(********************************************************************)
(*                                                                  *)
(*  Ancillary file to                                               *)
(*  "Bootstrapping a Five-Loop Amplitude from Steinmann Relations"  *)
(*  by S. Caron-Huot, L. Dixon, A. McLeod, and M. von Hippel        *)
(*  arXiv:1609.00669                                                *)
(*                                                                  *)
(*  This file contains expressions for the three functions          *)
(*  e = {\cal E} in the paper (BDS-like normalized MHV amplitude)   *)
(*  E  (BDS-like normalized NMHV amplitude, parity-even part)       *)
(*  Et = \tilde{E} in the paper                                     *)   
(*  (BDS-like normalized NMHV amplitude, parity-odd part)           *)
(*  from one through five loops in the near-collinear limit         *)
(*  v -> 0,     T -> 0                                              *)
(*  through order T^3.                                              *)
(*                                                                  *)
(*  The variables                                                   *)
(*     T = exp(-tau), S = exp(sigma) and F = exp(i*phi)             *)
(*  introduced by Basso, Sever and Vieira in arXiv:1303.1396        *)
(*  are related to the cross ratios u,v,w by                        *)
(*                                                                  *)
(*    1/v = 1 + 1/T^2                                               *)
(*    1/w = 1 + (T+F*S)*(T+S/F)                                     *)
(*  u/v/w = S^2/T^2                                                 *)
(*                                                                  *)
(*  Only one orientation of e is given for                          *)
(*  each loop, denoted by eLT for loop order L, since it is         *)
(*  totally symmetric in the cross ratios u, v, and w. Three        *)
(*  orientations of E and Et are given, using the following         *)
(*  notation:                                                       *)
(*                                                                  *)
(*                 F^{(L)}(u,v,w) -> FLuvwT                         *)
(*                                                                  *)
(*  We don't give EtLwuvT explicitly as it is given by              *)
(*         EtLwuvT = - EtLuvwT - EtLvwuT                            *)
(*                                                                  *)
(*  For the HPLs and MZVs, we use the notation of the HPL           *)
(*  package presented in arXiv:hep-ph/0507152.                      *)
(*                                                                  *)
(*------------------------------------------------------------------*)
(*                                                                  *)
(*  The standard framed bosonic Wilson loop  W_hex  defined in      *)
(*  arXiv:1303.1396 is related very simply to e:                    *)
(*                                                                  *)
(*  W_hex = e * exp( 1/2 * Gamma_cusp * F(T,S) )                    *)
(*                                                                  *)
(*  where Gamma_cusp = 4 * ( g^2 - 2*Zeta[2]*g^4 + ... )            *)
(*  is the cusp anomalous dimension, and                            *)
(*                                                                  *)
(*  F(T,S) = ln(T)^2 + ln(S)^2 + Zeta[2]                            *)
(*         = 1/4 * ( ln(v)^2 + ln(u/w)^2 )                          *)
(*           + 1/2 * ln(1-v) * ln((1-v)/v*w/u) + Zeta[2].           *)
(*                                                                  *)
(*  * The T^1 terms below agree with formulae from arXiv:1310.5735. *)
(*  * The T^2*F^{\pm2} terms agree with formulae provided to us by  *)
(*    G. Papathanasiou, based on                                    *)
(*    -  arXiv:1406.1123 for the bound-state (DF) contribution,     *)
(*    -  arXiv:1507.08982, appendix B.1, WFF = W_{2,1,1}/2 for the  *)
(*       contribution of a pair of gluonic excitations.             *)
(*  * The T^3*F^{\pm3} terms agree with formulae provided to us by  *)
(*    G. Papathanasiou as well, based on                            *)
(*    -  methods used in arXiv:1310.5735 and arXiv:1406.1123 for    *)
(*       the single-particle 3-gluon bound-state contribution, and  *)
(*    -  arXiv:1507.08982 for the contribution of a 2-particle      *)
(*       consisting of an elementary gluon and a DF state.          *)
(*                                                                  *)
(*------------------------------------------------------------------*)
(*                                                                  *)
(*  For the NMHV Wilson loop, it is more conventional to compare    *)
(*  using the ratio function, whose parity even (odd) components    *)
(*  are found by expanding   V = E/e    (Vt = Et/e).                *)
(*  * The T^1 term in the <6134> component agrees through           *)
(*    five loops with results in arXiv:1310.5735.                   *)
(*  * The T^2 terms in the <1114> and <1144> components agree       *)
(*    with results in arXiv:1410.2534 through four loops, the       *)
(*    last order they were compared so far.                         *)
(*                                                                  *)
(********************************************************************)

e1T0F0=-Pi^2/3 - HPL[{0}, S^2]^2/2 - 2*Log[T]^2;
e1T1F1=S*HPL[{0}, S^2] + ((1 + S^2)*HPL[{1}, -S^2])/S;
e1T2F0=2*HPL[{0}, S^2] + 2*HPL[{1}, -S^2];
e1T2F2=-1/2 - (S^2*HPL[{0}, S^2])/2 + ((-1 - S^4)*HPL[{1}, -S^2])/(2*S^2);
e1T3F1=(-3*S)/(2*(1 + S^2)) - S*HPL[{0}, S^2] - S*HPL[{1}, -S^2];
e1T3F3=(2 + S^2 + 2*S^4)/(6*S*(1 + S^2)) + (S^3*HPL[{0}, S^2])/3 + ((1 + S^6)*HPL[{1}, -S^2])/(3*S^3);
e1T=e1T0F0+T*e1T1F1*(F+1/F)+T^2*(e1T2F0+e1T2F2*(F^2+1/F^2))+T^3*(e1T3F1*(F+1/F)+e1T3F3*(F^3+1/F^3));
E1uvwT0F0=-Pi^2/3 - HPL[{0}, S^2]^2/2 - 2*HPL[{0}, S^2]*HPL[{1}, -S^2] - 2*HPL[{1}, -S^2]^2 + (2*HPL[{0}, S^2] + 4*HPL[{1}, -S^2])*Log[T] - 2*Log[T]^2;
E1uvwT1F1=(2*S*HPL[{0}, S^2])/(1 + S^2) + (4*S*HPL[{1}, -S^2])/(1 + S^2) - (4*S*Log[T])/(1 + S^2);
E1uvwT2F0=(-4*S^2)/(1 + S^2)^2 + (2*HPL[{0}, S^2])/(1 + S^2)^2 + (4*HPL[{1}, -S^2])/(1 + S^2)^2 - (4*Log[T])/(1 + S^2)^2;
E1uvwT2F2=(-2*S^2)/(1 + S^2)^2 - (S^2*HPL[{0}, S^2])/(1 + S^2)^2 - (2*S^2*HPL[{1}, -S^2])/(1 + S^2)^2 + (2*S^2*Log[T])/(1 + S^2)^2;
E1uvwT3F1=(2*S*(-2 + S^2))/(1 + S^2)^3 - (2*S*HPL[{0}, S^2])/(1 + S^2)^3 - (4*S*HPL[{1}, -S^2])/(1 + S^2)^3 + (4*S*Log[T])/(1 + S^2)^3;
E1uvwT3F3=(2*S^3)/(1 + S^2)^3 + (2*S^3*HPL[{0}, S^2])/(3*(1 + S^2)^3) + (4*S^3*HPL[{1}, -S^2])/(3*(1 + S^2)^3) - (4*S^3*Log[T])/(3*(1 + S^2)^3);
E1uvwT=E1uvwT0F0+T*E1uvwT1F1*(F+1/F)+T^2*(E1uvwT2F0+E1uvwT2F2*(F^2+1/F^2))+T^3*(E1uvwT3F1*(F+1/F)+E1uvwT3F3*(F^3+1/F^3));
E1vwuT0F0=-Pi^2/3 - HPL[{0}, S^2]^2/2 - 2*HPL[{0}, S^2]*Log[T] - 2*Log[T]^2;
E1vwuT2F0=2*HPL[{0}, S^2] + 4*Log[T];
E1vwuT=E1vwuT0F0+T^2*E1vwuT2F0;
E1wuvT0F0=-Pi^2/3 - HPL[{0}, S^2]^2/2 + 2*HPL[{0}, S^2]*Log[T] - 2*Log[T]^2;
E1wuvT=E1wuvT0F0;
e2T0F0=Pi^4/6 + (Pi^2*HPL[{0}, S^2]^2)/3 + HPL[{0}, S^2]^4/8 + ((4*Pi^2)/3 + HPL[{0}, S^2]^2)*Log[T]^2 + 2*Log[T]^4;
e2T1F1=-(S*HPL[{0}, S^2]^3)/2 + ((Pi^2*(-1 - S^2))/(3*S) - (4*(1 + S^2))/S)*HPL[{1}, -S^2] + ((-1 - S^2)*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/(2*S) - (2*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (2*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + HPL[{0}, S^2]*(-4*S - (2*Pi^2*S)/3 - (2*(1 + S^2)*HPL[{1}, -S^2])/S + ((-1 - S^2)*HPL[{1}, -S^2]^2)/S) - (2*(1 + S^2)*HPL[{3}, -S^2])/S + ((4*(1 + S^2)*HPL[{1}, -S^2])/S + (2*(1 + S^2)*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(4*S + (2*(1 + S^2)*HPL[{1}, -S^2])/S))*Log[T] + (-2*S*HPL[{0}, S^2] - (2*(1 + S^2)*HPL[{1}, -S^2])/S)*Log[T]^2;
e2T2F0=-2 + (Pi^2*S^2)/3 - HPL[{0}, S^2]^3 + HPL[{0}, S^2]^2*(S^2 - HPL[{1}, -S^2]) - (2*Pi^2*HPL[{1}, -S^2])/3 - (4*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]*((-4*Pi^2)/3 - 2*HPL[{1}, -S^2]^2) + (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - 4*HPL[{3}, -S^2] + (4*HPL[{0}, S^2]*HPL[{1}, -S^2] + 4*HPL[{1}, -S^2]^2)*Log[T] + (-4*HPL[{0}, S^2] - 4*HPL[{1}, -S^2])*Log[T]^2;
e2T2F2=1/2 + (Pi^2*(1 + S^2))/6 + (S^2*HPL[{0}, S^2]^3)/4 + ((Pi^2*(1 + S^4))/(6*S^2) + (1 + 2*S^2 + S^4)/(2*S^2))*HPL[{1}, -S^2] + ((1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(2*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^2*((1 + 2*S^2)/4 + ((1 + S^4)*HPL[{1}, -S^2])/(4*S^2)) + HPL[{0}, S^2]*((Pi^2*S^2)/3 + (1 + S^2)/2 + ((1 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^2)/(2*S^2)) + ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + ((1 + S^4)*HPL[{3}, -S^2])/S^2 + (-1 - ((1 + S^2)^2*HPL[{1}, -S^2])/S^2 + ((-1 - S^4)*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*(-1 - S^2 + ((-1 - S^4)*HPL[{1}, -S^2])/S^2))*Log[T] + (1 + S^2*HPL[{0}, S^2] + ((1 + S^4)*HPL[{1}, -S^2])/S^2)*Log[T]^2;
e2T3F1=-(Pi^2*S*(-7 - 3*S^2 + S^4))/(6*(1 + S^2)) + (S*HPL[{0}, S^2]^3)/2 + ((Pi^2*S)/3 + (-1 - S^6)/S^3)*HPL[{1}, -S^2] + (3*S*HPL[{1}, -S^2]^2)/(1 + S^2) + (2*S*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*(-(S*(-11 - 6*S^2 + 2*S^4))/(4*(1 + S^2)) + (S*HPL[{1}, -S^2])/2) + HPL[{0}, S^2]*((2*Pi^2*S)/3 - S^3 + (3*S*HPL[{1}, -S^2])/(1 + S^2) + S*HPL[{1}, -S^2]^2) + ((1 + 4*S^4 - S^6)*HPL[{2}, -S^2])/S^3 + 2*S*HPL[{3}, -S^2] + ((-6*S*HPL[{1}, -S^2])/(1 + S^2) - 2*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-3*S)/(1 + S^2) - 2*S*HPL[{1}, -S^2]))*Log[T] + ((3*S)/(1 + S^2) + 2*S*HPL[{0}, S^2] + 2*S*HPL[{1}, -S^2])*Log[T]^2;
e2T3F3=(-4*(1 + S^2))/(27*S) + (Pi^2*(-2 - S^2 - 5*S^4 - 3*S^6))/(18*S*(1 + S^2)) - (S^3*HPL[{0}, S^2]^3)/6 + ((-13 - 12*S^2 - 12*S^4 - 13*S^6)/(27*S^3) + (Pi^2*(-1 - S^6))/(9*S^3))*HPL[{1}, -S^2] + ((-2 - 8*S^2 - 3*S^4 - 8*S^6 - 2*S^8)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^2*((-2 - S^2 - 8*S^4 - 6*S^6)/(12*S*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2])/(6*S^3)) + HPL[{0}, S^2]*((-2*Pi^2*S^3)/9 + (-6 - 6*S^2 - 13*S^4)/(27*S) + ((-2 - 8*S^2 - 3*S^4 - 8*S^6 - 2*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2]^2)/(3*S^3)) - ((-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/S^3 - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + ((4*(1 + S^2))/(9*S) + (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]*((6 + 3*S^2 + 10*S^4 + 4*S^6)/(9*S*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(3*S^3)))*Log[T] + ((-2 - S^2 - 2*S^4)/(3*S*(1 + S^2)) - (2*S^3*HPL[{0}, S^2])/3 - (2*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3))*Log[T]^2;
e2T=e2T0F0+T*e2T1F1*(F+1/F)+T^2*(e2T2F0+e2T2F2*(F^2+1/F^2))+T^3*(e2T3F1*(F+1/F)+e2T3F3*(F^3+1/F^3));
E2uvwT0F0=(7*Pi^4)/36 + HPL[{0}, S^2]^4/8 + HPL[{0}, S^2]^3*HPL[{1}, -S^2] + (5*Pi^2*HPL[{1}, -S^2]^2)/3 + 2*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^2*((5*Pi^2)/12 + 2*HPL[{1}, -S^2]^2 + HPL[{2}, -S^2]/2) + (Pi^2*HPL[{2}, -S^2])/6 + HPL[{2}, -S^2]^2 + 4*HPL[{4}, -S^2] - 4*HPL[{3, 1}, -S^2] + ((5*Pi^2)/3 + 2*HPL[{0}, S^2]^2 + 12*HPL[{0}, S^2]*HPL[{1}, -S^2] + 12*HPL[{1}, -S^2]^2)*Log[T]^2 + (-4*HPL[{0}, S^2] - 8*HPL[{1}, -S^2])*Log[T]^3 + 2*Log[T]^4 - 4*HPL[{1}, -S^2]*Zeta[3] + HPL[{0}, S^2]*(4*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*(2*Pi^2 + 4*HPL[{2}, -S^2]) - 4*HPL[{2, 1}, -S^2] + 2*Zeta[3]) + Log[T]*(-HPL[{0}, S^2]^3 - (10*Pi^2*HPL[{1}, -S^2])/3 - 4*HPL[{0}, S^2]^2*HPL[{1}, -S^2] - 8*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]*(-2*Pi^2 - 12*HPL[{1}, -S^2]^2 - 4*HPL[{2}, -S^2]) + 4*Zeta[3]);
E2uvwT1F1=-((S*HPL[{0}, S^2]^3)/(1 + S^2)) + ((2 - 7*S^2 - S^4)*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/(2*S*(1 + S^2)) + (2*(1 - 10*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(3 - 17*S^2))/(6*S*(1 + S^2)) - (3*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]*((Pi^2*S*(-11 + S^2))/(6*(1 + S^2)) + ((1 - 10*S^2 + S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) + (S*(-3 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) + ((1 - 3*S^2)*HPL[{3}, -S^2])/S + (4*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + ((Pi^2*S*(11 + S^2))/(3*(1 + S^2)) + (S*(5 + S^2)*HPL[{0}, S^2]^2)/(1 + S^2) - (2*(1 - 10*S^2 + S^4)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(S*(1 + S^2)) - (2*(1 - 10*S^2 + S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) + (2*(-1 + S^2)*HPL[{2}, -S^2])/S)*Log[T] + ((2*S*(-5 + S^2)*HPL[{0}, S^2])/(1 + S^2) + (2*(1 - 10*S^2 + S^4)*HPL[{1}, -S^2])/(S*(1 + S^2)))*Log[T]^2 + (8*S*Log[T]^3)/(1 + S^2) - (4*S^3*Zeta[3])/(1 + S^2);
E2uvwT2F0=(Pi^2*(-3 + 19*S^2 + 2*S^4))/(6*(1 + S^2)^2) - HPL[{0}, S^2]^3/(1 + S^2)^2 - (6*(1 - 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (4*(-5 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^2*((-2 + 9*S^2 + 3*S^4)/(2*(1 + S^2)^2) + ((-5 - 2*S^2 - S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-10*Pi^2)/(3*(1 + S^2)^2) - (2*(1 + S^2)^2)/S^2 - 6*HPL[{2}, -S^2]) + (5*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{0}, S^2]*(-2*(1 + S^2) + (Pi^2*(-5 + 2*S^2 + S^4))/(3*(1 + S^2)^2) - (6*(1 - 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2 + (2*(-5 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (2*(-1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) - 6*HPL[{3}, -S^2] + 8*HPL[{2, 1}, -S^2] + ((2*Pi^2*(6 + 2*S^2 + S^4))/(3*(1 + S^2)^2) + (2*(3 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(1 + S^2)^2 + (12*(-1 + S^2)^2*HPL[{1}, -S^2])/(1 + S^2)^2 - (4*(-5 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]*((4*(-1 + S^2)*(-1 + 2*S^2))/(1 + S^2)^2 - (4*(-5 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) + 4*HPL[{2}, -S^2])*Log[T] + ((-2*(1 - 10*S^2 + S^4))/(1 + S^2)^2 + (4*(-2 + 2*S^2 + S^4)*HPL[{0}, S^2])/(1 + S^2)^2 + (4*(-5 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2)*Log[T]^2 + (8*Log[T]^3)/(1 + S^2)^2 - (4*(1 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2;
E2uvwT2F2=(Pi^2*(-3 + 19*S^2 + 2*S^4))/(12*(1 + S^2)^2) + (S^2*HPL[{0}, S^2]^3)/(2*(1 + S^2)^2) + ((1 - 2*S^2 + 18*S^4 - 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 10*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^2*((-2 + 9*S^2 + 3*S^4)/(4*(1 + S^2)^2) + ((-2 - 4*S^2 + 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2])/(4*S^2*(1 + S^2)^2)) + (5*(-1 + S^2)*HPL[{2}, -S^2])/(2*(1 + S^2)) + HPL[{1}, -S^2]*((1 + S^2)^2/(2*S^2) + (Pi^2*(-3 - 6*S^2 + 17*S^4))/(12*S^2*(1 + S^2)^2) + (3*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(2*S^2)) + HPL[{0}, S^2]*((1 + S^2)/2 + (Pi^2*(11*S^2 - 2*S^4 - S^6))/(12*(1 + S^2)^2) + ((1 - 2*S^2 + 18*S^4 - 2*S^6 + S^8)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 10*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2]^2)/(2*S^2*(1 + S^2)^2) - (S^2*(-1 + S^2)*(3 + S^2)*HPL[{2}, -S^2])/(2*(1 + S^2)^2)) + ((-1 + 3*S^4)*HPL[{3}, -S^2])/(2*S^2) - (2*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (-(Pi^2*S^2*(11 + 2*S^2 + S^4))/(6*(1 + S^2)^2) - (S^2*(5 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(2*(1 + S^2)^2) + ((-1 + 2*S^2 - 18*S^4 + 2*S^6 - S^8)*HPL[{1}, -S^2])/(S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 10*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + HPL[{0}, S^2]*((1 - 9*S^2 + S^4 - S^6)/(1 + S^2)^2 + ((1 + 2*S^2 - 10*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2])/(S^2*(1 + S^2)^2)) - ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2)*Log[T] + ((-1 + 10*S^2 - S^4)/(1 + S^2)^2 - (S^2*(-5 + 2*S^2 + S^4)*HPL[{0}, S^2])/(1 + S^2)^2 + ((-1 - 2*S^2 + 10*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2])/(S^2*(1 + S^2)^2))*Log[T]^2 - (4*S^2*Log[T]^3)/(1 + S^2)^2 + (2*(2*S^4 + S^6)*Zeta[3])/(1 + S^2)^2;
E2uvwT3F1=(3*(1 + S^2))/(4*S) - (Pi^2*S*(-47 + 15*S^2 + 4*S^4 + 2*S^6))/(12*(1 + S^2)^3) + (S*HPL[{0}, S^2]^3)/(1 + S^2)^3 + ((-3 + 38*S^2 - 30*S^4 + 6*S^6 + 5*S^8)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)^3) - (2*S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^2*(-(S*(-26 - 3*S^2 + S^4 + 2*S^6))/(4*(1 + S^2)^3) + (S*(9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(2*(1 + S^2)^3)) - ((2 + S^2)*(1 - 11*S^2 + 2*S^4)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((10*Pi^2*S)/(3*(1 + S^2)^3) + (3 + 25*S^4 - 40*S^6 + 25*S^8 + 3*S^12)/(4*S^3*(1 + S^2)^3) + 3*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*(-(Pi^2*S*(-11 + 3*S^2 + 3*S^4 + S^6))/(6*(1 + S^2)^3) + (S*(13 - 20*S^2 + 12*S^4 + 3*S^8))/(4*(1 + S^2)^3) + ((-3 + 38*S^2 - 30*S^4 + 6*S^6 + 5*S^8)*HPL[{1}, -S^2])/(2*S*(1 + S^2)^3) - (S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 - (S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + 3*S*HPL[{3}, -S^2] - 4*S*HPL[{2, 1}, -S^2] + ((-6*S*(1 - 2*S^2 + S^4))/(1 + S^2)^3 - (Pi^2*S*(11 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) - (S*(5 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(1 + S^2)^3 + ((3 - 38*S^2 + 30*S^4 - 6*S^6 - 5*S^8)*HPL[{1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 + HPL[{0}, S^2]*(-((S*(20 - 11*S^2 + 10*S^4 + 5*S^6))/(1 + S^2)^3) + (2*S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(1 + S^2)^3) - 2*S*HPL[{2}, -S^2])*Log[T] + ((-3*S*(-1 + S^2)*(7 + S^2))/(1 + S^2)^3 - (2*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2])/(1 + S^2)^3 - (2*S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(1 + S^2)^3)*Log[T]^2 - (8*S*Log[T]^3)/(1 + S^2)^3 + (4*S^3*(3 + 3*S^2 + S^4)*Zeta[3])/(1 + S^2)^3;
E2uvwT3F3=(-1 - S^2)/(12*S) + (Pi^2*(6 + 15*S^2 - 57*S^4 - 8*S^6 - 2*S^8))/(36*S*(1 + S^2)^3) - (S^3*HPL[{0}, S^2]^3)/(3*(1 + S^2)^3) + ((-1 - S^2 + 3*S^4 - 18*S^6 + 3*S^8 - S^10 - S^12)*HPL[{1}, -S^2]^2)/(2*S^3*(1 + S^2)^3) + (2*(1 + 3*S^2 + 3*S^4 - 10*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^2*(-((1 + 4*S^2)*(-4 + 6*S^2 + 3*S^4 + S^6))/(12*S*(1 + S^2)^3) + ((2 + 6*S^2 + 6*S^4 - 7*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{1}, -S^2])/(6*S^3*(1 + S^2)^3)) - ((-1 + S^2)*(8 + 23*S^2 + 8*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(3 + 9*S^2 + 9*S^4 - 17*S^6))/(18*S^3*(1 + S^2)^3) + (-5 - 32*S^2 - 31*S^4 - 104*S^6 - 31*S^8 - 32*S^10 - 5*S^12)/(12*S^3*(1 + S^2)^3) + ((1 - S^6)*HPL[{2}, -S^2])/S^3) + HPL[{0}, S^2]*((Pi^2*S^3*(-11 + 3*S^2 + 3*S^4 + S^6))/(18*(1 + S^2)^3) + (-6 - 7*S^2 - 52*S^4 - 24*S^6 - 26*S^8 - 5*S^10)/(12*S*(1 + S^2)^3) + ((-1 - S^2 + 3*S^4 - 18*S^6 + 3*S^8 - S^10 - S^12)*HPL[{1}, -S^2])/(2*S^3*(1 + S^2)^3) + ((1 + 3*S^2 + 3*S^4 - 10*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (S^3*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((1 - 3*S^6)*HPL[{3}, -S^2])/(3*S^3) + (4*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + ((Pi^2*S^3*(11 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (1 - 2*S^2 + 18*S^4 - 2*S^6 + S^8)/(3*S*(1 + S^2)^3) + (S^3*(5 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^3) + ((1 + S^2 - 3*S^4 + 18*S^6 - 3*S^8 + S^10 + S^12)*HPL[{1}, -S^2])/(S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 10*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + HPL[{0}, S^2]*((-2 - 5*S^2 + 27*S^4 - 4*S^6 + 5*S^8 + 3*S^10)/(3*S*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 10*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3)) + (2*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3))*Log[T] + (((-2 + 5*S^2 + S^4)*(-1 - 5*S^2 + 2*S^4))/(3*S*(1 + S^2)^3) + (2*S^3*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2])/(3*(1 + S^2)^3) + (2*(1 + 3*S^2 + 3*S^4 - 10*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3))*Log[T]^2 + (8*S^3*Log[T]^3)/(3*(1 + S^2)^3) - (4*S^5*(3 + 3*S^2 + S^4)*Zeta[3])/(3*(1 + S^2)^3);
E2uvwT=E2uvwT0F0+T*E2uvwT1F1*(F+1/F)+T^2*(E2uvwT2F0+E2uvwT2F2*(F^2+1/F^2))+T^3*(E2uvwT3F1*(F+1/F)+E2uvwT3F3*(F^3+1/F^3));
E2vwuT0F0=(5*Pi^4)/36 + HPL[{0}, S^2]^4/8 + HPL[{0}, S^2]^2*(Pi^2/4 - HPL[{2}, -S^2]/2) - (Pi^2*HPL[{2}, -S^2])/2 + 2*HPL[{4}, -S^2] + 4*HPL[{3, 1}, -S^2] - 8*HPL[{2, 1, 1}, -S^2] + (Pi^2 - 4*HPL[{2}, -S^2])*Log[T]^2 + 4*HPL[{0}, S^2]*Log[T]^3 + 2*Log[T]^4 + Log[T]*(HPL[{0}, S^2]^3 + HPL[{0}, S^2]*(2*Pi^2 + 4*HPL[{2}, -S^2]) - 4*HPL[{3}, -S^2] + 8*HPL[{2, 1}, -S^2] - 4*Zeta[3]) + HPL[{0}, S^2]*(-4*HPL[{2, 1}, -S^2] - 2*Zeta[3]);
E2vwuT1F1=((Pi^2*S)/2 + (2*(1 + S^2))/S)*HPL[{1}, -S^2] + (S*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/2 + ((1 + S^2)*HPL[{1}, -S^2]^2)/S + (4*S*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]*(2*S + (Pi^2*S)/3 + ((1 + S^2)*HPL[{1}, -S^2])/S + 2*S*HPL[{1}, -S^2]^2 + 2*S*HPL[{2}, -S^2]) - 3*S*HPL[{3}, -S^2] + 2*S*HPL[{2, 1}, -S^2] + (-(Pi^2*S)/3 - S*HPL[{0}, S^2]^2 - (2*(1 + S^2)*HPL[{1}, -S^2])/S - 4*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*(-2*S - 4*S*HPL[{1}, -S^2]) - 2*S*HPL[{2}, -S^2])*Log[T] + (4*S*HPL[{0}, S^2] + 4*S*HPL[{1}, -S^2])*Log[T]^2 - 2*S*Zeta[3];
E2vwuT2F0=-2 + Pi^2/(2*(1 + S^2)) - HPL[{0}, S^2]^3 + (Pi^2 + 2*(1 + S^2))*HPL[{1}, -S^2] - (2*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + (8*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*((2 + S^2)/(2*(1 + S^2)) + HPL[{1}, -S^2]) + HPL[{2}, -S^2] + HPL[{0}, S^2]*(-Pi^2 + 2*(1 + S^2) - (2*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2) + 4*HPL[{1}, -S^2]^2 + 2*HPL[{2}, -S^2]) - 4*HPL[{3}, -S^2] + (-4*Pi^2 - 6*HPL[{0}, S^2]^2 + HPL[{0}, S^2]*(-4/(1 + S^2) - 8*HPL[{1}, -S^2]) + (4*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2) - 8*HPL[{1}, -S^2]^2)*Log[T] + ((-2*(-1 + S^2))/(1 + S^2) + 8*HPL[{1}, -S^2])*Log[T]^2 - 8*Log[T]^3 + 4*Zeta[3];
E2vwuT2F2=-1/4 - (Pi^2*S^2)/(4*(1 + S^2)) + (-(Pi^2*S^2)/4 + (-1 - 4*S^2 - 3*S^4)/(4*S^2))*HPL[{1}, -S^2] + ((-1 - S^2 - 11*S^4 - 3*S^6)*HPL[{1}, -S^2]^2)/(4*S^2*(1 + S^2)) - (2*S^2*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*(-S^2/(4*(1 + S^2)) - (S^2*HPL[{1}, -S^2])/4) + HPL[{0}, S^2]*(-(Pi^2*S^2)/6 + (-1 - 3*S^2)/4 + ((-1 - S^2 - 11*S^4 - 3*S^6)*HPL[{1}, -S^2])/(4*S^2*(1 + S^2)) - S^2*HPL[{1}, -S^2]^2 - S^2*HPL[{2}, -S^2]) + (3*S^2*HPL[{3}, -S^2])/2 - S^2*HPL[{2, 1}, -S^2] + (1/2 + (Pi^2*S^2)/6 + (S^2*HPL[{0}, S^2]^2)/2 + ((1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)) + 2*S^2*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((S^2*(7 + 3*S^2))/(2*(1 + S^2)) + 2*S^2*HPL[{1}, -S^2]) + S^2*HPL[{2}, -S^2])*Log[T] + ((-2*S^2)/(1 + S^2) - 2*S^2*HPL[{0}, S^2] - 2*S^2*HPL[{1}, -S^2])*Log[T]^2 + S^2*Zeta[3];
E2vwuT3F1=(-3*S)/4 + (Pi^2*S*(-8 - S^2 + 4*S^4))/(12*(1 + S^2)^2) + (-(Pi^2*S)/2 + (1 - 8*S^2 + 2*S^4 - 8*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{1}, -S^2] + ((1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)^2) - (4*S*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*((S^3*(5 + 4*S^2))/(4*(1 + S^2)^2) - (S*HPL[{1}, -S^2])/2) + 2*S*HPL[{2}, -S^2] + HPL[{0}, S^2]*(-(Pi^2*S)/3 - (S*(4 + S^2 + 8*S^4 + 3*S^6))/(4*(1 + S^2)^2) + ((1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2])/(2*S*(1 + S^2)^2) - 2*S*HPL[{1}, -S^2]^2 - 2*S*HPL[{2}, -S^2]) + 3*S*HPL[{3}, -S^2] - 2*S*HPL[{2, 1}, -S^2] + ((Pi^2*S)/3 - (2*S*(-1 + S^2))/(1 + S^2)^2 + S*HPL[{0}, S^2]^2 + ((-1 + 12*S^2 + 7*S^4 - 2*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) + 4*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-2*S*(-3 - S^2 + S^4))/(1 + S^2)^2 + 4*S*HPL[{1}, -S^2]) + 2*S*HPL[{2}, -S^2])*Log[T] + ((-2*S*(4 + 3*S^2))/(1 + S^2)^2 - 4*S*HPL[{0}, S^2] - 4*S*HPL[{1}, -S^2])*Log[T]^2 + 2*S*Zeta[3];
E2vwuT3F3=(Pi^2*S^3*(3 + 2*S^2))/(12*(1 + S^2)^2) + (8 + 17*S^2)/(108*S) + ((Pi^2*S^3)/6 + (8 + 49*S^2 + 80*S^4 + 314*S^6 + 184*S^8 + 53*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] + ((2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + (4*S^3*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]^2*((S^3*(3 + 2*S^2))/(12*(1 + S^2)^2) + (S^3*HPL[{1}, -S^2])/6) + HPL[{0}, S^2]*((Pi^2*S^3)/9 + (12 + 18*S^2 + 143*S^4 + 118*S^6 + 53*S^8)/(108*S*(1 + S^2)^2) + ((2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)^2) + (2*S^3*HPL[{1}, -S^2]^2)/3 + (2*S^3*HPL[{2}, -S^2])/3) - S^3*HPL[{3}, -S^2] + (2*S^3*HPL[{2, 1}, -S^2])/3 + (-(Pi^2*S^3)/9 + (-2 - 3*S^2 - 18*S^4 - 5*S^6)/(9*S*(1 + S^2)^2) - (S^3*HPL[{0}, S^2]^2)/3 + ((-2 - 4*S^2 - 2*S^4 - 47*S^6 - 46*S^8 - 11*S^10)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*S^3*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*(-(S^3*(29 + 34*S^2 + 11*S^4))/(9*(1 + S^2)^2) - (4*S^3*HPL[{1}, -S^2])/3) - (2*S^3*HPL[{2}, -S^2])/3)*Log[T] + ((2*S^3*(3 + 2*S^2))/(3*(1 + S^2)^2) + (4*S^3*HPL[{0}, S^2])/3 + (4*S^3*HPL[{1}, -S^2])/3)*Log[T]^2 - (2*S^3*Zeta[3])/3;
E2vwuT=E2vwuT0F0+T*E2vwuT1F1*(F+1/F)+T^2*(E2vwuT2F0+E2vwuT2F2*(F^2+1/F^2))+T^3*(E2vwuT3F1*(F+1/F)+E2vwuT3F3*(F^3+1/F^3));
E2wuvT0F0=(7*Pi^4)/36 + HPL[{0}, S^2]^4/8 + HPL[{0}, S^2]^2*((5*Pi^2)/12 + HPL[{2}, -S^2]/2) + (Pi^2*HPL[{2}, -S^2])/2 - 2*HPL[{4}, -S^2] - 4*HPL[{3, 1}, -S^2] + 8*HPL[{2, 1, 1}, -S^2] + ((5*Pi^2)/3 + 2*HPL[{0}, S^2]^2 + 4*HPL[{2}, -S^2])*Log[T]^2 - 4*HPL[{0}, S^2]*Log[T]^3 + 2*Log[T]^4 + HPL[{0}, S^2]*(4*HPL[{2, 1}, -S^2] + 2*Zeta[3]) + Log[T]*(-HPL[{0}, S^2]^3 + HPL[{0}, S^2]*(-2*Pi^2 - 4*HPL[{2}, -S^2]) + 4*HPL[{3}, -S^2] - 8*HPL[{2, 1}, -S^2] + 4*Zeta[3]);
E2wuvT1F1=(Pi^2/(2*S) + (2*(1 + S^2))/S)*HPL[{1}, -S^2] + (HPL[{0}, S^2]^2*HPL[{1}, -S^2])/(2*S) + ((1 + S^2)*HPL[{1}, -S^2]^2)/S + (4*HPL[{1}, -S^2]^3)/(3*S) + HPL[{0}, S^2]*(2*S + ((1 + S^2)*HPL[{1}, -S^2])/S + (2*HPL[{1}, -S^2]^2)/S) - HPL[{3}, -S^2]/S - (2*HPL[{2, 1}, -S^2])/S + ((-2*(1 + S^2)*HPL[{1}, -S^2])/S - (4*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(-2*S - (4*HPL[{1}, -S^2])/S) + (2*HPL[{2}, -S^2])/S)*Log[T] + (4*HPL[{1}, -S^2]*Log[T]^2)/S;
E2wuvT2F0=-2 + (Pi^2*(-1 + 2*S^2))/(6*(1 + S^2)) + (S^2*HPL[{0}, S^2]^2)/(2*(1 + S^2)) + (2*(1 + S^2)*HPL[{1}, -S^2])/S^2 + (2*(-1 + S^2)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(1 + S^2) + (2*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - HPL[{2}, -S^2] + ((4*HPL[{0}, S^2])/(1 + S^2) - (4*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2))*Log[T] + (2*(-1 + S^2)*Log[T]^2)/(1 + S^2);
E2wuvT2F2=-1/4 - Pi^2/(4*(1 + S^2)) + (-Pi^2/(4*S^2) + (-3 - 4*S^2 - S^4)/(4*S^2))*HPL[{1}, -S^2] + ((-3 - 11*S^2 - S^4 - S^6)*HPL[{1}, -S^2]^2)/(4*S^2*(1 + S^2)) - (2*HPL[{1}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^2*(-1/(4*(1 + S^2)) - HPL[{1}, -S^2]/(4*S^2)) + HPL[{0}, S^2]*((-3 - S^2)/4 + ((-3 - 11*S^2 - S^4 - S^6)*HPL[{1}, -S^2])/(4*S^2*(1 + S^2)) - HPL[{1}, -S^2]^2/S^2) + HPL[{3}, -S^2]/(2*S^2) + HPL[{2, 1}, -S^2]/S^2 + (1/2 + ((3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)) + (2*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*((4 + S^2 + S^4)/(2*(1 + S^2)) + (2*HPL[{1}, -S^2])/S^2) - HPL[{2}, -S^2]/S^2)*Log[T] + (-2/(1 + S^2) - (2*HPL[{1}, -S^2])/S^2)*Log[T]^2;
E2wuvT3F1=-3/(4*S) + (Pi^2*S)/(4*(1 + S^2)^2) + (S*HPL[{0}, S^2]^2)/(4*(1 + S^2)^2) + ((-3 - 8*S^2 + 2*S^4 - 8*S^6 + S^8)*HPL[{1}, -S^2])/(4*S^3*(1 + S^2)^2) - (S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(2*(1 + S^2)^2) + HPL[{0}, S^2]*((S*(-3 + S^2)*(-1 + S^2))/(4*(1 + S^2)^2) - (S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(2*(1 + S^2)^2)) + ((2*S*(-1 + S^2))/(1 + S^2)^2 + (S*(-1 + 2*S^2 + S^4)*HPL[{0}, S^2])/(1 + S^2)^2 + (S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2)*Log[T] + (2*S*Log[T]^2)/(1 + S^2)^2;
E2wuvT3F3=(Pi^2*(2 + 3*S^2))/(12*S*(1 + S^2)^2) + (17 + 8*S^2)/(108*S) + (Pi^2/(6*S^3) + (53 + 184*S^2 + 314*S^4 + 80*S^6 + 49*S^8 + 8*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] + ((11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + (4*HPL[{1}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^2*((2 + 3*S^2)/(12*S*(1 + S^2)^2) + HPL[{1}, -S^2]/(6*S^3)) + HPL[{0}, S^2]*((66 + 171*S^2 + 62*S^4 + 37*S^6 + 8*S^8)/(108*S*(1 + S^2)^2) + ((11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)^2) + (2*HPL[{1}, -S^2]^2)/(3*S^3)) - HPL[{3}, -S^2]/(3*S^3) - (2*HPL[{2, 1}, -S^2])/(3*S^3) + ((-5 - 18*S^2 - 3*S^4 - 2*S^6)/(9*S*(1 + S^2)^2) + ((-11 - 46*S^2 - 47*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]*((-2*(6 + 9*S^2 + S^4 + 2*S^6 + S^8))/(9*S*(1 + S^2)^2) - (4*HPL[{1}, -S^2])/(3*S^3)) + (2*HPL[{2}, -S^2])/(3*S^3))*Log[T] + ((2*(2 + 3*S^2))/(3*S*(1 + S^2)^2) + (4*HPL[{1}, -S^2])/(3*S^3))*Log[T]^2;
E2wuvT=E2wuvT0F0+T*E2wuvT1F1*(F+1/F)+T^2*(E2wuvT2F0+E2wuvT2F2*(F^2+1/F^2))+T^3*(E2wuvT3F1*(F+1/F)+E2wuvT3F3*(F^3+1/F^3));
Et2uvwT1F1=-(Pi^2*S)/3 + HPL[{0}, S^2]^2*(-S + ((-1 - S^2)*HPL[{1}, -S^2])/(2*S)) - (2*(1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((Pi^2*(-1 - S^2))/(6*S) - (2*(1 + S^2)*HPL[{2}, -S^2])/S) + ((-1 - S^2)*HPL[{3}, -S^2])/S + (2*(1 + S^2)*HPL[{2, 1}, -S^2])/S + ((Pi^2*S)/3 + S*HPL[{0}, S^2]^2 + (2*(1 + S^2)*HPL[{2}, -S^2])/S)*Log[T] - 2*S*Zeta[3];
Et2uvwT2F2=(Pi^2*(1 + S^2))/12 + ((-1 + S^2)*(1 + S^2)*HPL[{1}, -S^2]^2)/(2*S^2) + HPL[{0}, S^2]*((-1 + 2*S^2)/2 + ((-1 + S^2)*(1 + S^2)*HPL[{1}, -S^2])/(2*S^2)) + HPL[{0}, S^2]^2*((1 + S^2)/4 + ((1 + S^4)*HPL[{1}, -S^2])/(4*S^2)) + ((1 + S^2)^2*HPL[{2}, -S^2])/(2*S^2) + HPL[{1}, -S^2]*((-1 + S^4)/S^2 + (Pi^2*(1 + S^4))/(12*S^2) + ((1 + S^4)*HPL[{2}, -S^2])/S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(2*S^2) + ((-1 - S^4)*HPL[{2, 1}, -S^2])/S^2 + (-(Pi^2*S^2)/6 - S^2*HPL[{0}, S^2] - (S^2*HPL[{0}, S^2]^2)/2 + ((1 - S^4)*HPL[{1}, -S^2])/S^2 + ((-1 - S^4)*HPL[{2}, -S^2])/S^2)*Log[T] + S^2*Zeta[3];
Et2uvwT3F1=(-1 + S^2)/(4*S) + (Pi^2*S)/(12*(1 + S^2)) + ((1 + 3*S^2)*HPL[{1}, -S^2]^2)/(2*S) + HPL[{0}, S^2]^2*(S/(4*(1 + S^2)) + (S*HPL[{1}, -S^2])/2) + HPL[{0}, S^2]*((S*(9 + S^2))/4 + ((1 + 3*S^2)*HPL[{1}, -S^2])/(2*S)) + (S*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((Pi^2*S)/6 + (-1 + 7*S^2 + 9*S^4 + S^6)/(4*S^3) + 2*S*HPL[{2}, -S^2]) + S*HPL[{3}, -S^2] - 2*S*HPL[{2, 1}, -S^2] + (-(Pi^2*S)/3 - 3*S*HPL[{0}, S^2] - S*HPL[{0}, S^2]^2 + ((-1 - 3*S^2)*HPL[{1}, -S^2])/S - 2*S*HPL[{2}, -S^2])*Log[T] + 2*S*Zeta[3];
Et2uvwT3F3=(-7*(-1 + S^2))/(36*S) + (Pi^2*(-6 - 3*S^2 - 10*S^4 - 4*S^6))/(108*S*(1 + S^2)) + ((1 - S^6)*HPL[{1}, -S^2]^2)/(2*S^3) + HPL[{0}, S^2]^2*((-6 - 3*S^2 - 10*S^4 - 4*S^6)/(36*S*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(6*S^3)) + HPL[{0}, S^2]*(-((1 + S^2)*(-2 + 3*S^2))/(4*S) + ((1 - S^6)*HPL[{1}, -S^2])/(2*S^3)) + ((-2 - 8*S^2 - 3*S^4 - 8*S^6 - 2*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-3*(-1 + S^2)*(1 + S^2)^2)/(4*S^3) - (Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + ((Pi^2*S^3)/9 + (-1 + S^2)/(3*S) + S^3*HPL[{0}, S^2] + (S^3*HPL[{0}, S^2]^2)/3 + ((-1 + S^6)*HPL[{1}, -S^2])/S^3 + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3))*Log[T] - (2*S^3*Zeta[3])/3;
Et2uvwT=T*Et2uvwT1F1*(F-1/F)+T^2*(Et2uvwT2F2*(F^2-1/F^2))+T^3*(Et2uvwT3F1*(F-1/F)+Et2uvwT3F3*(F^3-1/F^3));
Et2vwuT1F1=(Pi^2*S)/3 + ((1 + S^2)*HPL[{1}, -S^2]^2)/S + (2*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^2*(S + ((1 + S^2)*HPL[{1}, -S^2])/(2*S)) + 2*S*HPL[{2}, -S^2] + HPL[{0}, S^2]*((Pi^2*S)/6 + ((1 + S^2)*HPL[{1}, -S^2])/S + ((1 + S^2)*HPL[{1}, -S^2]^2)/S + S*HPL[{2}, -S^2]) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2))/(3*S) + ((1 + S^2)*HPL[{2}, -S^2])/S) - S*HPL[{3}, -S^2] - (2*HPL[{2, 1}, -S^2])/S + (-(Pi^2*S)/3 - S*HPL[{0}, S^2]^2 - (2*(1 + S^2)*HPL[{1}, -S^2])/S - (2*(1 + S^2)*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(-2*S - (2*(1 + S^2)*HPL[{1}, -S^2])/S) - 2*S*HPL[{2}, -S^2])*Log[T] + (2*S*HPL[{0}, S^2] + (2*(1 + S^2)*HPL[{1}, -S^2])/S)*Log[T]^2;
Et2vwuT2F2=(Pi^2*(-2 - S^2))/12 - ((1 + S^2)*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(4*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^2*((-1 - S^2)/4 + ((-1 - S^4)*HPL[{1}, -S^2])/(4*S^2)) + ((-1 - S^2)*HPL[{2}, -S^2])/2 + HPL[{0}, S^2]*(-(Pi^2*S^2)/12 + (-1 - 4*S^2)/4 - ((1 + S^2)*(1 + 3*S^2)*HPL[{1}, -S^2])/(4*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^2)/(2*S^2) - (S^2*HPL[{2}, -S^2])/2) + HPL[{1}, -S^2]*(-1 - S^2 + (Pi^2*(-1 - S^4))/(6*S^2) + ((-1 - S^4)*HPL[{2}, -S^2])/(2*S^2)) + (S^2*HPL[{3}, -S^2])/2 + HPL[{2, 1}, -S^2]/S^2 + (1/2 + (Pi^2*S^2)/6 + (S^2*HPL[{0}, S^2]^2)/2 + ((1 + 4*S^2 + 3*S^4)*HPL[{1}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*((2 + 3*S^2)/2 + ((1 + S^4)*HPL[{1}, -S^2])/S^2) + S^2*HPL[{2}, -S^2])*Log[T] + (-1 - S^2*HPL[{0}, S^2] + ((-1 - S^4)*HPL[{1}, -S^2])/S^2)*Log[T]^2;
Et2vwuT3F1=-S/4 - (Pi^2*S)/(6*(1 + S^2)) + ((-1 - 5*S^2 - 2*S^4)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)) - (2*S*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*(-S/(4*(1 + S^2)) - (S*HPL[{1}, -S^2])/2) - (S*HPL[{2}, -S^2])/(2*(1 + S^2)) + HPL[{1}, -S^2]*(-(Pi^2*S)/3 + (-7 - 8*S^2 - S^4)/(4*S) - S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*(-(Pi^2*S)/6 - (S*(8 + S^2))/4 + ((-1 - 5*S^2 - 2*S^4)*HPL[{1}, -S^2])/(2*S*(1 + S^2)) - S*HPL[{1}, -S^2]^2 - S*HPL[{2}, -S^2]) + S*HPL[{3}, -S^2] + ((Pi^2*S)/3 + S*HPL[{0}, S^2]^2 + ((1 + 5*S^2 + 2*S^4)*HPL[{1}, -S^2])/(S*(1 + S^2)) + 2*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((S*(3 + 2*S^2))/(1 + S^2) + 2*S*HPL[{1}, -S^2]) + 2*S*HPL[{2}, -S^2])*Log[T] + (-(S/(1 + S^2)) - 2*S*HPL[{0}, S^2] - 2*S*HPL[{1}, -S^2])*Log[T]^2;
Et2vwuT3F3=(7*S)/36 + (Pi^2*(6 + 3*S^2 + 8*S^4 + 2*S^6))/(54*S*(1 + S^2)) + ((2 + 14*S^2 + 6*S^4 + 23*S^6 + 11*S^8)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^2*((6 + 3*S^2 + 10*S^4 + 4*S^6)/(36*S*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(6*S^3)) + ((6 + 3*S^2 + 10*S^4 + 4*S^6)*HPL[{2}, -S^2])/(18*S*(1 + S^2)) + HPL[{0}, S^2]*((Pi^2*S^3)/18 + (4 + 10*S^2 + 27*S^4)/(36*S) + ((2 + 14*S^2 + 6*S^4 + 23*S^6 + 11*S^8)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S^3) + (S^3*HPL[{2}, -S^2])/3) + HPL[{1}, -S^2]*((5 + 32*S^2 + 27*S^4)/(36*S) + (Pi^2*(1 + S^6))/(9*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) - (S^3*HPL[{3}, -S^2])/3 - (2*HPL[{2, 1}, -S^2])/(3*S^3) + (-(Pi^2*S^3)/9 + (-2 - 5*S^2)/(9*S) - (S^3*HPL[{0}, S^2]^2)/3 + ((-2 - 14*S^2 - 6*S^4 - 23*S^6 - 11*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]*((-6 - 3*S^2 - 17*S^4 - 11*S^6)/(9*S*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3)) - (2*S^3*HPL[{2}, -S^2])/3)*Log[T] + ((2 + S^2 + 2*S^4)/(3*S*(1 + S^2)) + (2*S^3*HPL[{0}, S^2])/3 + (2*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3))*Log[T]^2;
Et2vwuT=T*Et2vwuT1F1*(F-1/F)+T^2*(Et2vwuT2F2*(F^2-1/F^2))+T^3*(Et2vwuT3F1*(F-1/F)+Et2vwuT3F3*(F^3-1/F^3));
e3T0F0=(-101*Pi^6)/810 - (47*Pi^4*HPL[{0}, S^2]^2)/180 - (Pi^2*HPL[{0}, S^2]^4)/8 - HPL[{0}, S^2]^6/48 + ((-47*Pi^4)/45 - Pi^2*HPL[{0}, S^2]^2 - HPL[{0}, S^2]^4/4)*Log[T]^2 + (-2*Pi^2 - HPL[{0}, S^2]^2)*Log[T]^4 - (4*Log[T]^6)/3;
e3T1F1=(Pi^4*S)/36 + (S*HPL[{0}, S^2]^5)/8 + ((1 + S^2)*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/(8*S) + ((20*(1 + S^2))/(3*S) + (5*Pi^2*(1 + S^2))/(9*S))*HPL[{1}, -S^2]^3 + (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S + (2*(1 + S^2)*HPL[{1}, -S^2]^5)/(5*S) + HPL[{0}, S^2]^3*(2*S + (Pi^2*S)/2 + ((1 + S^2)*HPL[{1}, -S^2])/S + ((1 + S^2)*HPL[{1}, -S^2]^2)/(2*S)) + ((1 + S^2)*HPL[{2}, -S^2]^2)/(2*S) + ((Pi^2*(1 + S^2))/(3*S) + (3 + S^2)/S)*HPL[{3}, -S^2] + ((3 + S^2)*HPL[{4}, -S^2])/S + (18*(1 + S^2)*HPL[{5}, -S^2])/S + ((Pi^2*(-1 - S^2))/(3*S) + (2*(-1 + S^2))/S)*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((Pi^2*S)/12 + (2*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (2*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (S*HPL[{2}, -S^2])/2 + HPL[{1}, -S^2]*((7*(1 + S^2))/(2*S) + (5*Pi^2*(1 + S^2))/(12*S) + ((1 + S^2)*HPL[{2}, -S^2])/(2*S)) + ((1 + S^2)*HPL[{3}, -S^2])/S + ((-1 - S^2)*HPL[{2, 1}, -S^2])/S) - 4*S*HPL[{3, 1}, -S^2] + (4*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (4*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (4*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((Pi^2*S)/3 + S*HPL[{0}, S^2]^3 + ((20*(1 + S^2))/S + (5*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2] + (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (4*(1 + S^2)*HPL[{1}, -S^2]^3)/S + HPL[{0}, S^2]^2*(S + (2*(1 + S^2)*HPL[{1}, -S^2])/S) + (2*(-1 + S^2)*HPL[{2}, -S^2])/S + HPL[{0}, S^2]*(20*S + 2*Pi^2*S + (12*(1 + S^2)*HPL[{1}, -S^2])/S + (6*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (2*(1 + S^2)*HPL[{2}, -S^2])/S))*Log[T]^2 + ((-8*(1 + S^2)*HPL[{1}, -S^2])/S - (4*(1 + S^2)*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(-8*S - (4*(1 + S^2)*HPL[{1}, -S^2])/S))*Log[T]^3 + (2*S*HPL[{0}, S^2] + (2*(1 + S^2)*HPL[{1}, -S^2])/S)*Log[T]^4 - 2*S*Zeta[3] + HPL[{1}, -S^2]*((36*(1 + S^2))/S + (17*Pi^2*(1 + S^2))/(6*S) + (7*Pi^4*(1 + S^2))/(36*S) + (Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(6*S) + ((1 + S^2)*HPL[{2}, -S^2]^2)/S + (4*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (4*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((18*(1 + S^2))/S + (5*Pi^2*(1 + S^2))/(3*S) - (2*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((Pi^2*(-1 + 2*S^2))/(6*S) - (2*(1 + S^2)*HPL[{3}, -S^2])/S - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]*(36*S + (11*Pi^2*S)/3 + (47*Pi^4*S)/90 + (4*(1 + S^2)*HPL[{1}, -S^2]^3)/S + ((1 + S^2)*HPL[{1}, -S^2]^4)/S + ((Pi^2*(1 + S^2))/(6*S) + (2*(1 + 2*S^2))/S)*HPL[{2}, -S^2] + ((1 + S^2)*HPL[{2}, -S^2]^2)/(2*S) + HPL[{1}, -S^2]^2*((10*(1 + S^2))/S + (Pi^2*(1 + S^2))/S + (2*(1 + S^2)*HPL[{2}, -S^2])/S) + ((1 + S^2)*HPL[{3}, -S^2])/S - (3*(1 + S^2)*HPL[{4}, -S^2])/S - (2*(3 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + 2*S*Zeta[3] + HPL[{1}, -S^2]*((18*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/S + (4*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (2*(1 + S^2)*Zeta[3])/S)) + Log[T]*(-(Pi^2*S)/3 + ((-20*(1 + S^2))/S - (5*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^2 - (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S + HPL[{0}, S^2]^3*(-2*S + ((-1 - S^2)*HPL[{1}, -S^2])/S) + HPL[{0}, S^2]^2*(-S - (4*(1 + S^2)*HPL[{1}, -S^2])/S - (2*(1 + S^2)*HPL[{1}, -S^2]^2)/S) - (2*(-1 + S^2)*HPL[{2}, -S^2])/S + (2*(-1 + S^2)*HPL[{3}, -S^2])/S - (4*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*(-36*S - 4*Pi^2*S - (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (4*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (2*(1 + 3*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((-20*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S - (4*(1 + S^2)*HPL[{2}, -S^2])/S) - (2*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + 4*S*Zeta[3] + HPL[{1}, -S^2]*((-36*(1 + S^2))/S - (10*Pi^2*(1 + S^2))/(3*S) + (4*(1 + S^2)*Zeta[3])/S));
e3T2F0=24 - (16*Pi^4*S^2)/45 + (Pi^2*(2 - 3*S^2))/3 + HPL[{0}, S^2]^5/4 + HPL[{0}, S^2]^4*(-S^2/2 + HPL[{1}, -S^2]/4) + (10*Pi^2*HPL[{1}, -S^2]^3)/9 + (4*HPL[{1}, -S^2]^5)/5 + HPL[{0}, S^2]^3*(Pi^2 + HPL[{1}, -S^2]^2) + (2*Pi^2*HPL[{3}, -S^2])/3 - (12*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + 36*HPL[{5}, -S^2] + HPL[{0}, S^2]^2*(1 - 3*S^2 - (7*Pi^2*S^2)/6 + (-1 - S^2)*HPL[{1}, -S^2]^2 + (4*HPL[{1}, -S^2]^3)/3 - ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((5*Pi^2)/6 - 2*(1 + S^2) + HPL[{2}, -S^2]) + 2*HPL[{3}, -S^2] - 2*HPL[{2, 1}, -S^2]) - (2*Pi^2*HPL[{2, 1}, -S^2])/3 + (4*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + 8*HPL[{3, 2}, -S^2] + 8*HPL[{4, 1}, -S^2] - (8*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 16*HPL[{2, 2, 1}, -S^2] + 48*HPL[{3, 1, 1}, -S^2] + (4 - (2*Pi^2*S^2)/3 + 2*HPL[{0}, S^2]^3 + (10*Pi^2*HPL[{1}, -S^2])/3 + 8*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*(-2*S^2 + 4*HPL[{1}, -S^2]) - (4*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + HPL[{0}, S^2]*(4*Pi^2 + 12*HPL[{1}, -S^2]^2 + 4*HPL[{2}, -S^2]))*Log[T]^2 + (-8*HPL[{0}, S^2]*HPL[{1}, -S^2] - 8*HPL[{1}, -S^2]^2)*Log[T]^3 + (4*HPL[{0}, S^2] + 4*HPL[{1}, -S^2])*Log[T]^4 + HPL[{1}, -S^2]^2*((Pi^2*(-1 - S^2))/3 + (2*(1 + 2*S^2 + S^4))/S^2 - (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - 4*Zeta[3]) + HPL[{2}, -S^2]*((-6*(-1 + S^4))/S^2 - (2*Pi^2*(-1 + S^4))/(3*S^2) - 4*HPL[{3}, -S^2] - 8*HPL[{2, 1}, -S^2] - 4*Zeta[3]) + HPL[{1}, -S^2]*((7*Pi^4)/18 - (2*Pi^2*(1 + S^2))/3 + (6*(1 + 2*S^2 + S^4))/S^2 + (Pi^2/3 - (4*(-1 + S^4))/S^2)*HPL[{2}, -S^2] + 2*HPL[{2}, -S^2]^2 - (2*(-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/S^2 + 8*HPL[{4}, -S^2] + (4*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - 8*HPL[{3, 1}, -S^2] - 4*(1 + S^2)*Zeta[3]) + HPL[{0}, S^2]*((47*Pi^4)/45 + 6*(1 + S^2) + 2*HPL[{1}, -S^2]^4 + (Pi^2/3 + (4*(1 + S^2))/S^2)*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*(2*Pi^2 + 4*HPL[{2}, -S^2]) + 2*(1 + S^2)*HPL[{3}, -S^2] - 6*HPL[{4}, -S^2] - 4*(1 + S^2)*HPL[{2, 1}, -S^2] + 8*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((2*(1 + 2*S^2 + S^4))/S^2 + (2*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 - 8*HPL[{2, 1}, -S^2] + 4*Zeta[3])) + Log[T]*(-12 + (4*Pi^2*S^2)/3 - 2*HPL[{0}, S^2]^3*HPL[{1}, -S^2] - (10*Pi^2*HPL[{1}, -S^2]^2)/3 - 4*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^2*(4*S^2 + 2*(1 + S^2)*HPL[{1}, -S^2] - 4*HPL[{1}, -S^2]^2) + (8*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + HPL[{0}, S^2]*(-4*(1 + S^2) - 8*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*(-4*Pi^2 - 8*HPL[{2}, -S^2]) - (4*(1 + S^2)*HPL[{2}, -S^2])/S^2 - 4*HPL[{3}, -S^2] + 8*HPL[{2, 1}, -S^2]) + HPL[{1}, -S^2]*((2*Pi^2*(1 + S^2))/3 - (4*(1 + 2*S^2 + S^4))/S^2 + (4*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + 8*Zeta[3]));
e3T2F2=-9/8 + (Pi^4*(-70 - 123*S^2))/720 + (Pi^2*(-5 - 24*S^2))/48 - (S^2*HPL[{0}, S^2]^5)/16 + ((-5*Pi^2*(1 + S^4))/(18*S^2) - (4*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{1}, -S^2]^3 + ((-1 - 2*S^2 - S^4)*HPL[{1}, -S^2]^4)/(2*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^5)/(5*S^2) + HPL[{0}, S^2]^4*((-1 - 4*S^2)/16 + ((-1 - S^4)*HPL[{1}, -S^2])/(16*S^2)) + HPL[{0}, S^2]^3*(-(Pi^2*S^2)/4 + (-1 - S^2)/4 + ((-1 - 2*S^2 - S^4)*HPL[{1}, -S^2])/(4*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^2)/(4*S^2)) + ((1 - 4*S^2 + S^4)*HPL[{2}, -S^2]^2)/(8*S^2) + ((15 + 8*S^2 - 7*S^4)/(8*S^2) + (Pi^2*(-1 - S^4))/(6*S^2))*HPL[{3}, -S^2] + ((27 - 8*S^2 - 23*S^4)*HPL[{4}, -S^2])/(4*S^2) - (9*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((11*(-1 + S^4))/(4*S^2) + (Pi^2*(1 + S^4))/(6*S^2))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((Pi^2*(-10 - 27*S^2))/48 + (5 - 24*S^2)/16 + ((-1 - 4*S^2 - 3*S^4)*HPL[{1}, -S^2]^2)/(4*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + ((4 - 2*S^2 - 3*S^4)*HPL[{2}, -S^2])/(8*S^2) + HPL[{1}, -S^2]*((5 - 12*S^2 - 17*S^4)/(16*S^2) - (5*Pi^2*(1 + S^4))/(24*S^2) + ((-1 - S^4)*HPL[{2}, -S^2])/(4*S^2)) + ((-1 - S^4)*HPL[{3}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{2, 1}, -S^2])/(2*S^2)) + ((-2 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (3*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (-5/2 + (Pi^2*(-10 - 3*S^2))/12 - (S^2*HPL[{0}, S^2]^3)/2 + ((-5*Pi^2*(1 + S^4))/(6*S^2) - (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2] - (3*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/S^2 - (2*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + HPL[{0}, S^2]^2*((-4 - 3*S^2)/4 + ((-1 - S^4)*HPL[{1}, -S^2])/S^2) - (3*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(2*S^2) + HPL[{0}, S^2]*(-(Pi^2*S^2) - 4*(1 + S^2) - (3*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + ((-1 - S^4)*HPL[{2}, -S^2])/S^2))*Log[T]^2 + (2 + (2*(1 + S^2)^2*HPL[{1}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*(2*(1 + S^2) + (2*(1 + S^4)*HPL[{1}, -S^2])/S^2))*Log[T]^3 + (-1 - S^2*HPL[{0}, S^2] + ((-1 - S^4)*HPL[{1}, -S^2])/S^2)*Log[T]^4 + ((12 - 11*S^2)*Zeta[3])/4 + HPL[{1}, -S^2]*((-7*Pi^4*(1 + S^4))/(72*S^2) - (15*(1 + 2*S^2 + S^4))/(4*S^2) - (11*Pi^2*(1 + 4*S^2 + 3*S^4))/(48*S^2) + ((Pi^2*(-1 - S^4))/(12*S^2) - (11*(-1 + S^4))/(4*S^2))*HPL[{2}, -S^2] + ((-1 - S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((1 - S^4)*HPL[{3}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (2*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (2*(1 + S^2)*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*((Pi^2*(-2 - 5*S^2 - 3*S^4))/(6*S^2) - (11*(1 + 2*S^2 + S^4))/(4*S^2) + ((1 - S^4)*HPL[{2}, -S^2])/S^2 + ((1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(7 - 2*S^2 - 6*S^4))/(24*S^2) - (3*(-1 + S^4))/S^2 + ((1 + S^4)*HPL[{3}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + ((1 + S^4)*Zeta[3])/S^2) + HPL[{0}, S^2]*((-47*Pi^4*S^2)/180 - (15*(1 + S^2))/4 - (7*Pi^2*(1 + S^2))/12 + ((-1 - 2*S^2 - S^4)*HPL[{1}, -S^2]^3)/S^2 + ((-1 - S^4)*HPL[{1}, -S^2]^4)/(2*S^2) + ((Pi^2*(-1 - S^4))/(12*S^2) - (5*(1 + 2*S^2 + S^4))/(4*S^2))*HPL[{2}, -S^2] + ((-1 - S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + HPL[{1}, -S^2]^2*((Pi^2*(-1 - S^4))/(2*S^2) - (2*(1 + 2*S^2 + S^4))/S^2 + ((-1 - S^4)*HPL[{2}, -S^2])/S^2) + ((-5 - S^4)*HPL[{3}, -S^2])/(4*S^2) + (3*(1 + S^4)*HPL[{4}, -S^2])/(2*S^2) + ((1 + S^2)*(3 + S^2)*HPL[{2, 1}, -S^2])/(2*S^2) - (2*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-2 + S^2)*Zeta[3])/2 + HPL[{1}, -S^2]*((Pi^2*(-1 - 2*S^2 - S^4))/(2*S^2) - (11*(1 + 2*S^2 + S^4))/(4*S^2) - ((1 + S^2)^2*HPL[{2}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + ((-1 - S^4)*Zeta[3])/S^2)) + Log[T]*(9/4 + (Pi^2*(16 + 11*S^2))/24 + ((5*Pi^2*(1 + S^4))/(6*S^2) + (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2]^2 + (2*(1 + S^2)^2*HPL[{1}, -S^2]^3)/S^2 + ((1 + S^4)*HPL[{1}, -S^2]^4)/S^2 + HPL[{0}, S^2]^3*((1 + S^2)/2 + ((1 + S^4)*HPL[{1}, -S^2])/(2*S^2)) + HPL[{0}, S^2]^2*((4 + 11*S^2)/8 + ((1 + S^2)*(1 + 3*S^2)*HPL[{1}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^2)/S^2) + (11*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(4*S^2) + ((-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(2*S^2) - ((-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + HPL[{0}, S^2]*((11*(1 + S^2))/2 + Pi^2*(1 + S^2) + (3*(1 + S^2)^2*HPL[{1}, -S^2]^2)/S^2 + (2*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + ((1 + S^2)*(1 + 3*S^2)*HPL[{2}, -S^2])/(2*S^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^4))/S^2 + (4*(1 + 2*S^2 + S^4))/S^2 + (2*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((1 + S^4)*HPL[{3}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) + (-2 + S^2)*Zeta[3] + HPL[{1}, -S^2]*((11*(1 + 2*S^2 + S^4))/(2*S^2) + (Pi^2*(2 + 5*S^2 + 3*S^4))/(3*S^2) + (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - (2*(1 + S^4)*Zeta[3])/S^2));
e3T3F1=(-27*(1 + S^2))/(16*S) + (Pi^2*S*(-44 + 15*S^2))/48 + (Pi^4*S*(-351 - 182*S^2 + 64*S^4))/(360*(1 + S^2)) - (S*HPL[{0}, S^2]^5)/8 + ((-5*Pi^2*S)/9 + (2*(1 - S^2 - S^4 + S^6))/(3*S^3))*HPL[{1}, -S^2]^3 - (3*S*HPL[{1}, -S^2]^4)/(1 + S^2) - (2*S*HPL[{1}, -S^2]^5)/5 + HPL[{0}, S^2]^4*((S*(-19 - 12*S^2 + 4*S^4))/(16*(1 + S^2)) - (S*HPL[{1}, -S^2])/8) + HPL[{0}, S^2]^3*(-(Pi^2*S)/2 + S^3 - (3*S*HPL[{1}, -S^2])/(2*(1 + S^2)) - (S*HPL[{1}, -S^2]^2)/2) + (S*(-2 + S^2)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)) + (-(Pi^2*S)/3 + (24 - 9*S^2 - 3*S^4 + 16*S^6)/(4*S^3))*HPL[{3}, -S^2] + ((-6 - 6*S^2 - 29*S^4 - 17*S^6 + 6*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 18*S*HPL[{5}, -S^2] + ((Pi^2*S)/3 + (-4 + 13*S^2 + 7*S^4 + 4*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((S*(-44 + 15*S^2))/16 + (Pi^2*S*(-69 - 40*S^2 + 14*S^4))/(24*(1 + S^2)) + ((-1 - 18*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(4*S*(1 + S^2)) - (2*S*HPL[{1}, -S^2]^3)/3 + ((-2 - 2*S^2 - 9*S^4 - 4*S^6 + 2*S^8)*HPL[{2}, -S^2])/(4*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-5*Pi^2*S)/12 + (2 - 4*S^2 - 3*S^4 + 3*S^6)/(4*S^3) - (S*HPL[{2}, -S^2])/2) - S*HPL[{3}, -S^2] + S*HPL[{2, 1}, -S^2]) - (2*(-1 - S^2 - 5*S^4 - S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 4*S*HPL[{3, 2}, -S^2] - 4*S*HPL[{4, 1}, -S^2] + (4*(-1 - 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - 8*S*HPL[{2, 2, 1}, -S^2] - 24*S*HPL[{3, 1, 1}, -S^2] + ((Pi^2*S*(-21 - 4*S^2 + 2*S^4))/(6*(1 + S^2)) - S*HPL[{0}, S^2]^3 + ((-5*Pi^2*S)/3 + (2*(1 - S^2 - S^4 + S^6))/S^3)*HPL[{1}, -S^2] - (18*S*HPL[{1}, -S^2]^2)/(1 + S^2) - 4*S*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*((S*(-6 - 2*S^2 + S^4))/(1 + S^2) - 2*S*HPL[{1}, -S^2]) + (2*(-1 - 3*S^4 + S^6)*HPL[{2}, -S^2])/S^3 + HPL[{0}, S^2]*(-2*Pi^2*S + 2*S*(-1 + S^2) - (18*S*HPL[{1}, -S^2])/(1 + S^2) - 6*S*HPL[{1}, -S^2]^2 - 2*S*HPL[{2}, -S^2]))*Log[T]^2 + ((12*S*HPL[{1}, -S^2])/(1 + S^2) + 4*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((6*S)/(1 + S^2) + 4*S*HPL[{1}, -S^2]))*Log[T]^3 + ((-3*S)/(1 + S^2) - 2*S*HPL[{0}, S^2] - 2*S*HPL[{1}, -S^2])*Log[T]^4 - (S*(7 + 4*S^2)*Zeta[3])/2 + HPL[{1}, -S^2]^2*(((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(8*S^3) + (Pi^2*(-1 - 36*S^2 - 3*S^4 + 2*S^6))/(12*S*(1 + S^2)) + ((-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 + 2*S*Zeta[3]) + HPL[{2}, -S^2]*((-15 - 36*S^2 - 44*S^4 + 15*S^6)/(8*S^3) + (Pi^2*(-4 - 4*S^2 - 15*S^4 - 8*S^6 + 4*S^8))/(12*S^3*(1 + S^2)) + 2*S*HPL[{3}, -S^2] + 4*S*HPL[{2, 1}, -S^2] + 2*S*Zeta[3]) + HPL[{1}, -S^2]*((-7*Pi^4*S)/36 + ((1 + S^2)*(3 - 62*S^2 + 3*S^4))/(16*S^3) + (Pi^2*(1 + S^2)*(4 - 10*S^2 + 5*S^4))/(12*S^3) + (-(Pi^2*S)/6 + (-1 - 11*S^2 - 9*S^4 + S^6)/(2*S^3))*HPL[{2}, -S^2] - S*HPL[{2}, -S^2]^2 + ((-1 - 4*S^4 + S^6)*HPL[{3}, -S^2])/S^3 - 4*S*HPL[{4}, -S^2] - (2*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 + 4*S*HPL[{3, 1}, -S^2] + ((-1 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + Log[T]*((5*(1 + S^2))/(4*S) - (Pi^2*S*(-11 + 6*S^2))/12 + ((5*Pi^2*S)/3 - (2*(1 - S^2 - S^4 + S^6))/S^3)*HPL[{1}, -S^2]^2 + (12*S*HPL[{1}, -S^2]^3)/(1 + S^2) + 2*S*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*((3*S)/(2*(1 + S^2)) + S*HPL[{1}, -S^2]) + HPL[{0}, S^2]^2*(-(S*(-11 + 6*S^2))/4 + ((1 + 18*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2])/(2*S*(1 + S^2)) + 2*S*HPL[{1}, -S^2]^2) + ((6 + 9*S^2 + 11*S^4 - 6*S^6)*HPL[{2}, -S^2])/(2*S^3) + 2*S*HPL[{3}, -S^2] - 4*S*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]*((3*Pi^2*S)/(1 + S^2) - (S*(-15 + 7*S^2))/4 + (18*S*HPL[{1}, -S^2]^2)/(1 + S^2) + 4*S*HPL[{1}, -S^2]^3 + ((2 + S^2 + 6*S^4 + S^6)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + HPL[{1}, -S^2]*(2*Pi^2*S - (2*(1 - S^2 - S^4 + S^6))/S^3 + 4*S*HPL[{2}, -S^2]) + 2*S*HPL[{3}, -S^2] - 4*S*HPL[{2, 1}, -S^2]) + (2*S*(-1 + 2*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(4*S^3) + (Pi^2*(1 + 36*S^2 + 3*S^4 - 2*S^6))/(6*S*(1 + S^2)) - (2*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 - 4*S*Zeta[3])) + HPL[{0}, S^2]*((-47*Pi^4*S)/90 + (Pi^2*S*(-1 + 7*S^2))/6 + (-10 - 49*S^2 + 3*S^4)/(16*S) - (6*S*HPL[{1}, -S^2]^3)/(1 + S^2) - S*HPL[{1}, -S^2]^4 + (-(Pi^2*S)/6 + (-6 - 5*S^2 - 9*S^4 + 4*S^6)/(4*S^3))*HPL[{2}, -S^2] - (S*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*(-(Pi^2*S) + (1 - S^2 - S^4 + S^6)/S^3 - 2*S*HPL[{2}, -S^2]) + ((1 + 3*S^2 - 2*S^4)*HPL[{3}, -S^2])/(2*S) + 3*S*HPL[{4}, -S^2] + ((-1 + 2*S^2 - S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - 4*S*HPL[{2, 1, 1}, -S^2] + (S*(-1 + 2*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*((-3*Pi^2*S)/(1 + S^2) + ((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(8*S^3) + ((-1 - 4*S^4 - S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + 4*S*HPL[{2, 1}, -S^2] - 2*S*Zeta[3]));
e3T3F3=(121*(1 + S^2))/(432*S) + (Pi^2*(-122 + 232*S^2 + 405*S^4))/(1296*S) + (Pi^4*(210 + 105*S^2 + 751*S^4 + 541*S^6))/(3240*S*(1 + S^2)) + (S^3*HPL[{0}, S^2]^5)/24 + ((5*Pi^2*(1 + S^6))/(27*S^3) + (121 + 171*S^2 + 171*S^4 + 121*S^6)/(162*S^3))*HPL[{1}, -S^2]^3 + ((2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2]^5)/(15*S^3) + HPL[{0}, S^2]^4*((2 + S^2 + 14*S^4 + 12*S^6)/(48*S*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2])/(24*S^3)) + HPL[{0}, S^2]^3*((Pi^2*S^3)/6 + (3 + 3*S^2 + 11*S^4)/(27*S) + ((2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2]^2)/(6*S^3)) + ((-7 + 5*S^2 + 6*S^4 + 5*S^6 - 7*S^8)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)) + ((Pi^2*(1 + S^6))/(9*S^3) + (39 - 153*S^2 + 99*S^4 + 247*S^6)/(108*S^3))*HPL[{3}, -S^2] + ((-129 - 105*S^2 + 12*S^4 + 125*S^6 + 101*S^8)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)) + (6*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((52 + 63*S^2 - 63*S^4 - 52*S^6)/(27*S^3) + (Pi^2*(-1 - S^6))/(9*S^3))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-232 + 122*S^2 + 405*S^4)/(432*S) + (Pi^2*(30 + 15*S^2 + 149*S^4 + 119*S^6))/(216*S*(1 + S^2)) + ((-1 + 23*S^2 + 12*S^4 + 41*S^6 + 17*S^8)*HPL[{1}, -S^2]^2)/(36*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((-18 - 12*S^2 + 3*S^4 + 17*S^6 + 11*S^8)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((5*Pi^2*(1 + S^6))/(36*S^3) + (-80 - 21*S^2 + 186*S^4 + 127*S^6)/(216*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(6*S^3)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) - (2*(-9 - 3*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (22*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 + ((55*(1 + S^2))/(54*S) + (Pi^2*(30 + 15*S^2 + 41*S^4 + 11*S^6))/(54*S*(1 + S^2)) + (S^3*HPL[{0}, S^2]^3)/3 + ((5*Pi^2*(1 + S^6))/(9*S^3) + (121 + 171*S^2 + 171*S^4 + 121*S^6)/(54*S^3))*HPL[{1}, -S^2] + (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{1}, -S^2]^3)/(3*S^3) + HPL[{0}, S^2]^2*((12 + 6*S^2 + 23*S^4 + 11*S^6)/(18*S*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3)) + (11*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((2*Pi^2*S^3)/3 + (108 + 63*S^2 + 121*S^4)/(54*S) + (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2]^2)/S^3 + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)))*Log[T]^2 + ((-8*(1 + S^2))/(9*S) - (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]*((-2*(6 + 3*S^2 + 10*S^4 + 4*S^6))/(9*S*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(3*S^3)))*Log[T]^3 + ((2 + S^2 + 2*S^4)/(3*S*(1 + S^2)) + (2*S^3*HPL[{0}, S^2])/3 + (2*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3))*Log[T]^4 + ((-57 + 6*S^2 + 52*S^4)*Zeta[3])/(27*S) + HPL[{1}, -S^2]^2*(((1 + S^2)*(93 + 16*S^2 + 93*S^4))/(54*S^3) + (Pi^2*(11 + 71*S^2 + 30*S^4 + 89*S^6 + 29*S^8))/(108*S^3*(1 + S^2)) + ((-1 + S^6)*HPL[{2}, -S^2])/S^3 - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-135 - 118*S^2 + 118*S^4 + 135*S^6)/(72*S^3) + (Pi^2*(-29 - 23*S^2 + 3*S^4 + 28*S^6 + 22*S^8))/(108*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((7*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(108*S^3) + (Pi^2*(1 + S^2)*(41 + 109*S^2 + 248*S^4))/(648*S^3) + ((1 + S^2)*(1279 + 42*S^2 + 1279*S^4))/(432*S^3) + ((23*(-1 + S^2)*(1 + S^2)^2)/(12*S^3) + (Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3))*HPL[{2}, -S^2] + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + ((-1 + S^6)*HPL[{3}, -S^2])/S^3 + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (2*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + ((-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]*((47*Pi^4*S^3)/270 + (5*Pi^2*(36 + 27*S^2 + 77*S^4))/(648*S) + (1184 + 137*S^2 + 1279*S^4)/(432*S) + (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2]^4)/(3*S^3) + ((Pi^2*(1 + S^6))/(18*S^3) + (98 + 111*S^2 + 66*S^4 + 97*S^6)/(108*S^3))*HPL[{2}, -S^2] + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(6*S^3) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^6))/(3*S^3) + (121 + 171*S^2 + 171*S^4 + 121*S^6)/(108*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + ((10 + S^6)*HPL[{3}, -S^2])/(9*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/S^3 - (2*(3 + 9*S^2 + 3*S^4 + 7*S^6 + S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((6 + 3*S^2 - S^4 - 7*S^6)*Zeta[3])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(93 + 16*S^2 + 93*S^4))/(54*S^3) + (Pi^2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8))/(9*S^3*(1 + S^2)) + (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + Log[T]*((-41*(1 + S^2))/(54*S) + (Pi^2*(-66 - 147*S^2 - 103*S^4))/(324*S) + ((-121 - 171*S^2 - 171*S^4 - 121*S^6)/(54*S^3) - (5*Pi^2*(1 + S^6))/(9*S^3))*HPL[{1}, -S^2]^2 - (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^4)/(3*S^3) + HPL[{0}, S^2]^3*((-6 - 3*S^2 - 10*S^4 - 4*S^6)/(18*S*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^2*((6 - 75*S^2 - 103*S^4)/(108*S) + ((1 - 23*S^2 - 12*S^4 - 41*S^6 - 17*S^8)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S^3)) - ((-1 + S^2)*(103 + 184*S^2 + 103*S^4)*HPL[{2}, -S^2])/(54*S^3) - (7*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (14*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((-169 - 49*S^2 - 186*S^4)/(54*S) + (Pi^2*(-6 - 3*S^2 - 10*S^4 - 4*S^6))/(9*S*(1 + S^2)) - (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*S^3) - (2*(1 + 7*S^2 + 3*S^4 + 9*S^6 + 3*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-121 - 171*S^2 - 171*S^4 - 121*S^6)/(54*S^3) - (2*Pi^2*(1 + S^6))/(3*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) - (2*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(93 + 16*S^2 + 93*S^4))/(27*S^3) + (Pi^2*(-11 - 71*S^2 - 30*S^4 - 89*S^6 - 29*S^8))/(54*S^3*(1 + S^2)) - (2*(-1 + S^6)*HPL[{2}, -S^2])/S^3 + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)));
e3T=e3T0F0+T*e3T1F1*(F+1/F)+T^2*(e3T2F0+e3T2F2*(F^2+1/F^2))+T^3*(e3T3F1*(F+1/F)+e3T3F3*(F^3+1/F^3));
E3uvwT0F0=(-283*Pi^6)/1620 - HPL[{0}, S^2]^6/48 - (HPL[{0}, S^2]^5*HPL[{1}, -S^2])/4 - (8*Pi^2*HPL[{1}, -S^2]^4)/3 - (4*HPL[{1}, -S^2]^6)/3 + HPL[{0}, S^2]^4*(-Pi^2/6 - (3*HPL[{1}, -S^2]^2)/4 - HPL[{2}, -S^2]/4) - (4*Pi^2*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((-151*Pi^4)/90 - (5*Pi^2*HPL[{2}, -S^2])/3 - 10*HPL[{2}, -S^2]^2) + 2*HPL[{3}, -S^2]^2 - (2*Pi^2*HPL[{4}, -S^2])/3 - 56*HPL[{6}, -S^2] + 20*HPL[{2, 1}, -S^2]^2 + 2*Pi^2*HPL[{3, 1}, -S^2] + 28*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-13*Pi^4)/45 - 4*HPL[{4}, -S^2] + 20*HPL[{3, 1}, -S^2] - 40*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]^2*((-151*Pi^4)/360 - 3*HPL[{1}, -S^2]^4 + HPL[{1}, -S^2]^2*(-3*Pi^2 - 5*HPL[{2}, -S^2]) - (11*Pi^2*HPL[{2}, -S^2])/12 - (3*HPL[{2}, -S^2]^2)/2 - 2*HPL[{4}, -S^2] + 10*HPL[{1}, -S^2]*HPL[{2, 1}, -S^2] + 6*HPL[{3, 1}, -S^2] - 10*HPL[{2, 1, 1}, -S^2]) - (10*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + ((-8*Pi^2)/3 - 3*HPL[{0}, S^2]^2 - 20*HPL[{0}, S^2]*HPL[{1}, -S^2] - 20*HPL[{1}, -S^2]^2)*Log[T]^4 + (4*HPL[{0}, S^2] + 8*HPL[{1}, -S^2])*Log[T]^5 - (4*Log[T]^6)/3 + Log[T]^3*((20*HPL[{0}, S^2]^3)/9 + (32*Pi^2*HPL[{1}, -S^2])/3 + 12*HPL[{0}, S^2]^2*HPL[{1}, -S^2] + (80*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]*((50*Pi^2)/9 + 40*HPL[{1}, -S^2]^2 + 16*HPL[{2}, -S^2]) - (40*HPL[{3}, -S^2])/3 - 16*Zeta[3]) + HPL[{0}, S^2]^3*((-20*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((-25*Pi^2)/18 - (7*HPL[{2}, -S^2])/3) + (7*HPL[{2, 1}, -S^2])/3 - 2*Zeta[3]) - 20*HPL[{2, 1}, -S^2]*Zeta[3] + 4*Zeta[3]^2 + HPL[{3}, -S^2]*(-20*HPL[{2, 1}, -S^2] + 4*Zeta[3]) + HPL[{1}, -S^2]^3*((40*HPL[{3}, -S^2])/3 + 16*Zeta[3]) + Log[T]^2*((-151*Pi^4)/90 - (3*HPL[{0}, S^2]^4)/4 - (20*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/3 - 16*Pi^2*HPL[{1}, -S^2]^2 - 20*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^2*(-3*Pi^2 - 18*HPL[{1}, -S^2]^2 - 5*HPL[{2}, -S^2]) - (5*Pi^2*HPL[{2}, -S^2])/3 - 10*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]*(-40*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*((-50*Pi^2)/3 - 48*HPL[{2}, -S^2]) - 4*HPL[{3}, -S^2] + 48*HPL[{2, 1}, -S^2]) + HPL[{1}, -S^2]*(40*HPL[{3}, -S^2] + 48*Zeta[3])) + Log[T]*(HPL[{0}, S^2]^5/4 + (3*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/2 + (32*Pi^2*HPL[{1}, -S^2]^3)/3 + 8*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^3*((25*Pi^2)/18 + (20*HPL[{1}, -S^2]^2)/3 + (7*HPL[{2}, -S^2])/3) + HPL[{1}, -S^2]*((151*Pi^4)/45 + (10*Pi^2*HPL[{2}, -S^2])/3 + 20*HPL[{2}, -S^2]^2) - (10*Pi^2*HPL[{3}, -S^2])/3 + 20*HPL[{5}, -S^2] + HPL[{0}, S^2]^2*(12*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*(6*Pi^2 + 10*HPL[{2}, -S^2]) - 10*HPL[{2, 1}, -S^2]) - (10*Pi^2*HPL[{2, 1}, -S^2])/3 + 40*HPL[{3, 2}, -S^2] + 120*HPL[{4, 1}, -S^2] + HPL[{0}, S^2]*((61*Pi^4)/30 + 20*HPL[{1}, -S^2]^4 + (19*Pi^2*HPL[{2}, -S^2])/3 + 10*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((50*Pi^2)/3 + 48*HPL[{2}, -S^2]) + 4*HPL[{4}, -S^2] + HPL[{1}, -S^2]*(8*HPL[{3}, -S^2] - 96*HPL[{2, 1}, -S^2]) - 48*HPL[{3, 1}, -S^2] + 96*HPL[{2, 1, 1}, -S^2]) + 80*HPL[{2, 2, 1}, -S^2] + 160*HPL[{3, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*(-40*HPL[{3}, -S^2] - 48*Zeta[3]) + HPL[{2}, -S^2]*(-20*HPL[{3}, -S^2] - 40*HPL[{2, 1}, -S^2] - 20*Zeta[3]) - 4*Pi^2*Zeta[3] - 32*Zeta[5]) + HPL[{0}, S^2]*(-4*HPL[{1}, -S^2]^5 + HPL[{1}, -S^2]^3*((-50*Pi^2)/9 - 16*HPL[{2}, -S^2]) - (Pi^2*HPL[{3}, -S^2])/3 + 6*HPL[{5}, -S^2] + (19*Pi^2*HPL[{2, 1}, -S^2])/3 + HPL[{1}, -S^2]^2*(-4*HPL[{3}, -S^2] + 48*HPL[{2, 1}, -S^2]) - 4*HPL[{3, 2}, -S^2] - 8*HPL[{4, 1}, -S^2] + HPL[{1}, -S^2]*((-61*Pi^4)/30 - (19*Pi^2*HPL[{2}, -S^2])/3 - 10*HPL[{2}, -S^2]^2 - 4*HPL[{4}, -S^2] + 48*HPL[{3, 1}, -S^2] - 96*HPL[{2, 1, 1}, -S^2]) - 40*HPL[{2, 2, 1}, -S^2] - 128*HPL[{3, 1, 1}, -S^2] + 96*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(2*HPL[{3}, -S^2] + 20*HPL[{2, 1}, -S^2] - 2*Zeta[3]) - 2*Pi^2*Zeta[3] - 16*Zeta[5]) + HPL[{1}, -S^2]*((10*Pi^2*HPL[{3}, -S^2])/3 - 20*HPL[{5}, -S^2] + (10*Pi^2*HPL[{2, 1}, -S^2])/3 - 40*HPL[{3, 2}, -S^2] - 120*HPL[{4, 1}, -S^2] - 80*HPL[{2, 2, 1}, -S^2] - 160*HPL[{3, 1, 1}, -S^2] + 4*Pi^2*Zeta[3] + HPL[{2}, -S^2]*(20*HPL[{3}, -S^2] + 40*HPL[{2, 1}, -S^2] + 20*Zeta[3]) + 32*Zeta[5]);
E3uvwT1F1=(S*HPL[{0}, S^2]^5)/(4*(1 + S^2)) + ((-2 + 5*S^2 + S^4)*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/(4*S*(1 + S^2)) - (4*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2]^5)/(5*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((Pi^2*(-13 + 77*S^2 - 6*S^4))/(9*S*(1 + S^2)) + (14*(-1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]^3*(-(Pi^2*S*(-49 + S^2))/(36*(1 + S^2)) + ((-6 + 33*S^2 - S^4)*HPL[{1}, -S^2]^2)/(6*S*(1 + S^2)) - (S*(-13 + S^2)*HPL[{2}, -S^2])/(6*(1 + S^2))) + (Pi^2*(-1 - 4*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (4*(-4 + 7*S^2 + 6*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*(-6 + 3*S^2 + 4*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*S*(-3 + 2*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (4*(-3 - 16*S^2 + 17*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (16*(1 - 3*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(13 - 26*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (48*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-2*Pi^2*S*(49 + S^2))/(9*(1 + S^2)) - (2*S*(19 + S^2)*HPL[{0}, S^2]^2)/(3*(1 + S^2)) + (8*(1 - 8*S^2 + S^4)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(S*(1 + S^2)) + (8*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) - (4*(-1 + S^2)*HPL[{2}, -S^2])/(3*S))*Log[T]^3 + ((-4*S*(-4 + S^2)*HPL[{0}, S^2])/(1 + S^2) - (4*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2])/(S*(1 + S^2)))*Log[T]^4 - (8*S*Log[T]^5)/(1 + S^2) + (4*Pi^2*S^3*Zeta[3])/(1 + S^2) + HPL[{0}, S^2]^2*(((-1 - S^2)*HPL[{1}, -S^2]^2)/S + ((-7 + 29*S^2)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((-2*(1 + S^2))/S + (Pi^2*(-19 + 59*S^2 + 6*S^4))/(12*S*(1 + S^2)) + ((-7 + 16*S^2 + 3*S^4)*HPL[{2}, -S^2])/(2*S*(1 + S^2))) + ((-1 + 3*S^2)*HPL[{3}, -S^2])/(2*S) - (2*(-3 + 3*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 6*S*Zeta[3]) + Log[T]^2*(-(S*(-19 + S^2)*HPL[{0}, S^2]^3)/(3*(1 + S^2)) + ((-7 + 29*S^2)*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/(S*(1 + S^2)) - (8*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-13 + 77*S^2 - 6*S^4))/(3*S*(1 + S^2)) + (14*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]*(-(Pi^2*S*(-43 + 7*S^2))/(3*(1 + S^2)) - (12*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) - (2*S*(-19 + 5*S^2)*HPL[{2}, -S^2])/(1 + S^2)) + (2*(-1 + S^2)*(1 + 11*S^2)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (24*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (24*S*(-1 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]*((-2*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-29 + 122*S^2))/(45*S*(1 + S^2)) + (Pi^2*(-7 + 8*S^2 + 5*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (2*(1 - 8*S^2 + S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) + (4*(-3 + 4*S^2)*HPL[{4}, -S^2])/S - (4*(-3 + 4*S^2)*HPL[{3, 1}, -S^2])/S + (28*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((4*S*(-3 + 2*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (8*(1 - 3*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*S*(-3 + 2*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(-1 - S^2))/(3*S) + (2*(-1 - 15*S^2 + 6*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (14*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (2*(-1 - 19*S^2 + 6*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]*(-(Pi^4*S*(-167 + 16*S^2))/(90*(1 + S^2)) - (2*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)) + ((4*(1 + S^2))/S - (Pi^2*S*(-16 + 3*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] - (2*S*(-4 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((Pi^2*(-12 + 81*S^2 - 7*S^4))/(6*S*(1 + S^2)) + ((-5 + 38*S^2 - 5*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + (2*(1 + S^2)*HPL[{3}, -S^2])/S - (4*S^3*HPL[{4}, -S^2])/(1 + S^2) - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (12*S*(-3 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (4*S*(-19 + 5*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((4*(1 + S^2)*HPL[{2}, -S^2])/S - (2*S*(-3 + S^2)*HPL[{3}, -S^2])/(1 + S^2) + (2*(5 - 38*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 2*S*Zeta[3])) + Log[T]*(-(Pi^4*S*(167 + 16*S^2))/(45*(1 + S^2)) - (S*(4 + S^2)*HPL[{0}, S^2]^4)/(2*(1 + S^2)) + ((6 - 33*S^2 + S^4)*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/(3*S*(1 + S^2)) + (4*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)) - (2*Pi^2*(-1 + 5*S^2 + S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (20*S*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((Pi^2*(13 - 77*S^2 + 6*S^4))/(3*S*(1 + S^2)) - (14*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^2*(-(Pi^2*S*(43 + 7*S^2))/(6*(1 + S^2)) + (2*(1 + S^2)*HPL[{1}, -S^2])/S + ((7 - 29*S^2)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) + ((1 - 10*S^2 - S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) - (12*(-1 + S^2)*HPL[{4}, -S^2])/S + HPL[{0}, S^2]*((8*(1 - 8*S^2 + S^4)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)) - (4*(1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((Pi^2*(12 - 81*S^2 + 7*S^4))/(3*S*(1 + S^2)) + (2*(5 - 38*S^2 + 5*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) - (8*S*HPL[{3}, -S^2])/(1 + S^2) + (4*(-5 + 19*S^2)*HPL[{2, 1}, -S^2])/(S*(1 + S^2))) + (4*(-1 + S^2)*HPL[{3, 1}, -S^2])/S - (8*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + HPL[{1}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) - (4*(-1 - 15*S^2 + 6*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (28*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(-1 - 19*S^2 + 6*S^4)*Zeta[3])/(S*(1 + S^2)))) + (32*S^3*Zeta[5])/(1 + S^2);
E3uvwT2F0=(-2*Pi^2*(-1 + S^2))/3 + (Pi^4*(29 - 138*S^2 - 16*S^4))/(45*(1 + S^2)^2) + HPL[{0}, S^2]^5/(4*(1 + S^2)^2) + (2*(13 - 34*S^2 + 13*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) - (8*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/(5*(1 + S^2)^2) + HPL[{0}, S^2]^4*((2 - 7*S^2 - 3*S^4)/(4*(1 + S^2)^2) + ((4 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(2*(1 + S^2)^2)) + (2*(1 - 8*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^3*((4*(1 + S^2)^2)/(3*S^2) - (4*Pi^2*(-7 + 2*S^2 + S^4))/(3*(1 + S^2)^2) + (28*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^3*(2*(1 + S^2) + (Pi^2*(24 - 2*S^2 - S^4))/(18*(1 + S^2)^2) + (2*(9 - 7*S^2 + 4*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + ((19 - 2*S^2 - S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + ((6 - 2*S^2 - S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((4*(1 + S^2)*(3 + 2*S^2))/S^2 + (2*Pi^2*(2 + 14*S^2 + 7*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (4*(-11 + 2*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (4*(17 + 24*S^2 + 12*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((4*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(13 + 16*S^2 + 8*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (36*HPL[{3, 1}, -S^2])/(1 + S^2) - (8*(-1 + 8*S^2 + 4*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (8*(2 + 34*S^2 + 17*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (36*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (16*(-3 + 4*S^2 + 2*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(-19 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 96*HPL[{2, 1, 1, 1}, -S^2] + ((-4*Pi^2*(25 + 2*S^2 + S^4))/(9*(1 + S^2)^2) - (4*(10 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^2) - (8*(13 - 34*S^2 + 13*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + (16*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]*((-4*(7 - 34*S^2 + 19*S^4))/(3*(1 + S^2)^2) + (16*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) - (8*HPL[{2}, -S^2])/3)*Log[T]^3 + ((4*(1 - 8*S^2 + S^4))/(1 + S^2)^2 - (4*(-3 + 4*S^2 + 2*S^4)*HPL[{0}, S^2])/(1 + S^2)^2 - (8*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2)*Log[T]^4 - (8*Log[T]^5)/(1 + S^2)^2 + (-4*(-1 + S^2) + (4*Pi^2*(1 + 4*S^2 + 2*S^4))/(1 + S^2)^2)*Zeta[3] + HPL[{0}, S^2]^2*(-2*(-1 + S^2) + (Pi^2*(19 - 73*S^2 - 20*S^4))/(12*(1 + S^2)^2) - (2*(-6 + 13*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (12*HPL[{1}, -S^2]^3)/(1 + S^2)^2 + ((9 - 16*S^2 - 5*S^4)*HPL[{2}, -S^2])/(2*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(((-1 + S^2)*(1 + S^2))/S^2) + (Pi^2*(7 + 2*S^2 + S^4))/(1 + S^2)^2 + ((13 + 6*S^2 + 3*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + 3*HPL[{3}, -S^2] - (2*(7 + 4*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + 12*Zeta[3]) + HPL[{1}, -S^2]^2*((4*(1 + S^2)^2)/S^2 + (Pi^2*(25 - 60*S^2 + 11*S^4))/(3*(1 + S^2)^2) - (28*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (8*(-2 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 28*HPL[{2, 1}, -S^2] + (24*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + Log[T]^2*((Pi^2*(13 - 79*S^2 + 4*S^4))/(3*(1 + S^2)^2) - (2*(-9 + 2*S^2 + S^4)*HPL[{0}, S^2]^3)/(3*(1 + S^2)^2) + (4*(13 - 34*S^2 + 13*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 - (16*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 + HPL[{0}, S^2]^2*((7 - 31*S^2 - 2*S^4)/(1 + S^2)^2 + (36*HPL[{1}, -S^2])/(1 + S^2)^2) - (18*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((4*(1 + S^2)^2)/S^2 - (4*Pi^2*(-7 + 2*S^2 + S^4))/(1 + S^2)^2 + 28*HPL[{2}, -S^2]) + HPL[{0}, S^2]*(4*(1 + S^2) - (2*Pi^2*(-18 + 14*S^2 + 7*S^4))/(3*(1 + S^2)^2) + (4*(13 - 34*S^2 + 13*S^4)*HPL[{1}, -S^2])/(1 + S^2)^2 - (24*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 - (4*(-7 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (4*(1 + 22*S^2 + 11*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 48*HPL[{2, 1}, -S^2] + (48*(2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-4*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(9 - 8*S^2 - 7*S^4))/(3*(1 + S^2)^2) + (4*(-1 + 8*S^2 + 4*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-3 + 4*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(-1 + 8*S^2 + 4*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((151*Pi^4)/(45*(1 + S^2)^2) + (2*Pi^2*(1 + S^2))/(3*S^2) + (8*(1 + S^2)^2)/S^2 + ((-4*(-1 + S^2)*(1 + S^2))/S^2 + (10*Pi^2*(2 + 2*S^2 + S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (4*(-4 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 - (4*(-7 - 20*S^2 + 7*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 32*HPL[{4}, -S^2] + (56*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 32*HPL[{3, 1}, -S^2] + 56*HPL[{2, 1, 1}, -S^2] - (4*(1 - 8*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]*(8*(1 + S^2) + (7*Pi^2*(1 + S^2))/3 + (Pi^4*(151 - 64*S^2 - 32*S^4))/(90*(1 + S^2)^2) + (4*(13 - 34*S^2 + 13*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) - (4*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(1 + S^2)^2 + ((2*(1 + S^2)^2)/S^2 + (Pi^2*(13 - 12*S^2 - 6*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (2*(-3 + 4*S^2 + 2*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((2*(1 + S^2)^2)/S^2 + (Pi^2*(43 - 14*S^2 - 7*S^4))/(3*(1 + S^2)^2) - (2*(-19 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (2*(3 + 3*S^2 + 4*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(1 + 4*S^2 + 2*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (2*(21 - 16*S^2 + 11*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (24*(-1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-7 + 10*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(5 + 4*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*((4*(1 + S^2)^2)/S^2 + (Pi^2*(31 - 48*S^2 + 21*S^4))/(3*(1 + S^2)^2) + (32*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 - (4*(-1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-19 + 10*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + 4*Zeta[3])) + Log[T]*((2*Pi^2*(-1 + S^2))/3 + (Pi^4*(-183 - 64*S^2 - 32*S^4))/(45*(1 + S^2)^2) + ((-5 - 4*S^2 - 2*S^4)*HPL[{0}, S^2]^4)/(2*(1 + S^2)^2) - (8*(13 - 34*S^2 + 13*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + (8*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(1 + S^2)^2 + HPL[{0}, S^2]^3*((-12 + 19*S^2 - 9*S^4)/(3*(1 + S^2)^2) + (2*(-19 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-4*(1 + S^2)^2)/S^2 + (4*Pi^2*(-7 + 2*S^2 + S^4))/(1 + S^2)^2 - 28*HPL[{2}, -S^2]) + ((4*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(7 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (20*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]^2*(2*(-1 + S^2) + (Pi^2*(-25 - 14*S^2 - 7*S^4))/(3*(1 + S^2)^2) + (4*(-6 + 13*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2 - (36*HPL[{1}, -S^2]^2)/(1 + S^2)^2 - (2*(6 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (4*(-7 - 15*S^2 + 12*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 24*HPL[{4}, -S^2] - (76*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + HPL[{0}, S^2]*(-8*(1 + S^2) + (Pi^2*(-19 + 53*S^2 - 28*S^4))/(3*(1 + S^2)^2) - (4*(13 - 34*S^2 + 13*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (16*(-4 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 - (2*(11 - 16*S^2 + 21*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-4*(1 + S^2)^2)/S^2 + (2*Pi^2*(-43 + 14*S^2 + 7*S^4))/(3*(1 + S^2)^2) + (4*(-19 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) - (8*HPL[{3}, -S^2])/(1 + S^2)^2 + (96*HPL[{2, 1}, -S^2])/(1 + S^2)^2) + 8*HPL[{3, 1}, -S^2] - 16*HPL[{2, 1, 1}, -S^2] + (4*(-1 - 7*S^2 + 18*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-8*(1 + S^2)^2)/S^2 - (2*Pi^2*(25 - 60*S^2 + 11*S^4))/(3*(1 + S^2)^2) + (56*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (16*(-2 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 56*HPL[{2, 1}, -S^2] - (48*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2)) + (32*(1 + 4*S^2 + 2*S^4)*Zeta[5])/(1 + S^2)^2;
E3uvwT2F2=(Pi^2*(1 - S^2))/3 + (Pi^4*(29 - 138*S^2 - 16*S^4))/(90*(1 + S^2)^2) - (S^2*HPL[{0}, S^2]^5)/(8*(1 + S^2)^2) + ((-1 + 22*S^2 - 74*S^4 + 22*S^6 - S^8)*HPL[{1}, -S^2]^4)/(6*S^2*(1 + S^2)^2) + (2*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^5)/(5*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^4*((2 - 7*S^2 - 3*S^4)/(8*(1 + S^2)^2) + ((2 + 4*S^2 - 5*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2])/(8*S^2*(1 + S^2)^2)) + ((1 - 8*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^3*(-(1 + S^2)^2/(3*S^2) + (Pi^2*(13 + 26*S^2 - 77*S^4 + 12*S^6 + 6*S^8))/(18*S^2*(1 + S^2)^2) - (7*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]^3*((-1 - S^2)/2 + (Pi^2*(-49*S^2 + 2*S^4 + S^6))/(72*(1 + S^2)^2) + ((-3 + 6*S^2 - 32*S^4 - 4*S^6 - 3*S^8)*HPL[{1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((6 + 12*S^2 - 33*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(12*S^2*(1 + S^2)^2) + (S^2*(-13 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(12*(1 + S^2)^2)) + (-((1 + S^2)*(3 + 7*S^2))/(2*S^2) + (Pi^2*(1 + 2*S^2 + 4*S^4 - 14*S^6 - 7*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-5 + 7*S^2 - 19*S^4 - 5*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) - (2*(-4 - 8*S^2 + 7*S^4 + 12*S^6 + 6*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-6 - 12*S^2 + 3*S^4 + 8*S^6 + 4*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((5 - 3*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (4*S^2*(-3 + 4*S^2 + 2*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (2*(-3 - 6*S^2 - 16*S^4 + 34*S^6 + 17*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (18*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (8*(1 + 2*S^2 - 3*S^4 + 2*S^6 + S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(13 + 26*S^2 - 26*S^4 + 2*S^6 + S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (24*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*S^2*(49 + 2*S^2 + S^4))/(9*(1 + S^2)^2) + (S^2*(19 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^2) + (2*(1 - 22*S^2 + 74*S^4 - 22*S^6 + S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + HPL[{0}, S^2]*((2*(-6 + 37*S^2 - 16*S^4 + S^6))/(3*(1 + S^2)^2) - (4*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2])/(S^2*(1 + S^2)^2)) + (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2))*Log[T]^3 + ((2*(1 - 8*S^2 + S^4))/(1 + S^2)^2 + (2*S^2*(-4 + 2*S^2 + S^4)*HPL[{0}, S^2])/(1 + S^2)^2 + (2*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2])/(S^2*(1 + S^2)^2))*Log[T]^4 + (4*S^2*Log[T]^5)/(1 + S^2)^2 + (-2*(-1 + S^2) - (2*Pi^2*(2*S^4 + S^6))/(1 + S^2)^2)*Zeta[3] + HPL[{0}, S^2]^2*(1 - S^2 + (Pi^2*(19 - 73*S^2 - 20*S^4))/(24*(1 + S^2)^2) + ((1 + 28*S^2 - 46*S^4 + S^8)*HPL[{1}, -S^2]^2)/(4*S^2*(1 + S^2)^2) + ((7 + 14*S^2 - 29*S^4)*HPL[{1}, -S^2]^3)/(6*S^2*(1 + S^2)^2) + ((9 - 16*S^2 - 5*S^4)*HPL[{2}, -S^2])/(4*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((-3 + S^2)*(1 + S^2))/(4*S^2) + (Pi^2*(19 + 38*S^2 - 59*S^4 - 12*S^6 - 6*S^8))/(24*S^2*(1 + S^2)^2) + ((7 + 14*S^2 - 16*S^4 - 6*S^6 - 3*S^8)*HPL[{2}, -S^2])/(4*S^2*(1 + S^2)^2)) + ((1 - 3*S^4)*HPL[{3}, -S^2])/(4*S^2) + ((-3 - 6*S^2 + 3*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - 3*S^2*Zeta[3]) + HPL[{2}, -S^2]*((-2*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(9 - 8*S^2 - 7*S^4))/(6*(1 + S^2)^2) - (2*S^2*(-3 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(1 + 2*S^2 - 3*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*S^2*(-3 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + Log[T]^2*((Pi^2*(13 - 79*S^2 + 4*S^4))/(6*(1 + S^2)^2) + (S^2*(-19 + 2*S^2 + S^4)*HPL[{0}, S^2]^3)/(6*(1 + S^2)^2) + ((-1 + 22*S^2 - 74*S^4 + 22*S^6 - S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)^2) + HPL[{0}, S^2]^2*((7 - 31*S^2 - 2*S^4)/(2*(1 + S^2)^2) + ((7 + 14*S^2 - 29*S^4)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)^2)) - (9*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)^2/S^2) + (Pi^2*(13 + 26*S^2 - 77*S^4 + 12*S^6 + 6*S^8))/(6*S^2*(1 + S^2)^2) - (7*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]*(-1 - S^2 + (Pi^2*(-43*S^2 + 14*S^4 + 7*S^6))/(6*(1 + S^2)^2) + ((-1 + 22*S^2 - 74*S^4 + 22*S^6 - S^8)*HPL[{1}, -S^2])/(S^2*(1 + S^2)^2) + (6*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + (S^2*(-19 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + ((1 + 2*S^2 + 10*S^4 - 22*S^6 - 11*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (12*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (12*(-S^2 + 2*S^4 + S^6)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-3*(1 + S^2)^2)/(2*S^2) + (Pi^2*(25 - 60*S^2 + 11*S^4))/(6*(1 + S^2)^2) - (14*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + ((1 + 2*S^2 + 15*S^4 - 12*S^6 - 6*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (7*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + ((1 + 2*S^2 + 19*S^4 - 12*S^6 - 6*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]*(-(Pi^2*(-1 + S^2)*(1 + S^2))/(6*S^2) - (7*(1 + S^2)^2)/(2*S^2) + (Pi^4*(29 + 58*S^2 - 122*S^4))/(90*S^2*(1 + S^2)^2) + ((-2*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(7 + 14*S^2 - 8*S^4 - 10*S^6 - 5*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-5 - 6*S^2 + 10*S^4 - 34*S^6 - 5*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-3 + 4*S^4)*HPL[{4}, -S^2])/S^2 + (28*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (2*(-3 + 4*S^4)*HPL[{3, 1}, -S^2])/S^2 - (14*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(1 + 3*S^2 + 14*S^4 - 11*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]*((-7*(1 + S^2))/2 - (7*Pi^2*(1 + S^2))/12 + (Pi^4*(-167*S^2 + 32*S^4 + 16*S^6))/(180*(1 + S^2)^2) + ((-1 + 22*S^2 - 74*S^4 + 22*S^6 - S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^4)/(S^2*(1 + S^2)^2) + (-((1 + S^2)^2/S^2) + (Pi^2*S^2*(-16 + 6*S^2 + 3*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2] + (S^2*(-4 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*(-(1 + S^2)^2/(2*S^2) + (Pi^2*(12 + 24*S^2 - 81*S^4 + 14*S^6 + 7*S^8))/(12*S^2*(1 + S^2)^2) + ((5 + 10*S^2 - 38*S^4 + 10*S^6 + 5*S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2)) + ((-1 - S^2 - 3*S^4 - S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (2*S^4*(2 + S^2)*HPL[{4}, -S^2])/(1 + S^2)^2 + ((2 - 13*S^2 + 28*S^4 - 3*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*S^2*(-3 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (2*S^2*(-19 + 10*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-6*S^2 - 5*S^4)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*((-3*(1 + S^2)^2)/(2*S^2) + (Pi^2*(-7 + 34*S^2 - 138*S^4 + 14*S^6 - 7*S^8))/(12*S^2*(1 + S^2)^2) - (2*(1 - 4*S^2 + 14*S^4 - 4*S^6 + S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2) + (S^2*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + ((-5 - 10*S^2 + 38*S^4 - 10*S^6 - 5*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - S^2*Zeta[3])) + Log[T]*((Pi^2*(-1 + S^2))/3 + (Pi^4*(167*S^2 + 32*S^4 + 16*S^6))/(90*(1 + S^2)^2) + (S^2*(4 + 2*S^2 + S^4)*HPL[{0}, S^2]^4)/(4*(1 + S^2)^2) + (2*(1 - 22*S^2 + 74*S^4 - 22*S^6 + S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) - (2*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^4)/(S^2*(1 + S^2)^2) + HPL[{0}, S^2]^3*((-6 + 37*S^2 + 9*S^4 + 6*S^6)/(6*(1 + S^2)^2) + ((-6 - 12*S^2 + 33*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2])/(6*S^2*(1 + S^2)^2)) + ((2*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-1 - 2*S^2 + 5*S^4 + 2*S^6 + S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (10*S^2*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((1 + S^2)^2/S^2 + (Pi^2*(-13 - 26*S^2 + 77*S^4 - 12*S^6 - 6*S^8))/(6*S^2*(1 + S^2)^2) + (7*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^2*(-1 + S^2 + (Pi^2*(43*S^2 + 14*S^4 + 7*S^6))/(12*(1 + S^2)^2) + ((-1 - 28*S^2 + 46*S^4 - S^8)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-7 - 14*S^2 + 29*S^4)*HPL[{1}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 10*S^4 + 2*S^6 + S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2)) + ((5 + 6*S^2 + 44*S^6 + 5*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (6*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - (38*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + HPL[{0}, S^2]*(3*(1 + S^2) + (Pi^2*(-12 + 74*S^2 - 7*S^4 + 7*S^6))/(6*(1 + S^2)^2) + ((1 - 22*S^2 + 74*S^4 - 22*S^6 + S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) - (4*(1 + 2*S^2 - 8*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)^2) + ((2 - 3*S^2 + 28*S^4 - 13*S^6 + 2*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((1 + S^2)^2/S^2 + (Pi^2*(-12 - 24*S^2 + 81*S^4 - 14*S^6 - 7*S^8))/(6*S^2*(1 + S^2)^2) + ((-5 - 10*S^2 + 38*S^4 - 10*S^6 - 5*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) + (4*S^2*HPL[{3}, -S^2])/(1 + S^2)^2 - (2*(-5 - 10*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2)) - (2*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (4*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(-1 - 7*S^2 + 18*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((3*(1 + S^2)^2)/S^2 + (Pi^2*(-25 + 60*S^2 - 11*S^4))/(3*(1 + S^2)^2) + (28*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (2*(-1 - 2*S^2 - 15*S^4 + 12*S^6 + 6*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (14*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (2*(-1 - 2*S^2 - 19*S^4 + 12*S^6 + 6*S^8)*Zeta[3])/(S^2*(1 + S^2)^2))) - (16*(2*S^4 + S^6)*Zeta[5])/(1 + S^2)^2;
E3uvwT3F1=(-9*(1 + S^2))/(4*S) + (Pi^2*(-6 - 35*S^2 - 13*S^4))/(24*S) + (Pi^4*S*(-363 + 106*S^2 + 32*S^4 + 16*S^6))/(90*(1 + S^2)^3) - (S*HPL[{0}, S^2]^5)/(4*(1 + S^2)^3) + ((13 - 180*S^2 + 186*S^4 + 4*S^6 - 15*S^8)*HPL[{1}, -S^2]^4)/(6*S*(1 + S^2)^3) + (4*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^5)/(5*(1 + S^2)^3) + HPL[{0}, S^2]^4*((S*(-22 - 5*S^2 + S^4 + 2*S^6))/(8*(1 + S^2)^3) - (S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(4*(1 + S^2)^3)) + (S*(-17 + 16*S^2 + 3*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^3*((2*Pi^2*S*(-15 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (-3 + 8*S^2 - 129*S^4 + 200*S^6 - 129*S^8 + 8*S^10 - 3*S^12)/(6*S^3*(1 + S^2)^3) - (14*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^3*((Pi^2*S*(-49 + 3*S^2 + 3*S^4 + S^6))/(36*(1 + S^2)^3) - (S*(39 - 31*S^2 + 6*S^4 + 5*S^6 + 9*S^8))/(12*(1 + S^2)^3) + ((9 - 80*S^2 + 18*S^4 - 23*S^6 - 10*S^8)*HPL[{1}, -S^2])/(6*S*(1 + S^2)^3) + (S*(-39 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(6*(1 + S^2)^3) + (S*(-13 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(6*(1 + S^2)^3)) + (-(Pi^2*S*(-3 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) + (-9 - 3*S^2 - 24*S^4 - 62*S^6 + 31*S^8 - 23*S^10 - 6*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((11 - 61*S^2 - 43*S^4 - 9*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - (4*S*(11 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(9 + 12*S^2 + 12*S^4 + 4*S^6))/(3*(1 + S^2)^3) + (3 - 15*S^2 + 102*S^4 - 54*S^6 + 31*S^8 - 3*S^10)/(2*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-7 + 49*S^2 + 47*S^4 + 13*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + (8*S*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-13 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (2*(2 - 41*S^2 - 19*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (16*S*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-39 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + 48*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*S*(13 - 34*S^2 + 13*S^4))/(3*(1 + S^2)^3) + (2*Pi^2*S*(49 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (2*S*(19 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^3) + (2*(-13 + 180*S^2 - 186*S^4 - 4*S^6 + 15*S^8)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^3) - (8*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 + HPL[{0}, S^2]*((2*S*(27 - 33*S^2 + 5*S^4 + 5*S^6))/(1 + S^2)^3 - (8*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(1 + S^2)^3) + (4*S*HPL[{2}, -S^2])/3)*Log[T]^3 + ((2*S*(-17 + 16*S^2 + 3*S^4))/(1 + S^2)^3 + (4*S*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2])/(1 + S^2)^3 + (4*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(1 + S^2)^3)*Log[T]^4 + (8*S*Log[T]^5)/(1 + S^2)^3 + ((-4*Pi^2*S^3*(3 + 3*S^2 + S^4))/(1 + S^2)^3 + (S*(-17 - 60*S^2 + 22*S^4 - 28*S^6 + 3*S^8))/(2*(1 + S^2)^3))*Zeta[3] + HPL[{0}, S^2]^2*((-3 - 32*S^2 - 13*S^4)/(8*S) + (Pi^2*S*(-215 - 3*S^2 + 10*S^4 + 14*S^6))/(24*(1 + S^2)^3) + ((6 - 81*S^2 + 22*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)^3) - (12*S*HPL[{1}, -S^2]^3)/(1 + S^2)^3 + ((2 - 63*S^2 - 12*S^4 - 5*S^6 + 2*S^8)*HPL[{2}, -S^2])/(4*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(-(Pi^2*S*(13 + 3*S^2 + 3*S^4 + S^6))/(2*(1 + S^2)^3) + (-3 + 14*S^2 - 123*S^4 + 132*S^6 - 37*S^8 - 18*S^10 + 3*S^12)/(8*S^3*(1 + S^2)^3) - (S*(23 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2}, -S^2])/(2*(1 + S^2)^3)) - (3*S*HPL[{3}, -S^2])/2 + (2*S*(6 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - 6*S*Zeta[3]) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(1 + 4*S^2 + S^4))/(2*S^3) + (Pi^2*(25 - 342*S^2 + 230*S^4 + 8*S^6 - 13*S^8))/(12*S*(1 + S^2)^3) + (7*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (4*S*(-7 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + 14*S*HPL[{2, 1}, -S^2] - (12*S*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + Log[T]^2*((-3*(1 + S^2))/(2*S) + (Pi^2*S*(-185 + 123*S^2 + 22*S^4 + 2*S^6))/(6*(1 + S^2)^3) + (S*(-19 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^3)/(3*(1 + S^2)^3) + ((13 - 180*S^2 + 186*S^4 + 4*S^6 - 15*S^8)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^3) + (8*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^3)/(1 + S^2)^3 + HPL[{0}, S^2]^2*((S*(-83 + 27*S^2 + 4*S^4 + 2*S^6))/(2*(1 + S^2)^3) - (36*S*HPL[{1}, -S^2])/(1 + S^2)^3) + ((2 - 41*S^2 - 19*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + HPL[{1}, -S^2]*((2*Pi^2*S*(-15 + 3*S^2 + 3*S^4 + S^6))/(1 + S^2)^3 + (-3 + 8*S^2 - 129*S^4 + 200*S^6 - 129*S^8 + 8*S^10 - 3*S^12)/(2*S^3*(1 + S^2)^3) - 14*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((Pi^2*S*(-43 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) - (S*(53 - 100*S^2 + 76*S^4 - 8*S^6 + 3*S^8))/(2*(1 + S^2)^3) + ((13 - 180*S^2 + 186*S^4 + 4*S^6 - 15*S^8)*HPL[{1}, -S^2])/(S*(1 + S^2)^3) + (12*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 + (2*S*(-19 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) - (2*S*(-9 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + 24*S*HPL[{2, 1}, -S^2] - (24*S*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*(-((1 + S^2)*(-13 + 16*S^2 + 13*S^4))/(4*S^3) + (Pi^2*(2 - 51*S^2 - 36*S^4 - 11*S^6 + 2*S^8))/(6*S*(1 + S^2)^3) - (4*S*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (8*S*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]*((-151*Pi^4*S)/(45*(1 + S^2)^3) - ((1 + S^2)*(1 + 4*S^2 + S^4))/S^3 + (Pi^2*(-3 + 11*S^2 - 126*S^4 + 166*S^6 - 83*S^8 - 5*S^10))/(12*S^3*(1 + S^2)^3) + ((-5*Pi^2*S*(3 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (-3 + 11*S^2 - 86*S^4 + 38*S^6 - 27*S^8 + 3*S^10)/(2*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + ((7 + 6*S^2 - 170*S^4 - 52*S^6 - 3*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - 16*S*HPL[{4}, -S^2] - (14*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 16*S*HPL[{3, 1}, -S^2] - 28*S*HPL[{2, 1, 1}, -S^2] + ((-1 + 18*S^2 - 142*S^4 + 17*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]*((-5 - 15*S^2 - 4*S^4)/(4*S) + (Pi^4*S*(-167 + 48*S^2 + 48*S^4 + 16*S^6))/(90*(1 + S^2)^3) - (Pi^2*S*(131 - 162*S^2 + 88*S^4 + 2*S^6 + 21*S^8))/(24*(1 + S^2)^3) + ((13 - 180*S^2 + 186*S^4 + 4*S^6 - 15*S^8)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^3) + (2*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^4)/(1 + S^2)^3 + ((Pi^2*S*(-16 + 9*S^2 + 9*S^4 + 3*S^6))/(3*(1 + S^2)^3) + (-3 - 2*S^2 - 69*S^4 + 20*S^6 - 93*S^8 + 6*S^10 - 3*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (2*S*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^2*((Pi^2*S*(-93 + 21*S^2 + 21*S^4 + 7*S^6))/(6*(1 + S^2)^3) + (-3 + 8*S^2 - 129*S^4 + 200*S^6 - 129*S^8 + 8*S^10 - 3*S^12)/(4*S^3*(1 + S^2)^3) + (S*(-43 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + ((3 - 4*S^2 + 16*S^4 - 6*S^6 - 5*S^8)*HPL[{3}, -S^2])/(2*S*(1 + S^2)^3) + (4*S^3*(3 + 3*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((-13 + 77*S^2 - 62*S^4 - 3*S^6 + 5*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-19 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (S*(19 + 33*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*(-((1 + S^2)*(1 + 4*S^2 + S^4))/(2*S^3) + (Pi^2*(31 - 340*S^2 + 222*S^4 - 42*S^6 - 35*S^8))/(12*S*(1 + S^2)^3) + ((8 - 67*S^2 + 72*S^4 - 7*S^6 - 10*S^8)*HPL[{2}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (2*S*(-43 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - 2*S*Zeta[3])) + Log[T]*((5*(1 + S^2))/(2*S) + (Pi^4*S*(167 + 48*S^2 + 48*S^4 + 16*S^6))/(45*(1 + S^2)^3) - (Pi^2*S*(-121 + 180*S^2 - 106*S^4 - 20*S^6 + 3*S^8))/(12*(1 + S^2)^3) + (S*(4 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^4)/(2*(1 + S^2)^3) + (2*(-13 + 180*S^2 - 186*S^4 - 4*S^6 + 15*S^8)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^3) - (4*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^4)/(1 + S^2)^3 + HPL[{0}, S^2]^3*((S*(96 + 11*S^2 + 55*S^4 + 20*S^6))/(6*(1 + S^2)^3) - (S*(-39 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(3*(1 + S^2)^3)) + ((2*Pi^2*S*(6 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (3 - 7*S^2 + 70*S^4 - 22*S^6 + 23*S^8 - 3*S^10)/(2*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (20*S*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^2*((-2*Pi^2*S*(-15 + 3*S^2 + 3*S^4 + S^6))/(1 + S^2)^3 + (3 - 8*S^2 + 129*S^4 - 200*S^6 + 129*S^8 - 8*S^10 + 3*S^12)/(2*S^3*(1 + S^2)^3) + 14*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*((Pi^2*S*(43 + 21*S^2 + 21*S^4 + 7*S^6))/(6*(1 + S^2)^3) - (S*(-69 + 44*S^2 - 54*S^4 - 20*S^6 + 3*S^8))/(4*(1 + S^2)^3) + ((-6 + 81*S^2 - 22*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2])/(S*(1 + S^2)^3) + (36*S*HPL[{1}, -S^2]^2)/(1 + S^2)^3 + (S*(11 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + ((-7 + 14*S^2 + 180*S^4 + 32*S^6 - 7*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + 12*S*HPL[{4}, -S^2] + (2*(12 - 71*S^2 - 9*S^4 + 12*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + HPL[{0}, S^2]*((3 + 7*S^2 + 2*S^4)/(2*S) + (Pi^2*S*(177 - 88*S^2 + 70*S^4 + 35*S^6))/(6*(1 + S^2)^3) + ((-13 + 180*S^2 - 186*S^4 - 4*S^6 + 15*S^8)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^3) - (8*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^3)/(1 + S^2)^3 + ((-3 + 57*S^2 - 82*S^4 + 17*S^6 + 15*S^8)*HPL[{2}, -S^2])/(S*(1 + S^2)^3) + HPL[{1}, -S^2]*(-(Pi^2*S*(-93 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) + (3 - 8*S^2 + 129*S^4 - 200*S^6 + 129*S^8 - 8*S^10 + 3*S^12)/(2*S^3*(1 + S^2)^3) - (2*S*(-43 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + (8*S*HPL[{3}, -S^2])/(1 + S^2)^3 - (96*S*HPL[{2, 1}, -S^2])/(1 + S^2)^3) - 4*S*HPL[{3, 1}, -S^2] + 8*S*HPL[{2, 1, 1}, -S^2] - (2*S*(-1 - 79*S^2 + 6*S^4 + 12*S^6)*Zeta[3])/(1 + S^2)^3 + HPL[{1}, -S^2]*(((1 + S^2)*(1 + 4*S^2 + S^4))/S^3 + (Pi^2*(-25 + 342*S^2 - 230*S^4 - 8*S^6 + 13*S^8))/(6*S*(1 + S^2)^3) - (14*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (8*S*(-7 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - 28*S*HPL[{2, 1}, -S^2] + (24*S*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3)) - (32*S^3*(3 + 3*S^2 + S^4)*Zeta[5])/(1 + S^2)^3;
E3uvwT3F3=(19*(1 + S^2))/(108*S) + (Pi^2*(1 + S^2)*(-232 + 297*S^2))/(648*S) + (Pi^4*(-58 - 145*S^2 + 414*S^4 + 64*S^6 + 16*S^8))/(270*S*(1 + S^2)^3) + (S^3*HPL[{0}, S^2]^5)/(12*(1 + S^2)^3) + ((1 - 9*S^2 - 33*S^4 + 74*S^6 - 33*S^8 - 9*S^10 + S^12)*HPL[{1}, -S^2]^4)/(6*S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^5)/(15*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^4*((-4 - 10*S^2 + 21*S^4 + 13*S^6 + 4*S^8)/(24*S*(1 + S^2)^3) + ((-2 - 6*S^2 - 6*S^4 + 5*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(12*S^3*(1 + S^2)^3)) + ((-2 - 5*S^2 + 24*S^4 - 5*S^6 - 2*S^8)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((Pi^2*(-13 - 39*S^2 - 39*S^4 + 77*S^6 - 18*S^8 - 18*S^10 - 6*S^12))/(27*S^3*(1 + S^2)^3) + (5 + 40*S^2 - 73*S^4 + 264*S^6 - 73*S^8 + 40*S^10 + 5*S^12)/(18*S^3*(1 + S^2)^3) + (14*(-1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]^3*(-(Pi^2*S^3*(-49 + 3*S^2 + 3*S^4 + S^6))/(108*(1 + S^2)^3) + (18 + 21*S^2 + 127*S^4 + 102*S^6 + 73*S^8 + 15*S^10)/(36*S*(1 + S^2)^3) + ((3 + 3*S^2 - 9*S^4 + 32*S^6 + 6*S^8 + 8*S^10 + 3*S^12)*HPL[{1}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-6 - 18*S^2 - 18*S^4 + 33*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)^3) - (S^3*(-13 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(18*(1 + S^2)^3)) + ((Pi^2*(-1 - 3*S^2 - 3*S^4 - 4*S^6 + 21*S^8 + 21*S^10 + 7*S^12))/(9*S^3*(1 + S^2)^3) + (2 + 45*S^2 + 87*S^4 + 122*S^6 + 232*S^8 + 97*S^10 + 23*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((15 + 12*S^2 - 21*S^4 + 57*S^6 + 52*S^8 + 15*S^10)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^2) + (4*(-4 - 12*S^2 - 12*S^4 + 7*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((21 + 31*S^2 + 114*S^4 - 114*S^6 - 31*S^8 - 21*S^10)/(6*S^3*(1 + S^2)^2) - (2*Pi^2*(-6 - 18*S^2 - 18*S^4 + 3*S^6 + 12*S^8 + 12*S^10 + 4*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-15 - 16*S^2 + 9*S^4 - 45*S^6 - 48*S^8 - 15*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (8*S^3*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) - (4*(-3 - 9*S^2 - 9*S^4 - 16*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-16 - 27*S^2 + 27*S^4 + 16*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)^2) - (16*(1 + 3*S^2 + 3*S^4 - 3*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 26*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-2*Pi^2*S^3*(49 + 3*S^2 + 3*S^4 + S^6))/(27*(1 + S^2)^3) - (2*(1 - 22*S^2 + 74*S^4 - 22*S^6 + S^8))/(9*S*(1 + S^2)^3) - (2*S^3*(19 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(9*(1 + S^2)^3) - (2*(1 - 9*S^2 - 33*S^4 + 74*S^6 - 33*S^8 - 9*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + HPL[{0}, S^2]*((-2*(-4 - 10*S^2 + 37*S^4 - 23*S^6 - 5*S^8 + S^10))/(3*S*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3)) - (4*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3))*Log[T]^3 + ((-2*(2 + 5*S^2 - 24*S^4 + 5*S^6 + 2*S^8))/(3*S*(1 + S^2)^3) - (4*S^3*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2])/(3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3))*Log[T]^4 - (8*S^3*Log[T]^5)/(3*(1 + S^2)^3) + ((4*Pi^2*S^5*(3 + 3*S^2 + S^4))/(3*(1 + S^2)^3) + (-26 - 77*S^2 - 48*S^4 + 358*S^6 + 130*S^8 + 63*S^10)/(18*S*(1 + S^2)^3))*Zeta[3] + HPL[{0}, S^2]^2*(((1 + S^2)*(-241 + 297*S^2))/(216*S) + (Pi^2*(-38 - 95*S^2 + 219*S^4 + 86*S^6 + 26*S^8))/(72*S*(1 + S^2)^3) + ((-2 - 66*S^2 - 183*S^4 + 212*S^6 + 6*S^8 - 3*S^10 - 2*S^12)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((-7 - 21*S^2 - 21*S^4 + 29*S^6)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + ((-16 - 43*S^2 + 48*S^4 + 23*S^6 + 8*S^8)*HPL[{2}, -S^2])/(12*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*(-19 - 57*S^2 - 57*S^4 + 59*S^6 + 18*S^8 + 18*S^10 + 6*S^12))/(36*S^3*(1 + S^2)^3) + (-205 - 546*S^2 - 1869*S^4 + 1300*S^6 + 525*S^8 + 462*S^10 + 173*S^12)/(216*S^3*(1 + S^2)^3) + ((-7 - 21*S^2 - 21*S^4 + 16*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)^3)) + ((-1 + 3*S^6)*HPL[{3}, -S^2])/(6*S^3) - (2*(-3 - 9*S^2 - 9*S^4 + 3*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + 2*S^3*Zeta[3]) + Log[T]^2*((1 + S^2)/(6*S) + (Pi^2*(-26 - 65*S^2 + 237*S^4 - 22*S^6 - 10*S^8))/(18*S*(1 + S^2)^3) - (S^3*(-19 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^3)/(9*(1 + S^2)^3) + ((1 - 9*S^2 - 33*S^4 + 74*S^6 - 33*S^8 - 9*S^10 + S^12)*HPL[{1}, -S^2]^2)/(S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^2*((-14 - 35*S^2 + 93*S^4 + 8*S^6 + 2*S^8)/(6*S*(1 + S^2)^3) + ((-7 - 21*S^2 - 21*S^4 + 29*S^6)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((-1 + S^2)*(16 + 43*S^2 + 16*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(-13 - 39*S^2 - 39*S^4 + 77*S^6 - 18*S^8 - 18*S^10 - 6*S^12))/(9*S^3*(1 + S^2)^3) + (5 + 40*S^2 - 73*S^4 + 264*S^6 - 73*S^8 + 40*S^10 + 5*S^12)/(6*S^3*(1 + S^2)^3) + (14*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]*(-(Pi^2*S^3*(-43 + 21*S^2 + 21*S^4 + 7*S^6))/(9*(1 + S^2)^3) + (6 - 33*S^2 + 132*S^4 - 40*S^6 + 34*S^8 + 5*S^10)/(6*S*(1 + S^2)^3) + ((1 - 9*S^2 - 33*S^4 + 74*S^6 - 33*S^8 - 9*S^10 + S^12)*HPL[{1}, -S^2])/(S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^2)/(S^3*(1 + S^2)^3) - (2*S^3*(-19 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + (2*(-1 - 3*S^2 - 3*S^4 - 10*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (8*S^3*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((11*(-1 + S^2)*(1 + S^2)^2)/(4*S^3) + (Pi^2*(-16 - 43*S^2 + 24*S^4 + 33*S^6 + 12*S^8))/(18*S*(1 + S^2)^3) + (4*S^3*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 3*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*S^3*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*(((1 + S^2)*(79 - 4*S^2 + 79*S^4))/(27*S^3) + (Pi^4*(-29 - 87*S^2 - 87*S^4 + 122*S^6))/(135*S^3*(1 + S^2)^3) + (Pi^2*(-80 - 93*S^2 - 1263*S^4 + 1838*S^6 - 66*S^8 + 411*S^10 + 109*S^12))/(324*S^3*(1 + S^2)^3) + ((7*(-3 - 5*S^2 - 14*S^4 + 14*S^6 + 5*S^8 + 3*S^10))/(6*S^3*(1 + S^2)^2) + (Pi^2*(-7 - 21*S^2 - 21*S^4 + 8*S^6 + 15*S^8 + 15*S^10 + 5*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((5 + 13*S^2 + 9*S^4 - 10*S^6 + 51*S^8 + 27*S^10 + 5*S^12)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-3 + 4*S^6)*HPL[{4}, -S^2])/(3*S^3) - (14*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (4*(-3 + 4*S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (28*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-13 - 51*S^2 - 69*S^4 - 242*S^6 + 309*S^8 + 75*S^10 - 13*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(25 - 4*S^2 + 25*S^4))/(18*S^3) + (Pi^2*(5 - 213*S^2 - 663*S^4 + 1090*S^6 - 285*S^8 - 87*S^10 + 5*S^12))/(108*S^3*(1 + S^2)^3) + (7*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (2*(-1 - 3*S^2 - 3*S^4 - 15*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (14*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (2*(-1 - 3*S^2 - 3*S^4 - 19*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]*((289 + 11*S^2 + 316*S^4)/(108*S) - (Pi^4*S^3*(-167 + 48*S^2 + 48*S^4 + 16*S^6))/(270*(1 + S^2)^3) + (Pi^2*(42 + 9*S^2 + 386*S^4 + 164*S^6 + 180*S^8 + 35*S^10))/(72*S*(1 + S^2)^3) + ((1 - 9*S^2 - 33*S^4 + 74*S^6 - 33*S^8 - 9*S^10 + S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) + (-(Pi^2*S^3*(-16 + 9*S^2 + 9*S^4 + 3*S^6))/(9*(1 + S^2)^3) + (61 + 366*S^2 + 123*S^4 + 1076*S^6 - 93*S^8 + 438*S^10 + 61*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*S^3*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(-12 - 36*S^2 - 36*S^4 + 81*S^6 - 21*S^8 - 21*S^10 - 7*S^12))/(18*S^3*(1 + S^2)^3) + (5 + 40*S^2 - 73*S^4 + 264*S^6 - 73*S^8 + 40*S^10 + 5*S^12)/(12*S^3*(1 + S^2)^3) + ((-5 - 15*S^2 - 15*S^4 + 38*S^6 - 15*S^8 - 15*S^10 - 5*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((13 + 33*S^2 + 15*S^4 + 44*S^6 - 15*S^8 + 21*S^10 + 13*S^12)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^3) - (4*S^5*(3 + 3*S^2 + S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + ((-13 + 27*S^2 + 180*S^4 - 242*S^6 + 60*S^8 - 3*S^10 - 13*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*S^3*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (4*S^3*(-19 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (S^3*(18 + 32*S^2 + 15*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(25 - 4*S^2 + 25*S^4))/(18*S^3) + (Pi^2*(7 - 3*S^2 - 51*S^4 + 138*S^6 - 21*S^8 + 7*S^10 + 7*S^12))/(12*S^3*(1 + S^2)^3) + ((13 - 12*S^2 - 120*S^4 + 242*S^6 - 120*S^8 - 12*S^10 + 13*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*S^3*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (2*(5 + 15*S^2 + 15*S^4 - 38*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*S^3*Zeta[3])/3)) + Log[T]*((-5*(1 + S^2))/(18*S) - (Pi^4*S^3*(167 + 48*S^2 + 48*S^4 + 16*S^6))/(135*(1 + S^2)^3) + (Pi^2*(14 + 341*S^2 - 744*S^4 - 22*S^6 - 166*S^8 - 63*S^10))/(108*S*(1 + S^2)^3) - (S^3*(4 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^4)/(6*(1 + S^2)^3) - (2*(1 - 9*S^2 - 33*S^4 + 74*S^6 - 33*S^8 - 9*S^10 + S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^3*((12 + 30*S^2 - 111*S^4 - 41*S^6 - 50*S^8 - 18*S^10)/(18*S*(1 + S^2)^3) + ((6 + 18*S^2 + 18*S^4 - 33*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((21 + 39*S^2 + 82*S^4 - 82*S^6 - 39*S^8 - 21*S^10)/(6*S^3*(1 + S^2)^2) - (2*Pi^2*(-1 - 3*S^2 - 3*S^4 + 5*S^6 + 3*S^8 + 3*S^10 + S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (20*S^3*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((-5 - 40*S^2 + 73*S^4 - 264*S^6 + 73*S^8 - 40*S^10 - 5*S^12)/(6*S^3*(1 + S^2)^3) + (Pi^2*(13 + 39*S^2 + 39*S^4 - 77*S^6 + 18*S^8 + 18*S^10 + 6*S^12))/(9*S^3*(1 + S^2)^3) - (14*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^2*(-(Pi^2*S^3*(43 + 21*S^2 + 21*S^4 + 7*S^6))/(18*(1 + S^2)^3) + (20 + 209*S^2 - 300*S^4 - 154*S^6 - 160*S^8 - 63*S^10)/(36*S*(1 + S^2)^3) + ((2 + 66*S^2 + 183*S^4 - 212*S^6 - 6*S^8 + 3*S^10 + 2*S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((7 + 21*S^2 + 21*S^4 - 29*S^6)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((1 + 3*S^2 + 3*S^4 - 10*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((-15 - 39*S^2 - 27*S^4 - 193*S^8 - 91*S^10 - 15*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{4}, -S^2])/S^3 + (2*(-26 - 57*S^2 + 57*S^4 + 26*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) + HPL[{0}, S^2]*((-41 - S^2 - 50*S^4)/(18*S) + (Pi^2*(24 + 60*S^2 - 222*S^4 + 28*S^6 - 35*S^8 - 21*S^10))/(18*S*(1 + S^2)^3) + ((-1 + 9*S^2 + 33*S^4 - 74*S^6 + 33*S^8 + 9*S^10 - S^12)*HPL[{1}, -S^2]^2)/(S^3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) + ((-13 - 3*S^2 + 60*S^4 - 242*S^6 + 180*S^8 + 27*S^10 - 13*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((-5 - 40*S^2 + 73*S^4 - 264*S^6 + 73*S^8 - 40*S^10 - 5*S^12)/(6*S^3*(1 + S^2)^3) + (Pi^2*(12 + 36*S^2 + 36*S^4 - 81*S^6 + 21*S^8 + 21*S^10 + 7*S^12))/(9*S^3*(1 + S^2)^3) + (2*(5 + 15*S^2 + 15*S^4 - 38*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) - (8*S^3*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (4*(-5 - 15*S^2 - 15*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3)) + (4*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (8*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(-2 - 5*S^2 - 21*S^4 + 78*S^6 + 24*S^8)*Zeta[3])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(-((1 + S^2)*(25 - 4*S^2 + 25*S^4))/(9*S^3) + (Pi^2*(-5 + 213*S^2 + 663*S^4 - 1090*S^6 + 285*S^8 + 87*S^10 - 5*S^12))/(54*S^3*(1 + S^2)^3) - (14*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (4*(-1 - 3*S^2 - 3*S^4 - 15*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (28*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (4*(-1 - 3*S^2 - 3*S^4 - 19*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3))) + (32*S^5*(3 + 3*S^2 + S^4)*Zeta[5])/(3*(1 + S^2)^3);
E3uvwT=E3uvwT0F0+T*E3uvwT1F1*(F+1/F)+T^2*(E3uvwT2F0+E3uvwT2F2*(F^2+1/F^2))+T^3*(E3uvwT3F1*(F+1/F)+E3uvwT3F3*(F^3+1/F^3));
E3vwuT0F0=(-121*Pi^6)/1620 - HPL[{0}, S^2]^6/48 + HPL[{0}, S^2]^4*(-Pi^2/12 + HPL[{2}, -S^2]/4) + (Pi^2*HPL[{2}, -S^2]^2)/3 + (4*HPL[{2}, -S^2]^3)/3 + 2*HPL[{3}, -S^2]^2 - 24*HPL[{6}, -S^2] - 6*Pi^2*HPL[{3, 1}, -S^2] + HPL[{2}, -S^2]*((29*Pi^4)/45 - 4*HPL[{4}, -S^2] + 4*HPL[{3, 1}, -S^2]) + 4*HPL[{5, 1}, -S^2] + (38*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{0}, S^2]^2*((-37*Pi^4)/360 + (13*Pi^2*HPL[{2}, -S^2])/12 + HPL[{2}, -S^2]^2 - HPL[{4}, -S^2] - 6*HPL[{3, 1}, -S^2] + 14*HPL[{2, 1, 1}, -S^2]) + 32*HPL[{3, 2, 1}, -S^2] + 104*HPL[{4, 1, 1}, -S^2] - 96*HPL[{3, 1, 1, 1}, -S^2] + 192*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-37*Pi^4)/90 + HPL[{0}, S^2]^4/4 + (19*Pi^2*HPL[{2}, -S^2])/3 + HPL[{0}, S^2]^2*(Pi^2 + 7*HPL[{2}, -S^2]) + 4*HPL[{4}, -S^2] + HPL[{0}, S^2]*(-4*HPL[{3}, -S^2] + 48*HPL[{2, 1}, -S^2]) - 48*HPL[{3, 1}, -S^2] + 96*HPL[{2, 1, 1}, -S^2])*Log[T]^2 + ((-4*Pi^2)/3 + HPL[{0}, S^2]^2 + 8*HPL[{2}, -S^2])*Log[T]^4 - 4*HPL[{0}, S^2]*Log[T]^5 - (4*Log[T]^6)/3 - 20*HPL[{2, 1}, -S^2]*Zeta[3] - 4*Zeta[3]^2 + HPL[{0}, S^2]^3*((7*HPL[{2, 1}, -S^2])/3 + 2*Zeta[3]) + HPL[{3}, -S^2]*(-20*HPL[{2, 1}, -S^2] + 4*Zeta[3]) + Log[T]^3*((-20*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]*((-50*Pi^2)/9 - 16*HPL[{2}, -S^2]) + 16*HPL[{3}, -S^2] - 32*HPL[{2, 1}, -S^2] + 16*Zeta[3]) + HPL[{0}, S^2]*(-(Pi^2*HPL[{3}, -S^2])/3 + 6*HPL[{5}, -S^2] + (19*Pi^2*HPL[{2, 1}, -S^2])/3 - 4*HPL[{3, 2}, -S^2] - 8*HPL[{4, 1}, -S^2] - 40*HPL[{2, 2, 1}, -S^2] - 128*HPL[{3, 1, 1}, -S^2] + 96*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(2*HPL[{3}, -S^2] + 20*HPL[{2, 1}, -S^2] - 2*Zeta[3]) + 2*Pi^2*Zeta[3] + 16*Zeta[5]) + Log[T]*(-HPL[{0}, S^2]^5/4 + HPL[{0}, S^2]^3*((-25*Pi^2)/18 - (7*HPL[{2}, -S^2])/3) + (14*Pi^2*HPL[{3}, -S^2])/3 + 4*HPL[{5}, -S^2] + HPL[{0}, S^2]^2*(2*HPL[{3}, -S^2] - 14*HPL[{2, 1}, -S^2]) - (38*Pi^2*HPL[{2, 1}, -S^2])/3 - 40*HPL[{3, 2}, -S^2] - 128*HPL[{4, 1}, -S^2] + HPL[{0}, S^2]*((-61*Pi^4)/30 - (19*Pi^2*HPL[{2}, -S^2])/3 - 10*HPL[{2}, -S^2]^2 - 4*HPL[{4}, -S^2] + 48*HPL[{3, 1}, -S^2] - 96*HPL[{2, 1, 1}, -S^2]) + 96*HPL[{3, 1, 1}, -S^2] - 192*HPL[{2, 1, 1, 1}, -S^2] + 4*Pi^2*Zeta[3] + HPL[{2}, -S^2]*(20*HPL[{3}, -S^2] + 20*Zeta[3]) + 32*Zeta[5]);
E3vwuT1F1=-(Pi^4*S)/9 - (S*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/4 + ((-19*Pi^2*S)/9 - (16*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^3 - (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (8*S*HPL[{1}, -S^2]^5)/5 - 2*S*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^3*(-2*S - (7*Pi^2*S)/36 + ((-1 - S^2)*HPL[{1}, -S^2])/S - (7*S*HPL[{1}, -S^2]^2)/6 - (7*S*HPL[{2}, -S^2])/6) + (-6*S + (7*Pi^2*S)/3)*HPL[{3}, -S^2] + 6*S*HPL[{4}, -S^2] + 14*S*HPL[{5}, -S^2] + ((-8*Pi^2*S)/3 + (4*(3 + S^2))/S)*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(-(Pi^2*S)/3 - (3*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (7*S*HPL[{1}, -S^2]^3)/3 - 2*S*HPL[{2}, -S^2] + HPL[{1}, -S^2]*((-13*Pi^2*S)/12 - (4*(1 + S^2))/S - 2*S*HPL[{2}, -S^2]) + (3*S*HPL[{3}, -S^2])/2 - 2*S*HPL[{2, 1}, -S^2]) + 6*S*HPL[{3, 1}, -S^2] + HPL[{1}, -S^2]*((-29*Pi^4*S)/45 - (24*(1 + S^2))/S - (8*Pi^2*(1 + S^2))/(3*S) + ((-2*Pi^2*S)/3 - (6*(1 + S^2))/S)*HPL[{2}, -S^2] - 4*S*HPL[{2}, -S^2]^2 + 4*S*HPL[{4}, -S^2] + (10*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 4*S*HPL[{3, 1}, -S^2]) - 16*S*HPL[{3, 2}, -S^2] - 58*S*HPL[{4, 1}, -S^2] - 16*S*HPL[{2, 1, 1}, -S^2] - 12*S*HPL[{2, 2, 1}, -S^2] + 8*S*HPL[{3, 1, 1}, -S^2] - 48*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S)/3 + 4*S*HPL[{0}, S^2]^2 + (8*(1 + S^2)*HPL[{1}, -S^2])/S + 16*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*(8*S + 16*S*HPL[{1}, -S^2]) + 8*S*HPL[{2}, -S^2])*Log[T]^3 + (-8*S*HPL[{0}, S^2] - 8*S*HPL[{1}, -S^2])*Log[T]^4 + (-4*S + 2*Pi^2*S)*Zeta[3] + HPL[{2}, -S^2]*((-4*Pi^2*S)/3 + 8*S*HPL[{3}, -S^2] + 6*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{1}, -S^2]^2*((-12*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S - (5*(1 + S^2)*HPL[{2}, -S^2])/S + 10*S*HPL[{3}, -S^2] + 10*S*Zeta[3]) + Log[T]^2*((-4*Pi^2*S)/3 - (7*S*HPL[{0}, S^2]^3)/3 + ((-19*Pi^2*S)/3 - (16*(1 + S^2))/S)*HPL[{1}, -S^2] - (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S - 16*S*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*(-4*S - 7*S*HPL[{1}, -S^2]) - 8*S*HPL[{2}, -S^2] + HPL[{0}, S^2]*(-16*S - (19*Pi^2*S)/3 - (12*(1 + S^2)*HPL[{1}, -S^2])/S - 24*S*HPL[{1}, -S^2]^2 - 22*S*HPL[{2}, -S^2]) + 22*S*HPL[{3}, -S^2] - 24*S*HPL[{2, 1}, -S^2] + 24*S*Zeta[3]) + Log[T]*((4*Pi^2*S)/3 + (19*Pi^4*S)/30 + (S*HPL[{0}, S^2]^4)/2 + ((19*Pi^2*S)/3 + (16*(1 + S^2))/S)*HPL[{1}, -S^2]^2 + (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S + 8*S*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*(2*S + (7*S*HPL[{1}, -S^2])/3) + (8*S + 4*Pi^2*S)*HPL[{2}, -S^2] + 5*S*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^2*(4*S + 2*Pi^2*S + (6*(1 + S^2)*HPL[{1}, -S^2])/S + 7*S*HPL[{1}, -S^2]^2 + 6*S*HPL[{2}, -S^2]) + 2*S*HPL[{3}, -S^2] + 2*S*HPL[{4}, -S^2] - (4*(5 + S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*(24*S + 4*Pi^2*S + (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S + 16*S*HPL[{1}, -S^2]^3 + 8*S*HPL[{2}, -S^2] + HPL[{1}, -S^2]*((19*Pi^2*S)/3 + (16*(1 + S^2))/S + 20*S*HPL[{2}, -S^2]) - 2*S*HPL[{3}, -S^2] + 4*S*HPL[{2, 1}, -S^2]) - 24*S*HPL[{3, 1}, -S^2] + 48*S*HPL[{2, 1, 1}, -S^2] + 4*S*Zeta[3] + HPL[{1}, -S^2]*((24*(1 + S^2))/S + (4*Pi^2*(1 + S^2))/S + (10*(1 + S^2)*HPL[{2}, -S^2])/S - 20*S*HPL[{3}, -S^2] - 20*S*Zeta[3])) + HPL[{0}, S^2]*(-24*S - (10*Pi^2*S)/3 - (89*Pi^4*S)/180 - (4*(1 + S^2)*HPL[{1}, -S^2]^3)/S - 4*S*HPL[{1}, -S^2]^4 + (-4*S - 3*Pi^2*S)*HPL[{2}, -S^2] - (9*S*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*((-19*Pi^2*S)/6 - (8*(1 + S^2))/S - 10*S*HPL[{2}, -S^2]) - S*HPL[{3}, -S^2] - 5*S*HPL[{4}, -S^2] + (2*(5 + S^2)*HPL[{2, 1}, -S^2])/S + 24*S*HPL[{3, 1}, -S^2] - 44*S*HPL[{2, 1, 1}, -S^2] + 2*S*Zeta[3] + HPL[{1}, -S^2]*((-12*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S - (5*(1 + S^2)*HPL[{2}, -S^2])/S - 2*S*HPL[{3}, -S^2] + 20*S*HPL[{2, 1}, -S^2] + 2*S*Zeta[3])) + 16*S*Zeta[5];
E3vwuT2F0=24 + (4*Pi^2*S^2)/3 - (29*Pi^4)/(45*(1 + S^2)) + HPL[{0}, S^2]^5/4 + HPL[{0}, S^2]^4*((-2 - S^2)/(4*(1 + S^2)) - HPL[{1}, -S^2]/2) + ((-38*Pi^2)/9 - (4*(1 + S^2))/3)*HPL[{1}, -S^2]^3 + (4*(-1 + S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) - (16*HPL[{1}, -S^2]^5)/5 + HPL[{0}, S^2]^3*((2*Pi^2)/3 - 2*(1 + S^2) + ((-6 + S^2)*HPL[{1}, -S^2])/(3*(1 + S^2)) - (7*HPL[{1}, -S^2]^2)/3 - 2*HPL[{2}, -S^2]) + (2*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + ((2*Pi^2)/3 - 8*S^2)*HPL[{3}, -S^2] - (4*S^2*HPL[{4}, -S^2])/(1 + S^2) + 36*HPL[{5}, -S^2] + ((-2*Pi^2)/3 - 4*S^2)*HPL[{2, 1}, -S^2] + (4*(2 + 3*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 8*HPL[{3, 2}, -S^2] + 8*HPL[{4, 1}, -S^2] - 20*HPL[{2, 1, 1}, -S^2] + 16*HPL[{2, 2, 1}, -S^2] + 48*HPL[{3, 1, 1}, -S^2] + (4 + (Pi^2*(-13 + 6*S^2))/(3*(1 + S^2)) - 2*HPL[{0}, S^2]^3 + HPL[{0}, S^2]^2*(-7/(1 + S^2) - 14*HPL[{1}, -S^2]) + ((-38*Pi^2)/3 - 4*(1 + S^2))*HPL[{1}, -S^2] + (24*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - 32*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]*(-4*Pi^2 - 4*(1 + S^2) + (24*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2) - 48*HPL[{1}, -S^2]^2 - 20*HPL[{2}, -S^2]) - 10*HPL[{2}, -S^2])*Log[T]^2 + ((100*Pi^2)/9 + (40*HPL[{0}, S^2]^2)/3 - (16*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2) + 32*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-4*(-7 + 5*S^2))/(3*(1 + S^2)) + 32*HPL[{1}, -S^2]))*Log[T]^3 + ((4*(-1 + S^2))/(1 + S^2) - 4*HPL[{0}, S^2] - 16*HPL[{1}, -S^2])*Log[T]^4 + 8*Log[T]^5 + HPL[{0}, S^2]^2*(-1 + 4*S^2 + (Pi^2*(-19 - 6*S^2))/(12*(1 + S^2)) + ((-6 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - (14*HPL[{1}, -S^2]^3)/3 + HPL[{1}, -S^2]*(-1 - (13*Pi^2)/6 - S^2 - 4*HPL[{2}, -S^2]) + ((-5 - S^2)*HPL[{2}, -S^2])/(2*(1 + S^2)) + 2*HPL[{3}, -S^2] - 2*HPL[{2, 1}, -S^2] - 12*Zeta[3]) + HPL[{2}, -S^2]*(8*S^2 + (Pi^2*(-5 - 3*S^2))/(3*(1 + S^2)) - 4*HPL[{3}, -S^2] - 8*HPL[{2, 1}, -S^2] - 4*Zeta[3]) + (-4*Pi^2 + 4*(-1 + S^2))*Zeta[3] + HPL[{1}, -S^2]^2*(-2*(1 + S^2) + (Pi^2*(-12 + 7*S^2))/(3*(1 + S^2)) - 10*HPL[{2}, -S^2] + 20*HPL[{3}, -S^2] + 20*Zeta[3]) + HPL[{1}, -S^2]*((-58*Pi^4)/45 - 12*(1 + S^2) - (2*Pi^2*(1 + S^2))/3 - (4*Pi^2*HPL[{2}, -S^2])/3 - 8*HPL[{2}, -S^2]^2 - (20*S^2*HPL[{3}, -S^2])/(1 + S^2) + 8*HPL[{4}, -S^2] + 20*HPL[{2, 1}, -S^2] - 8*HPL[{3, 1}, -S^2] - (20*S^2*Zeta[3])/(1 + S^2)) + Log[T]*(-12 + (61*Pi^4)/15 + (2*Pi^2*(1 + S^2))/3 + (5*HPL[{0}, S^2]^4)/2 + ((38*Pi^2)/3 + 4*(1 + S^2))*HPL[{1}, -S^2]^2 - (16*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) + 16*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*((12 + 5*S^2)/(3*(1 + S^2)) + (14*HPL[{1}, -S^2])/3) + ((10*Pi^2)/3 + 4*S^2)*HPL[{2}, -S^2] + 20*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^2*((25*Pi^2)/3 + 2*(1 + S^2) - (2*(-6 + S^2)*HPL[{1}, -S^2])/(1 + S^2) + 14*HPL[{1}, -S^2]^2 + 10*HPL[{2}, -S^2]) + (20*S^2*HPL[{3}, -S^2])/(1 + S^2) + HPL[{0}, S^2]*((19*Pi^2)/(3*(1 + S^2)) + 4*(1 + S^2) - (24*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + 32*HPL[{1}, -S^2]^3 - (10*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((38*Pi^2)/3 + 4*(1 + S^2) + 40*HPL[{2}, -S^2]) - 40*HPL[{2, 1}, -S^2]) - 20*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]*(4*(1 + S^2) - (2*Pi^2*(-12 + 7*S^2))/(3*(1 + S^2)) + 20*HPL[{2}, -S^2] - 40*HPL[{3}, -S^2] - 40*Zeta[3]) + (4*(1 + 6*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]*((37*Pi^4)/90 - (7*Pi^2*(1 + S^2))/3 - 2*(1 + 6*S^2) + (8*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) - 8*HPL[{1}, -S^2]^4 + HPL[{1}, -S^2]^2*((-19*Pi^2)/3 - 2*(1 + S^2) - 20*HPL[{2}, -S^2]) + ((-11*Pi^2)/3 - 2*S^2)*HPL[{2}, -S^2] - 4*HPL[{2}, -S^2]^2 + (2*S^2*HPL[{3}, -S^2])/(1 + S^2) - 8*HPL[{4}, -S^2] - (10*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 24*HPL[{3, 1}, -S^2] - 40*HPL[{2, 1, 1}, -S^2] - (2*(5 + 6*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-2*(1 + S^2) + (Pi^2*(-12 + 7*S^2))/(3*(1 + S^2)) + (10*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - 4*HPL[{3}, -S^2] + 40*HPL[{2, 1}, -S^2] + 4*Zeta[3])) - 32*Zeta[5];
E3vwuT2F2=3/4 + (Pi^2*(1 + 2*S^2))/3 + (Pi^4*(39*S^2 + 10*S^4))/(90*(1 + S^2)) + ((19*Pi^2*S^2)/18 + (2 + 11*S^2 + 9*S^4)/(3*S^2))*HPL[{1}, -S^2]^3 + ((1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) + (4*S^2*HPL[{1}, -S^2]^5)/5 + HPL[{0}, S^2]^4*(S^2/(8*(1 + S^2)) + (S^2*HPL[{1}, -S^2])/8) + (2*S^2*(2 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{0}, S^2]^3*((7*Pi^2*S^2)/72 + (1 + 3*S^2)/4 + ((3 + 3*S^2 + 23*S^4 + 9*S^6)*HPL[{1}, -S^2])/(12*S^2*(1 + S^2)) + (7*S^2*HPL[{1}, -S^2]^2)/12 + (7*S^2*HPL[{2}, -S^2])/12) + (-S^2/4 - (7*Pi^2*S^2)/6)*HPL[{3}, -S^2] - (S^2*(11 + 7*S^2)*HPL[{4}, -S^2])/(2*(1 + S^2)) - 7*S^2*HPL[{5}, -S^2] + ((4*Pi^2*S^2)/3 + (-3 - 13*S^2 + S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((1 + 4*S^2)/2 + (Pi^2*(21*S^2 + 8*S^4))/(24*(1 + S^2)) + ((3 + 3*S^2 + 23*S^4 + 9*S^6)*HPL[{1}, -S^2]^2)/(4*S^2*(1 + S^2)) + (7*S^2*HPL[{1}, -S^2]^3)/6 + (S^2*(3 + 2*S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((13*Pi^2*S^2)/24 + (2 + 11*S^2 + 9*S^4)/(4*S^2) + S^2*HPL[{2}, -S^2]) - (3*S^2*HPL[{3}, -S^2])/4 + S^2*HPL[{2, 1}, -S^2]) - (S^2*(13 + 17*S^2)*HPL[{3, 1}, -S^2])/(2*(1 + S^2)) + 8*S^2*HPL[{3, 2}, -S^2] + 29*S^2*HPL[{4, 1}, -S^2] + 16*S^2*HPL[{2, 1, 1}, -S^2] + 6*S^2*HPL[{2, 2, 1}, -S^2] - 4*S^2*HPL[{3, 1, 1}, -S^2] + 24*S^2*HPL[{2, 1, 1, 1}, -S^2] + (-2 - (2*Pi^2*S^2)/3 - 2*S^2*HPL[{0}, S^2]^2 - (2*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) - 8*S^2*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-2*S^2*(7 + 3*S^2))/(1 + S^2) - 8*S^2*HPL[{1}, -S^2]) - 4*S^2*HPL[{2}, -S^2])*Log[T]^3 + ((4*S^2)/(1 + S^2) + 4*S^2*HPL[{0}, S^2] + 4*S^2*HPL[{1}, -S^2])*Log[T]^4 + (-S^2/2 - Pi^2*S^2)*Zeta[3] + Log[T]^2*(2 + (Pi^2*(27*S^2 + 8*S^4))/(6*(1 + S^2)) + (7*S^2*HPL[{0}, S^2]^3)/6 + ((19*Pi^2*S^2)/6 + (2 + 11*S^2 + 9*S^4)/S^2)*HPL[{1}, -S^2] + (3*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) + 8*S^2*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*((S^2*(15 + 8*S^2))/(2*(1 + S^2)) + (7*S^2*HPL[{1}, -S^2])/2) + 8*S^2*HPL[{2}, -S^2] + HPL[{0}, S^2]*((19*Pi^2*S^2)/6 + 3*(1 + 3*S^2) + (3*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) + 12*S^2*HPL[{1}, -S^2]^2 + 11*S^2*HPL[{2}, -S^2]) - 11*S^2*HPL[{3}, -S^2] + 12*S^2*HPL[{2, 1}, -S^2] - 12*S^2*Zeta[3]) + HPL[{1}, -S^2]^2*(((1 + S^2)*(3 + 20*S^2))/(4*S^2) + (Pi^2*(3 + 3*S^2 + 28*S^4 + 9*S^6))/(6*S^2*(1 + S^2)) + (5*(1 + 3*S^4)*HPL[{2}, -S^2])/(4*S^2) - 5*S^2*HPL[{3}, -S^2] - 5*S^2*Zeta[3]) + HPL[{2}, -S^2]*((3 + 16*S^2)/4 + (Pi^2*(5*S^2 + 4*S^4))/(3*(1 + S^2)) - 4*S^2*HPL[{3}, -S^2] - 3*S^2*HPL[{2, 1}, -S^2] - 4*S^2*Zeta[3]) + HPL[{1}, -S^2]*((29*Pi^4*S^2)/90 + (3*(1 + S^2)*(1 + 8*S^2))/(4*S^2) + (Pi^2*(1 + S^2)*(2 + 9*S^2))/(6*S^2) + ((Pi^2*S^2)/3 + (3*(1 + 6*S^2 + 5*S^4))/(4*S^2))*HPL[{2}, -S^2] + 2*S^2*HPL[{2}, -S^2]^2 - (10*S^2*HPL[{3}, -S^2])/(1 + S^2) - 2*S^2*HPL[{4}, -S^2] - (5*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + 2*S^2*HPL[{3, 1}, -S^2] - (10*S^2*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]*((89*Pi^4*S^2)/360 + (Pi^2*(1 + 3*S^2))/2 + (3*(1 + 8*S^2))/4 + ((1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) + 2*S^2*HPL[{1}, -S^2]^4 + ((3*Pi^2*S^2)/2 + (5 + 16*S^2)/4)*HPL[{2}, -S^2] + (9*S^2*HPL[{2}, -S^2]^2)/4 + HPL[{1}, -S^2]^2*((19*Pi^2*S^2)/12 + (2 + 11*S^2 + 9*S^4)/(2*S^2) + 5*S^2*HPL[{2}, -S^2]) - (S^2*(-3 + S^2)*HPL[{3}, -S^2])/(4*(1 + S^2)) + (5*S^2*HPL[{4}, -S^2])/2 + ((-5 - 5*S^2 - 19*S^4 + S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 12*S^2*HPL[{3, 1}, -S^2] + 22*S^2*HPL[{2, 1, 1}, -S^2] + ((-S^2 + S^4)*Zeta[3])/(2*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(3 + 20*S^2))/(4*S^2) + (Pi^2*(3 + 3*S^2 + 28*S^4 + 9*S^6))/(6*S^2*(1 + S^2)) + (5*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(4*S^2*(1 + S^2)) + S^2*HPL[{3}, -S^2] - 10*S^2*HPL[{2, 1}, -S^2] - S^2*Zeta[3])) + Log[T]*(-3/2 - (19*Pi^4*S^2)/60 + (Pi^2*(-3 - 4*S^2))/3 - (S^2*HPL[{0}, S^2]^4)/4 + ((-19*Pi^2*S^2)/6 + (-2 - 11*S^2 - 9*S^4)/S^2)*HPL[{1}, -S^2]^2 - (2*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) - 4*S^2*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*(-(S^2*(16 + 9*S^2))/(6*(1 + S^2)) - (7*S^2*HPL[{1}, -S^2])/6) + (-2*Pi^2*S^2 + (-5 - 16*S^2)/2)*HPL[{2}, -S^2] - (5*S^2*HPL[{2}, -S^2]^2)/2 + HPL[{0}, S^2]^2*(-(Pi^2*S^2) + (-3 - 8*S^2)/2 + ((-3 - 3*S^2 - 23*S^4 - 9*S^6)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)) - (7*S^2*HPL[{1}, -S^2]^2)/2 - 3*S^2*HPL[{2}, -S^2]) + (S^2*(21 + S^2)*HPL[{3}, -S^2])/(2*(1 + S^2)) - S^2*HPL[{4}, -S^2] + ((5 - S^4)*HPL[{2, 1}, -S^2])/S^2 + HPL[{0}, S^2]*(-2*(1 + 5*S^2) + (Pi^2*(-37*S^2 - 18*S^4))/(6*(1 + S^2)) - (3*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) - 8*S^2*HPL[{1}, -S^2]^3 - (2*S^2*(9 + 4*S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((-19*Pi^2*S^2)/6 + (-2 - 11*S^2 - 9*S^4)/S^2 - 10*S^2*HPL[{2}, -S^2]) + S^2*HPL[{3}, -S^2] - 2*S^2*HPL[{2, 1}, -S^2]) + 12*S^2*HPL[{3, 1}, -S^2] - 24*S^2*HPL[{2, 1, 1}, -S^2] + ((11*S^2 + S^4)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(3 + 20*S^2))/(2*S^2) + (Pi^2*(-3 - 3*S^2 - 28*S^4 - 9*S^6))/(3*S^2*(1 + S^2)) - (5*(1 + 3*S^4)*HPL[{2}, -S^2])/(2*S^2) + 10*S^2*HPL[{3}, -S^2] + 10*S^2*Zeta[3])) - 8*S^2*Zeta[5];
E3vwuT3F1=(27*S)/8 + (Pi^2*S*(19 + 4*S^2))/12 - (Pi^4*S*(-99 - 53*S^2 + 17*S^4))/(90*(1 + S^2)^2) + ((19*Pi^2*S)/9 + (7 + 88*S^2 + 14*S^4 + 32*S^6 + 3*S^8)/(6*S*(1 + S^2)^2))*HPL[{1}, -S^2]^3 + ((-1 + 12*S^2 + 7*S^4 - 2*S^6)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)^2) + (8*S*HPL[{1}, -S^2]^5)/5 + HPL[{0}, S^2]^4*(-(S^3*(5 + 4*S^2))/(8*(1 + S^2)^2) + (S*HPL[{1}, -S^2])/4) + (S*(11 + 12*S^2 + 3*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]^3*((7*Pi^2*S)/36 + (S*(12 + 8*S^2 + 19*S^4 + 9*S^6))/(12*(1 + S^2)^2) + ((-3 + 26*S^2 + 26*S^4 + 4*S^6)*HPL[{1}, -S^2])/(6*S*(1 + S^2)^2) + (7*S*HPL[{1}, -S^2]^2)/6 + (7*S*HPL[{2}, -S^2])/6) + ((-7*Pi^2*S)/3 + (S*(-4 + S^2 - 2*S^4 + 3*S^6))/(1 + S^2)^2)*HPL[{3}, -S^2] - (2*S*(12 + 19*S^2 + 8*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - 14*S*HPL[{5}, -S^2] + ((8*Pi^2*S)/3 + (-8 - 36*S^2 + 11*S^4 + 3*S^6)/(2*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((S*(35 + 8*S^2))/8 - (Pi^2*S*(-36 - 7*S^2 + 16*S^4))/(24*(1 + S^2)^2) + ((-3 + 26*S^2 + 26*S^4 + 4*S^6)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)^2) + (7*S*HPL[{1}, -S^2]^3)/3 + (S*(2 + S^2)*(3 + 2*S^2)*HPL[{2}, -S^2])/(1 + S^2)^2 + HPL[{1}, -S^2]*((13*Pi^2*S)/12 + (7 + 88*S^2 + 46*S^4 + 24*S^6 + 3*S^8)/(8*S*(1 + S^2)^2) + 2*S*HPL[{2}, -S^2]) - (3*S*HPL[{3}, -S^2])/2 + 2*S*HPL[{2, 1}, -S^2]) - (2*S*(1 + 7*S^2 + 5*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + 16*S*HPL[{3, 2}, -S^2] + 58*S*HPL[{4, 1}, -S^2] + 16*S*HPL[{2, 1, 1}, -S^2] + 12*S*HPL[{2, 2, 1}, -S^2] - 8*S*HPL[{3, 1, 1}, -S^2] + 48*S*HPL[{2, 1, 1, 1}, -S^2] + ((-4*Pi^2*S)/3 + (8*S*(-1 + S^2))/(1 + S^2)^2 - 4*S*HPL[{0}, S^2]^2 + (4*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) - 16*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((8*S*(-3 - S^2 + S^4))/(1 + S^2)^2 - 16*S*HPL[{1}, -S^2]) - 8*S*HPL[{2}, -S^2])*Log[T]^3 + ((4*S*(4 + 3*S^2))/(1 + S^2)^2 + 8*S*HPL[{0}, S^2] + 8*S*HPL[{1}, -S^2])*Log[T]^4 + (-2*Pi^2*S - (S^3*(-9 + 14*S^2 + 3*S^4))/(2*(1 + S^2)^2))*Zeta[3] + Log[T]^2*((3*S)/2 + (Pi^2*S*(84 + 73*S^2 + 8*S^4))/(6*(1 + S^2)^2) + (7*S*HPL[{0}, S^2]^3)/3 + ((19*Pi^2*S)/3 + (7 + 88*S^2 + 14*S^4 + 32*S^6 + 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{1}, -S^2] - (6*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^2) + 16*S*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*((S*(36 + 37*S^2 + 8*S^4))/(2*(1 + S^2)^2) + 7*S*HPL[{1}, -S^2]) + 8*S*HPL[{2}, -S^2] + HPL[{0}, S^2]*((19*Pi^2*S)/3 + (S*(40 + 21*S^2 + 32*S^4 + 3*S^6))/(2*(1 + S^2)^2) - (6*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) + 24*S*HPL[{1}, -S^2]^2 + 22*S*HPL[{2}, -S^2]) - 22*S*HPL[{3}, -S^2] + 24*S*HPL[{2, 1}, -S^2] - 24*S*Zeta[3]) + HPL[{1}, -S^2]^2*((11*(1 + S^2)*(3 + S^2))/(8*S) + (Pi^2*(-6 + 62*S^2 + 47*S^4 - 2*S^6))/(6*S*(1 + S^2)^2) + (5*(-1 + 6*S^2)*HPL[{2}, -S^2])/(2*S) - 10*S*HPL[{3}, -S^2] - 10*S*Zeta[3]) + HPL[{2}, -S^2]*(2*S*(4 + S^2) + (Pi^2*S*(8 + 11*S^2 + 4*S^4))/(3*(1 + S^2)^2) - 8*S*HPL[{3}, -S^2] - 6*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{1}, -S^2]*((29*Pi^4*S)/45 + ((1 + S^2)*(3 + 7*S^2))/(8*S) + (Pi^2*(7 + 88*S^2 + 30*S^4 + 28*S^6 + 3*S^8))/(12*S*(1 + S^2)^2) + ((2*Pi^2*S)/3 + (2*(1 + 9*S^2 + S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] + 4*S*HPL[{2}, -S^2]^2 + (10*S*(-2 + S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 4*S*HPL[{4}, -S^2] - (5*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S + 4*S*HPL[{3, 1}, -S^2] + (10*S*(-2 + S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]*((89*Pi^4*S)/180 + (S*(5 + 7*S^2))/8 + (Pi^2*S*(64 + 37*S^2 + 70*S^4 + 21*S^6))/(24*(1 + S^2)^2) - (2*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)^2) + 4*S*HPL[{1}, -S^2]^4 + (3*Pi^2*S + (S*(36 + 23*S^2 + 30*S^4 + 3*S^6))/(4*(1 + S^2)^2))*HPL[{2}, -S^2] + (9*S*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*((19*Pi^2*S)/6 + (7 + 88*S^2 + 14*S^4 + 32*S^6 + 3*S^8)/(4*S*(1 + S^2)^2) + 10*S*HPL[{2}, -S^2]) + (S*(5 + 5*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 5*S*HPL[{4}, -S^2] + ((5 - 32*S^2 - 29*S^4 - 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 24*S*HPL[{3, 1}, -S^2] + 44*S*HPL[{2, 1, 1}, -S^2] + (S*(-2 + S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((11*(1 + S^2)*(3 + S^2))/(8*S) + (Pi^2*(-6 + 62*S^2 + 47*S^4 - 2*S^6))/(6*S*(1 + S^2)^2) - (5*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^2) + 2*S*HPL[{3}, -S^2] - 20*S*HPL[{2, 1}, -S^2] - 2*S*Zeta[3])) + Log[T]*((-5*S)/4 - (19*Pi^4*S)/30 - (Pi^2*S*(64 + 7*S^2 + 22*S^4 + 3*S^6))/(12*(1 + S^2)^2) - (S*HPL[{0}, S^2]^4)/2 + ((-19*Pi^2*S)/3 + (-7 - 88*S^2 - 14*S^4 - 32*S^6 - 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{1}, -S^2]^2 + (4*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)^2) - 8*S*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*(-(S*(36 + 37*S^2 + 8*S^4))/(6*(1 + S^2)^2) - (7*S*HPL[{1}, -S^2])/3) + (-4*Pi^2*S - (S*(36 + 19*S^2 + 3*S^4))/(2*(1 + S^2)))*HPL[{2}, -S^2] - 5*S*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^2*(-2*Pi^2*S - (S*(40 + 31*S^2 + 22*S^4 + 3*S^6))/(4*(1 + S^2)^2) + ((3 - 26*S^2 - 26*S^4 - 4*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) - 7*S*HPL[{1}, -S^2]^2 - 6*S*HPL[{2}, -S^2]) - (2*S*(1 + 27*S^2 + 21*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 2*S*HPL[{4}, -S^2] + (2*(-5 + 22*S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*(-(S*(38 + 11*S^2))/4 + (Pi^2*S*(-72 - 49*S^2 + 4*S^4))/(6*(1 + S^2)^2) + (6*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^2) - 16*S*HPL[{1}, -S^2]^3 + (2*S*(-14 - 3*S^2 + 6*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-19*Pi^2*S)/3 + (-7 - 88*S^2 - 14*S^4 - 32*S^6 - 3*S^8)/(2*S*(1 + S^2)^2) - 20*S*HPL[{2}, -S^2]) + 2*S*HPL[{3}, -S^2] - 4*S*HPL[{2, 1}, -S^2]) + 24*S*HPL[{3, 1}, -S^2] - 48*S*HPL[{2, 1, 1}, -S^2] - (2*S*(2 + 29*S^2 + 22*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-11*(1 + S^2)*(3 + S^2))/(4*S) + (Pi^2*(6 - 62*S^2 - 47*S^4 + 2*S^6))/(3*S*(1 + S^2)^2) - (5*(-1 + 6*S^2)*HPL[{2}, -S^2])/S + 20*S*HPL[{3}, -S^2] + 20*S*Zeta[3])) - 16*S*Zeta[5];
E3vwuT3F3=(-64 - 235*S^2)/(648*S) + (Pi^2*(-32 - 101*S^2 - 216*S^4))/(324*S) - (Pi^4*S^3*(677 + 658*S^2 + 155*S^4))/(1620*(1 + S^2)^2) + ((-19*Pi^2*S^3)/27 + (-32 - 253*S^2 - 428*S^4 - 1958*S^6 - 1324*S^8 - 437*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^3 + ((-2 - 4*S^2 - 2*S^4 - 47*S^6 - 46*S^8 - 11*S^10)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^2) - (8*S^3*HPL[{1}, -S^2]^5)/15 + HPL[{0}, S^2]^4*(-(S^3*(3 + 2*S^2))/(24*(1 + S^2)^2) - (S^3*HPL[{1}, -S^2])/12) - (S^3*(67 + 86*S^2 + 31*S^4)*HPL[{2}, -S^2]^2)/(18*(1 + S^2)^2) + HPL[{0}, S^2]^3*((-7*Pi^2*S^3)/108 + (-12 - 18*S^2 - 128*S^4 - 133*S^6 - 53*S^8)/(108*S*(1 + S^2)^2) + ((-2 - 4*S^2 - 2*S^4 - 32*S^6 - 36*S^8 - 11*S^10)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)^2) - (7*S^3*HPL[{1}, -S^2]^2)/18 - (7*S^3*HPL[{2}, -S^2])/18) + ((7*Pi^2*S^3)/9 + (S^3*(31 + 14*S^2 + 13*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*S^3*(7 + 10*S^2 + 4*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (14*S^3*HPL[{5}, -S^2])/3 + ((-8*Pi^2*S^3)/9 + (24 + 120*S^2 + 138*S^4 + 329*S^6 - 37*S^8)/(54*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-32 - 101*S^2 - 432*S^4)/(216*S) - (Pi^2*S^3*(179 + 202*S^2 + 62*S^4))/(216*(1 + S^2)^2) + ((-2 - 4*S^2 - 2*S^4 - 32*S^6 - 36*S^8 - 11*S^10)*HPL[{1}, -S^2]^2)/(6*S^3*(1 + S^2)^2) - (7*S^3*HPL[{1}, -S^2]^3)/9 - (S^3*(49 + 74*S^2 + 31*S^4)*HPL[{2}, -S^2])/(18*(1 + S^2)^2) + HPL[{1}, -S^2]*((-13*Pi^2*S^3)/36 + (-32 - 253*S^2 - 428*S^4 - 1670*S^6 - 1396*S^8 - 437*S^10)/(216*S^3*(1 + S^2)^2) - (2*S^3*HPL[{2}, -S^2])/3) + (S^3*HPL[{3}, -S^2])/2 - (2*S^3*HPL[{2, 1}, -S^2])/3) + (S^3*(17 + 42*S^2 + 23*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (16*S^3*HPL[{3, 2}, -S^2])/3 - (58*S^3*HPL[{4, 1}, -S^2])/3 - (124*S^3*HPL[{2, 1, 1}, -S^2])/9 - 4*S^3*HPL[{2, 2, 1}, -S^2] + (8*S^3*HPL[{3, 1, 1}, -S^2])/3 - 16*S^3*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S^3)/9 + (4*(2 + 3*S^2 + 18*S^4 + 5*S^6))/(9*S*(1 + S^2)^2) + (4*S^3*HPL[{0}, S^2]^2)/3 + (4*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*S^3*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*((4*S^3*(29 + 34*S^2 + 11*S^4))/(9*(1 + S^2)^2) + (16*S^3*HPL[{1}, -S^2])/3) + (8*S^3*HPL[{2}, -S^2])/3)*Log[T]^3 + ((-4*S^3*(3 + 2*S^2))/(3*(1 + S^2)^2) - (8*S^3*HPL[{0}, S^2])/3 - (8*S^3*HPL[{1}, -S^2])/3)*Log[T]^4 + ((2*Pi^2*S^3)/3 + (S^3*(145 + 2*S^2 + 37*S^4))/(54*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-2 - 7*S^2 - 36*S^4)/(9*S) - (Pi^2*S^3*(40 + 68*S^2 + 31*S^4))/(27*(1 + S^2)^2) + (8*S^3*HPL[{3}, -S^2])/3 + 2*S^3*HPL[{2, 1}, -S^2] + (8*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(32 + 111*S^2 + 953*S^4))/(216*S^3) + (Pi^2*(-4 - 8*S^2 - 4*S^4 - 79*S^6 - 82*S^8 - 22*S^10))/(18*S^3*(1 + S^2)^2) - (5*(2 + 11*S^6)*HPL[{2}, -S^2])/(18*S^3) + (10*S^3*HPL[{3}, -S^2])/3 + (10*S^3*Zeta[3])/3) + Log[T]^2*((-32 - 101*S^2)/(54*S) - (Pi^2*S^3*(233 + 238*S^2 + 62*S^4))/(54*(1 + S^2)^2) - (7*S^3*HPL[{0}, S^2]^3)/9 + ((-19*Pi^2*S^3)/9 + (-32 - 253*S^2 - 428*S^4 - 1958*S^6 - 1324*S^8 - 437*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] - (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) - (16*S^3*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*(-(S^3*(125 + 166*S^2 + 62*S^4))/(18*(1 + S^2)^2) - (7*S^3*HPL[{1}, -S^2])/3) - (62*S^3*HPL[{2}, -S^2])/9 + HPL[{0}, S^2]*((-19*Pi^2*S^3)/9 + (-72 - 108*S^2 - 995*S^4 - 964*S^6 - 437*S^8)/(54*S*(1 + S^2)^2) - (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) - 8*S^3*HPL[{1}, -S^2]^2 - (22*S^3*HPL[{2}, -S^2])/3) + (22*S^3*HPL[{3}, -S^2])/3 - 8*S^3*HPL[{2, 1}, -S^2] + 8*S^3*Zeta[3]) + HPL[{1}, -S^2]*((-29*Pi^4*S^3)/135 - ((1 + S^2)*(64 + 227*S^2 + 3175*S^4))/(648*S^3) + (Pi^2*(-32 - 253*S^2 - 428*S^4 - 1814*S^6 - 1360*S^8 - 437*S^10))/(324*S^3*(1 + S^2)^2) + ((-2*Pi^2*S^3)/9 + (-2 - 15*S^2 - 14*S^4 - 75*S^6 - 32*S^8)/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (4*S^3*HPL[{2}, -S^2]^2)/3 + (10*S^3*(3 + 2*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (4*S^3*HPL[{4}, -S^2])/3 + (5*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*S^3*HPL[{3, 1}, -S^2])/3 + (10*S^3*(3 + 2*S^2)*Zeta[3])/(3*(1 + S^2)^2)) + Log[T]*((19*Pi^4*S^3)/90 + (32 + 123*S^2)/(108*S) + (Pi^2*(144 + 216*S^2 + 1537*S^4 + 1202*S^6 + 421*S^8))/(324*S*(1 + S^2)^2) + (S^3*HPL[{0}, S^2]^4)/6 + ((19*Pi^2*S^3)/9 + (32 + 253*S^2 + 428*S^4 + 1958*S^6 + 1324*S^8 + 437*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^2 + (4*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) + (8*S^3*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*((S^3*(43 + 58*S^2 + 22*S^4))/(18*(1 + S^2)^2) + (7*S^3*HPL[{1}, -S^2])/9) + ((4*Pi^2*S^3)/3 + (60 + 30*S^2 + 571*S^4 + 421*S^6)/(54*S*(1 + S^2)))*HPL[{2}, -S^2] + (5*S^3*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((2*Pi^2*S^3)/3 + (72 + 108*S^2 + 889*S^4 + 1022*S^6 + 421*S^8)/(108*S*(1 + S^2)^2) + ((2 + 4*S^2 + 2*S^4 + 32*S^6 + 36*S^8 + 11*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) + (7*S^3*HPL[{1}, -S^2]^2)/3 + 2*S^3*HPL[{2}, -S^2]) - (S^3*(97 + 74*S^2 + 7*S^4)*HPL[{3}, -S^2])/(9*(1 + S^2)^2) + (2*S^3*HPL[{4}, -S^2])/3 + (2*(-10 + 7*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((Pi^2*S^3*(101 + 126*S^2 + 44*S^4))/(18*(1 + S^2)^2) + (64 + 202*S^2 + 953*S^4)/(108*S) + (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + (16*S^3*HPL[{1}, -S^2]^3)/3 + (2*S^3*(76 + 92*S^2 + 31*S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*((19*Pi^2*S^3)/9 + (32 + 253*S^2 + 428*S^4 + 1958*S^6 + 1324*S^8 + 437*S^10)/(54*S^3*(1 + S^2)^2) + (20*S^3*HPL[{2}, -S^2])/3) - (2*S^3*HPL[{3}, -S^2])/3 + (4*S^3*HPL[{2, 1}, -S^2])/3) - 8*S^3*HPL[{3, 1}, -S^2] + 16*S^3*HPL[{2, 1, 1}, -S^2] - (2*S^3*(52 + 44*S^2 + 7*S^4)*Zeta[3])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(32 + 111*S^2 + 953*S^4))/(108*S^3) + (Pi^2*(4 + 8*S^2 + 4*S^4 + 79*S^6 + 82*S^8 + 22*S^10))/(9*S^3*(1 + S^2)^2) + (5*(2 + 11*S^6)*HPL[{2}, -S^2])/(9*S^3) - (20*S^3*HPL[{3}, -S^2])/3 - (20*S^3*Zeta[3])/3)) + HPL[{0}, S^2]*((-89*Pi^4*S^3)/540 + (-96 - 369*S^2 - 3175*S^4)/(648*S) + (Pi^2*(-144 - 216*S^2 - 1763*S^4 - 1762*S^6 - 755*S^8))/(648*S*(1 + S^2)^2) - (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) - (4*S^3*HPL[{1}, -S^2]^4)/3 + (-(Pi^2*S^3) + (-60 - 90*S^2 - 889*S^4 - 920*S^6 - 421*S^8)/(108*S*(1 + S^2)^2))*HPL[{2}, -S^2] - (3*S^3*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*((-19*Pi^2*S^3)/18 + (-32 - 253*S^2 - 428*S^4 - 1958*S^6 - 1324*S^8 - 437*S^10)/(108*S^3*(1 + S^2)^2) - (10*S^3*HPL[{2}, -S^2])/3) + (S^3*(-11 + 2*S^2 + 7*S^4)*HPL[{3}, -S^2])/(18*(1 + S^2)^2) - (5*S^3*HPL[{4}, -S^2])/3 + ((10 + 20*S^2 + 10*S^4 + 83*S^6 + 46*S^8 - 7*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 8*S^3*HPL[{3, 1}, -S^2] - (44*S^3*HPL[{2, 1, 1}, -S^2])/3 - (S^3*(-2 + 8*S^2 + 7*S^4)*Zeta[3])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(32 + 111*S^2 + 953*S^4))/(216*S^3) + (Pi^2*(-4 - 8*S^2 - 4*S^4 - 79*S^6 - 82*S^8 - 22*S^10))/(18*S^3*(1 + S^2)^2) - (5*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^2) - (2*S^3*HPL[{3}, -S^2])/3 + (20*S^3*HPL[{2, 1}, -S^2])/3 + (2*S^3*Zeta[3])/3)) + (16*S^3*Zeta[5])/3;
E3vwuT=E3vwuT0F0+T*E3vwuT1F1*(F+1/F)+T^2*(E3vwuT2F0+E3vwuT2F2*(F^2+1/F^2))+T^3*(E3vwuT3F1*(F+1/F)+E3vwuT3F3*(F^3+1/F^3));
E3wuvT0F0=(-283*Pi^6)/1620 - HPL[{0}, S^2]^6/48 + HPL[{0}, S^2]^4*(-Pi^2/6 - HPL[{2}, -S^2]/4) - (Pi^2*HPL[{2}, -S^2]^2)/3 - (4*HPL[{2}, -S^2]^3)/3 - 2*HPL[{3}, -S^2]^2 + 24*HPL[{6}, -S^2] + HPL[{2}, -S^2]*((-29*Pi^4)/45 + 4*HPL[{4}, -S^2] - 4*HPL[{3, 1}, -S^2]) + 6*Pi^2*HPL[{3, 1}, -S^2] - 4*HPL[{5, 1}, -S^2] + HPL[{0}, S^2]^2*((-151*Pi^4)/360 - (13*Pi^2*HPL[{2}, -S^2])/12 - HPL[{2}, -S^2]^2 + HPL[{4}, -S^2] + 6*HPL[{3, 1}, -S^2] - 14*HPL[{2, 1, 1}, -S^2]) - (38*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 32*HPL[{3, 2, 1}, -S^2] - 104*HPL[{4, 1, 1}, -S^2] + 96*HPL[{3, 1, 1, 1}, -S^2] - 192*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-151*Pi^4)/90 - (3*HPL[{0}, S^2]^4)/4 + HPL[{0}, S^2]^2*(-3*Pi^2 - 7*HPL[{2}, -S^2]) - (19*Pi^2*HPL[{2}, -S^2])/3 - 4*HPL[{4}, -S^2] + HPL[{0}, S^2]*(4*HPL[{3}, -S^2] - 48*HPL[{2, 1}, -S^2]) + 48*HPL[{3, 1}, -S^2] - 96*HPL[{2, 1, 1}, -S^2])*Log[T]^2 + ((-8*Pi^2)/3 - 3*HPL[{0}, S^2]^2 - 8*HPL[{2}, -S^2])*Log[T]^4 + 4*HPL[{0}, S^2]*Log[T]^5 - (4*Log[T]^6)/3 + Log[T]^3*((20*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]*((50*Pi^2)/9 + 16*HPL[{2}, -S^2]) - 16*HPL[{3}, -S^2] + 32*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + HPL[{3}, -S^2]*(20*HPL[{2, 1}, -S^2] - 4*Zeta[3]) + HPL[{0}, S^2]^3*((-7*HPL[{2, 1}, -S^2])/3 - 2*Zeta[3]) + 20*HPL[{2, 1}, -S^2]*Zeta[3] + 4*Zeta[3]^2 + Log[T]*(HPL[{0}, S^2]^5/4 + HPL[{0}, S^2]^3*((25*Pi^2)/18 + (7*HPL[{2}, -S^2])/3) - (14*Pi^2*HPL[{3}, -S^2])/3 - 4*HPL[{5}, -S^2] + (38*Pi^2*HPL[{2, 1}, -S^2])/3 + HPL[{0}, S^2]^2*(-2*HPL[{3}, -S^2] + 14*HPL[{2, 1}, -S^2]) + 40*HPL[{3, 2}, -S^2] + 128*HPL[{4, 1}, -S^2] + HPL[{0}, S^2]*((61*Pi^4)/30 + (19*Pi^2*HPL[{2}, -S^2])/3 + 10*HPL[{2}, -S^2]^2 + 4*HPL[{4}, -S^2] - 48*HPL[{3, 1}, -S^2] + 96*HPL[{2, 1, 1}, -S^2]) - 96*HPL[{3, 1, 1}, -S^2] + 192*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-20*HPL[{3}, -S^2] - 20*Zeta[3]) - 4*Pi^2*Zeta[3] - 32*Zeta[5]) + HPL[{0}, S^2]*((Pi^2*HPL[{3}, -S^2])/3 - 6*HPL[{5}, -S^2] - (19*Pi^2*HPL[{2, 1}, -S^2])/3 + 4*HPL[{3, 2}, -S^2] + 8*HPL[{4, 1}, -S^2] + 40*HPL[{2, 2, 1}, -S^2] + 128*HPL[{3, 1, 1}, -S^2] - 96*HPL[{2, 1, 1, 1}, -S^2] - 2*Pi^2*Zeta[3] + HPL[{2}, -S^2]*(-2*HPL[{3}, -S^2] - 20*HPL[{2, 1}, -S^2] + 2*Zeta[3]) - 16*Zeta[5]);
E3wuvT1F1=-(HPL[{0}, S^2]^4*HPL[{1}, -S^2])/(4*S) + ((-19*Pi^2)/(9*S) - (16*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^3 - (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (8*HPL[{1}, -S^2]^5)/(5*S) + HPL[{0}, S^2]^3*(-S/3 + ((-1 - S^2)*HPL[{1}, -S^2])/(6*S) - (7*HPL[{1}, -S^2]^2)/(6*S)) - (2*HPL[{2}, -S^2]^2)/S + (2*(-1 + 6*S^2)*HPL[{3}, -S^2])/S - (2*HPL[{4}, -S^2])/S + (12*HPL[{5}, -S^2])/S + ((11*Pi^2)/(3*S) - (4*(1 + 3*S^2))/S)*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(((-1 - S^2)*HPL[{1}, -S^2]^2)/(2*S) - (7*HPL[{1}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]*((-13*Pi^2)/(12*S) + (-1 - S^2)/S - (2*HPL[{2}, -S^2])/S) + HPL[{3}, -S^2]/(2*S) + (5*HPL[{2, 1}, -S^2])/S) - (10*HPL[{3, 1}, -S^2])/S + (4*HPL[{3, 2}, -S^2])/S + (6*HPL[{4, 1}, -S^2])/S + (16*HPL[{2, 1, 1}, -S^2])/S - (12*HPL[{2, 2, 1}, -S^2])/S - (40*HPL[{3, 1, 1}, -S^2])/S + (48*HPL[{2, 1, 1, 1}, -S^2])/S + (((-19*Pi^2)/(3*S) - (16*(1 + S^2))/S)*HPL[{1}, -S^2] - (7*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/S - (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (16*HPL[{1}, -S^2]^3)/S + (8*HPL[{2}, -S^2])/S + HPL[{0}, S^2]*(-16*S - (12*(1 + S^2)*HPL[{1}, -S^2])/S - (24*HPL[{1}, -S^2]^2)/S + (2*HPL[{2}, -S^2])/S) - (2*HPL[{3}, -S^2])/S + (24*HPL[{2, 1}, -S^2])/S)*Log[T]^2 + ((8*(1 + S^2)*HPL[{1}, -S^2])/S + (16*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(8*S + (16*HPL[{1}, -S^2])/S) - (8*HPL[{2}, -S^2])/S)*Log[T]^3 - (8*HPL[{1}, -S^2]*Log[T]^4)/S + 12*S*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2)/(3*S) - (2*HPL[{3}, -S^2])/S + (6*HPL[{2, 1}, -S^2])/S - (2*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-12*(1 + S^2))/S - (7*Pi^2*(1 + S^2))/(6*S) + (5*(1 + S^2)*HPL[{2}, -S^2])/S + (10*HPL[{3}, -S^2])/S + (10*Zeta[3])/S) + HPL[{1}, -S^2]*((-29*Pi^4)/(45*S) - (24*(1 + S^2))/S - (5*Pi^2*(1 + S^2))/(3*S) + ((-2*Pi^2)/(3*S) + (6*(1 + S^2))/S)*HPL[{2}, -S^2] - (4*HPL[{2}, -S^2]^2)/S + (10*(1 + S^2)*HPL[{3}, -S^2])/S + (4*HPL[{4}, -S^2])/S - (10*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*HPL[{3, 1}, -S^2])/S + (10*(1 + S^2)*Zeta[3])/S) + Log[T]*(((19*Pi^2)/(3*S) + (16*(1 + S^2))/S)*HPL[{1}, -S^2]^2 + (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (8*HPL[{1}, -S^2]^4)/S + HPL[{0}, S^2]^3*(S/3 + (7*HPL[{1}, -S^2])/(3*S)) + (-8/S - (7*Pi^2)/(3*S))*HPL[{2}, -S^2] + (5*HPL[{2}, -S^2]^2)/S + HPL[{0}, S^2]^2*(((1 + S^2)*HPL[{1}, -S^2])/S + (7*HPL[{1}, -S^2]^2)/S - HPL[{2}, -S^2]/S) - (2*(1 + 10*S^2)*HPL[{3}, -S^2])/S - (2*HPL[{4}, -S^2])/S + (4*(1 + 5*S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*(24*S + (7*Pi^2*S)/3 + (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (16*HPL[{1}, -S^2]^3)/S + (2*(1 + 5*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((19*Pi^2)/(3*S) + (16*(1 + S^2))/S + (20*HPL[{2}, -S^2])/S) + (2*HPL[{3}, -S^2])/S - (44*HPL[{2, 1}, -S^2])/S) + (24*HPL[{3, 1}, -S^2])/S - (48*HPL[{2, 1, 1}, -S^2])/S - 20*S*Zeta[3] + HPL[{1}, -S^2]*((24*(1 + S^2))/S + (7*Pi^2*(1 + S^2))/(3*S) - (10*(1 + S^2)*HPL[{2}, -S^2])/S - (20*HPL[{3}, -S^2])/S - (20*Zeta[3])/S)) + HPL[{0}, S^2]*(-24*S - (5*Pi^2*S)/3 - (4*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (4*HPL[{1}, -S^2]^4)/S + (Pi^2/(6*S) - (2*(1 + 3*S^2))/S)*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(2*S) + HPL[{1}, -S^2]^2*((-19*Pi^2)/(6*S) - (8*(1 + S^2))/S - (10*HPL[{2}, -S^2])/S) - HPL[{3}, -S^2]/S - (3*HPL[{4}, -S^2])/S + (8*HPL[{2, 1}, -S^2])/S + (4*HPL[{2, 1, 1}, -S^2])/S + HPL[{1}, -S^2]*((-12*(1 + S^2))/S - (7*Pi^2*(1 + S^2))/(6*S) - (5*(1 + S^2)*HPL[{2}, -S^2])/S - (2*HPL[{3}, -S^2])/S + (20*HPL[{2, 1}, -S^2])/S + (2*Zeta[3])/S));
E3wuvT2F0=24 + (Pi^4*(13 - 16*S^2))/(45*(1 + S^2)) - (S^2*HPL[{0}, S^2]^4)/(4*(1 + S^2)) - (4*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S^2) - (4*(-1 + S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) + HPL[{0}, S^2]^3*(5/3 + ((6 - S^2)*HPL[{1}, -S^2])/(3*(1 + S^2))) + (-8/S^2 + (Pi^2*(5 + 3*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] - (2*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((Pi^2*(12 - 7*S^2))/(3*(1 + S^2)) - (2*(1 + S^2))/S^2 + 10*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*(-1 + (Pi^2*(5 - 8*S^2))/(12*(1 + S^2)) + ((-1 - S^2)*HPL[{1}, -S^2])/S^2 + ((6 - S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + ((5 + S^2)*HPL[{2}, -S^2])/(2*(1 + S^2))) - (12*HPL[{3}, -S^2])/S^2 + (4*S^2*HPL[{4}, -S^2])/(1 + S^2) + (4*HPL[{2, 1}, -S^2])/S^2 - (4*(2 + 3*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 20*HPL[{2, 1, 1}, -S^2] + (4 + (Pi^2*(11 - 8*S^2))/(3*(1 + S^2)) + ((5 - 2*S^2)*HPL[{0}, S^2]^2)/(1 + S^2) - (4*(1 + S^2)*HPL[{1}, -S^2])/S^2 - (24*(-1 + S^2)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(1 + S^2) - (24*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + 10*HPL[{2}, -S^2])*Log[T]^2 + ((4*(-7 + 5*S^2)*HPL[{0}, S^2])/(3*(1 + S^2)) + (16*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2))*Log[T]^3 - (4*(-1 + S^2)*Log[T]^4)/(1 + S^2) - 4*Zeta[3] + HPL[{1}, -S^2]*((-12*(1 + S^2))/S^2 - (2*Pi^2*(1 + S^2))/(3*S^2) + (20*S^2*HPL[{3}, -S^2])/(1 + S^2) - 20*HPL[{2, 1}, -S^2] + (20*S^2*Zeta[3])/(1 + S^2)) + Log[T]*(-12 + (2*Pi^2)/3 + ((-12 - 5*S^2)*HPL[{0}, S^2]^3)/(3*(1 + S^2)) + (4*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 + (16*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) + HPL[{0}, S^2]^2*(2 + (2*(-6 + S^2)*HPL[{1}, -S^2])/(1 + S^2)) + HPL[{1}, -S^2]*((4*(1 + S^2))/S^2 + (2*Pi^2*(-12 + 7*S^2))/(3*(1 + S^2)) - 20*HPL[{2}, -S^2]) - (4*HPL[{2}, -S^2])/S^2 + HPL[{0}, S^2]*((-19*Pi^2)/(3*(1 + S^2)) + (4*(1 + S^2)*HPL[{1}, -S^2])/S^2 + (24*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + (10*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) - (20*S^2*HPL[{3}, -S^2])/(1 + S^2) + 20*HPL[{2, 1}, -S^2] - (4*(-1 + 4*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]*(-10 + (5*Pi^2)/3 - (2*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 - (8*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) + (2*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((Pi^2*(12 - 7*S^2))/(3*(1 + S^2)) - (2*(1 + S^2))/S^2 - (10*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) - (2*S^2*HPL[{3}, -S^2])/(1 + S^2) + (10*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (2*(5 + 6*S^2)*Zeta[3])/(1 + S^2));
E3wuvT2F2=3/4 + (5*Pi^2)/24 + (29*Pi^4)/(90*(1 + S^2)) + ((19*Pi^2)/(18*S^2) + (9 + 11*S^2 + 2*S^4)/(3*S^2))*HPL[{1}, -S^2]^3 + ((3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) + (4*HPL[{1}, -S^2]^5)/(5*S^2) + HPL[{0}, S^2]^4*(1/(8*(1 + S^2)) + HPL[{1}, -S^2]/(8*S^2)) + HPL[{0}, S^2]^3*((3 + S^2)/24 + ((3 + 31*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(24*S^2*(1 + S^2)) + (7*HPL[{1}, -S^2]^2)/(12*S^2)) + (2*(1 + 2*S^2)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)) + ((1 - 26*S^2 - 6*S^4)*HPL[{3}, -S^2])/(4*S^2) + ((9 + 5*S^2)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - (6*HPL[{5}, -S^2])/S^2 + ((-11*Pi^2)/(6*S^2) + (-1 + 13*S^2 + 3*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(1/8 + (13*Pi^2)/(24*(1 + S^2)) + ((3 + 31*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(8*S^2*(1 + S^2)) + (7*HPL[{1}, -S^2]^3)/(6*S^2) + HPL[{2}, -S^2]/(1 + S^2) + HPL[{1}, -S^2]*((13*Pi^2)/(24*S^2) + (3 + 4*S^2 + S^4)/(8*S^2) + HPL[{2}, -S^2]/S^2) - HPL[{3}, -S^2]/(4*S^2) - (5*HPL[{2, 1}, -S^2])/(2*S^2)) + ((15 + 19*S^2)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) - (2*HPL[{3, 2}, -S^2])/S^2 - (3*HPL[{4, 1}, -S^2])/S^2 - (16*HPL[{2, 1, 1}, -S^2])/S^2 + (6*HPL[{2, 2, 1}, -S^2])/S^2 + (20*HPL[{3, 1, 1}, -S^2])/S^2 - (24*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (2 + (19*Pi^2)/(6*(1 + S^2)) + ((19*Pi^2)/(6*S^2) + (9 + 11*S^2 + 2*S^4)/S^2)*HPL[{1}, -S^2] + (3*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) + (8*HPL[{1}, -S^2]^3)/S^2 + HPL[{0}, S^2]^2*(7/(2*(1 + S^2)) + (7*HPL[{1}, -S^2])/(2*S^2)) - (8*HPL[{2}, -S^2])/S^2 + HPL[{0}, S^2]*(2*(4 + S^2) + (3*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) + (12*HPL[{1}, -S^2]^2)/S^2 - HPL[{2}, -S^2]/S^2) + HPL[{3}, -S^2]/S^2 - (12*HPL[{2, 1}, -S^2])/S^2)*Log[T]^2 + (-2 - (2*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) - (8*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*((-2*(4 + S^2 + S^4))/(1 + S^2) - (8*HPL[{1}, -S^2])/S^2) + (4*HPL[{2}, -S^2])/S^2)*Log[T]^3 + (4/(1 + S^2) + (4*HPL[{1}, -S^2])/S^2)*Log[T]^4 + ((-13 - 3*S^2)*Zeta[3])/2 + HPL[{1}, -S^2]^2*(((1 + S^2)*(20 + 3*S^2))/(4*S^2) + (Pi^2*(21 + 97*S^2 + 7*S^4 + 7*S^6))/(24*S^2*(1 + S^2)) - (5*(3 + S^4)*HPL[{2}, -S^2])/(4*S^2) - (5*HPL[{3}, -S^2])/S^2 - (5*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-16 - 3*S^2)/(4*S^2) + (Pi^2*(-2 - S^2))/(3*S^2*(1 + S^2)) + HPL[{3}, -S^2]/S^2 - (3*HPL[{2, 1}, -S^2])/S^2 + Zeta[3]/S^2) + HPL[{1}, -S^2]*((29*Pi^4)/(90*S^2) + (3*(1 + S^2)*(8 + S^2))/(4*S^2) + (Pi^2*(1 + S^2)*(21 + 5*S^2))/(24*S^2) + (Pi^2/(3*S^2) - (3*(5 + 6*S^2 + S^4))/(4*S^2))*HPL[{2}, -S^2] + (2*HPL[{2}, -S^2]^2)/S^2 - (5*(3 + 7*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - (2*HPL[{4}, -S^2])/S^2 + (5*(3 + S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + (2*HPL[{3, 1}, -S^2])/S^2 - (5*(3 + 7*S^2 + S^4 + S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{0}, S^2]*((3*(8 + S^2))/4 + (Pi^2*(19 + 5*S^2))/24 + ((3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) + (2*HPL[{1}, -S^2]^4)/S^2 + (-Pi^2/(12*S^2) + (-1 + 13*S^2 + 3*S^4)/(4*S^2))*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/(4*S^2) + HPL[{1}, -S^2]^2*((19*Pi^2)/(12*S^2) + (9 + 11*S^2 + 2*S^4)/(2*S^2) + (5*HPL[{2}, -S^2])/S^2) + ((-1 + 3*S^2)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) + (3*HPL[{4}, -S^2])/(2*S^2) - (2*(4 + 9*S^2)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (2*HPL[{2, 1, 1}, -S^2])/S^2 + Zeta[3]/(-1 - S^2) + HPL[{1}, -S^2]*(((1 + S^2)*(20 + 3*S^2))/(4*S^2) + (Pi^2*(21 + 97*S^2 + 7*S^4 + 7*S^6))/(24*S^2*(1 + S^2)) + (5*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(4*S^2*(1 + S^2)) + HPL[{3}, -S^2]/S^2 - (10*HPL[{2, 1}, -S^2])/S^2 - Zeta[3]/S^2)) + Log[T]*(-3/2 - (7*Pi^2)/12 + ((-19*Pi^2)/(6*S^2) + (-9 - 11*S^2 - 2*S^4)/S^2)*HPL[{1}, -S^2]^2 - (2*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) - (4*HPL[{1}, -S^2]^4)/S^2 + HPL[{0}, S^2]^3*((-14 - S^2 - S^4)/(12*(1 + S^2)) - (7*HPL[{1}, -S^2])/(6*S^2)) + ((7*Pi^2)/(6*S^2) + (16 + 5*S^2)/(2*S^2))*HPL[{2}, -S^2] - (5*HPL[{2}, -S^2]^2)/(2*S^2) + HPL[{0}, S^2]^2*(-1/4 + ((-3 - 31*S^2 - S^4 - S^6)*HPL[{1}, -S^2])/(4*S^2*(1 + S^2)) - (7*HPL[{1}, -S^2]^2)/(2*S^2) + HPL[{2}, -S^2]/(2*S^2)) + ((-1 + 19*S^2 + 10*S^4 + 10*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + HPL[{4}, -S^2]/S^2 + ((1 - 5*S^4)*HPL[{2, 1}, -S^2])/S^2 + HPL[{0}, S^2]*((-19 - 3*S^2)/2 + (Pi^2*(-38 - 7*S^2 - 7*S^4))/(12*(1 + S^2)) - (3*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) - (8*HPL[{1}, -S^2]^3)/S^2 + ((1 - 19*S^2 - 5*S^4 - 5*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-19*Pi^2)/(6*S^2) + (-9 - 11*S^2 - 2*S^4)/S^2 - (10*HPL[{2}, -S^2])/S^2) - HPL[{3}, -S^2]/S^2 + (22*HPL[{2, 1}, -S^2])/S^2) - (12*HPL[{3, 1}, -S^2])/S^2 + (24*HPL[{2, 1, 1}, -S^2])/S^2 + (5*(2 + S^2 + S^4)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(20 + 3*S^2))/(2*S^2) + (Pi^2*(-21 - 97*S^2 - 7*S^4 - 7*S^6))/(12*S^2*(1 + S^2)) + (5*(3 + S^4)*HPL[{2}, -S^2])/(2*S^2) + (10*HPL[{3}, -S^2])/S^2 + (10*Zeta[3])/S^2));
E3wuvT3F1=27/(8*S) + Pi^2/(4*S) - (29*Pi^4*S)/(90*(1 + S^2)^2) - (S*HPL[{0}, S^2]^4)/(8*(1 + S^2)^2) + ((3 + 16*S^2 - 34*S^4 + 40*S^6 - 9*S^8)*HPL[{1}, -S^2]^3)/(6*S^3*(1 + S^2)^2) + (S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(1 + S^2)^2 + HPL[{0}, S^2]^3*(-(S*(23 - 4*S^2 + S^4))/(24*(1 + S^2)^2) + (S*(-13 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(12*(1 + S^2)^2)) + (-2/S^3 - (Pi^2*S)/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (2*S*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*(((1 + S^2)*(11 + S^2))/(8*S^3) + (Pi^2*S*(-31 + 14*S^2 + 7*S^4))/(12*(1 + S^2)^2) - (5*S*HPL[{2}, -S^2])/2) + HPL[{0}, S^2]^2*(3/(8*S) - (13*Pi^2*S)/(24*(1 + S^2)^2) + ((3 + 16*S^2 - 34*S^4 + 8*S^6 - S^8)*HPL[{1}, -S^2])/(8*S^3*(1 + S^2)^2) + (S*(-13 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(4*(1 + S^2)^2) - (S*HPL[{2}, -S^2])/(1 + S^2)^2) + ((9 + 18*S^2 + 9*S^4 - 12*S^6 + 8*S^8)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^2) + (2*S*HPL[{4}, -S^2])/(1 + S^2)^2 + ((-3 - 11*S^2 + 20*S^4 - 8*S^6)*HPL[{2, 1}, -S^2])/(2*S^3*(1 + S^2)) - (2*S*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (3/(2*S) - (19*Pi^2*S)/(6*(1 + S^2)^2) - (7*S*HPL[{0}, S^2]^2)/(2*(1 + S^2)^2) + ((3 + 16*S^2 - 34*S^4 + 40*S^6 - 9*S^8)*HPL[{1}, -S^2])/(2*S^3*(1 + S^2)^2) + (6*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]*(-(S*(23 - 16*S^2 + 9*S^4))/(2*(1 + S^2)^2) + (6*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2))*Log[T]^2 + ((-8*S*(-1 + S^2))/(1 + S^2)^2 - (4*S*(-1 + 2*S^2 + S^4)*HPL[{0}, S^2])/(1 + S^2)^2 - (4*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2)*Log[T]^3 - (4*S*Log[T]^4)/(1 + S^2)^2 + (2*S^3*(-3 + 2*S^2)*Zeta[3])/(1 + S^2)^2 + HPL[{0}, S^2]*((5 + 3*S^2)/(8*S) - (Pi^2*S*(23 - 10*S^2 + 5*S^4))/(12*(1 + S^2)^2) + ((3 + 16*S^2 - 34*S^4 + 40*S^6 - 9*S^8)*HPL[{1}, -S^2]^2)/(4*S^3*(1 + S^2)^2) + (2*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 + ((-3 - 6*S^2 - 23*S^4 + 12*S^6 - 8*S^8)*HPL[{2}, -S^2])/(4*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(11 + S^2))/(8*S^3) + (Pi^2*S*(-31 + 14*S^2 + 7*S^4))/(12*(1 + S^2)^2) + (5*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(2*(1 + S^2)^2)) - (S*HPL[{3}, -S^2])/(1 + S^2)^2 + (10*S*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (S*Zeta[3])/(1 + S^2)^2) + Log[T]*(-5/(4*S) - (Pi^2*S*(-12 + 7*S^2))/(3*(1 + S^2)^2) - (S*(-6 + 2*S^2 + S^4)*HPL[{0}, S^2]^3)/(6*(1 + S^2)^2) + ((-3 - 16*S^2 + 34*S^4 - 40*S^6 + 9*S^8)*HPL[{1}, -S^2]^2)/(2*S^3*(1 + S^2)^2) - (4*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 + HPL[{0}, S^2]^2*(-((S*(-6 + S^2))/(1 + S^2)^2) - (S*(-13 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(2*(1 + S^2)^2)) + ((3 + 3*S^2 + 20*S^4)*HPL[{2}, -S^2])/(2*S^3*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(11 + S^2))/(4*S^3) - (Pi^2*S*(-31 + 14*S^2 + 7*S^4))/(6*(1 + S^2)^2) + 5*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((-6 - S^2)/(4*S) - (Pi^2*S*(-12 + 14*S^2 + 7*S^4))/(6*(1 + S^2)^2) + ((-3 - 16*S^2 + 34*S^4 - 40*S^6 + 9*S^8)*HPL[{1}, -S^2])/(2*S^3*(1 + S^2)^2) - (6*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 - (5*S*(-1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (10*S^3*(2 + S^2)*HPL[{3}, -S^2])/(1 + S^2)^2 - 10*S*HPL[{2, 1}, -S^2] + (10*S^3*(2 + S^2)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(7 + 3*S^2))/(8*S^3) + (Pi^2*(3 + 16*S^2 - 34*S^4 + 24*S^6 - 5*S^8))/(12*S^3*(1 + S^2)^2) + (2*(1 - 5*S^2 + S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) - (5*S*(-1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 5*S*HPL[{2, 1}, -S^2] - (5*S*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2);
E3wuvT3F3=(-235 - 64*S^2)/(648*S) + (Pi^2*(-59 - 20*S^2))/(324*S) - (29*Pi^4*(2 + 3*S^2))/(270*S*(1 + S^2)^2) + ((-19*Pi^2)/(27*S^3) + (-437 - 1324*S^2 - 1958*S^4 - 428*S^6 - 253*S^8 - 32*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^3 + ((-11 - 46*S^2 - 47*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^2) - (8*HPL[{1}, -S^2]^5)/(15*S^3) + HPL[{0}, S^2]^4*((-2 - 3*S^2)/(24*S*(1 + S^2)^2) - HPL[{1}, -S^2]/(12*S^3)) + HPL[{0}, S^2]^3*((-66 - 351*S^2 - 62*S^4 - 37*S^6 - 8*S^8)/(648*S*(1 + S^2)^2) + ((-11 - 106*S^2 - 137*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{1}, -S^2])/(108*S^3*(1 + S^2)^2) - (7*HPL[{1}, -S^2]^2)/(18*S^3)) + ((-31 - 86*S^2 - 67*S^4)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((41 + 376*S^2 + 653*S^4 + 258*S^6 + 144*S^8 + 24*S^10)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^2) - (2*(19 + 32*S^2 + 10*S^4)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{5}, -S^2])/S^3 + ((11*Pi^2)/(9*S^3) + (37 - 329*S^2 - 138*S^4 - 120*S^6 - 24*S^8)/(54*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-17 - 8*S^2)/(216*S) - (13*Pi^2*(2 + 3*S^2))/(72*S*(1 + S^2)^2) + ((-11 - 106*S^2 - 137*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{1}, -S^2]^2)/(36*S^3*(1 + S^2)^2) - (7*HPL[{1}, -S^2]^3)/(9*S^3) + ((-2 - 3*S^2)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((-13*Pi^2)/(36*S^3) + (-53 - 112*S^2 - 602*S^4 - 80*S^6 - 49*S^8 - 8*S^10)/(216*S^3*(1 + S^2)^2) - (2*HPL[{2}, -S^2])/(3*S^3)) + HPL[{3}, -S^2]/(6*S^3) + (5*HPL[{2, 1}, -S^2])/(3*S^3)) + ((-55 - 122*S^2 - 73*S^4)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{3, 2}, -S^2])/(3*S^3) + (2*HPL[{4, 1}, -S^2])/S^3 + (124*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (4*HPL[{2, 2, 1}, -S^2])/S^3 - (40*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (16*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-101 - 32*S^2)/(54*S) - (19*Pi^2*(2 + 3*S^2))/(18*S*(1 + S^2)^2) + ((-19*Pi^2)/(9*S^3) + (-437 - 1324*S^2 - 1958*S^4 - 428*S^6 - 253*S^8 - 32*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] - (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) - (16*HPL[{1}, -S^2]^3)/(3*S^3) + HPL[{0}, S^2]^2*((-7*(2 + 3*S^2))/(6*S*(1 + S^2)^2) - (7*HPL[{1}, -S^2])/(3*S^3)) + (62*HPL[{2}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((-360 - 963*S^2 - 320*S^4 - 181*S^6 - 32*S^8)/(54*S*(1 + S^2)^2) - (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) - (8*HPL[{1}, -S^2]^2)/S^3 + (2*HPL[{2}, -S^2])/(3*S^3)) - (2*HPL[{3}, -S^2])/(3*S^3) + (8*HPL[{2, 1}, -S^2])/S^3)*Log[T]^2 + ((4*(5 + 18*S^2 + 3*S^4 + 2*S^6))/(9*S*(1 + S^2)^2) + (4*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]*((8*(6 + 9*S^2 + S^4 + 2*S^6 + S^8))/(9*S*(1 + S^2)^2) + (16*HPL[{1}, -S^2])/(3*S^3)) - (8*HPL[{2}, -S^2])/(3*S^3))*Log[T]^3 + ((-4*(2 + 3*S^2))/(3*S*(1 + S^2)^2) - (8*HPL[{1}, -S^2])/(3*S^3))*Log[T]^4 + ((49 + 102*S^2 + 43*S^4 + 24*S^6 + 4*S^8)*Zeta[3])/(9*S*(1 + S^2)^2) + HPL[{2}, -S^2]*((36 + 7*S^2 + 2*S^4)/(9*S^3) + (Pi^2*(31 + 50*S^2 + 13*S^4))/(54*S^3*(1 + S^2)^2) - (2*HPL[{3}, -S^2])/(3*S^3) + (2*HPL[{2, 1}, -S^2])/S^3 - (2*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(953 + 111*S^2 + 32*S^4))/(216*S^3) + (Pi^2*(-77 - 382*S^2 - 419*S^4 - 14*S^6 - 28*S^8 - 14*S^10))/(108*S^3*(1 + S^2)^2) + (5*(11 + 2*S^6)*HPL[{2}, -S^2])/(18*S^3) + (10*HPL[{3}, -S^2])/(3*S^3) + (10*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((-29*Pi^4)/(135*S^3) - ((1 + S^2)*(3175 + 227*S^2 + 64*S^4))/(648*S^3) + (Pi^2*(-245 - 718*S^2 - 1280*S^4 - 254*S^6 - 151*S^8 - 20*S^10))/(324*S^3*(1 + S^2)^2) + ((-2*Pi^2)/(9*S^3) + (32 + 75*S^2 + 14*S^4 + 15*S^6 + 2*S^8)/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (4*HPL[{2}, -S^2]^2)/(3*S^3) + (5*(11 + 34*S^2 + 29*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{4}, -S^2])/(3*S^3) - (5*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*HPL[{3, 1}, -S^2])/(3*S^3) + (5*(11 + 34*S^2 + 29*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + Log[T]*((123 + 32*S^2)/(108*S) + (Pi^2*(35 + 156*S^2 + 21*S^4 + 14*S^6))/(54*S*(1 + S^2)^2) + ((19*Pi^2)/(9*S^3) + (437 + 1324*S^2 + 1958*S^4 + 428*S^6 + 253*S^8 + 32*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^2 + (4*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) + (8*HPL[{1}, -S^2]^4)/(3*S^3) + HPL[{0}, S^2]^3*((42 + 63*S^2 + 2*S^4 + 4*S^6 + 2*S^8)/(54*S*(1 + S^2)^2) + (7*HPL[{1}, -S^2])/(9*S^3)) + ((-7*Pi^2)/(9*S^3) + (-421 - 571*S^2 - 30*S^4 - 60*S^6)/(54*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (5*HPL[{2}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]^2*((5 + 48*S^2 + 3*S^4 + 2*S^6)/(18*S*(1 + S^2)^2) + ((11 + 106*S^2 + 137*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)^2) + (7*HPL[{1}, -S^2]^2)/(3*S^3) - HPL[{2}, -S^2]/(3*S^3)) + ((7 - 46*S^2 - 83*S^4 - 20*S^6 - 40*S^8 - 20*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*HPL[{4}, -S^2])/(3*S^3) + (2*(-7 + 10*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((862 + 79*S^2 + 32*S^4)/(108*S) + (Pi^2*(114 + 171*S^2 + 14*S^4 + 28*S^6 + 14*S^8))/(54*S*(1 + S^2)^2) + (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + (16*HPL[{1}, -S^2]^3)/(3*S^3) + ((-7 + 46*S^2 + 83*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((19*Pi^2)/(9*S^3) + (437 + 1324*S^2 + 1958*S^4 + 428*S^6 + 253*S^8 + 32*S^10)/(54*S^3*(1 + S^2)^2) + (20*HPL[{2}, -S^2])/(3*S^3)) + (2*HPL[{3}, -S^2])/(3*S^3) - (44*HPL[{2, 1}, -S^2])/(3*S^3)) + (8*HPL[{3, 1}, -S^2])/S^3 - (16*HPL[{2, 1, 1}, -S^2])/S^3 - (10*(6 + 9*S^2 + 2*S^4 + 4*S^6 + 2*S^8)*Zeta[3])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(953 + 111*S^2 + 32*S^4))/(108*S^3) + (Pi^2*(77 + 382*S^2 + 419*S^4 + 14*S^6 + 28*S^8 + 14*S^10))/(54*S^3*(1 + S^2)^2) - (5*(11 + 2*S^6)*HPL[{2}, -S^2])/(9*S^3) - (20*HPL[{3}, -S^2])/(3*S^3) - (20*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]*((-3033 - 195*S^2 - 64*S^4)/(648*S) + (Pi^2*(-213 - 657*S^2 - 191*S^4 - 109*S^6 - 20*S^8))/(324*S*(1 + S^2)^2) - (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) - (4*HPL[{1}, -S^2]^4)/(3*S^3) + (Pi^2/(18*S^3) + (37 - 220*S^2 - 755*S^4 - 258*S^6 - 144*S^8 - 24*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(6*S^3) + HPL[{1}, -S^2]^2*((-19*Pi^2)/(18*S^3) + (-437 - 1324*S^2 - 1958*S^4 - 428*S^6 - 253*S^8 - 32*S^10)/(108*S^3*(1 + S^2)^2) - (10*HPL[{2}, -S^2])/(3*S^3)) + ((7 + 2*S^2 - 11*S^4)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^2) - HPL[{4}, -S^2]/S^3 + (2*(31 + 92*S^2 + 76*S^4)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((2 + 3*S^2)*Zeta[3])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(953 + 111*S^2 + 32*S^4))/(216*S^3) + (Pi^2*(-77 - 382*S^2 - 419*S^4 - 14*S^6 - 28*S^8 - 14*S^10))/(108*S^3*(1 + S^2)^2) - (5*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^2) - (2*HPL[{3}, -S^2])/(3*S^3) + (20*HPL[{2, 1}, -S^2])/(3*S^3) + (2*Zeta[3])/(3*S^3)));
E3wuvT=E3wuvT0F0+T*E3wuvT1F1*(F+1/F)+T^2*(E3wuvT2F0+E3wuvT2F2*(F^2+1/F^2))+T^3*(E3wuvT3F1*(F+1/F)+E3wuvT3F3*(F^3+1/F^3));
Et3uvwT1F1=(14*Pi^2*S)/9 + (53*Pi^4*S)/135 + HPL[{0}, S^2]^4*(S/2 + ((1 + S^2)*HPL[{1}, -S^2])/(4*S)) + (2*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((5*Pi^2*S)/108 + (5*(1 + S^2)*HPL[{1}, -S^2])/(18*S) + (5*(1 + S^2)*HPL[{1}, -S^2]^2)/(18*S) + (5*S*HPL[{2}, -S^2])/18) + HPL[{1}, -S^2]^3*((7*Pi^2*(1 + S^2))/(27*S) + (28*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((14*(1 + S^2))/(3*S) + (Pi^2*(2 + 7*S^2))/(9*S))*HPL[{3}, -S^2] + (2*(17 + 15*S^2)*HPL[{4}, -S^2])/(3*S) + (2*(22 + 17*S^2)*HPL[{5}, -S^2])/(3*S) + ((Pi^2*(-13 - 8*S^2))/(9*S) - (28*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (2*(11 + 9*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(-1 + 4*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2*(3 + 13*S^2)*HPL[{4, 1}, -S^2])/S + (40*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (20*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(-4 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-16*Pi^2*S)/27 - (16*S*HPL[{0}, S^2]^2)/9 - (32*(1 + S^2)*HPL[{2}, -S^2])/(9*S))*Log[T]^3 + ((28*S)/3 + 2*Pi^2*S)*Zeta[3] + HPL[{0}, S^2]^2*((14*S)/3 + (23*Pi^2*S)/18 + (3*(1 + S^2)*HPL[{1}, -S^2]^2)/(2*S) + (7*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + ((3 + 5*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((7*(1 + S^2))/(3*S) + (25*Pi^2*(1 + S^2))/(36*S) + (5*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((1 + S^2)*HPL[{3}, -S^2])/(2*S) + ((-7 - 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) + 4*S*Zeta[3]) + Log[T]^2*((10*Pi^2*S)/9 + (5*S*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]^2*((10*S)/3 + (7*(1 + S^2)*HPL[{1}, -S^2])/(3*S)) + (20*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{0}, S^2]*((5*Pi^2*S)/9 + (2*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{1}, -S^2]*((7*Pi^2*(1 + S^2))/(9*S) + (28*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + (2*(1 + 11*S^2)*HPL[{3}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 8*S*Zeta[3]) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2))/(2*S) + (6*(1 + S^2)*HPL[{2}, -S^2])/S + (14*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (28*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (14*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]*((7*Pi^2*(1 + S^2))/(9*S) + (29*Pi^4*(1 + S^2))/(135*S) + ((28*(1 + S^2))/(3*S) + (4*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (6*(1 + S^2)*HPL[{3}, -S^2])/S + (28*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (12*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (28*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (56*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (6*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((28*(1 + S^2))/(3*S) + (2*Pi^2*(4 + 5*S^2))/(9*S) + (2*(-1 + 4*S^2)*HPL[{3}, -S^2])/(3*S) + (10*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-1 + 4*S^2)*Zeta[3])/(3*S)) + Log[T]*((-14*Pi^2*S)/9 - (121*Pi^4*S)/270 - (S*HPL[{0}, S^2]^4)/2 + HPL[{0}, S^2]^3*((-5*S)/9 - (5*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + ((Pi^2*(-11 - 16*S^2))/(9*S) - (28*(1 + S^2))/(3*S))*HPL[{2}, -S^2] - (5*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^2*((-14*S)/3 - (13*Pi^2*S)/9 - (3*(1 + S^2)*HPL[{1}, -S^2])/S - (7*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + ((-3 - 8*S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{1}, -S^2]^2*((-7*Pi^2*(1 + S^2))/(9*S) - (28*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (2*(3 + 13*S^2)*HPL[{3}, -S^2])/(3*S) - (26*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + HPL[{0}, S^2]*((-5*Pi^2*S)/9 - (5*Pi^2*(1 + S^2)*HPL[{1}, -S^2])/(9*S) - (2*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) + (32*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (64*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (32*S*Zeta[3])/3 + HPL[{1}, -S^2]*((Pi^2*(-1 - S^2))/S - (12*(1 + S^2)*HPL[{2}, -S^2])/S - (28*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (56*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (28*(1 + S^2)*Zeta[3])/(3*S))) + HPL[{0}, S^2]*((5*Pi^4*S)/108 + (5*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^2)/(18*S) + (Pi^2*(1 + 6*S^2)*HPL[{2}, -S^2])/(18*S) + ((1 + S^2)*HPL[{2}, -S^2]^2)/(6*S) + ((-3 - S^2)*HPL[{3}, -S^2])/(3*S) + ((-1 - S^2)*HPL[{4}, -S^2])/S + (2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (2*S*Zeta[3])/3 + HPL[{1}, -S^2]*((5*Pi^2*(1 + S^2))/(18*S) - (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (2*(1 + S^2)*Zeta[3])/(3*S))) + 16*S*Zeta[5];
Et3uvwT2F2=(Pi^4*(-29 - 34*S^2))/270 + (Pi^2*(-19 - 31*S^2))/72 - (4*(-1 + S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + HPL[{0}, S^2]^4*((-1 - S^2)/8 + ((-1 - S^4)*HPL[{1}, -S^2])/(8*S^2)) - (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^3*((-5*Pi^2*S^2)/216 + (7 - 24*S^2)/24 - ((1 + S^2)*(-21 + 41*S^2)*HPL[{1}, -S^2])/(72*S^2) - (5*(1 + S^4)*HPL[{1}, -S^2]^2)/(36*S^2) - (5*S^2*HPL[{2}, -S^2])/36) + HPL[{1}, -S^2]^3*((-4*(-1 + S^4))/(3*S^2) - (7*Pi^2*(1 + S^4))/(54*S^2) - (14*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((41 - 42*S^2 - 55*S^4)/(12*S^2) + (Pi^2*(-2 - 7*S^4))/(18*S^2))*HPL[{3}, -S^2] + ((11 - 28*S^2 - 31*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((-22 - 17*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((7*(1 + 6*S^2 + S^4))/(6*S^2) + (Pi^2*(13 + 8*S^4))/(18*S^2))*HPL[{2, 1}, -S^2] + ((1 + 28*S^2 + 43*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + (2*(-1 + 2*S^2)*(1 + 2*S^2)*HPL[{3, 2}, -S^2])/(3*S^2) + ((3 + 13*S^4)*HPL[{4, 1}, -S^2])/S^2 - (2*(11 + 14*S^2 + 11*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (10*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(-4 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((8*Pi^2*S^2)/27 + (16*S^2*HPL[{0}, S^2])/9 + (8*S^2*HPL[{0}, S^2]^2)/9 + (16*(-1 + S^4)*HPL[{1}, -S^2])/(9*S^2) + (16*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2))*Log[T]^3 + (-(Pi^2*S^2) - (7*(3 + S^2))/6)*Zeta[3] + Log[T]^2*((Pi^2*(-7 - 11*S^2))/18 - (5*S^2*HPL[{0}, S^2]^3)/18 - (8*(-1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^2*((-7 - 11*S^2)/6 - (7*(1 + S^4)*HPL[{1}, -S^2])/(6*S^2)) + ((-11 - 14*S^2 - 11*S^4)*HPL[{2}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((-5*Pi^2*S^2)/18 + (7 - 12*S^2)/3 - (8*(-1 + S^4)*HPL[{1}, -S^2])/(3*S^2) + ((-1 - S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{1}, -S^2]*((-4*(-1 + S^4))/S^2 - (7*Pi^2*(1 + S^4))/(18*S^2) - (14*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-1 - 11*S^4)*HPL[{3}, -S^2])/(3*S^2) + (4*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - 4*S^2*Zeta[3]) + HPL[{0}, S^2]^2*((-19 - 31*S^2)/24 + (Pi^2*(-25 - 29*S^2))/72 - (7*(1 + S^2)*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(24*S^2) - (7*(1 + S^4)*HPL[{1}, -S^2]^3)/(18*S^2) + ((-3 - 10*S^2 - 11*S^4)*HPL[{2}, -S^2])/(12*S^2) + HPL[{1}, -S^2]*((-7 - 34*S^2 - 27*S^4)/(24*S^2) - (25*Pi^2*(1 + S^4))/(72*S^2) - (5*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((-1 - S^4)*HPL[{3}, -S^2])/(4*S^2) + ((7 + 2*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) - 2*S^2*Zeta[3]) + HPL[{1}, -S^2]*((-14*(-1 + S^4))/(3*S^2) - (29*Pi^4*(1 + S^4))/(270*S^2) - (17*Pi^2*(-1 + 2*S^2 + 3*S^4))/(72*S^2) + ((-2*Pi^2*(1 + S^4))/(3*S^2) - (17*(1 + 2*S^2 + S^4))/(6*S^2))*HPL[{2}, -S^2] + ((1 - 28*S^2 - 29*S^4)*HPL[{3}, -S^2])/(6*S^2) - (14*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (14*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (28*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-23 - 28*S^2 - 5*S^4)*Zeta[3])/(6*S^2)) + HPL[{2}, -S^2]*((-31 - 38*S^2 - 31*S^4)/(12*S^2) + (Pi^2*(-7 - 12*S^2 - 11*S^4))/(18*S^2) - ((-1 + 2*S^2)*(1 + 2*S^2)*HPL[{3}, -S^2])/(3*S^2) - (5*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((1 - 4*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(9 - 28*S^2 - 37*S^4))/(72*S^2) - (17*(-1 + S^4))/(6*S^2) - (7*(1 + S^2)^2*HPL[{2}, -S^2])/(3*S^2) - (7*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (7*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]*((-5*Pi^4*S^2)/216 + (Pi^2*(35 - 96*S^2))/72 - (7*(-7 + 8*S^2))/12 + ((-2*(-1 + S^4))/S^2 - (5*Pi^2*(1 + S^4))/(36*S^2))*HPL[{1}, -S^2]^2 - (8*(-1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + ((Pi^2*(-1 - 6*S^4))/(36*S^2) + (1 + 2*S^2 - 6*S^4)/(3*S^2))*HPL[{2}, -S^2] + ((-1 - S^4)*HPL[{2}, -S^2]^2)/(12*S^2) - ((-5 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(12*S^2) + ((1 + S^4)*HPL[{4}, -S^2])/(2*S^2) + ((-17 + S^4)*HPL[{2, 1}, -S^2])/(6*S^2) - (2*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-2 - 21*S^2)*Zeta[3])/6 + HPL[{1}, -S^2]*((Pi^2*(37 - 20*S^2 - 57*S^4))/(72*S^2) - (17*(-1 + S^4))/(6*S^2) - (3*(-1 + S^4)*HPL[{2}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + ((-1 - S^4)*Zeta[3])/(3*S^2))) + Log[T]*((121*Pi^4*S^2)/540 + (Pi^2*(13 + 27*S^2))/36 + (S^2*HPL[{0}, S^2]^4)/4 + (16*(-1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + HPL[{0}, S^2]^3*((10 + 41*S^2)/36 + (5*(1 + S^4)*HPL[{1}, -S^2])/(18*S^2)) + ((Pi^2*(11 + 16*S^4))/(18*S^2) + (27 + 26*S^2 + 27*S^4)/(6*S^2))*HPL[{2}, -S^2] + (5*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^2*((4*(-1 + S^4))/S^2 + (7*Pi^2*(1 + S^4))/(18*S^2) + (14*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]^2*((13*Pi^2*S^2)/18 + (13 + 27*S^2)/12 + (7*(1 + 4*S^2 + 3*S^4)*HPL[{1}, -S^2])/(12*S^2) + (7*(1 + S^4)*HPL[{1}, -S^2]^2)/(6*S^2) + ((3 + 8*S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((-19 + 28*S^2 + 31*S^4)*HPL[{3}, -S^2])/(6*S^2) + (13*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (2*(3 + 14*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((-27 + 34*S^2)/6 + (Pi^2*(10 + 57*S^2))/36 + ((4*(-1 + S^4))/S^2 + (5*Pi^2*(1 + S^4))/(18*S^2))*HPL[{1}, -S^2] + (8*(-1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + ((-1 + 17*S^4)*HPL[{2}, -S^2])/(6*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/(3*S^2) + (2*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) - (16*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (32*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(7 + 3*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((17*(-1 + S^4))/(3*S^2) + (Pi^2*(-9 + 28*S^2 + 37*S^4))/(36*S^2) + (14*(1 + S^2)^2*HPL[{2}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (28*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (14*(1 + S^4)*Zeta[3])/(3*S^2))) - 8*S^2*Zeta[5];
Et3uvwT3F1=(-49*(-1 + S^2))/(24*S) - (Pi^4*S*(44 + 15*S^2))/(270*(1 + S^2)) + (Pi^2*(3 - 44*S^2 - 3*S^4))/(36*S) - (4*(1 + 3*S^2)*HPL[{1}, -S^2]^4)/(9*S) + HPL[{0}, S^2]^4*(-S/(8*(1 + S^2)) - (S*HPL[{1}, -S^2])/4) - S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^3*((-7*Pi^2*S)/27 + (3 - 37*S^2 - 43*S^4 - 3*S^6)/(18*S^3) - (28*S*HPL[{2}, -S^2])/9) + HPL[{0}, S^2]^3*((-5*Pi^2*S)/108 - (S*(157 + 18*S^2))/72 + ((-18 - 77*S^2 - 49*S^4)*HPL[{1}, -S^2])/(36*S*(1 + S^2)) - (5*S*HPL[{1}, -S^2]^2)/18 - (5*S*HPL[{2}, -S^2])/18) + ((-7*Pi^2*S)/9 + (3 - 16*S^2 - 22*S^4 - 2*S^6)/(2*S^3))*HPL[{3}, -S^2] - (2*(5 + 25*S^2 + 13*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (34*S*HPL[{5}, -S^2])/3 + ((8*Pi^2*S)/9 + (-1 + 14*S^2 + 6*S^4 - S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + (2*(5 + 34*S^2 + 22*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3, 2}, -S^2])/3 + 26*S*HPL[{4, 1}, -S^2] - (4*S*(13 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)) + (20*S*HPL[{2, 2, 1}, -S^2])/3 + (16*S*HPL[{3, 1, 1}, -S^2])/3 + 16*S*HPL[{2, 1, 1, 1}, -S^2] + ((16*Pi^2*S)/27 + (16*S*HPL[{0}, S^2])/3 + (16*S*HPL[{0}, S^2]^2)/9 + (16*(1 + 3*S^2)*HPL[{1}, -S^2])/(9*S) + (32*S*HPL[{2}, -S^2])/9)*Log[T]^3 + (-2*Pi^2*S + (S*(-6 + S^2))/2)*Zeta[3] + Log[T]^2*((1 - S^2)/(2*S) - (Pi^2*S*(19 + 12*S^2))/(18*(1 + S^2)) - (5*S*HPL[{0}, S^2]^3)/9 - (8*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^2*(-(S*(19 + 12*S^2))/(6*(1 + S^2)) - (7*S*HPL[{1}, -S^2])/3) - (2*S*(13 + 6*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((-7*Pi^2*S)/9 + (3 - 37*S^2 - 43*S^4 - 3*S^6)/(6*S^3) - (28*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]*((-5*Pi^2*S)/9 - (S*(43 + 3*S^2))/6 - (8*(1 + 3*S^2)*HPL[{1}, -S^2])/(3*S) - (2*S*HPL[{2}, -S^2])/3) - (22*S*HPL[{3}, -S^2])/3 + 8*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{1}, -S^2]^2*((Pi^2*(-14 - 65*S^2 - 37*S^4))/(36*S*(1 + S^2)) - ((1 + S^2)*(-13 + 112*S^2 + 13*S^4))/(24*S^3) + ((-5 - 38*S^2 - 5*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) - (14*S*HPL[{3}, -S^2])/3 + (28*S*HPL[{2, 1}, -S^2])/3 - (14*S*Zeta[3])/3) + HPL[{0}, S^2]^2*(-(Pi^2*S*(37 + 12*S^2))/(72*(1 + S^2)) + (3 - 85*S^2 - 6*S^4)/(24*S) + ((-6 - 33*S^2 - 13*S^4)*HPL[{1}, -S^2]^2)/(12*S*(1 + S^2)) - (7*S*HPL[{1}, -S^2]^3)/9 - (S*(11 + 6*S^2)*HPL[{2}, -S^2])/(6*(1 + S^2)) + HPL[{1}, -S^2]*((-25*Pi^2*S)/36 + (3 - 49*S^2 - 51*S^4 + S^6)/(24*S^3) - (5*S*HPL[{2}, -S^2])/3) - (S*HPL[{3}, -S^2])/2 + (2*S*HPL[{2, 1}, -S^2])/3 - 4*S*Zeta[3]) + HPL[{2}, -S^2]*((-2*Pi^2*S*(2 + S^2))/(3*(1 + S^2)) - ((1 + S^2)*(3 + 38*S^2 + 3*S^4))/(6*S^3) - (8*S*HPL[{3}, -S^2])/3 - (10*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-29*Pi^4*S)/135 - (Pi^2*(1 + S^2)*(-3 + 46*S^2 + S^4))/(36*S^3) - ((1 + S^2)*(-25 + 224*S^2 + 25*S^4))/(24*S^3) + ((-4*Pi^2*S)/3 + (1 - 17*S^2 - 17*S^4 + S^6)/(3*S^3))*HPL[{2}, -S^2] + ((-10 - 49*S^2 - 25*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (28*S*HPL[{4}, -S^2])/3 + ((5 + 38*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (28*S*HPL[{3, 1}, -S^2])/3 - (56*S*HPL[{2, 1, 1}, -S^2])/3 + ((2 - S^2 + 11*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{0}, S^2]*((-5*Pi^4*S)/108 - (Pi^2*S*(200 + 21*S^2))/72 + (15 - 234*S^2 - 25*S^4)/(24*S) + ((-5*Pi^2*S)/18 + (3 - 37*S^2 - 43*S^4 - 3*S^6)/(12*S^3))*HPL[{1}, -S^2]^2 - (8*(1 + 3*S^2)*HPL[{1}, -S^2]^3)/(9*S) + (-(Pi^2*S)/3 + (1 - 14*S^2 - 42*S^4 - 3*S^6)/(12*S^3))*HPL[{2}, -S^2] - (S*HPL[{2}, -S^2]^2)/6 + ((-1 - 2*S^2 - 2*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + S*HPL[{4}, -S^2] + ((7 + 4*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*S*HPL[{2, 1, 1}, -S^2])/3 - (S*(33 + 32*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-26 - 109*S^2 - 73*S^4))/(36*S*(1 + S^2)) - ((1 + S^2)*(-13 + 112*S^2 + 13*S^4))/(24*S^3) - (3*(1 + 3*S^2)*HPL[{2}, -S^2])/(2*S) + (2*S*HPL[{3}, -S^2])/3 - (2*S*Zeta[3])/3)) + Log[T]*((121*Pi^4*S)/270 - (Pi^2*S*(-50 + S^2))/36 + (5*(-1 + S^2))/(4*S) + (S*HPL[{0}, S^2]^4)/2 + (16*(1 + 3*S^2)*HPL[{1}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^3*((S*(54 + 49*S^2))/(18*(1 + S^2)) + (5*S*HPL[{1}, -S^2])/9) + ((16*Pi^2*S)/9 + (-1 + 26*S^2 + 50*S^4 - S^6)/(6*S^3))*HPL[{2}, -S^2] + (5*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((13*Pi^2*S)/9 - (S*(-50 + S^2))/12 + ((6 + 33*S^2 + 13*S^4)*HPL[{1}, -S^2])/(6*S*(1 + S^2)) + (7*S*HPL[{1}, -S^2]^2)/3 + (8*S*HPL[{2}, -S^2])/3) + HPL[{1}, -S^2]^2*((7*Pi^2*S)/9 + (-3 + 37*S^2 + 43*S^4 + 3*S^6)/(6*S^3) + (28*S*HPL[{2}, -S^2])/3) + (2*(5 + 21*S^2 + 9*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (26*S*HPL[{4}, -S^2])/3 + (2*(-5 - 12*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{0}, S^2]*((Pi^2*S*(78 + 73*S^2))/(18*(1 + S^2)) + (-6 + 119*S^2 + 13*S^4)/(12*S) + ((5*Pi^2*S)/9 + (-3 + 37*S^2 + 43*S^4 + 3*S^6)/(6*S^3))*HPL[{1}, -S^2] + (8*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(3*S) + ((2 + 23*S^2)*HPL[{2}, -S^2])/(3*S) - (2*S*HPL[{3}, -S^2])/3 + (4*S*HPL[{2, 1}, -S^2])/3) - (32*S*HPL[{3, 1}, -S^2])/3 + (64*S*HPL[{2, 1, 1}, -S^2])/3 - (14*S^3*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(-13 + 112*S^2 + 13*S^4))/(12*S^3) + (Pi^2*(14 + 65*S^2 + 37*S^4))/(18*S*(1 + S^2)) + ((5 + 38*S^2 + 5*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + (28*S*HPL[{3}, -S^2])/3 - (56*S*HPL[{2, 1}, -S^2])/3 + (28*S*Zeta[3])/3)) - 16*S*Zeta[5];
Et3uvwT3F3=(511*(-1 + S^2))/(1944*S) + (Pi^2*(507 + 264*S^2 + 1775*S^4))/(2916*S) + (Pi^4*(348 + 174*S^2 + 695*S^4 + 347*S^6))/(4860*S*(1 + S^2)) + (4*(-1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + HPL[{0}, S^2]^4*((6 + 3*S^2 + 10*S^4 + 4*S^6)/(72*S*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(12*S^3)) + (31*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^2)/(54*S^3) + HPL[{0}, S^2]^3*((5*Pi^2*S^3)/324 + (-214 + 167*S^2 + 486*S^4)/(648*S) + ((-107 - 47*S^2 + 30*S^4 + 232*S^6 + 172*S^8)*HPL[{1}, -S^2])/(324*S^3*(1 + S^2)) + (5*(1 + S^6)*HPL[{1}, -S^2]^2)/(54*S^3) + (5*S^3*HPL[{2}, -S^2])/54) + HPL[{1}, -S^2]^3*((7*Pi^2*(1 + S^6))/(81*S^3) + (67*(-1 - S^2 + S^4 + S^6))/(54*S^3) + (28*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((Pi^2*(2 + 7*S^6))/(27*S^3) + (-287 - 36*S^2 + 504*S^4 + 568*S^6)/(162*S^3))*HPL[{3}, -S^2] + (2*(-46 - 4*S^2 + 21*S^4 + 93*S^6 + 51*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (2*(22 + 17*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-281 - 468*S^2 - 468*S^4 - 281*S^6)/(162*S^3) + (Pi^2*(-13 - 8*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((23 - 61*S^2 - 42*S^4 - 255*S^6 - 171*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-1 + 4*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (2*(3 + 13*S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (4*(37 + 79*S^2 + 21*S^4 + 79*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (20*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(-4 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-16*Pi^2*S^3)/81 - (16*(-1 + S^2))/(27*S) - (16*S^3*HPL[{0}, S^2])/9 - (16*S^3*HPL[{0}, S^2]^2)/27 - (16*(-1 + S^6)*HPL[{1}, -S^2])/(9*S^3) - (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(27*S^3))*Log[T]^3 + ((2*Pi^2*S^3)/3 + (450 + 18*S^2 + 281*S^4)/(162*S))*Zeta[3] + HPL[{0}, S^2]^2*((1383 + 159*S^2 + 3550*S^4)/(1944*S) + (Pi^2*(150 + 75*S^2 + 296*S^4 + 146*S^6))/(648*S*(1 + S^2)) + ((3 + 31*S^2 + 14*S^4 + 52*S^6 + 24*S^8)*HPL[{1}, -S^2]^2)/(36*S^3*(1 + S^2)) + (7*(1 + S^6)*HPL[{1}, -S^2]^3)/(27*S^3) + ((6 + 36*S^2 + 15*S^4 + 67*S^6 + 37*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((25*Pi^2*(1 + S^6))/(108*S^3) + (281 + 153*S^2 + 675*S^4 + 803*S^6)/(648*S^3) + (5*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(6*S^3) + ((-7 - 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*S^3*Zeta[3])/3) + Log[T]^2*((41*(-1 + S^2))/(54*S) + (Pi^2*(42 + 21*S^2 + 116*S^4 + 74*S^6))/(162*S*(1 + S^2)) + (5*S^3*HPL[{0}, S^2]^3)/27 + (8*(-1 + S^6)*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]^2*((42 + 21*S^2 + 116*S^4 + 74*S^6)/(54*S*(1 + S^2)) + (7*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3)) + (2*(37 + 79*S^2 + 21*S^4 + 79*S^6 + 37*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{0}, S^2]*((5*Pi^2*S^3)/27 + (-44 + 23*S^2 + 67*S^4)/(18*S) + (8*(-1 + S^6)*HPL[{1}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{1}, -S^2]*((7*Pi^2*(1 + S^6))/(27*S^3) + (67*(-1 - S^2 + S^4 + S^6))/(18*S^3) + (28*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + (2*(1 + 11*S^6)*HPL[{3}, -S^2])/(9*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^2*((539*(-1 + S^2)*(1 + S^2)^2)/(216*S^3) + (Pi^2*(-21 + 7*S^2 + 14*S^4 + 76*S^6 + 48*S^8))/(108*S^3*(1 + S^2)) + ((27 + 83*S^2 + 28*S^4 + 83*S^6 + 27*S^8)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)) + (14*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (28*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (14*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*(((1 + S^2)*(1775 - 1004*S^2 + 1775*S^4))/(486*S^3) + (Pi^2*(43 + 115*S^2 + 36*S^4 + 146*S^6 + 74*S^8))/(162*S^3*(1 + S^2)) + (2*(-1 + 4*S^6)*HPL[{3}, -S^2])/(9*S^3) + (10*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(-1 + 4*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((29*(-1 + S^2)*(1 + S^2)^2)/(8*S^3) + (29*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (Pi^2*(1 + S^2)*(-161 - 64*S^2 + 703*S^4))/(972*S^3) + ((4*Pi^2*(1 + S^6))/(9*S^3) + (271 + 207*S^2 + 207*S^4 + 271*S^6)/(81*S^3))*HPL[{2}, -S^2] + ((-9 + 19*S^2 + 14*S^4 + 64*S^6 + 36*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (28*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-27 - 83*S^2 - 28*S^4 - 83*S^6 - 27*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (28*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (56*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((27 + 55*S^2 + 14*S^4 + 28*S^6)*Zeta[3])/(9*S^3*(1 + S^2))) + Log[T]*((-121*Pi^4*S^3)/810 - (191*(-1 + S^2))/(324*S) + (Pi^2*(-18 - 342*S^2 - 803*S^4))/(972*S) - (S^3*HPL[{0}, S^2]^4)/6 - (16*(-1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^3*((-30 - 15*S^2 - 202*S^4 - 172*S^6)/(162*S*(1 + S^2)) - (5*(1 + S^6)*HPL[{1}, -S^2])/(27*S^3)) + ((-803 - 360*S^2 - 360*S^4 - 803*S^6)/(162*S^3) + (Pi^2*(-11 - 16*S^6))/(27*S^3))*HPL[{2}, -S^2] - (5*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^2*((-13*Pi^2*S^3)/27 + (-162 - 198*S^2 - 803*S^4)/(324*S) + ((-3 - 31*S^2 - 14*S^4 - 52*S^6 - 24*S^8)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)) - (7*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + ((-3 - 8*S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{1}, -S^2]^2*((-7*Pi^2*(1 + S^6))/(27*S^3) - (67*(-1 - S^2 + S^4 + S^6))/(18*S^3) - (28*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((93 + 9*S^2 - 42*S^4 - 191*S^6 - 107*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (26*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + (14*(1 + 13*S^2 + 6*S^4 + 13*S^6 + S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{0}, S^2]*(-((1 + S^2)*(-454 + 539*S^2))/(108*S) + (Pi^2*(-30 - 15*S^2 - 274*S^4 - 244*S^6))/(162*S*(1 + S^2)) + ((-5*Pi^2*(1 + S^6))/(27*S^3) - (67*(-1 - S^2 + S^4 + S^6))/(18*S^3))*HPL[{1}, -S^2] - (8*(-1 + S^6)*HPL[{1}, -S^2]^2)/(3*S^3) + ((7 - 74*S^6)*HPL[{2}, -S^2])/(27*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (14*(6 + 3*S^2 + 7*S^4 + S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((-539*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(21 - 7*S^2 - 14*S^4 - 76*S^6 - 48*S^8))/(54*S^3*(1 + S^2)) + ((-27 - 83*S^2 - 28*S^4 - 83*S^6 - 27*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + HPL[{0}, S^2]*((5*Pi^4*S^3)/324 + (29*(1 + S^2)*(-25 + 27*S^2))/(216*S) + (Pi^2*(-346 + 236*S^2 + 687*S^4))/(648*S) + ((5*Pi^2*(1 + S^6))/(54*S^3) + (67*(-1 - S^2 + S^4 + S^6))/(36*S^3))*HPL[{1}, -S^2]^2 + (8*(-1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((Pi^2*(1 + 6*S^6))/(54*S^3) + (-9 - 44*S^2 + 32*S^4 + 67*S^6)/(36*S^3))*HPL[{2}, -S^2] + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(18*S^3) + ((-15 - 27*S^2 - 6*S^4 - 5*S^6 + 7*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((74 - 7*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((6 + 3*S^2 + 103*S^4 + 97*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((539*(-1 + S^2)*(1 + S^2)^2)/(216*S^3) + (Pi^2*(-179 - 119*S^2 + 30*S^4 + 304*S^6 + 244*S^8))/(324*S^3*(1 + S^2)) + (3*(-1 + S^6)*HPL[{2}, -S^2])/(2*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + (16*S^3*Zeta[5])/3;
Et3uvwT=T*Et3uvwT1F1*(F-1/F)+T^2*(Et3uvwT2F2*(F^2-1/F^2))+T^3*(Et3uvwT3F1*(F-1/F)+Et3uvwT3F3*(F^3-1/F^3));
Et3vwuT1F1=(-16*Pi^2*S)/9 - (58*Pi^4*S)/135 - (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (4*(1 + S^2)*HPL[{1}, -S^2]^5)/(5*S) + HPL[{0}, S^2]^4*(-S/2 + ((-1 - S^2)*HPL[{1}, -S^2])/(4*S)) - (2*(1 + 2*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((-13*Pi^2*S)/108 - (13*(1 + S^2)*HPL[{1}, -S^2])/(18*S) - (13*(1 + S^2)*HPL[{1}, -S^2]^2)/(18*S) - (13*S*HPL[{2}, -S^2])/18) + HPL[{1}, -S^2]^3*((-4*(1 + S^2))/S - (32*Pi^2*(1 + S^2))/(27*S) - (14*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((Pi^2*(-1 + 7*S^2))/(9*S) + (2*(1 + 10*S^2))/(3*S))*HPL[{3}, -S^2] - (2*(1 + 12*S^2)*HPL[{4}, -S^2])/(3*S) + (4*(-1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((Pi^2*(23 - 8*S^2))/(9*S) - (4*(-8 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (2*(-5 + 12*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(-1 + 4*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2*(-3 + 8*S^2)*HPL[{4, 1}, -S^2])/S - (8*(-2 + 7*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(7 + 2*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(-23 + 5*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (16*(-2 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((26*Pi^2*S)/27 + (26*S*HPL[{0}, S^2]^2)/9 + (8*(1 + S^2)*HPL[{1}, -S^2])/S + (8*(1 + S^2)*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(8*S + (8*(1 + S^2)*HPL[{1}, -S^2])/S) + (4*(-5 + 13*S^2)*HPL[{2}, -S^2])/(9*S))*Log[T]^3 + (-4*S*HPL[{0}, S^2] - (4*(1 + S^2)*HPL[{1}, -S^2])/S)*Log[T]^4 + (4*S*Zeta[3])/3 + HPL[{0}, S^2]^2*((-16*S)/3 - (25*Pi^2*S)/18 - (5*(1 + S^2)*HPL[{1}, -S^2]^2)/(2*S) - (14*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (7*S*HPL[{2}, -S^2])/3 + HPL[{1}, -S^2]*((-8*(1 + S^2))/(3*S) - (8*Pi^2*(1 + S^2))/(9*S) - (11*(1 + S^2)*HPL[{2}, -S^2])/(6*S)) + (S*HPL[{3}, -S^2])/2 + ((11 - 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) - 2*S*Zeta[3]) + Log[T]^2*((-14*Pi^2*S)/9 - (13*S*HPL[{0}, S^2]^3)/9 - (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S + HPL[{0}, S^2]^2*((-14*S)/3 - (14*(1 + S^2)*HPL[{1}, -S^2])/(3*S)) - (4*(-2 + 7*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-12*(1 + S^2))/S - (32*Pi^2*(1 + S^2))/(9*S) - (14*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]*(-12*S - (31*Pi^2*S)/9 - (12*(1 + S^2)*HPL[{1}, -S^2])/S - (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (2*(-1 + 17*S^2)*HPL[{2}, -S^2])/(3*S)) + (2*(-2 + 11*S^2)*HPL[{3}, -S^2])/(3*S) - (8*(-2 + S^2)*HPL[{2, 1}, -S^2])/S + 8*S*Zeta[3]) + HPL[{1}, -S^2]*((-17*Pi^2*(1 + S^2))/(9*S) - (58*Pi^4*(1 + S^2))/(135*S) + ((Pi^2*(-1 - S^2))/S - (14*(1 + S^2))/(3*S))*HPL[{2}, -S^2] - (2*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (2*(1 + S^2)*HPL[{3}, -S^2])/S - (8*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (6*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (28*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-6*(1 + S^2))/S - (11*Pi^2*(1 + S^2))/(6*S) - (3*(1 + S^2)*HPL[{2}, -S^2])/S + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (14*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((-2*Pi^2*(-1 + 7*S^2))/(9*S) - (4*(-1 + 8*S^2))/(3*S) + (2*(-1 + 4*S^2)*HPL[{3}, -S^2])/(3*S) + (2*(7 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-1 + 4*S^2)*Zeta[3])/(3*S)) + Log[T]*((16*Pi^2*S)/9 + (73*Pi^4*S)/135 + (S*HPL[{0}, S^2]^4)/2 + (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (4*(1 + S^2)*HPL[{1}, -S^2]^4)/S + HPL[{0}, S^2]^3*((13*S)/9 + (13*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + ((4*(-1 + 8*S^2))/(3*S) + (Pi^2*(-5 + 26*S^2))/(9*S))*HPL[{2}, -S^2] + (5*(1 + 2*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^2*((16*S)/3 + (31*Pi^2*S)/18 + (5*(1 + S^2)*HPL[{1}, -S^2])/S + (14*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (13*S*HPL[{2}, -S^2])/3) + HPL[{1}, -S^2]^2*((12*(1 + S^2))/S + (32*Pi^2*(1 + S^2))/(9*S) + (14*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (2*(-3 + 10*S^2)*HPL[{3}, -S^2])/(3*S) + (2*(5 + 8*S^2)*HPL[{4}, -S^2])/(3*S) + (4*(-13 + 5*S^2)*HPL[{2, 1}, -S^2])/(3*S) + HPL[{0}, S^2]*(12*S + (31*Pi^2*S)/9 + (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (2*(-1 + 17*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((12*(1 + S^2))/S + (31*Pi^2*(1 + S^2))/(9*S) + (10*(1 + S^2)*HPL[{2}, -S^2])/S) - (2*(-1 + 2*S^2)*HPL[{3}, -S^2])/(3*S) + (8*(-8 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) - (4*(-5 + 13*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (8*(-5 + 13*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (20*S*Zeta[3])/3 + HPL[{1}, -S^2]*((12*(1 + S^2))/S + (11*Pi^2*(1 + S^2))/(3*S) + (6*(1 + S^2)*HPL[{2}, -S^2])/S - (16*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (28*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (16*(1 + S^2)*Zeta[3])/(3*S))) + HPL[{0}, S^2]*(-(Pi^2*S) - (73*Pi^4*S)/270 - (4*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S + (-6*S + (Pi^2*(1 - 30*S^2))/(18*S))*HPL[{2}, -S^2] + ((1 - 14*S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^2*((-6*(1 + S^2))/S - (31*Pi^2*(1 + S^2))/(18*S) - (5*(1 + S^2)*HPL[{2}, -S^2])/S) + ((-3 + 2*S^2)*HPL[{3}, -S^2])/(3*S) + ((-1 - 2*S^2)*HPL[{4}, -S^2])/S - (4*(-8 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + 12*S*HPL[{3, 1}, -S^2] - (4*(-1 + 17*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*S*Zeta[3])/3 + HPL[{1}, -S^2]*((-6*(1 + S^2))/S - (31*Pi^2*(1 + S^2))/(18*S) - (5*(1 + S^2)*HPL[{2}, -S^2])/S - (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (10*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (2*(1 + S^2)*Zeta[3])/(3*S)));
Et3vwuT2F2=(Pi^4*(29 + 22*S^2))/135 + (Pi^2*(23 + 38*S^2))/72 + ((7 + 18*S^2 + 11*S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + (2*(1 + S^4)*HPL[{1}, -S^2]^5)/(5*S^2) + HPL[{0}, S^2]^4*((1 + S^2)/8 + ((1 + S^4)*HPL[{1}, -S^2])/(8*S^2)) + ((2 + 3*S^2 + 4*S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^3*((13*Pi^2*S^2)/216 + (1 + 24*S^2)/24 + ((1 + S^2)*(3 + 49*S^2)*HPL[{1}, -S^2])/(72*S^2) + (13*(1 + S^4)*HPL[{1}, -S^2]^2)/(36*S^2) + (13*S^2*HPL[{2}, -S^2])/36) + HPL[{1}, -S^2]^3*((16*Pi^2*(1 + S^4))/(27*S^2) + (7 + 22*S^2 + 15*S^4)/(6*S^2) + (7*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((Pi^2*(1 - 7*S^4))/(18*S^2) + (-7 - 18*S^2 + 20*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((-1 + 8*S^2 + 14*S^4)*HPL[{4}, -S^2])/(6*S^2) - (2*(-1 + S^2)*(1 + S^2)*HPL[{5}, -S^2])/(3*S^2) + ((7*(-2 - 3*S^2 + S^4))/(6*S^2) + (Pi^2*(-23 + 8*S^4))/(18*S^2))*HPL[{2, 1}, -S^2] + ((25 - 8*S^2 - 50*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + (2*(-1 + 2*S^2)*(1 + 2*S^2)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-3 + 8*S^4)*HPL[{4, 1}, -S^2])/S^2 + (2*(-8 + 7*S^2 + 19*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(7 + 2*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(-23 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (8*(-2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (-2 - (13*Pi^2*S^2)/27 - (13*S^2*HPL[{0}, S^2]^2)/9 - (4*(7 + 18*S^2 + 11*S^4)*HPL[{1}, -S^2])/(9*S^2) - (4*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*((-4*(9 + 11*S^2))/9 - (4*(1 + S^4)*HPL[{1}, -S^2])/S^2) - (2*(-5 + 13*S^4)*HPL[{2}, -S^2])/(9*S^2))*Log[T]^3 + (2 + 2*S^2*HPL[{0}, S^2] + (2*(1 + S^4)*HPL[{1}, -S^2])/S^2)*Log[T]^4 + ((-9 - 7*S^2)*Zeta[3])/6 + Log[T]^2*(3/2 + (Pi^2*(32 + 19*S^2))/18 + (13*S^2*HPL[{0}, S^2]^3)/18 + (2*(7 + 18*S^2 + 11*S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + (4*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + HPL[{0}, S^2]^2*((14 + 19*S^2)/6 + (7*(1 + S^4)*HPL[{1}, -S^2])/(3*S^2)) + ((-8 + 7*S^2 + 19*S^4)*HPL[{2}, -S^2])/(3*S^2) + HPL[{1}, -S^2]*((16*Pi^2*(1 + S^4))/(9*S^2) + (7 + 22*S^2 + 15*S^4)/(2*S^2) + (7*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]*((31*Pi^2*S^2)/18 + (26 + 45*S^2)/6 + (2*(7 + 18*S^2 + 11*S^4)*HPL[{1}, -S^2])/(3*S^2) + (6*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + ((-1 + 17*S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((2 - 11*S^4)*HPL[{3}, -S^2])/(3*S^2) + (4*(-2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - 4*S^2*Zeta[3]) + HPL[{0}, S^2]^2*((7 + 19*S^2)/12 + (Pi^2*(32 + 37*S^2))/72 + ((17 + 56*S^2 + 39*S^4)*HPL[{1}, -S^2]^2)/(24*S^2) + (7*(1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + ((11 + 19*S^2)*HPL[{2}, -S^2])/12 + HPL[{1}, -S^2]*((4*Pi^2*(1 + S^4))/(9*S^2) + (7*(1 + 4*S^2 + 3*S^4))/(12*S^2) + (11*(1 + S^4)*HPL[{2}, -S^2])/(12*S^2)) - (S^2*HPL[{3}, -S^2])/4 + ((-11 + 2*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + S^2*Zeta[3]) + HPL[{1}, -S^2]*((29*Pi^4*(1 + S^4))/(135*S^2) + (2*(1 + 9*S^2 + 8*S^4))/(3*S^2) + (Pi^2*(35 + 122*S^2 + 87*S^4))/(72*S^2) + ((Pi^2*(1 + S^4))/(2*S^2) + (-1 + 34*S^2 + 35*S^4)/(12*S^2))*HPL[{2}, -S^2] + ((1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((-23 - 16*S^2 + 7*S^4)*HPL[{3}, -S^2])/(6*S^2) + (4*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + ((1 - 28*S^2 - 29*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) - (4*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-11 - 16*S^2 - 5*S^4)*Zeta[3])/(6*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-4 + 9*S^2 + 19*S^4))/(18*S^2) + (-7 + 19*S^2 + 38*S^4)/(12*S^2) - ((-1 + 2*S^2)*(1 + 2*S^2)*HPL[{3}, -S^2])/(3*S^2) + ((-7 - 2*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((1 - 4*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(45 + 128*S^2 + 83*S^4))/(72*S^2) + (29 + 126*S^2 + 97*S^4)/(24*S^2) + ((-1 + 28*S^2 + 29*S^4)*HPL[{2}, -S^2])/(12*S^2) - (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (7*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]*((73*Pi^4*S^2)/540 + (Pi^2*(29 + 117*S^2))/72 + (23 + 128*S^2)/24 + (2*(7 + 18*S^2 + 11*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^4)/S^2 + ((Pi^2*(-1 + 30*S^4))/(36*S^2) + (-8 + 23*S^2 + 45*S^4)/(12*S^2))*HPL[{2}, -S^2] + ((-1 + 14*S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + HPL[{1}, -S^2]^2*((31*Pi^2*(1 + S^4))/(36*S^2) + (7 + 22*S^2 + 15*S^4)/(4*S^2) + (5*(1 + S^4)*HPL[{2}, -S^2])/(2*S^2)) - ((-1 + 2*S^2)^2*HPL[{3}, -S^2])/(12*S^2) + ((1 + 2*S^4)*HPL[{4}, -S^2])/(2*S^2) + ((-13 - 15*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - 6*S^2*HPL[{3, 1}, -S^2] + (2*(-1 + 17*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-1 + 6*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((31*Pi^2*(1 + 4*S^2 + 3*S^4))/(72*S^2) + (29 + 126*S^2 + 97*S^4)/(24*S^2) + ((7 + 20*S^2 + 13*S^4)*HPL[{2}, -S^2])/(4*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (5*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + ((-1 - S^4)*Zeta[3])/(3*S^2))) + Log[T]*(-3/4 - (73*Pi^4*S^2)/270 - (7*Pi^2*(5 + 6*S^2))/36 - (S^2*HPL[{0}, S^2]^4)/4 - (4*(7 + 18*S^2 + 11*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) - (2*(1 + S^4)*HPL[{1}, -S^2]^4)/S^2 + HPL[{0}, S^2]^3*((-26 - 49*S^2)/36 - (13*(1 + S^4)*HPL[{1}, -S^2])/(18*S^2)) + ((15 - 13*S^2 - 42*S^4)/(6*S^2) + (Pi^2*(5 - 26*S^4))/(18*S^2))*HPL[{2}, -S^2] - (5*(1 + 2*S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{0}, S^2]^2*((-31*Pi^2*S^2)/36 + (-17 - 42*S^2)/12 + ((-17 - 56*S^2 - 39*S^4)*HPL[{1}, -S^2])/(12*S^2) - (7*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) - (13*S^2*HPL[{2}, -S^2])/6) + HPL[{1}, -S^2]^2*((-7 - 22*S^2 - 15*S^4)/(2*S^2) - (16*Pi^2*(1 + S^4))/(9*S^2) - (7*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((5 + 16*S^2 + 4*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-5 - 8*S^4)*HPL[{4}, -S^2])/(3*S^2) + ((15 + 14*S^2 - 9*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((-36 - 97*S^2)/12 - (31*Pi^2*(2 + 3*S^2))/36 - (2*(7 + 18*S^2 + 11*S^4)*HPL[{1}, -S^2]^2)/(3*S^2) - (4*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + ((5 - 30*S^2 - 43*S^4)*HPL[{2}, -S^2])/(6*S^2) + HPL[{1}, -S^2]*((-7 - 22*S^2 - 15*S^4)/(2*S^2) - (31*Pi^2*(1 + S^4))/(18*S^2) - (5*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((-1 + 2*S^4)*HPL[{3}, -S^2])/(3*S^2) - (4*(-8 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) + (2*(-5 + 13*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (4*(-5 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((8 + 9*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((-29 - 126*S^2 - 97*S^4)/(12*S^2) + (Pi^2*(-45 - 128*S^2 - 83*S^4))/(36*S^2) - ((1 + S^2)*(-1 + 29*S^2)*HPL[{2}, -S^2])/(6*S^2) + (8*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*Zeta[3])/(3*S^2)));
Et3vwuT3F1=(Pi^2*S*(47 + 3*S^2))/72 + (7*(1 + 8*S^2))/(24*S) + (Pi^4*S*(44 + 15*S^2))/(135*(1 + S^2)) + ((13 + 70*S^2 + 21*S^4)*HPL[{1}, -S^2]^4)/(18*S*(1 + S^2)) + (4*S*HPL[{1}, -S^2]^5)/5 + HPL[{0}, S^2]^4*(S/(8*(1 + S^2)) + (S*HPL[{1}, -S^2])/4) + (S*(3 + 2*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{0}, S^2]^3*((13*Pi^2*S)/108 + (S*(149 + 18*S^2))/72 + ((18 + 85*S^2 + 41*S^4)*HPL[{1}, -S^2])/(36*S*(1 + S^2)) + (13*S*HPL[{1}, -S^2]^2)/18 + (13*S*HPL[{2}, -S^2])/18) + HPL[{1}, -S^2]^3*((32*Pi^2*S)/27 + (53 + 56*S^2 + 3*S^4)/(18*S) + (14*S*HPL[{2}, -S^2])/9) + ((-7*Pi^2*S)/9 + (8 + 15*S^2 + 2*S^4)/(2*S))*HPL[{3}, -S^2] + ((5 + 16*S^2 + 7*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{5}, -S^2])/3 + ((8*Pi^2*S)/9 + (-15 + S^2 + S^4)/(2*S))*HPL[{2, 1}, -S^2] + ((-5 - 52*S^2 - 43*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3, 2}, -S^2])/3 + 16*S*HPL[{4, 1}, -S^2] + (2*S*(31 + 24*S^2)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)) + (8*S*HPL[{2, 2, 1}, -S^2])/3 - (20*S*HPL[{3, 1, 1}, -S^2])/3 + 16*S*HPL[{2, 1, 1, 1}, -S^2] + ((-26*Pi^2*S)/27 - (26*S*HPL[{0}, S^2]^2)/9 - (2*(13 + 70*S^2 + 21*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) - 8*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-2*S*(13 + 7*S^2))/(3*(1 + S^2)) - 8*S*HPL[{1}, -S^2]) - (52*S*HPL[{2}, -S^2])/9)*Log[T]^3 + ((2*S)/(1 + S^2) + 4*S*HPL[{0}, S^2] + 4*S*HPL[{1}, -S^2])*Log[T]^4 - (S*(1 + S^2)*Zeta[3])/2 + Log[T]^2*(S/2 + (4*Pi^2*S*(7 + 3*S^2))/(9*(1 + S^2)) + (13*S*HPL[{0}, S^2]^3)/9 + ((13 + 70*S^2 + 21*S^4)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) + 8*S*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*((S*(19 + 12*S^2))/(3*(1 + S^2)) + (14*S*HPL[{1}, -S^2])/3) + (S*(31 + 24*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((32*Pi^2*S)/9 + (53 + 56*S^2 + 3*S^4)/(6*S) + (14*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]*((31*Pi^2*S)/9 + (S*(56 + 3*S^2))/6 + ((13 + 70*S^2 + 21*S^4)*HPL[{1}, -S^2])/(3*S*(1 + S^2)) + 12*S*HPL[{1}, -S^2]^2 + (34*S*HPL[{2}, -S^2])/3) - (22*S*HPL[{3}, -S^2])/3 + 8*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{1}, -S^2]^2*(((1 + S^2)*(1 + 125*S^2 + 14*S^4))/(24*S^3) + (Pi^2*(25 + 133*S^2 + 44*S^4))/(36*S*(1 + S^2)) + ((10 + 49*S^2 + 25*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) - (8*S*HPL[{3}, -S^2])/3 - (14*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{2}, -S^2]*((Pi^2*S*(11 + 8*S^2))/(6*(1 + S^2)) + ((1 + S^2)*(3 + 38*S^2 + 3*S^4))/(12*S^3) - (8*S*HPL[{3}, -S^2])/3 - (4*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{0}, S^2]^2*((Pi^2*S*(7 + 3*S^2))/(9*(1 + S^2)) + (S*(44 + 3*S^2))/24 + ((12 + 63*S^2 + 23*S^4)*HPL[{1}, -S^2]^2)/(12*S*(1 + S^2)) + (14*S*HPL[{1}, -S^2]^3)/9 + (S*(35 + 24*S^2)*HPL[{2}, -S^2])/(12*(1 + S^2)) + HPL[{1}, -S^2]*((8*Pi^2*S)/9 + (59 + 60*S^2 + S^4)/(24*S) + (11*S*HPL[{2}, -S^2])/6) - (S*HPL[{3}, -S^2])/2 + (2*S*HPL[{2, 1}, -S^2])/3 + 2*S*Zeta[3]) + HPL[{1}, -S^2]*((58*Pi^4*S)/135 + (Pi^2*(1 + S^2)*(28 + S^2))/(18*S) + ((1 + S^2)*(1 + 247*S^2 + 26*S^4))/(24*S^3) + (Pi^2*S + (-1 + 29*S^2 + 29*S^4 - S^6)/(6*S^3))*HPL[{2}, -S^2] + 2*S*HPL[{2}, -S^2]^2 + ((5 + 17*S^2 + 20*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (8*S*HPL[{4}, -S^2])/3 + ((-10 - 49*S^2 - 25*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*S*HPL[{3, 1}, -S^2])/3 + (28*S*HPL[{2, 1, 1}, -S^2])/3 + ((-1 - 7*S^2 + 2*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{0}, S^2]*((73*Pi^4*S)/270 + (Pi^2*S*(205 + 21*S^2))/72 + (-3 + 261*S^2 + 26*S^4)/(24*S) + ((13 + 70*S^2 + 21*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + 2*S*HPL[{1}, -S^2]^4 + ((5*Pi^2*S)/3 + (-2 + 7*S^2 + 57*S^4 + 3*S^6)/(12*S^3))*HPL[{2}, -S^2] + (7*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((31*Pi^2*S)/18 + (53 + 56*S^2 + 3*S^4)/(12*S) + 5*S*HPL[{2}, -S^2]) + ((1 + 2*S^2 - S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) + 2*S*HPL[{4}, -S^2] + ((-11 - 25*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 12*S*HPL[{3, 1}, -S^2] + (68*S*HPL[{2, 1, 1}, -S^2])/3 + (S*(18 + 19*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((31*Pi^2*(1 + 5*S^2 + 2*S^4))/(36*S*(1 + S^2)) + ((1 + S^2)*(1 + 125*S^2 + 14*S^4))/(24*S^3) + ((4 + 21*S^2 + 7*S^4)*HPL[{2}, -S^2])/(2*S*(1 + S^2)) + (2*S*HPL[{3}, -S^2])/3 - 10*S*HPL[{2, 1}, -S^2] - (2*S*Zeta[3])/3)) + Log[T]*((-73*Pi^4*S)/135 + (1 - 4*S^2)/(4*S) - (Pi^2*S*(61 + S^2))/36 - (S*HPL[{0}, S^2]^4)/2 - (2*(13 + 70*S^2 + 21*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) - 4*S*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*(-(S*(54 + 41*S^2))/(18*(1 + S^2)) - (13*S*HPL[{1}, -S^2])/9) + ((-26*Pi^2*S)/9 + (2 - 13*S^2 - 61*S^4 - S^6)/(6*S^3))*HPL[{2}, -S^2] - (10*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((-32*Pi^2*S)/9 + (-53 - 56*S^2 - 3*S^4)/(6*S) - (14*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^2*((-31*Pi^2*S)/18 - (S*(61 + S^2))/12 + ((-12 - 63*S^2 - 23*S^4)*HPL[{1}, -S^2])/(6*S*(1 + S^2)) - (14*S*HPL[{1}, -S^2]^2)/3 - (13*S*HPL[{2}, -S^2])/3) + ((-5 - 18*S^2 - 21*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{4}, -S^2])/3 + (2*(10 + 18*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{0}, S^2]*((-31*Pi^2*S*(3 + 2*S^2))/(18*(1 + S^2)) - (7*S*(19 + 2*S^2))/12 + ((-13 - 70*S^2 - 21*S^4)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) - 8*S*HPL[{1}, -S^2]^3 + ((-1 - 38*S^2 - 22*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((-31*Pi^2*S)/9 + (-53 - 56*S^2 - 3*S^4)/(6*S) - 10*S*HPL[{2}, -S^2]) + (4*S*HPL[{3}, -S^2])/3 - (8*S*HPL[{2, 1}, -S^2])/3) + (52*S*HPL[{3, 1}, -S^2])/3 - (104*S*HPL[{2, 1, 1}, -S^2])/3 - (2*S*(-3 + S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-25 - 133*S^2 - 44*S^4))/(18*S*(1 + S^2)) - ((1 + S^2)*(1 + 125*S^2 + 14*S^4))/(12*S^3) + ((-10 - 49*S^2 - 25*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3}, -S^2])/3 + (28*S*HPL[{2, 1}, -S^2])/3 + (16*S*Zeta[3])/3));
Et3vwuT3F3=(-73*(1 + 8*S^2))/(1944*S) + (Pi^2*(-1290 - 1317*S^2 - 3899*S^4))/(5832*S) + (Pi^4*(-348 - 174*S^2 - 599*S^4 - 251*S^6))/(2430*S*(1 + S^2)) + ((-9 - 33*S^2 - 12*S^4 - 41*S^6 - 17*S^8)*HPL[{1}, -S^2]^4)/(18*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^5)/(15*S^3) + HPL[{0}, S^2]^4*((-6 - 3*S^2 - 10*S^4 - 4*S^6)/(72*S*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(12*S^3)) + ((-31 - 67*S^2 - 18*S^4 - 98*S^6 - 62*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + HPL[{0}, S^2]^3*((-13*Pi^2*S^3)/324 + (38 - 175*S^2 - 486*S^4)/(648*S) + ((19 - 137*S^2 - 78*S^4 - 344*S^6 - 188*S^8)*HPL[{1}, -S^2])/(324*S^3*(1 + S^2)) - (13*(1 + S^6)*HPL[{1}, -S^2]^2)/(54*S^3) - (13*S^3*HPL[{2}, -S^2])/54) + HPL[{1}, -S^2]^3*((-48 - 73*S^2 - 140*S^4 - 115*S^6)/(54*S^3) - (32*Pi^2*(1 + S^6))/(81*S^3) - (14*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((67 + 459*S^2 - 216*S^4 - 203*S^6)/(162*S^3) + (Pi^2*(-1 + 7*S^6))/(27*S^3))*HPL[{3}, -S^2] + ((7 - 17*S^2 - 12*S^4 - 57*S^6 - 33*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{5}, -S^2])/(9*S^3) + ((298 - 171*S^2 + 639*S^4 - 17*S^6)/(162*S^3) + (Pi^2*(23 - 8*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((-100 - 76*S^2 + 12*S^4 + 219*S^6 + 195*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-1 + 4*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (2*(-3 + 8*S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (2*(-62 - 20*S^2 + 21*S^4 + 178*S^6 + 136*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(7 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (4*(-23 + 5*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (16*(-2 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((26*Pi^2*S^3)/81 + (2*(17 + 25*S^2))/(27*S) + (26*S^3*HPL[{0}, S^2]^2)/27 + (2*(9 + 33*S^2 + 12*S^4 + 41*S^6 + 17*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]*((2*(12 + 6*S^2 + 29*S^4 + 17*S^6))/(9*S*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3)) + (4*(-5 + 13*S^6)*HPL[{2}, -S^2])/(27*S^3))*Log[T]^3 + ((-2*(2 + S^2 + 2*S^4))/(3*S*(1 + S^2)) - (4*S^3*HPL[{0}, S^2])/3 - (4*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3))*Log[T]^4 + ((216 + 27*S^2 + 17*S^4)*Zeta[3])/(162*S) + HPL[{0}, S^2]^2*((-894 - 552*S^2 - 3899*S^4)/(1944*S) - (2*Pi^2*(12 + 6*S^2 + 25*S^4 + 13*S^6))/(81*S*(1 + S^2)) + ((-13 - 69*S^2 - 28*S^4 - 102*S^6 - 46*S^8)*HPL[{1}, -S^2]^2)/(36*S^3*(1 + S^2)) - (14*(1 + S^6)*HPL[{1}, -S^2]^3)/(27*S^3) + ((-66 - 33*S^2 - 202*S^4 - 136*S^6)*HPL[{2}, -S^2])/(108*S*(1 + S^2)) + HPL[{1}, -S^2]*((-298 - 369*S^2 - 1170*S^4 - 1099*S^6)/(648*S^3) - (8*Pi^2*(1 + S^6))/(27*S^3) - (11*(1 + S^6)*HPL[{2}, -S^2])/(18*S^3)) + (S^3*HPL[{3}, -S^2])/6 + ((11 - 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (2*S^3*Zeta[3])/3) + Log[T]^2*((-44 - 85*S^2)/(54*S) - (4*Pi^2*(24 + 12*S^2 + 41*S^4 + 17*S^6))/(81*S*(1 + S^2)) - (13*S^3*HPL[{0}, S^2]^3)/27 + ((-9 - 33*S^2 - 12*S^4 - 41*S^6 - 17*S^8)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{1}, -S^2]^3)/(3*S^3) + HPL[{0}, S^2]^2*((-42 - 21*S^2 - 110*S^4 - 68*S^6)/(27*S*(1 + S^2)) - (14*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3)) + ((62 + 20*S^2 - 21*S^4 - 178*S^6 - 136*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-48 - 73*S^2 - 140*S^4 - 115*S^6)/(18*S^3) - (32*Pi^2*(1 + S^6))/(27*S^3) - (14*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]*((-31*Pi^2*S^3)/27 + (-50 - 46*S^2 - 115*S^4)/(18*S) + ((-9 - 33*S^2 - 12*S^4 - 41*S^6 - 17*S^8)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^2)/S^3 - (2*(-1 + 17*S^6)*HPL[{2}, -S^2])/(9*S^3)) + (2*(-2 + 11*S^6)*HPL[{3}, -S^2])/(9*S^3) - (8*(-2 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(231 + 95*S^2 + 770*S^4))/(216*S^3) + (Pi^2*(-40 - 168*S^2 - 64*S^4 - 225*S^6 - 97*S^8))/(108*S^3*(1 + S^2)) + ((9 - 19*S^2 - 14*S^4 - 64*S^6 - 36*S^8)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (14*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((349 - 501*S^2 - 1041*S^4 - 3899*S^6)/(972*S^3) + (Pi^2*(31 - 23*S^2 - 27*S^4 - 190*S^6 - 136*S^8))/(162*S^3*(1 + S^2)) + (2*(-1 + 4*S^6)*HPL[{3}, -S^2])/(9*S^3) + (2*(7 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(-1 + 4*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((-58*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) - ((1 + S^2)*(135 + 65*S^2 + 918*S^4))/(216*S^3) - (Pi^2*(1 + S^2)*(365 + 148*S^2 + 1067*S^4))/(972*S^3) + ((-1 + 63*S^2 - 477*S^4 - 541*S^6)/(162*S^3) + (Pi^2*(-1 - S^6))/(3*S^3))*HPL[{2}, -S^2] - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + ((32 + 48*S^2 + 8*S^4 + 3*S^6 - 13*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-9 + 19*S^2 + 14*S^4 + 64*S^6 + 36*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (28*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((14 + 30*S^2 + 8*S^4 + 21*S^6 + 5*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + Log[T]*((73*Pi^4*S^3)/405 + (101 + 292*S^2)/(324*S) + (Pi^2*(540 + 837*S^2 + 1099*S^4))/(972*S) + (S^3*HPL[{0}, S^2]^4)/6 + (2*(9 + 33*S^2 + 12*S^4 + 41*S^6 + 17*S^8)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{1}, -S^2]^4)/(3*S^3) + HPL[{0}, S^2]^3*((78 + 39*S^2 + 266*S^4 + 188*S^6)/(162*S*(1 + S^2)) + (13*(1 + S^6)*HPL[{1}, -S^2])/(27*S^3)) + ((Pi^2*(-5 + 26*S^6))/(27*S^3) + (-296 + 45*S^2 + 315*S^4 + 1099*S^6)/(162*S^3))*HPL[{2}, -S^2] + (5*(1 + 2*S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^2*((31*Pi^2*S^3)/54 + (234 + 387*S^2 + 1099*S^4)/(324*S) + ((13 + 69*S^2 + 28*S^4 + 102*S^6 + 46*S^8)*HPL[{1}, -S^2])/(18*S^3*(1 + S^2)) + (14*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + (13*S^3*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]^2*((32*Pi^2*(1 + S^6))/(27*S^3) + (48 + 73*S^2 + 140*S^4 + 115*S^6)/(18*S^3) + (14*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-30 - 78*S^2 - 24*S^4 - 41*S^6 + 7*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (2*(5 + 8*S^6)*HPL[{4}, -S^2])/(9*S^3) + (14*(-5 - 11*S^2 - 3*S^4 - 2*S^6 + 4*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{0}, S^2]*((232 + 179*S^2 + 770*S^4)/(108*S) + (31*Pi^2*(6 + 3*S^2 + 17*S^4 + 11*S^6))/(162*S*(1 + S^2)) + ((9 + 33*S^2 + 12*S^4 + 41*S^6 + 17*S^8)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2]^3)/(3*S^3) + ((-20 + 70*S^2 + 45*S^4 + 241*S^6 + 151*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((31*Pi^2*(1 + S^6))/(27*S^3) + (48 + 73*S^2 + 140*S^4 + 115*S^6)/(18*S^3) + (10*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) - (2*(-1 + 2*S^6)*HPL[{3}, -S^2])/(9*S^3) + (8*(-8 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3)) - (4*(-5 + 13*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (8*(-5 + 13*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (8*(6 + 3*S^2 + 13*S^4 + 7*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(231 + 95*S^2 + 770*S^4))/(108*S^3) + (Pi^2*(40 + 168*S^2 + 64*S^4 + 225*S^6 + 97*S^8))/(54*S^3*(1 + S^2)) + ((-9 + 19*S^2 + 14*S^4 + 64*S^6 + 36*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (28*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + HPL[{0}, S^2]*((-73*Pi^4*S^3)/810 + (Pi^2*(-112 - 313*S^2 - 831*S^4))/(648*S) + (-49 - 37*S^2 - 306*S^4)/(72*S) + ((-9 - 33*S^2 - 12*S^4 - 41*S^6 - 17*S^8)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2]^4)/(3*S^3) + ((18 - 37*S^2 - 45*S^4 - 115*S^6)/(36*S^3) + (Pi^2*(1 - 30*S^6))/(54*S^3))*HPL[{2}, -S^2] + ((1 - 14*S^6)*HPL[{2}, -S^2]^2)/(18*S^3) + HPL[{1}, -S^2]^2*((-48 - 73*S^2 - 140*S^4 - 115*S^6)/(36*S^3) - (31*Pi^2*(1 + S^6))/(54*S^3) - (5*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + ((12 - 6*S^4 + S^6 + 13*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) + ((-1 - 2*S^6)*HPL[{4}, -S^2])/(3*S^3) + ((77 + 167*S^2 + 45*S^4 + 77*S^6 - 13*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + 4*S^3*HPL[{3, 1}, -S^2] - (4*(-1 + 17*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((6 + 3*S^2 - 53*S^4 - 59*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(231 + 95*S^2 + 770*S^4))/(216*S^3) - (31*Pi^2*(2 + 14*S^2 + 6*S^4 + 23*S^6 + 11*S^8))/(324*S^3*(1 + S^2)) + ((-19 - 79*S^2 - 30*S^4 - 106*S^6 - 46*S^8)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (10*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)));
Et3vwuT=T*Et3vwuT1F1*(F-1/F)+T^2*(Et3vwuT2F2*(F^2-1/F^2))+T^3*(Et3vwuT3F1*(F-1/F)+Et3vwuT3F3*(F^3-1/F^3));
e4T0F0=(7979*Pi^8)/68040 + (89*Pi^4*HPL[{0}, S^2]^4)/720 + (Pi^2*HPL[{0}, S^2]^6)/36 + HPL[{0}, S^2]^8/384 + ((89*Pi^4)/45 + (4*Pi^2*HPL[{0}, S^2]^2)/3 + HPL[{0}, S^2]^4/4)*Log[T]^4 + ((16*Pi^2)/9 + (2*HPL[{0}, S^2]^2)/3)*Log[T]^6 + (2*Log[T]^8)/3 + (8*Pi^2*Zeta[3]^2)/3 + HPL[{0}, S^2]^2*((1399*Pi^6)/5670 + 4*Zeta[3]^2) + Log[T]^2*((2798*Pi^6)/2835 + (89*Pi^4*HPL[{0}, S^2]^2)/90 + (Pi^2*HPL[{0}, S^2]^4)/3 + HPL[{0}, S^2]^6/24 + 16*Zeta[3]^2);
e4T1F1=(-4*Pi^4*S)/9 - (Pi^6*S)/20 - (S*HPL[{0}, S^2]^7)/48 + ((-1 - S^2)*HPL[{0}, S^2]^6*HPL[{1}, -S^2])/(48*S) + ((-32*(1 + S^2))/(5*S) - (8*Pi^2*(1 + S^2))/(15*S))*HPL[{1}, -S^2]^5 - (4*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) - (4*(1 + S^2)*HPL[{1}, -S^2]^7)/(21*S) + HPL[{0}, S^2]^5*(-S/2 - (Pi^2*S)/6 + ((-1 - S^2)*HPL[{1}, -S^2])/(4*S) + ((-1 - S^2)*HPL[{1}, -S^2]^2)/(8*S)) - (2*(-1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - 2*S*HPL[{3}, -S^2]^2 + ((-14*Pi^2*(1 + S^2))/(3*S) - (4*(7 + 10*S^2))/S)*HPL[{5}, -S^2] - (8*(5 + 2*S^2)*HPL[{6}, -S^2])/S - (200*(1 + S^2)*HPL[{7}, -S^2])/S + (18*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + HPL[{0}, S^2]^4*(-(Pi^2*S)/24 - (3*(1 + S^2)*HPL[{1}, -S^2]^2)/(4*S) + ((-1 - S^2)*HPL[{1}, -S^2]^3)/(4*S) - (S*HPL[{2}, -S^2])/4 + HPL[{1}, -S^2]*((Pi^2*(-1 - S^2))/(6*S) - (5*(1 + S^2))/(4*S) + ((-1 - S^2)*HPL[{2}, -S^2])/(4*S)) + ((-1 - S^2)*HPL[{3}, -S^2])/(4*S) + ((1 + S^2)*HPL[{2, 1}, -S^2])/(2*S)) + ((-8*Pi^2*(1 + S^2))/(3*S) - (8*(1 + 8*S^2))/S)*HPL[{3, 2}, -S^2] + ((-6*Pi^2*(1 + S^2))/S - (8*(3 + 22*S^2))/S)*HPL[{4, 1}, -S^2] + (40*(1 + S^2)*HPL[{4, 3}, -S^2])/S + (4*(4 + 3*S^2)*HPL[{5, 1}, -S^2])/S + (120*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (312*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((-72*(1 + S^2))/S - (20*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((-16*Pi^2*(1 + S^2))/S - (4*(49 + 27*S^2))/S)*HPL[{3, 1, 1}, -S^2] - (16*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (80*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (52*(-1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (80*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (272*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S + (552*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((-88*(-1 + S^2))/S + (4*Pi^2*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (48*(-1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (48*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (144*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (96*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (96*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (288*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (576*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + ((-2*Pi^2*S)/3 - S*HPL[{0}, S^2]^3 + ((-32*(1 + S^2))/S - (8*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2] - (20*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (20*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^2*(-2*S - (3*(1 + S^2)*HPL[{1}, -S^2])/S) - (4*(-1 + S^2)*HPL[{2}, -S^2])/S + HPL[{0}, S^2]*(-32*S - (8*Pi^2*S)/3 - (20*(1 + S^2)*HPL[{1}, -S^2])/S - (10*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (4*(1 + S^2)*HPL[{2}, -S^2])/S) + (4*(1 + S^2)*HPL[{3}, -S^2])/S)*Log[T]^4 + ((8*(1 + S^2)*HPL[{1}, -S^2])/S + (4*(1 + S^2)*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(8*S + (4*(1 + S^2)*HPL[{1}, -S^2])/S))*Log[T]^5 + ((-4*S*HPL[{0}, S^2])/3 - (4*(1 + S^2)*HPL[{1}, -S^2])/(3*S))*Log[T]^6 + (32*S + (10*Pi^2*S)/3)*Zeta[3] + 4*S*Zeta[3]^2 + HPL[{3}, -S^2]*((16*(-1 + S^2))/S + (Pi^4*(1 + S^2))/(45*S) + (2*Pi^2*(1 + 6*S^2))/(3*S) - (20*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(7 + 2*S^2)*HPL[{2, 1}, -S^2])/S - (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (4*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((32*(-1 + S^2))/S + (2*Pi^2*(-2 + 7*S^2))/(3*S) - (16*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((Pi^2*(-3 - 4*S^2))/(3*S) - (8*(1 + S^2))/S + (2*(1 + S^2)*HPL[{3}, -S^2])/S + (2*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^4*((-74*(1 + S^2))/(3*S) - (8*Pi^2*(1 + S^2))/(3*S) + (10*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (4*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((16*(-1 + S^2))/S + (16*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (12*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-232*(1 + S^2))/(3*S) - (77*Pi^2*(1 + S^2))/(9*S) - (151*Pi^4*(1 + S^2))/(270*S) - (5*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (10*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (40*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (16*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-64*(-1 + S^2))/S - (2*Pi^2*(-5 + 14*S^2))/(3*S) + (24*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-32*(-1 + S^2))/S + (7*Pi^4*(1 + S^2))/(15*S) - (2*Pi^2*(-13 + 4*S^2))/(3*S) - (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(7 + 2*S^2)*Zeta[3])/S) + Log[T]^3*((22*Pi^2*S)/9 + ((64*(1 + S^2))/S + (16*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^2 + (80*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (20*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + HPL[{0}, S^2]^3*((38*S)/9 + (20*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + ((44*(-1 + S^2))/(3*S) + (4*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (8*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^2*((22*S)/3 + (12*(1 + S^2)*HPL[{1}, -S^2])/S + (6*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (4*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (4*(5 + 17*S^2)*HPL[{3}, -S^2])/(3*S) + (16*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*((296*S)/3 + (98*Pi^2*S)/9 + (40*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (40*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (8*(1 + 3*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((64*(1 + S^2))/S + (50*Pi^2*(1 + S^2))/(9*S) + (16*(1 + S^2)*HPL[{2}, -S^2])/S) + (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{2, 1}, -S^2])/S) - 16*S*Zeta[3] + HPL[{1}, -S^2]*((296*(1 + S^2))/(3*S) + (32*Pi^2*(1 + S^2))/(3*S) - (40*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (16*(1 + S^2)*Zeta[3])/S)) + HPL[{0}, S^2]^3*((-58*S)/3 - (23*Pi^2*S)/9 - (89*Pi^4*S)/180 - (20*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (5*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + ((-3 - 7*S^2)/(3*S) + (Pi^2*(-1 - S^2))/(12*S))*HPL[{2}, -S^2] + ((-1 - S^2)*HPL[{2}, -S^2]^2)/(4*S) + HPL[{1}, -S^2]^2*((-11*(1 + S^2))/(2*S) - (25*Pi^2*(1 + S^2))/(36*S) - (7*(1 + S^2)*HPL[{2}, -S^2])/(6*S)) + ((-1 - S^2)*HPL[{3}, -S^2])/(2*S) + (3*(1 + S^2)*HPL[{4}, -S^2])/(2*S) + ((11 + 4*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 2*S*Zeta[3] + HPL[{1}, -S^2]*((-29*(1 + S^2))/(3*S) - (25*Pi^2*(1 + S^2))/(18*S) - (7*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (7*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(1 + S^2)*Zeta[3])/S)) + HPL[{0}, S^2]^2*((-4*Pi^2*S)/3 - (19*Pi^4*S)/120 - (3*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (3*(1 + S^2)*HPL[{1}, -S^2]^5)/(5*S) + ((-3 - 7*S^2)*HPL[{2}, -S^2]^2)/(4*S) + HPL[{1}, -S^2]^3*((Pi^2*(-1 - S^2))/S - (29*(1 + S^2))/(3*S) - (5*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-1 - 3*S^2)/(2*S) + (Pi^2*(-1 - S^2))/(2*S))*HPL[{3}, -S^2] + ((-1 + S^2)*HPL[{4}, -S^2])/(2*S) - (11*(1 + S^2)*HPL[{5}, -S^2])/S + ((3*Pi^2*(1 + S^2))/(2*S) + (3*(5 + S^2))/S)*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((-23*(1 + S^2))/S - (3*Pi^2*(1 + S^2))/S - (5*(1 + S^2)*HPL[{2}, -S^2])/S + (5*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + (2*(1 + 4*S^2)*HPL[{3, 1}, -S^2])/S - (2*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (2*(1 + 8*S^2)*HPL[{2, 1, 1}, -S^2])/S + HPL[{1}, -S^2]*((-38*(1 + S^2))/S - (59*Pi^2*(1 + S^2))/(12*S) - (151*Pi^4*(1 + S^2))/(360*S) + ((-8*(1 + S^2))/S - (11*Pi^2*(1 + S^2))/(12*S))*HPL[{2}, -S^2] - (3*(1 + S^2)*HPL[{2}, -S^2]^2)/(2*S) - (2*(1 + S^2)*HPL[{4}, -S^2])/S + (10*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (6*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (10*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S) - (8*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (24*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (12*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - S*Zeta[3] + HPL[{2}, -S^2]*(-8*S + (Pi^2*(-1 - 14*S^2))/(12*S) + ((1 + S^2)*HPL[{3}, -S^2])/S + (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (3*(1 + S^2)*Zeta[3])/S)) + Log[T]^2*((-16*Pi^2*S)/3 - (19*Pi^4*S)/30 - (S*HPL[{0}, S^2]^5)/4 + ((-64*(1 + S^2))/S - (16*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^3 - (20*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (4*(1 + S^2)*HPL[{1}, -S^2]^5)/S + HPL[{0}, S^2]^4*(-S/2 - (3*(1 + S^2)*HPL[{1}, -S^2])/(4*S)) - (9*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{0}, S^2]^3*((-32*S)/3 - (4*Pi^2*S)/3 - (20*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (10*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + ((-1 - S^2)*HPL[{2}, -S^2])/S) + ((2*Pi^2*(1 + S^2))/S + (2*(5 + 27*S^2))/S)*HPL[{3}, -S^2] - (2*(-1 + S^2)*HPL[{4}, -S^2])/S - (12*(1 + S^2)*HPL[{5}, -S^2])/S + ((-44*(-1 + S^2))/S + (2*Pi^2*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(-16*S - 2*Pi^2*S - (18*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (6*(1 + S^2)*HPL[{1}, -S^2]^3)/S + ((-1 - 8*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((-29*(1 + S^2))/S - (3*Pi^2*(1 + S^2))/S - (5*(1 + S^2)*HPL[{2}, -S^2])/S) + (6*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + (24*(-1 + S^2)*HPL[{3, 1}, -S^2])/S - (24*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (72*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (48*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + HPL[{0}, S^2]*(-232*S - (80*Pi^2*S)/3 - (89*Pi^4*S)/45 - (40*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (10*(1 + S^2)*HPL[{1}, -S^2]^4)/S + ((-3*Pi^2*(1 + S^2))/S - (4*(4 + 15*S^2))/S)*HPL[{2}, -S^2] - (5*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^2*((-96*(1 + S^2))/S - (25*Pi^2*(1 + S^2))/(3*S) - (24*(1 + S^2)*HPL[{2}, -S^2])/S) - (2*(3 + S^2)*HPL[{3}, -S^2])/S - (2*(1 + S^2)*HPL[{4}, -S^2])/S + (24*(3 + S^2)*HPL[{2, 1}, -S^2])/S + HPL[{1}, -S^2]*((-148*(1 + S^2))/S - (50*Pi^2*(1 + S^2))/(3*S) - (48*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(1 + S^2)*HPL[{3}, -S^2])/S + (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S) - (48*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (96*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + 44*S*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(5 - 14*S^2))/(3*S) - (32*(-1 + S^2))/S + (12*(1 + S^2)*HPL[{3}, -S^2])/S + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (12*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-148*(1 + S^2))/S - (16*Pi^2*(1 + S^2))/S + (20*(1 + S^2)*HPL[{3}, -S^2])/S + (24*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]*((-232*(1 + S^2))/S - (77*Pi^2*(1 + S^2))/(3*S) - (151*Pi^4*(1 + S^2))/(90*S) - (5*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (10*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (40*(1 + S^2)*HPL[{3}, -S^2])/S + (48*(1 + S^2)*Zeta[3])/S)) + 8*S*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(11 - 47*S^2))/(90*S) - (8*Pi^2*(-1 + 2*S^2))/(3*S) + ((4*Pi^2*(1 + S^2))/(3*S) + (4*(1 + 8*S^2))/S)*HPL[{3}, -S^2] + 4*S*HPL[{4}, -S^2] + (20*(1 + S^2)*HPL[{5}, -S^2])/S + ((36*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (4*(5 + 4*S^2)*HPL[{3, 1}, -S^2])/S - (8*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (40*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (36*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (48*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((2*Pi^2*(1 + S^2))/S + (4*(2 + 7*S^2))/S)*Zeta[3] + (16*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^2*((-200*(1 + S^2))/S - (20*Pi^2*(1 + S^2))/S - (151*Pi^4*(1 + S^2))/(90*S) - (10*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((30*(1 + S^2))/S + (5*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (10*(1 + S^2)*HPL[{5}, -S^2])/S + (5*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (20*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (60*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (80*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((38*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-5*Pi^2*(1 + S^2))/(3*S) + (10*(1 + S^2)*HPL[{3}, -S^2])/S + (20*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (10*(1 + S^2)*Zeta[3])/S) + (16*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]*((-400*(1 + S^2))/S - (32*Pi^2*(1 + S^2))/S - (122*Pi^4*(1 + S^2))/(45*S) - (283*Pi^6*(1 + S^2))/(1620*S) + ((-16*(1 + S^2))/S - (4*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 + (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-4*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] - (20*(1 + S^2)*HPL[{5}, -S^2])/S - (56*(1 + S^2)*HPL[{6}, -S^2])/S + (20*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((4*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (120*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (28*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (10*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (80*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (160*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((56*(1 + S^2))/S + (4*Pi^2*(1 + S^2))/S)*Zeta[3] + (4*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((10*Pi^2*(1 + S^2))/(3*S) - (20*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((32*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S) - (20*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-8*Pi^2*(1 + S^2))/(3*S) - (13*Pi^4*(1 + S^2))/(45*S) + (20*(1 + S^2)*HPL[{3}, -S^2])/S - (4*(1 + S^2)*HPL[{4}, -S^2])/S + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (20*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (20*(1 + S^2)*Zeta[3])/S) + (32*(1 + S^2)*Zeta[5])/S) + Log[T]*((16*Pi^2*S)/3 + (41*Pi^4*S)/45 + ((32*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^4 + (8*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (4*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + HPL[{0}, S^2]^5*(S/2 + ((1 + S^2)*HPL[{1}, -S^2])/(4*S)) + HPL[{0}, S^2]^4*(S/2 + (3*(1 + S^2)*HPL[{1}, -S^2])/(2*S) + (3*(1 + S^2)*HPL[{1}, -S^2]^2)/(4*S)) + ((14*(1 + S^2))/S + (Pi^2*(1 + S^2))/S)*HPL[{2}, -S^2]^2 + (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-8*(-1 + S^2))/S - (2*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] + (4*(6 + 5*S^2)*HPL[{5}, -S^2])/S - (16*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + HPL[{0}, S^2]^3*((58*S)/3 + (49*Pi^2*S)/18 + (20*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (20*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + ((3 + 10*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((11*(1 + S^2))/S + (25*Pi^2*(1 + S^2))/(18*S) + (7*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((1 + S^2)*HPL[{3}, -S^2])/S - (8*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) + HPL[{3}, -S^2]*(-64*S - (2*Pi^2*(2 + 9*S^2))/(3*S) + (16*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + ((-44*(-1 + S^2))/S - (4*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] + (8*(3 + 8*S^2)*HPL[{3, 2}, -S^2])/S + (4*(17 + 49*S^2)*HPL[{4, 1}, -S^2])/S + ((88*(-1 + S^2))/S + (8*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]^2*(16*S + (17*Pi^2*S)/6 + (12*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (3*(1 + S^2)*HPL[{1}, -S^2]^4)/S + ((Pi^2*(1 + S^2))/(3*S) + (1 + 13*S^2)/S)*HPL[{2}, -S^2] + ((1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^2*((29*(1 + S^2))/S + (3*Pi^2*(1 + S^2))/S + (5*(1 + S^2)*HPL[{2}, -S^2])/S) + ((1 - S^2)*HPL[{3}, -S^2])/S - (2*(1 + S^2)*HPL[{4}, -S^2])/S - (2*(9 + 2*S^2)*HPL[{2, 1}, -S^2])/S + HPL[{1}, -S^2]*((46*(1 + S^2))/S + (6*Pi^2*(1 + S^2))/S + (10*(1 + S^2)*HPL[{2}, -S^2])/S - (10*(1 + S^2)*HPL[{2, 1}, -S^2])/S) - (4*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (8*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S) + (88*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (32*(7 + 4*S^2)*HPL[{3, 1, 1}, -S^2])/S + (96*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + HPL[{0}, S^2]*(400*S + 44*Pi^2*S + (361*Pi^4*S)/90 + (20*(1 + S^2)*HPL[{1}, -S^2]^4)/S + (4*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (5*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((64*(1 + S^2))/S + (50*Pi^2*(1 + S^2))/(9*S) + (16*(1 + S^2)*HPL[{2}, -S^2])/S) + ((4*Pi^2*(1 + S^2))/(3*S) + (2*(5 + 3*S^2))/S)*HPL[{3}, -S^2] + (2*(1 + 3*S^2)*HPL[{4}, -S^2])/S + (12*(1 + S^2)*HPL[{5}, -S^2])/S + ((-20*Pi^2*(1 + S^2))/(3*S) - (8*(15 + 4*S^2))/S)*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((148*(1 + S^2))/S + (50*Pi^2*(1 + S^2))/(3*S) + (48*(1 + S^2)*HPL[{2}, -S^2])/S + (4*(1 + S^2)*HPL[{3}, -S^2])/S - (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + HPL[{2}, -S^2]*((8*(3 + 11*S^2))/S + (Pi^2*(9 + 28*S^2))/(3*S) - (20*(1 + S^2)*HPL[{2, 1}, -S^2])/S) - (24*(1 + 3*S^2)*HPL[{3, 1}, -S^2])/S - (4*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (48*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/S + HPL[{1}, -S^2]*((232*(1 + S^2))/S + (27*Pi^2*(1 + S^2))/S + (61*Pi^4*(1 + S^2))/(30*S) + ((76*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (10*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (8*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(1 + S^2)*HPL[{4}, -S^2])/S - (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S) + (40*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (128*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (96*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S) + (-64*S - 4*Pi^2*S)*Zeta[3] + HPL[{1}, -S^2]^2*((232*(1 + S^2))/S + (77*Pi^2*(1 + S^2))/(3*S) + (151*Pi^4*(1 + S^2))/(90*S) + (5*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (10*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (40*(1 + S^2)*HPL[{3}, -S^2])/S - (48*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((296*(1 + S^2))/(3*S) + (32*Pi^2*(1 + S^2))/(3*S) - (40*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (16*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((64*(-1 + S^2))/S + (2*Pi^2*(-15 + 4*S^2))/(3*S) + (16*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((32*(-1 + S^2))/S + (Pi^4*(1 + S^2))/(9*S) + (2*Pi^2*(-5 + 12*S^2))/(3*S) - (4*(3 + 8*S^2)*HPL[{3}, -S^2])/S - (8*(1 + S^2)*HPL[{4}, -S^2])/S - (44*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (32*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(3 + 8*S^2)*Zeta[3])/S) - 32*S*Zeta[5] + HPL[{1}, -S^2]*((400*(1 + S^2))/S + (40*Pi^2*(1 + S^2))/S + (151*Pi^4*(1 + S^2))/(45*S) + (20*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-60*(1 + S^2))/S - (10*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (20*(1 + S^2)*HPL[{5}, -S^2])/S - (10*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (120*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (80*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (160*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((-76*(1 + S^2))/S - (4*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((10*Pi^2*(1 + S^2))/(3*S) - (20*(1 + S^2)*HPL[{3}, -S^2])/S - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (20*(1 + S^2)*Zeta[3])/S) - (32*(1 + S^2)*Zeta[5])/S)) + HPL[{0}, S^2]*(-400*S - (116*Pi^2*S)/3 - (319*Pi^4*S)/90 - (1399*Pi^6*S)/2835 - (4*(1 + S^2)*HPL[{1}, -S^2]^5)/S - (2*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + ((-3 - 13*S^2)/S - (2*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 - (2*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^4*((-16*(1 + S^2))/S - (25*Pi^2*(1 + S^2))/(18*S) - (4*(1 + S^2)*HPL[{2}, -S^2])/S) + (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((4*(-1 + S^2))/S + (4*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] - 6*S*HPL[{5}, -S^2] + (40*(1 + S^2)*HPL[{6}, -S^2])/S + (10*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((-148*(1 + S^2))/(3*S) - (50*Pi^2*(1 + S^2))/(9*S) - (16*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + ((2*Pi^2*(1 + S^2))/S + (2*(7 + 29*S^2))/S)*HPL[{3, 1}, -S^2] - (4*HPL[{3, 2}, -S^2])/S + (2*(-3 + S^2)*HPL[{4, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-6*Pi^2*(1 + S^2))/S - (8*(4 + 15*S^2))/S)*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((-116*(1 + S^2))/S - (27*Pi^2*(1 + S^2))/(2*S) - (61*Pi^4*(1 + S^2))/(60*S) + ((-38*(1 + S^2))/S - (19*Pi^2*(1 + S^2))/(6*S))*HPL[{2}, -S^2] - (5*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (4*(1 + S^2)*HPL[{3}, -S^2])/S - (2*(1 + S^2)*HPL[{4}, -S^2])/S + (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S) - (20*(3 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (64*(3 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (52*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (48*(3 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (48*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (96*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - 2*Pi^2*S*Zeta[3] - 8*S*Zeta[3]^2 + HPL[{2}, -S^2]*((Pi^2*(-7 - 22*S^2))/(3*S) - (7*Pi^4*(1 + S^2))/(30*S) - (8*(3 + 7*S^2))/S + (2*HPL[{3}, -S^2])/S - (4*(1 + S^2)*HPL[{4}, -S^2])/S + (10*(3 + S^2)*HPL[{2, 1}, -S^2])/S + (12*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (20*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (2*Zeta[3])/S) + HPL[{3}, -S^2]*((Pi^2*(-3 - 2*S^2))/(3*S) - (12*(1 + S^2))/S - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((8*(11 + 3*S^2))/S + (Pi^2*(29 + 10*S^2))/(3*S) + (4*(1 + S^2)*Zeta[3])/S) - 16*S*Zeta[5] + HPL[{1}, -S^2]*((-200*(1 + S^2))/S - (22*Pi^2*(1 + S^2))/S - (61*Pi^4*(1 + S^2))/(30*S) - (10*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((Pi^2*(-1 - S^2))/(3*S) - (6*(1 + S^2))/S)*HPL[{3}, -S^2] - (4*(1 + S^2)*HPL[{4}, -S^2])/S + (6*(1 + S^2)*HPL[{5}, -S^2])/S + ((76*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (48*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (4*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (8*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (128*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (96*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-2*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-56*(1 + S^2))/S - (19*Pi^2*(1 + S^2))/(3*S) + (2*(1 + S^2)*HPL[{3}, -S^2])/S + (20*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2*(1 + S^2)*Zeta[3])/S) - (16*(1 + S^2)*Zeta[5])/S));
e4T2F0=-300 + (697*Pi^6*S^2)/1890 + (4*Pi^2*(-11 + 7*S^2))/3 + (Pi^4*(-20 + 63*S^2))/45 - HPL[{0}, S^2]^7/24 + HPL[{0}, S^2]^6*(S^2/8 - HPL[{1}, -S^2]/24) - (16*Pi^2*HPL[{1}, -S^2]^5)/15 - (8*HPL[{1}, -S^2]^7)/21 + HPL[{0}, S^2]^5*(-Pi^2/3 - HPL[{1}, -S^2]^2/4) + (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) - (2*(1 + S^2)^2*HPL[{3}, -S^2]^2)/S^2 - (28*Pi^2*HPL[{5}, -S^2])/3 + (120*(-1 + S^2)*(1 + S^2)*HPL[{6}, -S^2])/S^2 - 400*HPL[{7}, -S^2] + (8*(1 + S^2)^2*HPL[{2, 1}, -S^2]^2)/S^2 + HPL[{0}, S^2]^4*((17*Pi^2*S^2)/24 + (-1 + 6*S^2)/4 + ((1 + S^2)*HPL[{1}, -S^2]^2)/2 - HPL[{1}, -S^2]^3/2 + HPL[{1}, -S^2]*(1 - Pi^2/3 + S^2 - HPL[{2}, -S^2]/2) + ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(4*S^2) - HPL[{3}, -S^2]/2 + HPL[{2, 1}, -S^2]) - (16*Pi^2*HPL[{3, 2}, -S^2])/3 - 12*Pi^2*HPL[{4, 1}, -S^2] + 80*HPL[{4, 3}, -S^2] - (40*(-1 + S^2)*(1 + S^2)*HPL[{5, 1}, -S^2])/S^2 + 240*HPL[{5, 2}, -S^2] + 624*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((2*Pi^4)/45 + (12*(-1 + S^4))/S^2 - 40*HPL[{4}, -S^2] - 16*(1 + S^2)*HPL[{2, 1}, -S^2] - 48*HPL[{3, 1}, -S^2] + 48*HPL[{2, 1, 1}, -S^2]) - (40*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - 32*Pi^2*HPL[{3, 1, 1}, -S^2] + (16*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + 32*HPL[{3, 2, 2}, -S^2] + 160*HPL[{3, 3, 1}, -S^2] + (80*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 + 160*HPL[{4, 1, 2}, -S^2] + 544*HPL[{4, 2, 1}, -S^2] + 1104*HPL[{5, 1, 1}, -S^2] + 8*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - (48*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - 96*HPL[{3, 1, 1, 2}, -S^2] - 96*HPL[{3, 1, 2, 1}, -S^2] - 96*HPL[{3, 2, 1, 1}, -S^2] - 288*HPL[{4, 1, 1, 1}, -S^2] + (96*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + 192*HPL[{2, 1, 2, 1, 1}, -S^2] + 576*HPL[{2, 2, 1, 1, 1}, -S^2] + 1152*HPL[{3, 1, 1, 1, 1}, -S^2] + (-4 + (2*Pi^2*S^2)/3 - 2*HPL[{0}, S^2]^3 + HPL[{0}, S^2]^2*(2*S^2 - 6*HPL[{1}, -S^2]) - (16*Pi^2*HPL[{1}, -S^2])/3 - (40*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]*((-16*Pi^2)/3 - 20*HPL[{1}, -S^2]^2 - 8*HPL[{2}, -S^2]) + (4*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + 8*HPL[{3}, -S^2])*Log[T]^4 + (8*HPL[{0}, S^2]*HPL[{1}, -S^2] + 8*HPL[{1}, -S^2]^2)*Log[T]^5 + ((-8*HPL[{0}, S^2])/3 - (8*HPL[{1}, -S^2])/3)*Log[T]^6 + Log[T]^3*(24 - (8*Pi^2*S^2)/3 + (40*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/9 + (32*Pi^2*HPL[{1}, -S^2]^2)/3 + (40*HPL[{1}, -S^2]^4)/3 + ((8*Pi^2)/9 - (16*(-1 + S^4))/S^2)*HPL[{2}, -S^2] + (16*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*(-8*S^2 - 4*(1 + S^2)*HPL[{1}, -S^2] + 12*HPL[{1}, -S^2]^2 + (8*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]*(8*(1 + S^2) + (80*HPL[{1}, -S^2]^3)/3 + (8*(1 + S^2)*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((100*Pi^2)/9 + 32*HPL[{2}, -S^2]) + (8*HPL[{3}, -S^2])/3 - 32*HPL[{2, 1}, -S^2]) + HPL[{1}, -S^2]*((-4*Pi^2*(1 + S^2))/3 + (8*(1 + 2*S^2 + S^4))/S^2 - (8*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - (80*HPL[{3}, -S^2])/3 - 32*Zeta[3])) + HPL[{0}, S^2]^3*((-89*Pi^4)/90 - 3*(1 + S^2) + (4*(1 + S^2)*HPL[{1}, -S^2]^3)/9 - (10*HPL[{1}, -S^2]^4)/9 + HPL[{1}, -S^2]^2*((-25*Pi^2)/18 + (4*(1 + S^2))/3 - (7*HPL[{2}, -S^2])/3) + (-Pi^2/6 - (2*(1 + S^2))/S^2)*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/2 + (-1 - S^2)*HPL[{3}, -S^2] + 3*HPL[{4}, -S^2] + (2*(1 + S^2)*HPL[{2, 1}, -S^2])/3 - 4*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((Pi^2*(1 + S^2))/9 + (-3 + 2*S^2 + 5*S^4)/(3*S^2) - ((1 + S^2)*(3 + S^2)*HPL[{2}, -S^2])/(3*S^2) + (14*HPL[{2, 1}, -S^2])/3 - 4*Zeta[3])) + HPL[{3, 1}, -S^2]*((-24*(-1 + 2*S^4))/S^2 - (4*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) - 32*Zeta[3]) + 24*S^2*Zeta[3] + 8*S^2*Zeta[3]^2 + HPL[{2}, -S^2]^2*((Pi^2*(-2 - 3*S^2 - S^4))/(3*S^2) - (2*(3 + 8*S^2 + 3*S^4))/S^2 + 4*HPL[{3}, -S^2] + 4*Zeta[3]) + HPL[{1}, -S^2]^4*((Pi^2*(1 + S^2))/3 - (2*(1 + 2*S^2 + S^4))/S^2 + (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + (20*HPL[{3}, -S^2])/3 + 8*Zeta[3]) + HPL[{4}, -S^2]*((12*(-1 + 3*S^4))/S^2 + (2*Pi^2*(-4 + S^2 + 5*S^4))/(3*S^2) + 32*HPL[{2, 1}, -S^2] + 24*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((72*(-1 + S^4))/S^2 + (8*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) + 48*Zeta[3]) + HPL[{2, 1}, -S^2]*((14*Pi^4)/15 - (24*(-1 + S^4))/S^2 - 48*HPL[{3, 1}, -S^2] - 96*HPL[{2, 1, 1}, -S^2] - 16*(1 + S^2)*Zeta[3]) + HPL[{1}, -S^2]^3*((-151*Pi^4)/135 + (4*Pi^2*(1 + S^2))/3 - (12*(1 + 2*S^2 + S^4))/S^2 + ((-10*Pi^2)/9 + (8*(-1 + S^4))/S^2)*HPL[{2}, -S^2] - (20*HPL[{2}, -S^2]^2)/3 + (4*(1 + S^2)*(-1 + 5*S^2)*HPL[{3}, -S^2])/(3*S^2) - (8*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + 8*(1 + S^2)*Zeta[3]) + HPL[{0}, S^2]^2*((11*Pi^4*S^2)/9 + (Pi^2*(-2 + 9*S^2))/2 + 2*(-11 + 14*S^2) + (1 + S^2)*HPL[{1}, -S^2]^4 - (6*HPL[{1}, -S^2]^5)/5 + HPL[{1}, -S^2]^3*(-2*Pi^2 + 4*(1 + S^2) - (10*HPL[{2}, -S^2])/3) + ((-1 - S^2)*HPL[{2}, -S^2]^2)/S^2 - Pi^2*HPL[{3}, -S^2] + (2*(1 + S^2)*(-2 + 3*S^2)*HPL[{4}, -S^2])/S^2 - 22*HPL[{5}, -S^2] + 3*Pi^2*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((3*Pi^2*(1 + S^2))/2 + (3*(-1 + 2*S^2 + 3*S^4))/S^2 + ((-3 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + 10*HPL[{2, 1}, -S^2]) - (2*(-3 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - 4*HPL[{3, 2}, -S^2] + (4*(-3 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 16*HPL[{2, 2, 1}, -S^2] - 48*HPL[{3, 1, 1}, -S^2] + 24*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) + (-9 - 8*S^2 + 3*S^4)/S^2 + 2*HPL[{3}, -S^2] + 8*HPL[{2, 1}, -S^2] + 6*Zeta[3]) + HPL[{1}, -S^2]*((-151*Pi^4)/180 + 3*Pi^2*(1 + S^2) + (-9 + 4*S^2 + 13*S^4)/S^2 + ((-11*Pi^2)/6 + (2*(-3 - 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - 3*HPL[{2}, -S^2]^2 + ((-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/S^2 - 4*HPL[{4}, -S^2] - (2*(-3 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + 12*HPL[{3, 1}, -S^2] - 20*HPL[{2, 1, 1}, -S^2] + 6*(1 + S^2)*Zeta[3])) + Log[T]^2*(-88 + (14*Pi^4*S^2)/15 + 2*Pi^2*(-2 + 3*S^2) - HPL[{0}, S^2]^5/2 + HPL[{0}, S^2]^4*(S^2 - (3*HPL[{1}, -S^2])/2) - (32*Pi^2*HPL[{1}, -S^2]^3)/3 - 8*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^3*((-8*Pi^2)/3 + (4*(1 + S^2)*HPL[{1}, -S^2])/3 - (20*HPL[{1}, -S^2]^2)/3 - 2*HPL[{2}, -S^2]) - (4*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + 4*Pi^2*HPL[{3}, -S^2] + (16*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 24*HPL[{5}, -S^2] + 4*Pi^2*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(3*Pi^2*S^2 + 6*(-1 + 3*S^2) + 6*(1 + S^2)*HPL[{1}, -S^2]^2 - 12*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*(-6*Pi^2 + 12*(1 + S^2) - 10*HPL[{2}, -S^2]) + (2*(-3 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + 12*HPL[{2, 1}, -S^2]) - (24*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - 48*HPL[{3, 2}, -S^2] - 144*HPL[{4, 1}, -S^2] + HPL[{0}, S^2]*((-178*Pi^4)/45 - 36*(1 + S^2) - 20*HPL[{1}, -S^2]^4 + HPL[{1}, -S^2]^2*((-50*Pi^2)/3 - 48*HPL[{2}, -S^2]) + (-6*Pi^2 - (24*(1 + S^2))/S^2)*HPL[{2}, -S^2] - 10*HPL[{2}, -S^2]^2 - 4*(1 + S^2)*HPL[{3}, -S^2] - 4*HPL[{4}, -S^2] + 24*(1 + S^2)*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]*((4*Pi^2*(1 + S^2))/3 - (12*(1 + 2*S^2 + S^4))/S^2 - (12*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 - 8*HPL[{3}, -S^2] + 96*HPL[{2, 1}, -S^2]) + 48*HPL[{3, 1}, -S^2] - 96*HPL[{2, 1, 1}, -S^2]) + (48*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 96*HPL[{2, 2, 1}, -S^2] - 192*HPL[{3, 1, 1}, -S^2] + HPL[{2}, -S^2]*((36*(-1 + S^4))/S^2 + (4*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) + 24*HPL[{3}, -S^2] + 48*HPL[{2, 1}, -S^2] + 24*Zeta[3]) + HPL[{1}, -S^2]^2*(2*Pi^2*(1 + S^2) - (12*(1 + 2*S^2 + S^4))/S^2 + (12*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + 40*HPL[{3}, -S^2] + 48*Zeta[3]) + HPL[{1}, -S^2]*((-151*Pi^4)/45 + 4*Pi^2*(1 + S^2) - (36*(1 + 2*S^2 + S^4))/S^2 + ((-10*Pi^2)/3 + (24*(-1 + S^4))/S^2)*HPL[{2}, -S^2] - 20*HPL[{2}, -S^2]^2 + (4*(1 + S^2)*(-1 + 5*S^2)*HPL[{3}, -S^2])/S^2 - (24*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + 24*(1 + S^2)*Zeta[3])) + Log[T]*(200 - (28*Pi^4*S^2)/15 - (4*Pi^2*(-9 + 8*S^2))/3 + (HPL[{0}, S^2]^5*HPL[{1}, -S^2])/2 + (16*Pi^2*HPL[{1}, -S^2]^4)/3 + (8*HPL[{1}, -S^2]^6)/3 + HPL[{0}, S^2]^4*(-2*S^2 + (-1 - S^2)*HPL[{1}, -S^2] + (3*HPL[{1}, -S^2]^2)/2) + (2*Pi^2 + (8*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + 8*HPL[{3}, -S^2]^2 + ((-4*Pi^2)/3 - (32*(-1 + S^4))/S^2)*HPL[{4}, -S^2] + HPL[{0}, S^2]^3*((2*(3 + 4*S^2))/3 - (4*(1 + S^2)*HPL[{1}, -S^2]^2)/3 + (40*HPL[{1}, -S^2]^3)/9 + (2*(1 + S^2)*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((25*Pi^2)/9 - (8*(1 + S^2))/3 + (14*HPL[{2}, -S^2])/3) + 2*HPL[{3}, -S^2] - (16*HPL[{2, 1}, -S^2])/3) - 32*HPL[{2, 1}, -S^2]^2 + HPL[{3}, -S^2]*((-8*(-2 + S^4))/S^2 + 32*HPL[{2, 1}, -S^2]) + ((-8*Pi^2)/3 + (48*(-1 + S^4))/S^2)*HPL[{3, 1}, -S^2] + ((16*Pi^2)/3 - (96*(-1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]^2*(-6*Pi^2*S^2 - 2*(-9 + 16*S^2) - 4*(1 + S^2)*HPL[{1}, -S^2]^3 + 6*HPL[{1}, -S^2]^4 + ((2*Pi^2)/3 - (4*(-3 - 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + 2*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*(6*Pi^2 - 12*(1 + S^2) + 10*HPL[{2}, -S^2]) - 4*HPL[{4}, -S^2] + HPL[{1}, -S^2]*(-3*Pi^2*(1 + S^2) - (6*(-1 + 2*S^2 + 3*S^4))/S^2 - (2*(-3 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - 20*HPL[{2, 1}, -S^2]) - 8*HPL[{3, 1}, -S^2] + 16*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]*((2*Pi^4)/9 - (64*(-1 + S^4))/S^2 - (8*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) - 16*HPL[{4}, -S^2] - 32*HPL[{3, 1}, -S^2] + 64*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]*(88*(1 + S^2) + (2*Pi^2*(6 + 7*S^2))/3 + 8*HPL[{1}, -S^2]^5 + (4*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + HPL[{1}, -S^2]^3*((100*Pi^2)/9 + 32*HPL[{2}, -S^2]) + ((8*Pi^2)/3 + 8*(1 + S^2))*HPL[{3}, -S^2] + (16*(1 + S^2)*HPL[{4}, -S^2])/S^2 + 24*HPL[{5}, -S^2] + HPL[{1}, -S^2]^2*((-4*Pi^2*(1 + S^2))/3 + (12*(1 + 2*S^2 + S^4))/S^2 + (12*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 + 8*HPL[{3}, -S^2] - 96*HPL[{2, 1}, -S^2]) + HPL[{2}, -S^2]*((4*Pi^2*(1 + S^2))/S^2 + (12*(1 + S^2)*(3 + S^2))/S^2 - 40*HPL[{2, 1}, -S^2]) + ((-40*Pi^2)/3 - 48*(1 + S^2))*HPL[{2, 1}, -S^2] - (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - 8*HPL[{4, 1}, -S^2] + (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + HPL[{1}, -S^2]*((61*Pi^4)/15 - (8*Pi^2*(1 + S^2))/3 + (36*(1 + 2*S^2 + S^4))/S^2 + ((38*Pi^2)/3 + (24*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + 20*HPL[{2}, -S^2]^2 + (4*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 + 8*HPL[{4}, -S^2] - (24*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - 96*HPL[{3, 1}, -S^2] + 192*HPL[{2, 1, 1}, -S^2]) + 80*HPL[{2, 2, 1}, -S^2] + 256*HPL[{3, 1, 1}, -S^2] - 192*HPL[{2, 1, 1, 1}, -S^2]) + HPL[{1}, -S^2]^3*((-4*Pi^2*(1 + S^2))/3 + (8*(1 + 2*S^2 + S^4))/S^2 - (8*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - (80*HPL[{3}, -S^2])/3 - 32*Zeta[3]) - 24*S^2*Zeta[3] + HPL[{2, 1}, -S^2]*((24*(-1 + S^4))/S^2 + 32*Zeta[3]) + HPL[{1}, -S^2]^2*((151*Pi^4)/45 - 4*Pi^2*(1 + S^2) + (36*(1 + 2*S^2 + S^4))/S^2 + ((10*Pi^2)/3 - (24*(-1 + S^4))/S^2)*HPL[{2}, -S^2] + 20*HPL[{2}, -S^2]^2 - (4*(1 + S^2)*(-1 + 5*S^2)*HPL[{3}, -S^2])/S^2 + (24*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - 24*(1 + S^2)*Zeta[3]) + HPL[{1}, -S^2]*((-14*Pi^4*(1 + S^2))/15 - (4*Pi^2*(-1 + S^4))/S^2 + (88*(1 + 2*S^2 + S^4))/S^2 + (4*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((-20*Pi^2)/3 - (8*(-1 + 4*S^2 + 5*S^4))/S^2)*HPL[{3}, -S^2] - (16*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + 40*HPL[{5}, -S^2] + ((-20*Pi^2)/3 + (48*(-1 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (24*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + 80*HPL[{3, 2}, -S^2] + 240*HPL[{4, 1}, -S^2] - (48*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 160*HPL[{2, 2, 1}, -S^2] + 320*HPL[{3, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-48*(-1 + S^4))/S^2 - (4*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) - 40*HPL[{3}, -S^2] - 80*HPL[{2, 1}, -S^2] - 40*Zeta[3]) + (-8*Pi^2 - 48*(1 + S^2))*Zeta[3] - 64*Zeta[5])) + HPL[{0}, S^2]*((-2798*Pi^6)/2835 - 100*(1 + S^2) - 6*Pi^2*(1 + S^2) - (4*HPL[{1}, -S^2]^6)/3 + HPL[{1}, -S^2]^4*((-25*Pi^2)/9 - 8*HPL[{2}, -S^2]) + ((-4*Pi^2)/3 - (4*(1 + S^2))/S^2)*HPL[{2}, -S^2]^2 - (4*HPL[{2}, -S^2]^3)/3 + 4*HPL[{3}, -S^2]^2 + ((8*Pi^2)/3 - (16*(1 + S^2))/S^2)*HPL[{4}, -S^2] - 24*(1 + S^2)*HPL[{5}, -S^2] + 80*HPL[{6}, -S^2] + 20*HPL[{2, 1}, -S^2]^2 + HPL[{1}, -S^2]^3*((4*Pi^2*(1 + S^2))/9 - (4*(1 + 2*S^2 + S^4))/S^2 - (4*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 - (8*HPL[{3}, -S^2])/3 + 32*HPL[{2, 1}, -S^2]) + (4*Pi^2 + (24*(1 + S^2))/S^2)*HPL[{3, 1}, -S^2] + 16*(1 + S^2)*HPL[{4, 1}, -S^2] - 32*HPL[{5, 1}, -S^2] + HPL[{1}, -S^2]^2*((-61*Pi^4)/30 + (4*Pi^2*(1 + S^2))/3 - (18*(1 + 2*S^2 + S^4))/S^2 + ((-19*Pi^2)/3 - (12*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - 10*HPL[{2}, -S^2]^2 - (2*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 - 4*HPL[{4}, -S^2] + (12*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + 48*HPL[{3, 1}, -S^2] - 96*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]*((-7*Pi^4)/15 - (4*Pi^2*(1 + S^2))/S^2 - (4*(8 + 11*S^2 + 3*S^4))/S^2 - 8*HPL[{4}, -S^2] + 8*(1 + S^2)*HPL[{2, 1}, -S^2] + 24*HPL[{3, 1}, -S^2] - 40*HPL[{2, 1, 1}, -S^2]) + (-12*Pi^2 - (48*(1 + S^2))/S^2)*HPL[{2, 1, 1}, -S^2] - 16*(1 + S^2)*HPL[{2, 2, 1}, -S^2] - 56*(1 + S^2)*HPL[{3, 1, 1}, -S^2] - 32*HPL[{3, 2, 1}, -S^2] - 104*HPL[{4, 1, 1}, -S^2] + 48*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2] + 96*HPL[{3, 1, 1, 1}, -S^2] - 192*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((-4*Pi^2*(1 + S^2))/3 - (4*(2 + 2*S^2 + 3*S^4))/S^2 - 8*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + 12*S^2*Zeta[3] - 16*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((8*Pi^2*(1 + S^2))/3 + (12*(1 + 4*S^2 + 3*S^4))/S^2 + 8*Zeta[3]) + HPL[{1}, -S^2]*((Pi^4*(1 + S^2))/9 + (2*Pi^2*(-3 - 2*S^2 + S^4))/(3*S^2) - (44*(1 + 2*S^2 + S^4))/S^2 - (2*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((-2*Pi^2)/3 - (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2] - (8*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 + 12*HPL[{5}, -S^2] + ((38*Pi^2)/3 + (24*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (12*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 - 8*HPL[{3, 2}, -S^2] - 16*HPL[{4, 1}, -S^2] - (24*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 - 80*HPL[{2, 2, 1}, -S^2] - 256*HPL[{3, 1, 1}, -S^2] + 192*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-24*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(3 + 5*S^2 + 2*S^4))/(3*S^2) + 4*HPL[{3}, -S^2] + 40*HPL[{2, 1}, -S^2] - 4*Zeta[3]) - 4*Pi^2*Zeta[3] - 32*Zeta[5])) + HPL[{2}, -S^2]*((56*(-1 + S^4))/S^2 + (Pi^4*(-4 - S^2 + 3*S^4))/(9*S^2) + (2*Pi^2*(-9 - 4*S^2 + 6*S^4))/(3*S^2) + (8*Pi^2*HPL[{3}, -S^2])/3 + (4*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 + 40*HPL[{5}, -S^2] + (20*Pi^2*HPL[{2, 1}, -S^2])/3 + (8*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 - 16*HPL[{3, 2}, -S^2] - 80*HPL[{4, 1}, -S^2] - (16*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 + 48*HPL[{3, 1, 1}, -S^2] + 96*HPL[{2, 1, 1, 1}, -S^2] + 4*Pi^2*Zeta[3] + 32*Zeta[5]) + HPL[{1}, -S^2]^2*((7*Pi^4*(1 + S^2))/15 + (2*Pi^2*(-1 + S^4))/S^2 - (44*(1 + 2*S^2 + S^4))/S^2 - (2*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((10*Pi^2)/3 + (4*(-1 + 4*S^2 + 5*S^4))/S^2)*HPL[{3}, -S^2] + (8*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 20*HPL[{5}, -S^2] + ((10*Pi^2)/3 - (24*(-1 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (12*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - 40*HPL[{3, 2}, -S^2] - 120*HPL[{4, 1}, -S^2] + (24*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 80*HPL[{2, 2, 1}, -S^2] - 160*HPL[{3, 1, 1}, -S^2] + (4*Pi^2 + 24*(1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*((24*(-1 + S^4))/S^2 + (2*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) + 20*HPL[{3}, -S^2] + 40*HPL[{2, 1}, -S^2] + 20*Zeta[3]) + 32*Zeta[5]) + HPL[{1}, -S^2]*((-283*Pi^6)/810 + (14*Pi^4*(1 + S^2))/15 - (100*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(-9 - 7*S^2 + 2*S^4))/(3*S^2) + ((-8*Pi^2)/3 - (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + 4*HPL[{3}, -S^2]^2 + ((-4*Pi^2)/3 + (16*(-1 + S^4))/S^2)*HPL[{4}, -S^2] + (8*(1 + S^2)*(-3 + 2*S^2)*HPL[{5}, -S^2])/S^2 - 112*HPL[{6}, -S^2] + 40*HPL[{2, 1}, -S^2]^2 + (4*Pi^2 - (24*(-1 + S^4))/S^2)*HPL[{3, 1}, -S^2] - 16*(1 + S^2)*HPL[{3, 2}, -S^2] - (16*(1 + S^2)*(-1 + 4*S^2)*HPL[{4, 1}, -S^2])/S^2 + 56*HPL[{5, 1}, -S^2] + ((-20*Pi^2)/3 + (48*(-1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (16*(1 + S^2)^2*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(1 + S^2)*(7 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - (48*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + HPL[{2, 1}, -S^2]*((-48*(-1 + S^4))/S^2 - (4*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) - 40*Zeta[3]) + (48*(1 + S^2) + 4*Pi^2*(1 + S^2))*Zeta[3] + 8*Zeta[3]^2 + HPL[{3}, -S^2]*((2*Pi^2*(-1 + 2*S^2 + 3*S^4))/(3*S^2) + (8*(-1 + 4*S^2 + 5*S^4))/S^2 - 40*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + HPL[{2}, -S^2]*((-26*Pi^4)/45 + (44*(-1 + S^4))/S^2 + (4*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) + 8*(1 + S^2)*HPL[{3}, -S^2] - 8*HPL[{4}, -S^2] + (8*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + 40*HPL[{3, 1}, -S^2] - 80*HPL[{2, 1, 1}, -S^2] + 8*(1 + S^2)*Zeta[3]) + 32*(1 + S^2)*Zeta[5]);
e4T2F2=25/8 + (13*Pi^4*(2 + 19*S^2))/360 + (Pi^2*(-13 + 48*S^2))/12 + (Pi^6*(3962 + 7797*S^2))/45360 + (S^2*HPL[{0}, S^2]^7)/96 + ((4*Pi^2*(1 + S^4))/(15*S^2) + (7*(1 + 2*S^2 + S^4))/(5*S^2))*HPL[{1}, -S^2]^5 + ((1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + (2*(1 + S^4)*HPL[{1}, -S^2]^7)/(21*S^2) + HPL[{0}, S^2]^6*((1 + 6*S^2)/96 + ((1 + S^4)*HPL[{1}, -S^2])/(96*S^2)) + HPL[{0}, S^2]^5*((Pi^2*S^2)/12 + (1 + S^2)/16 + ((1 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(16*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^2)/(16*S^2)) + ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(6*S^2) + ((4 - 2*S^2 + 3*S^4)*HPL[{3}, -S^2]^2)/(2*S^2) + ((7*Pi^2*(1 + S^4))/(3*S^2) + (-31 + 2*S^2 + 28*S^4)/(2*S^2))*HPL[{5}, -S^2] + (14*(-5 + 2*S^2 + 4*S^4)*HPL[{6}, -S^2])/S^2 + (100*(1 + S^4)*HPL[{7}, -S^2])/S^2 + ((-7 - 20*S^2 - 7*S^4)*HPL[{2, 1}, -S^2]^2)/(2*S^2) + HPL[{0}, S^2]^4*((-7 + 24*S^2)/32 + (Pi^2*(8 + 33*S^2))/96 + ((1 + 6*S^2 + 5*S^4)*HPL[{1}, -S^2]^2)/(16*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^3)/(8*S^2) + ((-2 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(16*S^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^4))/(12*S^2) + (-7 + 8*S^2 + 15*S^4)/(32*S^2) + ((1 + S^4)*HPL[{2}, -S^2])/(8*S^2)) + ((1 + S^4)*HPL[{3}, -S^2])/(8*S^2) + ((-1 - S^4)*HPL[{2, 1}, -S^2])/(4*S^2)) + ((4*Pi^2*(1 + S^4))/(3*S^2) + (3 + 18*S^2 + 10*S^4)/S^2)*HPL[{3, 2}, -S^2] + ((3*Pi^2*(1 + S^4))/S^2 + (26 + 58*S^2 + 17*S^4)/S^2)*HPL[{4, 1}, -S^2] - (20*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + ((24 - 14*S^2 - 17*S^4)*HPL[{5, 1}, -S^2])/S^2 - (60*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 - (156*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((10*Pi^2*(1 + S^4))/(3*S^2) + (13 + 36*S^2 + 13*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((8*Pi^2*(1 + S^4))/S^2 + (31 + 136*S^2 + 65*S^4)/(2*S^2))*HPL[{3, 1, 1}, -S^2] + (4*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 - (8*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + (27*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 - (136*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 - (276*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((-17*(-1 + S^4))/S^2 - (2*Pi^2*(1 + S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (12*(-1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (72*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (24*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (144*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (288*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (4 + (Pi^2*(8 + S^2))/6 + (S^2*HPL[{0}, S^2]^3)/2 + ((4*Pi^2*(1 + S^4))/(3*S^2) + (7*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2] + (5*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/S^2 + (10*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^2*((3 + S^2)/2 + (3*(1 + S^4)*HPL[{1}, -S^2])/(2*S^2)) + ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + HPL[{0}, S^2]*((4*Pi^2*S^2)/3 + 7*(1 + S^2) + (5*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2])/S^2 + (5*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + (2*(1 + S^4)*HPL[{2}, -S^2])/S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/S^2)*Log[T]^4 + (-2 - (2*(1 + S^2)^2*HPL[{1}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*(-2*(1 + S^2) - (2*(1 + S^4)*HPL[{1}, -S^2])/S^2))*Log[T]^5 + (2/3 + (2*S^2*HPL[{0}, S^2])/3 + (2*(1 + S^4)*HPL[{1}, -S^2])/(3*S^2))*Log[T]^6 + ((Pi^2*(-36 + 23*S^2))/12 + (-71 + 37*S^2)/2)*Zeta[3] + (-2 + 5*S^2)*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^4*(-1 - S^4))/(90*S^2) + (Pi^2*(-20 - 26*S^2 - S^4))/(12*S^2) + (-28 - 36*S^2 + 9*S^4)/(2*S^2) + (10*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((5 + 10*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((1 - 2*S^2)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((3*(1 + S^4))/(4*S^2) + (Pi^2*(2 + 8*S^2 + 3*S^4))/(12*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/S^2 + ((-1 - S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((34*(-1 + S^4))/S^2 + (Pi^2*(-7 + 10*S^2 + 14*S^4))/(6*S^2) - (12*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(-11 + 2*S^2 + 7*S^4))/(6*S^2) + (-28 + 9*S^2 + 22*S^4)/(2*S^2) - (8*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (6*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*((14*(1 + 2*S^2 + S^4))/(3*S^2) + (Pi^2*(7 + 16*S^2 + 9*S^4))/(12*S^2) + ((-1 + S^4)*HPL[{2}, -S^2])/S^2 - (5*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((37 - 9*S^2 - 31*S^4)/(2*S^2) + (Pi^2*(4 - 6*S^2 - 7*S^4))/(6*S^2) + (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((151*Pi^4*(1 + S^4))/(540*S^2) + (25*(1 + 2*S^2 + S^4))/(2*S^2) + (Pi^2*(103 + 260*S^2 + 157*S^4))/(72*S^2) + ((9*(-1 + S^4))/(2*S^2) + (5*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2] + (5*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) - (4*(4 + 5*S^2 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (4*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (2*(3 + 4*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(9 - 18*S^2 - 22*S^4))/(12*S^2) - (37*(-1 + S^4))/(2*S^2) - (7*Pi^4*(1 + S^4))/(30*S^2) + (12*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((5 + 10*S^2 + 2*S^4)*Zeta[3])/S^2) + HPL[{0}, S^2]^2*((3*(-27 + 64*S^2))/16 + (Pi^2*(-25 + 212*S^2))/96 + (Pi^4*(302 + 823*S^2))/1440 + ((1 + 3*S^2 + 2*S^4)*HPL[{1}, -S^2]^4)/(2*S^2) + (3*(1 + S^4)*HPL[{1}, -S^2]^5)/(10*S^2) + ((1 + 12*S^2 + 5*S^4)*HPL[{2}, -S^2]^2)/(16*S^2) + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^4))/(2*S^2) + (19 + 92*S^2 + 73*S^4)/(24*S^2) + (5*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((Pi^2*(1 + S^4))/(4*S^2) + (3*(-11 - 8*S^2 + 3*S^4))/(16*S^2))*HPL[{3}, -S^2] + ((-29 + 8*S^2 + 13*S^4)*HPL[{4}, -S^2])/(8*S^2) + (11*(1 + S^4)*HPL[{5}, -S^2])/(2*S^2) + ((1 - 36*S^2 - 27*S^4)/(8*S^2) - (3*Pi^2*(1 + S^4))/(4*S^2))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((3*Pi^2*(1 + 4*S^2 + 3*S^4))/(8*S^2) + (3 + 55*S^2 + 52*S^4)/(8*S^2) + ((1 + 10*S^2 + 9*S^4)*HPL[{2}, -S^2])/(4*S^2) - (5*(1 + S^4)*HPL[{2, 1}, -S^2])/(2*S^2)) + ((1 - 6*S^2 - 4*S^4)*HPL[{3, 1}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + ((-1 + 10*S^2 + 8*S^4)*HPL[{2, 1, 1}, -S^2])/(2*S^2) + (4*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (6*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-24 + 29*S^2)*Zeta[3])/8 + HPL[{1}, -S^2]*((151*Pi^4*(1 + S^4))/(720*S^2) + (-19 + 54*S^2 + 73*S^4)/(8*S^2) + (Pi^2*(-23 + 140*S^2 + 163*S^4))/(96*S^2) + ((11*Pi^2*(1 + S^4))/(24*S^2) + (-5 + 28*S^2 + 33*S^4)/(8*S^2))*HPL[{2}, -S^2] + (3*(1 + S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + ((-1 + S^4)*HPL[{3}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{4}, -S^2])/S^2 + ((-1 - 10*S^2 - 9*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) - (3*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (5*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (3*(-1 + S^4)*Zeta[3])/(2*S^2)) + HPL[{2}, -S^2]*((-10 + 13*S^4)/(4*S^2) + (Pi^2*(-13 + 22*S^2 + 14*S^4))/(48*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/(2*S^2) - (2*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (3*(1 + S^4)*Zeta[3])/(2*S^2))) + HPL[{0}, S^2]^3*((89*Pi^4*S^2)/360 + (39 + 56*S^2)/24 + (Pi^2*(52 + 57*S^2))/144 + (2*(2 + 5*S^2 + 3*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + (5*(1 + S^4)*HPL[{1}, -S^2]^4)/(18*S^2) + ((Pi^2*(1 + S^4))/(24*S^2) + (15 + 28*S^2 + 18*S^4)/(24*S^2))*HPL[{2}, -S^2] + ((1 + S^4)*HPL[{2}, -S^2]^2)/(8*S^2) + HPL[{1}, -S^2]^2*((25*Pi^2*(1 + S^4))/(72*S^2) + (35 + 108*S^2 + 73*S^4)/(48*S^2) + (7*(1 + S^4)*HPL[{2}, -S^2])/(12*S^2)) + ((5 + S^4)*HPL[{3}, -S^2])/(8*S^2) - (3*(1 + S^4)*HPL[{4}, -S^2])/(4*S^2) + ((-7 - 14*S^2 - 10*S^4)*HPL[{2, 1}, -S^2])/(12*S^2) + ((1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((2 - S^2)*Zeta[3])/2 + HPL[{1}, -S^2]*((9 + 29*S^2 + 20*S^4)/(8*S^2) + (Pi^2*(23 + 50*S^2 + 27*S^4))/(72*S^2) + ((5 + 14*S^2 + 9*S^4)*HPL[{2}, -S^2])/(12*S^2) - (7*(1 + S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((1 + S^4)*Zeta[3])/S^2)) + Log[T]^3*(-37/6 + (Pi^2*(-92 - 37*S^2))/36 + ((-8*Pi^2*(1 + S^4))/(3*S^2) - (14*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2]^2 - (20*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) - (10*(1 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + HPL[{0}, S^2]^3*((-20 - 17*S^2)/18 - (10*(1 + S^4)*HPL[{1}, -S^2])/(9*S^2)) + ((-37*(-1 + S^4))/(6*S^2) - (2*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] - (4*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^2*((-32 - 37*S^2)/12 - (2*(1 + 3*S^2 + 2*S^4)*HPL[{1}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 - (2*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((19 + 20*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S^2) + (4*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + HPL[{0}, S^2]*((Pi^2*(-50 - 47*S^2))/18 - (56*(1 + S^2))/3 - (10*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/S^2 - (20*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) - (4*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((-25*Pi^2*(1 + S^4))/(9*S^2) - (14*(1 + 2*S^2 + S^4))/S^2 - (8*(1 + S^4)*HPL[{2}, -S^2])/S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) - 4*(-2 + S^2)*Zeta[3] + HPL[{1}, -S^2]*((Pi^2*(-7 - 16*S^2 - 9*S^4))/(3*S^2) - (56*(1 + 2*S^2 + S^4))/(3*S^2) - (4*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (8*(1 + S^4)*Zeta[3])/S^2)) + Log[T]^2*(29/4 + (Pi^2*(65 + 68*S^2))/24 + (Pi^4*(302 + 111*S^2))/360 + (S^2*HPL[{0}, S^2]^5)/8 + ((8*Pi^2*(1 + S^4))/(3*S^2) + (14*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2]^3 + (5*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/S^2 + (2*(1 + S^4)*HPL[{1}, -S^2]^5)/S^2 + HPL[{0}, S^2]^4*((3*(1 + S^2))/8 + (3*(1 + S^4)*HPL[{1}, -S^2])/(8*S^2)) + ((7 + 20*S^2 + 7*S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + HPL[{0}, S^2]^3*((2*Pi^2*S^2)/3 + (22 + 27*S^2)/12 + (2*(1 + S^2)*(2 + 3*S^2)*HPL[{1}, -S^2])/(3*S^2) + (5*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + ((1 + S^4)*HPL[{2}, -S^2])/(2*S^2)) + ((-47 - 80*S^2 - 13*S^4)/(4*S^2) + (Pi^2*(-1 - S^4))/S^2)*HPL[{3}, -S^2] + (15*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/(2*S^2) + (6*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((Pi^2*(-1 - S^4))/S^2 - (17*(-1 + S^4))/(2*S^2))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((Pi^2*(3 + 2*S^2))/2 + (17*(1 + 4*S^2))/8 + (3*(1 + S^2)*(1 + 2*S^2)*HPL[{1}, -S^2]^2)/S^2 + (3*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + ((-1 + 10*S^2 + 8*S^4)*HPL[{2}, -S^2])/(4*S^2) + HPL[{1}, -S^2]*((3*Pi^2*(1 + S^4))/(2*S^2) + (19 + 92*S^2 + 73*S^4)/(8*S^2) + (5*(1 + S^4)*HPL[{2}, -S^2])/(2*S^2)) - (3*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) - (6*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (36*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (12*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + HPL[{0}, S^2]*((89*Pi^4*S^2)/90 + (75*(1 + S^2))/2 + (Pi^2*(64 + 69*S^2))/12 + (10*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/S^2 + (5*(1 + S^4)*HPL[{1}, -S^2]^4)/S^2 + ((3*Pi^2*(1 + S^4))/(2*S^2) + (7 + 19*S^2 + 12*S^4)/S^2)*HPL[{2}, -S^2] + (5*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + HPL[{1}, -S^2]^2*((25*Pi^2*(1 + S^4))/(6*S^2) + (21*(1 + 2*S^2 + S^4))/S^2 + (12*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((1 + S^2)*(3 + S^2)*HPL[{3}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{4}, -S^2])/S^2 - (12*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + HPL[{1}, -S^2]*((28*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(23 + 50*S^2 + 27*S^4))/(6*S^2) + (12*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (24*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) - (12*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2) + (24*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (48*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((-48 + 17*S^2)*Zeta[3])/2 + HPL[{1}, -S^2]^2*((28*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(7 + 16*S^2 + 9*S^4))/(2*S^2) + (6*(-1 + S^4)*HPL[{2}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (12*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((17*(-1 + S^4))/S^2 + (Pi^2*(-7 + 10*S^2 + 14*S^4))/(12*S^2) - (6*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (6*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((151*Pi^4*(1 + S^4))/(180*S^2) + (75*(1 + 2*S^2 + S^4))/(2*S^2) + (Pi^2*(103 + 260*S^2 + 157*S^4))/(24*S^2) + ((27*(-1 + S^4))/(2*S^2) + (5*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2}, -S^2] + (5*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 - (4*(1 + S^2)*(4 + S^2)*HPL[{3}, -S^2])/S^2 - (12*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (6*(3 + 4*S^2 + S^4)*Zeta[3])/S^2)) + 3*(-8 + 9*S^2)*Zeta[5] + HPL[{1}, -S^2]*((283*Pi^6*(1 + S^4))/(3240*S^2) + (325*(1 + 2*S^2 + S^4))/(8*S^2) + (Pi^2*(14 + 51*S^2 + 37*S^4))/(6*S^2) + (Pi^4*(23 + 118*S^2 + 95*S^4))/(120*S^2) + ((2*Pi^2*(1 + S^4))/(3*S^2) + (7*(1 + 2*S^2 + S^4))/(2*S^2))*HPL[{2}, -S^2]^2 + ((-1 - S^4)*HPL[{3}, -S^2]^2)/S^2 + ((Pi^2*(1 + S^4))/(3*S^2) + (-27 - 4*S^2 + 23*S^4)/(2*S^2))*HPL[{4}, -S^2] + (5*(-1 + 2*S^2 + 3*S^4)*HPL[{5}, -S^2])/S^2 + (28*(1 + S^4)*HPL[{6}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((29 + 4*S^2 - 25*S^4)/(2*S^2) + (Pi^2*(-1 - S^4))/S^2)*HPL[{3, 1}, -S^2] + (2*(1 + S^2)*(7 + 3*S^2)*HPL[{3, 2}, -S^2])/S^2 + (10*(5 + 6*S^2 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (14*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((27*(-1 + S^4))/S^2 + (5*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (20*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (4*(7 + 20*S^2 + 13*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (24*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-2*Pi^2*(1 + S^2))/S^2 + (-53 - 57*S^2 - 4*S^4)/(2*S^2))*Zeta[3] - (2*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2}, -S^2]*((23*(-1 + S^4))/S^2 + (13*Pi^4*(1 + S^4))/(90*S^2) + (Pi^2*(-8 + 7*S^2 + 15*S^4))/(6*S^2) - ((1 + S^2)*(7 + 3*S^2)*HPL[{3}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (10*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-7 - 10*S^2 - 3*S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^2*(-9 - 10*S^2 - S^4))/(6*S^2) + (-37 - 25*S^2 + 12*S^4)/(2*S^2) + (10*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-49*(-1 + S^4))/(2*S^2) - (5*Pi^2*(-1 + 2*S^2 + 3*S^4))/(6*S^2) + (10*(1 + S^4)*Zeta[3])/S^2) - (16*(1 + S^2)*Zeta[5])/S^2) + HPL[{2}, -S^2]*((24*(-1 + S^4))/S^2 + (Pi^2*(-9 + 10*S^4))/(4*S^2) + (Pi^4*(-39 + 52*S^2 + 43*S^4))/(360*S^2) + ((-3 - 18*S^2 - 10*S^4)/(2*S^2) - (2*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] + ((-4 + 2*S^2 - 3*S^4)*HPL[{4}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-13 - 36*S^2 - 13*S^4)/(2*S^2) - (5*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + ((-3 - 10*S^2 - 4*S^4)*HPL[{3, 1}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + ((7 + 20*S^2 + 7*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (24*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-8 - 18*S^2 - 5*S^4)/(2*S^2) + (Pi^2*(-1 - S^4))/S^2)*Zeta[3] - (8*(1 + S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]^2*((213*(1 + 2*S^2 + S^4))/(8*S^2) + (Pi^2*(59 + 167*S^2 + 108*S^4))/(24*S^2) + (Pi^4*(109 + 302*S^2 + 193*S^4))/(360*S^2) + (5*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((-5*Pi^2*(1 + S^4))/(6*S^2) - (3*(19 + 20*S^2 + S^4))/(4*S^2))*HPL[{3}, -S^2] + (4*(-1 + S^4)*HPL[{4}, -S^2])/S^2 + (5*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-27*(-1 + S^4))/(2*S^2) - (5*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2, 1}, -S^2] - (6*(-1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (10*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (30*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (12*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (40*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((-65 - 76*S^2 - 11*S^4)/(4*S^2) + (Pi^2*(-1 - S^4))/S^2)*Zeta[3] + HPL[{2}, -S^2]*((49*(-1 + S^4))/(4*S^2) + (5*Pi^2*(-1 + 2*S^2 + 3*S^4))/(12*S^2) - (5*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (5*(1 + S^4)*Zeta[3])/S^2) - (8*(1 + S^4)*Zeta[5])/S^2) + HPL[{0}, S^2]*((1399*Pi^6*S^2)/5670 + (325*(1 + S^2))/8 + (Pi^4*(86 + 91*S^2))/144 + (Pi^2*(114 + 131*S^2))/24 + ((1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/S^2 + ((1 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + ((Pi^2*(1 + S^4))/(3*S^2) + (9 + 28*S^2 + 19*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 + ((1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^4*((25*Pi^2*(1 + S^4))/(36*S^2) + (7*(1 + 2*S^2 + S^4))/(2*S^2) + (2*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((-1 - S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-2*Pi^2*(1 + S^4))/(3*S^2) + (13 + 18*S^2 + 5*S^4)/(2*S^2))*HPL[{4}, -S^2] - (3*(-2 + S^2)*(4 + S^2)*HPL[{5}, -S^2])/(2*S^2) - (20*(1 + S^4)*HPL[{6}, -S^2])/S^2 - (5*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + HPL[{1}, -S^2]^3*((28*(1 + 2*S^2 + S^4))/(3*S^2) + (Pi^2*(23 + 50*S^2 + 27*S^4))/(18*S^2) + (4*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) + ((-33 - 80*S^2 - 47*S^4)/(4*S^2) + (Pi^2*(-1 - S^4))/S^2)*HPL[{3, 1}, -S^2] + ((-1 + 2*S^2)*HPL[{3, 2}, -S^2])/S^2 + ((-15 + 8*S^2 + 5*S^4)*HPL[{4, 1}, -S^2])/(2*S^2) + (8*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((3*Pi^2*(1 + S^4))/S^2 + (2*(7 + 19*S^2 + 12*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((61*Pi^4*(1 + S^4))/(120*S^2) + (75*(1 + 2*S^2 + S^4))/(4*S^2) + (Pi^2*(119 + 276*S^2 + 157*S^4))/(48*S^2) + ((19*Pi^2*(1 + S^4))/(12*S^2) + (19*(1 + 2*S^2 + S^4))/(2*S^2))*HPL[{2}, -S^2] + (5*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/S^2 + ((1 + S^4)*HPL[{4}, -S^2])/S^2 - (12*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2) + ((1 + S^2)*(9 + 11*S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (2*(15 + 32*S^2 + 17*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (26*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (24*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (24*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (48*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(2 - S^2))/2 - (3*(-3 + 2*S^2))/4)*Zeta[3] + 4*S^2*Zeta[3]^2 + HPL[{2}, -S^2]*((7*Pi^4*(1 + S^4))/(60*S^2) + (3*(13 + 32*S^2 + 19*S^4))/(4*S^2) + (Pi^2*(29 + 66*S^2 + 42*S^4))/(24*S^2) + ((1 - 2*S^2)*HPL[{3}, -S^2])/(2*S^2) + (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 - ((1 + S^2)*(9 + 11*S^2)*HPL[{2, 1}, -S^2])/(2*S^2) - (6*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (10*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-1 + 2*S^2)*Zeta[3])/(2*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-19 - 38*S^2 - 22*S^4))/(12*S^2) - (19*(2 + 3*S^2 + S^4))/(2*S^2) - (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^2*(9 + 2*S^2 + 2*S^4))/(12*S^2) + (23 + 23*S^2 + 15*S^4)/(4*S^2) + (2*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/S^2) - 4*(-2 + S^2)*Zeta[5] + HPL[{1}, -S^2]*((213*(1 + 2*S^2 + S^4))/(8*S^2) + (Pi^2*(83 + 199*S^2 + 116*S^4))/(24*S^2) + (Pi^4*(173 + 366*S^2 + 193*S^4))/(360*S^2) + (5*(1 + S^2)^2*HPL[{2}, -S^2]^2)/(2*S^2) + ((Pi^2*(1 + S^4))/(6*S^2) + (13 + 20*S^2 + 7*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-19*Pi^2*(1 + S^4))/(6*S^2) - (19*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (12*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (24*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (64*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(1 + S^4))/S^2 + (-5 - 4*S^2 + S^4)/(4*S^2))*Zeta[3] + HPL[{2}, -S^2]*((57*(1 + 2*S^2 + S^4))/(4*S^2) + (Pi^2*(17 + 38*S^2 + 21*S^4))/(12*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + ((1 + S^4)*Zeta[3])/S^2) + (8*(1 + S^4)*Zeta[5])/S^2)) + Log[T]*(-25/4 + (Pi^4*(-238 - 241*S^2))/360 + (Pi^2*(-12 - 55*S^2))/12 + ((-4*Pi^2*(1 + S^4))/(3*S^2) - (7*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2]^4 - (2*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/S^2 - (2*(1 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + HPL[{0}, S^2]^5*((-1 - S^2)/8 + ((-1 - S^4)*HPL[{1}, -S^2])/(8*S^2)) + HPL[{0}, S^2]^4*((-2 - 11*S^2)/16 - ((1 + S^2)*(1 + 5*S^2)*HPL[{1}, -S^2])/(8*S^2) - (3*(1 + S^4)*HPL[{1}, -S^2]^2)/(8*S^2)) + ((Pi^2*(-1 - S^4))/(2*S^2) - (5*(3 + 4*S^2 + 3*S^4))/(4*S^2))*HPL[{2}, -S^2]^2 - (2*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-10*(-1 + S^4))/S^2 + (Pi^2*(1 + S^4))/(3*S^2))*HPL[{4}, -S^2] + ((-6 - 10*S^2 - 7*S^4)*HPL[{5}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + HPL[{3}, -S^2]*((31 + 59*S^2 + S^4)/(2*S^2) + (Pi^2*(10 + 10*S^2 + 3*S^4))/(6*S^2) - (8*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) + HPL[{0}, S^2]^3*((-53 - 80*S^2)/24 + (Pi^2*(-50 - 47*S^2))/72 - (2*(1 + S^2)*(2 + 3*S^2)*HPL[{1}, -S^2]^2)/(3*S^2) - (10*(1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) - ((3 + 2*S^2)*(1 + 4*S^2)*HPL[{2}, -S^2])/(12*S^2) + HPL[{1}, -S^2]*((-35 - 108*S^2 - 73*S^4)/(24*S^2) - (25*Pi^2*(1 + S^4))/(36*S^2) - (7*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((-1 - S^4)*HPL[{3}, -S^2])/(2*S^2) + (4*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) + ((37*(-1 + S^4))/(2*S^2) + (2*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1}, -S^2] - (2*(9 + 10*S^2 + 4*S^4)*HPL[{3, 2}, -S^2])/S^2 + ((-55 - 60*S^2 - 23*S^4)*HPL[{4, 1}, -S^2])/S^2 + ((-37*(-1 + S^4))/S^2 - (4*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]^2*((13 - 110*S^2)/8 + (Pi^2*(-44 - 103*S^2))/48 - (2*(1 + 3*S^2 + 2*S^4)*HPL[{1}, -S^2]^3)/S^2 - (3*(1 + S^4)*HPL[{1}, -S^2]^4)/(2*S^2) + ((9 - 20*S^2 - 39*S^4)/(8*S^2) + (Pi^2*(-1 - S^4))/(6*S^2))*HPL[{2}, -S^2] + ((-1 - S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + HPL[{1}, -S^2]^2*((-19 - 92*S^2 - 73*S^4)/(8*S^2) - (3*Pi^2*(1 + S^4))/(2*S^2) - (5*(1 + S^4)*HPL[{2}, -S^2])/(2*S^2)) - ((-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(4*S^2) + ((1 + S^4)*HPL[{4}, -S^2])/S^2 + ((3 + 10*S^2 + 10*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + HPL[{1}, -S^2]*((-3 - 55*S^2 - 52*S^4)/(4*S^2) - (3*Pi^2*(1 + 4*S^2 + 3*S^4))/(4*S^2) + ((-1 - 10*S^2 - 9*S^4)*HPL[{2}, -S^2])/(2*S^2) + (5*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) + (2*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2) - (2*(13 + 20*S^2 + 13*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(5 + 10*S^2 + 8*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (24*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + HPL[{0}, S^2]*((Pi^4*(-122 - 117*S^2))/120 + (Pi^2*(-55 - 64*S^2))/8 - (213*(1 + S^2))/4 - (5*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/S^2 - (2*(1 + S^4)*HPL[{1}, -S^2]^5)/S^2 - ((1 + S^2)*(11 + 9*S^2)*HPL[{2}, -S^2]^2)/(4*S^2) + HPL[{1}, -S^2]^3*((-25*Pi^2*(1 + S^4))/(9*S^2) - (14*(1 + 2*S^2 + S^4))/S^2 - (8*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((-11 - 16*S^2 - 5*S^4)/(4*S^2) - (2*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] - ((1 + S^2)*(-5 + 9*S^2)*HPL[{4}, -S^2])/(2*S^2) - (6*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((10*Pi^2*(1 + S^4))/(3*S^2) + (2*(12 + 19*S^2 + 7*S^4))/S^2)*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(-15 - 38*S^2 - 20*S^4))/(12*S^2) - (19*(1 + 3*S^2 + 2*S^4))/(2*S^2) + (10*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) + HPL[{1}, -S^2]^2*((Pi^2*(-23 - 50*S^2 - 27*S^4))/(6*S^2) - (28*(1 + 2*S^2 + S^4))/S^2 - (12*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) + (12*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (24*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 + HPL[{1}, -S^2]*((Pi^2*(-119 - 276*S^2 - 157*S^4))/(24*S^2) - (61*Pi^4*(1 + S^4))/(60*S^2) - (75*(1 + 2*S^2 + S^4))/(2*S^2) + ((-19*Pi^2*(1 + S^4))/(6*S^2) - (19*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - (5*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 - (2*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (24*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2) - (20*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (64*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (48*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2) + ((83 - 30*S^2)/2 + Pi^2*(2 - S^2))*Zeta[3] + HPL[{2, 1}, -S^2]*((15*(-1 + S^4))/S^2 + (Pi^2*(-3 + 10*S^2 + 16*S^4))/(6*S^2) - (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((Pi^2*(-7 - 16*S^2 - 9*S^4))/(3*S^2) - (56*(1 + 2*S^2 + S^4))/(3*S^2) - (4*(-1 + S^4)*HPL[{2}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*((Pi^2*(-103 - 260*S^2 - 157*S^4))/(24*S^2) - (151*Pi^4*(1 + S^4))/(180*S^2) - (75*(1 + 2*S^2 + S^4))/(2*S^2) + ((-27*(-1 + S^4))/(2*S^2) - (5*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2}, -S^2] - (5*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + (4*(4 + 5*S^2 + S^4)*HPL[{3}, -S^2])/S^2 + (12*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (6*(3 + 4*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(23 - 10*S^2 - 38*S^4))/(12*S^2) + (Pi^4*(-1 - S^4))/(18*S^2) - (55*(-1 + S^4))/(2*S^2) + ((9 + 10*S^2 + 4*S^4)*HPL[{3}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((13 + 20*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (16*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((9 + 10*S^2 + 4*S^4)*Zeta[3])/S^2) - 8*(-2 + S^2)*Zeta[5] + HPL[{1}, -S^2]*((Pi^4*(-109 - 302*S^2 - 193*S^4))/(180*S^2) + (Pi^2*(-59 - 167*S^2 - 108*S^4))/(12*S^2) - (213*(1 + 2*S^2 + S^4))/(4*S^2) - (5*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((5*Pi^2*(1 + S^4))/(3*S^2) + (3*(19 + 20*S^2 + S^4))/(2*S^2))*HPL[{3}, -S^2] - (8*(-1 + S^4)*HPL[{4}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((27*(-1 + S^4))/S^2 + (5*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (12*(-1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (20*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (60*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (24*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (80*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((2*Pi^2*(1 + S^4))/S^2 + (65 + 76*S^2 + 11*S^4)/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-49*(-1 + S^4))/(2*S^2) - (5*Pi^2*(-1 + 2*S^2 + 3*S^4))/(6*S^2) + (10*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (10*(1 + S^4)*Zeta[3])/S^2) + (16*(1 + S^4)*Zeta[5])/S^2));
e4T3F1=(183*(1 + S^2))/(8*S) - (Pi^4*S*(-432 + 155*S^2))/360 + (Pi^2*(25 + 144*S^2 - 27*S^4))/(16*S) - (Pi^6*S*(-7179 - 3804*S^2 + 1394*S^4))/(7560*(1 + S^2)) + (S*HPL[{0}, S^2]^7)/48 + ((8*Pi^2*S)/15 - (2*(1 - 2*S^2 - 2*S^4 + S^6))/(5*S^3))*HPL[{1}, -S^2]^5 + (2*S*HPL[{1}, -S^2]^6)/(1 + S^2) + (4*S*HPL[{1}, -S^2]^7)/21 + HPL[{0}, S^2]^6*(-(S*(-9 - 6*S^2 + 2*S^4))/(32*(1 + S^2)) + (S*HPL[{1}, -S^2])/48) + HPL[{0}, S^2]^5*((Pi^2*S)/6 - (3*S^3)/8 + (3*S*HPL[{1}, -S^2])/(8*(1 + S^2)) + (S*HPL[{1}, -S^2]^2)/8) + ((1 + 2*S^4 - S^6)*HPL[{2}, -S^2]^3)/(3*S^3) + ((1 - 3*S^4 + 2*S^6 + S^8)*HPL[{3}, -S^2]^2)/(S^3*(1 + S^2)) + ((14*Pi^2*S)/3 + (-60 + 31*S^2 + 10*S^4 - 40*S^6)/S^3)*HPL[{5}, -S^2] - (4*(-15 - 15*S^2 - 77*S^4 - 41*S^6 + 15*S^8)*HPL[{6}, -S^2])/(S^3*(1 + S^2)) + 200*S*HPL[{7}, -S^2] - (2*(2 + 10*S^4 - S^6 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)) + HPL[{0}, S^2]^4*(-(S*(-44 + 15*S^2))/32 - (Pi^2*S*(-78 - 49*S^2 + 17*S^4))/(48*(1 + S^2)) + ((1 + 15*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2]^2)/(8*S*(1 + S^2)) + (S*HPL[{1}, -S^2]^3)/4 + ((1 + S^2 + 5*S^4 + S^6 - S^8)*HPL[{2}, -S^2])/(8*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*S)/6 + (-1 + 4*S^2 + 3*S^4 - 2*S^6)/(8*S^3) + (S*HPL[{2}, -S^2])/4) + (S*HPL[{3}, -S^2])/4 - (S*HPL[{2, 1}, -S^2])/2) + ((8*Pi^2*S)/3 - 2*S*(-5 + 4*S^2))*HPL[{3, 2}, -S^2] + (6*Pi^2*S - (2*(-10 + 11*S^2 - 8*S^4 + 10*S^6))/S^3)*HPL[{4, 1}, -S^2] - 40*S*HPL[{4, 3}, -S^2] + (2*(-10 - 10*S^2 - 55*S^4 - 24*S^6 + 10*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)) - 120*S*HPL[{5, 2}, -S^2] - 312*S*HPL[{6, 1}, -S^2] + ((20*Pi^2*S)/3 - (2*(4 - 13*S^2 - 5*S^4 + 4*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + (16*Pi^2*S + (-40 + 87*S^2 + 29*S^4 - 16*S^6)/S^3)*HPL[{3, 1, 1}, -S^2] - (8*(-1 - 2*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 - 16*S*HPL[{3, 2, 2}, -S^2] - 80*S*HPL[{3, 3, 1}, -S^2] - (4*(-10 - 27*S^4 + 10*S^6)*HPL[{4, 1, 1}, -S^2])/S^3 - 80*S*HPL[{4, 1, 2}, -S^2] - 272*S*HPL[{4, 2, 1}, -S^2] - 552*S*HPL[{5, 1, 1}, -S^2] + (-4*Pi^2*S - (2*(-12 + 39*S^2 + 13*S^4 + 12*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] + (24*(-1 - 2*S^4 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/S^3 + 48*S*HPL[{3, 1, 1, 2}, -S^2] + 48*S*HPL[{3, 1, 2, 1}, -S^2] + 48*S*HPL[{3, 2, 1, 1}, -S^2] + 144*S*HPL[{4, 1, 1, 1}, -S^2] - (48*(-1 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 - 96*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 288*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 576*S*HPL[{3, 1, 1, 1, 1}, -S^2] + (-(Pi^2*S*(-14 - S^2 + S^4))/(3*(1 + S^2)) + S*HPL[{0}, S^2]^3 + ((8*Pi^2*S)/3 - (2*(1 - 2*S^2 - 2*S^4 + S^6))/S^3)*HPL[{1}, -S^2] + (30*S*HPL[{1}, -S^2]^2)/(1 + S^2) + (20*S*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*(-(S*(-13 - 2*S^2 + 2*S^4))/(2*(1 + S^2)) + 3*S*HPL[{1}, -S^2]) - (2*(-1 - 2*S^4 + S^6)*HPL[{2}, -S^2])/S^3 + HPL[{0}, S^2]*((8*Pi^2*S)/3 - 2*S*(-2 + S^2) + (30*S*HPL[{1}, -S^2])/(1 + S^2) + 10*S*HPL[{1}, -S^2]^2 + 4*S*HPL[{2}, -S^2]) - 4*S*HPL[{3}, -S^2])*Log[T]^4 + ((-12*S*HPL[{1}, -S^2])/(1 + S^2) - 4*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-6*S)/(1 + S^2) - 4*S*HPL[{1}, -S^2]))*Log[T]^5 + ((2*S)/(1 + S^2) + (4*S*HPL[{0}, S^2])/3 + (4*S*HPL[{1}, -S^2])/3)*Log[T]^6 + ((S*(95 + 4*S^2))/4 + (Pi^2*S*(13 + 12*S^2))/6)*Zeta[3] - (2*S*(-7 - 8*S^2 + 2*S^4)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1, 1}, -S^2]*((43 + 68*S^2 + 108*S^4 - 43*S^6)/(2*S^3) + (Pi^2*(12 + 10*S^2 + 31*S^4 + 10*S^6 - 8*S^8))/(3*S^3*(1 + S^2)) - 24*S*Zeta[3]) + HPL[{4}, -S^2]*((8 + 63*S^2 + 67*S^4 - 23*S^6)/(2*S^3) + (Pi^2*(8 + 9*S^2 + 40*S^4 + 23*S^6 - 10*S^8))/(6*S^3*(1 + S^2)) - 16*S*HPL[{2, 1}, -S^2] - 12*S*Zeta[3]) + HPL[{1}, -S^2]^4*((-7*(1 + S^2)*(3 - 14*S^2 + 3*S^4))/(24*S^3) + (Pi^2*(1 + 54*S^2 + 3*S^4 - 2*S^6))/(12*S*(1 + S^2)) + ((1 + 4*S^4 - S^6)*HPL[{2}, -S^2])/S^3 - (10*S*HPL[{3}, -S^2])/3 - 4*S*Zeta[3]) + HPL[{2}, -S^2]^2*((7 - 11*S^2 - 3*S^4 + 7*S^6)/(4*S^3) + (Pi^2*(4 + S^2 + 18*S^4 - S^6 + 2*S^8))/(12*S^3*(1 + S^2)) - 2*S*HPL[{3}, -S^2] - 2*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((-14 - 51*S^2 - 71*S^4 + 29*S^6)/(2*S^3) + (Pi^2*(-6 - 5*S^2 - 17*S^4 - 5*S^6 + 4*S^8))/(3*S^3*(1 + S^2)) + 16*S*Zeta[3]) + HPL[{3}, -S^2]*(-(Pi^4*S)/45 + (Pi^2*(-16 + 5*S^2 + S^4))/(12*S^3) + (-1 + 99*S^2 + 34*S^4 + 3*S^6)/(4*S^3) + 20*S*HPL[{4}, -S^2] + (2*(-2 + 7*S^2 - 2*S^4 + 4*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 24*S*HPL[{3, 1}, -S^2] - 24*S*HPL[{2, 1, 1}, -S^2] - (6*S*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((151*Pi^4*S)/270 - (11*(1 + S^2)*(1 - 26*S^2 + S^4))/(24*S^3) - (Pi^2*(1 + S^2)*(4 - 14*S^2 + 5*S^4))/(6*S^3) + ((5*Pi^2*S)/9 + (3 + 29*S^2 + 23*S^4 - 3*S^6)/(3*S^3))*HPL[{2}, -S^2] + (10*S*HPL[{2}, -S^2]^2)/3 - (2*(-1 - 3*S^2 + 14*S^4 - 9*S^6 + 5*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) + (4*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (2*(-1 + 6*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-7*Pi^4*S)/15 + (Pi^2*(12 - 39*S^2 - 14*S^4 - 8*S^6))/(6*S^3) + (4 - 225*S^2 - 95*S^4 - 4*S^6)/(4*S^3) + 24*S*HPL[{3, 1}, -S^2] + 48*S*HPL[{2, 1, 1}, -S^2] + (2*(-2 + 7*S^2 - 2*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^3*((89*Pi^4*S)/180 - (Pi^2*S*(-5 + 98*S^2))/72 + (30 + 191*S^2 - 7*S^4)/(96*S) + ((1 + 36*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + (5*S*HPL[{1}, -S^2]^4)/9 + ((Pi^2*S)/12 + (18 + 15*S^2 + 25*S^4 - 4*S^6)/(24*S^3))*HPL[{2}, -S^2] + (S*HPL[{2}, -S^2]^2)/4 + HPL[{1}, -S^2]^2*((25*Pi^2*S)/36 + (-6 + 19*S^2 + 11*S^4 - 14*S^6)/(12*S^3) + (7*S*HPL[{2}, -S^2])/6) + ((-1 - 3*S^2 + 2*S^4)*HPL[{3}, -S^2])/(4*S) - (3*S*HPL[{4}, -S^2])/2 + ((1 - 23*S^2 - 5*S^4 - 2*S^6)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) + 2*S*HPL[{2, 1, 1}, -S^2] - (S*(-1 + 2*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(21 - 188*S^2 + 71*S^4))/(48*S^3) + (Pi^2*(1 + 81*S^2 + 3*S^4 - 2*S^6))/(36*S*(1 + S^2)) + ((3 + S^2 + 21*S^4 + 3*S^6 + S^8)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)) - (7*S*HPL[{2, 1}, -S^2])/3 + 2*S*Zeta[3])) + Log[T]^3*((-5*(1 + S^2))/(2*S) + (Pi^2*S*(-11 + 6*S^2))/6 + ((-16*Pi^2*S)/3 + (4*(1 - 2*S^2 - 2*S^4 + S^6))/S^3)*HPL[{1}, -S^2]^2 - (40*S*HPL[{1}, -S^2]^3)/(1 + S^2) - (20*S*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*((2*S*(-14 + S^2))/(9*(1 + S^2)) - (20*S*HPL[{1}, -S^2])/9) + ((-4*Pi^2*S)/9 + (-18 - 19*S^2 - 33*S^4 + 18*S^6)/(3*S^3))*HPL[{2}, -S^2] - (8*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((S*(-11 + 6*S^2))/2 + ((-1 - 24*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)) - 6*S*HPL[{1}, -S^2]^2 - (4*S*HPL[{2}, -S^2])/3) - (20*S*(-2 + S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + 16*S*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]*((Pi^2*S*(-73 + 2*S^2))/(9*(1 + S^2)) + (7*S*(-11 + 3*S^2))/6 - (60*S*HPL[{1}, -S^2]^2)/(1 + S^2) - (40*S*HPL[{1}, -S^2]^3)/3 + (2*(-2 - S^2 - 10*S^4 + S^6)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-50*Pi^2*S)/9 + (4*(1 - 2*S^2 - 2*S^4 + S^6))/S^3 - 16*S*HPL[{2}, -S^2]) - (4*S*HPL[{3}, -S^2])/3 + 16*S*HPL[{2, 1}, -S^2]) - (8*S*(-1 + 2*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*((7*(1 + S^2)*(3 - 14*S^2 + 3*S^4))/(6*S^3) + (Pi^2*(-1 - 54*S^2 - 3*S^4 + 2*S^6))/(3*S*(1 + S^2)) + (4*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 + (40*S*HPL[{3}, -S^2])/3 + 16*S*Zeta[3])) + HPL[{0}, S^2]^2*(-(Pi^2*S*(-372 + 133*S^2))/96 - (3*(-25 - 263*S^2 + 54*S^4))/(32*S) - (Pi^4*S*(-2099 - 1206*S^2 + 440*S^4))/(720*(1 + S^2)) + ((1 + 24*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2]^4)/(4*S*(1 + S^2)) + (3*S*HPL[{1}, -S^2]^5)/5 + ((2 + S^2 + 8*S^4)*HPL[{2}, -S^2]^2)/(4*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*(Pi^2*S + (-2 + 6*S^2 + 5*S^4 - 3*S^6)/(2*S^3) + (5*S*HPL[{2}, -S^2])/3) + ((Pi^2*S)/2 + (-16 + S^2 + 3*S^4 - 8*S^6)/(8*S^3))*HPL[{3}, -S^2] + ((4 + 5*S^2 + 25*S^4 + 12*S^6 - 6*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)) + 11*S*HPL[{5}, -S^2] + ((-3*Pi^2*S)/2 + (12 - 39*S^2 - 15*S^4 - 4*S^6)/(4*S^3))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*(-((1 + S^2)*(21 - 136*S^2 + 43*S^4))/(16*S^3) - (3*Pi^2*(-1 - 18*S^2 - 3*S^4 + 2*S^6))/(8*S*(1 + S^2)) + ((3 + 2*S^2 + 21*S^4 + 6*S^6 - S^8)*HPL[{2}, -S^2])/(2*S^3*(1 + S^2)) - 5*S*HPL[{2, 1}, -S^2]) + ((-3 - 2*S^2 - 11*S^4 - 2*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 2*S*HPL[{3, 2}, -S^2] + ((6 + 4*S^2 + 19*S^4 + 4*S^6 - 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 8*S*HPL[{2, 2, 1}, -S^2] + 24*S*HPL[{3, 1, 1}, -S^2] - 12*S*HPL[{2, 1, 1, 1}, -S^2] + (S*(13 + 12*S^2)*Zeta[3])/4 + HPL[{2}, -S^2]*((43 + 30*S^2 + 70*S^4 - 15*S^6)/(16*S^3) + (Pi^2*(12 + 10*S^2 + 49*S^4 + 10*S^6 - 8*S^8))/(24*S^3*(1 + S^2)) - S*HPL[{3}, -S^2] - 4*S*HPL[{2, 1}, -S^2] - 3*S*Zeta[3]) + HPL[{1}, -S^2]*((151*Pi^4*S)/360 + (-11 + 391*S^2 + 307*S^4 - 95*S^6)/(32*S^3) + (Pi^2*(-4 + 14*S^2 + 11*S^4 - 7*S^6))/(8*S^3) + ((11*Pi^2*S)/12 + (3 + 25*S^2 + 21*S^4 - S^6)/(4*S^3))*HPL[{2}, -S^2] + (3*S*HPL[{2}, -S^2]^2)/2 + ((1 + 4*S^4 - S^6)*HPL[{3}, -S^2])/(2*S^3) + 2*S*HPL[{4}, -S^2] + ((-3 - 2*S^2 - 21*S^4 - 6*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 6*S*HPL[{3, 1}, -S^2] + 10*S*HPL[{2, 1, 1}, -S^2] - (3*(-1 - 5*S^2 + 2*S^4)*Zeta[3])/(2*S))) + Log[T]^2*((75*(1 + S^2))/(8*S) - (Pi^2*S*(-108 + 43*S^2))/24 - (Pi^4*S*(-225 - 46*S^2 + 28*S^4))/(60*(1 + S^2)) + (S*HPL[{0}, S^2]^5)/4 + ((16*Pi^2*S)/3 - (4*(1 - 2*S^2 - 2*S^4 + S^6))/S^3)*HPL[{1}, -S^2]^3 + (30*S*HPL[{1}, -S^2]^4)/(1 + S^2) + 4*S*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^4*(-(S*(-7 + 2*S^2)*(3 + 2*S^2))/(8*(1 + S^2)) + (3*S*HPL[{1}, -S^2])/4) + ((2 + 10*S^4 - S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + HPL[{0}, S^2]^3*((4*Pi^2*S)/3 - (S*(-5 + 8*S^2))/6 + ((1 + 36*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2])/(3*S*(1 + S^2)) + (10*S*HPL[{1}, -S^2]^2)/3 + S*HPL[{2}, -S^2]) + (-2*Pi^2*S + (-16 + 9*S^2 - S^4 + 8*S^6)/(2*S^3))*HPL[{3}, -S^2] - (2*(-4 - 15*S^4 + 4*S^6)*HPL[{4}, -S^2])/S^3 + 12*S*HPL[{5}, -S^2] + (-2*Pi^2*S + (12 - 39*S^2 - 13*S^4 - 12*S^6)/S^3)*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(-(S*(-108 + 43*S^2))/8 - (Pi^2*S*(-17 - 5*S^2 + 3*S^4))/(2*(1 + S^2)) - (3*(-1 - 24*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)) + 6*S*HPL[{1}, -S^2]^3 + ((6 + 4*S^2 + 19*S^4 + 4*S^6 - 2*S^8)*HPL[{2}, -S^2])/(2*S^3*(1 + S^2)) + HPL[{1}, -S^2]*(3*Pi^2*S - (3*(2 - 6*S^2 - 5*S^4 + 3*S^6))/(2*S^3) + 5*S*HPL[{2}, -S^2]) - 6*S*HPL[{2, 1}, -S^2]) + (12*(-1 - 2*S^4 + S^6)*HPL[{3, 1}, -S^2])/S^3 + 24*S*HPL[{3, 2}, -S^2] + 72*S*HPL[{4, 1}, -S^2] - (24*(-1 - 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + HPL[{0}, S^2]*((89*Pi^4*S)/45 + (Pi^2*(17*S - 14*S^3))/6 + (30 + 245*S^2 - 11*S^4)/(8*S) + (60*S*HPL[{1}, -S^2]^3)/(1 + S^2) + 10*S*HPL[{1}, -S^2]^4 + (3*Pi^2*S + (18 + 7*S^2 + 27*S^4 - 12*S^6)/(2*S^3))*HPL[{2}, -S^2] + 5*S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((25*Pi^2*S)/3 - (6*(1 - 2*S^2 - 2*S^4 + S^6))/S^3 + 24*S*HPL[{2}, -S^2]) + ((-1 + 2*S^2)*(1 + S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + 2*S*HPL[{4}, -S^2] - (6*(-1 + 10*S^2 + S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + HPL[{1}, -S^2]*((-7*(1 + S^2)*(3 - 14*S^2 + 3*S^4))/(4*S^3) + (Pi^2*(1 + 81*S^2 + 3*S^4 - 2*S^6))/(3*S*(1 + S^2)) + (6*(1 + 10*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + 4*S*HPL[{3}, -S^2] - 48*S*HPL[{2, 1}, -S^2]) - 24*S*HPL[{3, 1}, -S^2] + 48*S*HPL[{2, 1, 1}, -S^2]) + 48*S*HPL[{2, 2, 1}, -S^2] + 96*S*HPL[{3, 1, 1}, -S^2] + S*(13 + 12*S^2)*Zeta[3] + HPL[{1}, -S^2]^2*((-7*(1 + S^2)*(3 - 14*S^2 + 3*S^4))/(4*S^3) + (Pi^2*(1 + 54*S^2 + 3*S^4 - 2*S^6))/(2*S*(1 + S^2)) - (6*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 - 20*S*HPL[{3}, -S^2] - 24*S*Zeta[3]) + HPL[{2}, -S^2]*((43 + 68*S^2 + 108*S^4 - 43*S^6)/(4*S^3) + (Pi^2*(12 + 10*S^2 + 31*S^4 + 10*S^6 - 8*S^8))/(6*S^3*(1 + S^2)) - 12*S*HPL[{3}, -S^2] - 24*S*HPL[{2, 1}, -S^2] - 12*S*Zeta[3]) + HPL[{1}, -S^2]*((151*Pi^4*S)/90 - (11*(1 + S^2)*(1 - 26*S^2 + S^4))/(8*S^3) - (Pi^2*(1 + S^2)*(4 - 14*S^2 + 5*S^4))/(2*S^3) + ((5*Pi^2*S)/3 + (3 + 29*S^2 + 23*S^4 - 3*S^6)/S^3)*HPL[{2}, -S^2] + 10*S*HPL[{2}, -S^2]^2 - (2*(-1 - 3*S^2 + 14*S^4 - 9*S^6 + 5*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + (12*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (6*(-1 + 6*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2)))) + 4*S*(9 + 4*S^2)*Zeta[5] + HPL[{2}, -S^2]*((81 + 283*S^2 + 357*S^4 - 81*S^6)/(8*S^3) + (Pi^2*(43 + 49*S^2 + 89*S^4 - 29*S^6))/(24*S^3) + (Pi^4*(40 + 35*S^2 + 134*S^4 + 31*S^6 - 30*S^8))/(180*S^3*(1 + S^2)) + ((-4*Pi^2*S)/3 + S*(-5 + 4*S^2))*HPL[{3}, -S^2] - (2*(1 - 3*S^4 + 2*S^6 + S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 20*S*HPL[{5}, -S^2] + ((-10*Pi^2*S)/3 + (4 - 13*S^2 - 5*S^4 + 4*S^6)/S^3)*HPL[{2, 1}, -S^2] - (2*(2 + 11*S^4 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 8*S*HPL[{3, 2}, -S^2] + 40*S*HPL[{4, 1}, -S^2] + (4*(2 + 10*S^4 - S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 24*S*HPL[{3, 1, 1}, -S^2] - 48*S*HPL[{2, 1, 1, 1}, -S^2] + (-2*Pi^2*S + S*(-1 + 4*S^2))*Zeta[3] - 16*S*Zeta[5]) + HPL[{1}, -S^2]^2*(((1 + S^2)*(8 + 101*S^2 + 8*S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(21 - 117*S^2 + 32*S^4))/(24*S^3) + (Pi^4*(7 + 193*S^2 + 21*S^4 - 14*S^6))/(60*S*(1 + S^2)) + ((1 + 13*S^4 + S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((-5*Pi^2*S)/3 + (-5 + 17*S^2 + 11*S^4 - 11*S^6)/(2*S^3))*HPL[{3}, -S^2] - (4*(-1 - 4*S^4 + S^6)*HPL[{4}, -S^2])/S^3 + 10*S*HPL[{5}, -S^2] + ((-5*Pi^2*S)/3 + (-3 - 29*S^2 - 23*S^4 + 3*S^6)/S^3)*HPL[{2, 1}, -S^2] + (6*(-1 - 4*S^4 + S^6)*HPL[{3, 1}, -S^2])/S^3 + 20*S*HPL[{3, 2}, -S^2] + 60*S*HPL[{4, 1}, -S^2] - (12*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + 40*S*HPL[{2, 2, 1}, -S^2] + 80*S*HPL[{3, 1, 1}, -S^2] + (-2*Pi^2*S - (3*(-2 + S^2)*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-11*(1 + S^2)*(-1 - 8*S^2 + S^4))/(4*S^3) + (Pi^2*(6 + 5*S^2 + 33*S^4 + 15*S^6 - 4*S^8))/(6*S^3*(1 + S^2)) - 10*S*HPL[{3}, -S^2] - 20*S*HPL[{2, 1}, -S^2] - 10*S*Zeta[3]) - 16*S*Zeta[5]) + HPL[{1}, -S^2]*((283*Pi^6*S)/1620 + ((1 + S^2)*(9 + 31*S^2 + 9*S^4))/S^3 - (Pi^2*(1 + S^2)*(11 - 344*S^2 + 53*S^4))/(48*S^3) - (Pi^4*(1 + S^2)*(40 - 166*S^2 + 61*S^4))/(180*S^3) + ((4*Pi^2*S)/3 + (1 + 5*S^2 + 5*S^4 + S^6)/(2*S^3))*HPL[{2}, -S^2]^2 - 2*S*HPL[{3}, -S^2]^2 + ((2*Pi^2*S)/3 - (2*(2 - 11*S^2 - 9*S^4 + 4*S^6))/S^3)*HPL[{4}, -S^2] - (2*(-6 - 5*S^2 - 33*S^4 - 15*S^6 + 4*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) + 56*S*HPL[{6}, -S^2] - 20*S*HPL[{2, 1}, -S^2]^2 + (-2*Pi^2*S + (3*(1 - 9*S^2 - 7*S^4 + 3*S^6))/S^3)*HPL[{3, 1}, -S^2] + (4*(-1 + 9*S^2 - 3*S^4 + 2*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (4*(-2 - 5*S^2 + 19*S^4 - 15*S^6 + 8*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) - 28*S*HPL[{5, 1}, -S^2] + ((10*Pi^2*S)/3 - (2*(-3 - 29*S^2 - 23*S^4 + 3*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (8*(1 + 13*S^4 + S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) + (4*(7 + 3*S^2 + 64*S^4 + 9*S^6 + S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (24*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + (-((1 + S^2)*(-19 + 11*S^2))/(2*S) + (Pi^2*(1 + 3*S^4 - 2*S^6))/(S*(1 + S^2)))*Zeta[3] - 4*S*Zeta[3]^2 + HPL[{3}, -S^2]*(-((1 + S^2)*(7 - 61*S^2 + 18*S^4))/(2*S^3) + (Pi^2*(1 + 2*S^2 - 5*S^4 + 6*S^6 - 3*S^8))/(3*S^3*(1 + S^2)) + 20*S*HPL[{2, 1}, -S^2] - 4*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((11*(1 + S^2)*(-1 - 8*S^2 + S^4))/(2*S^3) + (Pi^2*(-6 - 5*S^2 - 33*S^4 - 15*S^6 + 4*S^8))/(3*S^3*(1 + S^2)) + 20*S*Zeta[3]) + HPL[{2}, -S^2]*((13*Pi^4*S)/45 - (Pi^2*(1 + S^2)*(-3 - 24*S^2 + 2*S^4))/(6*S^3) - ((1 + S^2)*(-21 - 160*S^2 + 21*S^4))/(4*S^3) - (2*(-1 + 9*S^2 - 3*S^4 + 2*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)) + 4*S*HPL[{4}, -S^2] - (4*(1 + 13*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 20*S*HPL[{3, 1}, -S^2] + 40*S*HPL[{2, 1, 1}, -S^2] - (2*(-1 + 9*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) - (8*(-1 - 3*S^4 + 2*S^6)*Zeta[5])/(S*(1 + S^2))) + HPL[{0}, S^2]*((1399*Pi^6*S)/2835 - (Pi^4*S*(-79 + 420*S^2))/360 + (Pi^2*(30 + 218*S^2 - 9*S^4))/(48*S) + (41 + 119*S^2 + 36*S^4)/(4*S) + (6*S*HPL[{1}, -S^2]^5)/(1 + S^2) + (2*S*HPL[{1}, -S^2]^6)/3 + ((2*Pi^2*S)/3 + (6 + S^2 + 9*S^4 - 4*S^6)/(4*S^3))*HPL[{2}, -S^2]^2 + (2*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((25*Pi^2*S)/18 + (-1 + 2*S^2 + 2*S^4 - S^6)/S^3 + 4*S*HPL[{2}, -S^2]) - 2*S*HPL[{3}, -S^2]^2 + ((-4*Pi^2*S)/3 + (2*(3 + 2*S^2 + 6*S^4 + S^6))/S^3)*HPL[{4}, -S^2] + (3*(-2 - 13*S^2 - 4*S^4 + 4*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)) - 40*S*HPL[{6}, -S^2] - 10*S*HPL[{2, 1}, -S^2]^2 + HPL[{1}, -S^2]^3*((-7*(1 + S^2)*(3 - 14*S^2 + 3*S^4))/(12*S^3) + (Pi^2*(1 + 81*S^2 + 3*S^4 - 2*S^6))/(9*S*(1 + S^2)) + (2*(1 + 10*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + (4*S*HPL[{3}, -S^2])/3 - 16*S*HPL[{2, 1}, -S^2]) + (-2*Pi^2*S + (-18 - S^2 - 33*S^4)/(2*S^3))*HPL[{3, 1}, -S^2] + (6*S*HPL[{3, 2}, -S^2])/(1 + S^2) - (2*(-2 - 17*S^2 - 5*S^4 + 4*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + 16*S*HPL[{5, 1}, -S^2] + (6*Pi^2*S + (18 + 7*S^2 + 27*S^4 - 12*S^6)/S^3)*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((61*Pi^4*S)/60 + (Pi^2*(-12 + 31*S^2 + 23*S^4 - 20*S^6))/(12*S^3) - (11*(1 - 25*S^2 - 25*S^4 + S^6))/(16*S^3) + ((19*Pi^2*S)/6 + (3 + 17*S^2 + 17*S^4 + 3*S^6)/(2*S^3))*HPL[{2}, -S^2] + 5*S*HPL[{2}, -S^2]^2 + ((1 + 4*S^4 + S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + 2*S*HPL[{4}, -S^2] - (6*(1 + 10*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 24*S*HPL[{3, 1}, -S^2] + 48*S*HPL[{2, 1, 1}, -S^2]) + (4*(-1 + 14*S^2 + 2*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (2*(-7 + 86*S^2 + 11*S^4 + 14*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + 16*S*HPL[{3, 2, 1}, -S^2] + 52*S*HPL[{4, 1, 1}, -S^2] - (12*(-1 + 10*S^2 + S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 48*S*HPL[{3, 1, 1, 1}, -S^2] + 96*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((Pi^2*S*(-1 + 2*S^2))/(1 + S^2)) - (S*(-34 + 15*S^2))/4)*Zeta[3] + 8*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((21 - 92*S^2 - 30*S^4 - 43*S^6)/(4*S^3) + (Pi^2*(4 - 53*S^2 - 8*S^4 - 8*S^6))/(6*S*(1 + S^2)) - 4*S*Zeta[3]) + HPL[{3}, -S^2]*((Pi^2*(-2 - 5*S^2 - 2*S^4 + 4*S^6))/(6*S*(1 + S^2)) + (-14 + 9*S^2 + 19*S^4 + 15*S^6)/(4*S^3) + 4*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2}, -S^2]*((7*Pi^4*S)/30 + (Pi^2*(18 + 11*S^2 + 26*S^4 - 8*S^6))/(12*S^3) + (46 + 79*S^2 + 167*S^4 - 4*S^6)/(8*S^3) - (3*S*HPL[{3}, -S^2])/(1 + S^2) + 4*S*HPL[{4}, -S^2] - (2*(-1 + 14*S^2 + 2*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - 12*S*HPL[{3, 1}, -S^2] + 20*S*HPL[{2, 1, 1}, -S^2] + (3*S*Zeta[3])/(1 + S^2)) - (8*S*(-1 + 2*S^2)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*(((1 + S^2)*(8 + 101*S^2 + 8*S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(21 - 143*S^2 + 46*S^4))/(24*S^3) + (Pi^4*(5 + 579*S^2 + 15*S^4 - 10*S^6))/(180*S*(1 + S^2)) + ((1 + 13*S^4 + S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((Pi^2*S)/3 + (-5 - S^2 + 11*S^4 + 7*S^6)/(2*S^3))*HPL[{3}, -S^2] + (2*(2 - S^4 + 2*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 6*S*HPL[{5}, -S^2] + ((-19*Pi^2*S)/3 + (-3 - 17*S^2 - 17*S^4 - 3*S^6)/S^3)*HPL[{2, 1}, -S^2] - (6*(1 + 10*S^4 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 4*S*HPL[{3, 2}, -S^2] + 8*S*HPL[{4, 1}, -S^2] + (12*(1 + 10*S^4 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 40*S*HPL[{2, 2, 1}, -S^2] + 128*S*HPL[{3, 1, 1}, -S^2] - 96*S*HPL[{2, 1, 1, 1}, -S^2] + (2*Pi^2*S - (3*(1 + S^2)*(-1 + 2*S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(11 + 50*S^2 + 11*S^4))/(4*S^3) + (Pi^2*(6 + S^2 + 51*S^4 + 3*S^6 + 4*S^8))/(6*S^3*(1 + S^2)) - 2*S*HPL[{3}, -S^2] - 20*S*HPL[{2, 1}, -S^2] + 2*S*Zeta[3]) + 16*S*Zeta[5])) + Log[T]*((-41*(1 + S^2))/(2*S) + (7*Pi^4*S*(-11 + 6*S^2))/60 + (Pi^2*(-30 - 213*S^2 + 46*S^4))/(24*S) + ((-8*Pi^2*S)/3 + (2*(1 - 2*S^2 - 2*S^4 + S^6))/S^3)*HPL[{1}, -S^2]^4 - (12*S*HPL[{1}, -S^2]^5)/(1 + S^2) - (4*S*HPL[{1}, -S^2]^6)/3 + HPL[{0}, S^2]^5*((-3*S)/(8*(1 + S^2)) - (S*HPL[{1}, -S^2])/4) + HPL[{0}, S^2]^4*((S*(-11 + 6*S^2))/8 + ((-1 - 15*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2])/(4*S*(1 + S^2)) - (3*S*HPL[{1}, -S^2]^2)/4) + (-(Pi^2*S) + (-6 + 3*S^2 - 5*S^4 - 6*S^6)/(2*S^3))*HPL[{2}, -S^2]^2 - 4*S*HPL[{3}, -S^2]^2 + ((2*Pi^2*S)/3 + (2*(-6 - 11*S^2 - 11*S^4 + 6*S^6))/S^3)*HPL[{4}, -S^2] - (2*S*(17 + 2*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 16*S*HPL[{2, 1}, -S^2]^2 + HPL[{3}, -S^2]*(-((Pi^2*S*(-3 + 2*S^2))/(1 + S^2)) + (14 - 35*S^2 - 9*S^4 - 7*S^6)/(2*S^3) - 16*S*HPL[{2, 1}, -S^2]) + HPL[{0}, S^2]^3*((Pi^2*S*(-73 + 2*S^2))/(36*(1 + S^2)) + (7*S*(-7 + 4*S^2))/24 + ((-1 - 36*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) - (20*S*HPL[{1}, -S^2]^3)/9 + ((-6 - 3*S^2 - 19*S^4 - S^6)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-25*Pi^2*S)/18 + (6 - 19*S^2 - 11*S^4 + 14*S^6)/(6*S^3) - (7*S*HPL[{2}, -S^2])/3) - S*HPL[{3}, -S^2] + (8*S*HPL[{2, 1}, -S^2])/3) + ((4*Pi^2*S)/3 + (18 + 19*S^2 + 33*S^4 - 18*S^6)/S^3)*HPL[{3, 1}, -S^2] + (4*S*(-11 + 4*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (4*S*(-32 + 13*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + ((-8*Pi^2*S)/3 + (2*(-18 - 19*S^2 - 33*S^4 + 18*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]^2*((3*Pi^2*(-11*S + 6*S^3))/8 + (-15 - 198*S^2 + 46*S^4)/(8*S) + ((-1 - 24*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)) - 3*S*HPL[{1}, -S^2]^4 + (-(Pi^2*S)/3 + (-18 - 11*S^2 - 27*S^4 + 6*S^6)/(4*S^3))*HPL[{2}, -S^2] - S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*(-3*Pi^2*S + (3*(2 - 6*S^2 - 5*S^4 + 3*S^6))/(2*S^3) - 5*S*HPL[{2}, -S^2]) - S*HPL[{3}, -S^2] + 2*S*HPL[{4}, -S^2] + (S*(23 + 8*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*(((1 + S^2)*(21 - 136*S^2 + 43*S^4))/(8*S^3) + (3*Pi^2*(-1 - 18*S^2 - 3*S^4 + 2*S^6))/(4*S*(1 + S^2)) + ((-3 - 2*S^2 - 21*S^4 - 6*S^6 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + 10*S*HPL[{2, 1}, -S^2]) + 4*S*HPL[{3, 1}, -S^2] - 8*S*HPL[{2, 1, 1}, -S^2]) - (8*S*(16 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (16*S*(19 + 4*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 96*S*HPL[{2, 1, 1, 1}, -S^2] + HPL[{0}, S^2]*((7*Pi^2*S*(-18 + 7*S^2))/24 + (Pi^4*S*(-539 + 10*S^2))/(180*(1 + S^2)) + (-75 - 361*S^2 - 32*S^4)/(8*S) - (30*S*HPL[{1}, -S^2]^4)/(1 + S^2) - 4*S*HPL[{1}, -S^2]^5 + ((-2 - S^2 - 12*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-50*Pi^2*S)/9 + (4*(1 - 2*S^2 - 2*S^4 + S^6))/S^3 - 16*S*HPL[{2}, -S^2]) + ((-4*Pi^2*S)/3 + (16 + S^2 - 7*S^4 - 6*S^6)/(2*S^3))*HPL[{3}, -S^2] - (2*(4 + 2*S^2 + 6*S^4 + 5*S^6)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 12*S*HPL[{5}, -S^2] + ((20*Pi^2*S)/3 + (-12 + 27*S^2 + 7*S^4 + 18*S^6)/S^3)*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(-12 - 6*S^2 - 49*S^4 + 2*S^6))/(6*S^3*(1 + S^2)) + (-43 - 30*S^2 - 92*S^4 + 21*S^6)/(4*S^3) + 20*S*HPL[{2, 1}, -S^2]) + HPL[{1}, -S^2]^2*((7*(1 + S^2)*(3 - 14*S^2 + 3*S^4))/(4*S^3) + (Pi^2*(-1 - 81*S^2 - 3*S^4 + 2*S^6))/(3*S*(1 + S^2)) - (6*(1 + 10*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) - 4*S*HPL[{3}, -S^2] + 48*S*HPL[{2, 1}, -S^2]) - (6*(-2 - S^2 - 10*S^4 + S^6)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 4*S*HPL[{4, 1}, -S^2] + (12*(-2 - S^2 - 10*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-61*Pi^4*S)/30 + (11*(1 - 25*S^2 - 25*S^4 + S^6))/(8*S^3) + (Pi^2*(12 - 31*S^2 - 23*S^4 + 20*S^6))/(6*S^3) + ((-19*Pi^2*S)/3 + (-3 - 17*S^2 - 17*S^4 - 3*S^6)/S^3)*HPL[{2}, -S^2] - 10*S*HPL[{2}, -S^2]^2 - (2*(1 + 4*S^4 + S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - 4*S*HPL[{4}, -S^2] + (12*(1 + 10*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 48*S*HPL[{3, 1}, -S^2] - 96*S*HPL[{2, 1, 1}, -S^2]) - 40*S*HPL[{2, 2, 1}, -S^2] - 128*S*HPL[{3, 1, 1}, -S^2] + 96*S*HPL[{2, 1, 1, 1}, -S^2]) + ((-2*Pi^2*S*(-1 + 2*S^2))/(1 + S^2) - (S*(46 + 21*S^2))/2)*Zeta[3] + HPL[{2, 1}, -S^2]*((5*Pi^2*S*(7 + 4*S^2))/(3*(1 + S^2)) + (-21 + 130*S^2 + 46*S^4 + 21*S^6)/(2*S^3) - 16*S*Zeta[3]) + HPL[{1}, -S^2]^3*((7*(1 + S^2)*(3 - 14*S^2 + 3*S^4))/(6*S^3) + (Pi^2*(-1 - 54*S^2 - 3*S^4 + 2*S^6))/(3*S*(1 + S^2)) + (4*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 + (40*S*HPL[{3}, -S^2])/3 + 16*S*Zeta[3]) + HPL[{2}, -S^2]*(-(Pi^4*S)/9 + (Pi^2*(-6 - 5*S^2 - 10*S^4 + 4*S^6))/(2*S^3) + (-46 - 137*S^2 - 183*S^4 + 46*S^6)/(4*S^3) - (2*S*(-11 + 4*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 8*S*HPL[{4}, -S^2] + (4*S*(16 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 16*S*HPL[{3, 1}, -S^2] - 32*S*HPL[{2, 1, 1}, -S^2] - (2*S*(-11 + 4*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-151*Pi^4*S)/90 + (11*(1 + S^2)*(1 - 26*S^2 + S^4))/(8*S^3) + (Pi^2*(1 + S^2)*(4 - 14*S^2 + 5*S^4))/(2*S^3) + ((-5*Pi^2*S)/3 + (-3 - 29*S^2 - 23*S^4 + 3*S^6)/S^3)*HPL[{2}, -S^2] - 10*S*HPL[{2}, -S^2]^2 + (2*(-1 - 3*S^2 + 14*S^4 - 9*S^6 + 5*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - (12*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (6*(-1 + 6*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) - (16*S*(-1 + 2*S^2)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(8 + 101*S^2 + 8*S^4))/(2*S^3) + (Pi^2*(1 + S^2)*(21 - 117*S^2 + 32*S^4))/(12*S^3) + (Pi^4*(-7 - 193*S^2 - 21*S^4 + 14*S^6))/(30*S*(1 + S^2)) - (2*(1 + 13*S^4 + S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((10*Pi^2*S)/3 + (5 - 17*S^2 - 11*S^4 + 11*S^6)/S^3)*HPL[{3}, -S^2] + (8*(-1 - 4*S^4 + S^6)*HPL[{4}, -S^2])/S^3 - 20*S*HPL[{5}, -S^2] + ((10*Pi^2*S)/3 - (2*(-3 - 29*S^2 - 23*S^4 + 3*S^6))/S^3)*HPL[{2, 1}, -S^2] - (12*(-1 - 4*S^4 + S^6)*HPL[{3, 1}, -S^2])/S^3 - 40*S*HPL[{3, 2}, -S^2] - 120*S*HPL[{4, 1}, -S^2] + (24*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - 80*S*HPL[{2, 2, 1}, -S^2] - 160*S*HPL[{3, 1, 1}, -S^2] + (4*Pi^2*S + (6*(-2 + S^2)*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((11*(1 + S^2)*(-1 - 8*S^2 + S^4))/(2*S^3) + (Pi^2*(-6 - 5*S^2 - 33*S^4 - 15*S^6 + 4*S^8))/(3*S^3*(1 + S^2)) + 20*S*HPL[{3}, -S^2] + 40*S*HPL[{2, 1}, -S^2] + 20*S*Zeta[3]) + 32*S*Zeta[5]));
e4T3F3=(-12371*(1 + S^2))/(17496*S) + (Pi^2*(5463 - 1546*S^2 - 10611*S^4))/(3888*S) - (13*Pi^4*(-129 + 222*S^2 + 470*S^4))/(14580*S) + (Pi^6*(-3962 - 1981*S^2 - 15185*S^4 - 11223*S^6))/(68040*S*(1 + S^2)) - (S^3*HPL[{0}, S^2]^7)/144 + ((-95 - 147*S^2 - 147*S^4 - 95*S^6)/(135*S^3) - (8*Pi^2*(1 + S^6))/(45*S^3))*HPL[{1}, -S^2]^5 - (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^7)/(63*S^3) + HPL[{0}, S^2]^6*((-2 - S^2 - 20*S^4 - 18*S^6)/(288*S*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2])/(144*S^3)) + HPL[{0}, S^2]^5*(-(Pi^2*S^3)/18 + (-6 - 6*S^2 - 31*S^4)/(216*S) + ((-2 - 8*S^2 - 3*S^4 - 8*S^6 - 2*S^8)*HPL[{1}, -S^2])/(72*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2]^2)/(24*S^3)) - (2*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^3)/(27*S^3) + ((-18 - 12*S^2 + 3*S^4 - 5*S^6 - 11*S^8)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-244 + 282*S^2 - 348*S^4 - 589*S^6)/(27*S^3) - (14*Pi^2*(1 + S^6))/(9*S^3))*HPL[{5}, -S^2] - (4*(-170 - 128*S^2 + 21*S^4 + 163*S^6 + 121*S^8)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)) - (200*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/(3*S^3) + ((3 + 23*S^2 + 10*S^4 + 23*S^6 + 3*S^8)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)) + HPL[{0}, S^2]^4*((248 - 106*S^2 - 405*S^4)/(864*S) + (Pi^2*(-12 - 6*S^2 - 85*S^4 - 73*S^6))/(216*S*(1 + S^2)) + ((1 - 5*S^2 - 3*S^4 - 11*S^6 - 5*S^8)*HPL[{1}, -S^2]^2)/(24*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2]^3)/(12*S^3) + ((9 + 3*S^2 - 3*S^4 - 8*S^6 - 2*S^8)*HPL[{2}, -S^2])/(72*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((106 + 45*S^2 - 162*S^4 - 101*S^6)/(432*S^3) + (Pi^2*(-1 - S^6))/(18*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(12*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(12*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(6*S^3)) + ((-8*Pi^2*(1 + S^6))/(9*S^3) - (2*(58 + 150*S^2 + 24*S^4 + 59*S^6))/(27*S^3))*HPL[{3, 2}, -S^2] + ((-492 - 1179*S^2 + 81*S^4 - 68*S^6)/(27*S^3) - (2*Pi^2*(1 + S^6))/S^3)*HPL[{4, 1}, -S^2] + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/(3*S^3) + (2*(-118 - 76*S^2 + 21*S^4 + 111*S^6 + 69*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/S^3 + (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/S^3 + ((-20*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (2*(1 + S^2)*(39 + 19*S^2 + 39*S^4))/(9*S^3))*HPL[{2, 2, 1}, -S^2] + ((-241 - 291*S^2 - 1047*S^4 - 837*S^6)/(27*S^3) - (16*Pi^2*(1 + S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] - (16*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^3) + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (178*(-1 + S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^3) + (272*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^3) + (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/S^3 + ((4*Pi^2*(1 + S^6))/(3*S^3) + (4*(-149 - 189*S^2 + 189*S^4 + 149*S^6))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (16*(-1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^3 - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^3 - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^3 - (48*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^3 - (32*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^3 + (96*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (192*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 + ((-47*(1 + S^2))/(27*S) - (2*Pi^2*(12 + 6*S^2 + 13*S^4 + S^6))/(27*S*(1 + S^2)) - (S^3*HPL[{0}, S^2]^3)/3 + ((-95 - 147*S^2 - 147*S^4 - 95*S^6)/(27*S^3) - (8*Pi^2*(1 + S^6))/(9*S^3))*HPL[{1}, -S^2] - (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)) - (20*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^2*((-18 - 9*S^2 - 22*S^4 - 4*S^6)/(18*S*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2])/S^3) - (4*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((-8*Pi^2*S^3)/9 + (-96 - 51*S^2 - 95*S^4)/(27*S) - (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) - (10*(1 + S^6)*HPL[{1}, -S^2]^2)/(3*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3))*Log[T]^4 + ((8*(1 + S^2))/(9*S) + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]*((2*(6 + 3*S^2 + 10*S^4 + 4*S^6))/(9*S*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(3*S^3)))*Log[T]^5 + ((-2*(2 + S^2 + 2*S^4))/(9*S*(1 + S^2)) - (4*S^3*HPL[{0}, S^2])/9 - (4*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3))*Log[T]^6 + ((23748 + 879*S^2 - 14218*S^4)/(972*S) + (Pi^2*(171 - 18*S^2 - 107*S^4))/(81*S))*Zeta[3] - (2*(-6 - 3*S^2 + 19*S^4 + 25*S^6)*Zeta[3]^2)/(9*S*(1 + S^2)) + HPL[{3, 1}, -S^2]*((-1342 - 534*S^2 + 1032*S^4 + 1873*S^6)/(162*S^3) + (Pi^2*(-13 + 5*S^2 + 9*S^4 + 32*S^6 + 14*S^8))/(27*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(14 + 187*S^2 + 14*S^4))/(324*S^3) + (Pi^2*(-3 - 51*S^2 - 24*S^4 - 55*S^6 - 7*S^8))/(108*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^4*((-187*(1 + S^2)*(7 + 2*S^2 + 7*S^4))/(486*S^3) + (Pi^2*(-23 - 119*S^2 - 48*S^4 - 137*S^6 - 41*S^8))/(108*S^3*(1 + S^2)) + ((1 - S^6)*HPL[{2}, -S^2])/S^3 + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((1057 + 1218*S^2 - 1716*S^4 - 1588*S^6)/(162*S^3) + (Pi^2*(33 + 29*S^2 - 2*S^4 - 25*S^6 - 21*S^8))/(18*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 1, 1}, -S^2]*((3215 + 1566*S^2 - 1566*S^4 - 3215*S^6)/(162*S^3) + (Pi^2*(19 - 11*S^2 - 15*S^4 - 58*S^6 - 28*S^8))/(27*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{3}, -S^2]*((Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (7622 + 15648*S^2 - 7221*S^4 - 6596*S^6)/(972*S^3) + (Pi^2*(341 + 480*S^2 - 24*S^4 - 159*S^6))/(324*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (2*(5 + 35*S^2 + 15*S^4 + 34*S^6 + 4*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(-7 - S^2 + 3*S^4 + 6*S^6)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((-151*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) - (Pi^2*(1 + S^2)*(587 + 529*S^2 + 1118*S^4))/(972*S^3) - ((1 + S^2)*(47207 + 6490*S^2 + 47207*S^4))/(5832*S^3) + ((-5*Pi^2*(1 + S^6))/(27*S^3) - (59*(-1 - S^2 + S^4 + S^6))/(18*S^3))*HPL[{2}, -S^2] - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) - (2*(-47 - 107*S^2 - 30*S^4 - 53*S^6 + 7*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (2*(-17 - 41*S^2 - 12*S^4 - 23*S^6 + S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((7*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(45*S^3) + (Pi^2*(-191 - 228*S^2 + 402*S^4 + 308*S^6))/(162*S^3) + (-14218 - 22869*S^2 + 22869*S^4 + 14218*S^6)/(972*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 - (2*(5 + 35*S^2 + 15*S^4 + 34*S^6 + 4*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + Log[T]^3*((605*(1 + S^2))/(243*S) + (Pi^2*(486 + 639*S^2 + 233*S^4))/(486*S) + ((16*Pi^2*(1 + S^6))/(9*S^3) + (2*(95 + 147*S^2 + 147*S^4 + 95*S^6))/(27*S^3))*HPL[{1}, -S^2]^2 + (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^4)/(9*S^3) + HPL[{0}, S^2]^3*((60 + 30*S^2 + 89*S^4 + 29*S^6)/(81*S*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(27*S^3)) + ((4*Pi^2*(1 + S^6))/(27*S^3) + (-233 - 153*S^2 + 153*S^4 + 233*S^6)/(81*S^3))*HPL[{2}, -S^2] + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^2*((126 + 279*S^2 + 233*S^4)/(162*S) + ((1 + 13*S^2 + 6*S^4 + 19*S^6 + 7*S^8)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/S^3 + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + (2*(-73 - 133*S^2 - 30*S^4 - 49*S^6 + 11*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (56*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((2*(1260 + 423*S^2 + 1309*S^4))/(243*S) + (Pi^2*(150 + 75*S^2 + 239*S^4 + 89*S^6))/(81*S*(1 + S^2)) + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^3)/(9*S^3) + (2*(13 + 37*S^2 + 12*S^4 + 27*S^6 + 3*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((50*Pi^2*(1 + S^6))/(27*S^3) + (2*(95 + 147*S^2 + 147*S^4 + 95*S^6))/(27*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) + (8*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((374*(1 + S^2)*(7 + 2*S^2 + 7*S^4))/(243*S^3) + (Pi^2*(23 + 119*S^2 + 48*S^4 + 137*S^6 + 41*S^8))/(27*S^3*(1 + S^2)) + (4*(-1 + S^6)*HPL[{2}, -S^2])/S^3 - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]^3*((-89*Pi^4*S^3)/540 + (-33024 - 3819*S^2 - 45155*S^4)/(23328*S) + (Pi^2*(-600 - 627*S^2 - 2267*S^4))/(3888*S) + ((-11 - 71*S^2 - 30*S^4 - 89*S^6 - 29*S^8)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)) - (5*(1 + S^6)*HPL[{1}, -S^2]^4)/(27*S^3) + ((-294 - 249*S^2 - 276*S^4 - 227*S^6)/(648*S^3) + (Pi^2*(-1 - S^6))/(36*S^3))*HPL[{2}, -S^2] - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(12*S^3) + HPL[{1}, -S^2]^2*((-77 - 130*S^2 - 253*S^4 - 200*S^6)/(216*S^3) - (25*Pi^2*(1 + S^6))/(108*S^3) - (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(18*S^3)) + ((-10 - S^6)*HPL[{3}, -S^2])/(18*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(2*S^3) + ((4 + 46*S^2 + 21*S^4 + 77*S^6 + 35*S^8)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(881 - 8*S^2 + 1592*S^4))/(972*S^3) + (Pi^2*(-41 - 191*S^2 - 75*S^4 - 209*S^6 - 59*S^8))/(324*S^3*(1 + S^2)) + ((-5 - 47*S^2 - 21*S^4 - 65*S^6 - 23*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) + (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]^2*((37835 - 4219*S^2 - 63666*S^4)/(7776*S) + (Pi^2*(4614 - 3324*S^2 - 10505*S^4))/(7776*S) + (Pi^4*(-302 - 151*S^2 - 1489*S^4 - 1187*S^6))/(2160*S*(1 + S^2)) + ((-1 - 13*S^2 - 6*S^4 - 19*S^6 - 7*S^8)*HPL[{1}, -S^2]^4)/(12*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2]^5)/(5*S^3) + ((3 - 33*S^2 - 18*S^4 - 41*S^6 - 5*S^8)*HPL[{2}, -S^2]^2)/(72*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-17 - 234*S^2 - 765*S^4 - 548*S^6)/(324*S^3) + (Pi^2*(-1 - S^6))/(3*S^3) - (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + ((221 + 207*S^2 - 45*S^4 - 183*S^6)/(216*S^3) + (Pi^2*(-1 - S^6))/(6*S^3))*HPL[{3}, -S^2] + ((133 + 109*S^2 - 12*S^4 - 85*S^6 - 61*S^8)*HPL[{4}, -S^2])/(36*S^3*(1 + S^2)) - (11*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((Pi^2*(1 + S^6))/(2*S^3) + (-14 - 13*S^2 + 71*S^4 + 53*S^6)/(18*S^3))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*(-((1 + S^2)*(-151 + 247*S^2 + 1289*S^4))/(324*S^3) + (Pi^2*(1 - 23*S^2 - 12*S^4 - 41*S^6 - 17*S^8))/(24*S^3*(1 + S^2)) + ((8 - 22*S^2 - 15*S^4 - 58*S^6 - 28*S^8)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) + ((-7 + 11*S^2 + 9*S^4 + 26*S^6 + 8*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + ((7 - 23*S^2 - 15*S^4 - 46*S^6 - 16*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((135 - 54*S^2 - 65*S^4)*Zeta[3])/(54*S) + HPL[{2}, -S^2]*((2187 + 912*S^2 - 1716*S^4 - 2243*S^6)/(1296*S^3) + (Pi^2*(61 - 5*S^2 - 33*S^4 - 94*S^6 - 28*S^8))/(216*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]*((16541 + 10263*S^2 - 53277*S^4 - 46999*S^6)/(7776*S^3) + (Pi^2*(619 + 36*S^2 - 1737*S^4 - 1154*S^6))/(1296*S^3) - (151*Pi^4*(1 + S^6))/(1080*S^3) + ((-11*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(36*S^3) - ((1 + S^2)*(-179 + 104*S^2 + 559*S^4))/(216*S^3))*HPL[{2}, -S^2] - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(2*S^3) + ((1 - S^6)*HPL[{3}, -S^2])/(2*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((-8 + 22*S^2 + 15*S^4 + 58*S^6 + 28*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (3*(-1 + S^6)*Zeta[3])/(2*S^3))) + Log[T]^2*((-5057*(1 + S^2))/(1944*S) + (Pi^2*(-1542 - 3108*S^2 - 3215*S^4))/(1944*S) + (Pi^4*(-302 - 151*S^2 - 421*S^4 - 119*S^6))/(540*S*(1 + S^2)) - (S^3*HPL[{0}, S^2]^5)/12 + ((-16*Pi^2*(1 + S^6))/(9*S^3) - (2*(95 + 147*S^2 + 147*S^4 + 95*S^6))/(27*S^3))*HPL[{1}, -S^2]^3 - (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^5)/(3*S^3) + HPL[{0}, S^2]^4*((-18 - 9*S^2 - 40*S^4 - 22*S^6)/(72*S*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2])/(4*S^3)) + ((-3 - 23*S^2 - 10*S^4 - 23*S^6 - 3*S^8)*HPL[{2}, -S^2]^2)/(6*S^3*(1 + S^2)) + HPL[{0}, S^2]^3*((-4*Pi^2*S^3)/9 + (-240 - 267*S^2 - 407*S^4)/(324*S) + ((-11 - 71*S^2 - 30*S^4 - 89*S^6 - 29*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) - (10*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + ((461 + 753*S^2 - 3*S^4 - 135*S^6)/(54*S^3) + (2*Pi^2*(1 + S^6))/(3*S^3))*HPL[{3}, -S^2] - (65*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((2*Pi^2*(1 + S^6))/(3*S^3) + (2*(-149 - 189*S^2 + 189*S^4 + 149*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((150 - 1416*S^2 - 3215*S^4)/(648*S) + (Pi^2*(-18 - 9*S^2 - 31*S^4 - 13*S^6))/(18*S*(1 + S^2)) + ((-1 - 13*S^2 - 6*S^4 - 19*S^6 - 7*S^8)*HPL[{1}, -S^2]^2)/(2*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2]^3)/S^3 + ((7 - 23*S^2 - 15*S^4 - 46*S^6 - 16*S^8)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-17 - 234*S^2 - 765*S^4 - 548*S^6)/(108*S^3) + (Pi^2*(-1 - S^6))/S^3 - (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3) + (8*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 - (24*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 - (16*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + HPL[{0}, S^2]*((-89*Pi^4*S^3)/135 + (-45528 - 8169*S^2 - 47207*S^4)/(1944*S) + (Pi^2*(-816 - 573*S^2 - 977*S^4))/(324*S) - (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)) - (10*(1 + S^6)*HPL[{1}, -S^2]^4)/(3*S^3) + ((Pi^2*(-1 - S^6))/S^3 - (5*(64 + 99*S^2 + 54*S^4 + 51*S^6))/(54*S^3))*HPL[{2}, -S^2] - (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + HPL[{1}, -S^2]^2*((-95 - 147*S^2 - 147*S^4 - 95*S^6)/(9*S^3) - (25*Pi^2*(1 + S^6))/(9*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/S^3) - (2*(3 + 9*S^2 + 3*S^4 + 7*S^6 + S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (2*(3 + 27*S^2 + 12*S^4 + 37*S^6 + 13*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-187*(1 + S^2)*(7 + 2*S^2 + 7*S^4))/(81*S^3) + (Pi^2*(-41 - 191*S^2 - 75*S^4 - 209*S^6 - 59*S^8))/(27*S^3*(1 + S^2)) - (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^3 - (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 - (2*(-207 - 18*S^2 + 149*S^4)*Zeta[3])/(27*S) + HPL[{2}, -S^2]*((3215 + 1566*S^2 - 1566*S^4 - 3215*S^6)/(324*S^3) + (Pi^2*(19 - 11*S^2 - 15*S^4 - 58*S^6 - 28*S^8))/(54*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/S^3 + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]^2*((-187*(1 + S^2)*(7 + 2*S^2 + 7*S^4))/(81*S^3) + (Pi^2*(-23 - 119*S^2 - 48*S^4 - 137*S^6 - 41*S^8))/(18*S^3*(1 + S^2)) - (6*(-1 + S^6)*HPL[{2}, -S^2])/S^3 + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]*((-151*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) - (Pi^2*(1 + S^2)*(587 + 529*S^2 + 1118*S^4))/(324*S^3) - ((1 + S^2)*(47207 + 6490*S^2 + 47207*S^4))/(1944*S^3) + ((-59*(-1 + S^2)*(1 + S^2)^2)/(6*S^3) - (5*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3))*HPL[{2}, -S^2] - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) - (2*(-47 - 107*S^2 - 30*S^4 - 53*S^6 + 7*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (12*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (2*(-17 - 41*S^2 - 12*S^4 - 23*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2)))) - (2*(-228 + 24*S^2 + 257*S^4)*Zeta[5])/(27*S) + HPL[{2}, -S^2]*((10611 + 7009*S^2 - 7009*S^4 - 10611*S^6)/(648*S^3) + (Pi^2*(2701 + 1239*S^2 - 1641*S^4 - 2729*S^6))/(1944*S^3) + (Pi^4*(74 - 4*S^2 - 39*S^4 - 116*S^6 - 38*S^8))/(810*S^3*(1 + S^2)) + ((4*Pi^2*(1 + S^6))/(9*S^3) + (58 + 150*S^2 + 24*S^4 + 59*S^6)/(27*S^3))*HPL[{3}, -S^2] + (2*(18 + 12*S^2 - 3*S^4 + 5*S^6 + 11*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((10*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + ((1 + S^2)*(39 + 19*S^2 + 39*S^4))/(9*S^3))*HPL[{2, 1}, -S^2] + (2*(1 + 31*S^2 + 15*S^4 + 38*S^6 + 8*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (2*(3 + 23*S^2 + 10*S^4 + 23*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (107 + 150*S^2 + 24*S^4 + 10*S^6)/(27*S^3))*Zeta[3] + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(386 + 207*S^2 + 866*S^4))/(324*S^3) - ((1 + S^2)*(54530 + 3127*S^2 + 54530*S^4))/(2916*S^3) + (Pi^4*(-113 - 1019*S^2 - 453*S^4 - 1397*S^6 - 491*S^8))/(1620*S^3*(1 + S^2)) - (5*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((140 + 191*S^2 + 14*S^4 - 37*S^6)/(18*S^3) + (5*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3}, -S^2] - (4*(-1 + S^6)*HPL[{4}, -S^2])/S^3 - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((5*Pi^2*(1 + S^6))/(9*S^3) + (59*(-1 - S^2 + S^4 + S^6))/(6*S^3))*HPL[{2, 1}, -S^2] + (6*(-1 + S^6)*HPL[{3, 1}, -S^2])/S^3 - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 - (12*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + ((1 + S^2)*(553 + 95*S^2 + 22*S^4))/(54*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-80*(-1 + S^2)*(1 + S^2)^2)/(9*S^3) - (5*Pi^2*(-7 - S^2 + 3*S^4 + 17*S^6 + 11*S^8))/(54*S^3*(1 + S^2)) + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]*((-283*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(4860*S^3) - (Pi^4*(1 + S^2)*(-79 + 1036*S^2 + 1982*S^4))/(4860*S^3) - (Pi^2*(1 + S^2)*(5111 + 2128*S^2 + 15701*S^4))/(3888*S^3) - ((1 + S^2)*(136907 + 4642*S^2 + 136907*S^4))/(4374*S^3) + ((-4*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(95 + 52*S^2 + 95*S^4))/(54*S^3))*HPL[{2}, -S^2]^2 + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((194 + 243*S^2 - 216*S^4 - 265*S^6)/(27*S^3) - (2*Pi^2*(1 + S^6))/(9*S^3))*HPL[{4}, -S^2] - (10*(-7 - S^2 + 3*S^4 + 17*S^6 + 11*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((2*Pi^2*(1 + S^6))/(3*S^3) + (-230 - 279*S^2 + 252*S^4 + 301*S^6)/(27*S^3))*HPL[{3, 1}, -S^2] - (4*(19 + 49*S^2 + 15*S^4 + 31*S^6 + S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + (20*(-5 - 11*S^2 - 3*S^4 - 5*S^6 + S^8)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((-10*Pi^2*(1 + S^6))/(9*S^3) - (59*(-1 - S^2 + S^4 + S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(13 + 133*S^2 + 60*S^4 + 187*S^6 + 67*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (24*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + (((1 + S^2)*(1460 + 127*S^2 + 20*S^4))/(81*S^3) + (Pi^2*(13 + 25*S^2 + 6*S^4 + 7*S^6 - 5*S^8))/(9*S^3*(1 + S^2)))*Zeta[3] + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*((160*(-1 + S^2)*(1 + S^2)^2)/(9*S^3) + (5*Pi^2*(-7 - S^2 + 3*S^4 + 17*S^6 + 11*S^8))/(27*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*(-((1 + S^2)*(-1585 - 764*S^2 + 1295*S^4))/(162*S^3) + (Pi^2*(28 + 58*S^2 + 15*S^4 + 22*S^6 - 8*S^8))/(27*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-1765*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) - (13*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - (Pi^2*(1 + S^2)*(-355 + 52*S^2 + 545*S^4))/(324*S^3) + (2*(19 + 49*S^2 + 15*S^4 + 31*S^6 + S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(19 + 49*S^2 + 15*S^4 + 31*S^6 + S^8)*Zeta[3])/(9*S^3*(1 + S^2))) - (8*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + Log[T]*((1357*(1 + S^2))/(729*S) + (Pi^4*(858 + 2334*S^2 + 1973*S^4))/(4860*S) + (Pi^2*(-1944 + 6957*S^2 + 17552*S^4))/(5832*S) + ((8*Pi^2*(1 + S^6))/(9*S^3) + (95 + 147*S^2 + 147*S^4 + 95*S^6)/(27*S^3))*HPL[{1}, -S^2]^4 + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^6)/(9*S^3) + HPL[{0}, S^2]^5*((6 + 3*S^2 + 10*S^4 + 4*S^6)/(72*S*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(12*S^3)) + HPL[{0}, S^2]^4*((-18 + 63*S^2 + 103*S^4)/(216*S) + ((-1 + 5*S^2 + 3*S^4 + 11*S^6 + 5*S^8)*HPL[{1}, -S^2])/(12*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(4*S^3)) + ((Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + ((1 + S^2)*(73 + 47*S^2 + 73*S^4))/(54*S^3))*HPL[{2}, -S^2]^2 + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((-2*Pi^2*(1 + S^6))/(9*S^3) + (-244 - 207*S^2 + 207*S^4 + 244*S^6)/(27*S^3))*HPL[{4}, -S^2] + (2*(12 + 42*S^2 + 15*S^4 + 49*S^6 + 19*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]^3*((2250 + 1152*S^2 + 4181*S^4)/(1944*S) + (Pi^2*(150 + 75*S^2 + 239*S^4 + 89*S^6))/(324*S*(1 + S^2)) + ((11 + 71*S^2 + 30*S^4 + 89*S^6 + 29*S^8)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^3)/(27*S^3) + ((6 + 48*S^2 + 21*S^4 + 53*S^6 + 11*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((25*Pi^2*(1 + S^6))/(54*S^3) + (77 + 130*S^2 + 253*S^4 + 200*S^6)/(108*S^3) + (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3)) + HPL[{3}, -S^2]*((-1800 - 3762*S^2 + 432*S^4 + 745*S^6)/(162*S^3) + (Pi^2*(-40 - 70*S^2 - 15*S^4 - 21*S^6 + 9*S^8))/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) + ((233 + 153*S^2 - 153*S^4 - 233*S^6)/(27*S^3) - (4*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (4*(-33 - 63*S^2 - 15*S^4 - 28*S^6 + 2*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (2*(-205 - 385*S^2 - 90*S^4 - 161*S^6 + 19*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + ((8*Pi^2*(1 + S^6))/(9*S^3) + (2*(-233 - 153*S^2 + 153*S^4 + 233*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]^2*((Pi^2*(18 + 657*S^2 + 851*S^4))/(648*S) + (-5574 + 3327*S^2 + 17552*S^4)/(1944*S) + ((1 + 13*S^2 + 6*S^4 + 19*S^6 + 7*S^8)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^4)/S^3 + ((Pi^2*(1 + S^6))/(9*S^3) + (-95 + 3*S^2 + 237*S^4 + 241*S^6)/(108*S^3))*HPL[{2}, -S^2] + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^6))/S^3 + (17 + 234*S^2 + 765*S^4 + 548*S^6)/(108*S^3) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + (7*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3}, -S^2])/(18*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((9 - 21*S^2 - 15*S^4 - 70*S^6 - 40*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(-151 + 247*S^2 + 1289*S^4))/(162*S^3) + (Pi^2*(-1 + 23*S^2 + 12*S^4 + 41*S^6 + 17*S^8))/(12*S^3*(1 + S^2)) + ((-8 + 22*S^2 + 15*S^4 + 58*S^6 + 28*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3)) + (4*(31 + 91*S^2 + 30*S^4 + 91*S^6 + 31*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (16*(5 + 35*S^2 + 15*S^4 + 56*S^6 + 26*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (112*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + HPL[{0}, S^2]*((Pi^2*(2430 + 948*S^2 + 3139*S^4))/(648*S) + (212739 + 17889*S^2 + 218120*S^4)/(5832*S) + (Pi^4*(1098 + 549*S^2 + 1775*S^4 + 677*S^6))/(1620*S*(1 + S^2)) + (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^5)/(3*S^3) + ((37 + 97*S^2 + 30*S^4 + 63*S^6 + 3*S^8)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((50*Pi^2*(1 + S^6))/(27*S^3) + (2*(95 + 147*S^2 + 147*S^4 + 95*S^6))/(27*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + ((4*Pi^2*(1 + S^6))/(9*S^3) + (155 + 75*S^2 + 75*S^4 + 111*S^6)/(54*S^3))*HPL[{3}, -S^2] + ((-25 - 13*S^2 + 6*S^4 + 45*S^6 + 33*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((-20*Pi^2*(1 + S^6))/(9*S^3) - (5*(51 + 54*S^2 + 99*S^4 + 64*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((187*(1 + S^2)*(7 + 2*S^2 + 7*S^4))/(81*S^3) + (Pi^2*(41 + 191*S^2 + 75*S^4 + 209*S^6 + 59*S^8))/(27*S^3*(1 + S^2)) + (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3) + HPL[{2}, -S^2]*((2625 + 4782*S^2 + 2154*S^4 + 3295*S^6)/(324*S^3) + (Pi^2*(45 + 159*S^2 + 57*S^4 + 134*S^6 + 20*S^8))/(54*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) - (2*(13 + 37*S^2 + 12*S^4 + 27*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (4*(13 + 37*S^2 + 12*S^4 + 27*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((61*Pi^4*(1 + S^6))/(90*S^3) + (Pi^2*(267 + 424*S^2 + 547*S^4 + 390*S^6))/(108*S^3) + (47207 + 53697*S^2 + 53697*S^4 + 47207*S^6)/(1944*S^3) + ((19*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (5*(1 + S^2)*(115 + 38*S^2 + 115*S^4))/(54*S^3))*HPL[{2}, -S^2] + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (16*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (128*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3) + ((-4506 - 312*S^2 + 2545*S^4)/(162*S) + (2*Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(9*S*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^3*((374*(1 + S^2)*(7 + 2*S^2 + 7*S^4))/(243*S^3) + (Pi^2*(23 + 119*S^2 + 48*S^4 + 137*S^6 + 41*S^8))/(27*S^3*(1 + S^2)) + (4*(-1 + S^6)*HPL[{2}, -S^2])/S^3 - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((2545 + 4194*S^2 - 4194*S^4 - 2545*S^6)/(162*S^3) + (Pi^2*(51 + 21*S^2 - 15*S^4 - 112*S^6 - 82*S^8))/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^2*((151*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(1 + S^2)*(587 + 529*S^2 + 1118*S^4))/(324*S^3) + ((1 + S^2)*(47207 + 6490*S^2 + 47207*S^4))/(1944*S^3) + ((5*Pi^2*(1 + S^6))/(9*S^3) + (59*(-1 - S^2 + S^4 + S^6))/(6*S^3))*HPL[{2}, -S^2] + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + (2*(-47 - 107*S^2 - 30*S^4 - 53*S^6 + 7*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (12*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (2*(-17 - 41*S^2 - 12*S^4 - 23*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (Pi^2*(-164 - 75*S^2 + 195*S^4 + 237*S^6))/(162*S^3) + (-17552 - 8901*S^2 + 8901*S^4 + 17552*S^6)/(972*S^3) + (2*(-33 - 63*S^2 - 15*S^4 - 28*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (2*(31 + 91*S^2 + 30*S^4 + 91*S^6 + 31*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(-33 - 63*S^2 - 15*S^4 - 28*S^6 + 2*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + (16*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(386 + 207*S^2 + 866*S^4))/(162*S^3) + ((1 + S^2)*(54530 + 3127*S^2 + 54530*S^4))/(1458*S^3) + (Pi^4*(113 + 1019*S^2 + 453*S^4 + 1397*S^6 + 491*S^8))/(810*S^3*(1 + S^2)) + (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-10*Pi^2*(1 + S^6))/(9*S^3) + (-140 - 191*S^2 - 14*S^4 + 37*S^6)/(9*S^3))*HPL[{3}, -S^2] + (8*(-1 + S^6)*HPL[{4}, -S^2])/S^3 + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-10*Pi^2*(1 + S^6))/(9*S^3) - (59*(-1 - S^2 + S^4 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (12*(-1 + S^6)*HPL[{3, 1}, -S^2])/S^3 + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 + (24*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - ((1 + S^2)*(553 + 95*S^2 + 22*S^4))/(27*S^3))*Zeta[3] + HPL[{2}, -S^2]*((160*(-1 + S^2)*(1 + S^2)^2)/(9*S^3) + (5*Pi^2*(-7 - S^2 + 3*S^4 + 17*S^6 + 11*S^8))/(27*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) - (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3))) + HPL[{0}, S^2]*((-1399*Pi^6*S^3)/8505 + (-269511 - 13587*S^2 - 273814*S^4)/(8748*S) + (Pi^2*(-39276 - 5994*S^2 - 46181*S^4))/(11664*S) + (Pi^4*(-2682 - 2142*S^2 - 6001*S^4))/(9720*S) - (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2]^6)/(9*S^3) + ((-111 - 192*S^2 - 102*S^4 - 79*S^6)/(108*S^3) - (2*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2}, -S^2]^2 - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{1}, -S^2]^4*((-95 - 147*S^2 - 147*S^4 - 95*S^6)/(54*S^3) - (25*Pi^2*(1 + S^6))/(54*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((-170 - 177*S^2 - 87*S^4 - 154*S^6)/(54*S^3) + (4*Pi^2*(1 + S^6))/(9*S^3))*HPL[{4}, -S^2] + ((-36 - 30*S^2 + 3*S^4 + 13*S^6 + 7*S^8)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + HPL[{1}, -S^2]^3*((-187*(1 + S^2)*(7 + 2*S^2 + 7*S^4))/(243*S^3) + (Pi^2*(-41 - 191*S^2 - 75*S^4 - 209*S^6 - 59*S^8))/(81*S^3*(1 + S^2)) - (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3)) + ((2*Pi^2*(1 + S^6))/(3*S^3) + (307 + 531*S^2 + 261*S^4 + 197*S^6)/(54*S^3))*HPL[{3, 1}, -S^2] - (2*(-7 - S^2 + 3*S^4 + 6*S^6)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + ((75 + 51*S^2 - 12*S^4 - 49*S^6 - 25*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((-2*Pi^2*(1 + S^6))/S^3 - (5*(64 + 99*S^2 + 54*S^4 + 51*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((-61*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(180*S^3) - (Pi^2*(1 + S^2)*(267 + 157*S^2 + 390*S^4))/(216*S^3) - ((1 + S^2)*(47207 + 6490*S^2 + 47207*S^4))/(3888*S^3) + ((-19*Pi^2*(1 + S^6))/(18*S^3) - (5*(115 + 153*S^2 + 153*S^4 + 115*S^6))/(108*S^3))*HPL[{2}, -S^2] - (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) - (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3) - (2*(3 + 63*S^2 + 30*S^4 + 97*S^6 + 37*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2*(15 + 207*S^2 + 96*S^4 + 305*S^6 + 113*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (4*(3 + 27*S^2 + 12*S^4 + 37*S^6 + 13*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^3 - (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-230 + 64*S^2 - 177*S^4)/(108*S) + (Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(9*S*(1 + S^2)))*Zeta[3] - (8*S^3*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((-316 - 126*S^2 - 258*S^4 - 397*S^6)/(108*S^3) + (Pi^2*(-33 - 39*S^2 - 3*S^4 - 10*S^6 - 4*S^8))/(54*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((3295 + 2154*S^2 + 4782*S^4 + 2625*S^6)/(324*S^3) + (Pi^2*(13 + 127*S^2 + 57*S^4 + 188*S^6 + 74*S^8))/(54*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-7*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(90*S^3) + (-14322 - 23079*S^2 - 9111*S^4 - 17656*S^6)/(1944*S^3) + (Pi^2*(-307 - 372*S^2 - 273*S^4 - 241*S^6))/(324*S^3) + ((-7 - S^2 + 3*S^4 + 6*S^6)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((3 + 63*S^2 + 30*S^4 + 97*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((7 + S^2 - 3*S^4 - 6*S^6)*Zeta[3])/(9*S^3*(1 + S^2))) + (8*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(730 + 122*S^2 + 967*S^4))/(324*S^3) - ((1 + S^2)*(54530 + 3127*S^2 + 54530*S^4))/(2916*S^3) + (Pi^4*(-107 - 473*S^2 - 183*S^4 - 503*S^6 - 137*S^8))/(540*S^3*(1 + S^2)) - (5*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-40 - 37*S^2 - 22*S^4 - 25*S^6)/(18*S^3) + (Pi^2*(-1 - S^6))/(9*S^3))*HPL[{3}, -S^2] - (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((19*Pi^2*(1 + S^6))/(9*S^3) + (5*(115 + 153*S^2 + 153*S^4 + 115*S^6))/(54*S^3))*HPL[{2, 1}, -S^2] + (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (16*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (128*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - ((1 + S^2)*(13 - 49*S^2 + 58*S^4))/(54*S^3))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(740 + 127*S^2 + 740*S^4))/(81*S^3) + (Pi^2*(-29 - 143*S^2 - 57*S^4 - 161*S^6 - 47*S^8))/(54*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)));
e4T=e4T0F0+T*e4T1F1*(F+1/F)+T^2*(e4T2F0+e4T2F2*(F^2+1/F^2))+T^3*(e4T3F1*(F+1/F)+e4T3F3*(F^3+1/F^3));
E4uvwT0F0=(20621*Pi^8)/108864 + HPL[{0}, S^2]^8/384 + (HPL[{0}, S^2]^7*HPL[{1}, -S^2])/24 + (22*Pi^2*HPL[{1}, -S^2]^6)/9 + (2*HPL[{1}, -S^2]^8)/3 + HPL[{0}, S^2]^6*((11*Pi^2)/288 + HPL[{1}, -S^2]^2/6 + HPL[{2}, -S^2]/16) + (23*Pi^2*HPL[{2}, -S^2]^3)/18 + (23*HPL[{2}, -S^2]^4)/6 - (Pi^2*HPL[{3}, -S^2]^2)/3 + 32*HPL[{4}, -S^2]^2 + (33*Pi^2*HPL[{6}, -S^2])/2 + 771*HPL[{8}, -S^2] - (134*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + 216*HPL[{3, 1}, -S^2]^2 + HPL[{2}, -S^2]^2*((263*Pi^4)/144 - 4*HPL[{4}, -S^2] + 4*HPL[{3, 1}, -S^2]) + HPL[{1}, -S^2]^4*((1849*Pi^4)/540 + (43*Pi^2*HPL[{2}, -S^2])/9 + (86*HPL[{2}, -S^2]^2)/3 - (56*HPL[{4}, -S^2])/3 + (56*HPL[{3, 1}, -S^2])/3) + 3*Pi^2*HPL[{4, 2}, -S^2] + (26*Pi^2*HPL[{5, 1}, -S^2])/3 + 6*HPL[{5, 3}, -S^2] + 15*HPL[{6, 2}, -S^2] - 416*HPL[{7, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-59*Pi^4)/20 - 688*HPL[{2, 1, 1}, -S^2]) + HPL[{4}, -S^2]*((-28*Pi^4)/45 - 12*HPL[{3, 1}, -S^2] - 56*HPL[{2, 1, 1}, -S^2]) + (707*Pi^4*HPL[{2, 1, 1}, -S^2])/90 + 688*HPL[{2, 1, 1}, -S^2]^2 + (92*Pi^2*HPL[{3, 2, 1}, -S^2])/3 - 28*HPL[{3, 3, 2}, -S^2] + (220*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 68*HPL[{4, 1, 3}, -S^2] - 40*HPL[{4, 2, 2}, -S^2] + 52*HPL[{4, 3, 1}, -S^2] + 8*HPL[{5, 1, 2}, -S^2] + 248*HPL[{5, 2, 1}, -S^2] + 860*HPL[{6, 1, 1}, -S^2] - (112*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 24*HPL[{3, 1, 2, 2}, -S^2] + 24*HPL[{3, 2, 1, 2}, -S^2] - 40*HPL[{3, 2, 2, 1}, -S^2] - 192*HPL[{3, 3, 1, 1}, -S^2] + 72*HPL[{4, 1, 1, 2}, -S^2] - 120*HPL[{4, 1, 2, 1}, -S^2] - 504*HPL[{4, 2, 1, 1}, -S^2] - 800*HPL[{5, 1, 1, 1}, -S^2] + (344*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 - 448*HPL[{4, 1, 1, 1, 1}, -S^2] + 448*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + ((22*Pi^2)/9 + (8*HPL[{0}, S^2]^2)/3 + (56*HPL[{0}, S^2]*HPL[{1}, -S^2])/3 + (56*HPL[{1}, -S^2]^2)/3)*Log[T]^6 + ((-8*HPL[{0}, S^2])/3 - (16*HPL[{1}, -S^2])/3)*Log[T]^7 + (2*Log[T]^8)/3 + Log[T]^4*((1849*Pi^4)/540 + (23*HPL[{0}, S^2]^4)/18 + (110*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/9 + (110*Pi^2*HPL[{1}, -S^2]^2)/3 + (140*HPL[{1}, -S^2]^4)/3 + (43*Pi^2*HPL[{2}, -S^2])/9 + (86*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((53*Pi^2)/9 + 40*HPL[{1}, -S^2]^2 + (43*HPL[{2}, -S^2])/3) - (56*HPL[{4}, -S^2])/3 + (56*HPL[{3, 1}, -S^2])/3 + HPL[{1}, -S^2]*((-400*HPL[{3}, -S^2])/3 - 120*Zeta[3]) + HPL[{0}, S^2]*((280*HPL[{1}, -S^2]^3)/3 + HPL[{1}, -S^2]*((320*Pi^2)/9 + 120*HPL[{2}, -S^2]) + (8*HPL[{3}, -S^2])/3 - 120*HPL[{2, 1}, -S^2] - (28*Zeta[3])/3)) + HPL[{5}, -S^2]*(40*HPL[{2, 1}, -S^2] - 56*Zeta[3]) + HPL[{1}, -S^2]^5*((-80*HPL[{3}, -S^2])/3 - 24*Zeta[3]) + HPL[{0}, S^2]^5*((11*HPL[{1}, -S^2]^3)/18 + HPL[{1}, -S^2]*((4*Pi^2)/9 + (2*HPL[{2}, -S^2])/3) - (2*HPL[{2, 1}, -S^2])/3 + (3*Zeta[3])/4) + 48*HPL[{3, 2}, -S^2]*Zeta[3] + 160*HPL[{4, 1}, -S^2]*Zeta[3] - 304*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 960*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 688*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] + (2*Pi^2*Zeta[3]^2)/3 + Log[T]^5*((-22*HPL[{0}, S^2]^3)/9 - (44*Pi^2*HPL[{1}, -S^2])/3 - 16*HPL[{0}, S^2]^2*HPL[{1}, -S^2] - (112*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]*((-64*Pi^2)/9 - 56*HPL[{1}, -S^2]^2 - 24*HPL[{2}, -S^2]) + (80*HPL[{3}, -S^2])/3 + 24*Zeta[3]) + HPL[{1}, -S^2]^2*((8699*Pi^6)/4536 + (67*Pi^2*HPL[{2}, -S^2]^2)/3 + 8*HPL[{3}, -S^2]^2 - (28*Pi^2*HPL[{4}, -S^2])/3 + 70*HPL[{6}, -S^2] - 344*HPL[{2, 1}, -S^2]^2 - (56*Pi^2*HPL[{3, 1}, -S^2])/3 + 36*HPL[{4, 2}, -S^2] + 176*HPL[{5, 1}, -S^2] + (172*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((707*Pi^4)/180 - 28*HPL[{4}, -S^2] - 344*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]) - 224*HPL[{4, 1, 1}, -S^2] + 224*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(344*HPL[{2, 1}, -S^2] - 24*Zeta[3]) + 344*HPL[{2, 1}, -S^2]*Zeta[3] + 4*Zeta[3]^2) + HPL[{2}, -S^2]*((2047*Pi^6)/5040 - 2*HPL[{3}, -S^2]^2 - (Pi^2*HPL[{4}, -S^2])/3 + 79*HPL[{6}, -S^2] - 46*Pi^2*HPL[{3, 1}, -S^2] + 24*HPL[{4, 2}, -S^2] + 48*HPL[{5, 1}, -S^2] + (268*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 24*HPL[{3, 1, 2}, -S^2] + 344*HPL[{3, 2, 1}, -S^2] + 1048*HPL[{4, 1, 1}, -S^2] - 688*HPL[{3, 1, 1, 1}, -S^2] + 1376*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(192*HPL[{2, 1}, -S^2] - 24*Zeta[3]) + 152*HPL[{2, 1}, -S^2]*Zeta[3] + 6*Zeta[3]^2) + HPL[{0}, S^2]^4*((1849*Pi^4)/8640 + (23*HPL[{1}, -S^2]^4)/18 + (19*Pi^2*HPL[{2}, -S^2])/36 + (31*HPL[{2}, -S^2]^2)/48 + HPL[{1}, -S^2]^2*((53*Pi^2)/36 + (31*HPL[{2}, -S^2])/12) + HPL[{4}, -S^2]/2 - (31*HPL[{3, 1}, -S^2])/12 + (31*HPL[{2, 1, 1}, -S^2])/6 + HPL[{1}, -S^2]*((-31*HPL[{2, 1}, -S^2])/6 + (7*Zeta[3])/6)) + HPL[{0}, S^2]^2*((8699*Pi^6)/18144 + (8*HPL[{1}, -S^2]^6)/3 + (79*Pi^2*HPL[{2}, -S^2]^2)/24 + (23*HPL[{2}, -S^2]^3)/6 + HPL[{1}, -S^2]^4*((53*Pi^2)/9 + (43*HPL[{2}, -S^2])/3) - 3*HPL[{3}, -S^2]^2 + Pi^2*HPL[{4}, -S^2] + 32*HPL[{6}, -S^2] - 48*HPL[{2, 1}, -S^2]^2 - (73*Pi^2*HPL[{3, 1}, -S^2])/6 - 18*HPL[{5, 1}, -S^2] + (74*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((473*Pi^4)/360 + 6*HPL[{4}, -S^2] - 52*HPL[{3, 1}, -S^2] + 96*HPL[{2, 1, 1}, -S^2]) + HPL[{1}, -S^2]^2*((359*Pi^4)/90 + (37*Pi^2*HPL[{2}, -S^2])/3 + 24*HPL[{2}, -S^2]^2 - 84*HPL[{3, 1}, -S^2] + 172*HPL[{2, 1, 1}, -S^2]) + 92*HPL[{3, 2, 1}, -S^2] + 276*HPL[{4, 1, 1}, -S^2] - 168*HPL[{3, 1, 1, 1}, -S^2] + 344*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(6*HPL[{2, 1}, -S^2] - 6*Zeta[3]) + HPL[{1}, -S^2]^3*(-4*HPL[{3}, -S^2] - (172*HPL[{2, 1}, -S^2])/3 - (16*Zeta[3])/3) + 8*HPL[{2, 1}, -S^2]*Zeta[3] + Zeta[3]^2 + HPL[{1}, -S^2]*(-(Pi^2*HPL[{3}, -S^2]) + 6*HPL[{5}, -S^2] - (74*Pi^2*HPL[{2, 1}, -S^2])/3 + 12*HPL[{3, 2}, -S^2] + 36*HPL[{4, 1}, -S^2] + 192*HPL[{2, 2, 1}, -S^2] + 552*HPL[{3, 1, 1}, -S^2] - 344*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-6*HPL[{3}, -S^2] - 96*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + Pi^2*Zeta[3])) + Log[T]^2*((8699*Pi^6)/4536 + HPL[{0}, S^2]^6/6 + (11*HPL[{0}, S^2]^5*HPL[{1}, -S^2])/6 + (110*Pi^2*HPL[{1}, -S^2]^4)/3 + (56*HPL[{1}, -S^2]^6)/3 + (67*Pi^2*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^4*((53*Pi^2)/36 + (23*HPL[{1}, -S^2]^2)/3 + (31*HPL[{2}, -S^2])/12) + 8*HPL[{3}, -S^2]^2 - (28*Pi^2*HPL[{4}, -S^2])/3 + 70*HPL[{6}, -S^2] - 344*HPL[{2, 1}, -S^2]^2 - (56*Pi^2*HPL[{3, 1}, -S^2])/3 + HPL[{1}, -S^2]^2*((1849*Pi^4)/90 + (86*Pi^2*HPL[{2}, -S^2])/3 + 172*HPL[{2}, -S^2]^2 - 112*HPL[{4}, -S^2] + 112*HPL[{3, 1}, -S^2]) + 36*HPL[{4, 2}, -S^2] + 176*HPL[{5, 1}, -S^2] + (172*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((707*Pi^4)/180 - 28*HPL[{4}, -S^2] - 344*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]) - 224*HPL[{4, 1, 1}, -S^2] + 224*HPL[{3, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^2*((359*Pi^4)/90 + 40*HPL[{1}, -S^2]^4 + (37*Pi^2*HPL[{2}, -S^2])/3 + 24*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((106*Pi^2)/3 + 86*HPL[{2}, -S^2]) - 84*HPL[{3, 1}, -S^2] + 172*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*(-12*HPL[{3}, -S^2] - 172*HPL[{2, 1}, -S^2] - 16*Zeta[3])) + HPL[{1}, -S^2]^3*((-800*HPL[{3}, -S^2])/3 - 240*Zeta[3]) + HPL[{3}, -S^2]*(344*HPL[{2, 1}, -S^2] - 24*Zeta[3]) + 344*HPL[{2, 1}, -S^2]*Zeta[3] + 4*Zeta[3]^2 + HPL[{0}, S^2]^3*((220*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((110*Pi^2)/9 + 30*HPL[{2}, -S^2]) + 2*HPL[{3}, -S^2] - 30*HPL[{2, 1}, -S^2] + (8*Zeta[3])/3) + HPL[{0}, S^2]*(56*HPL[{1}, -S^2]^5 + HPL[{1}, -S^2]^3*((640*Pi^2)/9 + 240*HPL[{2}, -S^2]) + (10*Pi^2*HPL[{3}, -S^2])/3 + 20*HPL[{5}, -S^2] - 90*Pi^2*HPL[{2, 1}, -S^2] + 40*HPL[{3, 2}, -S^2] + 64*HPL[{4, 1}, -S^2] + HPL[{1}, -S^2]*((937*Pi^4)/45 + 90*Pi^2*HPL[{2}, -S^2] + 172*HPL[{2}, -S^2]^2 + 56*HPL[{4}, -S^2] - 720*HPL[{3, 1}, -S^2] + 1440*HPL[{2, 1, 1}, -S^2]) + 688*HPL[{2, 2, 1}, -S^2] + 2096*HPL[{3, 1, 1}, -S^2] - 1440*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*(16*HPL[{3}, -S^2] - 720*HPL[{2, 1}, -S^2] - 56*Zeta[3]) + HPL[{2}, -S^2]*(-20*HPL[{3}, -S^2] - 344*HPL[{2, 1}, -S^2] - 20*Zeta[3]) - 2*Pi^2*Zeta[3]) + HPL[{1}, -S^2]*((-212*Pi^2*HPL[{3}, -S^2])/3 - 48*HPL[{5}, -S^2] - (172*Pi^2*HPL[{2, 1}, -S^2])/3 + 688*HPL[{3, 2}, -S^2] + 2288*HPL[{4, 1}, -S^2] + 1376*HPL[{2, 2, 1}, -S^2] + 2528*HPL[{3, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-344*HPL[{3}, -S^2] - 688*HPL[{2, 1}, -S^2] - 344*Zeta[3]) - (196*Pi^2*Zeta[3])/3 - 440*Zeta[5])) + HPL[{1}, -S^2]^3*((-212*Pi^2*HPL[{3}, -S^2])/9 - 16*HPL[{5}, -S^2] - (172*Pi^2*HPL[{2, 1}, -S^2])/9 + (688*HPL[{3, 2}, -S^2])/3 + (2288*HPL[{4, 1}, -S^2])/3 + (1376*HPL[{2, 2, 1}, -S^2])/3 + (2528*HPL[{3, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((-344*HPL[{3}, -S^2])/3 - (688*HPL[{2, 1}, -S^2])/3 - (344*Zeta[3])/3) - (196*Pi^2*Zeta[3])/9 - (440*Zeta[5])/3) + HPL[{3}, -S^2]*(-70*HPL[{5}, -S^2] + (92*Pi^2*HPL[{2, 1}, -S^2])/3 + 8*HPL[{3, 2}, -S^2] - 28*HPL[{4, 1}, -S^2] - 384*HPL[{2, 2, 1}, -S^2] - 1120*HPL[{3, 1, 1}, -S^2] + 688*HPL[{2, 1, 1, 1}, -S^2] - 4*Pi^2*Zeta[3] - 32*Zeta[5]) - 64*Zeta[3]*Zeta[5] + HPL[{0}, S^2]^3*((22*HPL[{1}, -S^2]^5)/9 + HPL[{1}, -S^2]^3*((110*Pi^2)/27 + 10*HPL[{2}, -S^2]) + (Pi^2*HPL[{3}, -S^2])/6 - 3*HPL[{5}, -S^2] - (85*Pi^2*HPL[{2, 1}, -S^2])/18 + 2*HPL[{3, 2}, -S^2] + 4*HPL[{4, 1}, -S^2] + HPL[{1}, -S^2]*((937*Pi^4)/540 + (85*Pi^2*HPL[{2}, -S^2])/18 + (19*HPL[{2}, -S^2]^2)/3 + 2*HPL[{4}, -S^2] - (88*HPL[{3, 1}, -S^2])/3 + 60*HPL[{2, 1, 1}, -S^2]) + (76*HPL[{2, 2, 1}, -S^2])/3 + 80*HPL[{3, 1, 1}, -S^2] - 60*HPL[{2, 1, 1, 1}, -S^2] + (49*Pi^2*Zeta[3])/18 + HPL[{2}, -S^2]*(-HPL[{3}, -S^2] - (38*HPL[{2, 1}, -S^2])/3 + (4*Zeta[3])/3) + HPL[{1}, -S^2]^2*(2*HPL[{3}, -S^2] - 30*HPL[{2, 1}, -S^2] + (8*Zeta[3])/3) + (55*Zeta[5])/3) + Log[T]^3*((-11*HPL[{0}, S^2]^5)/18 - (46*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/9 - (440*Pi^2*HPL[{1}, -S^2]^3)/9 - (112*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^3*((-110*Pi^2)/27 - (220*HPL[{1}, -S^2]^2)/9 - 10*HPL[{2}, -S^2]) + (212*Pi^2*HPL[{3}, -S^2])/9 + 16*HPL[{5}, -S^2] + (172*Pi^2*HPL[{2, 1}, -S^2])/9 + HPL[{1}, -S^2]*((-1849*Pi^4)/135 - (172*Pi^2*HPL[{2}, -S^2])/9 - (344*HPL[{2}, -S^2]^2)/3 + (224*HPL[{4}, -S^2])/3 - (224*HPL[{3, 1}, -S^2])/3) - (688*HPL[{3, 2}, -S^2])/3 - (2288*HPL[{4, 1}, -S^2])/3 - (1376*HPL[{2, 2, 1}, -S^2])/3 - (2528*HPL[{3, 1, 1}, -S^2])/3 + (196*Pi^2*Zeta[3])/9 + HPL[{0}, S^2]^2*((-160*HPL[{1}, -S^2]^3)/3 + HPL[{1}, -S^2]*((-212*Pi^2)/9 - (172*HPL[{2}, -S^2])/3) + 4*HPL[{3}, -S^2] + (172*HPL[{2, 1}, -S^2])/3 + (16*Zeta[3])/3) + HPL[{2}, -S^2]*((344*HPL[{3}, -S^2])/3 + (688*HPL[{2, 1}, -S^2])/3 + (344*Zeta[3])/3) + HPL[{1}, -S^2]^2*((800*HPL[{3}, -S^2])/3 + 240*Zeta[3]) + HPL[{0}, S^2]*((-937*Pi^4)/135 - (280*HPL[{1}, -S^2]^4)/3 + HPL[{1}, -S^2]^2*((-640*Pi^2)/9 - 240*HPL[{2}, -S^2]) - 30*Pi^2*HPL[{2}, -S^2] - (172*HPL[{2}, -S^2]^2)/3 - (56*HPL[{4}, -S^2])/3 + 240*HPL[{3, 1}, -S^2] - 480*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((-32*HPL[{3}, -S^2])/3 + 480*HPL[{2, 1}, -S^2] + (112*Zeta[3])/3)) + (440*Zeta[5])/3) + HPL[{2, 1}, -S^2]*(-360*HPL[{3, 2}, -S^2] - 1096*HPL[{4, 1}, -S^2] + 688*HPL[{3, 1, 1}, -S^2] - 1376*HPL[{2, 1, 1, 1}, -S^2] + (94*Pi^2*Zeta[3])/3 + 172*Zeta[5]) + HPL[{1}, -S^2]*(-2*Pi^2*HPL[{5}, -S^2] + 288*HPL[{7}, -S^2] + (184*Pi^2*HPL[{3, 2}, -S^2])/3 + (608*Pi^2*HPL[{4, 1}, -S^2])/3 - 44*HPL[{4, 3}, -S^2] - 120*HPL[{5, 2}, -S^2] - 300*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((-196*Pi^4)/45 + 28*HPL[{4}, -S^2] + 352*HPL[{3, 1}, -S^2] - 688*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-707*Pi^4)/90 + 688*HPL[{3, 1}, -S^2] + 1376*HPL[{2, 1, 1}, -S^2]) + (536*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (1184*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 696*HPL[{3, 2, 2}, -S^2] - 2144*HPL[{3, 3, 1}, -S^2] - 2120*HPL[{4, 1, 2}, -S^2] - 6536*HPL[{4, 2, 1}, -S^2] - 13344*HPL[{5, 1, 1}, -S^2] - (344*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 1376*HPL[{3, 1, 1, 2}, -S^2] + 1376*HPL[{3, 1, 2, 1}, -S^2] + 1376*HPL[{3, 2, 1, 1}, -S^2] + 4576*HPL[{4, 1, 1, 1}, -S^2] - 2752*HPL[{2, 1, 2, 1, 1}, -S^2] - 8256*HPL[{2, 2, 1, 1, 1}, -S^2] - 16960*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^2*(-96*HPL[{3}, -S^2] - 76*Zeta[3]) + HPL[{4}, -S^2]*(56*HPL[{2, 1}, -S^2] - 16*Zeta[3]) - (157*Pi^4*Zeta[3])/45 + 352*HPL[{3, 1}, -S^2]*Zeta[3] - 688*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]*((-92*Pi^2*HPL[{3}, -S^2])/3 - 40*HPL[{5}, -S^2] - (268*Pi^2*HPL[{2, 1}, -S^2])/3 + 360*HPL[{3, 2}, -S^2] + 1096*HPL[{4, 1}, -S^2] - 688*HPL[{3, 1, 1}, -S^2] - 1376*HPL[{2, 1, 1, 1}, -S^2] - (94*Pi^2*Zeta[3])/3 - 172*Zeta[5]) - (110*Pi^2*Zeta[5])/3 - 300*Zeta[7]) + HPL[{0}, S^2]*((8*HPL[{1}, -S^2]^7)/3 + HPL[{1}, -S^2]^5*((64*Pi^2)/9 + 24*HPL[{2}, -S^2]) - (4*Pi^2*HPL[{5}, -S^2])/3 - 120*HPL[{7}, -S^2] + (16*Pi^2*HPL[{3, 2}, -S^2])/3 + (28*Pi^2*HPL[{4, 1}, -S^2])/3 - 48*HPL[{4, 3}, -S^2] - 144*HPL[{5, 2}, -S^2] - 240*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((26*Pi^4)/45 + 24*HPL[{4}, -S^2] + 40*HPL[{3, 1}, -S^2] - 40*HPL[{2, 1, 1}, -S^2]) + HPL[{1}, -S^2]^3*((937*Pi^4)/135 + 30*Pi^2*HPL[{2}, -S^2] + (172*HPL[{2}, -S^2]^2)/3 + (56*HPL[{4}, -S^2])/3 - 240*HPL[{3, 1}, -S^2] + 480*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-377*Pi^4)/45 + 344*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]) + (248*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (764*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 64*HPL[{3, 2, 2}, -S^2] - 208*HPL[{3, 3, 1}, -S^2] - 208*HPL[{4, 1, 2}, -S^2] - 640*HPL[{4, 2, 1}, -S^2] - 1256*HPL[{5, 1, 1}, -S^2] - 180*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 608*HPL[{2, 2, 2, 1}, -S^2] + 1904*HPL[{3, 1, 1, 2}, -S^2] + 1904*HPL[{3, 1, 2, 1}, -S^2] + 3728*HPL[{3, 2, 1, 1}, -S^2] + 11072*HPL[{4, 1, 1, 1}, -S^2] - 1376*HPL[{2, 1, 2, 1, 1}, -S^2] - 4128*HPL[{2, 2, 1, 1, 1}, -S^2] - 6816*HPL[{3, 1, 1, 1, 1}, -S^2] - 2880*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^4*((8*HPL[{3}, -S^2])/3 - 120*HPL[{2, 1}, -S^2] - (28*Zeta[3])/3) + HPL[{2}, -S^2]^2*(-8*HPL[{3}, -S^2] - 76*HPL[{2, 1}, -S^2] - 2*Zeta[3]) + (157*Pi^4*Zeta[3])/90 - 40*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-8*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{1}, -S^2]^2*((10*Pi^2*HPL[{3}, -S^2])/3 + 20*HPL[{5}, -S^2] - 90*Pi^2*HPL[{2, 1}, -S^2] + 40*HPL[{3, 2}, -S^2] + 64*HPL[{4, 1}, -S^2] + 688*HPL[{2, 2, 1}, -S^2] + 2096*HPL[{3, 1, 1}, -S^2] - 1440*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-20*HPL[{3}, -S^2] - 344*HPL[{2, 1}, -S^2] - 20*Zeta[3]) - 2*Pi^2*Zeta[3]) + HPL[{1}, -S^2]*((12907*Pi^6)/5670 + (62*Pi^2*HPL[{2}, -S^2]^2)/3 + (76*HPL[{2}, -S^2]^3)/3 - 4*HPL[{3}, -S^2]^2 + (20*Pi^2*HPL[{4}, -S^2])/3 - 344*HPL[{2, 1}, -S^2]^2 - (268*Pi^2*HPL[{3, 1}, -S^2])/3 - 56*HPL[{5, 1}, -S^2] + 180*Pi^2*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((377*Pi^4)/45 + 8*HPL[{4}, -S^2] - 344*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]) + 608*HPL[{3, 2, 1}, -S^2] + 1936*HPL[{4, 1, 1}, -S^2] - 1440*HPL[{3, 1, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1, 1}, -S^2] + 40*HPL[{2, 1}, -S^2]*Zeta[3] + 16*Zeta[3]^2 + HPL[{3}, -S^2]*(40*HPL[{2, 1}, -S^2] + 8*Zeta[3])) + (55*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((-8*Pi^2*HPL[{3}, -S^2])/3 - 24*HPL[{5}, -S^2] - (124*Pi^2*HPL[{2, 1}, -S^2])/3 + 32*HPL[{3, 2}, -S^2] + 104*HPL[{4, 1}, -S^2] + 304*HPL[{2, 2, 1}, -S^2] - 952*HPL[{3, 1, 1}, -S^2] - 688*HPL[{2, 1, 1, 1}, -S^2] - (Pi^2*Zeta[3])/3 + 24*Zeta[5]) + 150*Zeta[7]) + Log[T]*(-HPL[{0}, S^2]^7/24 - (HPL[{0}, S^2]^6*HPL[{1}, -S^2])/3 - (44*Pi^2*HPL[{1}, -S^2]^5)/3 - (16*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^5*((-4*Pi^2)/9 - (11*HPL[{1}, -S^2]^2)/6 - (2*HPL[{2}, -S^2])/3) + 2*Pi^2*HPL[{5}, -S^2] - 288*HPL[{7}, -S^2] + HPL[{1}, -S^2]^3*((-1849*Pi^4)/135 - (172*Pi^2*HPL[{2}, -S^2])/9 - (344*HPL[{2}, -S^2]^2)/3 + (224*HPL[{4}, -S^2])/3 - (224*HPL[{3, 1}, -S^2])/3) - (184*Pi^2*HPL[{3, 2}, -S^2])/3 - (608*Pi^2*HPL[{4, 1}, -S^2])/3 + 44*HPL[{4, 3}, -S^2] + 120*HPL[{5, 2}, -S^2] + 300*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((707*Pi^4)/90 - 688*HPL[{3, 1}, -S^2] - 1376*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((196*Pi^4)/45 - 28*HPL[{4}, -S^2] - 352*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]) - (536*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (1184*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 696*HPL[{3, 2, 2}, -S^2] + 2144*HPL[{3, 3, 1}, -S^2] + 2120*HPL[{4, 1, 2}, -S^2] + 6536*HPL[{4, 2, 1}, -S^2] + 13344*HPL[{5, 1, 1}, -S^2] + (344*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 1376*HPL[{3, 1, 1, 2}, -S^2] - 1376*HPL[{3, 1, 2, 1}, -S^2] - 1376*HPL[{3, 2, 1, 1}, -S^2] - 4576*HPL[{4, 1, 1, 1}, -S^2] + 2752*HPL[{2, 1, 2, 1, 1}, -S^2] + 8256*HPL[{2, 2, 1, 1, 1}, -S^2] + 16960*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^3*((-937*Pi^4)/540 - (110*HPL[{1}, -S^2]^4)/9 + HPL[{1}, -S^2]^2*((-110*Pi^2)/9 - 30*HPL[{2}, -S^2]) - (85*Pi^2*HPL[{2}, -S^2])/18 - (19*HPL[{2}, -S^2]^2)/3 - 2*HPL[{4}, -S^2] + (88*HPL[{3, 1}, -S^2])/3 - 60*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*(-4*HPL[{3}, -S^2] + 60*HPL[{2, 1}, -S^2] - (16*Zeta[3])/3)) + HPL[{0}, S^2]^4*((-46*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((-53*Pi^2)/18 - (31*HPL[{2}, -S^2])/6) + (31*HPL[{2, 1}, -S^2])/6 - (7*Zeta[3])/6) + (157*Pi^4*Zeta[3])/45 - 352*HPL[{3, 1}, -S^2]*Zeta[3] + 688*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-56*HPL[{2, 1}, -S^2] + 16*Zeta[3]) + HPL[{2}, -S^2]^2*(96*HPL[{3}, -S^2] + 76*Zeta[3]) + HPL[{1}, -S^2]^4*((400*HPL[{3}, -S^2])/3 + 120*Zeta[3]) + HPL[{0}, S^2]^2*(-16*HPL[{1}, -S^2]^5 + HPL[{1}, -S^2]^3*((-212*Pi^2)/9 - (172*HPL[{2}, -S^2])/3) + Pi^2*HPL[{3}, -S^2] - 6*HPL[{5}, -S^2] + (74*Pi^2*HPL[{2, 1}, -S^2])/3 - 12*HPL[{3, 2}, -S^2] - 36*HPL[{4, 1}, -S^2] + HPL[{1}, -S^2]*((-359*Pi^4)/45 - (74*Pi^2*HPL[{2}, -S^2])/3 - 48*HPL[{2}, -S^2]^2 + 168*HPL[{3, 1}, -S^2] - 344*HPL[{2, 1, 1}, -S^2]) - 192*HPL[{2, 2, 1}, -S^2] - 552*HPL[{3, 1, 1}, -S^2] + 344*HPL[{2, 1, 1, 1}, -S^2] - Pi^2*Zeta[3] + HPL[{2}, -S^2]*(6*HPL[{3}, -S^2] + 96*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + HPL[{1}, -S^2]^2*(12*HPL[{3}, -S^2] + 172*HPL[{2, 1}, -S^2] + 16*Zeta[3])) + HPL[{1}, -S^2]*((-8699*Pi^6)/2268 - (134*Pi^2*HPL[{2}, -S^2]^2)/3 - 16*HPL[{3}, -S^2]^2 + (56*Pi^2*HPL[{4}, -S^2])/3 - 140*HPL[{6}, -S^2] + 688*HPL[{2, 1}, -S^2]^2 + (112*Pi^2*HPL[{3, 1}, -S^2])/3 - 72*HPL[{4, 2}, -S^2] - 352*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-707*Pi^4)/90 + 56*HPL[{4}, -S^2] + 688*HPL[{3, 1}, -S^2] - 1376*HPL[{2, 1, 1}, -S^2]) - (344*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 448*HPL[{4, 1, 1}, -S^2] - 448*HPL[{3, 1, 1, 1}, -S^2] - 688*HPL[{2, 1}, -S^2]*Zeta[3] - 8*Zeta[3]^2 + HPL[{3}, -S^2]*(-688*HPL[{2, 1}, -S^2] + 48*Zeta[3])) + HPL[{0}, S^2]*((-12907*Pi^6)/5670 - (56*HPL[{1}, -S^2]^6)/3 + HPL[{1}, -S^2]^4*((-320*Pi^2)/9 - 120*HPL[{2}, -S^2]) - (62*Pi^2*HPL[{2}, -S^2]^2)/3 - (76*HPL[{2}, -S^2]^3)/3 + 4*HPL[{3}, -S^2]^2 - (20*Pi^2*HPL[{4}, -S^2])/3 + 344*HPL[{2, 1}, -S^2]^2 + (268*Pi^2*HPL[{3, 1}, -S^2])/3 + 56*HPL[{5, 1}, -S^2] + HPL[{1}, -S^2]^2*((-937*Pi^4)/45 - 90*Pi^2*HPL[{2}, -S^2] - 172*HPL[{2}, -S^2]^2 - 56*HPL[{4}, -S^2] + 720*HPL[{3, 1}, -S^2] - 1440*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]*((-377*Pi^4)/45 - 8*HPL[{4}, -S^2] + 344*HPL[{3, 1}, -S^2] - 688*HPL[{2, 1, 1}, -S^2]) - 180*Pi^2*HPL[{2, 1, 1}, -S^2] - 608*HPL[{3, 2, 1}, -S^2] - 1936*HPL[{4, 1, 1}, -S^2] + 1440*HPL[{3, 1, 1, 1}, -S^2] - 2880*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-40*HPL[{2, 1}, -S^2] - 8*Zeta[3]) - 40*HPL[{2, 1}, -S^2]*Zeta[3] - 16*Zeta[3]^2 + HPL[{1}, -S^2]^3*((-32*HPL[{3}, -S^2])/3 + 480*HPL[{2, 1}, -S^2] + (112*Zeta[3])/3) + HPL[{1}, -S^2]*((-20*Pi^2*HPL[{3}, -S^2])/3 - 40*HPL[{5}, -S^2] + 180*Pi^2*HPL[{2, 1}, -S^2] - 80*HPL[{3, 2}, -S^2] - 128*HPL[{4, 1}, -S^2] - 1376*HPL[{2, 2, 1}, -S^2] - 4192*HPL[{3, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1}, -S^2] + 4*Pi^2*Zeta[3] + HPL[{2}, -S^2]*(40*HPL[{3}, -S^2] + 688*HPL[{2, 1}, -S^2] + 40*Zeta[3]))) + (110*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((92*Pi^2*HPL[{3}, -S^2])/3 + 40*HPL[{5}, -S^2] + (268*Pi^2*HPL[{2, 1}, -S^2])/3 - 360*HPL[{3, 2}, -S^2] - 1096*HPL[{4, 1}, -S^2] + 688*HPL[{3, 1, 1}, -S^2] + 1376*HPL[{2, 1, 1, 1}, -S^2] + (94*Pi^2*Zeta[3])/3 + 172*Zeta[5]) + HPL[{1}, -S^2]^2*((212*Pi^2*HPL[{3}, -S^2])/3 + 48*HPL[{5}, -S^2] + (172*Pi^2*HPL[{2, 1}, -S^2])/3 - 688*HPL[{3, 2}, -S^2] - 2288*HPL[{4, 1}, -S^2] - 1376*HPL[{2, 2, 1}, -S^2] - 2528*HPL[{3, 1, 1}, -S^2] + (196*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*(344*HPL[{3}, -S^2] + 688*HPL[{2, 1}, -S^2] + 344*Zeta[3]) + 440*Zeta[5]) + 300*Zeta[7]);
E4uvwT1F1=-(S*HPL[{0}, S^2]^7)/(24*(1 + S^2)) + ((6 - 13*S^2 - 3*S^4)*HPL[{0}, S^2]^6*HPL[{1}, -S^2])/(48*S*(1 + S^2)) + (4*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^7)/(21*S*(1 + S^2)) + HPL[{1}, -S^2]^5*((Pi^2*(29 - 173*S^2 + 18*S^4))/(15*S*(1 + S^2)) - (22*(-1 + S^2)*HPL[{2}, -S^2])/(5*S)) + HPL[{0}, S^2]^5*(-(Pi^2*S*(65 + S^2))/(144*(1 + S^2)) + ((9 - 36*S^2 - S^4)*HPL[{1}, -S^2]^2)/(24*S*(1 + S^2)) - (S*(17 + S^2)*HPL[{2}, -S^2])/(24*(1 + S^2))) - (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + (Pi^2*(20 - 45*S^2 - 77*S^4)*HPL[{5}, -S^2])/(6*S*(1 + S^2)) - (3*(-75 + 115*S^2 + 94*S^4)*HPL[{7}, -S^2])/(S*(1 + S^2)) + (8*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + (Pi^2*(5 - 224*S^2 + 139*S^4)*HPL[{3, 2}, -S^2])/(6*S*(1 + S^2)) + (Pi^2*(-7 - 372*S^2 + 243*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (4*S*(16 + 5*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) + (3*(2 + 67*S^2 + 25*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) + (2*(-58 + 287*S^2 + 195*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) + HPL[{3}, -S^2]*((Pi^2*(1 + S^2))/(3*S) + (Pi^4*(49 + 898*S^2 - 719*S^4))/(360*S*(1 + S^2)) - (4*S*(8 + S^2)*HPL[{4}, -S^2])/(1 + S^2) - (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (2*(-3 - 120*S^2 + 59*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (4*(-3 - 108*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) + (8*Pi^2*(17 - 42*S^2 + 8*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*Pi^2*(209 - 370*S^2 + 13*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + ((29 + 466*S^2 - 259*S^4)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) - (8*(-8 - 181*S^2 + 95*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) - (2*(-29 - 706*S^2 + 383*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) - (2*(-77 - 2206*S^2 + 1139*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-82 - 2237*S^2 + 1181*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*Pi^2*(-38 + 27*S^2 + 22*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (288*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S - (4*(-213 + 216*S^2 + 85*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(-213 + 216*S^2 + 85*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-429 + 216*S^2 + 301*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(-639 + 364*S^2 + 431*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (64*(8 - 27*S^2 + 8*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (192*(8 - 27*S^2 + 8*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(79 - 334*S^2 + 117*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (1216*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((-2*Pi^2*S*(-65 + S^2))/(9*(1 + S^2)) - (2*S*(-23 + S^2)*HPL[{0}, S^2]^2)/(3*(1 + S^2)) - (4*(3 - 22*S^2 + 3*S^4)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(S*(1 + S^2)) - (4*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) - (4*(-1 + S^2)*HPL[{2}, -S^2])/(3*S))*Log[T]^5 + ((4*S*(-11 + 3*S^2)*HPL[{0}, S^2])/(3*(1 + S^2)) + (4*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2])/(3*S*(1 + S^2)))*Log[T]^6 + (16*S*Log[T]^7)/(3*(1 + S^2)) - (157*Pi^4*S^3*Zeta[3])/(45*(1 + S^2)) + HPL[{2, 1}, -S^2]*((Pi^4*(-474 + 425*S^2 + 192*S^4))/(90*S*(1 + S^2)) + (4*(33 - 108*S^2 + 31*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (32*(8 - 27*S^2 + 8*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((10*Pi^2*(1 + S^2))/(9*S) + (Pi^4*(1152 - 5849*S^2 + 395*S^4))/(540*S*(1 + S^2)) - (2*Pi^2*(-36 + 67*S^2 + 17*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (2*(19 - 134*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (2*(-9 - 84*S^2 + 37*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (8*(-13 - 21*S^2 + 20*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (88*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-4*Pi^2*(1 + S^2))/(3*S) - (16*S*(-27 + 16*S^2)*Zeta[3])/(1 + S^2)) + Log[T]^4*((S*(-101 + 9*S^2)*HPL[{0}, S^2]^3)/(9*(1 + S^2)) + ((14 - 63*S^2 + 3*S^4)*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/(S*(1 + S^2)) + (20*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(29 - 173*S^2 + 18*S^4))/(3*S*(1 + S^2)) - (22*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]*((2*Pi^2*S*(-133 + 27*S^2))/(9*(1 + S^2)) + (10*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) + (2*(-2 - 141*S^2 + 41*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) - (4*(-1 - 64*S^2 + 37*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (152*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*S*(-26 + 19*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{0}, S^2]^4*((5*(1 + S^2)*HPL[{1}, -S^2]^2)/(12*S) + ((43 - 147*S^2 - 6*S^4)*HPL[{1}, -S^2]^3)/(36*S*(1 + S^2)) + HPL[{1}, -S^2]*((5*(1 + S^2))/(6*S) + (Pi^2*(133 - 342*S^2 - 51*S^4))/(144*S*(1 + S^2)) + ((37 - 99*S^2 - 12*S^4)*HPL[{2}, -S^2])/(24*S*(1 + S^2))) + ((1 - 3*S^2)*HPL[{3}, -S^2])/(8*S) + ((-17 + 17*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) - (S*(26 + 19*S^2)*Zeta[3])/(6*(1 + S^2))) + HPL[{4}, -S^2]*((Pi^2*(1 + S^2))/(3*S) + (4*(-1 - 14*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(-1 + 2*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]^2*((Pi^2*(-1 - S^2))/(2*S) + ((5 + 130*S^2 - 67*S^4)*HPL[{3}, -S^2])/(2*S*(1 + S^2)) + (36*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(-1 - 12*S^2 + 8*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^4*((Pi^2*(1 + S^2))/(3*S) - (2*(6 - 155*S^2 + 39*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (22*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (2*(1 - 47*S^2 + 12*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) + (8*(1 - 28*S^2 + 15*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^3*((Pi^4*S*(-3723 + 25*S^2))/(2160*(1 + S^2)) + (2*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + ((36 - 175*S^2 + 9*S^4)*HPL[{1}, -S^2]^4)/(18*S*(1 + S^2)) + ((-2*(1 + S^2))/S + (Pi^2*S*(-167 + 3*S^2))/(36*(1 + S^2)))*HPL[{2}, -S^2] + (S*(-69 + 7*S^2)*HPL[{2}, -S^2]^2)/(12*(1 + S^2)) + HPL[{1}, -S^2]^2*((1 + S^2)/(3*S) + (Pi^2*(81 - 355*S^2 + 4*S^4))/(36*S*(1 + S^2)) + ((15 - 71*S^2 + 4*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + ((-1 - S^2)*HPL[{3}, -S^2])/S + (2*S^3*HPL[{4}, -S^2])/(1 + S^2) + (4*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (S*(-75 + 13*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) + (4*S*(-41 + 4*S^2)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2))/(18*S) - (5*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (S*(-3 + S^2)*HPL[{3}, -S^2])/(1 + S^2) - (2*(15 - 71*S^2 + 4*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (2*(-2 + 9*S^2 + 3*S^4)*Zeta[3])/(3*S*(1 + S^2)))) + Log[T]^3*((Pi^4*S*(3723 + 25*S^2))/(270*(1 + S^2)) + (S*(101 + 9*S^2)*HPL[{0}, S^2]^4)/(18*(1 + S^2)) - (2*(36 - 175*S^2 + 9*S^4)*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/(9*S*(1 + S^2)) - (20*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)) - (4*Pi^2*(-2 - 40*S^2 + 5*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - (4*(3 - 80*S^2 + 3*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^2*((-2*Pi^2*(29 - 173*S^2 + 18*S^4))/(3*S*(1 + S^2)) + (44*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^2*((4*Pi^2*S*(54 + S^2))/(9*(1 + S^2)) - (4*(1 + S^2)*HPL[{1}, -S^2])/S - (2*(14 - 63*S^2 + 3*S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) - (2*(1 - 80*S^2 + 5*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + (4*(-9 - 44*S^2 + 21*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (16*(-4 + 11*S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (80*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + HPL[{0}, S^2]*((-40*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) + (8*(1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((-2*Pi^2*(81 - 505*S^2 + 54*S^4))/(9*S*(1 + S^2)) - (4*(13 - 94*S^2 + 13*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + (8*(-1 + 4*S^2 + S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (8*(-41 + 141*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*S*(-11 + 3*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]*((-4*Pi^2*(1 + S^2))/(3*S) + (8*(6 - 155*S^2 + 39*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (88*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 - 47*S^2 + 12*S^4)*Zeta[3])/(S*(1 + S^2)))) - (110*Pi^2*S^3*Zeta[5])/(3*(1 + S^2)) + HPL[{0}, S^2]^2*(((1 + S^2)*HPL[{1}, -S^2]^4)/S + ((14 - 63*S^2 + 3*S^4)*HPL[{1}, -S^2]^5)/(5*S*(1 + S^2)) + ((-1 - S^2)*HPL[{2}, -S^2]^2)/(2*S) + HPL[{1}, -S^2]^3*((10*(1 + S^2))/(3*S) + (Pi^2*(85 - 336*S^2 + 3*S^4))/(18*S*(1 + S^2)) + ((39 - 134*S^2 - S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + ((1 + S^2)/S + (Pi^2*(1 - 3*S^4))/(2*S*(1 + S^2)))*HPL[{3}, -S^2] + ((1 + S^2)*HPL[{4}, -S^2])/S + ((5 - 16*S^2 - 15*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + (2*Pi^2*(-18 + 22*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (4*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (2*(1 - 4*S^2 + 13*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (4*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (24*(-3 + 5*S^2)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (6*(-37 + 58*S^2 + 3*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*(-19 + 27*S^2 + 3*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (Pi^2*S*(26 + 23*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{2}, -S^2]*((Pi^2*(-1 - S^2))/(6*S) - (2*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (12*(-3 + 5*S^2)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*S*(-3 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]*((18*(1 + S^2))/S + (5*Pi^2*(1 + S^2))/(2*S) + (Pi^4*(739 - 2305*S^2 - 172*S^4))/(360*S*(1 + S^2)) + ((-1 - S^2)/S + (Pi^2*(76 - 233*S^2 - 13*S^4))/(12*S*(1 + S^2)))*HPL[{2}, -S^2] + ((17 - 75*S^2 + 4*S^4)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)) - (2*(-4 + 5*S^2)*HPL[{4}, -S^2])/S + (2*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(-10 + 33*S^2 + S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (2*(-39 + 134*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((9*(1 + S^2))/S + (4*Pi^2*(1 + S^2))/(3*S) + ((-1 - S^2)*HPL[{2}, -S^2])/S - (3*(-1 - 3*S^2 + 2*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + ((-39 + 134*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-1 - 3*S^2 + 2*S^4)*Zeta[3])/(S*(1 + S^2))) - 55*S*Zeta[5]) + Log[T]^2*(-(S*(23 + S^2)*HPL[{0}, S^2]^5)/(12*(1 + S^2)) + ((43 - 147*S^2 - 6*S^4)*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/(12*S*(1 + S^2)) + (4*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)) - (4*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((2*Pi^2*(29 - 173*S^2 + 18*S^4))/(3*S*(1 + S^2)) - (44*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^3*((2*Pi^2*S*(-54 + S^2))/(9*(1 + S^2)) + (2*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + ((36 - 175*S^2 + 9*S^4)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) + (2*S*(-41 + 4*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) + (Pi^2*(5 + 134*S^2 - 83*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (2*(-10 + 13*S^2 + 47*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*(-38 + 27*S^2 + 22*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(-3 - 216*S^2 + 131*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (4*(-9 - 364*S^2 + 217*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (32*(8 - 27*S^2 + 8*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(49 - 98*S^2 + 11*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (608*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (4*Pi^2*S*(-26 + 23*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{0}, S^2]^2*((6*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (2*(14 - 63*S^2 + 3*S^4)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)) - (2*(1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((10*(1 + S^2))/S + (Pi^2*(85 - 336*S^2 + 3*S^4))/(6*S*(1 + S^2)) + ((39 - 134*S^2 - S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) - (3*(-1 + S^2)*(1 + 3*S^2)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (4*(-19 + 27*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (16*S^3*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]*((10*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(1152 - 5849*S^2 + 395*S^4))/(180*S*(1 + S^2)) - (2*Pi^2*(-36 + 67*S^2 + 17*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + (2*(19 - 134*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) + (8*(1 + S^2)*HPL[{3}, -S^2])/S - (2*(-9 - 84*S^2 + 37*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (8*(-13 - 21*S^2 + 20*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (264*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (24*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-2*Pi^2*(1 + S^2))/(3*S) - (2*(-3 - 108*S^2 + 67*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (16*(8 - 27*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (8*S*(-27 + 16*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((2*Pi^2*(1 + S^2))/S - (4*(6 - 155*S^2 + 39*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (132*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (12*(1 - 47*S^2 + 12*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]*((Pi^4*S*(-1655 + 219*S^2))/(90*(1 + S^2)) + (10*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)) + ((-20*(1 + S^2))/S + (Pi^2*(-2 - 223*S^2 + 49*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2] + (2*S*(-67 + 19*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((Pi^2*(81 - 505*S^2 + 54*S^4))/(3*S*(1 + S^2)) + (6*(13 - 94*S^2 + 13*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) - (8*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(1 - 10*S^2 + 3*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(-1 - 70*S^2 + 21*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (8*(-2 - 141*S^2 + 41*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + HPL[{1}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) - (24*(1 + S^2)*HPL[{2}, -S^2])/S + (4*S*(-7 + S^2)*HPL[{3}, -S^2])/(1 + S^2) - (12*(13 - 94*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(3 - 21*S^2 + 4*S^4)*Zeta[3])/(S*(1 + S^2)))) - (220*S*(-1 + S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]*((6*Pi^2*(1 + S^2))/S + (14*Pi^4*(1 + S^2))/(15*S) + (Pi^6*(35130 - 138409*S^2 + 441*S^4))/(45360*S*(1 + S^2)) + ((-2*(1 + S^2))/S + (Pi^2*(36 - 209*S^2 + 23*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2]^2 - (13*(-1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + ((-1 - 10*S^2 + 7*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + (Pi^2*(25 + 80*S^2 - 57*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - (4*(1 + S^2)*HPL[{5}, -S^2])/S + ((138 - 161*S^2 - 159*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) - (4*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + (2*Pi^2*(-33 + 45*S^2 + 22*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (24*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (9*(1 - 6*S^2 + S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) + (4*(-13 - 59*S^2 + 42*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) - (4*Pi^2*(-36 + 67*S^2 + 17*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (16*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (32*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (104*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (4*(-87 - 84*S^2 + 115*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*(-13 - 21*S^2 + 20*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (528*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((36*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (2*(-6 + S^2 + 3*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{2}, -S^2]*((Pi^2*(-1 - S^2))/(3*S) + (Pi^4*(976 - 2225*S^2 - 373*S^4))/(360*S*(1 + S^2)) + (4*(1 + S^2)*HPL[{3}, -S^2])/S + ((-1 + 38*S^2 - 17*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(21 - 134*S^2 + 17*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (8*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) + (8*(4 - 67*S^2 + 15*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(-1 + 5*S^2)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) + (8*(3 - 67*S^2 + 16*S^4)*Zeta[3])/(S*(1 + S^2))) + (36*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((Pi^4*(-1 - S^2))/(18*S) + (Pi^2*(-1 + 112*S^2 - 71*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) + (4*(1 + S^2)*HPL[{4}, -S^2])/S + ((-6 + 23*S^2 - 11*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) - (4*Pi^2*(17 - 42*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S + ((-13 - 242*S^2 + 131*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (2*(-13 - 362*S^2 + 199*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (16*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (144*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (4*(-105 + 108*S^2 + 41*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(8 - 27*S^2 + 8*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*S*(-30 + 17*S^2)*Zeta[3])/(3*(1 + S^2)) - (2*S*(-47 + 39*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^2*((3*Pi^2*(1 + S^2))/S + (89*Pi^4*(1 + S^2))/(180*S) - (2*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((4*(1 + S^2))/S + (Pi^2*(-3 + 164*S^2 - 45*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] - (2*(-18 - 13*S^2 + 29*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + (2*Pi^2*(-36 + 67*S^2 + 17*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(4 - 67*S^2 + 15*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (2*(39 - 888*S^2 + 217*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (8*(19 - 134*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(51 - 247*S^2 + 18*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (264*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((20*(1 + S^2))/S + (Pi^2*(1 + 153*S^2 - 44*S^4))/(3*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-1 - S^2))/(3*S) - (4*(4 - 67*S^2 + 15*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (4*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(3 - 67*S^2 + 16*S^4)*Zeta[3])/(S*(1 + S^2))) - (2*(-10 - 173*S^2 + 57*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{0}, S^2]*((Pi^6*S*(-95123 + 8133*S^2))/(45360*(1 + S^2)) + (2*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)) + ((-1 - S^2)/S + (Pi^2*S*(-203 + 45*S^2))/(12*(1 + S^2)))*HPL[{2}, -S^2]^2 + ((-3 + S^2)*(1 + 20*S^2)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(81 - 505*S^2 + 54*S^4))/(18*S*(1 + S^2)) + ((13 - 94*S^2 + 13*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + (2*(-1 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((-18*(1 + S^2))/S + (Pi^2*(1 - 10*S^2 + 9*S^4))/(3*S*(1 + S^2)))*HPL[{4}, -S^2] - (18*(1 + S^2)*HPL[{5}, -S^2])/S + (2*(-5 + 23*S^2)*HPL[{6}, -S^2])/S - (4*S*(-67 + 19*S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((20*(1 + S^2))/S + (Pi^2*(2 + 215*S^2 - 55*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] + (16*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (4*(-1 - 6*S^2 + 9*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((-40*(1 + S^2))/S + (2*Pi^2*(-2 - 223*S^2 + 49*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-36*(1 + S^2))/S - (11*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(5 - 1321*S^2 + 182*S^4))/(180*S*(1 + S^2)) - (4*(-1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(1 - 67*S^2 + 18*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (8*S*(-67 + 19*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2))/(3*S) + (Pi^4*(535 - 2994*S^2 + 219*S^4))/(180*S*(1 + S^2)) + ((-20*(1 + S^2))/S + (Pi^2*(69 - 424*S^2 + 47*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2] + ((19 - 134*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) - (8*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(1 - 11*S^2 + 2*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(19 - 141*S^2 + 20*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (12*(13 - 94*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) - (8*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (8*(-3 + S^2)*(1 + 20*S^2)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(-8 - 187*S^2 + 63*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (48*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (16*(-1 - 70*S^2 + 21*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*(-2 - 141*S^2 + 41*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (2*S*(-5 + 3*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1}, -S^2]*((36*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S) + (4*(1 - 7*S^2 + 2*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((-18*(1 + S^2))/S - (5*Pi^2*(1 + S^2))/(3*S) - (8*(-2 + 4*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-1 + 4*S^2 + 3*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((2*Pi^2*(1 + S^2))/(9*S) - (8*(1 + S^2)*HPL[{2}, -S^2])/S + (4*S*(-7 + S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (4*(13 - 94*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(3 - 21*S^2 + 4*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]*((Pi^4*(1 + S^2))/(18*S) - (2*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((4*Pi^2*S*(-4 + S^2))/(3*(1 + S^2)) - (16*(1 + S^2))/S)*HPL[{3}, -S^2] - (16*(1 + S^2)*HPL[{4}, -S^2])/S + (8*(-1 - 3*S^2 + 3*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((40*(1 + S^2))/S + (Pi^2*(-69 + 424*S^2 - 47*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (16*(-1 + 4*S^2)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (8*(-5 + 13*S^2 + 2*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(19 - 134*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(57 - 409*S^2 + 58*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (24*(13 - 94*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (Pi^2*(1 + 3*S^2 - 10*S^4)*Zeta[3])/(3*S*(1 + S^2)) + HPL[{2}, -S^2]*((-36*(1 + S^2))/S - (11*Pi^2*(1 + S^2))/(3*S) + (8*(-1 + 4*S^2)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (4*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*(1 - 14*S^2 + 5*S^4)*Zeta[3])/(S*(1 + S^2))) - (4*(-1 + 5*S^2)*Zeta[5])/S)) + Log[T]*((Pi^6*S*(95123 + 8133*S^2))/(22680*(1 + S^2)) + (S*(11 + 3*S^2)*HPL[{0}, S^2]^6)/(24*(1 + S^2)) + ((-9 + 36*S^2 + S^4)*HPL[{0}, S^2]^5*HPL[{1}, -S^2])/(12*S*(1 + S^2)) - (4*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)) + ((4*(1 + S^2))/S + (Pi^2*(-2 + 125*S^2 - 7*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2]^2 - (10*(-1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^4*((Pi^2*(-29 + 173*S^2 - 18*S^4))/(3*S*(1 + S^2)) + (22*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^4*((Pi^2*S*(133 + 27*S^2))/(36*(1 + S^2)) - (5*(1 + S^2)*HPL[{1}, -S^2])/(6*S) + ((-43 + 147*S^2 + 6*S^4)*HPL[{1}, -S^2]^2)/(12*S*(1 + S^2)) + ((-3 + 65*S^2 + 6*S^4)*HPL[{2}, -S^2])/(12*S*(1 + S^2))) - (2*S*(-5 + 3*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + (Pi^2*(-15 - 44*S^2 + 27*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (2*(-50 + 79*S^2 + 59*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) + (8*(3 - 80*S^2 + 3*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + (14*Pi^2*(-1 - 8*S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (6*(-1 + S^2)*(-1 + 5*S^2)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (4*(-14 - 49*S^2 + 53*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) - (8*Pi^2*(-2 - 40*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{2}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-28 + 1375*S^2 - 11*S^4))/(180*S*(1 + S^2)) + (2*(3 - 10*S^2 + 15*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (4*(9 - 160*S^2 + 3*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (16*(3 - 80*S^2 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) + (12*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (68*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (8*(-21 + 44*S^2 + 9*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (32*(-4 + 11*S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (160*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (16*(-3 + 40*S^2)*HPL[{2, 1}, -S^2]*Zeta[3])/(S*(1 + S^2)) + (4*S*(5 + 3*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((-10*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-1152 + 5849*S^2 - 395*S^4))/(180*S*(1 + S^2)) + (2*Pi^2*(-36 + 67*S^2 + 17*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (2*(19 - 134*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) - (8*(1 + S^2)*HPL[{3}, -S^2])/S + (2*(-9 - 84*S^2 + 37*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (8*(-13 - 21*S^2 + 20*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (264*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (24*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]^3*((-2*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (2*(36 - 175*S^2 + 9*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((-2*(1 + S^2))/(3*S) + (Pi^2*(-81 + 355*S^2 - 4*S^4))/(18*S*(1 + S^2)) - (2*(15 - 71*S^2 + 4*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + (4*S*HPL[{3}, -S^2])/(1 + S^2) - (20*(-1 + 2*S^2)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*S*(11 + 3*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{3}, -S^2]*((4*(-19 + 160*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(-1 - 6*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-4*Pi^2*(1 + S^2))/(3*S) + (8*(6 - 155*S^2 + 39*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (88*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 - 47*S^2 + 12*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^2*((Pi^4*S*(1655 + 219*S^2))/(180*(1 + S^2)) - (4*(1 + S^2)*HPL[{1}, -S^2]^3)/S + ((-14 + 63*S^2 - 3*S^4)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)) + ((2*(1 + S^2))/S + (Pi^2*(-4 + 145*S^2 + S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2] + ((1 + 45*S^2 - 4*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) + HPL[{1}, -S^2]^2*((-10*(1 + S^2))/S + (Pi^2*(-85 + 336*S^2 - 3*S^4))/(6*S*(1 + S^2)) + ((-39 + 134*S^2 + S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + (6*(-1 + S^2)*HPL[{4}, -S^2])/S + (2*(1 - 78*S^2 + 5*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (4*(1 - 80*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + HPL[{1}, -S^2]*((-18*(1 + S^2))/S - (8*Pi^2*(1 + S^2))/(3*S) + (2*(1 + S^2)*HPL[{2}, -S^2])/S + (6*(-1 - 3*S^2 + 2*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (2*(-39 + 134*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(-1 - 3*S^2 + 2*S^4)*Zeta[3])/(S*(1 + S^2)))) + HPL[{0}, S^2]*((-4*(3 - 22*S^2 + 3*S^4)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)) + (2*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((-2*Pi^2*(81 - 505*S^2 + 54*S^4))/(9*S*(1 + S^2)) - (4*(13 - 94*S^2 + 13*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + ((16*(1 + S^2))/S + (2*Pi^2*(-1 + 10*S^2 + S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + (16*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(-1 - 10*S^2 + S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((-40*(1 + S^2))/S - (2*Pi^2*(-71 + 201*S^2 + 2*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (16*S*(-4 + S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (8*(-1 - 12*S^2 + 5*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + HPL[{1}, -S^2]*((-2*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-535 + 2994*S^2 - 219*S^4))/(90*S*(1 + S^2)) + ((40*(1 + S^2))/S + (Pi^2*(-69 + 424*S^2 - 47*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2] - (2*(19 - 134*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) + (16*(1 + S^2)*HPL[{3}, -S^2])/S - (8*(1 - 11*S^2 + 2*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(19 - 141*S^2 + 20*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (24*(13 - 94*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) + (16*(-19 + 67*S^2)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(-58 + 205*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*(-41 + 141*S^2 + 2*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*S^3*Zeta[3])/(1 + S^2) + HPL[{2}, -S^2]*((36*(1 + S^2))/S + (4*Pi^2*(1 + S^2))/S + (8*S*(-4 + S^2)*HPL[{3}, -S^2])/(1 + S^2) - (8*(-19 + 67*S^2)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*S*(-7 + 3*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-2*Pi^2*(1 + S^2))/(3*S) + (24*(1 + S^2)*HPL[{2}, -S^2])/S - (4*S*(-7 + S^2)*HPL[{3}, -S^2])/(1 + S^2) + (12*(13 - 94*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*(3 - 21*S^2 + 4*S^4)*Zeta[3])/(S*(1 + S^2)))) + HPL[{1}, -S^2]*((-6*Pi^2*(1 + S^2))/S - (89*Pi^4*(1 + S^2))/(90*S) + (4*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-8*(1 + S^2))/S + (2*Pi^2*(3 - 164*S^2 + 45*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + (4*(-18 - 13*S^2 + 29*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) - (4*Pi^2*(-36 + 67*S^2 + 17*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (16*(4 - 67*S^2 + 15*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (4*(39 - 888*S^2 + 217*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (16*(19 - 134*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (16*(51 - 247*S^2 + 18*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (528*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-40*(1 + S^2))/S + (2*Pi^2*(-1 - 153*S^2 + 44*S^4))/(3*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) + (8*(4 - 67*S^2 + 15*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (8*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(3 - 67*S^2 + 16*S^4)*Zeta[3])/(S*(1 + S^2))) + (4*(-10 - 173*S^2 + 57*S^4)*Zeta[5])/(S*(1 + S^2)))) - (300*S^3*Zeta[7])/(1 + S^2);
E4uvwT2F0=(Pi^2*(-17 + 7*S^2))/2 + (Pi^4*(-115 + 221*S^2))/180 + (Pi^6*(-35571 + 153793*S^2 + 15384*S^4))/(45360*(1 + S^2)^2) - HPL[{0}, S^2]^7/(24*(1 + S^2)^2) - (4*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^6)/(9*(1 + S^2)^2) + (8*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^7)/(21*(1 + S^2)^2) + HPL[{0}, S^2]^6*((-6 + 19*S^2 + 9*S^4)/(48*(1 + S^2)^2) + ((-11 - 6*S^2 - 3*S^4)*HPL[{1}, -S^2])/(24*(1 + S^2)^2)) + HPL[{1}, -S^2]^5*((-4*(1 + S^2)^2)/(5*S^2) + (4*Pi^2*(-46 + 18*S^2 + 9*S^4))/(15*(1 + S^2)^2) - (44*HPL[{2}, -S^2])/5) + ((-1 + S^2)*HPL[{2}, -S^2]^3)/(1 + S^2) + HPL[{0}, S^2]^5*((-3*(1 + S^2))/4 + (Pi^2*(-33 - 2*S^2 - S^4))/(72*(1 + S^2)^2) + ((-27 + 10*S^2 - 7*S^4)*HPL[{1}, -S^2])/(12*(1 + S^2)^2) + ((-23 - 2*S^2 - S^4)*HPL[{1}, -S^2]^2)/(12*(1 + S^2)^2) + ((-9 - 2*S^2 - S^4)*HPL[{2}, -S^2])/(12*(1 + S^2)^2)) - ((-1 + S^2)*(3 + 11*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*(-71 - 154*S^2 - 77*S^4))/(3*(1 + S^2)^2) - (8*(15 + 24*S^2 + 10*S^4))/S^2)*HPL[{5}, -S^2] + ((-539 - 423*S^2 - 24*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (12*(71 + 94*S^2 + 47*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 + (8*(13 - 60*S^2 + 13*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + (-16*S^2 + (Pi^2*(-45 + 278*S^2 + 139*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-8*(-5 - 6*S^2 + 5*S^4))/S^2 + (2*Pi^2*(-61 + 486*S^2 + 243*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (3*(-1 - 18*S^2 + 7*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (4*(21 + 20*S^2 + 10*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 - (4*(-91 - 148*S^2 + 31*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (30*(9 + 10*S^2 + 5*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 + (60*(18 + 26*S^2 + 13*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((-16*(1 + S^4))/S^2 + (8*Pi^2*(-51 + 32*S^2 + 16*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-16*(5 + 3*S^2 + 2*S^4))/S^2 + (4*Pi^2*(-283 + 26*S^2 + 13*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (12*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(1 + S^2) + (36*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) - (2*(-89 + 518*S^2 + 259*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 - (16*(-39 + 190*S^2 + 95*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (4*(-73 - 116*S^2 + 69*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(-147 + 766*S^2 + 383*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 - (4*(-495 + 2278*S^2 + 1139*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(-487 + 2362*S^2 + 1181*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((-48*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(87 + 88*S^2 + 44*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 576*HPL[{2, 2, 2, 1}, -S^2] - (16*(-12 - 29*S^2 + 11*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(257 + 170*S^2 + 85*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (8*(257 + 170*S^2 + 85*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (344*(11 + 14*S^2 + 7*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(717 + 862*S^2 + 431*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (368*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) - (64*(-27 + 32*S^2 + 16*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (192*(-27 + 32*S^2 + 16*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(-148 + 234*S^2 + 117*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 2432*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-4*Pi^2*(-32 + 2*S^2 + S^4))/(9*(1 + S^2)^2) - (4*(-11 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^2) + (8*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) - (8*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]*((8*(4 - 25*S^2 + 13*S^4))/(3*(1 + S^2)^2) - (8*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) - (8*HPL[{2}, -S^2])/3)*Log[T]^5 + ((-4*(3 - 22*S^2 + 3*S^4))/(3*(1 + S^2)^2) + (8*(-4 + 6*S^2 + 3*S^4)*HPL[{0}, S^2])/(3*(1 + S^2)^2) + (8*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2))*Log[T]^6 + (16*Log[T]^7)/(3*(1 + S^2)^2) + ((4*Pi^2*(-2 + 3*S^2))/3 + 8*(-4 + 5*S^2) - (157*Pi^4*(1 + 4*S^2 + 2*S^4))/(45*(1 + S^2)^2))*Zeta[3] + (2*(-3 + 13*S^2 + 12*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((-8*(1 + S^2)*(6 + S^2))/S^2 - (2*Pi^2*(4 + 5*S^2))/(3*S^2) + (Pi^4*(65 - 1438*S^2 - 719*S^4))/(180*(1 + S^2)^2) - (4*(9 + 4*S^2 + 2*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (16*(7 - 30*S^2 + 6*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(-29 + 118*S^2 + 59*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-19 + 134*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*S^2*(-5 + S^2)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^4*((-1 + 19*S^2)/12 + (Pi^2*(-141 + 434*S^2 + 151*S^4))/(144*(1 + S^2)^2) + ((-81 + 120*S^2 + 17*S^4)*HPL[{1}, -S^2]^2)/(12*(1 + S^2)^2) + ((-49 - 6*S^2 - 3*S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) + ((-51 + 89*S^2 + 16*S^4)*HPL[{2}, -S^2])/(24*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(-3 + 7*S^2))/(12*S^2) + (Pi^2*(-263 - 102*S^2 - 51*S^4))/(72*(1 + S^2)^2) + ((-37 - 12*S^2 - 6*S^4)*HPL[{2}, -S^2])/(6*(1 + S^2)^2)) - (3*HPL[{3}, -S^2])/4 + ((37 + 12*S^2 + 6*S^4)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)^2) + ((-45 - 76*S^2 - 38*S^4)*Zeta[3])/(6*(1 + S^2)^2)) + HPL[{4}, -S^2]*((2*(1 + S^2)*(-27 + 11*S^2))/S^2 + (Pi^2*(-87 - 120*S^2 + 79*S^4))/(6*(1 + S^2)^2) + (8*(-6 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(2 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*((-4*(1 + S^2)^2)/S^2 - (2*Pi^2*(79 - 205*S^2 + 46*S^4))/(9*(1 + S^2)^2) + (44*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (4*(-61 + 78*S^2 + 39*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + 44*HPL[{2, 1}, -S^2] - (24*(-3 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-40*(1 + S^2)^2)/(3*S^2) - (4*Pi^2*(3 + 4*S^2))/(9*S^2) + (Pi^4*(-3303 + 790*S^2 + 395*S^4))/(270*(1 + S^2)^2) + ((8*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(60 + 34*S^2 + 17*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(-67 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + (16*(1 - 65*S^2 + 34*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (4*(-19 + 74*S^2 + 37*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (176*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (32*(3 + 20*S^2 + 10*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - 176*HPL[{2, 1, 1}, -S^2] + (16*(2 - 15*S^2 + 13*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((32*(1 + S^2))/S^2 + (Pi^2*(71 - 52*S^2 - 11*S^4))/(3*(1 + S^2)^2) + (16*(-7 + 30*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*(4 + (Pi^2*(-81 + 380*S^2 - 75*S^4))/(12*(1 + S^2)^2) + ((29 - 134*S^2 - 67*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 72*HPL[{2, 1}, -S^2] - (4*(-3 + 32*S^2 + 16*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((32*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-65 + 120*S^2 + 13*S^4))/(3*(1 + S^2)^2) - (16*(-11 + 64*S^2 + 32*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-40*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-3 + 2*S^4))/(3*S^2) + (Pi^4*(1091 + 768*S^2 + 384*S^4))/(90*(1 + S^2)^2) + (8*(-55 + 62*S^2 + 31*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (32*(-27 + 32*S^2 + 16*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(19 - 120*S^2 + 33*S^4)*Zeta[3])/(1 + S^2)^2) + Log[T]^4*((Pi^2*(-82 + 519*S^2 - 59*S^4))/(9*(1 + S^2)^2) + (2*(-46 + 18*S^2 + 9*S^4)*HPL[{0}, S^2]^3)/(9*(1 + S^2)^2) - (20*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + (40*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^2*((-37 + 189*S^2 - 14*S^4)/(3*(1 + S^2)^2) + (2*(-37 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-4*(1 + S^2)^2)/S^2 + (4*Pi^2*(-46 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2) - 44*HPL[{2}, -S^2]) + (46*(-1 + S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + HPL[{0}, S^2]*(-4*(1 + S^2) + (4*Pi^2*(-53 + 54*S^2 + 27*S^4))/(9*(1 + S^2)^2) - (20*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + (20*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (4*(-49 + 82*S^2 + 41*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) - (8*(-13 + 74*S^2 + 37*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (304*HPL[{2, 1}, -S^2])/3 - (8*(-7 + 76*S^2 + 38*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + Log[T]^3*((-4*Pi^2*(-1 + S^2))/3 + (Pi^4*(1874 + 50*S^2 + 25*S^4))/(135*(1 + S^2)^2) + ((55 + 18*S^2 + 9*S^4)*HPL[{0}, S^2]^4)/(9*(1 + S^2)^2) + (80*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) - (40*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^3*((2*(45 - 139*S^2 + 36*S^4))/(9*(1 + S^2)^2) - (4*(-101 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2])/(9*(1 + S^2)^2)) + ((-8*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-33 + 20*S^2 + 10*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*(-40 + 6*S^2 + 3*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((8*(1 + S^2)^2)/S^2 - (8*Pi^2*(-46 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2) + 88*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*(-4*(-1 + S^2) + (4*Pi^2*(55 + 4*S^2 + 2*S^4))/(9*(1 + S^2)^2) + (4*(73 - 160*S^2 + 7*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) - (4*(-37 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 - (4*(-38 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) - (8*(-10 - 111*S^2 + 99*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (56*(-1 + 6*S^2 + 3*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (872*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (32*(8 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (160*HPL[{2, 1, 1}, -S^2])/3 - (8*(-2 - 75*S^2 + 107*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((16*(1 + S^2)^2)/S^2 + (8*Pi^2*(79 - 205*S^2 + 46*S^4))/(9*(1 + S^2)^2) - (176*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (16*(-61 + 78*S^2 + 39*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 176*HPL[{2, 1}, -S^2] + (96*(-3 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]*(16*(1 + S^2) + (2*Pi^2*(85 - 389*S^2 + 166*S^4))/(9*(1 + S^2)^2) + (40*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) - (80*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + (4*(-1 + S^2)*(-47 + 133*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((8*(1 + S^2)^2)/S^2 - (8*Pi^2*(-133 + 54*S^2 + 27*S^4))/(9*(1 + S^2)^2) - (8*(-47 + 26*S^2 + 13*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (16*(3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (32*(46 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (16*(-4 + 6*S^2 + 3*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + HPL[{0}, S^2]^3*((Pi^2*(-51 - 49*S^2))/18 - 8*(1 + S^2) + (Pi^4*(-1849 + 50*S^2 + 25*S^4))/(1080*(1 + S^2)^2) - (2*(77 - 120*S^2 + 23*S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) + ((-101 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^4)/(9*(1 + S^2)^2) + ((-3 - 6*S^2 - S^4)/(3*S^2) + (Pi^2*(-82 + 6*S^2 + 3*S^4))/(18*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-31 + 14*S^2 + 7*S^4)*HPL[{2}, -S^2]^2)/(6*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-3 - 10*S^2 - 5*S^4)/(3*S^2) + (2*Pi^2*(-54 + 2*S^2 + S^4))/(9*(1 + S^2)^2) + (2*(-41 + 8*S^2 + 4*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-3 - 3*S^2 - 4*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (2*(1 + 4*S^2 + 2*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + ((103 - 56*S^2 + 21*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (2*(-31 + 26*S^2 + 13*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(-37 + 16*S^2 + 8*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((-39 - 46*S^2 - 23*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(-106 + 85*S^2 - 29*S^4))/(9*(1 + S^2)^2) - (2*(3 + 11*S^2 + 6*S^4))/(3*S^2) + ((-77 + 70*S^2 - 33*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + (2*(-1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(-41 + 8*S^2 + 4*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (4*(7 + 6*S^2 + 3*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + HPL[{0}, S^2]^2*((3*(-17 + 7*S^2))/2 + (Pi^2*(-7 + 23*S^2))/6 + (Pi^4*(-1547 + 5348*S^2 + 1151*S^4))/(720*(1 + S^2)^2) + ((-73 + 160*S^2 - 7*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + (2*(-37 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^5)/(5*(1 + S^2)^2) + ((-29 + 140*S^2 - 23*S^4)*HPL[{2}, -S^2]^2)/(4*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((2*(-3 - 2*S^2 + 3*S^4))/(3*S^2) + (Pi^2*(-209 + 6*S^2 + 3*S^4))/(9*(1 + S^2)^2) - (2*(87 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((Pi^2*(-2 - 6*S^2 - 3*S^4))/(1 + S^2)^2 - (2*(2 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2] + (2*(-8 + 7*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (6*(6 + 10*S^2 + 5*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-2*(-3 + S^4))/S^2 + (2*Pi^2*(43 + 12*S^2 + 6*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((47 - 110*S^2 + 11*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (4*(-1 + 4*S^2 + 2*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(4 + 26*S^2 + 13*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (4*(21 - 60*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (192*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (12*(49 + 6*S^2 + 3*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(49 + 12*S^2 + 6*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(-1 + 3*S^2) + (Pi^2*(-49 - 92*S^2 - 46*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*((2*(-3 - 2*S^2 + 2*S^4))/S^2 + (Pi^2*(-77 + 140*S^2 + 5*S^4))/(3*(1 + S^2)^2) + ((-75 + 102*S^2 + 5*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 - (12*(2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (2*(87 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (16*S^2*(2 + S^2)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((2*(-2 + S^2 + 2*S^4))/S^2 + (Pi^2*(-93 + 209*S^2 + 6*S^4))/(12*(1 + S^2)^2) - (2*(-1 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (96*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((2*(1 + S^2)*(-5 + 4*S^2))/S^2 + (Pi^4*(-402 - 86*S^2 - 43*S^4))/(45*(1 + S^2)^2) + (Pi^2*(-3 + S^2 + 5*S^4))/(3*S^2) + ((Pi^2*(-161 - 26*S^2 - 13*S^4))/(6*(1 + S^2)^2) + (2*(-3 + 2*S^4))/S^2)*HPL[{2}, -S^2] + (4*(-11 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + (6*(-3 - 4*S^2 + 3*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 20*HPL[{4}, -S^2] - (2*(-75 + 102*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(22 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*(87 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-1 + 5*S^4)*Zeta[3])/(1 + S^2)^2) - 110*Zeta[5]) + (8*(-5 + 4*S^2) - (110*Pi^2*(1 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{0}, S^2]*((Pi^4*(-22 - 21*S^2))/9 - 36*(1 + S^2) - (34*Pi^2*(1 + S^2))/3 + (Pi^6*(-43495 + 16266*S^2 + 8133*S^4))/(22680*(1 + S^2)^2) - (4*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) + (4*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) + (-2*S^2 + (Pi^2*(-79 + 90*S^2 + 45*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (4*(-9 + 20*S^2 + 10*S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((-2*(1 + S^2)^2)/S^2 + (2*Pi^2*(-133 + 54*S^2 + 27*S^4))/(9*(1 + S^2)^2) + (2*(-47 + 26*S^2 + 13*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (4*(2 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((4*(-3 - 3*S^2 + S^4))/S^2 + (2*Pi^2*(-1 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] - (8*(4 + 8*S^2 + 9*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + 92*HPL[{6}, -S^2] - (8*(-24 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((8*(2 + S^2))/S^2 - (2*Pi^2*(-79 + 110*S^2 + 55*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (8*(1 - 8*S^2 + S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(5 + 27*S^2 + 6*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (8*(2 + 18*S^2 + 9*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-8*(3 + 4*S^2 + 3*S^4))/S^2 + (4*Pi^2*(-86 + 98*S^2 + 49*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (16*(27 - 51*S^2 + 8*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(173 - 295*S^2 + 56*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-9 + 20*S^2 + 10*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(-58 + 126*S^2 + 63*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(133 - 180*S^2 + 47*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (96*(-8 + 14*S^2 + 7*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-49 + 82*S^2 + 41*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-16*(1 + S^2) + (Pi^2*(-43 - 75*S^2 - 20*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (4*(-1 + 6*S^2 + 3*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((-20*(1 + S^2)^2)/S^2 - (2*Pi^2*(3 + 8*S^2 + 4*S^4))/(3*S^2) + (Pi^4*(-1655 + 438*S^2 + 219*S^4))/(90*(1 + S^2)^2) + ((-4*(3 + 4*S^2 + 3*S^4))/S^2 + (Pi^2*(-223 + 94*S^2 + 47*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*(-67 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 - (4*(9 + 12*S^2 + 11*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-5 + 4*S^2 + 2*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (360*(1 - 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (80*(-7 + 4*S^2 + 2*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (24*(-47 + 26*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-1 - 28*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-8*(1 + S^2)^2)/S^2 - (4*Pi^2*(81 - 185*S^2 + 54*S^4))/(9*(1 + S^2)^2) - (120*(1 - 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + (8*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (8*(-47 + 26*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (16*(-5 + 4*S^2 + 2*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((8*(3 + 4*S^2 + 2*S^4))/S^2 + (4*Pi^2*(59 - 59*S^2 + 17*S^4))/(3*(1 + S^2)^2) + (8*(-3 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-2*Pi^2*(1 + S^2)*(3 + 2*S^2))/(3*S^2) - (4*(1 + S^2)*(4 + 5*S^2))/S^2 + (13*Pi^4*(-22 + 14*S^2 + 7*S^4))/(45*(1 + S^2)^2) + (4*(1 - 8*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*(2 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(27 - 51*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-25 + 36*S^2 + 18*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-24 + 38*S^2 + 19*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(-7 - 24*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((-4*(4 + 5*S^2))/S^2 - (20*Pi^2*(1 + S^2 + S^4))/(3*(1 + S^2)^2) - (8*(7 + 4*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(4 + 6*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-36*(1 + S^2)^2)/S^2 + (Pi^4*(-1269 + 1842*S^2 - 637*S^4))/(90*(1 + S^2)^2) - (2*Pi^2*(6 + 17*S^2 + 9*S^4))/(3*S^2) - (2*(35 - 102*S^2 + 35*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((-16*(1 + S^2))/S^2 + (4*Pi^2*(-3 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (16*(4 + 2*S^2 + 5*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(1 + 12*S^2 + 6*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((8*(3 + 4*S^2 + 3*S^4))/S^2 - (2*Pi^2*(-223 + 94*S^2 + 47*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(22 - 45*S^2 + 23*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (80*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (32*(5 + 2*S^2 + S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (720*(1 - 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-102 + 58*S^2 + 29*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (48*(-47 + 26*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-16*(1 + S^2) - (4*Pi^2*(2 + 10*S^2 + 5*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-167 + 250*S^2 - 123*S^4))/(3*(1 + S^2)^2) - (4*(5 + 8*S^2 + 5*S^4))/S^2 + (40*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (20*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) - 40*Zeta[5]) - (2*(47 + 35*S^2)*Zeta[5])/(1 + S^2)) + Log[T]^2*((4*Pi^2*(-3 + 2*S^2))/3 + (Pi^4*(-1134 + 5935*S^2 - 327*S^4))/(180*(1 + S^2)^2) + ((-12 - 2*S^2 - S^4)*HPL[{0}, S^2]^5)/(6*(1 + S^2)^2) - (20*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + (8*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 + HPL[{0}, S^2]^4*((-51 + 149*S^2 + 16*S^4)/(12*(1 + S^2)^2) + ((-49 - 6*S^2 - 3*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-8*(1 + S^2)^2)/S^2 + (8*Pi^2*(-46 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2) - 88*HPL[{2}, -S^2]) - (4*(13 - 60*S^2 + 13*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]^3*((-4*(3 + 2*S^2))/3 + (2*Pi^2*(-53 + 4*S^2 + 2*S^4))/(9*(1 + S^2)^2) - (2*(77 - 120*S^2 + 23*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + (2*(-101 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + (2*(-37 + 16*S^2 + 8*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((8*(-2 - 3*S^2 + S^4))/S^2 - (2*Pi^2*(-23 + 166*S^2 + 83*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(-55 - 116*S^2 + 51*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (4*(35 + 94*S^2 + 47*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-24*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(87 + 88*S^2 + 44*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(-12 - 29*S^2 + 11*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (4*(-41 + 262*S^2 + 131*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(-69 + 434*S^2 + 217*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (184*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (32*(-27 + 32*S^2 + 16*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-68 + 22*S^2 + 11*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 1216*HPL[{2, 1, 1, 1}, -S^2] + (24*(-1 + S^2) - (4*Pi^2*(-3 + 92*S^2 + 46*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*((-24*(1 + S^2)^2)/S^2 - (4*Pi^2*(79 - 205*S^2 + 46*S^4))/(3*(1 + S^2)^2) + (264*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (8*(-61 + 78*S^2 + 39*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 264*HPL[{2, 1}, -S^2] - (144*(-3 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^2*(4*(-3 + 2*S^2) + (Pi^2*(-44 + 169*S^2 + S^4))/(3*(1 + S^2)^2) - (2*(73 - 160*S^2 + 7*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (4*(-37 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 - (2*(21 - 60*S^2 + 5*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + HPL[{1}, -S^2]*((2*(-3 - 2*S^2 + 3*S^4))/S^2 + (Pi^2*(-209 + 6*S^2 + 3*S^4))/(3*(1 + S^2)^2) - (2*(87 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) - (6*(1 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(49 + 12*S^2 + 6*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (16*(1 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-40*(1 + S^2)^2)/S^2 - (4*Pi^2*(3 + 4*S^2))/(3*S^2) + (Pi^4*(-3303 + 790*S^2 + 395*S^4))/(90*(1 + S^2)^2) + ((24*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(60 + 34*S^2 + 17*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(-67 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + (16*(1 - 65*S^2 + 34*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(-19 + 74*S^2 + 37*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (528*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (32*(3 + 20*S^2 + 10*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - 528*HPL[{2, 1, 1}, -S^2] + (48*(2 - 15*S^2 + 13*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((16*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-65 + 120*S^2 + 13*S^4))/(3*(1 + S^2)^2) - (4*(-19 + 134*S^2 + 67*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (16*(-27 + 32*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-11 + 64*S^2 + 32*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]*(-40*(1 + S^2) - (2*Pi^2*(9 + 7*S^2))/3 + (Pi^4*(-718 + 438*S^2 + 219*S^4))/(45*(1 + S^2)^2) - (40*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + (20*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^4)/(1 + S^2)^2 + ((-4*(3 + 4*S^2 + 3*S^4))/S^2 + (2*Pi^2*(-86 + 98*S^2 + 49*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(-24 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((-12*(1 + S^2)^2)/S^2 + (4*Pi^2*(-133 + 54*S^2 + 27*S^4))/(3*(1 + S^2)^2) + (12*(-47 + 26*S^2 + 13*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) - (4*(11 + 11*S^2 + 8*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-4 + 6*S^2 + 3*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (4*(133 - 180*S^2 + 47*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (48*(-8 + 14*S^2 + 7*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-49 + 82*S^2 + 41*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-4 - 29*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-24*(1 + S^2)^2)/S^2 - (4*Pi^2*(81 - 185*S^2 + 54*S^4))/(3*(1 + S^2)^2) - (360*(1 - 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + (8*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (24*(-47 + 26*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (16*(-5 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2)) - (440*(2*S^2 + S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]*((21*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-4 + S^2 + 4*S^4))/(3*S^2) + (Pi^4*(-1074 + 2063*S^2 + 309*S^4))/(360*(1 + S^2)^2) + (8*S^2 + (Pi^2*(21 - 142*S^2 - 71*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-3 - 22*S^2 + 37*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (2*(-9 + 22*S^2 + 11*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((8*(1 + S^4))/S^2 - (4*Pi^2*(-51 + 32*S^2 + 16*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(31 - 120*S^2 + 21*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (2*(-49 + 262*S^2 + 131*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(-75 + 398*S^2 + 199*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (16*(13 - 60*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - 288*HPL[{2, 2, 1}, -S^2] + (8*(127 + 82*S^2 + 41*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(-27 + 32*S^2 + 16*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (8*S^2 - (2*Pi^2*(-13 + 68*S^2 + 34*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (4*(-4 + 78*S^2 + 39*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-36*(1 + S^2)^2)/S^2 + (Pi^4*(-1036 + 2383*S^2 - 279*S^4))/(90*(1 + S^2)^2) - (2*Pi^2*(6 + 8*S^2 + S^4))/(3*S^2) - (2*(35 - 102*S^2 + 35*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((8*(-2 - 2*S^2 + S^4))/S^2 - (2*Pi^2*(-61 + 90*S^2 + 45*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*(-23 - 56*S^2 + 23*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (4*(17 + 58*S^2 + 29*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-24*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(60 + 34*S^2 + 17*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(-33 - 28*S^2 + 33*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-28 + 30*S^2 + 15*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(-355 + 434*S^2 + 217*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (528*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (16*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-70 + 18*S^2 + 9*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 528*HPL[{2, 1, 1, 1}, -S^2] + (8*(2 + 3*S^2) - (4*Pi^2*(-27 + 44*S^2 + 22*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((20*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-141 + 102*S^2 + 71*S^4))/(3*(1 + S^2)^2) - (8*(-28 + 30*S^2 + 15*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-27 + 32*S^2 + 16*S^4)*Zeta[3])/(1 + S^2)^2) - (4*(-53 + 114*S^2 + 57*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-36*(1 + S^2)^2)/S^2 - (2*Pi^2*(1 + S^2)*(10 + S^2))/(3*S^2) + (Pi^4*(-40 - S^2 + 49*S^4))/(90*S^2) + (Pi^6*(-86549 + 882*S^2 + 441*S^4))/(22680*(1 + S^2)^2) + ((-2*(1 + S^4))/S^2 + (Pi^2*(-111 + 46*S^2 + 23*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (26*HPL[{2}, -S^2]^3)/3 + (2*(-1 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-32*(1 + S^2))/S^2 + (Pi^2*(-1 - 114*S^2 - 57*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] + (8*(-41 - 47*S^2 + 6*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 - (2*(229 + 318*S^2 + 159*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (8*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-8*(-5 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(25 + 22*S^2 + 11*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (8*(13 - 102*S^2 + 57*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (16*(8 - 181*S^2 + 97*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (18*(-3 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (16*(-1 + 42*S^2 + 21*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((48*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(60 + 34*S^2 + 17*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (16*(35 - 102*S^2 + 35*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(103 - 176*S^2 + 37*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 208*HPL[{3, 2, 1}, -S^2] - (8*(59 + 230*S^2 + 115*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (1056*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (64*(3 + 20*S^2 + 10*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 1056*HPL[{2, 1, 1, 1, 1}, -S^2] + (8*(4 + 5*S^2) + (4*Pi^2*(4 - 45*S^2 + 49*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (4*(5 + 6*S^2 + 3*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((8*(-4 - 5*S^2 + S^4))/S^2 + (2*Pi^2*(-7 - 142*S^2 + 77*S^4))/(3*(1 + S^2)^2) + (16*(-28 + 30*S^2 + 15*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (48*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-40*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(-141 + 102*S^2 + 71*S^4))/(3*(1 + S^2)^2) + (16*(-27 + 32*S^2 + 16*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((36*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(-1787 - 746*S^2 - 373*S^4))/(180*(1 + S^2)^2) + (2*Pi^2*(-6 + 5*S^4))/(3*S^2) + (4*(13 - 102*S^2 + 57*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (2*(-11 + 34*S^2 + 17*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(35 - 102*S^2 + 35*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-69 + 34*S^2 + 17*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(9 - 102*S^2 + 61*S^4)*Zeta[3])/(1 + S^2)^2) + (8*(3 - 37*S^2 + 70*S^4)*Zeta[5])/(1 + S^2)^2) + Log[T]*((Pi^4*(42 - 47*S^2))/45 - (4*Pi^2*(-5 + 4*S^2))/3 + (Pi^6*(51628 + 16266*S^2 + 8133*S^4))/(11340*(1 + S^2)^2) + ((7 + 6*S^2 + 3*S^4)*HPL[{0}, S^2]^6)/(12*(1 + S^2)^2) + (8*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) - (8*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^5*((9 - 10*S^2 + 3*S^4)/(6*(1 + S^2)^2) + ((23 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(6*(1 + S^2)^2)) - (2*Pi^2*(-60 + 14*S^2 + 7*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (20*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((4*(1 + S^2)^2)/S^2 - (4*Pi^2*(-46 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2) + 44*HPL[{2}, -S^2]) + HPL[{0}, S^2]^4*((3 - 2*S^2)/3 + (Pi^2*(80 + 54*S^2 + 27*S^4))/(18*(1 + S^2)^2) + ((81 - 120*S^2 - 17*S^4)*HPL[{1}, -S^2])/(6*(1 + S^2)^2) + ((49 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + ((37 + 12*S^2 + 6*S^4)*HPL[{2}, -S^2])/(6*(1 + S^2)^2)) - (4*(-1 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-8*(-3 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-1 + 54*S^2 + 27*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] - (8*(-35 - 30*S^2 + 17*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (4*(94 + 118*S^2 + 59*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (16*(-40 + 6*S^2 + 3*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((16*(-2 + S^2)*(1 + S^2))/S^2 + (28*Pi^2*(-3 + 2*S^2 + S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(-1 - 168*S^2 + 177*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(-49 - 612*S^2 + 581*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (12*(-1 + 10*S^2 + 5*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (8*(9 + 106*S^2 + 53*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-48*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-33 + 20*S^2 + 10*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (64*(11 - 21*S^2 + 11*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(142 - 141*S^2 + 33*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 24*HPL[{3, 1, 2}, -S^2] - 136*HPL[{3, 2, 1}, -S^2] - (16*(37 + 18*S^2 + 9*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (1744*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (64*(8 + 2*S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 320*HPL[{2, 1, 1, 1, 1}, -S^2] + (-16*(-2 + 3*S^2) - (2*Pi^2*(-9 - 77*S^2 + 128*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (8*(4 + 6*S^2 + 3*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((48*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-217 + 84*S^2 + 129*S^4))/(3*(1 + S^2)^2) + (688*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((-16*(-2 - 2*S^2 + S^4))/S^2 - (2*Pi^2*(-19 - 120*S^2 + 111*S^4))/(3*(1 + S^2)^2) + (8*(93 + 14*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-2 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((16*(1 + S^2)^2)/S^2 + (8*Pi^2*(79 - 205*S^2 + 46*S^4))/(9*(1 + S^2)^2) - (176*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (16*(-61 + 78*S^2 + 39*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 176*HPL[{2, 1}, -S^2] + (96*(-3 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^3*((4*(5 + 4*S^2))/3 + (Pi^2*(135 - 239*S^2 + 66*S^4))/(18*(1 + S^2)^2) + (2*(77 - 120*S^2 + 23*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) - (4*(-101 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) + ((17 - 28*S^2 + 15*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-4*Pi^2*(-54 + 2*S^2 + S^4))/(9*(1 + S^2)^2) + (2*(3 + 10*S^2 + 5*S^4))/(3*S^2) - (4*(-41 + 8*S^2 + 4*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + (4*HPL[{3}, -S^2])/(1 + S^2)^2 - (60*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(7 + 6*S^2 + 3*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((40*(1 + S^2)^2)/S^2 + (4*Pi^2*(3 + 4*S^2))/(3*S^2) + (Pi^4*(3303 - 790*S^2 - 395*S^4))/(90*(1 + S^2)^2) + ((-24*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(60 + 34*S^2 + 17*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (4*(-67 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 - (16*(1 - 65*S^2 + 34*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-19 + 74*S^2 + 37*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (528*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (32*(3 + 20*S^2 + 10*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + 528*HPL[{2, 1, 1}, -S^2] - (48*(2 - 15*S^2 + 13*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-32*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(696 - 22*S^2 - 11*S^4))/(90*(1 + S^2)^2) - (8*(-1 - 42*S^2 + 45*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(1 + 30*S^2 + 15*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (32*(11 - 21*S^2 + 11*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(-83 + 6*S^2 + 3*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (32*(-40 + 6*S^2 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(-1 - 84*S^2 + 89*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^2*((Pi^2*(9 - 7*S^2))/3 - 4*(-5 + 4*S^2) + (Pi^4*(937 + 438*S^2 + 219*S^4))/(90*(1 + S^2)^2) + (4*(73 - 160*S^2 + 7*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) - (2*(-37 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^4)/(1 + S^2)^2 + ((-6*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(75 + 2*S^2 + S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*(-5 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((Pi^2*(209 - 6*S^2 - 3*S^4))/(3*(1 + S^2)^2) - (2*(-3 - 2*S^2 + 3*S^4))/S^2 + (2*(87 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) - (6*(-3 - 3*S^2 + 4*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 12*HPL[{4}, -S^2] + (8*(-27 + 21*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(-37 + 10*S^2 + 5*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-38 + 10*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(-7 - 2*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-4*(-3 - 2*S^2 + 2*S^4))/S^2 - (2*Pi^2*(-77 + 140*S^2 + 5*S^4))/(3*(1 + S^2)^2) - (2*(-75 + 102*S^2 + 5*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + (24*(2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(87 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (32*S^2*(2 + S^2)*Zeta[3])/(1 + S^2)^2)) + HPL[{0}, S^2]*(72*(1 + S^2) + (4*Pi^2*(8 + 7*S^2))/3 + (Pi^4*(377 - 1059*S^2 + 438*S^4))/(45*(1 + S^2)^2) + (20*(17 - 50*S^2 + 17*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) - (8*(-11 + 6*S^2 + 3*S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 + (4*(8 - 51*S^2 + 27*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^3*((8*(1 + S^2)^2)/S^2 - (8*Pi^2*(-133 + 54*S^2 + 27*S^4))/(9*(1 + S^2)^2) - (8*(-47 + 26*S^2 + 13*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + ((8*(1 + S^2)*(2 + S^2))/S^2 + (4*Pi^2*(6 + 2*S^2 + S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (8*(8 + 5*S^2 + 11*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(-4 + 2*S^2 + S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-4*Pi^2*(137 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2) - (8*(3 + 4*S^2 + 3*S^4))/S^2)*HPL[{2, 1}, -S^2] - (8*(23 - 89*S^2 + 68*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (16*(-3 + 4*S^2 + 2*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (16*(-3 + 10*S^2 + 5*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (8*(47 - 180*S^2 + 133*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (1376*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(132 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(46 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(1 + S^2) + (4*Pi^2*(1 + 4*S^2 + 2*S^4))/(1 + S^2)^2)*Zeta[3] + HPL[{1}, -S^2]*((40*(1 + S^2)^2)/S^2 + (Pi^4*(1655 - 438*S^2 - 219*S^4))/(45*(1 + S^2)^2) + (4*Pi^2*(3 + 8*S^2 + 4*S^4))/(3*S^2) + ((8*(3 + 4*S^2 + 3*S^4))/S^2 - (2*Pi^2*(-223 + 94*S^2 + 47*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (4*(-67 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + (8*(9 + 12*S^2 + 11*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (16*(-5 + 4*S^2 + 2*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (720*(1 - 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (160*(-7 + 4*S^2 + 2*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (48*(-47 + 26*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(-1 - 28*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((24*(1 + S^2)^2)/S^2 + (4*Pi^2*(81 - 185*S^2 + 54*S^4))/(3*(1 + S^2)^2) + (360*(1 - 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 - (8*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (24*(-47 + 26*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-5 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((8*(2 + 4*S^2 + 3*S^4))/S^2 + (2*Pi^2*(49 - 132*S^2 + 89*S^4))/(3*(1 + S^2)^2) + (8*(-3 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (688*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(-2 + 6*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2)) - (4*(-8 - 59*S^2 + 169*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((72*(1 + S^2)^2)/S^2 + (4*Pi^2*(6 + 8*S^2 + S^4))/(3*S^2) + (Pi^4*(1036 - 2383*S^2 + 279*S^4))/(45*(1 + S^2)^2) + (4*(35 - 102*S^2 + 35*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((-16*(-2 - 2*S^2 + S^4))/S^2 + (4*Pi^2*(-61 + 90*S^2 + 45*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (8*(-23 - 56*S^2 + 23*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(17 + 58*S^2 + 29*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((48*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(60 + 34*S^2 + 17*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(-33 - 28*S^2 + 33*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (32*(-28 + 30*S^2 + 15*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (8*(-355 + 434*S^2 + 217*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (1056*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (32*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (64*(-70 + 18*S^2 + 9*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 1056*HPL[{2, 1, 1, 1}, -S^2] + (-16*(2 + 3*S^2) + (8*Pi^2*(-27 + 44*S^2 + 22*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-40*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(-141 + 102*S^2 + 71*S^4))/(3*(1 + S^2)^2) + (16*(-28 + 30*S^2 + 15*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (16*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-27 + 32*S^2 + 16*S^4)*Zeta[3])/(1 + S^2)^2) + (8*(-53 + 114*S^2 + 57*S^4)*Zeta[5])/(1 + S^2)^2)) - (300*(1 + 4*S^2 + 2*S^4)*Zeta[7])/(1 + S^2)^2;
E4uvwT2F2=(Pi^2*(-13 + 11*S^2))/4 + (Pi^4*(-103 + 121*S^2))/240 + (Pi^6*(-35130 + 155116*S^2 + 16707*S^4 + 441*S^6))/(90720*(1 + S^2)^2) + (S^2*HPL[{0}, S^2]^7)/(48*(1 + S^2)^2) + ((-1 - 38*S^2 + 94*S^4 - 38*S^6 - S^8)*HPL[{1}, -S^2]^6)/(9*S^2*(1 + S^2)^2) - (2*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^7)/(21*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^6*((-6 + 19*S^2 + 9*S^4)/(96*(1 + S^2)^2) + ((-6 - 12*S^2 + 13*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2])/(96*S^2*(1 + S^2)^2)) - ((-1 + S^2)*(3 + 4*S^2 + 3*S^4)*HPL[{2}, -S^2]^3)/(4*S^2*(1 + S^2)) + HPL[{1}, -S^2]^5*(-(1 + S^2)^2/(5*S^2) + (Pi^2*(-29 - 58*S^2 + 173*S^4 - 36*S^6 - 18*S^8))/(30*S^2*(1 + S^2)^2) + (11*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(5*S^2)) + HPL[{0}, S^2]^5*((3*(1 + S^2))/16 + (Pi^2*(65*S^2 + 2*S^4 + S^6))/(288*(1 + S^2)^2) + ((9 - 18*S^2 + 74*S^4 + 22*S^6 + 9*S^8)*HPL[{1}, -S^2])/(48*S^2*(1 + S^2)^2) + ((-9 - 18*S^2 + 36*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(48*S^2*(1 + S^2)^2) + (S^2*(17 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(48*(1 + S^2)^2)) + ((-1 - 3*S^2 - 4*S^4 - 21*S^6 - 3*S^8)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((27 + 102*S^2 + 67*S^4)/(2*S^2) + (Pi^2*(-20 - 40*S^2 + 45*S^4 + 154*S^6 + 77*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((165 + 92*S^2 + 480*S^4 + 549*S^6 + 136*S^8)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)^2) + (3*(-75 - 150*S^2 + 115*S^4 + 188*S^6 + 94*S^8)*HPL[{7}, -S^2])/(2*S^2*(1 + S^2)^2) + ((1 + 56*S^2 - 234*S^4 + 56*S^6 + S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((3 - 11*S^4)/S^2 + (Pi^2*(-5 - 10*S^2 + 224*S^4 - 278*S^6 - 139*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-1 - 36*S^2 - 59*S^4)/S^2 + (Pi^2*(7 + 14*S^2 + 372*S^4 - 486*S^6 - 243*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (3*(-1 + 3*S^2 + 27*S^6 + 7*S^8)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*S^2*(16 + 10*S^2 + 5*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 - (2*(21 + 15*S^2 + 44*S^4 + 181*S^6 + 43*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) - (3*(2 + 4*S^2 + 67*S^4 + 50*S^6 + 25*S^8)*HPL[{5, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((58 + 116*S^2 - 287*S^4 - 390*S^6 - 195*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-8*(1 + S^4))/S^2 - (4*Pi^2*(17 + 34*S^2 - 42*S^4 + 16*S^6 + 8*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((4*(-4 + 9*S^2 + 5*S^4))/S^2 + (Pi^2*(-209 - 418*S^2 + 370*S^4 - 26*S^6 - 13*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (6*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{3, 1, 2}, -S^2])/(S^2*(1 + S^2)) - (6*(-2 + S^2 - S^4 + 2*S^6)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-29 - 58*S^2 - 466*S^4 + 518*S^6 + 259*S^8)*HPL[{3, 2, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + (4*(-8 - 16*S^2 - 181*S^4 + 190*S^6 + 95*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-30 - 15*S^2 + 32*S^4 - 93*S^6 + 2*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-29 - 58*S^2 - 706*S^4 + 766*S^6 + 383*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-77 - 154*S^2 - 2206*S^4 + 2278*S^6 + 1139*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-82 - 164*S^2 - 2237*S^4 + 2362*S^6 + 1181*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-36*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-38 - 76*S^2 + 27*S^4 + 44*S^6 + 22*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (144*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (8*(6 + 7*S^2 - 8*S^4 + 20*S^6 + S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-213 - 426*S^2 + 216*S^4 + 170*S^6 + 85*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-213 - 426*S^2 + 216*S^4 + 170*S^6 + 85*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-429 - 858*S^2 + 216*S^4 + 602*S^6 + 301*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-639 - 1278*S^2 + 364*S^4 + 862*S^6 + 431*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-5 + 18*S^2 - 18*S^4 + 5*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (32*(8 + 16*S^2 - 27*S^4 + 16*S^6 + 8*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (96*(8 + 16*S^2 - 27*S^4 + 16*S^6 + 8*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(79 + 158*S^2 - 334*S^4 + 234*S^6 + 117*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (608*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*S^2*(-65 + 2*S^2 + S^4))/(9*(1 + S^2)^2) + (S^2*(-23 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^2) + (2*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + HPL[{0}, S^2]*((2*(9 - 47*S^2 + 29*S^4 + S^6))/(3*(1 + S^2)^2) + (2*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2])/(S^2*(1 + S^2)^2)) + (2*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2))*Log[T]^5 + ((-2*(3 - 22*S^2 + 3*S^4))/(3*(1 + S^2)^2) - (2*S^2*(-11 + 6*S^2 + 3*S^4)*HPL[{0}, S^2])/(3*(1 + S^2)^2) - (2*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2))*Log[T]^6 - (8*S^2*Log[T]^7)/(3*(1 + S^2)^2) + ((5*Pi^2*(-1 + 3*S^2))/6 + (-67 + 77*S^2)/4 + (157*Pi^4*(2*S^4 + S^6))/(90*(1 + S^2)^2))*Zeta[3] + ((-6 + 4*S^2 + 3*S^4 - 3*S^6)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1, 1}, -S^2]*((17*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(8 - 50*S^2 + 117*S^4 - 6*S^6 - 9*S^8))/(3*S^2*(1 + S^2)^2) + (8*S^2*(-27 + 32*S^2 + 16*S^4)*Zeta[3])/(1 + S^2)^2) + Log[T]^4*((Pi^2*(-87 + 504*S^2 - 74*S^4 - 5*S^6))/(18*(1 + S^2)^2) - (S^2*(-101 + 18*S^2 + 9*S^4)*HPL[{0}, S^2]^3)/(18*(1 + S^2)^2) - (5*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) - (10*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^2*((-42 + 174*S^2 - 29*S^4 - 5*S^6)/(6*(1 + S^2)^2) + ((-14 - 28*S^2 + 63*S^4 - 6*S^6 - 3*S^8)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)^2)) - ((-1 + S^2)*(5 - 13*S^2 + 5*S^4)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)^2/S^2) + (Pi^2*(-29 - 58*S^2 + 173*S^4 - 36*S^6 - 18*S^8))/(6*S^2*(1 + S^2)^2) + (11*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]*(-1 - S^2 + (Pi^2*(133*S^2 - 54*S^4 - 27*S^6))/(9*(1 + S^2)^2) - (5*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) - (5*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((2 + 4*S^2 + 141*S^4 - 82*S^6 - 41*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + (2*(-1 - 2*S^2 - 64*S^4 + 74*S^6 + 37*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (76*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(-26*S^2 + 38*S^4 + 19*S^6)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{0}, S^2]^4*((-7 + 13*S^2)/24 + (Pi^2*(-133 + 458*S^2 + 175*S^4 + 8*S^6))/(288*(1 + S^2)^2) + ((-81 + 120*S^2 + 17*S^4)*HPL[{1}, -S^2]^2)/(24*(1 + S^2)^2) + ((-43 - 86*S^2 + 147*S^4 + 12*S^6 + 6*S^8)*HPL[{1}, -S^2]^3)/(72*S^2*(1 + S^2)^2) + ((-43 + 113*S^2 + 40*S^4 + 8*S^6)*HPL[{2}, -S^2])/(48*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(-11 + 9*S^2))/(48*S^2) + (Pi^2*(-133 - 266*S^2 + 342*S^4 + 102*S^6 + 51*S^8))/(288*S^2*(1 + S^2)^2) + ((-37 - 74*S^2 + 99*S^4 + 24*S^6 + 12*S^8)*HPL[{2}, -S^2])/(48*S^2*(1 + S^2)^2)) + ((-1 + 3*S^4)*HPL[{3}, -S^2])/(16*S^2) + ((17 + 34*S^2 - 17*S^4 - 6*S^6 - 3*S^8)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((26*S^2 + 38*S^4 + 19*S^6)*Zeta[3])/(12*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((23*(1 + S^2)^2)/(6*S^2) + (Pi^2*(-29 - 42*S^2 - 5*S^4))/(36*S^2) + (Pi^4*(-1152 - 2304*S^2 + 5849*S^4 - 790*S^6 - 395*S^8))/(1080*S^2*(1 + S^2)^2) + ((4*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-36 - 72*S^2 + 67*S^4 + 34*S^6 + 17*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-19 - 38*S^2 + 134*S^4 - 38*S^6 - 19*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (2*(11 + 48*S^2 - 194*S^4 + 180*S^6 + 11*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-9 - 18*S^2 - 84*S^4 + 74*S^6 + 37*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) - (88*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(-13 - 26*S^2 - 21*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (44*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(1 - 4*S^2 + 66*S^4 - 48*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-77*(-1 + S^2)*(1 + S^2))/(4*S^2) + (Pi^2*(9 - 7*S^4))/(3*S^2) + (Pi^4*(474 + 948*S^2 - 425*S^4 - 384*S^6 - 192*S^8))/(180*S^2*(1 + S^2)^2) - (2*(33 + 66*S^2 - 108*S^4 + 62*S^6 + 31*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(8 + 16*S^2 - 27*S^4 + 16*S^6 + 8*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-2 - 24*S^2 + 117*S^4 - 32*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*((3*(1 + S^2)*(-1 + 33*S^2))/(4*S^2) + (Pi^2*(6 - 41*S^2 - 18*S^4 + 169*S^6 + 28*S^8))/(12*S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 - 14*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1 - 2*S^2 + 2*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*(((1 + S^2)*(15 + 169*S^2))/(8*S^2) + (Pi^2*(3 + 54*S^2 + 59*S^4))/(24*S^2) + (Pi^4*(-49 - 98*S^2 - 898*S^4 + 1438*S^6 + 719*S^8))/(720*S^2*(1 + S^2)^2) + (2*S^2*(8 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(-7 - 43*S^2 + 117*S^4 - 13*S^6 + 6*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((3 + 6*S^2 + 120*S^4 - 118*S^6 - 59*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-3 - 6*S^2 - 108*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-1 - 2*S^2 - 5*S^4 + 3*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((1 + 18*S^2 + S^4)/(8*S^2) + (Pi^2*(2 - 82*S^2 + 365*S^4 - 94*S^6 - 7*S^8))/(24*S^2*(1 + S^2)^2) + ((-5 - 10*S^2 - 130*S^4 + 134*S^6 + 67*S^8)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)^2) - (18*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (2*(-1 - 2*S^2 - 12*S^4 + 16*S^6 + 8*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((1 + S^2)^2/(2*S^2) + (Pi^2*(-13 - 368*S^2 + 742*S^4 - 236*S^6 - 13*S^8))/(36*S^2*(1 + S^2)^2) + (22*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + ((6 + 12*S^2 - 155*S^4 + 78*S^6 + 39*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (11*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + ((1 + 2*S^2 - 47*S^4 + 24*S^6 + 12*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(7 + 41*S^2))/(2*S^2) + (Pi^2*(-18 + 18*S^2 - 103*S^4 - 26*S^6 + S^8))/(6*S^2*(1 + S^2)^2) - (4*(1 + 2*S^2 - 28*S^4 + 30*S^6 + 15*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((23*(1 + S^2))/8 + (Pi^2*(51 + 55*S^2))/72 + (Pi^4*(3723*S^2 - 50*S^4 - 25*S^6))/(4320*(1 + S^2)^2) + ((3 - 65*S^2 + 138*S^4 - 11*S^6 + 3*S^8)*HPL[{1}, -S^2]^3)/(9*S^2*(1 + S^2)^2) + ((-36 - 72*S^2 + 175*S^4 - 18*S^6 - 9*S^8)*HPL[{1}, -S^2]^4)/(36*S^2*(1 + S^2)^2) + (-(Pi^2*S^2*(-167 + 6*S^2 + 3*S^4))/(72*(1 + S^2)^2) + (3 + 6*S^2 + 5*S^4)/(6*S^2))*HPL[{2}, -S^2] - (S^2*(-69 + 14*S^2 + 7*S^4)*HPL[{2}, -S^2]^2)/(24*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((17 + 18*S^2 + 9*S^4)/(24*S^2) + (Pi^2*(-81 - 162*S^2 + 355*S^4 - 8*S^6 - 4*S^8))/(72*S^2*(1 + S^2)^2) + ((-15 - 30*S^2 + 71*S^4 - 8*S^6 - 4*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2)) + ((1 + S^2 + 3*S^4 + S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) - (S^4*(2 + S^2)*HPL[{4}, -S^2])/(1 + S^2)^2 + ((-6 + 82*S^2 - 83*S^4 + 6*S^6 - 3*S^8)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + (S^2*(-75 + 26*S^2 + 13*S^4)*HPL[{3, 1}, -S^2])/(6*(1 + S^2)^2) - (2*S^2*(-41 + 8*S^2 + 4*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((-4 + 59*S^2 + 82*S^4 + 35*S^6)*Zeta[3])/(6*(1 + S^2)^2) + HPL[{1}, -S^2]*((45 + 50*S^2 + 21*S^4)/(24*S^2) + (Pi^2*(51 - 220*S^2 + 646*S^4 + 88*S^6 + 51*S^8))/(72*S^2*(1 + S^2)^2) + ((6 - 53*S^2 + 106*S^4 - 9*S^6 + 6*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2) - (S^2*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) + ((15 + 30*S^2 - 71*S^4 + 8*S^6 + 4*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-2 - 4*S^2 + 9*S^4 + 6*S^6 + 3*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2))) + Log[T]^3*((Pi^2*(3 - S^2))/3 + (Pi^4*(-3723*S^2 - 50*S^4 - 25*S^6))/(540*(1 + S^2)^2) - (S^2*(101 + 18*S^2 + 9*S^4)*HPL[{0}, S^2]^4)/(36*(1 + S^2)^2) + (20*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2]^3)/(9*S^2*(1 + S^2)^2) + (10*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^3*((36 - 166*S^2 + 9*S^4 - 9*S^6)/(9*(1 + S^2)^2) + ((36 + 72*S^2 - 175*S^4 + 18*S^6 + 9*S^8)*HPL[{1}, -S^2])/(9*S^2*(1 + S^2)^2)) + ((-2*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-2 - 4*S^2 - 40*S^4 + 10*S^6 + 5*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*(3 + 6*S^2 - 80*S^4 + 6*S^6 + 3*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((2*(1 + S^2)^2)/S^2 + (Pi^2*(29 + 58*S^2 - 173*S^4 + 36*S^6 + 18*S^8))/(3*S^2*(1 + S^2)^2) - (22*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^2*(3 - S^2 - (2*Pi^2*(54*S^2 + 2*S^4 + S^6))/(9*(1 + S^2)^2) + (2*(4 + 89*S^2 - 136*S^4 + 23*S^6 + 4*S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((14 + 28*S^2 - 63*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 80*S^4 + 10*S^6 + 5*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) - (2*(9 + 26*S^2 - 138*S^4 + 264*S^6 + 19*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(-9 - 18*S^2 - 44*S^4 + 42*S^6 + 21*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-5 - 114*S^2 + 114*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) - (8*(-4 - 8*S^2 + 11*S^4 + 2*S^6 + S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (40*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (4*(3 - 60*S^2 + 122*S^4 + 5*S^6)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{0}, S^2]*(-2*(1 + S^2) + (Pi^2*(81 - 401*S^2 + 154*S^4 - 4*S^6))/(9*(1 + S^2)^2) + (10*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (20*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + (2*(-8 + 25*S^2 - 198*S^4 + 131*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((2*(1 + S^2)^2)/S^2 + (Pi^2*(81 + 162*S^2 - 505*S^4 + 108*S^6 + 54*S^8))/(9*S^2*(1 + S^2)^2) + (2*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) - (4*(-1 - 2*S^2 + 4*S^4 + 2*S^6 + S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-41 - 82*S^2 + 141*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(-11*S^2 + 6*S^4 + 3*S^6)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]*((-2*(1 + S^2)^2)/S^2 + (Pi^2*(13 + 368*S^2 - 742*S^4 + 236*S^6 + 13*S^8))/(9*S^2*(1 + S^2)^2) - (88*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (4*(6 + 12*S^2 - 155*S^4 + 78*S^6 + 39*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (44*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + 2*S^2 - 47*S^4 + 24*S^6 + 12*S^8)*Zeta[3])/(S^2*(1 + S^2)^2))) + (-17 + 19*S^2 + (55*Pi^2*(2*S^4 + S^6))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{0}, S^2]^2*((3*(-13 + 11*S^2))/4 + (Pi^2*(-17 + 23*S^2))/16 + (Pi^4*(-1478 + 5555*S^2 + 1358*S^4 + 69*S^6))/(1440*(1 + S^2)^2) + ((-4 - 89*S^2 + 136*S^4 - 23*S^6 - 4*S^8)*HPL[{1}, -S^2]^4)/(6*S^2*(1 + S^2)^2) + ((-14 - 28*S^2 + 63*S^4 - 6*S^6 - 3*S^8)*HPL[{1}, -S^2]^5)/(10*S^2*(1 + S^2)^2) + ((3 - 26*S^2 + 131*S^4 - 38*S^6 - 6*S^8)*HPL[{2}, -S^2]^2)/(8*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-23 - 30*S^2 + S^4)/(12*S^2) + (Pi^2*(-85 - 170*S^2 + 336*S^4 - 6*S^6 - 3*S^8))/(36*S^2*(1 + S^2)^2) + ((-39 - 78*S^2 + 134*S^4 + 2*S^6 + S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2)) + ((-5 + 18*S^2 + 15*S^4)/(8*S^2) + (Pi^2*(-1 - 2*S^2 + 6*S^6 + 3*S^8))/(4*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((3 - 23*S^2 + 37*S^4 + 3*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + ((-5 - 10*S^2 + 16*S^4 + 30*S^6 + 15*S^8)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)^2) + ((9 - 5*S^4)/(2*S^2) + (Pi^2*(18 + 36*S^2 - 22*S^4 - 6*S^6 - 3*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-6 + 32*S^2 - 119*S^4 + 14*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*(1 - S^2 + S^4)*(1 + 3*S^2 + S^4)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 4*S^4 - 26*S^6 - 13*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((3 - 37*S^2 + 117*S^4 - 19*S^6 - 4*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(-3 - 6*S^2 + 5*S^4)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (3*(-37 - 74*S^2 + 58*S^4 + 6*S^6 + 3*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-19 - 38*S^2 + 27*S^4 + 6*S^6 + 3*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (-1 + 3*S^2 + (Pi^2*(26*S^2 + 46*S^4 + 23*S^6))/(6*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-16 + 9*S^2 + 17*S^4)/(8*S^2) + (Pi^2*(3 - 80*S^2 + 230*S^4 + 21*S^6 + 4*S^8))/(24*S^2*(1 + S^2)^2) + ((1 - S^2 + S^4)*(1 + 3*S^2 + S^4)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (6*(-3 - 6*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (S^2*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(-43 + 29*S^2))/(8*S^2) + (Pi^2*(-45 - 34*S^2 + 19*S^4))/(48*S^2) + (Pi^4*(-739 - 1478*S^2 + 2305*S^4 + 344*S^6 + 172*S^8))/(720*S^2*(1 + S^2)^2) + ((-23 + 2*S^2 + 17*S^4)/(8*S^2) + (Pi^2*(-76 - 152*S^2 + 233*S^4 + 26*S^6 + 13*S^8))/(24*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-17 - 34*S^2 + 75*S^4 - 8*S^6 - 4*S^8)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)^2) + (3*(1 - 2*S^2 - 2*S^4 + 10*S^6 + S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-4 + 5*S^4)*HPL[{4}, -S^2])/S^2 + ((2 + 83*S^2 - 90*S^4 + 3*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-10 - 20*S^2 + 33*S^4 + 2*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-39 - 78*S^2 + 134*S^4 + 2*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 - 8*S^2 - 6*S^4 + 16*S^6 - S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-55 - 46*S^2 + 25*S^4)/(16*S^2) + (Pi^2*(-2 - 85*S^2 + 128*S^4 - 3*S^6 - 2*S^8))/(6*S^2*(1 + S^2)^2) + ((-2 - 83*S^2 + 90*S^4 - 3*S^6 - 2*S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2) + (3*(-1 - 2*S^2 - 3*S^4 + 4*S^6 + 2*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((39 + 78*S^2 - 134*S^4 - 2*S^6 - S^8)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 3*S^4 + 4*S^6 + 2*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + (55*S^2*Zeta[5])/2) + HPL[{2}, -S^2]*((33*(-1 + S^2)*(1 + S^2))/(2*S^2) + (Pi^2*(-33 + 9*S^2 + 34*S^4))/(24*S^2) + (Pi^4*(41 - 970*S^2 + 2129*S^4 + 293*S^6 - 19*S^8))/(720*S^2*(1 + S^2)^2) + ((-3 + 7*S^4)/S^2 + (Pi^2*(1 + 2*S^2 - 112*S^4 + 142*S^6 + 71*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-1 + 9*S^2 + 20*S^4 + 81*S^6 + 15*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((6 + 12*S^2 - 23*S^4 + 22*S^6 + 11*S^8)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)^2) + ((4*(1 + S^4))/S^2 + (2*Pi^2*(17 + 34*S^2 - 42*S^4 + 16*S^6 + 8*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((5 + 74*S^2 - 234*S^4 + 38*S^6 - 3*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((13 + 26*S^2 + 242*S^4 - 262*S^6 - 131*S^8)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((13 + 26*S^2 + 362*S^4 - 398*S^6 - 199*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(1 + 56*S^2 - 234*S^4 + 56*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (72*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (2*(-105 - 210*S^2 + 108*S^4 + 82*S^6 + 41*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(8 + 16*S^2 - 27*S^4 + 16*S^6 + 8*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*S^2 + (Pi^2*S^2*(-30 + 34*S^2 + 17*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (S^2*(-47 + 78*S^2 + 39*S^4)*Zeta[5])/(1 + S^2)^2) + Log[T]^2*((Pi^2*(-23 + 17*S^2))/12 + (Pi^4*(-1152 + 5881*S^2 - 381*S^4 - 18*S^6))/(360*(1 + S^2)^2) + (S^2*(23 + 2*S^2 + S^4)*HPL[{0}, S^2]^5)/(24*(1 + S^2)^2) - (5*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) - (2*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)^2) + HPL[{0}, S^2]^4*((-43 + 173*S^2 + 40*S^4 + 8*S^6)/(24*(1 + S^2)^2) + ((-43 - 86*S^2 + 147*S^4 + 12*S^6 + 6*S^8)*HPL[{1}, -S^2])/(24*S^2*(1 + S^2)^2)) + ((-1 - 56*S^2 + 234*S^4 - 56*S^6 - S^8)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-2*(1 + S^2)^2)/S^2 + (Pi^2*(-29 - 58*S^2 + 173*S^4 - 36*S^6 - 18*S^8))/(3*S^2*(1 + S^2)^2) + (22*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^3*((3 + 5*S^2)/3 + (Pi^2*(54*S^2 - 2*S^4 - S^6))/(9*(1 + S^2)^2) + ((3 - 65*S^2 + 138*S^4 - 11*S^6 + 3*S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-36 - 72*S^2 + 175*S^4 - 18*S^6 - 9*S^8)*HPL[{1}, -S^2]^2)/(6*S^2*(1 + S^2)^2) - (S^2*(-41 + 8*S^2 + 4*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((2*(2 + 9*S^2 + 11*S^4))/S^2 + (Pi^2*(-5 - 10*S^2 - 134*S^4 + 166*S^6 + 83*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((3 - 21*S^2 - 32*S^4 + 129*S^6 + 25*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((-10 - 20*S^2 + 13*S^4 + 94*S^6 + 47*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-18*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(-38 - 76*S^2 + 27*S^4 + 44*S^6 + 22*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(6 + 7*S^2 - 8*S^4 + 20*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((3 + 6*S^2 + 216*S^4 - 262*S^6 - 131*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-9 - 18*S^2 - 364*S^4 + 434*S^6 + 217*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-5 + 18*S^2 - 18*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (16*(8 + 16*S^2 - 27*S^4 + 16*S^6 + 8*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(49 + 98*S^2 - 98*S^4 + 22*S^6 + 11*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (304*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (6*(-1 + 3*S^2) + (2*Pi^2*(-26*S^2 + 46*S^4 + 23*S^6))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((17*(-1 + S^2)*(1 + S^2))/(2*S^2) + (Pi^2*(8 - 50*S^2 + 117*S^4 - 6*S^6 - 9*S^8))/(6*S^2*(1 + S^2)^2) + ((-3 - 6*S^2 - 108*S^4 + 134*S^6 + 67*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (8*(8 + 16*S^2 - 27*S^4 + 16*S^6 + 8*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*S^2*(-27 + 32*S^2 + 16*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^2*((-23 + 17*S^2)/4 + (Pi^2*(-85 + 347*S^2 + 11*S^4 + 3*S^6))/(12*(1 + S^2)^2) + ((-4 - 89*S^2 + 136*S^4 - 23*S^6 - 4*S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-14 - 28*S^2 + 63*S^4 - 6*S^6 - 3*S^8)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)^2) + ((3 - 37*S^2 + 117*S^4 - 19*S^6 - 4*S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((-23 - 30*S^2 + S^4)/(4*S^2) + (Pi^2*(-85 - 170*S^2 + 336*S^4 - 6*S^6 - 3*S^8))/(12*S^2*(1 + S^2)^2) + ((-39 - 78*S^2 + 134*S^4 + 2*S^6 + S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2)) + (3*(-1 - 2*S^2 - 2*S^4 + 6*S^6 + 3*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*(-19 - 38*S^2 + 27*S^4 + 6*S^6 + 3*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(2*S^4 + S^6)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((23*(1 + S^2)^2)/(2*S^2) + (Pi^2*(-29 - 42*S^2 - 5*S^4))/(12*S^2) + (Pi^4*(-1152 - 2304*S^2 + 5849*S^4 - 790*S^6 - 395*S^8))/(360*S^2*(1 + S^2)^2) + ((12*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-36 - 72*S^2 + 67*S^4 + 34*S^6 + 17*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-19 - 38*S^2 + 134*S^4 - 38*S^6 - 19*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + (2*(11 + 48*S^2 - 194*S^4 + 180*S^6 + 11*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((-9 - 18*S^2 - 84*S^4 + 74*S^6 + 37*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (264*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(-13 - 26*S^2 - 21*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (132*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (6*(1 - 4*S^2 + 66*S^4 - 48*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((3*(1 + S^2)^2)/S^2 + (Pi^2*(-13 - 368*S^2 + 742*S^4 - 236*S^6 - 13*S^8))/(6*S^2*(1 + S^2)^2) + (132*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (2*(6 + 12*S^2 - 155*S^4 + 78*S^6 + 39*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (66*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (6*(1 + 2*S^2 - 47*S^4 + 24*S^6 + 12*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]*((23*(1 + S^2))/2 + (Pi^2*(3 + 7*S^2))/6 + (Pi^4*(1655*S^2 - 438*S^4 - 219*S^6))/(180*(1 + S^2)^2) - (10*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) - (5*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^4)/(S^2*(1 + S^2)^2) + ((11 + 18*S^2 - S^4)/(2*S^2) + (Pi^2*(2 + 4*S^2 + 223*S^4 - 98*S^6 - 49*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] - (S^2*(-67 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((-3*(1 + S^2)^2)/S^2 + (Pi^2*(-81 - 162*S^2 + 505*S^4 - 108*S^6 - 54*S^8))/(6*S^2*(1 + S^2)^2) - (3*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) + ((5 + 2*S^2 + 20*S^4 + 16*S^6 + 9*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(1 + 2*S^2 - 10*S^4 + 6*S^6 + 3*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-2 - 131*S^2 + 198*S^4 - 25*S^6 + 8*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-1 - 2*S^2 - 70*S^4 + 42*S^6 + 21*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-2 - 4*S^2 - 141*S^4 + 82*S^6 + 41*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 - 8*S^2 + 24*S^4 + 7*S^6)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((3*(1 + S^2)^2)/S^2 + (Pi^2*(1 - 320*S^2 + 746*S^4 - 212*S^6 + S^8))/(6*S^2*(1 + S^2)^2) + (6*(1 - 26*S^2 + 66*S^4 - 26*S^6 + S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2) - (2*S^2*(-7 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (6*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 21*S^4 + 8*S^6 + 4*S^8)*Zeta[3])/(S^2*(1 + S^2)^2))) + (110*(-S^2 + 2*S^4 + S^6)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*((255*(1 + S^2)^2)/(8*S^2) + (Pi^2*(1 + S^2)*(-5 + 13*S^2))/(6*S^2) + (Pi^4*(-301 - 286*S^2 + 55*S^4))/(720*S^2) + (Pi^6*(-35130 - 70260*S^2 + 138409*S^4 - 882*S^6 - 441*S^8))/(90720*S^2*(1 + S^2)^2) + ((-3 + 2*S^2 - 3*S^4)/(4*S^2) + (Pi^2*(-36 - 72*S^2 + 209*S^4 - 46*S^6 - 23*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (13*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(6*S^2) + ((1 + 2*S^2 + 10*S^4 - 14*S^6 - 7*S^8)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((8*(1 + S^2)*(1 + 3*S^2))/S^2 + (Pi^2*(-25 - 50*S^2 - 80*S^4 + 114*S^6 + 57*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((45 + 16*S^2 + 82*S^4 + 204*S^6 + 45*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-138 - 276*S^2 + 161*S^4 + 318*S^6 + 159*S^8)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-4*(1 + S^2)*(1 + 7*S^2))/S^2 + (Pi^2*(33 + 66*S^2 - 45*S^4 - 44*S^6 - 22*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(2 + 21*S^2 - 90*S^4 + 65*S^6 + 2*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(13 + 68*S^2 - 284*S^4 + 246*S^6 + 13*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (9*(1 + 2*S^2 - 6*S^4 + 2*S^6 + S^8)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*(-13 - 26*S^2 - 59*S^4 + 84*S^6 + 42*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((24*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-36 - 72*S^2 + 67*S^4 + 34*S^6 + 17*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(2 + 43*S^2 - 90*S^4 + 43*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(1 + 210*S^2 - 346*S^4 + 78*S^6 + S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (52*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + (2*(-87 - 174*S^2 - 84*S^4 + 230*S^6 + 115*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (528*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - (8*(-13 - 26*S^2 - 21*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (264*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-67 - 70*S^2 + 13*S^4)/(4*S^2) + (Pi^2*(-5 - 4*S^2 - 210*S^4 + 176*S^6 - 5*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + ((-6 - 12*S^2 + S^4 + 6*S^6 + 3*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{3}, -S^2]*((7 + 38*S^2 + 47*S^4)/(2*S^2) + (Pi^2*(7 + 21*S^2 - 100*S^4 + 105*S^6 + 7*S^8))/(3*S^2*(1 + S^2)^2) - (4*(4 + 8*S^2 - 67*S^4 + 30*S^6 + 15*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1 - 2*S^2 + 5*S^4)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((18*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-47 + 2*S^2 + 41*S^4))/(24*S^2) + (Pi^4*(-976 - 1952*S^2 + 2225*S^4 + 746*S^6 + 373*S^8))/(720*S^2*(1 + S^2)^2) + (2*(2 + 21*S^2 - 90*S^4 + 65*S^6 + 2*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 38*S^4 + 34*S^6 + 17*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + (4*(2 + 43*S^2 - 90*S^4 + 43*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(21 + 42*S^2 - 134*S^4 + 34*S^6 + 17*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(2 + 17*S^2 - 90*S^4 + 69*S^6 + 2*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-20*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(2 + 149*S^2 - 90*S^4 - 63*S^6 + 2*S^8))/(3*S^2*(1 + S^2)^2) - (4*(3 + 6*S^2 - 67*S^4 + 32*S^6 + 16*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-17 - 56*S^2 - 250*S^4 + 212*S^6 - 17*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((111*(1 + S^2)^2)/(8*S^2) + (Pi^2*(-43 - 22*S^2 + 37*S^4))/(48*S^2) + (Pi^4*(-143 - 4716*S^2 + 8674*S^4 - 1688*S^6 - 143*S^8))/(720*S^2*(1 + S^2)^2) + ((-2 - 43*S^2 + 90*S^4 - 43*S^6 - 2*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((7 + 30*S^2 + 31*S^4)/(2*S^2) + (Pi^2*(3 + 6*S^2 - 164*S^4 + 90*S^6 + 45*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(7 + 5*S^2 - 14*S^4 + 51*S^6 + 7*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((-18 - 36*S^2 - 13*S^4 + 58*S^6 + 29*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-12*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(36 + 72*S^2 - 67*S^4 - 34*S^6 - 17*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(7 - 38*S^2 - 14*S^4 + 94*S^6 + 7*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(4 + 8*S^2 - 67*S^4 + 30*S^6 + 15*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-39 - 78*S^2 + 888*S^4 - 434*S^6 - 217*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (264*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(51 + 102*S^2 - 247*S^4 + 36*S^6 + 18*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (132*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-17 - 18*S^2 + 7*S^4)/(2*S^2) + (Pi^2*(-1 - 2*S^2 - 153*S^4 + 88*S^6 + 44*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((10*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-2 - 149*S^2 + 90*S^4 + 63*S^6 - 2*S^8))/(6*S^2*(1 + S^2)^2) + (2*(4 + 8*S^2 - 67*S^4 + 30*S^6 + 15*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 67*S^4 + 32*S^6 + 16*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-10 - 20*S^2 - 173*S^4 + 114*S^6 + 57*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]*((255*(1 + S^2))/8 + (23*Pi^2*(1 + S^2))/6 + (Pi^4*(199 + 219*S^2))/360 + (Pi^6*(95123*S^2 - 16266*S^4 - 8133*S^6))/(90720*(1 + S^2)^2) + ((-1 - 38*S^2 + 94*S^4 - 38*S^6 - S^8)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)^2) + ((-3 - 6*S^2 + 22*S^4 - 6*S^6 - 3*S^8)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 7*S^4)/(8*S^2) - (Pi^2*S^2*(-203 + 90*S^2 + 45*S^4))/(24*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + ((3 + 6*S^2 + 59*S^4 - 40*S^6 - 20*S^8)*HPL[{2}, -S^2]^3)/(6*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^4*(-(1 + S^2)^2/(2*S^2) + (Pi^2*(-81 - 162*S^2 + 505*S^4 - 108*S^6 - 54*S^8))/(36*S^2*(1 + S^2)^2) + ((-13 - 26*S^2 + 94*S^4 - 26*S^6 - 13*S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2)) + ((1 + 2*S^2 - 2*S^4 - 2*S^6 - S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-3 + 18*S^2 + 29*S^4)/(4*S^2) + (Pi^2*(-1 - 2*S^2 + 10*S^4 - 18*S^6 - 9*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((11 + 16*S^2 + 14*S^4 - 16*S^6 + 15*S^8)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)^2) + ((5 - 23*S^4)*HPL[{6}, -S^2])/S^2 + (2*S^2*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-1 - 14*S^2 - 5*S^4)/(2*S^2) + (Pi^2*(-2 - 4*S^2 - 215*S^4 + 110*S^6 + 55*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(-1 - 5*S^4 + 6*S^6 + 2*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-1 + 2*S^2 - 12*S^4 + 32*S^6 + 15*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 6*S^4 + 18*S^6 + 9*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((11 + 18*S^2 - S^4)/S^2 + (Pi^2*(2 + 4*S^2 + 223*S^4 - 98*S^6 - 49*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(7 + 130*S^2 - 180*S^4 + 42*S^6 + S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-8 - 194*S^2 + 280*S^4 - 55*S^6 + 3*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-3 - 6*S^2 - 59*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-8 - 16*S^2 - 187*S^4 + 126*S^6 + 63*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-2 - 131*S^2 + 198*S^4 - 25*S^6 + 8*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-1 - 2*S^2 - 70*S^4 + 42*S^6 + 21*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-2 - 4*S^2 - 141*S^4 + 82*S^6 + 41*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(1 + S^2) + (Pi^2*(-1 + 51*S^2 + 106*S^4 + 42*S^6))/(6*(1 + S^2)^2))*Zeta[3] + ((5*S^2 - 6*S^4 - 3*S^6)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((-21 - 70*S^2 - 33*S^4)/(4*S^2) + (Pi^2*(-4 + 213*S^2 - 281*S^4 + 31*S^6 - 11*S^8))/(6*S^2*(1 + S^2)^2) - (2*(1 + 2*S^2 - 7*S^4 + 4*S^6 + 2*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((1 + 50*S^2 + 65*S^4)/(8*S^2) + (Pi^2*(11 + 8*S^2 + 38*S^4 + 16*S^6 + 15*S^8))/(12*S^2*(1 + S^2)^2) + (4*(-2 - 4*S^2 + 4*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 + 4*S^4 + 6*S^6 + 3*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((1 + S^2)^2/S^2 + (Pi^2*(1 - 320*S^2 + 746*S^4 - 212*S^6 + S^8))/(18*S^2*(1 + S^2)^2) + (2*(1 - 26*S^2 + 66*S^4 - 26*S^6 + S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2) - (2*S^2*(-7 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (2*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 21*S^4 + 8*S^6 + 4*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((5*(1 + S^2)*(13 + 11*S^2))/(8*S^2) + (Pi^2*(1 + S^2)*(23 + 19*S^2))/(24*S^2) + (Pi^4*(-5 - 10*S^2 + 1321*S^4 - 364*S^6 - 182*S^8))/(360*S^2*(1 + S^2)^2) + (2*(-1 - 5*S^4 + 6*S^6 + 2*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 + 2*S^4 + 2*S^6 + S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((7 + 130*S^2 - 180*S^4 + 42*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1 + 2*S^2 - 67*S^4 + 36*S^6 + 18*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*S^2*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((2 + 5*S^2 + 23*S^6 + 6*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((23*(1 + S^2)^2)/(4*S^2) + (Pi^2*(11 + 6*S^2 + 3*S^4))/(24*S^2) + (Pi^4*(-535 - 1070*S^2 + 2994*S^4 - 438*S^6 - 219*S^8))/(360*S^2*(1 + S^2)^2) + ((5 + 18*S^2 + 5*S^4)/(2*S^2) + (Pi^2*(-69 - 138*S^2 + 424*S^4 - 94*S^6 - 47*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-19 - 38*S^2 + 134*S^4 - 38*S^6 - 19*S^8)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((7 + 10*S^2 + 18*S^4 + 6*S^6 + 7*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(1 + 2*S^2 - 11*S^4 + 4*S^6 + 2*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (6*(1 - 26*S^2 + 66*S^4 - 26*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(19 + 38*S^2 - 141*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((7 + 26*S^2 - 14*S^4 + 30*S^6 + 7*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-2 + 55*S^2 + 45*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*((111*(1 + S^2)^2)/(8*S^2) + (Pi^2*(51 + 62*S^2 + 27*S^4))/(24*S^2) + (Pi^4*(102 - 861*S^2 + 2454*S^4 - 229*S^6 + 102*S^8))/(180*S^2*(1 + S^2)^2) + ((-2 - 43*S^2 + 90*S^4 - 43*S^6 - 2*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + (8*(1 + S^2) - (2*Pi^2*(-4*S^2 + 2*S^4 + S^6))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (8*(1 + 4*S^4 - S^6 + S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1 - 2*S^2 - 3*S^4 + 6*S^6 + 3*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-5 - 18*S^2 - 5*S^4)/S^2 + (Pi^2*(69 + 138*S^2 - 424*S^4 + 94*S^6 + 47*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(3 - 76*S^2 + 198*S^4 - 80*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-1 - 2*S^2 + 4*S^4)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-5 - 10*S^2 + 13*S^4 + 4*S^6 + 2*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(1 - 26*S^2 + 66*S^4 - 26*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(57 + 114*S^2 - 409*S^4 + 116*S^6 + 58*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((4*(1 + S^2)*(3 + S^2))/S^2 + (Pi^2*(-1 - 2*S^2 - 3*S^4 + 20*S^6 + 10*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((27 + 70*S^2 + 27*S^4)/(4*S^2) + (Pi^2*(9 - 131*S^2 + 304*S^4 - 87*S^6 + 9*S^8))/(6*S^2*(1 + S^2)^2) - (4*(-1 - 2*S^2 + 4*S^4)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 14*S^4 + 10*S^6 + 5*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + (2*(-1 + 5*S^4)*Zeta[5])/S^2)) + Log[T]*((Pi^4*(171 - 185*S^2))/360 + (Pi^2*(77 - 67*S^2))/24 + (Pi^6*(-95123*S^2 - 16266*S^4 - 8133*S^6))/(45360*(1 + S^2)^2) - (S^2*(11 + 6*S^2 + 3*S^4)*HPL[{0}, S^2]^6)/(48*(1 + S^2)^2) + (2*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^5*((9 - 47*S^2 - 21*S^4 - 9*S^6)/(24*(1 + S^2)^2) + ((9 + 18*S^2 - 36*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2])/(24*S^2*(1 + S^2)^2)) + (-(1 + S^2)^2/(2*S^2) + (Pi^2*(2 + 4*S^2 - 125*S^4 + 14*S^6 + 7*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (5*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^4*((1 + S^2)^2/S^2 + (Pi^2*(29 + 58*S^2 - 173*S^4 + 36*S^6 + 18*S^8))/(6*S^2*(1 + S^2)^2) - (11*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^4*((3 - 17*S^2)/24 + (Pi^2*(-133*S^2 - 54*S^4 - 27*S^6))/(72*(1 + S^2)^2) + ((81 - 120*S^2 - 17*S^4)*HPL[{1}, -S^2])/(12*(1 + S^2)^2) + ((43 + 86*S^2 - 147*S^4 - 12*S^6 - 6*S^8)*HPL[{1}, -S^2]^2)/(24*S^2*(1 + S^2)^2) + ((3 + 6*S^2 - 65*S^4 - 12*S^6 - 6*S^8)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)^2)) + (S^2*(-5 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + (-(((1 + S^2)*(-3 + 31*S^2))/S^2) + (Pi^2*(15 + 30*S^2 + 44*S^4 - 54*S^6 - 27*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(19 + 10*S^2 + 66*S^4 + 122*S^6 + 23*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((50 + 100*S^2 - 79*S^4 - 118*S^6 - 59*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) - (4*(3 + 6*S^2 - 80*S^4 + 6*S^6 + 3*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((4*(1 + S^2)*(2 + 5*S^2))/S^2 - (7*Pi^2*(-1 - 2*S^2 - 8*S^4 + 2*S^6 + S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (2*(-3 + 7*S^2 - 126*S^4 + 225*S^6 + 17*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(7 + 35*S^2 - 402*S^4 + 777*S^6 + 63*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (3*(1 + 2*S^2 - 6*S^4 + 10*S^6 + 5*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-14 - 28*S^2 - 49*S^4 + 106*S^6 + 53*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-12*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-2 - 4*S^2 - 40*S^4 + 10*S^6 + 5*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(7 + 116*S^2 - 126*S^4 + 116*S^6 + 7*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(6 + 161*S^2 - 120*S^4 + 42*S^6 + S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 + (34*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + (4*(-21 - 42*S^2 + 44*S^4 + 18*S^6 + 9*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-5 - 114*S^2 + 114*S^4 + 5*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (16*(-4 - 8*S^2 + 11*S^4 + 2*S^6 + S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (80*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (17 - 23*S^2 + (Pi^2*(1 + 53*S^2 - 152*S^4 - 8*S^6))/(3*(1 + S^2)^2))*Zeta[3] - (2*(5*S^2 + 6*S^4 + 3*S^6)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((23*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-12 - 248*S^2 + 63*S^4 + 132*S^6 + 5*S^8))/(3*S^2*(1 + S^2)^2) - (8*(-3 - 6*S^2 + 40*S^4)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((-29 - 37*S^2)/12 + (Pi^2*(81 - 401*S^2 - 96*S^4 - 54*S^6))/(36*(1 + S^2)^2) + ((-3 + 65*S^2 - 138*S^4 + 11*S^6 - 3*S^8)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((36 + 72*S^2 - 175*S^4 + 18*S^6 + 9*S^8)*HPL[{1}, -S^2]^3)/(9*S^2*(1 + S^2)^2) + ((-2 + 8*S^2 - 43*S^4 + 4*S^6 - 3*S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((-17 - 18*S^2 - 9*S^4)/(12*S^2) + (Pi^2*(81 + 162*S^2 - 355*S^4 + 8*S^6 + 4*S^8))/(36*S^2*(1 + S^2)^2) + ((15 + 30*S^2 - 71*S^4 + 8*S^6 + 4*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) - (2*S^2*HPL[{3}, -S^2])/(1 + S^2)^2 + (10*(-1 - 2*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-11*S^2 - 6*S^4 - 3*S^6)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-23*(1 + S^2)^2)/(2*S^2) + (Pi^2*(29 + 42*S^2 + 5*S^4))/(12*S^2) + (Pi^4*(1152 + 2304*S^2 - 5849*S^4 + 790*S^6 + 395*S^8))/(360*S^2*(1 + S^2)^2) + ((-12*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(36 + 72*S^2 - 67*S^4 - 34*S^6 - 17*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) - (2*(11 + 48*S^2 - 194*S^4 + 180*S^6 + 11*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((9 + 18*S^2 + 84*S^4 - 74*S^6 - 37*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (264*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(-13 - 26*S^2 - 21*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (132*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (6*(1 - 4*S^2 + 66*S^4 - 48*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-4 - 23*S^2 - 27*S^4)/S^2 + (Pi^2*(-6 - 10*S^2 + 69*S^4 - 150*S^6 - 11*S^8))/(3*S^2*(1 + S^2)^2) - (2*(-19 - 38*S^2 + 160*S^4 + 14*S^6 + 7*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1 - 2*S^2 - 6*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-67*(-1 + S^2)*(1 + S^2))/(4*S^2) - (Pi^2*(1 + S^2)*(-11 + 13*S^2))/(12*S^2) + (Pi^4*(28 + 56*S^2 - 1375*S^4 + 22*S^6 + 11*S^8))/(360*S^2*(1 + S^2)^2) - (2*(-3 - S^2 - 63*S^4 + 117*S^6 + 10*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((-3 - 6*S^2 + 10*S^4 - 30*S^6 - 15*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (2*(7 + 116*S^2 - 126*S^4 + 116*S^6 + 7*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(9 + 18*S^2 - 160*S^4 + 6*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(3 + 6*S^2 - 80*S^4 + 6*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(2 + 10*S^2 - 63*S^4 + 106*S^6 + 5*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-2*(1 + S^2)^2)/S^2 + (Pi^2*(13 + 368*S^2 - 742*S^4 + 236*S^6 + 13*S^8))/(9*S^2*(1 + S^2)^2) - (88*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (4*(6 + 12*S^2 - 155*S^4 + 78*S^6 + 39*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (44*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + 2*S^2 - 47*S^4 + 24*S^6 + 12*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((77 - 67*S^2)/8 + (Pi^2*(3 - 5*S^2))/3 + (Pi^4*(-1655*S^2 - 438*S^4 - 219*S^6))/(360*(1 + S^2)^2) + (2*(4 + 89*S^2 - 136*S^4 + 23*S^6 + 4*S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + ((14 + 28*S^2 - 63*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)^2) + (-((1 + S^2)*(-5 + 7*S^2))/(4*S^2) + (Pi^2*(4 + 8*S^2 - 145*S^4 - 2*S^6 - S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-1 - 2*S^2 - 45*S^4 + 8*S^6 + 4*S^8)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((23 + 30*S^2 - S^4)/(4*S^2) + (Pi^2*(85 + 170*S^2 - 336*S^4 + 6*S^6 + 3*S^8))/(12*S^2*(1 + S^2)^2) + ((39 + 78*S^2 - 134*S^4 - 2*S^6 - S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2)) - (3*(1 - 2*S^2 + 12*S^6 + S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) - (3*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + ((-7 - 129*S^2 + 63*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 78*S^4 - 10*S^6 - 5*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1 + 2*S^2 - 80*S^4 + 10*S^6 + 5*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((4 - 7*S^2 - 30*S^4 - 3*S^6)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((55 + 46*S^2 - 25*S^4)/(8*S^2) + (Pi^2*(2 + 85*S^2 - 128*S^4 + 3*S^6 + 2*S^8))/(3*S^2*(1 + S^2)^2) + ((2 + 83*S^2 - 90*S^4 + 3*S^6 + 2*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2) - (3*(-1 - 2*S^2 - 3*S^4 + 4*S^6 + 2*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((-39 - 78*S^2 + 134*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1 - 2*S^2 - 3*S^4 + 4*S^6 + 2*S^8)*Zeta[3])/(S^2*(1 + S^2)^2))) + HPL[{0}, S^2]*((Pi^2*(-35 - 43*S^2))/12 - (111*(1 + S^2))/4 + (Pi^4*(535 - 2775*S^2 + 219*S^4 - 219*S^6))/(180*(1 + S^2)^2) + (5*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 22*S^4 + 6*S^6 + 3*S^8)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)^2) + ((-1 + S^2)*(-1 - 43*S^2 + 137*S^4 + 7*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((2*(1 + S^2)^2)/S^2 + (Pi^2*(81 + 162*S^2 - 505*S^4 + 108*S^6 + 54*S^8))/(9*S^2*(1 + S^2)^2) + (2*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) + (-10*(1 + S^2) + (Pi^2*(1 + 2*S^2 - 10*S^4 - 2*S^6 - S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] - (2*(3 - 2*S^2 + 14*S^4 - 4*S^6 + 5*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 10*S^4 + 2*S^6 + S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 + 18*S^2 + 11*S^4)/S^2 + (Pi^2*(-71 - 142*S^2 + 201*S^4 + 4*S^6 + 2*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(-4 + 12*S^2 - 98*S^4 + 67*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*S^2*(-4 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(-1 - 2*S^2 - 12*S^4 + 10*S^6 + 5*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-8 + 25*S^2 - 198*S^4 + 131*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-19 - 38*S^2 + 67*S^4)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-58 - 116*S^2 + 205*S^4 + 2*S^6 + S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-41 - 82*S^2 + 141*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (-14*(1 + S^2) - (2*Pi^2*(2*S^4 + S^6))/(1 + S^2)^2)*Zeta[3] + HPL[{2}, -S^2]*((-33 - 70*S^2 - 21*S^4)/(4*S^2) + (Pi^2*(-14 + 49*S^2 - 327*S^4 + 143*S^6 - 7*S^8))/(6*S^2*(1 + S^2)^2) - (4*S^2*(-4 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-19 - 38*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*S^2*(-7 + 6*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-3*(1 + S^2)^2)/S^2 + (Pi^2*(-1 + 320*S^2 - 746*S^4 + 212*S^6 - S^8))/(6*S^2*(1 + S^2)^2) - (6*(1 - 26*S^2 + 66*S^4 - 26*S^6 + S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2) + (2*S^2*(-7 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (6*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(3 + 6*S^2 - 21*S^4 + 8*S^6 + 4*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]*((-23*(1 + S^2)^2)/(2*S^2) + (Pi^2*(-11 - 6*S^2 - 3*S^4))/(12*S^2) + (Pi^4*(535 + 1070*S^2 - 2994*S^4 + 438*S^6 + 219*S^8))/(180*S^2*(1 + S^2)^2) + ((-5 - 18*S^2 - 5*S^4)/S^2 + (Pi^2*(69 + 138*S^2 - 424*S^4 + 94*S^6 + 47*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) - (2*(7 + 10*S^2 + 18*S^4 + 6*S^6 + 7*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 - 11*S^4 + 4*S^6 + 2*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (12*(1 - 26*S^2 + 66*S^4 - 26*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(19 + 38*S^2 - 141*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(13 + 26*S^2 - 94*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(7 + 26*S^2 - 14*S^4 + 30*S^6 + 7*S^8)*Zeta[3])/(S^2*(1 + S^2)^2))) + (2*(10 + 65*S^2 - 163*S^4 + 2*S^6)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-111*(1 + S^2)^2)/(4*S^2) + (Pi^2*(43 + 22*S^2 - 37*S^4))/(24*S^2) + (Pi^4*(143 + 4716*S^2 - 8674*S^4 + 1688*S^6 + 143*S^8))/(360*S^2*(1 + S^2)^2) + (2*(2 + 43*S^2 - 90*S^4 + 43*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-7 - 30*S^2 - 31*S^4)/S^2 + (Pi^2*(-3 - 6*S^2 + 164*S^4 - 90*S^6 - 45*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] - (4*(7 + 5*S^2 - 14*S^4 + 51*S^6 + 7*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-18 - 36*S^2 - 13*S^4 + 58*S^6 + 29*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((24*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-36 - 72*S^2 + 67*S^4 + 34*S^6 + 17*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(7 - 38*S^2 - 14*S^4 + 94*S^6 + 7*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(4 + 8*S^2 - 67*S^4 + 30*S^6 + 15*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(39 + 78*S^2 - 888*S^4 + 434*S^6 + 217*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (528*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (8*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(51 + 102*S^2 - 247*S^4 + 36*S^6 + 18*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (264*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((17 + 18*S^2 - 7*S^4)/S^2 + (Pi^2*(1 + 2*S^2 + 153*S^4 - 88*S^6 - 44*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-20*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(2 + 149*S^2 - 90*S^4 - 63*S^6 + 2*S^8))/(3*S^2*(1 + S^2)^2) - (4*(4 + 8*S^2 - 67*S^4 + 30*S^6 + 15*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(3 + 6*S^2 - 67*S^4 + 32*S^6 + 16*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) - (2*(-10 - 20*S^2 - 173*S^4 + 114*S^6 + 57*S^8)*Zeta[5])/(S^2*(1 + S^2)^2))) + (150*(2*S^4 + S^6)*Zeta[7])/(1 + S^2)^2;
E4uvwT3F1=(405*(1 + S^2))/(32*S) + (Pi^2*(120 + 395*S^2 + 67*S^4))/(64*S) + (Pi^4*(120 + 1576*S^2 + 1761*S^4 + 365*S^6))/(720*S*(1 + S^2)) - (Pi^6*S*(-415181 + 121702*S^2 + 29886*S^4 + 14943*S^6))/(90720*(1 + S^2)^3) + (S*HPL[{0}, S^2]^7)/(24*(1 + S^2)^3) + ((-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^6)/(9*S*(1 + S^2)^3) - (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^7)/(21*(1 + S^2)^3) + HPL[{0}, S^2]^6*(-(S*(-62 - 17*S^2 + 3*S^4 + 6*S^6))/(96*(1 + S^2)^3) + (S*(19 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2])/(48*(1 + S^2)^3)) + ((11 + 25*S^2 + 35*S^4 - 7*S^6)*HPL[{2}, -S^2]^3)/(12*S*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-2*Pi^2*S*(-101 + 27*S^2 + 27*S^4 + 9*S^6))/(15*(1 + S^2)^3) + (9 - 62*S^2 + 803*S^4 - 1612*S^6 + 803*S^8 - 62*S^10 + 9*S^12)/(30*S^3*(1 + S^2)^3) + (22*S*HPL[{2}, -S^2])/5) + HPL[{0}, S^2]^5*((Pi^2*S*(65 + 3*S^2 + 3*S^4 + S^6))/(144*(1 + S^2)^3) + (S*(117 - 64*S^2 - 12*S^4 + 20*S^6 + 27*S^8))/(96*(1 + S^2)^3) + ((-27 + 206*S^2 + 18*S^4 + 74*S^6 + 25*S^8)*HPL[{1}, -S^2])/(48*S*(1 + S^2)^3) + (S*(45 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(24*(1 + S^2)^3) + (S*(17 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(24*(1 + S^2)^3)) - (S*(19 + 102*S^2 + 39*S^4 + 4*S^6)*HPL[{3}, -S^2]^2)/(2*(1 + S^2)^3) + ((Pi^2*S*(65 + 231*S^2 + 231*S^4 + 77*S^6))/(6*(1 + S^2)^3) + (90 - 16*S^2 + 149*S^4 + 284*S^6 + 79*S^8 + 206*S^10 + 60*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((-265 + 1203*S^2 + 2058*S^4 + 1300*S^6 + 290*S^8)*HPL[{6}, -S^2])/(2*S*(1 + S^2)^3) + (6*S*(95 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 + ((13 - 542*S^2 + 590*S^4 + 106*S^6 - 7*S^8)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^3) + (-(Pi^2*S*(-229 + 417*S^2 + 417*S^4 + 139*S^6))/(6*(1 + S^2)^3) + (2*(-2 - 8*S^2 - 168*S^4 + 149*S^6 - 30*S^8 + 3*S^10))/(S*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + (-(Pi^2*S*(-365 + 729*S^2 + 729*S^4 + 243*S^6))/(3*(1 + S^2)^3) + (-15 + 9*S^2 - 185*S^4 - 1412*S^6 + 817*S^8 - 253*S^10 + 15*S^12)/(S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] - (3*(3 + 5*S^2 + 116*S^4 + 53*S^6 + 11*S^8)*HPL[{4, 2}, -S^2])/(2*S*(1 + S^2)^3) - (4*S*(16 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 - (2*(-35 + 177*S^2 + 786*S^4 + 386*S^6 + 76*S^8)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^3) - (15*S*(13 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{5, 2}, -S^2])/(1 + S^2)^3 - (30*S*(23 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(-59 + 24*S^2 + 24*S^4 + 8*S^6))/(3*(1 + S^2)^3) + (2*(3 - 24*S^2 + 165*S^4 - 312*S^6 + 149*S^8 - 32*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((-2*Pi^2*S*(-579 + 39*S^2 + 39*S^4 + 13*S^6))/(3*(1 + S^2)^3) + (2*(15 - 68*S^2 + 596*S^4 - 398*S^6 + 171*S^8 - 10*S^10 + 6*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + (12*S*(4 + 3*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^2 - (2*(-11 - 49*S^2 - 53*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (S*(-437 + 777*S^2 + 777*S^4 + 259*S^6)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^3 + (8*S*(-173 + 285*S^2 + 285*S^4 + 95*S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 + (2*(12 + 191*S^2 + 836*S^4 + 333*S^6 + 12*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-677 + 1149*S^2 + 1149*S^4 + 383*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 + (2*S*(-2129 + 3417*S^2 + 3417*S^4 + 1139*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-2155 + 3543*S^2 + 3543*S^4 + 1181*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(65 + 66*S^2 + 66*S^4 + 22*S^6))/(3*(1 + S^2)^3) + (2*(-9 + 59*S^2 - 548*S^4 + 404*S^6 - 107*S^8 + 9*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 288*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(2 + 18*S^2 + 162*S^4 + 67*S^6 + 5*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(429 + 255*S^2 + 255*S^4 + 85*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (4*S*(429 + 255*S^2 + 255*S^4 + 85*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (172*S*(15 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (8*S*(1003 + 1293*S^2 + 1293*S^4 + 431*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (8*(-5 - 110*S^2 - 74*S^4 + 5*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (64*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (192*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-413 + 351*S^2 + 351*S^4 + 117*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - 1216*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-4*S*(17 - 50*S^2 + 17*S^4))/(3*(1 + S^2)^3) + (2*Pi^2*S*(-65 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (2*S*(-23 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^3) - (2*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 + HPL[{0}, S^2]*((-2*S*(34 - 55*S^2 + 5*S^6))/(1 + S^2)^3 + (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2])/(1 + S^2)^3) + (4*S*HPL[{2}, -S^2])/3)*Log[T]^5 + ((-2*S*(-47 + 46*S^2 + 9*S^4))/(3*(1 + S^2)^3) - (4*S*(-11 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2])/(3*(1 + S^2)^3) - (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2])/(3*(1 + S^2)^3))*Log[T]^6 - (16*S*Log[T]^7)/(3*(1 + S^2)^3) + ((157*Pi^4*S^3*(3 + 3*S^2 + S^4))/(45*(1 + S^2)^3) - (S*(-160 - 131*S^2 + 5*S^4))/(4*(1 + S^2)) - (Pi^2*S*(-74 - 285*S^2 + 81*S^4 - 91*S^6 + 9*S^8))/(6*(1 + S^2)^3))*Zeta[3] - (S*(-29 - 2*S^2 + 30*S^4 + 15*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^4*((1 + S^2)^3/(2*S^3) + (Pi^2*(-79 + 1089*S^2 - 948*S^4 - 100*S^6 + 36*S^8))/(18*S*(1 + S^2)^3) - (11*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (2*S*(-161 + 117*S^2 + 117*S^4 + 39*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - 22*S*HPL[{2, 1}, -S^2] + (24*S*(-4 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4}, -S^2]*((-114 - 57*S^2 + 329*S^4 + 82*S^6)/(4*S^3) + (Pi^2*(-35 + 207*S^2 + 860*S^4 + 313*S^6 + 31*S^8))/(12*S*(1 + S^2)^3) - (4*S*(-13 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((Pi^4*S*(-849 + 2157*S^2 + 2157*S^4 + 719*S^6))/(360*(1 + S^2)^3) + (-57 + 252*S^2 + 778*S^4 + 200*S^6 - 77*S^8)/(16*S^3*(1 + S^2)) + (Pi^2*(12 + 7*S^2 + 158*S^4 + 610*S^6 - 294*S^8 + 107*S^10))/(12*S^3*(1 + S^2)^3) + (4*S*(8 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (2*(-13 + 281*S^2 - 279*S^4 - 47*S^6 + 10*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-117 + 177*S^2 + 177*S^4 + 59*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-105 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-5 + 19*S^2 + 8*S^4 + 2*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*((21 + 2*S^2 + 5*S^4)/(8*S*(1 + S^2)) + (Pi^2*(-13 + 865*S^2 - 893*S^4 - 159*S^6 + 4*S^8))/(24*S*(1 + S^2)^3) + (S*(-125 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{3}, -S^2])/(2*(1 + S^2)^3) - 36*S*HPL[{2, 1}, -S^2] + (4*S*(-11 + 24*S^2 + 24*S^4 + 8*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((10 - 81*S^2 - 63*S^4 + 6*S^6)/(2*S^3) + (Pi^2*(5 - 377*S^2 - 165*S^4 - 129*S^6 - 10*S^8))/(6*S*(1 + S^2)^3) - (8*S*(-29 + 45*S^2 + 45*S^4 + 15*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((-2 + 49*S^2 + 31*S^4 + 2*S^6)/S^3 + (Pi^2*(-1 + 457*S^2 - S^4 + 49*S^6 - 8*S^8))/(3*S*(1 + S^2)^3) + (16*S*(-27 + 48*S^2 + 48*S^4 + 16*S^6)*Zeta[3])/(1 + S^2)^3) + Log[T]^4*((3*(1 + S^2))/(2*S) - (Pi^2*S*(-1156 + 1006*S^2 + 187*S^4 + 5*S^6))/(18*(1 + S^2)^3) - (S*(-101 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{0}, S^2]^3)/(9*(1 + S^2)^3) + (5*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)^3) - (20*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^2*(-(S*(-451 + 316*S^2 + 52*S^4 + 5*S^6))/(6*(1 + S^2)^3) - (S*(-77 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2])/(1 + S^2)^3) + ((5 + 110*S^2 + 74*S^4 - 5*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((-2*Pi^2*S*(-101 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (9 - 62*S^2 + 803*S^4 - 1612*S^6 + 803*S^8 - 62*S^10 + 9*S^12)/(6*S^3*(1 + S^2)^3) + 22*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((-2*Pi^2*S*(-133 + 81*S^2 + 81*S^4 + 27*S^6))/(9*(1 + S^2)^3) + (S*(297 - 806*S^2 + 506*S^4 - 62*S^6 + 9*S^8))/(6*(1 + S^2)^3) + (5*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^3) - (10*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 - (2*S*(-139 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + (4*S*(-63 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (152*S*HPL[{2, 1}, -S^2])/3 + (8*S*(-26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{0}, S^2]^4*((9 + 271*S^2 + 98*S^4)/(96*S) - (Pi^2*S*(-475 - 82*S^2 - 3*S^4 + 28*S^6))/(96*(1 + S^2)^3) + ((-81 + 914*S^2 - 70*S^4 + 32*S^6 - 7*S^8)*HPL[{1}, -S^2]^2)/(48*S*(1 + S^2)^3) + (S*(95 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(18*(1 + S^2)^3) + ((-2 + 127*S^2 + 29*S^4 + 28*S^6 + 4*S^8)*HPL[{2}, -S^2])/(16*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*S*(475 + 153*S^2 + 153*S^4 + 51*S^6))/(144*(1 + S^2)^3) + (9 - 126*S^2 + 837*S^4 - 406*S^6 + 227*S^8 + 112*S^10 - 21*S^12)/(96*S^3*(1 + S^2)^3) + (S*(34 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2}, -S^2])/(6*(1 + S^2)^3)) + (3*S*HPL[{3}, -S^2])/8 - (S*(34 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)^3) + (S*(26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(6*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-5 - 152*S^2 - 136*S^4 + 5*S^6)/(4*S^3) - (Pi^4*S*(899 + 576*S^2 + 576*S^4 + 192*S^6))/(90*(1 + S^2)^3) + (Pi^2*(-9 + 50*S^2 - 480*S^4 + 24*S^6 + 147*S^8 - 66*S^10 + 6*S^12))/(6*S^3*(1 + S^2)^3) - (4*S*(-141 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (32*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(-11 + 227*S^2 - 369*S^4 - 89*S^6 + 2*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(((1 + S^2)*(25 + 66*S^2 + 25*S^4))/(12*S^3) - (Pi^4*S*(-7001 + 1185*S^2 + 1185*S^4 + 395*S^6))/(540*(1 + S^2)^3) + (Pi^2*(9 - 62*S^2 + 771*S^4 - 1283*S^6 + 504*S^8 - 11*S^10))/(18*S^3*(1 + S^2)^3) + ((2*Pi^2*S*(103 + 51*S^2 + 51*S^4 + 17*S^6))/(9*(1 + S^2)^3) + (9 - 32*S^2 + 403*S^4 - 259*S^6 + 80*S^8 - 9*S^10)/(3*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (2*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) - (4*(-1 + 170*S^2 - 536*S^4 - 85*S^6 + 22*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (2*S*(-75 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + (44*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (32*S*(-2 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + 88*S*HPL[{2, 1, 1}, -S^2] - (4*(-2 + 47*S^2 - 154*S^4 - 10*S^6 + 13*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + Log[T]^3*((-5*(1 + S^2))/S - (Pi^4*S*(3723 + 75*S^2 + 75*S^4 + 25*S^6))/(270*(1 + S^2)^3) + (Pi^2*S*(-659 + 1484*S^2 - 550*S^4 - 44*S^6 + 9*S^8))/(18*(1 + S^2)^3) - (S*(101 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{0}, S^2]^4)/(18*(1 + S^2)^3) - (20*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)^3) + (20*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^3*(-(S*(431 - 184*S^2 + 90*S^4 + 45*S^6))/(9*(1 + S^2)^3) + (2*S*(-211 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{1}, -S^2])/(9*(1 + S^2)^3)) + ((4*Pi^2*S*(-38 + 15*S^2 + 15*S^4 + 5*S^6))/(9*(1 + S^2)^3) + (-9 + 5*S^2 - 258*S^4 + 114*S^6 - 53*S^8 + 9*S^10)/(3*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*S*(-83 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((4*Pi^2*S*(-101 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (-9 + 62*S^2 - 803*S^4 + 1612*S^6 - 803*S^8 + 62*S^10 - 9*S^12)/(3*S^3*(1 + S^2)^3) - 44*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*((-4*Pi^2*S*(54 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (S*(-319 + 484*S^2 - 210*S^4 - 44*S^6 + 9*S^8))/(6*(1 + S^2)^3) + ((73 - 948*S^2 + 486*S^4 + 70*S^6 + 3*S^8)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^3) + (2*S*(-77 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 + (2*S*(-81 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + (2*(13 + 174*S^2 - 1230*S^4 - 100*S^6 + 91*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (28*S*(-5 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) - (4*(71 - 418*S^2 - 58*S^4 + 61*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (16*S*(15 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + (80*S*HPL[{2, 1, 1}, -S^2])/3 + (4*S*(52 - 550*S^2 - S^4 + 61*S^6)*Zeta[3])/(3*(1 + S^2)^3) + HPL[{1}, -S^2]*((-2*(1 + S^2)^3)/S^3 - (2*Pi^2*(-79 + 1089*S^2 - 948*S^4 - 100*S^6 + 36*S^8))/(9*S*(1 + S^2)^3) + (44*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (8*S*(-161 + 117*S^2 + 117*S^4 + 39*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + 88*S*HPL[{2, 1}, -S^2] - (96*S*(-4 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{0}, S^2]*((-3 - 3*S^2 - 2*S^4)/S - (Pi^2*S*(941 - 1009*S^2 + 90*S^4 + 120*S^6))/(9*(1 + S^2)^3) - (10*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)^3) + (40*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^3) - (2*(-7 + 397*S^2 - 740*S^4 + 9*S^6 + 73*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((4*Pi^2*S*(-293 + 81*S^2 + 81*S^4 + 27*S^6))/(9*(1 + S^2)^3) + (-9 + 62*S^2 - 803*S^4 + 1612*S^6 - 803*S^8 + 62*S^10 - 9*S^12)/(3*S^3*(1 + S^2)^3) + (4*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) - (8*S*(5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (16*S*(91 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (8*S*(-11 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(3*(1 + S^2)^3))) + HPL[{0}, S^2]^3*((60 + 283*S^2 + 110*S^4 - 17*S^6)/(96*S*(1 + S^2)) - (Pi^4*S*(-3723 + 75*S^2 + 75*S^4 + 25*S^6))/(2160*(1 + S^2)^3) + (Pi^2*S*(945 - 636*S^2 + 144*S^4 + 112*S^6 + 147*S^8))/(144*(1 + S^2)^3) + ((-77 + 848*S^2 - 398*S^4 + 34*S^6 + 37*S^8)*HPL[{1}, -S^2]^3)/(18*S*(1 + S^2)^3) - (S*(-211 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{1}, -S^2]^4)/(18*(1 + S^2)^3) + (-(Pi^2*S*(-167 + 9*S^2 + 9*S^4 + 3*S^6))/(36*(1 + S^2)^3) + (9 + 6*S^2 + 369*S^4 - 74*S^6 + 279*S^8 + 8*S^10 + 3*S^12)/(24*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (S*(-69 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2}, -S^2]^2)/(12*(1 + S^2)^3) + HPL[{1}, -S^2]^2*(-(Pi^2*S*(-109 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (9 - 74*S^2 + 751*S^4 - 690*S^6 + 209*S^8 - 12*S^10 + 15*S^12)/(24*S^3*(1 + S^2)^3) - (2*S*(-43 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((-3 + 4*S^2 - 16*S^4 + 6*S^6 + 5*S^8)*HPL[{3}, -S^2])/(4*S*(1 + S^2)^3) - (2*S^3*(3 + 3*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((68 - 341*S^2 + 149*S^4 + 11*S^6 - 7*S^8)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)^3) + (S*(-75 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) - (4*S*(-41 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (S*(59 + 117*S^2 + 107*S^4 + 33*S^6)*Zeta[3])/(2*(1 + S^2)^3) + HPL[{1}, -S^2]*((6 + 31*S^2 + 69*S^4 + 17*S^6 - 3*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-106 + 939*S^2 - 154*S^4 + 202*S^6 + 81*S^8))/(36*S*(1 + S^2)^3) + ((-77 + 664*S^2 - 326*S^4 + 60*S^6 + 47*S^8)*HPL[{2}, -S^2])/(12*S*(1 + S^2)^3) - (S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (4*S*(-43 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (2*S*(11 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(3*(1 + S^2)^3))) + ((110*Pi^2*S^3*(3 + 3*S^2 + S^4))/(3*(1 + S^2)^3) - (S*(-80 - 269*S^2 + 106*S^4 - 133*S^6 + 12*S^8))/(1 + S^2)^3)*Zeta[5] + HPL[{0}, S^2]^2*((3*(60 + 335*S^2 + 67*S^4))/(64*S) + (Pi^2*(18 + 341*S^2 + 411*S^4 + 100*S^6))/(48*S*(1 + S^2)) - (Pi^4*S*(-16301 + 361*S^2 + 99*S^4 + 669*S^6))/(1440*(1 + S^2)^3) + ((-73 + 948*S^2 - 486*S^4 - 70*S^6 - 3*S^8)*HPL[{1}, -S^2]^4)/(12*S*(1 + S^2)^3) - (S*(-77 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^5)/(5*(1 + S^2)^3) - (S*(-323 + 303*S^2 + 53*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(8*(1 + S^2)^3) + HPL[{1}, -S^2]^3*(-(Pi^2*S*(-421 + 9*S^2 + 9*S^4 + 3*S^6))/(18*(1 + S^2)^3) + (9 - 62*S^2 + 739*S^4 - 954*S^6 + 205*S^8 + 40*S^10 - 9*S^12)/(12*S^3*(1 + S^2)^3) + (S*(173 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((Pi^2*S*(1 + 9*S^2 + 9*S^4 + 3*S^6))/(2*(1 + S^2)^3) + (3*(2 + S^2 + 19*S^4 + 24*S^6 - 6*S^8 + 7*S^10 + S^12))/(4*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-7 + 69*S^2 + 33*S^4 - S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) + (3*S*(7 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(40 + 9*S^2 + 9*S^4 + 3*S^6))/(3*(1 + S^2)^3) + (-9 + 50*S^2 - 471*S^4 + 192*S^6 - 3*S^8 - 34*S^10 + 3*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((9 - 341*S^2 + 159*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(2*S*(1 + S^2)^3) - (4*S*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (2*S*(-5 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + ((-6 + 342*S^2 - 185*S^4 - 20*S^6 - 3*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (192*S*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (6*S*(95 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (8*S*(46 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((Pi^2*S*(26 + 69*S^2 + 69*S^4 + 23*S^6))/(3*(1 + S^2)^3) - (S*(-127 - 260*S^2 - 162*S^4 - 84*S^6 + 9*S^8))/(4*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-2 + 48*S^2 + 73*S^4 + 37*S^6 + 2*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-12 + 723*S^2 - 98*S^4 + 64*S^6 + 9*S^8))/(24*S*(1 + S^2)^3) + (2*S*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (96*S*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(-77 + 931*S^2 - 278*S^4 - 19*S^6 - 5*S^8))/(12*S*(1 + S^2)^3) + (6 + 34*S^2 + 75*S^4 + 28*S^6 + 5*S^8)/(8*S^3*(1 + S^2)) + ((-75 + 774*S^2 - 202*S^4 - 34*S^6 - 15*S^8)*HPL[{2}, -S^2])/(4*S*(1 + S^2)^3) + (6*S*(-1 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (S*(173 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^4*S*(761 + 129*S^2 + 129*S^4 + 43*S^6))/(90*(1 + S^2)^3) + (25 + 151*S^2 + 275*S^4 + 125*S^6 + 24*S^8)/(16*S^3*(1 + S^2)) + (Pi^2*(9 - 94*S^2 + 788*S^4 - 680*S^6 + 216*S^8 + 76*S^10 - 15*S^12))/(24*S^3*(1 + S^2)^3) + ((Pi^2*S*(309 + 39*S^2 + 39*S^4 + 13*S^6))/(12*(1 + S^2)^3) + (9 - 19*S^2 + 411*S^4 - 203*S^6 + 90*S^8 + 38*S^10 - 6*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*S*(-23 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 - (3*(3 - 10*S^2 - 50*S^4 - 12*S^6 + S^8)*HPL[{3}, -S^2])/(2*S*(1 + S^2)^3) + 10*S*HPL[{4}, -S^2] + ((75 - 774*S^2 + 202*S^4 + 34*S^6 + 15*S^8)*HPL[{2, 1}, -S^2])/(2*S*(1 + S^2)^3) - (4*S*(43 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (2*S*(173 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(1 - 12*S^2 - 44*S^4 - 2*S^6 + 5*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + 55*S*Zeta[5]) + Log[T]^2*((45*(1 + S^2))/(4*S) + (Pi^2*(18 + 79*S^2 + 51*S^4 + 2*S^6))/(12*S*(1 + S^2)) - (Pi^4*S*(-14410 + 9121*S^2 + 1447*S^4 + 104*S^6))/(360*(1 + S^2)^3) + (S*(23 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^5)/(12*(1 + S^2)^3) + (5*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)^3) - (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^5)/(1 + S^2)^3 + HPL[{0}, S^2]^4*((S*(165 - 3*S^2 + 18*S^4 + 2*S^6))/(8*(1 + S^2)^3) + (S*(95 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2])/(6*(1 + S^2)^3)) + ((-13 + 542*S^2 - 590*S^4 - 106*S^6 + 7*S^8)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-4*Pi^2*S*(-101 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (9 - 62*S^2 + 803*S^4 - 1612*S^6 + 803*S^8 - 62*S^10 + 9*S^12)/(3*S^3*(1 + S^2)^3) + 44*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^3*((-2*Pi^2*S*(-54 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (S*(90 - 79*S^2 + 51*S^4 + 3*S^6 + 3*S^8))/(3*(1 + S^2)^3) + ((-77 + 848*S^2 - 398*S^4 + 34*S^6 + 37*S^8)*HPL[{1}, -S^2])/(6*S*(1 + S^2)^3) - (S*(-211 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^3) - (2*S*(-41 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((Pi^2*S*(-129 + 249*S^2 + 249*S^4 + 83*S^6))/(3*(1 + S^2)^3) + (6 + 4*S^2 + 101*S^4 + 538*S^6 - 276*S^8 + 86*S^10 - 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-21 + 83*S^2 + 656*S^4 + 249*S^6 + 33*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (2*S*(23 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(65 + 66*S^2 + 66*S^4 + 22*S^6))/(3*(1 + S^2)^3) + (-9 + 59*S^2 - 548*S^4 + 404*S^6 - 107*S^8 + 9*S^10)/(S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(2 + 18*S^2 + 162*S^4 + 67*S^6 + 5*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-213 + 393*S^2 + 393*S^4 + 131*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-355 + 651*S^2 + 651*S^4 + 217*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (4*(-5 - 110*S^2 - 74*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (32*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-147 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - 608*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S*(-26 + 69*S^2 + 69*S^4 + 23*S^6))/(3*(1 + S^2)^3) - (S*(-21 - 310*S^2 + 324*S^4 - 98*S^6 + 9*S^8))/(1 + S^2)^3)*Zeta[3] + HPL[{0}, S^2]^2*((Pi^2*S*(946 - 325*S^2 + 2*S^4 + S^6))/(12*(1 + S^2)^3) + (9 + 61*S^2 + 42*S^4 + 2*S^6)/(4*S*(1 + S^2)) + ((-73 + 948*S^2 - 486*S^4 - 70*S^6 - 3*S^8)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)^3) - (2*S*(-77 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(1 + S^2)^3 + ((-6 + 342*S^2 - 185*S^4 - 20*S^6 - 3*S^8)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(-(Pi^2*S*(-421 + 9*S^2 + 9*S^4 + 3*S^6))/(6*(1 + S^2)^3) + (9 - 62*S^2 + 739*S^4 - 954*S^6 + 205*S^8 + 40*S^10 - 9*S^12)/(4*S^3*(1 + S^2)^3) + (S*(173 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + (3*S*(-1 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (4*S*(46 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (16*S^3*(3 + 3*S^2 + S^4)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*((3*(1 + S^2)^3)/S^3 + (Pi^2*(-79 + 1089*S^2 - 948*S^4 - 100*S^6 + 36*S^8))/(3*S*(1 + S^2)^3) - (66*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-161 + 117*S^2 + 117*S^4 + 39*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - 132*S*HPL[{2, 1}, -S^2] + (144*S*(-4 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((-2 + 49*S^2 + 31*S^4 + 2*S^6)/(2*S^3) + (Pi^2*(-1 + 457*S^2 - S^4 + 49*S^6 - 8*S^8))/(6*S*(1 + S^2)^3) + (2*S*(-105 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (16*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-27 + 48*S^2 + 48*S^4 + 16*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]*(((1 + S^2)*(25 + 66*S^2 + 25*S^4))/(4*S^3) - (Pi^4*S*(-7001 + 1185*S^2 + 1185*S^4 + 395*S^6))/(180*(1 + S^2)^3) + (Pi^2*(9 - 62*S^2 + 771*S^4 - 1283*S^6 + 504*S^8 - 11*S^10))/(6*S^3*(1 + S^2)^3) + ((2*Pi^2*S*(103 + 51*S^2 + 51*S^4 + 17*S^6))/(3*(1 + S^2)^3) + (9 - 32*S^2 + 403*S^4 - 259*S^6 + 80*S^8 - 9*S^10)/(S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (2*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 - (4*(-1 + 170*S^2 - 536*S^4 - 85*S^6 + 22*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-75 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (132*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (32*S*(-2 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + 264*S*HPL[{2, 1, 1}, -S^2] - (12*(-2 + 47*S^2 - 154*S^4 - 10*S^6 + 13*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]*((30 + 61*S^2 + 25*S^4)/(4*S) - (Pi^4*S*(-1655 + 657*S^2 + 657*S^4 + 219*S^6))/(90*(1 + S^2)^3) + (Pi^2*S*(657 - 1122*S^2 + 710*S^4 - 50*S^6 + 21*S^8))/(12*(1 + S^2)^3) + (10*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^3) - (10*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(1 + S^2)^3 + (-(Pi^2*S*(-221 + 147*S^2 + 147*S^4 + 49*S^6))/(3*(1 + S^2)^3) + (9 + 4*S^2 + 317*S^4 - 514*S^6 + 537*S^8 - 58*S^10 + 9*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*S*(-67 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^2*((-2*Pi^2*S*(-293 + 81*S^2 + 81*S^4 + 27*S^6))/(3*(1 + S^2)^3) + (9 - 62*S^2 + 803*S^4 - 1612*S^6 + 803*S^8 - 62*S^10 + 9*S^12)/(2*S^3*(1 + S^2)^3) - (6*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + ((-11 + 36*S^2 + 32*S^4 + 54*S^6 + 21*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-11 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (2*(-83 + 629*S^2 - 448*S^4 - 63*S^6 + 17*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (24*S*(-23 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-139 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*S*(-10 + 122*S^2 + 63*S^4 + 15*S^6)*Zeta[3])/(1 + S^2)^3 + HPL[{1}, -S^2]*((3*(1 + S^2)^3)/S^3 + (Pi^2*(-81 + 1039*S^2 - 904*S^4 - 48*S^6 + 56*S^8))/(3*S*(1 + S^2)^3) + (18*(-5 + 57*S^2 - 66*S^4 - 3*S^6 + 5*S^8)*HPL[{2}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (12*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-6 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3)) + (220*S*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2}, -S^2]*((3*(-67 + 493*S^2 + 275*S^4 + 67*S^6))/(32*S^3) + (Pi^4*(-107 + 7860*S^2 + 439*S^4 + 911*S^6 - 45*S^8))/(720*S*(1 + S^2)^3) + (Pi^2*(-4 + 95*S^2 + 153*S^4 + 70*S^6 + 4*S^8))/(24*S^3*(1 + S^2)) + ((Pi^2*S*(-113 + 213*S^2 + 213*S^4 + 71*S^6))/(6*(1 + S^2)^3) + (2 + 11*S^2 + 168*S^4 - 152*S^6 + 30*S^8 - 3*S^10)/(S*(1 + S^2)^3))*HPL[{3}, -S^2] + ((9 + 71*S^2 + 348*S^4 + 135*S^6 + 17*S^8)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^3) + (S*(-29 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(-59 + 24*S^2 + 24*S^4 + 8*S^6))/(3*(1 + S^2)^3) + (-3 + 24*S^2 - 165*S^4 + 312*S^6 - 149*S^8 + 32*S^10 - 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((15 - 598*S^2 + 498*S^4 + 66*S^6 - 13*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (S*(-229 + 393*S^2 + 393*S^4 + 131*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (2*S*(-349 + 597*S^2 + 597*S^4 + 199*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (2*(-13 + 542*S^2 - 590*S^4 - 106*S^6 + 7*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 144*S*HPL[{2, 2, 1}, -S^2] - (4*S*(213 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-30 + 51*S^2 + 51*S^4 + 17*S^6))/(3*(1 + S^2)^3) - (S*(-9 - 168*S^2 + 150*S^4 - 32*S^6 + 3*S^8))/(1 + S^2)^3)*Zeta[3] + (2*S*(-47 + 117*S^2 + 117*S^4 + 39*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*((3*(1 + S^2)*(27 + 86*S^2 + 27*S^4))/(16*S^3) + (Pi^2*(12 + 58*S^2 + 111*S^4 + 52*S^6 + 11*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(-1036 + 13752*S^2 - 8414*S^4 - 789*S^6 + 225*S^8))/(360*S*(1 + S^2)^3) + ((-35 + 494*S^2 - 602*S^4 - 74*S^6 + 25*S^8)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^3) + ((Pi^2*S*(-167 + 135*S^2 + 135*S^4 + 45*S^6))/(3*(1 + S^2)^3) + (6 + 36*S^4 + 557*S^6 - 231*S^8 + 51*S^10 - 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-23 + 7*S^2 + 510*S^4 + 149*S^6 + 5*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (2*S*(5 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(103 + 51*S^2 + 51*S^4 + 17*S^6))/(3*(1 + S^2)^3) + (-9 + 32*S^2 - 403*S^4 + 259*S^6 - 80*S^8 + 9*S^10)/(S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(33 - 154*S^2 - 470*S^4 - 96*S^6 + 19*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-71 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (2*S*(-927 + 651*S^2 + 651*S^4 + 217*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (132*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-149 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - 264*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S*(-38 + 33*S^2 + 33*S^4 + 11*S^6))/(3*(1 + S^2)^3) - (S*(32 - 329*S^2 + 299*S^4 - 51*S^6 + 9*S^8))/(1 + S^2)^3)*Zeta[3] + HPL[{2}, -S^2]*((1 + 93*S^2 + 67*S^4 - S^6)/(4*S^3) + (Pi^2*(-141 + 1236*S^2 + 458*S^4 + 32*S^6 - 81*S^8))/(12*S*(1 + S^2)^3) + (4*S*(-71 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (4*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*Zeta[3])/(1 + S^2)^3) + (2*S*(-163 + 171*S^2 + 171*S^4 + 57*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]*((3*(1 + S^2)*(2 + 23*S^2 + 2*S^4))/S^3 - (Pi^6*S*(-173539 + 1323*S^2 + 1323*S^4 + 441*S^6))/(45360*(1 + S^2)^3) + (Pi^2*(50 + 267*S^2 + 457*S^4 + 241*S^6 + 49*S^8))/(48*S^3*(1 + S^2)) + (Pi^4*(120 - 1016*S^2 + 10591*S^4 - 13169*S^6 + 5330*S^8 + 495*S^10 - 147*S^12))/(720*S^3*(1 + S^2)^3) + (-(Pi^2*S*(-245 + 69*S^2 + 69*S^4 + 23*S^6))/(6*(1 + S^2)^3) + (3 - 17*S^2 + 349*S^4 - 646*S^6 + 333*S^8 - 25*S^10 + 3*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (13*S*HPL[{2}, -S^2]^3)/3 - (S*(-9 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(-55 + 171*S^2 + 171*S^4 + 57*S^6))/(6*(1 + S^2)^3) + (12 - 21*S^2 + 148*S^4 + 420*S^6 + 80*S^8 + 65*S^10)/(S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(-41 + 142*S^2 + 424*S^4 + 207*S^6 + 38*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) + (S*(299 + 477*S^2 + 477*S^4 + 159*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 + (4*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((-4*Pi^2*S*(39 + 33*S^2 + 33*S^4 + 11*S^6))/(3*(1 + S^2)^3) + (-15 + 17*S^2 - 421*S^4 - 468*S^6 + 129*S^8 - 77*S^10 + 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (2*(-13 + 340*S^2 - 822*S^4 - 96*S^6 + 47*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + (2*(-16 + 1013*S^2 - 2976*S^4 - 437*S^6 + 136*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) - (9*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 - (8*S*(-23 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(103 + 51*S^2 + 51*S^4 + 17*S^6))/(3*(1 + S^2)^3) - (2*(-9 + 32*S^2 - 403*S^4 + 259*S^6 - 80*S^8 + 9*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(-35 + 494*S^2 - 602*S^4 - 74*S^6 + 25*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*(-103 + 1142*S^2 - 734*S^4 - 52*S^6 + 31*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 104*S*HPL[{3, 2, 1}, -S^2] + (4*S*(3 + 345*S^2 + 345*S^4 + 115*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (264*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (64*S*(-2 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + 528*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((10 + 39*S^2 + 4*S^4 - S^6)/(2*S*(1 + S^2)) + (Pi^2*(4 - 117*S^2 + 550*S^4 + 34*S^6 - 49*S^8))/(3*S*(1 + S^2)^3))*Zeta[3] + (2*S*(7 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{3}, -S^2]*((Pi^2*(-7 - 310*S^2 + 1222*S^4 + 206*S^6 - 47*S^8))/(6*S*(1 + S^2)^3) + (-4 + 63*S^2 + 161*S^4 + 65*S^6 - 5*S^8)/(2*S^3*(1 + S^2)) - (8*S*(-71 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (48*S*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((-1 - 93*S^2 - 67*S^4 + S^6)/(2*S^3) + (Pi^2*(141 - 1236*S^2 - 458*S^4 - 32*S^6 + 81*S^8))/(6*S*(1 + S^2)^3) - (16*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((1 + 313*S^2 + 263*S^4 - S^6)/(8*S^3) + (Pi^4*S*(3201 + 1119*S^2 + 1119*S^4 + 373*S^6))/(360*(1 + S^2)^3) + (Pi^2*(18 - 42*S^2 + 782*S^4 - 59*S^6 - 89*S^8 + 109*S^10 - 15*S^12))/(12*S^3*(1 + S^2)^3) + ((13 - 340*S^2 + 822*S^4 + 96*S^6 - 47*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (S*(-39 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (2*(-35 + 494*S^2 - 602*S^4 - 74*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-155 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((9 - 312*S^2 + 862*S^4 + 100*S^6 - 51*S^8)*Zeta[3])/(S*(1 + S^2)^3)) - (2*(-3 + 70*S^2 - 672*S^4 - 7*S^6 + 78*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]*((3*(51 + 349*S^2 + 32*S^4))/(16*S) + (Pi^2*(40 + 155*S^2 + 94*S^4 + 11*S^6))/(32*S*(1 + S^2)) - (Pi^6*S*(-95123 + 24399*S^2 + 24399*S^4 + 8133*S^6))/(45360*(1 + S^2)^3) + (Pi^4*S*(5389 - 6093*S^2 + 3037*S^4 + 157*S^6 + 630*S^8))/(720*(1 + S^2)^3) + ((-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)^3) - (2*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^3) + (-(Pi^2*S*(-203 + 135*S^2 + 135*S^4 + 45*S^6))/(12*(1 + S^2)^3) + (3 + 126*S^2 - 323*S^4 + 215*S^6 - 24*S^8 + 3*S^10)/(4*S*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (4*S*(-14 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*(-(Pi^2*S*(-293 + 81*S^2 + 81*S^4 + 27*S^6))/(9*(1 + S^2)^3) + (9 - 62*S^2 + 803*S^4 - 1612*S^6 + 803*S^8 - 62*S^10 + 9*S^12)/(12*S^3*(1 + S^2)^3) - (S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) - (2*S*(3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(-11 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (9 + 11*S^2 + 119*S^4 + 186*S^6 + 203*S^8 + 19*S^10 - 3*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (4*(-2 + S^2)*(1 + 4*S^2 + 13*S^4 + 5*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - 46*S*HPL[{6}, -S^2] + (4*S*(-67 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(-213 + 165*S^2 + 165*S^4 + 55*S^6))/(3*(1 + S^2)^3) + (-6 - 5*S^2 - 173*S^4 + 201*S^6 - 325*S^8 + 20*S^10)/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*(1 - 9*S^2 + 31*S^4 + 15*S^6 + 4*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) - (6*(-1 - 10*S^2 + 44*S^4 + 32*S^6 + 11*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-5 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-221 + 147*S^2 + 147*S^4 + 49*S^6))/(3*(1 + S^2)^3) + (9 + 4*S^2 + 317*S^4 - 514*S^6 + 537*S^8 - 58*S^10 + 9*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(35 - 294*S^2 + 245*S^4 + 60*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (2*(-221 + 1800*S^2 - 1438*S^4 - 306*S^6 + 9*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (32*S*(-14 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-179 + 189*S^2 + 189*S^4 + 63*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 - (4*(-83 + 629*S^2 - 448*S^4 - 63*S^6 + 17*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (48*S*(-23 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-139 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (-4*S*(-4 + S^2) + (Pi^2*S*(167 + 473*S^2 + 384*S^4 + 114*S^6))/(6*(1 + S^2)^3))*Zeta[3] - (2*S*(-5 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^3*((1 + S^2)^3/S^3 + (Pi^2*(-81 + 1039*S^2 - 904*S^4 - 48*S^6 + 56*S^8))/(9*S*(1 + S^2)^3) + (6*(-5 + 57*S^2 - 66*S^4 - 3*S^6 + 5*S^8)*HPL[{2}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-6 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((Pi^2*(151 - 970*S^2 + 597*S^4 + 74*S^6 - 24*S^8))/(6*S*(1 + S^2)^3) + (-3 - 37*S^2 - 41*S^4 - 29*S^6 + 2*S^8)/(2*S^3*(1 + S^2)) - (8*S*(-4 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((2 + 55*S^2 + 67*S^4 + 6*S^6)/(4*S^3) + (Pi^2*(-5 + 12*S^2 - 4*S^4 + 18*S^6 + 9*S^8))/(3*S*(1 + S^2)^3) + (8*S*(6 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(5 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((-13*Pi^4*S*(-51 + 21*S^2 + 21*S^4 + 7*S^6))/(90*(1 + S^2)^3) + (-4 + 122*S^2 + 195*S^4 + 122*S^6 + 5*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(9 + 5*S^2 + 343*S^4 - 294*S^6 + 408*S^8 - 25*S^10 + 6*S^12))/(12*S^3*(1 + S^2)^3) + (2*(1 - 9*S^2 + 31*S^4 + 15*S^6 + 4*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (4*S*(3 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (2*(35 - 294*S^2 + 245*S^4 + 60*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-34 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-67 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((-2 + 3*S^2 + 108*S^4 + 55*S^6 + 12*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(25 + 66*S^2 + 25*S^4))/(8*S^3) - (Pi^4*S*(-3529 + 657*S^2 + 657*S^4 + 219*S^6))/(180*(1 + S^2)^3) + (Pi^2*(9 - 68*S^2 + 777*S^4 - 1151*S^6 + 506*S^8 - 37*S^10 + 12*S^12))/(12*S^3*(1 + S^2)^3) + (-(Pi^2*S*(-493 + 141*S^2 + 141*S^4 + 47*S^6))/(6*(1 + S^2)^3) + (9 - 23*S^2 + 435*S^4 - 514*S^6 + 419*S^8 - 31*S^10 + 9*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + ((-9 + 12*S^2 - 2*S^4 + 46*S^6 + 21*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-6 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (18*(-5 + 57*S^2 - 66*S^4 - 3*S^6 + 5*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (80*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (12*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((-1 - 70*S^2 + 150*S^4 + 64*S^6 + 13*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + (3*S*(59 + 100*S^2 + 45*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((3*(1 + S^2)*(27 + 86*S^2 + 27*S^4))/(16*S^3) + (Pi^2*(12 + 55*S^2 + 105*S^4 + 41*S^6 + 3*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(-1269 + 13454*S^2 - 7606*S^4 + 1214*S^6 + 1055*S^8))/(360*S*(1 + S^2)^3) + ((-35 + 494*S^2 - 602*S^4 - 74*S^6 + 25*S^8)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^3) + ((-4*Pi^2*S*(-4 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (2*(3 + S^2 + 27*S^4 + 57*S^6 + 48*S^8 + 4*S^10))/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (4*(-4 + 13*S^2 - 22*S^4 + 10*S^6 + 7*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-2 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((Pi^2*S*(-493 + 141*S^2 + 141*S^4 + 47*S^6))/(3*(1 + S^2)^3) + (-9 + 23*S^2 - 435*S^4 + 514*S^6 - 419*S^8 + 31*S^10 - 9*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(-22 + 253*S^2 - 302*S^4 - 14*S^6 + 23*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (80*S*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (16*S*(9 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (36*(-5 + 57*S^2 - 66*S^4 - 3*S^6 + 5*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-233 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (24*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-1 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) + (2*(-1 + 7*S^2 + 57*S^4 - 14*S^6 - 4*S^8 + 3*S^10))/(S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((1 + 74*S^2 + 82*S^4 + 58*S^6 + S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-167 + 1690*S^2 - 1514*S^4 + 6*S^6 + 137*S^8))/(12*S*(1 + S^2)^3) - (40*S*HPL[{3}, -S^2])/(1 + S^2)^3 + (4*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (10*S*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + 20*S*Zeta[5])) + Log[T]*((-153*(1 + S^2))/(8*S) + (Pi^2*(-60 - 271*S^2 - 191*S^4 - 4*S^6))/(24*S*(1 + S^2)) - (Pi^6*S*(95123 + 24399*S^2 + 24399*S^4 + 8133*S^6))/(22680*(1 + S^2)^3) + (Pi^4*S*(-5052 + 6710*S^2 - 3995*S^4 - 824*S^6 + 141*S^8))/(360*(1 + S^2)^3) - (S*(11 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2]^6)/(24*(1 + S^2)^3) - (2*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)^3) + (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^5*(-(S*(132 + 55*S^2 + 80*S^4 + 25*S^6))/(24*(1 + S^2)^3) - (S*(45 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(12*(1 + S^2)^3)) + ((Pi^2*S*(-127 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) + (-7 - 184*S^2 + 334*S^4 - 184*S^6 - 7*S^8)/(2*S*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (10*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((2*Pi^2*S*(-101 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (-9 + 62*S^2 - 803*S^4 + 1612*S^6 - 803*S^8 + 62*S^10 - 9*S^12)/(6*S^3*(1 + S^2)^3) - 22*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^4*(-(Pi^2*S*(133 + 81*S^2 + 81*S^4 + 27*S^6))/(36*(1 + S^2)^3) + (S*(-251 + 22*S^2 - 165*S^4 - 64*S^6 + 6*S^8))/(24*(1 + S^2)^3) + ((81 - 914*S^2 + 70*S^4 - 32*S^6 + 7*S^8)*HPL[{1}, -S^2])/(24*S*(1 + S^2)^3) - (S*(95 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(6*(1 + S^2)^3) - (S*(34 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2}, -S^2])/(6*(1 + S^2)^3)) + (2*S*(-5 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(-29 + 81*S^2 + 81*S^4 + 27*S^6))/(3*(1 + S^2)^3) + (-9 + 21*S^2 - 177*S^4 - 436*S^6 - 65*S^8 - 57*S^10 + 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(-29 + 192*S^2 + 452*S^4 + 181*S^6 + 22*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - (2*S*(129 + 177*S^2 + 177*S^4 + 59*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 - (8*S*(-83 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((-14*Pi^2*S*(-7 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) - (2*(-6 - 3*S^2 - 155*S^4 - 242*S^6 + 2*S^8 - 23*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*S*(71 - 522*S^2 - 37*S^4 + 40*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (2*(25 + 423*S^2 - 3622*S^4 - 343*S^6 + 245*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + (6*S*(-7 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-35 + 159*S^2 + 159*S^4 + 53*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((8*Pi^2*S*(-38 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) + (2*(-9 + 5*S^2 - 258*S^4 + 114*S^6 - 53*S^8 + 9*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (4*(-57 + 446*S^2 - 614*S^4 - 42*S^6 + 43*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (8*(-92 + 582*S^2 - 306*S^4 - 13*S^6 + 19*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 12*S*HPL[{3, 1, 2}, -S^2] + 68*S*HPL[{3, 2, 1}, -S^2] + (8*S*(65 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 - (8*(71 - 418*S^2 - 58*S^4 + 61*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (32*S*(15 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + 160*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((3*S*(-16 - 11*S^2 + S^4))/(1 + S^2) + (Pi^2*S*(7 - 669*S^2 - 20*S^4 + 68*S^6))/(3*(1 + S^2)^3))*Zeta[3] - (4*S*(5 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{2, 1}, -S^2]*((3 + 44*S^2 + 36*S^4 - 3*S^6)/S^3 + (Pi^2*(-140 + 779*S^2 + 459*S^4 - 17*S^6 - 73*S^8))/(3*S*(1 + S^2)^3) - (688*S*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((-1 - 38*S^2 - 90*S^4 - 39*S^6 + 2*S^8)/(S^3*(1 + S^2)) + (Pi^2*(11 + 66*S^2 - 693*S^4 - 62*S^6 + 50*S^8))/(3*S*(1 + S^2)^3) - (4*S*(179 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-5 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-2*(1 + S^2)^3)/S^3 - (2*Pi^2*(-79 + 1089*S^2 - 948*S^4 - 100*S^6 + 36*S^8))/(9*S*(1 + S^2)^3) + (44*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (8*S*(-161 + 117*S^2 + 117*S^4 + 39*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + 88*S*HPL[{2, 1}, -S^2] - (96*S*(-4 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{0}, S^2]^3*((-9 - 76*S^2 - 60*S^4 - 5*S^6)/(12*S*(1 + S^2)) - (Pi^2*S*(1091 + 91*S^2 + 490*S^4 + 170*S^6))/(36*(1 + S^2)^3) + ((77 - 848*S^2 + 398*S^4 - 34*S^6 - 37*S^8)*HPL[{1}, -S^2]^2)/(6*S*(1 + S^2)^3) + (2*S*(-211 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^3) + ((9 - 323*S^2 + 177*S^4 - 71*S^6 - 40*S^8)*HPL[{2}, -S^2])/(6*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((2*Pi^2*S*(-109 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (-9 + 74*S^2 - 751*S^4 + 690*S^6 - 209*S^8 + 12*S^10 - 15*S^12)/(12*S^3*(1 + S^2)^3) + (4*S*(-43 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) - (4*S*HPL[{3}, -S^2])/(1 + S^2)^3 + (60*S*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (2*S*(11 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(25 + 66*S^2 + 25*S^4))/(4*S^3) + (Pi^4*S*(-7001 + 1185*S^2 + 1185*S^4 + 395*S^6))/(180*(1 + S^2)^3) + (Pi^2*(-9 + 62*S^2 - 771*S^4 + 1283*S^6 - 504*S^8 + 11*S^10))/(6*S^3*(1 + S^2)^3) + ((-2*Pi^2*S*(103 + 51*S^2 + 51*S^4 + 17*S^6))/(3*(1 + S^2)^3) + (-9 + 32*S^2 - 403*S^4 + 259*S^6 - 80*S^8 + 9*S^10)/(S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + (4*(-1 + 170*S^2 - 536*S^4 - 85*S^6 + 22*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-75 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (132*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (32*S*(-2 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - 264*S*HPL[{2, 1, 1}, -S^2] + (12*(-2 + 47*S^2 - 154*S^4 - 10*S^6 + 13*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2}, -S^2]*((4 - 161*S^2 - 127*S^4 - 4*S^6)/(4*S^3) + (Pi^4*S*(-1403 + 33*S^2 + 33*S^4 + 11*S^6))/(180*(1 + S^2)^3) + (Pi^2*(-9 - 8*S^2 - 302*S^4 + 35*S^6 - 58*S^8 - 43*S^10 + 9*S^12))/(6*S^3*(1 + S^2)^3) + (2*S*(59 - 543*S^2 - 49*S^4 + 37*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (2*S*(-13 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (2*(-57 + 446*S^2 - 614*S^4 - 42*S^6 + 43*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-169 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-83 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(2 + 85*S^2 - 493*S^4 - 11*S^6 + 49*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]^2*((-30 - 211*S^2 - 161*S^4 - 4*S^6)/(8*S*(1 + S^2)) - (Pi^4*S*(1655 + 657*S^2 + 657*S^4 + 219*S^6))/(180*(1 + S^2)^3) + (Pi^2*S*(-821 + 528*S^2 - 540*S^4 - 172*S^6 + 21*S^8))/(24*(1 + S^2)^3) + ((73 - 948*S^2 + 486*S^4 + 70*S^6 + 3*S^8)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^3) + (S*(-77 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(1 + S^2)^3 + (-(Pi^2*S*(149 + 3*S^2 + 3*S^4 + S^6))/(6*(1 + S^2)^3) + (-9 - 12*S^2 - 351*S^4 + 214*S^6 - 177*S^8 - 42*S^10 + 9*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (4*S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^2*((Pi^2*S*(-421 + 9*S^2 + 9*S^4 + 3*S^6))/(6*(1 + S^2)^3) + (-9 + 62*S^2 - 739*S^4 + 954*S^6 - 205*S^8 - 40*S^10 + 9*S^12)/(4*S^3*(1 + S^2)^3) - (S*(173 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + (3*(3 - 14*S^2 - 52*S^4 - 8*S^6 + 3*S^8)*HPL[{3}, -S^2])/(2*S*(1 + S^2)^3) - 6*S*HPL[{4}, -S^2] + ((-69 + 432*S^2 - 17*S^4 - 14*S^6 - 12*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-79 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-81 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (S*(-45 - 119*S^2 - 19*S^4 + 7*S^6)*Zeta[3])/(1 + S^2)^3 + HPL[{1}, -S^2]*((-6 - 34*S^2 - 75*S^4 - 28*S^6 - 5*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(77 - 931*S^2 + 278*S^4 + 19*S^6 + 5*S^8))/(6*S*(1 + S^2)^3) + ((75 - 774*S^2 + 202*S^4 + 34*S^6 + 15*S^8)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^3) - (12*S*(-1 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (2*S*(173 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3)) + HPL[{0}, S^2]*((-3*(30 + 83*S^2 + 27*S^4))/(8*S) + (Pi^2*(-18 - 94*S^2 - 75*S^4 - 11*S^6))/(12*S*(1 + S^2)) - (Pi^4*S*(2312 - 1071*S^2 + 730*S^4 + 365*S^6))/(60*(1 + S^2)^3) - (5*(-17 + 246*S^2 - 282*S^4 - 26*S^6 + 15*S^8)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)^3) + (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{1}, -S^2]^5)/(1 + S^2)^3 - (S*(200 - 357*S^2 - 14*S^4 + 27*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^3*((4*Pi^2*S*(-293 + 81*S^2 + 81*S^4 + 27*S^6))/(9*(1 + S^2)^3) + (-9 + 62*S^2 - 803*S^4 + 1612*S^6 - 803*S^8 + 62*S^10 - 9*S^12)/(3*S^3*(1 + S^2)^3) + (4*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + ((-2*Pi^2*S*(11 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (-6 - 2*S^2 - 61*S^4 - 106*S^6 - 82*S^8 - 12*S^10 - 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(-7 + 28*S^2 - 34*S^4 + 34*S^6 + 19*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(136 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (9 - 50*S^2 + 553*S^4 - 514*S^6 + 301*S^8 - 4*S^10 + 9*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(-7 + 388*S^2 - 750*S^4 + 10*S^6 + 75*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (8*S*(-11 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (4*(-7 + 397*S^2 - 740*S^4 + 9*S^6 + 73*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (1376*S*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(263 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (32*S*(91 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S^3*(3 + 3*S^2 + S^4))/(1 + S^2)^3 - (S*(47 + 170*S^2 + 10*S^4 + 2*S^6 + 3*S^8))/(1 + S^2)^3)*Zeta[3] + HPL[{1}, -S^2]^2*((-3*(1 + S^2)^3)/S^3 + (Pi^2*(81 - 1039*S^2 + 904*S^4 + 48*S^6 - 56*S^8))/(3*S*(1 + S^2)^3) - (18*(-5 + 57*S^2 - 66*S^4 - 3*S^6 + 5*S^8)*HPL[{2}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (12*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-6 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((Pi^2*(16 - 720*S^2 + 917*S^4 - 80*S^6 - 113*S^8))/(6*S*(1 + S^2)^3) + (2 - 37*S^2 - 41*S^4 - 29*S^6 - 3*S^8)/(2*S^3*(1 + S^2)) - (8*S*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (688*S*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-7 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]*(-((1 + S^2)*(25 + 66*S^2 + 25*S^4))/(4*S^3) + (Pi^4*S*(-3529 + 657*S^2 + 657*S^4 + 219*S^6))/(90*(1 + S^2)^3) + (Pi^2*(-9 + 68*S^2 - 777*S^4 + 1151*S^6 - 506*S^8 + 37*S^10 - 12*S^12))/(6*S^3*(1 + S^2)^3) + ((Pi^2*S*(-493 + 141*S^2 + 141*S^4 + 47*S^6))/(3*(1 + S^2)^3) + (-9 + 23*S^2 - 435*S^4 + 514*S^6 - 419*S^8 + 31*S^10 - 9*S^12)/(S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (2*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 - (2*(-9 + 12*S^2 - 2*S^4 + 46*S^6 + 21*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (16*S*(-6 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (36*(-5 + 57*S^2 - 66*S^4 - 3*S^6 + 5*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (160*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (24*S*(-107 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(-1 - 70*S^2 + 150*S^4 + 64*S^6 + 13*S^8)*Zeta[3])/(S*(1 + S^2)^3))) + (2*S*(-12 - 721*S^2 + 67*S^4 + 116*S^6)*Zeta[5])/(1 + S^2)^3 + HPL[{1}, -S^2]*((-3*(1 + S^2)*(27 + 86*S^2 + 27*S^4))/(8*S^3) + (Pi^4*(1036 - 13752*S^2 + 8414*S^4 + 789*S^6 - 225*S^8))/(180*S*(1 + S^2)^3) + (Pi^2*(-12 - 58*S^2 - 111*S^4 - 52*S^6 - 11*S^8))/(12*S^3*(1 + S^2)) + ((35 - 494*S^2 + 602*S^4 + 74*S^6 - 25*S^8)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(-167 + 135*S^2 + 135*S^4 + 45*S^6))/(3*(1 + S^2)^3) + (2*(-6 - 36*S^4 - 557*S^6 + 231*S^8 - 51*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(-23 + 7*S^2 + 510*S^4 + 149*S^6 + 5*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (4*S*(5 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(103 + 51*S^2 + 51*S^4 + 17*S^6))/(3*(1 + S^2)^3) - (2*(-9 + 32*S^2 - 403*S^4 + 259*S^6 - 80*S^8 + 9*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(33 - 154*S^2 - 470*S^4 - 96*S^6 + 19*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(-71 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-927 + 651*S^2 + 651*S^4 + 217*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (264*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (16*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-149 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + 528*S*HPL[{2, 1, 1, 1}, -S^2] + ((-8*Pi^2*S*(-38 + 33*S^2 + 33*S^4 + 11*S^6))/(3*(1 + S^2)^3) + (2*S*(32 - 329*S^2 + 299*S^4 - 51*S^6 + 9*S^8))/(1 + S^2)^3)*Zeta[3] + HPL[{2}, -S^2]*((-1 - 93*S^2 - 67*S^4 + S^6)/(2*S^3) + (Pi^2*(141 - 1236*S^2 - 458*S^4 - 32*S^6 + 81*S^8))/(6*S*(1 + S^2)^3) - (8*S*(-71 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-35 + 24*S^2 + 24*S^4 + 8*S^6)*Zeta[3])/(1 + S^2)^3) - (4*S*(-163 + 171*S^2 + 171*S^4 + 57*S^6)*Zeta[5])/(1 + S^2)^3)) + (300*S^3*(3 + 3*S^2 + S^4)*Zeta[7])/(1 + S^2)^3;
E4uvwT3F3=(-395*(1 + S^2))/(864*S) + (Pi^2*(15806 - 475*S^2 - 14985*S^4))/(5184*S) + (Pi^4*(6404 + 5221*S^2 - 9976*S^4 - 8433*S^6))/(12960*S*(1 + S^2)) + (Pi^6*(23420 + 58550*S^2 - 155116*S^4 - 22276*S^6 - 6451*S^8 - 441*S^10))/(90720*S*(1 + S^2)^3) - (S^3*HPL[{0}, S^2]^7)/(72*(1 + S^2)^3) + ((1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^6)/(9*S^3*(1 + S^2)^3) + (4*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^7)/(63*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^6*((4 + 10*S^2 - 19*S^4 - 13*S^6 - 4*S^8)/(96*S*(1 + S^2)^3) + ((6 + 18*S^2 + 18*S^4 - 13*S^6 - 9*S^8 - 9*S^10 - 3*S^12)*HPL[{1}, -S^2])/(144*S^3*(1 + S^2)^3)) + ((-1 + S^2)*(27 + 49*S^2 + 58*S^4 + 49*S^6 + 27*S^8)*HPL[{2}, -S^2]^3)/(36*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((Pi^2*(29 + 87*S^2 + 87*S^4 - 173*S^6 + 54*S^8 + 54*S^10 + 18*S^12))/(45*S^3*(1 + S^2)^3) + (25 + 58*S^2 + 1139*S^4 - 1148*S^6 + 1139*S^8 + 58*S^10 + 25*S^12)/(90*S^3*(1 + S^2)^3) - (22*(-1 + S^6)*HPL[{2}, -S^2])/(15*S^3)) + HPL[{0}, S^2]^5*(-(Pi^2*S^3*(65 + 3*S^2 + 3*S^4 + S^6))/(432*(1 + S^2)^3) + (-54 - 63*S^2 - 352*S^4 - 336*S^6 - 214*S^8 - 45*S^10)/(288*S*(1 + S^2)^3) + ((-9 - 9*S^2 + 27*S^4 - 74*S^6 - 33*S^8 - 29*S^10 - 9*S^12)*HPL[{1}, -S^2])/(48*S^3*(1 + S^2)^3) + ((9 + 27*S^2 + 27*S^4 - 36*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{1}, -S^2]^2)/(72*S^3*(1 + S^2)^3) - (S^3*(17 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(72*(1 + S^2)^3)) + ((14 + 42*S^2 + 51*S^4 + 46*S^6 + 297*S^8 + 162*S^10 + 32*S^12)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((171 - 542*S^2 - 1487*S^4 - 3948*S^6 - 6014*S^8 - 3344*S^10 - 792*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(20 + 60*S^2 + 60*S^4 - 45*S^6 - 231*S^8 - 231*S^10 - 77*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((-495 - 1109*S^2 - 395*S^4 - 1440*S^6 - 2491*S^8 - 1660*S^10 - 408*S^12)*HPL[{6}, -S^2])/(6*S^3*(1 + S^2)^3) + ((75 + 225*S^2 + 225*S^4 - 115*S^6 - 282*S^8 - 282*S^10 - 94*S^12)*HPL[{7}, -S^2])/(S^3*(1 + S^2)^3) + ((-19 - 333*S^2 - 819*S^4 + 2086*S^6 - 819*S^8 - 333*S^10 - 19*S^12)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((Pi^2*(5 + 15*S^2 + 15*S^4 - 224*S^6 + 417*S^8 + 417*S^10 + 139*S^12))/(18*S^3*(1 + S^2)^3) + (-15 - 20*S^2 + 196*S^4 - 240*S^6 + 1879*S^8 + 412*S^10 + 156*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((Pi^2*(-7 - 21*S^2 - 21*S^4 - 372*S^6 + 729*S^8 + 729*S^10 + 243*S^12))/(9*S^3*(1 + S^2)^3) + (-49 + 158*S^2 + 845*S^4 + 280*S^6 + 5341*S^8 + 1642*S^10 + 519*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((-3 - S^2 + 14*S^4 + 118*S^8 + 79*S^10 + 21*S^12)*HPL[{4, 2}, -S^2])/(2*S^3*(1 + S^2)^3) + (4*S^3*(16 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{4, 3}, -S^2])/(3*(1 + S^2)^3) + (2*(63 + 149*S^2 + 68*S^4 + 132*S^6 + 809*S^8 + 524*S^10 + 129*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2 + 6*S^2 + 6*S^4 + 67*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{5, 2}, -S^2])/(S^3*(1 + S^2)^3) + (2*(-58 - 174*S^2 - 174*S^4 + 287*S^6 + 585*S^8 + 585*S^10 + 195*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*Pi^2*(17 + 51*S^2 + 51*S^4 - 42*S^6 + 24*S^8 + 24*S^10 + 8*S^12))/(9*S^3*(1 + S^2)^3) + (141 + 392*S^2 + 2075*S^4 - 480*S^6 + 2075*S^8 + 392*S^10 + 141*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((339 + 448*S^2 + 4585*S^4 - 2100*S^6 + 661*S^8 - 404*S^10 - 57*S^12)/(9*S^3*(1 + S^2)^3) + (2*Pi^2*(209 + 627*S^2 + 627*S^4 - 370*S^6 + 39*S^8 + 39*S^10 + 13*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (2*(-3 - 7*S^2 - 6*S^4 + 6*S^6 + 7*S^8 + 3*S^10)*HPL[{3, 1, 2}, -S^2])/(S^3*(1 + S^2)^2) + (2*(-18 - S^2 + 9*S^4 - 9*S^6 + S^8 + 18*S^10)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + ((29 + 87*S^2 + 87*S^4 + 466*S^6 - 777*S^8 - 777*S^10 - 259*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-8 - 24*S^2 - 24*S^4 - 181*S^6 + 285*S^8 + 285*S^10 + 95*S^12)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-90 - 138*S^2 - 3*S^4 + 96*S^6 - 485*S^8 - 194*S^10 + 6*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-29 - 87*S^2 - 87*S^4 - 706*S^6 + 1149*S^8 + 1149*S^10 + 383*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-77 - 231*S^2 - 231*S^4 - 2206*S^6 + 3417*S^8 + 3417*S^10 + 1139*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-82 - 246*S^2 - 246*S^4 - 2237*S^6 + 3543*S^8 + 3543*S^10 + 1181*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*(-33 - 38*S^2 - 289*S^4 + 289*S^6 + 38*S^8 + 33*S^10))/(3*S^3*(1 + S^2)^2) + (8*Pi^2*(-38 - 114*S^2 - 114*S^4 + 27*S^6 + 66*S^8 + 66*S^10 + 22*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] + (96*(-1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/S^3 + (8*(18 + 36*S^2 + 21*S^4 - 24*S^6 + 101*S^8 + 47*S^10 + 3*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-213 - 639*S^2 - 639*S^4 + 216*S^6 + 255*S^8 + 255*S^10 + 85*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-213 - 639*S^2 - 639*S^4 + 216*S^6 + 255*S^8 + 255*S^10 + 85*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-429 - 1287*S^2 - 1287*S^4 + 216*S^6 + 903*S^8 + 903*S^10 + 301*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-639 - 1917*S^2 - 1917*S^4 + 364*S^6 + 1293*S^8 + 1293*S^10 + 431*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-15 + 26*S^2 + 54*S^4 - 54*S^6 - 26*S^8 + 15*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (64*(8 + 24*S^2 + 24*S^4 - 27*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(8 + 24*S^2 + 24*S^4 - 27*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (32*(79 + 237*S^2 + 237*S^4 - 334*S^6 + 351*S^8 + 351*S^10 + 117*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (1216*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-2*Pi^2*S^3*(-65 + 3*S^2 + 3*S^4 + S^6))/(27*(1 + S^2)^3) - (2*(1 + 38*S^2 - 94*S^4 + 38*S^6 + S^8))/(9*S*(1 + S^2)^3) - (2*S^3*(-23 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(9*(1 + S^2)^3) - (2*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + HPL[{0}, S^2]*((-2*(6 + 15*S^2 - 47*S^4 + 42*S^6 + 15*S^8 + S^10))/(3*S*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3)) - (4*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3))*Log[T]^5 + ((2*(2 + 5*S^2 - 22*S^4 + 5*S^6 + 2*S^8))/(3*S*(1 + S^2)^3) + (4*S^3*(-11 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2])/(9*(1 + S^2)^3) + (4*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3))*Log[T]^6 + (16*S^3*Log[T]^7)/(9*(1 + S^2)^3) + ((-157*Pi^4*S^5*(3 + 3*S^2 + S^4))/(135*(1 + S^2)^3) + (3714 + 3227*S^2 - 5390*S^4 - 4471*S^6)/(216*S*(1 + S^2)) + (Pi^2*(20 + 32*S^2 - 63*S^4 - 1657*S^6 - 661*S^8 - 255*S^10))/(54*S*(1 + S^2)^3))*Zeta[3] + ((4 + 10*S^2 - 4*S^4 - 4*S^6 + 5*S^8 + 3*S^10)*Zeta[3]^2)/(S*(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((-3*(-13 - 15*S^2 + 15*S^4 + 13*S^6))/(2*S^3) + (Pi^2*(-67 + 213*S^2 + 807*S^4 - 1043*S^6 + 12*S^8 + 120*S^10 + 86*S^12))/(27*S^3*(1 + S^2)^3) - (16*S^3*(-27 + 48*S^2 + 48*S^4 + 16*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + Log[T]^4*((1 + S^2)/(6*S) + (Pi^2*(174 + 435*S^2 - 1512*S^4 + 355*S^6 + 163*S^8 + 15*S^10))/(54*S*(1 + S^2)^3) + (S^3*(-101 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{0}, S^2]^3)/(27*(1 + S^2)^3) + (5*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (20*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^2*((84 + 210*S^2 - 522*S^4 + 130*S^6 + 73*S^8 + 15*S^10)/(18*S*(1 + S^2)^3) + ((14 + 42*S^2 + 42*S^4 - 63*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((-1 + S^2)*(15 - 11*S^2 - 65*S^4 - 11*S^6 + 15*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(29 + 87*S^2 + 87*S^4 - 173*S^6 + 54*S^8 + 54*S^10 + 18*S^12))/(9*S^3*(1 + S^2)^3) + (25 + 58*S^2 + 1139*S^4 - 1148*S^6 + 1139*S^8 + 58*S^10 + 25*S^12)/(18*S^3*(1 + S^2)^3) - (22*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]*((2*Pi^2*S^3*(-133 + 81*S^2 + 81*S^4 + 27*S^6))/(27*(1 + S^2)^3) + (22 + 413*S^2 - 574*S^4 + 726*S^6 + 36*S^8 + 25*S^10)/(18*S*(1 + S^2)^3) + (5*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3) + (10*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (2*(-2 - 6*S^2 - 6*S^4 - 141*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) - (4*(-1 - 3*S^2 - 3*S^4 - 64*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (152*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (8*S^3*(-26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{0}, S^2]^4*((1133 - 757*S^2 - 2214*S^4)/(2592*S) + (Pi^2*(266 + 665*S^2 - 1374*S^4 - 759*S^6 - 282*S^8 - 24*S^10))/(864*S*(1 + S^2)^3) + ((-25 + 669*S^2 + 2127*S^4 - 2210*S^6 - 519*S^8 - 213*S^10 - 25*S^12)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)^3) + ((43 + 129*S^2 + 129*S^4 - 147*S^6 - 18*S^8 - 18*S^10 - 6*S^12)*HPL[{1}, -S^2]^3)/(108*S^3*(1 + S^2)^3) + ((80 + 209*S^2 - 339*S^4 - 180*S^6 - 108*S^8 - 24*S^10)*HPL[{2}, -S^2])/(144*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((1025 + 1974*S^2 + 9345*S^4 - 8606*S^6 - 6765*S^8 - 4380*S^10 - 1369*S^12)/(2592*S^3*(1 + S^2)^3) + (Pi^2*(133 + 399*S^2 + 399*S^4 - 342*S^6 - 153*S^8 - 153*S^10 - 51*S^12))/(432*S^3*(1 + S^2)^3) + ((37 + 111*S^2 + 111*S^4 - 99*S^6 - 36*S^8 - 36*S^10 - 12*S^12)*HPL[{2}, -S^2])/(72*S^3*(1 + S^2)^3)) + ((1 - 3*S^6)*HPL[{3}, -S^2])/(24*S^3) + ((-17 - 51*S^2 - 51*S^4 + 17*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^3) - (S^3*(26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(18*(1 + S^2)^3)) + HPL[{4}, -S^2]*((57 - 5*S^2 - 251*S^4 - 249*S^6)/(8*S^3) + (Pi^2*(-59 + 57*S^2 + 534*S^4 + 152*S^6 - 2298*S^8 - 1281*S^10 - 257*S^12))/(108*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 - 14*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-1 - 3*S^2 - 3*S^4 + 2*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(1013 - 566*S^2 + 1013*S^4))/(324*S^3) + (Pi^2*(895 + 2580*S^2 + 21291*S^4 - 15670*S^6 + 12831*S^8 + 618*S^10 + 31*S^12))/(972*S^3*(1 + S^2)^3) + (Pi^4*(1152 + 3456*S^2 + 3456*S^4 - 5849*S^6 + 1185*S^8 + 1185*S^10 + 395*S^12))/(1620*S^3*(1 + S^2)^3) + ((48 + 61*S^2 + 409*S^4 - 409*S^6 - 61*S^8 - 48*S^10)/(9*S^3*(1 + S^2)^2) - (2*Pi^2*(-36 - 108*S^2 - 108*S^4 + 67*S^6 + 51*S^8 + 51*S^10 + 17*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (2*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) - (4*(52 + 213*S^2 + 330*S^4 - 868*S^6 + 1221*S^8 + 510*S^10 + 52*S^12)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^3) - (2*(-9 - 27*S^2 - 27*S^4 - 84*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (44*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (8*(-13 - 39*S^2 - 39*S^4 - 21*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (88*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(2 - 6*S^2 - 33*S^4 + 292*S^6 - 330*S^8 - 105*S^10 + 2*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-648 - 1361*S^2 - 5195*S^4 - 10465*S^6 - 5119*S^8)/(216*S^3*(1 + S^2)) + (Pi^2*(-50 - 1149*S^2 - 2589*S^4 - 1774*S^6 - 10122*S^8 - 3129*S^10 - 923*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(49 + 147*S^2 + 147*S^4 + 898*S^6 - 2157*S^8 - 2157*S^10 - 719*S^12))/(1080*S^3*(1 + S^2)^3) - (4*S^3*(8 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) - (2*(-68 - 315*S^2 - 576*S^4 + 1043*S^6 - 243*S^8 - 18*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-3 - 9*S^2 - 9*S^4 - 120*S^6 + 177*S^8 + 177*S^10 + 59*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-3 - 9*S^2 - 9*S^4 - 108*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-3 - 8*S^2 - 8*S^4 - 15*S^6 + 13*S^8 + 10*S^10 + 3*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-4471 - 4633*S^2 + 4633*S^4 + 4471*S^6)/(216*S^3) + (Pi^4*(-474 - 1422*S^2 - 1422*S^4 + 425*S^6 + 576*S^8 + 576*S^10 + 192*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(-420 - 982*S^2 - 4273*S^4 + 240*S^6 + 2198*S^8 + 590*S^10 + 279*S^12))/(108*S^3*(1 + S^2)^3) + (4*(33 + 99*S^2 + 99*S^4 - 108*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(8 + 24*S^2 + 24*S^4 - 27*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-23 - 147*S^2 - 327*S^4 + 1043*S^6 - 492*S^8 - 186*S^10 + 4*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((-297 + 80*S^2 + 322*S^4 + 80*S^6 - 297*S^8)/(432*S^3*(1 + S^2)) + (Pi^2*(-1 + 155*S^2 + 413*S^4 - 1085*S^6 + 444*S^8 + 204*S^10 + 26*S^12))/(72*S^3*(1 + S^2)^3) + ((5 + 15*S^2 + 15*S^4 + 130*S^6 - 201*S^8 - 201*S^10 - 67*S^12)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^3) + (12*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (4*(-1 - 3*S^2 - 3*S^4 - 12*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(18*S^3) + (Pi^2*(17 + 309*S^2 + 822*S^4 - 1118*S^6 + 525*S^8 + 210*S^10 + 17*S^12))/(54*S^3*(1 + S^2)^3) - (11*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (2*(6 + 18*S^2 + 18*S^4 - 155*S^6 + 117*S^8 + 117*S^10 + 39*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (22*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (2*(1 + 3*S^2 + 3*S^4 - 47*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((9 + 19*S^2 + 109*S^4 + 87*S^6)/(4*S^3) + (Pi^2*(157 + 111*S^2 - 375*S^4 + 917*S^6 + 426*S^8 + 174*S^10 - 14*S^12))/(54*S^3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 28*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^3*((-5898 - 6089*S^2 - 8848*S^4 - 7793*S^6)/(2592*S*(1 + S^2)) + (Pi^4*S^3*(-3723 + 75*S^2 + 75*S^4 + 25*S^6))/(6480*(1 + S^2)^3) + (Pi^2*(-464 - 194*S^2 - 3666*S^4 - 2891*S^6 - 2036*S^8 - 441*S^10))/(648*S*(1 + S^2)^3) + ((-59 + 465*S^2 + 1743*S^4 - 2494*S^6 + 285*S^8 - 21*S^10 - 59*S^12)*HPL[{1}, -S^2]^3)/(162*S^3*(1 + S^2)^3) + ((36 + 108*S^2 + 108*S^4 - 175*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{1}, -S^2]^4)/(54*S^3*(1 + S^2)^3) + ((Pi^2*S^3*(-167 + 9*S^2 + 9*S^4 + 3*S^6))/(108*(1 + S^2)^3) + (-61 - 376*S^2 + 200*S^4 - 1646*S^6 - 613*S^8 - 790*S^10 - 178*S^12)/(216*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (S^3*(-69 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2}, -S^2]^2)/(36*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((-185 - 1245*S^2 + 1734*S^4 - 5041*S^6 - 732*S^8 - 966*S^10 - 149*S^12)/(324*S^3*(1 + S^2)^3) + (Pi^2*(81 + 243*S^2 + 243*S^4 - 355*S^6 + 12*S^8 + 12*S^10 + 4*S^12))/(108*S^3*(1 + S^2)^3) + ((15 + 45*S^2 + 45*S^4 - 71*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((-13 - 33*S^2 - 15*S^4 - 44*S^6 + 15*S^8 - 21*S^10 - 13*S^12)*HPL[{3}, -S^2])/(36*S^3*(1 + S^2)^3) + (2*S^5*(3 + 3*S^2 + S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + ((44 - 240*S^2 - 1086*S^4 + 727*S^6 - 117*S^8 - 9*S^10 + 17*S^12)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)^3) - (S^3*(-75 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 1}, -S^2])/(9*(1 + S^2)^3) + (4*S^3*(-41 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{2, 1, 1}, -S^2])/(9*(1 + S^2)^3) + ((8 + 20*S^2 - 177*S^4 - 369*S^6 - 333*S^8 - 105*S^10)*Zeta[3])/(18*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((-705 - 1316*S^2 - 942*S^4 - 972*S^6 - 497*S^8)/(432*S^3*(1 + S^2)) + (Pi^2*(-232 + 30*S^2 + 1479*S^4 - 2912*S^6 - 600*S^8 - 663*S^10 - 232*S^12))/(324*S^3*(1 + S^2)^3) + ((-83 + 321*S^2 + 1491*S^4 - 1858*S^6 + 303*S^8 - 75*S^10 - 83*S^12)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)^3) + (S^3*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (2*(15 + 45*S^2 + 45*S^4 - 71*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-2 - 6*S^2 - 6*S^4 + 9*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3))) + Log[T]^3*((2*(1 + S^2))/(9*S) + (Pi^4*S^3*(3723 + 75*S^2 + 75*S^4 + 25*S^6))/(810*(1 + S^2)^3) + (Pi^2*(-26 - 405*S^2 + 682*S^4 - 262*S^6 + 12*S^8 + 15*S^10))/(27*S*(1 + S^2)^3) + (S^3*(101 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{0}, S^2]^4)/(54*(1 + S^2)^3) - (20*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) - (20*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^3*((-24 - 60*S^2 + 166*S^4 - 12*S^6 + 15*S^8 + 9*S^10)/(9*S*(1 + S^2)^3) - (2*(36 + 108*S^2 + 108*S^4 - 175*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^3)) + ((2*(-15 - 23*S^2 - 120*S^4 + 120*S^6 + 23*S^8 + 15*S^10))/(9*S^3*(1 + S^2)^2) - (4*Pi^2*(-2 - 6*S^2 - 6*S^4 - 40*S^6 + 15*S^8 + 15*S^10 + 5*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (4*(3 + 9*S^2 + 9*S^4 - 80*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((-25 - 58*S^2 - 1139*S^4 + 1148*S^6 - 1139*S^8 - 58*S^10 - 25*S^12)/(9*S^3*(1 + S^2)^3) - (2*Pi^2*(29 + 87*S^2 + 87*S^4 - 173*S^6 + 54*S^8 + 54*S^10 + 18*S^12))/(9*S^3*(1 + S^2)^3) + (44*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^2*((4*Pi^2*S^3*(54 + 3*S^2 + 3*S^4 + S^6))/(27*(1 + S^2)^3) + (-21 - 215*S^2 + 212*S^4 - 72*S^6 + 17*S^8 + 15*S^10)/(9*S*(1 + S^2)^3) + ((-19 - 303*S^2 - 789*S^4 + 826*S^6 - 195*S^8 - 105*S^10 - 19*S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(14 + 42*S^2 + 42*S^4 - 63*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 80*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + (2*(27 + 101*S^2 + 125*S^4 - 414*S^6 + 1153*S^8 + 475*S^10 + 57*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-9 - 27*S^2 - 27*S^4 - 44*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-15 - 172*S^2 - 342*S^4 + 342*S^6 + 172*S^8 + 15*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*(-4 - 12*S^2 - 12*S^4 + 11*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (80*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(6 + 15*S^2 - 180*S^4 + 529*S^6 + 193*S^8 + 15*S^10)*Zeta[3])/(9*S*(1 + S^2)^3) + HPL[{0}, S^2]*((5 - 35*S^2 + 14*S^4)/(9*S) + (Pi^2*(-54 - 135*S^2 + 401*S^4 - 222*S^6 - 60*S^8 + 4*S^10))/(9*S*(1 + S^2)^3) - (10*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) - (40*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) - (2*(-19 + 23*S^2 + 146*S^4 - 584*S^6 + 580*S^8 + 199*S^10 + 11*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((-25 - 58*S^2 - 1139*S^4 + 1148*S^6 - 1139*S^8 - 58*S^10 - 25*S^12)/(9*S^3*(1 + S^2)^3) - (2*Pi^2*(81 + 243*S^2 + 243*S^4 - 505*S^6 + 162*S^8 + 162*S^10 + 54*S^12))/(27*S^3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + (8*(-1 - 3*S^2 - 3*S^4 + 4*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(-41 - 123*S^2 - 123*S^4 + 141*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*S^3*(-11 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{1}, -S^2]*((2*(1 + S^2)*(7 - 22*S^2 + 7*S^4))/(9*S^3) - (2*Pi^2*(17 + 309*S^2 + 822*S^4 - 1118*S^6 + 525*S^8 + 210*S^10 + 17*S^12))/(27*S^3*(1 + S^2)^3) + (44*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (8*(6 + 18*S^2 + 18*S^4 - 155*S^6 + 117*S^8 + 117*S^10 + 39*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (88*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + 3*S^2 + 3*S^4 - 47*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3))) + ((-110*Pi^2*S^5*(3 + 3*S^2 + S^4))/(9*(1 + S^2)^3) + (36 + 112*S^2 + 67*S^4 - 544*S^6 - 189*S^8 - 94*S^10)/(3*S*(1 + S^2)^3))*Zeta[5] + HPL[{0}, S^2]^2*((16078 - 203*S^2 - 14985*S^4)/(1728*S) + (Pi^2*(1186 + 779*S^2 - 2306*S^4 - 1827*S^6))/(864*S*(1 + S^2)) + (Pi^4*(2956 + 7390*S^2 - 16665*S^4 - 5845*S^6 - 2185*S^8 - 207*S^10))/(4320*S*(1 + S^2)^3) + ((19 + 303*S^2 + 789*S^4 - 826*S^6 + 195*S^8 + 105*S^10 + 19*S^12)*HPL[{1}, -S^2]^4)/(36*S^3*(1 + S^2)^3) + ((14 + 42*S^2 + 42*S^4 - 63*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^5)/(15*S^3*(1 + S^2)^3) + ((-22 + 132*S^2 + 420*S^4 - 1169*S^6 + 513*S^8 + 279*S^10 + 59*S^12)*HPL[{2}, -S^2]^2)/(72*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((335 + 1029*S^2 + 5520*S^4 - 2669*S^6 + 1290*S^8 + 48*S^10 - 97*S^12)/(162*S^3*(1 + S^2)^3) + (Pi^2*(85 + 255*S^2 + 255*S^4 - 336*S^6 + 9*S^8 + 9*S^10 + 3*S^12))/(54*S^3*(1 + S^2)^3) + ((39 + 117*S^2 + 117*S^4 - 134*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((76 - 57*S^2 - 129*S^4 - 784*S^6 - 1776*S^8 - 759*S^10 - 203*S^12)/(108*S^3*(1 + S^2)^3) + (Pi^2*(1 + 3*S^2 + 3*S^4 - 9*S^8 - 9*S^10 - 3*S^12))/(6*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-16 + 31*S^2 + 101*S^4 - 169*S^6 - 113*S^8 - 16*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) + ((5 + 15*S^2 + 15*S^4 - 16*S^6 - 45*S^8 - 45*S^10 - 15*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-18 - 54*S^2 - 54*S^4 + 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12))/(9*S^3*(1 + S^2)^3) + (-222 - 556*S^2 - 2311*S^4 + 240*S^6 + 236*S^8 + 164*S^10 + 81*S^12)/(36*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((49 - 105*S^2 - 501*S^4 + 1061*S^6 - 180*S^8 - 108*S^10 - 32*S^12)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(1 + 3*S^2 + 3*S^4 - 4*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-22 + 180*S^2 + 567*S^4 - 1043*S^6 + 252*S^8 + 153*S^10 + 41*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(-3 - 9*S^2 - 9*S^4 + 5*S^6)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)^3) - (2*(-37 - 111*S^2 - 111*S^4 + 58*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (8*(-19 - 57*S^2 - 57*S^4 + 27*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (-(Pi^2*S^3*(26 + 69*S^2 + 69*S^4 + 23*S^6))/(9*(1 + S^2)^3) - (2*(-2 - 14*S^2 + 51*S^4 + 163*S^6 + 115*S^8 + 39*S^10))/(9*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((756 + 1930*S^2 + 161*S^4 - 1850*S^6 - 1053*S^8)/(432*S^3*(1 + S^2)) + (Pi^2*(-22 + 420*S^2 + 1194*S^4 - 2060*S^6 - 288*S^8 - 171*S^10 - 31*S^12))/(216*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-3 - 9*S^2 - 9*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^3) - (2*S^3*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((5247 + 11036*S^2 + 3570*S^4 - 6276*S^6 - 3193*S^8)/(864*S^3*(1 + S^2)) + (Pi^2*(565 + 1344*S^2 + 6795*S^4 - 4648*S^6 - 1395*S^8 - 1428*S^10 - 521*S^12))/(432*S^3*(1 + S^2)^3) + (Pi^4*(739 + 2217*S^2 + 2217*S^4 - 2305*S^6 - 516*S^8 - 516*S^10 - 172*S^12))/(1080*S^3*(1 + S^2)^3) + ((847 + 2238*S^2 + 10527*S^4 - 3310*S^6 - 597*S^8 - 1056*S^10 - 521*S^12)/(216*S^3*(1 + S^2)^3) + (Pi^2*(76 + 228*S^2 + 228*S^4 - 233*S^6 - 39*S^8 - 39*S^10 - 13*S^12))/(36*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((17 + 51*S^2 + 51*S^4 - 75*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{2}, -S^2]^2)/(6*S^3*(1 + S^2)^3) - (3*(1 + S^2 - 3*S^4 - 2*S^6 + 15*S^8 + 7*S^10 + S^12)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^3) - (2*(-4 + 5*S^6)*HPL[{4}, -S^2])/(3*S^3) + ((-41 - 831*S^2 - 2253*S^4 + 1610*S^6 - 93*S^8 - 111*S^10 - 41*S^12)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + (4*(-10 - 30*S^2 - 30*S^4 + 33*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-39 - 117*S^2 - 117*S^4 + 134*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(2 + 21*S^2 + 48*S^4 + 22*S^6 - 114*S^8 - 33*S^10 + 2*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((535 + 1250*S^2 + 702*S^4 - 422*S^6 - 265*S^8)/(144*S^3*(1 + S^2)) + (Pi^2*(16 + 789*S^2 + 2247*S^4 - 2344*S^6 + 33*S^8 + 51*S^10 + 16*S^12))/(108*S^3*(1 + S^2)^3) + ((41 + 831*S^2 + 2253*S^4 - 1610*S^6 + 93*S^8 + 111*S^10 + 41*S^12)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)^3) + ((1 + 3*S^2 + 3*S^4 + 3*S^6 - 6*S^8 - 6*S^10 - 2*S^12)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^3) + ((-39 - 117*S^2 - 117*S^4 + 134*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 3*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) - (55*S^3*Zeta[5])/3) + Log[T]^2*((-17*(1 + S^2))/(27*S) + (Pi^2*(1346 + 1693*S^2 - 922*S^4 - 1053*S^6))/(648*S*(1 + S^2)) + (Pi^4*(2304 + 5760*S^2 - 17643*S^4 + 1937*S^6 + 902*S^8 + 54*S^10))/(1080*S*(1 + S^2)^3) - (S^3*(23 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^5)/(36*(1 + S^2)^3) + (5*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) + (4*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^4*((86 + 215*S^2 - 519*S^4 - 174*S^6 - 102*S^8 - 24*S^10)/(72*S*(1 + S^2)^3) + ((43 + 129*S^2 + 129*S^4 - 147*S^6 - 18*S^8 - 18*S^10 - 6*S^12)*HPL[{1}, -S^2])/(36*S^3*(1 + S^2)^3)) + ((19 + 333*S^2 + 819*S^4 - 2086*S^6 + 819*S^8 + 333*S^10 + 19*S^12)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((2*Pi^2*(29 + 87*S^2 + 87*S^4 - 173*S^6 + 54*S^8 + 54*S^10 + 18*S^12))/(9*S^3*(1 + S^2)^3) + (25 + 58*S^2 + 1139*S^4 - 1148*S^6 + 1139*S^8 + 58*S^10 + 25*S^12)/(9*S^3*(1 + S^2)^3) - (44*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^3*((2*Pi^2*S^3*(-54 + 3*S^2 + 3*S^4 + S^6))/(27*(1 + S^2)^3) + (-118 + 557*S^2 - 2052*S^4 - 742*S^6 - 862*S^8 - 207*S^10)/(108*S*(1 + S^2)^3) + ((-59 + 465*S^2 + 1743*S^4 - 2494*S^6 + 285*S^8 - 21*S^10 - 59*S^12)*HPL[{1}, -S^2])/(54*S^3*(1 + S^2)^3) + ((36 + 108*S^2 + 108*S^4 - 175*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + (2*S^3*(-41 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{2}, -S^2])/(9*(1 + S^2)^3)) + ((Pi^2*(5 + 15*S^2 + 15*S^4 + 134*S^6 - 249*S^8 - 249*S^10 - 83*S^12))/(9*S^3*(1 + S^2)^3) - (2*(21 + 182*S^2 + 410*S^4 + 165*S^6 + 1391*S^8 + 395*S^10 + 120*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-9 + 9*S^2 + 90*S^4 + 96*S^6 - 578*S^8 - 341*S^10 - 75*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-10 - 30*S^2 - 30*S^4 + 13*S^6 + 141*S^8 + 141*S^10 + 47*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*(-33 - 38*S^2 - 289*S^4 + 289*S^6 + 38*S^8 + 33*S^10))/(3*S^3*(1 + S^2)^2) + (4*Pi^2*(-38 - 114*S^2 - 114*S^4 + 27*S^6 + 66*S^8 + 66*S^10 + 22*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(18 + 36*S^2 + 21*S^4 - 24*S^6 + 101*S^8 + 47*S^10 + 3*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-3 - 9*S^2 - 9*S^4 - 216*S^6 + 393*S^8 + 393*S^10 + 131*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-9 - 27*S^2 - 27*S^4 - 364*S^6 + 651*S^8 + 651*S^10 + 217*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-15 + 26*S^2 + 54*S^4 - 54*S^6 - 26*S^8 + 15*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (32*(8 + 24*S^2 + 24*S^4 - 27*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(49 + 147*S^2 + 147*S^4 - 98*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (608*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*S^3*(-26 + 69*S^2 + 69*S^4 + 23*S^6))/(9*(1 + S^2)^3) - (2*(-4 + 8*S^2 - 47*S^4 + 335*S^6 + 67*S^8 + 33*S^10))/(3*S*(1 + S^2)^3))*Zeta[3] + HPL[{0}, S^2]^2*((1292 + 1585*S^2 - 976*S^4 - 1053*S^6)/(216*S*(1 + S^2)) + (Pi^2*(170 + 425*S^2 - 1041*S^4 - 44*S^6 - 29*S^8 - 9*S^10))/(36*S*(1 + S^2)^3) + ((19 + 303*S^2 + 789*S^4 - 826*S^6 + 195*S^8 + 105*S^10 + 19*S^12)*HPL[{1}, -S^2]^2)/(6*S^3*(1 + S^2)^3) + (2*(14 + 42*S^2 + 42*S^4 - 63*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) + ((-22 + 180*S^2 + 567*S^4 - 1043*S^6 + 252*S^8 + 153*S^10 + 41*S^12)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((335 + 1029*S^2 + 5520*S^4 - 2669*S^6 + 1290*S^8 + 48*S^10 - 97*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(85 + 255*S^2 + 255*S^4 - 336*S^6 + 9*S^8 + 9*S^10 + 3*S^12))/(18*S^3*(1 + S^2)^3) + ((39 + 117*S^2 + 117*S^4 - 134*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((1 + 3*S^2 + 3*S^4 + 2*S^6 - 9*S^8 - 9*S^10 - 3*S^12)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-19 - 57*S^2 - 57*S^4 + 27*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*S^5*(3 + 3*S^2 + S^4)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-3*(-13 - 15*S^2 + 15*S^4 + 13*S^6))/(4*S^3) + (Pi^2*(-67 + 213*S^2 + 807*S^4 - 1043*S^6 + 12*S^8 + 120*S^10 + 86*S^12))/(54*S^3*(1 + S^2)^3) - (2*(-3 - 9*S^2 - 9*S^4 - 108*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(8 + 24*S^2 + 24*S^4 - 27*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*S^3*(-27 + 48*S^2 + 48*S^4 + 16*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*(-((1 + S^2)*(1013 - 566*S^2 + 1013*S^4))/(108*S^3) + (Pi^2*(895 + 2580*S^2 + 21291*S^4 - 15670*S^6 + 12831*S^8 + 618*S^10 + 31*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(1152 + 3456*S^2 + 3456*S^4 - 5849*S^6 + 1185*S^8 + 1185*S^10 + 395*S^12))/(540*S^3*(1 + S^2)^3) + ((48 + 61*S^2 + 409*S^4 - 409*S^6 - 61*S^8 - 48*S^10)/(3*S^3*(1 + S^2)^2) - (2*Pi^2*(-36 - 108*S^2 - 108*S^4 + 67*S^6 + 51*S^8 + 51*S^10 + 17*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (2*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) - (4*(52 + 213*S^2 + 330*S^4 - 868*S^6 + 1221*S^8 + 510*S^10 + 52*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-9 - 27*S^2 - 27*S^4 - 84*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (132*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (8*(-13 - 39*S^2 - 39*S^4 - 21*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (88*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(2 - 6*S^2 - 33*S^4 + 292*S^6 - 330*S^8 - 105*S^10 + 2*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(3*S^3) + (Pi^2*(17 + 309*S^2 + 822*S^4 - 1118*S^6 + 525*S^8 + 210*S^10 + 17*S^12))/(9*S^3*(1 + S^2)^3) - (66*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (4*(6 + 18*S^2 + 18*S^4 - 155*S^6 + 117*S^8 + 117*S^10 + 39*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (44*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (4*(1 + 3*S^2 + 3*S^4 - 47*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*Zeta[3])/(S^3*(1 + S^2)^3)) + HPL[{0}, S^2]*((-878 + 431*S^2 - 1013*S^4)/(108*S) + (Pi^4*S^3*(-1655 + 657*S^2 + 657*S^4 + 219*S^6))/(270*(1 + S^2)^3) + (Pi^2*(-26 + 898*S^2 - 1887*S^4 + 718*S^6 - 377*S^8 - 66*S^10))/(54*S*(1 + S^2)^3) + (10*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) + (10*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-2 - 6*S^2 - 6*S^4 - 223*S^6 + 147*S^8 + 147*S^10 + 49*S^12))/(9*S^3*(1 + S^2)^3) + (-175 - 852*S^2 + 1785*S^4 - 4994*S^6 + 5097*S^8 - 258*S^10 + 149*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (2*S^3*(-67 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((25 + 58*S^2 + 1139*S^4 - 1148*S^6 + 1139*S^8 + 58*S^10 + 25*S^12)/(6*S^3*(1 + S^2)^3) + (Pi^2*(81 + 243*S^2 + 243*S^4 - 505*S^6 + 162*S^8 + 162*S^10 + 54*S^12))/(9*S^3*(1 + S^2)^3) + (2*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2}, -S^2])/(S^3*(1 + S^2)^3)) + ((-35 - 81*S^2 - 9*S^4 - 160*S^6 - 183*S^8 - 201*S^10 - 71*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - 10*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-11 - 199*S^2 - 580*S^4 + 584*S^6 - 146*S^8 - 23*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-1 - 3*S^2 - 3*S^4 - 70*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-2 - 6*S^2 - 6*S^4 - 141*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(6 + 15*S^2 - 24*S^4 + 107*S^6 + 77*S^8 + 21*S^10)*Zeta[3])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(-((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(3*S^3) + (Pi^2*(-7 + 705*S^2 + 2154*S^4 - 3362*S^6 + 1425*S^8 + 462*S^10 - 7*S^12))/(27*S^3*(1 + S^2)^3) - (2*(4 - 111*S^2 - 363*S^4 + 584*S^6 - 363*S^8 - 111*S^10 + 4*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*S^3*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 21*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3))) - (220*S^3*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-3*(-185 - 201*S^2 + 201*S^4 + 185*S^6))/(32*S^3) + (Pi^2*(1809 + 4198*S^2 + 161*S^4 - 4118*S^6 - 2106*S^8))/(1296*S^3*(1 + S^2)) + (Pi^4*(-319 + 5127*S^2 + 14595*S^4 - 19061*S^6 - 4428*S^8 - 1449*S^10 + 221*S^12))/(6480*S^3*(1 + S^2)^3) + ((42 + 110*S^2 - 79*S^4 + 240*S^6 - 1996*S^8 - 502*S^10 - 183*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(-1 - 3*S^2 - 3*S^4 + 112*S^6 - 213*S^8 - 213*S^10 - 71*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-1 - 39*S^2 - 138*S^4 - 200*S^6 - 1098*S^8 - 639*S^10 - 145*S^12)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^3) + ((-6 - 18*S^2 - 18*S^4 + 23*S^6 - 33*S^8 - 33*S^10 - 11*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-141 - 392*S^2 - 2075*S^4 + 480*S^6 - 2075*S^8 - 392*S^10 - 141*S^12)/(18*S^3*(1 + S^2)^3) - (4*Pi^2*(17 + 51*S^2 + 51*S^4 - 42*S^6 + 24*S^8 + 24*S^10 + 8*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-55 - 483*S^2 - 1059*S^4 + 2086*S^6 - 579*S^8 - 183*S^10 + 17*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-13 - 39*S^2 - 39*S^4 - 242*S^6 + 393*S^8 + 393*S^10 + 131*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-13 - 39*S^2 - 39*S^4 - 362*S^6 + 597*S^8 + 597*S^10 + 199*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(19 + 333*S^2 + 819*S^4 - 2086*S^6 + 819*S^8 + 333*S^10 + 19*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (48*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 + (4*(-105 - 315*S^2 - 315*S^4 + 108*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(8 + 24*S^2 + 24*S^4 - 27*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*S^3*(-30 + 51*S^2 + 51*S^4 + 17*S^6))/(9*(1 + S^2)^3) + (-24 - 130*S^2 - 349*S^4 + 240*S^6 - 1726*S^8 - 262*S^10 - 117*S^12)/(18*S^3*(1 + S^2)^3))*Zeta[3] - (2*S^3*(-47 + 117*S^2 + 117*S^4 + 39*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((-17*(1 + S^2)*(38 - 5*S^2 + 38*S^4))/(27*S^3) + (Pi^2*(3221 + 8116*S^2 + 1782*S^4 - 9196*S^6 - 5219*S^8))/(2592*S^3*(1 + S^2)) + (Pi^4*(3227 + 8430*S^2 + 47322*S^4 - 34631*S^6 + 9099*S^8 - 4917*S^10 - 2014*S^12))/(6480*S^3*(1 + S^2)^3) + (Pi^6*(35130 + 105390*S^2 + 105390*S^4 - 138409*S^6 + 1323*S^8 + 1323*S^10 + 441*S^12))/(136080*S^3*(1 + S^2)^3) + ((Pi^2*(36 + 108*S^2 + 108*S^4 - 209*S^6 + 69*S^8 + 69*S^10 + 23*S^12))/(18*S^3*(1 + S^2)^3) + (163 + 591*S^2 + 4965*S^4 - 3310*S^6 + 4965*S^8 + 591*S^10 + 163*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (13*(-1 + S^6)*HPL[{2}, -S^2]^3)/(9*S^3) + ((-1 - 3*S^2 - 3*S^4 - 10*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((25 - 158*S^2 - 379*S^4 - 680*S^6 - 1525*S^8 - 794*S^10 - 201*S^12)/(6*S^3*(1 + S^2)^3) + (Pi^2*(25 + 75*S^2 + 75*S^4 + 80*S^6 - 171*S^8 - 171*S^10 - 57*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(200 + 435*S^2 + 102*S^4 + 364*S^6 + 1371*S^8 + 858*S^10 + 200*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + ((138 + 414*S^2 + 414*S^4 - 161*S^6 - 477*S^8 - 477*S^10 - 159*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-33 - 99*S^2 - 99*S^4 + 45*S^6 + 66*S^8 + 66*S^10 + 22*S^12))/(9*S^3*(1 + S^2)^3) + (-4 + 129*S^2 + 6*S^4 + 340*S^6 + 946*S^8 + 347*S^10 + 92*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (2*(41 + 273*S^2 + 579*S^4 - 1610*S^6 + 1767*S^8 + 669*S^10 + 41*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(83 + 372*S^2 + 624*S^4 - 1694*S^6 + 2226*S^8 + 906*S^10 + 83*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (3*(1 + 3*S^2 + 3*S^4 - 6*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-13 - 39*S^2 - 39*S^4 - 59*S^6 + 126*S^8 + 126*S^10 + 42*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*(-48 - 61*S^2 - 409*S^4 + 409*S^6 + 61*S^8 + 48*S^10))/(3*S^3*(1 + S^2)^2) - (4*Pi^2*(-36 - 108*S^2 - 108*S^4 + 67*S^6 + 51*S^8 + 51*S^10 + 17*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (4*(41 + 471*S^2 + 1173*S^4 - 1610*S^6 + 1173*S^8 + 471*S^10 + 41*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(19 + 987*S^2 + 2859*S^4 - 3094*S^6 + 1077*S^8 + 393*S^10 + 19*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (104*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (4*(-87 - 261*S^2 - 261*S^4 - 84*S^6 + 345*S^8 + 345*S^10 + 115*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (264*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (16*(-13 - 39*S^2 - 39*S^4 - 21*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (176*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((619 + 1154*S^2 + 342*S^4 - 518*S^6 - 181*S^8)/(36*S^3*(1 + S^2)) + (Pi^2*(10 + 24*S^2 - 3*S^4 + 920*S^6 - 1218*S^8 - 381*S^10 + 10*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] - (2*(-6 - 18*S^2 - 18*S^4 + S^6 + 9*S^8 + 9*S^10 + 3*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((-117 - 404*S^2 - 1302*S^4 - 2076*S^6 - 917*S^8)/(36*S^3*(1 + S^2)) + (Pi^2*(-131 - 453*S^2 - 579*S^4 + 1790*S^6 - 2847*S^8 - 1209*S^10 - 131*S^12))/(54*S^3*(1 + S^2)^3) + (8*(4 + 12*S^2 + 12*S^4 - 67*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-1 - 3*S^2 - 3*S^4 + 5*S^6)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((1055 + 1109*S^2 - 1109*S^4 - 1055*S^6)/(54*S^3) + (Pi^2*(1711 + 4200*S^2 + 18987*S^4 - 3310*S^6 - 9057*S^8 - 3018*S^10 - 1385*S^12))/(648*S^3*(1 + S^2)^3) + (Pi^4*(976 + 2928*S^2 + 2928*S^4 - 2225*S^6 - 1119*S^8 - 1119*S^10 - 373*S^12))/(1080*S^3*(1 + S^2)^3) + ((-41 - 273*S^2 - 579*S^4 + 1610*S^6 - 1767*S^8 - 669*S^10 - 41*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-1 - 3*S^2 - 3*S^4 + 38*S^6 - 51*S^8 - 51*S^10 - 17*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(41 + 471*S^2 + 1173*S^4 - 1610*S^6 + 1173*S^8 + 471*S^10 + 41*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(21 + 63*S^2 + 63*S^4 - 134*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-41 - 237*S^2 - 471*S^4 + 1610*S^6 - 1875*S^8 - 705*S^10 - 41*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((2*(-100 - 109*S^2 + 109*S^4 + 100*S^6))/(9*S^3) + (Pi^2*(-41 - 1425*S^2 - 4035*S^4 + 1610*S^6 + 1689*S^8 + 483*S^10 - 41*S^12))/(54*S^3*(1 + S^2)^3) + (8*(3 + 9*S^2 + 9*S^4 - 67*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + (2*(6 + 25*S^2 + 36*S^4 + 120*S^6 - 165*S^8 - 42*S^10 + 6*S^12)*Zeta[5])/(S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(1559 - 338*S^2 + 1559*S^4))/(144*S^3) + (Pi^2*(451 + 1346*S^2 + 1062*S^4 - 326*S^6 - 349*S^8))/(432*S^3*(1 + S^2)) + (Pi^4*(421 + 11364*S^2 + 31299*S^4 - 39478*S^6 + 10860*S^8 + 4551*S^10 + 421*S^12))/(3240*S^3*(1 + S^2)^3) + ((41 + 471*S^2 + 1173*S^4 - 1610*S^6 + 1173*S^8 + 471*S^10 + 41*S^12)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((-127 - 1752*S^2 - 5019*S^4 + 250*S^6 - 13479*S^8 - 3714*S^10 - 991*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(-3 - 9*S^2 - 9*S^4 + 164*S^6 - 135*S^8 - 135*S^10 - 45*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-14 - 33*S^2 - 15*S^4 + 28*S^6 - 153*S^8 - 79*S^10 - 14*S^12)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^3) - (2*(-18 - 54*S^2 - 54*S^4 - 13*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-48 - 61*S^2 - 409*S^4 + 409*S^6 + 61*S^8 + 48*S^10)/(3*S^3*(1 + S^2)^2) + (2*Pi^2*(-36 - 108*S^2 - 108*S^4 + 67*S^6 + 51*S^8 + 51*S^10 + 17*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(7 - 5*S^2 - 57*S^4 - 14*S^6 + 141*S^8 + 61*S^10 + 7*S^12)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^3) + (8*(4 + 12*S^2 + 12*S^4 - 67*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(39 + 117*S^2 + 117*S^4 - 888*S^6 + 651*S^8 + 651*S^10 + 217*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (132*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(51 + 153*S^2 + 153*S^4 - 247*S^6 + 54*S^8 + 54*S^10 + 18*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (88*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((445 + 1536*S^2 + 789*S^4 + 4994*S^6 - 7671*S^8 - 426*S^10 - 419*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(1 + 3*S^2 + 3*S^4 + 153*S^6 - 132*S^8 - 132*S^10 - 44*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((100 + 109*S^2 - 109*S^4 - 100*S^6)/(9*S^3) + (Pi^2*(41 + 1425*S^2 + 4035*S^4 - 1610*S^6 - 1689*S^8 - 483*S^10 + 41*S^12))/(108*S^3*(1 + S^2)^3) - (4*(4 + 12*S^2 + 12*S^4 - 67*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 67*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) - (2*(-10 - 30*S^2 - 30*S^4 - 173*S^6 + 171*S^8 + 171*S^10 + 57*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]*((-10093 + 1117*S^2 - 10336*S^4)/(432*S) + (Pi^2*(-7654 - 6983*S^2 - 10012*S^4 - 9819*S^6))/(2592*S*(1 + S^2)) + (Pi^6*S^3*(-95123 + 24399*S^2 + 24399*S^4 + 8133*S^6))/(136080*(1 + S^2)^3) + (Pi^4*(-3662 + 3640*S^2 - 39315*S^4 - 15455*S^6 - 17351*S^8 - 3537*S^10))/(6480*S*(1 + S^2)^3) + ((1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^3) + (2*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^6)/(9*S^3*(1 + S^2)^3) + ((Pi^2*S^3*(-203 + 135*S^2 + 135*S^4 + 45*S^6))/(36*(1 + S^2)^3) + (32 + 255*S^2 + 1866*S^4 - 1655*S^6 + 3099*S^8 + 336*S^10 + 131*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + ((-3 - 9*S^2 - 9*S^4 - 59*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{2}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*((25 + 58*S^2 + 1139*S^4 - 1148*S^6 + 1139*S^8 + 58*S^10 + 25*S^12)/(36*S^3*(1 + S^2)^3) + (Pi^2*(81 + 243*S^2 + 243*S^4 - 505*S^6 + 162*S^8 + 162*S^10 + 54*S^12))/(54*S^3*(1 + S^2)^3) + ((13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + (2*(-1 - 3*S^2 - 3*S^4 + 2*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((13 + 5*S^2 + 19*S^4 - 70*S^6 - 85*S^8 - 135*S^10 - 35*S^12)/(6*S^3*(1 + S^2)^3) + (Pi^2*(1 + 3*S^2 + 3*S^4 - 10*S^6 + 27*S^8 + 27*S^10 + 9*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((-9 - 28*S^2 - 19*S^4 - 6*S^6 + 59*S^8 - 10*S^10 - 15*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-5 + 23*S^6)*HPL[{6}, -S^2])/(3*S^3) - (4*S^3*(-67 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^3) + ((Pi^2*(2 + 6*S^2 + 6*S^4 + 215*S^6 - 165*S^8 - 165*S^10 - 55*S^12))/(9*S^3*(1 + S^2)^3) + (-34 + 57*S^2 - 1257*S^4 + 2317*S^6 - 2481*S^8 + 354*S^10 + 20*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (4*(-3 - 5*S^2 + S^4 - 15*S^6 + 26*S^8 + 20*S^10 + 6*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-19 - 15*S^2 + 21*S^4 - 128*S^6 + 387*S^8 + 369*S^10 + 125*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 6*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-2 - 6*S^2 - 6*S^4 - 223*S^6 + 147*S^8 + 147*S^10 + 49*S^12))/(9*S^3*(1 + S^2)^3) + (-175 - 852*S^2 + 1785*S^4 - 4994*S^6 + 5097*S^8 - 258*S^10 + 149*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (4*(34 + 333*S^2 + 855*S^4 - 805*S^6 + 318*S^8 + 138*S^10 + 7*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-169 - 1917*S^2 - 5121*S^4 + 4990*S^6 - 1725*S^8 - 627*S^10 + 29*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(-3 - 9*S^2 - 9*S^4 - 59*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-8 - 24*S^2 - 24*S^4 - 187*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-11 - 199*S^2 - 580*S^4 + 584*S^6 - 146*S^8 - 23*S^10 + 19*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-1 - 3*S^2 - 3*S^4 - 70*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-2 - 6*S^2 - 6*S^4 - 141*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*(3 + S^2 + 3*S^4))/S + (Pi^2*(2 + 5*S^2 - 153*S^4 - 476*S^6 - 410*S^8 - 126*S^10))/(18*S*(1 + S^2)^3))*Zeta[3] + (2*S^3*(-5 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3]^2)/(3*(1 + S^2)^3) + HPL[{2}, -S^2]*((-1652 - 2874*S^2 - 2679*S^4 - 2426*S^6 - 1401*S^8)/(216*S^3*(1 + S^2)) + (Pi^2*(-358 - 1980*S^2 + 2385*S^4 - 9932*S^6 + 3258*S^8 - 2628*S^10 - 385*S^12))/(648*S^3*(1 + S^2)^3) + (Pi^4*(5 + 15*S^2 + 15*S^4 - 1321*S^6 + 546*S^8 + 546*S^10 + 182*S^12))/(540*S^3*(1 + S^2)^3) - (2*(-3 - 5*S^2 + S^4 - 15*S^6 + 26*S^8 + 20*S^10 + 6*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 + 2*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(34 + 333*S^2 + 855*S^4 - 805*S^6 + 318*S^8 + 138*S^10 + 7*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 67*S^6 + 54*S^8 + 54*S^10 + 18*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*S^3*(-67 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + ((-6 - 20*S^2 - 23*S^4 - 103*S^8 - 70*S^10 - 18*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(1013 - 566*S^2 + 1013*S^4))/(216*S^3) + (Pi^2*(-145 - 1968*S^2 + 13719*S^4 - 20414*S^6 + 8787*S^8 - 1410*S^10 - 73*S^12))/(648*S^3*(1 + S^2)^3) + (Pi^4*(535 + 1605*S^2 + 1605*S^4 - 2994*S^6 + 657*S^8 + 657*S^10 + 219*S^12))/(540*S^3*(1 + S^2)^3) + ((-13 - 555*S^2 + 3441*S^4 - 4994*S^6 + 3441*S^8 - 555*S^10 - 13*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(69 + 207*S^2 + 207*S^4 - 424*S^6 + 141*S^8 + 141*S^10 + 47*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-53 - 147*S^2 - 111*S^4 - 142*S^6 - 57*S^8 - 129*S^10 - 53*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - 11*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(4 - 111*S^2 - 363*S^4 + 584*S^6 - 363*S^8 - 111*S^10 + 4*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(19 + 57*S^2 + 57*S^4 - 141*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((-7 - 27*S^2 - 39*S^4 + 14*S^6 - 45*S^8 - 29*S^10 - 7*S^12)*Zeta[3])/(S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((85 + 119*S^2 + 171*S^4 + 199*S^6 + 134*S^8)/(18*S^3*(1 + S^2)) + (Pi^2*(11 - 837*S^2 - 2826*S^4 + 2479*S^6 - 555*S^8 - 78*S^10 + 74*S^12))/(54*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*(-((1 + S^2)*(26 - 29*S^2 + 278*S^4))/(36*S^3) + (Pi^2*(-37 - 90*S^2 - 27*S^4 - 146*S^6 - 69*S^8 - 132*S^10 - 55*S^12))/(54*S^3*(1 + S^2)^3) - (8*(-2 - 6*S^2 - 6*S^4 + 4*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 + 4*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(9*S^3) + (Pi^2*(-7 + 705*S^2 + 2154*S^4 - 3362*S^6 + 1425*S^8 + 462*S^10 - 7*S^12))/(81*S^3*(1 + S^2)^3) - (2*(4 - 111*S^2 - 363*S^4 + 584*S^6 - 363*S^8 - 111*S^10 + 4*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*S^3*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(9*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 21*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + ((4 + 6*S^2 - 165*S^4 - 290*S^6 - 135*S^8)*Zeta[5])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(1559 - 338*S^2 + 1559*S^4))/(144*S^3) + (Pi^2*(-789 - 1220*S^2 - 582*S^4 - 876*S^6 - 581*S^8))/(432*S^3*(1 + S^2)) + (Pi^4*(-1861 + 4017*S^2 + 23187*S^4 - 44222*S^6 + 6123*S^8 - 1671*S^10 - 1861*S^12))/(3240*S^3*(1 + S^2)^3) + ((41 + 471*S^2 + 1173*S^4 - 1610*S^6 + 1173*S^8 + 471*S^10 + 41*S^12)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((4*Pi^2*S^3*(-4 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) - (2*(-10 + 138*S^2 + 273*S^4 + 421*S^6 + 489*S^8 + 435*S^10 + 98*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (4*(13 + 24*S^2 - 12*S^4 + 62*S^6 - 39*S^8 + 15*S^10 + 13*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(-1 - 3*S^2 - 3*S^4 - 3*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-69 - 207*S^2 - 207*S^4 + 424*S^6 - 141*S^8 - 141*S^10 - 47*S^12))/(9*S^3*(1 + S^2)^3) + (13 + 555*S^2 - 3441*S^4 + 4994*S^6 - 3441*S^8 + 555*S^10 + 13*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(2 - 54*S^2 - 177*S^4 + 292*S^6 - 186*S^8 - 57*S^10 + 2*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-1 - 3*S^2 - 3*S^4 + 4*S^6)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-5 - 15*S^2 - 15*S^4 + 13*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(4 - 111*S^2 - 363*S^4 + 584*S^6 - 363*S^8 - 111*S^10 + 4*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(57 + 171*S^2 + 171*S^4 - 409*S^6 + 174*S^8 + 174*S^10 + 58*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((Pi^2*(1 + 3*S^2 + 3*S^4 + 3*S^6 - 30*S^8 - 30*S^10 - 10*S^12))/(9*S^3*(1 + S^2)^3) - (2*(17 + 76*S^2 + 131*S^4 + 85*S^6 + 107*S^8 + 43*S^10 + 5*S^12))/(3*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-73 - 106*S^2 - 114*S^4 - 106*S^6 - 73*S^8)/(12*S^3*(1 + S^2)) + (Pi^2*(-107 + 987*S^2 + 3669*S^4 - 5362*S^6 + 2481*S^8 + 591*S^10 - 107*S^12))/(108*S^3*(1 + S^2)^3) + (8*(-1 - 3*S^2 - 3*S^4 + 4*S^6)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 14*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) - (4*(-1 + 5*S^6)*Zeta[5])/(3*S^3))) + Log[T]*((7*(1 + S^2))/(9*S) + (Pi^2*(-4078 - 4349*S^2 + 4130*S^4 + 3969*S^6))/(1296*S*(1 + S^2)) + (Pi^6*S^3*(95123 + 24399*S^2 + 24399*S^4 + 8133*S^6))/(68040*(1 + S^2)^3) + (Pi^4*(-1010 - 15857*S^2 + 26340*S^4 + 751*S^6 + 6616*S^8 + 2676*S^10))/(3240*S*(1 + S^2)^3) + (S^3*(11 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2]^6)/(72*(1 + S^2)^3) - (2*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^6)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^5*((-18 - 45*S^2 + 141*S^4 + 94*S^6 + 85*S^8 + 27*S^10)/(72*S*(1 + S^2)^3) + ((-9 - 27*S^2 - 27*S^4 + 36*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(36*S^3*(1 + S^2)^3)) + ((Pi^2*(-2 - 6*S^2 - 6*S^4 + 125*S^6 - 21*S^8 - 21*S^10 - 7*S^12))/(9*S^3*(1 + S^2)^3) + (97 - 6*S^2 - 3705*S^4 + 5180*S^6 - 3705*S^8 - 6*S^10 + 97*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (10*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{1}, -S^2]^4*((-25 - 58*S^2 - 1139*S^4 + 1148*S^6 - 1139*S^8 - 58*S^10 - 25*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(-29 - 87*S^2 - 87*S^4 + 173*S^6 - 54*S^8 - 54*S^10 - 18*S^12))/(9*S^3*(1 + S^2)^3) + (22*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^4*((Pi^2*S^3*(133 + 81*S^2 + 81*S^4 + 27*S^6))/(108*(1 + S^2)^3) + (7 - 473*S^2 + 1110*S^4 + 1027*S^6 + 805*S^8 + 264*S^10)/(216*S*(1 + S^2)^3) + ((25 - 669*S^2 - 2127*S^4 + 2210*S^6 + 519*S^8 + 213*S^10 + 25*S^12)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)^3) + ((-43 - 129*S^2 - 129*S^4 + 147*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{1}, -S^2]^2)/(36*S^3*(1 + S^2)^3) + ((-3 - 9*S^2 - 9*S^4 + 65*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)^3)) - (2*S^3*(-5 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2]^2)/(3*(1 + S^2)^3) + ((Pi^2*(-15 - 45*S^2 - 45*S^4 - 44*S^6 + 81*S^8 + 81*S^10 + 27*S^12))/(9*S^3*(1 + S^2)^3) + (-85 - 62*S^2 + 71*S^4 + 600*S^6 + 1701*S^8 + 950*S^10 + 249*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(57 + 125*S^2 + 41*S^4 + 198*S^6 + 540*S^8 + 312*S^10 + 69*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-50 - 150*S^2 - 150*S^4 + 79*S^6 + 177*S^8 + 177*S^10 + 59*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(3 + 9*S^2 + 9*S^4 - 80*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-11 - 146*S^2 - 157*S^4 - 300*S^6 - 729*S^8 - 298*S^10 - 71*S^12)/(3*S^3*(1 + S^2)^3) + (14*Pi^2*(-1 - 3*S^2 - 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (2*(-9 + 2*S^2 + 41*S^4 - 378*S^6 + 977*S^8 + 404*S^10 + 51*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(21 + 123*S^2 + 186*S^4 - 1206*S^6 + 3388*S^8 + 1435*S^10 + 189*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 6*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) - (4*(-14 - 42*S^2 - 42*S^4 - 49*S^6 + 159*S^8 + 159*S^10 + 53*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*(-15 - 23*S^2 - 120*S^4 + 120*S^6 + 23*S^8 + 15*S^10))/(3*S^3*(1 + S^2)^2) - (8*Pi^2*(-2 - 6*S^2 - 6*S^4 - 40*S^6 + 15*S^8 + 15*S^10 + 5*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(21 + 203*S^2 + 509*S^4 - 378*S^6 + 509*S^8 + 203*S^10 + 21*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(18 + 254*S^2 + 701*S^4 - 360*S^6 + 187*S^8 + 67*S^10 + 3*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-1 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 - (68*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (8*(-21 - 63*S^2 - 63*S^4 + 44*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-15 - 172*S^2 - 342*S^4 + 342*S^6 + 172*S^8 + 15*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (32*(-4 - 12*S^2 - 12*S^4 + 11*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (160*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-818 - 451*S^2 + 1930*S^4 + 1347*S^6)/(54*S*(1 + S^2)) + (Pi^2*(-2 - 5*S^2 - 159*S^4 + 660*S^6 + 252*S^8 + 24*S^10))/(9*S*(1 + S^2)^3))*Zeta[3] + (4*S^3*(5 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3]^2)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^3*((1208 + 1477*S^2 + 2840*S^4 + 2355*S^6)/(648*S*(1 + S^2)) + (Pi^2*(-162 - 405*S^2 + 1203*S^4 + 434*S^6 + 470*S^8 + 162*S^10))/(108*S*(1 + S^2)^3) + ((59 - 465*S^2 - 1743*S^4 + 2494*S^6 - 285*S^8 + 21*S^10 + 59*S^12)*HPL[{1}, -S^2]^2)/(54*S^3*(1 + S^2)^3) - (2*(36 + 108*S^2 + 108*S^4 - 175*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^3) + ((13 - 27*S^2 - 135*S^4 + 377*S^6 - 62*S^8 + 28*S^10 + 22*S^12)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*(-81 - 243*S^2 - 243*S^4 + 355*S^6 - 12*S^8 - 12*S^10 - 4*S^12))/(54*S^3*(1 + S^2)^3) + (185 + 1245*S^2 - 1734*S^4 + 5041*S^6 + 732*S^8 + 966*S^10 + 149*S^12)/(162*S^3*(1 + S^2)^3) - (2*(15 + 45*S^2 + 45*S^4 - 71*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + (4*S^3*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (20*(-1 - 3*S^2 - 3*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*S^3*(11 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((449 + 467*S^2 - 467*S^4 - 449*S^6)/(18*S^3) + (Pi^2*(36 + 404*S^2 + 1076*S^4 - 189*S^6 - 567*S^8 - 201*S^10 - 15*S^12))/(9*S^3*(1 + S^2)^3) + (16*(-3 - 9*S^2 - 9*S^4 + 40*S^6)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((378 + 794*S^2 + 2017*S^4 + 3542*S^6 + 1725*S^8)/(54*S^3*(1 + S^2)) + (Pi^2*(18 + 55*S^2 + 49*S^4 - 207*S^6 + 656*S^8 + 272*S^10 + 33*S^12))/(9*S^3*(1 + S^2)^3) + (4*(-19 - 57*S^2 - 57*S^4 + 160*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-1 - 3*S^2 - 3*S^4 - 6*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(1013 - 566*S^2 + 1013*S^4))/(108*S^3) + (Pi^4*(-1152 - 3456*S^2 - 3456*S^4 + 5849*S^6 - 1185*S^8 - 1185*S^10 - 395*S^12))/(540*S^3*(1 + S^2)^3) + (Pi^2*(-895 - 2580*S^2 - 21291*S^4 + 15670*S^6 - 12831*S^8 - 618*S^10 - 31*S^12))/(324*S^3*(1 + S^2)^3) + ((-48 - 61*S^2 - 409*S^4 + 409*S^6 + 61*S^8 + 48*S^10)/(3*S^3*(1 + S^2)^2) + (2*Pi^2*(-36 - 108*S^2 - 108*S^4 + 67*S^6 + 51*S^8 + 51*S^10 + 17*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (4*(52 + 213*S^2 + 330*S^4 - 868*S^6 + 1221*S^8 + 510*S^10 + 52*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-9 - 27*S^2 - 27*S^4 - 84*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (132*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (8*(-13 - 39*S^2 - 39*S^4 - 21*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (88*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (4*(2 - 6*S^2 - 33*S^4 + 292*S^6 - 330*S^8 - 105*S^10 + 2*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((2*(1 + S^2)*(7 - 22*S^2 + 7*S^4))/(9*S^3) - (2*Pi^2*(17 + 309*S^2 + 822*S^4 - 1118*S^6 + 525*S^8 + 210*S^10 + 17*S^12))/(27*S^3*(1 + S^2)^3) + (44*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (8*(6 + 18*S^2 + 18*S^4 - 155*S^6 + 117*S^8 + 117*S^10 + 39*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (88*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + 3*S^2 + 3*S^4 - 47*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-147 - 157*S^2 + 157*S^4 + 147*S^6)/(8*S^3) + (Pi^4*(-28 - 84*S^2 - 84*S^4 + 1375*S^6 - 33*S^8 - 33*S^10 - 11*S^12))/(540*S^3*(1 + S^2)^3) + (Pi^2*(-451 - 1254*S^2 - 6168*S^4 + 2590*S^6 + 2463*S^8 + 1248*S^10 + 548*S^12))/(324*S^3*(1 + S^2)^3) + (2*(-9 - 14*S^2 + S^4 - 189*S^6 + 508*S^8 + 217*S^10 + 30*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(3 + 9*S^2 + 9*S^4 - 10*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(21 + 203*S^2 + 509*S^4 - 378*S^6 + 509*S^8 + 203*S^10 + 21*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(9 + 27*S^2 + 27*S^4 - 160*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(3 + 9*S^2 + 9*S^4 - 80*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(6 + 30*S^2 + 48*S^4 - 189*S^6 + 461*S^8 + 173*S^10 + 15*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^2*((Pi^4*S^3*(1655 + 657*S^2 + 657*S^4 + 219*S^6))/(540*(1 + S^2)^3) + (-4150 - 4493*S^2 + 4058*S^4 + 3969*S^6)/(432*S*(1 + S^2)) + (Pi^2*(-56 - 1118*S^2 + 1746*S^4 + 811*S^6 + 856*S^8 + 309*S^10))/(108*S*(1 + S^2)^3) + ((-19 - 303*S^2 - 789*S^4 + 826*S^6 - 195*S^8 - 105*S^10 - 19*S^12)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + ((-14 - 42*S^2 - 42*S^4 + 63*S^6 - 9*S^8 - 9*S^10 - 3*S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-4 - 12*S^2 - 12*S^4 + 145*S^6 + 3*S^8 + 3*S^10 + S^12))/(18*S^3*(1 + S^2)^3) + (-181 - 570*S^2 - 3594*S^4 + 2590*S^6 - 111*S^8 + 564*S^10 + 278*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((1 + 3*S^2 + 3*S^4 + 45*S^6 - 12*S^8 - 12*S^10 - 4*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(-85 - 255*S^2 - 255*S^4 + 336*S^6 - 9*S^8 - 9*S^10 - 3*S^12))/(18*S^3*(1 + S^2)^3) + (-335 - 1029*S^2 - 5520*S^4 + 2669*S^6 - 1290*S^8 - 48*S^10 + 97*S^12)/(54*S^3*(1 + S^2)^3) + ((-39 - 117*S^2 - 117*S^4 + 134*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((3 + 3*S^2 - 9*S^4 + 53*S^8 + 23*S^10 + 3*S^12)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^3) + (2*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{4}, -S^2])/S^3 + ((21 + 217*S^2 + 562*S^4 - 189*S^6 - 53*S^8 - 14*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(1 + 3*S^2 + 3*S^4 - 78*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 80*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-8 - 20*S^2 + 21*S^4 + 131*S^6 + 59*S^8 + 9*S^10)*Zeta[3])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((-535 - 1250*S^2 - 702*S^4 + 422*S^6 + 265*S^8)/(72*S^3*(1 + S^2)) + (Pi^2*(-16 - 789*S^2 - 2247*S^4 + 2344*S^6 - 33*S^8 - 51*S^10 - 16*S^12))/(54*S^3*(1 + S^2)^3) + ((-41 - 831*S^2 - 2253*S^4 + 1610*S^6 - 93*S^8 - 111*S^10 - 41*S^12)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^3) + (2*(-1 - 3*S^2 - 3*S^4 - 3*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^3) - (2*(-39 - 117*S^2 - 117*S^4 + 134*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-1 - 3*S^2 - 3*S^4 - 3*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3))) + HPL[{0}, S^2]*((1478 - 257*S^2 + 1559*S^4)/(72*S) + (Pi^2*(1298 + 937*S^2 + 2462*S^4 + 2607*S^6))/(648*S*(1 + S^2)) + (Pi^4*(-1070 - 2675*S^2 + 8325*S^4 - 876*S^6 + 1095*S^8 + 657*S^10))/(540*S*(1 + S^2)^3) - (5*(1 + 21*S^2 + 57*S^4 - 94*S^6 + 57*S^8 + 21*S^10 + S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 22*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^3) + ((-7 - 138*S^2 - 318*S^4 + 805*S^6 - 855*S^8 - 333*S^10 - 34*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-25 - 58*S^2 - 1139*S^4 + 1148*S^6 - 1139*S^8 - 58*S^10 - 25*S^12)/(9*S^3*(1 + S^2)^3) - (2*Pi^2*(81 + 243*S^2 + 243*S^4 - 505*S^6 + 162*S^8 + 162*S^10 + 54*S^12))/(27*S^3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((2*Pi^2*(-1 - 3*S^2 - 3*S^4 + 10*S^6 + 3*S^8 + 3*S^10 + S^12))/(9*S^3*(1 + S^2)^3) + (-38 + 240*S^2 + 483*S^4 + 1022*S^6 + 1338*S^8 + 1050*S^10 + 241*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(17 + 21*S^2 - 51*S^4 + 106*S^6 - 75*S^8 + 51*S^10 + 35*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 10*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((149 - 258*S^2 + 5097*S^4 - 4994*S^6 + 1785*S^8 - 852*S^10 - 175*S^12)/(27*S^3*(1 + S^2)^3) - (2*Pi^2*(-71 - 213*S^2 - 213*S^4 + 201*S^6 + 6*S^8 + 6*S^10 + 2*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(-19 + 21*S^2 + 141*S^4 - 578*S^6 + 593*S^8 + 203*S^10 + 11*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*S^3*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) - (8*(-1 - 3*S^2 - 3*S^4 - 12*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-19 + 23*S^2 + 146*S^4 - 584*S^6 + 580*S^8 + 199*S^10 + 11*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-19 - 57*S^2 - 57*S^4 + 67*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-58 - 174*S^2 - 174*S^4 + 205*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-41 - 123*S^2 - 123*S^4 + 141*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*S^5*(3 + 3*S^2 + S^4))/(3*(1 + S^2)^3) + (42 + 129*S^2 + 150*S^4 + 314*S^6 + 180*S^8 + 41*S^10)/(3*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((134 + 199*S^2 + 171*S^4 + 119*S^6 + 85*S^8)/(18*S^3*(1 + S^2)) + (Pi^2*(32 - 50*S^2 - 281*S^4 + 961*S^6 - 642*S^8 - 171*S^10 + 11*S^12))/(18*S^3*(1 + S^2)^3) + (8*S^3*(-4 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (8*(-19 - 57*S^2 - 57*S^4 + 67*S^6)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*S^3*(-7 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(7 - 22*S^2 + 7*S^4))/(3*S^3) + (Pi^2*(7 - 705*S^2 - 2154*S^4 + 3362*S^6 - 1425*S^8 - 462*S^10 + 7*S^12))/(27*S^3*(1 + S^2)^3) + (2*(4 - 111*S^2 - 363*S^4 + 584*S^6 - 363*S^8 - 111*S^10 + 4*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*S^3*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (4*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(3 + 9*S^2 + 9*S^4 - 21*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]*(((1 + S^2)*(1013 - 566*S^2 + 1013*S^4))/(108*S^3) + (Pi^4*(-535 - 1605*S^2 - 1605*S^4 + 2994*S^6 - 657*S^8 - 657*S^10 - 219*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(145 + 1968*S^2 - 13719*S^4 + 20414*S^6 - 8787*S^8 + 1410*S^10 + 73*S^12))/(324*S^3*(1 + S^2)^3) + ((Pi^2*(-69 - 207*S^2 - 207*S^4 + 424*S^6 - 141*S^8 - 141*S^10 - 47*S^12))/(9*S^3*(1 + S^2)^3) + (13 + 555*S^2 - 3441*S^4 + 4994*S^6 - 3441*S^8 + 555*S^10 + 13*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (2*(53 + 147*S^2 + 111*S^4 + 142*S^6 + 57*S^8 + 129*S^10 + 53*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 11*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(4 - 111*S^2 - 363*S^4 + 584*S^6 - 363*S^8 - 111*S^10 + 4*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(19 + 57*S^2 + 57*S^4 - 141*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(13 + 39*S^2 + 39*S^4 - 94*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (2*(7 + 27*S^2 + 39*S^4 - 14*S^6 + 45*S^8 + 29*S^10 + 7*S^12)*Zeta[3])/(S^3*(1 + S^2)^3))) - (2*(20 + 50*S^2 + 195*S^4 - 707*S^6 - 206*S^8 + 6*S^10)*Zeta[5])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(((1 + S^2)*(1559 - 338*S^2 + 1559*S^4))/(72*S^3) + (Pi^2*(-451 - 1346*S^2 - 1062*S^4 + 326*S^6 + 349*S^8))/(216*S^3*(1 + S^2)) + (Pi^4*(-421 - 11364*S^2 - 31299*S^4 + 39478*S^6 - 10860*S^8 - 4551*S^10 - 421*S^12))/(1620*S^3*(1 + S^2)^3) + ((-41 - 471*S^2 - 1173*S^4 + 1610*S^6 - 1173*S^8 - 471*S^10 - 41*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((2*Pi^2*(3 + 9*S^2 + 9*S^4 - 164*S^6 + 135*S^8 + 135*S^10 + 45*S^12))/(9*S^3*(1 + S^2)^3) + (127 + 1752*S^2 + 5019*S^4 - 250*S^6 + 13479*S^8 + 3714*S^10 + 991*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(14 + 33*S^2 + 15*S^4 - 28*S^6 + 153*S^8 + 79*S^10 + 14*S^12)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-18 - 54*S^2 - 54*S^4 - 13*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*(-48 - 61*S^2 - 409*S^4 + 409*S^6 + 61*S^8 + 48*S^10))/(3*S^3*(1 + S^2)^2) - (4*Pi^2*(-36 - 108*S^2 - 108*S^4 + 67*S^6 + 51*S^8 + 51*S^10 + 17*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(7 - 5*S^2 - 57*S^4 - 14*S^6 + 141*S^8 + 61*S^10 + 7*S^12)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^3) - (16*(4 + 12*S^2 + 12*S^4 - 67*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(39 + 117*S^2 + 117*S^4 - 888*S^6 + 651*S^8 + 651*S^10 + 217*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (264*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (16*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(51 + 153*S^2 + 153*S^4 - 247*S^6 + 54*S^8 + 54*S^10 + 18*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (176*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((2*Pi^2*(-1 - 3*S^2 - 3*S^4 - 153*S^6 + 132*S^8 + 132*S^10 + 44*S^12))/(9*S^3*(1 + S^2)^3) + (-445 - 1536*S^2 - 789*S^4 - 4994*S^6 + 7671*S^8 + 426*S^10 + 419*S^12)/(27*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((2*(-100 - 109*S^2 + 109*S^4 + 100*S^6))/(9*S^3) + (Pi^2*(-41 - 1425*S^2 - 4035*S^4 + 1610*S^6 + 1689*S^8 + 483*S^10 - 41*S^12))/(54*S^3*(1 + S^2)^3) + (8*(4 + 12*S^2 + 12*S^4 - 67*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(3 + 9*S^2 + 9*S^4 - 67*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + (4*(-10 - 30*S^2 - 30*S^4 - 173*S^6 + 171*S^8 + 171*S^10 + 57*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3))) - (100*S^5*(3 + 3*S^2 + S^4)*Zeta[7])/(1 + S^2)^3;
E4uvwT=E4uvwT0F0+T*E4uvwT1F1*(F+1/F)+T^2*(E4uvwT2F0+E4uvwT2F2*(F^2+1/F^2))+T^3*(E4uvwT3F1*(F+1/F)+E4uvwT3F3*(F^3+1/F^3));
E4vwuT0F0=(24559*Pi^8)/544320 + HPL[{0}, S^2]^8/384 + HPL[{0}, S^2]^6*((5*Pi^2)/288 - HPL[{2}, -S^2]/16) - (59*Pi^2*HPL[{2}, -S^2]^3)/18 - (5*Pi^2*HPL[{3}, -S^2]^2)/3 + 24*HPL[{4}, -S^2]^2 + (7*Pi^2*HPL[{6}, -S^2])/2 + 279*HPL[{8}, -S^2] + (38*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + 32*HPL[{3, 1}, -S^2]^2 - 4*Pi^2*HPL[{4, 2}, -S^2] - 12*Pi^2*HPL[{5, 1}, -S^2] - 6*HPL[{5, 3}, -S^2] - 3*HPL[{6, 2}, -S^2] - 40*HPL[{7, 1}, -S^2] + HPL[{2}, -S^2]^2*((-67*Pi^4)/80 + 9*HPL[{4}, -S^2] + 76*HPL[{3, 1}, -S^2] - 152*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 1}, -S^2]*((1483*Pi^4)/180 - 112*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]^4*((287*Pi^4)/8640 - (41*Pi^2*HPL[{2}, -S^2])/72 - (25*HPL[{2}, -S^2]^2)/48 + HPL[{4}, -S^2]/4 + (31*HPL[{3, 1}, -S^2])/12 - (37*HPL[{2, 1, 1}, -S^2])/6) - (1547*Pi^4*HPL[{2, 1, 1}, -S^2])/90 + HPL[{4}, -S^2]*((-7*Pi^4)/36 - 80*HPL[{3, 1}, -S^2] + 112*HPL[{2, 1, 1}, -S^2]) + 4*Pi^2*HPL[{3, 1, 2}, -S^2] - (224*Pi^2*HPL[{3, 2, 1}, -S^2])/3 - 36*HPL[{3, 3, 2}, -S^2] - (712*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 60*HPL[{4, 1, 3}, -S^2] - 30*HPL[{4, 2, 2}, -S^2] + 204*HPL[{4, 3, 1}, -S^2] + 108*HPL[{5, 1, 2}, -S^2] + 828*HPL[{5, 2, 1}, -S^2] + 2100*HPL[{6, 1, 1}, -S^2] + (560*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 608*HPL[{3, 2, 2, 1}, -S^2] + 1824*HPL[{3, 3, 1, 1}, -S^2] - 96*HPL[{4, 1, 1, 2}, -S^2] + 1728*HPL[{4, 1, 2, 1}, -S^2] + 5376*HPL[{4, 2, 1, 1}, -S^2] + 10672*HPL[{5, 1, 1, 1}, -S^2] - 376*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] + 1216*HPL[{2, 2, 1, 2, 1}, -S^2] + 3648*HPL[{2, 2, 2, 1, 1}, -S^2] - 7200*HPL[{3, 1, 1, 1, 2}, -S^2] - 12064*HPL[{3, 1, 1, 2, 1}, -S^2] - 14496*HPL[{3, 1, 2, 1, 1}, -S^2] - 30304*HPL[{3, 2, 1, 1, 1}, -S^2] - 91136*HPL[{4, 1, 1, 1, 1}, -S^2] + 2880*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 5760*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((10*Pi^2)/9 - (4*HPL[{0}, S^2]^2)/3 - 8*HPL[{2}, -S^2])*Log[T]^6 + (8*HPL[{0}, S^2]*Log[T]^7)/3 + (2*Log[T]^8)/3 + HPL[{5}, -S^2]*(44*HPL[{2, 1}, -S^2] - 32*Zeta[3]) + Log[T]^5*((22*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]*((64*Pi^2)/9 + 24*HPL[{2}, -S^2]) - 24*HPL[{3}, -S^2] + 48*HPL[{2, 1}, -S^2] - 24*Zeta[3]) + HPL[{0}, S^2]^5*((-2*HPL[{2, 1}, -S^2])/3 - (3*Zeta[3])/4) - 16*HPL[{3, 2}, -S^2]*Zeta[3] - 16*HPL[{4, 1}, -S^2]*Zeta[3] - 304*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 928*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 624*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] + (14*Pi^2*Zeta[3]^2)/3 + HPL[{0}, S^2]^2*((1273*Pi^6)/90720 - (21*Pi^2*HPL[{2}, -S^2]^2)/8 - (7*HPL[{2}, -S^2]^3)/2 - HPL[{3}, -S^2]^2 + 18*HPL[{6}, -S^2] + 38*HPL[{2, 1}, -S^2]^2 + (27*Pi^2*HPL[{3, 1}, -S^2])/2 - 2*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-63*Pi^4)/40 + 2*HPL[{4}, -S^2] + 36*HPL[{3, 1}, -S^2] - 76*HPL[{2, 1, 1}, -S^2]) - (88*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 84*HPL[{3, 2, 1}, -S^2] - 264*HPL[{4, 1, 1}, -S^2] + 200*HPL[{3, 1, 1, 1}, -S^2] - 408*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(6*HPL[{2, 1}, -S^2] - 6*Zeta[3]) + 8*HPL[{2, 1}, -S^2]*Zeta[3] + 7*Zeta[3]^2) + HPL[{2}, -S^2]*((-11857*Pi^6)/15120 - 6*HPL[{3}, -S^2]^2 + (16*Pi^2*HPL[{4}, -S^2])/3 + 21*HPL[{6}, -S^2] + 152*HPL[{2, 1}, -S^2]^2 + (22*Pi^2*HPL[{3, 1}, -S^2])/3 - 18*HPL[{4, 2}, -S^2] - 116*HPL[{5, 1}, -S^2] - (76*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 112*HPL[{4, 1, 1}, -S^2] + 7184*HPL[{3, 1, 1, 1}, -S^2] + 152*HPL[{2, 1}, -S^2]*Zeta[3] - 6*Zeta[3]^2 + HPL[{3}, -S^2]*(152*HPL[{2, 1}, -S^2] + 8*Zeta[3])) + Log[T]^4*((287*Pi^4)/540 - (7*HPL[{0}, S^2]^4)/9 + HPL[{0}, S^2]^2*((-29*Pi^2)/9 - 17*HPL[{2}, -S^2]) - (47*Pi^2*HPL[{2}, -S^2])/3 + (8*HPL[{4}, -S^2])/3 + 120*HPL[{3, 1}, -S^2] - 240*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]*(8*HPL[{3}, -S^2] - 120*HPL[{2, 1}, -S^2] + (28*Zeta[3])/3)) + Log[T]^2*((1273*Pi^6)/22680 - HPL[{0}, S^2]^6/12 + HPL[{0}, S^2]^4*((-29*Pi^2)/36 - (37*HPL[{2}, -S^2])/12) - (19*Pi^2*HPL[{2}, -S^2]^2)/3 - (76*HPL[{2}, -S^2]^3)/3 - 16*HPL[{3}, -S^2]^2 - (2*Pi^2*HPL[{4}, -S^2])/3 - 30*HPL[{6}, -S^2] + HPL[{2}, -S^2]*((-1547*Pi^4)/180 + 56*HPL[{4}, -S^2] - 56*HPL[{3, 1}, -S^2]) + (280*Pi^2*HPL[{3, 1}, -S^2])/3 - 48*HPL[{4, 2}, -S^2] - 136*HPL[{5, 1}, -S^2] + HPL[{0}, S^2]^2*((-181*Pi^4)/90 - (44*Pi^2*HPL[{2}, -S^2])/3 - 19*HPL[{2}, -S^2]^2 - 6*HPL[{4}, -S^2] + 100*HPL[{3, 1}, -S^2] - 204*HPL[{2, 1, 1}, -S^2]) - 188*Pi^2*HPL[{2, 1, 1}, -S^2] + 48*HPL[{3, 1, 2}, -S^2] - 560*HPL[{3, 2, 1}, -S^2] - 1792*HPL[{4, 1, 1}, -S^2] + 1440*HPL[{3, 1, 1, 1}, -S^2] - 2880*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(360*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + HPL[{0}, S^2]^3*(2*HPL[{3}, -S^2] - 30*HPL[{2, 1}, -S^2] - (8*Zeta[3])/3) + 312*HPL[{2, 1}, -S^2]*Zeta[3] + 28*Zeta[3]^2 + HPL[{0}, S^2]*(6*Pi^2*HPL[{3}, -S^2] + 4*HPL[{5}, -S^2] - 90*Pi^2*HPL[{2, 1}, -S^2] + 8*HPL[{3, 2}, -S^2] - 32*HPL[{4, 1}, -S^2] + 624*HPL[{2, 2, 1}, -S^2] + 1968*HPL[{3, 1, 1}, -S^2] - 1440*HPL[{2, 1, 1, 1}, -S^2] + 2*Pi^2*Zeta[3] + HPL[{2}, -S^2]*(-4*HPL[{3}, -S^2] - 312*HPL[{2, 1}, -S^2] + 28*Zeta[3]))) + Log[T]^3*((11*HPL[{0}, S^2]^5)/18 + HPL[{0}, S^2]^3*((110*Pi^2)/27 + 10*HPL[{2}, -S^2]) - (68*Pi^2*HPL[{3}, -S^2])/3 - 40*HPL[{5}, -S^2] + (188*Pi^2*HPL[{2, 1}, -S^2])/3 + 224*HPL[{3, 2}, -S^2] + (2128*HPL[{4, 1}, -S^2])/3 + HPL[{0}, S^2]*((937*Pi^4)/135 + 30*Pi^2*HPL[{2}, -S^2] + 52*HPL[{2}, -S^2]^2 + (56*HPL[{4}, -S^2])/3 - 240*HPL[{3, 1}, -S^2] + 480*HPL[{2, 1, 1}, -S^2]) - 480*HPL[{3, 1, 1}, -S^2] + 960*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-120*HPL[{3}, -S^2] - 104*Zeta[3]) + HPL[{0}, S^2]^2*(-8*HPL[{3}, -S^2] + 68*HPL[{2, 1}, -S^2] - (16*Zeta[3])/3) - (196*Pi^2*Zeta[3])/9 - (440*Zeta[5])/3) + HPL[{3}, -S^2]*(-42*HPL[{5}, -S^2] + 32*Pi^2*HPL[{2, 1}, -S^2] + 24*HPL[{3, 2}, -S^2] + 44*HPL[{4, 1}, -S^2] - 304*HPL[{2, 2, 1}, -S^2] - 976*HPL[{3, 1, 1}, -S^2] + 720*HPL[{2, 1, 1, 1}, -S^2] - (8*Pi^2*Zeta[3])/3 - 40*Zeta[5]) + HPL[{0}, S^2]^3*((Pi^2*HPL[{3}, -S^2])/6 - 3*HPL[{5}, -S^2] - (85*Pi^2*HPL[{2, 1}, -S^2])/18 + 2*HPL[{3, 2}, -S^2] + 4*HPL[{4, 1}, -S^2] + (76*HPL[{2, 2, 1}, -S^2])/3 + 80*HPL[{3, 1, 1}, -S^2] - 60*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-HPL[{3}, -S^2] - (38*HPL[{2, 1}, -S^2])/3 + (2*Zeta[3])/3) - (49*Pi^2*Zeta[3])/18 - (55*Zeta[5])/3) + 64*Zeta[3]*Zeta[5] + HPL[{2, 1}, -S^2]*(-304*HPL[{3, 2}, -S^2] - 1024*HPL[{4, 1}, -S^2] - 608*HPL[{2, 2, 1}, -S^2] - 1104*HPL[{3, 1, 1}, -S^2] + (86*Pi^2*Zeta[3])/3 + 188*Zeta[5]) + Log[T]*(HPL[{0}, S^2]^7/24 + HPL[{0}, S^2]^5*((4*Pi^2)/9 + (2*HPL[{2}, -S^2])/3) - (32*Pi^2*HPL[{5}, -S^2])/3 + 88*HPL[{7}, -S^2] + HPL[{2, 1}, -S^2]*((1547*Pi^4)/90 + 112*HPL[{3, 1}, -S^2]) + 60*Pi^2*HPL[{3, 2}, -S^2] + (580*Pi^2*HPL[{4, 1}, -S^2])/3 - 76*HPL[{4, 3}, -S^2] - 228*HPL[{5, 2}, -S^2] - 380*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((-44*Pi^4)/9 + 44*HPL[{4}, -S^2] + 368*HPL[{3, 1}, -S^2] - 720*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]^3*((937*Pi^4)/540 + (85*Pi^2*HPL[{2}, -S^2])/18 + (19*HPL[{2}, -S^2]^2)/3 + 2*HPL[{4}, -S^2] - (88*HPL[{3, 1}, -S^2])/3 + 60*HPL[{2, 1, 1}, -S^2]) - (152*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - 288*Pi^2*HPL[{3, 1, 1}, -S^2] - 608*HPL[{3, 2, 2}, -S^2] - 1952*HPL[{3, 3, 1}, -S^2] - 1952*HPL[{4, 1, 2}, -S^2] - 5984*HPL[{4, 2, 1}, -S^2] - 12336*HPL[{5, 1, 1}, -S^2] + 376*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + 1216*HPL[{2, 2, 2, 1}, -S^2] - 2304*HPL[{3, 1, 1, 2}, -S^2] - 2304*HPL[{3, 1, 2, 1}, -S^2] - 5952*HPL[{3, 2, 1, 1}, -S^2] - 17632*HPL[{4, 1, 1, 1}, -S^2] - 2880*HPL[{3, 1, 1, 1, 1}, -S^2] + 5760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^2*(-76*HPL[{3}, -S^2] + 152*HPL[{2, 1}, -S^2] - 76*Zeta[3]) + HPL[{4}, -S^2]*(-112*HPL[{2, 1}, -S^2] - 32*Zeta[3]) - (157*Pi^4*Zeta[3])/45 + 320*HPL[{3, 1}, -S^2]*Zeta[3] - 624*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{0}, S^2]^4*(-HPL[{3}, -S^2]/2 + (37*HPL[{2, 1}, -S^2])/6 + (7*Zeta[3])/6) + HPL[{0}, S^2]^2*(-3*Pi^2*HPL[{3}, -S^2] - 2*HPL[{5}, -S^2] + (88*Pi^2*HPL[{2, 1}, -S^2])/3 + 12*HPL[{3, 2}, -S^2] + 48*HPL[{4, 1}, -S^2] - 152*HPL[{2, 2, 1}, -S^2] - 504*HPL[{3, 1, 1}, -S^2] + 408*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-6*HPL[{3}, -S^2] + 76*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + Pi^2*Zeta[3]) + HPL[{0}, S^2]*((12907*Pi^6)/5670 + (58*Pi^2*HPL[{2}, -S^2]^2)/3 + (76*HPL[{2}, -S^2]^3)/3 - 12*HPL[{3}, -S^2]^2 + (20*Pi^2*HPL[{4}, -S^2])/3 - 312*HPL[{2, 1}, -S^2]^2 - (268*Pi^2*HPL[{3, 1}, -S^2])/3 - 56*HPL[{5, 1}, -S^2] + 180*Pi^2*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((377*Pi^4)/45 + 24*HPL[{4}, -S^2] - 312*HPL[{3, 1}, -S^2] + 624*HPL[{2, 1, 1}, -S^2]) + 608*HPL[{3, 2, 1}, -S^2] + 1936*HPL[{4, 1, 1}, -S^2] - 1440*HPL[{3, 1, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1, 1}, -S^2] - 56*HPL[{2, 1}, -S^2]*Zeta[3] + 16*Zeta[3]^2 + HPL[{3}, -S^2]*(8*HPL[{2, 1}, -S^2] + 8*Zeta[3])) + HPL[{2}, -S^2]*(-32*Pi^2*HPL[{3}, -S^2] - 44*HPL[{5}, -S^2] + (76*Pi^2*HPL[{2, 1}, -S^2])/3 + 304*HPL[{3, 2}, -S^2] + 1024*HPL[{4, 1}, -S^2] - 608*HPL[{2, 2, 1}, -S^2] + 1104*HPL[{3, 1, 1}, -S^2] - (86*Pi^2*Zeta[3])/3 - 188*Zeta[5]) - (110*Pi^2*Zeta[5])/3 - 300*Zeta[7]) + HPL[{0}, S^2]*((-8*Pi^2*HPL[{5}, -S^2])/3 - 80*HPL[{7}, -S^2] + (8*Pi^2*HPL[{3, 2}, -S^2])/3 + (4*Pi^2*HPL[{4, 1}, -S^2])/3 - 32*HPL[{4, 3}, -S^2] - 96*HPL[{5, 2}, -S^2] - 160*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((7*Pi^4)/15 + 16*HPL[{4}, -S^2] + 8*HPL[{3, 1}, -S^2] - 8*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-377*Pi^4)/45 + 312*HPL[{3, 1}, -S^2] + 624*HPL[{2, 1, 1}, -S^2]) + (232*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + 244*Pi^2*HPL[{3, 1, 1}, -S^2] + 32*HPL[{3, 2, 2}, -S^2] + 48*HPL[{3, 3, 1}, -S^2] + 48*HPL[{4, 1, 2}, -S^2] + 96*HPL[{4, 2, 1}, -S^2] + 152*HPL[{5, 1, 1}, -S^2] - 180*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 608*HPL[{2, 2, 2, 1}, -S^2] + 1840*HPL[{3, 1, 1, 2}, -S^2] + 1840*HPL[{3, 1, 2, 1}, -S^2] + 3664*HPL[{3, 2, 1, 1}, -S^2] + 10880*HPL[{4, 1, 1, 1}, -S^2] - 1248*HPL[{2, 1, 2, 1, 1}, -S^2] - 3744*HPL[{2, 2, 1, 1, 1}, -S^2] - 6048*HPL[{3, 1, 1, 1, 1}, -S^2] - 2880*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (157*Pi^4*Zeta[3])/90 - 32*HPL[{3, 1}, -S^2]*Zeta[3] + 56*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]^2*(4*HPL[{3}, -S^2] - 76*HPL[{2, 1}, -S^2] + 6*Zeta[3]) + HPL[{4}, -S^2]*(-24*HPL[{2, 1}, -S^2] + 16*Zeta[3]) - (55*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((-4*Pi^2*HPL[{3}, -S^2])/3 - 16*HPL[{5}, -S^2] - (116*Pi^2*HPL[{2, 1}, -S^2])/3 - 16*HPL[{3, 2}, -S^2] - 24*HPL[{4, 1}, -S^2] + 304*HPL[{2, 2, 1}, -S^2] - 920*HPL[{3, 1, 1}, -S^2] - 624*HPL[{2, 1, 1, 1}, -S^2] + 3*Pi^2*Zeta[3] + 16*Zeta[5]) - 150*Zeta[7]);
E4vwuT1F1=(5*Pi^4*S)/6 + (13*Pi^6*S)/60 + (S*HPL[{0}, S^2]^6*HPL[{1}, -S^2])/16 + ((47*Pi^2*S)/15 + (104*(1 + S^2))/(15*S))*HPL[{1}, -S^2]^5 + (2*(1 + S^2)*HPL[{1}, -S^2]^6)/S + (8*S*HPL[{1}, -S^2]^7)/7 + ((-6 + 13*S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^5*((3*S)/4 + (Pi^2*S)/18 + (3*(1 + S^2)*HPL[{1}, -S^2])/(8*S) + (S*HPL[{1}, -S^2]^2)/3 + (S*HPL[{2}, -S^2])/3) + ((-2 + S^2)*HPL[{3}, -S^2]^2)/S + ((-47*Pi^2*S)/6 + (2*(-1 + 35*S^2))/S)*HPL[{5}, -S^2] - (2*(5 + 21*S^2)*HPL[{6}, -S^2])/S - 106*S*HPL[{7}, -S^2] - (4*(3 + 16*S^2)*HPL[{2, 1}, -S^2]^2)/S + HPL[{4}, -S^2]*((Pi^2*(11 - 8*S^2))/(6*S) - (6*(-1 + 8*S^2))/S + 2*S*HPL[{2, 1}, -S^2]) + ((83*Pi^2*S)/3 + (5*(1 + 7*S^2))/S)*HPL[{3, 2}, -S^2] + (93*Pi^2*S + (2*(3 + 44*S^2))/S)*HPL[{4, 1}, -S^2] + (3*(1 + 2*S^2)*HPL[{4, 2}, -S^2])/S + 10*S*HPL[{4, 3}, -S^2] + (4*(-2 + 5*S^2)*HPL[{5, 1}, -S^2])/S + 33*S*HPL[{5, 2}, -S^2] + 142*S*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((-103*Pi^4*S)/45 + (Pi^2*(5 - S^2))/(6*S) + (2*(3 + 14*S^2))/S - 2*S*HPL[{4}, -S^2] + (2*(23 + 5*S^2)*HPL[{2, 1}, -S^2])/S + 156*S*HPL[{3, 1}, -S^2] - 328*S*HPL[{2, 1, 1}, -S^2]) + ((76*Pi^2*S)/3 + (8*(16 + 3*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((32*Pi^2*S)/3 + (4*(95 + 7*S^2))/S)*HPL[{3, 1, 1}, -S^2] - (6*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (14*(-3 + 7*S^2)*HPL[{3, 2, 1}, -S^2])/S - 310*S*HPL[{3, 2, 2}, -S^2] - 944*S*HPL[{3, 3, 1}, -S^2] + (4*(-31 + 72*S^2)*HPL[{4, 1, 1}, -S^2])/S - 938*S*HPL[{4, 1, 2}, -S^2] - 2858*S*HPL[{4, 2, 1}, -S^2] - 5868*S*HPL[{5, 1, 1}, -S^2] + ((208*Pi^2*S)/3 + (16*(-18 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + 304*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(-11 + 26*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - 280*S*HPL[{3, 1, 1, 2}, -S^2] - 280*S*HPL[{3, 1, 2, 1}, -S^2] - 1192*S*HPL[{3, 2, 1, 1}, -S^2] - 3408*S*HPL[{4, 1, 1, 1}, -S^2] + (32*(-4 + 15*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - 592*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 1776*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 4384*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 1440*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (-2*Pi^2*S - 6*S*HPL[{0}, S^2]^2 - (12*(1 + S^2)*HPL[{1}, -S^2])/S - 24*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*(-12*S - 24*S*HPL[{1}, -S^2]) - 12*S*HPL[{2}, -S^2])*Log[T]^5 + (8*S*HPL[{0}, S^2] + 8*S*HPL[{1}, -S^2])*Log[T]^6 + (16*S + Pi^2*S - (157*Pi^4*S)/90)*Zeta[3] + 4*S*Zeta[3]^2 + HPL[{2, 1, 1}, -S^2]*((8*(-4 + 15*S^2))/S + (4*Pi^2*(-5 + 31*S^2))/(3*S) - 304*S*Zeta[3]) + Log[T]^4*((10*Pi^2*S)/3 + (46*S*HPL[{0}, S^2]^3)/9 + ((47*Pi^2*S)/3 + (104*(1 + S^2))/(3*S))*HPL[{1}, -S^2] + (30*(1 + S^2)*HPL[{1}, -S^2]^2)/S + 40*S*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*(10*S + 17*S*HPL[{1}, -S^2]) + (4*(-4 + 15*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{0}, S^2]*((104*S)/3 + (136*Pi^2*S)/9 + (30*(1 + S^2)*HPL[{1}, -S^2])/S + 60*S*HPL[{1}, -S^2]^2 + 56*S*HPL[{2}, -S^2]) - (178*S*HPL[{3}, -S^2])/3 + 60*S*HPL[{2, 1}, -S^2] - 60*S*Zeta[3]) + HPL[{2}, -S^2]^2*((4 + 15*S^2)/S + (Pi^2*(2 + 31*S^2))/(6*S) - 41*S*HPL[{3}, -S^2] + 38*S*HPL[{2, 1}, -S^2] - 36*S*Zeta[3]) + HPL[{1}, -S^2]^4*((22*(1 + S^2))/S + (14*Pi^2*(1 + S^2))/(3*S) + (9*(1 + S^2)*HPL[{2}, -S^2])/S - 30*S*HPL[{3}, -S^2] - 26*S*Zeta[3]) + HPL[{0}, S^2]^4*((5*Pi^2*S)/24 + (37*(1 + S^2)*HPL[{1}, -S^2]^2)/(24*S) + (37*S*HPL[{1}, -S^2]^3)/36 + (5*S*HPL[{2}, -S^2])/4 + HPL[{1}, -S^2]*((41*Pi^2*S)/72 + (11*(1 + S^2))/(6*S) + (25*S*HPL[{2}, -S^2])/24) - (3*S*HPL[{3}, -S^2])/8 + (3*S*HPL[{2, 1}, -S^2])/4 + (7*S*Zeta[3])/12) + HPL[{3, 1}, -S^2]*((Pi^2*(11 - 57*S^2))/(3*S) - (6*(-3 + 7*S^2))/S + 152*S*Zeta[3]) + HPL[{1}, -S^2]^3*((1547*Pi^4*S)/540 + (188*(1 + S^2))/(3*S) + (32*Pi^2*(1 + S^2))/(3*S) + ((38*Pi^2*S)/9 + (56*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (76*S*HPL[{2}, -S^2]^2)/3 - (12*(1 + S^2)*HPL[{3}, -S^2])/S - (56*S*HPL[{4}, -S^2])/3 - (36*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (56*S*HPL[{3, 1}, -S^2])/3 - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((14*Pi^4*S)/5 - (4*Pi^2*(19 + S^2))/(3*S) - (4*(23 + 4*S^2))/S + 176*S*HPL[{3, 1}, -S^2] + 296*S*HPL[{2, 1, 1}, -S^2] + (8*(3 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]^3*(19*S + (133*Pi^2*S)/36 + (403*Pi^4*S)/1080 + (34*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + (5*S*HPL[{1}, -S^2]^4)/2 + ((25*S)/6 + (41*Pi^2*S)/18)*HPL[{2}, -S^2] + (35*S*HPL[{2}, -S^2]^2)/12 + HPL[{1}, -S^2]^2*((85*Pi^2*S)/36 + (41*(1 + S^2))/(6*S) + (19*S*HPL[{2}, -S^2])/3) + (S*HPL[{3}, -S^2])/2 + (5*S*HPL[{4}, -S^2])/2 + ((-28 - S^2)*HPL[{2, 1}, -S^2])/(3*S) - (44*S*HPL[{3, 1}, -S^2])/3 + 28*S*HPL[{2, 1, 1}, -S^2] + S*Zeta[3] + HPL[{1}, -S^2]*((19*(1 + S^2))/(2*S) + (79*Pi^2*(1 + S^2))/(36*S) + (14*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + S*HPL[{3}, -S^2] - (38*S*HPL[{2, 1}, -S^2])/3 - (2*S*Zeta[3])/3)) + Log[T]^3*((-20*Pi^2*S)/3 - (781*Pi^4*S)/270 - (37*S*HPL[{0}, S^2]^4)/18 + ((-94*Pi^2*S)/3 - (208*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^2 - (40*(1 + S^2)*HPL[{1}, -S^2]^3)/S - 40*S*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*(-8*S - 10*S*HPL[{1}, -S^2]) + (-20*Pi^2*S - (8*(-4 + 15*S^2))/(3*S))*HPL[{2}, -S^2] - 26*S*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^2*(-20*S - (82*Pi^2*S)/9 - (26*(1 + S^2)*HPL[{1}, -S^2])/S - 34*S*HPL[{1}, -S^2]^2 - 30*S*HPL[{2}, -S^2]) + (4*(1 + 12*S^2)*HPL[{3}, -S^2])/(3*S) + (64*S*HPL[{4}, -S^2])/3 - (8*(-35 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (304*S*HPL[{3, 1}, -S^2])/3 - 240*S*HPL[{2, 1, 1}, -S^2] + 8*S*Zeta[3] + HPL[{0}, S^2]*(-88*S - 18*Pi^2*S - (60*(1 + S^2)*HPL[{1}, -S^2]^2)/S - 80*S*HPL[{1}, -S^2]^3 - (8*(-1 + 18*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*(-30*Pi^2*S - (208*(1 + S^2))/(3*S) - 104*S*HPL[{2}, -S^2]) + (20*S*HPL[{3}, -S^2])/3 - 16*S*HPL[{2, 1}, -S^2] + (56*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-88*(1 + S^2))/S - (56*Pi^2*(1 + S^2))/(3*S) - (36*(1 + S^2)*HPL[{2}, -S^2])/S + 120*S*HPL[{3}, -S^2] + 104*S*Zeta[3])) + HPL[{0}, S^2]^2*((5*Pi^2*S)/2 + (89*Pi^4*S)/120 + (13*(1 + S^2)*HPL[{1}, -S^2]^4)/(2*S) + (17*S*HPL[{1}, -S^2]^5)/5 + ((-1 + 15*S^2)*HPL[{2}, -S^2]^2)/(2*S) + HPL[{1}, -S^2]^3*((44*Pi^2*S)/9 + (44*(1 + S^2))/(3*S) + (38*S*HPL[{2}, -S^2])/3) + ((-3*Pi^2*S)/2 + (3 + 5*S^2)/S)*HPL[{3}, -S^2] + ((3 - S^2)*HPL[{4}, -S^2])/S - 10*S*HPL[{5}, -S^2] + ((8*Pi^2*S)/3 - (2*(20 + 3*S^2))/S)*HPL[{2, 1}, -S^2] - 31*S*HPL[{3, 1}, -S^2] + 4*S*HPL[{3, 2}, -S^2] + 21*S*HPL[{4, 1}, -S^2] + (4*(-1 + 16*S^2)*HPL[{2, 1, 1}, -S^2])/S + 2*S*HPL[{2, 2, 1}, -S^2] - 12*S*HPL[{3, 1, 1}, -S^2] + 28*S*HPL[{2, 1, 1, 1}, -S^2] + (5*S + (Pi^2*S)/2)*Zeta[3] + HPL[{1}, -S^2]^2*((27*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/(3*S) + (35*(1 + S^2)*HPL[{2}, -S^2])/(2*S) - 3*S*HPL[{3}, -S^2] - 38*S*HPL[{2, 1}, -S^2] - 4*S*Zeta[3]) + HPL[{2}, -S^2]*(15*S + (Pi^2*(-1 + 31*S^2))/(6*S) - 2*S*HPL[{3}, -S^2] - S*HPL[{2, 1}, -S^2] - S*Zeta[3]) + HPL[{1}, -S^2]*((63*Pi^4*S)/40 + (39*(1 + S^2))/S + (22*Pi^2*(1 + S^2))/(3*S) + ((21*Pi^2*S)/4 + (19*(1 + S^2))/S)*HPL[{2}, -S^2] + (21*S*HPL[{2}, -S^2]^2)/2 + (2*(1 + S^2)*HPL[{3}, -S^2])/S - 2*S*HPL[{4}, -S^2] - (35*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 36*S*HPL[{3, 1}, -S^2] + 76*S*HPL[{2, 1, 1}, -S^2] + ((1 + S^2)*Zeta[3])/S)) + (44*S - (55*Pi^2*S)/3)*Zeta[5] + Log[T]^2*(10*Pi^2*S + (89*Pi^4*S)/30 + (2*S*HPL[{0}, S^2]^5)/3 + ((94*Pi^2*S)/3 + (208*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^3 + (30*(1 + S^2)*HPL[{1}, -S^2]^4)/S + 24*S*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^4*((5*S)/2 + (37*S*HPL[{1}, -S^2])/12) + (2*(3 + 16*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{0}, S^2]^3*((43*S)/3 + (43*Pi^2*S)/9 + (34*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + 15*S*HPL[{1}, -S^2]^2 + 14*S*HPL[{2}, -S^2]) + ((-98*Pi^2*S)/3 - (2*(1 + 11*S^2))/S)*HPL[{3}, -S^2] - (2*(-5 + 6*S^2)*HPL[{4}, -S^2])/S - 54*S*HPL[{5}, -S^2] + ((104*Pi^2*S)/3 + (8*(-18 + S^2))/S)*HPL[{2, 1}, -S^2] - (4*(-11 + 26*S^2)*HPL[{3, 1}, -S^2])/S + 316*S*HPL[{3, 2}, -S^2] + 1032*S*HPL[{4, 1}, -S^2] + (16*(-4 + 15*S^2)*HPL[{2, 1, 1}, -S^2])/S + 296*S*HPL[{2, 2, 1}, -S^2] + 176*S*HPL[{3, 1, 1}, -S^2] + 720*S*HPL[{2, 1, 1, 1}, -S^2] + (-8*S - (98*Pi^2*S)/3)*Zeta[3] + HPL[{1}, -S^2]^2*((132*(1 + S^2))/S + (28*Pi^2*(1 + S^2))/S + (54*(1 + S^2)*HPL[{2}, -S^2])/S - 180*S*HPL[{3}, -S^2] - 156*S*Zeta[3]) + HPL[{2}, -S^2]*((4*(-4 + 15*S^2))/S + (2*Pi^2*(-5 + 31*S^2))/(3*S) - 164*S*HPL[{3}, -S^2] - 148*S*HPL[{2, 1}, -S^2] - 152*S*Zeta[3]) + HPL[{0}, S^2]^2*(30*S + 10*Pi^2*S + (39*(1 + S^2)*HPL[{1}, -S^2]^2)/S + 34*S*HPL[{1}, -S^2]^3 + (2*(-1 + 16*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((44*Pi^2*S)/3 + (44*(1 + S^2))/S + 38*S*HPL[{2}, -S^2]) - 9*S*HPL[{3}, -S^2] + 14*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{1}, -S^2]*((1547*Pi^4*S)/180 + (188*(1 + S^2))/S + (32*Pi^2*(1 + S^2))/S + ((38*Pi^2*S)/3 + (56*(1 + S^2))/S)*HPL[{2}, -S^2] + 76*S*HPL[{2}, -S^2]^2 - (36*(1 + S^2)*HPL[{3}, -S^2])/S - 56*S*HPL[{4}, -S^2] - (108*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 56*S*HPL[{3, 1}, -S^2] - (24*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]*(188*S + (95*Pi^2*S)/3 + (253*Pi^4*S)/30 + (60*(1 + S^2)*HPL[{1}, -S^2]^3)/S + 60*S*HPL[{1}, -S^2]^4 + (76*S + 42*Pi^2*S)*HPL[{2}, -S^2] + 77*S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*(45*Pi^2*S + (104*(1 + S^2))/S + 156*S*HPL[{2}, -S^2]) + (2*(4 + S^2)*HPL[{3}, -S^2])/S + 26*S*HPL[{4}, -S^2] - (4*(41 + 3*S^2)*HPL[{2, 1}, -S^2])/S - 336*S*HPL[{3, 1}, -S^2] + 672*S*HPL[{2, 1, 1}, -S^2] - 16*S*Zeta[3] + HPL[{1}, -S^2]*((132*(1 + S^2))/S + (79*Pi^2*(1 + S^2))/(3*S) + (78*(1 + S^2)*HPL[{2}, -S^2])/S + 4*S*HPL[{3}, -S^2] - 312*S*HPL[{2, 1}, -S^2] - 28*S*Zeta[3])) - 220*S*Zeta[5]) + HPL[{1}, -S^2]^2*((150*(1 + S^2))/S + (20*Pi^2*(1 + S^2))/S + (89*Pi^4*(1 + S^2))/(30*S) + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (-16*Pi^2*S - (18*(1 + S^2))/S)*HPL[{3}, -S^2] + ((1 + S^2)*HPL[{4}, -S^2])/S - 22*S*HPL[{5}, -S^2] + ((-38*Pi^2*S)/3 - (56*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (40*(1 + S^2)*HPL[{3, 1}, -S^2])/S + 152*S*HPL[{3, 2}, -S^2] + 512*S*HPL[{4, 1}, -S^2] + (108*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + 304*S*HPL[{2, 2, 1}, -S^2] + 552*S*HPL[{3, 1, 1}, -S^2] + ((-43*Pi^2*S)/3 - (16*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((30*(1 + S^2))/S + (31*Pi^2*(1 + S^2))/(3*S) - 76*S*HPL[{3}, -S^2] - 152*S*HPL[{2, 1}, -S^2] - 76*S*Zeta[3]) - 94*S*Zeta[5]) + HPL[{2}, -S^2]*((2*Pi^2*(-2 + 15*S^2))/(3*S) + (Pi^4*(-13 + 197*S^2))/(90*S) + ((-43*Pi^2*S)/3 + (-1 - 19*S^2)/S)*HPL[{3}, -S^2] + ((1 - 2*S^2)*HPL[{4}, -S^2])/S - S*HPL[{5}, -S^2] + ((-38*Pi^2*S)/3 - (4*(16 + 3*S^2))/S)*HPL[{2, 1}, -S^2] - (2*(11 + 31*S^2)*HPL[{3, 1}, -S^2])/S + 158*S*HPL[{3, 2}, -S^2] + 490*S*HPL[{4, 1}, -S^2] + (8*(3 + 16*S^2)*HPL[{2, 1, 1}, -S^2])/S - 152*S*HPL[{2, 2, 1}, -S^2] + 128*S*HPL[{3, 1, 1}, -S^2] - 296*S*HPL[{2, 1, 1, 1}, -S^2] + (-13*Pi^2*S - (8*(1 + 2*S^2))/S)*Zeta[3] - 74*S*Zeta[5]) + HPL[{1}, -S^2]*((11857*Pi^6*S)/15120 + (300*(1 + S^2))/S + (86*Pi^2*(1 + S^2))/(3*S) + (18*Pi^4*(1 + S^2))/(5*S) + ((59*Pi^2*S)/6 + (19*(1 + S^2))/S)*HPL[{2}, -S^2]^2 + 6*S*HPL[{3}, -S^2]^2 + ((-16*Pi^2*S)/3 + (5*(1 + S^2))/S)*HPL[{4}, -S^2] + (16*(1 + S^2)*HPL[{5}, -S^2])/S - 21*S*HPL[{6}, -S^2] - 152*S*HPL[{2, 1}, -S^2]^2 + ((-22*Pi^2*S)/3 - (40*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (118*(1 + S^2)*HPL[{4, 1}, -S^2])/S + 18*S*HPL[{4, 2}, -S^2] + 116*S*HPL[{5, 1}, -S^2] + ((76*Pi^2*S)/3 + (112*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (152*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (384*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - 112*S*HPL[{4, 1, 1}, -S^2] - (216*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 112*S*HPL[{3, 1, 1, 1}, -S^2] + ((-24*(1 + S^2))/S - (5*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + 6*S*Zeta[3]^2 + HPL[{3}, -S^2]*((-18*(1 + S^2))/S - (7*Pi^2*(1 + S^2))/(3*S) + 152*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-60*(1 + S^2))/S - (62*Pi^2*(1 + S^2))/(3*S) + 152*S*Zeta[3]) + HPL[{2}, -S^2]*((67*Pi^4*S)/40 + (38*(1 + S^2))/S + (11*Pi^2*(1 + S^2))/S - (20*(1 + S^2)*HPL[{3}, -S^2])/S - 18*S*HPL[{4}, -S^2] - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 152*S*HPL[{3, 1}, -S^2] + 304*S*HPL[{2, 1, 1}, -S^2] - (16*(1 + S^2)*Zeta[3])/S) + (4*(1 + S^2)*Zeta[5])/S) + HPL[{0}, S^2]*(300*S + (104*Pi^2*S)/3 + (22*Pi^4*S)/5 + (2437*Pi^6*S)/3780 + (6*(1 + S^2)*HPL[{1}, -S^2]^5)/S + 4*S*HPL[{1}, -S^2]^6 + ((28*Pi^2*S)/3 + (2 + 19*S^2)/S)*HPL[{2}, -S^2]^2 + 12*S*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*((15*Pi^2*S)/2 + (52*(1 + S^2))/(3*S) + 26*S*HPL[{2}, -S^2]) - 2*S*HPL[{3}, -S^2]^2 + ((14*Pi^2*S)/3 - (4*(1 + 2*S^2))/S)*HPL[{4}, -S^2] + (4*(-2 + 3*S^2)*HPL[{5}, -S^2])/S + 40*S*HPL[{6}, -S^2] + ((Pi^2*(-69 - 4*S^2))/(3*S) - (4*(25 + 6*S^2))/S)*HPL[{2, 1}, -S^2] - 154*S*HPL[{2, 1}, -S^2]^2 + ((-128*Pi^2*S)/3 - (4*(-1 + 17*S^2))/S)*HPL[{3, 1}, -S^2] - (4*(1 + 2*S^2)*HPL[{4, 1}, -S^2])/S - 44*S*HPL[{5, 1}, -S^2] + (152*S + 84*Pi^2*S)*HPL[{2, 1, 1}, -S^2] + (8*(18 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (28*(16 + S^2)*HPL[{3, 1, 1}, -S^2])/S + 288*S*HPL[{3, 2, 1}, -S^2] + 916*S*HPL[{4, 1, 1}, -S^2] - (8*(41 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 672*S*HPL[{3, 1, 1, 1}, -S^2] + 1344*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-18*S - (Pi^2*S)/3)*Zeta[3] + HPL[{1}, -S^2]^3*((44*(1 + S^2))/S + (79*Pi^2*(1 + S^2))/(9*S) + (26*(1 + S^2)*HPL[{2}, -S^2])/S + (4*S*HPL[{3}, -S^2])/3 - 104*S*HPL[{2, 1}, -S^2] - (28*S*Zeta[3])/3) + HPL[{3}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) + (4*(1 + 3*S^2))/S + 8*S*HPL[{2, 1}, -S^2] - 4*S*Zeta[3]) + HPL[{1}, -S^2]^2*((377*Pi^4*S)/90 + (94*(1 + S^2))/S + (31*Pi^2*(1 + S^2))/(2*S) + ((58*Pi^2*S)/3 + (44*(1 + S^2))/S)*HPL[{2}, -S^2] + 38*S*HPL[{2}, -S^2]^2 + 12*S*HPL[{4}, -S^2] - (78*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 156*S*HPL[{3, 1}, -S^2] + 312*S*HPL[{2, 1, 1}, -S^2] - (6*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((21*Pi^2*S)/2 + (178*Pi^4*S)/45 + (2*(4 + 23*S^2))/S + 4*S*HPL[{4}, -S^2] - (4*(18 + S^2)*HPL[{2, 1}, -S^2])/S - 152*S*HPL[{3, 1}, -S^2] + 308*S*HPL[{2, 1, 1}, -S^2] - (2*(-2 + 3*S^2)*Zeta[3])/S) - 20*S*Zeta[5] + HPL[{1}, -S^2]*((150*(1 + S^2))/S + (41*Pi^2*(1 + S^2))/(2*S) + (35*Pi^4*(1 + S^2))/(12*S) + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (4*Pi^2*S*HPL[{3}, -S^2])/3 + (4*(1 + S^2)*HPL[{4}, -S^2])/S + 16*S*HPL[{5}, -S^2] + ((-116*Pi^2*S)/3 - (88*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (76*(1 + S^2)*HPL[{3, 1}, -S^2])/S + 16*S*HPL[{3, 2}, -S^2] + 24*S*HPL[{4, 1}, -S^2] + (156*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + 304*S*HPL[{2, 2, 1}, -S^2] + 920*S*HPL[{3, 1, 1}, -S^2] - 624*S*HPL[{2, 1, 1, 1}, -S^2] + (-3*Pi^2*S - (2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((54*(1 + S^2))/S + (67*Pi^2*(1 + S^2))/(6*S) - 8*S*HPL[{3}, -S^2] - 152*S*HPL[{2, 1}, -S^2] - 12*S*Zeta[3]) - 16*S*Zeta[5])) + Log[T]*(-10*Pi^2*S - (89*Pi^4*S)/30 - (7037*Pi^6*S)/7560 - (S*HPL[{0}, S^2]^6)/8 + ((-47*Pi^2*S)/3 - (104*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^4 - (12*(1 + S^2)*HPL[{1}, -S^2]^5)/S - 8*S*HPL[{1}, -S^2]^6 + HPL[{0}, S^2]^5*((-3*S)/4 - (2*S*HPL[{1}, -S^2])/3) + ((-40*Pi^2*S)/3 - (2*(3 + 16*S^2))/S)*HPL[{2}, -S^2]^2 - (38*S*HPL[{2}, -S^2]^3)/3 + HPL[{0}, S^2]^4*((-5*S)/2 - (41*Pi^2*S)/36 - (37*(1 + S^2)*HPL[{1}, -S^2])/(12*S) - (37*S*HPL[{1}, -S^2]^2)/12 - (17*S*HPL[{2}, -S^2])/6) - 8*S*HPL[{3}, -S^2]^2 + ((11*Pi^2*S)/3 + (2*(-5 + 8*S^2))/S)*HPL[{4}, -S^2] - (8*(1 + 6*S^2)*HPL[{5}, -S^2])/S - 50*S*HPL[{6}, -S^2] + (152/S + (48*Pi^2)/S)*HPL[{2, 1}, -S^2] + 156*S*HPL[{2, 1}, -S^2]^2 + ((164*Pi^2*S)/3 + (4*(-11 + 25*S^2))/S)*HPL[{3, 1}, -S^2] - (6*(-1 + 9*S^2)*HPL[{3, 2}, -S^2])/S - (4*(-5 + 38*S^2)*HPL[{4, 1}, -S^2])/S - 42*S*HPL[{4, 2}, -S^2] - 156*S*HPL[{5, 1}, -S^2] + (-120*Pi^2*S - (16*(-4 + 15*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (16*(16 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/S - (8*(95 + 6*S^2)*HPL[{3, 1, 1}, -S^2])/S + 24*S*HPL[{3, 1, 2}, -S^2] - 280*S*HPL[{3, 2, 1}, -S^2] - 784*S*HPL[{4, 1, 1}, -S^2] - (16*(-35 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 608*S*HPL[{3, 1, 1, 1}, -S^2] - 1440*S*HPL[{2, 1, 1, 1, 1}, -S^2] - (2*Pi^2*S*Zeta[3])/3 + 12*S*Zeta[3]^2 + HPL[{0}, S^2]^3*(-19*S - (9*Pi^2*S)/2 - (34*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - 10*S*HPL[{1}, -S^2]^3 - 9*S*HPL[{2}, -S^2] + HPL[{1}, -S^2]*((-85*Pi^2*S)/18 - (41*(1 + S^2))/(3*S) - (38*S*HPL[{2}, -S^2])/3) + S*HPL[{3}, -S^2] - (8*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(-1 + 9*S^2))/(3*S) + (2*(1 + 9*S^2))/S + 24*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{1}, -S^2]^3*((-88*(1 + S^2))/S - (56*Pi^2*(1 + S^2))/(3*S) - (36*(1 + S^2)*HPL[{2}, -S^2])/S + 120*S*HPL[{3}, -S^2] + 104*S*Zeta[3]) + HPL[{1}, -S^2]^2*((-1547*Pi^4*S)/180 - (188*(1 + S^2))/S - (32*Pi^2*(1 + S^2))/S + ((-38*Pi^2*S)/3 - (56*(1 + S^2))/S)*HPL[{2}, -S^2] - 76*S*HPL[{2}, -S^2]^2 + (36*(1 + S^2)*HPL[{3}, -S^2])/S + 56*S*HPL[{4}, -S^2] + (108*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 56*S*HPL[{3, 1}, -S^2] + (24*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-123*Pi^4*S)/20 - (4*(-4 + 15*S^2))/S - (2*Pi^2*(-5 + 31*S^2))/(3*S) + (6*(-1 + 5*S^2)*HPL[{3}, -S^2])/S + 34*S*HPL[{4}, -S^2] + (8*(16 + 3*S^2)*HPL[{2, 1}, -S^2])/S + 128*S*HPL[{3, 1}, -S^2] - 312*S*HPL[{2, 1, 1}, -S^2] + (8*(1 + 3*S^2)*Zeta[3])/S) + HPL[{0}, S^2]^2*(-30*S - 10*Pi^2*S - 3*Pi^4*S - (26*(1 + S^2)*HPL[{1}, -S^2]^3)/S - 17*S*HPL[{1}, -S^2]^4 + ((-79*Pi^2*S)/6 - (2*(-1 + 16*S^2))/S)*HPL[{2}, -S^2] - (41*S*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*((-44*Pi^2*S)/3 - (44*(1 + S^2))/S - 38*S*HPL[{2}, -S^2]) + ((-2 - 3*S^2)*HPL[{3}, -S^2])/S - 5*S*HPL[{4}, -S^2] + (2*(37 + 3*S^2)*HPL[{2, 1}, -S^2])/S + 88*S*HPL[{3, 1}, -S^2] - 180*S*HPL[{2, 1, 1}, -S^2] - 8*S*Zeta[3] + HPL[{1}, -S^2]*((-54*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/(3*S) - (35*(1 + S^2)*HPL[{2}, -S^2])/S + 6*S*HPL[{3}, -S^2] + 76*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3])) + HPL[{0}, S^2]*(-300*S - 41*Pi^2*S - (107*Pi^4*S)/18 - (30*(1 + S^2)*HPL[{1}, -S^2]^4)/S - 24*S*HPL[{1}, -S^2]^5 - (2*(1 + 18*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*(-30*Pi^2*S - (208*(1 + S^2))/(3*S) - 104*S*HPL[{2}, -S^2]) + ((8*Pi^2*S)/3 - (4*(3 + 2*S^2))/S)*HPL[{3}, -S^2] - (4*HPL[{4}, -S^2])/S + 4*S*HPL[{5}, -S^2] + ((-20*Pi^2*S)/3 + (8*(22 + 3*S^2))/S)*HPL[{2, 1}, -S^2] + (4*(-2 + 35*S^2)*HPL[{3, 1}, -S^2])/S - 16*S*HPL[{3, 2}, -S^2] - 52*S*HPL[{4, 1}, -S^2] - (16*(-1 + 18*S^2)*HPL[{2, 1, 1}, -S^2])/S + 8*S*HPL[{2, 2, 1}, -S^2] + 64*S*HPL[{3, 1, 1}, -S^2] - 96*S*HPL[{2, 1, 1, 1}, -S^2] + (20*S + 2*Pi^2*S)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(2 - 63*S^2))/(3*S) - (4*(2 + 21*S^2))/S + 8*S*HPL[{3}, -S^2] - 4*S*HPL[{2, 1}, -S^2] + 24*S*Zeta[3]) + HPL[{1}, -S^2]^2*((-132*(1 + S^2))/S - (79*Pi^2*(1 + S^2))/(3*S) - (78*(1 + S^2)*HPL[{2}, -S^2])/S - 4*S*HPL[{3}, -S^2] + 312*S*HPL[{2, 1}, -S^2] + 28*S*Zeta[3]) + HPL[{1}, -S^2]*((-377*Pi^4*S)/45 - (188*(1 + S^2))/S - (31*Pi^2*(1 + S^2))/S + ((-116*Pi^2*S)/3 - (88*(1 + S^2))/S)*HPL[{2}, -S^2] - 76*S*HPL[{2}, -S^2]^2 - 24*S*HPL[{4}, -S^2] + (156*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 312*S*HPL[{3, 1}, -S^2] - 624*S*HPL[{2, 1, 1}, -S^2] + (12*(1 + S^2)*Zeta[3])/S)) - 40*S*Zeta[5] + HPL[{1}, -S^2]*((-300*(1 + S^2))/S - (40*Pi^2*(1 + S^2))/S - (89*Pi^4*(1 + S^2))/(15*S) - (38*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (32*Pi^2*S + (36*(1 + S^2))/S)*HPL[{3}, -S^2] - (2*(1 + S^2)*HPL[{4}, -S^2])/S + 44*S*HPL[{5}, -S^2] + ((76*Pi^2*S)/3 + (112*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (80*(1 + S^2)*HPL[{3, 1}, -S^2])/S - 304*S*HPL[{3, 2}, -S^2] - 1024*S*HPL[{4, 1}, -S^2] - (216*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 608*S*HPL[{2, 2, 1}, -S^2] - 1104*S*HPL[{3, 1, 1}, -S^2] + ((86*Pi^2*S)/3 + (32*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-60*(1 + S^2))/S - (62*Pi^2*(1 + S^2))/(3*S) + 152*S*HPL[{3}, -S^2] + 304*S*HPL[{2, 1}, -S^2] + 152*S*Zeta[3]) + 188*S*Zeta[5])) - 150*S*Zeta[7];
E4vwuT2F0=-300 + (Pi^2*(-37 - 81*S^2))/6 + (11857*Pi^6)/(15120*(1 + S^2)) - (7*Pi^4*(-5 + 29*S^2))/180 - HPL[{0}, S^2]^7/24 + HPL[{0}, S^2]^6*((2 + S^2)/(16*(1 + S^2)) + HPL[{1}, -S^2]/8) + ((94*Pi^2)/15 + (4*(1 + S^2))/5)*HPL[{1}, -S^2]^5 - (4*(-1 + S^2)*HPL[{1}, -S^2]^6)/(1 + S^2) + (16*HPL[{1}, -S^2]^7)/7 + HPL[{0}, S^2]^5*((-5*Pi^2)/24 + (3*(1 + S^2))/4 + ((9 + S^2)*HPL[{1}, -S^2])/(12*(1 + S^2)) + (2*HPL[{1}, -S^2]^2)/3 + (3*HPL[{2}, -S^2])/4) + (2*HPL[{2}, -S^2]^3)/3 + ((-7 - 13*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((-5*Pi^2)/3 + 4*(-3 + 20*S^2))*HPL[{5}, -S^2] + ((-11 + 10*S^2)*HPL[{6}, -S^2])/(1 + S^2) - 398*HPL[{7}, -S^2] + (76*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((8*Pi^2)/3 + 16*(1 + S^2))*HPL[{3, 2}, -S^2] + ((64*Pi^2)/3 + 8*(4 + 5*S^2))*HPL[{4, 1}, -S^2] - (3*(5 + 11*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) + 76*HPL[{4, 3}, -S^2] - (4*(25 + 54*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + 198*HPL[{5, 2}, -S^2] + 400*HPL[{6, 1}, -S^2] + ((56*Pi^2)/3 + 16*(1 + S^2))*HPL[{2, 2, 1}, -S^2] + ((104*Pi^2)/3 + 16*(3 + 2*S^2))*HPL[{3, 1, 1}, -S^2] + 24*HPL[{3, 1, 2}, -S^2] + 40*HPL[{3, 2, 1}, -S^2] - 172*HPL[{3, 2, 2}, -S^2] - 432*HPL[{3, 3, 1}, -S^2] + (28*(5 + 9*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) - 384*HPL[{4, 1, 2}, -S^2] - 1200*HPL[{4, 2, 1}, -S^2] - 2344*HPL[{5, 1, 1}, -S^2] + ((-40*Pi^2)/3 + 48*S^2)*HPL[{2, 1, 1, 1}, -S^2] - (16*(5 + 12*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) + 160*HPL[{3, 1, 1, 2}, -S^2] + 160*HPL[{3, 1, 2, 1}, -S^2] + 160*HPL[{3, 2, 1, 1}, -S^2] + 672*HPL[{4, 1, 1, 1}, -S^2] + 272*HPL[{2, 1, 1, 1, 1}, -S^2] - 320*HPL[{2, 1, 2, 1, 1}, -S^2] - 960*HPL[{2, 2, 1, 1, 1}, -S^2] - 2112*HPL[{3, 1, 1, 1, 1}, -S^2] + ((-128*Pi^2)/9 - (44*HPL[{0}, S^2]^2)/3 + HPL[{0}, S^2]*((8*(-4 + 5*S^2))/(3*(1 + S^2)) - 48*HPL[{1}, -S^2]) + (24*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2) - 48*HPL[{1}, -S^2]^2)*Log[T]^5 + ((-4*(-1 + S^2))/(1 + S^2) + (16*HPL[{0}, S^2])/3 + 16*HPL[{1}, -S^2])*Log[T]^6 - (16*Log[T]^7)/3 + HPL[{2, 1, 1}, -S^2]*(-16/S^2 + (2*Pi^2*(43 + 5*S^2))/(3*(1 + S^2)) - 80*Zeta[3]) + HPL[{1}, -S^2]^4*((Pi^2*(28 - 19*S^2))/(3*(1 + S^2)) + 2*(1 + S^2) + 18*HPL[{2}, -S^2] - 60*HPL[{3}, -S^2] - 52*Zeta[3]) + Log[T]^4*(-4 + (Pi^2*(82 - 59*S^2))/(9*(1 + S^2)) + (56*HPL[{0}, S^2]^3)/9 + ((94*Pi^2)/3 + 4*(1 + S^2))*HPL[{1}, -S^2] - (60*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + 80*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*((37 - 14*S^2)/(3*(1 + S^2)) + 34*HPL[{1}, -S^2]) + (34*HPL[{2}, -S^2])/3 + HPL[{0}, S^2]*((116*Pi^2)/9 + 4*(1 + S^2) - (60*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2) + 120*HPL[{1}, -S^2]^2 + 52*HPL[{2}, -S^2]) - (64*HPL[{3}, -S^2])/3 - (56*Zeta[3])/3) + HPL[{2}, -S^2]^2*(-2 + (Pi^2*(63 - 55*S^2))/(12*(1 + S^2)) - 26*HPL[{3}, -S^2] - 12*Zeta[3]) + ((157*Pi^4)/45 - 16*(-2 + S^2) - (4*Pi^2*(-2 + 3*S^2))/3)*Zeta[3] + (6*Zeta[3]^2)/(1 + S^2) + HPL[{0}, S^2]^4*((-2 - 29*S^2)/12 + (Pi^2*(141 + 59*S^2))/(144*(1 + S^2)) + (37*HPL[{1}, -S^2]^2)/(12*(1 + S^2)) + (37*HPL[{1}, -S^2]^3)/18 + ((39 + 14*S^2)*HPL[{2}, -S^2])/(24*(1 + S^2)) + HPL[{1}, -S^2]*((41*Pi^2)/36 + (1 + S^2)/12 + (25*HPL[{2}, -S^2])/12) - HPL[{3}, -S^2]/2 + (3*HPL[{2, 1}, -S^2])/2 + (15*Zeta[3])/2) + HPL[{3, 1}, -S^2]*((Pi^2*(-39 - 17*S^2))/(3*(1 + S^2)) - 8*(1 + S^2) + 32*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(39 + 71*S^2))/(6*(1 + S^2)) - (2*(-9 + 17*S^2 + 25*S^4))/S^2 + 120*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{3}, -S^2]*((4*Pi^2)/3 - (49*Pi^4)/90 + (2*(9 - S^2 + 22*S^4))/S^2 - 44*HPL[{4}, -S^2] - (4*(-25 + 13*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 32*HPL[{3, 1}, -S^2] - 80*HPL[{2, 1, 1}, -S^2] + (8*S^2*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((1547*Pi^4)/270 + (4*Pi^2*(1 + S^2))/3 + (8*(1 + S^2)*(-1 + 3*S^2))/(3*S^2) + (76*Pi^2*HPL[{2}, -S^2])/9 + (152*HPL[{2}, -S^2]^2)/3 + (24*(-1 + 4*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (112*HPL[{4}, -S^2])/3 - 72*HPL[{2, 1}, -S^2] + (112*HPL[{3, 1}, -S^2])/3 + (8*(-2 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((5*Pi^4)/18 + (8*Pi^2*(-1 + S^2))/3 + 8*(3 + 2*S^2) + 80*HPL[{3, 1}, -S^2] + 160*HPL[{2, 1, 1}, -S^2] - (4*(-9 + 29*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^3*((-287*Pi^4)/1080 + (15 + 32*S^2)/3 + (Pi^2*(51 + 49*S^2))/18 - (2*(-34 + 11*S^2)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)) + 5*HPL[{1}, -S^2]^4 + ((38*Pi^2)/9 + S^2/3)*HPL[{2}, -S^2] + (25*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*(1 + (85*Pi^2)/18 + S^2 + (38*HPL[{2}, -S^2])/3) - (S^2*HPL[{3}, -S^2])/(1 + S^2) + 4*HPL[{4}, -S^2] + ((-23 + 15*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) - (62*HPL[{3, 1}, -S^2])/3 + (124*HPL[{2, 1, 1}, -S^2])/3 + HPL[{1}, -S^2]*((Pi^2*(79 - 6*S^2))/(18*(1 + S^2)) + (5*(1 + S^2))/3 - (2*(-14 + 5*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + 2*HPL[{3}, -S^2] - (76*HPL[{2, 1}, -S^2])/3 - (4*Zeta[3])/3) + ((39 + 41*S^2)*Zeta[3])/(3*(1 + S^2))) + Log[T]^3*(24 - (1874*Pi^4)/135 - (4*Pi^2*(1 + S^2))/3 - (55*HPL[{0}, S^2]^4)/9 + HPL[{0}, S^2]^3*(-10/(1 + S^2) - 20*HPL[{1}, -S^2]) + ((-188*Pi^2)/3 - 8*(1 + S^2))*HPL[{1}, -S^2]^2 + (80*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) - 80*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^2*((-220*Pi^2)/9 - 4*(1 + S^2) + (4*(-13 + 4*S^2)*HPL[{1}, -S^2])/(1 + S^2) - 68*HPL[{1}, -S^2]^2 - 44*HPL[{2}, -S^2]) + ((-44*Pi^2)/3 - 8*S^2)*HPL[{2}, -S^2] - 88*HPL[{2}, -S^2]^2 - (8*(-4 + 41*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (128*HPL[{4}, -S^2])/3 + (296*HPL[{2, 1}, -S^2])/3 - (128*HPL[{3, 1}, -S^2])/3 - (8*(2 + 41*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{0}, S^2]*(-8*(1 + S^2) + (10*Pi^2*(-17 + 10*S^2))/(9*(1 + S^2)) + (120*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - 160*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*(-60*Pi^2 - 8*(1 + S^2) - 208*HPL[{2}, -S^2]) + (4*(-29 + 49*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) - (16*HPL[{3}, -S^2])/3 + 208*HPL[{2, 1}, -S^2] + (64*Zeta[3])/3) + HPL[{1}, -S^2]*(-8*(1 + S^2) + (4*Pi^2*(-28 + 19*S^2))/(3*(1 + S^2)) - 72*HPL[{2}, -S^2] + 240*HPL[{3}, -S^2] + 208*Zeta[3])) + Log[T]^2*(-88 - (7*Pi^4*(-162 + 59*S^2))/(180*(1 + S^2)) + HPL[{0}, S^2]^5 + ((188*Pi^2)/3 + 8*(1 + S^2))*HPL[{1}, -S^2]^3 - (60*(-1 + S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) + 48*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^4*((51 + 14*S^2)/(12*(1 + S^2)) + (37*HPL[{1}, -S^2])/6) - (38*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{0}, S^2]^3*((58*Pi^2)/9 + (4*(3 + 2*S^2))/3 - (2*(-34 + 11*S^2)*HPL[{1}, -S^2])/(3*(1 + S^2)) + 30*HPL[{1}, -S^2]^2 + (62*HPL[{2}, -S^2])/3) + ((-32*Pi^2)/3 - 8*S^2)*HPL[{3}, -S^2] + (2*(23 + 51*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 52*HPL[{5}, -S^2] + ((-20*Pi^2)/3 + 24*S^2)*HPL[{2, 1}, -S^2] - (8*(5 + 12*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 80*HPL[{3, 2}, -S^2] + 336*HPL[{4, 1}, -S^2] + 136*HPL[{2, 1, 1}, -S^2] + 160*HPL[{2, 2, 1}, -S^2] + 224*HPL[{3, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*(12*(1 + S^2) - (2*Pi^2*(-28 + 19*S^2))/(1 + S^2) + 108*HPL[{2}, -S^2] - 360*HPL[{3}, -S^2] - 312*Zeta[3]) + HPL[{2}, -S^2]*(-8/S^2 + (Pi^2*(43 + 5*S^2))/(3*(1 + S^2)) - 40*HPL[{3}, -S^2] - 80*HPL[{2, 1}, -S^2] - 40*Zeta[3]) + (-4*Pi^2 - 24*(-1 + S^2))*Zeta[3] + HPL[{0}, S^2]^2*(6 + (44*Pi^2)/(3*(1 + S^2)) - (6*(-13 + 4*S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + 68*HPL[{1}, -S^2]^3 - (2*(-13 + 6*S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((88*Pi^2)/3 + 6*(1 + S^2) + 76*HPL[{2}, -S^2]) - 20*HPL[{2, 1}, -S^2] + 16*Zeta[3]) + HPL[{1}, -S^2]*((1547*Pi^4)/90 + 4*Pi^2*(1 + S^2) + (8*(1 + S^2)*(-1 + 3*S^2))/S^2 + (76*Pi^2*HPL[{2}, -S^2])/3 + 152*HPL[{2}, -S^2]^2 + (72*(-1 + 4*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 112*HPL[{4}, -S^2] - 216*HPL[{2, 1}, -S^2] + 112*HPL[{3, 1}, -S^2] + (24*(-2 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]*((362*Pi^4)/45 + 4*(1 + 6*S^2) + (2*Pi^2*(9 + 7*S^2))/3 - (120*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) + 120*HPL[{1}, -S^2]^4 + ((140*Pi^2)/3 + 12*S^2)*HPL[{2}, -S^2] + 76*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*(90*Pi^2 + 12*(1 + S^2) + 312*HPL[{2}, -S^2]) + (4*(4 + 3*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 16*HPL[{4}, -S^2] + (4*(-49 + 29*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 304*HPL[{3, 1}, -S^2] + 624*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*(12*(1 + S^2) - (2*Pi^2*(-79 + 56*S^2))/(3*(1 + S^2)) - (156*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + 8*HPL[{3}, -S^2] - 624*HPL[{2, 1}, -S^2] - 56*Zeta[3]) + (4*(4 + 11*S^2)*Zeta[3])/(1 + S^2))) + HPL[{1}, -S^2]^2*((Pi^4*(1068 - 479*S^2))/(180*(1 + S^2)) + (4*Pi^2*(1 + S^2))/3 + (12*(1 + S^2)*(-1 + 2*S^2))/S^2 - (38*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) - 32*Pi^2*HPL[{3}, -S^2] + (2*(1 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 44*HPL[{5}, -S^2] - (76*Pi^2*HPL[{2, 1}, -S^2])/3 - (8*(10 + 17*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 304*HPL[{3, 2}, -S^2] + 1024*HPL[{4, 1}, -S^2] + 216*HPL[{2, 1, 1}, -S^2] + 608*HPL[{2, 2, 1}, -S^2] + 1104*HPL[{3, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-4*(1 + S^2)^2)/S^2 + (2*Pi^2*(31 + 12*S^2))/(3*(1 + S^2)) - 152*HPL[{3}, -S^2] - 304*HPL[{2, 1}, -S^2] - 152*Zeta[3]) - (86*Pi^2*Zeta[3])/3 - 188*Zeta[5]) + ((110*Pi^2)/3 - 8*(-5 + 4*S^2))*Zeta[5] + HPL[{2}, -S^2]*((-2*Pi^2*(2 + S^2))/(3*S^2) + (Pi^4*(84 + 17*S^2))/(40*(1 + S^2)) + (-13 + 22*S^2 - 81*S^4)/S^2 + ((-4*Pi^2)/3 - 8*(1 + S^2))*HPL[{3}, -S^2] + ((23 + 41*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 74*HPL[{5}, -S^2] + ((-28*Pi^2)/3 - 8*(1 + S^2))*HPL[{2, 1}, -S^2] + (4*(-27 + 11*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 92*HPL[{3, 2}, -S^2] + 192*HPL[{4, 1}, -S^2] - (152*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 80*HPL[{3, 1, 1}, -S^2] - 160*HPL[{2, 1, 1, 1}, -S^2] + ((-2*Pi^2)/3 - 8*(2 + S^2))*Zeta[3] + 48*Zeta[5]) + HPL[{0}, S^2]^2*((7 - 81*S^2)/2 + (Pi^2*(1 - 29*S^2))/6 + (7*Pi^4*(221 + 59*S^2))/(720*(1 + S^2)) + ((13 - 4*S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) + (34*HPL[{1}, -S^2]^5)/5 + ((25 - 17*S^2)*HPL[{2}, -S^2]^2)/(4*(1 + S^2)) + HPL[{1}, -S^2]^3*((88*Pi^2)/9 + 2*(1 + S^2) + (76*HPL[{2}, -S^2])/3) + (-Pi^2 + 2*(2 + S^2))*HPL[{3}, -S^2] + (2*(4 + 5*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 18*HPL[{5}, -S^2] + ((4*Pi^2)/3 + 2*(-4 + S^2))*HPL[{2, 1}, -S^2] + ((-29 + 7*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 12*HPL[{3, 2}, -S^2] - 20*HPL[{4, 1}, -S^2] - (4*(-13 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 16*HPL[{2, 2, 1}, -S^2] + 48*HPL[{3, 1, 1}, -S^2] - 40*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*(1 + S^2 - (2*Pi^2*(-19 + 3*S^2))/(3*(1 + S^2)) + ((35 - 3*S^2)*HPL[{2}, -S^2])/(1 + S^2) - 6*HPL[{3}, -S^2] - 76*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + ((49*Pi^2)/3 - 2*(-1 + 3*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-2*(1 + S^2))/S^2 + (Pi^2*(65 + 2*S^2))/(12*(1 + S^2)) + 6*HPL[{3}, -S^2] - 8*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + HPL[{1}, -S^2]*((63*Pi^4)/20 + (2*Pi^2*(1 + S^2))/3 - (2*(1 + S^2))/S^2 + ((21*Pi^2)/2 + 2*(1 + S^2))*HPL[{2}, -S^2] + 21*HPL[{2}, -S^2]^2 + (2*(2 + 5*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 4*HPL[{4}, -S^2] + (2*(-35 + 3*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 72*HPL[{3, 1}, -S^2] + 152*HPL[{2, 1, 1}, -S^2] + (2*(1 + 5*S^2)*Zeta[3])/(1 + S^2)) + 110*Zeta[5]) + HPL[{1}, -S^2]*((11857*Pi^6)/7560 + (Pi^4*(1 + S^2))/2 + (2*Pi^2*(1 + S^2)*(-2 + 3*S^2))/(3*S^2) + (4*(1 + S^2)*(-11 + 36*S^2))/S^2 + ((59*Pi^2)/3 + 2*(1 + S^2))*HPL[{2}, -S^2]^2 + 12*HPL[{3}, -S^2]^2 + ((-32*Pi^2)/3 + 8*(1 + S^2))*HPL[{4}, -S^2] + (4*(8 + 19*S^2)*HPL[{5}, -S^2])/(1 + S^2) - 42*HPL[{6}, -S^2] - 304*HPL[{2, 1}, -S^2]^2 + ((-44*Pi^2)/3 - 8*(1 + S^2))*HPL[{3, 1}, -S^2] - (16*(-5 + 14*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (4*(-59 + 197*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 36*HPL[{4, 2}, -S^2] + 232*HPL[{5, 1}, -S^2] + (152*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - (304*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (48*(-16 + 7*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 224*HPL[{4, 1, 1}, -S^2] - 432*HPL[{2, 1, 1, 1}, -S^2] + 224*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((2*Pi^2*(-7 + 41*S^2))/(3*(1 + S^2)) + 304*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + (-8*(1 + S^2) + (2*Pi^2*(-5 + 38*S^2))/(3*(1 + S^2)))*Zeta[3] + 12*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((8*(1 + S^2)^2)/S^2 - (4*Pi^2*(31 + 12*S^2))/(3*(1 + S^2)) + 304*Zeta[3]) + HPL[{2}, -S^2]*((67*Pi^4)/20 + (2*Pi^2*(1 + S^2))/3 - (4*(1 + S^2)*(2 + 3*S^2))/S^2 + (8*(-5 + 14*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 36*HPL[{4}, -S^2] + (152*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 304*HPL[{3, 1}, -S^2] + 608*HPL[{2, 1, 1}, -S^2] + (8*(-4 + 15*S^2)*Zeta[3])/(1 + S^2)) + (4*(2 + 49*S^2)*Zeta[5])/(1 + S^2)) + HPL[{0}, S^2]*((-1273*Pi^6)/22680 + 16*(-4 + 9*S^2) + (2*Pi^2*(8 + 19*S^2))/3 + (Pi^4*(22 + 21*S^2))/9 - (12*(-1 + S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) + 8*HPL[{1}, -S^2]^6 + ((21*Pi^2)/2 + 2*(3 + S^2))*HPL[{2}, -S^2]^2 + (34*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*(15*Pi^2 + 2*(1 + S^2) + 52*HPL[{2}, -S^2]) + 4*HPL[{3}, -S^2]^2 + ((16*Pi^2)/3 - 4*(2 + S^2))*HPL[{4}, -S^2] - (16*(1 + 2*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 88*HPL[{6}, -S^2] - 152*HPL[{2, 1}, -S^2]^2 + (8 - 46*Pi^2)*HPL[{3, 1}, -S^2] - (8*(1 + 3*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (24*(1 + 2*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 56*HPL[{5, 1}, -S^2] + ((280*Pi^2)/3 + 24*S^2)*HPL[{2, 1, 1}, -S^2] - (16*(-10 + 9*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (8*(-64 + 51*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 272*HPL[{3, 2, 1}, -S^2] + 848*HPL[{4, 1, 1}, -S^2] + (8*(-49 + 29*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 608*HPL[{3, 1, 1, 1}, -S^2] + 1248*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^3*(4*(1 + S^2) - (2*Pi^2*(-79 + 56*S^2))/(9*(1 + S^2)) - (52*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (8*HPL[{3}, -S^2])/3 - 208*HPL[{2, 1}, -S^2] - (56*Zeta[3])/3) + HPL[{3}, -S^2]*(-4*S^2 + (4*Pi^2)/(3*(1 + S^2)) + 8*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + (8*(2 + S^2) + (Pi^2*(43 + 52*S^2))/(3*(1 + S^2)))*Zeta[3] - 28*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(8 + (4*Pi^2*(-18 + 11*S^2))/(3*(1 + S^2)) + 32*Zeta[3]) + HPL[{1}, -S^2]^2*((377*Pi^4)/45 + 2*Pi^2*(1 + S^2) + (4*(1 + S^2)*(-1 + 3*S^2))/S^2 + (116*Pi^2*HPL[{2}, -S^2])/3 + 76*HPL[{2}, -S^2]^2 - (4*S^2*HPL[{3}, -S^2])/(1 + S^2) + 24*HPL[{4}, -S^2] + (156*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 312*HPL[{3, 1}, -S^2] + 624*HPL[{2, 1, 1}, -S^2] + (4*(-3 + 4*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((161*Pi^4)/30 + (4*Pi^2*S^2)/3 + (4*(-2 + S^2 + 2*S^4))/S^2 + (4*(1 + 3*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 8*HPL[{4}, -S^2] + (8*(-10 + 9*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 144*HPL[{3, 1}, -S^2] + 304*HPL[{2, 1, 1}, -S^2] + (2*(7 + 13*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(525 - 229*S^2))/(90*(1 + S^2)) + (8*Pi^2*(1 + S^2))/3 + (12*(1 + S^2)*(-1 + 2*S^2))/S^2 - (38*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + ((8*Pi^2)/3 - 8*(1 + S^2))*HPL[{3}, -S^2] - (8*(-1 + 2*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 32*HPL[{5}, -S^2] - (232*Pi^2*HPL[{2, 1}, -S^2])/3 + (8*(-19 + 20*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 32*HPL[{3, 2}, -S^2] + 48*HPL[{4, 1}, -S^2] - (312*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 608*HPL[{2, 2, 1}, -S^2] + 1840*HPL[{3, 1, 1}, -S^2] - 1248*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(67 - 49*S^2))/(3*(1 + S^2)) + (4*(-1 + S^2)*(1 + S^2))/S^2 - 16*HPL[{3}, -S^2] - 304*HPL[{2, 1}, -S^2] - 24*Zeta[3]) + (-6*Pi^2 + 8*(1 + S^2))*Zeta[3] - 32*Zeta[5]) + (2*(47 + 55*S^2)*Zeta[5])/(1 + S^2)) + Log[T]*(200 - (12907*Pi^6)/2835 + (Pi^4*(-42 - 47*S^2))/45 + (4*Pi^2*(4 + S^2))/3 - (7*HPL[{0}, S^2]^6)/12 + HPL[{0}, S^2]^5*((-9 - 5*S^2)/(6*(1 + S^2)) - (4*HPL[{1}, -S^2])/3) + ((-94*Pi^2)/3 - 4*(1 + S^2))*HPL[{1}, -S^2]^4 + (24*(-1 + S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) - 16*HPL[{1}, -S^2]^6 + HPL[{0}, S^2]^4*((-40*Pi^2)/9 + (-3 - 2*S^2)/3 - (37*HPL[{1}, -S^2])/(6*(1 + S^2)) - (37*HPL[{1}, -S^2]^2)/6 - (17*HPL[{2}, -S^2])/3) - (104*Pi^2*HPL[{2}, -S^2]^2)/3 + 12*HPL[{3}, -S^2]^2 + (8*Pi^2 - 8*S^2)*HPL[{4}, -S^2] - (4*(16 + 27*S^2)*HPL[{5}, -S^2])/(1 + S^2) - 176*HPL[{6}, -S^2] + 528*HPL[{2, 1}, -S^2]^2 + (32*Pi^2 + 16*S^2)*HPL[{3, 1}, -S^2] + (16*(1 + 20*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (4*(9 + 265*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 40*HPL[{5, 1}, -S^2] + (-88*Pi^2 - 48*S^2)*HPL[{2, 1, 1}, -S^2] + (304*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (16*(-53 + 16*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 256*HPL[{4, 1, 1}, -S^2] + 592*HPL[{2, 1, 1, 1}, -S^2] - 256*HPL[{3, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*(-16*(2 + S^2) + (2*Pi^2*(81 + 43*S^2))/(3*(1 + S^2)) - 528*Zeta[3]) + HPL[{0}, S^2]^3*((-2*(7 + 3*S^2))/3 - (5*Pi^2*(27 + 10*S^2))/(18*(1 + S^2)) + (2*(-34 + 11*S^2)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)) - 20*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*((-85*Pi^2)/9 - 2*(1 + S^2) - (76*HPL[{2}, -S^2])/3) + ((-33 + 5*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + (28*HPL[{2, 1}, -S^2])/3 - (28*Zeta[3])/3) + (16*(-2 + S^2) - (2*Pi^2*(9 + 52*S^2))/(3*(1 + S^2)))*Zeta[3] - 32*Zeta[3]^2 + HPL[{3}, -S^2]*(8*(2 + S^2) - (4*Pi^2*(-1 + 23*S^2))/(3*(1 + S^2)) - 528*HPL[{2, 1}, -S^2] + 48*Zeta[3]) + HPL[{1}, -S^2]^3*(-8*(1 + S^2) + (4*Pi^2*(-28 + 19*S^2))/(3*(1 + S^2)) - 72*HPL[{2}, -S^2] + 240*HPL[{3}, -S^2] + 208*Zeta[3]) + HPL[{1}, -S^2]^2*((-1547*Pi^4)/90 - 4*Pi^2*(1 + S^2) - (8*(1 + S^2)*(-1 + 3*S^2))/S^2 - (76*Pi^2*HPL[{2}, -S^2])/3 - 152*HPL[{2}, -S^2]^2 - (72*(-1 + 4*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 112*HPL[{4}, -S^2] + 216*HPL[{2, 1}, -S^2] - 112*HPL[{3, 1}, -S^2] - (24*(-2 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((-314*Pi^4)/45 - (4*Pi^2*(-1 + 3*S^2))/3 + (8*(2 + 2*S^2 + S^4))/S^2 - (4*(5 + 43*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 48*HPL[{4}, -S^2] - (152*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 528*HPL[{3, 1}, -S^2] - 1056*HPL[{2, 1, 1}, -S^2] - (4*(-7 + 31*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^2*((-937*Pi^4)/90 + (Pi^2*(-9 - 7*S^2))/3 + 2*(-1 + 2*S^2) + (4*(-13 + 4*S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) - 34*HPL[{1}, -S^2]^4 + HPL[{1}, -S^2]^2*((-88*Pi^2)/3 - 6*(1 + S^2) - 76*HPL[{2}, -S^2]) + ((-67*Pi^2)/3 - 2*(-2 + 3*S^2))*HPL[{2}, -S^2] - 38*HPL[{2}, -S^2]^2 - (2*(2 + 5*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 8*HPL[{4}, -S^2] + (4*(22 + 3*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 128*HPL[{3, 1}, -S^2] - 264*HPL[{2, 1, 1}, -S^2] - (2*(7 + 11*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-2*(1 + S^2) + (4*Pi^2*(-19 + 3*S^2))/(3*(1 + S^2)) + (2*(-35 + 3*S^2)*HPL[{2}, -S^2])/(1 + S^2) + 12*HPL[{3}, -S^2] + 152*HPL[{2, 1}, -S^2] + 16*Zeta[3])) + HPL[{0}, S^2]*((-377*Pi^4)/(45*(1 + S^2)) - 16*(-1 + 3*S^2) - (4*Pi^2*(5 + 3*S^2))/3 + (60*(-1 + S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) - 48*HPL[{1}, -S^2]^5 + HPL[{1}, -S^2]^3*(-60*Pi^2 - 8*(1 + S^2) - 208*HPL[{2}, -S^2]) + (4*(-9 + 10*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + ((-4*Pi^2)/3 + 8*(-2 + S^2))*HPL[{3}, -S^2] + (8*(-2 + S^2)*HPL[{4}, -S^2])/(1 + S^2) + 8*HPL[{5}, -S^2] + ((184*Pi^2)/3 - 24*S^2)*HPL[{2, 1}, -S^2] - (8*(-14 + 25*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 48*HPL[{3, 2}, -S^2] - 80*HPL[{4, 1}, -S^2] + (8*(-29 + 49*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 608*HPL[{2, 2, 1}, -S^2] - 1856*HPL[{3, 1, 1}, -S^2] + 1248*HPL[{2, 1, 1, 1}, -S^2] + (-4*Pi^2 + 8*(-1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2*(-31 + 27*S^2))/(3*(1 + S^2)) - (8*(-1 + S^2 + S^4))/S^2 + 24*HPL[{3}, -S^2] + 304*HPL[{2, 1}, -S^2] + 16*Zeta[3]) + HPL[{1}, -S^2]^2*(-12*(1 + S^2) + (2*Pi^2*(-79 + 56*S^2))/(3*(1 + S^2)) + (156*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - 8*HPL[{3}, -S^2] + 624*HPL[{2, 1}, -S^2] + 56*Zeta[3]) + HPL[{1}, -S^2]*((-754*Pi^4)/45 - 4*Pi^2*(1 + S^2) - (8*(1 + S^2)*(-1 + 3*S^2))/S^2 - (232*Pi^2*HPL[{2}, -S^2])/3 - 152*HPL[{2}, -S^2]^2 + (8*S^2*HPL[{3}, -S^2])/(1 + S^2) - 48*HPL[{4}, -S^2] - (312*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 624*HPL[{3, 1}, -S^2] - 1248*HPL[{2, 1, 1}, -S^2] - (8*(-3 + 4*S^2)*Zeta[3])/(1 + S^2))) - (4*(8 + 55*S^2)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*((-8*Pi^2*(1 + S^2))/3 - (24*(1 + S^2)*(-1 + 2*S^2))/S^2 + (Pi^4*(-1068 + 479*S^2))/(90*(1 + S^2)) + (76*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + 64*Pi^2*HPL[{3}, -S^2] - (4*(1 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 88*HPL[{5}, -S^2] + (152*Pi^2*HPL[{2, 1}, -S^2])/3 + (16*(10 + 17*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 608*HPL[{3, 2}, -S^2] - 2048*HPL[{4, 1}, -S^2] - 432*HPL[{2, 1, 1}, -S^2] - 1216*HPL[{2, 2, 1}, -S^2] - 2208*HPL[{3, 1, 1}, -S^2] + (172*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*((8*(1 + S^2)^2)/S^2 - (4*Pi^2*(31 + 12*S^2))/(3*(1 + S^2)) + 304*HPL[{3}, -S^2] + 608*HPL[{2, 1}, -S^2] + 304*Zeta[3]) + 376*Zeta[5])) + 300*Zeta[7];
E4vwuT2F2=-75/32 + (Pi^2*(-77 - 552*S^2))/96 + (Pi^4*(-111 - 355*S^2))/240 + (Pi^6*(-18423*S^2 - 6566*S^4))/(30240*(1 + S^2)) + ((-47*Pi^2*S^2)/30 + (-17 - 84*S^2 - 67*S^4)/(15*S^2))*HPL[{1}, -S^2]^5 + ((-1 - S^2 - 11*S^4 - 3*S^6)*HPL[{1}, -S^2]^6)/(2*S^2*(1 + S^2)) - (4*S^2*HPL[{1}, -S^2]^7)/7 + HPL[{0}, S^2]^6*(-S^2/(32*(1 + S^2)) - (S^2*HPL[{1}, -S^2])/32) + ((6 - 41*S^4)*HPL[{2}, -S^2]^3)/(12*S^2) + HPL[{0}, S^2]^5*(-(Pi^2*S^2)/36 - (3*(1 + 3*S^2))/32 + ((-9 - 9*S^2 - 59*S^4 - 27*S^6)*HPL[{1}, -S^2])/(96*S^2*(1 + S^2)) - (S^2*HPL[{1}, -S^2]^2)/6 - (S^2*HPL[{2}, -S^2])/6) + ((2 + 2*S^2 - 11*S^4 + S^6)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((47*Pi^2*S^2)/12 + (-21 - 4*S^2 - 37*S^4)/(4*S^2))*HPL[{5}, -S^2] + ((5 + 5*S^2 + 62*S^4 + 41*S^6)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)) + 53*S^2*HPL[{7}, -S^2] + ((3 + 3*S^2 + 126*S^4 + 50*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + HPL[{4}, -S^2]*((-4 + 45*S^2 - 31*S^4)/(8*S^2) + (Pi^2*(-11 - 11*S^2 + 68*S^4 + 4*S^6))/(24*S^2*(1 + S^2)) - S^2*HPL[{2, 1}, -S^2]) + ((-83*Pi^2*S^2)/6 + (7 - 68*S^2 - 97*S^4)/(8*S^2))*HPL[{3, 2}, -S^2] + ((-93*Pi^2*S^2)/2 + (-5 - 106*S^2 - 150*S^4)/(4*S^2))*HPL[{4, 1}, -S^2] - (3*(1 + S^2 + 18*S^4 + 6*S^6)*HPL[{4, 2}, -S^2])/(4*S^2*(1 + S^2)) - 5*S^2*HPL[{4, 3}, -S^2] + ((2 + 2*S^2 - 63*S^4 - 5*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) - (33*S^2*HPL[{5, 2}, -S^2])/2 - 71*S^2*HPL[{6, 1}, -S^2] + ((-38*Pi^2*S^2)/3 + (-27 - 94*S^2 - 10*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((-16*Pi^2*S^2)/3 + (-141 - 532*S^2 + S^4)/(2*S^2))*HPL[{3, 1, 1}, -S^2] + (3*(-1 + 3*S^4)*HPL[{3, 1, 2}, -S^2])/(2*S^2) + ((21 - 155*S^4)*HPL[{3, 2, 1}, -S^2])/(2*S^2) + 155*S^2*HPL[{3, 2, 2}, -S^2] + 472*S^2*HPL[{3, 3, 1}, -S^2] + ((31 + 31*S^2 - 180*S^4 - 236*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 469*S^2*HPL[{4, 1, 2}, -S^2] + 1429*S^2*HPL[{4, 2, 1}, -S^2] + 2934*S^2*HPL[{5, 1, 1}, -S^2] + ((-104*Pi^2*S^2)/3 - (2*(-23 - 91*S^2 + 16*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - 152*S^2*HPL[{2, 2, 2, 1}, -S^2] + (2*(-11 - 11*S^2 + 70*S^4 + 98*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 140*S^2*HPL[{3, 1, 1, 2}, -S^2] + 140*S^2*HPL[{3, 1, 2, 1}, -S^2] + 596*S^2*HPL[{3, 2, 1, 1}, -S^2] + 1704*S^2*HPL[{4, 1, 1, 1}, -S^2] - (8*(-4 + 55*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + 296*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] + 888*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] + 2192*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] - 720*S^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (3 + Pi^2*S^2 + 3*S^2*HPL[{0}, S^2]^2 + (3*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) + 12*S^2*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((3*S^2*(7 + 3*S^2))/(1 + S^2) + 12*S^2*HPL[{1}, -S^2]) + 6*S^2*HPL[{2}, -S^2])*Log[T]^5 + ((-4*S^2)/(1 + S^2) - 4*S^2*HPL[{0}, S^2] - 4*S^2*HPL[{1}, -S^2])*Log[T]^6 + ((157*Pi^4*S^2)/180 + (5*Pi^2*(2 + 3*S^2))/24 + (46 + 31*S^2)/8)*Zeta[3] + ((2*S^2 + 5*S^4)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((-59 - 28*S^2 + 441*S^4)/(8*S^2) + (Pi^2*(-11 - 11*S^2 + 251*S^4 + 207*S^6))/(12*S^2*(1 + S^2)) - 76*S^2*Zeta[3]) + HPL[{0}, S^2]^4*((-7*(1 + 10*S^2))/48 + (Pi^2*(-137*S^2 - 55*S^4))/(288*(1 + S^2)) - (37*(1 + S^2 + 7*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(96*S^2*(1 + S^2)) - (37*S^2*HPL[{1}, -S^2]^3)/72 - (5*S^2*(16 + 11*S^2)*HPL[{2}, -S^2])/(48*(1 + S^2)) + HPL[{1}, -S^2]*((-41*Pi^2*S^2)/144 - (7*(1 + 10*S^2 + 9*S^4))/(48*S^2) - (25*S^2*HPL[{2}, -S^2])/48) + (3*S^2*HPL[{3}, -S^2])/16 - (3*S^2*HPL[{2, 1}, -S^2])/8 - (7*S^2*Zeta[3])/24) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(53 + 285*S^2))/(24*S^2) + (Pi^2*(-7 - 7*S^2 - 68*S^4 - 21*S^6))/(6*S^2*(1 + S^2)) - (9*(1 + 3*S^4)*HPL[{2}, -S^2])/(4*S^2) + 15*S^2*HPL[{3}, -S^2] + 13*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((3 - 74*S^2 - 230*S^4)/(16*S^2) + (Pi^2*(-2 - 2*S^2 - 217*S^4 - 99*S^6))/(24*S^2*(1 + S^2)) + (41*S^2*HPL[{3}, -S^2])/2 - 19*S^2*HPL[{2, 1}, -S^2] + 18*S^2*Zeta[3]) + Log[T]^4*(-13/3 + (Pi^2*(-196*S^2 - 55*S^4))/(18*(1 + S^2)) - (23*S^2*HPL[{0}, S^2]^3)/9 + ((-47*Pi^2*S^2)/6 + (-17 - 84*S^2 - 67*S^4)/(3*S^2))*HPL[{1}, -S^2] - (15*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(2*S^2*(1 + S^2)) - 20*S^2*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*(-(S^2*(106 + 55*S^2))/(6*(1 + S^2)) - (17*S^2*HPL[{1}, -S^2])/2) + ((4 - 55*S^4)*HPL[{2}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((-68*Pi^2*S^2)/9 + (-45 - 134*S^2)/6 - (15*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)) - 30*S^2*HPL[{1}, -S^2]^2 - 28*S^2*HPL[{2}, -S^2]) + (89*S^2*HPL[{3}, -S^2])/3 - 30*S^2*HPL[{2, 1}, -S^2] + 30*S^2*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((13 - 20*S^2 - 230*S^4)/(2*S^2) + (Pi^2*(5 + 5*S^2 - 149*S^4 - 111*S^6))/(3*S^2*(1 + S^2)) + 152*S^2*Zeta[3]) + HPL[{3}, -S^2]*((103*Pi^4*S^2)/90 + (Pi^2*(23 + 8*S^2 + 43*S^4))/(48*S^2) + (96 + 80*S^2 + 95*S^4)/(16*S^2) + S^2*HPL[{4}, -S^2] + ((-23 - 23*S^2 - 159*S^4 - 7*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 78*S^2*HPL[{3, 1}, -S^2] + 164*S^2*HPL[{2, 1, 1}, -S^2] + (4*S^2*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((-7*Pi^4*S^2)/5 + (14 + 426*S^2 - 31*S^4)/(8*S^2) + (Pi^2*(52 + 190*S^2 - 15*S^4))/(12*S^2) - 88*S^2*HPL[{3, 1}, -S^2] - 148*S^2*HPL[{2, 1, 1}, -S^2] - (2*(3 + 3*S^2 + 39*S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^3*((-1547*Pi^4*S^2)/1080 - (Pi^2*(1 + S^2)*(21 + 83*S^2))/(12*S^2) - ((1 + S^2)*(95 + 629*S^2))/(24*S^2) + ((-19*Pi^2*S^2)/9 + (-7 - 53*S^2 - 46*S^4)/(3*S^2))*HPL[{2}, -S^2] - (38*S^2*HPL[{2}, -S^2]^2)/3 + (3*(1 + S^2 + 23*S^4 + 3*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (28*S^2*HPL[{4}, -S^2])/3 + (9*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 - (28*S^2*HPL[{3, 1}, -S^2])/3 + (2*(1 + S^2 + 29*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + Log[T]^3*(11/2 + (781*Pi^4*S^2)/540 + (2*Pi^2*(7 + 9*S^2))/3 + (37*S^2*HPL[{0}, S^2]^4)/36 + ((47*Pi^2*S^2)/3 + (2*(17 + 84*S^2 + 67*S^4))/(3*S^2))*HPL[{1}, -S^2]^2 + (10*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) + 20*S^2*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*((S^2*(101 + 56*S^2))/(9*(1 + S^2)) + 5*S^2*HPL[{1}, -S^2]) + (10*Pi^2*S^2 + (-3 + 5*S^2 + 36*S^4)/S^2)*HPL[{2}, -S^2] + 13*S^2*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^2*((41*Pi^2*S^2)/9 + (13 + 36*S^2)/2 + ((13 + 13*S^2 + 107*S^4 + 39*S^6)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)) + 17*S^2*HPL[{1}, -S^2]^2 + 15*S^2*HPL[{2}, -S^2]) + ((-1 - S^2 - 232*S^4 - 52*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (32*S^2*HPL[{4}, -S^2])/3 + (2*(-35 + 29*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (152*S^2*HPL[{3, 1}, -S^2])/3 + 120*S^2*HPL[{2, 1, 1}, -S^2] - (2*(107*S^2 + 29*S^4)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(53 + 285*S^2))/(6*S^2) + (2*Pi^2*(7 + 7*S^2 + 68*S^4 + 21*S^6))/(3*S^2*(1 + S^2)) + (9*(1 + 3*S^4)*HPL[{2}, -S^2])/S^2 - 60*S^2*HPL[{3}, -S^2] - 52*S^2*Zeta[3]) + HPL[{0}, S^2]*((64 + 285*S^2)/6 + (Pi^2*(517*S^2 + 247*S^4))/(18*(1 + S^2)) + (15*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) + 40*S^2*HPL[{1}, -S^2]^3 + (2*(-1 - S^2 + 142*S^4 + 64*S^6)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)) + HPL[{1}, -S^2]*(15*Pi^2*S^2 + (2*(17 + 84*S^2 + 67*S^4))/(3*S^2) + 52*S^2*HPL[{2}, -S^2]) - (10*S^2*HPL[{3}, -S^2])/3 + 8*S^2*HPL[{2, 1}, -S^2] - (28*S^2*Zeta[3])/3)) + HPL[{0}, S^2]^3*((-403*Pi^4*S^2)/2160 + (-47 - 565*S^2)/96 + (Pi^2*(-158 - 509*S^2))/288 + ((-17 - 17*S^2 - 141*S^4 - 51*S^6)*HPL[{1}, -S^2]^3)/(18*S^2*(1 + S^2)) - (5*S^2*HPL[{1}, -S^2]^4)/4 + ((-41*Pi^2*S^2)/36 + (-56 - 209*S^2)/48)*HPL[{2}, -S^2] - (35*S^2*HPL[{2}, -S^2]^2)/24 + HPL[{1}, -S^2]^2*((-85*Pi^2*S^2)/72 + (-35 - 256*S^2 - 221*S^4)/(48*S^2) - (19*S^2*HPL[{2}, -S^2])/6) + (S^2*(-3 + S^2)*HPL[{3}, -S^2])/(8*(1 + S^2)) - (5*S^2*HPL[{4}, -S^2])/4 + ((28 + 28*S^2 + 63*S^4 - 13*S^6)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)) + (22*S^2*HPL[{3, 1}, -S^2])/3 - 14*S^2*HPL[{2, 1, 1}, -S^2] + ((-25*S^2 - 29*S^4)*Zeta[3])/(12*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(47 + 485*S^2))/(96*S^2) + (Pi^2*(-79 - 79*S^2 - 577*S^4 - 237*S^6))/(144*S^2*(1 + S^2)) + ((-7 - 7*S^2 - 59*S^4 - 21*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) - (S^2*HPL[{3}, -S^2])/2 + (19*S^2*HPL[{2, 1}, -S^2])/3 + (S^2*Zeta[3])/3)) + HPL[{0}, S^2]^2*((Pi^2*(-41 - 255*S^2))/48 - (3*(5 + 92*S^2))/16 + (Pi^4*(-2153*S^2 - 1019*S^4))/(1440*(1 + S^2)) + ((-13 - 13*S^2 - 107*S^4 - 39*S^6)*HPL[{1}, -S^2]^4)/(8*S^2*(1 + S^2)) - (17*S^2*HPL[{1}, -S^2]^5)/10 + ((1 + S^2 - 91*S^4 - 49*S^6)*HPL[{2}, -S^2]^2)/(8*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((-22*Pi^2*S^2)/9 + (-29 - 144*S^2 - 115*S^4)/(12*S^2) - (19*S^2*HPL[{2}, -S^2])/3) + ((3*Pi^2*S^2)/4 + (1 - 12*S^2 - 9*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((-3 - 3*S^2 + S^4 - 3*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + 5*S^2*HPL[{5}, -S^2] + ((-4*Pi^2*S^2)/3 + (29 + 99*S^2 + S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + (S^2*(181 + 109*S^2)*HPL[{3, 1}, -S^2])/(4*(1 + S^2)) - 2*S^2*HPL[{3, 2}, -S^2] - (21*S^2*HPL[{4, 1}, -S^2])/2 + ((1 + S^2 - 94*S^4 - 56*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - S^2*HPL[{2, 2, 1}, -S^2] + 6*S^2*HPL[{3, 1, 1}, -S^2] - 14*S^2*HPL[{2, 1, 1, 1}, -S^2] + (-(Pi^2*S^2)/4 + (-2 - 17*S^2)/8)*Zeta[3] + HPL[{2}, -S^2]*((8 - 30*S^2 - 115*S^4)/(8*S^2) + (Pi^2*(1 + S^2 - 174*S^4 - 111*S^6))/(24*S^2*(1 + S^2)) + S^2*HPL[{3}, -S^2] + (S^2*HPL[{2, 1}, -S^2])/2 + (S^2*Zeta[3])/2) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(21 + 124*S^2))/(8*S^2) + (Pi^2*(-19 - 19*S^2 - 145*S^4 - 57*S^6))/(12*S^2*(1 + S^2)) + ((-35 - 35*S^2 - 257*S^4 - 105*S^6)*HPL[{2}, -S^2])/(8*S^2*(1 + S^2)) + (3*S^2*HPL[{3}, -S^2])/2 + 19*S^2*HPL[{2, 1}, -S^2] + 2*S^2*Zeta[3]) + HPL[{1}, -S^2]*((-63*Pi^4*S^2)/80 - (3*(1 + S^2)*(7 + 93*S^2))/(16*S^2) - (Pi^2*(1 + S^2)*(43 + 241*S^2))/(48*S^2) + ((-21*Pi^2*S^2)/8 + (-12 - 67*S^2 - 55*S^4)/(4*S^2))*HPL[{2}, -S^2] - (21*S^2*HPL[{2}, -S^2]^2)/4 + ((-1 - S^2 + 3*S^4 - 3*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + S^2*HPL[{4}, -S^2] + ((35 + 35*S^2 + 257*S^4 + 105*S^6)*HPL[{2, 1}, -S^2])/(4*S^2*(1 + S^2)) + 18*S^2*HPL[{3, 1}, -S^2] - 38*S^2*HPL[{2, 1, 1}, -S^2] + ((-1 - S^2 + 13*S^4 - 3*S^6)*Zeta[3])/(4*S^2*(1 + S^2)))) + ((55*Pi^2*S^2)/6 + (-2 + 11*S^2)/2)*Zeta[5] + HPL[{2}, -S^2]*((56 - 31*S^2 - 552*S^4)/(16*S^2) + (Pi^2*(29 - 80*S^2 - 460*S^4))/(48*S^2) + (Pi^4*(26 + 26*S^2 - 2101*S^4 - 1498*S^6))/(720*S^2*(1 + S^2)) + ((43*Pi^2*S^2)/6 + (-11 + 28*S^2 + 53*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((-1 - S^2 + 34*S^4 - 2*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + (S^2*HPL[{5}, -S^2])/2 + ((19*Pi^2*S^2)/3 + (27 + 94*S^2 + 10*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((11 + 11*S^2 + 241*S^4 + 89*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) - 79*S^2*HPL[{3, 2}, -S^2] - 245*S^2*HPL[{4, 1}, -S^2] - (2*(3 + 3*S^2 + 126*S^4 + 50*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 76*S^2*HPL[{2, 2, 1}, -S^2] - 64*S^2*HPL[{3, 1, 1}, -S^2] + 148*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((13*Pi^2*S^2)/2 + (6 + 8*S^2 + 17*S^4)/(2*S^2))*Zeta[3] + 37*S^2*Zeta[5]) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(95 + 533*S^2))/(48*S^2) - ((1 + S^2)*(211 + 1461*S^2))/(32*S^2) + (Pi^4*(-267 - 267*S^2 - 2348*S^4 - 801*S^6))/(360*S^2*(1 + S^2)) - (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + (8*Pi^2*S^2 + (31 + 64*S^2 + 33*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((-1 - S^2 + 109*S^4 - 3*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + 11*S^2*HPL[{5}, -S^2] + ((19*Pi^2*S^2)/3 + (7 + 53*S^2 + 46*S^4)/S^2)*HPL[{2, 1}, -S^2] + (2*(5 + 5*S^2 + S^4 + 15*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 76*S^2*HPL[{3, 2}, -S^2] - 256*S^2*HPL[{4, 1}, -S^2] - (27*(1 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - 152*S^2*HPL[{2, 2, 1}, -S^2] - 276*S^2*HPL[{3, 1, 1}, -S^2] + ((43*Pi^2*S^2)/6 + ((1 + S^2)*(5 + 19*S^2))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-3*(1 + S^2)*(5 + 71*S^2))/(8*S^2) + (Pi^2*(-31 - 31*S^2 - 169*S^4 - 93*S^6))/(12*S^2*(1 + S^2)) + 38*S^2*HPL[{3}, -S^2] + 76*S^2*HPL[{2, 1}, -S^2] + 38*S^2*Zeta[3]) + 47*S^2*Zeta[5]) + Log[T]^2*(-47/8 + (Pi^2*(-53 - 115*S^2))/12 + (Pi^4*(-2566*S^2 - 1019*S^4))/(360*(1 + S^2)) - (S^2*HPL[{0}, S^2]^5)/3 + ((-47*Pi^2*S^2)/3 - (2*(17 + 84*S^2 + 67*S^4))/(3*S^2))*HPL[{1}, -S^2]^3 - (15*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) - 12*S^2*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^4*(-(S^2*(92 + 55*S^2))/(24*(1 + S^2)) - (37*S^2*HPL[{1}, -S^2])/24) + ((-3 - 3*S^2 - 126*S^4 - 50*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + HPL[{0}, S^2]^3*((-43*Pi^2*S^2)/18 + (-68 - 239*S^2)/24 + ((-17 - 17*S^2 - 141*S^4 - 51*S^6)*HPL[{1}, -S^2])/(6*S^2*(1 + S^2)) - (15*S^2*HPL[{1}, -S^2]^2)/2 - 7*S^2*HPL[{2}, -S^2]) + ((49*Pi^2*S^2)/3 + (21 + 32*S^2 + 61*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((-5 - 5*S^2 + 66*S^4 + 10*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + 27*S^2*HPL[{5}, -S^2] + ((-52*Pi^2*S^2)/3 + (23 + 91*S^2 - 16*S^4)/S^2)*HPL[{2, 1}, -S^2] + ((-11 - 11*S^2 + 70*S^4 + 98*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 158*S^2*HPL[{3, 2}, -S^2] - 516*S^2*HPL[{4, 1}, -S^2] - (4*(-4 + 55*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - 148*S^2*HPL[{2, 2, 1}, -S^2] - 88*S^2*HPL[{3, 1, 1}, -S^2] - 360*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((49*Pi^2*S^2)/3 + 2*(3 + 8*S^2))*Zeta[3] + HPL[{0}, S^2]^2*((-27 - 115*S^2)/4 - (11*Pi^2*(9*S^2 + 5*S^4))/(6*(1 + S^2)) - (3*(13 + 13*S^2 + 107*S^4 + 39*S^6)*HPL[{1}, -S^2]^2)/(4*S^2*(1 + S^2)) - 17*S^2*HPL[{1}, -S^2]^3 + ((1 + S^2 - 94*S^4 - 56*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-22*Pi^2*S^2)/3 + (-29 - 144*S^2 - 115*S^4)/(4*S^2) - 19*S^2*HPL[{2}, -S^2]) + (9*S^2*HPL[{3}, -S^2])/2 - 7*S^2*HPL[{2, 1}, -S^2] + 4*S^2*Zeta[3]) + HPL[{2}, -S^2]*((13 - 20*S^2 - 230*S^4)/(4*S^2) + (Pi^2*(5 + 5*S^2 - 149*S^4 - 111*S^6))/(6*S^2*(1 + S^2)) + 82*S^2*HPL[{3}, -S^2] + 74*S^2*HPL[{2, 1}, -S^2] + 76*S^2*Zeta[3]) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(53 + 285*S^2))/(4*S^2) + (Pi^2*(-7 - 7*S^2 - 68*S^4 - 21*S^6))/(S^2*(1 + S^2)) - (27*(1 + 3*S^4)*HPL[{2}, -S^2])/(2*S^2) + 90*S^2*HPL[{3}, -S^2] + 78*S^2*Zeta[3]) + HPL[{1}, -S^2]*((-1547*Pi^4*S^2)/360 - (Pi^2*(1 + S^2)*(21 + 83*S^2))/(4*S^2) - ((1 + S^2)*(95 + 629*S^2))/(8*S^2) + ((-19*Pi^2*S^2)/3 + (-7 - 53*S^2 - 46*S^4)/S^2)*HPL[{2}, -S^2] - 38*S^2*HPL[{2}, -S^2]^2 + (9*(1 + S^2 + 23*S^4 + 3*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + 28*S^2*HPL[{4}, -S^2] + (27*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 - 28*S^2*HPL[{3, 1}, -S^2] + (6*(1 + S^2 + 29*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]*((-253*Pi^4*S^2)/60 + (-106 - 629*S^2)/8 + (Pi^2*(-158 - 507*S^2))/24 - (15*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) - 30*S^2*HPL[{1}, -S^2]^4 + (-21*Pi^2*S^2 + (4 - 39*S^2 - 127*S^4)/(2*S^2))*HPL[{2}, -S^2] - (77*S^2*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*((-45*Pi^2*S^2)/2 + (-17 - 84*S^2 - 67*S^4)/S^2 - 78*S^2*HPL[{2}, -S^2]) + ((-4 - 4*S^2 + S^4 + 5*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - 13*S^2*HPL[{4}, -S^2] + ((41 + 41*S^2 + 145*S^4 - 11*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 168*S^2*HPL[{3, 1}, -S^2] - 336*S^2*HPL[{2, 1, 1}, -S^2] + (2*(13*S^2 + 6*S^4)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(53 + 285*S^2))/(4*S^2) + (Pi^2*(-79 - 79*S^2 - 777*S^4 - 237*S^6))/(12*S^2*(1 + S^2)) - (39*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - 2*S^2*HPL[{3}, -S^2] + 156*S^2*HPL[{2, 1}, -S^2] + 14*S^2*Zeta[3])) + 110*S^2*Zeta[5]) + HPL[{1}, -S^2]*((-11857*Pi^6*S^2)/30240 - (5*(1 + S^2)*(55 + 369*S^2))/(32*S^2) - (Pi^2*(1 + S^2)*(137 + 1187*S^2))/(96*S^2) - (Pi^4*(1 + S^2)*(359 + 1599*S^2))/(720*S^2) + ((-59*Pi^2*S^2)/12 + (-31 - 144*S^2 - 113*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 - 3*S^2*HPL[{3}, -S^2]^2 + ((8*Pi^2*S^2)/3 + (35 + 8*S^2 - 27*S^4)/(8*S^2))*HPL[{4}, -S^2] - (2*(2 + 2*S^2 - 5*S^4 + 6*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) + (21*S^2*HPL[{6}, -S^2])/2 + 76*S^2*HPL[{2, 1}, -S^2]^2 + ((11*Pi^2*S^2)/3 + 40*(1 + S^2))*HPL[{3, 1}, -S^2] - (2*(5 + 5*S^2 + 91*S^4 + 15*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((-59 - 59*S^2 - 1201*S^4 - 177*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) - 9*S^2*HPL[{4, 2}, -S^2] - 58*S^2*HPL[{5, 1}, -S^2] + ((-38*Pi^2*S^2)/3 - (2*(7 + 53*S^2 + 46*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (38*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (24*(4 + 4*S^2 + 35*S^4 + 12*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 56*S^2*HPL[{4, 1, 1}, -S^2] + (54*(1 + 3*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - 56*S^2*HPL[{3, 1, 1, 1}, -S^2] + (((1 + S^2)*(11 + 37*S^2))/(4*S^2) + (Pi^2*(5 + 5*S^2 + 187*S^4 + 15*S^6))/(12*S^2*(1 + S^2)))*Zeta[3] - 3*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((3*(1 + S^2)*(5 + 71*S^2))/(4*S^2) + (Pi^2*(31 + 31*S^2 + 169*S^4 + 93*S^6))/(6*S^2*(1 + S^2)) - 76*S^2*Zeta[3]) + HPL[{3}, -S^2]*(((1 + S^2)*(59 + 53*S^2))/(8*S^2) + (Pi^2*(7 + 7*S^2 + 213*S^4 + 21*S^6))/(12*S^2*(1 + S^2)) - 76*S^2*HPL[{2, 1}, -S^2] + 4*S^2*Zeta[3]) + HPL[{2}, -S^2]*((-67*Pi^4*S^2)/80 - (Pi^2*(1 + S^2)*(19 + 101*S^2))/(12*S^2) - ((1 + S^2)*(-11 + 475*S^2))/(16*S^2) + ((5 + 5*S^2 + 91*S^4 + 15*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + 9*S^2*HPL[{4}, -S^2] + (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 76*S^2*HPL[{3, 1}, -S^2] - 152*S^2*HPL[{2, 1, 1}, -S^2] + (4*(1 + S^2 + 22*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-1 - S^2 + 91*S^4 - 3*S^6)*Zeta[5])/(S^2*(1 + S^2))) + Log[T]*(75/16 + (7037*Pi^6*S^2)/15120 + (23*Pi^2*(3 + 11*S^2))/24 + (Pi^4*(1068 + 2039*S^2))/720 + (S^2*HPL[{0}, S^2]^6)/16 + ((47*Pi^2*S^2)/6 + (17 + 84*S^2 + 67*S^4)/(3*S^2))*HPL[{1}, -S^2]^4 + (3*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)) + 4*S^2*HPL[{1}, -S^2]^6 + HPL[{0}, S^2]^5*((S^2*(43 + 27*S^2))/(48*(1 + S^2)) + (S^2*HPL[{1}, -S^2])/3) + ((20*Pi^2*S^2)/3 + (4 + 50*S^2 + 103*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 + (19*S^2*HPL[{2}, -S^2]^3)/3 + HPL[{0}, S^2]^4*((41*Pi^2*S^2)/72 + (37 + 125*S^2)/48 + (37*(1 + S^2 + 7*S^4 + 3*S^6)*HPL[{1}, -S^2])/(48*S^2*(1 + S^2)) + (37*S^2*HPL[{1}, -S^2]^2)/24 + (17*S^2*HPL[{2}, -S^2])/12) + 4*S^2*HPL[{3}, -S^2]^2 + ((-11*Pi^2*S^2)/6 + (3 + 14*S^2 + 18*S^4)/(4*S^2))*HPL[{4}, -S^2] + (2*(1 + S^2 + 4*S^4 + 15*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) + 25*S^2*HPL[{6}, -S^2] + ((-28 - 208*S^2 + 17*S^4)/(2*S^2) + (2*Pi^2*(-18 - 18*S^2 - 10*S^4 + 9*S^6))/(3*S^2*(1 + S^2)))*HPL[{2, 1}, -S^2] - 78*S^2*HPL[{2, 1}, -S^2]^2 + ((-82*Pi^2*S^2)/3 + (33 - 4*S^2 - 201*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-3 - 3*S^2 + 401*S^4 + 97*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((-5 - 5*S^2 + 658*S^4 + 146*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) + 21*S^2*HPL[{4, 2}, -S^2] + 78*S^2*HPL[{5, 1}, -S^2] + (60*Pi^2*S^2 + (6*(-3 + 5*S^2 + 36*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(16 + 16*S^2 + 83*S^4 + 7*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (2*(-95 - 95*S^2 - 266*S^4 + 10*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 12*S^2*HPL[{3, 1, 2}, -S^2] + 140*S^2*HPL[{3, 2, 1}, -S^2] + 392*S^2*HPL[{4, 1, 1}, -S^2] + (4*(-35 + 29*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - 304*S^2*HPL[{3, 1, 1, 1}, -S^2] + 720*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-14 - 17*S^2)/2 + (Pi^2*(-103*S^2 - 17*S^4))/(6*(1 + S^2)))*Zeta[3] - 6*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^3*(((1 + S^2)*(53 + 285*S^2))/(6*S^2) + (2*Pi^2*(7 + 7*S^2 + 68*S^4 + 21*S^6))/(3*S^2*(1 + S^2)) + (9*(1 + 3*S^4)*HPL[{2}, -S^2])/S^2 - 60*S^2*HPL[{3}, -S^2] - 52*S^2*Zeta[3]) + HPL[{3}, -S^2]*((-65 - 48*S^2 - 87*S^4)/(8*S^2) + (Pi^2*(1 + S^2 - 243*S^4 - 51*S^6))/(12*S^2*(1 + S^2)) - 12*S^2*HPL[{2, 1}, -S^2] - 4*S^2*Zeta[3]) + HPL[{0}, S^2]^3*((70 + 517*S^2)/48 + (Pi^2*(417*S^2 + 247*S^4))/(72*(1 + S^2)) + ((17 + 17*S^2 + 141*S^4 + 51*S^6)*HPL[{1}, -S^2]^2)/(6*S^2*(1 + S^2)) + 5*S^2*HPL[{1}, -S^2]^3 + (S^2*(173 + 97*S^2)*HPL[{2}, -S^2])/(12*(1 + S^2)) + HPL[{1}, -S^2]*((85*Pi^2*S^2)/36 + (35 + 256*S^2 + 221*S^4)/(24*S^2) + (19*S^2*HPL[{2}, -S^2])/3) - (S^2*HPL[{3}, -S^2])/2 + (4*S^2*HPL[{2, 1}, -S^2])/3 + (4*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^2*((1547*Pi^4*S^2)/360 + (Pi^2*(1 + S^2)*(21 + 83*S^2))/(4*S^2) + ((1 + S^2)*(95 + 629*S^2))/(8*S^2) + ((19*Pi^2*S^2)/3 + (7 + 53*S^2 + 46*S^4)/S^2)*HPL[{2}, -S^2] + 38*S^2*HPL[{2}, -S^2]^2 - (9*(1 + S^2 + 23*S^4 + 3*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - 28*S^2*HPL[{4}, -S^2] - (27*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 + 28*S^2*HPL[{3, 1}, -S^2] - (6*(1 + S^2 + 29*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]*((123*Pi^4*S^2)/40 + (Pi^2*(-14 + 50*S^2 + 217*S^4))/(12*S^2) + (-25 + 38*S^2 + 506*S^4)/(8*S^2) + ((3 + 3*S^2 - 205*S^4 - 53*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - 17*S^2*HPL[{4}, -S^2] - (2*(16 + 16*S^2 + 83*S^4 + 7*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 64*S^2*HPL[{3, 1}, -S^2] + 156*S^2*HPL[{2, 1, 1}, -S^2] - (2*(1 + S^2 + 49*S^4 + 11*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^2*((3*Pi^4*S^2)/2 + (Pi^2*(76 + 233*S^2))/24 + (36 + 253*S^2)/8 + ((13 + 13*S^2 + 107*S^4 + 39*S^6)*HPL[{1}, -S^2]^3)/(2*S^2*(1 + S^2)) + (17*S^2*HPL[{1}, -S^2]^4)/2 + ((79*Pi^2*S^2)/12 + (-5 + 35*S^2 + 109*S^4)/(4*S^2))*HPL[{2}, -S^2] + (41*S^2*HPL[{2}, -S^2]^2)/4 + HPL[{1}, -S^2]^2*((22*Pi^2*S^2)/3 + (29 + 144*S^2 + 115*S^4)/(4*S^2) + 19*S^2*HPL[{2}, -S^2]) + ((2 + 2*S^2 - 11*S^4 + S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) + (5*S^2*HPL[{4}, -S^2])/2 + ((-37 - 37*S^2 - 69*S^4 + 7*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 44*S^2*HPL[{3, 1}, -S^2] + 90*S^2*HPL[{2, 1, 1}, -S^2] + (2*(S^2 + 3*S^4)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(((1 + S^2)*(21 + 124*S^2))/(4*S^2) + (Pi^2*(19 + 19*S^2 + 145*S^4 + 57*S^6))/(6*S^2*(1 + S^2)) + ((35 + 35*S^2 + 257*S^4 + 105*S^6)*HPL[{2}, -S^2])/(4*S^2*(1 + S^2)) - 3*S^2*HPL[{3}, -S^2] - 38*S^2*HPL[{2, 1}, -S^2] - 4*S^2*Zeta[3])) + HPL[{0}, S^2]*((3*(74 + 487*S^2))/16 + (Pi^2*(198 + 1087*S^2))/48 + (13*Pi^4*(241*S^2 + 125*S^4))/(360*(1 + S^2)) + (15*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) + 12*S^2*HPL[{1}, -S^2]^5 + ((1 + S^2 + 136*S^4 + 60*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*(15*Pi^2*S^2 + (2*(17 + 84*S^2 + 67*S^4))/(3*S^2) + 52*S^2*HPL[{2}, -S^2]) + ((-4*Pi^2*S^2)/3 + (3 + 8*S^2 + 10*S^4)/(2*S^2))*HPL[{3}, -S^2] + ((1 + S^2 + 16*S^4 + 4*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) - 2*S^2*HPL[{5}, -S^2] + ((10*Pi^2*S^2)/3 + (-28 - 115*S^2 - 3*S^4)/S^2)*HPL[{2, 1}, -S^2] + ((2 + 2*S^2 - 281*S^4 - 125*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 8*S^2*HPL[{3, 2}, -S^2] + 26*S^2*HPL[{4, 1}, -S^2] + (4*(-1 - S^2 + 142*S^4 + 64*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 4*S^2*HPL[{2, 2, 1}, -S^2] - 32*S^2*HPL[{3, 1, 1}, -S^2] + 48*S^2*HPL[{2, 1, 1, 1}, -S^2] + (-(Pi^2*S^2) - (3*(2 + 5*S^2))/2)*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(53 + 285*S^2))/(4*S^2) + (Pi^2*(79 + 79*S^2 + 777*S^4 + 237*S^6))/(12*S^2*(1 + S^2)) + (39*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) + 2*S^2*HPL[{3}, -S^2] - 156*S^2*HPL[{2, 1}, -S^2] - 14*S^2*Zeta[3]) + HPL[{2}, -S^2]*((-2 + 68*S^2 + 267*S^4)/(4*S^2) + (Pi^2*(-2 - 2*S^2 + 457*S^4 + 225*S^6))/(12*S^2*(1 + S^2)) - 4*S^2*HPL[{3}, -S^2] + 2*S^2*HPL[{2, 1}, -S^2] - 12*S^2*Zeta[3]) + HPL[{1}, -S^2]*((377*Pi^4*S^2)/90 + (Pi^2*(1 + S^2)*(103 + 489*S^2))/(24*S^2) + ((1 + S^2)*(95 + 629*S^2))/(8*S^2) + ((58*Pi^2*S^2)/3 + (12 + 77*S^2 + 65*S^4)/S^2)*HPL[{2}, -S^2] + 38*S^2*HPL[{2}, -S^2]^2 + (4*S^2*HPL[{3}, -S^2])/(1 + S^2) + 12*S^2*HPL[{4}, -S^2] - (39*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 156*S^2*HPL[{3, 1}, -S^2] + 312*S^2*HPL[{2, 1, 1}, -S^2] + ((-3 - 3*S^2 - 37*S^4 - 9*S^6)*Zeta[3])/(S^2*(1 + S^2)))) - (2*(50*S^2 + 3*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(95 + 533*S^2))/(24*S^2) + ((1 + S^2)*(211 + 1461*S^2))/(16*S^2) + (Pi^4*(267 + 267*S^2 + 2348*S^4 + 801*S^6))/(180*S^2*(1 + S^2)) + (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + (-16*Pi^2*S^2 + (-31 - 64*S^2 - 33*S^4)/(2*S^2))*HPL[{3}, -S^2] + ((1 + S^2 - 109*S^4 + 3*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - 22*S^2*HPL[{5}, -S^2] + ((-38*Pi^2*S^2)/3 - (2*(7 + 53*S^2 + 46*S^4))/S^2)*HPL[{2, 1}, -S^2] - (4*(5 + 5*S^2 + S^4 + 15*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 152*S^2*HPL[{3, 2}, -S^2] + 512*S^2*HPL[{4, 1}, -S^2] + (54*(1 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + 304*S^2*HPL[{2, 2, 1}, -S^2] + 552*S^2*HPL[{3, 1, 1}, -S^2] + ((-43*Pi^2*S^2)/3 - ((1 + S^2)*(5 + 19*S^2))/S^2)*Zeta[3] + HPL[{2}, -S^2]*((3*(1 + S^2)*(5 + 71*S^2))/(4*S^2) + (Pi^2*(31 + 31*S^2 + 169*S^4 + 93*S^6))/(6*S^2*(1 + S^2)) - 76*S^2*HPL[{3}, -S^2] - 152*S^2*HPL[{2, 1}, -S^2] - 76*S^2*Zeta[3]) - 94*S^2*Zeta[5])) + HPL[{0}, S^2]*((-2437*Pi^6*S^2)/7560 + (Pi^2*(-51 - 398*S^2))/32 - (7*Pi^4*(25 + 79*S^2))/240 - (5*(55 + 369*S^2))/32 - (3*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^5)/(2*S^2*(1 + S^2)) - 2*S^2*HPL[{1}, -S^2]^6 + ((-14*Pi^2*S^2)/3 + (-6 - 38*S^2 - 119*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 - 6*S^2*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*((-15*Pi^2*S^2)/4 + (-17 - 84*S^2 - 67*S^4)/(6*S^2) - 13*S^2*HPL[{2}, -S^2]) + S^2*HPL[{3}, -S^2]^2 + ((-7*Pi^2*S^2)/3 + (-1 - 2*S^2 - 5*S^4)/(2*S^2))*HPL[{4}, -S^2] - (2*(-1 - S^2 + 6*S^4 + 2*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - 20*S^2*HPL[{6}, -S^2] + ((39 + 256*S^2 + 20*S^4)/(4*S^2) + (Pi^2*(69 + 69*S^2 + 208*S^4 - 24*S^6))/(12*S^2*(1 + S^2)))*HPL[{2, 1}, -S^2] + 77*S^2*HPL[{2, 1}, -S^2]^2 + ((64*Pi^2*S^2)/3 + (-5 + 38*S^2 + 125*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] - (8*S^2*HPL[{3, 2}, -S^2])/(1 + S^2) + ((1 + S^2 - 10*S^4 + 2*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) + 22*S^2*HPL[{5, 1}, -S^2] + (-42*Pi^2*S^2 + (4 - 39*S^2 - 127*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (2*(-18 - 18*S^2 - 73*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-112 - 112*S^2 - 437*S^4 + 23*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 144*S^2*HPL[{3, 2, 1}, -S^2] - 458*S^2*HPL[{4, 1, 1}, -S^2] - (2*(-41 - 41*S^2 - 145*S^4 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 336*S^2*HPL[{3, 1, 1, 1}, -S^2] - 672*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((18 + 19*S^2)/8 + (Pi^2*(S^2 - 17*S^4))/(12*(1 + S^2)))*Zeta[3] + HPL[{3}, -S^2]*((-7 - 8*S^2 - 18*S^4)/(4*S^2) + (Pi^2*(-1 - S^2 - 2*S^4 + 2*S^6))/(6*S^2*(1 + S^2)) - 4*S^2*HPL[{2, 1}, -S^2] + 2*S^2*Zeta[3]) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(53 + 285*S^2))/(12*S^2) + (Pi^2*(-79 - 79*S^2 - 777*S^4 - 237*S^6))/(36*S^2*(1 + S^2)) - (13*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - (2*S^2*HPL[{3}, -S^2])/3 + 52*S^2*HPL[{2, 1}, -S^2] + (14*S^2*Zeta[3])/3) + HPL[{2}, -S^2]*((-89*Pi^4*S^2)/45 + (-28 - 162*S^2 - 577*S^4)/(16*S^2) + (Pi^2*(8 - 134*S^2 - 463*S^4))/(48*S^2) + (4*S^2*HPL[{3}, -S^2])/(1 + S^2) - 2*S^2*HPL[{4}, -S^2] + ((18 + 18*S^2 + 73*S^4 - 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 76*S^2*HPL[{3, 1}, -S^2] - 154*S^2*HPL[{2, 1, 1}, -S^2] + ((-2 - 2*S^2 + 21*S^4 + 9*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{1}, -S^2]^2*((-377*Pi^4*S^2)/180 - (Pi^2*(1 + S^2)*(103 + 489*S^2))/(48*S^2) - ((1 + S^2)*(95 + 629*S^2))/(16*S^2) + ((-29*Pi^2*S^2)/3 + (-12 - 77*S^2 - 65*S^4)/(2*S^2))*HPL[{2}, -S^2] - 19*S^2*HPL[{2}, -S^2]^2 - (2*S^2*HPL[{3}, -S^2])/(1 + S^2) - 6*S^2*HPL[{4}, -S^2] + (39*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 78*S^2*HPL[{3, 1}, -S^2] - 156*S^2*HPL[{2, 1, 1}, -S^2] + ((3 + 3*S^2 + 37*S^4 + 9*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + ((5*S^2 - 3*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(153 + 1055*S^2))/(96*S^2) - ((1 + S^2)*(211 + 1461*S^2))/(32*S^2) + (Pi^4*(-525 - 525*S^2 - 4591*S^4 - 1575*S^6))/(720*S^2*(1 + S^2)) - (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((-2*Pi^2*S^2)/3 - (2*(-1 + S^2 + 2*S^4))/S^2)*HPL[{3}, -S^2] + ((-1 - S^2 - 15*S^4 - 3*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) - 8*S^2*HPL[{5}, -S^2] + ((58*Pi^2*S^2)/3 + (12 + 77*S^2 + 65*S^4)/S^2)*HPL[{2, 1}, -S^2] + ((19 + 19*S^2 + 213*S^4 + 57*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 8*S^2*HPL[{3, 2}, -S^2] - 12*S^2*HPL[{4, 1}, -S^2] - (39*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 152*S^2*HPL[{2, 2, 1}, -S^2] - 460*S^2*HPL[{3, 1, 1}, -S^2] + 312*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((3*Pi^2*S^2)/2 + ((1 + S^2)*(13 + 11*S^2))/(4*S^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(37 + 287*S^2))/(8*S^2) + (Pi^2*(-67 - 67*S^2 - 665*S^4 - 201*S^6))/(24*S^2*(1 + S^2)) + 4*S^2*HPL[{3}, -S^2] + 76*S^2*HPL[{2, 1}, -S^2] + 6*S^2*Zeta[3]) + 8*S^2*Zeta[5])) + 75*S^2*Zeta[7];
E4vwuT3F1=(-3*(-7 + 45*S^2))/(4*S) - (Pi^4*S*(2025 + 377*S^2))/720 + (Pi^2*(8 - 347*S^2 + 16*S^4))/(32*S) + (Pi^6*S*(-45544 - 31803*S^2 + 1884*S^4))/(30240*(1 + S^2)^2) + ((-47*Pi^2*S)/15 + (-41 - 592*S^2 + 10*S^4 - 168*S^6 - 9*S^8)/(30*S*(1 + S^2)^2))*HPL[{1}, -S^2]^5 + ((1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^6)/(S*(1 + S^2)^2) - (8*S*HPL[{1}, -S^2]^7)/7 + HPL[{0}, S^2]^6*((S^3*(5 + 4*S^2))/(32*(1 + S^2)^2) - (S*HPL[{1}, -S^2])/16) + ((-1 - S^2)*HPL[{2}, -S^2]^3)/S + HPL[{0}, S^2]^5*(-(Pi^2*S)/18 - (S*(36 + 29*S^2 + 52*S^4 + 27*S^6))/(96*(1 + S^2)^2) + ((9 - 68*S^2 - 83*S^4 - 22*S^6)*HPL[{1}, -S^2])/(48*S*(1 + S^2)^2) - (S*HPL[{1}, -S^2]^2)/3 - (S*HPL[{2}, -S^2])/3) + ((-1 - 5*S^2 + 8*S^4 + 9*S^6)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^2) + ((47*Pi^2*S)/6 + (34 + 86*S^2 + 15*S^4 - 53*S^6 - 60*S^8)/(2*S*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-10 + 328*S^2 + 581*S^4 + 264*S^6)*HPL[{6}, -S^2])/(2*S*(1 + S^2)^2) + 106*S*HPL[{7}, -S^2] + (2*(-3 + 168*S^2 + 155*S^4 + 22*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + HPL[{4}, -S^2]*((-36 + 215*S^2 - 504*S^4 - 88*S^6)/(8*S^3) + (Pi^2*(11 + 114*S^2 + 35*S^4 - 36*S^6))/(12*S*(1 + S^2)^2) - 2*S*HPL[{2, 1}, -S^2]) + ((-83*Pi^2*S)/3 + (3 + 37*S^2 + 319*S^4 - 31*S^6 - 12*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + (-93*Pi^2*S + (19 + 116*S^2 + 604*S^4 - 20*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (3*(1 - 6*S^2 + 15*S^4 + 16*S^6)*HPL[{4, 2}, -S^2])/(2*S*(1 + S^2)^2) - 10*S*HPL[{4, 3}, -S^2] + (2*(-2 - 52*S^2 + 47*S^4 + 68*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) - 33*S*HPL[{5, 2}, -S^2] - 142*S*HPL[{6, 1}, -S^2] + ((-76*Pi^2*S)/3 - (2*(8 + 95*S^2 - 59*S^4 + 9*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-32*Pi^2*S)/3 - (4*(22 + 169*S^2 + 9*S^4 + 3*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (3*(-1 + 2*S^2)*HPL[{3, 1, 2}, -S^2])/S - (3*(7 + 10*S^2)*HPL[{3, 2, 1}, -S^2])/S + 310*S*HPL[{3, 2, 2}, -S^2] + 944*S*HPL[{3, 3, 1}, -S^2] - (2*(31 + 30*S^2 + 107*S^4 + 80*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 938*S*HPL[{4, 1, 2}, -S^2] + 2858*S*HPL[{4, 2, 1}, -S^2] + 5868*S*HPL[{5, 1, 1}, -S^2] + ((-208*Pi^2*S)/3 - (2*(-48 - 238*S^2 + 55*S^4 + 9*S^6))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - 304*S*HPL[{2, 2, 2, 1}, -S^2] + (4*(11 + 10*S^2 + 57*S^4 + 44*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 280*S*HPL[{3, 1, 1, 2}, -S^2] + 280*S*HPL[{3, 1, 2, 1}, -S^2] + 1192*S*HPL[{3, 2, 1, 1}, -S^2] + 3408*S*HPL[{4, 1, 1, 1}, -S^2] - (64*(1 + 5*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + 592*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 1776*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 4384*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 1440*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (2*Pi^2*S - (12*S*(-1 + S^2))/(1 + S^2)^2 + 6*S*HPL[{0}, S^2]^2 - (6*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) + 24*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-12*S*(-3 - S^2 + S^4))/(1 + S^2)^2 + 24*S*HPL[{1}, -S^2]) + 12*S*HPL[{2}, -S^2])*Log[T]^5 + ((-4*S*(4 + 3*S^2))/(1 + S^2)^2 - 8*S*HPL[{0}, S^2] - 8*S*HPL[{1}, -S^2])*Log[T]^6 + ((157*Pi^4*S)/90 + (S*(-55 + 4*S^2))/2 + (Pi^2*S*(-22 - 97*S^2 + 20*S^4 + 9*S^6))/(6*(1 + S^2)^2))*Zeta[3] + (S*(-4 + 7*S^2 + 8*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3, 1}, -S^2]*((43 + 136*S^2 - S^4)/(2*S) + (Pi^2*(11 + 196*S^2 + 249*S^4 + 86*S^6))/(6*S*(1 + S^2)^2) - 152*S*Zeta[3]) + HPL[{0}, S^2]^4*((-5*S*(79 + 14*S^2))/96 + (Pi^2*S*(-110 - 15*S^2 + 54*S^4))/(144*(1 + S^2)^2) - (37*(-1 + 8*S^2 + 9*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(48*S*(1 + S^2)^2) - (37*S*HPL[{1}, -S^2]^3)/36 - (S*(184 + 243*S^2 + 84*S^4)*HPL[{2}, -S^2])/(48*(1 + S^2)^2) + HPL[{1}, -S^2]*((-41*Pi^2*S)/72 + (-91 - 744*S^2 - 564*S^4 - 210*S^6 - 3*S^8)/(96*S*(1 + S^2)^2) - (25*S*HPL[{2}, -S^2])/24) + (3*S*HPL[{3}, -S^2])/8 - (3*S*HPL[{2, 1}, -S^2])/4 - (7*S*Zeta[3])/12) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(191 + 33*S^2))/(24*S) + (Pi^2*(14 - 150*S^2 - 107*S^4 + 10*S^6))/(6*S*(1 + S^2)^2) - (9*(-1 + 6*S^2)*HPL[{2}, -S^2])/(2*S) + 30*S*HPL[{3}, -S^2] + 26*S*Zeta[3]) + HPL[{2}, -S^2]^2*((1 - 126*S^2)/(8*S) + (Pi^2*(2 - 270*S^2 - 251*S^4 - 38*S^6))/(12*S*(1 + S^2)^2) + 41*S*HPL[{3}, -S^2] - 38*S*HPL[{2, 1}, -S^2] + 36*S*Zeta[3]) + Log[T]^4*((-3*S)/2 - (Pi^2*S*(604 + 503*S^2 + 40*S^4))/(18*(1 + S^2)^2) - (46*S*HPL[{0}, S^2]^3)/9 + ((-47*Pi^2*S)/3 + (-41 - 592*S^2 + 10*S^4 - 168*S^6 - 9*S^8)/(6*S*(1 + S^2)^2))*HPL[{1}, -S^2] + (15*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^2) - 40*S*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*(-(S*(244 + 233*S^2 + 40*S^4))/(6*(1 + S^2)^2) - 17*S*HPL[{1}, -S^2]) - (8*(1 + 5*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{0}, S^2]*((-136*Pi^2*S)/9 - (S*(84 + 17*S^2 + 56*S^4 + 3*S^6))/(2*(1 + S^2)^2) + (15*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) - 60*S*HPL[{1}, -S^2]^2 - 56*S*HPL[{2}, -S^2]) + (178*S*HPL[{3}, -S^2])/3 - 60*S*HPL[{2, 1}, -S^2] + 60*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-2*(-2 + 22*S^2 + 65*S^4 + 6*S^6))/S^3 - (2*Pi^2*(5 + 128*S^2 + 146*S^4 + 42*S^6))/(3*S*(1 + S^2)^2) + 304*S*Zeta[3]) + HPL[{3}, -S^2]*((103*Pi^4*S)/45 + (Pi^2*(-25 - 85*S^2 - 243*S^4 + 9*S^6))/(12*S*(1 + S^2)^2) + (18 + 117*S^2 + 86*S^4 + 89*S^6)/(16*S^3) + 2*S*HPL[{4}, -S^2] + ((23 - 296*S^2 - 281*S^4 - 38*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 156*S*HPL[{3, 1}, -S^2] + 328*S*HPL[{2, 1, 1}, -S^2] - (4*S*(-2 + S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-14*Pi^4*S)/5 + (137 + 55*S^2 - 4*S^4)/(2*S) + (Pi^2*(38 + 273*S^2 + 126*S^4 - 39*S^6 - 6*S^8))/(6*S*(1 + S^2)^2) - 176*S*HPL[{3, 1}, -S^2] - 296*S*HPL[{2, 1, 1}, -S^2] - (4*(-3 + 72*S^2 + 58*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-1547*Pi^4*S)/540 - ((1 + S^2)*(2 + 205*S^2 + 27*S^4))/(12*S^3) + (Pi^2*(-39 - 555*S^2 - 76*S^4 - 133*S^6 - 9*S^8))/(18*S*(1 + S^2)^2) + ((-38*Pi^2*S)/9 - (2*(13 + 106*S^2 + 13*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2] - (76*S*HPL[{2}, -S^2]^2)/3 - (6*(1 - 24*S^2 - S^4 + 14*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + (56*S*HPL[{4}, -S^2])/3 + (18*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S - (56*S*HPL[{3, 1}, -S^2])/3 - (4*(1 - 30*S^2 + 2*S^4 + 20*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + Log[T]^3*((5*S)/2 + (781*Pi^4*S)/270 + (Pi^2*S*(422 - 35*S^2 + 116*S^4 + 9*S^6))/(18*(1 + S^2)^2) + (37*S*HPL[{0}, S^2]^4)/18 + ((94*Pi^2*S)/3 + (41 + 592*S^2 - 10*S^4 + 168*S^6 + 9*S^8)/(3*S*(1 + S^2)^2))*HPL[{1}, -S^2]^2 - (20*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)^2) + 40*S*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*((5*S*(4 + S^2)*(11 + 8*S^2))/(9*(1 + S^2)^2) + 10*S*HPL[{1}, -S^2]) + (20*Pi^2*S + (4 + 186*S^2 + 107*S^4 + 9*S^6)/(3*S*(1 + S^2)))*HPL[{2}, -S^2] + 26*S*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^2*((82*Pi^2*S)/9 + (S*(242 + 145*S^2 + 116*S^4 + 9*S^6))/(6*(1 + S^2)^2) + ((-13 + 120*S^2 + 109*S^4 + 10*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) + 34*S*HPL[{1}, -S^2]^2 + 30*S*HPL[{2}, -S^2]) + (2*(1 - 106*S^2 + 235*S^4 + 252*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (64*S*HPL[{4}, -S^2])/3 - (4*(-35 + 122*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (304*S*HPL[{3, 1}, -S^2])/3 + 240*S*HPL[{2, 1, 1}, -S^2] + (4*S*(-34 + 127*S^2 + 122*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(191 + 33*S^2))/(6*S) - (2*Pi^2*(14 - 150*S^2 - 107*S^4 + 10*S^6))/(3*S*(1 + S^2)^2) + (18*(-1 + 6*S^2)*HPL[{2}, -S^2])/S - 120*S*HPL[{3}, -S^2] - 104*S*Zeta[3]) + HPL[{0}, S^2]*((S*(206 + 33*S^2))/6 - (5*Pi^2*S*(-98 - 61*S^2 + 10*S^4))/(9*(1 + S^2)^2) - (30*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^2) + 80*S*HPL[{1}, -S^2]^3 - (4*(-1 - 118*S^2 - 38*S^4 + 40*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(30*Pi^2*S + (41 + 592*S^2 - 10*S^4 + 168*S^6 + 9*S^8)/(3*S*(1 + S^2)^2) + 104*S*HPL[{2}, -S^2]) - (20*S*HPL[{3}, -S^2])/3 + 16*S*HPL[{2, 1}, -S^2] - (56*S*Zeta[3])/3)) + HPL[{0}, S^2]^3*((-403*Pi^4*S)/1080 + (S*(-128 + 19*S^2))/96 - (Pi^2*S*(466 + 429*S^2 + 450*S^4 + 147*S^6))/(144*(1 + S^2)^2) + ((17 - 158*S^2 - 142*S^4 - 12*S^6)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)^2) - (5*S*HPL[{1}, -S^2]^4)/2 + ((-41*Pi^2*S)/18 - (S*(262 + 277*S^2 + 170*S^4 + 3*S^6))/(24*(1 + S^2)^2))*HPL[{2}, -S^2] - (35*S*HPL[{2}, -S^2]^2)/12 + HPL[{1}, -S^2]^2*((-85*Pi^2*S)/36 + (-63 - 596*S^2 - 336*S^4 - 172*S^6 - 9*S^8)/(24*S*(1 + S^2)^2) - (19*S*HPL[{2}, -S^2])/3) - (S*(5 + 5*S^2 + S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) - (5*S*HPL[{4}, -S^2])/2 + ((-14 + 43*S^2 + 33*S^4 - 5*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) + (44*S*HPL[{3, 1}, -S^2])/3 - 28*S*HPL[{2, 1, 1}, -S^2] - (S*(17 + 39*S^2 + 21*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(277 + 19*S^2))/(48*S) + (Pi^2*(79 - 656*S^2 - 699*S^4 - 134*S^6))/(72*S*(1 + S^2)^2) + ((7 - 66*S^2 - 58*S^4 - 4*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) - S*HPL[{3}, -S^2] + (38*S*HPL[{2, 1}, -S^2])/3 + (2*S*Zeta[3])/3)) + HPL[{0}, S^2]^2*(-(Pi^2*S*(267 + 41*S^2))/24 + (3*(4 - 329*S^2 + 16*S^4))/(32*S) + (Pi^4*S*(-2146 - 1457*S^2 + 122*S^4))/(720*(1 + S^2)^2) + ((13 - 120*S^2 - 109*S^4 - 10*S^6)*HPL[{1}, -S^2]^4)/(4*S*(1 + S^2)^2) - (17*S*HPL[{1}, -S^2]^5)/5 + ((-1 - 102*S^2 - 96*S^4 - 16*S^6)*HPL[{2}, -S^2]^2)/(4*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-44*Pi^2*S)/9 + (-37 - 518*S^2 - 162*S^4 - 98*S^6 - 9*S^8)/(12*S*(1 + S^2)^2) - (38*S*HPL[{2}, -S^2])/3) + ((3*Pi^2*S)/2 + (-5 - 32*S^2 - 48*S^4 - 12*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((3 + 18*S^2 + 17*S^4 + 4*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) + 10*S*HPL[{5}, -S^2] + ((-8*Pi^2*S)/3 + (28 + 260*S^2 + 69*S^4 - 14*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (3*S*(31 + 32*S^2 + 7*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - 4*S*HPL[{3, 2}, -S^2] - 21*S*HPL[{4, 1}, -S^2] - (2*(1 + 100*S^2 + 102*S^4 + 22*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 2*S*HPL[{2, 2, 1}, -S^2] + 12*S*HPL[{3, 1, 1}, -S^2] - 28*S*HPL[{2, 1, 1, 1}, -S^2] + (-(Pi^2*S)/2 + (S*(-50 - 99*S^2 - 24*S^4 + 9*S^6))/(4*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-2 - 384*S^2 - 447*S^4 - 128*S^6))/(24*S*(1 + S^2)^2) + (4 - 43*S^2 - 120*S^4 - 12*S^6)/(8*S^3) + 2*S*HPL[{3}, -S^2] + S*HPL[{2, 1}, -S^2] + S*Zeta[3]) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(229 + 23*S^2))/(16*S) + (Pi^2*(19 - 164*S^2 - 165*S^4 - 26*S^6))/(6*S*(1 + S^2)^2) + ((35 - 292*S^2 - 309*S^4 - 58*S^6)*HPL[{2}, -S^2])/(4*S*(1 + S^2)^2) + 3*S*HPL[{3}, -S^2] + 38*S*HPL[{2, 1}, -S^2] + 4*S*Zeta[3]) + HPL[{1}, -S^2]*((-63*Pi^4*S)/40 - ((1 + S^2)*(1 + 156*S^2 + 10*S^4))/(8*S^3) + (Pi^2*(-64 - 631*S^2 - 363*S^4 - 154*S^6 - 6*S^8))/(24*S*(1 + S^2)^2) + ((-21*Pi^2*S)/4 + (-21 - 253*S^2 - 124*S^4 - 47*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{2}, -S^2] - (21*S*HPL[{2}, -S^2]^2)/2 + ((1 + 2*S^2 - 14*S^4 - 12*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 2*S*HPL[{4}, -S^2] + ((-35 + 292*S^2 + 309*S^4 + 58*S^6)*HPL[{2, 1}, -S^2])/(2*S*(1 + S^2)^2) + 36*S*HPL[{3, 1}, -S^2] - 76*S*HPL[{2, 1, 1}, -S^2] + ((1 + 12*S^2 - 19*S^4 - 22*S^6)*Zeta[3])/(2*S*(1 + S^2)^2))) + ((55*Pi^2*S)/3 + (S*(4 - 31*S^2 + 71*S^4 + 12*S^6))/(1 + S^2)^2)*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-52 - 4080*S^2 - 4989*S^4 - 1564*S^6))/(720*S*(1 + S^2)^2) + (Pi^2*(8 - 87*S^2 - 250*S^4 - 24*S^6))/(24*S^3) + (85 - 342*S^2 - 933*S^4 + 48*S^6)/(16*S^3) + ((43*Pi^2*S)/3 + (3 - 23*S^2 - 179*S^4 + 5*S^6 + 6*S^8)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((1 + 2*S^2 - 89*S^4 - 72*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) + S*HPL[{5}, -S^2] + ((38*Pi^2*S)/3 + (8 + 95*S^2 - 59*S^4 + 9*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-11 + 332*S^2 + 317*S^4 + 50*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 158*S*HPL[{3, 2}, -S^2] - 490*S*HPL[{4, 1}, -S^2] - (4*(-3 + 168*S^2 + 155*S^4 + 22*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 152*S*HPL[{2, 2, 1}, -S^2] - 128*S*HPL[{3, 1, 1}, -S^2] + 296*S*HPL[{2, 1, 1, 1}, -S^2] + (13*Pi^2*S + (-10 - 13*S^2 - 57*S^4 + 25*S^6 + 3*S^8)/(S*(1 + S^2)^2))*Zeta[3] + 74*S*Zeta[5]) + HPL[{1}, -S^2]^2*((-7*Pi^2*(1 + S^2)*(15 + 2*S^2))/(12*S) - ((1 + S^2)*(-1 + 118*S^2 + 21*S^4))/(4*S^3) + (Pi^4*(534 - 5230*S^2 - 4327*S^4 - 110*S^6))/(360*S*(1 + S^2)^2) + (19*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^2) + (16*Pi^2*S + (-13 - 20*S^2 - 191*S^4 - 4*S^6)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((1 + 108*S^2 - 67*S^4 - 118*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) + 22*S*HPL[{5}, -S^2] + ((38*Pi^2*S)/3 + (2*(13 + 106*S^2 + 13*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (4*(-5 + 6*S^2 + 62*S^4 + 44*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 152*S*HPL[{3, 2}, -S^2] - 512*S*HPL[{4, 1}, -S^2] - (54*(-1 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/S - 304*S*HPL[{2, 2, 1}, -S^2] - 552*S*HPL[{3, 1, 1}, -S^2] + ((43*Pi^2*S)/3 + (2 + 37*S^2 - 86*S^4 + 35*S^6)/(S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(4 - 171*S^2 + 5*S^4))/(4*S^3) + (Pi^2*(31 - 200*S^2 - 303*S^4 - 110*S^6))/(6*S*(1 + S^2)^2) + 76*S*HPL[{3}, -S^2] + 152*S*HPL[{2, 1}, -S^2] + 76*S*Zeta[3]) + 94*S*Zeta[5]) + Log[T]^2*(-(Pi^2*S*(37 + 3*S^2))/3 - (3*(-2 + 9*S^2))/(4*S) - (119*Pi^4*S*(60 + 55*S^2 + 8*S^4))/(360*(1 + S^2)^2) - (2*S*HPL[{0}, S^2]^5)/3 + ((-94*Pi^2*S)/3 + (-41 - 592*S^2 + 10*S^4 - 168*S^6 - 9*S^8)/(3*S*(1 + S^2)^2))*HPL[{1}, -S^2]^3 + (15*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)^2) - 24*S*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^4*(-(S*(220 + 255*S^2 + 72*S^4))/(24*(1 + S^2)^2) - (37*S*HPL[{1}, -S^2])/12) + ((3 - 168*S^2 - 155*S^4 - 22*S^6)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^2) + HPL[{0}, S^2]^3*((-43*Pi^2*S)/9 - (S*(143 + 142*S^2 + 95*S^4 + 6*S^6))/(6*(1 + S^2)^2) + ((17 - 158*S^2 - 142*S^4 - 12*S^6)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^2) - 15*S*HPL[{1}, -S^2]^2 - 14*S*HPL[{2}, -S^2]) + ((98*Pi^2*S)/3 + (-20 - 53*S^2 - 195*S^4 + 21*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((5 + 78*S^2 + S^4 - 44*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) + 54*S*HPL[{5}, -S^2] + ((-104*Pi^2*S)/3 + (48 + 238*S^2 - 55*S^4 - 9*S^6)/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (2*(11 + 10*S^2 + 57*S^4 + 44*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 316*S*HPL[{3, 2}, -S^2] - 1032*S*HPL[{4, 1}, -S^2] - (32*(1 + 5*S^2)*HPL[{2, 1, 1}, -S^2])/S - 296*S*HPL[{2, 2, 1}, -S^2] - 176*S*HPL[{3, 1, 1}, -S^2] - 720*S*HPL[{2, 1, 1, 1}, -S^2] + ((98*Pi^2*S)/3 + (S*(6 - 95*S^2 + 64*S^4 + 9*S^6))/(1 + S^2)^2)*Zeta[3] + HPL[{0}, S^2]^2*(-(S*(139 + 12*S^2))/4 - (2*Pi^2*S*(58 + 61*S^2 + 14*S^4))/(3*(1 + S^2)^2) - (3*(-13 + 120*S^2 + 109*S^4 + 10*S^6)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)^2) - 34*S*HPL[{1}, -S^2]^3 + ((-1 - 100*S^2 - 102*S^4 - 22*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + HPL[{1}, -S^2]*((-44*Pi^2*S)/3 + (-37 - 518*S^2 - 162*S^4 - 98*S^6 - 9*S^8)/(4*S*(1 + S^2)^2) - 38*S*HPL[{2}, -S^2]) + 9*S*HPL[{3}, -S^2] - 14*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2}, -S^2]*((Pi^2*(-5 - 128*S^2 - 146*S^4 - 42*S^6))/(3*S*(1 + S^2)^2) + (2 - 22*S^2 - 65*S^4 - 6*S^6)/S^3 + 164*S*HPL[{3}, -S^2] + 148*S*HPL[{2, 1}, -S^2] + 152*S*Zeta[3]) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(191 + 33*S^2))/(4*S) + (Pi^2*(14 - 150*S^2 - 107*S^4 + 10*S^6))/(S*(1 + S^2)^2) - (27*(-1 + 6*S^2)*HPL[{2}, -S^2])/S + 180*S*HPL[{3}, -S^2] + 156*S*Zeta[3]) + HPL[{1}, -S^2]*((-1547*Pi^4*S)/180 - ((1 + S^2)*(2 + 205*S^2 + 27*S^4))/(4*S^3) + (Pi^2*(-39 - 555*S^2 - 76*S^4 - 133*S^6 - 9*S^8))/(6*S*(1 + S^2)^2) + ((-38*Pi^2*S)/3 - (2*(13 + 106*S^2 + 13*S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] - 76*S*HPL[{2}, -S^2]^2 - (18*(1 - 24*S^2 - S^4 + 14*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 56*S*HPL[{4}, -S^2] + (54*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S - 56*S*HPL[{3, 1}, -S^2] - (12*(1 - 30*S^2 + 2*S^4 + 20*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]*((-253*Pi^4*S)/30 - (S*(217 + 27*S^2))/4 - (Pi^2*S*(538 + 335*S^2 + 358*S^4 + 21*S^6))/(12*(1 + S^2)^2) + (30*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)^2) - 60*S*HPL[{1}, -S^2]^4 + (-42*Pi^2*S + (-8 - 264*S^2 - 121*S^4 - 186*S^6 - 9*S^8)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2] - 77*S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*(-45*Pi^2*S + (-41 - 592*S^2 + 10*S^4 - 168*S^6 - 9*S^8)/(2*S*(1 + S^2)^2) - 156*S*HPL[{2}, -S^2]) - (2*(-2 + 5*S^2 + 11*S^4 + 5*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - 26*S*HPL[{4}, -S^2] + (2*(-41 + 232*S^2 + 197*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 336*S*HPL[{3, 1}, -S^2] - 672*S*HPL[{2, 1, 1}, -S^2] - (2*S*(-24 - 13*S^2 + 4*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*(-((1 + S^2)*(191 + 33*S^2))/(4*S) + (Pi^2*(79 - 856*S^2 - 599*S^4 + 66*S^6))/(6*S*(1 + S^2)^2) + (39*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - 4*S*HPL[{3}, -S^2] + 312*S*HPL[{2, 1}, -S^2] + 28*S*Zeta[3])) + 220*S*Zeta[5]) + HPL[{1}, -S^2]*((-11857*Pi^6*S)/15120 - (Pi^2*(1 + S^2)*(4 + 517*S^2 + 47*S^4))/(48*S^3) - ((1 + S^2)*(-53 + 390*S^2 + 213*S^4))/(16*S^3) + (Pi^4*(-655 - 7802*S^2 - 2789*S^4 - 1965*S^6 - 135*S^8))/(720*S*(1 + S^2)^2) + ((-59*Pi^2*S)/6 + (-13 - 228*S^2 + 36*S^4 - 56*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - 6*S*HPL[{3}, -S^2]^2 + ((16*Pi^2*S)/3 + (-35 - 165*S^2 - 321*S^4 - 85*S^6 - 6*S^8)/(2*S*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(-4 - 6*S^2 + 55*S^4 + 46*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) + 21*S*HPL[{6}, -S^2] + 152*S*HPL[{2, 1}, -S^2]^2 + ((22*Pi^2*S)/3 + (39 + 268*S^2 + 346*S^4 + 64*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(5 - 96*S^2 - 17*S^4 + 46*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + ((59 - 1260*S^2 - 137*S^4 + 670*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) - 18*S*HPL[{4, 2}, -S^2] - 116*S*HPL[{5, 1}, -S^2] + ((-76*Pi^2*S)/3 - (4*(13 + 106*S^2 + 13*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (76*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (24*(-8 + 78*S^2 + 65*S^4 + 2*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 112*S*HPL[{4, 1, 1}, -S^2] + (108*(-1 + 6*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 112*S*HPL[{3, 1, 1, 1}, -S^2] + (((1 + S^2)*(-19 + 5*S^2))/(2*S) + (Pi^2*(-5 + 192*S^2 - 31*S^4 - 142*S^6))/(6*S*(1 + S^2)^2))*Zeta[3] - 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(4 - 171*S^2 + 5*S^4))/(2*S^3) + (Pi^2*(-31 + 200*S^2 + 303*S^4 + 110*S^6))/(3*S*(1 + S^2)^2) - 152*S*Zeta[3]) + HPL[{3}, -S^2]*(((1 + S^2)*(-29 + 3*S^2))/S + (Pi^2*(-7 + 220*S^2 - 19*S^4 - 150*S^6))/(6*S*(1 + S^2)^2) - 152*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2}, -S^2]*((-67*Pi^4*S)/40 + ((1 + S^2)*(12 - 447*S^2 + 7*S^4))/(8*S^3) + (Pi^2*(-47 - 491*S^2 - 362*S^4 - 73*S^6 - 3*S^8))/(12*S*(1 + S^2)^2) - (2*(5 - 96*S^2 - 17*S^4 + 46*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 18*S*HPL[{4}, -S^2] - (38*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 152*S*HPL[{3, 1}, -S^2] - 304*S*HPL[{2, 1, 1}, -S^2] - (4*(2 - 46*S^2 - 3*S^4 + 26*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - (2*(-1 - 90*S^2 + 58*S^4 + 100*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + Log[T]*((7037*Pi^6*S)/7560 + (Pi^2*S*(360 + S^2))/24 + (-14 + 51*S^2)/(4*S) + (Pi^4*S*(3194 + 1338*S^2 + 1379*S^4 + 141*S^6))/(360*(1 + S^2)^2) + (S*HPL[{0}, S^2]^6)/8 + ((47*Pi^2*S)/3 + (41 + 592*S^2 - 10*S^4 + 168*S^6 + 9*S^8)/(6*S*(1 + S^2)^2))*HPL[{1}, -S^2]^4 - (6*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)^2) + 8*S*HPL[{1}, -S^2]^6 + HPL[{0}, S^2]^5*((S*(27 + 34*S^2 + 11*S^4))/(12*(1 + S^2)^2) + (2*S*HPL[{1}, -S^2])/3) + ((40*Pi^2*S)/3 + (5 + 133*S^2 + 23*S^4 + 47*S^6)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (38*S*HPL[{2}, -S^2]^3)/3 + HPL[{0}, S^2]^4*((41*Pi^2*S)/36 + (S*(174 + 203*S^2 + 109*S^4 + 6*S^6))/(24*(1 + S^2)^2) + (37*(-1 + 8*S^2 + 9*S^4 + 2*S^6)*HPL[{1}, -S^2])/(24*S*(1 + S^2)^2) + (37*S*HPL[{1}, -S^2]^2)/12 + (17*S*HPL[{2}, -S^2])/6) + 8*S*HPL[{3}, -S^2]^2 + ((-11*Pi^2*S)/3 + (7 + 118*S^2 + 254*S^4 + 90*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(-2 + 66*S^2 + 193*S^4 + 114*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) + 50*S*HPL[{6}, -S^2] + ((-123 - 36*S^2 + 17*S^4)/S - (2*Pi^2*(-36 + 72*S^2 + 157*S^4 + 68*S^6))/(3*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - 156*S*HPL[{2, 1}, -S^2]^2 + ((-164*Pi^2*S)/3 - (2*(11 + 120*S^2 + 210*S^4 + 76*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((3 + 176*S^2 - 417*S^4 - 438*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) - (2*(-5 - 294*S^2 + 707*S^4 + 740*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + 42*S*HPL[{4, 2}, -S^2] + 156*S*HPL[{5, 1}, -S^2] + (120*Pi^2*S + (2*(4 + 186*S^2 + 107*S^4 + 9*S^6))/(S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (16*(8 - 30*S^2 + 11*S^4 + 30*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (4*(95 - 254*S^2 - 103*S^4 + 108*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 24*S*HPL[{3, 1, 2}, -S^2] + 280*S*HPL[{3, 2, 1}, -S^2] + 784*S*HPL[{4, 1, 1}, -S^2] - (8*(-35 + 122*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 608*S*HPL[{3, 1, 1, 1}, -S^2] + 1440*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-(S*(-36 + 17*S^2)) + (Pi^2*S*(-10 + 195*S^2 + 162*S^4))/(3*(1 + S^2)^2))*Zeta[3] - 12*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*(((1 + S^2)*(191 + 33*S^2))/(6*S) - (2*Pi^2*(14 - 150*S^2 - 107*S^4 + 10*S^6))/(3*S*(1 + S^2)^2) + (18*(-1 + 6*S^2)*HPL[{2}, -S^2])/S - 120*S*HPL[{3}, -S^2] - 104*S*Zeta[3]) + HPL[{3}, -S^2]*((72 + 94*S^2 - 11*S^4)/(2*S) + (Pi^2*(-1 - 96*S^2 + 291*S^4 + 290*S^6))/(6*S*(1 + S^2)^2) - 24*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{0}, S^2]^3*((S*(322 + 45*S^2))/24 + (5*Pi^2*S*(98 + 111*S^2 + 30*S^4))/(36*(1 + S^2)^2) + ((-17 + 158*S^2 + 142*S^4 + 12*S^6)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)^2) + 10*S*HPL[{1}, -S^2]^3 + (S*(89 + 83*S^2 + 13*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((85*Pi^2*S)/18 + (63 + 596*S^2 + 336*S^4 + 172*S^6 + 9*S^8)/(12*S*(1 + S^2)^2) + (38*S*HPL[{2}, -S^2])/3) - S*HPL[{3}, -S^2] + (8*S*HPL[{2, 1}, -S^2])/3 + (8*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((1547*Pi^4*S)/180 + ((1 + S^2)*(2 + 205*S^2 + 27*S^4))/(4*S^3) + (Pi^2*(39 + 555*S^2 + 76*S^4 + 133*S^6 + 9*S^8))/(6*S*(1 + S^2)^2) + ((38*Pi^2*S)/3 + (2*(13 + 106*S^2 + 13*S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] + 76*S*HPL[{2}, -S^2]^2 + (18*(1 - 24*S^2 - S^4 + 14*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - 56*S*HPL[{4}, -S^2] - (54*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S + 56*S*HPL[{3, 1}, -S^2] + (12*(1 - 30*S^2 + 2*S^4 + 20*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2}, -S^2]*((123*Pi^4*S)/20 + (-12 + 161*S^2 + 330*S^4 + S^6)/(4*S^3) + (Pi^2*(9 + 218*S^2 + 236*S^4 + 112*S^6 + 9*S^8))/(6*S*(1 + S^2)^2) + ((-3 - 88*S^2 + 213*S^4 + 222*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - 34*S*HPL[{4}, -S^2] + (8*(8 - 30*S^2 + 11*S^4 + 30*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 128*S*HPL[{3, 1}, -S^2] + 312*S*HPL[{2, 1, 1}, -S^2] + (4*(1 - 20*S^2 + 52*S^4 + 54*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]^2*(3*Pi^4*S + (S*(345 + S^2))/8 + (Pi^2*S*(590 + 551*S^2 + 334*S^4 + 21*S^6))/(24*(1 + S^2)^2) + ((-13 + 120*S^2 + 109*S^4 + 10*S^6)*HPL[{1}, -S^2]^3)/(S*(1 + S^2)^2) + 17*S*HPL[{1}, -S^2]^4 + ((79*Pi^2*S)/6 + (14 + 246*S^2 + 179*S^4 + 108*S^6 + 9*S^8)/(4*S*(1 + S^2)^2))*HPL[{2}, -S^2] + (41*S*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*((44*Pi^2*S)/3 + (37 + 518*S^2 + 162*S^4 + 98*S^6 + 9*S^8)/(4*S*(1 + S^2)^2) + 38*S*HPL[{2}, -S^2]) + ((-1 + 5*S^2 + 28*S^4 + 19*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 5*S*HPL[{4}, -S^2] + ((37 - 92*S^2 - 105*S^4 - 14*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 88*S*HPL[{3, 1}, -S^2] + 180*S*HPL[{2, 1, 1}, -S^2] + (4*S*(6 + 17*S^2 + 10*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*(((1 + S^2)*(229 + 23*S^2))/(8*S) + (Pi^2*(-19 + 164*S^2 + 165*S^4 + 26*S^6))/(3*S*(1 + S^2)^2) + ((-35 + 292*S^2 + 309*S^4 + 58*S^6)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^2) - 6*S*HPL[{3}, -S^2] - 76*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3])) + HPL[{0}, S^2]*((Pi^2*S*(88 + 13*S^2))/4 + (-6 + 251*S^2 + 42*S^4)/(4*S) + (Pi^4*S*(1615 + 1345*S^2 + 107*S^4))/(90*(1 + S^2)^2) - (15*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)^2) + 24*S*HPL[{1}, -S^2]^5 + ((-1 + 116*S^2 + 45*S^4 - 34*S^6)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*(30*Pi^2*S + (41 + 592*S^2 - 10*S^4 + 168*S^6 + 9*S^8)/(3*S*(1 + S^2)^2) + 104*S*HPL[{2}, -S^2]) + ((-8*Pi^2*S)/3 + (1 + 32*S^2 + 50*S^4 + 20*S^6 - 3*S^8)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] - (2*(1 - 4*S^2 + 19*S^4 + 18*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - 4*S*HPL[{5}, -S^2] + ((20*Pi^2*S)/3 + (-52 - 360*S^2 - 11*S^4 - 6*S^6 + 9*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(-1 - 115*S^2 - 32*S^4 + 43*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 16*S*HPL[{3, 2}, -S^2] + 52*S*HPL[{4, 1}, -S^2] - (8*(-1 - 118*S^2 - 38*S^4 + 40*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 8*S*HPL[{2, 2, 1}, -S^2] - 64*S*HPL[{3, 1, 1}, -S^2] + 96*S*HPL[{2, 1, 1, 1}, -S^2] + (-2*Pi^2*S - (S*(-36 - 103*S^2 - 36*S^4 + 3*S^6))/(1 + S^2)^2)*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(191 + 33*S^2))/(4*S) + (Pi^2*(-79 + 856*S^2 + 599*S^4 - 66*S^6))/(6*S*(1 + S^2)^2) - (39*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + 4*S*HPL[{3}, -S^2] - 312*S*HPL[{2, 1}, -S^2] - 28*S*Zeta[3]) + HPL[{2}, -S^2]*((Pi^2*(1 + 207*S^2 + 121*S^4 - 27*S^6))/(3*S*(1 + S^2)^2) + (-4 + 25*S^2 + 116*S^4 + 17*S^6)/(2*S^3) - 8*S*HPL[{3}, -S^2] + 4*S*HPL[{2, 1}, -S^2] - 24*S*Zeta[3]) + HPL[{1}, -S^2]*((377*Pi^4*S)/45 + ((1 + S^2)*(2 + 205*S^2 + 27*S^4))/(4*S^3) + (Pi^2*(52 + 594*S^2 + 163*S^4 + 170*S^6 + 9*S^8))/(6*S*(1 + S^2)^2) + ((116*Pi^2*S)/3 + (6*(5 + 52*S^2 + 11*S^4 + 16*S^6))/(S*(1 + S^2)^2))*HPL[{2}, -S^2] + 76*S*HPL[{2}, -S^2]^2 - (4*S*(-2 + S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 24*S*HPL[{4}, -S^2] + (78*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 312*S*HPL[{3, 1}, -S^2] + 624*S*HPL[{2, 1, 1}, -S^2] + (2*(3 - 40*S^2 - 19*S^4 + 10*S^6)*Zeta[3])/(S*(1 + S^2)^2))) + (2*S*(20 + 275*S^2 + 208*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((7*Pi^2*(1 + S^2)*(15 + 2*S^2))/(6*S) + ((1 + S^2)*(-1 + 118*S^2 + 21*S^4))/(2*S^3) + (Pi^4*(-534 + 5230*S^2 + 4327*S^4 + 110*S^6))/(180*S*(1 + S^2)^2) - (19*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^2) + (-32*Pi^2*S + (2*(13 + 20*S^2 + 191*S^4 + 4*S^6))/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-1 - 108*S^2 + 67*S^4 + 118*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - 44*S*HPL[{5}, -S^2] + ((-76*Pi^2*S)/3 - (4*(13 + 106*S^2 + 13*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (8*(-5 + 6*S^2 + 62*S^4 + 44*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 304*S*HPL[{3, 2}, -S^2] + 1024*S*HPL[{4, 1}, -S^2] + (108*(-1 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/S + 608*S*HPL[{2, 2, 1}, -S^2] + 1104*S*HPL[{3, 1, 1}, -S^2] + ((-86*Pi^2*S)/3 - (2*(2 + 37*S^2 - 86*S^4 + 35*S^6))/(S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(4 - 171*S^2 + 5*S^4))/(2*S^3) + (Pi^2*(-31 + 200*S^2 + 303*S^4 + 110*S^6))/(3*S*(1 + S^2)^2) - 152*S*HPL[{3}, -S^2] - 304*S*HPL[{2, 1}, -S^2] - 152*S*Zeta[3]) - 188*S*Zeta[5])) + HPL[{0}, S^2]*((-2437*Pi^6*S)/3780 - (Pi^2*S*(562 + 35*S^2))/96 + (28 - 501*S^2 - 213*S^4)/(16*S) - (Pi^4*S*(1611 + 1166*S^2 + 1378*S^4 + 315*S^6))/(360*(1 + S^2)^2) + (3*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)^2) - 4*S*HPL[{1}, -S^2]^6 + ((-28*Pi^2*S)/3 + (10 - 92*S^2 - 23*S^4 - 76*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - 12*S*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*((-15*Pi^2*S)/2 + (-41 - 592*S^2 + 10*S^4 - 168*S^6 - 9*S^8)/(12*S*(1 + S^2)^2) - 26*S*HPL[{2}, -S^2]) + 2*S*HPL[{3}, -S^2]^2 + ((-14*Pi^2*S)/3 + (-2 - 20*S^2 + S^4 - 2*S^6 + 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{4}, -S^2] - (4*(1 + 15*S^2 + 17*S^4 + 5*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) - 40*S*HPL[{6}, -S^2] + ((52 + 11*S^2 - 6*S^4)/S + (Pi^2*(-69 + 318*S^2 + 263*S^4 - 8*S^6))/(6*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + 154*S*HPL[{2, 1}, -S^2]^2 + ((128*Pi^2*S)/3 + (7 + 140*S^2 + 65*S^4 + 88*S^6)/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (8*S*(-2 + S^2 + 2*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (2*(-1 + 4*S^2 + 41*S^4 + 30*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + 44*S*HPL[{5, 1}, -S^2] + (-84*Pi^2*S + (-8 - 264*S^2 - 121*S^4 - 186*S^6 - 9*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(9 - 56*S^2 - 44*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*(56 - 341*S^2 - 275*S^4 + 7*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 288*S*HPL[{3, 2, 1}, -S^2] - 916*S*HPL[{4, 1, 1}, -S^2] + (4*(-41 + 232*S^2 + 197*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 672*S*HPL[{3, 1, 1, 1}, -S^2] - 1344*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((S*(-6 + 13*S^2))/2 - (Pi^2*S*(10 + 65*S^2 + 46*S^4))/(6*(1 + S^2)^2))*Zeta[3] + HPL[{3}, -S^2]*((-12 - 64*S^2 - S^4)/(4*S) + (Pi^2*(1 - 10*S^2 - 13*S^4 - 4*S^6))/(3*S*(1 + S^2)^2) - 8*S*HPL[{2, 1}, -S^2] + 4*S*Zeta[3]) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(191 + 33*S^2))/(12*S) + (Pi^2*(79 - 856*S^2 - 599*S^4 + 66*S^6))/(18*S*(1 + S^2)^2) + (13*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (4*S*HPL[{3}, -S^2])/3 + 104*S*HPL[{2, 1}, -S^2] + (28*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-377*Pi^4*S)/90 - ((1 + S^2)*(2 + 205*S^2 + 27*S^4))/(8*S^3) + (Pi^2*(-52 - 594*S^2 - 163*S^4 - 170*S^6 - 9*S^8))/(12*S*(1 + S^2)^2) + ((-58*Pi^2*S)/3 - (3*(5 + 52*S^2 + 11*S^4 + 16*S^6))/(S*(1 + S^2)^2))*HPL[{2}, -S^2] - 38*S*HPL[{2}, -S^2]^2 + (2*S*(-2 + S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 12*S*HPL[{4}, -S^2] - (39*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 156*S*HPL[{3, 1}, -S^2] - 312*S*HPL[{2, 1, 1}, -S^2] + ((-3 + 40*S^2 + 19*S^4 - 10*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-178*Pi^4*S)/45 + (6 - 27*S^2 - 115*S^4 - 4*S^6)/(4*S^3) + (Pi^2*(-4 - 263*S^2 - 199*S^4 - 178*S^6 - 6*S^8))/(12*S*(1 + S^2)^2) - (4*S*(-2 + S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 4*S*HPL[{4}, -S^2] - (4*(9 - 56*S^2 - 44*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 152*S*HPL[{3, 1}, -S^2] - 308*S*HPL[{2, 1, 1}, -S^2] - (2*(-1 - 11*S^2 - 4*S^4 + 3*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - (4*S*(-5 + 3*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-13*Pi^2*(1 + S^2)*(9 + S^2))/(12*S) - ((1 + S^2)*(-1 + 118*S^2 + 21*S^4))/(4*S^3) + (Pi^4*(525 - 5116*S^2 - 4267*S^4 - 134*S^6))/(360*S*(1 + S^2)^2) + (19*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^2) + ((-4*Pi^2*S)/3 + (-9 - 40*S^2 - 46*S^4 - 16*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(1 - 16*S^2 - 5*S^4 + 6*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - 16*S*HPL[{5}, -S^2] + ((116*Pi^2*S)/3 + (6*(5 + 52*S^2 + 11*S^4 + 16*S^6))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(19 - 232*S^2 - 131*S^4 + 42*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 16*S*HPL[{3, 2}, -S^2] - 24*S*HPL[{4, 1}, -S^2] + (78*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 304*S*HPL[{2, 2, 1}, -S^2] - 920*S*HPL[{3, 1, 1}, -S^2] + 624*S*HPL[{2, 1, 1, 1}, -S^2] + (3*Pi^2*S + (-6 - 17*S^2 - 59*S^4 - 23*S^6 - 3*S^8)/(S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-4 + 133*S^2 + 5*S^4))/(4*S^3) + (Pi^2*(67 - 732*S^2 - 505*S^4 + 62*S^6))/(12*S*(1 + S^2)^2) + 8*S*HPL[{3}, -S^2] + 152*S*HPL[{2, 1}, -S^2] + 12*S*Zeta[3]) + 16*S*Zeta[5])) + 150*S*Zeta[7];
E4vwuT3F3=(1472 + 5255*S^2)/(5832*S) + (Pi^6*S^3*(52539 + 57650*S^2 + 16968*S^4))/(90720*(1 + S^2)^2) + (Pi^4*(2910 + 8880*S^2 + 28451*S^4))/(19440*S) + (Pi^2*(5374 + 17611*S^2 + 129762*S^4))/(23328*S) + ((47*Pi^2*S^3)/45 + (352 + 2135*S^2 + 3376*S^4 + 14698*S^6 + 9848*S^8 + 3223*S^10)/(810*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^5 + ((2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^6)/(9*S^3*(1 + S^2)^2) + (8*S^3*HPL[{1}, -S^2]^7)/21 + HPL[{0}, S^2]^6*((S^3*(3 + 2*S^2))/(96*(1 + S^2)^2) + (S^3*HPL[{1}, -S^2])/48) + (2*(-3 + 38*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^5*((Pi^2*S^3)/54 + (12 + 18*S^2 + 123*S^4 + 138*S^6 + 53*S^8)/(288*S*(1 + S^2)^2) + ((6 + 12*S^2 + 6*S^4 + 81*S^6 + 98*S^8 + 33*S^10)*HPL[{1}, -S^2])/(144*S^3*(1 + S^2)^2) + (S^3*HPL[{1}, -S^2]^2)/9 + (S^3*HPL[{2}, -S^2])/9) + ((-4 - 8*S^2 - 4*S^4 + 47*S^6 + 22*S^8 - 7*S^10)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((-47*Pi^2*S^3)/18 + (194 + 457*S^2 + 230*S^4 - 22*S^6 + 475*S^8 + 68*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-20 - 40*S^2 - 20*S^4 - 453*S^6 - 654*S^8 - 264*S^10)*HPL[{6}, -S^2])/(18*S^3*(1 + S^2)^2) - (106*S^3*HPL[{7}, -S^2])/3 - (2*(6 + 12*S^2 + 6*S^4 + 527*S^6 + 598*S^8 + 185*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + HPL[{4}, -S^2]*((-326 - 521*S^2 + 88*S^4 + 1150*S^6)/(216*S^3) + (Pi^2*(11 + 22*S^2 + 11*S^4 - 143*S^6 - 94*S^8 + S^10))/(54*S^3*(1 + S^2)^2) + (2*S^3*HPL[{2, 1}, -S^2])/3) + ((83*Pi^2*S^3)/9 + (-88 + 277*S^2 + 524*S^4 + 5540*S^6 + 796*S^8 + 887*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + (31*Pi^2*S^3 + (30 + 741*S^2 + 984*S^4 + 9203*S^6 + 1060*S^8 + 1346*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((1 + 2*S^2 + S^4 + 38*S^6 + 40*S^8 + 11*S^10)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (10*S^3*HPL[{4, 3}, -S^2])/3 + (2*(-4 - 8*S^2 - 4*S^4 + 271*S^6 + 194*S^8 + 10*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 11*S^3*HPL[{5, 2}, -S^2] + (142*S^3*HPL[{6, 1}, -S^2])/3 + ((76*Pi^2*S^3)/9 + (2*(163 + 680*S^2 + 1009*S^4 + 2712*S^6 + 882*S^8 + 30*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((32*Pi^2*S^3)/9 + (794 + 3505*S^2 + 5582*S^4 + 12844*S^6 + 4448*S^8 - 557*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + ((2 - 11*S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + ((-42 + 575*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (310*S^3*HPL[{3, 2, 2}, -S^2])/3 - (944*S^3*HPL[{3, 3, 1}, -S^2])/3 + (4*(-31 - 62*S^2 - 31*S^4 + 315*S^6 + 798*S^8 + 441*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (938*S^3*HPL[{4, 1, 2}, -S^2])/3 - (2858*S^3*HPL[{4, 2, 1}, -S^2])/3 - 1956*S^3*HPL[{5, 1, 1}, -S^2] + ((208*Pi^2*S^3)/9 + (2*(-234 - 846*S^2 - 1026*S^4 - 1999*S^6 + 539*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (304*S^3*HPL[{2, 2, 2, 1}, -S^2])/3 - (8*(-11 - 22*S^2 - 11*S^4 + 125*S^6 + 334*S^8 + 188*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (280*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 - (280*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 - (1192*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 - 1136*S^3*HPL[{4, 1, 1, 1}, -S^2] + (32*(-4 + 105*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) - (592*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 592*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] - (4384*S^3*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + 480*S^3*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*S^3)/3 - (2*(2 + 3*S^2 + 18*S^4 + 5*S^6))/(3*S*(1 + S^2)^2) - 2*S^3*HPL[{0}, S^2]^2 - (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) - 8*S^3*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((-2*S^3*(29 + 34*S^2 + 11*S^4))/(3*(1 + S^2)^2) - 8*S^3*HPL[{1}, -S^2]) - 4*S^3*HPL[{2}, -S^2])*Log[T]^5 + ((4*S^3*(3 + 2*S^2))/(3*(1 + S^2)^2) + (8*S^3*HPL[{0}, S^2])/3 + (8*S^3*HPL[{1}, -S^2])/3)*Log[T]^6 + ((-157*Pi^4*S^3)/270 + (-1494 - 1791*S^2 - 2564*S^4)/(972*S) + (Pi^2*(-20 - 30*S^2 - 413*S^4 + 72*S^6 - 41*S^8))/(108*S*(1 + S^2)^2))*Zeta[3] - (S^3*(23 + 82*S^2 + 50*S^4)*Zeta[3]^2)/(9*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-41 + 282*S^2 + 939*S^4 + 9084*S^6)/(81*S^3) + (2*Pi^2*(-10 - 20*S^2 - 10*S^4 + 593*S^6 + 958*S^8 + 422*S^10))/(27*S^3*(1 + S^2)^2) - (304*S^3*Zeta[3])/3) + Log[T]^4*((256 + 739*S^2)/(162*S) + (Pi^2*S^3*(563 + 562*S^2 + 140*S^4))/(54*(1 + S^2)^2) + (46*S^3*HPL[{0}, S^2]^3)/27 + ((47*Pi^2*S^3)/9 + (352 + 2135*S^2 + 3376*S^4 + 14698*S^6 + 9848*S^8 + 3223*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] + (5*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + (40*S^3*HPL[{1}, -S^2]^3)/3 + HPL[{0}, S^2]^2*((S^3*(293 + 382*S^2 + 140*S^4))/(18*(1 + S^2)^2) + (17*S^3*HPL[{1}, -S^2])/3) + (4*(-4 + 105*S^6)*HPL[{2}, -S^2])/(27*S^3) + HPL[{0}, S^2]*((136*Pi^2*S^3)/27 + (540 + 810*S^2 + 7381*S^4 + 7094*S^6 + 3223*S^8)/(162*S*(1 + S^2)^2) + (5*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) + 20*S^3*HPL[{1}, -S^2]^2 + (56*S^3*HPL[{2}, -S^2])/3) - (178*S^3*HPL[{3}, -S^2])/9 + 20*S^3*HPL[{2, 1}, -S^2] - 20*S^3*Zeta[3]) + HPL[{2}, -S^2]^2*((-283 + 915*S^2 + 2733*S^4 + 8760*S^6)/(648*S^3) + (Pi^2*(4 + 8*S^2 + 4*S^4 + 899*S^6 + 1090*S^8 + 368*S^10))/(108*S^3*(1 + S^2)^2) - (41*S^3*HPL[{3}, -S^2])/3 + (38*S^3*HPL[{2, 1}, -S^2])/3 - 12*S^3*Zeta[3]) + HPL[{1}, -S^2]^4*(((1 + S^2)*(512 + 917*S^2 + 6791*S^4))/(648*S^3) + (Pi^2*(28 + 56*S^2 + 28*S^4 + 577*S^6 + 590*S^8 + 154*S^10))/(54*S^3*(1 + S^2)^2) + ((2 + 11*S^6)*HPL[{2}, -S^2])/(2*S^3) - 10*S^3*HPL[{3}, -S^2] - (26*S^3*Zeta[3])/3) + HPL[{0}, S^2]^4*((Pi^2*S^3*(193 + 222*S^2 + 70*S^4))/(432*(1 + S^2)^2) + (32 + 725*S^2 + 3618*S^4)/(2592*S) + (37*(2 + 4*S^2 + 2*S^4 + 29*S^6 + 34*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)^2) + (37*S^3*HPL[{1}, -S^2]^3)/108 + (5*S^3*(43 + 66*S^2 + 28*S^4)*HPL[{2}, -S^2])/(144*(1 + S^2)^2) + HPL[{1}, -S^2]*((41*Pi^2*S^3)/216 + (32 + 1249*S^2 + 2552*S^4 + 10580*S^6 + 9790*S^8 + 3209*S^10)/(2592*S^3*(1 + S^2)^2) + (25*S^3*HPL[{2}, -S^2])/72) - (S^3*HPL[{3}, -S^2])/8 + (S^3*HPL[{2, 1}, -S^2])/4 + (7*S^3*Zeta[3])/36) + HPL[{3, 1}, -S^2]*((366 + 179*S^2 - 226*S^4 - 5933*S^6)/(108*S^3) + (Pi^2*(22 + 44*S^2 + 22*S^4 - 987*S^6 - 1710*S^8 - 789*S^10))/(54*S^3*(1 + S^2)^2) + (152*S^3*Zeta[3])/3) + HPL[{3}, -S^2]*((-103*Pi^4*S^3)/135 + (-15240 - 11403*S^2 - 2772*S^4 - 5771*S^6)/(3888*S^3) + (Pi^2*(-232 - 587*S^2 - 304*S^4 - 3118*S^6 - 392*S^8 - 679*S^10))/(648*S^3*(1 + S^2)^2) - (2*S^3*HPL[{4}, -S^2])/3 + ((46 + 92*S^2 + 46*S^4 + 703*S^6 + 494*S^8 + 19*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 52*S^3*HPL[{3, 1}, -S^2] - (328*S^3*HPL[{2, 1, 1}, -S^2])/3 - (4*S^3*(3 + 2*S^2)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((14*Pi^4*S^3)/15 + (-1187 - 1764*S^2 - 51399*S^4 + 2564*S^6)/(972*S^3) + (Pi^2*(-139 - 608*S^2 - 994*S^4 - 1894*S^6 - 851*S^8 + 176*S^10))/(81*S^3*(1 + S^2)^2) + (176*S^3*HPL[{3, 1}, -S^2])/3 + (296*S^3*HPL[{2, 1, 1}, -S^2])/3 + (4*(6 + 12*S^2 + 6*S^4 + 173*S^6 + 118*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((1547*Pi^4*S^3)/1620 + ((1 + S^2)*(3632 + 6115*S^2 + 66623*S^4))/(2916*S^3) + (Pi^2*(109 + 662*S^2 + 1045*S^4 + 4318*S^6 + 3134*S^8 + 1000*S^10))/(162*S^3*(1 + S^2)^2) + ((38*Pi^2*S^3)/27 + (56 + 497*S^2 + 513*S^4 + 2639*S^6 + 1127*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (76*S^3*HPL[{2}, -S^2]^2)/9 - (2*(2 + 4*S^2 + 2*S^4 + 101*S^6 + 82*S^8 + 11*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) - (56*S^3*HPL[{4}, -S^2])/9 - (2*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/S^3 + (56*S^3*HPL[{3, 1}, -S^2])/9 - (4*(2 + 4*S^2 + 2*S^4 + 128*S^6 + 100*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((403*Pi^4*S^3)/3240 + (876 + 3726*S^2 + 44201*S^4)/(7776*S) + (Pi^2*(474 + 711*S^2 + 5630*S^4 + 6568*S^6 + 2705*S^8))/(1944*S*(1 + S^2)^2) + ((34 + 68*S^2 + 34*S^4 + 592*S^6 + 644*S^8 + 187*S^10)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)^2) + (5*S^3*HPL[{1}, -S^2]^4)/6 + ((41*Pi^2*S^3)/54 + (168 + 252*S^2 + 2534*S^4 + 3175*S^6 + 1409*S^8)/(324*S*(1 + S^2)^2))*HPL[{2}, -S^2] + (35*S^3*HPL[{2}, -S^2]^2)/36 + HPL[{1}, -S^2]^2*((85*Pi^2*S^3)/108 + (55 + 653*S^2 + 1207*S^4 + 5086*S^6 + 4226*S^8 + 1369*S^10)/(324*S^3*(1 + S^2)^2) + (19*S^3*HPL[{2}, -S^2])/9) - (S^3*(-11 + 2*S^2 + 7*S^4)*HPL[{3}, -S^2])/(36*(1 + S^2)^2) + (5*S^3*HPL[{4}, -S^2])/6 + ((-56 - 112*S^2 - 56*S^4 - 281*S^6 - 106*S^8 + 61*S^10)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)^2) - (44*S^3*HPL[{3, 1}, -S^2])/9 + (28*S^3*HPL[{2, 1, 1}, -S^2])/3 + (S^3*(35 + 78*S^2 + 41*S^4)*Zeta[3])/(18*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(73 + 216*S^2 + 3085*S^4))/(648*S^3) + (Pi^2*(158 + 316*S^2 + 158*S^4 + 2399*S^6 + 2758*S^8 + 869*S^10))/(648*S^3*(1 + S^2)^2) + ((14 + 28*S^2 + 14*S^4 + 248*S^6 + 268*S^8 + 77*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) + (S^3*HPL[{3}, -S^2])/3 - (38*S^3*HPL[{2, 1}, -S^2])/9 - (2*S^3*Zeta[3])/9)) + Log[T]^3*((-781*Pi^4*S^3)/810 + (-244 - 845*S^2)/(162*S) + (Pi^2*(-336 - 504*S^2 - 3595*S^4 - 2666*S^6 - 931*S^8))/(162*S*(1 + S^2)^2) - (37*S^3*HPL[{0}, S^2]^4)/54 + ((-94*Pi^2*S^3)/9 + (-352 - 2135*S^2 - 3376*S^4 - 14698*S^6 - 9848*S^8 - 3223*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^2 - (20*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) - (40*S^3*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*(-(S^3*(91 + 122*S^2 + 46*S^4))/(9*(1 + S^2)^2) - (10*S^3*HPL[{1}, -S^2])/3) + ((-20*Pi^2*S^3)/3 + (122 - 148*S^2 - 3279*S^6 - 2793*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (26*S^3*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((-82*Pi^2*S^3)/27 + (-156 - 234*S^2 - 1975*S^4 - 2216*S^6 - 931*S^8)/(54*S*(1 + S^2)^2) + ((-26 - 52*S^2 - 26*S^4 - 449*S^6 - 490*S^8 - 143*S^10)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) - (34*S^3*HPL[{1}, -S^2]^2)/3 - 10*S^3*HPL[{2}, -S^2]) + (4*(1 + 2*S^2 + S^4 + 507*S^6 + 474*S^8 + 102*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (64*S^3*HPL[{4}, -S^2])/9 - (4*(-70 + 123*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (304*S^3*HPL[{3, 1}, -S^2])/9 - 80*S^3*HPL[{2, 1, 1}, -S^2] + (4*S^3*(158 + 160*S^2 + 41*S^4)*Zeta[3])/(9*(1 + S^2)^2) + HPL[{0}, S^2]*((-656 - 1442*S^2 - 6791*S^4)/(162*S) - (Pi^2*S^3*(236 + 292*S^2 + 101*S^4))/(9*(1 + S^2)^2) - (10*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) - (80*S^3*HPL[{1}, -S^2]^3)/3 - (4*(-2 - 4*S^2 - 2*S^4 + 594*S^6 + 720*S^8 + 243*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-10*Pi^2*S^3 + (-352 - 2135*S^2 - 3376*S^4 - 14698*S^6 - 9848*S^8 - 3223*S^10)/(81*S^3*(1 + S^2)^2) - (104*S^3*HPL[{2}, -S^2])/3) + (20*S^3*HPL[{3}, -S^2])/9 - (16*S^3*HPL[{2, 1}, -S^2])/3 + (56*S^3*Zeta[3])/9) + HPL[{1}, -S^2]*(-((1 + S^2)*(512 + 917*S^2 + 6791*S^4))/(162*S^3) - (2*Pi^2*(28 + 56*S^2 + 28*S^4 + 577*S^6 + 590*S^8 + 154*S^10))/(27*S^3*(1 + S^2)^2) - (2*(2 + 11*S^6)*HPL[{2}, -S^2])/S^3 + 40*S^3*HPL[{3}, -S^2] + (104*S^3*Zeta[3])/3)) + HPL[{0}, S^2]^2*((Pi^4*S^3*(3007 + 3746*S^2 + 1306*S^4))/(2160*(1 + S^2)^2) + (Pi^2*(310 + 1345*S^2 + 6646*S^4))/(1296*S) + (1022 + 2915*S^2 + 43254*S^4)/(2592*S) + ((26 + 52*S^2 + 26*S^4 + 449*S^6 + 490*S^8 + 143*S^10)*HPL[{1}, -S^2]^4)/(36*S^3*(1 + S^2)^2) + (17*S^3*HPL[{1}, -S^2]^5)/15 + ((-2 - 4*S^2 - 2*S^4 + 372*S^6 + 492*S^8 + 183*S^10)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((44*Pi^2*S^3)/27 + (302 + 1837*S^2 + 2894*S^4 + 11210*S^6 + 8956*S^8 + 2777*S^10)/(324*S^3*(1 + S^2)^2) + (38*S^3*HPL[{2}, -S^2])/9) + (-(Pi^2*S^3)/2 + (-24 - 6*S^2 + 84*S^4 + 155*S^6 + 226*S^8 + 29*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((3 + 6*S^2 + 3*S^4 - S^6 + 10*S^8 + 8*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (10*S^3*HPL[{5}, -S^2])/3 + ((8*Pi^2*S^3)/9 + (-322 - 1352*S^2 - 2104*S^4 - 4551*S^6 - 1944*S^8 + 165*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (S^3*(737 + 1042*S^2 + 413*S^4)*HPL[{3, 1}, -S^2])/(18*(1 + S^2)^2) + (4*S^3*HPL[{3, 2}, -S^2])/3 + 7*S^3*HPL[{4, 1}, -S^2] + (2*(-2 - 4*S^2 - 2*S^4 + 383*S^6 + 538*S^8 + 212*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*S^3*HPL[{2, 2, 1}, -S^2])/3 - 4*S^3*HPL[{3, 1, 1}, -S^2] + (28*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((Pi^2*S^3)/6 + (6 + 9*S^2 + 172*S^4 + 449*S^6 + 208*S^8)/(54*S*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(522 + 641*S^2 + 6045*S^4))/(432*S^3) + (Pi^2*(38 + 76*S^2 + 38*S^4 + 605*S^6 + 682*S^8 + 209*S^10))/(54*S^3*(1 + S^2)^2) + ((70 + 140*S^2 + 70*S^4 + 1069*S^6 + 1226*S^8 + 385*S^10)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)^2) - S^3*HPL[{3}, -S^2] - (38*S^3*HPL[{2, 1}, -S^2])/3 - (4*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((-108 + 209*S^2 + 719*S^4 + 3028*S^6)/(216*S^3) + (Pi^2*(-4 - 8*S^2 - 4*S^4 + 1411*S^6 + 2066*S^8 + 844*S^10))/(216*S^3*(1 + S^2)^2) - (2*S^3*HPL[{3}, -S^2])/3 - (S^3*HPL[{2, 1}, -S^2])/3 - (S^3*Zeta[3])/3) + HPL[{1}, -S^2]*((21*Pi^4*S^3)/40 + ((1 + S^2)*(1015 + 1289*S^2 + 20074*S^4))/(1296*S^3) + (Pi^2*(167 + 1543*S^2 + 2723*S^4 + 10895*S^6 + 9373*S^8 + 2993*S^10))/(648*S^3*(1 + S^2)^2) + ((7*Pi^2*S^3)/4 + (121 + 806*S^2 + 1327*S^4 + 4936*S^6 + 4244*S^8 + 1318*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (7*S^3*HPL[{2}, -S^2]^2)/2 + ((2 + 4*S^2 + 2*S^4 - 16*S^6 + 4*S^8 + 11*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*S^3*HPL[{4}, -S^2])/3 + ((-70 - 140*S^2 - 70*S^4 - 1069*S^6 - 1226*S^8 - 385*S^10)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^2) - 12*S^3*HPL[{3, 1}, -S^2] + (76*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((2 + 4*S^2 + 2*S^4 - 61*S^6 - 26*S^8 + 11*S^10)*Zeta[3])/(18*S^3*(1 + S^2)^2))) + ((-55*Pi^2*S^3)/9 + (12 + 18*S^2 - 676*S^4 - 53*S^6 - 217*S^8)/(27*S*(1 + S^2)^2))*Zeta[5] + Log[T]^2*((1154 + 4433*S^2)/(972*S) + (Pi^4*S^3*(7253 + 8318*S^2 + 2612*S^4))/(1080*(1 + S^2)^2) + (Pi^2*(534 + 1359*S^2 + 3028*S^4))/(324*S) + (2*S^3*HPL[{0}, S^2]^5)/9 + ((94*Pi^2*S^3)/9 + (352 + 2135*S^2 + 3376*S^4 + 14698*S^6 + 9848*S^8 + 3223*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^3 + (5*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^2) + 8*S^3*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^4*((S^3*(251 + 354*S^2 + 140*S^4))/(72*(1 + S^2)^2) + (37*S^3*HPL[{1}, -S^2])/36) + ((6 + 12*S^2 + 6*S^4 + 527*S^6 + 598*S^8 + 185*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + HPL[{0}, S^2]^3*((43*Pi^2*S^3)/27 + (408 + 612*S^2 + 5725*S^4 + 6926*S^6 + 3025*S^8)/(324*S*(1 + S^2)^2) + ((34 + 68*S^2 + 34*S^4 + 592*S^6 + 644*S^8 + 187*S^10)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^2) + 5*S^3*HPL[{1}, -S^2]^2 + (14*S^3*HPL[{2}, -S^2])/3) + ((-98*Pi^2*S^3)/9 + (-184 - 575*S^2 - 472*S^4 - 3428*S^6 - 844*S^8 - 737*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (2*(-5 - 10*S^2 - 5*S^4 + 141*S^6 + 114*S^8 + 15*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - 18*S^3*HPL[{5}, -S^2] + ((104*Pi^2*S^3)/9 + (-234 - 846*S^2 - 1026*S^4 - 1999*S^6 + 539*S^8)/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (4*(-11 - 22*S^2 - 11*S^4 + 125*S^6 + 334*S^8 + 188*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (316*S^3*HPL[{3, 2}, -S^2])/3 + 344*S^3*HPL[{4, 1}, -S^2] + (16*(-4 + 105*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (296*S^3*HPL[{2, 2, 1}, -S^2])/3 + (176*S^3*HPL[{3, 1, 1}, -S^2])/3 + 240*S^3*HPL[{2, 1, 1, 1}, -S^2] + ((-98*Pi^2*S^3)/9 + (-72 - 108*S^2 - 1583*S^4 - 682*S^6 - 539*S^8)/(27*S*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(512 + 917*S^2 + 6791*S^4))/(108*S^3) + (Pi^2*(28 + 56*S^2 + 28*S^4 + 577*S^6 + 590*S^8 + 154*S^10))/(9*S^3*(1 + S^2)^2) + (3*(2 + 11*S^6)*HPL[{2}, -S^2])/S^3 - 60*S^3*HPL[{3}, -S^2] - 52*S^3*Zeta[3]) + HPL[{2}, -S^2]*((-41 + 282*S^2 + 939*S^4 + 9084*S^6)/(162*S^3) + (Pi^2*(-10 - 20*S^2 - 10*S^4 + 593*S^6 + 958*S^8 + 422*S^10))/(27*S^3*(1 + S^2)^2) - (164*S^3*HPL[{3}, -S^2])/3 - (148*S^3*HPL[{2, 1}, -S^2])/3 - (152*S^3*Zeta[3])/3) + HPL[{0}, S^2]^2*((2*Pi^2*S^3*(68 + 92*S^2 + 35*S^4))/(9*(1 + S^2)^2) + (139 + 310*S^2 + 1514*S^4)/(54*S) + ((26 + 52*S^2 + 26*S^4 + 449*S^6 + 490*S^8 + 143*S^10)*HPL[{1}, -S^2]^2)/(6*S^3*(1 + S^2)^2) + (34*S^3*HPL[{1}, -S^2]^3)/3 + ((-2 - 4*S^2 - 2*S^4 + 383*S^6 + 538*S^8 + 212*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((44*Pi^2*S^3)/9 + (302 + 1837*S^2 + 2894*S^4 + 11210*S^6 + 8956*S^8 + 2777*S^10)/(108*S^3*(1 + S^2)^2) + (38*S^3*HPL[{2}, -S^2])/3) - 3*S^3*HPL[{3}, -S^2] + (14*S^3*HPL[{2, 1}, -S^2])/3 - (8*S^3*Zeta[3])/3) + HPL[{1}, -S^2]*((1547*Pi^4*S^3)/540 + ((1 + S^2)*(3632 + 6115*S^2 + 66623*S^4))/(972*S^3) + (Pi^2*(109 + 662*S^2 + 1045*S^4 + 4318*S^6 + 3134*S^8 + 1000*S^10))/(54*S^3*(1 + S^2)^2) + ((38*Pi^2*S^3)/9 + (56 + 497*S^2 + 513*S^4 + 2639*S^6 + 1127*S^8)/(27*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (76*S^3*HPL[{2}, -S^2]^2)/3 - (2*(2 + 4*S^2 + 2*S^4 + 101*S^6 + 82*S^8 + 11*S^10)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) - (56*S^3*HPL[{4}, -S^2])/3 - (6*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/S^3 + (56*S^3*HPL[{3, 1}, -S^2])/3 - (4*(2 + 4*S^2 + 2*S^4 + 128*S^6 + 100*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((253*Pi^4*S^3)/90 + (4176 + 8865*S^2 + 66623*S^4)/(972*S) + (Pi^2*(474 + 711*S^2 + 6553*S^4 + 7010*S^6 + 3124*S^8))/(162*S*(1 + S^2)^2) + (10*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^2) + 20*S^3*HPL[{1}, -S^2]^4 + (14*Pi^2*S^3 + (-72 + 324*S^2 + 630*S^4 + 6767*S^6 + 6964*S^8 + 3239*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (77*S^3*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*(15*Pi^2*S^3 + (352 + 2135*S^2 + 3376*S^4 + 14698*S^6 + 9848*S^8 + 3223*S^10)/(54*S^3*(1 + S^2)^2) + 52*S^3*HPL[{2}, -S^2]) + ((8 + 16*S^2 + 8*S^4 - 7*S^6 - 38*S^8 - 25*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (26*S^3*HPL[{4}, -S^2])/3 + (2*(-82 - 164*S^2 - 82*S^4 - 645*S^6 - 354*S^8 + 57*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 112*S^3*HPL[{3, 1}, -S^2] + 224*S^3*HPL[{2, 1, 1}, -S^2] - (2*S^3*(107 + 130*S^2 + 44*S^4)*Zeta[3])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(512 + 917*S^2 + 6791*S^4))/(108*S^3) + (Pi^2*(158 + 316*S^2 + 158*S^4 + 3299*S^6 + 3358*S^8 + 869*S^10))/(54*S^3*(1 + S^2)^2) + (13*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^2) + (4*S^3*HPL[{3}, -S^2])/3 - 104*S^3*HPL[{2, 1}, -S^2] - (28*S^3*Zeta[3])/3)) - (220*S^3*Zeta[5])/3) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(517 + 779*S^2 + 6418*S^4))/(648*S^3) + ((1 + S^2)*(3985 + 4812*S^2 + 75721*S^4))/(1944*S^3) + (Pi^4*(356 + 712*S^2 + 356*S^4 + 6599*S^6 + 7010*S^8 + 1958*S^10))/(1080*S^3*(1 + S^2)^2) + (19*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((-16*Pi^2*S^3)/3 + (-26 - 83*S^2 - 90*S^4 - 450*S^6 - 92*S^8 - 35*S^10)/(6*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((2 + 4*S^2 + 2*S^4 - 493*S^6 - 314*S^8 + 11*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - (22*S^3*HPL[{5}, -S^2])/3 + ((-38*Pi^2*S^3)/9 + (-56 - 497*S^2 - 513*S^4 - 2639*S^6 - 1127*S^8)/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (4*(10 + 20*S^2 + 10*S^4 - 8*S^6 + 68*S^8 + 55*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (152*S^3*HPL[{3, 2}, -S^2])/3 + (512*S^3*HPL[{4, 1}, -S^2])/3 + (6*(2 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (304*S^3*HPL[{2, 2, 1}, -S^2])/3 + 184*S^3*HPL[{3, 1, 1}, -S^2] + ((-43*Pi^2*S^3)/9 + (-25 - 149*S^2 - 241*S^4 - 1744*S^6 - 446*S^8 - 223*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(80 + 47*S^2 + 1376*S^4))/(54*S^3) + (Pi^2*(62 + 124*S^2 + 62*S^4 + 683*S^6 + 910*S^8 + 341*S^10))/(54*S^3*(1 + S^2)^2) - (76*S^3*HPL[{3}, -S^2])/3 - (152*S^3*HPL[{2, 1}, -S^2])/3 - (76*S^3*Zeta[3])/3) - (94*S^3*Zeta[5])/3) + HPL[{2}, -S^2]*((Pi^2*(-365 + 909*S^2 + 3096*S^4 + 18168*S^6))/(1944*S^3) + (-243 - 1960*S^2 + 13199*S^4 + 129762*S^6)/(3888*S^3) + (Pi^4*(-104 - 208*S^2 - 104*S^4 + 16939*S^6 + 26642*S^8 + 11512*S^10))/(6480*S^3*(1 + S^2)^2) + ((-43*Pi^2*S^3)/9 + (104 - 5*S^2 - 148*S^4 - 2668*S^6 - 356*S^8 - 463*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((1 + 2*S^2 + S^4 - 74*S^6 - 40*S^8 + 7*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (S^3*HPL[{5}, -S^2])/3 + ((-38*Pi^2*S^3)/9 + (-163 - 680*S^2 - 1009*S^4 - 2712*S^6 - 882*S^8 - 30*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-22 - 44*S^2 - 22*S^4 - 1007*S^6 - 1102*S^8 - 323*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (158*S^3*HPL[{3, 2}, -S^2])/3 + (490*S^3*HPL[{4, 1}, -S^2])/3 + (4*(6 + 12*S^2 + 6*S^4 + 527*S^6 + 598*S^8 + 185*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (152*S^3*HPL[{2, 2, 1}, -S^2])/3 + (128*S^3*HPL[{3, 1, 1}, -S^2])/3 - (296*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-13*Pi^2*S^3)/3 + (-44 - 136*S^2 - 116*S^4 - 763*S^6 - 242*S^8 - 187*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] - (74*S^3*Zeta[5])/3) + HPL[{1}, -S^2]*((11857*Pi^6*S^3)/45360 + (Pi^2*(1 + S^2)*(6677 + 9982*S^2 + 126845*S^4))/(11664*S^3) + ((1 + S^2)*(38053 + 24644*S^2 + 540781*S^4))/(11664*S^3) + (Pi^4*(358 + 2585*S^2 + 4274*S^4 + 17579*S^6 + 13713*S^8 + 4369*S^10))/(2160*S^3*(1 + S^2)^2) + ((59*Pi^2*S^3)/18 + (184 + 977*S^2 + 1480*S^4 + 6196*S^6 + 4100*S^8 + 1327*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + 2*S^3*HPL[{3}, -S^2]^2 + ((-16*Pi^2*S^3)/9 + (-340 - 683*S^2 - 412*S^4 - 1186*S^6 + 1468*S^8 + 569*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(8 + 16*S^2 + 8*S^4 - 55*S^6 + 22*S^8 + 44*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - 7*S^3*HPL[{6}, -S^2] - (152*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((-22*Pi^2*S^3)/9 - (2*(-25 + 115*S^2 + 335*S^4 + 1073*S^6 + 1636*S^8 + 506*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(10 + 20*S^2 + 10*S^4 + 397*S^6 + 338*S^8 + 55*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((118 + 236*S^2 + 118*S^4 + 5257*S^6 + 4370*S^8 + 649*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 6*S^3*HPL[{4, 2}, -S^2] + (116*S^3*HPL[{5, 1}, -S^2])/3 + ((76*Pi^2*S^3)/9 + (2*(56 + 497*S^2 + 513*S^4 + 2639*S^6 + 1127*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (76*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*(16 + 32*S^2 + 16*S^4 + 295*S^6 + 314*S^8 + 88*S^10)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (112*S^3*HPL[{4, 1, 1}, -S^2])/3 - (12*(2 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + (112*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 + (-((1 + S^2)*(-5 + 138*S^2 + 373*S^4))/(54*S^3) + (Pi^2*(-10 - 20*S^2 - 10*S^4 - 829*S^6 - 626*S^8 - 55*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] + 2*S^3*Zeta[3]^2 + HPL[{3}, -S^2]*(-((1 + S^2)*(122 + 149*S^2 + 81*S^4))/(36*S^3) + (Pi^2*(-14 - 28*S^2 - 14*S^4 - 941*S^6 - 730*S^8 - 77*S^10))/(54*S^3*(1 + S^2)^2) + (152*S^3*HPL[{2, 1}, -S^2])/3 - (8*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(80 + 47*S^2 + 1376*S^4))/(27*S^3) + (Pi^2*(-62 - 124*S^2 - 62*S^4 - 683*S^6 - 910*S^8 - 341*S^10))/(27*S^3*(1 + S^2)^2) + (152*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((67*Pi^4*S^3)/120 + ((1 + S^2)*(1996 + 731*S^2 + 56833*S^4))/(1944*S^3) + (Pi^2*(59 + 453*S^2 + 779*S^4 + 2696*S^6 + 2670*S^8 + 815*S^10))/(108*S^3*(1 + S^2)^2) - (2*(10 + 20*S^2 + 10*S^4 + 397*S^6 + 338*S^8 + 55*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - 6*S^3*HPL[{4}, -S^2] - (38*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (152*S^3*HPL[{3, 1}, -S^2])/3 + (304*S^3*HPL[{2, 1, 1}, -S^2])/3 - (4*(4 + 8*S^2 + 4*S^4 + 193*S^6 + 158*S^8 + 22*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (2*(2 + 4*S^2 + 2*S^4 - 412*S^6 - 260*S^8 + 11*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((2437*Pi^6*S^3)/11340 + (Pi^2*(10980 + 28908*S^2 + 265849*S^4))/(23328*S) + (37614 + 30621*S^2 + 540781*S^4)/(11664*S) + (Pi^4*(700 + 1050*S^2 + 8905*S^4 + 9702*S^6 + 4163*S^8))/(2160*S*(1 + S^2)^2) + ((2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^2) + (4*S^3*HPL[{1}, -S^2]^6)/3 + ((28*Pi^2*S^3)/9 + (22 + 158*S^2 + 193*S^4 + 1613*S^6 + 1612*S^8 + 740*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + 4*S^3*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*((5*Pi^2*S^3)/2 + (352 + 2135*S^2 + 3376*S^4 + 14698*S^6 + 9848*S^8 + 3223*S^10)/(324*S^3*(1 + S^2)^2) + (26*S^3*HPL[{2}, -S^2])/3) - (2*S^3*HPL[{3}, -S^2]^2)/3 + ((14*Pi^2*S^3)/9 + (14 + 40*S^2 + 32*S^4 + 235*S^6 + 212*S^8 + 91*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-8 - 16*S^2 - 8*S^4 + 93*S^6 + 90*S^8 + 21*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (40*S^3*HPL[{6}, -S^2])/3 + ((-506 - 879*S^2 - 9132*S^4 - 291*S^6)/(162*S^3) + (Pi^2*(-69 - 138*S^2 - 69*S^4 - 463*S^6 - 230*S^8 + 59*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (154*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((-128*Pi^2*S^3)/9 + (40 - 148*S^2 - 302*S^4 - 3371*S^6 - 3478*S^8 - 1625*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (8*S^3*(3 + 2*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) - (4*(1 + 2*S^2 + S^4 - 25*S^6 - 14*S^8 + 2*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (44*S^3*HPL[{5, 1}, -S^2])/3 + (28*Pi^2*S^3 + (-72 + 324*S^2 + 630*S^4 + 6767*S^6 + 6964*S^8 + 3239*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(-18 - 36*S^2 - 18*S^4 - 163*S^6 - 98*S^8 + 8*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(-224 - 448*S^2 - 224*S^4 - 1949*S^6 - 1138*S^8 + 121*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 96*S^3*HPL[{3, 2, 1}, -S^2] + (916*S^3*HPL[{4, 1, 1}, -S^2])/3 + (4*(-82 - 164*S^2 - 82*S^4 - 645*S^6 - 354*S^8 + 57*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 224*S^3*HPL[{3, 1, 1, 1}, -S^2] + 448*S^3*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-176 - 26*S^2 - 123*S^4)/(108*S) + (Pi^2*S^3*(-2 + 104*S^2 + 79*S^4))/(54*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^3*(((1 + S^2)*(512 + 917*S^2 + 6791*S^4))/(324*S^3) + (Pi^2*(158 + 316*S^2 + 158*S^4 + 3299*S^6 + 3358*S^8 + 869*S^10))/(162*S^3*(1 + S^2)^2) + (13*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*S^3*HPL[{3}, -S^2])/9 - (104*S^3*HPL[{2, 1}, -S^2])/3 - (28*S^3*Zeta[3])/9) + HPL[{3}, -S^2]*((134 - 135*S^2 + 540*S^4 + 591*S^6)/(162*S^3) + (Pi^2*(4 + 8*S^2 + 4*S^4 + 13*S^6 - 22*S^8 - 23*S^10))/(54*S^3*(1 + S^2)^2) + (8*S^3*HPL[{2, 1}, -S^2])/3 - (4*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((178*Pi^4*S^3)/135 + (698 + 1899*S^2 + 7407*S^4 + 32899*S^6)/(972*S^3) + (Pi^2*(-24 + 220*S^2 + 378*S^4 + 3945*S^6 + 4438*S^8 + 2019*S^10))/(216*S^3*(1 + S^2)^2) - (4*S^3*(3 + 2*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (4*S^3*HPL[{4}, -S^2])/3 + (4*(-18 - 36*S^2 - 18*S^4 - 163*S^6 - 98*S^8 + 8*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (152*S^3*HPL[{3, 1}, -S^2])/3 + (308*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((4 + 8*S^2 + 4*S^4 - 87*S^6 - 102*S^8 - 33*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((377*Pi^4*S^3)/270 + ((1 + S^2)*(3632 + 6115*S^2 + 66623*S^4))/(1944*S^3) + (Pi^2*(154 + 1147*S^2 + 1930*S^4 + 8290*S^6 + 6100*S^8 + 1987*S^10))/(216*S^3*(1 + S^2)^2) + ((58*Pi^2*S^3)/9 + (106 + 851*S^2 + 1492*S^4 + 6640*S^6 + 4658*S^8 + 1573*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (38*S^3*HPL[{2}, -S^2]^2)/3 + (2*S^3*(3 + 2*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + 4*S^3*HPL[{4}, -S^2] - (13*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - 52*S^3*HPL[{3, 1}, -S^2] + 104*S^3*HPL[{2, 1, 1}, -S^2] + ((-2 - 4*S^2 - 2*S^4 - 53*S^6 - 50*S^8 - 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + (4*S^3*(-5 + 14*S^2 + 13*S^4)*Zeta[5])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(658 + 1349*S^2 + 12961*S^4))/(1296*S^3) + ((1 + S^2)*(3985 + 4812*S^2 + 75721*S^4))/(1944*S^3) + (Pi^4*(350 + 700*S^2 + 350*S^4 + 6449*S^6 + 6866*S^8 + 1925*S^10))/(1080*S^3*(1 + S^2)^2) + (19*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((4*Pi^2*S^3)/9 + (-4 - 7*S^2 + 22*S^6 + 28*S^8 + 13*S^10)/(3*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(2 + 4*S^2 + 2*S^4 + 65*S^6 + 58*S^8 + 11*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*S^3*HPL[{5}, -S^2])/3 + ((-116*Pi^2*S^3)/9 + (-106 - 851*S^2 - 1492*S^4 - 6640*S^6 - 4658*S^8 - 1573*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(38 + 76*S^2 + 38*S^4 + 911*S^6 + 886*S^8 + 209*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*S^3*HPL[{3, 2}, -S^2])/3 + 8*S^3*HPL[{4, 1}, -S^2] + (26*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (304*S^3*HPL[{2, 2, 1}, -S^2])/3 + (920*S^3*HPL[{3, 1, 1}, -S^2])/3 - 208*S^3*HPL[{2, 1, 1, 1}, -S^2] + (-(Pi^2*S^3) + (-112 - 323*S^2 - 328*S^4 - 958*S^6 - 440*S^8 - 103*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(75 + 185*S^2 + 1749*S^4))/(54*S^3) + (Pi^2*(134 + 268*S^2 + 134*S^4 + 2825*S^6 + 2866*S^8 + 737*S^10))/(108*S^3*(1 + S^2)^2) - (8*S^3*HPL[{3}, -S^2])/3 - (152*S^3*HPL[{2, 1}, -S^2])/3 - 4*S^3*Zeta[3]) - (16*S^3*Zeta[5])/3)) + Log[T]*((-7037*Pi^6*S^3)/22680 + (-702 - 2689*S^2)/(972*S) + (Pi^2*(-1962 - 4863*S^2 - 19799*S^4))/(1944*S) + (Pi^4*(-2136 - 3204*S^2 - 24494*S^4 - 23065*S^6 - 8921*S^8))/(3240*S*(1 + S^2)^2) - (S^3*HPL[{0}, S^2]^6)/24 + ((-47*Pi^2*S^3)/9 + (-352 - 2135*S^2 - 3376*S^4 - 14698*S^6 - 9848*S^8 - 3223*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^4 - (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^2) - (8*S^3*HPL[{1}, -S^2]^6)/3 + HPL[{0}, S^2]^5*(-(S^3*(57 + 82*S^2 + 33*S^4))/(72*(1 + S^2)^2) - (2*S^3*HPL[{1}, -S^2])/9) + ((-40*Pi^2*S^3)/9 + (-21 - 297*S^2 - 471*S^4 - 3484*S^6 - 3218*S^8 - 1297*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (38*S^3*HPL[{2}, -S^2]^3)/9 + HPL[{0}, S^2]^4*((-41*Pi^2*S^3)/108 + (-74 - 111*S^2 - 1001*S^4 - 1290*S^6 - 548*S^8)/(216*S*(1 + S^2)^2) - (37*(2 + 4*S^2 + 2*S^4 + 29*S^6 + 34*S^8 + 11*S^10)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)^2) - (37*S^3*HPL[{1}, -S^2]^2)/36 - (17*S^3*HPL[{2}, -S^2])/18) - (8*S^3*HPL[{3}, -S^2]^2)/3 + ((11*Pi^2*S^3)/9 + (-2 - 43*S^2 - 128*S^4 - 13*S^6 - 1460*S^8 - 526*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(4 + 8*S^2 + 4*S^4 + 6*S^6 + 144*S^8 + 105*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (50*S^3*HPL[{6}, -S^2])/3 + ((521 + 480*S^2 + 7599*S^4 - 828*S^6)/(81*S^3) - (2*Pi^2*(-24 - 48*S^2 - 24*S^4 - 30*S^6 + 16*S^8 + 27*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + 52*S^3*HPL[{2, 1}, -S^2]^2 + ((164*Pi^2*S^3)/9 + (-242 - 325*S^2 - 206*S^4 + 2296*S^6 + 5624*S^8 + 2701*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((2 + 4*S^2 + 2*S^4 - 579*S^6 - 550*S^8 - 123*S^10)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*(-5 - 10*S^2 - 5*S^4 + 1433*S^6 + 1330*S^8 + 281*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 14*S^3*HPL[{4, 2}, -S^2] - 52*S^3*HPL[{5, 1}, -S^2] + (-40*Pi^2*S^3 - (2*(-122 + 148*S^2 + 3279*S^6 + 2793*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (16*(16 + 32*S^2 + 16*S^4 + 183*S^6 + 138*S^8 + 12*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*(-95 - 190*S^2 - 95*S^4 - 591*S^6 - 354*S^8 + 30*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 8*S^3*HPL[{3, 1, 2}, -S^2] - (280*S^3*HPL[{3, 2, 1}, -S^2])/3 - (784*S^3*HPL[{4, 1, 1}, -S^2])/3 - (8*(-70 + 123*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + (608*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 - 480*S^3*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*S^3*(466 + 416*S^2 + 79*S^4))/(27*(1 + S^2)^2) + (74 + 95*S^2 + 276*S^4)/(27*S))*Zeta[3] + 4*S^3*Zeta[3]^2 + HPL[{0}, S^2]^3*((-110 - 623*S^2 - 3382*S^4)/(324*S) - (Pi^2*S^3*(558 + 776*S^2 + 303*S^4))/(108*(1 + S^2)^2) + ((-34 - 68*S^2 - 34*S^4 - 592*S^6 - 644*S^8 - 187*S^10)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)^2) - (10*S^3*HPL[{1}, -S^2]^3)/3 - (S^3*(237 + 322*S^2 + 123*S^4)*HPL[{2}, -S^2])/(18*(1 + S^2)^2) + HPL[{1}, -S^2]*((-85*Pi^2*S^3)/54 + (-55 - 653*S^2 - 1207*S^4 - 5086*S^6 - 4226*S^8 - 1369*S^10)/(162*S^3*(1 + S^2)^2) - (38*S^3*HPL[{2}, -S^2])/9) + (S^3*HPL[{3}, -S^2])/3 - (8*S^3*HPL[{2, 1}, -S^2])/9 - (8*S^3*Zeta[3])/9) + HPL[{3}, -S^2]*((1664 + 2511*S^2 - 648*S^4 + 1737*S^6)/(324*S^3) + (Pi^2*(-2 - 4*S^2 - 2*S^4 + 1071*S^6 + 990*S^8 + 207*S^10))/(54*S^3*(1 + S^2)^2) + 8*S^3*HPL[{2, 1}, -S^2] + (8*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(512 + 917*S^2 + 6791*S^4))/(162*S^3) - (2*Pi^2*(28 + 56*S^2 + 28*S^4 + 577*S^6 + 590*S^8 + 154*S^10))/(27*S^3*(1 + S^2)^2) - (2*(2 + 11*S^6)*HPL[{2}, -S^2])/S^3 + 40*S^3*HPL[{3}, -S^2] + (104*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-1547*Pi^4*S^3)/540 - ((1 + S^2)*(3632 + 6115*S^2 + 66623*S^4))/(972*S^3) + (Pi^2*(-109 - 662*S^2 - 1045*S^4 - 4318*S^6 - 3134*S^8 - 1000*S^10))/(54*S^3*(1 + S^2)^2) + ((-38*Pi^2*S^3)/9 + (-56 - 497*S^2 - 513*S^4 - 2639*S^6 - 1127*S^8)/(27*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (76*S^3*HPL[{2}, -S^2]^2)/3 + (2*(2 + 4*S^2 + 2*S^4 + 101*S^6 + 82*S^8 + 11*S^10)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) + (56*S^3*HPL[{4}, -S^2])/3 + (6*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/S^3 - (56*S^3*HPL[{3, 1}, -S^2])/3 + (4*(2 + 4*S^2 + 2*S^4 + 128*S^6 + 100*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-41*Pi^4*S^3)/20 + (-809 - 963*S^2 - 6165*S^4 - 59397*S^6)/(972*S^3) + (Pi^2*(101 - 143*S^2 - 349*S^4 - 4300*S^6 - 6308*S^8 - 2797*S^10))/(162*S^3*(1 + S^2)^2) + ((-2 - 4*S^2 - 2*S^4 + 295*S^6 + 286*S^8 + 67*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) + (34*S^3*HPL[{4}, -S^2])/3 + (8*(16 + 32*S^2 + 16*S^4 + 183*S^6 + 138*S^8 + 12*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (128*S^3*HPL[{3, 1}, -S^2])/3 - 104*S^3*HPL[{2, 1, 1}, -S^2] + (4*(2 + 4*S^2 + 2*S^4 + 213*S^6 + 198*S^8 + 42*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*(-(Pi^4*S^3) + (-1230 - 2328*S^2 - 19799*S^4)/(648*S) + (Pi^2*(-304 - 456*S^2 - 3977*S^4 - 4796*S^6 - 2027*S^8))/(216*S*(1 + S^2)^2) + ((-26 - 52*S^2 - 26*S^4 - 449*S^6 - 490*S^8 - 143*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) - (17*S^3*HPL[{1}, -S^2]^4)/3 + ((-79*Pi^2*S^3)/18 + (80 - 260*S^2 - 550*S^4 - 5321*S^6 - 6544*S^8 - 2801*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (41*S^3*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((-44*Pi^2*S^3)/9 + (-302 - 1837*S^2 - 2894*S^4 - 11210*S^6 - 8956*S^8 - 2777*S^10)/(108*S^3*(1 + S^2)^2) - (38*S^3*HPL[{2}, -S^2])/3) + ((-4 - 8*S^2 - 4*S^4 + 57*S^6 + 42*S^8 + 3*S^10)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^2) - (5*S^3*HPL[{4}, -S^2])/3 + ((74 + 148*S^2 + 74*S^4 + 303*S^6 + 150*S^8 - 39*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (88*S^3*HPL[{3, 1}, -S^2])/3 - 60*S^3*HPL[{2, 1, 1}, -S^2] - (4*S^3*(2 + 16*S^2 + 11*S^4)*Zeta[3])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(522 + 641*S^2 + 6045*S^4))/(216*S^3) + (Pi^2*(-38 - 76*S^2 - 38*S^4 - 605*S^6 - 682*S^8 - 209*S^10))/(27*S^3*(1 + S^2)^2) + ((-70 - 140*S^2 - 70*S^4 - 1069*S^6 - 1226*S^8 - 385*S^10)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^2) + 2*S^3*HPL[{3}, -S^2] + (76*S^3*HPL[{2, 1}, -S^2])/3 + (8*S^3*Zeta[3])/3)) + HPL[{0}, S^2]*((-4160 - 6476*S^2 - 75721*S^4)/(972*S) + (Pi^2*(-876 - 2688*S^2 - 13555*S^4))/(648*S) - (Pi^4*S^3*(12761 + 16474*S^2 + 5975*S^4))/(1620*(1 + S^2)^2) - (5*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^2) - 8*S^3*HPL[{1}, -S^2]^5 + ((-2 - 4*S^2 - 2*S^4 - 567*S^6 - 678*S^8 - 225*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*(-10*Pi^2*S^3 + (-352 - 2135*S^2 - 3376*S^4 - 14698*S^6 - 9848*S^8 - 3223*S^10)/(81*S^3*(1 + S^2)^2) - (104*S^3*HPL[{2}, -S^2])/3) + ((8*Pi^2*S^3)/9 + (-12 - 42*S^2 - 84*S^4 - 251*S^6 - 250*S^8 - 89*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (4*(1 + 2*S^2 + S^4 + 36*S^6 + 36*S^8 + 9*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*S^3*HPL[{5}, -S^2])/3 + ((-20*Pi^2*S^3)/9 + (284 + 1378*S^2 + 2354*S^4 + 6513*S^6 + 2352*S^8 - 93*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(-4 - 8*S^2 - 4*S^4 + 1177*S^6 + 1418*S^8 + 475*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*S^3*HPL[{3, 2}, -S^2])/3 - (52*S^3*HPL[{4, 1}, -S^2])/3 - (8*(-2 - 4*S^2 - 2*S^4 + 594*S^6 + 720*S^8 + 243*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*S^3*HPL[{2, 2, 1}, -S^2])/3 + (64*S^3*HPL[{3, 1, 1}, -S^2])/3 - 32*S^3*HPL[{2, 1, 1, 1}, -S^2] + ((2*Pi^2*S^3)/3 + (2*(18 + 27*S^2 + 199*S^4 + 110*S^6 + 46*S^8))/(27*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((56 - 681*S^2 - 2472*S^4 - 10203*S^6)/(162*S^3) + (Pi^2*(4 + 8*S^2 + 4*S^4 - 1899*S^6 - 2406*S^8 - 855*S^10))/(54*S^3*(1 + S^2)^2) + (8*S^3*HPL[{3}, -S^2])/3 - (4*S^3*HPL[{2, 1}, -S^2])/3 + 8*S^3*Zeta[3]) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(512 + 917*S^2 + 6791*S^4))/(108*S^3) + (Pi^2*(-158 - 316*S^2 - 158*S^4 - 3299*S^6 - 3358*S^8 - 869*S^10))/(54*S^3*(1 + S^2)^2) - (13*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*S^3*HPL[{3}, -S^2])/3 + 104*S^3*HPL[{2, 1}, -S^2] + (28*S^3*Zeta[3])/3) + HPL[{1}, -S^2]*((-377*Pi^4*S^3)/135 - ((1 + S^2)*(3632 + 6115*S^2 + 66623*S^4))/(972*S^3) + (Pi^2*(-154 - 1147*S^2 - 1930*S^4 - 8290*S^6 - 6100*S^8 - 1987*S^10))/(108*S^3*(1 + S^2)^2) + ((-116*Pi^2*S^3)/9 + (-106 - 851*S^2 - 1492*S^4 - 6640*S^6 - 4658*S^8 - 1573*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (76*S^3*HPL[{2}, -S^2]^2)/3 - (4*S^3*(3 + 2*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 8*S^3*HPL[{4}, -S^2] + (26*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + 104*S^3*HPL[{3, 1}, -S^2] - 208*S^3*HPL[{2, 1, 1}, -S^2] + (2*(2 + 4*S^2 + 2*S^4 + 53*S^6 + 50*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2))) + (2*S^3*(475 + 386*S^2 + 52*S^4)*Zeta[5])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(517 + 779*S^2 + 6418*S^4))/(324*S^3) - ((1 + S^2)*(3985 + 4812*S^2 + 75721*S^4))/(972*S^3) + (Pi^4*(-356 - 712*S^2 - 356*S^4 - 6599*S^6 - 7010*S^8 - 1958*S^10))/(540*S^3*(1 + S^2)^2) - (19*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((32*Pi^2*S^3)/3 + (26 + 83*S^2 + 90*S^4 + 450*S^6 + 92*S^8 + 35*S^10)/(3*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-2 - 4*S^2 - 2*S^4 + 493*S^6 + 314*S^8 - 11*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (44*S^3*HPL[{5}, -S^2])/3 + ((76*Pi^2*S^3)/9 + (2*(56 + 497*S^2 + 513*S^4 + 2639*S^6 + 1127*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(10 + 20*S^2 + 10*S^4 - 8*S^6 + 68*S^8 + 55*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (304*S^3*HPL[{3, 2}, -S^2])/3 - (1024*S^3*HPL[{4, 1}, -S^2])/3 - (12*(2 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (608*S^3*HPL[{2, 2, 1}, -S^2])/3 - 368*S^3*HPL[{3, 1, 1}, -S^2] + ((86*Pi^2*S^3)/9 + (2*(25 + 149*S^2 + 241*S^4 + 1744*S^6 + 446*S^8 + 223*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(80 + 47*S^2 + 1376*S^4))/(27*S^3) + (Pi^2*(-62 - 124*S^2 - 62*S^4 - 683*S^6 - 910*S^8 - 341*S^10))/(27*S^3*(1 + S^2)^2) + (152*S^3*HPL[{3}, -S^2])/3 + (304*S^3*HPL[{2, 1}, -S^2])/3 + (152*S^3*Zeta[3])/3) + (188*S^3*Zeta[5])/3)) - 50*S^3*Zeta[7];
E4vwuT=E4vwuT0F0+T*E4vwuT1F1*(F+1/F)+T^2*(E4vwuT2F0+E4vwuT2F2*(F^2+1/F^2))+T^3*(E4vwuT3F1*(F+1/F)+E4vwuT3F3*(F^3+1/F^3));
E4wuvT0F0=(20621*Pi^8)/108864 + HPL[{0}, S^2]^8/384 + HPL[{0}, S^2]^6*((11*Pi^2)/288 + HPL[{2}, -S^2]/16) + (59*Pi^2*HPL[{2}, -S^2]^3)/18 + (5*Pi^2*HPL[{3}, -S^2]^2)/3 - 24*HPL[{4}, -S^2]^2 - (7*Pi^2*HPL[{6}, -S^2])/2 - 279*HPL[{8}, -S^2] - (38*Pi^2*HPL[{2, 1}, -S^2]^2)/3 - 32*HPL[{3, 1}, -S^2]^2 + 4*Pi^2*HPL[{4, 2}, -S^2] + 12*Pi^2*HPL[{5, 1}, -S^2] + 6*HPL[{5, 3}, -S^2] + 3*HPL[{6, 2}, -S^2] + 40*HPL[{7, 1}, -S^2] + HPL[{4}, -S^2]*((7*Pi^4)/36 + 80*HPL[{3, 1}, -S^2] - 112*HPL[{2, 1, 1}, -S^2]) + (1547*Pi^4*HPL[{2, 1, 1}, -S^2])/90 + HPL[{0}, S^2]^4*((1849*Pi^4)/8640 + (41*Pi^2*HPL[{2}, -S^2])/72 + (25*HPL[{2}, -S^2]^2)/48 - HPL[{4}, -S^2]/4 - (31*HPL[{3, 1}, -S^2])/12 + (37*HPL[{2, 1, 1}, -S^2])/6) + HPL[{3, 1}, -S^2]*((-1483*Pi^4)/180 + 112*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]^2*((67*Pi^4)/80 - 9*HPL[{4}, -S^2] - 76*HPL[{3, 1}, -S^2] + 152*HPL[{2, 1, 1}, -S^2]) - 4*Pi^2*HPL[{3, 1, 2}, -S^2] + (224*Pi^2*HPL[{3, 2, 1}, -S^2])/3 + 36*HPL[{3, 3, 2}, -S^2] + (712*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 60*HPL[{4, 1, 3}, -S^2] + 30*HPL[{4, 2, 2}, -S^2] - 204*HPL[{4, 3, 1}, -S^2] - 108*HPL[{5, 1, 2}, -S^2] - 828*HPL[{5, 2, 1}, -S^2] - 2100*HPL[{6, 1, 1}, -S^2] - (560*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 - 608*HPL[{3, 2, 2, 1}, -S^2] - 1824*HPL[{3, 3, 1, 1}, -S^2] + 96*HPL[{4, 1, 1, 2}, -S^2] - 1728*HPL[{4, 1, 2, 1}, -S^2] - 5376*HPL[{4, 2, 1, 1}, -S^2] - 10672*HPL[{5, 1, 1, 1}, -S^2] + 376*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] - 1216*HPL[{2, 2, 1, 2, 1}, -S^2] - 3648*HPL[{2, 2, 2, 1, 1}, -S^2] + 7200*HPL[{3, 1, 1, 1, 2}, -S^2] + 12064*HPL[{3, 1, 1, 2, 1}, -S^2] + 14496*HPL[{3, 1, 2, 1, 1}, -S^2] + 30304*HPL[{3, 2, 1, 1, 1}, -S^2] + 91136*HPL[{4, 1, 1, 1, 1}, -S^2] - 2880*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 5760*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((22*Pi^2)/9 + (8*HPL[{0}, S^2]^2)/3 + 8*HPL[{2}, -S^2])*Log[T]^6 - (8*HPL[{0}, S^2]*Log[T]^7)/3 + (2*Log[T]^8)/3 + Log[T]^4*((1849*Pi^4)/540 + (23*HPL[{0}, S^2]^4)/18 + (47*Pi^2*HPL[{2}, -S^2])/3 + HPL[{0}, S^2]^2*((53*Pi^2)/9 + 17*HPL[{2}, -S^2]) - (8*HPL[{4}, -S^2])/3 - 120*HPL[{3, 1}, -S^2] + 240*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]*(-8*HPL[{3}, -S^2] + 120*HPL[{2, 1}, -S^2] - (28*Zeta[3])/3)) + HPL[{0}, S^2]^5*((2*HPL[{2, 1}, -S^2])/3 + (3*Zeta[3])/4) + 16*HPL[{3, 2}, -S^2]*Zeta[3] + 16*HPL[{4, 1}, -S^2]*Zeta[3] + 304*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 928*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 624*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] + (2*Pi^2*Zeta[3]^2)/3 + Log[T]^5*((-22*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]*((-64*Pi^2)/9 - 24*HPL[{2}, -S^2]) + 24*HPL[{3}, -S^2] - 48*HPL[{2, 1}, -S^2] + 24*Zeta[3]) + HPL[{5}, -S^2]*(-44*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{2}, -S^2]*((11857*Pi^6)/15120 + 6*HPL[{3}, -S^2]^2 - (16*Pi^2*HPL[{4}, -S^2])/3 - 21*HPL[{6}, -S^2] - 152*HPL[{2, 1}, -S^2]^2 - (22*Pi^2*HPL[{3, 1}, -S^2])/3 + 18*HPL[{4, 2}, -S^2] + 116*HPL[{5, 1}, -S^2] + (76*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 112*HPL[{4, 1, 1}, -S^2] - 7184*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-152*HPL[{2, 1}, -S^2] - 8*Zeta[3]) - 152*HPL[{2, 1}, -S^2]*Zeta[3] + 6*Zeta[3]^2) + HPL[{0}, S^2]^2*((8699*Pi^6)/18144 + (21*Pi^2*HPL[{2}, -S^2]^2)/8 + (7*HPL[{2}, -S^2]^3)/2 + HPL[{3}, -S^2]^2 - 18*HPL[{6}, -S^2] - 38*HPL[{2, 1}, -S^2]^2 - (27*Pi^2*HPL[{3, 1}, -S^2])/2 + 2*HPL[{5, 1}, -S^2] + (88*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((63*Pi^4)/40 - 2*HPL[{4}, -S^2] - 36*HPL[{3, 1}, -S^2] + 76*HPL[{2, 1, 1}, -S^2]) + 84*HPL[{3, 2, 1}, -S^2] + 264*HPL[{4, 1, 1}, -S^2] - 200*HPL[{3, 1, 1, 1}, -S^2] + 408*HPL[{2, 1, 1, 1, 1}, -S^2] - 8*HPL[{2, 1}, -S^2]*Zeta[3] + Zeta[3]^2 + HPL[{3}, -S^2]*(-6*HPL[{2, 1}, -S^2] + 6*Zeta[3])) + Log[T]^2*((8699*Pi^6)/4536 + HPL[{0}, S^2]^6/6 + (19*Pi^2*HPL[{2}, -S^2]^2)/3 + (76*HPL[{2}, -S^2]^3)/3 + HPL[{0}, S^2]^4*((53*Pi^2)/36 + (37*HPL[{2}, -S^2])/12) + 16*HPL[{3}, -S^2]^2 + (2*Pi^2*HPL[{4}, -S^2])/3 + 30*HPL[{6}, -S^2] - (280*Pi^2*HPL[{3, 1}, -S^2])/3 + HPL[{2}, -S^2]*((1547*Pi^4)/180 - 56*HPL[{4}, -S^2] + 56*HPL[{3, 1}, -S^2]) + 48*HPL[{4, 2}, -S^2] + 136*HPL[{5, 1}, -S^2] + 188*Pi^2*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]^2*((359*Pi^4)/90 + (44*Pi^2*HPL[{2}, -S^2])/3 + 19*HPL[{2}, -S^2]^2 + 6*HPL[{4}, -S^2] - 100*HPL[{3, 1}, -S^2] + 204*HPL[{2, 1, 1}, -S^2]) - 48*HPL[{3, 1, 2}, -S^2] + 560*HPL[{3, 2, 1}, -S^2] + 1792*HPL[{4, 1, 1}, -S^2] - 1440*HPL[{3, 1, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1, 1}, -S^2] - 312*HPL[{2, 1}, -S^2]*Zeta[3] + 4*Zeta[3]^2 + HPL[{0}, S^2]^3*(-2*HPL[{3}, -S^2] + 30*HPL[{2, 1}, -S^2] + (8*Zeta[3])/3) + HPL[{3}, -S^2]*(-360*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + HPL[{0}, S^2]*(-6*Pi^2*HPL[{3}, -S^2] - 4*HPL[{5}, -S^2] + 90*Pi^2*HPL[{2, 1}, -S^2] - 8*HPL[{3, 2}, -S^2] + 32*HPL[{4, 1}, -S^2] - 624*HPL[{2, 2, 1}, -S^2] - 1968*HPL[{3, 1, 1}, -S^2] + 1440*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(4*HPL[{3}, -S^2] + 312*HPL[{2, 1}, -S^2] - 28*Zeta[3]) - 2*Pi^2*Zeta[3])) + HPL[{2, 1}, -S^2]*(304*HPL[{3, 2}, -S^2] + 1024*HPL[{4, 1}, -S^2] + 608*HPL[{2, 2, 1}, -S^2] + 1104*HPL[{3, 1, 1}, -S^2] - (86*Pi^2*Zeta[3])/3 - 188*Zeta[5]) - 64*Zeta[3]*Zeta[5] + HPL[{0}, S^2]^3*(-(Pi^2*HPL[{3}, -S^2])/6 + 3*HPL[{5}, -S^2] + (85*Pi^2*HPL[{2, 1}, -S^2])/18 - 2*HPL[{3, 2}, -S^2] - 4*HPL[{4, 1}, -S^2] - (76*HPL[{2, 2, 1}, -S^2])/3 - 80*HPL[{3, 1, 1}, -S^2] + 60*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(HPL[{3}, -S^2] + (38*HPL[{2, 1}, -S^2])/3 - (2*Zeta[3])/3) + (49*Pi^2*Zeta[3])/18 + (55*Zeta[5])/3) + HPL[{3}, -S^2]*(42*HPL[{5}, -S^2] - 32*Pi^2*HPL[{2, 1}, -S^2] - 24*HPL[{3, 2}, -S^2] - 44*HPL[{4, 1}, -S^2] + 304*HPL[{2, 2, 1}, -S^2] + 976*HPL[{3, 1, 1}, -S^2] - 720*HPL[{2, 1, 1, 1}, -S^2] + (8*Pi^2*Zeta[3])/3 + 40*Zeta[5]) + Log[T]^3*((-11*HPL[{0}, S^2]^5)/18 + HPL[{0}, S^2]^3*((-110*Pi^2)/27 - 10*HPL[{2}, -S^2]) + (68*Pi^2*HPL[{3}, -S^2])/3 + 40*HPL[{5}, -S^2] - (188*Pi^2*HPL[{2, 1}, -S^2])/3 - 224*HPL[{3, 2}, -S^2] - (2128*HPL[{4, 1}, -S^2])/3 + HPL[{0}, S^2]*((-937*Pi^4)/135 - 30*Pi^2*HPL[{2}, -S^2] - 52*HPL[{2}, -S^2]^2 - (56*HPL[{4}, -S^2])/3 + 240*HPL[{3, 1}, -S^2] - 480*HPL[{2, 1, 1}, -S^2]) + 480*HPL[{3, 1, 1}, -S^2] - 960*HPL[{2, 1, 1, 1}, -S^2] + (196*Pi^2*Zeta[3])/9 + HPL[{0}, S^2]^2*(8*HPL[{3}, -S^2] - 68*HPL[{2, 1}, -S^2] + (16*Zeta[3])/3) + HPL[{2}, -S^2]*(120*HPL[{3}, -S^2] + 104*Zeta[3]) + (440*Zeta[5])/3) + HPL[{0}, S^2]*((8*Pi^2*HPL[{5}, -S^2])/3 + 80*HPL[{7}, -S^2] - (8*Pi^2*HPL[{3, 2}, -S^2])/3 - (4*Pi^2*HPL[{4, 1}, -S^2])/3 + 32*HPL[{4, 3}, -S^2] + 96*HPL[{5, 2}, -S^2] + 160*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((377*Pi^4)/45 - 312*HPL[{3, 1}, -S^2] - 624*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-7*Pi^4)/15 - 16*HPL[{4}, -S^2] - 8*HPL[{3, 1}, -S^2] + 8*HPL[{2, 1, 1}, -S^2]) - (232*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - 244*Pi^2*HPL[{3, 1, 1}, -S^2] - 32*HPL[{3, 2, 2}, -S^2] - 48*HPL[{3, 3, 1}, -S^2] - 48*HPL[{4, 1, 2}, -S^2] - 96*HPL[{4, 2, 1}, -S^2] - 152*HPL[{5, 1, 1}, -S^2] + 180*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + 608*HPL[{2, 2, 2, 1}, -S^2] - 1840*HPL[{3, 1, 1, 2}, -S^2] - 1840*HPL[{3, 1, 2, 1}, -S^2] - 3664*HPL[{3, 2, 1, 1}, -S^2] - 10880*HPL[{4, 1, 1, 1}, -S^2] + 1248*HPL[{2, 1, 2, 1, 1}, -S^2] + 3744*HPL[{2, 2, 1, 1, 1}, -S^2] + 6048*HPL[{3, 1, 1, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(24*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + HPL[{2}, -S^2]^2*(-4*HPL[{3}, -S^2] + 76*HPL[{2, 1}, -S^2] - 6*Zeta[3]) + (157*Pi^4*Zeta[3])/90 + 32*HPL[{3, 1}, -S^2]*Zeta[3] - 56*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]*((4*Pi^2*HPL[{3}, -S^2])/3 + 16*HPL[{5}, -S^2] + (116*Pi^2*HPL[{2, 1}, -S^2])/3 + 16*HPL[{3, 2}, -S^2] + 24*HPL[{4, 1}, -S^2] - 304*HPL[{2, 2, 1}, -S^2] + 920*HPL[{3, 1, 1}, -S^2] + 624*HPL[{2, 1, 1, 1}, -S^2] - 3*Pi^2*Zeta[3] - 16*Zeta[5]) + (55*Pi^2*Zeta[5])/3 + 150*Zeta[7]) + Log[T]*(-HPL[{0}, S^2]^7/24 + HPL[{0}, S^2]^5*((-4*Pi^2)/9 - (2*HPL[{2}, -S^2])/3) + (32*Pi^2*HPL[{5}, -S^2])/3 - 88*HPL[{7}, -S^2] + HPL[{2, 1}, -S^2]*((-1547*Pi^4)/90 - 112*HPL[{3, 1}, -S^2]) - 60*Pi^2*HPL[{3, 2}, -S^2] - (580*Pi^2*HPL[{4, 1}, -S^2])/3 + 76*HPL[{4, 3}, -S^2] + 228*HPL[{5, 2}, -S^2] + 380*HPL[{6, 1}, -S^2] + HPL[{0}, S^2]^3*((-937*Pi^4)/540 - (85*Pi^2*HPL[{2}, -S^2])/18 - (19*HPL[{2}, -S^2]^2)/3 - 2*HPL[{4}, -S^2] + (88*HPL[{3, 1}, -S^2])/3 - 60*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((44*Pi^4)/9 - 44*HPL[{4}, -S^2] - 368*HPL[{3, 1}, -S^2] + 720*HPL[{2, 1, 1}, -S^2]) + (152*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + 288*Pi^2*HPL[{3, 1, 1}, -S^2] + 608*HPL[{3, 2, 2}, -S^2] + 1952*HPL[{3, 3, 1}, -S^2] + 1952*HPL[{4, 1, 2}, -S^2] + 5984*HPL[{4, 2, 1}, -S^2] + 12336*HPL[{5, 1, 1}, -S^2] - 376*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 1216*HPL[{2, 2, 2, 1}, -S^2] + 2304*HPL[{3, 1, 1, 2}, -S^2] + 2304*HPL[{3, 1, 2, 1}, -S^2] + 5952*HPL[{3, 2, 1, 1}, -S^2] + 17632*HPL[{4, 1, 1, 1}, -S^2] + 2880*HPL[{3, 1, 1, 1, 1}, -S^2] - 5760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^4*(HPL[{3}, -S^2]/2 - (37*HPL[{2, 1}, -S^2])/6 - (7*Zeta[3])/6) + (157*Pi^4*Zeta[3])/45 - 320*HPL[{3, 1}, -S^2]*Zeta[3] + 624*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(112*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{2}, -S^2]^2*(76*HPL[{3}, -S^2] - 152*HPL[{2, 1}, -S^2] + 76*Zeta[3]) + HPL[{0}, S^2]*((-12907*Pi^6)/5670 - (58*Pi^2*HPL[{2}, -S^2]^2)/3 - (76*HPL[{2}, -S^2]^3)/3 + 12*HPL[{3}, -S^2]^2 - (20*Pi^2*HPL[{4}, -S^2])/3 + 312*HPL[{2, 1}, -S^2]^2 + (268*Pi^2*HPL[{3, 1}, -S^2])/3 + 56*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-377*Pi^4)/45 - 24*HPL[{4}, -S^2] + 312*HPL[{3, 1}, -S^2] - 624*HPL[{2, 1, 1}, -S^2]) - 180*Pi^2*HPL[{2, 1, 1}, -S^2] - 608*HPL[{3, 2, 1}, -S^2] - 1936*HPL[{4, 1, 1}, -S^2] + 1440*HPL[{3, 1, 1, 1}, -S^2] - 2880*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-8*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + 56*HPL[{2, 1}, -S^2]*Zeta[3] - 16*Zeta[3]^2) + HPL[{0}, S^2]^2*(3*Pi^2*HPL[{3}, -S^2] + 2*HPL[{5}, -S^2] - (88*Pi^2*HPL[{2, 1}, -S^2])/3 - 12*HPL[{3, 2}, -S^2] - 48*HPL[{4, 1}, -S^2] + 152*HPL[{2, 2, 1}, -S^2] + 504*HPL[{3, 1, 1}, -S^2] - 408*HPL[{2, 1, 1, 1}, -S^2] - Pi^2*Zeta[3] + HPL[{2}, -S^2]*(6*HPL[{3}, -S^2] - 76*HPL[{2, 1}, -S^2] + 8*Zeta[3])) + (110*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*(32*Pi^2*HPL[{3}, -S^2] + 44*HPL[{5}, -S^2] - (76*Pi^2*HPL[{2, 1}, -S^2])/3 - 304*HPL[{3, 2}, -S^2] - 1024*HPL[{4, 1}, -S^2] + 608*HPL[{2, 2, 1}, -S^2] - 1104*HPL[{3, 1, 1}, -S^2] + (86*Pi^2*Zeta[3])/3 + 188*Zeta[5]) + 300*Zeta[7]);
E4wuvT1F1=(2*Pi^4*S)/9 + (7*Pi^6*S)/720 + (HPL[{0}, S^2]^6*HPL[{1}, -S^2])/(16*S) + ((47*Pi^2)/(15*S) + (104*(1 + S^2))/(15*S))*HPL[{1}, -S^2]^5 + (2*(1 + S^2)*HPL[{1}, -S^2]^6)/S + (8*HPL[{1}, -S^2]^7)/(7*S) + HPL[{0}, S^2]^5*(-S/12 + ((-1 - S^2)*HPL[{1}, -S^2])/(24*S) + HPL[{1}, -S^2]^2/(3*S)) + ((-13 + 6*S^2)*HPL[{2}, -S^2]^3)/(3*S) + ((2 + 5*S^2)*HPL[{3}, -S^2]^2)/S + ((-5*Pi^2)/(2*S) - (21*(-1 + 3*S^2))/S)*HPL[{5}, -S^2] + ((30 + S^2)*HPL[{6}, -S^2])/S - (150*HPL[{7}, -S^2])/S - (4*(16 + 3*S^2)*HPL[{2, 1}, -S^2]^2)/S + HPL[{0}, S^2]^4*((-5*Pi^2*S)/144 + (37*HPL[{1}, -S^2]^3)/(36*S) - (5*S*HPL[{2}, -S^2])/24 + HPL[{1}, -S^2]*((41*Pi^2)/(72*S) + (5*(1 + S^2))/(24*S) + (25*HPL[{2}, -S^2])/(24*S)) - HPL[{3}, -S^2]/(8*S) - (7*HPL[{2, 1}, -S^2])/(3*S)) + ((-7*Pi^2)/(3*S) + (-11 + 123*S^2)/S)*HPL[{3, 2}, -S^2] + ((-11*Pi^2)/(3*S) + (2*(4 + 209*S^2))/S)*HPL[{4, 1}, -S^2] + (3*(-2 + 5*S^2)*HPL[{4, 2}, -S^2])/S + (48*HPL[{4, 3}, -S^2])/S + (2*(9 + 43*S^2)*HPL[{5, 1}, -S^2])/S + (147*HPL[{5, 2}, -S^2])/S + (332*HPL[{6, 1}, -S^2])/S + ((152*Pi^2)/(3*S) + (8*(3 + 16*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((464*Pi^2)/(3*S) + (4*(11 + 23*S^2))/S)*HPL[{3, 1, 1}, -S^2] - (6*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (14*(-7 + 3*S^2)*HPL[{3, 2, 1}, -S^2])/S - (6*HPL[{3, 2, 2}, -S^2])/S + (32*HPL[{3, 3, 1}, -S^2])/S + (4*(-88 + 19*S^2)*HPL[{4, 1, 1}, -S^2])/S + (38*HPL[{4, 1, 2}, -S^2])/S + (134*HPL[{4, 2, 1}, -S^2])/S + (300*HPL[{5, 1, 1}, -S^2])/S + ((-356*Pi^2)/(3*S) + (16*(-1 + 18*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - (304*HPL[{2, 2, 2, 1}, -S^2])/S - (8*(-34 + 5*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (872*HPL[{3, 1, 1, 2}, -S^2])/S + (872*HPL[{3, 1, 2, 1}, -S^2])/S + (1784*HPL[{3, 2, 1, 1}, -S^2])/S + (5408*HPL[{4, 1, 1, 1}, -S^2])/S + (32*(-15 + 4*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (592*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (1776*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (2944*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (1440*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((8*Pi^2*S)/9 + ((47*Pi^2)/(3*S) + (104*(1 + S^2))/(3*S))*HPL[{1}, -S^2] + (30*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (40*HPL[{1}, -S^2]^3)/S + HPL[{0}, S^2]^2*((8*S)/3 + (17*HPL[{1}, -S^2])/S) + (4*(-15 + 4*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{0}, S^2]*((104*S)/3 + (30*(1 + S^2)*HPL[{1}, -S^2])/S + (60*HPL[{1}, -S^2]^2)/S - (4*HPL[{2}, -S^2])/S) + (2*HPL[{3}, -S^2])/(3*S) - (60*HPL[{2, 1}, -S^2])/S)*Log[T]^4 + ((-12*(1 + S^2)*HPL[{1}, -S^2])/S - (24*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(-12*S - (24*HPL[{1}, -S^2])/S) + (12*HPL[{2}, -S^2])/S)*Log[T]^5 + (8*HPL[{1}, -S^2]*Log[T]^6)/S + (-92*S - (44*Pi^2*S)/3)*Zeta[3] - 6*S*Zeta[3]^2 + HPL[{1}, -S^2]^4*((22*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/(6*S) - (9*(1 + S^2)*HPL[{2}, -S^2])/S - (30*HPL[{3}, -S^2])/S - (26*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((Pi^2*(37 - 13*S^2))/(3*S) - (2*(-39 + 7*S^2))/S - (8*Zeta[3])/S) + HPL[{2}, -S^2]^2*((Pi^2*(9 + 4*S^2))/(3*S) + (15 + 4*S^2)/S - (3*HPL[{3}, -S^2])/S - (38*HPL[{2, 1}, -S^2])/S + (2*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((8*(-15 + 4*S^2))/S + (4*Pi^2*(-15 + 8*S^2))/(3*S) + (8*Zeta[3])/S) + HPL[{4}, -S^2]*((Pi^2*(-16 - 19*S^2))/(6*S) - (2*(-6 + 5*S^2))/S + (58*HPL[{2, 1}, -S^2])/S + (16*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-1043*Pi^4)/(180*S) + (2*Pi^2*(-1 + 22*S^2))/(3*S) + (4*(4 + 23*S^2))/S + (120*HPL[{3, 1}, -S^2])/S + (296*HPL[{2, 1, 1}, -S^2])/S + (120*Zeta[3])/S) + HPL[{3}, -S^2]*((7*Pi^4)/(45*S) + (Pi^2*(-13 - 87*S^2))/(6*S) - (2*(-6 + 43*S^2))/S - (24*HPL[{4}, -S^2])/S - (2*(-59 + 11*S^2)*HPL[{2, 1}, -S^2])/S - (28*HPL[{3, 1}, -S^2])/S + (32*HPL[{2, 1, 1}, -S^2])/S - 8*S*Zeta[3]) + HPL[{1}, -S^2]^3*((1547*Pi^4)/(540*S) + (188*(1 + S^2))/(3*S) + (68*Pi^2*(1 + S^2))/(9*S) + ((38*Pi^2)/(9*S) - (56*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (76*HPL[{2}, -S^2]^2)/(3*S) - (48*(1 + S^2)*HPL[{3}, -S^2])/S - (56*HPL[{4}, -S^2])/(3*S) + (36*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (56*HPL[{3, 1}, -S^2])/(3*S) - (44*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]^3*(9*S + (5*Pi^2*S)/36 + (11*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + (5*HPL[{1}, -S^2]^4)/(2*S) + (-Pi^2/(12*S) + (6 + 13*S^2)/(6*S))*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/(4*S) + HPL[{1}, -S^2]^2*((85*Pi^2)/(36*S) + (17*(1 + S^2))/(6*S) + (19*HPL[{2}, -S^2])/(3*S)) + HPL[{3}, -S^2]/(2*S) + (3*HPL[{4}, -S^2])/(2*S) + ((-7 - 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*HPL[{2, 1, 1}, -S^2])/S - (5*S*Zeta[3])/3 + HPL[{1}, -S^2]*((9*(1 + S^2))/(2*S) + (Pi^2*(1 + S^2))/(6*S) + (5*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{3}, -S^2]/S - (38*HPL[{2, 1}, -S^2])/(3*S) - (2*Zeta[3])/(3*S))) + Log[T]^3*((-16*Pi^2*S)/9 + ((-94*Pi^2)/(3*S) - (208*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^2 - (40*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (40*HPL[{1}, -S^2]^4)/S + HPL[{0}, S^2]^3*(-2*S - (10*HPL[{1}, -S^2])/S) + ((34*Pi^2)/(3*S) - (8*(-15 + 4*S^2))/(3*S))*HPL[{2}, -S^2] - (26*HPL[{2}, -S^2]^2)/S + HPL[{0}, S^2]^2*((-16*S)/3 - (8*(1 + S^2)*HPL[{1}, -S^2])/S - (34*HPL[{1}, -S^2]^2)/S + (4*HPL[{2}, -S^2])/S) + (4*(6 + 71*S^2)*HPL[{3}, -S^2])/(3*S) + (16*HPL[{4}, -S^2])/S - (8*(-3 + 35*S^2)*HPL[{2, 1}, -S^2])/(3*S) + HPL[{0}, S^2]*(-88*S - 12*Pi^2*S - (60*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (80*HPL[{1}, -S^2]^3)/S - (4*(3 + 41*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-30*Pi^2)/S - (208*(1 + S^2))/(3*S) - (104*HPL[{2}, -S^2])/S) - (28*HPL[{3}, -S^2])/(3*S) + (224*HPL[{2, 1}, -S^2])/S) - (416*HPL[{3, 1}, -S^2])/(3*S) + (240*HPL[{2, 1, 1}, -S^2])/S + (280*S*Zeta[3])/3 + HPL[{1}, -S^2]*((-88*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/(3*S) + (36*(1 + S^2)*HPL[{2}, -S^2])/S + (120*HPL[{3}, -S^2])/S + (104*Zeta[3])/S)) + HPL[{0}, S^2]^2*((2*Pi^2*S)/3 - (Pi^4*S)/40 + (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S + (17*HPL[{1}, -S^2]^5)/(5*S) + ((2 + 5*S^2)*HPL[{2}, -S^2]^2)/(2*S) + HPL[{1}, -S^2]^3*((44*Pi^2)/(9*S) + (16*(1 + S^2))/(3*S) + (38*HPL[{2}, -S^2])/(3*S)) + ((-3 - 7*S^2)*HPL[{3}, -S^2])/S + ((-3 - S^2)*HPL[{4}, -S^2])/S - (9*HPL[{5}, -S^2])/S + ((-12*Pi^2)/S + 8*S)*HPL[{2, 1}, -S^2] + ((3 - 8*S^2)*HPL[{3, 1}, -S^2])/S - (2*HPL[{3, 2}, -S^2])/S - (3*HPL[{4, 1}, -S^2])/S + 16*S*HPL[{2, 1, 1}, -S^2] + (78*HPL[{2, 2, 1}, -S^2])/S + (240*HPL[{3, 1, 1}, -S^2])/S - (176*HPL[{2, 1, 1, 1}, -S^2])/S - 8*S*Zeta[3] + HPL[{1}, -S^2]^2*((12*(1 + S^2))/S + (Pi^2*(1 + S^2))/S + (3*(1 + S^2)*HPL[{2}, -S^2])/(2*S) - (3*HPL[{3}, -S^2])/S - (38*HPL[{2, 1}, -S^2])/S - (4*Zeta[3])/S) + HPL[{2}, -S^2]*(4*S + (Pi^2*S)/4 + HPL[{3}, -S^2]/S - (39*HPL[{2, 1}, -S^2])/S + (3*Zeta[3])/S) + HPL[{1}, -S^2]*((63*Pi^4)/(40*S) + (20*(1 + S^2))/S + (7*Pi^2*(1 + S^2))/(4*S) + (21*Pi^2*HPL[{2}, -S^2])/(4*S) + (21*HPL[{2}, -S^2]^2)/(2*S) - (5*(1 + S^2)*HPL[{3}, -S^2])/S - (2*HPL[{4}, -S^2])/S - (3*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (36*HPL[{3, 1}, -S^2])/S + (76*HPL[{2, 1, 1}, -S^2])/S - (5*(1 + S^2)*Zeta[3])/S)) + Log[T]^2*((8*Pi^2*S)/3 + (23*Pi^4*S)/60 + ((94*Pi^2)/(3*S) + (208*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^3 + (30*(1 + S^2)*HPL[{1}, -S^2]^4)/S + (24*HPL[{1}, -S^2]^5)/S + HPL[{0}, S^2]^4*((-5*S)/12 + (37*HPL[{1}, -S^2])/(12*S)) + (2*(16 + 3*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{0}, S^2]^3*(5*S + (11*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + (15*HPL[{1}, -S^2]^2)/S - HPL[{2}, -S^2]/S) + ((4*Pi^2)/(3*S) - (2*(7 + 73*S^2))/S)*HPL[{3}, -S^2] - (2*(10 + 17*S^2)*HPL[{4}, -S^2])/S + (6*HPL[{5}, -S^2])/S + ((-178*Pi^2)/(3*S) + (8*(-1 + 18*S^2))/S)*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(8*S + (Pi^2*S)/2 + (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (34*HPL[{1}, -S^2]^3)/S + 8*S*HPL[{2}, -S^2] + HPL[{1}, -S^2]*((44*Pi^2)/(3*S) + (16*(1 + S^2))/S + (38*HPL[{2}, -S^2])/S) + (3*HPL[{3}, -S^2])/S - (88*HPL[{2, 1}, -S^2])/S) - (4*(-34 + 5*S^2)*HPL[{3, 1}, -S^2])/S - (20*HPL[{3, 2}, -S^2])/S - (32*HPL[{4, 1}, -S^2])/S + (16*(-15 + 4*S^2)*HPL[{2, 1, 1}, -S^2])/S + (296*HPL[{2, 2, 1}, -S^2])/S + (896*HPL[{3, 1, 1}, -S^2])/S - (720*HPL[{2, 1, 1, 1}, -S^2])/S - 144*S*Zeta[3] + HPL[{1}, -S^2]^2*((132*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/S - (54*(1 + S^2)*HPL[{2}, -S^2])/S - (180*HPL[{3}, -S^2])/S - (156*Zeta[3])/S) + HPL[{2}, -S^2]*((4*(-15 + 4*S^2))/S + (2*Pi^2*(-15 + 8*S^2))/(3*S) + (16*HPL[{3}, -S^2])/S - (148*HPL[{2, 1}, -S^2])/S + (4*Zeta[3])/S) + HPL[{1}, -S^2]*((1547*Pi^4)/(180*S) + (188*(1 + S^2))/S + (68*Pi^2*(1 + S^2))/(3*S) + ((38*Pi^2)/(3*S) - (56*(1 + S^2))/S)*HPL[{2}, -S^2] + (76*HPL[{2}, -S^2]^2)/S - (144*(1 + S^2)*HPL[{3}, -S^2])/S - (56*HPL[{4}, -S^2])/S + (108*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (56*HPL[{3, 1}, -S^2])/S - (132*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]*(188*S + (67*Pi^2*S)/3 + (60*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (60*HPL[{1}, -S^2]^4)/S + ((-3*Pi^2)/S + (4*(3 + 22*S^2))/S)*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/S + HPL[{1}, -S^2]^2*((45*Pi^2)/S + (104*(1 + S^2))/S + (156*HPL[{2}, -S^2])/S) - (2*(-1 + 4*S^2)*HPL[{3}, -S^2])/S - (2*HPL[{4}, -S^2])/S + (8*(-18 + S^2)*HPL[{2, 1}, -S^2])/S + (24*HPL[{3, 1}, -S^2])/S - (48*HPL[{2, 1, 1}, -S^2])/S - 12*S*Zeta[3] + HPL[{1}, -S^2]*((132*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/(3*S) + (78*(1 + S^2)*HPL[{2}, -S^2])/S + (4*HPL[{3}, -S^2])/S - (312*HPL[{2, 1}, -S^2])/S - (28*Zeta[3])/S))) - 114*S*Zeta[5] + HPL[{1}, -S^2]^2*((150*(1 + S^2))/S + (15*Pi^2*(1 + S^2))/S + (479*Pi^4*(1 + S^2))/(360*S) + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-16*Pi^2)/S - (74*(1 + S^2))/S)*HPL[{3}, -S^2] - (29*(1 + S^2)*HPL[{4}, -S^2])/S - (22*HPL[{5}, -S^2])/S + ((-38*Pi^2)/(3*S) + (56*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (68*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (152*HPL[{3, 2}, -S^2])/S + (512*HPL[{4, 1}, -S^2])/S - (108*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (304*HPL[{2, 2, 1}, -S^2])/S + (552*HPL[{3, 1, 1}, -S^2])/S + ((-43*Pi^2)/(3*S) - (72*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-30*(1 + S^2))/S - (4*Pi^2*(1 + S^2))/S - (76*HPL[{3}, -S^2])/S - (152*HPL[{2, 1}, -S^2])/S - (76*Zeta[3])/S) - (94*Zeta[5])/S) + HPL[{2}, -S^2]*((Pi^2*(-15 + 8*S^2))/(3*S) + (Pi^4*(-234 + 101*S^2))/(360*S) + ((5*Pi^2)/(3*S) - (7*(-1 + 9*S^2))/S)*HPL[{3}, -S^2] + ((2 - 19*S^2)*HPL[{4}, -S^2])/S + (21*HPL[{5}, -S^2])/S + ((-76*Pi^2)/(3*S) - (4*(3 + 16*S^2))/S)*HPL[{2, 1}, -S^2] - (2*(33 + S^2)*HPL[{3, 1}, -S^2])/S + (6*HPL[{3, 2}, -S^2])/S - (22*HPL[{4, 1}, -S^2])/S + (8*(16 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/S + (152*HPL[{2, 2, 1}, -S^2])/S - (424*HPL[{3, 1, 1}, -S^2])/S - (296*HPL[{2, 1, 1, 1}, -S^2])/S + ((4*Pi^2)/(3*S) - (4*(-1 + 14*S^2))/S)*Zeta[3] + (20*Zeta[5])/S) + HPL[{1}, -S^2]*((11857*Pi^6)/(15120*S) + (300*(1 + S^2))/S + (67*Pi^2*(1 + S^2))/(3*S) + (623*Pi^4*(1 + S^2))/(360*S) + ((59*Pi^2)/(6*S) + (19*(1 + S^2))/S)*HPL[{2}, -S^2]^2 + (6*HPL[{3}, -S^2]^2)/S + ((-16*Pi^2)/(3*S) - (37*(1 + S^2))/S)*HPL[{4}, -S^2] - (38*(1 + S^2)*HPL[{5}, -S^2])/S - (21*HPL[{6}, -S^2])/S - (152*HPL[{2, 1}, -S^2]^2)/S + ((-22*Pi^2)/(3*S) + (72*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (112*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (394*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (18*HPL[{4, 2}, -S^2])/S + (116*HPL[{5, 1}, -S^2])/S + ((76*Pi^2)/(3*S) - (112*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (152*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (168*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (112*HPL[{4, 1, 1}, -S^2])/S + (216*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (112*HPL[{3, 1, 1, 1}, -S^2])/S + ((-84*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (6*Zeta[3]^2)/S + HPL[{3}, -S^2]*((-78*(1 + S^2))/S - (41*Pi^2*(1 + S^2))/(3*S) + (152*HPL[{2, 1}, -S^2])/S - (8*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((60*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/S + (152*Zeta[3])/S) + HPL[{2}, -S^2]*((67*Pi^4)/(40*S) - (38*(1 + S^2))/S - (14*Pi^2*(1 + S^2))/(3*S) - (56*(1 + S^2)*HPL[{3}, -S^2])/S - (18*HPL[{4}, -S^2])/S - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (152*HPL[{3, 1}, -S^2])/S + (304*HPL[{2, 1, 1}, -S^2])/S - (60*(1 + S^2)*Zeta[3])/S) - (98*(1 + S^2)*Zeta[5])/S) + HPL[{0}, S^2]*(300*S + (74*Pi^2*S)/3 + (29*Pi^4*S)/18 + (6*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (4*HPL[{1}, -S^2]^6)/S + (-Pi^2/(3*S) + 17*S)*HPL[{2}, -S^2]^2 - (2*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^4*((15*Pi^2)/(2*S) + (52*(1 + S^2))/(3*S) + (26*HPL[{2}, -S^2])/S) + (4*HPL[{3}, -S^2]^2)/S + ((4*Pi^2)/(3*S) + (4*(3 + 4*S^2))/S)*HPL[{4}, -S^2] + (12*HPL[{5}, -S^2])/S + (40*HPL[{6}, -S^2])/S + (2*HPL[{2, 1}, -S^2]^2)/S + ((2*Pi^2)/S - (16*(1 + 6*S^2))/S)*HPL[{3, 1}, -S^2] + 16*S*HPL[{3, 2}, -S^2] + (4*(-2 + 11*S^2)*HPL[{4, 1}, -S^2])/S - (16*HPL[{5, 1}, -S^2])/S + ((-6*Pi^2)/S + (8*(3 + 22*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (8*(18 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (4*(109 + 2*S^2)*HPL[{3, 1, 1}, -S^2])/S - (16*HPL[{3, 2, 1}, -S^2])/S - (52*HPL[{4, 1, 1}, -S^2])/S + (16*(-18 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (48*HPL[{3, 1, 1, 1}, -S^2])/S - (96*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (-2*S - (8*Pi^2*S)/3)*Zeta[3] + HPL[{1}, -S^2]^3*((44*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/(9*S) + (26*(1 + S^2)*HPL[{2}, -S^2])/S + (4*HPL[{3}, -S^2])/(3*S) - (104*HPL[{2, 1}, -S^2])/S - (28*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-2*Pi^2*(-1 + S^2))/(3*S) + (4*(3 + S^2))/S + (4*HPL[{2, 1}, -S^2])/S - (8*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-43*Pi^2)/(3*S) - (4*(21 + 2*S^2))/S + (28*Zeta[3])/S) + HPL[{1}, -S^2]^2*((377*Pi^4)/(90*S) + (94*(1 + S^2))/S + (23*Pi^2*(1 + S^2))/(2*S) + ((58*Pi^2)/(3*S) + (44*(1 + S^2))/S)*HPL[{2}, -S^2] + (38*HPL[{2}, -S^2]^2)/S + (2*(1 + S^2)*HPL[{3}, -S^2])/S + (12*HPL[{4}, -S^2])/S - (78*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (156*HPL[{3, 1}, -S^2])/S + (312*HPL[{2, 1, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-7*Pi^4)/(30*S) + (Pi^2*(4 + 19*S^2))/(2*S) + (2*(12 + 31*S^2))/S - 8*S*HPL[{3}, -S^2] - (8*HPL[{4}, -S^2])/S - (4*(18 + S^2)*HPL[{2, 1}, -S^2])/S + (4*HPL[{3, 1}, -S^2])/S - (4*HPL[{2, 1, 1}, -S^2])/S - (2*(2 + 3*S^2)*Zeta[3])/S) + 4*S*Zeta[5] + HPL[{1}, -S^2]*((150*(1 + S^2))/S + (31*Pi^2*(1 + S^2))/(2*S) + (229*Pi^4*(1 + S^2))/(180*S) + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((4*Pi^2)/(3*S) + (12*(1 + S^2))/S)*HPL[{3}, -S^2] + (8*(1 + S^2)*HPL[{4}, -S^2])/S + (16*HPL[{5}, -S^2])/S + ((-116*Pi^2)/(3*S) - (88*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (80*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (16*HPL[{3, 2}, -S^2])/S + (24*HPL[{4, 1}, -S^2])/S + (156*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (304*HPL[{2, 2, 1}, -S^2])/S + (920*HPL[{3, 1, 1}, -S^2])/S - (624*HPL[{2, 1, 1, 1}, -S^2])/S + ((-3*Pi^2)/S - (14*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((54*(1 + S^2))/S + (49*Pi^2*(1 + S^2))/(6*S) - (8*HPL[{3}, -S^2])/S - (152*HPL[{2, 1}, -S^2])/S - (12*Zeta[3])/S) - (16*Zeta[5])/S)) + Log[T]*((-8*Pi^2*S)/3 - (23*Pi^4*S)/60 + ((-47*Pi^2)/(3*S) - (104*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^4 - (12*(1 + S^2)*HPL[{1}, -S^2]^5)/S - (8*HPL[{1}, -S^2]^6)/S + HPL[{0}, S^2]^5*(S/12 - (2*HPL[{1}, -S^2])/(3*S)) + ((-7*Pi^2)/S - (2*(16 + 3*S^2))/S)*HPL[{2}, -S^2]^2 + (38*HPL[{2}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^4*((5*S)/12 - (37*HPL[{1}, -S^2]^2)/(12*S) + HPL[{2}, -S^2]/(4*S)) + (8*HPL[{3}, -S^2]^2)/S + ((13*Pi^2)/(3*S) + (2*(12 + 17*S^2))/S)*HPL[{4}, -S^2] + (2*(9 + 41*S^2)*HPL[{5}, -S^2])/S - (20*HPL[{6}, -S^2])/S + (156*HPL[{2, 1}, -S^2]^2)/S + HPL[{0}, S^2]^3*(-9*S - (2*Pi^2*S)/9 - (11*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (10*HPL[{1}, -S^2]^3)/S + ((-3 - 8*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-85*Pi^2)/(18*S) - (17*(1 + S^2))/(3*S) - (38*HPL[{2}, -S^2])/(3*S)) - HPL[{3}, -S^2]/S + (82*HPL[{2, 1}, -S^2])/(3*S)) + ((-116*Pi^2)/(3*S) + (20*(-7 + S^2))/S)*HPL[{3, 1}, -S^2] - (2*(-3 + 131*S^2)*HPL[{3, 2}, -S^2])/S - (4*(10 + 213*S^2)*HPL[{4, 1}, -S^2])/S + (6*HPL[{4, 2}, -S^2])/S - (20*HPL[{5, 1}, -S^2])/S + ((68*Pi^2)/S - (16*(-15 + 4*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (16*(3 + 16*S^2)*HPL[{2, 2, 1}, -S^2])/S - (8*(12 + 25*S^2)*HPL[{3, 1, 1}, -S^2])/S - (24*HPL[{3, 1, 2}, -S^2])/S + (280*HPL[{3, 2, 1}, -S^2])/S + (1008*HPL[{4, 1, 1}, -S^2])/S - (16*(-3 + 35*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (832*HPL[{3, 1, 1, 1}, -S^2])/S + (1440*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (152*S + 28*Pi^2*S)*Zeta[3] + HPL[{2, 1}, -S^2]*(-152*S - (4*Pi^2*(-3 + 20*S^2))/(3*S) - (312*Zeta[3])/S) + HPL[{3}, -S^2]*((2*(9 + 77*S^2))/S + (Pi^2*(9 + 79*S^2))/(3*S) - (336*HPL[{2, 1}, -S^2])/S + (16*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-88*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/(3*S) + (36*(1 + S^2)*HPL[{2}, -S^2])/S + (120*HPL[{3}, -S^2])/S + (104*Zeta[3])/S) + HPL[{2}, -S^2]*((22*Pi^4)/(9*S) - (4*(-15 + 4*S^2))/S - (2*Pi^2*(-15 + 8*S^2))/(3*S) + (2*(-3 + 67*S^2)*HPL[{3}, -S^2])/S - (22*HPL[{4}, -S^2])/S + (8*(3 + 16*S^2)*HPL[{2, 1}, -S^2])/S + (184*HPL[{3, 1}, -S^2])/S - (312*HPL[{2, 1, 1}, -S^2])/S + 120*S*Zeta[3]) + HPL[{1}, -S^2]^2*((-1547*Pi^4)/(180*S) - (188*(1 + S^2))/S - (68*Pi^2*(1 + S^2))/(3*S) + ((-38*Pi^2)/(3*S) + (56*(1 + S^2))/S)*HPL[{2}, -S^2] - (76*HPL[{2}, -S^2]^2)/S + (144*(1 + S^2)*HPL[{3}, -S^2])/S + (56*HPL[{4}, -S^2])/S - (108*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (56*HPL[{3, 1}, -S^2])/S + (132*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]^2*(-8*S - (Pi^2*S)/2 - (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (17*HPL[{1}, -S^2]^4)/S + ((3*Pi^2)/(2*S) - 8*S)*HPL[{2}, -S^2] - (3*HPL[{2}, -S^2]^2)/(2*S) + HPL[{1}, -S^2]^2*((-44*Pi^2)/(3*S) - (16*(1 + S^2))/S - (38*HPL[{2}, -S^2])/S) + ((3 + 8*S^2)*HPL[{3}, -S^2])/S + HPL[{4}, -S^2]/S - (2*(-3 + 5*S^2)*HPL[{2, 1}, -S^2])/S - (12*HPL[{3, 1}, -S^2])/S + (24*HPL[{2, 1, 1}, -S^2])/S + 14*S*Zeta[3] + HPL[{1}, -S^2]*((-24*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S - (3*(1 + S^2)*HPL[{2}, -S^2])/S + (6*HPL[{3}, -S^2])/S + (76*HPL[{2, 1}, -S^2])/S + (8*Zeta[3])/S)) + HPL[{0}, S^2]*(-300*S - 31*Pi^2*S - (73*Pi^4*S)/30 - (30*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (24*HPL[{1}, -S^2]^5)/S - (2*(1 + 18*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((-30*Pi^2)/S - (208*(1 + S^2))/(3*S) - (104*HPL[{2}, -S^2])/S) + ((-10*Pi^2)/(3*S) + (4*(-2 + S^2))/S)*HPL[{3}, -S^2] - (4*(2 + 3*S^2)*HPL[{4}, -S^2])/S + (152/S + (250*Pi^2)/(3*S))*HPL[{2, 1}, -S^2] + (12*(1 + 14*S^2)*HPL[{3, 1}, -S^2])/S - (24*HPL[{3, 2}, -S^2])/S - (20*HPL[{4, 1}, -S^2])/S - (8*(3 + 41*S^2)*HPL[{2, 1, 1}, -S^2])/S - (616*HPL[{2, 2, 1}, -S^2])/S - (1904*HPL[{3, 1, 1}, -S^2])/S + (1344*HPL[{2, 1, 1, 1}, -S^2])/S + 12*S*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-6 - 49*S^2))/(3*S) - (4*(6 + 25*S^2))/S + (12*HPL[{3}, -S^2])/S + (308*HPL[{2, 1}, -S^2])/S - (4*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-132*(1 + S^2))/S - (56*Pi^2*(1 + S^2))/(3*S) - (78*(1 + S^2)*HPL[{2}, -S^2])/S - (4*HPL[{3}, -S^2])/S + (312*HPL[{2, 1}, -S^2])/S + (28*Zeta[3])/S) + HPL[{1}, -S^2]*((-377*Pi^4)/(45*S) - (188*(1 + S^2))/S - (23*Pi^2*(1 + S^2))/S + ((-116*Pi^2)/(3*S) - (88*(1 + S^2))/S)*HPL[{2}, -S^2] - (76*HPL[{2}, -S^2]^2)/S - (4*(1 + S^2)*HPL[{3}, -S^2])/S - (24*HPL[{4}, -S^2])/S + (156*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (312*HPL[{3, 1}, -S^2])/S - (624*HPL[{2, 1, 1}, -S^2])/S + (16*(1 + S^2)*Zeta[3])/S)) + 180*S*Zeta[5] + HPL[{1}, -S^2]*((-300*(1 + S^2))/S - (30*Pi^2*(1 + S^2))/S - (479*Pi^4*(1 + S^2))/(180*S) - (38*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((32*Pi^2)/S + (148*(1 + S^2))/S)*HPL[{3}, -S^2] + (58*(1 + S^2)*HPL[{4}, -S^2])/S + (44*HPL[{5}, -S^2])/S + ((76*Pi^2)/(3*S) - (112*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (136*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (304*HPL[{3, 2}, -S^2])/S - (1024*HPL[{4, 1}, -S^2])/S + (216*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (608*HPL[{2, 2, 1}, -S^2])/S - (1104*HPL[{3, 1, 1}, -S^2])/S + ((86*Pi^2)/(3*S) + (144*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((60*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/S + (152*HPL[{3}, -S^2])/S + (304*HPL[{2, 1}, -S^2])/S + (152*Zeta[3])/S) + (188*Zeta[5])/S));
E4wuvT2F0=-300 + (Pi^4*(64 + 3*S^2))/60 + (Pi^2*(-59 + 13*S^2))/6 + (Pi^6*(-6141 + 5716*S^2))/(15120*(1 + S^2)) + (S^2*HPL[{0}, S^2]^6)/(16*(1 + S^2)) + (4*(1 + S^2)*HPL[{1}, -S^2]^5)/(5*S^2) + (4*(-1 + S^2)*HPL[{1}, -S^2]^6)/(1 + S^2) + HPL[{0}, S^2]^5*(-5/6 + ((-9 - S^2)*HPL[{1}, -S^2])/(12*(1 + S^2))) + HPL[{1}, -S^2]^4*((2*(1 + S^2))/S^2 + (Pi^2*(-28 + 19*S^2))/(3*(1 + S^2)) - 18*HPL[{2}, -S^2]) + (-2 + (59*Pi^2*(-1 + S^2))/(12*(1 + S^2)))*HPL[{2}, -S^2]^2 - (2*HPL[{2}, -S^2]^3)/3 + HPL[{0}, S^2]^4*((17 - 5*S^2)/12 + (Pi^2*(-43 + 39*S^2))/(144*(1 + S^2)) + ((1 + S^2)*HPL[{1}, -S^2])/(4*S^2) - (37*HPL[{1}, -S^2]^2)/(12*(1 + S^2)) + ((-43 - 18*S^2)*HPL[{2}, -S^2])/(24*(1 + S^2))) + ((7 + 13*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((Pi^2*(-31 - 63*S^2))/(6*(1 + S^2)) - (2*(-33 - 25*S^2 + S^4))/S^2)*HPL[{4}, -S^2] + (4*(30 + S^2)*HPL[{5}, -S^2])/S^2 + ((11 - 10*S^2)*HPL[{6}, -S^2])/(1 + S^2) - (76*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((Pi^2*(35 + 13*S^2))/(3*(1 + S^2)) - (8*(1 + S^2 + 2*S^4))/S^2)*HPL[{3, 1}, -S^2] - (8*(5 + 2*S^2)*HPL[{4, 1}, -S^2])/S^2 + (3*(5 + 11*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) + (4*(25 + 54*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]^2*((-12*(-2 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(1 + S^2)*(3 + S^2))/(3*S^2) + (Pi^4*(-1068 + 479*S^2))/(180*(1 + S^2)) + ((4*(1 + S^2)^2)/S^2 - (2*Pi^2*(31 + 12*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] + (38*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) - (2*(1 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (8*(10 + 17*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 216*HPL[{2, 1, 1}, -S^2]) + (16*S^2 - (2*Pi^2*(43 + 5*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (16*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (16*(5 + 3*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - 24*HPL[{3, 1, 2}, -S^2] - 40*HPL[{3, 2, 1}, -S^2] - (28*(5 + 9*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) - (48*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (16*(5 + 12*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - 272*HPL[{2, 1, 1, 1, 1}, -S^2] + (-4 + (Pi^2*(-76 + 65*S^2))/(9*(1 + S^2)) + ((-31 + 20*S^2)*HPL[{0}, S^2]^2)/(3*(1 + S^2)) + (4*(1 + S^2)*HPL[{1}, -S^2])/S^2 + (60*(-1 + S^2)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(1 + S^2) + (60*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - (34*HPL[{2}, -S^2])/3)*Log[T]^4 + ((-8*(-4 + 5*S^2)*HPL[{0}, S^2])/(3*(1 + S^2)) - (24*(-1 + S^2)*HPL[{1}, -S^2])/(1 + S^2))*Log[T]^5 + (4*(-1 + S^2)*Log[T]^6)/(1 + S^2) + (56 + 4*Pi^2)*Zeta[3] - (6*Zeta[3]^2)/(1 + S^2) + HPL[{2}, -S^2]*((4*Pi^2*S^2)/3 + (Pi^4*(-736 - 133*S^2))/(360*(1 + S^2)) + (81 - 22*S^2 + 13*S^4)/S^2 + ((-23 - 41*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (4*(-27 + 11*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (152*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 8*Zeta[3]) + HPL[{0}, S^2]^3*((-53*Pi^2)/18 + (-6 + 7*S^2)/3 + ((1 + S^2)*HPL[{1}, -S^2]^2)/S^2 + (2*(-34 + 11*S^2)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)) + ((-3 + 2*S^2)*HPL[{2}, -S^2])/(3*S^2) + HPL[{1}, -S^2]*(((1 + S^2)*(3 + 2*S^2))/(3*S^2) + (Pi^2*(-79 + 6*S^2))/(18*(1 + S^2)) + (2*(-14 + 5*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) + (S^2*HPL[{3}, -S^2])/(1 + S^2) + ((23 - 15*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + ((-43 - 45*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{3}, -S^2]*((-4*Pi^2*(-2 + S^2))/(3*S^2) + (2*(30 + 11*S^2 + 9*S^4))/S^2 + (4*(-25 + 13*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (8*(2 + 3*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((4*Pi^2*(1 + S^2))/(3*S^2) - (8*(-3 + S^2)*(1 + S^2))/(3*S^2) - (24*(-1 + 4*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 72*HPL[{2, 1}, -S^2] - (8*(-2 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((4*Pi^2*(-3 + S^2))/(3*S^2) - (8*(2 + 3*S^2))/S^2 + (4*(-9 + 29*S^2)*Zeta[3])/(1 + S^2)) + Log[T]^3*(24 - (4*Pi^2)/3 + (10*HPL[{0}, S^2]^3)/(1 + S^2) - (8*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 - (80*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) + HPL[{0}, S^2]^2*(-4 - (4*(-13 + 4*S^2)*HPL[{1}, -S^2])/(1 + S^2)) + (8*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((-8*(1 + S^2))/S^2 - (4*Pi^2*(-28 + 19*S^2))/(3*(1 + S^2)) + 72*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((-10*Pi^2*(-17 + 10*S^2))/(9*(1 + S^2)) - (8*(1 + S^2)*HPL[{1}, -S^2])/S^2 - (120*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - (4*(-29 + 49*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) + (8*(-4 + 41*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (296*HPL[{2, 1}, -S^2])/3 + (8*(-4 + 35*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{0}, S^2]^2*((Pi^2*(20 - 3*S^2))/6 + (-15 + 13*S^2)/2 + (7*Pi^4*(-101 + 61*S^2))/(720*(1 + S^2)) + (2*(1 + S^2)*HPL[{1}, -S^2]^3)/S^2 + ((-13 + 4*S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) + (2*S^2 + (Pi^2*(-23 - 2*S^2))/(4*(1 + S^2)))*HPL[{2}, -S^2] + (21*(-1 + S^2)*HPL[{2}, -S^2]^2)/(4*(1 + S^2)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(3 + 2*S^2))/S^2 + (2*Pi^2*(-19 + 3*S^2))/(3*(1 + S^2)) + ((-35 + 3*S^2)*HPL[{2}, -S^2])/(1 + S^2)) - (4*(-1 + S^2)*HPL[{3}, -S^2])/S^2 - (2*(2 + 3*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (2*(-3 + 2*S^2)*HPL[{2, 1}, -S^2])/S^2 + ((25 - 11*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (4*(-13 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 6*Zeta[3] + HPL[{1}, -S^2]*((Pi^2*(1 + S^2))/S^2 + (2*(1 + S^2)*(3 + S^2))/S^2 - (2*(2 + 5*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (2*(-35 + 3*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (2*(1 + 5*S^2)*Zeta[3])/(1 + S^2))) + Log[T]^2*(-88 + (4*Pi^2*S^2)/3 + (Pi^4*(-946 + 601*S^2))/(180*(1 + S^2)) + ((-43 - 6*S^2)*HPL[{0}, S^2]^4)/(12*(1 + S^2)) + (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S^2 + (60*(-1 + S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) + HPL[{0}, S^2]^3*(-2 + (2*(-34 + 11*S^2)*HPL[{1}, -S^2])/(3*(1 + S^2))) + HPL[{1}, -S^2]^2*((12*(1 + S^2))/S^2 + (2*Pi^2*(-28 + 19*S^2))/(1 + S^2) - 108*HPL[{2}, -S^2]) + (8*S^2 + (Pi^2*(-43 - 5*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] + (38*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{0}, S^2]^2*(2*(3 + 2*S^2) + (Pi^2*(-37 + 7*S^2))/(3*(1 + S^2)) + (6*(1 + S^2)*HPL[{1}, -S^2])/S^2 + (6*(-13 + 4*S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + (2*(-13 + 6*S^2)*HPL[{2}, -S^2])/(1 + S^2)) + (16*HPL[{3}, -S^2])/S^2 - (2*(23 + 51*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (24*HPL[{2, 1}, -S^2])/S^2 + (8*(5 + 12*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 136*HPL[{2, 1, 1}, -S^2] + 24*Zeta[3] + HPL[{1}, -S^2]*((4*Pi^2*(1 + S^2))/S^2 - (8*(-3 + S^2)*(1 + S^2))/S^2 - (72*(-1 + 4*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 216*HPL[{2, 1}, -S^2] - (24*(-2 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]*(-2*Pi^2 - 4*(-3 + 2*S^2) + (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 + (120*(-1 + S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) - (12*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((12*(1 + S^2))/S^2 + (2*Pi^2*(-79 + 56*S^2))/(3*(1 + S^2)) + (156*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) - (4*(4 + 3*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (4*(-49 + 29*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(4 + 11*S^2)*Zeta[3])/(1 + S^2))) + 32*Zeta[5] + Log[T]*(200 - (52*Pi^4)/45 - (8*Pi^2*(-1 + S^2))/3 + ((9 + 5*S^2)*HPL[{0}, S^2]^5)/(6*(1 + S^2)) - (4*(1 + S^2)*HPL[{1}, -S^2]^4)/S^2 - (24*(-1 + S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) + HPL[{0}, S^2]^4*(-1/3 + (37*HPL[{1}, -S^2])/(6*(1 + S^2))) + HPL[{1}, -S^2]^3*((-8*(1 + S^2))/S^2 - (4*Pi^2*(-28 + 19*S^2))/(3*(1 + S^2)) + 72*HPL[{2}, -S^2]) + HPL[{0}, S^2]^3*(8/3 + (5*Pi^2*(27 + 10*S^2))/(18*(1 + S^2)) - (2*(1 + S^2)*HPL[{1}, -S^2])/S^2 - (2*(-34 + 11*S^2)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)) + ((33 - 5*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) + ((-8*(1 + 2*S^2))/S^2 + (4*Pi^2*(-1 + 23*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] + (24*HPL[{4}, -S^2])/S^2 + (4*(16 + 27*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((16*(1 + 2*S^2))/S^2 - (2*Pi^2*(81 + 43*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (32*HPL[{3, 1}, -S^2])/S^2 - (16*(1 + 20*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (4*(9 + 265*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + (48*HPL[{2, 1, 1}, -S^2])/S^2 + HPL[{1}, -S^2]*((Pi^4*(1068 - 479*S^2))/(90*(1 + S^2)) + (24*(-2 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(1 + S^2)*(3 + S^2))/(3*S^2) + ((-8*(1 + S^2)^2)/S^2 + (4*Pi^2*(31 + 12*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] - (76*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + (4*(1 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (16*(10 + 17*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 432*HPL[{2, 1, 1}, -S^2]) - (304*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (16*(-53 + 16*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 592*HPL[{2, 1, 1, 1}, -S^2] + (-64 + (2*Pi^2*(1 + 44*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{0}, S^2]^2*((-5*Pi^2)/3 - 2*(5 + 4*S^2) - (6*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 - (4*(-13 + 4*S^2)*HPL[{1}, -S^2]^3)/(1 + S^2) - (2*(-3 + 2*S^2)*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((-2*(1 + S^2)*(3 + 2*S^2))/S^2 - (4*Pi^2*(-19 + 3*S^2))/(3*(1 + S^2)) - (2*(-35 + 3*S^2)*HPL[{2}, -S^2])/(1 + S^2)) + (2*(2 + 5*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (4*(22 + 3*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (2*(5 + 9*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-4*Pi^2*(1 + S^2))/S^2 + (8*(-3 + S^2)*(1 + S^2))/S^2 + (72*(-1 + 4*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 216*HPL[{2, 1}, -S^2] + (24*(-2 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((-4*Pi^2*(-3 + S^2))/(3*S^2) - (8*(1 + 2*S^2 + 2*S^4))/S^2 + (4*(5 + 43*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (152*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(-7 + 31*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]*((8*Pi^2)/3 + (377*Pi^4)/(45*(1 + S^2)) + 8*(-5 + 3*S^2) - (8*(1 + S^2)*HPL[{1}, -S^2]^3)/S^2 - (60*(-1 + S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) + (8 - (2*Pi^2*(-31 + 27*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] - (4*(-9 + 10*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((-12*(1 + S^2))/S^2 - (2*Pi^2*(-79 + 56*S^2))/(3*(1 + S^2)) - (156*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) + (16*(-1 + S^2)*HPL[{3}, -S^2])/S^2 - (8*(-2 + S^2)*HPL[{4}, -S^2])/(1 + S^2) + (24*HPL[{2, 1}, -S^2])/S^2 + (8*(-14 + 25*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (8*(-29 + 49*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 8*Zeta[3] + HPL[{1}, -S^2]*((-4*Pi^2*(1 + S^2))/S^2 + (8*(-3 + S^2)*(1 + S^2))/S^2 - (8*S^2*HPL[{3}, -S^2])/(1 + S^2) + (312*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (8*(-3 + 4*S^2)*Zeta[3])/(1 + S^2))) + (4*(-12 + 35*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]*((4*Pi^2*(1 + S^2))/S^2 + (4*Pi^4*(1 + S^2))/(9*S^2) - (4*(1 + S^2)*(-36 + 11*S^2))/S^2 + (2*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + ((8*(1 + S^2)^2)/S^2 - (2*Pi^2*(-7 + 41*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] + (8*(1 + S^2)*HPL[{4}, -S^2])/S^2 - (4*(8 + 19*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((-8*(1 + S^2)^2)/S^2 + (4*Pi^2*(31 + 12*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (16*(-5 + 14*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (4*(-59 + 197*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + (304*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (48*(-16 + 7*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 432*HPL[{2, 1, 1, 1}, -S^2] + (8*(1 + S^2) - (2*Pi^2*(-5 + 38*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((4*(1 + S^2)*(3 + 2*S^2))/S^2 - (8*(-5 + 14*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (152*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (8*(-4 + 15*S^2)*Zeta[3])/(1 + S^2)) - (4*(2 + 49*S^2)*Zeta[5])/(1 + S^2)) + HPL[{0}, S^2]*((-98*Pi^4)/45 + (Pi^2*(-3 + 5*S^2))/3 - 4*(-41 + 11*S^2) + (2*(1 + S^2)*HPL[{1}, -S^2]^4)/S^2 + (12*(-1 + S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) - 4*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^3*((4*(1 + S^2))/S^2 + (2*Pi^2*(-79 + 56*S^2))/(9*(1 + S^2)) + (52*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) + ((-4*Pi^2)/(3*(1 + S^2)) - (4*(-1 + 2*S^4))/S^2)*HPL[{3}, -S^2] - (12*HPL[{4}, -S^2])/S^2 + (16*S^2*HPL[{5}, -S^2])/(1 + S^2) + ((-4*Pi^2*(-18 + 11*S^2))/(3*(1 + S^2)) + (8*(-1 - S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (16*HPL[{3, 1}, -S^2])/S^2 + (8*(3 + 5*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (24*(3 + 4*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - (24*HPL[{2, 1, 1}, -S^2])/S^2 + HPL[{1}, -S^2]*((-12*(-2 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(1 + S^2)*(3 + S^2))/(3*S^2) + (Pi^4*(-525 + 229*S^2))/(90*(1 + S^2)) + ((-4*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-67 + 49*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] + (38*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + (8*(-1 + 2*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (8*(-19 + 20*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (312*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)) + (16*(-10 + 9*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (8*(-64 + 51*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - (8*(-49 + 29*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (8*(-1 + S^2) + (Pi^2*(-47 - 56*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*(4/S^2 + (2*Pi^2*(-3 + S^2))/(3*S^2) - (4*(3 + 5*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (8*(-10 + 9*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (6*(1 + 3*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((2*Pi^2*(1 + S^2))/S^2 - (4*(-3 + S^2)*(1 + S^2))/S^2 + (4*S^2*HPL[{3}, -S^2])/(1 + S^2) - (156*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(-3 + 4*S^2)*Zeta[3])/(1 + S^2)) - (2*(43 + 51*S^2)*Zeta[5])/(1 + S^2));
E4wuvT2F2=-75/32 + (Pi^4*(-701 - 42*S^2))/2880 + (Pi^2*(-23 - 28*S^2))/48 + (Pi^6*(-23714 - 147*S^2 - 147*S^4))/(60480*(1 + S^2)) + ((-47*Pi^2)/(30*S^2) + (-67 - 84*S^2 - 17*S^4)/(15*S^2))*HPL[{1}, -S^2]^5 + ((-3 - 11*S^2 - S^4 - S^6)*HPL[{1}, -S^2]^6)/(2*S^2*(1 + S^2)) - (4*HPL[{1}, -S^2]^7)/(7*S^2) + HPL[{0}, S^2]^6*(-1/(32*(1 + S^2)) - HPL[{1}, -S^2]/(32*S^2)) + HPL[{0}, S^2]^5*((3 + S^2)/96 + ((3 - 29*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(96*S^2*(1 + S^2)) - HPL[{1}, -S^2]^2/(6*S^2)) + ((41 - 6*S^4)*HPL[{2}, -S^2]^3)/(12*S^2) + ((14 + 2*S^2 - 5*S^4 - 5*S^6)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((5*Pi^2)/(4*S^2) + (21 + 168*S^2 + 67*S^4)/(8*S^2))*HPL[{5}, -S^2] + ((-270 - 228*S^2 - S^4 - S^6)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)) + (75*HPL[{7}, -S^2])/S^2 + ((50 + 126*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + HPL[{0}, S^2]^4*((-11 + 40*S^2)/192 + (Pi^2*(-164 + 5*S^2 + 5*S^4))/(576*(1 + S^2)) - (37*HPL[{1}, -S^2]^2)/(24*(1 + S^2)) - (37*HPL[{1}, -S^2]^3)/(72*S^2) + (5*(-10 + S^2 + S^4)*HPL[{2}, -S^2])/(96*(1 + S^2)) + HPL[{1}, -S^2]*((-41*Pi^2)/(144*S^2) + (-23 - 8*S^2 + 15*S^4)/(192*S^2) - (25*HPL[{2}, -S^2])/(48*S^2)) + HPL[{3}, -S^2]/(16*S^2) + (7*HPL[{2, 1}, -S^2])/(6*S^2)) + ((7*Pi^2)/(6*S^2) + (17 - 684*S^2 - 223*S^4)/(8*S^2))*HPL[{3, 2}, -S^2] + ((11*Pi^2)/(6*S^2) + (-6 - 1126*S^2 - 371*S^4)/(4*S^2))*HPL[{4, 1}, -S^2] - (3*(-6 + 6*S^2 + 5*S^4 + 5*S^6)*HPL[{4, 2}, -S^2])/(4*S^2*(1 + S^2)) - (24*HPL[{4, 3}, -S^2])/S^2 + ((9 - 107*S^2 - 43*S^4 - 43*S^6)*HPL[{5, 1}, -S^2])/(2*S^2*(1 + S^2)) - (147*HPL[{5, 2}, -S^2])/(2*S^2) - (166*HPL[{6, 1}, -S^2])/S^2 + ((-76*Pi^2)/(3*S^2) + (-10 - 94*S^2 - 27*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((-232*Pi^2)/(3*S^2) - (7*(9 + 24*S^2 + 7*S^4))/(2*S^2))*HPL[{3, 1, 1}, -S^2] + (3*(-3 + S^4)*HPL[{3, 1, 2}, -S^2])/(2*S^2) + ((155 - 21*S^4)*HPL[{3, 2, 1}, -S^2])/(2*S^2) + (3*HPL[{3, 2, 2}, -S^2])/S^2 - (16*HPL[{3, 3, 1}, -S^2])/S^2 + ((284 + 340*S^2 - 19*S^4 - 19*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (19*HPL[{4, 1, 2}, -S^2])/S^2 - (67*HPL[{4, 2, 1}, -S^2])/S^2 - (150*HPL[{5, 1, 1}, -S^2])/S^2 + ((178*Pi^2)/(3*S^2) - (2*(-16 + 91*S^2 + 23*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (152*HPL[{2, 2, 2, 1}, -S^2])/S^2 + (2*(-122 - 150*S^2 + 5*S^4 + 5*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (436*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (436*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (892*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (2704*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (8*(-55 + 4*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (296*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (888*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (1472*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (720*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (-13/3 + (Pi^2*(-141 - 4*S^2 - 4*S^4))/(18*(1 + S^2)) + ((-47*Pi^2)/(6*S^2) + (-67 - 84*S^2 - 17*S^4)/(3*S^2))*HPL[{1}, -S^2] - (15*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(2*S^2*(1 + S^2)) - (20*HPL[{1}, -S^2]^3)/S^2 + HPL[{0}, S^2]^2*((-51 - 4*S^2 - 4*S^4)/(6*(1 + S^2)) - (17*HPL[{1}, -S^2])/(2*S^2)) + ((55 - 4*S^4)*HPL[{2}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((-123 - 34*S^2)/6 - (15*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)) - (30*HPL[{1}, -S^2]^2)/S^2 + (2*HPL[{2}, -S^2])/S^2) - HPL[{3}, -S^2]/(3*S^2) + (30*HPL[{2, 1}, -S^2])/S^2)*Log[T]^4 + (3 + (3*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) + (12*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*((3*(4 + S^2 + S^4))/(1 + S^2) + (12*HPL[{1}, -S^2])/S^2) - (6*HPL[{2}, -S^2])/S^2)*Log[T]^5 + (-4/(1 + S^2) - (4*HPL[{1}, -S^2])/S^2)*Log[T]^6 + ((236 + 7*S^2)/4 + (Pi^2*(53 + 17*S^2))/6)*Zeta[3] + (3*(-2 + S^2 + S^4)*Zeta[3]^2)/(2*(1 + S^2)) + HPL[{4}, -S^2]*((69 + 91*S^2 + 70*S^4)/(8*S^2) + (Pi^2*(28 + 92*S^2 + 19*S^4 + 19*S^6))/(24*S^2*(1 + S^2)) - (29*HPL[{2, 1}, -S^2])/S^2 - (8*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((230 + 20*S^2 - 13*S^4)/(2*S^2) + (Pi^2*(61 + 23*S^2 - 8*S^4 - 8*S^6))/(3*S^2*(1 + S^2)) - (4*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((-230 - 74*S^2 + 3*S^4)/(16*S^2) + (Pi^2*(-29 - 88*S^2 - 4*S^4 - 4*S^6))/(12*S^2*(1 + S^2)) + (3*HPL[{3}, -S^2])/(2*S^2) + (19*HPL[{2, 1}, -S^2])/S^2 - Zeta[3]/S^2) + HPL[{3, 1}, -S^2]*((-479 - 108*S^2 - 7*S^4)/(8*S^2) + (Pi^2*(-135 - 91*S^2 + 13*S^4 + 13*S^6))/(12*S^2*(1 + S^2)) + (4*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(285 + 53*S^2))/(24*S^2) + (Pi^2*(-57 - 245*S^2 - 19*S^4 - 19*S^6))/(24*S^2*(1 + S^2)) + (9*(3 + S^4)*HPL[{2}, -S^2])/(4*S^2) + (15*HPL[{3}, -S^2])/S^2 + (13*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((1043*Pi^4)/(360*S^2) + (Pi^2*(25 - 96*S^2 - 25*S^4))/(12*S^2) + (31 - 426*S^2 - 14*S^4)/(8*S^2) - (60*HPL[{3, 1}, -S^2])/S^2 - (148*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(49 + 87*S^2)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((-7*Pi^4)/(90*S^2) + (33 + 932*S^2 + 124*S^4)/(16*S^2) + (Pi^2*(-13 + 432*S^2 + 127*S^4))/(48*S^2) + (12*HPL[{4}, -S^2])/S^2 + ((-193 - 345*S^2 + 11*S^4 + 11*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (14*HPL[{3, 1}, -S^2])/S^2 - (16*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(4 + 6*S^2 + S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^3*((-1547*Pi^4)/(1080*S^2) - (Pi^2*(1 + S^2)*(157 + 49*S^2))/(36*S^2) - ((1 + S^2)*(629 + 95*S^2))/(24*S^2) + ((-19*Pi^2)/(9*S^2) + (46 + 53*S^2 + 7*S^4)/(3*S^2))*HPL[{2}, -S^2] - (38*HPL[{2}, -S^2]^2)/(3*S^2) + (12*(3 + 8*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (28*HPL[{4}, -S^2])/(3*S^2) - (9*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (28*HPL[{3, 1}, -S^2])/(3*S^2) + ((33 + 85*S^2 + 11*S^4 + 11*S^6)*Zeta[3])/(S^2*(1 + S^2))) + Log[T]^3*(11/2 + (Pi^2*(23 + 3*S^2))/6 + ((47*Pi^2)/(3*S^2) + (2*(67 + 84*S^2 + 17*S^4))/(3*S^2))*HPL[{1}, -S^2]^2 + (10*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) + (20*HPL[{1}, -S^2]^4)/S^2 + HPL[{0}, S^2]^3*((10 + S^2 + S^4)/(2*(1 + S^2)) + (5*HPL[{1}, -S^2])/S^2) + ((-17*Pi^2)/(3*S^2) + (-36 - 5*S^2 + 3*S^4)/S^2)*HPL[{2}, -S^2] + (13*HPL[{2}, -S^2]^2)/S^2 + HPL[{0}, S^2]^2*((8 + 3*S^2)/2 + (2*(3 + 20*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) + (17*HPL[{1}, -S^2]^2)/S^2 - (2*HPL[{2}, -S^2])/S^2) + ((6 - 174*S^2 - 71*S^4 - 71*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (8*HPL[{4}, -S^2])/S^2 + (2*(-29 + 35*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((274 + 53*S^2)/6 + (3*Pi^2*(5 + S^2 + S^4))/(1 + S^2) + (15*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) + (40*HPL[{1}, -S^2]^3)/S^2 + ((-11 + 145*S^2 + 41*S^4 + 41*S^6)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((15*Pi^2)/S^2 + (2*(67 + 84*S^2 + 17*S^4))/(3*S^2) + (52*HPL[{2}, -S^2])/S^2) + (14*HPL[{3}, -S^2])/(3*S^2) - (112*HPL[{2, 1}, -S^2])/S^2) + (208*HPL[{3, 1}, -S^2])/(3*S^2) - (120*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(78 + 35*S^2 + 35*S^4)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(285 + 53*S^2))/(6*S^2) + (Pi^2*(57 + 245*S^2 + 19*S^4 + 19*S^6))/(6*S^2*(1 + S^2)) - (9*(3 + S^4)*HPL[{2}, -S^2])/S^2 - (60*HPL[{3}, -S^2])/S^2 - (52*Zeta[3])/S^2)) + HPL[{0}, S^2]^3*((Pi^2*(-8 + 3*S^2))/96 + (-57 + 5*S^2)/32 + ((-33 - 213*S^2 - 11*S^4 - 11*S^6)*HPL[{1}, -S^2]^3)/(36*S^2*(1 + S^2)) - (5*HPL[{1}, -S^2]^4)/(4*S^2) + (Pi^2/(24*S^2) + (6 - 48*S^2 + S^4)/(48*S^2))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(8*S^2) + HPL[{1}, -S^2]^2*((-85*Pi^2)/(72*S^2) + (-65 - 76*S^2 - 11*S^4)/(48*S^2) - (19*HPL[{2}, -S^2])/(6*S^2)) + ((1 - 3*S^2)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)) - (3*HPL[{4}, -S^2])/(4*S^2) + ((33 + 109*S^2 + 2*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]/S^2 + ((4 + 5*S^2 + 5*S^4)*Zeta[3])/(12*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(123 + 17*S^2))/(96*S^2) + (Pi^2*(-9 - 179*S^2 - 3*S^4 - 3*S^6))/(72*S^2*(1 + S^2)) + ((-15 - 91*S^2 - 5*S^4 - 5*S^6)*HPL[{2}, -S^2])/(12*S^2*(1 + S^2)) - HPL[{3}, -S^2]/(2*S^2) + (19*HPL[{2, 1}, -S^2])/(3*S^2) + Zeta[3]/(3*S^2))) + HPL[{0}, S^2]^2*((1 - 56*S^2)/32 + (3*Pi^2*(-5 + 3*S^2))/32 + (Pi^4*(-126 + S^2 + S^4))/(160*(1 + S^2)) + ((-3 - 20*S^2 - S^4 - S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) - (17*HPL[{1}, -S^2]^5)/(10*S^2) + ((-8 - 50*S^2 - 5*S^4 - 5*S^6)*HPL[{2}, -S^2]^2)/(8*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((-22*Pi^2)/(9*S^2) + (-23 - 38*S^2 - 15*S^4)/(12*S^2) - (19*HPL[{2}, -S^2])/(3*S^2)) + ((-5 + 18*S^2 + 7*S^4)*HPL[{3}, -S^2])/(8*S^2) + ((-5 - S^2 + S^4 + S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + (9*HPL[{5}, -S^2])/(2*S^2) + ((6*Pi^2)/S^2 + (9 - 5*S^2 - 2*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + ((-13 + 59*S^2 + 8*S^4 + 8*S^6)*HPL[{3, 1}, -S^2])/(4*S^2*(1 + S^2)) + HPL[{3, 2}, -S^2]/S^2 + (3*HPL[{4, 1}, -S^2])/(2*S^2) - (2*(-3 + 16*S^2 + 2*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (39*HPL[{2, 2, 1}, -S^2])/S^2 - (120*HPL[{3, 1, 1}, -S^2])/S^2 + (88*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((9 + 11*S^2)*Zeta[3])/4 + HPL[{2}, -S^2]*((-14 - 13*S^2)/16 + (Pi^2*(4 - 38*S^2 - S^4 - S^6))/(16*S^2*(1 + S^2)) - HPL[{3}, -S^2]/(2*S^2) + (39*HPL[{2, 1}, -S^2])/(2*S^2) - (3*Zeta[3])/(2*S^2)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(35 + 27*S^2))/(16*S^2) + (Pi^2*(-9 - 97*S^2 - 3*S^4 - 3*S^6))/(12*S^2*(1 + S^2)) + ((-9 - 161*S^2 - 3*S^4 - 3*S^6)*HPL[{2}, -S^2])/(8*S^2*(1 + S^2)) + (3*HPL[{3}, -S^2])/(2*S^2) + (19*HPL[{2, 1}, -S^2])/S^2 + (2*Zeta[3])/S^2) + HPL[{1}, -S^2]*((-63*Pi^4)/(80*S^2) - (Pi^2*(1 + S^2)*(23 + 5*S^2))/(32*S^2) - ((1 + S^2)*(83 + 53*S^2))/(32*S^2) + ((-21*Pi^2)/(8*S^2) + (-3 - 10*S^2 - 7*S^4)/(8*S^2))*HPL[{2}, -S^2] - (21*HPL[{2}, -S^2]^2)/(4*S^2) + ((15 + 27*S^2 + 5*S^4 + 5*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) + HPL[{4}, -S^2]/S^2 + ((9 + 161*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(4*S^2*(1 + S^2)) + (18*HPL[{3, 1}, -S^2])/S^2 - (38*HPL[{2, 1, 1}, -S^2])/S^2 + ((15 + 31*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(4*S^2*(1 + S^2)))) + Log[T]^2*(-47/8 + (Pi^2*(-86 - 13*S^2))/24 + (Pi^4*(-3094 - 69*S^2 - 69*S^4))/(720*(1 + S^2)) + ((-47*Pi^2)/(3*S^2) - (2*(67 + 84*S^2 + 17*S^4))/(3*S^2))*HPL[{1}, -S^2]^3 - (15*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) - (12*HPL[{1}, -S^2]^5)/S^2 + HPL[{0}, S^2]^4*((-74 + 5*S^2 + 5*S^4)/(48*(1 + S^2)) - (37*HPL[{1}, -S^2])/(24*S^2)) + ((-50 - 126*S^2 - 3*S^4 - 3*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + HPL[{0}, S^2]^3*((-54 - S^2)/24 + ((-33 - 213*S^2 - 11*S^4 - 11*S^6)*HPL[{1}, -S^2])/(12*S^2*(1 + S^2)) - (15*HPL[{1}, -S^2]^2)/(2*S^2) + HPL[{2}, -S^2]/(2*S^2)) + ((-2*Pi^2)/(3*S^2) + (-3 + 396*S^2 + 113*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((38 + 94*S^2 + 17*S^4 + 17*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - (3*HPL[{5}, -S^2])/S^2 + ((89*Pi^2)/(3*S^2) + (16 - 91*S^2 - 23*S^4)/S^2)*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-34 - 13*S^2)/8 + (Pi^2*(-176 - 3*S^2 - 3*S^4))/(24*(1 + S^2)) - (3*(3 + 20*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) - (17*HPL[{1}, -S^2]^3)/S^2 + ((3 - 16*S^2 - 2*S^4 - 2*S^6)*HPL[{2}, -S^2])/(S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-22*Pi^2)/(3*S^2) + (-23 - 38*S^2 - 15*S^4)/(4*S^2) - (19*HPL[{2}, -S^2])/S^2) - (3*HPL[{3}, -S^2])/(2*S^2) + (44*HPL[{2, 1}, -S^2])/S^2) + ((-122 - 150*S^2 + 5*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (10*HPL[{3, 2}, -S^2])/S^2 + (16*HPL[{4, 1}, -S^2])/S^2 - (4*(-55 + 4*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (148*HPL[{2, 2, 1}, -S^2])/S^2 - (448*HPL[{3, 1, 1}, -S^2])/S^2 + (360*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (97 + 23*S^2)*Zeta[3] + HPL[{2}, -S^2]*((230 + 20*S^2 - 13*S^4)/(4*S^2) + (Pi^2*(61 + 23*S^2 - 8*S^4 - 8*S^6))/(6*S^2*(1 + S^2)) - (8*HPL[{3}, -S^2])/S^2 + (74*HPL[{2, 1}, -S^2])/S^2 - (2*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(285 + 53*S^2))/(4*S^2) + (Pi^2*(-57 - 245*S^2 - 19*S^4 - 19*S^6))/(4*S^2*(1 + S^2)) + (27*(3 + S^4)*HPL[{2}, -S^2])/(2*S^2) + (90*HPL[{3}, -S^2])/S^2 + (78*Zeta[3])/S^2) + HPL[{1}, -S^2]*((-1547*Pi^4)/(360*S^2) - (Pi^2*(1 + S^2)*(157 + 49*S^2))/(12*S^2) - ((1 + S^2)*(629 + 95*S^2))/(8*S^2) + ((-19*Pi^2)/(3*S^2) + (46 + 53*S^2 + 7*S^4)/S^2)*HPL[{2}, -S^2] - (38*HPL[{2}, -S^2]^2)/S^2 + (36*(3 + 8*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (28*HPL[{4}, -S^2])/S^2 - (27*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (28*HPL[{3, 1}, -S^2])/S^2 + (3*(33 + 85*S^2 + 11*S^4 + 11*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]*((-618 - 95*S^2)/8 + (Pi^2*(-100 - 23*S^2))/8 - (15*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) - (30*HPL[{1}, -S^2]^4)/S^2 + ((3*Pi^2)/(2*S^2) + (-3 - 115*S^2 - 28*S^4)/(2*S^2))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(2*S^2) + HPL[{1}, -S^2]^2*((-45*Pi^2)/(2*S^2) + (-67 - 84*S^2 - 17*S^4)/S^2 - (78*HPL[{2}, -S^2])/S^2) + ((-11 - 15*S^2 + 4*S^4 + 4*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + HPL[{4}, -S^2]/S^2 - (2*(-64 - 142*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (12*HPL[{3, 1}, -S^2])/S^2 + (24*HPL[{2, 1, 1}, -S^2])/S^2 + ((14 + 3*S^2 + 3*S^4)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(285 + 53*S^2))/(4*S^2) + (Pi^2*(-42 - 177*S^2 - 14*S^4 - 14*S^6))/(3*S^2*(1 + S^2)) - (39*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - (2*HPL[{3}, -S^2])/S^2 + (156*HPL[{2, 1}, -S^2])/S^2 + (14*Zeta[3])/S^2))) + ((254 + 45*S^2)*Zeta[5])/4 + HPL[{2}, -S^2]*((552 + 31*S^2 - 56*S^4)/(16*S^2) + (Pi^2*(115 + 3*S^2 - 13*S^4))/(24*S^2) + (Pi^4*(1058 - 148*S^2 - 101*S^4 - 101*S^6))/(1440*S^2*(1 + S^2)) + ((-5*Pi^2)/(6*S^2) + (-13 + 348*S^2 + 119*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((-46 - 10*S^2 + 19*S^4 + 19*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) - (21*HPL[{5}, -S^2])/(2*S^2) + ((38*Pi^2)/(3*S^2) + (10 + 94*S^2 + 27*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((111 + 263*S^2 + S^4 + S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) - (3*HPL[{3, 2}, -S^2])/S^2 + (11*HPL[{4, 1}, -S^2])/S^2 - (2*(50 + 126*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (76*HPL[{2, 2, 1}, -S^2])/S^2 + (212*HPL[{3, 1, 1}, -S^2])/S^2 + (148*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-2*Pi^2)/(3*S^2) + (-7 + 86*S^2 + 21*S^4)/(2*S^2))*Zeta[3] - (10*Zeta[5])/S^2) + HPL[{1}, -S^2]^2*((-5*Pi^2*(1 + S^2)*(4 + S^2))/(3*S^2) - ((1 + S^2)*(1461 + 211*S^2))/(32*S^2) + (Pi^4*(-1437 - 7625*S^2 - 479*S^4 - 479*S^6))/(1440*S^2*(1 + S^2)) - (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((8*Pi^2)/S^2 + (217 + 276*S^2 + 59*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((87 + 199*S^2 + 29*S^4 + 29*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + (11*HPL[{5}, -S^2])/S^2 + ((19*Pi^2)/(3*S^2) + (-46 - 53*S^2 - 7*S^4)/S^2)*HPL[{2, 1}, -S^2] + ((-51 - 79*S^2 - 17*S^4 - 17*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (76*HPL[{3, 2}, -S^2])/S^2 - (256*HPL[{4, 1}, -S^2])/S^2 + (27*(3 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (152*HPL[{2, 2, 1}, -S^2])/S^2 - (276*HPL[{3, 1, 1}, -S^2])/S^2 + ((43*Pi^2)/(6*S^2) + ((1 + S^2)*(111 + 19*S^2))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((3*(1 + S^2)*(71 + 5*S^2))/(8*S^2) + (Pi^2*(9 - 10*S^2 + 3*S^4 + 3*S^6))/(3*S^2*(1 + S^2)) + (38*HPL[{3}, -S^2])/S^2 + (76*HPL[{2, 1}, -S^2])/S^2 + (38*Zeta[3])/S^2) + (47*Zeta[5])/S^2) + HPL[{1}, -S^2]*((-11857*Pi^6)/(30240*S^2) - (Pi^2*(1 + S^2)*(178 + 37*S^2))/(24*S^2) - (5*(1 + S^2)*(369 + 55*S^2))/(32*S^2) - (Pi^4*(1 + S^2)*(2593 + 783*S^2))/(2880*S^2) + ((-59*Pi^2)/(12*S^2) + (-113 - 144*S^2 - 31*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 - (3*HPL[{3}, -S^2]^2)/S^2 + ((8*Pi^2)/(3*S^2) + (123 + 200*S^2 + 77*S^4)/(8*S^2))*HPL[{4}, -S^2] + ((57 + 101*S^2 + 19*S^4 + 19*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) + (21*HPL[{6}, -S^2])/(2*S^2) + (76*HPL[{2, 1}, -S^2]^2)/S^2 + ((11*Pi^2)/(3*S^2) - (2*(26 + 33*S^2 + 7*S^4))/S^2)*HPL[{3, 1}, -S^2] - (4*(21 + 59*S^2 + 7*S^4 + 7*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((-591 - 1615*S^2 - 197*S^4 - 197*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) - (9*HPL[{4, 2}, -S^2])/S^2 - (58*HPL[{5, 1}, -S^2])/S^2 + ((-38*Pi^2)/(3*S^2) + (2*(46 + 53*S^2 + 7*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (38*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (6*(21 + 113*S^2 + 7*S^4 + 7*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (56*HPL[{4, 1, 1}, -S^2])/S^2 - (54*(3 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (56*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (((1 + S^2)*(125 + 13*S^2))/(2*S^2) + (Pi^2*(57 + 143*S^2 + 19*S^4 + 19*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] - (3*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((-3*(1 + S^2)*(71 + 5*S^2))/(4*S^2) - (2*Pi^2*(9 - 10*S^2 + 3*S^4 + 3*S^6))/(3*S^2*(1 + S^2)) - (76*Zeta[3])/S^2) + HPL[{3}, -S^2]*(((1 + S^2)*(479 + 89*S^2))/(8*S^2) + (Pi^2*(123 + 315*S^2 + 41*S^4 + 41*S^6))/(12*S^2*(1 + S^2)) - (76*HPL[{2, 1}, -S^2])/S^2 + (4*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-67*Pi^4)/(80*S^2) + (Pi^2*(1 + S^2)*(89 + 7*S^2))/(24*S^2) - ((1 + S^2)*(-475 + 11*S^2))/(16*S^2) + (2*(21 + 59*S^2 + 7*S^4 + 7*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (9*HPL[{4}, -S^2])/S^2 + (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (76*HPL[{3, 1}, -S^2])/S^2 - (152*HPL[{2, 1, 1}, -S^2])/S^2 + ((45 + 121*S^2 + 15*S^4 + 15*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((147 + 335*S^2 + 49*S^4 + 49*S^6)*Zeta[5])/(2*S^2*(1 + S^2))) + Log[T]*(75/16 + (25*Pi^2*(4 + S^2))/48 + (Pi^4*(1114 + 125*S^2))/1440 + ((47*Pi^2)/(6*S^2) + (67 + 84*S^2 + 17*S^4)/(3*S^2))*HPL[{1}, -S^2]^4 + (3*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)) + (4*HPL[{1}, -S^2]^6)/S^2 + HPL[{0}, S^2]^5*((16 - S^2 - S^4)/(48*(1 + S^2)) + HPL[{1}, -S^2]/(3*S^2)) + ((7*Pi^2)/(2*S^2) + (103 + 50*S^2 + 4*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 - (19*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^4*((-12 - 25*S^2)/96 + (37*HPL[{1}, -S^2])/(12*(1 + S^2)) + (37*HPL[{1}, -S^2]^2)/(24*S^2) - HPL[{2}, -S^2]/(8*S^2)) - (4*HPL[{3}, -S^2]^2)/S^2 + ((-13*Pi^2)/(6*S^2) + (-78 - 118*S^2 - 63*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((-23 - 67*S^2 - 41*S^4 - 41*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) + (10*HPL[{6}, -S^2])/S^2 - (78*HPL[{2, 1}, -S^2]^2)/S^2 + HPL[{0}, S^2]^3*((142 - 15*S^2)/48 + (Pi^2*(85 + 2*S^2 + 2*S^4))/(36*(1 + S^2)) + ((33 + 213*S^2 + 11*S^4 + 11*S^6)*HPL[{1}, -S^2]^2)/(12*S^2*(1 + S^2)) + (5*HPL[{1}, -S^2]^3)/S^2 + ((-3 + 73*S^2 + 8*S^4 + 8*S^6)*HPL[{2}, -S^2])/(12*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((85*Pi^2)/(36*S^2) + (65 + 76*S^2 + 11*S^4)/(24*S^2) + (19*HPL[{2}, -S^2])/(3*S^2)) + HPL[{3}, -S^2]/(2*S^2) - (41*HPL[{2, 1}, -S^2])/(3*S^2)) + ((58*Pi^2)/(3*S^2) + (231 + 56*S^2 - 3*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-41 + 263*S^2 + 131*S^4 + 131*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((-26 + 486*S^2 + 213*S^4 + 213*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - (3*HPL[{4, 2}, -S^2])/S^2 + (10*HPL[{5, 1}, -S^2])/S^2 + ((-34*Pi^2)/S^2 + (6*(-36 - 5*S^2 + 3*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(7 + 83*S^2 + 16*S^4 + 16*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (2*(48 + 324*S^2 + 25*S^4 + 25*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (12*HPL[{3, 1, 2}, -S^2])/S^2 - (140*HPL[{3, 2, 1}, -S^2])/S^2 - (504*HPL[{4, 1, 1}, -S^2])/S^2 + (4*(-29 + 35*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (416*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (720*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (-111 - 14*S^2 + (Pi^2*(-43 - 21*S^2 - 21*S^4))/(3*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^3*(((1 + S^2)*(285 + 53*S^2))/(6*S^2) + (Pi^2*(57 + 245*S^2 + 19*S^4 + 19*S^6))/(6*S^2*(1 + S^2)) - (9*(3 + S^4)*HPL[{2}, -S^2])/S^2 - (60*HPL[{3}, -S^2])/S^2 - (52*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-19 - 880*S^2 - 177*S^4)/(8*S^2) + (Pi^2*(5 - 187*S^2 - 79*S^4 - 79*S^6))/(12*S^2*(1 + S^2)) + (168*HPL[{2, 1}, -S^2])/S^2 - (8*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-17 + 208*S^2 + 28*S^4)/(2*S^2) + (Pi^2*(-25 - 63*S^2 + 20*S^4 + 20*S^6))/(3*S^2*(1 + S^2)) + (156*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*((1547*Pi^4)/(360*S^2) + (Pi^2*(1 + S^2)*(157 + 49*S^2))/(12*S^2) + ((1 + S^2)*(629 + 95*S^2))/(8*S^2) + ((19*Pi^2)/(3*S^2) + (-46 - 53*S^2 - 7*S^4)/S^2)*HPL[{2}, -S^2] + (38*HPL[{2}, -S^2]^2)/S^2 - (36*(3 + 8*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - (28*HPL[{4}, -S^2])/S^2 + (27*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (28*HPL[{3, 1}, -S^2])/S^2 - (3*(33 + 85*S^2 + 11*S^4 + 11*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]*((-11*Pi^4)/(9*S^2) + (Pi^2*(-19 + 3*S^4))/(2*S^2) + (-506 - 38*S^2 + 25*S^4)/(8*S^2) + ((25 - 127*S^2 - 67*S^4 - 67*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + (11*HPL[{4}, -S^2])/S^2 - (2*(7 + 83*S^2 + 16*S^4 + 16*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (92*HPL[{3, 1}, -S^2])/S^2 + (156*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(-4 + 34*S^2 + 15*S^4 + 15*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^2*((Pi^2*(36 - 7*S^2))/48 + (34 + 25*S^2)/16 + (2*(3 + 20*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^3)/(S^2*(1 + S^2)) + (17*HPL[{1}, -S^2]^4)/(2*S^2) + ((-3*Pi^2)/(4*S^2) + (3*(-2 + 5*S^2 + 3*S^4))/(4*S^2))*HPL[{2}, -S^2] + (3*HPL[{2}, -S^2]^2)/(4*S^2) + HPL[{1}, -S^2]^2*((22*Pi^2)/(3*S^2) + (23 + 38*S^2 + 15*S^4)/(4*S^2) + (19*HPL[{2}, -S^2])/S^2) + ((-1 - 13*S^2 - 8*S^4 - 8*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) - HPL[{4}, -S^2]/(2*S^2) + ((-21 - 97*S^2 + 5*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (6*HPL[{3, 1}, -S^2])/S^2 - (12*HPL[{2, 1, 1}, -S^2])/S^2 + ((-8 - 7*S^2 - 7*S^4)*Zeta[3])/(2*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(35 + 27*S^2))/(8*S^2) + (Pi^2*(9 + 97*S^2 + 3*S^4 + 3*S^6))/(6*S^2*(1 + S^2)) + ((9 + 161*S^2 + 3*S^4 + 3*S^6)*HPL[{2}, -S^2])/(4*S^2*(1 + S^2)) - (3*HPL[{3}, -S^2])/S^2 - (38*HPL[{2, 1}, -S^2])/S^2 - (4*Zeta[3])/S^2)) + HPL[{0}, S^2]*((Pi^2*(690 + 91*S^2))/48 + (1450 + 211*S^2)/16 + (Pi^4*(1508 + 219*S^2 + 219*S^4))/(360*(1 + S^2)) + (15*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) + (12*HPL[{1}, -S^2]^5)/S^2 + ((-3 + 73*S^2 + 18*S^4 + 18*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((15*Pi^2)/S^2 + (2*(67 + 84*S^2 + 17*S^4))/(3*S^2) + (52*HPL[{2}, -S^2])/S^2) + ((5*Pi^2)/(3*S^2) + (10 + 2*S^2 - 9*S^4)/(2*S^2))*HPL[{3}, -S^2] + ((2 + 14*S^2 + 3*S^4 + 3*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) + ((-125*Pi^2)/(3*S^2) + (-127 - 39*S^2 + 4*S^4)/S^2)*HPL[{2, 1}, -S^2] + ((11 - 145*S^2 - 42*S^4 - 42*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (12*HPL[{3, 2}, -S^2])/S^2 + (10*HPL[{4, 1}, -S^2])/S^2 + (2*(-11 + 145*S^2 + 41*S^4 + 41*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (308*HPL[{2, 2, 1}, -S^2])/S^2 + (952*HPL[{3, 1, 1}, -S^2])/S^2 - (672*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (5*(4 + 3*S^2)*Zeta[3])/2 + HPL[{1}, -S^2]^2*(((1 + S^2)*(285 + 53*S^2))/(4*S^2) + (Pi^2*(42 + 177*S^2 + 14*S^4 + 14*S^6))/(3*S^2*(1 + S^2)) + (39*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) + (2*HPL[{3}, -S^2])/S^2 - (156*HPL[{2, 1}, -S^2])/S^2 - (14*Zeta[3])/S^2) + HPL[{2}, -S^2]*((20 + 256*S^2 + 39*S^4)/(4*S^2) + (Pi^2*(-14 + 218*S^2 + 49*S^4 + 49*S^6))/(12*S^2*(1 + S^2)) - (6*HPL[{3}, -S^2])/S^2 - (154*HPL[{2, 1}, -S^2])/S^2 + (2*Zeta[3])/S^2) + HPL[{1}, -S^2]*((377*Pi^4)/(90*S^2) + (Pi^2*(1 + S^2)*(333 + 79*S^2))/(24*S^2) + ((1 + S^2)*(629 + 95*S^2))/(8*S^2) + ((58*Pi^2)/(3*S^2) + (65 + 77*S^2 + 12*S^4)/S^2)*HPL[{2}, -S^2] + (38*HPL[{2}, -S^2]^2)/S^2 + ((3 + 7*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (12*HPL[{4}, -S^2])/S^2 - (39*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (156*HPL[{3, 1}, -S^2])/S^2 + (312*HPL[{2, 1, 1}, -S^2])/S^2 - (4*(3 + 10*S^2 + S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2)))) + ((-94 - 45*S^2 - 45*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*((10*Pi^2*(1 + S^2)*(4 + S^2))/(3*S^2) + ((1 + S^2)*(1461 + 211*S^2))/(16*S^2) + (Pi^4*(1437 + 7625*S^2 + 479*S^4 + 479*S^6))/(720*S^2*(1 + S^2)) + (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((-16*Pi^2)/S^2 + (-217 - 276*S^2 - 59*S^4)/(2*S^2))*HPL[{3}, -S^2] + ((-87 - 199*S^2 - 29*S^4 - 29*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - (22*HPL[{5}, -S^2])/S^2 + ((-38*Pi^2)/(3*S^2) + (2*(46 + 53*S^2 + 7*S^4))/S^2)*HPL[{2, 1}, -S^2] + (2*(51 + 79*S^2 + 17*S^4 + 17*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (152*HPL[{3, 2}, -S^2])/S^2 + (512*HPL[{4, 1}, -S^2])/S^2 - (54*(3 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (304*HPL[{2, 2, 1}, -S^2])/S^2 + (552*HPL[{3, 1, 1}, -S^2])/S^2 + ((-43*Pi^2)/(3*S^2) - ((1 + S^2)*(111 + 19*S^2))/S^2)*Zeta[3] + HPL[{2}, -S^2]*((-3*(1 + S^2)*(71 + 5*S^2))/(4*S^2) - (2*Pi^2*(9 - 10*S^2 + 3*S^4 + 3*S^6))/(3*S^2*(1 + S^2)) - (76*HPL[{3}, -S^2])/S^2 - (152*HPL[{2, 1}, -S^2])/S^2 - (76*Zeta[3])/S^2) - (94*Zeta[5])/S^2)) + HPL[{0}, S^2]*((Pi^2*(-789 - 80*S^2))/96 + (Pi^4*(-67 - 14*S^2))/80 - (5*(369 + 55*S^2))/32 - (3*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^5)/(2*S^2*(1 + S^2)) - (2*HPL[{1}, -S^2]^6)/S^2 + (Pi^2/(6*S^2) + (6 - 106*S^2 - 25*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 + HPL[{2}, -S^2]^3/(3*S^2) + HPL[{1}, -S^2]^4*((-15*Pi^2)/(4*S^2) + (-67 - 84*S^2 - 17*S^4)/(6*S^2) - (13*HPL[{2}, -S^2])/S^2) - (2*HPL[{3}, -S^2]^2)/S^2 + ((-2*Pi^2)/(3*S^2) + (3 - 2*S^2 - S^4)/S^2)*HPL[{4}, -S^2] + (8*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (20*HPL[{6}, -S^2])/S^2 - HPL[{2, 1}, -S^2]^2/S^2 + (-(Pi^2/S^2) + (1 + 58*S^2 + 14*S^4)/S^2)*HPL[{3, 1}, -S^2] - (4*(2 + 4*S^2 + S^4 + S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((-14 - 26*S^2 - 11*S^4 - 11*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) + (8*HPL[{5, 1}, -S^2])/S^2 + ((3*Pi^2)/S^2 + (-3 - 115*S^2 - 28*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] - (2*(60 + 136*S^2 + S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-371 - 831*S^2 - 2*S^4 - 2*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (8*HPL[{3, 2, 1}, -S^2])/S^2 + (26*HPL[{4, 1, 1}, -S^2])/S^2 - (4*(-64 - 142*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (24*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (48*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((50 + 33*S^2)/8 + (Pi^2*(9 + 4*S^2 + 4*S^4))/(6*(1 + S^2)))*Zeta[3] + HPL[{2, 1}, -S^2]*((Pi^2*(161 + 393*S^2))/(12*S^2*(1 + S^2)) + (267 + 68*S^2 - 2*S^4)/(4*S^2) - (14*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-2 - 18*S^2 + 9*S^4)/(4*S^2) + (Pi^2*(-2 - 6*S^2 + S^4 + S^6))/(6*S^2*(1 + S^2)) - (2*HPL[{2, 1}, -S^2])/S^2 + (4*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(285 + 53*S^2))/(12*S^2) + (Pi^2*(-42 - 177*S^2 - 14*S^4 - 14*S^6))/(9*S^2*(1 + S^2)) - (13*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - (2*HPL[{3}, -S^2])/(3*S^2) + (52*HPL[{2, 1}, -S^2])/S^2 + (14*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((-377*Pi^4)/(180*S^2) - (Pi^2*(1 + S^2)*(333 + 79*S^2))/(48*S^2) - ((1 + S^2)*(629 + 95*S^2))/(16*S^2) + ((-29*Pi^2)/(3*S^2) + (-65 - 77*S^2 - 12*S^4)/(2*S^2))*HPL[{2}, -S^2] - (19*HPL[{2}, -S^2]^2)/S^2 + ((-3 - 7*S^2 - S^4 - S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - (6*HPL[{4}, -S^2])/S^2 + (39*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (78*HPL[{3, 1}, -S^2])/S^2 - (156*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(3 + 10*S^2 + S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]*((7*Pi^4)/(60*S^2) + (Pi^2*(-278 - 55*S^2))/48 + (-40 - 550*S^2 - 67*S^4)/(16*S^2) + (2*(2 + 4*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (4*HPL[{4}, -S^2])/S^2 + ((60 + 136*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (2*HPL[{3, 1}, -S^2])/S^2 + (2*HPL[{2, 1, 1}, -S^2])/S^2 + ((-2 + 10*S^2 + 3*S^4 + 3*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + ((8 - S^2 - S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(231 + 41*S^2))/(32*S^2) - ((1 + S^2)*(1461 + 211*S^2))/(32*S^2) + (Pi^4*(-687 - 3703*S^2 - 229*S^4 - 229*S^6))/(720*S^2*(1 + S^2)) - (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((-2*Pi^2)/(3*S^2) + (3*(-3 - 2*S^2 + S^4))/(2*S^2))*HPL[{3}, -S^2] - (2*(3 + 9*S^2 + S^4 + S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) - (8*HPL[{5}, -S^2])/S^2 + ((58*Pi^2)/(3*S^2) + (65 + 77*S^2 + 12*S^4)/S^2)*HPL[{2, 1}, -S^2] + (4*(15 + 54*S^2 + 5*S^4 + 5*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (8*HPL[{3, 2}, -S^2])/S^2 - (12*HPL[{4, 1}, -S^2])/S^2 - (39*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (152*HPL[{2, 2, 1}, -S^2])/S^2 - (460*HPL[{3, 1, 1}, -S^2])/S^2 + (312*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((3*Pi^2)/(2*S^2) + ((1 + S^2)*(13 + 15*S^2))/(4*S^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(287 + 37*S^2))/(8*S^2) + (Pi^2*(-147 - 611*S^2 - 49*S^4 - 49*S^6))/(24*S^2*(1 + S^2)) + (4*HPL[{3}, -S^2])/S^2 + (76*HPL[{2, 1}, -S^2])/S^2 + (6*Zeta[3])/S^2) + (8*Zeta[5])/S^2));
E4wuvT3F1=(3*(-45 + 7*S^2))/(4*S) + (Pi^2*(-108 - 82*S^2 - 85*S^4))/(96*S) + (Pi^4*(-480 + 497*S^2 - 36*S^4))/(2880*S) - (Pi^6*S*(-11710 + 294*S^2 + 147*S^4))/(30240*(1 + S^2)^2) + (S*HPL[{0}, S^2]^6)/(32*(1 + S^2)^2) + ((-9 - 80*S^2 + 274*S^4 - 328*S^6 + 47*S^8)*HPL[{1}, -S^2]^5)/(30*S^3*(1 + S^2)^2) - (S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^6)/(1 + S^2)^2 + HPL[{0}, S^2]^5*(-(S*(-37 - 4*S^2 + S^4))/(96*(1 + S^2)^2) + (S*(17 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(48*(1 + S^2)^2)) + ((5*(-6 + 5*S^2))/(8*S) - (Pi^2*S*(-51 + 16*S^2 + 8*S^4))/(12*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - S*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*(-((1 + S^2)*(11 + 5*S^2))/(8*S^3) - (Pi^2*S*(-75 + 38*S^2 + 19*S^4))/(12*(1 + S^2)^2) + (9*S*HPL[{2}, -S^2])/2) + HPL[{0}, S^2]^4*((Pi^2*S*(87 + 10*S^2 + 5*S^4))/(288*(1 + S^2)^2) + (-18 + 31*S^2 + 20*S^4)/(192*S) + ((-9 - 104*S^2 + 210*S^4 + 42*S^6 + 33*S^8)*HPL[{1}, -S^2])/(96*S^3*(1 + S^2)^2) + (37*S*HPL[{1}, -S^2]^2)/(24*(1 + S^2)^2) + (5*S*(6 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(48*(1 + S^2)^2)) - (S*(-1 + 10*S^2 + 5*S^4)*HPL[{3}, -S^2]^2)/(2*(1 + S^2)^2) + ((Pi^2*S*(-13 + 38*S^2 + 19*S^4))/(12*(1 + S^2)^2) + (192 + 24*S^2 + 33*S^4 + 4*S^6)/(8*S^3))*HPL[{4}, -S^2] + ((-90 - 158*S^2 - 12*S^4 + 85*S^6 - 15*S^8)*HPL[{5}, -S^2])/(2*S^3*(1 + S^2)^2) - (S*(22 + 2*S^2 + S^4)*HPL[{6}, -S^2])/(2*(1 + S^2)^2) + (2*S*(-35 + 6*S^2 + 3*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*S*(-9 + 26*S^2 + 13*S^4))/(6*(1 + S^2)^2) + (-25 - 24*S^2 - 33*S^4 + 8*S^6)/(2*S^3))*HPL[{3, 1}, -S^2] + ((-3 - S^2 - 259*S^4 + 43*S^6)*HPL[{3, 2}, -S^2])/(2*S*(1 + S^2)^2) + ((15 + 34*S^2 + 14*S^4 - 458*S^6 + 59*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^2) - (3*S*(-1 + 10*S^2 + 5*S^4)*HPL[{4, 2}, -S^2])/(2*(1 + S^2)^2) - (S*(-15 + 86*S^2 + 43*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-2*Pi^2*S*(-11 + 16*S^2 + 8*S^4))/(3*(1 + S^2)^2) - (2*(-6 - 9*S^2 - 10*S^4 + 2*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (2*(-3 - 25*S^2 + 47*S^4 - 71*S^6 + 12*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)^2) + (2*(-15 - 96*S^2 + 115*S^4 - 74*S^6 + 6*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + 3*S*HPL[{3, 1, 2}, -S^2] - 21*S*HPL[{3, 2, 1}, -S^2] - (2*S*(47 + 38*S^2 + 19*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(9 + 63*S^2 - 134*S^4 + 48*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (4*S*(19 + 10*S^2 + 5*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 64*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-3/(2*S) - (Pi^2*S*(-133 + 16*S^2 + 8*S^4))/(18*(1 + S^2)^2) - (S*(-43 + 16*S^2 + 8*S^4)*HPL[{0}, S^2]^2)/(6*(1 + S^2)^2) + ((-9 - 80*S^2 + 274*S^4 - 328*S^6 + 47*S^8)*HPL[{1}, -S^2])/(6*S^3*(1 + S^2)^2) - (15*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + HPL[{0}, S^2]*((S*(149 - 164*S^2 + 47*S^4))/(6*(1 + S^2)^2) - (15*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) - (8*S*HPL[{2}, -S^2])/3)*Log[T]^4 + ((12*S*(-1 + S^2))/(1 + S^2)^2 + (6*S*(-1 + 2*S^2 + S^4)*HPL[{0}, S^2])/(1 + S^2)^2 + (6*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(1 + S^2)^2)*Log[T]^5 + (4*S*Log[T]^6)/(1 + S^2)^2 + ((-7*S)/2 - (Pi^2*S*(-4 - 39*S^2 + 8*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (3*S*(2 + 2*S^2 + S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((4 + S^2 + 7*S^4)/(2*S^3) + (Pi^2*(9 + 68*S^2 - 85*S^4 - 38*S^6 + 30*S^8))/(6*S^3*(1 + S^2)^2) + (76*S*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((57 - 50*S^2 + 285*S^4 + 18*S^6)/(16*S^3) + (Pi^2*(-12 - 39*S^2 - 31*S^4 + 155*S^6 - 33*S^8))/(12*S^3*(1 + S^2)^2) + (S*(87 + 22*S^2 + 11*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*S^3*(2 + S^2)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^3*((5*Pi^2*S*(34 + 3*S^2 + 3*S^4))/(72*(1 + S^2)^2) + (-30 + 251*S^2 + 14*S^4)/(96*S) + ((-9 - 84*S^2 + 200*S^4 - 60*S^6 + 25*S^8)*HPL[{1}, -S^2]^2)/(24*S^3*(1 + S^2)^2) - (S*(-79 + 22*S^2 + 11*S^4)*HPL[{1}, -S^2]^3)/(18*(1 + S^2)^2) + ((9 + 18*S^2 + 141*S^4 + 14*S^6 + 34*S^8)*HPL[{2}, -S^2])/(24*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*S*(-82 + 6*S^2 + 3*S^4))/(36*(1 + S^2)^2) - ((1 + S^2)*(33 - 45*S^2 + 8*S^4))/(48*S^3) - (S*(-33 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(6*(1 + S^2)^2)) + (S*HPL[{3}, -S^2])/(2*(1 + S^2)^2) + (S*(-18 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (S*(3 + 10*S^2 + 5*S^4)*Zeta[3])/(6*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*(-((1 + S^2)^2*(27 + 2*S^2))/(12*S^3) + (Pi^2*(-9 - 75*S^2 + 258*S^4 - 221*S^6 + 19*S^8))/(18*S^3*(1 + S^2)^2) - (2*(13 - 54*S^2 + 13*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + (12*S*(-3 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 18*S*HPL[{2, 1}, -S^2] + (2*S*(-15 + 22*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2) + Log[T]^3*(5/(2*S) + (2*Pi^2*S*(-80 + 62*S^2 + S^4))/(9*(1 + S^2)^2) + (S*(-4 + 2*S^2 + S^4)*HPL[{0}, S^2]^3)/(1 + S^2)^2 + ((9 + 80*S^2 - 274*S^4 + 328*S^6 - 47*S^8)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + (20*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 + HPL[{0}, S^2]^2*((2*S*(-35 + 17*S^2 + S^4))/(3*(1 + S^2)^2) + (2*S*(-15 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) + ((-9 - 11*S^2 - 82*S^4 + 4*S^6)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(11 + 5*S^2))/(2*S^3) + (Pi^2*S*(-75 + 38*S^2 + 19*S^4))/(3*(1 + S^2)^2) - 18*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((6 + 5*S^2)/(2*S) + (3*Pi^2*S*(-3 + 4*S^2 + 2*S^4))/(1 + S^2)^2 + ((9 + 80*S^2 - 274*S^4 + 328*S^6 - 47*S^8)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) + (30*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (2*S*(-37 + 82*S^2 + 41*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) - (2*S*(-19 + 142*S^2 + 71*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (140*S*HPL[{2, 1}, -S^2])/3 - (4*S*(-4 + 70*S^2 + 35*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(-21 - 30*S^2 + S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(33 - 9*S^2 + 4*S^4))/(24*S^3) - (Pi^4*S*(-2615 + 958*S^2 + 479*S^4))/(720*(1 + S^2)^2) + (-((1 + S^2)*(5 - 35*S^2 + 4*S^4))/(4*S^3) + (Pi^2*S*(25 + 12*S^2 + 6*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] - (19*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)^2) + ((-4 - 31*S^2 + 140*S^4 - 13*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + (S*(-27 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + (2*(13 - 54*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*S*(3 + 34*S^2 + 17*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + 54*S*HPL[{2, 1, 1}, -S^2] + ((5 - 16*S^2 + 107*S^4 - 28*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2}, -S^2]*(-(Pi^4*S*(-502 + 202*S^2 + 101*S^4))/(720*(1 + S^2)^2) + (-48 - 219*S^2 - 106*S^4 - 85*S^6)/(16*S^3) + (Pi^2*(6 + 3*S^2 + 10*S^4 - 2*S^6))/(6*S^3) + ((3 + 11*S^2 + 143*S^4 - 17*S^6)*HPL[{3}, -S^2])/(2*S*(1 + S^2)^2) + (S*(1 + 38*S^2 + 19*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((3 + 25*S^2 - 47*S^4 + 71*S^6 - 12*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-75 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-35 + 6*S^2 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(2 + 7*S^2 - 24*S^4 + 9*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((-54 - 94*S^2 - 85*S^4)/(32*S) + (Pi^4*S*(64 + 2*S^2 + S^4))/(80*(1 + S^2)^2) + (Pi^2*(-36 + 71*S^2 + 12*S^4))/(96*S) + ((-9 - 70*S^2 + 242*S^4 - 114*S^6 - 9*S^8)*HPL[{1}, -S^2]^3)/(12*S^3*(1 + S^2)^2) - (S*(-15 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^4)/(2*(1 + S^2)^2) + (-(Pi^2*S*(-20 + 2*S^2 + S^4))/(8*(1 + S^2)^2) + (6 - 3*S^2 + 10*S^4 - 2*S^6)/(4*S^3))*HPL[{2}, -S^2] - (S*(-16 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2]^2)/(4*(1 + S^2)^2) + HPL[{1}, -S^2]^2*(-(Pi^2*S*(-41 + 6*S^2 + 3*S^4))/(6*(1 + S^2)^2) - ((1 + S^2)*(33 - 33*S^2 + 8*S^4))/(16*S^3) - (S*(-73 + 6*S^2 + 3*S^4)*HPL[{2}, -S^2])/(4*(1 + S^2)^2)) + ((-6 - 18*S^2 - 5*S^4 + 16*S^6 - 3*S^8)*HPL[{3}, -S^2])/(4*S^3*(1 + S^2)^2) + (S*(-1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((9 + 64*S^2 - 99*S^4 + 10*S^6 + 12*S^8)*HPL[{2, 1}, -S^2])/(4*S^3*(1 + S^2)^2) + (2*S*(-7 + 4*S^2 + 2*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-15 + 8*S^2 + 4*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (2*S*(3 + 7*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*(-((1 + S^2)*(27 - 23*S^2 + 14*S^4))/(16*S^3) + (Pi^2*(-9 - 87*S^2 + 226*S^4 - 36*S^6 + 12*S^8))/(24*S^3*(1 + S^2)^2) + ((-25 + 112*S^2 - 23*S^4 - 8*S^6)*HPL[{2}, -S^2])/(4*S*(1 + S^2)^2) + (S*(-1 + 10*S^2 + 5*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) + (S*(-73 + 6*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(2*(1 + S^2)^2) + (S*(-3 + 10*S^2 + 5*S^4)*Zeta[3])/(2*(1 + S^2)^2))) + Log[T]^2*((3*(-9 + 2*S^2))/(4*S) + (Pi^2*(-9 + 10*S^2 - 2*S^4))/(6*S) - (Pi^4*S*(-1478 + 138*S^2 + 69*S^4))/(360*(1 + S^2)^2) + (S*(42 + 10*S^2 + 5*S^4)*HPL[{0}, S^2]^4)/(24*(1 + S^2)^2) + ((-9 - 80*S^2 + 274*S^4 - 328*S^6 + 47*S^8)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^2) - (15*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(1 + S^2)^2 + HPL[{0}, S^2]^3*((5*S*(31 + 2*S^2 + 7*S^4))/(12*(1 + S^2)^2) - (S*(-79 + 22*S^2 + 11*S^4)*HPL[{1}, -S^2])/(6*(1 + S^2)^2)) + (-(Pi^2*S*(-11 + 16*S^2 + 8*S^4))/(3*(1 + S^2)^2) + (6 + 9*S^2 + 10*S^4 - 2*S^6)/S^3)*HPL[{2}, -S^2] - (S*(-35 + 6*S^2 + 3*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((-3*(1 + S^2)*(11 + 5*S^2))/(4*S^3) - (Pi^2*S*(-75 + 38*S^2 + 19*S^4))/(2*(1 + S^2)^2) + 27*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*((-9 + 20*S^2 - 4*S^4)/(4*S) - (Pi^2*S*(-85 + 6*S^2 + 3*S^4))/(12*(1 + S^2)^2) + ((-9 - 70*S^2 + 242*S^4 - 114*S^6 - 9*S^8)*HPL[{1}, -S^2])/(4*S^3*(1 + S^2)^2) - (3*S*(-15 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 - (S*(-15 + 8*S^2 + 4*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + ((-6 - 21*S^2 - 26*S^4 + 139*S^6 - 30*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-11 + 34*S^2 + 17*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + ((9 + 63*S^2 - 134*S^4 + 48*S^6)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + (2*S*(19 + 10*S^2 + 5*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - 32*S*HPL[{2, 1, 1}, -S^2] - (4*S*(2 - 25*S^2 + 12*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{0}, S^2]*((-15 - 31*S^2 - 2*S^4)/(4*S) + (Pi^2*S*(152 - 77*S^2 + 41*S^4))/(6*(1 + S^2)^2) + ((-9 - 80*S^2 + 274*S^4 - 328*S^6 + 47*S^8)*HPL[{1}, -S^2]^2)/(2*S^3*(1 + S^2)^2) - (30*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 + ((9 + 10*S^2 + 125*S^4 - 136*S^6 + 52*S^8)*HPL[{2}, -S^2])/(2*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-3*(1 + S^2)*(11 + 5*S^2))/(4*S^3) - (Pi^2*S*(-107 + 56*S^2 + 28*S^4))/(3*(1 + S^2)^2) - (39*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (2*S*(3 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*S*(40 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(-4 + 6*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)^2*(27 + 2*S^2))/(4*S^3) + (Pi^2*(-9 - 75*S^2 + 258*S^4 - 221*S^6 + 19*S^8))/(6*S^3*(1 + S^2)^2) - (2*(13 - 54*S^2 + 13*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) + (36*S*(-3 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 54*S*HPL[{2, 1}, -S^2] + (6*S*(-15 + 22*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2)) - (S*(2 - 47*S^2 + 45*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{0}, S^2]*((Pi^2*(-60 + 189*S^2 + 10*S^4))/(96*S) + (-102 - 365*S^2 + 53*S^4)/(16*S) + (Pi^4*S*(1056 - 259*S^2 + 193*S^4))/(360*(1 + S^2)^2) + ((-9 - 80*S^2 + 274*S^4 - 328*S^6 + 47*S^8)*HPL[{1}, -S^2]^4)/(12*S^3*(1 + S^2)^2) - (3*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 + ((4 + 71*S^2 - 64*S^4 + 21*S^6)*HPL[{2}, -S^2]^2)/(4*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(11 + 5*S^2))/(4*S^3) - (Pi^2*S*(-107 + 56*S^2 + 28*S^4))/(9*(1 + S^2)^2) - (13*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + ((Pi^2*S*(3 + 2*S^2 + S^4))/(3*(1 + S^2)^2) + (-23 - 4*S^4 + 8*S^6)/(4*S^3))*HPL[{3}, -S^2] + ((9 + 18*S^2 + 21*S^4 - 8*S^6 + 4*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)^2) + (8*S*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-58*Pi^2*S)/(3*(1 + S^2)^2) + (17 + 12*S^2 + 9*S^4 - 4*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] - (2*(3 + 3*S^2 + 30*S^4 - 34*S^6 + 14*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) - (8*S^3*(2 + S^2)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (2*S*(5 + 22*S^2 + 11*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + ((9 + 10*S^2 + 125*S^4 - 136*S^6 + 52*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (4*S*(-37 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-114 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (8*S*(40 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-(S*(-13 + 4*S^2))/2 + (Pi^2*S*(-1 + 16*S^2 + 8*S^4))/(6*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((1 - 10*S^2 + 9*S^4)/(8*S^3) + (Pi^2*(9 + 14*S^2 + 133*S^4 - 61*S^6 + 43*S^8))/(12*S^3*(1 + S^2)^2) + (4*S^3*(2 + S^2)*HPL[{3}, -S^2])/(1 + S^2)^2 + (2*S*(-37 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (3*S*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*(-((1 + S^2)^2*(27 + 2*S^2))/(8*S^3) + (Pi^2*(-9 - 82*S^2 + 237*S^4 - 194*S^6 + 36*S^8))/(12*S^3*(1 + S^2)^2) + (3*(-6 + 19*S^2 - 22*S^4 + 5*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (S*(-1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (39*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(-5 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(-21 - 30*S^2 + S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(33 - 15*S^2 + 4*S^4))/(24*S^3) - (Pi^4*S*(-1279 + 458*S^2 + 229*S^4))/(360*(1 + S^2)^2) + (((1 + S^2)*(-5 - 13*S^2 + 4*S^4))/(4*S^3) - (Pi^2*S*(-183 + 98*S^2 + 49*S^4))/(12*(1 + S^2)^2))*HPL[{2}, -S^2] - (19*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)^2) + (4*(-2 - 2*S^2 + S^4 + 2*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - (4*S*(-2 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (6*(-6 + 19*S^2 - 22*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-29 + 20*S^2 + 10*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (78*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-1 - 7*S^2 + 29*S^4 + 7*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - (2*S*(5 + 2*S^2 + S^4)*Zeta[5])/(1 + S^2)^2) + Log[T]*((51 - 14*S^2)/(4*S) + (Pi^2*(30 - 49*S^2 + 12*S^4))/(24*S) - (Pi^4*S*(2115 - 961*S^2 + 18*S^4))/(360*(1 + S^2)^2) - (S*(9 + 2*S^2 + S^4)*HPL[{0}, S^2]^5)/(24*(1 + S^2)^2) + ((9 + 80*S^2 - 274*S^4 + 328*S^6 - 47*S^8)*HPL[{1}, -S^2]^4)/(6*S^3*(1 + S^2)^2) + (6*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 + HPL[{0}, S^2]^4*(-(S*(91 + 31*S^2 + 14*S^4))/(24*(1 + S^2)^2) - (37*S*HPL[{1}, -S^2])/(12*(1 + S^2)^2)) - ((-1 + S^2)*(3 - 70*S^2 + 3*S^4)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*(((1 + S^2)*(11 + 5*S^2))/(2*S^3) + (Pi^2*S*(-75 + 38*S^2 + 19*S^4))/(3*(1 + S^2)^2) - 18*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^3*((18 - 47*S^2)/(24*S) + (Pi^2*S*(-81 + 8*S^2 + 4*S^4))/(36*(1 + S^2)^2) + ((9 + 84*S^2 - 200*S^4 + 60*S^6 - 25*S^8)*HPL[{1}, -S^2])/(12*S^3*(1 + S^2)^2) + (S*(-79 + 22*S^2 + 11*S^4)*HPL[{1}, -S^2]^2)/(6*(1 + S^2)^2) + (S*(-15 + 8*S^2 + 4*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((23 - 6*S^2 - 42*S^4)/(2*S^3) - (Pi^2*S*(-17 + 158*S^2 + 79*S^4))/(6*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-9 - 14*S^2 - 50*S^4 - 130*S^6 - 29*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^2) - (S*(19 + 82*S^2 + 41*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-17 + 12*S^2 + 11*S^4)/S^3 + (2*Pi^2*S*(39 + 40*S^2 + 20*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(6 + 10*S^2 + 37*S^4 + 68*S^6 + 7*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-21 + 262*S^2 + 131*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (2*S*(-43 + 426*S^2 + 213*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (2*(-9 - 11*S^2 - 82*S^4 + 4*S^6)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (16*S*(-11 + 16*S^2 + 8*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (4*S*(-113 + 50*S^2 + 25*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 280*S*HPL[{2, 1, 1, 1}, -S^2] + (-11*S - (Pi^2*S*(-1 + 84*S^2 + 42*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{0}, S^2]^2*((15 - 49*S^2 + 12*S^4)/(8*S) - (Pi^2*S*(161 - 3*S^2 + 12*S^4))/(12*(1 + S^2)^2) + ((9 + 70*S^2 - 242*S^4 + 114*S^6 + 9*S^8)*HPL[{1}, -S^2]^2)/(4*S^3*(1 + S^2)^2) + (2*S*(-15 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^3)/(1 + S^2)^2 + ((-9 - 14*S^2 - 125*S^4 + 36*S^6 + 4*S^8)*HPL[{2}, -S^2])/(4*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*S*(-41 + 6*S^2 + 3*S^4))/(3*(1 + S^2)^2) + ((1 + S^2)*(33 - 33*S^2 + 8*S^4))/(8*S^3) + (S*(-73 + 6*S^2 + 3*S^4)*HPL[{2}, -S^2])/(2*(1 + S^2)^2)) - (S*(1 + 8*S^2 + 4*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (S*(43 + 10*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (S*(3 + 14*S^2 + 7*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*(((1 + S^2)^2*(27 + 2*S^2))/(4*S^3) + (Pi^2*(9 + 75*S^2 - 258*S^4 + 221*S^6 - 19*S^8))/(6*S^3*(1 + S^2)^2) + (2*(13 - 54*S^2 + 13*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) - (36*S*(-3 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 54*S*HPL[{2, 1}, -S^2] - (6*S*(-15 + 22*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-1 - 42*S^2 - 49*S^4 + 12*S^6)/(4*S^3) + (Pi^2*(-9 - 17*S^2 - 109*S^4 - 21*S^6 + 4*S^8))/(6*S^3*(1 + S^2)^2) - (S*(-9 + 134*S^2 + 67*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*S*(-11 + 16*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-4 + 30*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(-21 - 30*S^2 + S^4))/(2*S^3) + (Pi^2*(1 + S^2)*(33 - 9*S^2 + 4*S^4))/(12*S^3) + (Pi^4*S*(-2615 + 958*S^2 + 479*S^4))/(360*(1 + S^2)^2) + (((1 + S^2)*(5 - 35*S^2 + 4*S^4))/(2*S^3) - (2*Pi^2*S*(25 + 12*S^2 + 6*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (19*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + (2*(4 + 31*S^2 - 140*S^4 + 13*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - (S*(-27 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (4*(13 - 54*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*S*(3 + 34*S^2 + 17*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - 108*S*HPL[{2, 1, 1}, -S^2] + (2*(-5 + 16*S^2 - 107*S^4 + 28*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]*((Pi^2*(9 - 8*S^2))/(6*S) + (27 + 64*S^2 - 2*S^4)/(4*S) + (Pi^4*S*(-535 + 438*S^2 + 219*S^4))/(180*(1 + S^2)^2) + ((9 + 80*S^2 - 274*S^4 + 328*S^6 - 47*S^8)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^2) + (15*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(1 + S^2)^2 + ((3*(-2 + S^2))/S^3 + (Pi^2*S*(-67 + 98*S^2 + 49*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*S*(-10 + 18*S^2 + 9*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^2*((3*(1 + S^2)*(11 + 5*S^2))/(4*S^3) + (Pi^2*S*(-107 + 56*S^2 + 28*S^4))/(3*(1 + S^2)^2) + (39*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + ((6 + 18*S^2 + 5*S^4 - 12*S^6 - 9*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) + (6*S*(-1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + ((-9 - 82*S^2 + 103*S^4 - 128*S^6 + 8*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (12*S*(-6 + 14*S^2 + 7*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (4*S*(-37 + 82*S^2 + 41*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*S*(6 + 29*S^2 + 9*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*(((1 + S^2)^2*(27 + 2*S^2))/(4*S^3) + (Pi^2*(9 + 82*S^2 - 237*S^4 + 194*S^6 - 36*S^8))/(6*S^3*(1 + S^2)^2) - (6*(-6 + 19*S^2 - 22*S^4 + 5*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (2*S*(-1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (78*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-5 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2)) - (2*S*(-2 + 90*S^2 + 45*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(27 + 3*S^2 + 8*S^4))/(24*S^3) + ((1 + S^2)*(-213 - 390*S^2 + 53*S^4))/(16*S^3) + (Pi^4*(-120 - 1050*S^2 + 3272*S^4 - 1771*S^6 + 215*S^8))/(720*S^3*(1 + S^2)^2) + ((-3 - 28*S^2 + 120*S^4 - 144*S^6 + 15*S^8)*HPL[{2}, -S^2]^2)/(4*S^3*(1 + S^2)^2) + (-((1 + S^2)*(-1 - 29*S^2 + 4*S^4))/(2*S^3) + (Pi^2*S*(-55 + 82*S^2 + 41*S^4))/(6*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-6 - 29*S^2 + 3*S^4 + 159*S^6 + 21*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(-3 + 38*S^2 + 19*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (((1 + S^2)*(5 - 35*S^2 + 4*S^4))/(2*S^3) - (2*Pi^2*S*(25 + 12*S^2 + 6*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((3 + 36*S^2 - 58*S^4 - 136*S^6 + 11*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) - (8*S*(-12 + 14*S^2 + 7*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (S*(-315 + 394*S^2 + 197*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (4*(13 - 54*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (76*S*(-3 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (12*S*(-39 + 14*S^2 + 7*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 108*S*HPL[{2, 1, 1, 1}, -S^2] + ((-2*(-6 + S^2)*(1 + S^2))/S + (Pi^2*S*(-24 + 38*S^2 + 19*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(7 - 47*S^2 + 12*S^4))/(8*S^3) + (Pi^2*(-51 + 194*S^2 + 59*S^4 - 34*S^6))/(12*S*(1 + S^2)^2) + (4*S*(-12 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (38*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(-23 + 30*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + (S*(-45 + 98*S^2 + 49*S^4)*Zeta[5])/(1 + S^2)^2);
E4wuvT3F3=(5255 + 1472*S^2)/(5832*S) + (Pi^4*(49566 + 20289*S^2 - 2744*S^4))/(233280*S) + (Pi^2*(4412 + 7334*S^2 + 243*S^4))/(23328*S) + (Pi^6*(23714 + 35571*S^2 + 98*S^4 + 196*S^6 + 98*S^8))/(90720*S*(1 + S^2)^2) + ((47*Pi^2)/(45*S^3) + (3223 + 9848*S^2 + 14698*S^4 + 3376*S^6 + 2135*S^8 + 352*S^10)/(810*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^5 + ((11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^6)/(9*S^3*(1 + S^2)^2) + (8*HPL[{1}, -S^2]^7)/(21*S^3) + HPL[{0}, S^2]^6*((2 + 3*S^2)/(96*S*(1 + S^2)^2) + HPL[{1}, -S^2]/(48*S^3)) + HPL[{0}, S^2]^5*((-66 + 189*S^2 - 62*S^4 - 37*S^6 - 8*S^8)/(2592*S*(1 + S^2)^2) + ((-11 + 74*S^2 + 133*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{1}, -S^2])/(432*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^2/(9*S^3)) + (2*(-38 + 3*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + ((-34 - 50*S^2 - 7*S^4 + 5*S^6 + 10*S^8 + 5*S^10)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-5*Pi^2)/(6*S^3) + (-683 - 1986*S^2 - 1850*S^4 - 600*S^6 - 413*S^8 - 96*S^10)/(36*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((1140 + 2154*S^2 + 951*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{6}, -S^2])/(18*S^3*(1 + S^2)^2) - (50*HPL[{7}, -S^2])/S^3 - (2*(185 + 598*S^2 + 527*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + HPL[{0}, S^2]^4*((364 - 299*S^2 - 540*S^4)/(5184*S) + (Pi^2*(246 + 369*S^2 - 5*S^4 - 10*S^6 - 5*S^8))/(1296*S*(1 + S^2)^2) + (37*(2 + 3*S^2)*HPL[{1}, -S^2]^2)/(72*S*(1 + S^2)^2) + (37*HPL[{1}, -S^2]^3)/(108*S^3) - (5*(-30 - 45*S^2 + 2*S^4 + 4*S^6 + 2*S^8)*HPL[{2}, -S^2])/(432*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((41*Pi^2)/(216*S^3) + (145 + 29*S^2 + 1243*S^4 - 44*S^6 - 151*S^8 - 80*S^10)/(1296*S^3*(1 + S^2)^2) + (25*HPL[{2}, -S^2])/(72*S^3)) - HPL[{3}, -S^2]/(24*S^3) - (7*HPL[{2, 1}, -S^2])/(9*S^3)) + ((-7*Pi^2)/(9*S^3) + (-647 + 6260*S^2 + 16156*S^4 + 7548*S^6 + 5163*S^8 + 1392*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-11*Pi^2)/(9*S^3) + (-434 + 11684*S^2 + 27457*S^4 + 12428*S^6 + 8599*S^8 + 2294*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((-11 - 4*S^2 + 16*S^4 + 5*S^6 + 10*S^8 + 5*S^10)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (16*HPL[{4, 3}, -S^2])/S^3 + ((-63 + 222*S^2 + 459*S^4 + 86*S^6 + 172*S^8 + 86*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (49*HPL[{5, 2}, -S^2])/S^3 + (332*HPL[{6, 1}, -S^2])/(3*S^3) + ((152*Pi^2)/(9*S^3) + (2*(30 + 882*S^2 + 2712*S^4 + 1009*S^6 + 680*S^8 + 163*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((464*Pi^2)/(9*S^3) + (521 + 1528*S^2 + 6794*S^4 + 1838*S^6 + 1345*S^8 + 326*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + ((11 - 2*S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + ((-575 + 42*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (2*HPL[{3, 2, 2}, -S^2])/S^3 + (32*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (4*(-529 - 1142*S^2 - 655*S^4 + 19*S^6 + 38*S^8 + 19*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (38*HPL[{4, 1, 2}, -S^2])/(3*S^3) + (134*HPL[{4, 2, 1}, -S^2])/(3*S^3) + (100*HPL[{5, 1, 1}, -S^2])/S^3 + ((-356*Pi^2)/(9*S^3) + (2*(-539 + 1999*S^2 + 1026*S^4 + 846*S^6 + 234*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - (304*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) - (8*(-232 - 506*S^2 - 295*S^4 + 5*S^6 + 10*S^8 + 5*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (872*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (872*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (1784*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (5408*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (32*(-105 + 4*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) - (592*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (592*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (2944*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) - (480*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((739 + 256*S^2)/(162*S) + (Pi^2*(846 + 1269*S^2 + 16*S^4 + 32*S^6 + 16*S^8))/(162*S*(1 + S^2)^2) + ((47*Pi^2)/(9*S^3) + (3223 + 9848*S^2 + 14698*S^4 + 3376*S^6 + 2135*S^8 + 352*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] + (5*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + (40*HPL[{1}, -S^2]^3)/(3*S^3) + HPL[{0}, S^2]^2*((306 + 459*S^2 + 16*S^4 + 32*S^6 + 16*S^8)/(54*S*(1 + S^2)^2) + (17*HPL[{1}, -S^2])/(3*S^3)) + (4*(-105 + 4*S^6)*HPL[{2}, -S^2])/(27*S^3) + HPL[{0}, S^2]*((2754 + 7317*S^2 + 2566*S^4 + 1595*S^6 + 352*S^8)/(162*S*(1 + S^2)^2) + (5*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) + (20*HPL[{1}, -S^2]^2)/S^3 - (4*HPL[{2}, -S^2])/(3*S^3)) + (2*HPL[{3}, -S^2])/(9*S^3) - (20*HPL[{2, 1}, -S^2])/S^3)*Log[T]^4 + ((-2*(5 + 18*S^2 + 3*S^4 + 2*S^6))/(3*S*(1 + S^2)^2) - (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) - (8*HPL[{1}, -S^2]^2)/S^3 + HPL[{0}, S^2]*((-4*(6 + 9*S^2 + S^4 + 2*S^6 + S^8))/(3*S*(1 + S^2)^2) - (8*HPL[{1}, -S^2])/S^3) + (4*HPL[{2}, -S^2])/S^3)*Log[T]^5 + ((4*(2 + 3*S^2))/(3*S*(1 + S^2)^2) + (8*HPL[{1}, -S^2])/(3*S^3))*Log[T]^6 + ((-53190 - 3258*S^2 - 1187*S^4)/(972*S) + (Pi^2*(-1182 - 2529*S^2 - 1150*S^4 - 773*S^6 - 196*S^8))/(162*S*(1 + S^2)^2))*Zeta[3] + ((6 + 9*S^2 - 2*S^4 - 4*S^6 - 2*S^8)*Zeta[3]^2)/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]^4*(((1 + S^2)*(6791 + 917*S^2 + 512*S^4))/(648*S^3) + (Pi^2*(209 + 982*S^2 + 1055*S^4 + 38*S^6 + 76*S^8 + 38*S^10))/(108*S^3*(1 + S^2)^2) + ((-11 - 2*S^6)*HPL[{2}, -S^2])/(2*S^3) - (10*HPL[{3}, -S^2])/S^3 - (26*Zeta[3])/(3*S^3)) + HPL[{3, 1}, -S^2]*((18537 + 3078*S^2 + 1665*S^4 + 934*S^6)/(324*S^3) + (Pi^2*(515 + 898*S^2 + 317*S^4 - 26*S^6 - 52*S^8 - 26*S^10))/(54*S^3*(1 + S^2)^2) - (8*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((8760 + 2733*S^2 + 915*S^4 - 283*S^6)/(648*S^3) + (Pi^2*(216 + 786*S^2 + 747*S^4 + 16*S^6 + 32*S^8 + 16*S^10))/(108*S^3*(1 + S^2)^2) - HPL[{3}, -S^2]/S^3 - (38*HPL[{2, 1}, -S^2])/(3*S^3) + (2*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((-9084 - 939*S^2 - 282*S^4 + 41*S^6)/(81*S^3) + (2*Pi^2*(-237 - 360*S^2 - 66*S^4 + 16*S^6 + 32*S^8 + 16*S^10))/(27*S^3*(1 + S^2)^2) + (8*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-4926 - 5064*S^2 - 2841*S^4 - 3086*S^6)/(648*S^3) + (Pi^2*(-43 - 182*S^2 - 187*S^4 - 19*S^6 - 38*S^8 - 19*S^10))/(54*S^3*(1 + S^2)^2) + (58*HPL[{2, 1}, -S^2])/(3*S^3) + (16*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-1043*Pi^4)/(540*S^3) + (-2564 + 51399*S^2 + 1764*S^4 + 1187*S^6)/(972*S^3) + (Pi^2*(-382 + 820*S^2 + 1076*S^4 + 979*S^6 + 536*S^8 + 115*S^10))/(162*S^3*(1 + S^2)^2) + (40*HPL[{3, 1}, -S^2])/S^3 + (296*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(61 + 160*S^2 + 118*S^4)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((7*Pi^4)/(135*S^3) + (4485 - 208368*S^2 - 18459*S^4 - 19988*S^6)/(3888*S^3) + (Pi^2*(425 - 4112*S^2 - 10294*S^4 - 4596*S^6 - 3003*S^8 - 708*S^10))/(648*S^3*(1 + S^2)^2) - (8*HPL[{4}, -S^2])/S^3 + ((721 + 1898*S^2 + 1405*S^4 - 22*S^6 - 44*S^8 - 22*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (28*HPL[{3, 1}, -S^2])/(3*S^3) + (32*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(18 + 42*S^2 + 27*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((1547*Pi^4)/(1620*S^3) + ((1 + S^2)*(66623 + 6115*S^2 + 3632*S^4))/(2916*S^3) + (Pi^2*(1873 + 5636*S^2 + 9802*S^4 + 2125*S^6 + 1433*S^8 + 271*S^10))/(486*S^3*(1 + S^2)^2) + ((38*Pi^2)/(27*S^3) + (-1127 - 2639*S^2 - 513*S^4 - 497*S^6 - 56*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (76*HPL[{2}, -S^2]^2)/(9*S^3) - (4*(22 + 74*S^2 + 67*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) - (56*HPL[{4}, -S^2])/(9*S^3) + (2*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/S^3 + (56*HPL[{3, 1}, -S^2])/(9*S^3) - (2*(121 + 398*S^2 + 355*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((3192 + 215*S^2 - 1150*S^4)/(2592*S) + (Pi^2*(288 + 3465*S^2 + 110*S^4 - 113*S^6 - 106*S^8))/(3888*S*(1 + S^2)^2) + ((121 + 782*S^2 + 931*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*HPL[{1}, -S^2]^3)/(162*S^3*(1 + S^2)^2) + (5*HPL[{1}, -S^2]^4)/(6*S^3) + (-Pi^2/(36*S^3) + (-111 + 330*S^2 + 2058*S^4 + 358*S^6 + 35*S^8 - 74*S^10)/(648*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/(12*S^3) + HPL[{1}, -S^2]^2*((85*Pi^2)/(108*S^3) + (412 + 1028*S^2 + 2410*S^4 + 349*S^6 + 182*S^8 + 7*S^10)/(324*S^3*(1 + S^2)^2) + (19*HPL[{2}, -S^2])/(9*S^3)) + ((-7 - 2*S^2 + 11*S^4)*HPL[{3}, -S^2])/(36*S^3*(1 + S^2)^2) + HPL[{4}, -S^2]/(2*S^3) + ((-131 - 490*S^2 - 473*S^4 - 4*S^6 - 8*S^8 - 4*S^10)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)^2) - (2*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-6 - 9*S^2 - 5*S^4 - 10*S^6 - 5*S^8)*Zeta[3])/(27*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(-711 - 160*S^2 + 87*S^4))/(648*S^3) + (Pi^2*(11 + 192*S^2 + 266*S^4 + 2*S^6 + 4*S^8 + 2*S^10))/(108*S^3*(1 + S^2)^2) + ((55 + 338*S^2 + 397*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)^2) + HPL[{3}, -S^2]/(3*S^3) - (38*HPL[{2, 1}, -S^2])/(9*S^3) - (2*Zeta[3])/(9*S^3))) + Log[T]^3*((-845 - 244*S^2)/(162*S) + (Pi^2*(-963 - 3753*S^2 - 682*S^4 - 491*S^6 - 61*S^8))/(243*S*(1 + S^2)^2) + ((-94*Pi^2)/(9*S^3) + (-3223 - 9848*S^2 - 14698*S^4 - 3376*S^6 - 2135*S^8 - 352*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^2 - (20*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) - (40*HPL[{1}, -S^2]^4)/(3*S^3) + HPL[{0}, S^2]^3*((-30 - 45*S^2 - 2*S^4 - 4*S^6 - 2*S^8)/(9*S*(1 + S^2)^2) - (10*HPL[{1}, -S^2])/(3*S^3)) + ((34*Pi^2)/(9*S^3) + (2793 + 3279*S^2 + 148*S^6 - 122*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (26*HPL[{2}, -S^2]^2)/(3*S^3) + HPL[{0}, S^2]^2*((-288 - 1323*S^2 - 277*S^4 - 221*S^6 - 61*S^8)/(81*S*(1 + S^2)^2) - (2*(22 + 146*S^2 + 175*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) - (34*HPL[{1}, -S^2]^2)/(3*S^3) + (4*HPL[{2}, -S^2])/(3*S^3)) + (4*(-21 + 228*S^2 + 384*S^4 + 71*S^6 + 142*S^8 + 71*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (16*HPL[{4}, -S^2])/(3*S^3) - (4*(-123 + 70*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + HPL[{0}, S^2]*((-6266 - 773*S^2 - 512*S^4)/(162*S) + (Pi^2*(-30 - 45*S^2 - 4*S^4 - 8*S^6 - 4*S^8))/(3*S*(1 + S^2)^2) - (10*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) - (80*HPL[{1}, -S^2]^3)/(3*S^3) - (2*(-57 + 354*S^2 + 645*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-10*Pi^2)/S^3 + (-3223 - 9848*S^2 - 14698*S^4 - 3376*S^6 - 2135*S^8 - 352*S^10)/(81*S^3*(1 + S^2)^2) - (104*HPL[{2}, -S^2])/(3*S^3)) - (28*HPL[{3}, -S^2])/(9*S^3) + (224*HPL[{2, 1}, -S^2])/(3*S^3)) - (416*HPL[{3, 1}, -S^2])/(9*S^3) + (80*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(234 + 351*S^2 + 70*S^4 + 140*S^6 + 70*S^8)*Zeta[3])/(27*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(6791 + 917*S^2 + 512*S^4))/(162*S^3) + (Pi^2*(-209 - 982*S^2 - 1055*S^4 - 38*S^6 - 76*S^8 - 38*S^10))/(27*S^3*(1 + S^2)^2) + (2*(11 + 2*S^6)*HPL[{2}, -S^2])/S^3 + (40*HPL[{3}, -S^2])/S^3 + (104*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]^2*((Pi^2*(2934 + 207*S^2 - 1538*S^4))/(7776*S) + (-4454 + 5026*S^2 + 243*S^4)/(7776*S) + (Pi^4*(378 + 567*S^2 - 2*S^4 - 4*S^6 - 2*S^8))/(720*S*(1 + S^2)^2) + ((22 + 146*S^2 + 175*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{1}, -S^2]^4)/(18*S^3*(1 + S^2)^2) + (17*HPL[{1}, -S^2]^5)/(15*S^3) + ((31 + 188*S^2 + 220*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((44*Pi^2)/(27*S^3) + (523 + 1424*S^2 + 4906*S^4 + 874*S^6 + 731*S^8 + 190*S^10)/(324*S^3*(1 + S^2)^2) + (38*HPL[{2}, -S^2])/(9*S^3)) + ((21 - 87*S^2 - 204*S^4 - 95*S^6 - 67*S^8 - 14*S^10)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^2) + ((15 + 24*S^2 + 6*S^4 - S^6 - 2*S^8 - S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (3*HPL[{5}, -S^2])/S^3 + ((-4*Pi^2)/S^3 + (-225 + 180*S^2 - 873*S^4 + 86*S^6 - 8*S^8 - 4*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((51 - 114*S^2 - 273*S^4 - 16*S^6 - 32*S^8 - 16*S^10)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^2) - (2*HPL[{3, 2}, -S^2])/(3*S^3) - HPL[{4, 1}, -S^2]/S^3 + (2*(-27 + 60*S^2 + 144*S^4 + 8*S^6 + 16*S^8 + 8*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (26*HPL[{2, 2, 1}, -S^2])/S^3 + (80*HPL[{3, 1, 1}, -S^2])/S^3 - (176*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-111 - 225*S^2 - 160*S^4 - 197*S^6 - 79*S^8)*Zeta[3])/(54*S*(1 + S^2)^2) + HPL[{1}, -S^2]^2*(((1 + S^2)*(541 + 453*S^2 + 202*S^4))/(432*S^3) + (Pi^2*(11 + 110*S^2 + 143*S^4 + 2*S^6 + 4*S^8 + 2*S^10))/(18*S^3*(1 + S^2)^2) + ((11 + 174*S^2 + 239*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(12*S^3*(1 + S^2)^2) - HPL[{3}, -S^2]/S^3 - (38*HPL[{2, 1}, -S^2])/(3*S^3) - (4*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-324 + 576*S^2 + 288*S^4 + 41*S^6)/(648*S^3) + (Pi^2*(-18 + 90*S^2 + 171*S^4 + 2*S^6 + 4*S^8 + 2*S^10))/(72*S^3*(1 + S^2)^2) + HPL[{3}, -S^2]/(3*S^3) - (13*HPL[{2, 1}, -S^2])/S^3 + Zeta[3]/S^3) + HPL[{1}, -S^2]*((21*Pi^4)/(40*S^3) + ((1 + S^2)*(3389 + 3136*S^2 + 1049*S^4))/(3888*S^3) + (Pi^2*(271 + 494*S^2 + 2464*S^4 + 262*S^6 + 143*S^8 + 10*S^10))/(432*S^3*(1 + S^2)^2) + ((7*Pi^2)/(4*S^3) + (1 - 16*S^2 + 140*S^4 + 17*S^6 + 19*S^8 + 7*S^10)/(12*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (7*HPL[{2}, -S^2]^2)/(2*S^3) + ((-55 - 146*S^2 - 109*S^4 - 10*S^6 - 20*S^8 - 10*S^10)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^2) - (2*HPL[{4}, -S^2])/(3*S^3) + ((-11 - 174*S^2 - 239*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{2, 1}, -S^2])/(6*S^3*(1 + S^2)^2) - (12*HPL[{3, 1}, -S^2])/S^3 + (76*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-55 - 158*S^2 - 127*S^4 - 10*S^6 - 20*S^8 - 10*S^10)*Zeta[3])/(18*S^3*(1 + S^2)^2))) + Log[T]^2*((4433 + 1154*S^2)/(972*S) + (Pi^2*(3138 + 1320*S^2 + 41*S^4))/(972*S) + (Pi^4*(3094 + 4641*S^2 + 46*S^4 + 92*S^6 + 46*S^8))/(1080*S*(1 + S^2)^2) + ((94*Pi^2)/(9*S^3) + (3223 + 9848*S^2 + 14698*S^4 + 3376*S^6 + 2135*S^8 + 352*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^3 + (5*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^2) + (8*HPL[{1}, -S^2]^5)/S^3 + HPL[{0}, S^2]^4*((222 + 333*S^2 - 10*S^4 - 20*S^6 - 10*S^8)/(216*S*(1 + S^2)^2) + (37*HPL[{1}, -S^2])/(36*S^3)) + ((185 + 598*S^2 + 527*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + HPL[{0}, S^2]^3*((103 + 420*S^2 + 70*S^4 + 12*S^6 - 11*S^8)/(54*S*(1 + S^2)^2) + ((121 + 782*S^2 + 931*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*HPL[{1}, -S^2])/(54*S^3*(1 + S^2)^2) + (5*HPL[{1}, -S^2]^2)/S^3 - HPL[{2}, -S^2]/(3*S^3)) + ((4*Pi^2)/(9*S^3) + (341 - 3764*S^2 - 9478*S^4 - 4216*S^6 - 2735*S^8 - 652*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (2*(73 + 230*S^2 + 199*S^4 + 17*S^6 + 34*S^8 + 17*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*HPL[{5}, -S^2])/S^3 + ((-178*Pi^2)/(9*S^3) + (-539 + 1999*S^2 + 1026*S^4 + 846*S^6 + 234*S^8)/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((921 + 552*S^2 + 41*S^4)/(324*S) + (Pi^2*(88 + 132*S^2 + S^4 + 2*S^6 + S^8))/(18*S*(1 + S^2)^2) + ((22 + 146*S^2 + 175*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + (34*HPL[{1}, -S^2]^3)/(3*S^3) + ((-27 + 60*S^2 + 144*S^4 + 8*S^6 + 16*S^8 + 8*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((44*Pi^2)/(9*S^3) + (523 + 1424*S^2 + 4906*S^4 + 874*S^6 + 731*S^8 + 190*S^10)/(108*S^3*(1 + S^2)^2) + (38*HPL[{2}, -S^2])/(3*S^3)) + HPL[{3}, -S^2]/S^3 - (88*HPL[{2, 1}, -S^2])/(3*S^3)) - (4*(-232 - 506*S^2 - 295*S^4 + 5*S^6 + 10*S^8 + 5*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (20*HPL[{3, 2}, -S^2])/(3*S^3) - (32*HPL[{4, 1}, -S^2])/(3*S^3) + (16*(-105 + 4*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (296*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (896*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (240*HPL[{2, 1, 1, 1}, -S^2])/S^3 - (2*(119 + 256*S^2 + 110*S^4 + 64*S^6 + 13*S^8)*Zeta[3])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]^2*(((1 + S^2)*(6791 + 917*S^2 + 512*S^4))/(108*S^3) + (Pi^2*(209 + 982*S^2 + 1055*S^4 + 38*S^6 + 76*S^8 + 38*S^10))/(18*S^3*(1 + S^2)^2) - (3*(11 + 2*S^6)*HPL[{2}, -S^2])/S^3 - (60*HPL[{3}, -S^2])/S^3 - (52*Zeta[3])/S^3) + HPL[{2}, -S^2]*((-9084 - 939*S^2 - 282*S^4 + 41*S^6)/(162*S^3) + (Pi^2*(-237 - 360*S^2 - 66*S^4 + 16*S^6 + 32*S^8 + 16*S^10))/(27*S^3*(1 + S^2)^2) + (16*HPL[{3}, -S^2])/(3*S^3) - (148*HPL[{2, 1}, -S^2])/(3*S^3) + (4*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((1547*Pi^4)/(540*S^3) + ((1 + S^2)*(66623 + 6115*S^2 + 3632*S^4))/(972*S^3) + (Pi^2*(1873 + 5636*S^2 + 9802*S^4 + 2125*S^6 + 1433*S^8 + 271*S^10))/(162*S^3*(1 + S^2)^2) + ((38*Pi^2)/(9*S^3) + (-1127 - 2639*S^2 - 513*S^4 - 497*S^6 - 56*S^8)/(27*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (76*HPL[{2}, -S^2]^2)/(3*S^3) - (4*(22 + 74*S^2 + 67*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) - (56*HPL[{4}, -S^2])/(3*S^3) + (6*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/S^3 + (56*HPL[{3, 1}, -S^2])/(3*S^3) - (2*(121 + 398*S^2 + 355*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((63873 + 5571*S^2 + 3632*S^4)/(972*S) + (Pi^2*(3372 + 9837*S^2 + 2986*S^4 + 1667*S^6 + 286*S^8))/(324*S*(1 + S^2)^2) + (10*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^2) + (20*HPL[{1}, -S^2]^4)/S^3 + (-(Pi^2/S^3) + (-93 + 2352*S^2 + 6513*S^4 + 2354*S^6 + 1378*S^8 + 284*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/(3*S^3) + HPL[{1}, -S^2]^2*((15*Pi^2)/S^3 + (3223 + 9848*S^2 + 14698*S^4 + 3376*S^6 + 2135*S^8 + 352*S^10)/(54*S^3*(1 + S^2)^2) + (52*HPL[{2}, -S^2])/S^3) + ((47 + 106*S^2 + 65*S^4 - 8*S^6 - 16*S^8 - 8*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*HPL[{4}, -S^2])/(3*S^3) + (4*(-243 - 720*S^2 - 594*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*HPL[{3, 1}, -S^2])/S^3 - (16*HPL[{2, 1, 1}, -S^2])/S^3 - (2*(14 + 21*S^2 + 2*S^4 + 4*S^6 + 2*S^8)*Zeta[3])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(6791 + 917*S^2 + 512*S^4))/(108*S^3) + (Pi^2*(308 + 1426*S^2 + 1523*S^4 + 56*S^6 + 112*S^8 + 56*S^10))/(27*S^3*(1 + S^2)^2) + (13*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^2) + (4*HPL[{3}, -S^2])/(3*S^3) - (104*HPL[{2, 1}, -S^2])/S^3 - (28*Zeta[3])/(3*S^3)))) + ((-958 - 1971*S^2 - 802*S^4 - 393*S^6 - 40*S^8)*Zeta[5])/(18*S*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(3666 + 685*S^2 + 357*S^4))/(648*S^3) + ((1 + S^2)*(75721 + 4812*S^2 + 3985*S^4))/(1944*S^3) + (Pi^4*(5269 + 29102*S^2 + 33115*S^4 + 958*S^6 + 1916*S^8 + 958*S^10))/(6480*S^3*(1 + S^2)^2) + (19*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((-16*Pi^2)/(3*S^3) + (-2569 - 8360*S^2 - 10354*S^4 - 2830*S^6 - 1853*S^8 - 346*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-319 - 974*S^2 - 823*S^4 - 58*S^6 - 116*S^8 - 58*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - (22*HPL[{5}, -S^2])/(3*S^3) + ((-38*Pi^2)/(9*S^3) + (1127 + 2639*S^2 + 513*S^4 + 497*S^6 + 56*S^8)/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (2*(187 + 458*S^2 + 313*S^4 + 34*S^6 + 68*S^8 + 34*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (152*HPL[{3, 2}, -S^2])/(3*S^3) + (512*HPL[{4, 1}, -S^2])/(3*S^3) - (6*(11 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (304*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (184*HPL[{3, 1, 1}, -S^2])/S^3 + ((-43*Pi^2)/(9*S^3) + (-150 - 468*S^2 - 544*S^4 - 139*S^6 - 78*S^8 - 9*S^10)/(3*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(1376 + 47*S^2 + 80*S^4))/(54*S^3) + (Pi^2*(-22 - 6*S^2 + 35*S^4 - 4*S^6 - 8*S^8 - 4*S^10))/(9*S^3*(1 + S^2)^2) - (76*HPL[{3}, -S^2])/(3*S^3) - (152*HPL[{2, 1}, -S^2])/(3*S^3) - (76*Zeta[3])/(3*S^3)) - (94*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((Pi^2*(-9408 - 363*S^2 + 6*S^4 + 82*S^6))/(1944*S^3) + (-129762 - 13199*S^2 + 1960*S^4 + 243*S^6)/(3888*S^3) + (Pi^4*(-4176 - 4734*S^2 + 1251*S^4 + 202*S^6 + 404*S^8 + 202*S^10))/(6480*S^3*(1 + S^2)^2) + ((5*Pi^2)/(9*S^3) + (343 - 3172*S^2 - 8180*S^4 - 3888*S^6 - 2715*S^8 - 756*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((101 + 148*S^2 + 20*S^4 - 19*S^6 - 38*S^8 - 19*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (7*HPL[{5}, -S^2])/S^3 + ((-76*Pi^2)/(9*S^3) + (-30 - 882*S^2 - 2712*S^4 - 1009*S^6 - 680*S^8 - 163*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-417 - 1290*S^2 - 1101*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*HPL[{3, 2}, -S^2])/S^3 - (22*HPL[{4, 1}, -S^2])/(3*S^3) + (4*(185 + 598*S^2 + 527*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (152*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (424*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (296*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((4*Pi^2)/(9*S^3) + (157 - 640*S^2 - 1949*S^4 - 893*S^6 - 544*S^8 - 119*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + (20*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]*((11857*Pi^6)/(45360*S^3) + (Pi^2*(1 + S^2)*(70012 + 9251*S^2 + 4681*S^4))/(11664*S^3) + ((1 + S^2)*(540781 + 24644*S^2 + 38053*S^4))/(11664*S^3) + (Pi^4*(31301 + 88462*S^2 + 184148*S^4 + 34316*S^6 + 22645*S^8 + 3932*S^10))/(38880*S^3*(1 + S^2)^2) + ((59*Pi^2)/(18*S^3) + (1327 + 4100*S^2 + 6196*S^4 + 1480*S^6 + 977*S^8 + 184*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (2*HPL[{3}, -S^2]^2)/S^3 + ((-16*Pi^2)/(9*S^3) + (-1489 - 5420*S^2 - 6862*S^4 - 2308*S^6 - 1901*S^8 - 508*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-209 - 550*S^2 - 407*S^4 - 38*S^6 - 76*S^8 - 38*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (7*HPL[{6}, -S^2])/S^3 - (152*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-22*Pi^2)/(9*S^3) + (2*(207 + 710*S^2 + 693*S^4 + 225*S^6 + 146*S^8 + 27*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (8*(77 + 268*S^2 + 248*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((2167 + 7406*S^2 + 6775*S^4 + 394*S^6 + 788*S^8 + 394*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (6*HPL[{4, 2}, -S^2])/S^3 + (116*HPL[{5, 1}, -S^2])/(3*S^3) + ((76*Pi^2)/(9*S^3) - (2*(1127 + 2639*S^2 + 513*S^4 + 497*S^6 + 56*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (76*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*(77 + 430*S^2 + 491*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (112*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (12*(11 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + (112*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (-((1 + S^2)*(3125 + 232*S^2 + 155*S^4))/(54*S^3) + (Pi^2*(-209 - 676*S^2 - 596*S^4 - 38*S^6 - 76*S^8 - 38*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + (2*Zeta[3]^2)/S^3 + HPL[{3}, -S^2]*(-((1 + S^2)*(5747 + 635*S^2 + 686*S^4))/(108*S^3) + (Pi^2*(-451 - 1478*S^2 - 1315*S^4 - 82*S^6 - 164*S^8 - 82*S^10))/(54*S^3*(1 + S^2)^2) + (152*HPL[{2, 1}, -S^2])/(3*S^3) - (8*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(1376 + 47*S^2 + 80*S^4))/(27*S^3) + (2*Pi^2*(22 + 6*S^2 - 35*S^4 + 4*S^6 + 8*S^8 + 4*S^10))/(9*S^3*(1 + S^2)^2) + (152*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((67*Pi^4)/(120*S^3) - ((1 + S^2)*(56833 + 731*S^2 + 1996*S^4))/(1944*S^3) + (Pi^2*(-1118 - 3910*S^2 - 1892*S^4 - 857*S^6 - 382*S^8 + 7*S^10))/(324*S^3*(1 + S^2)^2) - (4*(77 + 268*S^2 + 248*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (6*HPL[{4}, -S^2])/S^3 - (38*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (152*HPL[{3, 1}, -S^2])/(3*S^3) + (304*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(55 + 186*S^2 + 169*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + ((-539 - 1642*S^2 - 1385*S^4 - 98*S^6 - 196*S^8 - 98*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((Pi^2*(156474 + 13077*S^2 - 3086*S^4))/(23328*S) + (534804 + 25083*S^2 + 38053*S^4)/(11664*S) + (Pi^4*(13602 + 47169*S^2 + 11672*S^4 + 6067*S^6 + 818*S^8))/(19440*S*(1 + S^2)^2) + ((11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^2) + (4*HPL[{1}, -S^2]^6)/(3*S^3) + (-Pi^2/(9*S^3) + (-153 + 876*S^2 + 2970*S^4 + 1094*S^6 + 661*S^8 + 140*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (2*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{1}, -S^2]^4*((5*Pi^2)/(2*S^3) + (3223 + 9848*S^2 + 14698*S^4 + 3376*S^6 + 2135*S^8 + 352*S^10)/(324*S^3*(1 + S^2)^2) + (26*HPL[{2}, -S^2])/(3*S^3)) + (4*HPL[{3}, -S^2]^2)/(3*S^3) + ((4*Pi^2)/(9*S^3) - (2*(12 - 6*S^2 - 78*S^4 - 17*S^6 - 10*S^8 + S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-29 - 42*S^2 - 5*S^4)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^2) + (40*HPL[{6}, -S^2])/(3*S^3) + (2*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((2*Pi^2)/(3*S^3) + (29 - 1226*S^2 - 3292*S^4 - 1176*S^6 - 675*S^8 - 132*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (8*(9 + 24*S^2 + 18*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*(34 + 86*S^2 + 61*S^4 + 11*S^6 + 22*S^8 + 11*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*HPL[{5, 1}, -S^2])/(3*S^3) + ((-2*Pi^2)/S^3 + (-93 + 2352*S^2 + 6513*S^4 + 2354*S^6 + 1378*S^8 + 284*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(225 + 678*S^2 + 567*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*(1397 + 4174*S^2 + 3467*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (52*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (8*(-243 - 720*S^2 - 594*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*HPL[{3, 1, 1, 1}, -S^2])/S^3 - (32*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-1122 - 573*S^2 - 1016*S^4)/(324*S) + (Pi^2*(-54 - 81*S^2 - 16*S^4 - 32*S^6 - 16*S^8))/(54*S*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^3*(((1 + S^2)*(6791 + 917*S^2 + 512*S^4))/(324*S^3) + (Pi^2*(308 + 1426*S^2 + 1523*S^4 + 56*S^6 + 112*S^8 + 56*S^10))/(81*S^3*(1 + S^2)^2) + (13*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{3}, -S^2])/(9*S^3) - (104*HPL[{2, 1}, -S^2])/(3*S^3) - (28*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((348 + 558*S^2 - 135*S^4 - 190*S^6)/(162*S^3) + (Pi^2*(13 + 50*S^2 + 49*S^4 - 4*S^6 - 8*S^8 - 4*S^10))/(54*S^3*(1 + S^2)^2) + (4*HPL[{2, 1}, -S^2])/(3*S^3) - (8*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((Pi^2*(-617 - 1930*S^2 - 1661*S^4))/(54*S^3*(1 + S^2)^2) + (-10203 - 2472*S^2 - 681*S^4 + 56*S^6)/(162*S^3) + (28*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-7*Pi^4)/(90*S^3) + (3837 + 60048*S^2 + 4599*S^4 + 1774*S^6)/(1944*S^3) + (Pi^2*(-68 + 894*S^2 + 2857*S^4 + 904*S^6 + 471*S^8 + 70*S^10))/(216*S^3*(1 + S^2)^2) - (4*(9 + 24*S^2 + 18*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*HPL[{4}, -S^2])/(3*S^3) - (2*(225 + 678*S^2 + 567*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{3, 1}, -S^2])/(3*S^3) - (4*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(-7 + 4*S^2 + 20*S^4 + 3*S^6 + 6*S^8 + 3*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((377*Pi^4)/(270*S^3) + ((1 + S^2)*(66623 + 6115*S^2 + 3632*S^4))/(1944*S^3) + (Pi^2*(1349 + 3968*S^2 + 6506*S^4 + 1358*S^6 + 833*S^8 + 122*S^10))/(216*S^3*(1 + S^2)^2) + ((58*Pi^2)/(9*S^3) + (1573 + 4658*S^2 + 6640*S^4 + 1492*S^6 + 851*S^8 + 106*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (38*HPL[{2}, -S^2]^2)/(3*S^3) + ((11 + 34*S^2 + 29*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{4}, -S^2])/S^3 - (13*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (52*HPL[{3, 1}, -S^2])/S^3 + (104*HPL[{2, 1, 1}, -S^2])/S^3 - (2*(22 + 86*S^2 + 85*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (4*(-12 - 18*S^2 + S^4 + 2*S^6 + S^8)*Zeta[5])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(8213 + 1237*S^2 + 338*S^4))/(1296*S^3) + ((1 + S^2)*(75721 + 4812*S^2 + 3985*S^4))/(1944*S^3) + (Pi^4*(2519 + 14086*S^2 + 16091*S^4 + 458*S^6 + 916*S^8 + 458*S^10))/(3240*S^3*(1 + S^2)^2) + (19*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((4*Pi^2)/(9*S^3) + (43 + 102*S^2 + 82*S^4 + 4*S^6 - 21*S^8 - 14*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*(11 + 40*S^2 + 38*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*HPL[{5}, -S^2])/(3*S^3) + ((-116*Pi^2)/(9*S^3) + (-1573 - 4658*S^2 - 6640*S^4 - 1492*S^6 - 851*S^8 - 106*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(110 + 454*S^2 + 461*S^4 + 20*S^6 + 40*S^8 + 20*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*HPL[{3, 2}, -S^2])/(3*S^3) + (8*HPL[{4, 1}, -S^2])/S^3 + (26*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (304*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (920*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (208*HPL[{2, 1, 1, 1}, -S^2])/S^3 + (-(Pi^2/S^3) + (-127 - 548*S^2 - 1054*S^4 - 352*S^6 - 323*S^8 - 100*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(1749 + 185*S^2 + 75*S^4))/(54*S^3) + (Pi^2*(539 + 2470*S^2 + 2627*S^4 + 98*S^6 + 196*S^8 + 98*S^10))/(108*S^3*(1 + S^2)^2) - (8*HPL[{3}, -S^2])/(3*S^3) - (152*HPL[{2, 1}, -S^2])/(3*S^3) - (4*Zeta[3])/S^3) - (16*Zeta[5])/(3*S^3))) + Log[T]*((-2689 - 702*S^2)/(972*S) + (Pi^2*(-8424 - 4923*S^2 + 809*S^4))/(5832*S) + (Pi^4*(-5258 - 25131*S^2 - 3602*S^4 - 2553*S^6 - 260*S^8))/(6480*S*(1 + S^2)^2) + ((-47*Pi^2)/(9*S^3) + (-3223 - 9848*S^2 - 14698*S^4 - 3376*S^6 - 2135*S^8 - 352*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^4 - (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^2) - (8*HPL[{1}, -S^2]^6)/(3*S^3) + HPL[{0}, S^2]^5*((-24 - 36*S^2 + S^4 + 2*S^6 + S^8)/(108*S*(1 + S^2)^2) - (2*HPL[{1}, -S^2])/(9*S^3)) + ((-7*Pi^2)/(3*S^3) + (-1297 - 3218*S^2 - 3484*S^4 - 471*S^6 - 297*S^8 - 21*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (38*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^4*((108 - 1143*S^2 + 308*S^4 + 427*S^6 + 200*S^8)/(1296*S*(1 + S^2)^2) - (37*(2 + 3*S^2)*HPL[{1}, -S^2])/(36*S*(1 + S^2)^2) - (37*HPL[{1}, -S^2]^2)/(36*S^3) + HPL[{2}, -S^2]/(12*S^3)) + (8*HPL[{3}, -S^2]^2)/(3*S^3) + ((13*Pi^2)/(9*S^3) + (894 + 3252*S^2 + 3945*S^4 + 1544*S^6 + 1447*S^8 + 482*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((81 + 294*S^2 + 279*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (20*HPL[{6}, -S^2])/(3*S^3) + (52*HPL[{2, 1}, -S^2]^2)/S^3 + HPL[{0}, S^2]^3*((13*(-62 - 2*S^2 + 15*S^4))/(324*S) + (Pi^2*(-510 - 765*S^2 - 8*S^4 - 16*S^6 - 8*S^8))/(324*S*(1 + S^2)^2) + ((-121 - 782*S^2 - 931*S^4 - 22*S^6 - 44*S^8 - 22*S^10)*HPL[{1}, -S^2]^2)/(54*S^3*(1 + S^2)^2) - (10*HPL[{1}, -S^2]^3)/(3*S^3) + ((21 - 186*S^2 - 321*S^4 - 16*S^6 - 32*S^8 - 16*S^10)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-85*Pi^2)/(54*S^3) + (-412 - 1028*S^2 - 2410*S^4 - 349*S^6 - 182*S^8 - 7*S^10)/(162*S^3*(1 + S^2)^2) - (38*HPL[{2}, -S^2])/(9*S^3)) - HPL[{3}, -S^2]/(3*S^3) + (82*HPL[{2, 1}, -S^2])/(9*S^3)) + ((-116*Pi^2)/(9*S^3) + (-2885 - 6520*S^2 - 4262*S^4 - 502*S^6 - 377*S^8 + 2*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((177 - 558*S^2 - 1191*S^4 - 262*S^6 - 524*S^8 - 262*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*(-71 + 626*S^2 + 1081*S^4 + 213*S^6 + 426*S^8 + 213*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*HPL[{4, 2}, -S^2])/S^3 - (20*HPL[{5, 1}, -S^2])/(3*S^3) + ((68*Pi^2)/(3*S^3) - (2*(-2793 - 3279*S^2 - 148*S^6 + 122*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (16*(12 + 138*S^2 + 183*S^4 + 16*S^6 + 32*S^8 + 16*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*(93 + 600*S^2 + 714*S^4 + 25*S^6 + 50*S^8 + 25*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*HPL[{3, 1, 2}, -S^2])/S^3 + (280*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (336*HPL[{4, 1, 1}, -S^2])/S^3 - (8*(-123 + 70*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) - (832*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (480*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((7884 + 702*S^2 + 521*S^4)/(81*S) + (Pi^2*(86 + 129*S^2 + 28*S^4 + 56*S^6 + 28*S^8))/(9*S*(1 + S^2)^2))*Zeta[3] + HPL[{2, 1}, -S^2]*((828 - 7599*S^2 - 480*S^4 - 521*S^6)/(81*S^3) - (2*Pi^2*(-105 - 324*S^2 - 276*S^4 + 40*S^6 + 80*S^8 + 40*S^10))/(27*S^3*(1 + S^2)^2) - (104*Zeta[3])/S^3) + HPL[{3}, -S^2]*((-1575 + 29748*S^2 + 4431*S^4 + 3748*S^6)/(324*S^3) + (Pi^2*(-45 + 486*S^2 + 819*S^4 + 158*S^6 + 316*S^8 + 158*S^10))/(54*S^3*(1 + S^2)^2) - (112*HPL[{2, 1}, -S^2])/S^3 + (16*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(6791 + 917*S^2 + 512*S^4))/(162*S^3) + (Pi^2*(-209 - 982*S^2 - 1055*S^4 - 38*S^6 - 76*S^8 - 38*S^10))/(27*S^3*(1 + S^2)^2) + (2*(11 + 2*S^6)*HPL[{2}, -S^2])/S^3 + (40*HPL[{3}, -S^2])/S^3 + (104*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((22*Pi^4)/(27*S^3) + (59397 + 6165*S^2 + 963*S^4 + 809*S^6)/(972*S^3) + (Pi^2*(750 + 1545*S^2 + 408*S^4 - 61*S^6 - 77*S^8 - 61*S^10))/(81*S^3*(1 + S^2)^2) + ((-105 + 246*S^2 + 579*S^4 + 134*S^6 + 268*S^8 + 134*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (22*HPL[{4}, -S^2])/(3*S^3) + (8*(12 + 138*S^2 + 183*S^4 + 16*S^6 + 32*S^8 + 16*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (184*HPL[{3, 1}, -S^2])/(3*S^3) - (104*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(-6 + 26*S^2 + 51*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-1547*Pi^4)/(540*S^3) - ((1 + S^2)*(66623 + 6115*S^2 + 3632*S^4))/(972*S^3) + (Pi^2*(-1873 - 5636*S^2 - 9802*S^4 - 2125*S^6 - 1433*S^8 - 271*S^10))/(162*S^3*(1 + S^2)^2) + ((-38*Pi^2)/(9*S^3) + (1127 + 2639*S^2 + 513*S^4 + 497*S^6 + 56*S^8)/(27*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (76*HPL[{2}, -S^2]^2)/(3*S^3) + (4*(22 + 74*S^2 + 67*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) + (56*HPL[{4}, -S^2])/(3*S^3) - (6*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/S^3 - (56*HPL[{3, 1}, -S^2])/(3*S^3) + (2*(121 + 398*S^2 + 355*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((-819 - 2727*S^2 + 809*S^4)/(1944*S) + (Pi^2*(-156 - 1263*S^2 - 82*S^4 - 5*S^6 + 26*S^8))/(216*S*(1 + S^2)^2) - (2*(22 + 146*S^2 + 175*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) - (17*HPL[{1}, -S^2]^4)/(3*S^3) + (Pi^2/(2*S^3) + (207 + 108*S^2 - 1647*S^4 - 392*S^6 - 334*S^8 - 122*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/(2*S^3) + HPL[{1}, -S^2]^2*((-44*Pi^2)/(9*S^3) + (-523 - 1424*S^2 - 4906*S^4 - 874*S^6 - 731*S^8 - 190*S^10)/(108*S^3*(1 + S^2)^2) - (38*HPL[{2}, -S^2])/(3*S^3)) + ((-3 + 30*S^2 + 51*S^4 + 16*S^6 + 32*S^8 + 16*S^10)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^2) + HPL[{4}, -S^2]/(3*S^3) + ((87 + 402*S^2 + 429*S^4 - 10*S^6 - 20*S^8 - 10*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*HPL[{3, 1}, -S^2])/S^3 + (8*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(12 + 18*S^2 + 7*S^4 + 14*S^6 + 7*S^8)*Zeta[3])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(541 + 453*S^2 + 202*S^4))/(216*S^3) + (Pi^2*(-11 - 110*S^2 - 143*S^4 - 2*S^6 - 4*S^8 - 2*S^10))/(9*S^3*(1 + S^2)^2) + ((-11 - 174*S^2 - 239*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)^2) + (2*HPL[{3}, -S^2])/S^3 + (76*HPL[{2, 1}, -S^2])/(3*S^3) + (8*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]*((-74057 - 4637*S^2 - 3985*S^4)/(972*S) + (Pi^2*(-7878 - 825*S^2 - 122*S^4))/(648*S) + (Pi^4*(-754 - 1131*S^2 - 73*S^4 - 146*S^6 - 73*S^8))/(270*S*(1 + S^2)^2) - (5*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^2) - (8*HPL[{1}, -S^2]^5)/S^3 - (2*(-8 + 98*S^2 + 163*S^4 + 18*S^6 + 36*S^8 + 18*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-10*Pi^2)/S^3 + (-3223 - 9848*S^2 - 14698*S^4 - 3376*S^6 - 2135*S^8 - 352*S^10)/(81*S^3*(1 + S^2)^2) - (104*HPL[{2}, -S^2])/(3*S^3)) + ((-10*Pi^2)/(9*S^3) + (2*(-67 - 131*S^2 - 85*S^4 + 29*S^6 + 70*S^8 + 38*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (4*(2 + 22*S^2 + 29*S^4 + 3*S^6 + 6*S^8 + 3*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + ((250*Pi^2)/(9*S^3) + (3239 + 6964*S^2 + 6767*S^4 + 630*S^6 + 324*S^8 - 72*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(-19 + 118*S^2 + 215*S^4 + 28*S^6 + 56*S^8 + 28*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (8*HPL[{3, 2}, -S^2])/S^3 - (20*HPL[{4, 1}, -S^2])/(3*S^3) - (4*(-57 + 354*S^2 + 645*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (616*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (1904*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (448*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((76 + 195*S^2 + 100*S^4 + 105*S^6 + 40*S^8)*Zeta[3])/(9*S*(1 + S^2)^2) + HPL[{2}, -S^2]*((-291 - 9132*S^2 - 879*S^4 - 506*S^6)/(162*S^3) + (Pi^2*(39 - 270*S^2 - 483*S^4 - 49*S^6 - 98*S^8 - 49*S^10))/(27*S^3*(1 + S^2)^2) + (4*HPL[{3}, -S^2])/S^3 + (308*HPL[{2, 1}, -S^2])/(3*S^3) - (4*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(6791 + 917*S^2 + 512*S^4))/(108*S^3) + (Pi^2*(-308 - 1426*S^2 - 1523*S^4 - 56*S^6 - 112*S^8 - 56*S^10))/(27*S^3*(1 + S^2)^2) - (13*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*HPL[{3}, -S^2])/(3*S^3) + (104*HPL[{2, 1}, -S^2])/S^3 + (28*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((-377*Pi^4)/(135*S^3) - ((1 + S^2)*(66623 + 6115*S^2 + 3632*S^4))/(972*S^3) + (Pi^2*(-1349 - 3968*S^2 - 6506*S^4 - 1358*S^6 - 833*S^8 - 122*S^10))/(108*S^3*(1 + S^2)^2) + ((-116*Pi^2)/(9*S^3) + (-1573 - 4658*S^2 - 6640*S^4 - 1492*S^6 - 851*S^8 - 106*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (76*HPL[{2}, -S^2]^2)/(3*S^3) - (2*(11 + 34*S^2 + 29*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*HPL[{4}, -S^2])/S^3 + (26*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (104*HPL[{3, 1}, -S^2])/S^3 - (208*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(22 + 86*S^2 + 85*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2))) + (2*(94 + 141*S^2 + 30*S^4 + 60*S^6 + 30*S^8)*Zeta[5])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(3666 + 685*S^2 + 357*S^4))/(324*S^3) - ((1 + S^2)*(75721 + 4812*S^2 + 3985*S^4))/(972*S^3) + (Pi^4*(-5269 - 29102*S^2 - 33115*S^4 - 958*S^6 - 1916*S^8 - 958*S^10))/(3240*S^3*(1 + S^2)^2) - (19*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((32*Pi^2)/(3*S^3) + (2569 + 8360*S^2 + 10354*S^4 + 2830*S^6 + 1853*S^8 + 346*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((319 + 974*S^2 + 823*S^4 + 58*S^6 + 116*S^8 + 58*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (44*HPL[{5}, -S^2])/(3*S^3) + ((76*Pi^2)/(9*S^3) - (2*(1127 + 2639*S^2 + 513*S^4 + 497*S^6 + 56*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (4*(187 + 458*S^2 + 313*S^4 + 34*S^6 + 68*S^8 + 34*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (304*HPL[{3, 2}, -S^2])/(3*S^3) - (1024*HPL[{4, 1}, -S^2])/(3*S^3) + (12*(11 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (608*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (368*HPL[{3, 1, 1}, -S^2])/S^3 + ((86*Pi^2)/(9*S^3) + (2*(150 + 468*S^2 + 544*S^4 + 139*S^6 + 78*S^8 + 9*S^10))/(3*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(1376 + 47*S^2 + 80*S^4))/(27*S^3) + (2*Pi^2*(22 + 6*S^2 - 35*S^4 + 4*S^6 + 8*S^8 + 4*S^10))/(9*S^3*(1 + S^2)^2) + (152*HPL[{3}, -S^2])/(3*S^3) + (304*HPL[{2, 1}, -S^2])/(3*S^3) + (152*Zeta[3])/(3*S^3)) + (188*Zeta[5])/(3*S^3)));
E4wuvT=E4wuvT0F0+T*E4wuvT1F1*(F+1/F)+T^2*(E4wuvT2F0+E4wuvT2F2*(F^2+1/F^2))+T^3*(E4wuvT3F1*(F+1/F)+E4wuvT3F3*(F^3+1/F^3));
Et4uvwT1F1=(-130*Pi^2*S)/9 - (251*Pi^4*S)/108 - (20137*Pi^6*S)/45360 + HPL[{0}, S^2]^6*(-S/8 + ((-1 - S^2)*HPL[{1}, -S^2])/(16*S)) - (13*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^5*((-5*Pi^2*S)/216 - (5*(1 + S^2)*HPL[{1}, -S^2])/(36*S) - (5*(1 + S^2)*HPL[{1}, -S^2]^2)/(36*S) - (5*S*HPL[{2}, -S^2])/36) + HPL[{1}, -S^2]^5*((-11*Pi^2*(1 + S^2))/(45*S) - (44*(1 + S^2)*HPL[{2}, -S^2])/(15*S)) + (8*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(-55 - 107*S^2))/(18*S) + (-133 - 81*S^2)/(3*S))*HPL[{5}, -S^2] + ((-320 - 317*S^2)*HPL[{6}, -S^2])/(3*S) - (2*(300 + 229*S^2)*HPL[{7}, -S^2])/(3*S) + (52*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((104*S)/3 + (4*Pi^2*(-3 + 14*S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((Pi^2*(1 + 69*S^2))/(3*S) + (2*(53 + 209*S^2))/(3*S))*HPL[{4, 1}, -S^2] + (3*(-1 + S^2)*HPL[{4, 2}, -S^2])/S + (2*(8 + 5*S^2)*HPL[{4, 3}, -S^2])/S + (2*(73 + 93*S^2)*HPL[{5, 1}, -S^2])/(3*S) + (3*(15 + 13*S^2)*HPL[{5, 2}, -S^2])/S + (2*(282 + 319*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((104*(-1 + S^2))/(3*S) + (4*Pi^2*(-30 + 13*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + (-416/(3*S) + (4*Pi^2*(-93 + 5*S^2))/(9*S))*HPL[{3, 1, 1}, -S^2] - (104*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (16*(4 + 13*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) - (32*(1 + 6*S^2)*HPL[{3, 3, 1}, -S^2])/S - (4*(117 + 113*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (2*(13 + 99*S^2)*HPL[{4, 1, 2}, -S^2])/S - (2*(29 + 283*S^2)*HPL[{4, 2, 1}, -S^2])/S - (4*(89 + 895*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((416*(1 + S^2))/(3*S) + (4*Pi^2*(7 + 4*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (272*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + (8*(41 + 39*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (16*(52 + 25*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) - (16*(52 + 25*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) - (16*(103 + 76*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) - (16*(301 + 218*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) - (640*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) - (144*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (432*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (32*(-66 + 97*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) + (992*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S) + ((14*Pi^2*S)/27 + (14*S*HPL[{0}, S^2]^2)/9 + (28*(1 + S^2)*HPL[{2}, -S^2])/(9*S))*Log[T]^5 + ((-260*S)/3 - (79*Pi^2*S)/9 - (157*Pi^4*S)/90)*Zeta[3] - 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((260*(1 + S^2))/(3*S) + (26*Pi^2*(4 + 3*S^2))/(9*S) + (Pi^4*(853 + 264*S^2))/(540*S) + (24*(-2 + S^2)*HPL[{3, 1}, -S^2])/S + (72*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (104*Zeta[3])/(3*S)) + Log[T]^4*((-40*Pi^2*S)/27 - (28*S*HPL[{0}, S^2]^3)/27 + HPL[{0}, S^2]^2*((-40*S)/9 - (11*(1 + S^2)*HPL[{1}, -S^2])/(3*S)) - (80*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((-11*Pi^2*(1 + S^2))/(9*S) - (44*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]*((-28*Pi^2*S)/27 - (4*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) - (2*(3 + 59*S^2)*HPL[{3}, -S^2])/(9*S) + (124*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (124*S*Zeta[3])/9) + HPL[{0}, S^2]^4*((-79*S)/36 - (37*Pi^2*S)/48 - (19*(1 + S^2)*HPL[{1}, -S^2]^2)/(24*S) - (49*(1 + S^2)*HPL[{1}, -S^2]^3)/(108*S) + ((-2 - 5*S^2)*HPL[{2}, -S^2])/(8*S) + HPL[{1}, -S^2]*((-79*(1 + S^2))/(72*S) - (23*Pi^2*(1 + S^2))/(54*S) - (49*(1 + S^2)*HPL[{2}, -S^2])/(72*S)) + ((-1 - S^2)*HPL[{3}, -S^2])/(8*S) + ((40 + 3*S^2)*HPL[{2, 1}, -S^2])/(36*S) - (83*S*Zeta[3])/36) + HPL[{1}, -S^2]^3*((-52*Pi^2*(1 + S^2))/(27*S) - (757*Pi^4*(1 + S^2))/(1620*S) + ((-208*(1 + S^2))/(9*S) - (106*Pi^2*(1 + S^2))/(27*S))*HPL[{2}, -S^2] - (52*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (92*(1 + S^2)*HPL[{4}, -S^2])/(9*S) + (104*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (88*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (176*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (52*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^4*((-13*Pi^2*(1 + S^2))/(18*S) - (26*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (22*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (44*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (22*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((-44*(1 + S^2))/S - (73*Pi^2*(1 + S^2))/(18*S) + (2*(11 + S^2)*HPL[{2, 1}, -S^2])/S + (16*(2 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((Pi^4*(-21 - 307*S^2))/(540*S) - (130*(1 + S^2))/(3*S) - (26*Pi^2*(1 + 2*S^2))/(9*S) - (2*(4 + S^2)*HPL[{4}, -S^2])/S - (8*(-11 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (16*(-1 + 5*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(-1 + 26*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*(-1 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((52*(1 + S^2))/S + (2*Pi^2*(29 + 42*S^2))/(9*S) + (8*(-3 + 11*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((Pi^2*(15 - 28*S^2))/(18*S) - (13*(-1 + S^2))/(3*S) - (2*(4 + 13*S^2)*HPL[{3}, -S^2])/(3*S) + (34*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(3 + 14*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((-104*(1 + S^2))/S - (4*Pi^2*(27 + 40*S^2))/(9*S) - (8*(-1 + 26*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^3*((-13*Pi^2*S)/54 - (7*Pi^4*S)/60 + ((-1 - S^2)*HPL[{1}, -S^2]^3)/S + ((-1 - S^2)*HPL[{1}, -S^2]^4)/(2*S) + ((-13*S)/9 + (Pi^2*(-3 - 76*S^2))/(108*S))*HPL[{2}, -S^2] + ((-1 - 7*S^2)*HPL[{2}, -S^2]^2)/(12*S) + HPL[{1}, -S^2]^2*((-14*(1 + S^2))/(9*S) - (77*Pi^2*(1 + S^2))/(108*S) - (11*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((3 + S^2)*HPL[{3}, -S^2])/(6*S) + ((1 + S^2)*HPL[{4}, -S^2])/(2*S) + ((19 - 3*S^2)*HPL[{2, 1}, -S^2])/(9*S) + 2*S*HPL[{3, 1}, -S^2] - (2*(3 + 26*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + HPL[{1}, -S^2]*((-5*(1 + S^2))/(3*S) - (77*Pi^2*(1 + S^2))/(108*S) - (11*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + ((1 + S^2)*HPL[{3}, -S^2])/(3*S) + (22*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (10*(1 + S^2)*Zeta[3])/(9*S))) + Log[T]^3*((104*Pi^2*S)/27 + (277*Pi^4*S)/270 + (55*S*HPL[{0}, S^2]^4)/54 + HPL[{0}, S^2]^3*(2*S + (2*(1 + S^2)*HPL[{1}, -S^2])/S) + ((208*(1 + S^2))/(9*S) + (2*Pi^2*(43 + 70*S^2))/(27*S))*HPL[{2}, -S^2] + (6*(-1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^2*((22*Pi^2*(1 + S^2))/(9*S) + (88*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]^2*((104*S)/9 + (10*Pi^2*S)/3 + (26*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + (22*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (2*(8 + 35*S^2)*HPL[{2}, -S^2])/(9*S)) + (4*(11 + 65*S^2)*HPL[{3}, -S^2])/(9*S) + (8*(15 + 13*S^2)*HPL[{4}, -S^2])/(9*S) - (304*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (16*(18 + 17*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (560*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (304*S*Zeta[3])/9 + HPL[{0}, S^2]*(2*Pi^2*S + (2*Pi^2*(1 + S^2)*HPL[{1}, -S^2])/S + (4*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (4*(3 + S^2)*HPL[{3}, -S^2])/(9*S) + (16*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (8*S*Zeta[3])/9) + HPL[{1}, -S^2]*((26*Pi^2*(1 + S^2))/(9*S) + (104*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (88*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (176*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (88*(1 + S^2)*Zeta[3])/(3*S))) + ((-262*S)/3 - (55*Pi^2*S)/3)*Zeta[5] + Log[T]^2*((-26*Pi^2*S)/3 - (1009*Pi^4*S)/540 - (5*S*HPL[{0}, S^2]^5)/18 + HPL[{0}, S^2]^4*((-7*S)/4 - (49*(1 + S^2)*HPL[{1}, -S^2])/(36*S)) - (26*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((-26*S)/9 - (13*Pi^2*S)/9 - (3*(1 + S^2)*HPL[{1}, -S^2])/S - (3*(1 + S^2)*HPL[{1}, -S^2]^2)/S + ((-3 - 26*S^2)*HPL[{2}, -S^2])/(9*S)) + HPL[{1}, -S^2]^3*((-22*Pi^2*(1 + S^2))/(9*S) - (88*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-52*(1 + 3*S^2))/(3*S) - (2*Pi^2*(3 + 34*S^2))/(9*S))*HPL[{3}, -S^2] - (2*(39 + 35*S^2)*HPL[{4}, -S^2])/(3*S) - (2*(17 + 67*S^2)*HPL[{5}, -S^2])/(3*S) + ((208*(1 + S^2))/(3*S) + (2*Pi^2*(7 + 4*S^2))/S)*HPL[{2, 1}, -S^2] + (4*(41 + 39*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (8*(-1 + 26*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (8*(5 + 88*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (320*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (72*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (16*(-42 + 11*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (496*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-208*S)/3 - (86*Pi^2*S)/9)*Zeta[3] + HPL[{0}, S^2]^2*(-26*S - (103*Pi^2*S)/18 - (13*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (22*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (2*(7 + 20*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-52*(1 + S^2))/(3*S) - (41*Pi^2*(1 + S^2))/(9*S) - (40*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-1 - 3*S^2)*HPL[{3}, -S^2])/S + (2*(32 + 5*S^2)*HPL[{2, 1}, -S^2])/(3*S) - 8*S*Zeta[3]) + HPL[{1}, -S^2]*((-52*Pi^2*(1 + S^2))/(9*S) - (757*Pi^4*(1 + S^2))/(540*S) + ((-208*(1 + S^2))/(3*S) - (106*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (52*(1 + S^2)*HPL[{3}, -S^2])/S - (92*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (104*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (88*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (176*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (52*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-13*Pi^2*(1 + S^2))/(3*S) - (52*(1 + S^2)*HPL[{2}, -S^2])/S - (44*(1 + S^2)*HPL[{3}, -S^2])/S + (88*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (44*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-52*(1 + S^2))/S - (2*Pi^2*(27 + 40*S^2))/(9*S) - (4*(-1 + 26*S^2)*HPL[{3}, -S^2])/(3*S) - (36*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(-1 + 26*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]*((-26*Pi^2*S)/9 - (107*Pi^4*S)/90 - (3*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (Pi^2*(-5 - 28*S^2)*HPL[{2}, -S^2])/(9*S) + ((-1 - S^2)*HPL[{2}, -S^2]^2)/(3*S) + (2*(3 + S^2)*HPL[{3}, -S^2])/(3*S) - (2*(5 + S^2)*HPL[{4}, -S^2])/(3*S) - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*HPL[{3, 1}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*S*Zeta[3])/3 + HPL[{1}, -S^2]*((-3*Pi^2*(1 + S^2))/S + (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (4*(1 + S^2)*Zeta[3])/(3*S))) - (220*S*Zeta[5])/3) + HPL[{0}, S^2]^2*((-130*S)/3 - (59*Pi^2*S)/9 - (389*Pi^4*S)/270 - (13*(1 + S^2)*HPL[{1}, -S^2]^4)/(6*S) - (11*(1 + S^2)*HPL[{1}, -S^2]^5)/(15*S) + ((2 - 15*S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^3*((-52*(1 + S^2))/(9*S) - (41*Pi^2*(1 + S^2))/(27*S) - (40*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((Pi^2*(-2 - 3*S^2))/(6*S) - (13*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + ((-17 - 19*S^2)*HPL[{4}, -S^2])/(3*S) + ((-19 - 20*S^2)*HPL[{5}, -S^2])/(3*S) + ((26*(2 + S^2))/(3*S) + (4*Pi^2*(9 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + ((17 + 45*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(-5 + 2*S^2)*HPL[{3, 2}, -S^2])/(3*S) + ((-7 + 31*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (4*(7 + 20*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (2*(33 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4*(17 + 2*S^2)*HPL[{3, 1, 1}, -S^2])/S + (4*(32 + 5*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (-9*S - (95*Pi^2*S)/18)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-32 - 85*S^2))/(36*S) - (13*(2 + 3*S^2))/(3*S) + ((5 - 2*S^2)*HPL[{3}, -S^2])/(3*S) + ((33 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + ((1 - S^2)*Zeta[3])/S) + HPL[{1}, -S^2]*((-65*(1 + S^2))/(3*S) - (131*Pi^2*(1 + S^2))/(36*S) - (911*Pi^4*(1 + S^2))/(1080*S) + ((-13*(1 + S^2))/S - (89*Pi^2*(1 + S^2))/(36*S))*HPL[{2}, -S^2] - (13*(1 + S^2)*HPL[{2}, -S^2]^2)/(6*S) - (5*(1 + S^2)*HPL[{3}, -S^2])/S - (6*(1 + S^2)*HPL[{4}, -S^2])/S + (52*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (44*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (80*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (14*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-13*(1 + S^2))/S - (8*Pi^2*(1 + S^2))/(3*S) - (26*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (3*(1 + S^2)*HPL[{3}, -S^2])/S + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(1 + S^2)*Zeta[3])/S) - (110*S*Zeta[5])/3) + HPL[{1}, -S^2]*((-65*Pi^2*(1 + S^2))/(9*S) - (277*Pi^4*(1 + S^2))/(216*S) - (11563*Pi^6*(1 + S^2))/(45360*S) - (13*Pi^2*(1 + S^2)*HPL[{2}, -S^2]^2)/(18*S) - (26*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-106*(1 + S^2))/(3*S) - (41*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] - (118*(1 + S^2)*HPL[{5}, -S^2])/(3*S) - (99*(1 + S^2)*HPL[{6}, -S^2])/S + ((208*(1 + S^2))/(3*S) + (110*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] + (88*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (388*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (220*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-416*(1 + S^2))/(3*S) - (212*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (104*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (208*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (808*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (208*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (176*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (352*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-52*(1 + S^2))/S - (53*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (6*(1 + S^2)*Zeta[3]^2)/S + HPL[{2}, -S^2]*((-260*(1 + S^2))/(3*S) - (91*Pi^2*(1 + S^2))/(9*S) - (1349*Pi^4*(1 + S^2))/(1080*S) - (44*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (52*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-52*(1 + S^2))/S - (6*Pi^2*(1 + S^2))/S + (88*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((104*(1 + S^2))/S + (130*Pi^2*(1 + S^2))/(9*S) + (104*(1 + S^2)*Zeta[3])/(3*S)) - (58*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^2*((-13*Pi^2*(1 + S^2))/(3*S) - (7*Pi^4*(1 + S^2))/(8*S) + ((-104*(1 + S^2))/(3*S) - (14*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (62*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (94*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((208*(1 + S^2))/(3*S) + (106*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (52*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (88*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (356*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (104*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (88*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (176*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-104*(1 + S^2))/(3*S) - (5*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-52*(1 + S^2))/S - (65*Pi^2*(1 + S^2))/(9*S) - (44*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (52*(1 + S^2)*Zeta[3])/(3*S)) - (134*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((Pi^4*(-642 - 1187*S^2))/(1080*S) - (260*(1 + S^2))/(3*S) - (13*Pi^2*(5 + 6*S^2))/(9*S) + ((-52*S)/3 - (2*Pi^2*(-3 + 14*S^2))/(9*S))*HPL[{3}, -S^2] + ((-7 - 25*S^2)*HPL[{4}, -S^2])/(3*S) + ((11 - 7*S^2)*HPL[{5}, -S^2])/S + ((-52*(-1 + S^2))/(3*S) - (2*Pi^2*(-30 + 13*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (4*(-9 + 17*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (8*(4 + 13*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2*(5 + 51*S^2)*HPL[{4, 1}, -S^2])/S - (104*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (8*(52 + 25*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (72*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-52*S)/3 + (Pi^2*(4 - 29*S^2))/(9*S))*Zeta[3] - (2*(-10 + 41*S^2)*Zeta[5])/(3*S)) + HPL[{0}, S^2]*((-13*Pi^4*S)/54 - (103*Pi^6*S)/1080 + (Pi^2*(-1 - S^2)*HPL[{1}, -S^2]^4)/(2*S) + (Pi^2*(-2 - 11*S^2)*HPL[{2}, -S^2]^2)/(18*S) + (4*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + (2*(4 + 3*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((4*(1 + S^2))/(3*S) + (2*Pi^2*(1 + 2*S^2))/(9*S))*HPL[{4}, -S^2] + (32*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (4*(15 + 13*S^2)*HPL[{6}, -S^2])/(3*S) + (2*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-4*(1 + S^2))/(3*S) + (2*Pi^2*(1 + 9*S^2))/(9*S))*HPL[{3, 1}, -S^2] - (16*S*HPL[{3, 2}, -S^2])/3 - (20*(1 + 3*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (4*(6 + 7*S^2)*HPL[{5, 1}, -S^2])/(3*S) - (2*Pi^2*(5 + 28*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (4*(3 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (4*(19 + 23*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (16*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (32*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (Pi^2*S*Zeta[3])/9 + 4*S*Zeta[3]^2 + HPL[{1}, -S^2]^2*((-14*Pi^2*(1 + S^2))/(9*S) - (79*Pi^4*(1 + S^2))/(135*S) - (11*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (4*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (2*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((Pi^2*(-1 - S^2))/S + (4*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (4*(1 + S^2)*Zeta[3])/(9*S)) + HPL[{2}, -S^2]*((-13*Pi^2*S)/9 + (Pi^4*(-13 - 87*S^2))/(135*S) + (8*S*HPL[{3}, -S^2])/3 - (4*(4 + 3*S^2)*HPL[{4}, -S^2])/(3*S) + (4*(3 + 2*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(1 + 3*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-2*Pi^2*(-9 + 2*S^2))/(9*S) + (4*(5 + 4*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((4*(1 + S^2))/(3*S) + (2*Pi^2*(3 + S^2))/(9*S) - (4*(7 + 6*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(4 + 5*S^2)*Zeta[3])/(3*S)) + (8*S*Zeta[5])/3 + HPL[{1}, -S^2]*((-5*Pi^2*(1 + S^2))/(3*S) - (79*Pi^4*(1 + S^2))/(135*S) + ((4*(1 + S^2))/(3*S) + (4*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (4*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (22*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (4*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (56*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (8*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + ((-4*(1 + S^2))/(3*S) - (11*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-11*Pi^2*(1 + S^2))/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (8*(1 + S^2)*Zeta[3])/(3*S)) - (8*(1 + S^2)*Zeta[5])/S)) + Log[T]*((130*Pi^2*S)/9 + (277*Pi^4*S)/108 + (4153*Pi^6*S)/7560 + (S*HPL[{0}, S^2]^6)/8 + HPL[{0}, S^2]^5*((5*S)/18 + (5*(1 + S^2)*HPL[{1}, -S^2])/(18*S)) + ((26*(-1 + S^2))/(3*S) + (Pi^2*(-17 + 26*S^2))/(9*S))*HPL[{2}, -S^2]^2 + (2*(1 + S^2)*HPL[{2}, -S^2]^3)/S + HPL[{1}, -S^2]^4*((11*Pi^2*(1 + S^2))/(9*S) + (44*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]^4*((79*S)/36 + (95*Pi^2*S)/108 + (19*(1 + S^2)*HPL[{1}, -S^2])/(12*S) + (49*(1 + S^2)*HPL[{1}, -S^2]^2)/(36*S) + ((9 + 46*S^2)*HPL[{2}, -S^2])/(36*S)) - (4*(-2 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((106*(1 + S^2))/(3*S) + (43*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + (2*(25 + 77*S^2)*HPL[{5}, -S^2])/(3*S) + (2*(90 + 143*S^2)*HPL[{6}, -S^2])/(3*S) - (36*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-208*(1 + S^2))/(3*S) - (8*Pi^2*(11 + 17*S^2))/(9*S))*HPL[{3, 1}, -S^2] - (208*S*HPL[{3, 2}, -S^2])/3 - (4*(23 + 183*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (6*(-1 + S^2)*HPL[{4, 2}, -S^2])/S - (4*(33 + 67*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((416*(1 + S^2))/(3*S) + (4*Pi^2*(43 + 70*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (208*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(-89 + 13*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (48*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (32*(21 + 20*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (608*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (32*(18 + 17*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (1120*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (104*S + (34*Pi^2*S)/3)*Zeta[3] + 4*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-104*(1 + S^2))/S - (4*Pi^2*(38 + 25*S^2))/(9*S) - (72*Zeta[3])/S) + HPL[{0}, S^2]^3*((26*S)/9 + (77*Pi^2*S)/54 + (3*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (2*(1 + S^2)*HPL[{1}, -S^2]^3)/S + ((3 + 25*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((28*(1 + S^2))/(9*S) + (77*Pi^2*(1 + S^2))/(54*S) + (22*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((-1 - S^2)*HPL[{3}, -S^2])/(3*S) + (2*(-19 + 4*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (20*S*Zeta[3])/9) + HPL[{2}, -S^2]*((260*(1 + S^2))/(3*S) + (26*Pi^2*(3 + 4*S^2))/(9*S) + (31*Pi^4*(16 + 35*S^2))/(540*S) + (104*S*HPL[{3}, -S^2])/3 + (2*(-17 + 13*S^2)*HPL[{4}, -S^2])/(3*S) + (104*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(-14 + 13*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (72*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (104*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((26*Pi^2*(1 + S^2))/(9*S) + (104*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (88*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (176*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (88*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((52*Pi^2*(1 + S^2))/(9*S) + (757*Pi^4*(1 + S^2))/(540*S) + ((208*(1 + S^2))/(3*S) + (106*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (52*(1 + S^2)*HPL[{3}, -S^2])/S + (92*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (104*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (88*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (176*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (52*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((104*(1 + 2*S^2))/(3*S) + (20*Pi^2*(1 + 4*S^2))/(9*S) + (8*(-23 + 4*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(4 + S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]*((26*Pi^2*S)/9 + (158*Pi^4*S)/135 + (2*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^3)/S + ((-4*(1 + S^2))/(3*S) - (2*Pi^2*(3 + 2*S^2))/(9*S))*HPL[{3}, -S^2] + (4*(3 + S^2)*HPL[{4}, -S^2])/(3*S) - (4*(2 + 3*S^2)*HPL[{5}, -S^2])/(3*S) + (2*Pi^2*(-17 + 6*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (4*(-1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(3 + 2*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(9 + 7*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (8*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(3 + 2*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + 2*Pi^2*S*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2*(2 + 13*S^2))/(9*S) + (4*(3 + 2*S^2)*HPL[{3}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((3*Pi^2*(1 + S^2))/S - (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (4*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]*((28*Pi^2*(1 + S^2))/(9*S) + (158*Pi^4*(1 + S^2))/(135*S) + (22*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (4*(1 + S^2)*Zeta[3])/(3*S))) + HPL[{0}, S^2]^2*((130*S)/3 + (131*Pi^2*S)/18 + (163*Pi^4*S)/90 + (26*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (11*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + ((26*(1 + 2*S^2))/(3*S) + (Pi^2*(17 + 81*S^2))/(18*S))*HPL[{2}, -S^2] + ((-7 + 25*S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^2*((52*(1 + S^2))/(3*S) + (41*Pi^2*(1 + S^2))/(9*S) + (40*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((3 + 5*S^2)*HPL[{3}, -S^2])/S + ((13 + 17*S^2)*HPL[{4}, -S^2])/(3*S) - (4*(19 + 6*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(4 + 17*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (4*(8 + 35*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (26*S*Zeta[3])/3 + HPL[{1}, -S^2]*((26*(1 + S^2))/S + (16*Pi^2*(1 + S^2))/(3*S) + (52*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (6*(1 + S^2)*HPL[{3}, -S^2])/S - (80*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*Zeta[3])/S)) + 100*S*Zeta[5] + HPL[{1}, -S^2]*((26*Pi^2*(1 + S^2))/(3*S) + (7*Pi^4*(1 + S^2))/(4*S) + ((208*(1 + S^2))/(3*S) + (28*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (124*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (188*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-416*(1 + S^2))/(3*S) - (212*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (104*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (176*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (712*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (208*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (176*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (352*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((208*(1 + S^2))/(3*S) + (10*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((104*(1 + S^2))/S + (130*Pi^2*(1 + S^2))/(9*S) + (88*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (104*(1 + S^2)*Zeta[3])/(3*S)) + (268*(1 + S^2)*Zeta[5])/(3*S))) - 150*S*Zeta[7];
Et4uvwT2F2=(Pi^2*(721 + 1095*S^2))/288 + (Pi^4*(3143 + 7059*S^2))/8640 + (Pi^6*(23126 + 30581*S^2))/181440 + (7*(-1 + S^4)*HPL[{1}, -S^2]^6)/(27*S^2) + HPL[{0}, S^2]^6*((1 + S^2)/32 + ((1 + S^4)*HPL[{1}, -S^2])/(32*S^2)) + ((23 + 52*S^2 + 23*S^4)*HPL[{2}, -S^2]^3)/(36*S^2) + HPL[{0}, S^2]^5*((5*Pi^2*S^2)/432 + (-2 + 9*S^2)/24 + ((1 + S^2)*(-3 + 8*S^2)*HPL[{1}, -S^2])/(36*S^2) + (5*(1 + S^4)*HPL[{1}, -S^2]^2)/(72*S^2) + (5*S^2*HPL[{2}, -S^2])/72) + HPL[{1}, -S^2]^5*((53*(-1 + S^4))/(45*S^2) + (11*Pi^2*(1 + S^4))/(90*S^2) + (22*(1 + S^4)*HPL[{2}, -S^2])/(15*S^2)) + ((8 - 13*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((Pi^2*(55 + 107*S^4))/(36*S^2) + (-741 + 368*S^2 + 1097*S^4)/(24*S^2))*HPL[{5}, -S^2] + ((-580 + 594*S^2 + 821*S^4)*HPL[{6}, -S^2])/(12*S^2) + ((300 + 229*S^4)*HPL[{7}, -S^2])/(3*S^2) - (41*(-1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-27 - 260*S^2 - 95*S^4)/(12*S^2) - (2*Pi^2*(-3 + 14*S^4))/(9*S^2))*HPL[{3, 2}, -S^2] + ((75 - 1004*S^2 - 569*S^4)/(12*S^2) + (Pi^2*(-1 - 69*S^4))/(6*S^2))*HPL[{4, 1}, -S^2] - (3*(-1 + 3*S^2)*(1 + 3*S^2)*HPL[{4, 2}, -S^2])/(4*S^2) + ((-8 - 5*S^4)*HPL[{4, 3}, -S^2])/S^2 + ((113 - 220*S^2 - 437*S^4)*HPL[{5, 1}, -S^2])/(6*S^2) - (3*(15 + 13*S^4)*HPL[{5, 2}, -S^2])/(2*S^2) + ((-282 - 319*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((-17*(-1 + S^4))/(3*S^2) - (2*Pi^2*(-30 + 13*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((-2*Pi^2*(-93 + 5*S^4))/(9*S^2) + (13 + 206*S^2 + 55*S^4)/(3*S^2))*HPL[{3, 1, 1}, -S^2] + (3*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((55 + 104*S^2 + 55*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (8*(4 + 13*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) + (16*(1 + 6*S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + ((193 + 404*S^2 + 269*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + ((13 + 99*S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + ((29 + 283*S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (2*(89 + 895*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((-2*Pi^2*(7 + 4*S^4))/S^2 - (4*(17 + 103*S^2 + 17*S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (136*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) - (2*(81 + 132*S^2 + 119*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (8*(52 + 25*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + (8*(52 + 25*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + (8*(103 + 76*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (8*(301 + 218*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) + (16*(25 + 33*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (72*(-1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (216*(-1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (16*(-66 + 97*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) - (496*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((-7*Pi^2*S^2)/27 - (14*S^2*HPL[{0}, S^2])/9 - (7*S^2*HPL[{0}, S^2]^2)/9 - (14*(-1 + S^4)*HPL[{1}, -S^2])/(9*S^2) - (14*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2))*Log[T]^5 + ((157*Pi^4*S^2)/180 + (Pi^2*(242 + 125*S^2))/72 + (738 + 337*S^2)/24)*Zeta[3] + ((6 - 5*S^2)*Zeta[3]^2)/2 + HPL[{0}, S^2]^4*((Pi^2*(368 + 445*S^2))/1728 + (129 + 463*S^2)/576 + ((37 + 204*S^2 + 151*S^4)*HPL[{1}, -S^2]^2)/(288*S^2) + (49*(1 + S^4)*HPL[{1}, -S^2]^3)/(216*S^2) + ((18 + 98*S^2 + 157*S^4)*HPL[{2}, -S^2])/(288*S^2) + HPL[{1}, -S^2]*((23*Pi^2*(1 + S^4))/(108*S^2) + (57 + 480*S^2 + 359*S^4)/(576*S^2) + (49*(1 + S^4)*HPL[{2}, -S^2])/(144*S^2)) + ((1 + S^4)*HPL[{3}, -S^2])/(16*S^2) + ((-40 - 3*S^4)*HPL[{2, 1}, -S^2])/(72*S^2) + (83*S^2*Zeta[3])/72) + Log[T]^4*((Pi^2*(33 + 50*S^2))/54 + (14*S^2*HPL[{0}, S^2]^3)/27 + (35*(-1 + S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + HPL[{0}, S^2]^2*((33 + 50*S^2)/18 + (11*(1 + S^4)*HPL[{1}, -S^2])/(6*S^2)) + (2*(25 + 33*S^2 + 25*S^4)*HPL[{2}, -S^2])/(9*S^2) + HPL[{0}, S^2]*((14*Pi^2*S^2)/27 + (-33 + 53*S^2)/9 + (35*(-1 + S^4)*HPL[{1}, -S^2])/(9*S^2) + (2*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + HPL[{1}, -S^2]*((53*(-1 + S^4))/(9*S^2) + (11*Pi^2*(1 + S^4))/(18*S^2) + (22*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((3 + 59*S^4)*HPL[{3}, -S^2])/(9*S^2) - (62*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (62*S^2*Zeta[3])/9) + HPL[{2, 1}, -S^2]*((-337 - 1476*S^2 - 337*S^4)/(24*S^2) + (Pi^4*(-853 - 264*S^4))/(1080*S^2) + (Pi^2*(-76 - 310*S^2 - 59*S^4))/(36*S^2) - (12*(-2 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (36*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(41 + 26*S^2)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^4*((143*(-1 + S^4))/(36*S^2) + (Pi^2*(-35 + 132*S^2 + 167*S^4))/(216*S^2) + (11*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(3*S^2) + (11*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (22*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (11*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((Pi^2*(57 + 148*S^2 + 193*S^4))/(72*S^2) + (-1 + 103*S^2 + 245*S^4)/(12*S^2) + ((-11 - S^4)*HPL[{2, 1}, -S^2])/S^2 - (8*(2 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-49 + 236*S^2 + 167*S^4))/(72*S^2) + (Pi^4*(21 + 307*S^4))/(1080*S^2) + (-105 + 1476*S^2 + 779*S^4)/(48*S^2) + ((4 + S^4)*HPL[{4}, -S^2])/S^2 + ((-57 - 52*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (8*(-1 + 5*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(-1 + 26*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((17 + 3*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((395*(-1 + S^4))/(36*S^2) + (757*Pi^4*(1 + S^4))/(3240*S^2) + (Pi^2*(-36 + 77*S^2 + 113*S^4))/(54*S^2) + ((53*Pi^2*(1 + S^4))/(27*S^2) + (77*(1 + 2*S^2 + S^4))/(9*S^2))*HPL[{2}, -S^2] + ((21 + 44*S^2 + 23*S^4)*HPL[{3}, -S^2])/(3*S^2) + (46*(1 + S^4)*HPL[{4}, -S^2])/(9*S^2) - (44*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (88*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((35 + 44*S^2 + 9*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((-85 - 116*S^2 - 208*S^4)/(6*S^2) + (Pi^2*(-44 - 106*S^2 - 113*S^4))/(18*S^2) - (4*(-3 + 11*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((73*(-1 + S^4))/(16*S^2) + (Pi^2*(-53 + 26*S^2 + 76*S^4))/(72*S^2) + ((4 + 13*S^4)*HPL[{3}, -S^2])/(3*S^2) - (17*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((3 + 14*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(59 + 106*S^2 + 100*S^4))/(9*S^2) + (293 + 232*S^2 + 293*S^4)/(6*S^2) + (4*(-1 + 26*S^4)*Zeta[3])/(3*S^2)) + Log[T]^3*((-277*Pi^4*S^2)/540 + (Pi^2*(-17 - 40*S^2))/18 - (55*S^2*HPL[{0}, S^2]^4)/108 - (140*(-1 + S^4)*HPL[{1}, -S^2]^3)/(27*S^2) + HPL[{0}, S^2]^3*((-54 - 139*S^2)/54 + ((-1 - S^4)*HPL[{1}, -S^2])/S^2) + ((Pi^2*(-43 - 70*S^4))/(27*S^2) - (2*(20 + 17*S^2 + 20*S^4))/(3*S^2))*HPL[{2}, -S^2] - (3*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + HPL[{0}, S^2]^2*((-5*Pi^2*S^2)/3 + (-17 - 40*S^2)/6 + ((-35 - 132*S^2 - 97*S^4)*HPL[{1}, -S^2])/(18*S^2) - (11*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + ((-8 - 35*S^4)*HPL[{2}, -S^2])/(9*S^2)) + HPL[{1}, -S^2]^2*((-106*(-1 + S^4))/(9*S^2) - (11*Pi^2*(1 + S^4))/(9*S^2) - (44*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((37 - 132*S^2 - 101*S^4)*HPL[{3}, -S^2])/(9*S^2) - (4*(15 + 13*S^4)*HPL[{4}, -S^2])/(9*S^2) + (8*(8 + 33*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (8*(18 + 17*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (280*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) - (4*(33 + 16*S^2)*Zeta[3])/9 + HPL[{0}, S^2]*((Pi^2*(-54 - 209*S^2))/54 - (13*(-9 + 11*S^2))/9 + ((Pi^2*(-1 - S^4))/S^2 - (106*(-1 + S^4))/(9*S^2))*HPL[{1}, -S^2] - (70*(-1 + S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + ((5 - 73*S^4)*HPL[{2}, -S^2])/(9*S^2) + (2*(3 + S^4)*HPL[{3}, -S^2])/(9*S^2) - (8*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (4*S^2*Zeta[3])/9) + HPL[{1}, -S^2]*((Pi^2*(35 - 132*S^2 - 167*S^4))/(54*S^2) - (143*(-1 + S^4))/(9*S^2) - (44*(1 + S^2)^2*HPL[{2}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (88*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (44*(1 + S^4)*Zeta[3])/(3*S^2))) + HPL[{0}, S^2]^3*((7*Pi^4*S^2)/120 + (-169 + 308*S^2)/72 + (Pi^2*(-137 + 718*S^2))/432 + ((-23 + 116*S^2 + 123*S^4)*HPL[{1}, -S^2]^3)/(108*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^4)/(4*S^2) + ((-6 + 2*S^2 + 71*S^4)/(36*S^2) + (Pi^2*(3 + 76*S^4))/(216*S^2))*HPL[{2}, -S^2] + ((1 + 7*S^4)*HPL[{2}, -S^2]^2)/(24*S^2) + HPL[{1}, -S^2]^2*((77*Pi^2*(1 + S^4))/(216*S^2) + (-67 + 102*S^2 + 153*S^4)/(72*S^2) + (11*(1 + S^4)*HPL[{2}, -S^2])/(18*S^2)) + ((-5 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(24*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/(4*S^2) + ((23 - 52*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(36*S^2) - S^2*HPL[{3, 1}, -S^2] + ((3 + 26*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + ((10 + 83*S^2)*Zeta[3])/18 + HPL[{1}, -S^2]*((-62 + 33*S^2 + 95*S^4)/(36*S^2) + (Pi^2*(-143 + 316*S^2 + 443*S^4))/(432*S^2) + ((-13 + 48*S^2 + 53*S^4)*HPL[{2}, -S^2])/(36*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/(6*S^2) - (11*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (5*(1 + S^4)*Zeta[3])/(9*S^2))) + ((55*Pi^2*S^2)/6 + (394 + 139*S^2)/12)*Zeta[5] + HPL[{0}, S^2]^2*((7*Pi^2*(35 + 108*S^2))/288 + (721 + 1095*S^2)/96 + (Pi^4*(911 + 1223*S^2))/2160 + ((35 + 132*S^2 + 97*S^4)*HPL[{1}, -S^2]^4)/(72*S^2) + (11*(1 + S^4)*HPL[{1}, -S^2]^5)/(30*S^2) + ((-12 + 26*S^2 + 35*S^4)*HPL[{2}, -S^2]^2)/(24*S^2) + HPL[{1}, -S^2]^3*((41*Pi^2*(1 + S^4))/(54*S^2) + (17 + 77*S^2 + 60*S^4)/(18*S^2) + (20*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((Pi^2*(2 + 3*S^4))/(12*S^2) + (-11 + 30*S^2 + 61*S^4)/(24*S^2))*HPL[{3}, -S^2] + ((1 + 28*S^2 + 31*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((19 + 20*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-42 - 104*S^2 - 25*S^4)/(12*S^2) - (2*Pi^2*(9 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((-7 - 80*S^2 - 107*S^4)*HPL[{3, 1}, -S^2])/(12*S^2) + ((5 - 2*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((7 - 31*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((9 + 40*S^2 + 50*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((33 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (2*(17 + 2*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (2*(32 + 5*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((95*Pi^2*S^2)/36 + (12 + 19*S^2)/8)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(36 + 178*S^2 + 257*S^4))/(144*S^2) + (74 + 206*S^2 + 293*S^4)/(48*S^2) + ((-5 + 2*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-33 - S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((-1 + S^4)*Zeta[3])/(2*S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(9 + 42*S^2 + 31*S^4))/(18*S^2) + (95 + 396*S^2 + 301*S^4)/(48*S^2) + ((33 + 76*S^2 + 51*S^4)*HPL[{2}, -S^2])/(12*S^2) + (3*(1 + S^4)*HPL[{3}, -S^2])/(2*S^2) - (20*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((911*Pi^4*(1 + S^4))/(2160*S^2) + (Pi^2*(125 + 788*S^2 + 599*S^4))/(288*S^2) + (305 + 1112*S^2 + 807*S^4)/(96*S^2) + ((89*Pi^2*(1 + S^4))/(72*S^2) + (67 + 180*S^2 + 145*S^4)/(24*S^2))*HPL[{2}, -S^2] + (13*(1 + S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + ((13 + 28*S^2 + 31*S^4)*HPL[{3}, -S^2])/(12*S^2) + (3*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((-33 - 76*S^2 - 51*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) - (22*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (40*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(3 + 7*S^2 + 2*S^4)*Zeta[3])/(3*S^2)) + (55*S^2*Zeta[5])/3) + Log[T]^2*((Pi^2*(116 + 293*S^2))/72 + (Pi^4*(1514 + 2441*S^2))/2160 + (5*S^2*HPL[{0}, S^2]^5)/36 + (35*(-1 + S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + HPL[{0}, S^2]^4*((7*(14 + 25*S^2))/144 + (49*(1 + S^4)*HPL[{1}, -S^2])/(72*S^2)) + (41*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^3*((106*(-1 + S^4))/(9*S^2) + (11*Pi^2*(1 + S^4))/(9*S^2) + (44*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]^3*((13*Pi^2*S^2)/18 + (-17 + 178*S^2)/36 + ((-23 + 116*S^2 + 123*S^4)*HPL[{1}, -S^2])/(36*S^2) + (3*(1 + S^4)*HPL[{1}, -S^2]^2)/(2*S^2) + ((3 + 26*S^4)*HPL[{2}, -S^2])/(18*S^2)) + ((Pi^2*(3 + 34*S^4))/(9*S^2) + (-19 + 103*S^2 + 53*S^4)/(3*S^2))*HPL[{3}, -S^2] + ((55 + 92*S^2 + 131*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((17 + 67*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((Pi^2*(-7 - 4*S^4))/S^2 - (2*(17 + 103*S^2 + 17*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + ((-81 - 132*S^2 - 119*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (4*(-1 + 26*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (4*(5 + 88*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (8*(25 + 33*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (36*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(-42 + 11*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((43*Pi^2*S^2)/9 + (103 + 34*S^2)/3)*Zeta[3] + HPL[{0}, S^2]^2*((Pi^2*(164 + 275*S^2))/72 + (116 + 293*S^2)/24 + ((35 + 132*S^2 + 97*S^4)*HPL[{1}, -S^2]^2)/(12*S^2) + (11*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + ((9 + 40*S^2 + 50*S^4)*HPL[{2}, -S^2])/(6*S^2) + HPL[{1}, -S^2]*((41*Pi^2*(1 + S^4))/(18*S^2) + (17 + 77*S^2 + 60*S^4)/(6*S^2) + (20*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((1 + 3*S^4)*HPL[{3}, -S^2])/(2*S^2) + ((-32 - 5*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + 4*S^2*Zeta[3]) + HPL[{1}, -S^2]^2*((143*(-1 + S^4))/(6*S^2) + (Pi^2*(-35 + 132*S^2 + 167*S^4))/(36*S^2) + (22*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 + (22*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (44*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (22*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((395*(-1 + S^4))/(12*S^2) + (757*Pi^4*(1 + S^4))/(1080*S^2) + (Pi^2*(-36 + 77*S^2 + 113*S^4))/(18*S^2) + ((53*Pi^2*(1 + S^4))/(9*S^2) + (77*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2}, -S^2] + ((21 + 44*S^2 + 23*S^4)*HPL[{3}, -S^2])/S^2 + (46*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (44*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - (44*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (88*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((35 + 44*S^2 + 9*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(59 + 106*S^2 + 100*S^4))/(18*S^2) + (293 + 232*S^2 + 293*S^4)/(12*S^2) + (2*(-1 + 26*S^4)*HPL[{3}, -S^2])/(3*S^2) + (18*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (2*(-1 + 26*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]*((107*Pi^4*S^2)/180 + (Pi^2*(-83 + 284*S^2))/36 + (-356 + 395*S^2)/12 + ((53*(-1 + S^4))/(3*S^2) + (3*Pi^2*(1 + S^4))/(2*S^2))*HPL[{1}, -S^2]^2 + (70*(-1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + ((Pi^2*(5 + 28*S^4))/(18*S^2) + (-10 - 26*S^2 + 53*S^4)/(3*S^2))*HPL[{2}, -S^2] + ((1 + S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + ((-25 - 12*S^2 + 21*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((5 + S^4)*HPL[{4}, -S^2])/(3*S^2) + ((73 - 5*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*HPL[{3, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((2 + 19*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((143*(-1 + S^4))/(6*S^2) + (Pi^2*(-93 + 116*S^2 + 193*S^4))/(36*S^2) + (13*(-1 + S^4)*HPL[{2}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (2*(1 + S^4)*Zeta[3])/(3*S^2))) + (110*S^2*Zeta[5])/3) + HPL[{1}, -S^2]^2*((393*(-1 + S^4))/(16*S^2) + (Pi^2*(-191 + 396*S^2 + 587*S^4))/(144*S^2) + (Pi^4*(203 + 2988*S^2 + 2865*S^4))/(4320*S^2) + (3*(-1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((7*Pi^2*(1 + S^4))/(3*S^2) + (73 + 154*S^2 + 81*S^4)/(6*S^2))*HPL[{3}, -S^2] + (2*(1 + 23*S^2 + 22*S^4)*HPL[{4}, -S^2])/(3*S^2) + (47*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-53*Pi^2*(1 + S^4))/(9*S^2) - (77*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + ((-15 - 44*S^2 - 29*S^4)*HPL[{3, 1}, -S^2])/S^2 - (44*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (178*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (44*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (44*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((5*Pi^2*(1 + S^4))/(2*S^2) + (7*(10 + 11*S^2 + S^4))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*((33*(1 + 2*S^2 + S^4))/(2*S^2) + (Pi^2*(99 + 208*S^2 + 117*S^4))/(36*S^2) + (22*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (26*(1 + S^4)*Zeta[3])/(3*S^2)) + (67*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(367 + 438*S^2 + 586*S^4))/(144*S^2) + (1095 + 1442*S^2 + 1095*S^4)/(48*S^2) + (Pi^4*(1342 + 2698*S^2 + 3279*S^4))/(4320*S^2) + ((Pi^2*(-3 + 14*S^4))/(9*S^2) + (27 + 112*S^2 + 61*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((-41 + 97*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((-11 + 7*S^4)*HPL[{5}, -S^2])/(2*S^2) + ((17*(-1 + S^4))/(6*S^2) + (Pi^2*(-30 + 13*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] - (2*(-17 + 24*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (4*(4 + 13*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-5 - 51*S^4)*HPL[{4, 1}, -S^2])/S^2 + (82*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (68*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (4*(52 + 25*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (36*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-8 + 102*S^2 + 9*S^4)/(6*S^2) + (Pi^2*(-4 + 29*S^4))/(18*S^2))*Zeta[3] + ((-10 + 41*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]*((124*(-1 + S^4))/(3*S^2) + (11563*Pi^6*(1 + S^4))/(90720*S^2) + (Pi^2*(-485 + 1112*S^2 + 1597*S^4))/(288*S^2) + (Pi^4*(291 + 7064*S^2 + 7093*S^4))/(8640*S^2) + ((13*(-1 + S^4))/(4*S^2) + (13*Pi^2*(1 + S^4))/(36*S^2))*HPL[{2}, -S^2]^2 + (13*(1 + S^4)*HPL[{2}, -S^2]^3)/(9*S^2) - (4*(1 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((41*Pi^2*(1 + S^4))/(18*S^2) + (-15 + 56*S^2 + 71*S^4)/(3*S^2))*HPL[{4}, -S^2] + ((-79 + 204*S^2 + 251*S^4)*HPL[{5}, -S^2])/(6*S^2) + (99*(1 + S^4)*HPL[{6}, -S^2])/(2*S^2) + ((-55*Pi^2*(1 + S^4))/(9*S^2) - (2*(17 + 77*S^2 + 60*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] - (2*(29 + 48*S^2 + 11*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(89 + 190*S^2 + 77*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (110*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((106*Pi^2*(1 + S^4))/(9*S^2) + (154*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (12*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (2*(3 + 44*S^2 + 41*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (104*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (404*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (88*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (176*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((127 + 132*S^2 + 5*S^4)/(4*S^2) + (Pi^2*(129 + 188*S^2 + 43*S^4))/(36*S^2))*Zeta[3] + (3*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-99 - 208*S^2 - 117*S^4))/(18*S^2) - (33*(1 + 2*S^2 + S^4))/S^2 - (52*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(19 + 40*S^2 + 25*S^4))/(9*S^2) + (85 + 198*S^2 + 113*S^4)/(6*S^2) - (44*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((1349*Pi^4*(1 + S^4))/(2160*S^2) + (139*(1 + 2*S^2 + S^4))/(6*S^2) + (Pi^2*(221 + 488*S^2 + 299*S^4))/(72*S^2) + ((29 + 48*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (6*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (8*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((33 + 56*S^2 + 15*S^4)*Zeta[3])/(3*S^2)) + ((217 + 260*S^2 + 59*S^4)*Zeta[5])/(6*S^2)) + Log[T]*((-4153*Pi^6*S^2)/15120 + (Pi^4*(-2390 - 6017*S^2))/4320 + (Pi^2*(-374 - 775*S^2))/144 - (S^2*HPL[{0}, S^2]^6)/16 - (14*(-1 + S^4)*HPL[{1}, -S^2]^5)/(9*S^2) + HPL[{0}, S^2]^5*((-5 - 16*S^2)/36 - (5*(1 + S^4)*HPL[{1}, -S^2])/(36*S^2)) + ((Pi^2*(17 - 26*S^4))/(18*S^2) - (95*(-1 + S^4))/(12*S^2))*HPL[{2}, -S^2]^2 + ((-1 - S^4)*HPL[{2}, -S^2]^3)/S^2 + HPL[{0}, S^2]^4*((-95*Pi^2*S^2)/216 + (-110 - 431*S^2)/288 + ((-37 - 204*S^2 - 151*S^4)*HPL[{1}, -S^2])/(144*S^2) - (49*(1 + S^4)*HPL[{1}, -S^2]^2)/(72*S^2) + ((-9 - 46*S^4)*HPL[{2}, -S^2])/(72*S^2)) + HPL[{1}, -S^2]^4*((-53*(-1 + S^4))/(9*S^2) - (11*Pi^2*(1 + S^4))/(18*S^2) - (22*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + (2*(-2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((-117 - 116*S^2 - 365*S^4)/(12*S^2) - (43*Pi^2*(1 + S^4))/(18*S^2))*HPL[{4}, -S^2] + ((113 - 188*S^2 - 297*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-90 - 143*S^4)*HPL[{6}, -S^2])/(3*S^2) + (18*(-1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((4*Pi^2*(11 + 17*S^4))/(9*S^2) + (89 + 102*S^2 + 151*S^4)/(3*S^2))*HPL[{3, 1}, -S^2] + ((-7 + 88*S^2 + 85*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-41 + 356*S^2 + 327*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (3*(-1 + S^2)*(1 + S^2)*HPL[{4, 2}, -S^2])/S^2 + (2*(33 + 67*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-4*(20 + 17*S^2 + 20*S^4))/S^2 - (2*Pi^2*(43 + 70*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + (92*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (2*(-101 - 132*S^2 + 37*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (24*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (16*(21 + 20*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (16*(8 + 33*S^2 + 8*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(18 + 17*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (560*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((-280 - 103*S^2)/6 - (5*Pi^2*(18 + 13*S^2))/18)*Zeta[3] - 2*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(40 + 102*S^2 + 17*S^4))/(9*S^2) + (103 + 560*S^2 + 103*S^4)/(6*S^2) + (36*Zeta[3])/S^2) + HPL[{0}, S^2]^3*((Pi^2*(-154 - 459*S^2))/216 + (76 - 219*S^2)/36 + ((23 - 116*S^2 - 123*S^4)*HPL[{1}, -S^2]^2)/(36*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^3)/S^2 - ((3 + 7*S^2)*(-1 + 17*S^2)*HPL[{2}, -S^2])/(36*S^2) + HPL[{1}, -S^2]*((67 - 102*S^2 - 153*S^4)/(36*S^2) - (77*Pi^2*(1 + S^4))/(108*S^2) - (11*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((1 + S^4)*HPL[{3}, -S^2])/(6*S^2) + ((19 - 4*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (10*S^2*Zeta[3])/9) + HPL[{1}, -S^2]^2*((Pi^2*(36 - 77*S^2 - 113*S^4))/(18*S^2) - (395*(-1 + S^4))/(12*S^2) - (757*Pi^4*(1 + S^4))/(1080*S^2) + ((-53*Pi^2*(1 + S^4))/(9*S^2) - (77*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2}, -S^2] + ((-21 - 44*S^2 - 23*S^4)*HPL[{3}, -S^2])/S^2 - (46*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (44*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (44*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-35 - 44*S^2 - 9*S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((Pi^2*(35 - 132*S^2 - 167*S^4))/(54*S^2) - (143*(-1 + S^4))/(9*S^2) - (44*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (88*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (44*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((49 - 560*S^2 - 255*S^4)/(12*S^2) + (Pi^2*(21 - 80*S^2 - 63*S^4))/(18*S^2) - (4*(-23 + 4*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(4 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((-775 - 748*S^2 - 775*S^4)/(24*S^2) + (Pi^2*(-145 - 178*S^2 - 240*S^4))/(36*S^2) - (31*Pi^4*(16 + 35*S^4))/(1080*S^2) + ((-1 - 44*S^2 - 47*S^4)*HPL[{3}, -S^2])/(3*S^2) + ((17 - 13*S^4)*HPL[{4}, -S^2])/(3*S^2) - (46*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(-14 + 13*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (36*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(-8 + 30*S^2 + 15*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^2*((-163*Pi^4*S^2)/180 + (-374 - 775*S^2)/48 + (Pi^2*(-212 - 671*S^2))/144 + ((-35 - 132*S^2 - 97*S^4)*HPL[{1}, -S^2]^3)/(18*S^2) - (11*(1 + S^4)*HPL[{1}, -S^2]^4)/(6*S^2) + ((-25 - 76*S^2 - 120*S^4)/(12*S^2) + (Pi^2*(-17 - 81*S^4))/(36*S^2))*HPL[{2}, -S^2] + ((7 - 25*S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + HPL[{1}, -S^2]^2*((-17 - 77*S^2 - 60*S^4)/(6*S^2) - (41*Pi^2*(1 + S^4))/(18*S^2) - (20*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((5 - 28*S^2 - 25*S^4)*HPL[{3}, -S^2])/(12*S^2) + ((-13 - 17*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((24 + 36*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(4 + 17*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (2*(8 + 35*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-8 - 11*S^2)*Zeta[3])/2 + HPL[{1}, -S^2]*((-95 - 396*S^2 - 301*S^4)/(24*S^2) + (Pi^2*(-9 - 42*S^2 - 31*S^4))/(9*S^2) + ((-33 - 76*S^2 - 51*S^4)*HPL[{2}, -S^2])/(6*S^2) - (3*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (40*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(1 + S^4)*Zeta[3])/S^2)) + HPL[{0}, S^2]*((1114 - 1179*S^2)/24 + (Pi^4*(-316 - 1141*S^2))/540 + (Pi^2*(193 - 362*S^2))/36 + ((Pi^2*(-1 - S^4))/S^2 - (106*(-1 + S^4))/(9*S^2))*HPL[{1}, -S^2]^3 - (35*(-1 + S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + ((-4 + 2*S^2 - 13*S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((27 - 2*S^2 - 45*S^4)/(6*S^2) + (Pi^2*(3 + 2*S^4))/(9*S^2))*HPL[{3}, -S^2] + ((1 + 4*S^2 - 17*S^4)*HPL[{4}, -S^2])/(3*S^2) + (2*(2 + 3*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((Pi^2*(17 - 6*S^4))/(9*S^2) + (2*(-53 + 26*S^2 + 10*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + ((-5 - 4*S^2 + 69*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(3 + 2*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (2*(9 + 7*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (2*(-5 + 73*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (4*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(3 + 2*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (16*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (-(Pi^2*S^2) + (21 - 31*S^2)/3)*Zeta[3] + HPL[{2}, -S^2]*((44 + 82*S^2 - 139*S^4)/(6*S^2) + (Pi^2*(2 - 11*S^2 - 48*S^4))/(9*S^2) - (2*(3 + 2*S^4)*HPL[{3}, -S^2])/(3*S^2) - (2*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]*((Pi^2*(173 - 102*S^2 - 259*S^4))/(36*S^2) - (395*(-1 + S^4))/(12*S^2) - (79*Pi^4*(1 + S^4))/(135*S^2) + ((-21*(-1 + S^4))/S^2 - (11*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] + ((23 + 4*S^2 - 19*S^4)*HPL[{3}, -S^2])/(3*S^2) + (4*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (26*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((19 - 4*S^2 - 23*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(93 - 116*S^2 - 193*S^4))/(36*S^2) - (143*(-1 + S^4))/(6*S^2) - (13*(-1 + S^4)*HPL[{2}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (2*(1 + S^4)*Zeta[3])/(3*S^2))) + ((-134 - 51*S^2)*Zeta[5])/3 + HPL[{1}, -S^2]*((Pi^4*(-203 - 2988*S^2 - 2865*S^4))/(2160*S^2) + (Pi^2*(191 - 396*S^2 - 587*S^4))/(72*S^2) - (393*(-1 + S^4))/(8*S^2) - (3*(-1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((-73 - 154*S^2 - 81*S^4)/(3*S^2) - (14*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] - (4*(1 + 23*S^2 + 22*S^4)*HPL[{4}, -S^2])/(3*S^2) - (94*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((106*Pi^2*(1 + S^4))/(9*S^2) + (154*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (2*(15 + 44*S^2 + 29*S^4)*HPL[{3, 1}, -S^2])/S^2 + (88*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (356*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (88*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (176*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-5*Pi^2*(1 + S^4))/S^2 - (14*(10 + 11*S^2 + S^4))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-99 - 208*S^2 - 117*S^4))/(18*S^2) - (33*(1 + 2*S^2 + S^4))/S^2 - (44*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (52*(1 + S^4)*Zeta[3])/(3*S^2)) - (134*(1 + S^4)*Zeta[5])/(3*S^2))) + HPL[{0}, S^2]*((103*Pi^6*S^2)/2160 + (Pi^2*(-694 + 1011*S^2))/144 + (-1919 + 1984*S^2)/48 + (Pi^4*(-874 + 3463*S^2))/2160 + ((53*(-1 + S^4))/(18*S^2) + (Pi^2*(1 + S^4))/(4*S^2))*HPL[{1}, -S^2]^4 + (7*(-1 + S^4)*HPL[{1}, -S^2]^5)/(9*S^2) + ((Pi^2*(2 + 11*S^4))/(36*S^2) + (4 - 38*S^2 + 43*S^4)/(12*S^2))*HPL[{2}, -S^2]^2 - (2*(1 + S^4)*HPL[{2}, -S^2]^3)/(9*S^2) + ((-4 - 3*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((Pi^2*(-1 - 2*S^4))/(9*S^2) + (13 + 26*S^2 + 21*S^4)/(6*S^2))*HPL[{4}, -S^2] + ((1 - 10*S^2 - S^4)*HPL[{5}, -S^2])/(3*S^2) - (2*(15 + 13*S^4)*HPL[{6}, -S^2])/(3*S^2) + ((-1 - S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((3 + 26*S^2 - 99*S^4)/(6*S^2) + (Pi^2*(-1 - 9*S^4))/(9*S^2))*HPL[{3, 1}, -S^2] - (4*(4 - 2*S^2 + 3*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-23 + 28*S^2 - 37*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (2*(6 + 7*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((Pi^2*(5 + 28*S^4))/(9*S^2) + (2*(-10 - 26*S^2 + 53*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (4*(13 - 2*S^2 + 4*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + ((-181 + 12*S^2 - 27*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (16*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (2*(19 + 23*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (2*(-73 + 5*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (8*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (16*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((-28 + 41*S^2)/4 + (Pi^2*(22 + 185*S^2))/36)*Zeta[3] - 2*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^3*((143*(-1 + S^4))/(18*S^2) + (Pi^2*(-93 + 116*S^2 + 193*S^4))/(108*S^2) + (13*(-1 + S^4)*HPL[{2}, -S^2])/(3*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) + (2*(1 + S^4)*Zeta[3])/(9*S^2)) + HPL[{2, 1}, -S^2]*((139 - 82*S^2 - 44*S^4)/(6*S^2) + (Pi^2*(24 - 13*S^2 + 2*S^4))/(9*S^2) - (2*(5 + 4*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-5 - 3*S^2 + 3*S^4))/(9*S^2) + (-15 + 42*S^2 + 73*S^4)/(12*S^2) + (2*(7 + 6*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(4 + 5*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-4 - 6*S^2 + 31*S^4))/(9*S^2) + (Pi^4*(13 + 87*S^4))/(270*S^2) + (-160 - 182*S^2 + 379*S^4)/(24*S^2) + (2*(4 - 2*S^2 + 3*S^4)*HPL[{3}, -S^2])/(3*S^2) + (2*(4 + 3*S^4)*HPL[{4}, -S^2])/(3*S^2) + (2*(13 - 2*S^2 + 4*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(3 + 2*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-5 + 12*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((395*(-1 + S^4))/(24*S^2) + (79*Pi^4*(1 + S^4))/(270*S^2) + (Pi^2*(-173 + 102*S^2 + 259*S^4))/(72*S^2) + ((21*(-1 + S^4))/(2*S^2) + (11*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2] + ((-23 - 4*S^2 + 19*S^4)*HPL[{3}, -S^2])/(6*S^2) - (2*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (13*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((-19 + 4*S^2 + 23*S^4)*Zeta[3])/(6*S^2)) + 4*(1 + 8*S^2)*Zeta[5] + HPL[{1}, -S^2]*((393*(-1 + S^4))/(16*S^2) + (Pi^2*(-89 + 22*S^2 + 111*S^4))/(24*S^2) + (Pi^4*(-489 + 652*S^2 + 1101*S^4))/(1080*S^2) + (3*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^2)/(2*S^2) + ((-2*Pi^2*(1 + S^4))/(9*S^2) + (-19 + 26*S^2 + 29*S^4)/(6*S^2))*HPL[{3}, -S^2] + ((-13 - 4*S^2 + 9*S^4)*HPL[{4}, -S^2])/(3*S^2) - (16*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-21*(-1 + S^4))/S^2 - (11*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((41 + 4*S^2 - 37*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (28*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (26*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((11*Pi^2*(1 + S^4))/(18*S^2) + (-24 - 13*S^2 + 19*S^4)/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*((61*(-1 + S^4))/(4*S^2) + (Pi^2*(-13 + 12*S^2 + 23*S^4))/(9*S^2) - (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (4*(1 + S^4)*Zeta[3])/(3*S^2)) + (4*(1 + S^4)*Zeta[5])/S^2)) + 75*S^2*Zeta[7];
Et4uvwT3F1=(907*(-1 + S^2))/(48*S) + (Pi^6*S*(22448 + 10885*S^2))/(90720*(1 + S^2)) + (Pi^2*(-182 + 1032*S^2 + 21*S^4))/(144*S) + (Pi^4*(-480 + 14435*S^2 + 15427*S^4 + 672*S^6))/(8640*S*(1 + S^2)) + (7*(1 + 3*S^2)*HPL[{1}, -S^2]^6)/(27*S) + HPL[{0}, S^2]^6*(S/(32*(1 + S^2)) + (S*HPL[{1}, -S^2])/16) + ((3 + 42*S^2 + 13*S^4)*HPL[{2}, -S^2]^3)/(18*S*(1 + S^2)) + HPL[{0}, S^2]^5*((5*Pi^2*S)/216 + (S*(233 + 27*S^2))/288 + ((27 + 118*S^2 + 71*S^4)*HPL[{1}, -S^2])/(144*S*(1 + S^2)) + (5*S*HPL[{1}, -S^2]^2)/36 + (5*S*HPL[{2}, -S^2])/36) + HPL[{1}, -S^2]^5*((11*Pi^2*S)/45 + (-9 + 151*S^2 + 169*S^4 + 9*S^6)/(90*S^3) + (44*S*HPL[{2}, -S^2])/15) + ((2 - 39*S^2 - 33*S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((107*Pi^2*S)/18 + (-45 + 235*S^2 + 649*S^4 + 407*S^6 + 30*S^8)/(3*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((320 + 1414*S^2 + 797*S^4)*HPL[{6}, -S^2])/(6*S*(1 + S^2)) + (458*S*HPL[{7}, -S^2])/3 - (56*S*HPL[{2, 1}, -S^2]^2)/3 + ((-56*Pi^2*S)/9 + (23 + 10*S^2 - 15*S^4 + 6*S^6)/(3*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + (-23*Pi^2*S + (5 - 30*S^2 - 106*S^4 - 74*S^6 + 5*S^8)/(S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] - (3*(-1 + 11*S^2)*HPL[{4, 2}, -S^2])/(2*S) - 10*S*HPL[{4, 3}, -S^2] + ((-88 - 675*S^2 - 477*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - 39*S*HPL[{5, 2}, -S^2] - (638*S*HPL[{6, 1}, -S^2])/3 + ((-52*Pi^2*S)/9 + (2*(-3 + 65*S^2 - 13*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + ((-20*Pi^2*S)/9 + (2*(-15 + 236*S^2 + 36*S^4 + 6*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] + (3*(-1 + 3*S^2)*HPL[{3, 1, 2}, -S^2])/S + ((3 + 186*S^2 + 79*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (208*S*HPL[{3, 2, 2}, -S^2])/3 + 192*S*HPL[{3, 3, 1}, -S^2] + (2*(29 + 434*S^2 + 203*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 198*S*HPL[{4, 1, 2}, -S^2] + 566*S*HPL[{4, 2, 1}, -S^2] + (3580*S*HPL[{5, 1, 1}, -S^2])/3 + (-16*Pi^2*S + (2*(9 - 136*S^2 - 24*S^4 + 9*S^6))/(3*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (272*S*HPL[{2, 2, 2, 1}, -S^2])/3 - (4*(13 + 172*S^2 + 93*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (400*S*HPL[{3, 1, 1, 2}, -S^2])/3 + (400*S*HPL[{3, 1, 2, 1}, -S^2])/3 + (1216*S*HPL[{3, 2, 1, 1}, -S^2])/3 + (3488*S*HPL[{4, 1, 1, 1}, -S^2])/3 + (16*(1 + 65*S^2 + 31*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 144*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 432*S*HPL[{2, 2, 1, 1, 1}, -S^2] + (3104*S*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - (992*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + ((-14*Pi^2*S)/27 - (14*S*HPL[{0}, S^2])/3 - (14*S*HPL[{0}, S^2]^2)/9 - (14*(1 + 3*S^2)*HPL[{1}, -S^2])/(9*S) - (28*S*HPL[{2}, -S^2])/9)*Log[T]^5 + ((157*Pi^4*S)/90 - (S*(-133 + 15*S^2))/6 - (Pi^2*S*(-78 - 73*S^2 + 9*S^4))/(18*(1 + S^2)))*Zeta[3] - (S*(8 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((Pi^2*(-19 - 296*S^2 - 167*S^4))/(18*S*(1 + S^2)) + (-1 - 69*S^2 - 103*S^4 + S^6)/(2*S^3) - (88*S*Zeta[3])/3) + HPL[{4}, -S^2]*((Pi^2*(17 + 266*S^2 + 167*S^4))/(36*S*(1 + S^2)) + (36 + 509*S^2 + 437*S^4 + 28*S^6)/(8*S^3) - 2*S*HPL[{2, 1}, -S^2] - (16*S*Zeta[3])/3) + HPL[{0}, S^2]^4*((Pi^2*S*(303 + 119*S^2))/(864*(1 + S^2)) + (-18 + 1157*S^2 + 1303*S^4 + 96*S^6)/(576*S*(1 + S^2)) + ((51 + 249*S^2 + 100*S^4)*HPL[{1}, -S^2]^2)/(144*S*(1 + S^2)) + (49*S*HPL[{1}, -S^2]^3)/108 + (7*S*(24 + 17*S^2)*HPL[{2}, -S^2])/(144*(1 + S^2)) + HPL[{1}, -S^2]*((23*Pi^2*S)/54 + (-9 + 356*S^2 + 686*S^4 + 324*S^6 - 13*S^8)/(288*S^3*(1 + S^2)) + (49*S*HPL[{2}, -S^2])/72) + (S*HPL[{3}, -S^2])/8 - (S*HPL[{2, 1}, -S^2])/12 + (83*S*Zeta[3])/36) + HPL[{1}, -S^2]^4*((13*(1 + S^2)*(-3 + 32*S^2 + 3*S^4))/(72*S^3) + (Pi^2*(64 + 295*S^2 + 165*S^4))/(108*S*(1 + S^2)) + ((9 + 62*S^2 + 9*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) + (22*S*HPL[{3}, -S^2])/3 - (44*S*HPL[{2, 1}, -S^2])/3 + (22*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((-45 + 149*S^2)/(24*S) + (Pi^2*(1 + 64*S^2 + 50*S^4))/(36*S*(1 + S^2)) + (26*S*HPL[{3}, -S^2])/3 - (34*S*HPL[{2, 1}, -S^2])/3 + (28*S*Zeta[3])/3) + Log[T]^4*((-1 + S^2)/(2*S) + (Pi^2*S*(95 + 62*S^2))/(54*(1 + S^2)) + (28*S*HPL[{0}, S^2]^3)/27 + (35*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(9*S) + HPL[{0}, S^2]^2*((S*(95 + 62*S^2))/(18*(1 + S^2)) + (11*S*HPL[{1}, -S^2])/3) + (2*(1 + 65*S^2 + 31*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{0}, S^2]*((28*Pi^2*S)/27 + (S*(169 + 9*S^2))/18 + (35*(1 + 3*S^2)*HPL[{1}, -S^2])/(9*S) + (4*S*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]*((11*Pi^2*S)/9 + (-9 + 151*S^2 + 169*S^4 + 9*S^6)/(18*S^3) + (44*S*HPL[{2}, -S^2])/3) + (118*S*HPL[{3}, -S^2])/9 - (124*S*HPL[{2, 1}, -S^2])/9 + (124*S*Zeta[3])/9) + HPL[{2, 1, 1}, -S^2]*((2*(53 + 105*S^2))/(3*S) + (2*Pi^2*(2 + 117*S^2 + 62*S^4))/(9*S*(1 + S^2)) + (208*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-22*Pi^4*S)/45 + (15 - 237*S^2 - 133*S^4 + 15*S^6)/(6*S^3) + (Pi^2*(9 - 123*S^2 - 159*S^4 - 17*S^6 + 6*S^8))/(18*S^3*(1 + S^2)) - 24*S*HPL[{3, 1}, -S^2] - 72*S*HPL[{2, 1, 1}, -S^2] - (52*S*Zeta[3])/(3*(1 + S^2))) + HPL[{3}, -S^2]*((307*Pi^4*S)/540 + (-21 + 1517*S^2 + 1563*S^4 - 99*S^6)/(48*S^3) + (Pi^2*(-6 + 27*S^2 + 104*S^4 + 67*S^6))/(18*S^3*(1 + S^2)) + 2*S*HPL[{4}, -S^2] + ((-17 - 10*S^2 + 51*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (80*S*HPL[{3, 1}, -S^2])/3 + (208*S*HPL[{2, 1, 1}, -S^2])/3 + (4*(-1 - S^2 + S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((757*Pi^4*S)/1620 + ((1 + S^2)*(-67 + 624*S^2 + 67*S^4))/(36*S^3) + (Pi^2*(-9 + 156*S^2 + 164*S^4 + 3*S^6))/(54*S^3) + ((106*Pi^2*S)/27 - (2*(3 - 50*S^2 - 50*S^4 + 3*S^6))/(9*S^3))*HPL[{2}, -S^2] + (2*(5 + 33*S^2 + 6*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (92*S*HPL[{4}, -S^2])/9 - (2*(9 + 62*S^2 + 9*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (88*S*HPL[{3, 1}, -S^2])/3 + (176*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(2 - 5*S^2 + 15*S^4)*Zeta[3])/(3*S*(1 + S^2))) + Log[T]^3*((-277*Pi^4*S)/270 - (5*(-1 + S^2))/(2*S) + (Pi^2*S*(-176 + 3*S^2))/54 - (55*S*HPL[{0}, S^2]^4)/54 - (140*(1 + 3*S^2)*HPL[{1}, -S^2]^3)/(27*S) + HPL[{0}, S^2]^3*(-(S*(166 + 139*S^2))/(27*(1 + S^2)) - 2*S*HPL[{1}, -S^2]) + ((-140*Pi^2*S)/27 + (3 - 64*S^2 - 176*S^4 + 3*S^6)/(9*S^3))*HPL[{2}, -S^2] - 6*S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((-22*Pi^2*S)/9 + (9 - 151*S^2 - 169*S^4 - 9*S^6)/(9*S^3) - (88*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^2*((-10*Pi^2*S)/3 + (S*(-176 + 3*S^2))/18 + ((-29 - 155*S^2 - 60*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) - (22*S*HPL[{1}, -S^2]^2)/3 - (70*S*HPL[{2}, -S^2])/9) + (2*(-17 - 82*S^2 + S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (104*S*HPL[{4}, -S^2])/9 - (4*(-25 - 56*S^2 + 35*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (272*S*HPL[{3, 1}, -S^2])/9 - (560*S*HPL[{2, 1, 1}, -S^2])/9 + (4*S*(2 + 35*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-64 - 295*S^2 - 165*S^4))/(27*S*(1 + S^2)) - (13*(1 + S^2)*(-3 + 32*S^2 + 3*S^4))/(18*S^3) - (2*(9 + 62*S^2 + 9*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (88*S*HPL[{3}, -S^2])/3 + (176*S*HPL[{2, 1}, -S^2])/3 - (88*S*Zeta[3])/3) + HPL[{0}, S^2]*(-(Pi^2*S*(271 + 244*S^2))/(27*(1 + S^2)) + (18 - 437*S^2 - 39*S^4)/(18*S) + (-2*Pi^2*S + (9 - 151*S^2 - 169*S^4 - 9*S^6)/(9*S^3))*HPL[{1}, -S^2] - (70*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(9*S) - (2*(8 + 107*S^2)*HPL[{2}, -S^2])/(9*S) + (4*S*HPL[{3}, -S^2])/9 - (16*S*HPL[{2, 1}, -S^2])/9 + (8*S*Zeta[3])/9)) + HPL[{0}, S^2]^3*((7*Pi^4*S)/60 + (-90 + 2323*S^2 + 95*S^4)/(288*S) + (Pi^2*S*(1452 + 1607*S^2 + 147*S^4))/(432*(1 + S^2)) + ((52 + 223*S^2 + 117*S^4)*HPL[{1}, -S^2]^3)/(54*S*(1 + S^2)) + (S*HPL[{1}, -S^2]^4)/2 + ((19*Pi^2*S)/27 + (-3 + 39*S^2 + 250*S^4 + 219*S^6 + 3*S^8)/(72*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (7*S*HPL[{2}, -S^2]^2)/12 + HPL[{1}, -S^2]^2*((77*Pi^2*S)/108 + (-9 + 220*S^2 + 448*S^4 + 248*S^6 + 13*S^8)/(72*S^3*(1 + S^2)) + (11*S*HPL[{2}, -S^2])/9) + ((1 + 2*S^2 + 2*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) - (S*HPL[{4}, -S^2])/2 + ((-20 - 26*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - 2*S*HPL[{3, 1}, -S^2] + (52*S*HPL[{2, 1, 1}, -S^2])/9 + (S*(237 + 227*S^2)*Zeta[3])/(18*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(187 + 813*S^2 + 472*S^4))/(216*S*(1 + S^2)) + (-39 + 500*S^2 + 1110*S^4 + 644*S^6 + 41*S^8)/(144*S^3*(1 + S^2)) + ((23 + 97*S^2 + 52*S^4)*HPL[{2}, -S^2])/(18*S*(1 + S^2)) - (S*HPL[{3}, -S^2])/3 - (22*S*HPL[{2, 1}, -S^2])/9 + (10*S*Zeta[3])/9)) + ((55*Pi^2*S)/3 - (2*S*(-47 - 39*S^2 + 6*S^4))/(3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*(((1 + S^2)*(21 + 829*S^2 + 21*S^4))/(24*S^3) + (Pi^2*(173 + 615*S^2 + 426*S^4))/(72*S*(1 + S^2)) + (Pi^4*(10 + 3534*S^2 + 2175*S^4))/(2160*S*(1 + S^2)) + ((28*Pi^2*S)/9 + (-16 - 5*S^2 + 12*S^4 - 3*S^6)/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + ((-13 + 114*S^2 + 111*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) + 7*S*HPL[{5}, -S^2] + ((26*Pi^2*S)/9 + (3 - 65*S^2 + 13*S^4 - 3*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + ((11 - 74*S^2 - 77*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (104*S*HPL[{3, 2}, -S^2])/3 - 102*S*HPL[{4, 1}, -S^2] + (112*S*HPL[{2, 1, 1}, -S^2])/3 + (136*S*HPL[{2, 2, 1}, -S^2])/3 - (200*S*HPL[{3, 1, 1}, -S^2])/3 + 72*S*HPL[{2, 1, 1, 1}, -S^2] + ((29*Pi^2*S)/9 + (4 + S^2 - 2*S^4 - 3*S^6)/(3*S*(1 + S^2)))*Zeta[3] + (82*S*Zeta[5])/3) + HPL[{0}, S^2]^2*((Pi^4*S*(1831 + 920*S^2))/(2160*(1 + S^2)) + (-91 + 941*S^2 + 21*S^4)/(48*S) + (Pi^2*(-36 + 1577*S^2 + 1741*S^4 + 96*S^6))/(288*S*(1 + S^2)) + ((29 + 155*S^2 + 60*S^4)*HPL[{1}, -S^2]^4)/(36*S*(1 + S^2)) + (11*S*HPL[{1}, -S^2]^5)/15 + ((1 + 36*S^2 + 22*S^4)*HPL[{2}, -S^2]^2)/(12*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((41*Pi^2*S)/27 + (-9 + 161*S^2 + 159*S^4 - 3*S^6)/(36*S^3) + (40*S*HPL[{2}, -S^2])/9) + ((Pi^2*S)/2 + (-6 + 19*S^2 + 92*S^4 + 62*S^6 + 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((1 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(2*S*(1 + S^2)) + (20*S*HPL[{5}, -S^2])/3 + ((-4*Pi^2*S)/9 + (9 - 119*S^2 - 158*S^4 - 19*S^6 + 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-3 - 62*S^2 - 37*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{3, 2}, -S^2])/3 - (31*S*HPL[{4, 1}, -S^2])/3 + (2*(1 + 52*S^2 + 31*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2*S*HPL[{2, 2, 1}, -S^2])/3 + 8*S*HPL[{3, 1, 1}, -S^2] - (20*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((95*Pi^2*S)/18 - (S*(-132 - 131*S^2 + 9*S^4))/(12*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(2 + 272*S^2 + 181*S^4))/(72*S*(1 + S^2)) + (67 + 299*S^2 + 216*S^4)/(24*S*(1 + S^2)) + (2*S*HPL[{3}, -S^2])/3 - (S*HPL[{2, 1}, -S^2])/3 + S*Zeta[3]) + HPL[{1}, -S^2]^2*((Pi^2*(20 + 101*S^2 + 40*S^4))/(18*S*(1 + S^2)) + (-39 + 375*S^2 + 403*S^4 + 5*S^6)/(48*S^3) + ((21 + 148*S^2 + 47*S^4)*HPL[{2}, -S^2])/(12*S*(1 + S^2)) + 3*S*HPL[{3}, -S^2] - (40*S*HPL[{2, 1}, -S^2])/3 + 4*S*Zeta[3]) + HPL[{1}, -S^2]*((911*Pi^4*S)/1080 + ((1 + S^2)*(-67 + 561*S^2 + 30*S^4))/(48*S^3) + (Pi^2*(-9 + 254*S^2 + 503*S^4 + 240*S^6 - 8*S^8))/(72*S^3*(1 + S^2)) + ((89*Pi^2*S)/36 + (-6 + 74*S^2 + 187*S^4 + 96*S^6 - 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (13*S*HPL[{2}, -S^2]^2)/6 + ((4 + 43*S^2 + 21*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) + 6*S*HPL[{4}, -S^2] + ((-21 - 148*S^2 - 47*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) - (44*S*HPL[{3, 1}, -S^2])/3 + (80*S*HPL[{2, 1, 1}, -S^2])/3 + ((5 + 22*S^2 - 7*S^4)*Zeta[3])/(6*S*(1 + S^2))) + (110*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*(((1 + S^2)*(-29 + 260*S^2 + 29*S^4))/(6*S^3) + (Pi^4*(940 + 4765*S^2 + 2311*S^4))/(2160*S*(1 + S^2)) + (Pi^2*(-39 + 376*S^2 + 429*S^4 + 22*S^6))/(72*S^3) + (3*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(2*S) + ((14*Pi^2*S)/3 + (-4 + 57*S^2 + 59*S^4 - 2*S^6)/(3*S^3))*HPL[{3}, -S^2] + ((57 + 290*S^2 + 141*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) + (94*S*HPL[{5}, -S^2])/3 + ((-106*Pi^2*S)/9 + (2*(3 - 50*S^2 - 50*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(8 + 45*S^2 + 15*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (88*S*HPL[{3, 2}, -S^2])/3 - (356*S*HPL[{4, 1}, -S^2])/3 + (2*(9 + 62*S^2 + 9*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + 88*S*HPL[{3, 1, 1}, -S^2] - 176*S*HPL[{2, 1, 1, 1}, -S^2] + (5*Pi^2*S + (5 - 5*S^2 - 6*S^4)/(3*S))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(17 - 286*S^2 + 17*S^4))/(12*S^3) + (Pi^2*(24 + 167*S^2 + 37*S^4))/(18*S*(1 + S^2)) + (44*S*HPL[{3}, -S^2])/3 + (52*S*Zeta[3])/3) + (134*S*Zeta[5])/3) + Log[T]^2*((91*(-1 + S^2))/(12*S) + (Pi^2*(-3 + 38*S^2))/(6*S) + (Pi^4*S*(2282 + 1525*S^2))/(1080*(1 + S^2)) + (5*S*HPL[{0}, S^2]^5)/18 + (35*(1 + 3*S^2)*HPL[{1}, -S^2]^4)/(9*S) + HPL[{0}, S^2]^4*((7*S*(24 + 17*S^2))/(72*(1 + S^2)) + (49*S*HPL[{1}, -S^2])/36) + (28*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^3*((13*Pi^2*S)/9 + (S*(287 + 307*S^2 + 12*S^4))/(36*(1 + S^2)) + ((52 + 223*S^2 + 117*S^4)*HPL[{1}, -S^2])/(18*S*(1 + S^2)) + 3*S*HPL[{1}, -S^2]^2 + (26*S*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]^3*((22*Pi^2*S)/9 + (-9 + 151*S^2 + 169*S^4 + 9*S^6)/(9*S^3) + (88*S*HPL[{2}, -S^2])/3) + ((68*Pi^2*S)/9 + (-6 + 41*S^2 + 75*S^4 - 3*S^6)/(3*S^3))*HPL[{3}, -S^2] + ((11 + 182*S^2 + 125*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (134*S*HPL[{5}, -S^2])/3 + (-8*Pi^2*S + (9 - 136*S^2 - 24*S^4 + 9*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(13 + 172*S^2 + 93*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (208*S*HPL[{3, 2}, -S^2])/3 - (704*S*HPL[{4, 1}, -S^2])/3 + (8*(1 + 65*S^2 + 31*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 72*S*HPL[{2, 2, 1}, -S^2] - (176*S*HPL[{3, 1, 1}, -S^2])/3 - (496*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((86*Pi^2*S)/9 - S*(-8 + 3*S^2))*Zeta[3] + HPL[{0}, S^2]^2*((-3 + 73*S^2)/(4*S) + (Pi^2*S*(263 + 181*S^2))/(36*(1 + S^2)) + ((29 + 155*S^2 + 60*S^4)*HPL[{1}, -S^2]^2)/(6*S*(1 + S^2)) + (22*S*HPL[{1}, -S^2]^3)/3 + ((1 + 52*S^2 + 31*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((41*Pi^2*S)/9 + (-9 + 161*S^2 + 159*S^4 - 3*S^6)/(12*S^3) + (40*S*HPL[{2}, -S^2])/3) + 3*S*HPL[{3}, -S^2] - (10*S*HPL[{2, 1}, -S^2])/3 + 8*S*Zeta[3]) + HPL[{2}, -S^2]*((53 + 105*S^2)/(3*S) + (Pi^2*(2 + 117*S^2 + 62*S^4))/(9*S*(1 + S^2)) + (104*S*HPL[{3}, -S^2])/3 + 36*S*HPL[{2, 1}, -S^2] + (104*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((13*(1 + S^2)*(-3 + 32*S^2 + 3*S^4))/(12*S^3) + (Pi^2*(64 + 295*S^2 + 165*S^4))/(18*S*(1 + S^2)) + ((9 + 62*S^2 + 9*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) + 44*S*HPL[{3}, -S^2] - 88*S*HPL[{2, 1}, -S^2] + 44*S*Zeta[3]) + HPL[{1}, -S^2]*((757*Pi^4*S)/540 + ((1 + S^2)*(-67 + 624*S^2 + 67*S^4))/(12*S^3) + (Pi^2*(-9 + 156*S^2 + 164*S^4 + 3*S^6))/(18*S^3) + ((106*Pi^2*S)/9 - (2*(3 - 50*S^2 - 50*S^4 + 3*S^6))/(3*S^3))*HPL[{2}, -S^2] + (2*(5 + 33*S^2 + 6*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (92*S*HPL[{4}, -S^2])/3 - (2*(9 + 62*S^2 + 9*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - 88*S*HPL[{3, 1}, -S^2] + 176*S*HPL[{2, 1, 1}, -S^2] - (2*(2 - 5*S^2 + 15*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]*((107*Pi^4*S)/90 + (Pi^2*S*(456 + 485*S^2 + 21*S^4))/(36*(1 + S^2)) + (-45 + 646*S^2 + 67*S^4)/(12*S) + (3*Pi^2*S + (-9 + 151*S^2 + 169*S^4 + 9*S^6)/(6*S^3))*HPL[{1}, -S^2]^2 + (70*(1 + 3*S^2)*HPL[{1}, -S^2]^3)/(9*S) + ((28*Pi^2*S)/9 + (-1 + 18*S^2 + 62*S^4 + 3*S^6)/(2*S^3))*HPL[{2}, -S^2] + (S*HPL[{2}, -S^2]^2)/3 + (2*(3 + 18*S^2 + 16*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (2*S*HPL[{4}, -S^2])/3 - (2*(31 + 10*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (16*S*HPL[{2, 1, 1}, -S^2])/3 + (2*S*(32 + 31*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((13*(1 + S^2)*(-3 + 32*S^2 + 3*S^4))/(12*S^3) + (Pi^2*(29 + 121*S^2 + 74*S^4))/(6*S*(1 + S^2)) + (13*(1 + 3*S^2)*HPL[{2}, -S^2])/S - (4*S*HPL[{3}, -S^2])/3 + (4*S*Zeta[3])/3)) + (220*S*Zeta[5])/3) + HPL[{1}, -S^2]*((11563*Pi^6*S)/45360 + ((1 + S^2)*(-53 + 520*S^2 + 53*S^4))/(6*S^3) + (Pi^2*(1 + S^2)*(-134 + 1185*S^2 + 97*S^4))/(144*S^3) + (Pi^4*(-120 + 2587*S^2 + 5541*S^4 + 2741*S^6 - 53*S^8))/(2160*S^3*(1 + S^2)) + ((13*Pi^2*S)/18 + (-3 + 49*S^2 + 55*S^4 + 3*S^6)/(12*S^3))*HPL[{2}, -S^2]^2 + (26*S*HPL[{2}, -S^2]^3)/9 - (8*S*HPL[{3}, -S^2]^2)/3 + ((41*Pi^2*S)/9 + (-9 + 153*S^2 + 163*S^4 + S^6)/(3*S^3))*HPL[{4}, -S^2] + ((104 + 451*S^2 + 253*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + 99*S*HPL[{6}, -S^2] + ((-110*Pi^2*S)/9 + (11 - 163*S^2 - 173*S^4 + S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + (4*(-2 - 13*S^2 + 11*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + ((-81 - 446*S^2 - 9*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - (220*S*HPL[{5, 1}, -S^2])/3 + ((212*Pi^2*S)/9 - (4*(3 - 50*S^2 - 50*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (12*(1 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/S + (4*(14 + 69*S^2 + 33*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (208*S*HPL[{3, 2, 1}, -S^2])/3 + (808*S*HPL[{4, 1, 1}, -S^2])/3 - (4*(9 + 62*S^2 + 9*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 176*S*HPL[{3, 1, 1, 1}, -S^2] + 352*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(-1 + 37*S^2 - 52*S^4))/(18*S*(1 + S^2)) + (-1 - 26*S^2 - 17*S^4)/(6*S))*Zeta[3] + 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-24 - 167*S^2 - 37*S^4))/(9*S*(1 + S^2)) + ((1 + S^2)*(17 - 286*S^2 + 17*S^4))/(6*S^3) - (104*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(19 + 142*S^2 + 39*S^4))/(18*S*(1 + S^2)) + (-9 + 186*S^2 + 179*S^4 - 8*S^6)/(6*S^3) - (88*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{2}, -S^2]*((1349*Pi^4*S)/1080 - ((1 + S^2)*(37 - 850*S^2 + 37*S^4))/(24*S^3) + (Pi^2*(-12 + 168*S^2 + 387*S^4 + 190*S^6 - 9*S^8))/(36*S^3*(1 + S^2)) - (2*(-2 - 13*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{4}, -S^2])/3 - (6*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/S - (16*S*HPL[{3, 1}, -S^2])/3 - (2*(-3 - 19*S^2 + 10*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-18 + 27*S^2 - 89*S^4)*Zeta[5])/(3*S*(1 + S^2))) + Log[T]*((-4153*Pi^6*S)/7560 - (59*(-1 + S^2))/(4*S) + (Pi^2*(90 - 637*S^2 + 7*S^4))/(72*S) + (Pi^4*S*(-2547 - 2480*S^2 + 47*S^4))/(1080*(1 + S^2)) - (S*HPL[{0}, S^2]^6)/8 - (14*(1 + 3*S^2)*HPL[{1}, -S^2]^5)/(9*S) + HPL[{0}, S^2]^5*(-(S*(81 + 71*S^2))/(72*(1 + S^2)) - (5*S*HPL[{1}, -S^2])/18) + ((-26*Pi^2*S)/9 - (2*(-4 + 17*S^2))/(3*S))*HPL[{2}, -S^2]^2 - 2*S*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*((-11*Pi^2*S)/9 + (9 - 151*S^2 - 169*S^4 - 9*S^6)/(18*S^3) - (44*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^4*((-95*Pi^2*S)/108 + (S*(-197 - 199*S^2 + 2*S^4))/(72*(1 + S^2)) + ((-51 - 249*S^2 - 100*S^4)*HPL[{1}, -S^2])/(72*S*(1 + S^2)) - (49*S*HPL[{1}, -S^2]^2)/36 - (23*S*HPL[{2}, -S^2])/18) + (4*S*HPL[{3}, -S^2]^2)/3 + ((-43*Pi^2*S)/9 + (3 - 105*S^2 - 179*S^4 + S^6)/(3*S^3))*HPL[{4}, -S^2] + ((-80 - 449*S^2 - 275*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (286*S*HPL[{6}, -S^2])/3 + ((-2*Pi^2*(-22 - 50*S^2 + 25*S^4))/(9*S*(1 + S^2)) + (-17 + 163*S^2 + 59*S^4 - 17*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + 36*S*HPL[{2, 1}, -S^2]^2 + ((136*Pi^2*S)/9 - (2*(2 - 57*S^2 - 111*S^4 + S^6))/(3*S^3))*HPL[{3, 1}, -S^2] + ((-9 + 66*S^2 - 13*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (2*(19 + 234*S^2 + 37*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 6*S*HPL[{4, 2}, -S^2] + (268*S*HPL[{5, 1}, -S^2])/3 + ((-280*Pi^2*S)/9 + (2*(3 - 64*S^2 - 176*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (8*(-9 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(-71 - 130*S^2 + 7*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 48*S*HPL[{3, 2, 1}, -S^2] - (640*S*HPL[{4, 1, 1}, -S^2])/3 - (8*(-25 - 56*S^2 + 35*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (544*S*HPL[{3, 1, 1, 1}, -S^2])/3 - (1120*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((Pi^2*S*(-29 + 16*S^2))/(9*(1 + S^2)) + (S*(-59 + 17*S^2))/3)*Zeta[3] - 4*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((Pi^2*(-64 - 295*S^2 - 165*S^4))/(27*S*(1 + S^2)) - (13*(1 + S^2)*(-3 + 32*S^2 + 3*S^4))/(18*S^3) - (2*(9 + 62*S^2 + 9*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (88*S*HPL[{3}, -S^2])/3 + (176*S*HPL[{2, 1}, -S^2])/3 - (88*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(-21 - 116*S^2 - 11*S^4))/(18*S*(1 + S^2)) + (21 - 120*S^2 - 198*S^4 + 13*S^6)/(6*S^3) - (32*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{0}, S^2]^3*(-(Pi^2*S*(571 + 494*S^2))/(108*(1 + S^2)) + (18 - 681*S^2 - 762*S^4 - 47*S^6)/(72*S*(1 + S^2)) + ((-52 - 223*S^2 - 117*S^4)*HPL[{1}, -S^2]^2)/(18*S*(1 + S^2)) - 2*S*HPL[{1}, -S^2]^3 + ((-3 - 71*S^2 - 57*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((-77*Pi^2*S)/54 + (9 - 220*S^2 - 448*S^4 - 248*S^6 - 13*S^8)/(36*S^3*(1 + S^2)) - (22*S*HPL[{2}, -S^2])/9) + (S*HPL[{3}, -S^2])/3 - (8*S*HPL[{2, 1}, -S^2])/9 - (20*S*Zeta[3])/9) + HPL[{2}, -S^2]*((-217*Pi^4*S)/108 + (7 - 339*S^2 - 547*S^4 + 7*S^6)/(12*S^3) + (Pi^2*(3 - 45*S^2 - 228*S^4 - 173*S^6 + 3*S^8))/(18*S^3*(1 + S^2)) + ((9 - 42*S^2 - 7*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (26*S*HPL[{4}, -S^2])/3 - (4*(-9 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (104*S*HPL[{3, 1}, -S^2])/3 - 72*S*HPL[{2, 1, 1}, -S^2] + (4*(-3 - 6*S^2 + 10*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^2*((-757*Pi^4*S)/540 - ((1 + S^2)*(-67 + 624*S^2 + 67*S^4))/(12*S^3) + (Pi^2*(9 - 156*S^2 - 164*S^4 - 3*S^6))/(18*S^3) + ((-106*Pi^2*S)/9 + (2*(3 - 50*S^2 - 50*S^4 + 3*S^6))/(3*S^3))*HPL[{2}, -S^2] - (2*(5 + 33*S^2 + 6*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (92*S*HPL[{4}, -S^2])/3 + (2*(9 + 62*S^2 + 9*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 88*S*HPL[{3, 1}, -S^2] - 176*S*HPL[{2, 1, 1}, -S^2] + (2*(2 - 5*S^2 + 15*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^2*((-163*Pi^4*S)/90 + (45 - 592*S^2 + 7*S^4)/(24*S) + (Pi^2*S*(-570 - 571*S^2 + 7*S^4))/(72*(1 + S^2)) + ((-29 - 155*S^2 - 60*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) - (11*S*HPL[{1}, -S^2]^4)/3 + ((-9*Pi^2*S)/2 + (3 - 29*S^2 - 216*S^4 - 173*S^6 + 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (25*S*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((-41*Pi^2*S)/9 + (9 - 161*S^2 - 159*S^4 + 3*S^6)/(12*S^3) - (40*S*HPL[{2}, -S^2])/3) + ((-2 - 17*S^2 - 6*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (17*S*HPL[{4}, -S^2])/3 + ((19 + 44*S^2 - 15*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (68*S*HPL[{3, 1}, -S^2])/3 - (140*S*HPL[{2, 1, 1}, -S^2])/3 - (S*(31 + 19*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-20 - 101*S^2 - 40*S^4))/(9*S*(1 + S^2)) + (39 - 375*S^2 - 403*S^4 - 5*S^6)/(24*S^3) + ((-21 - 148*S^2 - 47*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) - 6*S*HPL[{3}, -S^2] + (80*S*HPL[{2, 1}, -S^2])/3 - 8*S*Zeta[3])) + HPL[{0}, S^2]*(-(Pi^4*S*(2939 + 2623*S^2))/(540*(1 + S^2)) + (91 - 1065*S^2 - 116*S^4)/(12*S) + (Pi^2*(18 - 550*S^2 - 619*S^4 - 43*S^6))/(36*S*(1 + S^2)) + (-2*Pi^2*S + (9 - 151*S^2 - 169*S^4 - 9*S^6)/(9*S^3))*HPL[{1}, -S^2]^3 - (35*(1 + 3*S^2)*HPL[{1}, -S^2]^4)/(9*S) + ((3 - 38*S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((4*Pi^2*S)/9 + (6 - 29*S^2 - 47*S^4 - S^6)/(3*S^3))*HPL[{3}, -S^2] - (2*(3 + 24*S^2 + 23*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + 4*S*HPL[{5}, -S^2] + ((-4*Pi^2*S)/3 + (-9 + 126*S^2 + 34*S^4 + 3*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(-14 - 257*S^2 - 221*S^4))/(18*S*(1 + S^2)) + (-107 - 236*S^2 - 17*S^4)/(6*S) - (8*S*HPL[{3}, -S^2])/3 - (4*S*HPL[{2, 1}, -S^2])/3) + (4*(4 + 56*S^2 + 53*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3, 2}, -S^2])/3 + (28*S*HPL[{4, 1}, -S^2])/3 - (4*(8 + 107*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*S*HPL[{2, 2, 1}, -S^2])/3 + (32*S*HPL[{3, 1, 1}, -S^2])/3 - (32*S*HPL[{2, 1, 1, 1}, -S^2])/3 + (-2*Pi^2*S - (S*(46 + S^2))/3)*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-29 - 121*S^2 - 74*S^4))/(6*S*(1 + S^2)) - (13*(1 + S^2)*(-3 + 32*S^2 + 3*S^4))/(12*S^3) - (13*(1 + 3*S^2)*HPL[{2}, -S^2])/S + (4*S*HPL[{3}, -S^2])/3 - (4*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-158*Pi^4*S)/135 - ((1 + S^2)*(-67 + 624*S^2 + 67*S^4))/(12*S^3) + (Pi^2*(9 - 181*S^2 - 384*S^4 - 213*S^6 - 11*S^8))/(18*S^3*(1 + S^2)) + ((-22*Pi^2*S)/9 - (2*(-3 + 45*S^2 + 55*S^4 + 3*S^6))/(3*S^3))*HPL[{2}, -S^2] - (2*(10 + 39*S^2 + 31*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (8*S*HPL[{4}, -S^2])/3 + (26*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/S - (8*S*HPL[{3, 1}, -S^2])/3 - (2*(11 + 45*S^2 + 32*S^4)*Zeta[3])/(3*S*(1 + S^2)))) + (2*S*(2 + 69*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(-940 - 4765*S^2 - 2311*S^4))/(1080*S*(1 + S^2)) - ((1 + S^2)*(-29 + 260*S^2 + 29*S^4))/(3*S^3) + (Pi^2*(39 - 376*S^2 - 429*S^4 - 22*S^6))/(36*S^3) - (3*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/S + ((-28*Pi^2*S)/3 + (2*(4 - 57*S^2 - 59*S^4 + 2*S^6))/(3*S^3))*HPL[{3}, -S^2] + ((-57 - 290*S^2 - 141*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (188*S*HPL[{5}, -S^2])/3 + ((212*Pi^2*S)/9 - (4*(3 - 50*S^2 - 50*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (4*(8 + 45*S^2 + 15*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (176*S*HPL[{3, 2}, -S^2])/3 + (712*S*HPL[{4, 1}, -S^2])/3 - (4*(9 + 62*S^2 + 9*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - 176*S*HPL[{3, 1, 1}, -S^2] + 352*S*HPL[{2, 1, 1, 1}, -S^2] + (-10*Pi^2*S + (2*(-5 + 5*S^2 + 6*S^4))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-24 - 167*S^2 - 37*S^4))/(9*S*(1 + S^2)) + ((1 + S^2)*(17 - 286*S^2 + 17*S^4))/(6*S^3) - (88*S*HPL[{3}, -S^2])/3 - (104*S*Zeta[3])/3) - (268*S*Zeta[5])/3)) + HPL[{0}, S^2]*((103*Pi^6*S)/1080 + (-177 + 2115*S^2 + 212*S^4)/(24*S) + (Pi^2*(-180 + 3615*S^2 + 229*S^4))/(288*S) + (Pi^4*S*(3394 + 3729*S^2 + 315*S^4))/(1080*(1 + S^2)) + ((Pi^2*S)/2 + (-9 + 151*S^2 + 169*S^4 + 9*S^6)/(36*S^3))*HPL[{1}, -S^2]^4 + (7*(1 + 3*S^2)*HPL[{1}, -S^2]^5)/(9*S) + ((11*Pi^2*S)/18 + (-4 + 67*S^2 + 3*S^4)/(12*S))*HPL[{2}, -S^2]^2 - (4*S*HPL[{2}, -S^2]^3)/9 - 2*S*HPL[{3}, -S^2]^2 + ((-4*Pi^2*S)/9 + (-3 + 34*S^2 + 32*S^4 - 3*S^6)/(6*S^3))*HPL[{4}, -S^2] + (4*(1 - S^2 + 2*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (52*S*HPL[{6}, -S^2])/3 - (2*S*HPL[{2, 1}, -S^2]^2)/3 + (-2*Pi^2*S + (2 - 33*S^2 - 84*S^4)/(3*S^3))*HPL[{3, 1}, -S^2] - (8*(-1 + S^2 + 3*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (2*(-5 + 26*S^2 + 45*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (28*S*HPL[{5, 1}, -S^2])/3 + ((56*Pi^2*S)/9 + (-1 + 18*S^2 + 62*S^4 + 3*S^6)/S^3)*HPL[{2, 1, 1}, -S^2] - (4*(-12 + 11*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4*(-39 - 21*S^2 + 17*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (32*S*HPL[{3, 2, 1}, -S^2])/3 - (92*S*HPL[{4, 1, 1}, -S^2])/3 - (4*(31 + 10*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (32*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((Pi^2*S*(269 + 258*S^2))/(18*(1 + S^2)) - (S*(-107 - 96*S^2 + 3*S^4))/(6*(1 + S^2)))*Zeta[3] - 4*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-71 - 93*S^2))/(18*S*(1 + S^2)) + (17 - 164*S^2 - 85*S^4)/(6*S^3) - (16*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((13*(1 + S^2)*(-3 + 32*S^2 + 3*S^4))/(36*S^3) + (Pi^2*(29 + 121*S^2 + 74*S^4))/(18*S*(1 + S^2)) + (13*(1 + 3*S^2)*HPL[{2}, -S^2])/(3*S) - (4*S*HPL[{3}, -S^2])/9 + (4*S*Zeta[3])/9) + HPL[{3}, -S^2]*((Pi^2*(3 + 12*S^2 + 11*S^4))/(9*S*(1 + S^2)) + (-21 + 97*S^2 + 240*S^4 + 141*S^6 + 3*S^8)/(12*S^3*(1 + S^2)) + 8*S*HPL[{2, 1}, -S^2] + (20*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((79*Pi^4*S)/135 + ((1 + S^2)*(-67 + 624*S^2 + 67*S^4))/(24*S^3) + (Pi^2*(-9 + 181*S^2 + 384*S^4 + 213*S^6 + 11*S^8))/(36*S^3*(1 + S^2)) + ((11*Pi^2*S)/9 + (-3 + 45*S^2 + 55*S^4 + 3*S^6)/(3*S^3))*HPL[{2}, -S^2] + ((10 + 39*S^2 + 31*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{4}, -S^2])/3 - (13*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/S + (4*S*HPL[{3, 1}, -S^2])/3 + ((11 + 45*S^2 + 32*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]*((29*Pi^4*S)/45 + (-7 + 402*S^2 + 647*S^4 + 30*S^6)/(24*S^3) + (Pi^2*(-3 + 45*S^2 + 245*S^4 + 207*S^6 + 6*S^8))/(36*S^3*(1 + S^2)) + (4*(-1 + S^2 + 3*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + 4*S*HPL[{4}, -S^2] + (2*(-12 + 11*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*S*HPL[{3, 1}, -S^2])/3 + (4*S*HPL[{2, 1, 1}, -S^2])/3 + ((2 + 41*S^2 + 35*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (4*S*(76 + 73*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(-29 + 260*S^2 + 29*S^4))/(6*S^3) + (Pi^4*(963 + 4108*S^2 + 2513*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(-39 + 419*S^2 + 971*S^4 + 569*S^6 + 40*S^8))/(72*S^3*(1 + S^2)) + (3*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(2*S) + ((-4*Pi^2*S)/9 + (-4 + 33*S^2 + 32*S^4 - S^6)/(3*S^3))*HPL[{3}, -S^2] + (2*(5 + 19*S^2 + 16*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (32*S*HPL[{5}, -S^2])/3 + ((-22*Pi^2*S)/9 - (2*(-3 + 45*S^2 + 55*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(19 + 75*S^2 + 58*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3, 2}, -S^2])/3 + (56*S*HPL[{4, 1}, -S^2])/3 + (26*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*S*HPL[{3, 1, 1}, -S^2])/3 + ((11*Pi^2*S)/9 + (19 + 32*S^2 + 5*S^4)/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(85 + 350*S^2 + 221*S^4))/(36*S*(1 + S^2)) + (-17 + 271*S^2 + 321*S^4 + 17*S^6)/(12*S^3) - (8*S*HPL[{3}, -S^2])/3 + (8*S*Zeta[3])/3) + 8*S*Zeta[5])) + 150*S*Zeta[7];
Et4uvwT3F3=(-21883*(-1 + S^2))/(34992*S) + (Pi^2*(-219354 - 9924*S^2 - 403993*S^4))/(104976*S) + (Pi^4*(-198858 - 255885*S^2 - 781987*S^4 - 712000*S^6))/(699840*S*(1 + S^2)) + (Pi^6*(-69378 - 34689*S^2 - 156650*S^4 - 87272*S^6))/(816480*S*(1 + S^2)) - (7*(-1 + S^6)*HPL[{1}, -S^2]^6)/(27*S^3) + HPL[{0}, S^2]^6*((-6 - 3*S^2 - 10*S^4 - 4*S^6)/(288*S*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(48*S^3)) + ((-71 - 227*S^2 - 78*S^4 - 227*S^6 - 71*S^8)*HPL[{2}, -S^2]^3)/(162*S^3*(1 + S^2)) + HPL[{0}, S^2]^5*((-5*Pi^2*S^3)/648 + (266 - 253*S^2 - 729*S^4)/(2592*S) + ((133 + 13*S^2 - 60*S^4 - 383*S^6 - 263*S^8)*HPL[{1}, -S^2])/(1296*S^3*(1 + S^2)) - (5*(1 + S^6)*HPL[{1}, -S^2]^2)/(108*S^3) - (5*S^3*HPL[{2}, -S^2])/108) + HPL[{1}, -S^2]^5*((-11*Pi^2*(1 + S^6))/(135*S^3) - (61*(-1 - S^2 + S^4 + S^6))/(54*S^3) - (44*(1 + S^6)*HPL[{2}, -S^2])/(45*S^3)) + ((-92 - 68*S^2 - 24*S^4 + 121*S^6 + 97*S^8)*HPL[{3}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((Pi^2*(-55 - 107*S^6))/(54*S^3) + (1583 + 6269*S^2 - 5271*S^4 - 23061*S^6 - 13968*S^8)/(324*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((3410 + 1628*S^2 - 891*S^4 - 4684*S^6 - 2902*S^8)*HPL[{6}, -S^2])/(54*S^3*(1 + S^2)) - (2*(300 + 229*S^6)*HPL[{7}, -S^2])/(9*S^3) + (304*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(27*S^3) + ((4*Pi^2*(-3 + 14*S^6))/(27*S^3) + (-135 + 5718*S^2 + 6306*S^4 + 2750*S^6 + 3161*S^8)/(324*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((Pi^2*(1 + 69*S^6))/(9*S^3) + (-454 + 7571*S^2 + 12162*S^4 + 11795*S^6 + 8954*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-1 + 19*S^6)*HPL[{4, 2}, -S^2])/(3*S^3) + (2*(8 + 5*S^6)*HPL[{4, 3}, -S^2])/(3*S^3) + ((-691 - 31*S^2 + 330*S^4 + 2394*S^6 + 1734*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((15 + 13*S^6)*HPL[{5, 2}, -S^2])/S^3 + (2*(282 + 319*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(-30 + 13*S^6))/(27*S^3) + (2*(-412 + 783*S^2 - 783*S^4 + 412*S^6))/(81*S^3))*HPL[{2, 2, 1}, -S^2] + ((-1163 + 1899*S^2 - 6471*S^4 - 99*S^6)/(81*S^3) + (4*Pi^2*(-93 + 5*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] - (3*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 + ((-365 - 989*S^2 - 312*S^4 - 989*S^6 - 365*S^8)*HPL[{3, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(4 + 13*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) - (32*(1 + 6*S^6)*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (4*(288 + 894*S^2 + 303*S^4 + 1070*S^6 + 464*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(13 + 99*S^6)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (2*(29 + 283*S^6)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (4*(89 + 895*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(7 + 4*S^6))/(3*S^3) + (2*(631 + 2286*S^2 + 2286*S^4 + 631*S^6))/(81*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (272*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + (8*(131 + 329*S^2 + 99*S^4 + 417*S^6 + 219*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(52 + 25*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) - (16*(52 + 25*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) - (16*(103 + 76*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) - (16*(301 + 218*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3) - (16*(175 + 373*S^2 + 99*S^4 + 373*S^6 + 175*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (48*(-1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^3 - (144*(-1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (32*(-66 + 97*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3) + (992*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((14*Pi^2*S^3)/81 + (14*(-1 + S^2))/(27*S) + (14*S^3*HPL[{0}, S^2])/9 + (14*S^3*HPL[{0}, S^2]^2)/27 + (14*(-1 + S^6)*HPL[{1}, -S^2])/(9*S^3) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(27*S^3))*Log[T]^5 + ((-157*Pi^4*S^3)/270 + (-43245 + 324*S^2 - 20950*S^4)/(1458*S) + (Pi^2*(-2544 - 2928*S^2 - 2905*S^4 - 2737*S^6))/(972*S*(1 + S^2)))*Zeta[3] + ((-6 - 3*S^2 + 4*S^4 + 10*S^6)*Zeta[3]^2)/(3*S*(1 + S^2)) + Log[T]^4*((-179*(-1 + S^2))/(162*S) + (Pi^2*(-198 - 99*S^2 - 548*S^4 - 350*S^6))/(486*S*(1 + S^2)) - (28*S^3*HPL[{0}, S^2]^3)/81 - (35*(-1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^2*((-198 - 99*S^2 - 548*S^4 - 350*S^6)/(162*S*(1 + S^2)) - (11*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3)) - (2*(175 + 373*S^2 + 99*S^4 + 373*S^6 + 175*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-11*Pi^2*(1 + S^6))/(27*S^3) - (305*(-1 - S^2 + S^4 + S^6))/(54*S^3) - (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]*((-28*Pi^2*S^3)/81 + (202 - 103*S^2 - 305*S^4)/(54*S) - (35*(-1 + S^6)*HPL[{1}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(27*S^3)) - (2*(3 + 59*S^6)*HPL[{3}, -S^2])/(27*S^3) + (124*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(27*S^3) - (124*S^3*Zeta[3])/27) + HPL[{0}, S^2]^4*((-12048 - 14979*S^2 - 56611*S^4 - 56272*S^6)/(46656*S*(1 + S^2)) + (Pi^2*(-184 - 92*S^2 - 379*S^4 - 195*S^6))/(1296*S*(1 + S^2)) + ((-8 - 208*S^2 - 106*S^4 - 379*S^6 - 179*S^8)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)) - (49*(1 + S^6)*HPL[{1}, -S^2]^3)/(324*S^3) + ((-12 - 110*S^2 - 49*S^4 - 296*S^6 - 198*S^8)*HPL[{2}, -S^2])/(432*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-23*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (-1468 - 2209*S^2 - 6117*S^4 - 10831*S^6 - 5887*S^8)/(7776*S^3*(1 + S^2)) - (49*(1 + S^6)*HPL[{2}, -S^2])/(216*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(24*S^3) + ((40 + 3*S^6)*HPL[{2, 1}, -S^2])/(108*S^3) - (83*S^3*Zeta[3])/108) + HPL[{1}, -S^2]^4*((-2357*(-1 + S^2)*(1 + S^2)^2)/(648*S^3) + (Pi^2*(85 - 47*S^2 - 66*S^4 - 350*S^6 - 218*S^8))/(324*S^3*(1 + S^2)) + ((-133 - 397*S^2 - 132*S^4 - 397*S^6 - 133*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) - (22*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (44*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (22*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{4}, -S^2]*((-7462 + 2635*S^2 - 9425*S^4 - 17482*S^6)/(648*S^3) + (Pi^2*(-37 - 271*S^2 - 99*S^4 - 577*S^6 - 343*S^8))/(162*S^3*(1 + S^2)) + (2*(11 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (16*(2 + S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((5743 + 145*S^2 + 6175*S^4 + 10753*S^6)/(324*S^3) + (Pi^2*(251 + 899*S^2 + 306*S^4 + 1455*S^6 + 807*S^8))/(162*S^3*(1 + S^2)) + (8*(-3 + 11*S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((9428 - 351*S^2 + 351*S^4 - 9428*S^6)/(1944*S^3) + (Pi^2*(201 + 123*S^2 - 39*S^4 - 350*S^6 - 272*S^8))/(324*S^3*(1 + S^2)) - (2*(4 + 13*S^6)*HPL[{3}, -S^2])/(9*S^3) + (34*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (2*(3 + 14*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((-4*(1 + S^2)*(1031 - 636*S^2 + 1031*S^4))/(81*S^3) - (2*Pi^2*(198 + 516*S^2 + 159*S^4 + 668*S^6 + 350*S^8))/(81*S^3*(1 + S^2)) - (8*(-1 + 26*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(20950 + 21971*S^2 + 20950*S^4))/(1458*S^3) + (Pi^4*(853 + 264*S^6))/(1620*S^3) + (Pi^2*(874 + 2260*S^2 + 3447*S^4 + 2631*S^6 + 462*S^8))/(486*S^3*(1 + S^2)) + (8*(-2 + S^6)*HPL[{3, 1}, -S^2])/S^3 + (24*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(152 + 230*S^2 + 39*S^4 + 78*S^6)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((-1027*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) - (757*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(4860*S^3) + (Pi^2*(985 + 1035*S^2 - 2970*S^4 - 2912*S^6))/(1458*S^3) + ((-106*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) - ((1 + S^2)*(1927 + 8*S^2 + 1927*S^4))/(243*S^3))*HPL[{2}, -S^2] - (2*(62 + 194*S^2 + 66*S^4 + 203*S^6 + 71*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (92*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) + (2*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (176*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(125 + 257*S^2 + 66*S^4 + 140*S^6 + 8*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((26117 - 195597*S^2 - 147771*S^4 - 193717*S^6)/(11664*S^3) + (Pi^4*(-21 - 307*S^6))/(1620*S^3) + (Pi^2*(1457 - 1510*S^2 - 5196*S^4 - 6398*S^6 - 3737*S^8))/(1944*S^3*(1 + S^2)) - (2*(4 + S^6)*HPL[{4}, -S^2])/(3*S^3) + ((403 + 691*S^2 + 180*S^4 + 83*S^6 - 205*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(-1 + 5*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (8*(-1 + 26*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (4*(37 + 34*S^2 + 3*S^4 + 10*S^6 + 13*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^3*((-7*Pi^4*S^3)/180 + (14936 - 893*S^2 - 30699*S^4)/(7776*S) + (Pi^2*(4908 - 417*S^2 - 20729*S^4 - 15620*S^6))/(11664*S*(1 + S^2)) + ((57 - 55*S^2 - 62*S^4 - 274*S^6 - 162*S^8)*HPL[{1}, -S^2]^3)/(162*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2]^4)/(6*S^3) + ((Pi^2*(-3 - 76*S^6))/(324*S^3) + (243 + 1005*S^2 - 753*S^4 - 5255*S^6 - 3956*S^8)/(1944*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((-1 - 7*S^6)*HPL[{2}, -S^2]^2)/(36*S^3) + HPL[{1}, -S^2]^2*((-77*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(324*S^3) + (889 + 1606*S^2 - 1581*S^4 - 3992*S^6 - 1910*S^8)/(972*S^3*(1 + S^2)) - (11*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((15 + 27*S^2 + 6*S^4 + 5*S^6 - 7*S^8)*HPL[{3}, -S^2])/(108*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(6*S^3) + ((-151 - 7*S^2 + 90*S^4 + 93*S^6 - 51*S^8)*HPL[{2, 1}, -S^2])/(162*S^3*(1 + S^2)) + (2*S^3*HPL[{3, 1}, -S^2])/3 - (2*(3 + 26*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + ((-20 - 10*S^2 - 269*S^4 - 249*S^6)*Zeta[3])/(54*S*(1 + S^2)) + HPL[{1}, -S^2]*((2897 + 5778*S^2 - 2494*S^4 - 9654*S^6 - 4711*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(836 - 100*S^2 - 486*S^4 - 2737*S^6 - 1801*S^8))/(1944*S^3*(1 + S^2)) + ((86 - 52*S^2 - 78*S^4 - 349*S^6 - 211*S^8)*HPL[{2}, -S^2])/(162*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (22*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3))) + Log[T]^3*((277*Pi^4*S^3)/810 + (793*(-1 + S^2))/(486*S) + (Pi^2*(18 + 1566*S^2 + 3223*S^4))/(1458*S) + (55*S^3*HPL[{0}, S^2]^4)/162 + (140*(-1 + S^6)*HPL[{1}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^3*((18 + 9*S^2 + 80*S^4 + 62*S^6)/(27*S*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3)) + ((2*Pi^2*(43 + 70*S^6))/(81*S^3) + (11*(293 + 144*S^2 + 144*S^4 + 293*S^6))/(243*S^3))*HPL[{2}, -S^2] + (2*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^2)/S^3 + HPL[{1}, -S^2]^2*((22*Pi^2*(1 + S^6))/(27*S^3) + (305*(-1 - S^2 + S^4 + S^6))/(27*S^3) + (88*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]^2*((10*Pi^2*S^3)/9 + (648 + 936*S^2 + 3223*S^4)/(486*S) + ((20 + 152*S^2 + 66*S^4 + 245*S^6 + 113*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) + (22*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + (2*(8 + 35*S^6)*HPL[{2}, -S^2])/(27*S^3)) + (4*(-97 + 101*S^2 + 99*S^4 + 344*S^6 + 146*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (8*(15 + 13*S^6)*HPL[{4}, -S^2])/(27*S^3) - (4*(49 + 445*S^2 + 198*S^4 + 445*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) - (16*(18 + 17*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (560*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + (4*(198 + 99*S^2 + 247*S^4 + 49*S^6)*Zeta[3])/(81*S*(1 + S^2)) + HPL[{0}, S^2]*(((1 + S^2)*(-2002 + 2357*S^2))/(162*S) + (Pi^2*(18 + 9*S^2 + 115*S^4 + 97*S^6))/(27*S*(1 + S^2)) + ((2*Pi^2*(1 + S^6))/(3*S^3) + (305*(-1 - S^2 + S^4 + S^6))/(27*S^3))*HPL[{1}, -S^2] + (70*(-1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + (2*(-25 + 326*S^6)*HPL[{2}, -S^2])/(81*S^3) - (4*(3 + S^6)*HPL[{3}, -S^2])/(27*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(27*S^3) - (8*S^3*Zeta[3])/27) + HPL[{1}, -S^2]*((2357*(-1 + S^2)*(1 + S^2)^2)/(162*S^3) + (Pi^2*(-85 + 47*S^2 + 66*S^4 + 350*S^6 + 218*S^8))/(81*S^3*(1 + S^2)) + (2*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (176*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (88*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + ((-55*Pi^2*S^3)/9 + (-4194 - 4347*S^2 - 2855*S^4 - 2486*S^6)/(162*S*(1 + S^2)))*Zeta[5] + Log[T]^2*((-589*(-1 + S^2))/(324*S) + (Pi^2*(-311 - 479*S^2 - 2062*S^4))/(486*S) + (Pi^4*(-4542 - 2271*S^2 - 13004*S^4 - 8462*S^6))/(9720*S*(1 + S^2)) - (5*S^3*HPL[{0}, S^2]^5)/54 - (35*(-1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + HPL[{0}, S^2]^4*((-7*(14 + 7*S^2 + 44*S^4 + 30*S^6))/(216*S*(1 + S^2)) - (49*(1 + S^6)*HPL[{1}, -S^2])/(108*S^3)) - (152*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^2)/(27*S^3) + HPL[{0}, S^2]^3*((-13*Pi^2*S^3)/27 + (918 - 612*S^2 - 5999*S^4 - 4685*S^6)/(972*S*(1 + S^2)) + ((57 - 55*S^2 - 62*S^4 - 274*S^6 - 162*S^8)*HPL[{1}, -S^2])/(54*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{1}, -S^2]^2)/S^3 + ((-3 - 26*S^6)*HPL[{2}, -S^2])/(27*S^3)) + HPL[{1}, -S^2]^3*((-305*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) - (22*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (88*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((1309 - 2799*S^2 - 1773*S^4 - 2571*S^6)/(162*S^3) - (2*Pi^2*(3 + 34*S^6))/(27*S^3))*HPL[{3}, -S^2] - (2*(75 + 213*S^2 + 69*S^4 + 389*S^6 + 251*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (2*(17 + 67*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((2*Pi^2*(7 + 4*S^6))/(3*S^3) + (631 + 2286*S^2 + 2286*S^4 + 631*S^6)/(81*S^3))*HPL[{2, 1}, -S^2] + (4*(131 + 329*S^2 + 99*S^4 + 417*S^6 + 219*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-1 + 26*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (8*(5 + 88*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (8*(175 + 373*S^2 + 99*S^4 + 373*S^6 + 175*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (24*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 + (16*(-42 + 11*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (496*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-86*Pi^2*S^3)/27 + (-2214 - 72*S^2 - 631*S^4)/(81*S))*Zeta[3] + HPL[{0}, S^2]^2*((-1159 - 421*S^2 - 4124*S^4)/(324*S) + (Pi^2*(-246 - 123*S^2 - 736*S^4 - 490*S^6))/(162*S*(1 + S^2)) + ((-20 - 152*S^2 - 66*S^4 - 245*S^6 - 113*S^8)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)) - (22*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((-23 - 143*S^2 - 60*S^4 - 295*S^6 - 175*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-775 - 675*S^2 - 3195*S^4 - 3079*S^6)/(324*S^3) - (41*Pi^2*(1 + S^6))/(27*S^3) - (40*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-1 - 3*S^6)*HPL[{3}, -S^2])/(3*S^3) + (2*(32 + 5*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (8*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-2357*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(85 - 47*S^2 - 66*S^4 - 350*S^6 - 218*S^8))/(54*S^3*(1 + S^2)) + ((-133 - 397*S^2 - 132*S^4 - 397*S^6 - 133*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (44*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (88*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (44*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-2*(1 + S^2)*(1031 - 636*S^2 + 1031*S^4))/(81*S^3) + (Pi^2*(-198 - 516*S^2 - 159*S^4 - 668*S^6 - 350*S^8))/(81*S^3*(1 + S^2)) - (4*(-1 + 26*S^6)*HPL[{3}, -S^2])/(9*S^3) - (12*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (4*(-1 + 26*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((-1027*(-1 + S^2)*(1 + S^2)^2)/(36*S^3) - (757*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (Pi^2*(985 + 1035*S^2 - 2970*S^4 - 2912*S^6))/(486*S^3) + ((-1927 - 1935*S^2 - 1935*S^4 - 1927*S^6)/(81*S^3) - (106*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2] - (2*(62 + 194*S^2 + 66*S^4 + 203*S^6 + 71*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (92*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (2*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (176*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(125 + 257*S^2 + 66*S^4 + 140*S^6 + 8*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]*((-107*Pi^4*S^3)/270 - ((1 + S^2)*(-2855 + 3081*S^2))/(108*S) + (Pi^2*(2736 + 279*S^2 - 9671*S^4 - 7430*S^6))/(972*S*(1 + S^2)) + ((Pi^2*(-1 - S^6))/S^3 - (305*(-1 - S^2 + S^4 + S^6))/(18*S^3))*HPL[{1}, -S^2]^2 - (70*(-1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((11 + 68*S^2 - 42*S^4 - 107*S^6)/(6*S^3) + (Pi^2*(-5 - 28*S^6))/(27*S^3))*HPL[{2}, -S^2] - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + ((105 + 129*S^2 + 30*S^4 - 73*S^6 - 97*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (2*(5 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (2*(-326 + 25*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (8*HPL[{3, 1}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(6 + 3*S^2 + 94*S^4 + 88*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((-2357*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(162 + 50*S^2 - 62*S^4 - 379*S^6 - 267*S^8))/(54*S^3*(1 + S^2)) - (13*(-1 + S^6)*HPL[{2}, -S^2])/S^3 + (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) - (220*S^3*Zeta[5])/9) + HPL[{0}, S^2]^2*((-235257 + 5979*S^2 - 403993*S^4)/(34992*S) + (Pi^2*(-19002 - 24459*S^2 - 83881*S^4 - 81016*S^6))/(23328*S*(1 + S^2)) + (Pi^4*(-5466 - 2733*S^2 - 12583*S^4 - 7117*S^6))/(19440*S*(1 + S^2)) + ((-20 - 152*S^2 - 66*S^4 - 245*S^6 - 113*S^8)*HPL[{1}, -S^2]^4)/(108*S^3*(1 + S^2)) - (11*(1 + S^6)*HPL[{1}, -S^2]^5)/(45*S^3) + ((49 - 29*S^2 - 39*S^4 - 198*S^6 - 120*S^8)*HPL[{2}, -S^2]^2)/(108*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-775 - 675*S^2 - 3195*S^4 - 3079*S^6)/(972*S^3) - (41*Pi^2*(1 + S^6))/(81*S^3) - (40*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((Pi^2*(-2 - 3*S^6))/(18*S^3) + (74 - 10*S^2 - 312*S^4 - 1027*S^6 - 583*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((19 - 29*S^2 - 15*S^4 - 94*S^6 - 46*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + ((-19 - 20*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((4*Pi^2*(9 + S^6))/(27*S^3) + (1117 + 1603*S^2 + 2322*S^4 + 2345*S^6 + 293*S^8)/(324*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-11 + 241*S^2 + 108*S^4 + 621*S^6 + 369*S^8)*HPL[{3, 1}, -S^2])/(54*S^3*(1 + S^2)) + (2*(-5 + 2*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + ((-7 + 31*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (2*(23 + 143*S^2 + 60*S^4 + 295*S^6 + 175*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(33 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (4*(17 + 2*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (4*(32 + 5*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-95*Pi^2*S^3)/54 + (-55 - 107*S^2 - 367*S^4 - 351*S^6)/(54*S*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((-2887 - 2323*S^2 - 7669*S^4 - 7801*S^6)/(1296*S^3) + (Pi^2*(-7 - 90*S^2 - 43*S^4 - 156*S^6 - 73*S^8))/(54*S^3*(1 + S^2)) + ((-167 - 635*S^2 - 216*S^4 - 797*S^6 - 329*S^8)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{3}, -S^2])/S^3 + (40*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-2944 - 7309*S^2 - 7083*S^4 - 16386*S^6 - 12372*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-82 - 616*S^2 - 267*S^4 - 1478*S^6 - 944*S^8))/(648*S^3*(1 + S^2)) + ((5 - 2*S^6)*HPL[{3}, -S^2])/(9*S^3) + ((33 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + ((1 - S^6)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((-911*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(3240*S^3) - ((1 + S^2)*(47003 - 6035*S^2 + 90824*S^4))/(11664*S^3) + (Pi^2*(-2243 - 3659*S^2 - 9987*S^4 - 17105*S^6 - 8966*S^8))/(3888*S^3*(1 + S^2)) + ((-89*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(108*S^3) + (-283 - 528*S^2 - 721*S^4 - 1134*S^6 - 586*S^8)/(108*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (13*(1 + S^6)*HPL[{2}, -S^2]^2)/(18*S^3) + ((-7 - 39*S^2 - 10*S^4 - 66*S^6 - 34*S^8)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{4}, -S^2])/S^3 + ((167 + 635*S^2 + 216*S^4 + 797*S^6 + 329*S^8)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)) + (44*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (80*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-73 - 229*S^2 - 96*S^4 - 193*S^6 - 37*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) - (110*S^3*Zeta[5])/9) + HPL[{1}, -S^2]^2*((-1087*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^2*(1046 + 1187*S^2 - 3685*S^4 - 3718*S^6))/(972*S^3) + (Pi^4*(483 - 2525*S^2 - 1474*S^4 - 6518*S^6 - 3510*S^8))/(6480*S^3*(1 + S^2)) - (3*(-1 + S^6)*HPL[{2}, -S^2]^2)/(2*S^3) + ((-14*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(1873 + 8*S^2 + 1981*S^4))/(162*S^3))*HPL[{3}, -S^2] + ((119 - 433*S^2 - 276*S^4 - 1189*S^6 - 637*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) - (94*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((106*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(1927 + 8*S^2 + 1927*S^4))/(81*S^3))*HPL[{2, 1}, -S^2] + (2*(35 + 167*S^2 + 66*S^4 + 230*S^6 + 98*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (356*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (2*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (88*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (176*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-5*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (-1760 - 1710*S^2 - 225*S^4 - 167*S^6)/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(1336 - 87*S^2 + 1336*S^4))/(81*S^3) + (Pi^2*(-283 - 913*S^2 - 306*S^4 - 994*S^6 - 364*S^8))/(162*S^3*(1 + S^2)) - (44*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (52*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (134*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*(-((1 + S^2)*(403993 - 174715*S^2 + 403993*S^4))/(17496*S^3) + (Pi^2*(-15316 - 24421*S^2 - 16563*S^4 - 33498*S^6 - 24744*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(-4434 - 12528*S^2 - 4047*S^4 - 19882*S^6 - 11788*S^8))/(19440*S^3*(1 + S^2)) + ((-2*Pi^2*(-3 + 14*S^6))/(27*S^3) + (-297 - 3102*S^2 - 2910*S^4 - 1618*S^6 - 1945*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((101 + 77*S^2 + 24*S^4 - 211*S^6 - 187*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + ((11 - 7*S^6)*HPL[{5}, -S^2])/(3*S^3) + ((412 - 783*S^2 + 783*S^4 - 412*S^6)/(81*S^3) - (2*Pi^2*(-30 + 13*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((-261 - 237*S^2 - 24*S^4 + 371*S^6 + 347*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(4 + 13*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (2*(5 + 51*S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (608*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (136*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (8*(52 + 25*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (24*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((Pi^2*(4 - 29*S^6))/(27*S^3) + (243 - 657*S^2 - 1125*S^4 - 286*S^6 - 169*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (2*(-10 + 41*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((-253*(-1 + S^2)*(1 + S^2)^2)/(8*S^3) - (11563*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(136080*S^3) - (Pi^2*(1 + S^2)*(-36184 - 6035*S^2 + 174011*S^4))/(34992*S^3) + (Pi^4*(-5027 + 163*S^2 - 86991*S^4 - 195659*S^6 - 101318*S^8))/(116640*S^3*(1 + S^2)) + ((-101*(-1 + S^2)*(1 + S^2)^2)/(36*S^3) - (13*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3))*HPL[{2}, -S^2]^2 - (26*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(27*S^3) + (8*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((-1009 + 1149*S^2 - 6555*S^4 - 8713*S^6)/(324*S^3) - (41*Pi^2*(1 + S^6))/(27*S^3))*HPL[{4}, -S^2] + ((503 - 85*S^2 - 330*S^4 - 1570*S^6 - 982*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) - (33*(1 + S^6)*HPL[{6}, -S^2])/S^3 + ((110*Pi^2*(1 + S^6))/(27*S^3) + (2*(482 + 486*S^2 + 1449*S^4 + 1445*S^6))/(81*S^3))*HPL[{3, 1}, -S^2] + (4*(103 + 241*S^2 + 78*S^4 + 160*S^6 + 22*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((1117 + 3325*S^2 + 1212*S^4 + 3109*S^6 + 901*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + (220*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-212*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (2*(1 + S^2)*(1927 + 8*S^2 + 1927*S^4))/(81*S^3))*HPL[{2, 1, 1}, -S^2] - (12*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 - (4*(-19 + 113*S^2 + 66*S^4 + 284*S^6 + 152*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (208*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (808*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (4*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (176*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (352*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-4979 - 4697*S^2 - 299*S^4 - 365*S^6)/(162*S^3) + (Pi^2*(-448 - 1000*S^2 - 294*S^4 - 613*S^6 - 61*S^8))/(162*S^3*(1 + S^2)))*Zeta[3] - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/S^3 + HPL[{3}, -S^2]*((-4807 - 4243*S^2 - 5749*S^4 - 5881*S^6)/(324*S^3) + (Pi^2*(-69 - 233*S^2 - 76*S^4 - 269*S^6 - 105*S^8))/(54*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((2*(1 + S^2)*(1336 - 87*S^2 + 1336*S^4))/(81*S^3) + (Pi^2*(283 + 913*S^2 + 306*S^4 + 994*S^6 + 364*S^8))/(81*S^3*(1 + S^2)) + (104*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((-1349*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(3240*S^3) - ((1 + S^2)*(137827 - 12070*S^2 + 137827*S^4))/(5832*S^3) + (Pi^2*(-2776 - 5446*S^2 - 6033*S^4 - 7264*S^6 - 3685*S^8))/(972*S^3*(1 + S^2)) - (2*(103 + 241*S^2 + 78*S^4 + 160*S^6 + 22*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (16*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (6*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (16*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (2*(116 + 278*S^2 + 90*S^4 + 197*S^6 + 35*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((-253 - 517*S^2 - 126*S^4 - 280*S^6 - 16*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]*((-103*Pi^6*S^3)/3240 - ((1 + S^2)*(-60293 + 61479*S^2))/(1944*S) + (Pi^2*(32066 - 2249*S^2 - 49185*S^4))/(7776*S) + (Pi^4*(29274 + 2433*S^2 - 104464*S^4 - 78703*S^6))/(58320*S*(1 + S^2)) + ((-305*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) - (Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(6*S^3))*HPL[{1}, -S^2]^4 - (7*(-1 + S^6)*HPL[{1}, -S^2]^5)/(9*S^3) + ((-81 + 242*S^2 - 61*S^4 - 384*S^6)/(108*S^3) + (Pi^2*(-2 - 11*S^6))/(54*S^3))*HPL[{2}, -S^2]^2 + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(27*S^3) + (2*(4 + 3*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((-122 + 99*S^2 - 225*S^4 - 329*S^6)/(81*S^3) + (2*Pi^2*(1 + 2*S^6))/(27*S^3))*HPL[{4}, -S^2] + ((-49 + 29*S^2 + 12*S^4 + 47*S^6 - 31*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (4*(15 + 13*S^6)*HPL[{6}, -S^2])/(9*S^3) + (2*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((2*Pi^2*(1 + 9*S^6))/(27*S^3) + (41 - 810*S^2 + 585*S^4 + 1481*S^6)/(81*S^3))*HPL[{3, 1}, -S^2] + (8*(18 + 12*S^2 - 3*S^4 + 10*S^6 + 16*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + (4*(58 + 16*S^2 - 21*S^4 + 60*S^6 + 102*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(6 + 7*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((11 + 68*S^2 - 42*S^4 - 107*S^6)/(3*S^3) - (2*Pi^2*(5 + 28*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(39 - 2*S^2 - 2*S^4 + 12*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (2*(807 + 795*S^2 - 42*S^4 + 107*S^6 + 119*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (4*(19 + 23*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (4*(-326 + 25*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3) + (16*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (32*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((2402 + 2221*S^2 - 3118*S^4 - 2505*S^6)/(324*S*(1 + S^2)) + (Pi^2*(-66 - 33*S^2 - 901*S^4 - 835*S^6))/(162*S*(1 + S^2)))*Zeta[3] + (4*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((-2357*(-1 + S^2)*(1 + S^2)^2)/(324*S^3) + (Pi^2*(162 + 50*S^2 - 62*S^4 - 379*S^6 - 267*S^8))/(162*S^3*(1 + S^2)) - (13*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3) + (4*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) + HPL[{2, 1}, -S^2]*((-1253 - 427*S^2 + 1039*S^4 + 285*S^6)/(54*S^3) + (Pi^2*(-477 - 333*S^2 + 90*S^4 + 118*S^6 - 26*S^8))/(162*S^3*(1 + S^2)) + (4*(5 + 4*S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((809 + 2030*S^2 - 1410*S^4 - 5143*S^6 - 3160*S^8)/(486*S^3*(1 + S^2)) + (Pi^2*(75 + 105*S^2 + 24*S^4 - 29*S^6 - 59*S^8))/(162*S^3*(1 + S^2)) - (4*(7 + 6*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(4 + 5*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((-1027*(-1 + S^2)*(1 + S^2)^2)/(72*S^3) - (79*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (Pi^2*(4523 + 8702*S^2 - 3162*S^4 - 13474*S^6 - 6565*S^8))/(1944*S^3*(1 + S^2)) + ((59 + 55*S^2 - 55*S^4 - 59*S^6)/(6*S^3) - (11*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2] + ((101 + 113*S^2 + 6*S^4 - 76*S^6 - 88*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (13*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (4*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + ((88 + 76*S^2 - 6*S^4 - 113*S^6 - 101*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]*(-((1 + S^2)*(-423 - 617*S^2 + 1090*S^4))/(72*S^3) + (Pi^4*(-13 - 87*S^6))/(405*S^3) + (Pi^2*(540 + 3138*S^2 - 51*S^4 - 9278*S^6 - 6845*S^8))/(1944*S^3*(1 + S^2)) - (4*(18 + 12*S^2 - 3*S^4 + 10*S^6 + 16*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (4*(4 + 3*S^6)*HPL[{4}, -S^2])/(9*S^3) - (2*(39 - 2*S^2 - 2*S^4 + 12*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(3 + 2*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (4*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((50 + 38*S^2 + 12*S^4 - 105*S^6 - 93*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) - (2*(36 + 18*S^2 + 473*S^4 + 437*S^6)*Zeta[5])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((-1087*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^2*(12865 + 25698*S^2 - 4988*S^4 - 33450*S^6 - 16493*S^8))/(3888*S^3*(1 + S^2)) + (Pi^4*(5191 + 1339*S^2 - 2016*S^4 - 12971*S^6 - 9119*S^8))/(9720*S^3*(1 + S^2)) - (3*(-1 + S^6)*HPL[{2}, -S^2]^2)/(2*S^3) + ((229 + 225*S^2 - 351*S^4 - 455*S^6)/(81*S^3) + (4*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3}, -S^2] - (2*(-56 - 68*S^2 - 6*S^4 + 31*S^6 + 43*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((22*Pi^2*(1 + S^6))/(27*S^3) + (-59 - 55*S^2 + 55*S^4 + 59*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + (2*(-182 - 194*S^2 - 6*S^4 + 157*S^6 + 169*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) - (56*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (26*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (8*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((-11*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(-1189 + 100*S^2 + 737*S^4))/(162*S^3))*Zeta[3] + HPL[{2}, -S^2]*((769 + 733*S^2 - 733*S^4 - 769*S^6)/(54*S^3) + (Pi^2*(523 + 247*S^2 - 156*S^4 - 1049*S^6 - 773*S^8))/(324*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3))) + Log[T]*((4153*Pi^6*S^3)/22680 + (2087*(-1 + S^2))/(1458*S) + (Pi^2*(32868 + 7047*S^2 + 95927*S^4))/(17496*S) + (Pi^4*(9162 + 35937*S^2 + 113369*S^4 + 85514*S^6))/(58320*S*(1 + S^2)) + (S^3*HPL[{0}, S^2]^6)/24 + (14*(-1 + S^6)*HPL[{1}, -S^2]^5)/(9*S^3) + HPL[{0}, S^2]^5*((60 + 30*S^2 + 323*S^4 + 263*S^6)/(648*S*(1 + S^2)) + (5*(1 + S^6)*HPL[{1}, -S^2])/(54*S^3)) + ((Pi^2*(-17 + 26*S^6))/(27*S^3) + (-1321 - 126*S^2 + 126*S^4 + 1321*S^6)/(162*S^3))*HPL[{2}, -S^2]^2 + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(3*S^3) + HPL[{1}, -S^2]^4*((305*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (11*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (44*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]^4*((95*Pi^2*S^3)/324 + (468 + 2151*S^2 + 8083*S^4 + 6616*S^6)/(3888*S*(1 + S^2)) + ((8 + 208*S^2 + 106*S^4 + 379*S^6 + 179*S^8)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)) + (49*(1 + S^6)*HPL[{1}, -S^2]^2)/(108*S^3) + ((9 + 46*S^6)*HPL[{2}, -S^2])/(108*S^3)) - (4*(-2 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((43*Pi^2*(1 + S^6))/(27*S^3) + (2354 - 759*S^2 + 2733*S^4 + 5594*S^6)/(162*S^3))*HPL[{4}, -S^2] + ((-571 - 7*S^2 + 282*S^4 + 1708*S^6 + 1144*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (2*(90 + 143*S^6)*HPL[{6}, -S^2])/(9*S^3) - (12*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/S^3 + ((-2413 - 711*S^2 - 2457*S^4 - 4033*S^6)/(81*S^3) - (8*Pi^2*(11 + 17*S^6))/(27*S^3))*HPL[{3, 1}, -S^2] + ((63 - 465*S^2 - 264*S^4 - 1033*S^6 - 505*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-121 + 413*S^2 + 267*S^4 + 1041*S^6 + 507*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 - (4*(33 + 67*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(43 + 70*S^6))/(27*S^3) + (22*(293 + 144*S^2 + 144*S^4 + 293*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] - (568*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) - (8*(-116 - 314*S^2 - 99*S^4 - 131*S^6 + 67*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/S^3 + (32*(21 + 20*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (8*(49 + 445*S^2 + 198*S^4 + 445*S^6 + 49*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (32*(18 + 17*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (1120*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((4*(844 + 10*S^2 + 305*S^4))/(81*S) + (5*Pi^2*(18 + 9*S^2 + 29*S^4 + 11*S^6))/(27*S*(1 + S^2)))*Zeta[3] + (4*S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((-244*(1 + S^2)*(5 + 9*S^2 + 5*S^4))/(81*S^3) - (2*Pi^2*(85 + 397*S^2 + 147*S^4 + 326*S^6 + 14*S^8))/(81*S^3*(1 + S^2)) - (24*Zeta[3])/S^3) + HPL[{0}, S^2]^3*((Pi^2*(462 + 231*S^2 + 2335*S^4 + 1873*S^6))/(972*S*(1 + S^2)) + (-1509 - 858*S^2 + 4961*S^4 + 4472*S^6)/(729*S*(1 + S^2)) + ((-57 + 55*S^2 + 62*S^4 + 274*S^6 + 162*S^8)*HPL[{1}, -S^2]^2)/(54*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2]^3)/(3*S^3) + ((-21 + 111*S^2 + 66*S^4 + 605*S^6 + 473*S^8)*HPL[{2}, -S^2])/(162*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((77*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (-889 - 1606*S^2 + 1581*S^4 + 3992*S^6 + 1910*S^8)/(486*S^3*(1 + S^2)) + (22*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(27*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (2*(-19 + 4*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (20*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^3*((2357*(-1 + S^2)*(1 + S^2)^2)/(162*S^3) + (Pi^2*(-85 + 47*S^2 + 66*S^4 + 350*S^6 + 218*S^8))/(81*S^3*(1 + S^2)) + (2*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (176*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (88*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((-7243 + 25725*S^2 + 15267*S^4 + 21883*S^6)/(972*S^3) + (Pi^2*(-239 + 253*S^2 + 228*S^4 + 859*S^6 + 367*S^8))/(162*S^3*(1 + S^2)) + (8*(-23 + 4*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(4 + S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((1027*(-1 + S^2)*(1 + S^2)^2)/(36*S^3) + (757*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (Pi^2*(-985 - 1035*S^2 + 2970*S^4 + 2912*S^6))/(486*S^3) + ((106*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(1927 + 8*S^2 + 1927*S^4))/(81*S^3))*HPL[{2}, -S^2] + (2*(62 + 194*S^2 + 66*S^4 + 203*S^6 + 71*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (92*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (2*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (88*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (176*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(125 + 257*S^2 + 66*S^4 + 140*S^6 + 8*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*(((1 + S^2)*(95927 - 56012*S^2 + 95927*S^4))/(2916*S^3) + (31*Pi^4*(16 + 35*S^6))/(1620*S^3) + (Pi^2*(1902 + 3186*S^2 + 2586*S^4 + 4633*S^6 + 3223*S^8))/(486*S^3*(1 + S^2)) + ((9 + 273*S^2 + 132*S^4 + 557*S^6 + 293*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-17 + 13*S^6)*HPL[{4}, -S^2])/(9*S^3) + (284*(-1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (8*(-14 + 13*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (24*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(-36 + 48*S^2 + 51*S^4 + 119*S^6 + 35*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^2*((163*Pi^4*S^3)/270 + (40005 - 90*S^2 + 95927*S^4)/(5832*S) + (Pi^2*(1116 + 3735*S^2 + 12242*S^4 + 9839*S^6))/(1944*S*(1 + S^2)) + ((20 + 152*S^2 + 66*S^4 + 245*S^6 + 113*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) + (11*(1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + ((Pi^2*(17 + 81*S^6))/(54*S^3) + (581 + 1565*S^2 + 2004*S^4 + 4459*S^6 + 3223*S^8)/(324*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((-7 + 25*S^6)*HPL[{2}, -S^2]^2)/(18*S^3) + HPL[{1}, -S^2]^2*((41*Pi^2*(1 + S^6))/(27*S^3) + (775 + 675*S^2 + 3195*S^4 + 3079*S^6)/(324*S^3) + (40*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-15 + 17*S^2 + 10*S^4 + 57*S^6 + 25*S^8)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)) + ((13 + 17*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-121 - 349*S^2 - 96*S^4 - 207*S^6 + 21*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(4 + 17*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (4*(8 + 35*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(18 + 9*S^2 + 47*S^4 + 29*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((2887 + 2323*S^2 + 7669*S^4 + 7801*S^6)/(648*S^3) + (Pi^2*(7 + 90*S^2 + 43*S^4 + 156*S^6 + 73*S^8))/(27*S^3*(1 + S^2)) + ((167 + 635*S^2 + 216*S^4 + 797*S^6 + 329*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{3}, -S^2])/S^3 - (80*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]*(((1 + S^2)*(-12553 + 13044*S^2))/(324*S) + (Pi^4*(1896 + 948*S^2 + 11375*S^4 + 9479*S^6))/(4860*S*(1 + S^2)) + (Pi^2*(-30090 - 21687*S^2 + 64096*S^4 + 56989*S^6))/(5832*S*(1 + S^2)) + ((305*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) + (2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3))*HPL[{1}, -S^2]^3 + (35*(-1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + ((12 - 2*S^2 - 2*S^4 + 39*S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((-2*Pi^2*(3 + 2*S^6))/(27*S^3) + (-256 - 366*S^2 + 300*S^4 + 581*S^6)/(81*S^3))*HPL[{3}, -S^2] + (4*(-6 - 12*S^2 - 3*S^4 + 31*S^6 + 37*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (4*(2 + 3*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((107 + 42*S^2 - 68*S^4 - 11*S^6)/(3*S^3) + (2*Pi^2*(-17 + 6*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (2*(-25 - 37*S^2 - 6*S^4 + 301*S^6 + 313*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(3 + 2*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (4*(9 + 7*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(-25 + 326*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(3 + 2*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (32*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((2*Pi^2*S^3)/3 + (-188 + 103*S^2 + 270*S^4)/(27*S))*Zeta[3] + HPL[{2}, -S^2]*((-285 - 1039*S^2 + 427*S^4 + 1253*S^6)/(54*S^3) + (Pi^2*(-46 + 86*S^2 + 66*S^4 + 931*S^6 + 799*S^8))/(162*S^3*(1 + S^2)) + (4*(3 + 2*S^6)*HPL[{3}, -S^2])/(9*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((2357*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(-162 - 50*S^2 + 62*S^4 + 379*S^6 + 267*S^8))/(54*S^3*(1 + S^2)) + (13*(-1 + S^6)*HPL[{2}, -S^2])/S^3 - (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((1027*(-1 + S^2)*(1 + S^2)^2)/(36*S^3) + (158*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (Pi^2*(-4523 - 8702*S^2 + 3162*S^4 + 13474*S^6 + 6565*S^8))/(972*S^3*(1 + S^2)) + ((22*Pi^2*(1 + S^6))/(27*S^3) + (-59 - 55*S^2 + 55*S^4 + 59*S^6)/(3*S^3))*HPL[{2}, -S^2] + (2*(-101 - 113*S^2 - 6*S^4 + 76*S^6 + 88*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (26*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (8*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (2*(-88 - 76*S^2 + 6*S^4 + 113*S^6 + 101*S^8)*Zeta[3])/(27*S^3*(1 + S^2)))) + (2*(134 + 67*S^2 + 148*S^4 + 14*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((1087*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) + (Pi^2*(-1046 - 1187*S^2 + 3685*S^4 + 3718*S^6))/(486*S^3) + (Pi^4*(-483 + 2525*S^2 + 1474*S^4 + 6518*S^6 + 3510*S^8))/(3240*S^3*(1 + S^2)) + (3*(-1 + S^6)*HPL[{2}, -S^2]^2)/S^3 + ((28*Pi^2*(1 + S^6))/(9*S^3) + (1873 + 1881*S^2 + 1989*S^4 + 1981*S^6)/(81*S^3))*HPL[{3}, -S^2] + ((-119 + 433*S^2 + 276*S^4 + 1189*S^6 + 637*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (188*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-212*Pi^2*(1 + S^6))/(27*S^3) - (2*(1927 + 1935*S^2 + 1935*S^4 + 1927*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] - (4*(35 + 167*S^2 + 66*S^4 + 230*S^6 + 98*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (176*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (712*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(133 + 397*S^2 + 132*S^4 + 397*S^6 + 133*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (176*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (352*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((10*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (2*(1760 + 1710*S^2 + 225*S^4 + 167*S^6))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*((2*(1 + S^2)*(1336 - 87*S^2 + 1336*S^4))/(81*S^3) + (Pi^2*(283 + 913*S^2 + 306*S^4 + 994*S^6 + 364*S^8))/(81*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (104*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (268*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) - 50*S^3*Zeta[7];
Et4uvwT=T*Et4uvwT1F1*(F-1/F)+T^2*(Et4uvwT2F2*(F^2-1/F^2))+T^3*(Et4uvwT3F1*(F-1/F)+Et4uvwT3F3*(F^3-1/F^3));
Et4vwuT1F1=(140*Pi^2*S)/9 + (1469*Pi^4*S)/540 + (23567*Pi^6*S)/45360 + (2*(1 + S^2)*HPL[{1}, -S^2]^6)/S + (4*(1 + S^2)*HPL[{1}, -S^2]^7)/(7*S) + HPL[{0}, S^2]^6*(S/8 + ((1 + S^2)*HPL[{1}, -S^2])/(16*S)) + ((-25 + 38*S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^5*((17*Pi^2*S)/432 + (17*(1 + S^2)*HPL[{1}, -S^2])/(72*S) + (17*(1 + S^2)*HPL[{1}, -S^2]^2)/(72*S) + (17*S*HPL[{2}, -S^2])/72) + HPL[{1}, -S^2]^5*((92*(1 + S^2))/(15*S) + (76*Pi^2*(1 + S^2))/(45*S) + (22*(1 + S^2)*HPL[{2}, -S^2])/(15*S)) + ((2 - S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-31 - 111*S^2)/(3*S) + (Pi^2*(5 - 17*S^2))/(18*S))*HPL[{5}, -S^2] + ((10 + 277*S^2)*HPL[{6}, -S^2])/(3*S) + (5*(15 + 14*S^2)*HPL[{7}, -S^2])/(3*S) - (4*(22 + 35*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-33 + 161*S^2)/(3*S) + (Pi^2*(-9 + 193*S^2))/(18*S))*HPL[{3, 2}, -S^2] + ((Pi^2*(-2 + 35*S^2))/S + (2*(-34 + 281*S^2))/(3*S))*HPL[{4, 1}, -S^2] + 9*S*HPL[{4, 2}, -S^2] + (16*HPL[{4, 3}, -S^2])/S + (2*(1 + 3*S^2)*HPL[{5, 1}, -S^2])/(3*S) - (3*(-17 + S^2)*HPL[{5, 2}, -S^2])/S - (2*(-108 + 53*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((8*Pi^2*(36 + 11*S^2))/(9*S) + (8*(29 + 16*S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((-4*(-181 + 3*S^2))/(3*S) + (2*Pi^2*(441 + 19*S^2))/(9*S))*HPL[{3, 1, 1}, -S^2] - (6*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (26*(-7 + 11*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + ((23 - 361*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) - (8*(-4 + 47*S^2)*HPL[{3, 3, 1}, -S^2])/S + (4*(-150 + 223*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (2*(-16 + 185*S^2)*HPL[{4, 1, 2}, -S^2])/S - (6*(-16 + 191*S^2)*HPL[{4, 2, 1}, -S^2])/S - (4*(-157 + 1753*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((20*Pi^2*(-11 + 4*S^2))/(3*S) + (32*(-23 + 10*S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] + (16*(-37 + 20*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) - (8*(-56 + 75*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (4*(-431 + 55*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) - (4*(-431 + 55*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) - (20*(-175 + 59*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) - (8*(-1315 + 421*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) + (32*(-23 + 43*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) - (16*(23 + 14*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (48*(23 + 14*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (32*(171 + 157*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) + (32*(-83 + 52*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S) + ((-34*Pi^2*S)/27 - (34*S*HPL[{0}, S^2]^2)/9 - (12*(1 + S^2)*HPL[{1}, -S^2])/S - (12*(1 + S^2)*HPL[{1}, -S^2]^2)/S + HPL[{0}, S^2]*(-12*S - (12*(1 + S^2)*HPL[{1}, -S^2])/S) - (4*(-10 + 17*S^2)*HPL[{2}, -S^2])/(9*S))*Log[T]^5 + (4*S*HPL[{0}, S^2] + (4*(1 + S^2)*HPL[{1}, -S^2])/S)*Log[T]^6 + ((-20*S)/3 - (34*Pi^2*S)/9)*Zeta[3] + 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((20*(-14 + S^2))/(3*S) + (2*Pi^2*(-89 + 21*S^2))/(9*S) + (Pi^4*(-1991 + 624*S^2))/(540*S) + (4*(21 + 19*S^2)*HPL[{3, 1}, -S^2])/S + (8*(23 + 14*S^2)*HPL[{2, 1, 1}, -S^2])/S + (176*Zeta[3])/(3*S)) + Log[T]^4*((86*Pi^2*S)/27 + (83*S*HPL[{0}, S^2]^3)/27 + (30*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (20*(1 + S^2)*HPL[{1}, -S^2]^3)/S + HPL[{0}, S^2]^2*((86*S)/9 + (31*(1 + S^2)*HPL[{1}, -S^2])/(3*S)) + (4*(-23 + 43*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((92*(1 + S^2))/(3*S) + (76*Pi^2*(1 + S^2))/(9*S) + (22*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]*((92*S)/3 + (218*Pi^2*S)/27 + (30*(1 + S^2)*HPL[{1}, -S^2])/S + (30*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (2*(-8 + 127*S^2)*HPL[{2}, -S^2])/(9*S)) - (2*(-3 + 104*S^2)*HPL[{3}, -S^2])/(9*S) + (4*(-83 + 52*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (208*S*Zeta[3])/9) + HPL[{0}, S^2]^4*((95*S)/36 + (119*Pi^2*S)/144 + (7*(1 + S^2)*HPL[{1}, -S^2]^2)/(6*S) + (20*(1 + S^2)*HPL[{1}, -S^2]^3)/(27*S) + (23*S*HPL[{2}, -S^2])/24 + HPL[{1}, -S^2]*((95*(1 + S^2))/(72*S) + (215*Pi^2*(1 + S^2))/(432*S) + (31*(1 + S^2)*HPL[{2}, -S^2])/(36*S)) - (S*HPL[{3}, -S^2])/8 + ((-31 + 6*S^2)*HPL[{2, 1}, -S^2])/(18*S) + (13*S*Zeta[3])/9) + HPL[{3, 1}, -S^2]*((Pi^2*(61 - 165*S^2))/(9*S) - (2*(-15 + 31*S^2))/S + (184*S*Zeta[3])/3) + HPL[{4}, -S^2]*((8*(-1 + 4*S^2))/S + (Pi^2*(-4 + 29*S^2))/(18*S) + (18*HPL[{2, 1}, -S^2])/S - (8*(-1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((100*(1 + S^2))/(3*S) + (242*Pi^2*(1 + S^2))/(27*S) + (2699*Pi^4*(1 + S^2))/(1620*S) + ((104*(1 + S^2))/(9*S) + (110*Pi^2*(1 + S^2))/(27*S))*HPL[{2}, -S^2] + (38*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (64*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (38*(1 + S^2)*HPL[{4}, -S^2])/(9*S) - (52*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (88*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (52*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^4*((16*(1 + S^2))/S + (77*Pi^2*(1 + S^2))/(18*S) + (13*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (34*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (22*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (28*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((Pi^4*(105 - 929*S^2))/(1080*S) + (Pi^2*(11 - 113*S^2))/(18*S) - (10*(1 + 16*S^2))/(3*S) - (8*HPL[{4}, -S^2])/S - (2*(-101 + 5*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-17 + 97*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(-11 + 97*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(-2 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((19 + 32*S^2)/(3*S) + (Pi^2*(21 + 74*S^2))/(18*S) + ((-1 - 97*S^2)*HPL[{3}, -S^2])/(6*S) + (2*(-37 + 20*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(-3 + 20*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((8*(-5 + 18*S^2))/S + (8*Pi^2*(-12 + 43*S^2))/(9*S) - (8*(-1 + 44*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^3*((79*Pi^2*S)/108 + (529*Pi^4*S)/2160 + (3*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (3*(1 + S^2)*HPL[{1}, -S^2]^4)/(2*S) + ((79*S)/18 + (Pi^2*(-3 + 161*S^2))/(108*S))*HPL[{2}, -S^2] + ((-1 + 21*S^2)*HPL[{2}, -S^2]^2)/(12*S) + HPL[{1}, -S^2]^2*((83*(1 + S^2))/(18*S) + (83*Pi^2*(1 + S^2))/(54*S) + (34*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((3 - 2*S^2)*HPL[{3}, -S^2])/(6*S) + ((1 + 2*S^2)*HPL[{4}, -S^2])/(2*S) + ((-71 + 6*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (25*S*HPL[{3, 1}, -S^2])/3 + (2*(-3 + 76*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) - (S*Zeta[3])/3 + HPL[{1}, -S^2]*((29*(1 + S^2))/(6*S) + (83*Pi^2*(1 + S^2))/(54*S) + (34*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + ((1 + S^2)*HPL[{3}, -S^2])/(3*S) - (68*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (2*(1 + S^2)*Zeta[3])/(9*S))) + Log[T]^3*((-184*Pi^2*S)/27 - (529*Pi^4*S)/270 - (83*S*HPL[{0}, S^2]^4)/54 - (40*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (20*(1 + S^2)*HPL[{1}, -S^2]^4)/S + HPL[{0}, S^2]^3*(-6*S - (6*(1 + S^2)*HPL[{1}, -S^2])/S) + ((-16*(-10 + 23*S^2))/(9*S) - (10*Pi^2*(-11 + 34*S^2))/(27*S))*HPL[{2}, -S^2] - (2*(5 + 8*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^2*((-184*(1 + S^2))/(3*S) - (152*Pi^2*(1 + S^2))/(9*S) - (44*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]^2*((-184*S)/9 - (56*Pi^2*S)/9 - (64*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (62*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (10*(-1 + 17*S^2)*HPL[{2}, -S^2])/(9*S)) + (4*(-4 + 101*S^2)*HPL[{3}, -S^2])/(9*S) + (4*(3 + 11*S^2)*HPL[{4}, -S^2])/(9*S) - (8*(-85 + 47*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (16*(-30 + 37*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (80*(-10 + 17*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (376*S*Zeta[3])/9 + HPL[{0}, S^2]*(-64*S - 16*Pi^2*S - (60*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (40*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (4*(-7 + 125*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((-184*(1 + S^2))/(3*S) - (16*Pi^2*(1 + S^2))/S - (52*(1 + S^2)*HPL[{2}, -S^2])/S) + (4*(-9 + 8*S^2)*HPL[{3}, -S^2])/(9*S) - (40*(-25 + 2*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (88*S*Zeta[3])/9) + HPL[{1}, -S^2]*((-64*(1 + S^2))/S - (154*Pi^2*(1 + S^2))/(9*S) - (52*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (136*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (88*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (112*(1 + S^2)*Zeta[3])/(3*S))) - (34*S*Zeta[5])/3 + Log[T]^2*(12*Pi^2*S + (1661*Pi^4*S)/540 + (17*S*HPL[{0}, S^2]^5)/36 + (30*(1 + S^2)*HPL[{1}, -S^2]^4)/S + (12*(1 + S^2)*HPL[{1}, -S^2]^5)/S + HPL[{0}, S^2]^4*((29*S)/12 + (20*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + (2*(22 + 35*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((184*(1 + S^2))/(3*S) + (152*Pi^2*(1 + S^2))/(9*S) + (44*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]^3*((79*S)/9 + (28*Pi^2*S)/9 + (9*(1 + S^2)*HPL[{1}, -S^2])/S + (9*(1 + S^2)*HPL[{1}, -S^2]^2)/S + ((-3 + 76*S^2)*HPL[{2}, -S^2])/(9*S)) + ((Pi^2*(9 - 113*S^2))/(9*S) - (2*(-7 + 99*S^2))/(3*S))*HPL[{3}, -S^2] - (10*S*HPL[{4}, -S^2])/3 - (2*(-13 + 7*S^2)*HPL[{5}, -S^2])/(3*S) + ((10*Pi^2*(-11 + 4*S^2))/(3*S) + (16*(-23 + 10*S^2))/(3*S))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(36*S + (173*Pi^2*S)/18 + (32*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (62*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (2*(-1 + 43*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((104*(1 + S^2))/(3*S) + (173*Pi^2*(1 + S^2))/(18*S) + (77*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((2 - 3*S^2)*HPL[{3}, -S^2])/S + (4*(-41 + 4*S^2)*HPL[{2, 1}, -S^2])/(3*S)) - (4*(-56 + 75*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(-13 + 185*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(-17 + 299*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (16*(-23 + 43*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*(23 + 14*S^2)*HPL[{2, 2, 1}, -S^2])/S + (16*(105 + 11*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (16*(-83 + 52*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-160*S)/3 - (104*Pi^2*S)/9)*Zeta[3] + HPL[{1}, -S^2]^2*((96*(1 + S^2))/S + (77*Pi^2*(1 + S^2))/(3*S) + (26*(1 + S^2)*HPL[{2}, -S^2])/S - (68*(1 + S^2)*HPL[{3}, -S^2])/S - (44*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (56*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]*((100*(1 + S^2))/S + (242*Pi^2*(1 + S^2))/(9*S) + (2699*Pi^4*(1 + S^2))/(540*S) + ((104*(1 + S^2))/(3*S) + (110*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (38*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (64*(1 + S^2)*HPL[{3}, -S^2])/S - (38*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (52*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (88*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (52*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((4*(-5 + 18*S^2))/S + (4*Pi^2*(-12 + 43*S^2))/(9*S) - (2*(-11 + 97*S^2)*HPL[{3}, -S^2])/(3*S) - (4*(23 + 14*S^2)*HPL[{2, 1}, -S^2])/S - (4*(-1 + 44*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]*(100*S + (217*Pi^2*S)/9 + (433*Pi^4*S)/90 + (60*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (30*(1 + S^2)*HPL[{1}, -S^2]^4)/S + ((4*(-1 + 21*S^2))/S + (Pi^2*(-11 + 203*S^2))/(9*S))*HPL[{2}, -S^2] + ((-1 + 116*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^2*((92*(1 + S^2))/S + (24*Pi^2*(1 + S^2))/S + (78*(1 + S^2)*HPL[{2}, -S^2])/S) - (2*(-9 + 8*S^2)*HPL[{3}, -S^2])/(3*S) + (2*(1 + 20*S^2)*HPL[{4}, -S^2])/(3*S) + (16*(-31 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(-4 + 63*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (8*(-8 + 127*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (44*S*Zeta[3])/3 + HPL[{1}, -S^2]*((96*(1 + S^2))/S + (24*Pi^2*(1 + S^2))/S + (78*(1 + S^2)*HPL[{2}, -S^2])/S + (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (156*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (40*(1 + S^2)*Zeta[3])/(3*S))) - (220*S*Zeta[5])/3) + HPL[{0}, S^2]^2*((140*S)/3 + (149*Pi^2*S)/18 + (365*Pi^4*S)/216 + (16*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + (31*(1 + S^2)*HPL[{1}, -S^2]^5)/(15*S) + ((-1 + 39*S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^3*((104*(1 + S^2))/(9*S) + (173*Pi^2*(1 + S^2))/(54*S) + (77*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((2 - 7*S^2)/(3*S) + (Pi^2*(1 - 3*S^2))/(6*S))*HPL[{3}, -S^2] + ((-2 + 17*S^2)*HPL[{4}, -S^2])/(3*S) + ((-4 - 5*S^2)*HPL[{5}, -S^2])/(3*S) + ((2*(-43 + S^2))/(3*S) + (2*Pi^2*(-36 + 5*S^2))/(9*S))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((20*(1 + S^2))/S + (5*Pi^2*(1 + S^2))/S + (83*(1 + S^2)*HPL[{2}, -S^2])/(6*S) - (77*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) - (5*(-1 + 18*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(1 + 2*S^2)*HPL[{3, 2}, -S^2])/(3*S) + ((-1 + 16*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (4*(-1 + 43*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(75 + 2*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2*(-77 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (8*(-41 + 4*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (2*S + (26*Pi^2*S)/9)*Zeta[3] + HPL[{2}, -S^2]*((2*(2 + 27*S^2))/(3*S) + (Pi^2*(-2 + 155*S^2))/(36*S) + ((-1 - 2*S^2)*HPL[{3}, -S^2])/(3*S) + ((-75 - 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) + Zeta[3]/S) + HPL[{1}, -S^2]*((70*(1 + S^2))/(3*S) + (199*Pi^2*(1 + S^2))/(36*S) + (653*Pi^4*(1 + S^2))/(540*S) + ((15*(1 + S^2))/S + (139*Pi^2*(1 + S^2))/(36*S))*HPL[{2}, -S^2] + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((1 + S^2)*HPL[{3}, -S^2])/S + (2*(1 + S^2)*HPL[{4}, -S^2])/S - (83*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (76*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (154*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + ((1 + S^2)*Zeta[3])/(3*S)) + (55*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*((50*(1 + S^2))/S + (44*Pi^2*(1 + S^2))/(3*S) + (931*Pi^4*(1 + S^2))/(360*S) + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-86*(1 + S^2))/(3*S) - (17*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (11*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (14*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-104*(1 + S^2))/(3*S) - (110*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (12*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (184*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (590*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (52*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (152*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (320*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (88*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-68*(1 + S^2))/(3*S) - (14*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((26*(1 + S^2))/S + (61*Pi^2*(1 + S^2))/(9*S) - (92*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (88*(1 + S^2)*Zeta[3])/(3*S)) - (74*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]*((145*Pi^2*(1 + S^2))/(9*S) + (3151*Pi^4*(1 + S^2))/(1080*S) + (23567*Pi^6*(1 + S^2))/(45360*S) + ((17*(1 + S^2))/S + (95*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2]^2 + (13*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + (5*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-19*(1 + S^2))/(3*S) - (7*Pi^2*(1 + S^2))/(18*S))*HPL[{4}, -S^2] + (26*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (39*(1 + S^2)*HPL[{6}, -S^2])/S - (76*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-32*(1 + S^2))/(3*S) - (88*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] + (184*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (574*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (9*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (64*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((208*(1 + S^2))/(3*S) + (220*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (152*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (328*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (104*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (236*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (104*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (32*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (176*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-16*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (6*(1 + S^2)*Zeta[3]^2)/S + HPL[{2}, -S^2]*((130*(1 + S^2))/(3*S) + (71*Pi^2*(1 + S^2))/(9*S) + (1579*Pi^4*(1 + S^2))/(1080*S) - (92*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (19*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (236*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (152*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (88*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-22*(1 + S^2))/S - (5*Pi^2*(1 + S^2))/S + (184*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (16*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-52*(1 + S^2))/S - (122*Pi^2*(1 + S^2))/(9*S) + (176*(1 + S^2)*Zeta[3])/(3*S)) - (18*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((20*(-1 + 14*S^2))/(3*S) + (Pi^2*(-11 + 108*S^2))/(9*S) + (Pi^4*(-318 + 2137*S^2))/(1080*S) + ((Pi^2*(9 - 101*S^2))/(18*S) + (21 - 85*S^2)/(3*S))*HPL[{3}, -S^2] + ((-4 - 7*S^2)*HPL[{4}, -S^2])/(3*S) + ((5 + 3*S^2)*HPL[{5}, -S^2])/S + ((-4*Pi^2*(36 + 11*S^2))/(9*S) - (4*(29 + 16*S^2))/(3*S))*HPL[{2, 1}, -S^2] - (2*(51 + 71*S^2)*HPL[{3, 1}, -S^2])/(3*S) + ((-7 + 185*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2*(-8 + 97*S^2)*HPL[{4, 1}, -S^2])/S + (8*(22 + 35*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(-37 + 20*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(-211 + 23*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (8*(23 + 14*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-4*Pi^2*(-1 + 11*S^2))/(9*S) - (4*(-3 + 19*S^2))/(3*S))*Zeta[3] - (10*(-2 + 7*S^2)*Zeta[5])/(3*S)) + HPL[{0}, S^2]*((25*Pi^2*S)/3 + (493*Pi^4*S)/270 + (373*Pi^6*S)/1008 + (6*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (2*(1 + S^2)*HPL[{1}, -S^2]^6)/S + ((-1 + 18*S^2)/S + (Pi^2*(-4 + 179*S^2))/(36*S))*HPL[{2}, -S^2]^2 + ((-5 + 52*S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{1}, -S^2]^4*((46*(1 + S^2))/(3*S) + (4*Pi^2*(1 + S^2))/S + (13*(1 + S^2)*HPL[{2}, -S^2])/S) - (2*(-1 + 3*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(5 + 19*S^2))/(9*S) + (2*(11 + 23*S^2))/(3*S))*HPL[{4}, -S^2] - (2*(-13 + 17*S^2)*HPL[{5}, -S^2])/(3*S) + (2*(15 + 17*S^2)*HPL[{6}, -S^2])/(3*S) - (2*(-1 + 116*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((Pi^2*(8 - 201*S^2))/(9*S) - (4*(1 + 67*S^2))/(3*S))*HPL[{3, 1}, -S^2] + (32*S*HPL[{3, 2}, -S^2])/3 + (4*(-8 + 27*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (4*(3 + 13*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((8*(-1 + 21*S^2))/S + (2*Pi^2*(-11 + 203*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (152*HPL[{2, 2, 1}, -S^2])/S - (4*(-351 + 8*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (8*(-5 + 52*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (4*(-29 + 332*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (32*(-31 + 2*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (16*(-4 + 63*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (16*(-8 + 127*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (-10*S - (14*Pi^2*S)/9)*Zeta[3] - 2*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((4*(-22 + S^2))/S + (Pi^2*(-195 + 14*S^2))/(9*S) - (8*(-4 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((Pi^2*(9 - 7*S^2))/(9*S) - (2*(-11 + 7*S^2))/(3*S) + (4*(5 + 6*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((50*(1 + S^2))/S + (221*Pi^2*(1 + S^2))/(18*S) + (1289*Pi^4*(1 + S^2))/(540*S) + ((40*(1 + S^2))/S + (185*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2] + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (78*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (232*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (156*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (20*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((32*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/S + (26*(1 + S^2)*HPL[{2}, -S^2])/S + (4*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (52*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (40*(1 + S^2)*Zeta[3])/(9*S)) + HPL[{2}, -S^2]*(50*S + (Pi^2*(-6 + 205*S^2))/(18*S) + (Pi^4*(-37 + 1242*S^2))/(540*S) - (16*S*HPL[{3}, -S^2])/3 + (4*(-1 + 3*S^2)*HPL[{4}, -S^2])/(3*S) - (76*HPL[{2, 1}, -S^2])/S - (232*S*HPL[{3, 1}, -S^2])/3 + (4*(-1 + 116*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (2*(2 + 3*S^2)*Zeta[3])/(3*S)) - (28*S*Zeta[5])/3 + HPL[{1}, -S^2]*((50*(1 + S^2))/S + (77*Pi^2*(1 + S^2))/(6*S) + (1289*Pi^4*(1 + S^2))/(540*S) + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((16*(1 + S^2))/(3*S) + (4*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (16*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (8*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-80*(1 + S^2))/S - (185*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (232*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (64*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (156*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (152*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (1376*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (312*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-34*(1 + S^2))/(3*S) - (8*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((42*(1 + S^2))/S + (185*Pi^2*(1 + S^2))/(18*S) - (16*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (14*(1 + S^2)*Zeta[3])/(3*S)) - (4*(1 + S^2)*Zeta[5])/S)) + Log[T]*((-140*Pi^2*S)/9 - (1849*Pi^4*S)/540 - (373*Pi^6*S)/504 - (S*HPL[{0}, S^2]^6)/8 - (12*(1 + S^2)*HPL[{1}, -S^2]^5)/S - (4*(1 + S^2)*HPL[{1}, -S^2]^6)/S + HPL[{0}, S^2]^5*((-17*S)/36 - (17*(1 + S^2)*HPL[{1}, -S^2])/(36*S)) + ((Pi^2*(-23 - 73*S^2))/(9*S) - (2*(22 + 35*S^2))/(3*S))*HPL[{2}, -S^2]^2 - (2*(-8 + 11*S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^4*((-95*S)/36 - (109*Pi^2*S)/108 - (7*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (20*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) - (37*S*HPL[{2}, -S^2])/18) + HPL[{1}, -S^2]^4*((-92*(1 + S^2))/(3*S) - (76*Pi^2*(1 + S^2))/(9*S) - (22*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (2*(-4 + 5*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(-2 - 5*S^2))/(9*S) - (2*(10 + 7*S^2))/(3*S))*HPL[{4}, -S^2] + (2*(-23 + 5*S^2)*HPL[{5}, -S^2])/(3*S) - (2*(60 + 109*S^2)*HPL[{6}, -S^2])/(3*S) + (12*(5 + 8*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((4*(-49 + 83*S^2))/(3*S) + (2*Pi^2*(-65 + 157*S^2))/(9*S))*HPL[{3, 1}, -S^2] - (2*(-9 + 185*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(-16 + 297*S^2)*HPL[{4, 1}, -S^2])/(3*S) - 18*S*HPL[{4, 2}, -S^2] - (4*(-9 + 25*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-32*(-10 + 23*S^2))/(3*S) - (20*Pi^2*(-11 + 34*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (16*(35 + 22*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(214 + 31*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (12*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (4*(-29 + 41*S^2)*HPL[{3, 2, 1}, -S^2])/S - (8*(-147 + 187*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (16*(-85 + 47*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (32*(-30 + 37*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (160*(-10 + 17*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (40*S + (32*Pi^2*S)/3)*Zeta[3] + 4*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-8*(-18 + 5*S^2))/S - (20*Pi^2*(-17 + 5*S^2))/(9*S) - (120*Zeta[3])/S) + HPL[{0}, S^2]^3*((-79*S)/9 - (83*Pi^2*S)/27 - (9*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (6*(1 + S^2)*HPL[{1}, -S^2]^3)/S + ((3 - 74*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((-83*(1 + S^2))/(9*S) - (83*Pi^2*(1 + S^2))/(27*S) - (68*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((-1 + 2*S^2)*HPL[{3}, -S^2])/(3*S) - (2*(-71 + 8*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (22*S*Zeta[3])/9) + HPL[{0}, S^2]^2*((-140*S)/3 - (187*Pi^2*S)/18 - (433*Pi^4*S)/180 - (64*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (31*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + ((Pi^2*(5 - 159*S^2))/(18*S) - (4*(1 + 23*S^2))/(3*S))*HPL[{2}, -S^2] + ((-1 - 74*S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^2*((-104*(1 + S^2))/(3*S) - (173*Pi^2*(1 + S^2))/(18*S) - (77*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-3 + 2*S^2)*HPL[{3}, -S^2])/S + ((-5 - 16*S^2)*HPL[{4}, -S^2])/(3*S) - (2*(-85 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-40*(1 + S^2))/S - (10*Pi^2*(1 + S^2))/S - (83*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (154*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) + (2*(-5 + 83*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (20*(-1 + 17*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*S*Zeta[3])/3) + HPL[{2}, -S^2]*((Pi^4*(412 - 2203*S^2))/(540*S) - (20*(-1 + 14*S^2))/(3*S) - (4*Pi^2*(-9 + 46*S^2))/(9*S) + (2*(-9 + 97*S^2)*HPL[{3}, -S^2])/(3*S) + (2*(-8 + 19*S^2)*HPL[{4}, -S^2])/(3*S) + (8*(35 + 22*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(55 + 61*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (24*(5 + 8*S^2)*HPL[{2, 1, 1}, -S^2])/S + (176*S*Zeta[3])/3) + HPL[{3}, -S^2]*((2*(-17 + 95*S^2))/(3*S) + (Pi^2*(-13 + 107*S^2))/(9*S) + (4*(-103 + 5*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((-64*(1 + S^2))/S - (154*Pi^2*(1 + S^2))/(9*S) - (52*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (136*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (88*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (112*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-100*(1 + S^2))/S - (242*Pi^2*(1 + S^2))/(9*S) - (2699*Pi^4*(1 + S^2))/(540*S) + ((-104*(1 + S^2))/(3*S) - (110*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (38*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (64*(1 + S^2)*HPL[{3}, -S^2])/S + (38*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (52*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (88*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (52*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]*(-100*S - (223*Pi^2*S)/9 - (1289*Pi^4*S)/270 - (30*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (12*(1 + S^2)*HPL[{1}, -S^2]^5)/S - 38*S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^3*((-184*(1 + S^2))/(3*S) - (16*Pi^2*(1 + S^2))/S - (52*(1 + S^2)*HPL[{2}, -S^2])/S) + ((4*(-4 + 5*S^2))/(3*S) + (2*Pi^2*(-6 + 7*S^2))/(9*S))*HPL[{3}, -S^2] - (44*S*HPL[{4}, -S^2])/3 + (4*(1 + 3*S^2)*HPL[{5}, -S^2])/(3*S) + ((-8*(-21 + S^2))/S - (4*Pi^2*(-98 + 9*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (4*(-7 + 124*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(3 + 2*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(3 + 16*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (8*(-7 + 125*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*(-115 + 2*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (16*(-177 + 7*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (80*(-25 + 2*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + 12*S*Zeta[3] + HPL[{1}, -S^2]^2*((-96*(1 + S^2))/S - (24*Pi^2*(1 + S^2))/S - (78*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (156*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (40*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]*((-100*(1 + S^2))/S - (221*Pi^2*(1 + S^2))/(9*S) - (1289*Pi^4*(1 + S^2))/(270*S) + ((-80*(1 + S^2))/S - (185*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (38*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (32*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (156*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (464*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (312*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (40*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((Pi^2*(10 - 199*S^2))/(9*S) - (4*(-1 + 22*S^2))/S + (4*(3 + 2*S^2)*HPL[{3}, -S^2])/(3*S) - (4*(-115 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-1 + 9*S^2)*Zeta[3])/(3*S))) + 60*S*Zeta[5] + HPL[{1}, -S^2]*((-100*(1 + S^2))/S - (88*Pi^2*(1 + S^2))/(3*S) - (931*Pi^4*(1 + S^2))/(180*S) - (38*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((172*(1 + S^2))/(3*S) + (34*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (22*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (28*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((208*(1 + S^2))/(3*S) + (220*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (24*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (368*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (1180*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (104*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (304*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (640*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (176*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((136*(1 + S^2))/(3*S) + (28*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-52*(1 + S^2))/S - (122*Pi^2*(1 + S^2))/(9*S) + (184*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (152*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (176*(1 + S^2)*Zeta[3])/(3*S)) + (148*(1 + S^2)*Zeta[5])/(3*S)));
Et4vwuT2F2=(Pi^6*(-47134 - 43573*S^2))/181440 + (Pi^4*(-4201 - 9807*S^2))/8640 + (Pi^2*(-512 - 1335*S^2))/288 + ((-47 - 108*S^2 - 61*S^4)*HPL[{1}, -S^2]^6)/(54*S^2) - (2*(1 + S^4)*HPL[{1}, -S^2]^7)/(7*S^2) + HPL[{0}, S^2]^6*((-1 - S^2)/32 + ((-1 - S^4)*HPL[{1}, -S^2])/(32*S^2)) + ((62 - 26*S^2 - 85*S^4)*HPL[{2}, -S^2]^3)/(36*S^2) + HPL[{0}, S^2]^5*((-17*Pi^2*S^2)/864 + (1 - 36*S^2)/96 - ((1 + S^2)*(-3 + 71*S^2)*HPL[{1}, -S^2])/(288*S^2) - (17*(1 + S^4)*HPL[{1}, -S^2]^2)/(144*S^2) - (17*S^2*HPL[{2}, -S^2])/144) + HPL[{1}, -S^2]^5*((-199 - 504*S^2 - 305*S^4)/(90*S^2) - (38*Pi^2*(1 + S^4))/(45*S^2) - (11*(1 + S^4)*HPL[{2}, -S^2])/(15*S^2)) + ((10 - 18*S^2 + 13*S^4)*HPL[{3}, -S^2]^2)/(12*S^2) + ((141 + 56*S^2 - 649*S^4)/(24*S^2) + (Pi^2*(-5 + 17*S^4))/(36*S^2))*HPL[{5}, -S^2] + ((80 - 234*S^2 - 469*S^4)*HPL[{6}, -S^2])/(12*S^2) - (5*(15 + 14*S^4)*HPL[{7}, -S^2])/(6*S^2) + ((59 + 114*S^2 + 100*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((87 - 868*S^2 - 361*S^4)/(24*S^2) + (Pi^2*(9 - 193*S^4))/(36*S^2))*HPL[{3, 2}, -S^2] + ((24 - 1346*S^2 - 491*S^4)/(12*S^2) + (Pi^2*(2 - 35*S^4))/(2*S^2))*HPL[{4, 1}, -S^2] - (3*(-2 + 6*S^2 + S^4)*HPL[{4, 2}, -S^2])/(4*S^2) - (8*HPL[{4, 3}, -S^2])/S^2 + ((-67 - 64*S^2 + 169*S^4)*HPL[{5, 1}, -S^2])/(6*S^2) + (3*(-17 + S^4)*HPL[{5, 2}, -S^2])/(2*S^2) + ((-108 + 53*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((-58 - 282*S^2 - 41*S^4)/(3*S^2) - (4*Pi^2*(36 + 11*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((-325 - 1256*S^2 - 79*S^4)/(6*S^2) + (Pi^2*(-441 - 19*S^4))/(9*S^2))*HPL[{3, 1, 1}, -S^2] + (3*(-3 + S^4)*HPL[{3, 1, 2}, -S^2])/(2*S^2) + ((221 - 104*S^2 - 331*S^4)*HPL[{3, 2, 1}, -S^2])/(6*S^2) + ((-23 + 361*S^4)*HPL[{3, 2, 2}, -S^2])/(6*S^2) + (4*(-4 + 47*S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + ((406 - 118*S^2 - 547*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + ((-16 + 185*S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (3*(-16 + 191*S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (2*(-157 + 1753*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((-10*Pi^2*(-11 + 4*S^4))/(3*S^2) - (2*(-89 - 103*S^2 + 55*S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (8*(-37 + 20*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) + (2*(-168 + 24*S^2 + 223*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (2*(-431 + 55*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + (2*(-431 + 55*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + (10*(-175 + 59*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (4*(-1315 + 421*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) - (8*(-68 + 33*S^2 + 118*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (8*(23 + 14*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (24*(23 + 14*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (16*(171 + 157*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) - (16*(-83 + 52*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) + (3 + (17*Pi^2*S^2)/27 + (17*S^2*HPL[{0}, S^2]^2)/9 + ((47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2])/(9*S^2) + (6*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + HPL[{0}, S^2]*((54 + 61*S^2)/9 + (6*(1 + S^4)*HPL[{1}, -S^2])/S^2) + (2*(-10 + 17*S^4)*HPL[{2}, -S^2])/(9*S^2))*Log[T]^5 + (-2 - 2*S^2*HPL[{0}, S^2] - (2*(1 + S^4)*HPL[{1}, -S^2])/S^2)*Log[T]^6 + ((171 + 2*S^2)/12 + (Pi^2*(106 + 49*S^2))/36)*Zeta[3] + ((-6 + 7*S^2)*Zeta[3]^2)/2 + HPL[{3, 1}, -S^2]*((Pi^2*(-193 + 172*S^2 + 461*S^4))/(36*S^2) + (-637 + 4*S^2 + 1115*S^4)/(24*S^2) - (92*S^2*Zeta[3])/3) + HPL[{0}, S^2]^4*((Pi^2*(-430 - 533*S^2))/1728 - (5*(21 + 115*S^2))/576 + ((-37 - 162*S^2 - 121*S^4)*HPL[{1}, -S^2]^2)/(144*S^2) - (10*(1 + S^4)*HPL[{1}, -S^2]^3)/(27*S^2) + ((-124 - 245*S^2)*HPL[{2}, -S^2])/288 + HPL[{1}, -S^2]*((-105 - 672*S^2 - 535*S^4)/(576*S^2) - (215*Pi^2*(1 + S^4))/(864*S^2) - (31*(1 + S^4)*HPL[{2}, -S^2])/(72*S^2)) + (S^2*HPL[{3}, -S^2])/16 + ((31 - 6*S^4)*HPL[{2, 1}, -S^2])/(36*S^2) - (13*S^2*Zeta[3])/18) + Log[T]^4*(-23/6 + (Pi^2*(-114 - 59*S^2))/27 - (83*S^2*HPL[{0}, S^2]^3)/54 - (5*(47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2]^2)/(18*S^2) - (10*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + HPL[{0}, S^2]^2*((-93 - 118*S^2)/18 - (31*(1 + S^4)*HPL[{1}, -S^2])/(6*S^2)) + ((68 - 33*S^2 - 118*S^4)*HPL[{2}, -S^2])/(9*S^2) + HPL[{0}, S^2]*((-109*Pi^2*S^2)/27 + (-219 - 305*S^2)/18 - (5*(47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2])/(18*S^2) - (15*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + ((8 - 127*S^4)*HPL[{2}, -S^2])/(9*S^2)) + HPL[{1}, -S^2]*((-199 - 504*S^2 - 305*S^4)/(18*S^2) - (38*Pi^2*(1 + S^4))/(9*S^2) - (11*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-3 + 104*S^4)*HPL[{3}, -S^2])/(9*S^2) - (2*(-83 + 52*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (104*S^2*Zeta[3])/9) + HPL[{2, 1}, -S^2]*((Pi^4*(1991 - 624*S^4))/(1080*S^2) + (Pi^2*(173 + 296*S^2 - 56*S^4))/(36*S^2) + (341 + 738*S^2 - 4*S^4)/(24*S^2) - (2*(21 + 19*S^4)*HPL[{3, 1}, -S^2])/S^2 - (4*(23 + 14*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(59 + 44*S^2)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((31 + 125*S^2 - 167*S^4)/(24*S^2) + (Pi^2*(30 + 22*S^2 - 95*S^4))/(72*S^2) - (9*HPL[{2, 1}, -S^2])/S^2 + (4*(-1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(-365 - 912*S^2 - 547*S^4))/(216*S^2) + (-173 - 489*S^2 - 316*S^4)/(36*S^2) + ((5 - 44*S^2 - 49*S^4)*HPL[{2}, -S^2])/(12*S^2) + (17*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (11*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (14*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((48 + 732*S^2 - 49*S^4)/(48*S^2) + (Pi^2*(-5 + 424*S^2 + 109*S^4))/(144*S^2) + (Pi^4*(-105 + 929*S^4))/(2160*S^2) + (4*HPL[{4}, -S^2])/S^2 + ((-267 - 176*S^2 - 19*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((17 - 97*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(-11 + 97*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((2 + 6*S^2 + 3*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((-613 - 2016*S^2 - 1403*S^4)/(72*S^2) - (2699*Pi^4*(1 + S^4))/(3240*S^2) - (7*Pi^2*(21 + 61*S^2 + 40*S^4))/(54*S^2) + ((20 - 77*S^2 - 97*S^4)/(9*S^2) - (55*Pi^2*(1 + S^4))/(27*S^2))*HPL[{2}, -S^2] - (19*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (4*(12 + 17*S^2 + 5*S^4)*HPL[{3}, -S^2])/(3*S^2) + (19*(1 + S^4)*HPL[{4}, -S^2])/(9*S^2) + ((-5 + 44*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (7*(5 + 8*S^2 + 3*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((-86 - 70*S^2 - 159*S^4)/(16*S^2) + (Pi^2*(-31 - 95*S^2 - 100*S^4))/(36*S^2) + ((1 + 97*S^4)*HPL[{3}, -S^2])/(12*S^2) + ((37 - 20*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((-3 + 20*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((230 - 116*S^2 - 523*S^4)/(6*S^2) + (Pi^2*(77 - 110*S^2 - 236*S^4))/(9*S^2) + (4*(-1 + 44*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^3*((-529*Pi^4*S^2)/4320 + (Pi^2*(-136 - 1633*S^2))/864 - (13*(-5 + 112*S^2))/288 + ((-89 - 328*S^2 - 231*S^4)*HPL[{1}, -S^2]^3)/(108*S^2) - (3*(1 + S^4)*HPL[{1}, -S^2]^4)/(4*S^2) + ((48 - 160*S^2 - 481*S^4)/(144*S^2) + (Pi^2*(3 - 161*S^4))/(216*S^2))*HPL[{2}, -S^2] + ((1 - 21*S^4)*HPL[{2}, -S^2]^2)/(24*S^2) + HPL[{1}, -S^2]^2*((-83 - 600*S^2 - 501*S^4)/(144*S^2) - (83*Pi^2*(1 + S^4))/(108*S^2) - (17*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((-1 + 2*S^2)^2*HPL[{3}, -S^2])/(24*S^2) + ((-1 - 2*S^4)*HPL[{4}, -S^2])/(4*S^2) + ((89 + 140*S^2 - 32*S^4)*HPL[{2, 1}, -S^2])/(36*S^2) + (25*S^2*HPL[{3, 1}, -S^2])/6 + ((3 - 76*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + ((-4 - 119*S^2)*Zeta[3])/36 + HPL[{1}, -S^2]*((29 - 1068*S^2 - 1097*S^4)/(288*S^2) + (Pi^2*(-37 - 334*S^2 - 293*S^4))/(216*S^2) + ((-37 - 138*S^2 - 97*S^4)*HPL[{2}, -S^2])/(36*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/(6*S^2) + (34*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + ((-1 - S^4)*Zeta[3])/(9*S^2))) + Log[T]^3*(4 + (529*Pi^4*S^2)/540 + (Pi^2*(85 + 83*S^2))/18 + (83*S^2*HPL[{0}, S^2]^4)/108 + (10*(47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2]^3)/(27*S^2) + (10*(1 + S^4)*HPL[{1}, -S^2]^4)/S^2 + HPL[{0}, S^2]^3*((162 + 251*S^2)/54 + (3*(1 + S^4)*HPL[{1}, -S^2])/S^2) + ((5*Pi^2*(-11 + 34*S^4))/(27*S^2) + (-43 + 17*S^2 + 83*S^4)/(3*S^2))*HPL[{2}, -S^2] + ((5 + 8*S^4)*HPL[{2}, -S^2]^2)/S^2 + HPL[{1}, -S^2]^2*((76*Pi^2*(1 + S^4))/(9*S^2) + (199 + 504*S^2 + 305*S^4)/(9*S^2) + (22*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]^2*((28*Pi^2*S^2)/9 + (40 + 83*S^2)/6 + ((65 + 186*S^2 + 121*S^4)*HPL[{1}, -S^2])/(9*S^2) + (31*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + (5*(-1 + 17*S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((-2 - 204*S^2 - 143*S^4)*HPL[{3}, -S^2])/(9*S^2) - (2*(3 + 11*S^4)*HPL[{4}, -S^2])/(9*S^2) + (2*(-121 - 66*S^2 + 89*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (8*(-30 + 37*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (40*(-10 + 17*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) - (2*(84 + 89*S^2)*Zeta[3])/9 + HPL[{0}, S^2]*((2*Pi^2*(108 + 139*S^2))/27 + (2*(93 + 158*S^2))/9 + (5*(47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + (20*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + ((-31 + 234*S^2 + 299*S^4)*HPL[{2}, -S^2])/(9*S^2) + HPL[{1}, -S^2]*((8*Pi^2*(1 + S^4))/S^2 + (199 + 504*S^2 + 305*S^4)/(9*S^2) + (26*(1 + S^4)*HPL[{2}, -S^2])/S^2) - (2*(-9 + 8*S^4)*HPL[{3}, -S^2])/(9*S^2) + (20*(-25 + 2*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (44*S^2*Zeta[3])/9) + HPL[{1}, -S^2]*((173 + 489*S^2 + 316*S^4)/(9*S^2) + (Pi^2*(365 + 912*S^2 + 547*S^4))/(54*S^2) + ((-5 + 44*S^2 + 49*S^4)*HPL[{2}, -S^2])/(3*S^2) - (68*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (56*(1 + S^4)*Zeta[3])/(3*S^2))) + ((178 + 121*S^2)*Zeta[5])/12 + HPL[{0}, S^2]^2*((Pi^4*(-1306 - 1699*S^2))/2160 + (-437 - 1335*S^2)/96 + (Pi^2*(-283 - 1098*S^2))/288 + ((-65 - 186*S^2 - 121*S^4)*HPL[{1}, -S^2]^4)/(36*S^2) - (31*(1 + S^4)*HPL[{1}, -S^2]^5)/(30*S^2) + ((-3 - 76*S^2 - 100*S^4)*HPL[{2}, -S^2]^2)/(24*S^2) + HPL[{1}, -S^2]^3*((-173*Pi^2*(1 + S^4))/(108*S^2) - (5*(19 + 70*S^2 + 51*S^4))/(36*S^2) - (77*(1 + S^4)*HPL[{2}, -S^2])/(18*S^2)) + ((-14 - 6*S^2 - 29*S^4)/(24*S^2) + (Pi^2*(-1 + 3*S^4))/(12*S^2))*HPL[{3}, -S^2] + ((-2 - 8*S^2 - 29*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((4 + 5*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((Pi^2*(36 - 5*S^4))/(9*S^2) + (84 + 193*S^2 - S^4)/(12*S^2))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((-157 - 702*S^2 - 545*S^4)/(48*S^2) + (Pi^2*(-51 - 174*S^2 - 121*S^4))/(36*S^2) + ((-99 - 304*S^2 - 213*S^4)*HPL[{2}, -S^2])/(24*S^2) + (77*(1 + S^4)*HPL[{2, 1}, -S^2])/(6*S^2)) + ((-25 + 148*S^2 + 238*S^4)*HPL[{3, 1}, -S^2])/(12*S^2) + ((-1 - 2*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((1 - 16*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((9 - 77*S^2 - 118*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-75 - 2*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + ((-77 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (4*(-41 + 4*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-13*Pi^2*S^2)/9 + (1 - 2*S^2)/4)*Zeta[3] + HPL[{2}, -S^2]*((-28 - 208*S^2 - 523*S^4)/(48*S^2) + (Pi^2*(18 - 278*S^2 - 481*S^4))/(144*S^2) + ((1 + 2*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((75 + 2*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) - Zeta[3]/(2*S^2)) + HPL[{1}, -S^2]*((-373 - 1612*S^2 - 1239*S^4)/(96*S^2) + (Pi^2*(-295 - 1372*S^2 - 1045*S^4))/(288*S^2) - (653*Pi^4*(1 + S^4))/(1080*S^2) + ((-37 - 153*S^2 - 124*S^4)/(12*S^2) - (139*Pi^2*(1 + S^4))/(72*S^2))*HPL[{2}, -S^2] - (19*(1 + S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + ((13 + 4*S^2 - 17*S^4)*HPL[{3}, -S^2])/(12*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/S^2 + ((99 + 304*S^2 + 213*S^4)*HPL[{2, 1}, -S^2])/(12*S^2) + (38*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (77*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((9 - 4*S^2 - 5*S^4)*Zeta[3])/(12*S^2)) - (55*S^2*Zeta[5])/6) + Log[T]^2*(-25/8 + (Pi^4*(-5398 - 4633*S^2))/2160 + (Pi^2*(-316 - 523*S^2))/72 - (17*S^2*HPL[{0}, S^2]^5)/72 - (5*(47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2]^4)/(18*S^2) - (6*(1 + S^4)*HPL[{1}, -S^2]^5)/S^2 + HPL[{0}, S^2]^4*((-160 - 263*S^2)/144 - (10*(1 + S^4)*HPL[{1}, -S^2])/(9*S^2)) + ((-59 - 114*S^2 - 100*S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{0}, S^2]^3*((-14*Pi^2*S^2)/9 + (-166 - 553*S^2)/72 + ((-89 - 328*S^2 - 231*S^4)*HPL[{1}, -S^2])/(36*S^2) - (9*(1 + S^4)*HPL[{1}, -S^2]^2)/(2*S^2) + ((3 - 76*S^4)*HPL[{2}, -S^2])/(18*S^2)) + HPL[{1}, -S^2]^3*((-199 - 504*S^2 - 305*S^4)/(9*S^2) - (76*Pi^2*(1 + S^4))/(9*S^2) - (22*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((Pi^2*(-9 + 113*S^4))/(18*S^2) + (23 + 436*S^2 + 167*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((34 + 38*S^2 - 37*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((-13 + 7*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((89 + 103*S^2 - 55*S^4)/(3*S^2) - (5*Pi^2*(-11 + 4*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-178 - 523*S^2)/24 + (Pi^2*(-346 - 499*S^2))/72 + ((-65 - 186*S^2 - 121*S^4)*HPL[{1}, -S^2]^2)/(6*S^2) - (31*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + ((9 - 77*S^2 - 118*S^4)*HPL[{2}, -S^2])/(6*S^2) + HPL[{1}, -S^2]*((-173*Pi^2*(1 + S^4))/(36*S^2) - (5*(19 + 70*S^2 + 51*S^4))/(12*S^2) - (77*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((-2 + 3*S^4)*HPL[{3}, -S^2])/(2*S^2) - (2*(-41 + 4*S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) + ((-168 + 24*S^2 + 223*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((13 - 185*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(-17 + 299*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (4*(-68 + 33*S^2 + 118*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (4*(23 + 14*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(105 + 11*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (8*(-83 + 52*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((52*Pi^2*S^2)/9 + (103 + 55*S^2)/3)*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-365 - 912*S^2 - 547*S^4))/(36*S^2) + (-173 - 489*S^2 - 316*S^4)/(6*S^2) + ((5 - 44*S^2 - 49*S^4)*HPL[{2}, -S^2])/(2*S^2) + (34*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (22*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (28*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((-613 - 2016*S^2 - 1403*S^4)/(24*S^2) - (2699*Pi^4*(1 + S^4))/(1080*S^2) - (7*Pi^2*(21 + 61*S^2 + 40*S^4))/(18*S^2) + ((20 - 77*S^2 - 97*S^4)/(3*S^2) - (55*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] - (19*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + (4*(1 + S^2)*(12 + 5*S^2)*HPL[{3}, -S^2])/S^2 + (19*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + ((1 + S^2)*(-5 + 49*S^2)*HPL[{2, 1}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (44*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (7*(5 + 8*S^2 + 3*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((230 - 116*S^2 - 523*S^4)/(12*S^2) + (Pi^2*(77 - 110*S^2 - 236*S^4))/(18*S^2) + ((-11 + 97*S^4)*HPL[{3}, -S^2])/(3*S^2) + (2*(23 + 14*S^4)*HPL[{2, 1}, -S^2])/S^2 + (2*(-1 + 44*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]*((-433*Pi^4*S^2)/180 + (-652 - 1403*S^2)/24 + (Pi^2*(-604 - 1163*S^2))/72 - (5*(47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) - (15*(1 + S^4)*HPL[{1}, -S^2]^4)/S^2 + ((25 - 205*S^2 - 299*S^4)/(6*S^2) + (Pi^2*(11 - 203*S^4))/(18*S^2))*HPL[{2}, -S^2] + ((1 - 116*S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^2*((-199 - 504*S^2 - 305*S^4)/(6*S^2) - (12*Pi^2*(1 + S^4))/S^2 - (39*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((-13 + 6*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-1 - 20*S^4)*HPL[{4}, -S^2])/(3*S^2) - (2*(-113 - 117*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(-4 + 63*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (4*(-8 + 127*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((20 + 13*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((-173 - 489*S^2 - 316*S^4)/(6*S^2) + (Pi^2*(-81 - 217*S^2 - 134*S^4))/(9*S^2) - (13*(5 + 12*S^2 + 7*S^4)*HPL[{2}, -S^2])/(2*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (78*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (20*(1 + S^4)*Zeta[3])/(3*S^2))) + (110*S^2*Zeta[5])/3) + HPL[{1}, -S^2]^2*((Pi^4*(-3859 - 10776*S^2 - 6957*S^4))/(4320*S^2) + (Pi^2*(-503 - 1680*S^2 - 1177*S^4))/(144*S^2) + (-343 - 1472*S^2 - 1129*S^4)/(32*S^2) + ((-35 - 76*S^2 - 41*S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + ((17*Pi^2*(1 + S^4))/(6*S^2) + (299 + 356*S^2 + 57*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((125 + 76*S^2 - 49*S^4)*HPL[{4}, -S^2])/(12*S^2) - (7*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((55*Pi^2*(1 + S^4))/(9*S^2) + (-20 + 77*S^2 + 97*S^4)/(3*S^2))*HPL[{2, 1}, -S^2] + ((-13 + 8*S^2 + 21*S^4)*HPL[{3, 1}, -S^2])/S^2 - (92*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (295*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((5 - 44*S^2 - 49*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (76*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (160*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (44*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((7*Pi^2*(1 + S^4))/(3*S^2) + (52 + 77*S^2 + 25*S^4)/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*((29 - 132*S^2 - 161*S^4)/(8*S^2) + (Pi^2*(-21 - 109*S^2 - 90*S^4))/(18*S^2) + (46*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (38*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (44*(1 + S^4)*Zeta[3])/(3*S^2)) + (37*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^4*(1204 - 3158*S^2 - 6495*S^4))/(4320*S^2) + (240 - 721*S^2 - 1335*S^4)/(48*S^2) + (Pi^2*(101 - 162*S^2 - 523*S^4))/(72*S^2) + ((Pi^2*(-9 + 101*S^4))/(36*S^2) + (-75 + 452*S^2 + 185*S^4)/(24*S^2))*HPL[{3}, -S^2] + ((-38 + 54*S^2 - 35*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((-5 - 3*S^4)*HPL[{5}, -S^2])/(2*S^2) + ((2*Pi^2*(36 + 11*S^4))/(9*S^2) + (58 + 282*S^2 + 41*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + ((143 + 228*S^2 + 189*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + ((7 - 185*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((8 - 97*S^4)*HPL[{4, 1}, -S^2])/S^2 - (2*(59 + 114*S^2 + 100*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (4*(-37 + 20*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(-211 + 23*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (4*(23 + 14*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((2*Pi^2*(-1 + 11*S^4))/(9*S^2) + (-5 + 90*S^2 + 54*S^4)/(6*S^2))*Zeta[3] + (5*(-2 + 7*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]*((Pi^4*(-6189 - 20344*S^2 - 14315*S^4))/(8640*S^2) + (Pi^2*(-493 - 1814*S^2 - 1321*S^4))/(144*S^2) - (23567*Pi^6*(1 + S^4))/(90720*S^2) - (2*(11 + 84*S^2 + 73*S^4))/(3*S^2) + ((-59 - 144*S^2 - 85*S^4)/(8*S^2) - (95*Pi^2*(1 + S^4))/(36*S^2))*HPL[{2}, -S^2]^2 - (13*(1 + S^4)*HPL[{2}, -S^2]^3)/(18*S^2) - (5*(1 + S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((7*Pi^2*(1 + S^4))/(36*S^2) - (11*(-27 - 8*S^2 + 19*S^4))/(24*S^2))*HPL[{4}, -S^2] + ((113 - 36*S^2 - 133*S^4)*HPL[{5}, -S^2])/(6*S^2) - (39*(1 + S^4)*HPL[{6}, -S^2])/(2*S^2) + (38*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((44*Pi^2*(1 + S^4))/(9*S^2) + (-61 + 38*S^2 + 99*S^4)/(3*S^2))*HPL[{3, 1}, -S^2] - (4*(28 + 45*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-797 - 1156*S^2 - 407*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) - (9*(1 + S^4)*HPL[{4, 2}, -S^2])/(2*S^2) - (32*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-110*Pi^2*(1 + S^4))/(9*S^2) - (2*(-20 + 77*S^2 + 97*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (2*(35 + 76*S^2 + 41*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (2*(57 + 160*S^2 + 103*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (52*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (118*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (2*(-5 + 44*S^2 + 49*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (16*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(57 + 82*S^2 + 29*S^4))/(18*S^2) + (63 + 92*S^2 + 29*S^4)/(4*S^2))*Zeta[3] - (3*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((Pi^2*(21 + 109*S^2 + 90*S^4))/(9*S^2) + (-29 + 132*S^2 + 161*S^4)/(4*S^2) - (88*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((625 + 624*S^2 - S^4)/(24*S^2) + (Pi^2*(157 + 208*S^2 + 43*S^4))/(36*S^2) - (92*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((59 - 1112*S^2 - 1171*S^4)/(48*S^2) + (Pi^2*(-17 - 230*S^2 - 221*S^4))/(36*S^2) - (1579*Pi^4*(1 + S^4))/(2160*S^2) + (2*(28 + 45*S^2 + 19*S^4)*HPL[{3}, -S^2])/(3*S^2) + (19*(1 + S^4)*HPL[{4}, -S^2])/(6*S^2) + ((35 + 76*S^2 + 41*S^4)*HPL[{2, 1}, -S^2])/S^2 + (118*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (76*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((57 + 86*S^2 + 33*S^4)*Zeta[3])/(3*S^2)) + ((109 + 152*S^2 + 35*S^4)*Zeta[5])/(6*S^2)) + Log[T]*(25/16 + (373*Pi^6*S^2)/1008 + (Pi^2*(478 + 1175*S^2))/144 + (Pi^4*(6070 + 10069*S^2))/4320 + (S^2*HPL[{0}, S^2]^6)/16 + ((47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2]^5)/(9*S^2) + (2*(1 + S^4)*HPL[{1}, -S^2]^6)/S^2 + HPL[{0}, S^2]^5*((34 + 71*S^2)/144 + (17*(1 + S^4)*HPL[{1}, -S^2])/(72*S^2)) + ((Pi^2*(23 + 73*S^4))/(18*S^2) + (119 + 150*S^2 + 214*S^4)/(12*S^2))*HPL[{2}, -S^2]^2 + ((-8 + 11*S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^4*((109*Pi^2*S^2)/216 + (148 + 607*S^2)/288 + ((37 + 162*S^2 + 121*S^4)*HPL[{1}, -S^2])/(72*S^2) + (10*(1 + S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + (37*S^2*HPL[{2}, -S^2])/36) + HPL[{1}, -S^2]^4*((38*Pi^2*(1 + S^4))/(9*S^2) + (199 + 504*S^2 + 305*S^4)/(18*S^2) + (11*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-4 + 5*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((Pi^2*(2 + 5*S^4))/(18*S^2) + (-96 - 98*S^2 + 145*S^4)/(12*S^2))*HPL[{4}, -S^2] + ((-67 + 28*S^2 + 159*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((60 + 109*S^4)*HPL[{6}, -S^2])/(3*S^2) - (6*(5 + 8*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((337 - 24*S^2 - 481*S^4)/(6*S^2) + (Pi^2*(65 - 157*S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + ((-59 + 368*S^2 + 257*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((-38 + 590*S^2 + 387*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + 9*S^2*HPL[{4, 2}, -S^2] + (2*(-9 + 25*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((10*Pi^2*(-11 + 34*S^4))/(9*S^2) + (2*(-43 + 17*S^2 + 83*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(46 + 114*S^2 + 23*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(-274 - 480*S^2 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (6*(-1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (2*(-29 + 41*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (4*(-147 + 187*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (4*(-121 - 66*S^2 + 89*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (16*(-30 + 37*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (80*(-10 + 17*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((-4*(26 + 5*S^2))/3 - (2*Pi^2*(21 + 17*S^2))/9)*Zeta[3] - 2*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-143 - 280*S^2 + 40*S^4)/(6*S^2) + (Pi^2*(-119 - 108*S^2 + 56*S^4))/(9*S^2) + (60*Zeta[3])/S^2) + HPL[{0}, S^2]^3*((5*(26 + 237*S^2))/144 + (Pi^2*(166 + 303*S^2))/108 + ((89 + 328*S^2 + 231*S^4)*HPL[{1}, -S^2]^2)/(36*S^2) + (3*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + ((-15 + 136*S^2 + 226*S^4)*HPL[{2}, -S^2])/(36*S^2) + HPL[{1}, -S^2]*((83*Pi^2*(1 + S^4))/(54*S^2) + (83 + 600*S^2 + 501*S^4)/(72*S^2) + (34*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((1 - 2*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-71 + 8*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (11*S^2*Zeta[3])/9) + HPL[{0}, S^2]^2*((433*Pi^4*S^2)/360 + (Pi^2*(388 + 1105*S^2))/144 + (334 + 1175*S^2)/48 + ((65 + 186*S^2 + 121*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + (31*(1 + S^4)*HPL[{1}, -S^2]^4)/(6*S^2) + ((Pi^2*(-5 + 159*S^4))/(36*S^2) + (-10 + 113*S^2 + 249*S^4)/(12*S^2))*HPL[{2}, -S^2] + ((1 + 74*S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + HPL[{1}, -S^2]^2*((173*Pi^2*(1 + S^4))/(36*S^2) + (5*(19 + 70*S^2 + 51*S^4))/(12*S^2) + (77*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((5 - 4*S^2 - 4*S^4)*HPL[{3}, -S^2])/(12*S^2) + ((5 + 16*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((-117 - 150*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + HPL[{1}, -S^2]*((Pi^2*(51 + 174*S^2 + 121*S^4))/(18*S^2) + (157 + 702*S^2 + 545*S^4)/(24*S^2) + ((99 + 304*S^2 + 213*S^4)*HPL[{2}, -S^2])/(12*S^2) - (77*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) + ((5 - 83*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (10*(-1 + 17*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (7*S^2*Zeta[3])/2) + HPL[{1}, -S^2]^3*((173 + 489*S^2 + 316*S^4)/(9*S^2) + (Pi^2*(365 + 912*S^2 + 547*S^4))/(54*S^2) + ((-5 + 44*S^2 + 49*S^4)*HPL[{2}, -S^2])/(3*S^2) - (68*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (56*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((-97 - 832*S^2 - 159*S^4)/(24*S^2) + (Pi^2*(3 - 208*S^2 - 147*S^4))/(36*S^2) - (2*(-103 + 5*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((2699*Pi^4*(1 + S^4))/(1080*S^2) + (7*Pi^2*(21 + 61*S^2 + 40*S^4))/(18*S^2) + (613 + 2016*S^2 + 1403*S^4)/(24*S^2) + ((55*Pi^2*(1 + S^4))/(9*S^2) + (-20 + 77*S^2 + 97*S^4)/(3*S^2))*HPL[{2}, -S^2] + (19*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 - (4*(12 + 17*S^2 + 5*S^4)*HPL[{3}, -S^2])/S^2 - (19*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + ((5 - 44*S^2 - 49*S^4)*HPL[{2, 1}, -S^2])/S^2 - (8*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (44*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (7*(5 + 8*S^2 + 3*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(-139 + 164*S^2 + 498*S^4))/(36*S^2) + (-400 + 374*S^2 + 1175*S^4)/(24*S^2) + (Pi^4*(-412 + 2203*S^4))/(1080*S^2) + ((43 - 184*S^2 - 133*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((8 - 19*S^4)*HPL[{4}, -S^2])/(3*S^2) - (2*(46 + 114*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(55 + 61*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (12*(5 + 8*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(-2 + 42*S^2 + 33*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]*((Pi^2*(874 + 2449*S^2))/144 + (1094 + 3387*S^2)/48 + (Pi^4*(2578 + 3907*S^2))/1080 + (5*(47 + 108*S^2 + 61*S^4)*HPL[{1}, -S^2]^4)/(18*S^2) + (6*(1 + S^4)*HPL[{1}, -S^2]^5)/S^2 + ((-2 + 112*S^2 + 133*S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^3*((8*Pi^2*(1 + S^4))/S^2 + (199 + 504*S^2 + 305*S^4)/(9*S^2) + (26*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((Pi^2*(6 - 7*S^4))/(9*S^2) + (12 + 16*S^2 + 21*S^4)/(6*S^2))*HPL[{3}, -S^2] + ((-2 + 16*S^2 + 25*S^4)*HPL[{4}, -S^2])/(3*S^2) - (2*(1 + 3*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-193 - 257*S^2 + 5*S^4)/(3*S^2) + (2*Pi^2*(-98 + 9*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((31 - 232*S^2 - 294*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(3 + 2*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (2*(3 + 16*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (2*(-31 + 234*S^2 + 299*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (4*(-115 + 2*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (8*(-177 + 7*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (40*(-25 + 2*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-60 - 17*S^2)*Zeta[3])/6 + HPL[{1}, -S^2]^2*((Pi^2*(81 + 217*S^2 + 134*S^4))/(9*S^2) + (173 + 489*S^2 + 316*S^4)/(6*S^2) + (13*(5 + 12*S^2 + 7*S^4)*HPL[{2}, -S^2])/(2*S^2) + (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (78*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (20*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]*((1289*Pi^4*(1 + S^4))/(540*S^2) + (Pi^2*(481 + 1608*S^2 + 1111*S^4))/(72*S^2) + (613 + 2016*S^2 + 1403*S^4)/(24*S^2) + ((185*Pi^2*(1 + S^4))/(18*S^2) + (7*(4 + 11*S^2 + 7*S^4))/S^2)*HPL[{2}, -S^2] + (19*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((-7 + 4*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*S^2) + (16*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (13*(5 + 12*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/S^2 - (232*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (156*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (8*(4 + 5*S^2 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-46 + 370*S^2 + 525*S^4))/(36*S^2) + (-41 + 392*S^2 + 610*S^4)/(12*S^2) - (2*(3 + 2*S^4)*HPL[{3}, -S^2])/(3*S^2) + (2*(-115 + 2*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(-1 + 9*S^4)*Zeta[3])/(3*S^2))) + ((-74 - 81*S^2)*Zeta[5])/3 + HPL[{1}, -S^2]*((343 + 1472*S^2 + 1129*S^4)/(16*S^2) + (Pi^2*(503 + 1680*S^2 + 1177*S^4))/(72*S^2) + (Pi^4*(3859 + 10776*S^2 + 6957*S^4))/(2160*S^2) + ((35 + 76*S^2 + 41*S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((-299 - 356*S^2 - 57*S^4)/(6*S^2) - (17*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] + ((-125 - 76*S^2 + 49*S^4)*HPL[{4}, -S^2])/(6*S^2) + (14*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-110*Pi^2*(1 + S^4))/(9*S^2) - (2*(-20 + 77*S^2 + 97*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(-13 + 8*S^2 + 21*S^4)*HPL[{3, 1}, -S^2])/S^2 + (184*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (590*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (2*(-5 + 44*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (152*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (320*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-14*Pi^2*(1 + S^4))/(3*S^2) - (2*(52 + 77*S^2 + 25*S^4))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(21 + 109*S^2 + 90*S^4))/(9*S^2) + (-29 + 132*S^2 + 161*S^4)/(4*S^2) - (92*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (76*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (88*(1 + S^4)*Zeta[3])/(3*S^2)) - (74*(1 + S^4)*Zeta[5])/(3*S^2))) + HPL[{0}, S^2]*((-373*Pi^6*S^2)/2016 + (Pi^4*(-1255 - 4718*S^2))/2160 + (-769 - 4672*S^2)/96 + (Pi^2*(-587 - 2859*S^2))/288 + ((-47 - 108*S^2 - 61*S^4)*HPL[{1}, -S^2]^5)/(18*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^6)/S^2 + ((5 - 178*S^2 - 268*S^4)/(24*S^2) + (Pi^2*(4 - 179*S^4))/(72*S^2))*HPL[{2}, -S^2]^2 + ((5 - 52*S^4)*HPL[{2}, -S^2]^3)/(18*S^2) + HPL[{1}, -S^2]^4*((-199 - 504*S^2 - 305*S^4)/(36*S^2) - (2*Pi^2*(1 + S^4))/S^2 - (13*(1 + S^4)*HPL[{2}, -S^2])/(2*S^2)) + ((-1 + 3*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((23 - 44*S^2 - 57*S^4)/(12*S^2) + (Pi^2*(-5 - 19*S^4))/(18*S^2))*HPL[{4}, -S^2] + ((11 - 14*S^2 + 7*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-15 - 17*S^4)*HPL[{6}, -S^2])/(3*S^2) + ((-1 + 116*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(-8 + 201*S^4))/(18*S^2) + (-21 + 218*S^2 + 291*S^4)/(6*S^2))*HPL[{3, 1}, -S^2] - (4*(1 + 4*S^2)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-2 - 32*S^2 - S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (2*(3 + 13*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((25 - 205*S^2 - 299*S^4)/(3*S^2) + (Pi^2*(11 - 203*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + (2*(-107 - 116*S^2 + 10*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + ((-655 - 696*S^2 + 66*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (4*(-5 + 52*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (2*(-29 + 332*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (4*(-113 - 117*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (8*(-4 + 63*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (8*(-8 + 127*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(8 - 53*S^2))/18 + (66 - 23*S^2)/8)*Zeta[3] + S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(315 + 374*S^2 - 58*S^4))/(36*S^2) + (332 + 556*S^2 + 47*S^4)/(12*S^2) + (4*(-4 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((15 - 120*S^2 - 91*S^4)/(24*S^2) + (Pi^2*(-5 - 6*S^2 + 9*S^4))/(36*S^2) - (2*(5 + 6*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(-1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((-173 - 489*S^2 - 316*S^4)/(18*S^2) + (Pi^2*(-81 - 217*S^2 - 134*S^4))/(27*S^2) - (13*(5 + 12*S^2 + 7*S^4)*HPL[{2}, -S^2])/(6*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) + (26*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (20*(1 + S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]^2*((-613 - 2016*S^2 - 1403*S^4)/(48*S^2) + (Pi^2*(-481 - 1608*S^2 - 1111*S^4))/(144*S^2) - (1289*Pi^4*(1 + S^4))/(1080*S^2) + ((-185*Pi^2*(1 + S^4))/(36*S^2) - (7*(4 + 11*S^2 + 7*S^4))/(2*S^2))*HPL[{2}, -S^2] - (19*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((7 - 4*S^2 - 11*S^4)*HPL[{3}, -S^2])/(6*S^2) - (8*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (13*(5 + 12*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + (116*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (78*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(4 + 5*S^2 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((160 - 778*S^2 - 1339*S^4)/(48*S^2) + (Pi^4*(37 - 1242*S^4))/(1080*S^2) + (Pi^2*(98 - 570*S^2 - 1079*S^4))/(144*S^2) + (2*(1 + 4*S^2)*HPL[{3}, -S^2])/(3*S^2) - (2*(-1 + 3*S^4)*HPL[{4}, -S^2])/(3*S^2) + ((107 + 116*S^2 - 10*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (116*S^2*HPL[{3, 1}, -S^2])/3 - (2*(-1 + 116*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((2 + 18*S^2 + 3*S^4)*Zeta[3])/(6*S^2)) - 2*(-1 + 9*S^2)*Zeta[5] + HPL[{1}, -S^2]*((Pi^4*(-1329 - 5176*S^2 - 3807*S^4))/(2160*S^2) + (-343 - 1472*S^2 - 1129*S^4)/(32*S^2) + (Pi^2*(-221 - 1008*S^2 - 787*S^4))/(96*S^2) - ((1 + S^2)*(35 + 41*S^2)*HPL[{2}, -S^2]^2)/(4*S^2) + ((1 - 14*S^2 - 11*S^4)/(3*S^2) - (2*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3}, -S^2] - (4*(1 + S^2)*(1 + 3*S^2)*HPL[{4}, -S^2])/(3*S^2) - (4*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((185*Pi^2*(1 + S^4))/(18*S^2) + (7*(4 + 11*S^2 + 7*S^4))/S^2)*HPL[{2, 1}, -S^2] + (2*(49 + 116*S^2 + 67*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (16*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (32*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (13*(5 + 12*S^2 + 7*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (76*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (688*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (156*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((4*Pi^2*(1 + S^4))/(9*S^2) + (87 + 104*S^2 + S^4)/(12*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-269 - 744*S^2 - 467*S^4))/(72*S^2) + (-97 - 316*S^2 - 219*S^4)/(8*S^2) + (8*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (38*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (7*(1 + S^4)*Zeta[3])/(3*S^2)) + (2*(1 + S^4)*Zeta[5])/S^2));
Et4vwuT3F1=(-557 - 2371*S^2)/(96*S) - (Pi^6*S*(43573 + 20006*S^2))/(90720*(1 + S^2)) + (Pi^2*(112 - 1737*S^2 + 111*S^4))/(576*S) - (Pi^4*S*(11713 + 12233*S^2 + 600*S^4))/(8640*(1 + S^2)) + ((-17 - 95*S^2 - 24*S^4)*HPL[{1}, -S^2]^6)/(27*S*(1 + S^2)) - (4*S*HPL[{1}, -S^2]^7)/7 + HPL[{0}, S^2]^6*(-S/(32*(1 + S^2)) - (S*HPL[{1}, -S^2])/16) + ((15 - 108*S^2 - 97*S^4)*HPL[{2}, -S^2]^3)/(36*S*(1 + S^2)) + HPL[{1}, -S^2]^5*((-76*Pi^2*S)/45 + (-293 - 302*S^2 - 9*S^4)/(90*S) - (22*S*HPL[{2}, -S^2])/15) + HPL[{0}, S^2]^5*((-17*Pi^2*S)/432 - (S*(226 + 27*S^2))/288 + ((-27 - 125*S^2 - 64*S^4)*HPL[{1}, -S^2])/(144*S*(1 + S^2)) - (17*S*HPL[{1}, -S^2]^2)/72 - (17*S*HPL[{2}, -S^2])/72) + ((2 + 30*S^2 + 33*S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((17*Pi^2*S)/18 + (-232 - 751*S^2 - 587*S^4 - 60*S^6)/(6*S*(1 + S^2)))*HPL[{5}, -S^2] + ((-145 - 629*S^2 - 367*S^4)*HPL[{6}, -S^2])/(6*S*(1 + S^2)) - (70*S*HPL[{7}, -S^2])/3 + ((9 + 244*S^2 + 121*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((-193*Pi^2*S)/18 + (-41 - 40*S^2 - 3*S^4 - 12*S^6)/(6*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + (-35*Pi^2*S + (14 + 41*S^2 + 26*S^4 - 5*S^6)/(S*(1 + S^2)))*HPL[{4, 1}, -S^2] + (3*(-1 + 2*S^2 + 6*S^4)*HPL[{4, 2}, -S^2])/(2*S*(1 + S^2)) + ((50 + 327*S^2 + 309*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + 3*S*HPL[{5, 2}, -S^2] + (106*S*HPL[{6, 1}, -S^2])/3 + ((-88*Pi^2*S)/9 - (2*(106 - 11*S^2 + 3*S^4))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((-38*Pi^2*S)/9 - (2*(349 - 12*S^2 + 6*S^4))/(3*S))*HPL[{3, 1, 1}, -S^2] - 3*S*HPL[{3, 1, 2}, -S^2] + ((30 - 225*S^2 - 203*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (361*S*HPL[{3, 2, 2}, -S^2])/3 + 376*S*HPL[{3, 3, 1}, -S^2] - (2*(-32 + 394*S^2 + 367*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 370*S*HPL[{4, 1, 2}, -S^2] + 1146*S*HPL[{4, 2, 1}, -S^2] + (7012*S*HPL[{5, 1, 1}, -S^2])/3 + ((-80*Pi^2*S)/3 - (2*(-239 + 39*S^2 + 9*S^4))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] - (320*S*HPL[{2, 2, 2, 1}, -S^2])/3 + (4*(-10 + 155*S^2 + 153*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (220*S*HPL[{3, 1, 1, 2}, -S^2])/3 + (220*S*HPL[{3, 1, 2, 1}, -S^2])/3 + (1180*S*HPL[{3, 2, 1, 1}, -S^2])/3 + (3368*S*HPL[{4, 1, 1, 1}, -S^2])/3 - (8*(-11 + 167*S^2 + 145*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 224*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 672*S*HPL[{2, 2, 1, 1, 1}, -S^2] + (5024*S*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - (1664*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + ((34*Pi^2*S)/27 + (34*S*HPL[{0}, S^2]^2)/9 + (2*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) + 12*S*HPL[{1}, -S^2]^2 + HPL[{0}, S^2]*((2*S*(17 + 8*S^2))/(3*(1 + S^2)) + 12*S*HPL[{1}, -S^2]) + (68*S*HPL[{2}, -S^2])/9)*Log[T]^5 + ((-2*S)/(1 + S^2) - 4*S*HPL[{0}, S^2] - 4*S*HPL[{1}, -S^2])*Log[T]^6 + ((S*(-52 + 27*S^2))/12 + (Pi^2*S*(-12 - 5*S^2 + 9*S^4))/(18*(1 + S^2)))*Zeta[3] + (S*(7 + 10*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((-3 + 31*S^2 + 108*S^4)/(2*S^3) + (Pi^2*(-7 + 388*S^2 + 307*S^4))/(18*S*(1 + S^2)) - (184*S*Zeta[3])/3) + HPL[{0}, S^2]^4*(-(Pi^2*S*(396 + 181*S^2))/(864*(1 + S^2)) - (S*(757 + 821*S^2 + 48*S^4))/(576*(1 + S^2)) + ((-81 - 402*S^2 - 161*S^4)*HPL[{1}, -S^2]^2)/(144*S*(1 + S^2)) - (20*S*HPL[{1}, -S^2]^3)/27 - (S*(243 + 181*S^2)*HPL[{2}, -S^2])/(144*(1 + S^2)) + HPL[{1}, -S^2]*((-215*Pi^2*S)/432 + (-421 - 817*S^2 - 399*S^4 + 5*S^6)/(288*S*(1 + S^2)) - (31*S*HPL[{2}, -S^2])/36) + (S*HPL[{3}, -S^2])/8 - (S*HPL[{2, 1}, -S^2])/3 - (13*S*Zeta[3])/9) + HPL[{4}, -S^2]*((Pi^2*(-25 - 136*S^2 - 118*S^4))/(36*S*(1 + S^2)) + (-12 - 176*S^2 - 149*S^4 - 8*S^6)/(8*S^3) + (8*S*Zeta[3])/3) + HPL[{1}, -S^2]^4*((Pi^2*(-158 - 863*S^2 - 249*S^4))/(108*S*(1 + S^2)) - ((1 + S^2)*(3 + 643*S^2 + 42*S^4))/(72*S^3) + ((-18 - 85*S^2 - 45*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) + (34*S*HPL[{3}, -S^2])/3 + (22*S*HPL[{2, 1}, -S^2])/3 + (28*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((9 - 268*S^2)/(24*S) + (Pi^2*(-7 - 439*S^2 - 242*S^4))/(72*S*(1 + S^2)) + (97*S*HPL[{3}, -S^2])/6 - (40*S*HPL[{2, 1}, -S^2])/3 + (40*S*Zeta[3])/3) + Log[T]^4*(-S/2 - (Pi^2*S*(373 + 145*S^2))/(54*(1 + S^2)) - (83*S*HPL[{0}, S^2]^3)/27 - (5*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)) - 20*S*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]^2*(-(S*(238 + 145*S^2))/(18*(1 + S^2)) - (31*S*HPL[{1}, -S^2])/3) + ((11 - 167*S^2 - 145*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{0}, S^2]*((-218*Pi^2*S)/27 - (S*(302 + 9*S^2))/18 - (5*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) - 30*S*HPL[{1}, -S^2]^2 - (254*S*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]*((-76*Pi^2*S)/9 + (-293 - 302*S^2 - 9*S^4)/(18*S) - (22*S*HPL[{2}, -S^2])/3) + (208*S*HPL[{3}, -S^2])/9 - (208*S*HPL[{2, 1}, -S^2])/9 + (208*S*Zeta[3])/9) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(13 - 387*S^2 - 290*S^4))/(9*S*(1 + S^2)) + (6 - 65*S^2 - 273*S^4 - 6*S^6)/(3*S^3) + (352*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-52*Pi^4*S)/45 + (-3 + 486*S^2 + 52*S^4 - 27*S^6)/(12*S^3) + (Pi^2*(237 + 207*S^2 - 38*S^4 - 6*S^6))/(18*S*(1 + S^2)) - 76*S*HPL[{3, 1}, -S^2] - 112*S*HPL[{2, 1, 1}, -S^2] - (2*(9 + 53*S^2)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-2699*Pi^4*S)/1620 + (Pi^2*(-279 - 283*S^2 - 6*S^4))/(54*S) - ((1 + S^2)*(-2 + 867*S^2 + 65*S^4))/(36*S^3) + ((-110*Pi^2*S)/27 + (3 - 128*S^2 - 128*S^4 + 3*S^6)/(9*S^3))*HPL[{2}, -S^2] - (38*S*HPL[{2}, -S^2]^2)/3 - (4*(-1 - 12*S^2 + 6*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (38*S*HPL[{4}, -S^2])/9 + (2*(18 + 85*S^2 + 45*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3, 1}, -S^2])/3 - (88*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(-4 - 29*S^2 + 3*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((929*Pi^4*S)/1080 + (Pi^2*(-63 - 128*S^2 - 61*S^4))/(36*S*(1 + S^2)) + (-12 - 439*S^2 - 1050*S^4 + 75*S^6)/(48*S^3) + ((-26 - 151*S^2 - 33*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (194*S*HPL[{3, 1}, -S^2])/3 + (388*S*HPL[{2, 1, 1}, -S^2])/3 + (2*(1 + 10*S^2 + 5*S^4)*Zeta[3])/(3*S*(1 + S^2))) + Log[T]^3*((529*Pi^4*S)/270 + (Pi^2*S*(295 + 3*S^2))/54 + (-1 + 4*S^2)/(2*S) + (83*S*HPL[{0}, S^2]^4)/54 + (20*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2]^3)/(27*S*(1 + S^2)) + 20*S*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^3*((S*(251 + 170*S^2))/(27*(1 + S^2)) + 6*S*HPL[{1}, -S^2]) + ((340*Pi^2*S)/27 + (-6 + 17*S^2 + 295*S^4 + 3*S^6)/(9*S^3))*HPL[{2}, -S^2] + 16*S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((152*Pi^2*S)/9 + (293 + 302*S^2 + 9*S^4)/(9*S) + (44*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^2*((56*Pi^2*S)/9 + (S*(295 + 3*S^2))/18 + ((73 + 388*S^2 + 129*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) + (62*S*HPL[{1}, -S^2]^2)/3 + (170*S*HPL[{2}, -S^2])/9) + (2*(7 - 55*S^2 + 40*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (44*S*HPL[{4}, -S^2])/9 + (4*(-65 - 88*S^2 + 10*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (592*S*HPL[{3, 1}, -S^2])/9 + (1360*S*HPL[{2, 1, 1}, -S^2])/9 - (8*S*(26 + 5*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(3 + 643*S^2 + 42*S^4))/(18*S^3) + (Pi^2*(158 + 863*S^2 + 249*S^4))/(27*S*(1 + S^2)) + (2*(18 + 85*S^2 + 45*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (136*S*HPL[{3}, -S^2])/3 - (88*S*HPL[{2, 1}, -S^2])/3 - (112*S*Zeta[3])/3) + HPL[{0}, S^2]*((S*(667 + 42*S^2))/18 + (2*Pi^2*S*(253 + 145*S^2))/(27*(1 + S^2)) + (10*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)) + 40*S*HPL[{1}, -S^2]^3 + (2*(1 + 254*S^2 + 136*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(16*Pi^2*S + (293 + 302*S^2 + 9*S^4)/(9*S) + 52*S*HPL[{2}, -S^2]) - (32*S*HPL[{3}, -S^2])/9 + (80*S*HPL[{2, 1}, -S^2])/9 - (88*S*Zeta[3])/9)) + HPL[{0}, S^2]^3*((-529*Pi^4*S)/2160 + (18 - 2738*S^2 - 109*S^4)/(288*S) - (Pi^2*S*(1509 + 1660*S^2 + 147*S^4))/(432*(1 + S^2)) + ((-77 - 383*S^2 - 144*S^4)*HPL[{1}, -S^2]^3)/(54*S*(1 + S^2)) - (3*S*HPL[{1}, -S^2]^4)/2 + ((-161*Pi^2*S)/108 + (6 - 15*S^2 - 326*S^4 - 312*S^6 - 3*S^8)/(72*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (7*S*HPL[{2}, -S^2]^2)/4 + HPL[{1}, -S^2]^2*((-83*Pi^2*S)/54 + (-317 - 629*S^2 - 331*S^4 - 11*S^6)/(72*S*(1 + S^2)) - (34*S*HPL[{2}, -S^2])/9) + ((-1 - 2*S^2 + S^4)*HPL[{3}, -S^2])/(12*S*(1 + S^2)) - S*HPL[{4}, -S^2] + ((62 + 101*S^2 - 29*S^4)*HPL[{2, 1}, -S^2])/(18*S*(1 + S^2)) + (25*S*HPL[{3, 1}, -S^2])/3 - (152*S*HPL[{2, 1, 1}, -S^2])/9 - (S*(78 + 77*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-53 - 252*S^2 - 116*S^4))/(54*S*(1 + S^2)) + (-3 - 703*S^2 - 1413*S^4 - 769*S^6 - 40*S^8)/(144*S^3*(1 + S^2)) + ((-65 - 322*S^2 - 121*S^4)*HPL[{2}, -S^2])/(36*S*(1 + S^2)) - (S*HPL[{3}, -S^2])/3 + (68*S*HPL[{2, 1}, -S^2])/9 - (2*S*Zeta[3])/9)) + (2*S*(5 + 12*S^2 + 6*S^4)*Zeta[5])/(3*(1 + S^2)) + HPL[{0}, S^2]^2*(-(Pi^4*S*(5725 + 3113*S^2))/(4320*(1 + S^2)) - (Pi^2*S*(1321 + 1397*S^2 + 60*S^4))/(288*(1 + S^2)) + (56 - 1429*S^2 + 111*S^4)/(192*S) + ((-73 - 388*S^2 - 129*S^4)*HPL[{1}, -S^2]^4)/(36*S*(1 + S^2)) - (31*S*HPL[{1}, -S^2]^5)/15 + ((2 - 195*S^2 - 121*S^4)*HPL[{2}, -S^2]^2)/(24*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((-173*Pi^2*S)/54 + (-265 - 264*S^2 - 3*S^4)/(36*S) - (77*S*HPL[{2}, -S^2])/9) + ((Pi^2*S)/2 + (-32 - 76*S^2 - 43*S^4 - 3*S^6)/(12*S*(1 + S^2)))*HPL[{3}, -S^2] + ((-2 - 11*S^2 - 7*S^4)*HPL[{4}, -S^2])/(2*S*(1 + S^2)) + (5*S*HPL[{5}, -S^2])/3 + ((-10*Pi^2*S)/9 + (235 + 214*S^2 - 28*S^4 - 3*S^6)/(12*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(2 - 463*S^2 - 326*S^4))/(72*S*(1 + S^2)) + (6 - 50*S^2 - 343*S^4 - 285*S^6 - 6*S^8)/(24*S^3*(1 + S^2)) + (2*S*HPL[{3}, -S^2])/3 + (2*S*HPL[{2, 1}, -S^2])/3) + HPL[{1}, -S^2]^2*((Pi^2*(-77 - 395*S^2 - 145*S^4))/(36*S*(1 + S^2)) + (-3 - 528*S^2 - 533*S^4 - 16*S^6)/(48*S^3) + ((-63 - 341*S^2 - 124*S^4)*HPL[{2}, -S^2])/(12*S*(1 + S^2)) + (77*S*HPL[{2, 1}, -S^2])/3) + ((3 + 233*S^2 + 154*S^4)*HPL[{3, 1}, -S^2])/(6*S*(1 + S^2)) - (4*S*HPL[{3, 2}, -S^2])/3 - (16*S*HPL[{4, 1}, -S^2])/3 + ((2 - 220*S^2 - 145*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{2, 2, 1}, -S^2])/3 + 2*S*HPL[{3, 1, 1}, -S^2] - (32*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-26*Pi^2*S)/9 + (S*(-63 - 58*S^2 + 9*S^4))/(12*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]*((-653*Pi^4*S)/540 - ((1 + S^2)*(-1 + 309*S^2 + 15*S^4))/(24*S^3) + (Pi^2*(-343 - 673*S^2 - 333*S^4 + S^6))/(72*S*(1 + S^2)) + ((-139*Pi^2*S)/36 + (3 - 121*S^2 - 263*S^4 - 135*S^6)/(12*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (19*S*HPL[{2}, -S^2]^2)/3 + ((-5 - 24*S^2)*HPL[{3}, -S^2])/(6*S) - 2*S*HPL[{4}, -S^2] + ((63 + 341*S^2 + 124*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) + (76*S*HPL[{3, 1}, -S^2])/3 - (154*S*HPL[{2, 1, 1}, -S^2])/3 + ((-4 - 7*S^2)*Zeta[3])/(6*S)) - (55*S*Zeta[5])/3) + HPL[{2}, -S^2]*((Pi^4*(73 - 5814*S^2 - 4308*S^4))/(2160*S*(1 + S^2)) + (-195 - 2279*S^2 - 1121*S^4 + 111*S^6)/(96*S^3) + (Pi^2*(12 - 109*S^2 - 681*S^4 - 564*S^6 - 12*S^8))/(72*S^3*(1 + S^2)) + ((101*Pi^2*S)/18 + (25 + 20*S^2 - 3*S^4 + 6*S^6)/(6*S*(1 + S^2)))*HPL[{3}, -S^2] + ((5 - 78*S^2 - 102*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - 3*S*HPL[{5}, -S^2] + ((44*Pi^2*S)/9 + (106 - 11*S^2 + 3*S^4)/(3*S))*HPL[{2, 1}, -S^2] + ((11 + 259*S^2 + 130*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (185*S*HPL[{3, 2}, -S^2])/3 - 194*S*HPL[{4, 1}, -S^2] - (2*(9 + 244*S^2 + 121*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (160*S*HPL[{2, 2, 1}, -S^2])/3 - (92*S*HPL[{3, 1, 1}, -S^2])/3 + 112*S*HPL[{2, 1, 1, 1}, -S^2] + ((44*Pi^2*S)/9 + (-2 + 7*S^2 + 10*S^4 + 3*S^6)/(3*S*(1 + S^2)))*Zeta[3] + (70*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*((Pi^4*(-2072 - 11111*S^2 - 3641*S^4))/(2160*S*(1 + S^2)) - ((1 + S^2)*(1 + 2630*S^2 + 233*S^4))/(48*S^3) + (Pi^2*(-3 - 587*S^2 - 609*S^4 - 29*S^6))/(72*S^3) + ((-11 - 63*S^2 - 14*S^4)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)) + ((17*Pi^2*S)/3 + (2 - 27*S^2 - 28*S^4 + S^6)/(3*S^3))*HPL[{3}, -S^2] + ((-30 - 109*S^2 - 117*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - (14*S*HPL[{5}, -S^2])/3 + ((110*Pi^2*S)/9 + (-3 + 128*S^2 + 128*S^4 - 3*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + (2*(9 + 39*S^2 + 26*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (184*S*HPL[{3, 2}, -S^2])/3 - (590*S*HPL[{4, 1}, -S^2])/3 - (2*(18 + 85*S^2 + 45*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - 152*S*HPL[{2, 2, 1}, -S^2] - 320*S*HPL[{3, 1, 1}, -S^2] + 88*S*HPL[{2, 1, 1, 1}, -S^2] + ((14*Pi^2*S)/3 + (14 + 19*S^2 + 3*S^4)/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-117 - 596*S^2 - 259*S^4))/(36*S*(1 + S^2)) + ((1 + S^2)*(4 - 299*S^2 + 13*S^4))/(12*S^3) + (92*S*HPL[{3}, -S^2])/3 + 76*S*HPL[{2, 1}, -S^2] + (88*S*Zeta[3])/3) + (74*S*Zeta[5])/3) + Log[T]^2*(-(Pi^2*S*(97 + 2*S^2))/12 - (7*(-2 + 11*S^2))/(12*S) - (Pi^4*S*(5704 + 3005*S^2))/(1080*(1 + S^2)) - (17*S*HPL[{0}, S^2]^5)/36 - (5*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2]^4)/(9*S*(1 + S^2)) - 12*S*HPL[{1}, -S^2]^5 + HPL[{0}, S^2]^4*(-(S*(261 + 181*S^2))/(72*(1 + S^2)) - (20*S*HPL[{1}, -S^2])/9) + ((-9 - 244*S^2 - 121*S^4)*HPL[{2}, -S^2]^2)/(6*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((-152*Pi^2*S)/9 + (-293 - 302*S^2 - 9*S^4)/(9*S) - (44*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^3*((-28*Pi^2*S)/9 - (S*(379 + 395*S^2 + 12*S^4))/(36*(1 + S^2)) + ((-77 - 383*S^2 - 144*S^4)*HPL[{1}, -S^2])/(18*S*(1 + S^2)) - 9*S*HPL[{1}, -S^2]^2 - (76*S*HPL[{2}, -S^2])/9) + ((113*Pi^2*S)/9 + (-31 - 21*S^2 + 3*S^4)/(3*S))*HPL[{3}, -S^2] + ((-13 - 70*S^2 - 76*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (14*S*HPL[{5}, -S^2])/3 + ((-40*Pi^2*S)/3 + (239 - 39*S^2 - 9*S^4)/(3*S))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(-(S*(47 + S^2))/2 - (Pi^2*S*(499 + 326*S^2))/(36*(1 + S^2)) + ((-73 - 388*S^2 - 129*S^4)*HPL[{1}, -S^2]^2)/(6*S*(1 + S^2)) - (62*S*HPL[{1}, -S^2]^3)/3 + ((2 - 220*S^2 - 145*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) + HPL[{1}, -S^2]*((-173*Pi^2*S)/18 + (-265 - 264*S^2 - 3*S^4)/(12*S) - (77*S*HPL[{2}, -S^2])/3) + 3*S*HPL[{3}, -S^2] - (16*S*HPL[{2, 1}, -S^2])/3) + (2*(-10 + 155*S^2 + 153*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (370*S*HPL[{3, 2}, -S^2])/3 - (1196*S*HPL[{4, 1}, -S^2])/3 - (4*(-11 + 167*S^2 + 145*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 112*S*HPL[{2, 2, 1}, -S^2] - (176*S*HPL[{3, 1, 1}, -S^2])/3 - (832*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((104*Pi^2*S)/9 + S*(13 + 3*S^2))*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-158 - 863*S^2 - 249*S^4))/(18*S*(1 + S^2)) - ((1 + S^2)*(3 + 643*S^2 + 42*S^4))/(12*S^3) + ((-18 - 85*S^2 - 45*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) + 68*S*HPL[{3}, -S^2] + 44*S*HPL[{2, 1}, -S^2] + 56*S*Zeta[3]) + HPL[{2}, -S^2]*((Pi^2*(13 - 387*S^2 - 290*S^4))/(18*S*(1 + S^2)) + (6 - 65*S^2 - 273*S^4 - 6*S^6)/(6*S^3) + (194*S*HPL[{3}, -S^2])/3 + 56*S*HPL[{2, 1}, -S^2] + (176*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-2699*Pi^4*S)/540 + (Pi^2*(-279 - 283*S^2 - 6*S^4))/(18*S) - ((1 + S^2)*(-2 + 867*S^2 + 65*S^4))/(12*S^3) + ((-110*Pi^2*S)/9 + (3 - 128*S^2 - 128*S^4 + 3*S^6)/(3*S^3))*HPL[{2}, -S^2] - 38*S*HPL[{2}, -S^2]^2 - (4*(-1 - 12*S^2 + 6*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (38*S*HPL[{4}, -S^2])/3 + (2*(18 + 85*S^2 + 45*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 16*S*HPL[{3, 1}, -S^2] - 88*S*HPL[{2, 1, 1}, -S^2] - (2*(-4 - 29*S^2 + 3*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]*((-433*Pi^4*S)/90 + (9 - 896*S^2 - 65*S^4)/(12*S) - (Pi^2*S*(681 + 706*S^2 + 21*S^4))/(36*(1 + S^2)) - (10*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) - 30*S*HPL[{1}, -S^2]^4 + ((-203*Pi^2*S)/9 + (2 - 15*S^2 - 111*S^4 - 3*S^6)/(2*S^3))*HPL[{2}, -S^2] - (116*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*(-24*Pi^2*S + (-293 - 302*S^2 - 9*S^4)/(6*S) - 78*S*HPL[{2}, -S^2]) + ((-9 - 18*S^2 - 7*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (40*S*HPL[{4}, -S^2])/3 - (2*(-77 - 175*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 168*S*HPL[{3, 1}, -S^2] - (1016*S*HPL[{2, 1, 1}, -S^2])/3 - (4*S*(-1 + 4*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-27 - 143*S^2 - 44*S^4))/(3*S*(1 + S^2)) - ((1 + S^2)*(3 + 643*S^2 + 42*S^4))/(12*S^3) - (13*(2 + 11*S^2 + 3*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) - (4*S*HPL[{3}, -S^2])/3 + 156*S*HPL[{2, 1}, -S^2] + (40*S*Zeta[3])/3)) + (220*S*Zeta[5])/3) + HPL[{1}, -S^2]*((-23567*Pi^6*S)/45360 - (Pi^2*(1 + S^2)*(-4 + 1485*S^2 + 95*S^4))/(144*S^3) - ((1 + S^2)*(97 + 5836*S^2 + 521*S^4))/(48*S^3) + (Pi^4*(-4076 - 8223*S^2 - 4168*S^4 - 41*S^6))/(2160*S*(1 + S^2)) + ((-95*Pi^2*S)/18 + (-104 - 107*S^2 - 3*S^4)/(12*S))*HPL[{2}, -S^2]^2 - (13*S*HPL[{2}, -S^2]^3)/9 - (5*S*HPL[{3}, -S^2]^2)/3 + ((7*Pi^2*S)/18 + (6 - 177*S^2 - 187*S^4 - 4*S^6)/(6*S^3))*HPL[{4}, -S^2] + ((-64 - 257*S^2 - 179*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - 39*S*HPL[{6}, -S^2] + 76*S*HPL[{2, 1}, -S^2]^2 + ((88*Pi^2*S)/9 + (-4 + 158*S^2 + 163*S^4 + S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + (2*(-13 - 104*S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + ((-48 - 515*S^2 + 123*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - 9*S*HPL[{4, 2}, -S^2] - (64*S*HPL[{5, 1}, -S^2])/3 + ((-220*Pi^2*S)/9 + (2*(3 - 128*S^2 - 128*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(11 + 63*S^2 + 14*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(31 + 165*S^2 + 54*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (104*S*HPL[{3, 2, 1}, -S^2])/3 - (236*S*HPL[{4, 1, 1}, -S^2])/3 + (4*(18 + 85*S^2 + 45*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 32*S*HPL[{3, 1, 1, 1}, -S^2] - 176*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*(-2 - 19*S^2 + 4*S^4))/(9*S*(1 + S^2)) + (59 + 76*S^2 + 13*S^4)/(6*S))*Zeta[3] - 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(4 - 299*S^2 + 13*S^4))/(6*S^3) + (Pi^2*(117 + 596*S^2 + 259*S^4))/(18*S*(1 + S^2)) - (176*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(1 + 43*S^2 - 60*S^4))/(18*S*(1 + S^2)) + (3 - 81*S^2 - 73*S^4 + 7*S^6)/(6*S^3) - (184*S*HPL[{2, 1}, -S^2])/3 + (16*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-1579*Pi^4*S)/1080 + ((1 + S^2)*(2 - 689*S^2 + 35*S^4))/(24*S^3) + (Pi^2*(6 - 246*S^2 - 519*S^4 - 260*S^6 + 3*S^8))/(36*S^3*(1 + S^2)) + ((13 + 104*S^2 - S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (19*S*HPL[{4}, -S^2])/3 + (2*(11 + 63*S^2 + 14*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (236*S*HPL[{3, 1}, -S^2])/3 - 152*S*HPL[{2, 1, 1}, -S^2] + ((9 + 86*S^2 - 11*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((6 + 45*S^2 - 35*S^4)*Zeta[5])/(3*S*(1 + S^2))) + Log[T]*((373*Pi^6*S)/504 + (-11 + 107*S^2)/(8*S) + (Pi^2*(-9 + 337*S^2 - 4*S^4))/(36*S) + (Pi^4*S*(3435 + 3472*S^2 + 47*S^4))/(1080*(1 + S^2)) + (S*HPL[{0}, S^2]^6)/8 + (2*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2]^5)/(9*S*(1 + S^2)) + 4*S*HPL[{1}, -S^2]^6 + HPL[{0}, S^2]^5*((S*(81 + 64*S^2))/(72*(1 + S^2)) + (17*S*HPL[{1}, -S^2])/36) + ((73*Pi^2*S)/9 + (-1 + 59*S^2)/(3*S))*HPL[{2}, -S^2]^2 + (22*S*HPL[{2}, -S^2]^3)/3 + HPL[{0}, S^2]^4*((109*Pi^2*S)/108 + (S*(113 + 115*S^2 + S^4))/(36*(1 + S^2)) + ((81 + 402*S^2 + 161*S^4)*HPL[{1}, -S^2])/(72*S*(1 + S^2)) + (20*S*HPL[{1}, -S^2]^2)/9 + (37*S*HPL[{2}, -S^2])/18) + HPL[{1}, -S^2]^4*((76*Pi^2*S)/9 + (293 + 302*S^2 + 9*S^4)/(18*S) + (22*S*HPL[{2}, -S^2])/3) + (10*S*HPL[{3}, -S^2]^2)/3 + ((5*Pi^2*S)/9 + (-6 + 60*S^2 + 121*S^4 + S^6)/(3*S^3))*HPL[{4}, -S^2] + ((46 + 319*S^2 + 259*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (218*S*HPL[{6}, -S^2])/3 + ((Pi^2*(-130 - 209*S^2 + 31*S^4))/(9*S*(1 + S^2)) + (-2 - 230*S^2 - 13*S^4 + 19*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] - 96*S*HPL[{2, 1}, -S^2]^2 + ((-314*Pi^2*S)/9 - (2*(-4 + 21*S^2 + 153*S^4 + S^6))/(3*S^3))*HPL[{3, 1}, -S^2] - (S*(-123 + 61*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) - (2*(17 - 132*S^2 + 146*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 18*S*HPL[{4, 2}, -S^2] + (100*S*HPL[{5, 1}, -S^2])/3 + ((680*Pi^2*S)/9 + (2*(-6 + 17*S^2 + 295*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(-57 - 134*S^2 + 37*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(-178 - 347*S^2 + 71*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 12*S*HPL[{3, 1, 2}, -S^2] + 164*S*HPL[{3, 2, 1}, -S^2] + (1496*S*HPL[{4, 1, 1}, -S^2])/3 + (8*(-65 - 88*S^2 + 10*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (1184*S*HPL[{3, 1, 1, 1}, -S^2])/3 + (2720*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((2*Pi^2*S*(-10 + 11*S^2))/(9*(1 + S^2)) - (S*(-13 + 19*S^2))/3)*Zeta[3] - 4*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*(((1 + S^2)*(3 + 643*S^2 + 42*S^4))/(18*S^3) + (Pi^2*(158 + 863*S^2 + 249*S^4))/(27*S*(1 + S^2)) + (2*(18 + 85*S^2 + 45*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (136*S*HPL[{3}, -S^2])/3 - (88*S*HPL[{2, 1}, -S^2])/3 - (112*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(12 - 35*S^2 + 55*S^4))/(18*S*(1 + S^2)) + (3 + 60*S^2 + 90*S^4 - 14*S^6)/(6*S^3) - (20*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{0}, S^2]^3*((Pi^2*S*(328 + 245*S^2))/(54*(1 + S^2)) + (S*(813 + 873*S^2 + 52*S^4))/(72*(1 + S^2)) + ((77 + 383*S^2 + 144*S^4)*HPL[{1}, -S^2]^2)/(18*S*(1 + S^2)) + 6*S*HPL[{1}, -S^2]^3 + ((3 + 221*S^2 + 150*S^4)*HPL[{2}, -S^2])/(18*S*(1 + S^2)) + HPL[{1}, -S^2]*((83*Pi^2*S)/27 + (317 + 629*S^2 + 331*S^4 + 11*S^6)/(36*S*(1 + S^2)) + (68*S*HPL[{2}, -S^2])/9) - (2*S*HPL[{3}, -S^2])/3 + (16*S*HPL[{2, 1}, -S^2])/9 + (22*S*Zeta[3])/9) + HPL[{0}, S^2]^2*((433*Pi^4*S)/180 + (-9 + 638*S^2 - 8*S^4)/(24*S) + (Pi^2*S*(747 + 758*S^2 + 7*S^4))/(72*(1 + S^2)) + ((73 + 388*S^2 + 129*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + (31*S*HPL[{1}, -S^2]^4)/3 + ((53*Pi^2*S)/6 + (-6 + 7*S^2 + 312*S^4 + 298*S^6 + 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (37*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((173*Pi^2*S)/18 + (265 + 264*S^2 + 3*S^4)/(12*S) + (77*S*HPL[{2}, -S^2])/3) + (5*(1 + 3*S^2)*HPL[{3}, -S^2])/(6*S) + (16*S*HPL[{4}, -S^2])/3 + ((-65 - 121*S^2 + 21*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(77 + 395*S^2 + 145*S^4))/(18*S*(1 + S^2)) + (3 + 528*S^2 + 533*S^4 + 16*S^6)/(24*S^3) + ((63 + 341*S^2 + 124*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) - (154*S*HPL[{2, 1}, -S^2])/3) - (166*S*HPL[{3, 1}, -S^2])/3 + (340*S*HPL[{2, 1, 1}, -S^2])/3 + (32*S*Zeta[3])/3) + HPL[{2}, -S^2]*((2203*Pi^4*S)/540 + (1 + 201*S^2 + 602*S^4 - 8*S^6)/(12*S^3) + (Pi^2*(-6 + 9*S^2 + 312*S^4 + 298*S^6 + 3*S^8))/(18*S^3*(1 + S^2)) + (S*(-57 + 35*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (38*S*HPL[{4}, -S^2])/3 + (2*(-57 - 134*S^2 + 37*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (244*S*HPL[{3, 1}, -S^2])/3 + 192*S*HPL[{2, 1, 1}, -S^2] + (22*S*(-3 + S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]^2*((2699*Pi^4*S)/540 + (Pi^2*(279 + 283*S^2 + 6*S^4))/(18*S) + ((1 + S^2)*(-2 + 867*S^2 + 65*S^4))/(12*S^3) + ((110*Pi^2*S)/9 + (-3 + 128*S^2 + 128*S^4 - 3*S^6)/(3*S^3))*HPL[{2}, -S^2] + 38*S*HPL[{2}, -S^2]^2 + (4*(-1 - 12*S^2 + 6*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (38*S*HPL[{4}, -S^2])/3 - (2*(18 + 85*S^2 + 45*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - 16*S*HPL[{3, 1}, -S^2] + 88*S*HPL[{2, 1, 1}, -S^2] + (2*(-4 - 29*S^2 + 3*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]*((Pi^4*S*(3907 + 2618*S^2))/(540*(1 + S^2)) + (Pi^2*S*(740 + 791*S^2 + 47*S^4))/(36*(1 + S^2)) + (-28 + 2709*S^2 + 233*S^4)/(24*S) + (5*(17 + 95*S^2 + 24*S^4)*HPL[{1}, -S^2]^4)/(9*S*(1 + S^2)) + 12*S*HPL[{1}, -S^2]^5 + (S*(112 + 55*S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + HPL[{1}, -S^2]^3*(16*Pi^2*S + (293 + 302*S^2 + 9*S^4)/(9*S) + 52*S*HPL[{2}, -S^2]) + ((-14*Pi^2*S)/9 + (37 + 31*S^2 - S^4)/(3*S))*HPL[{3}, -S^2] + (2*(3 + 21*S^2 + 10*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - 4*S*HPL[{5}, -S^2] + (4*Pi^2*S + (-267 + S^2 + 3*S^4)/(3*S))*HPL[{2, 1}, -S^2] - (2*(1 + 248*S^2 + 131*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3, 2}, -S^2])/3 + (64*S*HPL[{4, 1}, -S^2])/3 + (4*(1 + 254*S^2 + 136*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{2, 2, 1}, -S^2])/3 - (112*S*HPL[{3, 1, 1}, -S^2])/3 + (160*S*HPL[{2, 1, 1, 1}, -S^2])/3 - (S*(-11 + S^2)*Zeta[3])/3 + HPL[{1}, -S^2]^2*(((1 + S^2)*(3 + 643*S^2 + 42*S^4))/(12*S^3) + (Pi^2*(27 + 143*S^2 + 44*S^4))/(3*S*(1 + S^2)) + (13*(2 + 11*S^2 + 3*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) + (4*S*HPL[{3}, -S^2])/3 - 156*S*HPL[{2, 1}, -S^2] - (40*S*Zeta[3])/3) + HPL[{2}, -S^2]*((Pi^2*(4 + 475*S^2 + 286*S^4))/(18*S*(1 + S^2)) + (-6 + 124*S^2 + 349*S^4 + 19*S^6)/(6*S^3) - (8*S*HPL[{3}, -S^2])/3 + (8*S*HPL[{2, 1}, -S^2])/3 - 12*S*Zeta[3]) + HPL[{1}, -S^2]*((1289*Pi^4*S)/270 + ((1 + S^2)*(-2 + 867*S^2 + 65*S^4))/(12*S^3) + (Pi^2*(305 + 612*S^2 + 321*S^4 + 10*S^6))/(18*S*(1 + S^2)) + ((185*Pi^2*S)/9 + (-3 + 156*S^2 + 166*S^4 + 3*S^6)/(3*S^3))*HPL[{2}, -S^2] + 38*S*HPL[{2}, -S^2]^2 + (2*(5 + 21*S^2 + 14*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (32*S*HPL[{4}, -S^2])/3 - (26*(2 + 11*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (464*S*HPL[{3, 1}, -S^2])/3 + 312*S*HPL[{2, 1, 1}, -S^2] + (2*(1 - 6*S^2 + 13*S^4)*Zeta[3])/(3*S*(1 + S^2)))) + (2*S*(-22 + 15*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(1 + 2630*S^2 + 233*S^4))/(24*S^3) + (Pi^4*(2072 + 11111*S^2 + 3641*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(3 + 587*S^2 + 609*S^4 + 29*S^6))/(36*S^3) + ((11 + 63*S^2 + 14*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) + ((-34*Pi^2*S)/3 - (2*(2 - 27*S^2 - 28*S^4 + S^6))/(3*S^3))*HPL[{3}, -S^2] + ((30 + 109*S^2 + 117*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (28*S*HPL[{5}, -S^2])/3 + ((-220*Pi^2*S)/9 + (2*(3 - 128*S^2 - 128*S^4 + 3*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (4*(9 + 39*S^2 + 26*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (368*S*HPL[{3, 2}, -S^2])/3 + (1180*S*HPL[{4, 1}, -S^2])/3 + (4*(18 + 85*S^2 + 45*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + 304*S*HPL[{2, 2, 1}, -S^2] + 640*S*HPL[{3, 1, 1}, -S^2] - 176*S*HPL[{2, 1, 1, 1}, -S^2] + ((-28*Pi^2*S)/3 - (2*(14 + 19*S^2 + 3*S^4))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(4 - 299*S^2 + 13*S^4))/(6*S^3) + (Pi^2*(117 + 596*S^2 + 259*S^4))/(18*S*(1 + S^2)) - (184*S*HPL[{3}, -S^2])/3 - 152*S*HPL[{2, 1}, -S^2] - (176*S*Zeta[3])/3) - (148*S*Zeta[5])/3)) + HPL[{0}, S^2]*((-373*Pi^6*S)/1008 + (33 - 6036*S^2 - 521*S^4)/(48*S) + (Pi^2*(36 - 4530*S^2 - 239*S^4))/(288*S) - (Pi^4*S*(7633 + 8283*S^2 + 630*S^4))/(2160*(1 + S^2)) + ((-17 - 95*S^2 - 24*S^4)*HPL[{1}, -S^2]^5)/(9*S*(1 + S^2)) - 2*S*HPL[{1}, -S^2]^6 + ((-179*Pi^2*S)/36 + (2 - 125*S^2 - 3*S^4)/(12*S))*HPL[{2}, -S^2]^2 - (52*S*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*(-4*Pi^2*S + (-293 - 302*S^2 - 9*S^4)/(36*S) - 13*S*HPL[{2}, -S^2]) + 2*S*HPL[{3}, -S^2]^2 + ((-19*Pi^2*S)/9 + (6 - 11*S^2 - 31*S^4 + 3*S^6)/(6*S^3))*HPL[{4}, -S^2] + (2*(2 + S^2 + S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (34*S*HPL[{6}, -S^2])/3 + (232*S*HPL[{2, 1}, -S^2]^2)/3 + ((67*Pi^2*S)/3 + (-4 + 27*S^2 + 156*S^4)/(3*S^3))*HPL[{3, 1}, -S^2] - (4*(1 + 5*S^2)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (2*(-1 - 11*S^2 + 6*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (52*S*HPL[{5, 1}, -S^2])/3 + ((-406*Pi^2*S)/9 + (2 - 15*S^2 - 111*S^4 - 3*S^6)/S^3)*HPL[{2, 1, 1}, -S^2] + (4*(-33 - 77*S^2 + 13*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(-207 - 480*S^2 + 71*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (416*S*HPL[{3, 2, 1}, -S^2])/3 - (1328*S*HPL[{4, 1, 1}, -S^2])/3 - (4*(-77 - 175*S^2 + 19*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 336*S*HPL[{3, 1, 1, 1}, -S^2] - (2032*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + (-(Pi^2*S*(77 + 81*S^2))/(9*(1 + S^2)) + (S*(-55 - 45*S^2 + 6*S^4))/(6*(1 + S^2)))*Zeta[3] + 2*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-3 - 6*S^2 - S^4))/(9*S*(1 + S^2)) + (-3 - 113*S^2 - 234*S^4 - 132*S^6)/(12*S^3*(1 + S^2)) - 8*S*HPL[{2, 1}, -S^2] - (4*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((Pi^2*(139 + 276*S^2 - 48*S^4))/(18*S*(1 + S^2)) + (2 + 289*S^2 + 89*S^4 - 6*S^6)/(6*S^3) + (8*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((Pi^2*(-27 - 143*S^2 - 44*S^4))/(9*S*(1 + S^2)) - ((1 + S^2)*(3 + 643*S^2 + 42*S^4))/(36*S^3) - (13*(2 + 11*S^2 + 3*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{3}, -S^2])/9 + 52*S*HPL[{2, 1}, -S^2] + (40*S*Zeta[3])/9) + HPL[{2}, -S^2]*((-23*Pi^4*S)/10 + (-1 - 450*S^2 - 886*S^4 - 27*S^6)/(24*S^3) + (Pi^2*(6 - 27*S^2 - 352*S^4 - 327*S^6 - 6*S^8))/(36*S^3*(1 + S^2)) + (2*(1 + 5*S^2)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 4*S*HPL[{4}, -S^2] - (2*(-33 - 77*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (232*S*HPL[{3, 1}, -S^2])/3 - (464*S*HPL[{2, 1, 1}, -S^2])/3 + ((-4 - 16*S^2 - 19*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^2*((-1289*Pi^4*S)/540 - ((1 + S^2)*(-2 + 867*S^2 + 65*S^4))/(24*S^3) + (Pi^2*(-305 - 612*S^2 - 321*S^4 - 10*S^6))/(36*S*(1 + S^2)) + ((-185*Pi^2*S)/18 + (3 - 156*S^2 - 166*S^4 - 3*S^6)/(6*S^3))*HPL[{2}, -S^2] - 19*S*HPL[{2}, -S^2]^2 + ((-5 - 21*S^2 - 14*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{4}, -S^2])/3 + (13*(2 + 11*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (232*S*HPL[{3, 1}, -S^2])/3 - 156*S*HPL[{2, 1, 1}, -S^2] + ((-1 + 6*S^2 - 13*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (S*(167 + 173*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(-1269 - 6335*S^2 - 2488*S^4))/(1080*S*(1 + S^2)) - ((1 + S^2)*(1 + 2630*S^2 + 233*S^4))/(48*S^3) + (Pi^2*(-3 - 676*S^2 - 1372*S^4 - 748*S^6 - 41*S^8))/(72*S^3*(1 + S^2)) + ((-11 - 63*S^2 - 14*S^4)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)) + ((-4*Pi^2*S)/9 + (2 - 33*S^2 - 31*S^4 + 2*S^6)/(3*S^3))*HPL[{3}, -S^2] - (8*(1 + 5*S^2 + 2*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (8*S*HPL[{5}, -S^2])/3 + ((185*Pi^2*S)/9 + (-3 + 156*S^2 + 166*S^4 + 3*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + (4*(19 + 105*S^2 + 28*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (32*S*HPL[{3, 2}, -S^2])/3 - (64*S*HPL[{4, 1}, -S^2])/3 - (26*(2 + 11*S^2 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - 152*S*HPL[{2, 2, 1}, -S^2] - (1376*S*HPL[{3, 1, 1}, -S^2])/3 + 312*S*HPL[{2, 1, 1, 1}, -S^2] + ((8*Pi^2*S)/9 - (4*(2 + 4*S^2 + S^4))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-143 - 751*S^2 - 238*S^4))/(36*S*(1 + S^2)) + (4 - 413*S^2 - 438*S^4 - 13*S^6)/(12*S^3) + (16*S*HPL[{3}, -S^2])/3 + 76*S*HPL[{2, 1}, -S^2] + (14*S*Zeta[3])/3) + 4*S*Zeta[5]));
Et4vwuT3F3=(6563 + 50329*S^2)/(69984*S) + (Pi^2*(556266 + 217731*S^2 + 1953401*S^4))/(419904*S) + (Pi^6*(141402 + 70701*S^2 + 278563*S^4 + 137161*S^6))/(816480*S*(1 + S^2)) + (Pi^4*(223638 + 439905*S^2 + 1118333*S^4 + 895586*S^6))/(699840*S*(1 + S^2)) + ((16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{1}, -S^2]^7)/(21*S^3) + HPL[{0}, S^2]^6*((6 + 3*S^2 + 10*S^4 + 4*S^6)/(288*S*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(48*S^3)) + ((-433 - 277*S^2 + 78*S^4 + 731*S^6 + 575*S^8)*HPL[{2}, -S^2]^3)/(324*S^3*(1 + S^2)) + HPL[{0}, S^2]^5*((17*Pi^2*S^3)/1296 + (-112 + 260*S^2 + 729*S^4)/(2592*S) + ((-56 + 148*S^2 + 102*S^4 + 481*S^6 + 277*S^8)*HPL[{1}, -S^2])/(1296*S^3*(1 + S^2)) + (17*(1 + S^6)*HPL[{1}, -S^2]^2)/(216*S^3) + (17*S^3*HPL[{2}, -S^2])/216) + HPL[{1}, -S^2]^5*((76*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + ((1 + S^2)*(1360 + 599*S^2 + 2275*S^4))/(810*S^3) + (22*(1 + S^6)*HPL[{2}, -S^2])/(45*S^3)) + ((-50 - 8*S^2 + 39*S^4 - 14*S^6 - 56*S^8)*HPL[{3}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((Pi^2*(5 - 17*S^6))/(54*S^3) + (-871 - 5797*S^2 + 75*S^4 + 12945*S^6 + 8376*S^8)/(324*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-385 + 317*S^2 + 351*S^4 + 2120*S^6 + 1418*S^8)*HPL[{6}, -S^2])/(54*S^3*(1 + S^2)) + (5*(15 + 14*S^6)*HPL[{7}, -S^2])/(9*S^3) + ((-421 - 1105*S^2 - 342*S^4 - 1409*S^6 - 725*S^8)*HPL[{2, 1}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((Pi^2*(-9 + 193*S^6))/(54*S^3) + (-1131 + 7953*S^2 + 10959*S^4 + 4049*S^6 + 1742*S^8)/(324*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((Pi^2*(-2 + 35*S^6))/(3*S^3) + (-991 + 14846*S^2 + 17337*S^4 + 3047*S^6 + 899*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-3 + 3*S^2 + 3*S^4 + 5*S^6 - S^8)*HPL[{4, 2}, -S^2])/(2*S^3*(1 + S^2)) + (16*HPL[{4, 3}, -S^2])/(3*S^3) + ((299 + 491*S^2 + 96*S^4 - 576*S^6 - 768*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((17 - S^6)*HPL[{5, 2}, -S^2])/S^3 - (2*(-108 + 53*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((8*Pi^2*(36 + 11*S^6))/(27*S^3) + (943 + 2745*S^2 + 4311*S^4 + 119*S^6)/(81*S^3))*HPL[{2, 2, 1}, -S^2] + ((2758 + 2655*S^2 + 12618*S^4 - 489*S^6)/(81*S^3) + (2*Pi^2*(441 + 19*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + ((11 - 2*S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + ((-767 - 455*S^2 + 156*S^4 + 1444*S^6 + 1132*S^8)*HPL[{3, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((23 - 361*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) - (8*(-4 + 47*S^6)*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (2*(-1452 - 1098*S^2 + 177*S^4 + 2258*S^6 + 1904*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-16 + 185*S^6)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (2*(-16 + 191*S^6)*HPL[{4, 2, 1}, -S^2])/S^3 - (4*(-157 + 1753*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((20*Pi^2*(-11 + 4*S^6))/(9*S^3) + (2*(-1673 + 1746*S^2 - 4032*S^4 + 1042*S^6))/(81*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (16*(-37 + 20*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) - (16*(-154 - 136*S^2 + 9*S^4 + 222*S^6 + 204*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-431 + 55*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) - (4*(-431 + 55*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) - (20*(-175 + 59*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) - (8*(-1315 + 421*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3) + (8*(-497 - 299*S^2 + 99*S^4 + 1045*S^6 + 847*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(23 + 14*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (16*(23 + 14*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (32*(171 + 157*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3) + (32*(-83 + 52*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-34*Pi^2*S^3)/81 - (14*(4 + 5*S^2))/(27*S) - (34*S^3*HPL[{0}, S^2]^2)/27 - (2*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^2)/S^3 + HPL[{0}, S^2]*((-2*(18 + 9*S^2 + 41*S^4 + 23*S^6))/(9*S*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2])/S^3) - (4*(-10 + 17*S^6)*HPL[{2}, -S^2])/(27*S^3))*Log[T]^5 + ((2*(2 + S^2 + 2*S^4))/(3*S*(1 + S^2)) + (4*S^3*HPL[{0}, S^2])/3 + (4*(1 + S^6)*HPL[{1}, -S^2])/(3*S^3))*Log[T]^6 + ((-73458 - 15687*S^2 + 21341*S^4)/(5832*S) + (Pi^2*(-1182 - 1311*S^2 - 17*S^4 + 166*S^6))/(486*S*(1 + S^2)))*Zeta[3] + ((6 + 3*S^2 - 7*S^4 - 13*S^6)*Zeta[3]^2)/(3*S*(1 + S^2)) + Log[T]^4*((402 + 581*S^2)/(162*S) + (Pi^2*(1368 + 684*S^2 + 2215*S^4 + 847*S^6))/(486*S*(1 + S^2)) + (83*S^3*HPL[{0}, S^2]^3)/81 + (5*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)) + (20*(1 + S^6)*HPL[{1}, -S^2]^3)/(3*S^3) + HPL[{0}, S^2]^2*((558 + 279*S^2 + 1405*S^4 + 847*S^6)/(162*S*(1 + S^2)) + (31*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3)) + ((-497 - 299*S^2 + 99*S^4 + 1045*S^6 + 847*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((76*Pi^2*(1 + S^6))/(27*S^3) + (1360 + 1959*S^2 + 2874*S^4 + 2275*S^6)/(162*S^3) + (22*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]*((218*Pi^2*S^3)/81 + (7*(192 + 132*S^2 + 325*S^4))/(162*S) + (5*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) + (10*(1 + S^6)*HPL[{1}, -S^2]^2)/S^3 + (2*(-8 + 127*S^6)*HPL[{2}, -S^2])/(27*S^3)) - (2*(-3 + 104*S^6)*HPL[{3}, -S^2])/(27*S^3) + (4*(-83 + 52*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (208*S^3*Zeta[3])/27) + HPL[{0}, S^2]^4*((Pi^2*(430 + 215*S^2 + 932*S^4 + 502*S^6))/(2592*S*(1 + S^2)) + (7842 + 14379*S^2 + 67097*S^4 + 61856*S^6)/(46656*S*(1 + S^2)) + ((41 + 363*S^2 + 164*S^4 + 615*S^6 + 293*S^8)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)) + (20*(1 + S^6)*HPL[{1}, -S^2]^3)/(81*S^3) + (31*(2 + S^2 + 7*S^4 + 5*S^6)*HPL[{2}, -S^2])/(216*S*(1 + S^2)) + HPL[{1}, -S^2]*((215*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(1296*S^3) + (1307 + 2672*S^2 + 9138*S^4 + 15164*S^6 + 7607*S^8)/(7776*S^3*(1 + S^2)) + (31*(1 + S^6)*HPL[{2}, -S^2])/(108*S^3)) - (S^3*HPL[{3}, -S^2])/24 + ((-31 + 6*S^6)*HPL[{2, 1}, -S^2])/(54*S^3) + (13*S^3*Zeta[3])/27) + HPL[{3, 1}, -S^2]*((7266 + 1759*S^2 - 2570*S^4 - 14237*S^6)/(324*S^3) + (Pi^2*(358 + 97*S^2 - 126*S^4 - 1092*S^6 - 831*S^8))/(81*S^3*(1 + S^2)) + (184*S^3*Zeta[3])/9) + HPL[{1}, -S^2]^4*(((1 + S^2)*(2497 + 869*S^2 + 4854*S^4))/(648*S^3) + (Pi^2*(355 + 1267*S^2 + 456*S^4 + 1540*S^6 + 628*S^8))/(324*S^3*(1 + S^2)) + ((-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) - (34*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (22*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{4}, -S^2]*((197 - 4679*S^2 + 3376*S^4 + 9721*S^6)/(648*S^3) + (Pi^2*(-125 - 179*S^2 - 45*S^4 + 301*S^6 + 355*S^8))/(324*S^3*(1 + S^2)) + (6*HPL[{2, 1}, -S^2])/S^3 - (8*(-1 + S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((17521 + 11223*S^2 + 10521*S^4 + 36377*S^6)/(3888*S^3) + (Pi^2*(453 + 1593*S^2 + 570*S^4 + 2570*S^6 + 1430*S^8))/(648*S^3*(1 + S^2)) + ((-1 - 97*S^6)*HPL[{3}, -S^2])/(18*S^3) + (2*(-37 + 20*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (2*(-3 + 20*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((-5375 + 923*S^2 + 2237*S^4 + 13623*S^6)/(162*S^3) + (Pi^2*(-573 + 87*S^2 + 330*S^4 + 2354*S^6 + 1694*S^8))/(81*S^3*(1 + S^2)) - (8*(-1 + 44*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((-62459 + 59067*S^2 - 230751*S^4 - 21341*S^6)/(5832*S^3) + (Pi^4*(-1991 + 624*S^6))/(1620*S^3) + (Pi^2*(-3160 - 1774*S^2 - 6975*S^4 - 7176*S^6 + 1293*S^8))/(972*S^3*(1 + S^2)) + (4*(21 + 19*S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (8*(23 + 14*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(421 + 685*S^2 + 132*S^4 + 264*S^6)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^4*(105 - 929*S^6))/(3240*S^3) + (-11275 - 226404*S^2 + 39501*S^4 + 57524*S^6)/(11664*S^3) + (Pi^2*(197 - 5947*S^2 - 5961*S^4 + 163*S^6 - 236*S^8))/(1944*S^3*(1 + S^2)) - (8*HPL[{4}, -S^2])/(3*S^3) + ((949 + 1489*S^2 + 252*S^4 + 638*S^6 + 98*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-17 + 97*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (4*(-11 + 97*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(-14 - 35*S^2 - 6*S^4 - 17*S^6 + 4*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((2699*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(4860*S^3) + ((1 + S^2)*(20794 + 5693*S^2 + 48523*S^4))/(2916*S^3) + (Pi^2*(5765 + 8631*S^2 + 15849*S^4 + 12875*S^6))/(2916*S^3) + ((110*Pi^2*(1 + S^6))/(81*S^3) + (-643 - 639*S^2 + 2574*S^4 + 2570*S^6)/(243*S^3))*HPL[{2}, -S^2] + (38*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) - (4*(88 + 190*S^2 + 51*S^4 + 127*S^6 + 25*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (38*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) - (2*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (88*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(125 + 293*S^2 + 84*S^4 + 230*S^6 + 62*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^3*((529*Pi^4*S^3)/6480 + (-2458 + 2416*S^2 + 36369*S^4)/(7776*S) + (Pi^2*(-600 + 5685*S^2 + 24133*S^4 + 17956*S^6))/(11664*S*(1 + S^2)) + ((66 + 392*S^2 + 166*S^4 + 605*S^6 + 279*S^8)*HPL[{1}, -S^2]^3)/(162*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2]^4)/(2*S^3) + ((Pi^2*(-3 + 161*S^6))/(324*S^3) + (-486 + 465*S^2 + 3054*S^4 + 8287*S^6 + 6292*S^8)/(1944*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((-1 + 21*S^6)*HPL[{2}, -S^2]^2)/(36*S^3) + HPL[{1}, -S^2]^2*((83*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (301 + 1063*S^2 + 4395*S^4 + 6589*S^6 + 3064*S^8)/(972*S^3*(1 + S^2)) + (34*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((-12 + 6*S^4 - S^6 - 13*S^8)*HPL[{3}, -S^2])/(108*S^3*(1 + S^2)) + ((1 + 2*S^6)*HPL[{4}, -S^2])/(6*S^3) + ((-223 - 637*S^2 - 216*S^4 - 285*S^6 + 129*S^8)*HPL[{2, 1}, -S^2])/(162*S^3*(1 + S^2)) - (25*S^3*HPL[{3, 1}, -S^2])/9 + (2*(-3 + 76*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + ((4 + 2*S^2 + 185*S^4 + 181*S^6)*Zeta[3])/(54*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-41 + 958*S^2 + 504*S^4 + 2110*S^6 + 1111*S^8))/(972*S^3*(1 + S^2)) + (-473 + 54*S^2 + 15952*S^4 + 28770*S^6 + 13777*S^8)/(3888*S^3*(1 + S^2)) + ((163 + 985*S^2 + 420*S^4 + 1525*S^6 + 703*S^8)*HPL[{2}, -S^2])/(324*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (68*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3))) + Log[T]^3*((-529*Pi^4*S^3)/810 + (-1129 - 1922*S^2)/(486*S) + (Pi^2*(-2205 - 2754*S^2 - 3091*S^4))/(729*S) - (83*S^3*HPL[{0}, S^2]^4)/162 - (20*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) - (20*(1 + S^6)*HPL[{1}, -S^2]^4)/(3*S^3) + HPL[{0}, S^2]^3*((-54 - 27*S^2 - 157*S^4 - 103*S^6)/(27*S*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2])/S^3) + ((2959 - 468*S^2 - 1116*S^4 - 6182*S^6)/(243*S^3) - (10*Pi^2*(-11 + 34*S^6))/(81*S^3))*HPL[{2}, -S^2] - (2*(5 + 8*S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + HPL[{1}, -S^2]^2*((-1360 - 1959*S^2 - 2874*S^4 - 2275*S^6)/(81*S^3) - (152*Pi^2*(1 + S^6))/(27*S^3) - (44*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]^2*((-56*Pi^2*S^3)/27 + (-945 - 1179*S^2 - 3091*S^4)/(243*S) + ((-115 - 487*S^2 - 186*S^4 - 655*S^6 - 283*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) - (62*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) - (10*(-1 + 17*S^6)*HPL[{2}, -S^2])/(27*S^3)) + (2*(19 + 631*S^2 + 306*S^4 + 1003*S^6 + 391*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (4*(3 + 11*S^6)*HPL[{4}, -S^2])/(27*S^3) - (4*(-332 - 530*S^2 - 99*S^4 + 85*S^6 + 283*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) + (16*(-30 + 37*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (80*(-10 + 17*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + (4*(252 + 126*S^2 + 535*S^4 + 283*S^6)*Zeta[3])/(81*S*(1 + S^2)) + HPL[{0}, S^2]*((-2448 - 1273*S^2 - 4854*S^4)/(162*S) - (2*Pi^2*(72 + 36*S^2 + 181*S^4 + 109*S^6))/(27*S*(1 + S^2)) - (10*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)) - (40*(1 + S^6)*HPL[{1}, -S^2]^3)/(3*S^3) - (2*(-122 + 580*S^2 + 351*S^4 + 1735*S^6 + 1033*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-1360 - 1959*S^2 - 2874*S^4 - 2275*S^6)/(81*S^3) - (16*Pi^2*(1 + S^6))/(3*S^3) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + (4*(-9 + 8*S^6)*HPL[{3}, -S^2])/(27*S^3) - (40*(-25 + 2*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (88*S^3*Zeta[3])/27) + HPL[{1}, -S^2]*(-((1 + S^2)*(2497 + 869*S^2 + 4854*S^4))/(162*S^3) + (Pi^2*(-355 - 1267*S^2 - 456*S^4 - 1540*S^6 - 628*S^8))/(81*S^3*(1 + S^2)) - (2*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (136*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (88*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (112*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + ((-2178 - 2367*S^2 - 329*S^4 - 248*S^6)*Zeta[5])/(162*S*(1 + S^2)) + Log[T]^2*((1543 + 3310*S^2)/(972*S) + (Pi^2*(5302 + 6295*S^2 + 13623*S^4))/(1944*S) + (Pi^4*(16194 + 8097*S^2 + 32890*S^4 + 16696*S^6))/(9720*S*(1 + S^2)) + (17*S^3*HPL[{0}, S^2]^5)/108 + (5*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{1}, -S^2]^5)/S^3 + HPL[{0}, S^2]^4*((80 + 40*S^2 + 241*S^4 + 161*S^6)/(108*S*(1 + S^2)) + (20*(1 + S^6)*HPL[{1}, -S^2])/(27*S^3)) + ((421 + 1105*S^2 + 342*S^4 + 1409*S^6 + 725*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((152*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(1360 + 599*S^2 + 2275*S^4))/(81*S^3) + (44*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]^3*((28*Pi^2*S^3)/27 + (1080 + 3465*S^2 + 9298*S^4 + 7021*S^6)/(972*S*(1 + S^2)) + ((66 + 392*S^2 + 166*S^4 + 605*S^6 + 279*S^8)*HPL[{1}, -S^2])/(54*S^3*(1 + S^2)) + (3*(1 + S^6)*HPL[{1}, -S^2]^2)/S^3 + ((-3 + 76*S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((-71 - 5580*S^2 - 315*S^4 - 846*S^6)/(162*S^3) + (Pi^2*(9 - 113*S^6))/(27*S^3))*HPL[{3}, -S^2] + ((-153 - 267*S^2 - 57*S^4 + 65*S^6 + 179*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-13 + 7*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((10*Pi^2*(-11 + 4*S^6))/(9*S^3) + (-1673 + 1746*S^2 - 4032*S^4 + 1042*S^6)/(81*S^3))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((2890 + 2809*S^2 + 13623*S^4)/(648*S) + (Pi^2*(1038 + 519*S^2 + 2851*S^4 + 1813*S^6))/(324*S*(1 + S^2)) + ((115 + 487*S^2 + 186*S^4 + 655*S^6 + 283*S^8)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)) + (62*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((-76 + 386*S^2 + 231*S^4 + 1309*S^6 + 847*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((173*Pi^2*(1 + S^6))/(54*S^3) + (1685 + 2754*S^2 + 7227*S^4 + 6050*S^6)/(324*S^3) + (77*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((2 - 3*S^6)*HPL[{3}, -S^2])/(3*S^3) + (4*(-41 + 4*S^6)*HPL[{2, 1}, -S^2])/(9*S^3)) - (8*(-154 - 136*S^2 + 9*S^4 + 222*S^6 + 204*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-13 + 185*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (4*(-17 + 299*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(-497 - 299*S^2 + 99*S^4 + 1045*S^6 + 847*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(23 + 14*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (16*(105 + 11*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (16*(-83 + 52*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-104*Pi^2*S^3)/27 - (2*(1107 + 198*S^2 + 521*S^4))/(81*S))*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(2497 + 869*S^2 + 4854*S^4))/(108*S^3) + (Pi^2*(355 + 1267*S^2 + 456*S^4 + 1540*S^6 + 628*S^8))/(54*S^3*(1 + S^2)) + ((-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (68*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (44*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (56*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-5375 + 923*S^2 + 2237*S^4 + 13623*S^6)/(324*S^3) + (Pi^2*(-573 + 87*S^2 + 330*S^4 + 2354*S^6 + 1694*S^8))/(162*S^3*(1 + S^2)) - (2*(-11 + 97*S^6)*HPL[{3}, -S^2])/(9*S^3) - (4*(23 + 14*S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (4*(-1 + 44*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((2699*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + ((1 + S^2)*(20794 + 5693*S^2 + 48523*S^4))/(972*S^3) + (Pi^2*(5765 + 8631*S^2 + 15849*S^4 + 12875*S^6))/(972*S^3) + ((110*Pi^2*(1 + S^6))/(27*S^3) + (-643 - 639*S^2 + 2574*S^4 + 2570*S^6)/(81*S^3))*HPL[{2}, -S^2] + (38*(1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) - (4*(88 + 190*S^2 + 51*S^4 + 127*S^6 + 25*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (38*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) - (2*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (88*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(125 + 293*S^2 + 84*S^4 + 230*S^6 + 62*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]*((433*Pi^4*S^3)/270 + (20601 + 7920*S^2 + 48523*S^4)/(972*S) + (Pi^2*(5112 + 10269*S^2 + 18895*S^4 + 13846*S^6))/(972*S*(1 + S^2)) + (10*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)) + (10*(1 + S^6)*HPL[{1}, -S^2]^4)/S^3 + ((Pi^2*(-11 + 203*S^6))/(27*S^3) + (-188 + 1197*S^2 + 837*S^4 + 2319*S^6)/(54*S^3))*HPL[{2}, -S^2] + ((-1 + 116*S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{1}, -S^2]^2*((8*Pi^2*(1 + S^6))/S^3 + (1360 + 1959*S^2 + 2874*S^4 + 2275*S^6)/(54*S^3) + (26*(1 + S^6)*HPL[{2}, -S^2])/S^3) + ((36 + 42*S^2 - 6*S^4 - S^6 - 7*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (2*(1 + 20*S^6)*HPL[{4}, -S^2])/(9*S^3) + (2*(-707 - 1409*S^2 - 351*S^4 - 605*S^6 + 97*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-4 + 63*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (8*(-8 + 127*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(60 + 30*S^2 + 91*S^4 + 31*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(2497 + 869*S^2 + 4854*S^4))/(108*S^3) + (Pi^2*(153 + 586*S^2 + 218*S^4 + 745*S^6 + 312*S^8))/(27*S^3*(1 + S^2)) + (13*(5 + 17*S^2 + 6*S^4 + 20*S^6 + 8*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (52*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) - (220*S^3*Zeta[5])/9) + HPL[{0}, S^2]^2*((500718 + 98571*S^2 + 1953401*S^4)/(139968*S) + (Pi^4*(15672 + 7836*S^2 + 37129*S^4 + 21457*S^6))/(38880*S*(1 + S^2)) + (Pi^2*(16512 + 31476*S^2 + 116393*S^4 + 102725*S^6))/(23328*S*(1 + S^2)) + ((115 + 487*S^2 + 186*S^4 + 655*S^6 + 283*S^8)*HPL[{1}, -S^2]^4)/(108*S^3*(1 + S^2)) + (31*(1 + S^6)*HPL[{1}, -S^2]^5)/(45*S^3) + ((32 + 488*S^2 + 228*S^4 + 1161*S^6 + 705*S^8)*HPL[{2}, -S^2]^2)/(216*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((173*Pi^2*(1 + S^6))/(162*S^3) + (1685 + 2754*S^2 + 7227*S^4 + 6050*S^6)/(972*S^3) + (77*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((Pi^2*(1 - 3*S^6))/(18*S^3) + (134 - 148*S^2 - 33*S^4 + 662*S^6 + 305*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((7 + 22*S^2 + 3*S^4 + 59*S^6 + 44*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + ((-4 - 5*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((2*Pi^2*(-36 + 5*S^6))/(27*S^3) + (-1487 - 1847*S^2 - 4689*S^4 - 4186*S^6 + 251*S^8)/(324*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((3086 + 4349*S^2 + 14798*S^4 + 13319*S^6)/(1296*S^3) + (Pi^2*(78 + 425*S^2 + 175*S^4 + 635*S^6 + 288*S^8))/(108*S^3*(1 + S^2)) + ((238 + 1156*S^2 + 450*S^4 + 1669*S^6 + 751*S^8)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)) - (77*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3)) + ((50 - 175*S^2 - 108*S^4 - 648*S^6 - 423*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(1 + 2*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + ((-1 + 16*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + ((-76 + 386*S^2 + 231*S^4 + 1309*S^6 + 847*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(75 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (2*(-77 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (8*(-41 + 4*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((26*Pi^2*S^3)/27 + (-25 - 2*S^2 + 234*S^4 + 229*S^6)/(54*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-76 + 758*S^2 + 417*S^4 + 2611*S^6 + 1777*S^8))/(648*S^3*(1 + S^2)) + (1396 + 9334*S^2 + 17955*S^4 + 52182*S^6 + 40869*S^8)/(3888*S^3*(1 + S^2)) + ((-1 - 2*S^6)*HPL[{3}, -S^2])/(9*S^3) + ((-75 - 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + Zeta[3]/(3*S^3)) + HPL[{1}, -S^2]*((653*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + ((1 + S^2)*(69749 + 12880*S^2 + 271655*S^4))/(23328*S^3) + (Pi^2*(2992 + 7111*S^2 + 19119*S^4 + 28441*S^6 + 13657*S^8))/(3888*S^3*(1 + S^2)) + ((139*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(108*S^3) + (423 + 1070*S^2 + 2776*S^4 + 4178*S^6 + 1977*S^8)/(216*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (19*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((-22 - 2*S^2 - 2*S^4 + 23*S^6)*HPL[{3}, -S^2])/(18*S^3) + (2*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + ((-238 - 1156*S^2 - 450*S^4 - 1669*S^6 - 751*S^8)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)) - (76*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (154*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-43 + 6*S^2 + 6*S^4 + 20*S^6)*Zeta[3])/(54*S^3)) + (55*S^3*Zeta[5])/9) + HPL[{1}, -S^2]^2*(((1 + S^2)*(112301 + 26842*S^2 + 347093*S^4))/(11664*S^3) + (Pi^2*(10577 + 14447*S^2 + 31967*S^4 + 27881*S^6))/(3888*S^3) + (Pi^4*(3461 + 14247*S^2 + 5378*S^4 + 18894*S^6 + 8108*S^8))/(6480*S^3*(1 + S^2)) + ((110 + 338*S^2 + 114*S^4 + 365*S^6 + 137*S^8)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)) + ((-17*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(3268 + 1043*S^2 + S^4))/(162*S^3))*HPL[{3}, -S^2] + ((-535 - 763*S^2 - 114*S^4 + 20*S^6 + 248*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) + (14*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-110*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(-643 + 4*S^2 + 2570*S^4))/(81*S^3))*HPL[{2, 1}, -S^2] - (2*(-22 - 14*S^2 + 4*S^4 + 37*S^6 + 29*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) + (184*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (590*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (2*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (152*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (320*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (88*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-14*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (-2395 - 3123*S^2 - 1395*S^4 - 775*S^6)/(162*S^3))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-608 - 87*S^2 + 3280*S^4))/(162*S^3) + (Pi^2*(73 + 1387*S^2 + 648*S^4 + 2629*S^6 + 1315*S^8))/(324*S^3*(1 + S^2)) - (92*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (76*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (88*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (74*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*((-337429 + 378231*S^2 + 538881*S^4 + 1953401*S^6)/(69984*S^3) + (Pi^4*(-4623 + 4851*S^2 + 4737*S^4 + 33359*S^6 + 23885*S^8))/(19440*S^3*(1 + S^2)) + (Pi^2*(-14729 - 4022*S^2 + 27435*S^4 + 99762*S^6 + 81738*S^8))/(11664*S^3*(1 + S^2)) + ((Pi^2*(9 - 101*S^6))/(54*S^3) + (867 - 3837*S^2 - 5601*S^4 - 1921*S^6 - 808*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((181 + 43*S^2 - 105*S^4 + 37*S^6 + 175*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) + ((5 + 3*S^6)*HPL[{5}, -S^2])/(3*S^3) + ((-943 - 2745*S^2 - 4311*S^4 - 119*S^6)/(162*S^3) - (4*Pi^2*(36 + 11*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((-516 - 1212*S^2 - 330*S^4 - 1369*S^6 - 673*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-7 + 185*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (2*(-8 + 97*S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (2*(421 + 1105*S^2 + 342*S^4 + 1409*S^6 + 725*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-37 + 20*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (4*(-211 + 23*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (8*(23 + 14*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*(-1 + 11*S^6))/(27*S^3) + (186 - 1920*S^2 - 2403*S^4 - 1196*S^6 - 791*S^8)/(162*S^3*(1 + S^2)))*Zeta[3] - (10*(-2 + 7*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((23567*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(136080*S^3) + ((1 + S^2)*(82377 + 23554*S^2 + 451251*S^4))/(11664*S^3) + (Pi^2*(1 + S^2)*(194513 + 47038*S^2 + 562793*S^4))/(69984*S^3) + (Pi^4*(61231 + 147889*S^2 + 289245*S^4 + 380287*S^6 + 176620*S^8))/(116640*S^3*(1 + S^2)) + ((95*Pi^2*(1 + S^6))/(54*S^3) + (614 + 876*S^2 + 1179*S^4 + 917*S^6)/(108*S^3))*HPL[{2}, -S^2]^2 + (13*(1 + S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + (5*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((-7*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + ((1 + S^2)*(-2119 - 2123*S^2 + 4568*S^4))/(324*S^3))*HPL[{4}, -S^2] + ((-541 - 445*S^2 + 66*S^4 + 662*S^6 + 566*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (13*(1 + S^6)*HPL[{6}, -S^2])/S^3 - (76*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-88*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(-1426 - 257*S^2 + 2750*S^4))/(81*S^3))*HPL[{3, 1}, -S^2] + (2*(389 + 935*S^2 + 264*S^4 + 773*S^6 + 227*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((2869 + 6373*S^2 + 1698*S^4 + 4618*S^6 + 1114*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + (3*(1 + S^6)*HPL[{4, 2}, -S^2])/S^3 + (64*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((220*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2*(1 + S^2)*(-643 + 4*S^2 + 2570*S^4))/(81*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(110 + 338*S^2 + 114*S^4 + 365*S^6 + 137*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(154 + 634*S^2 + 240*S^4 + 841*S^6 + 361*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (104*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (236*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (4*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (32*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (176*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-4405 - 5749*S^2 - 2371*S^4 - 1243*S^6)/(324*S^3) + (Pi^2*(-209 - 458*S^2 - 120*S^4 - 332*S^6 - 83*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/S^3 + HPL[{3}, -S^2]*((-6766 - 8671*S^2 - 142*S^4 + 1547*S^6)/(324*S^3) + (Pi^2*(-198 - 404*S^2 - 106*S^4 - 233*S^6 - 27*S^8))/(54*S^3*(1 + S^2)) + (184*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(-608 - 87*S^2 + 3280*S^4))/(81*S^3) + (Pi^2*(-73 - 1387*S^2 - 648*S^4 - 2629*S^6 - 1315*S^8))/(162*S^3*(1 + S^2)) + (176*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((1579*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(3240*S^3) + ((1 + S^2)*(-10129 - 6035*S^2 + 147956*S^4))/(5832*S^3) + (Pi^2*(-17 + 646*S^2 + 12198*S^4 + 22822*S^6 + 11071*S^8))/(1944*S^3*(1 + S^2)) + ((-389 - 935*S^2 - 264*S^4 - 773*S^6 - 227*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (19*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (2*(110 + 338*S^2 + 114*S^4 + 365*S^6 + 137*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (236*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (152*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-403 - 925*S^2 - 252*S^4 - 709*S^6 - 187*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((-47 - 97*S^2 - 26*S^4 - 60*S^6 - 10*S^8)*Zeta[5])/(3*S^3*(1 + S^2))) + HPL[{0}, S^2]*((373*Pi^6*S^3)/3024 + (Pi^2*(33828 + 23088*S^2 + 206153*S^4))/(23328*S) + (83639 + 29408*S^2 + 451251*S^4)/(11664*S) + (Pi^4*(15216 + 53859*S^2 + 143954*S^4 + 105851*S^6))/(58320*S*(1 + S^2)) + ((16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2]^6)/(3*S^3) + ((Pi^2*(-4 + 179*S^6))/(108*S^3) + (-31 + 584*S^2 + 353*S^4 + 1029*S^6)/(108*S^3))*HPL[{2}, -S^2]^2 + ((-5 + 52*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{1}, -S^2]^4*((4*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + ((1 + S^2)*(1360 + 599*S^2 + 2275*S^4))/(324*S^3) + (13*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) - (2*(-1 + 3*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((Pi^2*(5 + 19*S^6))/(27*S^3) + (-127 + 117*S^2 + 387*S^4 + 641*S^6)/(162*S^3))*HPL[{4}, -S^2] + ((-82 - 49*S^2 + 30*S^4 + 44*S^6 + 11*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (2*(15 + 17*S^6)*HPL[{6}, -S^2])/(9*S^3) - (2*(-1 + 116*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((203 - 1863*S^2 - 1251*S^4 - 3454*S^6)/(81*S^3) + (Pi^2*(8 - 201*S^6))/(27*S^3))*HPL[{3, 1}, -S^2] - (4*(-9 - 33*S^2 - 12*S^4 - 14*S^6 + 10*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-29 - 125*S^2 - 48*S^4 - 33*S^6 + 63*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(3 + 13*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((2*Pi^2*(-11 + 203*S^6))/(27*S^3) + (-188 + 1197*S^2 + 837*S^4 + 2319*S^6)/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(-113 - 228*S^2 - 59*S^4 - 100*S^6 + 15*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2*(-2070 - 4146*S^2 - 1056*S^4 - 1799*S^6 + 277*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-5 + 52*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (4*(-29 + 332*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (4*(-707 - 1409*S^2 - 351*S^4 - 605*S^6 + 97*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(-4 + 63*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (16*(-8 + 127*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(-6 - 3*S^2 + 58*S^4 + 64*S^6))/(81*S*(1 + S^2)) + (-2038 - 2285*S^2 + 583*S^4 + 614*S^6)/(324*S*(1 + S^2)))*Zeta[3] - (2*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*(((1 + S^2)*(2497 + 869*S^2 + 4854*S^4))/(324*S^3) + (Pi^2*(153 + 586*S^2 + 218*S^4 + 745*S^6 + 312*S^8))/(81*S^3*(1 + S^2)) + (13*(5 + 17*S^2 + 6*S^4 + 20*S^6 + 8*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) - (52*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) + HPL[{2, 1}, -S^2]*((-3674 - 1023*S^2 - 6453*S^4 - 370*S^6)/(162*S^3) + (Pi^2*(-930 - 2046*S^2 - 567*S^4 - 890*S^6 + 226*S^8))/(162*S^3*(1 + S^2)) - (8*(-4 + S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((Pi^2*(21 + 6*S^2 - 2*S^4 - 23*S^6))/(162*S*(1 + S^2)) + (197 + 221*S^2 + 1947*S^4 + 3857*S^6 + 2258*S^8)/(486*S^3*(1 + S^2)) + (4*(5 + 6*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(-1 + S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((1289*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + ((1 + S^2)*(20794 + 5693*S^2 + 48523*S^4))/(1944*S^3) + (Pi^2*(4682 + 12083*S^2 + 23289*S^4 + 28625*S^6 + 12953*S^8))/(1944*S^3*(1 + S^2)) + ((185*Pi^2*(1 + S^6))/(54*S^3) + (584 + 828*S^2 + 1323*S^4 + 1115*S^6)/(54*S^3))*HPL[{2}, -S^2] + (19*(1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + ((-34 - 22*S^2 + 6*S^4 + 59*S^6 + 47*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (13*(5 + 17*S^2 + 6*S^4 + 20*S^6 + 8*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (232*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (52*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + ((-119 - 239*S^2 - 60*S^4 - 131*S^6 - 11*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^4*(-37 + 1242*S^6))/(1620*S^3) + (-4617 + 17172*S^2 + 15642*S^4 + 49009*S^6)/(1944*S^3) + (Pi^2*(-1050 + 3492*S^2 + 9156*S^4 + 17755*S^6 + 13249*S^8))/(1944*S^3*(1 + S^2)) + (2*(-9 - 33*S^2 - 12*S^4 - 14*S^6 + 10*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-1 + 3*S^6)*HPL[{4}, -S^2])/(9*S^3) + (2*(-113 - 228*S^2 - 59*S^4 - 100*S^6 + 15*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (232*S^3*HPL[{3, 1}, -S^2])/9 + (4*(-1 + 116*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-4 - 52*S^2 - 33*S^4 - 54*S^6 - 6*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((-36 - 18*S^2 + 485*S^4 + 521*S^6)*Zeta[5])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(112301 + 26842*S^2 + 347093*S^4))/(11664*S^3) + (Pi^4*(2758 + 18256*S^2 + 7794*S^4 + 29407*S^6 + 13909*S^8))/(9720*S^3*(1 + S^2)) + (Pi^2*(7018 + 17643*S^2 + 43219*S^4 + 60501*S^6 + 28339*S^8))/(3888*S^3*(1 + S^2)) + ((110 + 338*S^2 + 114*S^4 + 365*S^6 + 137*S^8)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)) + ((4*Pi^2*(1 + S^6))/(27*S^3) + (25 - 27*S^2 + 234*S^4 + 340*S^6)/(81*S^3))*HPL[{3}, -S^2] + (8*(2 + 14*S^2 + 6*S^4 + 23*S^6 + 11*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(9*S^3) + ((-584 - 828*S^2 - 1323*S^4 - 1115*S^6)/(27*S^3) - (185*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (4*(148 + 496*S^2 + 174*S^4 + 577*S^6 + 229*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) + (64*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (26*(5 + 17*S^2 + 6*S^4 + 20*S^6 + 8*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (152*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (1376*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (104*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-8*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(-923 - 211*S^2 + 94*S^4))/(162*S^3))*Zeta[3] + HPL[{2}, -S^2]*((1063 + 1453*S^2 + 2919*S^4 + 2601*S^6)/(108*S^3) + (Pi^2*(748 + 2974*S^2 + 1122*S^4 + 3865*S^6 + 1639*S^8))/(324*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (76*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (14*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3))) + Log[T]*((-373*Pi^6*S^3)/1512 + (-1907 - 6081*S^2)/(2916*S) + (Pi^2*(-74502 - 61857*S^2 - 274571*S^4))/(34992*S) + (Pi^4*(-47466 - 117009*S^2 - 199843*S^4 - 129760*S^6))/(58320*S*(1 + S^2)) - (S^3*HPL[{0}, S^2]^6)/24 - (2*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^6)/(3*S^3) + HPL[{0}, S^2]^5*((-102 - 51*S^2 - 379*S^4 - 277*S^6)/(648*S*(1 + S^2)) - (17*(1 + S^6)*HPL[{1}, -S^2])/(108*S^3)) + ((-2741 - 2511*S^2 - 2763*S^4 - 5383*S^6)/(324*S^3) + (Pi^2*(-23 - 73*S^6))/(27*S^3))*HPL[{2}, -S^2]^2 - (2*(-8 + 11*S^6)*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^4*((-109*Pi^2*S^3)/324 + (-738 - 3285*S^2 - 10775*S^4 - 8336*S^6)/(3888*S*(1 + S^2)) + ((-41 - 363*S^2 - 164*S^4 - 615*S^6 - 293*S^8)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)) - (20*(1 + S^6)*HPL[{1}, -S^2]^2)/(27*S^3) - (37*S^3*HPL[{2}, -S^2])/54) + HPL[{1}, -S^2]^4*((-76*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(1360 + 599*S^2 + 2275*S^4))/(162*S^3) - (22*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) - (2*(-4 + 5*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((509 + 2517*S^2 - 1254*S^4 - 3043*S^6)/(162*S^3) + (Pi^2*(-2 - 5*S^6))/(27*S^3))*HPL[{4}, -S^2] + ((359 + 275*S^2 - 42*S^4 - 812*S^6 - 728*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) - (2*(60 + 109*S^6)*HPL[{6}, -S^2])/(9*S^3) + (4*(5 + 8*S^6)*HPL[{2, 1}, -S^2]^2)/S^3 + ((2*Pi^2*(-65 + 157*S^6))/(27*S^3) + (-3724 - 531*S^2 + 990*S^4 + 6227*S^6)/(81*S^3))*HPL[{3, 1}, -S^2] + ((243 - 861*S^2 - 552*S^4 - 1798*S^6 - 694*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-131 + 1639*S^2 + 885*S^4 + 2769*S^6 + 999*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) - 6*S^3*HPL[{4, 2}, -S^2] - (4*(-9 + 25*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-20*Pi^2*(-11 + 34*S^6))/(27*S^3) - (2*(-2959 + 468*S^2 + 1116*S^4 + 6182*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(239 + 923*S^2 + 342*S^4 + 781*S^6 + 97*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-349 - 1069*S^2 - 360*S^4 - 670*S^6 + 50*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-1 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 - (4*(-29 + 41*S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (8*(-147 + 187*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (8*(-332 - 530*S^2 - 99*S^4 + 85*S^6 + 283*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(-30 + 37*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (160*(-10 + 17*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((4718 + 935*S^2 + 503*S^4)/(162*S) + (2*Pi^2*(42 + 21*S^2 + 73*S^4 + 31*S^6))/(27*S*(1 + S^2)))*Zeta[3] + (4*S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((2943 - 3703*S^2 + 10535*S^4 - 503*S^6)/(162*S^3) + (Pi^2*(646 + 1300*S^2 + 318*S^4 + 275*S^6 - 379*S^8))/(81*S^3*(1 + S^2)) - (40*Zeta[3])/S^3) + HPL[{0}, S^2]^2*((-433*Pi^4*S^3)/540 + (-54180 - 27261*S^2 - 274571*S^4)/(11664*S) + (Pi^2*(-2628 - 7533*S^2 - 19315*S^4 - 14518*S^6))/(1944*S*(1 + S^2)) + ((-115 - 487*S^2 - 186*S^4 - 655*S^6 - 283*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) - (31*(1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + ((Pi^2*(5 - 159*S^6))/(54*S^3) + (218 - 1363*S^2 - 3639*S^4 - 8348*S^6 - 6182*S^8)/(324*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((-1 - 74*S^6)*HPL[{2}, -S^2]^2)/(18*S^3) + HPL[{1}, -S^2]^2*((-1685 - 2754*S^2 - 7227*S^4 - 6050*S^6)/(324*S^3) - (173*Pi^2*(1 + S^6))/(54*S^3) - (77*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(18*S) + ((-5 - 16*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((314 + 770*S^2 + 219*S^4 + 360*S^6 - 96*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-3086 - 4349*S^2 - 14798*S^4 - 13319*S^6)/(648*S^3) + (Pi^2*(-78 - 425*S^2 - 175*S^4 - 635*S^6 - 288*S^8))/(54*S^3*(1 + S^2)) + ((-238 - 1156*S^2 - 450*S^4 - 1669*S^6 - 751*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) + (154*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3)) + (2*(-5 + 83*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (20*(-1 + 17*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (97*S^3*Zeta[3])/27) + HPL[{0}, S^2]^3*((-2100 - 10437*S^2 - 55832*S^4 - 48143*S^6)/(5832*S*(1 + S^2)) + (Pi^2*(-498 - 249*S^2 - 1654*S^4 - 1156*S^6))/(486*S*(1 + S^2)) + ((-66 - 392*S^2 - 166*S^4 - 605*S^6 - 279*S^8)*HPL[{1}, -S^2]^2)/(54*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{1}, -S^2]^3)/S^3 - (2*(-15 + 87*S^2 + 51*S^4 + 310*S^6 + 208*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-83*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + (-301 - 1063*S^2 - 4395*S^4 - 6589*S^6 - 3064*S^8)/(486*S^3*(1 + S^2)) - (68*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((-1 + 2*S^6)*HPL[{3}, -S^2])/(9*S^3) - (2*(-71 + 8*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (22*S^3*Zeta[3])/27) + HPL[{3}, -S^2]*((1277 + 35526*S^2 - 1959*S^4 - 2948*S^6)/(972*S^3) + (Pi^2*(19 + 637*S^2 + 318*S^4 + 1012*S^6 + 394*S^8))/(162*S^3*(1 + S^2)) + (4*(-103 + 5*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(2497 + 869*S^2 + 4854*S^4))/(162*S^3) + (Pi^2*(-355 - 1267*S^2 - 456*S^4 - 1540*S^6 - 628*S^8))/(81*S^3*(1 + S^2)) - (2*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (136*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (88*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (112*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((-2699*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) - ((1 + S^2)*(20794 + 5693*S^2 + 48523*S^4))/(972*S^3) + (Pi^2*(-5765 - 8631*S^2 - 15849*S^4 - 12875*S^6))/(972*S^3) + ((-110*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(-643 + 4*S^2 + 2570*S^4))/(81*S^3))*HPL[{2}, -S^2] - (38*(1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + (4*(88 + 190*S^2 + 51*S^4 + 127*S^6 + 25*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (38*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (2*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (16*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (88*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(125 + 293*S^2 + 84*S^4 + 230*S^6 + 62*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((82717 - 26739*S^2 - 53091*S^4 - 274571*S^6)/(5832*S^3) + (Pi^4*(412 - 2203*S^6))/(1620*S^3) + (Pi^2*(3177 + 1128*S^2 - 5223*S^4 - 15646*S^6 - 12364*S^8))/(972*S^3*(1 + S^2)) + ((-171 + 381*S^2 + 276*S^4 + 908*S^6 + 356*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-8 + 19*S^6)*HPL[{4}, -S^2])/(9*S^3) + (2*(239 + 923*S^2 + 342*S^4 + 781*S^6 + 97*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(55 + 61*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (8*(5 + 8*S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(-18 + 240*S^2 + 120*S^4 + 445*S^6 + 187*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]*((-112344 - 35637*S^2 - 347093*S^4)/(5832*S) + (Pi^2*(-24132 - 43926*S^2 - 110975*S^4 - 91829*S^6))/(5832*S*(1 + S^2)) + (Pi^4*(-7734 - 3867*S^2 - 22093*S^4 - 14359*S^6))/(4860*S*(1 + S^2)) - (5*(16 + 52*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^5)/S^3 + ((3 - 110*S^2 - 55*S^4 - 265*S^6 - 152*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-16*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - ((1 + S^2)*(1360 + 599*S^2 + 2275*S^4))/(81*S^3) - (52*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + ((-160 + 165*S^2 - 276*S^4 - 313*S^6)/(81*S^3) + (2*Pi^2*(-6 + 7*S^6))/(27*S^3))*HPL[{3}, -S^2] - (2*(-9 + 39*S^2 + 24*S^4 + 133*S^6 + 85*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (4*(1 + 3*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((1356 + 459*S^2 + 1809*S^4 - 89*S^6)/(27*S^3) - (4*Pi^2*(-98 + 9*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + (2*(-122 + 574*S^2 + 348*S^4 + 1709*S^6 + 1013*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(3 + 2*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (4*(3 + 16*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (4*(-122 + 580*S^2 + 351*S^4 + 1735*S^6 + 1033*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-115 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (16*(-177 + 7*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (80*(-25 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((226 + 4*S^2 - 15*S^4)*Zeta[3])/(27*S) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(2497 + 869*S^2 + 4854*S^4))/(108*S^3) + (Pi^2*(-153 - 586*S^2 - 218*S^4 - 745*S^6 - 312*S^8))/(27*S^3*(1 + S^2)) - (13*(5 + 17*S^2 + 6*S^4 + 20*S^6 + 8*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (52*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((485 - 3336*S^2 - 2304*S^4 - 7433*S^6)/(162*S^3) + (Pi^2*(182 - 928*S^2 - 555*S^4 - 2975*S^6 - 1865*S^8))/(162*S^3*(1 + S^2)) + (4*(3 + 2*S^6)*HPL[{3}, -S^2])/(9*S^3) - (4*(-115 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(-1 + 9*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((-1289*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) - ((1 + S^2)*(20794 + 5693*S^2 + 48523*S^4))/(972*S^3) + (Pi^2*(-4682 - 12083*S^2 - 23289*S^4 - 28625*S^6 - 12953*S^8))/(972*S^3*(1 + S^2)) + ((-584 - 828*S^2 - 1323*S^4 - 1115*S^6)/(27*S^3) - (185*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2] - (38*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) - (2*(-34 - 22*S^2 + 6*S^4 + 59*S^6 + 47*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (32*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (26*(5 + 17*S^2 + 6*S^4 + 20*S^6 + 8*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (464*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (104*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(119 + 239*S^2 + 60*S^4 + 131*S^6 + 11*S^8)*Zeta[3])/(27*S^3*(1 + S^2)))) + (2*(74 + 37*S^2 + 158*S^4 + 84*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(112301 + 26842*S^2 + 347093*S^4))/(5832*S^3) + (Pi^2*(-10577 - 14447*S^2 - 31967*S^4 - 27881*S^6))/(1944*S^3) + (Pi^4*(-3461 - 14247*S^2 - 5378*S^4 - 18894*S^6 - 8108*S^8))/(3240*S^3*(1 + S^2)) + ((-110 - 338*S^2 - 114*S^4 - 365*S^6 - 137*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((34*Pi^2*(1 + S^6))/(9*S^3) + (3268 + 4311*S^2 + 1044*S^4 + S^6)/(81*S^3))*HPL[{3}, -S^2] + ((535 + 763*S^2 + 114*S^4 - 20*S^6 - 248*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (28*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((220*Pi^2*(1 + S^6))/(27*S^3) + (2*(-643 - 639*S^2 + 2574*S^4 + 2570*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] + (4*(-22 - 14*S^2 + 4*S^4 + 37*S^6 + 29*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (368*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (1180*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (4*(-55 + 77*S^2 + 66*S^4 + 320*S^6 + 188*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (304*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (640*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (176*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((28*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (2395 + 3123*S^2 + 1395*S^4 + 775*S^6)/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-608 - 87*S^2 + 3280*S^4))/(81*S^3) + (Pi^2*(-73 - 1387*S^2 - 648*S^4 - 2629*S^6 - 1315*S^8))/(162*S^3*(1 + S^2)) + (184*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (152*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (176*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (148*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)));
Et4vwuT=T*Et4vwuT1F1*(F-1/F)+T^2*(Et4vwuT2F2*(F^2-1/F^2))+T^3*(Et4vwuT3F1*(F-1/F)+Et4vwuT3F3*(F^3-1/F^3));
e5T0F0=(-42709*Pi^10)/340200 - (47*Pi^4*HPL[{0}, S^2]^6)/1440 - (5*Pi^2*HPL[{0}, S^2]^8)/1152 - HPL[{0}, S^2]^10/3840 + ((-94*Pi^4)/45 - (10*Pi^2*HPL[{0}, S^2]^2)/9 - HPL[{0}, S^2]^4/6)*Log[T]^6 + ((-10*Pi^2)/9 - HPL[{0}, S^2]^2/3)*Log[T]^8 - (4*Log[T]^10)/15 - (8*Pi^4*Zeta[3]^2)/3 + Log[T]^4*((-6023*Pi^6)/2835 - (47*Pi^4*HPL[{0}, S^2]^2)/30 - (5*Pi^2*HPL[{0}, S^2]^4)/12 - HPL[{0}, S^2]^6/24 - 32*Zeta[3]^2) + HPL[{0}, S^2]^4*((-6023*Pi^6)/45360 - 2*Zeta[3]^2) - (160*Pi^2*Zeta[3]*Zeta[5])/3 + Log[T]^2*((-179327*Pi^8)/170100 - (47*Pi^4*HPL[{0}, S^2]^4)/120 - (5*Pi^2*HPL[{0}, S^2]^6)/72 - HPL[{0}, S^2]^8/192 - (64*Pi^2*Zeta[3]^2)/3 + HPL[{0}, S^2]^2*((-6023*Pi^6)/5670 - 16*Zeta[3]^2) - 320*Zeta[3]*Zeta[5]) + HPL[{0}, S^2]^2*((-179327*Pi^8)/680400 - (16*Pi^2*Zeta[3]^2)/3 - 80*Zeta[3]*Zeta[5]);
e5T1F1=(25*Pi^4*S)/4 + (8*Pi^6*S)/9 + (13091*Pi^8*S)/181440 + (S*HPL[{0}, S^2]^9)/384 + ((1 + S^2)*HPL[{0}, S^2]^8*HPL[{1}, -S^2])/(384*S) + ((88*(1 + S^2))/(21*S) + (22*Pi^2*(1 + S^2))/(63*S))*HPL[{1}, -S^2]^7 + (2*(1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) + (2*(1 + S^2)*HPL[{1}, -S^2]^9)/(27*S) + HPL[{0}, S^2]^7*(S/12 + (5*Pi^2*S)/144 + ((1 + S^2)*HPL[{1}, -S^2])/(24*S) + ((1 + S^2)*HPL[{1}, -S^2]^2)/(48*S)) + (43*(1 + S^2)*HPL[{2}, -S^2]^4)/(12*S) - (14*(1 + S^2)*HPL[{3}, -S^2]^3)/(3*S) - (12*(-1 + S^2)*HPL[{4}, -S^2]^2)/S + ((125*Pi^2*(1 + S^2))/(2*S) + (325 + 552*S^2)/S)*HPL[{7}, -S^2] + (3*(175 + 82*S^2)*HPL[{8}, -S^2])/S + (2450*(1 + S^2)*HPL[{9}, -S^2])/S + HPL[{0}, S^2]^6*((Pi^2*S)/96 + ((1 + S^2)*HPL[{1}, -S^2]^2)/(6*S) + ((1 + S^2)*HPL[{1}, -S^2]^3)/(18*S) + (S*HPL[{2}, -S^2])/16 + HPL[{1}, -S^2]*((13*(1 + S^2))/(48*S) + (11*Pi^2*(1 + S^2))/(288*S) + ((1 + S^2)*HPL[{2}, -S^2])/(16*S)) + ((1 + S^2)*HPL[{3}, -S^2])/(24*S) + ((-1 - S^2)*HPL[{2, 1}, -S^2])/(8*S)) + (4*(49 + 41*S^2)*HPL[{3, 1}, -S^2]^2)/S + ((-16*Pi^2*(1 + S^2))/S - (2*(7 + 88*S^2))/S)*HPL[{4, 3}, -S^2] + ((-38 - 509*S^2)/S - (283*Pi^2*(1 + S^2))/(6*S))*HPL[{5, 2}, -S^2] + 6*S*HPL[{5, 3}, -S^2] + (490*(1 + S^2)*HPL[{5, 4}, -S^2])/S + ((-118*Pi^2*(1 + S^2))/S - (4*(43 + 285*S^2))/S)*HPL[{6, 1}, -S^2] + (3*(2 + 3*S^2)*HPL[{6, 2}, -S^2])/S + (1948*(1 + S^2)*HPL[{6, 3}, -S^2])/S - (4*(57 + 47*S^2)*HPL[{7, 1}, -S^2])/S + (4860*(1 + S^2)*HPL[{7, 2}, -S^2])/S + (8720*(1 + S^2)*HPL[{8, 1}, -S^2])/S + (664*(1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((-205 - 893*S^2)/S - (61*Pi^2*(1 + S^2))/(2*S))*HPL[{3, 2, 2}, -S^2] + ((-320*Pi^2*(1 + S^2))/(3*S) - (8*(77 + 358*S^2))/S)*HPL[{3, 3, 1}, -S^2] + (4*(-8 + S^2)*HPL[{3, 3, 2}, -S^2])/S + ((-104*Pi^2*(1 + S^2))/S - (4*(149 + 711*S^2))/S)*HPL[{4, 1, 2}, -S^2] + (4*(16 + S^2)*HPL[{4, 1, 3}, -S^2])/S + ((-340*Pi^2*(1 + S^2))/S - (4*(473 + 2205*S^2))/S)*HPL[{4, 2, 1}, -S^2] - (5*(7 + S^2)*HPL[{4, 2, 2}, -S^2])/S - (4*(-32 + 19*S^2)*HPL[{4, 3, 1}, -S^2])/S - (84*(1 + S^2)*HPL[{4, 3, 2}, -S^2])/S + (168*(1 + S^2)*HPL[{4, 4, 1}, -S^2])/S + ((-2134*Pi^2*(1 + S^2))/(3*S) - (4*(976 + 4517*S^2))/S)*HPL[{5, 1, 1}, -S^2] - (2*(-29 + 25*S^2)*HPL[{5, 1, 2}, -S^2])/S + (336*(1 + S^2)*HPL[{5, 1, 3}, -S^2])/S - (2*(-269 + 145*S^2)*HPL[{5, 2, 1}, -S^2])/S + (78*(1 + S^2)*HPL[{5, 2, 2}, -S^2])/S + (1152*(1 + S^2)*HPL[{5, 3, 1}, -S^2])/S - (20*(-74 + 31*S^2)*HPL[{6, 1, 1}, -S^2])/S + (808*(1 + S^2)*HPL[{6, 1, 2}, -S^2])/S + (3688*(1 + S^2)*HPL[{6, 2, 1}, -S^2])/S + (9040*(1 + S^2)*HPL[{7, 1, 1}, -S^2])/S + ((688*(-1 + S^2))/S - (104*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 2, 1}, -S^2] + ((506*Pi^2*(1 + S^2))/(3*S) - (12*(-199 + 15*S^2))/S)*HPL[{3, 1, 1, 2}, -S^2] + ((506*Pi^2*(1 + S^2))/(3*S) - (12*(-199 + 15*S^2))/S)*HPL[{3, 1, 2, 1}, -S^2] + (12*(1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/S + ((818*Pi^2*(1 + S^2))/(3*S) - (12*(-371 + 187*S^2))/S)*HPL[{3, 2, 1, 1}, -S^2] + (12*(1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/S - (4*(-71 + 81*S^2)*HPL[{3, 2, 2, 1}, -S^2])/S + (416*(1 + S^2)*HPL[{3, 2, 2, 2}, -S^2])/S + (1192*(1 + S^2)*HPL[{3, 2, 3, 1}, -S^2])/S - (48*(-17 + 21*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (1168*(1 + S^2)*HPL[{3, 3, 1, 2}, -S^2])/S + (3496*(1 + S^2)*HPL[{3, 3, 2, 1}, -S^2])/S + ((2584*Pi^2*(1 + S^2))/(3*S) - (32*(-429 + 197*S^2))/S)*HPL[{4, 1, 1, 1}, -S^2] + (12*(-1 + 7*S^2)*HPL[{4, 1, 1, 2}, -S^2])/S - (7160*(1 + S^2)*HPL[{4, 1, 1, 3}, -S^2])/S - (12*(-67 + 77*S^2)*HPL[{4, 1, 2, 1}, -S^2])/S - (5992*(1 + S^2)*HPL[{4, 1, 2, 2}, -S^2])/S - (10624*(1 + S^2)*HPL[{4, 1, 3, 1}, -S^2])/S - (84*(-29 + 35*S^2)*HPL[{4, 2, 1, 1}, -S^2])/S - (3736*(1 + S^2)*HPL[{4, 2, 1, 2}, -S^2])/S - (3664*(1 + S^2)*HPL[{4, 2, 2, 1}, -S^2])/S - (20912*(1 + S^2)*HPL[{4, 3, 1, 1}, -S^2])/S - (8*(-617 + 717*S^2)*HPL[{5, 1, 1, 1}, -S^2])/S - (21688*(1 + S^2)*HPL[{5, 1, 1, 2}, -S^2])/S - (35368*(1 + S^2)*HPL[{5, 1, 2, 1}, -S^2])/S - (83464*(1 + S^2)*HPL[{5, 2, 1, 1}, -S^2])/S - (208480*(1 + S^2)*HPL[{6, 1, 1, 1}, -S^2])/S + ((-2208*(1 + S^2))/S - (192*Pi^2*(1 + S^2))/S)*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-6624*(1 + S^2))/S - (576*Pi^2*(1 + S^2))/S)*HPL[{2, 2, 1, 1, 1}, -S^2] - (608*(-1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S - (1824*(-1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S + (832*(1 + S^2)*HPL[{2, 2, 2, 2, 1}, -S^2])/S + ((-3416*Pi^2*(1 + S^2))/(3*S) - (32*(379 + 474*S^2))/S)*HPL[{3, 1, 1, 1, 1}, -S^2] + (3600*(-1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S + (6032*(-1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S + (1744*(1 + S^2)*HPL[{3, 1, 1, 2, 2}, -S^2])/S + (7248*(-1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S + (1744*(1 + S^2)*HPL[{3, 1, 2, 1, 2}, -S^2])/S - (48*(1 + S^2)*HPL[{3, 1, 2, 2, 1}, -S^2])/S - (12928*(1 + S^2)*HPL[{3, 1, 3, 1, 1}, -S^2])/S + (15152*(-1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S + (4240*(1 + S^2)*HPL[{3, 2, 1, 1, 2}, -S^2])/S + (2448*(1 + S^2)*HPL[{3, 2, 1, 2, 1}, -S^2])/S - (3696*(1 + S^2)*HPL[{3, 2, 2, 1, 1}, -S^2])/S - (13440*(1 + S^2)*HPL[{3, 3, 1, 1, 1}, -S^2])/S + (32*(-1431 + 1417*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S + (12608*(1 + S^2)*HPL[{4, 1, 1, 1, 2}, -S^2])/S + (7232*(1 + S^2)*HPL[{4, 1, 1, 2, 1}, -S^2])/S - (11200*(1 + S^2)*HPL[{4, 1, 2, 1, 1}, -S^2])/S - (40576*(1 + S^2)*HPL[{4, 2, 1, 1, 1}, -S^2])/S - (81792*(1 + S^2)*HPL[{5, 1, 1, 1, 1}, -S^2])/S + ((3040*(-1 + S^2))/S - (368*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (64*(-26 + 19*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + (1472*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/S + (1472*(1 + S^2)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/S + (1472*(1 + S^2)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/S + (1472*(1 + S^2)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/S + (1472*(1 + S^2)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/S + (5312*(1 + S^2)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S + (2880*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (2944*(1 + S^2)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S + (11776*(1 + S^2)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S + (29440*(1 + S^2)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S + (57984*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((2*Pi^2*S)/3 + (2*S*HPL[{0}, S^2]^3)/3 + ((88*(1 + S^2))/(3*S) + (22*Pi^2*(1 + S^2))/(9*S))*HPL[{1}, -S^2] + (56*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (56*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^2*(2*S + (8*(1 + S^2)*HPL[{1}, -S^2])/(3*S)) + (4*(-1 + S^2)*HPL[{2}, -S^2])/S + HPL[{0}, S^2]*((88*S)/3 + (20*Pi^2*S)/9 + (56*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + (28*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (4*(1 + S^2)*HPL[{2}, -S^2])/S) - (16*(1 + S^2)*HPL[{3}, -S^2])/(3*S))*Log[T]^6 + ((-16*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + HPL[{0}, S^2]*((-16*S)/3 - (8*(1 + S^2)*HPL[{1}, -S^2])/(3*S)))*Log[T]^7 + ((2*S*HPL[{0}, S^2])/3 + (2*(1 + S^2)*HPL[{1}, -S^2])/(3*S))*Log[T]^8 + (-32*S - 2*Pi^2*S)*Zeta[3]^2 + HPL[{2, 1, 1, 1, 1}, -S^2]*((2256*(-1 + S^2))/S + (8*Pi^2*(-29 + 112*S^2))/(3*S) - (736*(1 + S^2)*Zeta[3])/S) + HPL[{4, 1, 1}, -S^2]*((2*Pi^2*(-63 + 293*S^2))/(3*S) + (4*(-427 + 319*S^2))/S - (680*(1 + S^2)*Zeta[3])/S) + HPL[{3, 2, 1}, -S^2]*((498*(-1 + S^2))/S + (Pi^2*(-29 + 195*S^2))/(3*S) - (196*(1 + S^2)*Zeta[3])/S) + HPL[{6}, -S^2]*((205 - 87*S^2)/S + (Pi^2*(40 + 19*S^2))/(6*S) - (226*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (140*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^5*((1316*(1 + S^2))/(15*S) + (173*Pi^2*(1 + S^2))/(15*S) + (1849*Pi^4*(1 + S^2))/(2700*S) + (43*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(45*S) + (86*(1 + S^2)*HPL[{2}, -S^2]^2)/(15*S) - (80*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (56*(1 + S^2)*HPL[{4}, -S^2])/(15*S) + (56*(1 + S^2)*HPL[{3, 1}, -S^2])/(15*S) - (24*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]^2*((Pi^2*(3 + 13*S^2))/(6*S) + (7 + 38*S^2)/S + (10*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (10*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^3*((133*(-1 + S^2))/(6*S) + (Pi^2*(-8 + 51*S^2))/(18*S) - (26*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (52*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (26*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{4, 2}, -S^2]*((Pi^2*(-1 + 7*S^2))/(2*S) + (4*(-1 + 16*S^2))/S - (6*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^6*((188*(1 + S^2))/(9*S) + (22*Pi^2*(1 + S^2))/(9*S) - (40*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (4*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(1 - 3*S^2))/S - (34*(-1 + S^2))/S + (12*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]^2*((-346*(1 + S^2))/S - (2*Pi^2*(55 + 74*S^2))/(3*S) + (80*(1 + S^2)*Zeta[3])/S) + HPL[{5, 1}, -S^2]*((2*Pi^2*(-1 + 17*S^2))/(3*S) + (2*(-5 + 166*S^2))/S + (80*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1, 1, 1}, -S^2]*((-48*(-28 + 19*S^2))/S - (4*Pi^2*(-33 + 107*S^2))/(3*S) + (432*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((109*Pi^4*(1 + S^2))/(90*S) + (7*Pi^2*(1 + 3*S^2))/(6*S) + (3*(55 + 89*S^2))/S - (4*(-9 + 2*S^2)*HPL[{2, 1}, -S^2])/S + (174*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (92*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(5 + S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((988*(1 + S^2))/S + (707*Pi^4*(1 + S^2))/(90*S) + (2*Pi^2*(259 + 173*S^2))/(3*S) - (16*(28 + 9*S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((1464*(-1 + S^2))/S - (133*Pi^4*(1 + S^2))/(15*S) + (4*Pi^2*(-217 + 79*S^2))/(3*S) + (16*(61 + 22*S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((119*Pi^4*(1 + S^2))/(60*S) + (38*(1 + 25*S^2))/S + (Pi^2*(86 + 511*S^2))/(6*S) + (376*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (2*(15 + 23*S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((308*Pi^4*(1 + S^2))/(45*S) + (4*(66 + 703*S^2))/S + (Pi^2*(177 + 811*S^2))/(3*S) + (1184*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (4*(21 + 25*S^2)*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((1607*Pi^4*(1 + S^2))/(90*S) + (12*(221 + 99*S^2))/S + (2*Pi^2*(705 + 242*S^2))/(3*S) - (8*(171 + 55*S^2)*Zeta[3])/S) + HPL[{0}, S^2]^5*((31*S)/6 + (59*Pi^2*S)/72 + (47*Pi^4*S)/240 + (11*(1 + S^2)*HPL[{1}, -S^2]^3)/(18*S) + (11*(1 + S^2)*HPL[{1}, -S^2]^4)/(72*S) + ((Pi^2*(1 + S^2))/(48*S) + (3 + 8*S^2)/(12*S))*HPL[{2}, -S^2] + ((1 + S^2)*HPL[{2}, -S^2]^2)/(16*S) + HPL[{1}, -S^2]^2*((3*(1 + S^2))/(2*S) + (2*Pi^2*(1 + S^2))/(9*S) + ((1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((1 + S^2)*HPL[{3}, -S^2])/(8*S) - (3*(1 + S^2)*HPL[{4}, -S^2])/(8*S) + ((-13 - 5*S^2)*HPL[{2, 1}, -S^2])/(12*S) + ((1 + S^2)*HPL[{2, 1, 1}, -S^2])/(2*S) + (3*S*Zeta[3])/4 + HPL[{1}, -S^2]*((31*(1 + S^2))/(12*S) + (4*Pi^2*(1 + S^2))/(9*S) + (2*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (3*(1 + S^2)*Zeta[3])/(4*S))) + HPL[{0}, S^2]^4*((11*Pi^2*S)/16 + (781*Pi^4*S)/8640 + (23*(1 + S^2)*HPL[{1}, -S^2]^4)/(18*S) + (23*(1 + S^2)*HPL[{1}, -S^2]^5)/(90*S) + (5*(3 + 8*S^2)*HPL[{2}, -S^2]^2)/(48*S) + HPL[{1}, -S^2]^3*((49*(1 + S^2))/(12*S) + (53*Pi^2*(1 + S^2))/(108*S) + (31*(1 + S^2)*HPL[{2}, -S^2])/(36*S)) + ((5*Pi^2*(1 + S^2))/(24*S) + (-1 + 5*S^2)/(8*S))*HPL[{3}, -S^2] + ((-1 - 3*S^2)*HPL[{4}, -S^2])/(8*S) + (13*(1 + S^2)*HPL[{5}, -S^2])/(4*S) + ((-45 - 11*S^2)/(6*S) - (8*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + ((-12 - 43*S^2)*HPL[{3, 1}, -S^2])/(12*S) + ((1 + S^2)*HPL[{3, 2}, -S^2])/(2*S) + ((-1 - S^2)*HPL[{4, 1}, -S^2])/(2*S) + ((9 + 46*S^2)*HPL[{2, 1, 1}, -S^2])/(6*S) + (19*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(6*S) + (19*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(2*S) - (19*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (17*S*Zeta[3])/12 + HPL[{2}, -S^2]*((33*S)/8 + (Pi^2*(9 + 91*S^2))/(144*S) + ((-1 - S^2)*HPL[{3}, -S^2])/(4*S) - (19*(1 + S^2)*HPL[{2, 1}, -S^2])/(12*S) - (5*(1 + S^2)*Zeta[3])/(4*S)) + HPL[{1}, -S^2]^2*((113*(1 + S^2))/(12*S) + (53*Pi^2*(1 + S^2))/(36*S) + (31*(1 + S^2)*HPL[{2}, -S^2])/(12*S) - (31*(1 + S^2)*HPL[{2, 1}, -S^2])/(12*S) + (7*(1 + S^2)*Zeta[3])/(12*S)) + HPL[{1}, -S^2]*((353*(1 + S^2))/(24*S) + (19*Pi^2*(1 + S^2))/(8*S) + (1849*Pi^4*(1 + S^2))/(8640*S) + ((33*(1 + S^2))/(8*S) + (19*Pi^2*(1 + S^2))/(36*S))*HPL[{2}, -S^2] + (31*(1 + S^2)*HPL[{2}, -S^2]^2)/(48*S) + ((1 + S^2)*HPL[{4}, -S^2])/(2*S) - (31*(1 + S^2)*HPL[{2, 1}, -S^2])/(6*S) - (31*(1 + S^2)*HPL[{3, 1}, -S^2])/(12*S) + (31*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(6*S) + (7*(1 + S^2)*Zeta[3])/(6*S))) + Log[T]^5*((-38*Pi^2*S)/9 + ((-88*(1 + S^2))/S - (22*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^2 - (112*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (28*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + HPL[{0}, S^2]^3*((-40*S)/9 - (22*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + ((-76*(-1 + S^2))/(3*S) - (8*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (16*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^2*((-38*S)/3 - (16*(1 + S^2)*HPL[{1}, -S^2])/S - (8*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (8*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + (4*(13 + 31*S^2)*HPL[{3}, -S^2])/(3*S) - (24*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*((-376*S)/3 - (124*Pi^2*S)/9 - (56*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (56*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (12*(1 + 3*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((-88*(1 + S^2))/S - (64*Pi^2*(1 + S^2))/(9*S) - (24*(1 + S^2)*HPL[{2}, -S^2])/S) + (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S) + 24*S*Zeta[3] + HPL[{1}, -S^2]*((-376*(1 + S^2))/(3*S) - (44*Pi^2*(1 + S^2))/(3*S) + (80*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (24*(1 + S^2)*Zeta[3])/S)) + Log[T]^4*((47*Pi^2*S)/3 + (781*Pi^4*S)/540 + (S*HPL[{0}, S^2]^5)/4 + ((440*(1 + S^2))/(3*S) + (110*Pi^2*(1 + S^2))/(9*S))*HPL[{1}, -S^2]^3 + (140*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + (28*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) + HPL[{0}, S^2]^4*((37*S)/36 + (23*(1 + S^2)*HPL[{1}, -S^2])/(18*S)) + (83*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((167*S)/9 + (5*Pi^2*S)/3 + (110*(1 + S^2)*HPL[{1}, -S^2])/(9*S) + (55*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + (7*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-67*Pi^2*(1 + S^2))/(9*S) - (4*(34 + 129*S^2))/(3*S))*HPL[{3}, -S^2] - (8*(3 + 4*S^2)*HPL[{4}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{5}, -S^2])/S + ((380*(-1 + S^2))/(3*S) - (46*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*(47*S + (41*Pi^2*S)/9 + (40*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (40*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + ((16 + 67*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((63*(1 + S^2))/S + (53*Pi^2*(1 + S^2))/(9*S) + (43*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (7*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (46*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) - (8*(-26 + 19*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (184*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (664*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (120*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (368*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (208*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (380*S*Zeta[3])/3 + HPL[{1}, -S^2]*((1316*(1 + S^2))/(3*S) + (173*Pi^2*(1 + S^2))/(3*S) + (1849*Pi^4*(1 + S^2))/(540*S) + (43*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (86*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (400*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (56*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (56*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (120*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((940*(1 + S^2))/(3*S) + (110*Pi^2*(1 + S^2))/(3*S) - (200*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (60*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((94*(-1 + S^2))/S + (Pi^2*(-29 + 112*S^2))/(9*S) - (92*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (184*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (92*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]*((1316*S)/3 + (497*Pi^2*S)/9 + (47*Pi^4*S)/15 + (280*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (70*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + ((22*Pi^2*(1 + S^2))/(3*S) + (4*(23 + 118*S^2))/(3*S))*HPL[{2}, -S^2] + (43*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^2*((220*(1 + S^2))/S + (160*Pi^2*(1 + S^2))/(9*S) + (60*(1 + S^2)*HPL[{2}, -S^2])/S) - (2*(-1 + 3*S^2)*HPL[{3}, -S^2])/S + (8*(1 + S^2)*HPL[{4}, -S^2])/S - (60*(3 + S^2)*HPL[{2, 1}, -S^2])/S - (208*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (120*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (28*S*Zeta[3])/3 + HPL[{1}, -S^2]*((940*(1 + S^2))/(3*S) + (320*Pi^2*(1 + S^2))/(9*S) + (120*(1 + S^2)*HPL[{2}, -S^2])/S + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (120*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (28*(1 + S^2)*Zeta[3])/(3*S)))) + (-182*S - (85*Pi^2*S)/3)*Zeta[5] + Zeta[3]*(-450*S - (181*Pi^2*S)/3 - (307*Pi^4*S)/90 - 64*S*Zeta[5]) + HPL[{2, 1, 1}, -S^2]*((900*(-1 + S^2))/S + (7*Pi^4*(-16 + 205*S^2))/(90*S) + (2*Pi^2*(-133 + 306*S^2))/(3*S) - (736*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (1472*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-36*Pi^2*(1 + S^2))/S - (24*(9 + 37*S^2))/S)*Zeta[3] - (208*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^3*((2900*(1 + S^2))/(3*S) + (1045*Pi^2*(1 + S^2))/(9*S) + (5849*Pi^4*(1 + S^2))/(540*S) + (8699*Pi^6*(1 + S^2))/(13608*S) + ((268*(1 + S^2))/(3*S) + (67*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2]^2 + (8*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-56*(1 + S^2))/S - (28*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] - (16*(1 + S^2)*HPL[{5}, -S^2])/S + (70*(1 + S^2)*HPL[{6}, -S^2])/(3*S) - (344*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((56*(1 + S^2))/S - (56*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] + (688*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2288*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (12*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (176*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + (172*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (1376*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (2528*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (224*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (224*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + ((-264*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (4*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{2}, -S^2]*((134*Pi^2*(1 + S^2))/(9*S) + (707*Pi^4*(1 + S^2))/(540*S) - (344*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (28*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (688*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (344*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (344*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-824*(1 + S^2))/(3*S) - (212*Pi^2*(1 + S^2))/(9*S) + (344*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-172*Pi^2*(1 + S^2))/(9*S) + (344*(1 + S^2)*Zeta[3])/(3*S)) - (440*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{4}, -S^2]*((Pi^4*(-51 - 37*S^2))/(72*S) + (Pi^2*(-6 - 19*S^2))/S - (25*(-5 + 13*S^2))/S - (245*(1 + S^2)*HPL[{5}, -S^2])/S + ((-4*Pi^2*(1 + S^2))/S - (8*(-11 + 7*S^2))/S)*HPL[{2, 1}, -S^2] + (2*(-3 + 37*S^2)*HPL[{3, 1}, -S^2])/S + (42*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (84*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (4*(5 + 33*S^2)*HPL[{2, 1, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (136*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-32*Pi^2*(1 + S^2))/(3*S) - (2*(9 + 22*S^2))/S)*Zeta[3] - (110*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^4*((950*(1 + S^2))/(3*S) + (371*Pi^2*(1 + S^2))/(9*S) + (1849*Pi^4*(1 + S^2))/(540*S) + (86*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-310*(1 + S^2))/(3*S) - (53*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (56*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (4*(1 + S^2)*HPL[{5}, -S^2])/S - (43*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (56*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (172*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (572*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (344*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (632*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + ((-94*(1 + S^2))/S - (49*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((43*Pi^2*(1 + S^2))/(9*S) - (86*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (172*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (86*(1 + S^2)*Zeta[3])/(3*S)) - (110*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]^2*((225*(1 + S^2))/(2*S) + (Pi^2*(201 + 334*S^2))/(12*S) + (Pi^4*(964 + 1567*S^2))/(720*S) + ((-4*Pi^2*(1 + S^2))/S - (2*(16 + 59*S^2))/S)*HPL[{3}, -S^2] + ((-7 - 25*S^2)*HPL[{4}, -S^2])/(2*S) + (15*(1 + S^2)*HPL[{5}, -S^2])/(2*S) + ((86*(-1 + S^2))/S - (13*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (2*(-23 + 15*S^2)*HPL[{3, 1}, -S^2])/S + (52*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (152*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (76*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (104*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (212*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((-17 - 103*S^2)/S - (7*Pi^2*(1 + S^2))/(2*S))*Zeta[3] - (18*(1 + S^2)*Zeta[5])/S) + HPL[{3, 1}, -S^2]*((Pi^4*(138 - 1345*S^2))/(180*S) - (50*(-11 + 7*S^2))/S - (16*Pi^2*(-10 + 17*S^2))/(3*S) - (180*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (680*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (16*(45 + 38*S^2)*HPL[{2, 1, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (2976*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (736*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((70*Pi^2*(1 + S^2))/(3*S) + (4*(29 + 118*S^2))/S)*Zeta[3] + (152*(1 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((Pi^4*(-561 - 1979*S^2))/(360*S) - (6067*Pi^6*(1 + S^2))/(45360*S) - (43*Pi^2*(1 + 5*S^2))/(3*S) - (25*(-5 + 13*S^2))/S + ((8*Pi^2*(1 + S^2))/S + (7 + 97*S^2)/S)*HPL[{4}, -S^2] + (6*(-4 + 3*S^2)*HPL[{5}, -S^2])/S + (251*(1 + S^2)*HPL[{6}, -S^2])/S + (100*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((70*Pi^2*(1 + S^2))/(3*S) + (4*(22 + 131*S^2))/S)*HPL[{3, 1}, -S^2] - (2*(-5 + 7*S^2)*HPL[{3, 2}, -S^2])/S - (4*(14 + 25*S^2)*HPL[{4, 1}, -S^2])/S - (168*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-100*Pi^2*(1 + S^2))/(3*S) - (8*(17 + 121*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (16*(33 + 14*S^2)*HPL[{2, 2, 1}, -S^2])/S - (16*(96 + 35*S^2)*HPL[{3, 1, 1}, -S^2])/S + (12*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (196*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (6448*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (16*(64 + 19*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (464*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (736*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-8*Pi^2)/(3*S) - (2*(11 + 12*S^2))/S)*Zeta[3] - (6*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((8*Pi^2*(17 + 5*S^2))/(3*S) + (4*(165 + 8*S^2))/S + (40*(1 + S^2)*Zeta[3])/S) + (4*(-7 + 3*S^2)*Zeta[5])/S) + HPL[{2, 1}, -S^2]*((450*(-1 + S^2))/S - (881*Pi^6*(1 + S^2))/(1512*S) + (Pi^2*(-406 + 159*S^2))/(3*S) + (Pi^4*(-2739 + 359*S^2))/(180*S) + ((152*Pi^2*(1 + S^2))/(3*S) + (48*(10 + 13*S^2))/S)*HPL[{3, 1}, -S^2] - (8*(63 + 25*S^2)*HPL[{3, 2}, -S^2])/S - (4*(391 + 135*S^2)*HPL[{4, 1}, -S^2])/S - (24*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (36*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((1104*(1 + S^2))/S + (96*Pi^2*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (304*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (16*(7 + 76*S^2)*HPL[{3, 1, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (392*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (1232*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (1328*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (736*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (1472*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((2*Pi^2*(65 + 22*S^2))/(3*S) + (4*(149 + 24*S^2))/S)*Zeta[3] - (20*(1 + S^2)*Zeta[3]^2)/S + (4*(62 + 15*S^2)*Zeta[5])/S) + Log[T]^2*(75*Pi^2*S + (51*Pi^4*S)/4 + (7037*Pi^6*S)/7560 + (S*HPL[{0}, S^2]^7)/24 + ((88*(1 + S^2))/S + (22*Pi^2*(1 + S^2))/(3*S))*HPL[{1}, -S^2]^5 + (56*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + (8*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) + HPL[{0}, S^2]^6*(S/8 + ((1 + S^2)*HPL[{1}, -S^2])/(6*S)) + (38*(-1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^5*((17*S)/6 + (5*Pi^2*S)/12 + (11*(1 + S^2)*HPL[{1}, -S^2])/(6*S) + (11*(1 + S^2)*HPL[{1}, -S^2]^2)/(12*S) + ((1 + S^2)*HPL[{2}, -S^2])/(4*S)) + (4*(3 + 7*S^2)*HPL[{3}, -S^2]^2)/S + ((-5*Pi^2*(1 + S^2))/(3*S) - (2*(4 + 35*S^2))/S)*HPL[{5}, -S^2] + (10*(2 + 5*S^2)*HPL[{6}, -S^2])/S + (200*(1 + S^2)*HPL[{7}, -S^2])/S - (332*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + HPL[{0}, S^2]^4*((33*S)/4 + (41*Pi^2*S)/36 + (23*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (23*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + ((9 + 46*S^2)*HPL[{2}, -S^2])/(12*S) + HPL[{1}, -S^2]*((49*(1 + S^2))/(4*S) + (53*Pi^2*(1 + S^2))/(36*S) + (31*(1 + S^2)*HPL[{2}, -S^2])/(12*S)) - (19*(1 + S^2)*HPL[{2, 1}, -S^2])/(6*S)) + ((97*Pi^2*(1 + S^2))/(3*S) + (6*(27 + 157*S^2))/S)*HPL[{3, 2}, -S^2] + ((356*Pi^2*(1 + S^2))/(3*S) + (32*(21 + 95*S^2))/S)*HPL[{4, 1}, -S^2] + (6*(-1 + 7*S^2)*HPL[{4, 2}, -S^2])/S - (88*(1 + S^2)*HPL[{4, 3}, -S^2])/S + (4*(5 + 39*S^2)*HPL[{5, 1}, -S^2])/S - (260*(1 + S^2)*HPL[{5, 2}, -S^2])/S - (560*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((1104*(1 + S^2))/S + (96*Pi^2*(1 + S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((596*Pi^2*(1 + S^2))/(3*S) + (16*(173 + 78*S^2))/S)*HPL[{3, 1, 1}, -S^2] - (24*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (280*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (376*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (1216*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (112*(-9 + 7*S^2)*HPL[{4, 1, 1}, -S^2])/S - (1184*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (3776*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (7872*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((1520*(-1 + S^2))/S - (184*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] - (32*(-26 + 19*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (736*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (736*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (736*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (2656*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (1440*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (1472*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (4416*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (9280*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (-732*S - (202*Pi^2*S)/3)*Zeta[3] - 12*S*Zeta[3]^2 + HPL[{2, 1, 1}, -S^2]*((1128*(-1 + S^2))/S + (4*Pi^2*(-29 + 112*S^2))/(3*S) - (368*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((2632*(1 + S^2))/(3*S) + (346*Pi^2*(1 + S^2))/(3*S) + (1849*Pi^4*(1 + S^2))/(270*S) + (86*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (172*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (800*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (112*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (112*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (240*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^4*((940*(1 + S^2))/(3*S) + (110*Pi^2*(1 + S^2))/(3*S) - (200*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (60*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((173*(1 + S^2))/S + (Pi^2*(55 + 74*S^2))/(3*S) - (50*(1 + S^2)*HPL[{3}, -S^2])/S - (40*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((Pi^2*(-15 - 13*S^2))/(3*S) - (8*(7 + 20*S^2))/S + (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (28*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-24*(-28 + 19*S^2))/S - (2*Pi^2*(-33 + 107*S^2))/(3*S) + (216*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((Pi^2*(-72 - 277*S^2))/(3*S) - (257*Pi^4*(1 + S^2))/(90*S) - (12*(13 + 74*S^2))/S + (44*(1 + S^2)*HPL[{4}, -S^2])/S + (8*(64 + 19*S^2)*HPL[{2, 1}, -S^2])/S + (232*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (368*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(3 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((732*(-1 + S^2))/S - (133*Pi^4*(1 + S^2))/(30*S) + (2*Pi^2*(-217 + 79*S^2))/(3*S) + (368*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (736*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(61 + 22*S^2)*Zeta[3])/S) + HPL[{0}, S^2]^2*(225*S + 40*Pi^2*S + 3*Pi^4*S + (40*(1 + S^2)*HPL[{1}, -S^2]^4)/S + (8*(1 + S^2)*HPL[{1}, -S^2]^5)/S + ((27 + 65*S^2)*HPL[{2}, -S^2]^2)/(2*S) + HPL[{1}, -S^2]^3*((126*(1 + S^2))/S + (106*Pi^2*(1 + S^2))/(9*S) + (86*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-4 - 19*S^2)/S - (7*Pi^2*(1 + S^2))/(6*S))*HPL[{3}, -S^2] + (3*(-1 + S^2)*HPL[{4}, -S^2])/S + (7*(1 + S^2)*HPL[{5}, -S^2])/S + ((-14*Pi^2*(1 + S^2))/S - (4*(61 + 8*S^2))/S)*HPL[{2, 1}, -S^2] - (2*(19 + 69*S^2)*HPL[{3, 1}, -S^2])/S + (5*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (24*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (4*(16 + 67*S^2)*HPL[{2, 1, 1}, -S^2])/S + (104*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (284*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (184*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 12*S*Zeta[3] + HPL[{1}, -S^2]*((387*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/S + (359*Pi^4*(1 + S^2))/(90*S) + ((134*(1 + S^2))/S + (37*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (24*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (12*(1 + S^2)*HPL[{3}, -S^2])/S - (172*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (84*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (172*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (16*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((272*(1 + S^2))/S + (106*Pi^2*(1 + S^2))/(3*S) + (86*(1 + S^2)*HPL[{2}, -S^2])/S - (6*(1 + S^2)*HPL[{3}, -S^2])/S - (86*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((Pi^2*(25 + 113*S^2))/(6*S) + (8 + 165*S^2)/S - (4*(1 + S^2)*HPL[{3}, -S^2])/S - (52*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S)) + HPL[{0}, S^2]^3*((397*S)/3 + (337*Pi^2*S)/18 + (47*Pi^4*S)/30 + (220*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + (55*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + ((2*Pi^2*(1 + S^2))/S + (2*(13 + 56*S^2))/(3*S))*HPL[{2}, -S^2] + (3*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^2*((175*(1 + S^2))/(3*S) + (55*Pi^2*(1 + S^2))/(9*S) + (15*(1 + S^2)*HPL[{2}, -S^2])/S) + (2*(4 + S^2)*HPL[{3}, -S^2])/(3*S) + (2*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (2*(23 + 8*S^2)*HPL[{2, 1}, -S^2])/S - (44*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (28*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*S*Zeta[3])/3 + HPL[{1}, -S^2]*((88*(1 + S^2))/S + (110*Pi^2*(1 + S^2))/(9*S) + (30*(1 + S^2)*HPL[{2}, -S^2])/S + (2*(1 + S^2)*HPL[{3}, -S^2])/S - (30*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/(3*S))) + HPL[{0}, S^2]*(2900*S + (1055*Pi^2*S)/3 + (971*Pi^4*S)/30 + (6023*Pi^6*S)/2835 + (56*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (28*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + ((61*Pi^2*(1 + S^2))/(6*S) + (2*(25 + 109*S^2))/S)*HPL[{2}, -S^2]^2 + (38*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^4*((220*(1 + S^2))/S + (160*Pi^2*(1 + S^2))/(9*S) + (60*(1 + S^2)*HPL[{2}, -S^2])/S) - (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((14*Pi^2*(1 + S^2))/(3*S) + (2*(22 + 29*S^2))/S)*HPL[{4}, -S^2] + (2*(15 + 13*S^2)*HPL[{5}, -S^2])/S - (20*(1 + S^2)*HPL[{6}, -S^2])/S - (172*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-148*Pi^2*(1 + S^2))/(3*S) - (40*(5 + 24*S^2))/S)*HPL[{3, 1}, -S^2] + (4*(7 + 5*S^2)*HPL[{3, 2}, -S^2])/S + (8*(7 + 11*S^2)*HPL[{4, 1}, -S^2])/S + (6*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (20*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((88*Pi^2*(1 + S^2))/S + (16*(23 + 118*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (8*(125 + 47*S^2)*HPL[{2, 2, 1}, -S^2])/S + (48*(63 + 22*S^2)*HPL[{3, 1, 1}, -S^2])/S - (24*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (280*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (1008*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (720*(3 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (832*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (1440*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (-108*S - 2*Pi^2*S)*Zeta[3] + 32*S*Zeta[3]^2 + HPL[{1}, -S^2]^2*((1316*(1 + S^2))/S + (505*Pi^2*(1 + S^2))/(3*S) + (937*Pi^4*(1 + S^2))/(90*S) + ((564*(1 + S^2))/S + (45*Pi^2*(1 + S^2))/S)*HPL[{2}, -S^2] + (86*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (16*(1 + S^2)*HPL[{3}, -S^2])/S + (28*(1 + S^2)*HPL[{4}, -S^2])/S - (720*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (360*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (720*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (56*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((1880*(1 + S^2))/(3*S) + (640*Pi^2*(1 + S^2))/(9*S) + (240*(1 + S^2)*HPL[{2}, -S^2])/S + (16*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (240*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (56*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-12*(113 + 19*S^2))/S - (2*Pi^2*(68 + 23*S^2))/S + (16*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((Pi^2*(11 - 7*S^2))/(3*S) + (2*(35 + 3*S^2))/S + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (16*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((349*Pi^4*(1 + S^2))/(90*S) + (4*Pi^2*(6 + 29*S^2))/S + (4*(44 + 227*S^2))/S - (4*(5 + 4*S^2)*HPL[{3}, -S^2])/S + (8*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(125 + 47*S^2)*HPL[{2, 1}, -S^2])/S - (176*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(2 + 9*S^2)*Zeta[3])/S) + HPL[{1}, -S^2]*((1900*(1 + S^2))/S + (734*Pi^2*(1 + S^2))/(3*S) + (937*Pi^4*(1 + S^2))/(45*S) + (172*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((28*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (56*(1 + S^2)*HPL[{4}, -S^2])/S + (20*(1 + S^2)*HPL[{5}, -S^2])/S + ((-1128*(1 + S^2))/S - (90*Pi^2*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (720*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (64*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (1440*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (2096*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (1440*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-84*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((792*(1 + S^2))/S + (90*Pi^2*(1 + S^2))/S - (20*(1 + S^2)*HPL[{3}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (20*(1 + S^2)*Zeta[3])/S))) - 384*S*Zeta[5] + HPL[{1}, -S^2]*((2900*(1 + S^2))/S + (1045*Pi^2*(1 + S^2))/(3*S) + (5849*Pi^4*(1 + S^2))/(180*S) + (8699*Pi^6*(1 + S^2))/(4536*S) + ((268*(1 + S^2))/S + (67*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 + (8*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-168*(1 + S^2))/S - (28*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] - (48*(1 + S^2)*HPL[{5}, -S^2])/S + (70*(1 + S^2)*HPL[{6}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((168*(1 + S^2))/S - (56*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] + (688*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (2288*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (36*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (176*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (172*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (1376*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (2528*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (224*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (224*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + ((-792*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (4*(1 + S^2)*Zeta[3]^2)/S + HPL[{2}, -S^2]*((134*Pi^2*(1 + S^2))/(3*S) + (707*Pi^4*(1 + S^2))/(180*S) - (344*(1 + S^2)*HPL[{3}, -S^2])/S - (28*(1 + S^2)*HPL[{4}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (344*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-824*(1 + S^2))/S - (212*Pi^2*(1 + S^2))/(3*S) + (344*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (24*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-172*Pi^2*(1 + S^2))/(3*S) + (344*(1 + S^2)*Zeta[3])/S) - (440*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^2*((1900*(1 + S^2))/S + (742*Pi^2*(1 + S^2))/(3*S) + (1849*Pi^4*(1 + S^2))/(90*S) + (172*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-620*(1 + S^2))/S - (106*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (112*(1 + S^2)*HPL[{4}, -S^2])/S - (24*(1 + S^2)*HPL[{5}, -S^2])/S - (86*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (112*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (1144*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (1264*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((-564*(1 + S^2))/S - (98*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((86*Pi^2*(1 + S^2))/(3*S) - (172*(1 + S^2)*HPL[{3}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (172*(1 + S^2)*Zeta[3])/S) - (220*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((450*(-1 + S^2))/S + (7*Pi^4*(-16 + 205*S^2))/(180*S) + (Pi^2*(-133 + 306*S^2))/(3*S) + ((-50*Pi^2*(1 + S^2))/(3*S) - (4*(17 + 121*S^2))/S)*HPL[{3}, -S^2] - (2*(5 + 33*S^2)*HPL[{4}, -S^2])/S - (46*(1 + S^2)*HPL[{5}, -S^2])/S + ((-552*(1 + S^2))/S - (48*Pi^2*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (8*(45 + 38*S^2)*HPL[{3, 1}, -S^2])/S + (188*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (592*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (664*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (368*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (736*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-18*Pi^2*(1 + S^2))/S - (12*(9 + 37*S^2))/S)*Zeta[3] - (104*(1 + S^2)*Zeta[5])/S)) + HPL[{0}, S^2]^2*((75*Pi^2*S)/4 + (45*Pi^4*S)/16 + (7037*Pi^6*S)/30240 + (8*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + (8*(1 + S^2)*HPL[{1}, -S^2]^7)/(21*S) + ((11 + 32*S^2)*HPL[{2}, -S^2]^3)/(6*S) + HPL[{1}, -S^2]^5*((63*(1 + S^2))/(5*S) + (53*Pi^2*(1 + S^2))/(45*S) + (43*(1 + S^2)*HPL[{2}, -S^2])/(15*S)) + ((-3 - S^2)*HPL[{3}, -S^2]^2)/(2*S) + ((85*Pi^2*(1 + S^2))/(12*S) + (11 + 56*S^2)/(2*S))*HPL[{5}, -S^2] - (3*(-5 + S^2)*HPL[{6}, -S^2])/S + (275*(1 + S^2)*HPL[{7}, -S^2])/(2*S) + ((-27 - 65*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((17*Pi^2*(1 + S^2))/(12*S) + (5*(1 + 8*S^2))/(2*S))*HPL[{3, 2}, -S^2] + ((Pi^2*(1 + S^2))/S + (3*(3 + 17*S^2))/S)*HPL[{4, 1}, -S^2] - (26*(1 + S^2)*HPL[{4, 3}, -S^2])/S + ((-7 - 5*S^2)*HPL[{5, 1}, -S^2])/S - (153*(1 + S^2)*HPL[{5, 2}, -S^2])/(2*S) - (214*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((15*Pi^2*(1 + S^2))/S + (2*(121 + 35*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((128*Pi^2*(1 + S^2))/(3*S) + (2*(359 + 86*S^2))/S)*HPL[{3, 1, 1}, -S^2] - (3*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + ((41 + 125*S^2)*HPL[{3, 2, 1}, -S^2])/S + (5*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/(2*S) - (16*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (6*(21 + 65*S^2)*HPL[{4, 1, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (76*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (166*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((-28*Pi^2*(1 + S^2))/S - (8*(61 + 8*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - (104*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S - (4*(19 + 69*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (322*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (322*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (634*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (1920*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (8*(16 + 67*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (208*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (624*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (1096*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (368*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (2*S + (11*Pi^2*S)/6)*Zeta[3] - 3*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-223 - 24*S^2)/S + (Pi^2*(-106 - 19*S^2))/(3*S) - (343*Pi^4*(1 + S^2))/(180*S) + (60*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (104*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*Zeta[3])/S) + HPL[{2}, -S^2]^2*((7*Pi^2*(2 + 5*S^2))/(8*S) + (7*(4 + 23*S^2))/(4*S) + ((1 + S^2)*HPL[{3}, -S^2])/(2*S) - (13*(1 + S^2)*HPL[{2, 1}, -S^2])/S + ((-1 - S^2)*Zeta[3])/(2*S)) + HPL[{3}, -S^2]*((Pi^2*(-7 - 4*S^2))/(12*S) + (59*Pi^4*(1 + S^2))/(240*S) + (-4 + 7*S^2)/S + (13*(1 + S^2)*HPL[{4}, -S^2])/S + (2*(4 + S^2)*HPL[{2, 1}, -S^2])/S + (12*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (8*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + ((-5 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-4 - 17*S^2)/S + (Pi^2*(-1 - S^2))/(2*S) - (14*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (25*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(25 + 113*S^2))/(3*S) + (2*(8 + 165*S^2))/S - (16*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((129*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/(3*S) + (359*Pi^4*(1 + S^2))/(270*S) + ((134*(1 + S^2))/(3*S) + (37*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (8*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (4*(1 + S^2)*HPL[{3}, -S^2])/S - (172*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (28*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (172*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (16*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^4*((136*(1 + S^2))/(3*S) + (53*Pi^2*(1 + S^2))/(9*S) + (43*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + ((-1 - S^2)*HPL[{3}, -S^2])/S - (43*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((Pi^2*(-31 - 112*S^2))/(6*S) - (2*(4 + 79*S^2))/S + (16*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((575*(1 + S^2))/(2*S) + (83*Pi^2*(1 + S^2))/(2*S) + (359*Pi^4*(1 + S^2))/(90*S) + (24*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((Pi^2*(-1 - S^2))/(2*S) - (9*(1 + S^2))/S)*HPL[{3}, -S^2] + (3*(1 + S^2)*HPL[{5}, -S^2])/S + ((-134*(1 + S^2))/S - (37*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (84*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (6*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (18*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (172*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (96*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (276*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (172*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-12*(1 + S^2))/S + (Pi^2*(1 + S^2))/(2*S))*Zeta[3] + HPL[{2}, -S^2]*((91*(1 + S^2))/S + (37*Pi^2*(1 + S^2))/(3*S) - (3*(1 + S^2)*HPL[{3}, -S^2])/S - (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(1 + S^2)*Zeta[3])/S)) + HPL[{1}, -S^2]*((925*(1 + S^2))/(2*S) + (185*Pi^2*(1 + S^2))/(3*S) + (461*Pi^4*(1 + S^2))/(72*S) + (8699*Pi^6*(1 + S^2))/(18144*S) + ((75*(1 + S^2))/(2*S) + (79*Pi^2*(1 + S^2))/(24*S))*HPL[{2}, -S^2]^2 + (23*(1 + S^2)*HPL[{2}, -S^2]^3)/(6*S) - (3*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((2*(1 + S^2))/S + (Pi^2*(1 + S^2))/S)*HPL[{4}, -S^2] + (6*(1 + S^2)*HPL[{5}, -S^2])/S + (32*(1 + S^2)*HPL[{6}, -S^2])/S - (48*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-132*(1 + S^2))/S - (73*Pi^2*(1 + S^2))/(6*S))*HPL[{3, 1}, -S^2] + (12*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (36*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (18*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((268*(1 + S^2))/S + (74*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (192*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (552*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (92*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (276*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (168*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-14*(1 + S^2))/S + (Pi^2*(1 + S^2))/S)*Zeta[3] + ((1 + S^2)*Zeta[3]^2)/S + HPL[{2}, -S^2]*((231*(1 + S^2))/(2*S) + (233*Pi^2*(1 + S^2))/(12*S) + (473*Pi^4*(1 + S^2))/(360*S) - (6*(1 + S^2)*HPL[{3}, -S^2])/S + (6*(1 + S^2)*HPL[{4}, -S^2])/S - (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (52*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((Pi^2*(-1 - S^2))/S - (10*(1 + S^2))/S + (6*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (6*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-182*(1 + S^2))/S - (74*Pi^2*(1 + S^2))/(3*S) + (8*(1 + S^2)*Zeta[3])/S)) + 11*S*Zeta[5] + HPL[{2}, -S^2]*((225*S)/2 + (2*Pi^2*(1 + 33*S^2))/(3*S) + (Pi^4*(83 + 650*S^2))/(360*S) + ((-5*Pi^2*(1 + S^2))/(6*S) - (2*(1 + 5*S^2))/S)*HPL[{3}, -S^2] + ((3 + S^2)*HPL[{4}, -S^2])/S - (13*(1 + S^2)*HPL[{5}, -S^2])/S + ((-121 - 35*S^2)/S - (15*Pi^2*(1 + S^2))/(2*S))*HPL[{2, 1}, -S^2] - (6*(5 + 11*S^2)*HPL[{3, 1}, -S^2])/S - (2*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (8*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (2*(27 + 65*S^2)*HPL[{2, 1, 1}, -S^2])/S + (52*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (164*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (104*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-19*Pi^2*(1 + S^2))/(6*S) - (2*(3 + 8*S^2))/S)*Zeta[3] - (29*(1 + S^2)*Zeta[5])/S)) + HPL[{0}, S^2]^3*(225*S + (113*Pi^2*S)/4 + (6529*Pi^4*S)/2160 + (6023*Pi^6*S)/11340 + (22*(1 + S^2)*HPL[{1}, -S^2]^5)/(9*S) + (11*(1 + S^2)*HPL[{1}, -S^2]^6)/(27*S) + ((11*Pi^2*(1 + S^2))/(24*S) + (10 + 49*S^2)/(6*S))*HPL[{2}, -S^2]^2 + (5*(1 + S^2)*HPL[{2}, -S^2]^3)/(12*S) + HPL[{1}, -S^2]^4*((175*(1 + S^2))/(18*S) + (55*Pi^2*(1 + S^2))/(54*S) + (5*(1 + S^2)*HPL[{2}, -S^2])/(2*S)) + ((-1 - S^2)*HPL[{3}, -S^2]^2)/S + ((14 - 15*S^2)/(6*S) - (43*Pi^2*(1 + S^2))/(36*S))*HPL[{4}, -S^2] + ((1 + 7*S^2)*HPL[{5}, -S^2])/(2*S) - (125*(1 + S^2)*HPL[{6}, -S^2])/(6*S) - (6*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-25 - 106*S^2)/(3*S) - (11*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] + ((11 - S^2)*HPL[{3, 2}, -S^2])/(6*S) - (4*(-2 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + ((-1 - S^2)*HPL[{4, 2}, -S^2])/(6*S) + (9*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((4*Pi^2*(1 + S^2))/S + (4*(13 + 56*S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (4*(29 + 10*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(91 + 31*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + ((-1 - S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (29*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (94*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (4*(23 + 8*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (88*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (56*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (5*S + (49*Pi^2*S)/18)*Zeta[3] + 8*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-134 - 49*S^2))/(18*S) - (5*(34 + 9*S^2))/(3*S) - (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((88*(1 + S^2))/(3*S) + (110*Pi^2*(1 + S^2))/(27*S) + (10*(1 + S^2)*HPL[{2}, -S^2])/S + (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (10*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/(9*S)) + HPL[{1}, -S^2]^2*((403*(1 + S^2))/(6*S) + (355*Pi^2*(1 + S^2))/(36*S) + (937*Pi^4*(1 + S^2))/(1080*S) + ((71*(1 + S^2))/(3*S) + (85*Pi^2*(1 + S^2))/(36*S))*HPL[{2}, -S^2] + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/(6*S) + (2*(1 + S^2)*HPL[{3}, -S^2])/S + ((1 + S^2)*HPL[{4}, -S^2])/S - (30*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (44*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (30*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((12 + 13*S^2)/(2*S) + (Pi^2*(23 + 17*S^2))/(36*S) + (2*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (6*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((37*Pi^4*(1 + S^2))/(240*S) + (2*Pi^2*(7 + 24*S^2))/(9*S) + (72 + 203*S^2)/(6*S) - HPL[{3}, -S^2]/S + (2*(1 + S^2)*HPL[{4}, -S^2])/S - (2*(29 + 10*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (7*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (12*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + ((3 + S^2)*Zeta[3])/(3*S)) + (55*S*Zeta[5])/3 + HPL[{1}, -S^2]*((225*(1 + S^2))/(2*S) + (287*Pi^2*(1 + S^2))/(18*S) + (937*Pi^4*(1 + S^2))/(540*S) + (19*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((3*(1 + S^2))/S + (Pi^2*(1 + S^2))/(6*S))*HPL[{3}, -S^2] + (2*(1 + S^2)*HPL[{4}, -S^2])/S - (3*(1 + S^2)*HPL[{5}, -S^2])/S + ((-142*(1 + S^2))/(3*S) - (85*Pi^2*(1 + S^2))/(18*S))*HPL[{2, 1}, -S^2] - (88*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (4*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (60*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (76*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (80*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (60*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((6*(1 + S^2))/S + (49*Pi^2*(1 + S^2))/(18*S))*Zeta[3] + HPL[{2}, -S^2]*((103*(1 + S^2))/(3*S) + (85*Pi^2*(1 + S^2))/(18*S) + ((-1 - S^2)*HPL[{3}, -S^2])/S - (38*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(1 + S^2)*Zeta[3])/(3*S)) + (55*(1 + S^2)*Zeta[5])/(3*S))) + Log[T]^3*((-122*Pi^2*S)/3 - (779*Pi^4*S)/135 + ((-440*(1 + S^2))/(3*S) - (110*Pi^2*(1 + S^2))/(9*S))*HPL[{1}, -S^2]^4 - (112*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) - (56*(1 + S^2)*HPL[{1}, -S^2]^6)/(9*S) + HPL[{0}, S^2]^5*((-10*S)/9 - (11*(1 + S^2)*HPL[{1}, -S^2])/(18*S)) + ((-260*(1 + S^2))/(3*S) - (62*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^4*((-34*S)/9 - (46*(1 + S^2)*HPL[{1}, -S^2])/(9*S) - (23*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) - (2*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (32*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + (8*(9 + 25*S^2)*HPL[{4}, -S^2])/(3*S) + (4*(1 + 11*S^2)*HPL[{5}, -S^2])/S + (320*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((-172*S)/3 - (200*Pi^2*S)/27 - (220*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) - (220*(1 + S^2)*HPL[{1}, -S^2]^3)/(27*S) - (2*(7 + 22*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-350*(1 + S^2))/(9*S) - (110*Pi^2*(1 + S^2))/(27*S) - (10*(1 + S^2)*HPL[{2}, -S^2])/S) - (4*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (32*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) + ((92*Pi^2*(1 + S^2))/(9*S) + (16*(-56 + 39*S^2))/(3*S))*HPL[{3, 1}, -S^2] - (8*(47 + 131*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (16*(88 + 221*S^2)*HPL[{4, 1}, -S^2])/(3*S) + ((-1520*(-1 + S^2))/(3*S) - (160*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (1424*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (32*(101 + 56*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (480*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (376*S + (196*Pi^2*S)/9)*Zeta[3] + HPL[{2, 1}, -S^2]*((-376*(-1 + S^2))/S - (4*Pi^2*(-115 + 26*S^2))/(9*S) - (320*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((2*Pi^2*(23 + 57*S^2))/(3*S) + (4*(71 + 353*S^2))/(3*S) - (320*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((-3760*(1 + S^2))/(9*S) - (440*Pi^2*(1 + S^2))/(9*S) + (800*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (80*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-2632*(1 + S^2))/(3*S) - (346*Pi^2*(1 + S^2))/(3*S) - (1849*Pi^4*(1 + S^2))/(270*S) - (86*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (172*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (800*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (112*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (112*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (240*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-244*(-1 + S^2))/S - (154*Pi^4*(1 + S^2))/(135*S) - (2*Pi^2*(-83 + 213*S^2))/(9*S) + (8*(22 + 67*S^2)*HPL[{3}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{4}, -S^2])/S + (712*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (320*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (640*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*(25 + 64*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^2*(-122*S - (163*Pi^2*S)/9 - (160*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (40*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + ((-32*Pi^2*(1 + S^2))/(9*S) - (4*(6 + 59*S^2))/(3*S))*HPL[{2}, -S^2] - (22*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^2*((-126*(1 + S^2))/S - (106*Pi^2*(1 + S^2))/(9*S) - (86*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + (8*(1 + 4*S^2)*HPL[{3}, -S^2])/(3*S) + (4*(70 + 19*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (92*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (160*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (16*S*Zeta[3])/3 + HPL[{1}, -S^2]*((-544*(1 + S^2))/(3*S) - (212*Pi^2*(1 + S^2))/(9*S) - (172*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/S + (172*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (16*(1 + S^2)*Zeta[3])/(3*S))) + HPL[{0}, S^2]*((-3800*S)/3 - (1456*Pi^2*S)/9 - (1783*Pi^4*S)/135 - (280*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) - (56*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) - (2*(47 + 125*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((-880*(1 + S^2))/(3*S) - (640*Pi^2*(1 + S^2))/(27*S) - (80*(1 + S^2)*HPL[{2}, -S^2])/S) + ((2*Pi^2*(1 + S^2))/(3*S) + (8*(-7 + 4*S^2))/(3*S))*HPL[{3}, -S^2] - (8*(6 + 13*S^2)*HPL[{4}, -S^2])/(3*S) - (12*(1 + S^2)*HPL[{5}, -S^2])/S + ((92*Pi^2*(1 + S^2))/(3*S) + (16*(118 + 23*S^2))/(3*S))*HPL[{2, 1}, -S^2] + (16*(26 + 71*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (80*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (240*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (1984*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (480*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (136*S*Zeta[3])/3 + HPL[{2}, -S^2]*((-2*Pi^2*(22 + 67*S^2))/(3*S) - (4*(19 + 113*S^2))/S + (16*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (344*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-1880*(1 + S^2))/(3*S) - (640*Pi^2*(1 + S^2))/(9*S) - (240*(1 + S^2)*HPL[{2}, -S^2])/S - (16*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (240*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (56*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]*((-2632*(1 + S^2))/(3*S) - (1010*Pi^2*(1 + S^2))/(9*S) - (937*Pi^4*(1 + S^2))/(135*S) + ((-376*(1 + S^2))/S - (30*Pi^2*(1 + S^2))/S)*HPL[{2}, -S^2] - (172*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (32*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (56*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (480*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (240*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (480*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (112*(1 + S^2)*Zeta[3])/(3*S))) + (440*S*Zeta[5])/3 + HPL[{1}, -S^2]*((-3800*(1 + S^2))/(3*S) - (1484*Pi^2*(1 + S^2))/(9*S) - (1849*Pi^4*(1 + S^2))/(135*S) - (344*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((1240*(1 + S^2))/(3*S) + (212*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (224*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{5}, -S^2])/S + (172*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (224*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (688*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2288*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (1376*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2528*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + ((376*(1 + S^2))/S + (196*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-172*Pi^2*(1 + S^2))/(9*S) + (344*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (688*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (344*(1 + S^2)*Zeta[3])/(3*S)) + (440*(1 + S^2)*Zeta[5])/(3*S))) - 30*S*Zeta[7] + HPL[{1}, -S^2]*((4900*(1 + S^2))/S + (2375*Pi^2*(1 + S^2))/(6*S) + (845*Pi^4*(1 + S^2))/(24*S) + (138409*Pi^6*(1 + S^2))/(45360*S) + (20621*Pi^8*(1 + S^2))/(108864*S) + (23*Pi^2*(1 + S^2)*HPL[{2}, -S^2]^3)/(18*S) + (23*(1 + S^2)*HPL[{2}, -S^2]^4)/(6*S) + ((Pi^2*(-1 - S^2))/(3*S) + (10*(1 + S^2))/S)*HPL[{3}, -S^2]^2 + (32*(1 + S^2)*HPL[{4}, -S^2]^2)/S + ((161*(1 + S^2))/S + (33*Pi^2*(1 + S^2))/(2*S))*HPL[{6}, -S^2] + (288*(1 + S^2)*HPL[{7}, -S^2])/S + (771*(1 + S^2)*HPL[{8}, -S^2])/S + ((-536*(1 + S^2))/S - (134*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2]^2 + (216*(1 + S^2)*HPL[{3, 1}, -S^2]^2)/S + ((54*(1 + S^2))/S + (3*Pi^2*(1 + S^2))/S)*HPL[{4, 2}, -S^2] - (44*(1 + S^2)*HPL[{4, 3}, -S^2])/S + ((236*(1 + S^2))/S + (26*Pi^2*(1 + S^2))/(3*S))*HPL[{5, 1}, -S^2] - (120*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (6*(1 + S^2)*HPL[{5, 3}, -S^2])/S - (300*(1 + S^2)*HPL[{6, 1}, -S^2])/S + (15*(1 + S^2)*HPL[{6, 2}, -S^2])/S - (416*(1 + S^2)*HPL[{7, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + (92*Pi^2*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (696*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (2144*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (28*(1 + S^2)*HPL[{3, 3, 2}, -S^2])/S + ((-336*(1 + S^2))/S + (220*Pi^2*(1 + S^2))/(3*S))*HPL[{4, 1, 1}, -S^2] - (2120*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (68*(1 + S^2)*HPL[{4, 1, 3}, -S^2])/S - (6536*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{4, 2, 2}, -S^2])/S + (52*(1 + S^2)*HPL[{4, 3, 1}, -S^2])/S - (13344*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + (8*(1 + S^2)*HPL[{5, 1, 2}, -S^2])/S + (248*(1 + S^2)*HPL[{5, 2, 1}, -S^2])/S + (860*(1 + S^2)*HPL[{6, 1, 1}, -S^2])/S + ((336*(1 + S^2))/S - (112*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1, 1}, -S^2] + (1376*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (1376*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/S + (1376*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/S - (40*(1 + S^2)*HPL[{3, 2, 2, 1}, -S^2])/S - (192*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (4576*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (72*(1 + S^2)*HPL[{4, 1, 1, 2}, -S^2])/S - (120*(1 + S^2)*HPL[{4, 1, 2, 1}, -S^2])/S - (504*(1 + S^2)*HPL[{4, 2, 1, 1}, -S^2])/S - (800*(1 + S^2)*HPL[{5, 1, 1, 1}, -S^2])/S + (344*Pi^2*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) - (2752*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (8256*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (16960*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (448*(1 + S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S + (448*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + ((2*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/(3*S))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((2720*(1 + S^2))/S + (1184*Pi^2*(1 + S^2))/(3*S) - (960*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((268*Pi^2*(1 + S^2))/(3*S) + (707*Pi^4*(1 + S^2))/(90*S) - (688*(1 + S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((1456*(1 + S^2))/S + (536*Pi^2*(1 + S^2))/(3*S) - (304*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((231*(1 + S^2))/S + (209*Pi^2*(1 + S^2))/(6*S) + (263*Pi^4*(1 + S^2))/(144*S) - (96*(1 + S^2)*HPL[{3}, -S^2])/S - (4*(1 + S^2)*HPL[{4}, -S^2])/S + (4*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (76*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((48*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (56*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-96*(1 + S^2))/S - (40*Pi^2*(1 + S^2))/(3*S) - (28*Pi^4*(1 + S^2))/(45*S) + (56*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (12*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (56*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (16*(1 + S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((728*(1 + S^2))/S + (184*Pi^2*(1 + S^2))/(3*S) + (48*(1 + S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((2376*(1 + S^2))/S + (608*Pi^2*(1 + S^2))/(3*S) + (160*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((96*(1 + S^2))/S - (30*Pi^2*(1 + S^2))/S - (59*Pi^4*(1 + S^2))/(20*S) - (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (352*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((-344*Pi^2*(1 + S^2))/(3*S) + (688*(1 + S^2)*Zeta[3])/S) + ((-496*(1 + S^2))/S - (110*Pi^2*(1 + S^2))/(3*S))*Zeta[5] + HPL[{2}, -S^2]*((77*Pi^2*(1 + S^2))/(2*S) + (445*Pi^4*(1 + S^2))/(72*S) + (2047*Pi^6*(1 + S^2))/(5040*S) - (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((Pi^2*(-1 - S^2))/(3*S) - (38*(1 + S^2))/S)*HPL[{4}, -S^2] - (40*(1 + S^2)*HPL[{5}, -S^2])/S + (79*(1 + S^2)*HPL[{6}, -S^2])/S + ((-536*(1 + S^2))/S - (46*Pi^2*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (360*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (1096*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (48*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((1072*(1 + S^2))/S + (268*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] - (688*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (24*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (344*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (1048*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (1376*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-364*(1 + S^2))/S - (94*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (6*(1 + S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((-364*(1 + S^2))/S - (92*Pi^2*(1 + S^2))/(3*S) + (192*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (24*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-728*(1 + S^2))/S - (268*Pi^2*(1 + S^2))/(3*S) + (152*(1 + S^2)*Zeta[3])/S) - (172*(1 + S^2)*Zeta[5])/S) + Zeta[3]*((-750*(1 + S^2))/S - (212*Pi^2*(1 + S^2))/(3*S) - (157*Pi^4*(1 + S^2))/(45*S) - (64*(1 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((-550*(1 + S^2))/S - (72*Pi^2*(1 + S^2))/S - (196*Pi^4*(1 + S^2))/(45*S) + (28*(1 + S^2)*HPL[{4}, -S^2])/S - (70*(1 + S^2)*HPL[{5}, -S^2])/S + ((536*(1 + S^2))/S + (92*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (352*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (8*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (28*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (384*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (1120*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-40*(1 + S^2))/S - (4*Pi^2*(1 + S^2))/S)*Zeta[3] - (32*(1 + S^2)*Zeta[5])/S) + HPL[{2, 1}, -S^2]*((-182*Pi^2*(1 + S^2))/(3*S) - (707*Pi^4*(1 + S^2))/(90*S) + (688*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (360*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (1096*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (1376*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((536*(1 + S^2))/S + (94*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (172*(1 + S^2)*Zeta[5])/S) - (300*(1 + S^2)*Zeta[7])/S) + HPL[{2}, -S^2]*((75*Pi^2*(-1 + 2*S^2))/(2*S) + (Pi^4*(-191 + 714*S^2))/(72*S) + (Pi^6*(-1122 + 10735*S^2))/(15120*S) + ((-1 + 5*S^2)*HPL[{3}, -S^2]^2)/S + ((-13 - 113*S^2)/S - (49*Pi^2*(1 + S^2))/(6*S))*HPL[{5}, -S^2] + ((16 - 5*S^2)*HPL[{6}, -S^2])/S - (261*(1 + S^2)*HPL[{7}, -S^2])/S - (76*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((15*Pi^2*(1 + S^2))/S + (2*(55 + 227*S^2))/S)*HPL[{3, 2}, -S^2] + ((52*Pi^2*(1 + S^2))/S + (8*(37 + 184*S^2))/S)*HPL[{4, 1}, -S^2] + (3*(5 + 11*S^2)*HPL[{4, 2}, -S^2])/S + (42*(1 + S^2)*HPL[{4, 3}, -S^2])/S + (4*(8 + 37*S^2)*HPL[{5, 1}, -S^2])/S + (129*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (436*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((-344*(-1 + S^2))/S + (52*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((-256*Pi^2*(1 + S^2))/(3*S) + (16*(-73 + 4*S^2))/S)*HPL[{3, 1, 1}, -S^2] - (24*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (320*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (208*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (584*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (4*(253 + 225*S^2)*HPL[{4, 1, 1}, -S^2])/S - (584*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (1712*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (3476*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((-1104*(1 + S^2))/S - (96*Pi^2*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - (416*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S - (16*(-183 + 266*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (872*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (872*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (2120*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (6304*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (1328*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (736*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (1472*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((Pi^2*(-33 - 127*S^2))/(3*S) - (157*Pi^4*(1 + S^2))/(90*S) - (2*(40 + 207*S^2))/S)*Zeta[3] + (2*(-2 + S^2)*Zeta[3]^2)/S + HPL[{2, 1, 1}, -S^2]*((692*(1 + S^2))/S + (4*Pi^2*(55 + 74*S^2))/(3*S) - (160*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((Pi^2*(1 - 31*S^2))/(6*S) - (2*(5 + 53*S^2))/S - (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (20*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-2*Pi^2*(60 + 71*S^2))/(3*S) - (2*(197 + 149*S^2))/S + (64*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((Pi^2*(-19 - 131*S^2))/(3*S) - (31*Pi^4*(1 + S^2))/(30*S) - (2*(6 + 241*S^2))/S - (18*(1 + S^2)*HPL[{4}, -S^2])/S + (8*(33 + 14*S^2)*HPL[{2, 1}, -S^2])/S + (84*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (200*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(3 + 5*S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((Pi^2*(-259 - 173*S^2))/(3*S) - (494*(1 + S^2))/S - (707*Pi^4*(1 + S^2))/(180*S) + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (8*(28 + 9*S^2)*Zeta[3])/S) + ((-55*Pi^2*(1 + S^2))/(3*S) - (28*(2 + 9*S^2))/S)*Zeta[5] - (150*(1 + S^2)*Zeta[7])/S) + HPL[{1}, -S^2]^2*((2450*(1 + S^2))/S + (1525*Pi^2*(1 + S^2))/(6*S) + (215*Pi^4*(1 + S^2))/(9*S) + (8699*Pi^6*(1 + S^2))/(4536*S) + (8*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((Pi^2*(-1 - S^2))/S - (26*(1 + S^2))/S)*HPL[{5}, -S^2] + (70*(1 + S^2)*HPL[{6}, -S^2])/S + (144*(1 + S^2)*HPL[{7}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((536*(1 + S^2))/S + (92*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((1776*(1 + S^2))/S + (304*Pi^2*(1 + S^2))/(3*S))*HPL[{4, 1}, -S^2] + (36*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (22*(1 + S^2)*HPL[{4, 3}, -S^2])/S + (176*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (60*(1 + S^2)*HPL[{5, 2}, -S^2])/S - (150*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((1072*(1 + S^2))/S + (268*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((1976*(1 + S^2))/S + (592*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] - (348*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (1072*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (224*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (1060*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (3268*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (6672*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S - (172*Pi^2*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (224*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (688*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (2288*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (4128*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (8480*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + ((-542*(1 + S^2))/S - (51*Pi^2*(1 + S^2))/S - (157*Pi^4*(1 + S^2))/(90*S))*Zeta[3] + (4*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1, 1}, -S^2]*((172*Pi^2*(1 + S^2))/(3*S) - (344*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((182*(1 + S^2))/S + (67*Pi^2*(1 + S^2))/(3*S) - (48*(1 + S^2)*HPL[{3}, -S^2])/S - (38*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-510*(1 + S^2))/S - (164*Pi^2*(1 + S^2))/(3*S) - (98*Pi^4*(1 + S^2))/(45*S) + (14*(1 + S^2)*HPL[{4}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (176*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (24*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-96*(1 + S^2))/S - (28*Pi^2*(1 + S^2))/(3*S) + (28*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((96*(1 + S^2))/S - (56*Pi^2*(1 + S^2))/(3*S) + (176*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-134*Pi^2*(1 + S^2))/(3*S) - (707*Pi^4*(1 + S^2))/(180*S) + (344*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (344*(1 + S^2)*Zeta[3])/S) + ((-346*(1 + S^2))/S - (55*Pi^2*(1 + S^2))/(3*S))*Zeta[5] + HPL[{2}, -S^2]*((91*Pi^2*(1 + S^2))/(3*S) + (707*Pi^4*(1 + S^2))/(180*S) + ((-268*(1 + S^2))/S - (46*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (28*(1 + S^2)*HPL[{4}, -S^2])/S - (20*(1 + S^2)*HPL[{5}, -S^2])/S + ((-536*(1 + S^2))/S - (134*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (344*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (180*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (548*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-268*(1 + S^2))/S - (47*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (86*(1 + S^2)*Zeta[5])/S) - (150*(1 + S^2)*Zeta[7])/S) + HPL[{0}, S^2]*(4900*S + (1400*Pi^2*S)/3 + (3781*Pi^4*S)/90 + (4979*Pi^6*S)/1296 + (179327*Pi^8*S)/340200 + (8*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) + ((1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) + ((53*Pi^2*(1 + S^2))/(36*S) + (2*(8 + 51*S^2))/(3*S))*HPL[{2}, -S^2]^3 + (23*(1 + S^2)*HPL[{2}, -S^2]^4)/(12*S) + HPL[{1}, -S^2]^6*((44*(1 + S^2))/(3*S) + (32*Pi^2*(1 + S^2))/(27*S) + (4*(1 + S^2)*HPL[{2}, -S^2])/S) + (-12*S - (4*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2]^2 + (28*(1 + S^2)*HPL[{4}, -S^2]^2)/S + (-94*S - (45*Pi^2*(1 + S^2))/(2*S))*HPL[{6}, -S^2] + (10*(-5 + 3*S^2)*HPL[{7}, -S^2])/S - (525*(1 + S^2)*HPL[{8}, -S^2])/S + ((-61*Pi^2*(1 + S^2))/(3*S) - (4*(25 + 109*S^2))/S)*HPL[{2, 1}, -S^2]^2 + (100*(1 + S^2)*HPL[{3, 1}, -S^2]^2)/S + ((-3*(-2 + S^2))/S + (Pi^2*(1 + S^2))/(3*S))*HPL[{4, 2}, -S^2] - (32*HPL[{4, 3}, -S^2])/S + ((22*Pi^2*(1 + S^2))/(3*S) - (2*(11 + 14*S^2))/S)*HPL[{5, 1}, -S^2] + (3*(-31 + S^2)*HPL[{5, 2}, -S^2])/S - (20*(9 + S^2)*HPL[{6, 1}, -S^2])/S - (6*(1 + S^2)*HPL[{6, 2}, -S^2])/S + (228*(1 + S^2)*HPL[{7, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((-6*(1 + S^2))/S - (7*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 2}, -S^2] + ((33*Pi^2*(1 + S^2))/S + (2*(61 + 405*S^2))/S)*HPL[{3, 2, 1}, -S^2] - (2*(19 + 35*S^2)*HPL[{3, 2, 2}, -S^2])/S - (16*(8 + 11*S^2)*HPL[{3, 3, 1}, -S^2])/S + (32*(1 + S^2)*HPL[{3, 3, 2}, -S^2])/S + ((346*Pi^2*(1 + S^2))/(3*S) + (4*(118 + 641*S^2))/S)*HPL[{4, 1, 1}, -S^2] - (2*(61 + 85*S^2)*HPL[{4, 1, 2}, -S^2])/S - (64*(1 + S^2)*HPL[{4, 1, 3}, -S^2])/S - (2*(205 + 253*S^2)*HPL[{4, 2, 1}, -S^2])/S + (35*(1 + S^2)*HPL[{4, 2, 2}, -S^2])/S - (128*(1 + S^2)*HPL[{4, 3, 1}, -S^2])/S - (4*(201 + 239*S^2)*HPL[{5, 1, 1}, -S^2])/S - (58*(1 + S^2)*HPL[{5, 1, 2}, -S^2])/S - (538*(1 + S^2)*HPL[{5, 2, 1}, -S^2])/S - (1480*(1 + S^2)*HPL[{6, 1, 1}, -S^2])/S - (304*(3 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((-296*Pi^2*(1 + S^2))/(3*S) - (80*(5 + 24*S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] + (8*(349 + 119*S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (8*(349 + 119*S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (12*(1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/S + (8*(691 + 233*S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (12*(1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/S - (284*(1 + S^2)*HPL[{3, 2, 2, 1}, -S^2])/S - (816*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (16*(1033 + 353*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (12*(1 + S^2)*HPL[{4, 1, 1, 2}, -S^2])/S - (804*(1 + S^2)*HPL[{4, 1, 2, 1}, -S^2])/S - (2436*(1 + S^2)*HPL[{4, 2, 1, 1}, -S^2])/S - (4936*(1 + S^2)*HPL[{5, 1, 1, 1}, -S^2])/S + ((176*Pi^2*(1 + S^2))/S + (32*(23 + 118*S^2))/S)*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(125 + 47*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (48*(125 + 47*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (608*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S - (1824*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (32*(311 + 122*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (3600*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S + (6032*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S + (7248*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S + (15152*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S + (45792*(1 + S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S - (1440*(3 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - (1664*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + (2880*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (38*S + (32*Pi^2*S)/3)*Zeta[3]^2 + HPL[{2}, -S^2]^2*((33*Pi^4*(1 + S^2))/(40*S) + (Pi^2*(35 + 158*S^2))/(6*S) + (32 + 199*S^2)/S - (4*(1 + 2*S^2)*HPL[{3}, -S^2])/S - (4*(1 + S^2)*HPL[{4}, -S^2])/S - (38*(3 + S^2)*HPL[{2, 1}, -S^2])/S - (34*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (76*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + ((-1 - 7*S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^4*((658*(1 + S^2))/(3*S) + (505*Pi^2*(1 + S^2))/(18*S) + (937*Pi^4*(1 + S^2))/(540*S) + ((94*(1 + S^2))/S + (15*Pi^2*(1 + S^2))/(2*S))*HPL[{2}, -S^2] + (43*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (14*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (120*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (60*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (120*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (28*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^5*((188*(1 + S^2))/(3*S) + (64*Pi^2*(1 + S^2))/(9*S) + (24*(1 + S^2)*HPL[{2}, -S^2])/S + (8*(1 + S^2)*HPL[{3}, -S^2])/(15*S) - (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (28*(1 + S^2)*Zeta[3])/(15*S)) + HPL[{4, 1}, -S^2]*((2*Pi^2*(11 + 9*S^2))/(3*S) + (2*(-9 + 38*S^2))/S + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((4*(307 + 57*S^2))/S + (2*Pi^2*(183 + 67*S^2))/(3*S) + (8*(1 + S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((Pi^2*(25 + 9*S^2))/(6*S) + (19 + 51*S^2)/S + (28*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((-24*(113 + 19*S^2))/S - (4*Pi^2*(68 + 23*S^2))/S + (32*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((8*(478 + 87*S^2))/S + (4*Pi^2*(280 + 97*S^2))/(3*S) + (56*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((Pi^2*(9 + 17*S^2))/(3*S) + (3*(15 + 34*S^2))/S + (56*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (84*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-187*Pi^4*(1 + S^2))/(360*S) - (2*(-40 + 7*S^2))/S + (Pi^2*(18 + 7*S^2))/(3*S) + (8*(-2 + S^2)*HPL[{2, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (2*(11 + 3*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((Pi^2*(-75 - 346*S^2))/(3*S) - (164*Pi^4*(1 + S^2))/(45*S) - (12*(13 + 74*S^2))/S - (352*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (4*(1 + 9*S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((349*Pi^4*(1 + S^2))/(45*S) + (8*Pi^2*(6 + 29*S^2))/S + (8*(44 + 227*S^2))/S - (8*(2 + 9*S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((1900*(1 + S^2))/(3*S) + (734*Pi^2*(1 + S^2))/(9*S) + (937*Pi^4*(1 + S^2))/(135*S) + (172*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((28*(1 + S^2))/(3*S) + (10*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (56*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (20*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-376*(1 + S^2))/S - (30*Pi^2*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (240*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (40*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (64*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (480*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (2096*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (480*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-28*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((264*(1 + S^2))/S + (30*Pi^2*(1 + S^2))/S - (20*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (344*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (20*(1 + S^2)*Zeta[3])/(3*S))) + HPL[{1}, -S^2]^2*((1450*(1 + S^2))/S + (1061*Pi^2*(1 + S^2))/(6*S) + (499*Pi^4*(1 + S^2))/(30*S) + (12907*Pi^6*(1 + S^2))/(11340*S) + ((134*(1 + S^2))/S + (31*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 + (38*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((44*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] + (20*(1 + S^2)*HPL[{5}, -S^2])/S - (172*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-564*(1 + S^2))/S - (134*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] + (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (64*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (28*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((1128*(1 + S^2))/S + (90*Pi^2*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (688*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (2096*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (304*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (968*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (1440*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (720*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (1440*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-48*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/S)*Zeta[3] + (8*(1 + S^2)*Zeta[3]^2)/S + HPL[{2}, -S^2]*((542*(1 + S^2))/S + (212*Pi^2*(1 + S^2))/(3*S) + (377*Pi^4*(1 + S^2))/(90*S) - (20*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(1 + S^2)*HPL[{4}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (172*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (20*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((32*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S) + (20*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-792*(1 + S^2))/S - (90*Pi^2*(1 + S^2))/S + (20*(1 + S^2)*Zeta[3])/S)) + (-10*S + (55*Pi^2*S)/3)*Zeta[5] + Zeta[3]*(-100*S - 4*Pi^2*S + (157*Pi^4*S)/90 + 160*S*Zeta[5]) + HPL[{2, 1}, -S^2]*((Pi^4*(-1159 - 405*S^2))/(90*S) + (Pi^2*(-509 - 102*S^2))/(3*S) - (300*(4 + S^2))/S + (8*(62 + 23*S^2)*HPL[{3, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (160*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (8*(125 + 47*S^2)*HPL[{2, 1, 1}, -S^2])/S + (304*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (960*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-12*(-5 + S^2))/S - (4*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (48*(1 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((150*(1 + S^2))/S + (Pi^2*(71 + 42*S^2))/(6*S) + (Pi^4*(167 + 83*S^2))/(180*S) + (16*HPL[{4}, -S^2])/S - (56*(1 + S^2)*HPL[{5}, -S^2])/S + ((4*Pi^2*(1 + S^2))/S + (8*(5 + 4*S^2))/S)*HPL[{2, 1}, -S^2] + (8*(4 + 3*S^2)*HPL[{3, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (72*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (8*(5 + 4*S^2)*HPL[{2, 1, 1}, -S^2])/S - (48*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (160*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (48*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((22*Pi^2*(1 + S^2))/(3*S) + (2*(7 + 11*S^2))/S)*Zeta[3] + (74*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((4447*Pi^6*(1 + S^2))/(15120*S) + (150*(2 + 5*S^2))/S + (Pi^2*(160 + 657*S^2))/(6*S) + (Pi^4*(232 + 913*S^2))/(90*S) + (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S + (24*S + (8*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] - (16*HPL[{5}, -S^2])/S + (56*(1 + S^2)*HPL[{6}, -S^2])/S - (76*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-65*Pi^2*(1 + S^2))/(3*S) - (8*(13 + 55*S^2))/S)*HPL[{3, 1}, -S^2] + (16*(1 + 2*S^2)*HPL[{3, 2}, -S^2])/S + (8*(8 + 11*S^2)*HPL[{4, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((122*Pi^2*(1 + S^2))/(3*S) + (8*(25 + 109*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (152*(3 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (8*(176 + 61*S^2)*HPL[{3, 1, 1}, -S^2])/S + (184*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (568*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (8*(125 + 47*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (4000*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((Pi^2*(1 - 8*S^2))/(3*S) - (8*(-1 + 5*S^2))/S)*Zeta[3] + (2*(1 + S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((-4*Pi^2*(2 + S^2))/(3*S) - (8*(1 + 3*S^2))/S + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (12*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((Pi^2*(-183 - 67*S^2))/(3*S) - (2*(307 + 57*S^2))/S - (4*(1 + S^2)*Zeta[3])/S) + (4*(5 + S^2)*Zeta[5])/S) + 150*S*Zeta[7] + HPL[{1}, -S^2]*((2450*(1 + S^2))/S + (1625*Pi^2*(1 + S^2))/(6*S) + (257*Pi^4*(1 + S^2))/(10*S) + (12907*Pi^6*(1 + S^2))/(5670*S) + (76*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((24*(1 + S^2))/S - (4*Pi^2*(1 + S^2))/(3*S))*HPL[{5}, -S^2] - (120*(1 + S^2)*HPL[{7}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-792*(1 + S^2))/S - (268*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] + ((64*(1 + S^2))/S + (16*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((104*(1 + S^2))/S + (28*Pi^2*(1 + S^2))/(3*S))*HPL[{4, 1}, -S^2] - (48*(1 + S^2)*HPL[{4, 3}, -S^2])/S - (56*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (144*(1 + S^2)*HPL[{5, 2}, -S^2])/S - (240*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((1072*(1 + S^2))/S + (248*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((3272*(1 + S^2))/S + (764*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + (608*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (64*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (208*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (1936*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (208*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (640*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (1256*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((-2256*(1 + S^2))/S - (180*Pi^2*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - (608*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S - (1440*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (1904*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (1904*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (3728*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (11072*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (2880*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (4128*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (6816*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (2880*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((Pi^2*(-1 - S^2))/S - (48*(1 + S^2))/S + (157*Pi^4*(1 + S^2))/(90*S))*Zeta[3] + (16*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1, 1}, -S^2]*((1584*(1 + S^2))/S + (180*Pi^2*(1 + S^2))/S - (40*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((182*(1 + S^2))/S + (62*Pi^2*(1 + S^2))/(3*S) - (8*(1 + S^2)*HPL[{3}, -S^2])/S - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((80*(1 + S^2))/S + (16*Pi^2*(1 + S^2))/(3*S) + (26*Pi^4*(1 + S^2))/(45*S) + (24*(1 + S^2)*HPL[{4}, -S^2])/S + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (40*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((64*(1 + S^2))/S + (20*Pi^2*(1 + S^2))/(3*S) - (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (32*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-1084*(1 + S^2))/S - (424*Pi^2*(1 + S^2))/(3*S) - (377*Pi^4*(1 + S^2))/(45*S) + (344*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (40*(1 + S^2)*Zeta[3])/S) + ((16*(1 + S^2))/S + (55*Pi^2*(1 + S^2))/(3*S))*Zeta[5] + HPL[{2}, -S^2]*((750*(1 + S^2))/S + (301*Pi^2*(1 + S^2))/(3*S) + (377*Pi^4*(1 + S^2))/(45*S) + ((-32*(1 + S^2))/S - (8*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (8*(1 + S^2)*HPL[{4}, -S^2])/S - (24*(1 + S^2)*HPL[{5}, -S^2])/S + ((-536*(1 + S^2))/S - (124*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (344*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (32*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (104*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (304*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (952*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((Pi^2*(-1 - S^2))/(3*S) - (28*(1 + S^2))/S)*Zeta[3] + (24*(1 + S^2)*Zeta[5])/S) + (150*(1 + S^2)*Zeta[7])/S)) + Log[T]*(-75*Pi^2*S - (181*Pi^4*S)/12 - (1151*Pi^6*S)/756 + ((-88*(1 + S^2))/(3*S) - (22*Pi^2*(1 + S^2))/(9*S))*HPL[{1}, -S^2]^6 - (16*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) - (2*(1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) + HPL[{0}, S^2]^7*(-S/12 + ((-1 - S^2)*HPL[{1}, -S^2])/(24*S)) + HPL[{0}, S^2]^6*(-S/8 + ((-1 - S^2)*HPL[{1}, -S^2])/(3*S) + ((-1 - S^2)*HPL[{1}, -S^2]^2)/(6*S)) + ((-86*(-1 + S^2))/(3*S) - (10*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2]^3 - (10*(1 + S^2)*HPL[{2}, -S^2]^4)/(3*S) + (-46*S - (3*Pi^2*(1 + S^2))/S)*HPL[{3}, -S^2]^2 + (32*(1 + S^2)*HPL[{4}, -S^2]^2)/S + ((8*(-20 + S^2))/S + (20*Pi^2*(1 + S^2))/(3*S))*HPL[{6}, -S^2] - (4*(75 + 97*S^2)*HPL[{7}, -S^2])/S + ((520*(1 + S^2))/S + (124*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*((-31*S)/6 - (31*Pi^2*S)/36 - (11*(1 + S^2)*HPL[{1}, -S^2]^2)/(6*S) - (11*(1 + S^2)*HPL[{1}, -S^2]^3)/(18*S) + ((-3 - 11*S^2)*HPL[{2}, -S^2])/(12*S) + HPL[{1}, -S^2]*((-3*(1 + S^2))/S - (4*Pi^2*(1 + S^2))/(9*S) - (2*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-1 - S^2)*HPL[{3}, -S^2])/(4*S) + (5*(1 + S^2)*HPL[{2, 1}, -S^2])/(6*S)) - (144*(1 + S^2)*HPL[{3, 1}, -S^2]^2)/S - (4*(-1 + 25*S^2)*HPL[{4, 2}, -S^2])/S + (4*(18 + 37*S^2)*HPL[{4, 3}, -S^2])/S + ((-2*Pi^2*(1 + S^2))/S - (4*(-2 + 117*S^2))/S)*HPL[{5, 1}, -S^2] + (2*(103 + 217*S^2)*HPL[{5, 2}, -S^2])/S + (20*(26 + 45*S^2)*HPL[{6, 1}, -S^2])/S - (640*(1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((52*(-1 + S^2))/S + (2*Pi^2*(1 + S^2))/S)*HPL[{3, 1, 2}, -S^2] + ((-636*(-1 + S^2))/S - (74*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 2, 1}, -S^2] + (4*(105 + 257*S^2)*HPL[{3, 2, 2}, -S^2])/S + (32*(41 + 102*S^2)*HPL[{3, 3, 1}, -S^2])/S + ((-80*Pi^2*(1 + S^2))/S - (32*(-69 + 52*S^2))/S)*HPL[{4, 1, 1}, -S^2] + (4*(317 + 805*S^2)*HPL[{4, 1, 2}, -S^2])/S + (4*(1013 + 2509*S^2)*HPL[{4, 2, 1}, -S^2])/S + (24*(349 + 863*S^2)*HPL[{5, 1, 1}, -S^2])/S - (608*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((184*Pi^2*(1 + S^2))/(3*S) + (32*(-56 + 39*S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] - (16*(161 + 17*S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (16*(161 + 17*S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (16*(-275 + 97*S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (32*(-430 + 121*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + ((-3040*(-1 + S^2))/S - (320*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1, 1}, -S^2] + (2848*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (8544*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (960*(17 + 20*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (2880*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (900*S + (296*Pi^2*S)/3 + (157*Pi^4*S)/45)*Zeta[3] + 40*S*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((-2256*(-1 + S^2))/S - (8*Pi^2*(-115 + 26*S^2))/(3*S) - (640*(1 + S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((-3*Pi^2*(11 + 31*S^2))/S - (2*(85 + 679*S^2))/S - (28*(1 + S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((-10*Pi^2*(37 + 95*S^2))/(3*S) - (40*(17 + 106*S^2))/S - (24*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((-18*(5 + 2*S^2))/S + (8*Pi^2*(-1 + 3*S^2))/(3*S) + (12*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^5*((-376*(1 + S^2))/(3*S) - (44*Pi^2*(1 + S^2))/(3*S) + (80*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (24*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^4*((-1316*(1 + S^2))/(3*S) - (173*Pi^2*(1 + S^2))/(3*S) - (1849*Pi^4*(1 + S^2))/(540*S) - (43*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (86*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (400*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (56*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (56*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (120*(1 + S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((-1528*(1 + S^2))/S - (8*Pi^2*(79 + 60*S^2))/(3*S) + (288*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((-36*Pi^2*(15 + 7*S^2))/S - (16*(251 + 110*S^2))/S + (848*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*(272*S + (3*Pi^4*(1 + S^2))/(5*S) + (Pi^2*(17 + 55*S^2))/(3*S) + (4*(-23 + 5*S^2)*HPL[{2, 1}, -S^2])/S - (80*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (4*(5 + 13*S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((Pi^2*(-159 - 245*S^2))/(6*S) - (215*(1 + S^2))/S - (76*Pi^4*(1 + S^2))/(45*S) + (4*(15 + 34*S^2)*HPL[{3}, -S^2])/S + (12*(1 + S^2)*HPL[{4}, -S^2])/S - (76*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (12*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (4*(10 + 29*S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-1464*(-1 + S^2))/S - (308*Pi^4*(1 + S^2))/(45*S) - (4*Pi^2*(-83 + 213*S^2))/(3*S) + (16*(25 + 64*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((169*Pi^4*(1 + S^2))/(45*S) + (194*Pi^2*(-1 + 2*S^2))/(3*S) + (4*(-217 + 149*S^2))/S + (640*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(29 + 69*S^2)*Zeta[3])/S) + HPL[{0}, S^2]^3*(-225*S - (284*Pi^2*S)/9 - (1783*Pi^4*S)/540 - (110*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) - (22*(1 + S^2)*HPL[{1}, -S^2]^5)/(9*S) + ((-9 - 28*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((-350*(1 + S^2))/(9*S) - (110*Pi^2*(1 + S^2))/(27*S) - (10*(1 + S^2)*HPL[{2}, -S^2])/S) + ((-13 - 10*S^2)/(3*S) - (17*Pi^2*(1 + S^2))/(18*S))*HPL[{3}, -S^2] - (2*(1 + 4*S^2)*HPL[{4}, -S^2])/(3*S) - (7*(1 + S^2)*HPL[{5}, -S^2])/S + ((49*Pi^2*(1 + S^2))/(9*S) + (4*(58 + 15*S^2))/(3*S))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((-36 - 161*S^2)/(3*S) + (Pi^2*(-36 - 121*S^2))/(18*S) + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) + (44*(1 + 3*S^2)*HPL[{3, 1}, -S^2])/(3*S) + ((1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (8*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (4*(7 + 22*S^2)*HPL[{2, 1, 1}, -S^2])/S - (80*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (248*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (64*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (16*S*Zeta[3])/3 + HPL[{1}, -S^2]*((-403*(1 + S^2))/(3*S) - (355*Pi^2*(1 + S^2))/(18*S) - (937*Pi^4*(1 + S^2))/(540*S) + ((-142*(1 + S^2))/(3*S) - (85*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2] - (19*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (4*(1 + S^2)*HPL[{3}, -S^2])/S - (2*(1 + S^2)*HPL[{4}, -S^2])/S + (60*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (88*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (60*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (16*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-88*(1 + S^2))/S - (110*Pi^2*(1 + S^2))/(9*S) - (30*(1 + S^2)*HPL[{2}, -S^2])/S - (2*(1 + S^2)*HPL[{3}, -S^2])/S + (30*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/(3*S))) + HPL[{0}, S^2]^4*((-33*S)/4 - (113*Pi^2*S)/72 - (46*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (23*(1 + S^2)*HPL[{1}, -S^2]^4)/(18*S) + ((-9 - 77*S^2)/(12*S) + (Pi^2*(-1 - S^2))/(6*S))*HPL[{2}, -S^2] + ((-1 - S^2)*HPL[{2}, -S^2]^2)/(2*S) + HPL[{1}, -S^2]^2*((-49*(1 + S^2))/(4*S) - (53*Pi^2*(1 + S^2))/(36*S) - (31*(1 + S^2)*HPL[{2}, -S^2])/(12*S)) + ((-1 + S^2)*HPL[{3}, -S^2])/(4*S) + ((1 + S^2)*HPL[{4}, -S^2])/S + ((53 + 16*S^2)*HPL[{2, 1}, -S^2])/(6*S) + (2*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (4*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (7*S*Zeta[3])/6 + HPL[{1}, -S^2]*((-113*(1 + S^2))/(6*S) - (53*Pi^2*(1 + S^2))/(18*S) - (31*(1 + S^2)*HPL[{2}, -S^2])/(6*S) + (31*(1 + S^2)*HPL[{2, 1}, -S^2])/(6*S) - (7*(1 + S^2)*Zeta[3])/(6*S))) + HPL[{0}, S^2]^2*(-225*S - 47*Pi^2*S - (73*Pi^4*S)/15 - (16*(1 + S^2)*HPL[{1}, -S^2]^5)/S - (8*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + ((-29 - 115*S^2)/(2*S) - (17*Pi^2*(1 + S^2))/(6*S))*HPL[{2}, -S^2]^2 - (10*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^4*((-63*(1 + S^2))/S - (53*Pi^2*(1 + S^2))/(9*S) - (43*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-1 - S^2)*HPL[{3}, -S^2]^2)/S + ((2*Pi^2*(1 + S^2))/S + (-1 + 5*S^2)/S)*HPL[{4}, -S^2] + ((-11 - 9*S^2)*HPL[{5}, -S^2])/S + (20*(1 + S^2)*HPL[{6}, -S^2])/S + ((2*(174 + 17*S^2))/S + (Pi^2*(123 + 35*S^2))/(3*S))*HPL[{2, 1}, -S^2] + (44*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((35*Pi^2*(1 + S^2))/(3*S) + (2*(15 + 116*S^2))/S)*HPL[{3, 1}, -S^2] + ((-5 - 17*S^2)*HPL[{3, 2}, -S^2])/S - (6*(3 + 11*S^2)*HPL[{4, 1}, -S^2])/S - (6*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-64*Pi^2*(1 + S^2))/(3*S) - (8*(6 + 59*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (4*(69 + 31*S^2)*HPL[{2, 2, 1}, -S^2])/S - (28*(29 + 11*S^2)*HPL[{3, 1, 1}, -S^2])/S + (6*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (74*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (240*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (8*(70 + 19*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (184*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (320*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (14*S - Pi^2*S)*Zeta[3] + HPL[{3}, -S^2]*(17*S + (Pi^2*(1 + 19*S^2))/(6*S) - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-544*(1 + S^2))/(3*S) - (212*Pi^2*(1 + S^2))/(9*S) - (172*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/S + (172*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (16*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-387*(1 + S^2))/S - (56*Pi^2*(1 + S^2))/S - (359*Pi^4*(1 + S^2))/(90*S) + ((-134*(1 + S^2))/S - (37*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2] - (24*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (12*(1 + S^2)*HPL[{3}, -S^2])/S + (172*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (84*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (172*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (16*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-8 - 207*S^2)/S + (Pi^2*(-7 - 65*S^2))/(2*S) - (13*Pi^4*(1 + S^2))/(18*S) + (2*(2 + 5*S^2)*HPL[{3}, -S^2])/S + (2*(1 + S^2)*HPL[{4}, -S^2])/S + (2*(69 + 31*S^2)*HPL[{2, 1}, -S^2])/S + (44*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (88*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(1 + 2*S^2)*Zeta[3])/S) + HPL[{1}, -S^2]*((-575*(1 + S^2))/S - (83*Pi^2*(1 + S^2))/S - (359*Pi^4*(1 + S^2))/(45*S) - (48*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((18*(1 + S^2))/S + (Pi^2*(1 + S^2))/S)*HPL[{3}, -S^2] - (6*(1 + S^2)*HPL[{5}, -S^2])/S + ((268*(1 + S^2))/S + (74*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (168*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (12*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (36*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (192*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (552*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((Pi^2*(-1 - S^2))/S + (24*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-182*(1 + S^2))/S - (74*Pi^2*(1 + S^2))/(3*S) + (6*(1 + S^2)*HPL[{3}, -S^2])/S + (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/S))) + HPL[{0}, S^2]*(-4900*S - (1625*Pi^2*S)/3 - (766*Pi^4*S)/15 - (24953*Pi^6*S)/5670 - (56*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) - (8*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) - (38*(1 + 3*S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^5*((-88*(1 + S^2))/S - (64*Pi^2*(1 + S^2))/(9*S) - (24*(1 + S^2)*HPL[{2}, -S^2])/S) + 12*S*HPL[{3}, -S^2]^2 + ((-10*Pi^2*(1 + S^2))/S - (2*(13 + 34*S^2))/S)*HPL[{5}, -S^2] + (20*(1 + S^2)*HPL[{6}, -S^2])/S - (100*(1 + S^2)*HPL[{7}, -S^2])/S + (4*(47 + 125*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((Pi^2*(-1 - S^2))/(3*S) - (2*(21 + 29*S^2))/S)*HPL[{3, 2}, -S^2] + ((-4*Pi^2*(1 + S^2))/S - (4*(14 + 33*S^2))/S)*HPL[{4, 1}, -S^2] - (6*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (16*(1 + S^2)*HPL[{4, 3}, -S^2])/S + (4*(5 + 19*S^2)*HPL[{5, 1}, -S^2])/S - (54*(1 + S^2)*HPL[{5, 2}, -S^2])/S - (40*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((-84*Pi^2*(1 + S^2))/S - (16*(109 + 25*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-248*Pi^2*(1 + S^2))/S - (16*(334 + 71*S^2))/S)*HPL[{3, 1, 1}, -S^2] + (24*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (8*(35 + 111*S^2)*HPL[{3, 2, 1}, -S^2])/S + (44*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (96*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (16*(63 + 184*S^2)*HPL[{4, 1, 1}, -S^2])/S + (84*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (276*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S + (504*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((184*Pi^2*(1 + S^2))/S + (32*(118 + 23*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (608*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + (32*(26 + 71*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (1840*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (1840*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (3664*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (11104*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (1440*(1 + 3*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (1376*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (4128*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (7040*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (2880*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (136*S + 6*Pi^2*S)*Zeta[3] - 48*S*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((24*(9 + 56*S^2))/S + (4*Pi^2*(37 + 104*S^2))/(3*S) - (40*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-2*Pi^2*(7 + 17*S^2))/(3*S) - (2*(31 + 30*S^2))/S + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-57 - 307*S^2)/S + (Pi^2*(-65 - 181*S^2))/(6*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/S + (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (6*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^4*((-940*(1 + S^2))/(3*S) - (320*Pi^2*(1 + S^2))/(9*S) - (120*(1 + S^2)*HPL[{2}, -S^2])/S - (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (120*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (28*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((-2632*(1 + S^2))/(3*S) - (1010*Pi^2*(1 + S^2))/(9*S) - (937*Pi^4*(1 + S^2))/(135*S) + ((-376*(1 + S^2))/S - (30*Pi^2*(1 + S^2))/S)*HPL[{2}, -S^2] - (172*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (32*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (56*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (480*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (240*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (480*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (112*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((-4*Pi^2*(22 + 67*S^2))/S - (24*(19 + 113*S^2))/S + (48*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((9*Pi^4*(1 + S^2))/S + (8*Pi^2*(88 + 19*S^2))/(3*S) + (8*(227 + 44*S^2))/S - (336*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(8 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((Pi^2*(-27 - 2*S^2))/(3*S) - (73*Pi^4*(1 + S^2))/(90*S) - (4*(33 + 17*S^2))/S + (8*(1 + S^2)*HPL[{4}, -S^2])/S - (8*(5 + 6*S^2)*HPL[{2, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (32*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(2 + 3*S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((Pi^4*(-349 - 1103*S^2))/(90*S) + (Pi^2*(-93 - 500*S^2))/(3*S) - (300*(1 + 4*S^2))/S + ((4*Pi^2*(1 + S^2))/(3*S) + (8*(3 + 4*S^2))/S)*HPL[{3}, -S^2] - 24*S*HPL[{4}, -S^2] - (8*(1 + S^2)*HPL[{5}, -S^2])/S + ((42*Pi^2*(1 + S^2))/S + (8*(109 + 25*S^2))/S)*HPL[{2, 1}, -S^2] + (24*(8 + 21*S^2)*HPL[{3, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (48*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (8*(47 + 125*S^2)*HPL[{2, 1, 1}, -S^2])/S - (304*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (944*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((2*Pi^2*(1 + S^2))/S + (4*(-1 + 17*S^2))/S)*Zeta[3]) + HPL[{1}, -S^2]^2*((-1900*(1 + S^2))/S - (734*Pi^2*(1 + S^2))/(3*S) - (937*Pi^4*(1 + S^2))/(45*S) - (172*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-28*(1 + S^2))/S - (10*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (56*(1 + S^2)*HPL[{4}, -S^2])/S - (20*(1 + S^2)*HPL[{5}, -S^2])/S + ((1128*(1 + S^2))/S + (90*Pi^2*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (720*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (64*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (1440*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (2096*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (1440*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((84*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-792*(1 + S^2))/S - (90*Pi^2*(1 + S^2))/S + (20*(1 + S^2)*HPL[{3}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (20*(1 + S^2)*Zeta[3])/S)) + HPL[{1}, -S^2]*((-2900*(1 + S^2))/S - (1061*Pi^2*(1 + S^2))/(3*S) - (499*Pi^4*(1 + S^2))/(15*S) - (12907*Pi^6*(1 + S^2))/(5670*S) + ((-268*(1 + S^2))/S - (62*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 - (76*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-88*(1 + S^2))/S - (20*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] - (40*(1 + S^2)*HPL[{5}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((1128*(1 + S^2))/S + (268*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] - (80*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (128*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (56*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-2256*(1 + S^2))/S - (180*Pi^2*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (1376*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (4192*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (608*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (1936*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (2880*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (1440*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (2880*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((96*(1 + S^2))/S + (4*Pi^2*(1 + S^2))/S)*Zeta[3] - (16*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((1584*(1 + S^2))/S + (180*Pi^2*(1 + S^2))/S - (40*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-64*(1 + S^2))/S - (20*Pi^2*(1 + S^2))/(3*S) - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-1084*(1 + S^2))/S - (424*Pi^2*(1 + S^2))/(3*S) - (377*Pi^4*(1 + S^2))/(45*S) + (40*(1 + S^2)*HPL[{3}, -S^2])/S - (8*(1 + S^2)*HPL[{4}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (40*(1 + S^2)*Zeta[3])/S))) + (532*S + (110*Pi^2*S)/3)*Zeta[5] + HPL[{2, 1}, -S^2]*((-900*(-1 + S^2))/S - (7*Pi^4*(-218 + 3*S^2))/(90*S) - (2*Pi^2*(-315 + 124*S^2))/(3*S) - (16*(41 + 48*S^2)*HPL[{3, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (1008*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (1424*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (640*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (1280*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-80*Pi^2*(1 + S^2))/(3*S) - (8*(107 + 23*S^2))/S)*Zeta[3] - (136*(1 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((100*(1 + 10*S^2))/S + (Pi^2*(71 + 370*S^2))/(3*S) + (Pi^4*(233 + 673*S^2))/(90*S) - (4*(9 + 20*S^2)*HPL[{4}, -S^2])/S - (64*(1 + S^2)*HPL[{5}, -S^2])/S + ((-28*Pi^2*(1 + S^2))/S - (104*(9 + S^2))/S)*HPL[{2, 1}, -S^2] - (16*(14 + 37*S^2)*HPL[{3, 1}, -S^2])/S + (12*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (128*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (16*(22 + 67*S^2)*HPL[{2, 1, 1}, -S^2])/S + (368*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (976*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (640*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-4*Pi^2*(1 + S^2))/(3*S) + (4*(8 + 5*S^2))/S)*Zeta[3] - (16*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^3*((-3800*(1 + S^2))/(3*S) - (1484*Pi^2*(1 + S^2))/(9*S) - (1849*Pi^4*(1 + S^2))/(135*S) - (344*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((1240*(1 + S^2))/(3*S) + (212*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (224*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{5}, -S^2])/S + (172*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (224*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (688*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2288*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (1376*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2528*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + ((376*(1 + S^2))/S + (196*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-172*Pi^2*(1 + S^2))/(9*S) + (344*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (688*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (344*(1 + S^2)*Zeta[3])/(3*S)) + (440*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]^2*((-2900*(1 + S^2))/S - (1045*Pi^2*(1 + S^2))/(3*S) - (5849*Pi^4*(1 + S^2))/(180*S) - (8699*Pi^6*(1 + S^2))/(4536*S) + ((-268*(1 + S^2))/S - (67*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 - (8*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((168*(1 + S^2))/S + (28*Pi^2*(1 + S^2))/(3*S))*HPL[{4}, -S^2] + (48*(1 + S^2)*HPL[{5}, -S^2])/S - (70*(1 + S^2)*HPL[{6}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-168*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] - (688*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (2288*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (36*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (176*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (172*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (1376*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (2528*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (224*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (224*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + ((792*(1 + S^2))/S + (196*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (4*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((172*Pi^2*(1 + S^2))/(3*S) - (344*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((824*(1 + S^2))/S + (212*Pi^2*(1 + S^2))/(3*S) - (344*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (24*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-134*Pi^2*(1 + S^2))/(3*S) - (707*Pi^4*(1 + S^2))/(180*S) + (344*(1 + S^2)*HPL[{3}, -S^2])/S + (28*(1 + S^2)*HPL[{4}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (344*(1 + S^2)*Zeta[3])/S) + (440*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((Pi^4*(257 - 1292*S^2))/(90*S) - (450*(-1 + S^2))/S - (31*Pi^6*(1 + S^2))/(135*S) - (5*Pi^2*(-35 + 78*S^2))/(3*S) - (6*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((14*Pi^2*(1 + S^2))/(3*S) + (12*(-1 + 11*S^2))/S)*HPL[{4}, -S^2] + (44*(1 + 2*S^2)*HPL[{5}, -S^2])/S + (68*(1 + S^2)*HPL[{6}, -S^2])/S + ((124*Pi^2*(1 + S^2))/(3*S) + (16*(37 + 28*S^2))/S)*HPL[{3, 1}, -S^2] - (8*(27 + 65*S^2)*HPL[{3, 2}, -S^2])/S - (4*(157 + 413*S^2)*HPL[{4, 1}, -S^2])/S - (24*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (132*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-1040*(1 + S^2))/S - (248*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (304*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (16*(79 + 10*S^2)*HPL[{3, 1, 1}, -S^2])/S + (24*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (296*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (864*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (1424*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (640*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (1280*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((2*Pi^2*(29 + 72*S^2))/(3*S) + (4*(33 + 158*S^2))/S)*Zeta[3] + (8*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((764*(1 + S^2))/S + (4*Pi^2*(79 + 60*S^2))/(3*S) - (144*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((16*Pi^2*(1 + 3*S^2))/S + (4*(17 + 174*S^2))/S - (184*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/S) + (4*(24 + 71*S^2)*Zeta[5])/S) + 300*S*Zeta[7] + HPL[{1}, -S^2]*((-4900*(1 + S^2))/S - (1525*Pi^2*(1 + S^2))/(3*S) - (430*Pi^4*(1 + S^2))/(9*S) - (8699*Pi^6*(1 + S^2))/(2268*S) - (16*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((52*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/S)*HPL[{5}, -S^2] - (140*(1 + S^2)*HPL[{6}, -S^2])/S - (288*(1 + S^2)*HPL[{7}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-1072*(1 + S^2))/S - (184*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((-3552*(1 + S^2))/S - (608*Pi^2*(1 + S^2))/(3*S))*HPL[{4, 1}, -S^2] - (72*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (44*(1 + S^2)*HPL[{4, 3}, -S^2])/S - (352*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (120*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (300*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((-2144*(1 + S^2))/S - (536*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((-3952*(1 + S^2))/S - (1184*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + (696*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (2144*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (448*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (2120*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (6536*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S + (13344*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + (344*Pi^2*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (448*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (1376*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (4576*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (2752*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (8256*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (16960*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + ((1084*(1 + S^2))/S + (102*Pi^2*(1 + S^2))/S + (157*Pi^4*(1 + S^2))/(45*S))*Zeta[3] - (8*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((268*Pi^2*(1 + S^2))/(3*S) + (707*Pi^4*(1 + S^2))/(90*S) - (688*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (688*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-192*(1 + S^2))/S + (112*Pi^2*(1 + S^2))/(3*S) - (352*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((192*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/(3*S) - (56*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (16*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((1020*(1 + S^2))/S + (328*Pi^2*(1 + S^2))/(3*S) + (196*Pi^4*(1 + S^2))/(45*S) - (28*(1 + S^2)*HPL[{4}, -S^2])/S - (688*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (352*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (48*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-364*(1 + S^2))/S - (134*Pi^2*(1 + S^2))/(3*S) + (96*(1 + S^2)*HPL[{3}, -S^2])/S + (76*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-344*Pi^2*(1 + S^2))/(3*S) + (688*(1 + S^2)*Zeta[3])/S) + ((692*(1 + S^2))/S + (110*Pi^2*(1 + S^2))/(3*S))*Zeta[5] + HPL[{2}, -S^2]*((-182*Pi^2*(1 + S^2))/(3*S) - (707*Pi^4*(1 + S^2))/(90*S) + ((536*(1 + S^2))/S + (92*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (56*(1 + S^2)*HPL[{4}, -S^2])/S + (40*(1 + S^2)*HPL[{5}, -S^2])/S + ((1072*(1 + S^2))/S + (268*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (688*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (360*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (1096*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (1376*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (1376*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((536*(1 + S^2))/S + (94*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (172*(1 + S^2)*Zeta[5])/S) + (300*(1 + S^2)*Zeta[7])/S));
e5T2F0=3920 - (17429*Pi^8*S^2)/42525 + (Pi^6*(10192 - 38931*S^2))/22680 + (Pi^4*(1320 - 1351*S^2))/90 + (Pi^2*(713 - 311*S^2))/3 + HPL[{0}, S^2]^9/192 + HPL[{0}, S^2]^8*(-S^2/48 + HPL[{1}, -S^2]/192) + (44*Pi^2*HPL[{1}, -S^2]^7)/63 + (4*HPL[{1}, -S^2]^9)/27 + HPL[{0}, S^2]^7*((5*Pi^2)/72 + HPL[{1}, -S^2]^2/24) + (2*(1 + S^2)^2*HPL[{2}, -S^2]^4)/(3*S^2) - (28*HPL[{3}, -S^2]^3)/3 - (24*(1 + S^2)^2*HPL[{4}, -S^2]^2)/S^2 + 125*Pi^2*HPL[{7}, -S^2] - (1400*(-1 + S^2)*(1 + S^2)*HPL[{8}, -S^2])/S^2 + 4900*HPL[{9}, -S^2] + HPL[{0}, S^2]^6*((-31*Pi^2*S^2)/144 + (1 - 9*S^2)/24 + ((-1 - S^2)*HPL[{1}, -S^2]^2)/8 + HPL[{1}, -S^2]^3/9 + HPL[{1}, -S^2]*((11*Pi^2)/144 + (-1 - S^2)/4 + HPL[{2}, -S^2]/8) - ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(24*S^2) + HPL[{3}, -S^2]/12 - HPL[{2, 1}, -S^2]/4) + (40*(1 + S^2)^2*HPL[{3, 1}, -S^2]^2)/S^2 - 32*Pi^2*HPL[{4, 3}, -S^2] - (283*Pi^2*HPL[{5, 2}, -S^2])/3 + (12*(-1 + S^2)*(1 + S^2)*HPL[{5, 3}, -S^2])/S^2 + 980*HPL[{5, 4}, -S^2] - 236*Pi^2*HPL[{6, 1}, -S^2] + (52*(-1 + S^2)*(1 + S^2)*HPL[{6, 2}, -S^2])/S^2 + 3896*HPL[{6, 3}, -S^2] + (624*(-1 + S^2)*(1 + S^2)*HPL[{7, 1}, -S^2])/S^2 + 9720*HPL[{7, 2}, -S^2] + 17440*HPL[{8, 1}, -S^2] + (192*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2]^2)/S^2 - 61*Pi^2*HPL[{3, 2, 2}, -S^2] - (640*Pi^2*HPL[{3, 3, 1}, -S^2])/3 + (20*(-1 + S^2)*(1 + S^2)*HPL[{3, 3, 2}, -S^2])/S^2 - 208*Pi^2*HPL[{4, 1, 2}, -S^2] - (40*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 3}, -S^2])/S^2 - 680*Pi^2*HPL[{4, 2, 1}, -S^2] + (20*(-1 + S^2)*(1 + S^2)*HPL[{4, 2, 2}, -S^2])/S^2 - (56*(-1 + S^2)*(1 + S^2)*HPL[{4, 3, 1}, -S^2])/S^2 - 168*HPL[{4, 3, 2}, -S^2] + 336*HPL[{4, 4, 1}, -S^2] - (4268*Pi^2*HPL[{5, 1, 1}, -S^2])/3 - (20*(-1 + S^2)*(1 + S^2)*HPL[{5, 1, 2}, -S^2])/S^2 + 672*HPL[{5, 1, 3}, -S^2] - (260*(-1 + S^2)*(1 + S^2)*HPL[{5, 2, 1}, -S^2])/S^2 + 156*HPL[{5, 2, 2}, -S^2] + 2304*HPL[{5, 3, 1}, -S^2] - (1040*(-1 + S^2)*(1 + S^2)*HPL[{6, 1, 1}, -S^2])/S^2 + 1616*HPL[{6, 1, 2}, -S^2] + 7376*HPL[{6, 2, 1}, -S^2] + 18080*HPL[{7, 1, 1}, -S^2] - (208*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 + (1012*Pi^2*HPL[{3, 1, 1, 2}, -S^2])/3 + (1012*Pi^2*HPL[{3, 1, 2, 1}, -S^2])/3 + (1636*Pi^2*HPL[{3, 2, 1, 1}, -S^2])/3 + (160*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 2, 1}, -S^2])/S^2 + 832*HPL[{3, 2, 2, 2}, -S^2] + 2384*HPL[{3, 2, 3, 1}, -S^2] + (480*(-1 + S^2)*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + 2336*HPL[{3, 3, 1, 2}, -S^2] + 6992*HPL[{3, 3, 2, 1}, -S^2] + (5168*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 - (32*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 1, 2}, -S^2])/S^2 - 14320*HPL[{4, 1, 1, 3}, -S^2] + (448*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 2, 1}, -S^2])/S^2 - 11984*HPL[{4, 1, 2, 2}, -S^2] - 21248*HPL[{4, 1, 3, 1}, -S^2] + (1408*(-1 + S^2)*(1 + S^2)*HPL[{4, 2, 1, 1}, -S^2])/S^2 - 7472*HPL[{4, 2, 1, 2}, -S^2] - 7328*HPL[{4, 2, 2, 1}, -S^2] - 41824*HPL[{4, 3, 1, 1}, -S^2] + (3024*(-1 + S^2)*(1 + S^2)*HPL[{5, 1, 1, 1}, -S^2])/S^2 - 43376*HPL[{5, 1, 1, 2}, -S^2] - 70736*HPL[{5, 1, 2, 1}, -S^2] - 166928*HPL[{5, 2, 1, 1}, -S^2] - 416960*HPL[{6, 1, 1, 1}, -S^2] - 384*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2] - 1152*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] + (320*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (960*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + 1664*HPL[{2, 2, 2, 2, 1}, -S^2] - (6832*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - (1888*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 - (3168*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 + 3488*HPL[{3, 1, 1, 2, 2}, -S^2] - (3808*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 + 3488*HPL[{3, 1, 2, 1, 2}, -S^2] - 96*HPL[{3, 1, 2, 2, 1}, -S^2] - 25856*HPL[{3, 1, 3, 1, 1}, -S^2] - (7968*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 + 8480*HPL[{3, 2, 1, 1, 2}, -S^2] + 4896*HPL[{3, 2, 1, 2, 1}, -S^2] - 7392*HPL[{3, 2, 2, 1, 1}, -S^2] - 26880*HPL[{3, 3, 1, 1, 1}, -S^2] - (24192*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + 25216*HPL[{4, 1, 1, 1, 2}, -S^2] + 14464*HPL[{4, 1, 1, 2, 1}, -S^2] - 22400*HPL[{4, 1, 2, 1, 1}, -S^2] - 81152*HPL[{4, 2, 1, 1, 1}, -S^2] - 163584*HPL[{5, 1, 1, 1, 1}, -S^2] - (736*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + (960*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + 2944*HPL[{3, 1, 1, 1, 1, 2}, -S^2] + 2944*HPL[{3, 1, 1, 1, 2, 1}, -S^2] + 2944*HPL[{3, 1, 1, 2, 1, 1}, -S^2] + 2944*HPL[{3, 1, 2, 1, 1, 1}, -S^2] + 2944*HPL[{3, 2, 1, 1, 1, 1}, -S^2] + 10624*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - (1920*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + 5888*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] + 23552*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] + 58880*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] + 115968*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + (8/3 - (4*Pi^2*S^2)/9 + (4*HPL[{0}, S^2]^3)/3 + (44*Pi^2*HPL[{1}, -S^2])/9 + (112*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]^2*((-4*S^2)/3 + (16*HPL[{1}, -S^2])/3) - (8*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((40*Pi^2)/9 + (56*HPL[{1}, -S^2]^2)/3 + 8*HPL[{2}, -S^2]) - (32*HPL[{3}, -S^2])/3)*Log[T]^6 + ((-16*HPL[{0}, S^2]*HPL[{1}, -S^2])/3 - (16*HPL[{1}, -S^2]^2)/3)*Log[T]^7 + ((4*HPL[{0}, S^2])/3 + (4*HPL[{1}, -S^2])/3)*Log[T]^8 + HPL[{2, 1, 1, 1, 1}, -S^2]*((-1440*(-1 + S^4))/S^2 - (32*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - 1472*Zeta[3]) + HPL[{4, 1, 1}, -S^2]*((-8*Pi^2*(-37 - 14*S^2 + 23*S^4))/(3*S^2) - (8*(-101 + 4*S^2 + 121*S^4))/S^2 - 1360*Zeta[3]) + HPL[{3, 2, 1}, -S^2]*((-224*(-1 + S^4))/S^2 - (2*Pi^2*(-37 - 15*S^2 + 22*S^4))/(3*S^2) - 392*Zeta[3]) + HPL[{6}, -S^2]*((-20*Pi^2*(-4 + S^2 + 5*S^4))/(3*S^2) - (2*(-30 + 4*S^2 + 205*S^4))/S^2 - 452*HPL[{2, 1}, -S^2] - 280*Zeta[3]) + HPL[{3}, -S^2]^2*((Pi^2*(-1 + S^4))/(3*S^2) + (2*(1 - S^2 + S^4))/S^2 + 20*HPL[{2, 1}, -S^2] - 20*Zeta[3]) + HPL[{2}, -S^2]^3*((-10*(-1 + S^4))/S^2 - (2*Pi^2*(-5 - 2*S^2 + 3*S^4))/(9*S^2) - (52*HPL[{3}, -S^2])/3 - (104*HPL[{2, 1}, -S^2])/3 - (52*Zeta[3])/3) + HPL[{4, 2}, -S^2]*((-2*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) - (2*(-11 + 5*S^4))/S^2 - 12*Zeta[3]) + HPL[{1}, -S^2]^6*((-2*Pi^2*(1 + S^2))/9 + (4*(1 + 2*S^2 + S^4))/(3*S^2) - (4*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2) - (80*HPL[{3}, -S^2])/9 - 8*Zeta[3]) + (-8*Pi^2*S^2 - 4*(2 + 7*S^2))*Zeta[3]^2 + HPL[{3, 1, 2}, -S^2]*((16*(-1 + S^4))/S^2 + (2*Pi^2*(-3 - S^2 + 2*S^4))/(3*S^2) + 24*Zeta[3]) + HPL[{2, 1}, -S^2]^2*((-48*(3 + 8*S^2 + 3*S^4))/S^2 - (4*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) + 160*Zeta[3]) + HPL[{5, 1}, -S^2]*((2*Pi^2*(-20 - S^2 + 19*S^4))/(3*S^2) + (4*(1 + 5*S^2 + 71*S^4))/S^2 + 160*Zeta[3]) + HPL[{3, 1, 1, 1}, -S^2]*((8*Pi^2*(-31 - 13*S^2 + 18*S^4))/(3*S^2) + (32*(-20 + S^2 + 25*S^4))/S^2 + 864*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((1607*Pi^4)/45 + (8*Pi^2*(1 + S^2))/3 + (8*(113 - 6*S^2 + 33*S^4))/S^2 - 496*(1 + S^2)*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((707*Pi^4)/45 + (272*(1 + S^4))/S^2 - 160*(1 + S^2)*Zeta[3]) + HPL[{4, 1}, -S^2]*((616*Pi^4)/45 - (8*Pi^2*(1 + S^2))/3 + (4*(1 + 12*S^2 + 183*S^4))/S^2 + 2368*HPL[{2, 1, 1}, -S^2] - 24*(1 + S^2)*Zeta[3]) + HPL[{3, 2}, -S^2]*((119*Pi^4)/30 + (2*Pi^2*(1 + S^2))/3 + (2*(11 + 125*S^4))/S^2 + 752*HPL[{2, 1, 1}, -S^2] - 12*(1 + S^2)*Zeta[3]) + HPL[{1}, -S^2]^5*((1849*Pi^4)/1350 - (4*Pi^2*(1 + S^2))/3 + (12*(1 + 2*S^2 + S^4))/S^2 + ((86*Pi^2)/45 - (8*(-1 + S^4))/S^2)*HPL[{2}, -S^2] + (172*HPL[{2}, -S^2]^2)/15 - (4*(1 + S^2)*(-1 + 9*S^2)*HPL[{3}, -S^2])/(5*S^2) - (112*HPL[{4}, -S^2])/15 + (8*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (112*HPL[{3, 1}, -S^2])/15 - 8*(1 + S^2)*Zeta[3]) + HPL[{5}, -S^2]*((109*Pi^4)/45 + 2*Pi^2*(1 + S^2) + (2*(30 + 3*S^2 + 43*S^4))/S^2 + (4*(1 + S^2)*(-6 + 13*S^2)*HPL[{2, 1}, -S^2])/S^2 + 348*HPL[{3, 1}, -S^2] - 184*HPL[{2, 1, 1}, -S^2] + 24*(1 + S^2)*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((-266*Pi^4)/15 + (640*(-1 + S^4))/S^2 + 384*(1 + S^2)*Zeta[3]) + HPL[{0}, S^2]^5*((47*Pi^4)/120 + (3*(1 + S^2))/4 - (2*(1 + S^2)*HPL[{1}, -S^2]^3)/9 + (11*HPL[{1}, -S^2]^4)/36 + HPL[{1}, -S^2]^2*((4*Pi^2)/9 - (2*(1 + S^2))/3 + (2*HPL[{2}, -S^2])/3) + (Pi^2/24 + (1 + S^2)/(2*S^2))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/8 + ((1 + S^2)*HPL[{3}, -S^2])/4 - (3*HPL[{4}, -S^2])/4 + ((1 + S^2)*HPL[{2, 1}, -S^2])/6 + HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((Pi^2*(-1 - S^2))/18 + (3 - 10*S^2 - 13*S^4)/(12*S^2) - ((-3 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(12*S^2) - (4*HPL[{2, 1}, -S^2])/3 + (3*Zeta[3])/2)) + Log[T]^5*(-24 + (8*Pi^2*S^2)/3 - (44*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/9 - (44*Pi^2*HPL[{1}, -S^2]^2)/3 - (56*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^2*(8*S^2 + 4*(1 + S^2)*HPL[{1}, -S^2] - 16*HPL[{1}, -S^2]^2 - (16*HPL[{2}, -S^2])/3) + ((-16*Pi^2)/9 + (16*(-1 + S^4))/S^2)*HPL[{2}, -S^2] - (32*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]*(-8*(1 + S^2) - (112*HPL[{1}, -S^2]^3)/3 + HPL[{1}, -S^2]*((-128*Pi^2)/9 - 48*HPL[{2}, -S^2]) - (8*(1 + S^2)*HPL[{2}, -S^2])/S^2 + (8*HPL[{3}, -S^2])/3 + 48*HPL[{2, 1}, -S^2]) + HPL[{1}, -S^2]*((4*Pi^2*(1 + S^2))/3 - (8*(1 + 2*S^2 + S^4))/S^2 + (8*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + (160*HPL[{3}, -S^2])/3 + 48*Zeta[3])) + HPL[{3}, -S^2]*((-6067*Pi^6)/22680 + (Pi^4*(1 + S^2))/9 - (2*Pi^2*(-15 + 37*S^4))/(3*S^2) - (2*(-74 + 35*S^2 + 176*S^4))/S^2 + (16*Pi^2 - (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{4}, -S^2] + (4*(1 + S^2)*(13 + 10*S^2)*HPL[{5}, -S^2])/S^2 + 502*HPL[{6}, -S^2] + 200*HPL[{2, 1}, -S^2]^2 + ((140*Pi^2)/3 - (8*(1 + 2*S^2 + S^4))/S^2)*HPL[{3, 1}, -S^2] - (4*(1 + S^2)*(-2 + 3*S^2)*HPL[{3, 2}, -S^2])/S^2 + (4*(-9 + S^2)*(1 + S^2)*HPL[{4, 1}, -S^2])/S^2 - 336*HPL[{5, 1}, -S^2] + ((-200*Pi^2)/3 + (16*(-1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (8*(1 + S^2)*(-1 + 19*S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (24*(1 + S^2)*(-1 + 19*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + 24*HPL[{3, 1, 2}, -S^2] - 392*HPL[{3, 2, 1}, -S^2] + 12896*HPL[{4, 1, 1}, -S^2] + (16*(1 + S^2)*(1 + 23*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + 928*HPL[{3, 1, 1, 1}, -S^2] - 1472*HPL[{2, 1, 1, 1, 1}, -S^2] - (4*(1 + 5*S^2 + 7*S^4)*Zeta[3])/S^2 - 12*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((2*Pi^2*(1 + 10*S^2 + 9*S^4))/S^2 + (16*(1 + 24*S^2 + 17*S^4))/S^2 + 80*Zeta[3])) + Log[T]^4*(128 - (52*Pi^4*S^2)/45 - (10*Pi^2*(-2 + 3*S^2))/3 + HPL[{0}, S^2]^5/2 + (220*Pi^2*HPL[{1}, -S^2]^3)/9 + (56*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^4*(-S^2 + (23*HPL[{1}, -S^2])/9) + (8*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + HPL[{0}, S^2]^3*((10*Pi^2)/3 - (8*(1 + S^2)*HPL[{1}, -S^2])/3 + (110*HPL[{1}, -S^2]^2)/9 + (14*HPL[{2}, -S^2])/3) - (134*Pi^2*HPL[{3}, -S^2])/9 - (8*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 16*HPL[{5}, -S^2] + HPL[{0}, S^2]^2*((-11*Pi^2*S^2)/3 - 10*(-1 + 3*S^2) - 10*(1 + S^2)*HPL[{1}, -S^2]^2 + (80*HPL[{1}, -S^2]^3)/3 - (2*(-5 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((106*Pi^2)/9 - 20*(1 + S^2) + (86*HPL[{2}, -S^2])/3) - (14*HPL[{3}, -S^2])/3 - (92*HPL[{2, 1}, -S^2])/3) - (92*Pi^2*HPL[{2, 1}, -S^2])/9 + (40*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (368*HPL[{3, 2}, -S^2])/3 + (1328*HPL[{4, 1}, -S^2])/3 - (80*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (736*HPL[{2, 2, 1}, -S^2])/3 + 416*HPL[{3, 1, 1}, -S^2] + HPL[{0}, S^2]*((94*Pi^4)/15 + 60*(1 + S^2) + (140*HPL[{1}, -S^2]^4)/3 + ((44*Pi^2)/3 + (40*(1 + S^2))/S^2)*HPL[{2}, -S^2] + (86*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((320*Pi^2)/9 + 120*HPL[{2}, -S^2]) + 4*(1 + S^2)*HPL[{3}, -S^2] + 16*HPL[{4}, -S^2] - 40*(1 + S^2)*HPL[{2, 1}, -S^2] - (416*HPL[{3, 1}, -S^2])/3 + 240*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((-8*Pi^2*(1 + S^2))/3 + (20*(1 + 2*S^2 + S^4))/S^2 + (20*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 + (16*HPL[{3}, -S^2])/3 - 240*HPL[{2, 1}, -S^2] - (56*Zeta[3])/3)) + HPL[{1}, -S^2]^2*((-10*Pi^2*(1 + S^2))/3 + (20*(1 + 2*S^2 + S^4))/S^2 - (20*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - (400*HPL[{3}, -S^2])/3 - 120*Zeta[3]) + HPL[{2}, -S^2]*((-60*(-1 + S^4))/S^2 - (4*Pi^2*(-5 - 2*S^2 + 3*S^4))/(3*S^2) - (184*HPL[{3}, -S^2])/3 - (368*HPL[{2, 1}, -S^2])/3 - (184*Zeta[3])/3) + HPL[{1}, -S^2]*((1849*Pi^4)/270 - (20*Pi^2*(1 + S^2))/3 + (60*(1 + 2*S^2 + S^4))/S^2 + ((86*Pi^2)/9 - (40*(-1 + S^4))/S^2)*HPL[{2}, -S^2] + (172*HPL[{2}, -S^2]^2)/3 - (4*(1 + S^2)*(-1 + 9*S^2)*HPL[{3}, -S^2])/S^2 - (112*HPL[{4}, -S^2])/3 + (40*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (112*HPL[{3, 1}, -S^2])/3 - 40*(1 + S^2)*Zeta[3])) + HPL[{0}, S^2]^4*((-77*Pi^4*S^2)/90 + (Pi^2*(15 - 97*S^2))/36 - (4*(-6 + 13*S^2))/3 - (7*(1 + S^2)*HPL[{1}, -S^2]^4)/12 + (23*HPL[{1}, -S^2]^5)/45 + ((1 + S^2)*HPL[{2}, -S^2]^2)/(2*S^2) + HPL[{1}, -S^2]^3*((53*Pi^2)/54 - (7*(1 + S^2))/3 + (31*HPL[{2}, -S^2])/18) + (5*Pi^2*HPL[{3}, -S^2])/12 - ((1 + S^2)*(-1 + 3*S^2)*HPL[{4}, -S^2])/(2*S^2) + (13*HPL[{5}, -S^2])/2 + (1 - (16*Pi^2)/9 + S^2)*HPL[{2, 1}, -S^2] + ((-5 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/(2*S^2) + HPL[{3, 2}, -S^2] - HPL[{4, 1}, -S^2] - ((-5 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (19*HPL[{2, 2, 1}, -S^2])/3 + 19*HPL[{3, 1, 1}, -S^2] - (38*HPL[{2, 1, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((45 + 48*S^2 - 14*S^4)/(12*S^2) + (Pi^2*(5 + 2*S^2 - 3*S^4))/(12*S^2) - HPL[{3}, -S^2]/2 - (19*HPL[{2, 1}, -S^2])/6 - (5*Zeta[3])/2) + HPL[{1}, -S^2]^2*((-11*Pi^2*(1 + S^2))/12 + (5 - 18*S^2 - 23*S^4)/(4*S^2) - ((1 + S^2)*(-5 + 2*S^2)*HPL[{2}, -S^2])/(4*S^2) - (31*HPL[{2, 1}, -S^2])/6 + (7*Zeta[3])/6) + HPL[{1}, -S^2]*((1849*Pi^4)/4320 - (11*Pi^2*(1 + S^2))/6 + (45 - 61*S^2 - 106*S^4)/(12*S^2) + ((19*Pi^2)/18 + (5 + 3*S^2 - 2*S^4)/(2*S^2))*HPL[{2}, -S^2] + (31*HPL[{2}, -S^2]^2)/24 - ((-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(4*S^2) + HPL[{4}, -S^2] + ((1 + S^2)*(-5 + 2*S^2)*HPL[{2, 1}, -S^2])/(2*S^2) - (31*HPL[{3, 1}, -S^2])/6 + (31*HPL[{2, 1, 1}, -S^2])/3 - (23*(1 + S^2)*Zeta[3])/6)) + HPL[{2, 1, 1}, -S^2]*((-824*(-1 + S^4))/S^2 - (4*Pi^4*(-104 - 57*S^2 + 47*S^4))/(45*S^2) - (4*Pi^2*(-89 - 48*S^2 + 53*S^4))/(3*S^2) - 1472*HPL[{3, 1, 1}, -S^2] - 2944*HPL[{2, 1, 1, 1}, -S^2] - 72*Pi^2*Zeta[3] - 416*Zeta[5]) + HPL[{4}, -S^2]*((Pi^4*(41 - 17*S^2 - 58*S^4))/(45*S^2) - (2*Pi^2*(-15 - 5*S^2 + 24*S^4))/(3*S^2) - (4*(-26 + 10*S^2 + 97*S^4))/S^2 - 490*HPL[{5}, -S^2] + (-8*Pi^2 + (8*(1 + 6*S^2 + 5*S^4))/S^2)*HPL[{2, 1}, -S^2] - (4*(-5 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + 84*HPL[{3, 2}, -S^2] - 168*HPL[{4, 1}, -S^2] + 32*(1 + S^2)*HPL[{2, 1, 1}, -S^2] + 32*HPL[{2, 2, 1}, -S^2] + 272*HPL[{3, 1, 1}, -S^2] + 32*HPL[{2, 1, 1, 1}, -S^2] + ((-64*Pi^2)/3 - (8*(1 + S^2))/S^2)*Zeta[3] - 220*Zeta[5]) + HPL[{1}, -S^2]^4*((-37*Pi^4*(1 + S^2))/60 - (10*Pi^2*(-1 + S^4))/(3*S^2) + (66*(1 + 2*S^2 + S^4))/S^2 + (4*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((-106*Pi^2)/9 - (4*(-1 + 8*S^2 + 9*S^4))/S^2)*HPL[{3}, -S^2] - (6*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 8*HPL[{5}, -S^2] + ((-86*Pi^2)/9 + (40*(-1 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (20*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (344*HPL[{3, 2}, -S^2])/3 + (1144*HPL[{4, 1}, -S^2])/3 - (40*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (688*HPL[{2, 2, 1}, -S^2])/3 + (1264*HPL[{3, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((-40*(-1 + S^4))/S^2 - (2*Pi^2*(-5 - 2*S^2 + 3*S^4))/(3*S^2) - (172*HPL[{3}, -S^2])/3 - (344*HPL[{2, 1}, -S^2])/3 - (172*Zeta[3])/3) + ((-98*Pi^2)/9 - 40*(1 + S^2))*Zeta[3] - (220*Zeta[5])/3) + HPL[{2}, -S^2]^2*((2*Pi^4*(21 + 29*S^2 + 8*S^4))/(45*S^2) + (3*(25 + 96*S^2 + 25*S^4))/S^2 + (Pi^2*(73 + 152*S^2 + 43*S^4))/(6*S^2) + (-8*Pi^2 - (2*(1 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2] - (2*(1 + S^2)*(-1 + 3*S^2)*HPL[{4}, -S^2])/S^2 + 15*HPL[{5}, -S^2] - (26*Pi^2*HPL[{2, 1}, -S^2])/3 + (2*(1 + S^2)*(-9 + 11*S^2)*HPL[{3, 1}, -S^2])/S^2 + 104*HPL[{3, 2}, -S^2] + 304*HPL[{4, 1}, -S^2] - (40*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 208*HPL[{2, 2, 1}, -S^2] + 424*HPL[{3, 1, 1}, -S^2] - 7*Pi^2*Zeta[3] - 36*Zeta[5]) - 12*(-2 + 19*S^2)*Zeta[5] + HPL[{3, 1}, -S^2]*((2*Pi^2*(-84 - 49*S^2 + 60*S^4))/(3*S^2) + (Pi^4*(-213 - 119*S^2 + 94*S^4))/(45*S^2) + (2*(-135 + 20*S^2 + 277*S^4))/S^2 - 360*HPL[{3, 2}, -S^2] - 1360*HPL[{4, 1}, -S^2] - (16*(1 + S^2)*(11 + 13*S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 32*HPL[{2, 2, 1}, -S^2] + 5952*HPL[{3, 1, 1}, -S^2] + 1472*HPL[{2, 1, 1, 1}, -S^2] + ((140*Pi^2)/3 - (16*(1 + S^2))/S^2)*Zeta[3] + 304*Zeta[5]) + Zeta[3]*(-50*(1 + 10*S^2) - (2*Pi^2*(-3 + 34*S^2))/3 - 160*S^2*Zeta[5]) + HPL[{1}, -S^2]^3*((8699*Pi^6)/6804 - (37*Pi^4*(1 + S^2))/15 + (260*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(-89 - 70*S^2 + 19*S^4))/(9*S^2) + ((134*Pi^2)/9 + (16*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + (16*HPL[{3}, -S^2]^2)/3 + ((-56*Pi^2)/9 - (24*(-1 + S^4))/S^2)*HPL[{4}, -S^2] - (4*(1 + S^2)*(-9 + 25*S^2)*HPL[{5}, -S^2])/(3*S^2) + (140*HPL[{6}, -S^2])/3 - (688*HPL[{2, 1}, -S^2]^2)/3 + ((-112*Pi^2)/9 + (80*(-1 + S^4))/S^2)*HPL[{3, 1}, -S^2] + (16*(1 + S^2)*(1 + 11*S^2)*HPL[{3, 2}, -S^2])/(3*S^2) + (8*(1 + S^2)*(-1 + 25*S^2)*HPL[{4, 1}, -S^2])/S^2 + 24*HPL[{4, 2}, -S^2] + (352*HPL[{5, 1}, -S^2])/3 + ((344*Pi^2)/9 - (160*(-1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (64*(1 + S^2)^2*HPL[{2, 2, 1}, -S^2])/S^2 + (16*(1 + S^2)*(13 + 3*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - (448*HPL[{4, 1, 1}, -S^2])/3 + (160*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (448*HPL[{3, 1, 1, 1}, -S^2])/3 + HPL[{3}, -S^2]*((-40*(-1 + 10*S^2 + 11*S^4))/(3*S^2) - (2*Pi^2*(-7 + 24*S^2 + 31*S^4))/(9*S^2) + (688*HPL[{2, 1}, -S^2])/3 - 16*Zeta[3]) + (-160*(1 + S^2) - (76*Pi^2*(1 + S^2))/9)*Zeta[3] + (8*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((160*(-1 + S^4))/S^2 + (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/(3*S^2) + (688*Zeta[3])/3) + HPL[{2}, -S^2]*((707*Pi^4)/270 - (144*(-1 + S^4))/S^2 - (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/(3*S^2) - (8*(1 + S^2)*(1 + 11*S^2)*HPL[{3}, -S^2])/(3*S^2) - (56*HPL[{4}, -S^2])/3 - (32*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - (688*HPL[{3, 1}, -S^2])/3 + (1376*HPL[{2, 1, 1}, -S^2])/3 - 32*(1 + S^2)*Zeta[3]) - (232*(1 + S^2)*Zeta[5])/3) + HPL[{2, 1}, -S^2]*((-881*Pi^6)/756 + (7*Pi^4*(1 + S^2))/15 + (500*(-1 + S^4))/S^2 + (4*Pi^2*(-42 + 25*S^4))/(3*S^2) + ((304*Pi^2)/3 - (16*(-1 + S^4))/S^2)*HPL[{3, 1}, -S^2] - (4*(1 + S^2)*(-3 + 37*S^2)*HPL[{3, 2}, -S^2])/S^2 - (8*(1 + S^2)*(-3 + 61*S^2)*HPL[{4, 1}, -S^2])/S^2 - 48*HPL[{4, 2}, -S^2] + 72*HPL[{5, 1}, -S^2] + 192*Pi^2*HPL[{2, 1, 1}, -S^2] - (160*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (16*(1 + S^2)*(-31 + 7*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + 48*HPL[{3, 1, 2}, -S^2] - 784*HPL[{3, 2, 1}, -S^2] - 2464*HPL[{4, 1, 1}, -S^2] - (384*(1 + S^2)^2*HPL[{2, 1, 1, 1}, -S^2])/S^2 + 1472*HPL[{3, 1, 1, 1}, -S^2] + 2944*HPL[{2, 1, 1, 1, 1}, -S^2] + (16*Pi^2*(1 + S^2) + (8*(-1 + 48*S^2 + 37*S^4))/S^2)*Zeta[3] - 40*Zeta[3]^2 + 152*(1 + S^2)*Zeta[5]) + HPL[{0}, S^2]^3*((6023*Pi^6)/5670 + (Pi^2*(87 + 61*S^2))/18 + (355 + 288*S^2)/6 - (8*(1 + S^2)*HPL[{1}, -S^2]^5)/15 + (22*HPL[{1}, -S^2]^6)/27 + ((11*Pi^2)/12 + (11*(1 + S^2))/(3*S^2))*HPL[{2}, -S^2]^2 + (5*HPL[{2}, -S^2]^3)/6 + HPL[{1}, -S^2]^4*((55*Pi^2)/27 - (8*(1 + S^2))/3 + 5*HPL[{2}, -S^2]) - 2*HPL[{3}, -S^2]^2 + ((-43*Pi^2)/18 + (6*(1 + S^2))/S^2)*HPL[{4}, -S^2] + (29*(1 + S^2)*HPL[{5}, -S^2])/3 - (125*HPL[{6}, -S^2])/3 - 12*HPL[{2, 1}, -S^2]^2 + ((-22*Pi^2)/9 - (20*(1 + S^2))/S^2)*HPL[{3, 1}, -S^2] + ((1 + S^2)*HPL[{3, 2}, -S^2])/3 - 6*(1 + S^2)*HPL[{4, 1}, -S^2] - HPL[{4, 2}, -S^2]/3 + 18*HPL[{5, 1}, -S^2] + (8*Pi^2 + (112*(1 + S^2))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((37*Pi^4)/120 + (29*Pi^2*(1 + S^2))/(9*S^2) + (62 + 101*S^2 + 7*S^4)/(3*S^2) + 4*HPL[{4}, -S^2] - 2*(1 + S^2)*HPL[{2, 1}, -S^2] - 14*HPL[{3, 1}, -S^2] + 24*HPL[{2, 1, 1}, -S^2]) + 4*(1 + S^2)*HPL[{2, 2, 1}, -S^2] + (52*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/3 - (2*HPL[{3, 1, 2}, -S^2])/3 + (58*HPL[{3, 2, 1}, -S^2])/3 + (188*HPL[{4, 1, 1}, -S^2])/3 - (32*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/3 - (176*HPL[{3, 1, 1, 1}, -S^2])/3 + 112*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((Pi^2*(1 + S^2))/9 - (2*(15 + 16*S^2 + 13*S^4))/(3*S^2) - (16*Zeta[3])/3) - (40*S^2*Zeta[3])/3 + 16*Zeta[3]^2 + HPL[{1}, -S^2]^3*((-32*Pi^2*(1 + S^2))/27 - (4*(-7 + 10*S^2 + 17*S^4))/(9*S^2) + (4*(1 + S^2)*(7 + 2*S^2)*HPL[{2}, -S^2])/(9*S^2) + (4*HPL[{3}, -S^2])/3 - 20*HPL[{2, 1}, -S^2] + (16*Zeta[3])/9) + HPL[{3}, -S^2]*((19*Pi^2*(1 + S^2))/18 + (9 + 15*S^2 + 17*S^4)/(3*S^2) + 4*HPL[{2, 1}, -S^2] + 12*Zeta[3]) + HPL[{1}, -S^2]^2*((937*Pi^4)/540 - (32*Pi^2*(1 + S^2))/9 + (41 - 2*S^2 - 43*S^4)/(3*S^2) + ((85*Pi^2)/18 + (4*(7 + 9*S^2 + 2*S^4))/(3*S^2))*HPL[{2}, -S^2] + (19*HPL[{2}, -S^2]^2)/3 + (4*(1 + S^2)^2*HPL[{3}, -S^2])/(3*S^2) + 2*HPL[{4}, -S^2] - (4*(1 + S^2)*(7 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S^2) - (88*HPL[{3, 1}, -S^2])/3 + 60*HPL[{2, 1, 1}, -S^2] - 2*(1 + S^2)*Zeta[3]) + HPL[{1}, -S^2]*((-77*Pi^4*(1 + S^2))/270 + (Pi^2*(29 - 70*S^2 - 99*S^4))/(18*S^2) + (177 + 82*S^2 - 95*S^4)/(6*S^2) + ((1 + S^2)*(11 + 3*S^2)*HPL[{2}, -S^2]^2)/(6*S^2) + (Pi^2/3 + (8*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{3}, -S^2] + (3*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 - 6*HPL[{5}, -S^2] + ((-85*Pi^2)/9 - (8*(7 + 9*S^2 + 2*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(1 + S^2)*(15 + 7*S^2)*HPL[{3, 1}, -S^2])/(3*S^2) + 4*HPL[{3, 2}, -S^2] + 8*HPL[{4, 1}, -S^2] + (8*(1 + S^2)*(7 + 2*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (152*HPL[{2, 2, 1}, -S^2])/3 + 160*HPL[{3, 1, 1}, -S^2] - 120*HPL[{2, 1, 1, 1}, -S^2] + ((49*Pi^2)/9 - 4*(1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(29 + 28*S^2 - S^4))/(18*S^2) + (8*(7 + 9*S^2 + 2*S^4))/(3*S^2) - 2*HPL[{3}, -S^2] - (76*HPL[{2, 1}, -S^2])/3 + (8*Zeta[3])/3) + (110*Zeta[5])/3)) + Log[T]^3*(-1480/3 + (208*Pi^4*S^2)/45 + (8*Pi^2*(-45 + 34*S^2))/9 - (11*HPL[{0}, S^2]^5*HPL[{1}, -S^2])/9 - (220*Pi^2*HPL[{1}, -S^2]^4)/9 - (112*HPL[{1}, -S^2]^6)/9 + HPL[{0}, S^2]^4*(4*S^2 + (7*(1 + S^2)*HPL[{1}, -S^2])/3 - (46*HPL[{1}, -S^2]^2)/9 - (4*HPL[{2}, -S^2])/3) + ((-124*Pi^2)/9 - (32*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 - (64*HPL[{3}, -S^2]^2)/3 + (32*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + (640*HPL[{2, 1}, -S^2]^2)/3 + HPL[{0}, S^2]^3*((-8*(7 + 3*S^2))/9 + (16*(1 + S^2)*HPL[{1}, -S^2]^2)/3 - (440*HPL[{1}, -S^2]^3)/27 + HPL[{1}, -S^2]*((-220*Pi^2)/27 + (32*(1 + S^2))/3 - 20*HPL[{2}, -S^2]) - (56*(1 + S^2)*HPL[{2}, -S^2])/(9*S^2) - (8*HPL[{3}, -S^2])/9 + (64*HPL[{2, 1}, -S^2])/3) + ((184*Pi^2)/9 - (160*(-1 + S^4))/S^2)*HPL[{3, 1}, -S^2] + HPL[{2}, -S^2]*((-308*Pi^4)/135 + (544*(-1 + S^4))/(3*S^2) + (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/(3*S^2) - (8*(-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(3*S^2) + 32*HPL[{4}, -S^2] + (640*HPL[{3, 1}, -S^2])/3 - (1280*HPL[{2, 1, 1}, -S^2])/3) + ((-320*Pi^2)/9 + (320*(-1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-80*(-1 + S^4))/S^2 - (640*Zeta[3])/3) + HPL[{3}, -S^2]*((-4*Pi^2*(1 + S^2))/9 + (16*(-3 + S^2 + 12*S^4))/(3*S^2) - (640*HPL[{2, 1}, -S^2])/3 - (16*Zeta[3])/3) + 80*S^2*Zeta[3] + HPL[{1}, -S^2]^3*((40*Pi^2*(1 + S^2))/9 - (80*(1 + 2*S^2 + S^4))/(3*S^2) + (80*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2) + (1600*HPL[{3}, -S^2])/9 + 160*Zeta[3]) + HPL[{1}, -S^2]^2*((-1849*Pi^4)/135 + (40*Pi^2*(1 + S^2))/3 - (120*(1 + 2*S^2 + S^4))/S^2 + ((-172*Pi^2)/9 + (80*(-1 + S^4))/S^2)*HPL[{2}, -S^2] - (344*HPL[{2}, -S^2]^2)/3 + (8*(1 + S^2)*(-1 + 9*S^2)*HPL[{3}, -S^2])/S^2 + (224*HPL[{4}, -S^2])/3 - (80*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (224*HPL[{3, 1}, -S^2])/3 + 80*(1 + S^2)*Zeta[3]) + HPL[{0}, S^2]^2*((44*Pi^2*S^2)/3 + (4*(-45 + 68*S^2))/3 + (40*(1 + S^2)*HPL[{1}, -S^2]^3)/3 - (80*HPL[{1}, -S^2]^4)/3 + HPL[{1}, -S^2]^2*((-212*Pi^2)/9 + 40*(1 + S^2) - (172*HPL[{2}, -S^2])/3) + ((-64*Pi^2)/9 + (8*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - (44*HPL[{2}, -S^2]^2)/3 - (4*(1 + S^2)*HPL[{3}, -S^2])/3 + (184*HPL[{3, 1}, -S^2])/3 - (320*HPL[{2, 1, 1}, -S^2])/3 + HPL[{1}, -S^2]*(8*Pi^2*(1 + S^2) + (20*(-1 + 2*S^2 + 3*S^4))/S^2 + (4*(-5 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + 8*HPL[{3}, -S^2] + (344*HPL[{2, 1}, -S^2])/3 + (32*Zeta[3])/3)) + HPL[{0}, S^2]*(-264*(1 + S^2) - (4*Pi^2*(29 + 21*S^2))/9 - (112*HPL[{1}, -S^2]^5)/3 + HPL[{1}, -S^2]^3*((-1280*Pi^2)/27 - 160*HPL[{2}, -S^2]) - (16*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + ((4*Pi^2)/3 - 16*(1 + S^2))*HPL[{3}, -S^2] - (24*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 24*HPL[{5}, -S^2] + ((184*Pi^2)/3 + 160*(1 + S^2))*HPL[{2, 1}, -S^2] + (80*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - (16*HPL[{3, 2}, -S^2])/3 - (160*HPL[{4, 1}, -S^2])/3 + HPL[{1}, -S^2]*((-1874*Pi^4)/135 + (32*Pi^2*(1 + S^2))/3 - (120*(1 + 2*S^2 + S^4))/S^2 + (-60*Pi^2 - (80*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - (344*HPL[{2}, -S^2]^2)/3 - (8*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 - (112*HPL[{4}, -S^2])/3 + (80*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + 480*HPL[{3, 1}, -S^2] - 960*HPL[{2, 1, 1}, -S^2]) - (160*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (1376*HPL[{2, 2, 1}, -S^2])/3 - (3968*HPL[{3, 1, 1}, -S^2])/3 + 960*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-116*Pi^2*(1 + S^2))/(9*S^2) - (40*(3 + 4*S^2 + S^4))/S^2 + (32*HPL[{3}, -S^2])/3 + (688*HPL[{2, 1}, -S^2])/3 + 16*Zeta[3]) + HPL[{1}, -S^2]^2*((16*Pi^2*(1 + S^2))/3 - (40*(1 + 2*S^2 + S^4))/S^2 - (40*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 - (32*HPL[{3}, -S^2])/3 + 480*HPL[{2, 1}, -S^2] + (112*Zeta[3])/3)) + HPL[{1}, -S^2]*((37*Pi^4*(1 + S^2))/15 + (40*Pi^2*(-1 + S^4))/(3*S^2) - (264*(1 + 2*S^2 + S^4))/S^2 - (16*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((424*Pi^2)/9 + (16*(-1 + 8*S^2 + 9*S^4))/S^2)*HPL[{3}, -S^2] + (24*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + 32*HPL[{5}, -S^2] + ((344*Pi^2)/9 - (160*(-1 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (80*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - (1376*HPL[{3, 2}, -S^2])/3 - (4576*HPL[{4, 1}, -S^2])/3 + (160*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (2752*HPL[{2, 2, 1}, -S^2])/3 - (5056*HPL[{3, 1, 1}, -S^2])/3 + ((392*Pi^2)/9 + 160*(1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*((160*(-1 + S^4))/S^2 + (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/(3*S^2) + (688*HPL[{3}, -S^2])/3 + (1376*HPL[{2, 1}, -S^2])/3 + (688*Zeta[3])/3) + (880*Zeta[5])/3)) + Log[T]^2*(1440 - (215*Pi^6*S^2)/189 + (Pi^4*(416 - 947*S^2))/90 - (2*Pi^2*(-192 + 103*S^2))/3 + HPL[{0}, S^2]^7/12 + HPL[{0}, S^2]^6*(-S^2/4 + HPL[{1}, -S^2]/3) + (44*Pi^2*HPL[{1}, -S^2]^5)/3 + (16*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^5*((5*Pi^2)/6 - (2*(1 + S^2)*HPL[{1}, -S^2])/3 + (11*HPL[{1}, -S^2]^2)/6 + HPL[{2}, -S^2]/2) - (20*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) - (10*Pi^2*HPL[{5}, -S^2])/3 - (160*(-1 + S^2)*(1 + S^2)*HPL[{6}, -S^2])/S^2 + 400*HPL[{7}, -S^2] + HPL[{0}, S^2]^4*((-7*Pi^2*S^2)/4 + (15 - 59*S^2)/6 - (7*(1 + S^2)*HPL[{1}, -S^2]^2)/2 + (46*HPL[{1}, -S^2]^3)/9 - ((-5 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(2*S^2) + HPL[{1}, -S^2]*((53*Pi^2)/18 - 7*(1 + S^2) + (31*HPL[{2}, -S^2])/6) - (19*HPL[{2, 1}, -S^2])/3) - (96*(1 + S^2)^2*HPL[{2, 1}, -S^2]^2)/S^2 + (194*Pi^2*HPL[{3, 2}, -S^2])/3 + (712*Pi^2*HPL[{4, 1}, -S^2])/3 - (16*(-1 + S^2)*(1 + S^2)*HPL[{4, 2}, -S^2])/S^2 - 176*HPL[{4, 3}, -S^2] + (72*(-1 + S^2)*(1 + S^2)*HPL[{5, 1}, -S^2])/S^2 - 520*HPL[{5, 2}, -S^2] - 1120*HPL[{6, 1}, -S^2] + 192*Pi^2*HPL[{2, 2, 1}, -S^2] + (1192*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + (16*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 - (144*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 - 752*HPL[{3, 2, 2}, -S^2] - 2432*HPL[{3, 3, 1}, -S^2] - (576*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 - 2368*HPL[{4, 1, 2}, -S^2] - 7552*HPL[{4, 2, 1}, -S^2] - 15744*HPL[{5, 1, 1}, -S^2] - (368*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + (480*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + 1472*HPL[{3, 1, 1, 2}, -S^2] + 1472*HPL[{3, 1, 2, 1}, -S^2] + 1472*HPL[{3, 2, 1, 1}, -S^2] + 5312*HPL[{4, 1, 1, 1}, -S^2] - (960*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - 2944*HPL[{2, 1, 2, 1, 1}, -S^2] - 8832*HPL[{2, 2, 1, 1, 1}, -S^2] - 18560*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1}, -S^2]*((-720*(-1 + S^4))/S^2 - (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - 736*Zeta[3]) + HPL[{1}, -S^2]^4*((-10*Pi^2*(1 + S^2))/3 + (20*(1 + 2*S^2 + S^4))/S^2 - (20*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - (400*HPL[{3}, -S^2])/3 - 120*Zeta[3]) + HPL[{2}, -S^2]^2*((24*(3 + 8*S^2 + 3*S^4))/S^2 + (2*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) - 100*HPL[{3}, -S^2] - 80*Zeta[3]) + HPL[{4}, -S^2]*((-4*Pi^2*(-7 - 2*S^2 + 5*S^4))/(3*S^2) - (4*(-11 + 4*S^2 + 31*S^4))/S^2 + 16*HPL[{2, 1}, -S^2] - 56*Zeta[3]) - 320*S^2*Zeta[3] - 16*S^2*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((4*Pi^2*(-31 - 13*S^2 + 18*S^4))/(3*S^2) + (16*(-20 + S^2 + 25*S^4))/S^2 + 432*Zeta[3]) + HPL[{1}, -S^2]^3*((1849*Pi^4)/135 - (40*Pi^2*(1 + S^2))/3 + (120*(1 + 2*S^2 + S^4))/S^2 + ((172*Pi^2)/9 - (80*(-1 + S^4))/S^2)*HPL[{2}, -S^2] + (344*HPL[{2}, -S^2]^2)/3 - (8*(1 + S^2)*(-1 + 9*S^2)*HPL[{3}, -S^2])/S^2 - (224*HPL[{4}, -S^2])/3 + (80*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (224*HPL[{3, 1}, -S^2])/3 - 80*(1 + S^2)*Zeta[3]) + HPL[{3}, -S^2]*((-257*Pi^4)/45 + (4*Pi^2*(1 + S^2))/3 - (4*(-11 + 6*S^2 + 69*S^4))/S^2 + 88*HPL[{4}, -S^2] + (8*(1 + S^2)*(1 + 23*S^2)*HPL[{2, 1}, -S^2])/S^2 + 464*HPL[{3, 1}, -S^2] - 736*HPL[{2, 1, 1}, -S^2] - 8*(1 + S^2)*Zeta[3]) + HPL[{2, 1}, -S^2]*((-133*Pi^4)/15 + (320*(-1 + S^4))/S^2 + 736*HPL[{3, 1}, -S^2] + 1472*HPL[{2, 1, 1}, -S^2] + 192*(1 + S^2)*Zeta[3]) + HPL[{0}, S^2]^3*((47*Pi^4)/15 + (4*(21 + 8*S^2))/3 - (16*(1 + S^2)*HPL[{1}, -S^2]^3)/3 + (110*HPL[{1}, -S^2]^4)/9 + (4*Pi^2 + (56*(1 + S^2))/(3*S^2))*HPL[{2}, -S^2] + 6*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((110*Pi^2)/9 - 16*(1 + S^2) + 30*HPL[{2}, -S^2]) + (8*(1 + S^2)*HPL[{3}, -S^2])/3 + (4*HPL[{4}, -S^2])/3 - (16*(1 + S^2)*HPL[{2, 1}, -S^2])/3 - (88*HPL[{3, 1}, -S^2])/3 + 56*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((-32*Pi^2*(1 + S^2))/9 - (4*(-7 + 10*S^2 + 17*S^4))/(3*S^2) + (4*(1 + S^2)*(7 + 2*S^2)*HPL[{2}, -S^2])/(3*S^2) + 4*HPL[{3}, -S^2] - 60*HPL[{2, 1}, -S^2] + (16*Zeta[3])/3)) + HPL[{0}, S^2]^2*((-167*Pi^4*S^2)/45 - (2*Pi^2*(-15 + 52*S^2))/3 - 2*(-96 + 103*S^2) - 10*(1 + S^2)*HPL[{1}, -S^2]^4 + 16*HPL[{1}, -S^2]^5 + (2*(1 + S^2)*(6 + S^2)*HPL[{2}, -S^2]^2)/S^2 + HPL[{1}, -S^2]^3*((212*Pi^2)/9 - 40*(1 + S^2) + (172*HPL[{2}, -S^2])/3) + ((-7*Pi^2)/3 + 4*(1 + S^2))*HPL[{3}, -S^2] - (8*(-2 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + 14*HPL[{5}, -S^2] - 28*Pi^2*HPL[{2, 1}, -S^2] + (4*(1 + S^2)*(-16 + 3*S^2)*HPL[{3, 1}, -S^2])/S^2 + 10*HPL[{3, 2}, -S^2] + 48*HPL[{4, 1}, -S^2] - (24*(-5 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 208*HPL[{2, 2, 1}, -S^2] + 568*HPL[{3, 1, 1}, -S^2] - 368*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*(-12*Pi^2*(1 + S^2) - (30*(-1 + 2*S^2 + 3*S^4))/S^2 - (6*(-5 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - 12*HPL[{3}, -S^2] - 172*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + HPL[{2}, -S^2]*((-2*Pi^2*(-5 - 4*S^2 + S^4))/S^2 - (8*(-11 - 12*S^2 + 2*S^4))/S^2 - 8*HPL[{3}, -S^2] - 104*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + HPL[{1}, -S^2]*((359*Pi^4)/45 - 24*Pi^2*(1 + S^2) - (8*(-11 + 5*S^2 + 16*S^4))/S^2 + ((74*Pi^2)/3 - (12*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + 48*HPL[{2}, -S^2]^2 - (8*(-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/S^2 + (12*(-5 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - 168*HPL[{3, 1}, -S^2] + 344*HPL[{2, 1, 1}, -S^2] - 16*(1 + S^2)*Zeta[3])) + HPL[{0}, S^2]*((12046*Pi^6)/2835 + 780*(1 + S^2) + (2*Pi^2*(87 + 61*S^2))/3 + (56*HPL[{1}, -S^2]^6)/3 + ((61*Pi^2)/3 + (48*(1 + S^2))/S^2)*HPL[{2}, -S^2]^2 + (76*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((320*Pi^2)/9 + 120*HPL[{2}, -S^2]) - 8*HPL[{3}, -S^2]^2 + ((28*Pi^2)/3 + (72*(1 + S^2))/S^2)*HPL[{4}, -S^2] + 36*(1 + S^2)*HPL[{5}, -S^2] - 40*HPL[{6}, -S^2] - 344*HPL[{2, 1}, -S^2]^2 + ((-296*Pi^2)/3 - (240*(1 + S^2))/S^2)*HPL[{3, 1}, -S^2] + 16*(1 + S^2)*HPL[{3, 2}, -S^2] - 24*(1 + S^2)*HPL[{4, 1}, -S^2] + 12*HPL[{4, 2}, -S^2] - 40*HPL[{5, 1}, -S^2] + (176*Pi^2 + (480*(1 + S^2))/S^2)*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((937*Pi^4)/45 - 16*Pi^2*(1 + S^2) + (180*(1 + 2*S^2 + S^4))/S^2 + (90*Pi^2 + (120*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + 172*HPL[{2}, -S^2]^2 + (12*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 + 56*HPL[{4}, -S^2] - (120*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - 720*HPL[{3, 1}, -S^2] + 1440*HPL[{2, 1, 1}, -S^2]) + 192*(1 + S^2)*HPL[{2, 2, 1}, -S^2] + 624*(1 + S^2)*HPL[{3, 1, 1}, -S^2] - 48*HPL[{3, 1, 2}, -S^2] + 560*HPL[{3, 2, 1}, -S^2] + 2016*HPL[{4, 1, 1}, -S^2] - 480*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2] - 1664*HPL[{3, 1, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^3*((-16*Pi^2*(1 + S^2))/3 + (40*(1 + 2*S^2 + S^4))/S^2 + (40*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 + (32*HPL[{3}, -S^2])/3 - 480*HPL[{2, 1}, -S^2] - (112*Zeta[3])/3) - 8*(1 + 5*S^2)*Zeta[3] + 64*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-76*Pi^2*(1 + S^2))/3 - (120*(1 + 4*S^2 + 3*S^4))/S^2 + 32*Zeta[3]) + HPL[{3}, -S^2]*((14*Pi^2*(1 + S^2))/3 + (4*(9 + 12*S^2 + 11*S^4))/S^2 + 48*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{1}, -S^2]*((-26*Pi^4*(1 + S^2))/9 + (396*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(-29 - 10*S^2 + 19*S^4))/(3*S^2) + (24*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((20*Pi^2)/3 + (24*(1 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2] + (36*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 + 40*HPL[{5}, -S^2] + (-180*Pi^2 - (240*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (120*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 + 80*HPL[{3, 2}, -S^2] + 128*HPL[{4, 1}, -S^2] + (240*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 + 1376*HPL[{2, 2, 1}, -S^2] + 4192*HPL[{3, 1, 1}, -S^2] - 2880*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((240*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) - 40*HPL[{3}, -S^2] - 688*HPL[{2, 1}, -S^2] - 40*Zeta[3]) - 4*Pi^2*Zeta[3]) + HPL[{2}, -S^2]*((349*Pi^4)/45 + (116*Pi^2*(1 + S^2))/(3*S^2) + (4*(69 + 110*S^2 + 41*S^4))/S^2 - 8*(1 + S^2)*HPL[{3}, -S^2] + 16*HPL[{4}, -S^2] - 96*(1 + S^2)*HPL[{2, 1}, -S^2] - 352*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2] - (8*(1 + S^2)*Zeta[3])/S^2)) + HPL[{1}, -S^2]^2*((-37*Pi^4*(1 + S^2))/10 - (20*Pi^2*(-1 + S^4))/S^2 + (396*(1 + 2*S^2 + S^4))/S^2 + (24*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((-212*Pi^2)/3 - (24*(-1 + 8*S^2 + 9*S^4))/S^2)*HPL[{3}, -S^2] - (36*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 48*HPL[{5}, -S^2] + ((-172*Pi^2)/3 + (240*(-1 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (120*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + 688*HPL[{3, 2}, -S^2] + 2288*HPL[{4, 1}, -S^2] - (240*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 1376*HPL[{2, 2, 1}, -S^2] + 2528*HPL[{3, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-240*(-1 + S^4))/S^2 - (4*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - 344*HPL[{3}, -S^2] - 688*HPL[{2, 1}, -S^2] - 344*Zeta[3]) + ((-196*Pi^2)/3 - 240*(1 + S^2))*Zeta[3] - 440*Zeta[5]) + HPL[{2}, -S^2]*((-412*(-1 + S^4))/S^2 - (2*Pi^4*(-104 - 57*S^2 + 47*S^4))/(45*S^2) - (2*Pi^2*(-89 - 48*S^2 + 53*S^4))/(3*S^2) + ((-100*Pi^2)/3 + (8*(-1 + S^4))/S^2)*HPL[{3}, -S^2] + 16*(1 + S^2)*HPL[{4}, -S^2] - 92*HPL[{5}, -S^2] - 96*Pi^2*HPL[{2, 1}, -S^2] - (8*(1 + S^2)*(11 + 13*S^2)*HPL[{3, 1}, -S^2])/S^2 + 376*HPL[{3, 2}, -S^2] + 1184*HPL[{4, 1}, -S^2] + (192*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 - 736*HPL[{3, 1, 1}, -S^2] - 1472*HPL[{2, 1, 1, 1}, -S^2] - 36*Pi^2*Zeta[3] - 208*Zeta[5]) + HPL[{1}, -S^2]*((8699*Pi^6)/2268 - (37*Pi^4*(1 + S^2))/5 + (780*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(-89 - 70*S^2 + 19*S^4))/(3*S^2) + ((134*Pi^2)/3 + (48*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + 16*HPL[{3}, -S^2]^2 + ((-56*Pi^2)/3 - (72*(-1 + S^4))/S^2)*HPL[{4}, -S^2] - (4*(1 + S^2)*(-9 + 25*S^2)*HPL[{5}, -S^2])/S^2 + 140*HPL[{6}, -S^2] - 688*HPL[{2, 1}, -S^2]^2 + ((-112*Pi^2)/3 + (240*(-1 + S^4))/S^2)*HPL[{3, 1}, -S^2] + (16*(1 + S^2)*(1 + 11*S^2)*HPL[{3, 2}, -S^2])/S^2 + (24*(1 + S^2)*(-1 + 25*S^2)*HPL[{4, 1}, -S^2])/S^2 + 72*HPL[{4, 2}, -S^2] + 352*HPL[{5, 1}, -S^2] + ((344*Pi^2)/3 - (480*(-1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (192*(1 + S^2)^2*HPL[{2, 2, 1}, -S^2])/S^2 + (48*(1 + S^2)*(13 + 3*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - 448*HPL[{4, 1, 1}, -S^2] + (480*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + 448*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((-40*(-1 + 10*S^2 + 11*S^4))/S^2 - (2*Pi^2*(-7 + 24*S^2 + 31*S^4))/(3*S^2) + 688*HPL[{2, 1}, -S^2] - 48*Zeta[3]) + (-480*(1 + S^2) - (76*Pi^2*(1 + S^2))/3)*Zeta[3] + 8*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((480*(-1 + S^4))/S^2 + (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + 688*Zeta[3]) + HPL[{2}, -S^2]*((707*Pi^4)/90 - (432*(-1 + S^4))/S^2 - (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - (8*(1 + S^2)*(1 + 11*S^2)*HPL[{3}, -S^2])/S^2 - 56*HPL[{4}, -S^2] - (96*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - 688*HPL[{3, 1}, -S^2] + 1376*HPL[{2, 1, 1}, -S^2] - 96*(1 + S^2)*Zeta[3]) - 232*(1 + S^2)*Zeta[5])) + HPL[{0}, S^2]^2*(353 - 311*S^2 - (15271*Pi^6*S^2)/11340 + (Pi^2*(192 - 311*S^2))/6 - (13*Pi^4*(-16 + 79*S^2))/180 - (2*(1 + S^2)*HPL[{1}, -S^2]^6)/3 + (16*HPL[{1}, -S^2]^7)/21 - ((-5 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^5*((106*Pi^2)/45 - 4*(1 + S^2) + (86*HPL[{2}, -S^2])/15) + ((-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2]^2)/S^2 + ((85*Pi^2)/6 + 6*(1 + S^2))*HPL[{5}, -S^2] - (20*(1 + S^2)*(-2 + 3*S^2)*HPL[{6}, -S^2])/S^2 + 275*HPL[{7}, -S^2] - (4*(1 + S^2)*(6 + S^2)*HPL[{2, 1}, -S^2]^2)/S^2 + ((17*Pi^2)/6 + 2*(1 + S^2))*HPL[{3, 2}, -S^2] + (2*Pi^2 - 8*(1 + S^2))*HPL[{4, 1}, -S^2] + (2*(1 + S^2)*HPL[{4, 2}, -S^2])/S^2 - 52*HPL[{4, 3}, -S^2] + (2*(1 + S^2)*(-11 + 10*S^2)*HPL[{5, 1}, -S^2])/S^2 - 153*HPL[{5, 2}, -S^2] - 428*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-343*Pi^4)/90 + 2*Pi^2*(1 + S^2) + (4*(-22 + 5*S^4))/S^2 + 120*HPL[{3, 1}, -S^2] + 208*HPL[{2, 1, 1}, -S^2]) + 30*Pi^2*HPL[{2, 2, 1}, -S^2] + ((256*Pi^2)/3 + 8*(1 + S^2))*HPL[{3, 1, 1}, -S^2] - (2*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 - (2*(1 + S^2)*(-19 + 4*S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + 5*HPL[{3, 2, 2}, -S^2] - 32*HPL[{3, 3, 1}, -S^2] - (8*(1 + S^2)*(-19 + 5*S^2)*HPL[{4, 1, 1}, -S^2])/S^2 - 32*HPL[{4, 1, 2}, -S^2] - 152*HPL[{4, 2, 1}, -S^2] - 332*HPL[{5, 1, 1}, -S^2] - 56*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 208*HPL[{2, 2, 2, 1}, -S^2] + (8*(1 + S^2)*(-16 + 3*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + 644*HPL[{3, 1, 1, 2}, -S^2] + 644*HPL[{3, 1, 2, 1}, -S^2] + 1268*HPL[{3, 2, 1, 1}, -S^2] + 3840*HPL[{4, 1, 1, 1}, -S^2] - (48*(-5 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - 416*HPL[{2, 1, 2, 1, 1}, -S^2] - 1248*HPL[{2, 2, 1, 1, 1}, -S^2] - 2192*HPL[{3, 1, 1, 1, 1}, -S^2] - 736*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*((19 + 14*S^2 - 17*S^4)/S^2 + (Pi^2*(7 - 4*S^2 - 11*S^4))/(3*S^2) - 28*HPL[{2, 1}, -S^2] - 50*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-4*Pi^2*(-5 - 4*S^2 + S^4))/S^2 - (16*(-11 - 12*S^2 + 2*S^4))/S^2 - 32*Zeta[3]) + HPL[{1}, -S^2]^4*(-2*Pi^2*(1 + S^2) - (5*(-1 + 2*S^2 + 3*S^4))/S^2 - ((-5 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 - 2*HPL[{3}, -S^2] - (86*HPL[{2, 1}, -S^2])/3 - (8*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(12 + 13*S^2 + S^4))/(6*S^2) + (37 + 56*S^2 + 7*S^4)/(2*S^2) + HPL[{3}, -S^2] - 26*HPL[{2, 1}, -S^2] - Zeta[3]) + 6*(1 + 2*S^2)*Zeta[3] - 20*S^2*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((Pi^2*(-31 - 25*S^2 + 6*S^4))/(3*S^2) + (2*(-44 - 51*S^2 + 10*S^4))/S^2 + 32*Zeta[3]) + HPL[{1}, -S^2]^3*((359*Pi^4)/135 - 8*Pi^2*(1 + S^2) - (8*(-11 + 5*S^2 + 16*S^4))/(3*S^2) + ((74*Pi^2)/9 - (4*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + 16*HPL[{2}, -S^2]^2 - (8*(-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(3*S^2) + (4*(-5 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - 56*HPL[{3, 1}, -S^2] + (344*HPL[{2, 1, 1}, -S^2])/3 - (16*(1 + S^2)*Zeta[3])/3) + HPL[{3}, -S^2]*((59*Pi^4)/120 + (Pi^2*(1 + S^2))/3 + (19 + 6*S^2 - 5*S^4)/S^2 + 26*HPL[{4}, -S^2] + (4*(1 + S^2)*(1 + 2*S^2)*HPL[{2, 1}, -S^2])/S^2 + 24*HPL[{3, 1}, -S^2] - 16*HPL[{2, 1, 1}, -S^2] + 2*(1 + S^2)*Zeta[3]) + HPL[{1}, -S^2]^2*((-349*Pi^4*(1 + S^2))/180 + (187 + 10*S^2 - 177*S^4)/(2*S^2) + (Pi^2*(5 - 14*S^2 - 19*S^4))/S^2 + ((1 + S^2)*(6 + S^2)*HPL[{2}, -S^2]^2)/S^2 + (-Pi^2 - (8*(-1 + S^4))/S^2)*HPL[{3}, -S^2] - (2*(-4 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + 6*HPL[{5}, -S^2] + ((-74*Pi^2)/3 + (12*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (4*(-8 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + 12*HPL[{3, 2}, -S^2] + 36*HPL[{4, 1}, -S^2] - (12*(-5 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 192*HPL[{2, 2, 1}, -S^2] + 552*HPL[{3, 1, 1}, -S^2] - 344*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(10 + 7*S^2 - 3*S^4))/(2*S^2) - (12*(-5 - 4*S^2 + S^4))/S^2 - 6*HPL[{3}, -S^2] - 96*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + (Pi^2 - 16*(1 + S^2))*Zeta[3]) + HPL[{2}, -S^2]*((Pi^4*(104 + 57*S^2 - 47*S^4))/(90*S^2) + (98 + 144*S^2 - 23*S^4)/S^2 + (Pi^2*(89 + 96*S^2 - 22*S^4))/(6*S^2) - (5*Pi^2*HPL[{3}, -S^2])/3 - (2*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 26*HPL[{5}, -S^2] - 15*Pi^2*HPL[{2, 1}, -S^2] - (4*(1 + S^2)*(6 + S^2)*HPL[{3, 1}, -S^2])/S^2 - 4*HPL[{3, 2}, -S^2] + 16*HPL[{4, 1}, -S^2] + (8*(1 + S^2)*(6 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 104*HPL[{2, 2, 1}, -S^2] - 328*HPL[{3, 1, 1}, -S^2] - 208*HPL[{2, 1, 1, 1}, -S^2] + ((-19*Pi^2)/3 + (4*(1 + S^2))/S^2)*Zeta[3] - 58*Zeta[5]) + HPL[{1}, -S^2]*((8699*Pi^6)/9072 - (349*Pi^4*(1 + S^2))/90 + (Pi^2*(89 - 81*S^2 - 170*S^4))/(6*S^2) - (59*(-3 - S^2 + 2*S^4))/S^2 + ((79*Pi^2)/12 + (2*(6 + 7*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + (23*HPL[{2}, -S^2]^3)/3 - 6*HPL[{3}, -S^2]^2 + (2*Pi^2 - (4*(-4 - 3*S^2 + S^4))/S^2)*HPL[{4}, -S^2] - ((1 + S^2)*(-9 + 5*S^2)*HPL[{5}, -S^2])/S^2 + 64*HPL[{6}, -S^2] - 96*HPL[{2, 1}, -S^2]^2 + ((-73*Pi^2)/3 + (8*(-8 - 7*S^2 + S^4))/S^2)*HPL[{3, 1}, -S^2] + ((1 + S^2)*(5 + 9*S^2)*HPL[{3, 2}, -S^2])/S^2 + (4*(1 + S^2)*(-1 + 7*S^2)*HPL[{4, 1}, -S^2])/S^2 - 36*HPL[{5, 1}, -S^2] + ((148*Pi^2)/3 - (24*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (8*(1 + S^2)*(6 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (8*(1 + S^2)*(20 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + 184*HPL[{3, 2, 1}, -S^2] + 552*HPL[{4, 1, 1}, -S^2] + (24*(-5 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - 336*HPL[{3, 1, 1, 1}, -S^2] + 688*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((15 - 2*S^2 - 17*S^4)/S^2 - (7*Pi^2*(-1 + S^4))/(6*S^2) + 12*HPL[{2, 1}, -S^2] - 12*Zeta[3]) + (-9*Pi^2*(1 + S^2) - (2*(-1 + 14*S^2 + 15*S^4))/S^2)*Zeta[3] + 2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((24*(-5 - 4*S^2 + S^4))/S^2 + (Pi^2*(-10 - 7*S^2 + 3*S^4))/S^2 + 16*Zeta[3]) + HPL[{2}, -S^2]*((473*Pi^4)/180 + (109 + 86*S^2 - 23*S^4)/S^2 + (Pi^2*(10 + 7*S^2 - 3*S^4))/S^2 - (2*(1 + S^2)*(1 + 2*S^2)*HPL[{3}, -S^2])/S^2 + 12*HPL[{4}, -S^2] - (4*(1 + S^2)*(6 + S^2)*HPL[{2, 1}, -S^2])/S^2 - 104*HPL[{3, 1}, -S^2] + 192*HPL[{2, 1, 1}, -S^2] + (2*(1 + S^2)*Zeta[3])/S^2) - 52*(1 + S^2)*Zeta[5])) + HPL[{1}, -S^2]^2*((-4447*Pi^6*(1 + S^2))/7560 + (Pi^4*(104 - 125*S^2 - 229*S^4))/(45*S^2) + (755*(1 + 2*S^2 + S^4))/S^2 + (7*Pi^2*(55 + 58*S^2 + 3*S^4))/(6*S^2) - (10*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) + (2*(1 + S^2)^2*HPL[{3}, -S^2]^2)/S^2 + (-2*Pi^2 - (4*(-9 + 16*S^2 + 25*S^4))/S^2)*HPL[{5}, -S^2] - (30*(1 + S^2)*(-2 + 3*S^2)*HPL[{6}, -S^2])/S^2 + 288*HPL[{7}, -S^2] - (48*(1 + S^2)^2*HPL[{2, 1}, -S^2]^2)/S^2 + ((184*Pi^2)/3 + (16*(1 + 12*S^2 + 11*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((608*Pi^2)/3 + (24*(-1 + 24*S^2 + 25*S^4))/S^2)*HPL[{4, 1}, -S^2] + (6*(1 + S^2)^2*HPL[{4, 2}, -S^2])/S^2 - 44*HPL[{4, 3}, -S^2] + (4*(1 + S^2)*(-11 + 23*S^2)*HPL[{5, 1}, -S^2])/S^2 - 120*HPL[{5, 2}, -S^2] - 300*HPL[{6, 1}, -S^2] + ((536*Pi^2)/3 + (192*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((1184*Pi^2)/3 + (48*(13 + 16*S^2 + 3*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] - (80*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 - 696*HPL[{3, 2, 2}, -S^2] - 2144*HPL[{3, 3, 1}, -S^2] - (312*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 - 2120*HPL[{4, 1, 2}, -S^2] - 6536*HPL[{4, 2, 1}, -S^2] - 13344*HPL[{5, 1, 1}, -S^2] + ((-344*Pi^2)/3 + (480*(-1 + S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (240*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + 1376*HPL[{3, 1, 1, 2}, -S^2] + 1376*HPL[{3, 1, 2, 1}, -S^2] + 1376*HPL[{3, 2, 1, 1}, -S^2] + 4576*HPL[{4, 1, 1, 1}, -S^2] - (480*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - 2752*HPL[{2, 1, 2, 1, 1}, -S^2] - 8256*HPL[{2, 2, 1, 1, 1}, -S^2] - 16960*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1}, -S^2]*((-480*(-1 + S^4))/S^2 - (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - 688*Zeta[3]) + HPL[{2}, -S^2]^2*((48*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) - 96*HPL[{3}, -S^2] - 76*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(17 + 6*S^2 - 11*S^4))/(3*S^2) - (16*(-4 + S^2 + 5*S^4))/S^2 + 56*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + ((-157*Pi^4)/45 - (76*Pi^2*(1 + S^2))/3 - (4*(1 + 110*S^2 + 109*S^4))/S^2)*Zeta[3] - 4*(1 + S^2)*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((2*Pi^2*(-31 - 14*S^2 + 17*S^4))/(3*S^2) + (8*(-29 + 2*S^2 + 31*S^4))/S^2 + 352*Zeta[3]) + HPL[{2, 1}, -S^2]*((-707*Pi^4)/90 + (432*(-1 + S^4))/S^2 + (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + 688*HPL[{3, 1}, -S^2] + 1376*HPL[{2, 1, 1}, -S^2] + 96*(1 + S^2)*Zeta[3]) + HPL[{3}, -S^2]*((-196*Pi^4)/45 - (16*(-2 + 23*S^2 + 25*S^4))/S^2 - (2*Pi^2*(-7 + 24*S^2 + 31*S^4))/(3*S^2) + 28*HPL[{4}, -S^2] + (8*(1 + S^2)*(1 + 11*S^2)*HPL[{2, 1}, -S^2])/S^2 + 352*HPL[{3, 1}, -S^2] - 688*HPL[{2, 1, 1}, -S^2] - (4*(-1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^4*(416 + 207*S^2 - 209*S^4))/(180*S^2) - (364*(-1 + S^4))/S^2 - (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + ((-92*Pi^2)/3 - (8*(1 + 12*S^2 + 11*S^4))/S^2)*HPL[{3}, -S^2] - (2*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 - 40*HPL[{5}, -S^2] + ((-268*Pi^2)/3 - (96*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (48*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 + 360*HPL[{3, 2}, -S^2] + 1096*HPL[{4, 1}, -S^2] + (96*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 - 688*HPL[{3, 1, 1}, -S^2] - 1376*HPL[{2, 1, 1, 1}, -S^2] + ((-94*Pi^2)/3 - 96*(1 + S^2))*Zeta[3] - 172*Zeta[5]) + ((-110*Pi^2)/3 - 232*(1 + S^2))*Zeta[5] - 300*Zeta[7]) + HPL[{2}, -S^2]*((Pi^4*(1238 + 912*S^2 - 565*S^4))/(180*S^2) + (Pi^6*(182 + 81*S^2 - 101*S^4))/(405*S^2) + (Pi^2*(67 + 48*S^2 - 42*S^4))/S^2 - (622*(-1 + S^4))/S^2 + (2*(1 + S^2)*(-1 + 2*S^2)*HPL[{3}, -S^2]^2)/S^2 + ((-49*Pi^2)/3 + (4*(4 + 7*S^2 + 3*S^4))/S^2)*HPL[{5}, -S^2] - (8*(1 + S^2)*(6 + 5*S^2)*HPL[{6}, -S^2])/S^2 - 522*HPL[{7}, -S^2] + (40*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S^2 + (30*Pi^2 + (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{3, 2}, -S^2] + (104*Pi^2 - (16*(-1 + S^4))/S^2)*HPL[{4, 1}, -S^2] + (4*(1 + S^2)^2*HPL[{4, 2}, -S^2])/S^2 + 84*HPL[{4, 3}, -S^2] - (4*(-4 + S^2)*(1 + S^2)*HPL[{5, 1}, -S^2])/S^2 + 258*HPL[{5, 2}, -S^2] + 872*HPL[{6, 1}, -S^2] + (104*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + ((-512*Pi^2)/3 + (16*(-1 + S^4))/S^2)*HPL[{3, 1, 1}, -S^2] - (4*(1 + S^2)^2*HPL[{3, 1, 2}, -S^2])/S^2 + (60*(1 + S^2)^2*HPL[{3, 2, 1}, -S^2])/S^2 - 416*HPL[{3, 2, 2}, -S^2] - 1168*HPL[{3, 3, 1}, -S^2] + (32*(1 + S^2)*(6 + 7*S^2)*HPL[{4, 1, 1}, -S^2])/S^2 - 1168*HPL[{4, 1, 2}, -S^2] - 3424*HPL[{4, 2, 1}, -S^2] - 6952*HPL[{5, 1, 1}, -S^2] - 192*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 832*HPL[{2, 2, 2, 1}, -S^2] + (16*(1 + S^2)*(-131 + 107*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - 1744*HPL[{3, 1, 1, 2}, -S^2] - 1744*HPL[{3, 1, 2, 1}, -S^2] - 4240*HPL[{3, 2, 1, 1}, -S^2] - 12608*HPL[{4, 1, 1, 1}, -S^2] + (384*(1 + S^2)^2*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - 1472*HPL[{3, 1, 1, 1, 1}, -S^2] - 2944*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1}, -S^2]*((96*(3 + 8*S^2 + 3*S^4))/S^2 + (8*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) - 320*Zeta[3]) + ((-157*Pi^4)/45 + (4*Pi^2*(1 + S^2))/(3*S^2) - (8*(2 + 15*S^4))/S^2)*Zeta[3] - (8*(1 + S^2)*Zeta[3]^2)/S^2 + HPL[{4}, -S^2]*((2*Pi^2*(1 + 2*S^2 + S^4))/(3*S^2) + (2*(-1 + 16*S^2 + 7*S^4))/S^2 - 16*HPL[{2, 1}, -S^2] + 40*Zeta[3]) + HPL[{3, 1}, -S^2]*((-2*Pi^2*(23 + 38*S^2 + 15*S^4))/(3*S^2) - (8*(17 + 48*S^2 + 19*S^4))/S^2 + 128*Zeta[3]) + HPL[{3}, -S^2]*((-31*Pi^4)/15 + (2*Pi^2*(-1 + S^4))/(3*S^2) - (2*(7 + 61*S^4))/S^2 - 36*HPL[{4}, -S^2] + (4*(1 + S^2)*(-1 + 19*S^2)*HPL[{2, 1}, -S^2])/S^2 + 168*HPL[{3, 1}, -S^2] - 400*HPL[{2, 1, 1}, -S^2] + 8*(1 + S^2)*Zeta[3]) + HPL[{2, 1}, -S^2]*((-707*Pi^4)/90 - (136*(1 + S^4))/S^2 + 16*HPL[{3, 1}, -S^2] + 80*(1 + S^2)*Zeta[3]) + ((-110*Pi^2)/3 + (16*(1 + S^2))/S^2)*Zeta[5] - 300*Zeta[7]) + HPL[{1}, -S^2]*((20621*Pi^8)/54432 - (4447*Pi^6*(1 + S^2))/3780 + (Pi^4*(1238 + 51*S^2 - 1187*S^4))/(180*S^2) + (1526*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(372 + 449*S^2 + 77*S^4))/(3*S^2) + ((23*Pi^2)/9 - (20*(-1 + S^4))/(3*S^2))*HPL[{2}, -S^2]^3 + (23*HPL[{2}, -S^2]^4)/3 + ((-2*Pi^2)/3 + (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2]^2 + 64*HPL[{4}, -S^2]^2 + (33*Pi^2 - (60*(-2 + S^2 + 3*S^4))/S^2)*HPL[{6}, -S^2] - (12*(1 + S^2)*(-25 + 16*S^2)*HPL[{7}, -S^2])/S^2 + 1542*HPL[{8}, -S^2] + ((-268*Pi^2)/3 - (96*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2]^2 + 432*HPL[{3, 1}, -S^2]^2 + (6*Pi^2 + (12*(1 + 2*S^2 + S^4))/S^2)*HPL[{4, 2}, -S^2] - (4*(1 + S^2)*(-6 + 5*S^2)*HPL[{4, 3}, -S^2])/S^2 + ((52*Pi^2)/3 + (8*(-11 + 12*S^2 + 23*S^4))/S^2)*HPL[{5, 1}, -S^2] - (6*(1 + S^2)*(-13 + 7*S^2)*HPL[{5, 2}, -S^2])/S^2 + 12*HPL[{5, 3}, -S^2] + 140*(1 + S^2)*HPL[{6, 1}, -S^2] + 30*HPL[{6, 2}, -S^2] - 832*HPL[{7, 1}, -S^2] + 1376*HPL[{2, 1, 1}, -S^2]^2 + ((184*Pi^2)/3 - (160*(-1 + S^4))/S^2)*HPL[{3, 2, 1}, -S^2] - (16*(1 + S^2)*(-1 + 9*S^2)*HPL[{3, 2, 2}, -S^2])/S^2 - (32*(1 + S^2)*(-1 + 14*S^2)*HPL[{3, 3, 1}, -S^2])/S^2 - 56*HPL[{3, 3, 2}, -S^2] + ((440*Pi^2)/3 - (624*(-1 + S^4))/S^2)*HPL[{4, 1, 1}, -S^2] - (20*(1 + S^2)*(-1 + 23*S^2)*HPL[{4, 1, 2}, -S^2])/S^2 + 136*HPL[{4, 1, 3}, -S^2] - (4*(1 + S^2)*(-17 + 343*S^2)*HPL[{4, 2, 1}, -S^2])/S^2 - 80*HPL[{4, 2, 2}, -S^2] + 104*HPL[{4, 3, 1}, -S^2] - (8*(1 + S^2)*(-27 + 367*S^2)*HPL[{5, 1, 1}, -S^2])/S^2 + 16*HPL[{5, 1, 2}, -S^2] + 496*HPL[{5, 2, 1}, -S^2] + 1720*HPL[{6, 1, 1}, -S^2] + (160*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((-224*Pi^2)/3 + (480*(-1 + S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] - (128*(-4 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (128*(-4 + S^2)*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + 48*HPL[{3, 1, 2, 2}, -S^2] - (32*(1 + S^2)*(-31 + 19*S^2)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + 48*HPL[{3, 2, 1, 2}, -S^2] - 80*HPL[{3, 2, 2, 1}, -S^2] - 384*HPL[{3, 3, 1, 1}, -S^2] - (48*(1 + S^2)*(-59 + 35*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + 144*HPL[{4, 1, 1, 2}, -S^2] - 240*HPL[{4, 1, 2, 1}, -S^2] - 1008*HPL[{4, 2, 1, 1}, -S^2] - 1600*HPL[{5, 1, 1, 1}, -S^2] + ((688*Pi^2)/3 - (960*(-1 + S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - (384*(1 + S^2)^2*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (1152*(1 + S^2)^2*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (96*(1 + S^2)*(19 + 29*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - 896*HPL[{4, 1, 1, 1, 1}, -S^2] + (960*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + 896*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + HPL[{3, 1, 1}, -S^2]*((4*Pi^2*(79 + 90*S^2 + 11*S^4))/(3*S^2) + (16*(77 + 94*S^2 + 17*S^4))/S^2 - 1920*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((384*(1 + 2*S^2 + S^4))/S^2 + (8*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) - 608*Zeta[3]) + HPL[{5}, -S^2]*((-2*Pi^2*(-3 + 2*S^2 + 5*S^4))/S^2 - (2*(-37 + 62*S^2 + 99*S^4))/S^2 + 80*HPL[{2, 1}, -S^2] - 112*Zeta[3]) + ((4*Pi^2)/3 - 8*(1 + S^2))*Zeta[3]^2 + HPL[{3, 2}, -S^2]*((32*(1 + 12*S^2 + 11*S^4))/S^2 + (Pi^2*(9 + 62*S^2 + 53*S^4))/(3*S^2) + 96*Zeta[3]) + HPL[{4, 1}, -S^2]*((32*(-1 + 37*S^2 + 38*S^4))/S^2 + (2*Pi^2*(-5 + 84*S^2 + 89*S^4))/(3*S^2) + 320*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((960*(-1 + S^4))/S^2 + (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + 1376*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((707*Pi^4)/45 - (864*(-1 + S^4))/S^2 - (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - 192*(1 + S^2)*Zeta[3]) + HPL[{2}, -S^2]^2*((263*Pi^4)/72 + (86*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) - 20*(1 + S^2)*HPL[{3}, -S^2] - 8*HPL[{4}, -S^2] + (20*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + 8*HPL[{3, 1}, -S^2] - 20*(1 + S^2)*Zeta[3]) + HPL[{4}, -S^2]*((-56*Pi^4)/45 - (2*Pi^2*(-17 - 6*S^2 + 11*S^4))/(3*S^2) - (2*(-55 + 24*S^2 + 79*S^4))/S^2 + (4*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - 24*HPL[{3, 1}, -S^2] - 112*HPL[{2, 1, 1}, -S^2] - (4*(1 + 4*S^2 + 3*S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((-59*Pi^4)/10 + (4*Pi^2*(-31 - 14*S^2 + 17*S^4))/(3*S^2) + (24*(-17 + 2*S^2 + 19*S^4))/S^2 - 1376*HPL[{2, 1, 1}, -S^2] + (8*(-1 + 10*S^2 + 11*S^4)*Zeta[3])/S^2) + Zeta[3]*((-157*Pi^4*(1 + S^2))/45 - (2*Pi^2*(-1 + 74*S^2 + 75*S^4))/(3*S^2) - (2*(11 + 386*S^2 + 375*S^4))/S^2 - 128*Zeta[5]) + HPL[{3}, -S^2]*((Pi^2*(25 - 102*S^2 - 127*S^4))/(3*S^2) + (Pi^4*(5 - 12*S^2 - 17*S^4))/(10*S^2) - (2*(-25 + 314*S^2 + 339*S^4))/S^2 + (4*(1 + S^2)*(-4 + 3*S^2)*HPL[{4}, -S^2])/S^2 - 140*HPL[{5}, -S^2] + ((184*Pi^2)/3 + (16*(1 + 12*S^2 + 11*S^4))/S^2)*HPL[{2, 1}, -S^2] + (8*(1 + S^2)*(-1 + 9*S^2)*HPL[{3, 1}, -S^2])/S^2 + 16*HPL[{3, 2}, -S^2] - 56*HPL[{4, 1}, -S^2] - (16*(1 + S^2)*(1 + 11*S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 768*HPL[{2, 2, 1}, -S^2] - 2240*HPL[{3, 1, 1}, -S^2] + 1376*HPL[{2, 1, 1, 1}, -S^2] + (-8*Pi^2 - (8*(-1 + S^4))/S^2)*Zeta[3] - 64*Zeta[5]) + ((-110*Pi^2*(1 + S^2))/3 - (8*(-1 + 56*S^2 + 57*S^4))/S^2)*Zeta[5] + HPL[{2, 1}, -S^2]*((728*(-1 + S^4))/S^2 + (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + (Pi^4*(-416 - 207*S^2 + 209*S^4))/(90*S^2) + (96*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 - 720*HPL[{3, 2}, -S^2] - 2192*HPL[{4, 1}, -S^2] + (192*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 + 1376*HPL[{3, 1, 1}, -S^2] - 2752*HPL[{2, 1, 1, 1}, -S^2] + ((188*Pi^2)/3 + 192*(1 + S^2))*Zeta[3] + 344*Zeta[5]) + HPL[{2}, -S^2]*((2047*Pi^6)/2520 + (Pi^4*(416 + 207*S^2 - 209*S^4))/(90*S^2) + (Pi^2*(217 + 86*S^2 - 131*S^4))/(3*S^2) - (590*(-1 + S^4))/S^2 - 4*HPL[{3}, -S^2]^2 + ((-2*Pi^2)/3 - (4*(1 + 2*S^2 + S^4))/S^2)*HPL[{4}, -S^2] - (20*(-1 + S^2)*(1 + S^2)*HPL[{5}, -S^2])/S^2 + 158*HPL[{6}, -S^2] + (-92*Pi^2 - (96*(1 + 2*S^2 + S^4))/S^2)*HPL[{3, 1}, -S^2] + (4*(1 + S^2)*(-1 + 19*S^2)*HPL[{3, 2}, -S^2])/S^2 + (4*(1 + S^2)*(-1 + 59*S^2)*HPL[{4, 1}, -S^2])/S^2 + 48*HPL[{4, 2}, -S^2] + 96*HPL[{5, 1}, -S^2] + ((536*Pi^2)/3 + (192*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (80*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (64*(-4 + S^2)*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - 48*HPL[{3, 1, 2}, -S^2] + 688*HPL[{3, 2, 1}, -S^2] + 2096*HPL[{4, 1, 1}, -S^2] - (192*(1 + S^2)^2*HPL[{2, 1, 1, 1}, -S^2])/S^2 - 1376*HPL[{3, 1, 1, 1}, -S^2] + 2752*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((-16*(1 + 12*S^2 + 11*S^4))/S^2 - (2*Pi^2*(2 + 15*S^2 + 13*S^4))/(3*S^2) + 384*HPL[{2, 1}, -S^2] - 48*Zeta[3]) + (-192*(1 + S^2) - (2*Pi^2*(-1 + 11*S^2 + 12*S^4))/(3*S^2))*Zeta[3] + 12*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-192*(1 + 2*S^2 + S^4))/S^2 - (4*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) + 304*Zeta[3]) - (4*(-2 + 17*S^2 + 19*S^4)*Zeta[5])/S^2) - 300*(1 + S^2)*Zeta[7]) + HPL[{0}, S^2]*((179327*Pi^8)/170100 + 1526*(1 + S^2) + (Pi^4*(609 + 491*S^2))/90 + (Pi^2*(745 + 678*S^2))/6 + (2*HPL[{1}, -S^2]^8)/3 + ((53*Pi^2)/18 + (20*(1 + S^2))/(3*S^2))*HPL[{2}, -S^2]^3 + (23*HPL[{2}, -S^2]^4)/6 + HPL[{1}, -S^2]^6*((64*Pi^2)/27 + 8*HPL[{2}, -S^2]) + ((-8*Pi^2)/3 - (4*(1 + S^2))/S^2)*HPL[{3}, -S^2]^2 + 56*HPL[{4}, -S^2]^2 + (-45*Pi^2 + (120*(1 + S^2))/S^2)*HPL[{6}, -S^2] + 300*(1 + S^2)*HPL[{7}, -S^2] - 1050*HPL[{8}, -S^2] + ((-122*Pi^2)/3 - (96*(1 + S^2))/S^2)*HPL[{2, 1}, -S^2]^2 + 200*HPL[{3, 1}, -S^2]^2 + ((2*Pi^2)/3 + (12*(1 + S^2))/S^2)*HPL[{4, 2}, -S^2] + 24*(1 + S^2)*HPL[{4, 3}, -S^2] + ((44*Pi^2)/3 - (88*(1 + S^2))/S^2)*HPL[{5, 1}, -S^2] + 78*(1 + S^2)*HPL[{5, 2}, -S^2] - 12*HPL[{6, 2}, -S^2] + 456*HPL[{7, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]^2 + HPL[{1}, -S^2]^4*((937*Pi^4)/270 - (8*Pi^2*(1 + S^2))/3 + (30*(1 + 2*S^2 + S^4))/S^2 + (15*Pi^2 + (20*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + (86*HPL[{2}, -S^2]^2)/3 + (2*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 + (28*HPL[{4}, -S^2])/3 - (20*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - 120*HPL[{3, 1}, -S^2] + 240*HPL[{2, 1, 1}, -S^2]) - (14*Pi^2*HPL[{3, 1, 2}, -S^2])/3 + (66*Pi^2 + (160*(1 + S^2))/S^2)*HPL[{3, 2, 1}, -S^2] + 16*(1 + S^2)*HPL[{3, 2, 2}, -S^2] + 32*(1 + S^2)*HPL[{3, 3, 1}, -S^2] + 64*HPL[{3, 3, 2}, -S^2] + ((692*Pi^2)/3 + (624*(1 + S^2))/S^2)*HPL[{4, 1, 1}, -S^2] + 20*(1 + S^2)*HPL[{4, 1, 2}, -S^2] - 128*HPL[{4, 1, 3}, -S^2] + 68*(1 + S^2)*HPL[{4, 2, 1}, -S^2] + 70*HPL[{4, 2, 2}, -S^2] - 256*HPL[{4, 3, 1}, -S^2] + 216*(1 + S^2)*HPL[{5, 1, 1}, -S^2] - 116*HPL[{5, 1, 2}, -S^2] - 1076*HPL[{5, 2, 1}, -S^2] - 2960*HPL[{6, 1, 1}, -S^2] - 160*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2] + ((-592*Pi^2)/3 - (480*(1 + S^2))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + 512*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2] + 512*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2] - 24*HPL[{3, 1, 2, 2}, -S^2] + 992*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2] - 24*HPL[{3, 2, 1, 2}, -S^2] - 568*HPL[{3, 2, 2, 1}, -S^2] - 1632*HPL[{3, 3, 1, 1}, -S^2] + 2832*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2] + 24*HPL[{4, 1, 1, 2}, -S^2] - 1608*HPL[{4, 1, 2, 1}, -S^2] - 4872*HPL[{4, 2, 1, 1}, -S^2] - 9872*HPL[{5, 1, 1, 1}, -S^2] + (352*Pi^2 + (960*(1 + S^2))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - 384*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2] - 1152*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2] - 1216*HPL[{2, 2, 1, 2, 1}, -S^2] - 3648*HPL[{2, 2, 2, 1, 1}, -S^2] - 1824*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2] + 7200*HPL[{3, 1, 1, 1, 2}, -S^2] + 12064*HPL[{3, 1, 1, 2, 1}, -S^2] + 14496*HPL[{3, 1, 2, 1, 1}, -S^2] + 30304*HPL[{3, 2, 1, 1, 1}, -S^2] + 91584*HPL[{4, 1, 1, 1, 1}, -S^2] - 960*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 3328*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 5760*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^5*((-8*Pi^2*(1 + S^2))/15 + (4*(1 + 2*S^2 + S^4))/S^2 + (4*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 + (16*HPL[{3}, -S^2])/15 - 48*HPL[{2, 1}, -S^2] - (56*Zeta[3])/15) + (64*Pi^2*Zeta[3]^2)/3 + HPL[{4, 1}, -S^2]*(-8*Pi^2*(1 + S^2) - (4*(11 + 9*S^2 + 5*S^4))/S^2 + 8*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*(20*Pi^2*(1 + S^2) + (16*(5 + 24*S^2 + 19*S^4))/S^2 + 16*Zeta[3]) + HPL[{3, 2}, -S^2]*((5*Pi^2*(1 + S^2))/3 + (2*(3 + 16*S^2 + 19*S^4))/S^2 + 56*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((-152*Pi^2*(1 + S^2))/3 - (240*(1 + 4*S^2 + 3*S^4))/S^2 + 64*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((208*Pi^2*(1 + S^2))/3 + (8*(39 + 156*S^2 + 125*S^4))/S^2 + 112*Zeta[3]) + HPL[{5}, -S^2]*((38*Pi^2*(1 + S^2))/3 + (2*(30 + 33*S^2 + 52*S^4))/S^2 + 112*HPL[{2, 1}, -S^2] + 168*Zeta[3]) + HPL[{1}, -S^2]^3*((-26*Pi^4*(1 + S^2))/27 + (132*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(-29 - 10*S^2 + 19*S^4))/(9*S^2) + (8*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((20*Pi^2)/9 + (8*(1 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2] + (12*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 + (40*HPL[{5}, -S^2])/3 + (-60*Pi^2 - (80*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (40*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 + (80*HPL[{3, 2}, -S^2])/3 + (128*HPL[{4, 1}, -S^2])/3 + (80*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 + (1376*HPL[{2, 2, 1}, -S^2])/3 + (4192*HPL[{3, 1, 1}, -S^2])/3 - 960*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((80*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(29 + 48*S^2 + 19*S^4))/(9*S^2) - (40*HPL[{3}, -S^2])/3 - (688*HPL[{2, 1}, -S^2])/3 - (40*Zeta[3])/3) - (4*Pi^2*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*((698*Pi^4)/45 + (232*Pi^2*(1 + S^2))/(3*S^2) + (8*(69 + 110*S^2 + 41*S^4))/S^2 - (16*(1 + S^2)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((33*Pi^4)/20 + (23*Pi^2*(1 + S^2))/(3*S^2) + (59 + 86*S^2 + 27*S^4)/S^2 + 2*(1 + S^2)*HPL[{3}, -S^2] - 8*HPL[{4}, -S^2] - 20*(1 + S^2)*HPL[{2, 1}, -S^2] - 68*HPL[{3, 1}, -S^2] + 152*HPL[{2, 1, 1}, -S^2] - (2*(1 + S^2)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((-328*Pi^4)/45 - (40*Pi^2*(1 + S^2))/S^2 - (4*(61 + 110*S^2 + 33*S^4))/S^2 - 704*HPL[{2, 1, 1}, -S^2] + (8*(1 + 3*S^2 + 2*S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((-187*Pi^4)/180 + (12*Pi^2*(1 + S^2))/S^2 - (14*(-7 - 8*S^2 + S^4))/S^2 - 8*(1 + S^2)*HPL[{2, 1}, -S^2] - 80*HPL[{3, 1}, -S^2] + 32*HPL[{2, 1, 1}, -S^2] - (4*(-1 + 3*S^2 + 4*S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*((12907*Pi^6)/5670 - (26*Pi^4*(1 + S^2))/9 + (390*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(43 + 44*S^2 + S^4))/(3*S^2) + ((62*Pi^2)/3 + (24*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + (76*HPL[{2}, -S^2]^3)/3 - 4*HPL[{3}, -S^2]^2 + ((20*Pi^2)/3 + (36*(1 + 2*S^2 + S^4))/S^2)*HPL[{4}, -S^2] + (18*(1 + S^2)^2*HPL[{5}, -S^2])/S^2 - 344*HPL[{2, 1}, -S^2]^2 + ((-268*Pi^2)/3 - (120*(1 + 2*S^2 + S^4))/S^2)*HPL[{3, 1}, -S^2] + (8*(1 + S^2)^2*HPL[{3, 2}, -S^2])/S^2 - (12*(1 + S^2)^2*HPL[{4, 1}, -S^2])/S^2 - 56*HPL[{5, 1}, -S^2] + (180*Pi^2 + (240*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (96*(1 + S^2)^2*HPL[{2, 2, 1}, -S^2])/S^2 + (312*(1 + S^2)^2*HPL[{3, 1, 1}, -S^2])/S^2 + 608*HPL[{3, 2, 1}, -S^2] + 1936*HPL[{4, 1, 1}, -S^2] - (240*(1 + S^2)^2*HPL[{2, 1, 1, 1}, -S^2])/S^2 - 1440*HPL[{3, 1, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1, 1}, -S^2] + (-2*Pi^2*(1 + S^2) - (4*(1 + 2*S^2 + S^4))/S^2)*Zeta[3] + 16*Zeta[3]^2 + HPL[{3}, -S^2]*((24*(1 + 2*S^2 + S^4))/S^2 + (7*Pi^2*(1 + 2*S^2 + S^4))/(3*S^2) + 40*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + HPL[{2, 1}, -S^2]*((-240*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) + 40*Zeta[3]) + HPL[{2}, -S^2]*((377*Pi^4)/45 + (220*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) - (4*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 + 8*HPL[{4}, -S^2] - (48*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 - 344*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2] - (4*(1 + 2*S^2 + S^4)*Zeta[3])/S^2)) + HPL[{2, 1}, -S^2]*((-83*Pi^4*(1 + S^2))/45 - (4*Pi^2*(15 + 38*S^2 + 29*S^4))/(3*S^2) - (2*(169 + 386*S^2 + 217*S^4))/S^2 + 96*(1 + S^2)*HPL[{3, 1}, -S^2] - 96*HPL[{3, 2}, -S^2] - 320*HPL[{4, 1}, -S^2] + 192*(1 + S^2)*HPL[{2, 1, 1}, -S^2] + 608*HPL[{2, 2, 1}, -S^2] + 1920*HPL[{3, 1, 1}, -S^2] - 1376*HPL[{2, 1, 1, 1}, -S^2] + ((-8*Pi^2)/3 + 16*(1 + S^2))*Zeta[3] - 96*Zeta[5]) - 8*(1 + 14*S^2)*Zeta[5] + HPL[{3}, -S^2]*((11*Pi^4*(1 + S^2))/10 + (Pi^2*(18 + 27*S^2 + 28*S^4))/(3*S^2) + (117 + 92*S^2 + 97*S^4)/S^2 - 12*(1 + S^2)*HPL[{4}, -S^2] - 112*HPL[{5}, -S^2] + (8*Pi^2 + (16*(1 + S^2))/S^2)*HPL[{2, 1}, -S^2] - 32*HPL[{3, 2}, -S^2] + 144*HPL[{4, 1}, -S^2] - 16*(1 + S^2)*HPL[{2, 1, 1}, -S^2] - 96*HPL[{2, 2, 1}, -S^2] - 320*HPL[{3, 1, 1}, -S^2] + 96*HPL[{2, 1, 1, 1}, -S^2] + (44*Pi^2*Zeta[3])/3 + 148*Zeta[5]) + Zeta[3]*((-2*Pi^2*(1 + 25*S^2))/3 - 2*(10 + 71*S^2) + 320*Zeta[5]) + HPL[{2}, -S^2]*((4447*Pi^6)/7560 + (203*Pi^4*(1 + S^2))/(45*S^2) + (Pi^2*(131 + 211*S^2 + 48*S^4))/(3*S^2) + (2*(188 + 331*S^2 + 143*S^4))/S^2 + 8*HPL[{3}, -S^2]^2 + ((16*Pi^2)/3 + (8*(1 + S^2))/S^2)*HPL[{4}, -S^2] + 12*(1 + S^2)*HPL[{5}, -S^2] + 112*HPL[{6}, -S^2] - 152*HPL[{2, 1}, -S^2]^2 + ((-130*Pi^2)/3 - (96*(1 + S^2))/S^2)*HPL[{3, 1}, -S^2] - 8*(1 + S^2)*HPL[{3, 2}, -S^2] - 16*(1 + S^2)*HPL[{4, 1}, -S^2] - 80*HPL[{5, 1}, -S^2] + ((244*Pi^2)/3 + (192*(1 + S^2))/S^2)*HPL[{2, 1, 1}, -S^2] + 80*(1 + S^2)*HPL[{2, 2, 1}, -S^2] - 256*(1 + S^2)*HPL[{3, 1, 1}, -S^2] + 368*HPL[{3, 2, 1}, -S^2] + 1136*HPL[{4, 1, 1}, -S^2] - 192*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2] - 8000*HPL[{3, 1, 1, 1}, -S^2] + 1376*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-16*(1 + S^2) - (2*Pi^2*(1 + S^2))/3 + 48*HPL[{2, 1}, -S^2] - 24*Zeta[3]) + HPL[{2, 1}, -S^2]*(-10*Pi^2*(1 + S^2) - (8*(5 + 24*S^2 + 19*S^4))/S^2 - 8*Zeta[3]) + ((-2*Pi^2*(1 + S^2))/(3*S^2) - (4*(3 + 4*S^2 + S^4))/S^2)*Zeta[3] + 4*Zeta[3]^2 - (8*(1 + S^2)*Zeta[5])/S^2) + HPL[{1}, -S^2]*((-31*Pi^6*(1 + S^2))/135 + (Pi^4*(203 - 114*S^2 - 317*S^4))/(90*S^2) + (755*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(375 + 478*S^2 + 103*S^4))/(6*S^2) + (10*(1 + S^2)^2*HPL[{2}, -S^2]^3)/(3*S^2) - (2*(1 + S^2)^2*HPL[{3}, -S^2]^2)/S^2 + ((-8*Pi^2)/3 + (36*(1 + 2*S^2 + S^4))/S^2)*HPL[{5}, -S^2] + (60*(1 + S^2)^2*HPL[{6}, -S^2])/S^2 - 240*HPL[{7}, -S^2] - (48*(1 + S^2)^2*HPL[{2, 1}, -S^2]^2)/S^2 + ((-240*(1 + 2*S^2 + S^4))/S^2 - (4*Pi^2*(15 + 26*S^2 + 11*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + ((32*Pi^2)/3 + (16*(1 + 2*S^2 + S^4))/S^2)*HPL[{3, 2}, -S^2] + ((56*Pi^2)/3 - (24*(1 + 2*S^2 + S^4))/S^2)*HPL[{4, 1}, -S^2] + (6*(1 + S^2)^2*HPL[{4, 2}, -S^2])/S^2 - 96*HPL[{4, 3}, -S^2] - (44*(1 + S^2)^2*HPL[{5, 1}, -S^2])/S^2 - 288*HPL[{5, 2}, -S^2] - 480*HPL[{6, 1}, -S^2] + ((496*Pi^2)/3 + (192*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((1528*Pi^2)/3 + (624*(1 + 2*S^2 + S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (80*(1 + S^2)^2*HPL[{3, 2, 1}, -S^2])/S^2 - 128*HPL[{3, 2, 2}, -S^2] - 416*HPL[{3, 3, 1}, -S^2] + (312*(1 + S^2)^2*HPL[{4, 1, 1}, -S^2])/S^2 - 416*HPL[{4, 1, 2}, -S^2] - 1280*HPL[{4, 2, 1}, -S^2] - 2512*HPL[{5, 1, 1}, -S^2] + (-360*Pi^2 - (480*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - 1216*HPL[{2, 2, 2, 1}, -S^2] - (240*(1 + S^2)^2*HPL[{3, 1, 1, 1}, -S^2])/S^2 + 3808*HPL[{3, 1, 1, 2}, -S^2] + 3808*HPL[{3, 1, 2, 1}, -S^2] + 7456*HPL[{3, 2, 1, 1}, -S^2] + 22144*HPL[{4, 1, 1, 1}, -S^2] + (480*(1 + S^2)^2*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - 2752*HPL[{2, 1, 2, 1, 1}, -S^2] - 8256*HPL[{2, 2, 1, 1, 1}, -S^2] - 13632*HPL[{3, 1, 1, 1, 1}, -S^2] - 5760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1}, -S^2]*((480*(1 + 2*S^2 + S^4))/S^2 + (4*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) - 80*Zeta[3]) + HPL[{2}, -S^2]^2*((48*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(23 + 38*S^2 + 15*S^4))/(6*S^2) - 16*HPL[{3}, -S^2] - 152*HPL[{2, 1}, -S^2] - 4*Zeta[3]) + ((157*Pi^4)/45 - 4*Pi^2*(1 + S^2) - (12*(1 + 2*S^2 + S^4))/S^2)*Zeta[3] + 8*(1 + S^2)*Zeta[3]^2 + HPL[{4}, -S^2]*((66*(1 + 2*S^2 + S^4))/S^2 + (6*Pi^2*(1 + 2*S^2 + S^4))/S^2 - 16*HPL[{2, 1}, -S^2] + 64*Zeta[3]) + HPL[{3}, -S^2]*((52*Pi^4)/45 + (48*(1 + 2*S^2 + S^4))/S^2 + (14*Pi^2*(1 + 2*S^2 + S^4))/(3*S^2) + 48*HPL[{4}, -S^2] + (8*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + 80*HPL[{3, 1}, -S^2] - 80*HPL[{2, 1, 1}, -S^2] - 8*(1 + S^2)*Zeta[3]) + HPL[{2, 1}, -S^2]*((-754*Pi^4)/45 - (440*(1 + 2*S^2 + S^4))/S^2 - (4*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) + 688*HPL[{3, 1}, -S^2] + 1376*HPL[{2, 1, 1}, -S^2] + (8*(1 + 2*S^2 + S^4)*Zeta[3])/S^2) + (110*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((386*(1 + 2*S^2 + S^4))/S^2 + (4*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) + (Pi^4*(203 + 286*S^2 + 83*S^4))/(90*S^2) + ((-16*Pi^2)/3 - (8*(1 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2] + (4*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 - 48*HPL[{5}, -S^2] + ((-248*Pi^2)/3 - (96*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (48*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 + 64*HPL[{3, 2}, -S^2] + 208*HPL[{4, 1}, -S^2] + (96*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 + 608*HPL[{2, 2, 1}, -S^2] - 1904*HPL[{3, 1, 1}, -S^2] - 1376*HPL[{2, 1, 1, 1}, -S^2] + ((-2*Pi^2)/3 - (8*(1 + 2*S^2 + S^4))/S^2)*Zeta[3] + 48*Zeta[5]) + 300*Zeta[7])) + Log[T]*(-2940 + (430*Pi^6*S^2)/189 + (5*Pi^2*(-147 + 68*S^2))/3 + (Pi^4*(-416 + 535*S^2))/30 - (HPL[{0}, S^2]^7*HPL[{1}, -S^2])/12 - (44*Pi^2*HPL[{1}, -S^2]^6)/9 - (4*HPL[{1}, -S^2]^8)/3 + HPL[{0}, S^2]^6*(S^2/2 + ((1 + S^2)*HPL[{1}, -S^2])/4 - HPL[{1}, -S^2]^2/3) + ((-20*Pi^2)/9 + (40*(-1 + S^4))/(3*S^2))*HPL[{2}, -S^2]^3 - (20*HPL[{2}, -S^2]^4)/3 - 6*Pi^2*HPL[{3}, -S^2]^2 + 64*HPL[{4}, -S^2]^2 + ((40*Pi^2)/3 + (320*(-1 + S^4))/S^2)*HPL[{6}, -S^2] + ((248*Pi^2)/3 + (192*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*((-3 - 5*S^2)/6 + (2*(1 + S^2)*HPL[{1}, -S^2]^2)/3 - (11*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((-8*Pi^2)/9 + (4*(1 + S^2))/3 - (4*HPL[{2}, -S^2])/3) + ((-1 - S^2)*HPL[{2}, -S^2])/(2*S^2) - HPL[{3}, -S^2]/2 + (5*HPL[{2, 1}, -S^2])/3) + HPL[{2}, -S^2]^2*((-152*Pi^4)/45 - (4*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) - (8*(13 + 43*S^2 + 13*S^4))/S^2 + (2*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 + 24*HPL[{4}, -S^2] - 24*HPL[{3, 1}, -S^2]) - 288*HPL[{3, 1}, -S^2]^2 + (32*(-1 + S^2)*(1 + S^2)*HPL[{4, 2}, -S^2])/S^2 + (-4*Pi^2 - (144*(-1 + S^4))/S^2)*HPL[{5, 1}, -S^2] + ((-616*Pi^4)/45 + (1088*(-1 + S^4))/S^2 + (32*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - 1280*HPL[{2, 1, 1}, -S^2]^2 + (4*Pi^2 - (32*(-1 + S^4))/S^2)*HPL[{3, 1, 2}, -S^2] + ((-148*Pi^2)/3 + (288*(-1 + S^4))/S^2)*HPL[{3, 2, 1}, -S^2] + (-160*Pi^2 + (1152*(-1 + S^4))/S^2)*HPL[{4, 1, 1}, -S^2] + ((368*Pi^2)/3 - (960*(-1 + S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + ((-640*Pi^2)/3 + (1920*(-1 + S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^4*((7*Pi^2*S^2)/2 + (5*(-9 + 23*S^2))/6 + (7*(1 + S^2)*HPL[{1}, -S^2]^3)/3 - (23*HPL[{1}, -S^2]^4)/9 + HPL[{1}, -S^2]^2*((-53*Pi^2)/18 + 7*(1 + S^2) - (31*HPL[{2}, -S^2])/6) + (-Pi^2/3 + (-5 - 4*S^2 + S^4)/S^2)*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2 + 2*HPL[{4}, -S^2] + (-1 - S^2)*HPL[{2, 1}, -S^2] + 4*HPL[{3, 1}, -S^2] - 8*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((11*Pi^2*(1 + S^2))/6 + (-5 + 18*S^2 + 23*S^4)/(2*S^2) + ((1 + S^2)*(-5 + 2*S^2)*HPL[{2}, -S^2])/(2*S^2) + (31*HPL[{2, 1}, -S^2])/3 - (7*Zeta[3])/3)) + HPL[{2, 1, 1, 1}, -S^2]*((-480*(-1 + S^4))/S^2 - 1280*Zeta[3]) + HPL[{3, 2}, -S^2]*((-2*Pi^2*(1 + S^2))/3 - (16*(1 + 11*S^4))/S^2 - 56*Zeta[3]) + HPL[{4, 1}, -S^2]*((8*Pi^2*(1 + S^2))/3 - (8*(-9 + 4*S^2 + 69*S^4))/S^2 - 48*Zeta[3]) + HPL[{5}, -S^2]*(-2*Pi^2*(1 + S^2) - (4*(40 + S^2 + 6*S^4))/S^2 + 24*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + ((4*Pi^2*(-1 + 19*S^2))/3 + 8*(3 + 79*S^2))*Zeta[3] + 32*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^5*((4*Pi^2*(1 + S^2))/3 - (8*(1 + 2*S^2 + S^4))/S^2 + (8*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + (160*HPL[{3}, -S^2])/3 + 48*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((-192*(1 + S^4))/S^2 + 576*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((-8*Pi^2*(1 + S^2))/3 - (32*(21 - S^2 + 6*S^4))/S^2 + 1696*Zeta[3]) + HPL[{1}, -S^2]^4*((-1849*Pi^4)/270 + (20*Pi^2*(1 + S^2))/3 - (60*(1 + 2*S^2 + S^4))/S^2 + ((-86*Pi^2)/9 + (40*(-1 + S^4))/S^2)*HPL[{2}, -S^2] - (172*HPL[{2}, -S^2]^2)/3 + (4*(1 + S^2)*(-1 + 9*S^2)*HPL[{3}, -S^2])/S^2 + (112*HPL[{4}, -S^2])/3 - (40*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (112*HPL[{3, 1}, -S^2])/3 + 40*(1 + S^2)*Zeta[3]) + HPL[{4}, -S^2]*((6*Pi^4)/5 + (8*Pi^2*(-7 - 2*S^2 + 5*S^4))/(3*S^2) + (4*(-35 + 12*S^2 + 79*S^4))/S^2 - (8*(1 + S^2)*(1 + 5*S^2)*HPL[{2, 1}, -S^2])/S^2 - 160*HPL[{3, 1}, -S^2] + 192*HPL[{2, 1, 1}, -S^2] + (8*(1 + S^2)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((338*Pi^4)/45 - (8*Pi^2*(-31 - 13*S^2 + 18*S^4))/(3*S^2) - (8*(-57 + 6*S^2 + 79*S^4))/S^2 + 1280*HPL[{2, 1, 1}, -S^2] + (16*(1 + S^2)*Zeta[3])/S^2) + HPL[{0}, S^2]^3*((Pi^2*(-29 - 31*S^2))/9 - (7*(26 + 15*S^2))/3 + (8*(1 + S^2)*HPL[{1}, -S^2]^4)/3 - (44*HPL[{1}, -S^2]^5)/9 + HPL[{1}, -S^2]^3*((-220*Pi^2)/27 + (32*(1 + S^2))/3 - 20*HPL[{2}, -S^2]) - (11*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-17*Pi^2)/9 - (16*(1 + S^2))/3)*HPL[{3}, -S^2] - (6*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 14*HPL[{5}, -S^2] + ((98*Pi^2)/9 + (32*(1 + S^2))/3)*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((-29*Pi^2*(1 + S^2))/(9*S^2) - (2*(41 + 56*S^2 + 3*S^4))/(3*S^2) + (80*HPL[{2, 1}, -S^2])/3) + (20*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (2*HPL[{3, 2}, -S^2])/3 + (16*HPL[{4, 1}, -S^2])/3 - (112*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (160*HPL[{2, 2, 1}, -S^2])/3 - (496*HPL[{3, 1, 1}, -S^2])/3 + 128*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((32*Pi^2*(1 + S^2))/9 + (4*(-7 + 10*S^2 + 17*S^4))/(3*S^2) - (4*(1 + S^2)*(7 + 2*S^2)*HPL[{2}, -S^2])/(3*S^2) - 4*HPL[{3}, -S^2] + 60*HPL[{2, 1}, -S^2] - (16*Zeta[3])/3) + HPL[{1}, -S^2]*((-937*Pi^4)/270 + (64*Pi^2*(1 + S^2))/9 + (2*(-41 + 2*S^2 + 43*S^4))/(3*S^2) + ((-85*Pi^2)/9 - (8*(7 + 9*S^2 + 2*S^4))/(3*S^2))*HPL[{2}, -S^2] - (38*HPL[{2}, -S^2]^2)/3 - (8*(1 + S^2)^2*HPL[{3}, -S^2])/(3*S^2) - 4*HPL[{4}, -S^2] + (8*(1 + S^2)*(7 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S^2) + (176*HPL[{3, 1}, -S^2])/3 - 120*HPL[{2, 1, 1}, -S^2] + 4*(1 + S^2)*Zeta[3])) + HPL[{0}, S^2]^2*((334*Pi^4*S^2)/45 + Pi^2*(-30 + 61*S^2) + 5*(-73 + 68*S^2) + 4*(1 + S^2)*HPL[{1}, -S^2]^5 - (16*HPL[{1}, -S^2]^6)/3 + HPL[{1}, -S^2]^4*((-106*Pi^2)/9 + 20*(1 + S^2) - (86*HPL[{2}, -S^2])/3) + ((-17*Pi^2)/3 - (4*(6 + 7*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 - (20*HPL[{2}, -S^2]^3)/3 - 2*HPL[{3}, -S^2]^2 + (4*Pi^2 + (16*(-2 - S^2 + S^4))/S^2)*HPL[{4}, -S^2] - 6*(1 + S^2)*HPL[{5}, -S^2] + 40*HPL[{6}, -S^2] + (-2*Pi^2*(1 + S^2) - (16*(-4 + S^4))/S^2)*HPL[{2, 1}, -S^2] + 88*HPL[{2, 1}, -S^2]^2 + ((70*Pi^2)/3 - (8*(-16 - 13*S^2 + 3*S^4))/S^2)*HPL[{3, 1}, -S^2] - 2*(1 + S^2)*HPL[{3, 2}, -S^2] + 8*(1 + S^2)*HPL[{4, 1}, -S^2] - 12*HPL[{5, 1}, -S^2] + ((-128*Pi^2)/3 + (48*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - 8*(1 + S^2)*HPL[{3, 1, 1}, -S^2] + 12*HPL[{3, 1, 2}, -S^2] - 148*HPL[{3, 2, 1}, -S^2] - 480*HPL[{4, 1, 1}, -S^2] + 368*HPL[{3, 1, 1, 1}, -S^2] - 640*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((Pi^2*(-1 - S^2))/3 - (2*(8 + 3*S^2))/S^2 - 8*HPL[{2, 1}, -S^2] - 4*Zeta[3]) + 4*(-1 + 4*S^2)*Zeta[3] + HPL[{1}, -S^2]^3*(8*Pi^2*(1 + S^2) + (20*(-1 + 2*S^2 + 3*S^4))/S^2 + (4*(-5 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2 + 8*HPL[{3}, -S^2] + (344*HPL[{2, 1}, -S^2])/3 + (32*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-359*Pi^4)/45 + 24*Pi^2*(1 + S^2) + (8*(-11 + 5*S^2 + 16*S^4))/S^2 + ((-74*Pi^2)/3 + (12*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - 48*HPL[{2}, -S^2]^2 + (8*(-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/S^2 - (12*(-5 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + 168*HPL[{3, 1}, -S^2] - 344*HPL[{2, 1, 1}, -S^2] + 16*(1 + S^2)*Zeta[3]) + HPL[{2}, -S^2]*((-13*Pi^4)/9 + (4*Pi^2*(-5 - 4*S^2 + S^4))/S^2 + (2*(-65 - 86*S^2 + 13*S^4))/S^2 + 4*HPL[{4}, -S^2] + 88*HPL[{3, 1}, -S^2] - 176*HPL[{2, 1, 1}, -S^2] - (4*(1 + S^2)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((349*Pi^4*(1 + S^2))/90 + (2*Pi^2*(-5 + 14*S^2 + 19*S^4))/S^2 + (-187 - 10*S^2 + 177*S^4)/S^2 - (2*(1 + S^2)*(6 + S^2)*HPL[{2}, -S^2]^2)/S^2 + (2*Pi^2 + (16*(-1 + S^4))/S^2)*HPL[{3}, -S^2] + (4*(-4 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 12*HPL[{5}, -S^2] + ((148*Pi^2)/3 - (24*(-5 - 4*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (8*(-8 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - 24*HPL[{3, 2}, -S^2] - 72*HPL[{4, 1}, -S^2] + (24*(-5 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 384*HPL[{2, 2, 1}, -S^2] - 1104*HPL[{3, 1, 1}, -S^2] + 688*HPL[{2, 1, 1, 1}, -S^2] + (-2*Pi^2 + 32*(1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*((24*(-5 - 4*S^2 + S^4))/S^2 + (Pi^2*(-10 - 7*S^2 + 3*S^4))/S^2 + 12*HPL[{3}, -S^2] + 192*HPL[{2, 1}, -S^2] + 16*Zeta[3]))) + HPL[{0}, S^2]*((Pi^2*(-380 - 303*S^2))/3 + (Pi^4*(-203 - 204*S^2))/45 - 1510*(1 + S^2) - (16*HPL[{1}, -S^2]^7)/3 + HPL[{1}, -S^2]^5*((-128*Pi^2)/9 - 48*HPL[{2}, -S^2]) - (20*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) + (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S^2 + (-20*Pi^2 - 72*(1 + S^2))*HPL[{5}, -S^2] - (120*(1 + S^2)*HPL[{6}, -S^2])/S^2 - 200*HPL[{7}, -S^2] + (96*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-2*Pi^2)/3 - 32*(1 + S^2))*HPL[{3, 2}, -S^2] + (-8*Pi^2 + 48*(1 + S^2))*HPL[{4, 1}, -S^2] - (12*(1 + S^2)*HPL[{4, 2}, -S^2])/S^2 - 32*HPL[{4, 3}, -S^2] + (88*(1 + S^2)*HPL[{5, 1}, -S^2])/S^2 - 108*HPL[{5, 2}, -S^2] - 80*HPL[{6, 1}, -S^2] + HPL[{1}, -S^2]^3*((-1874*Pi^4)/135 + (32*Pi^2*(1 + S^2))/3 - (120*(1 + 2*S^2 + S^4))/S^2 + (-60*Pi^2 - (80*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - (344*HPL[{2}, -S^2]^2)/3 - (8*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 - (112*HPL[{4}, -S^2])/3 + (80*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + 480*HPL[{3, 1}, -S^2] - 960*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-73*Pi^4)/45 - (28*Pi^2*(1 + S^2))/3 - (8*(11 + 12*S^2 + 9*S^4))/S^2 + 16*HPL[{4}, -S^2] - (16*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - 32*HPL[{3, 1}, -S^2] + 64*HPL[{2, 1, 1}, -S^2]) + (-168*Pi^2 - 384*(1 + S^2))*HPL[{2, 2, 1}, -S^2] + (-496*Pi^2 - 1248*(1 + S^2))*HPL[{3, 1, 1}, -S^2] - (160*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + 88*HPL[{3, 2, 2}, -S^2] + 192*HPL[{3, 3, 1}, -S^2] - (624*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 + 168*HPL[{4, 1, 2}, -S^2] + 552*HPL[{4, 2, 1}, -S^2] + 1008*HPL[{5, 1, 1}, -S^2] + (368*Pi^2 + 960*(1 + S^2))*HPL[{2, 1, 1, 1}, -S^2] + 1216*HPL[{2, 2, 2, 1}, -S^2] + (480*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - 3680*HPL[{3, 1, 1, 2}, -S^2] - 3680*HPL[{3, 1, 2, 1}, -S^2] - 7328*HPL[{3, 2, 1, 1}, -S^2] - 22208*HPL[{4, 1, 1, 1}, -S^2] - (960*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + 2752*HPL[{2, 1, 2, 1, 1}, -S^2] + 8256*HPL[{2, 2, 1, 1, 1}, -S^2] + 14080*HPL[{3, 1, 1, 1, 1}, -S^2] + 5760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{3, 1}, -S^2]*((40*Pi^2*(1 + S^2))/S^2 + (8*(41 + 60*S^2 + 11*S^4))/S^2 - 80*Zeta[3]) + 8*(3 + 11*S^2)*Zeta[3] + HPL[{4}, -S^2]*((-12*Pi^2*(1 + S^2))/S^2 - (4*(22 + 33*S^2 + 4*S^4))/S^2 + 8*Zeta[3]) + HPL[{2}, -S^2]^2*((-23*Pi^2*(1 + S^2))/(3*S^2) - (4*(19 + 24*S^2 + 5*S^4))/S^2 + 8*HPL[{3}, -S^2] + 152*HPL[{2, 1}, -S^2] + 12*Zeta[3]) + HPL[{1}, -S^2]^4*((8*Pi^2*(1 + S^2))/3 - (20*(1 + 2*S^2 + S^4))/S^2 - (20*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 - (16*HPL[{3}, -S^2])/3 + 240*HPL[{2, 1}, -S^2] + (56*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*((-232*Pi^2*(1 + S^2))/(3*S^2) - (240*(3 + 4*S^2 + S^4))/S^2 + 96*Zeta[3]) + HPL[{2, 1}, -S^2]*(18*Pi^4 + (152*Pi^2*(1 + S^2))/3 + (8*(41 + 110*S^2 + 69*S^4))/S^2 - 672*HPL[{3, 1}, -S^2] - 1376*HPL[{2, 1, 1}, -S^2] - 16*(1 + S^2)*Zeta[3]) + HPL[{2}, -S^2]*((-203*Pi^4*(1 + S^2))/(45*S^2) - (4*Pi^2*(43 + 58*S^2 + 9*S^4))/(3*S^2) - (2*(217 + 386*S^2 + 169*S^4))/S^2 + ((8*Pi^2)/3 + 16*(1 + S^2))*HPL[{3}, -S^2] - (8*(1 + S^2)*HPL[{4}, -S^2])/S^2 - 16*HPL[{5}, -S^2] + (84*Pi^2 + 192*(1 + S^2))*HPL[{2, 1}, -S^2] + (96*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - 32*HPL[{3, 2}, -S^2] - 96*HPL[{4, 1}, -S^2] - (192*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 608*HPL[{2, 2, 1}, -S^2] + 1888*HPL[{3, 1, 1}, -S^2] + 1376*HPL[{2, 1, 1, 1}, -S^2] + (4*Pi^2 + (16*(1 + S^2))/S^2)*Zeta[3]) + HPL[{1}, -S^2]^2*((26*Pi^4*(1 + S^2))/9 - (396*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(-29 - 10*S^2 + 19*S^4))/(3*S^2) - (24*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((-20*Pi^2)/3 - (24*(1 + 2*S^2 + S^4))/S^2)*HPL[{3}, -S^2] - (36*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 - 40*HPL[{5}, -S^2] + (180*Pi^2 + (240*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (120*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 - 80*HPL[{3, 2}, -S^2] - 128*HPL[{4, 1}, -S^2] - (240*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 - 1376*HPL[{2, 2, 1}, -S^2] - 4192*HPL[{3, 1, 1}, -S^2] + 2880*HPL[{2, 1, 1, 1}, -S^2] + 4*Pi^2*Zeta[3] + HPL[{2}, -S^2]*((-240*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) + 40*HPL[{3}, -S^2] + 688*HPL[{2, 1}, -S^2] + 40*Zeta[3])) + HPL[{1}, -S^2]*((-12907*Pi^6)/2835 + (52*Pi^4*(1 + S^2))/9 - (780*(1 + 2*S^2 + S^4))/S^2 - (4*Pi^2*(43 + 44*S^2 + S^4))/(3*S^2) + ((-124*Pi^2)/3 - (48*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 - (152*HPL[{2}, -S^2]^3)/3 + 8*HPL[{3}, -S^2]^2 + ((-40*Pi^2)/3 - (72*(1 + 2*S^2 + S^4))/S^2)*HPL[{4}, -S^2] - (36*(1 + S^2)^2*HPL[{5}, -S^2])/S^2 + 688*HPL[{2, 1}, -S^2]^2 + ((536*Pi^2)/3 + (240*(1 + 2*S^2 + S^4))/S^2)*HPL[{3, 1}, -S^2] - (16*(1 + S^2)^2*HPL[{3, 2}, -S^2])/S^2 + (24*(1 + S^2)^2*HPL[{4, 1}, -S^2])/S^2 + 112*HPL[{5, 1}, -S^2] + (-360*Pi^2 - (480*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (192*(1 + S^2)^2*HPL[{2, 2, 1}, -S^2])/S^2 - (624*(1 + S^2)^2*HPL[{3, 1, 1}, -S^2])/S^2 - 1216*HPL[{3, 2, 1}, -S^2] - 3872*HPL[{4, 1, 1}, -S^2] + (480*(1 + S^2)^2*HPL[{2, 1, 1, 1}, -S^2])/S^2 + 2880*HPL[{3, 1, 1, 1}, -S^2] - 5760*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((480*(1 + 2*S^2 + S^4))/S^2 + (4*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) - 80*Zeta[3]) + HPL[{3}, -S^2]*((-48*(1 + 2*S^2 + S^4))/S^2 - (14*Pi^2*(1 + 2*S^2 + S^4))/(3*S^2) - 80*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + (4*Pi^2*(1 + S^2) + (8*(1 + 2*S^2 + S^4))/S^2)*Zeta[3] - 32*Zeta[3]^2 + HPL[{2}, -S^2]*((-754*Pi^4)/45 - (440*(1 + 2*S^2 + S^4))/S^2 - (4*Pi^2*(29 + 48*S^2 + 19*S^4))/(3*S^2) + (8*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 - 16*HPL[{4}, -S^2] + (96*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + 688*HPL[{3, 1}, -S^2] - 1376*HPL[{2, 1, 1}, -S^2] + (8*(1 + 2*S^2 + S^4)*Zeta[3])/S^2))) + HPL[{2, 1}, -S^2]*((-7*Pi^4*(1 + S^2))/15 - (632*(-1 + S^4))/S^2 - (4*Pi^2*(-31 + 19*S^4))/(3*S^2) + (16*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + 688*HPL[{3, 2}, -S^2] + 2016*HPL[{4, 1}, -S^2] - 1280*HPL[{3, 1, 1}, -S^2] + 2560*HPL[{2, 1, 1, 1}, -S^2] + ((-160*Pi^2)/3 - 384*(1 + S^2))*Zeta[3] - 272*Zeta[5]) + HPL[{3}, -S^2]*((Pi^4*(-1 - S^2))/9 + (2*Pi^2*(-14 - S^2 + 24*S^4))/(3*S^2) + (2*(-65 + 32*S^2 + 251*S^4))/S^2 + (4*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 - 128*HPL[{5}, -S^2] + (-56*Pi^2 - (16*(1 + 24*S^2 + 23*S^4))/S^2)*HPL[{2, 1}, -S^2] + (8*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 + 24*HPL[{3, 2}, -S^2] + 256*HPL[{4, 1}, -S^2] - (16*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 736*HPL[{2, 2, 1}, -S^2] + 1952*HPL[{3, 1, 1}, -S^2] - 1280*HPL[{2, 1, 1, 1}, -S^2] + ((-8*Pi^2)/3 + 16*(1 + S^2))*Zeta[3] - 32*Zeta[5]) + 8*(-2 + 29*S^2)*Zeta[5] + HPL[{1}, -S^2]^3*((37*Pi^4*(1 + S^2))/15 + (40*Pi^2*(-1 + S^4))/(3*S^2) - (264*(1 + 2*S^2 + S^4))/S^2 - (16*(1 + S^2)^2*HPL[{2}, -S^2]^2)/S^2 + ((424*Pi^2)/9 + (16*(-1 + 8*S^2 + 9*S^4))/S^2)*HPL[{3}, -S^2] + (24*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/S^2 + 32*HPL[{5}, -S^2] + ((344*Pi^2)/9 - (160*(-1 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (80*(-1 + S^2)*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - (1376*HPL[{3, 2}, -S^2])/3 - (4576*HPL[{4, 1}, -S^2])/3 + (160*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (2752*HPL[{2, 2, 1}, -S^2])/3 - (5056*HPL[{3, 1, 1}, -S^2])/3 + ((392*Pi^2)/9 + 160*(1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*((160*(-1 + S^4))/S^2 + (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/(3*S^2) + (688*HPL[{3}, -S^2])/3 + (1376*HPL[{2, 1}, -S^2])/3 + (688*Zeta[3])/3) + (880*Zeta[5])/3) + HPL[{1}, -S^2]^2*((-8699*Pi^6)/2268 + (37*Pi^4*(1 + S^2))/5 - (780*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(-89 - 70*S^2 + 19*S^4))/(3*S^2) + ((-134*Pi^2)/3 - (48*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 - 16*HPL[{3}, -S^2]^2 + ((56*Pi^2)/3 + (72*(-1 + S^4))/S^2)*HPL[{4}, -S^2] + (4*(1 + S^2)*(-9 + 25*S^2)*HPL[{5}, -S^2])/S^2 - 140*HPL[{6}, -S^2] + 688*HPL[{2, 1}, -S^2]^2 + ((112*Pi^2)/3 - (240*(-1 + S^4))/S^2)*HPL[{3, 1}, -S^2] - (16*(1 + S^2)*(1 + 11*S^2)*HPL[{3, 2}, -S^2])/S^2 - (24*(1 + S^2)*(-1 + 25*S^2)*HPL[{4, 1}, -S^2])/S^2 - 72*HPL[{4, 2}, -S^2] - 352*HPL[{5, 1}, -S^2] + ((-344*Pi^2)/3 + (480*(-1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (192*(1 + S^2)^2*HPL[{2, 2, 1}, -S^2])/S^2 - (48*(1 + S^2)*(13 + 3*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + 448*HPL[{4, 1, 1}, -S^2] - (480*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - 448*HPL[{3, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-480*(-1 + S^4))/S^2 - (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - 688*Zeta[3]) + (480*(1 + S^2) + (76*Pi^2*(1 + S^2))/3)*Zeta[3] - 8*Zeta[3]^2 + HPL[{3}, -S^2]*((40*(-1 + 10*S^2 + 11*S^4))/S^2 + (2*Pi^2*(-7 + 24*S^2 + 31*S^4))/(3*S^2) - 688*HPL[{2, 1}, -S^2] + 48*Zeta[3]) + HPL[{2}, -S^2]*((-707*Pi^4)/90 + (432*(-1 + S^4))/S^2 + (8*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + (8*(1 + S^2)*(1 + 11*S^2)*HPL[{3}, -S^2])/S^2 + 56*HPL[{4}, -S^2] + (96*(1 + S^2)^2*HPL[{2, 1}, -S^2])/S^2 + 688*HPL[{3, 1}, -S^2] - 1376*HPL[{2, 1, 1}, -S^2] + 96*(1 + S^2)*Zeta[3]) + 232*(1 + S^2)*Zeta[5]) + HPL[{2}, -S^2]*((-62*Pi^6)/135 + (680*(-1 + S^4))/S^2 + (4*Pi^4*(-104 - 57*S^2 + 47*S^4))/(45*S^2) + (2*Pi^2*(-133 - 86*S^2 + 81*S^4))/(3*S^2) - 12*HPL[{3}, -S^2]^2 + ((28*Pi^2)/3 - 32*(1 + S^2))*HPL[{4}, -S^2] - (4*(1 + S^2)*(4 + 3*S^2)*HPL[{5}, -S^2])/S^2 + 136*HPL[{6}, -S^2] + ((248*Pi^2)/3 + (16*(11 + 24*S^2 + 13*S^4))/S^2)*HPL[{3, 1}, -S^2] - (4*(1 + S^2)^2*HPL[{3, 2}, -S^2])/S^2 + (16*(-1 + S^2)*(1 + S^2)*HPL[{4, 1}, -S^2])/S^2 - 48*HPL[{4, 2}, -S^2] - 264*HPL[{5, 1}, -S^2] + ((-496*Pi^2)/3 - (384*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (16*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + 48*HPL[{3, 1, 2}, -S^2] - 592*HPL[{3, 2, 1}, -S^2] - 1728*HPL[{4, 1, 1}, -S^2] + 1280*HPL[{3, 1, 1, 1}, -S^2] - 2560*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((96*(1 + S^4))/S^2 - 288*Zeta[3]) + ((-4*Pi^2*(1 + S^2))/(3*S^2) + (8*(1 + 11*S^4))/S^2)*Zeta[3] + 16*Zeta[3]^2 + HPL[{3}, -S^2]*((-2*Pi^2*(-1 + S^4))/(3*S^2) + (16*(1 + 5*S^4))/S^2 - 368*HPL[{2, 1}, -S^2] + 16*Zeta[3]) - (16*(1 + S^2)*Zeta[5])/S^2) + HPL[{1}, -S^2]*((4447*Pi^6*(1 + S^2))/3780 - (1510*(1 + 2*S^2 + S^4))/S^2 - (7*Pi^2*(55 + 58*S^2 + 3*S^4))/(3*S^2) + (2*Pi^4*(-104 + 125*S^2 + 229*S^4))/(45*S^2) + (20*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) - (4*(1 + S^2)^2*HPL[{3}, -S^2]^2)/S^2 + (4*Pi^2 + (8*(-9 + 16*S^2 + 25*S^4))/S^2)*HPL[{5}, -S^2] + (60*(1 + S^2)*(-2 + 3*S^2)*HPL[{6}, -S^2])/S^2 - 576*HPL[{7}, -S^2] + (96*(1 + S^2)^2*HPL[{2, 1}, -S^2]^2)/S^2 + ((-368*Pi^2)/3 - (32*(1 + 12*S^2 + 11*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((-1216*Pi^2)/3 - (48*(-1 + 24*S^2 + 25*S^4))/S^2)*HPL[{4, 1}, -S^2] - (12*(1 + S^2)^2*HPL[{4, 2}, -S^2])/S^2 + 88*HPL[{4, 3}, -S^2] - (8*(1 + S^2)*(-11 + 23*S^2)*HPL[{5, 1}, -S^2])/S^2 + 240*HPL[{5, 2}, -S^2] + 600*HPL[{6, 1}, -S^2] + ((-1072*Pi^2)/3 - (384*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((-2368*Pi^2)/3 - (96*(13 + 16*S^2 + 3*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (160*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + 1392*HPL[{3, 2, 2}, -S^2] + 4288*HPL[{3, 3, 1}, -S^2] + (624*(-1 + S^2)*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 + 4240*HPL[{4, 1, 2}, -S^2] + 13072*HPL[{4, 2, 1}, -S^2] + 26688*HPL[{5, 1, 1}, -S^2] + ((688*Pi^2)/3 - (960*(-1 + S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (480*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - 2752*HPL[{3, 1, 1, 2}, -S^2] - 2752*HPL[{3, 1, 2, 1}, -S^2] - 2752*HPL[{3, 2, 1, 1}, -S^2] - 9152*HPL[{4, 1, 1, 1}, -S^2] + (960*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + 5504*HPL[{2, 1, 2, 1, 1}, -S^2] + 16512*HPL[{2, 2, 1, 1, 1}, -S^2] + 33920*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-4*Pi^2*(-31 - 14*S^2 + 17*S^4))/(3*S^2) - (16*(-29 + 2*S^2 + 31*S^4))/S^2 - 704*Zeta[3]) + ((314*Pi^4)/45 + (152*Pi^2*(1 + S^2))/3 + (8*(1 + 110*S^2 + 109*S^4))/S^2)*Zeta[3] + 8*(1 + S^2)*Zeta[3]^2 + HPL[{4}, -S^2]*((32*(-4 + S^2 + 5*S^4))/S^2 + (2*Pi^2*(-17 - 6*S^2 + 11*S^4))/(3*S^2) - 112*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{2}, -S^2]^2*((-96*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(12 + 19*S^2 + 7*S^4))/(3*S^2) + 192*HPL[{3}, -S^2] + 152*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((960*(-1 + S^4))/S^2 + (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + 1376*Zeta[3]) + HPL[{2, 1}, -S^2]*((707*Pi^4)/45 - (864*(-1 + S^4))/S^2 - (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 - 1376*HPL[{3, 1}, -S^2] - 2752*HPL[{2, 1, 1}, -S^2] - 192*(1 + S^2)*Zeta[3]) + HPL[{3}, -S^2]*((392*Pi^4)/45 + (32*(-2 + 23*S^2 + 25*S^4))/S^2 + (4*Pi^2*(-7 + 24*S^2 + 31*S^4))/(3*S^2) - 56*HPL[{4}, -S^2] - (16*(1 + S^2)*(1 + 11*S^2)*HPL[{2, 1}, -S^2])/S^2 - 704*HPL[{3, 1}, -S^2] + 1376*HPL[{2, 1, 1}, -S^2] + (8*(-1 + S^4)*Zeta[3])/S^2) + ((220*Pi^2)/3 + 464*(1 + S^2))*Zeta[5] + HPL[{2}, -S^2]*((728*(-1 + S^4))/S^2 + (16*Pi^2*(-5 - 2*S^2 + 3*S^4))/S^2 + (Pi^4*(-416 - 207*S^2 + 209*S^4))/(90*S^2) + ((184*Pi^2)/3 + (16*(1 + 12*S^2 + 11*S^4))/S^2)*HPL[{3}, -S^2] + (4*(1 + S^2)^2*HPL[{4}, -S^2])/S^2 + 80*HPL[{5}, -S^2] + ((536*Pi^2)/3 + (192*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (96*(1 + S^2)^2*HPL[{3, 1}, -S^2])/S^2 - 720*HPL[{3, 2}, -S^2] - 2192*HPL[{4, 1}, -S^2] - (192*(1 + S^2)^2*HPL[{2, 1, 1}, -S^2])/S^2 + 1376*HPL[{3, 1, 1}, -S^2] + 2752*HPL[{2, 1, 1, 1}, -S^2] + ((188*Pi^2)/3 + 192*(1 + S^2))*Zeta[3] + 344*Zeta[5]) + 600*Zeta[7]));
e5T2F2=-1225/128 + (Pi^8*(-1031050 - 2034547*S^2))/10886400 + (Pi^6*(-40813 - 309138*S^2))/362880 + (Pi^4*(14993 - 78059*S^2))/11520 + (Pi^2*(14529 - 31616*S^2))/768 - (S^2*HPL[{0}, S^2]^9)/768 + ((-11*Pi^2*(1 + S^4))/(63*S^2) - (20*(1 + 2*S^2 + S^4))/(21*S^2))*HPL[{1}, -S^2]^7 + ((-1 - 2*S^2 - S^4)*HPL[{1}, -S^2]^8)/(6*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^9)/(27*S^2) + HPL[{0}, S^2]^8*((-1 - 8*S^2)/768 + ((-1 - S^4)*HPL[{1}, -S^2])/(768*S^2)) + HPL[{0}, S^2]^7*((-5*Pi^2*S^2)/288 + (-1 - S^2)/96 + ((-1 - 2*S^2 - S^4)*HPL[{1}, -S^2])/(96*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^2)/(96*S^2)) + ((-37 - 92*S^2 - 37*S^4)*HPL[{2}, -S^2]^4)/(48*S^2) + (7*(1 + S^4)*HPL[{3}, -S^2]^3)/(3*S^2) + ((19 - 16*S^2 + 13*S^4)*HPL[{4}, -S^2]^2)/S^2 + ((1325 - 348*S^2 - 1516*S^4)/(8*S^2) - (125*Pi^2*(1 + S^4))/(4*S^2))*HPL[{7}, -S^2] + ((3325 - 1542*S^2 - 2554*S^4)*HPL[{8}, -S^2])/(4*S^2) - (1225*(1 + S^4)*HPL[{9}, -S^2])/S^2 + HPL[{0}, S^2]^6*((23 - 72*S^2)/384 - (11*Pi^2*(2 + 11*S^2))/1152 + ((-1 - 8*S^2 - 7*S^4)*HPL[{1}, -S^2]^2)/(96*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^3)/(36*S^2) + ((4 - 6*S^2 - S^4)*HPL[{2}, -S^2])/(192*S^2) + HPL[{1}, -S^2]*((23 - 20*S^2 - 43*S^4)/(384*S^2) - (11*Pi^2*(1 + S^4))/(576*S^2) + ((-1 - S^4)*HPL[{2}, -S^2])/(32*S^2)) + ((-1 - S^4)*HPL[{3}, -S^2])/(48*S^2) + ((1 + S^4)*HPL[{2, 1}, -S^2])/(16*S^2)) + ((-23 - 108*S^2 - 31*S^4)*HPL[{3, 1}, -S^2]^2)/S^2 + ((8*Pi^2*(1 + S^4))/S^2 + (-113 + 4*S^2 + 244*S^4)/(4*S^2))*HPL[{4, 3}, -S^2] + ((283*Pi^2*(1 + S^4))/(12*S^2) + (3*(-218 - 28*S^2 + 481*S^4))/(8*S^2))*HPL[{5, 2}, -S^2] + (3*(-4 - 2*S^2 + 5*S^4)*HPL[{5, 3}, -S^2])/(2*S^2) - (245*(1 + S^4)*HPL[{5, 4}, -S^2])/S^2 + ((59*Pi^2*(1 + S^4))/S^2 + (-559 - 124*S^2 + 960*S^4)/(2*S^2))*HPL[{6, 1}, -S^2] + ((-98 - 30*S^2 + 113*S^4)*HPL[{6, 2}, -S^2])/(4*S^2) - (974*(1 + S^4)*HPL[{6, 3}, -S^2])/S^2 + ((-369 + 208*S^2 + 265*S^4)*HPL[{7, 1}, -S^2])/S^2 - (2430*(1 + S^4)*HPL[{7, 2}, -S^2])/S^2 - (4360*(1 + S^4)*HPL[{8, 1}, -S^2])/S^2 - (2*(77 + 172*S^2 + 77*S^4)*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((61*Pi^2*(1 + S^4))/(4*S^2) + (1207 + 2312*S^2 + 807*S^4)/(8*S^2))*HPL[{3, 2, 2}, -S^2] + ((160*Pi^2*(1 + S^4))/(3*S^2) + (429 + 884*S^2 + 360*S^4)/S^2)*HPL[{3, 3, 1}, -S^2] + ((-18 + 14*S^2 + 11*S^4)*HPL[{3, 3, 2}, -S^2])/S^2 + ((52*Pi^2*(1 + S^4))/S^2 + (417 + 884*S^2 + 348*S^4)/S^2)*HPL[{4, 1, 2}, -S^2] + ((36 - 34*S^2 - 19*S^4)*HPL[{4, 1, 3}, -S^2])/S^2 + ((170*Pi^2*(1 + S^4))/S^2 + (1275 + 2696*S^2 + 1149*S^4)/S^2)*HPL[{4, 2, 1}, -S^2] + (5*(-15 + 16*S^2 + 7*S^4)*HPL[{4, 2, 2}, -S^2])/(4*S^2) + ((60 - 26*S^2 - 47*S^4)*HPL[{4, 3, 1}, -S^2])/S^2 + (42*(1 + S^4)*HPL[{4, 3, 2}, -S^2])/S^2 - (84*(1 + S^4)*HPL[{4, 4, 1}, -S^2])/S^2 + ((1067*Pi^2*(1 + S^4))/(3*S^2) + (5348 + 11068*S^2 + 4715*S^4)/(2*S^2))*HPL[{5, 1, 1}, -S^2] + ((49 - 8*S^2 - 45*S^4)*HPL[{5, 1, 2}, -S^2])/(2*S^2) - (168*(1 + S^4)*HPL[{5, 1, 3}, -S^2])/S^2 + ((529 - 248*S^2 - 405*S^4)*HPL[{5, 2, 1}, -S^2])/(2*S^2) - (39*(1 + S^4)*HPL[{5, 2, 2}, -S^2])/S^2 - (576*(1 + S^4)*HPL[{5, 3, 1}, -S^2])/S^2 - (5*(-178 + 86*S^2 + 135*S^4)*HPL[{6, 1, 1}, -S^2])/S^2 - (404*(1 + S^4)*HPL[{6, 1, 2}, -S^2])/S^2 - (1844*(1 + S^4)*HPL[{6, 2, 1}, -S^2])/S^2 - (4520*(1 + S^4)*HPL[{7, 1, 1}, -S^2])/S^2 + ((50*(-1 + S^4))/S^2 + (52*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 2, 2, 1}, -S^2] + ((-187 - 1200*S^2 - 749*S^4)/(2*S^2) - (253*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1, 1, 2}, -S^2] + ((-187 - 1200*S^2 - 749*S^4)/(2*S^2) - (253*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1, 2, 1}, -S^2] + (3*(1 - 4*S^2 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/S^2 + ((113 - 1200*S^2 - 1049*S^4)/(2*S^2) - (409*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 2, 1, 1}, -S^2] + (3*(1 - 4*S^2 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/S^2 + ((-9 + 20*S^2 - S^4)*HPL[{3, 2, 2, 1}, -S^2])/S^2 - (208*(1 + S^4)*HPL[{3, 2, 2, 2}, -S^2])/S^2 - (596*(1 + S^4)*HPL[{3, 2, 3, 1}, -S^2])/S^2 - (12*(3 - 8*S^2 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (584*(1 + S^4)*HPL[{3, 3, 1, 2}, -S^2])/S^2 - (1748*(1 + S^4)*HPL[{3, 3, 2, 1}, -S^2])/S^2 + ((-1292*Pi^2*(1 + S^4))/(3*S^2) - (2*(27 + 988*S^2 + 821*S^4))/S^2)*HPL[{4, 1, 1, 1}, -S^2] + ((13 - 36*S^2 + 5*S^4)*HPL[{4, 1, 1, 2}, -S^2])/S^2 + (3580*(1 + S^4)*HPL[{4, 1, 1, 3}, -S^2])/S^2 + ((-23 + 60*S^2 - 7*S^4)*HPL[{4, 1, 2, 1}, -S^2])/S^2 + (2996*(1 + S^4)*HPL[{4, 1, 2, 2}, -S^2])/S^2 + (5312*(1 + S^4)*HPL[{4, 1, 3, 1}, -S^2])/S^2 + ((-95 + 252*S^2 - 31*S^4)*HPL[{4, 2, 1, 1}, -S^2])/S^2 + (1868*(1 + S^4)*HPL[{4, 2, 1, 2}, -S^2])/S^2 + (1832*(1 + S^4)*HPL[{4, 2, 2, 1}, -S^2])/S^2 + (10456*(1 + S^4)*HPL[{4, 3, 1, 1}, -S^2])/S^2 + (2*(-139 + 200*S^2 + 39*S^4)*HPL[{5, 1, 1, 1}, -S^2])/S^2 + (10844*(1 + S^4)*HPL[{5, 1, 1, 2}, -S^2])/S^2 + (17684*(1 + S^4)*HPL[{5, 1, 2, 1}, -S^2])/S^2 + (41732*(1 + S^4)*HPL[{5, 2, 1, 1}, -S^2])/S^2 + (104240*(1 + S^4)*HPL[{6, 1, 1, 1}, -S^2])/S^2 + ((96*Pi^2*(1 + S^4))/S^2 + (12*(39 + 100*S^2 + 39*S^4))/S^2)*HPL[{2, 1, 2, 1, 1}, -S^2] + ((288*Pi^2*(1 + S^4))/S^2 + (36*(39 + 100*S^2 + 39*S^4))/S^2)*HPL[{2, 2, 1, 1, 1}, -S^2] + (8*(-1 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (24*(-1 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 - (416*(1 + S^4)*HPL[{2, 2, 2, 2, 1}, -S^2])/S^2 + ((1708*Pi^2*(1 + S^4))/(3*S^2) + (4*(765 + 1844*S^2 + 712*S^4))/S^2)*HPL[{3, 1, 1, 1, 1}, -S^2] - (44*(-1 + S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 - (76*(-1 + S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 - (872*(1 + S^4)*HPL[{3, 1, 1, 2, 2}, -S^2])/S^2 - (92*(-1 + S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 - (872*(1 + S^4)*HPL[{3, 1, 2, 1, 2}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{3, 1, 2, 2, 1}, -S^2])/S^2 + (6464*(1 + S^4)*HPL[{3, 1, 3, 1, 1}, -S^2])/S^2 - (196*(-1 + S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 - (2120*(1 + S^4)*HPL[{3, 2, 1, 1, 2}, -S^2])/S^2 - (1224*(1 + S^4)*HPL[{3, 2, 1, 2, 1}, -S^2])/S^2 + (1848*(1 + S^4)*HPL[{3, 2, 2, 1, 1}, -S^2])/S^2 + (6720*(1 + S^4)*HPL[{3, 3, 1, 1, 1}, -S^2])/S^2 - (8*(-81 - 28*S^2 + 95*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 - (6304*(1 + S^4)*HPL[{4, 1, 1, 1, 2}, -S^2])/S^2 - (3616*(1 + S^4)*HPL[{4, 1, 1, 2, 1}, -S^2])/S^2 + (5600*(1 + S^4)*HPL[{4, 1, 2, 1, 1}, -S^2])/S^2 + (20288*(1 + S^4)*HPL[{4, 2, 1, 1, 1}, -S^2])/S^2 + (40896*(1 + S^4)*HPL[{5, 1, 1, 1, 1}, -S^2])/S^2 + ((212*(-1 + S^4))/S^2 + (184*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (16*(-4 - 14*S^2 + 11*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 - (736*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/S^2 - (736*(1 + S^4)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/S^2 - (736*(1 + S^4)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/S^2 - (736*(1 + S^4)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/S^2 - (736*(1 + S^4)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/S^2 - (2656*(1 + S^4)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S^2 - (240*(-1 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 - (1472*(1 + S^4)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S^2 - (5888*(1 + S^4)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S^2 - (14720*(1 + S^4)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S^2 - (28992*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (-11/3 + (Pi^2*(-22 - S^2))/18 - (S^2*HPL[{0}, S^2]^3)/3 + ((-11*Pi^2*(1 + S^4))/(9*S^2) - (20*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{1}, -S^2] - (14*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) - (28*(1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + HPL[{0}, S^2]^2*((-8 - S^2)/6 - (4*(1 + S^4)*HPL[{1}, -S^2])/(3*S^2)) - ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((-10*Pi^2*S^2)/9 - (20*(1 + S^2))/3 - (14*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(3*S^2) - (14*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) - (2*(1 + S^4)*HPL[{2}, -S^2])/S^2) + (8*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2))*Log[T]^6 + (4/3 + (4*(1 + S^2)^2*HPL[{1}, -S^2])/(3*S^2) + (4*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]*((4*(1 + S^2))/3 + (4*(1 + S^4)*HPL[{1}, -S^2])/(3*S^2)))*Log[T]^7 + (-1/3 - (S^2*HPL[{0}, S^2])/3 + ((-1 - S^4)*HPL[{1}, -S^2])/(3*S^2))*Log[T]^8 + ((35 - 48*S^2)/4 + (Pi^2*(-2 - 27*S^2))/6)*Zeta[3]^2 + HPL[{5}, -S^2]*((3337 + 1212*S^2 - 2541*S^4)/(32*S^2) + (Pi^2*(473 + 396*S^2 - 207*S^4))/(48*S^2) - (109*Pi^4*(1 + S^4))/(180*S^2) + ((-4 - 20*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/S^2 - (87*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (46*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(-5 + 7*S^2)*Zeta[3])/S^2) + HPL[{3, 2}, -S^2]*((-415 - 4648*S^2 - 1759*S^4)/(16*S^2) - (119*Pi^4*(1 + S^4))/(120*S^2) - (5*Pi^2*(88 + 256*S^2 + 97*S^4))/(48*S^2) - (188*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-7 - 48*S^2 - 11*S^4)*Zeta[3])/(2*S^2)) + HPL[{3, 1, 1, 1}, -S^2]*((Pi^2*(27 + 56*S^2 + 83*S^4))/(3*S^2) + (-441 - 90*S^2 + 362*S^4)/S^2 - (216*(1 + S^4)*Zeta[3])/S^2) + HPL[{5, 1}, -S^2]*((Pi^2*(-23 - 13*S^2 + 25*S^4))/(3*S^2) + (-565 - 684*S^2 + 184*S^4)/(8*S^2) - (40*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]^2*((Pi^2*(59 + 134*S^2 + 60*S^4))/(6*S^2) + (731 + 712*S^2 + 731*S^4)/(8*S^2) - (40*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 1, 2}, -S^2]*((73*(-1 + S^4))/(8*S^2) + (Pi^2*(5 + 13*S^4))/(12*S^2) - (6*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^6*((Pi^2*(-5 - 11*S^2 - 6*S^4))/(9*S^2) - (79*(1 + 2*S^2 + S^4))/(18*S^2) - (2*(-1 + S^4)*HPL[{2}, -S^2])/(3*S^2) + (20*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) + (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{4, 2}, -S^2]*((29 - 111*S^2 - 44*S^4)/(4*S^2) + (Pi^2*(17 - 36*S^2 + S^4))/(24*S^2) + (3*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^3*((Pi^2*(-16 - 46*S^2 - 21*S^4))/(72*S^2) - (217*(-1 + S^4))/(32*S^2) + (13*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (26*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (13*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]^2*((Pi^2*(-37 + 4*S^2 - 19*S^4))/(24*S^2) - (3*(65 + 76*S^2 + 94*S^4))/(16*S^2) - (5*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (5*(1 + S^4)*Zeta[3])/S^2) + HPL[{6}, -S^2]*((2005 - 1146*S^2 - 2075*S^4)/(16*S^2) + (Pi^2*(160 - 66*S^2 - 87*S^4))/(8*S^2) + (113*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (70*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 2, 1}, -S^2]*((Pi^2*(-59 - 184*S^2 - 71*S^4))/(12*S^2) - (1229*(-1 + S^4))/(8*S^2) + (98*(1 + S^4)*Zeta[3])/S^2) + HPL[{4, 1, 1}, -S^2]*((2325 + 360*S^2 - 2009*S^4)/(4*S^2) + (Pi^2*(-63 - 220*S^2 - 187*S^4))/(6*S^2) + (340*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-803*(-1 + S^4))/S^2 - (2*Pi^2*(13 + 86*S^2 + 64*S^4))/(3*S^2) + (368*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^5*((Pi^2*(-267 - 620*S^2 - 353*S^4))/(120*S^2) - (1849*Pi^4*(1 + S^4))/(5400*S^2) - (499*(1 + 2*S^2 + S^4))/(30*S^2) + ((-43*(-1 + S^4))/(10*S^2) - (43*Pi^2*(1 + S^4))/(90*S^2))*HPL[{2}, -S^2] - (43*(1 + S^4)*HPL[{2}, -S^2]^2)/(15*S^2) + (2*(13 + 20*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S^2) + (28*(1 + S^4)*HPL[{4}, -S^2])/(15*S^2) + (4*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (28*(1 + S^4)*HPL[{3, 1}, -S^2])/(15*S^2) + (4*(2 + 3*S^2 + S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((-1692 - 7620*S^2 - 1997*S^4)/(8*S^2) + (Pi^2*(-1015 - 2144*S^2 - 765*S^4))/(24*S^2) - (154*Pi^4*(1 + S^4))/(45*S^2) - (592*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((15 - 80*S^2 + 7*S^4)*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((-1087 - 4648*S^2 - 1087*S^4)/(8*S^2) + (Pi^2*(-331 - 920*S^2 - 381*S^4))/(12*S^2) - (707*Pi^4*(1 + S^4))/(180*S^2) + (4*(18 + 38*S^2 + 17*S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((425*(-1 + S^4))/(4*S^2) + (133*Pi^4*(1 + S^4))/(30*S^2) + (Pi^2*(29 + 300*S^2 + 205*S^4))/(6*S^2) - (4*(43 + 86*S^2 + 34*S^4)*Zeta[3])/S^2) + HPL[{3, 1, 1}, -S^2]*((-1535 - 8648*S^2 - 2385*S^4)/(8*S^2) + (Pi^2*(-575 - 2024*S^2 - 880*S^4))/(12*S^2) - (1607*Pi^4*(1 + S^4))/(180*S^2) + (2*(103 + 240*S^2 + 95*S^4)*Zeta[3])/S^2) + Log[T]^5*(47/6 + (Pi^2*(136 + 41*S^2))/36 + ((11*Pi^2*(1 + S^4))/(3*S^2) + (20*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2]^2 + (28*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + (14*(1 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + HPL[{0}, S^2]^3*((11 + 8*S^2)/9 + (11*(1 + S^4)*HPL[{1}, -S^2])/(9*S^2)) + ((41*(-1 + S^4))/(6*S^2) + (4*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] + (8*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^2*((52 + 41*S^2)/12 + ((3 + 8*S^2 + 5*S^4)*HPL[{1}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + (4*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-35 - 40*S^2 - 17*S^4)*HPL[{3}, -S^2])/(3*S^2) - (6*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + HPL[{0}, S^2]*((79*(1 + S^2))/3 + (Pi^2*(32 + 29*S^2))/9 + (14*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/S^2 + (28*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + ((1 + S^2)*(7 + 5*S^2)*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((32*Pi^2*(1 + S^4))/(9*S^2) + (20*(1 + 2*S^2 + S^4))/S^2 + (12*(1 + S^4)*HPL[{2}, -S^2])/S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (12*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2) + 6*(-2 + S^2)*Zeta[3] + HPL[{1}, -S^2]*((79*(1 + 2*S^2 + S^4))/(3*S^2) + (2*Pi^2*(5 + 11*S^2 + 6*S^4))/(3*S^2) + (4*(-1 + S^4)*HPL[{2}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (12*(1 + S^4)*Zeta[3])/S^2)) + HPL[{0}, S^2]^5*((-47*Pi^4*S^2)/480 + (-33 - 67*S^2)/96 + (Pi^2*(-31 - 36*S^2))/288 + ((-7 - 22*S^2 - 15*S^4)*HPL[{1}, -S^2]^3)/(72*S^2) - (11*(1 + S^4)*HPL[{1}, -S^2]^4)/(144*S^2) + ((-15 - 26*S^2 - 21*S^4)/(96*S^2) + (Pi^2*(-1 - S^4))/(96*S^2))*HPL[{2}, -S^2] + ((-1 - S^4)*HPL[{2}, -S^2]^2)/(32*S^2) + HPL[{1}, -S^2]^2*((-11 - 60*S^2 - 49*S^4)/(96*S^2) + (Pi^2*(-1 - S^4))/(9*S^2) + ((-1 - S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((-5 - S^4)*HPL[{3}, -S^2])/(32*S^2) + (3*(1 + S^4)*HPL[{4}, -S^2])/(16*S^2) + ((5 + 16*S^2 + 17*S^4)*HPL[{2, 1}, -S^2])/(48*S^2) + ((-1 - S^4)*HPL[{2, 1, 1}, -S^2])/(4*S^2) + (3*(-2 + S^2)*Zeta[3])/16 + HPL[{1}, -S^2]*((-7 - 36*S^2 - 29*S^4)/(32*S^2) + (Pi^2*(-7 - 16*S^2 - 9*S^4))/(72*S^2) + ((-1 - 4*S^2 - 3*S^4)*HPL[{2}, -S^2])/(12*S^2) + ((1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (3*(1 + S^4)*Zeta[3])/(8*S^2))) + HPL[{0}, S^2]^4*((Pi^4*(-3698 - 14003*S^2))/34560 + (1939 - 5504*S^2)/768 + (Pi^2*(572 - 3065*S^2))/2304 + ((-25 - 92*S^2 - 67*S^4)*HPL[{1}, -S^2]^4)/(144*S^2) - (23*(1 + S^4)*HPL[{1}, -S^2]^5)/(180*S^2) + ((-9 - 62*S^2 - 32*S^4)*HPL[{2}, -S^2]^2)/(192*S^2) + HPL[{1}, -S^2]^3*((-53 - 484*S^2 - 431*S^4)/(288*S^2) - (53*Pi^2*(1 + S^4))/(216*S^2) - (31*(1 + S^4)*HPL[{2}, -S^2])/(72*S^2)) + ((51 + 40*S^2 - 11*S^4)/(64*S^2) - (5*Pi^2*(1 + S^4))/(48*S^2))*HPL[{3}, -S^2] + ((31 - 8*S^2 - 3*S^4)*HPL[{4}, -S^2])/(32*S^2) - (13*(1 + S^4)*HPL[{5}, -S^2])/(8*S^2) + ((4*Pi^2*(1 + S^4))/(9*S^2) + (7 + 126*S^2 + 81*S^4)/(48*S^2))*HPL[{2, 1}, -S^2] + ((62 + 41*S^2)*HPL[{3, 1}, -S^2])/48 + ((-1 - S^4)*HPL[{3, 2}, -S^2])/(4*S^2) + ((1 + S^4)*HPL[{4, 1}, -S^2])/(4*S^2) + ((-3 - 62*S^2 - 38*S^4)*HPL[{2, 1, 1}, -S^2])/(24*S^2) - (19*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(12*S^2) - (19*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(4*S^2) + (19*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(6*S^2) + ((124 - 165*S^2)*Zeta[3])/96 + HPL[{1}, -S^2]*((1159 - 2604*S^2 - 3763*S^4)/(768*S^2) + (Pi^2*(73 - 196*S^2 - 269*S^4))/(288*S^2) - (1849*Pi^4*(1 + S^4))/(17280*S^2) + ((-19*Pi^2*(1 + S^4))/(72*S^2) - (7*(-1 + 52*S^2 + 53*S^4))/(192*S^2))*HPL[{2}, -S^2] - (31*(1 + S^4)*HPL[{2}, -S^2]^2)/(96*S^2) + ((1 - S^4)*HPL[{3}, -S^2])/(8*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/(4*S^2) + ((5 + 31*S^2 + 26*S^4)*HPL[{2, 1}, -S^2])/(12*S^2) + (31*(1 + S^4)*HPL[{3, 1}, -S^2])/(24*S^2) - (31*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(12*S^2) + ((8 - 7*S^2 - 15*S^4)*Zeta[3])/(12*S^2)) + HPL[{1}, -S^2]^2*((29 - 622*S^2 - 651*S^4)/(192*S^2) + (Pi^2*(-10 - 53*S^2 - 43*S^4))/(72*S^2) + ((-5 - 31*S^2 - 26*S^4)*HPL[{2}, -S^2])/(24*S^2) + (31*(1 + S^4)*HPL[{2, 1}, -S^2])/(24*S^2) - (7*(1 + S^4)*Zeta[3])/(24*S^2)) + HPL[{2}, -S^2]*((336 + 26*S^2 - 569*S^4)/(384*S^2) + (Pi^2*(57 - 152*S^2 - 53*S^4))/(576*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(8*S^2) + (19*(1 + S^4)*HPL[{2, 1}, -S^2])/(24*S^2) + (5*(1 + S^4)*Zeta[3])/(8*S^2))) + Log[T]^4*(-329/24 + (Pi^2*(-1118 - 803*S^2))/144 + (Pi^4*(-3698 - 467*S^2))/2160 - (S^2*HPL[{0}, S^2]^5)/8 + ((-55*Pi^2*(1 + S^4))/(9*S^2) - (100*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{1}, -S^2]^3 - (35*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) - (14*(1 + S^4)*HPL[{1}, -S^2]^5)/(3*S^2) + HPL[{0}, S^2]^4*((-92 - 35*S^2)/144 - (23*(1 + S^4)*HPL[{1}, -S^2])/(36*S^2)) + ((-77 - 172*S^2 - 77*S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + HPL[{0}, S^2]^3*((-5*Pi^2*S^2)/6 + (-256 - 293*S^2)/72 + ((-43 - 110*S^2 - 67*S^4)*HPL[{1}, -S^2])/(18*S^2) - (55*(1 + S^4)*HPL[{1}, -S^2]^2)/(18*S^2) - (7*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((67*Pi^2*(1 + S^4))/(18*S^2) + (180 + 344*S^2 + 127*S^4)/(6*S^2))*HPL[{3}, -S^2] - (2*(-3 - 14*S^2 + 10*S^4)*HPL[{4}, -S^2])/(3*S^2) + (4*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((53*(-1 + S^4))/(6*S^2) + (23*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-458 - 803*S^2)/48 + (Pi^2*(-106 - 25*S^2))/36 - (5*(3 + 8*S^2 + 5*S^4)*HPL[{1}, -S^2]^2)/(2*S^2) - (20*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + ((-28 - 86*S^2 - 49*S^4)*HPL[{2}, -S^2])/(12*S^2) + HPL[{1}, -S^2]*((-67 - 220*S^2 - 153*S^4)/(8*S^2) - (53*Pi^2*(1 + S^4))/(18*S^2) - (43*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + (7*(1 + S^4)*HPL[{3}, -S^2])/(6*S^2) + (23*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) + (2*(-4 - 14*S^2 + 11*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (92*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (332*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (10*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (184*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (104*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((332 - 53*S^2)*Zeta[3])/6 + HPL[{2}, -S^2]*((Pi^2*(-13 - 86*S^2 - 64*S^4))/(36*S^2) - (803*(-1 + S^4))/(24*S^2) + (46*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (92*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (46*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((-395*(1 + 2*S^2 + S^4))/(6*S^2) - (5*Pi^2*(5 + 11*S^2 + 6*S^4))/(3*S^2) - (10*(-1 + S^4)*HPL[{2}, -S^2])/S^2 + (100*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (30*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((Pi^2*(-267 - 620*S^2 - 353*S^4))/(24*S^2) - (1849*Pi^4*(1 + S^4))/(1080*S^2) - (499*(1 + 2*S^2 + S^4))/(6*S^2) + ((-43*(-1 + S^4))/(2*S^2) - (43*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2] - (43*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (10*(13 + 20*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S^2) + (28*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (20*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (28*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (20*(2 + 3*S^2 + S^4)*Zeta[3])/S^2) + HPL[{0}, S^2]*((-47*Pi^4*S^2)/30 + (Pi^2*(-856 - 893*S^2))/72 - (499*(1 + S^2))/6 - (70*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) - (35*(1 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + ((-97 - 270*S^2 - 173*S^4)/(6*S^2) - (11*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2}, -S^2] - (43*(1 + S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^2*((-80*Pi^2*(1 + S^4))/(9*S^2) - (50*(1 + 2*S^2 + S^4))/S^2 - (30*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((17 - 8*S^2 + 17*S^4)*HPL[{3}, -S^2])/(6*S^2) - (4*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (5*(1 + S^2)*(5 + 7*S^2)*HPL[{2, 1}, -S^2])/S^2 + (104*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (60*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (7*(-2 + S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((-395*(1 + 2*S^2 + S^4))/(6*S^2) - (2*Pi^2*(37 + 80*S^2 + 43*S^4))/(9*S^2) - (30*(1 + S^2)^2*HPL[{2}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (60*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (14*(1 + S^4)*Zeta[3])/(3*S^2)))) + ((5188 - 3233*S^2)/16 - (5*Pi^2*(-132 + 91*S^2))/24)*Zeta[5] + Zeta[3]*((Pi^2*(3920 - 1039*S^2))/96 + (Pi^4*(1884 - 977*S^2))/720 - (3*(-8294 + 3613*S^2))/64 - 32*(-1 + 3*S^2)*Zeta[5]) + HPL[{2, 1}, -S^2]*((10839*(-1 + S^4))/(64*S^2) + (881*Pi^6*(1 + S^4))/(3024*S^2) + (Pi^2*(-326 + 2324*S^2 + 1413*S^4))/(96*S^2) + (Pi^4*(531 + 5004*S^2 + 3161*S^4))/(1440*S^2) + ((-91 - 300*S^2 - 143*S^4)/S^2 - (76*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + (2*(43 + 90*S^2 + 41*S^4)*HPL[{3, 2}, -S^2])/S^2 + ((241 + 548*S^2 + 241*S^4)*HPL[{4, 1}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (18*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-48*Pi^2*(1 + S^4))/S^2 - (6*(39 + 100*S^2 + 39*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (4*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (4*(35 + 86*S^2 + 42*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (196*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (616*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (4*(77 + 172*S^2 + 77*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (368*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (736*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-39 - 94*S^2 - 34*S^4))/(6*S^2) + (-711 - 356*S^2 - 20*S^4)/(4*S^2))*Zeta[3] + (10*(1 + S^4)*Zeta[3]^2)/S^2 + ((-44 - 86*S^2 - 15*S^4)*Zeta[5])/S^2) + HPL[{3}, -S^2]*((17101 + 26212*S^2 - 4577*S^4)/(128*S^2) + (6067*Pi^6*(1 + S^4))/(90720*S^2) + (Pi^2*(1389 + 3068*S^2 + 209*S^4))/(96*S^2) + (Pi^4*(4483 + 6680*S^2 + 1629*S^4))/(2880*S^2) + ((113 - 40*S^2 - 241*S^4)/(8*S^2) - (4*Pi^2*(1 + S^4))/S^2)*HPL[{4}, -S^2] + ((-70 + 70*S^2 - 61*S^4)*HPL[{5}, -S^2])/(2*S^2) - (251*(1 + S^4)*HPL[{6}, -S^2])/(2*S^2) - (50*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-125 - 288*S^2 - 156*S^4)/(2*S^2) - (35*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + ((27 - 8*S^2 - 5*S^4)*HPL[{3, 2}, -S^2])/(2*S^2) + ((40 + 14*S^2 + 49*S^4)*HPL[{4, 1}, -S^2])/S^2 + (84*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((50*Pi^2*(1 + S^4))/(3*S^2) + (2*(58 + 150*S^2 + 59*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(23 + 48*S^2 + 22*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (4*(56 + 140*S^2 + 57*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (6*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (98*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (3224*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (4*(38 + 86*S^2 + 39*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (232*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (368*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((3 - 8*S^2 - 44*S^4)/(8*S^2) - (2*Pi^2*(2 - 3*S^2 + S^4))/(3*S^2))*Zeta[3] + (3*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((-731 - 356*S^2)/(4*S^2) - (2*Pi^2*(10 + 23*S^2 + 10*S^4))/(3*S^2) - (20*(1 + S^4)*Zeta[3])/S^2) + ((-15 + 16*S^2 - 5*S^4)*Zeta[5])/S^2) + HPL[{3, 1}, -S^2]*((Pi^2*(-493 + 86*S^2 + 764*S^4))/(24*S^2) + (Pi^4*(262 + 1062*S^2 + 1235*S^4))/(720*S^2) + (-7757 + 208*S^2 + 5905*S^4)/(32*S^2) + (90*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (340*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (4*(37 + 86*S^2 + 40*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (1488*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (368*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-129 - 288*S^2 - 122*S^4)/(2*S^2) - (35*Pi^2*(1 + S^4))/(3*S^2))*Zeta[3] - (76*(1 + S^4)*Zeta[5])/S^2) + HPL[{2}, -S^2]^2*((-1839 + 1556*S^2 - 1839*S^4)/(128*S^2) + (Pi^2*(-771 - 1052*S^2 - 1422*S^4))/(192*S^2) + (Pi^4*(-1052 - 2630*S^2 - 1281*S^4))/(2880*S^2) + ((2*Pi^2*(1 + S^4))/S^2 + (161 + 316*S^2 + 111*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((57 + 16*S^2 + 7*S^4)*HPL[{4}, -S^2])/(8*S^2) - (15*(1 + S^4)*HPL[{5}, -S^2])/(4*S^2) + ((25*(-1 + S^4))/(4*S^2) + (13*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2, 1}, -S^2] + ((-9 - 4*S^2 - 7*S^4)*HPL[{3, 1}, -S^2])/(2*S^2) - (26*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (76*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + ((1 - S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (52*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (106*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((7*Pi^2*(1 + S^4))/(4*S^2) + (137 + 280*S^2 + 87*S^4)/(8*S^2))*Zeta[3] + (9*(1 + S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]^4*((Pi^4*(-758 - 1849*S^2 - 1091*S^4))/(1080*S^2) - (2545*(1 + 2*S^2 + S^4))/(48*S^2) - (5*Pi^2*(98 + 241*S^2 + 143*S^4))/(72*S^2) - (43*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + ((53*Pi^2*(1 + S^4))/(18*S^2) + (419 + 580*S^2 + 161*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((23 + 28*S^2 + 5*S^4)*HPL[{4}, -S^2])/(3*S^2) + (2*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((43*(-1 + S^4))/(2*S^2) + (43*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2, 1}, -S^2] + (4*(-11 - 7*S^2 + 4*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (86*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (286*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (20*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (316*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((49*Pi^2*(1 + S^4))/(18*S^2) + (133 + 180*S^2 + 47*S^4)/(4*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(5 - 86*S^2 - 91*S^4))/(36*S^2) - (75*(-1 + S^4))/(4*S^2) + (43*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (86*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (43*(1 + S^4)*Zeta[3])/(3*S^2)) + (55*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{4}, -S^2]*((6925 - 416*S^2 - 3221*S^4)/(64*S^2) + (Pi^4*(969 + 448*S^2 - 545*S^4))/(1440*S^2) + (Pi^2*(432 + 272*S^2 - 9*S^4))/(48*S^2) + (245*(1 + S^4)*HPL[{5}, -S^2])/(2*S^2) + ((2*Pi^2*(1 + S^4))/S^2 + (2*(-19 - 7*S^2 + 7*S^4))/S^2)*HPL[{2, 1}, -S^2] + ((-71 + 12*S^2 - 55*S^4)*HPL[{3, 1}, -S^2])/(2*S^2) - (21*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (42*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + ((35 + 28*S^2 + 23*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (8*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (68*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (8*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((16*Pi^2*(1 + S^4))/(3*S^2) + (-31 - 16*S^2 + 38*S^4)/(4*S^2))*Zeta[3] + (55*(1 + S^4)*Zeta[5])/S^2) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(895 - 356*S^2 - 1626*S^4))/(24*S^2) + (Pi^4*(-136 - 1414*S^2 - 1005*S^4))/(360*S^2) - (6831*(-1 + S^4))/(16*S^2) + (368*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (736*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((18*Pi^2*(1 + S^4))/S^2 + (3*(45 + 100*S^2 + 33*S^4))/S^2)*Zeta[3] + (104*(1 + S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]^3*((Pi^4*(-7177 - 20228*S^2 - 13051*S^4))/(4320*S^2) + (Pi^2*(-4543 - 11936*S^2 - 7393*S^4))/(288*S^2) - (8699*Pi^6*(1 + S^4))/(27216*S^2) - (851*(1 + 2*S^2 + S^4))/(6*S^2) + ((-67*Pi^2*(1 + S^4))/(18*S^2) - (62*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2}, -S^2]^2 - (4*(1 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((57 + 56*S^2 - S^4)/(2*S^2) + (14*Pi^2*(1 + S^4))/(9*S^2))*HPL[{4}, -S^2] - (2*(-23 - 12*S^2 + 11*S^4)*HPL[{5}, -S^2])/(3*S^2) - (35*(1 + S^4)*HPL[{6}, -S^2])/(3*S^2) + (172*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((28*Pi^2*(1 + S^4))/(9*S^2) + (-57 - 28*S^2 + 29*S^4)/S^2)*HPL[{3, 1}, -S^2] - (4*(53 + 86*S^2 + 33*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (104*(7 + 11*S^2 + 4*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (6*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-86*(-1 + S^4))/S^2 - (86*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] - (344*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (16*(32 + 79*S^2 + 47*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (112*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (80*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (112*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + ((25*(4 + 5*S^2 + S^4))/S^2 + (2*Pi^2*(34 + 49*S^2 + 15*S^4))/(9*S^2))*Zeta[3] - (2*(1 + S^4)*Zeta[3]^2)/(3*S^2) + HPL[{2, 1}, -S^2]*((75*(-1 + S^4))/S^2 + (Pi^2*(-5 + 86*S^2 + 91*S^4))/(9*S^2) - (172*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((5*(59 + 73*S^2 + 14*S^4))/(3*S^2) + (2*Pi^2*(36 + 53*S^2 + 17*S^4))/(9*S^2) - (172*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(83 - 248*S^2 - 331*S^4))/(36*S^2) - (475*(-1 + S^4))/(8*S^2) - (707*Pi^4*(1 + S^4))/(1080*S^2) + (2*(53 + 86*S^2 + 33*S^4)*HPL[{3}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (172*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (172*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(55 + 86*S^2 + 31*S^4)*Zeta[3])/(3*S^2)) + (4*(42 + 55*S^2 + 13*S^4)*Zeta[5])/(3*S^2)) + Log[T]^3*(475/24 + (19*Pi^4*(16 + 9*S^2))/90 + (Pi^2*(1564 + 2425*S^2))/144 + ((55*Pi^2*(1 + S^4))/(9*S^2) + (100*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{1}, -S^2]^4 + (28*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/(3*S^2) + (28*(1 + S^4)*HPL[{1}, -S^2]^6)/(9*S^2) + HPL[{0}, S^2]^5*((11 + 8*S^2)/36 + (11*(1 + S^4)*HPL[{1}, -S^2])/(36*S^2)) + ((31*Pi^2*(1 + S^4))/(9*S^2) + (131 + 196*S^2 + 131*S^4)/(6*S^2))*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^4*((74 + 115*S^2)/72 + ((25 + 92*S^2 + 67*S^4)*HPL[{1}, -S^2])/(36*S^2) + (23*(1 + S^4)*HPL[{1}, -S^2]^2)/(18*S^2) + ((1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + (16*(1 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + (2*(-21 - 40*S^2 + 10*S^4)*HPL[{4}, -S^2])/(3*S^2) + ((-15 - 8*S^2 - 5*S^4)*HPL[{5}, -S^2])/S^2 - (160*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^3*((5*Pi^2*(11 + 8*S^2))/27 + (283 + 465*S^2)/36 + ((43 + 110*S^2 + 67*S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + (110*(1 + S^4)*HPL[{1}, -S^2]^3)/(27*S^2) + ((35 + 90*S^2 + 46*S^4)*HPL[{2}, -S^2])/(18*S^2) + HPL[{1}, -S^2]*((55*Pi^2*(1 + S^4))/(27*S^2) + (5*(41 + 124*S^2 + 83*S^4))/(36*S^2) + (5*(1 + S^4)*HPL[{2}, -S^2])/S^2) + (2*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) - (16*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) + ((-46*Pi^2*(1 + S^4))/(9*S^2) - (2*(-108 - 40*S^2 + 97*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + (2*(137 + 172*S^2 + 53*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (4*(244 + 286*S^2 + 111*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((410*(-1 + S^4))/(3*S^2) + (80*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + (4*(95 + 172*S^2 + 95*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(55 + 158*S^2 + 100*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (120*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((49*Pi^2*(-2 + S^2))/9 + (-1058 + 97*S^2)/6)*Zeta[3] + HPL[{1}, -S^2]^3*((790*(1 + 2*S^2 + S^4))/(9*S^2) + (20*Pi^2*(5 + 11*S^2 + 6*S^4))/(9*S^2) + (40*(-1 + S^4)*HPL[{2}, -S^2])/(3*S^2) - (400*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) - (40*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-747 - 2028*S^2 - 553*S^4)/(12*S^2) + (Pi^2*(-197 - 212*S^2 - 99*S^4))/(18*S^2) + (160*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(23 - 86*S^2 - 118*S^4))/(9*S^2) - (97*(-1 + S^4))/(6*S^2) + (160*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((1849*Pi^4*(1 + S^4))/(540*S^2) + (499*(1 + 2*S^2 + S^4))/(3*S^2) + (Pi^2*(267 + 620*S^2 + 353*S^4))/(12*S^2) + ((43*(-1 + S^4))/S^2 + (43*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] + (86*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) - (20*(13 + 20*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S^2) - (56*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (40*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (56*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (40*(2 + 3*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((2425*(-1 + S^4))/(24*S^2) + (77*Pi^4*(1 + S^4))/(135*S^2) + (Pi^2*(-195 + 196*S^2 + 457*S^4))/(36*S^2) - (2*(68 + 86*S^2 + 27*S^4)*HPL[{3}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (2*(95 + 172*S^2 + 95*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (160*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (320*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(67 + 86*S^2 + 28*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^2*((Pi^2*(136 + 145*S^2))/24 + (624 + 2425*S^2)/48 + (10*(3 + 8*S^2 + 5*S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + (20*(1 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + ((16*Pi^2*(1 + S^4))/(9*S^2) + (5 + 98*S^2 + 126*S^4)/(6*S^2))*HPL[{2}, -S^2] + (11*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{1}, -S^2]^2*((53*Pi^2*(1 + S^4))/(9*S^2) + (67 + 220*S^2 + 153*S^4)/(4*S^2) + (43*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-11 - 6*S^2 - 7*S^4)*HPL[{3}, -S^2])/(3*S^2) + ((-22 - 86*S^2 - 73*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (46*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (80*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (4*(-2 + S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((5*(19 + 83*S^2 + 64*S^4))/(6*S^2) + (Pi^2*(35 + 106*S^2 + 71*S^4))/(9*S^2) + ((25 + 86*S^2 + 61*S^4)*HPL[{2}, -S^2])/(3*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (86*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (8*(1 + S^4)*Zeta[3])/(3*S^2))) + HPL[{0}, S^2]*((2545*(1 + S^2))/12 + (Pi^2*(1073 + 1255*S^2))/36 + (Pi^4*(1874 + 1601*S^2))/540 + (70*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + (28*(1 + S^4)*HPL[{1}, -S^2]^5)/(3*S^2) + ((1 + S^2)*(101 + 71*S^2)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^3*((320*Pi^2*(1 + S^4))/(27*S^2) + (200*(1 + 2*S^2 + S^4))/(3*S^2) + (40*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((2 + 20*S^2 - 11*S^4)/(3*S^2) + (Pi^2*(-1 - S^4))/(3*S^2))*HPL[{3}, -S^2] + (2*(9 + 14*S^2 + 20*S^4)*HPL[{4}, -S^2])/(3*S^2) + (6*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-46*Pi^2*(1 + S^4))/(3*S^2) - (2*(173 + 270*S^2 + 97*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (4*(21 + 30*S^2 + 16*S^4)*HPL[{3, 1}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (40*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (20*(7 + 12*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (992*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (240*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-40 - 11*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]^2*((395*(1 + 2*S^2 + S^4))/(3*S^2) + (4*Pi^2*(37 + 80*S^2 + 43*S^4))/(9*S^2) + (60*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (120*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (28*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(140 + 270*S^2 + 121*S^4))/(18*S^2) + (397 + 1500*S^2 + 1103*S^4)/(12*S^2) - (8*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (172*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((937*Pi^4*(1 + S^4))/(270*S^2) + (499*(1 + 2*S^2 + S^4))/(3*S^2) + (35*Pi^2*(23 + 52*S^2 + 29*S^4))/(36*S^2) + ((15*Pi^2*(1 + S^4))/S^2 + (90*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + (86*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (8*(1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (28*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (120*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (120*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (240*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (28*(1 + 2*S^2 + S^4)*Zeta[3])/(3*S^2))) + (110*(-2 + S^2)*Zeta[5])/3 + HPL[{1}, -S^2]*((2545*(1 + 2*S^2 + S^4))/(12*S^2) + (5*Pi^2*(98 + 241*S^2 + 143*S^4))/(18*S^2) + (Pi^4*(758 + 1849*S^2 + 1091*S^4))/(270*S^2) + (86*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-419 - 580*S^2 - 161*S^4)/(3*S^2) - (106*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3}, -S^2] - (4*(23 + 28*S^2 + 5*S^4)*HPL[{4}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-86*(-1 + S^4))/S^2 - (86*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] - (16*(-11 - 7*S^2 + 4*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (344*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (1144*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (80*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (1264*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((-133 - 180*S^2 - 47*S^4)/S^2 - (98*Pi^2*(1 + S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((75*(-1 + S^4))/S^2 + (Pi^2*(-5 + 86*S^2 + 91*S^4))/(9*S^2) - (172*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (344*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (172*(1 + S^4)*Zeta[3])/(3*S^2)) - (220*(1 + S^4)*Zeta[5])/(3*S^2))) + HPL[{0}, S^2]^3*((-6023*Pi^6*S^2)/22680 + (-7063 - 10485*S^2)/384 + (Pi^4*(-7596 - 8975*S^2))/17280 + (Pi^2*(-2664 - 5371*S^2))/1152 + ((-43 - 110*S^2 - 67*S^4)*HPL[{1}, -S^2]^5)/(90*S^2) - (11*(1 + S^4)*HPL[{1}, -S^2]^6)/(54*S^2) + ((-10 - 45*S^2 - 46*S^4)/(24*S^2) - (11*Pi^2*(1 + S^4))/(48*S^2))*HPL[{2}, -S^2]^2 - (5*(1 + S^4)*HPL[{2}, -S^2]^3)/(24*S^2) + HPL[{1}, -S^2]^4*((-55*Pi^2*(1 + S^4))/(108*S^2) - (5*(41 + 124*S^2 + 83*S^4))/(144*S^2) - (5*(1 + S^4)*HPL[{2}, -S^2])/(4*S^2)) + ((1 + S^4)*HPL[{3}, -S^2]^2)/(2*S^2) + ((-182 - 216*S^2 - 25*S^4)/(48*S^2) + (43*Pi^2*(1 + S^4))/(72*S^2))*HPL[{4}, -S^2] + ((-139 + 36*S^2 - 5*S^4)*HPL[{5}, -S^2])/(24*S^2) + (125*(1 + S^4)*HPL[{6}, -S^2])/(12*S^2) + (3*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((11*Pi^2*(1 + S^4))/(18*S^2) + (91 + 252*S^2 + 214*S^4)/(24*S^2))*HPL[{3, 1}, -S^2] + ((13 - 24*S^2 + 5*S^4)*HPL[{3, 2}, -S^2])/(24*S^2) + ((7 - 4*S^2 - S^4)*HPL[{4, 1}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{4, 2}, -S^2])/(12*S^2) - (9*(1 + S^4)*HPL[{5, 1}, -S^2])/(2*S^2) + ((-35 - 118*S^2 - 110*S^4)/(6*S^2) - (2*Pi^2*(1 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + ((-14 - 38*S^2 - 27*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(23 + 60*S^2 + 40*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((1 + S^4)*HPL[{3, 1, 2}, -S^2])/(6*S^2) - (29*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(6*S^2) - (47*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + ((35 + 90*S^2 + 64*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (44*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (28*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((49*Pi^2*(-2 + S^2))/72 - (5*(20 + 13*S^2))/48)*Zeta[3] - 4*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^2*((-1223 - 4712*S^2 - 3489*S^4)/(192*S^2) - (937*Pi^4*(1 + S^4))/(2160*S^2) - (5*Pi^2*(63 + 244*S^2 + 181*S^4))/(288*S^2) + ((-97 - 280*S^2 - 183*S^4)/(24*S^2) - (85*Pi^2*(1 + S^4))/(72*S^2))*HPL[{2}, -S^2] - (19*(1 + S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + ((-1 - 2*S^2 - S^4)*HPL[{3}, -S^2])/(2*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/(2*S^2) + (5*(7 + 18*S^2 + 11*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (22*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (15*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-1 - 8*S^2 - 7*S^4)*Zeta[3])/(6*S^2)) + HPL[{3}, -S^2]*((-340 - 340*S^2 - 271*S^4)/(96*S^2) + (Pi^2*(-83 - 12*S^2 - 13*S^4))/(144*S^2) + ((-1 - S^4)*HPL[{2, 1}, -S^2])/S^2 - (3*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((-121 - 425*S^2 - 304*S^4)/(36*S^2) + (Pi^2*(-39 - 110*S^2 - 71*S^4))/(54*S^2) - (5*(7 + 18*S^2 + 11*S^4)*HPL[{2}, -S^2])/(18*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/(3*S^2) + (5*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + S^4)*Zeta[3])/(9*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(60 + 170*S^2 + 149*S^4))/(72*S^2) + (340 + 1036*S^2 + 365*S^4)/(48*S^2) + (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((-968 - 2056*S^2 - 2245*S^4)/(192*S^2) + (Pi^2*(-110 - 248*S^2 - 215*S^4))/(144*S^2) - (37*Pi^4*(1 + S^4))/(480*S^2) + ((-1 + 2*S^2)*HPL[{3}, -S^2])/(4*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/S^2 + ((14 + 38*S^2 + 27*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (7*(1 + S^4)*HPL[{3, 1}, -S^2])/(2*S^2) - (6*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((3 - 8*S^2 + S^4)*Zeta[3])/(12*S^2)) + (55*(-2 + S^2)*Zeta[5])/12 + HPL[{1}, -S^2]*((-4087 - 14924*S^2 - 10837*S^4)/(384*S^2) + (Pi^4*(-783 - 1874*S^2 - 1091*S^4))/(2160*S^2) + (Pi^2*(-226 - 965*S^2 - 739*S^4))/(144*S^2) + ((-15 - 38*S^2 - 23*S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + ((-13 - 20*S^2 - 7*S^4)/(8*S^2) + (Pi^2*(-1 - S^4))/(12*S^2))*HPL[{3}, -S^2] + ((-1 - 2*S^2 - S^4)*HPL[{4}, -S^2])/(2*S^2) + (3*(1 + S^4)*HPL[{5}, -S^2])/(2*S^2) + ((85*Pi^2*(1 + S^4))/(36*S^2) + (97 + 280*S^2 + 183*S^4)/(12*S^2))*HPL[{2, 1}, -S^2] + (2*(9 + 22*S^2 + 13*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((-1 - S^4)*HPL[{3, 2}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (5*(7 + 18*S^2 + 11*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (38*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (40*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (30*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((2 - 5*S^2 - 7*S^4)/(3*S^2) - (49*Pi^2*(1 + S^4))/(36*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-5*Pi^2*(11 + 34*S^2 + 23*S^4))/(72*S^2) - (5*(13 + 41*S^2 + 28*S^4))/(12*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(2*S^2) + (19*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(1 + S^4)*Zeta[3])/(3*S^2)) - (55*(1 + S^4)*Zeta[5])/(6*S^2))) + HPL[{0}, S^2]^2*((Pi^6*(-17398 - 44645*S^2))/72576 + (Pi^4*(980 - 32527*S^2))/11520 + (Pi^2*(3720 - 17839*S^2))/768 - (19*(-841 + 1664*S^2))/256 + ((-3 - 8*S^2 - 5*S^4)*HPL[{1}, -S^2]^6)/(6*S^2) - (4*(1 + S^4)*HPL[{1}, -S^2]^7)/(21*S^2) + ((-17 - 46*S^2 - 20*S^4)*HPL[{2}, -S^2]^3)/(24*S^2) + HPL[{1}, -S^2]^5*((-67 - 220*S^2 - 153*S^4)/(40*S^2) - (53*Pi^2*(1 + S^4))/(90*S^2) - (43*(1 + S^4)*HPL[{2}, -S^2])/(30*S^2)) - ((-11 + S^2)*(-1 + S^2)*HPL[{3}, -S^2]^2)/(8*S^2) + ((273 + 200*S^2 - 116*S^4)/(16*S^2) - (85*Pi^2*(1 + S^4))/(24*S^2))*HPL[{5}, -S^2] + ((155 - 64*S^2 - 63*S^4)*HPL[{6}, -S^2])/(4*S^2) - (275*(1 + S^4)*HPL[{7}, -S^2])/(4*S^2) + ((41 + 96*S^2 + 43*S^4)*HPL[{2, 1}, -S^2]^2)/(4*S^2) + ((47 - 80*S^2 - 36*S^4)/(16*S^2) - (17*Pi^2*(1 + S^4))/(24*S^2))*HPL[{3, 2}, -S^2] + ((-61 - 168*S^2 - 23*S^4)/(8*S^2) + (Pi^2*(-1 - S^4))/(2*S^2))*HPL[{4, 1}, -S^2] - ((-1 + S^2)*(1 + S^2)*HPL[{4, 2}, -S^2])/(2*S^2) + (13*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + ((-61 + 36*S^2 + 25*S^4)*HPL[{5, 1}, -S^2])/(4*S^2) + (153*(1 + S^4)*HPL[{5, 2}, -S^2])/(4*S^2) + (107*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((-97 - 320*S^2 - 147*S^4)/(4*S^2) - (15*Pi^2*(1 + S^4))/(2*S^2))*HPL[{2, 2, 1}, -S^2] + ((-233 - 912*S^2 - 432*S^4)/(4*S^2) - (64*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] + ((7 + 11*S^4)*HPL[{3, 1, 2}, -S^2])/(4*S^2) + ((-61 - 184*S^2 - 69*S^4)*HPL[{3, 2, 1}, -S^2])/(4*S^2) - (5*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/(4*S^2) + (8*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 - (3*(27 + 92*S^2 + 47*S^4)*HPL[{4, 1, 1}, -S^2])/(2*S^2) + (8*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (38*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (83*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((14*Pi^2*(1 + S^4))/S^2 + (41 + 150*S^2 + 76*S^4)/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (52*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((35 + 84*S^2 + 61*S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (161*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (161*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (317*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (960*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (2*(28 + 86*S^2 + 49*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (104*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (312*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (548*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (184*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((454 - 307*S^2)/16 + (Pi^2*(172 - 199*S^2))/48)*Zeta[3] + ((-2 - 43*S^2)*Zeta[3]^2)/4 + HPL[{1}, -S^2]^3*((Pi^2*(-127 - 572*S^2 - 445*S^4))/(72*S^2) - (359*Pi^4*(1 + S^4))/(540*S^2) - (19*(29 + 208*S^2 + 179*S^4))/(96*S^2) + ((-23 - 124*S^2 - 101*S^4)/(6*S^2) - (37*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2] - (4*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((7 + 6*S^2 - S^4)*HPL[{3}, -S^2])/(3*S^2) + ((25 + 86*S^2 + 61*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (86*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (8*(1 + S^2)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((343*Pi^4*(1 + S^4))/(360*S^2) + (Pi^2*(48 + 276*S^2 + 157*S^4))/(24*S^2) + (99 + 2324*S^2 + 988*S^4)/(32*S^2) - (30*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (52*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(-1 + 2*S^2)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((526 + 420*S^2 - 229*S^4)/(32*S^2) + (Pi^2*(211 + 168*S^2 - 24*S^4))/(96*S^2) - (59*Pi^4*(1 + S^4))/(480*S^2) - (13*(1 + S^4)*HPL[{4}, -S^2])/(2*S^2) + ((-2 - 6*S^2 - S^4)*HPL[{2, 1}, -S^2])/(2*S^2) - (6*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-11 + 12*S^2 - S^4)*Zeta[3])/(4*S^2)) + HPL[{3, 1}, -S^2]*((Pi^2*(35 + 146*S^2 + 102*S^4))/(24*S^2) + (-26 + 88*S^2 + 201*S^4)/(4*S^2) - (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((-40 - 340*S^2 - 691*S^4)/(64*S^2) + (Pi^2*(-50 - 158*S^2 - 75*S^4))/(96*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/(4*S^2) + (13*(1 + S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + ((1 + S^4)*Zeta[3])/(4*S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(-35 - 106*S^2 - 71*S^4))/(36*S^2) - (5*(19 + 83*S^2 + 64*S^4))/(24*S^2) + ((-25 - 86*S^2 - 61*S^4)*HPL[{2}, -S^2])/(12*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(2*S^2) + (43*(1 + S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (2*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((92 - 356*S^2 - 823*S^4)/(8*S^2) + (Pi^2*(-31 - 148*S^2 - 87*S^4))/(12*S^2) + (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(19 - 4*S^2 - 5*S^4))/(8*S^2) + (246 + 92*S^2 + 19*S^4)/(16*S^2) + (7*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (25*(1 + S^4)*Zeta[3])/(2*S^2)) + HPL[{1}, -S^2]^2*((-151 - 9228*S^2 - 9077*S^4)/(128*S^2) + (Pi^2*(-161 - 1452*S^2 - 1291*S^4))/(96*S^2) + (Pi^4*(-369 - 1436*S^2 - 1067*S^4))/(720*S^2) + ((-19 - 48*S^2 - 29*S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + ((53 + 36*S^2 - 17*S^4)/(8*S^2) + (Pi^2*(1 + S^4))/(4*S^2))*HPL[{3}, -S^2] - (5*(-1 + S^4)*HPL[{4}, -S^2])/(2*S^2) - (3*(1 + S^4)*HPL[{5}, -S^2])/(2*S^2) + ((37*Pi^2*(1 + S^4))/(6*S^2) + (23 + 124*S^2 + 101*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + (6*(2 + 7*S^2 + 5*S^4)*HPL[{3, 1}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (9*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + ((-25 - 86*S^2 - 61*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (138*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (86*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((9 + 7*S^2 - 2*S^4)/S^2 + (Pi^2*(-1 - S^4))/(4*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-10 - 157*S^2 - 147*S^4)/(4*S^2) + (Pi^2*(-35 - 148*S^2 - 113*S^4))/(24*S^2) + (3*(1 + S^4)*HPL[{3}, -S^2])/(2*S^2) + (24*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (2*(1 + S^4)*Zeta[3])/S^2)) + ((220 - 281*S^2)*Zeta[5])/8 + HPL[{1}, -S^2]*((5259 - 19952*S^2 - 25211*S^4)/(256*S^2) + (Pi^4*(265 - 6332*S^2 - 6597*S^4))/(2880*S^2) + (Pi^2*(152 - 1639*S^2 - 1791*S^4))/(96*S^2) - (8699*Pi^6*(1 + S^4))/(36288*S^2) + ((-85 - 268*S^2 - 183*S^4)/(16*S^2) - (79*Pi^2*(1 + S^4))/(48*S^2))*HPL[{2}, -S^2]^2 - (23*(1 + S^4)*HPL[{2}, -S^2]^3)/(12*S^2) + (3*(1 + S^4)*HPL[{3}, -S^2]^2)/(2*S^2) + ((19 + 6*S^2 - 13*S^4)/(2*S^2) + (Pi^2*(-1 - S^4))/(2*S^2))*HPL[{4}, -S^2] + ((2 - 3*S^2 - 5*S^4)*HPL[{5}, -S^2])/S^2 - (16*(1 + S^4)*HPL[{6}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((73*Pi^2*(1 + S^4))/(12*S^2) + (2*(4 + 29*S^2 + 25*S^4))/S^2)*HPL[{3, 1}, -S^2] - (2*(1 + S^2)*(2 + S^2)*HPL[{3, 2}, -S^2])/S^2 + ((-17 - 18*S^2 - S^4)*HPL[{4, 1}, -S^2])/S^2 + (9*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-23 - 124*S^2 - 101*S^4)/S^2 - (37*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (2*(1 + S^2)*(19 + 29*S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (4*(25 + 69*S^2 + 44*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (46*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (138*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (2*(25 + 86*S^2 + 61*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (84*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((135 + 92*S^2 - 43*S^4)/(8*S^2) + (Pi^2*(4 - S^2 - 5*S^4))/(2*S^2))*Zeta[3] + ((-1 - S^4)*Zeta[3]^2)/(2*S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(35 + 148*S^2 + 113*S^4))/(12*S^2) + (10 + 157*S^2 + 147*S^4)/(2*S^2) - (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((79 + 34*S^2 - 45*S^4)/(8*S^2) + (Pi^2*(5 + 3*S^2 - 2*S^4))/(6*S^2) - (3*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (3*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((409 - 2784*S^2 - 3193*S^4)/(64*S^2) - (473*Pi^4*(1 + S^4))/(720*S^2) - (5*Pi^2*(17 + 172*S^2 + 155*S^4))/(96*S^2) + ((1 + S^2)*(2 + S^2)*HPL[{3}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((1 + S^2)*(19 + 29*S^2)*HPL[{2, 1}, -S^2])/S^2 + (26*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((5 + 8*S^2 + 3*S^4)*Zeta[3])/(2*S^2)) - (13*(-1 + S^4)*Zeta[5])/S^2) + HPL[{2}, -S^2]*((2944 + 778*S^2 - 4783*S^4)/(128*S^2) + (Pi^2*(214 - 165*S^2 - 696*S^4))/(96*S^2) + (Pi^4*(167 - 946*S^2 - 474*S^4))/(1440*S^2) + ((5*Pi^2*(1 + S^4))/(12*S^2) + (-2 + 5*S^2 + 3*S^4)/(2*S^2))*HPL[{3}, -S^2] + ((-11 + S^2)*(-1 + S^2)*HPL[{4}, -S^2])/(4*S^2) + (13*(1 + S^4)*HPL[{5}, -S^2])/(2*S^2) + ((15*Pi^2*(1 + S^4))/(4*S^2) + (97 + 320*S^2 + 147*S^4)/(8*S^2))*HPL[{2, 1}, -S^2] + ((19 + 52*S^2 + 21*S^4)*HPL[{3, 1}, -S^2])/(2*S^2) + ((1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + ((-41 - 96*S^2 - 43*S^4)*HPL[{2, 1, 1}, -S^2])/(2*S^2) - (26*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (82*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (52*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((19*Pi^2*(1 + S^4))/(12*S^2) + (7 + 12*S^2 + 6*S^4)/(4*S^2))*Zeta[3] + (29*(1 + S^4)*Zeta[5])/(2*S^2))) + Log[T]^2*(-725/32 + (Pi^6*(-86990 - 30489*S^2))/90720 + (Pi^4*(-10786 - 15709*S^2))/2880 - (11*Pi^2*(134 + 621*S^2))/192 - (S^2*HPL[{0}, S^2]^7)/48 + ((-11*Pi^2*(1 + S^4))/(3*S^2) - (20*(1 + 2*S^2 + S^4))/S^2)*HPL[{1}, -S^2]^5 - (14*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) - (4*(1 + S^4)*HPL[{1}, -S^2]^7)/(3*S^2) + HPL[{0}, S^2]^6*((-8 - 9*S^2)/96 + ((-1 - S^4)*HPL[{1}, -S^2])/(12*S^2)) - ((-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(6*S^2) + HPL[{0}, S^2]^5*((-5*Pi^2*S^2)/24 - (5*(2 + 3*S^2))/24 + ((-7 - 22*S^2 - 15*S^4)*HPL[{1}, -S^2])/(24*S^2) - (11*(1 + S^4)*HPL[{1}, -S^2]^2)/(24*S^2) + ((-1 - S^4)*HPL[{2}, -S^2])/(8*S^2)) + ((-13 - 4*S^2 - 9*S^4)*HPL[{3}, -S^2]^2)/S^2 + ((200 + 196*S^2 - 91*S^4)/(4*S^2) + (5*Pi^2*(1 + S^4))/(6*S^2))*HPL[{5}, -S^2] - (5*(-34 + 14*S^2 + 27*S^4)*HPL[{6}, -S^2])/(2*S^2) - (100*(1 + S^4)*HPL[{7}, -S^2])/S^2 + ((77 + 172*S^2 + 77*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + HPL[{0}, S^2]^4*((-118 - 905*S^2)/192 + (Pi^2*(-106 - 85*S^2))/144 + ((-25 - 92*S^2 - 67*S^4)*HPL[{1}, -S^2]^2)/(24*S^2) - (23*(1 + S^4)*HPL[{1}, -S^2]^3)/(18*S^2) + ((-3 - 62*S^2 - 38*S^4)*HPL[{2}, -S^2])/(48*S^2) + HPL[{1}, -S^2]*((-53 - 484*S^2 - 431*S^4)/(96*S^2) - (53*Pi^2*(1 + S^4))/(72*S^2) - (31*(1 + S^4)*HPL[{2}, -S^2])/(24*S^2)) + (19*(1 + S^4)*HPL[{2, 1}, -S^2])/(12*S^2)) + ((-487 - 1200*S^2 - 449*S^4)/(4*S^2) - (97*Pi^2*(1 + S^4))/(6*S^2))*HPL[{3, 2}, -S^2] + ((-477 - 988*S^2 - 371*S^4)/S^2 - (178*Pi^2*(1 + S^4))/(3*S^2))*HPL[{4, 1}, -S^2] + ((13 - 36*S^2 + 5*S^4)*HPL[{4, 2}, -S^2])/(2*S^2) + (44*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + ((-31 - 88*S^2 + 75*S^4)*HPL[{5, 1}, -S^2])/S^2 + (130*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 + (280*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((-48*Pi^2*(1 + S^4))/S^2 - (6*(39 + 100*S^2 + 39*S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((-298*Pi^2*(1 + S^4))/(3*S^2) - (2*(171 + 556*S^2 + 224*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (2*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 - (2*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + (188*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (608*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 - (4*(-9 - 28*S^2 + 23*S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (592*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (1888*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (3936*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((106*(-1 + S^4))/S^2 + (92*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] + (8*(-4 - 14*S^2 + 11*S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (368*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (368*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (368*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (1328*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (120*(-1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (736*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (2208*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (4640*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + ((3012 - 425*S^2)/8 + (Pi^2*(380 - 87*S^2))/12)*Zeta[3] + (-2 - 11*S^2)*Zeta[3]^2 + HPL[{3}, -S^2]*((257*Pi^4*(1 + S^4))/(180*S^2) + (Pi^2*(418 + 736*S^2 + 263*S^4))/(24*S^2) + (863 + 2648*S^2 + 438*S^4)/(8*S^2) - (22*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (2*(38 + 86*S^2 + 39*S^4)*HPL[{2, 1}, -S^2])/S^2 - (116*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (184*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-5 + 12*S^2 - 7*S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((Pi^2*(27 + 56*S^2 + 83*S^4))/(6*S^2) + (-441 - 90*S^2 + 362*S^4)/(2*S^2) - (108*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(33 + 56*S^2 - 61*S^4))/(12*S^2) + (93 + 90*S^2 - 14*S^4)/(2*S^2) - (4*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (14*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((-731 - 712*S^2 - 731*S^4)/(16*S^2) + (Pi^2*(-59 - 134*S^2 - 60*S^4))/(12*S^2) + (25*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (20*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*((-395*(1 + 2*S^2 + S^4))/(6*S^2) - (5*Pi^2*(5 + 11*S^2 + 6*S^4))/(3*S^2) - (10*(-1 + S^4)*HPL[{2}, -S^2])/S^2 + (100*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (30*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-13 - 86*S^2 - 64*S^4))/(3*S^2) - (803*(-1 + S^4))/(2*S^2) + (184*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((Pi^2*(-267 - 620*S^2 - 353*S^4))/(12*S^2) - (1849*Pi^4*(1 + S^4))/(540*S^2) - (499*(1 + 2*S^2 + S^4))/(3*S^2) + ((-43*(-1 + S^4))/S^2 - (43*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] - (86*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (20*(13 + 20*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S^2) + (56*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (40*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (56*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (40*(2 + 3*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((425*(-1 + S^4))/(8*S^2) + (133*Pi^4*(1 + S^4))/(60*S^2) + (Pi^2*(29 + 300*S^2 + 205*S^4))/(12*S^2) - (184*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (368*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(43 + 86*S^2 + 34*S^4)*Zeta[3])/S^2) + HPL[{0}, S^2]^3*((-47*Pi^4*S^2)/60 + (-448 - 897*S^2)/32 + (Pi^2*(-456 - 593*S^2))/144 + ((-43 - 110*S^2 - 67*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) - (55*(1 + S^4)*HPL[{1}, -S^2]^4)/(18*S^2) + ((-35 - 118*S^2 - 110*S^4)/(12*S^2) + (Pi^2*(-1 - S^4))/S^2)*HPL[{2}, -S^2] - (3*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + HPL[{1}, -S^2]^2*((-55*Pi^2*(1 + S^4))/(18*S^2) - (5*(41 + 124*S^2 + 83*S^4))/(24*S^2) - (15*(1 + S^4)*HPL[{2}, -S^2])/(2*S^2)) + ((-4 - 6*S^2 + S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/(3*S^2) + ((35 + 90*S^2 + 64*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (22*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (14*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(-2 + S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((-121 - 425*S^2 - 304*S^4)/(12*S^2) + (Pi^2*(-39 - 110*S^2 - 71*S^4))/(18*S^2) - (5*(7 + 18*S^2 + 11*S^4)*HPL[{2}, -S^2])/(6*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/S^2 + (15*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + S^4)*Zeta[3])/(3*S^2))) + HPL[{0}, S^2]^2*((-158 - 6831*S^2)/64 + (Pi^2*(-144 - 427*S^2))/24 + (Pi^4*(-359 - 199*S^2))/180 - (5*(3 + 8*S^2 + 5*S^4)*HPL[{1}, -S^2]^4)/(2*S^2) - (4*(1 + S^4)*HPL[{1}, -S^2]^5)/S^2 + ((-41 - 96*S^2 - 43*S^4)*HPL[{2}, -S^2]^2)/(8*S^2) + HPL[{1}, -S^2]^3*((-67 - 220*S^2 - 153*S^4)/(4*S^2) - (53*Pi^2*(1 + S^4))/(9*S^2) - (43*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((7*Pi^2*(1 + S^4))/(12*S^2) + (58 + 48*S^2 + 9*S^4)/(8*S^2))*HPL[{3}, -S^2] - (21*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/(4*S^2) - (7*(1 + S^4)*HPL[{5}, -S^2])/(2*S^2) + ((7*Pi^2*(1 + S^4))/S^2 + (41 + 150*S^2 + 76*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((35 + 84*S^2 + 61*S^4)*HPL[{3, 1}, -S^2])/(2*S^2) - (5*(1 + S^4)*HPL[{3, 2}, -S^2])/(2*S^2) - (12*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + ((-28 - 86*S^2 - 49*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (52*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (142*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (92*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((24 - 17*S^2)*Zeta[3])/2 + HPL[{1}, -S^2]*((Pi^2*(-127 - 572*S^2 - 445*S^4))/(24*S^2) - (359*Pi^4*(1 + S^4))/(180*S^2) - (19*(29 + 208*S^2 + 179*S^4))/(32*S^2) + ((-23 - 124*S^2 - 101*S^4)/(2*S^2) - (37*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2}, -S^2] - (12*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((7 + 6*S^2 - S^4)*HPL[{3}, -S^2])/S^2 + ((25 + 86*S^2 + 61*S^4)*HPL[{2, 1}, -S^2])/S^2 + (42*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (86*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (8*(1 + S^2)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((92 - 356*S^2 - 823*S^4)/(16*S^2) + (Pi^2*(-31 - 148*S^2 - 87*S^4))/(24*S^2) + (2*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (26*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*((Pi^2*(-35 - 106*S^2 - 71*S^4))/(6*S^2) - (5*(19 + 83*S^2 + 64*S^4))/(4*S^2) + ((-25 - 86*S^2 - 61*S^4)*HPL[{2}, -S^2])/(2*S^2) + (3*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (43*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/S^2)) + HPL[{0}, S^2]*((-6023*Pi^6*S^2)/5670 + (Pi^2*(-5336 - 6683*S^2))/96 + (Pi^4*(-4624 - 5147*S^2))/720 - (851*(1 + S^2))/2 - (14*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/S^2 - (14*(1 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + ((-91 - 248*S^2 - 157*S^4)/(4*S^2) - (61*Pi^2*(1 + S^4))/(12*S^2))*HPL[{2}, -S^2]^2 - (19*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^4*((-80*Pi^2*(1 + S^4))/(9*S^2) - (50*(1 + 2*S^2 + S^4))/S^2 - (30*(1 + S^4)*HPL[{2}, -S^2])/S^2) + (2*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-74 - 120*S^2 - 81*S^4)/(4*S^2) - (7*Pi^2*(1 + S^4))/(3*S^2))*HPL[{4}, -S^2] + ((-39 - 20*S^2 - 5*S^4)*HPL[{5}, -S^2])/(2*S^2) + (10*(1 + S^4)*HPL[{6}, -S^2])/S^2 + (86*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((74*Pi^2*(1 + S^4))/(3*S^2) + (114 + 272*S^2 + 187*S^4)/S^2)*HPL[{3, 1}, -S^2] + ((-1 - 20*S^2 + 5*S^4)*HPL[{3, 2}, -S^2])/S^2 - (4*(5 + 8*S^2 + 6*S^4)*HPL[{4, 1}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (10*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-44*Pi^2*(1 + S^4))/S^2 - (2*(97 + 270*S^2 + 173*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (2*(1 + S^2)*(71 + 101*S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (4*(98 + 262*S^2 + 143*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 - (140*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (504*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (60*(5 + 12*S^2 + 7*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (416*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (720*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(2 - S^2))/2 + (90 + 79*S^2)/4)*Zeta[3] - 16*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(110 + 270*S^2 + 169*S^4))/(6*S^2) + (1103 + 1500*S^2 + 397*S^4)/(4*S^2) - (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-127 - 220*S^2 - 71*S^4)/(8*S^2) + (Pi^2*(9 - 20*S^2 + 19*S^4))/(12*S^2) - (12*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((-395*(1 + 2*S^2 + S^4))/(3*S^2) - (4*Pi^2*(37 + 80*S^2 + 43*S^4))/(9*S^2) - (60*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 - (8*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (120*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (28*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((-937*Pi^4*(1 + S^4))/(180*S^2) - (499*(1 + 2*S^2 + S^4))/(2*S^2) - (35*Pi^2*(23 + 52*S^2 + 29*S^4))/(24*S^2) + ((-45*Pi^2*(1 + S^4))/(2*S^2) - (135*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] - (43*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 - (4*(1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/S^2 - (14*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (180*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (180*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (360*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (14*(1 + 2*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-127 - 504*S^2 - 377*S^4)/(2*S^2) + (Pi^2*(-132 - 388*S^2 - 283*S^4))/(12*S^2) - (349*Pi^4*(1 + S^4))/(180*S^2) + ((5 + 10*S^2 + 2*S^4)*HPL[{3}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((1 + S^2)*(71 + 101*S^2)*HPL[{2, 1}, -S^2])/S^2 + (88*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((8 + 10*S^2 + 5*S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((Pi^4*(-807 - 1874*S^2 - 1067*S^4))/(180*S^2) + (Pi^2*(-172 - 405*S^2 - 233*S^4))/(4*S^2) - (2545*(1 + 2*S^2 + S^4))/(8*S^2) - (43*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((-25 - 44*S^2 - 19*S^4)/(2*S^2) - (5*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] - (14*(1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/S^2 - (10*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((45*Pi^2*(1 + S^4))/S^2 + (270*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (180*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (20*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (32*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (360*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (1048*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (720*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(1 + S^4))/S^2 + (3*(15 + 28*S^2 + 13*S^4))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-375*(1 + 2*S^2 + S^4))/(2*S^2) - (5*Pi^2*(25 + 54*S^2 + 29*S^4))/(6*S^2) + (10*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (10*(1 + S^4)*Zeta[3])/S^2))) + (220 - 87*S^2)*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(895 - 356*S^2 - 1626*S^4))/(48*S^2) + (Pi^4*(-136 - 1414*S^2 - 1005*S^4))/(720*S^2) - (6831*(-1 + S^4))/(32*S^2) + ((25*Pi^2*(1 + S^4))/(3*S^2) + (58 + 150*S^2 + 59*S^4)/S^2)*HPL[{3}, -S^2] + ((35 + 28*S^2 + 23*S^4)*HPL[{4}, -S^2])/(2*S^2) + (23*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((24*Pi^2*(1 + S^4))/S^2 + (3*(39 + 100*S^2 + 39*S^4))/S^2)*HPL[{2, 1}, -S^2] + (2*(37 + 86*S^2 + 40*S^4)*HPL[{3, 1}, -S^2])/S^2 - (94*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (296*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (2*(77 + 172*S^2 + 77*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (184*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (368*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((9*Pi^2*(1 + S^4))/S^2 + (3*(45 + 100*S^2 + 33*S^4))/(2*S^2))*Zeta[3] + (52*(1 + S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]^2*((Pi^4*(-758 - 1849*S^2 - 1091*S^4))/(180*S^2) - (2545*(1 + 2*S^2 + S^4))/(8*S^2) - (5*Pi^2*(98 + 241*S^2 + 143*S^4))/(12*S^2) - (43*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((53*Pi^2*(1 + S^4))/(3*S^2) + (419 + 580*S^2 + 161*S^4)/(2*S^2))*HPL[{3}, -S^2] + (2*(23 + 28*S^2 + 5*S^4)*HPL[{4}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((129*(-1 + S^4))/S^2 + (43*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (8*(-11 - 7*S^2 + 4*S^4)*HPL[{3, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (572*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (120*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (632*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((49*Pi^2*(1 + S^4))/(3*S^2) + (3*(133 + 180*S^2 + 47*S^4))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(5 - 86*S^2 - 91*S^4))/(6*S^2) - (225*(-1 + S^4))/(2*S^2) + (86*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (86*(1 + S^4)*Zeta[3])/S^2) + (110*(1 + S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]*((Pi^4*(-7177 - 20228*S^2 - 13051*S^4))/(1440*S^2) + (Pi^2*(-4543 - 11936*S^2 - 7393*S^4))/(96*S^2) - (8699*Pi^6*(1 + S^4))/(9072*S^2) - (851*(1 + 2*S^2 + S^4))/(2*S^2) + ((-67*Pi^2*(1 + S^4))/(6*S^2) - (62*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 - (4*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((14*Pi^2*(1 + S^4))/(3*S^2) - (3*(-57 - 56*S^2 + S^4))/(2*S^2))*HPL[{4}, -S^2] - (2*(1 + S^2)*(-23 + 11*S^2)*HPL[{5}, -S^2])/S^2 - (35*(1 + S^4)*HPL[{6}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((28*Pi^2*(1 + S^4))/(3*S^2) + (3*(-57 - 28*S^2 + 29*S^4))/S^2)*HPL[{3, 1}, -S^2] - (4*(53 + 86*S^2 + 33*S^4)*HPL[{3, 2}, -S^2])/S^2 - (104*(1 + S^2)*(7 + 4*S^2)*HPL[{4, 1}, -S^2])/S^2 - (18*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-258*(-1 + S^4))/S^2 - (86*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (344*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (16*(32 + 79*S^2 + 47*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (112*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (240*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (112*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + ((75*(4 + 5*S^2 + S^4))/S^2 + (2*Pi^2*(34 + 49*S^2 + 15*S^4))/(3*S^2))*Zeta[3] - (2*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((225*(-1 + S^4))/S^2 + (Pi^2*(-5 + 86*S^2 + 91*S^4))/(3*S^2) - (172*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((5*(59 + 73*S^2 + 14*S^4))/S^2 + (2*Pi^2*(36 + 53*S^2 + 17*S^4))/(3*S^2) - (172*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (12*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(83 - 248*S^2 - 331*S^4))/(12*S^2) - (1425*(-1 + S^4))/(8*S^2) - (707*Pi^4*(1 + S^4))/(360*S^2) + (2*(53 + 86*S^2 + 33*S^4)*HPL[{3}, -S^2])/S^2 + (14*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (172*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(55 + 86*S^2 + 31*S^4)*Zeta[3])/S^2) + (4*(42 + 55*S^2 + 13*S^4)*Zeta[5])/S^2)) - (225*(-4 + 5*S^2)*Zeta[7])/4 + HPL[{1}, -S^2]*((Pi^6*(-80077 - 421652*S^2 - 341575*S^4))/(362880*S^2) + (Pi^4*(-24285 - 120548*S^2 - 96263*S^4))/(11520*S^2) + (Pi^2*(-21973 - 74416*S^2 - 52443*S^4))/(768*S^2) - (20621*Pi^8*(1 + S^4))/(217728*S^2) - (15995*(1 + 2*S^2 + S^4))/(32*S^2) + ((-49*(-1 + S^4))/(12*S^2) - (23*Pi^2*(1 + S^4))/(36*S^2))*HPL[{2}, -S^2]^3 - (23*(1 + S^4)*HPL[{2}, -S^2]^4)/(12*S^2) + ((-13 - 14*S^2 - S^4)/(2*S^2) + (Pi^2*(1 + S^4))/(6*S^2))*HPL[{3}, -S^2]^2 - (16*(1 + S^4)*HPL[{4}, -S^2]^2)/S^2 + ((943 - 196*S^2 - 1139*S^4)/(8*S^2) - (33*Pi^2*(1 + S^4))/(4*S^2))*HPL[{6}, -S^2] - (3*(-17 + 48*S^2 + 65*S^4)*HPL[{7}, -S^2])/S^2 - (771*(1 + S^4)*HPL[{8}, -S^2])/(2*S^2) + ((67*Pi^2*(1 + S^4))/(3*S^2) + (124*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2]^2 - (108*(1 + S^4)*HPL[{3, 1}, -S^2]^2)/S^2 + ((-3*Pi^2*(1 + S^4))/(2*S^2) - (27*(1 + 2*S^2 + S^4))/(2*S^2))*HPL[{4, 2}, -S^2] + (22*(1 + S^2)*HPL[{4, 3}, -S^2])/S^2 + ((-13*Pi^2*(1 + S^4))/(3*S^2) + (-345 - 292*S^2 + 53*S^4)/(2*S^2))*HPL[{5, 1}, -S^2] + (60*(1 + S^2)*HPL[{5, 2}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{5, 3}, -S^2])/S^2 + (10*(4 + 15*S^2 + 11*S^4)*HPL[{6, 1}, -S^2])/S^2 - (15*(1 + S^4)*HPL[{6, 2}, -S^2])/(2*S^2) + (208*(1 + S^4)*HPL[{7, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((-98*(-1 + S^4))/S^2 - (46*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 2, 1}, -S^2] + (2*(107 + 174*S^2 + 67*S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (16*(41 + 67*S^2 + 26*S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + (14*(1 + S^4)*HPL[{3, 3, 2}, -S^2])/S^2 + ((-110*Pi^2*(1 + S^4))/(3*S^2) - (3*(-155 - 56*S^2 + 99*S^4))/S^2)*HPL[{4, 1, 1}, -S^2] + (10*(65 + 106*S^2 + 41*S^4)*HPL[{4, 1, 2}, -S^2])/S^2 - (34*(1 + S^4)*HPL[{4, 1, 3}, -S^2])/S^2 + (2*(997 + 1634*S^2 + 637*S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{4, 2, 2}, -S^2])/S^2 - (26*(1 + S^4)*HPL[{4, 3, 1}, -S^2])/S^2 + (4*(1031 + 1668*S^2 + 637*S^4)*HPL[{5, 1, 1}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{5, 1, 2}, -S^2])/S^2 - (124*(1 + S^4)*HPL[{5, 2, 1}, -S^2])/S^2 - (430*(1 + S^4)*HPL[{6, 1, 1}, -S^2])/S^2 + (80*(-1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((56*Pi^2*(1 + S^4))/(3*S^2) + (6*(-57 - 28*S^2 + 29*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] - (8*(23 + 86*S^2 + 63*S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (8*(23 + 86*S^2 + 63*S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/S^2 - (8*(-7 + 86*S^2 + 93*S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3, 2, 2, 1}, -S^2])/S^2 + (96*(1 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (16*(1 + 143*S^2 + 142*S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (36*(1 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/S^2 + (60*(1 + S^4)*HPL[{4, 1, 2, 1}, -S^2])/S^2 + (252*(1 + S^4)*HPL[{4, 2, 1, 1}, -S^2])/S^2 + (400*(1 + S^4)*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((-516*(-1 + S^4))/S^2 - (172*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (688*(1 + 2*S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (2064*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (160*(28 + 53*S^2 + 25*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (224*(1 + S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + (480*(-1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 - (224*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((19 - 20*S^2 - 39*S^4)/(4*S^2) + (Pi^2*(-1 - S^4))/(3*S^2))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((450*(-1 + S^4))/S^2 + (2*Pi^2*(-5 + 86*S^2 + 91*S^4))/(3*S^2) - (344*(1 + S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((-829 - 1044*S^2 - 215*S^4)/S^2 + (Pi^2*(-199 - 304*S^2 - 105*S^4))/(3*S^2) - (80*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 2}, -S^2]*((Pi^2*(-57 - 92*S^2 - 35*S^4))/(3*S^2) - (2*(116 + 157*S^2 + 41*S^4))/S^2 - (24*(1 + S^4)*Zeta[3])/S^2) + HPL[{5}, -S^2]*((275 - 134*S^2 - 409*S^4)/(4*S^2) + (Pi^2*(9 + 2*S^2 - 7*S^4))/(2*S^2) - (20*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (28*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((-314*(1 + 2*S^2 + S^4))/S^2 - (4*Pi^2*(31 + 67*S^2 + 36*S^4))/(3*S^2) + (152*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 1, 1}, -S^2]*((-4*Pi^2*(57 + 148*S^2 + 91*S^4))/(3*S^2) - (2*(176 + 577*S^2 + 401*S^4))/S^2 + (480*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((475 + 244*S^2 - 231*S^4)/(4*S^2) + (Pi^2*(247 + 192*S^2 - 55*S^4))/(24*S^2) + (14*Pi^4*(1 + S^4))/(45*S^2) - (14*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (6*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (28*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(3 + 4*S^2 + S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((59*Pi^4*(1 + S^4))/(40*S^2) + (Pi^2*(-139 + 148*S^2 + 287*S^4))/(12*S^2) + (-1669 - 488*S^2 + 1181*S^4)/(8*S^2) + (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (16*(7 + 11*S^2 + 4*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((Pi^2*(-333 - 764*S^2 - 431*S^4))/(48*S^2) - (263*Pi^4*(1 + S^4))/(288*S^2) - (87*(1 + 2*S^2 + S^4))/(2*S^2) + ((29 + 48*S^2 + 19*S^4)*HPL[{3}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (10*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (2*(12 + 19*S^2 + 7*S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(83 - 248*S^2 - 331*S^4))/(6*S^2) - (1425*(-1 + S^4))/(4*S^2) - (707*Pi^4*(1 + S^4))/(180*S^2) + (4*(55 + 86*S^2 + 31*S^4)*Zeta[3])/S^2) + ((55*Pi^2*(1 + S^2))/(3*S^2) + (997 + 1066*S^2 + 69*S^4)/(4*S^2))*Zeta[5] + HPL[{2, 1}, -S^2]*((4463*(-1 + S^4))/(16*S^2) + (Pi^2*(-205 + 314*S^2 + 519*S^4))/(12*S^2) + (Pi^4*(41 + 707*S^2 + 666*S^4))/(180*S^2) - (172*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (180*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (548*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (344*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-175 - 248*S^2 - 73*S^4)/S^2 - (47*Pi^2*(1 + S^4))/(3*S^2))*Zeta[3] - (86*(1 + S^4)*Zeta[5])/S^2) + HPL[{3}, -S^2]*((7181 + 5436*S^2 - 1745*S^4)/(32*S^2) + (Pi^2*(669 + 764*S^2 + 95*S^4))/(24*S^2) + (Pi^4*(295 + 392*S^2 + 97*S^4))/(180*S^2) - (14*(1 + S^2)*HPL[{4}, -S^2])/S^2 + (35*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-167 - 248*S^2 - 81*S^4)/S^2 - (46*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (4*(27 + 44*S^2 + 17*S^4)*HPL[{3, 1}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (14*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (4*(53 + 86*S^2 + 33*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (192*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (560*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((2*Pi^2*(1 + S^4))/S^2 + (2*(1 + 4*S^2 + 3*S^4))/S^2)*Zeta[3] + (16*(1 + S^4)*Zeta[5])/S^2) + Zeta[3]*((157*Pi^4*(1 + S^2))/(90*S^2) + (Pi^2*(735 + 842*S^2 + 107*S^4))/(24*S^2) + (10029 + 11132*S^2 + 1103*S^4)/(32*S^2) + (32*(1 + S^4)*Zeta[5])/S^2) + HPL[{2}, -S^2]*((Pi^4*(1303 - 7988*S^2 - 9291*S^4))/(2880*S^2) + (Pi^2*(3259 - 2784*S^2 - 6043*S^4))/(192*S^2) - (15235*(-1 + S^4))/(64*S^2) - (2047*Pi^6*(1 + S^4))/(10080*S^2) + ((1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((Pi^2*(1 + S^4))/(6*S^2) + (35 + 46*S^2 + 11*S^4)/(2*S^2))*HPL[{4}, -S^2] + (20*(1 + S^2)*HPL[{5}, -S^2])/S^2 - (79*(1 + S^4)*HPL[{6}, -S^2])/(2*S^2) + ((23*Pi^2*(1 + S^4))/S^2 + (2*(59 + 124*S^2 + 65*S^4))/S^2)*HPL[{3, 1}, -S^2] - (10*(11 + 18*S^2 + 7*S^4)*HPL[{3, 2}, -S^2])/S^2 - (2*(167 + 274*S^2 + 107*S^4)*HPL[{4, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (24*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-134*Pi^2*(1 + S^4))/(3*S^2) - (248*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (40*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (4*(23 + 86*S^2 + 63*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (524*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (344*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (688*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(30 + 47*S^2 + 17*S^4))/(3*S^2) + (245 + 314*S^2 + 69*S^4)/(2*S^2))*Zeta[3] - (3*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((157*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(31 + 67*S^2 + 36*S^4))/(3*S^2) - (76*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^2*(57 + 92*S^2 + 35*S^4))/(6*S^2) + (116 + 157*S^2 + 41*S^4)/S^2 - (96*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (12*(1 + S^4)*Zeta[3])/S^2) + (2*(32 + 43*S^2 + 11*S^4)*Zeta[5])/S^2) + (150*(1 + S^2)*Zeta[7])/S^2) + HPL[{2}, -S^2]*((Pi^6*(7498 - 36846*S^2 - 20323*S^4))/(181440*S^2) + (Pi^4*(10285 - 3186*S^2 - 19226*S^4))/(5760*S^2) + (Pi^2*(9775 + 778*S^2 - 11614*S^4))/(384*S^2) - (247*(-1 + S^4))/S^2 + ((-19 + 4*S^2 - S^4)*HPL[{3}, -S^2]^2)/(4*S^2) + ((49*Pi^2*(1 + S^4))/(12*S^2) + (-123 + 148*S^2 + 239*S^4)/(8*S^2))*HPL[{5}, -S^2] + ((144 - 158*S^2 + 139*S^4)*HPL[{6}, -S^2])/(4*S^2) + (261*(1 + S^4)*HPL[{7}, -S^2])/(2*S^2) + ((-1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-76 - 149*S^2 - 51*S^4)/S^2 - (15*Pi^2*(1 + S^4))/(2*S^2))*HPL[{3, 2}, -S^2] + ((-407 - 920*S^2 - 361*S^4)/(2*S^2) - (26*Pi^2*(1 + S^4))/S^2)*HPL[{4, 1}, -S^2] - (3*(1 + S^2)*(11 + 5*S^2)*HPL[{4, 2}, -S^2])/(4*S^2) - (21*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + ((-53 - 24*S^2 - 34*S^4)*HPL[{5, 1}, -S^2])/S^2 - (129*(1 + S^4)*HPL[{5, 2}, -S^2])/(2*S^2) - (218*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((-25*(-1 + S^4))/S^2 - (26*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 2, 1}, -S^2] + ((128*Pi^2*(1 + S^4))/(3*S^2) + (41 + 300*S^2 + 193*S^4)/S^2)*HPL[{3, 1, 1}, -S^2] + (6*(1 + S^2)^2*HPL[{3, 1, 2}, -S^2])/S^2 - (4*(17 + 43*S^2 + 17*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (104*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (292*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + ((-187 - 524*S^2 - 199*S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (292*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (856*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (1738*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((48*Pi^2*(1 + S^4))/S^2 + (6*(39 + 100*S^2 + 39*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (208*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + (4*(25 + 86*S^2 + 52*S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (436*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (436*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (1060*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (3152*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (4*(77 + 172*S^2 + 77*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (368*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (736*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((157*Pi^4*(1 + S^4))/(180*S^2) + (Pi^2*(149 + 324*S^2 + 111*S^4))/(24*S^2) + (524 + 2324*S^2 + 563*S^4)/(16*S^2))*Zeta[3] + ((2 - 6*S^2 + 13*S^4)*Zeta[3]^2)/(2*S^2) + HPL[{3, 1}, -S^2]*((Pi^2*(56 + 138*S^2 + 61*S^4))/(6*S^2) + (811 + 712*S^2 + 651*S^4)/(8*S^2) - (32*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(57 + 4*S^2 + 25*S^4))/(24*S^2) + (169 + 398*S^2 + 329*S^4)/(8*S^2) + (4*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (10*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((-731 - 712*S^2 - 731*S^4)/(4*S^2) + (Pi^2*(-59 - 134*S^2 - 60*S^4))/(3*S^2) + (80*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((31*Pi^4*(1 + S^4))/(60*S^2) + (Pi^2*(54 + 160*S^2 + 65*S^4))/(12*S^2) + (182 + 2324*S^2 + 905*S^4)/(16*S^2) + (9*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (2*(23 + 48*S^2 + 22*S^4)*HPL[{2, 1}, -S^2])/S^2 - (42*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (100*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-1 + 12*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((707*Pi^4*(1 + S^4))/(360*S^2) + (Pi^2*(331 + 920*S^2 + 381*S^4))/(24*S^2) + (1087 + 4648*S^2 + 1087*S^4)/(16*S^2) - (4*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (2*(18 + 38*S^2 + 17*S^4)*Zeta[3])/S^2) + ((55*Pi^2*(1 + S^4))/(6*S^2) + (35 + 82*S^2 + 20*S^4)/S^2)*Zeta[5] + (75*(1 + S^4)*Zeta[7])/S^2) + HPL[{1}, -S^2]^2*((Pi^6*(-15077 - 43495*S^2 - 28418*S^4))/(45360*S^2) + (Pi^2*(-10331 - 29588*S^2 - 19257*S^4))/(384*S^2) + (Pi^4*(-7571 - 25578*S^2 - 18007*S^4))/(2880*S^2) - (9899*(1 + 2*S^2 + S^4))/(32*S^2) - (5*(-1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) - (2*(1 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((221 + 92*S^2 - 129*S^4)/(4*S^2) + (Pi^2*(1 + S^4))/(2*S^2))*HPL[{5}, -S^2] - (5*(-4 + 7*S^2 + 11*S^4)*HPL[{6}, -S^2])/S^2 - (72*(1 + S^4)*HPL[{7}, -S^2])/S^2 + (86*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-167 - 248*S^2 - 81*S^4)/S^2 - (46*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 2}, -S^2] + ((-152*Pi^2*(1 + S^4))/(3*S^2) - (69*(17 + 24*S^2 + 7*S^4))/(2*S^2))*HPL[{4, 1}, -S^2] - (9*(1 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (11*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 - (2*(39 + 44*S^2 + 5*S^4)*HPL[{5, 1}, -S^2])/S^2 + (30*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 + (75*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((-134*Pi^2*(1 + S^4))/(3*S^2) - (248*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((-325 - 908*S^2 - 583*S^4)/S^2 - (296*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] - (40*(-1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (174*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (536*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 - (4*(-53 - 28*S^2 + 25*S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (530*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (1634*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (3336*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((258*(-1 + S^4))/S^2 + (86*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] + (16*(-11 - 7*S^2 + 4*S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (1144*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (240*(-1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (2064*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (4240*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + ((157*Pi^4*(1 + S^4))/(180*S^2) + (Pi^2*(471 + 596*S^2 + 125*S^4))/(24*S^2) + (3*(1147 + 1344*S^2 + 197*S^4))/(16*S^2))*Zeta[3] - 2*(1 + S^2)*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((2*Pi^2*(-5 + 14*S^2 + 19*S^4))/(3*S^2) + (3*(-46 - 17*S^2 + 29*S^4))/S^2 - (88*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((14*Pi^2*(1 + S^2))/(3*S^2) + (133 + 102*S^2 - 31*S^4)/(2*S^2) - (14*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((Pi^2*(-31 - 67*S^2 - 36*S^4))/(6*S^2) - (157*(1 + 2*S^2 + S^4))/(4*S^2) + (24*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (19*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(5 - 86*S^2 - 91*S^4))/(3*S^2) - (225*(-1 + S^4))/S^2 + (172*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((49*Pi^4*(1 + S^4))/(45*S^2) + (Pi^2*(59 + 77*S^2 + 18*S^4))/(3*S^2) + (3061 + 3272*S^2 + 211*S^4)/(16*S^2) - (7*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (2*(53 + 86*S^2 + 33*S^4)*HPL[{2, 1}, -S^2])/S^2 - (88*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(2 + 3*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((1425*(-1 + S^4))/(8*S^2) + (707*Pi^4*(1 + S^4))/(360*S^2) + (Pi^2*(-83 + 248*S^2 + 331*S^4))/(12*S^2) - (172*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(55 + 86*S^2 + 31*S^4)*Zeta[3])/S^2) + ((55*Pi^2*(1 + S^4))/(6*S^2) + (613 + 708*S^2 + 95*S^4)/(4*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-41 - 707*S^2 - 666*S^4))/(360*S^2) + (Pi^2*(205 - 314*S^2 - 519*S^4))/(24*S^2) - (4463*(-1 + S^4))/(32*S^2) + ((23*Pi^2*(1 + S^4))/(3*S^2) + (167 + 248*S^2 + 81*S^4)/(2*S^2))*HPL[{3}, -S^2] + (7*(1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/S^2 + (10*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((67*Pi^2*(1 + S^4))/(3*S^2) + (124*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (86*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (90*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (274*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (172*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((47*Pi^2*(1 + S^4))/(6*S^2) + (175 + 248*S^2 + 73*S^4)/(2*S^2))*Zeta[3] + (43*(1 + S^4)*Zeta[5])/S^2) + (75*(1 + S^4)*Zeta[7])/S^2) + Log[T]*(1225/64 + (Pi^4*(1732 + 9877*S^2))/1152 + (Pi^2*(-2438 + 19631*S^2))/384 + (Pi^6*(35362 + 38499*S^2))/45360 + ((11*Pi^2*(1 + S^4))/(9*S^2) + (20*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{1}, -S^2]^6 + (4*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^7)/(3*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^8)/(3*S^2) + HPL[{0}, S^2]^7*((1 + S^2)/48 + ((1 + S^4)*HPL[{1}, -S^2])/(48*S^2)) + HPL[{0}, S^2]^6*((4 + 33*S^2)/192 + ((1 + S^2)*(1 + 7*S^2)*HPL[{1}, -S^2])/(48*S^2) + ((1 + S^4)*HPL[{1}, -S^2]^2)/(12*S^2)) + ((73*(-1 + S^4))/(12*S^2) + (5*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2]^3 + (5*(1 + S^4)*HPL[{2}, -S^2]^4)/(3*S^2) + ((3*Pi^2*(1 + S^4))/(2*S^2) + (16 + 28*S^2 + 49*S^4)/(4*S^2))*HPL[{3}, -S^2]^2 - (16*(1 + S^4)*HPL[{4}, -S^2]^2)/S^2 + ((-10*Pi^2*(1 + S^4))/(3*S^2) + (-170 + 52*S^2 + 217*S^4)/(2*S^2))*HPL[{6}, -S^2] + ((125 + 144*S^2 + 103*S^4)*HPL[{7}, -S^2])/S^2 + ((-131 - 196*S^2 - 131*S^4)/S^2 - (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*((Pi^2*(32 + 29*S^2))/144 + (20 + 47*S^2)/48 + ((1 + S^2)*(7 + 15*S^2)*HPL[{1}, -S^2]^2)/(24*S^2) + (11*(1 + S^4)*HPL[{1}, -S^2]^3)/(36*S^2) + ((3 + 16*S^2 + 7*S^4)*HPL[{2}, -S^2])/(48*S^2) + HPL[{1}, -S^2]*((2*Pi^2*(1 + S^4))/(9*S^2) + (11 + 60*S^2 + 49*S^4)/(48*S^2) + ((1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((1 + S^4)*HPL[{3}, -S^2])/(8*S^2) - (5*(1 + S^4)*HPL[{2, 1}, -S^2])/(12*S^2)) + (72*(1 + S^4)*HPL[{3, 1}, -S^2]^2)/S^2 + ((-10 + 36*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/S^2 + ((-70 - 22*S^2 - 51*S^4)*HPL[{4, 3}, -S^2])/S^2 + ((98 + 332*S^2 - 61*S^4)/(2*S^2) + (Pi^2*(1 + S^4))/S^2)*HPL[{5, 1}, -S^2] - (3*(139 + 40*S^2 + 101*S^4)*HPL[{5, 2}, -S^2])/(2*S^2) - (5*(86 + 30*S^2 + 67*S^4)*HPL[{6, 1}, -S^2])/S^2 + (320*(1 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((Pi^2*(-1 - S^4))/S^2 - (23*(-1 + S^4))/(2*S^2))*HPL[{3, 1, 2}, -S^2] + ((269*(-1 + S^4))/(2*S^2) + (37*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 2, 1}, -S^2] + ((-271 - 348*S^2 - 119*S^4)*HPL[{3, 2, 2}, -S^2])/S^2 - (8*(111 + 134*S^2 + 50*S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + ((40*Pi^2*(1 + S^4))/S^2 + (2*(-261 - 80*S^2 + 239*S^4))/S^2)*HPL[{4, 1, 1}, -S^2] + ((-867 - 1060*S^2 - 379*S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + ((-2763 - 3268*S^2 - 1267*S^4)*HPL[{4, 2, 1}, -S^2])/S^2 - (6*(963 + 1112*S^2 + 449*S^4)*HPL[{5, 1, 1}, -S^2])/S^2 - (152*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((-92*Pi^2*(1 + S^4))/(3*S^2) - (4*(-108 - 40*S^2 + 97*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (4*(23 + 172*S^2 + 167*S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (4*(23 + 172*S^2 + 167*S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (4*(-91 + 172*S^2 + 281*S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (8*(-98 + 286*S^2 + 453*S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + ((820*(-1 + S^4))/S^2 + (160*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1, 1, 1}, -S^2] - (8*(95 + 172*S^2 + 95*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (24*(95 + 172*S^2 + 95*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (80*(65 + 106*S^2 + 56*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (720*(-1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((157*Pi^4*(-2 + S^2))/180 + (Pi^2*(-625 + 119*S^2))/12 + (-8358 + 2095*S^2)/16)*Zeta[3] + 2*(-2 + 3*S^2)*Zeta[3]^2 + HPL[{4}, -S^2]*((-3*Pi^4*(1 + S^4))/(10*S^2) + (Pi^2*(-127 - 160*S^2 + 95*S^4))/(24*S^2) + (-377 - 164*S^2 + 103*S^4)/(4*S^2) + ((-7 + 28*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/S^2 + (40*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-21 - 8*S^2 - 17*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((38*Pi^4*(1 + S^4))/(45*S^2) + (Pi^2*(335 + 608*S^2 + 481*S^4))/(48*S^2) + (1697 + 920*S^2 + 1697*S^4)/(32*S^2) - ((5 + 4*S^2)*(7 + 4*S^2)*HPL[{3}, -S^2])/S^2 - (6*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (19*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (6*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + ((-30 - 38*S^2 - 11*S^4)*Zeta[3])/S^2) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(193 + 592*S^2 + 405*S^4))/(3*S^2) + (414 + 1686*S^2 + 511*S^4)/S^2 - (424*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((75*(7 + 24*S^2 + 7*S^4))/(2*S^2) + (2*Pi^2*(65 + 134*S^2 + 84*S^4))/(3*S^2) - (144*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^5*((79*(1 + 2*S^2 + S^4))/(3*S^2) + (2*Pi^2*(5 + 11*S^2 + 6*S^4))/(3*S^2) + (4*(-1 + S^4)*HPL[{2}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (12*(1 + S^4)*Zeta[3])/S^2) + HPL[{5}, -S^2]*((Pi^2*(-11 - 6*S^2 - S^4))/(6*S^2) + (-717 - 596*S^2 + 512*S^4)/(8*S^2) - (6*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((Pi^2*(523 + 608*S^2 + 241*S^4))/(6*S^2) + (937 + 2928*S^2 + 888*S^4)/(2*S^2) + (12*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 2}, -S^2]*((Pi^2*(291 + 368*S^2 + 107*S^4))/(12*S^2) + (3*(287 + 1200*S^2 + 413*S^4))/(8*S^2) + (14*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((-97*(-1 + S^4))/S^2 - (2*Pi^2*(-23 + 86*S^2 + 118*S^4))/(3*S^2) + (320*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*((1849*Pi^4*(1 + S^4))/(1080*S^2) + (499*(1 + 2*S^2 + S^4))/(6*S^2) + (Pi^2*(267 + 620*S^2 + 353*S^4))/(24*S^2) + ((43*(-1 + S^4))/(2*S^2) + (43*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2] + (43*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) - (10*(13 + 20*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S^2) - (28*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (20*(-1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (28*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (20*(2 + 3*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((2425*(-1 + S^4))/(4*S^2) + (154*Pi^4*(1 + S^4))/(45*S^2) + (Pi^2*(-195 + 196*S^2 + 457*S^4))/(6*S^2) - (4*(67 + 86*S^2 + 28*S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((2699 + 328*S^2 - 2151*S^4)/(8*S^2) + (Pi^2*(191 - 112*S^2 - 456*S^4))/(12*S^2) - (169*Pi^4*(1 + S^4))/(90*S^2) - (320*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(81 + 88*S^2 + 37*S^4)*Zeta[3])/S^2) + HPL[{0}, S^2]^4*((Pi^2*(208 + 725*S^2))/576 + (-416 + 3097*S^2)/384 + ((25 + 92*S^2 + 67*S^4)*HPL[{1}, -S^2]^3)/(36*S^2) + (23*(1 + S^4)*HPL[{1}, -S^2]^4)/(36*S^2) + ((Pi^2*(1 + S^4))/(12*S^2) + (-21 + 112*S^2 + 209*S^4)/(96*S^2))*HPL[{2}, -S^2] + ((1 + S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + HPL[{1}, -S^2]^2*((53*Pi^2*(1 + S^4))/(72*S^2) + (53 + 484*S^2 + 431*S^4)/(96*S^2) + (31*(1 + S^4)*HPL[{2}, -S^2])/(24*S^2)) + ((-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(16*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/(2*S^2) + ((-17 - 62*S^2 - 66*S^4)*HPL[{2, 1}, -S^2])/(24*S^2) + ((-1 - S^4)*HPL[{3, 1}, -S^2])/S^2 + (2*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (7*(-2 + S^2)*Zeta[3])/24 + HPL[{1}, -S^2]*((Pi^2*(10 + 53*S^2 + 43*S^4))/(36*S^2) + (-29 + 622*S^2 + 651*S^4)/(96*S^2) + ((5 + 31*S^2 + 26*S^4)*HPL[{2}, -S^2])/(12*S^2) - (31*(1 + S^4)*HPL[{2, 1}, -S^2])/(12*S^2) + (7*(1 + S^4)*Zeta[3])/(12*S^2))) + HPL[{0}, S^2]^3*((Pi^2*(483 + 935*S^2))/144 + (Pi^4*(1874 + 1601*S^2))/2160 + (3862 + 7509*S^2)/192 + ((43 + 110*S^2 + 67*S^4)*HPL[{1}, -S^2]^4)/(18*S^2) + (11*(1 + S^4)*HPL[{1}, -S^2]^5)/(9*S^2) + ((16 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(12*S^2) + HPL[{1}, -S^2]^3*((55*Pi^2*(1 + S^4))/(27*S^2) + (5*(41 + 124*S^2 + 83*S^4))/(36*S^2) + (5*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((17*Pi^2*(1 + S^4))/(36*S^2) + (9 + 16*S^2 + 4*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((-2 + 2*S^2 + 3*S^4)*HPL[{4}, -S^2])/(2*S^2) + (7*(1 + S^4)*HPL[{5}, -S^2])/(2*S^2) + ((-62 - 162*S^2 - 73*S^4)/(6*S^2) - (49*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(50 + 170*S^2 + 81*S^4))/(72*S^2) + (180 + 604*S^2 + 755*S^4)/(48*S^2) - (20*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) - (2*(9 + 22*S^2 + 13*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((-1 - S^4)*HPL[{3, 2}, -S^2])/(6*S^2) - (4*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((35 + 90*S^2 + 46*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (40*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (124*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (32*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((2 + 7*S^2)*Zeta[3])/6 + HPL[{1}, -S^2]^2*((Pi^2*(39 + 110*S^2 + 71*S^4))/(18*S^2) + (121 + 425*S^2 + 304*S^4)/(12*S^2) + (5*(7 + 18*S^2 + 11*S^4)*HPL[{2}, -S^2])/(6*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/S^2 - (15*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]*((937*Pi^4*(1 + S^4))/(1080*S^2) + (5*Pi^2*(63 + 244*S^2 + 181*S^4))/(144*S^2) + (1223 + 4712*S^2 + 3489*S^4)/(96*S^2) + ((85*Pi^2*(1 + S^4))/(36*S^2) + (97 + 280*S^2 + 183*S^4)/(12*S^2))*HPL[{2}, -S^2] + (19*(1 + S^4)*HPL[{2}, -S^2]^2)/(6*S^2) + ((1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/S^2 + ((1 + S^4)*HPL[{4}, -S^2])/S^2 - (5*(7 + 18*S^2 + 11*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (30*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((1 + 8*S^2 + 7*S^4)*Zeta[3])/(3*S^2))) + HPL[{0}, S^2]^2*((Pi^4*(998 + 1993*S^2))/720 + (Pi^2*(104 + 2761*S^2))/96 + (-4338 + 19631*S^2)/128 + ((3 + 8*S^2 + 5*S^4)*HPL[{1}, -S^2]^5)/S^2 + (4*(1 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + ((17*Pi^2*(1 + S^4))/(12*S^2) + (73 + 216*S^2 + 219*S^4)/(16*S^2))*HPL[{2}, -S^2]^2 + (5*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^4*((53*Pi^2*(1 + S^4))/(18*S^2) + (67 + 220*S^2 + 153*S^4)/(8*S^2) + (43*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((1 + S^4)*HPL[{3}, -S^2]^2)/(2*S^2) + ((Pi^2*(-1 - S^4))/S^2 + (-43 + 55*S^4)/(8*S^2))*HPL[{4}, -S^2] + ((23 + 12*S^2 + 13*S^4)*HPL[{5}, -S^2])/(4*S^2) - (10*(1 + S^4)*HPL[{6}, -S^2])/S^2 + ((-172 - 900*S^2 - 353*S^4)/(8*S^2) + (Pi^2*(-39 - 148*S^2 - 139*S^4))/(12*S^2))*HPL[{2, 1}, -S^2] - (22*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-25 - 192*S^2 - 262*S^4)/(4*S^2) - (35*Pi^2*(1 + S^4))/(6*S^2))*HPL[{3, 1}, -S^2] + ((17 + 24*S^2 + S^4)*HPL[{3, 2}, -S^2])/(4*S^2) + ((35 + 36*S^2 + 19*S^4)*HPL[{4, 1}, -S^2])/(2*S^2) + (3*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((32*Pi^2*(1 + S^4))/(3*S^2) + (5 + 98*S^2 + 126*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + ((35 + 96*S^2 + 73*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + ((83 + 276*S^2 + 205*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (3*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (37*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (120*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (2*(22 + 86*S^2 + 73*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (92*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (160*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(2 - S^2))/4 + (3*(-64 + 47*S^2))/8)*Zeta[3] + HPL[{1}, -S^2]^2*((359*Pi^4*(1 + S^4))/(180*S^2) + (19*(29 + 208*S^2 + 179*S^4))/(32*S^2) + (Pi^2*(127 + 572*S^2 + 445*S^4))/(24*S^2) + ((37*Pi^2*(1 + S^4))/(6*S^2) + (23 + 124*S^2 + 101*S^4)/(2*S^2))*HPL[{2}, -S^2] + (12*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((-7 - 6*S^2 + S^4)*HPL[{3}, -S^2])/S^2 + ((-25 - 86*S^2 - 61*S^4)*HPL[{2, 1}, -S^2])/S^2 - (42*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (86*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (8*(1 + S^2)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((13*Pi^4*(1 + S^4))/(36*S^2) + (Pi^2*(-11 + 308*S^2 + 461*S^4))/(48*S^2) + (-508 + 460*S^2 + 2205*S^4)/(32*S^2) - (3*(2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(2*S^2) + ((-1 - S^4)*HPL[{4}, -S^2])/S^2 + ((-35 - 96*S^2 - 73*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) - (22*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (44*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-7 - 4*S^2 - 3*S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((5*(19 + 83*S^2 + 64*S^4))/(6*S^2) + (Pi^2*(35 + 106*S^2 + 71*S^4))/(9*S^2) + ((25 + 86*S^2 + 61*S^4)*HPL[{2}, -S^2])/(3*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (86*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (8*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-25 - 12*S^2 - 11*S^4))/(24*S^2) + (-172 - 148*S^2 + 67*S^4)/(16*S^2) + (2*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + ((1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((Pi^4*(369 + 1436*S^2 + 1067*S^4))/(360*S^2) + (Pi^2*(161 + 1452*S^2 + 1291*S^4))/(48*S^2) + (151 + 9228*S^2 + 9077*S^4)/(64*S^2) + ((19 + 48*S^2 + 29*S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((Pi^2*(-1 - S^4))/(2*S^2) + (-53 - 36*S^2 + 17*S^4)/(4*S^2))*HPL[{3}, -S^2] + (5*(-1 + S^4)*HPL[{4}, -S^2])/S^2 + (3*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-23 - 124*S^2 - 101*S^4)/S^2 - (37*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (12*(2 + 7*S^2 + 5*S^4)*HPL[{3, 1}, -S^2])/S^2 + (6*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (18*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (2*(25 + 86*S^2 + 61*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (96*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (276*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(1 + S^4))/(2*S^2) + (2*(-9 - 7*S^2 + 2*S^4))/S^2)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(35 + 148*S^2 + 113*S^4))/(12*S^2) + (10 + 157*S^2 + 147*S^4)/(2*S^2) - (3*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + S^4)*Zeta[3])/S^2))) + HPL[{0}, S^2]*((9899*(1 + S^2))/16 + (7*Pi^2*(2006 + 2527*S^2))/192 + (Pi^4*(5622 + 7507*S^2))/720 + (Pi^6*(25814 + 23231*S^2))/22680 + (14*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + (4*(1 + S^4)*HPL[{1}, -S^2]^7)/(3*S^2) + ((1 + S^2)*(47 + 29*S^2)*HPL[{2}, -S^2]^3)/(6*S^2) + HPL[{1}, -S^2]^5*((32*Pi^2*(1 + S^4))/(9*S^2) + (20*(1 + 2*S^2 + S^4))/S^2 + (12*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((-3 - 2*S^2 - 2*S^4)*HPL[{3}, -S^2]^2)/S^2 + ((5*Pi^2*(1 + S^4))/S^2 + (65 + 88*S^2 + 54*S^4)/(4*S^2))*HPL[{5}, -S^2] + (15*(-3 + S^4)*HPL[{6}, -S^2])/S^2 + (50*(1 + S^4)*HPL[{7}, -S^2])/S^2 + ((-101 - 172*S^2 - 71*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((Pi^2*(1 + S^4))/(6*S^2) + (37 + 112*S^2 + 13*S^4)/(4*S^2))*HPL[{3, 2}, -S^2] + ((2*Pi^2*(1 + S^4))/S^2 + (46 + 64*S^2 + 41*S^4)/(2*S^2))*HPL[{4, 1}, -S^2] + (3*(1 + 5*S^4)*HPL[{4, 2}, -S^2])/(2*S^2) + (8*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + ((7 - 28*S^2 - 23*S^4)*HPL[{5, 1}, -S^2])/S^2 + (27*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((42*Pi^2*(1 + S^4))/S^2 + (2*(157 + 248*S^2 + 91*S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((124*Pi^2*(1 + S^4))/S^2 + (2*(473 + 764*S^2 + 262*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] - (18*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (2*(85 + 152*S^2 + 49*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (22*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 - (48*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + (4*(150 + 242*S^2 + 107*S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (42*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 - (138*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 - (252*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((-92*Pi^2*(1 + S^4))/S^2 - (4*(173 + 270*S^2 + 97*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (304*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (24*(21 + 30*S^2 + 16*S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (920*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (920*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (1832*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (5552*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (120*(7 + 12*S^2 + 5*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (688*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (2064*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (3520*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (1440*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-82 - 137*S^2)/4 + (Pi^2*(-12 + S^2))/4)*Zeta[3] + 4*(2 + 5*S^2)*Zeta[3]^2 + HPL[{2, 1, 1}, -S^2]*((Pi^2*(140 + 270*S^2 + 121*S^4))/(3*S^2) + (397 + 1500*S^2 + 1103*S^4)/(2*S^2) - (24*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*((395*(1 + 2*S^2 + S^4))/(6*S^2) + (2*Pi^2*(37 + 80*S^2 + 43*S^4))/(9*S^2) + (30*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (60*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (14*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(133 + 248*S^2 + 109*S^4))/(24*S^2) + (289 + 1256*S^2 + 967*S^4)/(16*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (38*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (3*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(3 + 20*S^2 + 29*S^4))/(6*S^2) + (251 + 456*S^2 + 186*S^4)/(8*S^2) - (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((-217 - 762*S^2 - 556*S^4)/(2*S^2) + (Pi^2*(-81 - 134*S^2 - 74*S^4))/(3*S^2) + (20*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((937*Pi^4*(1 + S^4))/(270*S^2) + (499*(1 + 2*S^2 + S^4))/(3*S^2) + (35*Pi^2*(23 + 52*S^2 + 29*S^4))/(36*S^2) + ((15*Pi^2*(1 + S^4))/S^2 + (90*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2] + (86*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (8*(1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (28*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (120*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (120*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (240*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (28*(1 + 2*S^2 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(31 + 88*S^2 - 10*S^4))/(24*S^2) + (73*Pi^4*(1 + S^4))/(180*S^2) + (325 + 544*S^2 + 329*S^4)/(8*S^2) - (4*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (2*(5 + 10*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (16*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(6 + 2*S^2 + 5*S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(-235 - 432*S^2 - 170*S^4))/(6*S^2) + (-377 - 504*S^2 - 127*S^4)/S^2 - (9*Pi^4*(1 + S^4))/(2*S^2) + (168*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(2 + 10*S^2 + 5*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^4*(641 + 1508*S^2 + 699*S^4))/(360*S^2) + (Pi^2*(577 + 2104*S^2 + 1858*S^4))/(48*S^2) + (1599 + 5566*S^2 + 3967*S^4)/(16*S^2) + ((-8 - 14*S^2 - 5*S^4)/S^2 - (2*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] + (2*(3 + 2*S^2 + 2*S^4)*HPL[{4}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-157 - 248*S^2 - 91*S^4)/S^2 - (21*Pi^2*(1 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (2*(52 + 86*S^2 + 37*S^4)*HPL[{3, 1}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (2*(101 + 172*S^2 + 71*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (152*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (472*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-3 - 32*S^2 - 31*S^4)/(2*S^2) + (Pi^2*(-1 - S^4))/S^2)*Zeta[3]) + HPL[{1}, -S^2]^2*((2545*(1 + 2*S^2 + S^4))/(8*S^2) + (Pi^2*(172 + 405*S^2 + 233*S^4))/(4*S^2) + (Pi^4*(807 + 1874*S^2 + 1067*S^4))/(180*S^2) + (43*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((5*Pi^2*(1 + S^4))/(3*S^2) + (25 + 44*S^2 + 19*S^4)/(2*S^2))*HPL[{3}, -S^2] + (14*(1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/S^2 + (10*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-45*Pi^2*(1 + S^4))/S^2 - (270*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (180*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (32*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (360*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (1048*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (720*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-1 - S^4))/S^2 - (3*(15 + 28*S^2 + 13*S^4))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((375*(1 + 2*S^2 + S^4))/(2*S^2) + (5*Pi^2*(25 + 54*S^2 + 29*S^4))/(6*S^2) - (10*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (10*(1 + S^4)*Zeta[3])/S^2)) + HPL[{1}, -S^2]*((12907*Pi^6*(1 + S^4))/(11340*S^2) + (851*(1 + 2*S^2 + S^4))/(2*S^2) + (Pi^4*(253 + 657*S^2 + 404*S^4))/(45*S^2) + (Pi^2*(5215 + 12696*S^2 + 7481*S^4))/(96*S^2) + ((31*Pi^2*(1 + S^4))/(3*S^2) + (62*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + (38*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((10*Pi^2*(1 + S^4))/(3*S^2) + (31 + 56*S^2 + 25*S^4)/S^2)*HPL[{4}, -S^2] + (10*(1 + 2*S^2 + S^4)*HPL[{5}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-134*Pi^2*(1 + S^4))/(3*S^2) - (3*(91 + 180*S^2 + 89*S^4))/S^2)*HPL[{3, 1}, -S^2] + (20*(1 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (32*(1 + 2*S^2 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (28*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((90*Pi^2*(1 + S^4))/S^2 + (540*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (344*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (1048*(1 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (304*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (968*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (720*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (720*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (1440*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-2*Pi^2*(1 + S^2))/S^2 + (-29 - 51*S^2 - 22*S^4)/S^2)*Zeta[3] + (8*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((5*Pi^2*(1 + 2*S^2 + S^4))/(3*S^2) + (34 + 61*S^2 + 27*S^4)/S^2 + (20*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-375*(1 + 2*S^2 + S^4))/S^2 - (5*Pi^2*(25 + 54*S^2 + 29*S^4))/(3*S^2) + (20*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((377*Pi^4*(1 + S^4))/(90*S^2) + (252*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(367 + 820*S^2 + 453*S^4))/(12*S^2) - (10*(1 + S^2)^2*HPL[{3}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (172*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (10*(1 + 2*S^2 + S^4)*Zeta[3])/S^2))) + ((55*Pi^2*(-2 + S^2))/6 + (9*(-170 + 69*S^2))/4)*Zeta[5] + HPL[{2}, -S^2]*((19631*(-1 + S^4))/(64*S^2) + (31*Pi^6*(1 + S^4))/(270*S^2) + (Pi^4*(-917 + 1492*S^2 + 3065*S^4))/(720*S^2) + (Pi^2*(-2933 + 460*S^2 + 4630*S^4))/(96*S^2) + (3*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((3 - 32*S^2 - 25*S^4)/S^2 - (7*Pi^2*(1 + S^4))/(3*S^2))*HPL[{4}, -S^2] + ((-36 - 20*S^2 - 23*S^4)*HPL[{5}, -S^2])/S^2 - (34*(1 + S^4)*HPL[{6}, -S^2])/S^2 + ((-145 - 196*S^2 - 117*S^4)/S^2 - (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + (2*(67 + 90*S^2 + 29*S^4)*HPL[{3, 2}, -S^2])/S^2 + ((427 + 548*S^2 + 187*S^4)*HPL[{4, 1}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (66*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((124*Pi^2*(1 + S^4))/(3*S^2) + (2*(131 + 196*S^2 + 131*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (76*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (4*(11 + 86*S^2 + 84*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (12*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (148*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (432*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (4*(95 + 172*S^2 + 95*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (320*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (640*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-269 - 900*S^2 - 256*S^4)/(4*S^2) + (Pi^2*(-81 - 94*S^2 - 34*S^4))/(6*S^2))*Zeta[3] - (4*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((-197 - 900*S^2 - 328*S^4)/(4*S^2) + (Pi^2*(-37 - 46*S^2 - 15*S^4))/(3*S^2) + (92*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(-65 - 134*S^2 - 84*S^4))/(3*S^2) - (75*(7 + 24*S^2 + 7*S^4))/(4*S^2) + (72*(1 + S^4)*Zeta[3])/S^2) + ((-84 - 86*S^2 - 29*S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]^3*((2545*(1 + 2*S^2 + S^4))/(12*S^2) + (5*Pi^2*(98 + 241*S^2 + 143*S^4))/(18*S^2) + (Pi^4*(758 + 1849*S^2 + 1091*S^4))/(270*S^2) + (86*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-419 - 580*S^2 - 161*S^4)/(3*S^2) - (106*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3}, -S^2] - (4*(23 + 28*S^2 + 5*S^4)*HPL[{4}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-86*(-1 + S^4))/S^2 - (86*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] - (16*(-11 - 7*S^2 + 4*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (344*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (1144*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (80*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (1264*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((-133 - 180*S^2 - 47*S^4)/S^2 - (98*Pi^2*(1 + S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((75*(-1 + S^4))/S^2 + (Pi^2*(-5 + 86*S^2 + 91*S^4))/(9*S^2) - (172*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (344*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (172*(1 + S^4)*Zeta[3])/(3*S^2)) - (220*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-919 - 2176*S^2 - 486*S^4))/(48*S^2) + (Pi^4*(-785 - 784*S^2 - 365*S^4))/(360*S^2) + (-2383 - 6318*S^2 - 288*S^4)/(16*S^2) + ((35 + 14*S^2 + 24*S^4)*HPL[{4}, -S^2])/S^2 + (32*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((14*Pi^2*(1 + S^4))/S^2 + (2*(109 + 98*S^2 + 22*S^4))/S^2)*HPL[{2, 1}, -S^2] + (4*(44 + 44*S^2 + 21*S^4)*HPL[{3, 1}, -S^2])/S^2 - (6*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (64*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (4*(68 + 86*S^2 + 27*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (184*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (488*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (320*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((2*Pi^2*(1 + S^4))/(3*S^2) + (-16 - 24*S^2 + 11*S^4)/(2*S^2))*Zeta[3] + (8*(1 + S^4)*Zeta[5])/S^2) + HPL[{2, 1}, -S^2]*((-2095*(-1 + S^4))/(16*S^2) - (25*Pi^2*(1 + 12*S^2 + 6*S^4))/(8*S^2) - (7*Pi^4*(4 + 202*S^2 + 237*S^4))/(360*S^2) + (4*(49 + 86*S^2 + 46*S^4)*HPL[{3, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (504*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (4*(95 + 172*S^2 + 95*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (320*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (640*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((40*Pi^2*(1 + S^4))/(3*S^2) + (215 + 196*S^2 + 47*S^4)/S^2)*Zeta[3] + (68*(1 + S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]^2*((8699*Pi^6*(1 + S^4))/(9072*S^2) + (851*(1 + 2*S^2 + S^4))/(2*S^2) + (Pi^2*(4543 + 11936*S^2 + 7393*S^4))/(96*S^2) + (Pi^4*(7177 + 20228*S^2 + 13051*S^4))/(1440*S^2) + ((67*Pi^2*(1 + S^4))/(6*S^2) + (62*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + (4*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-14*Pi^2*(1 + S^4))/(3*S^2) + (3*(-57 - 56*S^2 + S^4))/(2*S^2))*HPL[{4}, -S^2] + (2*(-23 - 12*S^2 + 11*S^4)*HPL[{5}, -S^2])/S^2 + (35*(1 + S^4)*HPL[{6}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-28*Pi^2*(1 + S^4))/(3*S^2) - (3*(-57 - 28*S^2 + 29*S^4))/S^2)*HPL[{3, 1}, -S^2] + (4*(53 + 86*S^2 + 33*S^4)*HPL[{3, 2}, -S^2])/S^2 + (104*(7 + 11*S^2 + 4*S^4)*HPL[{4, 1}, -S^2])/S^2 + (18*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (88*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((258*(-1 + S^4))/S^2 + (86*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (344*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (16*(32 + 79*S^2 + 47*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (112*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (240*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (112*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + ((-75*(4 + 5*S^2 + S^4))/S^2 - (2*Pi^2*(34 + 49*S^2 + 15*S^4))/(3*S^2))*Zeta[3] + (2*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((-5*(59 + 73*S^2 + 14*S^4))/S^2 - (2*Pi^2*(36 + 53*S^2 + 17*S^4))/(3*S^2) + (172*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (12*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(5 - 86*S^2 - 91*S^4))/(3*S^2) - (225*(-1 + S^4))/S^2 + (172*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((1425*(-1 + S^4))/(8*S^2) + (707*Pi^4*(1 + S^4))/(360*S^2) + (Pi^2*(-83 + 248*S^2 + 331*S^4))/(12*S^2) - (2*(53 + 86*S^2 + 33*S^4)*HPL[{3}, -S^2])/S^2 - (14*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (172*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(55 + 86*S^2 + 31*S^4)*Zeta[3])/S^2) - (4*(42 + 55*S^2 + 13*S^4)*Zeta[5])/S^2) + 75*(-2 + S^2)*Zeta[7] + HPL[{1}, -S^2]*((9899*(1 + 2*S^2 + S^4))/(16*S^2) + (Pi^4*(7571 + 25578*S^2 + 18007*S^4))/(1440*S^2) + (Pi^2*(10331 + 29588*S^2 + 19257*S^4))/(192*S^2) + (Pi^6*(15077 + 43495*S^2 + 28418*S^4))/(22680*S^2) + (10*(-1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + (4*(1 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((Pi^2*(-1 - S^4))/S^2 + (-221 - 92*S^2 + 129*S^4)/(2*S^2))*HPL[{5}, -S^2] + (10*(-4 + 7*S^2 + 11*S^4)*HPL[{6}, -S^2])/S^2 + (144*(1 + S^4)*HPL[{7}, -S^2])/S^2 - (172*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((92*Pi^2*(1 + S^4))/(3*S^2) + (2*(167 + 248*S^2 + 81*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((304*Pi^2*(1 + S^4))/(3*S^2) + (69*(17 + 24*S^2 + 7*S^4))/S^2)*HPL[{4, 1}, -S^2] + (18*(1 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (22*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + (4*(39 + 44*S^2 + 5*S^4)*HPL[{5, 1}, -S^2])/S^2 - (60*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 - (150*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((268*Pi^2*(1 + S^4))/(3*S^2) + (496*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((592*Pi^2*(1 + S^4))/(3*S^2) + (2*(325 + 908*S^2 + 583*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (80*(-1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (348*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 - (1072*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + (8*(-53 - 28*S^2 + 25*S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (1060*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 - (3268*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 - (6672*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((-516*(-1 + S^4))/S^2 - (172*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (32*(-11 - 7*S^2 + 4*S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (2288*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (480*(-1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (1376*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (4128*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (8480*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-471 - 596*S^2 - 125*S^4))/(12*S^2) - (157*Pi^4*(1 + S^4))/(90*S^2) - (3*(1147 + 1344*S^2 + 197*S^4))/(8*S^2))*Zeta[3] + 4*(1 + S^2)*Zeta[3]^2 + HPL[{2, 1, 1}, -S^2]*((450*(-1 + S^4))/S^2 + (2*Pi^2*(-5 + 86*S^2 + 91*S^4))/(3*S^2) - (344*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((157*(1 + 2*S^2 + S^4))/(2*S^2) + (Pi^2*(31 + 67*S^2 + 36*S^4))/(3*S^2) - (48*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (38*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((-28*Pi^2*(1 + S^2))/(3*S^2) + (-133 - 102*S^2 + 31*S^4)/S^2 + (28*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (8*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((-4*Pi^2*(-5 + 14*S^2 + 19*S^4))/(3*S^2) - (6*(-46 - 17*S^2 + 29*S^4))/S^2 + (176*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-3061 - 3272*S^2 - 211*S^4)/(8*S^2) - (98*Pi^4*(1 + S^4))/(45*S^2) - (2*Pi^2*(59 + 77*S^2 + 18*S^4))/(3*S^2) + (14*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (4*(53 + 86*S^2 + 33*S^4)*HPL[{2, 1}, -S^2])/S^2 + (176*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (8*(2 + 3*S^2 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(83 - 248*S^2 - 331*S^4))/(6*S^2) - (1425*(-1 + S^4))/(4*S^2) - (707*Pi^4*(1 + S^4))/(180*S^2) + (344*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(55 + 86*S^2 + 31*S^4)*Zeta[3])/S^2) + ((-613 - 708*S^2 - 95*S^4)/(2*S^2) - (55*Pi^2*(1 + S^4))/(3*S^2))*Zeta[5] + HPL[{2}, -S^2]*((4463*(-1 + S^4))/(16*S^2) + (Pi^2*(-205 + 314*S^2 + 519*S^4))/(12*S^2) + (Pi^4*(41 + 707*S^2 + 666*S^4))/(180*S^2) + ((-167 - 248*S^2 - 81*S^4)/S^2 - (46*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] - (14*(1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/S^2 - (20*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-134*Pi^2*(1 + S^4))/(3*S^2) - (248*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (172*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (180*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (548*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (344*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (688*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-175 - 248*S^2 - 73*S^4)/S^2 - (47*Pi^2*(1 + S^4))/(3*S^2))*Zeta[3] - (86*(1 + S^4)*Zeta[5])/S^2) - (150*(1 + S^4)*Zeta[7])/S^2)) + HPL[{0}, S^2]*((-179327*Pi^8*S^2)/680400 + (Pi^6*(-239044 - 261199*S^2))/362880 + (Pi^4*(-29776 - 41607*S^2))/5760 + (Pi^2*(-20679 - 24101*S^2))/384 - (15995*(1 + S^2))/32 - (2*(1 + 2*S^2 + S^4)*HPL[{1}, -S^2]^7)/(3*S^2) + ((-1 - S^4)*HPL[{1}, -S^2]^8)/(6*S^2) + ((-15 - 38*S^2 - 23*S^4)/(4*S^2) - (53*Pi^2*(1 + S^4))/(72*S^2))*HPL[{2}, -S^2]^3 - (23*(1 + S^4)*HPL[{2}, -S^2]^4)/(24*S^2) + HPL[{1}, -S^2]^6*((-16*Pi^2*(1 + S^4))/(27*S^2) - (10*(1 + 2*S^2 + S^4))/(3*S^2) - (2*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((2*Pi^2*(1 + S^4))/(3*S^2) + (-13 - 4*S^2 + 11*S^4)/(4*S^2))*HPL[{3}, -S^2]^2 - (14*(1 + S^4)*HPL[{4}, -S^2]^2)/S^2 + ((-250 - 312*S^2 - 27*S^4)/(4*S^2) + (45*Pi^2*(1 + S^4))/(4*S^2))*HPL[{6}, -S^2] + (5*(-55 + 24*S^2 + 13*S^4)*HPL[{7}, -S^2])/(2*S^2) + (525*(1 + S^4)*HPL[{8}, -S^2])/(2*S^2) + ((61*Pi^2*(1 + S^4))/(6*S^2) + (91 + 248*S^2 + 157*S^4)/(2*S^2))*HPL[{2, 1}, -S^2]^2 - (50*(1 + S^4)*HPL[{3, 1}, -S^2]^2)/S^2 + ((Pi^2*(-1 - S^4))/(6*S^2) - (9*(2 + S^4))/(8*S^2))*HPL[{4, 2}, -S^2] - (2*(-11 + S^2)*(-1 + S^2)*HPL[{4, 3}, -S^2])/S^2 + ((-11*Pi^2*(1 + S^4))/(3*S^2) + (131 + 200*S^2 + 46*S^4)/(4*S^2))*HPL[{5, 1}, -S^2] - (9*(31 - 32*S^2 + 3*S^4)*HPL[{5, 2}, -S^2])/(4*S^2) - (5*(13 - 24*S^2 + 5*S^4)*HPL[{6, 1}, -S^2])/S^2 + (3*(1 + S^4)*HPL[{6, 2}, -S^2])/S^2 - (114*(1 + S^4)*HPL[{7, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((27*(1 + S^4))/(4*S^2) + (7*Pi^2*(1 + S^4))/(6*S^2))*HPL[{3, 1, 2}, -S^2] + ((-33*Pi^2*(1 + S^4))/(2*S^2) - (3*(111 + 304*S^2 + 175*S^4))/(4*S^2))*HPL[{3, 2, 1}, -S^2] + ((17 + 64*S^2 + 17*S^4)*HPL[{3, 2, 2}, -S^2])/(2*S^2) + (4*(2 + 26*S^2 + 3*S^4)*HPL[{3, 3, 1}, -S^2])/S^2 - (16*(1 + S^4)*HPL[{3, 3, 2}, -S^2])/S^2 + ((-614 - 1488*S^2 - 909*S^4)/(2*S^2) - (173*Pi^2*(1 + S^4))/(3*S^2))*HPL[{4, 1, 1}, -S^2] + ((13 + 208*S^2 + 9*S^4)*HPL[{4, 1, 2}, -S^2])/(2*S^2) + (32*(1 + S^4)*HPL[{4, 1, 3}, -S^2])/S^2 + ((37 + 640*S^2 + 57*S^4)*HPL[{4, 2, 1}, -S^2])/(2*S^2) - (35*(1 + S^4)*HPL[{4, 2, 2}, -S^2])/(2*S^2) + (64*(1 + S^4)*HPL[{4, 3, 1}, -S^2])/S^2 + ((-3 + 628*S^2 + 67*S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + (29*(1 + S^4)*HPL[{5, 1, 2}, -S^2])/S^2 + (269*(1 + S^4)*HPL[{5, 2, 1}, -S^2])/S^2 + (740*(1 + S^4)*HPL[{6, 1, 1}, -S^2])/S^2 + (4*(1 + S^2)*(29 + 47*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((148*Pi^2*(1 + S^4))/(3*S^2) + (2*(114 + 272*S^2 + 187*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] - (2*(175 + 476*S^2 + 277*S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (2*(175 + 476*S^2 + 277*S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (6*(1 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/S^2 - (2*(349 + 932*S^2 + 559*S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (6*(1 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/S^2 + (142*(1 + S^4)*HPL[{3, 2, 2, 1}, -S^2])/S^2 + (408*(1 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (8*(266 + 692*S^2 + 429*S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (6*(1 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/S^2 + (402*(1 + S^4)*HPL[{4, 1, 2, 1}, -S^2])/S^2 + (1218*(1 + S^4)*HPL[{4, 2, 1, 1}, -S^2])/S^2 + (2468*(1 + S^4)*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((-88*Pi^2*(1 + S^4))/S^2 - (4*(97 + 270*S^2 + 173*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + (4*(71 + 172*S^2 + 101*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (12*(71 + 172*S^2 + 101*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (304*(1 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (912*(1 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (24*(62 + 142*S^2 + 87*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (1800*(1 + S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 - (3016*(1 + S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 - (3624*(1 + S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 - (7576*(1 + S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 - (22896*(1 + S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + (120*(5 + 12*S^2 + 7*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (832*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 - (1440*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-16*Pi^2*S^2)/3 + (-28 - 29*S^2)/4)*Zeta[3]^2 + HPL[{4}, -S^2]*((-776 - 1224*S^2 - 309*S^4)/(16*S^2) + (Pi^2*(-128 - 168*S^2 - 53*S^4))/(24*S^2) + (187*Pi^4*(1 + S^4))/(720*S^2) + (2*(-1 + 2*S^2)*HPL[{2, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (8*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((25 - 32*S^2 - 3*S^4)*Zeta[3])/(2*S^2)) + HPL[{5}, -S^2]*((-769 - 640*S^2 - 490*S^4)/(16*S^2) + (Pi^2*(-89 + 8*S^2 - 5*S^4))/(12*S^2) - (28*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (42*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 1, 1}, -S^2]*((-1514 - 1994*S^2 - 469*S^4)/(2*S^2) + (Pi^2*(-144 - 382*S^2 - 223*S^4))/(3*S^2) - (28*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((Pi^2*(110 + 270*S^2 + 169*S^4))/(3*S^2) + (1103 + 1500*S^2 + 397*S^4)/(2*S^2) - (16*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 2}, -S^2]*((21 - 160*S^2 - 27*S^4)/(16*S^2) + (Pi^2*(11 - 64*S^2 + 15*S^4))/(24*S^2) - (14*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((-967 - 1256*S^2 - 289*S^4)/(4*S^2) + (Pi^2*(-99 - 248*S^2 - 155*S^4))/(6*S^2) - (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((Pi^2*(11 - 28*S^2 - 15*S^4))/(6*S^2) + (213 + 120*S^2 + 94*S^4)/(8*S^2) - (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^5*((-79*(1 + 2*S^2 + S^4))/(6*S^2) - (2*Pi^2*(37 + 80*S^2 + 43*S^4))/(45*S^2) - (6*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{3}, -S^2])/(15*S^2) + (12*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (14*(1 + S^4)*Zeta[3])/(15*S^2)) + HPL[{1}, -S^2]^4*((-937*Pi^4*(1 + S^4))/(1080*S^2) - (499*(1 + 2*S^2 + S^4))/(12*S^2) - (35*Pi^2*(23 + 52*S^2 + 29*S^4))/(144*S^2) + ((-15*Pi^2*(1 + S^4))/(4*S^2) - (45*(1 + 2*S^2 + S^4))/(2*S^2))*HPL[{2}, -S^2] - (43*(1 + S^4)*HPL[{2}, -S^2]^2)/(6*S^2) - (2*(1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (7*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (30*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (30*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (60*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (7*(1 + 2*S^2 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((82*Pi^4*(1 + S^4))/(45*S^2) + (Pi^2*(319 + 796*S^2 + 588*S^4))/(24*S^2) + (535 + 2096*S^2 + 1451*S^4)/(8*S^2) + (176*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (3*(7 + 3*S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((-127 - 504*S^2 - 377*S^4)/S^2 + (Pi^2*(-132 - 388*S^2 - 283*S^4))/(6*S^2) - (349*Pi^4*(1 + S^4))/(90*S^2) + (2*(8 + 10*S^2 + 5*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((Pi^2*(-111 - 338*S^2 - 249*S^4))/(48*S^2) + (-19 - 174*S^2 - 155*S^4)/(4*S^2) - (33*Pi^4*(1 + S^4))/(80*S^2) + ((1 + 8*S^2 + S^4)*HPL[{3}, -S^2])/(2*S^2) + (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((29 + 76*S^2 + 47*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + (17*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (38*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((9 + 4*S^2 + 7*S^4)*Zeta[3])/(4*S^2)) + HPL[{1}, -S^2]^3*((Pi^4*(-807 - 1874*S^2 - 1067*S^4))/(540*S^2) + (Pi^2*(-172 - 405*S^2 - 233*S^4))/(12*S^2) - (2545*(1 + 2*S^2 + S^4))/(24*S^2) - (43*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-25 - 44*S^2 - 19*S^4)/(6*S^2) - (5*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3}, -S^2] - (14*(1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (10*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((15*Pi^2*(1 + S^4))/S^2 + (90*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (60*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (20*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (32*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (120*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (1048*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (240*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(1 + S^4))/(3*S^2) + (15 + 28*S^2 + 13*S^4)/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-125*(1 + 2*S^2 + S^4))/(2*S^2) - (5*Pi^2*(25 + 54*S^2 + 29*S^4))/(18*S^2) + (10*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (172*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (10*(1 + S^4)*Zeta[3])/(3*S^2))) + HPL[{1}, -S^2]^2*((Pi^2*(-5215 - 12696*S^2 - 7481*S^4))/(192*S^2) + (Pi^4*(-253 - 657*S^2 - 404*S^4))/(90*S^2) - (12907*Pi^6*(1 + S^4))/(22680*S^2) - (851*(1 + 2*S^2 + S^4))/(4*S^2) + ((-31*Pi^2*(1 + S^4))/(6*S^2) - (31*(1 + 2*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 - (19*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + ((1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-31 - 56*S^2 - 25*S^4)/(2*S^2) - (5*Pi^2*(1 + S^4))/(3*S^2))*HPL[{4}, -S^2] - (5*(1 + 2*S^2 + S^4)*HPL[{5}, -S^2])/S^2 + (86*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((67*Pi^2*(1 + S^4))/(3*S^2) + (3*(91 + 180*S^2 + 89*S^4))/(2*S^2))*HPL[{3, 1}, -S^2] - (10*(1 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (16*(1 + 2*S^2 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (14*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-45*Pi^2*(1 + S^4))/S^2 - (270*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (172*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (524*(1 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (152*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (484*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (360*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (360*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (720*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(1 + S^2))/S^2 + (29 + 51*S^2 + 22*S^4)/(2*S^2))*Zeta[3] - (4*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((375*(1 + 2*S^2 + S^4))/(2*S^2) + (5*Pi^2*(25 + 54*S^2 + 29*S^4))/(6*S^2) - (10*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-34 - 61*S^2 - 27*S^4)/(2*S^2) - (5*Pi^2*(1 + 2*S^2 + S^4))/(6*S^2) - (10*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(-367 - 820*S^2 - 453*S^4))/(24*S^2) - (377*Pi^4*(1 + S^4))/(180*S^2) - (126*(1 + 2*S^2 + S^4))/S^2 + (5*(1 + 2*S^2 + S^4)*HPL[{3}, -S^2])/S^2 - (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (86*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (86*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (5*(1 + 2*S^2 + S^4)*Zeta[3])/S^2)) + ((55*Pi^2*(-2 + S^2))/12 + (-152 + 119*S^2)/8)*Zeta[5] + Zeta[3]*((157*Pi^4*(-2 + S^2))/360 + (Pi^2*(-5 + 7*S^2))/24 + (-52 + 463*S^2)/16 - 80*S^2*Zeta[5]) + HPL[{3}, -S^2]*((-1791 - 2744*S^2 - 1983*S^4)/(32*S^2) + (Pi^2*(-467 - 560*S^2 - 342*S^4))/(96*S^2) + (Pi^4*(-323 - 208*S^2 - 11*S^4))/(720*S^2) + ((-11 + S^2)*(-1 + S^2)*HPL[{4}, -S^2])/S^2 + (28*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((4 - 6*S^2 - 11*S^4)/S^2 - (2*Pi^2*(1 + S^4))/S^2)*HPL[{2, 1}, -S^2] - 2*(10 + S^2)*HPL[{3, 1}, -S^2] + (8*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (36*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (2*(5 + 10*S^2 + 2*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (80*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (24*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((17 + 24*S^2 - 27*S^4)/(4*S^2) - (11*Pi^2*(1 + S^4))/(3*S^2))*Zeta[3] - (37*(1 + S^4)*Zeta[5])/S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(1443 + 2536*S^2 + 762*S^4))/(48*S^2) + (Pi^4*(627 + 1508*S^2 + 1049*S^4))/(360*S^2) + (3967 + 5566*S^2 + 1599*S^4)/(16*S^2) - (2*(34 + 86*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/S^2 + (24*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (80*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (2*(71 + 172*S^2 + 101*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (152*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (480*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((2*Pi^2*(1 + S^4))/(3*S^2) + (-49 - 48*S^2 + 3*S^4)/(2*S^2))*Zeta[3] + (24*(1 + S^4)*Zeta[5])/S^2) + HPL[{2}, -S^2]*((-3215 - 8628*S^2 - 5413*S^4)/(32*S^2) + (Pi^2*(-1984 - 6088*S^2 - 5261*S^4))/(192*S^2) + (Pi^4*(-863 - 2258*S^2 - 1699*S^4))/(720*S^2) - (4447*Pi^6*(1 + S^4))/(30240*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((13 + 4*S^2 - 11*S^4)/(2*S^2) - (4*Pi^2*(1 + S^4))/(3*S^2))*HPL[{4}, -S^2] - ((-11 + S^2)*(-1 + S^2)*HPL[{5}, -S^2])/S^2 - (28*(1 + S^4)*HPL[{6}, -S^2])/S^2 + (38*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((65*Pi^2*(1 + S^4))/(6*S^2) + (41 + 120*S^2 + 80*S^4)/S^2)*HPL[{3, 1}, -S^2] - (2*(1 + 8*S^2 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (2*(2 + 26*S^2 + 3*S^4)*HPL[{4, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-91 - 248*S^2 - 157*S^4)/S^2 - (61*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (2*(29 + 76*S^2 + 47*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (2*(92 + 238*S^2 + 143*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (92*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (284*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (2*(71 + 172*S^2 + 101*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (2000*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(11 + 2*S^2 + 6*S^4))/(12*S^2) + (3 + 19*S^2 + 23*S^4)/(2*S^2))*Zeta[3] + ((-1 - S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((Pi^2*(99 + 248*S^2 + 155*S^4))/(12*S^2) + (967 + 1256*S^2 + 289*S^4)/(8*S^2) + (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((10 + 3*S^2)/2 + (Pi^2*(1 + 8*S^2 + S^4))/(6*S^2) - (12*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (6*(1 + S^4)*Zeta[3])/S^2) + (3*(1 - 4*S^2 + S^4)*Zeta[5])/S^2) + (75*(-2 + S^2)*Zeta[7])/2 + HPL[{1}, -S^2]*((Pi^2*(-14267 - 35284*S^2 - 21017*S^4))/(384*S^2) + (Pi^6*(-11605 - 25814*S^2 - 14209*S^4))/(22680*S^2) + (Pi^4*(-2723 - 7558*S^2 - 4835*S^4))/(720*S^2) - (9899*(1 + 2*S^2 + S^4))/(32*S^2) - (19*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + ((1 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-31 - 38*S^2 - 7*S^4)/S^2 + (2*Pi^2*(1 + S^4))/(3*S^2))*HPL[{5}, -S^2] + (60*(1 + S^4)*HPL[{7}, -S^2])/S^2 + (86*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((Pi^2*(63 + 134*S^2 + 71*S^4))/(3*S^2) + (191 + 375*S^2 + 184*S^4)/S^2)*HPL[{3, 1}, -S^2] + ((-8*Pi^2*(1 + S^4))/(3*S^2) - (4*(1 + 5*S^2 + 4*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((19 - 4*S^2 - 23*S^4)/S^2 - (14*Pi^2*(1 + S^4))/(3*S^2))*HPL[{4, 1}, -S^2] + (24*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + (14*(1 + 2*S^2 + S^4)*HPL[{5, 1}, -S^2])/S^2 + (72*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 + (120*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((-124*Pi^2*(1 + S^4))/(3*S^2) - (248*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((-769 - 1532*S^2 - 763*S^4)/S^2 - (382*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] - (152*(1 + 2*S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (32*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (104*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 - (484*(1 + 2*S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (104*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (320*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (628*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((90*Pi^2*(1 + S^4))/S^2 + (540*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (304*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + (360*(1 + 2*S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (952*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (952*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (1864*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (5536*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (720*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (688*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (2064*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (3408*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (1440*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(61 + 44*S^2 - 17*S^4))/(24*S^2) - (157*Pi^4*(1 + S^4))/(180*S^2) + (41 + 61*S^2 + 20*S^4)/(2*S^2))*Zeta[3] - (2*(3 + 4*S^2 + S^4)*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((Pi^2*(-8 - 13*S^2 - 5*S^4))/(3*S^2) - (13*Pi^4*(1 + S^4))/(45*S^2) - (3*(59 + 104*S^2 + 45*S^4))/(4*S^2) - (12*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (10*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (20*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - 4*(1 + S^2)*Zeta[3]) + HPL[{4}, -S^2]*((-29 - 51*S^2 - 22*S^4)/S^2 - (5*Pi^2*(1 + 2*S^2 + S^4))/(3*S^2) + (4*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (16*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((Pi^2*(-29 - 62*S^2 - 33*S^4))/(6*S^2) - (157*(1 + 2*S^2 + S^4))/(4*S^2) + (4*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (38*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + ((1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((-375*(1 + 2*S^2 + S^4))/S^2 - (5*Pi^2*(25 + 54*S^2 + 29*S^4))/(3*S^2) + (20*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((377*Pi^4*(1 + S^4))/(90*S^2) + (252*(1 + 2*S^2 + S^4))/S^2 + (Pi^2*(367 + 820*S^2 + 453*S^4))/(12*S^2) - (172*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (10*(1 + 2*S^2 + S^4)*Zeta[3])/S^2) + ((-55*Pi^2*(1 + S^4))/(6*S^2) - (3*(-5 - 4*S^2 + S^4))/S^2)*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-317 - 754*S^2 - 437*S^4))/(180*S^2) - (2783*(1 + 2*S^2 + S^4))/(16*S^2) - (5*Pi^2*(101 + 232*S^2 + 131*S^4))/(24*S^2) + ((4*Pi^2*(1 + S^4))/(3*S^2) + (2*(1 + 5*S^2 + 4*S^4))/S^2)*HPL[{3}, -S^2] - (2*(1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/S^2 + (12*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((62*Pi^2*(1 + S^4))/(3*S^2) + (124*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (86*(1 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (16*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (52*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (172*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (152*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (476*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (344*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(1 + S^4))/(6*S^2) + (13 + 20*S^2 + 7*S^4)/S^2)*Zeta[3] - (12*(1 + S^4)*Zeta[5])/S^2) - (75*(1 + S^4)*Zeta[7])/S^2));
e5T3F1=(-77607*(1 + S^2))/(256*S) + (Pi^6*S*(-174213 + 60433*S^2))/120960 + (Pi^2*(-20008 - 78861*S^2 + 12838*S^4))/(768*S) + (Pi^4*(-21028 - 148930*S^2 + 29279*S^4))/(11520*S) + (Pi^8*S*(-5615669 - 2953638*S^2 + 1115456*S^4))/(5443200*(1 + S^2)) - (S*HPL[{0}, S^2]^9)/384 + ((-22*Pi^2*S)/63 + (4*(1 - 3*S^2 - 3*S^4 + S^6))/(21*S^3))*HPL[{1}, -S^2]^7 - (S*HPL[{1}, -S^2]^8)/(1 + S^2) - (2*S*HPL[{1}, -S^2]^9)/27 + HPL[{0}, S^2]^8*((S*(-35 - 24*S^2 + 8*S^4))/(768*(1 + S^2)) - (S*HPL[{1}, -S^2])/384) + HPL[{0}, S^2]^7*((-5*Pi^2*S)/144 + S^3/12 - (S*HPL[{1}, -S^2])/(16*(1 + S^2)) - (S*HPL[{1}, -S^2]^2)/48) + ((-4 - 58*S^4 + 3*S^6 - 4*S^8)*HPL[{2}, -S^2]^4)/(12*S^3*(1 + S^2)) + (14*S*HPL[{3}, -S^2]^3)/3 + (4*(3 - 13*S^4 + 5*S^6 + 3*S^8)*HPL[{4}, -S^2]^2)/(S^3*(1 + S^2)) + ((-125*Pi^2*S)/2 + (1400 - 825*S^2 - 252*S^4 + 908*S^6)/(2*S^3))*HPL[{7}, -S^2] + ((-1400 - 1400*S^2 - 7421*S^4 - 3708*S^6 + 1400*S^8)*HPL[{8}, -S^2])/(2*S^3*(1 + S^2)) - 2450*S*HPL[{9}, -S^2] + HPL[{0}, S^2]^6*((S*(-44 + 15*S^2))/128 + (Pi^2*S*(-275 - 180*S^2 + 62*S^4))/(576*(1 + S^2)) + ((-1 - 14*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(32*S*(1 + S^2)) - (S*HPL[{1}, -S^2]^3)/18 + ((-2 - 2*S^2 - 11*S^4 + 2*S^8)*HPL[{2}, -S^2])/(96*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-11*Pi^2*S)/288 + (2 - 12*S^2 - 9*S^4 + 5*S^6)/(96*S^3) - (S*HPL[{2}, -S^2])/16) - (S*HPL[{3}, -S^2])/24 + (S*HPL[{2, 1}, -S^2])/8) - (4*(5 + 66*S^4 - 5*S^6 + 5*S^8)*HPL[{3, 1}, -S^2]^2)/(S^3*(1 + S^2)) + (16*Pi^2*S + (-12 - 30*S^2 + 137*S^4 - 56*S^6)/(2*S^3))*HPL[{4, 3}, -S^2] + ((283*Pi^2*S)/6 + (-104 - 219*S^2 + 785*S^4 - 344*S^6)/(4*S^3))*HPL[{5, 2}, -S^2] - (3*(-2 - 2*S^2 - 7*S^4 - 8*S^6 + 2*S^8)*HPL[{5, 3}, -S^2])/(S^3*(1 + S^2)) - 490*S*HPL[{5, 4}, -S^2] + (118*Pi^2*S + (-624 + 232*S^2 + 957*S^4 - 484*S^6)/(2*S^3))*HPL[{6, 1}, -S^2] + ((52 + 52*S^2 + 181*S^4 + 174*S^6 - 52*S^8)*HPL[{6, 2}, -S^2])/(2*S^3*(1 + S^2)) - 1948*S*HPL[{6, 3}, -S^2] - (4*(-78 - 78*S^2 - 421*S^4 - 187*S^6 + 78*S^8)*HPL[{7, 1}, -S^2])/(S^3*(1 + S^2)) - 4860*S*HPL[{7, 2}, -S^2] - 8720*S*HPL[{8, 1}, -S^2] - (24*(4 + 34*S^4 - S^6 + 4*S^8)*HPL[{2, 1, 1}, -S^2]^2)/(S^3*(1 + S^2)) + ((61*Pi^2*S)/2 + (10 - 39*S^2 + 40*S^4 - 70*S^6)/S^3)*HPL[{3, 2, 2}, -S^2] + ((320*Pi^2*S)/3 - (4*(-2 + 21*S^2 - 44*S^4 + 58*S^6))/S^3)*HPL[{3, 3, 1}, -S^2] - (2*(-5 - 5*S^2 - 43*S^4 - 17*S^6 + 5*S^8)*HPL[{3, 3, 2}, -S^2])/(S^3*(1 + S^2)) + (104*Pi^2*S + (20 - 141*S^2 + 339*S^4 - 460*S^6)/(2*S^3))*HPL[{4, 1, 2}, -S^2] + (2*(-10 - 10*S^2 - 89*S^4 - 28*S^6 + 10*S^8)*HPL[{4, 1, 3}, -S^2])/(S^3*(1 + S^2)) + (340*Pi^2*S + (20 - 393*S^2 + 1191*S^4 - 1420*S^6)/(2*S^3))*HPL[{4, 2, 1}, -S^2] - (5*(-2 - 2*S^2 - 19*S^4 - 5*S^6 + 2*S^8)*HPL[{4, 2, 2}, -S^2])/(S^3*(1 + S^2)) + (2*(-14 - 14*S^2 - 133*S^4 - 80*S^6 + 14*S^8)*HPL[{4, 3, 1}, -S^2])/(S^3*(1 + S^2)) + 84*S*HPL[{4, 3, 2}, -S^2] - 168*S*HPL[{4, 4, 1}, -S^2] + ((2134*Pi^2*S)/3 + (160 - 463*S^2 + 1235*S^4 - 1416*S^6)/S^3)*HPL[{5, 1, 1}, -S^2] + (2*(-5 - 5*S^2 - 51*S^4 - 40*S^6 + 5*S^8)*HPL[{5, 1, 2}, -S^2])/(S^3*(1 + S^2)) - 336*S*HPL[{5, 1, 3}, -S^2] + (2*(-65 - 65*S^2 - 591*S^4 - 340*S^6 + 65*S^8)*HPL[{5, 2, 1}, -S^2])/(S^3*(1 + S^2)) - 78*S*HPL[{5, 2, 2}, -S^2] - 1152*S*HPL[{5, 3, 1}, -S^2] + (10*(-52 - 52*S^2 - 399*S^4 - 218*S^6 + 52*S^8)*HPL[{6, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 808*S*HPL[{6, 1, 2}, -S^2] - 3688*S*HPL[{6, 2, 1}, -S^2] - 9040*S*HPL[{7, 1, 1}, -S^2] + ((104*Pi^2*S)/3 + (4*(-20 + 97*S^2 + 27*S^4 + 20*S^6))/S^3)*HPL[{2, 2, 2, 1}, -S^2] + ((-506*Pi^2*S)/3 - (4*(-64 + 293*S^2 + 112*S^4 + 16*S^6))/S^3)*HPL[{3, 1, 1, 2}, -S^2] + ((-506*Pi^2*S)/3 - (4*(-64 + 293*S^2 + 112*S^4 + 16*S^6))/S^3)*HPL[{3, 1, 2, 1}, -S^2] + (12*S*(-2 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2) + ((-818*Pi^2*S)/3 - (4*(-124 + 584*S^2 + 193*S^4 + 76*S^6))/S^3)*HPL[{3, 2, 1, 1}, -S^2] + (12*S*(-2 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2) - (4*(-20 - 20*S^2 - 14*S^4 + 21*S^6 + 20*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(S^3*(1 + S^2)) - 416*S*HPL[{3, 2, 2, 2}, -S^2] - 1192*S*HPL[{3, 2, 3, 1}, -S^2] - (48*(-5 - 5*S^2 - 5*S^4 + 6*S^6 + 5*S^8)*HPL[{3, 3, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 1168*S*HPL[{3, 3, 1, 2}, -S^2] - 3496*S*HPL[{3, 3, 2, 1}, -S^2] + ((-2584*Pi^2*S)/3 - (6*(-228 + 1147*S^2 + 389*S^4 + 148*S^6))/S^3)*HPL[{4, 1, 1, 1}, -S^2] + (4*(-4 - 4*S^2 - 22*S^4 + 9*S^6 + 4*S^8)*HPL[{4, 1, 1, 2}, -S^2])/(S^3*(1 + S^2)) + 7160*S*HPL[{4, 1, 1, 3}, -S^2] - (4*(-56 - 56*S^2 - 38*S^4 + 63*S^6 + 56*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(S^3*(1 + S^2)) + 5992*S*HPL[{4, 1, 2, 2}, -S^2] + 10624*S*HPL[{4, 1, 3, 1}, -S^2] - (4*(-176 - 176*S^2 - 158*S^4 + 207*S^6 + 176*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 3736*S*HPL[{4, 2, 1, 2}, -S^2] + 3664*S*HPL[{4, 2, 2, 1}, -S^2] + 20912*S*HPL[{4, 3, 1, 1}, -S^2] - (24*(-63 - 63*S^2 - 63*S^4 + 50*S^6 + 63*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 21688*S*HPL[{5, 1, 1, 2}, -S^2] + 35368*S*HPL[{5, 1, 2, 1}, -S^2] + 83464*S*HPL[{5, 2, 1, 1}, -S^2] + 208480*S*HPL[{6, 1, 1, 1}, -S^2] + (192*Pi^2*S - (16*(12 - 47*S^2 - 23*S^4 + 12*S^6))/S^3)*HPL[{2, 1, 2, 1, 1}, -S^2] + (576*Pi^2*S - (48*(12 - 47*S^2 - 23*S^4 + 12*S^6))/S^3)*HPL[{2, 2, 1, 1, 1}, -S^2] - (32*(-5 - S^4 + 5*S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^3 - (96*(-5 - S^4 + 5*S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 - 832*S*HPL[{2, 2, 2, 2, 1}, -S^2] + ((3416*Pi^2*S)/3 - (4*(216 - 917*S^2 - 523*S^4 + 336*S^6))/S^3)*HPL[{3, 1, 1, 1, 1}, -S^2] + (16*(-59 - 11*S^4 + 59*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 + (16*(-99 - 19*S^4 + 99*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^3 - 1744*S*HPL[{3, 1, 1, 2, 2}, -S^2] + (16*(-119 - 23*S^4 + 119*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^3 - 1744*S*HPL[{3, 1, 2, 1, 2}, -S^2] + 48*S*HPL[{3, 1, 2, 2, 1}, -S^2] + 12928*S*HPL[{3, 1, 3, 1, 1}, -S^2] + (16*(-249 - 49*S^4 + 249*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^3 - 4240*S*HPL[{3, 2, 1, 1, 2}, -S^2] - 2448*S*HPL[{3, 2, 1, 2, 1}, -S^2] + 3696*S*HPL[{3, 2, 2, 1, 1}, -S^2] + 13440*S*HPL[{3, 3, 1, 1, 1}, -S^2] + (32*(-378 - 378*S^2 - 74*S^4 + 283*S^6 + 378*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 12608*S*HPL[{4, 1, 1, 1, 2}, -S^2] - 7232*S*HPL[{4, 1, 1, 2, 1}, -S^2] + 11200*S*HPL[{4, 1, 2, 1, 1}, -S^2] + 40576*S*HPL[{4, 2, 1, 1, 1}, -S^2] + 81792*S*HPL[{5, 1, 1, 1, 1}, -S^2] + ((368*Pi^2*S)/3 + (8*(-60 + 227*S^2 + 57*S^4 + 60*S^6))/S^3)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (32*(-15 - 15*S^2 - S^4 - 7*S^6 + 15*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 1472*S*HPL[{3, 1, 1, 1, 1, 2}, -S^2] - 1472*S*HPL[{3, 1, 1, 1, 2, 1}, -S^2] - 1472*S*HPL[{3, 1, 1, 2, 1, 1}, -S^2] - 1472*S*HPL[{3, 1, 2, 1, 1, 1}, -S^2] - 1472*S*HPL[{3, 2, 1, 1, 1, 1}, -S^2] - 5312*S*HPL[{4, 1, 1, 1, 1, 1}, -S^2] + (960*(-1 - S^4 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 - 2944*S*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] - 11776*S*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] - 29440*S*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] - 57984*S*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + ((Pi^2*S*(-35 + 2*S^4))/(9*(1 + S^2)) - (2*S*HPL[{0}, S^2]^3)/3 + ((-22*Pi^2*S)/9 + (4*(1 - 3*S^2 - 3*S^4 + S^6))/(3*S^3))*HPL[{1}, -S^2] - (28*S*HPL[{1}, -S^2]^2)/(1 + S^2) - (56*S*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]^2*((2*S*(-7 + S^4))/(3*(1 + S^2)) - (8*S*HPL[{1}, -S^2])/3) + (4*(-1 - S^4 + S^6)*HPL[{2}, -S^2])/(3*S^3) + HPL[{0}, S^2]*((-20*Pi^2*S)/9 + (4*S*(-3 + S^2))/3 - (28*S*HPL[{1}, -S^2])/(1 + S^2) - (28*S*HPL[{1}, -S^2]^2)/3 - 4*S*HPL[{2}, -S^2]) + (16*S*HPL[{3}, -S^2])/3)*Log[T]^6 + ((8*S*HPL[{1}, -S^2])/(1 + S^2) + (8*S*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*((4*S)/(1 + S^2) + (8*S*HPL[{1}, -S^2])/3))*Log[T]^7 + (-(S/(1 + S^2)) - (2*S*HPL[{0}, S^2])/3 - (2*S*HPL[{1}, -S^2])/3)*Log[T]^8 + ((9*S*(-11 + 7*S^2))/4 + (Pi^2*S*(-19 - 14*S^2 + 4*S^4))/(1 + S^2))*Zeta[3]^2 + HPL[{3, 1, 1, 1}, -S^2]*((184 + 219*S^2 + 595*S^4 - 242*S^6)/S^3 - (2*Pi^2*(-62 - 49*S^2 - 132*S^4 - 25*S^6 + 36*S^8))/(3*S^3*(1 + S^2)) - 432*S*Zeta[3]) + HPL[{5, 1}, -S^2]*((-52 + 724*S^2 + 925*S^4 - 88*S^6)/(4*S^3) + (Pi^2*(40 + 39*S^2 + 132*S^4 + 173*S^6 - 38*S^8))/(6*S^3*(1 + S^2)) - 80*S*Zeta[3]) + HPL[{2, 1}, -S^2]^2*((105 - 11*S^2 + 177*S^4 + 105*S^6)/(2*S^3) + (Pi^2*(24 + 5*S^2 + 159*S^4 - 9*S^6 + 14*S^8))/(3*S^3*(1 + S^2)) - 80*S*Zeta[3]) + HPL[{3, 1, 2}, -S^2]*((62 + S^2 + 23*S^4 - 62*S^6)/(4*S^3) + (Pi^2*(6 - S^2 + 13*S^4 - 4*S^6))/(6*S^3) - 12*S*Zeta[3]) + HPL[{1}, -S^2]^6*(((1 + S^2)*(21 - 130*S^2 + 21*S^4))/(36*S^3) + (Pi^2*(-1 - 72*S^2 - 3*S^4 + 2*S^6))/(18*S*(1 + S^2)) + (2*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/(3*S^3) + (40*S*HPL[{3}, -S^2])/9 + 4*S*Zeta[3]) + HPL[{4, 2}, -S^2]*((-79 - 107*S^2 - 7*S^4 + 169*S^6)/(8*S^3) + (Pi^2*(-6 - 5*S^2 - 24*S^4 + 6*S^6 + 4*S^8))/(6*S^3*(1 + S^2)) + 6*S*Zeta[3]) + HPL[{2}, -S^2]^3*((-71 - 40*S^2 - 212*S^4 + 71*S^6)/(24*S^3) + (Pi^2*(-20 - 16*S^2 - 63*S^4 + 14*S^6 + 12*S^8))/(36*S^3*(1 + S^2)) + (26*S*HPL[{3}, -S^2])/3 + (52*S*HPL[{2, 1}, -S^2])/3 + (26*S*Zeta[3])/3) + HPL[{3}, -S^2]^2*((-42 - 143*S^2 - 154*S^4 + 34*S^6)/(8*S^3) + (Pi^2*(1 + S^2 + 2*S^4 - 2*S^6 - S^8))/(6*S^3*(1 + S^2)) - 10*S*HPL[{2, 1}, -S^2] + 10*S*Zeta[3]) + HPL[{6}, -S^2]*((-370 - 2730*S^2 - 3141*S^4 + 961*S^6)/(8*S^3) + (Pi^2*(-160 - 180*S^2 - 939*S^4 - 422*S^6 + 200*S^8))/(12*S^3*(1 + S^2)) + 226*S*HPL[{2, 1}, -S^2] + 140*S*Zeta[3]) + HPL[{3, 2, 1}, -S^2]*((3*(-74 - 53*S^2 - 275*S^4 + 74*S^6))/(4*S^3) + (Pi^2*(-74 - 59*S^2 - 240*S^4 + 65*S^6 + 44*S^8))/(6*S^3*(1 + S^2)) + 196*S*Zeta[3]) + HPL[{4, 1, 1}, -S^2]*((-411 - 551*S^2 - 1597*S^4 + 527*S^6)/(2*S^3) + (2*Pi^2*(-74 - 60*S^2 - 204*S^4 - 7*S^6 + 46*S^8))/(3*S^3*(1 + S^2)) + 680*S*Zeta[3]) + HPL[{2, 1, 1, 1, 1}, -S^2]*((2*(-213 - 212*S^2 - 564*S^4 + 213*S^6))/S^3 + (4*Pi^2*(-20 - 16*S^2 - 51*S^4 + 12*S^8))/(S^3*(1 + S^2)) + 736*S*Zeta[3]) + HPL[{1}, -S^2]^5*((-1849*Pi^4*S)/2700 + ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(40*S^3) + (Pi^2*(1 + S^2)*(20 - 86*S^2 + 25*S^4))/(30*S^3) + ((-43*Pi^2*S)/45 + (-5 - 47*S^2 - 37*S^4 + 5*S^6)/(5*S^3))*HPL[{2}, -S^2] - (86*S*HPL[{2}, -S^2]^2)/15 + (2*(-1 - 5*S^2 + 72*S^4 - 15*S^6 + 9*S^8)*HPL[{3}, -S^2])/(5*S^3*(1 + S^2)) + (56*S*HPL[{4}, -S^2])/15 - (4*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (56*S*HPL[{3, 1}, -S^2])/15 + (2*(-1 + 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 2}, -S^2]*((-119*Pi^4*S)/60 + (17 + 12*S^2 - 1088*S^4 + 175*S^6)/(16*S^3) + (Pi^2*(24 - 49*S^2 - 137*S^4 + 198*S^6))/(24*S^3) - 376*S*HPL[{2, 1, 1}, -S^2] + (3*(-1 - 24*S^2 + 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{5}, -S^2]*((-109*Pi^4*S)/90 + (30 - 3867*S^2 - 1023*S^4 - S^6)/(16*S^3) + (Pi^2*(160 - 43*S^2 - 31*S^4 + 49*S^6))/(12*S^3) + ((12 + 19*S^2 + 34*S^4 + 61*S^6 - 26*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 174*S*HPL[{3, 1}, -S^2] + 92*S*HPL[{2, 1, 1}, -S^2] - (2*(-3 - 52*S^2 - S^4 + 6*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{4, 1}, -S^2]*((-308*Pi^4*S)/45 + (3 + 738*S^2 - 389*S^4 + 135*S^6)/(4*S^3) + (Pi^2*(-80 + 37*S^2 - 197*S^4 + 348*S^6))/(12*S^3) - 1184*S*HPL[{2, 1, 1}, -S^2] + (2*(-3 - 100*S^2 + 29*S^4 + 6*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((133*Pi^4*S)/15 + (2*Pi^2*(-62 + 225*S^2 + 71*S^4 + 38*S^6))/(3*S^3) + (-52 + 2093*S^2 + 451*S^4 + 52*S^6)/(2*S^3) - (24*(-4 + 31*S^2 + 8*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((-707*Pi^4*S)/90 + (Pi^2*(46 - 192*S^2 - 81*S^4 + 26*S^6))/(3*S^3) + (48 - 1373*S^2 - 301*S^4 + 48*S^6)/(4*S^3) + (8*(-5 + 45*S^2 + 3*S^4 + 10*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((-1607*Pi^4*S)/90 + (Pi^2*(332 - 1195*S^2 - 431*S^4 + 34*S^6))/(6*S^3) + (151 - 4825*S^2 - 1039*S^4 + 47*S^6)/(4*S^3) + (4*(-31 + 276*S^2 + 9*S^4 + 62*S^6)*Zeta[3])/(S*(1 + S^2))) + Log[T]^5*((5*(1 + S^2))/(2*S) - (Pi^2*S*(-11 + 6*S^2))/6 + ((22*Pi^2*S)/3 - (4*(1 - 3*S^2 - 3*S^4 + S^6))/S^3)*HPL[{1}, -S^2]^2 + (56*S*HPL[{1}, -S^2]^3)/(1 + S^2) + (28*S*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*(-(S*(-29 + 4*S^2))/(9*(1 + S^2)) + (22*S*HPL[{1}, -S^2])/9) + ((8*Pi^2*S)/9 + (18 + 11*S^2 + 33*S^4 - 18*S^6)/(3*S^3))*HPL[{2}, -S^2] + (16*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*(-(S*(-11 + 6*S^2))/2 + ((1 + 30*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)) + 8*S*HPL[{1}, -S^2]^2 + (8*S*HPL[{2}, -S^2])/3) + (4*S*(-23 + 7*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - 24*S*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]*((-4*Pi^2*S*(-23 + S^2))/(9*(1 + S^2)) - (S*(-109 + 21*S^2))/6 + (84*S*HPL[{1}, -S^2]^2)/(1 + S^2) + (56*S*HPL[{1}, -S^2]^3)/3 - (2*(-2 - S^2 - 14*S^4 + 3*S^6)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + HPL[{1}, -S^2]*((64*Pi^2*S)/9 - (4*(1 - 3*S^2 - 3*S^4 + S^6))/S^3 + 24*S*HPL[{2}, -S^2]) - (4*S*HPL[{3}, -S^2])/3 - 24*S*HPL[{2, 1}, -S^2]) + (12*S*(-1 + 2*S^2)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(21 - 130*S^2 + 21*S^4))/(6*S^3) + (Pi^2*(1 + 72*S^2 + 3*S^4 - 2*S^6))/(3*S*(1 + S^2)) - (4*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 - (80*S*HPL[{3}, -S^2])/3 - 24*S*Zeta[3])) + HPL[{0}, S^2]^5*((-47*Pi^4*S)/240 + (Pi^2*S*(-2 + 89*S^2))/144 + (5*(-6 - 47*S^2 + S^4))/(384*S) + ((-2 - 45*S^2 - 6*S^4 + 4*S^6)*HPL[{1}, -S^2]^3)/(36*S*(1 + S^2)) - (11*S*HPL[{1}, -S^2]^4)/72 + (-(Pi^2*S)/48 + (-18 - 15*S^2 - 23*S^4 - 4*S^6)/(96*S^3))*HPL[{2}, -S^2] - (S*HPL[{2}, -S^2]^2)/16 + HPL[{1}, -S^2]^2*((-2*Pi^2*S)/9 + (3 - 16*S^2 - 8*S^4 + 11*S^6)/(24*S^3) - (S*HPL[{2}, -S^2])/3) + ((1 + 3*S^2 - 2*S^4)*HPL[{3}, -S^2])/(16*S) + (3*S*HPL[{4}, -S^2])/8 + ((1 + 40*S^2 + 13*S^4 - 2*S^6)*HPL[{2, 1}, -S^2])/(24*S*(1 + S^2)) - (S*HPL[{2, 1, 1}, -S^2])/2 + (3*S*(-1 + 2*S^2)*Zeta[3])/(8*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(21 - 310*S^2 + 121*S^4))/(192*S^3) + (Pi^2*(-1 - 54*S^2 - 3*S^4 + 2*S^6))/(72*S*(1 + S^2)) + ((-3 - 2*S^2 - 30*S^4 - 6*S^6 + S^8)*HPL[{2}, -S^2])/(24*S^3*(1 + S^2)) + (2*S*HPL[{2, 1}, -S^2])/3 - (3*S*Zeta[3])/4)) + HPL[{0}, S^2]^4*((Pi^2*S*(-2737 + 898*S^2))/1152 + (-738 - 11574*S^2 + 2237*S^4)/(768*S) + (Pi^4*S*(-33553 - 20614*S^2 + 7392*S^4))/(17280*(1 + S^2)) + ((-7 - 134*S^2 - 21*S^4 + 14*S^6)*HPL[{1}, -S^2]^4)/(48*S*(1 + S^2)) - (23*S*HPL[{1}, -S^2]^5)/90 + ((-24 - 12*S^2 - 85*S^4 - 4*S^6)*HPL[{2}, -S^2]^2)/(96*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-53*Pi^2*S)/108 + (30 - 128*S^2 - 91*S^4 + 67*S^6)/(72*S^3) - (31*S*HPL[{2}, -S^2])/36) + ((-5*Pi^2*S)/24 + (8 + 7*S^2 - 3*S^4)/(32*S^3))*HPL[{3}, -S^2] + ((-2 - 4*S^2 - 21*S^4 - 7*S^6 + 6*S^8)*HPL[{4}, -S^2])/(8*S^3*(1 + S^2)) - (13*S*HPL[{5}, -S^2])/4 + ((8*Pi^2*S)/9 + (-60 + 247*S^2 + 86*S^4 - 38*S^6)/(48*S^3))*HPL[{2, 1}, -S^2] + ((30 + 18*S^2 + 103*S^4 + 16*S^6 - 6*S^8)*HPL[{3, 1}, -S^2])/(24*S^3*(1 + S^2)) - (S*HPL[{3, 2}, -S^2])/2 + (S*HPL[{4, 1}, -S^2])/2 + ((-30 - 18*S^2 - 97*S^4 - 10*S^6 + 6*S^8)*HPL[{2, 1, 1}, -S^2])/(12*S^3*(1 + S^2)) - (19*S*HPL[{2, 2, 1}, -S^2])/6 - (19*S*HPL[{3, 1, 1}, -S^2])/2 + (19*S*HPL[{2, 1, 1, 1}, -S^2])/3 - (S*(49 + 92*S^2)*Zeta[3])/48 + HPL[{1}, -S^2]^2*(((1 + S^2)*(105 - 967*S^2 + 378*S^4))/(192*S^3) + (Pi^2*(-11 - 172*S^2 - 33*S^4 + 22*S^6))/(48*S*(1 + S^2)) + ((-10 - 7*S^2 - 84*S^4 - 21*S^6 + 4*S^8)*HPL[{2}, -S^2])/(16*S^3*(1 + S^2)) + (31*S*HPL[{2, 1}, -S^2])/12 - (7*S*Zeta[3])/12) + HPL[{2}, -S^2]*((-213 - 72*S^2 - 397*S^4 + 10*S^6)/(192*S^3) + (Pi^2*(-30 - 24*S^2 - 131*S^4 - 5*S^6 + 18*S^8))/(144*S^3*(1 + S^2)) + (S*HPL[{3}, -S^2])/4 + (19*S*HPL[{2, 1}, -S^2])/12 + (5*S*Zeta[3])/4) + HPL[{1}, -S^2]*((-1849*Pi^4*S)/8640 + (Pi^2*(1 + S^2)*(30 - 184*S^2 + 71*S^4))/(144*S^3) + ((1 + S^2)*(19 - 952*S^2 + 389*S^4))/(128*S^3) + ((-19*Pi^2*S)/36 + (-15 - 143*S^2 - 106*S^4 + 22*S^6)/(48*S^3))*HPL[{2}, -S^2] - (31*S*HPL[{2}, -S^2]^2)/48 + ((-1 - 4*S^4 + S^6)*HPL[{3}, -S^2])/(8*S^3) - (S*HPL[{4}, -S^2])/2 + ((10 + 7*S^2 + 84*S^4 + 21*S^6 - 4*S^8)*HPL[{2, 1}, -S^2])/(8*S^3*(1 + S^2)) + (31*S*HPL[{3, 1}, -S^2])/12 - (31*S*HPL[{2, 1, 1}, -S^2])/6 + ((-23 - 180*S^2 - 69*S^4 + 46*S^6)*Zeta[3])/(24*S*(1 + S^2)))) + Log[T]^4*((-123*(1 + S^2))/(8*S) + (Pi^2*S*(-188 + 71*S^2))/24 + (Pi^4*S*(-6481 - 310*S^2 + 624*S^4))/(1080*(1 + S^2)) - (S*HPL[{0}, S^2]^5)/4 + ((-110*Pi^2*S)/9 + (20*(1 - 3*S^2 - 3*S^4 + S^6))/(3*S^3))*HPL[{1}, -S^2]^3 - (70*S*HPL[{1}, -S^2]^4)/(1 + S^2) - (28*S*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^4*((S*(-104 - 17*S^2 + 18*S^4))/(36*(1 + S^2)) - (23*S*HPL[{1}, -S^2])/18) + ((-4 - 34*S^4 + S^6 - 4*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + HPL[{0}, S^2]^3*((-5*Pi^2*S)/3 + (S*(-5 + 2*S^2))/3 + ((-2 - 67*S^2 - 6*S^4 + 4*S^6)*HPL[{1}, -S^2])/(3*S*(1 + S^2)) - (55*S*HPL[{1}, -S^2]^2)/9 - (7*S*HPL[{2}, -S^2])/3) + ((67*Pi^2*S)/9 + (24 - 23*S^2 + 63*S^4 - 96*S^6)/(6*S^3))*HPL[{3}, -S^2] + (4*(-3 - 3*S^2 + S^4 - 17*S^6 + 3*S^8)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)) + 8*S*HPL[{5}, -S^2] + ((46*Pi^2*S)/9 + (-60 + 227*S^2 + 57*S^4 + 60*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((S*(-188 + 71*S^2))/8 + (Pi^2*S*(-209 - 17*S^2 + 33*S^4))/(18*(1 + S^2)) + (5*(-1 - 30*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(2*S*(1 + S^2)) - (40*S*HPL[{1}, -S^2]^3)/3 + ((-10 - 6*S^2 - 41*S^4 + 2*S^8)*HPL[{2}, -S^2])/(2*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-53*Pi^2*S)/9 + (10 - 36*S^2 - 31*S^4 + 15*S^6)/(2*S^3) - (43*S*HPL[{2}, -S^2])/3) + (7*S*HPL[{3}, -S^2])/3 + (46*S*HPL[{2, 1}, -S^2])/3) - (4*(-15 - 15*S^2 - S^4 - 7*S^6 + 15*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (184*S*HPL[{3, 2}, -S^2])/3 - (664*S*HPL[{4, 1}, -S^2])/3 + (40*(-1 - S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (368*S*HPL[{2, 2, 1}, -S^2])/3 - 208*S*HPL[{3, 1, 1}, -S^2] - S*(19 + 20*S^2)*Zeta[3] + HPL[{2}, -S^2]*((-213 - 212*S^2 - 564*S^4 + 213*S^6)/(12*S^3) + (Pi^2*(-20 - 16*S^2 - 51*S^4 + 12*S^8))/(6*S^3*(1 + S^2)) + (92*S*HPL[{3}, -S^2])/3 + (184*S*HPL[{2, 1}, -S^2])/3 + (92*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(21 - 130*S^2 + 21*S^4))/(12*S^3) + (5*Pi^2*(-1 - 72*S^2 - 3*S^4 + 2*S^6))/(6*S*(1 + S^2)) + (10*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 + (200*S*HPL[{3}, -S^2])/3 + 60*S*Zeta[3]) + HPL[{1}, -S^2]*((-1849*Pi^4*S)/540 + ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(8*S^3) + (Pi^2*(1 + S^2)*(20 - 86*S^2 + 25*S^4))/(6*S^3) + ((-43*Pi^2*S)/9 + (-5 - 47*S^2 - 37*S^4 + 5*S^6)/S^3)*HPL[{2}, -S^2] - (86*S*HPL[{2}, -S^2]^2)/3 + (2*(-1 - 5*S^2 + 72*S^4 - 15*S^6 + 9*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + (56*S*HPL[{4}, -S^2])/3 - (20*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (56*S*HPL[{3, 1}, -S^2])/3 + (10*(-1 + 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]*((-47*Pi^4*S)/15 + (Pi^2*S*(-20 + 7*S^2))/3 + (-50 - 521*S^2 + 19*S^4)/(8*S) - (140*S*HPL[{1}, -S^2]^3)/(1 + S^2) - (70*S*HPL[{1}, -S^2]^4)/3 + ((-22*Pi^2*S)/3 + (-90 - 19*S^2 - 159*S^4 + 60*S^6)/(6*S^3))*HPL[{2}, -S^2] - (43*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((-160*Pi^2*S)/9 + (10*(1 - 3*S^2 - 3*S^4 + S^6))/S^3 - 60*S*HPL[{2}, -S^2]) + ((3 + 8*S^2 + 11*S^4 - 6*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 8*S*HPL[{4}, -S^2] + (10*(-1 + 18*S^2 + 3*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (208*S*HPL[{3, 1}, -S^2])/3 - 120*S*HPL[{2, 1, 1}, -S^2] - (14*S*(-1 + 2*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((5*(1 + S^2)*(21 - 130*S^2 + 21*S^4))/(12*S^3) + (2*Pi^2*(-1 - 86*S^2 - 3*S^4 + 2*S^6))/(3*S*(1 + S^2)) - (10*(1 + 16*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) - (8*S*HPL[{3}, -S^2])/3 + 120*S*HPL[{2, 1}, -S^2] + (28*S*Zeta[3])/3))) + ((-5*Pi^2*S*(53 + 44*S^2))/12 + (-52 - 2079*S^2 - 78*S^4)/(8*S))*Zeta[5] + HPL[{3, 1}, -S^2]*((522 + 3835*S^2 + 5173*S^4 - 2250*S^6)/(16*S^3) + (Pi^2*(415 + 376*S^2 + 1148*S^4 - 250*S^6))/(24*S^3) + (Pi^4*(852 + 614*S^2 + 2235*S^4 + 504*S^6 - 376*S^8))/(360*S^3*(1 + S^2)) + 180*S*HPL[{3, 2}, -S^2] + 680*S*HPL[{4, 1}, -S^2] + (8*(11 - S^2 + 105*S^4 + S^6 + 13*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 16*S*HPL[{2, 2, 1}, -S^2] - 2976*S*HPL[{3, 1, 1}, -S^2] - 736*S*HPL[{2, 1, 1, 1}, -S^2] + ((-70*Pi^2*S)/3 + (14 + 9*S^2 - 35*S^4 + 36*S^6)/S^3)*Zeta[3] - 152*S*Zeta[5]) + HPL[{2}, -S^2]^2*((-1042 + 1099*S^2 - 1109*S^4 - 1042*S^6)/(64*S^3) + (Pi^2*(-405 + 34*S^2 - 718*S^4 - 263*S^6))/(96*S^3) + (Pi^4*(-672 - 208*S^2 - 3147*S^4 + 78*S^6 - 256*S^8))/(1440*S^3*(1 + S^2)) + (4*Pi^2*S + (9 - 14*S^2 + 24*S^4 - 31*S^6)/(4*S^3))*HPL[{3}, -S^2] + ((-2 - 4*S^2 - 9*S^4 - 13*S^6 + 6*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)) - (15*S*HPL[{5}, -S^2])/2 + ((13*Pi^2*S)/3 + (-20 + 97*S^2 + 27*S^4 + 20*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + ((9 + 10*S^2 - 6*S^4 - 12*S^6 - 11*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 52*S*HPL[{3, 2}, -S^2] - 152*S*HPL[{4, 1}, -S^2] + (4*(-5 - S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - 104*S*HPL[{2, 2, 1}, -S^2] - 212*S*HPL[{3, 1, 1}, -S^2] + ((7*Pi^2*S)/2 + (-2 - 4*S^2 + 11*S^4 - 22*S^6)/(2*S^3))*Zeta[3] + 18*S*Zeta[5]) + HPL[{1}, -S^2]^4*((Pi^2*(1 + S^2)*(107 - 700*S^2 + 161*S^4))/(72*S^3) - ((1 + S^2)*(343 + 4730*S^2 + 343*S^4))/(96*S^3) + (Pi^4*(-111 - 4364*S^2 - 333*S^4 + 222*S^6))/(720*S*(1 + S^2)) + ((-2 - 39*S^4 - 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((53*Pi^2*S)/9 + (7 - 39*S^2 - 9*S^4 + 37*S^6)/(6*S^3))*HPL[{3}, -S^2] + ((-3 - 3*S^2 + 16*S^4 - 9*S^6 + 3*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 4*S*HPL[{5}, -S^2] + ((43*Pi^2*S)/9 + (5 + 47*S^2 + 37*S^4 - 5*S^6)/S^3)*HPL[{2, 1}, -S^2] - (2*(-5 - 5*S^2 - 6*S^4 - 15*S^6 + 5*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - (172*S*HPL[{3, 2}, -S^2])/3 - (572*S*HPL[{4, 1}, -S^2])/3 + (20*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (344*S*HPL[{2, 2, 1}, -S^2])/3 - (632*S*HPL[{3, 1, 1}, -S^2])/3 + ((49*Pi^2*S)/9 + ((1 + S^2)*(-6 + 5*S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-9 - 68*S^2 + 9*S^4))/(2*S^3) + (Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(6*S^3*(1 + S^2)) + (86*S*HPL[{3}, -S^2])/3 + (172*S*HPL[{2, 1}, -S^2])/3 + (86*S*Zeta[3])/3) + (110*S*Zeta[5])/3) + HPL[{4}, -S^2]*((Pi^2*(-64 - 391*S^2 - 471*S^4 + 168*S^6))/(48*S^3) + (897 - 6093*S^2 - 8051*S^4 + 2559*S^6)/(32*S^3) + (Pi^4*(-164 - 198*S^2 - 493*S^4 - 563*S^6 + 232*S^8))/(360*S^3*(1 + S^2)) + 245*S*HPL[{5}, -S^2] + (4*Pi^2*S + (-14 + 43*S^2 + 35*S^4 - 86*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + (2*(-5 - 3*S^2 - 2*S^4 - 12*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 42*S*HPL[{3, 2}, -S^2] + 84*S*HPL[{4, 1}, -S^2] - (4*(-2 - 24*S^2 + 3*S^4 + 4*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - 16*S*HPL[{2, 2, 1}, -S^2] - 136*S*HPL[{3, 1, 1}, -S^2] - 16*S*HPL[{2, 1, 1, 1}, -S^2] + ((32*Pi^2*S)/3 + (14 + 9*S^2 + 3*S^4 - 20*S^6)/(2*S^3))*Zeta[3] + 110*S*Zeta[5]) + HPL[{2, 1, 1}, -S^2]*((7*(-198 - 469*S^2 - 651*S^4 + 198*S^6))/(8*S^3) + (Pi^2*(-441 - 360*S^2 - 1058*S^4 + 231*S^6))/(12*S^3) + (Pi^4*(-832 - 604*S^2 - 2443*S^4 - 174*S^6 + 376*S^8))/(180*S^3*(1 + S^2)) + 736*S*HPL[{3, 1, 1}, -S^2] + 1472*S*HPL[{2, 1, 1, 1}, -S^2] + (36*Pi^2*S - (8*(1 + S^2 - 7*S^4 + 11*S^6))/S^3)*Zeta[3] + 208*S*Zeta[5]) + HPL[{3}, -S^2]*((6067*Pi^6*S)/45360 + (Pi^4*(328 - 47*S^2 + 161*S^4 - 594*S^6))/(720*S^3) + (Pi^2*(28 - 971*S^2 - 729*S^4 - 329*S^6))/(96*S^3) + (778 - 6525*S^2 - 751*S^4 + 1605*S^6)/(32*S^3) + (-8*Pi^2*S + (9 + 16*S^2 - 69*S^4 + 37*S^6)/(2*S^3))*HPL[{4}, -S^2] + ((-26 - 3*S^2 + 93*S^4 - 55*S^6 - 20*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) - 251*S*HPL[{6}, -S^2] - 100*S*HPL[{2, 1}, -S^2]^2 + ((-70*Pi^2*S)/3 + (9 + 7*S^2 - 47*S^4 + 49*S^6)/S^3)*HPL[{3, 1}, -S^2] + ((-4 - 5*S^2 - 36*S^4 - 17*S^6 + 6*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) - (2*(-9 - 5*S^2 - 47*S^4 - 29*S^6 + S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) + 168*S*HPL[{5, 1}, -S^2] + ((100*Pi^2*S)/3 - (2*(-5 - 3*S^2 - 33*S^4 + 53*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (4*(-1 - 10*S^2 + 122*S^4 + 6*S^6 + 19*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) + (4*(-3 - 30*S^2 + 350*S^4 + 14*S^6 + 57*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 12*S*HPL[{3, 1, 2}, -S^2] + 196*S*HPL[{3, 2, 1}, -S^2] - 6448*S*HPL[{4, 1, 1}, -S^2] - (8*(1 - 11*S^2 + 103*S^4 + 9*S^6 + 23*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 464*S*HPL[{3, 1, 1, 1}, -S^2] + 736*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*S*(-7 + 2*S^2))/(3*(1 + S^2)) + (-15 - 109*S^2 - 89*S^4 + 30*S^6)/(4*S^3))*Zeta[3] + 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((1 + 145*S^2 + 59*S^4 - 421*S^6)/(4*S^3) + (Pi^2*(-3 + 12*S^2 - 104*S^4 - 8*S^6 - 27*S^8))/(3*S^3*(1 + S^2)) - 40*S*Zeta[3]) - (4*S*(-11 + S^2)*Zeta[5])/(1 + S^2)) + Zeta[3]*(-(Pi^4*S*(499 + 628*S^2))/360 + (Pi^2*(-26 - 665*S^2 - 53*S^4))/(48*S) + (64 - 7762*S^2 + 827*S^4)/(32*S) + (16*S*(-18 - 19*S^2 + 5*S^4)*Zeta[5])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((881*Pi^6*S)/1512 + (827 + 19374*S^2 + 7826*S^4 - 827*S^6)/(32*S^3) + (Pi^2*(-111 + 3898*S^2 + 1075*S^4 + 63*S^6))/(48*S^3) + (Pi^4*(-1704 + 5940*S^2 + 1931*S^4 + 538*S^6))/(720*S^3) + ((-152*Pi^2*S)/3 + (2*(15 - 100*S^2 - 60*S^4 + 33*S^6))/S^3)*HPL[{3, 1}, -S^2] + (2*(-3 - 20*S^2 + 228*S^4 + 12*S^6 + 37*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) + (4*(-3 - 32*S^2 + 342*S^4 + 21*S^6 + 61*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) + 24*S*HPL[{4, 2}, -S^2] - 36*S*HPL[{5, 1}, -S^2] + (-96*Pi^2*S + (8*(12 - 47*S^2 - 23*S^4 + 12*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (16*(-5 - S^4 + 5*S^6)*HPL[{2, 2, 1}, -S^2])/S^3 + (8*(-31 - 19*S^2 - 109*S^4 + 15*S^6 + 7*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 24*S*HPL[{3, 1, 2}, -S^2] + 392*S*HPL[{3, 2, 1}, -S^2] + 1232*S*HPL[{4, 1, 1}, -S^2] + (48*(4 + 34*S^4 - S^6 + 4*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 736*S*HPL[{3, 1, 1, 1}, -S^2] - 1472*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-15 + 64*S^2 + 70*S^4 - 195*S^6)/(2*S^3) + (Pi^2*(4 - 35*S^2 - 8*S^6))/(S*(1 + S^2)))*Zeta[3] + 20*S*Zeta[3]^2 - (2*(-19 + 53*S^2 - 19*S^4 + 38*S^6)*Zeta[5])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-8699*Pi^6*S)/13608 + (Pi^2*(1 + S^2)*(115 - 3850*S^2 + 559*S^4))/(144*S^3) + (Pi^4*(1 + S^2)*(832 - 3646*S^2 + 1229*S^4))/(1080*S^3) - ((1 + S^2)*(2377 + 12838*S^2 + 2377*S^4))/(96*S^3) + ((-67*Pi^2*S)/9 - (4*(2 + 11*S^2 + 11*S^4 + 2*S^6))/(3*S^3))*HPL[{2}, -S^2]^2 - (8*S*HPL[{3}, -S^2]^2)/3 + ((28*Pi^2*S)/9 + (-3 - 25*S^2 - 11*S^4 + 11*S^6)/S^3)*HPL[{4}, -S^2] + (2*(-9 - 17*S^2 - 48*S^4 - 51*S^6 + 25*S^8)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)) - (70*S*HPL[{6}, -S^2])/3 + (344*S*HPL[{2, 1}, -S^2]^2)/3 + ((56*Pi^2*S)/9 - (2*(-9 - 127*S^2 - 97*S^4 + 21*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] - (8*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)) - (4*(-1 - 13*S^2 + 210*S^4 - 39*S^6 + 25*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) - 12*S*HPL[{4, 2}, -S^2] - (176*S*HPL[{5, 1}, -S^2])/3 + ((-172*Pi^2*S)/9 + (4*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (16*(2 + 39*S^4 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) - (8*(13 + 5*S^2 + 162*S^4 + 15*S^6 + 3*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (224*S*HPL[{4, 1, 1}, -S^2])/3 - (80*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 - (224*S*HPL[{3, 1, 1, 1}, -S^2])/3 + ((2*(1 + S^2)*(1 - 25*S^2 + 28*S^4))/(3*S^3) + (Pi^2*(-19 + 180*S^2 - 57*S^4 + 38*S^6))/(9*S*(1 + S^2)))*Zeta[3] - (4*S*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((-2*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 - (2*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(3*S^3*(1 + S^2)) - (344*S*Zeta[3])/3) + HPL[{3}, -S^2]*((2*(1 + S^2)*(7 - 57*S^2 + 34*S^4))/(3*S^3) + (Pi^2*(-7 - 19*S^2 + 218*S^4 - 57*S^6 + 31*S^8))/(9*S^3*(1 + S^2)) - (344*S*HPL[{2, 1}, -S^2])/3 + 8*S*Zeta[3]) + HPL[{2}, -S^2]*((-707*Pi^4*S)/540 + (Pi^2*(1 + S^2)*(-15 - 119*S^2 + 7*S^4))/(9*S^3) + ((1 + S^2)*(-111 - 628*S^2 + 111*S^4))/(6*S^3) + (4*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) + (28*S*HPL[{4}, -S^2])/3 + (8*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + (344*S*HPL[{3, 1}, -S^2])/3 - (688*S*HPL[{2, 1, 1}, -S^2])/3 + (4*(-2 + 31*S^2 - 6*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2))) + (2*(-29 + 156*S^2 - 87*S^4 + 58*S^6)*Zeta[5])/(3*S*(1 + S^2))) + Log[T]^3*((469*(1 + S^2))/(8*S) - (Pi^4*S*(-1137 + 596*S^2))/360 + (Pi^2*(308 + 1925*S^2 - 496*S^4))/(72*S) + ((110*Pi^2*S)/9 - (20*(1 - 3*S^2 - 3*S^4 + S^6))/(3*S^3))*HPL[{1}, -S^2]^4 + (56*S*HPL[{1}, -S^2]^5)/(1 + S^2) + (56*S*HPL[{1}, -S^2]^6)/9 + HPL[{0}, S^2]^5*(-(S*(-29 + 4*S^2))/(36*(1 + S^2)) + (11*S*HPL[{1}, -S^2])/18) + ((62*Pi^2*S)/9 + (2*(20 - 3*S^2 + 21*S^4 + 20*S^6))/(3*S^3))*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^4*(-(S*(-65 + 32*S^2))/24 + ((7 + 134*S^2 + 21*S^4 - 14*S^6)*HPL[{1}, -S^2])/(12*S*(1 + S^2)) + (23*S*HPL[{1}, -S^2]^2)/9 + (2*S*HPL[{2}, -S^2])/3) + (32*S*HPL[{3}, -S^2]^2)/3 + ((8 + 27*S^2 + 21*S^4 - 8*S^6)*HPL[{4}, -S^2])/S^3 + (12*S*(-1 + S^2)*HPL[{5}, -S^2])/(1 + S^2) - (320*S*HPL[{2, 1}, -S^2]^2)/3 + HPL[{0}, S^2]^3*((-5*Pi^2*S*(-29 + 4*S^2))/(27*(1 + S^2)) - (S*(-172 + 15*S^2))/18 - (2*(-2 - 67*S^2 - 6*S^4 + 4*S^6)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) + (220*S*HPL[{1}, -S^2]^3)/27 + ((28 + 14*S^2 + 115*S^4 - 6*S^6)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((110*Pi^2*S)/27 + (-28 + 103*S^2 + 77*S^4 - 54*S^6)/(9*S^3) + 10*S*HPL[{2}, -S^2]) + (4*S*HPL[{3}, -S^2])/9 - (32*S*HPL[{2, 1}, -S^2])/3) + ((-92*Pi^2*S)/9 + (2*(-90 - 43*S^2 - 165*S^4 + 90*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] - (8*S*(-30 + 13*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (88*S*(-29 + 10*S^2)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)) + ((160*Pi^2*S)/9 - (20*(-18 - 11*S^2 - 33*S^4 + 18*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (16*S*(44 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (16*S*(281 + 44*S^2)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)) - 480*S*HPL[{2, 1, 1, 1}, -S^2] + ((98*Pi^2*S*(-1 + 2*S^2))/(9*(1 + S^2)) + S*(48 + 35*S^2))*Zeta[3] + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(21 - 130*S^2 + 21*S^4))/(9*S^3) - (10*Pi^2*(-1 - 72*S^2 - 3*S^4 + 2*S^6))/(9*S*(1 + S^2)) - (40*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/(3*S^3) - (800*S*HPL[{3}, -S^2])/9 - 80*S*Zeta[3]) + HPL[{3}, -S^2]*((Pi^2*(-1 - 250*S^2 + 71*S^4 + 2*S^6))/(9*S*(1 + S^2)) + (-10 + 53*S^2 - 19*S^4 + 60*S^6)/(2*S^3) + (320*S*HPL[{2, 1}, -S^2])/3 + (8*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-2*Pi^2*S*(91 + 48*S^2))/(3*(1 + S^2)) + (105 - 712*S^2 - 144*S^4 - 105*S^6)/(3*S^3) + (320*S*Zeta[3])/3) + HPL[{2}, -S^2]*((154*Pi^4*S)/135 + (496 + 863*S^2 + 1617*S^4 - 496*S^6)/(12*S^3) + (Pi^2*(92 + 43*S^2 + 153*S^4 - 52*S^6))/(9*S^3) + (4*(-1 - S^2 - 91*S^4 + 39*S^6 + S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) - 16*S*HPL[{4}, -S^2] - (8*S*(44 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (320*S*HPL[{3, 1}, -S^2])/3 + (640*S*HPL[{2, 1, 1}, -S^2])/3 + (4*S*(-31 + 12*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((1849*Pi^4*S)/270 - ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(20 - 86*S^2 + 25*S^4))/(3*S^3) + ((86*Pi^2*S)/9 - (2*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2}, -S^2] + (172*S*HPL[{2}, -S^2]^2)/3 - (4*(-1 - 5*S^2 + 72*S^4 - 15*S^6 + 9*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - (112*S*HPL[{4}, -S^2])/3 + (40*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (112*S*HPL[{3, 1}, -S^2])/3 - (20*(-1 + 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^2*(-(Pi^2*S*(-60 + 31*S^2))/6 + (158 + 1775*S^2 - 496*S^4)/(24*S) - (10*(-1 - 30*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) + (40*S*HPL[{1}, -S^2]^4)/3 + ((32*Pi^2*S)/9 + (94 + 31*S^2 + 141*S^4 - 14*S^6)/(6*S^3))*HPL[{2}, -S^2] + (22*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((106*Pi^2*S)/9 + (-10 + 36*S^2 + 31*S^4 - 15*S^6)/S^3 + (86*S*HPL[{2}, -S^2])/3) + ((-1 - 20*S^2 + S^4 + 2*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (2*S*(61 + 18*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (92*S*HPL[{3, 1}, -S^2])/3 + (160*S*HPL[{2, 1, 1}, -S^2])/3 + (8*S*(-1 + 2*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(109 - 750*S^2 + 217*S^4))/(12*S^3) - (2*Pi^2*(-3 - 71*S^2 - 9*S^4 + 6*S^6))/(3*S*(1 + S^2)) - (2*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) - 4*S*HPL[{3}, -S^2] - (172*S*HPL[{2, 1}, -S^2])/3 - (16*S*Zeta[3])/3)) + HPL[{0}, S^2]*(-(Pi^2*S*(-889 + 135*S^2))/36 - (Pi^4*S*(-2629 + 182*S^2))/(270*(1 + S^2)) + (754 + 4319*S^2 + 343*S^4)/(24*S) + (140*S*HPL[{1}, -S^2]^4)/(1 + S^2) + (56*S*HPL[{1}, -S^2]^5)/3 - (2*(-4 - 2*S^2 - 34*S^4 + 7*S^6)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((640*Pi^2*S)/27 - (40*(1 - 3*S^2 - 3*S^4 + S^6))/(3*S^3) + 80*S*HPL[{2}, -S^2]) + ((-2*Pi^2*S)/3 + (-36 + 9*S^2 + 5*S^4 + 22*S^6)/(3*S^3))*HPL[{3}, -S^2] + (2*(18 + 9*S^2 + 56*S^4 + 23*S^6)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)) + 12*S*HPL[{5}, -S^2] + ((-92*Pi^2*S)/3 - (2*(-60 + 191*S^2 + 51*S^4 + 90*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (4*(-30 - 15*S^2 - 224*S^4 + 31*S^6)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) + (8*S*HPL[{3, 2}, -S^2])/3 + (80*S*HPL[{4, 1}, -S^2])/3 - (40*(-2 - S^2 - 14*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (688*S*HPL[{2, 2, 1}, -S^2])/3 + (1984*S*HPL[{3, 1, 1}, -S^2])/3 - 480*S*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(21 - 130*S^2 + 21*S^4))/(6*S^3) - (4*Pi^2*(-1 - 86*S^2 - 3*S^4 + 2*S^6))/(3*S*(1 + S^2)) + (20*(1 + 16*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + (16*S*HPL[{3}, -S^2])/3 - 240*S*HPL[{2, 1}, -S^2] - (56*S*Zeta[3])/3) + HPL[{2}, -S^2]*((217 + 116*S^2 + 576*S^4 - 101*S^6)/(6*S^3) + (Pi^2*(58 + 29*S^2 + 325*S^4 - 51*S^6))/(9*S^3*(1 + S^2)) - (16*S*HPL[{3}, -S^2])/3 - (344*S*HPL[{2, 1}, -S^2])/3 - 8*S*Zeta[3]) + HPL[{1}, -S^2]*((937*Pi^4*S)/135 - ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(58 - 251*S^2 + 84*S^4))/(9*S^3) + (30*Pi^2*S + (10*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2}, -S^2] + (172*S*HPL[{2}, -S^2]^2)/3 + (4*(1 + 2*S^4 + S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + (56*S*HPL[{4}, -S^2])/3 - (40*(1 + 16*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 240*S*HPL[{3, 1}, -S^2] + 480*S*HPL[{2, 1, 1}, -S^2] - (56*S*Zeta[3])/(1 + S^2))) + (220*S*(-1 + 2*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(107 - 700*S^2 + 161*S^4))/(18*S^3) + ((1 + S^2)*(343 + 4730*S^2 + 343*S^4))/(24*S^3) + (Pi^4*(111 + 4364*S^2 + 333*S^4 - 222*S^6))/(180*S*(1 + S^2)) + (4*(2 + 39*S^4 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((-212*Pi^2*S)/9 - (2*(7 - 39*S^2 - 9*S^4 + 37*S^6))/(3*S^3))*HPL[{3}, -S^2] - (4*(-3 - 3*S^2 + 16*S^4 - 9*S^6 + 3*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 16*S*HPL[{5}, -S^2] + ((-172*Pi^2*S)/9 + (4*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1}, -S^2] + (8*(-5 - 5*S^2 - 6*S^4 - 15*S^6 + 5*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + (688*S*HPL[{3, 2}, -S^2])/3 + (2288*S*HPL[{4, 1}, -S^2])/3 - (80*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (1376*S*HPL[{2, 2, 1}, -S^2])/3 + (2528*S*HPL[{3, 1, 1}, -S^2])/3 + ((-196*Pi^2*S)/9 - (4*(1 + S^2)*(-6 + 5*S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-2*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 - (2*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(3*S^3*(1 + S^2)) - (344*S*HPL[{3}, -S^2])/3 - (688*S*HPL[{2, 1}, -S^2])/3 - (344*S*Zeta[3])/3) - (440*S*Zeta[5])/3)) + HPL[{0}, S^2]^3*((-6023*Pi^6*S)/11340 + (Pi^4*S*(-235 + 3388*S^2))/2160 + (-1922 - 6969*S^2 + 6*S^4)/(384*S) + (Pi^2*(-282 - 2441*S^2 + 37*S^4))/(576*S) + ((-2 - 67*S^2 - 6*S^4 + 4*S^6)*HPL[{1}, -S^2]^5)/(15*S*(1 + S^2)) - (11*S*HPL[{1}, -S^2]^6)/27 + ((-11*Pi^2*S)/24 + (-62 - 7*S^2 - 99*S^4 + 8*S^6)/(48*S^3))*HPL[{2}, -S^2]^2 - (5*S*HPL[{2}, -S^2]^3)/12 + HPL[{1}, -S^2]^4*((-55*Pi^2*S)/54 + (28 - 103*S^2 - 77*S^4 + 54*S^6)/(36*S^3) - (5*S*HPL[{2}, -S^2])/2) + S*HPL[{3}, -S^2]^2 + ((43*Pi^2*S)/36 + (-66 - 65*S^2 - 85*S^4 - 8*S^6)/(24*S^3))*HPL[{4}, -S^2] + ((29 + 186*S^2 + 45*S^4 - 58*S^6)*HPL[{5}, -S^2])/(12*S*(1 + S^2)) + (125*S*HPL[{6}, -S^2])/6 + 6*S*HPL[{2, 1}, -S^2]^2 + ((11*Pi^2*S)/9 + (90 + 13*S^2 + 141*S^4)/(12*S^3))*HPL[{3, 1}, -S^2] + ((1 - 28*S^2 + 5*S^4 - 2*S^6)*HPL[{3, 2}, -S^2])/(12*S*(1 + S^2)) + ((-9 - 82*S^2 - 19*S^4 + 18*S^6)*HPL[{4, 1}, -S^2])/(6*S*(1 + S^2)) + (S*HPL[{4, 2}, -S^2])/6 - 9*S*HPL[{5, 1}, -S^2] + (-4*Pi^2*S + (-40 - 11*S^2 - 62*S^4 + 6*S^6)/(3*S^3))*HPL[{2, 1, 1}, -S^2] + ((3 - 136*S^2 - 31*S^4 - 6*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + ((13 - 406*S^2 - 85*S^4 - 26*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (S*HPL[{3, 1, 2}, -S^2])/3 - (29*S*HPL[{3, 2, 1}, -S^2])/3 - (94*S*HPL[{4, 1, 1}, -S^2])/3 + (2*(-4 + 159*S^2 + 36*S^4 + 8*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (88*S*HPL[{3, 1, 1, 1}, -S^2])/3 - 56*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((49*Pi^2*S*(-1 + 2*S^2))/(36*(1 + S^2)) + (5*S*(-59 + 8*S^2))/24)*Zeta[3] - 8*S*Zeta[3]^2 + HPL[{3}, -S^2]*((75 - 99*S^2 - 191*S^4 - 84*S^6)/(48*S^3) + (Pi^2*(19 + 62*S^2 + 23*S^4 - 38*S^6))/(72*S*(1 + S^2)) - 2*S*HPL[{2, 1}, -S^2] - 6*S*Zeta[3]) + HPL[{1}, -S^2]^3*(((1 + S^2)*(47 - 399*S^2 + 140*S^4))/(36*S^3) + (Pi^2*(-8 - 213*S^2 - 24*S^4 + 16*S^6))/(27*S*(1 + S^2)) + ((-14 - 5*S^2 - 137*S^4 - 15*S^6 - 4*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (2*S*HPL[{3}, -S^2])/3 + 10*S*HPL[{2, 1}, -S^2] - (8*S*Zeta[3])/9) + HPL[{2, 1}, -S^2]*((Pi^2*(1 + 359*S^2 + 101*S^4 - 2*S^6))/(36*S*(1 + S^2)) + (-105 + 624*S^2 + 137*S^4 + 2*S^6)/(24*S^3) + (8*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-37*Pi^4*S)/240 + (Pi^2*(-170 - 97*S^2 - 239*S^4 - 8*S^6))/(144*S^3) + (-283 - 521*S^2 - 1606*S^4 + 3*S^6)/(96*S^3) + (3*S*HPL[{3}, -S^2])/(2*(1 + S^2)) - 2*S*HPL[{4}, -S^2] + ((-3 + 136*S^2 + 31*S^4 + 6*S^6)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) + 7*S*HPL[{3, 1}, -S^2] - 12*S*HPL[{2, 1, 1}, -S^2] + (S*(-5 + S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]^2*((-937*Pi^4*S)/1080 + (Pi^2*(1 + S^2)*(58 - 321*S^2 + 164*S^4))/(72*S^3) + ((1 + S^2)*(25 - 1219*S^2 + 362*S^4))/(48*S^3) + ((-85*Pi^2*S)/36 + (-5 - 53*S^2 - 48*S^4)/(6*S^3))*HPL[{2}, -S^2] - (19*S*HPL[{2}, -S^2]^2)/6 + ((-2 - 5*S^4 - 2*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) - S*HPL[{4}, -S^2] + ((14 + 5*S^2 + 137*S^4 + 15*S^6 + 4*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (44*S*HPL[{3, 1}, -S^2])/3 - 30*S*HPL[{2, 1, 1}, -S^2] + ((-1 - 14*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(2*S*(1 + S^2))) + (55*S*(-1 + 2*S^2)*Zeta[5])/(6*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(199 - 2348*S^2 + 885*S^4))/(288*S^3) + ((1 + S^2)*(-167 - 7973*S^2 + 1916*S^4))/(192*S^3) + (Pi^4*(-77 - 3273*S^2 - 231*S^4 + 154*S^6))/(1080*S*(1 + S^2)) + ((-11 - 4*S^2 - 116*S^4 - 12*S^6 - 3*S^8)*HPL[{2}, -S^2]^2)/(12*S^3*(1 + S^2)) + (-(Pi^2*S)/6 + (2 - 3*S^2 - 13*S^4 - 8*S^6)/(6*S^3))*HPL[{3}, -S^2] - (3*(1 + S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)) + 3*S*HPL[{5}, -S^2] + ((85*Pi^2*S)/18 + (5 + 53*S^2 + 48*S^4)/(3*S^3))*HPL[{2, 1}, -S^2] + ((15 + 4*S^2 + 126*S^4 + 12*S^6 + 7*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - 2*S*HPL[{3, 2}, -S^2] - 4*S*HPL[{4, 1}, -S^2] - (2*(14 + 5*S^2 + 137*S^4 + 15*S^6 + 4*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (76*S*HPL[{2, 2, 1}, -S^2])/3 - 80*S*HPL[{3, 1, 1}, -S^2] + 60*S*HPL[{2, 1, 1, 1}, -S^2] + ((-49*Pi^2*S)/18 + ((1 + S^2)*(-41 + 49*S^2))/(6*S))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-65 - 646*S^2 + 7*S^4))/(48*S^3) + (Pi^2*(-29 - 15*S^2 - 287*S^4 - 45*S^6 + S^8))/(36*S^3*(1 + S^2)) + S*HPL[{3}, -S^2] + (38*S*HPL[{2, 1}, -S^2])/3 - (4*S*Zeta[3])/3) - (55*S*Zeta[5])/3)) + HPL[{0}, S^2]^2*((Pi^4*S*(-13945 + 4721*S^2))/2880 + (Pi^2*(-1534 - 16927*S^2 + 3623*S^4))/(384*S) + (-10006 - 68859*S^2 + 12838*S^4)/(256*S) + (Pi^6*S*(-576935 - 324282*S^2 + 122168*S^4))/(181440*(1 + S^2)) + ((-1 - 30*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^6)/(6*S*(1 + S^2)) - (8*S*HPL[{1}, -S^2]^7)/21 + ((-10 - 6*S^2 - 61*S^4 + 6*S^6 + 2*S^8)*HPL[{2}, -S^2]^3)/(12*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((-53*Pi^2*S)/45 + (10 - 36*S^2 - 31*S^4 + 15*S^6)/(10*S^3) - (43*S*HPL[{2}, -S^2])/15) + ((1 + S^2 + 10*S^4 - S^8)*HPL[{3}, -S^2]^2)/(2*S^3*(1 + S^2)) + ((-85*Pi^2*S)/12 + (160 - S^2 - 19*S^4 + 74*S^6)/(8*S^3))*HPL[{5}, -S^2] + ((-20 - 25*S^2 - 141*S^4 - 58*S^6 + 30*S^8)*HPL[{6}, -S^2])/(S^3*(1 + S^2)) - (275*S*HPL[{7}, -S^2])/2 + ((12 + 5*S^2 + 57*S^4 - 6*S^6 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)) + ((-17*Pi^2*S)/12 + (8 - 41*S^2 - 13*S^4 + 22*S^6)/(8*S^3))*HPL[{3, 2}, -S^2] + (-(Pi^2*S) + (-22 - 7*S^2 - S^4 + 36*S^6)/(2*S^3))*HPL[{4, 1}, -S^2] + ((-2 + S^2 - 3*S^4)*HPL[{4, 2}, -S^2])/(2*S^3) + 26*S*HPL[{4, 3}, -S^2] + ((22 + 21*S^2 + 114*S^4 + 41*S^6 - 20*S^8)*HPL[{5, 1}, -S^2])/(2*S^3*(1 + S^2)) + (153*S*HPL[{5, 2}, -S^2])/2 + 214*S*HPL[{6, 1}, -S^2] + (-15*Pi^2*S + (22 - 98*S^2 - 35*S^4 + 2*S^6)/S^3)*HPL[{2, 2, 1}, -S^2] + ((-128*Pi^2*S)/3 + (82 - 304*S^2 - 109*S^4 - 7*S^6)/S^3)*HPL[{3, 1, 1}, -S^2] + ((2 - S^2 + 9*S^4)*HPL[{3, 1, 2}, -S^2])/(2*S^3) + ((-38 - 23*S^2 - 236*S^4 + 33*S^6 + 8*S^8)*HPL[{3, 2, 1}, -S^2])/(2*S^3*(1 + S^2)) - (5*S*HPL[{3, 2, 2}, -S^2])/2 + 16*S*HPL[{3, 3, 1}, -S^2] + (2*(-38 - 24*S^2 - 200*S^4 + 3*S^6 + 10*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 16*S*HPL[{4, 1, 2}, -S^2] + 76*S*HPL[{4, 2, 1}, -S^2] + 166*S*HPL[{5, 1, 1}, -S^2] + (28*Pi^2*S + (-64 + 223*S^2 + 85*S^4 + 16*S^6)/S^3)*HPL[{2, 1, 1, 1}, -S^2] + 104*S*HPL[{2, 2, 2, 1}, -S^2] - (2*(-32 - 19*S^2 - 130*S^4 - 11*S^6 + 6*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 322*S*HPL[{3, 1, 1, 2}, -S^2] - 322*S*HPL[{3, 1, 2, 1}, -S^2] - 634*S*HPL[{3, 2, 1, 1}, -S^2] - 1920*S*HPL[{4, 1, 1, 1}, -S^2] + (12*(-10 - 6*S^2 - 41*S^4 + 2*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 208*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 624*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 1096*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 368*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (-(Pi^2*S*(23 + 36*S^2))/8 + (-18 - 206*S^2 - S^4)/(16*S))*Zeta[3] + (S*(-89 - 66*S^2 + 20*S^4)*Zeta[3]^2)/(2*(1 + S^2)) + HPL[{3, 1}, -S^2]*((231 + 157*S^2 + 553*S^4 - 8*S^6)/(8*S^3) + (Pi^2*(62 + 37*S^2 + 233*S^4 + 27*S^6 - 12*S^8))/(12*S^3*(1 + S^2)) - 16*S*Zeta[3]) + HPL[{2}, -S^2]^2*((-195 + 12*S^2 - 364*S^4 - 53*S^6)/(32*S^3) + (Pi^2*(-48 - 22*S^2 - 199*S^4 + 8*S^6 - 4*S^8))/(48*S^3*(1 + S^2)) - (S*HPL[{3}, -S^2])/2 + 13*S*HPL[{2, 1}, -S^2] + (S*Zeta[3])/2) + HPL[{1}, -S^2]^4*(((1 + S^2)*(109 - 750*S^2 + 217*S^4))/(48*S^3) + (Pi^2*(-3 - 71*S^2 - 9*S^4 + 6*S^6))/(6*S*(1 + S^2)) + ((-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2}, -S^2])/(2*S^3*(1 + S^2)) + S*HPL[{3}, -S^2] + (43*S*HPL[{2, 1}, -S^2])/3 + (4*S*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*((-114 - 74*S^2 - 247*S^4 + 9*S^6)/(2*S^3) + (Pi^2*(-30 - 18*S^2 - 110*S^4 - 5*S^6 + 6*S^8))/(3*S^3*(1 + S^2)) + 16*S*Zeta[3]) + HPL[{4}, -S^2]*((-79 - 80*S^2 - 146*S^4 + 67*S^6)/(16*S^3) + (Pi^2*(-7 - 9*S^2 - 40*S^4 - 18*S^6 + 11*S^8))/(6*S^3*(1 + S^2)) + 14*S*HPL[{2, 1}, -S^2] + 25*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((343*Pi^4*S)/180 + (Pi^2*(-124 + 470*S^2 + 171*S^4 - 22*S^6))/(24*S^3) + (-59 + 1805*S^2 + 624*S^4 + 11*S^6)/(16*S^3) - 60*S*HPL[{3, 1}, -S^2] - 104*S*HPL[{2, 1, 1}, -S^2] - (12*S*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((-59*Pi^4*S)/240 + (21 - 265*S^2 - 593*S^4 - 232*S^6)/(32*S^3) + (Pi^2*(56 + S^2 - 17*S^4 - 26*S^6))/(48*S^3) - 13*S*HPL[{4}, -S^2] + ((-2 + S^2 - S^4 + S^6 - 4*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 12*S*HPL[{3, 1}, -S^2] + 8*S*HPL[{2, 1, 1}, -S^2] + ((1 + 22*S^2 + S^4 - 2*S^6)*Zeta[3])/(2*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-359*Pi^4*S)/270 + (Pi^2*(1 + S^2)*(15 - 74*S^2 + 28*S^4))/(9*S^3) + ((1 + S^2)*(29 - 1040*S^2 + 251*S^4))/(24*S^3) + ((-37*Pi^2*S)/9 + (-15 - 127*S^2 - 113*S^4 - S^6)/(6*S^3))*HPL[{2}, -S^2] - 8*S*HPL[{2}, -S^2]^2 + (2*(-2 - 2*S^2 + S^4 - 6*S^6 + 2*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) - (2*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 28*S*HPL[{3, 1}, -S^2] - (172*S*HPL[{2, 1, 1}, -S^2])/3 + (4*(-1 - 3*S^4 + 2*S^6)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(214 - 1717*S^2 + 595*S^4))/(96*S^3) + ((1 + S^2)*(-349 - 5853*S^2 + 1210*S^4))/(64*S^3) + (Pi^4*(-349 - 6402*S^2 - 1047*S^4 + 698*S^6))/(720*S*(1 + S^2)) + ((-12 - 5*S^2 - 150*S^4 - 15*S^6 - 2*S^8)*HPL[{2}, -S^2]^2)/(4*S^3*(1 + S^2)) + ((Pi^2*S)/2 + (2 - 13*S^2 - 15*S^4)/(2*S^3))*HPL[{3}, -S^2] + ((-8 + 3*S^2 - 17*S^4 + 2*S^6)*HPL[{4}, -S^2])/(2*S^3) - 3*S*HPL[{5}, -S^2] + ((37*Pi^2*S)/3 + (15 + 127*S^2 + 113*S^4 + S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + ((16 + 9*S^2 + 148*S^4 + 27*S^6 - 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 6*S*HPL[{3, 2}, -S^2] - 18*S*HPL[{4, 1}, -S^2] + (6*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 96*S*HPL[{2, 2, 1}, -S^2] - 276*S*HPL[{3, 1, 1}, -S^2] + 172*S*HPL[{2, 1, 1, 1}, -S^2] + (-(Pi^2*S)/2 + ((1 + S^2)*(1 - 9*S^2 + 5*S^4))/S^3)*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(56 + 349*S^2 + 3*S^4))/(8*S^3) + (Pi^2*(-20 - 13*S^2 - 186*S^4 - 39*S^6 + 6*S^8))/(8*S^3*(1 + S^2)) + 3*S*HPL[{3}, -S^2] + 48*S*HPL[{2, 1}, -S^2] + 4*S*Zeta[3])) - (S*(67 + 52*S^2)*Zeta[5])/2 + HPL[{2}, -S^2]*((Pi^2*(-441 - 220*S^2 - 891*S^4 + 28*S^6))/(96*S^3) + (-1204 - 2102*S^2 - 3103*S^4 + 162*S^6)/(64*S^3) + (Pi^4*(-416 - 302*S^2 - 1619*S^4 - 126*S^6 + 188*S^8))/(720*S^3*(1 + S^2)) + ((5*Pi^2*S)/6 + (11 + 4*S^2 - 8*S^4)/(4*S))*HPL[{3}, -S^2] + ((-1 - S^2 - 10*S^4 + S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 13*S*HPL[{5}, -S^2] + ((15*Pi^2*S)/2 + (-22 + 98*S^2 + 35*S^4 - 2*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + ((12 + 5*S^2 + 62*S^4 - 7*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 2*S*HPL[{3, 2}, -S^2] - 8*S*HPL[{4, 1}, -S^2] - (2*(12 + 5*S^2 + 57*S^4 - 6*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 52*S*HPL[{2, 2, 1}, -S^2] + 164*S*HPL[{3, 1, 1}, -S^2] + 104*S*HPL[{2, 1, 1, 1}, -S^2] + ((19*Pi^2*S)/6 + (-10 - S^2 - 4*S^4 - 4*S^6)/(4*S^3))*Zeta[3] + 29*S*Zeta[5]) + HPL[{1}, -S^2]*((-8699*Pi^6*S)/18144 + (Pi^4*(1 + S^2)*(416 - 2212*S^2 + 845*S^4))/(720*S^3) + (Pi^2*(1 + S^2)*(115 - 4936*S^2 + 1669*S^4))/(192*S^3) + ((1 + S^2)*(-2047 - 16827*S^2 + 2734*S^4))/(128*S^3) + ((-79*Pi^2*S)/24 + (-8 - 48*S^2 - 43*S^4 - 3*S^6)/(4*S^3))*HPL[{2}, -S^2]^2 - (23*S*HPL[{2}, -S^2]^3)/6 + 3*S*HPL[{3}, -S^2]^2 + (-(Pi^2*S) + (-23 - 24*S^2 - S^4)/(2*S))*HPL[{4}, -S^2] + ((-9 - 7*S^2 - 42*S^4 - 21*S^6 + 5*S^8)*HPL[{5}, -S^2])/(2*S^3*(1 + S^2)) - 32*S*HPL[{6}, -S^2] + 48*S*HPL[{2, 1}, -S^2]^2 + ((73*Pi^2*S)/6 + (6 + 61*S^2 + 58*S^4 + 3*S^6)/S^3)*HPL[{3, 1}, -S^2] + ((-5 + 2*S^2 - 14*S^4 + 6*S^6 - 9*S^8)*HPL[{3, 2}, -S^2])/(2*S^3*(1 + S^2)) - (2*(-1 - 4*S^2 + 5*S^4 - 12*S^6 + 7*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) + 18*S*HPL[{5, 1}, -S^2] + ((-74*Pi^2*S)/3 + (-15 - 127*S^2 - 113*S^4 - S^6)/S^3)*HPL[{2, 1, 1}, -S^2] - (2*(12 + 5*S^2 + 150*S^4 + 15*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) - (2*(40 + 19*S^2 + 448*S^4 + 57*S^6 + 2*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 92*S*HPL[{3, 2, 1}, -S^2] - 276*S*HPL[{4, 1, 1}, -S^2] - (12*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 168*S*HPL[{3, 1, 1, 1}, -S^2] - 344*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(11 - 121*S^2 + 74*S^4))/(8*S^3) + (3*Pi^2*(-3 - 20*S^2 - 9*S^4 + 6*S^6))/(4*S*(1 + S^2)))*Zeta[3] - S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(56 + 349*S^2 + 3*S^4))/(4*S^3) + (Pi^2*(20 + 13*S^2 + 186*S^4 + 39*S^6 - 6*S^8))/(4*S^3*(1 + S^2)) - 8*S*Zeta[3]) + HPL[{3}, -S^2]*(-((1 + S^2)*(-8 + 145*S^2 + 7*S^4))/(8*S^3) + (Pi^2*(-7 - 7*S^2 - 10*S^4 - 21*S^6 + 7*S^8))/(12*S^3*(1 + S^2)) - 6*S*HPL[{2, 1}, -S^2] + 6*S*Zeta[3]) + HPL[{2}, -S^2]*((-473*Pi^4*S)/360 - ((1 + S^2)*(445 + 2018*S^2 + S^4))/(32*S^3) + (Pi^2*(1 + S^2)*(-10 - 80*S^2 + 7*S^4))/(8*S^3) + ((2 - S^2 + 8*S^4 - 3*S^6 + 4*S^8)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)) - 6*S*HPL[{4}, -S^2] + ((12 + 5*S^2 + 150*S^4 + 15*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 52*S*HPL[{3, 1}, -S^2] - 96*S*HPL[{2, 1, 1}, -S^2] + ((-2 - S^2 + 22*S^4 - 3*S^6)*Zeta[3])/(2*S^3*(1 + S^2))) + (13*(-1 - 5*S^2 + 2*S^4)*Zeta[5])/S)) + Log[T]^2*((-5001*(1 + S^2))/(32*S) + (Pi^4*S*(-11779 + 4087*S^2))/1440 + (Pi^2*(-1534 - 6091*S^2 + 1386*S^4))/(96*S) + (Pi^6*S*(-63821 - 11726*S^2 + 8600*S^4))/(15120*(1 + S^2)) - (S*HPL[{0}, S^2]^7)/24 + ((-22*Pi^2*S)/3 + (4*(1 - 3*S^2 - 3*S^4 + S^6))/S^3)*HPL[{1}, -S^2]^5 - (28*S*HPL[{1}, -S^2]^6)/(1 + S^2) - (8*S*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^6*((S*(-5 - 2*S^2 + S^4))/(8*(1 + S^2)) - (S*HPL[{1}, -S^2])/6) + (2*(-5 - S^4 + 5*S^6)*HPL[{2}, -S^2]^3)/(3*S^3) + HPL[{0}, S^2]^5*((-5*Pi^2*S)/12 + (S*(-2 + 5*S^2))/12 + ((-2 - 45*S^2 - 6*S^4 + 4*S^6)*HPL[{1}, -S^2])/(12*S*(1 + S^2)) - (11*S*HPL[{1}, -S^2]^2)/12 - (S*HPL[{2}, -S^2])/4) - (4*S*(4 + S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((5*Pi^2*S)/3 + (160 - 85*S^2 - 43*S^4 + 24*S^6)/(2*S^3))*HPL[{5}, -S^2] + (5*(-16 - 16*S^2 - 75*S^4 - 38*S^6 + 16*S^8)*HPL[{6}, -S^2])/(S^3*(1 + S^2)) - 200*S*HPL[{7}, -S^2] + (12*(4 + 34*S^4 - S^6 + 4*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)) + HPL[{0}, S^2]^4*((S*(-757 + 223*S^2))/96 + (Pi^2*S*(-329 - 107*S^2 + 63*S^4))/(72*(1 + S^2)) + ((-7 - 134*S^2 - 21*S^4 + 14*S^6)*HPL[{1}, -S^2]^2)/(8*S*(1 + S^2)) - (23*S*HPL[{1}, -S^2]^3)/9 + ((-30 - 18*S^2 - 97*S^4 - 10*S^6 + 6*S^8)*HPL[{2}, -S^2])/(24*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-53*Pi^2*S)/36 + (30 - 128*S^2 - 91*S^4 + 67*S^6)/(24*S^3) - (31*S*HPL[{2}, -S^2])/12) + (19*S*HPL[{2, 1}, -S^2])/6) + ((-97*Pi^2*S)/3 + (2*(4 - 2*S^2 - 31*S^4 + 44*S^6))/S^3)*HPL[{3, 2}, -S^2] + ((-356*Pi^2*S)/3 + (3*(-12 + 17*S^2 - 65*S^4 + 92*S^6))/S^3)*HPL[{4, 1}, -S^2] + (2*(-4 - 4*S^2 - 22*S^4 + 9*S^6 + 4*S^8)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)) + 88*S*HPL[{4, 3}, -S^2] - (12*(-3 - 3*S^2 - 3*S^4 - 22*S^6 + 3*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)) + 260*S*HPL[{5, 2}, -S^2] + 560*S*HPL[{6, 1}, -S^2] + (-96*Pi^2*S + (8*(12 - 47*S^2 - 23*S^4 + 12*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + ((-596*Pi^2*S)/3 + (2*(168 - 587*S^2 - 213*S^4 + 48*S^6))/S^3)*HPL[{3, 1, 1}, -S^2] - (8*(-1 - S^4 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 + (8*(-9 - S^4 + 9*S^6)*HPL[{3, 2, 1}, -S^2])/S^3 + 376*S*HPL[{3, 2, 2}, -S^2] + 1216*S*HPL[{3, 3, 1}, -S^2] + (16*(-18 - 18*S^2 - 2*S^4 - 5*S^6 + 18*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 1184*S*HPL[{4, 1, 2}, -S^2] + 3776*S*HPL[{4, 2, 1}, -S^2] + 7872*S*HPL[{5, 1, 1}, -S^2] + ((184*Pi^2*S)/3 + (4*(-60 + 227*S^2 + 57*S^4 + 60*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] - (16*(-15 - 15*S^2 - S^4 - 7*S^6 + 15*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 736*S*HPL[{3, 1, 1, 2}, -S^2] - 736*S*HPL[{3, 1, 2, 1}, -S^2] - 736*S*HPL[{3, 2, 1, 1}, -S^2] - 2656*S*HPL[{4, 1, 1, 1}, -S^2] + (480*(-1 - S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + 1472*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 4416*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 9280*S*HPL[{3, 1, 1, 1, 1}, -S^2] + (-(Pi^2*S*(77 + 76*S^2))/6 + (-8 - 459*S^2 - 52*S^4)/(4*S))*Zeta[3] + (2*S*(-25 - 18*S^2 + 4*S^4)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((184 + 219*S^2 + 595*S^4 - 242*S^6)/(2*S^3) + (Pi^2*(62 + 49*S^2 + 132*S^4 + 25*S^6 - 36*S^8))/(3*S^3*(1 + S^2)) - 216*S*Zeta[3]) + HPL[{4}, -S^2]*((15 - 311*S^2 - 325*S^4 + 101*S^6)/(4*S^3) + (Pi^2*(-14 - 12*S^2 - 15*S^4 - 49*S^6 + 10*S^8))/(3*S^3*(1 + S^2)) - 8*S*HPL[{2, 1}, -S^2] + 28*S*Zeta[3]) + HPL[{2}, -S^2]^2*((-105 + 11*S^2 - 177*S^4 - 105*S^6)/(4*S^3) + (Pi^2*(-24 - 5*S^2 - 159*S^4 + 9*S^6 - 14*S^8))/(6*S^3*(1 + S^2)) + 50*S*HPL[{3}, -S^2] + 40*S*Zeta[3]) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(21 - 130*S^2 + 21*S^4))/(12*S^3) + (5*Pi^2*(-1 - 72*S^2 - 3*S^4 + 2*S^6))/(6*S*(1 + S^2)) + (10*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 + (200*S*HPL[{3}, -S^2])/3 + 60*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-213 - 212*S^2 - 564*S^4 + 213*S^6)/S^3 + (2*Pi^2*(-20 - 16*S^2 - 51*S^4 + 12*S^8))/(S^3*(1 + S^2)) + 368*S*Zeta[3]) + HPL[{3}, -S^2]*((257*Pi^4*S)/90 + (Pi^2*(56 - 43*S^2 + 55*S^4 - 122*S^6))/(12*S^3) + (7 - 706*S^2 - 136*S^4 - 97*S^6)/(8*S^3) - 44*S*HPL[{4}, -S^2] - (4*(1 - 11*S^2 + 103*S^4 + 9*S^6 + 23*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 232*S*HPL[{3, 1}, -S^2] + 368*S*HPL[{2, 1, 1}, -S^2] + (2*(-1 + 6*S^2 - 9*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-1849*Pi^4*S)/270 + ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(4*S^3) + (Pi^2*(1 + S^2)*(20 - 86*S^2 + 25*S^4))/(3*S^3) + ((-86*Pi^2*S)/9 + (2*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2}, -S^2] - (172*S*HPL[{2}, -S^2]^2)/3 + (4*(-1 - 5*S^2 + 72*S^4 - 15*S^6 + 9*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + (112*S*HPL[{4}, -S^2])/3 - (40*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (112*S*HPL[{3, 1}, -S^2])/3 + (20*(-1 + 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((133*Pi^4*S)/30 + (Pi^2*(-62 + 225*S^2 + 71*S^4 + 38*S^6))/(3*S^3) + (-52 + 2093*S^2 + 451*S^4 + 52*S^6)/(4*S^3) - 368*S*HPL[{3, 1}, -S^2] - 736*S*HPL[{2, 1, 1}, -S^2] - (12*(-4 + 31*S^2 + 8*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^3*((-47*Pi^4*S)/30 + (Pi^2*S*(-25 + 31*S^2))/18 + (-22 - 211*S^2 + 2*S^4)/(8*S) + (2*(-2 - 67*S^2 - 6*S^4 + 4*S^6)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) - (55*S*HPL[{1}, -S^2]^4)/9 + (-2*Pi^2*S + (-40 - 11*S^2 - 62*S^4 + 6*S^6)/(6*S^3))*HPL[{2}, -S^2] - 3*S*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((-55*Pi^2*S)/9 + (28 - 103*S^2 - 77*S^4 + 54*S^6)/(6*S^3) - 15*S*HPL[{2}, -S^2]) + ((2 + S^2 + 4*S^4 - 4*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (2*S*HPL[{4}, -S^2])/3 + ((-4 + 159*S^2 + 36*S^4 + 8*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (44*S*HPL[{3, 1}, -S^2])/3 - 28*S*HPL[{2, 1, 1}, -S^2] + (4*S*(-1 + 2*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(47 - 399*S^2 + 140*S^4))/(12*S^3) + (Pi^2*(-8 - 213*S^2 - 24*S^4 + 16*S^6))/(9*S*(1 + S^2)) + ((-14 - 5*S^2 - 137*S^4 - 15*S^6 - 4*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) - 2*S*HPL[{3}, -S^2] + 30*S*HPL[{2, 1}, -S^2] - (8*S*Zeta[3])/3)) + HPL[{0}, S^2]^2*((Pi^2*S*(-1321 + 436*S^2))/48 + (Pi^4*S*(-1873 - 462*S^2 + 334*S^4))/(180*(1 + S^2)) + (-796 - 5353*S^2 + 1386*S^4)/(32*S) + (5*(-1 - 30*S^2 - 3*S^4 + 2*S^6)*HPL[{1}, -S^2]^4)/(2*S*(1 + S^2)) - 8*S*HPL[{1}, -S^2]^5 + ((-12 - 5*S^2 - 57*S^4 + 6*S^6 - 2*S^8)*HPL[{2}, -S^2]^2)/(2*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-106*Pi^2*S)/9 + (10 - 36*S^2 - 31*S^4 + 15*S^6)/S^3 - (86*S*HPL[{2}, -S^2])/3) + ((7*Pi^2*S)/6 + (16 - 10*S^2 - 4*S^4 - 13*S^6)/(2*S^3))*HPL[{3}, -S^2] + ((-8 + 2*S^2 - 19*S^4 + 4*S^6)*HPL[{4}, -S^2])/S^3 - 7*S*HPL[{5}, -S^2] + (14*Pi^2*S + (-64 + 223*S^2 + 85*S^4 + 16*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + ((32 + 19*S^2 + 130*S^4 + 11*S^6 - 6*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 5*S*HPL[{3, 2}, -S^2] - 24*S*HPL[{4, 1}, -S^2] + (6*(-10 - 6*S^2 - 41*S^4 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 104*S*HPL[{2, 2, 1}, -S^2] - 284*S*HPL[{3, 1, 1}, -S^2] + 184*S*HPL[{2, 1, 1, 1}, -S^2] - 2*S*(5 + 4*S^2)*Zeta[3] + HPL[{2}, -S^2]*((-114 - 74*S^2 - 247*S^4 + 9*S^6)/(4*S^3) + (Pi^2*(-30 - 18*S^2 - 110*S^4 - 5*S^6 + 6*S^8))/(6*S^3*(1 + S^2)) + 4*S*HPL[{3}, -S^2] + 52*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{1}, -S^2]^2*(((1 + S^2)*(109 - 750*S^2 + 217*S^4))/(8*S^3) + (Pi^2*(-3 - 71*S^2 - 9*S^4 + 6*S^6))/(S*(1 + S^2)) + (3*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + 6*S*HPL[{3}, -S^2] + 86*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{1}, -S^2]*((-359*Pi^4*S)/90 + (Pi^2*(1 + S^2)*(15 - 74*S^2 + 28*S^4))/(3*S^3) + ((1 + S^2)*(29 - 1040*S^2 + 251*S^4))/(8*S^3) + ((-37*Pi^2*S)/3 + (-15 - 127*S^2 - 113*S^4 - S^6)/(2*S^3))*HPL[{2}, -S^2] - 24*S*HPL[{2}, -S^2]^2 + (2*(-2 - 2*S^2 + S^4 - 6*S^6 + 2*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - (6*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 84*S*HPL[{3, 1}, -S^2] - 172*S*HPL[{2, 1, 1}, -S^2] + (4*(-1 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2)))) + HPL[{0}, S^2]*((-6023*Pi^6*S)/2835 + (Pi^4*S*(-201 + 136*S^2))/60 + (-3066 - 12149*S^2 - 2377*S^4)/(32*S) + (Pi^2*(-94 - 943*S^2 + 23*S^4))/(16*S) - (84*S*HPL[{1}, -S^2]^5)/(1 + S^2) - (28*S*HPL[{1}, -S^2]^6)/3 + ((-61*Pi^2*S)/6 + (2*(-9 - S^2 - 17*S^4 + 5*S^6))/S^3)*HPL[{2}, -S^2]^2 - (38*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((-160*Pi^2*S)/9 + (10*(1 - 3*S^2 - 3*S^4 + S^6))/S^3 - 60*S*HPL[{2}, -S^2]) + 4*S*HPL[{3}, -S^2]^2 + ((-14*Pi^2*S)/3 + (-58 - 25*S^2 - 77*S^4 + 16*S^6)/(2*S^3))*HPL[{4}, -S^2] + ((9 + 14*S^2 + 17*S^4 - 18*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)) + 20*S*HPL[{6}, -S^2] + 172*S*HPL[{2, 1}, -S^2]^2 + ((148*Pi^2*S)/3 + (86 + 9*S^2 + 181*S^4 - 44*S^6)/S^3)*HPL[{3, 1}, -S^2] - (4*(-1 + 6*S^2 - 6*S^4 + 2*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (2*(-3 - 62*S^2 - 5*S^4 + 6*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - 6*S*HPL[{4, 2}, -S^2] + 20*S*HPL[{5, 1}, -S^2] + (-88*Pi^2*S + (2*(-90 - 19*S^2 - 159*S^4 + 60*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (24*(-2 + 44*S^2 + 7*S^4 + 4*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-39 + 784*S^2 + 115*S^4 + 78*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + 24*S*HPL[{3, 1, 2}, -S^2] - 280*S*HPL[{3, 2, 1}, -S^2] - 1008*S*HPL[{4, 1, 1}, -S^2] + (120*(-1 + 18*S^2 + 3*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 832*S*HPL[{3, 1, 1, 1}, -S^2] - 1440*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((Pi^2*S*(-1 + 2*S^2))/(1 + S^2)) + (S*(-31 + 29*S^2))/2)*Zeta[3] - 32*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-19 + 429*S^2 + 81*S^4 + 38*S^6))/(3*S*(1 + S^2)) + (-101 + 616*S^2 + 156*S^4 + 217*S^6)/(2*S^3) - 16*S*Zeta[3]) + HPL[{3}, -S^2]*((67 - 32*S^2 - 122*S^4 - 77*S^6)/(4*S^3) + (Pi^2*(7 + 10*S^2 + 19*S^4 - 14*S^6))/(6*S*(1 + S^2)) - 24*S*HPL[{2, 1}, -S^2] - 16*S*Zeta[3]) + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(21 - 130*S^2 + 21*S^4))/(6*S^3) + (4*Pi^2*(-1 - 86*S^2 - 3*S^4 + 2*S^6))/(3*S*(1 + S^2)) - (20*(1 + 16*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) - (16*S*HPL[{3}, -S^2])/3 + 240*S*HPL[{2, 1}, -S^2] + (56*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-937*Pi^4*S)/90 + (3*(1 + S^2)*(19 - 590*S^2 + 19*S^4))/(8*S^3) + (Pi^2*(1 + S^2)*(58 - 251*S^2 + 84*S^4))/(6*S^3) + (-45*Pi^2*S - (15*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2}, -S^2] - 86*S*HPL[{2}, -S^2]^2 - (6*(1 + 2*S^4 + S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - 28*S*HPL[{4}, -S^2] + (60*(1 + 16*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 360*S*HPL[{3, 1}, -S^2] - 720*S*HPL[{2, 1, 1}, -S^2] + (84*S*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((-349*Pi^4*S)/90 + (-497 - 554*S^2 - 1752*S^4 + 51*S^6)/(8*S^3) + (Pi^2*(-170 - 41*S^2 - 283*S^4 + 72*S^6))/(12*S^3) + (2*(-1 + 9*S^2 - 3*S^4 + 2*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)) - 8*S*HPL[{4}, -S^2] + (12*(-2 + 44*S^2 + 7*S^4 + 4*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 176*S*HPL[{3, 1}, -S^2] - 344*S*HPL[{2, 1, 1}, -S^2] - (2*(-2 - S^2 - 11*S^4 + 3*S^6)*Zeta[3])/(S^3*(1 + S^2))) + HPL[{1}, -S^2]*(-((1 + S^2)*(343 + 4730*S^2 + 343*S^4))/(16*S^3) + (Pi^2*(1 + S^2)*(199 - 1448*S^2 + 385*S^4))/(24*S^3) + (Pi^4*(-65 - 3201*S^2 - 195*S^4 + 130*S^6))/(90*S*(1 + S^2)) - (6*(2 + 39*S^4 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((-10*Pi^2*S)/3 + (11 - 5*S^2 - 25*S^4 - 9*S^6)/S^3)*HPL[{3}, -S^2] - (6*(3 + 8*S^4 + 3*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 20*S*HPL[{5}, -S^2] + (90*Pi^2*S + (30*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2, 1}, -S^2] + (60*(1 + 16*S^4 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 40*S*HPL[{3, 2}, -S^2] - 64*S*HPL[{4, 1}, -S^2] - (120*(1 + 16*S^4 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 688*S*HPL[{2, 2, 1}, -S^2] - 2096*S*HPL[{3, 1, 1}, -S^2] + 1440*S*HPL[{2, 1, 1, 1}, -S^2] + (2*Pi^2*S + (2*(1 + S^2)*(-2 + 3*S^2 + 8*S^4))/S^3)*Zeta[3] + HPL[{2}, -S^2]*(-(((1 + S^2)*(29 + 154*S^2 + 29*S^4))/S^3) + (Pi^2*(-29 - 5*S^2 - 377*S^4 - 15*S^6 - 19*S^8))/(3*S^3*(1 + S^2)) + 20*S*HPL[{3}, -S^2] + 344*S*HPL[{2, 1}, -S^2] + 20*S*Zeta[3]))) - S*(131 + 116*S^2)*Zeta[5] + HPL[{2}, -S^2]*((7*(-198 - 469*S^2 - 651*S^4 + 198*S^6))/(16*S^3) + (Pi^2*(-441 - 360*S^2 - 1058*S^4 + 231*S^6))/(24*S^3) + (Pi^4*(-832 - 604*S^2 - 2443*S^4 - 174*S^6 + 376*S^8))/(360*S^3*(1 + S^2)) + ((50*Pi^2*S)/3 + (5 + 3*S^2 + 33*S^4 - 53*S^6)/S^3)*HPL[{3}, -S^2] - (2*(-2 - 24*S^2 + 3*S^4 + 4*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)) + 46*S*HPL[{5}, -S^2] + (48*Pi^2*S - (4*(12 - 47*S^2 - 23*S^4 + 12*S^6))/S^3)*HPL[{2, 1}, -S^2] + (4*(11 - S^2 + 105*S^4 + S^6 + 13*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 188*S*HPL[{3, 2}, -S^2] - 592*S*HPL[{4, 1}, -S^2] - (24*(4 + 34*S^4 - S^6 + 4*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 368*S*HPL[{3, 1, 1}, -S^2] + 736*S*HPL[{2, 1, 1, 1}, -S^2] + (18*Pi^2*S - (4*(1 + S^2 - 7*S^4 + 11*S^6))/S^3)*Zeta[3] + 104*S*Zeta[5]) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(107 - 700*S^2 + 161*S^4))/(12*S^3) - ((1 + S^2)*(343 + 4730*S^2 + 343*S^4))/(16*S^3) + (Pi^4*(-111 - 4364*S^2 - 333*S^4 + 222*S^6))/(120*S*(1 + S^2)) - (6*(2 + 39*S^4 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((106*Pi^2*S)/3 + (7 - 39*S^2 - 9*S^4 + 37*S^6)/S^3)*HPL[{3}, -S^2] + (6*(-3 - 3*S^2 + 16*S^4 - 9*S^6 + 3*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 24*S*HPL[{5}, -S^2] + ((86*Pi^2*S)/3 - (6*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1}, -S^2] - (12*(-5 - 5*S^2 - 6*S^4 - 15*S^6 + 5*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 344*S*HPL[{3, 2}, -S^2] - 1144*S*HPL[{4, 1}, -S^2] + (120*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - 688*S*HPL[{2, 2, 1}, -S^2] - 1264*S*HPL[{3, 1, 1}, -S^2] + ((98*Pi^2*S)/3 + (6*(1 + S^2)*(-6 + 5*S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((3*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 + (Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(S^3*(1 + S^2)) + 172*S*HPL[{3}, -S^2] + 344*S*HPL[{2, 1}, -S^2] + 172*S*Zeta[3]) + 220*S*Zeta[5]) + HPL[{1}, -S^2]*((-8699*Pi^6*S)/4536 + (Pi^2*(1 + S^2)*(115 - 3850*S^2 + 559*S^4))/(48*S^3) + (Pi^4*(1 + S^2)*(832 - 3646*S^2 + 1229*S^4))/(360*S^3) - ((1 + S^2)*(2377 + 12838*S^2 + 2377*S^4))/(32*S^3) + ((-67*Pi^2*S)/3 - (4*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2}, -S^2]^2 - 8*S*HPL[{3}, -S^2]^2 + ((28*Pi^2*S)/3 + (3*(-3 - 25*S^2 - 11*S^4 + 11*S^6))/S^3)*HPL[{4}, -S^2] + (2*(-9 - 17*S^2 - 48*S^4 - 51*S^6 + 25*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) - 70*S*HPL[{6}, -S^2] + 344*S*HPL[{2, 1}, -S^2]^2 + ((56*Pi^2*S)/3 - (2*(-9 - 127*S^2 - 97*S^4 + 21*S^6))/S^3)*HPL[{3, 1}, -S^2] - (8*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) - (12*(-1 - 13*S^2 + 210*S^4 - 39*S^6 + 25*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) - 36*S*HPL[{4, 2}, -S^2] - 176*S*HPL[{5, 1}, -S^2] + ((-172*Pi^2*S)/3 + (12*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (48*(2 + 39*S^4 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) - (24*(13 + 5*S^2 + 162*S^4 + 15*S^6 + 3*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 224*S*HPL[{4, 1, 1}, -S^2] - (240*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 - 224*S*HPL[{3, 1, 1, 1}, -S^2] + ((2*(1 + S^2)*(1 - 25*S^2 + 28*S^4))/S^3 + (Pi^2*(-19 + 180*S^2 - 57*S^4 + 38*S^6))/(3*S*(1 + S^2)))*Zeta[3] - 4*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-6*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 - (2*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(S^3*(1 + S^2)) - 344*S*Zeta[3]) + HPL[{3}, -S^2]*((2*(1 + S^2)*(7 - 57*S^2 + 34*S^4))/S^3 + (Pi^2*(-7 - 19*S^2 + 218*S^4 - 57*S^6 + 31*S^8))/(3*S^3*(1 + S^2)) - 344*S*HPL[{2, 1}, -S^2] + 24*S*Zeta[3]) + HPL[{2}, -S^2]*((-707*Pi^4*S)/180 + (Pi^2*(1 + S^2)*(-15 - 119*S^2 + 7*S^4))/(3*S^3) + ((1 + S^2)*(-111 - 628*S^2 + 111*S^4))/(2*S^3) + (4*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + 28*S*HPL[{4}, -S^2] + (24*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 344*S*HPL[{3, 1}, -S^2] - 688*S*HPL[{2, 1, 1}, -S^2] + (12*(-2 + 31*S^2 - 6*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2))) + (2*(-29 + 156*S^2 - 87*S^4 + 58*S^6)*Zeta[5])/(S*(1 + S^2)))) - (15*S*(51 + 20*S^2)*Zeta[7])/2 + HPL[{2}, -S^2]*((Pi^2*(-2590 - 5385*S^2 - 7660*S^4 + 1548*S^6))/(192*S^3) + (Pi^4*(-6054 - 4260*S^2 - 12451*S^4 + 2077*S^6))/(2880*S^3) + (-12838 - 49947*S^2 - 58853*S^4 + 12838*S^6)/(128*S^3) + (Pi^6*(-20384 - 15848*S^2 - 66011*S^4 - 3966*S^6 + 11312*S^8))/(90720*S^3*(1 + S^2)) + ((2 + 3*S^2 + 18*S^4 + 7*S^6 - 4*S^8)*HPL[{3}, -S^2]^2)/(2*S^3*(1 + S^2)) + ((49*Pi^2*S)/6 + (-16 - S^2 + 77*S^4 - 47*S^6)/(2*S^3))*HPL[{5}, -S^2] + ((48 + 4*S^2 - 183*S^4 + 138*S^6 + 40*S^8)*HPL[{6}, -S^2])/(2*S^3*(1 + S^2)) + 261*S*HPL[{7}, -S^2] - (4*(-5 - S^4 + 5*S^6)*HPL[{2, 1}, -S^2]^2)/S^3 + (-15*Pi^2*S + (-13 + 35*S^2 - 41*S^4 + 67*S^6)/(2*S^3))*HPL[{3, 2}, -S^2] + (-52*Pi^2*S + (-40 + 41*S^2 - 179*S^4 + 272*S^6)/(2*S^3))*HPL[{4, 1}, -S^2] + ((-2 - 23*S^4 + 9*S^6 - 2*S^8)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)) - 42*S*HPL[{4, 3}, -S^2] + ((-8 - 5*S^2 - 70*S^4 + S^6 + 2*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)) - 129*S*HPL[{5, 2}, -S^2] - 436*S*HPL[{6, 1}, -S^2] + ((-52*Pi^2*S)/3 - (2*(-20 + 97*S^2 + 27*S^4 + 20*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + ((256*Pi^2*S)/3 + (2*(-55 + 294*S^2 + 114*S^4 + 7*S^6))/S^3)*HPL[{3, 1, 1}, -S^2] + (2*(1 + 16*S^4 + S^8)*HPL[{3, 1, 2}, -S^2])/(S^3*(1 + S^2)) - (6*(5 + 72*S^4 - 4*S^6 + 5*S^8)*HPL[{3, 2, 1}, -S^2])/(S^3*(1 + S^2)) + 208*S*HPL[{3, 2, 2}, -S^2] + 584*S*HPL[{3, 3, 1}, -S^2] - (4*(24 - 2*S^2 + 324*S^4 - 15*S^6 + 28*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 584*S*HPL[{4, 1, 2}, -S^2] + 1712*S*HPL[{4, 2, 1}, -S^2] + 3476*S*HPL[{5, 1, 1}, -S^2] + (96*Pi^2*S - (8*(12 - 47*S^2 - 23*S^4 + 12*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] + 416*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(-131 - 119*S^2 - 129*S^4 + 95*S^6 + 107*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 872*S*HPL[{3, 1, 1, 2}, -S^2] + 872*S*HPL[{3, 1, 2, 1}, -S^2] + 2120*S*HPL[{3, 2, 1, 1}, -S^2] + 6304*S*HPL[{4, 1, 1, 1}, -S^2] - (48*(4 + 34*S^4 - S^6 + 4*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 736*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 1472*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((157*Pi^4*S)/90 + (Pi^2*(-14 - 5*S^2 + 24*S^4 - 48*S^6))/(12*S^3) + (-7 - 288*S^2 + 173*S^4 - 41*S^6)/(8*S^3))*Zeta[3] + ((4 + 2*S^2 + 5*S^4 + 16*S^6)*Zeta[3]^2)/(S^3*(1 + S^2)) + HPL[{3, 1}, -S^2]*((141 - 65*S^2 + 365*S^4 + 279*S^6)/(4*S^3) + (Pi^2*(23 + 4*S^2 + 167*S^4 - 6*S^6 + 15*S^8))/(3*S^3*(1 + S^2)) - 64*S*Zeta[3]) + HPL[{4}, -S^2]*((107 + 405*S^2 + 345*S^4 - 169*S^6)/(8*S^3) + (Pi^2*(-2 + 4*S^4 - 3*S^6 - 2*S^8))/(6*S^3*(1 + S^2)) + 8*S*HPL[{2, 1}, -S^2] - 20*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-105 + 11*S^2 - 177*S^4 - 105*S^6)/S^3 - (2*Pi^2*(24 + 5*S^2 + 159*S^4 - 9*S^6 + 14*S^8))/(3*S^3*(1 + S^2)) + 160*S*Zeta[3]) + HPL[{3}, -S^2]*((31*Pi^4*S)/30 + (107 + 78*S^2 + 191*S^4 - 155*S^6)/(8*S^3) + (Pi^2*(5 + 14*S^2 + 37*S^4 - 61*S^6))/(12*S^3) + 18*S*HPL[{4}, -S^2] - (2*(-1 - 10*S^2 + 122*S^4 + 6*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 84*S*HPL[{3, 1}, -S^2] + 200*S*HPL[{2, 1, 1}, -S^2] - (2*(-1 - 18*S^2 + 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((707*Pi^4*S)/180 + (-48 + 1373*S^2 + 301*S^4 - 48*S^6)/(8*S^3) + (Pi^2*(-46 + 192*S^2 + 81*S^4 - 26*S^6))/(6*S^3) - 8*S*HPL[{3, 1}, -S^2] - (4*(-5 + 45*S^2 + 3*S^4 + 10*S^6)*Zeta[3])/(S*(1 + S^2))) + ((55*Pi^2*S)/3 + (-28 - 10*S^2 + 19*S^4 - 76*S^6)/(2*S^3))*Zeta[5] + 150*S*Zeta[7]) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(-692 - 10583*S^2 + 867*S^4))/(192*S^3) + (Pi^4*(1 + S^2)*(2952 - 20219*S^2 + 5919*S^4))/(2880*S^3) - ((1 + S^2)*(11427 + 35402*S^2 + 11427*S^4))/(128*S^3) + (Pi^6*(-4447 - 113672*S^2 - 13341*S^4 + 8894*S^6))/(30240*S*(1 + S^2)) + (5*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) + ((-1 - 10*S^4 - S^8)*HPL[{3}, -S^2]^2)/(S^3*(1 + S^2)) + (Pi^2*S + (41 - 157*S^2 - 107*S^4 + 91*S^6)/(2*S^3))*HPL[{5}, -S^2] + (15*(-4 - 5*S^2 - 36*S^4 - 15*S^6 + 6*S^8)*HPL[{6}, -S^2])/(2*S^3*(1 + S^2)) - 144*S*HPL[{7}, -S^2] + (12*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)) + ((-92*Pi^2*S)/3 - (2*(1 - 5*S^2 + 9*S^4 + 15*S^6))/S^3)*HPL[{3, 2}, -S^2] + ((-304*Pi^2*S)/3 - (3*(3 - 31*S^2 + 3*S^4 + 37*S^6))/S^3)*HPL[{4, 1}, -S^2] - (3*(1 + 16*S^4 + S^8)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)) + 22*S*HPL[{4, 3}, -S^2] - (2*(-11 - 17*S^2 + 52*S^4 - 51*S^6 + 23*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)) + 60*S*HPL[{5, 2}, -S^2] + 150*S*HPL[{6, 1}, -S^2] + ((-268*Pi^2*S)/3 - (16*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + ((-592*Pi^2*S)/3 - (2*(41 + 303*S^2 + 273*S^4 + 11*S^6))/S^3)*HPL[{3, 1, 1}, -S^2] + (40*(-1 - 4*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 + 348*S*HPL[{3, 2, 2}, -S^2] + 1072*S*HPL[{3, 3, 1}, -S^2] + (12*(-13 - 13*S^2 - 24*S^4 - 39*S^6 + 13*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 1060*S*HPL[{4, 1, 2}, -S^2] + 3268*S*HPL[{4, 2, 1}, -S^2] + 6672*S*HPL[{5, 1, 1}, -S^2] + ((172*Pi^2*S)/3 - (12*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] - (24*(-5 - 5*S^2 - 6*S^4 - 15*S^6 + 5*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 688*S*HPL[{3, 1, 1, 2}, -S^2] - 688*S*HPL[{3, 1, 2, 1}, -S^2] - 688*S*HPL[{3, 2, 1, 1}, -S^2] - 2288*S*HPL[{4, 1, 1, 1}, -S^2] + (240*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + 1376*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 4128*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 8480*S*HPL[{3, 1, 1, 1, 1}, -S^2] + ((157*Pi^4*S)/90 + (Pi^2*(1 + S^2)*(2 - 36*S^2 + 25*S^4))/(6*S^3) + ((1 + S^2)*(1 - 310*S^2 + 445*S^4))/(8*S^3))*Zeta[3] + ((-1 - 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(-31 - 430*S^2 + 77*S^4))/(2*S^3) + (Pi^2*(31 + 24*S^2 + 166*S^4 + 72*S^6 - 17*S^8))/(3*S^3*(1 + S^2)) - 176*S*Zeta[3]) + HPL[{4}, -S^2]*(((1 + S^2)*(-71 - 664*S^2 + 255*S^4))/(8*S^3) + (Pi^2*(-17 - 14*S^2 + 34*S^4 - 42*S^6 + 11*S^8))/(6*S^3*(1 + S^2)) - 28*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(59 + 202*S^2 + 59*S^4))/(8*S^3) + (Pi^2*(-24 - 5*S^2 - 384*S^4 - 15*S^6 - 14*S^8))/(12*S^3*(1 + S^2)) + 48*S*HPL[{3}, -S^2] + 38*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((6*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 + (2*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(S^3*(1 + S^2)) + 344*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((707*Pi^4*S)/180 - (Pi^2*(1 + S^2)*(-15 - 119*S^2 + 7*S^4))/(3*S^3) - ((1 + S^2)*(-111 - 628*S^2 + 111*S^4))/(2*S^3) - 344*S*HPL[{3, 1}, -S^2] - 688*S*HPL[{2, 1, 1}, -S^2] - (12*(-2 + 31*S^2 - 6*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((98*Pi^4*S)/45 + (Pi^2*(1 + S^2)*(11 - 76*S^2 + 37*S^4))/(12*S^3) + ((1 + S^2)*(27 - 239*S^2 + 138*S^4))/(2*S^3) - 14*S*HPL[{4}, -S^2] - (4*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 176*S*HPL[{3, 1}, -S^2] + 344*S*HPL[{2, 1, 1}, -S^2] + (2*(-1 - S^2 + 14*S^4 - 3*S^6 + S^8)*Zeta[3])/(S^3*(1 + S^2))) + ((55*Pi^2*S)/3 + ((1 + S^2)*(4 - 60*S^2 + 29*S^4))/S^3)*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(-110 - 757*S^2 + 51*S^4))/(24*S^3) + ((1 + S^2)*(-1559 - 7904*S^2 + 1559*S^4))/(32*S^3) + (Pi^4*(-832 - 625*S^2 - 6328*S^4 - 1875*S^6 + 418*S^8))/(720*S^3*(1 + S^2)) + ((46*Pi^2*S)/3 + (3 - 3*S^2 + 7*S^4 + 13*S^6)/S^3)*HPL[{3}, -S^2] + ((1 + 40*S^4 + S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 20*S*HPL[{5}, -S^2] + ((134*Pi^2*S)/3 + (8*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 1}, -S^2] + (12*(2 + 39*S^4 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 180*S*HPL[{3, 2}, -S^2] - 548*S*HPL[{4, 1}, -S^2] - (24*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 344*S*HPL[{3, 1, 1}, -S^2] + 688*S*HPL[{2, 1, 1, 1}, -S^2] + ((47*Pi^2*S)/3 + (2*(1 + S^2)*(-7 + 8*S^2))/S)*Zeta[3] + 86*S*Zeta[5]) + 150*S*Zeta[7]) + HPL[{1}, -S^2]*((-20621*Pi^8*S)/108864 + (Pi^2*(1 + S^2)*(-4424 - 29665*S^2 + 357*S^4))/(384*S^3) - (31*(1 + S^2)*(1741 + 2870*S^2 + 1741*S^4))/(256*S^3) + (Pi^4*(1 + S^2)*(797 - 28423*S^2 + 6902*S^4))/(2880*S^3) + (Pi^6*(1 + S^2)*(20384 - 100850*S^2 + 35069*S^4))/(90720*S^3) + ((-23*Pi^2*S)/18 + (-5 - 51*S^2 - 41*S^4 + 5*S^6)/(6*S^3))*HPL[{2}, -S^2]^3 - (23*S*HPL[{2}, -S^2]^4)/6 + ((Pi^2*S)/3 + (-13 - 3*S^2 + 5*S^4 - 5*S^6)/(2*S^3))*HPL[{3}, -S^2]^2 - 32*S*HPL[{4}, -S^2]^2 + ((-33*Pi^2*S)/2 + (162 - 446*S^2 - 391*S^4 + 217*S^6)/(2*S^3))*HPL[{6}, -S^2] + (3*(-50 - 41*S^2 - 290*S^4 - 123*S^6 + 32*S^8)*HPL[{7}, -S^2])/(S^3*(1 + S^2)) - 771*S*HPL[{8}, -S^2] + ((134*Pi^2*S)/3 + (8*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 1}, -S^2]^2 - 216*S*HPL[{3, 1}, -S^2]^2 + (-3*Pi^2*S + (1 - 5*S^2 - 37*S^4 - 31*S^6)/(2*S^3))*HPL[{4, 2}, -S^2] + ((-12 - 11*S^2 + 24*S^4 - 33*S^6 + 10*S^8)*HPL[{4, 3}, -S^2])/(S^3*(1 + S^2)) + ((-26*Pi^2*S)/3 + (-31 + 163*S^2 + 65*S^4 - 129*S^6)/S^3)*HPL[{5, 1}, -S^2] + (3*(-13 - 10*S^2 + 26*S^4 - 30*S^6 + 7*S^8)*HPL[{5, 2}, -S^2])/(S^3*(1 + S^2)) - 6*S*HPL[{5, 3}, -S^2] - (5*(-7 - 132*S^2 - 21*S^4 + 14*S^6)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) - 15*S*HPL[{6, 2}, -S^2] + 416*S*HPL[{7, 1}, -S^2] - 688*S*HPL[{2, 1, 1}, -S^2]^2 + (8*(-1 - S^2 + S^4 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 + ((-92*Pi^2*S)/3 + (4*(-7 - 53*S^2 - 39*S^4 + 7*S^6))/S^3)*HPL[{3, 2, 1}, -S^2] + (4*(-2 - 10*S^2 + 205*S^4 - 30*S^6 + 18*S^8)*HPL[{3, 2, 2}, -S^2])/(S^3*(1 + S^2)) + (8*(-2 - 15*S^2 + 316*S^4 - 45*S^6 + 28*S^8)*HPL[{3, 3, 1}, -S^2])/(S^3*(1 + S^2)) + 28*S*HPL[{3, 3, 2}, -S^2] + ((-220*Pi^2*S)/3 + (6*(-13 - 127*S^2 - 93*S^4 + 21*S^6))/S^3)*HPL[{4, 1, 1}, -S^2] + (10*(-1 - 12*S^2 + 248*S^4 - 36*S^6 + 23*S^8)*HPL[{4, 1, 2}, -S^2])/(S^3*(1 + S^2)) - 68*S*HPL[{4, 1, 3}, -S^2] + (2*(-17 - 180*S^2 + 3856*S^4 - 540*S^6 + 343*S^8)*HPL[{4, 2, 1}, -S^2])/(S^3*(1 + S^2)) + 40*S*HPL[{4, 2, 2}, -S^2] - 52*S*HPL[{4, 3, 1}, -S^2] + (4*(-27 - 197*S^2 + 3876*S^4 - 591*S^6 + 367*S^8)*HPL[{5, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 8*S*HPL[{5, 1, 2}, -S^2] - 248*S*HPL[{5, 2, 1}, -S^2] - 860*S*HPL[{6, 1, 1}, -S^2] - (80*(-1 - 4*S^4 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/S^3 + ((112*Pi^2*S)/3 - (4*(-9 - 127*S^2 - 97*S^4 + 21*S^6))/S^3)*HPL[{3, 1, 1, 1}, -S^2] + (16*(-16 - 10*S^2 - 157*S^4 - 30*S^6 + 4*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^3*(1 + S^2)) + (16*(-16 - 10*S^2 - 157*S^4 - 30*S^6 + 4*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^3*(1 + S^2)) - 24*S*HPL[{3, 1, 2, 2}, -S^2] + (16*(-31 - 25*S^2 - 217*S^4 - 75*S^6 + 19*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 24*S*HPL[{3, 2, 1, 2}, -S^2] + 40*S*HPL[{3, 2, 2, 1}, -S^2] + 192*S*HPL[{3, 3, 1, 1}, -S^2] + (24*(-59 - 47*S^2 - 450*S^4 - 141*S^6 + 35*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 72*S*HPL[{4, 1, 1, 2}, -S^2] + 120*S*HPL[{4, 1, 2, 1}, -S^2] + 504*S*HPL[{4, 2, 1, 1}, -S^2] + 800*S*HPL[{5, 1, 1, 1}, -S^2] + ((-344*Pi^2*S)/3 + (24*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1, 1}, -S^2] + (96*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (288*(2 + 39*S^4 + 2*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (48*(19 - 5*S^2 + 462*S^4 - 15*S^6 + 29*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 448*S*HPL[{4, 1, 1, 1, 1}, -S^2] - (480*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 - 448*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*S)/3 - ((1 + S^2)*(4 + 10*S^2 + 3*S^4))/S^3)*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((-12*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 - (4*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(S^3*(1 + S^2)) - 688*S*Zeta[3]) + HPL[{4, 1}, -S^2]*(-((1 + S^2)*(67 - 1084*S^2 + 825*S^4))/(4*S^3) + (Pi^2*(5 + 47*S^2 - 640*S^4 + 141*S^6 - 89*S^8))/(3*S^3*(1 + S^2)) - 160*S*Zeta[3]) + HPL[{3, 2}, -S^2]*(-((1 + S^2)*(7 - 70*S^2 + 111*S^4))/(2*S^3) + (Pi^2*(-9 + 22*S^2 - 402*S^4 + 66*S^6 - 53*S^8))/(6*S^3*(1 + S^2)) - 48*S*Zeta[3]) + HPL[{5}, -S^2]*(((1 + S^2)*(98 - 1133*S^2 + 291*S^4))/(4*S^3) + (Pi^2*(-3 - 4*S^2 - 15*S^4 - 12*S^6 + 5*S^8))/(S^3*(1 + S^2)) - 40*S*HPL[{2, 1}, -S^2] + 56*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*(-(((1 + S^2)*(59 + 202*S^2 + 59*S^4))/S^3) - (2*Pi^2*(24 + 5*S^2 + 384*S^4 + 15*S^6 + 14*S^8))/(3*S^3*(1 + S^2)) + 304*S*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*(-(((1 + S^2)*(149 + 834*S^2 + 41*S^4))/S^3) - (2*Pi^2*(79 + 34*S^2 + 934*S^4 + 102*S^6 + 11*S^8))/(3*S^3*(1 + S^2)) + 960*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-707*Pi^4*S)/90 + (2*Pi^2*(1 + S^2)*(-15 - 119*S^2 + 7*S^4))/(3*S^3) + ((1 + S^2)*(-111 - 628*S^2 + 111*S^4))/S^3 + (24*(-2 + 31*S^2 - 6*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]^2*((-263*Pi^4*S)/144 - (Pi^2*(1 + S^2)*(16 + 76*S^2 + 11*S^4))/(12*S^3) - ((1 + S^2)*(223 + 442*S^2 + 223*S^4))/(16*S^3) + ((-5 + 114*S^2 - 15*S^4 + 10*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)) + 4*S*HPL[{4}, -S^2] - (10*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 - 4*S*HPL[{3, 1}, -S^2] + ((-5 + 84*S^2 - 15*S^4 + 10*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{4}, -S^2]*((28*Pi^4*S)/45 + (Pi^2*(1 + S^2)*(-9 - 112*S^2 + 31*S^4))/(12*S^3) + ((1 + S^2)*(-119 - 1484*S^2 + 547*S^4))/(8*S^3) - (2*(1 + 40*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 12*S*HPL[{3, 1}, -S^2] + 56*S*HPL[{2, 1, 1}, -S^2] + (2*(1 - S^2 + 4*S^4 - 3*S^6 + 3*S^8)*Zeta[3])/(S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((59*Pi^4*S)/20 - (Pi^2*(1 + S^2)*(-7 - 76*S^2 + 5*S^4))/(2*S^3) - ((1 + S^2)*(-115 - 1398*S^2 + 329*S^4))/(4*S^3) + 688*S*HPL[{2, 1, 1}, -S^2] - (4*(-1 - 6*S^2 + 98*S^4 - 18*S^6 + 11*S^8)*Zeta[3])/(S^3*(1 + S^2))) + (((1 + S^2)*(30 - 323*S^2 + 209*S^4))/(4*S^3) + (55*Pi^2*(-1 - 3*S^4 + 2*S^6))/(6*S*(1 + S^2)))*Zeta[5] + HPL[{2, 1}, -S^2]*(-(Pi^2*(1 + S^2)*(-110 - 757*S^2 + 51*S^4))/(12*S^3) - ((1 + S^2)*(-1559 - 7904*S^2 + 1559*S^4))/(16*S^3) + (Pi^4*(832 + 625*S^2 + 6328*S^4 + 1875*S^6 - 418*S^8))/(360*S^3*(1 + S^2)) - (24*(2 + 39*S^4 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 360*S*HPL[{3, 2}, -S^2] + 1096*S*HPL[{4, 1}, -S^2] - (48*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 688*S*HPL[{3, 1, 1}, -S^2] + 1376*S*HPL[{2, 1, 1, 1}, -S^2] + ((-94*Pi^2*S)/3 - (4*(1 + S^2)*(-7 + 8*S^2))/S)*Zeta[3] - 172*S*Zeta[5]) + HPL[{3}, -S^2]*((Pi^2*(1 + S^2)*(36 - 373*S^2 + 129*S^4))/(24*S^3) + ((1 + S^2)*(438 - 4395*S^2 + 1997*S^4))/(16*S^3) + (Pi^4*(-15 - 33*S^2 + 224*S^4 - 99*S^6 + 51*S^8))/(60*S^3*(1 + S^2)) + ((8 + 7*S^2 - 16*S^4 + 21*S^6 - 6*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 70*S*HPL[{5}, -S^2] + ((-92*Pi^2*S)/3 - (2*(3 - 3*S^2 + 7*S^4 + 13*S^6))/S^3)*HPL[{2, 1}, -S^2] - (4*(-1 - 5*S^2 + 104*S^4 - 15*S^6 + 9*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 8*S*HPL[{3, 2}, -S^2] + 28*S*HPL[{4, 1}, -S^2] + (8*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 384*S*HPL[{2, 2, 1}, -S^2] + 1120*S*HPL[{3, 1, 1}, -S^2] - 688*S*HPL[{2, 1, 1, 1}, -S^2] + (4*Pi^2*S + ((1 + S^2)*(-7 - 4*S^2 + 7*S^4))/S^3)*Zeta[3] + 32*S*Zeta[5]) + Zeta[3]*((Pi^2*(1 + S^2)*(15 - 221*S^2 + 186*S^4))/(24*S^3) + ((1 + S^2)*(-6 - 1123*S^2 + 1553*S^4))/(16*S^3) + (157*Pi^4*(-1 - 3*S^4 + 2*S^6))/(180*S*(1 + S^2)) + 64*S*Zeta[5]) + HPL[{2}, -S^2]*((-2047*Pi^6*S)/5040 + (Pi^4*(1 + S^2)*(-416 - 3194*S^2 + 233*S^4))/(720*S^3) + (Pi^2*(1 + S^2)*(-889 - 4530*S^2 + 443*S^4))/(96*S^3) + ((1 + S^2)*(-4781 - 27200*S^2 + 4781*S^4))/(64*S^3) + 2*S*HPL[{3}, -S^2]^2 + ((Pi^2*S)/3 + (17 + 3*S^2 + 3*S^4 + 17*S^6)/(2*S^3))*HPL[{4}, -S^2] + (10*(-1 - S^2 + 2*S^4 - 3*S^6 + S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) - 79*S*HPL[{6}, -S^2] + (46*Pi^2*S + (16*(1 + 6*S^2 + 6*S^4 + S^6))/S^3)*HPL[{3, 1}, -S^2] - (2*(-1 - 10*S^2 + 212*S^4 - 30*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) - (2*(-1 - 30*S^2 + 644*S^4 - 90*S^6 + 59*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) - 24*S*HPL[{4, 2}, -S^2] - 48*S*HPL[{5, 1}, -S^2] + ((-268*Pi^2*S)/3 - (16*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (40*(-1 - 4*S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 - (8*(-16 - 10*S^2 - 157*S^4 - 30*S^6 + 4*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 24*S*HPL[{3, 1, 2}, -S^2] - 344*S*HPL[{3, 2, 1}, -S^2] - 1048*S*HPL[{4, 1, 1}, -S^2] + (48*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 688*S*HPL[{3, 1, 1, 1}, -S^2] - 1376*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(2 - 59*S^2 + 57*S^4))/(2*S^3) + (Pi^2*(-2 - 13*S^2 + 208*S^4 - 39*S^6 + 24*S^8))/(6*S^3*(1 + S^2)))*Zeta[3] - 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(59 + 202*S^2 + 59*S^4))/(2*S^3) + (Pi^2*(24 + 5*S^2 + 384*S^4 + 15*S^6 + 14*S^8))/(3*S^3*(1 + S^2)) - 152*S*Zeta[3]) + HPL[{3}, -S^2]*(((1 + S^2)*(23 - 70*S^2 + 95*S^4))/(4*S^3) + (Pi^2*(4 - 11*S^2 + 202*S^4 - 33*S^6 + 26*S^8))/(6*S^3*(1 + S^2)) - 192*S*HPL[{2, 1}, -S^2] + 24*S*Zeta[3]) + ((-4 - 21*S^2 + 140*S^4 - 63*S^6 + 38*S^8)*Zeta[5])/(S^3*(1 + S^2))) + (75*(-1 - 3*S^4 + 2*S^6)*Zeta[7])/(S*(1 + S^2))) + Log[T]*((18471*(1 + S^2))/(64*S) - (Pi^6*S*(-47153 + 25212*S^2))/30240 + (Pi^4*(4240 + 41815*S^2 - 8606*S^4))/(2880*S) + (Pi^2*(5816 + 20409*S^2 - 3954*S^4))/(192*S) + ((22*Pi^2*S)/9 - (4*(1 - 3*S^2 - 3*S^4 + S^6))/(3*S^3))*HPL[{1}, -S^2]^6 + (8*S*HPL[{1}, -S^2]^7)/(1 + S^2) + (2*S*HPL[{1}, -S^2]^8)/3 + HPL[{0}, S^2]^7*(S/(16*(1 + S^2)) + (S*HPL[{1}, -S^2])/24) + HPL[{0}, S^2]^6*(-(S*(-11 + 6*S^2))/32 + ((1 + 14*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2])/(16*S*(1 + S^2)) + (S*HPL[{1}, -S^2]^2)/6) + ((10*Pi^2*S)/9 - (5*(-6 - S^2 - 11*S^4 + 6*S^6))/(6*S^3))*HPL[{2}, -S^2]^3 + (10*S*HPL[{2}, -S^2]^4)/3 + (3*Pi^2*S + (8 + 13*S^2 + 13*S^4 - 8*S^6)/(2*S^3))*HPL[{3}, -S^2]^2 - 32*S*HPL[{4}, -S^2]^2 + ((-20*Pi^2*S)/3 - (5*(-56 - 70*S^2 - 87*S^4 + 44*S^6))/(2*S^3))*HPL[{6}, -S^2] + (12*S*(37 + S^2)*HPL[{7}, -S^2])/(1 + S^2) + ((-124*Pi^2*S)/3 - (4*(20 - 3*S^2 + 21*S^4 + 20*S^6))/S^3)*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*(-(Pi^2*S*(-23 + S^2))/(36*(1 + S^2)) - (S*(-53 + 35*S^2))/96 + ((2 + 45*S^2 + 6*S^4 - 4*S^6)*HPL[{1}, -S^2]^2)/(12*S*(1 + S^2)) + (11*S*HPL[{1}, -S^2]^3)/18 + ((6 + 3*S^2 + 20*S^4 - S^6)*HPL[{2}, -S^2])/(24*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((4*Pi^2*S)/9 + (-3 + 16*S^2 + 8*S^4 - 11*S^6)/(12*S^3) + (2*S*HPL[{2}, -S^2])/3) + (S*HPL[{3}, -S^2])/4 - (5*S*HPL[{2, 1}, -S^2])/6) + 144*S*HPL[{3, 1}, -S^2]^2 + ((28 + 27*S^2 + 51*S^4 - 52*S^6)*HPL[{4, 2}, -S^2])/(2*S^3) - (2*S*(47 + 14*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) + (2*Pi^2*S + (-46 - 111*S^2 - 85*S^4 - 2*S^6)/S^3)*HPL[{5, 1}, -S^2] - (2*S*(133 + 43*S^2)*HPL[{5, 2}, -S^2])/(1 + S^2) - (10*S*(67 + 22*S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) + 640*S*HPL[{2, 1, 1}, -S^2]^2 + (-2*Pi^2*S + (4*(-5 + 3*S^2 - 6*S^4 + 5*S^6))/S^3)*HPL[{3, 1, 2}, -S^2] + ((74*Pi^2*S)/3 - (4*(-25 - 8*S^2 - 49*S^4 + 25*S^6))/S^3)*HPL[{3, 2, 1}, -S^2] + (12*S*(-64 + 23*S^2)*HPL[{3, 2, 2}, -S^2])/(1 + S^2) + (16*S*(-149 + 52*S^2)*HPL[{3, 3, 1}, -S^2])/(1 + S^2) + (80*Pi^2*S - (6*(-68 - 37*S^2 - 131*S^4 + 68*S^6))/S^3)*HPL[{4, 1, 1}, -S^2] + (12*S*(-194 + 71*S^2)*HPL[{4, 1, 2}, -S^2])/(1 + S^2) + (12*S*(-610 + 207*S^2)*HPL[{4, 2, 1}, -S^2])/(1 + S^2) + (72*S*(-209 + 69*S^2)*HPL[{5, 1, 1}, -S^2])/(1 + S^2) - 608*S*HPL[{2, 2, 2, 1}, -S^2] + ((-184*Pi^2*S)/3 + (4*(-90 - 43*S^2 - 165*S^4 + 90*S^6))/S^3)*HPL[{3, 1, 1, 1}, -S^2] + (48*S*(68 + 25*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2) + (48*S*(68 + 25*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2) + (48*S*(106 + 63*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2) + (16*S*(1003 + 574*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2) + ((320*Pi^2*S)/3 - (40*(-18 - 11*S^2 - 33*S^4 + 18*S^6))/S^3)*HPL[{2, 1, 1, 1, 1}, -S^2] - (96*S*(44 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2) - (288*S*(44 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2) + (160*S*(-155 + 4*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2) - 2880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((157*Pi^4*S*(-1 + 2*S^2))/(90*(1 + S^2)) + (5*Pi^2*S*(50 + 29*S^2))/12 + (42 + 1830*S^2 - 173*S^4)/(8*S))*Zeta[3] - S*(-23 + 16*S^2)*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((2*Pi^2*(-1 + 1100*S^2 + 215*S^4 + 2*S^6))/(3*S*(1 + S^2)) - (3*(102 - 597*S^2 - 149*S^4 + 32*S^6))/S^3 - 848*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((4*Pi^2*S*(75 + 8*S^2))/(1 + S^2) - (4*(23 - 136*S^2 - 42*S^4 + 23*S^6))/S^3 - 288*S*Zeta[3]) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(21 - 130*S^2 + 21*S^4))/(6*S^3) + (Pi^2*(1 + 72*S^2 + 3*S^4 - 2*S^6))/(3*S*(1 + S^2)) - (4*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2])/S^3 - (80*S*HPL[{3}, -S^2])/3 - 24*S*Zeta[3]) + HPL[{5}, -S^2]*((-320 + 584*S^2 + 303*S^4 - 22*S^6)/(4*S^3) + (Pi^2*(-3 - 8*S^2 + 19*S^4 + 6*S^6))/(6*S*(1 + S^2)) - 12*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((55 - 271*S^2 + 243*S^4 - 539*S^6)/(2*S^3) - (2*Pi^2*(-1 - 343*S^2 + 116*S^4 + 2*S^6))/(3*S*(1 + S^2)) + 24*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((-32 + 37*S^2 + 259*S^4 - 336*S^6)/(4*S^3) + (Pi^2*(-1 + 376*S^2 - 173*S^4 + 2*S^6))/(6*S*(1 + S^2)) + 28*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((-4*Pi^2*S*(91 + 48*S^2))/(1 + S^2) - (2*(-105 + 712*S^2 + 144*S^4 + 105*S^6))/S^3 + 640*S*Zeta[3]) + HPL[{2}, -S^2]^2*((76*Pi^4*S)/45 + (Pi^2*(78 - 8*S^2 + 93*S^4 + 48*S^6))/(12*S^3) + (494 - 43*S^2 + 1029*S^4 + 494*S^6)/(16*S^3) + ((-1 - 106*S^4 + 36*S^6 - S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - 12*S*HPL[{4}, -S^2] - 76*S*HPL[{2, 1}, -S^2] + 12*S*HPL[{3, 1}, -S^2] + (6*S*(-13 + 6*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((308*Pi^4*S)/45 + (496 + 863*S^2 + 1617*S^4 - 496*S^6)/(2*S^3) - (2*Pi^2*(-92 - 43*S^2 - 153*S^4 + 52*S^6))/(3*S^3) + (24*S*(-31 + 12*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^4*((1849*Pi^4*S)/540 - ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(8*S^3) - (Pi^2*(1 + S^2)*(20 - 86*S^2 + 25*S^4))/(6*S^3) + ((43*Pi^2*S)/9 + (5 + 47*S^2 + 37*S^4 - 5*S^6)/S^3)*HPL[{2}, -S^2] + (86*S*HPL[{2}, -S^2]^2)/3 - (2*(-1 - 5*S^2 + 72*S^4 - 15*S^6 + 9*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - (56*S*HPL[{4}, -S^2])/3 + (20*(-1 - 4*S^4 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (56*S*HPL[{3, 1}, -S^2])/3 - (10*(-1 + 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{4}, -S^2]*((-3*Pi^4*S)/5 + (-205 + 631*S^2 + 753*S^4 - 217*S^6)/(4*S^3) + (Pi^2*(68 + 121*S^2 + 137*S^4 - 44*S^6))/(12*S^3) + (4*(1 - 2*S^2 + 16*S^4 + 3*S^6 + 5*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 80*S*HPL[{3, 1}, -S^2] - 96*S*HPL[{2, 1, 1}, -S^2] - (2*(2 + S^2 + 16*S^4 + 5*S^6)*Zeta[3])/(S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-169*Pi^4*S)/45 + (Pi^2*(-190 - 71*S^2 - 319*S^4 + 100*S^6))/(6*S^3) + (-285 - 947*S^2 - 1701*S^4 + 707*S^6)/(4*S^3) - 640*S*HPL[{2, 1, 1}, -S^2] - (4*(2 + S^2 - 100*S^4 + 33*S^6)*Zeta[3])/(S^3*(1 + S^2))) + HPL[{0}, S^2]^4*(-(Pi^2*S*(-115 + 61*S^2))/48 + (150 + 2961*S^2 - 490*S^4)/(192*S) + ((7 + 134*S^2 + 21*S^4 - 14*S^6)*HPL[{1}, -S^2]^3)/(12*S*(1 + S^2)) + (23*S*HPL[{1}, -S^2]^4)/18 + ((Pi^2*S)/6 + (30 + 13*S^2 + 42*S^4 - 2*S^6)/(16*S^3))*HPL[{2}, -S^2] + (S*HPL[{2}, -S^2]^2)/2 + HPL[{1}, -S^2]^2*((53*Pi^2*S)/36 + (-30 + 128*S^2 + 91*S^4 - 67*S^6)/(24*S^3) + (31*S*HPL[{2}, -S^2])/12) + (S*HPL[{3}, -S^2])/4 - S*HPL[{4}, -S^2] + ((-3 - 155*S^2 - 53*S^4 + 6*S^6)*HPL[{2, 1}, -S^2])/(12*S*(1 + S^2)) - 2*S*HPL[{3, 1}, -S^2] + 4*S*HPL[{2, 1, 1}, -S^2] - (7*S*(-1 + 2*S^2)*Zeta[3])/(12*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(105 - 967*S^2 + 378*S^4))/(96*S^3) + (Pi^2*(11 + 172*S^2 + 33*S^4 - 22*S^6))/(24*S*(1 + S^2)) + ((10 + 7*S^2 + 84*S^4 + 21*S^6 - 4*S^8)*HPL[{2}, -S^2])/(8*S^3*(1 + S^2)) - (31*S*HPL[{2, 1}, -S^2])/6 + (7*S*Zeta[3])/6)) + HPL[{0}, S^2]^3*(-(Pi^4*S*(-2629 + 182*S^2))/(1080*(1 + S^2)) - (Pi^2*S*(-609 + 205*S^2))/144 + (580 + 3437*S^2 - 186*S^4)/(96*S) + ((2 + 67*S^2 + 6*S^4 - 4*S^6)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)) + (22*S*HPL[{1}, -S^2]^5)/9 + ((22 + 11*S^2 + 96*S^4 - 7*S^6)*HPL[{2}, -S^2]^2)/(12*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((110*Pi^2*S)/27 + (-28 + 103*S^2 + 77*S^4 - 54*S^6)/(9*S^3) + 10*S*HPL[{2}, -S^2]) + ((17*Pi^2*S)/18 + (-18 + 3*S^2 + 5*S^4 + 12*S^6)/(6*S^3))*HPL[{3}, -S^2] + ((18 + 9*S^2 + 28*S^4 + 19*S^6)*HPL[{4}, -S^2])/(6*S^3*(1 + S^2)) + 7*S*HPL[{5}, -S^2] + ((-49*Pi^2*S)/9 + (30 - 95*S^2 - 34*S^4 - 6*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(58 + 29*S^2 + 215*S^4 - 11*S^6))/(36*S^3*(1 + S^2)) + (170 + 87*S^2 + 502*S^4 - 9*S^6)/(24*S^3) - (40*S*HPL[{2, 1}, -S^2])/3) + ((-30 - 15*S^2 - 118*S^4 - S^6)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (S*HPL[{3, 2}, -S^2])/3 - (8*S*HPL[{4, 1}, -S^2])/3 - (2*(-28 - 14*S^2 - 115*S^4 + 6*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (80*S*HPL[{2, 2, 1}, -S^2])/3 + (248*S*HPL[{3, 1, 1}, -S^2])/3 - 64*S*HPL[{2, 1, 1, 1}, -S^2] + (S*(-1 + 4*S^2)*Zeta[3])/2 + HPL[{1}, -S^2]^2*(-((1 + S^2)*(47 - 399*S^2 + 140*S^4))/(12*S^3) + (Pi^2*(8 + 213*S^2 + 24*S^4 - 16*S^6))/(9*S*(1 + S^2)) + ((14 + 5*S^2 + 137*S^4 + 15*S^6 + 4*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + 2*S*HPL[{3}, -S^2] - 30*S*HPL[{2, 1}, -S^2] + (8*S*Zeta[3])/3) + HPL[{1}, -S^2]*((937*Pi^4*S)/540 - (Pi^2*(1 + S^2)*(58 - 321*S^2 + 164*S^4))/(36*S^3) - ((1 + S^2)*(25 - 1219*S^2 + 362*S^4))/(24*S^3) + ((85*Pi^2*S)/18 + (5 + 53*S^2 + 48*S^4)/(3*S^3))*HPL[{2}, -S^2] + (19*S*HPL[{2}, -S^2]^2)/3 + (2*(2 + 5*S^4 + 2*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) + 2*S*HPL[{4}, -S^2] - (2*(14 + 5*S^2 + 137*S^4 + 15*S^6 + 4*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (88*S*HPL[{3, 1}, -S^2])/3 + 60*S*HPL[{2, 1, 1}, -S^2] + ((1 + 14*S^2 + 3*S^4 - 2*S^6)*Zeta[3])/(S*(1 + S^2)))) + HPL[{0}, S^2]^2*(-(Pi^4*S*(-3659 + 1944*S^2))/720 + (3002 + 17595*S^2 - 3954*S^4)/(64*S) + (Pi^2*(154 + 2368*S^2 - 493*S^4))/(48*S) + ((1 + 30*S^2 + 3*S^4 - 2*S^6)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)) + (8*S*HPL[{1}, -S^2]^6)/3 + ((17*Pi^2*S)/6 + (38 - 2*S^2 + 51*S^4 + 8*S^6)/(4*S^3))*HPL[{2}, -S^2]^2 + (10*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((53*Pi^2*S)/9 + (-10 + 36*S^2 + 31*S^4 - 15*S^6)/(2*S^3) + (43*S*HPL[{2}, -S^2])/3) + S*HPL[{3}, -S^2]^2 + (-2*Pi^2*S + (22 + 20*S^2 + 37*S^4 - 10*S^6)/(2*S^3))*HPL[{4}, -S^2] + ((-3 + 10*S^2 + S^4 + 6*S^6)*HPL[{5}, -S^2])/(2*S*(1 + S^2)) - 20*S*HPL[{6}, -S^2] + ((58 - 331*S^2 - 105*S^4 - 12*S^6)/(2*S^3) + (Pi^2*(-3 - 338*S^2 - 107*S^4 + 6*S^6))/(6*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - 44*S*HPL[{2, 1}, -S^2]^2 + ((-35*Pi^2*S)/3 + (-50 - 14*S^2 - 77*S^4 + 5*S^6)/S^3)*HPL[{3, 1}, -S^2] + ((-1 + S^2)*(1 - 15*S^2 + 2*S^4)*HPL[{3, 2}, -S^2])/(2*S*(1 + S^2)) - (2*(-1 - 24*S^2 + 6*S^4 + 2*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + 6*S*HPL[{5, 1}, -S^2] + ((64*Pi^2*S)/3 + (94 + 31*S^2 + 141*S^4 - 14*S^6)/S^3)*HPL[{2, 1, 1}, -S^2] + (12*S*(31 + 7*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (2*(-1 + 538*S^2 + 127*S^4 + 2*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - 6*S*HPL[{3, 1, 2}, -S^2] + 74*S*HPL[{3, 2, 1}, -S^2] + 240*S*HPL[{4, 1, 1}, -S^2] - (12*S*(61 + 18*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 184*S*HPL[{3, 1, 1, 1}, -S^2] + 320*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-(Pi^2*S*(-1 + 2*S^2))/(2*(1 + S^2)) + (S*(53 + 20*S^2))/2)*Zeta[3] + HPL[{1}, -S^2]^3*(-((1 + S^2)*(109 - 750*S^2 + 217*S^4))/(12*S^3) - (2*Pi^2*(-3 - 71*S^2 - 9*S^4 + 6*S^6))/(3*S*(1 + S^2)) - (2*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) - 4*S*HPL[{3}, -S^2] - (172*S*HPL[{2, 1}, -S^2])/3 - (16*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(-1 - 14*S^2 + 7*S^4 + 2*S^6))/(12*S*(1 + S^2)) + (-52 + 105*S^2 + 115*S^4 + 75*S^6)/(8*S^3) + 4*S*HPL[{2, 1}, -S^2] + 2*S*Zeta[3]) + HPL[{1}, -S^2]^2*((359*Pi^4*S)/90 - (Pi^2*(1 + S^2)*(15 - 74*S^2 + 28*S^4))/(3*S^3) - ((1 + S^2)*(29 - 1040*S^2 + 251*S^4))/(8*S^3) + ((37*Pi^2*S)/3 + (15 + 127*S^2 + 113*S^4 + S^6)/(2*S^3))*HPL[{2}, -S^2] + 24*S*HPL[{2}, -S^2]^2 - (2*(-2 - 2*S^2 + S^4 - 6*S^6 + 2*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + (6*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 84*S*HPL[{3, 1}, -S^2] + 172*S*HPL[{2, 1, 1}, -S^2] - (4*(-1 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]*((13*Pi^4*S)/18 + (Pi^2*(184 + 70*S^2 + 267*S^4 - 20*S^6))/(24*S^3) + (504 + 658*S^2 + 1395*S^4 - 10*S^6)/(16*S^3) + (S*(-7 + 2*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 2*S*HPL[{4}, -S^2] - (6*S*(31 + 7*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 44*S*HPL[{3, 1}, -S^2] + 88*S*HPL[{2, 1, 1}, -S^2] + ((2 + S^2 - 10*S^4 + 3*S^6)*Zeta[3])/(S^3*(1 + S^2))) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(214 - 1717*S^2 + 595*S^4))/(48*S^3) - ((1 + S^2)*(-349 - 5853*S^2 + 1210*S^4))/(32*S^3) + (Pi^4*(349 + 6402*S^2 + 1047*S^4 - 698*S^6))/(360*S*(1 + S^2)) + ((12 + 5*S^2 + 150*S^4 + 15*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(2*S^3*(1 + S^2)) + (-(Pi^2*S) + (-2 + 13*S^2 + 15*S^4)/S^3)*HPL[{3}, -S^2] + ((8 - 3*S^2 + 17*S^4 - 2*S^6)*HPL[{4}, -S^2])/S^3 + 6*S*HPL[{5}, -S^2] + ((-74*Pi^2*S)/3 + (-15 - 127*S^2 - 113*S^4 - S^6)/S^3)*HPL[{2, 1}, -S^2] + (2*(-16 - 9*S^2 - 148*S^4 - 27*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 12*S*HPL[{3, 2}, -S^2] + 36*S*HPL[{4, 1}, -S^2] - (12*(-5 - 3*S^2 - 51*S^4 - 9*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 192*S*HPL[{2, 2, 1}, -S^2] + 552*S*HPL[{3, 1, 1}, -S^2] - 344*S*HPL[{2, 1, 1, 1}, -S^2] + (Pi^2*S - (2*(1 + S^2)*(1 - 9*S^2 + 5*S^4))/S^3)*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(56 + 349*S^2 + 3*S^4))/(4*S^3) + (Pi^2*(20 + 13*S^2 + 186*S^4 + 39*S^6 - 6*S^8))/(4*S^3*(1 + S^2)) - 6*S*HPL[{3}, -S^2] - 96*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]))) + HPL[{0}, S^2]*(-(Pi^6*S*(-12333 + 574*S^2))/(3780*(1 + S^2)) - (Pi^4*S*(-5107 + 1368*S^2))/720 + (Pi^2*(1334 + 7756*S^2 + 157*S^4))/(96*S) + (12042 + 34787*S^2 + 11427*S^4)/(64*S) + (28*S*HPL[{1}, -S^2]^6)/(1 + S^2) + (8*S*HPL[{1}, -S^2]^7)/3 + ((10 + 5*S^2 + 86*S^4 - 23*S^6)*HPL[{2}, -S^2]^3)/(3*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((64*Pi^2*S)/9 - (4*(1 - 3*S^2 - 3*S^4 + S^6))/S^3 + 24*S*HPL[{2}, -S^2]) + ((-2 - S^2 - 4*S^4 + S^6)*HPL[{3}, -S^2]^2)/(S^3*(1 + S^2)) + (10*Pi^2*S + (-120 - 23*S^2 + 57*S^4 + 66*S^6)/(2*S^3))*HPL[{5}, -S^2] + (10*(6 - 3*S^2 + 7*S^4)*HPL[{6}, -S^2])/S^3 + 100*S*HPL[{7}, -S^2] + (12*(-4 - 2*S^2 - 34*S^4 + 7*S^6)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)) + ((Pi^2*S)/3 + (2*(-3 + S^2 - 2*S^4 + 7*S^6))/S^3)*HPL[{3, 2}, -S^2] + (4*Pi^2*S + (44 - 7*S^2 - 11*S^4 - 26*S^6)/S^3)*HPL[{4, 1}, -S^2] + (3*(2 - S^2 + 5*S^4)*HPL[{4, 2}, -S^2])/S^3 + 16*S*HPL[{4, 3}, -S^2] - (2*(22 + 11*S^2 + 46*S^4 + 15*S^6)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)) + 54*S*HPL[{5, 2}, -S^2] + 40*S*HPL[{6, 1}, -S^2] + (84*Pi^2*S + (16*(-5 + 21*S^2 + 5*S^4 + 9*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + (248*Pi^2*S + (2*(-156 + 513*S^2 + 125*S^4 + 238*S^6))/S^3)*HPL[{3, 1, 1}, -S^2] - 24*S*HPL[{3, 1, 2}, -S^2] - (8*(-10 - 5*S^2 - 83*S^4 + 26*S^6)*HPL[{3, 2, 1}, -S^2])/(S^3*(1 + S^2)) - 44*S*HPL[{3, 2, 2}, -S^2] - 96*S*HPL[{3, 3, 1}, -S^2] - (4*(-78 - 39*S^2 - 572*S^4 + 115*S^6)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 84*S*HPL[{4, 1, 2}, -S^2] - 276*S*HPL[{4, 2, 1}, -S^2] - 504*S*HPL[{5, 1, 1}, -S^2] + (-184*Pi^2*S - (4*(-60 + 191*S^2 + 51*S^4 + 90*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] - 608*S*HPL[{2, 2, 2, 1}, -S^2] + (8*(-30 - 15*S^2 - 224*S^4 + 31*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 1840*S*HPL[{3, 1, 1, 2}, -S^2] + 1840*S*HPL[{3, 1, 2, 1}, -S^2] + 3664*S*HPL[{3, 2, 1, 1}, -S^2] + 11104*S*HPL[{4, 1, 1, 1}, -S^2] - (240*(-2 - S^2 - 14*S^4 + 3*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 1376*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 4128*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 7040*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 2880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((Pi^2*S*(-1 + 4*S^2))/2 + (-26 + 110*S^2 - 211*S^4)/(4*S))*Zeta[3] + (8*S*(5 + 2*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1, 1}, -S^2]*((217 + 116*S^2 + 576*S^4 - 101*S^6)/S^3 - (2*Pi^2*(-58 - 29*S^2 - 325*S^4 + 51*S^6))/(3*S^3*(1 + S^2)) - 48*S*Zeta[3]) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(21 - 130*S^2 + 21*S^4))/(12*S^3) - (2*Pi^2*(-1 - 86*S^2 - 3*S^4 + 2*S^6))/(3*S*(1 + S^2)) + (10*(1 + 16*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) + (8*S*HPL[{3}, -S^2])/3 - 120*S*HPL[{2, 1}, -S^2] - (28*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(46 + 23*S^2 + 300*S^4 - 49*S^6))/(12*S^3*(1 + S^2)) + (92 - 4*S^2 + 245*S^4 - 33*S^6)/(4*S^3) - 4*S*HPL[{3}, -S^2] - 76*S*HPL[{2, 1}, -S^2] - 6*S*Zeta[3]) + HPL[{4}, -S^2]*((125 + 117*S^2 + 251*S^4 - 24*S^6)/(4*S^3) + (Pi^2*(6 + 3*S^2 + 14*S^4 + 7*S^6))/(S^3*(1 + S^2)) - 4*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((2*Pi^2*(-10 - 5*S^2 - 57*S^4 + 5*S^6))/(S^3*(1 + S^2)) + (-173 - 78*S^2 - 638*S^4 + 69*S^6)/(2*S^3) + 40*S*Zeta[3]) + HPL[{1}, -S^2]^3*((937*Pi^4*S)/135 - ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(58 - 251*S^2 + 84*S^4))/(9*S^3) + (30*Pi^2*S + (10*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2}, -S^2] + (172*S*HPL[{2}, -S^2]^2)/3 + (4*(1 + 2*S^4 + S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + (56*S*HPL[{4}, -S^2])/3 - (40*(1 + 16*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 240*S*HPL[{3, 1}, -S^2] + 480*S*HPL[{2, 1, 1}, -S^2] - (56*S*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((73*Pi^4*S)/90 + (Pi^2*(-72 + 15*S^2 + 15*S^4 + 46*S^6))/(12*S^3) + (-29 + 132*S^2 + 714*S^4 + 237*S^6)/(8*S^3) - 8*S*HPL[{4}, -S^2] + (4*(2 + S^2 + 17*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 16*S*HPL[{3, 1}, -S^2] - 32*S*HPL[{2, 1, 1}, -S^2] + (4*S*(5 + 2*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*(-9*Pi^4*S + (51 - 1784*S^2 - 586*S^4 - 497*S^6)/(4*S^3) + (Pi^2*(120 - 381*S^2 - 119*S^4 - 102*S^6))/(6*S^3) + 336*S*HPL[{3, 1}, -S^2] + 688*S*HPL[{2, 1, 1}, -S^2] + (4*(-1 + 15*S^2 + 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^4*(406 + 203*S^2 + 1858*S^4 - 201*S^6))/(180*S^3*(1 + S^2)) + (Pi^2*(387 + 203*S^2 + 1078*S^4 - 110*S^6))/(24*S^3) + (1380 + 2154*S^2 + 4987*S^4 + 167*S^6)/(16*S^3) + ((-4*Pi^2*S)/3 + (-3 + S^2 - 6*S^4)/S)*HPL[{3}, -S^2] - (2*(-2 - S^2 - 4*S^4 + S^6)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 8*S*HPL[{5}, -S^2] + (-42*Pi^2*S - (8*(-5 + 21*S^2 + 5*S^4 + 9*S^6))/S^3)*HPL[{2, 1}, -S^2] + (4*(-12 - 6*S^2 - 103*S^4 + 20*S^6)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 16*S*HPL[{3, 2}, -S^2] + 48*S*HPL[{4, 1}, -S^2] - (24*(-4 - 2*S^2 - 34*S^4 + 7*S^6)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 304*S*HPL[{2, 2, 1}, -S^2] - 944*S*HPL[{3, 1, 1}, -S^2] - 688*S*HPL[{2, 1, 1, 1}, -S^2] + (-2*Pi^2*S + (-14 - 5*S^2 - 13*S^4 + 4*S^6)/S^3)*Zeta[3]) + HPL[{1}, -S^2]^2*(((1 + S^2)*(343 + 4730*S^2 + 343*S^4))/(16*S^3) - (Pi^2*(1 + S^2)*(199 - 1448*S^2 + 385*S^4))/(24*S^3) + (Pi^4*(65 + 3201*S^2 + 195*S^4 - 130*S^6))/(90*S*(1 + S^2)) + (6*(2 + 39*S^4 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((10*Pi^2*S)/3 + (-11 + 5*S^2 + 25*S^4 + 9*S^6)/S^3)*HPL[{3}, -S^2] + (6*(3 + 8*S^4 + 3*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 20*S*HPL[{5}, -S^2] + (-90*Pi^2*S - (30*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2, 1}, -S^2] - (60*(1 + 16*S^4 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 40*S*HPL[{3, 2}, -S^2] + 64*S*HPL[{4, 1}, -S^2] + (120*(1 + 16*S^4 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 688*S*HPL[{2, 2, 1}, -S^2] + 2096*S*HPL[{3, 1, 1}, -S^2] - 1440*S*HPL[{2, 1, 1, 1}, -S^2] + (-2*Pi^2*S - (2*(1 + S^2)*(-2 + 3*S^2 + 8*S^4))/S^3)*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(29 + 154*S^2 + 29*S^4))/S^3 + (Pi^2*(29 + 5*S^2 + 377*S^4 + 15*S^6 + 19*S^8))/(3*S^3*(1 + S^2)) - 20*S*HPL[{3}, -S^2] - 344*S*HPL[{2, 1}, -S^2] - 20*S*Zeta[3])) + HPL[{1}, -S^2]*((12907*Pi^6*S)/5670 - (Pi^4*(1 + S^2)*(203 - 941*S^2 + 414*S^4))/(90*S^3) - (Pi^2*(1 + S^2)*(107 - 4208*S^2 + 781*S^4))/(48*S^3) + ((1 + S^2)*(2377 + 12838*S^2 + 2377*S^4))/(32*S^3) + ((62*Pi^2*S)/3 + (4*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2}, -S^2]^2 + (76*S*HPL[{2}, -S^2]^3)/3 - 4*S*HPL[{3}, -S^2]^2 + ((20*Pi^2*S)/3 + (7 + 25*S^2 + 41*S^4 + 23*S^6)/S^3)*HPL[{4}, -S^2] + (6*(3 + 4*S^4 + 3*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) - 344*S*HPL[{2, 1}, -S^2]^2 + ((-268*Pi^2*S)/3 - (2*(5 + 93*S^2 + 113*S^4 + 25*S^6))/S^3)*HPL[{3, 1}, -S^2] + (8*(1 + 13*S^4 + S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) - (12*(1 - 18*S^4 + S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) - 56*S*HPL[{5, 1}, -S^2] + (180*Pi^2*S + (60*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (48*(2 + 39*S^4 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) + (24*(13 + 236*S^4 + 13*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 608*S*HPL[{3, 2, 1}, -S^2] + 1936*S*HPL[{4, 1, 1}, -S^2] - (240*(1 + 16*S^4 + S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 1440*S*HPL[{3, 1, 1, 1}, -S^2] + 2880*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((1 + S^2)*(-15 - 30*S^2 + 61*S^4))/(2*S^3) + (Pi^2*(1 + 3*S^4 - 2*S^6))/(S*(1 + S^2)))*Zeta[3] + 16*S*Zeta[3]^2 + HPL[{3}, -S^2]*(((1 + S^2)*(-39 + 98*S^2 + 37*S^4))/(2*S^3) + (Pi^2*(7 + 16*S^4 + 7*S^8))/(3*S^3*(1 + S^2)) + 40*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-2*(1 + S^2)*(29 + 154*S^2 + 29*S^4))/S^3 - (2*Pi^2*(29 + 5*S^2 + 377*S^4 + 15*S^6 + 19*S^8))/(3*S^3*(1 + S^2)) + 40*S*Zeta[3]) + HPL[{2}, -S^2]*((377*Pi^4*S)/45 + (Pi^2*(1 + S^2)*(25 + 186*S^2 + 15*S^4))/(6*S^3) + ((1 + S^2)*(223 + 946*S^2 + 223*S^4))/(4*S^3) - (4*(1 + 13*S^4 + S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) + 8*S*HPL[{4}, -S^2] - (24*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 344*S*HPL[{3, 1}, -S^2] + 688*S*HPL[{2, 1, 1}, -S^2] - (4*(1 + 13*S^4 + S^8)*Zeta[3])/(S^3*(1 + S^2))))) + ((55*Pi^2*S*(-1 + 2*S^2))/(3*(1 + S^2)) + (S*(461 + 203*S^2))/2)*Zeta[5] + HPL[{1}, -S^2]^3*(-(Pi^2*(1 + S^2)*(107 - 700*S^2 + 161*S^4))/(18*S^3) + ((1 + S^2)*(343 + 4730*S^2 + 343*S^4))/(24*S^3) + (Pi^4*(111 + 4364*S^2 + 333*S^4 - 222*S^6))/(180*S*(1 + S^2)) + (4*(2 + 39*S^4 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((-212*Pi^2*S)/9 - (2*(7 - 39*S^2 - 9*S^4 + 37*S^6))/(3*S^3))*HPL[{3}, -S^2] - (4*(-3 - 3*S^2 + 16*S^4 - 9*S^6 + 3*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 16*S*HPL[{5}, -S^2] + ((-172*Pi^2*S)/9 + (4*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1}, -S^2] + (8*(-5 - 5*S^2 - 6*S^4 - 15*S^6 + 5*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + (688*S*HPL[{3, 2}, -S^2])/3 + (2288*S*HPL[{4, 1}, -S^2])/3 - (80*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (1376*S*HPL[{2, 2, 1}, -S^2])/3 + (2528*S*HPL[{3, 1, 1}, -S^2])/3 + ((-196*Pi^2*S)/9 - (4*(1 + S^2)*(-6 + 5*S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-2*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 - (2*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(3*S^3*(1 + S^2)) - (344*S*HPL[{3}, -S^2])/3 - (688*S*HPL[{2, 1}, -S^2])/3 - (344*S*Zeta[3])/3) - (440*S*Zeta[5])/3) + HPL[{3}, -S^2]*((-178 + 1490*S^2 + 366*S^4 - 351*S^6)/(8*S^3) + (Pi^4*(-5 - 888*S^2 + 303*S^4 + 10*S^6))/(180*S*(1 + S^2)) + (Pi^2*(-82 + 264*S^2 + 58*S^4 + 255*S^6))/(24*S^3) - (2*(1 - 27*S^4 - 4*S^6 + S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 64*S*HPL[{5}, -S^2] + (28*Pi^2*S + (2*(1 - 9*S^2 - 19*S^4 + 79*S^6))/S^3)*HPL[{2, 1}, -S^2] - (4*(1 - 102*S^4 + 32*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 12*S*HPL[{3, 2}, -S^2] - 128*S*HPL[{4, 1}, -S^2] + (8*(-1 - S^2 - 91*S^4 + 39*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 368*S*HPL[{2, 2, 1}, -S^2] - 976*S*HPL[{3, 1, 1}, -S^2] + 640*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S)/3 + (4 + 21*S^2 + 7*S^4 - 6*S^6)/S^3)*Zeta[3] + 16*S*Zeta[5]) + HPL[{2, 1}, -S^2]*((Pi^2*(221 - 1374*S^2 - 354*S^4 - 129*S^6))/(12*S^3) + (7*Pi^4*(-1 - 185*S^2 - 81*S^4 + 2*S^6))/(60*S*(1 + S^2)) + (-173 - 6180*S^2 - 1788*S^4 + 173*S^6)/(8*S^3) - (8*(-1 - S^2 - 129*S^4 + S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 344*S*HPL[{3, 2}, -S^2] - 1008*S*HPL[{4, 1}, -S^2] + (48*S*(44 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 640*S*HPL[{3, 1, 1}, -S^2] - 1280*S*HPL[{2, 1, 1, 1}, -S^2] + ((80*Pi^2*S)/3 + (8*(1 - 6*S^2 - 6*S^4 + 19*S^6))/S^3)*Zeta[3] + 136*S*Zeta[5]) + HPL[{2}, -S^2]*((31*Pi^6*S)/135 + (3954 + 12607*S^2 + 14593*S^4 - 3954*S^6)/(32*S^3) + (Pi^4*(2536 + 1280*S^2 + 3991*S^4 - 1004*S^6))/(720*S^3) + (Pi^2*(1000 + 1521*S^2 + 3012*S^4 - 506*S^6))/(48*S^3) + 6*S*HPL[{3}, -S^2]^2 + ((-14*Pi^2*S)/3 + (-20 - 49*S^2 - 41*S^4 + 52*S^6)/(2*S^3))*HPL[{4}, -S^2] + ((8 + S^2 - 74*S^4 - S^6 + 6*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) - 68*S*HPL[{6}, -S^2] + ((-124*Pi^2*S)/3 - (2*(31 - 4*S^2 + 36*S^4 + 49*S^6))/S^3)*HPL[{3, 1}, -S^2] + (2*(1 + 196*S^4 - 72*S^6 + S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) - (4*(-2 - 2*S^2 - 302*S^4 + 111*S^6 + 2*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) + 24*S*HPL[{4, 2}, -S^2] + 132*S*HPL[{5, 1}, -S^2] + ((248*Pi^2*S)/3 + (8*(20 - 3*S^2 + 21*S^4 + 20*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + 304*S*HPL[{2, 2, 1}, -S^2] + (8*(-1 - S^2 - 205*S^4 - 75*S^6 + S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 24*S*HPL[{3, 1, 2}, -S^2] + 296*S*HPL[{3, 2, 1}, -S^2] + 864*S*HPL[{4, 1, 1}, -S^2] - (48*S*(44 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 640*S*HPL[{3, 1, 1, 1}, -S^2] + 1280*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(2 + S^2 - 103*S^4 + 39*S^6))/(3*S^3*(1 + S^2)) + (11 + 50*S^2 - 66*S^4 + 81*S^6)/(2*S^3))*Zeta[3] - 8*S*Zeta[3]^2 + HPL[{3}, -S^2]*((-47 - 51*S^2 - 109*S^4 + 231*S^6)/(4*S^3) + (Pi^2*(-1 - S^2 - 98*S^4 + 41*S^6 + S^8))/(3*S^3*(1 + S^2)) + 184*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-2*Pi^2*S*(75 + 8*S^2))/(1 + S^2) + (2*(23 - 136*S^2 - 42*S^4 + 23*S^6))/S^3 + 144*S*Zeta[3]) + (2*(4 + 2*S^2 - 87*S^4 + 44*S^6)*Zeta[5])/(S^3*(1 + S^2))) + HPL[{1}, -S^2]^2*((8699*Pi^6*S)/4536 - (Pi^2*(1 + S^2)*(115 - 3850*S^2 + 559*S^4))/(48*S^3) - (Pi^4*(1 + S^2)*(832 - 3646*S^2 + 1229*S^4))/(360*S^3) + ((1 + S^2)*(2377 + 12838*S^2 + 2377*S^4))/(32*S^3) + ((67*Pi^2*S)/3 + (4*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2}, -S^2]^2 + 8*S*HPL[{3}, -S^2]^2 + ((-28*Pi^2*S)/3 - (3*(-3 - 25*S^2 - 11*S^4 + 11*S^6))/S^3)*HPL[{4}, -S^2] - (2*(-9 - 17*S^2 - 48*S^4 - 51*S^6 + 25*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) + 70*S*HPL[{6}, -S^2] - 344*S*HPL[{2, 1}, -S^2]^2 + ((-56*Pi^2*S)/3 + (2*(-9 - 127*S^2 - 97*S^4 + 21*S^6))/S^3)*HPL[{3, 1}, -S^2] + (8*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) + (12*(-1 - 13*S^2 + 210*S^4 - 39*S^6 + 25*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) + 36*S*HPL[{4, 2}, -S^2] + 176*S*HPL[{5, 1}, -S^2] + ((172*Pi^2*S)/3 - (12*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (48*(2 + 39*S^4 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) + (24*(13 + 5*S^2 + 162*S^4 + 15*S^6 + 3*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 224*S*HPL[{4, 1, 1}, -S^2] + (240*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + 224*S*HPL[{3, 1, 1, 1}, -S^2] + ((-2*(1 + S^2)*(1 - 25*S^2 + 28*S^4))/S^3 + (Pi^2*(19 - 180*S^2 + 57*S^4 - 38*S^6))/(3*S*(1 + S^2)))*Zeta[3] + 4*S*Zeta[3]^2 + HPL[{3}, -S^2]*((-2*(1 + S^2)*(7 - 57*S^2 + 34*S^4))/S^3 + (Pi^2*(7 + 19*S^2 - 218*S^4 + 57*S^6 - 31*S^8))/(3*S^3*(1 + S^2)) + 344*S*HPL[{2, 1}, -S^2] - 24*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((6*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 + (2*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(S^3*(1 + S^2)) + 344*S*Zeta[3]) + HPL[{2}, -S^2]*((707*Pi^4*S)/180 - (Pi^2*(1 + S^2)*(-15 - 119*S^2 + 7*S^4))/(3*S^3) - ((1 + S^2)*(-111 - 628*S^2 + 111*S^4))/(2*S^3) - (4*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - 28*S*HPL[{4}, -S^2] - (24*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 344*S*HPL[{3, 1}, -S^2] + 688*S*HPL[{2, 1, 1}, -S^2] - (12*(-2 + 31*S^2 - 6*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2))) - (2*(-29 + 156*S^2 - 87*S^4 + 58*S^6)*Zeta[5])/(S*(1 + S^2))) + (150*S*(-1 + 2*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(-692 - 10583*S^2 + 867*S^4))/(96*S^3) - (Pi^4*(1 + S^2)*(2952 - 20219*S^2 + 5919*S^4))/(1440*S^3) + ((1 + S^2)*(11427 + 35402*S^2 + 11427*S^4))/(64*S^3) + (Pi^6*(4447 + 113672*S^2 + 13341*S^4 - 8894*S^6))/(15120*S*(1 + S^2)) - (10*(-1 - 4*S^4 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) + (2*(1 + 10*S^4 + S^8)*HPL[{3}, -S^2]^2)/(S^3*(1 + S^2)) + (-2*Pi^2*S + (-41 + 157*S^2 + 107*S^4 - 91*S^6)/S^3)*HPL[{5}, -S^2] - (15*(-4 - 5*S^2 - 36*S^4 - 15*S^6 + 6*S^8)*HPL[{6}, -S^2])/(S^3*(1 + S^2)) + 288*S*HPL[{7}, -S^2] - (24*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)) + ((184*Pi^2*S)/3 + (4*(1 - 5*S^2 + 9*S^4 + 15*S^6))/S^3)*HPL[{3, 2}, -S^2] + ((608*Pi^2*S)/3 + (6*(3 - 31*S^2 + 3*S^4 + 37*S^6))/S^3)*HPL[{4, 1}, -S^2] + (6*(1 + 16*S^4 + S^8)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)) - 44*S*HPL[{4, 3}, -S^2] + (4*(-11 - 17*S^2 + 52*S^4 - 51*S^6 + 23*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)) - 120*S*HPL[{5, 2}, -S^2] - 300*S*HPL[{6, 1}, -S^2] + ((536*Pi^2*S)/3 + (32*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + ((1184*Pi^2*S)/3 + (4*(41 + 303*S^2 + 273*S^4 + 11*S^6))/S^3)*HPL[{3, 1, 1}, -S^2] - (80*(-1 - 4*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 - 696*S*HPL[{3, 2, 2}, -S^2] - 2144*S*HPL[{3, 3, 1}, -S^2] - (24*(-13 - 13*S^2 - 24*S^4 - 39*S^6 + 13*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 2120*S*HPL[{4, 1, 2}, -S^2] - 6536*S*HPL[{4, 2, 1}, -S^2] - 13344*S*HPL[{5, 1, 1}, -S^2] + ((-344*Pi^2*S)/3 + (24*(-5 - 47*S^2 - 37*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] + (48*(-5 - 5*S^2 - 6*S^4 - 15*S^6 + 5*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 1376*S*HPL[{3, 1, 1, 2}, -S^2] + 1376*S*HPL[{3, 1, 2, 1}, -S^2] + 1376*S*HPL[{3, 2, 1, 1}, -S^2] + 4576*S*HPL[{4, 1, 1, 1}, -S^2] - (480*(-1 - 4*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 - 2752*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 8256*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 16960*S*HPL[{3, 1, 1, 1, 1}, -S^2] + ((-157*Pi^4*S)/45 - (Pi^2*(1 + S^2)*(2 - 36*S^2 + 25*S^4))/(3*S^3) - ((1 + S^2)*(1 - 310*S^2 + 445*S^4))/(4*S^3))*Zeta[3] - (2*(-1 - 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-12*(1 + S^2)*(-9 - 68*S^2 + 9*S^4))/S^3 - (4*Pi^2*(-10 - 8*S^2 - 71*S^4 - 24*S^6 + 6*S^8))/(S^3*(1 + S^2)) - 688*S*Zeta[3]) + HPL[{2}, -S^2]^2*(((1 + S^2)*(59 + 202*S^2 + 59*S^4))/(4*S^3) + (Pi^2*(24 + 5*S^2 + 384*S^4 + 15*S^6 + 14*S^8))/(6*S^3*(1 + S^2)) - 96*S*HPL[{3}, -S^2] - 76*S*Zeta[3]) + HPL[{4}, -S^2]*(-((1 + S^2)*(-71 - 664*S^2 + 255*S^4))/(4*S^3) + (Pi^2*(17 + 14*S^2 - 34*S^4 + 42*S^6 - 11*S^8))/(3*S^3*(1 + S^2)) + 56*S*HPL[{2, 1}, -S^2] - 16*S*Zeta[3]) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(-31 - 430*S^2 + 77*S^4))/S^3 + (2*Pi^2*(-31 - 24*S^2 - 166*S^4 - 72*S^6 + 17*S^8))/(3*S^3*(1 + S^2)) + 352*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-707*Pi^4*S)/90 + (2*Pi^2*(1 + S^2)*(-15 - 119*S^2 + 7*S^4))/(3*S^3) + ((1 + S^2)*(-111 - 628*S^2 + 111*S^4))/S^3 + 688*S*HPL[{3, 1}, -S^2] + 1376*S*HPL[{2, 1, 1}, -S^2] + (24*(-2 + 31*S^2 - 6*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((-196*Pi^4*S)/45 - (Pi^2*(1 + S^2)*(11 - 76*S^2 + 37*S^4))/(6*S^3) - ((1 + S^2)*(27 - 239*S^2 + 138*S^4))/S^3 + 28*S*HPL[{4}, -S^2] + (8*(1 - 5*S^2 + 97*S^4 - 15*S^6 + 11*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 352*S*HPL[{3, 1}, -S^2] - 688*S*HPL[{2, 1, 1}, -S^2] - (4*(-1 - S^2 + 14*S^4 - 3*S^6 + S^8)*Zeta[3])/(S^3*(1 + S^2))) + ((-110*Pi^2*S)/3 - (2*(1 + S^2)*(4 - 60*S^2 + 29*S^4))/S^3)*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(-110 - 757*S^2 + 51*S^4))/(12*S^3) - ((1 + S^2)*(-1559 - 7904*S^2 + 1559*S^4))/(16*S^3) + (Pi^4*(832 + 625*S^2 + 6328*S^4 + 1875*S^6 - 418*S^8))/(360*S^3*(1 + S^2)) + ((-92*Pi^2*S)/3 - (2*(3 - 3*S^2 + 7*S^4 + 13*S^6))/S^3)*HPL[{3}, -S^2] - (2*(1 + 40*S^4 + S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - 40*S*HPL[{5}, -S^2] + ((-268*Pi^2*S)/3 - (16*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 1}, -S^2] - (24*(2 + 39*S^4 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + 360*S*HPL[{3, 2}, -S^2] + 1096*S*HPL[{4, 1}, -S^2] + (48*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 688*S*HPL[{3, 1, 1}, -S^2] - 1376*S*HPL[{2, 1, 1, 1}, -S^2] + ((-94*Pi^2*S)/3 - (4*(1 + S^2)*(-7 + 8*S^2))/S)*Zeta[3] - 172*S*Zeta[5]) - 300*S*Zeta[7])) + HPL[{0}, S^2]*((-179327*Pi^8*S)/340200 + (Pi^6*S*(-5799 + 27938*S^2))/22680 + (-48710 - 94231*S^2 - 53971*S^4)/(256*S) + (Pi^2*(-4988 - 19118*S^2 - 2371*S^4))/(384*S) + (Pi^4*(-1990 - 18089*S^2 + 455*S^4))/(2880*S) - (4*S*HPL[{1}, -S^2]^7)/(1 + S^2) - (S*HPL[{1}, -S^2]^8)/3 + ((-53*Pi^2*S)/36 + (-30 + 3*S^2 - 57*S^4 + 20*S^6)/(12*S^3))*HPL[{2}, -S^2]^3 - (23*S*HPL[{2}, -S^2]^4)/12 + HPL[{1}, -S^2]^6*((-32*Pi^2*S)/27 + (2*(1 - 3*S^2 - 3*S^4 + S^6))/(3*S^3) - 4*S*HPL[{2}, -S^2]) + ((4*Pi^2*S)/3 + (6 + 3*S^2 + 7*S^4 - 8*S^6)/(4*S^3))*HPL[{3}, -S^2]^2 - 28*S*HPL[{4}, -S^2]^2 + ((45*Pi^2*S)/2 - (5*(14 + 3*S^2 + 47*S^4 + 24*S^6))/(2*S^3))*HPL[{6}, -S^2] - (5*(-15 - 112*S^2 - 31*S^4 + 30*S^6)*HPL[{7}, -S^2])/(S*(1 + S^2)) + 525*S*HPL[{8}, -S^2] + ((61*Pi^2*S)/3 - (4*(-9 - S^2 - 17*S^4 + 5*S^6))/S^3)*HPL[{2, 1}, -S^2]^2 - 100*S*HPL[{3, 1}, -S^2]^2 + (-(Pi^2*S)/3 + (-22 + S^2 - 19*S^4)/(4*S^3))*HPL[{4, 2}, -S^2] - (2*(-3 - 46*S^2 - S^4 + 6*S^6)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) + ((-22*Pi^2*S)/3 + (66 - 9*S^2 + 127*S^4 + 60*S^6)/(2*S^3))*HPL[{5, 1}, -S^2] - (3*(-13 - 188*S^2 - 5*S^4 + 26*S^6)*HPL[{5, 2}, -S^2])/(2*S*(1 + S^2)) - (60*S*(-5 + S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) + 6*S*HPL[{6, 2}, -S^2] - 228*S*HPL[{7, 1}, -S^2] - 344*S*HPL[{2, 1, 1}, -S^2]^2 + ((7*Pi^2*S)/3 + (2*(-1 - 2*S^2 + 5*S^4 + 3*S^6))/S^3)*HPL[{3, 1, 2}, -S^2] + (-33*Pi^2*S + (2*(-31 + S^2 - 52*S^4 + 23*S^6))/S^3)*HPL[{3, 2, 1}, -S^2] - (2*(-2 - 47*S^2 + 7*S^4 + 4*S^6)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) - (8*(-1 - 35*S^2 + 7*S^4 + 2*S^6)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) - 32*S*HPL[{3, 3, 2}, -S^2] + ((-346*Pi^2*S)/3 + (-238 - 7*S^2 - 419*S^4 + 136*S^6)/S^3)*HPL[{4, 1, 1}, -S^2] + ((5 + 256*S^2 - 71*S^4 - 10*S^6)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + 64*S*HPL[{4, 1, 3}, -S^2] + ((17 + 832*S^2 - 179*S^4 - 34*S^6)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) - 35*S*HPL[{4, 2, 2}, -S^2] + 128*S*HPL[{4, 3, 1}, -S^2] - (2*(-27 - 878*S^2 + 145*S^4 + 54*S^6)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) + 58*S*HPL[{5, 1, 2}, -S^2] + 538*S*HPL[{5, 2, 1}, -S^2] + 1480*S*HPL[{6, 1, 1}, -S^2] + (8*(-5 + 122*S^2 + 23*S^4 + 10*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)) + ((296*Pi^2*S)/3 - (2*(-86 - 9*S^2 - 181*S^4 + 44*S^6))/S^3)*HPL[{3, 1, 1, 1}, -S^2] - (8*(-16 + 372*S^2 + 63*S^4 + 32*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (8*(-16 + 372*S^2 + 63*S^4 + 32*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + 12*S*HPL[{3, 1, 2, 2}, -S^2] - (8*(-31 + 738*S^2 + 132*S^4 + 62*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + 12*S*HPL[{3, 2, 1, 2}, -S^2] + 284*S*HPL[{3, 2, 2, 1}, -S^2] + 816*S*HPL[{3, 3, 1, 1}, -S^2] - (4*(-177 + 4454*S^2 + 833*S^4 + 354*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 12*S*HPL[{4, 1, 1, 2}, -S^2] + 804*S*HPL[{4, 1, 2, 1}, -S^2] + 2436*S*HPL[{4, 2, 1, 1}, -S^2] + 4936*S*HPL[{5, 1, 1, 1}, -S^2] + (-176*Pi^2*S + (4*(-90 - 19*S^2 - 159*S^4 + 60*S^6))/S^3)*HPL[{2, 1, 1, 1, 1}, -S^2] + (48*(-2 + 44*S^2 + 7*S^4 + 4*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (144*(-2 + 44*S^2 + 7*S^4 + 4*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 608*S*HPL[{2, 2, 1, 2, 1}, -S^2] + 1824*S*HPL[{2, 2, 2, 1, 1}, -S^2] + (8*(-57 + 1328*S^2 + 221*S^4 + 114*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 3600*S*HPL[{3, 1, 1, 1, 2}, -S^2] - 6032*S*HPL[{3, 1, 1, 2, 1}, -S^2] - 7248*S*HPL[{3, 1, 2, 1, 1}, -S^2] - 15152*S*HPL[{3, 2, 1, 1, 1}, -S^2] - 45792*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (240*(-1 + 18*S^2 + 3*S^4 + 2*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 1664*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 2880*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((-32*Pi^2*S)/3 + S*(-5 + 24*S^2))*Zeta[3]^2 + HPL[{5}, -S^2]*((170 - 245*S^2 - 331*S^4 - 327*S^6)/(8*S^3) + (Pi^2*(19 + 100*S^2 + 31*S^4 - 38*S^6))/(6*S*(1 + S^2)) - 56*S*HPL[{2, 1}, -S^2] - 84*S*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((265 - 1622*S^2 - 218*S^4 - 629*S^6)/(2*S^3) - (2*Pi^2*(-26 + 595*S^2 + 100*S^4 + 52*S^6))/(3*S*(1 + S^2)) - 56*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((2*Pi^2*(-19 + 429*S^2 + 81*S^4 + 38*S^6))/(3*S*(1 + S^2)) + (-101 + 616*S^2 + 156*S^4 + 217*S^6)/S^3 - 32*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((25 - 8*S^2 + 116*S^4 - 115*S^6)/(8*S^3) + (Pi^2*(5 - 52*S^2 + 29*S^4 - 10*S^6))/(12*S*(1 + S^2)) - 28*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((33 - 265*S^2 - 16*S^4 - 92*S^6)/S^3 + (Pi^2*(15 - 400*S^2 - 73*S^4 - 30*S^6))/(3*S*(1 + S^2)) - 8*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((2*Pi^2*(-1 - 12*S^2 - 2*S^4 + 2*S^6))/(S*(1 + S^2)) + (-77 + 71*S^2 + 295*S^4 + 70*S^6)/(4*S^3) - 4*S*Zeta[3]) + HPL[{1}, -S^2]^5*(((1 + S^2)*(21 - 130*S^2 + 21*S^4))/(12*S^3) + (2*Pi^2*(-1 - 86*S^2 - 3*S^4 + 2*S^6))/(15*S*(1 + S^2)) - (2*(1 + 16*S^4 + S^8)*HPL[{2}, -S^2])/(S^3*(1 + S^2)) - (8*S*HPL[{3}, -S^2])/15 + 24*S*HPL[{2, 1}, -S^2] + (28*S*Zeta[3])/15) + HPL[{1}, -S^2]^4*((-937*Pi^4*S)/540 + ((1 + S^2)*(19 - 590*S^2 + 19*S^4))/(16*S^3) + (Pi^2*(1 + S^2)*(58 - 251*S^2 + 84*S^4))/(36*S^3) + ((-15*Pi^2*S)/2 - (5*(1 + 7*S^2 + 7*S^4 + S^6))/(2*S^3))*HPL[{2}, -S^2] - (43*S*HPL[{2}, -S^2]^2)/3 + ((-1 - 2*S^4 - S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - (14*S*HPL[{4}, -S^2])/3 + (10*(1 + 16*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 60*S*HPL[{3, 1}, -S^2] - 120*S*HPL[{2, 1, 1}, -S^2] + (14*S*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]^2*((-33*Pi^4*S)/40 + (-479 + 126*S^2 - 1424*S^4 + 33*S^6)/(32*S^3) + (Pi^2*(-134 - 15*S^2 - 235*S^4 + 48*S^6))/(48*S^3) + ((1 + 22*S^2 - 5*S^4 - 2*S^6)*HPL[{3}, -S^2])/(2*S*(1 + S^2)) + 4*S*HPL[{4}, -S^2] + ((-5 + 122*S^2 + 23*S^4 + 10*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 34*S*HPL[{3, 1}, -S^2] - 76*S*HPL[{2, 1, 1}, -S^2] + ((2 + S^2 + 6*S^4 + S^6)*Zeta[3])/(2*S^3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-349*Pi^4*S)/45 + (-497 - 554*S^2 - 1752*S^4 + 51*S^6)/(4*S^3) + (Pi^2*(-170 - 41*S^2 - 283*S^4 + 72*S^6))/(6*S^3) - (4*(-2 - S^2 - 11*S^4 + 3*S^6)*Zeta[3])/(S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((164*Pi^4*S)/45 + (Pi^2*(88 + 11*S^2 + 161*S^4 - 22*S^6))/(6*S^3) + (139 + 228*S^2 + 942*S^4 - 20*S^6)/(4*S^3) + 352*S*HPL[{2, 1, 1}, -S^2] - (2*(2 - 3*S^2 - 5*S^4 + 4*S^6)*Zeta[3])/S^3) + HPL[{4}, -S^2]*((187*Pi^4*S)/360 + (-236 - 863*S^2 - 1261*S^4 - 3*S^6)/(16*S^3) + (Pi^2*(-62 - 45*S^2 - 81*S^4 + 4*S^6))/(12*S^3) + (2*(-1 + 4*S^2 + S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + 40*S*HPL[{3, 1}, -S^2] - 16*S*HPL[{2, 1, 1}, -S^2] + ((-2 - 5*S^2 - 64*S^4 - 5*S^6 + 8*S^8)*Zeta[3])/(S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(343 + 4730*S^2 + 343*S^4))/(48*S^3) + (Pi^2*(1 + S^2)*(199 - 1448*S^2 + 385*S^4))/(72*S^3) + (Pi^4*(-65 - 3201*S^2 - 195*S^4 + 130*S^6))/(270*S*(1 + S^2)) - (2*(2 + 39*S^4 + 2*S^8)*HPL[{2}, -S^2]^2)/(S^3*(1 + S^2)) + ((-10*Pi^2*S)/9 + (11 - 5*S^2 - 25*S^4 - 9*S^6)/(3*S^3))*HPL[{3}, -S^2] - (2*(3 + 8*S^4 + 3*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) - (20*S*HPL[{5}, -S^2])/3 + (30*Pi^2*S + (10*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2, 1}, -S^2] + (20*(1 + 16*S^4 + S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - (40*S*HPL[{3, 2}, -S^2])/3 - (64*S*HPL[{4, 1}, -S^2])/3 - (40*(1 + 16*S^4 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - (688*S*HPL[{2, 2, 1}, -S^2])/3 - (2096*S*HPL[{3, 1, 1}, -S^2])/3 + 480*S*HPL[{2, 1, 1, 1}, -S^2] + ((2*Pi^2*S)/3 + (2*(1 + S^2)*(-2 + 3*S^2 + 8*S^4))/(3*S^3))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(29 + 154*S^2 + 29*S^4))/(3*S^3) + (Pi^2*(-29 - 5*S^2 - 377*S^4 - 15*S^6 - 19*S^8))/(9*S^3*(1 + S^2)) + (20*S*HPL[{3}, -S^2])/3 + (344*S*HPL[{2, 1}, -S^2])/3 + (20*S*Zeta[3])/3)) + HPL[{1}, -S^2]^2*((-12907*Pi^6*S)/11340 + (Pi^4*(1 + S^2)*(203 - 941*S^2 + 414*S^4))/(180*S^3) + (Pi^2*(1 + S^2)*(107 - 4208*S^2 + 781*S^4))/(96*S^3) - ((1 + S^2)*(2377 + 12838*S^2 + 2377*S^4))/(64*S^3) + ((-31*Pi^2*S)/3 - (2*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2}, -S^2]^2 - (38*S*HPL[{2}, -S^2]^3)/3 + 2*S*HPL[{3}, -S^2]^2 + ((-10*Pi^2*S)/3 + (-7 - 25*S^2 - 41*S^4 - 23*S^6)/(2*S^3))*HPL[{4}, -S^2] - (3*(3 + 4*S^4 + 3*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)) + 172*S*HPL[{2, 1}, -S^2]^2 + ((134*Pi^2*S)/3 + (5 + 93*S^2 + 113*S^4 + 25*S^6)/S^3)*HPL[{3, 1}, -S^2] - (4*(1 + 13*S^4 + S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) + (6*(1 - 18*S^4 + S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) + 28*S*HPL[{5, 1}, -S^2] + (-90*Pi^2*S - (30*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (24*(2 + 39*S^4 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) - (12*(13 + 236*S^4 + 13*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 304*S*HPL[{3, 2, 1}, -S^2] - 968*S*HPL[{4, 1, 1}, -S^2] + (120*(1 + 16*S^4 + S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 720*S*HPL[{3, 1, 1, 1}, -S^2] - 1440*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(-15 - 30*S^2 + 61*S^4))/(4*S^3) + (Pi^2*(-1 - 3*S^4 + 2*S^6))/(2*S*(1 + S^2)))*Zeta[3] - 8*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(29 + 154*S^2 + 29*S^4))/S^3 + (Pi^2*(29 + 5*S^2 + 377*S^4 + 15*S^6 + 19*S^8))/(3*S^3*(1 + S^2)) - 20*S*Zeta[3]) + HPL[{3}, -S^2]*(-((1 + S^2)*(-39 + 98*S^2 + 37*S^4))/(4*S^3) + (Pi^2*(-7 - 16*S^4 - 7*S^8))/(6*S^3*(1 + S^2)) - 20*S*HPL[{2, 1}, -S^2] - 4*S*Zeta[3]) + HPL[{2}, -S^2]*((-377*Pi^4*S)/90 - (Pi^2*(1 + S^2)*(25 + 186*S^2 + 15*S^4))/(12*S^3) - ((1 + S^2)*(223 + 946*S^2 + 223*S^4))/(8*S^3) + (2*(1 + 13*S^4 + S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - 4*S*HPL[{4}, -S^2] + (12*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) + 172*S*HPL[{3, 1}, -S^2] - 344*S*HPL[{2, 1, 1}, -S^2] + (2*(1 + 13*S^4 + S^8)*Zeta[3])/(S^3*(1 + S^2)))) + ((55*Pi^2*S*(-1 + 2*S^2))/(6*(1 + S^2)) + S*(-76 + 37*S^2))*Zeta[5] + Zeta[3]*((157*Pi^4*S*(-1 + 2*S^2))/(180*(1 + S^2)) + (Pi^2*S*(-326 + 69*S^2))/24 + (27 - 104*S^2 + 108*S^4)/(2*S) - 160*S*Zeta[5]) + HPL[{3}, -S^2]*((-89 - 573*S^2 - 1543*S^4 - 331*S^6)/(16*S^3) + (Pi^2*(142 - 131*S^2 - 313*S^4 - 161*S^6))/(48*S^3) + (Pi^4*(33 + 52*S^2 + 57*S^4 - 66*S^6))/(120*S*(1 + S^2)) + ((-3 - 46*S^2 - S^4 + 6*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)) + 56*S*HPL[{5}, -S^2] + (-4*Pi^2*S + (-6 - 7*S^2 - 11*S^4)/S^3)*HPL[{2, 1}, -S^2] + (4*S*(-13 + 2*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 16*S*HPL[{3, 2}, -S^2] - 72*S*HPL[{4, 1}, -S^2] + (4*(-1 + 9*S^2 - 3*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + 48*S*HPL[{2, 2, 1}, -S^2] + 160*S*HPL[{3, 1, 1}, -S^2] - 48*S*HPL[{2, 1, 1, 1}, -S^2] + ((-22*Pi^2*S)/3 + (2 - 2*S^2 + S^4 + 2*S^6)/S^3)*Zeta[3] - 74*S*Zeta[5]) + HPL[{2, 1}, -S^2]*((Pi^4*(-83 + 2574*S^2 + 561*S^4 + 166*S^6))/(180*S*(1 + S^2)) + (Pi^2*(-206 + 1240*S^2 + 293*S^4 + 219*S^6))/(24*S^3) + (167 + 5051*S^2 + 2218*S^4 + 1380*S^6)/(16*S^3) - (4*(-6 + 131*S^2 + 20*S^4 + 12*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + 48*S*HPL[{3, 2}, -S^2] + 160*S*HPL[{4, 1}, -S^2] - (24*(-2 + 44*S^2 + 7*S^4 + 4*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - 304*S*HPL[{2, 2, 1}, -S^2] - 960*S*HPL[{3, 1, 1}, -S^2] + 688*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S)/3 + (4 - 9*S^2 - S^4 - 14*S^6)/S^3)*Zeta[3] + 48*S*Zeta[5]) + HPL[{2}, -S^2]*((-4447*Pi^6*S)/15120 + (-4284 - 8948*S^2 - 15715*S^4 - 1157*S^6)/(64*S^3) + (Pi^2*(-780 - 1075*S^2 - 3358*S^4 + 54*S^6))/(96*S^3) + (Pi^4*(-1198 - 579*S^2 - 1831*S^4 + 312*S^6))/(720*S^3) - 4*S*HPL[{3}, -S^2]^2 + ((-8*Pi^2*S)/3 + (-6 - 3*S^2 - 7*S^4 + 8*S^6)/(2*S^3))*HPL[{4}, -S^2] + ((3 + 46*S^2 + S^4 - 6*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)) - 56*S*HPL[{6}, -S^2] + 76*S*HPL[{2, 1}, -S^2]^2 + ((65*Pi^2*S)/3 - (4*(-9 - S^2 - 17*S^4 + 5*S^6))/S^3)*HPL[{3, 1}, -S^2] + (2*(-1 - 22*S^2 + 5*S^4 + 2*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (4*(-1 - 35*S^2 + 7*S^4 + 2*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + 40*S*HPL[{5, 1}, -S^2] + ((-122*Pi^2*S)/3 + (8*(-9 - S^2 - 17*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (4*(-5 + 122*S^2 + 23*S^4 + 10*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*(-16 + 375*S^2 + 66*S^4 + 32*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - 184*S*HPL[{3, 2, 1}, -S^2] - 568*S*HPL[{4, 1, 1}, -S^2] + (24*(-2 + 44*S^2 + 7*S^4 + 4*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 4000*S*HPL[{3, 1, 1, 1}, -S^2] - 688*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((58 + 55*S^2 + 28*S^4 - 11*S^6)/(4*S^3) + (Pi^2*(2 + S^2 + S^4 - S^6))/(6*S^3*(1 + S^2)))*Zeta[3] - 2*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-15 + 400*S^2 + 73*S^4 + 30*S^6))/(6*S*(1 + S^2)) + (-33 + 265*S^2 + 16*S^4 + 92*S^6)/(2*S^3) + 4*S*Zeta[3]) + HPL[{3}, -S^2]*((10 - 31*S^2 + 19*S^4)/(4*S) + (Pi^2*(-1 + 18*S^2 - 3*S^4 + 2*S^6))/(6*S*(1 + S^2)) - 24*S*HPL[{2, 1}, -S^2] + 12*S*Zeta[3]) + (2*(2 + S^2 - 14*S^4 + 5*S^6)*Zeta[5])/(S^3*(1 + S^2))) + (75*S*(-1 + 2*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(-510 - 12703*S^2 + 1573*S^4))/(192*S^3) + (Pi^4*(1 + S^2)*(1401 - 12570*S^2 + 4153*S^4))/(1440*S^3) - ((1 + S^2)*(11427 + 35402*S^2 + 11427*S^4))/(128*S^3) + (Pi^6*(-217 - 14209*S^2 - 651*S^4 + 434*S^6))/(3780*S*(1 + S^2)) + ((-5 - 104*S^4 - 5*S^8)*HPL[{2}, -S^2]^3)/(3*S^3*(1 + S^2)) + ((1 + 4*S^4 + S^8)*HPL[{3}, -S^2]^2)/(S^3*(1 + S^2)) + ((4*Pi^2*S)/3 + (33 + 19*S^2 - 85*S^4 - 71*S^6)/(2*S^3))*HPL[{5}, -S^2] - (30*(1 + S^2)*(1 - 2*S^2 + S^4)*HPL[{6}, -S^2])/S^3 + 120*S*HPL[{7}, -S^2] + (12*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)) + ((2*(1 + S^2)*(5 + 75*S^2 + 24*S^4))/S^3 + (2*Pi^2*(15 + 2*S^2 + 183*S^4 + 6*S^6 + 11*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-16*Pi^2*S)/3 - (2*(1 + 3*S^2 + 7*S^4 + 5*S^6))/S^3)*HPL[{3, 2}, -S^2] + ((-28*Pi^2*S)/3 + (-11 - 5*S^2 + 11*S^4 + 5*S^6)/S^3)*HPL[{4, 1}, -S^2] - (3*(1 - S^2 - S^4 + S^6)*HPL[{4, 2}, -S^2])/S^3 + 48*S*HPL[{4, 3}, -S^2] + (2*(11 + 20*S^4 + 11*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)) + 144*S*HPL[{5, 2}, -S^2] + 240*S*HPL[{6, 1}, -S^2] + ((-248*Pi^2*S)/3 - (16*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + ((-764*Pi^2*S)/3 - (2*(37 + 269*S^2 + 289*S^4 + 57*S^6))/S^3)*HPL[{3, 1, 1}, -S^2] - (8*(5 + 104*S^4 + 5*S^8)*HPL[{3, 2, 1}, -S^2])/(S^3*(1 + S^2)) + 64*S*HPL[{3, 2, 2}, -S^2] + 208*S*HPL[{3, 3, 1}, -S^2] - (12*(13 + 216*S^4 + 13*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 208*S*HPL[{4, 1, 2}, -S^2] + 640*S*HPL[{4, 2, 1}, -S^2] + 1256*S*HPL[{5, 1, 1}, -S^2] + (180*Pi^2*S + (60*(1 + 7*S^2 + 7*S^4 + S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] + 608*S*HPL[{2, 2, 2, 1}, -S^2] + (120*(1 + 16*S^4 + S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 1904*S*HPL[{3, 1, 1, 2}, -S^2] - 1904*S*HPL[{3, 1, 2, 1}, -S^2] - 3728*S*HPL[{3, 2, 1, 1}, -S^2] - 11072*S*HPL[{4, 1, 1, 1}, -S^2] - (240*(1 + 16*S^4 + S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + 1376*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 4128*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 6816*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 2880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-157*Pi^4*S)/90 + (Pi^2*(1 + S^2)*(-2 - 38*S^2 + 57*S^4))/(6*S^3) + ((1 + S^2)*(-4 - 87*S^2 + 111*S^4))/(4*S^3))*Zeta[3] - (2*(-1 + 6*S^2 - 3*S^4 + 2*S^6)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{4}, -S^2]*(-(((1 + S^2)*(6 + 25*S^2 + 20*S^4))/S^3) + (Pi^2*(-3 - 4*S^4 - 3*S^8))/(S^3*(1 + S^2)) + 8*S*HPL[{2, 1}, -S^2] - 32*S*Zeta[3]) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(59 + 202*S^2 + 59*S^4))/(8*S^3) + (Pi^2*(-23 - 4*S^2 - 350*S^4 - 12*S^6 - 15*S^8))/(12*S^3*(1 + S^2)) + 8*S*HPL[{3}, -S^2] + 76*S*HPL[{2, 1}, -S^2] + 2*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-2*(1 + S^2)*(29 + 154*S^2 + 29*S^4))/S^3 - (2*Pi^2*(29 + 5*S^2 + 377*S^4 + 15*S^6 + 19*S^8))/(3*S^3*(1 + S^2)) + 40*S*Zeta[3]) + HPL[{3}, -S^2]*((-26*Pi^4*S)/45 - (Pi^2*(1 + S^2)*(-15 + 26*S^2 + 25*S^4))/(12*S^3) - ((1 + S^2)*(-115 + 472*S^2 + 115*S^4))/(8*S^3) - 24*S*HPL[{4}, -S^2] - (4*(1 + 13*S^4 + S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - 40*S*HPL[{3, 1}, -S^2] + 40*S*HPL[{2, 1, 1}, -S^2] + (2*(-1 - 12*S^2 - 3*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((377*Pi^4*S)/45 + (Pi^2*(1 + S^2)*(25 + 186*S^2 + 15*S^4))/(6*S^3) + ((1 + S^2)*(223 + 946*S^2 + 223*S^4))/(4*S^3) - 344*S*HPL[{3, 1}, -S^2] - 688*S*HPL[{2, 1, 1}, -S^2] - (4*(1 + 13*S^4 + S^8)*Zeta[3])/(S^3*(1 + S^2))) + ((-55*Pi^2*S)/3 + (4*(1 + S^2)*(-1 - 6*S^2 + 13*S^4))/S^3)*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(181 + 1262*S^2 + 109*S^4))/(48*S^3) - ((1 + S^2)*(1547 + 5658*S^2 + 1547*S^4))/(32*S^3) + (Pi^4*(-203 - 60*S^2 - 2216*S^4 - 180*S^6 - 83*S^8))/(180*S^3*(1 + S^2)) + ((8*Pi^2*S)/3 + (3 + 5*S^2 + 5*S^4 + 3*S^6)/S^3)*HPL[{3}, -S^2] - (2*(1 + 4*S^4 + S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)) + 24*S*HPL[{5}, -S^2] + ((124*Pi^2*S)/3 + (8*(2 + 11*S^2 + 11*S^4 + 2*S^6))/S^3)*HPL[{2, 1}, -S^2] + (12*(2 + 39*S^4 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - 32*S*HPL[{3, 2}, -S^2] - 104*S*HPL[{4, 1}, -S^2] - (24*(2 + 39*S^4 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - 304*S*HPL[{2, 2, 1}, -S^2] + 952*S*HPL[{3, 1, 1}, -S^2] + 688*S*HPL[{2, 1, 1, 1}, -S^2] + ((Pi^2*S)/3 + ((1 + S^2)*(5 + 2*S^2 + 5*S^4))/S^3)*Zeta[3] - 24*S*Zeta[5]) - 150*S*Zeta[7]));
e5T3F3=(10341169*(1 + S^2))/(5038848*S) + (Pi^6*(-524123 + 1132264*S^2 + 2480538*S^4))/(4898880*S) + (Pi^4*(-1596258 + 484076*S^2 + 4411995*S^4))/(933120*S) + (Pi^2*(-28932248 + 1981483*S^2 + 50699034*S^4))/(1679616*S) + (Pi^8*(1031050 + 515525*S^2 + 3919233*S^4 + 2888183*S^6))/(16329600*S*(1 + S^2)) + (S^3*HPL[{0}, S^2]^9)/1152 + ((22*Pi^2*(1 + S^6))/(189*S^3) + (259 + 417*S^2 + 417*S^4 + 259*S^6)/(567*S^3))*HPL[{1}, -S^2]^7 + ((2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^8)/(27*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{1}, -S^2]^9)/(81*S^3) + HPL[{0}, S^2]^8*((2 + S^2 + 26*S^4 + 24*S^6)/(2304*S*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2])/(1152*S^3)) + HPL[{0}, S^2]^7*((5*Pi^2*S^3)/432 + (3 + 3*S^2 + 20*S^4)/(648*S) + ((2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(432*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2]^2)/(144*S^3)) + ((59 + 335*S^2 + 138*S^4 + 335*S^6 + 59*S^8)*HPL[{2}, -S^2]^4)/(216*S^3*(1 + S^2)) - (14*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^3)/(9*S^3) - (2*(31 + 15*S^2 - 8*S^4 + S^6 + 17*S^8)*HPL[{4}, -S^2]^2)/(3*S^3*(1 + S^2)) + ((125*Pi^2*(1 + S^6))/(6*S^3) + (14350 - 13149*S^2 + 18522*S^4 + 27246*S^6)/(108*S^3))*HPL[{7}, -S^2] + ((-5425 - 3883*S^2 + 771*S^4 + 5168*S^6 + 3626*S^8)*HPL[{8}, -S^2])/(6*S^3*(1 + S^2)) + (2450*(1 + S^2)*(1 - S^2 + S^4)*HPL[{9}, -S^2])/(3*S^3) + HPL[{0}, S^2]^6*((-760 + 302*S^2 + 1215*S^4)/(10368*S) + (Pi^2*(22 + 11*S^2 + 201*S^4 + 179*S^6))/(1728*S*(1 + S^2)) + ((-11 + 37*S^2 + 24*S^4 + 91*S^6 + 43*S^8)*HPL[{1}, -S^2]^2)/(864*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2]^3)/(54*S^3) + ((-6 + 3*S^4 + 5*S^6 - S^8)*HPL[{2}, -S^2])/(288*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((11*Pi^2*(1 + S^6))/(864*S^3) + (-344 - 159*S^2 + 462*S^4 + 277*S^6)/(5184*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(48*S^3)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(72*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(24*S^3)) + (2*(-19 + 305*S^2 + 162*S^4 + 361*S^6 + 37*S^8)*HPL[{3, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((215 - 102*S^2 - 156*S^4 - 2503*S^6)/(54*S^3) - (16*Pi^2*(1 + S^6))/(3*S^3))*HPL[{4, 3}, -S^2] + ((703 + 126*S^2 - 819*S^4 - 14897*S^6)/(108*S^3) - (283*Pi^2*(1 + S^6))/(18*S^3))*HPL[{5, 2}, -S^2] + ((18 + 24*S^2 + 3*S^4 - 19*S^6 - 25*S^8)*HPL[{5, 3}, -S^2])/(3*S^3*(1 + S^2)) + (490*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 4}, -S^2])/(3*S^3) + ((520 + 6372*S^2 - 6273*S^4 - 20406*S^6)/(54*S^3) - (118*Pi^2*(1 + S^6))/(3*S^3))*HPL[{6, 1}, -S^2] + ((142 + 172*S^2 + 15*S^4 - 147*S^6 - 177*S^8)*HPL[{6, 2}, -S^2])/(6*S^3*(1 + S^2)) + (1948*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 3}, -S^2])/(3*S^3) - (2*(-1803 - 1179*S^2 + 312*S^4 + 1699*S^6 + 1075*S^8)*HPL[{7, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1620*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7, 2}, -S^2])/S^3 + (8720*(1 + S^2)*(1 - S^2 + S^4)*HPL[{8, 1}, -S^2])/(3*S^3) + (4*(139 + 655*S^2 + 258*S^4 + 655*S^6 + 139*S^8)*HPL[{2, 1, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-13330 - 19377*S^2 - 3537*S^4 - 818*S^6)/(108*S^3) - (61*Pi^2*(1 + S^6))/(6*S^3))*HPL[{3, 2, 2}, -S^2] + ((-320*Pi^2*(1 + S^6))/(9*S^3) - (2*(5123 + 7248*S^2 + 1533*S^4 + 775*S^6))/(27*S^3))*HPL[{3, 3, 1}, -S^2] - (2*(-101 - 59*S^2 + 21*S^4 + 94*S^6 + 52*S^8)*HPL[{3, 3, 2}, -S^2])/(9*S^3*(1 + S^2)) + ((-20002 - 28929*S^2 - 6069*S^4 - 2610*S^6)/(54*S^3) - (104*Pi^2*(1 + S^6))/(3*S^3))*HPL[{4, 1, 2}, -S^2] + (2*(-202 - 100*S^2 + 51*S^4 + 185*S^6 + 83*S^8)*HPL[{4, 1, 3}, -S^2])/(9*S^3*(1 + S^2)) + ((-62230 - 87393*S^2 - 19713*S^4 - 11430*S^6)/(54*S^3) - (340*Pi^2*(1 + S^6))/(3*S^3))*HPL[{4, 2, 1}, -S^2] - (5*(-85 - 37*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{4, 2, 2}, -S^2])/(18*S^3*(1 + S^2)) + (2*(-350 - 272*S^2 + 39*S^4 + 337*S^6 + 259*S^8)*HPL[{4, 3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3, 2}, -S^2])/S^3 + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 4, 1}, -S^2])/S^3 + ((-64411 - 90378*S^2 - 19359*S^4 - 11615*S^6)/(27*S^3) - (2134*Pi^2*(1 + S^6))/(9*S^3))*HPL[{5, 1, 1}, -S^2] + ((-293 - 269*S^2 + 12*S^4 + 289*S^6 + 265*S^8)*HPL[{5, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) + (112*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 3}, -S^2])/S^3 + ((-3053 - 2309*S^2 + 372*S^4 + 2929*S^6 + 2185*S^8)*HPL[{5, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (26*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2, 2}, -S^2])/S^3 + (384*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 3, 1}, -S^2])/S^3 + (10*(-986 - 728*S^2 + 129*S^4 + 943*S^6 + 685*S^8)*HPL[{6, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (808*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1, 2}, -S^2])/(3*S^3) + (3688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 2, 1}, -S^2])/(3*S^3) + (9040*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7, 1, 1}, -S^2])/(3*S^3) + ((-104*Pi^2*(1 + S^6))/(9*S^3) - (8*(-391 - 495*S^2 + 495*S^4 + 391*S^6))/(27*S^3))*HPL[{2, 2, 2, 1}, -S^2] + ((506*Pi^2*(1 + S^6))/(9*S^3) + (-1016 - 763*S^2 + 4667*S^4 + 3384*S^6)/(9*S^3))*HPL[{3, 1, 1, 2}, -S^2] + ((506*Pi^2*(1 + S^6))/(9*S^3) + (-1016 - 763*S^2 + 4667*S^4 + 3384*S^6)/(9*S^3))*HPL[{3, 1, 2, 1}, -S^2] - (2*(7 - 5*S^2 - 6*S^4 - 5*S^6 + 7*S^8)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^3*(1 + S^2)) + ((818*Pi^2*(1 + S^6))/(9*S^3) + (-4144 - 4723*S^2 + 8627*S^4 + 6512*S^6)/(9*S^3))*HPL[{3, 2, 1, 1}, -S^2] - (2*(7 - 5*S^2 - 6*S^4 - 5*S^6 + 7*S^8)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^3*(1 + S^2)) + (2*(-137 - 197*S^2 - 30*S^4 + 147*S^6 + 207*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (416*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2, 2}, -S^2])/(3*S^3) + (1192*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 3, 1}, -S^2])/(3*S^3) + (8*(-29 - 53*S^2 - 12*S^4 + 33*S^6 + 57*S^8)*HPL[{3, 3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (1168*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1, 2}, -S^2])/(3*S^3) + (3496*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 2, 1}, -S^2])/(3*S^3) + ((2584*Pi^2*(1 + S^6))/(9*S^3) + (2*(-16824 - 19479*S^2 + 38823*S^4 + 29716*S^6))/(27*S^3))*HPL[{4, 1, 1, 1}, -S^2] - (2*(17 - 19*S^2 - 18*S^4 - 11*S^6 + 25*S^8)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)) - (7160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 3}, -S^2])/(3*S^3) + (2*(-133 - 193*S^2 - 30*S^4 + 143*S^6 + 203*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (5992*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2, 2}, -S^2])/(3*S^3) - (10624*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 3, 1}, -S^2])/(3*S^3) + (2*(-365 - 617*S^2 - 126*S^4 + 407*S^6 + 659*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (3736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1, 2}, -S^2])/(3*S^3) - (3664*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 2, 1}, -S^2])/(3*S^3) - (20912*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3, 1, 1}, -S^2])/(3*S^3) + (4*(-917 - 1517*S^2 - 300*S^4 + 1017*S^6 + 1617*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (21688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1, 2}, -S^2])/(3*S^3) - (35368*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 2, 1}, -S^2])/(3*S^3) - (83464*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2, 1, 1}, -S^2])/(3*S^3) - (208480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1, 1, 1}, -S^2])/(3*S^3) + ((-64*Pi^2*(1 + S^6))/S^3 - (64*(37 + 61*S^2 + 61*S^4 + 37*S^6))/(9*S^3))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-192*Pi^2*(1 + S^6))/S^3 - (64*(37 + 61*S^2 + 61*S^4 + 37*S^6))/(3*S^3))*HPL[{2, 2, 1, 1, 1}, -S^2] + (688*(-1 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(9*S^3) + (688*(-1 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(3*S^3) + (832*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 2, 1}, -S^2])/(3*S^3) + ((-3416*Pi^2*(1 + S^6))/(9*S^3) - (4*(12995 + 20262*S^2 + 15762*S^4 + 9435*S^6))/(27*S^3))*HPL[{3, 1, 1, 1, 1}, -S^2] - (456*(-1 + S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 - (6856*(-1 + S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(9*S^3) + (1744*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2, 2}, -S^2])/(3*S^3) - (2744*(-1 + S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^3) + (1744*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1, 2}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 2, 1}, -S^2])/S^3 - (12928*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 3, 1, 1}, -S^2])/(3*S^3) - (17176*(-1 + S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(9*S^3) + (4240*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1, 2}, -S^2])/(3*S^3) + (816*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 2, 1}, -S^2])/S^3 - (1232*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2, 1, 1}, -S^2])/S^3 - (4480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1, 1, 1}, -S^2])/S^3 - (112*(-459 - 447*S^2 + 6*S^4 + 457*S^6 + 445*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (12608*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1, 2}, -S^2])/(3*S^3) + (7232*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 2, 1}, -S^2])/(3*S^3) - (11200*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2, 1, 1}, -S^2])/(3*S^3) - (40576*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1, 1, 1}, -S^2])/(3*S^3) - (27264*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1, 1, 1}, -S^2])/S^3 + ((-368*Pi^2*(1 + S^6))/(9*S^3) - (80*(-178 - 225*S^2 + 225*S^4 + 178*S^6))/(27*S^3))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (32*(47 + 5*S^2 - 21*S^4 - 40*S^6 + 2*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(3*S^3) + (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(3*S^3) + (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(3*S^3) + (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(3*S^3) + (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (5312*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (160*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + (2944*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(3*S^3) + (11776*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (29440*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + (19328*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((133*(1 + S^2))/(81*S) + (Pi^2*(22 + 11*S^2 + 21*S^4 - S^6))/(27*S*(1 + S^2)) + (2*S^3*HPL[{0}, S^2]^3)/9 + ((22*Pi^2*(1 + S^6))/(27*S^3) + (259 + 417*S^2 + 417*S^4 + 259*S^6)/(81*S^3))*HPL[{1}, -S^2] + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)) + (56*(1 + S^6)*HPL[{1}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^2*((8 + 4*S^2 + 7*S^4 - S^6)/(9*S*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3)) - (2*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((20*Pi^2*S^3)/27 + (276 + 141*S^2 + 259*S^4)/(81*S) + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) + (28*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3))*Log[T]^6 + ((-16*(1 + S^2))/(27*S) - (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]*((-4*(6 + 3*S^2 + 10*S^4 + 4*S^6))/(27*S*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(9*S^3)))*Log[T]^7 + ((2 + S^2 + 2*S^4)/(9*S*(1 + S^2)) + (2*S^3*HPL[{0}, S^2])/9 + (2*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3))*Log[T]^8 + ((-1167 + 354*S^2 + 1268*S^4)/(162*S) + (Pi^2*(2 + S^2 + 45*S^4 + 43*S^6))/(9*S*(1 + S^2)))*Zeta[3]^2 + HPL[{2, 1, 1, 1, 1}, -S^2]*((2*(-5557 - 987*S^2 + 987*S^4 + 5557*S^6))/(27*S^3) + (4*Pi^2*(131 + 389*S^2 + 129*S^4 + 266*S^6 + 8*S^8))/(27*S^3*(1 + S^2)) - (736*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4, 1, 1}, -S^2]*((-42314 - 14553*S^2 + 4005*S^4 + 43682*S^6)/(162*S^3) + (Pi^2*(441 + 1101*S^2 + 330*S^4 + 769*S^6 + 109*S^8))/(27*S^3*(1 + S^2)) - (680*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 2, 1}, -S^2]*((-7513 - 147*S^2 + 147*S^4 + 7513*S^6)/(108*S^3) + (Pi^2*(169 + 445*S^2 + 138*S^4 + 192*S^6 - 84*S^8))/(27*S^3*(1 + S^2)) - (196*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{6}, -S^2]*((-34090 - 42207*S^2 + 76503*S^4 + 71682*S^6)/(648*S^3) + (Pi^2*(-2260 - 1666*S^2 + 297*S^4 + 1721*S^6 + 1127*S^8))/(108*S^3*(1 + S^2)) - (226*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (140*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]^2*((5132 + 2436*S^2 + 1257*S^4 + 7909*S^6)/(648*S^3) + (Pi^2*(159 + 147*S^2 - 6*S^4 + 41*S^6 + 53*S^8))/(108*S^3*(1 + S^2)) + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^3*((-12044 + 9*S^2 - 9*S^4 + 12044*S^6)/(3888*S^3) + (Pi^2*(92 + 230*S^2 + 69*S^4 + 105*S^6 - 33*S^8))/(324*S^3*(1 + S^2)) - (26*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (26*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{4, 2}, -S^2]*((-1699 + 3537*S^2 + 2619*S^4 + 1399*S^6)/(324*S^3) + (Pi^2*(-23 + 13*S^2 + 18*S^4 + 17*S^6 - 19*S^8))/(36*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]^6*(((1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(729*S^3) + (Pi^2*(35 + 167*S^2 + 66*S^4 + 185*S^6 + 53*S^8))/(162*S^3*(1 + S^2)) + (2*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(27*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{5, 1}, -S^2]*((6323 + 31200*S^2 - 12297*S^4 - 17914*S^6)/(324*S^3) + (Pi^2*(419 + 575*S^2 + 78*S^4 - 379*S^6 - 535*S^8))/(54*S^3*(1 + S^2)) + (80*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]^2*((-5*(1 + S^2)*(2912 - 407*S^2 + 2912*S^4))/(324*S^3) + (Pi^2*(-128 - 530*S^2 - 201*S^4 - 487*S^6 - 85*S^8))/(27*S^3*(1 + S^2)) + (80*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 1, 1, 1}, -S^2]*((5443 + 1866*S^2 - 108*S^4 - 5671*S^6)/(27*S^3) - (4*Pi^2*(102 + 186*S^2 + 42*S^4 + 137*S^6 + 53*S^8))/(27*S^3*(1 + S^2)) + (144*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{3, 1, 2}, -S^2]*((1549 - 459*S^2 + 459*S^4 - 1549*S^6)/(324*S^3) + (Pi^2*(-5 - 6*S^6))/(9*S^3) + (4*(1 + S^6)*Zeta[3])/S^3) + HPL[{1}, -S^2]^5*((1849*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(8100*S^3) + (Pi^2*(1 + S^2)*(1547 + 1273*S^2 + 2402*S^4))/(1620*S^3) + ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(7290*S^3) + ((43*Pi^2*(1 + S^6))/(135*S^3) + (19*(-1 - S^2 + S^4 + S^6))/(6*S^3))*HPL[{2}, -S^2] + (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(45*S^3) - (2*(67 + 187*S^2 + 60*S^4 + 133*S^6 + 13*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(45*S^3) - (4*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(45*S^3) - (2*(7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{3, 2}, -S^2]*((119*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(180*S^3) + (Pi^2*(6158 + 10059*S^2 + 2445*S^4 + 847*S^6))/(648*S^3) + (147173 + 750840*S^2 + 95172*S^4 + 213983*S^6)/(3888*S^3) + (376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(3 - 69*S^2 - 36*S^4 - 68*S^6 + 4*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{5}, -S^2]*((109*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(-2177 - 4446*S^2 + 1647*S^4 + 3288*S^6))/(648*S^3) + (-60545 - 82287*S^2 + 104679*S^4 + 106160*S^6)/(1296*S^3) + ((-9 + 111*S^2 + 60*S^4 - 77*S^6 - 197*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (58*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (92*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(115 + 31*S^2 - 42*S^4 - 79*S^6 + 5*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{4, 1}, -S^2]*((308*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (Pi^2*(11985 + 17745*S^2 + 3111*S^4 + 1579*S^6))/(324*S^3) + (363147 + 1301355*S^2 + 47511*S^4 + 177791*S^6)/(1944*S^3) + (1184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(60 - 60*S^2 - 60*S^4 - 73*S^6 + 47*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + ((1 + S^2)*(90289 + 121214*S^2 + 90289*S^4))/(972*S^3) + (Pi^2*(1873 + 3522*S^2 + 5502*S^4 + 3437*S^6))/(162*S^3) - (8*(11 + 125*S^2 + 57*S^4 + 168*S^6 + 54*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((-133*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(45*S^3) + (24149 + 75483*S^2 - 75483*S^4 - 24149*S^6)/(162*S^3) + (Pi^2*(1931 + 2100*S^2 - 5028*S^4 - 3707*S^6))/(81*S^3) + (8*(41 + 299*S^2 + 129*S^4 + 356*S^6 + 98*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((1607*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(921 + 4305*S^2 + 15573*S^4 + 9788*S^6))/(162*S^3) + (36110 + 58865*S^2 + 209831*S^4 + 84408*S^6)/(324*S^3) - (8*(18 + 378*S^2 + 180*S^4 + 505*S^6 + 145*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]^5*((47*Pi^4*S^3)/720 + (Pi^2*(660 + 849*S^2 + 3811*S^4))/(15552*S) + (34080 + 3939*S^2 + 55777*S^4)/(93312*S) + ((4 + 70*S^2 + 33*S^4 + 106*S^6 + 40*S^8)*HPL[{1}, -S^2]^3)/(324*S^3*(1 + S^2)) + (11*(1 + S^6)*HPL[{1}, -S^2]^4)/(216*S^3) + ((Pi^2*(1 + S^6))/(144*S^3) + (294 + 165*S^2 + 354*S^4 + 163*S^6)/(2592*S^3))*HPL[{2}, -S^2] + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(48*S^3) + HPL[{1}, -S^2]^2*((2*Pi^2*(1 + S^6))/(27*S^3) + (33 + 89*S^2 + 335*S^4 + 279*S^6)/(864*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + ((10 + S^6)*HPL[{3}, -S^2])/(72*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(8*S^3) + ((5 - 19*S^2 - 12*S^4 - 56*S^6 - 32*S^8)*HPL[{2, 1}, -S^2])/(108*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(6*S^3) + ((6 + 3*S^2 - S^4 - 7*S^6)*Zeta[3])/(24*S*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(925 - 160*S^2 + 2347*S^4))/(3888*S^3) + (Pi^2*(23 + 119*S^2 + 48*S^4 + 137*S^6 + 41*S^8))/(648*S^3*(1 + S^2)) + ((-1 + 23*S^2 + 12*S^4 + 41*S^6 + 17*S^8)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(4*S^3))) + Log[T]^5*((-841*(1 + S^2))/(243*S) + (Pi^2*(-774 - 837*S^2 - 157*S^4))/(486*S) + ((-259 - 417*S^2 - 417*S^4 - 259*S^6)/(27*S^3) - (22*Pi^2*(1 + S^6))/(9*S^3))*HPL[{1}, -S^2]^2 - (56*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^4)/(9*S^3) + HPL[{0}, S^2]^3*((-11*(6 + 3*S^2 + 8*S^4 + 2*S^6))/(81*S*(1 + S^2)) - (22*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(27*S^3)) + ((157 + 63*S^2 - 63*S^4 - 157*S^6)/(81*S^3) - (8*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2] - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^2*((-270 - 333*S^2 - 157*S^4)/(162*S) + ((-7 - 55*S^2 - 24*S^4 - 73*S^6 - 25*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) - (2*(-125 - 245*S^2 - 60*S^4 - 119*S^6 + S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (28*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + HPL[{0}, S^2]*((-3519 - 1251*S^2 - 3562*S^4)/(243*S) - (2*Pi^2*(96 + 48*S^2 + 149*S^4 + 53*S^6))/(81*S*(1 + S^2)) - (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^3)/(9*S^3) - (4*(4 + 10*S^2 + 3*S^4 + 6*S^6)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-259 - 417*S^2 - 417*S^4 - 259*S^6)/(27*S^3) - (64*Pi^2*(1 + S^6))/(27*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3) - (4*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((-2*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) + (Pi^2*(-35 - 167*S^2 - 66*S^4 - 185*S^6 - 53*S^8))/(27*S^3*(1 + S^2)) - (4*(-1 + S^6)*HPL[{2}, -S^2])/S^3 + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3)) + HPL[{0}, S^2]^4*((Pi^2*(-4044 + 2365*S^2 + 8379*S^4))/(10368*S) + (-422810 + 17452*S^2 + 899343*S^4)/(186624*S) + (Pi^4*(11094 + 5547*S^2 + 72155*S^4 + 61061*S^6))/(155520*S*(1 + S^2)) + ((-5 + 547*S^2 + 276*S^4 + 925*S^6 + 373*S^8)*HPL[{1}, -S^2]^4)/(1296*S^3*(1 + S^2)) + (23*(1 + S^6)*HPL[{1}, -S^2]^5)/(270*S^3) + ((3 + 189*S^2 + 93*S^4 + 230*S^6 + 44*S^8)*HPL[{2}, -S^2]^2)/(864*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((53*Pi^2*(1 + S^6))/(324*S^3) + (-104 + 247*S^2 + 1486*S^4 + 1135*S^6)/(1296*S^3) + (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(108*S^3)) + ((5*Pi^2*(1 + S^6))/(72*S^3) + (-481 - 261*S^2 - 9*S^4 + 119*S^6)/(864*S^3))*HPL[{3}, -S^2] + ((-137 - 113*S^2 + 12*S^4 + 45*S^6 + 21*S^8)*HPL[{4}, -S^2])/(144*S^3*(1 + S^2)) + (13*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(12*S^3) + ((243 + 102*S^2 - 2454*S^4 - 2158*S^6)/(1296*S^3) - (8*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((30 - 156*S^2 - 93*S^4 - 263*S^6 - 77*S^8)*HPL[{3, 1}, -S^2])/(216*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(6*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(6*S^3) + ((-9 + 177*S^2 + 93*S^4 + 242*S^6 + 56*S^8)*HPL[{2, 1, 1}, -S^2])/(108*S^3*(1 + S^2)) + (19*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(18*S^3) + (19*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(6*S^3) - (19*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-807 + 462*S^2 + 106*S^4)*Zeta[3])/(648*S) + HPL[{2}, -S^2]*((-1053 - 288*S^2 + 811*S^4 + 1251*S^6)/(1728*S^3) + (Pi^2*(-279 + 177*S^2 + 228*S^4 + 467*S^6 + 11*S^8))/(2592*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(12*S^3) - (19*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(36*S^3) - (5*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(12*S^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(-5221 + 3979*S^2 + 34046*S^4))/(15552*S^3) + (Pi^2*(-85 + 551*S^2 + 318*S^4 + 1145*S^6 + 509*S^8))/(1296*S^3*(1 + S^2)) + ((-65 + 307*S^2 + 186*S^4 + 685*S^6 + 313*S^8)*HPL[{2}, -S^2])/(432*S^3*(1 + S^2)) - (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(36*S^3) + (7*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(36*S^3)) + HPL[{1}, -S^2]*((1849*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(25920*S^3) + (Pi^2*(1 + S^2)*(-456 + 319*S^2 + 630*S^4))/(1296*S^3) + ((1 + S^2)*(-114907 + 25201*S^2 + 322646*S^4))/(93312*S^3) + ((19*Pi^2*(1 + S^6))/(108*S^3) + (7*(-24 + S^2 + 178*S^4 + 153*S^6))/(864*S^3))*HPL[{2}, -S^2] + (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(144*S^3) + ((-1 + S^6)*HPL[{3}, -S^2])/(8*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(6*S^3) + ((65 - 307*S^2 - 186*S^4 - 685*S^6 - 313*S^8)*HPL[{2, 1}, -S^2])/(216*S^3*(1 + S^2)) - (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(36*S^3) + (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(18*S^3) + ((-179 - 95*S^2 + 42*S^4 + 319*S^6 + 235*S^8)*Zeta[3])/(216*S^3*(1 + S^2)))) + Log[T]^4*((16595*(1 + S^2))/(2916*S) + (Pi^2*(6030 + 7017*S^2 + 5557*S^4))/(1944*S) + (Pi^4*(11094 + 5547*S^2 + 11243*S^4 + 149*S^6))/(9720*S*(1 + S^2)) + (S^3*HPL[{0}, S^2]^5)/12 + ((110*Pi^2*(1 + S^6))/(27*S^3) + (5*(259 + 417*S^2 + 417*S^4 + 259*S^6))/(81*S^3))*HPL[{1}, -S^2]^3 + (70*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)) + (28*(1 + S^6)*HPL[{1}, -S^2]^5)/(9*S^3) + HPL[{0}, S^2]^4*((276 + 138*S^2 + 341*S^4 + 65*S^6)/(648*S*(1 + S^2)) + (23*(1 + S^6)*HPL[{1}, -S^2])/(54*S^3)) + ((139 + 655*S^2 + 258*S^4 + 655*S^6 + 139*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + HPL[{0}, S^2]^3*((5*Pi^2*S^3)/9 + (1428 + 1455*S^2 + 1550*S^4)/(972*S) + ((56 + 386*S^2 + 165*S^4 + 494*S^6 + 164*S^8)*HPL[{1}, -S^2])/(81*S^3*(1 + S^2)) + (55*(1 + S^6)*HPL[{1}, -S^2]^2)/(27*S^3) + (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + ((-4115 - 5622*S^2 - 1122*S^4 - 555*S^6)/(162*S^3) - (67*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3}, -S^2] + (4*(-6 - 48*S^2 - 21*S^4 + 13*S^6 + 55*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-46*Pi^2*(1 + S^6))/(27*S^3) - (10*(-178 - 225*S^2 + 225*S^4 + 178*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((2040 + 3027*S^2 + 5557*S^4)/(648*S) + (Pi^2*(318 + 159*S^2 + 328*S^4 + 10*S^6))/(162*S*(1 + S^2)) + (5*(7 + 55*S^2 + 24*S^4 + 73*S^6 + 25*S^8)*HPL[{1}, -S^2]^2)/(18*S^3*(1 + S^2)) + (40*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((86 + 344*S^2 + 129*S^4 + 311*S^6 + 53*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((53*Pi^2*(1 + S^6))/(27*S^3) + (84 + 245*S^2 + 530*S^4 + 369*S^6)/(36*S^3) + (43*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) - (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (46*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3)) - (4*(47 + 5*S^2 - 21*S^4 - 40*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) + (664*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(9*S^3) - (20*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (368*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (208*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (2*(-1359 - 234*S^2 + 890*S^4)*Zeta[3])/(81*S) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) + (5*Pi^2*(35 + 167*S^2 + 66*S^4 + 185*S^6 + 53*S^8))/(54*S^3*(1 + S^2)) + (10*(-1 + S^6)*HPL[{2}, -S^2])/S^3 - (200*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2}, -S^2]*((-5557 - 987*S^2 + 987*S^4 + 5557*S^6)/(324*S^3) + (Pi^2*(131 + 389*S^2 + 129*S^4 + 266*S^6 + 8*S^8))/(162*S^3*(1 + S^2)) - (92*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (92*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((1849*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (Pi^2*(1 + S^2)*(1547 + 1273*S^2 + 2402*S^4))/(324*S^3) + ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(1458*S^3) + ((95*(-1 + S^2)*(1 + S^2)^2)/(6*S^3) + (43*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3))*HPL[{2}, -S^2] + (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) - (10*(67 + 187*S^2 + 60*S^4 + 133*S^6 + 13*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) - (20*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (10*(7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{0}, S^2]*((47*Pi^4*S^3)/45 + (Pi^2*(5568 + 3570*S^2 + 5435*S^4))/(972*S) + (73878 + 16341*S^2 + 75523*S^4)/(1458*S) + (140*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) + (70*(1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + ((22*Pi^2*(1 + S^6))/(9*S^3) + (2344 + 3735*S^2 + 1800*S^4 + 1349*S^6)/(162*S^3))*HPL[{2}, -S^2] + (43*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{1}, -S^2]^2*((160*Pi^2*(1 + S^6))/(27*S^3) + (5*(259 + 417*S^2 + 417*S^4 + 259*S^6))/(54*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/S^3) - (2*(14 + 10*S^2 - 2*S^4 + 5*S^6 + 9*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (20*(6 + 3*S^2 + 10*S^4 + 4*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (208*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + (14*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((5*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) + (2*Pi^2*(133 + 613*S^2 + 240*S^4 + 667*S^6 + 187*S^8))/(81*S^3*(1 + S^2)) + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)))) + ((5*Pi^2*(-627 + 66*S^2 + 425*S^4))/(162*S) + (-219675 - 7599*S^2 + 152191*S^4)/(972*S))*Zeta[5] + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-19127 + 633*S^2 + 11892*S^4 + 33687*S^6))/(972*S^3) + (-48021 - 11198*S^2 + 11198*S^4 + 48021*S^6)/(162*S^3) + (Pi^4*(892 + 5134*S^2 + 2121*S^4 + 5177*S^6 + 935*S^8))/(1620*S^3*(1 + S^2)) - (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-12*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/S^3 - (2*(543 + 800*S^2 + 176*S^4 + 49*S^6))/(9*S^3))*Zeta[3] - (208*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{4}, -S^2]*((Pi^2*(-5673 - 7078*S^2 + 2786*S^4 + 2585*S^6))/(1296*S^3) + (-1292045 - 1223370*S^2 + 1519650*S^4 + 1235533*S^6)/(23328*S^3) + (Pi^4*(-3723 - 5067*S^2 - 672*S^4 + 1571*S^6 + 2915*S^8))/(6480*S^3*(1 + S^2)) - (245*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((365 + 426*S^2 + 246*S^4 - 607*S^6)/(54*S^3) - (4*Pi^2*(1 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + ((327 + 291*S^2 - 18*S^4 + 119*S^6 + 155*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (14*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 - (2*(145 + 229*S^2 + 42*S^4 + 105*S^6 + 21*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (136*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-32*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (36 + 156*S^2 - 132*S^4 - 277*S^6)/(54*S^3))*Zeta[3] - (110*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]^4*((Pi^2*(1 + S^2)*(40091 + 19300*S^2 + 66605*S^4))/(11664*S^3) + ((1 + S^2)*(1244177 + 139966*S^2 + 1244177*S^4))/(34992*S^3) + (Pi^4*(4399 + 26587*S^2 + 11094*S^4 + 32581*S^6 + 10393*S^8))/(19440*S^3*(1 + S^2)) + (43*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((-3041 - 4290*S^2 - 1725*S^4 - 476*S^6)/(162*S^3) - (53*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3}, -S^2] + ((-137 - 305*S^2 - 84*S^4 - 143*S^6 + 25*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-43*Pi^2*(1 + S^6))/(27*S^3) - (95*(-1 - S^2 + S^4 + S^6))/(6*S^3))*HPL[{2, 1}, -S^2] - (2*(-163 - 247*S^2 - 42*S^4 + 23*S^6 + 107*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) + (572*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(9*S^3) + (20*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (632*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((-49*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(1043 + 307*S^2 + 188*S^4))/(54*S^3))*Zeta[3] + HPL[{2}, -S^2]*((491*(-1 + S^2)*(1 + S^2)^2)/(36*S^3) + (Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(162*S^3*(1 + S^2)) - (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (86*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (110*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]^2*(((1 + S^2)*(4532 - 3891*S^2 + 4532*S^4))/(432*S^3) + (Pi^2*(15639 + 18843*S^2 + 18834*S^4 + 27683*S^6))/(7776*S^3) + (Pi^4*(2324 + 10214*S^2 + 3945*S^4 + 9737*S^6 + 1847*S^8))/(12960*S^3*(1 + S^2)) + ((-3379 - 5121*S^2 - 1161*S^4 - 251*S^6)/(216*S^3) - (4*Pi^2*(1 + S^6))/(3*S^3))*HPL[{3}, -S^2] + ((-239 - 287*S^2 - 24*S^4 - 17*S^6 + 31*S^8)*HPL[{4}, -S^2])/(36*S^3*(1 + S^2)) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(2*S^3) + ((391 + 495*S^2 - 495*S^4 - 391*S^6)/(27*S^3) - (13*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2] + ((-17 - 5*S^2 + 6*S^4 + 81*S^6 + 69*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (152*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (86*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (212*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((-7*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(6*S^3) + (-1679 - 2334*S^2 - 354*S^4 - 115*S^6)/(108*S^3))*Zeta[3] - (6*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/S^3) + HPL[{3, 1}, -S^2]*((871442 + 164529*S^2 - 238599*S^4 - 857314*S^6)/(5832*S^3) + (Pi^2*(17777 + 2376*S^2 - 9243*S^4 - 34423*S^6))/(1944*S^3) + (Pi^4*(-1524 - 4710*S^2 - 1593*S^4 - 5381*S^6 - 2195*S^8))/(3240*S^3*(1 + S^2)) - (60*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 - (680*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (8*(54 + 312*S^2 + 129*S^4 + 343*S^6 + 85*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (992*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 + (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((70*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (1682 + 2280*S^2 + 588*S^4 + 301*S^6)/(27*S^3))*Zeta[3] + (152*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + Zeta[3]*((Pi^4*(-8949 + 942*S^2 + 4489*S^4))/(4860*S) + (Pi^2*(-321864 - 22776*S^2 + 126083*S^4))/(11664*S) + (-1089906 - 27937*S^2 + 518557*S^4)/(3888*S) + (16*(-12 - 6*S^2 + 47*S^4 + 59*S^6)*Zeta[5])/(9*S*(1 + S^2))) + HPL[{3}, -S^2]*((-6067*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(136080*S^3) + (Pi^4*(-50232 - 55185*S^2 - 6369*S^4 - 1202*S^6))/(38880*S^3) + (Pi^2*(-240668 - 520335*S^2 + 25443*S^4 + 28445*S^6))/(23328*S^3) + (-11670346 - 27754221*S^2 + 10476663*S^4 + 6997706*S^6)/(139968*S^3) + ((8*Pi^2*(1 + S^6))/(3*S^3) + (-215 + 444*S^2 + 120*S^4 + 2485*S^6)/(108*S^3))*HPL[{4}, -S^2] + ((115 + 45*S^2 - 35*S^4 + 14*S^6 + 84*S^8)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)) + (251*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + (100*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((70*Pi^2*(1 + S^6))/(9*S^3) + (3659 + 4623*S^2 + 1113*S^4 + 1219*S^6)/(54*S^3))*HPL[{3, 1}, -S^2] + (2*(-67 - 55*S^2 + 6*S^4 + 32*S^6 + 20*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (2*(145 + 187*S^2 + 21*S^4 + 200*S^6 + 158*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/S^3 + ((-3097 - 4863*S^2 - 993*S^4 - 455*S^6)/(27*S^3) - (100*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] - (8*(21 + 165*S^2 + 72*S^4 + 208*S^6 + 64*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(12 + 432*S^2 + 210*S^4 + 589*S^6 + 169*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^3 - (196*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (6448*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (8*(11 + 269*S^2 + 129*S^4 + 386*S^6 + 128*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (464*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-457 - 156*S^2 + 78*S^4 + 1983*S^6)/(324*S^3) + (2*Pi^2*(23 + 5*S^2 - 9*S^4 - 9*S^6 + 9*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/S^3 + HPL[{2, 1}, -S^2]*((28767 + 11697*S^2 + 13353*S^4 + 353*S^6)/(324*S^3) + (2*Pi^2*(5 + 143*S^2 + 69*S^4 + 203*S^6 + 65*S^8))/(27*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + (2*(85 + 37*S^2 - 24*S^4 - 33*S^6 + 15*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-881*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(4536*S^3) + (518557 + 1061969*S^2 - 1061969*S^4 - 518557*S^6)/(3888*S^3) + (Pi^2*(85043 + 252498*S^2 - 464001*S^4 - 175332*S^6))/(11664*S^3) + (Pi^4*(18447 + 16908*S^2 - 65532*S^4 - 49396*S^6))/(19440*S^3) + ((152*Pi^2*(1 + S^6))/(9*S^3) + (511 + 961*S^2 + 991*S^4 + 673*S^6)/(9*S^3))*HPL[{3, 1}, -S^2] - (4*(36 + 306*S^2 + 135*S^4 + 392*S^6 + 122*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (2*(107 + 1751*S^2 + 822*S^4 + 2391*S^6 + 747*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 + (12*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/S^3 + ((32*Pi^2*(1 + S^6))/S^3 + (32*(37 + 61*S^2 + 61*S^4 + 37*S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] - (344*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (8*(-140 - 398*S^2 - 129*S^4 - 257*S^6 + S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^3 - (392*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (1232*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (8*(139 + 655*S^2 + 258*S^4 + 655*S^6 + 139*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((5*(2843 + 1311*S^2 + 1194*S^4 + 69*S^6))/(162*S^3) + (Pi^2*(13 + 295*S^2 + 141*S^4 + 380*S^6 + 98*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + (2*(43 + 301*S^2 + 129*S^4 + 288*S^6 + 30*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((8699*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(40824*S^3) + (Pi^4*(1 + S^2)*(34511 + 43567*S^2 + 92552*S^4))/(58320*S^3) + (Pi^2*(1 + S^2)*(314575 + 94913*S^2 + 571984*S^4))/(34992*S^3) + (11*(1 + S^2)*(951775 + 64742*S^2 + 951775*S^4))/(104976*S^3) + ((67*Pi^2*(1 + S^6))/(27*S^3) + (1571 + 2577*S^2 + 2577*S^4 + 1571*S^6)/(162*S^3))*HPL[{2}, -S^2]^2 + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(9*S^3) + ((-28*Pi^2*(1 + S^6))/(27*S^3) + (-811 - 1135*S^2 - 13*S^4 + 311*S^6)/(54*S^3))*HPL[{4}, -S^2] + (2*(-59 - 83*S^2 - 12*S^4 + 19*S^6 + 43*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (70*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(9*S^3) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-56*Pi^2*(1 + S^6))/(27*S^3) - (2*(-490 - 571*S^2 + 284*S^4 + 365*S^6))/(27*S^3))*HPL[{3, 1}, -S^2] + (8*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + (52*(71 + 203*S^2 + 66*S^4 + 149*S^6 + 17*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 + (176*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(9*S^3) + ((172*Pi^2*(1 + S^6))/(27*S^3) + (190*(-1 - S^2 + S^4 + S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (688*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(181 + 1129*S^2 + 474*S^4 + 1399*S^6 + 451*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (80*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + (224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (-((1 + S^2)*(3461 + 540*S^2 + 515*S^4))/(54*S^3) + (Pi^2*(-367 - 955*S^2 - 294*S^4 - 613*S^6 - 25*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(9*S^3) + HPL[{3}, -S^2]*(-((1 + S^2)*(28099 + 7448*S^2 + 1585*S^4))/(486*S^3) + (Pi^2*(-383 - 1019*S^2 - 318*S^4 - 677*S^6 - 41*S^8))/(81*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-491*(-1 + S^2)*(1 + S^2)^2)/(9*S^3) - (2*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(81*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((28601*(-1 + S^2)*(1 + S^2)^2)/(648*S^3) + (707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (Pi^2*(1 + S^2)*(-1271 + 503*S^2 + 2842*S^4))/(486*S^3) - (4*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) - (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (4*(140 + 398*S^2 + 129*S^4 + 290*S^6 + 32*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + (2*(-481 - 1141*S^2 - 330*S^4 - 619*S^6 + 41*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^3*((6023*Pi^6*S^3)/34020 + (Pi^4*(40332 + 50295*S^2 + 161116*S^4))/(233280*S) + (Pi^2*(88984 + 17518*S^2 + 163629*S^4))/(46656*S) + (1453428 + 71527*S^2 + 2066970*S^4)/(93312*S) + ((56 + 386*S^2 + 165*S^4 + 494*S^6 + 164*S^8)*HPL[{1}, -S^2]^5)/(405*S^3*(1 + S^2)) + (11*(1 + S^6)*HPL[{1}, -S^2]^6)/(81*S^3) + ((11*Pi^2*(1 + S^6))/(72*S^3) + (467 + 1020*S^2 + 993*S^4 + 860*S^6)/(1296*S^3))*HPL[{2}, -S^2]^2 + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(36*S^3) + HPL[{1}, -S^2]^4*((55*Pi^2*(1 + S^6))/(162*S^3) + (1087 + 2208*S^2 + 4287*S^4 + 3166*S^6)/(1944*S^3) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(6*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((-43*Pi^2*(1 + S^6))/(108*S^3) + (1397 + 1062*S^2 + 522*S^4 + 462*S^6)/(648*S^3))*HPL[{4}, -S^2] + ((103 + 85*S^2 - 9*S^4 - 23*S^6 - 5*S^8)*HPL[{5}, -S^2])/(18*S^3*(1 + S^2)) - (125*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(18*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/S^3 + ((-811 - 1461*S^2 - 1164*S^4 - 1117*S^6)/(324*S^3) - (11*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3, 1}, -S^2] + ((-43 - 7*S^2 + 18*S^4 + 26*S^6 - 10*S^8)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)) + ((-209 - 137*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{4, 1}, -S^2])/(54*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/(18*S^3) + (3*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/S^3 + ((4*Pi^2*(1 + S^6))/(3*S^3) + (761 + 1269*S^2 + 1269*S^4 + 1087*S^6)/(162*S^3))*HPL[{2, 1, 1}, -S^2] + ((-19 + 209*S^2 + 114*S^4 + 421*S^6 + 193*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-41 + 679*S^2 + 360*S^4 + 1285*S^6 + 565*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(9*S^3) + (29*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (94*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (2*(-5 + 85*S^2 + 45*S^4 + 166*S^6 + 76*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (88*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((1332 - 195*S^2 + 1513*S^4)/(648*S) - (49*Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(324*S*(1 + S^2)))*Zeta[3] + (8*S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((-6229 - 5442*S^2 - 25206*S^4 - 13608*S^6)/(1944*S^3) + (Pi^2*(65 - 445*S^2 - 255*S^4 - 1058*S^6 - 548*S^8))/(324*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^3*(((1 + S^2)*(1753 + 772*S^2 + 5173*S^4))/(972*S^3) + (Pi^2*(38 + 368*S^2 + 165*S^4 + 512*S^6 + 182*S^8))/(243*S^3*(1 + S^2)) + (5*(1 + 7*S^2 + 3*S^4 + 9*S^6 + 3*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) + HPL[{3}, -S^2]*((1419 + 594*S^2 + 666*S^4 + 1426*S^6)/(648*S^3) + (Pi^2*(158 + 176*S^2 + 9*S^4 + 26*S^6 + 8*S^8))/(324*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2}, -S^2]*((37*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(720*S^3) + (Pi^2*(2231 + 2094*S^2 + 3039*S^4 + 1902*S^6))/(3888*S^3) + (88245 + 99573*S^2 + 61197*S^4 + 176093*S^6)/(23328*S^3) + ((7 + S^2 - 3*S^4 - 6*S^6)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((19 - 209*S^2 - 114*S^4 - 421*S^6 - 193*S^8)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)) - (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + ((-21 + 3*S^2 + 12*S^4 + 17*S^6 - 7*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) + HPL[{1}, -S^2]^2*((937*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(3240*S^3) + (Pi^2*(1 + S^2)*(1582 + 1961*S^2 + 7351*S^4))/(3888*S^3) + ((1 + S^2)*(102073 + 15179*S^2 + 289660*S^4))/(23328*S^3) + ((85*Pi^2*(1 + S^6))/(108*S^3) + (617 + 990*S^2 + 1845*S^4 + 1472*S^6)/(324*S^3))*HPL[{2}, -S^2] + (19*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(18*S^3) + ((2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (5*(1 + 7*S^2 + 3*S^4 + 9*S^6 + 3*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + ((-11 + 37*S^2 + 24*S^4 + 91*S^6 + 43*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) - (55*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[5])/(54*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(14509 + 716*S^2 + 38989*S^4))/(11664*S^3) + ((1 + S^2)*(202248 - 8251*S^2 + 463041*S^4))/(23328*S^3) + (Pi^4*(1181 + 6803*S^2 + 2811*S^4 + 8189*S^6 + 2567*S^8))/(9720*S^3*(1 + S^2)) + ((20 + 134*S^2 + 57*S^4 + 170*S^6 + 56*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((Pi^2*(1 + S^6))/(18*S^3) + (40 + 37*S^2 + 22*S^4 + 25*S^6)/(36*S^3))*HPL[{3}, -S^2] + ((2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((-617 - 990*S^2 - 1845*S^4 - 1472*S^6)/(162*S^3) - (85*Pi^2*(1 + S^6))/(54*S^3))*HPL[{2, 1}, -S^2] - (4*(13 + 79*S^2 + 33*S^4 + 97*S^6 + 31*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (10*(1 + 7*S^2 + 3*S^4 + 9*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((49*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + ((1 + S^2)*(24 - 43*S^2 + 135*S^4))/(54*S^3))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(6197 + 1900*S^2 + 15035*S^4))/(1944*S^3) + (5*Pi^2*(7 + 109*S^2 + 51*S^4 + 163*S^6 + 61*S^8))/(324*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (38*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (55*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + Log[T]^3*((-64601*(1 + S^2))/(8748*S) + (Pi^2*(-10721 - 15881*S^2 - 30827*S^4))/(2916*S) + (Pi^4*(-37482 - 50595*S^2 - 19858*S^4))/(29160*S) + ((-110*Pi^2*(1 + S^6))/(27*S^3) - (5*(259 + 417*S^2 + 417*S^4 + 259*S^6))/(81*S^3))*HPL[{1}, -S^2]^4 - (56*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^5)/(27*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^6)/(27*S^3) + HPL[{0}, S^2]^5*((-11*(6 + 3*S^2 + 8*S^4 + 2*S^6))/(324*S*(1 + S^2)) - (11*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(54*S^3)) + ((-62*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(683 + 430*S^2 + 683*S^4))/(81*S^3))*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^4*((-402 - 1563*S^2 - 1316*S^4)/(1944*S) + ((5 - 547*S^2 - 276*S^4 - 925*S^6 - 373*S^8)*HPL[{1}, -S^2])/(324*S^3*(1 + S^2)) - (23*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(27*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) - (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(9*S^3) + ((396 + 1833*S^2 - 165*S^4 - 1132*S^6)*HPL[{4}, -S^2])/(81*S^3) - (2*(-65 - 89*S^2 - 12*S^4 - 19*S^6 + 5*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (320*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^3*((-1789 - 1258*S^2 - 3359*S^4)/(486*S) - (55*Pi^2*(6 + 3*S^2 + 8*S^4 + 2*S^6))/(243*S*(1 + S^2)) - (2*(56 + 386*S^2 + 165*S^4 + 494*S^6 + 164*S^8)*HPL[{1}, -S^2]^2)/(81*S^3*(1 + S^2)) - (220*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^3)/(81*S^3) + ((-35 - 125*S^2 - 45*S^4 - 104*S^6 - 14*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-1087 - 2208*S^2 - 4287*S^4 - 3166*S^6)/(486*S^3) - (110*Pi^2*(1 + S^6))/(81*S^3) - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(27*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3)) + ((92*Pi^2*(1 + S^6))/(27*S^3) + (2*(-601 - 732*S^2 - 102*S^4 + 969*S^6))/(81*S^3))*HPL[{3, 1}, -S^2] + (4*(-499 - 1015*S^2 - 258*S^4 - 427*S^6 + 89*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-878 - 1736*S^2 - 429*S^4 - 805*S^6 + 53*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-160*Pi^2*(1 + S^6))/(27*S^3) - (20*(-157 - 63*S^2 + 63*S^4 + 157*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] - (8*(205 + 721*S^2 + 258*S^4 + 721*S^6 + 205*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(-5 + 469*S^2 + 237*S^4 + 784*S^6 + 310*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (560*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((9054 + 1203*S^2 - 3281*S^4)/(81*S) - (98*Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(81*S*(1 + S^2)))*Zeta[3] + HPL[{2, 1}, -S^2]*((-3281 - 7851*S^2 + 7851*S^4 + 3281*S^6)/(81*S^3) + (2*Pi^2*(-391 - 133*S^2 + 129*S^4 + 854*S^6 + 596*S^8))/(81*S^3*(1 + S^2)) - (320*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((25309 + 52971*S^2 + 5865*S^4 + 5623*S^6)/(486*S^3) + (2*Pi^2*(119 + 225*S^2 + 53*S^4 + 109*S^6 + 3*S^8))/(27*S^3*(1 + S^2)) - (320*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^3*((-20*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(729*S^3) - (10*Pi^2*(35 + 167*S^2 + 66*S^4 + 185*S^6 + 53*S^8))/(81*S^3*(1 + S^2)) - (40*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3) + (800*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(27*S^3) + (80*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^2*((-1849*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) - (Pi^2*(1 + S^2)*(1547 + 1273*S^2 + 2402*S^4))/(162*S^3) - ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(729*S^3) + ((-86*Pi^2*(1 + S^6))/(27*S^3) - (95*(-1 - S^2 + S^4 + S^6))/(3*S^3))*HPL[{2}, -S^2] - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + (20*(67 + 187*S^2 + 60*S^4 + 133*S^6 + 13*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (112*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + (40*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (112*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) + (20*(7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((-154*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (30827 + 5160*S^2 - 5160*S^4 - 30827*S^6)/(486*S^3) + (Pi^2*(611 - 564*S^2 - 1662*S^4 - 1977*S^6))/(486*S^3) - (4*(-251 - 509*S^2 - 129*S^4 - 212*S^6 + 46*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (4*(205 + 721*S^2 + 258*S^4 + 721*S^6 + 205*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (320*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (4*(-239 - 497*S^2 - 129*S^4 - 224*S^6 + 34*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^2*((-2311 - 7471*S^2 - 30827*S^4)/(972*S) + (Pi^2*(-1752 - 3228*S^2 - 2101*S^4))/(972*S) - (10*(7 + 55*S^2 + 24*S^4 + 73*S^6 + 25*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^4)/(9*S^3) + ((-174 - 879*S^2 - 1347*S^4 - 1192*S^6)/(162*S^3) - (32*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2] - (22*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{1}, -S^2]^2*((-84 - 245*S^2 - 530*S^4 - 369*S^6)/(18*S^3) - (106*Pi^2*(1 + S^6))/(27*S^3) - (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + ((89 + 125*S^2 + 18*S^4 + 59*S^6 + 23*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-76 + 182*S^2 + 129*S^4 + 539*S^6 + 281*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (92*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (8*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(4471 + 7220*S^2 + 30985*S^4))/(972*S^3) - (2*Pi^2*(25 + 343*S^2 + 159*S^4 + 505*S^6 + 187*S^8))/(81*S^3*(1 + S^2)) - (2*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + HPL[{0}, S^2]*((-1223472 - 160671*S^2 - 1244177*S^4)/(8748*S) + (Pi^2*(-22962 - 10029*S^2 - 27887*S^4))/(1458*S) + (Pi^4*(-5622 - 2811*S^2 - 8369*S^4 - 2747*S^6))/(2430*S*(1 + S^2)) - (140*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^5)/(9*S^3) + ((-337 - 853*S^2 - 258*S^4 - 523*S^6 - 7*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-640*Pi^2*(1 + S^6))/(81*S^3) - (10*(259 + 417*S^2 + 417*S^4 + 259*S^6))/(81*S^3) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + ((2*Pi^2*(1 + S^6))/(9*S^3) + (106 - 87*S^2 - 267*S^4 + 86*S^6)/(81*S^3))*HPL[{3}, -S^2] - (2*(51 + 135*S^2 + 42*S^4 + 199*S^6 + 115*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((92*Pi^2*(1 + S^6))/(9*S^3) + (2*(1349 + 1800*S^2 + 3735*S^4 + 2344*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] + (4*(437 + 977*S^2 + 270*S^4 + 617*S^6 + 77*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(9*S^3) - (80*(4 + 10*S^2 + 3*S^4 + 6*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (1984*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 - (2*(-276 - 141*S^2 + 184*S^4)*Zeta[3])/(81*S) + HPL[{2}, -S^2]*((-2413 - 5508*S^2 - 2076*S^4 - 3551*S^6)/(81*S^3) + (Pi^2*(-155 - 425*S^2 - 135*S^4 - 284*S^6 - 14*S^8))/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^2*((-10*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) - (4*Pi^2*(133 + 613*S^2 + 240*S^4 + 667*S^6 + 187*S^8))/(81*S^3*(1 + S^2)) - (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 + (56*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((-937*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) - (Pi^2*(1 + S^2)*(4972 + 3491*S^2 + 7051*S^4))/(486*S^3) - ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(729*S^3) + ((-10*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/S^3 - ((1 + S^2)*(1231 + 614*S^2 + 1231*S^4))/(27*S^3))*HPL[{2}, -S^2] - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) - (16*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + (80*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + (56*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*Zeta[3])/(27*S^3*(1 + S^2)))) - (220*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[5])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(40091 + 19300*S^2 + 66605*S^4))/(2916*S^3) - ((1 + S^2)*(1244177 + 139966*S^2 + 1244177*S^4))/(8748*S^3) + (Pi^4*(-4399 - 26587*S^2 - 11094*S^4 - 32581*S^6 - 10393*S^8))/(4860*S^3*(1 + S^2)) - (172*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((212*Pi^2*(1 + S^6))/(27*S^3) + (2*(3041 + 4290*S^2 + 1725*S^4 + 476*S^6))/(81*S^3))*HPL[{3}, -S^2] - (4*(-137 - 305*S^2 - 84*S^4 - 143*S^6 + 25*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((172*Pi^2*(1 + S^6))/(27*S^3) + (190*(-1 - S^2 + S^4 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (8*(-163 - 247*S^2 - 42*S^4 + 23*S^6 + 107*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) - (2288*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(9*S^3) - (80*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (2528*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((196*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2*(1 + S^2)*(1043 + 307*S^2 + 188*S^4))/(27*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-491*(-1 + S^2)*(1 + S^2)^2)/(9*S^3) - (2*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(81*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (440*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + HPL[{0}, S^2]^2*((Pi^4*(-84704 + 86077*S^2 + 260238*S^4))/(155520*S) + (Pi^2*(-488732 + 85906*S^2 + 1475595*S^4))/(93312*S) + (-29966260 + 947471*S^2 + 50699034*S^4)/(559872*S) + (Pi^6*(17398 + 8699*S^2 + 80847*S^4 + 63449*S^6))/(108864*S*(1 + S^2)) + ((7 + 55*S^2 + 24*S^4 + 73*S^6 + 25*S^8)*HPL[{1}, -S^2]^6)/(54*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2]^7)/(63*S^3) + ((49 + 187*S^2 + 69*S^4 + 148*S^6 + 10*S^8)*HPL[{2}, -S^2]^3)/(108*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((53*Pi^2*(1 + S^6))/(135*S^3) + (84 + 245*S^2 + 530*S^4 + 369*S^6)/(180*S^3) + (43*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(45*S^3)) + ((57 + 21*S^2 - 18*S^4 - 29*S^6 + 7*S^8)*HPL[{3}, -S^2]^2)/(36*S^3*(1 + S^2)) + ((85*Pi^2*(1 + S^6))/(36*S^3) + (-1108 - 1764*S^2 + 540*S^4 + 1673*S^6)/(216*S^3))*HPL[{5}, -S^2] + ((-245 - 181*S^2 + 32*S^4 + 161*S^6 + 97*S^8)*HPL[{6}, -S^2])/(6*S^3*(1 + S^2)) + (275*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/(6*S^3) + ((-117 - 405*S^2 - 144*S^4 - 319*S^6 - 31*S^8)*HPL[{2, 1}, -S^2]^2)/(18*S^3*(1 + S^2)) + ((17*Pi^2*(1 + S^6))/(36*S^3) + (-178 + 468*S^2 + 324*S^4 + 79*S^6)/(216*S^3))*HPL[{3, 2}, -S^2] + ((Pi^2*(1 + S^6))/(3*S^3) + (219 + 528*S^2 - 24*S^4 + 5*S^6)/(36*S^3))*HPL[{4, 1}, -S^2] + ((-1 + S^2)*(1 + S^2 + S^4)*HPL[{4, 2}, -S^2])/(2*S^3) - (26*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/(3*S^3) + ((146 + 92*S^2 - 27*S^4 - 104*S^6 - 50*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (51*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/(2*S^3) - (214*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/(3*S^3) + ((5*Pi^2*(1 + S^6))/S^3 + (97 + 594*S^2 + 2574*S^4 + 1661*S^6)/(54*S^3))*HPL[{2, 2, 1}, -S^2] + ((128*Pi^2*(1 + S^6))/(9*S^3) + (-292 + 1143*S^2 + 7911*S^4 + 5015*S^6)/(54*S^3))*HPL[{3, 1, 1}, -S^2] + ((-4 - 7*S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + ((86 + 362*S^2 + 138*S^4 + 275*S^6 - S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/(6*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^3) + ((69 + 345*S^2 + 138*S^4 + 325*S^6 + 49*S^8)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (166*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((151 - 150*S^2 - 2778*S^4 - 1927*S^6)/(27*S^3) - (28*Pi^2*(1 + S^6))/(3*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) - (4*(55 + 181*S^2 + 63*S^4 + 177*S^6 + 51*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (322*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (322*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (634*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^3 + (4*(86 + 344*S^2 + 129*S^4 + 311*S^6 + 53*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (208*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (208*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (1096*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) - (368*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(-1035 + 486*S^2 + 265*S^4))/(324*S) + (-73734 - 1095*S^2 + 53636*S^4)/(3888*S))*Zeta[3] + ((2 + S^2 + 69*S^4 + 67*S^6)*Zeta[3]^2)/(6*S*(1 + S^2)) + HPL[{4}, -S^2]*((-10837 - 6654*S^2 + 4326*S^4 + 205*S^6)/(1296*S^3) + (Pi^2*(-83 - 71*S^2 + 6*S^4 + 37*S^6 + 25*S^8))/(36*S^3*(1 + S^2)) - (14*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (25*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((-2456 + 3594*S^2 + 8931*S^4 + 17016*S^6)/(324*S^3) + (Pi^2*(77 + 521*S^2 + 222*S^4 + 553*S^6 + 109*S^8))/(54*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^4*(((1 + S^2)*(4471 + 7220*S^2 + 30985*S^4))/(3888*S^3) + (Pi^2*(25 + 343*S^2 + 159*S^4 + 505*S^6 + 187*S^8))/(162*S^3*(1 + S^2)) + ((5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (43*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((1079 + 6318*S^2 + 6309*S^4 + 13123*S^6)/(2592*S^3) + (Pi^2*(40 + 198*S^2 + 79*S^4 + 183*S^6 + 25*S^8))/(144*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(6*S^3) - (13*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(6*S^3)) + HPL[{3, 1}, -S^2]*((1448 - 3222*S^2 - 8919*S^4 - 17410*S^6)/(648*S^3) + (Pi^2*(-80 - 518*S^2 - 219*S^4 - 617*S^6 - 179*S^8))/(108*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-343*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + (12596 + 26049*S^2 - 237552*S^4 - 102885*S^6)/(3888*S^3) + (Pi^2*(394 - 48*S^2 - 5232*S^4 - 4085*S^6))/(648*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 + (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(-7 - S^2 + 3*S^4 + 6*S^6)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((59*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(720*S^3) + (Pi^2*(-2026 - 1422*S^2 + 162*S^4 + 389*S^6))/(1296*S^3) + (-78131 - 62421*S^2 + 30459*S^4 + 46088*S^6)/(7776*S^3) + (13*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((-1 + 17*S^2 + 9*S^4 + 20*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((31 + 13*S^2 - 9*S^4 - 17*S^6 + S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((359*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(1 + S^2)*(74 + 417*S^2 + 1121*S^4))/(324*S^3) + ((1 + S^2)*(4161 + 12043*S^2 + 89964*S^4))/(3888*S^3) + ((37*Pi^2*(1 + S^6))/(27*S^3) + (23 + 1029*S^2 + 4125*S^4 + 3119*S^6)/(324*S^3))*HPL[{2}, -S^2] + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + (2*(-8 - 14*S^2 - 3*S^4 - 2*S^6 + 4*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (2*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(-250 + 3733*S^2 + 21677*S^4))/(2592*S^3) + ((1 + S^2)*(-83671 + 99511*S^2 + 1146314*S^4))/(23328*S^3) + (Pi^4*(-269 + 8347*S^2 + 4308*S^4 + 14629*S^6 + 6013*S^8))/(6480*S^3*(1 + S^2)) + ((17 + 113*S^2 + 48*S^4 + 143*S^6 + 47*S^8)*HPL[{2}, -S^2]^2)/(12*S^3*(1 + S^2)) + ((Pi^2*(-1 - S^6))/(6*S^3) + (-48 - 59*S^2 + 18*S^4 + 29*S^6)/(12*S^3))*HPL[{3}, -S^2] + (5*(-1 + S^6)*HPL[{4}, -S^2])/(2*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((-23 - 1029*S^2 - 4125*S^4 - 3119*S^6)/(108*S^3) - (37*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2] + ((-1 - 85*S^2 - 42*S^4 - 139*S^6 - 55*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 + (6*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 + (2*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^3 + (92*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(6*S^3) + ((1 + S^2)*(-199 - 30*S^2 + 77*S^4))/(36*S^3))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-2729 + 5624*S^2 + 30193*S^4))/(1296*S^3) + (Pi^2*(-55 + 833*S^2 + 444*S^4 + 1535*S^6 + 647*S^8))/(216*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/S^3 - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + ((-2448 + 963*S^2 + 1376*S^4)*Zeta[5])/(108*S) + HPL[{2}, -S^2]*((-7101 - 3647*S^2 + 4288*S^4 + 11633*S^6)/(432*S^3) + (Pi^2*(-11933 + 1002*S^2 + 16230*S^4 + 28275*S^6))/(7776*S^3) + (Pi^4*(-959 + 1879*S^2 + 1419*S^4 + 3346*S^6 + 508*S^8))/(6480*S^3*(1 + S^2)) + ((10 - 117*S^2 - 81*S^4 - 67*S^6)/(108*S^3) - (5*Pi^2*(1 + S^6))/(18*S^3))*HPL[{3}, -S^2] + ((-57 - 21*S^2 + 18*S^4 + 29*S^6 - 7*S^8)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)) - (13*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-97 - 594*S^2 - 2574*S^4 - 1661*S^6)/(108*S^3) - (5*Pi^2*(1 + S^6))/(2*S^3))*HPL[{2, 1}, -S^2] - (2*(8 + 34*S^2 + 13*S^4 + 28*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + ((117 + 405*S^2 + 144*S^4 + 319*S^6 + 31*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (164*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-19*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3) + (-285 - 186*S^2 - 60*S^4 - 46*S^6)/(108*S^3))*Zeta[3] - (29*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]*((8699*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(54432*S^3) + (Pi^4*(1 + S^2)*(-18608 + 21995*S^2 + 47515*S^4))/(38880*S^3) + (Pi^2*(1 + S^2)*(-51212 + 30665*S^2 + 296269*S^4))/(23328*S^3) + ((1 + S^2)*(-2595943 + 917773*S^2 + 9892808*S^4))/(139968*S^3) + ((79*Pi^2*(1 + S^6))/(72*S^3) + (115 + 312*S^2 + 627*S^4 + 430*S^6)/(72*S^3))*HPL[{2}, -S^2]^2 + (23*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(18*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/S^3 + ((Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + ((1 + S^2)*(-320 - 13*S^2 + 265*S^4))/(54*S^3))*HPL[{4}, -S^2] + ((-17 - 5*S^2 + 6*S^4 + 37*S^6 + 25*S^8)*HPL[{5}, -S^2])/(6*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/S^3 + ((29 - 135*S^2 - 681*S^4 - 517*S^6)/(18*S^3) - (73*Pi^2*(1 + S^6))/(18*S^3))*HPL[{3, 1}, -S^2] + ((7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)) - (2*(-6 - 12*S^2 - 3*S^4 - 4*S^6 + 2*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)) - (6*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/S^3 + ((74*Pi^2*(1 + S^6))/(9*S^3) + (23 + 1029*S^2 + 4125*S^4 + 3119*S^6)/(54*S^3))*HPL[{2, 1, 1}, -S^2] + (2*(17 + 113*S^2 + 48*S^4 + 143*S^6 + 47*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (2*(35 + 311*S^2 + 138*S^4 + 425*S^6 + 149*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (92*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (92*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/S^3 - (4*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^3 + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (((1 + S^2)*(-7411 - 509*S^2 + 2912*S^4))/(648*S^3) + (Pi^2*(-77 - 65*S^2 + 6*S^4 + 97*S^6 + 85*S^8))/(36*S^3*(1 + S^2)))*Zeta[3] + ((1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*(((1 + S^2)*(-4040 - 919*S^2 + 3583*S^4))/(648*S^3) + (Pi^2*(-25 - 37*S^2 - 6*S^4 + 5*S^6 + 17*S^8))/(36*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(-2729 + 5624*S^2 + 30193*S^4))/(648*S^3) + (Pi^2*(55 - 833*S^2 - 444*S^4 - 1535*S^6 - 647*S^8))/(108*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((473*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1080*S^3) + (Pi^2*(1 + S^2)*(-481 + 1531*S^2 + 6332*S^4))/(1296*S^3) + ((1 + S^2)*(-19660 + 9485*S^2 + 89807*S^4))/(2592*S^3) + ((-7 - 19*S^2 - 6*S^4 - 13*S^6 - S^8)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/S^3 + ((-17 - 113*S^2 - 48*S^4 - 143*S^6 - 47*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + ((-25 - 73*S^2 - 24*S^4 - 55*S^6 - 7*S^8)*Zeta[3])/(18*S^3*(1 + S^2))) + (13*(-1 + S^6)*Zeta[5])/S^3)) + Log[T]^2*((258503*(1 + S^2))/(34992*S) + (Pi^4*(42718 + 85171*S^2 + 115158*S^4))/(38880*S) + (Pi^2*(229 + 67417*S^2 + 288126*S^4))/(11664*S) + (Pi^6*(86990 + 43495*S^2 + 115131*S^4 + 28141*S^6))/(136080*S*(1 + S^2)) + (S^3*HPL[{0}, S^2]^7)/72 + ((22*Pi^2*(1 + S^6))/(9*S^3) + (259 + 417*S^2 + 417*S^4 + 259*S^6)/(27*S^3))*HPL[{1}, -S^2]^5 + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2]^7)/(9*S^3) + HPL[{0}, S^2]^6*((8 + 4*S^2 + 19*S^4 + 11*S^6)/(144*S*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2])/(18*S^3)) - (43*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^5*((5*Pi^2*S^3)/36 + (156 + 345*S^2 + 451*S^4)/(1296*S) + ((4 + 70*S^2 + 33*S^4 + 106*S^6 + 40*S^8)*HPL[{1}, -S^2])/(108*S^3*(1 + S^2)) + (11*(1 + S^6)*HPL[{1}, -S^2]^2)/(36*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(12*S^3)) + (2*(51 + 63*S^2 + 6*S^4 + 35*S^6 + 23*S^8)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-5*Pi^2*(1 + S^6))/(9*S^3) + (-1069 - 2682*S^2 + 1107*S^4 + 1615*S^6)/(54*S^3))*HPL[{5}, -S^2] + (5*(-158 - 116*S^2 + 21*S^4 + 151*S^6 + 109*S^8)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)) + (200*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/(3*S^3) - (2*(139 + 655*S^2 + 258*S^4 + 655*S^6 + 139*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + HPL[{0}, S^2]^4*((-244 + 855*S^2 + 2304*S^4)/(864*S) + (Pi^2*(318 + 159*S^2 + 598*S^4 + 280*S^6))/(648*S*(1 + S^2)) + ((-5 + 547*S^2 + 276*S^4 + 925*S^6 + 373*S^8)*HPL[{1}, -S^2]^2)/(216*S^3*(1 + S^2)) + (23*(1 + S^6)*HPL[{1}, -S^2]^3)/(27*S^3) + ((-9 + 177*S^2 + 93*S^4 + 242*S^6 + 56*S^8)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((53*Pi^2*(1 + S^6))/(108*S^3) + (-104 + 247*S^2 + 1486*S^4 + 1135*S^6)/(432*S^3) + (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(36*S^3)) - (19*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(18*S^3)) + ((97*Pi^2*(1 + S^6))/(9*S^3) + (2112 + 3197*S^2 + 707*S^4 + 256*S^6)/(18*S^3))*HPL[{3, 2}, -S^2] + ((356*Pi^2*(1 + S^6))/(9*S^3) + (11328 + 16161*S^2 + 3183*S^4 + 1564*S^6)/(27*S^3))*HPL[{4, 1}, -S^2] + ((-17 + 19*S^2 + 18*S^4 + 11*S^6 - 25*S^8)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)) - (88*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/(3*S^3) - (2*(-127 - 391*S^2 - 132*S^4 + 171*S^6 + 435*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (260*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/(3*S^3) - (560*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/(3*S^3) + ((32*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/S^3 + (32*(1 + S^2)*(37 + 24*S^2 + 37*S^4))/(9*S^3))*HPL[{2, 2, 1}, -S^2] + ((596*Pi^2*(1 + S^6))/(9*S^3) + (2*(1213 + 3162*S^2 + 7662*S^4 + 4773*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + (4*(-1 + S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) - (332*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (1216*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (8*(-117 - 33*S^2 + 42*S^4 + 103*S^6 + 19*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (3776*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (2624*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/S^3 + ((-184*Pi^2*(1 + S^6))/(9*S^3) - (40*(-178 - 225*S^2 + 225*S^4 + 178*S^6))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (16*(47 + 5*S^2 - 21*S^4 - 40*S^6 + 2*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (2656*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (80*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 - (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (9280*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(-1587 - 210*S^2 + 1049*S^4))/(81*S) + (-82710 - 7227*S^2 + 24149*S^4)/(324*S))*Zeta[3] + (2*(2 + S^2 + 21*S^4 + 19*S^6)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-5557 - 987*S^2 + 987*S^4 + 5557*S^6)/(27*S^3) + (2*Pi^2*(131 + 389*S^2 + 129*S^4 + 266*S^6 + 8*S^8))/(27*S^3*(1 + S^2)) - (368*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) + (5*Pi^2*(35 + 167*S^2 + 66*S^4 + 185*S^6 + 53*S^8))/(54*S^3*(1 + S^2)) + (10*(-1 + S^6)*HPL[{2}, -S^2])/S^3 - (200*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2}, -S^2]^2*((5*(1 + S^2)*(2912 - 407*S^2 + 2912*S^4))/(648*S^3) + (Pi^2*(128 + 530*S^2 + 201*S^4 + 487*S^6 + 85*S^8))/(54*S^3*(1 + S^2)) - (50*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-3091 - 7290*S^2 + 2016*S^4 + 3775*S^6)/(162*S^3) + (Pi^2*(-111 - 279*S^2 - 84*S^4 + 139*S^6 + 307*S^8))/(54*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 1}, -S^2]*((5443 + 1866*S^2 - 108*S^4 - 5671*S^6)/(54*S^3) - (2*Pi^2*(102 + 186*S^2 + 42*S^4 + 137*S^6 + 53*S^8))/(27*S^3*(1 + S^2)) + (72*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]^3*((1849*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(1 + S^2)*(1547 + 1273*S^2 + 2402*S^4))/(162*S^3) + ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(729*S^3) + ((86*Pi^2*(1 + S^6))/(27*S^3) + (95*(-1 - S^2 + S^4 + S^6))/(3*S^3))*HPL[{2}, -S^2] + (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) - (20*(67 + 187*S^2 + 60*S^4 + 133*S^6 + 13*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (112*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) - (40*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (112*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (20*(7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((-257*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (-54179 - 152638*S^2 - 1672*S^4 - 5881*S^6)/(648*S^3) + (Pi^2*(-4698 - 6261*S^2 - 933*S^4 - 523*S^6))/(324*S^3) + (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (4*(11 + 269*S^2 + 129*S^4 + 386*S^6 + 128*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (232*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (368*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(15 - 3*S^2 - 9*S^4 - S^6 + 17*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-133*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(90*S^3) + (24149 + 75483*S^2 - 75483*S^4 - 24149*S^6)/(324*S^3) + (Pi^2*(1931 + 2100*S^2 - 5028*S^4 - 3707*S^6))/(162*S^3) + (368*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(41 + 299*S^2 + 129*S^4 + 356*S^6 + 98*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]^3*((47*Pi^4*S^3)/90 + (Pi^2*(2208 + 3180*S^2 + 3805*S^4))/(1944*S) + (96552 + 32859*S^2 + 212002*S^4)/(11664*S) + (2*(56 + 386*S^2 + 165*S^4 + 494*S^6 + 164*S^8)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)) + (55*(1 + S^6)*HPL[{1}, -S^2]^4)/(27*S^3) + ((2*Pi^2*(1 + S^6))/(3*S^3) + (761 + 1269*S^2 + 1269*S^4 + 1087*S^6)/(324*S^3))*HPL[{2}, -S^2] + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/S^3 + HPL[{1}, -S^2]^2*((55*Pi^2*(1 + S^6))/(27*S^3) + (1087 + 2208*S^2 + 4287*S^4 + 3166*S^6)/(324*S^3) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/S^3) + ((8 + 26*S^2 + 9*S^4 + 11*S^6 - 7*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + ((5 - 85*S^2 - 45*S^4 - 166*S^6 - 76*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(1753 + 772*S^2 + 5173*S^4))/(324*S^3) + (Pi^2*(38 + 368*S^2 + 165*S^4 + 512*S^6 + 182*S^8))/(81*S^3*(1 + S^2)) + (5*(1 + 7*S^2 + 3*S^4 + 9*S^6 + 3*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + HPL[{0}, S^2]^2*((Pi^2*(1308 + 5592*S^2 + 12469*S^4))/(1296*S) + (-10987 + 11409*S^2 + 96042*S^4)/(1296*S) + (Pi^4*(718 + 359*S^2 + 1090*S^4 + 372*S^6))/(540*S*(1 + S^2)) + (5*(7 + 55*S^2 + 24*S^4 + 73*S^6 + 25*S^8)*HPL[{1}, -S^2]^4)/(18*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2]^5)/(3*S^3) + ((117 + 405*S^2 + 144*S^4 + 319*S^6 + 31*S^8)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((106*Pi^2*(1 + S^6))/(27*S^3) + (84 + 245*S^2 + 530*S^4 + 369*S^6)/(18*S^3) + (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + ((-7*Pi^2*(1 + S^6))/(18*S^3) + (-583 - 639*S^2 + 189*S^4 + 32*S^6)/(108*S^3))*HPL[{3}, -S^2] + (29*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{4}, -S^2])/(6*S^3) + (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((151 - 150*S^2 - 2778*S^4 - 1927*S^6)/(54*S^3) - (14*Pi^2*(1 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(55 + 181*S^2 + 63*S^4 + 177*S^6 + 51*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 + (2*(86 + 344*S^2 + 129*S^4 + 311*S^6 + 53*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (284*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-76 + 8*S^2 + 53*S^4)*Zeta[3])/(9*S) + HPL[{1}, -S^2]^2*(((1 + S^2)*(4471 + 7220*S^2 + 30985*S^4))/(648*S^3) + (Pi^2*(25 + 343*S^2 + 159*S^4 + 505*S^6 + 187*S^8))/(27*S^3*(1 + S^2)) + ((5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/S^3 - (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-2456 + 3594*S^2 + 8931*S^4 + 17016*S^6)/(648*S^3) + (Pi^2*(77 + 521*S^2 + 222*S^4 + 553*S^6 + 109*S^8))/(108*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((359*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(1 + S^2)*(74 + 417*S^2 + 1121*S^4))/(108*S^3) + ((1 + S^2)*(4161 + 12043*S^2 + 89964*S^4))/(1296*S^3) + ((37*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + ((1 + S^2)*(23 + 1006*S^2 + 3119*S^4))/(108*S^3))*HPL[{2}, -S^2] + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/S^3 + (2*(-8 - 14*S^2 - 3*S^4 - 2*S^6 + 4*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) - (2*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 + (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*Zeta[3])/(9*S^3*(1 + S^2)))) + HPL[{0}, S^2]*((6023*Pi^6*S^3)/8505 + (Pi^4*(9344 + 7619*S^2 + 11030*S^4))/(3240*S) + (Pi^2*(392064 + 98223*S^2 + 514094*S^4))/(11664*S) + (10359372 + 822315*S^2 + 10469525*S^4)/(34992*S) + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)) + (28*(1 + S^6)*HPL[{1}, -S^2]^6)/(9*S^3) + ((61*Pi^2*(1 + S^6))/(18*S^3) + (1018 + 1716*S^2 + 861*S^4 + 553*S^6)/(54*S^3))*HPL[{2}, -S^2]^2 + (38*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{1}, -S^2]^4*((160*Pi^2*(1 + S^6))/(27*S^3) + (5*(259 + 417*S^2 + 417*S^4 + 259*S^6))/(54*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((14*Pi^2*(1 + S^6))/(9*S^3) + (673 + 642*S^2 + 462*S^4 + 854*S^6)/(54*S^3))*HPL[{4}, -S^2] - (2*(-69 - 99*S^2 - 15*S^4 - 25*S^6 + 5*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-2738 - 3771*S^2 - 1791*S^4 - 1698*S^6)/(27*S^3) - (148*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (2*(13 - 47*S^2 - 30*S^4 - 25*S^6 + 35*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + (2*(55 + 151*S^2 + 48*S^4 + 149*S^6 + 53*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((88*Pi^2*(1 + S^6))/(3*S^3) + (2*(2344 + 3735*S^2 + 1800*S^4 + 1349*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(7 + 523*S^2 + 258*S^4 + 853*S^6 + 337*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(-21 + 503*S^2 + 262*S^4 + 843*S^6 + 319*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^3 + (280*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (336*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/S^3 - (80*(6 + 3*S^2 + 10*S^4 + 4*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (832*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-168 - 125*S^2 + 38*S^4)/(18*S) + (Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(9*S*(1 + S^2)))*Zeta[3] + (32*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((10*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) + (4*Pi^2*(133 + 613*S^2 + 240*S^4 + 667*S^6 + 187*S^8))/(81*S^3*(1 + S^2)) + (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (56*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((-3551 - 2076*S^2 - 5508*S^4 - 2413*S^6)/(27*S^3) + (Pi^2*(5 - 265*S^2 - 135*S^4 - 466*S^6 - 196*S^8))/(9*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((1256 + 1239*S^2 + 1860*S^4 + 1452*S^6)/(162*S^3) + (Pi^2*(-34 - 4*S^2 + 15*S^4 - 4*S^6 - 34*S^8))/(27*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((349*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(1035 + 1668*S^2 + 1023*S^4 + 812*S^6))/(108*S^3) + (104647 + 281304*S^2 + 85815*S^4 + 217162*S^6)/(1944*S^3) + (2*(-10 - 40*S^2 - 15*S^4 - 29*S^6 + S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (2*(7 + 523*S^2 + 258*S^4 + 853*S^6 + 337*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (176*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(31 + 61*S^2 + 15*S^4 + 30*S^6)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]^2*((937*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(1 + S^2)*(4972 + 3491*S^2 + 7051*S^4))/(324*S^3) + ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(486*S^3) + ((15*Pi^2*(1 + S^6))/S^3 + (1231 + 1845*S^2 + 1845*S^4 + 1231*S^6)/(18*S^3))*HPL[{2}, -S^2] + (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*S^3) + (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)) - (120*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 + (240*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 - (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(23069 + 8356*S^2 + 33329*S^4))/(972*S^3) + ((1 + S^2)*(1244177 + 139966*S^2 + 1244177*S^4))/(5832*S^3) + (Pi^4*(1289 + 6911*S^2 + 2811*S^4 + 8081*S^6 + 2459*S^8))/(810*S^3*(1 + S^2)) + (86*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((10*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + ((1 + S^2)*(298 - 85*S^2 + 253*S^4))/(27*S^3))*HPL[{3}, -S^2] + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-30*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/S^3 - ((1 + S^2)*(1231 + 614*S^2 + 1231*S^4))/(9*S^3))*HPL[{2, 1}, -S^2] - (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (80*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (2096*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - ((1 + S^2)*(70 + 81*S^2 + 55*S^4))/(9*S^3))*Zeta[3] + HPL[{2}, -S^2]*((2*(1 + S^2)*(497 + 135*S^2 + 497*S^4))/(9*S^3) + (5*Pi^2*(5 + 23*S^2 + 9*S^4 + 25*S^6 + 7*S^8))/(3*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)))) + ((-1274 - 101*S^2 + 958*S^4)*Zeta[5])/(9*S) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(40091 + 19300*S^2 + 66605*S^4))/(1944*S^3) + ((1 + S^2)*(1244177 + 139966*S^2 + 1244177*S^4))/(5832*S^3) + (Pi^4*(4399 + 26587*S^2 + 11094*S^4 + 32581*S^6 + 10393*S^8))/(3240*S^3*(1 + S^2)) + (86*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-3041 - 4290*S^2 - 1725*S^4 - 476*S^6)/(27*S^3) - (106*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3}, -S^2] + (2*(-137 - 305*S^2 - 84*S^4 - 143*S^6 + 25*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((-86*Pi^2*(1 + S^6))/(9*S^3) - (95*(-1 - S^2 + S^4 + S^6))/S^3)*HPL[{2, 1}, -S^2] - (4*(-163 - 247*S^2 - 42*S^4 + 23*S^6 + 107*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (1144*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (120*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (1264*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((-98*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(1043 + 307*S^2 + 188*S^4))/(9*S^3))*Zeta[3] + HPL[{2}, -S^2]*((491*(-1 + S^2)*(1 + S^2)^2)/(6*S^3) + (Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(27*S^3*(1 + S^2)) - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (172*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) - (220*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((Pi^2*(-19127 + 633*S^2 + 11892*S^4 + 33687*S^6))/(1944*S^3) + (-48021 - 11198*S^2 + 11198*S^4 + 48021*S^6)/(324*S^3) + (Pi^4*(892 + 5134*S^2 + 2121*S^4 + 5177*S^6 + 935*S^8))/(3240*S^3*(1 + S^2)) + ((-3097 - 4863*S^2 - 993*S^4 - 455*S^6)/(54*S^3) - (50*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3}, -S^2] + ((-145 - 229*S^2 - 42*S^4 - 105*S^6 - 21*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (46*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-16*Pi^2*(1 + S^6))/S^3 - (16*(37 + 61*S^2 + 61*S^4 + 37*S^6))/(9*S^3))*HPL[{2, 1}, -S^2] - (4*(54 + 312*S^2 + 129*S^4 + 343*S^6 + 85*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (188*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (592*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (4*(139 + 655*S^2 + 258*S^4 + 655*S^6 + 139*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (368*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-6*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/S^3 + (-543 - 800*S^2 - 176*S^4 - 49*S^6)/(9*S^3))*Zeta[3] - (104*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]*((8699*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(13608*S^3) + (Pi^4*(1 + S^2)*(34511 + 43567*S^2 + 92552*S^4))/(19440*S^3) + (Pi^2*(1 + S^2)*(314575 + 94913*S^2 + 571984*S^4))/(11664*S^3) + (11*(1 + S^2)*(951775 + 64742*S^2 + 951775*S^4))/(34992*S^3) + ((67*Pi^2*(1 + S^6))/(9*S^3) + (1571 + 2577*S^2 + 2577*S^4 + 1571*S^6)/(54*S^3))*HPL[{2}, -S^2]^2 + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((-28*Pi^2*(1 + S^6))/(9*S^3) + (-811 - 1135*S^2 - 13*S^4 + 311*S^6)/(18*S^3))*HPL[{4}, -S^2] + (2*(-59 - 83*S^2 - 12*S^4 + 19*S^6 + 43*S^8)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)) + (70*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-56*Pi^2*(1 + S^6))/(9*S^3) - (2*(-490 - 571*S^2 + 284*S^4 + 365*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] + (8*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + (52*(71 + 203*S^2 + 66*S^4 + 149*S^6 + 17*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + (12*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 + (176*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((172*Pi^2*(1 + S^6))/(9*S^3) + (190*(-1 - S^2 + S^4 + S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (688*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(181 + 1129*S^2 + 474*S^4 + 1399*S^6 + 451*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (240*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + (224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (-((1 + S^2)*(3461 + 540*S^2 + 515*S^4))/(18*S^3) + (Pi^2*(-367 - 955*S^2 - 294*S^4 - 613*S^6 - 25*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*(-((1 + S^2)*(28099 + 7448*S^2 + 1585*S^4))/(162*S^3) + (Pi^2*(-383 - 1019*S^2 - 318*S^4 - 677*S^6 - 41*S^8))/(27*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 1}, -S^2]*((-491*(-1 + S^2)*(1 + S^2)^2)/(3*S^3) - (2*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(27*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((28601*(-1 + S^2)*(1 + S^2)^2)/(216*S^3) + (707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + (Pi^2*(1 + S^2)*(-1271 + 503*S^2 + 2842*S^4))/(162*S^3) - (4*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(140 + 398*S^2 + 129*S^4 + 290*S^6 + 32*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + (2*(-481 - 1141*S^2 - 330*S^4 - 619*S^6 + 41*S^8)*Zeta[5])/(9*S^3*(1 + S^2)))) + (5*(-285 + 30*S^2 + 358*S^4)*Zeta[7])/(9*S) + HPL[{2}, -S^2]*((Pi^2*(-69324 - 22139*S^2 + 24062*S^4 + 82920*S^6))/(3888*S^3) + (-208638 - 127217*S^2 + 127217*S^4 + 208638*S^6)/(1152*S^3) + (Pi^4*(-249452 - 30147*S^2 + 189570*S^4 + 403230*S^6))/(233280*S^3) + (Pi^6*(-8442 + 28404*S^2 + 18423*S^4 + 40493*S^6 + 3647*S^8))/(272160*S^3*(1 + S^2)) + ((44 + 38*S^2 - 3*S^4 - 10*S^6 - 4*S^8)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((443 - 1182*S^2 - 237*S^4 - 2522*S^6)/(108*S^3) - (49*Pi^2*(1 + S^6))/(18*S^3))*HPL[{5}, -S^2] + ((-688 - 214*S^2 + 237*S^4 - 139*S^6 - 613*S^8)*HPL[{6}, -S^2])/(18*S^3*(1 + S^2)) - (87*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/S^3 + (86*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((5*Pi^2*(1 + S^6))/S^3 + (6587 + 9873*S^2 + 1953*S^4 + 331*S^6)/(108*S^3))*HPL[{3, 2}, -S^2] + ((52*Pi^2*(1 + S^6))/(3*S^3) + (9772 + 14937*S^2 + 3237*S^4 + 1360*S^6)/(54*S^3))*HPL[{4, 1}, -S^2] + ((37 + 85*S^2 + 24*S^4 + 43*S^6 - 5*S^8)*HPL[{4, 2}, -S^2])/(6*S^3*(1 + S^2)) + (14*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/S^3 + ((437 + 581*S^2 + 72*S^4 + 265*S^6 + 121*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) + (43*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/S^3 + (436*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/(3*S^3) + ((52*Pi^2*(1 + S^6))/(9*S^3) + (4*(-391 - 495*S^2 + 495*S^4 + 391*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((1595 + 1077*S^2 - 6933*S^4 - 5147*S^6)/(27*S^3) - (256*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3, 1, 1}, -S^2] - (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1, 2}, -S^2])/(3*S^3*(1 + S^2)) + (4*(53 + 311*S^2 + 129*S^4 + 311*S^6 + 53*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (208*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (584*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (2*(209 + 1781*S^2 + 786*S^4 + 1905*S^6 + 333*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (584*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (1712*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (3476*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((-32*Pi^2*(1 + S^6))/S^3 - (32*(37 + 61*S^2 + 61*S^4 + 37*S^6))/(9*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (416*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) + (8*(-570 - 828*S^2 - 129*S^4 + 173*S^6 + 431*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (872*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (872*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (2120*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (6304*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (8*(139 + 655*S^2 + 258*S^4 + 655*S^6 + 139*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (736*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) - (1472*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-157*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (-59851 - 200400*S^2 - 11103*S^4 - 30438*S^6)/(1944*S^3) + (Pi^2*(-1914 - 2586*S^2 - 588*S^4 - 193*S^6))/(324*S^3))*Zeta[3] + ((-4 + 14*S^2 + 9*S^4 - 43*S^6 - 61*S^8)*Zeta[3]^2)/(9*S^3*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((5*(1 + S^2)*(2912 - 407*S^2 + 2912*S^4))/(162*S^3) + (2*Pi^2*(128 + 530*S^2 + 201*S^4 + 487*S^6 + 85*S^8))/(27*S^3*(1 + S^2)) - (160*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-4405 - 4677*S^2 - 3039*S^4 - 8731*S^6)/(324*S^3) + (Pi^2*(-259 - 271*S^2 - 6*S^4 - 47*S^6 - 35*S^8))/(108*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 1}, -S^2]*((-16723 - 11706*S^2 - 13344*S^4 - 12397*S^6)/(324*S^3) + (Pi^2*(-102 - 516*S^2 - 207*S^4 - 511*S^6 - 97*S^8))/(27*S^3*(1 + S^2)) + (64*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((-31*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(90*S^3) + (-32811 - 184308*S^2 - 27195*S^4 - 57478*S^6)/(1944*S^3) + (Pi^2*(-3077 - 5097*S^2 - 1155*S^4 - 589*S^6))/(648*S^3) - (6*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/S^3 + (4*(21 + 165*S^2 + 72*S^4 + 208*S^6 + 64*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (200*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(6 - 12*S^2 - 9*S^4 - 14*S^6 + 4*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) - ((1 + S^2)*(90289 + 121214*S^2 + 90289*S^4))/(1944*S^3) + (Pi^2*(-1873 - 3522*S^2 - 5502*S^4 - 3437*S^6))/(324*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (4*(11 + 125*S^2 + 57*S^4 + 168*S^6 + 54*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((-55*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (-2074 - 2814*S^2 - 303*S^4 - 126*S^6)/(54*S^3))*Zeta[5] - (50*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3) + HPL[{1}, -S^2]^2*((Pi^4*(1 + S^2)*(250879 + 210773*S^2 + 867784*S^4))/(233280*S^3) + (Pi^2*(1 + S^2)*(1160506 + 239477*S^2 + 2390491*S^4))/(69984*S^3) + ((1 + S^2)*(23544041 + 1079542*S^2 + 23544041*S^4))/(104976*S^3) + (Pi^6*(53911 + 575851*S^2 + 260970*S^4 + 815989*S^6 + 294049*S^8))/(816480*S^3*(1 + S^2)) + (5*(-1 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((Pi^2*(-1 - S^6))/(3*S^3) + (-1591 - 2106*S^2 + 1233*S^4 + 1748*S^6)/(54*S^3))*HPL[{5}, -S^2] + (5*(-107 - 23*S^2 + 42*S^4 + 247*S^6 + 163*S^8)*HPL[{6}, -S^2])/(18*S^3*(1 + S^2)) + (48*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/S^3 - (172*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((92*Pi^2*(1 + S^6))/(9*S^3) + (2*(1213 + 1716*S^2 + 861*S^4 + 358*S^6))/(27*S^3))*HPL[{3, 2}, -S^2] + ((304*Pi^2*(1 + S^6))/(9*S^3) + (5663 + 7999*S^2 + 3457*S^4 + 1121*S^6)/(18*S^3))*HPL[{4, 1}, -S^2] + (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)) - (22*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/(3*S^3) - (2*(-241 - 505*S^2 - 132*S^4 - 199*S^6 + 65*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/S^3 - (50*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/S^3 + ((268*Pi^2*(1 + S^6))/(9*S^3) + (2*(1571 + 2577*S^2 + 2577*S^4 + 1571*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((592*Pi^2*(1 + S^6))/(9*S^3) + (2*(1672 + 3441*S^2 + 6006*S^4 + 4237*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + (40*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 - (116*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/S^3 - (1072*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (4*(-407 - 575*S^2 - 84*S^4 + 127*S^6 + 295*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1060*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (3268*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (2224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/S^3 + ((-172*Pi^2*(1 + S^6))/(9*S^3) - (190*(-1 - S^2 + S^4 + S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] - (8*(-163 - 247*S^2 - 42*S^4 + 23*S^6 + 107*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (2288*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (240*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (8480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-157*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) - (Pi^2*(1 + S^2)*(1242 + 337*S^2 + 111*S^4))/(108*S^3) - ((1 + S^2)*(289609 + 22655*S^2 + 32200*S^4))/(1944*S^3))*Zeta[3] + ((-5 + 7*S^2 + 6*S^4 + 25*S^6 + 13*S^8)*Zeta[3]^2)/(9*S^3*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((491*(-1 + S^2)*(1 + S^2)^2)/(3*S^3) + (2*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(27*S^3*(1 + S^2)) - (344*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(((1 + S^2)*(3433 + 1406*S^2 + 3433*S^4))/(162*S^3) + (Pi^2*(223 + 1027*S^2 + 402*S^4 + 1117*S^6 + 313*S^8))/(108*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/S^3 - (38*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*(((1 + S^2)*(-7867 - 2432*S^2 + 4907*S^4))/(216*S^3) + (7*Pi^2*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8))/(27*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(-4789 - 608*S^2 + 4049*S^4))/(54*S^3) - (4*Pi^2*(-40 + 2*S^2 + 21*S^4 + 110*S^6 + 68*S^8))/(27*S^3*(1 + S^2)) + (176*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((-98*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - (Pi^2*(1 + S^2)*(3473 + 1348*S^2 + 215*S^4))/(324*S^3) + ((1 + S^2)*(-78310 - 14535*S^2 + 7493*S^4))/(648*S^3) + (14*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (4*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (176*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-28601*(-1 + S^2)*(1 + S^2)^2)/(216*S^3) - (707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) - (Pi^2*(1 + S^2)*(-1271 + 503*S^2 + 2842*S^4))/(162*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(140 + 398*S^2 + 129*S^4 + 290*S^6 + 32*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((-55*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(5237 + 859*S^2 + 134*S^4))/(54*S^3))*Zeta[5] + HPL[{2}, -S^2]*((15185*(-1 + S^2)*(1 + S^2)^2)/(144*S^3) + (Pi^2*(1 + S^2)*(-29243 + 5624*S^2 + 56707*S^4))/(3888*S^3) + (Pi^4*(-2797 + 5687*S^2 + 4242*S^4 + 16937*S^6 + 8453*S^8))/(6480*S^3*(1 + S^2)) + ((-1213 - 1716*S^2 - 861*S^4 - 358*S^6)/(27*S^3) - (46*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3}, -S^2] - (14*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-1571 - 2577*S^2 - 2577*S^4 - 1571*S^6)/(27*S^3) - (134*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2] - (172*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (60*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 + (548*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-47*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(1294 + 503*S^2 + 277*S^4))/(27*S^3))*Zeta[3] - (86*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) - (50*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3) + HPL[{1}, -S^2]*((20621*Pi^8*(1 + S^2)*(1 - S^2 + S^4))/(326592*S^3) + (Pi^6*(1 + S^2)*(-153755 + 1229447*S^2 + 2367802*S^4))/(4898880*S^3) + (Pi^4*(1 + S^2)*(383263 + 369915*S^2 + 2546218*S^4))/(466560*S^3) + (Pi^2*(1 + S^2)*(7873582 + 1629935*S^2 + 20362333*S^4))/(419904*S^3) + (41*(1 + S^2)*(46195277 + 2035702*S^2 + 46195277*S^4))/(5038848*S^3) + ((23*Pi^2*(1 + S^6))/(54*S^3) + (35*(-1 - S^2 + S^4 + S^6))/(12*S^3))*HPL[{2}, -S^2]^3 + (23*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^4)/(18*S^3) + ((247 + 453*S^2 + 93*S^4 - 113*S^6)/(108*S^3) + (Pi^2*(-1 - S^6))/(9*S^3))*HPL[{3}, -S^2]^2 + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2]^2)/(3*S^3) + ((11*Pi^2*(1 + S^6))/(2*S^3) + (-6205 - 7986*S^2 + 10779*S^4 + 12560*S^6)/(108*S^3))*HPL[{6}, -S^2] + ((-91 + 5*S^2 + 48*S^4 + 251*S^6 + 155*S^8)*HPL[{7}, -S^2])/(S^3*(1 + S^2)) + (257*(1 + S^2)*(1 - S^2 + S^4)*HPL[{8}, -S^2])/S^3 + ((-1571 - 2577*S^2 - 2577*S^4 - 1571*S^6)/(27*S^3) - (134*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2]^2 + (72*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2]^2)/S^3 + ((Pi^2*(1 + S^6))/S^3 + (19 + 41*S^2 + 41*S^4 + 19*S^6)/(4*S^3))*HPL[{4, 2}, -S^2] + (11*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)) + ((2180 + 3297*S^2 - 402*S^4 - 1519*S^6)/(27*S^3) + (26*Pi^2*(1 + S^6))/(9*S^3))*HPL[{5, 1}, -S^2] + (10*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 3}, -S^2])/S^3 - (5*(-1 + 59*S^2 + 30*S^4 + 101*S^6 + 41*S^8)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 2}, -S^2])/S^3 - (416*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((92*Pi^2*(1 + S^6))/(9*S^3) + (70*(-1 - S^2 + S^4 + S^6))/S^3)*HPL[{3, 2, 1}, -S^2] - (4*(88 + 262*S^2 + 87*S^4 + 202*S^6 + 28*S^8)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)) - (8*(403 + 1207*S^2 + 402*S^4 + 937*S^6 + 133*S^8)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 2}, -S^2])/(3*S^3) + ((220*Pi^2*(1 + S^6))/(9*S^3) + (-2701 - 3025*S^2 + 1877*S^4 + 2201*S^6)/(9*S^3))*HPL[{4, 1, 1}, -S^2] - (20*(160 + 478*S^2 + 159*S^4 + 370*S^6 + 52*S^8)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) + (68*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^3) - (4*(2444 + 7346*S^2 + 2451*S^4 + 5726*S^6 + 824*S^8)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 2}, -S^2])/(3*S^3) + (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3, 1}, -S^2])/(3*S^3) - (4*(1703 + 5039*S^2 + 1668*S^4 + 3857*S^6 + 521*S^8)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 2}, -S^2])/(3*S^3) + (248*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2, 1}, -S^2])/(3*S^3) + (860*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^3) - (80*(-1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/S^3 + ((-112*Pi^2*(1 + S^6))/(9*S^3) - (4*(-490 - 571*S^2 + 284*S^4 + 365*S^6))/(9*S^3))*HPL[{3, 1, 1, 1}, -S^2] + (16*(-4 + 254*S^2 + 129*S^4 + 434*S^6 + 176*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) + (16*(-4 + 254*S^2 + 129*S^4 + 434*S^6 + 176*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/S^3 + (16*(-139 + 119*S^2 + 129*S^4 + 569*S^6 + 311*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/S^3 - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3) - (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^3 + (8*(-697 + 1019*S^2 + 858*S^4 + 3557*S^6 + 1841*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (24*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/S^3 - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2, 1}, -S^2])/S^3 - (168*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1, 1}, -S^2])/S^3 - (800*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((344*Pi^2*(1 + S^6))/(9*S^3) + (380*(-1 - S^2 + S^4 + S^6))/S^3)*HPL[{2, 1, 1, 1, 1}, -S^2] - (1376*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1376*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (80*(239 + 875*S^2 + 318*S^4 + 821*S^6 + 185*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (448*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3) - (480*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + (448*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + ((1 + S^2)*(-257 + 107*S^2 + 220*S^4))/(54*S^3))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*(((1 + S^2)*(13097 + 9424*S^2 + 39611*S^4))/(81*S^3) + (4*Pi^2*(143 + 1031*S^2 + 444*S^4 + 1337*S^6 + 449*S^8))/(27*S^3*(1 + S^2)) - (320*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 2, 1}, -S^2]*((4*(1 + S^2)*(3433 + 1406*S^2 + 3433*S^4))/(81*S^3) + (2*Pi^2*(223 + 1027*S^2 + 402*S^4 + 1117*S^6 + 313*S^8))/(27*S^3*(1 + S^2)) - (304*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*(((1 + S^2)*(-2978 - 3173*S^2 + 10291*S^4))/(108*S^3) + (Pi^2*(-38 - 44*S^2 - 3*S^4 + 28*S^6 + 34*S^8))/(9*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (56*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 2}, -S^2]*(((1 + S^2)*(11285 + 2812*S^2 + 2447*S^4))/(81*S^3) + (Pi^2*(283 + 835*S^2 + 276*S^4 + 637*S^6 + 85*S^8))/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{4, 1}, -S^2]*(((1 + S^2)*(17669 + 4560*S^2 + 1627*S^4))/(36*S^3) + (Pi^2*(1031 + 2855*S^2 + 912*S^4 + 2009*S^6 + 185*S^8))/(27*S^3*(1 + S^2)) + (160*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1, 1}, -S^2]*((-982*(-1 + S^2)*(1 + S^2)^2)/(3*S^3) - (4*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(27*S^3*(1 + S^2)) + (688*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((263*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(432*S^3) + (Pi^2*(1 + S^2)*(1916 + 1597*S^2 + 2861*S^4))/(648*S^3) + (7*(1 + S^2)*(10021 + 2710*S^2 + 10021*S^4))/(2592*S^3) + ((-47 - 143*S^2 - 48*S^4 - 113*S^6 - 17*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (10*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + ((-121 - 349*S^2 - 114*S^4 - 259*S^6 - 31*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{4}, -S^2]*((-28*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (Pi^2*(1 + S^2)*(-3713 - 1024*S^2 + 1993*S^4))/(648*S^3) + ((1 + S^2)*(-21263 - 5050*S^2 + 20593*S^4))/(324*S^3) + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(-17 - 41*S^2 - 12*S^4 - 23*S^6 + S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-59*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(60*S^3) - (Pi^2*(1 + S^2)*(-519 + 83*S^2 + 882*S^4))/(54*S^3) - ((1 + S^2)*(-86473 - 10100*S^2 + 85133*S^4))/(648*S^3) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (8*(71 + 203*S^2 + 66*S^4 + 149*S^6 + 17*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((28601*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(1 + S^2)*(-1271 + 503*S^2 + 2842*S^4))/(81*S^3) - (8*(140 + 398*S^2 + 129*S^4 + 290*S^6 + 32*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + (-((1 + S^2)*(55021 + 4763*S^2 + 508*S^4))/(324*S^3) + (55*Pi^2*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8))/(54*S^3*(1 + S^2)))*Zeta[5] + Zeta[3]*(-(Pi^2*(1 + S^2)*(38560 + 5369*S^2 + 1723*S^4))/(1944*S^3) - ((1 + S^2)*(442616 + 13485*S^2 + 32621*S^4))/(1944*S^3) + (157*Pi^4*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8))/(1620*S^3*(1 + S^2)) - (64*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{3}, -S^2]*((Pi^2*(1 + S^2)*(-10713 - 2789*S^2 + 666*S^4))/(648*S^3) + ((1 + S^2)*(-861236 - 164719*S^2 + 368749*S^4))/(5832*S^3) + (Pi^4*(-1675 - 4027*S^2 - 1176*S^4 - 2245*S^6 + 107*S^8))/(1620*S^3*(1 + S^2)) - (7*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (70*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((92*Pi^2*(1 + S^6))/(9*S^3) + (2*(1213 + 1716*S^2 + 861*S^4 + 358*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + (4*(133 + 397*S^2 + 132*S^4 + 307*S^6 + 43*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (8*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (128*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^3 - (1120*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - (2*(1 + S^2)*(-7 + 61*S^2 + 2*S^4))/(27*S^3))*Zeta[3] - (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-15185*(-1 + S^2)*(1 + S^2)^2)/(72*S^3) - (Pi^2*(1 + S^2)*(-29243 + 5624*S^2 + 56707*S^4))/(1944*S^3) + (Pi^4*(2797 - 5687*S^2 - 4242*S^4 - 16937*S^6 - 8453*S^8))/(3240*S^3*(1 + S^2)) + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (120*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 - (1096*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (688*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((94*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (2*(1 + S^2)*(1294 + 503*S^2 + 277*S^4))/(27*S^3))*Zeta[3] + (172*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((1387639*(-1 + S^2)*(1 + S^2)^2)/(7776*S^3) + (2047*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(15120*S^3) + (Pi^4*(1 + S^2)*(-26893 + 15847*S^2 + 78812*S^4))/(38880*S^3) + (Pi^2*(1 + S^2)*(-105463 + 9485*S^2 + 175610*S^4))/(7776*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((Pi^2*(-1 - S^6))/(9*S^3) + (5*(-133 - 255*S^2 - 111*S^4 + 11*S^6))/(108*S^3))*HPL[{4}, -S^2] + (10*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (79*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + ((-1481 - 2487*S^2 - 2667*S^4 - 1661*S^6)/(27*S^3) - (46*Pi^2*(1 + S^6))/(3*S^3))*HPL[{3, 1}, -S^2] + (20*(3 + 9*S^2 + 3*S^4 + 7*S^6 + S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)) + (4*(409 + 1231*S^2 + 411*S^4 + 961*S^6 + 139*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/S^3 + ((268*Pi^2*(1 + S^6))/(9*S^3) + (2*(1571 + 2577*S^2 + 2577*S^4 + 1571*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (40*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 - (8*(-4 + 254*S^2 + 129*S^4 + 434*S^6 + 176*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^3 + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (1048*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (688*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (-((1 + S^2)*(23785 + 5624*S^2 + 3679*S^4))/(324*S^3) + (Pi^2*(-305 - 869*S^2 - 282*S^4 - 635*S^6 - 71*S^8))/(54*S^3*(1 + S^2)))*Zeta[3] + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/S^3 + HPL[{3}, -S^2]*(-((1 + S^2)*(11285 + 2812*S^2 + 2447*S^4))/(162*S^3) + (Pi^2*(-283 - 835*S^2 - 276*S^4 - 637*S^6 - 85*S^8))/(54*S^3*(1 + S^2)) + (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 1}, -S^2]*((-2*(1 + S^2)*(3433 + 1406*S^2 + 3433*S^4))/(81*S^3) + (Pi^2*(-223 - 1027*S^2 - 402*S^4 - 1117*S^6 - 313*S^8))/(27*S^3*(1 + S^2)) + (152*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + ((-361 - 877*S^2 - 258*S^4 - 499*S^6 + 17*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + (25*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*Zeta[7])/(3*S^3*(1 + S^2))) + HPL[{0}, S^2]*((179327*Pi^8*S^3)/1020600 + (Pi^6*(1438116 + 1259619*S^2 + 3258856*S^4))/(4898880*S) + (Pi^4*(4946760 + 1021779*S^2 + 7002595*S^4))/(1399680*S) + (Pi^2*(33799596 + 2288373*S^2 + 39541780*S^4))/(839808*S) + (1887194832 + 90275307*S^2 + 1894006357*S^4)/(5038848*S) + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{1}, -S^2]^8)/(9*S^3) + ((53*Pi^2*(1 + S^6))/(108*S^3) + (1063 + 1686*S^2 + 651*S^4 + 444*S^6)/(324*S^3))*HPL[{2}, -S^2]^3 + (23*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^4)/(36*S^3) + HPL[{1}, -S^2]^6*((32*Pi^2*(1 + S^6))/(81*S^3) + (259 + 417*S^2 + 417*S^4 + 259*S^6)/(162*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + ((33 + 32*S^2 - 28*S^4 - 37*S^6)/(36*S^3) - (4*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3}, -S^2]^2 + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2]^2)/(3*S^3) + ((-15*Pi^2*(1 + S^6))/(2*S^3) + (1260 + 1683*S^2 + 423*S^4 + 667*S^6)/(54*S^3))*HPL[{6}, -S^2] - (10*(-130 - 94*S^2 + 18*S^4 + 69*S^6 + 33*S^8)*HPL[{7}, -S^2])/(9*S^3*(1 + S^2)) - (175*(1 + S^2)*(1 - S^2 + S^4)*HPL[{8}, -S^2])/S^3 + ((-1018 - 1716*S^2 - 861*S^4 - 553*S^6)/(27*S^3) - (61*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2]^2 + (100*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2]^2)/(3*S^3) + ((Pi^2*(1 + S^6))/(9*S^3) + (29 + 80*S^6)/(36*S^3))*HPL[{4, 2}, -S^2] + (2*(119 + 47*S^2 - 36*S^4 - 63*S^6 + 9*S^8)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)) + ((-620 - 1272*S^2 - 372*S^4 - 281*S^6)/(54*S^3) + (22*Pi^2*(1 + S^6))/(9*S^3))*HPL[{5, 1}, -S^2] + ((248 + 104*S^2 - 72*S^4 - 125*S^6 + 19*S^8)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)) + (10*(81 + 9*S^2 - 36*S^4 - 47*S^6 + 25*S^8)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 2}, -S^2])/S^3 + (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7, 1}, -S^2])/S^3 + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((-109*(1 + S^6))/(18*S^3) - (7*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3, 1, 2}, -S^2] + ((11*Pi^2*(1 + S^6))/S^3 + (3925 + 6744*S^2 + 2604*S^4 + 1449*S^6)/(54*S^3))*HPL[{3, 2, 1}, -S^2] + ((-29 - 221*S^2 - 96*S^4 - 181*S^6 + 11*S^8)*HPL[{3, 2, 2}, -S^2])/(9*S^3*(1 + S^2)) + (8*(11 - 67*S^2 - 39*S^4 - 64*S^6 + 14*S^8)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 2}, -S^2])/(3*S^3) + ((346*Pi^2*(1 + S^6))/(9*S^3) + (7051 + 10758*S^2 + 4368*S^4 + 3518*S^6)/(27*S^3))*HPL[{4, 1, 1}, -S^2] + (2*(47 - 265*S^2 - 156*S^4 - 226*S^6 + 86*S^8)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) - (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^3) + (2*(173 - 787*S^2 - 480*S^4 - 772*S^6 + 188*S^8)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (35*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 2}, -S^2])/(3*S^3) - (128*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3, 1}, -S^2])/(3*S^3) + (4*(258 - 684*S^2 - 471*S^4 - 794*S^6 + 148*S^8)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (58*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 2}, -S^2])/(3*S^3) - (538*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2, 1}, -S^2])/(3*S^3) - (1480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^3) - (16*(-6 + 108*S^2 + 57*S^4 + 196*S^6 + 82*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + ((-296*Pi^2*(1 + S^6))/(9*S^3) - (2*(2738 + 3771*S^2 + 1791*S^4 + 1698*S^6))/(27*S^3))*HPL[{3, 1, 1, 1}, -S^2] + (4*(-85 + 1343*S^2 + 714*S^4 + 2377*S^6 + 949*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) + (4*(-85 + 1343*S^2 + 714*S^4 + 2377*S^6 + 949*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/S^3 + (4*(-157 + 2639*S^2 + 1398*S^4 + 4729*S^6 + 1933*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/S^3 - (284*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3) - (272*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^3 + (4*(-377 + 7927*S^2 + 4152*S^4 + 14261*S^6 + 5957*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/S^3 - (268*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2, 1}, -S^2])/S^3 - (812*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1, 1}, -S^2])/S^3 - (4936*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((176*Pi^2*(1 + S^6))/(3*S^3) + (4*(2344 + 3735*S^2 + 1800*S^4 + 1349*S^6))/(27*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (8*(7 + 523*S^2 + 258*S^4 + 853*S^6 + 337*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(7 + 523*S^2 + 258*S^4 + 853*S^6 + 337*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (608*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3) - (608*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 - (8*(119 + 2675*S^2 + 1278*S^4 + 4295*S^6 + 1739*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1200*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 + (6032*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) + (2416*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^3 + (15152*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) + (15264*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^3 - (160*(6 + 3*S^2 + 10*S^4 + 4*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (1664*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + (960*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((32*Pi^2*S^3)/9 + (240 + 33*S^2 + 706*S^4)/(54*S))*Zeta[3]^2 + HPL[{1}, -S^2]^5*(((1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) + (2*Pi^2*(133 + 613*S^2 + 240*S^4 + 667*S^6 + 187*S^8))/(405*S^3*(1 + S^2)) + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(45*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(45*S^3)) + HPL[{4, 1}, -S^2]*((-2601 - 3036*S^2 - 408*S^4 - 6221*S^6)/(324*S^3) + (Pi^2*(-77 + 7*S^2 + 42*S^4 + 129*S^6 + 45*S^8))/(27*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 2, 1}, -S^2]*((17549 + 9888*S^2 + 28824*S^4 + 9915*S^6)/(162*S^3) + (2*Pi^2*(-6 + 366*S^2 + 186*S^4 + 637*S^6 + 265*S^8))/(27*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 2}, -S^2]*((193 + 696*S^2 + 1938*S^4 - 1029*S^6)/(324*S^3) + (Pi^2*(-56 + 40*S^2 + 48*S^4 + 51*S^6 - 45*S^8))/(54*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1, 1}, -S^2]*((-2*(3551 + 2076*S^2 + 5508*S^4 + 2413*S^6))/(27*S^3) - (2*Pi^2*(-5 + 265*S^2 + 135*S^4 + 466*S^6 + 196*S^8))/(9*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 1, 1}, -S^2]*((55159 + 32142*S^2 + 90192*S^4 + 32649*S^6)/(162*S^3) + (2*Pi^2*(-52 + 1094*S^2 + 573*S^4 + 1907*S^6 + 761*S^8))/(27*S^3*(1 + S^2)) + (56*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*((2226 + 930*S^2 + 1725*S^4 + 3265*S^6)/(108*S^3) + (Pi^2*(189 + 177*S^2 - 6*S^4 - 22*S^6 - 10*S^8))/(27*S^3*(1 + S^2)) + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{3, 1}, -S^2]*((-34676 - 95232*S^2 - 29679*S^4 - 71791*S^6)/(648*S^3) + (Pi^2*(-3549 - 5232*S^2 - 2955*S^4 - 2815*S^6))/(324*S^3) - (164*Pi^4*(1 + S^6))/(135*S^3) - (352*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(46 + 9*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((349*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (Pi^2*(1035 + 1668*S^2 + 1023*S^4 + 812*S^6))/(54*S^3) + (104647 + 281304*S^2 + 85815*S^4 + 217162*S^6)/(972*S^3) - (4*(31 + 61*S^2 + 15*S^4 + 30*S^6)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]^2*((11*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(40*S^3) + (Pi^2*(2503 + 4452*S^2 + 2715*S^4 + 1966*S^6))/(1296*S^3) + (41425 + 229764*S^2 + 37587*S^4 + 169016*S^6)/(7776*S^3) + ((1 - 47*S^2 - 24*S^4 - 37*S^6 + 11*S^8)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (2*(-6 + 108*S^2 + 57*S^4 + 196*S^6 + 82*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (34*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-19 - 25*S^2 - 3*S^4 - 13*S^6 - 7*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]^4*((937*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (Pi^2*(1 + S^2)*(4972 + 3491*S^2 + 7051*S^4))/(1944*S^3) + ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(2916*S^3) + ((5*Pi^2*(1 + S^6))/(2*S^3) + (1231 + 1845*S^2 + 1845*S^4 + 1231*S^6)/(108*S^3))*HPL[{2}, -S^2] + (43*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (14*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) - (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 - (14*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{4}, -S^2]*((-187*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1080*S^3) + (Pi^2*(1035 + 852*S^2 + 492*S^4 + 658*S^6))/(324*S^3) + (108416 + 96843*S^2 + 75297*S^4 + 71641*S^6)/(3888*S^3) - (2*(-19 - 7*S^2 + 6*S^4 + 17*S^6 + 5*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(-70 - 22*S^2 + 24*S^4 + 51*S^6 + 3*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^2)*(23069 + 8356*S^2 + 33329*S^4))/(2916*S^3) + ((1 + S^2)*(1244177 + 139966*S^2 + 1244177*S^4))/(17496*S^3) + (Pi^4*(1289 + 6911*S^2 + 2811*S^4 + 8081*S^6 + 2459*S^8))/(2430*S^3*(1 + S^2)) + (86*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((10*Pi^2*(1 + S^6))/(27*S^3) + (298 + 213*S^2 + 168*S^4 + 253*S^6)/(81*S^3))*HPL[{3}, -S^2] + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(9*S^3) + ((-1231 - 1845*S^2 - 1845*S^4 - 1231*S^6)/(27*S^3) - (10*Pi^2*(1 + S^6))/S^3)*HPL[{2, 1}, -S^2] - (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) + (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(9*S^3) + (80*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (2096*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(70 + 81*S^2 + 55*S^4))/(27*S^3))*Zeta[3] + HPL[{2}, -S^2]*((2*(1 + S^2)*(497 + 135*S^2 + 497*S^4))/(27*S^3) + (5*Pi^2*(5 + 23*S^2 + 9*S^4 + 25*S^6 + 7*S^8))/(9*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + HPL[{1}, -S^2]^2*((12907*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(34020*S^3) + (Pi^4*(1 + S^2)*(8249 + 6206*S^2 + 16109*S^4))/(6480*S^3) + (Pi^2*(1 + S^2)*(404165 + 73963*S^2 + 591752*S^4))/(23328*S^3) + (11*(1 + S^2)*(951775 + 64742*S^2 + 951775*S^4))/(69984*S^3) + ((31*Pi^2*(1 + S^6))/(9*S^3) + (1571 + 2577*S^2 + 2577*S^4 + 1571*S^6)/(108*S^3))*HPL[{2}, -S^2]^2 + (38*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(9*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((10*Pi^2*(1 + S^6))/(9*S^3) + (278 + 285*S^2 + 240*S^4 + 233*S^6)/(27*S^3))*HPL[{4}, -S^2] + (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-623 - 930*S^2 - 915*S^4 - 608*S^6)/(9*S^3) - (134*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3, 1}, -S^2] + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + (32*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((30*Pi^2*(1 + S^6))/S^3 + (1231 + 1845*S^2 + 1845*S^4 + 1231*S^6)/(9*S^3))*HPL[{2, 1, 1}, -S^2] + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1048*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (304*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (968*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (80*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - (240*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^3 + (480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + (-((1 + S^2)*(439 + 608*S^2 + 301*S^4))/(108*S^3) + (Pi^2*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8))/(18*S^3*(1 + S^2)))*Zeta[3] + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*(((1 + S^2)*(4367 - 764*S^2 + 3953*S^4))/(324*S^3) + (5*Pi^2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8))/(27*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-2*(1 + S^2)*(497 + 135*S^2 + 497*S^4))/(9*S^3) - (5*Pi^2*(5 + 23*S^2 + 9*S^4 + 25*S^6 + 7*S^8))/(3*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((377*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(1 + S^2)*(4927 + 2588*S^2 + 6637*S^4))/(648*S^3) + ((1 + S^2)*(321809 + 45310*S^2 + 321809*S^4))/(3888*S^3) - (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (172*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (10*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*Zeta[3])/(9*S^3*(1 + S^2)))) + ((5664 - 1599*S^2 + 5126*S^4)/(324*S) - (55*Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(54*S*(1 + S^2)))*Zeta[5] + Zeta[3]*((81612 - 44577*S^2 - 7064*S^4)/(5832*S) + (Pi^2*(828 - 570*S^2 + 1627*S^4))/(648*S) - (157*Pi^4*(-6 - 3*S^2 + S^4 + 7*S^6))/(1620*S*(1 + S^2)) + (160*S^3*Zeta[5])/3) + HPL[{2, 1}, -S^2]*((-320747 - 113294*S^2 - 388913*S^4 - 154490*S^6)/(1944*S^3) + (Pi^2*(-27535 - 17898*S^2 - 58254*S^4 - 28086*S^6))/(1944*S^3) + (Pi^4*(38 - 2224*S^2 - 1131*S^4 - 4116*S^6 - 1854*S^8))/(810*S^3*(1 + S^2)) + (4*(-2 + 256*S^2 + 129*S^4 + 421*S^6 + 163*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 - (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (4*(7 + 523*S^2 + 258*S^4 + 853*S^6 + 337*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (304*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (320*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (89 + 79*S^2 + 64*S^4 + 8*S^6)/(9*S^3))*Zeta[3] - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/S^3) + HPL[{3}, -S^2]*((Pi^2*(5513 + 3021*S^2 + 3858*S^4 + 5730*S^6))/(1944*S^3) + (132377 + 102812*S^2 + 100730*S^4 + 183407*S^6)/(3888*S^3) + (Pi^4*(518 + 830*S^2 + 156*S^4 + 233*S^6 - 79*S^8))/(1620*S^3*(1 + S^2)) + ((-119 - 47*S^2 + 36*S^4 + 63*S^6 - 9*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((4*Pi^2*(1 + S^6))/(3*S^3) + (-113 - 42*S^2 + 228*S^4 + 131*S^6)/(27*S^3))*HPL[{2, 1}, -S^2] - (4*(10 - 20*S^2 - 15*S^4 - 27*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (24*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 + (4*(-10 - 40*S^2 - 15*S^4 - 29*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^3 - (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((22*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (19 - 276*S^2 + 156*S^4 + 197*S^6)/(54*S^3))*Zeta[3] + (74*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((4447*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(45360*S^3) + (Pi^4*(19082 + 24981*S^2 + 21336*S^4 + 15485*S^6))/(19440*S^3) + (Pi^2*(192892 + 380877*S^2 + 147012*S^4 + 393255*S^6))/(23328*S^3) + (1747910 + 3309609*S^2 + 1100712*S^4 + 2799485*S^6)/(23328*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((8*Pi^2*(1 + S^6))/(9*S^3) + (-33 - 32*S^2 + 28*S^4 + 37*S^6)/(18*S^3))*HPL[{4}, -S^2] + ((119 + 47*S^2 - 36*S^4 - 63*S^6 + 9*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) - (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-950 - 1644*S^2 - 879*S^4 - 575*S^6)/(27*S^3) - (65*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (2*(1 - 47*S^2 - 24*S^4 - 37*S^6 + 11*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(11 - 67*S^2 - 39*S^4 - 64*S^6 + 14*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((122*Pi^2*(1 + S^6))/(9*S^3) + (2*(1018 + 1716*S^2 + 861*S^4 + 553*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (8*(-6 + 108*S^2 + 57*S^4 + 196*S^6 + 82*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(-26 + 688*S^2 + 357*S^4 + 1205*S^6 + 491*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (568*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (4*(7 + 523*S^2 + 258*S^4 + 853*S^6 + 337*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4000*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((653 - 1650*S^2 - 831*S^4 - 1510*S^6)/(324*S^3) + (Pi^2*(-52 - 58*S^2 - 3*S^4 - 13*S^6 - 7*S^8))/(54*S^3*(1 + S^2)))*Zeta[3] + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*((-410 - 348*S^2 - 969*S^4 + 201*S^6)/(324*S^3) + (Pi^2*(11 - 37*S^2 - 24*S^4 - 47*S^6 + S^8))/(54*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 1}, -S^2]*((-17549 - 9888*S^2 - 28824*S^4 - 9915*S^6)/(324*S^3) + (Pi^2*(6 - 366*S^2 - 186*S^4 - 637*S^6 - 265*S^8))/(27*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) - (4*(13 - 5*S^2 - 9*S^4 - 10*S^6 + 8*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) - (25*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[7])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(1 + S^2)*(15591 + 3382*S^2 + 26959*S^4))/(6480*S^3) + (Pi^2*(1 + S^2)*(1850921 + 115213*S^2 + 2633300*S^4))/(69984*S^3) + ((1 + S^2)*(23544041 + 1079542*S^2 + 23544041*S^4))/(104976*S^3) + (Pi^6*(19955 + 97397*S^2 + 38721*S^4 + 109115*S^6 + 31673*S^8))/(102060*S^3*(1 + S^2)) + (38*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^3)/(27*S^3*(1 + S^2)) - (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-4*Pi^2*(1 + S^6))/(9*S^3) + (185 + 163*S^2 + 43*S^4 + 65*S^6)/(9*S^3))*HPL[{5}, -S^2] - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/S^3 - (172*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + (-((1 + S^2)*(2011 + 540*S^2 + 1965*S^4))/(18*S^3) - (2*Pi^2*(116 + 518*S^2 + 201*S^4 + 554*S^6 + 152*S^8))/(27*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((16*Pi^2*(1 + S^6))/(9*S^3) + (2*(-13 + 75*S^2 + 165*S^4 + 77*S^6))/(27*S^3))*HPL[{3, 2}, -S^2] + ((28*Pi^2*(1 + S^6))/(9*S^3) - (2*(317 + 60*S^2 - 255*S^4 + 2*S^6))/(27*S^3))*HPL[{4, 1}, -S^2] - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/S^3 - (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (48*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/S^3 - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/S^3 + ((248*Pi^2*(1 + S^6))/(9*S^3) + (2*(1571 + 2577*S^2 + 2577*S^4 + 1571*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((764*Pi^2*(1 + S^6))/(9*S^3) + (2*(5011 + 7944*S^2 + 7899*S^4 + 4966*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + (304*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (208*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (968*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (208*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (1256*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((-60*Pi^2*(1 + S^6))/S^3 - (2*(1231 + 1845*S^2 + 1845*S^4 + 1231*S^6))/(9*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (608*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) - (80*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (1904*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (1904*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (3728*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (11072*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (160*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (2272*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 - (960*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((157*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) - (5*(1 + S^2)*(53 + 505*S^2 + 14*S^4))/(324*S^3) + (Pi^2*(1 + S^2)*(-22 - 167*S^2 + 215*S^4))/(108*S^3))*Zeta[3] - (2*(-17 - 41*S^2 - 12*S^4 - 23*S^6 + S^8)*Zeta[3]^2)/(9*S^3*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((4*(1 + S^2)*(497 + 135*S^2 + 497*S^4))/(9*S^3) + (10*Pi^2*(5 + 23*S^2 + 9*S^4 + 25*S^6 + 7*S^8))/(3*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(((1 + S^2)*(3433 + 1406*S^2 + 3433*S^4))/(162*S^3) + (Pi^2*(53 + 239*S^2 + 93*S^4 + 257*S^6 + 71*S^8))/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) - (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*(((1 + S^2)*(6475 + 206*S^2 + 5647*S^4))/(324*S^3) + (10*Pi^2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8))/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-377*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - (Pi^2*(1 + S^2)*(4927 + 2588*S^2 + 6637*S^4))/(324*S^3) - ((1 + S^2)*(321809 + 45310*S^2 + 321809*S^4))/(1944*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((26*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (Pi^2*(1 + S^2)*(329 - 56*S^2 + 239*S^4))/(162*S^3) + ((1 + S^2)*(56269 - 5800*S^2 + 55099*S^4))/(1944*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/S^3 + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(-5 + 7*S^2 + 6*S^4 + 25*S^6 + 13*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((55*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (2*(1 + S^2)*(-19 - 89*S^2 + 116*S^4))/(27*S^3))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(24089 + 6760*S^2 + 32927*S^4))/(1944*S^3) + ((1 + S^2)*(475237 + 26970*S^2 + 475237*S^4))/(3888*S^3) + (Pi^4*(484 + 2746*S^2 + 1131*S^4 + 3286*S^6 + 1024*S^8))/(810*S^3*(1 + S^2)) + ((-8*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(-13 + 88*S^2 + 77*S^4))/(27*S^3))*HPL[{3}, -S^2] + (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((-1571 - 2577*S^2 - 2577*S^4 - 1571*S^6)/(27*S^3) - (124*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2] - (172*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (304*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (952*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + (-(Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (5*(1 + S^2)*(67 + 26*S^2 + 31*S^4))/(54*S^3))*Zeta[3] + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/S^3) + (50*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3)) + Log[T]*((-275585*(1 + S^2))/(52488*S) + (Pi^2*(347492 - 141013*S^2 - 1303623*S^4))/(34992*S) + (Pi^4*(71050 - 383747*S^2 - 1291781*S^4))/(233280*S) + (Pi^6*(-170318 - 452405*S^2 - 370562*S^4))/(816480*S) + ((-259 - 417*S^2 - 417*S^4 - 259*S^6)/(81*S^3) - (22*Pi^2*(1 + S^6))/(27*S^3))*HPL[{1}, -S^2]^6 - (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^8)/(9*S^3) + HPL[{0}, S^2]^7*((-6 - 3*S^2 - 10*S^4 - 4*S^6)/(432*S*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(72*S^3)) + HPL[{0}, S^2]^6*((22 - 59*S^2 - 103*S^4)/(864*S) + ((11 - 37*S^2 - 24*S^4 - 91*S^6 - 43*S^8)*HPL[{1}, -S^2])/(432*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^2)/(18*S^3)) + ((163 - 45*S^2 + 45*S^4 - 163*S^6)/(162*S^3) - (10*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2]^3 - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^4)/(9*S^3) + ((-387 - 204*S^2 - 69*S^4 - 371*S^6)/(54*S^3) + (Pi^2*(-1 - S^6))/S^3)*HPL[{3}, -S^2]^2 + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2]^2)/(3*S^3) + ((5620 + 3084*S^2 - 4521*S^4 - 4394*S^6)/(54*S^3) + (20*Pi^2*(1 + S^6))/(9*S^3))*HPL[{6}, -S^2] - (2*(375 + 807*S^2 + 216*S^4 + 653*S^6 + 221*S^8)*HPL[{7}, -S^2])/(9*S^3*(1 + S^2)) + ((124*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (2*(1 + S^2)*(683 + 430*S^2 + 683*S^4))/(27*S^3))*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*((-729 - 711*S^2 - 2507*S^4)/(3888*S) + (Pi^2*(-96 - 48*S^2 - 149*S^4 - 53*S^6))/(648*S*(1 + S^2)) + ((-4 - 70*S^2 - 33*S^4 - 106*S^6 - 40*S^8)*HPL[{1}, -S^2]^2)/(108*S^3*(1 + S^2)) - (11*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^3)/(54*S^3) + ((-3 - 27*S^2 - 12*S^4 - 26*S^6 - 2*S^8)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-33 - 89*S^2 - 335*S^4 - 279*S^6)/(432*S^3) - (4*Pi^2*(1 + S^6))/(27*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(12*S^3) + (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(18*S^3)) - (48*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2]^2)/S^3 + ((458 - 945*S^2 - 405*S^4 - 110*S^6)*HPL[{4, 2}, -S^2])/(54*S^3) + (2*(270 + 336*S^2 + 33*S^4 + 203*S^6 + 137*S^8)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)) + ((-2*Pi^2*(1 + S^6))/(3*S^3) + (-991 - 3702*S^2 + 537*S^4 + 1899*S^6)/(27*S^3))*HPL[{5, 1}, -S^2] + ((1619 + 1979*S^2 + 180*S^4 + 1181*S^6 + 821*S^8)*HPL[{5, 2}, -S^2])/(9*S^3*(1 + S^2)) + (10*(322 + 412*S^2 + 45*S^4 + 279*S^6 + 189*S^8)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)) - (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((2*Pi^2*(1 + S^6))/(3*S^3) + (-142 + 135*S^2 - 135*S^4 + 142*S^6)/(27*S^3))*HPL[{3, 1, 2}, -S^2] + ((-74*Pi^2*(1 + S^6))/(9*S^3) - (5*(-34 + 3*S^2 - 3*S^4 + 34*S^6))/(9*S^3))*HPL[{3, 2, 1}, -S^2] - (2*(-957 - 2001*S^2 - 522*S^4 - 937*S^6 + 107*S^8)*HPL[{3, 2, 2}, -S^2])/(9*S^3*(1 + S^2)) - (16*(-397 - 799*S^2 - 201*S^4 - 372*S^6 + 30*S^8)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)) + ((-80*Pi^2*(1 + S^6))/(3*S^3) - (2*(-1374 - 1563*S^2 - 105*S^4 + 2110*S^6))/(27*S^3))*HPL[{4, 1, 1}, -S^2] - (2*(-3109 - 6289*S^2 - 1590*S^4 - 2873*S^6 + 307*S^8)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) - (2*(-9901 - 19705*S^2 - 4902*S^4 - 9233*S^6 + 571*S^8)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(-3461 - 6797*S^2 - 1668*S^4 - 3199*S^6 + 137*S^8)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (2128*(-1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + ((184*Pi^2*(1 + S^6))/(9*S^3) + (4*(-601 - 732*S^2 - 102*S^4 + 969*S^6))/(27*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (8*(-299 + 217*S^2 + 258*S^4 + 1225*S^6 + 709*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) - (8*(-299 + 217*S^2 + 258*S^4 + 1225*S^6 + 709*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(-1097 - 581*S^2 + 258*S^4 + 2023*S^6 + 1507*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(-1516 - 658*S^2 + 429*S^4 + 3199*S^6 + 2341*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + ((-320*Pi^2*(1 + S^6))/(9*S^3) - (40*(-157 - 63*S^2 + 63*S^4 + 157*S^6))/(27*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] + (16*(205 + 721*S^2 + 258*S^4 + 721*S^6 + 205*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (16*(205 + 721*S^2 + 258*S^4 + 721*S^6 + 205*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (160*(55 + 161*S^2 + 53*S^4 + 140*S^6 + 34*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (1120*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((361033 + 18226*S^2 - 121869*S^4)/(972*S) + (Pi^2*(32436 + 3618*S^2 - 14215*S^4))/(972*S) - (157*Pi^4*(-6 - 3*S^2 + S^4 + 7*S^6))/(810*S*(1 + S^2)))*Zeta[3] + ((102 - 69*S^2 - 356*S^4)*Zeta[3]^2)/(27*S) + HPL[{2, 1, 1, 1}, -S^2]*((2*(-3281 - 7851*S^2 + 7851*S^4 + 3281*S^6))/(27*S^3) + (4*Pi^2*(-391 - 133*S^2 + 129*S^4 + 854*S^6 + 596*S^8))/(27*S^3*(1 + S^2)) - (640*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 2}, -S^2]*((-34295 - 88923*S^2 - 15825*S^4 - 17321*S^6)/(324*S^3) + (Pi^2*(-177 - 361*S^2 - 92*S^4 - 148*S^6 + 36*S^8))/(9*S^3*(1 + S^2)) - (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*((-33269 - 75195*S^2 - 9828*S^4 - 10567*S^6)/(81*S^3) + (Pi^2*(-1891 - 3715*S^2 - 912*S^4 - 1721*S^6 + 103*S^8))/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{5}, -S^2]*((5331 + 9502*S^2 - 4547*S^4 - 7146*S^6)/(108*S^3) + (Pi^2*(119 + 155*S^2 + 18*S^4 - 15*S^6 - 51*S^8))/(54*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^5*((-2*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) + (Pi^2*(-35 - 167*S^2 - 66*S^4 - 185*S^6 - 53*S^8))/(27*S^3*(1 + S^2)) - (4*(-1 + S^6)*HPL[{2}, -S^2])/S^3 + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 2, 1}, -S^2]*(-((1 + S^2)*(12904 + 13283*S^2 + 12904*S^4))/(81*S^3) - (4*Pi^2*(95 + 497*S^2 + 201*S^4 + 630*S^6 + 228*S^8))/(27*S^3*(1 + S^2)) + (96*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{3, 1, 1}, -S^2]*((-13403 - 25590*S^2 - 72696*S^4 - 33089*S^6)/(81*S^3) - (4*Pi^2*(-24 + 272*S^2 + 148*S^4 + 521*S^6 + 225*S^8))/(9*S^3*(1 + S^2)) + (848*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^4*((-1849*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) - (Pi^2*(1 + S^2)*(1547 + 1273*S^2 + 2402*S^4))/(324*S^3) - ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(1458*S^3) + ((-43*Pi^2*(1 + S^6))/(27*S^3) - (95*(-1 - S^2 + S^4 + S^6))/(6*S^3))*HPL[{2}, -S^2] - (86*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + (10*(67 + 187*S^2 + 60*S^4 + 133*S^6 + 13*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + (20*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) + (10*(7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((169*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (Pi^2*(-289 + 123*S^2 + 1221*S^4 + 2378*S^6))/(162*S^3) + (-187171 - 43308*S^2 + 18612*S^4 + 182753*S^6)/(972*S^3) + (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (8*(-146 - 278*S^2 - 66*S^4 - 129*S^6 + 3*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{4}, -S^2]*((Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(5*S^3) + (88875 + 120249*S^2 - 70857*S^4 - 80039*S^6)/(1944*S^3) + (Pi^2*(959 + 2283*S^2 - 615*S^4 - 1805*S^6))/(324*S^3) - (2*(-89 - 5*S^2 + 42*S^4 + 119*S^6 + 35*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(41 + 53*S^2 + 6*S^4 + 34*S^6 + 22*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]^2*((-76*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - ((1 + S^2)*(15019 - 8038*S^2 + 15019*S^4))/(486*S^3) + (Pi^2*(-1959 - 3504*S^2 - 3414*S^4 - 2285*S^6))/(648*S^3) - (2*(-120 - 264*S^2 - 72*S^4 - 131*S^6 + 13*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/S^3 + (266*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (2*(-110 - 224*S^2 - 57*S^4 - 91*S^6 + 23*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-308*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (30827 + 5160*S^2 - 5160*S^4 - 30827*S^6)/(81*S^3) + (Pi^2*(611 - 564*S^2 - 1662*S^4 - 1977*S^6))/(81*S^3) - (8*(-239 - 497*S^2 - 129*S^4 - 224*S^6 + 34*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]^4*((20270 - 10621*S^2 - 80487*S^4)/(15552*S) + (Pi^2*(588 - 4218*S^2 - 5951*S^4))/(7776*S) + ((5 - 547*S^2 - 276*S^4 - 925*S^6 - 373*S^8)*HPL[{1}, -S^2]^3)/(324*S^3*(1 + S^2)) - (23*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^4)/(54*S^3) + ((261 - 123*S^2 - 1284*S^4 - 1055*S^6)/(1296*S^3) + (Pi^2*(-1 - S^6))/(18*S^3))*HPL[{2}, -S^2] - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(6*S^3) + HPL[{1}, -S^2]^2*((104 - 247*S^2 - 1486*S^4 - 1135*S^6)/(432*S^3) - (53*Pi^2*(1 + S^6))/(108*S^3) - (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(36*S^3)) - (7*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3}, -S^2])/(72*S^3) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((-56 + 130*S^2 + 93*S^4 + 443*S^6 + 257*S^8)*HPL[{2, 1}, -S^2])/(108*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (7*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[3])/(108*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(-5221 + 3979*S^2 + 34046*S^4))/(7776*S^3) + (Pi^2*(85 - 551*S^2 - 318*S^4 - 1145*S^6 - 509*S^8))/(648*S^3*(1 + S^2)) + ((65 - 307*S^2 - 186*S^4 - 685*S^6 - 313*S^8)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)) + (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(18*S^3) - (7*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(18*S^3))) + HPL[{0}, S^2]^3*((-167071 - 19528*S^2 - 334494*S^4)/(11664*S) + (Pi^2*(-9012 - 7329*S^2 - 22612*S^4))/(5832*S) + (Pi^4*(-5622 - 2811*S^2 - 8369*S^4 - 2747*S^6))/(9720*S*(1 + S^2)) + ((-56 - 386*S^2 - 165*S^4 - 494*S^6 - 164*S^8)*HPL[{1}, -S^2]^4)/(81*S^3*(1 + S^2)) - (22*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^5)/(27*S^3) + ((-99 - 327*S^2 - 114*S^4 - 259*S^6 - 31*S^8)*HPL[{2}, -S^2]^2)/(108*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-1087 - 2208*S^2 - 4287*S^4 - 3166*S^6)/(486*S^3) - (110*Pi^2*(1 + S^6))/(81*S^3) - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) + ((-376 - 225*S^2 - 225*S^4 - 193*S^6)/(324*S^3) - (17*Pi^2*(1 + S^6))/(54*S^3))*HPL[{3}, -S^2] + ((59 + 23*S^2 - 18*S^4 - 97*S^6 - 61*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) - (7*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((49*Pi^2*(1 + S^6))/(27*S^3) + (473 + 711*S^2 + 2421*S^4 + 1857*S^6)/(162*S^3))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((-6165 - 10752*S^2 - 8664*S^4 - 16462*S^6)/(1944*S^3) + (Pi^2*(-135 - 645*S^2 - 255*S^4 - 572*S^6 - 62*S^8))/(324*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3)) + ((107 + 371*S^2 + 132*S^4 + 333*S^6 + 69*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(9*S^3) - (2*(35 + 125*S^2 + 45*S^4 + 104*S^6 + 14*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (248*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((66 - 177*S^2 + 166*S^4)*Zeta[3])/(162*S) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(1753 + 772*S^2 + 5173*S^4))/(324*S^3) + (Pi^2*(-38 - 368*S^2 - 165*S^4 - 512*S^6 - 182*S^8))/(81*S^3*(1 + S^2)) - (5*(1 + 7*S^2 + 3*S^4 + 9*S^6 + 3*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((-937*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) - (Pi^2*(1 + S^2)*(1582 + 1961*S^2 + 7351*S^4))/(1944*S^3) - ((1 + S^2)*(102073 + 15179*S^2 + 289660*S^4))/(11664*S^3) + ((-85*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) - ((1 + S^2)*(617 + 373*S^2 + 1472*S^4))/(162*S^3))*HPL[{2}, -S^2] - (19*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) - (2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (10*(1 + 7*S^2 + 3*S^4 + 9*S^6 + 3*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (88*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + ((11 - 37*S^2 - 24*S^4 - 91*S^6 - 43*S^8)*Zeta[3])/(27*S^3*(1 + S^2)))) + HPL[{0}, S^2]^2*((412093 - 76412*S^2 - 1303623*S^4)/(11664*S) + (Pi^2*(15648 - 25563*S^2 - 142141*S^4))/(7776*S) + (Pi^4*(-1022 - 8495*S^2 - 9628*S^4))/(6480*S) + ((-7 - 55*S^2 - 24*S^4 - 73*S^6 - 25*S^8)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^6)/(9*S^3) + ((-593 - 1278*S^2 - 1188*S^4 - 919*S^6)/(216*S^3) - (17*Pi^2*(1 + S^6))/(18*S^3))*HPL[{2}, -S^2]^2 - (10*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{1}, -S^2]^4*((-84 - 245*S^2 - 530*S^4 - 369*S^6)/(36*S^3) - (53*Pi^2*(1 + S^6))/(27*S^3) - (43*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((563 + 450*S^2 - 450*S^4 - 673*S^6)/(108*S^3) + (2*Pi^2*(1 + S^6))/(3*S^3))*HPL[{4}, -S^2] + ((-38 - 56*S^2 - 9*S^4 - 36*S^6 - 18*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + ((-273 - 699*S^2 + 26886*S^4 + 13177*S^6)/(324*S^3) + (Pi^2*(-66 + 156*S^2 + 111*S^4 + 491*S^6 + 269*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((35*Pi^2*(1 + S^6))/(9*S^3) + (312 + 855*S^2 + 1323*S^4 + 1409*S^6)/(54*S^3))*HPL[{3, 1}, -S^2] + ((-32 - 68*S^2 - 18*S^4 - 17*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + ((-45 - 81*S^2 - 18*S^4 - 37*S^6 - S^8)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/S^3 + ((-174 - 879*S^2 - 1347*S^4 - 1192*S^6)/(27*S^3) - (64*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] - (2*(-15 + 273*S^2 + 144*S^4 + 539*S^6 + 251*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(-67 + 347*S^2 + 207*S^4 + 779*S^6 + 365*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^3 - (74*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/S^3 + (4*(-76 + 182*S^2 + 129*S^4 + 539*S^6 + 281*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (320*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((5274 + 9*S^2 - 4372*S^4)/(324*S) + (Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(18*S*(1 + S^2)))*Zeta[3] + HPL[{3}, -S^2]*((5553 + 6822*S^2 - 2718*S^4 - 2879*S^6)/(648*S^3) + (Pi^2*(55 + 73*S^2 + 9*S^4 + 19*S^6 + S^8))/(54*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(4471 + 7220*S^2 + 30985*S^4))/(972*S^3) - (2*Pi^2*(25 + 343*S^2 + 159*S^4 + 505*S^6 + 187*S^8))/(81*S^3*(1 + S^2)) - (2*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((-359*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) - (Pi^2*(1 + S^2)*(74 + 417*S^2 + 1121*S^4))/(108*S^3) - ((1 + S^2)*(4161 + 12043*S^2 + 89964*S^4))/(1296*S^3) + ((-23 - 1029*S^2 - 4125*S^4 - 3119*S^6)/(108*S^3) - (37*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2}, -S^2] - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/S^3 - (2*(-8 - 14*S^2 - 3*S^4 - 2*S^6 + 4*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) + (2*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((-13*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (11596 + 1119*S^2 - 15081*S^4 - 41634*S^6)/(972*S^3) + (Pi^2*(29 - 334*S^2 - 877*S^4 - 749*S^6))/(216*S^3) + ((22 + 40*S^2 + 9*S^4 + 19*S^6 + S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + ((-15 + 273*S^2 + 144*S^4 + 539*S^6 + 251*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (88*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((53 + 77*S^2 + 12*S^4 + 31*S^6 + 7*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(-250 + 3733*S^2 + 21677*S^4))/(1296*S^3) - ((1 + S^2)*(-83671 + 99511*S^2 + 1146314*S^4))/(11664*S^3) + (Pi^4*(269 - 8347*S^2 - 4308*S^4 - 14629*S^6 - 6013*S^8))/(3240*S^3*(1 + S^2)) + ((-17 - 113*S^2 - 48*S^4 - 143*S^6 - 47*S^8)*HPL[{2}, -S^2]^2)/(6*S^3*(1 + S^2)) + ((Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - ((1 + S^2)*(-48 - 11*S^2 + 29*S^4))/(6*S^3))*HPL[{3}, -S^2] - (5*(-1 + S^6)*HPL[{4}, -S^2])/S^3 - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((74*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + ((1 + S^2)*(23 + 1006*S^2 + 3119*S^4))/(54*S^3))*HPL[{2, 1}, -S^2] + (2*(1 + 85*S^2 + 42*S^4 + 139*S^6 + 55*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 - (12*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 - (4*(5 + 263*S^2 + 129*S^4 + 425*S^6 + 167*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^3 - (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/S^3 + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + (-(Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - ((1 + S^2)*(-199 - 30*S^2 + 77*S^4))/(18*S^3))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-2729 + 5624*S^2 + 30193*S^4))/(648*S^3) + (Pi^2*(55 - 833*S^2 - 444*S^4 - 1535*S^6 - 647*S^8))/(108*S^3*(1 + S^2)) + (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/S^3 + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)))) + HPL[{0}, S^2]*((-46795929 - 2451237*S^2 - 47088082*S^4)/(104976*S) + (Pi^2*(-1724685 - 219255*S^2 - 2247659*S^4))/(34992*S) + (Pi^4*(-78894 - 38934*S^2 - 117289*S^4))/(19440*S) + (Pi^6*(-77442 - 38721*S^2 - 119599*S^4 - 42157*S^6))/(102060*S*(1 + S^2)) - (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2]^7)/(9*S^3) + (2*(-82 - 196*S^2 - 57*S^4 - 108*S^6 + 6*S^8)*HPL[{2}, -S^2]^3)/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((-259 - 417*S^2 - 417*S^4 - 259*S^6)/(27*S^3) - (64*Pi^2*(1 + S^6))/(27*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/S^3) + ((9 + 13*S^2 + 2*S^4 + 5*S^6 + S^8)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)) + ((-1402 - 492*S^2 - 312*S^4 - 721*S^6)/(54*S^3) - (10*Pi^2*(1 + S^6))/(3*S^3))*HPL[{5}, -S^2] - (20*(-19 + 8*S^6)*HPL[{6}, -S^2])/(9*S^3) - (100*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/(3*S^3) + (2*(337 + 853*S^2 + 258*S^4 + 523*S^6 + 7*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((Pi^2*(-1 - S^6))/(9*S^3) + (-21 - 768*S^2 - 408*S^4 + 235*S^6)/(54*S^3))*HPL[{3, 2}, -S^2] + ((-83 - 654*S^2 - 114*S^4 - 60*S^6)/(27*S^3) - (4*Pi^2*(1 + S^6))/(3*S^3))*HPL[{4, 1}, -S^2] - (2*(1 + 10*S^6)*HPL[{4, 2}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/(3*S^3) + (4*(-22 + 20*S^2 + 21*S^4 + 70*S^6 + 28*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (18*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/S^3 - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/(3*S^3) + ((-28*Pi^2*(1 + S^6))/S^3 - (4*(553 + 861*S^2 + 1716*S^4 + 1018*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((-248*Pi^2*(1 + S^6))/(3*S^3) - (2*(3212 + 5253*S^2 + 10563*S^4 + 6022*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + (44*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + (4*(-295 - 751*S^2 - 228*S^4 - 399*S^6 + 57*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/S^3 - (4*(1035 + 2487*S^2 + 726*S^4 + 1495*S^6 + 43*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/S^3 + (92*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/S^3 + (168*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/S^3 + ((184*Pi^2*(1 + S^6))/(3*S^3) + (4*(1349 + 1800*S^2 + 3735*S^4 + 2344*S^6))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (608*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) + (8*(437 + 977*S^2 + 270*S^4 + 617*S^6 + 77*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1840*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (1840*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (3664*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (11104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (160*(4 + 10*S^2 + 3*S^4 + 6*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (7040*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + (960*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((Pi^2*(19 - 2*S^2 - S^4))/(9*S) + (2142 + 10206*S^2 + 2209*S^4)/(972*S))*Zeta[3] - (8*(2 + S^2 + 7*S^4 + 5*S^6)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{3, 1}, -S^2]*((5379 + 11184*S^2 + 4182*S^4 + 7517*S^6)/(54*S^3) + (2*Pi^2*(272 + 674*S^2 + 201*S^4 + 475*S^6 + 73*S^8))/(27*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-7889 - 8238*S^2 - 5484*S^4 - 6279*S^6)/(324*S^3) - (2*Pi^2*(-2 + 28*S^2 + 15*S^4 + 74*S^6 + 44*S^8))/(27*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((-9915 - 28824*S^2 - 9888*S^4 - 17549*S^6)/(648*S^3) + (Pi^2*(-218 - 590*S^2 - 186*S^4 - 391*S^6 - 19*S^8))/(54*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(1781 + 604*S^2 + 1781*S^4))/(243*S^3) - (2*Pi^2*(133 + 613*S^2 + 240*S^4 + 667*S^6 + 187*S^8))/(81*S^3*(1 + S^2)) - (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/S^3 + (28*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((-2*(2413 + 5508*S^2 + 2076*S^4 + 3551*S^6))/(27*S^3) - (2*Pi^2*(155 + 425*S^2 + 135*S^4 + 284*S^6 + 14*S^8))/(9*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]^3*((-937*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) - (Pi^2*(1 + S^2)*(4972 + 3491*S^2 + 7051*S^4))/(486*S^3) - ((1 + S^2)*(75523 + 14696*S^2 + 75523*S^4))/(729*S^3) + ((-1231 - 1845*S^2 - 1845*S^4 - 1231*S^6)/(27*S^3) - (10*Pi^2*(1 + S^6))/S^3)*HPL[{2}, -S^2] - (172*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) - (16*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + (80*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (160*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^3 + (56*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((-73*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (-49935 - 45006*S^2 - 47148*S^4 - 63841*S^6)/(1944*S^3) + (Pi^2*(-270 - 312*S^2 - 492*S^4 - 107*S^6))/(324*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (4*(10 + 40*S^2 + 15*S^4 + 51*S^6 + 21*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(22 + 28*S^2 + 3*S^4 + 21*S^6 + 15*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((3*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/S^3 + (Pi^2*(1822 + 2511*S^2 + 6156*S^4 + 4201*S^6))/(162*S^3) + (217162 + 85815*S^2 + 281304*S^4 + 104647*S^6)/(972*S^3) - (112*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/S^3 - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(-11 + 19*S^2 + 15*S^4 + 50*S^6 + 20*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((-154490 - 388913*S^2 - 113294*S^4 - 320747*S^6)/(1944*S^3) + (Pi^2*(-20643 - 43800*S^2 - 21120*S^4 - 37768*S^6))/(1944*S^3) + (Pi^4*(-1006 - 3268*S^2 - 1131*S^4 - 2456*S^6 - 194*S^8))/(810*S^3*(1 + S^2)) + ((4*Pi^2*(1 + S^6))/(9*S^3) + (87 + 192*S^2 + 102*S^4 + 23*S^6)/(27*S^3))*HPL[{3}, -S^2] - (2*(9 + 13*S^2 + 2*S^4 + 5*S^6 + S^8)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((14*Pi^2*(1 + S^6))/S^3 + (2*(553 + 861*S^2 + 1716*S^4 + 1018*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + (4*(58 + 144*S^2 + 43*S^4 + 89*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 - (4*(337 + 853*S^2 + 258*S^4 + 523*S^6 + 7*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (304*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (944*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (68 + 228*S^2 + 93*S^4 + 131*S^6)/(27*S^3))*Zeta[3]) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(23069 + 8356*S^2 + 33329*S^4))/(972*S^3) - ((1 + S^2)*(1244177 + 139966*S^2 + 1244177*S^4))/(5832*S^3) + (Pi^4*(-1289 - 6911*S^2 - 2811*S^4 - 8081*S^6 - 2459*S^8))/(810*S^3*(1 + S^2)) - (86*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-298 - 213*S^2 - 168*S^4 - 253*S^6)/(27*S^3) - (10*Pi^2*(1 + S^6))/(9*S^3))*HPL[{3}, -S^2] - (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((30*Pi^2*(1 + S^6))/S^3 + (1231 + 1845*S^2 + 1845*S^4 + 1231*S^6)/(9*S^3))*HPL[{2, 1}, -S^2] + (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) - (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (80*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (2096*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + ((1 + S^2)*(70 + 81*S^2 + 55*S^4))/(9*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-2*(1 + S^2)*(497 + 135*S^2 + 497*S^4))/(9*S^3) - (5*Pi^2*(5 + 23*S^2 + 9*S^4 + 25*S^6 + 7*S^8))/(3*S^3*(1 + S^2)) + (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + HPL[{1}, -S^2]*((-12907*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(17010*S^3) - (Pi^4*(1 + S^2)*(8249 + 6206*S^2 + 16109*S^4))/(3240*S^3) - (Pi^2*(1 + S^2)*(404165 + 73963*S^2 + 591752*S^4))/(11664*S^3) - (11*(1 + S^2)*(951775 + 64742*S^2 + 951775*S^4))/(34992*S^3) + ((-1571 - 2577*S^2 - 2577*S^4 - 1571*S^6)/(54*S^3) - (62*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2}, -S^2]^2 - (76*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(9*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((-20*Pi^2*(1 + S^6))/(9*S^3) - (2*(278 + 285*S^2 + 240*S^4 + 233*S^6))/(27*S^3))*HPL[{4}, -S^2] - (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((268*Pi^2*(1 + S^6))/(9*S^3) + (2*(623 + 930*S^2 + 915*S^4 + 608*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (40*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (64*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((-60*Pi^2*(1 + S^6))/S^3 - (2*(1231 + 1845*S^2 + 1845*S^4 + 1231*S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] - (688*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2096*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (608*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (1936*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (160*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (480*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^3 - (960*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + (((1 + S^2)*(439 + 608*S^2 + 301*S^4))/(54*S^3) + (Pi^2*(13 + 25*S^2 + 6*S^4 + 7*S^6 - 5*S^8))/(9*S^3*(1 + S^2)))*Zeta[3] - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*((4*(1 + S^2)*(497 + 135*S^2 + 497*S^4))/(9*S^3) + (10*Pi^2*(5 + 23*S^2 + 9*S^4 + 25*S^6 + 7*S^8))/(3*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*(-((1 + S^2)*(4367 - 764*S^2 + 3953*S^4))/(162*S^3) - (10*Pi^2*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8))/(27*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-377*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - (Pi^2*(1 + S^2)*(4927 + 2588*S^2 + 6637*S^4))/(324*S^3) - ((1 + S^2)*(321809 + 45310*S^2 + 321809*S^4))/(1944*S^3) + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (20*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*Zeta[3])/(9*S^3*(1 + S^2))))) + ((42006 + 2631*S^2 - 25414*S^4)/(162*S) - (55*Pi^2*(-6 - 3*S^2 + S^4 + 7*S^6))/(27*S*(1 + S^2)))*Zeta[5] + HPL[{2, 1}, -S^2]*((Pi^2*(-10116 - 24252*S^2 + 50439*S^4 + 23020*S^6))/(972*S^3) + (-40623 - 114269*S^2 + 114269*S^4 + 40623*S^6)/(324*S^3) + (7*Pi^4*(-527 + 79*S^2 + 303*S^4 + 1680*S^6 + 1074*S^8))/(1620*S^3*(1 + S^2)) - (8*(118 + 376*S^2 + 129*S^4 + 345*S^6 + 87*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (336*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/S^3 - (8*(205 + 721*S^2 + 258*S^4 + 721*S^6 + 205*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (1280*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-80*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (2*(959 + 1194*S^2 + 1032*S^4 + 407*S^6))/(27*S^3))*Zeta[3] - (136*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{3}, -S^2]*((606302 + 1852767*S^2 - 204075*S^4 - 124912*S^6)/(5832*S^3) + (Pi^2*(30862 + 59793*S^2 + 3147*S^4 + 2744*S^6))/(1944*S^3) + (Pi^4*(1475 + 2651*S^2 + 588*S^4 + 1156*S^6 - 20*S^8))/(810*S^3*(1 + S^2)) - (2*(135 + 177*S^2 + 21*S^4 + 100*S^6 + 58*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (64*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-1755 - 2001*S^2 - 2451*S^4 - 977*S^6)/(27*S^3) - (28*Pi^2*(1 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (8*(163 + 295*S^2 + 66*S^4 + 134*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 + (128*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (8*(-251 - 509*S^2 - 129*S^4 - 212*S^6 + 46*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (368*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (976*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (-31 + 270*S^2 + 18*S^4 - 178*S^6)/(27*S^3))*Zeta[3] - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]^3*(-(Pi^2*(1 + S^2)*(40091 + 19300*S^2 + 66605*S^4))/(2916*S^3) - ((1 + S^2)*(1244177 + 139966*S^2 + 1244177*S^4))/(8748*S^3) + (Pi^4*(-4399 - 26587*S^2 - 11094*S^4 - 32581*S^6 - 10393*S^8))/(4860*S^3*(1 + S^2)) - (172*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((212*Pi^2*(1 + S^6))/(27*S^3) + (2*(3041 + 4290*S^2 + 1725*S^4 + 476*S^6))/(81*S^3))*HPL[{3}, -S^2] - (4*(-137 - 305*S^2 - 84*S^4 - 143*S^6 + 25*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((172*Pi^2*(1 + S^6))/(27*S^3) + (190*(-1 - S^2 + S^4 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (8*(-163 - 247*S^2 - 42*S^4 + 23*S^6 + 107*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) - (2288*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(9*S^3) - (80*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (2528*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((196*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2*(1 + S^2)*(1043 + 307*S^2 + 188*S^4))/(27*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-491*(-1 + S^2)*(1 + S^2)^2)/(9*S^3) - (2*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(81*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (440*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]^2*((-8699*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(13608*S^3) - (Pi^4*(1 + S^2)*(34511 + 43567*S^2 + 92552*S^4))/(19440*S^3) - (Pi^2*(1 + S^2)*(314575 + 94913*S^2 + 571984*S^4))/(11664*S^3) - (11*(1 + S^2)*(951775 + 64742*S^2 + 951775*S^4))/(34992*S^3) + ((-1571 - 2577*S^2 - 2577*S^4 - 1571*S^6)/(54*S^3) - (67*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2}, -S^2]^2 - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(3*S^3) + ((811 + 1135*S^2 + 13*S^4 - 311*S^6)/(18*S^3) + (28*Pi^2*(1 + S^6))/(9*S^3))*HPL[{4}, -S^2] - (2*(-59 - 83*S^2 - 12*S^4 + 19*S^6 + 43*S^8)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)) - (70*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((56*Pi^2*(1 + S^6))/(9*S^3) + (2*(-490 - 571*S^2 + 284*S^4 + 365*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (8*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (52*(71 + 203*S^2 + 66*S^4 + 149*S^6 + 17*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (12*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 - (176*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((-172*Pi^2*(1 + S^6))/(9*S^3) - (190*(-1 - S^2 + S^4 + S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (688*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(181 + 1129*S^2 + 474*S^4 + 1399*S^6 + 451*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (240*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 - (224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (((1 + S^2)*(3461 + 540*S^2 + 515*S^4))/(18*S^3) + (Pi^2*(367 + 955*S^2 + 294*S^4 + 613*S^6 + 25*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*((491*(-1 + S^2)*(1 + S^2)^2)/(3*S^3) + (2*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(27*S^3*(1 + S^2)) - (344*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*(((1 + S^2)*(28099 + 7448*S^2 + 1585*S^4))/(162*S^3) + (Pi^2*(383 + 1019*S^2 + 318*S^4 + 677*S^6 + 41*S^8))/(27*S^3*(1 + S^2)) - (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2}, -S^2]*((-28601*(-1 + S^2)*(1 + S^2)^2)/(216*S^3) - (707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) - (Pi^2*(1 + S^2)*(-1271 + 503*S^2 + 2842*S^4))/(162*S^3) + (4*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (344*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(140 + 398*S^2 + 129*S^4 + 290*S^6 + 32*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) - (2*(-481 - 1141*S^2 - 330*S^4 - 619*S^6 + 41*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((-31*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (434541 + 162835*S^2 - 162835*S^4 - 434541*S^6)/(1944*S^3) + (Pi^2*(115673 + 17718*S^2 - 45642*S^4 - 175749*S^6))/(5832*S^3) + (Pi^4*(8446 - 5862*S^2 - 29127*S^4 - 29416*S^6))/(19440*S^3) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/S^3 + ((14*Pi^2*(1 + S^6))/(9*S^3) + (100 + 283*S^2 + 103*S^4 + 184*S^6)/(18*S^3))*HPL[{4}, -S^2] + ((269 + 389*S^2 + 60*S^4 + 217*S^6 + 97*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (68*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + ((124*Pi^2*(1 + S^6))/(9*S^3) + (1429 + 2091*S^2 + 2361*S^4 + 1303*S^6)/(27*S^3))*HPL[{3, 1}, -S^2] + (4*(-234 - 504*S^2 - 135*S^4 - 238*S^6 + 32*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + (2*(-1529 - 3173*S^2 - 822*S^4 - 1453*S^6 + 191*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 - (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/S^3 + ((-248*Pi^2*(1 + S^6))/(9*S^3) - (4*(683 + 1113*S^2 + 1113*S^4 + 683*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (1064*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (8*(-148 + 110*S^2 + 129*S^4 + 611*S^6 + 353*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^3 - (296*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (288*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/S^3 + (8*(205 + 721*S^2 + 258*S^4 + 721*S^6 + 205*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (640*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (1280*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((9570 + 22854*S^2 + 3333*S^4 + 3334*S^6)/(162*S^3) + (Pi^2*(292 + 574*S^2 + 141*S^4 + 255*S^6 - 27*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(12904 + 13283*S^2 + 12904*S^4))/(162*S^3) + (2*Pi^2*(95 + 497*S^2 + 201*S^4 + 630*S^6 + 228*S^8))/(27*S^3*(1 + S^2)) - (48*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{3}, -S^2]*((16373 + 44691*S^2 + 7683*S^4 + 9435*S^6)/(324*S^3) + (Pi^2*(91 + 183*S^2 + 46*S^4 + 77*S^6 - 15*S^8))/(9*S^3*(1 + S^2)) - (184*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) - (2*(-318 - 576*S^2 - 129*S^4 - 211*S^6 + 47*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) - (50*(-6 - 3*S^2 + S^4 + 7*S^6)*Zeta[7])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*(-(Pi^4*(1 + S^2)*(250879 + 210773*S^2 + 867784*S^4))/(116640*S^3) - (Pi^2*(1 + S^2)*(1160506 + 239477*S^2 + 2390491*S^4))/(34992*S^3) - ((1 + S^2)*(23544041 + 1079542*S^2 + 23544041*S^4))/(52488*S^3) + (Pi^6*(-53911 - 575851*S^2 - 260970*S^4 - 815989*S^6 - 294049*S^8))/(408240*S^3*(1 + S^2)) - (10*(-1 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) - (8*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((2*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - ((1 + S^2)*(-1591 - 515*S^2 + 1748*S^4))/(27*S^3))*HPL[{5}, -S^2] - (5*(-107 - 23*S^2 + 42*S^4 + 247*S^6 + 163*S^8)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)) - (96*(1 + S^2)*(1 - S^2 + S^4)*HPL[{7}, -S^2])/S^3 + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-184*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (4*(1 + S^2)*(1213 + 503*S^2 + 358*S^4))/(27*S^3))*HPL[{3, 2}, -S^2] + ((-608*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(5663 + 2336*S^2 + 1121*S^4))/(9*S^3))*HPL[{4, 1}, -S^2] - (4*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)) + (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/(3*S^3) + (4*(-241 - 505*S^2 - 132*S^4 - 199*S^6 + 65*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/S^3 + (100*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6, 1}, -S^2])/S^3 + ((-536*Pi^2*(1 + S^6))/(9*S^3) - (4*(1571 + 2577*S^2 + 2577*S^4 + 1571*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((-1184*Pi^2*(1 + S^6))/(9*S^3) - (4*(1672 + 3441*S^2 + 6006*S^4 + 4237*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] - (80*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 + (232*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 2}, -S^2])/S^3 + (2144*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (8*(-407 - 575*S^2 - 84*S^4 + 127*S^6 + 295*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2120*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^3) + (6536*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^3) + (4448*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1, 1}, -S^2])/S^3 + ((344*Pi^2*(1 + S^6))/(9*S^3) + (380*(-1 - S^2 + S^4 + S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] + (16*(-163 - 247*S^2 - 42*S^4 + 23*S^6 + 107*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (4576*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (480*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + (2752*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (2752*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (16960*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((157*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (Pi^2*(1 + S^2)*(1242 + 337*S^2 + 111*S^4))/(54*S^3) + ((1 + S^2)*(289609 + 22655*S^2 + 32200*S^4))/(972*S^3))*Zeta[3] - (2*(-5 + 7*S^2 + 6*S^4 + 25*S^6 + 13*S^8)*Zeta[3]^2)/(9*S^3*(1 + S^2)) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(-4789 - 608*S^2 + 4049*S^4))/(27*S^3) + (8*Pi^2*(-40 + 2*S^2 + 21*S^4 + 110*S^6 + 68*S^8))/(27*S^3*(1 + S^2)) - (352*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*(-((1 + S^2)*(-7867 - 2432*S^2 + 4907*S^4))/(108*S^3) - (14*Pi^2*(-13 - 25*S^2 - 6*S^4 - 7*S^6 + 5*S^8))/(27*S^3*(1 + S^2)) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) + (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(3433 + 1406*S^2 + 3433*S^4))/(81*S^3) + (Pi^2*(-223 - 1027*S^2 - 402*S^4 - 1117*S^6 - 313*S^8))/(54*S^3*(1 + S^2)) + (32*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/S^3 + (76*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((-982*(-1 + S^2)*(1 + S^2)^2)/(3*S^3) - (4*Pi^2*(-130 + 128*S^2 + 129*S^4 + 560*S^6 + 302*S^8))/(27*S^3*(1 + S^2)) + (688*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((196*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (Pi^2*(1 + S^2)*(3473 + 1348*S^2 + 215*S^4))/(162*S^3) - ((1 + S^2)*(-78310 - 14535*S^2 + 7493*S^4))/(324*S^3) - (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(3*S^3) - (8*(131 + 389*S^2 + 129*S^4 + 299*S^6 + 41*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (352*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(7 + 19*S^2 + 6*S^4 + 13*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((28601*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (707*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (Pi^2*(1 + S^2)*(-1271 + 503*S^2 + 2842*S^4))/(81*S^3) - (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (8*(140 + 398*S^2 + 129*S^4 + 290*S^6 + 32*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((110*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + ((1 + S^2)*(5237 + 859*S^2 + 134*S^4))/(27*S^3))*Zeta[5] + HPL[{2}, -S^2]*((-15185*(-1 + S^2)*(1 + S^2)^2)/(72*S^3) - (Pi^2*(1 + S^2)*(-29243 + 5624*S^2 + 56707*S^4))/(1944*S^3) + (Pi^4*(2797 - 5687*S^2 - 4242*S^4 - 16937*S^6 - 8453*S^8))/(3240*S^3*(1 + S^2)) + ((92*Pi^2*(1 + S^6))/(9*S^3) + (2*(1213 + 1716*S^2 + 861*S^4 + 358*S^6))/(27*S^3))*HPL[{3}, -S^2] + (28*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((268*Pi^2*(1 + S^6))/(9*S^3) + (2*(1571 + 2577*S^2 + 2577*S^4 + 1571*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + (344*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (120*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/S^3 - (1096*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) - (688*(2 + 8*S^2 + 3*S^4 + 8*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (688*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (1376*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((94*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (2*(1 + S^2)*(1294 + 503*S^2 + 277*S^4))/(27*S^3))*Zeta[3] + (172*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + (100*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3));
e5T=e5T0F0+T*e5T1F1*(F+1/F)+T^2*(e5T2F0+e5T2F2*(F^2+1/F^2))+T^3*(e5T3F1*(F+1/F)+e5T3F3*(F^3+1/F^3));
E5uvwT0F0=(-262799*Pi^10)/1166400 - HPL[{0}, S^2]^10/3840 - (HPL[{0}, S^2]^9*HPL[{1}, -S^2])/192 - (14*Pi^2*HPL[{1}, -S^2]^8)/9 - (4*HPL[{1}, -S^2]^10)/15 + HPL[{0}, S^2]^8*((-7*Pi^2)/1152 - (5*HPL[{1}, -S^2]^2)/192 - HPL[{2}, -S^2]/96) - (167*Pi^2*HPL[{2}, -S^2]^4)/18 - (47*Pi^2*HPL[{4}, -S^2]^2)/3 + 494*HPL[{5}, -S^2]^2 - (827*Pi^2*HPL[{8}, -S^2])/3 - 10816*HPL[{10}, -S^2] + HPL[{1}, -S^2]^6*((-1013*Pi^4)/270 - (58*Pi^2*HPL[{2}, -S^2])/9 - (116*HPL[{2}, -S^2]^2)/3 + 32*HPL[{4}, -S^2] - 32*HPL[{3, 1}, -S^2]) - (1520*Pi^2*HPL[{3, 1}, -S^2]^2)/3 + HPL[{2, 1}, -S^2]^2*((13303*Pi^4)/180 + 672*HPL[{3, 1}, -S^2]) + 16*HPL[{3, 2}, -S^2]^2 - 6328*HPL[{4, 1}, -S^2]^2 + (10*Pi^2*HPL[{5, 3}, -S^2])/3 + (25*Pi^2*HPL[{6, 2}, -S^2])/3 + 4*HPL[{6, 4}, -S^2] + (440*Pi^2*HPL[{7, 1}, -S^2])/3 - 52*HPL[{7, 3}, -S^2] - 196*HPL[{8, 2}, -S^2] + 6180*HPL[{9, 1}, -S^2] + HPL[{5, 1}, -S^2]*((-817*Pi^4)/30 - 5248*HPL[{2, 1, 1}, -S^2]) + HPL[{4, 2}, -S^2]*((-68*Pi^4)/15 - 1344*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]^3*((-1717*Pi^4)/540 + 32*HPL[{4}, -S^2] + (860*HPL[{3, 1}, -S^2])/3 - (1720*HPL[{2, 1, 1}, -S^2])/3) + HPL[{3}, -S^2]^2*((-19*Pi^4)/18 + 110*HPL[{4}, -S^2] + 104*HPL[{3, 1}, -S^2] - 336*HPL[{2, 1, 1}, -S^2]) - (5392*Pi^2*HPL[{2, 1, 1}, -S^2]^2)/3 + HPL[{6}, -S^2]*((-4*Pi^4)/45 + 540*HPL[{3, 1}, -S^2] + 20*HPL[{2, 1, 1}, -S^2]) - 6880*HPL[{2, 2, 1}, -S^2]^2 - 13824*HPL[{3, 1, 1}, -S^2]^2 - (3434*Pi^4*HPL[{3, 2, 1}, -S^2])/45 - (152*Pi^2*HPL[{3, 3, 2}, -S^2])/3 - (1786*Pi^4*HPL[{4, 1, 1}, -S^2])/9 + 72*Pi^2*HPL[{4, 1, 3}, -S^2] - (76*Pi^2*HPL[{4, 2, 2}, -S^2])/3 + (1000*Pi^2*HPL[{4, 3, 1}, -S^2])/3 + 944*HPL[{4, 3, 3}, -S^2] + 2828*HPL[{4, 4, 2}, -S^2] + (608*Pi^2*HPL[{5, 1, 2}, -S^2])/3 - 5660*HPL[{5, 1, 4}, -S^2] + (4088*Pi^2*HPL[{5, 2, 1}, -S^2])/3 - 2812*HPL[{5, 2, 3}, -S^2] + 3776*HPL[{5, 3, 2}, -S^2] - 15124*HPL[{5, 4, 1}, -S^2] + (10510*Pi^2*HPL[{6, 1, 1}, -S^2])/3 - 22628*HPL[{6, 1, 3}, -S^2] - 8484*HPL[{6, 2, 2}, -S^2] - 73668*HPL[{6, 3, 1}, -S^2] - 50984*HPL[{7, 1, 2}, -S^2] - 216184*HPL[{7, 2, 1}, -S^2] - 498252*HPL[{8, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2]^2 + (1769*Pi^4*HPL[{3, 1, 1, 1}, -S^2])/15 - (164*Pi^2*HPL[{3, 1, 2, 2}, -S^2])/3 - (164*Pi^2*HPL[{3, 2, 1, 2}, -S^2])/3 + 524*Pi^2*HPL[{3, 2, 2, 1}, -S^2] + 1736*Pi^2*HPL[{3, 3, 1, 1}, -S^2] + 528*HPL[{3, 3, 2, 2}, -S^2] + 1600*HPL[{3, 3, 3, 1}, -S^2] - 164*Pi^2*HPL[{4, 1, 1, 2}, -S^2] + 1572*Pi^2*HPL[{4, 1, 2, 1}, -S^2] - 1772*HPL[{4, 1, 2, 3}, -S^2] - 4436*HPL[{4, 1, 3, 2}, -S^2] + 5044*Pi^2*HPL[{4, 2, 1, 1}, -S^2] - 4460*HPL[{4, 2, 1, 3}, -S^2] - 5804*HPL[{4, 2, 2, 2}, -S^2] - 1788*HPL[{4, 2, 3, 1}, -S^2] - 11924*HPL[{4, 3, 1, 2}, -S^2] - 18308*HPL[{4, 3, 2, 1}, -S^2] - 19152*HPL[{4, 4, 1, 1}, -S^2] + (28376*Pi^2*HPL[{5, 1, 1, 1}, -S^2])/3 - 7992*HPL[{5, 1, 1, 3}, -S^2] - 16900*HPL[{5, 1, 2, 2}, -S^2] + 2216*HPL[{5, 1, 3, 1}, -S^2] - 38212*HPL[{5, 2, 1, 2}, -S^2] - 54148*HPL[{5, 2, 2, 1}, -S^2] - 47736*HPL[{5, 3, 1, 1}, -S^2] - 71820*HPL[{6, 1, 1, 2}, -S^2] - 87660*HPL[{6, 1, 2, 1}, -S^2] - 47340*HPL[{6, 2, 1, 1}, -S^2] + 50192*HPL[{7, 1, 1, 1}, -S^2] + HPL[{2, 1, 1}, -S^2]*((-16733*Pi^6)/1260 + 1344*HPL[{3, 1, 2}, -S^2] - 12416*HPL[{3, 2, 1}, -S^2] - 37440*HPL[{4, 1, 1}, -S^2] + 27840*HPL[{3, 1, 1, 1}, -S^2] - 55680*HPL[{2, 1, 1, 1, 1}, -S^2]) - (2708*Pi^4*HPL[{2, 1, 1, 1, 1}, -S^2])/9 + (3440*Pi^2*HPL[{2, 2, 1, 2, 1}, -S^2])/3 + 3440*Pi^2*HPL[{2, 2, 2, 1, 1}, -S^2] - 6880*Pi^2*HPL[{3, 1, 1, 1, 2}, -S^2] - (34400*Pi^2*HPL[{3, 1, 1, 2, 1}, -S^2])/3 - 13760*Pi^2*HPL[{3, 1, 2, 1, 1}, -S^2] - 672*HPL[{3, 1, 3, 1, 2}, -S^2] - (86000*Pi^2*HPL[{3, 2, 1, 1, 1}, -S^2])/3 + 672*HPL[{3, 2, 1, 3, 1}, -S^2] - 672*HPL[{3, 2, 2, 1, 2}, -S^2] + 672*HPL[{3, 2, 2, 2, 1}, -S^2] + 4032*HPL[{3, 2, 3, 1, 1}, -S^2] - 2016*HPL[{3, 3, 1, 1, 2}, -S^2] + 2688*HPL[{3, 3, 1, 2, 1}, -S^2] + 14112*HPL[{3, 3, 2, 1, 1}, -S^2] - (255056*Pi^2*HPL[{4, 1, 1, 1, 1}, -S^2])/3 - 32928*HPL[{4, 1, 1, 1, 3}, -S^2] - 31584*HPL[{4, 1, 1, 2, 2}, -S^2] - 61152*HPL[{4, 1, 1, 3, 1}, -S^2] - 33600*HPL[{4, 1, 2, 1, 2}, -S^2] - 59808*HPL[{4, 1, 2, 2, 1}, -S^2] - 81312*HPL[{4, 1, 3, 1, 1}, -S^2] - 37632*HPL[{4, 2, 1, 1, 2}, -S^2] - 53760*HPL[{4, 2, 1, 2, 1}, -S^2] - 49728*HPL[{4, 2, 2, 1, 1}, -S^2] - 121632*HPL[{4, 3, 1, 1, 1}, -S^2] - 138432*HPL[{5, 1, 1, 1, 2}, -S^2] - 231168*HPL[{5, 1, 1, 2, 1}, -S^2] - 283584*HPL[{5, 1, 2, 1, 1}, -S^2] - 485184*HPL[{5, 2, 1, 1, 1}, -S^2] - 1208736*HPL[{6, 1, 1, 1, 1}, -S^2] + (3968*Pi^2*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/3 - 1344*HPL[{3, 1, 1, 1, 2, 2}, -S^2] - 1344*HPL[{3, 1, 1, 2, 1, 2}, -S^2] - 1344*HPL[{3, 1, 1, 2, 2, 1}, -S^2] - 1344*HPL[{3, 1, 2, 1, 1, 2}, -S^2] - 1344*HPL[{3, 1, 2, 1, 2, 1}, -S^2] - 1344*HPL[{3, 1, 2, 2, 1, 1}, -S^2] - 1344*HPL[{3, 2, 1, 1, 1, 2}, -S^2] - 1344*HPL[{3, 2, 1, 1, 2, 1}, -S^2] - 1344*HPL[{3, 2, 1, 2, 1, 1}, -S^2] - 1344*HPL[{3, 2, 2, 1, 1, 1}, -S^2] - 4032*HPL[{4, 1, 1, 1, 1, 2}, -S^2] - 4032*HPL[{4, 1, 1, 1, 2, 1}, -S^2] - 4032*HPL[{4, 1, 1, 2, 1, 1}, -S^2] - 4032*HPL[{4, 1, 2, 1, 1, 1}, -S^2] - 4032*HPL[{4, 2, 1, 1, 1, 1}, -S^2] - 23040*HPL[{5, 1, 1, 1, 1, 1}, -S^2] - 4640*Pi^2*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + 23040*HPL[{4, 1, 1, 1, 1, 1, 1}, -S^2] - 23040*HPL[{3, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((-14*Pi^2)/9 - (5*HPL[{0}, S^2]^2)/3 - 12*HPL[{0}, S^2]*HPL[{1}, -S^2] - 12*HPL[{1}, -S^2]^2)*Log[T]^8 + ((4*HPL[{0}, S^2])/3 + (8*HPL[{1}, -S^2])/3)*Log[T]^9 - (4*Log[T]^10)/15 + HPL[{0}, S^2]^6*((-1013*Pi^4)/17280 - (11*HPL[{1}, -S^2]^4)/36 + HPL[{1}, -S^2]^2*((-19*Pi^2)/48 - (2*HPL[{2}, -S^2])/3) - (11*Pi^2*HPL[{2}, -S^2])/72 - (5*HPL[{2}, -S^2]^2)/32 - HPL[{4}, -S^2]/12 + (5*HPL[{3, 1}, -S^2])/8 - (4*HPL[{2, 1, 1}, -S^2])/3 + HPL[{1}, -S^2]*((4*HPL[{2, 1}, -S^2])/3 - Zeta[3]/2)) + Log[T]^7*((16*HPL[{0}, S^2]^3)/9 + (112*Pi^2*HPL[{1}, -S^2])/9 + (40*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/3 + 32*HPL[{1}, -S^2]^3 + HPL[{0}, S^2]*((52*Pi^2)/9 + 48*HPL[{1}, -S^2]^2 + (64*HPL[{2}, -S^2])/3) - (80*HPL[{3}, -S^2])/3 - (64*Zeta[3])/3) + HPL[{0}, S^2]^7*(-HPL[{1}, -S^2]^3/9 + HPL[{1}, -S^2]*((-13*Pi^2)/144 - HPL[{2}, -S^2]/8) + HPL[{2, 1}, -S^2]/8 - Zeta[3]/6) + 320*HPL[{4, 3}, -S^2]*Zeta[3] + 952*HPL[{5, 2}, -S^2]*Zeta[3] + 1404*HPL[{6, 1}, -S^2]*Zeta[3] + 440*HPL[{3, 2, 2}, -S^2]*Zeta[3] + 1328*HPL[{3, 3, 1}, -S^2]*Zeta[3] + 1288*HPL[{4, 1, 2}, -S^2]*Zeta[3] + 4072*HPL[{4, 2, 1}, -S^2]*Zeta[3] + 8480*HPL[{5, 1, 1}, -S^2]*Zeta[3] - 6880*HPL[{2, 2, 2, 1}, -S^2]*Zeta[3] + 20032*HPL[{3, 1, 1, 2}, -S^2]*Zeta[3] + 20032*HPL[{3, 1, 2, 1}, -S^2]*Zeta[3] + 40672*HPL[{3, 2, 1, 1}, -S^2]*Zeta[3] + 121504*HPL[{4, 1, 1, 1}, -S^2]*Zeta[3] - 12544*HPL[{2, 1, 2, 1, 1}, -S^2]*Zeta[3] - 37632*HPL[{2, 2, 1, 1, 1}, -S^2]*Zeta[3] - 60928*HPL[{3, 1, 1, 1, 1}, -S^2]*Zeta[3] - 27840*HPL[{2, 1, 1, 1, 1, 1}, -S^2]*Zeta[3] - (257*Pi^4*Zeta[3]^2)/90 + HPL[{1}, -S^2]^7*((80*HPL[{3}, -S^2])/3 + (64*Zeta[3])/3) + HPL[{7}, -S^2]*(-104*HPL[{2, 1}, -S^2] + 832*Zeta[3]) + HPL[{4}, -S^2]*((14729*Pi^6)/11340 - 992*HPL[{6}, -S^2] - 672*HPL[{2, 1}, -S^2]^2 - 58*Pi^2*HPL[{3, 1}, -S^2] - 24*HPL[{4, 2}, -S^2] + 6212*HPL[{5, 1}, -S^2] + (452*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 768*HPL[{3, 2, 1}, -S^2] + 2192*HPL[{4, 1, 1}, -S^2] - 1888*HPL[{3, 1, 1, 1}, -S^2] + 3840*HPL[{2, 1, 1, 1, 1}, -S^2] - 136*HPL[{2, 1}, -S^2]*Zeta[3] - 48*Zeta[3]^2) + HPL[{3, 1}, -S^2]*((28661*Pi^6)/5670 + 708*HPL[{4, 2}, -S^2] + 2432*HPL[{5, 1}, -S^2] + (5392*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 6208*HPL[{3, 2, 1}, -S^2] + 18752*HPL[{4, 1, 1}, -S^2] - 16640*HPL[{3, 1, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1, 1}, -S^2] - 20*Zeta[3]^2) + HPL[{2}, -S^2]^2*((-114271*Pi^6)/45360 - 26*HPL[{3}, -S^2]^2 + (71*Pi^2*HPL[{4}, -S^2])/3 - 98*HPL[{6}, -S^2] + 860*HPL[{2, 1}, -S^2]^2 + 45*Pi^2*HPL[{3, 1}, -S^2] - 132*HPL[{4, 2}, -S^2] - 650*HPL[{5, 1}, -S^2] - (430*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 672*HPL[{4, 1, 1}, -S^2] + 81888*HPL[{3, 1, 1, 1}, -S^2] - 860*HPL[{2, 1}, -S^2]*Zeta[3] - 17*Zeta[3]^2 + HPL[{3}, -S^2]*(-860*HPL[{2, 1}, -S^2] + 70*Zeta[3])) + HPL[{1}, -S^2]^4*((-121*Pi^6)/27 - (674*Pi^2*HPL[{2}, -S^2]^2)/9 - 52*HPL[{3}, -S^2]^2 + (368*Pi^2*HPL[{4}, -S^2])/9 + 36*HPL[{6}, -S^2] + 1160*HPL[{2, 1}, -S^2]^2 + (496*Pi^2*HPL[{3, 1}, -S^2])/9 - 168*HPL[{4, 2}, -S^2] - 960*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-677*Pi^4)/54 + 160*HPL[{4}, -S^2] + 1160*HPL[{3, 1}, -S^2] - 2320*HPL[{2, 1, 1}, -S^2]) - (580*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 960*HPL[{4, 1, 1}, -S^2] - 960*HPL[{3, 1, 1, 1}, -S^2] - 1160*HPL[{2, 1}, -S^2]*Zeta[3] - 28*Zeta[3]^2 + HPL[{3}, -S^2]*(-1160*HPL[{2, 1}, -S^2] + (224*Zeta[3])/3)) + Log[T]^6*((-1013*Pi^4)/270 - (11*HPL[{0}, S^2]^4)/9 - (112*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/9 - (392*Pi^2*HPL[{1}, -S^2]^2)/9 - 56*HPL[{1}, -S^2]^4 + HPL[{0}, S^2]^2*((-19*Pi^2)/3 - (140*HPL[{1}, -S^2]^2)/3 - (58*HPL[{2}, -S^2])/3) - (58*Pi^2*HPL[{2}, -S^2])/9 - (116*HPL[{2}, -S^2]^2)/3 + 32*HPL[{4}, -S^2] - 32*HPL[{3, 1}, -S^2] + HPL[{0}, S^2]*(-112*HPL[{1}, -S^2]^3 + HPL[{1}, -S^2]*((-364*Pi^2)/9 - (448*HPL[{2}, -S^2])/3) + (8*HPL[{3}, -S^2])/3 + (448*HPL[{2, 1}, -S^2])/3 + 16*Zeta[3]) + HPL[{1}, -S^2]*((560*HPL[{3}, -S^2])/3 + (448*Zeta[3])/3)) + HPL[{0}, S^2]^4*((-121*Pi^6)/432 - (11*HPL[{1}, -S^2]^6)/9 + HPL[{1}, -S^2]^4*((-55*Pi^2)/18 - (68*HPL[{2}, -S^2])/9) - (31*Pi^2*HPL[{2}, -S^2]^2)/18 - 2*HPL[{2}, -S^2]^3 + (5*HPL[{3}, -S^2]^2)/4 - (5*Pi^2*HPL[{4}, -S^2])/12 - 9*HPL[{6}, -S^2] + (271*HPL[{2, 1}, -S^2]^2)/12 + (245*Pi^2*HPL[{3, 1}, -S^2])/36 + (11*HPL[{5, 1}, -S^2])/2 + HPL[{1}, -S^2]^2*((-659*Pi^4)/288 - (64*Pi^2*HPL[{2}, -S^2])/9 - (271*HPL[{2}, -S^2]^2)/24 + (265*HPL[{3, 1}, -S^2])/6 - (272*HPL[{2, 1, 1}, -S^2])/3) + HPL[{2}, -S^2]*((-1823*Pi^4)/2160 - (5*HPL[{4}, -S^2])/2 + (49*HPL[{3, 1}, -S^2])/2 - (271*HPL[{2, 1, 1}, -S^2])/6) - (128*Pi^2*HPL[{2, 1, 1}, -S^2])/9 - 48*HPL[{3, 2, 1}, -S^2] - 144*HPL[{4, 1, 1}, -S^2] + (265*HPL[{3, 1, 1, 1}, -S^2])/3 - (544*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + HPL[{1}, -S^2]^3*(HPL[{3}, -S^2]/3 + (272*HPL[{2, 1}, -S^2])/9 - (7*Zeta[3])/9) - (7*Zeta[3]^2)/4 + HPL[{3}, -S^2]*(-HPL[{2, 1}, -S^2]/2 + (5*Zeta[3])/2) + HPL[{1}, -S^2]*((Pi^2*HPL[{3}, -S^2])/12 - HPL[{5}, -S^2]/2 + (128*Pi^2*HPL[{2, 1}, -S^2])/9 + HPL[{2}, -S^2]*(HPL[{3}, -S^2]/2 + (271*HPL[{2, 1}, -S^2])/6) - HPL[{3, 2}, -S^2] - 3*HPL[{4, 1}, -S^2] - (271*HPL[{2, 2, 1}, -S^2])/3 - 269*HPL[{3, 1, 1}, -S^2] + (544*HPL[{2, 1, 1, 1}, -S^2])/3 - (97*Pi^2*Zeta[3])/36 - (65*Zeta[5])/6)) + HPL[{2, 1, 1, 1}, -S^2]*((-3824*Pi^2*Zeta[3])/3 - 6464*Zeta[5]) + HPL[{4, 1}, -S^2]*(-23328*HPL[{2, 2, 1}, -S^2] - 69440*HPL[{3, 1, 1}, -S^2] + 45504*HPL[{2, 1, 1, 1}, -S^2] - 164*Pi^2*Zeta[3] - 1648*Zeta[5]) + HPL[{3, 2}, -S^2]*(-744*HPL[{4, 1}, -S^2] - 6880*HPL[{2, 2, 1}, -S^2] - 21312*HPL[{3, 1, 1}, -S^2] + 15104*HPL[{2, 1, 1, 1}, -S^2] - (136*Pi^2*Zeta[3])/3 - 528*Zeta[5]) + Log[T]^5*((163*HPL[{0}, S^2]^5)/225 + (22*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/3 + (784*Pi^2*HPL[{1}, -S^2]^3)/9 + (336*HPL[{1}, -S^2]^5)/5 + HPL[{0}, S^2]^3*((746*Pi^2)/135 + (112*HPL[{1}, -S^2]^2)/3 + (50*HPL[{2}, -S^2])/3) - (440*Pi^2*HPL[{3}, -S^2])/9 - (304*HPL[{5}, -S^2])/5 - (116*Pi^2*HPL[{2, 1}, -S^2])/3 + HPL[{1}, -S^2]*((1013*Pi^4)/45 + (116*Pi^2*HPL[{2}, -S^2])/3 + 232*HPL[{2}, -S^2]^2 - 192*HPL[{4}, -S^2] + 192*HPL[{3, 1}, -S^2]) + 464*HPL[{3, 2}, -S^2] + 1584*HPL[{4, 1}, -S^2] + 928*HPL[{2, 2, 1}, -S^2] + 1664*HPL[{3, 1, 1}, -S^2] + HPL[{0}, S^2]*((14057*Pi^4)/1350 + 168*HPL[{1}, -S^2]^4 + 54*Pi^2*HPL[{2}, -S^2] + 116*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^2*((364*Pi^2)/3 + 448*HPL[{2}, -S^2]) + 16*HPL[{4}, -S^2] - 448*HPL[{3, 1}, -S^2] + 896*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*(-16*HPL[{3}, -S^2] - 896*HPL[{2, 1}, -S^2] - 96*Zeta[3])) + HPL[{1}, -S^2]^2*(-560*HPL[{3}, -S^2] - 448*Zeta[3]) + HPL[{2}, -S^2]*(-232*HPL[{3}, -S^2] - 464*HPL[{2, 1}, -S^2] - 232*Zeta[3]) + HPL[{0}, S^2]^2*((280*HPL[{1}, -S^2]^3)/3 + HPL[{1}, -S^2]*(38*Pi^2 + 116*HPL[{2}, -S^2]) - (20*HPL[{3}, -S^2])/3 - 116*HPL[{2, 1}, -S^2] - 12*Zeta[3]) - (124*Pi^2*Zeta[3])/3 - 232*Zeta[5]) + HPL[{0}, S^2]^5*((-163*HPL[{1}, -S^2]^5)/225 + HPL[{1}, -S^2]^3*((-373*Pi^2)/270 - (271*HPL[{2}, -S^2])/90) - (Pi^2*HPL[{3}, -S^2])/24 + (3*HPL[{5}, -S^2])/4 + (293*Pi^2*HPL[{2, 1}, -S^2])/180 - HPL[{3, 2}, -S^2]/2 - HPL[{4, 1}, -S^2] + HPL[{1}, -S^2]*((-14057*Pi^4)/21600 - (293*Pi^2*HPL[{2}, -S^2])/180 - (77*HPL[{2}, -S^2]^2)/40 - HPL[{4}, -S^2]/2 + (87*HPL[{3, 1}, -S^2])/10 - (271*HPL[{2, 1, 1}, -S^2])/15) - (77*HPL[{2, 2, 1}, -S^2])/10 - (241*HPL[{3, 1, 1}, -S^2])/10 + (271*HPL[{2, 1, 1, 1}, -S^2])/15 + HPL[{1}, -S^2]^2*(-HPL[{3}, -S^2]/2 + (271*HPL[{2, 1}, -S^2])/30 - (3*Zeta[3])/2) + HPL[{2}, -S^2]*(HPL[{3}, -S^2]/4 + (77*HPL[{2, 1}, -S^2])/20 - Zeta[3]/2) - (31*Pi^2*Zeta[3])/24 - (29*Zeta[5])/4) + 260*Zeta[5]^2 + HPL[{1}, -S^2]^5*((440*Pi^2*HPL[{3}, -S^2])/9 + (304*HPL[{5}, -S^2])/5 + (116*Pi^2*HPL[{2, 1}, -S^2])/3 - 464*HPL[{3, 2}, -S^2] - 1584*HPL[{4, 1}, -S^2] - 928*HPL[{2, 2, 1}, -S^2] - 1664*HPL[{3, 1, 1}, -S^2] + (124*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*(232*HPL[{3}, -S^2] + 464*HPL[{2, 1}, -S^2] + 232*Zeta[3]) + 232*Zeta[5]) + HPL[{5}, -S^2]*(-66*Pi^2*HPL[{2, 1}, -S^2] - 400*HPL[{3, 2}, -S^2] - 1372*HPL[{4, 1}, -S^2] + 776*HPL[{2, 2, 1}, -S^2] + 2384*HPL[{3, 1, 1}, -S^2] - 1472*HPL[{2, 1, 1, 1}, -S^2] + 38*Pi^2*Zeta[3] + 532*Zeta[5]) + HPL[{2, 2, 1}, -S^2]*(-24832*HPL[{3, 1, 1}, -S^2] + 572*Pi^2*Zeta[3] + 2856*Zeta[5]) + HPL[{3, 1, 1}, -S^2]*(-27840*HPL[{2, 1, 1, 1}, -S^2] + (5404*Pi^2*Zeta[3])/3 + 8952*Zeta[5]) + HPL[{1}, -S^2]^2*((-456659*Pi^8)/194400 - (215*Pi^2*HPL[{2}, -S^2]^3)/9 - (215*HPL[{2}, -S^2]^4)/3 - 24*Pi^2*HPL[{3}, -S^2]^2 - 28*HPL[{4}, -S^2]^2 + (35*Pi^2*HPL[{6}, -S^2])/3 - 1326*HPL[{8}, -S^2] + (2696*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + HPL[{2}, -S^2]^2*((-13303*Pi^4)/360 + 336*HPL[{4}, -S^2] - 336*HPL[{3, 1}, -S^2]) - 4160*HPL[{3, 1}, -S^2]^2 - 82*Pi^2*HPL[{4, 2}, -S^2] - (1436*Pi^2*HPL[{5, 1}, -S^2])/3 + 36*HPL[{5, 3}, -S^2] + 90*HPL[{6, 2}, -S^2] + 616*HPL[{7, 1}, -S^2] - (1354*Pi^4*HPL[{2, 1, 1}, -S^2])/9 - 13920*HPL[{2, 1, 1}, -S^2]^2 + HPL[{4}, -S^2]*((686*Pi^4)/45 - 944*HPL[{3, 1}, -S^2] + 1920*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 1}, -S^2]*((1769*Pi^4)/30 + 13920*HPL[{2, 1, 1}, -S^2]) - (1720*Pi^2*HPL[{3, 2, 1}, -S^2])/3 - 1008*HPL[{3, 3, 2}, -S^2] - (3688*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 1680*HPL[{4, 1, 3}, -S^2] - 672*HPL[{4, 2, 2}, -S^2] + 5712*HPL[{4, 3, 1}, -S^2] + 3360*HPL[{5, 1, 2}, -S^2] + 23520*HPL[{5, 2, 1}, -S^2] + 60912*HPL[{6, 1, 1}, -S^2] + (1984*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 - 672*HPL[{3, 1, 2, 2}, -S^2] - 672*HPL[{3, 2, 1, 2}, -S^2] - 672*HPL[{3, 2, 2, 1}, -S^2] - 2016*HPL[{4, 1, 1, 2}, -S^2] - 2016*HPL[{4, 1, 2, 1}, -S^2] - 2016*HPL[{4, 2, 1, 1}, -S^2] - 11520*HPL[{5, 1, 1, 1}, -S^2] - 2320*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] + 11520*HPL[{4, 1, 1, 1, 1}, -S^2] - 11520*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 304*HPL[{3, 2}, -S^2]*Zeta[3] - 1168*HPL[{4, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 19712*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 13920*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (62*Pi^2*Zeta[3]^2)/3 + HPL[{5}, -S^2]*(-736*HPL[{2, 1}, -S^2] + 64*Zeta[3]) + HPL[{2}, -S^2]*((-16733*Pi^6)/2520 - 168*HPL[{3}, -S^2]^2 + (226*Pi^2*HPL[{4}, -S^2])/3 + 10*HPL[{6}, -S^2] + (2696*Pi^2*HPL[{3, 1}, -S^2])/3 - 672*HPL[{4, 2}, -S^2] - 2624*HPL[{5, 1}, -S^2] - (5392*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 672*HPL[{3, 1, 2}, -S^2] - 6208*HPL[{3, 2, 1}, -S^2] - 18720*HPL[{4, 1, 1}, -S^2] + 13920*HPL[{3, 1, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1, 1}, -S^2] - 3136*HPL[{2, 1}, -S^2]*Zeta[3] + HPL[{3}, -S^2]*(-4112*HPL[{2, 1}, -S^2] + 152*Zeta[3])) + HPL[{2, 1}, -S^2]*(7552*HPL[{3, 2}, -S^2] + 22752*HPL[{4, 1}, -S^2] - 13920*HPL[{3, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2] - (1912*Pi^2*Zeta[3])/3 - 3232*Zeta[5]) - 120*Zeta[3]*Zeta[5] + HPL[{3}, -S^2]*(28*HPL[{5}, -S^2] - 612*Pi^2*HPL[{2, 1}, -S^2] + 672*HPL[{3, 2}, -S^2] + 272*HPL[{4, 1}, -S^2] + 8224*HPL[{2, 2, 1}, -S^2] + 23424*HPL[{3, 1, 1}, -S^2] - 13920*HPL[{2, 1, 1, 1}, -S^2] + (128*Pi^2*Zeta[3])/3 + 192*Zeta[5])) + HPL[{2}, -S^2]*((-46931*Pi^8)/85050 - (29*Pi^2*HPL[{3}, -S^2]^2)/3 - 106*HPL[{4}, -S^2]^2 - 27*Pi^2*HPL[{6}, -S^2] - 1264*HPL[{8}, -S^2] + (430*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + 336*HPL[{3, 1}, -S^2]^2 - (164*Pi^2*HPL[{4, 2}, -S^2])/3 - (590*Pi^2*HPL[{5, 1}, -S^2])/3 + 20*HPL[{5, 3}, -S^2] + 56*HPL[{6, 2}, -S^2] + 696*HPL[{7, 1}, -S^2] + HPL[{3, 1}, -S^2]*((1126*Pi^4)/15 - 1344*HPL[{2, 1, 1}, -S^2]) - (13303*Pi^4*HPL[{2, 1, 1}, -S^2])/90 + HPL[{4}, -S^2]*((163*Pi^4)/45 - 564*HPL[{3, 1}, -S^2] + 1344*HPL[{2, 1, 1}, -S^2]) + (164*Pi^2*HPL[{3, 1, 2}, -S^2])/3 - 836*Pi^2*HPL[{3, 2, 1}, -S^2] - 216*HPL[{3, 3, 2}, -S^2] - (7564*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 244*HPL[{4, 1, 3}, -S^2] - 140*HPL[{4, 2, 2}, -S^2] + 1684*HPL[{4, 3, 1}, -S^2] + 1100*HPL[{5, 1, 2}, -S^2] + 6860*HPL[{5, 2, 1}, -S^2] + 17300*HPL[{6, 1, 1}, -S^2] + (26032*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 6880*HPL[{3, 2, 2, 1}, -S^2] + 20640*HPL[{3, 3, 1, 1}, -S^2] - 1344*HPL[{4, 1, 1, 2}, -S^2] + 19296*HPL[{4, 1, 2, 1}, -S^2] + 60576*HPL[{4, 2, 1, 1}, -S^2] + 118592*HPL[{5, 1, 1, 1}, -S^2] - (10784*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + 13760*HPL[{2, 2, 1, 2, 1}, -S^2] + 41280*HPL[{2, 2, 2, 1, 1}, -S^2] - 81216*HPL[{3, 1, 1, 1, 2}, -S^2] - 136256*HPL[{3, 1, 1, 2, 1}, -S^2] - 163776*HPL[{3, 1, 2, 1, 1}, -S^2] - 342656*HPL[{3, 2, 1, 1, 1}, -S^2] - 1028160*HPL[{4, 1, 1, 1, 1}, -S^2] + 27840*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 55680*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] - 240*HPL[{3, 2}, -S^2]*Zeta[3] - 704*HPL[{4, 1}, -S^2]*Zeta[3] + 3440*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 10016*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 6272*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (29*Pi^2*Zeta[3]^2)/3 + HPL[{5}, -S^2]*(-388*HPL[{2, 1}, -S^2] + 172*Zeta[3]) + HPL[{2, 1}, -S^2]*(3440*HPL[{3, 2}, -S^2] + 11664*HPL[{4, 1}, -S^2] - 6880*HPL[{2, 2, 1}, -S^2] + 12416*HPL[{3, 1, 1}, -S^2] - 286*Pi^2*Zeta[3] - 1428*Zeta[5]) - 116*Zeta[3]*Zeta[5] + HPL[{3}, -S^2]*(200*HPL[{5}, -S^2] - (1066*Pi^2*HPL[{2, 1}, -S^2])/3 + 200*HPL[{3, 2}, -S^2] + 372*HPL[{4, 1}, -S^2] + 3440*HPL[{2, 2, 1}, -S^2] - 10992*HPL[{3, 1, 1}, -S^2] - 8224*HPL[{2, 1, 1, 1}, -S^2] + (68*Pi^2*Zeta[3])/3 + 264*Zeta[5])) + Log[T]^4*((-121*Pi^6)/27 - (11*HPL[{0}, S^2]^6)/36 - (163*HPL[{0}, S^2]^5*HPL[{1}, -S^2])/45 - (980*Pi^2*HPL[{1}, -S^2]^4)/9 - 56*HPL[{1}, -S^2]^6 + HPL[{0}, S^2]^4*((-55*Pi^2)/18 - (55*HPL[{1}, -S^2]^2)/3 - (68*HPL[{2}, -S^2])/9) - (674*Pi^2*HPL[{2}, -S^2]^2)/9 - 52*HPL[{3}, -S^2]^2 + (368*Pi^2*HPL[{4}, -S^2])/9 + 36*HPL[{6}, -S^2] + 1160*HPL[{2, 1}, -S^2]^2 + HPL[{1}, -S^2]^2*((-1013*Pi^4)/18 - (290*Pi^2*HPL[{2}, -S^2])/3 - 580*HPL[{2}, -S^2]^2 + 480*HPL[{4}, -S^2] - 480*HPL[{3, 1}, -S^2]) + (496*Pi^2*HPL[{3, 1}, -S^2])/9 - 168*HPL[{4, 2}, -S^2] - 960*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-677*Pi^4)/54 + 160*HPL[{4}, -S^2] + 1160*HPL[{3, 1}, -S^2] - 2320*HPL[{2, 1, 1}, -S^2]) - (580*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 960*HPL[{4, 1, 1}, -S^2] - 960*HPL[{3, 1, 1, 1}, -S^2] - 1160*HPL[{2, 1}, -S^2]*Zeta[3] - 28*Zeta[3]^2 + HPL[{0}, S^2]^3*((-560*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((-746*Pi^2)/27 - (250*HPL[{2}, -S^2])/3) - 2*HPL[{3}, -S^2] + (250*HPL[{2, 1}, -S^2])/3 + (14*Zeta[3])/9) + HPL[{3}, -S^2]*(-1160*HPL[{2, 1}, -S^2] + (224*Zeta[3])/3) + HPL[{1}, -S^2]^3*((2800*HPL[{3}, -S^2])/3 + (2240*Zeta[3])/3) + HPL[{0}, S^2]^2*((-659*Pi^4)/72 - (350*HPL[{1}, -S^2]^4)/3 + HPL[{1}, -S^2]^2*(-95*Pi^2 - 290*HPL[{2}, -S^2]) - (707*Pi^2*HPL[{2}, -S^2])/18 - (239*HPL[{2}, -S^2]^2)/3 + (8*HPL[{4}, -S^2])/3 + (856*HPL[{3, 1}, -S^2])/3 - 580*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]*((100*HPL[{3}, -S^2])/3 + 580*HPL[{2, 1}, -S^2] + 60*Zeta[3])) + HPL[{0}, S^2]*(-168*HPL[{1}, -S^2]^5 + HPL[{1}, -S^2]^3*((-1820*Pi^2)/9 - (2240*HPL[{2}, -S^2])/3) + (4*Pi^2*HPL[{3}, -S^2])/3 - (112*HPL[{5}, -S^2])/3 + 270*Pi^2*HPL[{2, 1}, -S^2] - (344*HPL[{3, 2}, -S^2])/3 - 264*HPL[{4, 1}, -S^2] + HPL[{1}, -S^2]*((-14057*Pi^4)/270 - 270*Pi^2*HPL[{2}, -S^2] - 580*HPL[{2}, -S^2]^2 - 80*HPL[{4}, -S^2] + 2240*HPL[{3, 1}, -S^2] - 4480*HPL[{2, 1, 1}, -S^2]) - 2320*HPL[{2, 2, 1}, -S^2] - 6880*HPL[{3, 1, 1}, -S^2] + 4480*HPL[{2, 1, 1, 1}, -S^2] + (194*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*((172*HPL[{3}, -S^2])/3 + 1160*HPL[{2, 1}, -S^2] + 116*Zeta[3]) + HPL[{1}, -S^2]^2*(40*HPL[{3}, -S^2] + 2240*HPL[{2, 1}, -S^2] + 240*Zeta[3]) + (260*Zeta[5])/3) + HPL[{1}, -S^2]*((2200*Pi^2*HPL[{3}, -S^2])/9 + 304*HPL[{5}, -S^2] + (580*Pi^2*HPL[{2, 1}, -S^2])/3 - 2320*HPL[{3, 2}, -S^2] - 7920*HPL[{4, 1}, -S^2] - 4640*HPL[{2, 2, 1}, -S^2] - 8320*HPL[{3, 1, 1}, -S^2] + (620*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*(1160*HPL[{3}, -S^2] + 2320*HPL[{2, 1}, -S^2] + 1160*Zeta[3]) + 1160*Zeta[5])) + HPL[{0}, S^2]^2*((-456659*Pi^8)/777600 - (5*HPL[{1}, -S^2]^8)/3 + HPL[{1}, -S^2]^6*((-19*Pi^2)/3 - (58*HPL[{2}, -S^2])/3) - (359*Pi^2*HPL[{2}, -S^2]^3)/36 - (119*HPL[{2}, -S^2]^4)/12 + 3*Pi^2*HPL[{3}, -S^2]^2 - 40*HPL[{4}, -S^2]^2 - (235*Pi^2*HPL[{6}, -S^2])/12 - (991*HPL[{8}, -S^2])/2 + (749*Pi^2*HPL[{2, 1}, -S^2]^2)/6 - 480*HPL[{3, 1}, -S^2]^2 + (Pi^2*HPL[{4, 2}, -S^2])/2 + (34*Pi^2*HPL[{5, 1}, -S^2])/3 + HPL[{5, 3}, -S^2] + (5*HPL[{6, 2}, -S^2])/2 + 286*HPL[{7, 1}, -S^2] + HPL[{1}, -S^2]^4*((-659*Pi^4)/72 - (707*Pi^2*HPL[{2}, -S^2])/18 - (239*HPL[{2}, -S^2]^2)/3 + (8*HPL[{4}, -S^2])/3 + (856*HPL[{3, 1}, -S^2])/3 - 580*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]^2*((-7859*Pi^4)/1440 - 13*HPL[{4}, -S^2] + 219*HPL[{3, 1}, -S^2] - 430*HPL[{2, 1, 1}, -S^2]) + HPL[{4}, -S^2]*((-3*Pi^4)/20 + 62*HPL[{3, 1}, -S^2] - 28*HPL[{2, 1, 1}, -S^2]) - (853*Pi^4*HPL[{2, 1, 1}, -S^2])/20 - 1912*HPL[{2, 1, 1}, -S^2]^2 + HPL[{3, 1}, -S^2]*((2459*Pi^4)/120 + 1912*HPL[{2, 1, 1}, -S^2]) - (718*Pi^2*HPL[{3, 2, 1}, -S^2])/3 + 100*HPL[{3, 3, 2}, -S^2] - (2146*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 204*HPL[{4, 1, 3}, -S^2] + 92*HPL[{4, 2, 2}, -S^2] - 428*HPL[{4, 3, 1}, -S^2] - 232*HPL[{5, 1, 2}, -S^2] - 1792*HPL[{5, 2, 1}, -S^2] - 4718*HPL[{6, 1, 1}, -S^2] + 462*Pi^2*HPL[{3, 1, 1, 1}, -S^2] + 4*HPL[{3, 1, 2, 2}, -S^2] + 4*HPL[{3, 2, 1, 2}, -S^2] + 1740*HPL[{3, 2, 2, 1}, -S^2] + 5208*HPL[{3, 3, 1, 1}, -S^2] + 12*HPL[{4, 1, 1, 2}, -S^2] + 5220*HPL[{4, 1, 2, 1}, -S^2] + 15636*HPL[{4, 2, 1, 1}, -S^2] + 31256*HPL[{5, 1, 1, 1}, -S^2] - (2828*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + 3440*HPL[{2, 2, 1, 2, 1}, -S^2] + 10320*HPL[{2, 2, 2, 1, 1}, -S^2] - 20640*HPL[{3, 1, 1, 1, 2}, -S^2] - 34400*HPL[{3, 1, 1, 2, 1}, -S^2] - 41280*HPL[{3, 1, 2, 1, 1}, -S^2] - 86000*HPL[{3, 2, 1, 1, 1}, -S^2] - 257936*HPL[{4, 1, 1, 1, 1}, -S^2] + 6848*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 13920*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] - 60*HPL[{3, 2}, -S^2]*Zeta[3] - 200*HPL[{4, 1}, -S^2]*Zeta[3] + 148*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 476*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 344*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (31*Pi^2*Zeta[3]^2)/6 + HPL[{1}, -S^2]^5*((20*HPL[{3}, -S^2])/3 + 116*HPL[{2, 1}, -S^2] + 12*Zeta[3]) + HPL[{5}, -S^2]*(-14*HPL[{2, 1}, -S^2] + 98*Zeta[3]) + HPL[{1}, -S^2]^2*((-3413*Pi^6)/648 - (749*Pi^2*HPL[{2}, -S^2]^2)/12 - (215*HPL[{2}, -S^2]^3)/3 + 6*HPL[{3}, -S^2]^2 + (4*Pi^2*HPL[{4}, -S^2])/3 - 19*HPL[{6}, -S^2] + 956*HPL[{2, 1}, -S^2]^2 + 231*Pi^2*HPL[{3, 1}, -S^2] + 6*HPL[{4, 2}, -S^2] + 4*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-853*Pi^4)/40 - 14*HPL[{4}, -S^2] + 956*HPL[{3, 1}, -S^2] - 1912*HPL[{2, 1, 1}, -S^2]) - (1414*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 1720*HPL[{3, 2, 1}, -S^2] - 5128*HPL[{4, 1, 1}, -S^2] + 3424*HPL[{3, 1, 1, 1}, -S^2] - 6960*HPL[{2, 1, 1, 1, 1}, -S^2] - 172*HPL[{2, 1}, -S^2]*Zeta[3] - 20*Zeta[3]^2 + HPL[{3}, -S^2]*(-96*HPL[{2, 1}, -S^2] + 16*Zeta[3])) + HPL[{2}, -S^2]*((-162979*Pi^6)/90720 + 13*HPL[{3}, -S^2]^2 - (37*Pi^2*HPL[{4}, -S^2])/6 - (167*HPL[{6}, -S^2])/2 + 430*HPL[{2, 1}, -S^2]^2 + (386*Pi^2*HPL[{3, 1}, -S^2])/3 + 4*HPL[{4, 2}, -S^2] + 66*HPL[{5, 1}, -S^2] - (749*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 4*HPL[{3, 1, 2}, -S^2] - 956*HPL[{3, 2, 1}, -S^2] - 2884*HPL[{4, 1, 1}, -S^2] + 22552*HPL[{3, 1, 1, 1}, -S^2] - 3824*HPL[{2, 1, 1, 1, 1}, -S^2] - 74*HPL[{2, 1}, -S^2]*Zeta[3] - 29*Zeta[3]^2 + HPL[{3}, -S^2]*(-38*HPL[{2, 1}, -S^2] + 30*Zeta[3])) + HPL[{2, 1}, -S^2]*(80*HPL[{3, 2}, -S^2] + 256*HPL[{4, 1}, -S^2] - 1720*HPL[{2, 2, 1}, -S^2] - 5352*HPL[{3, 1, 1}, -S^2] + 3824*HPL[{2, 1, 1, 1}, -S^2] - (43*Pi^2*Zeta[3])/3 - 74*Zeta[5]) - 30*Zeta[3]*Zeta[5] + HPL[{1}, -S^2]^3*((56*Pi^2*HPL[{3}, -S^2])/9 + 12*HPL[{5}, -S^2] + (1414*Pi^2*HPL[{2, 1}, -S^2])/9 - 64*HPL[{3, 2}, -S^2] - (608*HPL[{4, 1}, -S^2])/3 - (3824*HPL[{2, 2, 1}, -S^2])/3 - (11072*HPL[{3, 1, 1}, -S^2])/3 + 2320*HPL[{2, 1, 1, 1}, -S^2] + (76*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*(32*HPL[{3}, -S^2] + (1912*HPL[{2, 1}, -S^2])/3 + (172*Zeta[3])/3) + 52*Zeta[5]) + HPL[{3}, -S^2]*(81*HPL[{5}, -S^2] - 9*Pi^2*HPL[{2, 1}, -S^2] - 52*HPL[{3, 2}, -S^2] + 42*HPL[{4, 1}, -S^2] + 76*HPL[{2, 2, 1}, -S^2] + 252*HPL[{3, 1, 1}, -S^2] - 192*HPL[{2, 1, 1, 1}, -S^2] + (19*Pi^2*Zeta[3])/3 + 58*Zeta[5]) + HPL[{1}, -S^2]*(2*Pi^2*HPL[{5}, -S^2] - 114*HPL[{7}, -S^2] - 18*Pi^2*HPL[{3, 2}, -S^2] - (170*Pi^2*HPL[{4, 1}, -S^2])/3 + 16*HPL[{4, 3}, -S^2] + 44*HPL[{5, 2}, -S^2] + 98*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((853*Pi^4)/20 - 1912*HPL[{3, 1}, -S^2] - 3824*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((241*Pi^4)/180 - 10*HPL[{4}, -S^2] - 100*HPL[{3, 1}, -S^2] + 192*HPL[{2, 1, 1}, -S^2]) - (1498*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (4382*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 164*HPL[{3, 2, 2}, -S^2] + 520*HPL[{3, 3, 1}, -S^2] + 524*HPL[{4, 1, 2}, -S^2] + 1580*HPL[{4, 2, 1}, -S^2] + 3240*HPL[{5, 1, 1}, -S^2] + (2828*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 3440*HPL[{2, 2, 2, 1}, -S^2] - 10704*HPL[{3, 1, 1, 2}, -S^2] - 10704*HPL[{3, 1, 2, 1}, -S^2] - 21024*HPL[{3, 2, 1, 1}, -S^2] - 63136*HPL[{4, 1, 1, 1}, -S^2] + 7648*HPL[{2, 1, 2, 1, 1}, -S^2] + 22944*HPL[{2, 2, 1, 1, 1}, -S^2] + 39040*HPL[{3, 1, 1, 1, 1}, -S^2] + 13920*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (373*Pi^4*Zeta[3])/180 - 180*HPL[{3, 1}, -S^2]*Zeta[3] + 344*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(28*HPL[{2, 1}, -S^2] + 20*Zeta[3]) + HPL[{2}, -S^2]^2*(19*HPL[{3}, -S^2] + 430*HPL[{2, 1}, -S^2] + 37*Zeta[3]) - (26*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*(9*Pi^2*HPL[{3}, -S^2] + 14*HPL[{5}, -S^2] + (749*Pi^2*HPL[{2, 1}, -S^2])/3 - 80*HPL[{3, 2}, -S^2] - 256*HPL[{4, 1}, -S^2] - 1720*HPL[{2, 2, 1}, -S^2] + 5352*HPL[{3, 1, 1}, -S^2] + 3824*HPL[{2, 1, 1, 1}, -S^2] + (43*Pi^2*Zeta[3])/3 + 74*Zeta[5]))) + HPL[{2, 1}, -S^2]*(656*Pi^2*HPL[{3, 2}, -S^2] + (5944*Pi^2*HPL[{4, 1}, -S^2])/3 - 172*HPL[{4, 3}, -S^2] - 324*HPL[{5, 2}, -S^2] + 260*HPL[{6, 1}, -S^2] - (1720*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - 2944*Pi^2*HPL[{3, 1, 1}, -S^2] - 6880*HPL[{3, 2, 2}, -S^2] - 21984*HPL[{3, 3, 1}, -S^2] - 21984*HPL[{4, 1, 2}, -S^2] - 67296*HPL[{4, 2, 1}, -S^2] - 137408*HPL[{5, 1, 1}, -S^2] + (10784*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 13760*HPL[{2, 2, 2, 1}, -S^2] - 26176*HPL[{3, 1, 1, 2}, -S^2] - 26176*HPL[{3, 1, 2, 1}, -S^2] - 67456*HPL[{3, 2, 1, 1}, -S^2] - 202176*HPL[{4, 1, 1, 1}, -S^2] - 27840*HPL[{3, 1, 1, 1, 1}, -S^2] + 55680*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (3383*Pi^4*Zeta[3])/90 + 3136*HPL[{3, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 1, 1}, -S^2]*Zeta[3] - 294*Pi^2*Zeta[5] - 1692*Zeta[7]) + Log[T]^3*(HPL[{0}, S^2]^7/9 + (11*HPL[{0}, S^2]^6*HPL[{1}, -S^2])/9 + (784*Pi^2*HPL[{1}, -S^2]^5)/9 + 32*HPL[{1}, -S^2]^7 + HPL[{0}, S^2]^5*((373*Pi^2)/270 + (326*HPL[{1}, -S^2]^2)/45 + (271*HPL[{2}, -S^2])/90) - (164*Pi^2*HPL[{5}, -S^2])/3 + 152*HPL[{7}, -S^2] + HPL[{1}, -S^2]^3*((2026*Pi^4)/27 + (1160*Pi^2*HPL[{2}, -S^2])/9 + (2320*HPL[{2}, -S^2]^2)/3 - 640*HPL[{4}, -S^2] + 640*HPL[{3, 1}, -S^2]) + 408*Pi^2*HPL[{3, 2}, -S^2] + (12488*Pi^2*HPL[{4, 1}, -S^2])/9 - (464*HPL[{4, 3}, -S^2])/3 - 352*HPL[{5, 2}, -S^2] - (208*HPL[{6, 1}, -S^2])/3 + HPL[{3}, -S^2]*((-3998*Pi^4)/135 + (400*HPL[{4}, -S^2])/3 + (6976*HPL[{3, 1}, -S^2])/3 - 4640*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-1354*Pi^4)/27 + 4640*HPL[{3, 1}, -S^2] + 9280*HPL[{2, 1, 1}, -S^2]) + (10784*Pi^2*HPL[{2, 2, 1}, -S^2])/9 + (23552*Pi^2*HPL[{3, 1, 1}, -S^2])/9 - (14432*HPL[{3, 2, 2}, -S^2])/3 - 14720*HPL[{3, 3, 1}, -S^2] - 14496*HPL[{4, 1, 2}, -S^2] - 44896*HPL[{4, 2, 1}, -S^2] - 92416*HPL[{5, 1, 1}, -S^2] - (2320*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 9280*HPL[{3, 1, 1, 2}, -S^2] + 9280*HPL[{3, 1, 2, 1}, -S^2] + 9280*HPL[{3, 2, 1, 1}, -S^2] + 31680*HPL[{4, 1, 1, 1}, -S^2] - 18560*HPL[{2, 1, 2, 1, 1}, -S^2] - 55680*HPL[{2, 2, 1, 1, 1}, -S^2] - 115200*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^3*((2467*Pi^4)/405 + (560*HPL[{1}, -S^2]^4)/9 + (646*Pi^2*HPL[{2}, -S^2])/27 + (356*HPL[{2}, -S^2]^2)/9 + HPL[{1}, -S^2]^2*((1492*Pi^2)/27 + (500*HPL[{2}, -S^2])/3) + (80*HPL[{4}, -S^2])/9 - (1496*HPL[{3, 1}, -S^2])/9 + (1000*HPL[{2, 1, 1}, -S^2])/3 + HPL[{1}, -S^2]*(8*HPL[{3}, -S^2] - (1000*HPL[{2, 1}, -S^2])/3 - (56*Zeta[3])/9)) + HPL[{1}, -S^2]^4*((-2800*HPL[{3}, -S^2])/3 - (2240*Zeta[3])/3) + HPL[{2}, -S^2]^2*((-2056*HPL[{3}, -S^2])/3 - (1568*Zeta[3])/3) + HPL[{4}, -S^2]*(640*HPL[{2, 1}, -S^2] - (256*Zeta[3])/3) + HPL[{0}, S^2]^4*((220*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((110*Pi^2)/9 + (272*HPL[{2}, -S^2])/9) - HPL[{3}, -S^2]/3 - (272*HPL[{2, 1}, -S^2])/9 + (7*Zeta[3])/9) - (3353*Pi^4*Zeta[3])/135 + (7168*HPL[{3, 1}, -S^2]*Zeta[3])/3 - 4640*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{1}, -S^2]*((484*Pi^6)/27 + (2696*Pi^2*HPL[{2}, -S^2]^2)/9 + 208*HPL[{3}, -S^2]^2 - (1472*Pi^2*HPL[{4}, -S^2])/9 - 144*HPL[{6}, -S^2] - 4640*HPL[{2, 1}, -S^2]^2 - (1984*Pi^2*HPL[{3, 1}, -S^2])/9 + 672*HPL[{4, 2}, -S^2] + 3840*HPL[{5, 1}, -S^2] + (2320*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((1354*Pi^4)/27 - 640*HPL[{4}, -S^2] - 4640*HPL[{3, 1}, -S^2] + 9280*HPL[{2, 1, 1}, -S^2]) - 3840*HPL[{4, 1, 1}, -S^2] + 3840*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(4640*HPL[{2, 1}, -S^2] - (896*Zeta[3])/3) + 4640*HPL[{2, 1}, -S^2]*Zeta[3] + 112*Zeta[3]^2) + HPL[{0}, S^2]*((2863*Pi^6)/324 + 112*HPL[{1}, -S^2]^6 + (1226*Pi^2*HPL[{2}, -S^2]^2)/9 + (1568*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((1820*Pi^2)/9 + (2240*HPL[{2}, -S^2])/3) - 8*HPL[{3}, -S^2]^2 + (200*Pi^2*HPL[{4}, -S^2])/9 + (292*HPL[{6}, -S^2])/3 - 2320*HPL[{2, 1}, -S^2]^2 - (4856*Pi^2*HPL[{3, 1}, -S^2])/9 - (544*HPL[{5, 1}, -S^2])/3 + 1080*Pi^2*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((12283*Pi^4)/270 + 16*HPL[{4}, -S^2] - 2320*HPL[{3, 1}, -S^2] + 4640*HPL[{2, 1, 1}, -S^2]) + HPL[{1}, -S^2]^2*((14057*Pi^4)/135 + 540*Pi^2*HPL[{2}, -S^2] + 1160*HPL[{2}, -S^2]^2 + 160*HPL[{4}, -S^2] - 4480*HPL[{3, 1}, -S^2] + 8960*HPL[{2, 1, 1}, -S^2]) + (12544*HPL[{3, 2, 1}, -S^2])/3 + 12864*HPL[{4, 1, 1}, -S^2] - 8960*HPL[{3, 1, 1, 1}, -S^2] + 17920*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^3*((-160*HPL[{3}, -S^2])/3 - (8960*HPL[{2, 1}, -S^2])/3 - 320*Zeta[3]) + HPL[{3}, -S^2]*((688*HPL[{2, 1}, -S^2])/3 - (16*Zeta[3])/3) + 464*HPL[{2, 1}, -S^2]*Zeta[3] + 56*Zeta[3]^2 + HPL[{1}, -S^2]*((-16*Pi^2*HPL[{3}, -S^2])/3 + (448*HPL[{5}, -S^2])/3 - 1080*Pi^2*HPL[{2, 1}, -S^2] + (1376*HPL[{3, 2}, -S^2])/3 + 1056*HPL[{4, 1}, -S^2] + 9280*HPL[{2, 2, 1}, -S^2] + 27520*HPL[{3, 1, 1}, -S^2] - 17920*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-688*HPL[{3}, -S^2])/3 - 4640*HPL[{2, 1}, -S^2] - 464*Zeta[3]) - (776*Pi^2*Zeta[3])/9 - (1040*Zeta[5])/3)) + HPL[{1}, -S^2]^2*((-4400*Pi^2*HPL[{3}, -S^2])/9 - 608*HPL[{5}, -S^2] - (1160*Pi^2*HPL[{2, 1}, -S^2])/3 + 4640*HPL[{3, 2}, -S^2] + 15840*HPL[{4, 1}, -S^2] + 9280*HPL[{2, 2, 1}, -S^2] + 16640*HPL[{3, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-2320*HPL[{3}, -S^2] - 4640*HPL[{2, 1}, -S^2] - 2320*Zeta[3]) - (1240*Pi^2*Zeta[3])/3 - 2320*Zeta[5]) + HPL[{2}, -S^2]*(-204*Pi^2*HPL[{3}, -S^2] - (736*HPL[{5}, -S^2])/3 - (5392*Pi^2*HPL[{2, 1}, -S^2])/9 + (7552*HPL[{3, 2}, -S^2])/3 + 7584*HPL[{4, 1}, -S^2] - 4640*HPL[{3, 1, 1}, -S^2] - 9280*HPL[{2, 1, 1, 1}, -S^2] - (1912*Pi^2*Zeta[3])/9 - (3232*Zeta[5])/3) + HPL[{0}, S^2]^2*((280*HPL[{1}, -S^2]^5)/3 + HPL[{1}, -S^2]^3*((380*Pi^2)/3 + (1160*HPL[{2}, -S^2])/3) - (56*Pi^2*HPL[{3}, -S^2])/9 - 12*HPL[{5}, -S^2] - (1414*Pi^2*HPL[{2, 1}, -S^2])/9 + 64*HPL[{3, 2}, -S^2] + (608*HPL[{4, 1}, -S^2])/3 + HPL[{1}, -S^2]*((659*Pi^4)/18 + (1414*Pi^2*HPL[{2}, -S^2])/9 + (956*HPL[{2}, -S^2]^2)/3 - (32*HPL[{4}, -S^2])/3 - (3424*HPL[{3, 1}, -S^2])/3 + 2320*HPL[{2, 1, 1}, -S^2]) + (3824*HPL[{2, 2, 1}, -S^2])/3 + (11072*HPL[{3, 1, 1}, -S^2])/3 - 2320*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((-200*HPL[{3}, -S^2])/3 - 1160*HPL[{2, 1}, -S^2] - 120*Zeta[3]) + HPL[{2}, -S^2]*(-32*HPL[{3}, -S^2] - (1912*HPL[{2, 1}, -S^2])/3 - (172*Zeta[3])/3) - (76*Pi^2*Zeta[3])/9 - 52*Zeta[5]) - (632*Pi^2*Zeta[5])/3 - 1488*Zeta[7]) + HPL[{0}, S^2]^3*((-16*HPL[{1}, -S^2]^7)/9 + HPL[{1}, -S^2]^5*((-746*Pi^2)/135 - (50*HPL[{2}, -S^2])/3) + (31*Pi^2*HPL[{5}, -S^2])/18 + (185*HPL[{7}, -S^2])/3 - (25*Pi^2*HPL[{3, 2}, -S^2])/9 - (40*Pi^2*HPL[{4, 1}, -S^2])/9 + (89*HPL[{4, 3}, -S^2])/3 + (268*HPL[{5, 2}, -S^2])/3 + 152*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((334*Pi^4)/45 - (712*HPL[{3, 1}, -S^2])/3 - (1424*HPL[{2, 1, 1}, -S^2])/3) + HPL[{1}, -S^2]^3*((-2467*Pi^4)/405 - (646*Pi^2*HPL[{2}, -S^2])/27 - (356*HPL[{2}, -S^2]^2)/9 - (80*HPL[{4}, -S^2])/9 + (1496*HPL[{3, 1}, -S^2])/9 - (1000*HPL[{2, 1, 1}, -S^2])/3) + HPL[{3}, -S^2]*((-131*Pi^4)/360 - (44*HPL[{4}, -S^2])/3 - 18*HPL[{3, 1}, -S^2] + (40*HPL[{2, 1, 1}, -S^2])/3) - (587*Pi^2*HPL[{2, 2, 1}, -S^2])/9 - 201*Pi^2*HPL[{3, 1, 1}, -S^2] + 30*HPL[{3, 2, 2}, -S^2] + (284*HPL[{3, 3, 1}, -S^2])/3 + (286*HPL[{4, 1, 2}, -S^2])/3 + (862*HPL[{4, 2, 1}, -S^2])/3 + (1672*HPL[{5, 1, 1}, -S^2])/3 + (1292*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/9 + 448*HPL[{2, 2, 2, 1}, -S^2] - (4112*HPL[{3, 1, 1, 2}, -S^2])/3 - (4112*HPL[{3, 1, 2, 1}, -S^2])/3 - (8144*HPL[{3, 2, 1, 1}, -S^2])/3 - (24272*HPL[{4, 1, 1, 1}, -S^2])/3 + (2848*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 2848*HPL[{2, 2, 1, 1, 1}, -S^2] + (14096*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + 2000*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*((14*HPL[{2, 1}, -S^2])/3 - 20*Zeta[3]) + HPL[{2}, -S^2]^2*((7*HPL[{3}, -S^2])/2 + 56*HPL[{2, 1}, -S^2] - (5*Zeta[3])/2) - (3353*Pi^4*Zeta[3])/1080 + 14*HPL[{3, 1}, -S^2]*Zeta[3] + (20*HPL[{2, 1, 1}, -S^2]*Zeta[3])/3 + HPL[{1}, -S^2]^4*(-2*HPL[{3}, -S^2] + (250*HPL[{2, 1}, -S^2])/3 + (14*Zeta[3])/9) + HPL[{1}, -S^2]*((-2863*Pi^6)/1296 - (587*Pi^2*HPL[{2}, -S^2]^2)/36 - (56*HPL[{2}, -S^2]^3)/3 + 2*HPL[{3}, -S^2]^2 - (35*Pi^2*HPL[{4}, -S^2])/9 - 2*HPL[{6}, -S^2] + (712*HPL[{2, 1}, -S^2]^2)/3 + (635*Pi^2*HPL[{3, 1}, -S^2])/9 + 2*HPL[{4, 2}, -S^2] + 32*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-334*Pi^4)/45 - (14*HPL[{4}, -S^2])/3 + (712*HPL[{3, 1}, -S^2])/3 - (1424*HPL[{2, 1, 1}, -S^2])/3) - (1292*Pi^2*HPL[{2, 1, 1}, -S^2])/9 - 448*HPL[{3, 2, 1}, -S^2] - (4192*HPL[{4, 1, 1}, -S^2])/3 + (2992*HPL[{3, 1, 1, 1}, -S^2])/3 - 2000*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((-40*HPL[{2, 1}, -S^2])/3 - 4*Zeta[3]) - (20*HPL[{2, 1}, -S^2]*Zeta[3])/3 - 14*Zeta[3]^2) + HPL[{1}, -S^2]^2*((-8*Pi^2*HPL[{3}, -S^2])/3 - (28*HPL[{5}, -S^2])/3 + (646*Pi^2*HPL[{2, 1}, -S^2])/9 - (40*HPL[{3, 2}, -S^2])/3 - (40*HPL[{4, 1}, -S^2])/3 - (1424*HPL[{2, 2, 1}, -S^2])/3 - 1448*HPL[{3, 1, 1}, -S^2] + 1000*HPL[{2, 1, 1, 1}, -S^2] - (38*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*((20*HPL[{3}, -S^2])/3 + (712*HPL[{2, 1}, -S^2])/3 + (10*Zeta[3])/3) - 26*Zeta[5]) + HPL[{2}, -S^2]*((25*Pi^2*HPL[{3}, -S^2])/18 + (43*HPL[{5}, -S^2])/3 + (587*Pi^2*HPL[{2, 1}, -S^2])/18 - (44*HPL[{3, 2}, -S^2])/3 - (140*HPL[{4, 1}, -S^2])/3 - 224*HPL[{2, 2, 1}, -S^2] + (2056*HPL[{3, 1, 1}, -S^2])/3 + (1424*HPL[{2, 1, 1, 1}, -S^2])/3 - (25*Pi^2*Zeta[3])/18 - (44*Zeta[5])/3) - (79*Pi^2*Zeta[5])/3 - 186*Zeta[7]) + HPL[{3}, -S^2]*((88*Pi^2*HPL[{5}, -S^2])/3 + 1072*HPL[{7}, -S^2] + (116*Pi^2*HPL[{3, 2}, -S^2])/3 + (110*Pi^2*HPL[{4, 1}, -S^2])/3 - 456*HPL[{4, 3}, -S^2] - 1368*HPL[{5, 2}, -S^2] - 3332*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-1661*Pi^4)/45 + 4112*HPL[{3, 1}, -S^2] + 8224*HPL[{2, 1, 1}, -S^2]) + (2132*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + 2036*Pi^2*HPL[{3, 1, 1}, -S^2] - 392*HPL[{3, 2, 2}, -S^2] - 1216*HPL[{3, 3, 1}, -S^2] + 564*HPL[{4, 1, 2}, -S^2] + 756*HPL[{4, 2, 1}, -S^2] + 632*HPL[{5, 1, 1}, -S^2] - 1224*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 6880*HPL[{2, 2, 2, 1}, -S^2] + 21984*HPL[{3, 1, 1, 2}, -S^2] + 21984*HPL[{3, 1, 2, 1}, -S^2] + 42624*HPL[{3, 2, 1, 1}, -S^2] + 160672*HPL[{4, 1, 1, 1}, -S^2] - 16448*HPL[{2, 1, 2, 1, 1}, -S^2] - 49344*HPL[{2, 2, 1, 1, 1}, -S^2] - 84736*HPL[{3, 1, 1, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(180*HPL[{2, 1}, -S^2] - 164*Zeta[3]) + (65*Pi^4*Zeta[3])/18 - 184*HPL[{3, 1}, -S^2]*Zeta[3] + 304*HPL[{2, 1, 1}, -S^2]*Zeta[3] + (106*Pi^2*Zeta[5])/3 + 300*Zeta[7]) + Zeta[3]*(-20*Pi^2*Zeta[5] + 600*Zeta[7]) + HPL[{1}, -S^2]^3*((164*Pi^2*HPL[{5}, -S^2])/3 - 152*HPL[{7}, -S^2] - 408*Pi^2*HPL[{3, 2}, -S^2] - (12488*Pi^2*HPL[{4, 1}, -S^2])/9 + (464*HPL[{4, 3}, -S^2])/3 + 352*HPL[{5, 2}, -S^2] + (208*HPL[{6, 1}, -S^2])/3 + HPL[{2, 1}, -S^2]*((1354*Pi^4)/27 - 4640*HPL[{3, 1}, -S^2] - 9280*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((3998*Pi^4)/135 - (400*HPL[{4}, -S^2])/3 - (6976*HPL[{3, 1}, -S^2])/3 + 4640*HPL[{2, 1, 1}, -S^2]) - (10784*Pi^2*HPL[{2, 2, 1}, -S^2])/9 - (23552*Pi^2*HPL[{3, 1, 1}, -S^2])/9 + (14432*HPL[{3, 2, 2}, -S^2])/3 + 14720*HPL[{3, 3, 1}, -S^2] + 14496*HPL[{4, 1, 2}, -S^2] + 44896*HPL[{4, 2, 1}, -S^2] + 92416*HPL[{5, 1, 1}, -S^2] + (2320*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 9280*HPL[{3, 1, 1, 2}, -S^2] - 9280*HPL[{3, 1, 2, 1}, -S^2] - 9280*HPL[{3, 2, 1, 1}, -S^2] - 31680*HPL[{4, 1, 1, 1}, -S^2] + 18560*HPL[{2, 1, 2, 1, 1}, -S^2] + 55680*HPL[{2, 2, 1, 1, 1}, -S^2] + 115200*HPL[{3, 1, 1, 1, 1}, -S^2] + (3353*Pi^4*Zeta[3])/135 - (7168*HPL[{3, 1}, -S^2]*Zeta[3])/3 + 4640*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-640*HPL[{2, 1}, -S^2] + (256*Zeta[3])/3) + HPL[{2}, -S^2]^2*((2056*HPL[{3}, -S^2])/3 + (1568*Zeta[3])/3) + (632*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*(204*Pi^2*HPL[{3}, -S^2] + (736*HPL[{5}, -S^2])/3 + (5392*Pi^2*HPL[{2, 1}, -S^2])/9 - (7552*HPL[{3, 2}, -S^2])/3 - 7584*HPL[{4, 1}, -S^2] + 4640*HPL[{3, 1, 1}, -S^2] + 9280*HPL[{2, 1, 1, 1}, -S^2] + (1912*Pi^2*Zeta[3])/9 + (3232*Zeta[5])/3) + 1488*Zeta[7]) + Log[T]^2*((-456659*Pi^8)/194400 - (5*HPL[{0}, S^2]^8)/192 - (HPL[{0}, S^2]^7*HPL[{1}, -S^2])/3 - (392*Pi^2*HPL[{1}, -S^2]^6)/9 - 12*HPL[{1}, -S^2]^8 + HPL[{0}, S^2]^6*((-19*Pi^2)/48 - (11*HPL[{1}, -S^2]^2)/6 - (2*HPL[{2}, -S^2])/3) - (215*Pi^2*HPL[{2}, -S^2]^3)/9 - (215*HPL[{2}, -S^2]^4)/3 - 24*Pi^2*HPL[{3}, -S^2]^2 - 28*HPL[{4}, -S^2]^2 + (35*Pi^2*HPL[{6}, -S^2])/3 - 1326*HPL[{8}, -S^2] + (2696*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + HPL[{1}, -S^2]^4*((-1013*Pi^4)/18 - (290*Pi^2*HPL[{2}, -S^2])/3 - 580*HPL[{2}, -S^2]^2 + 480*HPL[{4}, -S^2] - 480*HPL[{3, 1}, -S^2]) + HPL[{2}, -S^2]^2*((-13303*Pi^4)/360 + 336*HPL[{4}, -S^2] - 336*HPL[{3, 1}, -S^2]) - 4160*HPL[{3, 1}, -S^2]^2 - 82*Pi^2*HPL[{4, 2}, -S^2] - (1436*Pi^2*HPL[{5, 1}, -S^2])/3 + 36*HPL[{5, 3}, -S^2] + 90*HPL[{6, 2}, -S^2] + 616*HPL[{7, 1}, -S^2] - (1354*Pi^4*HPL[{2, 1, 1}, -S^2])/9 - 13920*HPL[{2, 1, 1}, -S^2]^2 + HPL[{4}, -S^2]*((686*Pi^4)/45 - 944*HPL[{3, 1}, -S^2] + 1920*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 1}, -S^2]*((1769*Pi^4)/30 + 13920*HPL[{2, 1, 1}, -S^2]) - (1720*Pi^2*HPL[{3, 2, 1}, -S^2])/3 - 1008*HPL[{3, 3, 2}, -S^2] - (3688*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 1680*HPL[{4, 1, 3}, -S^2] - 672*HPL[{4, 2, 2}, -S^2] + 5712*HPL[{4, 3, 1}, -S^2] + 3360*HPL[{5, 1, 2}, -S^2] + 23520*HPL[{5, 2, 1}, -S^2] + 60912*HPL[{6, 1, 1}, -S^2] + (1984*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 - 672*HPL[{3, 1, 2, 2}, -S^2] - 672*HPL[{3, 2, 1, 2}, -S^2] - 672*HPL[{3, 2, 2, 1}, -S^2] - 2016*HPL[{4, 1, 1, 2}, -S^2] - 2016*HPL[{4, 1, 2, 1}, -S^2] - 2016*HPL[{4, 2, 1, 1}, -S^2] - 11520*HPL[{5, 1, 1, 1}, -S^2] - 2320*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] + 11520*HPL[{4, 1, 1, 1, 1}, -S^2] - 11520*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^4*((-659*Pi^4)/288 - (55*HPL[{1}, -S^2]^4)/3 + HPL[{1}, -S^2]^2*((-55*Pi^2)/3 - (136*HPL[{2}, -S^2])/3) - (64*Pi^2*HPL[{2}, -S^2])/9 - (271*HPL[{2}, -S^2]^2)/24 + (265*HPL[{3, 1}, -S^2])/6 - (272*HPL[{2, 1, 1}, -S^2])/3 + HPL[{1}, -S^2]*(HPL[{3}, -S^2] + (272*HPL[{2, 1}, -S^2])/3 - (7*Zeta[3])/3)) + HPL[{0}, S^2]^5*((-326*HPL[{1}, -S^2]^3)/45 + HPL[{1}, -S^2]*((-373*Pi^2)/90 - (271*HPL[{2}, -S^2])/30) - HPL[{3}, -S^2]/2 + (271*HPL[{2, 1}, -S^2])/30 - (3*Zeta[3])/2) - 304*HPL[{3, 2}, -S^2]*Zeta[3] - 1168*HPL[{4, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 19712*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 13920*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (62*Pi^2*Zeta[3]^2)/3 + HPL[{5}, -S^2]*(-736*HPL[{2, 1}, -S^2] + 64*Zeta[3]) + HPL[{1}, -S^2]^5*(560*HPL[{3}, -S^2] + 448*Zeta[3]) + HPL[{2}, -S^2]*((-16733*Pi^6)/2520 - 168*HPL[{3}, -S^2]^2 + (226*Pi^2*HPL[{4}, -S^2])/3 + 10*HPL[{6}, -S^2] + (2696*Pi^2*HPL[{3, 1}, -S^2])/3 - 672*HPL[{4, 2}, -S^2] - 2624*HPL[{5, 1}, -S^2] - (5392*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 672*HPL[{3, 1, 2}, -S^2] - 6208*HPL[{3, 2, 1}, -S^2] - 18720*HPL[{4, 1, 1}, -S^2] + 13920*HPL[{3, 1, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1, 1}, -S^2] - 3136*HPL[{2, 1}, -S^2]*Zeta[3] + HPL[{3}, -S^2]*(-4112*HPL[{2, 1}, -S^2] + 152*Zeta[3])) + HPL[{1}, -S^2]^2*((-242*Pi^6)/9 - (1348*Pi^2*HPL[{2}, -S^2]^2)/3 - 312*HPL[{3}, -S^2]^2 + (736*Pi^2*HPL[{4}, -S^2])/3 + 216*HPL[{6}, -S^2] + 6960*HPL[{2, 1}, -S^2]^2 + (992*Pi^2*HPL[{3, 1}, -S^2])/3 - 1008*HPL[{4, 2}, -S^2] - 5760*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-677*Pi^4)/9 + 960*HPL[{4}, -S^2] + 6960*HPL[{3, 1}, -S^2] - 13920*HPL[{2, 1, 1}, -S^2]) - 1160*Pi^2*HPL[{2, 1, 1}, -S^2] + 5760*HPL[{4, 1, 1}, -S^2] - 5760*HPL[{3, 1, 1, 1}, -S^2] - 6960*HPL[{2, 1}, -S^2]*Zeta[3] - 168*Zeta[3]^2 + HPL[{3}, -S^2]*(-6960*HPL[{2, 1}, -S^2] + 448*Zeta[3])) + HPL[{2, 1}, -S^2]*(7552*HPL[{3, 2}, -S^2] + 22752*HPL[{4, 1}, -S^2] - 13920*HPL[{3, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2] - (1912*Pi^2*Zeta[3])/3 - 3232*Zeta[5]) + HPL[{0}, S^2]^3*((-112*HPL[{1}, -S^2]^5)/3 + HPL[{1}, -S^2]^3*((-1492*Pi^2)/27 - (500*HPL[{2}, -S^2])/3) - (8*Pi^2*HPL[{3}, -S^2])/3 - (28*HPL[{5}, -S^2])/3 + (646*Pi^2*HPL[{2, 1}, -S^2])/9 - (40*HPL[{3, 2}, -S^2])/3 - (40*HPL[{4, 1}, -S^2])/3 + HPL[{1}, -S^2]*((-2467*Pi^4)/135 - (646*Pi^2*HPL[{2}, -S^2])/9 - (356*HPL[{2}, -S^2]^2)/3 - (80*HPL[{4}, -S^2])/3 + (1496*HPL[{3, 1}, -S^2])/3 - 1000*HPL[{2, 1, 1}, -S^2]) - (1424*HPL[{2, 2, 1}, -S^2])/3 - 1448*HPL[{3, 1, 1}, -S^2] + 1000*HPL[{2, 1, 1, 1}, -S^2] - (38*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*((20*HPL[{3}, -S^2])/3 + (712*HPL[{2, 1}, -S^2])/3 + (10*Zeta[3])/3) + HPL[{1}, -S^2]^2*(-12*HPL[{3}, -S^2] + 500*HPL[{2, 1}, -S^2] + (28*Zeta[3])/3) - 26*Zeta[5]) - 120*Zeta[3]*Zeta[5] + HPL[{3}, -S^2]*(28*HPL[{5}, -S^2] - 612*Pi^2*HPL[{2, 1}, -S^2] + 672*HPL[{3, 2}, -S^2] + 272*HPL[{4, 1}, -S^2] + 8224*HPL[{2, 2, 1}, -S^2] + 23424*HPL[{3, 1, 1}, -S^2] - 13920*HPL[{2, 1, 1, 1}, -S^2] + (128*Pi^2*Zeta[3])/3 + 192*Zeta[5]) + HPL[{1}, -S^2]^3*((4400*Pi^2*HPL[{3}, -S^2])/9 + 608*HPL[{5}, -S^2] + (1160*Pi^2*HPL[{2, 1}, -S^2])/3 - 4640*HPL[{3, 2}, -S^2] - 15840*HPL[{4, 1}, -S^2] - 9280*HPL[{2, 2, 1}, -S^2] - 16640*HPL[{3, 1, 1}, -S^2] + (1240*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*(2320*HPL[{3}, -S^2] + 4640*HPL[{2, 1}, -S^2] + 2320*Zeta[3]) + 2320*Zeta[5]) + HPL[{0}, S^2]^2*((-3413*Pi^6)/648 - (140*HPL[{1}, -S^2]^6)/3 + HPL[{1}, -S^2]^4*(-95*Pi^2 - 290*HPL[{2}, -S^2]) - (749*Pi^2*HPL[{2}, -S^2]^2)/12 - (215*HPL[{2}, -S^2]^3)/3 + 6*HPL[{3}, -S^2]^2 + (4*Pi^2*HPL[{4}, -S^2])/3 - 19*HPL[{6}, -S^2] + 956*HPL[{2, 1}, -S^2]^2 + 231*Pi^2*HPL[{3, 1}, -S^2] + 6*HPL[{4, 2}, -S^2] + 4*HPL[{5, 1}, -S^2] + HPL[{1}, -S^2]^2*((-659*Pi^4)/12 - (707*Pi^2*HPL[{2}, -S^2])/3 - 478*HPL[{2}, -S^2]^2 + 16*HPL[{4}, -S^2] + 1712*HPL[{3, 1}, -S^2] - 3480*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]*((-853*Pi^4)/40 - 14*HPL[{4}, -S^2] + 956*HPL[{3, 1}, -S^2] - 1912*HPL[{2, 1, 1}, -S^2]) - (1414*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 1720*HPL[{3, 2, 1}, -S^2] - 5128*HPL[{4, 1, 1}, -S^2] + 3424*HPL[{3, 1, 1, 1}, -S^2] - 6960*HPL[{2, 1, 1, 1, 1}, -S^2] - 172*HPL[{2, 1}, -S^2]*Zeta[3] - 20*Zeta[3]^2 + HPL[{3}, -S^2]*(-96*HPL[{2, 1}, -S^2] + 16*Zeta[3]) + HPL[{1}, -S^2]^3*((200*HPL[{3}, -S^2])/3 + 1160*HPL[{2, 1}, -S^2] + 120*Zeta[3]) + HPL[{1}, -S^2]*((56*Pi^2*HPL[{3}, -S^2])/3 + 36*HPL[{5}, -S^2] + (1414*Pi^2*HPL[{2, 1}, -S^2])/3 - 192*HPL[{3, 2}, -S^2] - 608*HPL[{4, 1}, -S^2] - 3824*HPL[{2, 2, 1}, -S^2] - 11072*HPL[{3, 1, 1}, -S^2] + 6960*HPL[{2, 1, 1, 1}, -S^2] + (76*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*(96*HPL[{3}, -S^2] + 1912*HPL[{2, 1}, -S^2] + 172*Zeta[3]) + 156*Zeta[5])) + HPL[{0}, S^2]*(-48*HPL[{1}, -S^2]^7 + HPL[{1}, -S^2]^5*((-364*Pi^2)/3 - 448*HPL[{2}, -S^2]) - 28*Pi^2*HPL[{5}, -S^2] - 28*HPL[{7}, -S^2] - (212*Pi^2*HPL[{3, 2}, -S^2])/3 - (436*Pi^2*HPL[{4, 1}, -S^2])/3 + 44*HPL[{4, 3}, -S^2] + 120*HPL[{5, 2}, -S^2] + 452*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((12283*Pi^4)/90 - 6960*HPL[{3, 1}, -S^2] - 13920*HPL[{2, 1, 1}, -S^2]) + HPL[{1}, -S^2]^3*((-14057*Pi^4)/135 - 540*Pi^2*HPL[{2}, -S^2] - 1160*HPL[{2}, -S^2]^2 - 160*HPL[{4}, -S^2] + 4480*HPL[{3, 1}, -S^2] - 8960*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-127*Pi^4)/45 - 28*HPL[{4}, -S^2] - 352*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]) - (4904*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - 4888*Pi^2*HPL[{3, 1, 1}, -S^2] + 608*HPL[{3, 2, 2}, -S^2] + 1920*HPL[{3, 3, 1}, -S^2] + 1920*HPL[{4, 1, 2}, -S^2] + 5856*HPL[{4, 2, 1}, -S^2] + 11360*HPL[{5, 1, 1}, -S^2] + 3240*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + 12544*HPL[{2, 2, 2, 1}, -S^2] - 39008*HPL[{3, 1, 1, 2}, -S^2] - 39008*HPL[{3, 1, 2, 1}, -S^2] - 76640*HPL[{3, 2, 1, 1}, -S^2] - 228960*HPL[{4, 1, 1, 1}, -S^2] + 27840*HPL[{2, 1, 2, 1, 1}, -S^2] + 83520*HPL[{2, 2, 1, 1, 1}, -S^2] + 140160*HPL[{3, 1, 1, 1, 1}, -S^2] + 53760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(48*HPL[{2, 1}, -S^2] - 48*Zeta[3]) + (373*Pi^4*Zeta[3])/90 - 688*HPL[{3, 1}, -S^2]*Zeta[3] + 1392*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]^2*(76*HPL[{3}, -S^2] + 1568*HPL[{2, 1}, -S^2] + 168*Zeta[3]) + HPL[{1}, -S^2]^4*(40*HPL[{3}, -S^2] + 2240*HPL[{2, 1}, -S^2] + 240*Zeta[3]) + HPL[{1}, -S^2]*((-2863*Pi^6)/108 - (1226*Pi^2*HPL[{2}, -S^2]^2)/3 - (1568*HPL[{2}, -S^2]^3)/3 + 24*HPL[{3}, -S^2]^2 - (200*Pi^2*HPL[{4}, -S^2])/3 - 292*HPL[{6}, -S^2] + 6960*HPL[{2, 1}, -S^2]^2 + (4856*Pi^2*HPL[{3, 1}, -S^2])/3 + 544*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-12283*Pi^4)/90 - 48*HPL[{4}, -S^2] + 6960*HPL[{3, 1}, -S^2] - 13920*HPL[{2, 1, 1}, -S^2]) - 3240*Pi^2*HPL[{2, 1, 1}, -S^2] - 12544*HPL[{3, 2, 1}, -S^2] - 38592*HPL[{4, 1, 1}, -S^2] + 26880*HPL[{3, 1, 1, 1}, -S^2] - 53760*HPL[{2, 1, 1, 1, 1}, -S^2] - 1392*HPL[{2, 1}, -S^2]*Zeta[3] - 168*Zeta[3]^2 + HPL[{3}, -S^2]*(-688*HPL[{2, 1}, -S^2] + 16*Zeta[3])) + (52*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((106*Pi^2*HPL[{3}, -S^2])/3 + 40*HPL[{5}, -S^2] + (2452*Pi^2*HPL[{2, 1}, -S^2])/3 - 304*HPL[{3, 2}, -S^2] - 960*HPL[{4, 1}, -S^2] - 6272*HPL[{2, 2, 1}, -S^2] + 19504*HPL[{3, 1, 1}, -S^2] + 13920*HPL[{2, 1, 1, 1}, -S^2] + (184*Pi^2*Zeta[3])/3 + 164*Zeta[5]) + HPL[{1}, -S^2]^2*(8*Pi^2*HPL[{3}, -S^2] - 224*HPL[{5}, -S^2] + 1620*Pi^2*HPL[{2, 1}, -S^2] - 688*HPL[{3, 2}, -S^2] - 1584*HPL[{4, 1}, -S^2] - 13920*HPL[{2, 2, 1}, -S^2] - 41280*HPL[{3, 1, 1}, -S^2] + 26880*HPL[{2, 1, 1, 1}, -S^2] + (388*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*(344*HPL[{3}, -S^2] + 6960*HPL[{2, 1}, -S^2] + 696*Zeta[3]) + 520*Zeta[5])) + HPL[{1}, -S^2]*(164*Pi^2*HPL[{5}, -S^2] - 456*HPL[{7}, -S^2] - 1224*Pi^2*HPL[{3, 2}, -S^2] - (12488*Pi^2*HPL[{4, 1}, -S^2])/3 + 464*HPL[{4, 3}, -S^2] + 1056*HPL[{5, 2}, -S^2] + 208*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((1354*Pi^4)/9 - 13920*HPL[{3, 1}, -S^2] - 27840*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((3998*Pi^4)/45 - 400*HPL[{4}, -S^2] - 6976*HPL[{3, 1}, -S^2] + 13920*HPL[{2, 1, 1}, -S^2]) - (10784*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (23552*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 14432*HPL[{3, 2, 2}, -S^2] + 44160*HPL[{3, 3, 1}, -S^2] + 43488*HPL[{4, 1, 2}, -S^2] + 134688*HPL[{4, 2, 1}, -S^2] + 277248*HPL[{5, 1, 1}, -S^2] + 2320*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 27840*HPL[{3, 1, 1, 2}, -S^2] - 27840*HPL[{3, 1, 2, 1}, -S^2] - 27840*HPL[{3, 2, 1, 1}, -S^2] - 95040*HPL[{4, 1, 1, 1}, -S^2] + 55680*HPL[{2, 1, 2, 1, 1}, -S^2] + 167040*HPL[{2, 2, 1, 1, 1}, -S^2] + 345600*HPL[{3, 1, 1, 1, 1}, -S^2] + (3353*Pi^4*Zeta[3])/45 - 7168*HPL[{3, 1}, -S^2]*Zeta[3] + 13920*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-1920*HPL[{2, 1}, -S^2] + 256*Zeta[3]) + HPL[{2}, -S^2]^2*(2056*HPL[{3}, -S^2] + 1568*Zeta[3]) + 632*Pi^2*Zeta[5] + HPL[{2}, -S^2]*(612*Pi^2*HPL[{3}, -S^2] + 736*HPL[{5}, -S^2] + (5392*Pi^2*HPL[{2, 1}, -S^2])/3 - 7552*HPL[{3, 2}, -S^2] - 22752*HPL[{4, 1}, -S^2] + 13920*HPL[{3, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2] + (1912*Pi^2*Zeta[3])/3 + 3232*Zeta[5]) + 4464*Zeta[7])) + Log[T]*(HPL[{0}, S^2]^9/192 + (5*HPL[{0}, S^2]^8*HPL[{1}, -S^2])/96 + (112*Pi^2*HPL[{1}, -S^2]^7)/9 + (8*HPL[{1}, -S^2]^9)/3 + HPL[{0}, S^2]^7*((13*Pi^2)/144 + HPL[{1}, -S^2]^2/3 + HPL[{2}, -S^2]/8) + 76*Pi^2*HPL[{7}, -S^2] + 4044*HPL[{9}, -S^2] + HPL[{1}, -S^2]^5*((1013*Pi^4)/45 + (116*Pi^2*HPL[{2}, -S^2])/3 + 232*HPL[{2}, -S^2]^2 - 192*HPL[{4}, -S^2] + 192*HPL[{3, 1}, -S^2]) - 44*Pi^2*HPL[{4, 3}, -S^2] - (308*Pi^2*HPL[{5, 2}, -S^2])/3 + 348*HPL[{5, 4}, -S^2] - 50*Pi^2*HPL[{6, 1}, -S^2] + 1412*HPL[{6, 3}, -S^2] + 3536*HPL[{7, 2}, -S^2] + 4628*HPL[{8, 1}, -S^2] + HPL[{5}, -S^2]*((-983*Pi^4)/90 + 832*HPL[{3, 1}, -S^2] - 1472*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 2}, -S^2]*((3322*Pi^4)/45 + 15104*HPL[{2, 1, 1}, -S^2]) + HPL[{4, 1}, -S^2]*((11338*Pi^4)/45 + 45504*HPL[{2, 1, 1}, -S^2]) + (13303*Pi^4*HPL[{2, 2, 1}, -S^2])/45 + (31913*Pi^4*HPL[{3, 1, 1}, -S^2])/45 - (3772*Pi^2*HPL[{3, 2, 2}, -S^2])/3 - (11560*Pi^2*HPL[{3, 3, 1}, -S^2])/3 - (11396*Pi^2*HPL[{4, 1, 2}, -S^2])/3 - (35252*Pi^2*HPL[{4, 2, 1}, -S^2])/3 - 204*HPL[{4, 2, 3}, -S^2] - 212*HPL[{4, 3, 2}, -S^2] + 176*HPL[{4, 4, 1}, -S^2] - 24184*Pi^2*HPL[{5, 1, 1}, -S^2] + 232*HPL[{5, 1, 3}, -S^2] - 164*HPL[{5, 2, 2}, -S^2] + 1096*HPL[{5, 3, 1}, -S^2] + 980*HPL[{6, 1, 2}, -S^2] + 3220*HPL[{6, 2, 1}, -S^2] + 7632*HPL[{7, 1, 1}, -S^2] - (2708*Pi^4*HPL[{2, 1, 1, 1}, -S^2])/9 - (3440*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 + 5888*Pi^2*HPL[{3, 1, 1, 2}, -S^2] + 5888*Pi^2*HPL[{3, 1, 2, 1}, -S^2] + 9328*Pi^2*HPL[{3, 2, 1, 1}, -S^2] + 13760*HPL[{3, 2, 2, 2}, -S^2] + 43296*HPL[{3, 2, 3, 1}, -S^2] + 42624*HPL[{3, 3, 1, 2}, -S^2] + 131232*HPL[{3, 3, 2, 1}, -S^2] + (86896*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 - 266752*HPL[{4, 1, 1, 3}, -S^2] - 224128*HPL[{4, 1, 2, 2}, -S^2] - 400672*HPL[{4, 1, 3, 1}, -S^2] - 137536*HPL[{4, 2, 1, 2}, -S^2] - 135520*HPL[{4, 2, 2, 1}, -S^2] - 792352*HPL[{4, 3, 1, 1}, -S^2] - 805632*HPL[{5, 1, 1, 2}, -S^2] - 1329216*HPL[{5, 1, 2, 1}, -S^2] - 3167808*HPL[{5, 2, 1, 1}, -S^2] - 7914656*HPL[{6, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-16733*Pi^6)/1260 + (5392*Pi^2*HPL[{3, 1}, -S^2])/3 - 1344*HPL[{4, 2}, -S^2] - 5248*HPL[{5, 1}, -S^2] + (10784*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 1344*HPL[{3, 1, 2}, -S^2] - 12416*HPL[{3, 2, 1}, -S^2] - 37440*HPL[{4, 1, 1}, -S^2] + 27840*HPL[{3, 1, 1, 1}, -S^2] + 55680*HPL[{2, 1, 1, 1, 1}, -S^2]) - (21568*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 21568*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] + 27520*HPL[{2, 2, 2, 2, 1}, -S^2] - (125440*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + 53696*HPL[{3, 1, 1, 2, 2}, -S^2] + 53696*HPL[{3, 1, 2, 1, 2}, -S^2] - 1344*HPL[{3, 1, 2, 2, 1}, -S^2] - 407040*HPL[{3, 1, 3, 1, 1}, -S^2] + 136256*HPL[{3, 2, 1, 1, 2}, -S^2] + 81216*HPL[{3, 2, 1, 2, 1}, -S^2] - 105664*HPL[{3, 2, 2, 1, 1}, -S^2] - 395520*HPL[{3, 3, 1, 1, 1}, -S^2] + 408384*HPL[{4, 1, 1, 1, 2}, -S^2] + 243264*HPL[{4, 1, 1, 2, 1}, -S^2] - 317376*HPL[{4, 1, 2, 1, 1}, -S^2] - 1190976*HPL[{4, 2, 1, 1, 1}, -S^2] - 2397696*HPL[{5, 1, 1, 1, 1}, -S^2] - 4640*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + 55680*HPL[{3, 1, 1, 1, 1, 2}, -S^2] + 55680*HPL[{3, 1, 1, 1, 2, 1}, -S^2] + 55680*HPL[{3, 1, 1, 2, 1, 1}, -S^2] + 55680*HPL[{3, 1, 2, 1, 1, 1}, -S^2] + 55680*HPL[{3, 2, 1, 1, 1, 1}, -S^2] + 190080*HPL[{4, 1, 1, 1, 1, 1}, -S^2] + 111360*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] + 445440*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] + 1113600*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] + 2204160*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^3*((-860*HPL[{3}, -S^2])/3 - (1720*HPL[{2, 1}, -S^2])/3 - (860*Zeta[3])/3) + HPL[{6}, -S^2]*(20*HPL[{2, 1}, -S^2] - 156*Zeta[3]) + HPL[{1}, -S^2]^6*((-560*HPL[{3}, -S^2])/3 - (448*Zeta[3])/3) + HPL[{0}, S^2]^6*((11*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((19*Pi^2)/24 + (4*HPL[{2}, -S^2])/3) - (4*HPL[{2, 1}, -S^2])/3 + Zeta[3]/2) - (1847*Pi^6*Zeta[3])/567 + 3136*HPL[{2, 1}, -S^2]^2*Zeta[3] + 120*HPL[{4, 2}, -S^2]*Zeta[3] + 640*HPL[{5, 1}, -S^2]*Zeta[3] - 6880*HPL[{3, 2, 1}, -S^2]*Zeta[3] - 21152*HPL[{4, 1, 1}, -S^2]*Zeta[3] + 14336*HPL[{3, 1, 1, 1}, -S^2]*Zeta[3] - 27840*HPL[{2, 1, 1, 1, 1}, -S^2]*Zeta[3] - 64*Zeta[3]^3 + HPL[{3}, -S^2]^2*(-336*HPL[{2, 1}, -S^2] + 48*Zeta[3]) + HPL[{3}, -S^2]*((-18983*Pi^6)/3780 + (110*Pi^2*HPL[{4}, -S^2])/3 + 148*HPL[{6}, -S^2] + 4112*HPL[{2, 1}, -S^2]^2 + (1844*Pi^2*HPL[{3, 1}, -S^2])/3 + 180*HPL[{4, 2}, -S^2] - 168*HPL[{5, 1}, -S^2] - 1224*Pi^2*HPL[{2, 1, 1}, -S^2] - 6880*HPL[{3, 2, 1}, -S^2] + 245984*HPL[{4, 1, 1}, -S^2] + 13952*HPL[{3, 1, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1, 1}, -S^2] + 304*HPL[{2, 1}, -S^2]*Zeta[3] - 88*Zeta[3]^2) + HPL[{1}, -S^2]^3*((484*Pi^6)/27 + (2696*Pi^2*HPL[{2}, -S^2]^2)/9 + 208*HPL[{3}, -S^2]^2 - (1472*Pi^2*HPL[{4}, -S^2])/9 - 144*HPL[{6}, -S^2] - 4640*HPL[{2, 1}, -S^2]^2 - (1984*Pi^2*HPL[{3, 1}, -S^2])/9 + 672*HPL[{4, 2}, -S^2] + 3840*HPL[{5, 1}, -S^2] + (2320*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((1354*Pi^4)/27 - 640*HPL[{4}, -S^2] - 4640*HPL[{3, 1}, -S^2] + 9280*HPL[{2, 1, 1}, -S^2]) - 3840*HPL[{4, 1, 1}, -S^2] + 3840*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(4640*HPL[{2, 1}, -S^2] - (896*Zeta[3])/3) + 4640*HPL[{2, 1}, -S^2]*Zeta[3] + 112*Zeta[3]^2) + HPL[{0}, S^2]^5*((14057*Pi^4)/21600 + (163*HPL[{1}, -S^2]^4)/45 + (293*Pi^2*HPL[{2}, -S^2])/180 + (77*HPL[{2}, -S^2]^2)/40 + HPL[{1}, -S^2]^2*((373*Pi^2)/90 + (271*HPL[{2}, -S^2])/30) + HPL[{4}, -S^2]/2 - (87*HPL[{3, 1}, -S^2])/10 + (271*HPL[{2, 1, 1}, -S^2])/15 + HPL[{1}, -S^2]*(HPL[{3}, -S^2] - (271*HPL[{2, 1}, -S^2])/15 + 3*Zeta[3])) + HPL[{2, 1, 1}, -S^2]*(-27840*HPL[{3, 1, 1}, -S^2] - 55680*HPL[{2, 1, 1, 1}, -S^2] - (3824*Pi^2*Zeta[3])/3 - 6464*Zeta[5]) + HPL[{1}, -S^2]^4*((-2200*Pi^2*HPL[{3}, -S^2])/9 - 304*HPL[{5}, -S^2] - (580*Pi^2*HPL[{2, 1}, -S^2])/3 + 2320*HPL[{3, 2}, -S^2] + 7920*HPL[{4, 1}, -S^2] + 4640*HPL[{2, 2, 1}, -S^2] + 8320*HPL[{3, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-1160*HPL[{3}, -S^2] - 2320*HPL[{2, 1}, -S^2] - 1160*Zeta[3]) - (620*Pi^2*Zeta[3])/3 - 1160*Zeta[5]) + HPL[{2}, -S^2]^2*((-533*Pi^2*HPL[{3}, -S^2])/3 - 194*HPL[{5}, -S^2] - (430*Pi^2*HPL[{2, 1}, -S^2])/3 + 1720*HPL[{3, 2}, -S^2] + 5832*HPL[{4, 1}, -S^2] + 3440*HPL[{2, 2, 1}, -S^2] + 6208*HPL[{3, 1, 1}, -S^2] - 143*Pi^2*Zeta[3] - 714*Zeta[5]) + HPL[{4}, -S^2]*(-172*HPL[{5}, -S^2] + (452*Pi^2*HPL[{2, 1}, -S^2])/3 - 360*HPL[{3, 2}, -S^2] - 1192*HPL[{4, 1}, -S^2] - 2688*HPL[{2, 2, 1}, -S^2] - 7264*HPL[{3, 1, 1}, -S^2] + 3840*HPL[{2, 1, 1, 1}, -S^2] - 28*Pi^2*Zeta[3] - 64*Zeta[5]) - (1564*Pi^4*Zeta[5])/45 + HPL[{0}, S^2]^4*((22*HPL[{1}, -S^2]^5)/3 + HPL[{1}, -S^2]^3*((110*Pi^2)/9 + (272*HPL[{2}, -S^2])/9) - (Pi^2*HPL[{3}, -S^2])/12 + HPL[{5}, -S^2]/2 + HPL[{2}, -S^2]*(-HPL[{3}, -S^2]/2 - (271*HPL[{2, 1}, -S^2])/6) - (128*Pi^2*HPL[{2, 1}, -S^2])/9 + HPL[{3, 2}, -S^2] + 3*HPL[{4, 1}, -S^2] + HPL[{1}, -S^2]*((659*Pi^4)/144 + (128*Pi^2*HPL[{2}, -S^2])/9 + (271*HPL[{2}, -S^2]^2)/12 - (265*HPL[{3, 1}, -S^2])/3 + (544*HPL[{2, 1, 1}, -S^2])/3) + (271*HPL[{2, 2, 1}, -S^2])/3 + 269*HPL[{3, 1, 1}, -S^2] - (544*HPL[{2, 1, 1, 1}, -S^2])/3 + (97*Pi^2*Zeta[3])/36 + HPL[{1}, -S^2]^2*(-HPL[{3}, -S^2] - (272*HPL[{2, 1}, -S^2])/3 + (7*Zeta[3])/3) + (65*Zeta[5])/6) + HPL[{3, 1}, -S^2]*(-7552*HPL[{3, 2}, -S^2] - 22784*HPL[{4, 1}, -S^2] + 2688*HPL[{2, 2, 1}, -S^2] + 98816*HPL[{3, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2] + (1972*Pi^2*Zeta[3])/3 + 3240*Zeta[5]) + HPL[{0}, S^2]^2*((40*HPL[{1}, -S^2]^7)/3 + HPL[{1}, -S^2]^5*(38*Pi^2 + 116*HPL[{2}, -S^2]) - 2*Pi^2*HPL[{5}, -S^2] + 114*HPL[{7}, -S^2] + 18*Pi^2*HPL[{3, 2}, -S^2] + (170*Pi^2*HPL[{4, 1}, -S^2])/3 - 16*HPL[{4, 3}, -S^2] - 44*HPL[{5, 2}, -S^2] - 98*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((-241*Pi^4)/180 + 10*HPL[{4}, -S^2] + 100*HPL[{3, 1}, -S^2] - 192*HPL[{2, 1, 1}, -S^2]) + HPL[{1}, -S^2]^3*((659*Pi^4)/18 + (1414*Pi^2*HPL[{2}, -S^2])/9 + (956*HPL[{2}, -S^2]^2)/3 - (32*HPL[{4}, -S^2])/3 - (3424*HPL[{3, 1}, -S^2])/3 + 2320*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-853*Pi^4)/20 + 1912*HPL[{3, 1}, -S^2] + 3824*HPL[{2, 1, 1}, -S^2]) + (1498*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (4382*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 164*HPL[{3, 2, 2}, -S^2] - 520*HPL[{3, 3, 1}, -S^2] - 524*HPL[{4, 1, 2}, -S^2] - 1580*HPL[{4, 2, 1}, -S^2] - 3240*HPL[{5, 1, 1}, -S^2] - (2828*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 3440*HPL[{2, 2, 2, 1}, -S^2] + 10704*HPL[{3, 1, 1, 2}, -S^2] + 10704*HPL[{3, 1, 2, 1}, -S^2] + 21024*HPL[{3, 2, 1, 1}, -S^2] + 63136*HPL[{4, 1, 1, 1}, -S^2] - 7648*HPL[{2, 1, 2, 1, 1}, -S^2] - 22944*HPL[{2, 2, 1, 1, 1}, -S^2] - 39040*HPL[{3, 1, 1, 1, 1}, -S^2] - 13920*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^4*((-100*HPL[{3}, -S^2])/3 - 580*HPL[{2, 1}, -S^2] - 60*Zeta[3]) + HPL[{2}, -S^2]^2*(-19*HPL[{3}, -S^2] - 430*HPL[{2, 1}, -S^2] - 37*Zeta[3]) + HPL[{4}, -S^2]*(-28*HPL[{2, 1}, -S^2] - 20*Zeta[3]) + (373*Pi^4*Zeta[3])/180 + 180*HPL[{3, 1}, -S^2]*Zeta[3] - 344*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{1}, -S^2]*((3413*Pi^6)/324 + (749*Pi^2*HPL[{2}, -S^2]^2)/6 + (430*HPL[{2}, -S^2]^3)/3 - 12*HPL[{3}, -S^2]^2 - (8*Pi^2*HPL[{4}, -S^2])/3 + 38*HPL[{6}, -S^2] - 1912*HPL[{2, 1}, -S^2]^2 - 462*Pi^2*HPL[{3, 1}, -S^2] - 12*HPL[{4, 2}, -S^2] - 8*HPL[{5, 1}, -S^2] + (2828*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((853*Pi^4)/20 + 28*HPL[{4}, -S^2] - 1912*HPL[{3, 1}, -S^2] + 3824*HPL[{2, 1, 1}, -S^2]) + 3440*HPL[{3, 2, 1}, -S^2] + 10256*HPL[{4, 1, 1}, -S^2] - 6848*HPL[{3, 1, 1, 1}, -S^2] + 13920*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(192*HPL[{2, 1}, -S^2] - 32*Zeta[3]) + 344*HPL[{2, 1}, -S^2]*Zeta[3] + 40*Zeta[3]^2) + HPL[{1}, -S^2]^2*((-56*Pi^2*HPL[{3}, -S^2])/3 - 36*HPL[{5}, -S^2] - (1414*Pi^2*HPL[{2, 1}, -S^2])/3 + 192*HPL[{3, 2}, -S^2] + 608*HPL[{4, 1}, -S^2] + 3824*HPL[{2, 2, 1}, -S^2] + 11072*HPL[{3, 1, 1}, -S^2] - 6960*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*(-96*HPL[{3}, -S^2] - 1912*HPL[{2, 1}, -S^2] - 172*Zeta[3]) - (76*Pi^2*Zeta[3])/3 - 156*Zeta[5]) + HPL[{2}, -S^2]*(-9*Pi^2*HPL[{3}, -S^2] - 14*HPL[{5}, -S^2] - (749*Pi^2*HPL[{2, 1}, -S^2])/3 + 80*HPL[{3, 2}, -S^2] + 256*HPL[{4, 1}, -S^2] + 1720*HPL[{2, 2, 1}, -S^2] - 5352*HPL[{3, 1, 1}, -S^2] - 3824*HPL[{2, 1, 1, 1}, -S^2] - (43*Pi^2*Zeta[3])/3 - 74*Zeta[5]) + (26*Pi^2*Zeta[5])/3) + HPL[{0}, S^2]^3*((2863*Pi^6)/1296 + (112*HPL[{1}, -S^2]^6)/9 + (587*Pi^2*HPL[{2}, -S^2]^2)/36 + (56*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((746*Pi^2)/27 + (250*HPL[{2}, -S^2])/3) - 2*HPL[{3}, -S^2]^2 + (35*Pi^2*HPL[{4}, -S^2])/9 + 2*HPL[{6}, -S^2] - (712*HPL[{2, 1}, -S^2]^2)/3 - (635*Pi^2*HPL[{3, 1}, -S^2])/9 - 2*HPL[{4, 2}, -S^2] - 32*HPL[{5, 1}, -S^2] + (1292*Pi^2*HPL[{2, 1, 1}, -S^2])/9 + HPL[{2}, -S^2]*((334*Pi^4)/45 + (14*HPL[{4}, -S^2])/3 - (712*HPL[{3, 1}, -S^2])/3 + (1424*HPL[{2, 1, 1}, -S^2])/3) + HPL[{1}, -S^2]^2*((2467*Pi^4)/135 + (646*Pi^2*HPL[{2}, -S^2])/9 + (356*HPL[{2}, -S^2]^2)/3 + (80*HPL[{4}, -S^2])/3 - (1496*HPL[{3, 1}, -S^2])/3 + 1000*HPL[{2, 1, 1}, -S^2]) + 448*HPL[{3, 2, 1}, -S^2] + (4192*HPL[{4, 1, 1}, -S^2])/3 - (2992*HPL[{3, 1, 1, 1}, -S^2])/3 + 2000*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^3*(8*HPL[{3}, -S^2] - (1000*HPL[{2, 1}, -S^2])/3 - (56*Zeta[3])/9) + (20*HPL[{2, 1}, -S^2]*Zeta[3])/3 + 14*Zeta[3]^2 + HPL[{3}, -S^2]*((40*HPL[{2, 1}, -S^2])/3 + 4*Zeta[3]) + HPL[{1}, -S^2]*((16*Pi^2*HPL[{3}, -S^2])/3 + (56*HPL[{5}, -S^2])/3 - (1292*Pi^2*HPL[{2, 1}, -S^2])/9 + (80*HPL[{3, 2}, -S^2])/3 + (80*HPL[{4, 1}, -S^2])/3 + (2848*HPL[{2, 2, 1}, -S^2])/3 + 2896*HPL[{3, 1, 1}, -S^2] - 2000*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-40*HPL[{3}, -S^2])/3 - (1424*HPL[{2, 1}, -S^2])/3 - (20*Zeta[3])/3) + (76*Pi^2*Zeta[3])/9 + 52*Zeta[5])) + HPL[{1}, -S^2]*((456659*Pi^8)/97200 + (430*Pi^2*HPL[{2}, -S^2]^3)/9 + (430*HPL[{2}, -S^2]^4)/3 + 48*Pi^2*HPL[{3}, -S^2]^2 + 56*HPL[{4}, -S^2]^2 - (70*Pi^2*HPL[{6}, -S^2])/3 + 2652*HPL[{8}, -S^2] - (5392*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + 8320*HPL[{3, 1}, -S^2]^2 + HPL[{2}, -S^2]^2*((13303*Pi^4)/180 - 672*HPL[{4}, -S^2] + 672*HPL[{3, 1}, -S^2]) + 164*Pi^2*HPL[{4, 2}, -S^2] + (2872*Pi^2*HPL[{5, 1}, -S^2])/3 - 72*HPL[{5, 3}, -S^2] - 180*HPL[{6, 2}, -S^2] - 1232*HPL[{7, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-1769*Pi^4)/15 - 27840*HPL[{2, 1, 1}, -S^2]) + HPL[{4}, -S^2]*((-1372*Pi^4)/45 + 1888*HPL[{3, 1}, -S^2] - 3840*HPL[{2, 1, 1}, -S^2]) + (2708*Pi^4*HPL[{2, 1, 1}, -S^2])/9 + 27840*HPL[{2, 1, 1}, -S^2]^2 + (3440*Pi^2*HPL[{3, 2, 1}, -S^2])/3 + 2016*HPL[{3, 3, 2}, -S^2] + (7376*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 3360*HPL[{4, 1, 3}, -S^2] + 1344*HPL[{4, 2, 2}, -S^2] - 11424*HPL[{4, 3, 1}, -S^2] - 6720*HPL[{5, 1, 2}, -S^2] - 47040*HPL[{5, 2, 1}, -S^2] - 121824*HPL[{6, 1, 1}, -S^2] - (3968*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 1344*HPL[{3, 1, 2, 2}, -S^2] + 1344*HPL[{3, 2, 1, 2}, -S^2] + 1344*HPL[{3, 2, 2, 1}, -S^2] + 4032*HPL[{4, 1, 1, 2}, -S^2] + 4032*HPL[{4, 1, 2, 1}, -S^2] + 4032*HPL[{4, 2, 1, 1}, -S^2] + 23040*HPL[{5, 1, 1, 1}, -S^2] + 4640*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] - 23040*HPL[{4, 1, 1, 1, 1}, -S^2] + 23040*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + HPL[{5}, -S^2]*(1472*HPL[{2, 1}, -S^2] - 128*Zeta[3]) + 608*HPL[{3, 2}, -S^2]*Zeta[3] + 2336*HPL[{4, 1}, -S^2]*Zeta[3] - 12544*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 39424*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 27840*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] + (124*Pi^2*Zeta[3]^2)/3 + HPL[{2}, -S^2]*((16733*Pi^6)/1260 + 336*HPL[{3}, -S^2]^2 - (452*Pi^2*HPL[{4}, -S^2])/3 - 20*HPL[{6}, -S^2] - (5392*Pi^2*HPL[{3, 1}, -S^2])/3 + 1344*HPL[{4, 2}, -S^2] + 5248*HPL[{5, 1}, -S^2] + (10784*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 1344*HPL[{3, 1, 2}, -S^2] + 12416*HPL[{3, 2, 1}, -S^2] + 37440*HPL[{4, 1, 1}, -S^2] - 27840*HPL[{3, 1, 1, 1}, -S^2] + 55680*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(8224*HPL[{2, 1}, -S^2] - 304*Zeta[3]) + 6272*HPL[{2, 1}, -S^2]*Zeta[3]) + HPL[{3}, -S^2]*(-56*HPL[{5}, -S^2] + 1224*Pi^2*HPL[{2, 1}, -S^2] - 1344*HPL[{3, 2}, -S^2] - 544*HPL[{4, 1}, -S^2] - 16448*HPL[{2, 2, 1}, -S^2] - 46848*HPL[{3, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2] - (256*Pi^2*Zeta[3])/3 - 384*Zeta[5]) + 240*Zeta[3]*Zeta[5] + HPL[{2, 1}, -S^2]*(-15104*HPL[{3, 2}, -S^2] - 45504*HPL[{4, 1}, -S^2] + 27840*HPL[{3, 1, 1}, -S^2] - 55680*HPL[{2, 1, 1, 1}, -S^2] + (3824*Pi^2*Zeta[3])/3 + 6464*Zeta[5])) + HPL[{0}, S^2]*((177569*Pi^8)/64800 + 12*HPL[{1}, -S^2]^8 + (560*Pi^2*HPL[{2}, -S^2]^3)/9 + (215*HPL[{2}, -S^2]^4)/3 + HPL[{1}, -S^2]^6*((364*Pi^2)/9 + (448*HPL[{2}, -S^2])/3) - 4*Pi^2*HPL[{3}, -S^2]^2 + 22*HPL[{4}, -S^2]^2 + (79*Pi^2*HPL[{6}, -S^2])/3 - 298*HPL[{8}, -S^2] - (2452*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + 3488*HPL[{3, 1}, -S^2]^2 - 2*Pi^2*HPL[{4, 2}, -S^2] - (232*Pi^2*HPL[{5, 1}, -S^2])/3 - 12*HPL[{5, 3}, -S^2] - 30*HPL[{6, 2}, -S^2] - 216*HPL[{7, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-12191*Pi^4)/90 - 13920*HPL[{2, 1, 1}, -S^2]) + (12283*Pi^4*HPL[{2, 1, 1}, -S^2])/45 + 13920*HPL[{2, 1, 1}, -S^2]^2 + HPL[{4}, -S^2]*((143*Pi^4)/18 - 64*HPL[{3, 1}, -S^2] + 96*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]^2*((11683*Pi^4)/360 + 2*HPL[{4}, -S^2] - 1568*HPL[{3, 1}, -S^2] + 3136*HPL[{2, 1, 1}, -S^2]) + HPL[{1}, -S^2]^4*((14057*Pi^4)/270 + 270*Pi^2*HPL[{2}, -S^2] + 580*HPL[{2}, -S^2]^2 + 80*HPL[{4}, -S^2] - 2240*HPL[{3, 1}, -S^2] + 4480*HPL[{2, 1, 1}, -S^2]) + (4480*Pi^2*HPL[{3, 2, 1}, -S^2])/3 - 64*HPL[{3, 3, 2}, -S^2] + (13840*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 152*HPL[{4, 1, 3}, -S^2] - 52*HPL[{4, 2, 2}, -S^2] + 280*HPL[{4, 3, 1}, -S^2] + 176*HPL[{5, 1, 2}, -S^2] + 1136*HPL[{5, 2, 1}, -S^2] + 3464*HPL[{6, 1, 1}, -S^2] - (9712*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 - 12544*HPL[{3, 2, 2, 1}, -S^2] - 37632*HPL[{3, 3, 1, 1}, -S^2] - 37632*HPL[{4, 1, 2, 1}, -S^2] - 112896*HPL[{4, 2, 1, 1}, -S^2] - 226880*HPL[{5, 1, 1, 1}, -S^2] + 6480*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] - 25088*HPL[{2, 2, 1, 2, 1}, -S^2] - 75264*HPL[{2, 2, 2, 1, 1}, -S^2] + 150528*HPL[{3, 1, 1, 1, 2}, -S^2] + 250880*HPL[{3, 1, 1, 2, 1}, -S^2] + 301056*HPL[{3, 1, 2, 1, 1}, -S^2] + 627200*HPL[{3, 2, 1, 1, 1}, -S^2] + 1883520*HPL[{4, 1, 1, 1, 1}, -S^2] - 53760*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 107520*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^5*(-16*HPL[{3}, -S^2] - 896*HPL[{2, 1}, -S^2] - 96*Zeta[3]) + 64*HPL[{3, 2}, -S^2]*Zeta[3] + 96*HPL[{4, 1}, -S^2]*Zeta[3] - 1344*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 4064*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 2784*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] + 28*Pi^2*Zeta[3]^2 + HPL[{5}, -S^2]*(80*HPL[{2, 1}, -S^2] + 120*Zeta[3]) + HPL[{2}, -S^2]*((249449*Pi^6)/22680 - 8*HPL[{3}, -S^2]^2 + (26*Pi^2*HPL[{4}, -S^2])/3 + 50*HPL[{6}, -S^2] - 3136*HPL[{2, 1}, -S^2]^2 - (2452*Pi^2*HPL[{3, 1}, -S^2])/3 + 12*HPL[{4, 2}, -S^2] - 16*HPL[{5, 1}, -S^2] + (4904*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 6880*HPL[{3, 2, 1}, -S^2] + 20736*HPL[{4, 1, 1}, -S^2] - 164448*HPL[{3, 1, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(304*HPL[{2, 1}, -S^2] - 32*Zeta[3]) + 672*HPL[{2, 1}, -S^2]*Zeta[3] + 76*Zeta[3]^2) + HPL[{1}, -S^2]^2*((2863*Pi^6)/108 + (1226*Pi^2*HPL[{2}, -S^2]^2)/3 + (1568*HPL[{2}, -S^2]^3)/3 - 24*HPL[{3}, -S^2]^2 + (200*Pi^2*HPL[{4}, -S^2])/3 + 292*HPL[{6}, -S^2] - 6960*HPL[{2, 1}, -S^2]^2 - (4856*Pi^2*HPL[{3, 1}, -S^2])/3 - 544*HPL[{5, 1}, -S^2] + 3240*Pi^2*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((12283*Pi^4)/90 + 48*HPL[{4}, -S^2] - 6960*HPL[{3, 1}, -S^2] + 13920*HPL[{2, 1, 1}, -S^2]) + 12544*HPL[{3, 2, 1}, -S^2] + 38592*HPL[{4, 1, 1}, -S^2] - 26880*HPL[{3, 1, 1, 1}, -S^2] + 53760*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(688*HPL[{2, 1}, -S^2] - 16*Zeta[3]) + 1392*HPL[{2, 1}, -S^2]*Zeta[3] + 168*Zeta[3]^2) + HPL[{1}, -S^2]^3*((-16*Pi^2*HPL[{3}, -S^2])/3 + (448*HPL[{5}, -S^2])/3 - 1080*Pi^2*HPL[{2, 1}, -S^2] + (1376*HPL[{3, 2}, -S^2])/3 + 1056*HPL[{4, 1}, -S^2] + 9280*HPL[{2, 2, 1}, -S^2] + 27520*HPL[{3, 1, 1}, -S^2] - 17920*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-688*HPL[{3}, -S^2])/3 - 4640*HPL[{2, 1}, -S^2] - 464*Zeta[3]) - (776*Pi^2*Zeta[3])/9 - (1040*Zeta[5])/3) + 336*Zeta[3]*Zeta[5] + HPL[{3}, -S^2]*(-44*HPL[{5}, -S^2] + (212*Pi^2*HPL[{2, 1}, -S^2])/3 + 32*HPL[{3, 2}, -S^2] - 24*HPL[{4, 1}, -S^2] - 608*HPL[{2, 2, 1}, -S^2] - 1920*HPL[{3, 1, 1}, -S^2] + 1376*HPL[{2, 1, 1, 1}, -S^2] + (8*Pi^2*Zeta[3])/3 + 88*Zeta[5]) + HPL[{2, 1}, -S^2]*(-608*HPL[{3, 2}, -S^2] - 1920*HPL[{4, 1}, -S^2] + 12544*HPL[{2, 2, 1}, -S^2] + 39008*HPL[{3, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1}, -S^2] + (368*Pi^2*Zeta[3])/3 + 328*Zeta[5]) + HPL[{1}, -S^2]*(56*Pi^2*HPL[{5}, -S^2] + 56*HPL[{7}, -S^2] + (424*Pi^2*HPL[{3, 2}, -S^2])/3 + (872*Pi^2*HPL[{4, 1}, -S^2])/3 - 88*HPL[{4, 3}, -S^2] - 240*HPL[{5, 2}, -S^2] - 904*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((254*Pi^4)/45 + 56*HPL[{4}, -S^2] + 704*HPL[{3, 1}, -S^2] - 1376*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-12283*Pi^4)/45 + 13920*HPL[{3, 1}, -S^2] + 27840*HPL[{2, 1, 1}, -S^2]) + (9808*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + 9776*Pi^2*HPL[{3, 1, 1}, -S^2] - 1216*HPL[{3, 2, 2}, -S^2] - 3840*HPL[{3, 3, 1}, -S^2] - 3840*HPL[{4, 1, 2}, -S^2] - 11712*HPL[{4, 2, 1}, -S^2] - 22720*HPL[{5, 1, 1}, -S^2] - 6480*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 25088*HPL[{2, 2, 2, 1}, -S^2] + 78016*HPL[{3, 1, 1, 2}, -S^2] + 78016*HPL[{3, 1, 2, 1}, -S^2] + 153280*HPL[{3, 2, 1, 1}, -S^2] + 457920*HPL[{4, 1, 1, 1}, -S^2] - 55680*HPL[{2, 1, 2, 1, 1}, -S^2] - 167040*HPL[{2, 2, 1, 1, 1}, -S^2] - 280320*HPL[{3, 1, 1, 1, 1}, -S^2] - 107520*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^2*(-152*HPL[{3}, -S^2] - 3136*HPL[{2, 1}, -S^2] - 336*Zeta[3]) - (373*Pi^4*Zeta[3])/45 + 1376*HPL[{3, 1}, -S^2]*Zeta[3] - 2784*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-96*HPL[{2, 1}, -S^2] + 96*Zeta[3]) + HPL[{2}, -S^2]*((-212*Pi^2*HPL[{3}, -S^2])/3 - 80*HPL[{5}, -S^2] - (4904*Pi^2*HPL[{2, 1}, -S^2])/3 + 608*HPL[{3, 2}, -S^2] + 1920*HPL[{4, 1}, -S^2] + 12544*HPL[{2, 2, 1}, -S^2] - 39008*HPL[{3, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1}, -S^2] - (368*Pi^2*Zeta[3])/3 - 328*Zeta[5]) - (104*Pi^2*Zeta[5])/3)) + HPL[{1}, -S^2]^2*(-164*Pi^2*HPL[{5}, -S^2] + 456*HPL[{7}, -S^2] + 1224*Pi^2*HPL[{3, 2}, -S^2] + (12488*Pi^2*HPL[{4, 1}, -S^2])/3 - 464*HPL[{4, 3}, -S^2] - 1056*HPL[{5, 2}, -S^2] - 208*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((-3998*Pi^4)/45 + 400*HPL[{4}, -S^2] + 6976*HPL[{3, 1}, -S^2] - 13920*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-1354*Pi^4)/9 + 13920*HPL[{3, 1}, -S^2] + 27840*HPL[{2, 1, 1}, -S^2]) + (10784*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (23552*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 14432*HPL[{3, 2, 2}, -S^2] - 44160*HPL[{3, 3, 1}, -S^2] - 43488*HPL[{4, 1, 2}, -S^2] - 134688*HPL[{4, 2, 1}, -S^2] - 277248*HPL[{5, 1, 1}, -S^2] - 2320*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + 27840*HPL[{3, 1, 1, 2}, -S^2] + 27840*HPL[{3, 1, 2, 1}, -S^2] + 27840*HPL[{3, 2, 1, 1}, -S^2] + 95040*HPL[{4, 1, 1, 1}, -S^2] - 55680*HPL[{2, 1, 2, 1, 1}, -S^2] - 167040*HPL[{2, 2, 1, 1, 1}, -S^2] - 345600*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^2*(-2056*HPL[{3}, -S^2] - 1568*Zeta[3]) + HPL[{4}, -S^2]*(1920*HPL[{2, 1}, -S^2] - 256*Zeta[3]) - (3353*Pi^4*Zeta[3])/45 + 7168*HPL[{3, 1}, -S^2]*Zeta[3] - 13920*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]*(-612*Pi^2*HPL[{3}, -S^2] - 736*HPL[{5}, -S^2] - (5392*Pi^2*HPL[{2, 1}, -S^2])/3 + 7552*HPL[{3, 2}, -S^2] + 22752*HPL[{4, 1}, -S^2] - 13920*HPL[{3, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1}, -S^2] - (1912*Pi^2*Zeta[3])/3 - 3232*Zeta[5]) - 632*Pi^2*Zeta[5] - 4464*Zeta[7]) + HPL[{2}, -S^2]*(-66*Pi^2*HPL[{5}, -S^2] - 104*HPL[{7}, -S^2] + HPL[{2, 1}, -S^2]*((-13303*Pi^4)/90 - 1344*HPL[{3, 1}, -S^2]) + 656*Pi^2*HPL[{3, 2}, -S^2] + (5944*Pi^2*HPL[{4, 1}, -S^2])/3 - 172*HPL[{4, 3}, -S^2] - 324*HPL[{5, 2}, -S^2] + 260*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((-1661*Pi^4)/45 + 180*HPL[{4}, -S^2] + 4112*HPL[{3, 1}, -S^2] - 8224*HPL[{2, 1, 1}, -S^2]) + (1720*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - 2944*Pi^2*HPL[{3, 1, 1}, -S^2] - 6880*HPL[{3, 2, 2}, -S^2] - 21984*HPL[{3, 3, 1}, -S^2] - 21984*HPL[{4, 1, 2}, -S^2] - 67296*HPL[{4, 2, 1}, -S^2] - 137408*HPL[{5, 1, 1}, -S^2] - (10784*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 13760*HPL[{2, 2, 2, 1}, -S^2] - 26176*HPL[{3, 1, 1, 2}, -S^2] - 26176*HPL[{3, 1, 2, 1}, -S^2] - 67456*HPL[{3, 2, 1, 1}, -S^2] - 202176*HPL[{4, 1, 1, 1}, -S^2] - 27840*HPL[{3, 1, 1, 1, 1}, -S^2] - 55680*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(1344*HPL[{2, 1}, -S^2] - 136*Zeta[3]) - (3383*Pi^4*Zeta[3])/90 + 3136*HPL[{3, 1}, -S^2]*Zeta[3] - 6272*HPL[{2, 1, 1}, -S^2]*Zeta[3] - 294*Pi^2*Zeta[5] - 1692*Zeta[7]) - 372*Pi^2*Zeta[7] - 3136*Zeta[9]) + HPL[{0}, S^2]*((-4*HPL[{1}, -S^2]^9)/3 + HPL[{1}, -S^2]^7*((-52*Pi^2)/9 - (64*HPL[{2}, -S^2])/3) - 12*HPL[{3}, -S^2]^3 + (178*Pi^2*HPL[{7}, -S^2])/3 + 1946*HPL[{9}, -S^2] - (3136*HPL[{2, 1}, -S^2]^3)/3 + (100*Pi^2*HPL[{4, 3}, -S^2])/3 + (298*Pi^2*HPL[{5, 2}, -S^2])/3 - 690*HPL[{5, 4}, -S^2] + (569*Pi^2*HPL[{6, 1}, -S^2])/3 - 2754*HPL[{6, 3}, -S^2] - 6876*HPL[{7, 2}, -S^2] - 14746*HPL[{8, 1}, -S^2] + HPL[{4, 1}, -S^2]*((-827*Pi^4)/90 - 1920*HPL[{2, 1, 1}, -S^2]) + HPL[{1}, -S^2]^5*((-14057*Pi^4)/1350 - 54*Pi^2*HPL[{2}, -S^2] - 116*HPL[{2}, -S^2]^2 - 16*HPL[{4}, -S^2] + 448*HPL[{3, 1}, -S^2] - 896*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 2}, -S^2]*((-257*Pi^4)/45 - 608*HPL[{2, 1, 1}, -S^2]) + HPL[{5}, -S^2]*((-9*Pi^4)/4 - 240*HPL[{3, 1}, -S^2] + 80*HPL[{2, 1, 1}, -S^2]) - (11683*Pi^4*HPL[{2, 2, 1}, -S^2])/90 - (35557*Pi^4*HPL[{3, 1, 1}, -S^2])/90 + (242*Pi^2*HPL[{3, 2, 2}, -S^2])/3 + (764*Pi^2*HPL[{3, 3, 1}, -S^2])/3 + (766*Pi^2*HPL[{4, 1, 2}, -S^2])/3 + (2326*Pi^2*HPL[{4, 2, 1}, -S^2])/3 + 30*HPL[{4, 2, 3}, -S^2] - 242*HPL[{4, 3, 2}, -S^2] - 904*HPL[{4, 4, 1}, -S^2] + 1504*Pi^2*HPL[{5, 1, 1}, -S^2] - 348*HPL[{5, 1, 3}, -S^2] - 1146*HPL[{5, 2, 2}, -S^2] - 3516*HPL[{5, 3, 1}, -S^2] - 3150*HPL[{6, 1, 2}, -S^2] - 8350*HPL[{6, 2, 1}, -S^2] - 15656*HPL[{7, 1, 1}, -S^2] + (12283*Pi^4*HPL[{2, 1, 1, 1}, -S^2])/45 + (4480*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 - (13864*Pi^2*HPL[{3, 1, 1, 2}, -S^2])/3 - (13864*Pi^2*HPL[{3, 1, 2, 1}, -S^2])/3 - (27304*Pi^2*HPL[{3, 2, 1, 1}, -S^2])/3 - 736*HPL[{3, 2, 2, 2}, -S^2] - 2144*HPL[{3, 2, 3, 1}, -S^2] - 2144*HPL[{3, 3, 1, 2}, -S^2] - 6368*HPL[{3, 3, 2, 1}, -S^2] - (81512*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 + 12760*HPL[{4, 1, 1, 3}, -S^2] + 10604*HPL[{4, 1, 2, 2}, -S^2] + 19064*HPL[{4, 1, 3, 1}, -S^2] + 6380*HPL[{4, 2, 1, 2}, -S^2] + 6380*HPL[{4, 2, 2, 1}, -S^2] + 38104*HPL[{4, 3, 1, 1}, -S^2] + 38256*HPL[{5, 1, 1, 2}, -S^2] + 63600*HPL[{5, 1, 2, 1}, -S^2] + 152304*HPL[{5, 2, 1, 1}, -S^2] + 381064*HPL[{6, 1, 1, 1}, -S^2] + (9808*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 9808*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 13760*HPL[{2, 2, 2, 2, 1}, -S^2] + (49136*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - 40064*HPL[{3, 1, 1, 2, 2}, -S^2] - 40064*HPL[{3, 1, 2, 1, 2}, -S^2] + 281472*HPL[{3, 1, 3, 1, 1}, -S^2] - 81344*HPL[{3, 2, 1, 1, 2}, -S^2] - 41280*HPL[{3, 2, 1, 2, 1}, -S^2] + 117568*HPL[{3, 2, 2, 1, 1}, -S^2] + 393984*HPL[{3, 3, 1, 1, 1}, -S^2] - 243840*HPL[{4, 1, 1, 1, 2}, -S^2] - 123648*HPL[{4, 1, 1, 2, 1}, -S^2] + 352896*HPL[{4, 1, 2, 1, 1}, -S^2] + 1182144*HPL[{4, 2, 1, 1, 1}, -S^2] + 2363584*HPL[{5, 1, 1, 1, 1}, -S^2] + 6480*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 25088*HPL[{2, 2, 1, 2, 1, 1}, -S^2] - 75264*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + 122688*HPL[{3, 1, 1, 1, 1, 2}, -S^2] + 273216*HPL[{3, 1, 1, 1, 2, 1}, -S^2] + 373568*HPL[{3, 1, 1, 2, 1, 1}, -S^2] + 423744*HPL[{3, 1, 2, 1, 1, 1}, -S^2] + 749888*HPL[{3, 2, 1, 1, 1, 1}, -S^2] + 2251584*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - 55680*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] - 222720*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] - 556800*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] - 1167360*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + 107520*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{6}, -S^2]*(50*HPL[{2, 1}, -S^2] - 426*Zeta[3]) - (1847*Pi^6*Zeta[3])/1134 - 336*HPL[{2, 1}, -S^2]^2*Zeta[3] - 12*HPL[{4, 2}, -S^2]*Zeta[3] + 232*HPL[{5, 1}, -S^2]*Zeta[3] + 704*HPL[{3, 2, 1}, -S^2]*Zeta[3] + 2016*HPL[{4, 1, 1}, -S^2]*Zeta[3] - 1376*HPL[{3, 1, 1, 1}, -S^2]*Zeta[3] + 2784*HPL[{2, 1, 1, 1, 1}, -S^2]*Zeta[3] - 32*Zeta[3]^3 + HPL[{1}, -S^2]^6*((8*HPL[{3}, -S^2])/3 + (448*HPL[{2, 1}, -S^2])/3 + 16*Zeta[3]) + HPL[{2}, -S^2]^3*((46*HPL[{3}, -S^2])/3 + (860*HPL[{2, 1}, -S^2])/3 + (88*Zeta[3])/3) + HPL[{3}, -S^2]^2*(-8*HPL[{2, 1}, -S^2] + 36*Zeta[3]) + HPL[{3}, -S^2]*((-6239*Pi^6)/7560 - 17*Pi^2*HPL[{4}, -S^2] - 342*HPL[{6}, -S^2] - 152*HPL[{2, 1}, -S^2]^2 - (142*Pi^2*HPL[{3, 1}, -S^2])/3 - 18*HPL[{4, 2}, -S^2] + 180*HPL[{5, 1}, -S^2] + (212*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 368*HPL[{3, 2, 1}, -S^2] - 11624*HPL[{4, 1, 1}, -S^2] - 704*HPL[{3, 1, 1, 1}, -S^2] + 1376*HPL[{2, 1, 1, 1, 1}, -S^2] - 32*HPL[{2, 1}, -S^2]*Zeta[3] + 44*Zeta[3]^2) + HPL[{2, 1}, -S^2]*((249449*Pi^6)/22680 - (2452*Pi^2*HPL[{3, 1}, -S^2])/3 + 12*HPL[{4, 2}, -S^2] - 16*HPL[{5, 1}, -S^2] - (4904*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 6880*HPL[{3, 2, 1}, -S^2] + 20736*HPL[{4, 1, 1}, -S^2] - 13920*HPL[{3, 1, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1, 1}, -S^2] + 76*Zeta[3]^2) + HPL[{1}, -S^2]^3*((-2863*Pi^6)/324 - (1226*Pi^2*HPL[{2}, -S^2]^2)/9 - (1568*HPL[{2}, -S^2]^3)/9 + 8*HPL[{3}, -S^2]^2 - (200*Pi^2*HPL[{4}, -S^2])/9 - (292*HPL[{6}, -S^2])/3 + 2320*HPL[{2, 1}, -S^2]^2 + (4856*Pi^2*HPL[{3, 1}, -S^2])/9 + (544*HPL[{5, 1}, -S^2])/3 + HPL[{2}, -S^2]*((-12283*Pi^4)/270 - 16*HPL[{4}, -S^2] + 2320*HPL[{3, 1}, -S^2] - 4640*HPL[{2, 1, 1}, -S^2]) - 1080*Pi^2*HPL[{2, 1, 1}, -S^2] - (12544*HPL[{3, 2, 1}, -S^2])/3 - 12864*HPL[{4, 1, 1}, -S^2] + 8960*HPL[{3, 1, 1, 1}, -S^2] - 17920*HPL[{2, 1, 1, 1, 1}, -S^2] - 464*HPL[{2, 1}, -S^2]*Zeta[3] - 56*Zeta[3]^2 + HPL[{3}, -S^2]*((-688*HPL[{2, 1}, -S^2])/3 + (16*Zeta[3])/3)) + HPL[{4}, -S^2]*(342*HPL[{5}, -S^2] + (26*Pi^2*HPL[{2, 1}, -S^2])/3 + 172*HPL[{3, 2}, -S^2] + 560*HPL[{4, 1}, -S^2] - 8*HPL[{2, 2, 1}, -S^2] - 80*HPL[{3, 1, 1}, -S^2] + 96*HPL[{2, 1, 1, 1}, -S^2] - 24*Pi^2*Zeta[3] - 316*Zeta[5]) - (782*Pi^4*Zeta[5])/45 + HPL[{2}, -S^2]^2*((59*Pi^2*HPL[{3}, -S^2])/6 + 49*HPL[{5}, -S^2] + (560*Pi^2*HPL[{2, 1}, -S^2])/3 - 92*HPL[{3, 2}, -S^2] - 274*HPL[{4, 1}, -S^2] - 1720*HPL[{2, 2, 1}, -S^2] - 5008*HPL[{3, 1, 1}, -S^2] + 3136*HPL[{2, 1, 1, 1}, -S^2] + (23*Pi^2*Zeta[3])/2 + 17*Zeta[5]) + HPL[{3, 1}, -S^2]*(336*HPL[{3, 2}, -S^2] + 1072*HPL[{4, 1}, -S^2] + 6272*HPL[{2, 2, 1}, -S^2] - 60608*HPL[{3, 1, 1}, -S^2] - 13920*HPL[{2, 1, 1, 1}, -S^2] - (130*Pi^2*Zeta[3])/3 + 20*Zeta[5]) + HPL[{1}, -S^2]^4*((4*Pi^2*HPL[{3}, -S^2])/3 - (112*HPL[{5}, -S^2])/3 + 270*Pi^2*HPL[{2, 1}, -S^2] - (344*HPL[{3, 2}, -S^2])/3 - 264*HPL[{4, 1}, -S^2] - 2320*HPL[{2, 2, 1}, -S^2] - 6880*HPL[{3, 1, 1}, -S^2] + 4480*HPL[{2, 1, 1, 1}, -S^2] + (194*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*((172*HPL[{3}, -S^2])/3 + 1160*HPL[{2, 1}, -S^2] + 116*Zeta[3]) + (260*Zeta[5])/3) + HPL[{2, 1, 1}, -S^2]*(12544*HPL[{2, 2, 1}, -S^2] + 39008*HPL[{3, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2] + (368*Pi^2*Zeta[3])/3 + 328*Zeta[5]) + HPL[{1}, -S^2]*((-177569*Pi^8)/64800 - (560*Pi^2*HPL[{2}, -S^2]^3)/9 - (215*HPL[{2}, -S^2]^4)/3 + 4*Pi^2*HPL[{3}, -S^2]^2 - 22*HPL[{4}, -S^2]^2 - (79*Pi^2*HPL[{6}, -S^2])/3 + 298*HPL[{8}, -S^2] + (2452*Pi^2*HPL[{2, 1}, -S^2]^2)/3 - 3488*HPL[{3, 1}, -S^2]^2 + 2*Pi^2*HPL[{4, 2}, -S^2] + (232*Pi^2*HPL[{5, 1}, -S^2])/3 + 12*HPL[{5, 3}, -S^2] + 30*HPL[{6, 2}, -S^2] + 216*HPL[{7, 1}, -S^2] + HPL[{2}, -S^2]^2*((-11683*Pi^4)/360 - 2*HPL[{4}, -S^2] + 1568*HPL[{3, 1}, -S^2] - 3136*HPL[{2, 1, 1}, -S^2]) + HPL[{4}, -S^2]*((-143*Pi^4)/18 + 64*HPL[{3, 1}, -S^2] - 96*HPL[{2, 1, 1}, -S^2]) - (12283*Pi^4*HPL[{2, 1, 1}, -S^2])/45 - 13920*HPL[{2, 1, 1}, -S^2]^2 + HPL[{3, 1}, -S^2]*((12191*Pi^4)/90 + 13920*HPL[{2, 1, 1}, -S^2]) - (4480*Pi^2*HPL[{3, 2, 1}, -S^2])/3 + 64*HPL[{3, 3, 2}, -S^2] - (13840*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 152*HPL[{4, 1, 3}, -S^2] + 52*HPL[{4, 2, 2}, -S^2] - 280*HPL[{4, 3, 1}, -S^2] - 176*HPL[{5, 1, 2}, -S^2] - 1136*HPL[{5, 2, 1}, -S^2] - 3464*HPL[{6, 1, 1}, -S^2] + (9712*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 12544*HPL[{3, 2, 2, 1}, -S^2] + 37632*HPL[{3, 3, 1, 1}, -S^2] + 37632*HPL[{4, 1, 2, 1}, -S^2] + 112896*HPL[{4, 2, 1, 1}, -S^2] + 226880*HPL[{5, 1, 1, 1}, -S^2] - 6480*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] + 25088*HPL[{2, 2, 1, 2, 1}, -S^2] + 75264*HPL[{2, 2, 2, 1, 1}, -S^2] - 150528*HPL[{3, 1, 1, 1, 2}, -S^2] - 250880*HPL[{3, 1, 1, 2, 1}, -S^2] - 301056*HPL[{3, 1, 2, 1, 1}, -S^2] - 627200*HPL[{3, 2, 1, 1, 1}, -S^2] - 1883520*HPL[{4, 1, 1, 1, 1}, -S^2] + 53760*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 107520*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{5}, -S^2]*(-80*HPL[{2, 1}, -S^2] - 120*Zeta[3]) - 64*HPL[{3, 2}, -S^2]*Zeta[3] - 96*HPL[{4, 1}, -S^2]*Zeta[3] + 1344*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 4064*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 2784*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - 28*Pi^2*Zeta[3]^2 + HPL[{2}, -S^2]*((-249449*Pi^6)/22680 + 8*HPL[{3}, -S^2]^2 - (26*Pi^2*HPL[{4}, -S^2])/3 - 50*HPL[{6}, -S^2] + 3136*HPL[{2, 1}, -S^2]^2 + (2452*Pi^2*HPL[{3, 1}, -S^2])/3 - 12*HPL[{4, 2}, -S^2] + 16*HPL[{5, 1}, -S^2] - (4904*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 6880*HPL[{3, 2, 1}, -S^2] - 20736*HPL[{4, 1, 1}, -S^2] + 164448*HPL[{3, 1, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1, 1}, -S^2] - 672*HPL[{2, 1}, -S^2]*Zeta[3] - 76*Zeta[3]^2 + HPL[{3}, -S^2]*(-304*HPL[{2, 1}, -S^2] + 32*Zeta[3])) + HPL[{2, 1}, -S^2]*(608*HPL[{3, 2}, -S^2] + 1920*HPL[{4, 1}, -S^2] - 12544*HPL[{2, 2, 1}, -S^2] - 39008*HPL[{3, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1}, -S^2] - (368*Pi^2*Zeta[3])/3 - 328*Zeta[5]) + HPL[{3}, -S^2]*(44*HPL[{5}, -S^2] - (212*Pi^2*HPL[{2, 1}, -S^2])/3 - 32*HPL[{3, 2}, -S^2] + 24*HPL[{4, 1}, -S^2] + 608*HPL[{2, 2, 1}, -S^2] + 1920*HPL[{3, 1, 1}, -S^2] - 1376*HPL[{2, 1, 1, 1}, -S^2] - (8*Pi^2*Zeta[3])/3 - 88*Zeta[5]) - 336*Zeta[3]*Zeta[5]) + HPL[{1}, -S^2]^2*(-28*Pi^2*HPL[{5}, -S^2] - 28*HPL[{7}, -S^2] - (212*Pi^2*HPL[{3, 2}, -S^2])/3 - (436*Pi^2*HPL[{4, 1}, -S^2])/3 + 44*HPL[{4, 3}, -S^2] + 120*HPL[{5, 2}, -S^2] + 452*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((12283*Pi^4)/90 - 6960*HPL[{3, 1}, -S^2] - 13920*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-127*Pi^4)/45 - 28*HPL[{4}, -S^2] - 352*HPL[{3, 1}, -S^2] + 688*HPL[{2, 1, 1}, -S^2]) - (4904*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - 4888*Pi^2*HPL[{3, 1, 1}, -S^2] + 608*HPL[{3, 2, 2}, -S^2] + 1920*HPL[{3, 3, 1}, -S^2] + 1920*HPL[{4, 1, 2}, -S^2] + 5856*HPL[{4, 2, 1}, -S^2] + 11360*HPL[{5, 1, 1}, -S^2] + 3240*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + 12544*HPL[{2, 2, 2, 1}, -S^2] - 39008*HPL[{3, 1, 1, 2}, -S^2] - 39008*HPL[{3, 1, 2, 1}, -S^2] - 76640*HPL[{3, 2, 1, 1}, -S^2] - 228960*HPL[{4, 1, 1, 1}, -S^2] + 27840*HPL[{2, 1, 2, 1, 1}, -S^2] + 83520*HPL[{2, 2, 1, 1, 1}, -S^2] + 140160*HPL[{3, 1, 1, 1, 1}, -S^2] + 53760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(48*HPL[{2, 1}, -S^2] - 48*Zeta[3]) + (373*Pi^4*Zeta[3])/90 - 688*HPL[{3, 1}, -S^2]*Zeta[3] + 1392*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]^2*(76*HPL[{3}, -S^2] + 1568*HPL[{2, 1}, -S^2] + 168*Zeta[3]) + (52*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((106*Pi^2*HPL[{3}, -S^2])/3 + 40*HPL[{5}, -S^2] + (2452*Pi^2*HPL[{2, 1}, -S^2])/3 - 304*HPL[{3, 2}, -S^2] - 960*HPL[{4, 1}, -S^2] - 6272*HPL[{2, 2, 1}, -S^2] + 19504*HPL[{3, 1, 1}, -S^2] + 13920*HPL[{2, 1, 1, 1}, -S^2] + (184*Pi^2*Zeta[3])/3 + 164*Zeta[5])) + HPL[{2}, -S^2]*((53*Pi^2*HPL[{5}, -S^2])/3 + 348*HPL[{7}, -S^2] - 40*Pi^2*HPL[{3, 2}, -S^2] - (380*Pi^2*HPL[{4, 1}, -S^2])/3 + 154*HPL[{4, 3}, -S^2] + 462*HPL[{5, 2}, -S^2] + 690*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((11683*Pi^4)/180 - 3136*HPL[{3, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((257*Pi^4)/90 - 86*HPL[{4}, -S^2] - 168*HPL[{3, 1}, -S^2] + 304*HPL[{2, 1, 1}, -S^2]) - (2240*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (6932*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 368*HPL[{3, 2, 2}, -S^2] + 1072*HPL[{3, 3, 1}, -S^2] + 1084*HPL[{4, 1, 2}, -S^2] + 3196*HPL[{4, 2, 1}, -S^2] + 6416*HPL[{5, 1, 1}, -S^2] + (4904*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 6880*HPL[{2, 2, 2, 1}, -S^2] + 20032*HPL[{3, 1, 1, 2}, -S^2] + 20032*HPL[{3, 1, 2, 1}, -S^2] + 40672*HPL[{3, 2, 1, 1}, -S^2] + 121920*HPL[{4, 1, 1, 1}, -S^2] + 12544*HPL[{2, 1, 2, 1, 1}, -S^2] + 37632*HPL[{2, 2, 1, 1, 1}, -S^2] - 61344*HPL[{3, 1, 1, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(4*HPL[{2, 1}, -S^2] - 68*Zeta[3]) + (127*Pi^4*Zeta[3])/60 - 320*HPL[{3, 1}, -S^2]*Zeta[3] + 672*HPL[{2, 1, 1}, -S^2]*Zeta[3] - Pi^2*Zeta[5] - 270*Zeta[7]) - 186*Pi^2*Zeta[7] - 1568*Zeta[9]) + HPL[{1}, -S^2]*(-76*Pi^2*HPL[{7}, -S^2] - 4044*HPL[{9}, -S^2] + 44*Pi^2*HPL[{4, 3}, -S^2] + (308*Pi^2*HPL[{5, 2}, -S^2])/3 - 348*HPL[{5, 4}, -S^2] + 50*Pi^2*HPL[{6, 1}, -S^2] - 1412*HPL[{6, 3}, -S^2] - 3536*HPL[{7, 2}, -S^2] - 4628*HPL[{8, 1}, -S^2] + HPL[{4, 1}, -S^2]*((-11338*Pi^4)/45 - 45504*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 2}, -S^2]*((-3322*Pi^4)/45 - 15104*HPL[{2, 1, 1}, -S^2]) + HPL[{5}, -S^2]*((983*Pi^4)/90 - 832*HPL[{3, 1}, -S^2] + 1472*HPL[{2, 1, 1}, -S^2]) - (13303*Pi^4*HPL[{2, 2, 1}, -S^2])/45 - (31913*Pi^4*HPL[{3, 1, 1}, -S^2])/45 + (3772*Pi^2*HPL[{3, 2, 2}, -S^2])/3 + (11560*Pi^2*HPL[{3, 3, 1}, -S^2])/3 + (11396*Pi^2*HPL[{4, 1, 2}, -S^2])/3 + (35252*Pi^2*HPL[{4, 2, 1}, -S^2])/3 + 204*HPL[{4, 2, 3}, -S^2] + 212*HPL[{4, 3, 2}, -S^2] - 176*HPL[{4, 4, 1}, -S^2] + 24184*Pi^2*HPL[{5, 1, 1}, -S^2] - 232*HPL[{5, 1, 3}, -S^2] + 164*HPL[{5, 2, 2}, -S^2] - 1096*HPL[{5, 3, 1}, -S^2] - 980*HPL[{6, 1, 2}, -S^2] - 3220*HPL[{6, 2, 1}, -S^2] - 7632*HPL[{7, 1, 1}, -S^2] + (2708*Pi^4*HPL[{2, 1, 1, 1}, -S^2])/9 + (3440*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 - 5888*Pi^2*HPL[{3, 1, 1, 2}, -S^2] - 5888*Pi^2*HPL[{3, 1, 2, 1}, -S^2] - 9328*Pi^2*HPL[{3, 2, 1, 1}, -S^2] - 13760*HPL[{3, 2, 2, 2}, -S^2] - 43296*HPL[{3, 2, 3, 1}, -S^2] - 42624*HPL[{3, 3, 1, 2}, -S^2] - 131232*HPL[{3, 3, 2, 1}, -S^2] - (86896*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 + 266752*HPL[{4, 1, 1, 3}, -S^2] + 224128*HPL[{4, 1, 2, 2}, -S^2] + 400672*HPL[{4, 1, 3, 1}, -S^2] + 137536*HPL[{4, 2, 1, 2}, -S^2] + 135520*HPL[{4, 2, 2, 1}, -S^2] + 792352*HPL[{4, 3, 1, 1}, -S^2] + 805632*HPL[{5, 1, 1, 2}, -S^2] + 1329216*HPL[{5, 1, 2, 1}, -S^2] + 3167808*HPL[{5, 2, 1, 1}, -S^2] + 7914656*HPL[{6, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((16733*Pi^6)/1260 - (5392*Pi^2*HPL[{3, 1}, -S^2])/3 + 1344*HPL[{4, 2}, -S^2] + 5248*HPL[{5, 1}, -S^2] - (10784*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 1344*HPL[{3, 1, 2}, -S^2] + 12416*HPL[{3, 2, 1}, -S^2] + 37440*HPL[{4, 1, 1}, -S^2] - 27840*HPL[{3, 1, 1, 1}, -S^2] - 55680*HPL[{2, 1, 1, 1, 1}, -S^2]) + (21568*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 21568*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 27520*HPL[{2, 2, 2, 2, 1}, -S^2] + (125440*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - 53696*HPL[{3, 1, 1, 2, 2}, -S^2] - 53696*HPL[{3, 1, 2, 1, 2}, -S^2] + 1344*HPL[{3, 1, 2, 2, 1}, -S^2] + 407040*HPL[{3, 1, 3, 1, 1}, -S^2] - 136256*HPL[{3, 2, 1, 1, 2}, -S^2] - 81216*HPL[{3, 2, 1, 2, 1}, -S^2] + 105664*HPL[{3, 2, 2, 1, 1}, -S^2] + 395520*HPL[{3, 3, 1, 1, 1}, -S^2] - 408384*HPL[{4, 1, 1, 1, 2}, -S^2] - 243264*HPL[{4, 1, 1, 2, 1}, -S^2] + 317376*HPL[{4, 1, 2, 1, 1}, -S^2] + 1190976*HPL[{4, 2, 1, 1, 1}, -S^2] + 2397696*HPL[{5, 1, 1, 1, 1}, -S^2] + 4640*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 55680*HPL[{3, 1, 1, 1, 1, 2}, -S^2] - 55680*HPL[{3, 1, 1, 1, 2, 1}, -S^2] - 55680*HPL[{3, 1, 1, 2, 1, 1}, -S^2] - 55680*HPL[{3, 1, 2, 1, 1, 1}, -S^2] - 55680*HPL[{3, 2, 1, 1, 1, 1}, -S^2] - 190080*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - 111360*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] - 445440*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] - 1113600*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] - 2204160*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]^2*(336*HPL[{2, 1}, -S^2] - 48*Zeta[3]) + (1847*Pi^6*Zeta[3])/567 - 3136*HPL[{2, 1}, -S^2]^2*Zeta[3] - 120*HPL[{4, 2}, -S^2]*Zeta[3] - 640*HPL[{5, 1}, -S^2]*Zeta[3] + 6880*HPL[{3, 2, 1}, -S^2]*Zeta[3] + 21152*HPL[{4, 1, 1}, -S^2]*Zeta[3] - 14336*HPL[{3, 1, 1, 1}, -S^2]*Zeta[3] + 27840*HPL[{2, 1, 1, 1, 1}, -S^2]*Zeta[3] + 64*Zeta[3]^3 + HPL[{6}, -S^2]*(-20*HPL[{2, 1}, -S^2] + 156*Zeta[3]) + HPL[{2}, -S^2]^3*((860*HPL[{3}, -S^2])/3 + (1720*HPL[{2, 1}, -S^2])/3 + (860*Zeta[3])/3) + HPL[{3}, -S^2]*((18983*Pi^6)/3780 - (110*Pi^2*HPL[{4}, -S^2])/3 - 148*HPL[{6}, -S^2] - 4112*HPL[{2, 1}, -S^2]^2 - (1844*Pi^2*HPL[{3, 1}, -S^2])/3 - 180*HPL[{4, 2}, -S^2] + 168*HPL[{5, 1}, -S^2] + 1224*Pi^2*HPL[{2, 1, 1}, -S^2] + 6880*HPL[{3, 2, 1}, -S^2] - 245984*HPL[{4, 1, 1}, -S^2] - 13952*HPL[{3, 1, 1, 1}, -S^2] + 27840*HPL[{2, 1, 1, 1, 1}, -S^2] - 304*HPL[{2, 1}, -S^2]*Zeta[3] + 88*Zeta[3]^2) + HPL[{3, 1}, -S^2]*(7552*HPL[{3, 2}, -S^2] + 22784*HPL[{4, 1}, -S^2] - 2688*HPL[{2, 2, 1}, -S^2] - 98816*HPL[{3, 1, 1}, -S^2] - 27840*HPL[{2, 1, 1, 1}, -S^2] - (1972*Pi^2*Zeta[3])/3 - 3240*Zeta[5]) + (1564*Pi^4*Zeta[5])/45 + HPL[{4}, -S^2]*(172*HPL[{5}, -S^2] - (452*Pi^2*HPL[{2, 1}, -S^2])/3 + 360*HPL[{3, 2}, -S^2] + 1192*HPL[{4, 1}, -S^2] + 2688*HPL[{2, 2, 1}, -S^2] + 7264*HPL[{3, 1, 1}, -S^2] - 3840*HPL[{2, 1, 1, 1}, -S^2] + 28*Pi^2*Zeta[3] + 64*Zeta[5]) + HPL[{2}, -S^2]^2*((533*Pi^2*HPL[{3}, -S^2])/3 + 194*HPL[{5}, -S^2] + (430*Pi^2*HPL[{2, 1}, -S^2])/3 - 1720*HPL[{3, 2}, -S^2] - 5832*HPL[{4, 1}, -S^2] - 3440*HPL[{2, 2, 1}, -S^2] - 6208*HPL[{3, 1, 1}, -S^2] + 143*Pi^2*Zeta[3] + 714*Zeta[5]) + HPL[{2, 1, 1}, -S^2]*(27840*HPL[{3, 1, 1}, -S^2] + 55680*HPL[{2, 1, 1, 1}, -S^2] + (3824*Pi^2*Zeta[3])/3 + 6464*Zeta[5]) + 372*Pi^2*Zeta[7] + HPL[{2}, -S^2]*(66*Pi^2*HPL[{5}, -S^2] + 104*HPL[{7}, -S^2] + HPL[{2, 1}, -S^2]*((13303*Pi^4)/90 + 1344*HPL[{3, 1}, -S^2]) - 656*Pi^2*HPL[{3, 2}, -S^2] - (5944*Pi^2*HPL[{4, 1}, -S^2])/3 + 172*HPL[{4, 3}, -S^2] + 324*HPL[{5, 2}, -S^2] - 260*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((1661*Pi^4)/45 - 180*HPL[{4}, -S^2] - 4112*HPL[{3, 1}, -S^2] + 8224*HPL[{2, 1, 1}, -S^2]) - (1720*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + 2944*Pi^2*HPL[{3, 1, 1}, -S^2] + 6880*HPL[{3, 2, 2}, -S^2] + 21984*HPL[{3, 3, 1}, -S^2] + 21984*HPL[{4, 1, 2}, -S^2] + 67296*HPL[{4, 2, 1}, -S^2] + 137408*HPL[{5, 1, 1}, -S^2] + (10784*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 13760*HPL[{2, 2, 2, 1}, -S^2] + 26176*HPL[{3, 1, 1, 2}, -S^2] + 26176*HPL[{3, 1, 2, 1}, -S^2] + 67456*HPL[{3, 2, 1, 1}, -S^2] + 202176*HPL[{4, 1, 1, 1}, -S^2] + 27840*HPL[{3, 1, 1, 1, 1}, -S^2] + 55680*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (3383*Pi^4*Zeta[3])/90 - 3136*HPL[{3, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-1344*HPL[{2, 1}, -S^2] + 136*Zeta[3]) + 294*Pi^2*Zeta[5] + 1692*Zeta[7]) + 3136*Zeta[9]);
E5uvwT1F1=(S*HPL[{0}, S^2]^9)/(192*(1 + S^2)) + ((-2 + 4*S^2 + S^4)*HPL[{0}, S^2]^8*HPL[{1}, -S^2])/(96*S*(1 + S^2)) - (8*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^9)/(27*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{2}, -S^2]^4)/(3*S) + HPL[{1}, -S^2]^7*((-2*Pi^2*(51 - 305*S^2 + 36*S^4))/(63*S*(1 + S^2)) + (20*(-1 + S^2)*HPL[{2}, -S^2])/(7*S)) + HPL[{0}, S^2]^7*((Pi^2*S*(27 + S^2))/(288*(1 + S^2)) + ((-4 + 13*S^2 + S^4)*HPL[{1}, -S^2]^2)/(48*S*(1 + S^2)) + (S*(7 + S^2)*HPL[{2}, -S^2])/(48*(1 + S^2))) - (2*(-16 + 25*S^2)*HPL[{3}, -S^2]^3)/(3*S) - (24*(1 + S^2)*HPL[{4}, -S^2]^2)/S + (Pi^2*(-145 + 473*S^2 + 390*S^4)*HPL[{7}, -S^2])/(3*S*(1 + S^2)) + (4*(-784 + 1155*S^2 + 928*S^4)*HPL[{9}, -S^2])/(S*(1 + S^2)) + (1232*(-1 + S^2)*HPL[{2, 1}, -S^2]^3)/(3*S) + (40*(1 + S^2)*HPL[{3, 1}, -S^2]^2)/S - (44*Pi^2*(-1 + 2*S^2)*HPL[{4, 3}, -S^2])/(3*S*(1 + S^2)) + (Pi^2*(122 - 233*S^2 - 47*S^4)*HPL[{5, 2}, -S^2])/(3*S*(1 + S^2)) + (4*(-1 + 213*S^2 + 127*S^4)*HPL[{5, 4}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*(-178 + 186*S^2 + 289*S^4)*HPL[{6, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(-3 + 872*S^2 + 522*S^4)*HPL[{6, 3}, -S^2])/(S*(1 + S^2)) + (4*(-23 + 2164*S^2 + 1303*S^4)*HPL[{7, 2}, -S^2])/(S*(1 + S^2)) + (4*(369 + 3458*S^2 + 1932*S^4)*HPL[{8, 1}, -S^2])/(S*(1 + S^2)) + (192*(1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + (Pi^2*(-67 - 2578*S^2 + 1261*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S*(1 + S^2)) + (4*Pi^2*(-45 - 1966*S^2 + 969*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S*(1 + S^2)) + (4*Pi^2*(-44 - 1922*S^2 + 971*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S*(1 + S^2)) + (4*Pi^2*(-119 - 5990*S^2 + 2942*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(3 - 32*S^2 + 16*S^4)*HPL[{4, 2, 3}, -S^2])/(S*(1 + S^2)) - (4*(-76 + 55*S^2 + 78*S^4)*HPL[{4, 3, 2}, -S^2])/(S*(1 + S^2)) - (8*(-71 - 31*S^2 + 62*S^4)*HPL[{4, 4, 1}, -S^2])/(S*(1 + S^2)) + (2*Pi^2*(-474 - 24653*S^2 + 12097*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(-5 + 103*S^2 + 50*S^4)*HPL[{5, 1, 3}, -S^2])/(S*(1 + S^2)) - (4*(-212 + 31*S^2 + 202*S^4)*HPL[{5, 2, 2}, -S^2])/(S*(1 + S^2)) - (4*(-399 - 403*S^2 + 270*S^4)*HPL[{5, 3, 1}, -S^2])/(S*(1 + S^2)) - (4*(-419 - 324*S^2 + 340*S^4)*HPL[{6, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(-699 - 1304*S^2 + 200*S^4)*HPL[{6, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*(695 + 3441*S^2 + 838*S^4)*HPL[{7, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*Pi^2*(-154 + 147*S^2 + 86*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*Pi^2*(-3643 + 5928*S^2 + 739*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) + (2*Pi^2*(-3643 + 5928*S^2 + 739*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*Pi^2*(-7339 + 9456*S^2 + 2803*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(-59 - 2352*S^2 + 1147*S^4)*HPL[{3, 2, 2, 2}, -S^2])/(S*(1 + S^2)) - (4*(-218 - 7435*S^2 + 3607*S^4)*HPL[{3, 2, 3, 1}, -S^2])/(S*(1 + S^2)) - (8*(-106 - 3649*S^2 + 1785*S^4)*HPL[{3, 3, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(-722 - 22547*S^2 + 10983*S^4)*HPL[{3, 3, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*(-11017 + 14784*S^2 + 4077*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(-1522 - 45887*S^2 + 22323*S^4)*HPL[{4, 1, 1, 3}, -S^2])/(S*(1 + S^2)) + (4*(-1317 - 38589*S^2 + 18760*S^4)*HPL[{4, 1, 2, 2}, -S^2])/(S*(1 + S^2)) + (8*(-1162 - 34475*S^2 + 16771*S^4)*HPL[{4, 1, 3, 1}, -S^2])/(S*(1 + S^2)) + (4*(-825 - 23751*S^2 + 11458*S^4)*HPL[{4, 2, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(-807 - 23340*S^2 + 11347*S^4)*HPL[{4, 2, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(-1132 - 34037*S^2 + 16617*S^4)*HPL[{4, 3, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(-4634 - 138823*S^2 + 67219*S^4)*HPL[{5, 1, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(-7622 - 228673*S^2 + 111253*S^4)*HPL[{5, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*(-18134 - 544381*S^2 + 265705*S^4)*HPL[{5, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*(-22606 - 680185*S^2 + 331753*S^4)*HPL[{6, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (32*Pi^2*(152 - 447*S^2 + 75*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (32*Pi^2*(152 - 447*S^2 + 75*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (128*(34 - 147*S^2 + 34*S^4)*HPL[{2, 2, 2, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*Pi^2*(1513 - 5224*S^2 + 1103*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(3361 - 9166*S^2 + 897*S^4)*HPL[{3, 1, 1, 2, 2}, -S^2])/(S*(1 + S^2)) - (4*(3361 - 9166*S^2 + 897*S^4)*HPL[{3, 1, 2, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(31 - 274*S^2 + 31*S^4)*HPL[{3, 1, 2, 2, 1}, -S^2])/(S*(1 + S^2)) + (32*(2951 - 8708*S^2 + 1061*S^4)*HPL[{3, 1, 3, 1, 1}, -S^2])/(S*(1 + S^2)) - (4*(6625 - 23278*S^2 + 4161*S^4)*HPL[{3, 2, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(3233 - 13838*S^2 + 3233*S^4)*HPL[{3, 2, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-10455 + 18162*S^2 + 2201*S^4)*HPL[{3, 2, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (96*(-1439 + 2824*S^2 + 143*S^4)*HPL[{3, 3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(9979 - 34954*S^2 + 6115*S^4)*HPL[{4, 1, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (8*(4891 - 20794*S^2 + 4723*S^4)*HPL[{4, 1, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(-15641 + 27206*S^2 + 3175*S^4)*HPL[{4, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(-51809 + 102038*S^2 + 4975*S^4)*HPL[{4, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-25899 + 51365*S^2 + 2336*S^4)*HPL[{5, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*Pi^2*(-330 + 289*S^2 + 184*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (9856*(-1 + S^2)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/S + (29568*(-1 + S^2)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S - (32*(-1577 - 1156*S^2 + 2161*S^4)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (32*(-3425 - 1156*S^2 + 4009*S^4)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (32*(-4657 - 1156*S^2 + 5241*S^4)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-5273 - 1156*S^2 + 5857*S^4)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-9277 - 1156*S^2 + 9861*S^4)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (64*(-13897 - 2018*S^2 + 14849*S^4)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (256*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (1024*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (2560*(73 - 289*S^2 + 73*S^4)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (768*(511 - 1903*S^2 + 456*S^4)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (42240*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((4*Pi^2*S*(-27 + S^2))/(9*(1 + S^2)) + (4*S*(-9 + S^2)*HPL[{0}, S^2]^2)/(3*(1 + S^2)) + (32*(1 - 7*S^2 + S^4)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(3*S*(1 + S^2)) + (32*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) + (8*(-1 + S^2)*HPL[{2}, -S^2])/(3*S))*Log[T]^7 + ((-4*S*(-7 + 2*S^2)*HPL[{0}, S^2])/(3*(1 + S^2)) - (8*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2])/(3*S*(1 + S^2)))*Log[T]^8 - (8*S*Log[T]^9)/(3*(1 + S^2)) + (1847*Pi^6*S^3*Zeta[3])/(567*(1 + S^2)) + (64*S^3*Zeta[3]^3)/(1 + S^2) + HPL[{3, 1, 1}, -S^2]*((-16*Pi^2*(1 + S^2))/S + (Pi^4*(-22369 + 40592*S^2 - 865*S^4))/(90*S*(1 + S^2)) - (232*(1 + S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((-8*Pi^2*(1 + S^2))/S + (Pi^4*(-3684 + 8559*S^2 - 1060*S^4))/(45*S*(1 + S^2)) - (80*(1 + S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((-12*Pi^2*(1 + S^2))/S + (Pi^4*(-11 + 14594*S^2 - 8071*S^4))/(90*S*(1 + S^2)) - (8*(-95 - 3862*S^2 + 1921*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (28*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^5*((-16*Pi^2*(1 + S^2))/(15*S) + (Pi^4*(-4460 + 23717*S^2 - 2213*S^4))/(1350*S*(1 + S^2)) + (2*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2}, -S^2])/(45*S*(1 + S^2)) - (8*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(15*S*(1 + S^2)) - (16*(1 + S^2)*HPL[{3}, -S^2])/(5*S) + (4*(47 - 554*S^2 + 119*S^4)*HPL[{4}, -S^2])/(15*S*(1 + S^2)) - (8*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1}, -S^2])/(15*S*(1 + S^2)) + (120*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((-11*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-29 + 2064*S^2 - 1229*S^4))/(45*S*(1 + S^2)) - (4*(-25 - 2594*S^2 + 1207*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (6*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((-11*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(28 - 225*S^2 + 730*S^4))/(90*S*(1 + S^2)) + (14*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (16*(2 - 39*S^2 + 11*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (4*(14 - 195*S^2 + 159*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (10*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((-4*Pi^4*(-393 + 432*S^2 + 148*S^4))/(9*S*(1 + S^2)) + (192*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(-1 - S^2))/(3*S) + (4*(-1 + 9*S^2)*Zeta[3])/S) + Log[T]^6*((-4*S*(-25 + 3*S^2)*HPL[{0}, S^2]^3)/(9*(1 + S^2)) - (2*(23 - 109*S^2 + 8*S^4)*HPL[{0}, S^2]^2*HPL[{1}, -S^2])/(3*S*(1 + S^2)) - (224*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((-2*Pi^2*(51 - 305*S^2 + 36*S^4))/(9*S*(1 + S^2)) + (20*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]*((-4*Pi^2*S*(-74 + 17*S^2))/(9*(1 + S^2)) - (112*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) - (4*(-2 - 87*S^2 + 27*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + (16*S*(-24 + 11*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (176*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (16*S*(-17 + 11*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{0}, S^2]^6*(((-1 - S^2)*HPL[{1}, -S^2]^2)/(12*S) + ((-23 + 70*S^2 + 5*S^4)*HPL[{1}, -S^2]^3)/(72*S*(1 + S^2)) + HPL[{1}, -S^2]*((-1 - S^2)/(6*S) + (Pi^2*(-79 + 182*S^2 + 33*S^4))/(288*S*(1 + S^2)) + ((-19 + 51*S^2 + 6*S^4)*HPL[{2}, -S^2])/(48*S*(1 + S^2))) + ((-1 + 3*S^2)*HPL[{3}, -S^2])/(48*S) + ((9 - 8*S^2 - S^4)*HPL[{2, 1}, -S^2])/(12*S*(1 + S^2)) + (S*(17 + 11*S^2)*Zeta[3])/(12*(1 + S^2))) + HPL[{2}, -S^2]^3*((2*Pi^2*(1 + S^2))/(9*S) + (2*(-17 - 294*S^2 + 153*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (8*(34 - 147*S^2 + 34*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (4*S*(-147 + 68*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2, 1, 1, 1, 1}, -S^2]*((32*Pi^2*(1 + S^2))/S + (64*S*(-289 + 146*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4, 2}, -S^2]*((Pi^2*(1 + S^2))/(3*S) - (4*(-1 - 22*S^2 + 9*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]^2*((32*(1 + S^2))/S + (2*(29 - 121*S^2 + 18*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-3 - 4*S^2 + 11*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^6*((-2*Pi^2*(1 + S^2))/(9*S) + (20*(5 - 65*S^2 + 14*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (20*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(5 - 87*S^2 + 20*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{5, 1}, -S^2]*((Pi^2*(-1 - S^2))/(3*S) - (4*(17 - 117*S^2 + 26*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{6}, -S^2]*((-10*Pi^2*(1 + S^2))/(3*S) - (4*(-74 - 29*S^2 + 50*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-30 + 61*S^2 + 52*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]^2*((-128*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/(3*S) - (16*(-6 - 131*S^2 + 71*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1, 1, 1}, -S^2]*((-52*Pi^2*(1 + S^2))/(3*S) - (16*(1 - 602*S^2 + 293*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{4, 1, 1}, -S^2]*((56*Pi^2*(1 + S^2))/(3*S) + (16*(1 - 898*S^2 + 423*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 2, 1}, -S^2]*((5*Pi^2*(1 + S^2))/S + (4*(-1 - 1168*S^2 + 553*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^5*((Pi^4*S*(14626 + 569*S^2))/(21600*(1 + S^2)) + ((-1 - S^2)*HPL[{1}, -S^2]^3)/(12*S) + ((-275 + 1033*S^2 + 4*S^4)*HPL[{1}, -S^2]^4)/(360*S*(1 + S^2)) + ((1 + S^2)/(2*S) + (Pi^2*S*(319 + 26*S^2))/(180*(1 + S^2)))*HPL[{2}, -S^2] - (S*(-76 + S^2)*HPL[{2}, -S^2]^2)/(40*(1 + S^2)) + HPL[{1}, -S^2]^2*((-1 - S^2)/(8*S) + (Pi^2*(-695 + 2398*S^2 + 109*S^4))/(720*S*(1 + S^2)) + ((-230 + 853*S^2 - S^4)*HPL[{2}, -S^2])/(120*S*(1 + S^2))) + ((1 + S^2)*HPL[{3}, -S^2])/(4*S) - (S^3*HPL[{4}, -S^2])/(2*(1 + S^2)) + ((-1 - S^2)*HPL[{2, 1}, -S^2])/(4*S) + (3*S*(-27 + 2*S^2)*HPL[{3, 1}, -S^2])/(10*(1 + S^2)) - (S*(-541 + S^2)*HPL[{2, 1, 1}, -S^2])/(30*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-1 - S^2))/(48*S) + (3*(1 + S^2)*HPL[{2}, -S^2])/(8*S) - (S*(-3 + S^2)*HPL[{3}, -S^2])/(4*(1 + S^2)) + ((230 - 853*S^2 + S^4)*HPL[{2, 1}, -S^2])/(60*S*(1 + S^2)) + ((-1 + 3*S^2 + S^4)*Zeta[3])/(S*(1 + S^2)))) + Log[T]^5*((Pi^4*S*(-14626 + 569*S^2))/(675*(1 + S^2)) + (2*S*(-164 + S^2)*HPL[{0}, S^2]^4)/(45*(1 + S^2)) + (2*(56 - 263*S^2 + 17*S^4)*HPL[{0}, S^2]^3*HPL[{1}, -S^2])/(9*S*(1 + S^2)) + (112*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)) + (4*Pi^2*(-11 - 77*S^2 + 21*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (8*(5 - 77*S^2 + 5*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^2*((2*Pi^2*(51 - 305*S^2 + 36*S^4))/(3*S*(1 + S^2)) - (60*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^2*((Pi^2*S*(-1601 + 109*S^2))/(45*(1 + S^2)) + (4*(1 + S^2)*HPL[{1}, -S^2])/S + (2*(23 - 109*S^2 + 8*S^4)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)) + (2*(-1 - 154*S^2 + 21*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) - (8*(-1 - 90*S^2 + 31*S^4)*HPL[{4}, -S^2])/(5*S*(1 + S^2)) - (16*(-5 + 9*S^2 + 2*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (112*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + HPL[{0}, S^2]*((224*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) - (8*(1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((2*Pi^2*(140 - 851*S^2 + 101*S^4))/(9*S*(1 + S^2)) + (4*(25 - 174*S^2 + 25*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) - (4*(-3 - 10*S^2 + 5*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (8*(-27 + 87*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (24*S*(-3 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]*((4*Pi^2*(1 + S^2))/(3*S) - (40*(5 - 65*S^2 + 14*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (120*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(5 - 87*S^2 + 20*S^4)*Zeta[3])/(S*(1 + S^2)))) + (1564*Pi^4*S^3*Zeta[5])/(45*(1 + S^2)) + HPL[{1}, -S^2]^3*((-116*Pi^2*(1 + S^2))/(9*S) - (571*Pi^4*(1 + S^2))/(270*S) + (Pi^6*(-201706 + 958255*S^2 - 59719*S^4))/(68040*S*(1 + S^2)) + ((44*(1 + S^2))/(3*S) + (Pi^2*(-350 + 2089*S^2 - 257*S^4))/(9*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + (62*(-1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - (2*(37 - 238*S^2 + 37*S^4)*HPL[{3}, -S^2]^2)/(3*S*(1 + S^2)) + (Pi^2*(61 - 1132*S^2 + 279*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) - (32*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (2*(-194 - 127*S^2 + 283*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) + (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) - (8*Pi^2*(-116 + 193*S^2 + 61*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (32*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (96*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (6*(13 - 86*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (16*(50 - 551*S^2 + 119*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + (8*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) + (64*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (128*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (496*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (32*(-116 - 277*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (32*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2400*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-296*(1 + S^2))/(3*S) - (74*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (8*(5 - 32*S^2 + 5*S^4)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{2}, -S^2]*((22*Pi^2*(1 + S^2))/(9*S) + (Pi^4*(-7200 + 21017*S^2 + 1137*S^4))/(540*S*(1 + S^2)) - (16*(1 + S^2)*HPL[{3}, -S^2])/S + (2*(113 - 734*S^2 + 113*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (32*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (32*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (16*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-128*(1 + S^2))/(3*S) - (14*Pi^2*(1 + S^2))/(9*S) - (8*(103 - 1348*S^2 + 289*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(11 - 87*S^2 + 14*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-8*Pi^2*(1 + S^2))/(3*S) - (32*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (236*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((-4*Pi^2*(1 + S^2))/S + (Pi^4*(1 + S^2))/(30*S) + (Pi^6*(-1655 - 71000*S^2 + 44553*S^4))/(22680*S*(1 + S^2)) + ((-4*(1 + S^2))/S - (2*Pi^2*(11 - 34*S^2 + 10*S^4))/(3*S*(1 + S^2)))*HPL[{4}, -S^2] + (46*(1 + S^2)*HPL[{5}, -S^2])/S + (4*S*(84 + 47*S^2)*HPL[{6}, -S^2])/(1 + S^2) - (2*(7 - 1426*S^2 + 623*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + ((-8*(1 + S^2))/S - (4*Pi^2*(-12 - 310*S^2 + 163*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] - (2*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (16*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (4*(2 - 30*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (8*(-1 + 25*S^2 + 5*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + (2*Pi^2*(-49 - 1204*S^2 + 681*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (72*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (216*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (4*(5 + 3*S^2)*HPL[{3, 1, 2}, -S^2])/S + (4*(-63 - 1168*S^2 + 615*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-1322 - 42339*S^2 + 20479*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (192*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (8*(-69 - 1182*S^2 + 631*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (32*(-29 - 578*S^2 + 321*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((8*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (2*(-3 - 26*S^2 + 21*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{2, 1}, -S^2]*((128*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/S + (4*(-29 + 68*S^2 + 21*S^4)*Zeta[3])/(S*(1 + S^2))) + (8*(1 + S^2)*Zeta[5])/S) + HPL[{2, 1}, -S^2]*((17*Pi^4*(1 + S^2))/(30*S) + (Pi^6*(83308 - 90729*S^2 - 23440*S^4))/(11340*S*(1 + S^2)) - (2*Pi^2*(567 - 1792*S^2 + 337*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (68*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (232*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (12*(23 - 86*S^2 + 3*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (4*(-252 + 1079*S^2 + 19*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) - (16*Pi^2*(152 - 447*S^2 + 75*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (192*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (12*(13 - 86*S^2 + 13*S^4)*HPL[{3, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(505 - 2094*S^2 + 505*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) + (32*(175 - 778*S^2 + 217*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (384*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (32*(125 - 578*S^2 + 167*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (128*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((128*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/S)*Zeta[3] - (8*(-2 + 5*S^2)*Zeta[3]^2)/S + (76*(1 + S^2)*Zeta[5])/S) + Log[T]^4*((S*(164 + S^2)*HPL[{0}, S^2]^5)/(45*(1 + S^2)) + ((-137 + 518*S^2 - 5*S^4)*HPL[{0}, S^2]^4*HPL[{1}, -S^2])/(18*S*(1 + S^2)) - (112*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)) + (8*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((-10*Pi^2*(51 - 305*S^2 + 36*S^4))/(9*S*(1 + S^2)) + (100*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^3*(-(Pi^2*S*(-703 + 43*S^2))/(27*(1 + S^2)) - (4*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (5*(56 - 263*S^2 + 17*S^4)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)) + ((2 + 669*S^2 - 83*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2))) + (2*Pi^2*(-7 - 754*S^2 + 353*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (4*(-6 - 125*S^2 + 109*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (4*Pi^2*(-330 + 289*S^2 + 184*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (4*(-37 - 1156*S^2 + 621*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (8*(-37 - 2018*S^2 + 989*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - (32*(73 - 289*S^2 + 73*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (32*(73 - 169*S^2 + 18*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (1760*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (4*Pi^2*S*(-281 + 184*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((-16*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-4460 + 23717*S^2 - 2213*S^4))/(270*S*(1 + S^2)) + (2*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - (8*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) - (16*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(47 - 554*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (8*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (600*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (40*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]^2*((-10*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (10*(23 - 109*S^2 + 8*S^4)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)) + (4*(1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((-16*(1 + S^2))/S + (Pi^2*(-619 + 2671*S^2 - 130*S^4))/(18*S*(1 + S^2)) + ((-325 + 1348*S^2 - 67*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + (2*(-7 - 34*S^2 + 23*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (4*(-165 + 289*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (4*S*(-26 + 19*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2}, -S^2]*((4*Pi^2*(1 + S^2))/(3*S) + (4*(-29 - 578*S^2 + 321*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (16*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*S*(-289 + 146*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]^2*((-10*Pi^2*(1 + S^2))/(3*S) + (100*(5 - 65*S^2 + 14*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (300*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (20*(5 - 87*S^2 + 20*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]*(-(Pi^4*S*(-11971 + 2086*S^2))/(270*(1 + S^2)) - (280*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)) + ((32*(1 + S^2))/S - (2*Pi^2*(-16 - 987*S^2 + 244*S^4))/(9*S*(1 + S^2)))*HPL[{2}, -S^2] - (4*S*(-337 + 98*S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + HPL[{1}, -S^2]^2*((-5*Pi^2*(140 - 851*S^2 + 101*S^4))/(9*S*(1 + S^2)) - (10*(25 - 174*S^2 + 25*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + (12*(1 + S^2)*HPL[{3}, -S^2])/S - (4*(1 - 16*S^2 + 3*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(-35 - 1312*S^2 + 403*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (40*(-2 - 87*S^2 + 27*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + HPL[{1}, -S^2]*((-4*Pi^2*(1 + S^2))/(3*S) + (40*(1 + S^2)*HPL[{2}, -S^2])/S + (4*(10 - 43*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (20*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*(40 - 277*S^2 + 43*S^4)*Zeta[3])/(3*S*(1 + S^2)))) + (40*S*(-50 + 37*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{0}, S^2]^4*((-3*(1 + S^2)*HPL[{1}, -S^2]^4)/(8*S) + ((-137 + 518*S^2 - 5*S^4)*HPL[{1}, -S^2]^5)/(90*S*(1 + S^2)) + ((1 + S^2)*HPL[{2}, -S^2]^2)/(4*S) + HPL[{1}, -S^2]^3*((-25*(1 + S^2))/(18*S) + (Pi^2*(-619 + 2086*S^2 + 65*S^4))/(216*S*(1 + S^2)) + ((-249 + 847*S^2 + 8*S^4)*HPL[{2}, -S^2])/(36*S*(1 + S^2))) + ((-1 - S^2)/(2*S) + (Pi^2*(-5 + 4*S^2 + 11*S^4))/(24*S*(1 + S^2)))*HPL[{3}, -S^2] + ((-1 - S^2)*HPL[{4}, -S^2])/(2*S) + ((-1 + 9*S^2 + 9*S^4)*HPL[{5}, -S^2])/(2*S*(1 + S^2)) + ((-1 - S^2)/(2*S) + (Pi^2*(129 - 139*S^2 - 12*S^4))/(18*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2))/(12*S) + ((2 + S^2)*HPL[{3}, -S^2])/(2*S*(1 + S^2)) + ((118 - 159*S^2 - 6*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2))) + ((-1 - S^2)*HPL[{3, 1}, -S^2])/S + ((-2 - S^2)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + ((-5 - 8*S^2 - 9*S^4)*HPL[{4, 1}, -S^2])/(2*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + ((-118 + 159*S^2 + 6*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + ((-241 + 316*S^2 + 19*S^4)*HPL[{3, 1, 1}, -S^2])/(2*S*(1 + S^2)) - (2*(-123 + 158*S^2 + 9*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (Pi^2*S*(281 + 184*S^2)*Zeta[3])/(36*(1 + S^2)) + HPL[{1}, -S^2]*((-8*(1 + S^2))/S - (85*Pi^2*(1 + S^2))/(72*S) + (Pi^4*(-2959 + 7876*S^2 + 950*S^4))/(2160*S*(1 + S^2)) + ((3*(1 + S^2))/(4*S) + (Pi^2*(-267 + 806*S^2 + 49*S^4))/(72*S*(1 + S^2)))*HPL[{2}, -S^2] + ((-56 + 211*S^2 - 4*S^4)*HPL[{2}, -S^2]^2)/(12*S*(1 + S^2)) + ((-5 + 6*S^2)*HPL[{4}, -S^2])/(2*S) - (19*(1 + S^2)*HPL[{2, 1}, -S^2])/(12*S) + ((127 - 413*S^2 - 10*S^4)*HPL[{3, 1}, -S^2])/(6*S*(1 + S^2)) + ((-249 + 847*S^2 + 8*S^4)*HPL[{2, 1, 1}, -S^2])/(6*S*(1 + S^2)) - (7*(1 + S^2)*Zeta[3])/(4*S)) + HPL[{1}, -S^2]^2*((-4*(1 + S^2))/S - (29*Pi^2*(1 + S^2))/(48*S) + (19*(1 + S^2)*HPL[{2}, -S^2])/(24*S) + ((-5 - 3*S^2 + 6*S^4)*HPL[{3}, -S^2])/(4*S*(1 + S^2)) + ((249 - 847*S^2 - 8*S^4)*HPL[{2, 1}, -S^2])/(12*S*(1 + S^2)) + ((-19 + 14*S^2 + 19*S^4)*Zeta[3])/(6*S*(1 + S^2))) + (5*S*(50 + 37*S^2)*Zeta[5])/(6*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((64*Pi^2*(1 + S^2))/(3*S) + (38*Pi^4*(1 + S^2))/(15*S) - (4928*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (32*(-433 + 578*S^2 + 141*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (128*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*Pi^2*S*(-317 + 161*S^2)*Zeta[3])/(3*(1 + S^2)) + (8*S*(-493 + 315*S^2)*Zeta[5])/(1 + S^2)) + HPL[{4}, -S^2]*((-4*Pi^2*(1 + S^2))/S - (17*Pi^4*(1 + S^2))/(90*S) - (4*S*(106 + 63*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((24*(1 + S^2))/S + (2*Pi^2*(-41 + 204*S^2 + 19*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (12*(-11 - 16*S^2 + 25*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (8*(-31 - 104*S^2 + 76*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (16*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(55 - 250*S^2 + 31*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(163 - 690*S^2 + 55*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (32*(-29 + 104*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((12*(1 + S^2))/S + (2*Pi^2*(1 - 12*S^2 + S^4))/(S*(1 + S^2)))*Zeta[3] - (4*(-25 + 12*S^2 + 21*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{2}, -S^2]^2*((8*Pi^2*(1 + S^2))/S + (29*Pi^4*(1 + S^2))/(45*S) + ((-2*(1 + S^2))/S + (Pi^2*(-1 - 736*S^2 + 331*S^4))/(6*S*(1 + S^2)))*HPL[{3}, -S^2] - (2*(1 + S^2)*HPL[{4}, -S^2])/S + (2*(-19 - 62*S^2 + 54*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*(-154 + 147*S^2 + 86*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2*(-23 - 588*S^2 + 295*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (2*(-47 - 2014*S^2 + 949*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (16*(34 - 147*S^2 + 34*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (2*(809 - 2102*S^2 + 193*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (1232*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-12*(1 + S^2))/S + (Pi^2*(-6 - 95*S^2 + 54*S^4))/(S*(1 + S^2)))*Zeta[3] + (2*(-16 - 219*S^2 + 154*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{1}, -S^2]^4*((-37*Pi^2*(1 + S^2))/(9*S) - (47*Pi^4*(1 + S^2))/(72*S) + (4*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-44*(1 + S^2))/(3*S) + (Pi^2*(118 - 1703*S^2 + 379*S^4))/(9*S*(1 + S^2)))*HPL[{3}, -S^2] + (2*(-5 - 116*S^2 + 41*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (4*(103 - 1348*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (8*(178 - 2299*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(463 - 2419*S^2 + 238*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (600*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-32*(1 + S^2))/S + (Pi^2*(79 - 1444*S^2 + 337*S^4))/(9*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S) + (2*(103 - 1348*S^2 + 289*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (16*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (4*(11 - 680*S^2 + 179*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-12*Pi^2*(1 + S^2))/S - (119*Pi^4*(1 + S^2))/(90*S) + (4*(-41 - 1305*S^2 + 624*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (8*(-83 - 1961*S^2 + 970*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (192*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(-265 - 250*S^2 + 351*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (32*(647 - 2123*S^2 + 318*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(125 - 578*S^2 + 167*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-24*(1 + S^2))/S - (2*Pi^2*(3 - 662*S^2 + 321*S^4))/(3*S*(1 + S^2)))*Zeta[3] - (4*(25 - 498*S^2 + 287*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{0}, S^2]^3*((Pi^6*S*(5767 + 41*S^2))/(2592*(1 + S^2)) - (4*(1 + S^2)*HPL[{1}, -S^2]^5)/(15*S) + ((-56 + 263*S^2 - 17*S^4)*HPL[{1}, -S^2]^6)/(27*S*(1 + S^2)) + ((5*(1 + S^2))/(3*S) + (Pi^2*(4 + 1091*S^2 - 87*S^4))/(72*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + ((1 + 99*S^2 - 14*S^4)*HPL[{2}, -S^2]^3)/(6*S*(1 + S^2)) + HPL[{1}, -S^2]^4*((-11*(1 + S^2))/(9*S) + (Pi^2*(-555 + 2348*S^2 - 81*S^4))/(108*S*(1 + S^2)) + ((-43 + 195*S^2 - 12*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + ((12 - 13*S^2 - 13*S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((26*(1 + S^2))/(3*S) + (Pi^2*(-1 + 32*S^2 - 37*S^4))/(18*S*(1 + S^2)))*HPL[{4}, -S^2] + (43*(1 + S^2)*HPL[{5}, -S^2])/(6*S) + ((5 - 64*S^2 - 75*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) + ((-4 - 635*S^2 + 81*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((-38*(1 + S^2))/(3*S) + (Pi^2*(-2 - 1149*S^2 + 123*S^4))/(18*S*(1 + S^2)))*HPL[{3, 1}, -S^2] - (5*(1 + S^2)*HPL[{3, 2}, -S^2])/(2*S) - (41*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (2*S*(-2 + S^2)*HPL[{4, 2}, -S^2])/(3*(1 + S^2)) + (2*(-1 - 20*S^2 + 29*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + ((24*(1 + S^2))/S - (2*Pi^2*(-1 - 605*S^2 + 42*S^4))/(9*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((70*(1 + S^2))/(3*S) + (8*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-5 + 8037*S^2 + 26*S^4))/(1080*S*(1 + S^2)) + (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (2*(-6 + 7*S^2 + 6*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + ((-1 - S^2)*HPL[{2, 1}, -S^2])/S + (2*(3 - 318*S^2 + 35*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (2*(-4 - 635*S^2 + 81*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2))) + (2*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (52*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (2*S*HPL[{3, 1, 2}, -S^2])/3 - (2*(-6 - 593*S^2 + 85*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(-8 - 923*S^2 + 133*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (68*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (4*(-2 - 663*S^2 + 87*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(-2 - 669*S^2 + 83*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (14*S*Zeta[3]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((-16*(1 + S^2))/(3*S) - (37*Pi^2*(1 + S^2))/(36*S) + (Pi^4*(-4011 + 15739*S^2 + 14*S^4))/(1080*S*(1 + S^2)) + ((10*(1 + S^2))/S + (Pi^2*(-488 + 2023*S^2 - 73*S^4))/(36*S*(1 + S^2)))*HPL[{2}, -S^2] + ((-121 + 553*S^2 - 38*S^4)*HPL[{2}, -S^2]^2)/(6*S*(1 + S^2)) + (13*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + ((-6 + 63*S^2 - 11*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (12*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (2*(127 - 583*S^2 + 38*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(43 - 195*S^2 + 12*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (2*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((35*(1 + S^2))/(3*S) + (47*Pi^2*(1 + S^2))/(36*S) + (2*(-6 + 21*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (4*S*(3 + 2*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((-38*(1 + S^2))/(3*S) - (16*Pi^2*(1 + S^2))/(9*S) - (4*(-7 - 6*S^2 + 6*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((Pi^2*(-1 - S^2))/(2*S) - (32*(1 + S^2))/(9*S) + (4*(1 + S^2)*HPL[{2}, -S^2])/S + (4*(-1 + 5*S^2)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (4*(43 - 195*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(-6 - 17*S^2 + 17*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{1}, -S^2]*((-8*Pi^2*(1 + S^2))/(9*S) - (43*Pi^4*(1 + S^2))/(360*S) + (7*(1 + S^2)*HPL[{2}, -S^2]^2)/(6*S) + ((26*(1 + S^2))/(3*S) + (Pi^2*(-2 + 25*S^2 - 5*S^4))/(6*S*(1 + S^2)))*HPL[{3}, -S^2] + (7*(1 + S^2)*HPL[{4}, -S^2])/S + ((18 + 33*S^2 - 41*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + ((-20*(1 + S^2))/S + (Pi^2*(488 - 2023*S^2 + 73*S^4))/(18*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (40*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (2*(6 - 33*S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (8*(-3 + 9*S^2 + 2*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (24*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(121 - 553*S^2 + 38*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(123 - 563*S^2 + 38*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*(43 - 195*S^2 + 12*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-1 - S^2)/S + (Pi^2*(-66 + 163*S^2 + 77*S^4))/(18*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((18*(1 + S^2))/S + (9*Pi^2*(1 + S^2))/(4*S) + ((6 - 33*S^2 + S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (2*(121 - 553*S^2 + 38*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + ((-14 - 11*S^2 + 23*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (4*(-10 + 43*S^2 + 14*S^4)*Zeta[5])/(3*S*(1 + S^2)))) + Log[T]^3*((Pi^6*S*(-5767 + 41*S^2))/(324*(1 + S^2)) - (S*(25 + 3*S^2)*HPL[{0}, S^2]^6)/(18*(1 + S^2)) + ((275 - 1033*S^2 - 4*S^4)*HPL[{0}, S^2]^5*HPL[{1}, -S^2])/(90*S*(1 + S^2)) + (224*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^6)/(9*S*(1 + S^2)) + ((-88*(1 + S^2))/(3*S) + (2*Pi^2*(46 - 1195*S^2 + 107*S^4))/(9*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + (244*(-1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{1}, -S^2]^4*((10*Pi^2*(51 - 305*S^2 + 36*S^4))/(9*S*(1 + S^2)) - (100*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^4*(-(Pi^2*S*(703 + 43*S^2))/(54*(1 + S^2)) + (3*(1 + S^2)*HPL[{1}, -S^2])/(2*S) + ((137 - 518*S^2 + 5*S^4)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)) + ((3 - 531*S^2 + 10*S^4)*HPL[{2}, -S^2])/(18*S*(1 + S^2))) + (4*(-1 - 116*S^2 + 41*S^4)*HPL[{3}, -S^2]^2)/(3*S*(1 + S^2)) - (2*Pi^2*(-15 - 544*S^2 + 207*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) - (4*(-90 - 47*S^2 + 151*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) - (160*(5 - 77*S^2 + 5*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) - (8*Pi^2*(-79 - 246*S^2 + 81*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (4*(-1 - 114*S^2 + 55*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) + (16*(-12 - 511*S^2 + 221*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + (80*Pi^2*(-11 - 77*S^2 + 21*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) + HPL[{2}, -S^2]*((-44*Pi^2*(1 + S^2))/(9*S) + (Pi^4*(-660 - 12377*S^2 + 1823*S^4))/(270*S*(1 + S^2)) - (4*(-1 - 106*S^2 + 55*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (16*(71 - 770*S^2 + 29*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (320*(5 - 77*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2))) - (112*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (1616*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (960*(-2 + 3*S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (320*(-5 + 9*S^2 + 2*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (2240*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (160*(-10 + 77*S^2)*HPL[{2, 1}, -S^2]*Zeta[3])/(3*S*(1 + S^2)) - (112*S*Zeta[3]^2)/(1 + S^2) + HPL[{0}, S^2]^3*((8*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (20*(56 - 263*S^2 + 17*S^4)*HPL[{1}, -S^2]^3)/(27*S*(1 + S^2)) - (38*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((44*(1 + S^2))/(9*S) + (Pi^2*(555 - 2348*S^2 + 81*S^4))/(27*S*(1 + S^2)) + (4*(43 - 195*S^2 + 12*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) - (4*(-5 + 16*S^2 + 3*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (4*(-260 + 501*S^2 + 11*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (56*S^3*Zeta[3])/(9*(1 + S^2))) + HPL[{1}, -S^2]^2*((32*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(4460 - 23717*S^2 + 2213*S^4))/(135*S*(1 + S^2)) - (4*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (16*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + (32*(1 + S^2)*HPL[{3}, -S^2])/S - (8*(47 - 554*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (16*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (1200*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (80*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-22*Pi^2*(1 + S^2))/(9*S) - (32*(-66 + 385*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(-3 - 96*S^2 + 19*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((40*Pi^2*(1 + S^2))/(9*S) - (400*(5 - 65*S^2 + 14*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (400*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (80*(5 - 87*S^2 + 20*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^2*((Pi^4*S*(-19753 + 17*S^2))/(540*(1 + S^2)) + (40*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (10*(23 - 109*S^2 + 8*S^4)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)) + ((-44*(1 + S^2))/(3*S) + (Pi^2*(-2 - 1301*S^2 + 115*S^4))/(9*S*(1 + S^2)))*HPL[{2}, -S^2] + (2*(-4 - 425*S^2 + 57*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^2*((32*(1 + S^2))/S + (Pi^2*(619 - 2671*S^2 + 130*S^4))/(9*S*(1 + S^2)) + (2*(325 - 1348*S^2 + 67*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) - (22*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (2*(-9 - 4*S^2 + 21*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (8*(-4 - 381*S^2 + 51*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (40*(-1 - 154*S^2 + 21*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((148*(1 + S^2))/(3*S) + (19*Pi^2*(1 + S^2))/(3*S) - (8*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(-7 - 78*S^2 + 29*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (4*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(4 - 139*S^2 + 37*S^4)*Zeta[3])/(3*S*(1 + S^2)))) + HPL[{0}, S^2]*((224*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)) - (8*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((20*Pi^2*(140 - 851*S^2 + 101*S^4))/(27*S*(1 + S^2)) + (40*(25 - 174*S^2 + 25*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + ((-104*(1 + S^2))/(3*S) - (2*Pi^2*(-25 - 18*S^2 + 31*S^4))/(9*S*(1 + S^2)))*HPL[{3}, -S^2] - (20*(1 + S^2)*HPL[{4}, -S^2])/S + (4*(3 - 105*S^2 + 4*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + ((128*(1 + S^2))/S + (4*Pi^2*(-665 + 1806*S^2 + 41*S^4))/(9*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (80*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (4*(3 - 262*S^2 + 79*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (16*(-7 - 155*S^2 + 50*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - (160*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + HPL[{1}, -S^2]*((44*Pi^2*(1 + S^2))/(9*S) + (Pi^4*(8061 - 44045*S^2 + 4122*S^4))/(270*S*(1 + S^2)) + ((-128*(1 + S^2))/S + (2*Pi^2*(211 - 1260*S^2 + 149*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2] + (16*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) - (48*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(17 - 194*S^2 + 29*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (160*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (16*(62 - 435*S^2 + 63*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (80*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) - (64*(-98 + 337*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (16*(-1191 + 3994*S^2 + 25*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (160*(-27 + 87*S^2 + 2*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (4*Pi^2*S*(-135 + 59*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{2}, -S^2]*((-296*(1 + S^2))/(3*S) - (98*Pi^2*(1 + S^2))/(9*S) - (4*(-1 - 136*S^2 + 37*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (32*(-98 + 337*S^2)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (16*S*(-22 + 7*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((8*Pi^2*(1 + S^2))/(3*S) - (80*(1 + S^2)*HPL[{2}, -S^2])/S - (8*(10 - 43*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (40*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (8*(40 - 277*S^2 + 43*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (208*S*(-4 + S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{1}, -S^2]*((148*Pi^2*(1 + S^2))/(9*S) + (47*Pi^4*(1 + S^2))/(18*S) - (16*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((176*(1 + S^2))/(3*S) - (4*Pi^2*(118 - 1703*S^2 + 379*S^4))/(9*S*(1 + S^2)))*HPL[{3}, -S^2] - (8*(-5 - 116*S^2 + 41*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + (8*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (16*(103 - 1348*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (32*(178 - 2299*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (32*(463 - 2419*S^2 + 238*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2400*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((128*(1 + S^2))/S - (4*Pi^2*(79 - 1444*S^2 + 337*S^4))/(9*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-8*Pi^2*(1 + S^2))/(3*S) - (8*(103 - 1348*S^2 + 289*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (32*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (16*(11 - 680*S^2 + 179*S^4)*Zeta[5])/(3*S*(1 + S^2)))) + (372*Pi^2*S^3*Zeta[7])/(1 + S^2) + HPL[{0}, S^2]^2*((-2*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) - (2*(23 - 109*S^2 + 8*S^4)*HPL[{1}, -S^2]^7)/(21*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^5*((-16*(1 + S^2))/(5*S) + (Pi^2*(-619 + 2671*S^2 - 130*S^4))/(90*S*(1 + S^2)) + ((-325 + 1348*S^2 - 67*S^4)*HPL[{2}, -S^2])/(15*S*(1 + S^2))) + ((-11*(1 + S^2))/S + (Pi^2*(-24 + 113*S^2 + 161*S^4))/(12*S*(1 + S^2)))*HPL[{5}, -S^2] - (10*(1 + S^2)*HPL[{6}, -S^2])/S + ((-145 + 445*S^2 + 362*S^4)*HPL[{7}, -S^2])/(2*S*(1 + S^2)) - (14*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-11*(1 + S^2))/S + (Pi^2*(-69 + 64*S^2 - 83*S^4))/(12*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-36*(1 + S^2))/S + (Pi^2*(-33 + 116*S^2 - 191*S^4))/(6*S*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((1 + S^2)*HPL[{4, 2}, -S^2])/S - (2*(-20 + 9*S^2 + 21*S^4)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) + ((-1 - S^2)*HPL[{5, 1}, -S^2])/S + ((234 - 117*S^2 - 263*S^4)*HPL[{5, 2}, -S^2])/(2*S*(1 + S^2)) + ((282 - 227*S^2 - 411*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-1 - S^2))/S + (Pi^4*(1166 - 1513*S^2 - 120*S^4))/(60*S*(1 + S^2)) - (2*(317 - 636*S^2 + 3*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (16*(79 - 158*S^2 + 2*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) + ((-24*(1 + S^2))/S + (2*Pi^2*(-276 + 475*S^2 + 2*S^4))/(3*S*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((-48*(1 + S^2))/S + (Pi^2*(-1685 + 2776*S^2 + 79*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + ((-1 - S^2)*HPL[{3, 1, 2}, -S^2])/S + (15*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + ((-37 - 210*S^2 + 155*S^4)*HPL[{3, 2, 2}, -S^2])/(2*S*(1 + S^2)) + (8*(1 - 39*S^2 + 25*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) + (56*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + ((11 - 306*S^2 + 207*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + ((83 - 930*S^2 + 567*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) + (2*(96 - 931*S^2 + 593*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) - (4*Pi^2*(-288 + 447*S^2 + 28*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (16*(-77 + 147*S^2 + 9*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)) - (52*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (2*(-1869 + 3616*S^2 + 133*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) + (2*(-1869 + 3616*S^2 + 133*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + (2*(-3717 + 7144*S^2 + 349*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(-5547 + 10748*S^2 + 511*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (32*(79 - 158*S^2 + 2*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (96*(79 - 158*S^2 + 2*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*(783 - 1614*S^2 + 43*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-165 + 289*S^2 + 19*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (Pi^4*S*(1863 + 1490*S^2)*Zeta[3])/(180*(1 + S^2)) + HPL[{1}, -S^2]^3*((-116*(1 + S^2))/(3*S) - (49*Pi^2*(1 + S^2))/(9*S) + (Pi^4*(-8046 + 31091*S^2 - 403*S^4))/(1080*S*(1 + S^2)) + ((22*(1 + S^2))/(3*S) + (Pi^2*(-574 + 2195*S^2 - 59*S^4))/(18*S*(1 + S^2)))*HPL[{2}, -S^2] + ((-154 + 741*S^2 - 61*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + (10*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + ((-33 - 24*S^2 + 41*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (8*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(161 - 663*S^2 + 32*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (14*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-12*(1 + S^2))/S + (Pi^4*(-385 - 358*S^2 + 991*S^4))/(720*S*(1 + S^2)) + (2*(-10 + 4*S^2 + 9*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (6*(1 + S^2)*HPL[{2, 1}, -S^2])/S + ((-21 + 58*S^2 - 21*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (6*(3 - 16*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + ((1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((64*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/S + (8*S*(-28 + 15*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*((-12*(1 + S^2))/S - (2*Pi^2*(1 + S^2))/(3*S) - (2*(-17 + 4*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-1 + 10*S^2 + 6*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-36*(1 + S^2))/S - (25*Pi^2*(1 + S^2))/(6*S) - (4*(1 - 30*S^2 + 14*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]^2*((8*(1 + S^2))/S + (13*Pi^2*(1 + S^2))/(12*S) + ((-9 - 46*S^2 + 39*S^4)*HPL[{3}, -S^2])/(4*S*(1 + S^2)) - (2*(-77 + 147*S^2 + 9*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + ((-6 - 23*S^2 + 20*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^4*((-37*(1 + S^2))/(3*S) - (19*Pi^2*(1 + S^2))/(12*S) + (2*(1 + S^2)*HPL[{2}, -S^2])/S + ((-7 - 78*S^2 + 29*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + ((325 - 1348*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + ((4 - 139*S^2 + 37*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (2*Pi^2*S*(125 + 112*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((-200*(1 + S^2))/S - (77*Pi^2*(1 + S^2))/(3*S) - (101*Pi^4*(1 + S^2))/(36*S) + (Pi^6*(-240902 + 760225*S^2 + 45487*S^4))/(90720*S*(1 + S^2)) + ((3*(1 + S^2))/S + (Pi^2*(-266 + 1163*S^2 - 69*S^4))/(12*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + ((-149 + 668*S^2 - 43*S^4)*HPL[{2}, -S^2]^3)/(6*S*(1 + S^2)) + ((11 - 24*S^2 - 11*S^4)*HPL[{3}, -S^2]^2)/(2*S*(1 + S^2)) + ((-2*(1 + S^2))/S + (Pi^2*(-93 - 12*S^2 + 113*S^4))/(12*S*(1 + S^2)))*HPL[{4}, -S^2] - (3*(1 + S^2)*HPL[{5}, -S^2])/S + ((-162 + 121*S^2 + 207*S^4)*HPL[{6}, -S^2])/(2*S*(1 + S^2)) + (2*(154 - 741*S^2 + 61*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + ((-24*(1 + S^2))/S + (2*Pi^2*(144 - 538*S^2 + 11*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] - (3*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (18*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (3*(1 - 6*S^2 + S^4)*HPL[{4, 2}, -S^2])/(2*S*(1 + S^2)) - (8*(-9 + 3*S^2 + 11*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((44*(1 + S^2))/S + (Pi^2*(-574 + 2195*S^2 - 59*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (8*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (44*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (4*(149 - 668*S^2 + 43*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) - (2*(927 - 3984*S^2 + 217*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (8*(161 - 663*S^2 + 32*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-22*(1 + S^2))/S - (14*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + ((-30 + 31*S^2 + 21*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{2}, -S^2]*((16*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-7152 + 23977*S^2 + 421*S^4))/(720*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{3}, -S^2])/S + ((-23 + 54*S^2 + 21*S^4)*HPL[{4}, -S^2])/(2*S*(1 + S^2)) - (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (2*(154 - 743*S^2 + 59*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (4*(154 - 741*S^2 + 61*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + ((1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((4*(1 + S^2))/S + (5*Pi^2*(1 + S^2))/(6*S) - (2*(5 - 75*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*(-6 + 15*S^2 + 5*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-32*(1 + S^2))/S - (31*Pi^2*(1 + S^2))/(6*S) - (2*(8 - 133*S^2 + 31*S^4)*Zeta[3])/(S*(1 + S^2))) - (38*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((8*Pi^2*(1 + S^2))/(3*S) + (19*Pi^4*(1 + S^2))/(60*S) + ((6*(1 + S^2))/S + (Pi^2*(11 - 12*S^2 + 13*S^4))/(4*S*(1 + S^2)))*HPL[{3}, -S^2] + ((46 - 3*S^2 - 21*S^4)*HPL[{5}, -S^2])/(2*S*(1 + S^2)) + ((12*(1 + S^2))/S + (Pi^2*(276 - 475*S^2 - 2*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (14*(1 + S^2)*HPL[{3, 1}, -S^2])/S + ((17 + 98*S^2 - 79*S^4)*HPL[{3, 2}, -S^2])/(2*S*(1 + S^2)) + ((-7 + 146*S^2 - 103*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (28*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(-77 + 147*S^2 + 9*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (6*(-311 + 604*S^2 + 23*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*(79 - 158*S^2 + 2*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((2*(1 + S^2))/S + (Pi^2*S*(-28 + 15*S^2))/(3*(1 + S^2)))*Zeta[3] + (S*(-51 + 23*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-100*(1 + S^2))/S - (85*Pi^2*(1 + S^2))/(6*S) - (271*Pi^4*(1 + S^2))/(180*S) + ((1 + S^2)*HPL[{2}, -S^2]^2)/S + ((6*(1 + S^2))/S + (Pi^2*(-22 - 87*S^2 + 47*S^4))/(6*S*(1 + S^2)))*HPL[{3}, -S^2] + (3*(1 + S^2)*HPL[{4}, -S^2])/S + ((-23 - 24*S^2 + 35*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((-22*(1 + S^2))/S + (Pi^2*(574 - 2195*S^2 + 59*S^4))/(6*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (14*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2*(5 - 75*S^2 + 16*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + ((3 + 474*S^2 - 137*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(154 - 741*S^2 + 61*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(469 - 2145*S^2 + 154*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-12*(1 + S^2))/S + (Pi^2*(-34 - 111*S^2 + 75*S^4))/(6*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((16*(1 + S^2))/S + (31*Pi^2*(1 + S^2))/(12*S) + ((5 - 75*S^2 + 16*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (2*(154 - 741*S^2 + 61*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + ((8 - 133*S^2 + 31*S^4)*Zeta[3])/(S*(1 + S^2))) + ((-40 - 117*S^2 + 79*S^4)*Zeta[5])/(S*(1 + S^2))) + 558*S*Zeta[7]) + Log[T]^2*((S*(9 + S^2)*HPL[{0}, S^2]^7)/(24*(1 + S^2)) + ((-23 + 70*S^2 + 5*S^4)*HPL[{0}, S^2]^6*HPL[{1}, -S^2])/(24*S*(1 + S^2)) - (32*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^7)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^5*((-2*Pi^2*(51 - 305*S^2 + 36*S^4))/(3*S*(1 + S^2)) + (60*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^5*((Pi^2*S*(1601 + 109*S^2))/(360*(1 + S^2)) + ((-1 - S^2)*HPL[{1}, -S^2])/(4*S) + ((-275 + 1033*S^2 + 4*S^4)*HPL[{1}, -S^2]^2)/(60*S*(1 + S^2)) - (S*(-541 + S^2)*HPL[{2}, -S^2])/(60*(1 + S^2))) + (Pi^2*(-24 - 245*S^2 + 271*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (2*(-145 + 501*S^2 + 418*S^4)*HPL[{7}, -S^2])/(S*(1 + S^2)) - (96*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + (Pi^2*(53 + 2400*S^2 - 1325*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (2*Pi^2*(-71 - 4200*S^2 + 2115*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(2 - 35*S^2 + 21*S^4)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) + (2*(10 - 349*S^2 + 169*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) - (4*(-74 + 145*S^2 + 167*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) - (16*Pi^2*(152 - 447*S^2 + 75*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*Pi^2*(919 - 1928*S^2 + 97*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(-97 - 4946*S^2 + 2367*S^4)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) + (16*(-47 - 1888*S^2 + 919*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) + (4*(-187 - 7382*S^2 + 3677*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(-559 - 23030*S^2 + 11201*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(-285 - 11861*S^2 + 5752*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*Pi^2*(-330 + 289*S^2 + 184*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4928*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + (16*(-887 + 1156*S^2 + 303*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) + (16*(-887 + 1156*S^2 + 303*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(-1811 + 1156*S^2 + 1227*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (32*(-2735 + 2018*S^2 + 1783*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (128*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (384*(73 - 289*S^2 + 73*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (640*(73 - 361*S^2 + 106*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (21120*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (Pi^4*S*(-1863 + 1490*S^2)*Zeta[3])/(45*(1 + S^2)) + HPL[{1}, -S^2]^3*((-32*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-4460 + 23717*S^2 - 2213*S^4))/(135*S*(1 + S^2)) + (4*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - (16*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) - (32*(1 + S^2)*HPL[{3}, -S^2])/S + (8*(47 - 554*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (16*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (1200*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (80*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((4*Pi^2*(1 + S^2))/S + (Pi^4*(-265 - 10762*S^2 + 5495*S^4))/(180*S*(1 + S^2)) - (8*(1 - 30*S^2 + 19*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(-69 - 1182*S^2 + 631*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (16*(-29 - 578*S^2 + 321*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-2*Pi^4*(-393 + 432*S^2 + 148*S^4))/(9*S*(1 + S^2)) - (16*(125 - 578*S^2 + 167*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (64*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]^4*((-9*(1 + S^2)*HPL[{1}, -S^2]^2)/(4*S) + ((-137 + 518*S^2 - 5*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + ((1 + S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((-25*(1 + S^2))/(6*S) + (Pi^2*(-619 + 2086*S^2 + 65*S^4))/(72*S*(1 + S^2)) + ((-249 + 847*S^2 + 8*S^4)*HPL[{2}, -S^2])/(12*S*(1 + S^2))) + ((-1 + S^2)*(5 + 7*S^2)*HPL[{3}, -S^2])/(4*S*(1 + S^2)) + ((123 - 158*S^2 - 9*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (S*(26 + 19*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((16*Pi^2*(1 + S^2))/S + (32*S*(-289 + 146*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*((4*Pi^2*(1 + S^2))/(3*S) + (16*(-29 + 104*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(1 - 16*S^2 + 15*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^4*((-10*Pi^2*(1 + S^2))/(3*S) + (100*(5 - 65*S^2 + 14*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (300*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (20*(5 - 87*S^2 + 20*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]^2*((64*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/(3*S) + ((7 - 1426*S^2 + 623*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (616*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(-6 - 131*S^2 + 71*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-26*Pi^2*(1 + S^2))/(3*S) - (8*(1 - 602*S^2 + 293*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^3*((Pi^4*S*(19753 + 17*S^2))/(1080*(1 + S^2)) - (8*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (5*(56 - 263*S^2 + 17*S^4)*HPL[{1}, -S^2]^4)/(9*S*(1 + S^2)) + ((12*(1 + S^2))/S + (Pi^2*(1 + 605*S^2 - 42*S^4))/(9*S*(1 + S^2)))*HPL[{2}, -S^2] + ((4 + 635*S^2 - 81*S^4)*HPL[{2}, -S^2]^2)/(6*S*(1 + S^2)) + HPL[{1}, -S^2]^2*((-22*(1 + S^2))/(3*S) + (Pi^2*(-555 + 2348*S^2 - 81*S^4))/(18*S*(1 + S^2)) - (2*(43 - 195*S^2 + 12*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + (17*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (2*(1 - 32*S^2 + 7*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (34*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-2 - 663*S^2 + 87*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(-2 - 669*S^2 + 83*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((-32*(1 + S^2))/(3*S) - (3*Pi^2*(1 + S^2))/(2*S) + (12*(1 + S^2)*HPL[{2}, -S^2])/S + (4*(-1 + 5*S^2)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (4*(43 - 195*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*(-6 - 17*S^2 + 17*S^4)*Zeta[3])/(3*S*(1 + S^2)))) + (8*Pi^2*S*(-125 + 112*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{0}, S^2]^2*((-10*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (2*(23 - 109*S^2 + 8*S^4)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)) + (7*(1 + S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((-32*(1 + S^2))/S + (Pi^2*(-619 + 2671*S^2 - 130*S^4))/(9*S*(1 + S^2)) - (2*(325 - 1348*S^2 + 67*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + ((12*(1 + S^2))/S + (Pi^2*(-29 - 74*S^2 + 67*S^4))/(6*S*(1 + S^2)))*HPL[{3}, -S^2] + (4*(1 + S^2)*HPL[{4}, -S^2])/S + ((-12 + 5*S^2 + 53*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*(-288 + 447*S^2 + 28*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (26*(1 + S^2)*HPL[{3, 1}, -S^2])/S + ((-21 + 88*S^2 - 83*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (2*(3 - 164*S^2 + 137*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (16*(79 - 158*S^2 + 2*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(-481 + 914*S^2 + 11*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*(-165 + 289*S^2 + 19*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (76*Pi^2*S^3*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((-116*(1 + S^2))/S - (49*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-8046 + 31091*S^2 - 403*S^4))/(360*S*(1 + S^2)) + ((22*(1 + S^2))/S + (Pi^2*(-574 + 2195*S^2 - 59*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2] + ((-154 + 741*S^2 - 61*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) + (10*(1 + S^2)*HPL[{3}, -S^2])/S + ((-33 - 24*S^2 + 41*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(161 - 663*S^2 + 32*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (4*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (14*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((32*(1 + S^2))/S + (4*Pi^2*(1 + S^2))/S + (3*(-1 + S^2)*(-3 + 13*S^2)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (8*(79 - 158*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*S*(-28 + 15*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-74*(1 + S^2))/S - (19*Pi^2*(1 + S^2))/(2*S) + (12*(1 + S^2)*HPL[{2}, -S^2])/S + (2*(-7 - 78*S^2 + 29*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (2*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*(4 - 139*S^2 + 37*S^4)*Zeta[3])/(S*(1 + S^2))) + (156*S^3*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]*((-116*Pi^2*(1 + S^2))/(3*S) - (571*Pi^4*(1 + S^2))/(90*S) + (Pi^6*(-201706 + 958255*S^2 - 59719*S^4))/(22680*S*(1 + S^2)) + ((44*(1 + S^2))/S + (Pi^2*(-350 + 2089*S^2 - 257*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + (62*(-1 + S^2)*HPL[{2}, -S^2]^3)/S - (2*(37 - 238*S^2 + 37*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + (Pi^2*(61 - 1132*S^2 + 279*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (32*(1 + S^2)*HPL[{5}, -S^2])/S + (2*(-194 - 127*S^2 + 283*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) + (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) - (8*Pi^2*(-116 + 193*S^2 + 61*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (96*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (288*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (18*(13 - 86*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (16*(50 - 551*S^2 + 119*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + (8*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (192*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (384*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (1488*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (32*(-116 - 277*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (7200*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-296*(1 + S^2))/S - (74*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (8*(5 - 32*S^2 + 5*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{2}, -S^2]*((22*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-7200 + 21017*S^2 + 1137*S^4))/(180*S*(1 + S^2)) - (48*(1 + S^2)*HPL[{3}, -S^2])/S + (2*(113 - 734*S^2 + 113*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (32*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-128*(1 + S^2))/S - (14*Pi^2*(1 + S^2))/(3*S) - (8*(103 - 1348*S^2 + 289*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(11 - 87*S^2 + 14*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-8*Pi^2*(1 + S^2))/S - (32*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(S*(1 + S^2))) - (236*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((32*Pi^2*(1 + S^2))/(3*S) + (19*Pi^4*(1 + S^2))/(15*S) + (Pi^2*(-49 - 1204*S^2 + 681*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (8*(1 + S^2)*HPL[{4}, -S^2])/S + (2*(14 - 195*S^2 + 159*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + (8*Pi^2*(152 - 447*S^2 + 75*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (96*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2*(-25 - 2594*S^2 + 1207*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (4*(-95 - 3862*S^2 + 1921*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (192*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (2464*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (16*(-433 + 578*S^2 + 141*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (64*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*S*(-317 + 161*S^2)*Zeta[3])/(3*(1 + S^2)) + (4*S*(-493 + 315*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-74*Pi^2*(1 + S^2))/(3*S) - (47*Pi^4*(1 + S^2))/(12*S) + (24*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-88*(1 + S^2))/S + (2*Pi^2*(118 - 1703*S^2 + 379*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + (12*(-5 - 116*S^2 + 41*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) - (4*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(103 - 1348*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (16*(178 - 2299*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (16*(463 - 2419*S^2 + 238*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (3600*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-192*(1 + S^2))/S + (2*Pi^2*(79 - 1444*S^2 + 337*S^4))/(3*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((4*Pi^2*(1 + S^2))/S + (4*(103 - 1348*S^2 + 289*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (16*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(S*(1 + S^2))) + (8*(11 - 680*S^2 + 179*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{0}, S^2]*(-(Pi^6*S*(-15415 + 1763*S^2))/(648*(1 + S^2)) - (112*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)) + ((22*(1 + S^2))/S + (Pi^2*(4 + 1983*S^2 - 473*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2]^2 - (2*(-19 - 607*S^2 + 196*S^4)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^4*((-5*Pi^2*(140 - 851*S^2 + 101*S^4))/(9*S*(1 + S^2)) - (10*(25 - 174*S^2 + 25*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + (2*(2 - 5*S^2 + 5*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((56*(1 + S^2))/S - (8*Pi^2*(1 - 20*S^2 + 4*S^4))/(3*S*(1 + S^2)))*HPL[{4}, -S^2] + (48*(1 + S^2)*HPL[{5}, -S^2])/S - (4*(5 - 43*S^2 + 25*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) + (16*S*(-337 + 98*S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((-192*(1 + S^2))/S + (2*Pi^2*(-37 - 1975*S^2 + 490*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] - (28*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (156*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (4*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (4*(5 - 107*S^2 + 24*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((384*(1 + S^2))/S - (8*Pi^2*(-16 - 987*S^2 + 244*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((-22*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-8061 + 44045*S^2 - 4122*S^4))/(180*S*(1 + S^2)) + ((192*(1 + S^2))/S + (Pi^2*(-211 + 1260*S^2 - 149*S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] - (8*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) + (72*(1 + S^2)*HPL[{3}, -S^2])/S - (2*(17 - 194*S^2 + 29*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (240*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (24*(62 - 435*S^2 + 63*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (120*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) + (96*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (432*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (20*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (4*(-71 - 2418*S^2 + 789*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) - (48*(-18 - 623*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (480*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (16*(-35 - 1312*S^2 + 403*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (480*(-2 - 87*S^2 + 27*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (4*S*(-31 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2}, -S^2]*((232*(1 + S^2))/S + (28*Pi^2*(1 + S^2))/S + (Pi^4*(91 + 10416*S^2 - 1958*S^4))/(90*S*(1 + S^2)) + (12*(1 + S^2)*HPL[{3}, -S^2])/S - (4*(1 - 8*S^2 + 3*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(1 - 1346*S^2 + 393*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (32*S*(-337 + 98*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (4*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-296*(1 + S^2))/S - (94*Pi^2*(1 + S^2))/(3*S) + (8*(-41 + 134*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((84*(1 + S^2))/S + (35*Pi^2*(1 + S^2))/(3*S) - (4*(39 - 132*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*(-1 + 5*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-8*Pi^2*(1 + S^2))/(3*S) + (80*(1 + S^2)*HPL[{2}, -S^2])/S + (8*(10 - 43*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (40*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*(40 - 277*S^2 + 43*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]*((-32*Pi^2*(1 + S^2))/(3*S) - (83*Pi^4*(1 + S^2))/(60*S) + (24*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((104*(1 + S^2))/S + (2*Pi^2*(4 - 13*S^2 + 7*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + (72*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(6 - 89*S^2 + 17*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((-384*(1 + S^2))/S + (2*Pi^2*(211 - 1260*S^2 + 149*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (240*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (8*(19 - 134*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (4*(97 - 610*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (480*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (16*(578 - 4001*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (240*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*(17 - 147*S^2 + 30*S^4)*Zeta[3])/(3*S*(1 + S^2)) + HPL[{2}, -S^2]*((296*(1 + S^2))/S + (32*Pi^2*(1 + S^2))/S + (4*(19 - 134*S^2 + 19*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*(41 - 266*S^2 + 41*S^4)*Zeta[3])/(S*(1 + S^2))) + (4*(27 - 195*S^2 + 38*S^4)*Zeta[5])/(S*(1 + S^2)))) + (2232*S*(-1 + S^2)*Zeta[7])/(1 + S^2)) + HPL[{1}, -S^2]*((-200*Pi^2*(1 + S^2))/(3*S) - (439*Pi^4*(1 + S^2))/(45*S) - (8957*Pi^6*(1 + S^2))/(7560*S) + (Pi^8*(-655944 + 2526341*S^2 - 14328*S^4))/(680400*S*(1 + S^2)) + (Pi^2*(-121 + 334*S^2 + 25*S^4)*HPL[{2}, -S^2]^3)/(9*S*(1 + S^2)) - (2*(24 - 167*S^2 + 24*S^4)*HPL[{2}, -S^2]^4)/(3*S*(1 + S^2)) + ((14*(1 + S^2))/S + (Pi^2*(-13 + 107*S^2 - 24*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2]^2 + (2*(-21 + 37*S^2 + 30*S^4)*HPL[{4}, -S^2]^2)/(S*(1 + S^2)) + ((-30*(1 + S^2))/S + (Pi^2*(-178 - 3*S^2 + 245*S^4))/(3*S*(1 + S^2)))*HPL[{6}, -S^2] + (54*(1 + S^2)*HPL[{7}, -S^2])/S + (12*(-149 + 230*S^2 + 158*S^4)*HPL[{8}, -S^2])/(S*(1 + S^2)) + ((-88*(1 + S^2))/S + (2*Pi^2*(350 - 2089*S^2 + 257*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2]^2 - (4*(233 - 1614*S^2 + 233*S^4)*HPL[{3, 1}, -S^2]^2)/(S*(1 + S^2)) + ((12*(1 + S^2))/S + (Pi^2*(-19 + 126*S^2 - 19*S^4))/(S*(1 + S^2)))*HPL[{4, 2}, -S^2] + (2*(1 + S^2)*HPL[{4, 3}, -S^2])/S + ((48*(1 + S^2))/S - (4*Pi^2*(32 - 545*S^2 + 141*S^4))/(3*S*(1 + S^2)))*HPL[{5, 1}, -S^2] + (18*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (24*S*(-2 + S^2)*HPL[{5, 3}, -S^2])/(1 + S^2) + (70*(1 + S^2)*HPL[{6, 1}, -S^2])/S + (60*S*(-2 + S^2)*HPL[{6, 2}, -S^2])/(1 + S^2) - (4*(-315 + 335*S^2 + 342*S^4)*HPL[{7, 1}, -S^2])/(S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(S*(1 + S^2)) + (8*Pi^2*(-121 + 334*S^2 + 25*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (64*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (208*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (28*(5 - 53*S^2 + 14*S^4)*HPL[{3, 3, 2}, -S^2])/(S*(1 + S^2)) + (2*Pi^2*(-1391 + 2876*S^2 + 579*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (220*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (4*(61 - 613*S^2 + 166*S^4)*HPL[{4, 1, 3}, -S^2])/(S*(1 + S^2)) - (652*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (8*(4 - 121*S^2 + 43*S^4)*HPL[{4, 2, 2}, -S^2])/(S*(1 + S^2)) + (4*(257 - 2129*S^2 + 470*S^4)*HPL[{4, 3, 1}, -S^2])/(S*(1 + S^2)) - (1360*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + (8*(89 - 629*S^2 + 122*S^4)*HPL[{5, 1, 2}, -S^2])/(S*(1 + S^2)) + (8*(509 - 4379*S^2 + 992*S^4)*HPL[{5, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*(2326 - 22627*S^2 + 5503*S^4)*HPL[{6, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*Pi^2*(-116 + 193*S^2 + 61*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (192*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (192*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (12*(13 - 86*S^2 + 13*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(S*(1 + S^2)) + (192*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (12*(13 - 86*S^2 + 13*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(-325 - 242*S^2 + 419*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(S*(1 + S^2)) - (48*(-91 + 95*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (576*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (36*(13 - 86*S^2 + 13*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (12*(-325 - 242*S^2 + 419*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (36*(-351 - 70*S^2 + 393*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-769 - 515*S^2 + 974*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (384*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (1152*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (2976*(-1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S - (8928*(-1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (2304*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (17856*(-1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S + (29760*(-1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S + (35712*(-1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S + (74400*(-1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S + (64*(-3464 - 277*S^2 + 3547*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (64*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (14400*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((20*(1 + S^2))/S + (Pi^2*(-40 + 95*S^2 + 11*S^4))/(3*S*(1 + S^2)))*Zeta[3]^2 + HPL[{2, 1, 1}, -S^2]*((44*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-7200 + 21017*S^2 + 1137*S^4))/(90*S*(1 + S^2)) - (96*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((32*(1 + S^2))/S + (14*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-1952 + 10306*S^2 - 1045*S^4))/(180*S*(1 + S^2)) - (10*(1 + S^2)*HPL[{3}, -S^2])/S + (2*(29 - 254*S^2 + 53*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (4*(-26 - 127*S^2 + 67*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (372*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (20*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-2*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-37 - 1057*S^2 + 352*S^4))/(45*S*(1 + S^2)) + (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(50 - 351*S^2 + 71*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (4*(113 - 734*S^2 + 113*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-8*Pi^2*(1 + S^2))/S + (Pi^4*(1660 - 4113*S^2 - 466*S^4))/(45*S*(1 + S^2)) + (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((128*(1 + S^2))/S + (7*Pi^2*(1 + S^2))/S + (8*(-14 + 63*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{4, 1}, -S^2]*((384*(1 + S^2))/S + (18*Pi^2*(1 + S^2))/S - (4*(87 - 478*S^2 + 19*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{5}, -S^2]*((64*(1 + S^2))/S - (11*Pi^2*(1 + S^2))/(3*S) - (4*(17 - 286*S^2 + 65*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-15 + 38*S^2 + 21*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((-16*Pi^2*(1 + S^2))/S - (64*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((256*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/(3*S) + (16*(42 - 607*S^2 + 135*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((512*(1 + S^2))/S + (140*Pi^2*(1 + S^2))/(3*S) + (16*(137 - 1908*S^2 + 419*S^4)*Zeta[3])/(S*(1 + S^2))) + ((-360*(1 + S^2))/S - (97*Pi^2*(1 + S^2))/(3*S))*Zeta[5] + HPL[{2}, -S^2]*((16*Pi^2*(1 + S^2))/(3*S) + (113*Pi^4*(1 + S^2))/(180*S) + (Pi^6*(-9184 + 26123*S^2 + 1841*S^4))/(2520*S*(1 + S^2)) - (2*(14 - 125*S^2 + 29*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((-28*(1 + S^2))/S + (Pi^2*(45 - 340*S^2 + 67*S^4))/(3*S*(1 + S^2)))*HPL[{4}, -S^2] + (4*(-27 + 16*S^2 + 48*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) - (372*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-88*(1 + S^2))/S + (2*Pi^2*(350 - 2091*S^2 + 255*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] + (36*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (116*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (24*(6 - 43*S^2 + 7*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (4*(131 - 996*S^2 + 185*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((176*(1 + S^2))/S - (4*Pi^2*(350 - 2089*S^2 + 257*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (96*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (12*(13 - 86*S^2 + 13*S^4)*HPL[{3, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(345 - 2414*S^2 + 345*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(1039 - 7282*S^2 + 1039*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (192*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (64*(-328 + 337*S^2 + 230*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-64*(1 + S^2))/S - (11*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (2*(-4 + 7*S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((-64*(1 + S^2))/S - (10*Pi^2*(1 + S^2))/(3*S) - (8*(70 - 795*S^2 + 163*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-14 + 63*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-128*(1 + S^2))/S - (28*Pi^2*(1 + S^2))/(3*S) - (8*(42 - 607*S^2 + 135*S^4)*Zeta[3])/(S*(1 + S^2))) - (34*(1 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((-28*Pi^2*(1 + S^2))/(3*S) - (29*Pi^4*(1 + S^2))/(90*S) - (2*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(-23 + 28*S^2 + 37*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((88*(1 + S^2))/S - (2*Pi^2*(108 - 1423*S^2 + 305*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (32*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (8*(14 - 125*S^2 + 29*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (4*(24 - 109*S^2 + 3*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (16*(70 - 795*S^2 + 163*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(383 - 4532*S^2 + 941*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*(103 - 1348*S^2 + 289*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((40*(1 + S^2))/S + (2*Pi^2*(17 - 102*S^2 + 9*S^4))/(3*S*(1 + S^2)))*Zeta[3] + (8*(7 - 40*S^2 + S^4)*Zeta[5])/(S*(1 + S^2))) + Zeta[3]*((-400*(1 + S^2))/S - (32*Pi^2*(1 + S^2))/S - (467*Pi^4*(1 + S^2))/(180*S) + (4*(-57 + 29*S^2 + 26*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-32*Pi^2*(1 + S^2))/(3*S) - (157*Pi^4*(1 + S^2))/(180*S) + (96*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (4*(241 - 2922*S^2 + 613*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (4*(727 - 8806*S^2 + 1843*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (192*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (1488*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (32*(191 - 674*S^2 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((88*(1 + S^2))/S - (2*Pi^2*(108 - 1481*S^2 + 323*S^4))/(3*S*(1 + S^2)))*Zeta[3] - (4*(44 - 1255*S^2 + 317*S^4)*Zeta[5])/(S*(1 + S^2))) - (360*(1 + S^2)*Zeta[7])/S) + HPL[{2}, -S^2]*((8*Pi^4*(1 + S^2))/(9*S) + (Pi^6*(1 + S^2))/(10*S) + ((1 + S^2)*HPL[{3}, -S^2]^2)/S + ((14*(1 + S^2))/S + (Pi^2*(10 - 33*S^2 + 23*S^4))/(S*(1 + S^2)))*HPL[{5}, -S^2] - (44*(1 + S^2)*HPL[{6}, -S^2])/S - (8*(-10 + 6*S^2 + 3*S^4)*HPL[{7}, -S^2])/(S*(1 + S^2)) + ((4*(1 + S^2))/S + (Pi^2*(21 + 1346*S^2 - 643*S^4))/(3*S*(1 + S^2)))*HPL[{3, 2}, -S^2] - (8*Pi^2*(-11 - 501*S^2 + 253*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (4*(-34 - 19*S^2 + 58*S^4)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) + (6*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (4*(-98 - 24*S^2 + 155*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) + (4*(-224 + 71*S^2 + 230*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) + (8*Pi^2*(-154 + 147*S^2 + 86*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (2*Pi^2*(-1799 + 2968*S^2 + 351*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (60*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (4*(-35 - 1176*S^2 + 579*S^4)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) + (8*(-51 - 1885*S^2 + 914*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) + (208*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (4*(-97 - 3770*S^2 + 1823*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(-331 - 11552*S^2 + 5603*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*(-688 - 23541*S^2 + 11499*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*Pi^2*(152 - 447*S^2 + 75*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (64*(34 - 147*S^2 + 34*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)) - (192*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (4*(1657 - 4462*S^2 + 425*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(1657 - 4462*S^2 + 425*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*(3289 - 11518*S^2 + 2057*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*(4991 - 17306*S^2 + 2975*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (384*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (4928*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (14784*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (32*(-799 - 578*S^2 + 1091*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (128*(73 - 289*S^2 + 73*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((2*Pi^2*(1 + S^2))/(3*S) + (Pi^4*S*(-2207 + 1176*S^2))/(90*(1 + S^2)))*Zeta[3] - (4*(1 + S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((2*Pi^2*(1 + S^2))/S + (Pi^4*(-5 - 1037*S^2 + 629*S^4))/(45*S*(1 + S^2)) - (4*(-17 - 26*S^2 + 36*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (36*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(-5 - 709*S^2 + 324*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (4*(7 - 1426*S^2 + 623*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((4*Pi^2*(1 + S^2))/S + (Pi^4*(3684 - 8559*S^2 + 1060*S^4))/(90*S*(1 + S^2)) + (4*(-265 - 250*S^2 + 351*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (2464*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (40*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-64*(1 + S^2))/S + (2*Pi^2*(1 + S^2))/(3*S) - (4*(55 - 250*S^2 + 31*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*(-7 - 16*S^2 + 25*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((256*(1 + S^2))/S + (76*Pi^2*(1 + S^2))/(3*S) + (32*(-6 - 131*S^2 + 71*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-128*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/(3*S) - (4*(-29 - 520*S^2 + 293*S^4)*Zeta[3])/(S*(1 + S^2))) + ((8*(1 + S^2))/S + (2*Pi^2*S*(-272 + 169*S^2))/(3*(1 + S^2)))*Zeta[5] + (12*S*(-73 + 68*S^2)*Zeta[7])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-100*Pi^2*(1 + S^2))/(3*S) - (479*Pi^4*(1 + S^2))/(90*S) - (9853*Pi^6*(1 + S^2))/(15120*S) + (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((4*(1 + S^2))/S + (2*Pi^2*(-19 - 186*S^2 + 79*S^4))/(3*S*(1 + S^2)))*HPL[{5}, -S^2] - (15*(1 + S^2)*HPL[{6}, -S^2])/S + (6*(-87 + 81*S^2 + 92*S^4)*HPL[{7}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((88*(1 + S^2))/S - (2*Pi^2*(108 - 1423*S^2 + 305*S^4))/(3*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((264*(1 + S^2))/S + (Pi^2*(-709 + 9670*S^2 - 2109*S^4))/(3*S*(1 + S^2)))*HPL[{4, 1}, -S^2] + (6*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (2*(7 - 185*S^2 + 40*S^4)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (12*(2 - 71*S^2 + 15*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) - (2*(-184 + 153*S^2 + 233*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) + ((176*(1 + S^2))/S - (4*Pi^2*(350 - 2089*S^2 + 257*S^4))/(3*S*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((352*(1 + S^2))/S - (16*Pi^2*(233 - 1141*S^2 + 98*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + (2*(443 - 5586*S^2 + 1187*S^4)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) + (16*(172 - 2137*S^2 + 451*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) + (2*(1337 - 16838*S^2 + 3569*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + (2*(4253 - 52142*S^2 + 10949*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) + (48*(362 - 4471*S^2 + 943*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (1488*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S - (32*(191 - 674*S^2 + 5*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (32*(191 - 674*S^2 + 5*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(-661 + 1348*S^2 + 269*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (32*(-1015 + 2299*S^2 + 344*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (384*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (160*(221 - 1673*S^2 + 266*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (7200*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((-232*(1 + S^2))/S - (20*Pi^2*(1 + S^2))/S + (Pi^4*(231 - 10373*S^2 + 2808*S^4))/(180*S*(1 + S^2)))*Zeta[3] + (18*(1 + S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((-64*(1 + S^2))/S - (16*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(292 - 6193*S^2 + 1511*S^4))/(90*S*(1 + S^2)) - (2*(8 - 157*S^2 + 35*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(103 - 1352*S^2 + 289*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (8*(103 - 1348*S^2 + 289*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (28*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-22*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(7200 - 21017*S^2 - 1137*S^4))/(180*S*(1 + S^2)) - (32*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (48*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((Pi^2*(1 + S^2))/S - (2*(113 - 734*S^2 + 113*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*(3 - 100*S^2 + 25*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((8*Pi^2*(1 + S^2))/S + (32*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]^2*((32*(1 + S^2))/S + (7*Pi^2*(1 + S^2))/(3*S) + (2*(70 - 795*S^2 + 163*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (186*(-1 + S^2)*HPL[{2, 1}, -S^2])/S + (2*(42 - 607*S^2 + 135*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-14*Pi^2*(1 + S^2))/(3*S) - (8*(53 - 694*S^2 + 149*S^4)*Zeta[3])/(S*(1 + S^2))) + ((-196*(1 + S^2))/S + (Pi^2*(-18 - 1477*S^2 + 437*S^4))/(3*S*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((16*Pi^2*(1 + S^2))/(3*S) + (157*Pi^4*(1 + S^2))/(360*S) + ((-44*(1 + S^2))/S + (Pi^2*(108 - 1423*S^2 + 305*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] - (2*(1 + S^2)*HPL[{4}, -S^2])/S + (2*(17 - 286*S^2 + 65*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((-88*(1 + S^2))/S + (2*Pi^2*(350 - 2089*S^2 + 257*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (48*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2*(241 - 2922*S^2 + 613*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (2*(727 - 8806*S^2 + 1843*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (744*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (16*(191 - 674*S^2 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-44*(1 + S^2))/S + (Pi^2*(108 - 1481*S^2 + 323*S^4))/(3*S*(1 + S^2)))*Zeta[3] + (2*(44 - 1255*S^2 + 317*S^4)*Zeta[5])/(S*(1 + S^2))) + (6*(-35 - 583*S^2 + 196*S^4)*Zeta[7])/(S*(1 + S^2))) + HPL[{0}, S^2]*((-7*Pi^8*S*(-70669 + 5432*S^2))/(194400*(1 + S^2)) - (4*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^8)/(3*S*(1 + S^2)) + ((16*(1 + S^2))/(3*S) + (Pi^2*(11 + 452*S^2 - 119*S^4))/(9*S*(1 + S^2)))*HPL[{2}, -S^2]^3 - (S*(-167 + 48*S^2)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)) + HPL[{1}, -S^2]^6*((Pi^2*(-140 + 851*S^2 - 101*S^4))/(27*S*(1 + S^2)) - (2*(25 - 174*S^2 + 25*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + ((6*(1 + S^2))/S + (Pi^2*(7 - 9*S^2 - 4*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2]^2 + (2*(-14 + 19*S^2 + 22*S^4)*HPL[{4}, -S^2]^2)/(S*(1 + S^2)) + ((160*(1 + S^2))/S - (Pi^2*S*(21 + 100*S^2))/(3*(1 + S^2)))*HPL[{6}, -S^2] + (200*(1 + S^2)*HPL[{7}, -S^2])/S - (2*(-105 + 342*S^2 + 298*S^4)*HPL[{8}, -S^2])/(S*(1 + S^2)) + ((-44*(1 + S^2))/S + (Pi^2*(-4 - 1983*S^2 + 473*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2]^2 - (4*(3 - 673*S^2 + 196*S^4)*HPL[{3, 1}, -S^2]^2)/(S*(1 + S^2)) + ((10*(1 + S^2))/S + (Pi^2*(-1 - 6*S^2 + S^4))/(3*S*(1 + S^2)))*HPL[{4, 2}, -S^2] - (4*(1 + S^2)*HPL[{4, 3}, -S^2])/S + ((-82*(1 + S^2))/S + (Pi^2*(3 - 147*S^2 + 82*S^4))/(3*S*(1 + S^2)))*HPL[{5, 1}, -S^2] - (6*(1 + S^2)*HPL[{5, 2}, -S^2])/S - (2*S*(7 + S^2)*HPL[{5, 3}, -S^2])/(1 + S^2) - (140*(1 + S^2)*HPL[{6, 1}, -S^2])/S - (2*(-2 + 18*S^2 + 5*S^4)*HPL[{6, 2}, -S^2])/(S*(1 + S^2)) + (2*(-51 + 31*S^2 + 190*S^4)*HPL[{7, 1}, -S^2])/(S*(1 + S^2)) - (32*S*(-337 + 98*S^2)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2) + HPL[{1}, -S^2]^4*((-11*Pi^2*(1 + S^2))/(9*S) + (Pi^4*(-8061 + 44045*S^2 - 4122*S^4))/(1080*S*(1 + S^2)) + ((32*(1 + S^2))/S + (Pi^2*(-211 + 1260*S^2 - 149*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2] - (4*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + (12*(1 + S^2)*HPL[{3}, -S^2])/S + ((-17 + 194*S^2 - 29*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(62 - 435*S^2 + 63*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (20*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) + ((Pi^2*(-5 - 7*S^2))/(3*S) - (4*(1 + S^2))/S)*HPL[{3, 1, 2}, -S^2] + ((124*(1 + S^2))/S + (Pi^2*(83 + 3604*S^2 - 959*S^4))/(3*S*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + (48*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (128*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (2*(-35 - 5*S^2 + 62*S^4)*HPL[{3, 3, 2}, -S^2])/(S*(1 + S^2)) + ((496*(1 + S^2))/S - (8*Pi^2*(-31 - 1396*S^2 + 365*S^4))/(3*S*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + (122*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (4*(-35 - 7*S^2 + 66*S^4)*HPL[{4, 1, 3}, -S^2])/(S*(1 + S^2)) + (362*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S + (2*(-32 - 3*S^2 + 55*S^4)*HPL[{4, 2, 2}, -S^2])/(S*(1 + S^2)) - (4*(-73 - 9*S^2 + 134*S^4)*HPL[{4, 3, 1}, -S^2])/(S*(1 + S^2)) + (816*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S - (2*(-77 - 17*S^2 + 148*S^4)*HPL[{5, 1, 2}, -S^2])/(S*(1 + S^2)) - (2*(-617 - 77*S^2 + 1108*S^4)*HPL[{5, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(-400 - 88*S^2 + 745*S^4)*HPL[{6, 1, 1}, -S^2])/(S*(1 + S^2)) - (160*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((-384*(1 + S^2))/S + (4*Pi^2*(-37 - 1975*S^2 + 490*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1, 1, 1}, -S^2] + (424*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (424*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (2*(9 + 7*S^2)*HPL[{3, 1, 2, 2}, -S^2])/S + (904*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (2*(9 + 7*S^2)*HPL[{3, 2, 1, 2}, -S^2])/S + (2*(-161 - 4856*S^2 + 1577*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(S*(1 + S^2)) + (48*(-19 - 605*S^2 + 198*S^4)*HPL[{3, 3, 1, 1}, -S^2])/(S*(1 + S^2)) + (2568*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (8*(1 + S^2)*HPL[{4, 1, 1, 2}, -S^2])/S + (8*(-115 - 3632*S^2 + 1187*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + (56*(-49 - 1556*S^2 + 509*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*(-679 - 21887*S^2 + 7152*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((768*(1 + S^2))/S - (16*Pi^2*(-16 - 987*S^2 + 244*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] - (192*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (576*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (32*(-19 - 607*S^2 + 196*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(S*(1 + S^2)) + (96*(-19 - 607*S^2 + 196*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (672*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (8*(-451 - 14558*S^2 + 4709*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (40*(-151 - 4854*S^2 + 1569*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(-907 - 29126*S^2 + 9413*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (40*(-379 - 12138*S^2 + 3921*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (96*(-474 - 15191*S^2 + 4903*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (960*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (32*(-35 - 1312*S^2 + 403*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (960*(-2 - 87*S^2 + 27*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (Pi^2*S*(-73 + 11*S^2)*Zeta[3]^2)/(3*(1 + S^2)) + HPL[{2}, -S^2]^2*((16*(1 + S^2))/S + (7*Pi^2*(1 + S^2))/(2*S) + (Pi^4*(20 + 9811*S^2 - 1892*S^4))/(360*S*(1 + S^2)) + (6*(1 + S^2)*HPL[{3}, -S^2])/S + ((9 - 4*S^2 - 15*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (20*(1 + S^2)*HPL[{2, 1}, -S^2])/S + ((-39 - 1210*S^2 + 397*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (4*(-19 - 607*S^2 + 196*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-1 - S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((464*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/S + (Pi^4*(91 + 10416*S^2 - 1958*S^4))/(45*S*(1 + S^2)) - (8*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((160*(1 + S^2))/S + (40*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-115 + 944*S^2 - 371*S^4))/(180*S*(1 + S^2)) - (12*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(-10 + 13*S^2 + 7*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (8*(1 - 8*S^2 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (6*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-232*(1 + S^2))/S - (86*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-193 - 20356*S^2 + 4219*S^4))/(180*S*(1 + S^2)) + (8*(1 - 1346*S^2 + 393*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (12*(1 + S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((128*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/S + (8*(42 - 125*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((-592*(1 + S^2))/S - (188*Pi^2*(1 + S^2))/(3*S) + (16*(-41 + 134*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((552*(1 + S^2))/S + (160*Pi^2*(1 + S^2))/(3*S) + (8*(125 - 375*S^2 + 8*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{4, 1}, -S^2]*((-128*(1 + S^2))/S - (80*Pi^2*(1 + S^2))/(3*S) + (4*(-13 + 28*S^2 + 17*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 2}, -S^2]*((-29*Pi^2*(1 + S^2))/(6*S) + (2*(-19 + 44*S^2 + 31*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^5*((-4*Pi^2*(1 + S^2))/(15*S) + (8*(1 + S^2)*HPL[{2}, -S^2])/S + (4*(10 - 43*S^2 + 7*S^4)*HPL[{3}, -S^2])/(15*S*(1 + S^2)) + (4*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*(40 - 277*S^2 + 43*S^4)*Zeta[3])/(15*S*(1 + S^2))) + HPL[{5}, -S^2]*((140*(1 + S^2))/S + (67*Pi^2*(1 + S^2))/(6*S) + (2*(-41 + 47*S^2 + 48*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*(-26 + 93*S^2 + 59*S^4)*Zeta[3])/(S*(1 + S^2))) - (12*S*(-19 + 9*S^2)*Zeta[3]*Zeta[5])/(1 + S^2) + HPL[{2}, -S^2]*((400*(1 + S^2))/S + (128*Pi^2*(1 + S^2))/(3*S) + (329*Pi^4*(1 + S^2))/(90*S) + (Pi^6*(-1134 + 222663*S^2 - 25652*S^4))/(22680*S*(1 + S^2)) + ((-8 - S^2 + 15*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((-16*(1 + S^2))/S + (Pi^2*(-13 + 22*S^2 + 9*S^4))/(3*S*(1 + S^2)))*HPL[{4}, -S^2] - (3*(1 + S^2)*HPL[{5}, -S^2])/S + (2*(-30 + 33*S^2 + 38*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) + (4*(-19 - 607*S^2 + 196*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + ((-36*(1 + S^2))/S + (Pi^2*(7 - 1982*S^2 + 463*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] - (24*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (60*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (2*(-1 + 6*S^2 + S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (2*(-17 + 9*S^2 + 18*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((88*(1 + S^2))/S - (2*Pi^2*(-4 - 1983*S^2 + 473*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (80*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (216*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (2*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (2*(-1 - 2672*S^2 + 769*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(1 - 2012*S^2 + 579*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (96*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (8*(-455 - 15914*S^2 + 5097*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (64*S*(-337 + 98*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + ((Pi^2*(-1 - S^2))/(3*S) - (8*(1 + S^2))/S)*Zeta[3] - (4*(-1 - 15*S^2 + 5*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{2, 1}, -S^2]*((-64*(1 + S^2))/S - (5*Pi^2*(1 + S^2))/S - (4*(42 - 125*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((7*Pi^2*(1 + S^2))/(3*S) + (2*(-39 + 126*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*(-11 + 18*S^2 + 13*S^4)*Zeta[3])/(S*(1 + S^2))) - (4*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^2*((-16*Pi^2*(1 + S^2))/(3*S) - (349*Pi^4*(1 + S^2))/(360*S) + (Pi^6*(-187513 + 953473*S^2 - 61474*S^4))/(45360*S*(1 + S^2)) + ((22*(1 + S^2))/S + (Pi^2*(-317 + 1901*S^2 - 234*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + ((-177 + 1214*S^2 - 177*S^4)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)) + ((1 - 20*S^2 + 3*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((62*(1 + S^2))/S + (Pi^2*(-29 + 320*S^2 - 51*S^4))/(6*S*(1 + S^2)))*HPL[{4}, -S^2] + (52*(1 + S^2)*HPL[{5}, -S^2])/S + ((-9 + 219*S^2 - 64*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) + (16*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + ((-192*(1 + S^2))/S + (2*Pi^2*(313 - 1888*S^2 + 227*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] - (32*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (168*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (3*(-1 + S^2)*HPL[{4, 2}, -S^2])/S + (4*(5 - 109*S^2 + 22*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((384*(1 + S^2))/S - (2*Pi^2*(211 - 1260*S^2 + 149*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (96*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (432*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (8*(177 - 1214*S^2 + 177*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(1079 - 7478*S^2 + 1091*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (480*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (48*(62 - 435*S^2 + 63*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (240*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*(1 + S^2)*Zeta[3])/(3*S) - (2*(7 - 67*S^2 + 10*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{3}, -S^2]*((84*(1 + S^2))/S + (31*Pi^2*(1 + S^2))/(3*S) - (4*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (8*S*(-1 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((232*(1 + S^2))/S + (26*Pi^2*(1 + S^2))/S + (Pi^4*(-7131 + 38357*S^2 - 3644*S^4))/(360*S*(1 + S^2)) + (16*(1 + S^2)*HPL[{3}, -S^2])/S + ((-1 + 40*S^2 - 7*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (16*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-296*(1 + S^2))/S - (32*Pi^2*(1 + S^2))/S - (4*(41 - 266*S^2 + 41*S^4)*Zeta[3])/(S*(1 + S^2))) - (2*(1 + S^2)*Zeta[5])/S) + HPL[{2, 1}, -S^2]*((-400*(1 + S^2))/S - (112*Pi^2*(1 + S^2))/(3*S) - (191*Pi^4*(1 + S^2))/(60*S) + (56*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2*(-77 + 252*S^2 + 25*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (4*(-119 + 394*S^2 + 33*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (16*(-19 - 607*S^2 + 196*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(-75 - 3774*S^2 + 1177*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (64*S*(-337 + 98*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((24*(1 + S^2))/S - (2*Pi^2*(27 - 146*S^2 + 11*S^4))/(3*S*(1 + S^2)))*Zeta[3] - (4*(9 - 55*S^2 + 18*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-32*Pi^2*(1 + S^2))/(9*S) - (83*Pi^4*(1 + S^2))/(180*S) + (8*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((104*(1 + S^2))/(3*S) + (2*Pi^2*(4 - 13*S^2 + 7*S^4))/(9*S*(1 + S^2)))*HPL[{3}, -S^2] + (24*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(6 - 89*S^2 + 17*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + ((-128*(1 + S^2))/S + (2*Pi^2*(211 - 1260*S^2 + 149*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (80*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (8*(19 - 134*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (4*(97 - 610*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (160*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (16*(578 - 4001*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (80*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*(17 - 147*S^2 + 30*S^4)*Zeta[3])/(9*S*(1 + S^2)) + HPL[{2}, -S^2]*((296*(1 + S^2))/(3*S) + (32*Pi^2*(1 + S^2))/(3*S) + (4*(19 - 134*S^2 + 19*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(41 - 266*S^2 + 41*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (4*(27 - 195*S^2 + 38*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((200*(1 + S^2))/S + (56*Pi^2*(1 + S^2))/(3*S) + (33*Pi^4*(1 + S^2))/(20*S) + (2*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(-14 + 18*S^2 + 21*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((-28*(1 + S^2))/S + (Pi^2*(-51 + 174*S^2 + 13*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2*(-17 - 2*S^2 + 31*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (8*(-14 + 3*S^2 + 20*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(-39 + 126*S^2 + 13*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-121 + 388*S^2 + 29*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(39 - 132*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-8*(1 + S^2))/S + (Pi^2*(-1 + 36*S^2 + 29*S^4))/(3*S*(1 + S^2)))*Zeta[3] + (2*(-21 + 80*S^2 + 57*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{1}, -S^2]*((-8*Pi^4*(1 + S^2))/(9*S) - (79*Pi^6*(1 + S^2))/(720*S) + (20*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((126*(1 + S^2))/S - (2*Pi^2*(-6 - 61*S^2 + 29*S^4))/(3*S*(1 + S^2)))*HPL[{5}, -S^2] + (135*(1 + S^2)*HPL[{6}, -S^2])/S - (2*(-78 + 39*S^2 + 145*S^4)*HPL[{7}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-40*(1 + S^2))/S - (2*Pi^2*(25 - 167*S^2 + 20*S^4))/(3*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-244*(1 + S^2))/S + (Pi^2*(-121 + 682*S^2 - 69*S^4))/(3*S*(1 + S^2)))*HPL[{4, 1}, -S^2] + (6*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (2*(-32 + 57*S^2 + 45*S^4)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) - (112*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (4*(-47 + 81*S^2 + 68*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) - (2*(-159 + 459*S^2 + 166*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) + ((176*(1 + S^2))/S - (4*Pi^2*(317 - 1901*S^2 + 234*S^4))/(3*S*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((736*(1 + S^2))/S - (4*Pi^2*(947 - 5690*S^2 + 695*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + (160*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (2*(69 - 488*S^2 + 51*S^4)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) + (16*(27 - 193*S^2 + 20*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) + (624*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (2*(215 - 1544*S^2 + 161*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + (2*(659 - 4712*S^2 + 485*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(327 - 2287*S^2 + 226*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-768*(1 + S^2))/S + (4*Pi^2*(211 - 1260*S^2 + 149*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (16*(177 - 1214*S^2 + 177*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)) - (480*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (32*(275 - 1888*S^2 + 275*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (32*(275 - 1888*S^2 + 275*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (16*(1081 - 7418*S^2 + 1081*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(6469 - 44314*S^2 + 6457*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (960*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (384*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (96*(330 - 2261*S^2 + 329*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (480*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((Pi^2*(-1 - S^2))/S + (Pi^4*(-212 - 805*S^2 + 899*S^4))/(180*S*(1 + S^2)))*Zeta[3] + (6*(1 + S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((168*(1 + S^2))/S + (52*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-19 + 433*S^2 - 56*S^4))/(90*S*(1 + S^2)) + (2*(-17 + 33*S^2 + 22*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (32*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(19 - 142*S^2 + 15*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (8*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-464*(1 + S^2))/S - (52*Pi^2*(1 + S^2))/S + (Pi^4*(7131 - 38357*S^2 + 3644*S^4))/(180*S*(1 + S^2)) - (32*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((32*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/(6*S) + (2*(9 - 61*S^2 + 6*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (2*(177 - 1214*S^2 + 177*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*(19 - 127*S^2 + 22*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-296*(1 + S^2))/S - (100*Pi^2*(1 + S^2))/(3*S) - (8*(19 - 129*S^2 + 24*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{4}, -S^2]*((128*(1 + S^2))/S + (13*Pi^2*(1 + S^2))/S + (2*(1 - 40*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*(-23 + 52*S^2 + 27*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((592*(1 + S^2))/S + (64*Pi^2*(1 + S^2))/S + (8*(41 - 266*S^2 + 41*S^4)*Zeta[3])/(S*(1 + S^2))) + ((-6*(1 + S^2))/S + (Pi^2*(-13 - 23*S^2 + 94*S^4))/(3*S*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((400*(1 + S^2))/S + (128*Pi^2*(1 + S^2))/(3*S) + (259*Pi^4*(1 + S^2))/(72*S) + ((20*(1 + S^2))/S + (Pi^2*(25 - 167*S^2 + 20*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + (4*(1 + S^2)*HPL[{4}, -S^2])/S - (2*(-19 + 42*S^2 + 21*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((-88*(1 + S^2))/S + (2*Pi^2*(317 - 1901*S^2 + 234*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (48*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2*(35 - 244*S^2 + 25*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (2*(109 - 772*S^2 + 79*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(177 - 1214*S^2 + 177*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(275 - 1888*S^2 + 275*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-16*(1 + S^2))/S + (Pi^2*(27 - 277*S^2 + 64*S^4))/(3*S*(1 + S^2)))*Zeta[3] + (2*(9 - 111*S^2 + 44*S^4)*Zeta[5])/(S*(1 + S^2))) + (30*(-2 + 7*S^2)*Zeta[7])/S)) + Log[T]*((-7*Pi^8*S*(70669 + 5432*S^2))/(97200*(1 + S^2)) - (S*(7 + 2*S^2)*HPL[{0}, S^2]^8)/(96*(1 + S^2)) + ((4 - 13*S^2 - S^4)*HPL[{0}, S^2]^7*HPL[{1}, -S^2])/(24*S*(1 + S^2)) + (8*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^8)/(3*S*(1 + S^2)) + (2*Pi^2*(-33 - 187*S^2 + 61*S^4)*HPL[{2}, -S^2]^3)/(9*S*(1 + S^2)) + (2*(14 - 187*S^2 + 14*S^4)*HPL[{2}, -S^2]^4)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^6*((2*Pi^2*(51 - 305*S^2 + 36*S^4))/(9*S*(1 + S^2)) - (20*(-1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^6*(-(Pi^2*S*(74 + 17*S^2))/(72*(1 + S^2)) + ((1 + S^2)*HPL[{1}, -S^2])/(6*S) + ((23 - 70*S^2 - 5*S^4)*HPL[{1}, -S^2]^2)/(24*S*(1 + S^2)) + ((1 - 35*S^2 - 4*S^4)*HPL[{2}, -S^2])/(24*S*(1 + S^2))) + ((-20*(1 + S^2))/S + (Pi^2*(3 - 98*S^2 + 43*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2]^2 + (4*(1 - 11*S^2 + 2*S^4)*HPL[{4}, -S^2]^2)/(S*(1 + S^2)) - (2*Pi^2*(-70 - 4*S^2 + 101*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) - (4*(-245 + 778*S^2 + 360*S^4)*HPL[{8}, -S^2])/(S*(1 + S^2)) + ((176*(1 + S^2))/S - (4*Pi^2*(46 - 1195*S^2 + 107*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2]^2 + (16*(48 - 445*S^2 + 27*S^4)*HPL[{3, 1}, -S^2]^2)/(S*(1 + S^2)) + (164*Pi^2*S*(-2 + S^2)*HPL[{4, 2}, -S^2])/(3*(1 + S^2)) + (2*Pi^2*(-38 - 999*S^2 + 475*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(3 - S^2 + 14*S^4)*HPL[{5, 3}, -S^2])/(S*(1 + S^2)) - (4*(-9 - 34*S^2 + 20*S^4)*HPL[{6, 2}, -S^2])/(S*(1 + S^2)) + (4*(-177 + 437*S^2 + 306*S^4)*HPL[{7, 1}, -S^2])/(S*(1 + S^2)) + ((-88*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-660 - 12377*S^2 + 1823*S^4))/(45*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (320*(5 - 77*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(S*(1 + S^2)) - (2*Pi^2*(-45 + 37*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (2*Pi^2*(-219 - 1488*S^2 + 451*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (12*(4 - 121*S^2 + 43*S^4)*HPL[{3, 3, 2}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*(-381 - 1700*S^2 + 525*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(12 - 313*S^2 + 95*S^4)*HPL[{4, 1, 3}, -S^2])/(S*(1 + S^2)) + (4*(1 - 221*S^2 + 114*S^4)*HPL[{4, 2, 2}, -S^2])/(S*(1 + S^2)) - (8*(36 - 1039*S^2 + 353*S^4)*HPL[{4, 3, 1}, -S^2])/(S*(1 + S^2)) - (4*(54 - 1231*S^2 + 395*S^4)*HPL[{5, 1, 2}, -S^2])/(S*(1 + S^2)) - (28*(42 - 1213*S^2 + 425*S^4)*HPL[{5, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(270 - 10937*S^2 + 4021*S^4)*HPL[{6, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*Pi^2*(-79 - 246*S^2 + 81*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(47 - 242*S^2 + 47*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(S*(1 + S^2)) + (4*(47 - 242*S^2 + 47*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(-535 + 242*S^2 + 441*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(S*(1 + S^2)) - (5856*(-1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (24*(-1 - 114*S^2 + 55*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (72*(-81 + 38*S^2 + 63*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (24*(-731 + 114*S^2 + 677*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-1086 + 511*S^2 + 877*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (160*Pi^2*(-11 - 77*S^2 + 21*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (3904*(-1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S - (11712*(-1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S + (22752*(-1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S + (38368*(-1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S + (46176*(-1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S + (96928*(-1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S + (1152*(-254 + 15*S^2 + 249*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (1920*(-5 + 9*S^2 + 2*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (13440*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S - (320*(-10 + 77*S^2)*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3])/(S*(1 + S^2)) - (2*Pi^2*S*(73 + 11*S^2)*Zeta[3]^2)/(3*(1 + S^2)) + HPL[{4}, -S^2]*((4*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(219 + 2078*S^2 - 885*S^4))/(90*S*(1 + S^2)) - (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(-3 - 161*S^2 + 78*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (24*(-1 - 106*S^2 + 55*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (12*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-64*(1 + S^2))/S - (34*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(220 - 12053*S^2 + 1030*S^4))/(180*S*(1 + S^2)) + (2*(1 + S^2)*HPL[{3}, -S^2])/S - (6*(1 - 86*S^2 + 25*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (2*(-161 + 258*S^2 + 83*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (488*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (20*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((16*Pi^2*(1 + S^2))/S + (Pi^4*(993 + 10096*S^2 - 1511*S^4))/(90*S*(1 + S^2)) - (32*(71 - 770*S^2 + 29*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^4*((16*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(4460 - 23717*S^2 + 2213*S^4))/(270*S*(1 + S^2)) - (2*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (8*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + (16*(1 + S^2)*HPL[{3}, -S^2])/S - (4*(47 - 554*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (8*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (600*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (40*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]^5*(((1 + S^2)*HPL[{1}, -S^2]^2)/(4*S) + ((275 - 1033*S^2 - 4*S^4)*HPL[{1}, -S^2]^3)/(90*S*(1 + S^2)) + ((-1 - S^2)*HPL[{2}, -S^2])/(2*S) + HPL[{1}, -S^2]*((1 + S^2)/(4*S) + (Pi^2*(695 - 2398*S^2 - 109*S^4))/(360*S*(1 + S^2)) + ((230 - 853*S^2 + S^4)*HPL[{2}, -S^2])/(60*S*(1 + S^2))) - (S*HPL[{3}, -S^2])/(1 + S^2) + ((-115 + 156*S^2)*HPL[{2, 1}, -S^2])/(15*S*(1 + S^2)) - (3*S*(3 + S^2)*Zeta[3])/(2*(1 + S^2))) + HPL[{5}, -S^2]*((7*Pi^2*(1 + S^2))/(3*S) - (4*(-20 + 377*S^2 + 29*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*(7 + 39*S^2)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((40*Pi^2*(1 + S^2))/(3*S) + (32*(-54 + 345*S^2 + 7*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^5*((4*Pi^2*(1 + S^2))/(3*S) - (40*(5 - 65*S^2 + 14*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (120*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(5 - 87*S^2 + 20*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((76*Pi^2*(1 + S^2))/(3*S) + (16*(-321 + 2166*S^2 + 23*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{4, 1}, -S^2]*((64*Pi^2*(1 + S^2))/(3*S) + (16*(-1 - 121*S^2 + 26*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 2}, -S^2]*((19*Pi^2*(1 + S^2))/(3*S) + (4*(-1 - 124*S^2 + 29*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^4*(-(Pi^4*S*(11971 + 2086*S^2))/(2160*(1 + S^2)) + (3*(1 + S^2)*HPL[{1}, -S^2]^3)/(2*S) + ((137 - 518*S^2 + 5*S^4)*HPL[{1}, -S^2]^4)/(18*S*(1 + S^2)) + ((-1 - S^2)/S + (Pi^2*(9 - 528*S^2 - 25*S^4))/(36*S*(1 + S^2)))*HPL[{2}, -S^2] + ((-6 - 263*S^2 + 14*S^4)*HPL[{2}, -S^2]^2)/(12*S*(1 + S^2)) + HPL[{1}, -S^2]^2*((25*(1 + S^2))/(6*S) + (Pi^2*(619 - 2086*S^2 - 65*S^4))/(72*S*(1 + S^2)) + ((249 - 847*S^2 - 8*S^4)*HPL[{2}, -S^2])/(12*S*(1 + S^2))) - (3*(-1 + S^2)*HPL[{4}, -S^2])/(2*S) + (7*(1 + S^2)*HPL[{2, 1}, -S^2])/(6*S) + ((-3 + 514*S^2 - 13*S^4)*HPL[{3, 1}, -S^2])/(6*S*(1 + S^2)) + ((3 - 531*S^2 + 10*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((8*(1 + S^2))/S + (29*Pi^2*(1 + S^2))/(24*S) - (19*(1 + S^2)*HPL[{2}, -S^2])/(12*S) + ((5 + 3*S^2 - 6*S^4)*HPL[{3}, -S^2])/(2*S*(1 + S^2)) + ((-249 + 847*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) + ((19 - 14*S^2 - 19*S^4)*Zeta[3])/(3*S*(1 + S^2)))) - (24*S*(19 + 9*S^2)*Zeta[3]*Zeta[5])/(1 + S^2) + HPL[{2}, -S^2]*((-32*Pi^2*(1 + S^2))/(3*S) - (82*Pi^4*(1 + S^2))/(45*S) + (Pi^6*(-652 - 144378*S^2 + 6871*S^4))/(11340*S*(1 + S^2)) + (2*(-1 - 129*S^2 + 40*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((32*(1 + S^2))/S - (4*Pi^2*(2 - 68*S^2 + 43*S^4))/(3*S*(1 + S^2)))*HPL[{4}, -S^2] - (14*(1 + S^2)*HPL[{5}, -S^2])/S - (4*(20 + 61*S^2 + 46*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) - (488*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((176*(1 + S^2))/S - (2*Pi^2*(133 - 2390*S^2 + 173*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] - (4*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (12*(1 - 86*S^2 + 25*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) + (4*(10 - 913*S^2 + 389*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((-352*(1 + S^2))/S + (8*Pi^2*(46 - 1195*S^2 + 107*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (12*(13 - 86*S^2 + 13*S^4)*HPL[{3, 1, 2}, -S^2])/(S*(1 + S^2)) + (4*(185 - 2734*S^2 + 185*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) + (24*(113 - 1390*S^2 + 57*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-661 - 770*S^2 + 761*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (640*(5 - 77*S^2 + 5*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (2*Pi^2*(1 + S^2)*Zeta[3])/(3*S) + 12*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-20*Pi^2*(1 + S^2))/(3*S) - (16*(-54 + 345*S^2 + 7*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((-10*Pi^2*(1 + S^2))/(3*S) + (4*(273 - 1754*S^2 + 29*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-1 - 58*S^2 + 19*S^4)*Zeta[3])/(S*(1 + S^2))) - (8*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^2*((116*Pi^2*(1 + S^2))/(3*S) + (571*Pi^4*(1 + S^2))/(90*S) + (Pi^6*(201706 - 958255*S^2 + 59719*S^4))/(22680*S*(1 + S^2)) + ((-44*(1 + S^2))/S + (Pi^2*(350 - 2089*S^2 + 257*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2]^2 - (62*(-1 + S^2)*HPL[{2}, -S^2]^3)/S + (2*(37 - 238*S^2 + 37*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + (Pi^2*(-61 + 1132*S^2 - 279*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (32*(1 + S^2)*HPL[{5}, -S^2])/S - (2*(-194 - 127*S^2 + 283*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) - (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + (8*Pi^2*(-116 + 193*S^2 + 61*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (96*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (288*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (18*(13 - 86*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) + (16*(50 - 551*S^2 + 119*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) - (8*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (192*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (384*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (1488*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (32*(-116 - 277*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (32*(-71 - 277*S^2 + 154*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (7200*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((296*(1 + S^2))/S + (74*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (8*(5 - 32*S^2 + 5*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{2}, -S^2]*((-22*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(7200 - 21017*S^2 - 1137*S^4))/(180*S*(1 + S^2)) + (48*(1 + S^2)*HPL[{3}, -S^2])/S - (2*(113 - 734*S^2 + 113*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (32*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (48*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((128*(1 + S^2))/S + (14*Pi^2*(1 + S^2))/(3*S) + (8*(103 - 1348*S^2 + 289*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (8*(11 - 87*S^2 + 14*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((8*Pi^2*(1 + S^2))/S + (32*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(S*(1 + S^2))) + (236*(1 + S^2)*Zeta[5])/S) + HPL[{0}, S^2]^3*((4*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + (2*(56 - 263*S^2 + 17*S^4)*HPL[{1}, -S^2]^5)/(9*S*(1 + S^2)) - (11*(1 + S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^3*((44*(1 + S^2))/(9*S) + (Pi^2*(555 - 2348*S^2 + 81*S^4))/(27*S*(1 + S^2)) + (4*(43 - 195*S^2 + 12*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + ((-34*(1 + S^2))/(3*S) + (Pi^2*(5 - 46*S^2 - 3*S^4))/(9*S*(1 + S^2)))*HPL[{3}, -S^2] - (25*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (2*(-5 - 30*S^2 + 3*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + ((16*(1 + S^2))/S + (Pi^2*(-490 + 813*S^2 + 11*S^4))/(9*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (40*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*S*(-23 + 17*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) + (20*(-1 - S^2 + 4*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - (76*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(-246 + 471*S^2 + 5*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(-748 + 1445*S^2 + 21*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(-260 + 501*S^2 + 11*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (Pi^2*S*(135 + 59*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((32*(1 + S^2))/(3*S) + (37*Pi^2*(1 + S^2))/(18*S) + (Pi^4*(4011 - 15739*S^2 - 14*S^4))/(540*S*(1 + S^2)) + ((-20*(1 + S^2))/S + (Pi^2*(488 - 2023*S^2 + 73*S^4))/(18*S*(1 + S^2)))*HPL[{2}, -S^2] + ((121 - 553*S^2 + 38*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) - (26*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (2*(6 - 63*S^2 + 11*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(127 - 583*S^2 + 38*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(43 - 195*S^2 + 12*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((-70*(1 + S^2))/(3*S) - (49*Pi^2*(1 + S^2))/(18*S) - (8*S*(-3 + 2*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (2*(-246 + 471*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (2*S*(1 + 11*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]^2*((32*(1 + S^2))/(3*S) + (3*Pi^2*(1 + S^2))/(2*S) - (12*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(-1 + 5*S^2)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (4*(43 - 195*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*(-6 - 17*S^2 + 17*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (52*S*(4 + S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-71*Pi^4*(1 + S^2))/(90*S) - (4*(507 - 3250*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (48*(-137 + 824*S^2 + 13*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (1952*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (32*(-51 - 770*S^2 + 151*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (640*(5 - 77*S^2 + 5*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-176*(1 + S^2))/S + (4*Pi^2*(108 - 847*S^2 + S^4))/(3*S*(1 + S^2)))*Zeta[3] + (16*(22 - 381*S^2 + S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((-4*Pi^2*(1 + S^2))/(3*S) - (11*Pi^4*(1 + S^2))/(18*S) + (4*(1 + S^2)*HPL[{4}, -S^2])/S + (8*S*(12 + 5*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((-176*(1 + S^2))/S - (2*Pi^2*(-265 + 1642*S^2 + 71*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (4*(-3 + S^2)*(-1 + 83*S^2)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) - (32*(-3 - 14*S^2 + 6*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (8*(273 - 1754*S^2 + 29*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(821 - 5030*S^2 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (64*(-66 + 385*S^2 + 16*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((-8*(1 + S^2))/S - (2*Pi^2*(-5 - 112*S^2 + 21*S^4))/(3*S*(1 + S^2)))*Zeta[3] - (4*(-29 - 100*S^2 + 25*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((148*Pi^2*(1 + S^2))/(9*S) + (47*Pi^4*(1 + S^2))/(18*S) - (16*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((176*(1 + S^2))/(3*S) - (4*Pi^2*(118 - 1703*S^2 + 379*S^4))/(9*S*(1 + S^2)))*HPL[{3}, -S^2] - (8*(-5 - 116*S^2 + 41*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + (8*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (16*(103 - 1348*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (32*(178 - 2299*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (32*(463 - 2419*S^2 + 238*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2400*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((128*(1 + S^2))/S - (4*Pi^2*(79 - 1444*S^2 + 337*S^4))/(9*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-8*Pi^2*(1 + S^2))/(3*S) - (8*(103 - 1348*S^2 + 289*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (32*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (16*(11 - 680*S^2 + 179*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{0}, S^2]*((32*(1 - 7*S^2 + S^4)*HPL[{1}, -S^2]^7)/(3*S*(1 + S^2)) - (20*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^5*((2*Pi^2*(140 - 851*S^2 + 101*S^4))/(9*S*(1 + S^2)) + (4*(25 - 174*S^2 + 25*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2))) + ((-114*(1 + S^2))/S + (Pi^2*(-7 - 165*S^2 + 10*S^4))/(3*S*(1 + S^2)))*HPL[{5}, -S^2] - (140*(1 + S^2)*HPL[{6}, -S^2])/S + (2*(-25 - 29*S^2 + 24*S^4)*HPL[{7}, -S^2])/(S*(1 + S^2)) + (48*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((28*(1 + S^2))/S + (Pi^2*(3 - 308*S^2 + 113*S^4))/(3*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((208*(1 + S^2))/S + (8*Pi^2*(-6 - 80*S^2 + 35*S^4))/(3*S*(1 + S^2)))*HPL[{4, 1}, -S^2] - (14*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (8*(2 + 15*S^2 + 2*S^4)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) + (80*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (2*(25 + 169*S^2 + 24*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) + (8*(13 + 134*S^2 + 8*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) + HPL[{1}, -S^2]^3*((44*Pi^2*(1 + S^2))/(9*S) + (Pi^4*(8061 - 44045*S^2 + 4122*S^4))/(270*S*(1 + S^2)) + ((-128*(1 + S^2))/S + (2*Pi^2*(211 - 1260*S^2 + 149*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2] + (16*(49 - 337*S^2 + 49*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) - (48*(1 + S^2)*HPL[{3}, -S^2])/S + (4*(17 - 194*S^2 + 29*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (160*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (16*(62 - 435*S^2 + 63*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (80*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2))) + ((-176*(1 + S^2))/S - (4*Pi^2*(-638 + 1819*S^2 + 5*S^4))/(3*S*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((-736*(1 + S^2))/S - (4*Pi^2*(-1939 + 5439*S^2 + 46*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (152*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (2*(-23 - 488*S^2 + 143*S^4)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) - (96*(-1 - 32*S^2 + 9*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) - (600*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (8*(-11 - 380*S^2 + 111*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) - (8*(-35 - 1178*S^2 + 321*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(-75 - 2289*S^2 + 626*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) + ((768*(1 + S^2))/S + (8*Pi^2*(-665 + 1806*S^2 + 41*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (32*(-196 + 607*S^2 + 19*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)) + (480*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (8*(-2355 + 7546*S^2 + 149*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) - (8*(-2355 + 7546*S^2 + 149*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (8*(-4707 + 14830*S^2 + 377*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*(-3521 + 11081*S^2 + 292*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (960*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (128*(-98 + 337*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (384*(-98 + 337*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (160*(389 - 1358*S^2 + 5*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (960*(-27 + 87*S^2 + 2*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (373*Pi^4*S^3*Zeta[3])/(45*(1 + S^2)) + HPL[{2, 1}, -S^2]*((464*(1 + S^2))/S + (48*Pi^2*(1 + S^2))/S + (Pi^4*(-7313 + 17525*S^2 + 272*S^4))/(90*S*(1 + S^2)) - (8*(-391 + 1350*S^2 + S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (64*(-98 + 337*S^2)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (24*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-168*(1 + S^2))/S - (20*Pi^2*(1 + S^2))/S + (Pi^4*(229 - 998*S^2 - 211*S^4))/(180*S*(1 + S^2)) - (8*(1 + 8*S^2)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(-5 - 148*S^2 + 33*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (8*(-1 - 136*S^2 + 37*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-592*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/(3*S) - (96*S*(-22 + 7*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*((-128*(1 + S^2))/S - (40*Pi^2*(1 + S^2))/(3*S) - (4*(-1 - 24*S^2 + S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-3 + 26*S^2 + 5*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((296*(1 + S^2))/S + (100*Pi^2*(1 + S^2))/(3*S) + (8*(-3 - 133*S^2 + 42*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^4*((4*Pi^2*(1 + S^2))/(3*S) - (40*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(10 - 43*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (20*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(40 - 277*S^2 + 43*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]^2*((-32*(1 + S^2))/S - (23*Pi^2*(1 + S^2))/(6*S) + ((3 + 118*S^2 - 37*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (4*(-196 + 607*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*(-4 - 129*S^2 + 43*S^4)*Zeta[3])/(S*(1 + S^2))) - (104*Pi^2*S^3*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((32*Pi^2*(1 + S^2))/(3*S) + (349*Pi^4*(1 + S^2))/(180*S) + (Pi^6*(187513 - 953473*S^2 + 61474*S^4))/(22680*S*(1 + S^2)) + ((-44*(1 + S^2))/S + (Pi^2*(317 - 1901*S^2 + 234*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + (2*(177 - 1214*S^2 + 177*S^4)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)) - (2*(1 - 20*S^2 + 3*S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((-124*(1 + S^2))/S + (Pi^2*(29 - 320*S^2 + 51*S^4))/(3*S*(1 + S^2)))*HPL[{4}, -S^2] - (104*(1 + S^2)*HPL[{5}, -S^2])/S + (2*(9 - 219*S^2 + 64*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) - (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + ((384*(1 + S^2))/S - (4*Pi^2*(313 - 1888*S^2 + 227*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] + (64*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (336*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (6*(-1 + S^2)*HPL[{4, 2}, -S^2])/S - (8*(5 - 109*S^2 + 22*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((-768*(1 + S^2))/S + (4*Pi^2*(211 - 1260*S^2 + 149*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (192*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (864*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (16*(177 - 1214*S^2 + 177*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(1079 - 7478*S^2 + 1091*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (960*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (96*(62 - 435*S^2 + 63*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (480*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (4*Pi^2*(1 + S^2)*Zeta[3])/(3*S) + (4*(7 - 67*S^2 + 10*S^4)*Zeta[3]^2)/(S*(1 + S^2)) + HPL[{3}, -S^2]*((-168*(1 + S^2))/S - (62*Pi^2*(1 + S^2))/(3*S) + (8*(19 - 134*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (16*S*(-1 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((-464*(1 + S^2))/S - (52*Pi^2*(1 + S^2))/S + (Pi^4*(7131 - 38357*S^2 + 3644*S^4))/(180*S*(1 + S^2)) - (32*(1 + S^2)*HPL[{3}, -S^2])/S + (2*(1 - 40*S^2 + 7*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (32*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((592*(1 + S^2))/S + (64*Pi^2*(1 + S^2))/S + (8*(41 - 266*S^2 + 41*S^4)*Zeta[3])/(S*(1 + S^2))) + (4*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((-400*(1 + S^2))/S - (48*Pi^2*(1 + S^2))/S - (361*Pi^4*(1 + S^2))/(90*S) + ((-12*(1 + S^2))/S + (Pi^2*(1 + 160*S^2 - 53*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + (4*(1 + S^2)*HPL[{4}, -S^2])/S - (2*(-3 - 37*S^2 + 6*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((88*(1 + S^2))/S + (2*Pi^2*(-638 + 1819*S^2 + 5*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (40*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (2*(-7 - 236*S^2 + 75*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (8*(-5 - 189*S^2 + 56*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (96*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (16*(-196 + 607*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(-1175 + 3778*S^2 + 77*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + (64*(-98 + 337*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((8*(1 + S^2))/S - (2*Pi^2*S*(-131 + 53*S^2))/(3*(1 + S^2)))*Zeta[3] - (8*S*(-28 + 13*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^2*((32*Pi^2*(1 + S^2))/(3*S) + (83*Pi^4*(1 + S^2))/(60*S) - (24*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-104*(1 + S^2))/S - (2*Pi^2*(4 - 13*S^2 + 7*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] - (72*(1 + S^2)*HPL[{4}, -S^2])/S + (4*(6 - 89*S^2 + 17*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((384*(1 + S^2))/S - (2*Pi^2*(211 - 1260*S^2 + 149*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (240*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (8*(19 - 134*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (4*(97 - 610*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (480*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (64*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (16*(578 - 4001*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (240*(25 - 174*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (4*Pi^2*(17 - 147*S^2 + 30*S^4)*Zeta[3])/(3*S*(1 + S^2)) + HPL[{2}, -S^2]*((-296*(1 + S^2))/S - (32*Pi^2*(1 + S^2))/S - (4*(19 - 134*S^2 + 19*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (32*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(41 - 266*S^2 + 41*S^4)*Zeta[3])/(S*(1 + S^2))) - (4*(27 - 195*S^2 + 38*S^4)*Zeta[5])/(S*(1 + S^2)))) + HPL[{0}, S^2]^2*(-(Pi^6*S*(15415 + 1763*S^2))/(1296*(1 + S^2)) + (4*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (2*(23 - 109*S^2 + 8*S^4)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)) + ((-12*(1 + S^2))/S + (Pi^2*(-10 - 688*S^2 + 71*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2]^2 + ((-5 - 374*S^2 + 61*S^4)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)) + HPL[{1}, -S^2]^4*((16*(1 + S^2))/S + (Pi^2*(619 - 2671*S^2 + 130*S^4))/(18*S*(1 + S^2)) + ((325 - 1348*S^2 + 67*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2))) + (2*(2 + 9*S^2 + S^4)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)) + ((4*(1 + S^2))/S + (Pi^2*(27 + 4*S^2 - 39*S^4))/(6*S*(1 + S^2)))*HPL[{4}, -S^2] + (7*(1 + S^2)*HPL[{5}, -S^2])/S + ((50 - 39*S^2 - 51*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) - (4*(-4 - 425*S^2 + 57*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + ((48*(1 + S^2))/S + (Pi^2*(5 + 1276*S^2 - 115*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] + (19*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (64*(1 + S^2)*HPL[{4, 1}, -S^2])/S + ((3 + 14*S^2 - S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) + (2*(-14 + 23*S^2 + 33*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) + ((-88*(1 + S^2))/S + (2*Pi^2*(-2 - 1301*S^2 + 115*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (40*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (76*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (2*(3 + 5*S^2)*HPL[{3, 1, 2}, -S^2])/S + (2*(-17 - 1488*S^2 + 249*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) + (4*(-21 - 2240*S^2 + 345*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*(-4 - 381*S^2 + 51*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (80*(-1 - 154*S^2 + 21*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (2*S*(31 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2}, -S^2]*((-32*(1 + S^2))/S - (17*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(156 - 14899*S^2 + 299*S^4))/(360*S*(1 + S^2)) - (10*(1 + S^2)*HPL[{3}, -S^2])/S + ((-11 - 46*S^2 - 7*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (20*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2*(-9 - 850*S^2 + 115*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (8*(-4 - 425*S^2 + 57*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (2*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((116*(1 + S^2))/S + (49*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(8046 - 31091*S^2 + 403*S^4))/(360*S*(1 + S^2)) + ((-22*(1 + S^2))/S + (Pi^2*(574 - 2195*S^2 + 59*S^4))/(6*S*(1 + S^2)))*HPL[{2}, -S^2] + ((154 - 741*S^2 + 61*S^4)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)) - (10*(1 + S^2)*HPL[{3}, -S^2])/S + ((33 + 24*S^2 - 41*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) + (24*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(161 - 663*S^2 + 32*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (4*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (14*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((7*Pi^2*(1 + S^2))/(3*S) + (4*(8 - 77*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3}, -S^2]*((-4*(1 + S^2))/S - (11*Pi^2*(1 + S^2))/(6*S) - (2*(-1 + 102*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(-1 - 8*S^2 + S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((148*(1 + S^2))/(3*S) + (19*Pi^2*(1 + S^2))/(3*S) - (8*(1 + S^2)*HPL[{2}, -S^2])/S - (4*(-7 - 78*S^2 + 29*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (4*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(4 - 139*S^2 + 37*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]*((200*(1 + S^2))/S + (85*Pi^2*(1 + S^2))/(3*S) + (271*Pi^4*(1 + S^2))/(90*S) - (2*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-12*(1 + S^2))/S + (Pi^2*(22 + 87*S^2 - 47*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] - (6*(1 + S^2)*HPL[{4}, -S^2])/S - (2*(-23 - 24*S^2 + 35*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((44*(1 + S^2))/S + (Pi^2*(-574 + 2195*S^2 - 59*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (28*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (4*(5 - 75*S^2 + 16*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (2*(-3 - 474*S^2 + 137*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(154 - 741*S^2 + 61*S^4)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)) + (8*(469 - 2145*S^2 + 154*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (8*(325 - 1348*S^2 + 67*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((24*(1 + S^2))/S + (Pi^2*(34 + 111*S^2 - 75*S^4))/(3*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-32*(1 + S^2))/S - (31*Pi^2*(1 + S^2))/(6*S) - (2*(5 - 75*S^2 + 16*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) - (4*(154 - 741*S^2 + 61*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (2*(8 - 133*S^2 + 31*S^4)*Zeta[3])/(S*(1 + S^2))) - (2*(-40 - 117*S^2 + 79*S^4)*Zeta[5])/(S*(1 + S^2)))) + HPL[{1}, -S^2]*((200*Pi^2*(1 + S^2))/(3*S) + (479*Pi^4*(1 + S^2))/(45*S) + (9853*Pi^6*(1 + S^2))/(7560*S) - (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-8*(1 + S^2))/S - (4*Pi^2*(-19 - 186*S^2 + 79*S^4))/(3*S*(1 + S^2)))*HPL[{5}, -S^2] + (30*(1 + S^2)*HPL[{6}, -S^2])/S - (12*(-87 + 81*S^2 + 92*S^4)*HPL[{7}, -S^2])/(S*(1 + S^2)) + (96*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-176*(1 + S^2))/S + (4*Pi^2*(108 - 1423*S^2 + 305*S^4))/(3*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-528*(1 + S^2))/S + (2*Pi^2*(709 - 9670*S^2 + 2109*S^4))/(3*S*(1 + S^2)))*HPL[{4, 1}, -S^2] - (12*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (4*(7 - 185*S^2 + 40*S^4)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)) - (48*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (24*(2 - 71*S^2 + 15*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) + (4*(-184 + 153*S^2 + 233*S^4)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)) + ((-352*(1 + S^2))/S + (8*Pi^2*(350 - 2089*S^2 + 257*S^4))/(3*S*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((-704*(1 + S^2))/S + (32*Pi^2*(233 - 1141*S^2 + 98*S^4))/(3*S*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] - (4*(443 - 5586*S^2 + 1187*S^4)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)) - (32*(172 - 2137*S^2 + 451*S^4)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)) - (4*(1337 - 16838*S^2 + 3569*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) - (4*(4253 - 52142*S^2 + 10949*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) - (96*(362 - 4471*S^2 + 943*S^4)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)) + (16*Pi^2*(-275 + 674*S^2 + 79*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2976*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + (64*(191 - 674*S^2 + 5*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)) + (64*(191 - 674*S^2 + 5*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)) - (32*(-661 + 1348*S^2 + 269*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (64*(-1015 + 2299*S^2 + 344*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (256*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)) - (768*(49 - 337*S^2 + 49*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (320*(221 - 1673*S^2 + 266*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (14400*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((464*(1 + S^2))/S + (40*Pi^2*(1 + S^2))/S + (Pi^4*(-231 + 10373*S^2 - 2808*S^4))/(90*S*(1 + S^2)))*Zeta[3] - (36*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((44*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-7200 + 21017*S^2 + 1137*S^4))/(90*S*(1 + S^2)) + (64*(49 - 337*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) + (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (96*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((128*(1 + S^2))/S + (32*Pi^2*(1 + S^2))/(3*S) + (Pi^4*(-292 + 6193*S^2 - 1511*S^4))/(45*S*(1 + S^2)) + (4*(8 - 157*S^2 + 35*S^4)*HPL[{4}, -S^2])/(S*(1 + S^2)) - (96*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(103 - 1352*S^2 + 289*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (16*(103 - 1348*S^2 + 289*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (56*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-2*Pi^2*(1 + S^2))/S + (4*(113 - 734*S^2 + 113*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (4*(3 - 100*S^2 + 25*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-16*Pi^2*(1 + S^2))/S - (64*(25 - 337*S^2 + 73*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2}, -S^2]^2*((-64*(1 + S^2))/S - (14*Pi^2*(1 + S^2))/(3*S) - (4*(70 - 795*S^2 + 163*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + (372*(-1 + S^2)*HPL[{2, 1}, -S^2])/S - (4*(42 - 607*S^2 + 135*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((28*Pi^2*(1 + S^2))/(3*S) + (16*(53 - 694*S^2 + 149*S^4)*Zeta[3])/(S*(1 + S^2))) + ((392*(1 + S^2))/S - (2*Pi^2*(-18 - 1477*S^2 + 437*S^4))/(3*S*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((-32*Pi^2*(1 + S^2))/(3*S) - (157*Pi^4*(1 + S^2))/(180*S) + ((88*(1 + S^2))/S - (2*Pi^2*(108 - 1423*S^2 + 305*S^4))/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + (4*(1 + S^2)*HPL[{4}, -S^2])/S - (4*(17 - 286*S^2 + 65*S^4)*HPL[{5}, -S^2])/(S*(1 + S^2)) + ((176*(1 + S^2))/S - (4*Pi^2*(350 - 2089*S^2 + 257*S^4))/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (96*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (4*(241 - 2922*S^2 + 613*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (4*(727 - 8806*S^2 + 1843*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (192*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (1488*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (32*(191 - 674*S^2 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (128*(49 - 337*S^2 + 49*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + ((88*(1 + S^2))/S - (2*Pi^2*(108 - 1481*S^2 + 323*S^4))/(3*S*(1 + S^2)))*Zeta[3] - (4*(44 - 1255*S^2 + 317*S^4)*Zeta[5])/(S*(1 + S^2))) - (12*(-35 - 583*S^2 + 196*S^4)*Zeta[7])/(S*(1 + S^2)))) + (3136*S^3*Zeta[9])/(1 + S^2);
E5uvwT2F0=(Pi^6*(2553 - 6404*S^2))/3780 - (20*Pi^2*(-17 + 3*S^2))/3 - (2*Pi^4*(-232 + 207*S^2))/45 + (Pi^8*(670272 - 2763853*S^2 - 237512*S^4))/(680400*(1 + S^2)^2) + HPL[{0}, S^2]^9/(192*(1 + S^2)^2) + (2*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)^2) - (8*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^9)/(27*(1 + S^2)^2) + HPL[{0}, S^2]^8*((2 - 6*S^2 - 3*S^4)/(96*(1 + S^2)^2) + ((7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2])/(96*(1 + S^2)^2)) + ((63 - 304*S^2 + 63*S^4)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^7*((8*(1 + S^2)^2)/(21*S^2) - (16*Pi^2*(-40 + 18*S^2 + 9*S^4))/(63*(1 + S^2)^2) + (40*HPL[{2}, -S^2])/7) + HPL[{0}, S^2]^7*((1 + S^2)/6 + (Pi^2*(14 + 2*S^2 + S^4))/(144*(1 + S^2)^2) + ((6 - S^2 + S^4)*HPL[{1}, -S^2])/(12*(1 + S^2)^2) + ((9 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(24*(1 + S^2)^2) + ((4 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(24*(1 + S^2)^2)) - (100*HPL[{3}, -S^2]^3)/3 - (2*(-4 + 69*S^2 + 45*S^4)*HPL[{4}, -S^2]^2)/(1 + S^2)^2 + ((4*Pi^2*(84 + 130*S^2 + 65*S^4))/(1 + S^2)^2 + (4*(350 + 550*S^2 + 227*S^4))/S^2)*HPL[{7}, -S^2] + (4*(1786 + 1383*S^2 + 260*S^4)*HPL[{8}, -S^2])/(1 + S^2)^2 + (4*(2867 + 3712*S^2 + 1856*S^4)*HPL[{9}, -S^2])/(1 + S^2)^2 + (2464*HPL[{2, 1}, -S^2]^3)/3 + (4*(351 - 1462*S^2 + 267*S^4)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^2 + ((-44*Pi^2)/(1 + S^2)^2 - (4*(3 + 18*S^2 + 14*S^4))/S^2)*HPL[{4, 3}, -S^2] + ((-4*(13 + 65*S^2 + 43*S^4))/S^2 - (2*Pi^2*(201 + 94*S^2 + 47*S^4))/(3*(1 + S^2)^2))*HPL[{5, 2}, -S^2] - (4*(-12 - 25*S^2 + 5*S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 + (4*(341 + 508*S^2 + 254*S^4)*HPL[{5, 4}, -S^2])/(1 + S^2)^2 + ((-4*(156 + 312*S^2 + 121*S^4))/S^2 - (2*Pi^2*(653 + 1156*S^2 + 578*S^4))/(3*(1 + S^2)^2))*HPL[{6, 1}, -S^2] - (4*(-42 - 85*S^2 + 2*S^4)*HPL[{6, 2}, -S^2])/(1 + S^2)^2 + (4*(1397 + 2088*S^2 + 1044*S^4)*HPL[{6, 3}, -S^2])/(1 + S^2)^2 + (4*(-1091 - 734*S^2 + 49*S^4)*HPL[{7, 1}, -S^2])/(1 + S^2)^2 + (8*(1745 + 2606*S^2 + 1303*S^4)*HPL[{7, 2}, -S^2])/(1 + S^2)^2 + (4*(5021 + 7728*S^2 + 3864*S^4)*HPL[{8, 1}, -S^2])/(1 + S^2)^2 + (32*(131 - 608*S^2 + 131*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^2 + ((-4*(-5 - 2*S^2 + 35*S^4))/S^2 + (2*Pi^2*(-625 + 2522*S^2 + 1261*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2, 2}, -S^2] + ((-16*(-1 + 2*S^2 + 29*S^4))/S^2 + (136*Pi^2*(-28 + 114*S^2 + 57*S^4))/(3*(1 + S^2)^2))*HPL[{3, 3, 1}, -S^2] + (4*(-83 - 490*S^2 + 97*S^4)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^2 + ((-20*(-1 + 23*S^4))/S^2 + (4*Pi^2*(-907 + 3884*S^2 + 1942*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1, 2}, -S^2] - (4*(-154 - 877*S^2 + 117*S^4)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^2 + ((-4*(-5 + 24*S^2 + 355*S^4))/S^2 + (4*Pi^2*(-2929 + 11768*S^2 + 5884*S^4))/(3*(1 + S^2)^2))*HPL[{4, 2, 1}, -S^2] + (4*(-106 - 357*S^2 + 85*S^4)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^2 + (4*(-19 + 64*S^2 + 32*S^4)*HPL[{4, 2, 3}, -S^2])/(1 + S^2)^2 - (4*(-278 - 2565*S^2 + 569*S^4)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^2 - (4*(209 + 312*S^2 + 156*S^4)*HPL[{4, 3, 2}, -S^2])/(1 + S^2)^2 - (16*(51 + 124*S^2 + 62*S^4)*HPL[{4, 4, 1}, -S^2])/(1 + S^2)^2 + ((-16*(-20 - 13*S^2 + 177*S^4))/S^2 + (4*Pi^2*(-6041 + 24194*S^2 + 12097*S^4))/(3*(1 + S^2)^2))*HPL[{5, 1, 1}, -S^2] - (4*(-97 - 1467*S^2 + 310*S^4)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(79 + 100*S^2 + 50*S^4)*HPL[{5, 1, 3}, -S^2])/(1 + S^2)^2 - (4*(-1237 - 10587*S^2 + 2410*S^4)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^2 - (4*(445 + 808*S^2 + 404*S^4)*HPL[{5, 2, 2}, -S^2])/(1 + S^2)^2 - (8*(133 + 540*S^2 + 270*S^4)*HPL[{5, 3, 1}, -S^2])/(1 + S^2)^2 - (4*(-4095 - 27967*S^2 + 6584*S^4)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^2 - (20*(87 + 272*S^2 + 136*S^4)*HPL[{6, 1, 2}, -S^2])/(1 + S^2)^2 - (20*(-81 + 160*S^2 + 80*S^4)*HPL[{6, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(896 + 838*S^2 + 419*S^4)*HPL[{7, 1, 1}, -S^2])/(1 + S^2)^2 + ((160*(-1 + S^2)*(1 + S^2))/S^2 - (688*Pi^2*(9 + 8*S^2 + 4*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 2, 1}, -S^2] + ((-128*(-4 + S^4))/S^2 + (4*Pi^2*(5155 + 1478*S^2 + 739*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1, 2}, -S^2] + ((-128*(-4 + S^4))/S^2 + (4*Pi^2*(5155 + 1478*S^2 + 739*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 2, 1}, -S^2] + (8*(25 - 118*S^2 + 25*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2)^2 + ((-32*(-31 + 19*S^4))/S^2 + (4*Pi^2*(9799 + 5606*S^2 + 2803*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2, 1, 1}, -S^2] + (8*(25 - 118*S^2 + 25*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2)^2 - (8*(-49 + 186*S^2 + 67*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(-573 + 2294*S^2 + 1147*S^4)*HPL[{3, 2, 2, 2}, -S^2])/(1 + S^2)^2 - (8*(-1805 + 7214*S^2 + 3607*S^4)*HPL[{3, 2, 3, 1}, -S^2])/(1 + S^2)^2 - (96*(-6 + 23*S^2)*HPL[{3, 3, 1, 1}, -S^2])/(1 + S^2) - (48*(-293 + 1190*S^2 + 595*S^4)*HPL[{3, 3, 1, 2}, -S^2])/(1 + S^2)^2 - (24*(-1807 + 7322*S^2 + 3661*S^4)*HPL[{3, 3, 2, 1}, -S^2])/(1 + S^2)^2 + ((-48*(-57 + 4*S^2 + 37*S^4))/S^2 + (8*Pi^2*(14939 + 8154*S^2 + 4077*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1, 1, 1}, -S^2] + (12*(-1 - 226*S^2 + 111*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(-11021 + 44646*S^2 + 22323*S^4)*HPL[{4, 1, 1, 3}, -S^2])/(1 + S^2)^2 - (12*(-47 + 362*S^2 + 73*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (64*(-1157 + 4690*S^2 + 2345*S^4)*HPL[{4, 1, 2, 2}, -S^2])/(1 + S^2)^2 + (16*(-8271 + 33542*S^2 + 16771*S^4)*HPL[{4, 1, 3, 1}, -S^2])/(1 + S^2)^2 - (12*(-143 + 634*S^2 + 441*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-2867 + 11458*S^2 + 5729*S^4)*HPL[{4, 2, 1, 2}, -S^2])/(1 + S^2)^2 + (56*(-799 + 3242*S^2 + 1621*S^4)*HPL[{4, 2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-8144 + 33234*S^2 + 16617*S^4)*HPL[{4, 3, 1, 1}, -S^2])/(1 + S^2)^2 - (128*(-12 + 211*S^2 + 43*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-33485 + 134438*S^2 + 67219*S^4)*HPL[{5, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(-54899 + 222506*S^2 + 111253*S^4)*HPL[{5, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (8*(-130271 + 531410*S^2 + 265705*S^4)*HPL[{5, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-162913 + 663506*S^2 + 331753*S^4)*HPL[{6, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-384*(1 + S^4))/S^2 + (64*Pi^2*(-262 + 150*S^2 + 75*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-1152*(1 + S^4))/S^2 + (64*Pi^2*(-262 + 150*S^2 + 75*S^4))/(1 + S^2)^2)*HPL[{2, 2, 1, 1, 1}, -S^2] - (928*(-1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/(1 + S^2) - (2784*(-1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/(1 + S^2) - (128*(-147 + 136*S^2 + 68*S^4)*HPL[{2, 2, 2, 2, 1}, -S^2])/(1 + S^2)^2 + ((-192*(9 - S^2 + 14*S^4))/S^2 + (32*Pi^2*(-2817 + 2206*S^2 + 1103*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1, 1, 1}, -S^2] + (4896*(-1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/(1 + S^2) + (8608*(-1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/(1 + S^2) - (8*(-5815 + 1794*S^2 + 897*S^4)*HPL[{3, 1, 1, 2, 2}, -S^2])/(1 + S^2)^2 + (10464*(-1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/(1 + S^2) - (8*(-5815 + 1794*S^2 + 897*S^4)*HPL[{3, 1, 2, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(-137 + 62*S^2 + 31*S^4)*HPL[{3, 1, 2, 2, 1}, -S^2])/(1 + S^2)^2 + (64*(-5299 + 2122*S^2 + 1061*S^4)*HPL[{3, 1, 3, 1, 1}, -S^2])/(1 + S^2)^2 + (22528*(-1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/(1 + S^2) - (8*(-12871 + 8322*S^2 + 4161*S^4)*HPL[{3, 2, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (8*(-6919 + 6466*S^2 + 3233*S^4)*HPL[{3, 2, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(15409 + 4402*S^2 + 2201*S^4)*HPL[{3, 2, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (192*(2203 + 286*S^2 + 143*S^4)*HPL[{3, 3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (192*(-356 + 89*S^2 + 325*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-19409 + 12230*S^2 + 6115*S^4)*HPL[{4, 1, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (16*(-10481 + 9446*S^2 + 4723*S^4)*HPL[{4, 1, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(23011 + 6350*S^2 + 3175*S^4)*HPL[{4, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(79411 + 9950*S^2 + 4975*S^4)*HPL[{4, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (512*(4975 + 584*S^2 + 292*S^4)*HPL[{5, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((960*(-1 + S^2)*(1 + S^2))/S^2 - (32*Pi^2*(803 + 736*S^2 + 368*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + 19712*HPL[{2, 2, 1, 2, 1, 1}, -S^2] + 59136*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + (192*(13 - 89*S^2 + 18*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(1291 + 4322*S^2 + 2161*S^4)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (64*(3139 + 8018*S^2 + 4009*S^4)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (192*(1457 + 3494*S^2 + 1747*S^4)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(4987 + 11714*S^2 + 5857*S^4)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (192*(2997 + 6574*S^2 + 3287*S^4)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (128*(13364 + 29698*S^2 + 14849*S^4)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (960*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) - (256*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (1024*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (2560*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (1536*(-979 + 912*S^2 + 456*S^4)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 84480*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((8*Pi^2*(-13 + 2*S^2 + S^4))/(9*(1 + S^2)^2) + (8*(-4 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^2) - (16*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + (32*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{0}, S^2]*((-8*(3 - 22*S^2 + 11*S^4))/(3*(1 + S^2)^2) + (32*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2)) + (16*HPL[{2}, -S^2])/3)*Log[T]^7 + ((8*(1 - 7*S^2 + S^4))/(3*(1 + S^2)^2) - (4*(-1 + 2*S^2)*(5 + 2*S^2)*HPL[{0}, S^2])/(3*(1 + S^2)^2) - (8*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2))*Log[T]^8 - (8*Log[T]^9)/(3*(1 + S^2)^2) + (4*(-1 + 9*S^2) + (Pi^2*(29 - 139*S^2 - 44*S^4))/(3*(1 + S^2)^2))*Zeta[3]^2 + (64*(1 + 4*S^2 + 2*S^4)*Zeta[3]^3)/(1 + S^2)^2 + HPL[{3, 1, 2}, -S^2]*((-82*Pi^2*(-1 + S^2))/(3*(1 + S^2)) - (12*(-1 + S^2)*(1 + S^2))/S^2 + 72*Zeta[3]) + HPL[{4, 2}, -S^2]*((12*(-1 - 2*S^2 + S^4))/S^2 + (Pi^2*(-1 - 330*S^2 + 163*S^4))/(3*(1 + S^2)^2) - (24*(-2 + 6*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{5}, -S^2]*((16*Pi^2*(1 + S^2)*(5 + 2*S^2))/(3*S^2) + (8*(60 + 81*S^2 + 37*S^4))/S^2 + (Pi^4*(477 + 2920*S^2 + 1460*S^4))/(90*(1 + S^2)^2) - (4*(2 + 373*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (32*(-15 + 22*S^2 + 11*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*(-25 + 318*S^2 + 159*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-25 + 11*S^2 + 4*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^6*((8*(1 + S^2)^2)/(3*S^2) + (2*Pi^2*(265 - 736*S^2 + 175*S^4))/(27*(1 + S^2)^2) - (40*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (560*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(9*(1 + S^2)^2) - 40*HPL[{2, 1}, -S^2] + (32*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{6}, -S^2]*((Pi^2*(519 + 343*S^2 - 246*S^4))/(3*(1 + S^2)^2) - (4*(-160 - 113*S^2 + 62*S^4))/S^2 - (20*(19 + 40*S^2 + 20*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (52*(11 + 16*S^2 + 8*S^4)*Zeta[3])/(1 + S^2)^2) + Log[T]^6*((2*Pi^2*(46 - 301*S^2 + 45*S^4))/(9*(1 + S^2)^2) - (8*(-11 + 6*S^2 + 3*S^4)*HPL[{0}, S^2]^3)/(9*(1 + S^2)^2) + (56*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) - (224*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) + HPL[{0}, S^2]^2*((2*(-6 + S^2)*(-3 + 17*S^2))/(3*(1 + S^2)^2) - (8*(-31 + 8*S^2 + 4*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2)) - (4*(-1 + S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((8*(1 + S^2)^2)/(3*S^2) - (16*Pi^2*(-40 + 18*S^2 + 9*S^4))/(9*(1 + S^2)^2) + 40*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((8*(1 + S^2))/3 - (4*Pi^2*(-57 + 68*S^2 + 34*S^4))/(9*(1 + S^2)^2) + (56*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) - (112*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) - (8*(-29 + 54*S^2 + 27*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + (16*(-13 + 44*S^2 + 22*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (352*HPL[{2, 1}, -S^2])/3 + (32*(-3 + 22*S^2 + 11*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{3}, -S^2]^2*((2*(-2 + 19*S^2 + 3*S^4))/S^2 + (Pi^2*(-14 - 121*S^2 + 37*S^4))/(3*(1 + S^2)^2) + (24*(-11 + 6*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(5 + 22*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^6*((-5 - 13*S^2)/24 + (Pi^2*(29 - 78*S^2 - 31*S^4))/(96*(1 + S^2)^2) + ((6 - 6*S^2 - S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + ((49 + 10*S^2 + 5*S^4)*HPL[{1}, -S^2]^3)/(36*(1 + S^2)^2) + ((29 - 41*S^2 - 6*S^4)*HPL[{2}, -S^2])/(48*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(-1 + 3*S^2))/(24*S^2) + (Pi^2*(49 + 22*S^2 + 11*S^4))/(48*(1 + S^2)^2) + ((19 + 6*S^2 + 3*S^4)*HPL[{2}, -S^2])/(12*(1 + S^2)^2)) + HPL[{3}, -S^2]/8 + ((-9 - 2*S^2 - S^4)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)^2) + ((14 + 22*S^2 + 11*S^4)*Zeta[3])/(6*(1 + S^2)^2)) + HPL[{5, 1}, -S^2]*((4*(-82 - 101*S^2 + 5*S^4))/S^2 + (2*Pi^2*(-207 - 1119*S^2 + 524*S^4))/(3*(1 + S^2)^2) - (16*(-27 + 26*S^2 + 13*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 2}, -S^2]*((2*Pi^2*(3 - 3*S^2 + 26*S^4))/(3*S^2) + (4*(1 - 4*S^2 + 59*S^4))/S^2 - (2*Pi^4*(-432 + 2458*S^2 + 1229*S^4))/(45*(1 + S^2)^2) - (8*(-681 + 2414*S^2 + 1207*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(23 - 106*S^2 + 23*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]^2*((Pi^2*(-773 + 3788*S^2 - 831*S^4))/(3*(1 + S^2)^2) - (8*(1 + 12*S^2 + S^4))/S^2 - (32*(-27 + 142*S^2 + 71*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4, 1}, -S^2]*((Pi^4*(3267 - 16142*S^2 - 8071*S^4))/(45*(1 + S^2)^2) + (4*Pi^2*(-10 - 14*S^2 + 41*S^4))/(3*S^2) + (4*(-57 - 76*S^2 + 173*S^4))/S^2 - (16*(-923 + 3842*S^2 + 1921*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(59 - 426*S^2 + 99*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^5*((64*(1 + S^2)^2)/(5*S^2) + (4*Pi^2*(5 + 7*S^2))/(15*S^2) + (Pi^4*(12982 - 4426*S^2 - 2213*S^4))/(675*(1 + S^2)^2) + ((-8*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(514 + 158*S^2 + 79*S^4))/(45*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(15*(1 + S^2)^2) - (8*(11 - 88*S^2 + 41*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-241 + 238*S^2 + 119*S^4)*HPL[{4}, -S^2])/(15*(1 + S^2)^2) + (240*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (32*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1}, -S^2])/(15*(1 + S^2)^2) + 240*HPL[{2, 1, 1}, -S^2] - (8*(29 - 188*S^2 + 119*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 1, 1, 1}, -S^2]*((768*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-31 + 19*S^4))/(3*S^2) - (4*Pi^4*(973 + 592*S^2 + 296*S^4))/(9*(1 + S^2)^2) + (32*(133 - 608*S^2 + 129*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^3*((-4*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(21 - 152*S^2 + 42*S^4))/(9*(1 + S^2)^2) + (4*(-62 + 306*S^2 + 153*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (8*(-147 + 136*S^2 + 68*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(-79 + 272*S^2 + 136*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((4*Pi^2*(23 - 4*S^2 + 13*S^4))/(3*S^2) + (16*(15 - 2*S^2 + 15*S^4))/S^2 - (53*Pi^4*(-211 + 80*S^2 + 40*S^4))/(45*(1 + S^2)^2) - (8*(275 - 1076*S^2 + 217*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-576*(-1 + S^2)*(1 + S^2))/S^2 + (32*Pi^2*(74 - 304*S^2 + 57*S^4))/(3*(1 + S^2)^2) + (64*(-143 + 584*S^2 + 292*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1, 1, 1}, -S^2]*((16*(1 + S^2)*(-25 + 11*S^2))/S^2 - (4*Pi^2*(207 - 646*S^2 + 139*S^4))/(3*(1 + S^2)^2) - (32*(-155 + 586*S^2 + 293*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4, 1, 1}, -S^2]*((-8*(1 + S^2)*(-69 + 41*S^2))/S^2 + (2*Pi^2*(665 - 2516*S^2 + 507*S^4))/(3*(1 + S^2)^2) + (32*(-238 + 846*S^2 + 423*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 2, 1}, -S^2]*((-108*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(209 - 1216*S^2 + 295*S^4))/(3*(1 + S^2)^2) + (8*(-307 + 1106*S^2 + 553*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1, 1}, -S^2]*((Pi^4*(31048 - 1730*S^2 - 865*S^4))/(45*(1 + S^2)^2) + (32*(31 + 6*S^2 + 7*S^4))/S^2 + (4*Pi^2*(83 + 11*S^4))/(3*S^2) - (8*(817 - 3418*S^2 + 693*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^5*((11*(1 + S^2))/4 + (Pi^2*(91 + 88*S^2))/72 + (Pi^4*(15195 + 2276*S^2 + 1138*S^4))/(21600*(1 + S^2)^2) + ((605 - 652*S^2 + 47*S^4)*HPL[{1}, -S^2]^3)/(90*(1 + S^2)^2) + ((164 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(45*(1 + S^2)^2) + ((3 + 4*S^2 - 2*S^4)/(12*S^2) + (Pi^2*(345 + 104*S^2 + 52*S^4))/(180*(1 + S^2)^2))*HPL[{2}, -S^2] + ((75 - 4*S^2 - 2*S^4)*HPL[{2}, -S^2]^2)/(40*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((1 + 4*S^2 + 2*S^4)/(4*S^2) + (Pi^2*(1601 + 218*S^2 + 109*S^4))/(360*(1 + S^2)^2) + ((541 - 2*S^2 - S^4)*HPL[{2}, -S^2])/(60*(1 + S^2)^2)) + ((3 + 3*S^2 + 4*S^4)*HPL[{3}, -S^2])/(4*(1 + S^2)^2) + ((-1 - 4*S^2 - 2*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((-755 + 263*S^2 - 66*S^4)*HPL[{2, 1}, -S^2])/(60*(1 + S^2)^2) + (3*(-25 + 8*S^2 + 4*S^4)*HPL[{3, 1}, -S^2])/(10*(1 + S^2)^2) + ((270 - 2*S^2 - S^4)*HPL[{2, 1, 1}, -S^2])/(15*(1 + S^2)^2) + ((25 + 24*S^2 + 11*S^4)*Zeta[3])/(4*(1 + S^2)^2) + HPL[{1}, -S^2]*((2 + 9*S^2 + 5*S^4)/(4*S^2) + (Pi^2*(1865 - 862*S^2 + 257*S^4))/(360*(1 + S^2)^2) + ((280 - 211*S^2 + 51*S^4)*HPL[{2}, -S^2])/(30*(1 + S^2)^2) + ((1 - 2*S^2 - S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) + ((-541 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(30*(1 + S^2)^2) + ((5 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2)) + Log[T]^5*((4*Pi^2*(-1 + S^2))/3 + (Pi^4*(-14057 + 2276*S^2 + 1138*S^4))/(675*(1 + S^2)^2) + (2*(-163 + 4*S^2 + 2*S^4)*HPL[{0}, S^2]^4)/(45*(1 + S^2)^2) - (112*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + (112*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^3*((-2*(271 - 1153*S^2 + 256*S^4))/(45*(1 + S^2)^2) + (4*(-151 + 34*S^2 + 17*S^4)*HPL[{1}, -S^2])/(9*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-8*(1 + S^2)^2)/S^2 + (16*Pi^2*(-40 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2) - 120*HPL[{2}, -S^2]) + ((8*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-15 + 28*S^2 + 14*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (8*(-77 + 20*S^2 + 10*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^2*(4*(-1 + S^2) + (2*Pi^2*(-746 + 218*S^2 + 109*S^4))/(45*(1 + S^2)^2) - (8*(59 - 137*S^2 + 14*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + (8*(-31 + 8*S^2 + 4*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (4*(-22 + 14*S^2 + 7*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (8*(29 - 1157*S^2 + 914*S^4)*HPL[{3}, -S^2])/(15*(1 + S^2)^2) - (16*(-29 + 62*S^2 + 31*S^4)*HPL[{4}, -S^2])/(5*(1 + S^2)^2) - (472*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (64*(4 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + 224*HPL[{2, 1, 1}, -S^2] + (8*(-53*S^2 + 59*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{0}, S^2]*(-16*(1 + S^2) - (2*Pi^2*(586 - 3463*S^2 + 1411*S^4))/(45*(1 + S^2)^2) - (56*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 + (224*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) - (4*(61 - 376*S^2 + 235*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-8*(1 + S^2)^2)/S^2 + (4*Pi^2*(-445 + 202*S^2 + 101*S^4))/(9*(1 + S^2)^2) + (8*(-87 + 50*S^2 + 25*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) - (8*(-1 + 10*S^2 + 5*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (32*(29 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (48*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-16*(1 + S^2)^2)/S^2 - (4*Pi^2*(265 - 736*S^2 + 175*S^4))/(9*(1 + S^2)^2) + (240*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (1120*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + 240*HPL[{2, 1}, -S^2] - (64*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2)) + (-20*(-17 + 19*S^2) - (2*Pi^2*(-44 + 53*S^2))/3 + (1564*Pi^4*(1 + 4*S^2 + 2*S^4))/(45*(1 + S^2)^2))*Zeta[5] + HPL[{3}, -S^2]*((-32*(1 + S^2)*(-13 + 3*S^2))/S^2 + (Pi^4*(41 + 5*S^2 - 68*S^4))/(45*S^2) - (4*Pi^2*(-16 - 7*S^2 + 17*S^4))/(3*S^2) + (Pi^6*(-4132 + 29702*S^2 + 14851*S^4))/(3780*(1 + S^2)^2) + ((-10*Pi^2*(-7 + 8*S^2 + 4*S^4))/(3*(1 + S^2)^2) + (4*(1 + 8*S^2 + 8*S^4))/S^2)*HPL[{4}, -S^2] + (4*(-19 + 46*S^2 + 51*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (4*(131 + 188*S^2 + 94*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (4*(-405 + 1246*S^2 + 623*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((8*(1 + 2*S^2 + 11*S^4))/S^2 - (4*Pi^2*(-135 + 652*S^2 + 326*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(-39 - 304*S^2 + 71*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*(73 + 61*S^2 + 124*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (4*(-19 + 52*S^2 + 26*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (8*(31 + 20*S^2 + 10*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (-192*S^2 + (4*Pi^2*(-79 + 454*S^2 + 227*S^4))/(1 + S^2)^2)*HPL[{2, 1, 1}, -S^2] - (16*(157 - 743*S^2 + 128*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(941 - 4232*S^2 + 683*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 24*HPL[{3, 1, 2}, -S^2] + (40*(-49 + 246*S^2 + 123*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(-10269 + 40958*S^2 + 20479*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(333 - 1216*S^2 + 191*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-241 + 1262*S^2 + 631*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (192*(-38 + 214*S^2 + 107*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-5 + 11*S^2) - (4*Pi^2*(-2 - 59*S^2 + 7*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (4*(-1 + 42*S^2 + 21*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((8*(-3 + 12*S^2 + 5*S^4))/S^2 + (2*Pi^2*(353 - 1269*S^2 + 214*S^4))/(3*(1 + S^2)^2) + (8*(59 + 42*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) - (8*(-4 - 35*S^2 + 17*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{4}, -S^2]*((-4*(1 + S^2)*(-100 + 21*S^2))/S^2 + (Pi^4*(231 + 893*S^2 - 710*S^4))/(45*(1 + S^2)^2) - (2*Pi^2*(-29 - 8*S^2 + 11*S^4))/(3*S^2) - (4*(169 + 252*S^2 + 126*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-4*(1 + 9*S^4))/S^2 + (4*Pi^2*(132 + 38*S^2 + 19*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(-11 - 311*S^2 + 172*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (120*(2 + 10*S^2 + 5*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(3 + 304*S^2 + 152*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (4*(-19 - 662*S^2 + 317*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-137 + 62*S^2 + 31*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(-399 + 110*S^2 + 55*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(73 + 26*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((4*Pi^2*(-6 + 2*S^2 + S^4))/(1 + S^2)^2 - (8*(-1 + 3*S^2 + 5*S^4))/S^2)*Zeta[3] - (8*(29 + 42*S^2 + 21*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*((-2*Pi^2*(-1 - 9*S^2 + 2*S^4))/(3*S^2) + (2*(5 - 22*S^2 + 5*S^4))/S^2 + (Pi^4*(2004 - 9392*S^2 + 1907*S^4))/(180*(1 + S^2)^2) + ((-2*(-1 + 9*S^4))/S^2 + (Pi^2*(-202 + 662*S^2 + 331*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (6*(-5 - 90*S^2 + 27*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(11 + 216*S^2 + 108*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((20*(-1 + S^2)*(1 + S^2))/S^2 - (86*Pi^2*(9 + 8*S^2 + 4*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(31 - 135*S^2 + 2*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (20*(-27 + 118*S^2 + 59*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*(-509 + 1898*S^2 + 949*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (116*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (16*(-147 + 136*S^2 + 68*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (4*(-1359 + 386*S^2 + 193*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 2464*HPL[{2, 1, 1, 1}, -S^2] + ((-2*(1 + 4*S^2 + 11*S^4))/S^2 + (Pi^2*(-35 + 216*S^2 + 108*S^4))/(1 + S^2)^2)*Zeta[3] + (14*(-7 + 88*S^2 + 44*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((392*(1 + S^2)^2)/(3*S^2) + (4*Pi^2*(47 + 73*S^2 + 10*S^4))/(9*S^2) - (2*Pi^4*(-104 - 104*S^2 + 67*S^4))/(135*S^2) - (11*Pi^6*(-50011 + 10858*S^2 + 5429*S^4))/(34020*(1 + S^2)^2) + ((8*(3 + 5*S^2 + 3*S^4))/(3*S^2) - (2*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (124*HPL[{2}, -S^2]^3)/3 - (4*(-119 + 74*S^2 + 37*S^4)*HPL[{3}, -S^2]^2)/(3*(1 + S^2)^2) + ((32*(1 + S^2))/S^2 + (2*Pi^2*(-457 + 558*S^2 + 279*S^4))/(9*(1 + S^2)^2))*HPL[{4}, -S^2] - (8*(-103 - 386*S^2 + 173*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + (4*(175 + 566*S^2 + 283*S^4)*HPL[{6}, -S^2])/(3*(1 + S^2)^2) + (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^2) + ((32*(1 + S^2)*(-3 + 2*S^2))/S^2 - (16*Pi^2*(185 + 122*S^2 + 61*S^4))/(9*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (16*(157 - 1054*S^2 + 529*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) + (16*(493 - 3694*S^2 + 1753*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) - (12*(-43 + 26*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (32*(-241 + 238*S^2 + 119*S^4)*HPL[{5, 1}, -S^2])/(3*(1 + S^2)^2) + ((-160*(-1 + S^2)*(1 + S^2))/S^2 + (16*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (32*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) + (64*(144 - 307*S^2 + 69*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 992*HPL[{3, 2, 1}, -S^2] + (64*(19 + 398*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(3*(1 + S^2)^2) + (4800*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - (128*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*(1 + S^2)^2) + 4800*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-8*(1 + 28*S^2 + 49*S^4))/(3*S^2) - (8*Pi^2*(25 - 174*S^2 + 111*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (16*(-16 + 10*S^2 + 5*S^4)*Zeta[3]^2)/(3*(1 + S^2)^2) + HPL[{3}, -S^2]*((-8*(-19 - 2*S^2 + 29*S^4))/(3*S^2) - (4*Pi^2*(135 - 1408*S^2 + 657*S^4))/(9*(1 + S^2)^2) - (16*(-581 + 578*S^2 + 289*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (224*(-3 + 2*S^2 + S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((128*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(9*(1 + S^2)^2) - (32*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-296*(-1 + S^2)*(1 + S^2))/(3*S^2) - (4*Pi^2*(-30 - 5*S^2 + 24*S^4))/(9*S^2) + (Pi^4*(14677 + 2274*S^2 + 1137*S^4))/(270*(1 + S^2)^2) - (8*(157 - 1054*S^2 + 529*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (4*(-367 + 226*S^2 + 113*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (32*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(151 - 1054*S^2 + 535*S^4)*Zeta[3])/(3*(1 + S^2)^2)) - (32*(9 - 71*S^2 + 65*S^4)*Zeta[5])/(1 + S^2)^2) + Log[T]^4*((-4*Pi^2*(-5 + 3*S^2))/3 + (Pi^4*(4018 - 23463*S^2 + 2909*S^4))/(270*(1 + S^2)^2) + ((165 + 4*S^2 + 2*S^4)*HPL[{0}, S^2]^5)/(45*(1 + S^2)^2) + (140*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) - (112*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^4*((71 - 252*S^2 + 7*S^4)/(9*(1 + S^2)^2) - (5*(-65 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(9*(1 + S^2)^2)) + (4*(131 - 608*S^2 + 131*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((40*(1 + S^2)^2)/(3*S^2) - (80*Pi^2*(-40 + 18*S^2 + 9*S^4))/(9*(1 + S^2)^2) + 200*HPL[{2}, -S^2]) + HPL[{0}, S^2]^3*((4*(3 + S^2))/3 - (2*Pi^2*(-330 + 86*S^2 + 43*S^4))/(27*(1 + S^2)^2) + (20*(18 - 33*S^2 + 5*S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) - (10*(-151 + 34*S^2 + 17*S^4)*HPL[{1}, -S^2]^2)/(9*(1 + S^2)^2) - (2*(-292 + 166*S^2 + 83*S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2)) + ((-8*(-1 - S^2 + 4*S^4))/S^2 + (4*Pi^2*(-197 + 706*S^2 + 353*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] - (4*(-13 - 178*S^2 + 75*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(-5 + 218*S^2 + 109*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + ((40*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(803 + 736*S^2 + 368*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(13 - 89*S^2 + 18*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-83 + 414*S^2 + 207*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (16*(-496 + 1978*S^2 + 989*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) - (40*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (32*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (128*(-56 + 18*S^2 + 9*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 3520*HPL[{2, 1, 1, 1}, -S^2] + (-40*(-1 + S^2) + (4*Pi^2*(-97 + 736*S^2 + 368*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*((40*(1 + S^2)^2)/S^2 + (10*Pi^2*(265 - 736*S^2 + 175*S^4))/(9*(1 + S^2)^2) - (600*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (2800*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 600*HPL[{2, 1}, -S^2] + (160*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^2*(-4*(-5 + 3*S^2) + (Pi^2*(554 - 2583*S^2 + 283*S^4))/(18*(1 + S^2)^2) + (20*(59 - 137*S^2 + 14*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) - (40*(-31 + 8*S^2 + 4*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + ((281 - 1216*S^2 + 243*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-2*(-5 - 4*S^2 + 5*S^4))/S^2 - (10*Pi^2*(-158 + 26*S^2 + 13*S^4))/(9*(1 + S^2)^2) - (2*(-803 + 134*S^2 + 67*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + (4*(-2 + 46*S^2 + 23*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (4*(473 + 76*S^2 + 38*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(-7 + 76*S^2 + 38*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]*((64*(1 + S^2)^2)/S^2 + (4*Pi^2*(5 + 7*S^2))/(3*S^2) + (Pi^4*(12982 - 4426*S^2 - 2213*S^4))/(135*(1 + S^2)^2) + ((-40*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (40*(11 - 88*S^2 + 41*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-241 + 238*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (1200*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (32*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + 1200*HPL[{2, 1, 1}, -S^2] - (40*(29 - 188*S^2 + 119*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-24*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(74 - 304*S^2 + 57*S^4))/(9*(1 + S^2)^2) + (8*(-38 + 214*S^2 + 107*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (16*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(-143 + 584*S^2 + 292*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{0}, S^2]*(64*(1 + S^2) + (2*Pi^2*(11 + 7*S^2))/3 + (Pi^4*(9885 - 8344*S^2 - 4172*S^4))/(270*(1 + S^2)^2) + (280*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) - (280*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + ((4*(5 + 6*S^2 + 5*S^4))/S^2 - (2*Pi^2*(-727 + 976*S^2 + 488*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] - (4*(-239 + 392*S^2 + 196*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((20*(1 + S^2)^2)/S^2 - (10*Pi^2*(-445 + 202*S^2 + 101*S^4))/(9*(1 + S^2)^2) - (20*(-87 + 50*S^2 + 25*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (4*(45 + 113*S^2 + 8*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (8*(-7 + 6*S^2 + 3*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (20*(235 - 376*S^2 + 61*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(-437 + 806*S^2 + 403*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (80*(-29 + 54*S^2 + 27*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(-89*S^2 + 31*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*((40*(1 + S^2)^2)/S^2 + (10*Pi^2*(85 - 220*S^2 + 59*S^4))/(3*(1 + S^2)^2) + (80*(37 - 94*S^2 + 37*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + (8*(-23 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (40*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(-137 + 86*S^2 + 43*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + (40*(-13 + 148*S^2 + 74*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{0}, S^2]^4*((Pi^2*(-23 - 108*S^2))/36 + (27 - 37*S^2)/4 + (Pi^4*(6673 - 18414*S^2 - 5317*S^4))/(4320*(1 + S^2)^2) + ((175 - 266*S^2 - S^4)*HPL[{1}, -S^2]^4)/(12*(1 + S^2)^2) + ((65 - 2*S^2 - S^4)*HPL[{1}, -S^2]^5)/(9*(1 + S^2)^2) + ((109 - 388*S^2 + 45*S^4)*HPL[{2}, -S^2]^2)/(24*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((15 + 10*S^2 - 9*S^4)/(18*S^2) + (5*Pi^2*(277 + 26*S^2 + 13*S^4))/(108*(1 + S^2)^2) + (4*(69 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2)) + ((1 - S^2)/(2*S^2) + (Pi^2*(10 + 22*S^2 + 11*S^4))/(12*(1 + S^2)^2))*HPL[{3}, -S^2] + ((5 - 12*S^2)*HPL[{4}, -S^2])/(2*(1 + S^2)) + ((19 + 36*S^2 + 18*S^4)*HPL[{5}, -S^2])/(2*(1 + S^2)^2) + ((-15 - 4*S^2 - 2*S^4)/(6*S^2) - (4*Pi^2*(35 + 6*S^2 + 3*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(91 - 170*S^2 - 5*S^4))/(18*(1 + S^2)^2) + (9 - 4*S^2 - 4*S^4)/(6*S^2) - HPL[{3}, -S^2]/(2*(1 + S^2)^2) + ((-283 - 24*S^2 - 12*S^4)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)^2)) + ((-142 + 373*S^2 - 15*S^4)*HPL[{3, 1}, -S^2])/(6*(1 + S^2)^2) + HPL[{3, 2}, -S^2]/(1 + S^2)^2 - (3*(2 + 6*S^2 + 3*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + ((293 - 745*S^2 + 50*S^4)*HPL[{2, 1, 1}, -S^2])/(6*(1 + S^2)^2) + ((283 + 24*S^2 + 12*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) + ((288 + 38*S^2 + 19*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(145 + 18*S^2 + 9*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((-7*(1 + 4*S^2))/6 + (Pi^2*(465 + 736*S^2 + 368*S^4))/(36*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]*((-4*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(15 - 10*S^2 - 27*S^4))/(36*S^2) + (Pi^4*(2357 + 760*S^2 + 380*S^4))/(432*(1 + S^2)^2) + ((15 + S^2 - 4*S^4)/(6*S^2) + (Pi^2*(561 + 98*S^2 + 49*S^4))/(36*(1 + S^2)^2))*HPL[{2}, -S^2] + ((263 - 16*S^2 - 8*S^4)*HPL[{2}, -S^2]^2)/(12*(1 + S^2)^2) + ((11 + 4*S^2 - 11*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) + 6*HPL[{4}, -S^2] + ((-258 + 285*S^2 - S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (5*(55 + 4*S^2 + 2*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(69 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((77 - 26*S^2 - 75*S^4)*Zeta[3])/(6*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((Pi^2*(415 - 506*S^2 - 41*S^4))/(24*(1 + S^2)^2) + (30 + 17*S^2 - 17*S^4)/(12*S^2) + ((258 - 285*S^2 + S^4)*HPL[{2}, -S^2])/(6*(1 + S^2)^2) + ((2 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(69 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + ((26 + 38*S^2 + 19*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + (5*(87 + 148*S^2 + 74*S^4)*Zeta[5])/(6*(1 + S^2)^2)) + Zeta[3]*((Pi^4*(142 - 325*S^2))/90 - 32*(-9 + 16*S^2) - 2*Pi^2*(-13 + 19*S^2) + (1847*Pi^6*(1 + 4*S^2 + 2*S^4))/(567*(1 + S^2)^2) - (4*(-31 + 135*S^2 + 106*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*((148*(1 + S^2)^2)/(3*S^2) + (Pi^2*(59 + 92*S^2 + 11*S^4))/(9*S^2) + (Pi^4*(3904 - 9634*S^2 + 1657*S^4))/(135*(1 + S^2)^2) + (2*(343 - 1054*S^2 + 343*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + ((-8*(-6 + 2*S^2 + 9*S^4))/(3*S^2) + (2*Pi^2*(-721 + 758*S^2 + 379*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] - (8*(11 - 266*S^2 + 83*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (4*(-35 + 82*S^2 + 41*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((40*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(-89 - 133*S^2 + 136*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(-581 + 578*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) - (16*(-992 + 986*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) - (1200*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (32*(-661 + 238*S^2 + 119*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) - 1200*HPL[{2, 1, 1, 1}, -S^2] + (-8*(3 + 5*S^2) + (2*Pi^2*(-593 + 674*S^2 + 337*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-32*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(1051 - 1054*S^2 - 365*S^4))/(9*(1 + S^2)^2) + (4*(-581 + 578*S^2 + 289*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (16*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + (8*(-256 + 358*S^2 + 179*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-4*(1 + S^2)*(74 + 5*S^2))/S^2 + (Pi^4*(-1214 + 3753*S^2 - 340*S^4))/(45*(1 + S^2)^2) + (2*Pi^2*(-46 - 33*S^2 + 25*S^4))/(3*S^2) + (128*(-20 + 78*S^2 + 39*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (32*(-227 + 970*S^2 + 485*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (64*(76 - 304*S^2 + 55*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (48*(61 + 234*S^2 + 117*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (128*(-613 + 318*S^2 + 159*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(-268 + 334*S^2 + 167*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((16*(1 + 5*S^4))/S^2 - (4*Pi^2*(-172 + 642*S^2 + 321*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-118 + 574*S^2 + 287*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-276*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-18 - 6*S^2 + 17*S^4))/(3*S^2) + (Pi^4*(5698 - 19055*S^2 + 2327*S^4))/(90*(1 + S^2)^2) - 9856*HPL[{2, 2, 1}, -S^2] - (192*(192 + 94*S^2 + 47*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (128*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-16*(1 + 11*S^4))/S^2 + (16*Pi^2*(-78 + 322*S^2 + 161*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (16*(-89 + 630*S^2 + 315*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((512*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^6*(-197477 - 93760*S^2 - 46880*S^4))/(11340*(1 + S^2)^2) + (4*Pi^2*(-47 + S^2 + 32*S^4))/(3*S^2) + (Pi^4*(-426 + 20*S^2 + 187*S^4))/(90*S^2) + ((-1348*Pi^2*(-3 + 2*S^2 + S^4))/(3*(1 + S^2)^2) + (16*(5 + 7*S^4))/S^2)*HPL[{3, 1}, -S^2] - (8*(289 - 1368*S^2 + 231*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*(1903 - 8254*S^2 + 1219*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (24*(-53 + 6*S^2 + 3*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (8*(675 + 38*S^2 + 19*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((192*(1 + S^4))/S^2 - (32*Pi^2*(-262 + 150*S^2 + 75*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (464*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (32*(123 - 608*S^2 + 139*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (24*(-43 + 26*S^2 + 13*S^4)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(-1047 + 1010*S^2 + 505*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (64*(-368 + 434*S^2 + 217*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(131 - 608*S^2 + 131*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(-268 + 334*S^2 + 167*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (128*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(6 + S^2) + (2*Pi^2*(260 - 1391*S^2 + 261*S^4))/(3*(1 + S^2)^2))*Zeta[3] - 80*Zeta[3]^2 + (4*(170 - 1087*S^2 + 359*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{0}, S^2]^3*((178*(1 + S^2))/3 + (Pi^2*(231 + 199*S^2))/18 + (Pi^4*(1798 + 1669*S^2))/540 + (Pi^6*(2904 + 82*S^2 + 41*S^4))/(1296*(1 + S^2)^2) + (4*(18 - 33*S^2 + 5*S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) - (2*(-151 + 34*S^2 + 17*S^4)*HPL[{1}, -S^2]^6)/(27*(1 + S^2)^2) + ((Pi^2*(500 - 174*S^2 - 87*S^4))/(36*(1 + S^2)^2) + (1 + 10*S^2 + 3*S^4)/(6*S^2))*HPL[{2}, -S^2]^2 - (14*(-1 + S^2)*(3 + S^2)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((Pi^2*(1411 - 162*S^2 - 81*S^4))/(54*(1 + S^2)^2) + (2*(7 + 13*S^2 + 5*S^4))/(9*S^2) - (2*(-113 + 24*S^2 + 12*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-19 - 26*S^2 - 13*S^4)*HPL[{3}, -S^2]^2)/(3*(1 + S^2)^2) + ((Pi^2*(-2 - 74*S^2 - 37*S^4))/(9*(1 + S^2)^2) + (9 + 18*S^2 - S^4)/(3*S^2))*HPL[{4}, -S^2] + ((38 + 95*S^2 + 113*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) - (2*(4 + 5*S^2)*(6 + 5*S^2)*HPL[{6}, -S^2])/(1 + S^2)^2 + (2*(-275 + 162*S^2 + 81*S^4)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^2) + ((-4*(9 + 9*S^2 + S^4))/(3*S^2) + (Pi^2*(-512 + 246*S^2 + 123*S^4))/(9*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (8*(-1 + S^2)*(-1 + 4*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) - (4*(22 + 49*S^2 + 7*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + (2*(-1 + 4*S^2 + 2*S^4)*HPL[{4, 2}, -S^2])/(3*(1 + S^2)^2) + (4*(5 + 58*S^2 + 29*S^4)*HPL[{5, 1}, -S^2])/(3*(1 + S^2)^2) + ((16*(1 + S^2)*(4 + S^2))/(3*S^2) - (4*Pi^2*(-281 + 84*S^2 + 42*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (2*(735 - 622*S^2 + 67*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) + (2*(2291 - 1810*S^2 + 243*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (4*HPL[{3, 1, 2}, -S^2])/3 - (4*(-251 + 170*S^2 + 85*S^4)*HPL[{3, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(-391 + 266*S^2 + 133*S^4)*HPL[{4, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(405 - 304*S^2 + 41*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(-287 + 174*S^2 + 87*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(-292 + 166*S^2 + 83*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((2*(22 + 19*S^2))/3 + (Pi^2*(416 + 419*S^2 + 155*S^4))/(18*(1 + S^2)^2))*Zeta[3] + (14*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2}, -S^2]*((Pi^2*(31 + 40*S^2 - 6*S^4))/(18*S^2) + (Pi^4*(2017 + 26*S^2 + 13*S^4))/(270*(1 + S^2)^2) + (2*(18 + 47*S^2 + 13*S^4))/(3*S^2) + ((-4 + 21*S^2 - 15*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (2*(19 + 24*S^2 + 12*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + ((-735 + 622*S^2 - 67*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(-143 + 70*S^2 + 35*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (4*(-275 + 162*S^2 + 81*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((26 + 13*S^2 - 33*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((Pi^4*(4941 + 14*S^2 + 7*S^4))/(270*(1 + S^2)^2) + (2*(25 + 63*S^2 + 22*S^4))/(3*S^2) + (Pi^2*(29 + 86*S^2 + 40*S^4))/(18*S^2) + ((Pi^2*(1219 - 146*S^2 - 73*S^4))/(18*(1 + S^2)^2) + (31 + 30*S^2 + 11*S^4)/(3*S^2))*HPL[{2}, -S^2] - (2*(-159 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + (8*(10 + 8*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (2*(-29 + 22*S^2 + 11*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (2*(551 - 770*S^2 + 179*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(-168 + 38*S^2 + 19*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(-113 + 24*S^2 + 12*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(-21 - 33*S^2 + 2*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((15 + 37*S^2 + 4*S^4)/(3*S^2) + (Pi^2*(88 + 73*S^2 + 81*S^4))/(18*(1 + S^2)^2) + (4*(17 + 14*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(5 + 8*S^2 + 4*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((Pi^2*(-1565 + 871*S^2 - 148*S^4))/(18*(1 + S^2)^2) - (4*(15 + 9*S^2 + 5*S^4))/(3*S^2) - (4*(7 + 24*S^2 + 12*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((2*(29 + 62*S^2 + 21*S^4))/(9*S^2) + (Pi^2*(1145 - 1642*S^2 + 197*S^4))/(27*(1 + S^2)^2) + (2*(551 - 770*S^2 + 179*S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2) + (8*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-113 + 24*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(3 + 34*S^2 + 17*S^4)*Zeta[3])/(9*(1 + S^2)^2)) + (4*(95 + 114*S^2 + 58*S^4)*Zeta[5])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(59 + 197*S^2 + 96*S^4))/(18*S^2) + (85 + 254*S^2 + 105*S^4)/(3*S^2) + (Pi^4*(9805 - 8176*S^2 + 1755*S^4))/(540*(1 + S^2)^2) + ((237 - 404*S^2 + 71*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + ((2*(1 + S^2)*(13 + S^2))/(3*S^2) + (Pi^2*(11 - 10*S^2 - 5*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(51 + 32*S^2 + 61*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (2*(13 + 82*S^2 + 41*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + ((-2*(31 + 30*S^2 + 11*S^4))/(3*S^2) + (Pi^2*(-1219 + 146*S^2 + 73*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(277 - 372*S^2 + 99*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (4*(-19 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) + (16*(7 + 4*S^2 + 2*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(551 - 770*S^2 + 179*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(-159 + 38*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(-162 + 38*S^2 + 19*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-113 + 24*S^2 + 12*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((2*(20 + 19*S^2))/3 + (Pi^2*(153 + 154*S^2 + 77*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((53 + 64*S^2 + 23*S^4)/(3*S^2) + (Pi^2*(1111 - 1192*S^2 + 281*S^4))/(18*(1 + S^2)^2) + (2*(-19 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (8*(-159 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (2*(13 + 46*S^2 + 23*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + (4*(67 + 56*S^2 + 28*S^4)*Zeta[5])/(3*(1 + S^2)^2))) + Log[T]^3*((8*Pi^2*(-24 + 13*S^2))/9 + (Pi^4*(-322 + 383*S^2))/135 + (Pi^6*(-2863 + 82*S^2 + 41*S^4))/(162*(1 + S^2)^2) + ((-14 - 6*S^2 - 3*S^4)*HPL[{0}, S^2]^6)/(9*(1 + S^2)^2) - (112*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) + (224*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^6)/(9*(1 + S^2)^2) + HPL[{0}, S^2]^5*((-365 + 861*S^2 - 78*S^4)/(90*(1 + S^2)^2) - (4*(164 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(45*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((-40*(1 + S^2)^2)/(3*S^2) + (80*Pi^2*(-40 + 18*S^2 + 9*S^4))/(9*(1 + S^2)^2) - 200*HPL[{2}, -S^2]) + (-80/3 + (4*Pi^2*(-567 + 214*S^2 + 107*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (488*HPL[{2}, -S^2]^3)/9 + HPL[{0}, S^2]^4*((-16 + 11*S^2)/9 + (Pi^2*(-373 - 86*S^2 - 43*S^4))/(27*(1 + S^2)^2) + ((-175 + 266*S^2 + S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + (10*(-65 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(9*(1 + S^2)^2) + (2*(-131 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2)) + (8*(-37 + 82*S^2 + 41*S^4)*HPL[{3}, -S^2]^2)/(3*(1 + S^2)^2) + ((8*(-5 + S^2)*(1 + S^2))/S^2 - (92*Pi^2*(-7 + 18*S^2 + 9*S^4))/(9*(1 + S^2)^2))*HPL[{4}, -S^2] + (8*(-127 - 342*S^2 + 241*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) - (8*(97 + 302*S^2 + 151*S^4)*HPL[{6}, -S^2])/(3*(1 + S^2)^2) - (160*(-77 + 20*S^2 + 10*S^4)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^2) + ((-32*(1 + S^2)*(-3 + 2*S^2))/S^2 - (16*Pi^2*(-43 + 162*S^2 + 81*S^4))/(9*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (32*(1 - 446*S^2 + 423*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) - (32*(13 - 1603*S^2 + 1354*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(-29 + 110*S^2 + 55*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (32*(-139 + 442*S^2 + 221*S^4)*HPL[{5, 1}, -S^2])/(3*(1 + S^2)^2) + ((160*(-1 + S^2)*(1 + S^2))/S^2 + (80*Pi^2*(-15 + 28*S^2 + 14*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (128*(106 - 223*S^2 + 106*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (32*(1243 - 1519*S^2 + 358*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) - 224*HPL[{3, 1, 2}, -S^2] + (3232*HPL[{3, 2, 1}, -S^2])/3 + (1920*(3 + 2*S^2 + S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (9440*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - (1280*(4 + 2*S^2 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 4480*HPL[{2, 1, 1, 1, 1}, -S^2] + (32*(-3 + 5*S^2) + (4*Pi^2*(-11 - 888*S^2 + 983*S^4))/(9*(1 + S^2)^2))*Zeta[3] - (112*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((-160*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-903 + 446*S^2 + 479*S^4))/(9*(1 + S^2)^2) - (4640*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^3*((-4*(37 + 15*S^2))/9 - (2*Pi^2*(318 - 1007*S^2 + 167*S^4))/(27*(1 + S^2)^2) - (40*(18 - 33*S^2 + 5*S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + (40*(-151 + 34*S^2 + 17*S^4)*HPL[{1}, -S^2]^3)/(27*(1 + S^2)^2) - (8*(73 - 233*S^2 + 69*S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*((-8*(7 + 13*S^2 + 5*S^4))/(9*S^2) + (2*Pi^2*(-1411 + 162*S^2 + 81*S^4))/(27*(1 + S^2)^2) + (8*(-113 + 24*S^2 + 12*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) - (8*(4 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (8*(386 + 22*S^2 + 11*S^4)*HPL[{2, 1}, -S^2])/(9*(1 + S^2)^2) - (56*(1 + 4*S^2 + 2*S^4)*Zeta[3])/(9*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-160*(1 + S^2)^2)/(3*S^2) - (40*Pi^2*(265 - 736*S^2 + 175*S^4))/(27*(1 + S^2)^2) + (800*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (11200*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(9*(1 + S^2)^2) + 800*HPL[{2, 1}, -S^2] - (640*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((8*(-15 - 14*S^2 + 45*S^4))/(3*S^2) + (4*Pi^2*(-13 - 1245*S^2 + 968*S^4))/(9*(1 + S^2)^2) - (32*(467 + 64*S^2 + 32*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(-37 + 38*S^2 + 19*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-128*(1 + S^2)^2)/S^2 - (8*Pi^2*(5 + 7*S^2))/(3*S^2) + (2*Pi^4*(-12982 + 4426*S^2 + 2213*S^4))/(135*(1 + S^2)^2) + ((80*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] + (16*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + (80*(11 - 88*S^2 + 41*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (16*(-241 + 238*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (2400*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (64*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - 2400*HPL[{2, 1, 1}, -S^2] + (80*(29 - 188*S^2 + 119*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((208*(-1 + S^2)*(1 + S^2))/(3*S^2) + (4*Pi^2*(-29 - 10*S^2 + 29*S^4))/(9*S^2) + (Pi^4*(-4947 + 3646*S^2 + 1823*S^4))/(135*(1 + S^2)^2) + (8*(-19 - 892*S^2 + 867*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (40*(-5 + 22*S^2 + 11*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (64*(106 - 223*S^2 + 106*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (928*(-14 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (320*(-77 + 20*S^2 + 10*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + (32*(9 - 223*S^2 + 203*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((8*(-24 + 13*S^2))/3 + (2*Pi^2*(-31 + 26*S^2))/9 + (Pi^4*(-9868 + 34*S^2 + 17*S^4))/(270*(1 + S^2)^2) - (80*(59 - 137*S^2 + 14*S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) + (40*(-31 + 8*S^2 + 4*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + ((8*(-7 - 5*S^2 + 7*S^4))/(3*S^2) + (2*Pi^2*(-592 + 230*S^2 + 115*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(-182 + 114*S^2 + 57*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((4*(-5 - 4*S^2 + 5*S^4))/S^2 + (20*Pi^2*(-158 + 26*S^2 + 13*S^4))/(9*(1 + S^2)^2) + (4*(-803 + 134*S^2 + 67*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + (8*(-21 - 44*S^2 + 27*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (4*(13 + 42*S^2 + 21*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (4*(-921 + 892*S^2 + 73*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(-163 + 102*S^2 + 51*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (80*(-22 + 14*S^2 + 7*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-11 - 93*S^2 + 98*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((4*(-29 - 32*S^2 + 19*S^4))/(3*S^2) - (2*Pi^2*(1115 - 2168*S^2 + 137*S^4))/(9*(1 + S^2)^2) - (4*(601 - 1054*S^2 + 85*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) - (8*(-21 + 58*S^2 + 29*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (8*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(-53 + 74*S^2 + 37*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + (32*(-4 - 174*S^2 + 265*S^4)*Zeta[5])/(3*(1 + S^2)^2) + HPL[{0}, S^2]*((-592*(1 + S^2))/3 - (4*Pi^2*(67 + 45*S^2))/9 + (Pi^4*(-7994 + 35835*S^2 - 12399*S^4))/(270*(1 + S^2)^2) - (280*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + (224*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) - (4*(147 - 1054*S^2 + 539*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-80*(1 + S^2)^2)/(3*S^2) + (40*Pi^2*(-445 + 202*S^2 + 101*S^4))/(27*(1 + S^2)^2) + (80*(-87 + 50*S^2 + 25*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-8*(9 + 8*S^2 + 9*S^4))/(3*S^2) - (4*Pi^2*(19 + 62*S^2 + 31*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] - (4*(31 - 6*S^2 + 43*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (32*(-13 + 2*S^2 + S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + ((16*(5 + 6*S^2 + 5*S^4))/S^2 + (8*Pi^2*(1256 + 82*S^2 + 41*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(50 - 313*S^2 + 197*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*(-93 + 158*S^2 + 79*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) + (32*(-49 + 100*S^2 + 50*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) - (80*(61 - 376*S^2 + 235*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (9280*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (160*(521 + 10*S^2 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) + (640*(29 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-16*(1 + S^2) - (8*Pi^2*(-38 + 118*S^2 + 59*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-8*(19 + 28*S^2 + 31*S^4))/(3*S^2) - (2*Pi^2*(597 - 2812*S^2 + 1451*S^4))/(9*(1 + S^2)^2) - (8*(-49 + 74*S^2 + 37*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (4640*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (16*(-15 + 28*S^2 + 14*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-128*(1 + S^2)^2)/S^2 - (4*Pi^2*(29 + 56*S^2 + 25*S^4))/(9*S^2) + (2*Pi^4*(-11996 + 4122*S^2 + 2061*S^4))/(135*(1 + S^2)^2) + ((-16*(5 + 6*S^2 + 5*S^4))/S^2 + (4*Pi^2*(-661 + 298*S^2 + 149*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (16*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (32*(4 + 19*S^2 + 5*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-91 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (320*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (224*(-31 + 18*S^2 + 9*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (160*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(22 - 133*S^2 + 25*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-80*(1 + S^2)^2)/S^2 - (20*Pi^2*(85 - 220*S^2 + 59*S^4))/(3*(1 + S^2)^2) - (160*(37 - 94*S^2 + 37*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) - (16*(-23 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (80*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (16*(-137 + 86*S^2 + 43*S^4)*Zeta[3])/(3*(1 + S^2)^2)) - (208*(-3 + 4*S^2 + 2*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]*((-592*(1 + S^2)^2)/(3*S^2) - (4*Pi^2*(59 + 92*S^2 + 11*S^4))/(9*S^2) - (4*Pi^4*(3904 - 9634*S^2 + 1657*S^4))/(135*(1 + S^2)^2) - (8*(343 - 1054*S^2 + 343*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + ((32*(-6 + 2*S^2 + 9*S^4))/(3*S^2) - (8*Pi^2*(-721 + 758*S^2 + 379*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] + (32*(11 - 266*S^2 + 83*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (16*(-35 + 82*S^2 + 41*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-160*(-1 + S^2)*(1 + S^2))/S^2 + (16*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (64*(-89 - 133*S^2 + 136*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (32*(-581 + 578*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) + (64*(-992 + 986*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + (4800*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) + (128*(-661 + 238*S^2 + 119*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) + 4800*HPL[{2, 1, 1, 1}, -S^2] + (32*(3 + 5*S^2) - (8*Pi^2*(-593 + 674*S^2 + 337*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((128*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(9*(1 + S^2)^2) - (16*(-581 + 578*S^2 + 289*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (32*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(3*(1 + S^2)^2)) - (32*(-256 + 358*S^2 + 179*S^4)*Zeta[5])/(3*(1 + S^2)^2))) + (-60*(-7 + 5*S^2) + (372*Pi^2*(1 + 4*S^2 + 2*S^4))/(1 + S^2)^2)*Zeta[7] + HPL[{0}, S^2]^2*((Pi^4*(39 - 365*S^2))/72 + (Pi^2*(325 - 291*S^2))/12 - 20*(-17 + 3*S^2) + (Pi^6*(261425 - 842589*S^2 - 148374*S^4))/(90720*(1 + S^2)^2) + (4*(59 - 137*S^2 + 14*S^4)*HPL[{1}, -S^2]^6)/(9*(1 + S^2)^2) - (8*(-31 + 8*S^2 + 4*S^4)*HPL[{1}, -S^2]^7)/(21*(1 + S^2)^2) + ((113 - 608*S^2 + 139*S^4)*HPL[{2}, -S^2]^3)/(6*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-2*(-5 - 4*S^2 + 5*S^4))/(5*S^2) - (2*Pi^2*(-158 + 26*S^2 + 13*S^4))/(9*(1 + S^2)^2) - (2*(-803 + 134*S^2 + 67*S^4)*HPL[{2}, -S^2])/(15*(1 + S^2)^2)) + ((-29 - 16*S^2 - 11*S^4)*HPL[{3}, -S^2]^2)/(2*(1 + S^2)^2) + ((2*(20 + 25*S^2 + 13*S^4))/S^2 + (Pi^2*(149 + 322*S^2 + 161*S^4))/(6*(1 + S^2)^2))*HPL[{5}, -S^2] + ((363 + 79*S^2 - 208*S^4)*HPL[{6}, -S^2])/(2*(1 + S^2)^2) + (2*(238 + 362*S^2 + 181*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 + ((-249 + 1356*S^2 - 307*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*(25 - 166*S^2 - 83*S^4))/(6*(1 + S^2)^2) + (2*(1 - 3*S^2 + 4*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((Pi^2*(-21 - 382*S^2 - 191*S^4))/(3*(1 + S^2)^2) + (2*(-11 - 16*S^2 + 13*S^4))/S^2)*HPL[{4, 1}, -S^2] + ((1 + 18*S^2 - 7*S^4)*HPL[{4, 2}, -S^2])/(2*(1 + S^2)^2) - (4*(25 + 42*S^2 + 21*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + (2*(-87 - 43*S^2 + 40*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-307 - 526*S^2 - 263*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (2*(460 + 822*S^2 + 411*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((4*(11 - 4*S^2 + S^4))/S^2 + (2*Pi^2*(753 + 8*S^2 + 4*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-4*(-41 + 6*S^2 + S^4))/S^2 + (2*Pi^2*(2270 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (2*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(1 + S^2) + (2*(225 - 1216*S^2 + 279*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + ((-9 + 310*S^2 + 155*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 + (40*(-3 + 20*S^2 + 10*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (2*(761 - 3584*S^2 + 783*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(-55 + 414*S^2 + 207*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 + (2*(-223 + 1134*S^2 + 567*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (4*(-217 + 1186*S^2 + 593*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((32*(-4 + S^4))/S^2 - (28*Pi^2*(109 + 16*S^2 + 8*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (16*(233 + 36*S^2 + 18*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^2 - (4*(285 - 1180*S^2 + 247*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(2809 + 266*S^2 + 133*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (4*(2809 + 266*S^2 + 133*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (4*(5605 + 698*S^2 + 349*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(8403 + 1022*S^2 + 511*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(281 - 1216*S^2 + 243*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-235 + 8*S^2 + 4*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (96*(-235 + 8*S^2 + 4*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-1177 + 86*S^2 + 43*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(473 + 76*S^2 + 38*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-4*Pi^2*(1 + 8*S^2))/3 - 2*(-13 + 9*S^2) + (Pi^4*(3353 + 5960*S^2 + 2980*S^4))/(180*(1 + S^2)^2))*Zeta[3] + ((20 - 73*S^2 - 53*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((Pi^2*(7 - 2*S^4))/(3*S^2) - (2*(-15 + 4*S^2 + 3*S^4))/S^2 + (Pi^4*(509 + 1982*S^2 + 991*S^4))/(360*(1 + S^2)^2) + (2*(23 + 36*S^2 + 18*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(20 - 53*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (2*(-29 + 42*S^2 + 21*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (12*(-3 + 26*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (2*S^2*(23 + 7*S^2)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((Pi^4*(-933 - 160*S^2 - 80*S^4))/(20*(1 + S^2)^2) + (Pi^2*(-31 - 4*S^2 + 2*S^4))/(3*S^2) + (4*(-23 + S^2 + 8*S^4))/S^2 - (4*(-475 + 6*S^2 + 3*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (16*(-235 + 8*S^2 + 4*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(-6 - 175*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((Pi^2*(143 - 20*S^2 - 195*S^4))/(12*(1 + S^2)^2) + (25 - 12*S^2 - 17*S^4)/S^2 - (28*(2 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(17 + 24*S^2 + 12*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((Pi^2*(-569 + 1926*S^2 - 277*S^4))/(6*(1 + S^2)^2) + (2*(-21 - 19*S^2 + 14*S^4))/S^2 - (4*(-17 + 56*S^2 + 28*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-8*(-9 - 6*S^2 + 8*S^4))/S^2 + (Pi^2*(574 - 1961*S^2 + 293*S^4))/(3*(1 + S^2)^2) + (8*(-13 + 60*S^2 + 30*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*((29 + 32*S^2 - 19*S^4)/(3*S^2) + (Pi^2*(1115 - 2168*S^2 + 137*S^4))/(18*(1 + S^2)^2) + ((601 - 1054*S^2 + 85*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + (2*(-21 + 58*S^2 + 29*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (2*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (2*(-53 + 74*S^2 + 37*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((1 + 6*S^2 - 5*S^4)/S^2 + (Pi^2*(467 - 2132*S^2 + 397*S^4))/(24*(1 + S^2)^2) + ((1 + 78*S^2 + 39*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) - (2*(233 + 36*S^2 + 18*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + ((3 + 80*S^2 + 40*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((Pi^4*(19367 - 806*S^2 - 403*S^4))/(540*(1 + S^2)^2) - (2*Pi^2*(-15 - 11*S^2 + 12*S^4))/(9*S^2) - (4*(-23 - 25*S^2 + 14*S^4))/(3*S^2) + ((Pi^2*(1355 - 118*S^2 - 59*S^4))/(9*(1 + S^2)^2) - (4*(-15 - 5*S^2 + 9*S^4))/(3*S^2))*HPL[{2}, -S^2] - (2*(-417 + 122*S^2 + 61*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (8*(-15 - 44*S^2 + 21*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (2*(25 + 82*S^2 + 41*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (4*(601 - 1054*S^2 + 85*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (32*(-99 + 16*S^2 + 8*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (4*(5 - 104*S^2 + 71*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + (-4*(-7 + 12*S^2) + (2*Pi^2*(237 + 448*S^2 + 224*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((89 - 44*S^2 - 69*S^4)/(2*S^2) - (2*Pi^2*(-9 - S^2 + 6*S^4))/(3*S^2) + (Pi^4*(8482 - 21031*S^2 + 1195*S^4))/(720*(1 + S^2)^2) + (-4*(-1 + S^2) + (Pi^2*(-5 + 26*S^2 + 13*S^4))/(2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((55 + 18*S^2 + 19*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) - (7*(5 + 6*S^2 + 3*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((Pi^2*(-753 - 8*S^2 - 4*S^4))/(3*(1 + S^2)^2) - (2*(11 - 4*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (2*(133 - 661*S^2 + 162*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + ((1 - 158*S^2 - 79*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (2*(-25 + 206*S^2 + 103*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (2*(249 - 1356*S^2 + 307*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(233 + 36*S^2 + 18*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (12*(469 + 46*S^2 + 23*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-235 + 8*S^2 + 4*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-2/S^2 + (Pi^2*(-13 + 60*S^2 + 30*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (2*(-14 + 46*S^2 + 23*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((Pi^4*(7570 - 12273*S^2 - 73*S^4))/(180*(1 + S^2)^2) + (75 + 66*S^2 - 41*S^4)/S^2 + (Pi^2*(59 + 49*S^2 - 36*S^4))/(6*S^2) + (2*(136 - 299*S^2 + 43*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((-8*(-3 - S^2 + S^4))/S^2 + (Pi^2*(-9 + 94*S^2 + 47*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (2*(-43 - 28*S^2 + 31*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(17 + 70*S^2 + 35*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((4*(-15 - 5*S^2 + 9*S^4))/S^2 + (Pi^2*(-1355 + 118*S^2 + 59*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(151 - 255*S^2 + 22*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (64*(-2 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (2*(-167 + 274*S^2 + 137*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (4*(601 - 1054*S^2 + 85*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(-417 + 122*S^2 + 61*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(-615 + 154*S^2 + 77*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-2*(-1 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(-1 + 150*S^2 + 75*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((49 + 12*S^2 - 25*S^4)/S^2 + (Pi^2*(1117 - 1624*S^2 + 87*S^4))/(6*(1 + S^2)^2) + (32*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-417 + 122*S^2 + 61*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (2*(-55 + 62*S^2 + 31*S^4)*Zeta[3])/(1 + S^2)^2) + (2*(1 + 158*S^2 + 79*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-2*(1 + S^2)*(-57 + 43*S^2))/S^2 + (Pi^4*(208 - 37*S^2 - 319*S^4))/(180*S^2) + (Pi^2*(47 + 25*S^2 - 38*S^4))/(3*S^2) + (Pi^6*(523307 + 90974*S^2 + 45487*S^4))/(45360*(1 + S^2)^2) + ((Pi^2*(680 - 138*S^2 - 69*S^4))/(6*(1 + S^2)^2) - (2*(-3 - 2*S^2 + 2*S^4))/S^2)*HPL[{2}, -S^2]^2 - (43*(-9 + 2*S^2 + S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + ((-23 - 22*S^2 - 11*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-2*(-12 - S^2 + 3*S^4))/S^2 + (Pi^2*(97 + 226*S^2 + 113*S^4))/(6*(1 + S^2)^2))*HPL[{4}, -S^2] - (8*(-15 - 10*S^2 + 14*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((245 + 414*S^2 + 207*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (4*(-417 + 122*S^2 + 61*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((22*Pi^2*(-61 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2) + (8*(-9 - 4*S^2 + 4*S^4))/S^2)*HPL[{3, 1}, -S^2] + (2*(9 - 130*S^2 + 53*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(-31 - 226*S^2 + 109*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (3*(-3 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (8*(23 + 44*S^2 + 22*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-8*(-15 - 5*S^2 + 9*S^4))/S^2 - (2*Pi^2*(-1355 + 118*S^2 + 59*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (16*(136 - 299*S^2 + 43*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(423 - 853*S^2 + 108*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (344*(-9 + 2*S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (4*(-2347 + 434*S^2 + 217*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(601 - 1054*S^2 + 85*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-99 + 16*S^2 + 8*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-2*(-1 + 7*S^2 + 10*S^4))/S^2 - (2*Pi^2*(-36 - 39*S^2 + 73*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (2*(41 + 42*S^2 + 21*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((Pi^2*(63 + 100*S^2 - 75*S^4))/(3*(1 + S^2)^2) - (4*(-9 - 2*S^2 + 3*S^4))/S^2 - (64*(-2 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(13 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((Pi^2*(-1117 + 1624*S^2 - 87*S^4))/(3*(1 + S^2)^2) + (2*(-49 - 12*S^2 + 25*S^4))/S^2 - (4*(-55 + 62*S^2 + 31*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((Pi^2*(30 + 6*S^2 - 13*S^4))/(3*S^2) - (4*(-19 - S^2 + 10*S^4))/S^2 + (Pi^4*(15775 + 842*S^2 + 421*S^4))/(360*(1 + S^2)^2) - (4*(2 - 33*S^2 + 13*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (7*(7 + 6*S^2 + 3*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(136 - 299*S^2 + 43*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(-419 + 118*S^2 + 59*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-417 + 122*S^2 + 61*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(-7 - 140*S^2 + 39*S^4)*Zeta[3])/(1 + S^2)^2) - (4*(-21 - S^2 + 98*S^4)*Zeta[5])/(1 + S^2)^2) + 1116*Zeta[7]) + Log[T]^2*((Pi^4*(623 - 519*S^2))/90 + (Pi^2*(163 - 69*S^2))/3 + (Pi^6*(195415 - 962227*S^2 + 62038*S^4))/(22680*(1 + S^2)^2) + ((5 + 2*S^2 + S^4)*HPL[{0}, S^2]^7)/(12*(1 + S^2)^2) + (56*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) - (32*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^6*((31 - 66*S^2 - 9*S^4)/(24*(1 + S^2)^2) + ((49 + 10*S^2 + 5*S^4)*HPL[{1}, -S^2])/(12*(1 + S^2)^2)) + (58*(-1 + S^2)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)) + HPL[{1}, -S^2]^5*((8*(1 + S^2)^2)/S^2 - (16*Pi^2*(-40 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2) + 120*HPL[{2}, -S^2]) + HPL[{0}, S^2]^5*((7 + 4*S^2)/6 + (Pi^2*(855 + 218*S^2 + 109*S^4))/(180*(1 + S^2)^2) + ((605 - 652*S^2 + 47*S^4)*HPL[{1}, -S^2])/(30*(1 + S^2)^2) + (2*(164 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(15*(1 + S^2)^2) + ((270 - 2*S^2 - S^4)*HPL[{2}, -S^2])/(30*(1 + S^2)^2)) + (2*(1 - 226*S^2 + 85*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((8*(20 + 31*S^2 + 3*S^4))/S^2 + (2*Pi^2*(25 + 542*S^2 + 271*S^4))/(3*(1 + S^2)^2))*HPL[{5}, -S^2] - (2*(-675 - 607*S^2 + 284*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (152*(14 + 22*S^2 + 11*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 - (16*(131 - 608*S^2 + 131*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((16*(1 + 11*S^4))/S^2 - (2*Pi^2*(-511 + 2650*S^2 + 1325*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((24*(-3 - 4*S^2 + 23*S^4))/S^2 - (4*Pi^2*(-1007 + 4230*S^2 + 2115*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (6*(-1 - 226*S^2 + 111*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (16*(-8 + 42*S^2 + 21*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + (32*(-30 - 269*S^2 + 121*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (4*(-95 + 338*S^2 + 169*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (8*(193 + 334*S^2 + 167*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((192*(1 + S^4))/S^2 - (32*Pi^2*(-262 + 150*S^2 + 75*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((96*(7 + S^2 + 2*S^4))/S^2 - (16*Pi^2*(-1375 + 194*S^2 + 97*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (336*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(1 + S^2) + (128*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + (4*(-1241 + 4734*S^2 + 2367*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 + (32*(-461 + 1838*S^2 + 919*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 - (96*(8 - 89*S^2 + 23*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-1759 + 7354*S^2 + 3677*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 + (184*(-245 + 974*S^2 + 487*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (256*(-364 + 1438*S^2 + 719*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((480*(-1 + S^2)*(1 + S^2))/S^2 - (16*Pi^2*(803 + 736*S^2 + 368*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 9856*HPL[{2, 2, 2, 1}, -S^2] + (96*(13 - 89*S^2 + 18*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (96*(391 + 202*S^2 + 101*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (96*(391 + 202*S^2 + 101*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (96*(699 + 818*S^2 + 409*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(3268 + 3566*S^2 + 1783*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (480*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + (128*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (384*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (2560*(-82 + 106*S^2 + 53*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 42240*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-4*Pi^2*(-18 + 19*S^2))/3 - 16*(-13 + 24*S^2) + (Pi^4*(-373 + 5960*S^2 + 2980*S^4))/(45*(1 + S^2)^2))*Zeta[3] + (12*(3 - 22*S^2 + 3*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{1}, -S^2]^4*((40*(1 + S^2)^2)/S^2 + (10*Pi^2*(265 - 736*S^2 + 175*S^4))/(9*(1 + S^2)^2) - (600*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (2800*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 600*HPL[{2, 1}, -S^2] + (160*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((-4*(1 + S^2)*(-33 + 5*S^2))/S^2 + (Pi^2*(161 + 1132*S^2 - 501*S^4))/(3*(1 + S^2)^2) + (32*(73 + 26*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-1 + 30*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((-4*Pi^2*(-7 - 6*S^2 + 14*S^4))/(3*S^2) - (8*(-17 - 18*S^2 + 31*S^4))/S^2 + (Pi^4*(-2501 + 10990*S^2 + 5495*S^4))/(90*(1 + S^2)^2) - (16*(-6 + 38*S^2 + 19*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(333 - 1216*S^2 + 191*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-241 + 1262*S^2 + 631*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (96*(-38 + 214*S^2 + 107*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(-4 - 95*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^4*((29 - 21*S^2)/6 + (Pi^2*(749 - 1998*S^2 - 107*S^4))/(72*(1 + S^2)^2) + ((175 - 266*S^2 - S^4)*HPL[{1}, -S^2]^2)/(2*(1 + S^2)^2) - (10*(-65 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) + ((293 - 745*S^2 + 50*S^4)*HPL[{2}, -S^2])/(12*(1 + S^2)^2) + HPL[{1}, -S^2]*((15 + 10*S^2 - 9*S^4)/(6*S^2) + (5*Pi^2*(277 + 26*S^2 + 13*S^4))/(36*(1 + S^2)^2) + (4*(69 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((5 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) - (2*(145 + 18*S^2 + 9*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + ((45 + 76*S^2 + 38*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((4*(1 + 12*S^2 + S^4))/S^2 + (Pi^2*(773 - 3788*S^2 + 831*S^4))/(6*(1 + S^2)^2) + (2*(-405 + 1246*S^2 + 623*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 1232*HPL[{2, 1}, -S^2] + (16*(-27 + 142*S^2 + 71*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((128*(1 + S^2)^2)/S^2 + (8*Pi^2*(5 + 7*S^2))/(3*S^2) - (2*Pi^4*(-12982 + 4426*S^2 + 2213*S^4))/(135*(1 + S^2)^2) + ((-80*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] - (16*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (80*(11 - 88*S^2 + 41*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (16*(-241 + 238*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (2400*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (64*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + 2400*HPL[{2, 1, 1}, -S^2] - (80*(29 - 188*S^2 + 119*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((384*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-31 + 19*S^4))/(3*S^2) - (2*Pi^4*(973 + 592*S^2 + 296*S^4))/(9*(1 + S^2)^2) - (32*(-268 + 334*S^2 + 167*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (64*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(133 - 608*S^2 + 129*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-288*(-1 + S^2)*(1 + S^2))/S^2 + (16*Pi^2*(74 - 304*S^2 + 57*S^4))/(3*(1 + S^2)^2) + (32*(-143 + 584*S^2 + 292*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((8*(1 + S^2)*(-25 + 11*S^2))/S^2 - (2*Pi^2*(207 - 646*S^2 + 139*S^4))/(3*(1 + S^2)^2) - (16*(-155 + 586*S^2 + 293*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^3*((4*(33 + 17*S^2))/3 + (Pi^2*(53 + 26*S^2))/9 + (Pi^4*(9885 + 34*S^2 + 17*S^4))/(540*(1 + S^2)^2) + (40*(18 - 33*S^2 + 5*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) - (10*(-151 + 34*S^2 + 17*S^4)*HPL[{1}, -S^2]^4)/(9*(1 + S^2)^2) + ((8*(1 + S^2)*(4 + S^2))/(3*S^2) - (2*Pi^2*(-281 + 84*S^2 + 42*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] + ((275 - 162*S^2 - 81*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((Pi^2*(1411 - 162*S^2 - 81*S^4))/(9*(1 + S^2)^2) + (4*(7 + 13*S^2 + 5*S^4))/(3*S^2) - (4*(-113 + 24*S^2 + 12*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (2*(43 + 28*S^2 + 21*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (4*(-13 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (4*(405 - 304*S^2 + 41*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(-287 + 174*S^2 + 87*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(-292 + 166*S^2 + 83*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (2*(-41 - 59*S^2 + 10*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((2*(29 + 62*S^2 + 21*S^4))/(3*S^2) + (Pi^2*(1145 - 1642*S^2 + 197*S^4))/(9*(1 + S^2)^2) + (2*(551 - 770*S^2 + 179*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + (24*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-113 + 24*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(3 + 34*S^2 + 17*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + (-8*(-30 + 29*S^2) + (8*Pi^2*(-13 + 448*S^2 + 224*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{0}, S^2]^2*(163 - 69*S^2 + (Pi^2*(59 - 39*S^2))/3 + (Pi^4*(8449 - 30251*S^2 + 840*S^4))/(360*(1 + S^2)^2) + (20*(59 - 137*S^2 + 14*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) - (8*(-31 + 8*S^2 + 4*S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 + ((249 - 1356*S^2 + 307*S^4)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-4*(-5 - 4*S^2 + 5*S^4))/S^2 - (20*Pi^2*(-158 + 26*S^2 + 13*S^4))/(9*(1 + S^2)^2) - (4*(-803 + 134*S^2 + 67*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-4*(-4 - 3*S^2 + 2*S^4))/S^2 + (Pi^2*(11 + 134*S^2 + 67*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((83 + 64*S^2 - 51*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(35 + 106*S^2 + 53*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((16*(-4 + S^4))/S^2 - (14*Pi^2*(109 + 16*S^2 + 8*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(285 - 1180*S^2 + 247*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (2*(-13 + 166*S^2 + 83*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*(-15 + 274*S^2 + 137*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (4*(281 - 1216*S^2 + 243*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-235 + 8*S^2 + 4*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(703 + 22*S^2 + 11*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(473 + 76*S^2 + 38*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-4*(-3 + 4*S^2) + (76*Pi^2*(1 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-4*(-9 - 6*S^2 + 8*S^4))/S^2 + (Pi^2*(574 - 1961*S^2 + 293*S^4))/(6*(1 + S^2)^2) + (6*(-3 + 26*S^2 + 13*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-235 + 8*S^2 + 4*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(-13 + 60*S^2 + 30*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-2*(-29 - 32*S^2 + 19*S^4))/S^2 + (Pi^2*(1115 - 2168*S^2 + 137*S^4))/(3*(1 + S^2)^2) + (2*(601 - 1054*S^2 + 85*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2 + (4*(-21 + 58*S^2 + 29*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(-53 + 74*S^2 + 37*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^4*(19367 - 806*S^2 - 403*S^4))/(180*(1 + S^2)^2) - (2*Pi^2*(-15 - 11*S^2 + 12*S^4))/(3*S^2) - (4*(-23 - 25*S^2 + 14*S^4))/S^2 + ((Pi^2*(1355 - 118*S^2 - 59*S^4))/(3*(1 + S^2)^2) - (4*(-15 - 5*S^2 + 9*S^4))/S^2)*HPL[{2}, -S^2] - (2*(-417 + 122*S^2 + 61*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 - (8*(-15 - 44*S^2 + 21*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (2*(25 + 82*S^2 + 41*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (4*(601 - 1054*S^2 + 85*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (32*(-99 + 16*S^2 + 8*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(5 - 104*S^2 + 71*S^4)*Zeta[3])/(1 + S^2)^2) + (156*(1 + 4*S^2 + 2*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*((392*(1 + S^2)^2)/S^2 + (4*Pi^2*(47 + 73*S^2 + 10*S^4))/(3*S^2) - (2*Pi^4*(-104 - 104*S^2 + 67*S^4))/(45*S^2) - (11*Pi^6*(-50011 + 10858*S^2 + 5429*S^4))/(11340*(1 + S^2)^2) + ((8*(3 + 5*S^2 + 3*S^4))/S^2 - (2*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + 124*HPL[{2}, -S^2]^3 - (4*(-119 + 74*S^2 + 37*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((96*(1 + S^2))/S^2 + (2*Pi^2*(-457 + 558*S^2 + 279*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] - (8*(-103 - 386*S^2 + 173*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (4*(175 + 566*S^2 + 283*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((96*(1 + S^2)*(-3 + 2*S^2))/S^2 - (16*Pi^2*(185 + 122*S^2 + 61*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (16*(157 - 1054*S^2 + 529*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (16*(493 - 3694*S^2 + 1753*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (36*(-43 + 26*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (32*(-241 + 238*S^2 + 119*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-480*(-1 + S^2)*(1 + S^2))/S^2 + (16*Pi^2*(514 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (32*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (192*(144 - 307*S^2 + 69*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 2976*HPL[{3, 2, 1}, -S^2] + (64*(19 + 398*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (14400*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - (128*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 14400*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-8*(1 + 28*S^2 + 49*S^4))/S^2 - (8*Pi^2*(25 - 174*S^2 + 111*S^4))/(1 + S^2)^2)*Zeta[3] - (16*(-16 + 10*S^2 + 5*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((-8*(-19 - 2*S^2 + 29*S^4))/S^2 - (4*Pi^2*(135 - 1408*S^2 + 657*S^4))/(3*(1 + S^2)^2) - (16*(-581 + 578*S^2 + 289*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (224*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((384*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(3*(1 + S^2)^2) - (32*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-296*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-30 - 5*S^2 + 24*S^4))/(3*S^2) + (Pi^4*(14677 + 2274*S^2 + 1137*S^4))/(90*(1 + S^2)^2) - (8*(157 - 1054*S^2 + 529*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-367 + 226*S^2 + 113*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (32*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(151 - 1054*S^2 + 535*S^4)*Zeta[3])/(1 + S^2)^2) - (96*(9 - 71*S^2 + 65*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((296*(1 + S^2)^2)/S^2 + (2*Pi^2*(59 + 92*S^2 + 11*S^4))/(3*S^2) + (2*Pi^4*(3904 - 9634*S^2 + 1657*S^4))/(45*(1 + S^2)^2) + (4*(343 - 1054*S^2 + 343*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((-16*(-6 + 2*S^2 + 9*S^4))/S^2 + (4*Pi^2*(-721 + 758*S^2 + 379*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (16*(11 - 266*S^2 + 83*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (24*(-35 + 82*S^2 + 41*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((240*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(514 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (32*(-89 - 133*S^2 + 136*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (16*(-581 + 578*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (32*(-992 + 986*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (7200*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (64*(-661 + 238*S^2 + 119*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 7200*HPL[{2, 1, 1, 1}, -S^2] + (-48*(3 + 5*S^2) + (4*Pi^2*(-593 + 674*S^2 + 337*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-192*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(3*(1 + S^2)^2) + (8*(-581 + 578*S^2 + 289*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + (16*(-256 + 358*S^2 + 179*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-138*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-18 - 6*S^2 + 17*S^4))/(3*S^2) + (Pi^4*(5698 - 19055*S^2 + 2327*S^4))/(180*(1 + S^2)^2) + (-96*S^2 + (2*Pi^2*(-79 + 454*S^2 + 227*S^4))/(1 + S^2)^2)*HPL[{3}, -S^2] - (2*(-19 - 662*S^2 + 317*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (4*(-25 + 318*S^2 + 159*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-96*(1 + S^4))/S^2 + (16*Pi^2*(-262 + 150*S^2 + 75*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (32*(76 - 304*S^2 + 55*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*(-681 + 2414*S^2 + 1207*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (8*(-923 + 3842*S^2 + 1921*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (32*(131 - 608*S^2 + 131*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + 4928*HPL[{2, 2, 1}, -S^2] - (96*(192 + 94*S^2 + 47*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-8*(1 + 11*S^4))/S^2 + (8*Pi^2*(-78 + 322*S^2 + 161*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (8*(-89 + 630*S^2 + 315*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{0}, S^2]*(392*(1 + S^2) + (4*Pi^2*(57 + 41*S^2))/3 + (Pi^4*(646 + 397*S^2))/90 + (Pi^6*(6826 - 3526*S^2 - 1763*S^4))/(324*(1 + S^2)^2) + (56*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 - (112*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) + ((Pi^2*(753 - 946*S^2 - 473*S^4))/(3*(1 + S^2)^2) + (4*(1 + 5*S^2 + 5*S^4))/S^2)*HPL[{2}, -S^2]^2 - (784*(-1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((20*(1 + S^2)^2)/S^2 - (10*Pi^2*(-445 + 202*S^2 + 101*S^4))/(9*(1 + S^2)^2) - (20*(-87 + 50*S^2 + 25*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (4*(-1 + 10*S^2 + 5*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((4*(11 + 4*S^2 + S^4))/S^2 - (8*Pi^2*(-17 + 16*S^2 + 8*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(59 + 18*S^2 + 71*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 - (4*(-23 + 100*S^2 + 50*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (16*(-239 + 392*S^2 + 196*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-8*(19 + 18*S^2 + 11*S^4))/S^2 + (8*Pi^2*(-362 + 490*S^2 + 245*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(-7 - 282*S^2 + 69*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(-125 - 826*S^2 + 91*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - 8*HPL[{4, 2}, -S^2] + (32*(-11 + 12*S^2 + 6*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((48*(5 + 6*S^2 + 5*S^4))/S^2 - (8*Pi^2*(-727 + 976*S^2 + 488*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (16*(539 - 1054*S^2 + 147*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(1662 - 3049*S^2 + 449*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 40*HPL[{3, 1, 2}, -S^2] - (8*(-779 + 1578*S^2 + 789*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (96*(-203 + 398*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (80*(235 - 376*S^2 + 61*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-437 + 806*S^2 + 403*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (960*(-29 + 54*S^2 + 27*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (56*(1 + S^2) - (2*Pi^2*(-41 - 326*S^2 + 103*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-10 + 22*S^2 + 11*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((-8*(31 + 28*S^2 + 19*S^4))/S^2 - (2*Pi^2*(1985 - 2488*S^2 + 387*S^4))/(3*(1 + S^2)^2) + (16*(88 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((4*(17 + 16*S^2 + 9*S^4))/S^2 + (2*Pi^2*(88 + 141*S^2 + 29*S^4))/(3*(1 + S^2)^2) - (8*(-85 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(3 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((Pi^4*(8367 - 7832*S^2 - 3916*S^4))/(90*(1 + S^2)^2) + (2*Pi^2*(31 + 38*S^2 + 19*S^4))/(3*S^2) + (8*(14 + 23*S^2 + 25*S^4))/S^2 - (4*(-3 - 140*S^2 + 35*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (24*(-1 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(539 - 1054*S^2 + 147*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (24*(-159 + 262*S^2 + 131*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (32*(-239 + 392*S^2 + 196*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (24*(1 - 42*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((192*(1 + S^2)^2)/S^2 + (Pi^4*(11996 - 4122*S^2 - 2061*S^4))/(45*(1 + S^2)^2) + (2*Pi^2*(29 + 56*S^2 + 25*S^4))/(3*S^2) + ((24*(5 + 6*S^2 + 5*S^4))/S^2 - (2*Pi^2*(-661 + 298*S^2 + 149*S^4))/(1 + S^2)^2)*HPL[{2}, -S^2] - (8*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + (48*(4 + 19*S^2 + 5*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(-91 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (160*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (336*(-31 + 18*S^2 + 9*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (240*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(22 - 133*S^2 + 25*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((80*(1 + S^2)^2)/S^2 + (20*Pi^2*(85 - 220*S^2 + 59*S^4))/(3*(1 + S^2)^2) + (160*(37 - 94*S^2 + 37*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + (16*(-23 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (80*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-137 + 86*S^2 + 43*S^4)*Zeta[3])/(3*(1 + S^2)^2)) - (4*(-39 - 275*S^2 + 24*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((296*(1 + S^2)^2)/S^2 + (2*Pi^2*(59 + 122*S^2 + 51*S^4))/(3*S^2) + (Pi^4*(7838 - 16377*S^2 + 3899*S^4))/(45*(1 + S^2)^2) + (4*(343 - 1054*S^2 + 343*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((8*(13 + 8*S^2 + 5*S^4))/S^2 + (4*Pi^2*(-5 + 14*S^2 + 7*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (16*(25 - 4*S^2 + 31*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(-39 + 34*S^2 + 17*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-48*(5 + 6*S^2 + 5*S^4))/S^2 + (4*Pi^2*(-661 + 298*S^2 + 149*S^4))/(1 + S^2)^2)*HPL[{2, 1}, -S^2] - (16*(367 - 940*S^2 + 373*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (16*(-67 + 38*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (8*(-311 + 170*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (320*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (32*(-1999 + 1162*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (480*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((8*(1 + S^2)*(-1 + 7*S^2))/S^2 + (8*Pi^2*(-67 + 60*S^2 + 30*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((8*(25 + 28*S^2 + 25*S^4))/S^2 + (2*Pi^2*(1291 - 2650*S^2 + 919*S^4))/(3*(1 + S^2)^2) + (8*(-67 + 38*S^2 + 19*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(-133 + 82*S^2 + 41*S^4)*Zeta[3])/(1 + S^2)^2) + (16*(-46 + 38*S^2 + 19*S^4)*Zeta[5])/(1 + S^2)^2)) + (4464*(2*S^2 + S^4)*Zeta[7])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((260*(1 + S^2)^2)/S^2 + (Pi^4*(822 + 891*S^2 - 299*S^4))/(180*S^2) + (Pi^2*(149 + 214*S^2 + 33*S^4))/(3*S^2) + (Pi^6*(59726 - 131157*S^2 + 12397*S^4))/(3780*(1 + S^2)^2) - (124*(-1 + S^2)*HPL[{2}, -S^2]^3)/(1 + S^2) + (4*(23 - 110*S^2 + 23*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((8*(16 + 26*S^2 + S^4))/S^2 + (4*Pi^2*(-44 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{5}, -S^2] - (4*(-335 - 301*S^2 + 142*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (24*(65 + 92*S^2 + 46*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 - (8*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((8*(-3 + 10*S^2 + 15*S^4))/S^2 - (4*Pi^2*(-613 + 610*S^2 + 305*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((48*(-4 + 3*S^2 + 8*S^4))/S^2 - (2*Pi^2*(-4135 + 4218*S^2 + 2109*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (12*(25 - 118*S^2 + 25*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (16*(-19 + 20*S^2 + 10*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + (8*(35 - 1094*S^2 + 311*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (24*(-29 + 30*S^2 + 15*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (4*(285 + 466*S^2 + 233*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((32*(3 + 5*S^2 + 3*S^4))/S^2 - (8*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((32*(15 + 13*S^2))/S^2 - (64*Pi^2*(-319 + 98*S^2 + 49*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (2976*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + (4*(-2421 + 2374*S^2 + 1187*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 + (32*(-929 + 902*S^2 + 451*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 - (64*(-134 - 133*S^2 + 181*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-7303 + 7138*S^2 + 3569*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 + (4*(-22723 + 21898*S^2 + 10949*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (96*(-1945 + 1886*S^2 + 943*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((480*(-1 + S^2)*(1 + S^2))/S^2 - (16*Pi^2*(514 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 2976*HPL[{2, 2, 2, 1}, -S^2] + (64*(-89 - 133*S^2 + 136*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (320*(-86 + 2*S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (320*(-86 + 2*S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(1139 + 538*S^2 + 269*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(1829 + 688*S^2 + 344*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (14400*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (384*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (640*(-407 + 266*S^2 + 133*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 14400*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*(-1 + 20*S^2 + 35*S^4))/(3*S^2) - (8*(1 + 23*S^2 + 38*S^4))/S^2 + (Pi^4*(-1949 + 2808*S^2 + 1404*S^4))/(45*(1 + S^2)^2))*Zeta[3] + (8*(13 - 16*S^2 + 13*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((-4*Pi^2*(-12 + 11*S^4))/(3*S^2) - (8*(-18 - 15*S^2 + 19*S^4))/S^2 + (Pi^4*(-2487 + 3022*S^2 + 1511*S^4))/(45*(1 + S^2)^2) - (20*(-13 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(157 - 1054*S^2 + 529*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-583 + 578*S^2 + 289*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-581 + 578*S^2 + 289*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(5 - 96*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((2*(1 + S^2)*(53 + 3*S^2))/S^2 - (2*Pi^2*(-21 - 560*S^2 + 197*S^4))/(3*(1 + S^2)^2) - (4*(-367 + 226*S^2 + 113*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(-39 + 50*S^2 + 25*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*((24*(1 + S^2 + S^4))/S^2 + (Pi^2*(615 - 1652*S^2 + 429*S^4))/(3*(1 + S^2)^2) + (4*(-351 + 326*S^2 + 163*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - 372*HPL[{2, 1}, -S^2] + (4*(-257 + 270*S^2 + 135*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-384*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(3*(1 + S^2)^2) + (32*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((8*(1 + S^2)*(-31 + 17*S^2))/S^2 + (16*Pi^2*(-120 + 61*S^2 + 57*S^4))/(3*(1 + S^2)^2) - (16*(-299 + 298*S^2 + 149*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((296*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(-14677 - 2274*S^2 - 1137*S^4))/(90*(1 + S^2)^2) + (4*Pi^2*(-30 - 5*S^2 + 24*S^4))/(3*S^2) - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(151 - 1054*S^2 + 535*S^4)*Zeta[3])/(1 + S^2)^2) + ((-8*(-1 + 18*S^2 + 29*S^4))/S^2 + (2*Pi^2*(-511 + 874*S^2 + 437*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((-232*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(6880 - 8117*S^2 - 1457*S^4))/(90*(1 + S^2)^2) + (Pi^2*(97 + 12*S^2 - 73*S^4))/(3*S^2) + ((-8*(-2 + 5*S^2 + 8*S^4))/S^2 + (2*Pi^2*(-613 + 610*S^2 + 305*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (12*(23 - 114*S^2 + 23*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (4*(-119 + 130*S^2 + 65*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-16*(3 + 5*S^2 + 3*S^4))/S^2 + (4*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(343 - 1054*S^2 + 343*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*(-1275 + 1226*S^2 + 613*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*(-3845 + 3686*S^2 + 1843*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + 1488*HPL[{2, 2, 1}, -S^2] + (160*(-86 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-8*(5 + 6*S^2) + (2*Pi^2*(-633 + 646*S^2 + 323*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (4*(-491 + 634*S^2 + 317*S^4)*Zeta[5])/(1 + S^2)^2) + (48*(-44 + 98*S^2 + 49*S^4)*Zeta[7])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-120*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(248 + 32*S^2 - 263*S^4))/(90*S^2) + (Pi^2*(79 - 22*S^2 - 69*S^4))/(3*S^2) + (Pi^6*(84790 - 215793*S^2 + 611*S^4))/(22680*(1 + S^2)^2) + (8*(-5 - 38*S^2 + 9*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-4*(-1 + 8*S^4))/S^2 + (2*Pi^2*(-10 + 46*S^2 + 23*S^4))/(1 + S^2)^2)*HPL[{5}, -S^2] - (4*(-25 + 46*S^2 + 76*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (8*(19 + 12*S^2 + 6*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 - (116*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((8*(-1 + 9*S^4))/S^2 - (2*Pi^2*(-341 + 1286*S^2 + 643*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((4*(-5 + 63*S^4))/S^2 - (8*Pi^2*(-237 + 1012*S^2 + 506*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (4*(11 - 236*S^2 + 89*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (4*(73 + 232*S^2 + 116*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + (4*(2 - 875*S^2 + 435*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (4*(229 + 620*S^2 + 310*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 + (20*(105 + 184*S^2 + 92*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((-80*(-1 + S^2)*(1 + S^2))/S^2 + (344*Pi^2*(9 + 8*S^2 + 4*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((48*(-5 + S^4))/S^2 - (4*Pi^2*(853 + 234*S^2 + 117*S^4))/(1 + S^2)^2)*HPL[{3, 1, 1}, -S^2] - (8*(25 - 118*S^2 + 25*S^4)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(227 - 1098*S^2 + 227*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (8*(-281 + 1158*S^2 + 579*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 + (32*(-230 + 914*S^2 + 457*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (4*(1531 - 6634*S^2 + 1195*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-925 + 3646*S^2 + 1823*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(-2809 + 11206*S^2 + 5603*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (8*(-5677 + 22998*S^2 + 11499*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((-192*(1 + S^4))/S^2 + (32*Pi^2*(-262 + 150*S^2 + 75*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (64*(-147 + 136*S^2 + 68*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^2 - (64*(-11 - 304*S^2 + 142*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-2847 + 850*S^2 + 425*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(-2847 + 850*S^2 + 425*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (136*(-375 + 242*S^2 + 121*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-9661 + 5950*S^2 + 2975*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(131 - 608*S^2 + 131*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 9856*HPL[{2, 1, 2, 1, 1}, -S^2] - 29568*HPL[{2, 2, 1, 1, 1}, -S^2] + (64*(656 + 2182*S^2 + 1091*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (128*(-289 + 292*S^2 + 146*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-2*Pi^2*(2 + 11*S^4))/(3*S^2) - (8*(-1 - S^2 + 16*S^4))/S^2 + (Pi^4*(-1031 + 4704*S^2 + 2352*S^4))/(90*(1 + S^2)^2))*Zeta[3] - (2*(-2 + 3*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3}, -S^2]*((-4*Pi^2*(-1 + 7*S^2))/3 - (4*(-1 - 2*S^2 + 31*S^4))/S^2 + (Pi^4*(-403 + 2516*S^2 + 1258*S^4))/(45*(1 + S^2)^2) - (36*(3 + 16*S^2 + 8*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(157 - 743*S^2 + 128*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (16*(-95 + 324*S^2 + 162*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*(-405 + 1246*S^2 + 623*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(9 - 53*S^2 + 14*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((Pi^2*(37 + 340*S^2 - 149*S^4))/(3*(1 + S^2)^2) - (4*(-3 + 20*S^2 + 5*S^4))/S^2 - (8*(-137 + 62*S^2 + 31*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(8 + 50*S^2 + 25*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((16*(1 + 12*S^2 + S^4))/S^2 + (2*Pi^2*(773 - 3788*S^2 + 831*S^4))/(3*(1 + S^2)^2) + (64*(-27 + 142*S^2 + 71*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-2*Pi^2*(23 - 4*S^2 + 13*S^4))/(3*S^2) - (8*(15 - 2*S^2 + 15*S^4))/S^2 + (53*Pi^4*(-211 + 80*S^2 + 40*S^4))/(90*(1 + S^2)^2) + (24*(61 + 234*S^2 + 117*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + 4928*HPL[{2, 1, 1}, -S^2] + (4*(275 - 1076*S^2 + 217*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((8*(-3 - 12*S^2 + S^4))/S^2 - (2*Pi^2*(437 - 1877*S^2 + 382*S^4))/(3*(1 + S^2)^2) - (8*(-99 + 586*S^2 + 293*S^4)*Zeta[3])/(1 + S^2)^2) + ((-4*(4 + 17*S^4))/S^2 + (2*Pi^2*(-103 + 676*S^2 + 338*S^4))/(3*(1 + S^2)^2))*Zeta[5] + (12*(-5 + 272*S^2 + 136*S^4)*Zeta[7])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-160*(1 + S^2)^2)/S^2 + (4*Pi^2*(1 + S^2)*(53 + 3*S^2))/(3*S^2) + (Pi^8*(3167957 - 57312*S^2 - 28656*S^4))/(680400*(1 + S^2)^2) + (Pi^6*(5096 - 1679*S^2 - 9463*S^4))/(11340*S^2) + (Pi^4*(327 + 255*S^2 - 152*S^4))/(45*S^2) + ((-20*(-1 + S^2)*(1 + S^2))/(3*S^2) + (10*Pi^2*(48 + 10*S^2 + 5*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2]^3 - (2*(-167 + 96*S^2 + 48*S^4)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^2) + ((-16*Pi^2*(-2 + 2*S^2 + S^4))/(1 + S^2)^2 + (2*(-3 + 8*S^2 + S^4))/S^2)*HPL[{3}, -S^2]^2 + (8*(22 + 30*S^2 + 15*S^4)*HPL[{4}, -S^2]^2)/(1 + S^2)^2 + ((32*(1 + S^2)*(11 + S^2))/S^2 + (70*Pi^2*(6 + 14*S^2 + 7*S^4))/(3*(1 + S^2)^2))*HPL[{6}, -S^2] - (8*(-532 - 413*S^2 + 5*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 + (12*(537 + 632*S^2 + 316*S^4)*HPL[{8}, -S^2])/(1 + S^2)^2 + ((-16*(3 + 5*S^2 + 3*S^4))/S^2 + (4*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - (8*(-807 + 466*S^2 + 233*S^4)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^2 + ((-16*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(-63 + 38*S^2 + 19*S^4))/(1 + S^2)^2)*HPL[{4, 2}, -S^2] - (8*(-15 - 113*S^2 + 18*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + ((-72*(1 + S^2)*(3 + S^2))/S^2 - (8*Pi^2*(-218 + 282*S^2 + 141*S^4))/(3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] - (12*(-33 - 190*S^2 + 19*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 + (24*(-1 + 4*S^2 + 2*S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 + (8*(-245 - 21*S^2 + 172*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + (60*(-1 + 4*S^2 + 2*S^4)*HPL[{6, 2}, -S^2])/(1 + S^2)^2 - (16*(248 + 342*S^2 + 171*S^4)*HPL[{7, 1}, -S^2])/(1 + S^2)^2 - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^2 + (16*(-1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((-144*(-1 + S^2)*(1 + S^2))/S^2 + (80*Pi^2*(48 + 10*S^2 + 5*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] - (32*(77 - 562*S^2 + 263*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 - (192*(40 - 287*S^2 + 133*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 - (112*(-11 + 14*S^2 + 7*S^4)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^2 + ((-96*(1 + S^2)*(-7 + 5*S^2))/S^2 + (4*Pi^2*(2423 + 1158*S^2 + 579*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] - (24*(313 - 2254*S^2 + 1057*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 + (16*(-127 + 166*S^2 + 83*S^4)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^2 - (24*(989 - 7014*S^2 + 3221*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(-41 + 86*S^2 + 43*S^4)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^2 + (16*(-479 + 470*S^2 + 235*S^4)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^2 - (16*(2939 - 21806*S^2 + 9911*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-149 + 122*S^2 + 61*S^4)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^2 + (64*(-487 + 496*S^2 + 248*S^4)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^2 + (8*(-9725 + 11006*S^2 + 5503*S^4)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^2 + (5952*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2) + ((192*(1 + S^2)*(-3 + 2*S^2))/S^2 - (32*Pi^2*(185 + 122*S^2 + 61*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] - (32*(-715 + 1054*S^2 + 29*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (32*(-715 + 1054*S^2 + 29*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (24*(-43 + 26*S^2 + 13*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2)^2 - (32*(-1273 + 1054*S^2 + 587*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (24*(-43 + 26*S^2 + 13*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2)^2 - (8*(251 + 838*S^2 + 419*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^2 - 9120*HPL[{3, 3, 1, 1}, -S^2] - (32*(-3841 + 3694*S^2 + 1595*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (72*(-43 + 26*S^2 + 13*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (24*(251 + 838*S^2 + 419*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (72*(337 + 786*S^2 + 393*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (128*(307 + 974*S^2 + 487*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-960*(-1 + S^2)*(1 + S^2))/S^2 + (32*Pi^2*(514 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] - (64*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (192*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 5952*HPL[{2, 2, 1, 2, 1}, -S^2] - 17856*HPL[{2, 2, 2, 1, 1}, -S^2] - (640*(188 - 659*S^2 + 233*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 35712*HPL[{3, 1, 1, 1, 2}, -S^2] + 59520*HPL[{3, 1, 1, 2, 1}, -S^2] + 71424*HPL[{3, 1, 2, 1, 1}, -S^2] + 148800*HPL[{3, 2, 1, 1, 1}, -S^2] + (128*(3367 + 7094*S^2 + 3547*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (28800*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) - (256*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 28800*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((8*(-1 - 2*S^2 + 3*S^4))/S^2 + (2*Pi^2*(73 + 22*S^2 + 11*S^4))/(3*(1 + S^2)^2))*Zeta[3]^2 + HPL[{3, 2}, -S^2]*((16*(-1 + 6*S^2 + 13*S^4))/S^2 + (2*Pi^2*(323 - 2238*S^2 + 1111*S^4))/(3*(1 + S^2)^2) + (16*(39 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((8*(1 + S^2)*(33 + S^2))/S^2 - (2*Pi^2*(-24 - 13*S^2 + 3*S^4))/(3*S^2) + (4*Pi^4*(-167 + 352*S^2 + 176*S^4))/(45*(1 + S^2)^2) + (24*(23 - 114*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-165 + 142*S^2 + 71*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*(-367 + 226*S^2 + 113*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-2 - 25*S^2 + 9*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4, 1}, -S^2]*((56*Pi^2*(33 - 280*S^2 + 133*S^4))/(3*(1 + S^2)^2) + (4*(-71 + 16*S^2 + 159*S^4))/S^2 - (8*(-273 + 38*S^2 + 19*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{5}, -S^2]*((4*(70 + 115*S^2 + 17*S^4))/S^2 - (2*Pi^2*(-163 - 426*S^2 + 229*S^4))/(3*(1 + S^2)^2) - (8*(-119 + 130*S^2 + 65*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(37 + 42*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((16*(1 + S^2)*(-27 + 10*S^2))/S^2 + (Pi^4*(-6239 - 1864*S^2 - 932*S^4))/(45*(1 + S^2)^2) + (8*Pi^2*(-18 - 7*S^2 + 10*S^4))/(3*S^2) + (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(19 - 138*S^2 + 67*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 2, 1}, -S^2]*((192*(1 + S^2 + S^4))/S^2 + (8*Pi^2*(615 - 1652*S^2 + 429*S^4))/(3*(1 + S^2)^2) + (32*(-257 + 270*S^2 + 135*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1, 1}, -S^2]*((768*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(3*(1 + S^2)^2) - (64*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*((2*Pi^2*(1 + S^2)*(6 + S^2))/(3*S^2) + (Pi^4*(11213 - 4180*S^2 - 2090*S^4))/(180*(1 + S^2)^2) + (4*(9 + 2*S^2 + 9*S^4))/S^2 - (8*(48 - 325*S^2 + 141*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-115 + 106*S^2 + 53*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (744*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (8*(-17 + 134*S^2 + 67*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + 744*HPL[{2, 1, 1}, -S^2] - (4*(71 - 456*S^2 + 257*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1, 1}, -S^2]*((16*(55 + 38*S^2 + 7*S^4))/S^2 + (16*Pi^2*(855 - 1774*S^2 + 315*S^4))/(3*(1 + S^2)^2) + (32*(-813 + 838*S^2 + 419*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-592*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-30 - 5*S^2 + 24*S^4))/(3*S^2) + (Pi^4*(14677 + 2274*S^2 + 1137*S^4))/(45*(1 + S^2)^2) - (16*(151 - 1054*S^2 + 535*S^4)*Zeta[3])/(1 + S^2)^2) + (-4*(83 + 99*S^2) - (4*Pi^2*(33 - 427*S^2 + 488*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{3}, -S^2]*((-2*Pi^2*(-37 - 6*S^2 + 35*S^4))/(3*S^2) - (4*(-79 - 106*S^2 + 37*S^4))/S^2 - (2*Pi^4*(109 - 2561*S^2 + 1328*S^4))/(45*(1 + S^2)^2) + (8*(-7 - 87*S^2 + 20*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(44 + 74*S^2 + 37*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((16*(-2 + 5*S^2 + 8*S^4))/S^2 - (4*Pi^2*(-613 + 610*S^2 + 305*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(73 - 540*S^2 + 259*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-55 + 58*S^2 + 29*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(-65 + 6*S^2 + 3*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (16*(157 - 1054*S^2 + 529*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-351 + 326*S^2 + 163*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(-1987 + 1882*S^2 + 941*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(-581 + 578*S^2 + 289*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((8*(-1 + 5*S^4))/S^2 + (4*Pi^2*(-55 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (16*(-23 + 2*S^2 + S^4)*Zeta[5])/(1 + S^2)^2) + Zeta[3]*((-2*Pi^2*(35 + 59*S^2))/3 + (Pi^4*(-243 + 3643*S^2 - 2820*S^4))/(45*(1 + S^2)^2) - (4*(-1 + 82*S^2 + 115*S^4))/S^2 + (16*(28 + 26*S^2 + 13*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-400*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(416 + 45*S^2 - 327*S^4))/(90*S^2) - (2*Pi^2*(-75 - 2*S^2 + 57*S^4))/(3*S^2) + (Pi^6*(18574 + 3682*S^2 + 1841*S^4))/(1260*(1 + S^2)^2) - (4*(-55 + 58*S^2 + 29*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((4*(1 - 10*S^2 + S^4))/S^2 + (2*Pi^2*(-159 + 134*S^2 + 67*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] - (8*(-5 - 146*S^2 + 43*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (4*(91 + 192*S^2 + 96*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - 744*HPL[{2, 1}, -S^2]^2 + ((-16*(3 + 5*S^2 + 3*S^4))/S^2 + (4*Pi^2*(-1093 + 510*S^2 + 255*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (8*(167 - 1182*S^2 + 539*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (24*(169 - 1186*S^2 + 541*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (336*(-3 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (8*(-471 + 370*S^2 + 185*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((32*(3 + 5*S^2 + 3*S^4))/S^2 - (8*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2976*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (16*(-715 + 1054*S^2 + 29*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (24*(-43 + 26*S^2 + 13*S^4)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^2 - (8*(-1207 + 690*S^2 + 345*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(-3641 + 2078*S^2 + 1039*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (320*(179 + 184*S^2 + 92*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-4*(1 + 12*S^2 + 23*S^4))/S^2 - (4*Pi^2*(72 - 597*S^2 + 287*S^4))/(3*(1 + S^2)^2))*Zeta[3] + 28*Zeta[3]^2 + HPL[{3}, -S^2]*((-12*(-1 + 4*S^2 + 9*S^4))/S^2 - (2*Pi^2*(161 - 1120*S^2 + 555*S^4))/(3*(1 + S^2)^2) - (16*(-351 + 326*S^2 + 163*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(39 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-96*(1 + S^2 + S^4))/S^2 - (4*Pi^2*(615 - 1652*S^2 + 429*S^4))/(3*(1 + S^2)^2) - (16*(-257 + 270*S^2 + 135*S^4)*Zeta[3])/(1 + S^2)^2) - (8*(33 - 469*S^2 + 306*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((464*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-97 - 12*S^2 + 73*S^4))/(3*S^2) + (Pi^4*(-6880 + 8117*S^2 + 1457*S^4))/(45*(1 + S^2)^2) + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*(-1275 + 1226*S^2 + 613*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(-3845 + 3686*S^2 + 1843*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (32*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + 2976*HPL[{2, 2, 1}, -S^2] - (320*(-86 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(5 + 6*S^2) - (4*Pi^2*(-633 + 646*S^2 + 323*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-491 + 634*S^2 + 317*S^4)*Zeta[5])/(1 + S^2)^2) - (36*(5 - 84*S^2 + 159*S^4)*Zeta[7])/(1 + S^2)^2) + HPL[{0}, S^2]*(-160*(1 + S^2) + 92*Pi^2*(1 + S^2) + (Pi^4*(2591 + 2271*S^2))/180 + (Pi^6*(60622 + 55645*S^2))/22680 - (7*Pi^8*(-65237 + 21728*S^2 + 10864*S^4))/(194400*(1 + S^2)^2) + (8*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^2) - (4*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)^2) + ((2*(5 + 6*S^2 + 5*S^4))/(3*S^2) - (14*Pi^2*(-23 + 34*S^2 + 17*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2]^3 + ((119 - 192*S^2 - 96*S^4)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^6*((4*(1 + S^2)^2)/(3*S^2) - (2*Pi^2*(-445 + 202*S^2 + 101*S^4))/(27*(1 + S^2)^2) - (4*(-87 + 50*S^2 + 25*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-2*(1 - 6*S^2 + S^4))/S^2 - (4*Pi^2*(5 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + (22*(5 + 8*S^2 + 4*S^4)*HPL[{4}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*(-121 - 400*S^2 - 200*S^4))/(3*(1 + S^2)^2) - (10*(-14 - 6*S^2 + 13*S^4))/S^2)*HPL[{6}, -S^2] + (2*(93 + 430*S^2 + 365*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 - (298*(5 + 8*S^2 + 4*S^4)*HPL[{8}, -S^2])/(1 + S^2)^2 + ((-8*(1 + 5*S^2 + 5*S^4))/S^2 + (2*Pi^2*(-753 + 946*S^2 + 473*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - (32*(-60 + 98*S^2 + 49*S^4)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^2 + ((2*Pi^2*(-2 + 2*S^2 + S^4))/(3*(1 + S^2)^2) + (2*(3 + 14*S^2 + 7*S^4))/S^2)*HPL[{4, 2}, -S^2] + (2*(-74 - 27*S^2 + 3*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + ((4*(-20 + 24*S^2 + 29*S^4))/S^2 + (4*Pi^2*(-17 + 82*S^2 + 41*S^4))/(3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + (2*(-219 - 89*S^2 + 10*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (4*(4 + 2*S^2 + S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 - (2*(575 + 393*S^2 + 270*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 - (10*(5 + 4*S^2 + 2*S^4)*HPL[{6, 2}, -S^2])/(1 + S^2)^2 + (8*(68 + 190*S^2 + 95*S^4)*HPL[{7, 1}, -S^2])/(1 + S^2)^2 - (32*(-239 + 392*S^2 + 196*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^2 + ((-14*Pi^2)/3 + (4*(-3 - 4*S^2 + S^4))/S^2)*HPL[{3, 1, 2}, -S^2] + ((4*(17 + 20*S^2 + 21*S^4))/S^2 - (14*Pi^2*(-183 + 274*S^2 + 137*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] - (8*(-2 - 119*S^2 + 35*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 - (8*(3 - 368*S^2 + 109*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (8*(23 + 62*S^2 + 31*S^4)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^2 + ((8*(41 + 40*S^2 + 31*S^4))/S^2 - (80*Pi^2*(-100 + 146*S^2 + 73*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] - (2*(15 - 1456*S^2 + 449*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 - (8*(47 + 132*S^2 + 66*S^4)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^2 - (2*(75 - 4456*S^2 + 1325*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (4*(42 + 110*S^2 + 55*S^4)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^2 - (8*(99 + 268*S^2 + 134*S^4)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^2 - (16*(-7 - 1134*S^2 + 293*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(26 + 74*S^2 + 37*S^4)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^2 - (16*(206 + 554*S^2 + 277*S^4)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(1057 + 2980*S^2 + 1490*S^4)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(543 - 912*S^2 + 113*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^2 + ((-16*(19 + 18*S^2 + 11*S^4))/S^2 + (16*Pi^2*(-362 + 490*S^2 + 245*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (8*(3251 - 5754*S^2 + 747*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(3251 - 5754*S^2 + 747*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - 28*HPL[{3, 1, 2, 2}, -S^2] + (8*(6509 - 11226*S^2 + 1425*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - 28*HPL[{3, 2, 1, 2}, -S^2] + (4*(-1559 + 3154*S^2 + 1577*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^2 + (192*(-97 + 198*S^2 + 99*S^4)*HPL[{3, 3, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(19423 - 33658*S^2 + 4159*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 16*HPL[{4, 1, 1, 2}, -S^2] + (16*(-1165 + 2374*S^2 + 1187*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (112*(-499 + 1018*S^2 + 509*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-1757 + 3576*S^2 + 1788*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((96*(5 + 6*S^2 + 5*S^4))/S^2 - (16*Pi^2*(-727 + 976*S^2 + 488*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] - (32*(539 - 1054*S^2 + 147*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (96*(539 - 1054*S^2 + 147*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (12544*(-1 + 2*S^2 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (37632*(-1 + 2*S^2 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(2650 - 5383*S^2 + 727*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-4699 + 9418*S^2 + 4709*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (80*(-1567 + 3138*S^2 + 1569*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(-9403 + 18826*S^2 + 9413*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (80*(-3919 + 7842*S^2 + 3921*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (192*(-4907 + 9806*S^2 + 4903*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (160*(235 - 376*S^2 + 61*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-437 + 806*S^2 + 403*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (1920*(-29 + 54*S^2 + 27*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(8 + 11*S^2) - (2*Pi^2*(-31 + 22*S^2 + 11*S^4))/(3*(1 + S^2)^2))*Zeta[3]^2 + HPL[{2}, -S^2]^2*(4*(1 + 9*S^2) + (Pi^4*(7899 - 7568*S^2 - 3784*S^4))/(360*(1 + S^2)^2) + (Pi^2*(3 + 20*S^2 + 13*S^4))/(6*S^2) - (2*S^2*(-59 + 17*S^2)*HPL[{3}, -S^2])/(1 + S^2)^2 - (2*(14 + 30*S^2 + 15*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (2*(543 - 912*S^2 + 113*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (2*(-387 + 794*S^2 + 397*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (1568*(-1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((17 + 270*S^2 - 83*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 2, 1}, -S^2]*((24*(7 + 4*S^2 + S^4))/S^2 + (2*Pi^2*(1813 - 2730*S^2 + 361*S^4))/(3*(1 + S^2)^2) + (16*(-83 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1, 1}, -S^2]*((-16*(31 + 28*S^2 + 19*S^4))/S^2 - (4*Pi^2*(1985 - 2488*S^2 + 387*S^4))/(3*(1 + S^2)^2) + (32*(88 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1, 1}, -S^2]*((16*(40 + 26*S^2 + 9*S^4))/S^2 + (2*Pi^2*(5615 - 7908*S^2 + 1141*S^4))/(3*(1 + S^2)^2) + (32*(-123 + 8*S^2 + 4*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((2*Pi^2*(10 + 11*S^2))/(3*S^2) + (Pi^4*(344 - 742*S^2 - 371*S^4))/(90*(1 + S^2)^2) - (2*(-53 - 78*S^2 + 7*S^4))/S^2 - (2*(11 - 16*S^2 + 21*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(15 + 14*S^2 + 7*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (48*(-1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(-55 + 4*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(8367 - 7832*S^2 - 3916*S^4))/(45*(1 + S^2)^2) + (4*Pi^2*(31 + 38*S^2 + 19*S^4))/(3*S^2) + (16*(14 + 23*S^2 + 25*S^4))/S^2 - (48*(1 - 42*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4, 1}, -S^2]*((-8*(11 - S^2 + 17*S^4))/S^2 + (Pi^2*(-213 - 1022*S^2 + 63*S^4))/(3*(1 + S^2)^2) + (8*(29 + 34*S^2 + 17*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*((32*(1 + S^2)^2)/S^2 + (Pi^4*(11996 - 4122*S^2 - 2061*S^4))/(270*(1 + S^2)^2) + (Pi^2*(29 + 56*S^2 + 25*S^4))/(9*S^2) + ((Pi^2*(661 - 298*S^2 - 149*S^4))/(3*(1 + S^2)^2) + (4*(5 + 6*S^2 + 5*S^4))/S^2)*HPL[{2}, -S^2] - (4*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + (8*(4 + 19*S^2 + 5*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (2*(-91 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (80*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (56*(-31 + 18*S^2 + 9*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (40*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(22 - 133*S^2 + 25*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{3, 2}, -S^2]*((-2*(-5 - 22*S^2 + 23*S^4))/S^2 + (Pi^2*(1 - 322*S^2 + 101*S^4))/(3*(1 + S^2)^2) + (4*(47 + 62*S^2 + 31*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^5*((8*(1 + S^2)^2)/S^2 + (2*Pi^2*(85 - 220*S^2 + 59*S^4))/(3*(1 + S^2)^2) + (16*(37 - 94*S^2 + 37*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) + (8*(-23 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(15*(1 + S^2)^2) + (8*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(-137 + 86*S^2 + 43*S^4)*Zeta[3])/(15*(1 + S^2)^2)) + HPL[{5}, -S^2]*((-14*(-10 - 11*S^2 + S^4))/S^2 + (Pi^2*(97 + 113*S^2 + 184*S^4))/(3*(1 + S^2)^2) + (16*(17 + 24*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*(89 + 118*S^2 + 59*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-2*Pi^2*(37 + 36*S^2 + 13*S^4))/(3*S^2) - (8*(21 + 24*S^2 + 19*S^4))/S^2 + (Pi^4*(-7972 + 8438*S^2 + 4219*S^4))/(90*(1 + S^2)^2) + (48*(-159 + 262*S^2 + 131*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(1 - 242*S^2 + 101*S^4)*Zeta[3])/(1 + S^2)^2) + (4*(40 + 37*S^2) + (Pi^2*(419 + 731*S^2 + 208*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{1}, -S^2]^2*((196*(1 + S^2)^2)/S^2 + (Pi^6*(38554 - 8782*S^2 - 4391*S^4))/(1620*(1 + S^2)^2) + (2*Pi^2*(49 + 111*S^2 + 46*S^4))/(3*S^2) + (Pi^4*(406 + 1074*S^2 + 519*S^4))/(180*S^2) + ((4*(3 + 5*S^2 + 3*S^4))/S^2 - (2*Pi^2*(-496 + 234*S^2 + 117*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (2*(-607 + 354*S^2 + 177*S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + (6*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*(149 - 102*S^2 - 51*S^4))/(3*(1 + S^2)^2) + (10*(5 + 4*S^2 + S^4))/S^2)*HPL[{4}, -S^2] + (4*(61 + 32*S^2 + 83*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 - (4*(-41 + 64*S^2 + 32*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (16*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-8*(19 + 18*S^2 + 11*S^4))/S^2 + (4*Pi^2*(-987 + 454*S^2 + 227*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (8*(15 - 142*S^2 + 15*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (8*(5 + 418*S^2 + 17*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + 6*HPL[{4, 2}, -S^2] + (16*(-23 + 22*S^2 + 11*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((48*(5 + 6*S^2 + 5*S^4))/S^2 - (4*Pi^2*(-661 + 298*S^2 + 149*S^4))/(1 + S^2)^2)*HPL[{2, 1, 1}, -S^2] + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (48*(351 - 1016*S^2 + 353*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-607 + 354*S^2 + 177*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(-3733 + 2182*S^2 + 1091*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (320*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (672*(-31 + 18*S^2 + 9*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (480*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (56*(1 + S^2) - (4*Pi^2*(1 - 166*S^2 + 27*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-16 + 10*S^2 + 5*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((8*(10 + 8*S^2 + 3*S^4))/S^2 + (4*Pi^2*(32 + 73*S^2 + 29*S^4))/(3*(1 + S^2)^2) - (8*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*S^2*(2 + S^2)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-8*(25 + 28*S^2 + 25*S^4))/S^2 - (2*Pi^2*(1291 - 2650*S^2 + 919*S^4))/(3*(1 + S^2)^2) - (8*(-133 + 82*S^2 + 41*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((Pi^4*(10461 - 3644*S^2 - 1822*S^4))/(90*(1 + S^2)^2) + (4*(39 + 46*S^2 + 39*S^4))/S^2 + (Pi^2*(61 + 66*S^2 + 41*S^4))/(3*S^2) - (4*(15 - 142*S^2 + 15*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (2*(-17 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(49 - 250*S^2 + 49*S^4)*Zeta[3])/(1 + S^2)^2) - (8*(-6 - 131*S^2 + 5*S^4)*Zeta[5])/(1 + S^2)^2) + Zeta[3]*(158*(1 + S^2) + (2*Pi^2*(29 + 26*S^2))/3 + (Pi^4*(3039 + 4967*S^2 + 436*S^4))/(180*(1 + S^2)^2) - (24*(-5 + 18*S^2 + 9*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]*((112*(1 + S^2)*(1 + 2*S^2))/S^2 + (4*Pi^2*(1 + S^2)*(16 + 19*S^2))/(3*S^2) + (Pi^6*(198145 - 102608*S^2 - 51304*S^4))/(22680*(1 + S^2)^2) + (Pi^4*(426 + 602*S^2 + 155*S^4))/(180*S^2) + (2*(11 + 30*S^2 + 15*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-2*(1 + 22*S^2 + S^4))/S^2 + (2*Pi^2*(22 + 18*S^2 + 9*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(32 - 7*S^2 + S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (2*(101 + 152*S^2 + 76*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (1568*(-1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-4*(1 + 4*S^2 + 9*S^4))/S^2 + (2*Pi^2*(-763 + 926*S^2 + 463*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(-1 - 118*S^2 + 35*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (2*(11 - 724*S^2 + 225*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (4*(4 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (8*(11 + 18*S^2 + 9*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((16*(1 + 5*S^2 + 5*S^4))/S^2 - (4*Pi^2*(-753 + 946*S^2 + 473*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(543 - 912*S^2 + 113*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(813 - 1438*S^2 + 187*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 4*HPL[{3, 1, 2}, -S^2] - (4*(-951 + 1538*S^2 + 769*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (48*(-239 + 386*S^2 + 193*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(539 - 1054*S^2 + 147*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (48*(-1727 + 3398*S^2 + 1699*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(-239 + 392*S^2 + 196*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((Pi^2*(20 + 265*S^2 - 123*S^4))/(3*(1 + S^2)^2) + (4*(5 + 10*S^2 + S^4))/S^2)*Zeta[3] - (4*(-9 + 20*S^2 + 10*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-1813 + 2730*S^2 - 361*S^4))/(3*(1 + S^2)^2) - (12*(7 + 4*S^2 + S^4))/S^2 - (8*(-83 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((Pi^2*(-1 + 161*S^2 - 50*S^4))/(3*(1 + S^2)^2) + (8*(-1 - 4*S^2 + 2*S^4))/S^2 + (4*(89 + 26*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(21 + 26*S^2 + 13*S^4)*Zeta[3])/(1 + S^2)^2) - (2*(-70 - 217*S^2 + 17*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((Pi^4*(-22810 + 22169*S^2 - 4153*S^4))/(180*(1 + S^2)^2) - (2*Pi^2*(61 + 46*S^2 + 29*S^4))/(3*S^2) - (2*(161 + 164*S^2 + 67*S^4))/S^2 + (32*(135 - 263*S^2 + 37*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*(177 + 50*S^2 + 25*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (24*(91 + 22*S^2 + 11*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (16*(539 - 1054*S^2 + 147*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (6272*(-1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(-1261 + 2354*S^2 + 1177*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-239 + 392*S^2 + 196*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-8*(-1 - 2*S^2 + S^4))/S^2 - (4*Pi^2*(-81 + 22*S^2 + 11*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-23 + 36*S^2 + 18*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((296*(1 + S^2)^2)/(3*S^2) + (2*Pi^2*(59 + 122*S^2 + 51*S^4))/(9*S^2) + (Pi^4*(7838 - 16377*S^2 + 3899*S^4))/(135*(1 + S^2)^2) + (4*(343 - 1054*S^2 + 343*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + ((8*(13 + 8*S^2 + 5*S^4))/(3*S^2) + (4*Pi^2*(-5 + 14*S^2 + 7*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] + (16*(25 - 4*S^2 + 31*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (8*(-39 + 34*S^2 + 17*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + ((-16*(5 + 6*S^2 + 5*S^4))/S^2 + (4*Pi^2*(-661 + 298*S^2 + 149*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (16*(367 - 940*S^2 + 373*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(-67 + 38*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) - (8*(-311 + 170*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + (320*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (32*(-1999 + 1162*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) + (160*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((8*(1 + S^2)*(-1 + 7*S^2))/(3*S^2) + (8*Pi^2*(-67 + 60*S^2 + 30*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((8*(25 + 28*S^2 + 25*S^4))/(3*S^2) + (2*Pi^2*(1291 - 2650*S^2 + 919*S^4))/(9*(1 + S^2)^2) + (8*(-67 + 38*S^2 + 19*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (8*(-133 + 82*S^2 + 41*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + (16*(-46 + 38*S^2 + 19*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((Pi^2*(32 + 53*S^2 + 13*S^4))/(3*S^2) + (2*(62 + 109*S^2 + 15*S^4))/S^2 + (Pi^4*(698 + 705*S^2 + 515*S^4))/(90*(1 + S^2)^2) + (14*(5 + S^2)*HPL[{4}, -S^2])/(1 + S^2)^2 - (4*(53 + 84*S^2 + 42*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-4*(9 + 8*S^2 + S^4))/S^2 + (2*Pi^2*(119 + 26*S^2 + 13*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(5 - 132*S^2 + 39*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*(23 + 62*S^2 + 31*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(37 + 80*S^2 + 40*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (8*(-3 - 140*S^2 + 35*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(89 + 26*S^2 + 13*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (8*(269 + 58*S^2 + 29*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-85 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((4*(1 + S^2)^2)/S^2 + (2*Pi^2*(33 + 58*S^2 + 29*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (4*(79 + 114*S^2 + 57*S^4)*Zeta[5])/(1 + S^2)^2) + (6*(161 + 116*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((260*(1 + S^2)^2)/S^2 + (Pi^2*(159 + 402*S^2 + 179*S^4))/(3*S^2) + (Pi^4*(822 + 2377*S^2 + 1177*S^4))/(180*S^2) + (Pi^6*(70951 - 100521*S^2 + 28938*S^4))/(3780*(1 + S^2)^2) + (16*(41 - 114*S^2 + 41*S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) - (8*(1 - 3*S^2 + 2*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-4*(-30 - 34*S^2 + 7*S^4))/S^2 - (4*Pi^2*(-13 + 58*S^2 + 29*S^4))/(3*(1 + S^2)^2))*HPL[{5}, -S^2] + (4*(105 + 119*S^2 + 160*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (4*(131 + 290*S^2 + 145*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 - (8*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-8*(3 + 2*S^2 + 5*S^4))/S^2 - (8*Pi^2*(-43 + 20*S^2 + 10*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-4*(49 + 32*S^2 + 29*S^4))/S^2 - (2*Pi^2*(-367 + 138*S^2 + 69*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (24*HPL[{4, 2}, -S^2])/(1 + S^2) - (4*(67 + 90*S^2 + 45*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 - (8*(61 + 20*S^2 + 95*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 - (16*(49 + 68*S^2 + 34*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (8*(196 + 166*S^2 + 83*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((32*(3 + 5*S^2 + 3*S^4))/S^2 - (16*Pi^2*(-496 + 234*S^2 + 117*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((16*(31 + 38*S^2 + 23*S^4))/S^2 - (8*Pi^2*(-2971 + 1390*S^2 + 695*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (128*(41 - 114*S^2 + 41*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (4*(-253 + 102*S^2 + 51*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 + (640*(-5 + 2*S^2 + S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (32*(517 - 1372*S^2 + 523*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-799 + 322*S^2 + 161*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 + (4*(-2443 + 970*S^2 + 485*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-597 + 226*S^2 + 113*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((-96*(5 + 6*S^2 + 5*S^4))/S^2 + (8*Pi^2*(-661 + 298*S^2 + 149*S^4))/(1 + S^2)^2)*HPL[{2, 1, 1, 1}, -S^2] + (32*(-607 + 354*S^2 + 177*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^2 - (32*(367 - 940*S^2 + 373*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(-944 + 550*S^2 + 275*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (64*(-944 + 550*S^2 + 275*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (32*(-3709 + 2162*S^2 + 1081*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-22163 + 12914*S^2 + 6457*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (640*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (384*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (192*(-1131 + 658*S^2 + 329*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (960*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((8*(1 + S^2)*(2 + 15*S^2))/S^2 + (2*Pi^2*(-1 + 26*S^2 + 26*S^4))/(3*S^2) + (Pi^4*(153 + 1798*S^2 + 899*S^4))/(90*(1 + S^2)^2))*Zeta[3] + (8*(19 - S^2 + 22*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((8*(1 + S^2)*(17 + 4*S^2))/S^2 + (4*Pi^2*(13 + 11*S^2 + 3*S^4))/(3*S^2) - (2*Pi^4*(-99 + 56*S^2 + 28*S^4))/(45*(1 + S^2)^2) + (8*(18 + 22*S^2 + 11*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(15 - 142*S^2 + 15*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-73 + 30*S^2 + 15*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(1 + 2*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((2*(51 + 62*S^2 + 7*S^4))/S^2 + (2*Pi^2*(101 + 24*S^2 + 123*S^4))/(3*(1 + S^2)^2) + (4*(-17 + 14*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (12*(17 + 18*S^2 + 9*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*((24*(1 + S^2 + S^4))/S^2 + (2*Pi^2*(290 - 729*S^2 + 207*S^4))/(3*(1 + S^2)^2) + (8*(-16 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-607 + 354*S^2 + 177*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (8*(-31 + 22*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-16*(16 + 14*S^2 + 9*S^4))/S^2 - (16*Pi^2*(161 - 328*S^2 + 118*S^4))/(3*(1 + S^2)^2) - (32*(-31 + 24*S^2 + 12*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((16*(25 + 28*S^2 + 25*S^4))/S^2 + (4*Pi^2*(1291 - 2650*S^2 + 919*S^4))/(3*(1 + S^2)^2) + (16*(-133 + 82*S^2 + 41*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-8*(39 + 46*S^2 + 39*S^4))/S^2 - (2*Pi^2*(61 + 66*S^2 + 41*S^4))/(3*S^2) + (Pi^4*(-10461 + 3644*S^2 + 1822*S^4))/(45*(1 + S^2)^2) - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(49 - 250*S^2 + 49*S^4)*Zeta[3])/(1 + S^2)^2) + ((4*(-2 + 34*S^2 + 37*S^4))/S^2 + (4*Pi^2*(21 + 94*S^2 + 47*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((4*(57 + 82*S^2 + 57*S^4))/S^2 + (Pi^2*(103 + 120*S^2 + 73*S^4))/(3*S^2) + (Pi^4*(7807 - 12439*S^2 + 4320*S^4))/(90*(1 + S^2)^2) + ((8*(2 + S^2 + 2*S^4))/S^2 + (4*Pi^2*(-43 + 20*S^2 + 10*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (12*(1 - 4*S^2 + 3*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (4*(41 + 42*S^2 + 21*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-16*(3 + 5*S^2 + 3*S^4))/S^2 + (8*Pi^2*(-496 + 234*S^2 + 117*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(343 - 1054*S^2 + 343*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*(-127 + 50*S^2 + 25*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*(-401 + 158*S^2 + 79*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-607 + 354*S^2 + 177*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-944 + 550*S^2 + 275*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((4*(1 + S^2)^2)/S^2 + (16*Pi^2*(-15 + 16*S^2 + 8*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (8*(-19 + 44*S^2 + 22*S^4)*Zeta[5])/(1 + S^2)^2) + 420*Zeta[7])) + Log[T]*((16*Pi^2*(-16 + 9*S^2))/3 + (Pi^4*(-1019 + 897*S^2))/90 + (Pi^6*(-4370 + 5483*S^2))/3780 - (7*Pi^8*(76101 + 21728*S^2 + 10864*S^4))/(97200*(1 + S^2)^2) + ((-9 - 8*S^2 - 4*S^4)*HPL[{0}, S^2]^8)/(96*(1 + S^2)^2) - (16*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^2) + (8*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^7*((-8 + 7*S^2 - S^4)/(24*(1 + S^2)^2) + ((-9 - 2*S^2 - S^4)*HPL[{1}, -S^2])/(12*(1 + S^2)^2)) + HPL[{1}, -S^2]^6*((-8*(1 + S^2)^2)/(3*S^2) + (16*Pi^2*(-40 + 18*S^2 + 9*S^4))/(9*(1 + S^2)^2) - 40*HPL[{2}, -S^2]) + ((20*(-1 + S^2)*(1 + S^2))/(3*S^2) + (2*Pi^2*(-93 + 244*S^2 + 122*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2]^3 + (2*(-187 + 56*S^2 + 28*S^4)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^6*((-3 + S^2)/12 + (Pi^2*(-91 - 68*S^2 - 34*S^4))/(72*(1 + S^2)^2) + (2*(-6 + 6*S^2 + S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2) + ((-49 - 10*S^2 - 5*S^4)*HPL[{1}, -S^2]^2)/(12*(1 + S^2)^2) + ((-5 - 2*S^2 - S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-4*(-1 + 10*S^2 + 3*S^4))/S^2 + (2*Pi^2*(-29 + 86*S^2 + 43*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + (8*(-5 + 4*S^2 + 2*S^4)*HPL[{4}, -S^2]^2)/(1 + S^2)^2 + ((20*(-10 - 8*S^2 + 5*S^4))/S^2 - (2*Pi^2*(167 + 404*S^2 + 202*S^4))/(3*(1 + S^2)^2))*HPL[{6}, -S^2] + (4*(-847 - 366*S^2 + 253*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 - (12*(461 + 480*S^2 + 240*S^4)*HPL[{8}, -S^2])/(1 + S^2)^2 + (160 - (8*Pi^2*(-567 + 214*S^2 + 107*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 + (32*(-233 + 54*S^2 + 27*S^4)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^2 + ((-12*(1 + S^4))/S^2 + (164*Pi^2*(-1 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + (4*(-2 - 127*S^2 + 107*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + ((-16*(-11 - 11*S^2 + 6*S^4))/S^2 + (4*Pi^2*(-243 + 950*S^2 + 475*S^4))/(3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + (4*(-7 - 305*S^2 + 230*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (8*(5 + 28*S^2 + 14*S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 - (4*(-665 - 327*S^2 + 234*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 - (20*(-1 + 16*S^2 + 8*S^4)*HPL[{6, 2}, -S^2])/(1 + S^2)^2 + (16*(230 + 306*S^2 + 153*S^4)*HPL[{7, 1}, -S^2])/(1 + S^2)^2 + (320*(-77 + 20*S^2 + 10*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^2 - (148*Pi^2*HPL[{3, 1, 2}, -S^2])/3 + ((160*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-409 + 902*S^2 + 451*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] + (8*(63 - 1878*S^2 + 1667*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 + (48*(23 - 964*S^2 + 853*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (24*(-41 + 86*S^2 + 43*S^4)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^2 + ((48*(1 + S^2)*(-15 + 11*S^2))/S^2 + (8*Pi^2*(-397 + 1050*S^2 + 525*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + (4*(253 - 11278*S^2 + 10213*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 - (80*(-23 + 38*S^2 + 19*S^4)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^2 + (4*(841 - 35446*S^2 + 31057*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (48*(-9 + 38*S^2 + 19*S^4)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^2 - (16*(-361 + 706*S^2 + 353*S^4)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^2 + (32*(157 - 9234*S^2 + 7937*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 - (40*(-89 + 158*S^2 + 79*S^4)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^2 - (280*(-83 + 170*S^2 + 85*S^4)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(-3593 + 8042*S^2 + 4021*S^4)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^2 - (12832*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2) + ((-192*(1 + S^2)*(-3 + 2*S^2))/S^2 - (32*Pi^2*(-43 + 162*S^2 + 81*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (32*(-1205 + 892*S^2 + 357*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (32*(-1205 + 892*S^2 + 357*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (8*(-121 + 94*S^2 + 47*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2)^2 + (128*(-602 + 223*S^2 + 390*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-121 + 94*S^2 + 47*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2)^2 - (168*(29 + 42*S^2 + 21*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^2 - 11712*HPL[{3, 3, 1, 1}, -S^2] + (64*(-3622 + 1603*S^2 + 2255*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (48*(-29 + 110*S^2 + 55*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (1008*(13 + 18*S^2 + 9*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (48*(761 + 1354*S^2 + 677*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(1237 + 1754*S^2 + 877*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((960*(-1 + S^2)*(1 + S^2))/S^2 + (160*Pi^2*(-15 + 28*S^2 + 14*S^4))/(1 + S^2)^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + (256*(106 - 223*S^2 + 106*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (768*(106 - 223*S^2 + 106*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 7808*HPL[{2, 2, 1, 2, 1}, -S^2] - 23424*HPL[{2, 2, 2, 1, 1}, -S^2] + (64*(2149 - 5617*S^2 + 3034*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 45504*HPL[{3, 1, 1, 1, 2}, -S^2] + 76736*HPL[{3, 1, 1, 2, 1}, -S^2] + 92352*HPL[{3, 1, 2, 1, 1}, -S^2] + 193856*HPL[{3, 2, 1, 1, 1}, -S^2] + (2304*(259 + 498*S^2 + 249*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (56640*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) - (7680*(4 + 2*S^2 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 26880*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (-72*S^2 - (4*Pi^2*(42 + 22*S^2 + 11*S^4))/(3*(1 + S^2)^2))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((-960*(-1 + S^2)*(1 + S^2))/S^2 - (16*Pi^2*(-903 + 446*S^2 + 479*S^4))/(3*(1 + S^2)^2) - (27840*Zeta[3])/(1 + S^2)^2) + HPL[{5}, -S^2]*((-4*(70 + 83*S^2 + 17*S^4))/S^2 + (2*Pi^2*(-183 - 367*S^2 + 308*S^4))/(3*(1 + S^2)^2) - (8*(213 + 58*S^2 + 29*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (128*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^5*((-3 - 2*S^2)/2 + (Pi^2*(-1205 + 1596*S^2 - 183*S^4))/(360*(1 + S^2)^2) + ((-605 + 652*S^2 - 47*S^4)*HPL[{1}, -S^2]^2)/(30*(1 + S^2)^2) - (4*(164 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(45*(1 + S^2)^2) + ((-365 + 581*S^2 - 138*S^4)*HPL[{2}, -S^2])/(60*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(-1601 - 218*S^2 - 109*S^4))/(180*(1 + S^2)^2) + (-1 - 4*S^2 - 2*S^4)/(2*S^2) + ((-541 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(30*(1 + S^2)^2)) - HPL[{3}, -S^2]/(1 + S^2)^2 + (271*HPL[{2, 1}, -S^2])/(15*(1 + S^2)^2) - (3*(2 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 2, 1}, -S^2]*((-352*(1 + S^4))/S^2 - (4*Pi^2*(1687 - 2820*S^2 + 885*S^4))/(3*(1 + S^2)^2) + (448*(29 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-16*(1 + S^2)^2)/S^2 - (4*Pi^2*(265 - 736*S^2 + 175*S^4))/(9*(1 + S^2)^2) + (240*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (1120*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + 240*HPL[{2, 1}, -S^2] - (64*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1, 1}, -S^2]*((-16*(81 + 14*S^2 + 21*S^4))/S^2 - (4*Pi^2*(5087 - 5970*S^2 + 719*S^4))/(3*(1 + S^2)^2) + (32*(1255 + 46*S^2 + 23*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4, 1}, -S^2]*((-32*(-5 - 7*S^2 + 31*S^4))/S^2 - (2*Pi^2*(-109 - 6934*S^2 + 5663*S^4))/(3*(1 + S^2)^2) + (32*(-47 + 52*S^2 + 26*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 2}, -S^2]*((-4*(7 + 81*S^4))/S^2 - (2*Pi^2*(-19 - 1938*S^2 + 1753*S^4))/(3*(1 + S^2)^2) + (8*(-47 + 58*S^2 + 29*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((36*(-9 + S^2)*(1 + S^2))/S^2 + (Pi^4*(487 - 1770*S^2 - 885*S^4))/(45*(1 + S^2)^2) + (4*Pi^2*(-14 - 5*S^2 + 4*S^4))/(3*S^2) + (4*(-295 + 706*S^2 + 41*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (32*(-20 + 78*S^2 + 39*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (240*(-5 + 22*S^2 + 11*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-21 - 92*S^2 + 57*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*((-64*(1 + S^2)^2)/S^2 - (4*Pi^2*(5 + 7*S^2))/(3*S^2) + (Pi^4*(-12982 + 4426*S^2 + 2213*S^4))/(135*(1 + S^2)^2) + ((40*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] + (8*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + (40*(11 - 88*S^2 + 41*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*(-241 + 238*S^2 + 119*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (1200*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (32*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - 1200*HPL[{2, 1, 1}, -S^2] + (40*(29 - 188*S^2 + 119*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((416*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-29 - 10*S^2 + 29*S^4))/(3*S^2) + (2*Pi^4*(-4947 + 3646*S^2 + 1823*S^4))/(45*(1 + S^2)^2) + (64*(9 - 223*S^2 + 203*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*((-12*(1 + S^2)^2)/S^2 + (Pi^2*(-1 - 32*S^2 + 9*S^4))/(3*S^2) + (Pi^4*(-11243 + 4120*S^2 + 2060*S^4))/(180*(1 + S^2)^2) + (4*(35 - 557*S^2 + 436*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (12*(-31 + 50*S^2 + 25*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (1604*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(251 + 166*S^2 + 83*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + 976*HPL[{2, 1, 1}, -S^2] + (2*(9 - 748*S^2 + 811*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-32*(1 + S^2)*(-11 + 2*S^2))/S^2 + (Pi^4*(3796 - 3022*S^2 - 1511*S^4))/(45*(1 + S^2)^2) - (20*Pi^2*(-7 - 4*S^2 + 5*S^4))/(3*S^2) - (1856*(-14 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(37 - 942*S^2 + 813*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^4*((Pi^2*(-61 + 26*S^2))/36 + (-53 + 43*S^2)/6 + (Pi^4*(-14057 - 8344*S^2 - 4172*S^4))/(2160*(1 + S^2)^2) + ((-175 + 266*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + (5*(-65 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(9*(1 + S^2)^2) + ((Pi^2*(-281 - 50*S^2 - 25*S^4))/(18*(1 + S^2)^2) + (-15 + 2*S^2 + 10*S^4)/(6*S^2))*HPL[{2}, -S^2] + ((-243 + 56*S^2 + 28*S^4)*HPL[{2}, -S^2]^2)/(12*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-15 - 10*S^2 + 9*S^4)/(6*S^2) - (5*Pi^2*(277 + 26*S^2 + 13*S^4))/(36*(1 + S^2)^2) - (4*(69 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-11 - 3*S^2 + 12*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) - 3*HPL[{4}, -S^2] + ((739 - 395*S^2 - 46*S^4)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)^2) + ((252 - 26*S^2 - 13*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(-131 + 10*S^2 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((-83 + 14*S^2 + 69*S^4)*Zeta[3])/(6*(1 + S^2)^2) + HPL[{1}, -S^2]*((-30 - 17*S^2 + 17*S^4)/(6*S^2) + (Pi^2*(-415 + 506*S^2 + 41*S^4))/(12*(1 + S^2)^2) + ((-258 + 285*S^2 - S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) - (2*(2 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(69 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (2*(26 + 38*S^2 + 19*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + (16*(-20 + 29*S^2) + (2*Pi^2*(-81 - 707*S^2 + 1270*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2, 1}, -S^2]*((-652*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(21822 - 13413*S^2 - 8155*S^4))/(90*(1 + S^2)^2) - (4*Pi^2*(-61 + 39*S^4))/(3*S^2) - (32*(191 - 446*S^2 + 233*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-1869 + 38*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (96*(487 + 26*S^2 + 13*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (128*(106 - 223*S^2 + 106*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + 3904*HPL[{2, 2, 1}, -S^2] + (64*(-284 + 302*S^2 + 151*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (640*(-77 + 20*S^2 + 10*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((8*Pi^2*(-477 + 2*S^2 + S^4))/(3*(1 + S^2)^2) - (16*(-1 + 10*S^2 + S^4))/S^2)*Zeta[3] + (32*(-201 + 2*S^2 + S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{0}, S^2]^3*((-237 - 173*S^2)/3 + (Pi^2*(-82 - 45*S^2))/9 + (Pi^4*(-12183 + 23190*S^2 - 4099*S^4))/(1080*(1 + S^2)^2) - (20*(18 - 33*S^2 + 5*S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + (4*(-151 + 34*S^2 + 17*S^4)*HPL[{1}, -S^2]^5)/(9*(1 + S^2)^2) + ((-213 + 994*S^2 - 217*S^4)*HPL[{2}, -S^2]^2)/(6*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-8*(7 + 13*S^2 + 5*S^4))/(9*S^2) + (2*Pi^2*(-1411 + 162*S^2 + 81*S^4))/(27*(1 + S^2)^2) + (8*(-113 + 24*S^2 + 12*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-2*Pi^2*(9 + 2*S^2 + S^4))/(3*(1 + S^2)^2) - (2*(9 + 20*S^2 + 3*S^4))/(3*S^2))*HPL[{3}, -S^2] - (2*(46 + 29*S^2 + 63*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (4*(-11 + 6*S^2 + 3*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + ((4*(15 + 10*S^2 + 7*S^4))/(3*S^2) + (2*Pi^2*(657 + 22*S^2 + 11*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(287 - 922*S^2 + 287*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (4*(-3 + 34*S^2 + 17*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) + (80*(1 + 4*S^2 + 2*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(73 - 233*S^2 + 69*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(361 + 10*S^2 + 5*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(369 + 14*S^2 + 7*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(386 + 22*S^2 + 11*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((4*(-1 + S^2))/3 - (2*Pi^2*(97 + 118*S^2 + 59*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]*((Pi^2*(-29 - 86*S^2 - 40*S^4))/(9*S^2) + (Pi^4*(-4941 - 14*S^2 - 7*S^4))/(135*(1 + S^2)^2) - (4*(25 + 63*S^2 + 22*S^4))/(3*S^2) + ((-2*(31 + 30*S^2 + 11*S^4))/(3*S^2) + (Pi^2*(-1219 + 146*S^2 + 73*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(-159 + 38*S^2 + 19*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (16*(10 + 8*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (4*(-29 + 22*S^2 + 11*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (4*(551 - 770*S^2 + 179*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (16*(-168 + 38*S^2 + 19*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (16*(-113 + 24*S^2 + 12*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-21 - 33*S^2 + 2*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((Pi^2*(-657 + 1513*S^2 - 414*S^4))/(18*(1 + S^2)^2) - (2*(23 + 46*S^2 + 13*S^4))/(3*S^2) - (8*(-1 + 8*S^2 + 4*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (4*(361 + 10*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (4*(6 + 22*S^2 + 11*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((Pi^2*(-1145 + 1642*S^2 - 197*S^4))/(9*(1 + S^2)^2) - (2*(29 + 62*S^2 + 21*S^4))/(3*S^2) - (2*(551 - 770*S^2 + 179*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) - (24*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*(-113 + 24*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(3 + 34*S^2 + 17*S^4)*Zeta[3])/(3*(1 + S^2)^2)) - (52*(5 + 4*S^2 + 2*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + Zeta[3]*((20*Pi^2*(-5 + 7*S^2))/3 + 4*(-69 + 163*S^2) + (Pi^4*(-687 - 6249*S^2 + 7850*S^4))/(90*(1 + S^2)^2) - (48*(14 + 18*S^2 + 9*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{3}, -S^2]*((2*Pi^2*(-32 - 15*S^2 + 53*S^4))/(3*S^2) + (4*(-94 - 89*S^2 + 69*S^4))/S^2 + (Pi^4*(-354 - 4605*S^2 + 3745*S^4))/(45*(1 + S^2)^2) - (4*(-9 - 119*S^2 + 90*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(17 + 20*S^2 + 10*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-32*(-2 + 5*S^2 + 2*S^4))/S^2 - (4*Pi^2*(989 + 142*S^2 + 71*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(-21 - 900*S^2 + 865*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (8*(-85 + 166*S^2 + 83*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (32*(-5 + 24*S^2 + 12*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (16*(-19 - 892*S^2 + 867*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-999 + 58*S^2 + 29*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(-2923 + 10*S^2 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(467 + 64*S^2 + 32*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-8*(-1 - 4*S^2 + 9*S^4))/S^2 - (4*Pi^2*(-43 + 42*S^2 + 21*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-23 + 50*S^2 + 25*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-392*(1 + S^2)^2)/S^2 - (4*Pi^2*(47 + 73*S^2 + 10*S^4))/(3*S^2) + (2*Pi^4*(-104 - 104*S^2 + 67*S^4))/(45*S^2) + (11*Pi^6*(-50011 + 10858*S^2 + 5429*S^4))/(11340*(1 + S^2)^2) + ((-8*(3 + 5*S^2 + 3*S^4))/S^2 + (2*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - 124*HPL[{2}, -S^2]^3 + (4*(-119 + 74*S^2 + 37*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-96*(1 + S^2))/S^2 - (2*Pi^2*(-457 + 558*S^2 + 279*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] + (8*(-103 - 386*S^2 + 173*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 - (4*(175 + 566*S^2 + 283*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-96*(1 + S^2)*(-3 + 2*S^2))/S^2 + (16*Pi^2*(185 + 122*S^2 + 61*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (16*(157 - 1054*S^2 + 529*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (16*(493 - 3694*S^2 + 1753*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (36*(-43 + 26*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (32*(-241 + 238*S^2 + 119*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((480*(-1 + S^2)*(1 + S^2))/S^2 - (16*Pi^2*(514 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (32*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (192*(144 - 307*S^2 + 69*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 2976*HPL[{3, 2, 1}, -S^2] - (64*(19 + 398*S^2 + 199*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (14400*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (128*(-13 + 154*S^2 + 77*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 14400*HPL[{2, 1, 1, 1, 1}, -S^2] + ((8*(1 + 28*S^2 + 49*S^4))/S^2 + (8*Pi^2*(25 - 174*S^2 + 111*S^4))/(1 + S^2)^2)*Zeta[3] + (16*(-16 + 10*S^2 + 5*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((8*(-19 - 2*S^2 + 29*S^4))/S^2 + (4*Pi^2*(135 - 1408*S^2 + 657*S^4))/(3*(1 + S^2)^2) + (16*(-581 + 578*S^2 + 289*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (224*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-384*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(3*(1 + S^2)^2) + (32*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((296*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(-14677 - 2274*S^2 - 1137*S^4))/(90*(1 + S^2)^2) + (4*Pi^2*(-30 - 5*S^2 + 24*S^4))/(3*S^2) + (8*(157 - 1054*S^2 + 529*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (4*(-367 + 226*S^2 + 113*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(151 - 1054*S^2 + 535*S^4)*Zeta[3])/(1 + S^2)^2) + (96*(9 - 71*S^2 + 65*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-592*(1 + S^2)^2)/(3*S^2) - (4*Pi^2*(59 + 92*S^2 + 11*S^4))/(9*S^2) - (4*Pi^4*(3904 - 9634*S^2 + 1657*S^4))/(135*(1 + S^2)^2) - (8*(343 - 1054*S^2 + 343*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + ((32*(-6 + 2*S^2 + 9*S^4))/(3*S^2) - (8*Pi^2*(-721 + 758*S^2 + 379*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] + (32*(11 - 266*S^2 + 83*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (16*(-35 + 82*S^2 + 41*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-160*(-1 + S^2)*(1 + S^2))/S^2 + (16*Pi^2*(514 + 158*S^2 + 79*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (64*(-89 - 133*S^2 + 136*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + (32*(-581 + 578*S^2 + 289*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) + (64*(-992 + 986*S^2 + 493*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + (4800*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) + (128*(-661 + 238*S^2 + 119*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) + 4800*HPL[{2, 1, 1, 1}, -S^2] + (32*(3 + 5*S^2) - (8*Pi^2*(-593 + 674*S^2 + 337*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((128*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(9*(1 + S^2)^2) - (16*(-581 + 578*S^2 + 289*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (32*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(3*(1 + S^2)^2)) - (32*(-256 + 358*S^2 + 179*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((288*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(1 + S^2)*(-28 + 25*S^2))/(3*S^2) + (Pi^4*(-406 - 110*S^2 + 467*S^4))/(90*S^2) + (Pi^6*(-136855 + 27484*S^2 + 13742*S^4))/(11340*(1 + S^2)^2) + (16*(-11 + 20*S^2 + 10*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((4*(-1 + 20*S^2 + 7*S^4))/S^2 - (4*Pi^2*(-27 + 172*S^2 + 86*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(-9 + 7*S^2)*(2 + 25*S^2)*HPL[{5}, -S^2])/(1 + S^2)^2 - (4*(87 + 184*S^2 + 92*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - 976*HPL[{2, 1}, -S^2]^2 + ((-16*(-1 - 10*S^2 + S^4))/S^2 - (4*Pi^2*(-1175 + 346*S^2 + 173*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (8*(45 - 996*S^2 + 847*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*(125 - 5978*S^2 + 5273*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (24*(-31 + 50*S^2 + 25*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (8*(-267 + 778*S^2 + 389*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (-320 + (16*Pi^2*(-567 + 214*S^2 + 107*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (6416*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (64*(-296 + 223*S^2 + 84*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (24*(-43 + 26*S^2 + 13*S^4)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^2 + (8*(-1367 + 370*S^2 + 185*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (144*(-241 + 38*S^2 + 19*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (128*(106 - 223*S^2 + 106*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(326 + 1522*S^2 + 761*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (640*(-77 + 20*S^2 + 10*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((8*(1 + 21*S^4))/S^2 + (2*Pi^2*(28 - 997*S^2 + 887*S^4))/(3*(1 + S^2)^2))*Zeta[3] + 24*Zeta[3]^2 + HPL[{3}, -S^2]*(176*S^2 + (2*Pi^2*(-31 - 971*S^2 + 896*S^4))/(3*(1 + S^2)^2) + (8*(-999 + 58*S^2 + 29*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (152*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((176*(1 + S^4))/S^2 + (2*Pi^2*(1687 - 2820*S^2 + 885*S^4))/(3*(1 + S^2)^2) - (224*(29 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + (4*(-38 - 789*S^2 + 865*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{0}, S^2]*((Pi^4*(-1151 - 802*S^2))/90 + (Pi^2*(-385 - 321*S^2))/3 - 520*(1 + S^2) + (Pi^6*(-248987 + 707115*S^2 - 246358*S^4))/(22680*(1 + S^2)^2) - (56*(7 - 22*S^2 + 7*S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) + (32*(-7 + 4*S^2 + 2*S^4)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^2) - (2*(113 - 912*S^2 + 543*S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-8*(1 + S^2)^2)/S^2 + (4*Pi^2*(-445 + 202*S^2 + 101*S^4))/(9*(1 + S^2)^2) + (8*(-87 + 50*S^2 + 25*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (2*(3 - 10*S^2 + 11*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-20*(6 + 8*S^2 + S^4))/S^2 + (4*Pi^2*(-37 + 10*S^2 + 5*S^4))/(3*(1 + S^2)^2))*HPL[{5}, -S^2] - (2*(225 + 293*S^2 + 360*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (8*(5 + 24*S^2 + 12*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 + (8*(147 - 1054*S^2 + 539*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((4*(-3 - 4*S^2 + 17*S^4))/S^2 + (2*Pi^2*(-99 + 226*S^2 + 113*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((8*(11 + 4*S^2 + 25*S^4))/S^2 + (8*Pi^2*(-39 + 140*S^2 + 70*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (2*(19 + 13*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) + (8*(15 + 8*S^2 + 4*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + (32*(14 + 3*S^2 + 23*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (48*(7 + 4*S^2 + 2*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 + (8*(129 + 32*S^2 + 16*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((-32*(5 + 5*S^2 + S^4))/S^2 - (8*Pi^2*(1231 + 10*S^2 + 5*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-16*(39 + 38*S^2 + 15*S^4))/S^2 - (16*Pi^2*(1856 + 46*S^2 + 23*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + 8*HPL[{3, 1, 2}, -S^2] - (8*(225 - 1826*S^2 + 1085*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (4*(-161 + 286*S^2 + 143*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 - (192*(-11 + 18*S^2 + 9*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 - (24*(257 - 1830*S^2 + 1129*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (48*(-43 + 74*S^2 + 37*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 - (48*(-137 + 214*S^2 + 107*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 - (32*(-397 + 626*S^2 + 313*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((96*(5 + 6*S^2 + 5*S^4))/S^2 + (16*Pi^2*(1256 + 82*S^2 + 41*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (64*(411 + 38*S^2 + 19*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^2 + (96*(50 - 313*S^2 + 197*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(5025 + 298*S^2 + 149*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (16*(5025 + 298*S^2 + 149*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (16*(9957 + 754*S^2 + 377*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (64*(7447 + 584*S^2 + 292*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (160*(61 - 376*S^2 + 235*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (55680*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (167040*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (320*(-871 + 10*S^2 + 5*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (3840*(29 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-144*(1 + S^2) - (8*Pi^2*(2 + S^2))/3 - (373*Pi^4*(1 + 4*S^2 + 2*S^4))/(45*(1 + S^2)^2))*Zeta[3] - (4*(17 - 25*S^2 + 42*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((8*Pi^2*(15 + 14*S^2 + 11*S^4))/(3*S^2) + (16*(25 + 23*S^2 + 14*S^4))/S^2 + (Pi^4*(12555 + 544*S^2 + 272*S^4))/(45*(1 + S^2)^2) - (16*(871 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (27840*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(23 - 62*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((-8*(1 + S^2)*(13 + 7*S^2))/S^2 + (Pi^4*(-719 - 422*S^2 - 211*S^4))/(90*(1 + S^2)^2) - (4*Pi^2*(9 + 14*S^2 + 6*S^4))/(3*S^2) - (56*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(-33 + 144*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (88*(-5 + 6*S^2 + 3*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (16*(-49 + 74*S^2 + 37*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(-5 - 6*S^2 + 3*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((4*(-17 - 16*S^2 + 3*S^4))/S^2 - (5*Pi^2*(37 + 8*S^2 + 51*S^4))/(3*(1 + S^2)^2) - (8*(-11 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(17 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-16*(19 + 28*S^2 + 31*S^4))/S^2 - (4*Pi^2*(597 - 2812*S^2 + 1451*S^4))/(3*(1 + S^2)^2) - (96*(-15 + 28*S^2 + 14*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((16*(13 + 14*S^2 + 12*S^4))/S^2 + (2*Pi^2*(587 - 2800*S^2 + 1469*S^4))/(3*(1 + S^2)^2) + (32*(-22 + 42*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-128*(1 + S^2)^2)/S^2 - (4*Pi^2*(29 + 56*S^2 + 25*S^4))/(9*S^2) + (2*Pi^4*(-11996 + 4122*S^2 + 2061*S^4))/(135*(1 + S^2)^2) + ((-16*(5 + 6*S^2 + 5*S^4))/S^2 + (4*Pi^2*(-661 + 298*S^2 + 149*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (16*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (32*(4 + 19*S^2 + 5*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(-91 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (320*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (224*(-31 + 18*S^2 + 9*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (160*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(22 - 133*S^2 + 25*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((-40*(1 + S^2)^2)/S^2 - (10*Pi^2*(85 - 220*S^2 + 59*S^4))/(3*(1 + S^2)^2) - (80*(37 - 94*S^2 + 37*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) - (8*(-23 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (40*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-137 + 86*S^2 + 43*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((Pi^2*(-507 + 3102*S^2 - 1295*S^4))/(6*(1 + S^2)^2) - (6*(1 + 4*S^2 + 7*S^4))/S^2 - (2*(-39 + 74*S^2 + 37*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (8*(411 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(-41 + 86*S^2 + 43*S^4)*Zeta[3])/(1 + S^2)^2) + (-8*(12 + 11*S^2) - (104*Pi^2*(1 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{1}, -S^2]*((-392*(1 + S^2)^2)/S^2 + (Pi^4*(-406 - 1074*S^2 - 519*S^4))/(90*S^2) - (4*Pi^2*(49 + 111*S^2 + 46*S^4))/(3*S^2) + (Pi^6*(-38554 + 8782*S^2 + 4391*S^4))/(810*(1 + S^2)^2) + ((-8*(3 + 5*S^2 + 3*S^4))/S^2 + (4*Pi^2*(-496 + 234*S^2 + 117*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (4*(-607 + 354*S^2 + 177*S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) - (12*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-20*(5 + 4*S^2 + S^4))/S^2 + (2*Pi^2*(-149 + 102*S^2 + 51*S^4))/(3*(1 + S^2)^2))*HPL[{4}, -S^2] - (8*(61 + 32*S^2 + 83*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (8*(-41 + 64*S^2 + 32*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((16*(19 + 18*S^2 + 11*S^4))/S^2 - (8*Pi^2*(-987 + 454*S^2 + 227*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (16*(15 - 142*S^2 + 15*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (16*(5 + 418*S^2 + 17*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - 12*HPL[{4, 2}, -S^2] - (32*(-23 + 22*S^2 + 11*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-96*(5 + 6*S^2 + 5*S^4))/S^2 + (8*Pi^2*(-661 + 298*S^2 + 149*S^4))/(1 + S^2)^2)*HPL[{2, 1, 1}, -S^2] - (32*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (96*(351 - 1016*S^2 + 353*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (32*(-607 + 354*S^2 + 177*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(-3733 + 2182*S^2 + 1091*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (640*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (1344*(-31 + 18*S^2 + 9*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (960*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-112*(1 + S^2) + (8*Pi^2*(1 - 166*S^2 + 27*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (16*(-16 + 10*S^2 + 5*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((-16*(10 + 8*S^2 + 3*S^4))/S^2 - (8*Pi^2*(32 + 73*S^2 + 29*S^4))/(3*(1 + S^2)^2) + (16*(-67 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (32*S^2*(2 + S^2)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((16*(25 + 28*S^2 + 25*S^4))/S^2 + (4*Pi^2*(1291 - 2650*S^2 + 919*S^4))/(3*(1 + S^2)^2) + (16*(-133 + 82*S^2 + 41*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-8*(39 + 46*S^2 + 39*S^4))/S^2 - (2*Pi^2*(61 + 66*S^2 + 41*S^4))/(3*S^2) + (Pi^4*(-10461 + 3644*S^2 + 1822*S^4))/(45*(1 + S^2)^2) + (8*(15 - 142*S^2 + 15*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (4*(-17 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*(49 - 250*S^2 + 49*S^4)*Zeta[3])/(1 + S^2)^2) + (16*(-6 - 131*S^2 + 5*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-296*(1 + S^2)^2)/S^2 + (Pi^4*(-7838 + 16377*S^2 - 3899*S^4))/(45*(1 + S^2)^2) - (2*Pi^2*(59 + 122*S^2 + 51*S^4))/(3*S^2) - (4*(343 - 1054*S^2 + 343*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((-8*(13 + 8*S^2 + 5*S^4))/S^2 - (4*Pi^2*(-5 + 14*S^2 + 7*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] - (16*(25 - 4*S^2 + 31*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(-39 + 34*S^2 + 17*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((48*(5 + 6*S^2 + 5*S^4))/S^2 - (4*Pi^2*(-661 + 298*S^2 + 149*S^4))/(1 + S^2)^2)*HPL[{2, 1}, -S^2] + (16*(367 - 940*S^2 + 373*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-67 + 38*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(-311 + 170*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (320*(37 - 94*S^2 + 37*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (64*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-1999 + 1162*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (480*(-87 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-8*(1 + S^2)*(-1 + 7*S^2))/S^2 - (8*Pi^2*(-67 + 60*S^2 + 30*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-8*(25 + 28*S^2 + 25*S^4))/S^2 - (2*Pi^2*(1291 - 2650*S^2 + 919*S^4))/(3*(1 + S^2)^2) - (8*(-67 + 38*S^2 + 19*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (32*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-133 + 82*S^2 + 41*S^4)*Zeta[3])/(1 + S^2)^2) - (16*(-46 + 38*S^2 + 19*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]*((Pi^4*(-8418 + 27587*S^2 - 13127*S^4))/(180*(1 + S^2)^2) - (4*Pi^2*(21 + 37*S^2 + 22*S^4))/(3*S^2) - (2*(67 + 164*S^2 + 161*S^4))/S^2 + ((-106*Pi^2*(-1 + 2*S^2 + S^4))/(3*(1 + S^2)^2) - (4*(-1 - 4*S^2 + 7*S^4))/S^2)*HPL[{3}, -S^2] - (2*(1 - 32*S^2 + 15*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(-7 + 6*S^2 + 3*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((16*(5 + 5*S^2 + S^4))/S^2 + (4*Pi^2*(1231 + 10*S^2 + 5*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(73 - 528*S^2 + 269*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (4*(-77 + 150*S^2 + 75*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (128*(-8 + 14*S^2 + 7*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (16*(147 - 1054*S^2 + 539*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(411 + 38*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (16*(2515 + 154*S^2 + 77*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (27840*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-16*(1 + 2*S^2))/S^2 - (4*Pi^2*(-39 + 106*S^2 + 53*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-15 + 52*S^2 + 26*S^4)*Zeta[5])/(1 + S^2)^2)) + HPL[{0}, S^2]^2*(16*(-16 + 9*S^2) + (Pi^2*(-101 + 69*S^2))/3 + (Pi^4*(-162 + 109*S^2))/45 + (Pi^6*(-8589 - 3526*S^2 - 1763*S^4))/(648*(1 + S^2)^2) - (8*(59 - 137*S^2 + 14*S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) + (8*(-31 + 8*S^2 + 4*S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) + ((-1 - 12*S^2 + 9*S^4)/S^2 + (Pi^2*(-607 + 284*S^2 + 142*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (2*(-154 + 122*S^2 + 61*S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((2*(-5 - 4*S^2 + 5*S^4))/S^2 + (10*Pi^2*(-158 + 26*S^2 + 13*S^4))/(9*(1 + S^2)^2) + (2*(-803 + 134*S^2 + 67*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + (4*(4 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*(-31 - 78*S^2 - 39*S^4))/(3*(1 + S^2)^2) + (2*(-13 + 2*S^2 + 5*S^4))/S^2)*HPL[{4}, -S^2] + (2*(-56 - 25*S^2 + 67*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 - (2*(70 + 102*S^2 + 51*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (8*(-182 + 114*S^2 + 57*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-4*(-17 - 14*S^2 + 13*S^4))/S^2 - (2*Pi^2*(-578 + 230*S^2 + 115*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (2*(-23 - 154*S^2 + 61*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (2*(-161 - 522*S^2 + 247*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (2*(-5 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (4*(35 + 66*S^2 + 33*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((16*(-7 - 5*S^2 + 7*S^4))/S^2 + (4*Pi^2*(-592 + 230*S^2 + 115*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (4*(839 - 1036*S^2 + 37*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (4*(2601 - 2932*S^2 + 3*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 20*HPL[{3, 1, 2}, -S^2] + (4*(-611 + 498*S^2 + 249*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (8*(-937 + 690*S^2 + 345*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(-921 + 892*S^2 + 73*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (32*(-163 + 102*S^2 + 51*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (480*(-22 + 14*S^2 + 7*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-7 + 5*S^2) + (Pi^2*(-94 - 79*S^2 + 167*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (4*(21 + 22*S^2 + 11*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((Pi^2*(1660 - 1287*S^2 - 119*S^4))/(3*(1 + S^2)^2) - (4*(-31 + 9*S^4))/S^2 + (8*(-42 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((2*(-17 - S^2 + 8*S^4))/S^2 + (Pi^2*(-75 - 97*S^2 + 90*S^4))/(3*(1 + S^2)^2) - (4*(55 + 14*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((4*(-29 - 32*S^2 + 19*S^4))/(3*S^2) - (2*Pi^2*(1115 - 2168*S^2 + 137*S^4))/(9*(1 + S^2)^2) - (4*(601 - 1054*S^2 + 85*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2) - (8*(-21 + 58*S^2 + 29*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (8*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (8*(-53 + 74*S^2 + 37*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((2*Pi^2*(-15 - 11*S^2 + 12*S^4))/(3*S^2) + (4*(-23 - 25*S^2 + 14*S^4))/S^2 + (Pi^4*(-19367 + 806*S^2 + 403*S^4))/(180*(1 + S^2)^2) + ((4*(-15 - 5*S^2 + 9*S^4))/S^2 + (Pi^2*(-1355 + 118*S^2 + 59*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*(-417 + 122*S^2 + 61*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + (8*(-15 - 44*S^2 + 21*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (2*(25 + 82*S^2 + 41*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (4*(601 - 1054*S^2 + 85*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (32*(-99 + 16*S^2 + 8*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(5 - 104*S^2 + 71*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((12*(1 + S^2)*(-5 + 4*S^2))/S^2 + (Pi^2*(-29 - 8*S^2 + 24*S^4))/(3*S^2) + (Pi^4*(-7378 + 598*S^2 + 299*S^4))/(180*(1 + S^2)^2) + (2*(-12 - 79*S^2 + 29*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (14*(3 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(839 - 1036*S^2 + 37*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(-363 + 230*S^2 + 115*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*(-182 + 114*S^2 + 57*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(-8 - 105*S^2 + 75*S^4)*Zeta[3])/(1 + S^2)^2) + (2*(-65 - 11*S^2 + 210*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((Pi^2*(-59 - 49*S^2 + 36*S^4))/(3*S^2) + (2*(-75 - 66*S^2 + 41*S^4))/S^2 + (Pi^4*(-7570 + 12273*S^2 + 73*S^4))/(90*(1 + S^2)^2) - (4*(136 - 299*S^2 + 43*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((16*(-3 - S^2 + S^4))/S^2 - (2*Pi^2*(-9 + 94*S^2 + 47*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*(-43 - 28*S^2 + 31*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (4*(17 + 70*S^2 + 35*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-8*(-15 - 5*S^2 + 9*S^4))/S^2 - (2*Pi^2*(-1355 + 118*S^2 + 59*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(151 - 255*S^2 + 22*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (128*(-2 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*(-167 + 274*S^2 + 137*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (8*(601 - 1054*S^2 + 85*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-417 + 122*S^2 + 61*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (32*(-615 + 154*S^2 + 77*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(-803 + 134*S^2 + 67*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((4*(-1 + 2*S^2 + 5*S^4))/S^2 - (2*Pi^2*(-1 + 150*S^2 + 75*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-1117 + 1624*S^2 - 87*S^4))/(3*(1 + S^2)^2) + (2*(-49 - 12*S^2 + 25*S^4))/S^2 - (64*(-2 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*(-417 + 122*S^2 + 61*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*(-55 + 62*S^2 + 31*S^4)*Zeta[3])/(1 + S^2)^2) - (4*(1 + 158*S^2 + 79*S^4)*Zeta[5])/(1 + S^2)^2)) + (12*(-25 - 191*S^2 + 578*S^4)*Zeta[7])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-520*(1 + S^2)^2)/S^2 + (Pi^6*(-59726 + 131157*S^2 - 12397*S^4))/(1890*(1 + S^2)^2) - (2*Pi^2*(149 + 214*S^2 + 33*S^4))/(3*S^2) + (Pi^4*(-822 - 891*S^2 + 299*S^4))/(90*S^2) + (248*(-1 + S^2)*HPL[{2}, -S^2]^3)/(1 + S^2) - (8*(23 - 110*S^2 + 23*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-16*(16 + 26*S^2 + S^4))/S^2 - (8*Pi^2*(-44 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{5}, -S^2] + (8*(-335 - 301*S^2 + 142*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (48*(65 + 92*S^2 + 46*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-16*(-3 + 10*S^2 + 15*S^4))/S^2 + (8*Pi^2*(-613 + 610*S^2 + 305*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-96*(-4 + 3*S^2 + 8*S^4))/S^2 + (4*Pi^2*(-4135 + 4218*S^2 + 2109*S^4))/(3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (24*(25 - 118*S^2 + 25*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (32*(-19 + 20*S^2 + 10*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 - (16*(35 - 1094*S^2 + 311*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 - (48*(-29 + 30*S^2 + 15*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 + (8*(285 + 466*S^2 + 233*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((-64*(3 + 5*S^2 + 3*S^4))/S^2 + (16*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-64*(15 + 13*S^2))/S^2 + (128*Pi^2*(-319 + 98*S^2 + 49*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (5952*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) - (8*(-2421 + 2374*S^2 + 1187*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 - (64*(-929 + 902*S^2 + 451*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (128*(-134 - 133*S^2 + 181*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(-7303 + 7138*S^2 + 3569*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 - (8*(-22723 + 21898*S^2 + 10949*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 - (192*(-1945 + 1886*S^2 + 943*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((-960*(-1 + S^2)*(1 + S^2))/S^2 + (32*Pi^2*(514 + 158*S^2 + 79*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 5952*HPL[{2, 2, 2, 1}, -S^2] - (128*(-89 - 133*S^2 + 136*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (640*(-86 + 2*S^2 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (640*(-86 + 2*S^2 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (64*(1139 + 538*S^2 + 269*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (128*(1829 + 688*S^2 + 344*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (28800*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) - (256*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (768*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (1280*(-407 + 266*S^2 + 133*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 28800*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((4*Pi^2*(-1 + 20*S^2 + 35*S^4))/(3*S^2) + (16*(1 + 23*S^2 + 38*S^4))/S^2 - (2*Pi^4*(-1949 + 2808*S^2 + 1404*S^4))/(45*(1 + S^2)^2))*Zeta[3] - (16*(13 - 16*S^2 + 13*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((8*Pi^2*(-12 + 11*S^4))/(3*S^2) + (16*(-18 - 15*S^2 + 19*S^4))/S^2 - (2*Pi^4*(-2487 + 3022*S^2 + 1511*S^4))/(45*(1 + S^2)^2) + (40*(-13 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (16*(157 - 1054*S^2 + 529*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (16*(-583 + 578*S^2 + 289*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (32*(-581 + 578*S^2 + 289*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(5 - 96*S^2 + 11*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((-4*(1 + S^2)*(53 + 3*S^2))/S^2 + (4*Pi^2*(-21 - 560*S^2 + 197*S^4))/(3*(1 + S^2)^2) + (8*(-367 + 226*S^2 + 113*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (8*(-39 + 50*S^2 + 25*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*((-48*(1 + S^2 + S^4))/S^2 - (2*Pi^2*(615 - 1652*S^2 + 429*S^4))/(3*(1 + S^2)^2) - (8*(-351 + 326*S^2 + 163*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 744*HPL[{2, 1}, -S^2] - (8*(-257 + 270*S^2 + 135*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((768*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-1051 + 1054*S^2 + 365*S^4))/(3*(1 + S^2)^2) - (64*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-16*(1 + S^2)*(-31 + 17*S^2))/S^2 - (32*Pi^2*(-120 + 61*S^2 + 57*S^4))/(3*(1 + S^2)^2) + (32*(-299 + 298*S^2 + 149*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-592*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-30 - 5*S^2 + 24*S^4))/(3*S^2) + (Pi^4*(14677 + 2274*S^2 + 1137*S^4))/(45*(1 + S^2)^2) + (64*(-337 + 196*S^2 + 98*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (16*(151 - 1054*S^2 + 535*S^4)*Zeta[3])/(1 + S^2)^2) + ((16*(-1 + 18*S^2 + 29*S^4))/S^2 - (4*Pi^2*(-511 + 874*S^2 + 437*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((464*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-97 - 12*S^2 + 73*S^4))/(3*S^2) + (Pi^4*(-6880 + 8117*S^2 + 1457*S^4))/(45*(1 + S^2)^2) + ((16*(-2 + 5*S^2 + 8*S^4))/S^2 - (4*Pi^2*(-613 + 610*S^2 + 305*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + (24*(23 - 114*S^2 + 23*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(-119 + 130*S^2 + 65*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((32*(3 + 5*S^2 + 3*S^4))/S^2 - (8*Pi^2*(-1091 + 514*S^2 + 257*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(343 - 1054*S^2 + 343*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*(-1275 + 1226*S^2 + 613*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (8*(-3845 + 3686*S^2 + 1843*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (32*(343 - 1054*S^2 + 343*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - 2976*HPL[{2, 2, 1}, -S^2] - (320*(-86 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (128*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(5 + 6*S^2) - (4*Pi^2*(-633 + 646*S^2 + 323*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (8*(-491 + 634*S^2 + 317*S^4)*Zeta[5])/(1 + S^2)^2) - (96*(-44 + 98*S^2 + 49*S^4)*Zeta[7])/(1 + S^2)^2)) + (3136*(1 + 4*S^2 + 2*S^4)*Zeta[9])/(1 + S^2)^2;
E5uvwT2F2=(Pi^6*(32035 - 39621*S^2))/60480 + (Pi^4*(877 - 879*S^2))/180 - (10*Pi^2*(-11 + 9*S^2))/3 + (Pi^8*(655944 - 2806837*S^2 - 280496*S^4 - 14328*S^6))/(1360800*(1 + S^2)^2) - (S^2*HPL[{0}, S^2]^9)/(384*(1 + S^2)^2) + ((1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^8)/(6*S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^9)/(27*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^8*((2 - 6*S^2 - 3*S^4)/(192*(1 + S^2)^2) + ((2 + 4*S^2 - 4*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2])/(192*S^2*(1 + S^2)^2)) + ((15 + 186*S^2 - 518*S^4 + 186*S^6 + 15*S^8)*HPL[{2}, -S^2]^4)/(12*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^7*((10*(1 + S^2)^2)/(21*S^2) + (Pi^2*(51 + 102*S^2 - 305*S^4 + 72*S^6 + 36*S^8))/(63*S^2*(1 + S^2)^2) - (10*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(7*S^2)) + HPL[{0}, S^2]^7*((-1 - S^2)/24 + (Pi^2*(-27*S^2 - 2*S^4 - S^6))/(576*(1 + S^2)^2) + ((-1 + 2*S^2 - 7*S^4 - 3*S^6 - S^8)*HPL[{1}, -S^2])/(24*S^2*(1 + S^2)^2) + ((4 + 8*S^2 - 13*S^4 - 2*S^6 - S^8)*HPL[{1}, -S^2]^2)/(96*S^2*(1 + S^2)^2) - (S^2*(7 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(96*(1 + S^2)^2)) + ((-4 + 5*S^2)*(4 + 5*S^2)*HPL[{3}, -S^2]^3)/(3*S^2) + ((-8 - 5*S^2 - 48*S^4 - 8*S^6 + 15*S^8)*HPL[{4}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-280 - 1217*S^2 - 829*S^4)/(2*S^2) + (Pi^2*(145 + 290*S^2 - 473*S^4 - 780*S^6 - 390*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{7}, -S^2] - (2*(609 + 526*S^2 + 1899*S^4 + 1804*S^6 + 485*S^8)*HPL[{8}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-784 - 1568*S^2 + 1155*S^4 + 1856*S^6 + 928*S^8)*HPL[{9}, -S^2])/(S^2*(1 + S^2)^2) - (616*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2]^3)/(3*S^2) + (2*(58 + 551*S^2 - 1210*S^4 + 403*S^6 + 26*S^8)*HPL[{3, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((41 + 45*S^2)/2 + (22*Pi^2*(-1 - 2*S^2 + 2*S^4))/(3*S^2*(1 + S^2)^2))*HPL[{4, 3}, -S^2] + ((-19 + 139*S^2 + 194*S^4)/(2*S^2) + (Pi^2*(-122 - 244*S^2 + 233*S^4 + 94*S^6 + 47*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{5, 2}, -S^2] + ((-1 - 8*S^2 - 40*S^4 - 98*S^6 - 29*S^8)*HPL[{5, 3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 + 213*S^4 + 254*S^6 + 127*S^8)*HPL[{5, 4}, -S^2])/(S^2*(1 + S^2)^2) + ((166 + 1143*S^2 + 1117*S^4)/(2*S^2) + (Pi^2*(-178 - 356*S^2 + 186*S^4 + 578*S^6 + 289*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{6, 1}, -S^2] + ((-15 - 12*S^2 - 28*S^4 - 172*S^6 - 51*S^8)*HPL[{6, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-3 - 6*S^2 + 872*S^4 + 1044*S^6 + 522*S^8)*HPL[{6, 3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(275 + 58*S^2 + 1063*S^4 + 1296*S^6 + 324*S^8)*HPL[{7, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-23 - 46*S^2 + 2164*S^4 + 2606*S^6 + 1303*S^8)*HPL[{7, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(369 + 738*S^2 + 3458*S^4 + 3864*S^6 + 1932*S^8)*HPL[{8, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(23 + 354*S^2 - 1078*S^4 + 354*S^6 + 23*S^8)*HPL[{2, 1, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((29 - 182*S^2 - 275*S^4)/S^2 + (Pi^2*(67 + 134*S^2 + 2578*S^4 - 2522*S^6 - 1261*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 2, 2}, -S^2] + ((-4*(-35 + 131*S^2 + 218*S^4))/S^2 - (2*Pi^2*(-45 - 90*S^2 - 1966*S^4 + 1938*S^6 + 969*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 3, 1}, -S^2] + ((105 + 304*S^2 - 200*S^4 + 764*S^6 + 155*S^8)*HPL[{3, 3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((293 - 998*S^2 - 1731*S^4)/(2*S^2) - (2*Pi^2*(-44 - 88*S^2 - 1922*S^4 + 1942*S^6 + 971*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1, 2}, -S^2] - (2*(106 + 297*S^2 - 160*S^4 + 622*S^6 + 133*S^8)*HPL[{4, 1, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((893 - 3182*S^2 - 5379*S^4)/(2*S^2) - (2*Pi^2*(-119 - 238*S^2 - 5990*S^4 + 5884*S^6 + 2942*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 2, 1}, -S^2] + ((91 + 200*S^2 - 24*S^4 + 678*S^6 + 139*S^8)*HPL[{4, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(3 + 6*S^2 - 32*S^4 + 32*S^6 + 16*S^8)*HPL[{4, 2, 3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(220 + 769*S^2 - 744*S^4 + 1950*S^6 + 387*S^8)*HPL[{4, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-76 - 152*S^2 + 55*S^4 + 156*S^6 + 78*S^8)*HPL[{4, 3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-71 - 142*S^2 - 31*S^4 + 124*S^6 + 62*S^8)*HPL[{4, 4, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-8*(-101 + 451*S^2 + 722*S^4))/S^2 + (Pi^2*(474 + 948*S^2 + 24653*S^4 - 24194*S^6 - 12097*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{5, 1, 1}, -S^2] + ((-203 - 870*S^2 + 960*S^4 - 2188*S^6 - 455*S^8)*HPL[{5, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-5 - 10*S^2 + 103*S^4 + 100*S^6 + 50*S^8)*HPL[{5, 1, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((-1823 - 6270*S^2 + 5880*S^4 - 16468*S^6 - 3275*S^8)*HPL[{5, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-212 - 424*S^2 + 31*S^4 + 404*S^6 + 202*S^8)*HPL[{5, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-399 - 798*S^2 - 403*S^4 + 540*S^6 + 270*S^8)*HPL[{5, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(2495 + 7856*S^2 - 7084*S^4 + 22477*S^6 + 4466*S^8)*HPL[{6, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-419 - 838*S^2 - 324*S^4 + 680*S^6 + 340*S^8)*HPL[{6, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-699 - 1398*S^2 - 1304*S^4 + 400*S^6 + 200*S^8)*HPL[{6, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(695 + 1390*S^2 + 3441*S^4 + 1676*S^6 + 838*S^8)*HPL[{7, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((304*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-154 - 308*S^2 + 147*S^4 + 172*S^6 + 86*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 2, 1}, -S^2] + ((-2*(-389 - 124*S^2 + 169*S^4))/S^2 + (Pi^2*(3643 + 7286*S^2 - 5928*S^4 - 1478*S^6 - 739*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1, 2}, -S^2] + ((-2*(-389 - 124*S^2 + 169*S^4))/S^2 + (Pi^2*(3643 + 7286*S^2 - 5928*S^4 - 1478*S^6 - 739*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 2, 1}, -S^2] + (4*(9 + 61*S^2 - 64*S^4 + 61*S^6 + 9*S^8)*HPL[{3, 1, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-2*(-845 - 124*S^2 + 625*S^4))/S^2 + (Pi^2*(7339 + 14678*S^2 - 9456*S^4 - 5606*S^6 - 2803*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 2, 1, 1}, -S^2] + (4*(9 + 61*S^2 - 64*S^4 + 61*S^6 + 9*S^8)*HPL[{3, 2, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-113 - 331*S^2 + 18*S^4 + 125*S^6 + 57*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-59 - 118*S^2 - 2352*S^4 + 2294*S^6 + 1147*S^8)*HPL[{3, 2, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-218 - 436*S^2 - 7435*S^4 + 7214*S^6 + 3607*S^8)*HPL[{3, 2, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (24*(-52 - 83*S^2 + 60*S^4 + 33*S^6)*HPL[{3, 3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (4*(-106 - 212*S^2 - 3649*S^4 + 3570*S^6 + 1785*S^8)*HPL[{3, 3, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-722 - 1444*S^2 - 22547*S^4 + 21966*S^6 + 10983*S^8)*HPL[{3, 3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-2*(-2639 - 628*S^2 + 1723*S^4))/S^2 - (2*Pi^2*(-11017 - 22034*S^2 + 14784*S^4 + 8154*S^6 + 4077*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1, 1, 1}, -S^2] + (2*(-19 + 73*S^2 - 336*S^4 + 713*S^6 + 133*S^8)*HPL[{4, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-1522 - 3044*S^2 - 45887*S^4 + 44646*S^6 + 22323*S^8)*HPL[{4, 1, 1, 3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-605 - 1693*S^2 + 60*S^4 + 403*S^6 + 263*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-1317 - 2634*S^2 - 38589*S^4 + 37520*S^6 + 18760*S^8)*HPL[{4, 1, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1162 - 2324*S^2 - 34475*S^4 + 33542*S^6 + 16771*S^8)*HPL[{4, 1, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-1853 - 4933*S^2 - 492*S^4 + 2635*S^6 + 1055*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-825 - 1650*S^2 - 23751*S^4 + 22916*S^6 + 11458*S^8)*HPL[{4, 2, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-807 - 1614*S^2 - 23340*S^4 + 22694*S^6 + 11347*S^8)*HPL[{4, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-1132 - 2264*S^2 - 34037*S^4 + 33234*S^6 + 16617*S^8)*HPL[{4, 3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1903 - 5074*S^2 + 148*S^4 + 1266*S^6 + 827*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-4634 - 9268*S^2 - 138823*S^4 + 134438*S^6 + 67219*S^8)*HPL[{5, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-7622 - 15244*S^2 - 228673*S^4 + 222506*S^6 + 111253*S^8)*HPL[{5, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-18134 - 36268*S^2 - 544381*S^4 + 531410*S^6 + 265705*S^8)*HPL[{5, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-22606 - 45212*S^2 - 680185*S^4 + 663506*S^6 + 331753*S^8)*HPL[{6, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-8*(55 + 62*S^2 + 55*S^4))/S^2 - (16*Pi^2*(152 + 304*S^2 - 447*S^4 + 150*S^6 + 75*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-24*(55 + 62*S^2 + 55*S^4))/S^2 - (16*Pi^2*(152 + 304*S^2 - 447*S^4 + 150*S^6 + 75*S^8))/(S^2*(1 + S^2)^2))*HPL[{2, 2, 1, 1, 1}, -S^2] - (8*(-85 - 143*S^2 + 143*S^4 + 85*S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (24*(-85 - 143*S^2 + 143*S^4 + 85*S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (64*(34 + 68*S^2 - 147*S^4 + 68*S^6 + 34*S^8)*HPL[{2, 2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-16*(141 + 218*S^2 + 221*S^4))/S^2 - (8*Pi^2*(1513 + 3026*S^2 - 5224*S^4 + 2206*S^6 + 1103*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1, 1, 1}, -S^2] + (8*(-491 - 797*S^2 + 797*S^4 + 491*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (8*(-831 - 1369*S^2 + 1369*S^4 + 831*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (2*(3361 + 6722*S^2 - 9166*S^4 + 1794*S^6 + 897*S^8)*HPL[{3, 1, 1, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-1001 - 1655*S^2 + 1655*S^4 + 1001*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (2*(3361 + 6722*S^2 - 9166*S^4 + 1794*S^6 + 897*S^8)*HPL[{3, 1, 2, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(31 + 62*S^2 - 274*S^4 + 62*S^6 + 31*S^8)*HPL[{3, 1, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(2951 + 5902*S^2 - 8708*S^4 + 2122*S^6 + 1061*S^8)*HPL[{3, 1, 3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-1053 - 1757*S^2 + 1757*S^4 + 1053*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (2*(6625 + 13250*S^2 - 23278*S^4 + 8322*S^6 + 4161*S^8)*HPL[{3, 2, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3233 + 6466*S^2 - 13838*S^4 + 6466*S^6 + 3233*S^8)*HPL[{3, 2, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-10455 - 20910*S^2 + 18162*S^4 + 4402*S^6 + 2201*S^8)*HPL[{3, 2, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (48*(-1439 - 2878*S^2 + 2824*S^4 + 286*S^6 + 143*S^8)*HPL[{3, 3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-6387 - 17206*S^2 + 588*S^4 + 16194*S^6 + 6227*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(9979 + 19958*S^2 - 34954*S^4 + 12230*S^6 + 6115*S^8)*HPL[{4, 1, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(4891 + 9782*S^2 - 20794*S^4 + 9446*S^6 + 4723*S^8)*HPL[{4, 1, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-15641 - 31282*S^2 + 27206*S^4 + 6350*S^6 + 3175*S^8)*HPL[{4, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-51809 - 103618*S^2 + 102038*S^4 + 9950*S^6 + 4975*S^8)*HPL[{4, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-25899 - 51798*S^2 + 51365*S^4 + 4672*S^6 + 2336*S^8)*HPL[{5, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((1280*(-1 + S^2)*(1 + S^2))/S^2 + (16*Pi^2*(-330 - 660*S^2 + 289*S^4 + 368*S^6 + 184*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (4928*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/S^2 - (14784*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S^2 - (16*(-115 - 388*S^2 + 294*S^4 - 118*S^6 + 35*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-1577 - 3154*S^2 - 1156*S^4 + 4322*S^6 + 2161*S^8)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-3425 - 6850*S^2 - 1156*S^4 + 8018*S^6 + 4009*S^8)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-4657 - 9314*S^2 - 1156*S^4 + 10482*S^6 + 5241*S^8)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-5273 - 10546*S^2 - 1156*S^4 + 11714*S^6 + 5857*S^8)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-9277 - 18554*S^2 - 1156*S^4 + 19722*S^6 + 9861*S^8)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(-13897 - 27794*S^2 - 2018*S^4 + 29698*S^6 + 14849*S^8)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (480*(-5 - 4*S^2 + 4*S^4 + 5*S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (128*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (512*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (1280*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (384*(511 + 1022*S^2 - 1903*S^4 + 912*S^6 + 456*S^8)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (21120*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-2*Pi^2*S^2*(-27 + 2*S^2 + S^4))/(9*(1 + S^2)^2) - (2*S^2*(-9 + 2*S^2 + S^4)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^2) - (4*(-1 + S^2)^2*(1 + 20*S^2 + S^4)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]*((-4*(-1 + S^2)*(-4 + 15*S^2 + S^4))/(3*(1 + S^2)^2) - (16*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2)) - (4*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2))*Log[T]^7 + ((4*(1 - 7*S^2 + S^4))/(3*(1 + S^2)^2) + (2*S^2*(-7 + 4*S^2 + 2*S^4)*HPL[{0}, S^2])/(3*(1 + S^2)^2) + (4*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2))*Log[T]^8 + (4*S^2*Log[T]^9)/(3*(1 + S^2)^2) + ((1 + 41*S^2)/2 + (Pi^2*(40 - 106*S^2 - 11*S^4 + 11*S^6))/(6*(1 + S^2)^2))*Zeta[3]^2 - (32*(2*S^4 + S^6)*Zeta[3]^3)/(1 + S^2)^2 + HPL[{3, 1, 2}, -S^2]*((-29*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(89 + 267*S^2 - 225*S^4 - 75*S^6))/(12*S^2*(1 + S^2)) - (2*(-1 + 9*S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^3*(((-1 + S^2)*(1 + S^2))/(2*S^2) + (Pi^2*(-53 + 8*S^2 - 518*S^4 + 364*S^6 + 83*S^8))/(36*S^2*(1 + S^2)^2) + ((17 + 34*S^2 + 294*S^4 - 306*S^6 - 153*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(34 + 68*S^2 - 147*S^4 + 68*S^6 + 34*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*S^2*(-147 + 136*S^2 + 68*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-120*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-49 + 73*S^2 - 539*S^4 + 281*S^6 + 72*S^8))/(3*S^2*(1 + S^2)^2) - (32*S^2*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^6*((1 - 7*S^2)/48 + (Pi^2*(79 - 258*S^2 - 117*S^4 - 8*S^6))/(576*(1 + S^2)^2) + ((-1 + 20*S^2 - 30*S^4 - 8*S^6 - S^8)*HPL[{1}, -S^2]^2)/(24*S^2*(1 + S^2)^2) + ((23 + 46*S^2 - 70*S^4 - 10*S^6 - 5*S^8)*HPL[{1}, -S^2]^3)/(144*S^2*(1 + S^2)^2) + ((21 - 65*S^2 - 30*S^4 - 8*S^6)*HPL[{2}, -S^2])/(96*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(-1 + 7*S^2))/(96*S^2) + (Pi^2*(79 + 158*S^2 - 182*S^4 - 66*S^6 - 33*S^8))/(576*S^2*(1 + S^2)^2) + ((19 + 38*S^2 - 51*S^4 - 12*S^6 - 6*S^8)*HPL[{2}, -S^2])/(96*S^2*(1 + S^2)^2)) + ((1 - 3*S^4)*HPL[{3}, -S^2])/(96*S^2) + ((-9 - 18*S^2 + 8*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(24*S^2*(1 + S^2)^2) + ((-17*S^2 - 22*S^4 - 11*S^6)*Zeta[3])/(24*(1 + S^2)^2)) + Log[T]^6*((Pi^2*(51 - 286*S^2 + 60*S^4 + 5*S^6))/(9*(1 + S^2)^2) + (2*S^2*(-25 + 6*S^2 + 3*S^4)*HPL[{0}, S^2]^3)/(9*(1 + S^2)^2) + (14*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (112*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^3)/(9*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^2*((23 - 90*S^2 + 32*S^4 + 5*S^6)/(3*(1 + S^2)^2) + ((23 + 46*S^2 - 109*S^4 + 16*S^6 + 8*S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2)) + (2*(-1 + S^2)*(5 + 9*S^2 + 5*S^4)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((10*(1 + S^2)^2)/(3*S^2) + (Pi^2*(51 + 102*S^2 - 305*S^4 + 72*S^6 + 36*S^8))/(9*S^2*(1 + S^2)^2) - (10*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]*((10*(1 + S^2))/3 + (2*Pi^2*(-74*S^2 + 34*S^4 + 17*S^6))/(9*(1 + S^2)^2) + (14*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) + (56*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (2*(-2 - 4*S^2 - 87*S^4 + 54*S^6 + 27*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) - (8*S^2*(-24 + 22*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (88*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S^2) - (8*(-17*S^2 + 22*S^4 + 11*S^6)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{5}, -S^2]*(-(Pi^2*(1 + S^2)*(75 + 431*S^2))/(24*S^2) + (-147 - 1158*S^2 - 755*S^4)/(4*S^2) + (Pi^4*(-28 - 56*S^2 + 225*S^4 - 1460*S^6 - 730*S^8))/(180*S^2*(1 + S^2)^2) + ((215 + 592*S^2 - 982*S^4 + 68*S^6 - 45*S^8)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + (8*(2 + 4*S^2 - 39*S^4 + 22*S^6 + 11*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(14 + 28*S^2 - 195*S^4 + 318*S^6 + 159*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((77 + 132*S^2 + 278*S^4 + 96*S^6 + S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^5*((-8*(1 + S^2)^2)/(15*S^2) + (Pi^2*(55 + 98*S^2 + 35*S^4))/(30*S^2) + (Pi^4*(4460 + 8920*S^2 - 23717*S^4 + 4426*S^6 + 2213*S^8))/(2700*S^2*(1 + S^2)^2) + ((-4*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(275 + 550*S^2 - 674*S^4 - 158*S^6 - 79*S^8))/(45*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(15*S^2*(1 + S^2)^2) - (2*(91 + 694*S^2 - 2094*S^4 + 1594*S^6 + 91*S^8)*HPL[{3}, -S^2])/(15*S^2*(1 + S^2)^2) - (2*(47 + 94*S^2 - 554*S^4 + 238*S^6 + 119*S^8)*HPL[{4}, -S^2])/(15*S^2*(1 + S^2)^2) + (120*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1}, -S^2])/(15*S^2*(1 + S^2)^2) - (60*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (4*(2 + 37*S^2 - 176*S^4 + 127*S^6 + 2*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2, 1, 1, 1}, -S^2]*((367*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-161 - 31*S^2 + 106*S^4))/(3*S^2) + (2*Pi^4*(-393 - 786*S^2 + 432*S^4 + 296*S^6 + 148*S^8))/(9*S^2*(1 + S^2)^2) - (16*(-26 - 208*S^2 + 539*S^4 - 146*S^6 + 3*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4, 2}, -S^2]*((-23 + 138*S^2 + 209*S^4)/(4*S^2) + (Pi^2*(-23 + 70*S^2 - 306*S^4 + 726*S^6 + 141*S^8))/(12*S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 22*S^4 + 18*S^6 + 9*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]^2*((-15 + 38*S^2 + 17*S^4)/(2*S^2) + (Pi^2*(17 + 66*S^2 - 62*S^4 + 220*S^6 + 43*S^8))/(12*S^2*(1 + S^2)^2) + ((-29 - 58*S^2 + 121*S^4 - 36*S^6 - 18*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-3 - 6*S^2 - 4*S^4 + 22*S^6 + 11*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^6*((7*(1 + S^2)^2)/(9*S^2) + (Pi^2*(19 + 341*S^2 - 622*S^4 + 251*S^6 + 19*S^8))/(27*S^2*(1 + S^2)^2) - (20*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (10*(5 + 10*S^2 - 65*S^4 + 28*S^6 + 14*S^8)*HPL[{3}, -S^2])/(9*S^2*(1 + S^2)^2) + (10*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (2*(5 + 10*S^2 - 87*S^4 + 40*S^6 + 20*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((57 - 142*S^2 + 57*S^4)/S^2 + (Pi^2*(133 + 110*S^2 + 57*S^4))/(3*S^2) + (Pi^4*(3684 + 7368*S^2 - 8559*S^4 + 2120*S^6 + 1060*S^8))/(90*S^2*(1 + S^2)^2) + (4*(-60 - 430*S^2 + 971*S^4 - 202*S^6 + 25*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{5, 1}, -S^2]*((189 + 1582*S^2 + 1585*S^4)/(4*S^2) + (Pi^2*(115 + 332*S^2 - 1686*S^4 + 4656*S^6 + 815*S^8))/(12*S^2*(1 + S^2)^2) + (2*(17 + 34*S^2 - 117*S^4 + 52*S^6 + 26*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 2}, -S^2]*((-107 - 284*S^2 + 335*S^4)/(4*S^2) + (Pi^2*(-121 + 282*S^2 + 659*S^4))/(24*S^2) + (Pi^4*(29 + 58*S^2 - 2064*S^4 + 2458*S^6 + 1229*S^8))/(90*S^2*(1 + S^2)^2) + (2*(-25 - 50*S^2 - 2594*S^4 + 2414*S^6 + 1207*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-33 + 36*S^2 - 394*S^4 + 188*S^6 + 43*S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) + HPL[{6}, -S^2]*((-3*(40 + 359*S^2 + 359*S^4))/(4*S^2) + (Pi^2*(-70 + 168*S^2 - 290*S^4 - 739*S^6 - 141*S^8))/(6*S^2*(1 + S^2)^2) + (2*(-74 - 148*S^2 - 29*S^4 + 100*S^6 + 50*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-30 - 60*S^2 + 61*S^4 + 104*S^6 + 52*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]^2*((21 - 38*S^2 + 21*S^4)/(2*S^2) + (Pi^2*(-32 - 986*S^2 + 3341*S^4 - 1214*S^6 - 117*S^8))/(6*S^2*(1 + S^2)^2) + (8*(-6 - 12*S^2 - 131*S^4 + 142*S^6 + 71*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4, 1}, -S^2]*((Pi^2*(-85 + 762*S^2 + 1207*S^4))/(12*S^2) + (-113 + 164*S^2 + 1813*S^4)/(4*S^2) + (Pi^4*(11 + 22*S^2 - 14594*S^4 + 16142*S^6 + 8071*S^8))/(180*S^2*(1 + S^2)^2) + (4*(-95 - 190*S^2 - 3862*S^4 + 3842*S^6 + 1921*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-57 + 38*S^2 - 750*S^4 + 414*S^6 + 91*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1, 1}, -S^2]*((341 - 1076*S^2 - 393*S^4)/(2*S^2) - (2*Pi^2*(-197 - 87*S^2 + 16*S^4))/(3*S^2) + (Pi^4*(22369 + 44738*S^2 - 40592*S^4 + 1730*S^6 + 865*S^8))/(180*S^2*(1 + S^2)^2) + (2*(-353 - 2596*S^2 + 6068*S^4 - 1448*S^6 + 97*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1, 1, 1}, -S^2]*((2*(1 + S^2)*(53 + 113*S^2))/S^2 + (Pi^2*(291 + 260*S^2 + 1568*S^4 - 584*S^6 - 199*S^8))/(3*S^2*(1 + S^2)^2) + (8*(1 + 2*S^2 - 602*S^4 + 586*S^6 + 293*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4, 1, 1}, -S^2]*((-4*(1 + S^2)*(12 + 71*S^2))/S^2 + (Pi^2*(-337 - 17*S^2 - 2540*S^4 + 1157*S^6 + 329*S^8))/(3*S^2*(1 + S^2)^2) - (8*(1 + 2*S^2 - 898*S^4 + 846*S^6 + 423*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 2, 1}, -S^2]*((-17*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-335 + 420*S^2 - 4102*S^4 + 2612*S^6 + 589*S^8))/(12*S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 - 1168*S^4 + 1106*S^6 + 553*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^5*((Pi^2*(-193 - 205*S^2))/576 - (57*(1 + S^2))/64 + (Pi^4*(-14626*S^2 - 1138*S^4 - 569*S^6))/(43200*(1 + S^2)^2) + ((-125 + 1920*S^2 - 3358*S^4 - 312*S^6 - 125*S^8)*HPL[{1}, -S^2]^3)/(720*S^2*(1 + S^2)^2) + ((275 + 550*S^2 - 1033*S^4 - 8*S^6 - 4*S^8)*HPL[{1}, -S^2]^4)/(720*S^2*(1 + S^2)^2) + ((-12 - 31*S^2 - 31*S^4)/(96*S^2) - (Pi^2*S^2*(319 + 52*S^2 + 26*S^4))/(360*(1 + S^2)^2))*HPL[{2}, -S^2] + (S^2*(-76 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(80*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-59 - 70*S^2 - 35*S^4)/(192*S^2) + (Pi^2*(695 + 1390*S^2 - 2398*S^4 - 218*S^6 - 109*S^8))/(1440*S^2*(1 + S^2)^2) + ((230 + 460*S^2 - 853*S^4 + 2*S^6 + S^8)*HPL[{2}, -S^2])/(240*S^2*(1 + S^2)^2)) + ((-1 - S^2 - 3*S^4 - S^8)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)^2) + (S^4*(2 + S^2)*HPL[{4}, -S^2])/(4*(1 + S^2)^2) + ((95 - 1220*S^2 + 826*S^4 - 22*S^6 + 5*S^8)*HPL[{2, 1}, -S^2])/(240*S^2*(1 + S^2)^2) - (3*S^2*(-27 + 4*S^2 + 2*S^4)*HPL[{3, 1}, -S^2])/(20*(1 + S^2)^2) + (S^2*(-541 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(60*(1 + S^2)^2) + ((4 - 39*S^2 - 52*S^4 - 21*S^6)*Zeta[3])/(8*(1 + S^2)^2) + HPL[{1}, -S^2]*((-41 - 42*S^2 - 17*S^4)/(64*S^2) + (Pi^2*(-965 + 3600*S^2 - 9238*S^4 - 2832*S^6 - 965*S^8))/(2880*S^2*(1 + S^2)^2) + ((-155 + 1620*S^2 - 2618*S^4 - 212*S^6 - 155*S^8)*HPL[{2}, -S^2])/(480*S^2*(1 + S^2)^2) + (S^2*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(8*(1 + S^2)^2) + ((-230 - 460*S^2 + 853*S^4 - 2*S^6 - S^8)*HPL[{2, 1}, -S^2])/(120*S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 3*S^4 - 2*S^6 - S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2))) + Log[T]^5*((-4*Pi^2*(4 + S^2))/9 + (Pi^4*(14626*S^2 - 1138*S^4 - 569*S^6))/(1350*(1 + S^2)^2) - (S^2*(-164 + 2*S^2 + S^4)*HPL[{0}, S^2]^4)/(45*(1 + S^2)^2) - (28*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) - (56*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^3*((-280 + 1126*S^2 - 283*S^4 - 9*S^6)/(45*(1 + S^2)^2) + ((-56 - 112*S^2 + 263*S^4 - 34*S^6 - 17*S^8)*HPL[{1}, -S^2])/(9*S^2*(1 + S^2)^2)) + ((-8*(-1 + S^2)*(1 + S^2))/(3*S^2) - (2*Pi^2*(-11 - 22*S^2 - 77*S^4 + 42*S^6 + 21*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] - (4*(5 + 10*S^2 - 77*S^4 + 10*S^6 + 5*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-10*(1 + S^2)^2)/S^2 + (Pi^2*(-51 - 102*S^2 + 305*S^4 - 72*S^6 - 36*S^8))/(3*S^2*(1 + S^2)^2) + (30*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^2*((-4*(4 + S^2))/3 + (Pi^2*(1601*S^2 - 218*S^4 - 109*S^6))/(90*(1 + S^2)^2) + ((-17 - 304*S^2 + 446*S^4 - 124*S^6 - 17*S^8)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-23 - 46*S^2 + 109*S^4 - 16*S^6 - 8*S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((1 + 2*S^2 + 154*S^4 - 42*S^6 - 21*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + (2*(21 + 292*S^2 - 1738*S^4 + 2362*S^6 + 171*S^8)*HPL[{3}, -S^2])/(15*S^2*(1 + S^2)^2) + (4*(-1 + S^2)*(1 + 3*S^2 + 93*S^4 + 31*S^6)*HPL[{4}, -S^2])/(5*S^2*(1 + S^2)^2) - (4*(-5 - 64*S^2 + 64*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (8*(-1 + S^2)*(5 + 15*S^2 + 6*S^4 + 2*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (56*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(5 - 38*S^2 + 74*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^2 + HPL[{0}, S^2]*((-14*(1 + S^2))/3 + (Pi^2*(-700 + 3121*S^2 - 1753*S^4 - 114*S^6))/(45*(1 + S^2)^2) - (14*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)^2) - (112*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) - (2*(-11 + 47*S^2 - 352*S^4 + 281*S^6 + 19*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((-10*(1 + S^2)^2)/S^2 + (Pi^2*(-140 - 280*S^2 + 851*S^4 - 202*S^6 - 101*S^8))/(9*S^2*(1 + S^2)^2) - (2*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) + (2*(-3 - 6*S^2 - 10*S^4 + 10*S^6 + 5*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(-27 - 54*S^2 + 87*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(-3*S^2 + 2*S^4 + S^6)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-14*(1 + S^2)^2)/(3*S^2) - (2*Pi^2*(19 + 341*S^2 - 622*S^4 + 251*S^6 + 19*S^8))/(9*S^2*(1 + S^2)^2) + (120*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (20*(5 + 10*S^2 - 65*S^4 + 28*S^6 + 14*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (60*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (4*(5 + 10*S^2 - 87*S^4 + 40*S^6 + 20*S^8)*Zeta[3])/(S^2*(1 + S^2)^2))) + ((Pi^2*(107 - 281*S^2))/12 - (3*(-209 + 271*S^2))/4 - (782*Pi^4*(2*S^4 + S^6))/(45*(1 + S^2)^2))*Zeta[5] + HPL[{2, 1, 1}, -S^2]*((-222*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(53 + 19*S^2 - 74*S^4))/(6*S^2) + (Pi^4*(-857 + 4394*S^2 - 17825*S^4 + 5271*S^6 + 1267*S^8))/(180*S^2*(1 + S^2)^2) + (2464*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (16*(-433 - 866*S^2 + 578*S^4 + 282*S^6 + 141*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (64*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4*(1 + 31*S^2 + 54*S^4))/S^2 - (4*Pi^2*S^2*(-317 + 322*S^2 + 161*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (4*S^2*(-493 + 630*S^2 + 315*S^4)*Zeta[5])/(1 + S^2)^2) + Zeta[3]*((Pi^4*(-419 - 2287*S^2))/720 + (Pi^2*(247 - 521*S^2))/24 - 5*(-39 + 41*S^2) - (1847*Pi^6*(2*S^4 + S^6))/(1134*(1 + S^2)^2) + (2*(57 - 57*S^2 - 28*S^4 + 26*S^6)*Zeta[5])/(1 + S^2)^2) + Log[T]^4*((Pi^2*(27 - 5*S^2))/6 + (Pi^4*(4460 - 22137*S^2 + 4235*S^4 + 442*S^6))/(540*(1 + S^2)^2) - (S^2*(164 + 2*S^2 + S^4)*HPL[{0}, S^2]^5)/(90*(1 + S^2)^2) + (35*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + (56*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^4*((137 - 519*S^2 - S^4 - 5*S^6)/(36*(1 + S^2)^2) + ((137 + 274*S^2 - 518*S^4 + 10*S^6 + 5*S^8)*HPL[{1}, -S^2])/(36*S^2*(1 + S^2)^2)) + ((23 + 354*S^2 - 1078*S^4 + 354*S^6 + 23*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((50*(1 + S^2)^2)/(3*S^2) + (5*Pi^2*(51 + 102*S^2 - 305*S^4 + 72*S^6 + 36*S^8))/(9*S^2*(1 + S^2)^2) - (50*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^3*((-2*(-1 + S^2))/3 + (Pi^2*(-703*S^2 + 86*S^4 + 43*S^6))/(54*(1 + S^2)^2) + ((7 + 568*S^2 - 948*S^4 + 178*S^6 + 7*S^8)*HPL[{1}, -S^2])/(9*S^2*(1 + S^2)^2) + (5*(56 + 112*S^2 - 263*S^4 + 34*S^6 + 17*S^8)*HPL[{1}, -S^2]^2)/(18*S^2*(1 + S^2)^2) + ((-2 - 4*S^2 - 669*S^4 + 166*S^6 + 83*S^8)*HPL[{2}, -S^2])/(18*S^2*(1 + S^2)^2)) + ((-7 - 126*S^2 - 167*S^4)/(3*S^2) + (Pi^2*(7 + 14*S^2 + 754*S^4 - 706*S^6 - 353*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] - (2*(6 + 53*S^2 - 294*S^4 + 453*S^6 + 74*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(-6 - 12*S^2 - 125*S^4 + 218*S^6 + 109*S^8)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)^2) + ((160*(-1 + S^2)*(1 + S^2))/(3*S^2) + (2*Pi^2*(-330 - 660*S^2 + 289*S^4 + 368*S^6 + 184*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-115 - 388*S^2 + 294*S^4 - 118*S^6 + 35*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-37 - 74*S^2 - 1156*S^4 + 1242*S^6 + 621*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-37 - 74*S^2 - 2018*S^4 + 1978*S^6 + 989*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (20*(-5 - 4*S^2 + 4*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (16*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (16*(73 + 146*S^2 - 169*S^4 + 36*S^6 + 18*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (880*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-40*(1 + 4*S^2))/3 - (2*Pi^2*(-281*S^2 + 368*S^4 + 184*S^6))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-5*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-49 + 73*S^2 - 539*S^4 + 281*S^6 + 72*S^8))/(9*S^2*(1 + S^2)^2) - (2*(-29 - 58*S^2 - 578*S^4 + 642*S^6 + 321*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (8*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*S^2*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((27 - 5*S^2)/2 + (Pi^2*(619 - 2388*S^2 + 478*S^4 + 65*S^6))/(36*(1 + S^2)^2) + (5*(17 + 304*S^2 - 446*S^4 + 124*S^6 + 17*S^8)*HPL[{1}, -S^2]^2)/(6*S^2*(1 + S^2)^2) + (5*(23 + 46*S^2 - 109*S^4 + 16*S^6 + 8*S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + ((-23 + 281*S^2 - 1078*S^4 + 427*S^6 + 69*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((15 + 24*S^2 + 5*S^4)/S^2 + (Pi^2*(619 + 1238*S^2 - 2671*S^4 + 260*S^6 + 130*S^8))/(36*S^2*(1 + S^2)^2) + ((325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2)) + ((7 + 14*S^2 + 34*S^4 - 46*S^6 - 23*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-165 - 330*S^2 + 289*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(-26*S^2 + 38*S^4 + 19*S^6)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]*((-8*(1 + S^2)^2)/(3*S^2) + (Pi^2*(55 + 98*S^2 + 35*S^4))/(6*S^2) + (Pi^4*(4460 + 8920*S^2 - 23717*S^4 + 4426*S^6 + 2213*S^8))/(540*S^2*(1 + S^2)^2) + ((-20*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(275 + 550*S^2 - 674*S^4 - 158*S^6 - 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) - (2*(91 + 694*S^2 - 2094*S^4 + 1594*S^6 + 91*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(47 + 94*S^2 - 554*S^4 + 238*S^6 + 119*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (600*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (300*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (20*(2 + 37*S^2 - 176*S^4 + 127*S^6 + 2*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((35*(1 + S^2)^2)/(3*S^2) + (5*Pi^2*(19 + 341*S^2 - 622*S^4 + 251*S^6 + 19*S^8))/(9*S^2*(1 + S^2)^2) - (300*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (50*(5 + 10*S^2 - 65*S^4 + 28*S^6 + 14*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (150*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (10*(5 + 10*S^2 - 87*S^4 + 40*S^6 + 20*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]*((-8*(1 + S^2))/3 + (Pi^2*(29 + 21*S^2))/6 + (Pi^4*(-11971*S^2 + 4172*S^4 + 2086*S^6))/(540*(1 + S^2)^2) + (70*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + (140*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + ((-35 + 6*S^2 + 65*S^4)/(3*S^2) + (Pi^2*(-16 - 32*S^2 - 987*S^4 + 488*S^6 + 244*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*S^2*(-337 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((25*(1 + S^2)^2)/S^2 + (5*Pi^2*(140 + 280*S^2 - 851*S^4 + 202*S^6 + 101*S^8))/(18*S^2*(1 + S^2)^2) + (5*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) - (2*(7 - 20*S^4 + 71*S^6 + 24*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(1 + 2*S^2 - 16*S^4 + 6*S^6 + 3*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (10*(-19 - 281*S^2 + 352*S^4 - 47*S^6 + 11*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(-35 - 70*S^2 - 1312*S^4 + 806*S^6 + 403*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (20*(-2 - 4*S^2 - 87*S^4 + 54*S^6 + 27*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(40 - 147*S^2 + 213*S^4 + 40*S^6)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((35*(1 + S^2)^2)/(3*S^2) + (Pi^2*(119 + 3026*S^2 - 5886*S^4 + 2246*S^6 + 119*S^8))/(18*S^2*(1 + S^2)^2) + (40*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(10 + 20*S^2 - 43*S^4 + 14*S^6 + 7*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (10*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(40 + 80*S^2 - 277*S^4 + 86*S^6 + 43*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2))) - (20*(-50*S^2 + 74*S^4 + 37*S^6)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{0}, S^2]^4*((Pi^2*(113 - 567*S^2))/576 + (31 - 33*S^2)/8 + (Pi^4*(5918 - 20679*S^2 - 7582*S^4 - 755*S^6))/(8640*(1 + S^2)^2) + ((19 + 2176*S^2 - 3078*S^4 + 64*S^6 + 19*S^8)*HPL[{1}, -S^2]^4)/(288*S^2*(1 + S^2)^2) + ((137 + 274*S^2 - 518*S^4 + 10*S^6 + 5*S^8)*HPL[{1}, -S^2]^5)/(180*S^2*(1 + S^2)^2) + ((-9 + 88*S^2 - 397*S^4 + 54*S^6 + 6*S^8)*HPL[{2}, -S^2]^2)/(48*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((59 + 38*S^2 - 37*S^4)/(144*S^2) + (Pi^2*(619 + 1238*S^2 - 2086*S^4 - 130*S^6 - 65*S^8))/(432*S^2*(1 + S^2)^2) + ((249 + 498*S^2 - 847*S^4 - 16*S^6 - 8*S^8)*HPL[{2}, -S^2])/(72*S^2*(1 + S^2)^2)) + ((1 - S^2 - S^4)/(2*S^2) + (Pi^2*(5 + 10*S^2 - 4*S^4 - 22*S^6 - 11*S^8))/(48*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((1 + 8*S^2 - 9*S^4 + S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + ((1 + 2*S^2 - 9*S^4 - 18*S^6 - 9*S^8)*HPL[{5}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-31 + 57*S^2 + 36*S^4)/(48*S^2) + (Pi^2*(-129 - 258*S^2 + 139*S^4 + 24*S^6 + 12*S^8))/(36*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((72 - 119*S^2 - 119*S^4)/(96*S^2) + (Pi^2*(-9 + 273*S^2 - 899*S^4 - 221*S^6 - 64*S^8))/(144*S^2*(1 + S^2)^2) + ((-2 - 4*S^2 - S^4)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-118 - 236*S^2 + 159*S^4 + 12*S^6 + 6*S^8)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)^2)) + ((21 - 230*S^2 + 782*S^4 - 36*S^6 - 9*S^8)*HPL[{3, 1}, -S^2])/(24*S^2*(1 + S^2)^2) + ((2 + 4*S^2 + S^4)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((5 + 10*S^2 + 8*S^4 + 18*S^6 + 9*S^8)*HPL[{4, 1}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-18 + 231*S^2 - 823*S^4 + 8*S^6 - 8*S^8)*HPL[{2, 1, 1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((118 + 236*S^2 - 159*S^4 - 12*S^6 - 6*S^8)*HPL[{2, 2, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((241 + 482*S^2 - 316*S^4 - 38*S^6 - 19*S^8)*HPL[{3, 1, 1}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-123 - 246*S^2 + 158*S^4 + 18*S^6 + 9*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-23 - 107*S^2)/48 + (Pi^2*(-281*S^2 - 368*S^4 - 184*S^6))/(72*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]*(-((1 + S^2)*(-17 + 15*S^2))/(8*S^2) + (Pi^2*(89 - 142*S^2 - 247*S^4))/(576*S^2) + (Pi^4*(2959 + 5918*S^2 - 7876*S^4 - 1900*S^6 - 950*S^8))/(4320*S^2*(1 + S^2)^2) + ((49 - 134*S^2 - 103*S^4)/(96*S^2) + (Pi^2*(267 + 534*S^2 - 806*S^4 - 98*S^6 - 49*S^8))/(144*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((56 + 112*S^2 - 211*S^4 + 8*S^6 + 4*S^8)*HPL[{2}, -S^2]^2)/(24*S^2*(1 + S^2)^2) + ((-1 + 18*S^2 + 2*S^4 - 26*S^6 - S^8)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)^2) + ((5 - 6*S^4)*HPL[{4}, -S^2])/(4*S^2) + ((17 - 1996*S^2 + 2382*S^4 + 60*S^6 + 17*S^8)*HPL[{2, 1}, -S^2])/(48*S^2*(1 + S^2)^2) + ((-127 - 254*S^2 + 413*S^4 + 20*S^6 + 10*S^8)*HPL[{3, 1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((249 + 498*S^2 - 847*S^4 - 16*S^6 - 8*S^8)*HPL[{2, 1, 1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((-23 + 216*S^2 - 242*S^4 - 392*S^6 - 23*S^8)*Zeta[3])/(48*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((189 + 34*S^2 - 187*S^4)/(192*S^2) + (Pi^2*(-101 + 4576*S^2 - 6678*S^4 - 896*S^6 - 101*S^8))/(576*S^2*(1 + S^2)^2) + ((-17 + 1996*S^2 - 2382*S^4 - 60*S^6 - 17*S^8)*HPL[{2}, -S^2])/(96*S^2*(1 + S^2)^2) + ((5 + 10*S^2 + 3*S^4 - 12*S^6 - 6*S^8)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)^2) + ((-249 - 498*S^2 + 847*S^4 + 16*S^6 + 8*S^8)*HPL[{2, 1}, -S^2])/(24*S^2*(1 + S^2)^2) + ((19 + 38*S^2 - 14*S^4 - 38*S^6 - 19*S^8)*Zeta[3])/(12*S^2*(1 + S^2)^2)) - (5*(50*S^2 + 74*S^4 + 37*S^6)*Zeta[5])/(12*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-13 - 90*S^2 - 13*S^4)/(2*S^2) + (Pi^2*(-11 + 21*S^2 - 8*S^4))/(12*S^2) + (Pi^4*(-16 + 2256*S^2 - 8540*S^4 + 2791*S^6 + 300*S^8))/(360*S^2*(1 + S^2)^2) + ((-3 - 126*S^2 - 155*S^4)/(4*S^2) + (Pi^2*(1 + 2*S^2 + 736*S^4 - 662*S^6 - 331*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-29 - 124*S^2 + 252*S^4 - 392*S^6 - 67*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((19 + 38*S^2 + 62*S^4 - 108*S^6 - 54*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((38*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-154 - 308*S^2 + 147*S^4 + 172*S^6 + 86*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((133 + 486*S^2 - 252*S^4 + 30*S^6 - 37*S^8)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-23 - 46*S^2 - 588*S^4 + 590*S^6 + 295*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-47 - 94*S^2 - 2014*S^4 + 1898*S^6 + 949*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-85 - 143*S^2 + 143*S^4 + 85*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (8*(34 + 68*S^2 - 147*S^4 + 68*S^6 + 34*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((809 + 1618*S^2 - 2102*S^4 + 386*S^6 + 193*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (616*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((23 - 14*S^2 - 53*S^4)/(2*S^2) + (Pi^2*(6 + 12*S^2 + 95*S^4 - 108*S^6 - 54*S^8))/(2*S^2*(1 + S^2)^2))*Zeta[3] + ((16 + 32*S^2 + 219*S^4 - 308*S^6 - 154*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((205*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-352 + 71*S^2 + 295*S^4))/(12*S^2) + (Pi^4*(-3613 - 629*S^2 + 1948*S^4))/(720*S^2) + (Pi^6*(-83308 - 166616*S^2 + 90729*S^4 + 46880*S^6 + 23440*S^8))/(22680*S^2*(1 + S^2)^2) + ((2*(23 + 62*S^2 + 87*S^4))/S^2 + (Pi^2*(567 + 1134*S^2 - 1792*S^4 + 674*S^6 + 337*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-357 - 2244*S^2 + 4350*S^4 - 1332*S^6 - 17*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-588 - 3605*S^2 + 6676*S^4 - 1621*S^6 + 62*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(23 + 46*S^2 - 86*S^4 + 6*S^6 + 3*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-252 - 504*S^2 + 1079*S^4 + 38*S^6 + 19*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((4*(55 + 62*S^2 + 55*S^4))/S^2 + (8*Pi^2*(152 + 304*S^2 - 447*S^4 + 150*S^6 + 75*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(-85 - 143*S^2 + 143*S^4 + 85*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (4*(-89 + 406*S^2 - 2156*S^4 + 1010*S^6 + 181*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (6*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{3, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(505 + 1010*S^2 - 2094*S^4 + 1010*S^6 + 505*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(175 + 350*S^2 - 778*S^4 + 434*S^6 + 217*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(23 + 354*S^2 - 1078*S^4 + 354*S^6 + 23*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(125 + 250*S^2 - 578*S^4 + 334*S^6 + 167*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (64*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-7 + 19*S^2 - 14*S^4)/S^2 + (Pi^2*(72 + 480*S^2 - 1163*S^4 + 345*S^6 + 4*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + (4*(-2 + 5*S^4)*Zeta[3]^2)/S^2 + ((1 + 304*S^2 - 2288*S^4 + 602*S^6 - 39*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*(-((1 + S^2)*(-111 + 1529*S^2))/(8*S^2) + (Pi^4*(169 - 1370*S^2 - 1795*S^4))/(720*S^2) + (Pi^2*(13 - 84*S^2 - 129*S^4))/(6*S^2) + (Pi^6*(1655 + 3310*S^2 + 71000*S^4 - 89106*S^6 - 44553*S^8))/(45360*S^2*(1 + S^2)^2) + ((2 - S^2 + S^4)/(2*S^2) + (Pi^2*(11 + 22*S^2 - 34*S^4 + 20*S^6 + 10*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((33 + 20*S^2 + 274*S^4 + 228*S^6 - 3*S^8)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*S^2*(84 + 94*S^2 + 47*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + ((7 + 14*S^2 - 1426*S^4 + 1246*S^6 + 623*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-53 + 56*S^2 + 149*S^4)/S^2 + (2*Pi^2*(-12 - 24*S^2 - 310*S^4 + 326*S^6 + 163*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-99 - 324*S^2 + 370*S^4 - 932*S^6 - 183*S^8)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(50 + 96*S^2 + 146*S^4 - 17*S^6 + 19*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(2 + 4*S^2 - 30*S^4 + 26*S^6 + 13*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-1 - 2*S^2 + 25*S^4 + 10*S^6 + 5*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-2*(-53 + 62*S^2 + 163*S^4))/S^2 + (Pi^2*(49 + 98*S^2 + 1204*S^4 - 1362*S^6 - 681*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(193 + 1230*S^2 - 2324*S^4 + 774*S^6 + 23*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(577 + 3616*S^2 - 6724*S^4 + 1952*S^6 + 3*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(5 + 3*S^4)*HPL[{3, 1, 2}, -S^2])/S^2 - (2*(-63 - 126*S^2 - 1168*S^4 + 1230*S^6 + 615*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1322 - 2644*S^2 - 42339*S^4 + 40958*S^6 + 20479*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-83 - 545*S^2 + 1078*S^4 - 163*S^6 + 37*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-69 - 138*S^2 - 1182*S^4 + 1262*S^6 + 631*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(-29 - 58*S^2 - 578*S^4 + 642*S^6 + 321*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((19 - 28*S^2 + 17*S^4)/(2*S^2) + (Pi^2*(9 - 4*S^2 + 146*S^4 - 136*S^6 - 39*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + ((3 + 6*S^2 + 26*S^4 - 42*S^6 - 21*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((26 + 19*S^2 - 47*S^4)/S^2 + (Pi^2*(165 + 1106*S^2 - 2328*S^4 + 308*S^6 - 95*S^8))/(6*S^2*(1 + S^2)^2) - (2*(-29 - 58*S^2 + 68*S^4 + 42*S^6 + 21*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) - (2*(-28 - 73*S^2 - 97*S^4 + 63*S^6 + 19*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*(-((1 + S^2)*(1 + 689*S^2))/(4*S^2) + (Pi^2*(31 - 480*S^2 - 431*S^4))/(24*S^2) + (Pi^4*(177 + 906*S^2 + 2456*S^4 - 4310*S^6 - 549*S^8))/(360*S^2*(1 + S^2)^2) + (2*S^2*(106 + 126*S^2 + 63*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((193 + 170*S^2 - 63*S^4)/(2*S^2) + (Pi^2*(41 + 82*S^2 - 204*S^4 - 38*S^6 - 19*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(2 + 50*S^2 - 140*S^4 + 339*S^6 + 55*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(-11 - 22*S^2 - 16*S^4 + 50*S^6 + 25*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-31 - 62*S^2 - 104*S^4 + 152*S^6 + 76*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-9 + 85*S^2 - 296*S^4 + 701*S^6 + 131*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(55 + 110*S^2 - 250*S^4 + 62*S^6 + 31*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(163 + 326*S^2 - 690*S^4 + 110*S^6 + 55*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(-29 - 58*S^2 + 104*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((3 + 14*S^2 + 7*S^4)/S^2 + (Pi^2*(-1 - 2*S^2 + 12*S^4 - 2*S^6 - S^8))/(S^2*(1 + S^2)^2))*Zeta[3] + (2*(-25 - 50*S^2 + 12*S^4 + 42*S^6 + 21*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-185*(1 + S^2)^2)/(4*S^2) + (Pi^2*(189 + 210*S^2 - 107*S^4))/(36*S^2) + (Pi^4*(3979 + 6294*S^2 + 1243*S^4))/(2160*S^2) + (Pi^6*(201706 + 403412*S^2 - 958255*S^4 + 119438*S^6 + 59719*S^8))/(136080*S^2*(1 + S^2)^2) + ((71 + 134*S^2 + 71*S^4)/(6*S^2) + (Pi^2*(350 + 700*S^2 - 2089*S^4 + 514*S^6 + 257*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (31*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S^2) + ((37 + 74*S^2 - 238*S^4 + 74*S^6 + 37*S^8)*HPL[{3}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((-16*(1 + S^2)*(7 + 10*S^2))/(3*S^2) + (Pi^2*(-61 - 122*S^2 + 1132*S^4 - 558*S^6 - 279*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(77 + 102*S^2 - 310*S^4 + 654*S^6 + 77*S^8)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)^2) + ((194 + 388*S^2 + 127*S^4 - 566*S^6 - 283*S^8)*HPL[{6}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((16*(1 + S^2)*(1 + 16*S^2))/(3*S^2) + (4*Pi^2*(-116 - 232*S^2 + 193*S^4 + 122*S^6 + 61*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(237 + 1934*S^2 - 5966*S^4 + 4454*S^6 + 237*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (3*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(50 + 100*S^2 - 551*S^4 + 238*S^6 + 119*S^8)*HPL[{5, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-80*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (16*(37 + 1012*S^2 - 1620*S^4 + 562*S^6 + 37*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (248*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 - (16*(-116 - 232*S^2 - 277*S^4 + 398*S^6 + 199*S^8)*HPL[{4, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2400*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (16*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (1200*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((223 + 238*S^2 - 161*S^4)/(6*S^2) + (Pi^2*(-53 - 812*S^2 + 3858*S^4 - 2876*S^6 - 53*S^8))/(18*S^2*(1 + S^2)^2))*Zeta[3] + (4*(5 + 10*S^2 - 32*S^4 + 10*S^6 + 5*S^8)*Zeta[3]^2)/(3*S^2*(1 + S^2)^2) + HPL[{3}, -S^2]*((-19 - 182*S^2 - 211*S^4)/(3*S^2) + (Pi^2*(-209 - 1376*S^2 + 4378*S^4 - 3464*S^6 - 209*S^8))/(18*S^2*(1 + S^2)^2) + (4*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(11 + 22*S^2 - 87*S^4 + 28*S^6 + 14*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-148*(-1 + S^2)*(1 + S^2))/(3*S^2) + (Pi^2*(287 + 134*S^2 - 145*S^4))/(36*S^2) + (Pi^4*(7200 + 14400*S^2 - 21017*S^4 - 2274*S^6 - 1137*S^8))/(1080*S^2*(1 + S^2)^2) - (2*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-113 - 226*S^2 + 734*S^4 - 226*S^6 - 113*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(55 + 522*S^2 - 1778*S^4 + 1290*S^6 + 55*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((64*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-55 - 2322*S^2 + 1778*S^4 + 510*S^6 - 55*S^8))/(9*S^2*(1 + S^2)^2) + (16*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + ((23 - 52*S^2 + 1274*S^4 - 948*S^6 + 23*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((-81*(1 + S^2)^2)/(8*S^2) + (Pi^2*(503 + 798*S^2 + 119*S^4))/(144*S^2) + (Pi^4*(3743 + 77436*S^2 - 131686*S^4 + 41484*S^6 + 3743*S^8))/(4320*S^2*(1 + S^2)^2) + ((55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2}, -S^2]^2)/(6*S^2*(1 + S^2)^2) + ((-79 - 270*S^2 - 199*S^4)/(6*S^2) + (Pi^2*(-118 - 236*S^2 + 1703*S^4 - 758*S^6 - 379*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] - (4*(18 + 83*S^2 - 158*S^4 + 155*S^6 + 18*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + ((5 + 10*S^2 + 116*S^4 - 82*S^6 - 41*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((20*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(9 - 53*S^2 - 79*S^4 + 172*S^6 + 9*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(178 + 356*S^2 - 2299*S^4 + 986*S^6 + 493*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (600*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(463 + 926*S^2 - 2419*S^4 + 476*S^6 + 238*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (300*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((5 - 2*S^2 - 15*S^4)/S^2 + (Pi^2*(-79 - 158*S^2 + 1444*S^4 - 674*S^6 - 337*S^8))/(18*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-16*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(55 + 2322*S^2 - 1778*S^4 - 510*S^6 + 55*S^8))/(36*S^2*(1 + S^2)^2) + ((-103 - 206*S^2 + 1348*S^4 - 578*S^6 - 289*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (8*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) - (2*(11 + 22*S^2 - 680*S^4 + 358*S^6 + 179*S^8)*Zeta[5])/(3*S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((3*(1 + S^2)*(-33 + 263*S^2))/(4*S^2) + (Pi^2*(59 + 200*S^2 + 189*S^4))/(12*S^2) + (Pi^4*(1129 - 2634*S^2 + 14904*S^4 - 3726*S^6 - 1165*S^8))/(360*S^2*(1 + S^2)^2) - (2*(-41 - 82*S^2 - 1305*S^4 + 1248*S^6 + 624*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-83 - 166*S^2 - 1961*S^4 + 1940*S^6 + 970*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(81 + 862*S^2 - 2156*S^4 + 554*S^6 + 11*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-265 - 530*S^2 - 250*S^4 + 702*S^6 + 351*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(647 + 1294*S^2 - 2123*S^4 + 636*S^6 + 318*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(125 + 250*S^2 - 578*S^4 + 334*S^6 + 167*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((9 + 62*S^2 + 101*S^4)/S^2 + (Pi^2*(3 + 6*S^2 - 662*S^4 + 642*S^6 + 321*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + (2*(25 + 50*S^2 - 498*S^4 + 574*S^6 + 287*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((Pi^4*(-3685 - 4201*S^2))/4320 + (Pi^2*(-999 - 1255*S^2))/288 - (79*(1 + S^2))/3 + (Pi^6*(-5767*S^2 - 82*S^4 - 41*S^6))/(5184*(1 + S^2)^2) + ((7 + 568*S^2 - 948*S^4 + 178*S^6 + 7*S^8)*HPL[{1}, -S^2]^5)/(45*S^2*(1 + S^2)^2) + ((56 + 112*S^2 - 263*S^4 + 34*S^6 + 17*S^8)*HPL[{1}, -S^2]^6)/(54*S^2*(1 + S^2)^2) + ((-5 + 4*S^2 - 3*S^4)/(24*S^2) + (Pi^2*(-4 - 8*S^2 - 1091*S^4 + 174*S^6 + 87*S^8))/(144*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + ((-1 - 2*S^2 - 99*S^4 + 28*S^6 + 14*S^8)*HPL[{2}, -S^2]^3)/(12*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((19 + 30*S^2 + 3*S^4)/(72*S^2) + (Pi^2*(555 + 1110*S^2 - 2348*S^4 + 162*S^6 + 81*S^8))/(216*S^2*(1 + S^2)^2) + ((43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2)) + ((-12 - 24*S^2 + 13*S^4 + 26*S^6 + 13*S^8)*HPL[{3}, -S^2]^2)/(12*S^2*(1 + S^2)^2) + ((-19 - 34*S^2 - 35*S^4)/(12*S^2) + (Pi^2*(1 + 2*S^2 - 32*S^4 + 74*S^6 + 37*S^8))/(36*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-67 - 160*S^2 - 154*S^4 + 52*S^6 - 111*S^8)*HPL[{5}, -S^2])/(24*S^2*(1 + S^2)^2) + ((-5 - 10*S^2 + 64*S^4 + 150*S^6 + 75*S^8)*HPL[{6}, -S^2])/(6*S^2*(1 + S^2)^2) + ((4 + 8*S^2 + 635*S^4 - 162*S^6 - 81*S^8)*HPL[{2, 1}, -S^2]^2)/(6*S^2*(1 + S^2)^2) + ((1 + 50*S^2 + 41*S^4)/(12*S^2) + (Pi^2*(2 + 4*S^2 + 1149*S^4 - 246*S^6 - 123*S^8))/(36*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-81 - 144*S^2 - 202*S^4 + 248*S^6 + 67*S^8)*HPL[{3, 2}, -S^2])/(24*S^2*(1 + S^2)^2) + ((-43 - 160*S^2 - 86*S^4 + 336*S^6 + 145*S^8)*HPL[{4, 1}, -S^2])/(12*S^2*(1 + S^2)^2) - (S^2*(-2 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(3*(1 + S^2)^2) + ((1 + 2*S^2 + 20*S^4 - 58*S^6 - 29*S^8)*HPL[{5, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-8*(1 + S^2)*(1 + 2*S^2))/(3*S^2) + (Pi^2*(-1 - 2*S^2 - 605*S^4 + 84*S^6 + 42*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + ((29 + 1532*S^2 - 1232*S^4 + 88*S^6 - 25*S^8)*HPL[{2, 2, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((28 + 2316*S^2 - 1903*S^4 + 94*S^6 - 59*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (S^2*HPL[{3, 1, 2}, -S^2])/3 + ((-6 - 12*S^2 - 593*S^4 + 170*S^6 + 85*S^8)*HPL[{3, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-8 - 16*S^2 - 923*S^4 + 266*S^6 + 133*S^8)*HPL[{4, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-15 - 1620*S^2 + 1306*S^4 - 44*S^6 + 45*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(-2 - 4*S^2 - 663*S^4 + 174*S^6 + 87*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-2 - 4*S^2 - 669*S^4 + 166*S^6 + 83*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-211 - 235*S^2)/24 + (Pi^2*(66 - 631*S^2 - 895*S^4 - 350*S^6))/(36*(1 + S^2)^2))*Zeta[3] - (7*S^2*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((-107 - 174*S^2 - 211*S^4)/(48*S^2) + (Pi^2*(-91 - 24*S^2 - 290*S^4 - 76*S^6 - 103*S^8))/(144*S^2*(1 + S^2)^2) + ((6 + 12*S^2 - 21*S^4 - 14*S^6 - 7*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*S^2*(3 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-227 - 340*S^2 - 369*S^4)/(48*S^2) + (Pi^2*(-76 - 203*S^2 - 187*S^4))/(144*S^2) + (Pi^4*(5 + 10*S^2 - 8037*S^4 - 52*S^6 - 26*S^8))/(2160*S^2*(1 + S^2)^2) + ((10 + 18*S^2 + 27*S^4 - 29*S^6 - 8*S^8)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)^2) + ((6 + 12*S^2 - 7*S^4 - 12*S^6 - 6*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-29 - 1532*S^2 + 1232*S^4 - 88*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((-3 - 6*S^2 + 318*S^4 - 70*S^6 - 35*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-4 - 8*S^2 - 635*S^4 + 162*S^6 + 81*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((14 - 23*S^2 - 69*S^4 - 12*S^6)*Zeta[3])/(6*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-241 - 274*S^2 - 289*S^4)/(48*S^2) + (Pi^2*(-257 - 290*S^2 - 169*S^4))/(288*S^2) + (Pi^4*(4011 + 8022*S^2 - 15739*S^4 - 28*S^6 - 14*S^8))/(2160*S^2*(1 + S^2)^2) + ((1 - 62*S^2 - 39*S^4)/(12*S^2) + (Pi^2*(488 + 976*S^2 - 2023*S^4 + 146*S^6 + 73*S^8))/(72*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((121 + 242*S^2 - 553*S^4 + 76*S^6 + 38*S^8)*HPL[{2}, -S^2]^2)/(12*S^2*(1 + S^2)^2) + ((-43 - 12*S^2 - 130*S^4 - 60*S^6 - 43*S^8)*HPL[{3}, -S^2])/(12*S^2*(1 + S^2)^2) + ((6 + 12*S^2 - 63*S^4 + 22*S^6 + 11*S^8)*HPL[{4}, -S^2])/(6*S^2*(1 + S^2)^2) + ((17 - 1034*S^2 + 1642*S^4 - 290*S^6 + 17*S^8)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-127 - 254*S^2 + 583*S^4 - 76*S^6 - 38*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-31 - 40*S^2 - 54*S^4 - 132*S^6 - 31*S^8)*Zeta[3])/(6*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-29 - 42*S^2 - 61*S^4)/(36*S^2) + (Pi^2*(-97 + 4192*S^2 - 7150*S^4 + 400*S^6 - 97*S^8))/(216*S^2*(1 + S^2)^2) + ((-17 + 1034*S^2 - 1642*S^4 + 290*S^6 - 17*S^8)*HPL[{2}, -S^2])/(18*S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 + 5*S^4)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((6 + 12*S^2 + 17*S^4 - 34*S^6 - 17*S^8)*Zeta[3])/(9*S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((19 + 332*S^2 + 137*S^4)/(24*S^2) + (Pi^2*(40 - 1420*S^2 + 1066*S^4 - 33*S^6 + 25*S^8))/(36*S^2*(1 + S^2)^2) + (2*(-7 - 14*S^2 - 6*S^4 + 12*S^6 + 6*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) - (2*(-10 + 141*S^2 + 197*S^4 + 85*S^6)*Zeta[5])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(-673 - 714*S^2 - 377*S^4))/(288*S^2) + (-85 - 86*S^2 - 65*S^4)/(6*S^2) + (Pi^4*(-3695 + 24440*S^2 - 54874*S^4 - 7760*S^6 - 3695*S^8))/(4320*S^2*(1 + S^2)^2) + ((17 + 1016*S^2 - 1514*S^4 + 352*S^6 + 17*S^8)*HPL[{2}, -S^2]^2)/(24*S^2*(1 + S^2)^2) + (-((1 + S^2)*(1 + 17*S^2))/(4*S^2) + (Pi^2*(2 + 4*S^2 - 25*S^4 + 10*S^6 + 5*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-57 - 24*S^2 - 214*S^4 + 16*S^6 - 57*S^8)*HPL[{4}, -S^2])/(12*S^2*(1 + S^2)^2) + ((-18 - 36*S^2 - 33*S^4 + 82*S^6 + 41*S^8)*HPL[{5}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-1 + 62*S^2 + 39*S^4)/(6*S^2) + (Pi^2*(-488 - 976*S^2 + 2023*S^4 - 146*S^6 - 73*S^8))/(36*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((13 - 502*S^2 + 822*S^4 - 146*S^6 + 13*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((6 + 12*S^2 - 33*S^4 + 2*S^6 + S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(-3 - 6*S^2 + 9*S^4 + 4*S^6 + 2*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-17 + 1034*S^2 - 1642*S^4 + 290*S^6 - 17*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(121 + 242*S^2 - 553*S^4 + 76*S^6 + 38*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(123 + 246*S^2 - 563*S^4 + 76*S^6 + 38*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-211 - 262*S^2 - 59*S^4)/(24*S^2) + (Pi^2*(66 + 132*S^2 - 163*S^4 - 154*S^6 - 77*S^8))/(36*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-47 - 262*S^2 - 167*S^4)/(24*S^2) + (Pi^2*(-189 + 3688*S^2 - 5902*S^4 + 368*S^6 - 189*S^8))/(144*S^2*(1 + S^2)^2) + ((-6 - 12*S^2 + 33*S^4 - 2*S^6 - S^8)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-121 - 242*S^2 + 553*S^4 - 76*S^6 - 38*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((14 + 28*S^2 + 11*S^4 - 46*S^6 - 23*S^8)*Zeta[3])/(6*S^2*(1 + S^2)^2)) - (2*(-10 - 20*S^2 + 43*S^4 + 28*S^6 + 14*S^8)*Zeta[5])/(3*S^2*(1 + S^2)^2))) + Log[T]^3*((Pi^2*(-367 + 225*S^2))/36 + (Pi^4*(-2423 + 397*S^2))/1080 + (Pi^6*(5767*S^2 - 82*S^4 - 41*S^6))/(648*(1 + S^2)^2) + (S^2*(25 + 6*S^2 + 3*S^4)*HPL[{0}, S^2]^6)/(36*(1 + S^2)^2) - (28*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)^2) - (112*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^6)/(9*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^5*((-275 + 1131*S^2 + 192*S^4 + 90*S^6)/(180*(1 + S^2)^2) + ((-275 - 550*S^2 + 1033*S^4 + 8*S^6 + 4*S^8)*HPL[{1}, -S^2])/(180*S^2*(1 + S^2)^2)) + ((-8*(2 + 9*S^2 + 2*S^4))/(3*S^2) + (Pi^2*(-46 - 92*S^2 + 1195*S^4 - 214*S^6 - 107*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (122*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S^2) + HPL[{1}, -S^2]^4*((-50*(1 + S^2)^2)/(3*S^2) - (5*Pi^2*(51 + 102*S^2 - 305*S^4 + 72*S^6 + 36*S^8))/(9*S^2*(1 + S^2)^2) + (50*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^4*((-25 + 83*S^2)/72 + (Pi^2*(703*S^2 + 86*S^4 + 43*S^6))/(108*(1 + S^2)^2) + ((-19 - 2176*S^2 + 3078*S^4 - 64*S^6 - 19*S^8)*HPL[{1}, -S^2])/(72*S^2*(1 + S^2)^2) + ((-137 - 274*S^2 + 518*S^4 - 10*S^6 - 5*S^8)*HPL[{1}, -S^2]^2)/(18*S^2*(1 + S^2)^2) + ((-3 - 6*S^2 + 531*S^4 - 20*S^6 - 10*S^8)*HPL[{2}, -S^2])/(36*S^2*(1 + S^2)^2)) - (2*(-1 - 2*S^2 - 116*S^4 + 82*S^6 + 41*S^8)*HPL[{3}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (((1 + S^2)*(1 + 95*S^2))/S^2 + (Pi^2*(-15 - 30*S^2 - 544*S^4 + 414*S^6 + 207*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(81 + 108*S^2 - 84*S^4 + 920*S^6 + 119*S^8)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-90 - 180*S^2 - 47*S^4 + 302*S^6 + 151*S^8)*HPL[{6}, -S^2])/(3*S^2*(1 + S^2)^2) + (80*(5 + 10*S^2 - 77*S^4 + 10*S^6 + 5*S^8)*HPL[{2, 1}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((-32*(1 + S^2)*(7 + 2*S^2))/(3*S^2) + (4*Pi^2*(-79 - 158*S^2 - 246*S^4 + 162*S^6 + 81*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(-37 + 58*S^2 - 1400*S^4 + 2150*S^6 + 165*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(-9 + 123*S^2 - 1219*S^4 + 1756*S^6 + 137*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 - 114*S^4 + 110*S^6 + 55*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-12 - 24*S^2 - 511*S^4 + 442*S^6 + 221*S^8)*HPL[{5, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-160*(-1 + S^2)*(1 + S^2))/(3*S^2) - (40*Pi^2*(-11 - 22*S^2 - 77*S^4 + 42*S^6 + 21*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (64*(8 + 138*S^2 - 175*S^4 + 138*S^6 + 8*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (8*(171 + 3020*S^2 - 2462*S^4 + 950*S^6 + 21*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (56*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 - (808*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (480*(-2 - 4*S^2 + 3*S^4 + 2*S^6 + S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (80*(-5 - 64*S^2 + 64*S^4 + 5*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (160*(-5 - 10*S^2 + 9*S^4 + 4*S^6 + 2*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (1120*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (4*(-5 + 27*S^2) + (2*Pi^2*(79 - 618*S^2 + 1253*S^4 + 90*S^6))/(9*(1 + S^2)^2))*Zeta[3] + (56*S^2*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((-108*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(-153 - 2176*S^2 + 700*S^4 + 1072*S^6 + 89*S^8))/(9*S^2*(1 + S^2)^2) + (80*(-10 - 20*S^2 + 77*S^4)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((5 + 49*S^2)/9 + (Pi^2*(-555 + 2257*S^2 - 91*S^4 + 81*S^6))/(54*(1 + S^2)^2) - (2*(7 + 568*S^2 - 948*S^4 + 178*S^6 + 7*S^8)*HPL[{1}, -S^2]^2)/(9*S^2*(1 + S^2)^2) - (10*(56 + 112*S^2 - 263*S^4 + 34*S^6 + 17*S^8)*HPL[{1}, -S^2]^3)/(27*S^2*(1 + S^2)^2) + ((49 - 448*S^2 + 1978*S^4 - 536*S^6 - 11*S^8)*HPL[{2}, -S^2])/(18*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((-19 - 30*S^2 - 3*S^4)/(18*S^2) + (Pi^2*(-555 - 1110*S^2 + 2348*S^4 - 162*S^6 - 81*S^8))/(54*S^2*(1 + S^2)^2) - (2*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + (2*(-5 - 10*S^2 + 16*S^4 + 6*S^6 + 3*S^8)*HPL[{3}, -S^2])/(9*S^2*(1 + S^2)^2) - (2*(-260 - 520*S^2 + 501*S^4 + 22*S^6 + 11*S^8)*HPL[{2, 1}, -S^2])/(9*S^2*(1 + S^2)^2) + (28*(2*S^4 + S^6)*Zeta[3])/(9*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((16*(1 + S^2)^2)/(3*S^2) + (Pi^2*(-55 - 98*S^2 - 35*S^4))/(3*S^2) + (Pi^4*(-4460 - 8920*S^2 + 23717*S^4 - 4426*S^6 - 2213*S^8))/(270*S^2*(1 + S^2)^2) + ((40*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (4*(91 + 694*S^2 - 2094*S^4 + 1594*S^6 + 91*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(47 + 94*S^2 - 554*S^4 + 238*S^6 + 119*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) - (1200*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (8*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (600*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (40*(2 + 37*S^2 - 176*S^4 + 127*S^6 + 2*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((2*(3 + 80*S^2 + 165*S^4))/(3*S^2) + (Pi^2*(63 + 520*S^2 - 3642*S^4 + 5084*S^6 + 383*S^8))/(18*S^2*(1 + S^2)^2) + (16*(-66 - 132*S^2 + 385*S^4 + 32*S^6 + 16*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-3 - 6*S^2 - 96*S^4 + 38*S^6 + 19*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-140*(1 + S^2)^2)/(9*S^2) - (20*Pi^2*(19 + 341*S^2 - 622*S^4 + 251*S^6 + 19*S^8))/(27*S^2*(1 + S^2)^2) + (400*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (200*(5 + 10*S^2 - 65*S^4 + 28*S^6 + 14*S^8)*HPL[{3}, -S^2])/(9*S^2*(1 + S^2)^2) - (200*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (40*(5 + 10*S^2 - 87*S^4 + 40*S^6 + 20*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((75*(-1 + S^2)*(1 + S^2))/(2*S^2) + (Pi^2*(35 - 72*S^2 - 67*S^4))/(18*S^2) + (Pi^4*(660 + 1320*S^2 + 12377*S^4 - 3646*S^6 - 1823*S^8))/(540*S^2*(1 + S^2)^2) + (4*(-28 - 11*S^2 - 700*S^4 + 1115*S^6 + 92*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 106*S^4 + 110*S^6 + 55*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (32*(8 + 138*S^2 - 175*S^4 + 138*S^6 + 8*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (8*(71 + 142*S^2 - 770*S^4 + 58*S^6 + 29*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (160*(5 + 10*S^2 - 77*S^4 + 10*S^6 + 5*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(3 + 106*S^2 - 700*S^4 + 998*S^6 + 61*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((Pi^2*(-185 + 43*S^2))/36 + (-367 + 225*S^2)/12 + (Pi^4*(19753*S^2 - 34*S^4 - 17*S^6))/(1080*(1 + S^2)^2) - (10*(17 + 304*S^2 - 446*S^4 + 124*S^6 + 17*S^8)*HPL[{1}, -S^2]^3)/(9*S^2*(1 + S^2)^2) - (5*(23 + 46*S^2 - 109*S^4 + 16*S^6 + 8*S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + ((-5 - 72*S^2 - 27*S^4)/(6*S^2) + (Pi^2*(2 + 4*S^2 + 1301*S^4 - 230*S^6 - 115*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((4 + 8*S^2 + 425*S^4 - 114*S^6 - 57*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-2*(15 + 24*S^2 + 5*S^4))/S^2 + (Pi^2*(-619 - 1238*S^2 + 2671*S^4 - 260*S^6 - 130*S^8))/(18*S^2*(1 + S^2)^2) + ((-325 - 650*S^2 + 1348*S^4 - 134*S^6 - 67*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + ((21 - 64*S^2 - 166*S^4 + 360*S^6 + 41*S^8)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-9 - 18*S^2 - 4*S^4 + 42*S^6 + 21*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(-78 - 1141*S^2 + 700*S^4 + 37*S^6 + 14*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-4 - 8*S^2 - 381*S^4 + 102*S^6 + 51*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (20*(-1 - 2*S^2 - 154*S^4 + 42*S^6 + 21*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(4 - 48*S^2 + 143*S^4 + 15*S^6)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-363 - 518*S^2 + 21*S^4)/(12*S^2) + (Pi^2*(-189 - 5216*S^2 + 7538*S^4 - 1304*S^6 - 189*S^8))/(36*S^2*(1 + S^2)^2) + ((-55 - 1422*S^2 + 1778*S^4 - 390*S^6 - 55*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-7 - 14*S^2 - 78*S^4 + 58*S^6 + 29*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(4 + 8*S^2 - 139*S^4 + 74*S^6 + 37*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2))) + (8*(11 - 291*S^2 + 587*S^4 + 19*S^6)*Zeta[5])/(3*(1 + S^2)^2) + HPL[{0}, S^2]*((81*(1 + S^2))/2 + (2*Pi^2*(-15 + 7*S^2))/9 + (Pi^4*(-8061 + 35634*S^2 - 12600*S^4 - 67*S^6))/(540*(1 + S^2)^2) - (70*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)^2) - (112*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)^2) + ((3 - 398*S^2 + 1778*S^4 - 1414*S^6 - 113*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-100*(1 + S^2)^2)/(3*S^2) - (10*Pi^2*(140 + 280*S^2 - 851*S^4 + 202*S^6 + 101*S^8))/(27*S^2*(1 + S^2)^2) - (20*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + ((3 + 114*S^2 + 71*S^4)/(3*S^2) + (Pi^2*(-25 - 50*S^2 - 18*S^4 + 62*S^6 + 31*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((27 - 34*S^2 + 330*S^4 - 18*S^6 + 71*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(3 + 6*S^2 - 105*S^4 + 8*S^6 + 4*S^8)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-4*(-65 - 6*S^2 + 35*S^4))/(3*S^2) - (2*Pi^2*(-665 - 1330*S^2 + 1806*S^4 + 82*S^6 + 41*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(-59 + 214*S^2 - 1782*S^4 + 1396*S^6 + 91*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(3 + 6*S^2 - 262*S^4 + 158*S^6 + 79*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) - (8*(-7 - 14*S^2 - 155*S^4 + 100*S^6 + 50*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (40*(-11 + 47*S^2 - 352*S^4 + 281*S^6 + 19*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (32*(-98 - 196*S^2 + 337*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (8*(-1191 - 2382*S^2 + 3994*S^4 + 50*S^6 + 25*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (80*(-27 - 54*S^2 + 87*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (48*(1 + S^2) + (2*Pi^2*(-135*S^2 + 118*S^4 + 59*S^6))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((163 + 238*S^2 - 101*S^4)/(6*S^2) + (Pi^2*(159 - 918*S^2 + 5498*S^4 - 3346*S^6 - 201*S^8))/(18*S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 136*S^4 + 74*S^6 + 37*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(-98 - 196*S^2 + 337*S^4)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (8*S^2*(-22 + 14*S^2 + 7*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((16*(1 + S^2)^2)/(3*S^2) + (Pi^2*(-169 - 330*S^2 - 153*S^4))/(18*S^2) + (Pi^4*(-8061 - 16122*S^2 + 44045*S^4 - 8244*S^6 - 4122*S^8))/(540*S^2*(1 + S^2)^2) + ((-4*(5 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(-211 - 422*S^2 + 1260*S^4 - 298*S^6 - 149*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (4*(35 + 92*S^2 - 18*S^4 + 80*S^6 + 35*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(17 + 34*S^2 - 194*S^4 + 58*S^6 + 29*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (160*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (8*(62 + 124*S^2 - 435*S^4 + 126*S^6 + 63*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (40*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(9 + 58*S^2 - 79*S^4 + 61*S^6 + 9*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-70*(1 + S^2)^2)/(3*S^2) + (Pi^2*(-119 - 3026*S^2 + 5886*S^4 - 2246*S^6 - 119*S^8))/(9*S^2*(1 + S^2)^2) - (80*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(10 + 20*S^2 - 43*S^4 + 14*S^6 + 7*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (20*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(40 + 80*S^2 - 277*S^4 + 86*S^6 + 43*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + (104*(-4*S^2 + 2*S^4 + S^6)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]*((81*(1 + S^2)^2)/(2*S^2) + (Pi^2*(-503 - 798*S^2 - 119*S^4))/(36*S^2) + (Pi^4*(-3743 - 77436*S^2 + 131686*S^4 - 41484*S^6 - 3743*S^8))/(1080*S^2*(1 + S^2)^2) - (2*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((2*(79 + 270*S^2 + 199*S^4))/(3*S^2) + (2*Pi^2*(118 + 236*S^2 - 1703*S^4 + 758*S^6 + 379*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + (16*(18 + 83*S^2 - 158*S^4 + 155*S^6 + 18*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-5 - 10*S^2 - 116*S^4 + 82*S^6 + 41*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-80*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (32*(9 - 53*S^2 - 79*S^4 + 172*S^6 + 9*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (8*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(178 + 356*S^2 - 2299*S^4 + 986*S^6 + 493*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2400*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(463 + 926*S^2 - 2419*S^4 + 476*S^6 + 238*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (1200*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((4*(-5 + 2*S^2 + 15*S^4))/S^2 + (2*Pi^2*(79 + 158*S^2 - 1444*S^4 + 674*S^6 + 337*S^8))/(9*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((64*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-55 - 2322*S^2 + 1778*S^4 + 510*S^6 - 55*S^8))/(9*S^2*(1 + S^2)^2) + (4*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (16*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + (8*(11 + 22*S^2 - 680*S^4 + 358*S^6 + 179*S^8)*Zeta[5])/(3*S^2*(1 + S^2)^2))) + (-15*(-11 + 13*S^2) - (186*Pi^2*(2*S^4 + S^6))/(1 + S^2)^2)*Zeta[7] + HPL[{0}, S^2]^2*((Pi^2*(307 - 309*S^2))/24 + (Pi^4*(69 - 133*S^2))/72 - 10*(-11 + 9*S^2) + (Pi^6*(240902 - 904158*S^2 - 209943*S^4 - 20523*S^6))/(181440*(1 + S^2)^2) + ((17 + 304*S^2 - 446*S^4 + 124*S^6 + 17*S^8)*HPL[{1}, -S^2]^6)/(18*S^2*(1 + S^2)^2) + ((23 + 46*S^2 - 109*S^4 + 16*S^6 + 8*S^8)*HPL[{1}, -S^2]^7)/(21*S^2*(1 + S^2)^2) + ((-21 + 244*S^2 - 1036*S^4 + 500*S^6 + 81*S^8)*HPL[{2}, -S^2]^3)/(24*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((15 + 24*S^2 + 5*S^4)/(5*S^2) + (Pi^2*(619 + 1238*S^2 - 2671*S^4 + 260*S^6 + 130*S^8))/(180*S^2*(1 + S^2)^2) + ((325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2}, -S^2])/(30*S^2*(1 + S^2)^2)) + ((16 + 29*S^2 + 62*S^4 + 35*S^6 + 10*S^8)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)^2) + ((17 - 174*S^2 - 127*S^4)/(8*S^2) + (Pi^2*(24 + 48*S^2 - 113*S^4 - 322*S^6 - 161*S^8))/(24*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-75 + 92*S^2 - 284*S^4 - 421*S^6 - 46*S^8)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)^2) + ((145 + 290*S^2 - 445*S^4 - 724*S^6 - 362*S^8)*HPL[{7}, -S^2])/(4*S^2*(1 + S^2)^2) + ((14 - 278*S^2 + 1185*S^4 - 506*S^6 - 71*S^8)*HPL[{2, 1}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((13 + 34*S^2 + 85*S^4)/(8*S^2) + (Pi^2*(69 + 138*S^2 - 64*S^4 + 166*S^6 + 83*S^8))/(24*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((6 + 67*S^2 + 97*S^4)/(2*S^2) + (Pi^2*(33 + 66*S^2 - 116*S^4 + 382*S^6 + 191*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((-4 - 3*S^2 + 30*S^4 + 13*S^6 + 8*S^8)*HPL[{4, 2}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-20 - 40*S^2 + 9*S^4 + 42*S^6 + 21*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((53 - 96*S^2 + 266*S^4 + 492*S^6 + 93*S^8)*HPL[{5, 1}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-234 - 468*S^2 + 117*S^4 + 526*S^6 + 263*S^8)*HPL[{5, 2}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-282 - 564*S^2 + 227*S^4 + 822*S^6 + 411*S^8)*HPL[{6, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((2*(39 + 24*S^2 + S^4))/S^2 + (Pi^2*(276 + 552*S^2 - 475*S^4 - 4*S^6 - 2*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-2*(-118 - 57*S^2 + 15*S^4))/S^2 + (Pi^2*(1685 + 3370*S^2 - 2776*S^4 - 158*S^6 - 79*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + ((13 + 23*S^2 + 19*S^4 + S^6)*HPL[{3, 1, 2}, -S^2])/(4*S^2*(1 + S^2)) + ((-71 + 1012*S^2 - 4102*S^4 + 2020*S^6 + 325*S^8)*HPL[{3, 2, 1}, -S^2])/(4*S^2*(1 + S^2)^2) + ((37 + 74*S^2 + 210*S^4 - 310*S^6 - 155*S^8)*HPL[{3, 2, 2}, -S^2])/(4*S^2*(1 + S^2)^2) - (4*(1 + 2*S^2 - 39*S^4 + 50*S^6 + 25*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-70 + 773*S^2 - 3128*S^4 + 1379*S^6 + 222*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-11 - 22*S^2 + 306*S^4 - 414*S^6 - 207*S^8)*HPL[{4, 1, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-83 - 166*S^2 + 930*S^4 - 1134*S^6 - 567*S^8)*HPL[{4, 2, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-96 - 192*S^2 + 931*S^4 - 1186*S^6 - 593*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(-81 - 31*S^2 + 26*S^4))/S^2 + (2*Pi^2*(-288 - 576*S^2 + 447*S^4 + 56*S^6 + 28*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (8*(-77 - 154*S^2 + 147*S^4 + 18*S^6 + 9*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((61 - 516*S^2 + 2156*S^4 - 820*S^6 - 129*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((1869 + 3738*S^2 - 3616*S^4 - 266*S^6 - 133*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((1869 + 3738*S^2 - 3616*S^4 - 266*S^6 - 133*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((3717 + 7434*S^2 - 7144*S^4 - 698*S^6 - 349*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-5547 - 11094*S^2 + 10748*S^4 + 1022*S^6 + 511*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-23 + 281*S^2 - 1078*S^4 + 427*S^6 + 69*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(79 + 158*S^2 - 158*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (48*(79 + 158*S^2 - 158*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(783 + 1566*S^2 - 1614*S^4 + 86*S^6 + 43*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-165 - 330*S^2 + 289*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((Pi^2*(-9 - 37*S^2))/6 - (11*(-1 + 7*S^2))/4 + (Pi^4*(-1863*S^2 - 2980*S^4 - 1490*S^6))/(360*(1 + S^2)^2))*Zeta[3] + ((30 - 43*S^2 - 23*S^4 + 10*S^6)*Zeta[3]^2)/(2*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((23 + 19*S^2 - 44*S^4)/(2*S^2) + (Pi^2*(-41 + 512*S^2 - 1901*S^4 + 435*S^6 + 61*S^8))/(6*S^2*(1 + S^2)^2) - (4*S^2*(-28 + 30*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*((363 + 518*S^2 - 21*S^4)/(48*S^2) + (Pi^2*(189 + 5216*S^2 - 7538*S^4 + 1304*S^6 + 189*S^8))/(144*S^2*(1 + S^2)^2) + ((55 + 1422*S^2 - 1778*S^4 + 390*S^6 + 55*S^8)*HPL[{2}, -S^2])/(12*S^2*(1 + S^2)^2) + ((7 + 14*S^2 + 78*S^4 - 58*S^6 - 29*S^8)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-325 - 650*S^2 + 1348*S^4 - 134*S^6 - 67*S^8)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-4 - 8*S^2 + 139*S^4 - 74*S^6 - 37*S^8)*Zeta[3])/(6*S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((105 - 448*S^2 - 297*S^4)/(16*S^2) + (Pi^2*(13 - 27*S^2 - 30*S^4))/(12*S^2) + (Pi^4*(385 + 770*S^2 + 358*S^4 - 1982*S^6 - 991*S^8))/(1440*S^2*(1 + S^2)^2) + ((10 + 20*S^2 - 4*S^4 - 18*S^6 - 9*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 + 16*S^2 - 172*S^4 - 18*S^6 - 21*S^8)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((21 + 42*S^2 - 58*S^4 + 42*S^6 + 21*S^8)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)^2) - (3*(3 + 6*S^2 - 16*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((11 + 8*S^2 + 50*S^4 - 36*S^6 - 25*S^8)*Zeta[3])/(4*S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-23 + 46*S^2 - 11*S^4)/(16*S^2) + (Pi^2*(-32 + 454*S^2 - 1979*S^4 + 614*S^6 + 83*S^8))/(48*S^2*(1 + S^2)^2) + ((9 + 18*S^2 + 46*S^4 - 78*S^6 - 39*S^8)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)^2) + ((-77 - 154*S^2 + 147*S^4 + 18*S^6 + 9*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((6 + 12*S^2 + 23*S^4 - 40*S^6 - 20*S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((205 + 242*S^2 - 91*S^4)/(12*S^2) + (Pi^2*(239 + 326*S^2 + 23*S^4))/(72*S^2) + (Pi^4*(8046 + 16092*S^2 - 31091*S^4 + 806*S^6 + 403*S^8))/(2160*S^2*(1 + S^2)^2) + ((167 + 134*S^2 - 25*S^4)/(12*S^2) + (Pi^2*(574 + 1148*S^2 - 2195*S^4 + 118*S^6 + 59*S^8))/(36*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((154 + 308*S^2 - 741*S^4 + 122*S^6 + 61*S^8)*HPL[{2}, -S^2]^2)/(6*S^2*(1 + S^2)^2) + ((-27 + 12*S^2 + 190*S^4 - 276*S^6 - 27*S^8)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)^2) + ((33 + 66*S^2 + 24*S^4 - 82*S^6 - 41*S^8)*HPL[{4}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-55 - 1422*S^2 + 1778*S^4 - 390*S^6 - 55*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(161 + 322*S^2 - 663*S^4 + 64*S^6 + 32*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-13 - 72*S^2 + 338*S^4 - 336*S^6 - 13*S^8)*Zeta[3])/(6*S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*((43 - 148*S^2 - 111*S^4)/(8*S^2) + (Pi^2*(5 + 149*S^2 - 32*S^4 - 217*S^6 - 9*S^8))/(24*S^2*(1 + S^2)^2) + ((-17 - 34*S^2 + 4*S^4 + 14*S^6 + 7*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 + 10*S^4 + 12*S^6 + 6*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-193 - 5*S^2 + 88*S^4))/(24*S^2) + (-337 + 142*S^2 + 223*S^4)/(8*S^2) + (Pi^4*(-1166 - 2332*S^2 + 1513*S^4 + 240*S^6 + 120*S^8))/(120*S^2*(1 + S^2)^2) + ((317 + 634*S^2 - 636*S^4 + 6*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(79 + 158*S^2 - 158*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((20 + 64*S^2 - 85*S^4 + 53*S^6 + 10*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((3 + 17*S^2 + 38*S^4)/(2*S^2) + (Pi^2*(103 - 976*S^2 + 3720*S^4 - 892*S^6 - 147*S^8))/(24*S^2*(1 + S^2)^2) + (2*(1 + 2*S^2 - 30*S^4 + 28*S^6 + 14*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-19*(-1 + 3*S^2))/2 + (Pi^2*(-125*S^2 - 224*S^4 - 112*S^6))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(95 - 100*S^2 - 163*S^4))/(48*S^2) + (85 - 90*S^2 - 111*S^4)/(4*S^2) + (Pi^4*(-353 + 6986*S^2 - 23401*S^4 - 469*S^6 - 437*S^8))/(1440*S^2*(1 + S^2)^2) + (-2*(1 + 3*S^2) + (Pi^2*(-11 - 22*S^2 + 12*S^4 - 26*S^6 - 13*S^8))/(8*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-29 - 57*S^2 - 144*S^4 - 85*S^6 - 25*S^8)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-46 - 92*S^2 + 3*S^4 + 42*S^6 + 21*S^8)*HPL[{5}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-39 - 24*S^2 - S^4)/S^2 + (Pi^2*(-276 - 552*S^2 + 475*S^4 + 4*S^6 + 2*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((11 - 130*S^2 + 604*S^4 - 241*S^6 - 30*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-17 - 34*S^2 - 98*S^4 + 158*S^6 + 79*S^8)*HPL[{3, 2}, -S^2])/(4*S^2*(1 + S^2)^2) + ((7 + 14*S^2 - 146*S^4 + 206*S^6 + 103*S^8)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-14 + 278*S^2 - 1185*S^4 + 506*S^6 + 71*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-77 - 154*S^2 + 147*S^4 + 18*S^6 + 9*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (3*(-311 - 622*S^2 + 604*S^4 + 46*S^6 + 23*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(79 + 158*S^2 - 158*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-3 - 25*S^2 - 26*S^4)/(4*S^2) - (Pi^2*S^2*(-28 + 30*S^2 + 15*S^4))/(6*(1 + S^2)^2))*Zeta[3] - (S^2*(-51 + 46*S^2 + 23*S^4)*Zeta[5])/(2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((543 + 414*S^2 - 385*S^4)/(16*S^2) + (Pi^2*(69 + 69*S^2 - 26*S^4))/(12*S^2) + (Pi^4*(205 + 15960*S^2 - 23316*S^4 + 674*S^6 + 205*S^8))/(720*S^2*(1 + S^2)^2) + ((37 + 692*S^2 - 974*S^4 + 320*S^6 + 37*S^8)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)^2) + ((11 - 58*S^2 - 53*S^4)/(4*S^2) + (Pi^2*(22 + 44*S^2 + 87*S^4 - 94*S^6 - 47*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-17 + 104*S^2 + 10*S^4 - 192*S^6 - 17*S^8)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)^2) + ((23 + 46*S^2 + 24*S^4 - 70*S^6 - 35*S^8)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-167 - 134*S^2 + 25*S^4)/(4*S^2) + (Pi^2*(-574 - 1148*S^2 + 2195*S^4 - 118*S^6 - 59*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-47 - 1396*S^2 + 1758*S^4 - 364*S^6 - 47*S^8)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((5 + 10*S^2 - 75*S^4 + 32*S^6 + 16*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-3 - 6*S^2 - 474*S^4 + 274*S^6 + 137*S^8)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((55 + 1422*S^2 - 1778*S^4 + 390*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(154 + 308*S^2 - 741*S^4 + 122*S^6 + 61*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(469 + 938*S^2 - 2145*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 - 10*S^2 - 13*S^4)/(2*S^2) + (Pi^2*(34 + 68*S^2 + 111*S^4 - 150*S^6 - 75*S^8))/(12*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((45 + 4*S^2 - 29*S^4)/(2*S^2) + (Pi^2*(93 + 4840*S^2 - 5938*S^4 + 720*S^6 + 93*S^8))/(48*S^2*(1 + S^2)^2) + ((-5 - 10*S^2 + 75*S^4 - 32*S^6 - 16*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-154 - 308*S^2 + 741*S^4 - 122*S^6 - 61*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-8 - 16*S^2 + 133*S^4 - 62*S^6 - 31*S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) + ((40 + 80*S^2 + 117*S^4 - 158*S^6 - 79*S^8)*Zeta[5])/(2*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]*((-5*(1 + S^2)*(-183 + 137*S^2))/(16*S^2) + (Pi^2*(409 + 266*S^2 - 271*S^4))/(48*S^2) + (Pi^4*(337 + 221*S^2 - 190*S^4))/(360*S^2) + (Pi^6*(240902 + 481804*S^2 - 760225*S^4 - 90974*S^6 - 45487*S^8))/(181440*S^2*(1 + S^2)^2) + ((65 + 98*S^2 + 25*S^4)/(8*S^2) + (Pi^2*(266 + 532*S^2 - 1163*S^4 + 138*S^6 + 69*S^8))/(24*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + ((149 + 298*S^2 - 668*S^4 + 86*S^6 + 43*S^8)*HPL[{2}, -S^2]^3)/(12*S^2*(1 + S^2)^2) + ((-11 - 22*S^2 + 24*S^4 + 22*S^6 + 11*S^8)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)^2) + ((1 - 44*S^2 - 29*S^4)/(2*S^2) + (Pi^2*(93 + 186*S^2 + 12*S^4 - 226*S^6 - 113*S^8))/(24*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-31 + 116*S^2 - 26*S^4 - 348*S^6 - 31*S^8)*HPL[{5}, -S^2])/(4*S^2*(1 + S^2)^2) + ((162 + 324*S^2 - 121*S^4 - 414*S^6 - 207*S^8)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-154 - 308*S^2 + 741*S^4 - 122*S^6 - 61*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((2*(-19 - 10*S^2 + 7*S^4))/S^2 + (Pi^2*(-144 - 288*S^2 + 538*S^4 - 22*S^6 - 11*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((19 + 112*S^2 - 406*S^4 + 288*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(4*S^2*(1 + S^2)^2) + ((47 + 64*S^2 - 622*S^4 + 624*S^6 + 47*S^8)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)^2) - (3*(1 + 2*S^2 - 6*S^4 + 2*S^6 + S^8)*HPL[{4, 2}, -S^2])/(4*S^2*(1 + S^2)^2) + (4*(-9 - 18*S^2 + 3*S^4 + 22*S^6 + 11*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((167 + 134*S^2 - 25*S^4)/(2*S^2) + (Pi^2*(574 + 1148*S^2 - 2195*S^4 + 118*S^6 + 59*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (2*(37 + 692*S^2 - 974*S^4 + 320*S^6 + 37*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((195 + 4164*S^2 - 5654*S^4 + 1644*S^6 + 195*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(149 + 298*S^2 - 668*S^4 + 86*S^6 + 43*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((927 + 1854*S^2 - 3984*S^4 + 434*S^6 + 217*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(55 + 1422*S^2 - 1778*S^4 + 390*S^6 + 55*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(161 + 322*S^2 - 663*S^4 + 64*S^6 + 32*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((11 - 14*S^2 - 33*S^4)/(4*S^2) + (Pi^2*(-9 + 36*S^2 + 24*S^4 - 182*S^6 - 9*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + ((30 + 60*S^2 - 31*S^4 - 42*S^6 - 21*S^8)*Zeta[3]^2)/(2*S^2*(1 + S^2)^2) + HPL[{2}, -S^2]*((229 - 134*S^2 - 235*S^4)/(8*S^2) + (Pi^2*(27 - 16*S^4))/(6*S^2) + (Pi^4*(7152 + 14304*S^2 - 23977*S^4 - 842*S^6 - 421*S^8))/(1440*S^2*(1 + S^2)^2) + ((-5 - 28*S^2 + 102*S^4 - 72*S^6 - 5*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((23 + 46*S^2 - 54*S^4 - 42*S^6 - 21*S^8)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-37 - 692*S^2 + 974*S^4 - 320*S^6 - 37*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-154 - 308*S^2 + 743*S^4 - 118*S^6 - 59*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(154 + 308*S^2 - 741*S^4 + 122*S^6 + 61*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-45 - 152*S^2 + 290*S^4 - 336*S^6 - 45*S^8)*Zeta[3])/(4*S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((7 - 50*S^2 - 41*S^4)/(2*S^2) + (Pi^2*(-33 + 120*S^2 + 202*S^4 - 432*S^6 - 33*S^8))/(24*S^2*(1 + S^2)^2) + ((5 + 10*S^2 - 75*S^4 + 32*S^6 + 16*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-6 - 12*S^2 + 15*S^4 + 10*S^6 + 5*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-45 - 4*S^2 + 29*S^4)/S^2 + (Pi^2*(-93 - 4840*S^2 + 5938*S^4 - 720*S^6 - 93*S^8))/(24*S^2*(1 + S^2)^2) + ((8 + 16*S^2 - 133*S^4 + 62*S^6 + 31*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((19 + 160*S^2 + 118*S^4 - 316*S^6 + 19*S^8)*Zeta[5])/(2*S^2*(1 + S^2)^2)) - 279*S^2*Zeta[7]) + HPL[{2}, -S^2]*((-180*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(1308 - 319*S^2 - 2003*S^4))/(1440*S^2) + (Pi^2*(98 - 45*S^2 - 111*S^4))/(6*S^2) + (Pi^6*(-4575 + 74470*S^2 - 219303*S^4 + 6251*S^6 + 3405*S^8))/(45360*S^2*(1 + S^2)^2) + ((45 + 144*S^2 - 206*S^4 + 456*S^6 + 89*S^8)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)^2) + ((29 - 68*S^2 - 153*S^4)/(4*S^2) + (Pi^2*(-10 - 20*S^2 + 33*S^4 - 46*S^6 - 23*S^8))/(2*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((1 - 6*S^2 - 266*S^4 - 328*S^6 - 59*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-10 - 20*S^2 + 6*S^4 + 6*S^6 + 3*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) + ((85 + 143*S^2 - 143*S^4 - 85*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-17 + 206*S^2 + 287*S^4)/(2*S^2) + (Pi^2*(-21 - 42*S^2 - 1346*S^4 + 1286*S^6 + 643*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-175 + 586*S^2 + 993*S^4)/(2*S^2) + (4*Pi^2*(-11 - 22*S^2 - 501*S^4 + 506*S^6 + 253*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((5 + 90*S^2 - 298*S^4 + 342*S^6 + 53*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-34 - 68*S^2 - 19*S^4 + 116*S^6 + 58*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((-21 + 528*S^2 - 1814*S^4 + 3468*S^6 + 583*S^8)*HPL[{5, 1}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*(-98 - 196*S^2 - 24*S^4 + 310*S^6 + 155*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-224 - 448*S^2 + 71*S^4 + 460*S^6 + 230*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-152*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-154 - 308*S^2 + 147*S^4 + 172*S^6 + 86*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((2*(-175 - 62*S^2 + 65*S^4))/S^2 + (Pi^2*(-1799 - 3598*S^2 + 2968*S^4 + 702*S^6 + 351*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + ((-29 - 216*S^2 + 298*S^4 - 216*S^6 - 29*S^8)*HPL[{3, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((91 + 1272*S^2 - 3846*S^4 + 1272*S^6 + 91*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-35 - 70*S^2 - 1176*S^4 + 1158*S^6 + 579*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-51 - 102*S^2 - 1885*S^4 + 1828*S^6 + 914*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(189 + 2147*S^2 - 5920*S^4 + 1531*S^6 + 49*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-97 - 194*S^2 - 3770*S^4 + 3646*S^6 + 1823*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-331 - 662*S^2 - 11552*S^4 + 11206*S^6 + 5603*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-688 - 1376*S^2 - 23541*S^4 + 22998*S^6 + 11499*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4*(55 + 62*S^2 + 55*S^4))/S^2 - (8*Pi^2*(152 + 304*S^2 - 447*S^4 + 150*S^6 + 75*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (32*(34 + 68*S^2 - 147*S^4 + 68*S^6 + 34*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-939 - 1874*S^2 - 2156*S^4 + 3290*S^6 + 1031*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(1657 + 3314*S^2 - 4462*S^4 + 850*S^6 + 425*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(1657 + 3314*S^2 - 4462*S^4 + 850*S^6 + 425*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(3289 + 6578*S^2 - 11518*S^4 + 4114*S^6 + 2057*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(4991 + 9982*S^2 - 17306*S^4 + 5950*S^6 + 2975*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(23 + 354*S^2 - 1078*S^4 + 354*S^6 + 23*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2464*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (7392*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (16*(-799 - 1598*S^2 - 578*S^4 + 2182*S^6 + 1091*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (64*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((Pi^2*(-5 - 87*S^2 - 134*S^4))/(12*S^2) + (15 + 71*S^2 - 72*S^4)/(2*S^2) - (Pi^4*S^2*(-2207 + 2352*S^2 + 1176*S^4))/(180*(1 + S^2)^2))*Zeta[3] + ((2 - 3*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3}, -S^2]*((85 + 142*S^2 - 199*S^4)/(4*S^2) + (Pi^2*(53 - 70*S^2 - 187*S^4))/(12*S^2) + (Pi^4*(5 + 10*S^2 + 1037*S^4 - 1258*S^6 - 629*S^8))/(90*S^2*(1 + S^2)^2) + (2*(-17 - 34*S^2 - 26*S^4 + 72*S^6 + 36*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((193 + 1230*S^2 - 2324*S^4 + 774*S^6 + 23*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-5 - 10*S^2 - 709*S^4 + 648*S^6 + 324*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(7 + 14*S^2 - 1426*S^4 + 1246*S^6 + 623*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((9 - 6*S^2 + 88*S^4 - 64*S^6 - 15*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-133 - 110*S^2 - 57*S^4))/(6*S^2) + (-57 + 142*S^2 - 57*S^4)/(2*S^2) + (Pi^4*(-3684 - 7368*S^2 + 8559*S^4 - 2120*S^6 - 1060*S^8))/(180*S^2*(1 + S^2)^2) - (2*(-265 - 530*S^2 - 250*S^4 + 702*S^6 + 351*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (1232*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(-60 - 430*S^2 + 971*S^4 - 202*S^6 + 25*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*((83 - 222*S^2 - 161*S^4)/(4*S^2) + (Pi^2*(-10 - 71*S^2 + 76*S^4 - 393*S^6 - 78*S^8))/(6*S^2*(1 + S^2)^2) + (2*(55 + 110*S^2 - 250*S^4 + 62*S^6 + 31*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-7 - 14*S^2 - 16*S^4 + 50*S^6 + 25*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-21 + 38*S^2 - 21*S^4)/S^2 + (Pi^2*(32 + 986*S^2 - 3341*S^4 + 1214*S^6 + 117*S^8))/(3*S^2*(1 + S^2)^2) - (16*(-6 - 12*S^2 - 131*S^4 + 142*S^6 + 71*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-20 - 19*S^2 + 41*S^4)/S^2 + (Pi^2*(-59 - 1122*S^2 + 3364*S^4 - 1036*S^6 - 71*S^8))/(6*S^2*(1 + S^2)^2) + (2*(-29 - 58*S^2 - 520*S^4 + 586*S^6 + 293*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-10 - 5*S^2 - 79*S^4)/(2*S^2) - (Pi^2*S^2*(-272 + 338*S^2 + 169*S^4))/(3*(1 + S^2)^2))*Zeta[5] - (6*S^2*(-73 + 136*S^2 + 68*S^4)*Zeta[7])/(1 + S^2)^2) + Log[T]^2*((Pi^4*(2795 - 1773*S^2))/720 + (Pi^2*(121 - 111*S^2))/6 + (Pi^6*(201706 - 943354*S^2 + 80911*S^4 + 6291*S^6))/(45360*(1 + S^2)^2) - (S^2*(9 + 2*S^2 + S^4)*HPL[{0}, S^2]^7)/(48*(1 + S^2)^2) + (14*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)^2) + (16*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^6*((23 - 90*S^2 - 33*S^4 - 8*S^6)/(48*(1 + S^2)^2) + ((23 + 46*S^2 - 70*S^4 - 10*S^6 - 5*S^8)*HPL[{1}, -S^2])/(48*S^2*(1 + S^2)^2)) + ((-1 + S^2)*(85 + 228*S^2 + 85*S^4)*HPL[{2}, -S^2]^3)/(6*S^2*(1 + S^2)) + HPL[{1}, -S^2]^5*((10*(1 + S^2)^2)/S^2 + (Pi^2*(51 + 102*S^2 - 305*S^4 + 72*S^6 + 36*S^8))/(3*S^2*(1 + S^2)^2) - (30*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^5*((-25 - 37*S^2)/48 + (Pi^2*(-1601*S^2 - 218*S^4 - 109*S^6))/(720*(1 + S^2)^2) + ((-125 + 1920*S^2 - 3358*S^4 - 312*S^6 - 125*S^8)*HPL[{1}, -S^2])/(240*S^2*(1 + S^2)^2) + ((275 + 550*S^2 - 1033*S^4 - 8*S^6 - 4*S^8)*HPL[{1}, -S^2]^2)/(120*S^2*(1 + S^2)^2) + (S^2*(-541 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(120*(1 + S^2)^2)) + ((1 + 37*S^2 - 124*S^4 + 185*S^6 + 33*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-2*(23 + 83*S^2 + 76*S^4))/S^2 + (Pi^2*(24 + 48*S^2 + 245*S^4 - 542*S^6 - 271*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-65 + 244*S^2 - 296*S^4 - 1057*S^6 - 236*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) + ((145 + 290*S^2 - 501*S^4 - 836*S^6 - 418*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) - (4*(23 + 354*S^2 - 1078*S^4 + 354*S^6 + 23*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-67 + 124*S^2 + 287*S^4)/S^2 + (Pi^2*(-53 - 106*S^2 - 2400*S^4 + 2650*S^6 + 1325*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-97 + 628*S^2 + 1013*S^4)/S^2 + (Pi^2*(-71 - 142*S^2 - 4200*S^4 + 4230*S^6 + 2115*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((-19 + 73*S^2 - 336*S^4 + 713*S^6 + 133*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(2 + 4*S^2 - 35*S^4 + 42*S^6 + 21*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(31 + 214*S^2 - 976*S^4 + 2082*S^6 + 361*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-10 - 20*S^2 + 349*S^4 - 338*S^6 - 169*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-74 - 148*S^2 + 145*S^4 + 334*S^6 + 167*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((4*(55 + 62*S^2 + 55*S^4))/S^2 + (8*Pi^2*(152 + 304*S^2 - 447*S^4 + 150*S^6 + 75*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-8*(-79 - 30*S^2 + S^4))/S^2 + (4*Pi^2*(919 + 1838*S^2 - 1928*S^4 + 194*S^6 + 97*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (4*(-19 - 61*S^2 + 61*S^4 + 19*S^6)*HPL[{3, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (8*(-33 - 41*S^2 + 41*S^4 + 33*S^6)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((97 + 194*S^2 + 4946*S^4 - 4734*S^6 - 2367*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-47 - 94*S^2 - 1888*S^4 + 1838*S^6 + 919*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-267 - 790*S^2 + 588*S^4 - 222*S^6 + 107*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-187 - 374*S^2 - 7382*S^4 + 7354*S^6 + 3677*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-559 - 1118*S^2 - 23030*S^4 + 22402*S^6 + 11201*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-285 - 570*S^2 - 11861*S^4 + 11504*S^6 + 5752*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((640*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-330 - 660*S^2 + 289*S^4 + 368*S^6 + 184*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (2464*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (8*(-115 - 388*S^2 + 294*S^4 - 118*S^6 + 35*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-887 - 1774*S^2 + 1156*S^4 + 606*S^6 + 303*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-887 - 1774*S^2 + 1156*S^4 + 606*S^6 + 303*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-1811 - 3622*S^2 + 1156*S^4 + 2454*S^6 + 1227*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(-2735 - 5470*S^2 + 2018*S^4 + 3566*S^6 + 1783*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (240*(-5 - 4*S^2 + 4*S^4 + 5*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (64*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (192*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (320*(73 + 146*S^2 - 361*S^4 + 212*S^6 + 106*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (10560*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((225 - 367*S^2)/2 + (Pi^2*(-53 - 201*S^2))/6 + (Pi^4*(1863*S^2 - 2980*S^4 - 1490*S^6))/(90*(1 + S^2)^2))*Zeta[3] + (2*(10 - 63*S^2 + 12*S^4 + S^6)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1, 1}, -S^2]*((-60*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-49 + 73*S^2 - 539*S^4 + 281*S^6 + 72*S^8))/(3*S^2*(1 + S^2)^2) - (16*S^2*(-289 + 292*S^2 + 146*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^4*((53 - 147*S^2)/48 + (Pi^2*(619 - 2388*S^2 - 497*S^4 - 130*S^6))/(144*(1 + S^2)^2) + ((19 + 2176*S^2 - 3078*S^4 + 64*S^6 + 19*S^8)*HPL[{1}, -S^2]^2)/(48*S^2*(1 + S^2)^2) + ((137 + 274*S^2 - 518*S^4 + 10*S^6 + 5*S^8)*HPL[{1}, -S^2]^3)/(18*S^2*(1 + S^2)^2) + ((-18 + 231*S^2 - 823*S^4 + 8*S^6 - 8*S^8)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((59 + 38*S^2 - 37*S^4)/(48*S^2) + (Pi^2*(619 + 1238*S^2 - 2086*S^4 - 130*S^6 - 65*S^8))/(144*S^2*(1 + S^2)^2) + ((249 + 498*S^2 - 847*S^4 - 16*S^6 - 8*S^8)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)^2)) + ((5 + 10*S^2 + 2*S^4 - 14*S^6 - 7*S^8)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)^2) + ((-123 - 246*S^2 + 158*S^4 + 18*S^6 + 9*S^8)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-26*S^2 - 38*S^4 - 19*S^6)*Zeta[3])/(6*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-1 - 224*S^2 - 735*S^4)/(4*S^2) + (Pi^2*(-5 - 156*S^2 - 203*S^4))/(6*S^2) + (Pi^4*(265 + 530*S^2 + 10762*S^4 - 10990*S^6 - 5495*S^8))/(360*S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 - 30*S^4 + 38*S^6 + 19*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-83 - 545*S^2 + 1078*S^4 - 163*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-69 - 138*S^2 - 1182*S^4 + 1262*S^6 + 631*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-29 - 58*S^2 - 578*S^4 + 642*S^6 + 321*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((7 - 16*S^2 + 242*S^4 - 236*S^6 - 53*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-16*(1 + S^2)^2)/(3*S^2) + (Pi^2*(55 + 98*S^2 + 35*S^4))/(3*S^2) + (Pi^4*(4460 + 8920*S^2 - 23717*S^4 + 4426*S^6 + 2213*S^8))/(270*S^2*(1 + S^2)^2) + ((-40*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (8*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) - (4*(91 + 694*S^2 - 2094*S^4 + 1594*S^6 + 91*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(47 + 94*S^2 - 554*S^4 + 238*S^6 + 119*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (1200*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (8*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (600*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (40*(2 + 37*S^2 - 176*S^4 + 127*S^6 + 2*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((367*(-1 + S^2)*(1 + S^2))/(2*S^2) + (Pi^2*(-161 - 31*S^2 + 106*S^4))/(3*S^2) + (Pi^4*(-393 - 786*S^2 + 432*S^4 + 296*S^6 + 148*S^8))/(9*S^2*(1 + S^2)^2) + (8*(125 + 250*S^2 - 578*S^4 + 334*S^6 + 167*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-26 - 208*S^2 + 539*S^4 - 146*S^6 + 3*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*((-2*(1 + S^2)*(3 + 80*S^2))/S^2 + (Pi^2*(-19 - 65*S^2 + 568*S^4 - 1027*S^6 - 169*S^8))/(6*S^2*(1 + S^2)^2) - (8*(-29 - 58*S^2 + 104*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(1 + 2*S^2 - 16*S^4 + 30*S^6 + 15*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((35*(1 + S^2)^2)/(3*S^2) + (5*Pi^2*(19 + 341*S^2 - 622*S^4 + 251*S^6 + 19*S^8))/(9*S^2*(1 + S^2)^2) - (300*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (50*(5 + 10*S^2 - 65*S^4 + 28*S^6 + 14*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (150*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (10*(5 + 10*S^2 - 87*S^4 + 40*S^6 + 20*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-21 + 38*S^2 - 21*S^4)/(4*S^2) + (Pi^2*(32 + 986*S^2 - 3341*S^4 + 1214*S^6 + 117*S^8))/(12*S^2*(1 + S^2)^2) + ((-7 - 14*S^2 + 1426*S^4 - 1246*S^6 - 623*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + (308*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (4*(-6 - 12*S^2 - 131*S^4 + 142*S^6 + 71*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(53 + 113*S^2))/S^2 + (Pi^2*(291 + 260*S^2 + 1568*S^4 - 584*S^6 - 199*S^8))/(6*S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 - 602*S^4 + 586*S^6 + 293*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((Pi^2*(-101 - 209*S^2))/72 - (2*(9 + 25*S^2))/3 + (Pi^4*(-19753*S^2 - 34*S^4 - 17*S^6))/(2160*(1 + S^2)^2) + (2*(7 + 568*S^2 - 948*S^4 + 178*S^6 + 7*S^8)*HPL[{1}, -S^2]^3)/(9*S^2*(1 + S^2)^2) + (5*(56 + 112*S^2 - 263*S^4 + 34*S^6 + 17*S^8)*HPL[{1}, -S^2]^4)/(18*S^2*(1 + S^2)^2) + ((-4*(1 + S^2)*(1 + 2*S^2))/(3*S^2) + (Pi^2*(-1 - 2*S^2 - 605*S^4 + 84*S^6 + 42*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-4 - 8*S^2 - 635*S^4 + 162*S^6 + 81*S^8)*HPL[{2}, -S^2]^2)/(12*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((19 + 30*S^2 + 3*S^4)/(12*S^2) + (Pi^2*(555 + 1110*S^2 - 2348*S^4 + 162*S^6 + 81*S^8))/(36*S^2*(1 + S^2)^2) + ((43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) + ((-31 + 36*S^2 - 110*S^4 - 76*S^6 - 43*S^8)*HPL[{3}, -S^2])/(12*S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 32*S^4 + 14*S^6 + 7*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-15 - 1620*S^2 + 1306*S^4 - 44*S^6 + 45*S^8)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((2 + 4*S^2 + 663*S^4 - 174*S^6 - 87*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-2 - 4*S^2 - 669*S^4 + 166*S^6 + 83*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((6 - 46*S^2 - 115*S^4 - 35*S^6)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-29 - 42*S^2 - 61*S^4)/(12*S^2) + (Pi^2*(-97 + 4192*S^2 - 7150*S^4 + 400*S^6 - 97*S^8))/(72*S^2*(1 + S^2)^2) + ((-17 + 1034*S^2 - 1642*S^4 + 290*S^6 - 17*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 + 5*S^4)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((6 + 12*S^2 + 17*S^4 - 34*S^6 - 17*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2))) + (69 - 167*S^2 - (4*Pi^2*(-125*S^2 + 224*S^4 + 112*S^6))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((-111*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(53 + 19*S^2 - 74*S^4))/(12*S^2) + (Pi^4*(-857 + 4394*S^2 - 17825*S^4 + 5271*S^6 + 1267*S^8))/(360*S^2*(1 + S^2)^2) + ((53 - 62*S^2 - 163*S^4)/S^2 + (Pi^2*(49 + 98*S^2 + 1204*S^4 - 1362*S^6 - 681*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((9 - 85*S^2 + 296*S^4 - 701*S^6 - 131*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((-14 - 28*S^2 + 195*S^4 - 318*S^6 - 159*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-2*(55 + 62*S^2 + 55*S^4))/S^2 - (4*Pi^2*(152 + 304*S^2 - 447*S^4 + 150*S^6 + 75*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(81 + 862*S^2 - 2156*S^4 + 554*S^6 + 11*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-25 - 50*S^2 - 2594*S^4 + 2414*S^6 + 1207*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-95 - 190*S^2 - 3862*S^4 + 3842*S^6 + 1921*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(23 + 354*S^2 - 1078*S^4 + 354*S^6 + 23*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (1232*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (8*(-433 - 866*S^2 + 578*S^4 + 282*S^6 + 141*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(73 + 146*S^2 - 289*S^4 + 146*S^6 + 73*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-2*(1 + 31*S^2 + 54*S^4))/S^2 - (2*Pi^2*S^2*(-317 + 322*S^2 + 161*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (2*S^2*(-493 + 630*S^2 + 315*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{0}, S^2]^2*((Pi^2*(215 - 177*S^2))/24 + (121 - 111*S^2)/2 + (Pi^4*(8046 - 31460*S^2 - 369*S^4 - 403*S^6))/(720*(1 + S^2)^2) + (5*(17 + 304*S^2 - 446*S^4 + 124*S^6 + 17*S^8)*HPL[{1}, -S^2]^4)/(6*S^2*(1 + S^2)^2) + ((23 + 46*S^2 - 109*S^4 + 16*S^6 + 8*S^8)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)^2) + ((-14 + 278*S^2 - 1185*S^4 + 506*S^6 + 71*S^8)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((2*(15 + 24*S^2 + 5*S^4))/S^2 + (Pi^2*(619 + 1238*S^2 - 2671*S^4 + 260*S^6 + 130*S^8))/(18*S^2*(1 + S^2)^2) + ((325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + ((1 - 15*S^2 - 18*S^4)/S^2 + (Pi^2*(29 + 58*S^2 + 74*S^4 - 134*S^6 - 67*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-7 + 41*S^2 - 20*S^4 - 121*S^6 - 21*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((12 + 24*S^2 - 5*S^4 - 106*S^6 - 53*S^8)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-81 - 31*S^2 + 26*S^4)/S^2 + (Pi^2*(-288 - 576*S^2 + 447*S^4 + 56*S^6 + 28*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((61 - 516*S^2 + 2156*S^4 - 820*S^6 - 129*S^8)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((21 + 42*S^2 - 88*S^4 + 166*S^6 + 83*S^8)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((3 + 6*S^2 - 164*S^4 + 274*S^6 + 137*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-23 + 281*S^2 - 1078*S^4 + 427*S^6 + 69*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(79 + 158*S^2 - 158*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-481 - 962*S^2 + 914*S^4 + 22*S^6 + 11*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-165 - 330*S^2 + 289*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-13 - 41*S^2)/2 - (38*Pi^2*(2*S^4 + S^6))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((23 + 19*S^2 - 44*S^4)/(4*S^2) + (Pi^2*(-41 + 512*S^2 - 1901*S^4 + 435*S^6 + 61*S^8))/(12*S^2*(1 + S^2)^2) - (3*(3 + 6*S^2 - 16*S^4 + 26*S^6 + 13*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) - (4*(79 + 158*S^2 - 158*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*S^2*(-28 + 30*S^2 + 15*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((363 + 518*S^2 - 21*S^4)/(8*S^2) + (Pi^2*(189 + 5216*S^2 - 7538*S^4 + 1304*S^6 + 189*S^8))/(24*S^2*(1 + S^2)^2) + ((55 + 1422*S^2 - 1778*S^4 + 390*S^6 + 55*S^8)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((7 + 14*S^2 + 78*S^4 - 58*S^6 - 29*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((-325 - 650*S^2 + 1348*S^4 - 134*S^6 - 67*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4 - 8*S^2 + 139*S^4 - 74*S^6 - 37*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]*((205 + 242*S^2 - 91*S^4)/(4*S^2) + (Pi^2*(239 + 326*S^2 + 23*S^4))/(24*S^2) + (Pi^4*(8046 + 16092*S^2 - 31091*S^4 + 806*S^6 + 403*S^8))/(720*S^2*(1 + S^2)^2) + ((167 + 134*S^2 - 25*S^4)/(4*S^2) + (Pi^2*(574 + 1148*S^2 - 2195*S^4 + 118*S^6 + 59*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((154 + 308*S^2 - 741*S^4 + 122*S^6 + 61*S^8)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((-27 + 12*S^2 + 190*S^4 - 276*S^6 - 27*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((33 + 66*S^2 + 24*S^4 - 82*S^6 - 41*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-55 - 1422*S^2 + 1778*S^4 - 390*S^6 - 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(161 + 322*S^2 - 663*S^4 + 64*S^6 + 32*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-13 - 72*S^2 + 338*S^4 - 336*S^6 - 13*S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) - (78*(2*S^4 + S^6)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-555*(1 + S^2)^2)/(4*S^2) + (Pi^2*(189 + 210*S^2 - 107*S^4))/(12*S^2) + (Pi^4*(3979 + 6294*S^2 + 1243*S^4))/(720*S^2) + (Pi^6*(201706 + 403412*S^2 - 958255*S^4 + 119438*S^6 + 59719*S^8))/(45360*S^2*(1 + S^2)^2) + ((71 + 134*S^2 + 71*S^4)/(2*S^2) + (Pi^2*(350 + 700*S^2 - 2089*S^4 + 514*S^6 + 257*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (31*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/S^2 + ((37 + 74*S^2 - 238*S^4 + 74*S^6 + 37*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-16*(1 + S^2)*(7 + 10*S^2))/S^2 + (Pi^2*(-61 - 122*S^2 + 1132*S^4 - 558*S^6 - 279*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(77 + 102*S^2 - 310*S^4 + 654*S^6 + 77*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((194 + 388*S^2 + 127*S^4 - 566*S^6 - 283*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) - (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((16*(1 + S^2)*(1 + 16*S^2))/S^2 + (4*Pi^2*(-116 - 232*S^2 + 193*S^4 + 122*S^6 + 61*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(237 + 1934*S^2 - 5966*S^4 + 4454*S^6 + 237*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (9*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(50 + 100*S^2 - 551*S^4 + 238*S^6 + 119*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-240*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(37 + 1012*S^2 - 1620*S^4 + 562*S^6 + 37*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (744*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 - (16*(-116 - 232*S^2 - 277*S^4 + 398*S^6 + 199*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (7200*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (16*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (3600*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((223 + 238*S^2 - 161*S^4)/(2*S^2) + (Pi^2*(-53 - 812*S^2 + 3858*S^4 - 2876*S^6 - 53*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + (4*(5 + 10*S^2 - 32*S^4 + 10*S^6 + 5*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{3}, -S^2]*((-19 - 182*S^2 - 211*S^4)/S^2 + (Pi^2*(-209 - 1376*S^2 + 4378*S^4 - 3464*S^6 - 209*S^8))/(6*S^2*(1 + S^2)^2) + (4*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(11 + 22*S^2 - 87*S^4 + 28*S^6 + 14*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-148*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(287 + 134*S^2 - 145*S^4))/(12*S^2) + (Pi^4*(7200 + 14400*S^2 - 21017*S^4 - 2274*S^6 - 1137*S^8))/(360*S^2*(1 + S^2)^2) - (2*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((-113 - 226*S^2 + 734*S^4 - 226*S^6 - 113*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(55 + 522*S^2 - 1778*S^4 + 1290*S^6 + 55*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((192*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-55 - 2322*S^2 + 1778*S^4 + 510*S^6 - 55*S^8))/(3*S^2*(1 + S^2)^2) + (16*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + (3*(23 - 52*S^2 + 1274*S^4 - 948*S^6 + 23*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-243*(1 + S^2)^2)/(4*S^2) + (Pi^2*(503 + 798*S^2 + 119*S^4))/(24*S^2) + (Pi^4*(3743 + 77436*S^2 - 131686*S^4 + 41484*S^6 + 3743*S^8))/(720*S^2*(1 + S^2)^2) + ((55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-79 - 270*S^2 - 199*S^4)/S^2 + (Pi^2*(-118 - 236*S^2 + 1703*S^4 - 758*S^6 - 379*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] - (8*(18 + 83*S^2 - 158*S^4 + 155*S^6 + 18*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (6*(-5 - 10*S^2 - 116*S^4 + 82*S^6 + 41*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((120*(-1 + S^2)*(1 + S^2))/S^2 + (2*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(9 - 53*S^2 - 79*S^4 + 172*S^6 + 9*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(178 + 356*S^2 - 2299*S^4 + 986*S^6 + 493*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (3600*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(463 + 926*S^2 - 2419*S^4 + 476*S^6 + 238*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (1800*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-6*(-5 + 2*S^2 + 15*S^4))/S^2 + (Pi^2*(-79 - 158*S^2 + 1444*S^4 - 674*S^6 - 337*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-96*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(55 + 2322*S^2 - 1778*S^4 - 510*S^6 + 55*S^8))/(6*S^2*(1 + S^2)^2) - (2*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) - (4*(11 + 22*S^2 - 680*S^4 + 358*S^6 + 179*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]*((Pi^4*(93 - 239*S^2))/240 - (555*(1 + S^2))/4 - (2*Pi^2*(11 + 27*S^2))/3 + (Pi^6*(-15415*S^2 + 3526*S^4 + 1763*S^6))/(1296*(1 + S^2)^2) + (14*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)^2) + (56*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)^2) + ((-11 + 134*S^2 + 153*S^4)/(4*S^2) + (Pi^2*(-4 - 8*S^2 - 1983*S^4 + 946*S^6 + 473*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + ((-19 - 38*S^2 - 607*S^4 + 392*S^6 + 196*S^8)*HPL[{2}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((25*(1 + S^2)^2)/S^2 + (5*Pi^2*(140 + 280*S^2 - 851*S^4 + 202*S^6 + 101*S^8))/(18*S^2*(1 + S^2)^2) + (5*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) + ((-2 - 4*S^2 + 5*S^4 - 10*S^6 - 5*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-1 - 98*S^2 - 65*S^4)/(2*S^2) + (4*Pi^2*(1 + 2*S^2 - 20*S^4 + 8*S^6 + 4*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-31 - 20*S^2 - 192*S^4 - 24*S^6 - 45*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + (2*(5 + 10*S^2 - 43*S^4 + 50*S^6 + 25*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) - (8*S^2*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-2*(-29 + 2*S^2 + 55*S^4))/S^2 + (Pi^2*(37 + 74*S^2 + 1975*S^4 - 980*S^6 - 490*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-13 + 42*S^2 - 318*S^4 + 410*S^6 + 95*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((15 + 90*S^2 - 722*S^4 + 1082*S^6 + 295*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (2*(5 + 10*S^2 - 107*S^4 + 48*S^6 + 24*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((4*(-35 + 6*S^2 + 65*S^4))/S^2 + (4*Pi^2*(-16 - 32*S^2 - 987*S^4 + 488*S^6 + 244*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (4*(-113 - 1414*S^2 + 1778*S^4 - 398*S^6 + 3*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-325 - 4242*S^2 + 5294*S^4 - 1052*S^6 + 57*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (10*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (2*(-71 - 142*S^2 - 2418*S^4 + 1578*S^6 + 789*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (24*(-18 - 36*S^2 - 623*S^4 + 398*S^6 + 199*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (40*(-19 - 281*S^2 + 352*S^4 - 47*S^6 + 11*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-35 - 70*S^2 - 1312*S^4 + 806*S^6 + 403*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (240*(-2 - 4*S^2 - 87*S^4 + 54*S^6 + 27*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (-83*(1 + S^2) + (Pi^2*(-34 + 101*S^2 - 328*S^4 - 75*S^6))/(3*(1 + S^2)^2))*Zeta[3] + (2*(-31*S^2 + 22*S^4 + 11*S^6)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2}, -S^2]*((-217 - 548*S^2 - 75*S^4)/(4*S^2) + (Pi^2*(-43 - 18*S^2 + 49*S^4))/(6*S^2) + (Pi^4*(-91 - 182*S^2 - 10416*S^4 + 3916*S^6 + 1958*S^8))/(180*S^2*(1 + S^2)^2) + ((9 - 12*S^2 + 172*S^4 - 196*S^6 - 45*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1 + 2*S^2 - 8*S^4 + 6*S^6 + 3*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-113 - 1414*S^2 + 1778*S^4 - 398*S^6 + 3*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(1 + 2*S^2 - 1346*S^4 + 786*S^6 + 393*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*S^2*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-1 - 86*S^2 + 288*S^4 - 394*S^6 - 71*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-101 + 238*S^2 + 163*S^4)/(2*S^2) + (Pi^2*(-205 - 4430*S^2 + 4826*S^4 - 514*S^6 + 155*S^8))/(6*S^2*(1 + S^2)^2) - (4*(-41 - 82*S^2 + 134*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-9 - 270*S^2 - 181*S^4)/(4*S^2) + (Pi^2*(-59 + 36*S^2 - 30*S^4 - 360*S^6 - 139*S^8))/(12*S^2*(1 + S^2)^2) + (2*(39 + 78*S^2 - 132*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 + 10*S^6 + 5*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-8*(1 + S^2)^2)/S^2 + (Pi^2*(169 + 330*S^2 + 153*S^4))/(12*S^2) + (Pi^4*(8061 + 16122*S^2 - 44045*S^4 + 8244*S^6 + 4122*S^8))/(360*S^2*(1 + S^2)^2) + ((6*(5 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(211 + 422*S^2 - 1260*S^4 + 298*S^6 + 149*S^8))/(2*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (4*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) - (2*(35 + 92*S^2 - 18*S^4 + 80*S^6 + 35*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((17 + 34*S^2 - 194*S^4 + 58*S^6 + 29*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (80*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (12*(62 + 124*S^2 - 435*S^4 + 126*S^6 + 63*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (60*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(9 + 58*S^2 - 79*S^4 + 61*S^6 + 9*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((70*(1 + S^2)^2)/(3*S^2) + (Pi^2*(119 + 3026*S^2 - 5886*S^4 + 2246*S^6 + 119*S^8))/(9*S^2*(1 + S^2)^2) + (80*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(10 + 20*S^2 - 43*S^4 + 14*S^6 + 7*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (20*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(40 + 80*S^2 - 277*S^4 + 86*S^6 + 43*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) - (2*(27 - 77*S^2 + 222*S^4 + 66*S^6)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-243*(1 + S^2)^2)/(4*S^2) + (Pi^2*(41 + 98*S^2 + 9*S^4))/(12*S^2) + (Pi^4*(643 + 65276*S^2 - 127158*S^4 + 33764*S^6 + 643*S^8))/(720*S^2*(1 + S^2)^2) + ((55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-25 - 122*S^2 - 57*S^4)/S^2 + (Pi^2*(-4 - 8*S^2 + 13*S^4 - 14*S^6 - 7*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] - (8*(6 - S^2 + 40*S^4 - 7*S^6 + 6*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (2*(6 + 12*S^2 - 89*S^4 + 34*S^6 + 17*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-12*(5 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(-211 - 422*S^2 + 1260*S^4 - 298*S^6 - 149*S^8))/(S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(10 + 407*S^2 - 880*S^4 + 413*S^6 + 10*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(97 + 194*S^2 - 610*S^4 + 170*S^6 + 85*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (160*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(578 + 1156*S^2 - 4001*S^4 + 1162*S^6 + 581*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (120*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4*(1 + S^2)*(21 + 13*S^2))/S^2 - (2*Pi^2*(17 + 34*S^2 - 147*S^4 + 60*S^6 + 30*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-31 - 238*S^2 - 31*S^4)/(2*S^2) + (Pi^2*(23 + 2674*S^2 - 5162*S^4 + 1930*S^6 + 23*S^8))/(6*S^2*(1 + S^2)^2) - (2*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(41 + 82*S^2 - 266*S^4 + 82*S^6 + 41*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) - (2*(27 + 54*S^2 - 195*S^4 + 76*S^6 + 38*S^8)*Zeta[5])/(S^2*(1 + S^2)^2))) - (1116*(-S^2 + 2*S^4 + S^6)*Zeta[7])/(1 + S^2)^2) + HPL[{1}, -S^2]*((-2695*(1 + S^2)^2)/(8*S^2) - (5*Pi^2*(1 + S^2)*(-9 + 31*S^2))/(6*S^2) + (Pi^6*(107785 + 120602*S^2 - 8687*S^4))/(181440*S^2) + (Pi^4*(2443 + 1694*S^2 - 1389*S^4))/(720*S^2) + (Pi^8*(655944 + 1311888*S^2 - 2526341*S^4 + 28656*S^6 + 14328*S^8))/(1360800*S^2*(1 + S^2)^2) + ((-10*(-1 + S^2)*(1 + S^2))/(3*S^2) + (Pi^2*(121 + 242*S^2 - 334*S^4 - 50*S^6 - 25*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^3 + ((24 + 48*S^2 - 167*S^4 + 48*S^6 + 24*S^8)*HPL[{2}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + ((47 + 150*S^2 + 63*S^4)/(4*S^2) + (Pi^2*(13 + 26*S^2 - 107*S^4 + 48*S^6 + 24*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + ((21 + 42*S^2 - 37*S^4 - 60*S^6 - 30*S^8)*HPL[{4}, -S^2]^2)/(S^2*(1 + S^2)^2) + (-((1 + S^2)*(361 + 1001*S^2))/(4*S^2) + (Pi^2*(178 + 356*S^2 + 3*S^4 - 490*S^6 - 245*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{6}, -S^2] + ((-1057 + 28*S^2 - 3038*S^4 - 4268*S^6 - 1057*S^8)*HPL[{7}, -S^2])/(2*S^2*(1 + S^2)^2) - (6*(-149 - 298*S^2 + 230*S^4 + 316*S^6 + 158*S^8)*HPL[{8}, -S^2])/(S^2*(1 + S^2)^2) + ((-71 - 134*S^2 - 71*S^4)/S^2 + (Pi^2*(-350 - 700*S^2 + 2089*S^4 - 514*S^6 - 257*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 + (2*(233 + 466*S^2 - 1614*S^4 + 466*S^6 + 233*S^8)*HPL[{3, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + (((1 + S^2)*(85 + 53*S^2))/(2*S^2) + (Pi^2*(19 + 38*S^2 - 126*S^4 + 38*S^6 + 19*S^8))/(2*S^2*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + ((-87 - 228*S^2 + 382*S^4 - 492*S^6 - 87*S^8)*HPL[{4, 3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((8*(1 + S^2)*(35 + 44*S^2))/S^2 + (2*Pi^2*(32 + 64*S^2 - 545*S^4 + 282*S^6 + 141*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{5, 1}, -S^2] - (3*(79 + 184*S^2 - 286*S^4 + 392*S^6 + 79*S^8)*HPL[{5, 2}, -S^2])/(2*S^2*(1 + S^2)^2) - (12*S^2*(-2 + 2*S^2 + S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 + ((279 - 844*S^2 + 1506*S^4 + 2492*S^6 + 279*S^8)*HPL[{6, 1}, -S^2])/(2*S^2*(1 + S^2)^2) - (30*S^2*(-2 + 2*S^2 + S^4)*HPL[{6, 2}, -S^2])/(1 + S^2)^2 + (2*(-315 - 630*S^2 + 335*S^4 + 684*S^6 + 342*S^8)*HPL[{7, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + (8*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 + ((-72*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-121 - 242*S^2 + 334*S^4 + 50*S^6 + 25*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] - (2*(143 + 1188*S^2 - 3638*S^4 + 2676*S^6 + 143*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(221 + 1844*S^2 - 5562*S^4 + 4076*S^6 + 221*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (14*(5 + 10*S^2 - 53*S^4 + 28*S^6 + 14*S^8)*HPL[{3, 3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-16*(1 + S^2)*(-1 + 35*S^2))/S^2 + (Pi^2*(1391 + 2782*S^2 - 2876*S^4 - 1158*S^6 - 579*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((-851 - 7160*S^2 + 21942*S^4 - 16088*S^6 - 851*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(61 + 122*S^2 - 613*S^4 + 332*S^6 + 166*S^8)*HPL[{4, 1, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((-2735 - 22808*S^2 + 67758*S^4 - 49592*S^6 - 2735*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(4 + 8*S^2 - 121*S^4 + 86*S^6 + 43*S^8)*HPL[{4, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(257 + 514*S^2 - 2129*S^4 + 940*S^6 + 470*S^8)*HPL[{4, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(745 + 5919*S^2 - 17336*S^4 + 12891*S^6 + 745*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(89 + 178*S^2 - 629*S^4 + 244*S^6 + 122*S^8)*HPL[{5, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(509 + 1018*S^2 - 4379*S^4 + 1984*S^6 + 992*S^8)*HPL[{5, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(2326 + 4652*S^2 - 22627*S^4 + 11006*S^6 + 5503*S^8)*HPL[{6, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2976*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2) + ((32*(1 + S^2)*(1 + 16*S^2))/S^2 + (8*Pi^2*(-116 - 232*S^2 + 193*S^4 + 122*S^6 + 61*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (8*(55 + 1650*S^2 - 1778*S^4 + 162*S^6 + 55*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(55 + 1650*S^2 - 1778*S^4 + 162*S^6 + 55*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (6*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{3, 1, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(55 + 2766*S^2 - 1778*S^4 - 954*S^6 + 55*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (6*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{3, 2, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-325 - 650*S^2 - 242*S^4 + 838*S^6 + 419*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (24*(-91 + 95*S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (8*(237 + 8630*S^2 - 5966*S^4 - 2242*S^6 + 237*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (18*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{4, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (6*(-325 - 650*S^2 - 242*S^4 + 838*S^6 + 419*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (18*(-351 - 702*S^2 - 70*S^4 + 786*S^6 + 393*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-769 - 1538*S^2 - 515*S^4 + 1948*S^6 + 974*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-480*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (48*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (1488*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (4464*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 - (32*(183 + 2612*S^2 - 5492*S^4 + 3062*S^6 + 183*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8928*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 - (14880*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 - (17856*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 - (37200*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 - (32*(-3464 - 6928*S^2 - 277*S^4 + 7094*S^6 + 3547*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (14400*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) + (32*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (7200*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-5 - 10*S^2 + 27*S^4)/(2*S^2) + (Pi^2*(40 + 80*S^2 - 95*S^4 - 22*S^6 - 11*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3]^2 + HPL[{3, 2}, -S^2]*((8*(-3 + 2*S^2 + 11*S^4))/S^2 + (Pi^2*(239 + 2248*S^2 - 7518*S^4 + 5400*S^6 + 239*S^8))/(12*S^2*(1 + S^2)^2) - (4*(-14 - 28*S^2 + 63*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*(-((1 + S^2)*(111 + 367*S^2))/(2*S^2) + (Pi^2*(-55 - 180*S^2 - 109*S^4))/(6*S^2) + (Pi^4*(37 + 74*S^2 + 1057*S^4 - 704*S^6 - 352*S^8))/(90*S^2*(1 + S^2)^2) + ((89 + 632*S^2 - 834*S^4 + 632*S^6 + 89*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(50 + 100*S^2 - 351*S^4 + 142*S^6 + 71*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(113 + 226*S^2 - 734*S^4 + 226*S^6 + 113*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(3 + 8*S^2 - 32*S^4 + 30*S^6 + 3*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((Pi^2*(1 + S^2)*(17 + 12*S^2))/(3*S^2) + (-3 - 134*S^2 - 3*S^4)/(4*S^2) + (Pi^4*(1952 + 3904*S^2 - 10306*S^4 + 2090*S^6 + 1045*S^8))/(360*S^2*(1 + S^2)^2) + ((-93 - 756*S^2 + 2042*S^4 - 1500*S^6 - 93*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-29 - 58*S^2 + 254*S^4 - 106*S^6 - 53*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (372*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (2*(-26 - 52*S^2 - 127*S^4 + 134*S^6 + 67*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (186*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(9 + 107*S^2 - 402*S^4 + 293*S^6 + 9*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4, 1}, -S^2]*((4*(8 + 95*S^2 + 123*S^4))/S^2 + (Pi^2*(521 + 3932*S^2 - 12554*S^4 + 9532*S^6 + 521*S^8))/(6*S^2*(1 + S^2)^2) + (2*(87 + 174*S^2 - 478*S^4 + 38*S^6 + 19*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{5}, -S^2]*((-361 - 922*S^2 - 785*S^4)/(4*S^2) + (Pi^2*(-185 - 88*S^2 + 594*S^4 - 1656*S^6 - 185*S^8))/(12*S^2*(1 + S^2)^2) + (2*(17 + 34*S^2 - 286*S^4 + 130*S^6 + 65*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-15 - 30*S^2 + 38*S^4 + 42*S^6 + 21*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-296*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(287 + 134*S^2 - 145*S^4))/(6*S^2) + (Pi^4*(7200 + 14400*S^2 - 21017*S^4 - 2274*S^6 - 1137*S^8))/(180*S^2*(1 + S^2)^2) - (4*(55 + 522*S^2 - 1778*S^4 + 1290*S^6 + 55*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(-57 + 535*S^2))/(2*S^2) + (2*Pi^2*(-17 + 24*S^2 + 39*S^4))/(3*S^2) + (Pi^4*(-1660 - 3320*S^2 + 4113*S^4 + 932*S^6 + 466*S^8))/(90*S^2*(1 + S^2)^2) - (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(63 + 556*S^2 - 1830*S^4 + 1324*S^6 + 63*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1, 1}, -S^2]*((384*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(55 + 2322*S^2 - 1778*S^4 - 510*S^6 + 55*S^8))/(3*S^2*(1 + S^2)^2) + (32*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((32*(2 + S^2 + 2*S^4))/S^2 + (4*Pi^2*(46 + 799*S^2 - 1376*S^4 + 613*S^6 + 46*S^8))/(3*S^2*(1 + S^2)^2) - (8*(42 + 84*S^2 - 607*S^4 + 270*S^6 + 135*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1, 1}, -S^2]*((-2*(-77 + 134*S^2 + 115*S^4))/S^2 + (Pi^2*(343 + 8212*S^2 - 12134*S^4 + 3892*S^6 + 343*S^8))/(3*S^2*(1 + S^2)^2) - (8*(137 + 274*S^2 - 1908*S^4 + 838*S^6 + 419*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((623 + 582*S^2 - 169*S^4)/(4*S^2) + (Pi^2*(107 + 164*S^2 + 4058*S^4 - 3476*S^6 + 107*S^8))/(12*S^2*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((-200*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^4*(3721 + 1146*S^2 - 2223*S^4))/(1440*S^2) + (Pi^2*(525 - 134*S^2 - 531*S^4))/(24*S^2) + (Pi^6*(9184 + 18368*S^2 - 26123*S^4 - 3682*S^6 - 1841*S^8))/(5040*S^2*(1 + S^2)^2) + ((14 + 28*S^2 - 125*S^4 + 58*S^6 + 29*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-79 - 206*S^2 - 79*S^4)/(2*S^2) + (Pi^2*(-45 - 90*S^2 + 340*S^4 - 134*S^6 - 67*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] - (4*(11 + 39*S^2 - 80*S^4 + 87*S^6 + 11*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-27 - 54*S^2 + 16*S^4 + 96*S^6 + 48*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) + (186*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-71 - 134*S^2 - 71*S^4)/S^2 + (Pi^2*(-350 - 700*S^2 + 2091*S^4 - 510*S^6 - 255*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((157 + 1296*S^2 - 3786*S^4 + 2784*S^6 + 157*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((469 + 3904*S^2 - 11418*S^4 + 8368*S^6 + 469*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(6 + 12*S^2 - 43*S^4 + 14*S^6 + 7*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(131 + 262*S^2 - 996*S^4 + 370*S^6 + 185*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(71 + 134*S^2 + 71*S^4))/S^2 + (2*Pi^2*(350 + 700*S^2 - 2089*S^4 + 514*S^6 + 257*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (1488*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (4*(55 + 1650*S^2 - 1778*S^4 + 162*S^6 + 55*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{3, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(345 + 690*S^2 - 2414*S^4 + 690*S^6 + 345*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1039 + 2078*S^2 - 7282*S^4 + 2078*S^6 + 1039*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(-328 - 656*S^2 + 337*S^4 + 460*S^6 + 230*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-2*(-3 + 4*S^2 + 19*S^4))/S^2 + (Pi^2*(-155 - 1196*S^2 + 3846*S^4 - 2916*S^6 - 155*S^8))/(12*S^2*(1 + S^2)^2))*Zeta[3] + ((4 - 7*S^4)*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((-2*(-7 + 4*S^2 + 23*S^4))/S^2 + (Pi^2*(-30 - 281*S^2 + 940*S^4 - 675*S^6 - 30*S^8))/(3*S^2*(1 + S^2)^2) + (4*(70 + 140*S^2 - 795*S^4 + 326*S^6 + 163*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-14 - 28*S^2 + 63*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-16*(2 + S^2 + 2*S^4))/S^2 - (2*Pi^2*(46 + 799*S^2 - 1376*S^4 + 613*S^6 + 46*S^8))/(3*S^2*(1 + S^2)^2) + (4*(42 + 84*S^2 - 607*S^4 + 270*S^6 + 135*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-61 - 508*S^2 + 3386*S^4 - 2692*S^6 - 61*S^8)*Zeta[5])/(2*S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((107 - 202*S^2 - 821*S^4)/(4*S^2) + (Pi^2*(-5 - 282*S^2 - 293*S^4))/(12*S^2) + (Pi^4*(-761 - 3916*S^2 + 15922*S^4 - 13668*S^6 - 761*S^8))/(360*S^2*(1 + S^2)^2) + ((59 + 180*S^2 - 342*S^4 + 396*S^6 + 59*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(-23 - 46*S^2 + 28*S^4 + 74*S^6 + 37*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((31 + 134*S^2 + 111*S^4)/S^2 + (Pi^2*(108 + 216*S^2 - 1423*S^4 + 610*S^6 + 305*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(16 + 137*S^2 - 444*S^4 + 323*S^6 + 16*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(14 + 28*S^2 - 125*S^4 + 58*S^6 + 29*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(24 + 48*S^2 - 109*S^4 + 6*S^6 + 3*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(70 + 140*S^2 - 795*S^4 + 326*S^6 + 163*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(383 + 766*S^2 - 4532*S^4 + 1882*S^6 + 941*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-23 - 38*S^2 + S^4)/S^2 + (Pi^2*(-17 - 34*S^2 + 102*S^4 - 18*S^6 - 9*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] - (4*(7 + 14*S^2 - 40*S^4 + 2*S^6 + S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + Zeta[3]*((Pi^2*(245 + 210*S^2 - 227*S^4))/(24*S^2) + (393 + 450*S^2 - 71*S^4)/(2*S^2) + (Pi^4*(-419 - 3620*S^2 + 26630*S^4 - 24236*S^6 - 419*S^8))/(720*S^2*(1 + S^2)^2) - (2*(-57 - 114*S^2 + 29*S^4 + 52*S^6 + 26*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((232*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-93 - 4*S^2 + 77*S^4))/(3*S^2) + (Pi^4*(-1437 - 60788*S^2 + 56314*S^4 + 5908*S^6 - 1437*S^8))/(720*S^2*(1 + S^2)^2) + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(241 + 482*S^2 - 2922*S^4 + 1226*S^6 + 613*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(727 + 1454*S^2 - 8806*S^4 + 3686*S^6 + 1843*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (744*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (16*(191 + 382*S^2 - 674*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((47 + 134*S^2 + 95*S^4)/S^2 + (Pi^2*(108 + 216*S^2 - 1481*S^4 + 646*S^6 + 323*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + (2*(44 + 88*S^2 - 1255*S^4 + 634*S^6 + 317*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + (3*(55 + 190*S^2 + 834*S^4 - 734*S^6 + 55*S^8)*Zeta[7])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-1175*(1 + S^2)^2)/(8*S^2) + (Pi^4*(7841 + 9658*S^2 - 1127*S^4))/(2880*S^2) + (Pi^2*(75 - 18*S^2 - 157*S^4))/(12*S^2) + (Pi^6*(60553 + 1675636*S^2 - 2784450*S^4 + 539740*S^6 + 60553*S^8))/(181440*S^2*(1 + S^2)^2) - (62*(-1 + S^2)*HPL[{2}, -S^2]^3)/(1 + S^2) + ((29 + 208*S^2 - 266*S^4 + 208*S^6 + 29*S^8)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((-3*(35 + 86*S^2 + 75*S^4))/(2*S^2) + (Pi^2*(19 + 38*S^2 + 186*S^4 - 158*S^6 - 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-579 + 364*S^2 - 1066*S^4 - 3452*S^6 - 579*S^8)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)^2) - (3*(-87 - 174*S^2 + 81*S^4 + 184*S^6 + 92*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) - (2*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((35 + 134*S^2 + 107*S^4)/S^2 + (Pi^2*(108 + 216*S^2 - 1423*S^4 + 610*S^6 + 305*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((205 + 674*S^2 + 493*S^4)/S^2 + (Pi^2*(709 + 1418*S^2 - 9670*S^4 + 4218*S^6 + 2109*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (3*(29 + 216*S^2 - 298*S^4 + 216*S^6 + 29*S^8)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-7 - 14*S^2 + 185*S^4 - 80*S^6 - 40*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) + (4*(84 + 371*S^2 - 590*S^4 + 647*S^6 + 84*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(2 + 4*S^2 - 71*S^4 + 30*S^6 + 15*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-184 - 368*S^2 + 153*S^4 + 466*S^6 + 233*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(71 + 134*S^2 + 71*S^4))/S^2 + (2*Pi^2*(350 + 700*S^2 - 2089*S^4 + 514*S^6 + 257*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((4*(67 + 66*S^2 + 7*S^4))/S^2 + (8*Pi^2*(233 + 466*S^2 - 1141*S^4 + 196*S^6 + 98*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (1488*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + ((-443 - 886*S^2 + 5586*S^4 - 2374*S^6 - 1187*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (8*(172 + 344*S^2 - 2137*S^4 + 902*S^6 + 451*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(9 - 98*S^2 - 79*S^4 + 217*S^6 + 9*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-1337 - 2674*S^2 + 16838*S^4 - 7138*S^6 - 3569*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-4253 - 8506*S^2 + 52142*S^4 - 21898*S^6 - 10949*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (24*(362 + 724*S^2 - 4471*S^4 + 1886*S^6 + 943*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((240*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (744*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + (32*(9 - 53*S^2 - 79*S^4 + 172*S^6 + 9*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(191 + 382*S^2 - 674*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (16*(191 + 382*S^2 - 674*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-661 - 1322*S^2 + 1348*S^4 + 538*S^6 + 269*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(-1015 - 2030*S^2 + 2299*S^4 + 688*S^6 + 344*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (7200*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) - (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (192*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (80*(221 + 442*S^2 - 1673*S^4 + 532*S^6 + 266*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (3600*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((221 + 274*S^2 - 75*S^4)/(2*S^2) + (Pi^2*(7 - 8*S^2 - 29*S^4))/(3*S^2) + (Pi^4*(-231 - 462*S^2 + 10373*S^4 - 5616*S^6 - 2808*S^8))/(360*S^2*(1 + S^2)^2))*Zeta[3] + ((-3 + 92*S^2 - 146*S^4 + 92*S^6 - 3*S^8)*Zeta[3]^2)/(2*S^2*(1 + S^2)^2) + HPL[{2}, -S^2]^2*((4*(2 + S^2 + 2*S^4))/S^2 + (Pi^2*(46 + 799*S^2 - 1376*S^4 + 613*S^6 + 46*S^8))/(6*S^2*(1 + S^2)^2) + ((-70 - 140*S^2 + 795*S^4 - 326*S^6 - 163*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (93*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + ((-42 - 84*S^2 + 607*S^4 - 270*S^6 - 135*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((63 - 210*S^2 - 529*S^4)/(4*S^2) + (Pi^2*(-17 - 82*S^2 - 63*S^4))/(3*S^2) + (Pi^4*(-292 - 584*S^2 + 6193*S^4 - 3022*S^6 - 1511*S^8))/(180*S^2*(1 + S^2)^2) + ((8 + 16*S^2 - 157*S^4 + 70*S^6 + 35*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (2*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(103 + 206*S^2 - 1352*S^4 + 578*S^6 + 289*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-27 - 128*S^2 + 222*S^4 - 152*S^6 - 27*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*((-2*(1 + S^2)*(29 + 54*S^2))/S^2 + (Pi^2*(-161 - 560*S^2 + 1274*S^4 - 1432*S^6 - 161*S^8))/(12*S^2*(1 + S^2)^2) + ((113 + 226*S^2 - 734*S^4 + 226*S^6 + 113*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-3 - 6*S^2 + 100*S^4 - 50*S^6 - 25*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((148*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-287 - 134*S^2 + 145*S^4))/(12*S^2) + (Pi^4*(-7200 - 14400*S^2 + 21017*S^4 + 2274*S^6 + 1137*S^8))/(360*S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(55 + 522*S^2 - 1778*S^4 + 1290*S^6 + 55*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-192*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(55 + 2322*S^2 - 1778*S^4 - 510*S^6 + 55*S^8))/(3*S^2*(1 + S^2)^2) - (16*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(-13 + 179*S^2))/S^2 + (Pi^2*(25 - 1820*S^2 + 1126*S^4 + 1012*S^6 + 25*S^8))/(6*S^2*(1 + S^2)^2) + (4*(53 + 106*S^2 - 694*S^4 + 298*S^6 + 149*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((169 + 178*S^2 - 71*S^4)/(2*S^2) + (Pi^2*(18 + 36*S^2 + 1477*S^4 - 874*S^6 - 437*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((-116*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(93 + 4*S^2 - 77*S^4))/(6*S^2) + (Pi^4*(1437 + 60788*S^2 - 56314*S^4 - 5908*S^6 + 1437*S^8))/(1440*S^2*(1 + S^2)^2) + ((-31 - 134*S^2 - 111*S^4)/(2*S^2) + (Pi^2*(-108 - 216*S^2 + 1423*S^4 - 610*S^6 - 305*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-89 - 632*S^2 + 834*S^4 - 632*S^6 - 89*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-17 - 34*S^2 + 286*S^4 - 130*S^6 - 65*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-71 - 134*S^2 - 71*S^4)/S^2 + (Pi^2*(-350 - 700*S^2 + 2089*S^4 - 514*S^6 - 257*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((241 + 482*S^2 - 2922*S^4 + 1226*S^6 + 613*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((727 + 1454*S^2 - 8806*S^4 + 3686*S^6 + 1843*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (372*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(191 + 382*S^2 - 674*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-47 - 134*S^2 - 95*S^4)/(2*S^2) + (Pi^2*(-108 - 216*S^2 + 1481*S^4 - 646*S^6 - 323*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + ((-44 - 88*S^2 + 1255*S^4 - 634*S^6 - 317*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) - (3*(-35 - 70*S^2 - 583*S^4 + 392*S^6 + 196*S^8)*Zeta[7])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]*((Pi^6*(-14543 - 17387*S^2))/25920 + (Pi^4*(-9841 - 12401*S^2))/2880 - (2695*(1 + S^2))/8 - (1819*Pi^2*(1 + S^2))/48 + (7*Pi^8*(-70669*S^2 + 10864*S^4 + 5432*S^6))/(388800*(1 + S^2)^2) + (2*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)^2) + (2*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^8)/(3*S^2*(1 + S^2)^2) + ((-15 + 18*S^2 + 41*S^4)/(6*S^2) + (Pi^2*(-11 - 22*S^2 - 452*S^4 + 238*S^6 + 119*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^3 + (S^2*(-167 + 96*S^2 + 48*S^4)*HPL[{2}, -S^2]^4)/(6*(1 + S^2)^2) + HPL[{1}, -S^2]^6*((5*(1 + S^2)^2)/(3*S^2) + (Pi^2*(140 + 280*S^2 - 851*S^4 + 202*S^6 + 101*S^8))/(54*S^2*(1 + S^2)^2) + ((25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + ((-1 + 40*S^2 + 9*S^4)/(4*S^2) + (Pi^2*(-7 - 14*S^2 + 9*S^4 + 8*S^6 + 4*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + ((14 + 28*S^2 - 19*S^4 - 44*S^6 - 22*S^8)*HPL[{4}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((150 - 29*S^2 - 279*S^4)/(4*S^2) + (Pi^2*S^2*(21 + 200*S^2 + 100*S^4))/(6*(1 + S^2)^2))*HPL[{6}, -S^2] + ((-30 - 63*S^2 + 142*S^4 + 137*S^6 - 66*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) + ((-105 - 210*S^2 + 342*S^4 + 596*S^6 + 298*S^8)*HPL[{8}, -S^2])/(S^2*(1 + S^2)^2) + ((11 - 134*S^2 - 153*S^4)/(2*S^2) + (Pi^2*(4 + 8*S^2 + 1983*S^4 - 946*S^6 - 473*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 + (2*(3 + 6*S^2 - 673*S^4 + 392*S^6 + 196*S^8)*HPL[{3, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((1 - 7*S^2)/2 + (Pi^2*(1 + 2*S^2 + 6*S^4 - 2*S^6 - S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + ((45 + 64*S^2 + 117*S^4 + 57*S^6 + 3*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((-113 + 214*S^2 + 207*S^4)/(4*S^2) + (Pi^2*(-3 - 6*S^2 + 147*S^4 - 164*S^6 - 82*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + ((133 + 194*S^2 + 352*S^4 + 185*S^6 + 14*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) + (S^2*(7 + 2*S^2 + S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 + ((292 + 407*S^2 + 801*S^4 + 340*S^6 + 106*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-2 - 4*S^2 + 18*S^4 + 10*S^6 + 5*S^8)*HPL[{6, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((51 + 102*S^2 - 31*S^4 - 380*S^6 - 190*S^8)*HPL[{7, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*S^2*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*(5 + 7*S^4))/(6*S^2) + (-3 + 2*S^2 + 13*S^4)/(2*S^2))*HPL[{3, 1, 2}, -S^2] + ((-123 + 146*S^2 + 341*S^4)/(2*S^2) + (Pi^2*(-83 - 166*S^2 - 3604*S^4 + 1918*S^6 + 959*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] + ((19 + 16*S^2 + 386*S^4 - 268*S^6 - 49*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-19 - 12*S^2 - 299*S^4 + 216*S^6 + 42*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((35 + 70*S^2 + 5*S^4 - 124*S^6 - 62*S^8)*HPL[{3, 3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-181 + 118*S^2 + 427*S^4)/S^2 + (4*Pi^2*(-31 - 62*S^2 - 1396*S^4 + 730*S^6 + 365*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((159 + 98*S^2 + 2342*S^4 - 1786*S^6 - 349*S^8)*HPL[{4, 1, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(-35 - 70*S^2 - 7*S^4 + 132*S^6 + 66*S^8)*HPL[{4, 1, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((519 + 362*S^2 + 7334*S^4 - 5266*S^6 - 1045*S^8)*HPL[{4, 2, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((32 + 64*S^2 + 3*S^4 - 110*S^6 - 55*S^8)*HPL[{4, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-73 - 146*S^2 - 9*S^4 + 268*S^6 + 134*S^8)*HPL[{4, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-239 - 178*S^2 - 3552*S^4 + 2634*S^6 + 567*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-77 - 154*S^2 - 17*S^4 + 296*S^6 + 148*S^8)*HPL[{5, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-617 - 1234*S^2 - 77*S^4 + 2216*S^6 + 1108*S^8)*HPL[{5, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-400 - 800*S^2 - 88*S^4 + 1490*S^6 + 745*S^8)*HPL[{6, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-121 - 1400*S^2 + 1608*S^4 - 200*S^6 + 49*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4*(-29 + 2*S^2 + 55*S^4))/S^2 - (2*Pi^2*(-37 - 74*S^2 - 1975*S^4 + 980*S^6 + 490*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] - (2*(-713 - 8442*S^2 + 9966*S^4 - 1610*S^6 + 199*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-713 - 8442*S^2 + 9966*S^4 - 1610*S^6 + 199*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((9 + 7*S^4)*HPL[{3, 1, 2, 2}, -S^2])/S^2 - (2*(-1439 - 16842*S^2 + 19614*S^4 - 2810*S^6 + 493*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((9 + 7*S^4)*HPL[{3, 2, 1, 2}, -S^2])/S^2 + ((161 + 322*S^2 + 4856*S^4 - 3154*S^6 - 1577*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (24*(-19 - 38*S^2 - 605*S^4 + 396*S^6 + 198*S^8)*HPL[{3, 3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-4371 - 50490*S^2 + 58610*S^4 - 8282*S^6 + 1469*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(1 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/S^2 - (4*(-115 - 230*S^2 - 3632*S^4 + 2374*S^6 + 1187*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (28*(-49 - 98*S^2 - 1556*S^4 + 1018*S^6 + 509*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-679 - 1358*S^2 - 21887*S^4 + 14304*S^6 + 7152*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((8*(-35 + 6*S^2 + 65*S^4))/S^2 + (8*Pi^2*(-16 - 32*S^2 - 987*S^4 + 488*S^6 + 244*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (8*(-113 - 1414*S^2 + 1778*S^4 - 398*S^6 + 3*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (24*(-113 - 1414*S^2 + 1778*S^4 - 398*S^6 + 3*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(-19 - 38*S^2 - 607*S^4 + 392*S^6 + 196*S^8)*HPL[{2, 2, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (48*(-19 - 38*S^2 - 607*S^4 + 392*S^6 + 196*S^8)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(579 + 7070*S^2 - 8930*S^4 + 2132*S^6 + 33*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-451 - 902*S^2 - 14558*S^4 + 9418*S^6 + 4709*S^8)*HPL[{3, 1, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (20*(-151 - 302*S^2 - 4854*S^4 + 3138*S^6 + 1569*S^8)*HPL[{3, 1, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-907 - 1814*S^2 - 29126*S^4 + 18826*S^6 + 9413*S^8)*HPL[{3, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (20*(-379 - 758*S^2 - 12138*S^4 + 7842*S^6 + 3921*S^8)*HPL[{3, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (48*(-474 - 948*S^2 - 15191*S^4 + 9806*S^6 + 4903*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (80*(-19 - 281*S^2 + 352*S^4 - 47*S^6 + 11*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(-35 - 70*S^2 - 1312*S^4 + 806*S^6 + 403*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (480*(-2 - 4*S^2 - 87*S^4 + 54*S^6 + 27*S^8)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-49 - 37*S^2)/2 + (Pi^2*(-73*S^2 + 22*S^4 + 11*S^6))/(6*(1 + S^2)^2))*Zeta[3]^2 + HPL[{2}, -S^2]^2*((-13 - 67*S^2 + 10*S^4)/(4*S^2) + (Pi^2*(-21 + 142*S^2 + 147*S^4))/(48*S^2) + (Pi^4*(-20 - 40*S^2 - 9811*S^4 + 3784*S^6 + 1892*S^8))/(720*S^2*(1 + S^2)^2) + ((4 - S^2 + 91*S^4 - 69*S^6 - 13*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-9 - 18*S^2 + 4*S^4 + 30*S^6 + 15*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-121 - 1400*S^2 + 1608*S^4 - 200*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + ((39 + 78*S^2 + 1210*S^4 - 794*S^6 - 397*S^8)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(-19 - 38*S^2 - 607*S^4 + 392*S^6 + 196*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-9 - 80*S^2 + 252*S^4 - 436*S^6 - 87*S^8)*Zeta[3])/(4*S^2*(1 + S^2)^2)) + HPL[{5}, -S^2]*((125 - 218*S^2 - 455*S^4)/(8*S^2) + (Pi^2*(-129 - 200*S^2 - 538*S^4 + 4*S^6 - 201*S^8))/(24*S^2*(1 + S^2)^2) + ((41 + 82*S^2 - 47*S^4 - 96*S^6 - 48*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((26 + 52*S^2 - 93*S^4 - 118*S^6 - 59*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 2}, -S^2]*((-4 + 49*S^2 + 13*S^4)/S^2 + (Pi^2*(-107 - 60*S^2 - 838*S^4 + 1068*S^6 + 257*S^8))/(24*S^2*(1 + S^2)^2) + ((19 + 38*S^2 - 44*S^4 - 62*S^6 - 31*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*((-45 - 162*S^2 - 373*S^4)/(8*S^2) + (Pi^2*(-39 - 166*S^2 - 135*S^4))/(24*S^2) + (Pi^4*(115 + 230*S^2 - 944*S^4 + 742*S^6 + 371*S^8))/(360*S^2*(1 + S^2)^2) + ((17 + 29*S^2 + 34*S^4 - 37*S^6 - 11*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-10 - 20*S^2 + 13*S^4 + 14*S^6 + 7*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 - 8*S^4 + 6*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-35 - 18*S^2 - 182*S^4 - 126*S^6 - 23*S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((83 + 16*S^2 - 19*S^4)/S^2 + (Pi^2*(255 + 4360*S^2 - 4788*S^4 + 884*S^6 - 31*S^8))/(6*S^2*(1 + S^2)^2) - (4*(42 + 84*S^2 - 125*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1, 1}, -S^2]*((-101 + 238*S^2 + 163*S^4)/S^2 + (Pi^2*(-205 - 4430*S^2 + 4826*S^4 - 514*S^6 + 155*S^8))/(3*S^2*(1 + S^2)^2) - (8*(-41 - 82*S^2 + 134*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1, 1}, -S^2]*((489 - 174*S^2 - 295*S^4)/(2*S^2) + (Pi^2*(353 + 6558*S^2 - 7197*S^4 + 1146*S^6 - 116*S^8))/(3*S^2*(1 + S^2)^2) - (4*(125 + 250*S^2 - 375*S^4 + 16*S^6 + 8*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((-4*(1 + S^2)^2)/(3*S^2) + (Pi^2*(169 + 330*S^2 + 153*S^4))/(72*S^2) + (Pi^4*(8061 + 16122*S^2 - 44045*S^4 + 8244*S^6 + 4122*S^8))/(2160*S^2*(1 + S^2)^2) + ((5 + 2*S^2 + 5*S^4)/S^2 + (Pi^2*(211 + 422*S^2 - 1260*S^4 + 298*S^6 + 149*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + (2*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((-35 - 92*S^2 + 18*S^4 - 80*S^6 - 35*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + ((17 + 34*S^2 - 194*S^4 + 58*S^6 + 29*S^8)*HPL[{4}, -S^2])/(6*S^2*(1 + S^2)^2) - (40*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(62 + 124*S^2 - 435*S^4 + 126*S^6 + 63*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (10*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(9 + 58*S^2 - 79*S^4 + 61*S^6 + 9*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{4, 1}, -S^2]*((-63 + 746*S^2 + 345*S^4)/(4*S^2) + (Pi^2*(-14 - 35*S^2 - 404*S^4 + 709*S^6 + 220*S^8))/(6*S^2*(1 + S^2)^2) - (2*(-13 - 26*S^2 + 28*S^4 + 34*S^6 + 17*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^5*((7*(1 + S^2)^2)/(3*S^2) + (Pi^2*(119 + 3026*S^2 - 5886*S^4 + 2246*S^6 + 119*S^8))/(90*S^2*(1 + S^2)^2) + (8*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(10 + 20*S^2 - 43*S^4 + 14*S^6 + 7*S^8)*HPL[{3}, -S^2])/(15*S^2*(1 + S^2)^2) - (2*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(40 + 80*S^2 - 277*S^4 + 86*S^6 + 43*S^8)*Zeta[3])/(15*S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((Pi^2*(59 + 46*S^2 - 69*S^4))/(12*S^2) + (49 + 259*S^2 + 82*S^4)/(2*S^2) + (Pi^4*(193 + 386*S^2 + 20356*S^4 - 8438*S^6 - 4219*S^8))/(360*S^2*(1 + S^2)^2) - (4*(1 + 2*S^2 - 1346*S^4 + 786*S^6 + 393*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 + 68*S^2 - 280*S^4 + 408*S^6 + 69*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-217 - 548*S^2 - 75*S^4)/(2*S^2) + (Pi^2*(-43 - 18*S^2 + 49*S^4))/(3*S^2) + (Pi^4*(-91 - 182*S^2 - 10416*S^4 + 3916*S^6 + 1958*S^8))/(90*S^2*(1 + S^2)^2) - (2*(1 + 86*S^2 - 288*S^4 + 394*S^6 + 71*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-3*(153 + 161*S^2))/4 + (Pi^2*(13 - 487*S^2 - 1010*S^4 - 406*S^6))/(6*(1 + S^2)^2))*Zeta[5] + Zeta[3]*((Pi^2*(-377 - 401*S^2))/24 - (345*(1 + S^2))/4 + (Pi^4*(212 - 3514*S^2 - 8045*S^4 - 2827*S^6))/(360*(1 + S^2)^2) + (6*(-19*S^2 + 18*S^4 + 9*S^6)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-555*(1 + S^2)^2)/(8*S^2) + (Pi^2*(-273 - 338*S^2 - 321*S^4))/(48*S^2) + (Pi^4*(-217 + 1662*S^2 + 687*S^4))/(2880*S^2) + (Pi^6*(187513 + 375026*S^2 - 953473*S^4 + 122948*S^6 + 61474*S^8))/(90720*S^2*(1 + S^2)^2) + ((71 + 134*S^2 + 71*S^4)/(4*S^2) + (Pi^2*(317 + 634*S^2 - 1901*S^4 + 468*S^6 + 234*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + ((177 + 354*S^2 - 1214*S^4 + 354*S^6 + 177*S^8)*HPL[{2}, -S^2]^3)/(6*S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 20*S^4 - 6*S^6 - 3*S^8)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((-5*(5 + 34*S^2 + 21*S^4))/(4*S^2) + (Pi^2*(29 + 58*S^2 - 320*S^4 + 102*S^6 + 51*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(18 + 11*S^2 + 76*S^4 - 11*S^6 + 18*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((9 + 18*S^2 - 219*S^4 + 128*S^6 + 64*S^8)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)^2) - (8*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-2*(23 + 6*S^2 + 7*S^4))/S^2 + (Pi^2*(-313 - 626*S^2 + 1888*S^4 - 454*S^6 - 227*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (2*(19 + 106*S^2 - 170*S^4 + 106*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(81 + 314*S^2 - 350*S^4 + 290*S^6 + 81*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (3*(-1 + S^2)*(1 + S^2)*HPL[{4, 2}, -S^2])/(2*S^2) - (2*(5 + 10*S^2 - 109*S^4 + 44*S^6 + 22*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((12*(5 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(211 + 422*S^2 - 1260*S^4 + 298*S^6 + 149*S^8))/(S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(65 + 1313*S^2 - 2658*S^4 + 1319*S^6 + 65*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(177 + 354*S^2 - 1214*S^4 + 354*S^6 + 177*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1079 + 2158*S^2 - 7478*S^4 + 2182*S^6 + 1091*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (160*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (24*(62 + 124*S^2 - 435*S^4 + 126*S^6 + 63*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (120*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (-((1 + S^2)*(111 + 55*S^2))/(2*S^2) + (Pi^2*(-67 - 272*S^2 + 262*S^4 - 376*S^6 - 67*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + ((7 + 14*S^2 - 67*S^4 + 20*S^6 + 10*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{3}, -S^2]*((-39 - 270*S^2 - 151*S^4)/(4*S^2) + (Pi^2*(-113 - 196*S^2 - 94*S^4 - 220*S^6 - 113*S^8))/(12*S^2*(1 + S^2)^2) + (2*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*S^2*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((-73 - 274*S^2 - 73*S^4)/(2*S^2) + (Pi^2*(31 - 50*S^2 - 9*S^4))/(12*S^2) + (Pi^4*(7131 + 14262*S^2 - 38357*S^4 + 7288*S^6 + 3644*S^8))/(720*S^2*(1 + S^2)^2) + ((-19 - 106*S^2 + 170*S^4 - 106*S^6 - 19*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 40*S^4 + 14*S^6 + 7*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-35 - 238*S^2 + 290*S^4 - 238*S^6 - 35*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((31 + 238*S^2 + 31*S^4)/(2*S^2) + (Pi^2*(-23 - 2674*S^2 + 5162*S^4 - 1930*S^6 - 23*S^8))/(6*S^2*(1 + S^2)^2) + (2*(41 + 82*S^2 - 266*S^4 + 82*S^6 + 41*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-133 - 484*S^2 + 250*S^4 - 572*S^6 - 133*S^8)*Zeta[5])/(2*S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-37*Pi^2*(1 + S^2)^2)/(4*S^2) - (5*(1 + S^2)*(69 + 65*S^2))/(4*S^2) + (Pi^4*(-1234 - 2001*S^2 - 851*S^4))/(1440*S^2) + (Pi^6*(1134 + 2268*S^2 - 222663*S^4 + 51304*S^6 + 25652*S^8))/(45360*S^2*(1 + S^2)^2) + ((8 + 16*S^2 + S^4 - 30*S^6 - 15*S^8)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((5 - 92*S^2 - 17*S^4)/(4*S^2) + (Pi^2*(13 + 26*S^2 - 22*S^4 - 18*S^6 - 9*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((93 + 116*S^2 + 202*S^4 - 16*S^6 - 35*S^8)*HPL[{5}, -S^2])/(4*S^2*(1 + S^2)^2) + ((30 + 60*S^2 - 33*S^4 - 76*S^6 - 38*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-19 - 38*S^2 - 607*S^4 + 392*S^6 + 196*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((9 - 122*S^2 - 155*S^4)/(2*S^2) + (Pi^2*(-7 - 14*S^2 + 1982*S^4 - 926*S^6 - 463*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (2*(-4 - 91*S^4 + 70*S^6 + 13*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-41 - 23*S^2 - 580*S^4 + 451*S^6 + 89*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 6*S^4 - 2*S^6 - S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-17 - 34*S^2 + 9*S^4 + 36*S^6 + 18*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-11 + 134*S^2 + 153*S^4)/S^2 + (Pi^2*(-4 - 8*S^2 - 1983*S^4 + 946*S^6 + 473*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(-121 - 1400*S^2 + 1608*S^4 - 200*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-177 - 2106*S^2 + 2498*S^4 - 398*S^6 + 51*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 + ((-1 - 2*S^2 - 2672*S^4 + 1538*S^6 + 769*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 - 2012*S^4 + 1158*S^6 + 579*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-113 - 1414*S^2 + 1778*S^4 - 398*S^6 + 3*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-455 - 910*S^2 - 15914*S^4 + 10194*S^6 + 5097*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*S^2*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-6 - 57*S^2 - 67*S^4)/(2*S^2) + (Pi^2*(-1 - 58*S^2 + 242*S^4 - 532*S^6 - 95*S^8))/(12*S^2*(1 + S^2)^2))*Zeta[3] + (2*(-1 - 2*S^2 - 15*S^4 + 10*S^6 + 5*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-83 - 16*S^2 + 19*S^4)/(2*S^2) + (Pi^2*(-255 - 4360*S^2 + 4788*S^4 - 884*S^6 + 31*S^8))/(12*S^2*(1 + S^2)^2) + (2*(42 + 84*S^2 - 125*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((5 - 51*S^2 - 16*S^4)/(2*S^2) + (Pi^2*(29 + 24*S^2 + 226*S^4 - 254*S^6 - 61*S^8))/(12*S^2*(1 + S^2)^2) + ((39 + 78*S^2 - 126*S^4 - 26*S^6 - 13*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-11 - 22*S^2 + 18*S^4 + 26*S^6 + 13*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-20 - 51*S^2 - 26*S^4 - 220*S^6 - 61*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-65 - 206*S^2 - 269*S^4)/(4*S^2) + (Pi^2*(-29 - 111*S^2 - 98*S^4))/(12*S^2) + (Pi^4*(-683 - 238*S^2 - 2172*S^4 - 1566*S^6 - 981*S^8))/(720*S^2*(1 + S^2)^2) + ((-45 - 62*S^2 - 112*S^4 - 36*S^6 + 3*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(-14 - 28*S^2 + 18*S^4 + 42*S^6 + 21*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((51 + 50*S^2 - 9*S^4)/(2*S^2) + (Pi^2*(51 + 102*S^2 - 174*S^4 - 26*S^6 - 13*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(-11 - 12*S^2 - 117*S^4 + 76*S^6 + 16*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-17 - 34*S^2 - 2*S^4 + 62*S^6 + 31*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-14 - 28*S^2 + 3*S^4 + 40*S^6 + 20*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-9 + 12*S^2 - 172*S^4 + 196*S^6 + 45*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-39 - 78*S^2 + 126*S^4 + 26*S^6 + 13*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-121 - 242*S^2 + 388*S^4 + 58*S^6 + 29*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(39 + 78*S^2 - 132*S^4 + 2*S^6 + S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-2*(1 + S^2)*(3 + 4*S^2))/S^2 + (Pi^2*(1 + 2*S^2 - 36*S^4 - 58*S^6 - 29*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + ((21 + 42*S^2 - 80*S^4 - 114*S^6 - 57*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-41 + 285*S^2 + 150*S^4))/(12*S^2) + (151 + 450*S^2 + 171*S^4)/(2*S^2) + (Pi^4*(-447 - 45554*S^2 + 47218*S^4 - 4532*S^6 + 1407*S^8))/(720*S^2*(1 + S^2)^2) - (8*(-28 - 353*S^2 + 445*S^4 - 99*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-77 - 154*S^2 + 252*S^4 + 50*S^6 + 25*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-119 - 238*S^2 + 394*S^4 + 66*S^6 + 33*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-113 - 1414*S^2 + 1778*S^4 - 398*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-19 - 38*S^2 - 607*S^4 + 392*S^6 + 196*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-75 - 150*S^2 - 3774*S^4 + 2354*S^6 + 1177*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*S^2*(-337 + 196*S^2 + 98*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((63 + 70*S^2 - S^4)/S^2 + (Pi^2*(27 + 54*S^2 - 146*S^4 + 22*S^6 + 11*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + (2*(9 + 18*S^2 - 55*S^4 + 36*S^6 + 18*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-81*(1 + S^2)^2)/(4*S^2) + (Pi^2*(41 + 98*S^2 + 9*S^4))/(36*S^2) + (Pi^4*(643 + 65276*S^2 - 127158*S^4 + 33764*S^6 + 643*S^8))/(2160*S^2*(1 + S^2)^2) + ((55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((-25 - 122*S^2 - 57*S^4)/(3*S^2) + (Pi^2*(-4 - 8*S^2 + 13*S^4 - 14*S^6 - 7*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] - (8*(6 - S^2 + 40*S^4 - 7*S^6 + 6*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(6 + 12*S^2 - 89*S^4 + 34*S^6 + 17*S^8)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-4*(5 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(-211 - 422*S^2 + 1260*S^4 - 298*S^6 - 149*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(10 + 407*S^2 - 880*S^4 + 413*S^6 + 10*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(97 + 194*S^2 - 610*S^4 + 170*S^6 + 85*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (160*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (8*(578 + 1156*S^2 - 4001*S^4 + 1162*S^6 + 581*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (40*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4*(1 + S^2)*(21 + 13*S^2))/(3*S^2) - (2*Pi^2*(17 + 34*S^2 - 147*S^4 + 60*S^6 + 30*S^8))/(9*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-31 - 238*S^2 - 31*S^4)/(6*S^2) + (Pi^2*(23 + 2674*S^2 - 5162*S^4 + 1930*S^6 + 23*S^8))/(18*S^2*(1 + S^2)^2) - (2*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(41 + 82*S^2 - 266*S^4 + 82*S^6 + 41*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) - (2*(27 + 54*S^2 - 195*S^4 + 76*S^6 + 38*S^8)*Zeta[5])/(3*S^2*(1 + S^2)^2)) - (3*(-10 + 186*S^2 + 151*S^4)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((-1175*(1 + S^2)^2)/(8*S^2) + (Pi^4*(-5561 - 5258*S^2 - 2721*S^4))/(2880*S^2) + (Pi^2*(-923 - 1174*S^2 - 763*S^4))/(48*S^2) + (Pi^6*(-106337 + 1277476*S^2 - 3050526*S^4 + 269164*S^6 - 106337*S^8))/(181440*S^2*(1 + S^2)^2) + (2*(9 + 200*S^2 - 402*S^4 + 200*S^6 + 9*S^8)*HPL[{2}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + ((1 - 4*S^2 + 30*S^4 - 12*S^6 + S^8)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((67 - 74*S^2 - 229*S^4)/(4*S^2) + (Pi^2*(-6 - 12*S^2 - 61*S^4 + 58*S^6 + 29*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-249 - 156*S^2 - 542*S^4 + 284*S^6 - 249*S^8)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-78 - 156*S^2 + 39*S^4 + 290*S^6 + 145*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) - (2*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((23 + 62*S^2 + 15*S^4)/S^2 + (Pi^2*(25 + 50*S^2 - 167*S^4 + 40*S^6 + 20*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((139 + 542*S^2 + 219*S^4)/(2*S^2) + (Pi^2*(121 + 242*S^2 - 682*S^4 + 138*S^6 + 69*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (3*(1 - 5*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((-32 - 64*S^2 + 57*S^4 + 90*S^6 + 45*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(37 + 26*S^2 + 182*S^4 - 42*S^6 + 37*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-47 - 94*S^2 + 81*S^4 + 136*S^6 + 68*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-159 - 318*S^2 + 459*S^4 + 332*S^6 + 166*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(71 + 134*S^2 + 71*S^4))/S^2 + (2*Pi^2*(317 + 634*S^2 - 1901*S^4 + 468*S^6 + 234*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((8*(47 + 70*S^2 + 39*S^4))/S^2 + (2*Pi^2*(947 + 1894*S^2 - 5690*S^4 + 1390*S^6 + 695*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (16*(9 + 200*S^2 - 402*S^4 + 200*S^6 + 9*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-69 - 138*S^2 + 488*S^4 - 102*S^6 - 51*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) - (8*(27 + 54*S^2 - 193*S^4 + 40*S^6 + 20*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(21 + 601*S^2 - 1246*S^4 + 607*S^6 + 21*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-215 - 430*S^2 + 1544*S^4 - 322*S^6 - 161*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((-659 - 1318*S^2 + 4712*S^4 - 970*S^6 - 485*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(327 + 654*S^2 - 2287*S^4 + 452*S^6 + 226*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-24*(5 + 2*S^2 + 5*S^4))/S^2 - (2*Pi^2*(211 + 422*S^2 - 1260*S^4 + 298*S^6 + 149*S^8))/(S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (8*(177 + 354*S^2 - 1214*S^4 + 354*S^6 + 177*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(10 + 407*S^2 - 880*S^4 + 413*S^6 + 10*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(275 + 550*S^2 - 1888*S^4 + 550*S^6 + 275*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (16*(275 + 550*S^2 - 1888*S^4 + 550*S^6 + 275*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(1081 + 2162*S^2 - 7418*S^4 + 2162*S^6 + 1081*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(6469 + 12938*S^2 - 44314*S^4 + 12914*S^6 + 6457*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (320*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (192*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (48*(330 + 660*S^2 - 2261*S^4 + 658*S^6 + 329*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (240*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (-((1 + S^2)*(343 + 135*S^2))/(4*S^2) + (Pi^2*(-379 - 534*S^2 - 163*S^4))/(24*S^2) + (Pi^4*(212 + 424*S^2 + 805*S^4 - 1798*S^6 - 899*S^8))/(360*S^2*(1 + S^2)^2))*Zeta[3] + ((-45 - 28*S^2 - 278*S^4 - 4*S^6 - 45*S^8)*Zeta[3]^2)/(2*S^2*(1 + S^2)^2) + HPL[{4}, -S^2]*((1 - 158*S^2 - 175*S^4)/(4*S^2) + (Pi^2*(-105 - 16*S^2 - 534*S^4 + 72*S^6 - 105*S^8))/(12*S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 40*S^4 - 14*S^6 - 7*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((23 + 46*S^2 - 52*S^4 - 54*S^6 - 27*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((4*(2 + S^2 + 2*S^4))/S^2 + (Pi^2*(127 + 2828*S^2 - 5070*S^4 + 2164*S^6 + 127*S^8))/(24*S^2*(1 + S^2)^2) + ((-9 - 18*S^2 + 61*S^4 - 12*S^6 - 6*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((-177 - 354*S^2 + 1214*S^4 - 354*S^6 - 177*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-19 - 38*S^2 + 127*S^4 - 44*S^6 - 22*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*(-(((1 + S^2)*(9 + 61*S^2))/S^2) + (Pi^2*(-7 - 44*S^2 - 27*S^4))/(3*S^2) + (Pi^4*(19 + 38*S^2 - 433*S^4 + 112*S^6 + 56*S^8))/(180*S^2*(1 + S^2)^2) + ((17 + 34*S^2 - 33*S^4 - 44*S^6 - 22*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (2*(19 + 106*S^2 - 170*S^4 + 106*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(19 + 38*S^2 - 142*S^4 + 30*S^6 + 15*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1 - 2*S^4 - 8*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-25 + 238*S^2 + 87*S^4)/(2*S^2) + (Pi^2*(-7 - 1316*S^2 + 2582*S^4 - 972*S^6 - 7*S^8))/(3*S^2*(1 + S^2)^2) + (4*(19 + 38*S^2 - 129*S^4 + 48*S^6 + 24*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-31 + 50*S^2 + 9*S^4))/(6*S^2) + (73 + 274*S^2 + 73*S^4)/S^2 + (Pi^4*(-7131 - 14262*S^2 + 38357*S^4 - 7288*S^6 - 3644*S^8))/(360*S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(35 + 238*S^2 - 290*S^4 + 238*S^6 + 35*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-31 - 238*S^2 - 31*S^4)/S^2 + (Pi^2*(23 + 2674*S^2 - 5162*S^4 + 1930*S^6 + 23*S^8))/(3*S^2*(1 + S^2)^2) - (4*(41 + 82*S^2 - 266*S^4 + 82*S^6 + 41*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-463 - 622*S^2 - 151*S^4)/(4*S^2) + (Pi^2*(13 + 26*S^2 + 23*S^4 - 188*S^6 - 94*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((-161 - 450*S^2 - 161*S^4)/(2*S^2) + (Pi^2*(-39 - 250*S^2 - 99*S^4))/(12*S^2) + (Pi^4*(-1409 + 56820*S^2 - 107966*S^4 + 28924*S^6 - 1409*S^8))/(1440*S^2*(1 + S^2)^2) + ((-19 - 62*S^2 - 19*S^4)/(2*S^2) + (Pi^2*(-25 - 50*S^2 + 167*S^4 - 40*S^6 - 20*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-1 + 2*S^2 - 30*S^4 + 14*S^6 - S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((-19 - 38*S^2 + 42*S^4 + 42*S^6 + 21*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-71 - 134*S^2 - 71*S^4)/S^2 + (Pi^2*(-317 - 634*S^2 + 1901*S^4 - 468*S^6 - 234*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((35 + 70*S^2 - 244*S^4 + 50*S^6 + 25*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((109 + 218*S^2 - 772*S^4 + 158*S^6 + 79*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(177 + 354*S^2 - 1214*S^4 + 354*S^6 + 177*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(275 + 550*S^2 - 1888*S^4 + 550*S^6 + 275*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-32*(1 + S^2)^2)/S^2 + (Pi^2*(-27 - 54*S^2 + 277*S^4 - 128*S^6 - 64*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + ((-9 - 18*S^2 + 111*S^4 - 88*S^6 - 44*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) - (15*(-2 + 7*S^4)*Zeta[7])/S^2)) + Log[T]*((5*Pi^2*(-41 + 39*S^2))/6 + (Pi^4*(-7981 + 7347*S^2))/1440 + (Pi^6*(-19315 + 20097*S^2))/30240 + (7*Pi^8*(70669*S^2 + 10864*S^4 + 5432*S^6))/(194400*(1 + S^2)^2) + (S^2*(7 + 4*S^2 + 2*S^4)*HPL[{0}, S^2]^8)/(192*(1 + S^2)^2) - (4*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)^2) - (4*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^8)/(3*S^2*(1 + S^2)^2) + HPL[{0}, S^2]^7*((-4 + 19*S^2 + 11*S^4 + 4*S^6)/(48*(1 + S^2)^2) + ((-4 - 8*S^2 + 13*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2])/(48*S^2*(1 + S^2)^2)) + ((-6*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(33 + 66*S^2 + 187*S^4 - 122*S^6 - 61*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^3 + ((-14 - 28*S^2 + 187*S^4 - 28*S^6 - 14*S^8)*HPL[{2}, -S^2]^4)/(3*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^6*((-10*(1 + S^2)^2)/(3*S^2) + (Pi^2*(-51 - 102*S^2 + 305*S^4 - 72*S^6 - 36*S^8))/(9*S^2*(1 + S^2)^2) + (10*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^6*((3 + 11*S^2)/48 + (Pi^2*(74*S^2 + 34*S^4 + 17*S^6))/(144*(1 + S^2)^2) + ((1 - 20*S^2 + 30*S^4 + 8*S^6 + S^8)*HPL[{1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((-23 - 46*S^2 + 70*S^4 + 10*S^6 + 5*S^8)*HPL[{1}, -S^2]^2)/(48*S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 35*S^4 + 8*S^6 + 4*S^8)*HPL[{2}, -S^2])/(48*S^2*(1 + S^2)^2)) + ((9 - 80*S^2 - 57*S^4)/(2*S^2) + (Pi^2*(-3 - 6*S^2 + 98*S^4 - 86*S^6 - 43*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2]^2 - (2*(1 + 2*S^2 - 11*S^4 + 4*S^6 + 2*S^8)*HPL[{4}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((10 + 579*S^2 + 629*S^4)/(2*S^2) + (Pi^2*(-70 - 140*S^2 - 4*S^4 + 202*S^6 + 101*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{6}, -S^2] + (2*(160 - 86*S^2 + 957*S^4 + 1256*S^6 + 281*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-245 - 490*S^2 + 778*S^4 + 720*S^6 + 360*S^8)*HPL[{8}, -S^2])/(S^2*(1 + S^2)^2) + ((16*(2 + 9*S^2 + 2*S^4))/S^2 + (2*Pi^2*(46 + 92*S^2 - 1195*S^4 + 214*S^6 + 107*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - (8*(48 + 96*S^2 - 445*S^4 + 54*S^6 + 27*S^8)*HPL[{3, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((25 - 174*S^2 - 223*S^4)/(2*S^2) - (82*Pi^2*S^2*(-2 + 2*S^2 + S^4))/(3*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + (2*(5 + 25*S^2 - 76*S^4 + 148*S^6 + 12*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) + ((-16*(2 + 42*S^2 + 43*S^4))/S^2 + (Pi^2*(38 + 76*S^2 + 999*S^4 - 950*S^6 - 475*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + ((53 + 150*S^2 - 436*S^4 + 528*S^6 + 5*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - S^4 + 28*S^6 + 14*S^8)*HPL[{5, 3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(77 - 178*S^2 + 672*S^4 + 1079*S^6 + 256*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-9 - 18*S^2 - 34*S^4 + 40*S^6 + 20*S^8)*HPL[{6, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-177 - 354*S^2 + 437*S^4 + 612*S^6 + 306*S^8)*HPL[{7, 1}, -S^2])/(S^2*(1 + S^2)^2) - (160*(5 + 10*S^2 - 77*S^4 + 10*S^6 + 5*S^8)*HPL[{2, 1, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((62*(-1 + S^4))/S^2 + (Pi^2*(-45 + 37*S^4))/(3*S^2))*HPL[{3, 1, 2}, -S^2] + ((-82*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(219 + 438*S^2 + 1488*S^4 - 902*S^6 - 451*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] + (4*(-30 + 113*S^2 - 1548*S^4 + 2057*S^6 + 140*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-53 + 144*S^2 - 2349*S^4 + 3208*S^6 + 234*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(4 + 8*S^2 - 121*S^4 + 86*S^6 + 43*S^8)*HPL[{3, 3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((6*(1 + S^2)*(73 + 23*S^2))/S^2 - (2*Pi^2*(-381 - 762*S^2 - 1700*S^4 + 1050*S^6 + 525*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + (2*(-219 + 525*S^2 - 9148*S^4 + 12781*S^6 + 929*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(12 + 24*S^2 - 313*S^4 + 190*S^6 + 95*S^8)*HPL[{4, 1, 3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-639 + 1857*S^2 - 28564*S^4 + 39217*S^6 + 2933*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(1 + 2*S^2 - 221*S^4 + 228*S^6 + 114*S^8)*HPL[{4, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(36 + 72*S^2 - 1039*S^4 + 706*S^6 + 353*S^8)*HPL[{4, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-549 + 2106*S^2 - 29208*S^4 + 40574*S^6 + 3125*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(54 + 108*S^2 - 1231*S^4 + 790*S^6 + 395*S^8)*HPL[{5, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (14*(42 + 84*S^2 - 1213*S^4 + 850*S^6 + 425*S^8)*HPL[{5, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(270 + 540*S^2 - 10937*S^4 + 8042*S^6 + 4021*S^8)*HPL[{6, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(-85 - 887*S^2 + 887*S^4 + 85*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-64*(1 + S^2)*(7 + 2*S^2))/S^2 + (8*Pi^2*(-79 - 158*S^2 - 246*S^4 + 162*S^6 + 81*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (16*(-109 - 1487*S^2 + 700*S^4 + 383*S^6 + 45*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-109 - 1487*S^2 + 700*S^4 + 383*S^6 + 45*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(47 + 94*S^2 - 242*S^4 + 94*S^6 + 47*S^8)*HPL[{3, 1, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-473 - 5890*S^2 + 1400*S^4 + 3682*S^6 + 345*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(47 + 94*S^2 - 242*S^4 + 94*S^6 + 47*S^8)*HPL[{3, 2, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-535 - 1070*S^2 + 242*S^4 + 882*S^6 + 441*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2928*(-1 + S^2)*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (16*(-747 - 8994*S^2 + 2438*S^4 + 5236*S^6 + 491*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (12*(-1 - 2*S^2 - 114*S^4 + 110*S^6 + 55*S^8)*HPL[{4, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (36*(-81 - 162*S^2 + 38*S^4 + 126*S^6 + 63*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(-731 - 1462*S^2 + 114*S^4 + 1354*S^6 + 677*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-1086 - 2172*S^2 + 511*S^4 + 1754*S^6 + 877*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-320*(-1 + S^2)*(1 + S^2))/S^2 - (80*Pi^2*(-11 - 22*S^2 - 77*S^4 + 42*S^6 + 21*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (128*(8 + 138*S^2 - 175*S^4 + 138*S^6 + 8*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (384*(8 + 138*S^2 - 175*S^4 + 138*S^6 + 8*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (1952*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (5856*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (16*(341 + 5812*S^2 - 8738*S^4 + 7882*S^6 + 491*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (11376*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 - (19184*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 - (23088*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 - (48464*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 - (576*(-254 - 508*S^2 + 15*S^4 + 498*S^6 + 249*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (480*(-5 - 64*S^2 + 64*S^4 + 5*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (960*(-5 - 10*S^2 + 9*S^4 + 4*S^6 + 2*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6720*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (-3*(-1 + 11*S^2) + (Pi^2*(73*S^2 + 22*S^4 + 11*S^6))/(3*(1 + S^2)^2))*Zeta[3]^2 + HPL[{5}, -S^2]*((229 + 1126*S^2 + 865*S^4)/(4*S^2) + (Pi^2*(211 + 188*S^2 + 26*S^4 + 2304*S^6 + 287*S^8))/(12*S^2*(1 + S^2)^2) + (2*(-20 - 40*S^2 + 377*S^4 + 58*S^6 + 29*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(7 + 14*S^2 + 39*S^4)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1, 1}, -S^2]*((-648*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-153 - 2176*S^2 + 700*S^4 + 1072*S^6 + 89*S^8))/(3*S^2*(1 + S^2)^2) + (160*(-10 - 20*S^2 + 77*S^4)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^5*((83 + 107*S^2)/96 + (Pi^2*(-695 + 3126*S^2 + 1347*S^4 + 510*S^6))/(720*(1 + S^2)^2) + ((125 - 1920*S^2 + 3358*S^4 + 312*S^6 + 125*S^8)*HPL[{1}, -S^2]^2)/(240*S^2*(1 + S^2)^2) + ((-275 - 550*S^2 + 1033*S^4 + 8*S^6 + 4*S^8)*HPL[{1}, -S^2]^3)/(180*S^2*(1 + S^2)^2) + ((30 - 200*S^2 + 896*S^4 + 117*S^6 + 75*S^8)*HPL[{2}, -S^2])/(120*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]*((59 + 70*S^2 + 35*S^4)/(96*S^2) + (Pi^2*(-695 - 1390*S^2 + 2398*S^4 + 218*S^6 + 109*S^8))/(720*S^2*(1 + S^2)^2) + ((-230 - 460*S^2 + 853*S^4 - 2*S^6 - S^8)*HPL[{2}, -S^2])/(120*S^2*(1 + S^2)^2)) + (S^2*HPL[{3}, -S^2])/(2*(1 + S^2)^2) + ((115 + 230*S^2 - 156*S^4)*HPL[{2, 1}, -S^2])/(30*S^2*(1 + S^2)^2) + (3*(3*S^2 + 2*S^4 + S^6)*Zeta[3])/(4*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((8*(1 + S^2)^2)/(3*S^2) + (Pi^2*(-55 - 98*S^2 - 35*S^4))/(6*S^2) + (Pi^4*(-4460 - 8920*S^2 + 23717*S^4 - 4426*S^6 - 2213*S^8))/(540*S^2*(1 + S^2)^2) + ((20*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] - (4*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (2*(91 + 694*S^2 - 2094*S^4 + 1594*S^6 + 91*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(47 + 94*S^2 - 554*S^4 + 238*S^6 + 119*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) - (600*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (300*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (20*(2 + 37*S^2 - 176*S^4 + 127*S^6 + 2*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((-2*(85 - 6*S^2 + 85*S^4))/S^2 - (2*Pi^2*(152 + 2210*S^2 - 2163*S^4 + 1238*S^6 + 67*S^8))/(3*S^2*(1 + S^2)^2) - (16*(-54 - 108*S^2 + 345*S^4 + 14*S^6 + 7*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^5*((-14*(1 + S^2)^2)/(3*S^2) - (2*Pi^2*(19 + 341*S^2 - 622*S^4 + 251*S^6 + 19*S^8))/(9*S^2*(1 + S^2)^2) + (120*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (20*(5 + 10*S^2 - 65*S^4 + 28*S^6 + 14*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (60*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (4*(5 + 10*S^2 - 87*S^4 + 40*S^6 + 20*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1, 1}, -S^2]*((2*(-249 + 178*S^2 + 75*S^4))/S^2 + (Pi^2*(-849 - 12740*S^2 + 9336*S^4 - 2344*S^6 - 19*S^8))/(3*S^2*(1 + S^2)^2) - (8*(-321 - 642*S^2 + 2166*S^4 + 46*S^6 + 23*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*(((1 + S^2)*(47 + 849*S^2))/(4*S^2) + (Pi^2*(-13 + 378*S^2 + 351*S^4))/(12*S^2) + (Pi^4*(-219 - 438*S^2 - 2078*S^4 + 1770*S^6 + 885*S^8))/(180*S^2*(1 + S^2)^2) + (2*(-98 - 547*S^2 + 538*S^4 + 69*S^6 + 42*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-3 - 6*S^2 - 161*S^4 + 156*S^6 + 78*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(-1 - 2*S^2 - 106*S^4 + 110*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((27 + 62*S^2 - 34*S^4 + 210*S^6 + 23*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4, 1}, -S^2]*((-2*(-52 + 157*S^2 + 473*S^4))/S^2 + (Pi^2*(-7 - 549*S^2 + 5002*S^4 - 7581*S^6 - 637*S^8))/(3*S^2*(1 + S^2)^2) - (8*(-1 - 2*S^2 - 121*S^4 + 52*S^6 + 26*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 2}, -S^2]*((71 + 6*S^2 - 241*S^4)/S^2 + (Pi^2*(93 - 428*S^2 + 5682*S^4 - 9268*S^6 - 783*S^8))/(12*S^2*(1 + S^2)^2) - (2*(-1 - 2*S^2 - 124*S^4 + 58*S^6 + 29*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((63*(1 + S^2)^2)/(4*S^2) + (Pi^2*(-3 - 122*S^2 - 39*S^4))/(12*S^2) + (Pi^4*(-220 - 440*S^2 + 12053*S^4 - 2060*S^6 - 1030*S^8))/(360*S^2*(1 + S^2)^2) + ((-7 + 282*S^2 - 1760*S^4 + 2226*S^6 + 163*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + (3*(1 + 2*S^2 - 86*S^4 + 50*S^6 + 25*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((85 + 887*S^2 - 887*S^4 - 85*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-161 - 322*S^2 + 258*S^4 + 166*S^6 + 83*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (244*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-24 - 2*S^2 - 637*S^4 + 970*S^6 + 61*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((225*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(35 - 72*S^2 - 67*S^4))/(3*S^2) + (Pi^4*(660 + 1320*S^2 + 12377*S^4 - 3646*S^6 - 1823*S^8))/(90*S^2*(1 + S^2)^2) + (8*(3 + 106*S^2 - 700*S^4 + 998*S^6 + 61*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(-1 + 449*S^2))/(2*S^2) - (10*Pi^2*(6 + 5*S^2 + S^4))/(3*S^2) + (Pi^4*(-993 - 1986*S^2 - 10096*S^4 + 3022*S^6 + 1511*S^8))/(180*S^2*(1 + S^2)^2) + (16*(71 + 142*S^2 - 770*S^4 + 58*S^6 + 29*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(13 + 236*S^2 - 1476*S^4 + 2008*S^6 + 123*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^4*((-95 + 161*S^2)/32 + (Pi^2*(65 + 413*S^2))/288 + (Pi^4*(11971*S^2 + 4172*S^4 + 2086*S^6))/(4320*(1 + S^2)^2) + ((-19 - 2176*S^2 + 3078*S^4 - 64*S^6 - 19*S^8)*HPL[{1}, -S^2]^3)/(72*S^2*(1 + S^2)^2) + ((-137 - 274*S^2 + 518*S^4 - 10*S^6 - 5*S^8)*HPL[{1}, -S^2]^4)/(36*S^2*(1 + S^2)^2) + ((-18 + 77*S^2 + 67*S^4)/(48*S^2) + (Pi^2*(-9 - 18*S^2 + 528*S^4 + 50*S^6 + 25*S^8))/(72*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((6 + 12*S^2 + 263*S^4 - 28*S^6 - 14*S^8)*HPL[{2}, -S^2]^2)/(24*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-59 - 38*S^2 + 37*S^4)/(48*S^2) + (Pi^2*(-619 - 1238*S^2 + 2086*S^4 + 130*S^6 + 65*S^8))/(144*S^2*(1 + S^2)^2) + ((-249 - 498*S^2 + 847*S^4 + 16*S^6 + 8*S^8)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)^2)) + ((1 - 18*S^2 + 28*S^6 + S^8)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)^2) + (3*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/(4*S^2) + ((19 + 1534*S^2 - 736*S^4 - 76*S^6 - S^8)*HPL[{2, 1}, -S^2])/(24*S^2*(1 + S^2)^2) + ((3 + 6*S^2 - 514*S^4 + 26*S^6 + 13*S^8)*HPL[{3, 1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((-3 - 6*S^2 + 531*S^4 - 20*S^6 - 10*S^8)*HPL[{2, 1, 1}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-38 + 149*S^2 + 204*S^4 + 45*S^6)*Zeta[3])/(12*(1 + S^2)^2) + HPL[{1}, -S^2]*((-189 - 34*S^2 + 187*S^4)/(96*S^2) + (Pi^2*(101 - 4576*S^2 + 6678*S^4 + 896*S^6 + 101*S^8))/(288*S^2*(1 + S^2)^2) + ((17 - 1996*S^2 + 2382*S^4 + 60*S^6 + 17*S^8)*HPL[{2}, -S^2])/(48*S^2*(1 + S^2)^2) + ((-5 - 10*S^2 - 3*S^4 + 12*S^6 + 6*S^8)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)^2) + ((249 + 498*S^2 - 847*S^4 - 16*S^6 - 8*S^8)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)^2) + ((-19 - 38*S^2 + 14*S^4 + 38*S^6 + 19*S^8)*Zeta[3])/(6*S^2*(1 + S^2)^2))) + (-167 + 225*S^2 + (Pi^2*(-18 - 518*S^2 + 1459*S^4 + 63*S^6))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{0}, S^2]^3*((115 + 179*S^2)/6 + (Pi^2*(435 + 731*S^2))/144 + (Pi^4*(-8022 + 35673*S^2 + 8384*S^4 + 4161*S^6))/(2160*(1 + S^2)^2) + ((-7 - 568*S^2 + 948*S^4 - 178*S^6 - 7*S^8)*HPL[{1}, -S^2]^4)/(9*S^2*(1 + S^2)^2) + ((-56 - 112*S^2 + 263*S^4 - 34*S^6 - 17*S^8)*HPL[{1}, -S^2]^5)/(9*S^2*(1 + S^2)^2) + ((-5 - 500*S^2 + 1796*S^4 - 616*S^6 - 59*S^8)*HPL[{2}, -S^2]^2)/(24*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-19 - 30*S^2 - 3*S^4)/(18*S^2) + (Pi^2*(-555 - 1110*S^2 + 2348*S^4 - 162*S^6 - 81*S^8))/(54*S^2*(1 + S^2)^2) - (2*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2)) + ((15 + 50*S^2 + 67*S^4)/(12*S^2) + (Pi^2*(-5 - 10*S^2 + 46*S^4 + 6*S^6 + 3*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((37 - 8*S^2 + 190*S^4 - 20*S^6 + 65*S^8)*HPL[{4}, -S^2])/(12*S^2*(1 + S^2)^2) + ((5 + 10*S^2 + 30*S^4 - 6*S^6 - 3*S^8)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)^2) + ((9 - 38*S^2 - 23*S^4)/(3*S^2) + (Pi^2*(490 + 980*S^2 - 813*S^4 - 22*S^6 - 11*S^8))/(18*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-25 + 220*S^2 - 973*S^4 + 286*S^6 + 8*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (S^2*(-23 + 34*S^2 + 17*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) - (10*(-1 - 2*S^2 - S^4 + 8*S^6 + 4*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((49 - 448*S^2 + 1978*S^4 - 536*S^6 - 11*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-246 - 492*S^2 + 471*S^4 + 10*S^6 + 5*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-748 - 1496*S^2 + 1445*S^4 + 42*S^6 + 21*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(-260 - 520*S^2 + 501*S^4 + 22*S^6 + 11*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + ((31 + 35*S^2)/3 + (Pi^2*(135*S^2 + 118*S^4 + 59*S^6))/(18*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((75 + 192*S^2 + 197*S^4)/(24*S^2) + (Pi^2*(109 - 848*S^2 + 3770*S^4 - 302*S^6 + 139*S^8))/(72*S^2*(1 + S^2)^2) + (4*S^2*(-3 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + ((246 + 492*S^2 - 471*S^4 - 10*S^6 - 5*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (S^2*(1 + 22*S^2 + 11*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((29 + 42*S^2 + 61*S^4)/(12*S^2) + (Pi^2*(97 - 4192*S^2 + 7150*S^4 - 400*S^6 + 97*S^8))/(72*S^2*(1 + S^2)^2) + ((17 - 1034*S^2 + 1642*S^4 - 290*S^6 + 17*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 + 5*S^4)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-6 - 12*S^2 - 17*S^4 + 34*S^6 + 17*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]*((Pi^2*(257 + 290*S^2 + 169*S^4))/(144*S^2) + (241 + 274*S^2 + 289*S^4)/(24*S^2) + (Pi^4*(-4011 - 8022*S^2 + 15739*S^4 + 28*S^6 + 14*S^8))/(1080*S^2*(1 + S^2)^2) + ((-1 + 62*S^2 + 39*S^4)/(6*S^2) + (Pi^2*(-488 - 976*S^2 + 2023*S^4 - 146*S^6 - 73*S^8))/(36*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-121 - 242*S^2 + 553*S^4 - 76*S^6 - 38*S^8)*HPL[{2}, -S^2]^2)/(6*S^2*(1 + S^2)^2) + ((43 + 12*S^2 + 130*S^4 + 60*S^6 + 43*S^8)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)^2) + ((-6 - 12*S^2 + 63*S^4 - 22*S^6 - 11*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + ((-17 + 1034*S^2 - 1642*S^4 + 290*S^6 - 17*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(127 + 254*S^2 - 583*S^4 + 76*S^6 + 38*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (4*(43 + 86*S^2 - 195*S^4 + 24*S^6 + 12*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((31 + 40*S^2 + 54*S^4 + 132*S^6 + 31*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + (26*(4*S^2 + 2*S^4 + S^6)*Zeta[5])/(3*(1 + S^2)^2)) + Zeta[3]*((Pi^2*(-9 + 71*S^2))/2 + 2*(-111 + 121*S^2) + (Pi^4*(231 - 3495*S^2 + 10604*S^4 + 918*S^6))/(180*(1 + S^2)^2) + (12*(19*S^2 + 18*S^4 + 9*S^6)*Zeta[5])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-242*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(319 - 3*S^2 - 234*S^4))/(6*S^2) + (Pi^4*(3151 + 52000*S^2 - 20664*S^4 - 16450*S^6 - 1097*S^8))/(360*S^2*(1 + S^2)^2) - (4*(29 + 950*S^2 - 1400*S^4 + 1258*S^6 + 99*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(507 + 1014*S^2 - 3250*S^4 + 38*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (24*(-137 - 274*S^2 + 824*S^4 + 26*S^6 + 13*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (64*(8 + 138*S^2 - 175*S^4 + 138*S^6 + 8*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (976*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (16*(-51 - 102*S^2 - 770*S^4 + 302*S^6 + 151*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (320*(5 + 10*S^2 - 77*S^4 + 10*S^6 + 5*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(-45 - 72*S^2 + 13*S^4))/S^2 - (2*Pi^2*(108 + 216*S^2 - 847*S^4 + 2*S^6 + S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] - (8*(22 + 44*S^2 - 381*S^4 + 2*S^6 + S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((555*(1 + S^2)^2)/(4*S^2) + (Pi^4*(-3979 - 6294*S^2 - 1243*S^4))/(720*S^2) + (Pi^2*(-189 - 210*S^2 + 107*S^4))/(12*S^2) + (Pi^6*(-201706 - 403412*S^2 + 958255*S^4 - 119438*S^6 - 59719*S^8))/(45360*S^2*(1 + S^2)^2) + ((-71 - 134*S^2 - 71*S^4)/(2*S^2) + (Pi^2*(-350 - 700*S^2 + 2089*S^4 - 514*S^6 - 257*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (31*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^3)/S^2 + ((-37 - 74*S^2 + 238*S^4 - 74*S^6 - 37*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((16*(1 + S^2)*(7 + 10*S^2))/S^2 + (Pi^2*(61 + 122*S^2 - 1132*S^4 + 558*S^6 + 279*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(77 + 102*S^2 - 310*S^4 + 654*S^6 + 77*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-194 - 388*S^2 - 127*S^4 + 566*S^6 + 283*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-16*(1 + S^2)*(1 + 16*S^2))/S^2 - (4*Pi^2*(-116 - 232*S^2 + 193*S^4 + 122*S^6 + 61*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(237 + 1934*S^2 - 5966*S^4 + 4454*S^6 + 237*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (9*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) - (8*(50 + 100*S^2 - 551*S^4 + 238*S^6 + 119*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((240*(-1 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(37 + 1012*S^2 - 1620*S^4 + 562*S^6 + 37*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (744*(-1 + S^2)*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + (16*(-116 - 232*S^2 - 277*S^4 + 398*S^6 + 199*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (7200*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - (16*(-71 - 142*S^2 - 277*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (3600*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-223 - 238*S^2 + 161*S^4)/(2*S^2) + (Pi^2*(53 + 812*S^2 - 3858*S^4 + 2876*S^6 + 53*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] - (4*(5 + 10*S^2 - 32*S^4 + 10*S^6 + 5*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{3}, -S^2]*((19 + 182*S^2 + 211*S^4)/S^2 + (Pi^2*(209 + 1376*S^2 - 4378*S^4 + 3464*S^6 + 209*S^8))/(6*S^2*(1 + S^2)^2) - (4*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(11 + 22*S^2 - 87*S^4 + 28*S^6 + 14*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((148*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-287 - 134*S^2 + 145*S^4))/(12*S^2) + (Pi^4*(-7200 - 14400*S^2 + 21017*S^4 + 2274*S^6 + 1137*S^8))/(360*S^2*(1 + S^2)^2) + (2*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((113 + 226*S^2 - 734*S^4 + 226*S^6 + 113*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(55 + 522*S^2 - 1778*S^4 + 1290*S^6 + 55*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-192*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(55 + 2322*S^2 - 1778*S^4 - 510*S^6 + 55*S^8))/(3*S^2*(1 + S^2)^2) - (16*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) - (3*(23 - 52*S^2 + 1274*S^4 - 948*S^6 + 23*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((Pi^2*(-5 + 280*S^2 + 429*S^4))/(12*S^2) + (-11 + 434*S^2 + 957*S^4)/(4*S^2) + (Pi^4*(457 + 1442*S^2 - 12588*S^4 + 19898*S^6 + 1487*S^8))/(360*S^2*(1 + S^2)^2) + ((-5 - 32*S^2 + 118*S^4 - 290*S^6 - 35*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (4*S^2*(12 + 10*S^2 + 5*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((8*(-21 - 18*S^2 + 13*S^4))/S^2 + (Pi^2*(-265 - 530*S^2 + 1642*S^4 + 142*S^6 + 71*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-63 - 60*S^2 - 1476*S^4 + 2180*S^6 + 171*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 250*S^4 + 166*S^6 + 83*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-3 - 6*S^2 - 14*S^4 + 12*S^6 + 6*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-28 - 11*S^2 - 700*S^4 + 1115*S^6 + 92*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(273 + 546*S^2 - 1754*S^4 + 58*S^6 + 29*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(821 + 1642*S^2 - 5030*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(-66 - 132*S^2 + 385*S^4 + 32*S^6 + 16*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((3*(-3 + 14*S^2 + S^4))/S^2 + (Pi^2*(-5 - 10*S^2 - 112*S^4 + 42*S^6 + 21*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + (2*(-29 - 58*S^2 - 100*S^4 + 50*S^6 + 25*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*((195*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(1 + S^2)*(-173 + 236*S^2))/(12*S^2) + (Pi^4*(-108 - 517*S^2 + 275*S^4))/(720*S^2) + (Pi^6*(652 + 1304*S^2 + 144378*S^4 - 13742*S^6 - 6871*S^8))/(22680*S^2*(1 + S^2)^2) + ((1 + 2*S^2 + 129*S^4 - 80*S^6 - 40*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-35 + 242*S^2 + 221*S^4)/(2*S^2) + (2*Pi^2*(2 + 4*S^2 - 68*S^4 + 86*S^6 + 43*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-39 + 32*S^2 - 298*S^4 + 1324*S^6 + 221*S^8)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(20 + 40*S^2 + 61*S^4 + 92*S^6 + 46*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) + (244*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-16*(-6 - 9*S^2 + 2*S^4))/S^2 + (Pi^2*(133 + 266*S^2 - 2390*S^4 + 346*S^6 + 173*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((43 - 348*S^2 + 3222*S^4 - 4236*S^6 - 297*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-119 + 299*S^2 - 4742*S^4 + 6747*S^6 + 531*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (6*(1 + 2*S^2 - 86*S^4 + 50*S^6 + 25*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(10 + 20*S^2 - 913*S^4 + 778*S^6 + 389*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-32*(2 + 9*S^2 + 2*S^4))/S^2 - (4*Pi^2*(46 + 92*S^2 - 1195*S^4 + 214*S^6 + 107*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(-85 - 887*S^2 + 887*S^4 + 85*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (4*(-199 - 2894*S^2 + 1400*S^4 + 686*S^6 + 71*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (6*(13 + 26*S^2 - 86*S^4 + 26*S^6 + 13*S^8)*HPL[{3, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(185 + 370*S^2 - 2734*S^4 + 370*S^6 + 185*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (12*(113 + 226*S^2 - 1390*S^4 + 114*S^6 + 57*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (64*(8 + 138*S^2 - 175*S^4 + 138*S^6 + 8*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-661 - 1322*S^2 - 770*S^4 + 1522*S^6 + 761*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (320*(5 + 10*S^2 - 77*S^4 + 10*S^6 + 5*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-5 - 3*S^2 + 90*S^4)/S^2 + (Pi^2*(11 + 236*S^2 - 1520*S^4 + 2226*S^6 + 147*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] - 6*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((85 - 6*S^2 + 85*S^4)/S^2 + (Pi^2*(152 + 2210*S^2 - 2163*S^4 + 1238*S^6 + 67*S^8))/(3*S^2*(1 + S^2)^2) + (8*(-54 - 108*S^2 + 345*S^4 + 14*S^6 + 7*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-54 - 3*S^2 + 139*S^4)/S^2 + (Pi^2*(-45 + 18*S^2 - 1432*S^4 + 2392*S^6 + 215*S^8))/(6*S^2*(1 + S^2)^2) - (2*(273 + 546*S^2 - 1754*S^4 + 58*S^6 + 29*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 58*S^4 + 38*S^6 + 19*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + (2*(30 + 102*S^2 - 549*S^4 + 1045*S^6 + 50*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((81*(1 + S^2)^2)/(2*S^2) + (Pi^2*(-503 - 798*S^2 - 119*S^4))/(36*S^2) + (Pi^4*(-3743 - 77436*S^2 + 131686*S^4 - 41484*S^6 - 3743*S^8))/(1080*S^2*(1 + S^2)^2) - (2*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + ((2*(79 + 270*S^2 + 199*S^4))/(3*S^2) + (2*Pi^2*(118 + 236*S^2 - 1703*S^4 + 758*S^6 + 379*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + (16*(18 + 83*S^2 - 158*S^4 + 155*S^6 + 18*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (4*(-5 - 10*S^2 - 116*S^4 + 82*S^6 + 41*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-80*(-1 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(9*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (32*(9 - 53*S^2 - 79*S^4 + 172*S^6 + 9*S^8)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (8*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(178 + 356*S^2 - 2299*S^4 + 986*S^6 + 493*S^8)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2400*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (16*(463 + 926*S^2 - 2419*S^4 + 476*S^6 + 238*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)^2) - (1200*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((4*(-5 + 2*S^2 + 15*S^4))/S^2 + (2*Pi^2*(79 + 158*S^2 - 1444*S^4 + 674*S^6 + 337*S^8))/(9*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((64*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-55 - 2322*S^2 + 1778*S^4 + 510*S^6 - 55*S^8))/(9*S^2*(1 + S^2)^2) + (4*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (16*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + (8*(11 + 22*S^2 - 680*S^4 + 358*S^6 + 179*S^8)*Zeta[5])/(3*S^2*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((5*(-41 + 39*S^2))/2 + (Pi^2*(-163 + 177*S^2))/12 + (Pi^4*(-283 + 801*S^2))/360 + (Pi^6*(15415*S^2 + 3526*S^4 + 1763*S^6))/(2592*(1 + S^2)^2) + ((-17 - 304*S^2 + 446*S^4 - 124*S^6 - 17*S^8)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)^2) + ((-23 - 46*S^2 + 109*S^4 - 16*S^6 - 8*S^8)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)^2) + ((13 - 50*S^2 - 23*S^4)/(4*S^2) + (Pi^2*(10 + 20*S^2 + 688*S^4 - 142*S^6 - 71*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + ((5 + 10*S^2 + 374*S^4 - 122*S^6 - 61*S^8)*HPL[{2}, -S^2]^3)/(6*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((-15 - 24*S^2 - 5*S^4)/S^2 + (Pi^2*(-619 - 1238*S^2 + 2671*S^4 - 260*S^6 - 130*S^8))/(36*S^2*(1 + S^2)^2) + ((-325 - 650*S^2 + 1348*S^4 - 134*S^6 - 67*S^8)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)^2)) + ((-2 - 4*S^2 - 9*S^4 - 2*S^6 - S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-8 + 45*S^2 + 33*S^4)/(2*S^2) + (Pi^2*(-27 - 54*S^2 - 4*S^4 + 78*S^6 + 39*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + ((49 - 28*S^2 + 194*S^4 + 464*S^6 + 49*S^8)*HPL[{5}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-50 - 100*S^2 + 39*S^4 + 102*S^6 + 51*S^8)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)^2) + (2*(-4 - 8*S^2 - 425*S^4 + 114*S^6 + 57*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((2*(-2 + 11*S^2 + 3*S^4))/S^2 + (Pi^2*(-5 - 10*S^2 - 1276*S^4 + 230*S^6 + 115*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-55 - 196*S^2 + 82*S^4 - 668*S^6 - 123*S^8)*HPL[{3, 2}, -S^2])/(4*S^2*(1 + S^2)^2) + ((-43 - 57*S^2 + 126*S^4 - 557*S^6 - 89*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-3 - 6*S^2 - 14*S^4 + 2*S^6 + S^8)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)^2) + ((14 + 28*S^2 - 23*S^4 - 66*S^6 - 33*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-5 - 72*S^2 - 27*S^4)/S^2 + (Pi^2*(2 + 4*S^2 + 1301*S^4 - 230*S^6 - 115*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(88 + 1106*S^2 - 763*S^4 + 134*S^6 + 3*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-507 - 6700*S^2 + 4412*S^4 - 444*S^6 + 23*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-3 - 5*S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((17 + 34*S^2 + 1488*S^4 - 498*S^6 - 249*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-21 - 42*S^2 - 2240*S^4 + 690*S^6 + 345*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-78 - 1141*S^2 + 700*S^4 + 37*S^6 + 14*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-4 - 8*S^2 - 381*S^4 + 102*S^6 + 51*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (40*(-1 - 2*S^2 - 154*S^4 + 42*S^6 + 21*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((3*(1 + 17*S^2))/2 + (Pi^2*(-34 + 101*S^2 + 347*S^4 + 60*S^6))/(6*(1 + S^2)^2))*Zeta[3] + ((31*S^2 + 22*S^4 + 11*S^6)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((157 - 3*S^2 - 72*S^4)/(2*S^2) + (Pi^2*(175 + 3816*S^2 - 2136*S^4 - 150*S^6 - 29*S^8))/(12*S^2*(1 + S^2)^2) - (2*(8 + 16*S^2 - 77*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-11 + 120*S^2 + 99*S^4)/(4*S^2) + (Pi^2*(27 - 172*S^2 - 166*S^4 + 528*S^6 + 47*S^8))/(24*S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 102*S^4 + 14*S^6 + 7*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 8*S^4 + 2*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((Pi^2*(-239 - 326*S^2 - 23*S^4))/(24*S^2) + (-205 - 242*S^2 + 91*S^4)/(4*S^2) + (Pi^4*(-8046 - 16092*S^2 + 31091*S^4 - 806*S^6 - 403*S^8))/(720*S^2*(1 + S^2)^2) + ((-167 - 134*S^2 + 25*S^4)/(4*S^2) + (Pi^2*(-574 - 1148*S^2 + 2195*S^4 - 118*S^6 - 59*S^8))/(12*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] + ((-154 - 308*S^2 + 741*S^4 - 122*S^6 - 61*S^8)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((27 - 12*S^2 - 190*S^4 + 276*S^6 + 27*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-33 - 66*S^2 - 24*S^4 + 82*S^6 + 41*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((55 + 1422*S^2 - 1778*S^4 + 390*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(161 + 322*S^2 - 663*S^4 + 64*S^6 + 32*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((13 + 72*S^2 - 338*S^4 + 336*S^6 + 13*S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]*(((1 + S^2)*(-121 + 247*S^2))/(8*S^2) + (Pi^2*(-23 + 5*S^2 + 40*S^4))/(24*S^2) + (Pi^4*(-156 - 312*S^2 + 14899*S^4 - 598*S^6 - 299*S^8))/(720*S^2*(1 + S^2)^2) + ((11 + 40*S^2 - 32*S^4 + 162*S^6 + 31*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) + ((11 + 22*S^2 + 46*S^4 + 14*S^6 + 7*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((88 + 1106*S^2 - 763*S^4 + 134*S^6 + 3*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-9 - 18*S^2 - 850*S^4 + 230*S^6 + 115*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-4 - 8*S^2 - 425*S^4 + 114*S^6 + 57*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((5 + 24*S^2 - 120*S^4 + 230*S^6 + 25*S^8)*Zeta[3])/(2*S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-363 - 518*S^2 + 21*S^4)/(12*S^2) + (Pi^2*(-189 - 5216*S^2 + 7538*S^4 - 1304*S^6 - 189*S^8))/(36*S^2*(1 + S^2)^2) + ((-55 - 1422*S^2 + 1778*S^4 - 390*S^6 - 55*S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(-7 - 14*S^2 - 78*S^4 + 58*S^6 + 29*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(4 + 8*S^2 - 139*S^4 + 74*S^6 + 37*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + ((-40 + 64*S^2 + 285*S^4 + 25*S^6)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((Pi^2*(-69 - 69*S^2 + 26*S^4))/(6*S^2) + (-543 - 414*S^2 + 385*S^4)/(8*S^2) + (Pi^4*(-205 - 15960*S^2 + 23316*S^4 - 674*S^6 - 205*S^8))/(360*S^2*(1 + S^2)^2) + ((-37 - 692*S^2 + 974*S^4 - 320*S^6 - 37*S^8)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)^2) + ((-11 + 58*S^2 + 53*S^4)/(2*S^2) + (Pi^2*(-22 - 44*S^2 - 87*S^4 + 94*S^6 + 47*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((17 - 104*S^2 - 10*S^4 + 192*S^6 + 17*S^8)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)^2) + ((-23 - 46*S^2 - 24*S^4 + 70*S^6 + 35*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((167 + 134*S^2 - 25*S^4)/(2*S^2) + (Pi^2*(574 + 1148*S^2 - 2195*S^4 + 118*S^6 + 59*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((47 + 1396*S^2 - 1758*S^4 + 364*S^6 + 47*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(5 + 10*S^2 - 75*S^4 + 32*S^6 + 16*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) + ((3 + 6*S^2 + 474*S^4 - 274*S^6 - 137*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(55 + 1422*S^2 - 1778*S^4 + 390*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(154 + 308*S^2 - 741*S^4 + 122*S^6 + 61*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(469 + 938*S^2 - 2145*S^4 + 308*S^6 + 154*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(325 + 650*S^2 - 1348*S^4 + 134*S^6 + 67*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((1 + 10*S^2 + 13*S^4)/S^2 + (Pi^2*(-34 - 68*S^2 - 111*S^4 + 150*S^6 + 75*S^8))/(6*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-45 - 4*S^2 + 29*S^4)/S^2 + (Pi^2*(-93 - 4840*S^2 + 5938*S^4 - 720*S^6 - 93*S^8))/(24*S^2*(1 + S^2)^2) + ((5 + 10*S^2 - 75*S^4 + 32*S^6 + 16*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (2*(154 + 308*S^2 - 741*S^4 + 122*S^6 + 61*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((8 + 16*S^2 - 133*S^4 + 62*S^6 + 31*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-40 - 80*S^2 - 117*S^4 + 158*S^6 + 79*S^8)*Zeta[5])/(S^2*(1 + S^2)^2))) + HPL[{0}, S^2]*((1175*(1 + S^2))/4 + (Pi^2*(703 + 959*S^2))/24 + (Pi^4*(3013 + 5805*S^2))/1440 + (Pi^6*(-187513 + 891537*S^2 - 61936*S^4 + 61474*S^6))/(45360*(1 + S^2)^2) - (14*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)^2) - (16*(1 + 2*S^2 - 7*S^4 + 2*S^6 + S^8)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)^2) + ((49 - 200*S^2 + 1608*S^4 - 1400*S^6 - 121*S^8)*HPL[{2}, -S^2]^3)/(6*S^2*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-10*(1 + S^2)^2)/S^2 + (Pi^2*(-140 - 280*S^2 + 851*S^4 - 202*S^6 - 101*S^8))/(9*S^2*(1 + S^2)^2) - (2*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2}, -S^2])/(S^2*(1 + S^2)^2)) - ((-2 + S^2)*(3 + 10*S^2 + 3*S^4 + 4*S^6)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-49 + 190*S^2 + 279*S^4)/(4*S^2) + (Pi^2*(7 + 14*S^2 + 165*S^4 - 20*S^6 - 10*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((50 + S^2 + 85*S^4 - 82*S^6 + 76*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) + ((25 + 50*S^2 + 29*S^4 - 48*S^6 - 24*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-3 + 398*S^2 - 1778*S^4 + 1414*S^6 + 113*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((13 - 150*S^2 - 91*S^4)/(2*S^2) + (Pi^2*(-3 - 6*S^2 + 308*S^4 - 226*S^6 - 113*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((15 - 294*S^2 - 181*S^4)/S^2 - (4*Pi^2*(-6 - 12*S^2 - 80*S^4 + 70*S^6 + 35*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((11 - 17*S^2 - 17*S^4 - S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) - (4*(2 + 4*S^2 + 15*S^4 + 4*S^6 + 2*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) - (2*(17 - 6*S^2 + 192*S^4 - 2*S^6 + 55*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-25 - 50*S^2 - 169*S^4 - 48*S^6 - 24*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(13 + 26*S^2 + 134*S^4 + 16*S^6 + 8*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(-153 - 134*S^2 + 11*S^4))/S^2 + (2*Pi^2*(-638 - 1276*S^2 + 1819*S^4 + 10*S^6 + 5*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((16*(-57 - 36*S^2 + 13*S^4))/S^2 + (2*Pi^2*(-1939 - 3878*S^2 + 5439*S^4 + 92*S^6 + 46*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (2*(5 + 8*S^2 + 5*S^4)*HPL[{3, 1, 2}, -S^2])/S^2 - (2*(-93 + 418*S^2 - 3190*S^4 + 2818*S^6 + 247*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-23 - 46*S^2 - 488*S^4 + 286*S^6 + 143*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (48*(-1 - 2*S^2 - 32*S^4 + 18*S^6 + 9*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-321 + 1234*S^2 - 9978*S^4 + 8418*S^6 + 655*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-11 - 22*S^2 - 380*S^4 + 222*S^6 + 111*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-35 - 70*S^2 - 1178*S^4 + 642*S^6 + 321*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-75 - 150*S^2 - 2289*S^4 + 1252*S^6 + 626*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-8*(-65 - 6*S^2 + 35*S^4))/S^2 - (4*Pi^2*(-665 - 1330*S^2 + 1806*S^4 + 82*S^6 + 41*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (16*(-196 - 392*S^2 + 607*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-59 + 214*S^2 - 1782*S^4 + 1396*S^6 + 91*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-2355 - 4710*S^2 + 7546*S^4 + 298*S^6 + 149*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-2355 - 4710*S^2 + 7546*S^4 + 298*S^6 + 149*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-4707 - 9414*S^2 + 14830*S^4 + 754*S^6 + 377*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-3521 - 7042*S^2 + 11081*S^4 + 584*S^6 + 292*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (80*(-11 + 47*S^2 - 352*S^4 + 281*S^6 + 19*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (64*(-98 - 196*S^2 + 337*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (192*(-98 - 196*S^2 + 337*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (80*(389 + 778*S^2 - 1358*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (480*(-27 - 54*S^2 + 87*S^4 + 4*S^6 + 2*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (112*(1 + S^2) + (Pi^2*(67 + 71*S^2))/3 + (373*Pi^4*(2*S^4 + S^6))/(90*(1 + S^2)^2))*Zeta[3] + (2*(-7 + 55*S^2 - 12*S^4 + 10*S^6)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1, 1}, -S^2]*((163 + 238*S^2 - 101*S^4)/S^2 + (Pi^2*(159 - 918*S^2 + 5498*S^4 - 3346*S^6 - 201*S^8))/(3*S^2*(1 + S^2)^2) + (48*S^2*(-22 + 14*S^2 + 7*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-75 - 548*S^2 - 217*S^4)/(2*S^2) - (2*Pi^2*(-37 + 16*S^2 + 29*S^4))/(3*S^2) + (Pi^4*(7313 + 14626*S^2 - 17525*S^4 - 544*S^6 - 272*S^8))/(180*S^2*(1 + S^2)^2) + (4*(-391 - 782*S^2 + 1350*S^4 + 2*S^6 + S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(-98 - 196*S^2 + 337*S^4)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-69 - 390*S^2 + 292*S^4 - 82*S^6 + S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{4}, -S^2]*((1 + 182*S^2 + 197*S^4)/(4*S^2) + (Pi^2*(32 - 21*S^2 + 260*S^4 - 19*S^6 + 68*S^8))/(6*S^2*(1 + S^2)^2) + (2*(-1 - 2*S^2 - 24*S^4 + 2*S^6 + S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-3 - 6*S^2 + 26*S^4 + 10*S^6 + 5*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*(((1 + S^2)*(13 + 142*S^2))/(2*S^2) + (Pi^2*(9 + 82*S^2 + 69*S^4))/(6*S^2) + (Pi^4*(-229 - 458*S^2 + 998*S^4 + 422*S^6 + 211*S^8))/(360*S^2*(1 + S^2)^2) + (4*(1 + 2*S^2 + 8*S^4)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (2*(-47 - 200*S^2 + 168*S^4 - 16*S^6 + 7*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-5 - 10*S^2 - 148*S^4 + 66*S^6 + 33*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (4*(-1 - 2*S^2 - 136*S^4 + 74*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 + 18*S^4 + 30*S^6 + 7*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((16*(1 + S^2)^2)/(3*S^2) + (Pi^2*(-169 - 330*S^2 - 153*S^4))/(18*S^2) + (Pi^4*(-8061 - 16122*S^2 + 44045*S^4 - 8244*S^6 - 4122*S^8))/(540*S^2*(1 + S^2)^2) + ((-4*(5 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(-211 - 422*S^2 + 1260*S^4 - 298*S^6 - 149*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)^2) + (4*(35 + 92*S^2 - 18*S^4 + 80*S^6 + 35*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) - (2*(17 + 34*S^2 - 194*S^4 + 58*S^6 + 29*S^8)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)^2) + (160*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)^2) + (8*(62 + 124*S^2 - 435*S^4 + 126*S^6 + 63*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (40*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(9 + 58*S^2 - 79*S^4 + 61*S^6 + 9*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-107 - 238*S^2 + 45*S^4)/(2*S^2) + (Pi^2*(-84 + 434*S^2 - 2755*S^4 + 1682*S^6 + 99*S^8))/(3*S^2*(1 + S^2)^2) - (4*(-3 - 6*S^2 - 133*S^4 + 84*S^6 + 42*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((-35*(1 + S^2)^2)/(3*S^2) + (Pi^2*(-119 - 3026*S^2 + 5886*S^4 - 2246*S^6 - 119*S^8))/(18*S^2*(1 + S^2)^2) - (40*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)^2) + (2*(10 + 20*S^2 - 43*S^4 + 14*S^6 + 7*S^8)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)^2) + (10*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(40 + 80*S^2 - 277*S^4 + 86*S^6 + 43*S^8)*Zeta[3])/(3*S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((19 - 16*S^2 - 83*S^4)/(4*S^2) + (Pi^2*(1 - 1296*S^2 + 5352*S^4 - 3444*S^6 - 285*S^8))/(24*S^2*(1 + S^2)^2) + ((-3 - 6*S^2 - 118*S^4 + 74*S^6 + 37*S^8)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)^2) - (2*(-196 - 392*S^2 + 607*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4 - 8*S^2 - 129*S^4 + 86*S^6 + 43*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + (133 + 137*S^2 + (52*Pi^2*(2*S^4 + S^6))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(119 + 215*S^2 + 48*S^4))/(12*S^2) + (171 + 450*S^2 + 151*S^4)/(2*S^2) + (Pi^4*(928 - 5633*S^2 + 30374*S^4 - 12196*S^6 + S^8))/(360*S^2*(1 + S^2)^2) + ((-13 + 74*S^2 + 47*S^4)/(2*S^2) + (Pi^2*(-1 - 2*S^2 - 160*S^4 + 106*S^6 + 53*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-1 + S^2)*(15 + 48*S^2 + 22*S^4 + 13*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + ((-3 - 6*S^2 - 37*S^4 + 12*S^6 + 6*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((153 + 134*S^2 - 11*S^4)/S^2 + (Pi^2*(638 + 1276*S^2 - 1819*S^4 - 10*S^6 - 5*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(-1 + 200*S^2 - 888*S^4 + 708*S^6 + 57*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((7 + 14*S^2 + 236*S^4 - 150*S^6 - 75*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-5 - 10*S^2 - 189*S^4 + 112*S^6 + 56*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-3 + 398*S^2 - 1778*S^4 + 1414*S^6 + 113*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(-196 - 392*S^2 + 607*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(-1175 - 2350*S^2 + 3778*S^4 + 154*S^6 + 77*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(-98 - 196*S^2 + 337*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((Pi^2*S^2*(-131 + 106*S^2 + 53*S^4))/(3*(1 + S^2)^2) + (1 + 58*S^2 + 65*S^4)/S^2)*Zeta[3] + (4*S^2*(-28 + 26*S^2 + 13*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*((243*(1 + S^2)^2)/(4*S^2) + (Pi^2*(-41 - 98*S^2 - 9*S^4))/(12*S^2) + (Pi^4*(-643 - 65276*S^2 + 127158*S^4 - 33764*S^6 - 643*S^8))/(720*S^2*(1 + S^2)^2) + ((-55 - 906*S^2 + 1778*S^4 - 906*S^6 - 55*S^8)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((25 + 122*S^2 + 57*S^4)/S^2 + (Pi^2*(4 + 8*S^2 - 13*S^4 + 14*S^6 + 7*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + (8*(6 - S^2 + 40*S^4 - 7*S^6 + 6*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (2*(6 + 12*S^2 - 89*S^4 + 34*S^6 + 17*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((12*(5 + 2*S^2 + 5*S^4))/S^2 + (Pi^2*(211 + 422*S^2 - 1260*S^4 + 298*S^6 + 149*S^8))/(S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(10 + 407*S^2 - 880*S^4 + 413*S^6 + 10*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(97 + 194*S^2 - 610*S^4 + 170*S^6 + 85*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (160*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(578 + 1156*S^2 - 4001*S^4 + 1162*S^6 + 581*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (120*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((4*(1 + S^2)*(21 + 13*S^2))/S^2 + (2*Pi^2*(17 + 34*S^2 - 147*S^4 + 60*S^6 + 30*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((31 + 238*S^2 + 31*S^4)/(2*S^2) + (Pi^2*(-23 - 2674*S^2 + 5162*S^4 - 1930*S^6 - 23*S^8))/(6*S^2*(1 + S^2)^2) + (2*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(41 + 82*S^2 - 266*S^4 + 82*S^6 + 41*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + (2*(27 + 54*S^2 - 195*S^4 + 76*S^6 + 38*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + HPL[{1}, -S^2]*((555*(1 + S^2)^2)/(4*S^2) + (Pi^4*(217 - 1662*S^2 - 687*S^4))/(1440*S^2) + (Pi^2*(273 + 338*S^2 + 321*S^4))/(24*S^2) + (Pi^6*(-187513 - 375026*S^2 + 953473*S^4 - 122948*S^6 - 61474*S^8))/(45360*S^2*(1 + S^2)^2) + ((-71 - 134*S^2 - 71*S^4)/(2*S^2) + (Pi^2*(-317 - 634*S^2 + 1901*S^4 - 468*S^6 - 234*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + ((-177 - 354*S^2 + 1214*S^4 - 354*S^6 - 177*S^8)*HPL[{2}, -S^2]^3)/(3*S^2*(1 + S^2)^2) + ((1 + 2*S^2 - 20*S^4 + 6*S^6 + 3*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((5*(5 + 34*S^2 + 21*S^4))/(2*S^2) + (Pi^2*(-29 - 58*S^2 + 320*S^4 - 102*S^6 - 51*S^8))/(6*S^2*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(18 + 11*S^2 + 76*S^4 - 11*S^6 + 18*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((-9 - 18*S^2 + 219*S^4 - 128*S^6 - 64*S^8)*HPL[{6}, -S^2])/(S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((4*(23 + 6*S^2 + 7*S^4))/S^2 + (2*Pi^2*(313 + 626*S^2 - 1888*S^4 + 454*S^6 + 227*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(19 + 106*S^2 - 170*S^4 + 106*S^6 + 19*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (4*(81 + 314*S^2 - 350*S^4 + 290*S^6 + 81*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) + (3*(-1 + S^2)*(1 + S^2)*HPL[{4, 2}, -S^2])/S^2 + (4*(5 + 10*S^2 - 109*S^4 + 44*S^6 + 22*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-24*(5 + 2*S^2 + 5*S^4))/S^2 - (2*Pi^2*(211 + 422*S^2 - 1260*S^4 + 298*S^6 + 149*S^8))/(S^2*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (16*(65 + 1313*S^2 - 2658*S^4 + 1319*S^6 + 65*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(177 + 354*S^2 - 1214*S^4 + 354*S^6 + 177*S^8)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(1079 + 2158*S^2 - 7478*S^4 + 2182*S^6 + 1091*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (320*(1 + 41*S^2 - 88*S^4 + 41*S^6 + S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (48*(62 + 124*S^2 - 435*S^4 + 126*S^6 + 63*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (240*(25 + 50*S^2 - 174*S^4 + 50*S^6 + 25*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (((1 + S^2)*(111 + 55*S^2))/S^2 + (Pi^2*(67 + 272*S^2 - 262*S^4 + 376*S^6 + 67*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] - (2*(7 + 14*S^2 - 67*S^4 + 20*S^6 + 10*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{3}, -S^2]*((39 + 270*S^2 + 151*S^4)/(2*S^2) + (Pi^2*(113 + 196*S^2 + 94*S^4 + 220*S^6 + 113*S^8))/(6*S^2*(1 + S^2)^2) - (4*(19 + 38*S^2 - 134*S^4 + 38*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*S^2*(-1 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((Pi^2*(-31 + 50*S^2 + 9*S^4))/(6*S^2) + (73 + 274*S^2 + 73*S^4)/S^2 + (Pi^4*(-7131 - 14262*S^2 + 38357*S^4 - 7288*S^6 - 3644*S^8))/(360*S^2*(1 + S^2)^2) + (2*(19 + 106*S^2 - 170*S^4 + 106*S^6 + 19*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) + ((-1 - 2*S^2 + 40*S^4 - 14*S^6 - 7*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(35 + 238*S^2 - 290*S^4 + 238*S^6 + 35*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-31 - 238*S^2 - 31*S^4)/S^2 + (Pi^2*(23 + 2674*S^2 - 5162*S^4 + 1930*S^6 + 23*S^8))/(3*S^2*(1 + S^2)^2) - (4*(41 + 82*S^2 - 266*S^4 + 82*S^6 + 41*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((133 + 484*S^2 - 250*S^4 + 572*S^6 + 133*S^8)*Zeta[5])/(S^2*(1 + S^2)^2))) - (6*(35 + 221*S^2 - 548*S^4 + 10*S^6)*Zeta[7])/(1 + S^2)^2 + HPL[{1}, -S^2]*((1175*(1 + S^2)^2)/(4*S^2) + (Pi^2*(-75 + 18*S^2 + 157*S^4))/(6*S^2) + (Pi^4*(-7841 - 9658*S^2 + 1127*S^4))/(1440*S^2) + (Pi^6*(-60553 - 1675636*S^2 + 2784450*S^4 - 539740*S^6 - 60553*S^8))/(90720*S^2*(1 + S^2)^2) + (124*(-1 + S^2)*HPL[{2}, -S^2]^3)/(1 + S^2) + ((-29 - 208*S^2 + 266*S^4 - 208*S^6 - 29*S^8)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((3*(35 + 86*S^2 + 75*S^4))/S^2 + (2*Pi^2*(-19 - 38*S^2 - 186*S^4 + 158*S^6 + 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{5}, -S^2] + ((579 - 364*S^2 + 1066*S^4 + 3452*S^6 + 579*S^8)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)^2) + (6*(-87 - 174*S^2 + 81*S^4 + 184*S^6 + 92*S^8)*HPL[{7}, -S^2])/(S^2*(1 + S^2)^2) + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)^2) + ((-2*(35 + 134*S^2 + 107*S^4))/S^2 - (2*Pi^2*(108 + 216*S^2 - 1423*S^4 + 610*S^6 + 305*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-2*(205 + 674*S^2 + 493*S^4))/S^2 + (Pi^2*(-709 - 1418*S^2 + 9670*S^4 - 4218*S^6 - 2109*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (3*(29 + 216*S^2 - 298*S^4 + 216*S^6 + 29*S^8)*HPL[{4, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(7 + 14*S^2 - 185*S^4 + 80*S^6 + 40*S^8)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)^2) - (8*(84 + 371*S^2 - 590*S^4 + 647*S^6 + 84*S^8)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)^2) + (12*(2 + 4*S^2 - 71*S^4 + 30*S^6 + 15*S^8)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(-184 - 368*S^2 + 153*S^4 + 466*S^6 + 233*S^8)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-4*(71 + 134*S^2 + 71*S^4))/S^2 - (4*Pi^2*(350 + 700*S^2 - 2089*S^4 + 514*S^6 + 257*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-8*(67 + 66*S^2 + 7*S^4))/S^2 - (16*Pi^2*(233 + 466*S^2 - 1141*S^4 + 196*S^6 + 98*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (2976*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + (2*(443 + 886*S^2 - 5586*S^4 + 2374*S^6 + 1187*S^8)*HPL[{3, 2, 2}, -S^2])/(S^2*(1 + S^2)^2) + (16*(172 + 344*S^2 - 2137*S^4 + 902*S^6 + 451*S^8)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (64*(9 - 98*S^2 - 79*S^4 + 217*S^6 + 9*S^8)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(1337 + 2674*S^2 - 16838*S^4 + 7138*S^6 + 3569*S^8)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) + (2*(4253 + 8506*S^2 - 52142*S^4 + 21898*S^6 + 10949*S^8)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (48*(362 + 724*S^2 - 4471*S^4 + 1886*S^6 + 943*S^8)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((-480*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-275 - 550*S^2 + 674*S^4 + 158*S^6 + 79*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (1488*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (64*(9 - 53*S^2 - 79*S^4 + 172*S^6 + 9*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (32*(191 + 382*S^2 - 674*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)^2) - (32*(191 + 382*S^2 - 674*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (16*(-661 - 1322*S^2 + 1348*S^4 + 538*S^6 + 269*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (32*(-1015 - 2030*S^2 + 2299*S^4 + 688*S^6 + 344*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (14400*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + (128*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (384*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (160*(221 + 442*S^2 - 1673*S^4 + 532*S^6 + 266*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (7200*(-1 + S^2)*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((2*Pi^2*(-7 + 8*S^2 + 29*S^4))/(3*S^2) + (-221 - 274*S^2 + 75*S^4)/S^2 + (Pi^4*(231 + 462*S^2 - 10373*S^4 + 5616*S^6 + 2808*S^8))/(180*S^2*(1 + S^2)^2))*Zeta[3] + ((3 - 92*S^2 + 146*S^4 - 92*S^6 + 3*S^8)*Zeta[3]^2)/(S^2*(1 + S^2)^2) + HPL[{4}, -S^2]*((4*(1 + S^2)*(29 + 54*S^2))/S^2 + (Pi^2*(161 + 560*S^2 - 1274*S^4 + 1432*S^6 + 161*S^8))/(6*S^2*(1 + S^2)^2) - (2*(113 + 226*S^2 - 734*S^4 + 226*S^6 + 113*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(3 + 6*S^2 - 100*S^4 + 50*S^6 + 25*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3}, -S^2]*((2*Pi^2*(17 + 82*S^2 + 63*S^4))/(3*S^2) + (-63 + 210*S^2 + 529*S^4)/(2*S^2) + (Pi^4*(292 + 584*S^2 - 6193*S^4 + 3022*S^6 + 1511*S^8))/(90*S^2*(1 + S^2)^2) - (2*(8 + 16*S^2 - 157*S^4 + 70*S^6 + 35*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) - (4*(55 + 534*S^2 - 1778*S^4 + 1278*S^6 + 55*S^8)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(103 + 206*S^2 - 1352*S^4 + 578*S^6 + 289*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) + (8*(103 + 206*S^2 - 1348*S^4 + 578*S^6 + 289*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (2*(27 + 128*S^2 - 222*S^4 + 152*S^6 + 27*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-296*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(287 + 134*S^2 - 145*S^4))/(6*S^2) + (Pi^4*(7200 + 14400*S^2 - 21017*S^4 - 2274*S^6 - 1137*S^8))/(180*S^2*(1 + S^2)^2) - (32*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) - (4*(55 + 522*S^2 - 1778*S^4 + 1290*S^6 + 55*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((384*(-1 + S^2)*(1 + S^2))/S^2 - (2*Pi^2*(55 + 2322*S^2 - 1778*S^4 - 510*S^6 + 55*S^8))/(3*S^2*(1 + S^2)^2) + (32*(25 + 50*S^2 - 337*S^4 + 146*S^6 + 73*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-8*(2 + S^2 + 2*S^4))/S^2 + (Pi^2*(-46 - 799*S^2 + 1376*S^4 - 613*S^6 - 46*S^8))/(3*S^2*(1 + S^2)^2) + (2*(70 + 140*S^2 - 795*S^4 + 326*S^6 + 163*S^8)*HPL[{3}, -S^2])/(S^2*(1 + S^2)^2) - (186*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (2*(42 + 84*S^2 - 607*S^4 + 270*S^6 + 135*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-2*(1 + S^2)*(-13 + 179*S^2))/S^2 + (Pi^2*(-25 + 1820*S^2 - 1126*S^4 - 1012*S^6 - 25*S^8))/(3*S^2*(1 + S^2)^2) - (8*(53 + 106*S^2 - 694*S^4 + 298*S^6 + 149*S^8)*Zeta[3])/(S^2*(1 + S^2)^2)) + ((-169 - 178*S^2 + 71*S^4)/S^2 + (Pi^2*(-18 - 36*S^2 - 1477*S^4 + 874*S^6 + 437*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((232*(-1 + S^2)*(1 + S^2))/S^2 + (Pi^2*(-93 - 4*S^2 + 77*S^4))/(3*S^2) + (Pi^4*(-1437 - 60788*S^2 + 56314*S^4 + 5908*S^6 - 1437*S^8))/(720*S^2*(1 + S^2)^2) + ((31 + 134*S^2 + 111*S^4)/S^2 + (Pi^2*(108 + 216*S^2 - 1423*S^4 + 610*S^6 + 305*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{3}, -S^2] + ((89 + 632*S^2 - 834*S^4 + 632*S^6 + 89*S^8)*HPL[{4}, -S^2])/(S^2*(1 + S^2)^2) + (2*(17 + 34*S^2 - 286*S^4 + 130*S^6 + 65*S^8)*HPL[{5}, -S^2])/(S^2*(1 + S^2)^2) + ((2*(71 + 134*S^2 + 71*S^4))/S^2 + (2*Pi^2*(350 + 700*S^2 - 2089*S^4 + 514*S^6 + 257*S^8))/(3*S^2*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)^2) - (2*(241 + 482*S^2 - 2922*S^4 + 1226*S^6 + 613*S^8)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)^2) - (2*(727 + 1454*S^2 - 8806*S^4 + 3686*S^6 + 1843*S^8)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)^2) - (8*(55 + 906*S^2 - 1778*S^4 + 906*S^6 + 55*S^8)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (744*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (16*(191 + 382*S^2 - 674*S^4 + 10*S^6 + 5*S^8)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + (64*(49 + 98*S^2 - 337*S^4 + 98*S^6 + 49*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)^2) + ((47 + 134*S^2 + 95*S^4)/S^2 + (Pi^2*(108 + 216*S^2 - 1481*S^4 + 646*S^6 + 323*S^8))/(3*S^2*(1 + S^2)^2))*Zeta[3] + (2*(44 + 88*S^2 - 1255*S^4 + 634*S^6 + 317*S^8)*Zeta[5])/(S^2*(1 + S^2)^2)) + (6*(-35 - 70*S^2 - 583*S^4 + 392*S^6 + 196*S^8)*Zeta[7])/(S^2*(1 + S^2)^2))) - (1568*(2*S^4 + S^6)*Zeta[9])/(1 + S^2)^2;
E5uvwT3F1=(-2625*(1 + S^2))/(32*S) + (Pi^2*(-1559 - 4133*S^2 - 974*S^4))/(96*S) + (Pi^6*(-10192 - 164348*S^2 - 170275*S^4 - 26871*S^6))/(60480*S*(1 + S^2)) + (Pi^4*(-2943 - 21435*S^2 - 16945*S^4 - 373*S^6))/(1440*S*(1 + S^2)) + (Pi^8*S*(-7567178 + 2245845*S^2 + 446368*S^4 + 223184*S^6))/(1360800*(1 + S^2)^3) - (S*HPL[{0}, S^2]^9)/(192*(1 + S^2)^3) + ((7 - 104*S^2 + 126*S^4 + 16*S^6 - 5*S^8)*HPL[{1}, -S^2]^8)/(6*S*(1 + S^2)^3) + (8*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^9)/(27*(1 + S^2)^3) + HPL[{0}, S^2]^8*((S*(-20 - 6*S^2 + S^4 + 2*S^6))/(192*(1 + S^2)^3) - (S*(6 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(96*(1 + S^2)^3)) + ((43 - 1312*S^2 + 1538*S^4 + 304*S^6 - 9*S^8)*HPL[{2}, -S^2]^4)/(12*S*(1 + S^2)^3) + HPL[{1}, -S^2]^7*((8*Pi^2*S*(-89 + 27*S^2 + 27*S^4 + 9*S^6))/(63*(1 + S^2)^3) + (-3 + 38*S^2 - 441*S^4 + 1052*S^6 - 441*S^8 + 38*S^10 - 3*S^12)/(21*S^3*(1 + S^2)^3) - (20*S*HPL[{2}, -S^2])/7) + HPL[{0}, S^2]^7*(-(Pi^2*S*(27 + 3*S^2 + 3*S^4 + S^6))/(288*(1 + S^2)^3) - (S*(26 - 11*S^2 - 6*S^4 + 5*S^6 + 6*S^8))/(96*(1 + S^2)^3) + ((6 - 42*S^2 - 12*S^4 - 17*S^6 - 5*S^8)*HPL[{1}, -S^2])/(48*S*(1 + S^2)^3) - (S*(17 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(48*(1 + S^2)^3) - (S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(48*(1 + S^2)^3)) + (50*S*HPL[{3}, -S^2]^3)/3 + ((4 - 144*S^2 - 78*S^4 + 21*S^6 + 35*S^8)*HPL[{4}, -S^2]^2)/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(103 + 195*S^2 + 195*S^4 + 65*S^6))/(1 + S^2)^3 + (-1050 + 556*S^2 - 1352*S^4 - 2295*S^6 - 2113*S^8 - 2545*S^10 - 681*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{7}, -S^2] - (2*(-854 + 4017*S^2 + 6245*S^4 + 4458*S^6 + 1095*S^8)*HPL[{8}, -S^2])/(S*(1 + S^2)^3) - (4*S*(1939 + 2784*S^2 + 2784*S^4 + 928*S^6)*HPL[{9}, -S^2])/(1 + S^2)^3 - (1232*S*HPL[{2, 1}, -S^2]^3)/3 - (2*(-139 + 3321*S^2 - 3484*S^4 - 679*S^6 + 25*S^8)*HPL[{3, 1}, -S^2]^2)/(S*(1 + S^2)^3) + ((44*Pi^2*S)/(1 + S^2)^3 + (9 - 64*S^2 - 269*S^4 - 689*S^6 + 458*S^8 + 65*S^10 + 42*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4, 3}, -S^2] + ((Pi^2*S*(355 + 141*S^2 + 141*S^4 + 47*S^6))/(3*(1 + S^2)^3) + (39 - 151*S^2 - 682*S^4 - 1539*S^6 + 1262*S^8 + 326*S^10 + 129*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{5, 2}, -S^2] + ((-5 - 116*S^2 - 400*S^4 - 240*S^6 - 59*S^8)*HPL[{5, 3}, -S^2])/(S*(1 + S^2)^3) - (4*S*(214 + 381*S^2 + 381*S^4 + 127*S^6)*HPL[{5, 4}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(364 + 867*S^2 + 867*S^4 + 289*S^6))/(3*(1 + S^2)^3) + (468 - 730*S^2 + 2748*S^4 + 5729*S^6 + 4413*S^8 + 2577*S^10 + 363*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{6, 1}, -S^2] + ((33 - 128*S^2 - 772*S^4 - 454*S^6 - 113*S^8)*HPL[{6, 2}, -S^2])/(S*(1 + S^2)^3) - (4*S*(875 + 1566*S^2 + 1566*S^4 + 522*S^6)*HPL[{6, 3}, -S^2])/(1 + S^2)^3 + (2*(-452 + 3058*S^2 + 4975*S^4 + 3055*S^6 + 666*S^8)*HPL[{7, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(2187 + 3909*S^2 + 3909*S^4 + 1303*S^6)*HPL[{7, 2}, -S^2])/(1 + S^2)^3 - (4*S*(3089 + 5796*S^2 + 5796*S^4 + 1932*S^6)*HPL[{8, 1}, -S^2])/(1 + S^2)^3 - (8*(-83 + 2668*S^2 - 3090*S^4 - 596*S^6 + 25*S^8)*HPL[{2, 1, 1}, -S^2]^2)/(S*(1 + S^2)^3) + (-(Pi^2*S*(-2511 + 3783*S^2 + 3783*S^4 + 1261*S^6))/(3*(1 + S^2)^3) + (-15 + 62*S^2 + 387*S^4 - 14820*S^6 + 11547*S^8 - 2082*S^10 + 105*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3, 2, 2}, -S^2] + ((-68*Pi^2*S*(-113 + 171*S^2 + 171*S^4 + 57*S^6))/(3*(1 + S^2)^3) + (2*(-3 + 32*S^2 + 153*S^4 - 11430*S^6 + 8879*S^8 - 1566*S^10 + 87*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 3, 1}, -S^2] + (3*(-27 - 212*S^2 + 1208*S^4 + 454*S^6 + 69*S^8)*HPL[{3, 3, 2}, -S^2])/(S*(1 + S^2)^3) + ((-4*Pi^2*S*(-1878 + 2913*S^2 + 2913*S^4 + 971*S^6))/(3*(1 + S^2)^3) + (-15 + 81*S^2 + 415*S^4 - 44706*S^6 + 35271*S^8 - 6335*S^10 + 345*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4, 1, 2}, -S^2] - (2*(-82 - 616*S^2 + 2986*S^4 + 1209*S^6 + 209*S^8)*HPL[{4, 1, 3}, -S^2])/(S*(1 + S^2)^3) + ((-4*Pi^2*S*(-5871 + 8826*S^2 + 8826*S^4 + 2942*S^6))/(3*(1 + S^2)^3) + (-15 + 225*S^2 + 1519*S^4 - 140490*S^6 + 107607*S^8 - 18935*S^10 + 1065*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4, 2, 1}, -S^2] + ((-89 - 72*S^2 + 3064*S^4 + 1220*S^6 + 189*S^8)*HPL[{4, 2, 2}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-35 + 48*S^2 + 48*S^4 + 16*S^6)*HPL[{4, 2, 3}, -S^2])/(1 + S^2)^3 - (2*(-148 - 2176*S^2 + 9346*S^4 + 3261*S^6 + 455*S^8)*HPL[{4, 3, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(131 + 234*S^2 + 234*S^4 + 78*S^6)*HPL[{4, 3, 2}, -S^2])/(1 + S^2)^3 + (16*S*(20 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{4, 4, 1}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-24179 + 36291*S^2 + 36291*S^4 + 12097*S^6))/(3*(1 + S^2)^3) + (2*(-60 + 101*S^2 - 232*S^4 - 74362*S^6 + 54271*S^8 - 9853*S^10 + 531*S^12))/(S^3*(1 + S^2)^3))*HPL[{5, 1, 1}, -S^2] + ((95 + 2788*S^2 - 10588*S^4 - 3776*S^6 - 575*S^8)*HPL[{5, 1, 2}, -S^2])/(S*(1 + S^2)^3) - (8*S*(54 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{5, 1, 3}, -S^2])/(1 + S^2)^3 + ((1235 + 16948*S^2 - 78628*S^4 - 27656*S^6 - 3875*S^8)*HPL[{5, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(243 + 606*S^2 + 606*S^4 + 202*S^6)*HPL[{5, 2, 2}, -S^2])/(1 + S^2)^3 + (8*S*(-2 + 405*S^2 + 405*S^4 + 135*S^6)*HPL[{5, 3, 1}, -S^2])/(1 + S^2)^3 - (2*(-1955 - 19229*S^2 + 106862*S^4 + 38124*S^6 + 5356*S^8)*HPL[{6, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (20*S*(19 + 204*S^2 + 204*S^4 + 68*S^6)*HPL[{6, 1, 2}, -S^2])/(1 + S^2)^3 + (20*S*(-121 + 120*S^2 + 120*S^4 + 40*S^6)*HPL[{6, 2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(1373 + 1257*S^2 + 1257*S^4 + 419*S^6)*HPL[{7, 1, 1}, -S^2])/(1 + S^2)^3 + ((688*Pi^2*S*(7 + 6*S^2 + 6*S^4 + 2*S^6))/(3*(1 + S^2)^3) - (4*(-15 + 227*S^2 - 1814*S^4 + 1574*S^6 - 307*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 2, 2, 1}, -S^2] + ((-2*Pi^2*S*(9571 + 2217*S^2 + 2217*S^4 + 739*S^6))/(3*(1 + S^2)^3) + (2*(-96 + 1267*S^2 - 9462*S^4 + 5564*S^6 + 1774*S^8 - 671*S^10 + 24*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 2}, -S^2] + ((-2*Pi^2*S*(9571 + 2217*S^2 + 2217*S^4 + 739*S^6))/(3*(1 + S^2)^3) + (2*(-96 + 1267*S^2 - 9462*S^4 + 5564*S^6 + 1774*S^8 - 671*S^10 + 24*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 2, 1}, -S^2] + (2*(29 - 461*S^2 + 678*S^4 + 167*S^6 + 7*S^8)*HPL[{3, 1, 2, 2}, -S^2])/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(16795 + 8409*S^2 + 8409*S^4 + 2803*S^6))/(3*(1 + S^2)^3) + (2*(-186 + 2539*S^2 - 18984*S^4 + 4124*S^6 + 9376*S^8 - 2423*S^10 + 114*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 2, 1, 1}, -S^2] + (2*(29 - 461*S^2 + 678*S^4 + 167*S^6 + 7*S^8)*HPL[{3, 2, 1, 2}, -S^2])/(S*(1 + S^2)^3) + (2*(309 - 573*S^2 + 914*S^4 + 887*S^6 + 99*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-2293 + 3441*S^2 + 3441*S^4 + 1147*S^6)*HPL[{3, 2, 2, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-7217 + 10821*S^2 + 10821*S^4 + 3607*S^6)*HPL[{3, 2, 3, 1}, -S^2])/(1 + S^2)^3 + (24*(70 - 98*S^2 + 157*S^4 + 23*S^6)*HPL[{3, 3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (24*S*(-1181 + 1785*S^2 + 1785*S^4 + 595*S^6)*HPL[{3, 3, 1, 2}, -S^2])/(1 + S^2)^3 + (12*S*(-7275 + 10983*S^2 + 10983*S^4 + 3661*S^6)*HPL[{3, 3, 2, 1}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(25801 + 12231*S^2 + 12231*S^4 + 4077*S^6))/(3*(1 + S^2)^3) + (2*(-513 + 7631*S^2 - 56551*S^4 + 17636*S^6 + 27531*S^8 - 6947*S^10 + 333*S^12))/(S^3*(1 + S^2)^3))*HPL[{4, 1, 1, 1}, -S^2] + (2*(13 - 549*S^2 + 3300*S^4 + 907*S^6 + 69*S^8)*HPL[{4, 1, 1, 2}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-44365 + 66969*S^2 + 66969*S^4 + 22323*S^6)*HPL[{4, 1, 1, 3}, -S^2])/(1 + S^2)^3 + (2*(853 - 885*S^2 + 4008*S^4 + 3067*S^6 + 345*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (32*S*(-4659 + 7035*S^2 + 7035*S^4 + 2345*S^6)*HPL[{4, 1, 2, 2}, -S^2])/(1 + S^2)^3 - (8*S*(-33313 + 50313*S^2 + 50313*S^4 + 16771*S^6)*HPL[{4, 1, 3, 1}, -S^2])/(1 + S^2)^3 + (2*(2533 - 1557*S^2 + 5424*S^4 + 7387*S^6 + 897*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-11463 + 17187*S^2 + 17187*S^4 + 5729*S^6)*HPL[{4, 2, 1, 2}, -S^2])/(1 + S^2)^3 - (28*S*(-3219 + 4863*S^2 + 4863*S^4 + 1621*S^6)*HPL[{4, 2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-32905 + 49851*S^2 + 49851*S^4 + 16617*S^6)*HPL[{4, 3, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(2441 - 2306*S^2 + 12224*S^4 + 9358*S^6 + 1027*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-134189 + 201657*S^2 + 201657*S^4 + 67219*S^6)*HPL[{5, 1, 1, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-221051 + 333759*S^2 + 333759*S^4 + 111253*S^6)*HPL[{5, 1, 2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-526247 + 797115*S^2 + 797115*S^4 + 265705*S^6)*HPL[{5, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-657579 + 995259*S^2 + 995259*S^4 + 331753*S^6)*HPL[{6, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-32*Pi^2*S*(-599 + 225*S^2 + 225*S^4 + 75*S^6))/(3*(1 + S^2)^3) + (8*(18 - 207*S^2 + 1642*S^4 - 3274*S^6 + 1546*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-32*Pi^2*S*(-599 + 225*S^2 + 225*S^4 + 75*S^6))/(1 + S^2)^3 + (24*(18 - 207*S^2 + 1642*S^4 - 3274*S^6 + 1546*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1, 1, 1}, -S^2] - (8*(-159 + 227*S^2 - 207*S^4 + 11*S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (24*(-159 + 227*S^2 - 207*S^4 + 11*S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (128*S*(-181 + 102*S^2 + 102*S^4 + 34*S^6)*HPL[{2, 2, 2, 2, 1}, -S^2])/(1 + S^2)^3 + ((-16*Pi^2*S*(-6737 + 3309*S^2 + 3309*S^4 + 1103*S^6))/(3*(1 + S^2)^3) + (8*(81 - 1054*S^2 + 8100*S^4 - 21212*S^6 + 10741*S^8 - 1886*S^10 + 126*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1, 1}, -S^2] + (8*(-931 + 1141*S^2 - 1333*S^4 + 51*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(S*(1 + S^2)^2) + (8*(-1567 + 2049*S^2 - 2161*S^4 + 95*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-12527 + 2691*S^2 + 2691*S^4 + 897*S^6)*HPL[{3, 1, 1, 2, 2}, -S^2])/(1 + S^2)^3 + (8*(-1885 + 2503*S^2 - 2575*S^4 + 117*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-12527 + 2691*S^2 + 2691*S^4 + 897*S^6)*HPL[{3, 1, 2, 1, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-305 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{3, 1, 2, 2, 1}, -S^2])/(1 + S^2)^3 - (32*S*(-11659 + 3183*S^2 + 3183*S^4 + 1061*S^6)*HPL[{3, 1, 3, 1, 1}, -S^2])/(1 + S^2)^3 + (16*(-1976 + 2727*S^2 - 2633*S^4 + 130*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-29903 + 12483*S^2 + 12483*S^4 + 4161*S^6)*HPL[{3, 2, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-17071 + 9699*S^2 + 9699*S^4 + 3233*S^6)*HPL[{3, 2, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(28617 + 6603*S^2 + 6603*S^4 + 2201*S^6)*HPL[{3, 2, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (96*S*(4263 + 429*S^2 + 429*S^4 + 143*S^6)*HPL[{3, 3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (24*(-3967 + 1990*S^2 - 1064*S^4 - 5330*S^6 + 251*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-44933 + 18345*S^2 + 18345*S^4 + 6115*S^6)*HPL[{4, 1, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (8*S*(-25685 + 14169*S^2 + 14169*S^4 + 4723*S^6)*HPL[{4, 1, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(42847 + 9525*S^2 + 9525*S^4 + 3175*S^6)*HPL[{4, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (8*S*(153847 + 14925*S^2 + 14925*S^4 + 4975*S^6)*HPL[{4, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (512*S*(4829 + 438*S^2 + 438*S^4 + 146*S^6)*HPL[{5, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((32*Pi^2*S*(619 + 552*S^2 + 552*S^4 + 184*S^6))/(3*(1 + S^2)^3) - (8*(-45 + 469*S^2 - 4166*S^4 + 3446*S^6 - 709*S^8 + 45*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 9856*S*HPL[{2, 2, 1, 2, 1, 1}, -S^2] - 29568*S*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + (16*(185 - 756*S^2 + 1938*S^4 + 734*S^6 + 15*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(421 + 6483*S^2 + 6483*S^4 + 2161*S^6)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (32*S*(2269 + 12027*S^2 + 12027*S^4 + 4009*S^6)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (96*S*(1167 + 5241*S^2 + 5241*S^4 + 1747*S^6)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (32*S*(4117 + 17571*S^2 + 17571*S^4 + 5857*S^6)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (96*S*(2707 + 9861*S^2 + 9861*S^4 + 3287*S^6)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (64*S*(11879 + 44547*S^2 + 44547*S^4 + 14849*S^6)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (480*(-9 - 8*S^2 - 24*S^4 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (256*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (1024*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (2560*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (1536*S*(-1207 + 684*S^2 + 684*S^4 + 228*S^6)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + 42240*S*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((8*S*(7 - 22*S^2 + 7*S^4))/(3*(1 + S^2)^3) - (4*Pi^2*S*(-27 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) - (4*S*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^3) + (4*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^3) - (32*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{0}, S^2]*((4*S*(41 - 77*S^2 - 5*S^4 + 5*S^6))/(3*(1 + S^2)^3) - (32*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(3*(1 + S^2)^3)) - (8*S*HPL[{2}, -S^2])/3)*Log[T]^7 + ((4*S*(-5 + 5*S^2 + S^4))/(1 + S^2)^3 + (4*S*(-7 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{0}, S^2])/(3*(1 + S^2)^3) + (8*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(3*(1 + S^2)^3))*Log[T]^8 + (8*S*Log[T]^9)/(3*(1 + S^2)^3) + ((6 + 65*S^2 - 53*S^4 - 64*S^6)/(2*S*(1 + S^2)) + (Pi^2*S*(-343 + 84*S^2 + 110*S^4 + 55*S^6))/(6*(1 + S^2)^3))*Zeta[3]^2 - (64*S^3*(3 + 3*S^2 + S^4)*Zeta[3]^3)/(1 + S^2)^3 + HPL[{3, 1, 2}, -S^2]*((Pi^2*(45 - 441*S^2 - 197*S^4 - 39*S^6))/(6*S*(1 + S^2)^2) + (-25 + 239*S^2 - 207*S^4 + 25*S^6)/(4*S^3) - 36*S*Zeta[3]) + HPL[{4, 2}, -S^2]*((-11 - 206*S^2 + 288*S^4 - 61*S^6)/(4*S^3) + (Pi^2*(12 - 237*S^2 + 1670*S^4 + 491*S^6 + 48*S^8))/(6*S*(1 + S^2)^3) + (12*S*(-7 + 9*S^2 + 9*S^4 + 3*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{6}, -S^2]*((1380 + 912*S^2 - 3667*S^4 - 754*S^6)/(4*S^3) + (Pi^2*(205 - 1655*S^2 - 3394*S^4 - 1550*S^6 - 226*S^8))/(6*S*(1 + S^2)^3) + (20*S*(9 + 30*S^2 + 30*S^4 + 10*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (52*S*(7 + 12*S^2 + 12*S^4 + 4*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^6*(-((1 + S^2)*(3 - 4*S^2 + 3*S^4))/(9*S^3) + (Pi^2*(265 - 3726*S^2 + 3678*S^4 + 508*S^6 - 105*S^8))/(54*S*(1 + S^2)^3) + (10*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (280*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(9*(1 + S^2)^3) + 20*S*HPL[{2, 1}, -S^2] - (16*S*(-23 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + Log[T]^6*((-1 - S^2)/S + (Pi^2*S*(-648 + 652*S^2 + 125*S^4 + S^6))/(9*(1 + S^2)^3) + (4*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2]^3)/(9*(1 + S^2)^3) - (14*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)^3) + (224*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^3) + HPL[{0}, S^2]^2*((S*(-228 + 232*S^2 + 41*S^4 + S^6))/(3*(1 + S^2)^3) + (8*S*(-33 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{1}, -S^2])/(3*(1 + S^2)^3)) + (2*(-9 - 8*S^2 - 24*S^4 + S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((8*Pi^2*S*(-89 + 27*S^2 + 27*S^4 + 9*S^6))/(9*(1 + S^2)^3) + (-3 + 38*S^2 - 441*S^4 + 1052*S^6 - 441*S^8 + 38*S^10 - 3*S^12)/(3*S^3*(1 + S^2)^3) - 20*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((4*Pi^2*S*(-74 + 51*S^2 + 51*S^4 + 17*S^6))/(9*(1 + S^2)^3) - (S*(151 - 526*S^2 + 290*S^4 - 38*S^6 + 3*S^8))/(3*(1 + S^2)^3) - (14*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^3) + (112*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^3) + (4*S*(-85 + 81*S^2 + 81*S^4 + 27*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) - (16*S*(-24 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (176*S*HPL[{2, 1}, -S^2])/3 - (16*S*(-17 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{3}, -S^2]^2*((4 + 122*S^2 + 35*S^4 + 4*S^6 - 33*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-11 - 160*S^2 + 1014*S^4 + 342*S^6 + 43*S^8))/(12*S*(1 + S^2)^3) - (12*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-1 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{0}, S^2]^6*((-3 - 178*S^2 - 59*S^4)/(192*S) + (Pi^2*S*(-827 - 222*S^2 - 35*S^4 + 44*S^6))/(576*(1 + S^2)^3) + ((24 - 233*S^2 - 16*S^4 - 25*S^6 - 2*S^8)*HPL[{1}, -S^2]^2)/(48*S*(1 + S^2)^3) - (S*(93 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{1}, -S^2]^3)/(72*(1 + S^2)^3) + ((2 - 211*S^2 - 79*S^4 - 74*S^6 - 16*S^8)*HPL[{2}, -S^2])/(96*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(-(Pi^2*S*(87 + 33*S^2 + 33*S^4 + 11*S^6))/(96*(1 + S^2)^3) + (-3 + 84*S^2 - 493*S^4 + 50*S^6 - 141*S^8 - 58*S^10 + 9*S^12)/(192*S^3*(1 + S^2)^3) - (S*(35 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{2}, -S^2])/(24*(1 + S^2)^3)) - (S*HPL[{3}, -S^2])/16 + (S*(17 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(12*(1 + S^2)^3) - (S*(17 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(12*(1 + S^2)^3)) + HPL[{5, 1}, -S^2]*((-414 + 165*S^2 + 2510*S^4 - 149*S^6)/(4*S^3) + (Pi^2*(-67 - 334*S^2 + 5605*S^4 + 1700*S^6 + 136*S^8))/(3*S*(1 + S^2)^3) + (8*S*(-67 + 39*S^2 + 39*S^4 + 13*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^3*((-9 - 127*S^2 - S^4 + 9*S^6)/(12*S^3) + (Pi^2*(-77 - 1258*S^2 + 1562*S^4 + 170*S^6 + 7*S^8))/(36*S*(1 + S^2)^3) - (2*S*(-277 + 459*S^2 + 459*S^4 + 153*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (8*S*(-181 + 102*S^2 + 102*S^4 + 34*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (4*S*(-147 + 204*S^2 + 204*S^4 + 68*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]^2*((-13 - 17*S^2 + 48*S^4 + 63*S^6 - 13*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-171 + 8241*S^2 - 9605*S^4 - 1783*S^6 + 58*S^8))/(6*S*(1 + S^2)^3) + (16*S*(-125 + 213*S^2 + 213*S^4 + 71*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1, 1, 1}, -S^2]*((12*(-9 - 111*S^2 - 17*S^4 + 9*S^6))/S^3 + (8*Pi^2*(-58 - 1536*S^2 + 1175*S^4 + 52*S^6 + 9*S^8))/(3*S*(1 + S^2)^3) - (64*S*(-289 + 438*S^2 + 438*S^4 + 146*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1, 1, 1}, -S^2]*((41 + 875*S^2 + 311*S^4 - 67*S^6)/S^3 + (2*Pi^2*(164 + 2015*S^2 - 831*S^4 + 313*S^6 + 19*S^8))/(3*S*(1 + S^2)^3) + (16*S*(-603 + 879*S^2 + 879*S^4 + 293*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4, 1, 1}, -S^2]*((-27 - 895*S^2 - 515*S^4 + 53*S^6)/S^3 + (Pi^2*(-411 - 6929*S^2 + 4112*S^4 - 483*S^6 - 49*S^8))/(3*S*(1 + S^2)^3) - (16*S*(-899 + 1269*S^2 + 1269*S^4 + 423*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 2, 1}, -S^2]*((-97 - 777*S^2 - 215*S^4 + 97*S^6)/(4*S^3) + (Pi^2*(-263 - 5428*S^2 + 5610*S^4 + 444*S^6 - 11*S^8))/(6*S*(1 + S^2)^3) - (4*S*(-1167 + 1659*S^2 + 1659*S^4 + 553*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{5}, -S^2]*(-(Pi^4*S*(-253 + 2190*S^2 + 2190*S^4 + 730*S^6))/(90*(1 + S^2)^3) + (210 - 160*S^2 - 1109*S^4 - 326*S^6 + 77*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-120 - 21*S^2 - 1358*S^4 - 2864*S^6 + 2*S^8 - 607*S^10 - 48*S^12))/(12*S^3*(1 + S^2)^3) - (2*(32 + 739*S^2 - 505*S^4 - 105*S^6 + 3*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(-41 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-209 + 477*S^2 + 477*S^4 + 159*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(-11 + 111*S^2 + 75*S^4 + 51*S^6 + 2*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{3, 2}, -S^2]*((Pi^4*S*(-2093 + 3687*S^2 + 3687*S^4 + 1229*S^6))/(45*(1 + S^2)^3) + (-63 - 280*S^2 + 816*S^4 + 40*S^6 - 417*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-9 + 34*S^2 + 284*S^4 + 7782*S^6 - 5897*S^8 + 1172*S^10 - 78*S^12))/(12*S^3*(1 + S^2)^3) + (4*S*(-2569 + 3621*S^2 + 3621*S^4 + 1207*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((13 - 456*S^2 + 514*S^4 + 76*S^6 + 5*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2, 1, 1, 1}, -S^2]*((86 + 695*S^2 + 489*S^4 - 86*S^6)/S^3 + (4*Pi^4*S*(825 + 444*S^2 + 444*S^4 + 148*S^6))/(9*(1 + S^2)^3) + (Pi^2*(93 - 846*S^2 + 7515*S^4 - 1978*S^6 - 2599*S^8 + 816*S^10 - 57*S^12))/(3*S^3*(1 + S^2)^3) - (16*(-77 + 1281*S^2 - 1655*S^4 - 397*S^6 + 6*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{4, 1}, -S^2]*((Pi^4*S*(-14605 + 24213*S^2 + 24213*S^4 + 8071*S^6))/(90*(1 + S^2)^3) + (-383 + 956*S^2 + 6772*S^4 + 2444*S^6 - 1261*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(60 + 85*S^2 + 1838*S^4 + 29442*S^6 - 18052*S^8 + 4025*S^10 - 246*S^12))/(12*S^3*(1 + S^2)^3) + (8*S*(-3767 + 5763*S^2 + 5763*S^4 + 1921*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(21 - 763*S^2 + 1212*S^4 + 273*S^6 + 29*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2, 2, 1}, -S^2]*((53*Pi^4*S*(-231 + 60*S^2 + 60*S^4 + 20*S^6))/(45*(1 + S^2)^3) - (2*(30 + 143*S^2 + 26*S^4 + 15*S^6 + 30*S^8))/(S^3*(1 + S^2)) + (Pi^2*(-69 + 848*S^2 - 6553*S^4 + 10176*S^6 - 3379*S^8 + 504*S^10 - 39*S^12))/(6*S^3*(1 + S^2)^3) + (4*(-161 + 2431*S^2 - 2755*S^4 - 601*S^6 + 42*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{3, 1, 1}, -S^2]*((Pi^4*S*(-62961 + 2595*S^2 + 2595*S^4 + 865*S^6))/(90*(1 + S^2)^3) + (-601 - 4368*S^2 - 3922*S^4 - 1564*S^6 - 257*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-249 + 2490*S^2 - 20471*S^4 + 19672*S^6 - 4071*S^8 + 118*S^10 - 33*S^12))/(6*S^3*(1 + S^2)^3) + (4*(-480 + 7487*S^2 - 8953*S^4 - 2051*S^6 + 85*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^5*((-7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(30*S^3) + (Pi^4*S*(-28177 + 6639*S^2 + 6639*S^4 + 2213*S^6))/(1350*(1 + S^2)^3) + (Pi^2*(-45 + 521*S^2 - 6176*S^4 + 12364*S^6 - 4175*S^8 + 239*S^10))/(90*S^3*(1 + S^2)^3) + ((-2*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(45*(1 + S^2)^3) + (-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10)/(5*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (8*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(15*(1 + S^2)^3) + (2*(-165 + 4426*S^2 - 9882*S^4 - 1452*S^6 + 421*S^8)*HPL[{3}, -S^2])/(15*S*(1 + S^2)^3) - (4*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{4}, -S^2])/(15*(1 + S^2)^3) - (60*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (16*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1}, -S^2])/(15*(1 + S^2)^3) - 120*S*HPL[{2, 1, 1}, -S^2] + (2*(-29 + 642*S^2 - 1614*S^4 - 164*S^6 + 105*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + HPL[{0}, S^2]^5*((-60 - 89*S^2 + 296*S^4 + 181*S^6)/(384*S*(1 + S^2)) - (Pi^4*S*(14626 + 1707*S^2 + 1707*S^4 + 569*S^6))/(21600*(1 + S^2)^3) - (Pi^2*S*(8555 - 3477*S^2 - 123*S^4 + 1293*S^6 + 1320*S^8))/(2880*(1 + S^2)^3) + ((605 - 5844*S^2 + 1024*S^4 - 538*S^6 - 187*S^8)*HPL[{1}, -S^2]^3)/(360*S*(1 + S^2)^3) - (S*(327 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^4)/(90*(1 + S^2)^3) + (-(Pi^2*S*(319 + 78*S^2 + 78*S^4 + 26*S^6))/(180*(1 + S^2)^3) + (-45 - 30*S^2 - 2945*S^4 - 53*S^6 - 1632*S^8 - 173*S^10 + 30*S^12)/(480*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (S*(-76 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^2)/(40*(1 + S^2)^3) + HPL[{1}, -S^2]^2*(-(Pi^2*S*(3093 + 327*S^2 + 327*S^4 + 109*S^6))/(720*(1 + S^2)^3) + (-45 + 710*S^2 - 5930*S^4 + 3100*S^6 - 595*S^8 - 38*S^10 - 90*S^12)/(480*S^3*(1 + S^2)^3) + (S*(-1083 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(120*(1 + S^2)^3)) + ((3 - 4*S^2 + 16*S^4 - 6*S^6 - 5*S^8)*HPL[{3}, -S^2])/(16*S*(1 + S^2)^3) + (S^3*(3 + 3*S^2 + S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^3) + ((-515 + 2229*S^2 - 566*S^4 - 58*S^6)*HPL[{2, 1}, -S^2])/(120*S*(1 + S^2)^3) - (3*S*(-27 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3, 1}, -S^2])/(10*(1 + S^2)^3) + (S*(-541 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(30*(1 + S^2)^3) - (S*(119 + 215*S^2 + 189*S^4 + 57*S^6)*Zeta[3])/(8*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*(1865 - 14664*S^2 - 1496*S^4 - 4108*S^6 - 1237*S^8))/(1440*S*(1 + S^2)^3) + (-4 - 25*S^2 - 57*S^4 - 3*S^6 + 9*S^8)/(64*S^3*(1 + S^2)) + ((280 - 2347*S^2 + 467*S^4 - 264*S^6 - 106*S^8)*HPL[{2}, -S^2])/(120*S*(1 + S^2)^3) + (S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(4*(1 + S^2)^3) - (S*(-1083 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(60*(1 + S^2)^3) - (S*(4 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3)) + Log[T]^5*((5*(1 + S^2))/S - (Pi^4*S*(-14626 + 1707*S^2 + 1707*S^4 + 569*S^6))/(675*(1 + S^2)^3) - (Pi^2*S*(-5107 + 14084*S^2 - 4466*S^4 - 92*S^6 + 45*S^8))/(90*(1 + S^2)^3) - (2*S*(-164 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^4)/(45*(1 + S^2)^3) + (28*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^3) - (112*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^3*((S*(971 - 752*S^2 + 8*S^4 + 51*S^6))/(15*(1 + S^2)^3) - (2*S*(-319 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{1}, -S^2])/(9*(1 + S^2)^3)) + ((-4*Pi^2*S*(-22 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) + (45 + 103*S^2 + 1258*S^4 - 538*S^6 + 137*S^8 - 45*S^10)/(15*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*S*(-82 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((-8*Pi^2*S*(-89 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12)/(S^3*(1 + S^2)^3) + 60*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*(-(Pi^2*S*(-1601 + 327*S^2 + 327*S^4 + 109*S^6))/(45*(1 + S^2)^3) - (S*(-2167 + 4844*S^2 - 1526*S^4 - 92*S^6 + 45*S^8))/(30*(1 + S^2)^3) - (2*(59 - 771*S^2 + 516*S^4 + 86*S^6)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^3) - (8*S*(-33 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(1 + S^2)^3 - (2*S*(-51 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) - (2*(7 + 920*S^2 - 3882*S^4 - 326*S^6 + 269*S^8)*HPL[{3}, -S^2])/(5*S*(1 + S^2)^3) + (8*S*(-89 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{4}, -S^2])/(5*(1 + S^2)^3) + (4*(39 - 232*S^2 - 36*S^4 + 29*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (32*S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - 112*S*HPL[{2, 1, 1}, -S^2] - (4*S*(46 - 336*S^2 - 17*S^4 + 29*S^6)*Zeta[3])/(1 + S^2)^3 + HPL[{0}, S^2]*((9 - 11*S^2 + 6*S^4)/(3*S) + (Pi^2*S*(2406 - 3447*S^2 - 167*S^4 + 226*S^6))/(15*(1 + S^2)^3) + (14*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^3) - (224*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^3) + (2*(-2 + 693*S^2 - 1518*S^4 - 95*S^6 + 102*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((-2*Pi^2*S*(-991 + 303*S^2 + 303*S^4 + 101*S^6))/(9*(1 + S^2)^3) + (3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12)/(S^3*(1 + S^2)^3) - (4*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + (4*S*(-7 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (16*S*(57 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (24*S*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]*((2*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) + (Pi^2*(-265 + 3726*S^2 - 3678*S^4 - 508*S^6 + 105*S^8))/(9*S*(1 + S^2)^3) - (60*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (560*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - 120*S*HPL[{2, 1}, -S^2] + (32*S*(-23 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^3)) + ((-1564*Pi^4*S^3*(3 + 3*S^2 + S^4))/(45*(1 + S^2)^3) + (-48 - 3295*S^2 - 2788*S^4 + 75*S^6)/(8*S*(1 + S^2)) + (Pi^2*S*(-1404 - 5315*S^2 + 1685*S^4 - 1829*S^6 + 159*S^8))/(12*(1 + S^2)^3))*Zeta[5] + HPL[{4}, -S^2]*((-27 - 1197*S^2 - 2774*S^4 - 196*S^6)/(8*S^3) + (Pi^2*(72 - 271*S^2 - 1099*S^4 - 891*S^6 - 39*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(122 - 295*S^2 - 11637*S^4 - 2935*S^6 + 53*S^8))/(180*S*(1 + S^2)^3) + (4*S*(106 + 189*S^2 + 189*S^4 + 63*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(245 + 57*S^2 + 57*S^4 + 19*S^6))/(3*(1 + S^2)^3) + (3 - 21*S^2 - 1243*S^4 + 2610*S^6 - 147*S^8 - 109*S^10 + 27*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(-7 - 235*S^2 + 1576*S^4 + 398*S^6 + 10*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (60*S*(-1 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (8*S*(-73 + 228*S^2 + 228*S^4 + 76*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (2*(1 - 509*S^2 + 3168*S^4 + 859*S^6 + 61*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-305 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-853 + 165*S^2 + 165*S^4 + 55*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (32*S*(133 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-13 + 3*S^2 + 3*S^4 + S^6))/(1 + S^2)^3 + (-6 - 11*S^2 - 106*S^4 - 370*S^6 + 218*S^8 + 5*S^10 + 30*S^12)/(2*S^3*(1 + S^2)^3))*Zeta[3] + (4*S*(37 + 63*S^2 + 63*S^4 + 21*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*((Pi^2*(7 - 45*S^2 - 62*S^4 + 16*S^6))/(24*S^3) + (Pi^4*(98 - 7046*S^2 + 7524*S^4 + 1341*S^6 - 24*S^8))/(120*S*(1 + S^2)^3) + (21 - 596*S^2 + 46*S^4 - 84*S^6 + 21*S^8)/(16*S^3*(1 + S^2)) + (-(Pi^2*S*(-735 + 993*S^2 + 993*S^4 + 331*S^6))/(6*(1 + S^2)^3) + (-3 + 4*S^2 + 205*S^4 - 4472*S^6 + 2995*S^8 - 532*S^10 + 27*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((11 + 280*S^2 - 1011*S^4 - 298*S^6 - 26*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-43 + 162*S^2 + 162*S^4 + 54*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((86*Pi^2*S*(7 + 6*S^2 + 6*S^4 + 2*S^6))/(3*(1 + S^2)^3) + (15 - 227*S^2 + 1814*S^4 - 1574*S^6 + 307*S^8 - 15*S^10)/(2*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((95 - 503*S^2 + 719*S^4 + 337*S^6 + 28*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (10*S*(-113 + 177*S^2 + 177*S^4 + 59*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (2*S*(-1967 + 2847*S^2 + 2847*S^4 + 949*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + ((-159 + 227*S^2 - 207*S^4 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (16*S*(-181 + 102*S^2 + 102*S^4 + 34*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(-2911 + 579*S^2 + 579*S^4 + 193*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + 1232*S*HPL[{2, 1, 1, 1}, -S^2] + (-((Pi^2*S*(-89 + 162*S^2 + 162*S^4 + 54*S^6))/(1 + S^2)^3) + (3 + 20*S^2 + 15*S^4 - 2920*S^6 + 2805*S^8 - 516*S^10 + 33*S^12)/(4*S^3*(1 + S^2)^3))*Zeta[3] - (14*S*(-29 + 66*S^2 + 66*S^4 + 22*S^6)*Zeta[5])/(1 + S^2)^3) + Log[T]^4*((-18*(1 + S^2))/S + (Pi^2*(-30 - 101*S^2 - 38*S^4 + 9*S^6))/(12*S*(1 + S^2)) + (Pi^4*S*(-52786 + 46537*S^2 + 8341*S^4 + 188*S^6))/(540*(1 + S^2)^3) - (S*(164 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^5)/(45*(1 + S^2)^3) - (35*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)^3) + (112*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^4*(-(S*(1444 - 517*S^2 + 38*S^4 + 19*S^6))/(36*(1 + S^2)^3) + (5*S*(-131 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(18*(1 + S^2)^3)) + ((83 - 2668*S^2 + 3090*S^4 + 596*S^6 - 25*S^8)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((40*Pi^2*S*(-89 + 27*S^2 + 27*S^4 + 9*S^6))/(9*(1 + S^2)^3) - (5*(3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12))/(3*S^3*(1 + S^2)^3) - 100*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^3*((Pi^2*S*(-703 + 129*S^2 + 129*S^4 + 43*S^6))/(27*(1 + S^2)^3) - (S*(362 - 544*S^2 + 209*S^4 - 2*S^6 + 3*S^8))/(6*(1 + S^2)^3) + ((270 - 3142*S^2 + 1824*S^4 + 129*S^6 - 67*S^8)*HPL[{1}, -S^2])/(9*S*(1 + S^2)^3) + (5*S*(-319 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{1}, -S^2]^2)/(9*(1 + S^2)^3) + (S*(-667 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{2}, -S^2])/(9*(1 + S^2)^3)) + ((-2*Pi^2*S*(-747 + 1059*S^2 + 1059*S^4 + 353*S^6))/(9*(1 + S^2)^3) + (-9 - 19*S^2 - 110*S^4 - 4842*S^6 + 3011*S^8 - 611*S^10 + 36*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(-4 - 145*S^2 + 782*S^4 + 215*S^6 + 12*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-119 + 327*S^2 + 327*S^4 + 109*S^6)*HPL[{5}, -S^2])/(3*(1 + S^2)^3) + ((4*Pi^2*S*(619 + 552*S^2 + 552*S^4 + 184*S^6))/(9*(1 + S^2)^3) + (45 - 469*S^2 + 4166*S^4 - 3446*S^6 + 709*S^8 - 45*S^10)/(3*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(185 - 756*S^2 + 1938*S^4 + 734*S^6 + 15*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-373 + 621*S^2 + 621*S^4 + 207*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (8*S*(-1981 + 2967*S^2 + 2967*S^4 + 989*S^6)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) + (20*(-9 - 8*S^2 - 24*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (32*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) + (64*S*(-121 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + 1760*S*HPL[{2, 1, 1, 1}, -S^2] + ((-4*Pi^2*S*(-281 + 552*S^2 + 552*S^4 + 184*S^6))/(9*(1 + S^2)^3) + (S*(-15 - 3064*S^2 + 2962*S^4 - 664*S^6 + 45*S^8))/(3*(1 + S^2)^3))*Zeta[3] + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) - (5*Pi^2*(-265 + 3726*S^2 - 3678*S^4 - 508*S^6 + 105*S^8))/(18*S*(1 + S^2)^3) + (150*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (1400*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + 300*S*HPL[{2, 1}, -S^2] - (80*S*(-23 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{0}, S^2]^2*((-15 - 71*S^2 - 23*S^4 + 9*S^6)/(4*S*(1 + S^2)) - (Pi^2*S*(6308 - 4514*S^2 - 539*S^4 + 23*S^6))/(36*(1 + S^2)^3) + (5*(59 - 771*S^2 + 516*S^4 + 86*S^6)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)^3) + (40*S*(-33 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^3) + ((19 - 2817*S^2 + 2830*S^4 + 449*S^6 + 3*S^8)*HPL[{2}, -S^2])/(6*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((5*Pi^2*S*(-329 + 39*S^2 + 39*S^4 + 13*S^6))/(9*(1 + S^2)^3) + (-45 + 472*S^2 - 5737*S^4 + 8948*S^6 - 1735*S^8 - 92*S^10 + 45*S^12)/(12*S^3*(1 + S^2)^3) + (S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) - (2*S*(-27 + 69*S^2 + 69*S^4 + 23*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (4*S*(454 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (4*S*(-26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-9 - 111*S^2 - 17*S^4 + 9*S^6)/(2*S^3) + (Pi^2*(-58 - 1536*S^2 + 1175*S^4 + 52*S^6 + 9*S^8))/(9*S*(1 + S^2)^3) - (4*S*(-183 + 321*S^2 + 321*S^4 + 107*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (16*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (8*S*(-289 + 438*S^2 + 438*S^4 + 146*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((-7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(6*S^3) + (Pi^4*S*(-28177 + 6639*S^2 + 6639*S^4 + 2213*S^6))/(270*(1 + S^2)^3) + (Pi^2*(-45 + 521*S^2 - 6176*S^4 + 12364*S^6 - 4175*S^8 + 239*S^10))/(18*S^3*(1 + S^2)^3) + ((-2*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) + (-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10)/(S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (8*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + (2*(-165 + 4426*S^2 - 9882*S^4 - 1452*S^6 + 421*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) - (300*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (16*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) - 600*S*HPL[{2, 1, 1}, -S^2] + (10*(-29 + 642*S^2 - 1614*S^4 - 164*S^6 + 105*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + HPL[{0}, S^2]*((-75 - 58*S^2 - 63*S^4)/(6*S) + (Pi^4*S*(-11971 + 6258*S^2 + 6258*S^4 + 2086*S^6))/(270*(1 + S^2)^3) - (Pi^2*S*(1479 - 3718*S^2 + 1868*S^4 - 194*S^6 + 21*S^8))/(12*(1 + S^2)^3) - (70*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^3) + (280*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^3) + ((2*Pi^2*S*(-971 + 732*S^2 + 732*S^4 + 244*S^6))/(9*(1 + S^2)^3) + (-45 - 50*S^2 - 2239*S^4 + 6112*S^6 - 4479*S^8 + 570*S^10 - 45*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (4*S*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((5*Pi^2*S*(-991 + 303*S^2 + 303*S^4 + 101*S^6))/(9*(1 + S^2)^3) - (5*(3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12))/(2*S^3*(1 + S^2)^3) + (10*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + ((53 + 38*S^2 - 614*S^4 - 324*S^6 - 85*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-17 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (10*(-146 + 1221*S^2 - 810*S^4 - 143*S^6 + 18*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-1277 + 1209*S^2 + 1209*S^4 + 403*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + (40*S*(-85 + 81*S^2 + 81*S^4 + 27*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*S*(-96 + 357*S^2 + 103*S^4 + 10*S^6)*Zeta[3])/(1 + S^2)^3 + HPL[{1}, -S^2]*((-5*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) + (Pi^2*(1275 - 17204*S^2 + 16878*S^4 + 1938*S^6 - 659*S^8))/(18*S*(1 + S^2)^3) - (10*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-53 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (20*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-317 + 129*S^2 + 129*S^4 + 43*S^6)*Zeta[3])/(3*(1 + S^2)^3))) - (40*S*(-50 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{0}, S^2]^4*((-432 - 4159*S^2 - 127*S^4)/(384*S) + (Pi^2*(-90 - 3131*S^2 - 3905*S^4 - 888*S^6))/(576*S*(1 + S^2)) + (Pi^4*S*(-63667 - 10415*S^2 - 4151*S^4 + 1907*S^6))/(8640*(1 + S^2)^3) + ((525 - 5762*S^2 + 1680*S^4 + 42*S^6 - 5*S^8)*HPL[{1}, -S^2]^4)/(144*S*(1 + S^2)^3) + (S*(-131 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^5)/(18*(1 + S^2)^3) - (S*(1051 - 625*S^2 - 43*S^4 + 7*S^6)*HPL[{2}, -S^2]^2)/(48*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-5*Pi^2*S*(541 + 39*S^2 + 39*S^4 + 13*S^6))/(216*(1 + S^2)^3) + (-45 + 520*S^2 - 5359*S^4 + 4166*S^6 - 715*S^8 - 218*S^10 + 27*S^12)/(144*S^3*(1 + S^2)^3) - (2*S*(137 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(9*(1 + S^2)^3)) + (-(Pi^2*S*(9 + 33*S^2 + 33*S^4 + 11*S^6))/(24*(1 + S^2)^3) + (-3 - 3*S^2 - 90*S^4 - 82*S^6 + 5*S^8 - 19*S^10)/(16*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((3 - 77*S^2 - 23*S^4 + 11*S^6)*HPL[{4}, -S^2])/(8*S*(1 + S^2)^2) - (S*(10 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{5}, -S^2])/(2*(1 + S^2)^3) + ((2*Pi^2*S*(67 + 9*S^2 + 9*S^4 + 3*S^6))/(9*(1 + S^2)^3) + (45 - 394*S^2 + 3097*S^4 - 907*S^6 - 28*S^8 + 69*S^10 + 6*S^12)/(48*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(30 - 2764*S^2 - 185*S^4 - 602*S^6 - 139*S^8))/(144*S*(1 + S^2)^3) + (-27 - 318*S^2 - 322*S^4 - 95*S^6 + 56*S^8)/(96*S^3*(1 + S^2)) + (S*HPL[{3}, -S^2])/(2*(1 + S^2)^3) + (S*(277 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)^3)) + ((-33 + 2288*S^2 - 866*S^4 - 14*S^6 - 7*S^8)*HPL[{3, 1}, -S^2])/(24*S*(1 + S^2)^3) - (S*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (3*S*(1 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{4, 1}, -S^2])/(2*(1 + S^2)^3) + ((30 - 2363*S^2 + 815*S^4 - 94*S^6 - 38*S^8)*HPL[{2, 1, 1}, -S^2])/(12*S*(1 + S^2)^3) - (S*(277 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) - (S*(557 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 1, 1}, -S^2])/(2*(1 + S^2)^3) + (2*S*(281 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (-(Pi^2*S*(281 + 552*S^2 + 552*S^4 + 184*S^6))/(36*(1 + S^2)^3) + (S*(-1361 - 2441*S^2 - 1851*S^4 - 575*S^6 + 84*S^8))/(48*(1 + S^2)^3))*Zeta[3] + HPL[{1}, -S^2]^2*((-60 - 381*S^2 - 835*S^4 - 507*S^6 - 89*S^8)/(192*S^3*(1 + S^2)) + (Pi^2*(1245 - 12752*S^2 + 1200*S^4 - 708*S^6 - 65*S^8))/(288*S*(1 + S^2)^3) + ((258 - 2454*S^2 + 529*S^4 - 23*S^6)*HPL[{2}, -S^2])/(24*S*(1 + S^2)^3) - (S*(1 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2])/(2*(1 + S^2)^3) + (2*S*(137 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (S*(33 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(6*(1 + S^2)^3)) + HPL[{1}, -S^2]*(-(Pi^4*S*(2167 + 570*S^2 + 570*S^4 + 190*S^6))/(432*(1 + S^2)^3) + (-21 - 105*S^2 - 209*S^4 - 135*S^6 - 26*S^8)/(32*S^3*(1 + S^2)) + (Pi^2*(-45 + 890*S^2 - 6377*S^4 + 2458*S^6 - 1415*S^8 - 544*S^10 + 81*S^12))/(288*S^3*(1 + S^2)^3) + (-(Pi^2*S*(1073 + 147*S^2 + 147*S^4 + 49*S^6))/(72*(1 + S^2)^3) + (-45 + 155*S^2 - 2810*S^4 + 1016*S^6 - 469*S^8 - 131*S^10 + 12*S^12)/(48*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (S*(-267 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{2}, -S^2]^2)/(12*(1 + S^2)^3) + ((11 - 66*S^2 - 130*S^4 - 20*S^6 + 9*S^8)*HPL[{3}, -S^2])/(8*S*(1 + S^2)^3) - 3*S*HPL[{4}, -S^2] + ((-258 + 2454*S^2 - 529*S^4 + 23*S^6)*HPL[{2, 1}, -S^2])/(12*S*(1 + S^2)^3) + (5*S*(54 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) - (4*S*(137 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + ((77 - 686*S^2 - 836*S^4 - 210*S^6 + 31*S^8)*Zeta[3])/(24*S*(1 + S^2)^3)) - (5*S*(50 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[5])/(6*(1 + S^2)^3)) + Zeta[3]*((-1847*Pi^6*S^3*(3 + 3*S^2 + S^4))/(567*(1 + S^2)^3) + (Pi^2*(-24 - 2157*S^2 - 1472*S^4 + 85*S^6))/(48*S*(1 + S^2)) + (147 - 3493*S^2 - 2523*S^4 + 349*S^6)/(8*S*(1 + S^2)) + (Pi^4*S*(-11278 - 44189*S^2 + 9271*S^4 - 10491*S^6 + 975*S^8))/(720*(1 + S^2)^3) + (2*S*(-311 + S^2 + 264*S^4 + 132*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(417 + 802*S^2 + 417*S^4))/(48*S^3) + (Pi^4*(7808 - 104629*S^2 + 82905*S^4 + 11207*S^6 - 1795*S^8))/(1080*S*(1 + S^2)^3) + (Pi^2*(-127 - 274*S^2 - 518*S^4 - 114*S^6 - 31*S^8))/(144*S^3*(1 + S^2)) + ((343 - 4976*S^2 + 6198*S^4 + 856*S^6 - 221*S^8)*HPL[{2}, -S^2]^2)/(6*S*(1 + S^2)^3) + (-(Pi^2*S*(-1821 + 1137*S^2 + 1137*S^4 + 379*S^6))/(9*(1 + S^2)^3) + (-18 - 78*S^2 + 375*S^4 - 5182*S^6 + 2416*S^8 - 340*S^10 + 27*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(-11 + 773*S^2 - 1794*S^4 - 407*S^6 + 11*S^8)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^3) - (2*S*(-111 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) + (15 - 61*S^2 + 904*S^4 - 664*S^6 + 141*S^8 - 15*S^10)/(S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(89 - 275*S^2 - 1842*S^4 - 298*S^6 + 100*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) + (8*S*(-2477 + 1479*S^2 + 1479*S^4 + 493*S^6)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) + (300*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) + (16*S*(-1441 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^3) + 600*S*HPL[{2, 1, 1, 1}, -S^2] + (-(Pi^2*S*(-1523 + 1011*S^2 + 1011*S^4 + 337*S^6))/(9*(1 + S^2)^3) + (-49 + 439*S^2 - 3416*S^4 + 2440*S^6 - 331*S^8 + 45*S^10)/(3*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((2*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(1051 - 9932*S^2 - 882*S^4 + 148*S^6 + 487*S^8))/(36*S*(1 + S^2)^3) - (2*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (16*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (8*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(3*(1 + S^2)^3)) - (4*S*(-691 + 537*S^2 + 537*S^4 + 179*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((107 + 3349*S^2 + 1774*S^4 + 116*S^6)/(8*S^3) + (Pi^4*(369 + 21575*S^2 - 10567*S^4 - 227*S^6 - 296*S^8))/(180*S*(1 + S^2)^3) + (Pi^2*(16 + 406*S^2 + 533*S^4 + 121*S^6 - 34*S^8))/(6*S^3*(1 + S^2)) - (64*S*(-79 + 117*S^2 + 117*S^4 + 39*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (16*S*(-939 + 1455*S^2 + 1455*S^4 + 485*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (4*(-215 + 5714*S^2 - 5592*S^4 - 1010*S^6 + 71*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (24*S*(5 + 351*S^2 + 351*S^4 + 117*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (64*S*(-1385 + 477*S^2 + 477*S^4 + 159*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-703 + 501*S^2 + 501*S^4 + 167*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-665 + 963*S^2 + 963*S^4 + 321*S^6))/(3*(1 + S^2)^3) - (2*(3 - 2*S^2 + 61*S^4 - 1782*S^6 + 1477*S^8 - 244*S^10 + 15*S^12))/(S^3*(1 + S^2)^3))*Zeta[3] + (4*S*(-523 + 861*S^2 + 861*S^4 + 287*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((9 - 5287*S^2 - 2137*S^4 - 9*S^6)/(8*S^3) + (Pi^2*(-42 - 619*S^2 - 704*S^4 - 84*S^6 + 55*S^8))/(6*S^3*(1 + S^2)) + (Pi^4*(-349 - 51788*S^2 + 31545*S^4 + 2013*S^6 + 269*S^8))/(180*S*(1 + S^2)^3) + 4928*S*HPL[{2, 2, 1}, -S^2] + (96*S*(337 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (128*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(-317 + 483*S^2 + 483*S^4 + 161*S^6))/(3*(1 + S^2)^3) + (2*(3 + 2*S^2 + 121*S^4 - 3418*S^6 + 2875*S^8 - 512*S^10 + 33*S^12))/(S^3*(1 + S^2)^3))*Zeta[3] - (8*S*(-493 + 945*S^2 + 945*S^4 + 315*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{3}, -S^2]*(-(Pi^6*S*(-23115 + 44553*S^2 + 44553*S^4 + 14851*S^6))/(7560*(1 + S^2)^3) + (Pi^2*(51 - 1228*S^2 - 2598*S^4 - 924*S^6 + 299*S^8))/(48*S^3*(1 + S^2)) + (-33 - 1796*S^2 - 4881*S^4 - 1266*S^6 + 316*S^8)/(8*S^3*(1 + S^2)) + (Pi^4*(-123 - 204*S^2 - 3974*S^4 - 21958*S^6 + 10705*S^8 - 3010*S^10 + 204*S^12))/(360*S^3*(1 + S^2)^3) + ((10*Pi^2*S*(-9 + 6*S^2 + 6*S^4 + 2*S^6))/(3*(1 + S^2)^3) + (-3 + 37*S^2 + 239*S^4 + 715*S^6 - 244*S^8 + 16*S^10 - 24*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((-5 + 430*S^2 + 562*S^4 + 198*S^6 - 13*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - (4*S*(84 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 + (2*S*(-1433 + 1869*S^2 + 1869*S^4 + 623*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((4*Pi^2*S*(-298 + 489*S^2 + 489*S^4 + 163*S^6))/(3*(1 + S^2)^3) + (-3 - 8*S^2 + 113*S^4 + 3510*S^6 - 3033*S^8 + 518*S^10 - 33*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((43 + 476*S^2 - 2266*S^4 - 792*S^6 - 109*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + (2*(-28 + 87*S^2 - 196*S^4 + 200*S^6 + 103*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-32 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 + (8*S*(26 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-385 + 681*S^2 + 681*S^4 + 227*S^6))/(1 + S^2)^3 + (2*(7 - 108*S^2 - 3538*S^4 + 2944*S^6 - 557*S^8 + 36*S^10))/(S*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(181 - 3127*S^2 + 3795*S^4 + 945*S^6 + 10*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (4*(546 - 9128*S^2 + 10473*S^4 + 2592*S^6 + 13*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 12*S*HPL[{3, 1, 2}, -S^2] - (20*S*(-221 + 369*S^2 + 369*S^4 + 123*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-41017 + 61437*S^2 + 61437*S^4 + 20479*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 - (8*(-187 + 2891*S^2 - 2786*S^4 - 603*S^6 + 41*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-1113 + 1893*S^2 + 1893*S^4 + 631*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (96*S*(-183 + 321*S^2 + 321*S^4 + 107*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((Pi^2*(1 + 125*S^2 - 386*S^4 - 163*S^6 - 37*S^8))/(3*S*(1 + S^2)^3) + (6 + 22*S^2 + 48*S^4 + 9*S^6 + S^8)/(S^3*(1 + S^2)))*Zeta[3] - (2*S*(-23 + 63*S^2 + 63*S^4 + 21*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{2, 1}, -S^2]*((Pi^2*(190 - 3062*S^2 + 2897*S^4 + 577*S^6 - 64*S^8))/(3*S*(1 + S^2)^3) + (31 + 658*S^2 + 352*S^4 - 302*S^6 + 21*S^8)/(4*S^3*(1 + S^2)) - (4*S*(97 + 63*S^2 + 63*S^4 + 21*S^6)*Zeta[3])/(1 + S^2)^3) - (2*(-2 - 11*S^2 + 399*S^4 + 151*S^6 + 31*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((349 + 3381*S^2 + 3019*S^4 - 349*S^6)/(8*S^3) + (Pi^6*S*(174037 + 70320*S^2 + 70320*S^4 + 23440*S^6))/(11340*(1 + S^2)^3) + (Pi^2*(206 + 1691*S^2 + 2164*S^4 + 737*S^6 - 86*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(1278 - 10114*S^2 + 92938*S^4 - 31577*S^6 - 19479*S^8 + 7547*S^10 - 561*S^12))/(720*S^3*(1 + S^2)^3) + ((674*Pi^2*S*(-7 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) - (2*(15 - 205*S^2 + 1479*S^4 - 3298*S^6 + 1677*S^8 - 265*S^10 + 21*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (2*(337 - 5779*S^2 + 6930*S^4 + 1733*S^6 + 15*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + (2*(-1085 + 18253*S^2 - 19602*S^4 - 4811*S^6 + S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-109 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 + (4*S*(1331 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((16*Pi^2*S*(-599 + 225*S^2 + 225*S^4 + 75*S^6))/(3*(1 + S^2)^3) - (4*(18 - 207*S^2 + 1642*S^4 - 3274*S^6 + 1546*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (4*(-159 + 227*S^2 - 207*S^4 + 11*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (4*(103 + 5578*S^2 - 5632*S^4 - 618*S^6 + 49*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (12*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-2599 + 1515*S^2 + 1515*S^4 + 505*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 - (32*S*(-953 + 651*S^2 + 651*S^4 + 217*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (16*(-83 + 2668*S^2 - 3090*S^4 - 596*S^6 + 25*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-703 + 501*S^2 + 501*S^4 + 167*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (128*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((12 + 101*S^2 + 64*S^4 - 36*S^6 + S^8)/(S^3*(1 + S^2)) + (Pi^2*(150 - 2816*S^2 + 3707*S^4 + 953*S^6 + 16*S^8))/(3*S*(1 + S^2)^3))*Zeta[3] + 40*S*Zeta[3]^2 - (2*(-97 + 2022*S^2 - 3587*S^4 - 805*S^6 + 53*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(307 + 1070*S^2 + 307*S^4))/(12*S^3) + (11*Pi^6*S*(-105451 + 16287*S^2 + 16287*S^4 + 5429*S^6))/(68040*(1 + S^2)^3) + (Pi^2*(-255 - 981*S^2 - 1837*S^4 - 703*S^6 - 120*S^8))/(72*S^3*(1 + S^2)) + (Pi^4*(-624 + 6423*S^2 - 75934*S^4 + 122755*S^6 - 37642*S^8 + 144*S^10 + 402*S^12))/(1080*S^3*(1 + S^2)^3) + ((Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(9*(1 + S^2)^3) + (-18 + 247*S^2 - 3086*S^4 + 7226*S^6 - 3070*S^8 + 255*S^10 - 18*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (62*S*HPL[{2}, -S^2]^3)/3 + (2*S*(-275 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{3}, -S^2]^2)/(3*(1 + S^2)^3) + (-(Pi^2*S*(-1193 + 837*S^2 + 837*S^4 + 279*S^6))/(9*(1 + S^2)^3) - (2*(18 - 7*S^2 + 152*S^4 + 2562*S^6 - 346*S^8 + 149*S^10))/(3*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(103 + 302*S^2 - 3426*S^4 - 878*S^6 + 11*S^8)*HPL[{5}, -S^2])/(3*S*(1 + S^2)^3) - (2*S*(67 + 849*S^2 + 849*S^4 + 283*S^6)*HPL[{6}, -S^2])/(3*(1 + S^2)^3) - (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^3) + ((8*Pi^2*S*(309 + 183*S^2 + 183*S^4 + 61*S^6))/(9*(1 + S^2)^3) - (2*(-54 + 91*S^2 - 2336*S^4 - 3138*S^6 + 1762*S^8 - 425*S^10 + 36*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)^3) - (4*(-493 + 12568*S^2 - 27762*S^4 - 3940*S^6 + 1243*S^8)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)^3) + (6*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 + (16*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{5, 1}, -S^2])/(3*(1 + S^2)^3) + ((-8*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) + (4*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)^3) - (16*(-432 + 5251*S^2 - 4356*S^4 - 558*S^6 + 121*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)^3) - 496*S*HPL[{3, 2, 1}, -S^2] - (32*S*(-161 + 597*S^2 + 597*S^4 + 199*S^6)*HPL[{4, 1, 1}, -S^2])/(3*(1 + S^2)^3) - (1200*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (64*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*(1 + S^2)^3) - 2400*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-7 - 194*S^2 - 598*S^4 - 34*S^6 + 89*S^8)/(6*S^3*(1 + S^2)) + (2*Pi^2*(-25 + 580*S^2 - 1511*S^4 - 160*S^6 + 96*S^8))/(3*S*(1 + S^2)^3))*Zeta[3] + (8*S*(-37 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3]^2)/(3*(1 + S^2)^3) + HPL[{3}, -S^2]*((-17 - 672*S^2 - 1214*S^4 - 432*S^6 + 79*S^8)/(6*S^3*(1 + S^2)) + (Pi^2*(-135 + 4474*S^2 - 10640*S^4 - 1608*S^6 + 441*S^8))/(9*S*(1 + S^2)^3) + (8*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (112*S*(-7 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-8*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(-1051 + 9932*S^2 + 882*S^4 - 148*S^6 - 487*S^8))/(9*S*(1 + S^2)^3) + (32*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-135 - 1583*S^2 - 785*S^4 + 135*S^6)/(12*S^3) - (Pi^4*S*(28217 + 3411*S^2 + 3411*S^4 + 1137*S^6))/(540*(1 + S^2)^3) + (Pi^2*(-90 + 321*S^2 - 5585*S^4 + 2317*S^6 + 779*S^8 - 502*S^10 + 72*S^12))/(18*S^3*(1 + S^2)^3) + (2*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (2*S*(-847 + 339*S^2 + 339*S^4 + 113*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) - (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (2*(-151 + 3632*S^2 - 8118*S^4 - 1048*S^6 + 413*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + (4*(-54 + 1295*S^2 - 4545*S^4 - 279*S^6 + 395*S^8)*Zeta[5])/(3*S*(1 + S^2)^3)) + HPL[{0}, S^2]^3*((-708 - 4435*S^2 - 2522*S^4 - 331*S^6)/(96*S*(1 + S^2)) - (Pi^6*S*(5767 + 123*S^2 + 123*S^4 + 41*S^6))/(2592*(1 + S^2)^3) + (Pi^2*(-289 - 977*S^2 + 288*S^4 + 472*S^6))/(288*S*(1 + S^2)) - (Pi^4*S*(44809 - 26648*S^2 + 7440*S^4 + 4960*S^6 + 5007*S^8))/(4320*(1 + S^2)^3) + ((270 - 3142*S^2 + 1824*S^4 + 129*S^6 - 67*S^8)*HPL[{1}, -S^2]^5)/(45*S*(1 + S^2)^3) + (S*(-319 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{1}, -S^2]^6)/(27*(1 + S^2)^3) + ((Pi^2*S*(-1087 + 261*S^2 + 261*S^4 + 87*S^6))/(72*(1 + S^2)^3) + (-3 - 18*S^2 - 1789*S^4 + 2850*S^6 - 1039*S^8 + 24*S^10 - 9*S^12)/(48*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (7*S*(-1 + S^2)*(7 + 4*S^2 + S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*((Pi^2*S*(-2903 + 243*S^2 + 243*S^4 + 81*S^6))/(108*(1 + S^2)^3) + (-21 + 226*S^2 - 2669*S^4 + 3020*S^6 - 739*S^8 + 30*S^10 - 15*S^12)/(36*S^3*(1 + S^2)^3) + (2*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + (S*(25 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3}, -S^2]^2)/(6*(1 + S^2)^3) + ((Pi^2*S*(-33 + 111*S^2 + 111*S^4 + 37*S^6))/(18*(1 + S^2)^3) + (-27 - 42*S^2 - 675*S^4 - 916*S^6 - 941*S^8 - 42*S^10 + 3*S^12)/(24*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((35 + 184*S^2 + 484*S^4 - 158*S^6 - 157*S^8)*HPL[{5}, -S^2])/(12*S*(1 + S^2)^3) + (S*(23 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 - (S*(-631 + 243*S^2 + 243*S^4 + 81*S^6)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^3) + (-(Pi^2*S*(-1147 + 369*S^2 + 369*S^4 + 123*S^6))/(18*(1 + S^2)^3) + (27 + 30*S^2 + 1126*S^4 - 1087*S^6 + 776*S^8 - 3*S^10 + 3*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((33 + 610*S^4 + 188*S^6 + 25*S^8)*HPL[{3, 2}, -S^2])/(12*S*(1 + S^2)^3) + ((-19 + 112*S^2 + 638*S^4 + 384*S^6 + 117*S^8)*HPL[{4, 1}, -S^2])/(6*S*(1 + S^2)^3) - (2*S*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(3*(1 + S^2)^3) - (2*S*(-19 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{5, 1}, -S^2])/(3*(1 + S^2)^3) + ((4*Pi^2*S*(-302 + 63*S^2 + 63*S^4 + 21*S^6))/(9*(1 + S^2)^3) + (-24 - 20*S^2 - 1103*S^4 + 1182*S^6 - 697*S^8 + 8*S^10 - 6*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + ((479 - 2881*S^2 + 1065*S^4 + 127*S^6 - 26*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)^3) + ((1481 - 8807*S^2 + 3127*S^4 + 261*S^6 - 122*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)^3) + (2*S*HPL[{3, 1, 2}, -S^2])/3 + (2*S*(-587 + 255*S^2 + 255*S^4 + 85*S^6)*HPL[{3, 2, 1}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-915 + 399*S^2 + 399*S^4 + 133*S^6)*HPL[{4, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (2*(-521 + 3070*S^2 - 1030*S^4 - 84*S^6 + 37*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-661 + 261*S^2 + 261*S^4 + 87*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (8*S*(-667 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*(1 + S^2)^3) + ((S*(-230 - 25*S^2 + 193*S^4))/(24*(1 + S^2)) - (Pi^2*S*(1964 + 3721*S^2 + 3145*S^4 + 932*S^6))/(36*(1 + S^2)^3))*Zeta[3] - (14*S*Zeta[3]^2)/(1 + S^2)^3 + HPL[{3}, -S^2]*((-39 - 337*S^2 - 261*S^4 - 19*S^6)/(48*S^3) + (Pi^2*(89 - 224*S^2 + 172*S^4 - 210*S^6 - 119*S^8))/(72*S*(1 + S^2)^3) - (2*S*(27 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (4*S*(3 + 6*S^2 + 6*S^4 + 2*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((Pi^2*(-1036 + 5299*S^2 - 1596*S^4 - 142*S^6 + 37*S^8))/(36*S*(1 + S^2)^3) + (42 + 476*S^2 + 477*S^4 + 236*S^6 + 49*S^8)/(24*S^3*(1 + S^2)) + (4*S*(1 + 18*S^2 + 18*S^4 + 6*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]*(-(Pi^4*S*(4021 + 39*S^2 + 39*S^4 + 13*S^6))/(540*(1 + S^2)^3) + (-101 - 569*S^2 - 774*S^4 - 455*S^6 - 5*S^8)/(48*S^3*(1 + S^2)) + (Pi^2*(-93 - 70*S^2 - 5151*S^4 + 2311*S^6 - 3026*S^8 - 157*S^10 + 18*S^12))/(144*S^3*(1 + S^2)^3) + ((-8 + 4*S^2 - 147*S^4 - 45*S^6 - 6*S^8)*HPL[{3}, -S^2])/(6*S*(1 + S^2)^3) - (2*S*(13 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + ((-479 + 2881*S^2 - 1065*S^4 - 127*S^6 + 26*S^8)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)^3) - (2*S*(-321 + 105*S^2 + 105*S^4 + 35*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + (2*S*(-631 + 243*S^2 + 243*S^4 + 81*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) - (S*(146 + 325*S^2 + 133*S^4 + 14*S^6)*Zeta[3])/(6*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((Pi^2*(1145 - 12128*S^2 + 4672*S^4 - 280*S^6 - 321*S^8))/(108*S*(1 + S^2)^3) + (-43 - 240*S^2 - 534*S^4 - 304*S^6 - 15*S^8)/(72*S^3*(1 + S^2)) + ((551 - 5580*S^2 + 3126*S^4 + 80*S^6 - 177*S^8)*HPL[{2}, -S^2])/(18*S*(1 + S^2)^3) - (8*S*HPL[{3}, -S^2])/(1 + S^2)^3 - (8*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (2*S*(-11 + 51*S^2 + 51*S^4 + 17*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-(Pi^4*S*(9875 + 21*S^2 + 21*S^4 + 7*S^6))/(540*(1 + S^2)^3) + (-92 - 377*S^2 - 983*S^4 - 467*S^6 - 57*S^8)/(48*S^3*(1 + S^2)) + (Pi^2*(-87 + 1162*S^2 - 11268*S^4 + 9140*S^6 - 2073*S^8 + 22*S^10 - 120*S^12))/(144*S^3*(1 + S^2)^3) + ((Pi^2*S*(-2511 + 219*S^2 + 219*S^4 + 73*S^6))/(36*(1 + S^2)^3) + (-93 + 312*S^2 - 5681*S^4 + 3858*S^6 - 2025*S^8 - 2*S^10 - 33*S^12)/(24*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (S*(-337 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + ((20 - 65*S^2 - 21*S^4 - 73*S^6 - 29*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (S*(-69 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + ((-551 + 5580*S^2 - 3126*S^4 - 80*S^6 + 177*S^8)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)^3) - (4*S*(-355 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + (8*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((21 - 54*S^2 - 272*S^4 - 143*S^6 - 30*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) - (2*S*(425 + 847*S^2 + 781*S^4 + 242*S^6)*Zeta[5])/(3*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^4*(9805 - 87392*S^2 + 11732*S^4 - 15066*S^6 - 5579*S^8))/(2160*S*(1 + S^2)^3) + (-160 - 479*S^2 - 1529*S^4 - 597*S^6 - 155*S^8)/(48*S^3*(1 + S^2)) + (Pi^2*(-103 - 615*S^2 - 1389*S^4 - 349*S^6 + 120*S^8))/(288*S^3*(1 + S^2)) + ((237 - 2620*S^2 + 1620*S^4 + 158*S^6 - 47*S^8)*HPL[{2}, -S^2]^2)/(12*S*(1 + S^2)^3) + ((Pi^2*S*(-27 + 15*S^2 + 15*S^4 + 5*S^6))/(6*(1 + S^2)^3) + (-13 - 6*S^2 - 159*S^4 - 222*S^6 - 167*S^8 - 16*S^10 - S^12)/(4*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((51 - 158*S^2 + 204*S^4 - 164*S^6 - 97*S^8)*HPL[{4}, -S^2])/(6*S*(1 + S^2)^3) + (S*(-15 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{5}, -S^2])/(3*(1 + S^2)^3) + (-(Pi^2*S*(-2511 + 219*S^2 + 219*S^4 + 73*S^6))/(18*(1 + S^2)^3) + (93 - 312*S^2 + 5681*S^4 - 3858*S^6 + 2025*S^8 + 2*S^10 + 33*S^12)/(12*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-277 + 2750*S^2 - 1578*S^4 - 12*S^6 + 105*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) + (2*S*(-39 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) - (16*S*(6 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) + ((551 - 5580*S^2 + 3126*S^4 + 80*S^6 - 177*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-337 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) + (8*S*(-343 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(229 + 231*S^2 + 231*S^4 + 77*S^6))/(18*(1 + S^2)^3) + (82 - 433*S^2 - 602*S^4 + 262*S^6 + 68*S^8 - 57*S^10)/(12*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1111 - 10274*S^2 + 4060*S^4 - 448*S^6 - 389*S^8))/(72*S*(1 + S^2)^3) + (-107 - 882*S^2 - 944*S^4 - 486*S^6 - 29*S^8)/(48*S^3*(1 + S^2)) - (S*(-39 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (4*S*(-337 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (S*(3 + 69*S^2 + 69*S^4 + 23*S^6)*Zeta[3])/(3*(1 + S^2)^3)) - (4*S*(53 + 42*S^2 + 42*S^4 + 14*S^6)*Zeta[5])/(3*(1 + S^2)^3))) + Log[T]^3*((629*(1 + S^2))/(12*S) + (Pi^2*(301 + 1162*S^2 + 548*S^4 - 49*S^6))/(36*S*(1 + S^2)) - (Pi^6*S*(-5767 + 123*S^2 + 123*S^4 + 41*S^6))/(324*(1 + S^2)^3) - (Pi^4*S*(-63886 + 135867*S^2 - 48547*S^4 - 4031*S^6 + 1149*S^8))/(1080*(1 + S^2)^3) + (S*(25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2]^6)/(18*(1 + S^2)^3) + (28*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)^3) - (224*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^6)/(9*(1 + S^2)^3) + HPL[{0}, S^2]^5*((S*(3185 - 183*S^2 + 806*S^4 + 262*S^6))/(180*(1 + S^2)^3) + (2*S*(327 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(45*(1 + S^2)^3)) + ((-2*Pi^2*S*(-1241 + 321*S^2 + 321*S^4 + 107*S^6))/(9*(1 + S^2)^3) + (4*(-10 + 361*S^2 - 988*S^4 + 381*S^6))/(3*S*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (244*S*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((-40*Pi^2*S*(-89 + 27*S^2 + 27*S^4 + 9*S^6))/(9*(1 + S^2)^3) + (5*(3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12))/(3*S^3*(1 + S^2)^3) + 100*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^4*((Pi^2*S*(703 + 129*S^2 + 129*S^4 + 43*S^6))/(54*(1 + S^2)^3) - (S*(-2488 + 2045*S^2 - 1053*S^4 - 273*S^6 + 33*S^8))/(72*(1 + S^2)^3) + ((-525 + 5762*S^2 - 1680*S^4 - 42*S^6 + 5*S^8)*HPL[{1}, -S^2])/(36*S*(1 + S^2)^3) - (5*S*(-131 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(9*(1 + S^2)^3) - (S*(-267 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2}, -S^2])/(9*(1 + S^2)^3)) - (4*S*(-115 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{3}, -S^2]^2)/(3*(1 + S^2)^3) + ((46*Pi^2*S*(-23 + 27*S^2 + 27*S^4 + 9*S^6))/(9*(1 + S^2)^3) + (45 - 69*S^2 + 675*S^4 + 5200*S^6 - 967*S^8 + 373*S^10 - 9*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(105 - 176*S^2 - 3952*S^4 - 856*S^6 + 79*S^8)*HPL[{5}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(43 + 453*S^2 + 453*S^4 + 151*S^6)*HPL[{6}, -S^2])/(3*(1 + S^2)^3) + (160*S*(-82 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^3) + ((8*Pi^2*S*(-167 + 243*S^2 + 243*S^4 + 81*S^6))/(9*(1 + S^2)^3) + (4*(-27 - 97*S^2 - 584*S^4 - 1570*S^6 + 297*S^8 - 69*S^10 + 18*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (4*(37 + 1764*S^2 - 10232*S^4 - 772*S^6 + 747*S^8)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)^3) + (16*(28 + 1730*S^2 - 8529*S^4 - 743*S^6 + 578*S^8)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-113 + 165*S^2 + 165*S^4 + 55*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 - (16*S*(-499 + 663*S^2 + 663*S^4 + 221*S^6)*HPL[{5, 1}, -S^2])/(3*(1 + S^2)^3) + ((-80*Pi^2*S*(-22 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) - (4*(-45 - 103*S^2 - 1258*S^4 + 538*S^6 - 137*S^8 + 45*S^10))/(3*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (64*(-65 + 577*S^2 - 777*S^4 - 65*S^6 + 49*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)^3) + (8*(-527 + 3696*S^2 - 2334*S^4 - 194*S^6 + 123*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 112*S*HPL[{3, 1, 2}, -S^2] - (1616*S*HPL[{3, 2, 1}, -S^2])/3 - (960*S*(5 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (80*(39 - 232*S^2 - 36*S^4 + 29*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (640*S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 - 2240*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-2*S*(-95 - 64*S^2 + 7*S^4))/(1 + S^2) - (2*Pi^2*S*(709 - 5686*S^2 - 349*S^4 + 466*S^6))/(9*(1 + S^2)^3))*Zeta[3] + (112*S*Zeta[3]^2)/(1 + S^2)^3 + HPL[{2, 1}, -S^2]*((2*(-7 - 57*S^2 - 71*S^4 + 7*S^6))/S^3 + (2*Pi^2*(1167 - 6860*S^2 - 3232*S^4 + 44*S^6 + 469*S^8))/(9*S*(1 + S^2)^3) + (4640*S*Zeta[3])/(1 + S^2)^3) + HPL[{0}, S^2]^3*((28 + 147*S^2 + 106*S^4 - 5*S^6)/(12*S*(1 + S^2)) + (Pi^2*S*(6098 - 2439*S^2 + 830*S^4 + 415*S^6))/(54*(1 + S^2)^3) + (2*(-270 + 3142*S^2 - 1824*S^4 - 129*S^6 + 67*S^8)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)^3) - (20*S*(-319 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{1}, -S^2]^3)/(27*(1 + S^2)^3) + (2*(-15 + 1255*S^2 - 1048*S^4 + 2*S^6 + 70*S^8)*HPL[{2}, -S^2])/(9*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(-(Pi^2*S*(-2903 + 243*S^2 + 243*S^4 + 81*S^6))/(27*(1 + S^2)^3) + (21 - 226*S^2 + 2669*S^4 - 3020*S^6 + 739*S^8 - 30*S^10 + 15*S^12)/(9*S^3*(1 + S^2)^3) - (8*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + (4*S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (4*S*(761 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*(1 + S^2)^3) + (56*S^3*(3 + 3*S^2 + S^4)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((20*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(9*S^3) + (10*Pi^2*(-265 + 3726*S^2 - 3678*S^4 - 508*S^6 + 105*S^8))/(27*S*(1 + S^2)^3) - (200*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (5600*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(9*(1 + S^2)^3) - 400*S*HPL[{2, 1}, -S^2] + (320*S*(-23 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((Pi^2*(-65 - 2722*S^2 + 12506*S^4 + 1120*S^6 - 843*S^8))/(9*S*(1 + S^2)^3) + (-33 + 394*S^2 + 1338*S^4 + 746*S^6 - 117*S^8)/(6*S^3*(1 + S^2)) + (32*S*(451 + 48*S^2 + 48*S^4 + 16*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (8*S*(-93 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(3*S^3) - (Pi^4*S*(-28177 + 6639*S^2 + 6639*S^4 + 2213*S^6))/(135*(1 + S^2)^3) + (Pi^2*(45 - 521*S^2 + 6176*S^4 - 12364*S^6 + 4175*S^8 - 239*S^10))/(9*S^3*(1 + S^2)^3) + ((4*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) - (2*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (16*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) - (4*(-165 + 4426*S^2 - 9882*S^4 - 1452*S^6 + 421*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + (600*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (32*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + 1200*S*HPL[{2, 1, 1}, -S^2] - (20*(-29 + 642*S^2 - 1614*S^4 - 164*S^6 + 105*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + HPL[{2}, -S^2]*((49 + 888*S^2 + 296*S^4 - 49*S^6)/(6*S^3) - (Pi^4*S*(-11717 + 5469*S^2 + 5469*S^4 + 1823*S^6))/(270*(1 + S^2)^3) + (Pi^2*(87 + 204*S^2 + 3655*S^4 - 2656*S^6 + 1041*S^8 + 188*S^10 - 87*S^12))/(18*S^3*(1 + S^2)^3) - (4*(30 + 783*S^2 - 5272*S^4 - 439*S^6 + 366*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (20*S*(-21 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (32*(-65 + 577*S^2 - 777*S^4 - 65*S^6 + 49*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) + (464*S*(-29 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) - (320*S*(-82 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) - (4*(3 + 1070*S^2 - 4808*S^4 - 254*S^6 + 401*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + HPL[{0}, S^2]^2*((151 + 862*S^2 + 398*S^4 - 49*S^6)/(12*S*(1 + S^2)) - (Pi^4*S*(-19753 + 51*S^2 + 51*S^4 + 17*S^6))/(540*(1 + S^2)^3) - (Pi^2*S*(-4655 + 6889*S^2 - 2579*S^4 - 365*S^6 + 78*S^8))/(36*(1 + S^2)^3) - (20*(59 - 771*S^2 + 516*S^4 + 86*S^6)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)^3) - (40*S*(-33 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^3) + (-(Pi^2*S*(-1299 + 345*S^2 + 345*S^4 + 115*S^6))/(9*(1 + S^2)^3) + (21 + 28*S^2 + 1147*S^4 - 1688*S^6 + 721*S^8 + 48*S^10 - 21*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*S*(-421 + 171*S^2 + 171*S^4 + 57*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((-10*Pi^2*S*(-329 + 39*S^2 + 39*S^4 + 13*S^6))/(9*(1 + S^2)^3) + (45 - 472*S^2 + 5737*S^4 - 8948*S^6 + 1735*S^8 + 92*S^10 - 45*S^12)/(6*S^3*(1 + S^2)^3) - (2*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) - (2*(22 - 19*S^2 - 430*S^4 - 71*S^6 + 18*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (2*S*(5 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + (2*(582 - 3965*S^2 + 788*S^4 + 149*S^6 + 34*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-377 + 153*S^2 + 153*S^4 + 51*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) - (40*S*(-51 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*S*(19 - 646*S^2 - 94*S^4 + 31*S^6)*Zeta[3])/(3*(1 + S^2)^3) + HPL[{1}, -S^2]*((67 + 234*S^2 + 558*S^4 + 74*S^6 - 29*S^8)/(12*S^3*(1 + S^2)) + (Pi^2*(-1115 + 13472*S^2 - 6840*S^4 - 902*S^6 + 5*S^8))/(18*S*(1 + S^2)^3) + ((-601 + 6782*S^2 - 3618*S^4 - 598*S^6 - 37*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-71 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-143 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[3])/(3*(1 + S^2)^3))) - (8*S*(238 - 2653*S^2 + 32*S^4 + 313*S^6)*Zeta[5])/(3*(1 + S^2)^3) + HPL[{0}, S^2]*((454 + 765*S^2 + 417*S^4)/(12*S) + (Pi^2*(174 + 421*S^2 + 268*S^4 + 45*S^6))/(36*S*(1 + S^2)) + (Pi^4*S*(87140 - 85968*S^2 + 3719*S^4 + 8143*S^6))/(540*(1 + S^2)^3) + (70*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)^3) - (224*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^3) + ((-9 + 3844*S^2 - 7678*S^4 - 652*S^6 + 439*S^8)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-20*Pi^2*S*(-991 + 303*S^2 + 303*S^4 + 101*S^6))/(27*(1 + S^2)^3) + (10*(3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12))/(3*S^3*(1 + S^2)^3) - (40*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((2*Pi^2*S*(7 + 93*S^2 + 93*S^4 + 31*S^6))/(9*(1 + S^2)^3) + (27 + 6*S^2 + 509*S^4 + 1304*S^6 + 309*S^8 + 42*S^10 + 27*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(-11 + 115*S^2 - 72*S^4 + 87*S^6 + 45*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-27 + 3*S^2 + 3*S^4 + S^6)*HPL[{5}, -S^2])/(3*(1 + S^2)^3) + ((-4*Pi^2*S*(2471 + 123*S^2 + 123*S^4 + 41*S^6))/(9*(1 + S^2)^3) - (2*(45 - 522*S^2 + 4575*S^4 - 6112*S^6 + 2143*S^8 + 2*S^10 + 45*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (8*(-2 + 1729*S^2 - 3798*S^4 - 230*S^6 + 259*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-265 + 237*S^2 + 237*S^4 + 79*S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) - (32*S*(-74 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) + (40*(-2 + 693*S^2 - 1518*S^4 - 95*S^6 + 102*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)^3) + (9280*S*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (80*S*(1037 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^3) - (320*S*(57 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(-135 + 177*S^2 + 177*S^4 + 59*S^6))/(9*(1 + S^2)^3) + (2*S*(63 + 1210*S^2 - 256*S^4 + 46*S^6 + 9*S^8))/(3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((47 + 526*S^2 + 170*S^4 + 14*S^6 + 35*S^8)/(6*S^3*(1 + S^2)) + (Pi^2*(-40 + 5975*S^2 - 9686*S^4 - 471*S^6 + 650*S^8))/(9*S*(1 + S^2)^3) + (4*S*(-135 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (4640*S*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-22 + 21*S^2 + 21*S^4 + 7*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*((10*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) + (Pi^2*(-1275 + 17204*S^2 - 16878*S^4 - 1938*S^6 + 659*S^8))/(9*S*(1 + S^2)^3) + (20*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-53 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (40*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-317 + 129*S^2 + 129*S^4 + 43*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(3*S^3) - (Pi^4*S*(-26053 + 6183*S^2 + 6183*S^4 + 2061*S^6))/(135*(1 + S^2)^3) + (Pi^2*(87 - 1022*S^2 + 11953*S^4 - 21820*S^6 + 8093*S^8 - 630*S^10 + 75*S^12))/(18*S^3*(1 + S^2)^3) + ((-2*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(3*(1 + S^2)^3) + (2*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (16*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + (8*(-12 - 106*S^2 + 174*S^4 + 129*S^6 + 41*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-211 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) - (40*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) + (112*S*(-71 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (80*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (8*(22 - 502*S^2 + 732*S^4 + 187*S^6 + 11*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + (208*S*(-4 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*(((1 + S^2)*(417 + 802*S^2 + 417*S^4))/(12*S^3) + (Pi^2*(127 + 274*S^2 + 518*S^4 + 114*S^6 + 31*S^8))/(36*S^3*(1 + S^2)) + (Pi^4*(-7808 + 104629*S^2 - 82905*S^4 - 11207*S^6 + 1795*S^8))/(270*S*(1 + S^2)^3) + (2*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^3) + ((4*Pi^2*S*(-1821 + 1137*S^2 + 1137*S^4 + 379*S^6))/(9*(1 + S^2)^3) - (4*(-18 - 78*S^2 + 375*S^4 - 5182*S^6 + 2416*S^8 - 340*S^10 + 27*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (8*(-11 + 773*S^2 - 1794*S^4 - 407*S^6 + 11*S^8)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-111 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) + (4*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(89 - 275*S^2 - 1842*S^4 - 298*S^6 + 100*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) - (16*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) - (32*S*(-2477 + 1479*S^2 + 1479*S^4 + 493*S^6)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) - (1200*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) - (64*S*(-1441 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^3) - 2400*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S*(-1523 + 1011*S^2 + 1011*S^4 + 337*S^6))/(9*(1 + S^2)^3) - (4*(-49 + 439*S^2 - 3416*S^4 + 2440*S^6 - 331*S^8 + 45*S^10))/(3*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-8*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(-1051 + 9932*S^2 + 882*S^4 - 148*S^6 - 487*S^8))/(9*S*(1 + S^2)^3) + (8*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (32*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + (16*S*(-691 + 537*S^2 + 537*S^4 + 179*S^6)*Zeta[5])/(3*(1 + S^2)^3))) + ((-372*Pi^2*S^3*(3 + 3*S^2 + S^4))/(1 + S^2)^3 + (3*S*(-547 - 1798*S^2 + 736*S^4 - 914*S^6 + 75*S^8))/(2*(1 + S^2)^3))*Zeta[7] + HPL[{0}, S^2]^2*((-1393 - 6541*S^2 - 1948*S^4)/(64*S) + (Pi^4*(-156 - 3291*S^2 - 3802*S^4 - 778*S^6))/(360*S*(1 + S^2)) + (Pi^2*(-1692 - 14511*S^2 - 11546*S^4 - 263*S^6))/(384*S*(1 + S^2)) + (Pi^6*S*(-2642519 + 88212*S^2 - 74348*S^4 + 61841*S^6))/(181440*(1 + S^2)^3) + ((59 - 771*S^2 + 516*S^4 + 86*S^6)*HPL[{1}, -S^2]^6)/(9*S*(1 + S^2)^3) + (8*S*(-33 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{1}, -S^2]^7)/(21*(1 + S^2)^3) + ((5 - 2584*S^2 + 3104*S^4 + 536*S^6 + 3*S^8)*HPL[{2}, -S^2]^3)/(24*S*(1 + S^2)^3) + HPL[{1}, -S^2]^5*((Pi^2*S*(-329 + 39*S^2 + 39*S^4 + 13*S^6))/(9*(1 + S^2)^3) + (-45 + 472*S^2 - 5737*S^4 + 8948*S^6 - 1735*S^8 - 92*S^10 + 45*S^12)/(60*S^3*(1 + S^2)^3) + (S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2}, -S^2])/(15*(1 + S^2)^3)) + ((-8 + 93*S^2 + 102*S^4 + 99*S^6 + 26*S^8)*HPL[{3}, -S^2]^2)/(4*S*(1 + S^2)^3) + (-(Pi^2*S*(137 + 483*S^2 + 483*S^4 + 161*S^6))/(12*(1 + S^2)^3) + (-60 - 14*S^2 - 298*S^4 - 340*S^6 - 17*S^8 - 204*S^10 - 39*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((165 - 1299*S^2 - 1986*S^4 - 796*S^6 - 46*S^8)*HPL[{6}, -S^2])/(4*S*(1 + S^2)^3) - (S*(295 + 543*S^2 + 543*S^4 + 181*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 + ((-5 + 2905*S^2 - 3425*S^4 - 591*S^6 + 8*S^8)*HPL[{2, 1}, -S^2]^2)/(2*S*(1 + S^2)^3) + ((Pi^2*S*(-133 + 249*S^2 + 249*S^4 + 83*S^6))/(12*(1 + S^2)^3) + (-3 + 39*S^2 + 224*S^4 + 778*S^6 - 69*S^8 + 91*S^10 - 12*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((Pi^2*S*(-149 + 573*S^2 + 573*S^4 + 191*S^6))/(6*(1 + S^2)^3) + (33 + 86*S^2 + 1257*S^4 + 3166*S^6 + 29*S^8 + 460*S^10 - 39*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((11 + 75*S^2 + 40*S^4 + 75*S^6 + 27*S^8)*HPL[{4, 2}, -S^2])/(4*S*(1 + S^2)^3) + (2*S*(29 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 + ((-55 + 630*S^2 + 1110*S^4 + 522*S^6 + 73*S^8)*HPL[{5, 1}, -S^2])/(2*S*(1 + S^2)^3) + (S*(351 + 789*S^2 + 789*S^4 + 263*S^6)*HPL[{5, 2}, -S^2])/(2*(1 + S^2)^3) + (S*(509 + 1233*S^2 + 1233*S^4 + 411*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(751 + 6*S^2 + 6*S^4 + 2*S^6))/(3*(1 + S^2)^3) + (-33 + 434*S^2 - 3269*S^4 + 3628*S^6 - 287*S^8 - 6*S^10 - 3*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + (-(Pi^2*S*(4461 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) + (-123 + 1286*S^2 - 10399*S^4 + 9712*S^6 - 817*S^8 - 190*S^10 + 3*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + ((-1 + S^2 - 15*S^4 - 9*S^6)*HPL[{3, 1, 2}, -S^2])/(2*S*(1 + S^2)^2) + ((9 - 5168*S^2 + 6194*S^4 + 1048*S^6 - 3*S^8)*HPL[{3, 2, 1}, -S^2])/(2*S*(1 + S^2)^3) - (S*(-173 + 465*S^2 + 465*S^4 + 155*S^6)*HPL[{3, 2, 2}, -S^2])/(2*(1 + S^2)^3) - (40*S*(-8 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 + ((42 - 8003*S^2 + 8744*S^4 + 1395*S^6 - 10*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (S*(-317 + 621*S^2 + 621*S^4 + 207*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 - (S*(-1013 + 1701*S^2 + 1701*S^4 + 567*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 - (2*S*(-1027 + 1779*S^2 + 1779*S^4 + 593*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((28*Pi^2*S*(105 + 12*S^2 + 12*S^4 + 4*S^6))/(3*(1 + S^2)^3) - (2*(-24 + 211*S^2 - 1909*S^4 + 1349*S^6 - 69*S^8 - 76*S^10 + 6*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] + (16*S*(224 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^3 + (2*(-21 + 2771*S^2 - 2769*S^4 - 421*S^6 + 4*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(5485 + 399*S^2 + 399*S^4 + 133*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 - (2*S*(5485 + 399*S^2 + 399*S^4 + 133*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 - (2*S*(10861 + 1047*S^2 + 1047*S^4 + 349*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (4*S*(16295 + 1533*S^2 + 1533*S^4 + 511*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(19 - 2817*S^2 + 2830*S^4 + 449*S^6 + 3*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (32*S*(-237 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (96*S*(-237 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-2397 + 129*S^2 + 129*S^4 + 43*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (32*S*(454 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-22 - 647*S^2 - 664*S^4 - 87*S^6)/(16*S*(1 + S^2)) - (Pi^4*S*(1863 + 4470*S^2 + 4470*S^4 + 1490*S^6))/(180*(1 + S^2)^3) + (Pi^2*S*(-384 - 775*S^2 - 440*S^4 - 177*S^6 + 24*S^8))/(6*(1 + S^2)^3))*Zeta[3] + (S*(-208 - 69*S^2 + 71*S^4 + 52*S^6)*Zeta[3]^2)/(2*(1 + S^2)^3) + HPL[{4}, -S^2]*((45 - 165*S^2 - 457*S^4 - 381*S^6 - 38*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(45 - 695*S^2 - 1168*S^4 - 285*S^6 + 47*S^8))/(24*S*(1 + S^2)^3) + (14*S*(3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(11 + 18*S^2 + 18*S^4 + 6*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((23 + 708*S^2 + 946*S^4 + 240*S^6 - 69*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-54 + 5059*S^2 - 3635*S^4 - 435*S^6 - 3*S^8))/(12*S*(1 + S^2)^3) + (4*S*(-31 + 42*S^2 + 42*S^4 + 14*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(49 - 5180*S^2 + 3645*S^4 + 355*S^6 - 35*S^8))/(6*S*(1 + S^2)^3) + (-15 - 259*S^2 - 320*S^4 - 60*S^6 + 28*S^8)/(2*S^3*(1 + S^2)) - (8*S*(-28 + 45*S^2 + 45*S^4 + 15*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*((Pi^2*(5 - 5007*S^2 + 4675*S^4 + 677*S^6 - 22*S^8))/(48*S*(1 + S^2)^3) + (1 - 93*S^2 - 166*S^4 - 29*S^6 + 19*S^8)/(16*S^3*(1 + S^2)) - (S*(-37 + 117*S^2 + 117*S^4 + 39*S^6)*HPL[{3}, -S^2])/(4*(1 + S^2)^3) + (2*S*(224 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (S*(-17 + 60*S^2 + 60*S^4 + 20*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^4*((Pi^2*(1115 - 13472*S^2 + 6840*S^4 + 902*S^6 - 5*S^8))/(72*S*(1 + S^2)^3) + (-67 - 234*S^2 - 558*S^4 - 74*S^6 + 29*S^8)/(48*S^3*(1 + S^2)) + ((601 - 6782*S^2 + 3618*S^4 + 598*S^6 + 37*S^8)*HPL[{2}, -S^2])/(12*S*(1 + S^2)^3) - (S*(-71 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (S*(-143 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{3}, -S^2]*(-(Pi^4*S*(27 + 2973*S^2 + 2973*S^4 + 991*S^6))/(720*(1 + S^2)^3) + (-17 - 1520*S^2 - 1898*S^4 - 644*S^6 + 135*S^8)/(32*S^3*(1 + S^2)) + (Pi^2*(-21 - 17*S^2 - 566*S^4 - 832*S^6 + 37*S^8 - 143*S^10 + 6*S^12))/(24*S^3*(1 + S^2)^3) - (2*S*(14 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((3 - 171*S^2 + 111*S^4 - 26*S^6 - 23*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (S*(-79 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (6*S*(-19 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((-1 + 56*S^2 - 84*S^4 - 78*S^6 - 33*S^8)*Zeta[3])/(2*S*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((Pi^4*S*(893 + 120*S^2 + 120*S^4 + 40*S^6))/(20*(1 + S^2)^3) + (60 + 455*S^2 + 490*S^4 + 167*S^6)/(4*S^3*(1 + S^2)) + (Pi^2*(93 - 816*S^2 + 6915*S^4 - 3605*S^6 + 110*S^8 + 221*S^10 - 6*S^12))/(24*S^3*(1 + S^2)^3) + (2*S*(-953 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-237 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((-4 - 254*S^2 + 397*S^4 + 159*S^6 + 28*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((Pi^4*S*(-39137 + 1209*S^2 + 1209*S^4 + 403*S^6))/(1080*(1 + S^2)^3) + (-129 - 589*S^2 - 1305*S^4 - 311*S^6 + 6*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-45 + 496*S^2 - 5548*S^4 + 6557*S^6 - 1225*S^8 - 155*S^10 + 36*S^12))/(36*S^3*(1 + S^2)^3) + ((Pi^2*S*(-2769 + 177*S^2 + 177*S^4 + 59*S^6))/(18*(1 + S^2)^3) + (-45 + 183*S^2 - 3056*S^4 + 3037*S^6 - 790*S^8 - 124*S^10 + 27*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + (2*(15 + 24*S^2 - 379*S^4 - 78*S^6 + 10*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (S*(9 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + ((-601 + 6782*S^2 - 3618*S^4 - 598*S^6 - 37*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) - (32*S*(-103 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + ((-5 + 270*S^2 - 996*S^4 - 140*S^6 + 51*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + ((-2*Pi^2*S*(125 + 336*S^2 + 336*S^4 + 112*S^6))/(3*(1 + S^2)^3) + (S*(-604 - 1227*S^2 - 770*S^4 - 423*S^6 + 36*S^8))/(2*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(779 - 68852*S^2 + 18705*S^4 - 5583*S^6 - 1795*S^8))/(1440*S*(1 + S^2)^3) + (93 - 4994*S^2 - 6308*S^4 - 2766*S^6 - 9*S^8)/(64*S^3*(1 + S^2)) + (Pi^2*(-42 - 577*S^2 - 642*S^4 - 155*S^6 + 84*S^8))/(48*S^3*(1 + S^2)) + (-(Pi^2*S*(-23 + 39*S^2 + 39*S^4 + 13*S^6))/(4*(1 + S^2)^3) + (-23 - 118*S^2 - 402*S^4 + 24*S^6 - 47*S^8 + 6*S^10)/(4*S*(1 + S^2)^3))*HPL[{3}, -S^2] + ((7 - 235*S^2 - 244*S^4 - 231*S^6 - 61*S^8)*HPL[{4}, -S^2])/(4*S*(1 + S^2)^3) + (7*S*(7 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{5}, -S^2])/(2*(1 + S^2)^3) + ((Pi^2*S*(751 + 6*S^2 + 6*S^4 + 2*S^6))/(3*(1 + S^2)^3) + (33 - 434*S^2 + 3269*S^4 - 3628*S^6 + 287*S^8 + 6*S^10 + 3*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-11 + 2926*S^2 - 3326*S^4 - 484*S^6 + 43*S^8)*HPL[{3, 1}, -S^2])/(2*S*(1 + S^2)^3) + (S*(-81 + 237*S^2 + 237*S^4 + 79*S^6)*HPL[{3, 2}, -S^2])/(2*(1 + S^2)^3) + (S*(-153 + 309*S^2 + 309*S^4 + 103*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + ((5 - 2905*S^2 + 3425*S^4 + 591*S^6 - 8*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(224 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (6*S*(915 + 69*S^2 + 69*S^4 + 23*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-237 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(-28 + 45*S^2 + 45*S^4 + 15*S^6))/(3*(1 + S^2)^3) + (3 - 6*S^2 - 171*S^4 - 641*S^6 + 144*S^8 - 65*S^10)/(4*S^3*(1 + S^2)^3))*Zeta[3] - (S*(-51 + 69*S^2 + 69*S^4 + 23*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(-127 - 615*S^2 - 1393*S^4 - 581*S^6 - 60*S^8))/(96*S^3*(1 + S^2)) + (-181 - 1000*S^2 - 2156*S^4 - 628*S^6 - 59*S^8)/(16*S^3*(1 + S^2)) + (Pi^4*(7570 - 85792*S^2 + 26276*S^4 + 959*S^6 - 59*S^8))/(720*S*(1 + S^2)^3) + ((136 - 1698*S^2 + 1250*S^4 + 211*S^6 - 5*S^8)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^3) + (-(Pi^2*S*(-65 + 141*S^2 + 141*S^4 + 47*S^6))/(6*(1 + S^2)^3) + (-18 - 10*S^2 - 234*S^4 - 557*S^6 + 12*S^8 - 67*S^10 + 6*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((43 - 209*S^2 - 468*S^4 - 103*S^6 + 17*S^8)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^3) - (S*(-1 + 105*S^2 + 105*S^4 + 35*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(-2769 + 177*S^2 + 177*S^4 + 59*S^6))/(6*(1 + S^2)^3) + (45 - 183*S^2 + 3056*S^4 - 3037*S^6 + 790*S^8 + 124*S^10 - 27*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (2*(151 - 1674*S^2 + 871*S^4 + 133*S^6 + 5*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (S*(-471 + 411*S^2 + 411*S^4 + 137*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + ((601 - 6782*S^2 + 3618*S^4 + 598*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-1307 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(-77 + 225*S^2 + 225*S^4 + 75*S^6))/(6*(1 + S^2)^3) + (-3 + 38*S^2 - 27*S^4 - 986*S^6 + 379*S^8 - 128*S^10 + 15*S^12)/(4*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1117 - 11690*S^2 + 4676*S^4 + 552*S^6 + 37*S^8))/(24*S*(1 + S^2)^3) + (-89 - 930*S^2 - 1156*S^4 - 310*S^6 + 53*S^8)/(16*S^3*(1 + S^2)) - (16*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (2*S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (S*(-141 + 93*S^2 + 93*S^4 + 31*S^6)*Zeta[3])/(1 + S^2)^3) - (S*(-77 + 237*S^2 + 237*S^4 + 79*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]*(-(Pi^6*S*(1001127 + 136461*S^2 + 136461*S^4 + 45487*S^6))/(90720*(1 + S^2)^3) + (-213 - 1843*S^2 - 3603*S^4 - 1377*S^6 - 172*S^8)/(16*S^3*(1 + S^2)) + (Pi^2*(-255 - 1219*S^2 - 2559*S^4 - 1121*S^6 - 150*S^8))/(96*S^3*(1 + S^2)) + (Pi^4*(-624 + 8922*S^2 - 76993*S^4 + 59573*S^6 - 18146*S^8 - 5141*S^10 + 957*S^12))/(1440*S^3*(1 + S^2)^3) + ((Pi^2*S*(-1429 + 207*S^2 + 207*S^4 + 69*S^6))/(12*(1 + S^2)^3) + (-18 + 193*S^2 - 2644*S^4 + 3906*S^6 - 910*S^8 - 11*S^10 + 12*S^12)/(8*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (43*S*(-19 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^3)/(6*(1 + S^2)^3) + (S*(35 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{3}, -S^2]^2)/(2*(1 + S^2)^3) + (-(Pi^2*S*(81 + 339*S^2 + 339*S^4 + 113*S^6))/(12*(1 + S^2)^3) + (-36 + 3*S^2 - 623*S^4 - 826*S^6 - 214*S^8 - 169*S^10 + 9*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((30 - 164*S^2 - 413*S^4 - 100*S^6 + 11*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - (S*(283 + 621*S^2 + 621*S^4 + 207*S^6)*HPL[{6}, -S^2])/(2*(1 + S^2)^3) - (2*S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((-22*Pi^2*S*(-62 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (54 - 173*S^2 + 3112*S^4 - 2792*S^6 + 886*S^8 + 145*S^10 - 24*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((9 - 410*S^2 + 904*S^4 + 134*S^6 - 37*S^8)*HPL[{3, 2}, -S^2])/(2*S*(1 + S^2)^3) + ((-31 - 409*S^2 + 1824*S^4 + 307*S^6 - 71*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) - (3*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(2*(1 + S^2)^3) + (8*S*(12 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((Pi^2*S*(-2769 + 177*S^2 + 177*S^4 + 59*S^6))/(3*(1 + S^2)^3) + (-45 + 183*S^2 - 3056*S^4 + 3037*S^6 - 790*S^8 - 124*S^10 + 27*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(-136 + 1698*S^2 - 1250*S^4 - 211*S^6 + 5*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (4*(-423 + 5070*S^2 - 3371*S^4 - 555*S^6 + 5*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (172*S*(-19 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(-4911 + 651*S^2 + 651*S^4 + 217*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(601 - 6782*S^2 + 3618*S^4 + 598*S^6 + 37*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (64*S*(-103 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-17 - 15*S^2 - 125*S^4 - 173*S^6 - 94*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(36 - 208*S^2 - 916*S^4 - 175*S^6 + 41*S^8))/(6*S*(1 + S^2)^3))*Zeta[3] - (S*(61 + 63*S^2 + 63*S^4 + 21*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{3}, -S^2]*((-13 - 478*S^2 - 632*S^4 - 234*S^6 + 29*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(63 - 150*S^2 - 1148*S^4 - 216*S^6 + 47*S^8))/(12*S*(1 + S^2)^3) + (32*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(21 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((89 + 930*S^2 + 1156*S^4 + 310*S^6 - 53*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-1117 + 11690*S^2 - 4676*S^4 - 552*S^6 - 37*S^8))/(12*S*(1 + S^2)^3) + (2*S*(-141 + 93*S^2 + 93*S^4 + 31*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*(-(Pi^4*S*(31129 + 1263*S^2 + 1263*S^4 + 421*S^6))/(720*(1 + S^2)^3) + (-66 - 835*S^2 - 1007*S^4 - 357*S^6 + 25*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-90 + 338*S^2 - 5866*S^4 + 4053*S^6 - 1259*S^8 - 255*S^10 + 39*S^12))/(24*S^3*(1 + S^2)^3) + ((-2 + 103*S^2 - 226*S^4 - 34*S^6 + 9*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (7*S*(11 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{4}, -S^2])/(2*(1 + S^2)^3) + (2*(-136 + 1698*S^2 - 1250*S^4 - 211*S^6 + 5*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-897 + 177*S^2 + 177*S^4 + 59*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((7 + 334*S^2 - 940*S^4 - 240*S^6 - 5*S^8)*Zeta[3])/(2*S*(1 + S^2)^3)) + ((21 - 240*S^2 - 868*S^4 - 41*S^6 + 98*S^8)*Zeta[5])/(S*(1 + S^2)^3)) - 558*S*Zeta[7]) + Log[T]^2*((-1725*(1 + S^2))/(16*S) + (Pi^2*(-1692 - 7057*S^2 - 3838*S^4 - 9*S^6))/(96*S*(1 + S^2)) + (Pi^4*(-1248 - 7316*S^2 - 4019*S^4 + 441*S^6))/(720*S*(1 + S^2)) + (Pi^6*S*(-788699 + 500412*S^2 + 72852*S^4 + 3421*S^6))/(15120*(1 + S^2)^3) - (S*(3 + S^2)*(3 + S^4)*HPL[{0}, S^2]^7)/(24*(1 + S^2)^3) - (14*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)^3) + (32*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^6*(-(S*(89 + 18*S^2 + 21*S^4 + 4*S^6))/(16*(1 + S^2)^3) - (S*(93 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{1}, -S^2])/(24*(1 + S^2)^3)) + ((-159 + 227*S^2 - 207*S^4 + 11*S^6)*HPL[{2}, -S^2]^3)/(6*S*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((8*Pi^2*S*(-89 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (-3 + 38*S^2 - 441*S^4 + 1052*S^6 - 441*S^8 + 38*S^10 - 3*S^12)/(S^3*(1 + S^2)^3) - 60*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^5*(-(Pi^2*S*(1601 + 327*S^2 + 327*S^4 + 109*S^6))/(360*(1 + S^2)^3) - (S*(3095 - 1167*S^2 + 1137*S^4 + 243*S^6 + 60*S^8))/(240*(1 + S^2)^3) + ((605 - 5844*S^2 + 1024*S^4 - 538*S^6 - 187*S^8)*HPL[{1}, -S^2])/(120*S*(1 + S^2)^3) - (S*(327 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^2)/(15*(1 + S^2)^3) + (S*(-541 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(60*(1 + S^2)^3)) + ((-3 - 253*S^2 + 912*S^4 + 243*S^6 + 17*S^8)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^3) + (-(Pi^2*S*(-221 + 813*S^2 + 813*S^4 + 271*S^6))/(3*(1 + S^2)^3) + (-60 - 7*S^2 - 1060*S^4 - 2524*S^6 + 19*S^8 - 403*S^10 - 9*S^12)/(S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((245 - 2011*S^2 - 4802*S^4 - 2304*S^6 - 406*S^8)*HPL[{6}, -S^2])/(S*(1 + S^2)^3) - (76*S*(17 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 + (4*(-83 + 2668*S^2 - 3090*S^4 - 596*S^6 + 25*S^8)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^3) + ((Pi^2*S*(-2347 + 3975*S^2 + 3975*S^4 + 1325*S^6))/(3*(1 + S^2)^3) + (-6 - 5*S^2 + 60*S^4 + 7004*S^6 - 5828*S^8 + 1081*S^10 - 66*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((2*Pi^2*S*(-4129 + 6345*S^2 + 6345*S^4 + 2115*S^6))/(3*(1 + S^2)^3) + (27 - S^2 + 581*S^4 + 26276*S^6 - 18081*S^8 + 3565*S^10 - 207*S^12)/(S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((13 - 549*S^2 + 3300*S^4 + 907*S^6 + 69*S^8)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-37 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 + (2*(-79 - 1298*S^2 + 10100*S^4 + 2878*S^6 + 199*S^8)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-359 + 507*S^2 + 507*S^4 + 169*S^6)*HPL[{5, 2}, -S^2])/(1 + S^2)^3 + (4*S*(219 + 501*S^2 + 501*S^4 + 167*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((16*Pi^2*S*(-599 + 225*S^2 + 225*S^4 + 75*S^6))/(3*(1 + S^2)^3) - (4*(18 - 207*S^2 + 1642*S^4 - 3274*S^6 + 1546*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((8*Pi^2*S*(-2847 + 291*S^2 + 291*S^4 + 97*S^6))/(3*(1 + S^2)^3) - (4*(63 - 602*S^2 + 5036*S^4 - 4980*S^6 + 1627*S^8 - 154*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (4*(-23 + 221*S^2 + 91*S^4 + 15*S^6)*HPL[{3, 1, 2}, -S^2])/(S*(1 + S^2)^2) - (8*(68 - 3*S^2 + 149*S^4 + 2*S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (2*S*(-4849 + 7101*S^2 + 7101*S^4 + 2367*S^6)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^3 - (16*S*(-1841 + 2757*S^2 + 2757*S^4 + 919*S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 - (12*(151 - 358*S^2 + 1544*S^4 + 626*S^6 + 13*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-7195 + 11031*S^2 + 11031*S^4 + 3677*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 - (92*S*(-977 + 1461*S^2 + 1461*S^4 + 487*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 - (128*S*(-1447 + 2157*S^2 + 2157*S^4 + 719*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((16*Pi^2*S*(619 + 552*S^2 + 552*S^4 + 184*S^6))/(3*(1 + S^2)^3) - (4*(-45 + 469*S^2 - 4166*S^4 + 3446*S^6 - 709*S^8 + 45*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 4928*S*HPL[{2, 2, 2, 1}, -S^2] + (8*(185 - 756*S^2 + 1938*S^4 + 734*S^6 + 15*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (48*S*(681 + 303*S^2 + 303*S^4 + 101*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 - (48*S*(681 + 303*S^2 + 303*S^4 + 101*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 - (48*S*(989 + 1227*S^2 + 1227*S^4 + 409*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (32*S*(4753 + 5349*S^2 + 5349*S^4 + 1783*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (240*(-9 - 8*S^2 - 24*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (128*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (384*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (1280*S*(-217 + 159*S^2 + 159*S^4 + 53*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + 21120*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-1 - 755*S^2 - 404*S^4 + 86*S^6)/(2*S*(1 + S^2)) - (Pi^4*S*(-1863 + 4470*S^2 + 4470*S^4 + 1490*S^6))/(45*(1 + S^2)^3) + (Pi^2*S*(-190 - 3723*S^2 + 3053*S^4 - 797*S^6 + 57*S^8))/(6*(1 + S^2)^3))*Zeta[3] + (6*S*(-45 + 51*S^2 + 13*S^4 + S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) - (5*Pi^2*(-265 + 3726*S^2 - 3678*S^4 - 508*S^6 + 105*S^8))/(18*S*(1 + S^2)^3) + (150*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (1400*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + 300*S*HPL[{2, 1}, -S^2] - (80*S*(-23 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4}, -S^2]*((27 - 133*S^2 - 509*S^4 - S^6)/(2*S^3) + (Pi^2*(51 + 619*S^2 - 5260*S^4 - 1503*S^6 - 91*S^8))/(6*S*(1 + S^2)^3) - (16*S*(133 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-17 + 45*S^2 + 45*S^4 + 15*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{0}, S^2]^4*((-45 - 416*S^2 - 350*S^4 - 3*S^6)/(48*S*(1 + S^2)) - (Pi^2*S*(6893 - 224*S^2 + 1021*S^4 + 218*S^6))/(144*(1 + S^2)^3) + ((525 - 5762*S^2 + 1680*S^4 + 42*S^6 - 5*S^8)*HPL[{1}, -S^2]^2)/(24*S*(1 + S^2)^3) + (5*S*(-131 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^3) + ((30 - 2363*S^2 + 815*S^4 - 94*S^6 - 38*S^8)*HPL[{2}, -S^2])/(24*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((-5*Pi^2*S*(541 + 39*S^2 + 39*S^4 + 13*S^6))/(72*(1 + S^2)^3) + (-45 + 520*S^2 - 5359*S^4 + 4166*S^6 - 715*S^8 - 218*S^10 + 27*S^12)/(48*S^3*(1 + S^2)^3) - (2*S*(137 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) - (S*(3 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3}, -S^2])/(4*(1 + S^2)^3) + (S*(281 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (S*(26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((Pi^2*(171 - 8241*S^2 + 9605*S^4 + 1783*S^6 - 58*S^8))/(12*S*(1 + S^2)^3) + (13 + 17*S^2 - 48*S^4 - 63*S^6 + 13*S^8)/(4*S^3*(1 + S^2)) - (S*(-1433 + 1869*S^2 + 1869*S^4 + 623*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + 616*S*HPL[{2, 1}, -S^2] - (8*S*(-125 + 213*S^2 + 213*S^4 + 71*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((6*(-9 - 111*S^2 - 17*S^4 + 9*S^6))/S^3 + (4*Pi^2*(-58 - 1536*S^2 + 1175*S^4 + 52*S^6 + 9*S^8))/(3*S*(1 + S^2)^3) - (32*S*(-289 + 438*S^2 + 438*S^4 + 146*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((41 + 875*S^2 + 311*S^4 - 67*S^6)/(2*S^3) + (Pi^2*(164 + 2015*S^2 - 831*S^4 + 313*S^6 + 19*S^8))/(3*S*(1 + S^2)^3) + (8*S*(-603 + 879*S^2 + 879*S^4 + 293*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((86 + 695*S^2 + 489*S^4 - 86*S^6)/(2*S^3) + (2*Pi^4*S*(825 + 444*S^2 + 444*S^4 + 148*S^6))/(9*(1 + S^2)^3) + (Pi^2*(93 - 846*S^2 + 7515*S^4 - 1978*S^6 - 2599*S^8 + 816*S^10 - 57*S^12))/(6*S^3*(1 + S^2)^3) + (16*S*(-703 + 501*S^2 + 501*S^4 + 167*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (64*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (8*(-77 + 1281*S^2 - 1655*S^4 - 397*S^6 + 6*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{3}, -S^2]*(-(Pi^4*S*(-10497 + 16485*S^2 + 16485*S^4 + 5495*S^6))/(180*(1 + S^2)^3) + (119 - 936*S^2 - 3298*S^4 - 1204*S^6 + 463*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-21 - 27*S^2 - 406*S^4 - 5428*S^6 + 3033*S^8 - 697*S^10 + 42*S^12))/(6*S^3*(1 + S^2)^3) + (8*S*(-31 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (4*(-187 + 2891*S^2 - 2786*S^4 - 603*S^6 + 41*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-1113 + 1893*S^2 + 1893*S^4 + 631*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (48*S*(-183 + 321*S^2 + 321*S^4 + 107*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(-3 - 194*S^2 + 688*S^4 + 248*S^6 + 41*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((-7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(3*S^3) + (Pi^4*S*(-28177 + 6639*S^2 + 6639*S^4 + 2213*S^6))/(135*(1 + S^2)^3) + (Pi^2*(-45 + 521*S^2 - 6176*S^4 + 12364*S^6 - 4175*S^8 + 239*S^10))/(9*S^3*(1 + S^2)^3) + ((-4*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) + (2*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (16*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + (4*(-165 + 4426*S^2 - 9882*S^4 - 1452*S^6 + 421*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (8*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) - (600*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (32*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) - 1200*S*HPL[{2, 1, 1}, -S^2] + (20*(-29 + 642*S^2 - 1614*S^4 - 164*S^6 + 105*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + HPL[{0}, S^2]^3*(-(Pi^4*S*(19753 + 51*S^2 + 51*S^4 + 17*S^6))/(1080*(1 + S^2)^3) + (-278 - 1509*S^2 - 904*S^4 + 39*S^6)/(48*S*(1 + S^2)) - (Pi^2*S*(5267 - 4431*S^2 + 2391*S^4 + 231*S^6 + 78*S^8))/(72*(1 + S^2)^3) - (2*(-270 + 3142*S^2 - 1824*S^4 - 129*S^6 + 67*S^8)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)^3) + (5*S*(-319 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{1}, -S^2]^4)/(9*(1 + S^2)^3) + ((2*Pi^2*S*(-302 + 63*S^2 + 63*S^4 + 21*S^6))/(9*(1 + S^2)^3) + (-24 - 20*S^2 - 1103*S^4 + 1182*S^6 - 697*S^8 + 8*S^10 - 6*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (S*(-631 + 243*S^2 + 243*S^4 + 81*S^6)*HPL[{2}, -S^2]^2)/(6*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*S*(-2903 + 243*S^2 + 243*S^4 + 81*S^6))/(18*(1 + S^2)^3) + (-21 + 226*S^2 - 2669*S^4 + 3020*S^6 - 739*S^8 + 30*S^10 - 15*S^12)/(6*S^3*(1 + S^2)^3) + (4*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) - (2*(-11 + 41*S^2 + 17*S^4 + 30*S^6 + 11*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (2*S*(-33 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + ((-521 + 3070*S^2 - 1030*S^4 - 84*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) - (2*S*(-661 + 261*S^2 + 261*S^4 + 87*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-667 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) - (S*(179 + 496*S^2 + 310*S^4 + 77*S^6)*Zeta[3])/(3*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*(1145 - 12128*S^2 + 4672*S^4 - 280*S^6 - 321*S^8))/(36*S*(1 + S^2)^3) + (-43 - 240*S^2 - 534*S^4 - 304*S^6 - 15*S^8)/(24*S^3*(1 + S^2)) + ((551 - 5580*S^2 + 3126*S^4 + 80*S^6 - 177*S^8)*HPL[{2}, -S^2])/(6*S*(1 + S^2)^3) - (24*S*HPL[{3}, -S^2])/(1 + S^2)^3 - (8*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (2*S*(-11 + 51*S^2 + 51*S^4 + 17*S^6)*Zeta[3])/(3*(1 + S^2)^3))) + ((-8*Pi^2*S*(-125 + 336*S^2 + 336*S^4 + 112*S^6))/(3*(1 + S^2)^3) + (S*(-196 - 2861*S^2 + 3225*S^4 - 983*S^6 + 87*S^8))/(1 + S^2)^3)*Zeta[5] + HPL[{0}, S^2]^2*((-828 - 5329*S^2 - 2974*S^4 - 9*S^6)/(32*S*(1 + S^2)) + (Pi^2*(-90 - 629*S^2 - 419*S^4 + 24*S^6))/(24*S*(1 + S^2)) - (Pi^4*S*(86655 - 30722*S^2 + 2486*S^4 + 1243*S^6))/(720*(1 + S^2)^3) + (5*(59 - 771*S^2 + 516*S^4 + 86*S^6)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)^3) + (8*S*(-33 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{1}, -S^2]^5)/(1 + S^2)^3 + ((5 - 2905*S^2 + 3425*S^4 + 591*S^6 - 8*S^8)*HPL[{2}, -S^2]^2)/(4*S*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((10*Pi^2*S*(-329 + 39*S^2 + 39*S^4 + 13*S^6))/(9*(1 + S^2)^3) + (-45 + 472*S^2 - 5737*S^4 + 8948*S^6 - 1735*S^8 - 92*S^10 + 45*S^12)/(6*S^3*(1 + S^2)^3) + (2*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + (-(Pi^2*S*(-45 + 201*S^2 + 201*S^4 + 67*S^6))/(6*(1 + S^2)^3) + (-6 - 4*S^2 - 148*S^4 - 293*S^6 + 11*S^8 - 43*S^10 + 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((27 - 251*S^2 - 568*S^4 - 213*S^6 - 19*S^8)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^3) - (S*(17 + 159*S^2 + 159*S^4 + 53*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((14*Pi^2*S*(105 + 12*S^2 + 12*S^4 + 4*S^6))/(3*(1 + S^2)^3) + (24 - 211*S^2 + 1909*S^4 - 1349*S^6 + 69*S^8 + 76*S^10 - 6*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-21 + 2771*S^2 - 2769*S^4 - 421*S^6 + 4*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (S*(-109 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (2*S*(-167 + 411*S^2 + 411*S^4 + 137*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (2*(19 - 2817*S^2 + 2830*S^4 + 449*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(-237 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(1395 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (16*S*(454 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-76*Pi^2*S^3*(3 + 3*S^2 + S^4))/(3*(1 + S^2)^3) + (S*(-175 - 659*S^2 + 91*S^4 - 133*S^6 + 12*S^8))/(2*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(49 - 5180*S^2 + 3645*S^4 + 355*S^6 - 35*S^8))/(12*S*(1 + S^2)^3) + (-15 - 259*S^2 - 320*S^4 - 60*S^6 + 28*S^8)/(4*S^3*(1 + S^2)) - (3*S*(-19 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (8*S*(-237 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-28 + 45*S^2 + 45*S^4 + 15*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(1115 - 13472*S^2 + 6840*S^4 + 902*S^6 - 5*S^8))/(12*S*(1 + S^2)^3) + (-67 - 234*S^2 - 558*S^4 - 74*S^6 + 29*S^8)/(8*S^3*(1 + S^2)) + ((601 - 6782*S^2 + 3618*S^4 + 598*S^6 + 37*S^8)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^3) - (2*S*(-71 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (2*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (2*S*(-143 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^4*S*(-39137 + 1209*S^2 + 1209*S^4 + 403*S^6))/(360*(1 + S^2)^3) + (-129 - 589*S^2 - 1305*S^4 - 311*S^6 + 6*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-45 + 496*S^2 - 5548*S^4 + 6557*S^6 - 1225*S^8 - 155*S^10 + 36*S^12))/(12*S^3*(1 + S^2)^3) + ((Pi^2*S*(-2769 + 177*S^2 + 177*S^4 + 59*S^6))/(6*(1 + S^2)^3) + (-45 + 183*S^2 - 3056*S^4 + 3037*S^6 - 790*S^8 - 124*S^10 + 27*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 + (2*(15 + 24*S^2 - 379*S^4 - 78*S^6 + 10*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (S*(9 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((-601 + 6782*S^2 - 3618*S^4 - 598*S^6 - 37*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (32*S*(-103 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((-5 + 270*S^2 - 996*S^4 - 140*S^6 + 51*S^8)*Zeta[3])/(S*(1 + S^2)^3)) - (156*S^3*(3 + 3*S^2 + S^4)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(417 + 802*S^2 + 417*S^4))/(8*S^3) + (Pi^4*(7808 - 104629*S^2 + 82905*S^4 + 11207*S^6 - 1795*S^8))/(180*S*(1 + S^2)^3) + (Pi^2*(-127 - 274*S^2 - 518*S^4 - 114*S^6 - 31*S^8))/(24*S^3*(1 + S^2)) + ((343 - 4976*S^2 + 6198*S^4 + 856*S^6 - 221*S^8)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(-1821 + 1137*S^2 + 1137*S^4 + 379*S^6))/(3*(1 + S^2)^3) + (2*(-18 - 78*S^2 + 375*S^4 - 5182*S^6 + 2416*S^8 - 340*S^10 + 27*S^12))/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (4*(-11 + 773*S^2 - 1794*S^4 - 407*S^6 + 11*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-111 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) - (6*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(89 - 275*S^2 - 1842*S^4 - 298*S^6 + 100*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (16*S*(-2477 + 1479*S^2 + 1479*S^4 + 493*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (1800*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-1441 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + 3600*S*HPL[{2, 1, 1, 1}, -S^2] + ((-2*Pi^2*S*(-1523 + 1011*S^2 + 1011*S^4 + 337*S^6))/(3*(1 + S^2)^3) + (2*(-49 + 439*S^2 - 3416*S^4 + 2440*S^6 - 331*S^8 + 45*S^10))/(S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((12*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(1051 - 9932*S^2 - 882*S^4 + 148*S^6 + 487*S^8))/(6*S*(1 + S^2)^3) - (4*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(1 + S^2)^3) - (8*S*(-691 + 537*S^2 + 537*S^4 + 179*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2}, -S^2]*((9 - 5287*S^2 - 2137*S^4 - 9*S^6)/(16*S^3) + (Pi^2*(-42 - 619*S^2 - 704*S^4 - 84*S^6 + 55*S^8))/(12*S^3*(1 + S^2)) + (Pi^4*(-349 - 51788*S^2 + 31545*S^4 + 2013*S^6 + 269*S^8))/(360*S*(1 + S^2)^3) + (-((Pi^2*S*(-385 + 681*S^2 + 681*S^4 + 227*S^6))/(1 + S^2)^3) + (7 - 108*S^2 - 3538*S^4 + 2944*S^6 - 557*S^8 + 36*S^10)/(S*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-1 + 509*S^2 - 3168*S^4 - 859*S^6 - 61*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-209 + 477*S^2 + 477*S^4 + 159*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(-599 + 225*S^2 + 225*S^4 + 75*S^6))/(3*(1 + S^2)^3) + (2*(18 - 207*S^2 + 1642*S^4 - 3274*S^6 + 1546*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(-215 + 5714*S^2 - 5592*S^4 - 1010*S^6 + 71*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-2569 + 3621*S^2 + 3621*S^4 + 1207*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-3767 + 5763*S^2 + 5763*S^4 + 1921*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (8*(-83 + 2668*S^2 - 3090*S^4 - 596*S^6 + 25*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 2464*S*HPL[{2, 2, 1}, -S^2] + (48*S*(337 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (64*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(-317 + 483*S^2 + 483*S^4 + 161*S^6))/(3*(1 + S^2)^3) + (3 + 2*S^2 + 121*S^4 - 3418*S^6 + 2875*S^8 - 512*S^10 + 33*S^12)/(S^3*(1 + S^2)^3))*Zeta[3] - (4*S*(-493 + 945*S^2 + 945*S^4 + 315*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]*(-((1 + S^2)*(307 + 1070*S^2 + 307*S^4))/(4*S^3) + (11*Pi^6*S*(-105451 + 16287*S^2 + 16287*S^4 + 5429*S^6))/(22680*(1 + S^2)^3) + (Pi^2*(-255 - 981*S^2 - 1837*S^4 - 703*S^6 - 120*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(-624 + 6423*S^2 - 75934*S^4 + 122755*S^6 - 37642*S^8 + 144*S^10 + 402*S^12))/(360*S^3*(1 + S^2)^3) + ((Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) + (-18 + 247*S^2 - 3086*S^4 + 7226*S^6 - 3070*S^8 + 255*S^10 - 18*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - 62*S*HPL[{2}, -S^2]^3 + (2*S*(-275 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(-1193 + 837*S^2 + 837*S^4 + 279*S^6))/(3*(1 + S^2)^3) - (2*(18 - 7*S^2 + 152*S^4 + 2562*S^6 - 346*S^8 + 149*S^10))/(S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(103 + 302*S^2 - 3426*S^4 - 878*S^6 + 11*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - (2*S*(67 + 849*S^2 + 849*S^4 + 283*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 - (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((8*Pi^2*S*(309 + 183*S^2 + 183*S^4 + 61*S^6))/(3*(1 + S^2)^3) - (2*(-54 + 91*S^2 - 2336*S^4 - 3138*S^6 + 1762*S^8 - 425*S^10 + 36*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) - (4*(-493 + 12568*S^2 - 27762*S^4 - 3940*S^6 + 1243*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + (18*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 + (16*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) + (12*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (16*(-432 + 5251*S^2 - 4356*S^4 - 558*S^6 + 121*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 1488*S*HPL[{3, 2, 1}, -S^2] - (32*S*(-161 + 597*S^2 + 597*S^4 + 199*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 - (3600*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (64*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 - 7200*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-7 - 194*S^2 - 598*S^4 - 34*S^6 + 89*S^8)/(2*S^3*(1 + S^2)) + (2*Pi^2*(-25 + 580*S^2 - 1511*S^4 - 160*S^6 + 96*S^8))/(S*(1 + S^2)^3))*Zeta[3] + (8*S*(-37 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{3}, -S^2]*((-17 - 672*S^2 - 1214*S^4 - 432*S^6 + 79*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-135 + 4474*S^2 - 10640*S^4 - 1608*S^6 + 441*S^8))/(3*S*(1 + S^2)^3) + (8*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (112*S*(-7 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((-24*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(-1051 + 9932*S^2 + 882*S^4 - 148*S^6 - 487*S^8))/(3*S*(1 + S^2)^3) + (32*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((-135 - 1583*S^2 - 785*S^4 + 135*S^6)/(4*S^3) - (Pi^4*S*(28217 + 3411*S^2 + 3411*S^4 + 1137*S^6))/(180*(1 + S^2)^3) + (Pi^2*(-90 + 321*S^2 - 5585*S^4 + 2317*S^6 + 779*S^8 - 502*S^10 + 72*S^12))/(6*S^3*(1 + S^2)^3) + (2*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-847 + 339*S^2 + 339*S^4 + 113*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(-151 + 3632*S^2 - 8118*S^4 - 1048*S^6 + 413*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + (4*(-54 + 1295*S^2 - 4545*S^4 - 279*S^6 + 395*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]*((-691 - 2063*S^2 - 614*S^4)/(8*S) + (Pi^2*(-578 - 2041*S^2 - 1388*S^4 - 213*S^6))/(48*S*(1 + S^2)) + (Pi^6*S*(-15415 + 5289*S^2 + 5289*S^4 + 1763*S^6))/(648*(1 + S^2)^3) - (Pi^4*S*(62940 - 102383*S^2 + 55565*S^4 - 2833*S^6 + 1191*S^8))/(720*(1 + S^2)^3) - (14*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)^3) + (112*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^3) + ((Pi^2*S*(-1979 + 1419*S^2 + 1419*S^4 + 473*S^6))/(6*(1 + S^2)^3) + (-3 - 7*S^2 - 1038*S^4 + 3613*S^6 - 2040*S^8 + 258*S^10 - 15*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (392*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*((5*Pi^2*S*(-991 + 303*S^2 + 303*S^4 + 101*S^6))/(9*(1 + S^2)^3) - (5*(3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12))/(2*S^3*(1 + S^2)^3) + (10*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) - (2*S*(-7 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + ((8*Pi^2*S*(-21 + 12*S^2 + 12*S^4 + 4*S^6))/(3*(1 + S^2)^3) + (-33 - 17*S^2 - 669*S^4 - 686*S^6 - 999*S^8 - 41*S^10 - 3*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((49 - 302*S^2 + 212*S^4 - 240*S^6 - 131*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-48 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 - (16*S*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((-4*Pi^2*S*(-969 + 735*S^2 + 735*S^4 + 245*S^6))/(3*(1 + S^2)^3) + (57 + 68*S^2 + 2269*S^4 - 5918*S^6 + 4705*S^8 - 526*S^10 + 33*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (4*(3 - 134*S^2 + 537*S^4 + 188*S^6 + 30*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + (2*(-55 - 599*S^2 + 2706*S^4 + 1097*S^6 + 223*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + 4*S*HPL[{4, 2}, -S^2] - (32*S*(-14 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((8*Pi^2*S*(-971 + 732*S^2 + 732*S^4 + 244*S^6))/(3*(1 + S^2)^3) - (2*(45 + 50*S^2 + 2239*S^4 - 6112*S^6 + 4479*S^8 - 570*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(-677 + 6108*S^2 - 4718*S^4 - 1060*S^6 + 3*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (8*(-1042 + 9143*S^2 - 6770*S^4 - 1428*S^6 + 47*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 20*S*HPL[{3, 1, 2}, -S^2] + (4*S*(-2347 + 2367*S^2 + 2367*S^4 + 789*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 + (48*S*(-605 + 597*S^2 + 597*S^4 + 199*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (40*(-146 + 1221*S^2 - 810*S^4 - 143*S^6 + 18*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-1277 + 1209*S^2 + 1209*S^4 + 403*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (480*S*(-85 + 81*S^2 + 81*S^4 + 27*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((6 - 215*S^2 + 13*S^4)/(2*S) - (Pi^2*S*(-109 + 1567*S^2 + 619*S^4 + 107*S^6))/(3*(1 + S^2)^3))*Zeta[3] + (4*S*(-31 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{2, 1}, -S^2]*((35 + 190*S^2 + 170*S^4 + 350*S^6 + 47*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-1251 + 9175*S^2 - 5080*S^4 - 799*S^6 + 127*S^8))/(3*S*(1 + S^2)^3) - (8*S*(175 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((Pi^2*(97 - 126*S^2 - 682*S^4 - 444*S^6 - 129*S^8))/(6*S*(1 + S^2)^3) + (-25 - 404*S^2 - 422*S^4 - 304*S^6 - 21*S^8)/(4*S^3*(1 + S^2)) + (4*S*(-171 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(1 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((Pi^4*S*(-10325 + 5874*S^2 + 5874*S^4 + 1958*S^6))/(90*(1 + S^2)^3) + (-46 - 740*S^2 - 411*S^4 - 328*S^6 - 83*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-93 - 90*S^2 - 4445*S^4 + 8476*S^6 - 5873*S^8 + 586*S^10 - 57*S^12))/(12*S^3*(1 + S^2)^3) - (2*(2 - 138*S^2 + 531*S^4 + 184*S^6 + 29*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (12*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (2*(-677 + 6108*S^2 - 4718*S^4 - 1060*S^6 + 3*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-449 + 393*S^2 + 393*S^4 + 131*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*S*(-298 + 999*S^2 + 276*S^4 + 23*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-10*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) + (Pi^2*(1275 - 17204*S^2 + 16878*S^4 + 1938*S^6 - 659*S^8))/(9*S*(1 + S^2)^3) - (20*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) - (8*S*(-53 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (40*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-317 + 129*S^2 + 129*S^4 + 43*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((-7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(2*S^3) + (Pi^4*S*(-26053 + 6183*S^2 + 6183*S^4 + 2061*S^6))/(90*(1 + S^2)^3) + (Pi^2*(-87 + 1022*S^2 - 11953*S^4 + 21820*S^6 - 8093*S^8 + 630*S^10 - 75*S^12))/(12*S^3*(1 + S^2)^3) + ((Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(1 + S^2)^3 + (-45 + 236*S^2 - 3407*S^4 + 6112*S^6 - 3311*S^8 + 284*S^10 - 45*S^12)/(S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (8*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 - (4*(-12 - 106*S^2 + 174*S^4 + 129*S^6 + 41*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-211 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (20*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (168*S*(-71 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (120*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (4*(22 - 502*S^2 + 732*S^4 + 187*S^6 + 11*S^8)*Zeta[3])/(S*(1 + S^2)^3)) - (2*S*(-93 + 1145*S^2 + 604*S^4 + 146*S^6)*Zeta[5])/(1 + S^2)^3 + HPL[{1}, -S^2]*(-((1 + S^2)*(417 + 802*S^2 + 417*S^4))/(8*S^3) + (Pi^4*(7838 - 96034*S^2 + 73673*S^4 + 5159*S^6 - 3702*S^8))/(180*S*(1 + S^2)^3) + (Pi^2*(-103 - 280*S^2 - 494*S^4 - 344*S^6 - 75*S^8))/(24*S^3*(1 + S^2)) + ((343 - 4976*S^2 + 6198*S^4 + 856*S^6 - 221*S^8)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(-17 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) + (-39 - 30*S^2 - 351*S^4 - 1306*S^6 - 467*S^8 - 16*S^10 - 15*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(-50 + 287*S^2 - 348*S^4 + 127*S^6 + 92*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-95 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(1 + S^2)^3 + (2*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(-367 + 4764*S^2 - 5850*S^4 - 598*S^6 + 303*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-707 + 255*S^2 + 255*S^4 + 85*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (40*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-4579 + 1743*S^2 + 1743*S^4 + 581*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (240*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(-82 + 45*S^2 + 45*S^4 + 15*S^6))/(3*(1 + S^2)^3) + (3 - 28*S^2 + 223*S^4 - 2226*S^6 + 419*S^8 - 2*S^10 - 21*S^12)/(S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1291 - 15150*S^2 + 14766*S^4 + 1270*S^6 - 777*S^8))/(6*S*(1 + S^2)^3) + (-41 - 358*S^2 - 170*S^4 - 182*S^6 - 41*S^8)/(2*S^3*(1 + S^2)) - (4*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-307 + 123*S^2 + 123*S^4 + 41*S^6)*Zeta[3])/(1 + S^2)^3) - (8*S*(-111 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[5])/(1 + S^2)^3)) - (2232*S*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[7])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(289 + 1922*S^2 + 289*S^4))/(32*S^3) + (Pi^6*(179178 - 2312311*S^2 + 1340511*S^4 + 151266*S^6 - 21694*S^8))/(45360*S*(1 + S^2)^3) + (Pi^2*(-779 - 3636*S^2 - 6750*S^4 - 2892*S^6 - 535*S^8))/(96*S^3*(1 + S^2)) + (Pi^4*(-1734 - 6679*S^2 - 15617*S^4 - 4665*S^6 - 425*S^8))/(2880*S^3*(1 + S^2)) + (31*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2]^3)/(S*(1 + S^2)^2) + ((23 - 437*S^2 + 624*S^4 + 155*S^6 + 7*S^8)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(-167 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) + (-48 + 89*S^2 - 704*S^4 - 2290*S^6 + 117*S^8 - 261*S^10 - 3*S^12)/(S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((335 - 1475*S^2 - 3759*S^4 - 1456*S^6 - 155*S^8)*HPL[{6}, -S^2])/(S*(1 + S^2)^3) - (24*S*(42 + 69*S^2 + 69*S^4 + 23*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 + (2*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^3) + ((2*Pi^2*S*(-1531 + 915*S^2 + 915*S^4 + 305*S^6))/(3*(1 + S^2)^3) + (9 + 138*S^2 - 1009*S^4 + 7658*S^6 - 4571*S^8 + 508*S^10 - 45*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((Pi^2*S*(-10379 + 6327*S^2 + 6327*S^4 + 2109*S^6))/(3*(1 + S^2)^3) - (2*(-36 - 212*S^2 + 1327*S^4 - 14121*S^6 + 7141*S^8 - 923*S^10 + 72*S^12))/(S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + (3*(25 - 475*S^2 + 660*S^4 + 157*S^6 + 5*S^8)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-24 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 + (2*(35 - 3092*S^2 + 7314*S^4 + 1832*S^6 + 31*S^8)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-73 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{5, 2}, -S^2])/(1 + S^2)^3 + (2*S*(337 + 699*S^2 + 699*S^4 + 233*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) - (2*(18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((32*Pi^2*S*(-687 + 147*S^2 + 147*S^4 + 49*S^6))/(3*(1 + S^2)^3) + (2*(-90 + 585*S^2 - 8508*S^4 + 11314*S^6 - 4378*S^8 + 85*S^10))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + (744*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (2*S*(-6029 + 3561*S^2 + 3561*S^4 + 1187*S^6)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^3 - (16*S*(-2309 + 1353*S^2 + 1353*S^4 + 451*S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 + (16*(134 - 590*S^2 - 2292*S^4 - 343*S^6 + 145*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-18175 + 10707*S^2 + 10707*S^4 + 3569*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 - (2*S*(-56395 + 32847*S^2 + 32847*S^4 + 10949*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 - (48*S*(-4833 + 2829*S^2 + 2829*S^4 + 943*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((8*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) - (12*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 1488*S*HPL[{2, 2, 2, 1}, -S^2] - (16*(89 - 275*S^2 - 1842*S^4 - 298*S^6 + 100*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (160*S*(-173 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (160*S*(-173 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(2009 + 807*S^2 + 807*S^4 + 269*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (64*S*(1657 + 516*S^2 + 516*S^4 + 172*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (3600*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (384*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (320*S*(-947 + 399*S^2 + 399*S^4 + 133*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + 7200*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (-(Pi^4*S*(-2651 + 2106*S^2 + 2106*S^4 + 702*S^6))/(45*(1 + S^2)^3) + (-3 - 197*S^2 - 773*S^4 + 81*S^6 + 132*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-3 - 60*S^2 + 851*S^4 - 7818*S^6 + 5259*S^8 - 790*S^10 + 105*S^12))/(12*S^3*(1 + S^2)^3))*Zeta[3] - (2*(-13 + 109*S^2 - 153*S^4 - 13*S^6 + 10*S^8)*Zeta[3]^2)/(S*(1 + S^2)^3) + HPL[{4}, -S^2]*((131 - 1073*S^2 - 1399*S^4 - 27*S^6)/(8*S^3) + (Pi^2*(21 + 1337*S^2 - 4056*S^4 - 917*S^6 + 39*S^8))/(6*S*(1 + S^2)^3) + (2*S*(-847 + 339*S^2 + 339*S^4 + 113*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (2*S*(-103 + 75*S^2 + 75*S^4 + 25*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((24*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(1051 - 9932*S^2 - 882*S^4 + 148*S^6 + 487*S^8))/(3*S*(1 + S^2)^3) - (32*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*((Pi^2*(615 - 8372*S^2 + 8698*S^4 + 1278*S^6 - 231*S^8))/(12*S*(1 + S^2)^3) + (-9 - 38*S^2 + 14*S^4 + 10*S^6 - 9*S^8)/(4*S^3*(1 + S^2)) - (2*S*(-865 + 489*S^2 + 489*S^4 + 163*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + 186*S*HPL[{2, 1}, -S^2] - (2*S*(-649 + 405*S^2 + 405*S^4 + 135*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((35 + 713*S^2 + 473*S^4 - 61*S^6)/(2*S^3) - (2*Pi^2*(240 - 1949*S^2 - 971*S^4 - 165*S^6 + 105*S^8))/(3*S*(1 + S^2)^3) + (8*S*(-747 + 447*S^2 + 447*S^4 + 149*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*(-(Pi^4*S*(-6485 + 4533*S^2 + 4533*S^4 + 1511*S^6))/(90*(1 + S^2)^3) + (-16 - 713*S^2 - 1539*S^4 - 435*S^6 + 119*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-36 - 88*S^2 + 141*S^4 - 5739*S^6 + 2428*S^8 - 407*S^10 + 33*S^12))/(6*S^3*(1 + S^2)^3) + (10*S*(-33 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (2*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-1455 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(5 - 316*S^2 + 464*S^4 + 122*S^6 + 9*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((135 + 1583*S^2 + 785*S^4 - 135*S^6)/(4*S^3) + (Pi^4*S*(28217 + 3411*S^2 + 3411*S^4 + 1137*S^6))/(180*(1 + S^2)^3) + (Pi^2*(90 - 321*S^2 + 5585*S^4 - 2317*S^6 - 779*S^8 + 502*S^10 - 72*S^12))/(6*S^3*(1 + S^2)^3) + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(-151 + 3632*S^2 - 8118*S^4 - 1048*S^6 + 413*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + (-(Pi^2*S*(-1459 + 1311*S^2 + 1311*S^4 + 437*S^6))/(3*(1 + S^2)^3) + (-3 + 5*S^2 + 281*S^4 - 3093*S^6 + 2981*S^8 - 526*S^10 + 87*S^12)/(S^3*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((-61 - 1181*S^2 - 675*S^4 + 61*S^6)/(4*S^3) + (Pi^2*(-185 - 2034*S^2 - 2692*S^4 - 742*S^6 + 149*S^8))/(48*S^3*(1 + S^2)) + (Pi^4*(6880 - 68025*S^2 + 5975*S^4 + 1894*S^6 + 2254*S^8))/(360*S*(1 + S^2)^3) + (-(Pi^2*S*(-1531 + 915*S^2 + 915*S^4 + 305*S^6))/(3*(1 + S^2)^3) + (-6 - 73*S^2 + 493*S^4 - 3853*S^6 + 2265*S^8 - 258*S^10 + 24*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (3*(23 - 451*S^2 + 636*S^4 + 157*S^6 + 7*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-303 + 195*S^2 + 195*S^4 + 65*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) + (18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-3163 + 1839*S^2 + 1839*S^4 + 613*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (2*S*(-9533 + 5529*S^2 + 5529*S^4 + 1843*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 744*S*HPL[{2, 2, 1}, -S^2] - (80*S*(-173 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(-1589 + 969*S^2 + 969*S^4 + 323*S^6))/(3*(1 + S^2)^3) + (-45 + 527*S^2 - 3757*S^4 + 2359*S^6 - 254*S^8 + 18*S^10)/(S*(1 + S^2)^3))*Zeta[3] - (2*S*(-1299 + 951*S^2 + 951*S^4 + 317*S^6)*Zeta[5])/(1 + S^2)^3) - (24*S*(-137 + 147*S^2 + 147*S^4 + 49*S^6)*Zeta[7])/(1 + S^2)^3) + HPL[{2}, -S^2]*((487 - 5113*S^2 - 1287*S^4 - 487*S^6)/(8*S^3) + (Pi^6*(4405 - 695360*S^2 + 168775*S^4 - 37435*S^6 - 2393*S^8))/(45360*S*(1 + S^2)^3) + (Pi^2*(51 - 5136*S^2 - 6866*S^4 - 2456*S^6 - 9*S^8))/(96*S^3*(1 + S^2)) + (Pi^4*(-688 - 8540*S^2 - 10198*S^4 - 1769*S^6 + 1105*S^8))/(1440*S^3*(1 + S^2)) + ((-12 - 120*S^2 + 566*S^4 + 197*S^6 + 27*S^8)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^3) + (-((Pi^2*S*(-43 + 69*S^2 + 69*S^4 + 23*S^6))/(1 + S^2)^3) + (-3 - 82*S^2 - 481*S^4 - 1429*S^6 + 276*S^8 - 145*S^10 + 24*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] - (2*(26 + 413*S^2 + 694*S^4 + 340*S^6 + 48*S^8)*HPL[{6}, -S^2])/(S*(1 + S^2)^3) + (8*S*(16 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 + ((159 - 227*S^2 + 207*S^4 - 11*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + ((Pi^2*S*(-1325 + 1929*S^2 + 1929*S^4 + 643*S^6))/(3*(1 + S^2)^3) + (3 - 12*S^2 - 133*S^4 + 3960*S^6 - 2923*S^8 + 524*S^10 - 27*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((8*Pi^2*S*(-490 + 759*S^2 + 759*S^4 + 253*S^6))/(3*(1 + S^2)^3) + (15 - 3*S^2 + 13*S^4 + 24222*S^6 - 17823*S^8 + 3301*S^10 - 189*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + (2*(1 - 316*S^2 + 900*S^4 + 214*S^6 + 5*S^8)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^3) - (4*S*(15 + 174*S^2 + 174*S^4 + 58*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 + (2*(16 - 781*S^2 + 4187*S^4 + 1097*S^6 + 49*S^8)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(74 + 465*S^2 + 465*S^4 + 155*S^6)*HPL[{5, 2}, -S^2])/(1 + S^2)^3 - (20*S*(59 + 138*S^2 + 138*S^4 + 46*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((-344*Pi^2*S*(7 + 6*S^2 + 6*S^4 + 2*S^6))/(3*(1 + S^2)^3) + (2*(-15 + 227*S^2 - 1814*S^4 + 1574*S^6 - 307*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((2*Pi^2*S*(1589 + 351*S^2 + 351*S^4 + 117*S^6))/(1 + S^2)^3 - (2*(-45 + 629*S^2 - 4653*S^4 + 2818*S^6 + 857*S^8 - 319*S^10 + 9*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (2*(25 - 475*S^2 + 660*S^4 + 157*S^6 + 5*S^8)*HPL[{3, 1, 2}, -S^2])/(S*(1 + S^2)^3) - (2*(-147 + 4773*S^2 - 5492*S^4 - 1059*S^6 + 41*S^8)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-1141 + 1737*S^2 + 1737*S^4 + 579*S^6)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^3 - (16*S*(-917 + 1371*S^2 + 1371*S^4 + 457*S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 - (2*(-515 + 15235*S^2 - 15288*S^4 - 2789*S^6 + 169*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-3673 + 5469*S^2 + 5469*S^4 + 1823*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-11221 + 16809*S^2 + 16809*S^4 + 5603*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-22853 + 34497*S^2 + 34497*S^4 + 11499*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((-16*Pi^2*S*(-599 + 225*S^2 + 225*S^4 + 75*S^6))/(3*(1 + S^2)^3) + (4*(18 - 207*S^2 + 1642*S^4 - 3274*S^6 + 1546*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] - (64*S*(-181 + 102*S^2 + 102*S^4 + 34*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^3 - (4*(-1693 - 4898*S^2 + 5832*S^4 - 1342*S^6 + 61*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-6119 + 1275*S^2 + 1275*S^4 + 425*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-6119 + 1275*S^2 + 1275*S^4 + 425*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 - (68*S*(-871 + 363*S^2 + 363*S^4 + 121*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-22297 + 8925*S^2 + 8925*S^4 + 2975*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (16*(-83 + 2668*S^2 - 3090*S^4 - 596*S^6 + 25*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 4928*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 14784*S*HPL[{2, 2, 1, 1, 1}, -S^2] - (32*S*(221 + 3273*S^2 + 3273*S^4 + 1091*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (128*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (-(Pi^4*S*(-2207 + 3528*S^2 + 3528*S^4 + 1176*S^6))/(90*(1 + S^2)^3) + (34 + 129*S^2 - 204*S^4 - 69*S^6 + 86*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(6 - 4*S^2 - 50*S^4 - 4059*S^6 + 3019*S^8 - 577*S^10 + 33*S^12))/(12*S^3*(1 + S^2)^3))*Zeta[3] + ((-1 - 23*S^2 - 30*S^4 - 7*S^6)*Zeta[3]^2)/(S*(1 + S^2)^2) + HPL[{4}, -S^2]*((Pi^2*(3 + 137*S^2 - 1706*S^4 - 545*S^6 - 61*S^8))/(6*S*(1 + S^2)^3) + (-8 - 41*S^2 - 64*S^4 - 121*S^6 + 54*S^8)/(4*S^3*(1 + S^2)) + (4*S*(-305 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-9 + 75*S^2 + 75*S^4 + 25*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(171 - 8241*S^2 + 9605*S^4 + 1783*S^6 - 58*S^8))/(3*S*(1 + S^2)^3) + (13 + 17*S^2 - 48*S^4 - 63*S^6 + 13*S^8)/(S^3*(1 + S^2)) - (32*S*(-125 + 213*S^2 + 213*S^4 + 71*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((5 - 114*S^2 + 160*S^4 + 270*S^6 - 57*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-113 + 4320*S^2 - 4459*S^4 - 747*S^6 + 57*S^8))/(3*S*(1 + S^2)^3) + (4*S*(-491 + 879*S^2 + 879*S^4 + 293*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*(-(Pi^4*S*(-1032 + 1887*S^2 + 1887*S^4 + 629*S^6))/(45*(1 + S^2)^3) + (-13 + 102*S^2 - 408*S^4 + 18*S^6 + 253*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-8 - 113*S^2 - 1970*S^4 + 1484*S^6 - 302*S^8 + 21*S^10))/(6*S*(1 + S^2)^3) + (36*S*(-1 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (2*(181 - 3127*S^2 + 3795*S^4 + 945*S^6 + 10*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(-176 + 243*S^2 + 243*S^4 + 81*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-1433 + 1869*S^2 + 1869*S^4 + 623*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(3 - 98*S^2 + 153*S^4 + 29*S^6 + 3*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-53*Pi^4*S*(-231 + 60*S^2 + 60*S^4 + 20*S^6))/(90*(1 + S^2)^3) + (30 + 143*S^2 + 26*S^4 + 15*S^6 + 30*S^8)/(S^3*(1 + S^2)) + (Pi^2*(69 - 848*S^2 + 6553*S^4 - 10176*S^6 + 3379*S^8 - 504*S^10 + 39*S^12))/(12*S^3*(1 + S^2)^3) - (12*S*(5 + 351*S^2 + 351*S^4 + 117*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - 2464*S*HPL[{2, 1, 1}, -S^2] - (2*(-161 + 2431*S^2 - 2755*S^4 - 601*S^6 + 42*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + ((-2*Pi^2*S*(-272 + 507*S^2 + 507*S^4 + 169*S^6))/(3*(1 + S^2)^3) + (12 - 8*S^2 - 404*S^4 - 3263*S^6 + 2869*S^8 - 665*S^10 + 51*S^12)/(2*S^3*(1 + S^2)^3))*Zeta[5] - (12*S*(-73 + 204*S^2 + 204*S^4 + 68*S^6)*Zeta[7])/(1 + S^2)^3) + HPL[{1}, -S^2]*(-((1 + S^2)*(253 + 39546*S^2 + 253*S^4))/(32*S^3) + (Pi^8*S*(-3182285 + 42984*S^2 + 42984*S^4 + 14328*S^6))/(680400*(1 + S^2)^3) + (Pi^4*(-1763 - 8424*S^2 - 16834*S^4 - 6668*S^6 - 911*S^8))/(1440*S^3*(1 + S^2)) + (Pi^2*(-520 - 3527*S^2 - 6357*S^4 - 3061*S^6 - 479*S^8))/(48*S^3*(1 + S^2)) + (Pi^6*(-15288 + 175875*S^2 - 1833797*S^4 + 2187128*S^6 - 777308*S^8 - 82287*S^10 + 28389*S^12))/(90720*S^3*(1 + S^2)^3) + ((-5*Pi^2*S*(91 + 15*S^2 + 15*S^4 + 5*S^6))/(9*(1 + S^2)^3) + (-15 + 73*S^2 - 1108*S^4 + 868*S^6 - 153*S^8 + 15*S^10)/(6*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^3 + (2*S*(-191 + 72*S^2 + 72*S^4 + 24*S^6)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^3) + ((8*Pi^2*S*(-5 + 3*S^2 + 3*S^4 + S^6))/(1 + S^2)^3 + (9 + 52*S^2 - 113*S^4 + 2228*S^6 - 37*S^8 + 72*S^10 - 3*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{3}, -S^2]^2 - (4*S*(29 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{4}, -S^2]^2)/(1 + S^2)^3 + ((-35*Pi^2*S*(5 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) + (-132 + 300*S^2 - 1931*S^4 - 3496*S^6 - 1349*S^8 - 660*S^10 - 12*S^12)/(S^3*(1 + S^2)^3))*HPL[{6}, -S^2] - (2*(-532 + 2346*S^2 + 4047*S^4 + 2363*S^6 + 510*S^8)*HPL[{7}, -S^2])/(S*(1 + S^2)^3) - (12*S*(379 + 474*S^2 + 474*S^4 + 158*S^6)*HPL[{8}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) + (18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2]^2 + (4*S*(-1847 + 699*S^2 + 699*S^4 + 233*S^6)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(-145 + 57*S^2 + 57*S^4 + 19*S^6))/(1 + S^2)^3 + (2*(-3 + 4*S^2 - 131*S^4 + 720*S^6 - 149*S^8 + 4*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{4, 2}, -S^2] - (2*(-15 - 232*S^2 + 667*S^4 + 213*S^6 + 25*S^8)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)^3) + ((4*Pi^2*S*(-577 + 423*S^2 + 423*S^4 + 141*S^6))/(3*(1 + S^2)^3) + (81 - 102*S^2 + 695*S^4 + 10760*S^6 - 1079*S^8 + 586*S^10 + 27*S^12)/(S^3*(1 + S^2)^3))*HPL[{5, 1}, -S^2] - (3*(-33 - 358*S^2 + 1044*S^4 + 370*S^6 + 57*S^8)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)^3) - (24*S*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{5, 3}, -S^2])/(1 + S^2)^3 - (2*(245 - 1825*S^2 - 2599*S^4 - 826*S^6 + 15*S^8)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)^3) - (60*S*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{6, 2}, -S^2])/(1 + S^2)^3 + (8*S*(325 + 513*S^2 + 513*S^4 + 171*S^6)*HPL[{7, 1}, -S^2])/(1 + S^2)^3 + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^3 - (2*(-3 + S^2 - 17*S^4 + 3*S^6)*HPL[{3, 1, 2}, -S^2])/S^3 + ((-40*Pi^2*S*(91 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) + (2*(-27 + 151*S^2 - 2198*S^4 + 1766*S^6 - 295*S^8 + 27*S^10))/(S^3*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] + (2*(-308 + 7721*S^2 - 16732*S^4 - 2363*S^6 + 750*S^8)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)^3) + (48*(-40 + 991*S^2 - 2125*S^4 - 302*S^6 + 94*S^8)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)^3) + (56*S*(-29 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(4267 + 1737*S^2 + 1737*S^4 + 579*S^6))/(3*(1 + S^2)^3) + (4*(-63 + 181*S^2 - 3257*S^4 - 3282*S^6 + 2491*S^8 - 563*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{4, 1, 1}, -S^2] + (6*(-313 + 7767*S^2 - 16780*S^4 - 2361*S^6 + 755*S^8)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-337 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^3 + (6*(-989 + 24307*S^2 - 51708*S^4 - 7405*S^6 + 2255*S^8)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-125 + 129*S^2 + 129*S^4 + 43*S^6)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^3 - (8*S*(-1193 + 705*S^2 + 705*S^4 + 235*S^6)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^3 + (4*(-2939 + 74732*S^2 - 160602*S^4 - 23576*S^6 + 6761*S^8)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-359 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^3 - (64*S*(-611 + 372*S^2 + 372*S^4 + 124*S^6)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-24953 + 16509*S^2 + 16509*S^4 + 5503*S^6)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^3 - (1488*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + ((16*Pi^2*S*(309 + 183*S^2 + 183*S^4 + 61*S^6))/(3*(1 + S^2)^3) - (4*(-54 + 91*S^2 - 2336*S^4 - 3138*S^6 + 1762*S^8 - 425*S^10 + 36*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1}, -S^2] + (8*(715 - 7580*S^2 + 2478*S^4 + 484*S^6 + 151*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)^3) + (8*(715 - 7580*S^2 + 2478*S^4 + 484*S^6 + 151*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (12*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2)^3 + (8*(1273 - 11486*S^2 - 3102*S^4 - 74*S^6 + 709*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (12*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2)^3 + (4*S*(83 + 1257*S^2 + 1257*S^4 + 419*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^3 + 4560*S*HPL[{3, 3, 1, 1}, -S^2] + (8*(3841 - 36004*S^2 - 5718*S^4 + 592*S^6 + 2105*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (36*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (12*S*(83 + 1257*S^2 + 1257*S^4 + 419*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (36*S*(281 + 1179*S^2 + 1179*S^4 + 393*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (64*S*(127 + 1461*S^2 + 1461*S^4 + 487*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-16*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) + (24*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (16*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (48*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 2976*S*HPL[{2, 2, 1, 2, 1}, -S^2] + 8928*S*HPL[{2, 2, 2, 1, 1}, -S^2] + (32*(-940 + 14653*S^2 - 20436*S^4 - 2866*S^6 + 763*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 17856*S*HPL[{3, 1, 1, 1, 2}, -S^2] - 29760*S*HPL[{3, 1, 1, 2, 1}, -S^2] - 35712*S*HPL[{3, 1, 2, 1, 1}, -S^2] - 74400*S*HPL[{3, 2, 1, 1, 1}, -S^2] - (64*S*(3187 + 10641*S^2 + 10641*S^4 + 3547*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (7200*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (128*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - 14400*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (-(Pi^2*S*(135 + 33*S^2 + 33*S^4 + 11*S^6))/(3*(1 + S^2)^3) + (3 + 41*S^2 - 7*S^4 + 245*S^6 - 21*S^8 + 16*S^10 - 9*S^12)/(S^3*(1 + S^2)^3))*Zeta[3]^2 + HPL[{3, 2}, -S^2]*((Pi^2*(323 - 7758*S^2 + 17020*S^4 + 2218*S^6 - 851*S^8))/(6*S*(1 + S^2)^3) - (2*(-4 - 66*S^2 - 119*S^4 - 32*S^6 + 13*S^8))/(S^3*(1 + S^2)) - (8*S*(77 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4, 1}, -S^2]*((Pi^2*(462 - 12977*S^2 + 29586*S^4 + 4247*S^6 - 1314*S^8))/(3*S*(1 + S^2)^3) + (-5 + 2826*S^2 + 5520*S^4 + 2086*S^6 - 315*S^8)/(4*S^3*(1 + S^2)) + (4*S*(-565 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{5}, -S^2]*((172 - 771*S^2 - 2661*S^4 - 1317*S^6 - 31*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(163 - 26*S^2 - 4252*S^4 - 1078*S^6 + 33*S^8))/(6*S*(1 + S^2)^3) + (4*S*(-303 + 195*S^2 + 195*S^4 + 65*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(53 + 63*S^2 + 63*S^4 + 21*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1, 1}, -S^2]*((-48*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 - (2*Pi^2*(1051 - 9932*S^2 - 882*S^4 + 148*S^6 + 487*S^8))/(3*S*(1 + S^2)^3) + (64*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 2, 1}, -S^2]*((-2*(9 + 38*S^2 - 14*S^4 - 10*S^6 + 9*S^8))/(S^3*(1 + S^2)) - (2*Pi^2*(-615 + 8372*S^2 - 8698*S^4 - 1278*S^6 + 231*S^8))/(3*S*(1 + S^2)^3) - (16*S*(-649 + 405*S^2 + 405*S^4 + 135*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1, 1}, -S^2]*((-71 - 900*S^2 - 1130*S^4 - 372*S^6 + 25*S^8)/(S^3*(1 + S^2)) - (4*Pi^2*(-855 + 10321*S^2 - 7727*S^4 - 1113*S^6 + 126*S^8))/(3*S*(1 + S^2)^3) - (16*S*(-2045 + 1257*S^2 + 1257*S^4 + 419*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4}, -S^2]*((40 - 405*S^2 - 620*S^4 - 19*S^6)/(2*S^3) - (4*Pi^4*S*(-255 + 264*S^2 + 264*S^4 + 88*S^6))/(45*(1 + S^2)^3) + (Pi^2*(-72 + 17*S^2 - 927*S^4 - 5950*S^6 + 478*S^8 - 467*S^10 + 9*S^12))/(12*S^3*(1 + S^2)^3) + (6*(23 - 451*S^2 + 636*S^4 + 157*S^6 + 7*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-401 + 213*S^2 + 213*S^4 + 71*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-847 + 339*S^2 + 339*S^4 + 113*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(4 + 113*S^2 - 352*S^4 - 69*S^6 + 8*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((57 + 1048*S^2 + 649*S^4 - 78*S^6)/(2*S^3) + (Pi^4*S*(5773 + 1398*S^2 + 1398*S^4 + 466*S^6))/(45*(1 + S^2)^3) + (Pi^2*(54 - 132*S^2 + 2724*S^4 + 173*S^6 - 438*S^8 + 285*S^10 - 30*S^12))/(3*S^3*(1 + S^2)^3) - (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (8*(-38 + 948*S^2 - 2081*S^4 - 278*S^6 + 101*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((Pi^4*S*(-12258 + 3135*S^2 + 3135*S^4 + 1045*S^6))/(180*(1 + S^2)^3) + (-41 - 392*S^2 - 158*S^4 - 136*S^6 - 41*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-18 + 220*S^2 - 2865*S^4 + 5566*S^6 - 1990*S^8 + 122*S^10 - 3*S^12))/(12*S^3*(1 + S^2)^3) + (2*(-48 + 1143*S^2 - 2339*S^4 - 354*S^6 + 92*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-283 + 159*S^2 + 159*S^4 + 53*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (186*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-101 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - 372*S*HPL[{2, 1, 1}, -S^2] + ((-71 + 1580*S^2 - 3698*S^4 - 434*S^6 + 211*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((-135 - 1583*S^2 - 785*S^4 + 135*S^6)/(2*S^3) - (Pi^4*S*(28217 + 3411*S^2 + 3411*S^4 + 1137*S^6))/(90*(1 + S^2)^3) + (Pi^2*(-90 + 321*S^2 - 5585*S^4 + 2317*S^6 + 779*S^8 - 502*S^10 + 72*S^12))/(3*S^3*(1 + S^2)^3) + (4*(-151 + 3632*S^2 - 8118*S^4 - 1048*S^6 + 413*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + ((-48 - 369*S^2 - 923*S^4 - 95*S^6 + 27*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-33 + 1055*S^2 - 5413*S^4 - 320*S^6 + 493*S^8))/(3*S*(1 + S^2)^3))*Zeta[5] + HPL[{3}, -S^2]*((Pi^2*(-15 - 575*S^2 - 923*S^4 - 333*S^6 + 54*S^8))/(12*S^3*(1 + S^2)) + (-5 - 433*S^2 - 1243*S^4 - 375*S^6 + 56*S^8)/(2*S^3*(1 + S^2)) + (Pi^4*(-109 + 7189*S^2 - 20685*S^4 - 3062*S^6 + 933*S^8))/(90*S*(1 + S^2)^3) + (2*(-7 - 199*S^2 + 551*S^4 + 152*S^6 + 9*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (4*S*(51 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-1531 + 915*S^2 + 915*S^4 + 305*S^6))/(3*(1 + S^2)^3) - (2*(-6 - 73*S^2 + 493*S^4 - 3853*S^6 + 2265*S^8 - 258*S^10 + 24*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(-73 + 1849*S^2 - 4054*S^4 - 553*S^6 + 191*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-139 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-133 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (4*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-865 + 489*S^2 + 489*S^4 + 163*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-4915 + 2823*S^2 + 2823*S^4 + 941*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-119 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (3 + 10*S^2 + 99*S^4 - 582*S^6 + 269*S^8 + 32*S^10 - 15*S^12)/(S^3*(1 + S^2)^3))*Zeta[3] - (8*S*(-47 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(1 + S^2)^3) + Zeta[3]*((Pi^2*(-24 - 209*S^2 - 723*S^4 - 207*S^6 - 5*S^8))/(24*S^3*(1 + S^2)) + (55 - 364*S^2 - 1874*S^4 + 380*S^6 + 299*S^8)/(8*S^3*(1 + S^2)) + (Pi^4*(-243 + 9740*S^2 - 36743*S^4 - 4113*S^6 + 2377*S^8))/(180*S*(1 + S^2)^3) - (8*S*(43 + 39*S^2 + 39*S^4 + 13*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((61 + 1181*S^2 + 675*S^4 - 61*S^6)/(2*S^3) + (Pi^4*(-6880 + 68025*S^2 - 5975*S^4 - 1894*S^6 - 2254*S^8))/(180*S*(1 + S^2)^3) + (Pi^2*(185 + 2034*S^2 + 2692*S^4 + 742*S^6 - 149*S^8))/(24*S^3*(1 + S^2)) - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-3163 + 1839*S^2 + 1839*S^4 + 613*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-9533 + 5529*S^2 + 5529*S^4 + 1843*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (8*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 1488*S*HPL[{2, 2, 1}, -S^2] + (160*S*(-173 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-1589 + 969*S^2 + 969*S^4 + 323*S^6))/(3*(1 + S^2)^3) - (2*(-45 + 527*S^2 - 3757*S^4 + 2359*S^6 - 254*S^8 + 18*S^10))/(S*(1 + S^2)^3))*Zeta[3] + (4*S*(-1299 + 951*S^2 + 951*S^4 + 317*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2}, -S^2]*((-41 - 3625*S^2 - 2775*S^4 + 41*S^6)/(8*S^3) - (Pi^6*S*(35307 + 5523*S^2 + 5523*S^4 + 1841*S^6))/(2520*(1 + S^2)^3) + (Pi^2*(-267 - 3388*S^2 - 4382*S^4 - 1364*S^6 + 185*S^8))/(48*S^3*(1 + S^2)) + (Pi^4*(-1248 + 4005*S^2 - 74161*S^4 + 34998*S^6 - 964*S^8 - 6075*S^10 + 981*S^12))/(720*S^3*(1 + S^2)^3) + (2*S*(-139 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(-385 + 201*S^2 + 201*S^4 + 67*S^6))/(3*(1 + S^2)^3) + (-3 - 58*S^2 + 263*S^4 - 3216*S^6 + 239*S^8 - 70*S^10 - 3*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(-5 - 363*S^2 + 986*S^4 + 241*S^6 + S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - (4*S*(43 + 144*S^2 + 144*S^4 + 48*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 + 372*S*HPL[{2, 1}, -S^2]^2 + ((-2*Pi^2*S*(-2441 + 765*S^2 + 765*S^4 + 255*S^6))/(3*(1 + S^2)^3) + (2*(9 - 131*S^2 + 1528*S^4 - 3613*S^6 + 1550*S^8 - 120*S^10 + 9*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (2*(-167 + 4097*S^2 - 8696*S^4 - 1259*S^6 + 373*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) - (6*(-169 + 4121*S^2 - 8720*S^4 - 1259*S^6 + 375*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + (168*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-1127 + 555*S^2 + 555*S^4 + 185*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) - (2*(18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (744*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (4*(715 - 7580*S^2 + 2478*S^4 + 484*S^6 + 151*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-2759 + 1035*S^2 + 1035*S^4 + 345*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-8321 + 3117*S^2 + 3117*S^4 + 1039*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (8*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (320*S*(133 + 138*S^2 + 138*S^4 + 46*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-7 - 174*S^2 - 380*S^4 - 122*S^6 + 43*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-72 + 1983*S^2 - 4529*S^4 - 644*S^6 + 204*S^8))/(3*S*(1 + S^2)^3))*Zeta[3] - 14*S*Zeta[3]^2 + HPL[{3}, -S^2]*((-21 - 314*S^2 - 508*S^4 - 110*S^6 + 57*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-161 + 3880*S^2 - 8510*S^4 - 1110*S^6 + 425*S^8))/(6*S*(1 + S^2)^3) + (8*S*(-865 + 489*S^2 + 489*S^4 + 163*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(77 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((9 + 38*S^2 - 14*S^4 - 10*S^6 + 9*S^8)/(S^3*(1 + S^2)) + (Pi^2*(-615 + 8372*S^2 - 8698*S^4 - 1278*S^6 + 231*S^8))/(3*S*(1 + S^2)^3) + (8*S*(-649 + 405*S^2 + 405*S^4 + 135*S^6)*Zeta[3])/(1 + S^2)^3) + (2*(-33 + 1357*S^2 - 4181*S^4 - 456*S^6 + 267*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + (3*(-15 + 434*S^2 - 4614*S^4 - 72*S^6 + 527*S^8)*Zeta[7])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]*((-2223 - 37576*S^2 - 253*S^4)/(32*S) + (Pi^2*(-1399 - 7189*S^2 - 5199*S^4 - 945*S^6))/(96*S*(1 + S^2)) + (Pi^4*(-2700 - 9551*S^2 - 2996*S^4 + 831*S^6))/(1920*S*(1 + S^2)) + (7*Pi^8*S*(-70669 + 16296*S^2 + 16296*S^4 + 5432*S^6))/(194400*(1 + S^2)^3) - (Pi^6*S*(1822498 - 1949549*S^2 + 934695*S^4 + 63837*S^6 + 166935*S^8))/(181440*(1 + S^2)^3) - (2*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^7)/(3*S*(1 + S^2)^3) + (4*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)^3) + ((7*Pi^2*S*(-63 + 51*S^2 + 51*S^4 + 17*S^6))/(9*(1 + S^2)^3) + (-15 - 42*S^2 - 925*S^4 + 3080*S^6 - 1997*S^8 + 282*S^10 - 15*S^12)/(12*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^3 + (S*(-167 + 144*S^2 + 144*S^4 + 48*S^6)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^6*((Pi^2*S*(-991 + 303*S^2 + 303*S^4 + 101*S^6))/(27*(1 + S^2)^3) + (-3 + 38*S^2 - 441*S^4 + 1052*S^6 - 441*S^8 + 38*S^10 - 3*S^12)/(6*S^3*(1 + S^2)^3) + (2*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((4*Pi^2*S*(4 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (3 + 2*S^2 + 63*S^4 + 80*S^6 + 119*S^8 + 10*S^10 + 3*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{3}, -S^2]^2 - (22*S*(3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{4}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(21 + 300*S^2 + 300*S^4 + 100*S^6))/(3*(1 + S^2)^3) + (-210 - 310*S^2 - 2056*S^4 - 4435*S^6 - 4273*S^8 - 431*S^10 + 195*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{6}, -S^2] + ((55 + 742*S^2 + 966*S^4 + 23*S^6 - 172*S^8)*HPL[{7}, -S^2])/(S*(1 + S^2)^3) + (298*S*(3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{8}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(-1979 + 1419*S^2 + 1419*S^4 + 473*S^6))/(3*(1 + S^2)^3) + (3 + 7*S^2 + 1038*S^4 - 3613*S^6 + 2040*S^8 - 258*S^10 + 15*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2]^2 + (16*S*(-169 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(-5 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (-9 + 10*S^2 + 29*S^4 + 79*S^6 - 21*S^10)/(4*S^3*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + ((-38 + 186*S^2 + 189*S^4 + 97*S^6)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(-75 + 123*S^2 + 123*S^4 + 41*S^6))/(3*(1 + S^2)^3) + (60 + 92*S^2 + 1217*S^4 + 1986*S^6 + 2054*S^8 + 78*S^10 - 87*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{5, 1}, -S^2] + ((-219 + 1126*S^2 + 1286*S^4 + 694*S^6 + 33*S^8)*HPL[{5, 2}, -S^2])/(2*S*(1 + S^2)^3) + (2*S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{5, 3}, -S^2])/(1 + S^2)^3 + ((-275 + 1093*S^2 + 717*S^4 + 956*S^6 + 251*S^8)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)^3) + (10*S*(4 + 3*S^2 + 3*S^4 + S^6)*HPL[{6, 2}, -S^2])/(1 + S^2)^3 - (4*S*(41 + 285*S^2 + 285*S^4 + 95*S^6)*HPL[{7, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^3 + ((7*Pi^2*S)/3 + (9 - 14*S^2 - 14*S^4 + 18*S^6 - 3*S^8)/(2*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((7*Pi^2*S*(-503 + 411*S^2 + 411*S^4 + 137*S^6))/(3*(1 + S^2)^3) + (-51 - 164*S^2 - 3733*S^4 + 12296*S^6 - 7969*S^8 + 1140*S^10 - 63*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3, 2, 1}, -S^2] + ((16 + 639*S^2 - 1488*S^4 - 279*S^6 + 8*S^8)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)^3) - (4*(-1 - 487*S^2 + 1213*S^4 + 269*S^6 + 10*S^8)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(15 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^3 + ((40*Pi^2*S*(-273 + 219*S^2 + 219*S^4 + 73*S^6))/(3*(1 + S^2)^3) + (-123 - 269*S^2 - 6219*S^4 + 17794*S^6 - 12981*S^8 + 1651*S^10 - 93*S^12)/(S^3*(1 + S^2)^3))*HPL[{4, 1, 1}, -S^2] + ((-5 + 1883*S^2 - 4946*S^4 - 1123*S^6 - 49*S^8)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)^3) + (8*S*(14 + 99*S^2 + 99*S^4 + 33*S^6)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^3 + ((-29 + 5879*S^2 - 14954*S^4 - 3487*S^6 - 193*S^8)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(29 + 165*S^2 + 165*S^4 + 55*S^6)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^3 + (8*S*(32 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^3 - (2*(-13 - 5692*S^2 + 14800*S^4 + 3786*S^6 + 347*S^8)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(15 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^3 + (8*S*(135 + 831*S^2 + 831*S^4 + 277*S^6)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(312 + 2235*S^2 + 2235*S^4 + 745*S^6)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(-673 + 5832*S^2 - 3656*S^4 - 692*S^6 + 61*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)^3) + ((-8*Pi^2*S*(-969 + 735*S^2 + 735*S^4 + 245*S^6))/(3*(1 + S^2)^3) + (2*(57 + 68*S^2 + 2269*S^4 - 5918*S^6 + 4705*S^8 - 526*S^10 + 33*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1}, -S^2] - (4*(-2025 + 17764*S^2 - 12042*S^4 - 2452*S^6 + 123*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)^3) - (4*(-2025 + 17764*S^2 - 12042*S^4 - 2452*S^6 + 123*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)^3) + 14*S*HPL[{3, 1, 2, 2}, -S^2] - (8*(-2022 + 17630*S^2 - 11505*S^4 - 2264*S^6 + 153*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 14*S*HPL[{3, 2, 1, 2}, -S^2] - (2*S*(-4695 + 4731*S^2 + 4731*S^4 + 1577*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^3 - (96*S*(-293 + 297*S^2 + 297*S^4 + 99*S^6)*HPL[{3, 3, 1, 1}, -S^2])/(1 + S^2)^3 - (4*(-12059 + 105575*S^2 - 68514*S^4 - 13553*S^6 + 875*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 8*S*HPL[{4, 1, 1, 2}, -S^2] - (8*S*(-3517 + 3561*S^2 + 3561*S^4 + 1187*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^3 - (56*S*(-1507 + 1527*S^2 + 1527*S^4 + 509*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (64*S*(-2651 + 2682*S^2 + 2682*S^4 + 894*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((16*Pi^2*S*(-971 + 732*S^2 + 732*S^4 + 244*S^6))/(3*(1 + S^2)^3) - (4*(45 + 50*S^2 + 2239*S^4 - 6112*S^6 + 4479*S^8 - 570*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1, 1}, -S^2] + (8*(-677 + 6108*S^2 - 4718*S^4 - 1060*S^6 + 3*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (24*(-677 + 6108*S^2 - 4718*S^4 - 1060*S^6 + 3*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (6272*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(1 + S^2)^3 - (18816*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (16*(1666 - 15289*S^2 + 12102*S^4 + 2812*S^6 + 35*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-14107 + 14127*S^2 + 14127*S^4 + 4709*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (40*S*(-4703 + 4707*S^2 + 4707*S^4 + 1569*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-28219 + 28239*S^2 + 28239*S^4 + 9413*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (40*S*(-11759 + 11763*S^2 + 11763*S^4 + 3921*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (96*S*(-14717 + 14709*S^2 + 14709*S^4 + 4903*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (80*(-146 + 1221*S^2 - 810*S^4 - 143*S^6 + 18*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (32*S*(-1277 + 1209*S^2 + 1209*S^4 + 403*S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (960*S*(-85 + 81*S^2 + 81*S^4 + 27*S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((Pi^2*S*(-73 + 33*S^2 + 33*S^4 + 11*S^6))/(3*(1 + S^2)^3) - (S*(178 + 37*S^2 + 133*S^4 - 29*S^6 + 33*S^8))/(2*(1 + S^2)^3))*Zeta[3]^2 + HPL[{2, 2, 1}, -S^2]*((Pi^2*(1156 - 8989*S^2 + 5783*S^4 + 1187*S^6 - 29*S^8))/(3*S*(1 + S^2)^3) + (-21 + 44*S^2 + 28*S^4 - 100*S^6 - 15*S^8)/(2*S^3*(1 + S^2)) - (8*S*(-167 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1, 1}, -S^2]*((35 + 190*S^2 + 170*S^4 + 350*S^6 + 47*S^8)/(S^3*(1 + S^2)) + (2*Pi^2*(-1251 + 9175*S^2 - 5080*S^4 - 799*S^6 + 127*S^8))/(3*S*(1 + S^2)^3) - (16*S*(175 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(3565 - 27093*S^2 + 16667*S^4 + 3117*S^6 - 216*S^8))/(3*S*(1 + S^2)^3) + (-44 - 136*S^2 - 169*S^4 - 302*S^6 - 33*S^8)/(S^3*(1 + S^2)) - (32*S*(-125 + 6*S^2 + 6*S^4 + 2*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4, 1}, -S^2]*((-10 + 829*S^2 + 662*S^4 + 269*S^6 - 106*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-74 - 487*S^2 + 3344*S^4 + 1481*S^6 + 340*S^8))/(6*S*(1 + S^2)^3) - (4*S*(41 + 51*S^2 + 51*S^4 + 17*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((Pi^4*S*(-10325 + 5874*S^2 + 5874*S^4 + 1958*S^6))/(45*(1 + S^2)^3) + (-46 - 740*S^2 - 411*S^4 - 328*S^6 - 83*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-93 - 90*S^2 - 4445*S^4 + 8476*S^6 - 5873*S^8 + 586*S^10 - 57*S^12))/(6*S^3*(1 + S^2)^3) - (4*S*(-298 + 999*S^2 + 276*S^4 + 23*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 2}, -S^2]*((-13 + 178*S^2 - 38*S^4 + 66*S^6 + 7*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(45 - 536*S^2 + 2758*S^4 + 940*S^6 + 145*S^8))/(12*S*(1 + S^2)^3) - (2*S*(63 + 93*S^2 + 93*S^4 + 31*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) + (Pi^2*(1275 - 17204*S^2 + 16878*S^4 + 1938*S^6 - 659*S^8))/(90*S*(1 + S^2)^3) - (2*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-53 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3}, -S^2])/(15*(1 + S^2)^3) - (4*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-317 + 129*S^2 + 129*S^4 + 43*S^6)*Zeta[3])/(15*(1 + S^2)^3)) + HPL[{5}, -S^2]*((Pi^2*(42 - 59*S^2 + 348*S^4 - 199*S^6 - 144*S^8))/(6*S*(1 + S^2)^3) + (130 - 769*S^2 - 2149*S^4 - 831*S^6 + 155*S^8)/(8*S^3*(1 + S^2)) - (16*S*(11 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (2*S*(119 + 177*S^2 + 177*S^4 + 59*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*((Pi^4*S*(-9791 + 5676*S^2 + 5676*S^4 + 1892*S^6))/(360*(1 + S^2)^3) + (-33 - 518*S^2 - 158*S^4 - 10*S^6 - 49*S^8)/(16*S^3*(1 + S^2)) + (Pi^2*(-9 - 32*S^2 - 3865*S^4 + 10076*S^6 - 5119*S^8 + 540*S^10 - 39*S^12))/(48*S^3*(1 + S^2)^3) + ((2 + 161*S^2 - 369*S^4 - 71*S^6 + S^8)*HPL[{3}, -S^2])/(2*S*(1 + S^2)^3) + (S*(13 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((-673 + 5832*S^2 - 3656*S^4 - 692*S^6 + 61*S^8)*HPL[{2, 1}, -S^2])/(2*S*(1 + S^2)^3) - (S*(-1171 + 1191*S^2 + 1191*S^4 + 397*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (784*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((12 + 243*S^2 - 1081*S^4 - 349*S^6 - 45*S^8)*Zeta[3])/(2*S*(1 + S^2)^3)) + HPL[{4}, -S^2]*((Pi^4*S*(-1059 + 1113*S^2 + 1113*S^4 + 371*S^6))/(180*(1 + S^2)^3) + (239 - 1272*S^2 - 3550*S^4 - 1544*S^6 + 399*S^8)/(16*S^3*(1 + S^2)) + (Pi^2*(-60 - 59*S^2 - 1344*S^4 - 1602*S^6 - 1940*S^8 - 83*S^10))/(24*S^3*(1 + S^2)^3) + ((-18 - 31*S^2 - 268*S^4 - 145*S^6 - 34*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(23 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (24*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((22 - 235*S^2 - 240*S^4 - 153*S^6 - 26*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*((-7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(12*S^3) + (Pi^4*S*(-26053 + 6183*S^2 + 6183*S^4 + 2061*S^6))/(540*(1 + S^2)^3) + (Pi^2*(-87 + 1022*S^2 - 11953*S^4 + 21820*S^6 - 8093*S^8 + 630*S^10 - 75*S^12))/(72*S^3*(1 + S^2)^3) + ((Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(6*(1 + S^2)^3) + (-45 + 236*S^2 - 3407*S^4 + 6112*S^6 - 3311*S^8 + 284*S^10 - 45*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (4*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) - (2*(-12 - 106*S^2 + 174*S^4 + 129*S^6 + 41*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (S*(-211 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + (10*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) - (28*S*(-71 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (20*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(22 - 502*S^2 + 732*S^4 + 187*S^6 + 11*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*(-(Pi^4*S*(-20163 + 12657*S^2 + 12657*S^4 + 4219*S^6))/(180*(1 + S^2)^3) + (175 + 2072*S^2 + 1542*S^4 + 844*S^6 + 143*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(111 + 128*S^2 + 4521*S^4 - 8092*S^6 + 6257*S^8 - 532*S^10 + 39*S^12))/(12*S^3*(1 + S^2)^3) - (24*S*(-449 + 393*S^2 + 393*S^4 + 131*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(-4 - 255*S^2 + 1053*S^4 + 293*S^6 + 21*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + ((12 - 676*S^2 - 585*S^4 + 115*S^6)/(4*S*(1 + S^2)) - (Pi^2*S*(1607 + 4533*S^2 + 3728*S^4 + 1114*S^6))/(6*(1 + S^2)^3))*Zeta[5] + HPL[{2, 1}, -S^2]*((Pi^2*(77 + 666*S^2 + 647*S^4 + 586*S^6 + 96*S^8))/(24*S^3*(1 + S^2)) + (607 + 3930*S^2 + 3676*S^4 + 3526*S^6 + 101*S^8)/(16*S^3*(1 + S^2)) + (Pi^4*(-14689 + 93542*S^2 - 47056*S^4 - 6611*S^6 + 1280*S^8))/(360*S*(1 + S^2)^3) - (2*(-677 + 6108*S^2 - 4718*S^4 - 1060*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(329 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (12*S*(171 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (4*(-677 + 6108*S^2 - 4718*S^4 - 1060*S^6 + 3*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (3136*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-3699 + 3531*S^2 + 3531*S^4 + 1177*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (64*S*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-173 + 33*S^2 + 33*S^4 + 11*S^6))/(3*(1 + S^2)^3) + (-3 + 28*S^2 - 217*S^4 + 1200*S^6 + 61*S^8 + 8*S^10 + 3*S^12)/(S^3*(1 + S^2)^3))*Zeta[3] + (8*S*(-32 + 27*S^2 + 27*S^4 + 9*S^6)*Zeta[5])/(1 + S^2)^3) + Zeta[3]*((-16 - 1395*S^2 - 223*S^4)/(16*S) + (Pi^2*(6 - 439*S^2 - 227*S^4 + 206*S^6))/(24*S*(1 + S^2)) - (Pi^4*S*(12289 + 34932*S^2 + 25156*S^4 + 6989*S^6))/(360*(1 + S^2)^3) + (12*S*(-19 + 27*S^2 + 27*S^4 + 9*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(417 + 802*S^2 + 417*S^4))/(24*S^3) + (Pi^4*(7838 - 96034*S^2 + 73673*S^4 + 5159*S^6 - 3702*S^8))/(540*S*(1 + S^2)^3) + (Pi^2*(-103 - 280*S^2 - 494*S^4 - 344*S^6 - 75*S^8))/(72*S^3*(1 + S^2)) + ((343 - 4976*S^2 + 6198*S^4 + 856*S^6 - 221*S^8)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^3) + ((-2*Pi^2*S*(-17 + 21*S^2 + 21*S^4 + 7*S^6))/(9*(1 + S^2)^3) + (-39 - 30*S^2 - 351*S^4 - 1306*S^6 - 467*S^8 - 16*S^10 - 15*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(-50 + 287*S^2 - 348*S^4 + 127*S^6 + 92*S^8)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-95 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{5}, -S^2])/(3*(1 + S^2)^3) + ((-2*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(3*(1 + S^2)^3) + (2*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(-367 + 4764*S^2 - 5850*S^4 - 598*S^6 + 303*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-707 + 255*S^2 + 255*S^4 + 85*S^6)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) - (40*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)^3) + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) + (16*S*(-4579 + 1743*S^2 + 1743*S^4 + 581*S^6)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^3) - (80*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(-82 + 45*S^2 + 45*S^4 + 15*S^6))/(9*(1 + S^2)^3) + (3 - 28*S^2 + 223*S^4 - 2226*S^6 + 419*S^8 - 2*S^10 - 21*S^12)/(3*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1291 - 15150*S^2 + 14766*S^4 + 1270*S^6 - 777*S^8))/(18*S*(1 + S^2)^3) + (-41 - 358*S^2 - 170*S^4 - 182*S^6 - 41*S^8)/(6*S^3*(1 + S^2)) - (4*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) - (4*S*(-307 + 123*S^2 + 123*S^4 + 41*S^6)*Zeta[3])/(3*(1 + S^2)^3)) - (8*S*(-111 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-127 - 1671*S^2 - 1680*S^4 + 200*S^6)/(16*S^3) + (Pi^4*(719 - 1897*S^2 - 1177*S^4 - 2721*S^6 - 1112*S^8))/(360*S*(1 + S^2)^3) + (Pi^2*(-16 - 195*S^2 - 255*S^4 - 146*S^6 - 10*S^8))/(12*S^3*(1 + S^2)) + ((19 - 87*S^2 - 55*S^4 - 28*S^6 + 5*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (4*S*(32 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(225 + 39*S^2 + 39*S^4 + 13*S^6))/(3*(1 + S^2)^3) + (27 + 72*S^2 - 279*S^4 + 948*S^6 - 167*S^8 - 60*S^10 + 3*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(4 - 172*S^2 + 465*S^4 + 126*S^6 + 13*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(15 + 93*S^2 + 93*S^4 + 31*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (8*S*(17 + 60*S^2 + 60*S^4 + 20*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (4*(2 - 138*S^2 + 531*S^4 + 184*S^6 + 29*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(165 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(509 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-171 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (-(Pi^2*S*(37 + 87*S^2 + 87*S^4 + 29*S^6))/(3*(1 + S^2)^3) + (-3 + 14*S^2 - 65*S^4 - 184*S^6 - 121*S^8 - 54*S^10 - 3*S^12)/(2*S^3*(1 + S^2)^3))*Zeta[3] - (2*S*(101 + 171*S^2 + 171*S^4 + 57*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2}, -S^2]*((Pi^6*S*(-223797 + 76956*S^2 + 76956*S^4 + 25652*S^6))/(22680*(1 + S^2)^3) + (79 - 3284*S^2 - 4702*S^4 - 3412*S^6 - 537*S^8)/(16*S^3*(1 + S^2)) + (Pi^2*(-147 - 1309*S^2 - 1185*S^4 - 783*S^6 - 88*S^8))/(48*S^3*(1 + S^2)) + (Pi^4*(-1278 - 808*S^2 - 62596*S^4 + 67749*S^6 - 62189*S^8 + 3059*S^10 - 465*S^12))/(1440*S^3*(1 + S^2)^3) - (S*(7 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(35 + 27*S^2 + 27*S^4 + 9*S^6))/(3*(1 + S^2)^3) + (3 - 15*S^2 - 229*S^4 - 308*S^6 - 305*S^8 - 13*S^10 + 3*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (3*(7 - 24*S^2 + 12*S^4 + 10*S^6 + 7*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - (2*S*(63 + 114*S^2 + 114*S^4 + 38*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 - (784*S*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(-1989 + 1389*S^2 + 1389*S^4 + 463*S^6))/(3*(1 + S^2)^3) + (3 + 12*S^2 + 2129*S^4 - 7108*S^6 + 4161*S^8 - 504*S^10 + 27*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((-5 - 315*S^2 + 748*S^4 + 143*S^6 - 3*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + ((6 - 935*S^2 + 2482*S^4 + 571*S^6 + 28*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 + (4*S*(13 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-1979 + 1419*S^2 + 1419*S^4 + 473*S^6))/(3*(1 + S^2)^3) - (2*(3 + 7*S^2 + 1038*S^4 - 3613*S^6 + 2040*S^8 - 258*S^10 + 15*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (2*(-673 + 5832*S^2 - 3656*S^4 - 692*S^6 + 61*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (2*(-2023 + 17772*S^2 - 12030*S^4 - 2444*S^6 + 125*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 2*S*HPL[{3, 1, 2}, -S^2] + (2*S*(-2671 + 2307*S^2 + 2307*S^4 + 769*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 + (24*S*(-671 + 579*S^2 + 579*S^4 + 193*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(-677 + 6108*S^2 - 4718*S^4 - 1060*S^6 + 3*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (24*S*(-5153 + 5097*S^2 + 5097*S^4 + 1699*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (64*S*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-35 + 25*S^2 - 150*S^4 - 4*S^6)/(4*S^3) - (Pi^2*S*(-152 + 1324*S^2 + 409*S^4 + 37*S^6))/(6*(1 + S^2)^3))*Zeta[3] + (4*S*(-14 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{2, 1}, -S^2]*((21 - 44*S^2 - 28*S^4 + 100*S^6 + 15*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-1156 + 8989*S^2 - 5783*S^4 - 1187*S^6 + 29*S^8))/(6*S*(1 + S^2)^3) + (4*S*(-167 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((Pi^2*(-10 + 142*S^2 - 678*S^4 - 229*S^6 - 35*S^8))/(6*S*(1 + S^2)^3) + (7 - 166*S^2 - 78*S^4 - 42*S^6 + 7*S^8)/(8*S^3*(1 + S^2)) - (2*S*(165 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(29 + 39*S^2 + 39*S^4 + 13*S^6)*Zeta[3])/(1 + S^2)^3) + ((19 - 70*S^2 - 1010*S^4 - 561*S^6 - 132*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(307 + 1070*S^2 + 307*S^4))/(8*S^3) + (Pi^6*S*(-81499 + 13173*S^2 + 13173*S^4 + 4391*S^6))/(3240*(1 + S^2)^3) + (Pi^2*(-218 - 769*S^2 - 1515*S^4 - 859*S^6 - 183*S^8))/(48*S^3*(1 + S^2)) + (Pi^4*(-1218 + 14000*S^2 - 150075*S^4 + 205512*S^6 - 72402*S^8 + 5060*S^10 - 1557*S^12))/(1440*S^3*(1 + S^2)^3) + ((Pi^2*S*(-1109 + 351*S^2 + 351*S^4 + 117*S^6))/(3*(1 + S^2)^3) + (-18 + 247*S^2 - 3086*S^4 + 7226*S^6 - 3070*S^8 + 255*S^10 - 18*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (S*(-1391 + 531*S^2 + 531*S^4 + 177*S^6)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^3) - (3*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(-349 + 153*S^2 + 153*S^4 + 51*S^6))/(6*(1 + S^2)^3) + (-75 - 6*S^2 - 1157*S^4 - 1004*S^6 - 1753*S^8 - 70*S^10 - 15*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((61 - 204*S^2 + 334*S^4 - 202*S^6 - 129*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-57 + 48*S^2 + 48*S^4 + 16*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 - (16*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((-2*Pi^2*S*(-2201 + 681*S^2 + 681*S^4 + 227*S^6))/(3*(1 + S^2)^3) + (57 - 217*S^2 + 3437*S^4 - 5920*S^6 + 3537*S^8 - 239*S^10 + 33*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (2*(15 - 514*S^2 + 662*S^4 + 174*S^6 + 15*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + (2*(-5 - 1255*S^2 + 1638*S^4 + 649*S^6 + 137*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) - 3*S*HPL[{4, 2}, -S^2] - (8*S*(-57 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(1 + S^2)^3 - (2*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (4*(-1053 + 14716*S^2 - 18246*S^4 - 2310*S^6 + 745*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-1391 + 531*S^2 + 531*S^4 + 177*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-8557 + 3273*S^2 + 3273*S^4 + 1091*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (40*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (336*S*(-71 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (240*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((12 - 25*S^2 - 72*S^4 + S^6)/(2*S^3) + (Pi^2*(-1 + 448*S^2 - 1004*S^4 - 330*S^6 - 41*S^8))/(3*S*(1 + S^2)^3))*Zeta[3] + (4*S*(-37 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{3}, -S^2]*((Pi^2*(32 + 41*S^2 - 195*S^4 - 202*S^6 - 70*S^8))/(3*S*(1 + S^2)^3) + (-17 - 226*S^2 - 211*S^4 - 128*S^6 - 6*S^8)/(2*S^3*(1 + S^2)) + (4*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((41 + 358*S^2 + 170*S^4 + 182*S^6 + 41*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-1291 + 15150*S^2 - 14766*S^4 - 1270*S^6 + 777*S^8))/(6*S*(1 + S^2)^3) + (4*S*(-307 + 123*S^2 + 123*S^4 + 41*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((Pi^4*S*(-11372 + 2733*S^2 + 2733*S^4 + 911*S^6))/(90*(1 + S^2)^3) + (-129 - 1324*S^2 - 822*S^4 - 812*S^6 - 129*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-183 + 784*S^2 - 12495*S^4 + 16082*S^6 - 8647*S^8 + 566*S^10 - 123*S^12))/(24*S^3*(1 + S^2)^3) + ((-15 + 514*S^2 - 662*S^4 - 174*S^6 - 15*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (S*(-41 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (2*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((-49 + 974*S^2 - 1410*S^4 - 370*S^6 - 25*S^8)*Zeta[3])/(S*(1 + S^2)^3)) - (2*(-6 - 318*S^2 + 711*S^4 + 305*S^6 + 62*S^8)*Zeta[5])/(S*(1 + S^2)^3)) - (9*S*(201 + 337*S^2 + 151*S^4)*Zeta[7])/(1 + S^2)^2 + HPL[{1}, -S^2]*((-5*(1 + S^2)*(289 + 1922*S^2 + 289*S^4))/(32*S^3) + (Pi^6*(212853 - 2228566*S^2 + 1152255*S^4 - 156177*S^6 - 142471*S^8))/(45360*S*(1 + S^2)^3) + (Pi^2*(-737 - 2594*S^2 - 5496*S^4 - 2830*S^6 - 727*S^8))/(96*S^3*(1 + S^2)) + (Pi^4*(-1494 - 6193*S^2 - 13069*S^4 - 4667*S^6 + 127*S^8))/(2880*S^3*(1 + S^2)) + ((164 - 2231*S^2 + 2768*S^4 + 341*S^6 - 118*S^8)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)^3) + ((-2 + 29*S^2 - 46*S^4 - S^6 + 4*S^8)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^3) + ((2*Pi^2*S*(-55 + 87*S^2 + 87*S^4 + 29*S^6))/(3*(1 + S^2)^3) + (-90 - 44*S^2 - 727*S^4 - 1254*S^6 - 1560*S^8 - 162*S^10 + 21*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((105 - 74*S^2 + 615*S^4 - 299*S^6 - 217*S^8)*HPL[{6}, -S^2])/(S*(1 + S^2)^3) + (2*S*(117 + 435*S^2 + 435*S^4 + 145*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 + (2*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^3) + ((8*Pi^2*S*(-48 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) + (9 + 30*S^2 - 125*S^4 + 1018*S^6 - 251*S^8 - 24*S^10 + 15*S^12)/(S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((Pi^2*S*(-803 + 207*S^2 + 207*S^4 + 69*S^6))/(3*(1 + S^2)^3) + (147 + 234*S^2 + 545*S^4 + 7400*S^6 + 493*S^8 - 26*S^10 + 87*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] - (3*(-2 + 7*S^2 + 3*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^2) + (2*S*(89 + 135*S^2 + 135*S^4 + 45*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 + (2*(-61 + 234*S^2 - 466*S^4 + 196*S^6 + 141*S^8)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(32 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{5, 2}, -S^2])/(1 + S^2)^3 + (4*S*(309 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((8*Pi^2*S*(-1109 + 351*S^2 + 351*S^4 + 117*S^6))/(3*(1 + S^2)^3) - (2*(18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((4*Pi^2*S*(-6637 + 2085*S^2 + 2085*S^4 + 695*S^6))/(3*(1 + S^2)^3) - (2*(93 - 711*S^2 + 9609*S^4 - 20372*S^6 + 9677*S^8 - 749*S^10 + 69*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (8*(-164 + 2231*S^2 - 2768*S^4 - 341*S^6 + 118*S^8)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-557 + 153*S^2 + 153*S^4 + 51*S^6)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^3 - (320*S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 - (4*(-1034 + 13673*S^2 - 16956*S^4 - 1919*S^6 + 800*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-1759 + 483*S^2 + 483*S^4 + 161*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 - (2*S*(-5371 + 1455*S^2 + 1455*S^4 + 485*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-1307 + 339*S^2 + 339*S^4 + 113*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(1 + S^2)^3 + (4*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] - (16*S*(-1391 + 531*S^2 + 531*S^4 + 177*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^3 + (8*(-367 + 4764*S^2 - 5850*S^4 - 598*S^6 + 303*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-2163 + 825*S^2 + 825*S^4 + 275*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (32*S*(-2163 + 825*S^2 + 825*S^4 + 275*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-8499 + 3243*S^2 + 3243*S^4 + 1081*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-50783 + 19371*S^2 + 19371*S^4 + 6457*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (80*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (384*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (96*S*(-2591 + 987*S^2 + 987*S^4 + 329*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (480*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((37 + 26*S^2 - 123*S^4 - 16*S^6)/(4*S^3) - (Pi^4*S*(-593 + 2697*S^2 + 2697*S^4 + 899*S^6))/(180*(1 + S^2)^3) + (Pi^2*(3 + 54*S^2 - 210*S^4 - 2828*S^6 + 681*S^8 + 66*S^10 - 78*S^12))/(12*S^3*(1 + S^2)^3))*Zeta[3] - (2*(-19 + 112*S^2 - 87*S^4 + 77*S^6 + 43*S^8)*Zeta[3]^2)/(S*(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((26 + 264*S^2 + 197*S^4 + 118*S^6 + 15*S^8)/(S^3*(1 + S^2)) + (2*Pi^2*(-322 + 3757*S^2 - 3714*S^4 - 305*S^6 + 204*S^8))/(3*S*(1 + S^2)^3) + (32*S*(-37 + 18*S^2 + 18*S^4 + 6*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4}, -S^2]*((Pi^2*(101 - 445*S^2 + 552*S^4 - 291*S^6 - 189*S^8))/(6*S*(1 + S^2)^3) + (93 - 648*S^2 - 1246*S^4 - 624*S^6 + 121*S^8)/(8*S^3*(1 + S^2)) - (2*S*(-41 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (6*S*(25 + 27*S^2 + 27*S^4 + 9*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*((Pi^2*(290 - 3798*S^2 + 3909*S^4 + 507*S^6 - 134*S^8))/(6*S*(1 + S^2)^3) + (-9 - 38*S^2 + 14*S^4 + 10*S^6 - 9*S^8)/(4*S^3*(1 + S^2)) - (4*S*(-35 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (2*S*(-1391 + 531*S^2 + 531*S^4 + 177*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-73 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(1291 - 15150*S^2 + 14766*S^4 + 1270*S^6 - 777*S^8))/(3*S*(1 + S^2)^3) + (-41 - 358*S^2 - 170*S^4 - 182*S^6 - 41*S^8)/(S^3*(1 + S^2)) - (8*S*(-307 + 123*S^2 + 123*S^4 + 41*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((2*Pi^4*S*(-113 + 42*S^2 + 42*S^4 + 14*S^6))/(45*(1 + S^2)^3) + (-50 - 579*S^2 - 669*S^4 - 377*S^6 + 3*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-39 - 24*S^2 - 414*S^4 - 986*S^6 - 484*S^8 - 32*S^10 - 9*S^12))/(6*S^3*(1 + S^2)^3) - (4*S*(25 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (2*(15 - 514*S^2 + 662*S^4 + 174*S^6 + 15*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-161 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(-1 - 6*S^2 - 20*S^4 + 3*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*(-(Pi^4*S*(-11372 + 2733*S^2 + 2733*S^4 + 911*S^6))/(45*(1 + S^2)^3) + (129 + 1324*S^2 + 822*S^4 + 812*S^6 + 129*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(183 - 784*S^2 + 12495*S^4 - 16082*S^6 + 8647*S^8 - 566*S^10 + 123*S^12))/(12*S^3*(1 + S^2)^3) + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(49 - 974*S^2 + 1410*S^4 + 370*S^6 + 25*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + ((-2*Pi^2*S*(-5 + 141*S^2 + 141*S^4 + 47*S^6))/(3*(1 + S^2)^3) + (6 + 48*S^2 - 317*S^4 - 2192*S^6 + 514*S^8 + 156*S^10 - 111*S^12)/(2*S^3*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(7807 - 82236*S^2 + 63851*S^4 + 2121*S^6 - 4377*S^8))/(360*S*(1 + S^2)^3) + (-177 - 2120*S^2 - 1838*S^4 - 1608*S^6 - 177*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-189 - 1598*S^2 - 1284*S^4 - 850*S^6 - 111*S^8))/(48*S^3*(1 + S^2)) + ((-4*Pi^2*S*(-48 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) + (-6 - 19*S^2 + 51*S^4 - 533*S^6 + 105*S^8 + 8*S^10 - 6*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (3*(-1 + 17*S^2 - 34*S^4 - S^6 + 3*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (2*S*(61 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(-1109 + 351*S^2 + 351*S^4 + 117*S^6))/(3*(1 + S^2)^3) + (18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-279 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (2*S*(-881 + 237*S^2 + 237*S^4 + 79*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-1391 + 531*S^2 + 531*S^4 + 177*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-2163 + 825*S^2 + 825*S^4 + 275*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-16*Pi^2*S*(-19 + 12*S^2 + 12*S^4 + 4*S^6))/(3*(1 + S^2)^3) + (-3 - 24*S^2 + 221*S^4 - 2330*S^6 + 161*S^8 - 54*S^10 - 3*S^12)/(2*S^3*(1 + S^2)^3))*Zeta[3] - (8*S*(-30 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[5])/(1 + S^2)^3) - 210*S*Zeta[7])) + Log[T]*((2615*(1 + S^2))/(16*S) + (Pi^4*(8340 + 50973*S^2 + 31144*S^4 - 2657*S^6))/(2880*S*(1 + S^2)) + (Pi^2*(1173 + 5645*S^2 + 3971*S^4 + 267*S^6))/(48*S*(1 + S^2)) + (7*Pi^8*S*(70669 + 16296*S^2 + 16296*S^4 + 5432*S^6))/(97200*(1 + S^2)^3) - (Pi^6*S*(-573222 + 729257*S^2 - 425003*S^4 - 84793*S^6 + 16449*S^8))/(30240*(1 + S^2)^3) + (S*(7 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{0}, S^2]^8)/(96*(1 + S^2)^3) + (4*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^7)/(3*S*(1 + S^2)^3) - (8*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^7*((S*(56 + 33*S^2 + 35*S^4 + 10*S^6))/(48*(1 + S^2)^3) + (S*(17 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2])/(24*(1 + S^2)^3)) + ((-2*Pi^2*S*(-154 + 183*S^2 + 183*S^4 + 61*S^6))/(9*(1 + S^2)^3) + (15 + 81*S^2 + 402*S^4 - 162*S^6 - S^8 - 15*S^10)/(6*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^3 - (2*S*(-201 + 42*S^2 + 42*S^4 + 14*S^6)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^6*((-8*Pi^2*S*(-89 + 27*S^2 + 27*S^4 + 9*S^6))/(9*(1 + S^2)^3) + (3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12)/(3*S^3*(1 + S^2)^3) + 20*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^6*((Pi^2*S*(74 + 51*S^2 + 51*S^4 + 17*S^6))/(72*(1 + S^2)^3) - (S*(-307 - 64*S^2 - 180*S^4 - 68*S^6 + 3*S^8))/(96*(1 + S^2)^3) + ((-24 + 233*S^2 + 16*S^4 + 25*S^6 + 2*S^8)*HPL[{1}, -S^2])/(24*S*(1 + S^2)^3) + (S*(93 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{1}, -S^2]^2)/(24*(1 + S^2)^3) + (S*(3 + S^2)*(3 + S^4)*HPL[{2}, -S^2])/(6*(1 + S^2)^3)) + (-(Pi^2*S*(-101 + 129*S^2 + 129*S^4 + 43*S^6))/(3*(1 + S^2)^3) + (-3 - 48*S^2 - 205*S^4 - 1266*S^6 + 75*S^8 - 58*S^10 + 9*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3}, -S^2]^2 - (8*S*(-6 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2]^2)/(1 + S^2)^3 + ((2*Pi^2*S*(66 + 303*S^2 + 303*S^4 + 101*S^6))/(3*(1 + S^2)^3) + (150 - 390*S^2 + 5006*S^4 + 8245*S^6 + 3103*S^8 + 1193*S^10 - 75*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{6}, -S^2] + (2*(-305 + 3020*S^2 + 4577*S^4 + 2361*S^6 + 425*S^8)*HPL[{7}, -S^2])/(S*(1 + S^2)^3) + (12*S*(341 + 360*S^2 + 360*S^4 + 120*S^6)*HPL[{8}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(-1241 + 321*S^2 + 321*S^4 + 107*S^6))/(3*(1 + S^2)^3) - (8*(-10 + 361*S^2 - 988*S^4 + 381*S^6))/(S*(1 + S^2)^3))*HPL[{2, 1}, -S^2]^2 - (16*S*(-493 + 81*S^2 + 81*S^4 + 27*S^6)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^3 + ((-164*Pi^2*S*(-2 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (9 - 11*S^2 - 257*S^4 - 3354*S^6 + 703*S^8 - 203*S^10 + 9*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4, 2}, -S^2] - (2*(-3 + 122*S^2 - 674*S^4 - 55*S^6 + 48*S^8)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(-961 + 1425*S^2 + 1425*S^4 + 475*S^6))/(3*(1 + S^2)^3) + (2*(-33 + 55*S^2 - 1167*S^4 - 5902*S^6 + 652*S^8 - 443*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{5, 1}, -S^2] + ((-33 - 884*S^2 + 2496*S^4 - 144*S^6 - 323*S^8)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-2 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{5, 3}, -S^2])/(1 + S^2)^3 - (2*(-225 + 2529*S^2 + 4266*S^4 + 2258*S^6 + 434*S^8)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)^3) + (20*S*(-5 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{6, 2}, -S^2])/(1 + S^2)^3 - (8*S*(307 + 459*S^2 + 459*S^4 + 153*S^6)*HPL[{7, 1}, -S^2])/(1 + S^2)^3 - (320*S*(-82 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^3 + ((74*Pi^2*S)/3 + (2*(-25 + 135*S^2 - 159*S^4 + 17*S^6))/(S*(1 + S^2)^2))*HPL[{3, 1, 2}, -S^2] + ((-2*Pi^2*S*(-1269 + 1353*S^2 + 1353*S^4 + 451*S^6))/(3*(1 + S^2)^3) - (2*(-30 - 137*S^2 - 939*S^4 + 483*S^6 - 15*S^8 + 30*S^10))/(S^3*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] - (2*(37 + 4373*S^2 - 20246*S^4 - 1407*S^6 + 1527*S^8)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)^3) - (8*(41 + 3239*S^2 - 15687*S^4 - 1189*S^6 + 1136*S^8)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-125 + 129*S^2 + 129*S^4 + 43*S^6)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(-1319 + 1575*S^2 + 1575*S^4 + 525*S^6))/(3*(1 + S^2)^3) - (2*(-135 - 507*S^2 - 3573*S^4 - 6640*S^6 + 1945*S^8 - 277*S^10 + 99*S^12))/(S^3*(1 + S^2)^3))*HPL[{4, 1, 1}, -S^2] - (2*(155 + 12397*S^2 - 62136*S^4 - 4579*S^6 + 4567*S^8)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)^3) + (40*S*(-65 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^3 - (2*(479 + 39625*S^2 - 191568*S^4 - 15079*S^6 + 13603*S^8)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (24*S*(-37 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^3 + (8*S*(-1075 + 1059*S^2 + 1059*S^4 + 353*S^6)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^3 - (4*(591 + 40666*S^2 - 198100*S^4 - 16606*S^6 + 13633*S^8)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (20*S*(-257 + 237*S^2 + 237*S^4 + 79*S^6)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^3 + (140*S*(-251 + 255*S^2 + 255*S^4 + 85*S^6)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-11207 + 12063*S^2 + 12063*S^4 + 4021*S^6)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^3 + (8*(531 - 3203*S^2 - 537*S^4 + 361*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + ((16*Pi^2*S*(-167 + 243*S^2 + 243*S^4 + 81*S^6))/(3*(1 + S^2)^3) + (8*(-27 - 97*S^2 - 584*S^4 - 1570*S^6 + 297*S^8 - 69*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1}, -S^2] - (32*(389 - 2445*S^2 - 247*S^4 + 61*S^6 + 84*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)^3) - (32*(389 - 2445*S^2 - 247*S^4 + 61*S^6 + 84*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-289 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2)^3 - (8*(3149 - 17796*S^2 - 12208*S^4 - 284*S^6 + 1419*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-289 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2)^3 + (84*S*(37 + 63*S^2 + 63*S^4 + 21*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^3 + 5856*S*HPL[{3, 3, 1, 1}, -S^2] - (16*(4723 - 27508*S^2 - 16602*S^4 - 98*S^6 + 2093*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (24*S*(-113 + 165*S^2 + 165*S^4 + 55*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (504*S*(17 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (24*S*(845 + 2031*S^2 + 2031*S^4 + 677*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (32*S*(1597 + 2631*S^2 + 2631*S^4 + 877*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-160*Pi^2*S*(-22 + 21*S^2 + 21*S^4 + 7*S^6))/(1 + S^2)^3 - (8*(-45 - 103*S^2 - 1258*S^4 + 538*S^6 - 137*S^8 + 45*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] - (128*(-65 + 577*S^2 - 777*S^4 - 65*S^6 + 49*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (384*(-65 + 577*S^2 - 777*S^4 - 65*S^6 + 49*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 3904*S*HPL[{2, 2, 1, 2, 1}, -S^2] + 11712*S*HPL[{2, 2, 2, 1, 1}, -S^2] - (16*(-2579 + 25840*S^2 - 42726*S^4 - 3578*S^6 + 2767*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 22752*S*HPL[{3, 1, 1, 1, 2}, -S^2] - 38368*S*HPL[{3, 1, 1, 2, 1}, -S^2] - 46176*S*HPL[{3, 1, 2, 1, 1}, -S^2] - 96928*S*HPL[{3, 2, 1, 1, 1}, -S^2] - (1152*S*(269 + 747*S^2 + 747*S^4 + 249*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (480*(39 - 232*S^2 - 36*S^4 + 29*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (3840*S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - 13440*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((2*Pi^2*S*(73 + 33*S^2 + 33*S^4 + 11*S^6))/(3*(1 + S^2)^3) + (S*(20 - 361*S^2 - 83*S^4 - 11*S^6 + 27*S^8))/(1 + S^2)^3)*Zeta[3]^2 + HPL[{5}, -S^2]*((Pi^2*(-75 + 292*S^2 + 2429*S^4 + 532*S^6 - 54*S^8))/(3*S*(1 + S^2)^3) + (110 + 1387*S^2 + 2949*S^4 + 1217*S^6 - 23*S^8)/(4*S^3*(1 + S^2)) + (4*S*(397 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 - (128*S*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1, 1}, -S^2]*((12*(-7 - 57*S^2 - 71*S^4 + 7*S^6))/S^3 + (4*Pi^2*(1167 - 6860*S^2 - 3232*S^4 + 44*S^6 + 469*S^8))/(3*S*(1 + S^2)^3) + (27840*S*Zeta[3])/(1 + S^2)^3) + HPL[{0}, S^2]^5*((18 + 252*S^2 + 199*S^4 + S^6)/(96*S*(1 + S^2)) + (Pi^2*S*(9065 + 3282*S^2 + 4481*S^4 + 1312*S^6))/(720*(1 + S^2)^3) + ((-605 + 5844*S^2 - 1024*S^4 + 538*S^6 + 187*S^8)*HPL[{1}, -S^2]^2)/(120*S*(1 + S^2)^3) + (2*S*(327 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^3)/(45*(1 + S^2)^3) + ((-45 + 2465*S^2 - 368*S^4 + 586*S^6 + 212*S^8)*HPL[{2}, -S^2])/(120*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*S*(3093 + 327*S^2 + 327*S^4 + 109*S^6))/(360*(1 + S^2)^3) + (45 - 710*S^2 + 5930*S^4 - 3100*S^6 + 595*S^8 + 38*S^10 + 90*S^12)/(240*S^3*(1 + S^2)^3) - (S*(-1083 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(60*(1 + S^2)^3)) + (S*HPL[{3}, -S^2])/(1 + S^2)^3 - (271*S*HPL[{2, 1}, -S^2])/(15*(1 + S^2)^3) + (3*S*(3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(2*(1 + S^2)^3)) + HPL[{2, 2, 1}, -S^2]*((2*(31 + 93*S^2 - 76*S^4 - 83*S^6 + 31*S^8))/(S^3*(1 + S^2)) + (2*Pi^2*(-1059 + 8503*S^2 - 7791*S^4 - 773*S^6 + 404*S^8))/(3*S*(1 + S^2)^3) - (224*S*(57 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^5*((2*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) + (Pi^2*(-265 + 3726*S^2 - 3678*S^4 - 508*S^6 + 105*S^8))/(9*S*(1 + S^2)^3) - (60*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (560*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - 120*S*HPL[{2, 1}, -S^2] + (32*S*(-23 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{4, 1}, -S^2]*((2*(11 - 160*S^2 - 795*S^4 - 493*S^6 + 95*S^8))/(S^3*(1 + S^2)) + (Pi^2*(165 + 6963*S^2 - 36530*S^4 - 3529*S^6 + 2335*S^8))/(3*S*(1 + S^2)^3) - (32*S*(-60 + 39*S^2 + 39*S^4 + 13*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1, 1}, -S^2]*((153 + 952*S^2 + 882*S^4 + 248*S^6 + 69*S^8)/(S^3*(1 + S^2)) + (2*Pi^2*(-3242 + 22787*S^2 - 10867*S^4 - 1199*S^6 + 369*S^8))/(3*S*(1 + S^2)^3) - (16*S*(2487 + 69*S^2 + 69*S^4 + 23*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 2}, -S^2]*((23 + 46*S^2 - 1232*S^4 - 934*S^6 + 225*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(69 + 3664*S^2 - 21814*S^4 - 1892*S^6 + 1485*S^8))/(6*S*(1 + S^2)^3) - (4*S*(-123 + 87*S^2 + 87*S^4 + 29*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*(-(Pi^4*S*(-12273 + 3090*S^2 + 3090*S^4 + 1030*S^6))/(180*(1 + S^2)^3) + (-19 + 106*S^2 + 106*S^4 + 106*S^6 - 19*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(3 - 32*S^2 + 4907*S^4 - 12088*S^6 + 4581*S^8 + 16*S^10 - 27*S^12))/(24*S^3*(1 + S^2)^3) + ((11 - 1445*S^2 + 5561*S^4 + 471*S^6 - 378*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (6*S*(-87 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((531 - 3203*S^2 - 537*S^4 + 361*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (2*S*(419 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - 488*S*HPL[{2, 1, 1}, -S^2] + ((-19 - 729*S^2 + 4641*S^4 + 267*S^6 - 380*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{4}, -S^2]*((141 + 1211*S^2 + 2665*S^4 - 105*S^6)/(8*S^3) + (Pi^4*S*(-1859 + 2655*S^2 + 2655*S^4 + 885*S^6))/(90*(1 + S^2)^3) + (Pi^2*(84 - 23*S^2 + 1372*S^4 + 6098*S^6 - 712*S^8 + 533*S^10 - 24*S^12))/(12*S^3*(1 + S^2)^3) + (2*(-137 + 2197*S^2 - 648*S^4 - 83*S^6 + 19*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-79 + 117*S^2 + 117*S^4 + 39*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (120*S*(-21 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(11 + 51*S^2 - 410*S^4 - 39*S^6 + 27*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*((7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(6*S^3) - (Pi^4*S*(-28177 + 6639*S^2 + 6639*S^4 + 2213*S^6))/(270*(1 + S^2)^3) + (Pi^2*(45 - 521*S^2 + 6176*S^4 - 12364*S^6 + 4175*S^8 - 239*S^10))/(18*S^3*(1 + S^2)^3) + ((2*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) + (15 - 61*S^2 + 904*S^4 - 664*S^6 + 141*S^8 - 15*S^10)/(S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (8*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) - (2*(-165 + 4426*S^2 - 9882*S^4 - 1452*S^6 + 421*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + (300*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (16*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) + 600*S*HPL[{2, 1, 1}, -S^2] - (10*(-29 + 642*S^2 - 1614*S^4 - 164*S^6 + 105*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((49 + 888*S^2 + 296*S^4 - 49*S^6)/S^3 - (Pi^4*S*(-11717 + 5469*S^2 + 5469*S^4 + 1823*S^6))/(45*(1 + S^2)^3) + (Pi^2*(87 + 204*S^2 + 3655*S^4 - 2656*S^6 + 1041*S^8 + 188*S^10 - 87*S^12))/(3*S^3*(1 + S^2)^3) - (8*(3 + 1070*S^2 - 4808*S^4 - 254*S^6 + 401*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((-107 - 2233*S^2 - 1049*S^4 + 89*S^6)/(4*S^3) + (Pi^4*S*(-9103 + 4533*S^2 + 4533*S^4 + 1511*S^6))/(90*(1 + S^2)^3) + (Pi^2*(-105 - 266*S^2 - 3531*S^4 - 12*S^6 - 935*S^8 - 250*S^10 + 75*S^12))/(6*S^3*(1 + S^2)^3) + (928*S*(-29 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(6 + 1167*S^2 - 4881*S^4 - 263*S^6 + 403*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]^4*((300 + 2411*S^2 + 1820*S^4 - 195*S^6)/(192*S*(1 + S^2)) + (Pi^4*S*(11971 + 6258*S^2 + 6258*S^4 + 2086*S^6))/(2160*(1 + S^2)^3) - (Pi^2*S*(-7093 + 1085*S^2 - 3753*S^4 - 1293*S^6 + 78*S^8))/(288*(1 + S^2)^3) + ((-525 + 5762*S^2 - 1680*S^4 - 42*S^6 + 5*S^8)*HPL[{1}, -S^2]^3)/(36*S*(1 + S^2)^3) - (5*S*(-131 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^4)/(18*(1 + S^2)^3) + ((Pi^2*S*(537 + 75*S^2 + 75*S^4 + 25*S^6))/(36*(1 + S^2)^3) + (45 + 84*S^2 + 2523*S^4 - 1125*S^6 + 966*S^8 + 193*S^10 - 30*S^12)/(48*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (S*(-257 + 42*S^2 + 42*S^4 + 14*S^6)*HPL[{2}, -S^2]^2)/(12*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((5*Pi^2*S*(541 + 39*S^2 + 39*S^4 + 13*S^6))/(72*(1 + S^2)^3) + (45 - 520*S^2 + 5359*S^4 - 4166*S^6 + 715*S^8 + 218*S^10 - 27*S^12)/(48*S^3*(1 + S^2)^3) + (2*S*(137 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((-11 + 70*S^2 + 132*S^4 + 16*S^6 - 11*S^8)*HPL[{3}, -S^2])/(8*S*(1 + S^2)^3) + (3*S*HPL[{4}, -S^2])/2 + ((486 - 2545*S^2 + 243*S^4 + 48*S^6 + 38*S^8)*HPL[{2, 1}, -S^2])/(12*S*(1 + S^2)^3) + (S*(-517 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 1}, -S^2])/(6*(1 + S^2)^3) - (2*S*(-267 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (S*(533 + 757*S^2 + 367*S^4 + 59*S^6)*Zeta[3])/(12*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*(-1245 + 12752*S^2 - 1200*S^4 + 708*S^6 + 65*S^8))/(144*S*(1 + S^2)^3) + (60 + 381*S^2 + 835*S^4 + 507*S^6 + 89*S^8)/(96*S^3*(1 + S^2)) + ((-258 + 2454*S^2 - 529*S^4 + 23*S^6)*HPL[{2}, -S^2])/(12*S*(1 + S^2)^3) + (S*(1 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (4*S*(137 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (S*(33 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(3*(1 + S^2)^3))) + ((6 + 480*S^2 + 329*S^4 - 25*S^6)/(S*(1 + S^2)) - (Pi^2*S*(45 - 6436*S^2 - 86*S^4 + 707*S^6))/(3*(1 + S^2)^3))*Zeta[5] + HPL[{2, 1}, -S^2]*((-497 - 4161*S^2 - 3263*S^4 + 497*S^6)/(8*S^3) + (Pi^2*(-101 - 796*S^2 - 1284*S^4 - 574*S^6 + 39*S^8))/(12*S^3*(1 + S^2)) + (Pi^4*(14109 - 84262*S^2 - 19595*S^4 + 1775*S^6 + 4239*S^8))/(180*S*(1 + S^2)^3) + (4*(-471 + 4238*S^2 - 6804*S^4 - 702*S^6 + 371*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-3757 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (48*S*(961 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (64*(-65 + 577*S^2 - 777*S^4 - 65*S^6 + 49*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 1952*S*HPL[{2, 2, 1}, -S^2] - (32*S*(-719 + 453*S^2 + 453*S^4 + 151*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (640*S*(-82 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(-955 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (2*(-3 - 92*S^2 + 933*S^4 - 4096*S^6 + 1843*S^8 + 4*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*Zeta[3] - (16*S*(-403 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{0}, S^2]^3*((Pi^2*(174 + 1701*S^2 + 1313*S^4 - 10*S^6))/(144*S*(1 + S^2)) + (844 + 4479*S^2 + 2218*S^4 + 119*S^6)/(96*S*(1 + S^2)) + (Pi^4*S*(99629 + 6229*S^2 + 37465*S^4 + 12449*S^6))/(2160*(1 + S^2)^3) + ((-270 + 3142*S^2 - 1824*S^4 - 129*S^6 + 67*S^8)*HPL[{1}, -S^2]^4)/(9*S*(1 + S^2)^3) - (2*S*(-319 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{1}, -S^2]^5)/(9*(1 + S^2)^3) + ((5 + 2359*S^2 - 2175*S^4 - 189*S^6 + 68*S^8)*HPL[{2}, -S^2]^2)/(12*S*(1 + S^2)^3) + HPL[{1}, -S^2]^3*(-(Pi^2*S*(-2903 + 243*S^2 + 243*S^4 + 81*S^6))/(27*(1 + S^2)^3) + (21 - 226*S^2 + 2669*S^4 - 3020*S^6 + 739*S^8 - 30*S^10 + 15*S^12)/(9*S^3*(1 + S^2)^3) - (8*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) + ((Pi^2*S*(17 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (27 - 6*S^2 + 491*S^4 + 656*S^6 + 489*S^8 + 78*S^10 + 9*S^12)/(12*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-35 + 180*S^2 - 164*S^4 + 214*S^6 + 113*S^8)*HPL[{4}, -S^2])/(6*S*(1 + S^2)^3) - (2*S*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{5}, -S^2])/(3*(1 + S^2)^3) + (-(Pi^2*S*(1303 + 33*S^2 + 33*S^4 + 11*S^6))/(9*(1 + S^2)^3) + (-45 + 352*S^2 - 3475*S^4 + 1494*S^6 - 631*S^8 - 18*S^10 - 21*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((31 - 2455*S^2 + 2159*S^4 + 17*S^6 - 140*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) - (2*S*(-23 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) - (80*S^3*(3 + 3*S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) + (4*(-15 + 1255*S^2 - 1048*S^4 + 2*S^6 + 70*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(717 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) + (4*S*(731 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (8*S*(761 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)^3) + ((Pi^2*S*(135 + 177*S^2 + 177*S^4 + 59*S^6))/(9*(1 + S^2)^3) - (S*(-471 - 816*S^2 - 288*S^4 - 52*S^6 + 3*S^8))/(6*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((65 + 406*S^2 + 467*S^4 + 250*S^6 - 20*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-75 + 4975*S^2 - 2464*S^4 + 590*S^6 + 352*S^8))/(36*S*(1 + S^2)^3) + (8*S*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) - (2*S*(717 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (2*S*(1 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((43 + 240*S^2 + 534*S^4 + 304*S^6 + 15*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-1145 + 12128*S^2 - 4672*S^4 + 280*S^6 + 321*S^8))/(36*S*(1 + S^2)^3) + ((-551 + 5580*S^2 - 3126*S^4 - 80*S^6 + 177*S^8)*HPL[{2}, -S^2])/(6*S*(1 + S^2)^3) + (24*S*HPL[{3}, -S^2])/(1 + S^2)^3 + (8*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(-11 + 51*S^2 + 51*S^4 + 17*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((Pi^4*S*(9875 + 21*S^2 + 21*S^4 + 7*S^6))/(270*(1 + S^2)^3) + (92 + 377*S^2 + 983*S^4 + 467*S^6 + 57*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(87 - 1162*S^2 + 11268*S^4 - 9140*S^6 + 2073*S^8 - 22*S^10 + 120*S^12))/(72*S^3*(1 + S^2)^3) + (-(Pi^2*S*(-2511 + 219*S^2 + 219*S^4 + 73*S^6))/(18*(1 + S^2)^3) + (93 - 312*S^2 + 5681*S^4 - 3858*S^6 + 2025*S^8 + 2*S^10 + 33*S^12)/(12*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (2*S*(-337 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + (2*(-20 + 65*S^2 + 21*S^4 + 73*S^6 + 29*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (2*S*(-69 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) + ((551 - 5580*S^2 + 3126*S^4 + 80*S^6 - 177*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-355 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^3) - (16*S*(-119 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(-21 + 54*S^2 + 272*S^4 + 143*S^6 + 30*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + (52*S*(4 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(3*(1 + S^2)^3)) + Zeta[3]*((-80 + 4639*S^2 + 2686*S^4 - 497*S^6)/(8*S*(1 + S^2)) + (Pi^2*(6 + 727*S^2 + 486*S^4 - 67*S^6))/(12*S*(1 + S^2)) - (Pi^4*S*(1149 - 47059*S^2 - 4766*S^4 + 3206*S^6))/(180*(1 + S^2)^3) + (24*S*(19 + 27*S^2 + 27*S^4 + 9*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{3}, -S^2]*((Pi^4*(-521 - 8055*S^2 + 48163*S^4 + 4429*S^6 - 3292*S^8))/(180*S*(1 + S^2)^3) + (-109 + 1200*S^2 + 4729*S^4 + 1278*S^6 - 606*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-8 + 207*S^2 + 497*S^4 + 258*S^6 - 36*S^8))/(6*S^3*(1 + S^2)) + (2*(-1 + 73*S^2 - 656*S^4 - 106*S^6 + 24*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (8*S*(12 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(1907 + 213*S^2 + 213*S^4 + 71*S^6))/(3*(1 + S^2)^3) + (2*(-12 - 153*S^2 + 1094*S^4 - 4168*S^6 + 1586*S^8 + 41*S^10 + 12*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(38 + 824*S^2 - 5225*S^4 - 404*S^6 + 375*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-253 + 249*S^2 + 249*S^4 + 83*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 + (32*S*(-11 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (8*(30 + 783*S^2 - 5272*S^4 - 439*S^6 + 366*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(-2027 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-5851 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (64*S*(451 + 48*S^2 + 48*S^4 + 16*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-107 + 63*S^2 + 63*S^4 + 21*S^6))/(3*(1 + S^2)^3) + (-3 - 44*S^2 - 91*S^4 + 520*S^6 - 389*S^8 - 36*S^10 + 27*S^12)/(S^3*(1 + S^2)^3))*Zeta[3] + (4*S*(-71 + 75*S^2 + 75*S^4 + 25*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]^3*(((1 + S^2)*(417 + 802*S^2 + 417*S^4))/(12*S^3) + (Pi^2*(127 + 274*S^2 + 518*S^4 + 114*S^6 + 31*S^8))/(36*S^3*(1 + S^2)) + (Pi^4*(-7808 + 104629*S^2 - 82905*S^4 - 11207*S^6 + 1795*S^8))/(270*S*(1 + S^2)^3) + (2*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^3) + ((4*Pi^2*S*(-1821 + 1137*S^2 + 1137*S^4 + 379*S^6))/(9*(1 + S^2)^3) - (4*(-18 - 78*S^2 + 375*S^4 - 5182*S^6 + 2416*S^8 - 340*S^10 + 27*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (8*(-11 + 773*S^2 - 1794*S^4 - 407*S^6 + 11*S^8)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^3) + (8*S*(-111 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(9*(1 + S^2)^3) + (4*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (16*(89 - 275*S^2 - 1842*S^4 - 298*S^6 + 100*S^8)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^3) - (16*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^3) - (32*S*(-2477 + 1479*S^2 + 1479*S^4 + 493*S^6)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^3) - (1200*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^3) - (64*S*(-1441 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^3) - 2400*S*HPL[{2, 1, 1, 1}, -S^2] + ((4*Pi^2*S*(-1523 + 1011*S^2 + 1011*S^4 + 337*S^6))/(9*(1 + S^2)^3) - (4*(-49 + 439*S^2 - 3416*S^4 + 2440*S^6 - 331*S^8 + 45*S^10))/(3*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-8*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(-1051 + 9932*S^2 + 882*S^4 - 148*S^6 - 487*S^8))/(9*S*(1 + S^2)^3) + (8*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (32*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + (16*S*(-691 + 537*S^2 + 537*S^4 + 179*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(307 + 1070*S^2 + 307*S^4))/(4*S^3) - (11*Pi^6*S*(-105451 + 16287*S^2 + 16287*S^4 + 5429*S^6))/(22680*(1 + S^2)^3) + (Pi^2*(255 + 981*S^2 + 1837*S^4 + 703*S^6 + 120*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(624 - 6423*S^2 + 75934*S^4 - 122755*S^6 + 37642*S^8 - 144*S^10 - 402*S^12))/(360*S^3*(1 + S^2)^3) + (-(Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) + (18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + 62*S*HPL[{2}, -S^2]^3 - (2*S*(-275 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(-1193 + 837*S^2 + 837*S^4 + 279*S^6))/(3*(1 + S^2)^3) + (2*(18 - 7*S^2 + 152*S^4 + 2562*S^6 - 346*S^8 + 149*S^10))/(S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(103 + 302*S^2 - 3426*S^4 - 878*S^6 + 11*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) + (2*S*(67 + 849*S^2 + 849*S^4 + 283*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((-8*Pi^2*S*(309 + 183*S^2 + 183*S^4 + 61*S^6))/(3*(1 + S^2)^3) + (2*(-54 + 91*S^2 - 2336*S^4 - 3138*S^6 + 1762*S^8 - 425*S^10 + 36*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (4*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + (4*(-493 + 12568*S^2 - 27762*S^4 - 3940*S^6 + 1243*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) - (18*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 - (16*S*(-601 + 357*S^2 + 357*S^4 + 119*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((8*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) - (12*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (16*(-432 + 5251*S^2 - 4356*S^4 - 558*S^6 + 121*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 1488*S*HPL[{3, 2, 1}, -S^2] + (32*S*(-161 + 597*S^2 + 597*S^4 + 199*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (3600*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (64*S*(-103 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 + 7200*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((7 + 194*S^2 + 598*S^4 + 34*S^6 - 89*S^8)/(2*S^3*(1 + S^2)) - (2*Pi^2*(-25 + 580*S^2 - 1511*S^4 - 160*S^6 + 96*S^8))/(S*(1 + S^2)^3))*Zeta[3] - (8*S*(-37 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{3}, -S^2]*((Pi^2*(135 - 4474*S^2 + 10640*S^4 + 1608*S^6 - 441*S^8))/(3*S*(1 + S^2)^3) + (17 + 672*S^2 + 1214*S^4 + 432*S^6 - 79*S^8)/(2*S^3*(1 + S^2)) - (8*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (112*S*(-7 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((24*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 + (Pi^2*(1051 - 9932*S^2 - 882*S^4 + 148*S^6 + 487*S^8))/(3*S*(1 + S^2)^3) - (32*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*((135 + 1583*S^2 + 785*S^4 - 135*S^6)/(4*S^3) + (Pi^4*S*(28217 + 3411*S^2 + 3411*S^4 + 1137*S^6))/(180*(1 + S^2)^3) + (Pi^2*(90 - 321*S^2 + 5585*S^4 - 2317*S^6 - 779*S^8 + 502*S^10 - 72*S^12))/(6*S^3*(1 + S^2)^3) - (2*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-847 + 339*S^2 + 339*S^4 + 113*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (2*(-151 + 3632*S^2 - 8118*S^4 - 1048*S^6 + 413*S^8)*Zeta[3])/(S*(1 + S^2)^3)) - (4*(-54 + 1295*S^2 - 4545*S^4 - 279*S^6 + 395*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-267 + 3869*S^2 + 2531*S^4 + 267*S^6)/(8*S^3) - (Pi^6*S*(-143726 + 20613*S^2 + 20613*S^4 + 6871*S^6))/(11340*(1 + S^2)^3) + (Pi^2*(61 + 1697*S^2 + 2218*S^4 + 627*S^6 - 99*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(1218 + 2104*S^2 + 55384*S^4 - 38419*S^6 + 21407*S^8 + 4603*S^10 - 1401*S^12))/(720*S^3*(1 + S^2)^3) - (16*S*(-16 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + ((4*Pi^2*S*(-70 + 129*S^2 + 129*S^4 + 43*S^6))/(3*(1 + S^2)^3) + (3 + 137*S^2 + 717*S^4 + 3822*S^6 - 331*S^8 + 249*S^10 - 21*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(22 + 13*S^2 + 1467*S^4 + 377*S^6 + 5*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) + (4*S*(41 + 138*S^2 + 138*S^4 + 46*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 + 488*S*HPL[{2, 1}, -S^2]^2 + ((2*Pi^2*S*(-2523 + 519*S^2 + 519*S^4 + 173*S^6))/(3*(1 + S^2)^3) + (2*(-3 + 57*S^2 - 1577*S^4 + 3928*S^6 - 1423*S^8 - 25*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (2*(3 + 2415*S^2 - 10462*S^4 - 785*S^6 + 761*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) + (2*(71 + 6473*S^2 - 32718*S^4 - 2743*S^6 + 2249*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) - (12*S*(-87 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-923 + 1167*S^2 + 1167*S^4 + 389*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(-1241 + 321*S^2 + 321*S^4 + 107*S^6))/(3*(1 + S^2)^3) + (16*(-10 + 361*S^2 - 988*S^4 + 381*S^6))/(S*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(531 - 3203*S^2 - 537*S^4 + 361*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*(1533 - 9582*S^2 - 676*S^4 + 350*S^6 + 351*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (12*S*(-99 + 39*S^2 + 39*S^4 + 13*S^6)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-2919 + 555*S^2 + 555*S^4 + 185*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 - (72*S*(-501 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 - (64*(-65 + 577*S^2 - 777*S^4 - 65*S^6 + 49*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-109 + 2283*S^2 + 2283*S^4 + 761*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (640*S*(-82 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((Pi^2*(-6 - 1150*S^2 + 5351*S^4 + 335*S^6 - 424*S^8))/(3*S*(1 + S^2)^3) + (-17 - 28*S^2 + 252*S^4 + 194*S^6 - 45*S^8)/(2*S^3*(1 + S^2)))*Zeta[3] - 12*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-29 - 818*S^2 + 5613*S^4 + 533*S^6 - 361*S^8))/(3*S*(1 + S^2)^3) + (11 - 30*S^2 + 664*S^4 + 522*S^6 - 135*S^8)/(4*S^3*(1 + S^2)) - (4*S*(-2027 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (76*S*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((Pi^2*(1059 - 8503*S^2 + 7791*S^4 + 773*S^6 - 404*S^8))/(3*S*(1 + S^2)^3) + (-31 - 93*S^2 + 76*S^4 + 83*S^6 - 31*S^8)/(S^3*(1 + S^2)) + (112*S*(57 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) - (2*(31 + 692*S^2 - 4775*S^4 - 107*S^6 + 481*S^8)*Zeta[5])/(S*(1 + S^2)^3)) + HPL[{0}, S^2]^2*((Pi^2*(602 + 4135*S^2 + 2616*S^4 - 293*S^6))/(96*S*(1 + S^2)) + (544 + 4387*S^2 + 3342*S^4 + 267*S^6)/(16*S*(1 + S^2)) + (Pi^6*S*(15415 + 5289*S^2 + 5289*S^4 + 1763*S^6))/(1296*(1 + S^2)^3) - (Pi^4*S*(-38440 + 25327*S^2 - 22036*S^4 - 6069*S^6 + 654*S^8))/(720*(1 + S^2)^3) - (2*(59 - 771*S^2 + 516*S^4 + 86*S^6)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)^3) - (8*S*(-33 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^3) + (-(Pi^2*S*(-678 + 213*S^2 + 213*S^4 + 71*S^6))/(6*(1 + S^2)^3) + (3 + 48*S^2 + 2019*S^4 - 4184*S^6 + 1533*S^8 + 16*S^10 - 27*S^12)/(8*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (S*(-369 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*((-5*Pi^2*S*(-329 + 39*S^2 + 39*S^4 + 13*S^6))/(9*(1 + S^2)^3) + (45 - 472*S^2 + 5737*S^4 - 8948*S^6 + 1735*S^8 + 92*S^10 - 45*S^12)/(12*S^3*(1 + S^2)^3) - (S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2}, -S^2])/(3*(1 + S^2)^3)) - (2*S*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(23 + 117*S^2 + 117*S^4 + 39*S^6))/(6*(1 + S^2)^3) + (39 + 46*S^2 + 697*S^4 + 898*S^6 + 255*S^8 + 160*S^10 - 15*S^12)/(4*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((-45 + 408*S^2 + 906*S^4 + 208*S^6 - 29*S^8)*HPL[{5}, -S^2])/(2*S*(1 + S^2)^3) + (S*(89 + 153*S^2 + 153*S^4 + 51*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 + (4*S*(-421 + 171*S^2 + 171*S^4 + 57*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((Pi^2*S*(-1271 + 345*S^2 + 345*S^4 + 115*S^6))/(3*(1 + S^2)^3) + (-51 - 72*S^2 - 2363*S^4 + 3128*S^6 - 1529*S^8 - 112*S^10 + 39*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((-5 + 136*S^2 - 1350*S^4 - 348*S^6 - 9*S^8)*HPL[{3, 2}, -S^2])/(2*S*(1 + S^2)^3) + ((53 + 43*S^2 - 2414*S^4 - 557*S^6 + 23*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + (S*(-11 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(1 + S^2)^3 - (2*S*(37 + 99*S^2 + 99*S^4 + 33*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(-1299 + 345*S^2 + 345*S^4 + 115*S^6))/(3*(1 + S^2)^3) - (2*(-21 - 28*S^2 - 1147*S^4 + 1688*S^6 - 721*S^8 - 48*S^10 + 21*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (2*(-539 + 3887*S^2 - 1575*S^4 - 253*S^6 + 12*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) - (2*(1661 - 11699*S^2 + 3865*S^4 + 617*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) - 10*S*HPL[{3, 1, 2}, -S^2] - (2*S*(-1471 + 747*S^2 + 747*S^4 + 249*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-2219 + 1035*S^2 + 1035*S^4 + 345*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(582 - 3965*S^2 + 788*S^4 + 149*S^6 + 34*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(-377 + 153*S^2 + 153*S^4 + 51*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (240*S*(-51 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((6 + 157*S^2 + 102*S^4 - 25*S^6)/(4*S*(1 + S^2)) + (Pi^2*S*(514 + 1403*S^2 + 461*S^4 + 28*S^6))/(6*(1 + S^2)^3))*Zeta[3] + (2*S*(31 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{2, 1}, -S^2]*((-59 - 412*S^2 - 516*S^4 - 190*S^6 - 3*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(1068 - 6510*S^2 + 1031*S^4 + 197*S^6 + 72*S^8))/(6*S*(1 + S^2)^3) - (4*S*(-85 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((Pi^2*(-77 + 248*S^2 + 1256*S^4 + 190*S^6 - 69*S^8))/(12*S*(1 + S^2)^3) + (1 + 434*S^2 + 650*S^4 + 286*S^6 - 27*S^8)/(8*S^3*(1 + S^2)) + (2*S*(103 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-7 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^3*((67 + 234*S^2 + 558*S^4 + 74*S^6 - 29*S^8)/(12*S^3*(1 + S^2)) + (Pi^2*(-1115 + 13472*S^2 - 6840*S^4 - 902*S^6 + 5*S^8))/(18*S*(1 + S^2)^3) + ((-601 + 6782*S^2 - 3618*S^4 - 598*S^6 - 37*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-71 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^3) + (4*S*(-143 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-(Pi^4*S*(-39137 + 1209*S^2 + 1209*S^4 + 403*S^6))/(360*(1 + S^2)^3) + (129 + 589*S^2 + 1305*S^4 + 311*S^6 - 6*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(45 - 496*S^2 + 5548*S^4 - 6557*S^6 + 1225*S^8 + 155*S^10 - 36*S^12))/(12*S^3*(1 + S^2)^3) + (-(Pi^2*S*(-2769 + 177*S^2 + 177*S^4 + 59*S^6))/(6*(1 + S^2)^3) + (45 - 183*S^2 + 3056*S^4 - 3037*S^6 + 790*S^8 + 124*S^10 - 27*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2}, -S^2]^2)/(1 + S^2)^3 - (2*(15 + 24*S^2 - 379*S^4 - 78*S^6 + 10*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (S*(9 + 123*S^2 + 123*S^4 + 41*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((601 - 6782*S^2 + 3618*S^4 + 598*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-103 + 12*S^2 + 12*S^4 + 4*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (4*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((5 - 270*S^2 + 996*S^4 + 140*S^6 - 51*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2}, -S^2]*(-(Pi^4*S*(-15055 + 897*S^2 + 897*S^4 + 299*S^6))/(360*(1 + S^2)^3) + (6 + 380*S^2 + 517*S^4 + 190*S^6 - 25*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(87 + 140*S^2 + 4817*S^4 - 4501*S^6 + 2408*S^8 + 289*S^10 - 72*S^12))/(24*S^3*(1 + S^2)^3) + ((1 - 35*S^2 + 341*S^4 + 94*S^6 + 5*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) + (7*S*(5 + 3*S^2 + 3*S^4 + S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + ((539 - 3887*S^2 + 1575*S^4 + 253*S^6 - 12*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-841 + 345*S^2 + 345*S^4 + 115*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-421 + 171*S^2 + 171*S^4 + 57*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + ((-3 - 80*S^2 + 543*S^4 + 81*S^6 - 23*S^8)*Zeta[3])/(S*(1 + S^2)^3)) - (S*(-431 - 1130*S^2 - 150*S^4 + 81*S^6)*Zeta[5])/(1 + S^2)^3 + HPL[{1}, -S^2]*((Pi^4*(-7570 + 85792*S^2 - 26276*S^4 - 959*S^6 + 59*S^8))/(360*S*(1 + S^2)^3) + (181 + 1000*S^2 + 2156*S^4 + 628*S^6 + 59*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(127 + 615*S^2 + 1393*S^4 + 581*S^6 + 60*S^8))/(48*S^3*(1 + S^2)) + ((-136 + 1698*S^2 - 1250*S^4 - 211*S^6 + 5*S^8)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^3) + ((Pi^2*S*(-65 + 141*S^2 + 141*S^4 + 47*S^6))/(3*(1 + S^2)^3) + (18 + 10*S^2 + 234*S^4 + 557*S^6 - 12*S^8 + 67*S^10 - 6*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-43 + 209*S^2 + 468*S^4 + 103*S^6 - 17*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-1 + 105*S^2 + 105*S^4 + 35*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((Pi^2*S*(-2769 + 177*S^2 + 177*S^4 + 59*S^6))/(3*(1 + S^2)^3) + (-45 + 183*S^2 - 3056*S^4 + 3037*S^6 - 790*S^8 - 124*S^10 + 27*S^12)/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(151 - 1674*S^2 + 871*S^4 + 133*S^6 + 5*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (64*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (2*S*(-471 + 411*S^2 + 411*S^4 + 137*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 - (2*(601 - 6782*S^2 + 3618*S^4 + 598*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-1307 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-1673 + 201*S^2 + 201*S^4 + 67*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((Pi^2*S*(-77 + 225*S^2 + 225*S^4 + 75*S^6))/(3*(1 + S^2)^3) + (3 - 38*S^2 + 27*S^4 + 986*S^6 - 379*S^8 + 128*S^10 - 15*S^12)/(2*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((89 + 930*S^2 + 1156*S^4 + 310*S^6 - 53*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-1117 + 11690*S^2 - 4676*S^4 - 552*S^6 - 37*S^8))/(12*S*(1 + S^2)^3) + (32*S*(-5 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (4*S*(-895 + 183*S^2 + 183*S^4 + 61*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(-141 + 93*S^2 + 93*S^4 + 31*S^6)*Zeta[3])/(1 + S^2)^3) + (2*S*(-77 + 237*S^2 + 237*S^4 + 79*S^6)*Zeta[5])/(1 + S^2)^3)) + HPL[{0}, S^2]*((5*(363 + 1848*S^2 + 289*S^4))/(16*S) + (Pi^4*(2436 + 14474*S^2 + 10923*S^4 + 673*S^6))/(1440*S*(1 + S^2)) + (Pi^2*(1752 + 6917*S^2 + 4582*S^4 + 953*S^6))/(96*S*(1 + S^2)) + (Pi^6*S*(2284139 - 1015409*S^2 + 615664*S^4 + 307832*S^6))/(45360*(1 + S^2)^3) + (14*(-7 + 104*S^2 - 126*S^4 - 16*S^6 + 5*S^8)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)^3) - (32*S*(-8 + 3*S^2 + 3*S^4 + S^6)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^3) + ((17 + 3092*S^2 - 7416*S^4 - 672*S^6 + 411*S^8)*HPL[{2}, -S^2]^3)/(6*S*(1 + S^2)^3) + HPL[{1}, -S^2]^5*((-2*Pi^2*S*(-991 + 303*S^2 + 303*S^4 + 101*S^6))/(9*(1 + S^2)^3) + (3 - 38*S^2 + 441*S^4 - 1052*S^6 + 441*S^8 - 38*S^10 + 3*S^12)/(S^3*(1 + S^2)^3) - (4*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2}, -S^2])/(1 + S^2)^3) + ((-2 - 47*S^2 - 4*S^4 - 53*S^6 - 22*S^8)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^3) + ((-2*Pi^2*S*(-79 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) + (90 + 44*S^2 + 775*S^4 + 1274*S^6 + 1572*S^8 + 238*S^10 + 15*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((-105 + 75*S^2 - 487*S^4 + 502*S^6 + 293*S^8)*HPL[{6}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-1 + 18*S^2 + 18*S^4 + 6*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 - (2*(-9 + 3844*S^2 - 7678*S^4 - 652*S^6 + 439*S^8)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^3) + (-(Pi^2*S*(-311 + 339*S^2 + 339*S^4 + 113*S^6))/(3*(1 + S^2)^3) + (9 + 20*S^2 - 25*S^4 - 2152*S^6 + 651*S^8 - 36*S^10 - 51*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((-8*Pi^2*S*(-74 + 105*S^2 + 105*S^4 + 35*S^6))/(3*(1 + S^2)^3) + (-33 - S^2 - 713*S^4 - 3870*S^6 + 5*S^8 - 113*S^10 - 75*S^12)/(S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((-13 - 12*S^2 - 6*S^4 - S^6)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^2) - (8*S*(13 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 - (2*(-37 + 356*S^2 - 224*S^4 + 402*S^6 + 203*S^8)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^3) - (48*S*(6 + 3*S^2 + 3*S^4 + S^6)*HPL[{5, 2}, -S^2])/(1 + S^2)^3 - (8*S*(121 + 24*S^2 + 24*S^4 + 8*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(2457 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) + (4*(15 - 254*S^2 + 2048*S^4 - 3613*S^6 + 1030*S^8 + 3*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((8*Pi^2*S*(3689 + 69*S^2 + 69*S^4 + 23*S^6))/(3*(1 + S^2)^3) + (2*(117 - 1518*S^2 + 12797*S^4 - 20374*S^6 + 6489*S^8 + 60*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (8*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (4*(15 + 3084*S^2 - 7428*S^4 - 680*S^6 + 409*S^8)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (2*S*(-465 + 429*S^2 + 429*S^4 + 143*S^6)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^3 + (96*S*(-31 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 + (36*(2 + 1069*S^2 - 2496*S^4 - 195*S^6 + 152*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (24*S*(-123 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 + (24*S*(-381 + 321*S^2 + 321*S^4 + 107*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-1107 + 939*S^2 + 939*S^4 + 313*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(2471 + 123*S^2 + 123*S^4 + 41*S^6))/(3*(1 + S^2)^3) - (4*(45 - 522*S^2 + 4575*S^4 - 6112*S^6 + 2143*S^8 + 2*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] - (32*S*(803 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*(-2 + 1729*S^2 - 3798*S^4 - 230*S^6 + 259*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (8*S*(9901 + 447*S^2 + 447*S^4 + 149*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 + (8*S*(9901 + 447*S^2 + 447*S^4 + 149*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (8*S*(19537 + 1131*S^2 + 1131*S^4 + 377*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (64*S*(7301 + 438*S^2 + 438*S^4 + 146*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (80*(-2 + 693*S^2 - 1518*S^4 - 95*S^6 + 102*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (55680*S*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 - (167040*S*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (160*S*(-1747 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (1920*S*(57 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((373*Pi^4*S^3*(3 + 3*S^2 + S^4))/(45*(1 + S^2)^3) + (-24 + 481*S^2 + 9*S^4)/(4*S) + (Pi^2*S*(267 + 1013*S^2 + 16*S^4 + 49*S^6 + 3*S^8))/(3*(1 + S^2)^3))*Zeta[3] + (2*S*(121 - 79*S^2 + 104*S^4 + 52*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{4}, -S^2]*((-104 + 317*S^2 + 818*S^4 + 481*S^6 - 36*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(-68 + 525*S^2 - 380*S^4 + 475*S^6 + 248*S^8))/(6*S*(1 + S^2)^3) + (4*S*(-23 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(29 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((47 + 526*S^2 + 170*S^4 + 14*S^6 + 35*S^8)/(S^3*(1 + S^2)) + (2*Pi^2*(-40 + 5975*S^2 - 9686*S^4 - 471*S^6 + 650*S^8))/(3*S*(1 + S^2)^3) + (96*S*(-22 + 21*S^2 + 21*S^4 + 7*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((Pi^2*(35 - 5913*S^2 + 9755*S^4 + 477*S^6 - 658*S^8))/(3*S*(1 + S^2)^3) + (-29 - 348*S^2 - 197*S^4 - 34*S^6 - 12*S^8)/(S^3*(1 + S^2)) - (16*S*(-65 + 63*S^2 + 63*S^4 + 21*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(3 - 4*S^2 + 3*S^4))/(3*S^3) + (Pi^2*(-1275 + 17204*S^2 - 16878*S^4 - 1938*S^6 + 659*S^8))/(18*S*(1 + S^2)^3) + (10*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^3) + (4*S*(-53 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + (20*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-317 + 129*S^2 + 129*S^4 + 43*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((15 + 196*S^2 - 28*S^4 - 140*S^6 + 21*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(-4 + 6203*S^2 - 9853*S^4 - 841*S^6 + 507*S^8))/(12*S*(1 + S^2)^3) + (S*(-115 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - (4*S*(803 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (2*S*(-125 + 129*S^2 + 129*S^4 + 43*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*(-(Pi^4*S*(12419 + 408*S^2 + 408*S^4 + 136*S^6))/(45*(1 + S^2)^3) + (-83 - 584*S^2 - 411*S^4 - 484*S^6 - 46*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-45 + 437*S^2 - 4025*S^4 + 3803*S^6 - 1387*S^8 - 10*S^10 - 33*S^12))/(3*S^3*(1 + S^2)^3) + (8*S*(1741 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (27840*S*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 - (4*(49 - 676*S^2 + 411*S^4 + 94*S^6 + 2*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{3}, -S^2]*((Pi^4*S*(1227 + 633*S^2 + 633*S^4 + 211*S^6))/(180*(1 + S^2)^3) + (91 + 1280*S^2 + 1450*S^4 + 684*S^6 - 57*S^8)/(8*S^3*(1 + S^2)) + (Pi^2*(27 + 500*S^4 + 980*S^6 + 399*S^8 + 60*S^10 + 18*S^12))/(6*S^3*(1 + S^2)^3) + (56*S*HPL[{4}, -S^2])/(1 + S^2)^3 + (4*(-13 + 376*S^2 - 131*S^4 + 10*S^6 + 14*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (44*S*(-13 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (8*S*(-135 + 111*S^2 + 111*S^4 + 37*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (8*(-1 + 9*S^2 + 27*S^4 + 14*S^6 + 3*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((7*(1 + S^2)*(9 + 10*S^2 + 9*S^4))/(3*S^3) - (Pi^4*S*(-26053 + 6183*S^2 + 6183*S^4 + 2061*S^6))/(135*(1 + S^2)^3) + (Pi^2*(87 - 1022*S^2 + 11953*S^4 - 21820*S^6 + 8093*S^8 - 630*S^10 + 75*S^12))/(18*S^3*(1 + S^2)^3) + ((-2*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(3*(1 + S^2)^3) + (2*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (16*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^3) + (8*(-12 - 106*S^2 + 174*S^4 + 129*S^6 + 41*S^8)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^3) - (4*S*(-211 + 87*S^2 + 87*S^4 + 29*S^6)*HPL[{4}, -S^2])/(3*(1 + S^2)^3) - (40*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^3) + (112*S*(-71 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (80*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (8*(22 - 502*S^2 + 732*S^4 + 187*S^6 + 11*S^8)*Zeta[3])/(3*S*(1 + S^2)^3)) + ((104*Pi^2*S^3*(3 + 3*S^2 + S^4))/(3*(1 + S^2)^3) + (S*(448 + 1595*S^2 + 95*S^4 + 21*S^6 + 33*S^8))/(1 + S^2)^3)*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(112 + 932*S^2 + 637*S^4 + 264*S^6 + 15*S^8))/(24*S^3*(1 + S^2)) + (101 + 4550*S^2 + 3676*S^4 + 2906*S^6 + 607*S^8)/(16*S^3*(1 + S^2)) + (Pi^4*(-925 + 70930*S^2 - 80646*S^4 + 2369*S^6 + 7474*S^8))/(360*S*(1 + S^2)^3) + ((53*Pi^2*S*(-3 + 3*S^2 + 3*S^4 + S^6))/(3*(1 + S^2)^3) + (-3 + 4*S^2 + 75*S^4 + 1184*S^6 - 253*S^8 + 28*S^10 + 21*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((12 + 133*S^2 + 64*S^4 + 139*S^6 + 52*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-17 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((-2*Pi^2*S*(2457 + 15*S^2 + 15*S^4 + 5*S^6))/(3*(1 + S^2)^3) - (2*(15 - 254*S^2 + 2048*S^4 - 3613*S^6 + 1030*S^8 + 3*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (2*(-9 + 3844*S^2 - 7678*S^4 - 652*S^6 + 439*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-229 + 225*S^2 + 225*S^4 + 75*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (64*S*(-23 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (4*(-9 + 3844*S^2 - 7678*S^4 - 652*S^6 + 439*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (16*S*(803 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(4953 + 231*S^2 + 231*S^4 + 77*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 - (27840*S*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-131 + 159*S^2 + 159*S^4 + 53*S^6))/(3*(1 + S^2)^3) + (2*(3 - 2*S^2 - 2*S^4 + 565*S^6 - 111*S^8 + 23*S^10))/(S^3*(1 + S^2)^3))*Zeta[3] + (8*S*(-28 + 39*S^2 + 39*S^4 + 13*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]^2*(((1 + S^2)*(417 + 802*S^2 + 417*S^4))/(8*S^3) + (Pi^2*(103 + 280*S^2 + 494*S^4 + 344*S^6 + 75*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(-7838 + 96034*S^2 - 73673*S^4 - 5159*S^6 + 3702*S^8))/(180*S*(1 + S^2)^3) + ((-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^3) + ((2*Pi^2*S*(-17 + 21*S^2 + 21*S^4 + 7*S^6))/(3*(1 + S^2)^3) + (39 + 30*S^2 + 351*S^4 + 1306*S^6 + 467*S^8 + 16*S^10 + 15*S^12)/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(-50 + 287*S^2 - 348*S^4 + 127*S^6 + 92*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-95 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(1 + S^2)^3 - (2*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(-367 + 4764*S^2 - 5850*S^4 - 598*S^6 + 303*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-707 + 255*S^2 + 255*S^4 + 85*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (40*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^3 - (16*S*(-4579 + 1743*S^2 + 1743*S^4 + 581*S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (240*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((8*Pi^2*S*(-82 + 45*S^2 + 45*S^4 + 15*S^6))/(3*(1 + S^2)^3) + (-3 + 28*S^2 - 223*S^4 + 2226*S^6 - 419*S^8 + 2*S^10 + 21*S^12)/(S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((41 + 358*S^2 + 170*S^4 + 182*S^6 + 41*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-1291 + 15150*S^2 - 14766*S^4 - 1270*S^6 + 777*S^8))/(6*S*(1 + S^2)^3) + (4*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-307 + 123*S^2 + 123*S^4 + 41*S^6)*Zeta[3])/(1 + S^2)^3) + (8*S*(-111 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{1}, -S^2]*(((1 + S^2)*(307 + 1070*S^2 + 307*S^4))/(4*S^3) - (Pi^6*S*(-81499 + 13173*S^2 + 13173*S^4 + 4391*S^6))/(1620*(1 + S^2)^3) + (Pi^2*(218 + 769*S^2 + 1515*S^4 + 859*S^6 + 183*S^8))/(24*S^3*(1 + S^2)) + (Pi^4*(1218 - 14000*S^2 + 150075*S^4 - 205512*S^6 + 72402*S^8 - 5060*S^10 + 1557*S^12))/(720*S^3*(1 + S^2)^3) + ((-2*Pi^2*S*(-1109 + 351*S^2 + 351*S^4 + 117*S^6))/(3*(1 + S^2)^3) + (18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (2*S*(-1391 + 531*S^2 + 531*S^4 + 177*S^6)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^3) + (6*S*(-7 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2]^2)/(1 + S^2)^3 + (-(Pi^2*S*(-349 + 153*S^2 + 153*S^4 + 51*S^6))/(3*(1 + S^2)^3) + (75 + 6*S^2 + 1157*S^4 + 1004*S^6 + 1753*S^8 + 70*S^10 + 15*S^12)/(2*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(-61 + 204*S^2 - 334*S^4 + 202*S^6 + 129*S^8)*HPL[{5}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-57 + 48*S^2 + 48*S^4 + 16*S^6)*HPL[{6}, -S^2])/(1 + S^2)^3 + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^3 + ((4*Pi^2*S*(-2201 + 681*S^2 + 681*S^4 + 227*S^6))/(3*(1 + S^2)^3) - (2*(57 - 217*S^2 + 3437*S^4 - 5920*S^6 + 3537*S^8 - 239*S^10 + 33*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*(15 - 514*S^2 + 662*S^4 + 174*S^6 + 15*S^8)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^3) - (4*(-5 - 1255*S^2 + 1638*S^4 + 649*S^6 + 137*S^8)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^3) + 6*S*HPL[{4, 2}, -S^2] + (16*S*(-57 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{5, 1}, -S^2])/(1 + S^2)^3 + ((-4*Pi^2*S*(-1471 + 447*S^2 + 447*S^4 + 149*S^6))/(1 + S^2)^3 + (4*(45 - 236*S^2 + 3407*S^4 - 6112*S^6 + 3311*S^8 - 284*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (8*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^3) + (8*(-1053 + 14716*S^2 - 18246*S^4 - 2310*S^6 + 745*S^8)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (16*S*(-1391 + 531*S^2 + 531*S^4 + 177*S^6)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^3 - (8*S*(-8557 + 3273*S^2 + 3273*S^4 + 1091*S^6)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^3 - (80*(-74 + 957*S^2 - 1164*S^4 - 119*S^6 + 60*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (672*S*(-71 + 27*S^2 + 27*S^4 + 9*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (480*S*(-199 + 75*S^2 + 75*S^4 + 25*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((-12 + 25*S^2 + 72*S^4 - S^6)/S^3 + (2*Pi^2*(1 - 448*S^2 + 1004*S^4 + 330*S^6 + 41*S^8))/(3*S*(1 + S^2)^3))*Zeta[3] - (8*S*(-37 + 15*S^2 + 15*S^4 + 5*S^6)*Zeta[3]^2)/(1 + S^2)^3 + HPL[{3}, -S^2]*((17 + 226*S^2 + 211*S^4 + 128*S^6 + 6*S^8)/(S^3*(1 + S^2)) + (2*Pi^2*(-32 - 41*S^2 + 195*S^4 + 202*S^6 + 70*S^8))/(3*S*(1 + S^2)^3) - (8*S*(-153 + 57*S^2 + 57*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((Pi^2*(1291 - 15150*S^2 + 14766*S^4 + 1270*S^6 - 777*S^8))/(3*S*(1 + S^2)^3) + (-41 - 358*S^2 - 170*S^4 - 182*S^6 - 41*S^8)/(S^3*(1 + S^2)) - (8*S*(-307 + 123*S^2 + 123*S^4 + 41*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]*(-(Pi^4*S*(-11372 + 2733*S^2 + 2733*S^4 + 911*S^6))/(45*(1 + S^2)^3) + (129 + 1324*S^2 + 822*S^4 + 812*S^6 + 129*S^8)/(4*S^3*(1 + S^2)) + (Pi^2*(183 - 784*S^2 + 12495*S^4 - 16082*S^6 + 8647*S^8 - 566*S^10 + 123*S^12))/(12*S^3*(1 + S^2)^3) + (2*(15 - 514*S^2 + 662*S^4 + 174*S^6 + 15*S^8)*HPL[{3}, -S^2])/(S*(1 + S^2)^3) - (2*S*(-41 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (2*(49 - 974*S^2 + 1410*S^4 + 370*S^6 + 25*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + (4*(-6 - 318*S^2 + 711*S^4 + 305*S^6 + 62*S^8)*Zeta[5])/(S*(1 + S^2)^3))) - (18*S*(-15 - 811*S^2 + 82*S^4 + 134*S^6)*Zeta[7])/(1 + S^2)^3 + HPL[{1}, -S^2]*((5*(1 + S^2)*(289 + 1922*S^2 + 289*S^4))/(16*S^3) + (Pi^4*(1734 + 6679*S^2 + 15617*S^4 + 4665*S^6 + 425*S^8))/(1440*S^3*(1 + S^2)) + (Pi^2*(779 + 3636*S^2 + 6750*S^4 + 2892*S^6 + 535*S^8))/(48*S^3*(1 + S^2)) + (Pi^6*(-179178 + 2312311*S^2 - 1340511*S^4 - 151266*S^6 + 21694*S^8))/(22680*S*(1 + S^2)^3) - (62*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2}, -S^2]^3)/(S*(1 + S^2)^2) - (2*(23 - 437*S^2 + 624*S^4 + 155*S^6 + 7*S^8)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^3) + ((4*Pi^2*S*(-167 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) + (2*(48 - 89*S^2 + 704*S^4 + 2290*S^6 - 117*S^8 + 261*S^10 + 3*S^12))/(S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + (2*(-335 + 1475*S^2 + 3759*S^4 + 1456*S^6 + 155*S^8)*HPL[{6}, -S^2])/(S*(1 + S^2)^3) + (48*S*(42 + 69*S^2 + 69*S^4 + 23*S^6)*HPL[{7}, -S^2])/(1 + S^2)^3 - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^3) + ((-4*Pi^2*S*(-1531 + 915*S^2 + 915*S^4 + 305*S^6))/(3*(1 + S^2)^3) + (2*(-9 - 138*S^2 + 1009*S^4 - 7658*S^6 + 4571*S^8 - 508*S^10 + 45*S^12))/(S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((-2*Pi^2*S*(-10379 + 6327*S^2 + 6327*S^4 + 2109*S^6))/(3*(1 + S^2)^3) + (4*(-36 - 212*S^2 + 1327*S^4 - 14121*S^6 + 7141*S^8 - 923*S^10 + 72*S^12))/(S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] - (6*(25 - 475*S^2 + 660*S^4 + 157*S^6 + 5*S^8)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^3) + (32*S*(-24 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{4, 3}, -S^2])/(1 + S^2)^3 - (4*(35 - 3092*S^2 + 7314*S^4 + 1832*S^6 + 31*S^8)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^3) + (24*S*(-73 + 45*S^2 + 45*S^4 + 15*S^6)*HPL[{5, 2}, -S^2])/(1 + S^2)^3 - (4*S*(337 + 699*S^2 + 699*S^4 + 233*S^6)*HPL[{6, 1}, -S^2])/(1 + S^2)^3 + ((-8*Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) + (4*(18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((-64*Pi^2*S*(-687 + 147*S^2 + 147*S^4 + 49*S^6))/(3*(1 + S^2)^3) - (4*(-90 + 585*S^2 - 8508*S^4 + 11314*S^6 - 4378*S^8 + 85*S^10))/(S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (1488*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-6029 + 3561*S^2 + 3561*S^4 + 1187*S^6)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^3 + (32*S*(-2309 + 1353*S^2 + 1353*S^4 + 451*S^6)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^3 - (32*(134 - 590*S^2 - 2292*S^4 - 343*S^6 + 145*S^8)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-18175 + 10707*S^2 + 10707*S^4 + 3569*S^6)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^3 + (4*S*(-56395 + 32847*S^2 + 32847*S^4 + 10949*S^6)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^3 + (96*S*(-4833 + 2829*S^2 + 2829*S^4 + 943*S^6)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^3 + ((-16*Pi^2*S*(949 + 237*S^2 + 237*S^4 + 79*S^6))/(3*(1 + S^2)^3) + (24*(-15 + 61*S^2 - 904*S^4 + 664*S^6 - 141*S^8 + 15*S^10))/(S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 2976*S*HPL[{2, 2, 2, 1}, -S^2] + (32*(89 - 275*S^2 - 1842*S^4 - 298*S^6 + 100*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^3) - (320*S*(-173 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^3 - (320*S*(-173 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^3 + (32*S*(2009 + 807*S^2 + 807*S^4 + 269*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (128*S*(1657 + 516*S^2 + 516*S^4 + 172*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^3 - (7200*(1 - 8*S^2 - 2*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (256*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^3 + (768*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + (640*S*(-947 + 399*S^2 + 399*S^4 + 133*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^3 - 14400*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((2*Pi^4*S*(-2651 + 2106*S^2 + 2106*S^4 + 702*S^6))/(45*(1 + S^2)^3) + (3 + 197*S^2 + 773*S^4 - 81*S^6 - 132*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(3 + 60*S^2 - 851*S^4 + 7818*S^6 - 5259*S^8 + 790*S^10 - 105*S^12))/(6*S^3*(1 + S^2)^3))*Zeta[3] + (4*(-13 + 109*S^2 - 153*S^4 - 13*S^6 + 10*S^8)*Zeta[3]^2)/(S*(1 + S^2)^3) + HPL[{4}, -S^2]*((-131 + 1073*S^2 + 1399*S^4 + 27*S^6)/(4*S^3) + (Pi^2*(-21 - 1337*S^2 + 4056*S^4 + 917*S^6 - 39*S^8))/(3*S*(1 + S^2)^3) - (4*S*(-847 + 339*S^2 + 339*S^4 + 113*S^6)*HPL[{2, 1}, -S^2])/(1 + S^2)^3 + (4*S*(-103 + 75*S^2 + 75*S^4 + 25*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((-48*(-2 - 21*S^2 - 11*S^4 + 2*S^6))/S^3 - (2*Pi^2*(1051 - 9932*S^2 - 882*S^4 + 148*S^6 + 487*S^8))/(3*S*(1 + S^2)^3) + (64*S*(-362 + 219*S^2 + 219*S^4 + 73*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2}, -S^2]^2*((9 + 38*S^2 - 14*S^4 - 10*S^6 + 9*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(-615 + 8372*S^2 - 8698*S^4 - 1278*S^6 + 231*S^8))/(6*S*(1 + S^2)^3) + (4*S*(-865 + 489*S^2 + 489*S^4 + 163*S^6)*HPL[{3}, -S^2])/(1 + S^2)^3 - 372*S*HPL[{2, 1}, -S^2] + (4*S*(-649 + 405*S^2 + 405*S^4 + 135*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3, 1}, -S^2]*((-35 - 713*S^2 - 473*S^4 + 61*S^6)/S^3 + (4*Pi^2*(240 - 1949*S^2 - 971*S^4 - 165*S^6 + 105*S^8))/(3*S*(1 + S^2)^3) - (16*S*(-747 + 447*S^2 + 447*S^4 + 149*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{3}, -S^2]*((Pi^4*S*(-6485 + 4533*S^2 + 4533*S^4 + 1511*S^6))/(45*(1 + S^2)^3) + (16 + 713*S^2 + 1539*S^4 + 435*S^6 - 119*S^8)/(2*S^3*(1 + S^2)) + (Pi^2*(36 + 88*S^2 - 141*S^4 + 5739*S^6 - 2428*S^8 + 407*S^10 - 33*S^12))/(3*S^3*(1 + S^2)^3) - (20*S*(-33 + 21*S^2 + 21*S^4 + 7*S^6)*HPL[{4}, -S^2])/(1 + S^2)^3 + (4*(-157 + 3674*S^2 - 8058*S^4 - 1042*S^6 + 407*S^8)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^3) - (8*S*(-1455 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 + (16*S*(-1451 + 867*S^2 + 867*S^4 + 289*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(5 - 316*S^2 + 464*S^4 + 122*S^6 + 9*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-135 - 1583*S^2 - 785*S^4 + 135*S^6)/(2*S^3) - (Pi^4*S*(28217 + 3411*S^2 + 3411*S^4 + 1137*S^6))/(90*(1 + S^2)^3) + (Pi^2*(-90 + 321*S^2 - 5585*S^4 + 2317*S^6 + 779*S^8 - 502*S^10 + 72*S^12))/(3*S^3*(1 + S^2)^3) - (64*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{3, 1}, -S^2])/(1 + S^2)^3 - (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^3 + (4*(-151 + 3632*S^2 - 8118*S^4 - 1048*S^6 + 413*S^8)*Zeta[3])/(S*(1 + S^2)^3)) + ((2*Pi^2*S*(-1459 + 1311*S^2 + 1311*S^4 + 437*S^6))/(3*(1 + S^2)^3) - (2*(-3 + 5*S^2 + 281*S^4 - 3093*S^6 + 2981*S^8 - 526*S^10 + 87*S^12))/(S^3*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((61 + 1181*S^2 + 675*S^4 - 61*S^6)/(2*S^3) + (Pi^4*(-6880 + 68025*S^2 - 5975*S^4 - 1894*S^6 - 2254*S^8))/(180*S*(1 + S^2)^3) + (Pi^2*(185 + 2034*S^2 + 2692*S^4 + 742*S^6 - 149*S^8))/(24*S^3*(1 + S^2)) + ((2*Pi^2*S*(-1531 + 915*S^2 + 915*S^4 + 305*S^6))/(3*(1 + S^2)^3) - (2*(-6 - 73*S^2 + 493*S^4 - 3853*S^6 + 2265*S^8 - 258*S^10 + 24*S^12))/(S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (6*(23 - 451*S^2 + 636*S^4 + 157*S^6 + 7*S^8)*HPL[{4}, -S^2])/(S*(1 + S^2)^3) + (4*S*(-303 + 195*S^2 + 195*S^4 + 65*S^6)*HPL[{5}, -S^2])/(1 + S^2)^3 + ((4*Pi^2*S*(-2439 + 771*S^2 + 771*S^4 + 257*S^6))/(3*(1 + S^2)^3) - (2*(18 - 247*S^2 + 3086*S^4 - 7226*S^6 + 3070*S^8 - 255*S^10 + 18*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^3) - (4*S*(-3163 + 1839*S^2 + 1839*S^4 + 613*S^6)*HPL[{3, 2}, -S^2])/(1 + S^2)^3 - (4*S*(-9533 + 5529*S^2 + 5529*S^4 + 1843*S^6)*HPL[{4, 1}, -S^2])/(1 + S^2)^3 + (8*(-343 + 4976*S^2 - 6198*S^4 - 856*S^6 + 221*S^8)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^3) + 1488*S*HPL[{2, 2, 1}, -S^2] + (160*S*(-173 + 3*S^2 + 3*S^4 + S^6)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^3 + (128*S*(-386 + 147*S^2 + 147*S^4 + 49*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^3 + ((2*Pi^2*S*(-1589 + 969*S^2 + 969*S^4 + 323*S^6))/(3*(1 + S^2)^3) - (2*(-45 + 527*S^2 - 3757*S^4 + 2359*S^6 - 254*S^8 + 18*S^10))/(S*(1 + S^2)^3))*Zeta[3] + (4*S*(-1299 + 951*S^2 + 951*S^4 + 317*S^6)*Zeta[5])/(1 + S^2)^3) + (48*S*(-137 + 147*S^2 + 147*S^4 + 49*S^6)*Zeta[7])/(1 + S^2)^3)) - (3136*S^3*(3 + 3*S^2 + S^4)*Zeta[9])/(1 + S^2)^3;
E5uvwT3F3=(92015*(1 + S^2))/(69984*S) + (Pi^2*(-6654007 + 25091*S^2 + 5979258*S^4))/(209952*S) + (Pi^6*(-1000750 - 878591*S^2 + 1541771*S^4 + 1322844*S^6))/(1632960*S*(1 + S^2)) + (Pi^4*(-1657748 - 1767829*S^2 + 1750570*S^4 + 1705131*S^6))/(349920*S*(1 + S^2)) + (Pi^8*(-1311888 - 3279720*S^2 + 8420511*S^4 + 1121984*S^6 + 366464*S^8 + 42984*S^10))/(4082400*S*(1 + S^2)^3) + (S^3*HPL[{0}, S^2]^9)/(576*(1 + S^2)^3) + ((-1 - 11*S^2 - 27*S^4 + 38*S^6 - 27*S^8 - 11*S^10 - S^12)*HPL[{1}, -S^2]^8)/(6*S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^9)/(81*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^8*((-4 - 10*S^2 + 18*S^4 + 13*S^6 + 4*S^8)/(576*S*(1 + S^2)^3) + ((-2 - 6*S^2 - 6*S^4 + 4*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(288*S^3*(1 + S^2)^3)) + ((-145 - 1191*S^2 - 2595*S^4 + 4642*S^6 - 2595*S^8 - 1191*S^10 - 145*S^12)*HPL[{2}, -S^2]^4)/(108*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^7*((-35 - 146*S^2 - 889*S^4 + 460*S^6 - 889*S^8 - 146*S^10 - 35*S^12)/(63*S^3*(1 + S^2)^3) - (2*Pi^2*(51 + 153*S^2 + 153*S^4 - 305*S^6 + 108*S^8 + 108*S^10 + 36*S^12))/(189*S^3*(1 + S^2)^3) + (20*(-1 + S^6)*HPL[{2}, -S^2])/(21*S^3)) + HPL[{0}, S^2]^7*((Pi^2*S^3*(27 + 3*S^2 + 3*S^4 + S^6))/(864*(1 + S^2)^3) + (12 + 14*S^2 + 75*S^4 + 78*S^6 + 47*S^8 + 10*S^10)/(288*S*(1 + S^2)^3) + ((2 + 2*S^2 - 6*S^4 + 14*S^6 + 9*S^8 + 7*S^10 + 2*S^12)*HPL[{1}, -S^2])/(48*S^3*(1 + S^2)^3) + ((-4 - 12*S^2 - 12*S^4 + 13*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^2)/(144*S^3*(1 + S^2)^3) + (S^3*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(144*(1 + S^2)^3)) - (2*(-16 + 25*S^6)*HPL[{3}, -S^2]^3)/(9*S^3) + ((34 + 70*S^2 + 37*S^4 + 164*S^6 + 77*S^8 - 37*S^10 - 35*S^12)*HPL[{4}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-145 - 435*S^2 - 435*S^4 + 473*S^6 + 1170*S^8 + 1170*S^10 + 390*S^12))/(9*S^3*(1 + S^2)^3) + (-1326 - 62*S^2 + 2935*S^4 + 15735*S^6 + 24215*S^8 + 14603*S^10 + 3540*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{7}, -S^2] + (2*(1827 + 4342*S^2 + 2266*S^4 + 5697*S^6 + 8175*S^8 + 5673*S^10 + 1455*S^12)*HPL[{8}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-784 - 2352*S^2 - 2352*S^4 + 1155*S^6 + 2784*S^8 + 2784*S^10 + 928*S^12)*HPL[{9}, -S^2])/(3*S^3*(1 + S^2)^3) + (1232*(-1 + S^6)*HPL[{2, 1}, -S^2]^3)/(9*S^3) - (2*(547 + 3645*S^2 + 7560*S^4 - 10840*S^6 + 5688*S^8 + 2529*S^10 + 259*S^12)*HPL[{3, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((-44*Pi^2*(-1 - 3*S^2 - 3*S^4 + 2*S^6))/(9*S^3*(1 + S^2)^3) + (285 + 898*S^2 + 1012*S^4 - 1053*S^6 + 532*S^8 - 1157*S^10 - 357*S^12)/(18*S^3*(1 + S^2)^3))*HPL[{4, 3}, -S^2] + ((332 + 1019*S^2 + 944*S^4 - 1505*S^6 - 1087*S^8 - 2062*S^10 - 625*S^12)/(6*S^3*(1 + S^2)^3) + (Pi^2*(122 + 366*S^2 + 366*S^4 - 233*S^6 - 141*S^8 - 141*S^10 - 47*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{5, 2}, -S^2] + ((3 + 15*S^2 + 33*S^4 + 120*S^6 + 433*S^8 + 313*S^10 + 87*S^12)*HPL[{5, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 + 213*S^6 + 381*S^8 + 381*S^10 + 127*S^12)*HPL[{5, 4}, -S^2])/(3*S^3*(1 + S^2)^3) + ((3030 + 344*S^2 - 7651*S^4 - 43659*S^6 - 72979*S^8 - 48661*S^10 - 13128*S^12)/(18*S^3*(1 + S^2)^3) - (2*Pi^2*(-178 - 534*S^2 - 534*S^4 + 186*S^6 + 867*S^8 + 867*S^10 + 289*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{6, 1}, -S^2] + ((45 + 117*S^2 + 63*S^4 + 84*S^6 + 769*S^8 + 559*S^10 + 153*S^12)*HPL[{6, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-3 - 9*S^2 - 9*S^4 + 872*S^6 + 1566*S^8 + 1566*S^10 + 522*S^12)*HPL[{6, 3}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(275 + 556*S^2 + 64*S^4 + 1063*S^6 + 1950*S^8 + 1302*S^10 + 324*S^12)*HPL[{7, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-23 - 69*S^2 - 69*S^4 + 2164*S^6 + 3909*S^8 + 3909*S^10 + 1303*S^12)*HPL[{7, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(369 + 1107*S^2 + 1107*S^4 + 3458*S^6 + 5796*S^8 + 5796*S^10 + 1932*S^12)*HPL[{8, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(79 + 741*S^2 + 1665*S^4 - 3214*S^6 + 1665*S^8 + 741*S^10 + 79*S^12)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-67 - 201*S^2 - 201*S^4 - 2578*S^6 + 3783*S^8 + 3783*S^10 + 1261*S^12))/(9*S^3*(1 + S^2)^3) + (-1275 - 158*S^2 + 14887*S^4 - 8412*S^6 + 75439*S^8 + 16450*S^10 + 5421*S^12)/(18*S^3*(1 + S^2)^3))*HPL[{3, 2, 2}, -S^2] + ((4*Pi^2*(-45 - 135*S^2 - 135*S^4 - 1966*S^6 + 2907*S^8 + 2907*S^10 + 969*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-993 - 224*S^2 + 11059*S^4 - 6366*S^6 + 58369*S^8 + 13090*S^10 + 4305*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 3, 1}, -S^2] + ((-315 - 1109*S^2 - 1391*S^4 + 600*S^6 - 3407*S^8 - 2045*S^10 - 465*S^12)*HPL[{3, 3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(-44 - 132*S^2 - 132*S^4 - 1922*S^6 + 2913*S^8 + 2913*S^10 + 971*S^12))/(9*S^3*(1 + S^2)^3) + (-3942 - 1331*S^2 + 42190*S^4 - 24594*S^6 + 231430*S^8 + 51925*S^10 + 17250*S^12)/(18*S^3*(1 + S^2)^3))*HPL[{4, 1, 2}, -S^2] + (2*(318 + 1100*S^2 + 1355*S^4 - 480*S^6 + 2787*S^8 + 1719*S^10 + 399*S^12)*HPL[{4, 1, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(-119 - 357*S^2 - 357*S^4 - 5990*S^6 + 8826*S^8 + 8826*S^10 + 2942*S^12))/(9*S^3*(1 + S^2)^3) + (-11430 - 323*S^2 + 139390*S^4 - 74778*S^6 + 714694*S^8 + 162877*S^10 + 53250*S^12)/(18*S^3*(1 + S^2)^3))*HPL[{4, 2, 1}, -S^2] + ((-273 - 853*S^2 - 907*S^4 + 72*S^6 - 3023*S^8 - 1823*S^10 - 417*S^12)*HPL[{4, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(3 + 9*S^2 + 9*S^4 - 32*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{4, 2, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(660 + 2566*S^2 + 3553*S^4 - 2232*S^6 + 8657*S^8 + 5129*S^10 + 1161*S^12)*HPL[{4, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-76 - 228*S^2 - 228*S^4 + 55*S^6 + 234*S^8 + 234*S^10 + 78*S^12)*HPL[{4, 3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-71 - 213*S^2 - 213*S^4 - 31*S^6 + 186*S^8 + 186*S^10 + 62*S^12)*HPL[{4, 4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-474 - 1422*S^2 - 1422*S^4 - 24653*S^6 + 36291*S^8 + 36291*S^10 + 12097*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-5262 + 3757*S^2 + 78151*S^4 - 30894*S^6 + 377077*S^8 + 90019*S^10 + 28788*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{5, 1, 1}, -S^2] + ((609 + 2647*S^2 + 4039*S^4 - 2880*S^6 + 9695*S^8 + 5861*S^10 + 1365*S^12)*HPL[{5, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-5 - 15*S^2 - 15*S^4 + 103*S^6 + 150*S^8 + 150*S^10 + 50*S^12)*HPL[{5, 1, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + ((5469 + 21067*S^2 + 28939*S^4 - 17640*S^6 + 73115*S^8 + 43361*S^10 + 9825*S^12)*HPL[{5, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-212 - 636*S^2 - 636*S^4 + 31*S^6 + 606*S^8 + 606*S^10 + 202*S^12)*HPL[{5, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-399 - 1197*S^2 - 1197*S^4 - 403*S^6 + 810*S^8 + 810*S^10 + 270*S^12)*HPL[{5, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(7485 + 27647*S^2 + 36245*S^4 - 21252*S^6 + 99877*S^8 + 59242*S^10 + 13398*S^12)*HPL[{6, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-419 - 1257*S^2 - 1257*S^4 - 324*S^6 + 1020*S^8 + 1020*S^10 + 340*S^12)*HPL[{6, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-699 - 2097*S^2 - 2097*S^4 - 1304*S^6 + 600*S^8 + 600*S^10 + 200*S^12)*HPL[{6, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(695 + 2085*S^2 + 2085*S^4 + 3441*S^6 + 2514*S^8 + 2514*S^10 + 838*S^12)*HPL[{7, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*(-279 - 413*S^2 - 2110*S^4 + 2110*S^6 + 413*S^8 + 279*S^10))/(3*S^3*(1 + S^2)^2) - (16*Pi^2*(-154 - 462*S^2 - 462*S^4 + 147*S^6 + 258*S^8 + 258*S^10 + 86*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 2, 2, 1}, -S^2] + ((2*(-1475 - 4023*S^2 - 17083*S^4 + 1292*S^6 + 2469*S^8 + 1227*S^10 + 665*S^12))/(3*S^3*(1 + S^2)^3) + (2*Pi^2*(-3643 - 10929*S^2 - 10929*S^4 + 5928*S^6 + 2217*S^8 + 2217*S^10 + 739*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 2}, -S^2] + ((2*(-1475 - 4023*S^2 - 17083*S^4 + 1292*S^6 + 2469*S^8 + 1227*S^10 + 665*S^12))/(3*S^3*(1 + S^2)^3) + (2*Pi^2*(-3643 - 10929*S^2 - 10929*S^4 + 5928*S^6 + 2217*S^8 + 2217*S^10 + 739*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 2, 1}, -S^2] - (2*(54 + 287*S^2 + 545*S^4 - 384*S^6 + 545*S^8 + 287*S^10 + 54*S^12)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*(-3149 - 8175*S^2 - 32221*S^4 + 1292*S^6 + 17607*S^8 + 5379*S^10 + 2339*S^12))/(3*S^3*(1 + S^2)^3) + (2*Pi^2*(-7339 - 22017*S^2 - 22017*S^4 + 9456*S^6 + 8409*S^8 + 8409*S^10 + 2803*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 2, 1, 1}, -S^2] - (2*(54 + 287*S^2 + 545*S^4 - 384*S^6 + 545*S^8 + 287*S^10 + 54*S^12)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-678 - 1919*S^2 - 2549*S^4 + 108*S^6 + 695*S^8 + 629*S^10 + 342*S^12)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-59 - 177*S^2 - 177*S^4 - 2352*S^6 + 3441*S^8 + 3441*S^10 + 1147*S^12)*HPL[{3, 2, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-218 - 654*S^2 - 654*S^4 - 7435*S^6 + 10821*S^8 + 10821*S^10 + 3607*S^12)*HPL[{3, 2, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-156 - 252*S^2 - 249*S^4 + 180*S^6 + 130*S^8 + 99*S^10)*HPL[{3, 3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (8*(-106 - 318*S^2 - 318*S^4 - 3649*S^6 + 5355*S^8 + 5355*S^10 + 1785*S^12)*HPL[{3, 3, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-722 - 2166*S^2 - 2166*S^4 - 22547*S^6 + 32949*S^8 + 32949*S^10 + 10983*S^12)*HPL[{3, 3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(-11017 - 33051*S^2 - 33051*S^4 + 14784*S^6 + 12231*S^8 + 12231*S^10 + 4077*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-9711 - 26291*S^2 - 100835*S^4 + 2516*S^6 + 46625*S^8 + 13887*S^10 + 6513*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{4, 1, 1, 1}, -S^2] - (2*(-19 + 19*S^2 + 130*S^4 - 336*S^6 + 1034*S^8 + 587*S^10 + 133*S^12)*HPL[{4, 1, 1, 2}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-1522 - 4566*S^2 - 4566*S^4 - 45887*S^6 + 66969*S^8 + 66969*S^10 + 22323*S^12)*HPL[{4, 1, 1, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-605 - 1651*S^2 - 2134*S^4 + 60*S^6 + 206*S^8 + 329*S^10 + 263*S^12)*HPL[{4, 1, 2, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-1317 - 3951*S^2 - 3951*S^4 - 38589*S^6 + 56280*S^8 + 56280*S^10 + 18760*S^12)*HPL[{4, 1, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-1162 - 3486*S^2 - 3486*S^4 - 34475*S^6 + 50313*S^8 + 50313*S^10 + 16771*S^12)*HPL[{4, 1, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-1853 - 4915*S^2 - 6142*S^4 - 492*S^6 + 2686*S^8 + 2161*S^10 + 1055*S^12)*HPL[{4, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-825 - 2475*S^2 - 2475*S^4 - 23751*S^6 + 34374*S^8 + 34374*S^10 + 11458*S^12)*HPL[{4, 2, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-807 - 2421*S^2 - 2421*S^4 - 23340*S^6 + 34041*S^8 + 34041*S^10 + 11347*S^12)*HPL[{4, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-1132 - 3396*S^2 - 3396*S^4 - 34037*S^6 + 49851*S^8 + 49851*S^10 + 16617*S^12)*HPL[{4, 3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-5709 - 15319*S^2 - 19123*S^4 + 444*S^6 + 1995*S^8 + 3159*S^10 + 2481*S^12)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-4634 - 13902*S^2 - 13902*S^4 - 138823*S^6 + 201657*S^8 + 201657*S^10 + 67219*S^12)*HPL[{5, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-7622 - 22866*S^2 - 22866*S^4 - 228673*S^6 + 333759*S^8 + 333759*S^10 + 111253*S^12)*HPL[{5, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-18134 - 54402*S^2 - 54402*S^4 - 544381*S^6 + 797115*S^8 + 797115*S^10 + 265705*S^12)*HPL[{5, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-22606 - 67818*S^2 - 67818*S^4 - 680185*S^6 + 995259*S^8 + 995259*S^10 + 331753*S^12)*HPL[{6, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((32*Pi^2*(152 + 456*S^2 + 456*S^4 - 447*S^6 + 225*S^8 + 225*S^10 + 75*S^12))/(9*S^3*(1 + S^2)^3) + (4*(405 + 1398*S^2 + 7307*S^4 - 1292*S^6 + 7307*S^8 + 1398*S^10 + 405*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((32*Pi^2*(152 + 456*S^2 + 456*S^4 - 447*S^6 + 225*S^8 + 225*S^10 + 75*S^12))/(3*S^3*(1 + S^2)^3) + (4*(405 + 1398*S^2 + 7307*S^4 - 1292*S^6 + 7307*S^8 + 1398*S^10 + 405*S^12))/(S^3*(1 + S^2)^3))*HPL[{2, 2, 1, 1, 1}, -S^2] + (8*(-255 - 382*S^2 - 429*S^4 + 429*S^6 + 382*S^8 + 255*S^10)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (8*(-255 - 382*S^2 - 429*S^4 + 429*S^6 + 382*S^8 + 255*S^10)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (128*(34 + 102*S^2 + 102*S^4 - 147*S^6 + 102*S^8 + 102*S^10 + 34*S^12)*HPL[{2, 2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((16*Pi^2*(1513 + 4539*S^2 + 4539*S^4 - 5224*S^6 + 3309*S^8 + 3309*S^10 + 1103*S^12))/(9*S^3*(1 + S^2)^3) + (4*(2077 + 8136*S^2 + 41117*S^4 - 7072*S^6 + 51751*S^8 + 10648*S^10 + 3167*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(-491 - 712*S^2 - 797*S^4 + 797*S^6 + 712*S^8 + 491*S^10)*HPL[{3, 1, 1, 1, 2}, -S^2])/(S^3*(1 + S^2)^2) - (8*(-2493 - 3664*S^2 - 4107*S^4 + 4107*S^6 + 3664*S^8 + 2493*S^10)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*(3361 + 10083*S^2 + 10083*S^4 - 9166*S^6 + 2691*S^8 + 2691*S^10 + 897*S^12)*HPL[{3, 1, 1, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-1001 - 1476*S^2 - 1655*S^4 + 1655*S^6 + 1476*S^8 + 1001*S^10)*HPL[{3, 1, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (4*(3361 + 10083*S^2 + 10083*S^4 - 9166*S^6 + 2691*S^8 + 2691*S^10 + 897*S^12)*HPL[{3, 1, 2, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(31 + 93*S^2 + 93*S^4 - 274*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*HPL[{3, 1, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(2951 + 8853*S^2 + 8853*S^4 - 8708*S^6 + 3183*S^8 + 3183*S^10 + 1061*S^12)*HPL[{3, 1, 3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-3159 - 4697*S^2 - 5271*S^4 + 5271*S^6 + 4697*S^8 + 3159*S^10)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*(6625 + 19875*S^2 + 19875*S^4 - 23278*S^6 + 12483*S^8 + 12483*S^10 + 4161*S^12)*HPL[{3, 2, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(3233 + 9699*S^2 + 9699*S^4 - 13838*S^6 + 9699*S^8 + 9699*S^10 + 3233*S^12)*HPL[{3, 2, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-10455 - 31365*S^2 - 31365*S^4 + 18162*S^6 + 6603*S^8 + 6603*S^10 + 2201*S^12)*HPL[{3, 2, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-1439 - 4317*S^2 - 4317*S^4 + 2824*S^6 + 429*S^8 + 429*S^10 + 143*S^12)*HPL[{3, 3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (8*(-19161 - 48059*S^2 - 61355*S^4 + 1764*S^6 + 56815*S^8 + 45595*S^10 + 18681*S^12)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(9979 + 29937*S^2 + 29937*S^4 - 34954*S^6 + 18345*S^8 + 18345*S^10 + 6115*S^12)*HPL[{4, 1, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(4891 + 14673*S^2 + 14673*S^4 - 20794*S^6 + 14169*S^8 + 14169*S^10 + 4723*S^12)*HPL[{4, 1, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-15641 - 46923*S^2 - 46923*S^4 + 27206*S^6 + 9525*S^8 + 9525*S^10 + 3175*S^12)*HPL[{4, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-51809 - 155427*S^2 - 155427*S^4 + 102038*S^6 + 14925*S^8 + 14925*S^10 + 4975*S^12)*HPL[{4, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-25899 - 77697*S^2 - 77697*S^4 + 51365*S^6 + 7008*S^8 + 7008*S^10 + 2336*S^12)*HPL[{5, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-8*(-545 - 711*S^2 - 4606*S^4 + 4606*S^6 + 711*S^8 + 545*S^10))/(3*S^3*(1 + S^2)^2) - (32*Pi^2*(-330 - 990*S^2 - 990*S^4 + 289*S^6 + 552*S^8 + 552*S^10 + 184*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (9856*(-1 + S^6)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (9856*(-1 + S^6)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S^3 + (16*(-345 - 1051*S^2 - 1525*S^4 + 882*S^6 - 745*S^8 - 181*S^10 + 105*S^12)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-1577 - 4731*S^2 - 4731*S^4 - 1156*S^6 + 6483*S^8 + 6483*S^10 + 2161*S^12)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-3425 - 10275*S^2 - 10275*S^4 - 1156*S^6 + 12027*S^8 + 12027*S^10 + 4009*S^12)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-4657 - 13971*S^2 - 13971*S^4 - 1156*S^6 + 15723*S^8 + 15723*S^10 + 5241*S^12)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-5273 - 15819*S^2 - 15819*S^4 - 1156*S^6 + 17571*S^8 + 17571*S^10 + 5857*S^12)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-9277 - 27831*S^2 - 27831*S^4 - 1156*S^6 + 29583*S^8 + 29583*S^10 + 9861*S^12)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(-13897 - 41691*S^2 - 41691*S^4 - 2018*S^6 + 44547*S^8 + 44547*S^10 + 14849*S^12)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (160*(-15 - 14*S^2 - 12*S^4 + 12*S^6 + 14*S^8 + 15*S^10)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (256*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (1024*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2560*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (256*(511 + 1533*S^2 + 1533*S^4 - 1903*S^6 + 1368*S^8 + 1368*S^10 + 456*S^12)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (14080*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((4*Pi^2*S^3*(-27 + 3*S^2 + 3*S^4 + S^6))/(27*(1 + S^2)^3) + (4*(1 + 18*S^2 - 38*S^4 + 18*S^6 + S^8))/(9*S*(1 + S^2)^3) + (4*S^3*(-9 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^2)/(9*(1 + S^2)^3) + (4*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]*((4*(8 + 20*S^2 - 57*S^4 + 61*S^6 + 25*S^8 + 3*S^10))/(9*S*(1 + S^2)^3) + (32*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3)) + (8*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3))*Log[T]^7 + ((-4*(-2 + S^2)*(-1 + 2*S^2)*(1 + 5*S^2 + S^4))/(9*S*(1 + S^2)^3) - (4*S^3*(-7 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{0}, S^2])/(9*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3))*Log[T]^8 - (8*S^3*Log[T]^9)/(9*(1 + S^2)^3) + ((-524 - 517*S^2 - 677*S^4 - 252*S^6)/(54*S*(1 + S^2)) + (Pi^2*(-80 - 200*S^2 + 318*S^4 + 44*S^6 - 55*S^8 - 33*S^10))/(18*S*(1 + S^2)^3))*Zeta[3]^2 + (64*S^5*(3 + 3*S^2 + S^4)*Zeta[3]^3)/(3*(1 + S^2)^3) + HPL[{3, 1, 2}, -S^2]*((-1247 + 49*S^2 - 49*S^4 + 1247*S^6)/(36*S^3) + (Pi^2*(-398 - 1063*S^2 - 1199*S^4 + 1015*S^6 + 905*S^8 + 340*S^10))/(54*S^3*(1 + S^2)^2) + (4*(-1 + 9*S^6)*Zeta[3])/(3*S^3)) + Log[T]^6*((-5*(1 + S^2))/(9*S) + (Pi^2*(-102 - 255*S^2 + 858*S^4 - 281*S^6 - 131*S^8 - 15*S^10))/(27*S*(1 + S^2)^3) - (4*S^3*(-25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2]^3)/(27*(1 + S^2)^3) - (14*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) - (224*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^2*((-46 - 115*S^2 + 270*S^4 - 141*S^6 - 75*S^8 - 15*S^10)/(9*S*(1 + S^2)^3) - (2*(23 + 69*S^2 + 69*S^4 - 109*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3)) - (2*(-1 + S^2)*(15 + 29*S^2 + 41*S^4 + 29*S^6 + 15*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-35 - 146*S^2 - 889*S^4 + 460*S^6 - 889*S^8 - 146*S^10 - 35*S^12)/(9*S^3*(1 + S^2)^3) - (2*Pi^2*(51 + 153*S^2 + 153*S^4 - 305*S^6 + 108*S^8 + 108*S^10 + 36*S^12))/(27*S^3*(1 + S^2)^3) + (20*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]*((-4*Pi^2*S^3*(-74 + 51*S^2 + 51*S^4 + 17*S^6))/(27*(1 + S^2)^3) + (-34 - 307*S^2 + 230*S^4 - 582*S^6 - 112*S^8 - 35*S^10)/(9*S*(1 + S^2)^3) - (14*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^3) - (112*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) - (4*(-2 - 6*S^2 - 6*S^4 - 87*S^6 + 81*S^8 + 81*S^10 + 27*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + (16*S^3*(-24 + 33*S^2 + 33*S^4 + 11*S^6)*HPL[{3}, -S^2])/(9*(1 + S^2)^3) - (176*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (16*S^3*(-17 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{0}, S^2]^6*((-401 + 598*S^2 + 1323*S^4)/(5184*S) + (Pi^2*(-158 - 395*S^2 + 774*S^4 + 509*S^6 + 206*S^8 + 24*S^10))/(1728*S*(1 + S^2)^3) + ((23 - 132*S^2 - 528*S^4 + 550*S^6 + 228*S^8 + 120*S^10 + 23*S^12)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)^3) + ((-23 - 69*S^2 - 69*S^4 + 70*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{1}, -S^2]^3)/(216*S^3*(1 + S^2)^3) + ((-40 - 103*S^2 + 195*S^4 + 134*S^6 + 92*S^8 + 24*S^10)*HPL[{2}, -S^2])/(288*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*(-79 - 237*S^2 - 237*S^4 + 182*S^6 + 99*S^8 + 99*S^10 + 33*S^12))/(864*S^3*(1 + S^2)^3) + (-365 - 48*S^2 - 3459*S^4 + 5642*S^6 + 5469*S^8 + 3282*S^10 + 895*S^12)/(5184*S^3*(1 + S^2)^3) + ((-19 - 57*S^2 - 57*S^4 + 51*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{2}, -S^2])/(144*S^3*(1 + S^2)^3)) + ((-1 + 3*S^6)*HPL[{3}, -S^2])/(144*S^3) + ((9 + 27*S^2 + 27*S^4 - 8*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{2, 1}, -S^2])/(36*S^3*(1 + S^2)^3) + (S^3*(17 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(36*(1 + S^2)^3)) + HPL[{2}, -S^2]^3*((8 - 11*S^2 + 11*S^4 - 8*S^6)/(6*S^3) + (Pi^2*(467 + 333*S^2 - 693*S^4 + 4642*S^6 - 4497*S^8 - 2715*S^10 - 757*S^12))/(324*S^3*(1 + S^2)^3) + (2*(-17 - 51*S^2 - 51*S^4 - 294*S^6 + 459*S^8 + 459*S^10 + 153*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(34 + 102*S^2 + 102*S^4 - 147*S^6 + 102*S^8 + 102*S^10 + 34*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*S^3*(-147 + 204*S^2 + 204*S^4 + 68*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{2, 1, 1, 1, 1}, -S^2]*((8*(-8 - 41*S^2 + 41*S^4 + 8*S^6))/S^3 - (8*Pi^2*(-142 + 20*S^2 + 533*S^4 - 1607*S^6 + 1132*S^8 + 721*S^10 + 221*S^12))/(9*S^3*(1 + S^2)^3) + (64*S^3*(-289 + 438*S^2 + 438*S^4 + 146*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{3, 2}, -S^2]*((19485 + 52792*S^2 - 10012*S^4 - 129296*S^6 - 70425*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(1117 - 1368*S^2 - 21744*S^4 + 9326*S^6 - 124119*S^8 - 31050*S^10 - 10538*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(-29 - 87*S^2 - 87*S^4 + 2064*S^6 - 3687*S^8 - 3687*S^10 - 1229*S^12))/(135*S^3*(1 + S^2)^3) - (4*(-25 - 75*S^2 - 75*S^4 - 2594*S^6 + 3621*S^8 + 3621*S^10 + 1207*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((52 + 49*S^2 - 104*S^4 + 596*S^6 - 386*S^8 - 233*S^10 - 62*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{5}, -S^2]*((9879 + 34525*S^2 + 88571*S^4 + 148399*S^6 + 75402*S^8)/(324*S^3*(1 + S^2)) + (Pi^4*(28 + 84*S^2 + 84*S^4 - 225*S^6 + 2190*S^8 + 2190*S^10 + 730*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(397 + 9345*S^2 + 17679*S^4 + 29504*S^6 + 59637*S^8 + 28731*S^10 + 7579*S^12))/(324*S^3*(1 + S^2)^3) + ((-985 - 3300*S^2 - 4029*S^4 + 4384*S^6 - 783*S^8 - 72*S^10 + 185*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (16*(2 + 6*S^2 + 6*S^4 - 39*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(14 + 42*S^2 + 42*S^4 - 195*S^6 + 477*S^8 + 477*S^10 + 159*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-359 - 954*S^2 - 855*S^4 - 1276*S^6 - 741*S^8 - 318*S^10 - 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1, 1}, -S^2]*((20651 + 21569*S^2 - 21569*S^4 - 20651*S^6)/(54*S^3) + (Pi^2*(1107 + 2828*S^2 + 12142*S^4 - 646*S^6 - 4835*S^8 - 1430*S^10 - 702*S^12))/(9*S^3*(1 + S^2)^3) - (4*Pi^4*(-393 - 1179*S^2 - 1179*S^4 + 432*S^6 + 444*S^8 + 444*S^10 + 148*S^12))/(27*S^3*(1 + S^2)^3) + (16*(-83 - 455*S^2 - 923*S^4 + 1607*S^6 - 742*S^8 - 286*S^10 + 4*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4, 2}, -S^2]*((140 - 1455*S^2 - 1357*S^4 - 2354*S^6)/(36*S^3) + (Pi^2*(101 - 42*S^2 - 564*S^4 + 1372*S^6 - 4746*S^8 - 2748*S^10 - 637*S^12))/(54*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 22*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]^2*((3100 - 4178*S^2 - 22197*S^4 - 20432*S^6 - 8753*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(-51 - 211*S^2 - 307*S^4 + 186*S^6 - 971*S^8 - 569*S^10 - 129*S^12))/(36*S^3*(1 + S^2)^3) + (2*(29 + 87*S^2 + 87*S^4 - 121*S^6 + 54*S^8 + 54*S^10 + 18*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-3 - 9*S^2 - 9*S^4 - 4*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(270*S^3) + (Pi^4*(-4460 - 13380*S^2 - 13380*S^4 + 23717*S^6 - 6639*S^8 - 6639*S^10 - 2213*S^12))/(4050*S^3*(1 + S^2)^3) + (Pi^2*(-1619 - 6333*S^2 - 36216*S^4 + 15548*S^6 - 27729*S^8 - 5235*S^10 - 1016*S^12))/(810*S^3*(1 + S^2)^3) + ((-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10)/(15*S^3*(1 + S^2)^2) + (2*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(135*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (8*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(45*S^3*(1 + S^2)^3) + (2*(283 + 1611*S^2 + 3147*S^4 - 6262*S^6 + 7197*S^8 + 2961*S^10 + 283*S^12)*HPL[{3}, -S^2])/(45*S^3*(1 + S^2)^3) + (4*(47 + 141*S^2 + 141*S^4 - 554*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{4}, -S^2])/(45*S^3*(1 + S^2)^3) - (60*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (8*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1}, -S^2])/(45*S^3*(1 + S^2)^3) + (40*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(17 + 147*S^2 + 345*S^4 - 1046*S^6 + 1155*S^8 + 417*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^6*((-2*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(27*S^3) + (Pi^2*(-109 - 1239*S^2 - 3057*S^4 + 3742*S^6 - 2247*S^8 - 969*S^10 - 109*S^12))/(162*S^3*(1 + S^2)^3) + (10*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (20*(5 + 15*S^2 + 15*S^4 - 65*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^3) - (20*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (4*(5 + 15*S^2 + 15*S^4 - 87*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{5, 1}, -S^2]*((-431 - 8364*S^2 - 15883*S^4 - 17814*S^6)/(36*S^3) + (Pi^2*(-515 - 2082*S^2 - 2541*S^4 + 7592*S^6 - 30843*S^8 - 17226*S^10 - 3665*S^12))/(54*S^3*(1 + S^2)^3) - (4*(17 + 51*S^2 + 51*S^4 - 117*S^6 + 78*S^8 + 78*S^10 + 26*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{6}, -S^2]*((-1080 + 124*S^2 + 11976*S^4 + 12833*S^6)/(36*S^3) + (Pi^2*(655 + 507*S^2 - 2265*S^4 + 2660*S^6 + 10101*S^8 + 5988*S^10 + 1294*S^12))/(54*S^3*(1 + S^2)^3) - (4*(-74 - 222*S^2 - 222*S^4 - 29*S^6 + 150*S^8 + 150*S^10 + 50*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-30 - 90*S^2 - 90*S^4 + 61*S^6 + 156*S^8 + 156*S^10 + 52*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]^2*((-953 + 24388*S^2 + 49386*S^4 + 24388*S^6 - 953*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(383 + 6015*S^2 + 14313*S^4 - 29879*S^6 + 16746*S^8 + 7926*S^10 + 1148*S^12))/(54*S^3*(1 + S^2)^3) - (16*(-6 - 18*S^2 - 18*S^4 - 131*S^6 + 213*S^8 + 213*S^10 + 71*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 2, 1}, -S^2]*((-12735 - 19126*S^2 - 5006*S^4 - 19126*S^6 - 12735*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-2863 - 9192*S^2 - 42267*S^4 + 5488*S^6 - 27129*S^8 - 5040*S^10 - 1189*S^12))/(54*S^3*(1 + S^2)^3) + (Pi^4*(-3684 - 11052*S^2 - 11052*S^4 + 8559*S^6 - 3180*S^8 - 3180*S^10 - 1060*S^12))/(135*S^3*(1 + S^2)^3) - (4*(-565 - 2877*S^2 - 5667*S^4 + 8689*S^6 - 3234*S^8 - 966*S^10 + 200*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{3, 1, 1, 1}, -S^2]*((-2*(641 + 570*S^2 + 2046*S^4 + 929*S^6))/(9*S^3) + (2*Pi^2*(-1277 - 1956*S^2 - 507*S^4 - 6991*S^6 + 3168*S^8 + 2331*S^10 + 928*S^12))/(27*S^3*(1 + S^2)^3) - (16*(1 + 3*S^2 + 3*S^4 - 602*S^6 + 879*S^8 + 879*S^10 + 293*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1, 1}, -S^2]*((-36426 - 53333*S^2 + 46445*S^4 + 73327*S^6 + 25527*S^8)/(162*S^3*(1 + S^2)) + (Pi^4*(-22369 - 67107*S^2 - 67107*S^4 + 40592*S^6 - 2595*S^8 - 2595*S^10 - 865*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(-8519 - 23838*S^2 - 112851*S^4 + 15416*S^6 - 30885*S^8 - 2034*S^10 + 487*S^12))/(54*S^3*(1 + S^2)^3) - (4*(-1661 - 8640*S^2 - 17145*S^4 + 27161*S^6 - 11274*S^8 - 3885*S^10 + 364*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{4, 1}, -S^2]*((11129 + 21680*S^2 - 85288*S^4 - 226848*S^6 - 115457*S^8)/(216*S^3*(1 + S^2)) + (Pi^2*(723 - 6119*S^2 - 33125*S^4 + 4146*S^6 - 146747*S^8 - 39995*S^10 - 12675*S^12))/(108*S^3*(1 + S^2)^3) + (Pi^4*(-11 - 33*S^2 - 33*S^4 + 14594*S^6 - 24213*S^8 - 24213*S^10 - 8071*S^12))/(270*S^3*(1 + S^2)^3) - (8*(-95 - 285*S^2 - 285*S^4 - 3862*S^6 + 5763*S^8 + 5763*S^10 + 1921*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-274 - 333*S^2 + 351*S^4 - 3410*S^6 + 2625*S^8 + 1581*S^10 + 392*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{4, 1, 1}, -S^2]*((1187 + 1155*S^2 + 9309*S^4 + 5093*S^6)/(18*S^3) + (Pi^2*(2963 + 2745*S^2 - 3168*S^4 + 22720*S^6 - 13344*S^8 - 8853*S^10 - 3031*S^12))/(27*S^3*(1 + S^2)^3) + (16*(1 + 3*S^2 + 3*S^4 - 898*S^6 + 1269*S^8 + 1269*S^10 + 423*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 2, 1}, -S^2]*((5*(-19 - 307*S^2 + 307*S^4 + 19*S^6))/(36*S^3) + (Pi^2*(490 - 43*S^2 - 1678*S^4 + 6128*S^6 - 5356*S^8 - 3205*S^10 - 896*S^12))/(18*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 - 1168*S^6 + 1659*S^8 + 1659*S^10 + 553*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^5*((Pi^4*S^3*(14626 + 1707*S^2 + 1707*S^4 + 569*S^6))/(64800*(1 + S^2)^3) + (2254 + 2641*S^2 + 4622*S^4 + 3803*S^6)/(3456*S*(1 + S^2)) + (Pi^2*(2920 + 1770*S^2 + 21087*S^4 + 20203*S^6 + 12737*S^8 + 2835*S^10))/(8640*S*(1 + S^2)^3) + ((200 - 1035*S^2 - 4290*S^4 + 5062*S^6 + 732*S^8 + 639*S^10 + 200*S^12)*HPL[{1}, -S^2]^3)/(1080*S^3*(1 + S^2)^3) + ((-275 - 825*S^2 - 825*S^4 + 1033*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{1}, -S^2]^4)/(1080*S^3*(1 + S^2)^3) + ((Pi^2*S^3*(319 + 78*S^2 + 78*S^4 + 26*S^6))/(540*(1 + S^2)^3) + (305 + 2220*S^2 - 2040*S^4 + 12511*S^6 + 8844*S^8 + 7221*S^10 + 1835*S^12)/(4320*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (S^3*(-76 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2]^2)/(120*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(-695 - 2085*S^2 - 2085*S^4 + 2398*S^6 + 327*S^8 + 327*S^10 + 109*S^12))/(2160*S^3*(1 + S^2)^3) + (910 + 6930*S^2 - 7395*S^4 + 23600*S^6 + 11070*S^8 + 6546*S^10 + 1195*S^12)/(4320*S^3*(1 + S^2)^3) + ((-230 - 690*S^2 - 690*S^4 + 853*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{2}, -S^2])/(360*S^3*(1 + S^2)^3)) + ((13 + 33*S^2 + 15*S^4 + 44*S^6 - 15*S^8 + 21*S^10 + 13*S^12)*HPL[{3}, -S^2])/(144*S^3*(1 + S^2)^3) - (S^5*(3 + 3*S^2 + S^4)*HPL[{4}, -S^2])/(6*(1 + S^2)^3) + ((-130 + 545*S^2 + 2660*S^4 - 1214*S^6 + 80*S^8 + 32*S^10 + 5*S^12)*HPL[{2, 1}, -S^2])/(360*S^3*(1 + S^2)^3) + (S^3*(-27 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3, 1}, -S^2])/(10*(1 + S^2)^3) - (S^3*(-541 + 3*S^2 + 3*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(90*(1 + S^2)^3) + ((-8 - 20*S^2 + 117*S^4 + 233*S^6 + 203*S^8 + 63*S^10)*Zeta[3])/(24*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((283 + 581*S^2 + 543*S^4 + 583*S^6 + 266*S^8)/(576*S^3*(1 + S^2)) + (Pi^2*(1460 + 225*S^2 - 8070*S^4 + 13882*S^6 + 6402*S^8 + 5049*S^10 + 1460*S^12))/(4320*S^3*(1 + S^2)^3) + ((65 - 280*S^2 - 1245*S^4 + 1284*S^6 + 129*S^8 + 178*S^10 + 65*S^12)*HPL[{2}, -S^2])/(240*S^3*(1 + S^2)^3) - (S^3*(-3 + 3*S^2 + 3*S^4 + S^6)*HPL[{3}, -S^2])/(12*(1 + S^2)^3) + ((230 + 690*S^2 + 690*S^4 - 853*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(180*S^3*(1 + S^2)^3) + ((-1 - 3*S^2 - 3*S^4 + 3*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3))) + Log[T]^5*((1 + S^2)/(3*S) + (Pi^4*S^3*(-14626 + 1707*S^2 + 1707*S^4 + 569*S^6))/(2025*(1 + S^2)^3) + (Pi^2*(650 + 7575*S^2 - 10392*S^4 + 7234*S^6 + 1174*S^8 + 143*S^10))/(270*S*(1 + S^2)^3) + (2*S^3*(-164 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^4)/(135*(1 + S^2)^3) + (28*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) + (112*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^3*((560 + 1400*S^2 - 3378*S^4 + 1226*S^6 + 431*S^8 + 27*S^10)/(135*S*(1 + S^2)^3) + (2*(56 + 168*S^2 + 168*S^4 - 263*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^3)) + ((-143 - 381*S^2 + 722*S^4 - 722*S^6 + 381*S^8 + 143*S^10)/(45*S^3*(1 + S^2)^2) + (4*Pi^2*(-11 - 33*S^2 - 33*S^4 - 77*S^6 + 63*S^8 + 63*S^10 + 21*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (8*(5 + 15*S^2 + 15*S^4 - 77*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12)/(3*S^3*(1 + S^2)^3) + (2*Pi^2*(51 + 153*S^2 + 153*S^4 - 305*S^6 + 108*S^8 + 108*S^10 + 36*S^12))/(9*S^3*(1 + S^2)^3) - (20*(-1 + S^6)*HPL[{2}, -S^2])/S^3) + HPL[{0}, S^2]^2*((Pi^2*S^3*(-1601 + 327*S^2 + 327*S^4 + 109*S^6))/(135*(1 + S^2)^3) + (440 + 3795*S^2 - 2412*S^4 + 3454*S^6 + 964*S^8 + 143*S^10)/(90*S*(1 + S^2)^3) + (2*(23 + 273*S^2 + 678*S^4 - 674*S^6 + 273*S^8 + 138*S^10 + 23*S^12)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(23 + 69*S^2 + 69*S^4 - 109*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (2*(-1 - 3*S^2 - 3*S^4 - 154*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) - (2*(63 + 689*S^2 + 1439*S^4 - 5214*S^6 + 10319*S^8 + 4259*S^10 + 513*S^12)*HPL[{3}, -S^2])/(45*S^3*(1 + S^2)^3) - (8*(-1 - 3*S^2 - 3*S^4 - 90*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*HPL[{4}, -S^2])/(15*S^3*(1 + S^2)^3) + (4*(-15 - 104*S^2 - 192*S^4 + 192*S^6 + 104*S^8 + 15*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (16*(-5 - 15*S^2 - 15*S^4 + 9*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (112*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(10 + 25*S^2 - 114*S^4 + 321*S^6 + 129*S^8 + 15*S^10)*Zeta[3])/(3*S*(1 + S^2)^3) + HPL[{0}, S^2]*((61 + 107*S^2 + 52*S^4)/(9*S) + (Pi^2*(1400 + 3500*S^2 - 9363*S^4 + 7631*S^6 + 3056*S^8 + 342*S^10))/(135*S*(1 + S^2)^3) + (14*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^2)/(S^3*(1 + S^2)^3) + (224*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + (2*(-28 + 60*S^2 + 267*S^4 - 1046*S^6 + 1233*S^8 + 504*S^10 + 62*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12)/(3*S^3*(1 + S^2)^3) + (2*Pi^2*(140 + 420*S^2 + 420*S^4 - 851*S^6 + 303*S^8 + 303*S^10 + 101*S^12))/(27*S^3*(1 + S^2)^3) + (4*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) - (4*(-3 - 9*S^2 - 9*S^4 - 10*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(-27 - 81*S^2 - 81*S^4 + 87*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*S^3*(-3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{1}, -S^2]*((4*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) + (Pi^2*(109 + 1239*S^2 + 3057*S^4 - 3742*S^6 + 2247*S^8 + 969*S^10 + 109*S^12))/(27*S^3*(1 + S^2)^3) - (60*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (40*(5 + 15*S^2 + 15*S^4 - 65*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (40*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (8*(5 + 15*S^2 + 15*S^4 - 87*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3))) + ((1564*Pi^4*S^5*(3 + 3*S^2 + S^4))/(135*(1 + S^2)^3) + (-34958 - 30715*S^2 + 52354*S^4 + 44655*S^6)/(216*S*(1 + S^2)) + (Pi^2*(-478 - 1045*S^2 + 753*S^4 + 31367*S^6 + 12101*S^8 + 4806*S^10))/(108*S*(1 + S^2)^3))*Zeta[5] + Log[T]^4*((19*(1 + S^2))/(54*S) + (Pi^2*(-851 - 1441*S^2 - 410*S^4 + 72*S^6))/(162*S*(1 + S^2)) + (Pi^4*(-8920 - 22300*S^2 + 66411*S^4 - 19595*S^6 - 9542*S^8 - 1326*S^10))/(1620*S*(1 + S^2)^3) + (S^3*(164 + 3*S^2 + 3*S^4 + S^6)*HPL[{0}, S^2]^5)/(135*(1 + S^2)^3) - (35*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) - (112*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^4*((-274 - 685*S^2 + 1557*S^4 + 4*S^6 + 31*S^8 + 15*S^10)/(108*S*(1 + S^2)^3) + ((-137 - 411*S^2 - 411*S^4 + 518*S^6 - 15*S^8 - 15*S^10 - 5*S^12)*HPL[{1}, -S^2])/(54*S^3*(1 + S^2)^3)) + ((-79 - 741*S^2 - 1665*S^4 + 3214*S^6 - 1665*S^8 - 741*S^10 - 79*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-5*(35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12))/(9*S^3*(1 + S^2)^3) - (10*Pi^2*(51 + 153*S^2 + 153*S^4 - 305*S^6 + 108*S^8 + 108*S^10 + 36*S^12))/(27*S^3*(1 + S^2)^3) + (100*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^3*(-(Pi^2*S^3*(-703 + 129*S^2 + 129*S^4 + 43*S^6))/(81*(1 + S^2)^3) + (-28 - 1177*S^2 + 1572*S^4 - 541*S^6 + 134*S^8 + 36*S^10)/(54*S*(1 + S^2)^3) + ((-16 - 882*S^2 - 2544*S^4 + 2854*S^6 - 789*S^8 - 297*S^10 - 16*S^12)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^3) - (5*(56 + 168*S^2 + 168*S^4 - 263*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)^3) + ((2 + 6*S^2 + 6*S^4 + 669*S^6 - 249*S^8 - 249*S^10 - 83*S^12)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^3)) + ((2*Pi^2*(-7 - 21*S^2 - 21*S^4 - 754*S^6 + 1059*S^8 + 1059*S^10 + 353*S^12))/(27*S^3*(1 + S^2)^3) + (26 + 573*S^2 + 2291*S^4 - 306*S^6 + 7608*S^8 + 1829*S^10 + 571*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(18 + 142*S^2 + 265*S^4 - 882*S^6 + 2005*S^8 + 1090*S^10 + 222*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-6 - 18*S^2 - 18*S^4 - 125*S^6 + 327*S^8 + 327*S^10 + 109*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + ((545 + 711*S^2 + 4606*S^4 - 4606*S^6 - 711*S^8 - 545*S^10)/(9*S^3*(1 + S^2)^2) - (4*Pi^2*(-330 - 990*S^2 - 990*S^4 + 289*S^6 + 552*S^8 + 552*S^10 + 184*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(-345 - 1051*S^2 - 1525*S^4 + 882*S^6 - 745*S^8 - 181*S^10 + 105*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-37 - 111*S^2 - 111*S^4 - 1156*S^6 + 1863*S^8 + 1863*S^10 + 621*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(-37 - 111*S^2 - 111*S^4 - 2018*S^6 + 2967*S^8 + 2967*S^10 + 989*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (20*(-15 - 14*S^2 - 12*S^4 + 12*S^6 + 14*S^8 + 15*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (32*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (32*(73 + 219*S^2 + 219*S^4 - 169*S^6 + 54*S^8 + 54*S^10 + 18*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (1760*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((4*Pi^2*S^3*(-281 + 552*S^2 + 552*S^4 + 184*S^6))/(27*(1 + S^2)^3) + (170 + 1085*S^2 - 284*S^4 + 6402*S^6 + 1426*S^8 + 545*S^10)/(9*S*(1 + S^2)^3))*Zeta[3] + HPL[{0}, S^2]^2*((-1477 - 2432*S^2 - 595*S^4 + 144*S^6)/(108*S*(1 + S^2)) + (Pi^2*(-1238 - 3095*S^2 + 7164*S^4 - 2107*S^6 - 1063*S^8 - 195*S^10))/(108*S*(1 + S^2)^3) - (5*(23 + 273*S^2 + 678*S^4 - 674*S^6 + 273*S^8 + 138*S^10 + 23*S^12)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) - (10*(23 + 69*S^2 + 69*S^4 - 109*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + ((59 - 475*S^2 - 1456*S^4 + 3214*S^6 - 1874*S^8 - 1007*S^10 - 217*S^12)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((-1663 - 6096*S^2 - 32427*S^4 + 10396*S^6 - 15453*S^8 - 3900*S^10 - 457*S^12)/(108*S^3*(1 + S^2)^3) + (Pi^2*(-619 - 1857*S^2 - 1857*S^4 + 2671*S^6 - 390*S^8 - 390*S^10 - 130*S^12))/(54*S^3*(1 + S^2)^3) + ((-325 - 975*S^2 - 975*S^4 + 1348*S^6 - 201*S^8 - 201*S^10 - 67*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + (2*(-7 - 21*S^2 - 21*S^4 - 34*S^6 + 69*S^8 + 69*S^10 + 23*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-165 - 495*S^2 - 495*S^4 + 289*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*S^3*(-26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-8 - 41*S^2 + 41*S^4 + 8*S^6)/(3*S^3) + (Pi^2*(142 - 20*S^2 - 533*S^4 + 1607*S^6 - 1132*S^8 - 721*S^10 - 221*S^12))/(27*S^3*(1 + S^2)^3) + (4*(-29 - 87*S^2 - 87*S^4 - 578*S^6 + 963*S^8 + 963*S^10 + 321*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (16*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*S^3*(-289 + 438*S^2 + 438*S^4 + 146*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{1}, -S^2]*(-((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(54*S^3) + (Pi^4*(-4460 - 13380*S^2 - 13380*S^4 + 23717*S^6 - 6639*S^8 - 6639*S^10 - 2213*S^12))/(810*S^3*(1 + S^2)^3) + (Pi^2*(-1619 - 6333*S^2 - 36216*S^4 + 15548*S^6 - 27729*S^8 - 5235*S^10 - 1016*S^12))/(162*S^3*(1 + S^2)^3) + ((-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10)/(3*S^3*(1 + S^2)^2) + (2*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (8*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + (2*(283 + 1611*S^2 + 3147*S^4 - 6262*S^6 + 7197*S^8 + 2961*S^10 + 283*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(47 + 141*S^2 + 141*S^4 - 554*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (300*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (8*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (200*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (10*(17 + 147*S^2 + 345*S^4 - 1046*S^6 + 1155*S^8 + 417*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((-10*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) - (5*Pi^2*(109 + 1239*S^2 + 3057*S^4 - 3742*S^6 + 2247*S^8 + 969*S^10 + 109*S^12))/(54*S^3*(1 + S^2)^3) + (150*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (100*(5 + 15*S^2 + 15*S^4 - 65*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (100*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (20*(5 + 15*S^2 + 15*S^4 - 87*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]*((-173 - 1246*S^2 - 65*S^4)/(54*S) - (Pi^4*S^3*(-11971 + 6258*S^2 + 6258*S^4 + 2086*S^6))/(810*(1 + S^2)^3) + (Pi^2*(-566 - 6959*S^2 + 6594*S^4 - 9812*S^6 - 1412*S^8 - 453*S^10))/(108*S*(1 + S^2)^3) - (70*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^3) - (280*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^3) + ((517 + 1098*S^2 - 8601*S^4 + 10304*S^6 - 23529*S^8 - 4242*S^10 - 1547*S^12)/(54*S^3*(1 + S^2)^3) - (2*Pi^2*(-16 - 48*S^2 - 48*S^4 - 987*S^6 + 732*S^8 + 732*S^10 + 244*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (4*S^3*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2}, -S^2]^2)/(9*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((-5*(35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12))/(6*S^3*(1 + S^2)^3) - (5*Pi^2*(140 + 420*S^2 + 420*S^4 - 851*S^6 + 303*S^8 + 303*S^10 + 101*S^12))/(27*S^3*(1 + S^2)^3) - (10*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((27 + 73*S^2 - 11*S^4 - 150*S^6 + 585*S^8 + 447*S^10 + 129*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 16*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (10*(-62 - 504*S^2 - 1233*S^4 + 1046*S^6 - 267*S^8 - 60*S^10 + 28*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-35 - 105*S^2 - 105*S^4 - 1312*S^6 + 1209*S^8 + 1209*S^10 + 403*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (40*(-2 - 6*S^2 - 6*S^4 - 87*S^6 + 81*S^8 + 81*S^10 + 27*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(80 + 200*S^2 - 441*S^4 + 935*S^6 + 536*S^8 + 120*S^10)*Zeta[3])/(9*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((-10*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) + (Pi^2*(-347 - 5229*S^2 - 13593*S^4 + 17678*S^6 - 10083*S^8 - 4059*S^10 - 347*S^12))/(54*S^3*(1 + S^2)^3) - (10*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(10 + 30*S^2 + 30*S^4 - 43*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (20*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(40 + 120*S^2 + 120*S^4 - 277*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3))) + (40*S^3*(-50 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[5])/(9*(1 + S^2)^3)) + HPL[{0}, S^2]^4*((-120718 + 24191*S^2 + 148797*S^4)/(31104*S) + (Pi^2*(-8024 + 1913*S^2 + 35215*S^4 + 25062*S^6))/(15552*S*(1 + S^2)) + (Pi^4*(-11836 - 29590*S^2 + 62037*S^4 + 32983*S^6 + 14767*S^8 + 2265*S^10))/(25920*S*(1 + S^2)^3) + ((-2 - 545*S^2 - 1614*S^4 + 1554*S^6 - 30*S^8 - 17*S^10 - 2*S^12)*HPL[{1}, -S^2]^4)/(144*S^3*(1 + S^2)^3) + ((-137 - 411*S^2 - 411*S^4 + 518*S^6 - 15*S^8 - 15*S^10 - 5*S^12)*HPL[{1}, -S^2]^5)/(270*S^3*(1 + S^2)^3) + ((22 - 152*S^2 - 470*S^4 + 1181*S^6 - 245*S^8 - 119*S^10 - 23*S^12)*HPL[{2}, -S^2]^2)/(144*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((Pi^2*(-619 - 1857*S^2 - 1857*S^4 + 2086*S^6 + 195*S^8 + 195*S^10 + 65*S^12))/(648*S^3*(1 + S^2)^3) + (-2261 - 2172*S^2 - 54867*S^4 + 42206*S^6 + 6837*S^8 + 7026*S^10 + 2311*S^12)/(3888*S^3*(1 + S^2)^3) + ((-249 - 747*S^2 - 747*S^4 + 847*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)^3)) + ((Pi^2*(-5 - 15*S^2 - 15*S^4 + 4*S^6 + 33*S^8 + 33*S^10 + 11*S^12))/(72*S^3*(1 + S^2)^3) + (-170 - 291*S^2 - 525*S^4 + 470*S^6 + 1464*S^8 + 645*S^10 + 199*S^12)/(432*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-13 - 98*S^2 - 139*S^4 + 167*S^6 + 70*S^8 - 13*S^10)*HPL[{4}, -S^2])/(72*S^3*(1 + S^2)^2) + ((-1 + 3*S^4 + 3*S^6)*(1 + 3*S^2 + 6*S^4 + 3*S^6)*HPL[{5}, -S^2])/(6*S^3*(1 + S^2)^3) + ((625 + 388*S^2 + 10798*S^4 - 2839*S^6 - 1130*S^8 - 413*S^10 - 101*S^12)/(432*S^3*(1 + S^2)^3) + (Pi^2*(129 + 387*S^2 + 387*S^4 - 139*S^6 - 36*S^8 - 36*S^10 - 12*S^12))/(54*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + HPL[{2}, -S^2]*((-459 - 818*S^2 + 832*S^4 + 2129*S^6 + 1298*S^8)/(864*S^3*(1 + S^2)) + (Pi^2*(22 - 492*S^2 - 1365*S^4 + 2687*S^6 + 982*S^8 + 703*S^10 + 187*S^12))/(432*S^3*(1 + S^2)^3) + ((2 + 6*S^2 + 6*S^4 + S^6)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^3) + ((118 + 354*S^2 + 354*S^4 - 159*S^6 - 18*S^8 - 18*S^10 - 6*S^12)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^3)) + ((-53 + 367*S^2 + 1183*S^4 - 2326*S^6 + 163*S^8 + 109*S^10 + 37*S^12)*HPL[{3, 1}, -S^2])/(72*S^3*(1 + S^2)^3) + ((-2 - 6*S^2 - 6*S^4 - S^6)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-5 - 15*S^2 - 15*S^4 - 8*S^6 - 27*S^8 - 27*S^10 - 9*S^12)*HPL[{4, 1}, -S^2])/(6*S^3*(1 + S^2)^3) + ((44 - 384*S^2 - 1185*S^4 + 2449*S^6 - 46*S^8 + 26*S^10 + 14*S^12)*HPL[{2, 1, 1}, -S^2])/(36*S^3*(1 + S^2)^3) + ((-118 - 354*S^2 - 354*S^4 + 159*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-241 - 723*S^2 - 723*S^4 + 316*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3, 1, 1}, -S^2])/(6*S^3*(1 + S^2)^3) - (2*(-123 - 369*S^2 - 369*S^4 + 158*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((Pi^2*S^3*(281 + 552*S^2 + 552*S^4 + 184*S^6))/(108*(1 + S^2)^3) + (104 - 2*S^2 + 1861*S^4 + 3941*S^6 + 3019*S^8 + 933*S^10)/(144*S*(1 + S^2)^3))*Zeta[3] + HPL[{1}, -S^2]^2*((-6685 - 12613*S^2 + 219*S^4 + 13589*S^6 + 6578*S^8)/(5184*S^3*(1 + S^2)) + (Pi^2*(224 - 2955*S^2 - 10122*S^4 + 10162*S^6 + 2190*S^8 + 1149*S^10 + 224*S^12))/(864*S^3*(1 + S^2)^3) + ((29 - 4452*S^2 - 13587*S^4 + 10624*S^6 + 291*S^8 + 174*S^10 + 29*S^12)*HPL[{2}, -S^2])/(432*S^3*(1 + S^2)^3) + ((-5 - 15*S^2 - 15*S^4 - 3*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{3}, -S^2])/(12*S^3*(1 + S^2)^3) + ((249 + 747*S^2 + 747*S^4 - 847*S^6 - 24*S^8 - 24*S^10 - 8*S^12)*HPL[{2, 1}, -S^2])/(36*S^3*(1 + S^2)^3) + ((-19 - 57*S^2 - 57*S^4 + 14*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*Zeta[3])/(18*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((-40577 - 73514*S^2 + 240*S^4 + 67138*S^6 + 31369*S^8)/(15552*S^3*(1 + S^2)) + (Pi^4*(-2959 - 8877*S^2 - 8877*S^4 + 7876*S^6 + 2850*S^8 + 2850*S^10 + 950*S^12))/(6480*S^3*(1 + S^2)^3) + (Pi^2*(-1934 - 723*S^2 - 26688*S^4 + 31709*S^6 + 22218*S^8 + 14064*S^10 + 3934*S^12))/(3888*S^3*(1 + S^2)^3) + ((Pi^2*(-267 - 801*S^2 - 801*S^4 + 806*S^6 + 147*S^8 + 147*S^10 + 49*S^12))/(216*S^3*(1 + S^2)^3) + (-133 - 73*S^2 - 2738*S^4 + 1864*S^6 + 683*S^8 + 529*S^10 + 156*S^12)/(144*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((-56 - 168*S^2 - 168*S^4 + 211*S^6 - 12*S^8 - 12*S^10 - 4*S^12)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)^3) + ((1 - 7*S^2 - 27*S^4 - 2*S^6 + 39*S^8 + 15*S^10 + S^12)*HPL[{3}, -S^2])/(8*S^3*(1 + S^2)^3) + ((-5 + 6*S^6)*HPL[{4}, -S^2])/(6*S^3) + ((-29 + 4452*S^2 + 13587*S^4 - 10624*S^6 - 291*S^8 - 174*S^10 - 29*S^12)*HPL[{2, 1}, -S^2])/(216*S^3*(1 + S^2)^3) + ((127 + 381*S^2 + 381*S^4 - 413*S^6 - 30*S^8 - 30*S^10 - 10*S^12)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + ((-249 - 747*S^2 - 747*S^4 + 847*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 1, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + ((52 - 51*S^2 - 444*S^4 + 398*S^6 + 924*S^8 + 405*S^10 + 52*S^12)*Zeta[3])/(72*S^3*(1 + S^2)^3)) + (5*S^3*(50 + 111*S^2 + 111*S^4 + 37*S^6)*Zeta[5])/(18*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((-1651 - 1731*S^2 + 1731*S^4 + 1651*S^6)/(8*S^3) + (Pi^2*(-5621 - 42938*S^2 - 24693*S^4 + 18550*S^6 + 6574*S^8))/(972*S^3*(1 + S^2)) + (Pi^4*(2381 - 6165*S^2 - 24489*S^4 + 53095*S^6 - 21784*S^8 - 13573*S^10 - 3991*S^12))/(540*S^3*(1 + S^2)^3) - (4928*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (32*(-433 - 1299*S^2 - 1299*S^4 + 578*S^6 + 423*S^8 + 423*S^10 + 141*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*Pi^2*S^3*(-317 + 483*S^2 + 483*S^4 + 161*S^6))/(9*(1 + S^2)^3) + (2*(17 + 316*S^2 + 1508*S^4 - 646*S^6 + 5799*S^8 + 1082*S^10 + 388*S^12))/(3*S^3*(1 + S^2)^3))*Zeta[3] + (8*S^3*(-493 + 945*S^2 + 945*S^4 + 315*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + Zeta[3]*((1847*Pi^6*S^5*(3 + 3*S^2 + S^4))/(1701*(1 + S^2)^3) + (Pi^2*(-14610 - 4159*S^2 + 48958*S^4 + 33323*S^6))/(1296*S*(1 + S^2)) + (-1096205 - 1060747*S^2 + 1382905*S^4 + 1160823*S^6)/(5832*S*(1 + S^2)) + (Pi^4*(6106 + 23611*S^2 + 36471*S^4 + 251317*S^6 + 107671*S^8 + 36264*S^10))/(6480*S*(1 + S^2)^3) - (2*(114 + 285*S^2 - 171*S^4 - 112*S^6 + 128*S^8 + 78*S^10)*Zeta[5])/(3*S*(1 + S^2)^3)) + HPL[{4}, -S^2]*((-10651 + 14997*S^2 + 136092*S^4 + 118220*S^6)/(648*S^3) + (Pi^2*(-1856 + 3221*S^2 + 19931*S^4 + 27905*S^6 + 13915*S^8))/(648*S^3*(1 + S^2)) + (Pi^4*(-754 - 3312*S^2 - 5796*S^4 - 10967*S^6 + 28923*S^8 + 14469*S^10 + 2513*S^12))/(1620*S^3*(1 + S^2)^3) - (4*S^3*(106 + 189*S^2 + 189*S^4 + 63*S^6)*HPL[{5}, -S^2])/(3*(1 + S^2)^3) + ((2*Pi^2*(-41 - 123*S^2 - 123*S^4 + 204*S^6 + 57*S^8 + 57*S^10 + 19*S^12))/(9*S^3*(1 + S^2)^3) + (-1298 - 5737*S^2 - 13930*S^4 - 1150*S^6 - 3310*S^8 + 599*S^10 + 730*S^12)/(18*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (2*(23 + 357*S^2 + 771*S^4 - 1250*S^6 + 4461*S^8 + 2400*S^10 + 500*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-11 - 33*S^2 - 33*S^4 - 16*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)^3) + (8*(-31 - 93*S^2 - 93*S^4 - 104*S^6 + 228*S^8 + 228*S^10 + 76*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-91 + 375*S^2 + 1302*S^4 - 2684*S^6 + 9114*S^8 + 5163*S^10 + 1169*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(55 + 165*S^2 + 165*S^4 - 250*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(163 + 489*S^2 + 489*S^4 - 690*S^6 + 165*S^8 + 165*S^10 + 55*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(-29 - 87*S^2 - 87*S^4 + 104*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((143 + 541*S^2 + 577*S^4 - 410*S^6 + 709*S^8 - 299*S^10 - 61*S^12)/(18*S^3*(1 + S^2)^3) + (2*Pi^2*(1 + 3*S^2 + 3*S^4 - 12*S^6 + 3*S^8 + 3*S^10 + S^12))/(3*S^3*(1 + S^2)^3))*Zeta[3] - (4*(-25 - 75*S^2 - 75*S^4 + 12*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((386941 + 439429*S^2 - 439429*S^4 - 386941*S^6)/(1944*S^3) + (Pi^2*(61218 + 119993*S^2 + 2503*S^4 - 100867*S^6 - 48483*S^8))/(1944*S^3*(1 + S^2)) + (Pi^6*(83308 + 249924*S^2 + 249924*S^4 - 90729*S^6 - 70320*S^8 - 70320*S^10 - 23440*S^12))/(34020*S^3*(1 + S^2)^3) + (Pi^4*(37768 + 92044*S^2 + 435397*S^4 - 35341*S^6 - 104915*S^8 - 30479*S^10 - 17066*S^12))/(6480*S^3*(1 + S^2)^3) + ((-2*(118 + 435*S^2 + 3211*S^4 - 646*S^6 + 4096*S^8 + 963*S^10 + 287*S^12))/(3*S^3*(1 + S^2)^3) - (2*Pi^2*(567 + 1701*S^2 + 1701*S^4 - 1792*S^6 + 1011*S^8 + 1011*S^10 + 337*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (2*(1649 + 7965*S^2 + 14850*S^4 - 19490*S^6 + 9984*S^8 + 4143*S^10 + 119*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-5437 - 25779*S^2 - 47640*S^4 + 59794*S^6 - 25230*S^8 - 9525*S^10 + 413*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(23 + 69*S^2 + 69*S^4 - 86*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) - (4*(-252 - 756*S^2 - 756*S^4 + 1079*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-16*Pi^2*(152 + 456*S^2 + 456*S^4 - 447*S^6 + 225*S^8 + 225*S^10 + 75*S^12))/(9*S^3*(1 + S^2)^3) - (2*(405 + 1398*S^2 + 7307*S^4 - 1292*S^6 + 7307*S^8 + 1398*S^10 + 405*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(-255 - 382*S^2 - 429*S^4 + 429*S^6 + 382*S^8 + 255*S^10)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*(-247 + 607*S^2 + 2359*S^4 - 6428*S^6 + 4301*S^8 + 2357*S^10 + 563*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{3, 1, 2}, -S^2])/(S^3*(1 + S^2)^3) + (4*(505 + 1515*S^2 + 1515*S^4 - 2094*S^6 + 1515*S^8 + 1515*S^10 + 505*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(175 + 525*S^2 + 525*S^4 - 778*S^6 + 651*S^8 + 651*S^10 + 217*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(79 + 741*S^2 + 1665*S^4 - 3214*S^6 + 1665*S^8 + 741*S^10 + 79*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(125 + 375*S^2 + 375*S^4 - 578*S^6 + 501*S^8 + 501*S^10 + 167*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (128*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-437 - 11186*S^2 - 24693*S^4 - 13202*S^6 + 1390*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-226 - 1122*S^2 - 2130*S^4 + 3469*S^6 - 1737*S^8 - 726*S^10 - 22*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] - (8*(-2 + 5*S^6)*Zeta[3]^2)/(3*S^3) + (2*(-52 - 741*S^2 - 2100*S^4 + 10201*S^6 - 4647*S^8 - 1587*S^10 + 128*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((Pi^2*(809 - 7403*S^2 - 6215*S^4 - 55*S^6))/(1296*S^3) + (29889 + 2788*S^2 + 8006*S^4 + 2788*S^6 + 29889*S^8)/(3888*S^3*(1 + S^2)) + (Pi^4*(-146 - 13158*S^2 - 33750*S^4 + 76280*S^6 - 38397*S^8 - 18678*S^10 - 2990*S^12))/(3240*S^3*(1 + S^2)^3) + ((Pi^2*(-1 - 3*S^2 - 3*S^4 - 736*S^6 + 993*S^8 + 993*S^10 + 331*S^12))/(18*S^3*(1 + S^2)^3) + (-431 + 2628*S^2 + 18873*S^4 - 4408*S^6 + 64287*S^8 + 15084*S^10 + 4591*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((133 + 585*S^2 + 882*S^4 - 1129*S^6 + 2619*S^8 + 1458*S^10 + 304*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-19 - 57*S^2 - 57*S^4 - 62*S^6 + 162*S^8 + 162*S^10 + 54*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((279 + 413*S^2 + 2110*S^4 - 2110*S^6 - 413*S^8 - 279*S^10)/(6*S^3*(1 + S^2)^2) - (2*Pi^2*(-154 - 462*S^2 - 462*S^4 + 147*S^6 + 258*S^8 + 258*S^10 + 86*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-601 - 1977*S^2 - 2967*S^4 + 1129*S^6 - 534*S^8 - 66*S^10 + 164*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-23 - 69*S^2 - 69*S^4 - 588*S^6 + 885*S^8 + 885*S^10 + 295*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-47 - 141*S^2 - 141*S^4 - 2014*S^6 + 2847*S^8 + 2847*S^10 + 949*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((255 + 382*S^2 + 429*S^4 - 429*S^6 - 382*S^8 - 255*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (16*(34 + 102*S^2 + 102*S^4 - 147*S^6 + 102*S^8 + 102*S^10 + 34*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(809 + 2427*S^2 + 2427*S^4 - 2102*S^6 + 579*S^8 + 579*S^10 + 193*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (1232*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(-6 - 18*S^2 - 18*S^4 - 95*S^6 + 162*S^8 + 162*S^10 + 54*S^12))/(3*S^3*(1 + S^2)^3) + (-433 - 804*S^2 + 1575*S^4 - 2264*S^6 + 16713*S^8 + 3348*S^10 + 1241*S^12)/(36*S^3*(1 + S^2)^3))*Zeta[3] + (2*(-16 - 48*S^2 - 48*S^4 - 219*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(((1 + S^2)*(104305 - 46054*S^2 + 104305*S^4))/(2916*S^3) + (Pi^2*(-208091 - 675584*S^2 - 696558*S^4 - 70424*S^6 + 73105*S^8))/(34992*S^3*(1 + S^2)) + (Pi^6*(-201706 - 605118*S^2 - 605118*S^4 + 958255*S^6 - 179157*S^8 - 179157*S^10 - 59719*S^12))/(204120*S^3*(1 + S^2)^3) + (Pi^4*(-57670 - 197979*S^2 - 1196718*S^4 + 563503*S^6 - 659832*S^8 - 103578*S^10 - 11914*S^12))/(29160*S^3*(1 + S^2)^3) + ((-2522 - 11073*S^2 - 59790*S^4 + 22802*S^6 - 59790*S^8 - 11073*S^10 - 2522*S^12)/(162*S^3*(1 + S^2)^3) + (Pi^2*(-350 - 1050*S^2 - 1050*S^4 + 2089*S^6 - 771*S^8 - 771*S^10 - 257*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (62*(-1 + S^6)*HPL[{2}, -S^2]^3)/(9*S^3) - (2*(37 + 111*S^2 + 111*S^4 - 238*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((Pi^2*(61 + 183*S^2 + 183*S^4 - 1132*S^6 + 837*S^8 + 837*S^10 + 279*S^12))/(27*S^3*(1 + S^2)^3) + (249 + 1714*S^2 + 4217*S^4 + 1660*S^6 + 6643*S^8 + 2546*S^10 + 571*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(713 + 1893*S^2 + 1425*S^4 - 2750*S^6 + 8877*S^8 + 4377*S^10 + 713*S^12)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)^3) + (2*(-194 - 582*S^2 - 582*S^4 - 127*S^6 + 849*S^8 + 849*S^10 + 283*S^12)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((-8*Pi^2*(-116 - 348*S^2 - 348*S^4 + 193*S^6 + 183*S^8 + 183*S^10 + 61*S^12))/(27*S^3*(1 + S^2)^3) - (2*(4 + 699*S^2 - 114*S^4 + 830*S^6 + 5544*S^8 + 1431*S^10 + 406*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(247 + 1465*S^2 + 2925*S^4 - 5946*S^6 + 6705*S^8 + 2725*S^10 + 247*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) - (16*(50 + 150*S^2 + 150*S^4 - 551*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((4*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(3*S^3*(1 + S^2)^2) + (8*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (8*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (16*(121 + 1764*S^2 + 4578*S^4 - 4840*S^6 + 2553*S^8 + 1089*S^10 + 121*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (496*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (32*(-116 - 348*S^2 - 348*S^4 - 277*S^6 + 597*S^8 + 597*S^10 + 199*S^12)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (1200*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (32*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (800*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-7451 - 9824*S^2 + 8349*S^4 + 22198*S^6 + 7588*S^8)/(243*S^3*(1 + S^2)) + (Pi^2*(331 + 2526*S^2 + 5703*S^4 - 17176*S^6 + 19635*S^8 + 7170*S^10 + 331*S^12))/(81*S^3*(1 + S^2)^3))*Zeta[3] - (8*(5 + 15*S^2 + 15*S^4 - 32*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3]^2)/(9*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((3445 + 17641*S^2 + 44727*S^4 + 49663*S^6 + 18484*S^8)/(243*S^3*(1 + S^2)) + (Pi^2*(958 + 5019*S^2 + 9330*S^4 - 19666*S^6 + 23424*S^8 + 9717*S^10 + 958*S^12))/(81*S^3*(1 + S^2)^3) - (8*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(11 + 33*S^2 + 33*S^4 - 87*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((557 + 629*S^2 - 629*S^4 - 557*S^6)/(9*S^3) + (Pi^2*(175 + 3837*S^2 + 10473*S^4 - 5314*S^6 - 2271*S^8 - 411*S^10 + 175*S^12))/(27*S^3*(1 + S^2)^3) - (32*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-7811 - 8999*S^2 + 8999*S^4 + 7811*S^6)/(162*S^3) + (Pi^4*(-7200 - 21600*S^2 - 21600*S^4 + 21017*S^6 + 3411*S^8 + 3411*S^10 + 1137*S^12))/(1620*S^3*(1 + S^2)^3) + (Pi^2*(-8921 - 23394*S^2 - 141699*S^4 + 22802*S^6 + 22119*S^8 + 1248*S^10 + 3877*S^12))/(972*S^3*(1 + S^2)^3) + (2*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(113 + 339*S^2 + 339*S^4 - 734*S^6 + 339*S^8 + 339*S^10 + 113*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(175 + 1137*S^2 + 2373*S^4 - 5314*S^6 + 5829*S^8 + 2289*S^10 + 175*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) - (2*(163 - 84*S^2 - 1407*S^4 + 16904*S^6 - 19551*S^8 - 6132*S^10 + 163*S^12)*Zeta[5])/(27*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((Pi^2*(-2099 - 1341*S^2 + 45412*S^4 + 90339*S^6 + 44389*S^8))/(1944*S^3*(1 + S^2)) + (-20695 - 40592*S^2 + 275219*S^4 + 785778*S^6 + 366246*S^8)/(1944*S^3*(1 + S^2)) + (Pi^4*(19 + 8046*S^2 + 24270*S^4 + 2966*S^6 + 102243*S^8 + 28512*S^10 + 8944*S^12))/(3240*S^3*(1 + S^2)^3) + (Pi^6*(-1655 - 4965*S^2 - 4965*S^4 - 71000*S^6 + 133659*S^8 + 133659*S^10 + 44553*S^12))/(68040*S^3*(1 + S^2)^3) + ((-458 - 1863*S^2 - 2997*S^4 - 259*S^6 - 6885*S^8 - 1350*S^10 - 332*S^12)/(54*S^3*(1 + S^2)^3) - (2*Pi^2*(11 + 33*S^2 + 33*S^4 - 34*S^6 + 30*S^8 + 30*S^10 + 10*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((-206 - 411*S^2 - 204*S^4 - 1348*S^6 - 1758*S^8 - 705*S^10 - 44*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*S^3*(84 + 141*S^2 + 141*S^4 + 47*S^6)*HPL[{6}, -S^2])/(3*(1 + S^2)^3) - (2*(7 + 21*S^2 + 21*S^4 - 1426*S^6 + 1869*S^8 + 1869*S^10 + 623*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((1441 + 2376*S^2 - 5427*S^4 + 8138*S^6 - 56529*S^8 - 12654*S^10 - 4409*S^12)/(27*S^3*(1 + S^2)^3) - (4*Pi^2*(-12 - 36*S^2 - 36*S^4 - 310*S^6 + 489*S^8 + 489*S^10 + 163*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((448 + 1701*S^2 + 2268*S^4 - 1660*S^6 + 6222*S^8 + 3675*S^10 + 826*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(440 + 1236*S^2 + 1200*S^4 + 1294*S^6 - 186*S^8 + 309*S^10 + 161*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(2 + 6*S^2 + 6*S^4 - 30*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-1 - 3*S^2 - 3*S^4 + 25*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*(-161 - 257*S^2 + 688*S^4 - 646*S^6 + 6619*S^8 + 1655*S^10 + 566*S^12))/(3*S^3*(1 + S^2)^3) + (2*Pi^2*(-49 - 147*S^2 - 147*S^4 - 1204*S^6 + 2043*S^8 + 2043*S^10 + 681*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (4*(297 + 1453*S^2 + 2719*S^4 - 3471*S^6 + 1908*S^8 + 816*S^10 + 42*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(296 + 1426*S^2 + 2657*S^4 - 3347*S^6 + 1638*S^8 + 665*S^10 + 9*S^12)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(5 + 3*S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + (4*(-63 - 189*S^2 - 189*S^4 - 1168*S^6 + 1845*S^8 + 1845*S^10 + 615*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1322 - 3966*S^2 - 3966*S^4 - 42339*S^6 + 61437*S^8 + 61437*S^10 + 20479*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-259 - 1259*S^2 - 2396*S^4 + 3214*S^6 - 934*S^8 - 223*S^10 + 101*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-69 - 207*S^2 - 207*S^4 - 1182*S^6 + 1893*S^8 + 1893*S^10 + 631*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(-29 - 87*S^2 - 87*S^4 - 578*S^6 + 963*S^8 + 963*S^10 + 321*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-1784 + 1120*S^2 + 4251*S^4 - 212*S^6 - 263*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-43 - 45*S^2 + 54*S^4 - 662*S^6 + 894*S^8 + 633*S^10 + 173*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + (2*(-3 - 9*S^2 - 9*S^4 - 26*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((-15769 - 35962*S^2 - 49386*S^4 - 12814*S^6 + 17675*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(-260 - 1276*S^2 - 2440*S^4 + 3467*S^6 - 911*S^8 - 164*S^10 + 130*S^12))/(9*S^3*(1 + S^2)^3) + (4*(-29 - 87*S^2 - 87*S^4 + 68*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + (2*(-257 - 780*S^2 - 933*S^4 - 883*S^6 + 804*S^8 + 579*S^10 + 166*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*(((1 + S^2)*(27713 - 37886*S^2 + 27713*S^4))/(3888*S^3) + (Pi^2*(-21491 - 69224*S^2 - 82371*S^4 - 37202*S^6 - 6452*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(-5027 - 67896*S^2 - 172821*S^4 + 198704*S^6 - 91929*S^8 - 40932*S^10 - 5027*S^12))/(6480*S^3*(1 + S^2)^3) + ((-175 - 1713*S^2 - 4101*S^4 + 5314*S^6 - 4101*S^8 - 1713*S^10 - 175*S^12)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((Pi^2*(118 + 354*S^2 + 354*S^4 - 1703*S^6 + 1137*S^8 + 1137*S^10 + 379*S^12))/(27*S^3*(1 + S^2)^3) + (1279 + 8682*S^2 + 29382*S^4 - 7666*S^6 + 54843*S^8 + 11976*S^10 + 3088*S^12)/(81*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(36 + 155*S^2 + 249*S^4 - 316*S^6 + 465*S^8 + 227*S^10 + 36*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-5 - 15*S^2 - 15*S^4 - 116*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((67 + 55*S^2 + 888*S^4 - 888*S^6 - 55*S^8 - 67*S^10)/(3*S^3*(1 + S^2)^2) - (2*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(18 - 17*S^2 - 159*S^4 - 158*S^6 + 516*S^8 + 208*S^10 + 18*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(178 + 534*S^2 + 534*S^4 - 2299*S^6 + 1479*S^8 + 1479*S^10 + 493*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (300*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(463 + 1389*S^2 + 1389*S^4 - 2419*S^6 + 714*S^8 + 714*S^10 + 238*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (200*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((Pi^2*(79 + 237*S^2 + 237*S^4 - 1444*S^6 + 1011*S^8 + 1011*S^10 + 337*S^12))/(27*S^3*(1 + S^2)^3) + (-44 + 237*S^2 + 3789*S^4 - 5152*S^6 + 12276*S^8 + 1335*S^10 + 559*S^12)/(27*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-557 - 629*S^2 + 629*S^4 + 557*S^6)/(36*S^3) + (Pi^2*(-175 - 3837*S^2 - 10473*S^4 + 5314*S^6 + 2271*S^8 + 411*S^10 - 175*S^12))/(108*S^3*(1 + S^2)^3) + (2*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (16*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + (4*(11 + 33*S^2 + 33*S^4 - 680*S^6 + 537*S^8 + 537*S^10 + 179*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((13081 - 5439*S^2 - 145650*S^4 - 120650*S^6)/(648*S^3) + (Pi^2*(-741 - 150*S^2 - 1763*S^4 - 3718*S^6 - 1436*S^8))/(108*S^3*(1 + S^2)) + (Pi^4*(-4783 + 2949*S^2 + 24963*S^4 - 66473*S^6 + 22200*S^8 + 15918*S^10 + 5540*S^12))/(1620*S^3*(1 + S^2)^3) + (4*(-41 - 123*S^2 - 123*S^4 - 1305*S^6 + 1872*S^8 + 1872*S^10 + 624*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-83 - 249*S^2 - 249*S^4 - 1961*S^6 + 2910*S^8 + 2910*S^10 + 970*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(263 + 1881*S^2 + 3981*S^4 - 6428*S^6 + 2679*S^8 + 1083*S^10 + 53*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-265 - 795*S^2 - 795*S^4 - 250*S^6 + 1053*S^8 + 1053*S^10 + 351*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(647 + 1941*S^2 + 1941*S^4 - 2123*S^6 + 954*S^8 + 954*S^10 + 318*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(125 + 375*S^2 + 375*S^4 - 578*S^6 + 501*S^8 + 501*S^10 + 167*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(3 + 9*S^2 + 9*S^4 - 662*S^6 + 963*S^8 + 963*S^10 + 321*S^12))/(9*S^3*(1 + S^2)^3) - (2*(79 + 660*S^2 + 2514*S^4 - 1174*S^6 + 8571*S^8 + 1446*S^10 + 520*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] - (4*(25 + 75*S^2 + 75*S^4 - 498*S^6 + 861*S^8 + 861*S^10 + 287*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^3*((Pi^6*S^3*(5767 + 123*S^2 + 123*S^4 + 41*S^6))/(7776*(1 + S^2)^3) + (Pi^2*(58901 + 64612*S^2 + 136472*S^4 + 117153*S^6))/(23328*S*(1 + S^2)) + (463100 + 391721*S^2 + 607198*S^4 + 554161*S^6)/(23328*S*(1 + S^2)) + (Pi^4*(11280 - 3635*S^2 + 99782*S^4 + 77718*S^6 + 54250*S^8 + 12285*S^10))/(12960*S*(1 + S^2)^3) + ((-16 - 882*S^2 - 2544*S^4 + 2854*S^6 - 789*S^8 - 297*S^10 - 16*S^12)*HPL[{1}, -S^2]^5)/(135*S^3*(1 + S^2)^3) + ((-56 - 168*S^2 - 168*S^4 + 263*S^6 - 51*S^8 - 51*S^10 - 17*S^12)*HPL[{1}, -S^2]^6)/(81*S^3*(1 + S^2)^3) + ((-271 - 1902*S^2 - 21009*S^4 + 18394*S^6 - 15411*S^8 - 2532*S^10 - 613*S^12)/(1296*S^3*(1 + S^2)^3) + (Pi^2*(4 + 12*S^2 + 12*S^4 + 1091*S^6 - 261*S^8 - 261*S^10 - 87*S^12))/(216*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + ((1 + 3*S^2 + 3*S^4 + 99*S^6 - 42*S^8 - 42*S^10 - 14*S^12)*HPL[{2}, -S^2]^3)/(18*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*((Pi^2*(-555 - 1665*S^2 - 1665*S^4 + 2348*S^6 - 243*S^8 - 243*S^10 - 81*S^12))/(324*S^3*(1 + S^2)^3) + (-184 + 345*S^2 - 13713*S^4 + 11692*S^6 - 4182*S^8 + 129*S^10 + 5*S^12)/(486*S^3*(1 + S^2)^3) + ((-43 - 129*S^2 - 129*S^4 + 195*S^6 - 36*S^8 - 36*S^10 - 12*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((12 + 36*S^2 + 36*S^4 - 13*S^6 - 39*S^8 - 39*S^10 - 13*S^12)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((Pi^2*(-1 - 3*S^2 - 3*S^4 + 32*S^6 - 111*S^8 - 111*S^10 - 37*S^12))/(54*S^3*(1 + S^2)^3) + (505 + 3330*S^2 + 3105*S^4 + 5852*S^6 + 4599*S^8 + 6138*S^10 + 1351*S^12)/(648*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((194 + 729*S^2 + 846*S^4 + 478*S^6 - 714*S^8 + 519*S^10 + 392*S^12)*HPL[{5}, -S^2])/(108*S^3*(1 + S^2)^3) + ((5 + 15*S^2 + 15*S^4 - 64*S^6 - 225*S^8 - 225*S^10 - 75*S^12)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-4 - 12*S^2 - 12*S^4 - 635*S^6 + 243*S^8 + 243*S^10 + 81*S^12)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((140 - 258*S^2 + 8679*S^4 - 12203*S^6 + 4719*S^8 - 1095*S^10 - 166*S^12)/(162*S^3*(1 + S^2)^3) + (Pi^2*(-2 - 6*S^2 - 6*S^4 - 1149*S^6 + 369*S^8 + 369*S^10 + 123*S^12))/(54*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((134 + 369*S^2 + 342*S^4 + 328*S^6 - 496*S^8 - 325*S^10 - 88*S^12)*HPL[{3, 2}, -S^2])/(36*S^3*(1 + S^2)^3) + ((296 + 927*S^2 + 1260*S^4 + 592*S^6 - 1878*S^8 - 1671*S^10 - 550*S^12)*HPL[{4, 1}, -S^2])/(54*S^3*(1 + S^2)^3) + (2*S^3*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{4, 2}, -S^2])/(9*(1 + S^2)^3) + (2*(-1 - 3*S^2 - 3*S^4 - 20*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-2*Pi^2*(-1 - 3*S^2 - 3*S^4 - 605*S^6 + 126*S^8 + 126*S^10 + 42*S^12))/(27*S^3*(1 + S^2)^3) + (24 + 454*S^2 - 5633*S^4 + 8460*S^6 - 2768*S^8 + 850*S^10 + 141*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + ((-46 - 1117*S^2 - 3328*S^4 + 1843*S^6 - 247*S^8 - 40*S^10 + 35*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-317 - 9945*S^2 - 30285*S^4 + 16997*S^6 - 1830*S^8 + 78*S^10 + 466*S^12)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^3) - (2*S^3*HPL[{3, 1, 2}, -S^2])/9 - (2*(-6 - 18*S^2 - 18*S^4 - 593*S^6 + 255*S^8 + 255*S^10 + 85*S^12)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-8 - 24*S^2 - 24*S^4 - 923*S^6 + 399*S^8 + 399*S^10 + 133*S^12)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-110 - 3489*S^2 - 10644*S^4 + 5792*S^6 - 540*S^8 + 63*S^10 + 160*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^3) + (4*(-2 - 6*S^2 - 6*S^4 - 663*S^6 + 261*S^8 + 261*S^10 + 87*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(-2 - 6*S^2 - 6*S^4 - 669*S^6 + 249*S^8 + 249*S^10 + 83*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((1660 + 2406*S^2 + 3387*S^4 + 2605*S^6)/(216*S*(1 + S^2)) + (Pi^2*(-132 - 330*S^2 + 1893*S^4 + 4007*S^6 + 3422*S^8 + 1050*S^10))/(108*S*(1 + S^2)^3))*Zeta[3] + (14*S^3*Zeta[3]^2)/(3*(1 + S^2)^3) + HPL[{3}, -S^2]*((6347 - 495*S^2 + 12429*S^4 + 14735*S^6)/(3888*S^3) + (Pi^2*(292 + 603*S^2 - 108*S^4 + 1070*S^6 + 168*S^8 + 753*S^10 + 346*S^12))/(648*S^3*(1 + S^2)^3) + (2*(-6 - 18*S^2 - 18*S^4 + 21*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*S^3*(3 + 6*S^2 + 6*S^4 + 2*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((40315 + 47659*S^2 + 70155*S^4 + 130891*S^6 + 79744*S^8)/(11664*S^3*(1 + S^2)) + (Pi^4*(-5 - 15*S^2 - 15*S^4 + 8037*S^6 + 78*S^8 + 78*S^10 + 26*S^12))/(3240*S^3*(1 + S^2)^3) + (Pi^2*(329 + 2674*S^2 - 7673*S^4 + 20971*S^6 + 6076*S^8 + 8071*S^10 + 1976*S^12))/(1296*S^3*(1 + S^2)^3) + ((-100 - 276*S^2 - 258*S^4 - 263*S^6 + 345*S^8 + 228*S^10 + 62*S^12)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^3) + (2*(-6 - 18*S^2 - 18*S^4 + 7*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + ((46 + 1117*S^2 + 3328*S^4 - 1843*S^6 + 247*S^8 + 40*S^10 - 35*S^12)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + (2*(3 + 9*S^2 + 9*S^4 - 318*S^6 + 105*S^8 + 105*S^10 + 35*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-4 - 12*S^2 - 12*S^4 - 635*S^6 + 243*S^8 + 243*S^10 + 81*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-28 - 70*S^2 + 69*S^4 + 311*S^6 + 176*S^8 + 36*S^10)*Zeta[3])/(18*S*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-503 - 509*S^2 - 8229*S^4 - 10868*S^6 - 4589*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-280 + 5124*S^2 + 18624*S^4 - 9434*S^6 + 780*S^8 + 33*S^10 - 145*S^12))/(324*S^3*(1 + S^2)^3) - (4*(-7 - 21*S^2 - 21*S^4 - 6*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((2347 + 919*S^2 - 633*S^4 + 6985*S^6 + 5542*S^8)/(2916*S^3*(1 + S^2)) + (Pi^2*(56 - 933*S^2 - 3126*S^4 + 3590*S^6 - 282*S^8 + 15*S^10 + 56*S^12))/(108*S^3*(1 + S^2)^3) + ((7 - 507*S^2 - 1575*S^4 + 1622*S^6 - 459*S^8 - 135*S^10 + 7*S^12)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 + 5*S^6)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-6 - 18*S^2 - 18*S^4 - 17*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*Zeta[3])/(27*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((103501 + 166036*S^2 + 127878*S^4 + 249412*S^6 + 137413*S^8)/(23328*S^3*(1 + S^2)) + (Pi^4*(-4011 - 12033*S^2 - 12033*S^4 + 15739*S^6 + 42*S^8 + 42*S^10 + 14*S^12))/(3240*S^3*(1 + S^2)^3) + (Pi^2*(1994 + 22170*S^2 - 77037*S^4 + 117568*S^6 + 16482*S^8 + 20154*S^10 + 3605*S^12))/(3888*S^3*(1 + S^2)^3) + ((Pi^2*(-488 - 1464*S^2 - 1464*S^4 + 2023*S^6 - 219*S^8 - 219*S^10 - 73*S^12))/(108*S^3*(1 + S^2)^3) + (-131 + 576*S^2 - 8007*S^4 + 7007*S^6 - 1512*S^8 + 957*S^10 + 190*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((-121 - 363*S^2 - 363*S^4 + 553*S^6 - 114*S^8 - 114*S^10 - 38*S^12)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((161 + 336*S^2 + 3*S^4 + 520*S^6 + 327*S^8 + 444*S^10 + 161*S^12)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^3) + ((-6 - 18*S^2 - 18*S^4 + 63*S^6 - 33*S^8 - 33*S^10 - 11*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-7 + 507*S^2 + 1575*S^4 - 1622*S^6 + 459*S^8 + 135*S^10 - 7*S^12)*HPL[{2, 1}, -S^2])/(6*S^3*(1 + S^2)^3) + (2*(127 + 381*S^2 + 381*S^4 - 583*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((142 + 375*S^2 + 276*S^4 + 248*S^6 + 897*S^8 + 582*S^10 + 142*S^12)*Zeta[3])/(27*S^3*(1 + S^2)^3)) + (2*(-20 - 50*S^2 + 423*S^4 + 887*S^6 + 806*S^8 + 255*S^10)*Zeta[5])/(9*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((22612 + 40139*S^2 + 27027*S^4 + 39637*S^6 + 19769*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(42899 + 80273*S^2 + 72039*S^4 + 92675*S^6 + 46994*S^8))/(23328*S^3*(1 + S^2)) + (Pi^4*(5650 - 6987*S^2 - 54732*S^4 + 82526*S^6 + 17718*S^8 + 17163*S^10 + 5650*S^12))/(6480*S^3*(1 + S^2)^3) + ((-94 - 2481*S^2 - 6900*S^4 + 6778*S^6 - 2418*S^8 - 987*S^10 - 94*S^12)*HPL[{2}, -S^2]^2)/(108*S^3*(1 + S^2)^3) + ((Pi^2*(-2 - 6*S^2 - 6*S^4 + 25*S^6 - 15*S^8 - 15*S^10 - 5*S^12))/(18*S^3*(1 + S^2)^3) + (41 + 2298*S^2 + 2775*S^4 + 5518*S^6 + 6339*S^8 + 5052*S^10 + 1121*S^12)/(324*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((68 + 147*S^2 + 12*S^4 + 286*S^6 - 78*S^8 + 117*S^10 + 68*S^12)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^3) + ((18 + 54*S^2 + 54*S^4 + 33*S^6 - 123*S^8 - 123*S^10 - 41*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + ((131 - 576*S^2 + 8007*S^4 - 7007*S^6 + 1512*S^8 - 957*S^10 - 190*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(488 + 1464*S^2 + 1464*S^4 - 2023*S^6 + 219*S^8 + 219*S^10 + 73*S^12))/(54*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-67 + 2145*S^2 + 6897*S^4 - 7298*S^6 + 2091*S^8 + 543*S^10 - 67*S^12)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^3) - (2*(6 + 18*S^2 + 18*S^4 - 33*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(-3 - 9*S^2 - 9*S^4 + 9*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((7 - 507*S^2 - 1575*S^4 + 1622*S^6 - 459*S^8 - 135*S^10 + 7*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(121 + 363*S^2 + 363*S^4 - 553*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(123 + 369*S^2 + 369*S^4 - 563*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-66 - 198*S^2 - 198*S^4 + 163*S^6 + 231*S^8 + 231*S^10 + 77*S^12))/(54*S^3*(1 + S^2)^3) + (830 + 3930*S^2 + 5589*S^4 + 5494*S^6 + 5748*S^8 + 2340*S^10 + 269*S^12)/(108*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((583 + 366*S^2 + 2820*S^4 + 4714*S^6 + 2541*S^8)/(432*S^3*(1 + S^2)) + (Pi^2*(72 - 787*S^2 - 2820*S^4 + 2906*S^6 - 330*S^8 + 43*S^10 + 72*S^12))/(72*S^3*(1 + S^2)^3) + ((6 + 18*S^2 + 18*S^4 - 33*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(121 + 363*S^2 + 363*S^4 - 553*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-14 - 42*S^2 - 42*S^4 - 11*S^6 + 69*S^8 + 69*S^10 + 23*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + (4*(-10 - 30*S^2 - 30*S^4 + 43*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3))) + Log[T]^3*((-338*(1 + S^2))/(243*S) + (Pi^2*(61508 + 93991*S^2 - 13552*S^4 - 31779*S^6))/(5832*S*(1 + S^2)) + (Pi^6*S^3*(-5767 + 123*S^2 + 123*S^4 + 41*S^6))/(972*(1 + S^2)^3) + (Pi^4*(7414 + 87825*S^2 - 109161*S^4 + 59171*S^6 + 3847*S^8 - 1776*S^10))/(3240*S*(1 + S^2)^3) - (S^3*(25 + 9*S^2 + 9*S^4 + 3*S^6)*HPL[{0}, S^2]^6)/(54*(1 + S^2)^3) + (28*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^3) + (224*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^5*((550 + 1375*S^2 - 3393*S^4 - 862*S^6 - 826*S^8 - 270*S^10)/(540*S*(1 + S^2)^3) + ((275 + 825*S^2 + 825*S^4 - 1033*S^6 - 12*S^8 - 12*S^10 - 4*S^12)*HPL[{1}, -S^2])/(270*S^3*(1 + S^2)^3)) + ((2*Pi^2*(46 + 138*S^2 + 138*S^4 - 1195*S^6 + 321*S^8 + 321*S^10 + 107*S^12))/(27*S^3*(1 + S^2)^3) + (1399 + 9564*S^2 + 53817*S^4 - 33976*S^6 + 53817*S^8 + 9564*S^10 + 1399*S^12)/(162*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (244*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{1}, -S^2]^4*((5*(35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12))/(9*S^3*(1 + S^2)^3) + (10*Pi^2*(51 + 153*S^2 + 153*S^4 - 305*S^6 + 108*S^8 + 108*S^10 + 36*S^12))/(27*S^3*(1 + S^2)^3) - (100*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^4*(-(Pi^2*S^3*(703 + 129*S^2 + 129*S^4 + 43*S^6))/(162*(1 + S^2)^3) + (24 + 2201*S^2 - 3403*S^4 - 1059*S^6 - 1145*S^8 - 386*S^10)/(216*S*(1 + S^2)^3) + ((2 + 545*S^2 + 1614*S^4 - 1554*S^6 + 30*S^8 + 17*S^10 + 2*S^12)*HPL[{1}, -S^2])/(36*S^3*(1 + S^2)^3) + ((137 + 411*S^2 + 411*S^4 - 518*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)^3) + ((3 + 9*S^2 + 9*S^4 - 531*S^6 + 30*S^8 + 30*S^10 + 10*S^12)*HPL[{2}, -S^2])/(54*S^3*(1 + S^2)^3)) + (4*(-1 - 3*S^2 - 3*S^4 - 116*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((135 - 507*S^2 - 2555*S^4 - 1960*S^6 - 8797*S^8 - 3997*S^10 - 1007*S^12)/(9*S^3*(1 + S^2)^3) - (2*Pi^2*(-15 - 45*S^2 - 45*S^4 - 544*S^6 + 621*S^8 + 621*S^10 + 207*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(243 + 645*S^2 + 483*S^4 - 252*S^6 + 4045*S^8 + 1999*S^10 + 357*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-90 - 270*S^2 - 270*S^4 - 47*S^6 + 453*S^8 + 453*S^10 + 151*S^12)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^3) - (160*(5 + 15*S^2 + 15*S^4 - 77*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((2*(361 + 1650*S^2 + 2497*S^4 + 980*S^6 + 3179*S^8 + 602*S^10 + 75*S^12))/(9*S^3*(1 + S^2)^3) - (8*Pi^2*(-79 - 237*S^2 - 237*S^4 - 246*S^6 + 243*S^8 + 243*S^10 + 81*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (4*(-111 + 5*S^2 + 401*S^4 - 4200*S^6 + 9343*S^8 + 3883*S^10 + 495*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (16*(-27 + 238*S^2 + 661*S^4 - 3657*S^6 + 7654*S^8 + 3208*S^10 + 411*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 - 114*S^6 + 165*S^8 + 165*S^10 + 55*S^12)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-12 - 36*S^2 - 36*S^4 - 511*S^6 + 663*S^8 + 663*S^10 + 221*S^12)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((4*(-143 - 381*S^2 + 722*S^4 - 722*S^6 + 381*S^8 + 143*S^10))/(9*S^3*(1 + S^2)^2) + (80*Pi^2*(-11 - 33*S^2 - 33*S^4 - 77*S^6 + 63*S^8 + 63*S^10 + 21*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (64*(8 + 81*S^2 + 203*S^4 - 175*S^6 + 203*S^8 + 81*S^10 + 8*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(513 + 5143*S^2 + 13177*S^4 - 7386*S^6 + 4297*S^8 + 1573*S^10 + 63*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (112*(-1 + S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + (1616*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (320*(-2 - 6*S^2 - 6*S^4 + 3*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (80*(-15 - 104*S^2 - 192*S^4 + 192*S^6 + 104*S^8 + 15*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (320*(-5 - 15*S^2 - 15*S^4 + 9*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2240*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-2*(-70 + 793*S^2 + 2606*S^4 + 1527*S^6))/(27*S*(1 + S^2)) - (2*Pi^2*(158 + 395*S^2 - 1854*S^4 + 5439*S^6 + 2220*S^8 + 270*S^10))/(27*S*(1 + S^2)^3))*Zeta[3] - (112*S^3*Zeta[3]^2)/(3*(1 + S^2)^3) + HPL[{0}, S^2]^3*((116 + 1381*S^2 - 4498*S^4 - 5547*S^6)/(972*S*(1 + S^2)) + (Pi^2*(1110 + 2775*S^2 - 6771*S^4 + 364*S^6 - 395*S^8 - 243*S^10))/(162*S*(1 + S^2)^3) + (2*(16 + 882*S^2 + 2544*S^4 - 2854*S^6 + 789*S^8 + 297*S^10 + 16*S^12)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)^3) + (20*(56 + 168*S^2 + 168*S^4 - 263*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)^3) + ((-173 + 1074*S^2 + 3531*S^4 - 8806*S^6 + 3591*S^8 + 1278*S^10 + 97*S^12)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((-2*(-184 + 345*S^2 - 13713*S^4 + 11692*S^6 - 4182*S^8 + 129*S^10 + 5*S^12))/(243*S^3*(1 + S^2)^3) + (Pi^2*(555 + 1665*S^2 + 1665*S^4 - 2348*S^6 + 243*S^8 + 243*S^10 + 81*S^12))/(81*S^3*(1 + S^2)^3) + (4*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) - (4*(-5 - 15*S^2 - 15*S^4 + 16*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^3) + (4*(-260 - 780*S^2 - 780*S^4 + 501*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^3) - (56*S^5*(3 + 3*S^2 + S^4)*Zeta[3])/(27*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((2*(-509 - 383*S^2 + 383*S^4 + 509*S^6))/(9*S^3) + (2*Pi^2*(-459 - 3797*S^2 - 9407*S^4 + 2100*S^6 + 4535*S^8 + 1853*S^10 + 267*S^12))/(27*S^3*(1 + S^2)^3) - (160*(-10 - 30*S^2 - 30*S^4 + 77*S^6)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(27*S^3) + (Pi^2*(1619 + 6333*S^2 + 36216*S^4 - 15548*S^6 + 27729*S^8 + 5235*S^10 + 1016*S^12))/(81*S^3*(1 + S^2)^3) + (Pi^4*(4460 + 13380*S^2 + 13380*S^4 - 23717*S^6 + 6639*S^8 + 6639*S^10 + 2213*S^12))/(405*S^3*(1 + S^2)^3) + ((-2*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(3*S^3*(1 + S^2)^2) - (4*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (16*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) - (4*(283 + 1611*S^2 + 3147*S^4 - 6262*S^6 + 7197*S^8 + 2961*S^10 + 283*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(47 + 141*S^2 + 141*S^4 - 554*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (600*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (16*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (400*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (20*(17 + 147*S^2 + 345*S^4 - 1046*S^6 + 1155*S^8 + 417*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-1065 - 8126*S^2 - 27478*S^4 - 40238*S^6 - 19389*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-256 - 2067*S^2 - 3840*S^4 + 16444*S^6 - 33270*S^8 - 13839*S^10 - 1696*S^12))/(81*S^3*(1 + S^2)^3) - (32*(-66 - 198*S^2 - 198*S^4 + 385*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(-3 - 9*S^2 - 9*S^4 - 96*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((40*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(27*S^3) + (10*Pi^2*(109 + 1239*S^2 + 3057*S^4 - 3742*S^6 + 2247*S^8 + 969*S^10 + 109*S^12))/(81*S^3*(1 + S^2)^3) - (200*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (400*(5 + 15*S^2 + 15*S^4 - 65*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^3) + (400*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (80*(5 + 15*S^2 + 15*S^4 - 87*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((1177 + 1603*S^2 - 1603*S^4 - 1177*S^6)/(36*S^3) + (Pi^4*(-660 - 1980*S^2 - 1980*S^4 - 12377*S^6 + 5469*S^8 + 5469*S^10 + 1823*S^12))/(810*S^3*(1 + S^2)^3) + (Pi^2*(-1042 - 2058*S^2 + 32421*S^4 - 16988*S^6 + 21396*S^8 + 11622*S^10 + 2441*S^12))/(486*S^3*(1 + S^2)^3) - (4*(-84 - 104*S^2 + 31*S^4 - 2100*S^6 + 4841*S^8 + 2048*S^10 + 276*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 106*S^6 + 165*S^8 + 165*S^10 + 55*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(8 + 81*S^2 + 203*S^4 - 175*S^6 + 203*S^8 + 81*S^10 + 8*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(71 + 213*S^2 + 213*S^4 - 770*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (320*(5 + 15*S^2 + 15*S^4 - 77*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(9 + 227*S^2 + 527*S^4 - 2100*S^6 + 4345*S^8 + 1717*S^10 + 183*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^2*((59888 + 90751*S^2 - 15172*S^4 - 31779*S^6)/(1944*S*(1 + S^2)) + (Pi^4*S^3*(-19753 + 51*S^2 + 51*S^4 + 17*S^6))/(1620*(1 + S^2)^3) + (Pi^2*(464 + 5996*S^2 - 5815*S^4 + 2395*S^6 - 181*S^8 - 243*S^10))/(108*S*(1 + S^2)^3) + (20*(23 + 273*S^2 + 678*S^4 - 674*S^6 + 273*S^8 + 138*S^10 + 23*S^12)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^3) + (10*(23 + 69*S^2 + 69*S^4 - 109*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^3) + ((Pi^2*(-2 - 6*S^2 - 6*S^4 - 1301*S^6 + 345*S^8 + 345*S^10 + 115*S^12))/(27*S^3*(1 + S^2)^3) + (245 + 2658*S^2 + 29352*S^4 - 16988*S^6 + 24465*S^8 + 6906*S^10 + 1154*S^12)/(162*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (2*(-4 - 12*S^2 - 12*S^4 - 425*S^6 + 171*S^8 + 171*S^10 + 57*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(619 + 1857*S^2 + 1857*S^4 - 2671*S^6 + 390*S^8 + 390*S^10 + 130*S^12))/(27*S^3*(1 + S^2)^3) + (1663 + 6096*S^2 + 32427*S^4 - 10396*S^6 + 15453*S^8 + 3900*S^10 + 457*S^12)/(54*S^3*(1 + S^2)^3) + (2*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((-67 + 477*S^4 + 802*S^6 - 2313*S^8 - 1062*S^10 - 157*S^12)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^3) - (2*(-9 - 27*S^2 - 27*S^4 - 4*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-234 - 2012*S^2 - 4967*S^4 + 2100*S^6 + 95*S^8 + 68*S^10 + 42*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(-4 - 12*S^2 - 12*S^4 - 381*S^6 + 153*S^8 + 153*S^10 + 51*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (40*(-1 - 3*S^2 - 3*S^4 - 154*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(8 + 20*S^2 - 144*S^4 + 624*S^6 + 285*S^8 + 45*S^10)*Zeta[3])/(9*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((14471 + 39524*S^2 + 37011*S^4 + 7502*S^6 - 568*S^8)/(486*S^3*(1 + S^2)) + (Pi^2*(236 + 4365*S^2 + 11622*S^4 - 11402*S^6 + 2820*S^8 + 1431*S^10 + 236*S^12))/(54*S^3*(1 + S^2)^3) + ((175 + 2487*S^2 + 6423*S^4 - 5314*S^6 + 1779*S^8 + 939*S^10 + 175*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-7 - 21*S^2 - 21*S^4 - 78*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(4 + 12*S^2 + 12*S^4 - 139*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3))) - (8*(22 + 55*S^2 - 873*S^4 + 2546*S^6 + 899*S^8 + 57*S^10)*Zeta[5])/(9*S*(1 + S^2)^3) + HPL[{0}, S^2]*((-24716 + 34889*S^2 - 27713*S^4)/(972*S) + (Pi^2*(5606 + 16501*S^2 + 9812*S^4 - 867*S^6))/(972*S*(1 + S^2)) + (Pi^4*(16122 + 40305*S^2 - 106902*S^4 + 54589*S^6 + 17191*S^8 + 201*S^10))/(1620*S*(1 + S^2)^3) + (70*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^3) + (224*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)^3) + ((1 + 799*S^2 + 2011*S^4 - 5314*S^6 + 6191*S^8 + 2627*S^10 + 349*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((10*(35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12))/(9*S^3*(1 + S^2)^3) + (20*Pi^2*(140 + 420*S^2 + 420*S^4 - 851*S^6 + 303*S^8 + 303*S^10 + 101*S^12))/(81*S^3*(1 + S^2)^3) + (40*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((193 - 2550*S^2 - 5907*S^4 - 6760*S^6 - 15069*S^8 - 9066*S^10 - 1913*S^12)/(81*S^3*(1 + S^2)^3) - (2*Pi^2*(-25 - 75*S^2 - 75*S^4 - 18*S^6 + 93*S^8 + 93*S^10 + 31*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(28 + 23*S^2 - 109*S^4 + 470*S^6 - 67*S^8 + 173*S^10 + 94*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(3 + 9*S^2 + 9*S^4 - 105*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + ((4*Pi^2*(-665 - 1995*S^2 - 1995*S^4 + 1806*S^6 + 123*S^8 + 123*S^10 + 41*S^12))/(27*S^3*(1 + S^2)^3) + (2*(-1547 - 4242*S^2 - 23529*S^4 + 10304*S^6 - 8601*S^8 + 1098*S^10 + 517*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (8*(-76 + 124*S^2 + 622*S^4 - 2648*S^6 + 3064*S^8 + 1243*S^10 + 149*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(3 + 9*S^2 + 9*S^4 - 262*S^6 + 237*S^8 + 237*S^10 + 79*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (16*(-7 - 21*S^2 - 21*S^4 - 155*S^6 + 150*S^8 + 150*S^10 + 50*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (40*(-28 + 60*S^2 + 267*S^4 - 1046*S^6 + 1233*S^8 + 504*S^10 + 62*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (64*(-98 - 294*S^2 - 294*S^4 + 337*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (16*(-1191 - 3573*S^2 - 3573*S^4 + 3994*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (160*(-27 - 81*S^2 - 81*S^4 + 87*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*Pi^2*S^3*(-135 + 177*S^2 + 177*S^4 + 59*S^6))/(27*(1 + S^2)^3) - (4*(108 + 430*S^2 + 245*S^4 + 989*S^6 + 455*S^8 + 109*S^10))/(9*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-6155 - 1886*S^2 + 8349*S^4 + 14260*S^6 + 6292*S^8)/(243*S^3*(1 + S^2)) + (Pi^2*(-593 + 1974*S^2 + 7536*S^4 - 24496*S^6 + 22086*S^8 + 8838*S^10 + 1027*S^12))/(81*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 136*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(-98 - 294*S^2 - 294*S^4 + 337*S^6)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (16*S^3*(-22 + 21*S^2 + 21*S^4 + 7*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*(((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(27*S^3) + (Pi^4*(8061 + 24183*S^2 + 24183*S^4 - 44045*S^6 + 12366*S^8 + 12366*S^10 + 4122*S^12))/(810*S^3*(1 + S^2)^3) + (Pi^2*(5461 + 18330*S^2 + 174867*S^4 - 108868*S^6 + 136743*S^8 + 19194*S^10 + 4705*S^12))/(486*S^3*(1 + S^2)^3) + ((2*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(9*S^3*(1 + S^2)^3) + (2*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (16*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) - (8*(15 + 52*S^2 + 63*S^4 - 14*S^6 + 54*S^8 + 49*S^10 + 15*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(17 + 51*S^2 + 51*S^4 - 194*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (40*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (16*(62 + 186*S^2 + 186*S^4 - 435*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (80*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(18 + 94*S^2 + 174*S^4 - 158*S^6 + 183*S^8 + 97*S^10 + 18*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((20*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) + (Pi^2*(347 + 5229*S^2 + 13593*S^4 - 17678*S^6 + 10083*S^8 + 4059*S^10 + 347*S^12))/(27*S^3*(1 + S^2)^3) + (20*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(10 + 30*S^2 + 30*S^4 - 43*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (40*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(40 + 120*S^2 + 120*S^4 - 277*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) - (208*S^3*(-4 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(9*(1 + S^2)^3)) + HPL[{1}, -S^2]*(-((1 + S^2)*(27713 - 37886*S^2 + 27713*S^4))/(972*S^3) + (Pi^2*(21491 + 69224*S^2 + 82371*S^4 + 37202*S^6 + 6452*S^8))/(1458*S^3*(1 + S^2)) + (Pi^4*(5027 + 67896*S^2 + 172821*S^4 - 198704*S^6 + 91929*S^8 + 40932*S^10 + 5027*S^12))/(1620*S^3*(1 + S^2)^3) + (2*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((-4*Pi^2*(118 + 354*S^2 + 354*S^4 - 1703*S^6 + 1137*S^8 + 1137*S^10 + 379*S^12))/(27*S^3*(1 + S^2)^3) - (4*(1279 + 8682*S^2 + 29382*S^4 - 7666*S^6 + 54843*S^8 + 11976*S^10 + 3088*S^12))/(81*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (8*(36 + 155*S^2 + 249*S^4 - 316*S^6 + 465*S^8 + 227*S^10 + 36*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-5 - 15*S^2 - 15*S^4 - 116*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(3*S^3*(1 + S^2)^2) + (8*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (16*(18 - 17*S^2 - 159*S^4 - 158*S^6 + 516*S^8 + 208*S^10 + 18*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(178 + 534*S^2 + 534*S^4 - 2299*S^6 + 1479*S^8 + 1479*S^10 + 493*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (1200*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(463 + 1389*S^2 + 1389*S^4 - 2419*S^6 + 714*S^8 + 714*S^10 + 238*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (800*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-4*Pi^2*(79 + 237*S^2 + 237*S^4 - 1444*S^6 + 1011*S^8 + 1011*S^10 + 337*S^12))/(27*S^3*(1 + S^2)^3) - (4*(-44 + 237*S^2 + 3789*S^4 - 5152*S^6 + 12276*S^8 + 1335*S^10 + 559*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((557 + 629*S^2 - 629*S^4 - 557*S^6)/(9*S^3) + (Pi^2*(175 + 3837*S^2 + 10473*S^4 - 5314*S^6 - 2271*S^8 - 411*S^10 + 175*S^12))/(27*S^3*(1 + S^2)^3) - (8*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (32*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) - (16*(11 + 33*S^2 + 33*S^4 - 680*S^6 + 537*S^8 + 537*S^10 + 179*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3))) + ((124*Pi^2*S^5*(3 + 3*S^2 + S^4))/(1 + S^2)^3 + (-230 - 735*S^2 - 430*S^4 + 3668*S^6 + 1244*S^8 + 627*S^10)/(2*S*(1 + S^2)^3))*Zeta[7] + HPL[{0}, S^2]^2*((-13386809 - 28613*S^2 + 11958516*S^4)/(139968*S) + (Pi^4*(-110248 - 57113*S^2 + 274622*S^4 + 213495*S^6))/(77760*S*(1 + S^2)) + (Pi^2*(-1189582 - 1213493*S^2 + 1394480*S^4 + 1293975*S^6))/(93312*S*(1 + S^2)) + (Pi^6*(-481804 - 1204510*S^2 + 2712474*S^4 + 905782*S^6 + 399091*S^8 + 61569*S^10))/(544320*S*(1 + S^2)^3) + ((-23 - 273*S^2 - 678*S^4 + 674*S^6 - 273*S^8 - 138*S^10 - 23*S^12)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)^3) - (2*(23 + 69*S^2 + 69*S^4 - 109*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{1}, -S^2]^7)/(63*S^3*(1 + S^2)^3) + ((169 - 1245*S^2 - 3819*S^4 + 9284*S^6 - 6561*S^8 - 3519*S^10 - 749*S^12)*HPL[{2}, -S^2]^3)/(216*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^5*((-1663 - 6096*S^2 - 32427*S^4 + 10396*S^6 - 15453*S^8 - 3900*S^10 - 457*S^12)/(540*S^3*(1 + S^2)^3) + (Pi^2*(-619 - 1857*S^2 - 1857*S^4 + 2671*S^6 - 390*S^8 - 390*S^10 - 130*S^12))/(270*S^3*(1 + S^2)^3) + ((-325 - 975*S^2 - 975*S^4 + 1348*S^6 - 201*S^8 - 201*S^10 - 67*S^12)*HPL[{2}, -S^2])/(45*S^3*(1 + S^2)^3)) + ((-48 - 130*S^2 - 121*S^4 - 186*S^6 - 161*S^8 - 116*S^10 - 30*S^12)*HPL[{3}, -S^2]^2)/(12*S^3*(1 + S^2)^3) + ((Pi^2*(-24 - 72*S^2 - 72*S^4 + 113*S^6 + 483*S^8 + 483*S^10 + 161*S^12))/(36*S^3*(1 + S^2)^3) + (-665 + 342*S^2 + 1926*S^4 + 9272*S^6 + 15750*S^8 + 8316*S^10 + 2215*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((725 + 963*S^2 - 1215*S^4 + 2656*S^6 + 5961*S^8 + 3000*S^10 + 464*S^12)*HPL[{6}, -S^2])/(36*S^3*(1 + S^2)^3) + ((-145 - 435*S^2 - 435*S^4 + 445*S^6 + 1086*S^8 + 1086*S^10 + 362*S^12)*HPL[{7}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-91 + 1569*S^2 + 4323*S^4 - 10595*S^6 + 6756*S^8 + 3480*S^10 + 674*S^12)*HPL[{2, 1}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((-674 - 2529*S^2 - 4239*S^4 - 2302*S^6 - 10098*S^8 - 4725*S^10 - 1457*S^12)/(108*S^3*(1 + S^2)^3) + (Pi^2*(-69 - 207*S^2 - 207*S^4 + 64*S^6 - 249*S^8 - 249*S^10 - 83*S^12))/(36*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((-138 - 991*S^2 - 1552*S^4 - 1701*S^6 - 7069*S^8 - 3460*S^10 - 1041*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(-33 - 99*S^2 - 99*S^4 + 116*S^6 - 573*S^8 - 573*S^10 - 191*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((31 + 87*S^2 + 42*S^4 - 280*S^6 - 186*S^8 - 213*S^10 - 77*S^12)*HPL[{4, 2}, -S^2])/(36*S^3*(1 + S^2)^3) - (2*(-20 - 60*S^2 - 60*S^4 + 9*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-236 - 189*S^2 + 720*S^4 - 1192*S^6 - 3348*S^8 - 1971*S^10 - 416*S^12)*HPL[{5, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + ((234 + 702*S^2 + 702*S^4 - 117*S^6 - 789*S^8 - 789*S^10 - 263*S^12)*HPL[{5, 2}, -S^2])/(6*S^3*(1 + S^2)^3) + ((282 + 846*S^2 + 846*S^4 - 227*S^6 - 1233*S^8 - 1233*S^10 - 411*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-276 - 828*S^2 - 828*S^4 + 475*S^6 + 6*S^8 + 6*S^10 + 2*S^12))/(9*S^3*(1 + S^2)^3) + (-824 - 2499*S^2 - 10173*S^4 + 806*S^6 - 2604*S^8 - 423*S^10 + 13*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((Pi^2*(-1685 - 5055*S^2 - 5055*S^4 + 2776*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3) + (-2515 - 7347*S^2 - 30417*S^4 + 2812*S^6 - 5385*S^8 - 213*S^10 + 353*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + ((-56 - 127*S^2 - 101*S^4 - 83*S^6 - 31*S^8 - 2*S^10)*HPL[{3, 1, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + ((94 - 891*S^2 - 2622*S^4 + 6128*S^6 - 4412*S^8 - 2357*S^10 - 500*S^12)*HPL[{3, 2, 1}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-37 - 111*S^2 - 111*S^4 - 210*S^6 + 465*S^8 + 465*S^10 + 155*S^12)*HPL[{3, 2, 2}, -S^2])/(6*S^3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 39*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((560 - 3840*S^2 - 12057*S^4 + 28012*S^6 - 18075*S^8 - 9660*S^10 - 2068*S^12)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((11 + 33*S^2 + 33*S^4 - 306*S^6 + 621*S^8 + 621*S^10 + 207*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((83 + 249*S^2 + 249*S^4 - 930*S^6 + 1701*S^8 + 1701*S^10 + 567*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(96 + 288*S^2 + 288*S^4 - 931*S^6 + 1779*S^8 + 1779*S^10 + 593*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((562 + 1572*S^2 + 6825*S^4 - 646*S^6 + 482*S^8 - 174*S^10 - 157*S^12)/(3*S^3*(1 + S^2)^3) - (4*Pi^2*(-288 - 864*S^2 - 864*S^4 + 447*S^6 + 84*S^8 + 84*S^10 + 28*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] - (16*(-77 - 231*S^2 - 231*S^4 + 147*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-242 + 1197*S^2 + 4068*S^4 - 9637*S^6 + 5403*S^8 + 2874*S^10 + 613*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-1869 - 5607*S^2 - 5607*S^4 + 3616*S^6 + 399*S^8 + 399*S^10 + 133*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-1869 - 5607*S^2 - 5607*S^4 + 3616*S^6 + 399*S^8 + 399*S^10 + 133*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-3717 - 11151*S^2 - 11151*S^4 + 7144*S^6 + 1047*S^8 + 1047*S^10 + 349*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-5547 - 16641*S^2 - 16641*S^4 + 10748*S^6 + 1533*S^8 + 1533*S^10 + 511*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-59 + 475*S^2 + 1456*S^4 - 3214*S^6 + 1874*S^8 + 1007*S^10 + 217*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(79 + 237*S^2 + 237*S^4 - 158*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(79 + 237*S^2 + 237*S^4 - 158*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (16*(783 + 2349*S^2 + 2349*S^4 - 1614*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-165 - 495*S^2 - 495*S^4 + 289*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^4*S^3*(1863 + 4470*S^2 + 4470*S^4 + 1490*S^6))/(540*(1 + S^2)^3) + (-7139 - 1912*S^2 + 24883*S^4 + 19008*S^6)/(648*S*(1 + S^2)) + (Pi^2*(116 + 128*S^2 + 1581*S^4 + 3878*S^6 + 2687*S^8 + 834*S^10))/(54*S*(1 + S^2)^3))*Zeta[3] + ((-60 - 150*S^2 + 129*S^4 + 103*S^6 - 26*S^8 - 30*S^10)*Zeta[3]^2)/(6*S*(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((-3029 - 27062*S^2 - 24693*S^4 + 2674*S^6 + 3982*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(103 - 859*S^2 - 2641*S^4 + 5663*S^6 - 1920*S^8 - 981*S^10 - 203*S^12))/(18*S^3*(1 + S^2)^3) + (8*S^3*(-28 + 45*S^2 + 45*S^4 + 15*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((60483 + 113326*S^2 + 5006*S^4 - 75074*S^6 - 35013*S^8)/(1296*S^3*(1 + S^2)) + (Pi^2*(2311 + 5104*S^2 + 31273*S^4 - 4777*S^6 + 316*S^8 - 935*S^10 - 572*S^12))/(216*S^3*(1 + S^2)^3) + (Pi^4*(1166 + 3498*S^2 + 3498*S^4 - 1513*S^6 - 360*S^8 - 360*S^10 - 120*S^12))/(180*S^3*(1 + S^2)^3) - (2*(317 + 951*S^2 + 951*S^4 - 636*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(79 + 237*S^2 + 237*S^4 - 158*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-60 - 212*S^2 - 284*S^4 + 255*S^6 - 253*S^8 - 154*S^10 - 30*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4}, -S^2]*((-2089 - 2528*S^2 + 8470*S^4 + 14548*S^6 + 7367*S^8)/(432*S^3*(1 + S^2)) + (Pi^2*(-25 - 771*S^2 - 2022*S^4 + 328*S^6 + 3030*S^8 + 1239*S^10 + 101*S^12))/(216*S^3*(1 + S^2)^3) - (2*(-17 - 51*S^2 - 51*S^4 + 4*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 + 10*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((-100 + 1061*S^2 + 853*S^4 - 743*S^6 - 507*S^8)/(36*S^3*(1 + S^2)) + (Pi^2*(-401 + 2298*S^2 + 7617*S^4 - 16615*S^6 + 5892*S^8 + 3201*S^10 + 724*S^12))/(108*S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 30*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((3901 - 15176*S^2 - 32322*S^4 - 13232*S^6 - 1283*S^8)/(2592*S^3*(1 + S^2)) + (Pi^2*(223 - 2481*S^2 - 7143*S^4 + 17681*S^6 - 8226*S^8 - 4194*S^10 - 812*S^12))/(432*S^3*(1 + S^2)^3) + ((-9 - 27*S^2 - 27*S^4 - 46*S^6 + 117*S^8 + 117*S^10 + 39*S^12)*HPL[{3}, -S^2])/(12*S^3*(1 + S^2)^3) - (2*(-77 - 231*S^2 - 231*S^4 + 147*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-6 - 18*S^2 - 18*S^4 - 23*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*((-14471 - 39524*S^2 - 37011*S^4 - 7502*S^6 + 568*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-236 - 4365*S^2 - 11622*S^4 + 11402*S^6 - 2820*S^8 - 1431*S^10 - 236*S^12))/(216*S^3*(1 + S^2)^3) + ((-175 - 2487*S^2 - 6423*S^4 + 5314*S^6 - 1779*S^8 - 939*S^10 - 175*S^12)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)^3) + ((-7 - 21*S^2 - 21*S^4 - 78*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((4 + 12*S^2 + 12*S^4 - 139*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((-201071 - 515312*S^2 - 390054*S^4 + 89848*S^6 + 80125*S^8)/(11664*S^3*(1 + S^2)) + (Pi^4*(-8046 - 24138*S^2 - 24138*S^4 + 31091*S^6 - 1209*S^8 - 1209*S^10 - 403*S^12))/(3240*S^3*(1 + S^2)^3) + (Pi^2*(-3625 - 10230*S^2 - 76074*S^4 + 36697*S^6 - 19761*S^8 - 2337*S^10 + 470*S^12))/(972*S^3*(1 + S^2)^3) + ((Pi^2*(-574 - 1722*S^2 - 1722*S^4 + 2195*S^6 - 177*S^8 - 177*S^10 - 59*S^12))/(54*S^3*(1 + S^2)^3) + (-5303 - 16806*S^2 - 90777*S^4 + 22802*S^6 - 28803*S^8 - 5340*S^10 + 259*S^12)/(324*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((-154 - 462*S^2 - 462*S^4 + 741*S^6 - 183*S^8 - 183*S^10 - 61*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((109 + 186*S^2 - 111*S^4 - 880*S^6 + 1833*S^8 + 834*S^10 + 109*S^12)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^3) + ((-33 - 99*S^2 - 99*S^4 - 24*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + ((175 + 2487*S^2 + 6423*S^4 - 5314*S^6 + 1779*S^8 + 939*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(161 + 483*S^2 + 483*S^4 - 663*S^6 + 96*S^8 + 96*S^10 + 32*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((76 + 321*S^2 + 528*S^4 - 1486*S^6 + 2310*S^8 + 915*S^10 + 76*S^12)*Zeta[3])/(27*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-5977 - 6727*S^2 + 29361*S^4 + 49973*S^6 + 25046*S^8)/(1296*S^3*(1 + S^2)) + (Pi^2*(-71 - 47*S^2 - 141*S^4 + 288*S^6 + 1297*S^8 + 567*S^10 + 171*S^12))/(72*S^3*(1 + S^2)^3) + (Pi^4*(-385 - 1155*S^2 - 1155*S^4 - 358*S^6 + 2973*S^8 + 2973*S^10 + 991*S^12))/(2160*S^3*(1 + S^2)^3) + (2*(-10 - 30*S^2 - 30*S^4 + 4*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-1 - 17*S^2 - 44*S^4 + 253*S^6 + 23*S^8 + 59*S^10 + 29*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-21 - 63*S^2 - 63*S^4 + 58*S^6 - 63*S^8 - 63*S^10 - 21*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(3 + 9*S^2 + 9*S^4 - 16*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((-52 - 99*S^2 - 36*S^4 - 230*S^6 + 216*S^8 + 279*S^10 + 110*S^12)*Zeta[3])/(18*S^3*(1 + S^2)^3)) + ((2*Pi^2*S^3*(125 + 336*S^2 + 336*S^4 + 112*S^6))/(9*(1 + S^2)^3) + (-76 - 556*S^2 + 1929*S^4 + 6224*S^6 + 4373*S^8 + 1494*S^10)/(18*S*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(-11291 - 41786*S^2 - 9717*S^4 + 40996*S^6 + 27346*S^8))/(7776*S^3*(1 + S^2)) + (-281637 - 685030*S^2 + 16012*S^4 + 696182*S^6 + 401193*S^8)/(15552*S^3*(1 + S^2)) + (Pi^4*(869 - 12237*S^2 - 35313*S^4 + 69823*S^6 + 2164*S^8 + 3379*S^10 + 1121*S^12))/(4320*S^3*(1 + S^2)^3) + ((Pi^2*(11 + 33*S^2 + 33*S^4 - 12*S^6 + 39*S^8 + 39*S^10 + 13*S^12))/(12*S^3*(1 + S^2)^3) + (83 + 319*S^2 + 562*S^4 + 286*S^6 + 1687*S^8 + 835*S^10 + 260*S^12)/(36*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((87 + 237*S^2 + 234*S^4 + 432*S^6 + 386*S^8 + 281*S^10 + 75*S^12)*HPL[{4}, -S^2])/(12*S^3*(1 + S^2)^3) + ((46 + 138*S^2 + 138*S^4 - 3*S^6 - 63*S^8 - 63*S^10 - 21*S^12)*HPL[{5}, -S^2])/(6*S^3*(1 + S^2)^3) + ((824 + 2499*S^2 + 10173*S^4 - 806*S^6 + 2604*S^8 + 423*S^10 - 13*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(276 + 828*S^2 + 828*S^4 - 475*S^6 - 6*S^8 - 6*S^10 - 2*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-163 + 1347*S^2 + 4083*S^4 - 10802*S^6 + 6423*S^8 + 3165*S^10 + 575*S^12)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + ((17 + 51*S^2 + 51*S^4 + 98*S^6 - 237*S^8 - 237*S^10 - 79*S^12)*HPL[{3, 2}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-7 - 21*S^2 - 21*S^4 + 146*S^6 - 309*S^8 - 309*S^10 - 103*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((91 - 1569*S^2 - 4323*S^4 + 10595*S^6 - 6756*S^8 - 3480*S^10 - 674*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(-77 - 231*S^2 - 231*S^4 + 147*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-311 - 933*S^2 - 933*S^4 + 604*S^6 + 69*S^8 + 69*S^10 + 23*S^12)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (16*(79 + 237*S^2 + 237*S^4 - 158*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*S^3*(-28 + 45*S^2 + 45*S^4 + 15*S^6))/(9*(1 + S^2)^3) + (197 + 1458*S^2 + 3177*S^4 + 1825*S^6 + 8352*S^8 + 3069*S^10 + 818*S^12)/(108*S^3*(1 + S^2)^3))*Zeta[3] + (S^3*(-51 + 69*S^2 + 69*S^4 + 23*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((Pi^2*(-444533 - 956396*S^2 - 388614*S^4 + 492676*S^6 + 268339*S^8))/(46656*S^3*(1 + S^2)) + (-2026031 - 4363607*S^2 - 1581987*S^4 + 2662531*S^6 + 1347070*S^8)/(34992*S^3*(1 + S^2)) + (Pi^6*(-240902 - 722706*S^2 - 722706*S^4 + 760225*S^6 + 136461*S^8 + 136461*S^10 + 45487*S^12))/(272160*S^3*(1 + S^2)^3) + (Pi^4*(-56015 - 103512*S^2 - 871950*S^4 + 647561*S^6 + 162861*S^8 + 172473*S^10 + 58186*S^12))/(38880*S^3*(1 + S^2)^3) + ((-694 - 2661*S^2 - 14820*S^4 + 3742*S^6 - 8130*S^8 - 2097*S^10 - 316*S^12)/(72*S^3*(1 + S^2)^3) + (Pi^2*(-266 - 798*S^2 - 798*S^4 + 1163*S^6 - 207*S^8 - 207*S^10 - 69*S^12))/(36*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + ((-149 - 447*S^2 - 447*S^4 + 668*S^6 - 129*S^8 - 129*S^10 - 43*S^12)*HPL[{2}, -S^2]^3)/(18*S^3*(1 + S^2)^3) + ((11 + 33*S^2 + 33*S^4 - 24*S^6 - 33*S^8 - 33*S^10 - 11*S^12)*HPL[{3}, -S^2]^2)/(6*S^3*(1 + S^2)^3) + ((Pi^2*(-93 - 279*S^2 - 279*S^4 - 12*S^6 + 339*S^8 + 339*S^10 + 113*S^12))/(36*S^3*(1 + S^2)^3) + (-728 - 237*S^2 - 1011*S^4 + 5798*S^6 + 13614*S^8 + 7143*S^10 + 1981*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((49 + 12*S^2 - 255*S^4 + 44*S^6 + 789*S^8 + 360*S^10 + 49*S^12)*HPL[{5}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-162 - 486*S^2 - 486*S^4 + 121*S^6 + 621*S^8 + 621*S^10 + 207*S^12)*HPL[{6}, -S^2])/(6*S^3*(1 + S^2)^3) + (2*(154 + 462*S^2 + 462*S^4 - 741*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((851 + 2499*S^2 + 14427*S^4 - 4436*S^6 + 3777*S^8 + 261*S^10 - 187*S^12)/(18*S^3*(1 + S^2)^3) + (2*Pi^2*(144 + 432*S^2 + 432*S^4 - 538*S^6 + 33*S^8 + 33*S^10 + 11*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((-26 - 135*S^2 - 246*S^4 + 614*S^6 - 642*S^8 - 267*S^10 - 26*S^12)*HPL[{3, 2}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-21 - 57*S^2 - 42*S^4 + 316*S^6 - 462*S^8 - 197*S^10 - 21*S^12)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((1 + 3*S^2 + 3*S^4 - 6*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{4, 2}, -S^2])/(2*S^3*(1 + S^2)^3) - (8*(-9 - 27*S^2 - 27*S^4 + 3*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-574 - 1722*S^2 - 1722*S^4 + 2195*S^6 - 177*S^8 - 177*S^10 - 59*S^12))/(9*S^3*(1 + S^2)^3) + (-5303 - 16806*S^2 - 90777*S^4 + 22802*S^6 - 28803*S^8 - 5340*S^10 + 259*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(169 + 1896*S^2 + 4677*S^4 - 4378*S^6 + 2166*S^8 + 1059*S^10 + 169*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(905 + 11190*S^2 + 28173*S^4 - 25388*S^6 + 11163*S^8 + 5520*S^10 + 905*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(149 + 447*S^2 + 447*S^4 - 668*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(927 + 2781*S^2 + 2781*S^4 - 3984*S^6 + 651*S^8 + 651*S^10 + 217*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(175 + 2487*S^2 + 6423*S^4 - 5314*S^6 + 1779*S^8 + 939*S^10 + 175*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(161 + 483*S^2 + 483*S^4 - 663*S^6 + 96*S^8 + 96*S^10 + 32*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-7313 - 9371*S^2 + 9447*S^4 + 20023*S^6 + 7222*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(116 + 84*S^2 - 402*S^4 - 146*S^6 + 2541*S^8 + 1065*S^10 + 116*S^12))/(54*S^3*(1 + S^2)^3))*Zeta[3] + ((-30 - 90*S^2 - 90*S^4 + 31*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((-388 - 832*S^2 + 4125*S^4 + 7250*S^6 + 3329*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(136 - 3*S^2 - 840*S^4 - 934*S^6 + 2886*S^8 + 1239*S^10 + 136*S^12))/(108*S^3*(1 + S^2)^3) - (2*(5 + 15*S^2 + 15*S^4 - 75*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-6 - 18*S^2 - 18*S^4 + 15*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((30749 + 79526*S^2 + 44040*S^4 - 18430*S^6 - 14989*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(496 + 11913*S^2 + 32856*S^4 - 26566*S^6 + 5046*S^8 + 2643*S^10 + 496*S^12))/(108*S^3*(1 + S^2)^3) - (2*(8 + 24*S^2 + 24*S^4 - 133*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-116879 - 276680*S^2 - 48090*S^4 + 192472*S^6 + 104089*S^8)/(3888*S^3*(1 + S^2)) + (Pi^4*(-7152 - 21456*S^2 - 21456*S^4 + 23977*S^6 + 1263*S^8 + 1263*S^10 + 421*S^12))/(2160*S^3*(1 + S^2)^3) + (Pi^2*(-7697 - 18120*S^2 - 140061*S^4 + 56354*S^6 - 16509*S^8 + 4182*S^10 + 3067*S^12))/(1296*S^3*(1 + S^2)^3) + ((20 + 102*S^2 + 183*S^4 - 464*S^6 + 480*S^8 + 201*S^10 + 20*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-23 - 69*S^2 - 69*S^4 + 54*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{4}, -S^2])/(6*S^3*(1 + S^2)^3) + (2*(169 + 1896*S^2 + 4677*S^4 - 4378*S^6 + 2166*S^8 + 1059*S^10 + 169*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(154 + 462*S^2 + 462*S^4 - 743*S^6 + 177*S^8 + 177*S^10 + 59*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(154 + 462*S^2 + 462*S^4 - 741*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((200 + 741*S^2 + 1020*S^4 - 1310*S^6 + 2262*S^8 + 1155*S^10 + 200*S^12)*Zeta[3])/(18*S^3*(1 + S^2)^3)) + ((-38 - 417*S^2 - 966*S^4 - 436*S^6 + 2247*S^8 + 654*S^10 - 38*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((Pi^2*(-48997 - 116887*S^2 - 73365*S^4 + 25763*S^6 + 20870*S^8))/(7776*S^3*(1 + S^2)) + (-408157 - 967195*S^2 - 547413*S^4 + 454067*S^6 + 255818*S^8)/(11664*S^3*(1 + S^2)) + (Pi^4*(-490 - 72258*S^2 - 212208*S^4 + 212554*S^6 - 5847*S^8 - 3471*S^10 - 490*S^12))/(6480*S^3*(1 + S^2)^3) + ((-169 - 1896*S^2 - 4677*S^4 + 4378*S^6 - 2166*S^8 - 1059*S^10 - 169*S^12)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((Pi^2*(-22 - 66*S^2 - 66*S^4 - 87*S^6 + 141*S^8 + 141*S^10 + 47*S^12))/(18*S^3*(1 + S^2)^3) + (-157 + 162*S^2 + 393*S^4 + 694*S^6 + 4353*S^8 + 1836*S^10 + 503*S^12)/(36*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((23 - 33*S^2 - 240*S^4 - 20*S^6 + 426*S^8 + 189*S^10 + 23*S^12)*HPL[{4}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-23 - 69*S^2 - 69*S^4 - 24*S^6 + 105*S^8 + 105*S^10 + 35*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((5303 + 16806*S^2 + 90777*S^4 - 22802*S^6 + 28803*S^8 + 5340*S^10 - 259*S^12)/(108*S^3*(1 + S^2)^3) + (Pi^2*(574 + 1722*S^2 + 1722*S^4 - 2195*S^6 + 177*S^8 + 177*S^10 + 59*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((229 + 3606*S^2 + 9465*S^4 - 7876*S^6 + 2499*S^8 + 1284*S^10 + 229*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(5 + 15*S^2 + 15*S^4 - 75*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((3 + 9*S^2 + 9*S^4 + 474*S^6 - 411*S^8 - 411*S^10 - 137*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-175 - 2487*S^2 - 6423*S^4 + 5314*S^6 - 1779*S^8 - 939*S^10 - 175*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(154 + 462*S^2 + 462*S^4 - 741*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(469 + 1407*S^2 + 1407*S^4 - 2145*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-34 - 102*S^2 - 102*S^4 - 111*S^6 + 225*S^8 + 225*S^10 + 75*S^12))/(18*S^3*(1 + S^2)^3) + (-91 + 90*S^2 + 1041*S^4 + 106*S^6 + 4587*S^8 + 1440*S^10 + 419*S^12)/(36*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-30749 - 79526*S^2 - 44040*S^4 + 18430*S^6 + 14989*S^8)/(1296*S^3*(1 + S^2)) + (Pi^2*(-496 - 11913*S^2 - 32856*S^4 + 26566*S^6 - 5046*S^8 - 2643*S^10 - 496*S^12))/(216*S^3*(1 + S^2)^3) + ((5 + 15*S^2 + 15*S^4 - 75*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(154 + 462*S^2 + 462*S^4 - 741*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8 + 24*S^2 + 24*S^4 - 133*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((-40 - 120*S^2 - 120*S^4 - 117*S^6 + 237*S^8 + 237*S^10 + 79*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + 186*S^3*Zeta[7]) + Log[T]^2*((8755*(1 + S^2))/(3888*S) + (Pi^4*(-82022 - 115150*S^2 + 31021*S^4 + 49677*S^6))/(19440*S*(1 + S^2)) + (Pi^2*(-461170 - 626123*S^2 + 360656*S^4 + 401193*S^6))/(23328*S*(1 + S^2)) + (Pi^6*(-403412 - 1008530*S^2 + 2830062*S^4 - 389654*S^6 - 184667*S^8 - 18873*S^10))/(136080*S*(1 + S^2)^3) + (S^3*(3 + S^2)*(3 + S^4)*HPL[{0}, S^2]^7)/(72*(1 + S^2)^3) - (14*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^6)/(3*S^3*(1 + S^2)^3) - (32*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^7)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^6*((-46 - 115*S^2 + 270*S^4 + 145*S^6 + 94*S^8 + 24*S^10)/(144*S*(1 + S^2)^3) + ((-23 - 69*S^2 - 69*S^4 + 70*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{1}, -S^2])/(72*S^3*(1 + S^2)^3)) - ((-1 + S^2)*(255 + 637*S^2 + 1066*S^4 + 637*S^6 + 255*S^8)*HPL[{2}, -S^2]^3)/(18*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-35 - 146*S^2 - 889*S^4 + 460*S^6 - 889*S^8 - 146*S^10 - 35*S^12)/(3*S^3*(1 + S^2)^3) - (2*Pi^2*(51 + 153*S^2 + 153*S^4 - 305*S^6 + 108*S^8 + 108*S^10 + 36*S^12))/(9*S^3*(1 + S^2)^3) + (20*(-1 + S^6)*HPL[{2}, -S^2])/S^3) + HPL[{0}, S^2]^5*((Pi^2*S^3*(1601 + 327*S^2 + 327*S^4 + 109*S^6))/(1080*(1 + S^2)^3) + (400 - 1170*S^2 + 5337*S^4 + 3823*S^6 + 2867*S^8 + 735*S^10)/(720*S*(1 + S^2)^3) + ((200 - 1035*S^2 - 4290*S^4 + 5062*S^6 + 732*S^8 + 639*S^10 + 200*S^12)*HPL[{1}, -S^2])/(360*S^3*(1 + S^2)^3) + ((-275 - 825*S^2 - 825*S^4 + 1033*S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{1}, -S^2]^2)/(180*S^3*(1 + S^2)^3) - (S^3*(-541 + 3*S^2 + 3*S^4 + S^6)*HPL[{2}, -S^2])/(180*(1 + S^2)^3)) + ((-1 - 27*S^2 - 62*S^4 + 124*S^6 - 270*S^8 - 151*S^10 - 33*S^12)*HPL[{3}, -S^2]^2)/(S^3*(1 + S^2)^3) + ((Pi^2*(-24 - 72*S^2 - 72*S^4 - 245*S^6 + 813*S^8 + 813*S^10 + 271*S^12))/(9*S^3*(1 + S^2)^3) + (354 + 3001*S^2 + 5251*S^4 + 6744*S^6 + 14629*S^8 + 6805*S^10 + 1788*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((195 + 17*S^2 - 1105*S^4 + 888*S^6 + 4747*S^8 + 2992*S^10 + 708*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-145 - 435*S^2 - 435*S^4 + 501*S^6 + 1254*S^8 + 1254*S^10 + 418*S^12)*HPL[{7}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(79 + 741*S^2 + 1665*S^4 - 3214*S^6 + 1665*S^8 + 741*S^10 + 79*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(53 + 159*S^2 + 159*S^4 + 2400*S^6 - 3975*S^8 - 3975*S^10 - 1325*S^12))/(9*S^3*(1 + S^2)^3) + (199 + 129*S^2 - 1945*S^4 + 1292*S^6 - 12669*S^8 - 2925*S^10 - 1009*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((333 - 1379*S^2 - 10007*S^4 + 2516*S^6 - 44203*S^8 - 11025*S^10 - 3531*S^12)/(3*S^3*(1 + S^2)^3) - (2*Pi^2*(-71 - 213*S^2 - 213*S^4 - 4200*S^6 + 6345*S^8 + 6345*S^10 + 2115*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((19 - 19*S^2 - 130*S^4 + 336*S^6 - 1034*S^8 - 587*S^10 - 133*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) + (8*(2 + 6*S^2 + 6*S^4 - 35*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(93 + 631*S^2 + 1087*S^4 - 2928*S^6 + 9165*S^8 + 5085*S^10 + 1083*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(10 + 30*S^2 + 30*S^4 - 349*S^6 + 507*S^8 + 507*S^10 + 169*S^12)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-74 - 222*S^2 - 222*S^4 + 145*S^6 + 501*S^8 + 501*S^10 + 167*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-16*Pi^2*(152 + 456*S^2 + 456*S^4 - 447*S^6 + 225*S^8 + 225*S^10 + 75*S^12))/(9*S^3*(1 + S^2)^3) - (2*(405 + 1398*S^2 + 7307*S^4 - 1292*S^6 + 7307*S^8 + 1398*S^10 + 405*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((-2*(1163 + 3048*S^2 + 17339*S^4 - 3264*S^6 + 6705*S^8 + 536*S^10 + 73*S^12))/(3*S^3*(1 + S^2)^3) - (8*Pi^2*(919 + 2757*S^2 + 2757*S^4 - 1928*S^6 + 291*S^8 + 291*S^10 + 97*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + (4*(-19 - 52*S^2 - 61*S^4 + 61*S^6 + 52*S^8 + 19*S^10)*HPL[{3, 1, 2}, -S^2])/(S^3*(1 + S^2)^2) - (8*(-99 - 113*S^2 - 123*S^4 + 123*S^6 + 113*S^8 + 99*S^10)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (2*(-97 - 291*S^2 - 291*S^4 - 4946*S^6 + 7101*S^8 + 7101*S^10 + 2367*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-47 - 141*S^2 - 141*S^4 - 1888*S^6 + 2757*S^8 + 2757*S^10 + 919*S^12)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-801 - 2195*S^2 - 2963*S^4 + 1764*S^6 - 1577*S^8 - 269*S^10 + 321*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-187 - 561*S^2 - 561*S^4 - 7382*S^6 + 11031*S^8 + 11031*S^10 + 3677*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-559 - 1677*S^2 - 1677*S^4 - 23030*S^6 + 33603*S^8 + 33603*S^10 + 11201*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-285 - 855*S^2 - 855*S^4 - 11861*S^6 + 17256*S^8 + 17256*S^10 + 5752*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*(-545 - 711*S^2 - 4606*S^4 + 4606*S^6 + 711*S^8 + 545*S^10))/(3*S^3*(1 + S^2)^2) - (16*Pi^2*(-330 - 990*S^2 - 990*S^4 + 289*S^6 + 552*S^8 + 552*S^10 + 184*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] - (4928*(-1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) + (8*(-345 - 1051*S^2 - 1525*S^4 + 882*S^6 - 745*S^8 - 181*S^10 + 105*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-887 - 2661*S^2 - 2661*S^4 + 1156*S^6 + 909*S^8 + 909*S^10 + 303*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-887 - 2661*S^2 - 2661*S^4 + 1156*S^6 + 909*S^8 + 909*S^10 + 303*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-1811 - 5433*S^2 - 5433*S^4 + 1156*S^6 + 3681*S^8 + 3681*S^10 + 1227*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(-2735 - 8205*S^2 - 8205*S^4 + 2018*S^6 + 5349*S^8 + 5349*S^10 + 1783*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (80*(-15 - 14*S^2 - 12*S^4 + 12*S^6 + 14*S^8 + 15*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (128*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (640*(73 + 219*S^2 + 219*S^4 - 361*S^6 + 318*S^8 + 318*S^10 + 106*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (7040*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((Pi^4*S^3*(-1863 + 4470*S^2 + 4470*S^4 + 1490*S^6))/(135*(1 + S^2)^3) + (-29552 - 8653*S^2 + 97108*S^4 + 61953*S^6)/(324*S*(1 + S^2)) + (Pi^2*(662 + 3773*S^2 - 111*S^4 + 22895*S^6 + 5969*S^8 + 2172*S^10))/(54*S*(1 + S^2)^3))*Zeta[3] - (2*(20 + 50*S^2 - 189*S^4 + 59*S^6 + 29*S^8 + 3*S^10)*Zeta[3]^2)/(3*S*(1 + S^2)^3) + HPL[{0}, S^2]^4*((-2009 - 1042*S^2 + 6400*S^4 + 5217*S^6)/(1296*S*(1 + S^2)) + (Pi^2*(-1238 - 3095*S^2 + 7164*S^4 + 2183*S^6 + 1472*S^8 + 390*S^10))/(432*S*(1 + S^2)^3) + ((-2 - 545*S^2 - 1614*S^4 + 1554*S^6 - 30*S^8 - 17*S^10 - 2*S^12)*HPL[{1}, -S^2]^2)/(24*S^3*(1 + S^2)^3) + ((-137 - 411*S^2 - 411*S^4 + 518*S^6 - 15*S^8 - 15*S^10 - 5*S^12)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^3) + ((44 - 384*S^2 - 1185*S^4 + 2449*S^6 - 46*S^8 + 26*S^10 + 14*S^12)*HPL[{2}, -S^2])/(72*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((Pi^2*(-619 - 1857*S^2 - 1857*S^4 + 2086*S^6 + 195*S^8 + 195*S^10 + 65*S^12))/(216*S^3*(1 + S^2)^3) + (-2261 - 2172*S^2 - 54867*S^4 + 42206*S^6 + 6837*S^8 + 7026*S^10 + 2311*S^12)/(1296*S^3*(1 + S^2)^3) + ((-249 - 747*S^2 - 747*S^4 + 847*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)^3)) + ((-5 - 15*S^2 - 15*S^4 - 2*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3}, -S^2])/(12*S^3*(1 + S^2)^3) + ((123 + 369*S^2 + 369*S^4 - 158*S^6 - 27*S^8 - 27*S^10 - 9*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (S^3*(26 + 57*S^2 + 57*S^4 + 19*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((4*(-8 - 41*S^2 + 41*S^4 + 8*S^6))/S^3 - (4*Pi^2*(-142 + 20*S^2 + 533*S^4 - 1607*S^6 + 1132*S^8 + 721*S^10 + 221*S^12))/(9*S^3*(1 + S^2)^3) + (32*S^3*(-289 + 438*S^2 + 438*S^4 + 146*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((20651 + 21569*S^2 - 21569*S^4 - 20651*S^6)/(108*S^3) + (Pi^2*(1107 + 2828*S^2 + 12142*S^4 - 646*S^6 - 4835*S^8 - 1430*S^10 - 702*S^12))/(18*S^3*(1 + S^2)^3) - (2*Pi^4*(-393 - 1179*S^2 - 1179*S^4 + 432*S^6 + 444*S^8 + 444*S^10 + 148*S^12))/(27*S^3*(1 + S^2)^3) - (16*(125 + 375*S^2 + 375*S^4 - 578*S^6 + 501*S^8 + 501*S^10 + 167*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-83 - 455*S^2 - 923*S^4 + 1607*S^6 - 742*S^8 - 286*S^10 + 4*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4}, -S^2]*((-541 + 3531*S^2 + 6933*S^4 + 6821*S^6)/(36*S^3) + (Pi^2*(161 + 747*S^2 + 990*S^4 - 5132*S^6 + 13638*S^8 + 7437*S^10 + 1511*S^12))/(54*S^3*(1 + S^2)^3) + (16*(-29 - 87*S^2 - 87*S^4 + 104*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 16*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(27*S^3) + (Pi^4*(-4460 - 13380*S^2 - 13380*S^4 + 23717*S^6 - 6639*S^8 - 6639*S^10 - 2213*S^12))/(405*S^3*(1 + S^2)^3) + (Pi^2*(-1619 - 6333*S^2 - 36216*S^4 + 15548*S^6 - 27729*S^8 - 5235*S^10 - 1016*S^12))/(81*S^3*(1 + S^2)^3) + ((2*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(3*S^3*(1 + S^2)^2) + (4*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (16*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + (4*(283 + 1611*S^2 + 3147*S^4 - 6262*S^6 + 7197*S^8 + 2961*S^10 + 283*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(47 + 141*S^2 + 141*S^4 - 554*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (600*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (16*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (400*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (20*(17 + 147*S^2 + 345*S^4 - 1046*S^6 + 1155*S^8 + 417*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*((-10*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) - (5*Pi^2*(109 + 1239*S^2 + 3057*S^4 - 3742*S^6 + 2247*S^8 + 969*S^10 + 109*S^12))/(54*S^3*(1 + S^2)^3) + (150*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (100*(5 + 15*S^2 + 15*S^4 - 65*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (100*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (20*(5 + 15*S^2 + 15*S^4 - 87*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((953 - 24388*S^2 - 49386*S^4 - 24388*S^6 + 953*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(-383 - 6015*S^2 - 14313*S^4 + 29879*S^6 - 16746*S^8 - 7926*S^10 - 1148*S^12))/(108*S^3*(1 + S^2)^3) + ((7 + 21*S^2 + 21*S^4 - 1426*S^6 + 1869*S^8 + 1869*S^10 + 623*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (616*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(-6 - 18*S^2 - 18*S^4 - 131*S^6 + 213*S^8 + 213*S^10 + 71*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((1779 + 4045*S^2 + 61463*S^4 + 130705*S^6 + 63732*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(35 + 1869*S^2 + 6975*S^4 - 524*S^6 + 25251*S^8 + 6543*S^10 + 2027*S^12))/(54*S^3*(1 + S^2)^3) + (Pi^4*(-265 - 795*S^2 - 795*S^4 - 10762*S^6 + 16485*S^8 + 16485*S^10 + 5495*S^12))/(540*S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 30*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-259 - 1259*S^2 - 2396*S^4 + 3214*S^6 - 934*S^8 - 223*S^10 + 101*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-69 - 207*S^2 - 207*S^4 - 1182*S^6 + 1893*S^8 + 1893*S^10 + 631*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-29 - 87*S^2 - 87*S^4 - 578*S^6 + 963*S^8 + 963*S^10 + 321*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-34 + 9*S^2 + 144*S^4 - 1094*S^6 + 1572*S^8 + 987*S^10 + 236*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((-641 - 570*S^2 - 2046*S^4 - 929*S^6)/(9*S^3) + (Pi^2*(-1277 - 1956*S^2 - 507*S^4 - 6991*S^6 + 3168*S^8 + 2331*S^10 + 928*S^12))/(27*S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 602*S^6 + 879*S^8 + 879*S^10 + 293*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^3*((Pi^4*S^3*(19753 + 51*S^2 + 51*S^4 + 17*S^6))/(3240*(1 + S^2)^3) + (16372 + 10379*S^2 + 64954*S^4 + 63171*S^6)/(3888*S*(1 + S^2)) + (Pi^2*(344 - 3524*S^2 + 8481*S^4 + 2741*S^6 + 3135*S^8 + 807*S^10))/(216*S*(1 + S^2)^3) - (2*(16 + 882*S^2 + 2544*S^4 - 2854*S^6 + 789*S^8 + 297*S^10 + 16*S^12)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^3) - (5*(56 + 168*S^2 + 168*S^4 - 263*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)^3) + ((Pi^2*(1 + 3*S^2 + 3*S^4 + 605*S^6 - 126*S^8 - 126*S^10 - 42*S^12))/(27*S^3*(1 + S^2)^3) + (24 + 454*S^2 - 5633*S^4 + 8460*S^6 - 2768*S^8 + 850*S^10 + 141*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((4 + 12*S^2 + 12*S^4 + 635*S^6 - 243*S^8 - 243*S^10 - 81*S^12)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((Pi^2*(-555 - 1665*S^2 - 1665*S^4 + 2348*S^6 - 243*S^8 - 243*S^10 - 81*S^12))/(54*S^3*(1 + S^2)^3) + (-184 + 345*S^2 - 13713*S^4 + 11692*S^6 - 4182*S^8 + 129*S^10 + 5*S^12)/(81*S^3*(1 + S^2)^3) - (2*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((97 + 108*S^2 - 333*S^4 + 410*S^6 + 393*S^8 + 438*S^10 + 151*S^12)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 32*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + ((110 + 3489*S^2 + 10644*S^4 - 5792*S^6 + 540*S^8 - 63*S^10 - 160*S^12)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^3) + (2*(-2 - 6*S^2 - 6*S^4 - 663*S^6 + 261*S^8 + 261*S^10 + 87*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-2 - 6*S^2 - 6*S^4 - 669*S^6 + 249*S^8 + 249*S^10 + 83*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-12 - 30*S^2 + 138*S^4 + 512*S^6 + 377*S^8 + 105*S^10)*Zeta[3])/(9*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((2347 + 919*S^2 - 633*S^4 + 6985*S^6 + 5542*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(56 - 933*S^2 - 3126*S^4 + 3590*S^6 - 282*S^8 + 15*S^10 + 56*S^12))/(36*S^3*(1 + S^2)^3) + ((7 - 507*S^2 - 1575*S^4 + 1622*S^6 - 459*S^8 - 135*S^10 + 7*S^12)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 + 5*S^6)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-6 - 18*S^2 - 18*S^4 - 17*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3))) + ((8*Pi^2*S^3*(-125 + 336*S^2 + 336*S^4 + 112*S^6))/(9*(1 + S^2)^3) + (-326 + 67*S^2 - 3105*S^4 + 18919*S^6 + 3355*S^8 + 1818*S^10)/(9*S*(1 + S^2)^3))*Zeta[5] + HPL[{0}, S^2]^2*((Pi^2*(-6440 - 8338*S^2 + 4615*S^4 + 5649*S^6))/(648*S*(1 + S^2)) + (-465274 - 634331*S^2 + 356552*S^4 + 401193*S^6)/(7776*S*(1 + S^2)) + (Pi^4*(-5364 - 13410*S^2 + 31460*S^4 + 492*S^6 + 929*S^8 + 403*S^10))/(720*S*(1 + S^2)^3) - (5*(23 + 273*S^2 + 678*S^4 - 674*S^6 + 273*S^8 + 138*S^10 + 23*S^12)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^3) - (2*(23 + 69*S^2 + 69*S^4 - 109*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^3) + ((91 - 1569*S^2 - 4323*S^4 + 10595*S^6 - 6756*S^8 - 3480*S^10 - 674*S^12)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-1663 - 6096*S^2 - 32427*S^4 + 10396*S^6 - 15453*S^8 - 3900*S^10 - 457*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(-619 - 1857*S^2 - 1857*S^4 + 2671*S^6 - 390*S^8 - 390*S^10 - 130*S^12))/(27*S^3*(1 + S^2)^3) - (2*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((Pi^2*(-29 - 87*S^2 - 87*S^4 - 74*S^6 + 201*S^8 + 201*S^10 + 67*S^12))/(18*S^3*(1 + S^2)^3) + (-43 + 150*S^2 + 102*S^4 + 394*S^6 + 2427*S^8 + 1056*S^10 + 314*S^12)/(18*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((53 - 105*S^2 - 600*S^4 + 160*S^6 + 1608*S^8 + 897*S^10 + 179*S^12)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^3) + ((-12 - 36*S^2 - 36*S^4 + 5*S^6 + 159*S^8 + 159*S^10 + 53*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((562 + 1572*S^2 + 6825*S^4 - 646*S^6 + 482*S^8 - 174*S^10 - 157*S^12)/(6*S^3*(1 + S^2)^3) - (2*Pi^2*(-288 - 864*S^2 - 864*S^4 + 447*S^6 + 84*S^8 + 84*S^10 + 28*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((-242 + 1197*S^2 + 4068*S^4 - 9637*S^6 + 5403*S^8 + 2874*S^10 + 613*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-21 - 63*S^2 - 63*S^4 + 88*S^6 - 249*S^8 - 249*S^10 - 83*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(3 + 9*S^2 + 9*S^4 - 164*S^6 + 411*S^8 + 411*S^10 + 137*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-59 + 475*S^2 + 1456*S^4 - 3214*S^6 + 1874*S^8 + 1007*S^10 + 217*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(79 + 237*S^2 + 237*S^4 - 158*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-481 - 1443*S^2 - 1443*S^4 + 914*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-165 - 495*S^2 - 495*S^4 + 289*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((76*Pi^2*S^5*(3 + 3*S^2 + S^4))/(9*(1 + S^2)^3) + (152 + 518*S^2 + 741*S^4 + 3689*S^6 + 1691*S^8 + 537*S^10)/(18*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-3029 - 27062*S^2 - 24693*S^4 + 2674*S^6 + 3982*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(103 - 859*S^2 - 2641*S^4 + 5663*S^6 - 1920*S^8 - 981*S^10 - 203*S^12))/(36*S^3*(1 + S^2)^3) + ((3 + 9*S^2 + 9*S^4 - 16*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^3) + (8*(79 + 237*S^2 + 237*S^4 - 158*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*S^3*(-28 + 45*S^2 + 45*S^4 + 15*S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((-14471 - 39524*S^2 - 37011*S^4 - 7502*S^6 + 568*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(-236 - 4365*S^2 - 11622*S^4 + 11402*S^6 - 2820*S^8 - 1431*S^10 - 236*S^12))/(36*S^3*(1 + S^2)^3) + ((-175 - 2487*S^2 - 6423*S^4 + 5314*S^6 - 1779*S^8 - 939*S^10 - 175*S^12)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)^3) + (2*(-7 - 21*S^2 - 21*S^4 - 78*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(4 + 12*S^2 + 12*S^4 - 139*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((-201071 - 515312*S^2 - 390054*S^4 + 89848*S^6 + 80125*S^8)/(3888*S^3*(1 + S^2)) + (Pi^4*(-8046 - 24138*S^2 - 24138*S^4 + 31091*S^6 - 1209*S^8 - 1209*S^10 - 403*S^12))/(1080*S^3*(1 + S^2)^3) + (Pi^2*(-3625 - 10230*S^2 - 76074*S^4 + 36697*S^6 - 19761*S^8 - 2337*S^10 + 470*S^12))/(324*S^3*(1 + S^2)^3) + ((Pi^2*(-574 - 1722*S^2 - 1722*S^4 + 2195*S^6 - 177*S^8 - 177*S^10 - 59*S^12))/(18*S^3*(1 + S^2)^3) + (-5303 - 16806*S^2 - 90777*S^4 + 22802*S^6 - 28803*S^8 - 5340*S^10 + 259*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((-154 - 462*S^2 - 462*S^4 + 741*S^6 - 183*S^8 - 183*S^10 - 61*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((109 + 186*S^2 - 111*S^4 - 880*S^6 + 1833*S^8 + 834*S^10 + 109*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-33 - 99*S^2 - 99*S^4 - 24*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + ((175 + 2487*S^2 + 6423*S^4 - 5314*S^6 + 1779*S^8 + 939*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(161 + 483*S^2 + 483*S^4 - 663*S^6 + 96*S^8 + 96*S^10 + 32*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((76 + 321*S^2 + 528*S^4 - 1486*S^6 + 2310*S^8 + 915*S^10 + 76*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + (52*S^5*(3 + 3*S^2 + S^4)*Zeta[5])/(1 + S^2)^3) + HPL[{2}, -S^2]*((-1651 - 1731*S^2 + 1731*S^4 + 1651*S^6)/(16*S^3) + (Pi^2*(-5621 - 42938*S^2 - 24693*S^4 + 18550*S^6 + 6574*S^8))/(1944*S^3*(1 + S^2)) + (Pi^4*(2381 - 6165*S^2 - 24489*S^4 + 53095*S^6 - 21784*S^8 - 13573*S^10 - 3991*S^12))/(1080*S^3*(1 + S^2)^3) + ((-161 - 257*S^2 + 688*S^4 - 646*S^6 + 6619*S^8 + 1655*S^10 + 566*S^12)/(3*S^3*(1 + S^2)^3) + (Pi^2*(-49 - 147*S^2 - 147*S^4 - 1204*S^6 + 2043*S^8 + 2043*S^10 + 681*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-91 + 375*S^2 + 1302*S^4 - 2684*S^6 + 9114*S^8 + 5163*S^10 + 1169*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(14 + 42*S^2 + 42*S^4 - 195*S^6 + 477*S^8 + 477*S^10 + 159*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*Pi^2*(152 + 456*S^2 + 456*S^4 - 447*S^6 + 225*S^8 + 225*S^10 + 75*S^12))/(9*S^3*(1 + S^2)^3) + (405 + 1398*S^2 + 7307*S^4 - 1292*S^6 + 7307*S^8 + 1398*S^10 + 405*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(263 + 1881*S^2 + 3981*S^4 - 6428*S^6 + 2679*S^8 + 1083*S^10 + 53*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-25 - 75*S^2 - 75*S^4 - 2594*S^6 + 3621*S^8 + 3621*S^10 + 1207*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-95 - 285*S^2 - 285*S^4 - 3862*S^6 + 5763*S^8 + 5763*S^10 + 1921*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(79 + 741*S^2 + 1665*S^4 - 3214*S^6 + 1665*S^8 + 741*S^10 + 79*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2464*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (16*(-433 - 1299*S^2 - 1299*S^4 + 578*S^6 + 423*S^8 + 423*S^10 + 141*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*S^3*(-317 + 483*S^2 + 483*S^4 + 161*S^6))/(9*(1 + S^2)^3) + (17 + 316*S^2 + 1508*S^4 - 646*S^6 + 5799*S^8 + 1082*S^10 + 388*S^12)/(3*S^3*(1 + S^2)^3))*Zeta[3] + (4*S^3*(-493 + 945*S^2 + 945*S^4 + 315*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]*(((1 + S^2)*(104305 - 46054*S^2 + 104305*S^4))/(972*S^3) + (Pi^2*(-208091 - 675584*S^2 - 696558*S^4 - 70424*S^6 + 73105*S^8))/(11664*S^3*(1 + S^2)) + (Pi^6*(-201706 - 605118*S^2 - 605118*S^4 + 958255*S^6 - 179157*S^8 - 179157*S^10 - 59719*S^12))/(68040*S^3*(1 + S^2)^3) + (Pi^4*(-57670 - 197979*S^2 - 1196718*S^4 + 563503*S^6 - 659832*S^8 - 103578*S^10 - 11914*S^12))/(9720*S^3*(1 + S^2)^3) + ((-2522 - 11073*S^2 - 59790*S^4 + 22802*S^6 - 59790*S^8 - 11073*S^10 - 2522*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(-350 - 1050*S^2 - 1050*S^4 + 2089*S^6 - 771*S^8 - 771*S^10 - 257*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (62*(-1 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) - (2*(37 + 111*S^2 + 111*S^4 - 238*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(61 + 183*S^2 + 183*S^4 - 1132*S^6 + 837*S^8 + 837*S^10 + 279*S^12))/(9*S^3*(1 + S^2)^3) + (249 + 1714*S^2 + 4217*S^4 + 1660*S^6 + 6643*S^8 + 2546*S^10 + 571*S^12)/(3*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(713 + 1893*S^2 + 1425*S^4 - 2750*S^6 + 8877*S^8 + 4377*S^10 + 713*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-194 - 582*S^2 - 582*S^4 - 127*S^6 + 849*S^8 + 849*S^10 + 283*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-8*Pi^2*(-116 - 348*S^2 - 348*S^4 + 193*S^6 + 183*S^8 + 183*S^10 + 61*S^12))/(9*S^3*(1 + S^2)^3) - (2*(4 + 699*S^2 - 114*S^4 + 830*S^6 + 5544*S^8 + 1431*S^10 + 406*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(247 + 1465*S^2 + 2925*S^4 - 5946*S^6 + 6705*S^8 + 2725*S^10 + 247*S^12)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^3) - (6*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) - (16*(50 + 150*S^2 + 150*S^4 - 551*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(S^3*(1 + S^2)^2) + (8*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (8*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(121 + 1764*S^2 + 4578*S^4 - 4840*S^6 + 2553*S^8 + 1089*S^10 + 121*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (496*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 + (32*(-116 - 348*S^2 - 348*S^4 - 277*S^6 + 597*S^8 + 597*S^10 + 199*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (3600*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (32*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2400*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-7451 - 9824*S^2 + 8349*S^4 + 22198*S^6 + 7588*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(331 + 2526*S^2 + 5703*S^4 - 17176*S^6 + 19635*S^8 + 7170*S^10 + 331*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] - (8*(5 + 15*S^2 + 15*S^4 - 32*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((3445 + 17641*S^2 + 44727*S^4 + 49663*S^6 + 18484*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(958 + 5019*S^2 + 9330*S^4 - 19666*S^6 + 23424*S^8 + 9717*S^10 + 958*S^12))/(27*S^3*(1 + S^2)^3) - (8*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(11 + 33*S^2 + 33*S^4 - 87*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((557 + 629*S^2 - 629*S^4 - 557*S^6)/(3*S^3) + (Pi^2*(175 + 3837*S^2 + 10473*S^4 - 5314*S^6 - 2271*S^8 - 411*S^10 + 175*S^12))/(9*S^3*(1 + S^2)^3) - (32*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-7811 - 8999*S^2 + 8999*S^4 + 7811*S^6)/(54*S^3) + (Pi^4*(-7200 - 21600*S^2 - 21600*S^4 + 21017*S^6 + 3411*S^8 + 3411*S^10 + 1137*S^12))/(540*S^3*(1 + S^2)^3) + (Pi^2*(-8921 - 23394*S^2 - 141699*S^4 + 22802*S^6 + 22119*S^8 + 1248*S^10 + 3877*S^12))/(324*S^3*(1 + S^2)^3) + (2*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(113 + 339*S^2 + 339*S^4 - 734*S^6 + 339*S^8 + 339*S^10 + 113*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(175 + 1137*S^2 + 2373*S^4 - 5314*S^6 + 5829*S^8 + 2289*S^10 + 175*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) - (2*(163 - 84*S^2 - 1407*S^4 + 16904*S^6 - 19551*S^8 - 6132*S^10 + 163*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(27713 - 37886*S^2 + 27713*S^4))/(648*S^3) + (Pi^2*(-21491 - 69224*S^2 - 82371*S^4 - 37202*S^6 - 6452*S^8))/(972*S^3*(1 + S^2)) + (Pi^4*(-5027 - 67896*S^2 - 172821*S^4 + 198704*S^6 - 91929*S^8 - 40932*S^10 - 5027*S^12))/(1080*S^3*(1 + S^2)^3) + ((-175 - 1713*S^2 - 4101*S^4 + 5314*S^6 - 4101*S^8 - 1713*S^10 - 175*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(118 + 354*S^2 + 354*S^4 - 1703*S^6 + 1137*S^8 + 1137*S^10 + 379*S^12))/(9*S^3*(1 + S^2)^3) + (2*(1279 + 8682*S^2 + 29382*S^4 - 7666*S^6 + 54843*S^8 + 11976*S^10 + 3088*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (4*(36 + 155*S^2 + 249*S^4 - 316*S^6 + 465*S^8 + 227*S^10 + 36*S^12)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-5 - 15*S^2 - 15*S^4 - 116*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{5}, -S^2])/(S^3*(1 + S^2)^3) + ((-2*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(S^3*(1 + S^2)^2) - (4*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (8*(18 - 17*S^2 - 159*S^4 - 158*S^6 + 516*S^8 + 208*S^10 + 18*S^12)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^3) - (8*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(178 + 534*S^2 + 534*S^4 - 2299*S^6 + 1479*S^8 + 1479*S^10 + 493*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (1800*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(463 + 1389*S^2 + 1389*S^4 - 2419*S^6 + 714*S^8 + 714*S^10 + 238*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (1200*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((2*Pi^2*(79 + 237*S^2 + 237*S^4 - 1444*S^6 + 1011*S^8 + 1011*S^10 + 337*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-44 + 237*S^2 + 3789*S^4 - 5152*S^6 + 12276*S^8 + 1335*S^10 + 559*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-557 - 629*S^2 + 629*S^4 + 557*S^6)/(6*S^3) + (Pi^2*(-175 - 3837*S^2 - 10473*S^4 + 5314*S^6 + 2271*S^8 + 411*S^10 - 175*S^12))/(18*S^3*(1 + S^2)^3) + (4*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + (8*(11 + 33*S^2 + 33*S^4 - 680*S^6 + 537*S^8 + 537*S^10 + 179*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]*((201563 - 85061*S^2 + 208610*S^4)/(1944*S) - (Pi^6*S^3*(-15415 + 5289*S^2 + 5289*S^4 + 1763*S^6))/(1944*(1 + S^2)^3) + (Pi^2*(10144 - 40705*S^2 + 17758*S^4 + 60831*S^6))/(3888*S*(1 + S^2)) + (Pi^4*(-786 - 65773*S^2 + 102525*S^4 - 46001*S^6 + 14133*S^8 + 2734*S^10))/(2160*S*(1 + S^2)^3) - (14*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^5)/(S^3*(1 + S^2)^3) - (112*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^6)/(9*S^3*(1 + S^2)^3) + ((-10 - 2517*S^2 - 20553*S^4 + 11401*S^6 - 39237*S^8 - 8556*S^10 - 2512*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(4 + 12*S^2 + 12*S^4 + 1983*S^6 - 1419*S^8 - 1419*S^10 - 473*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (2*(-19 - 57*S^2 - 57*S^4 - 607*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*HPL[{2}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*((-5*(35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12))/(6*S^3*(1 + S^2)^3) - (5*Pi^2*(140 + 420*S^2 + 420*S^4 - 851*S^6 + 303*S^8 + 303*S^10 + 101*S^12))/(27*S^3*(1 + S^2)^3) - (10*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + (2*(2 + 6*S^2 + 6*S^4 - 5*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-8*Pi^2*(1 + 3*S^2 + 3*S^4 - 20*S^6 + 12*S^8 + 12*S^10 + 4*S^12))/(9*S^3*(1 + S^2)^3) + (-446 + 1005*S^2 + 1536*S^4 + 10214*S^6 + 8646*S^8 + 9285*S^10 + 2128*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((73 + 165*S^2 + 39*S^4 + 536*S^6 + 47*S^8 + 245*S^10 + 115*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(5 + 15*S^2 + 15*S^4 - 43*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*S^3*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1}, -S^2]^2)/(3*(1 + S^2)^3) + ((2*Pi^2*(-37 - 111*S^2 - 111*S^4 - 1975*S^6 + 1470*S^8 + 1470*S^10 + 490*S^12))/(9*S^3*(1 + S^2)^3) + (-403 - 852*S^2 + 8523*S^4 - 10754*S^6 + 22869*S^8 + 3630*S^10 + 1355*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (4*(-38 - 6*S^2 + 147*S^4 - 733*S^6 + 1332*S^8 + 837*S^10 + 205*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-10 + 97*S^2 + 187*S^4 - 1148*S^6 + 2299*S^8 + 1561*S^10 + 410*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/(3*S^3) + (4*(5 + 15*S^2 + 15*S^4 - 107*S^6 + 72*S^8 + 72*S^10 + 24*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-8*Pi^2*(-16 - 48*S^2 - 48*S^4 - 987*S^6 + 732*S^8 + 732*S^10 + 244*S^12))/(9*S^3*(1 + S^2)^3) - (2*(-517 - 1098*S^2 + 8601*S^4 - 10304*S^6 + 23529*S^8 + 4242*S^10 + 1547*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(349 + 2627*S^2 + 6191*S^4 - 5314*S^6 + 2011*S^8 + 799*S^10 + S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-510 - 3904*S^2 - 9292*S^4 + 7896*S^6 - 2724*S^8 - 975*S^10 + 63*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^3) - (4*(-71 - 213*S^2 - 213*S^4 - 2418*S^6 + 2367*S^8 + 2367*S^10 + 789*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-18 - 54*S^2 - 54*S^4 - 623*S^6 + 597*S^8 + 597*S^10 + 199*S^12)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (40*(-62 - 504*S^2 - 1233*S^4 + 1046*S^6 - 267*S^8 - 60*S^10 + 28*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-35 - 105*S^2 - 105*S^4 - 1312*S^6 + 1209*S^8 + 1209*S^10 + 403*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (160*(-2 - 6*S^2 - 6*S^4 - 87*S^6 + 81*S^8 + 81*S^10 + 27*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((770 + 538*S^2 + 785*S^4)/(9*S) + (Pi^2*(68 + 170*S^2 - 303*S^4 + 1447*S^6 + 913*S^8 + 225*S^10))/(9*S*(1 + S^2)^3))*Zeta[3] - (4*S^3*(-31 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3]^2)/(3*(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((6292 + 14260*S^2 + 8349*S^4 - 1886*S^6 - 6155*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(1040 + 11049*S^2 + 29139*S^4 - 21482*S^6 + 4545*S^8 + 837*S^10 - 580*S^12))/(27*S^3*(1 + S^2)^3) + (8*(-41 - 123*S^2 - 123*S^4 + 134*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((79 + 1720*S^2 + 8556*S^4 + 9784*S^6 + 5029*S^8)/(108*S^3*(1 + S^2)) + (Pi^2*(178 + 327*S^2 - 366*S^4 - 40*S^6 + 2148*S^8 + 1779*S^10 + 538*S^12))/(54*S^3*(1 + S^2)^3) - (4*(39 + 117*S^2 + 117*S^4 - 132*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(18*S^3) + (Pi^2*(-5461 - 18330*S^2 - 174867*S^4 + 108868*S^6 - 136743*S^8 - 19194*S^10 - 4705*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(-8061 - 24183*S^2 - 24183*S^4 + 44045*S^6 - 12366*S^8 - 12366*S^10 - 4122*S^12))/(540*S^3*(1 + S^2)^3) + ((-515 - 1572*S^2 - 16065*S^4 + 10304*S^6 - 16065*S^8 - 1572*S^10 - 515*S^12)/(9*S^3*(1 + S^2)^3) + (Pi^2*(-211 - 633*S^2 - 633*S^4 + 1260*S^6 - 447*S^8 - 447*S^10 - 149*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (8*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (4*(15 + 52*S^2 + 63*S^4 - 14*S^6 + 54*S^8 + 49*S^10 + 15*S^12)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^3) - (2*(17 + 51*S^2 + 51*S^4 - 194*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (20*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(62 + 186*S^2 + 186*S^4 - 435*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^3) - (40*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(18 + 94*S^2 + 174*S^4 - 158*S^6 + 183*S^8 + 97*S^10 + 18*S^12)*Zeta[3])/(S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((-20*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) + (Pi^2*(-347 - 5229*S^2 - 13593*S^4 + 17678*S^6 - 10083*S^8 - 4059*S^10 - 347*S^12))/(27*S^3*(1 + S^2)^3) - (20*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(10 + 30*S^2 + 30*S^4 - 43*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (40*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(40 + 120*S^2 + 120*S^4 - 277*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((49357 + 64930*S^2 + 41775*S^4 - 12470*S^6 + 4096*S^8)/(972*S^3*(1 + S^2)) + (Pi^4*(91 + 273*S^2 + 273*S^4 + 10416*S^6 - 5874*S^8 - 5874*S^10 - 1958*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(541 + 1552*S^2 - 14234*S^4 + 18764*S^6 - 26297*S^8 - 3392*S^10 - 1406*S^12))/(108*S^3*(1 + S^2)^3) + (2*(-16 - 14*S^2 + 31*S^4 - 263*S^6 + 426*S^8 + 267*S^10 + 65*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(349 + 2627*S^2 + 6191*S^4 - 5314*S^6 + 2011*S^8 + 799*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - 1346*S^6 + 1179*S^8 + 1179*S^10 + 393*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*S^3*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^3) + (2*(7 + 270*S^2 + 648*S^4 - 1291*S^6 + 2601*S^8 + 1467*S^10 + 322*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + (2*(54 + 135*S^2 - 231*S^4 + 992*S^6 + 722*S^8 + 198*S^10)*Zeta[5])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*(((1 + S^2)*(27713 - 37886*S^2 + 27713*S^4))/(648*S^3) + (Pi^2*(-4673 - 28781*S^2 - 45993*S^4 - 22715*S^6 - 1478*S^8))/(972*S^3*(1 + S^2)) + (Pi^4*(-757 - 50388*S^2 - 146373*S^4 + 191152*S^6 - 75471*S^8 - 26754*S^10 - 757*S^12))/(1080*S^3*(1 + S^2)^3) + ((-175 - 1713*S^2 - 4101*S^4 + 5314*S^6 - 4101*S^8 - 1713*S^10 - 175*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(4 + 12*S^2 + 12*S^4 - 13*S^6 + 21*S^8 + 21*S^10 + 7*S^12))/(9*S^3*(1 + S^2)^3) + (2*(259 + 2535*S^2 + 5361*S^4 + 4055*S^6 + 6234*S^8 + 3822*S^10 + 718*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(19 + 34*S^2 - 18*S^4 + 150*S^6 - 54*S^8 + 22*S^10 + 19*S^12)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^3) - (4*(6 + 18*S^2 + 18*S^4 - 89*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(3*S^3*(1 + S^2)^3) + (2*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(85 + 1401*S^2 + 3723*S^4 - 5230*S^6 + 3777*S^8 + 1419*S^10 + 85*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(97 + 291*S^2 + 291*S^4 - 610*S^6 + 255*S^8 + 255*S^10 + 85*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (40*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(578 + 1734*S^2 + 1734*S^4 - 4001*S^6 + 1743*S^8 + 1743*S^10 + 581*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (80*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((4*Pi^2*(17 + 51*S^2 + 51*S^4 - 147*S^6 + 90*S^8 + 90*S^10 + 30*S^12))/(9*S^3*(1 + S^2)^3) + (2*(128 + 604*S^2 + 1406*S^4 + 415*S^6 + 1309*S^8 + 461*S^10 + 77*S^12))/(3*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-137 - 12374*S^2 - 16698*S^4 - 12374*S^6 - 137*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-149 - 4341*S^2 - 12225*S^4 + 15326*S^6 - 8877*S^8 - 3225*S^10 - 149*S^12))/(18*S^3*(1 + S^2)^3) + (4*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(41 + 123*S^2 + 123*S^4 - 266*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + (4*(27 + 81*S^2 + 81*S^4 - 195*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3))) + (744*S^3*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[7])/(1 + S^2)^3) + HPL[{2}, -S^2]*((-1367 - 1527*S^2 + 1527*S^4 + 1367*S^6)/(8*S^3) + (Pi^4*(-81160 - 330718*S^2 - 116823*S^4 + 267251*S^6 + 148772*S^8))/(116640*S^3*(1 + S^2)) + (Pi^2*(-341415 - 753428*S^2 + 8006*S^4 + 759004*S^6 + 401193*S^8))/(23328*S^3*(1 + S^2)) + (Pi^6*(11835 - 130771*S^2 - 381631*S^4 + 654129*S^6 - 17510*S^8 - 19187*S^10 - 12105*S^12))/(136080*S^3*(1 + S^2)^3) + ((-205 - 780*S^2 - 1023*S^4 + 922*S^6 - 3051*S^8 - 1800*S^10 - 403*S^12)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^3) + ((Pi^2*(10 + 30*S^2 + 30*S^4 - 33*S^6 + 69*S^8 + 69*S^10 + 23*S^12))/(3*S^3*(1 + S^2)^3) + (127 + 1236*S^2 + 4152*S^4 + 5141*S^6 + 23034*S^8 + 10767*S^10 + 3079*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + (2*(23 + 36*S^4 + 1252*S^6 + 2283*S^8 + 1338*S^10 + 293*S^12)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(-10 - 30*S^2 - 30*S^4 + 6*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{7}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-255 - 382*S^2 - 429*S^4 + 429*S^6 + 382*S^8 + 255*S^10)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + ((769 - 852*S^2 - 13875*S^4 + 5480*S^6 - 59289*S^8 - 13308*S^10 - 4253*S^12)/(27*S^3*(1 + S^2)^3) + (Pi^2*(21 + 63*S^2 + 63*S^4 + 1346*S^6 - 1929*S^8 - 1929*S^10 - 643*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((2160 + 481*S^2 - 23816*S^4 + 9966*S^6 - 125264*S^8 - 30767*S^10 - 9912*S^12)/(18*S^3*(1 + S^2)^3) - (8*Pi^2*(-11 - 33*S^2 - 33*S^4 - 501*S^6 + 759*S^8 + 759*S^10 + 253*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] - (2*(25 + 303*S^2 + 663*S^4 - 1336*S^6 + 2265*S^8 + 1203*S^10 + 241*S^12)*HPL[{4, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-34 - 102*S^2 - 102*S^4 - 19*S^6 + 174*S^8 + 174*S^10 + 58*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + ((29 - 460*S^2 - 1315*S^4 + 2716*S^6 - 7605*S^8 - 4152*S^10 - 877*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-98 - 294*S^2 - 294*S^4 - 24*S^6 + 465*S^8 + 465*S^10 + 155*S^12)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-224 - 672*S^2 - 672*S^4 + 71*S^6 + 690*S^8 + 690*S^10 + 230*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*(-279 - 413*S^2 - 2110*S^4 + 2110*S^6 + 413*S^8 + 279*S^10))/(3*S^3*(1 + S^2)^2) + (8*Pi^2*(-154 - 462*S^2 - 462*S^4 + 147*S^6 + 258*S^8 + 258*S^10 + 86*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((-2*(-676 - 1819*S^2 - 8257*S^4 + 646*S^6 + 950*S^8 + 421*S^10 + 271*S^12))/(3*S^3*(1 + S^2)^3) - (2*Pi^2*(-1799 - 5397*S^2 - 5397*S^4 + 2968*S^6 + 1053*S^8 + 1053*S^10 + 351*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + (2*(133 + 753*S^2 + 1464*S^4 - 1336*S^6 + 1464*S^8 + 753*S^10 + 133*S^12)*HPL[{3, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(149 + 1337*S^2 + 2972*S^4 - 5744*S^6 + 2972*S^8 + 1337*S^10 + 149*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-35 - 105*S^2 - 105*S^4 - 1176*S^6 + 1737*S^8 + 1737*S^10 + 579*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-51 - 153*S^2 - 153*S^4 - 1885*S^6 + 2742*S^8 + 2742*S^10 + 914*S^12)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(1831 + 13917*S^2 + 29838*S^4 - 53020*S^6 + 22026*S^8 + 9129*S^10 + 571*S^12)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-97 - 291*S^2 - 291*S^4 - 3770*S^6 + 5469*S^8 + 5469*S^10 + 1823*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-331 - 993*S^2 - 993*S^4 - 11552*S^6 + 16809*S^8 + 16809*S^10 + 5603*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-688 - 2064*S^2 - 2064*S^4 - 23541*S^6 + 34497*S^8 + 34497*S^10 + 11499*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((16*Pi^2*(152 + 456*S^2 + 456*S^4 - 447*S^6 + 225*S^8 + 225*S^10 + 75*S^12))/(9*S^3*(1 + S^2)^3) + (2*(405 + 1398*S^2 + 7307*S^4 - 1292*S^6 + 7307*S^8 + 1398*S^10 + 405*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] + (64*(34 + 102*S^2 + 102*S^4 - 147*S^6 + 102*S^8 + 102*S^10 + 34*S^12)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-2797 - 5763*S^2 - 5751*S^4 - 6428*S^6 + 12411*S^8 + 8727*S^10 + 3113*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(1657 + 4971*S^2 + 4971*S^4 - 4462*S^6 + 1275*S^8 + 1275*S^10 + 425*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(1657 + 4971*S^2 + 4971*S^4 - 4462*S^6 + 1275*S^8 + 1275*S^10 + 425*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(3289 + 9867*S^2 + 9867*S^4 - 11518*S^6 + 6171*S^8 + 6171*S^10 + 2057*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(4991 + 14973*S^2 + 14973*S^4 - 17306*S^6 + 8925*S^8 + 8925*S^10 + 2975*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(79 + 741*S^2 + 1665*S^4 - 3214*S^6 + 1665*S^8 + 741*S^10 + 79*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4928*(-1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (4928*(-1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (32*(-799 - 2397*S^2 - 2397*S^4 - 578*S^6 + 3273*S^8 + 3273*S^10 + 1091*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(73 + 219*S^2 + 219*S^4 - 289*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^4*S^3*(-2207 + 3528*S^2 + 3528*S^4 + 1176*S^6))/(270*(1 + S^2)^3) + (-735 - 6667*S^2 + 2503*S^4 + 25793*S^6 + 13470*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(350 + 4302*S^2 + 16749*S^4 - 3989*S^6 + 60543*S^8 + 12807*S^10 + 4310*S^12))/(324*S^3*(1 + S^2)^3))*Zeta[3] + ((5 - 8*S^2 - 13*S^4 + 32*S^6 + 40*S^8 + 5*S^10)*Zeta[3]^2)/(9*S^3*(1 + S^2)^2) + HPL[{4}, -S^2]*((-3631 + 8465*S^2 + 32040*S^4 + 35501*S^6 + 19445*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(85 + 543*S^2 + 1002*S^4 - 694*S^6 + 5136*S^8 + 3003*S^10 + 697*S^12))/(54*S^3*(1 + S^2)^3) - (4*(55 + 165*S^2 + 165*S^4 - 250*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-7 - 21*S^2 - 21*S^4 - 16*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-15495 - 34418*S^2 + 5006*S^4 + 72670*S^6 + 40965*S^8)/(648*S^3*(1 + S^2)) + (Pi^4*(-5 - 15*S^2 - 15*S^4 - 1037*S^6 + 1887*S^8 + 1887*S^10 + 629*S^12))/(135*S^3*(1 + S^2)^3) + (Pi^2*(-200 - 226*S^2 + 1313*S^4 - 826*S^6 + 10772*S^8 + 2900*S^10 + 979*S^12))/(54*S^3*(1 + S^2)^3) - (4*(-17 - 51*S^2 - 51*S^4 - 26*S^6 + 108*S^8 + 108*S^10 + 36*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(297 + 1453*S^2 + 2719*S^4 - 3471*S^6 + 1908*S^8 + 816*S^10 + 42*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-5 - 15*S^2 - 15*S^4 - 709*S^6 + 972*S^8 + 972*S^10 + 324*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(7 + 21*S^2 + 21*S^4 - 1426*S^6 + 1869*S^8 + 1869*S^10 + 623*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-43 - 51*S^2 + 57*S^4 - 401*S^6 + 396*S^8 + 243*S^10 + 65*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((953 - 24388*S^2 - 49386*S^4 - 24388*S^6 + 953*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-383 - 6015*S^2 - 14313*S^4 + 29879*S^6 - 16746*S^8 - 7926*S^10 - 1148*S^12))/(27*S^3*(1 + S^2)^3) + (32*(-6 - 18*S^2 - 18*S^4 - 131*S^6 + 213*S^8 + 213*S^10 + 71*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((12735 + 19126*S^2 + 5006*S^4 + 19126*S^6 + 12735*S^8)/(324*S^3*(1 + S^2)) + (Pi^4*(3684 + 11052*S^2 + 11052*S^4 - 8559*S^6 + 3180*S^8 + 3180*S^10 + 1060*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(2863 + 9192*S^2 + 42267*S^4 - 5488*S^6 + 27129*S^8 + 5040*S^10 + 1189*S^12))/(108*S^3*(1 + S^2)^3) + (4*(-265 - 795*S^2 - 795*S^4 - 250*S^6 + 1053*S^8 + 1053*S^10 + 351*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2464*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(-565 - 2877*S^2 - 5667*S^4 + 8689*S^6 - 3234*S^8 - 966*S^10 + 200*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((10585 + 37906*S^2 + 49386*S^4 + 10870*S^6 - 12491*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(313 + 3495*S^2 + 8013*S^4 - 15043*S^6 + 7230*S^8 + 3207*S^10 + 367*S^12))/(27*S^3*(1 + S^2)^3) - (4*(-29 - 87*S^2 - 87*S^4 - 520*S^6 + 879*S^8 + 879*S^10 + 293*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((2*Pi^2*S^3*(-272 + 507*S^2 + 507*S^4 + 169*S^6))/(9*(1 + S^2)^3) + (1384 + 5982*S^2 + 11409*S^4 - 4657*S^6 + 51081*S^8 + 7971*S^10 + 3598*S^12)/(54*S^3*(1 + S^2)^3))*Zeta[5] + (4*S^3*(-73 + 204*S^2 + 204*S^4 + 68*S^6)*Zeta[7])/(1 + S^2)^3) + HPL[{1}, -S^2]*((5*(1 + S^2)*(3458815 - 640642*S^2 + 3458815*S^4))/(69984*S^3) + (Pi^4*(-1289744 - 3072533*S^2 - 1874739*S^4 + 916645*S^6 + 650899*S^8))/(349920*S^3*(1 + S^2)) + (Pi^2*(-1087286 - 2900603*S^2 - 533469*S^4 + 4125535*S^6 + 2285815*S^8))/(104976*S^3*(1 + S^2)) + (Pi^8*(-655944 - 1967832*S^2 - 1967832*S^4 + 2526341*S^6 - 42984*S^8 - 42984*S^10 - 14328*S^12))/(2041200*S^3*(1 + S^2)^3) + (Pi^6*(-551525 - 1546947*S^2 - 8534076*S^4 + 5030888*S^6 - 1888107*S^8 + 440415*S^10 + 261904*S^12))/(816480*S^3*(1 + S^2)^3) + ((-63 - 31*S^2 - 1084*S^4 + 1084*S^6 + 31*S^8 + 63*S^10)/(18*S^3*(1 + S^2)^2) + (Pi^2*(-121 - 363*S^2 - 363*S^4 + 334*S^6 + 75*S^8 + 75*S^10 + 25*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^3 - (2*(24 + 72*S^2 + 72*S^4 - 167*S^6 + 72*S^8 + 72*S^10 + 24*S^12)*HPL[{2}, -S^2]^4)/(9*S^3*(1 + S^2)^3) + ((-1033 - 6792*S^2 - 20571*S^4 - 8204*S^6 - 23667*S^8 - 9852*S^10 - 2041*S^12)/(108*S^3*(1 + S^2)^3) + (Pi^2*(-13 - 39*S^2 - 39*S^4 + 107*S^6 - 72*S^8 - 72*S^10 - 24*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2]^2 + (2*(-21 - 63*S^2 - 63*S^4 + 37*S^6 + 90*S^8 + 90*S^10 + 30*S^12)*HPL[{4}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-178 - 534*S^2 - 534*S^4 - 3*S^6 + 735*S^8 + 735*S^10 + 245*S^12))/(9*S^3*(1 + S^2)^3) + (-460 + 2508*S^2 + 4545*S^4 + 13504*S^6 + 22941*S^8 + 12948*S^10 + 3230*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{6}, -S^2] + ((521 + 1032*S^2 - 39*S^4 + 1504*S^6 + 3183*S^8 + 2106*S^10 + 521*S^12)*HPL[{7}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-149 - 447*S^2 - 447*S^4 + 230*S^6 + 474*S^8 + 474*S^10 + 158*S^12)*HPL[{8}, -S^2])/(S^3*(1 + S^2)^3) + ((2*Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2089*S^6 + 771*S^8 + 771*S^10 + 257*S^12))/(9*S^3*(1 + S^2)^3) + (2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2]^2 - (4*(233 + 699*S^2 + 699*S^4 - 1614*S^6 + 699*S^8 + 699*S^10 + 233*S^12)*HPL[{3, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-19 - 57*S^2 - 57*S^4 + 126*S^6 - 57*S^8 - 57*S^10 - 19*S^12))/(3*S^3*(1 + S^2)^3) - (4*(98 + 480*S^2 + 1281*S^4 + 268*S^6 + 1218*S^8 + 408*S^10 + 71*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 2}, -S^2] + ((389 + 1290*S^2 + 1533*S^4 - 1724*S^6 + 3315*S^8 + 1884*S^10 + 389*S^12)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-4*Pi^2*(32 + 96*S^2 + 96*S^4 - 545*S^6 + 423*S^8 + 423*S^10 + 141*S^12))/(9*S^3*(1 + S^2)^3) - (2*(913 + 6195*S^2 + 14760*S^4 + 7340*S^6 + 22146*S^8 + 8943*S^10 + 1939*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{5, 1}, -S^2] + ((116 + 369*S^2 + 408*S^4 - 434*S^6 + 876*S^8 + 525*S^10 + 116*S^12)*HPL[{5, 2}, -S^2])/(S^3*(1 + S^2)^3) + (8*S^3*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{5, 3}, -S^2])/(1 + S^2)^3 + ((-1343 - 822*S^2 + 5487*S^4 - 6952*S^6 - 17031*S^8 - 8328*S^10 - 1343*S^12)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (20*S^3*(-2 + 3*S^2 + 3*S^4 + S^6)*HPL[{6, 2}, -S^2])/(1 + S^2)^3 - (4*(-315 - 945*S^2 - 945*S^4 + 335*S^6 + 1026*S^8 + 1026*S^10 + 342*S^12)*HPL[{7, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) - (2*(-3 + S^2 - S^4 + 3*S^6)*HPL[{3, 1, 2}, -S^2])/S^3 + ((2*(-117 - 47*S^2 - 2162*S^4 + 2162*S^6 + 47*S^8 + 117*S^10))/(3*S^3*(1 + S^2)^2) + (8*Pi^2*(-121 - 363*S^2 - 363*S^4 + 334*S^6 + 75*S^8 + 75*S^10 + 25*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 2, 1}, -S^2] + (2*(1327 + 8016*S^2 + 16134*S^4 - 32662*S^6 + 36222*S^8 + 14712*S^10 + 1327*S^12)*HPL[{3, 2, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(1027 + 6216*S^2 + 12525*S^4 - 24964*S^6 + 27591*S^8 + 11238*S^10 + 1027*S^12)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (28*(5 + 15*S^2 + 15*S^4 - 53*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{3, 3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-1391 - 4173*S^2 - 4173*S^4 + 2876*S^6 + 1737*S^8 + 1737*S^10 + 579*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-129 + 1150*S^2 - 2473*S^4 + 1660*S^6 + 13333*S^8 + 3110*S^10 + 949*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{4, 1, 1}, -S^2] + (2*(3967 + 24099*S^2 + 48660*S^4 - 98464*S^6 + 108924*S^8 + 44187*S^10 + 3967*S^12)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(61 + 183*S^2 + 183*S^4 - 613*S^6 + 498*S^8 + 498*S^10 + 166*S^12)*HPL[{4, 1, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(12715 + 76911*S^2 + 154932*S^4 - 304096*S^6 + 335724*S^8 + 137175*S^10 + 12715*S^12)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(4 + 12*S^2 + 12*S^4 - 121*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*HPL[{4, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(257 + 771*S^2 + 771*S^4 - 2129*S^6 + 1410*S^8 + 1410*S^10 + 470*S^12)*HPL[{4, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(13835 + 81111*S^2 + 160833*S^4 - 311198*S^6 + 349077*S^8 + 143859*S^10 + 13835*S^12)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(89 + 267*S^2 + 267*S^4 - 629*S^6 + 366*S^8 + 366*S^10 + 122*S^12)*HPL[{5, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(509 + 1527*S^2 + 1527*S^4 - 4379*S^6 + 2976*S^8 + 2976*S^10 + 992*S^12)*HPL[{5, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(2326 + 6978*S^2 + 6978*S^4 - 22627*S^6 + 16509*S^8 + 16509*S^10 + 5503*S^12)*HPL[{6, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (1488*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + ((-16*Pi^2*(-116 - 348*S^2 - 348*S^4 + 193*S^6 + 183*S^8 + 183*S^10 + 61*S^12))/(9*S^3*(1 + S^2)^3) - (4*(4 + 699*S^2 - 114*S^4 + 830*S^6 + 5544*S^8 + 1431*S^10 + 406*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1}, -S^2] - (8*(175 + 2829*S^2 + 7449*S^4 - 5314*S^6 + 753*S^8 + 597*S^10 + 175*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(175 + 2829*S^2 + 7449*S^4 - 5314*S^6 + 753*S^8 + 597*S^10 + 175*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{3, 1, 2, 2}, -S^2])/(S^3*(1 + S^2)^3) - (8*(175 + 4503*S^2 + 12471*S^4 - 5314*S^6 - 4269*S^8 - 1077*S^10 + 175*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{3, 2, 1, 2}, -S^2])/(S^3*(1 + S^2)^3) - (4*(-325 - 975*S^2 - 975*S^4 - 242*S^6 + 1257*S^8 + 1257*S^10 + 419*S^12)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-91 + 95*S^6)*HPL[{3, 3, 1, 1}, -S^2])/S^3 - (8*(247 + 4813*S^2 + 12969*S^4 - 5946*S^6 - 3339*S^8 - 623*S^10 + 247*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (12*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{4, 1, 1, 2}, -S^2])/(S^3*(1 + S^2)^3) - (4*(-325 - 975*S^2 - 975*S^4 - 242*S^6 + 1257*S^8 + 1257*S^10 + 419*S^12)*HPL[{4, 1, 2, 1}, -S^2])/(S^3*(1 + S^2)^3) - (12*(-351 - 1053*S^2 - 1053*S^4 - 70*S^6 + 1179*S^8 + 1179*S^10 + 393*S^12)*HPL[{4, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (32*(-769 - 2307*S^2 - 2307*S^4 - 515*S^6 + 2922*S^8 + 2922*S^10 + 974*S^12)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(S^3*(1 + S^2)^2) + (16*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1, 1}, -S^2] + (16*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (992*(-1 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^3 - (2976*(-1 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 + (32*(193 + 1696*S^2 + 3942*S^4 - 5472*S^6 + 4617*S^8 + 1921*S^10 + 193*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (5952*(-1 + S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 + (9920*(-1 + S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^3 + (11904*(-1 + S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^3 + (24800*(-1 + S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^3 + (64*(-3464 - 10392*S^2 - 10392*S^4 - 277*S^6 + 10641*S^8 + 10641*S^10 + 3547*S^12)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (7200*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (64*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4800*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-223 - 789*S^2 - 2355*S^4 - 239*S^6 - 1599*S^8 - 222*S^10 - 97*S^12)/(27*S^3*(1 + S^2)^3) + (Pi^2*(-40 - 120*S^2 - 120*S^4 + 95*S^6 + 33*S^8 + 33*S^10 + 11*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3]^2 + HPL[{3, 2}, -S^2]*((263 - 6220*S^2 - 22020*S^4 - 24328*S^6 - 8143*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(-376 - 2445*S^2 - 5100*S^4 + 11242*S^6 - 12192*S^8 - 4809*S^10 - 376*S^12))/(18*S^3*(1 + S^2)^3) + (8*(-14 - 42*S^2 - 42*S^4 + 63*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4, 1}, -S^2]*((-8413 - 54814*S^2 - 148632*S^4 - 165394*S^6 - 60571*S^8)/(108*S^3*(1 + S^2)) + (Pi^2*(-268 - 1522*S^2 - 2967*S^4 + 6262*S^6 - 7167*S^8 - 2922*S^10 - 268*S^12))/(3*S^3*(1 + S^2)^3) - (4*(87 + 261*S^2 + 261*S^4 - 478*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{5}, -S^2]*((18175 + 45979*S^2 + 103083*S^4 + 161989*S^6 + 75046*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(860 + 1929*S^2 + 660*S^4 - 2618*S^6 + 11244*S^8 + 5457*S^10 + 860*S^12))/(54*S^3*(1 + S^2)^3) - (4*(17 + 51*S^2 + 51*S^4 - 286*S^6 + 195*S^8 + 195*S^10 + 65*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-15 - 45*S^2 - 45*S^4 + 38*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4}, -S^2]*((2049 + 5774*S^2 + 13015*S^4 + 10694*S^6)/(54*S^3) + (Pi^4*(-37 - 111*S^2 - 111*S^4 - 1057*S^6 + 1056*S^8 + 1056*S^10 + 352*S^12))/(135*S^3*(1 + S^2)^3) + (Pi^2*(1513 + 15189*S^2 + 36942*S^4 + 20738*S^6 + 73401*S^8 + 30057*S^10 + 7120*S^12))/(324*S^3*(1 + S^2)^3) - (2*(403 + 2229*S^2 + 4272*S^4 - 3748*S^6 + 4272*S^8 + 2229*S^10 + 403*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(50 + 150*S^2 + 150*S^4 - 351*S^6 + 213*S^8 + 213*S^10 + 71*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(113 + 339*S^2 + 339*S^4 - 734*S^6 + 339*S^8 + 339*S^10 + 113*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(49 + 168*S^2 + 204*S^4 - 586*S^6 + 798*S^8 + 366*S^10 + 49*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1, 1}, -S^2]*((-2*(-557 - 629*S^2 + 629*S^4 + 557*S^6))/(3*S^3) + (2*Pi^2*(175 + 3837*S^2 + 10473*S^4 - 5314*S^6 - 2271*S^8 - 411*S^10 + 175*S^12))/(9*S^3*(1 + S^2)^3) - (64*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((2879 - 791*S^2 - 36787*S^4 - 28365*S^6)/(108*S^3) + (Pi^2*(839 + 402*S^2 + 14769*S^4 - 6926*S^6 - 12855*S^8 - 4032*S^10 - 1405*S^12))/(54*S^3*(1 + S^2)^3) + (Pi^4*(1660 + 4980*S^2 + 4980*S^4 - 4113*S^6 - 1398*S^8 - 1398*S^10 - 466*S^12))/(135*S^3*(1 + S^2)^3) + (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(97 + 612*S^2 + 1257*S^4 - 2740*S^6 + 2985*S^8 + 1188*S^10 + 97*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 2, 1}, -S^2]*((-4*(1970 + 7637*S^2 + 11010*S^4 + 7637*S^6 + 1970*S^8))/(81*S^3*(1 + S^2)) - (2*Pi^2*(863 + 8931*S^2 + 21657*S^4 - 24698*S^6 + 16635*S^8 + 7257*S^10 + 863*S^12))/(27*S^3*(1 + S^2)^3) + (16*(42 + 126*S^2 + 126*S^4 - 607*S^6 + 405*S^8 + 405*S^10 + 135*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((-7811 - 8999*S^2 + 8999*S^4 + 7811*S^6)/(27*S^3) + (Pi^4*(-7200 - 21600*S^2 - 21600*S^4 + 21017*S^6 + 3411*S^8 + 3411*S^10 + 1137*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(-8921 - 23394*S^2 - 141699*S^4 + 22802*S^6 + 22119*S^8 + 1248*S^10 + 3877*S^12))/(162*S^3*(1 + S^2)^3) + (4*(175 + 1137*S^2 + 2373*S^4 - 5314*S^6 + 5829*S^8 + 2289*S^10 + 175*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((-6395 - 42104*S^2 - 48090*S^4 - 42104*S^6 - 6395*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-2302 - 9528*S^2 - 52125*S^4 + 17014*S^6 - 42090*S^8 - 8682*S^10 - 1735*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(-1952 - 5856*S^2 - 5856*S^4 + 10306*S^6 - 3135*S^8 - 3135*S^10 - 1045*S^12))/(540*S^3*(1 + S^2)^3) + ((431 + 2568*S^2 + 5133*S^4 - 9164*S^6 + 10155*S^8 + 4242*S^10 + 431*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(29 + 87*S^2 + 87*S^4 - 254*S^6 + 159*S^8 + 159*S^10 + 53*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (186*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (4*(-26 - 78*S^2 - 78*S^4 - 127*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (124*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + ((187 + 1347*S^2 + 2949*S^4 - 7186*S^6 + 7971*S^8 + 3021*S^10 + 187*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{3, 1, 1}, -S^2]*((2*(-8375 - 28181*S^2 - 21333*S^4 + 3841*S^6 + 6664*S^8))/(81*S^3*(1 + S^2)) - (2*Pi^2*(1631 + 21774*S^2 + 55641*S^4 - 54428*S^6 + 26481*S^8 + 12054*S^10 + 1631*S^12))/(27*S^3*(1 + S^2)^3) + (16*(137 + 411*S^2 + 411*S^4 - 1908*S^6 + 1257*S^8 + 1257*S^10 + 419*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((-5893 - 11023*S^2 - 3039*S^4 + 5543*S^6 + 2012*S^8)/(36*S^3*(1 + S^2)) + (Pi^2*(-239 - 750*S^2 - 525*S^4 - 17776*S^6 + 24045*S^8 + 7440*S^10 - 239*S^12))/(54*S^3*(1 + S^2)^3))*Zeta[5] + HPL[{3}, -S^2]*((Pi^2*(2669 + 15977*S^2 + 52977*S^4 + 64163*S^6 + 25142*S^8))/(972*S^3*(1 + S^2)) + (-8363 - 7953*S^2 + 64227*S^4 + 149965*S^6 + 65412*S^8)/(324*S^3*(1 + S^2)) + (Pi^4*(3497 + 15834*S^2 + 26607*S^4 - 71504*S^6 + 92433*S^8 + 37776*S^10 + 3497*S^12))/(1620*S^3*(1 + S^2)^3) + ((-263 - 930*S^2 - 1209*S^4 + 1544*S^6 - 2667*S^8 - 1416*S^10 - 263*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-23 - 69*S^2 - 69*S^4 + 28*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-1559 - 9930*S^2 - 40305*S^4 + 22802*S^6 - 79275*S^8 - 12216*S^10 - 3485*S^12)/(27*S^3*(1 + S^2)^3) - (2*Pi^2*(108 + 324*S^2 + 324*S^4 - 1423*S^6 + 915*S^8 + 915*S^10 + 305*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(298 + 1833*S^2 + 3723*S^4 - 7972*S^6 + 8745*S^8 + 3507*S^10 + 298*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(14 + 42*S^2 + 42*S^4 - 125*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(24 + 72*S^2 + 72*S^4 - 109*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(70 + 210*S^2 + 210*S^4 - 795*S^6 + 489*S^8 + 489*S^10 + 163*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(383 + 1149*S^2 + 1149*S^4 - 4532*S^6 + 2823*S^8 + 2823*S^10 + 941*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(17 + 51*S^2 + 51*S^4 - 102*S^6 + 27*S^8 + 27*S^10 + 9*S^12))/(9*S^3*(1 + S^2)^3) - (2*(-299 - 1416*S^2 - 3054*S^4 + 113*S^6 - 2505*S^8 - 507*S^10 + 16*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + (8*(7 + 21*S^2 + 21*S^4 - 40*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + Zeta[3]*((Pi^2*(-7405 - 9673*S^2 + 8715*S^4 + 21473*S^6 + 7466*S^8))/(648*S^3*(1 + S^2)) + (-1065731 - 2092250*S^2 - 911712*S^4 + 750274*S^6 + 262219*S^8)/(5832*S^3*(1 + S^2)) + (Pi^4*(3053 + 14718*S^2 + 27237*S^4 - 117500*S^6 + 166395*S^8 + 61104*S^10 + 3053*S^12))/(3240*S^3*(1 + S^2)^3) + (4*(-57 - 171*S^2 - 171*S^4 + 29*S^6 + 78*S^8 + 78*S^10 + 26*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((73775 + 84143*S^2 - 84143*S^4 - 73775*S^6)/(324*S^3) + (Pi^2*(60827 + 143570*S^2 + 44040*S^4 - 82474*S^6 - 45067*S^8))/(1944*S^3*(1 + S^2)) + (Pi^4*(6859 + 150648*S^2 + 411261*S^4 - 252628*S^6 - 38937*S^8 + 582*S^10 + 6859*S^12))/(3240*S^3*(1 + S^2)^3) - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(241 + 723*S^2 + 723*S^4 - 2922*S^6 + 1839*S^8 + 1839*S^10 + 613*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(727 + 2181*S^2 + 2181*S^4 - 8806*S^6 + 5529*S^8 + 5529*S^10 + 1843*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (496*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 - (32*(191 + 573*S^2 + 573*S^4 - 674*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-1685 - 10218*S^2 - 39855*S^4 + 22802*S^6 - 79725*S^8 - 11928*S^10 - 3359*S^12)/(27*S^3*(1 + S^2)^3) - (2*Pi^2*(108 + 324*S^2 + 324*S^4 - 1481*S^6 + 969*S^8 + 969*S^10 + 323*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] - (4*(44 + 132*S^2 + 132*S^4 - 1255*S^6 + 951*S^8 + 951*S^10 + 317*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-374789 - 405893*S^2 + 405893*S^4 + 374789*S^6)/(1944*S^3) + (Pi^2*(-257477 - 579260*S^2 - 48090*S^4 + 495052*S^6 + 244687*S^8))/(11664*S^3*(1 + S^2)) + (Pi^6*(-9184 - 27552*S^2 - 27552*S^4 + 26123*S^6 + 5523*S^8 + 5523*S^10 + 1841*S^12))/(7560*S^3*(1 + S^2)^3) + (Pi^4*(-59731 - 153123*S^2 - 919680*S^4 + 229342*S^6 + 83595*S^8 + 32709*S^10 + 29864*S^12))/(19440*S^3*(1 + S^2)^3) - (2*(14 + 42*S^2 + 42*S^4 - 125*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(45 + 135*S^2 + 135*S^4 - 340*S^6 + 201*S^8 + 201*S^10 + 67*S^12))/(9*S^3*(1 + S^2)^3) + (1879 + 10878*S^2 + 31065*S^4 + 10400*S^6 + 33405*S^8 + 13074*S^10 + 2563*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + (2*(22 + 83*S^2 + 117*S^4 - 160*S^6 + 261*S^8 + 131*S^10 + 22*S^12)*HPL[{5}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-27 - 81*S^2 - 81*S^4 + 16*S^6 + 144*S^8 + 144*S^10 + 48*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) - (124*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/S^3 + ((2*Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2091*S^6 + 765*S^8 + 765*S^10 + 255*S^12))/(9*S^3*(1 + S^2)^3) + (2693 + 11622*S^2 + 60375*S^4 - 22802*S^6 + 59205*S^8 + 10524*S^10 + 2351*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (2*(81 + 487*S^2 + 978*S^4 - 1888*S^6 + 2094*S^8 + 859*S^10 + 81*S^12)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)^3) - (2*(2183 + 13179*S^2 + 26526*S^4 - 51236*S^6 + 56658*S^8 + 23223*S^10 + 2183*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(6 + 18*S^2 + 18*S^4 - 43*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) - (4*(131 + 393*S^2 + 393*S^4 - 996*S^6 + 555*S^8 + 555*S^10 + 185*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2089*S^6 + 771*S^8 + 771*S^10 + 257*S^12))/(9*S^3*(1 + S^2)^3) - (2*(2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (744*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*(175 + 2829*S^2 + 7449*S^4 - 5314*S^6 + 753*S^8 + 597*S^10 + 175*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{3, 1, 2}, -S^2])/(S^3*(1 + S^2)^3) - (4*(345 + 1035*S^2 + 1035*S^4 - 2414*S^6 + 1035*S^8 + 1035*S^10 + 345*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(1039 + 3117*S^2 + 3117*S^4 - 7282*S^6 + 3117*S^8 + 3117*S^10 + 1039*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(-328 - 984*S^2 - 984*S^4 + 337*S^6 + 690*S^8 + 690*S^10 + 230*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((671 + 15482*S^2 + 44040*S^4 + 45614*S^6 + 15089*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(725 + 4152*S^2 + 8139*S^4 - 17252*S^6 + 19749*S^8 + 8022*S^10 + 725*S^12))/(54*S^3*(1 + S^2)^3))*Zeta[3] + (2*(-4 + 7*S^6)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*((-931 + 10982*S^2 + 44040*S^4 + 50114*S^6 + 16691*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(565 + 3669*S^2 + 7647*S^4 - 16870*S^6 + 18285*S^8 + 7215*S^10 + 565*S^12))/(54*S^3*(1 + S^2)^3) - (8*(70 + 210*S^2 + 210*S^4 - 795*S^6 + 489*S^8 + 489*S^10 + 163*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-14 - 42*S^2 - 42*S^4 + 63*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((2*(1970 + 7637*S^2 + 11010*S^4 + 7637*S^6 + 1970*S^8))/(81*S^3*(1 + S^2)) + (Pi^2*(863 + 8931*S^2 + 21657*S^4 - 24698*S^6 + 16635*S^8 + 7257*S^10 + 863*S^12))/(27*S^3*(1 + S^2)^3) - (8*(42 + 126*S^2 + 126*S^4 - 607*S^6 + 405*S^8 + 405*S^10 + 135*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((317 + 1794*S^2 + 3531*S^4 - 15152*S^6 + 18273*S^8 + 6708*S^10 + 317*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + ((-115 - 495*S^2 - 735*S^4 - 2402*S^6 + 3423*S^8 + 891*S^10 - 115*S^12)*Zeta[7])/(S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(523277 - 119846*S^2 + 523277*S^4))/(23328*S^3) + (Pi^4*(-664561 - 1784425*S^2 - 1582989*S^4 - 186799*S^6 + 102662*S^8))/(233280*S^3*(1 + S^2)) + (Pi^2*(-566897 - 1776530*S^2 - 1277940*S^4 + 1065994*S^6 + 761053*S^8))/(69984*S^3*(1 + S^2)) + (Pi^6*(-66197 - 1379268*S^2 - 3711063*S^4 + 4225940*S^6 - 1155297*S^8 - 527346*S^10 - 66197*S^12))/(272160*S^3*(1 + S^2)^3) + (31*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2]^3)/(S*(1 + S^2)^2) + ((-133 - 735*S^2 - 1410*S^4 + 1192*S^6 - 1410*S^8 - 735*S^10 - 133*S^12)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((2*Pi^2*(-19 - 57*S^2 - 57*S^4 - 186*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3) + (1061 + 14034*S^2 + 26013*S^4 + 27052*S^6 + 70257*S^8 + 30918*S^10 + 7505*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((881 + 1494*S^2 - 789*S^4 + 1624*S^6 + 7797*S^8 + 4356*S^10 + 881*S^12)*HPL[{6}, -S^2])/(6*S^3*(1 + S^2)^3) + (2*(-87 - 261*S^2 - 261*S^4 + 81*S^6 + 276*S^8 + 276*S^10 + 92*S^12)*HPL[{7}, -S^2])/(S^3*(1 + S^2)^3) + (2*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(108 + 324*S^2 + 324*S^4 - 1423*S^6 + 915*S^8 + 915*S^10 + 305*S^12))/(9*S^3*(1 + S^2)^3) - (2*(820 + 5073*S^2 + 20247*S^4 - 11401*S^6 + 39543*S^8 + 6000*S^10 + 1702*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((Pi^2*(-709 - 2127*S^2 - 2127*S^4 + 9670*S^6 - 6327*S^8 - 6327*S^10 - 2109*S^12))/(9*S^3*(1 + S^2)^3) - (2*(1153 + 7536*S^2 + 26478*S^4 - 8911*S^6 + 49602*S^8 + 9927*S^10 + 2599*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((-133 - 753*S^2 - 1464*S^4 + 1336*S^6 - 1464*S^8 - 753*S^10 - 133*S^12)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(7 + 21*S^2 + 21*S^4 - 185*S^6 + 120*S^8 + 120*S^10 + 40*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(509 + 2133*S^2 + 3351*S^4 - 3530*S^6 + 5835*S^8 + 2961*S^10 + 509*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(2 + 6*S^2 + 6*S^4 - 71*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{5, 2}, -S^2])/(S^3*(1 + S^2)^3) - (2*(-184 - 552*S^2 - 552*S^4 + 153*S^6 + 699*S^8 + 699*S^10 + 233*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2089*S^6 + 771*S^8 + 771*S^10 + 257*S^12))/(9*S^3*(1 + S^2)^3) - (2*(2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((-16*Pi^2*(233 + 699*S^2 + 699*S^4 - 1141*S^6 + 294*S^8 + 294*S^10 + 98*S^12))/(9*S^3*(1 + S^2)^3) - (2*(5008 + 15855*S^2 + 120606*S^4 - 53074*S^6 + 69684*S^8 + 9267*S^10 + 1390*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + (744*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (2*(443 + 1329*S^2 + 1329*S^4 - 5586*S^6 + 3561*S^8 + 3561*S^10 + 1187*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(172 + 516*S^2 + 516*S^4 - 2137*S^6 + 1353*S^8 + 1353*S^10 + 451*S^12)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(18 - 62*S^2 - 294*S^4 - 158*S^6 + 651*S^8 + 253*S^10 + 18*S^12)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (2*(1337 + 4011*S^2 + 4011*S^4 - 16838*S^6 + 10707*S^8 + 10707*S^10 + 3569*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(4253 + 12759*S^2 + 12759*S^4 - 52142*S^6 + 32847*S^8 + 32847*S^10 + 10949*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(362 + 1086*S^2 + 1086*S^4 - 4471*S^6 + 2829*S^8 + 2829*S^10 + 943*S^12)*HPL[{5, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((-4*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(S^3*(1 + S^2)^2) - (8*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] - (496*(-1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/S^3 - (16*(18 - 17*S^2 - 159*S^4 - 158*S^6 + 516*S^8 + 208*S^10 + 18*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (32*(191 + 573*S^2 + 573*S^4 - 674*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(191 + 573*S^2 + 573*S^4 - 674*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-661 - 1983*S^2 - 1983*S^4 + 1348*S^6 + 807*S^8 + 807*S^10 + 269*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(-1015 - 3045*S^2 - 3045*S^4 + 2299*S^6 + 1032*S^8 + 1032*S^10 + 344*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (3600*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (160*(221 + 663*S^2 + 663*S^4 - 1673*S^6 + 798*S^8 + 798*S^10 + 266*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2400*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-194051 - 355040*S^2 - 83550*S^4 + 250120*S^6 + 87145*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-179 + 564*S^2 + 8619*S^4 - 10198*S^6 + 29139*S^8 + 4110*S^10 + 1537*S^12))/(108*S^3*(1 + S^2)^3) + (Pi^4*(231 + 693*S^2 + 693*S^4 - 10373*S^6 + 8424*S^8 + 8424*S^10 + 2808*S^12))/(540*S^3*(1 + S^2)^3))*Zeta[3] + ((-1 - 26*S^2 - 75*S^4 + 68*S^6 - 75*S^8 - 26*S^10 - S^12)*Zeta[3]^2)/(S^3*(1 + S^2)^3) + HPL[{4}, -S^2]*((3425 + 7525*S^2 + 12659*S^4 + 9063*S^6)/(72*S^3) + (Pi^2*(239 + 897*S^2 + 1254*S^4 - 1916*S^6 + 3216*S^8 + 1551*S^10 + 239*S^12))/(18*S^3*(1 + S^2)^3) - (2*(113 + 339*S^2 + 339*S^4 - 734*S^6 + 339*S^8 + 339*S^10 + 113*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(3 + 9*S^2 + 9*S^4 - 100*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((-557 - 629*S^2 + 629*S^4 + 557*S^6)/(3*S^3) + (Pi^2*(-175 - 3837*S^2 - 10473*S^4 + 5314*S^6 + 2271*S^8 + 411*S^10 - 175*S^12))/(9*S^3*(1 + S^2)^3) + (32*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-13121 + 65416*S^2 + 434382*S^4 + 670576*S^6 + 268075*S^8)/(1944*S^3*(1 + S^2)) + (Pi^4*(292 + 876*S^2 + 876*S^4 - 6193*S^6 + 4533*S^8 + 4533*S^10 + 1511*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(2087 + 17850*S^2 + 59943*S^4 - 13250*S^6 + 122745*S^8 + 29460*S^10 + 7685*S^12))/(324*S^3*(1 + S^2)^3) - (2*(8 + 24*S^2 + 24*S^4 - 157*S^6 + 105*S^8 + 105*S^10 + 35*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(103 + 309*S^2 + 309*S^4 - 1352*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(104 + 489*S^2 + 822*S^4 - 1034*S^6 + 984*S^8 + 543*S^10 + 104*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((-1970 - 7637*S^2 - 11010*S^4 - 7637*S^6 - 1970*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-863 - 8931*S^2 - 21657*S^4 + 24698*S^6 - 16635*S^8 - 7257*S^10 - 863*S^12))/(108*S^3*(1 + S^2)^3) + (2*(70 + 210*S^2 + 210*S^4 - 795*S^6 + 489*S^8 + 489*S^10 + 163*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (62*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (2*(42 + 126*S^2 + 126*S^4 - 607*S^6 + 405*S^8 + 405*S^10 + 135*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((55 - 318*S^2 - 2205*S^4 - 1616*S^6)/(9*S^3) + (Pi^2*(-95 + 3912*S^2 + 12327*S^4 - 5032*S^6 - 6789*S^8 - 2460*S^10 - 95*S^12))/(27*S^3*(1 + S^2)^3) - (8*(53 + 159*S^2 + 159*S^4 - 694*S^6 + 447*S^8 + 447*S^10 + 149*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((7811 + 8999*S^2 - 8999*S^4 - 7811*S^6)/(54*S^3) + (Pi^2*(8921 + 23394*S^2 + 141699*S^4 - 22802*S^6 - 22119*S^8 - 1248*S^10 - 3877*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(7200 + 21600*S^2 + 21600*S^4 - 21017*S^6 - 3411*S^8 - 3411*S^10 - 1137*S^12))/(540*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(175 + 1137*S^2 + 2373*S^4 - 5314*S^6 + 5829*S^8 + 2289*S^10 + 175*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((Pi^2*(-18 - 54*S^2 - 54*S^4 - 1477*S^6 + 1311*S^8 + 1311*S^10 + 437*S^12))/(9*S^3*(1 + S^2)^3) + (-2320 - 8079*S^2 - 5352*S^4 - 24341*S^6 + 37758*S^8 + 1974*S^10 + 2108*S^12)/(27*S^3*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((-73775 - 84143*S^2 + 84143*S^4 + 73775*S^6)/(648*S^3) + (Pi^2*(-60827 - 143570*S^2 - 44040*S^4 + 82474*S^6 + 45067*S^8))/(3888*S^3*(1 + S^2)) + (Pi^4*(-6859 - 150648*S^2 - 411261*S^4 + 252628*S^6 + 38937*S^8 - 582*S^10 - 6859*S^12))/(6480*S^3*(1 + S^2)^3) + ((Pi^2*(108 + 324*S^2 + 324*S^4 - 1423*S^6 + 915*S^8 + 915*S^10 + 305*S^12))/(9*S^3*(1 + S^2)^3) + (1559 + 9930*S^2 + 40305*S^4 - 22802*S^6 + 79275*S^8 + 12216*S^10 + 3485*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((403 + 2229*S^2 + 4272*S^4 - 3748*S^6 + 4272*S^8 + 2229*S^10 + 403*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(17 + 51*S^2 + 51*S^4 - 286*S^6 + 195*S^8 + 195*S^10 + 65*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2089*S^6 + 771*S^8 + 771*S^10 + 257*S^12))/(9*S^3*(1 + S^2)^3) + (2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(241 + 723*S^2 + 723*S^4 - 2922*S^6 + 1839*S^8 + 1839*S^10 + 613*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(727 + 2181*S^2 + 2181*S^4 - 8806*S^6 + 5529*S^8 + 5529*S^10 + 1843*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (248*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 + (16*(191 + 573*S^2 + 573*S^4 - 674*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(108 + 324*S^2 + 324*S^4 - 1481*S^6 + 969*S^8 + 969*S^10 + 323*S^12))/(9*S^3*(1 + S^2)^3) + (1685 + 10218*S^2 + 39855*S^4 - 22802*S^6 + 79725*S^8 + 11928*S^10 + 3359*S^12)/(54*S^3*(1 + S^2)^3))*Zeta[3] + (2*(44 + 132*S^2 + 132*S^4 - 1255*S^6 + 951*S^8 + 951*S^10 + 317*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + (2*(-35 - 105*S^2 - 105*S^4 - 583*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*Zeta[7])/(S^3*(1 + S^2)^3)) + HPL[{0}, S^2]*((5*(3436945 - 618772*S^2 + 3458815*S^4))/(69984*S) - (7*Pi^8*S^3*(-70669 + 16296*S^2 + 16296*S^4 + 5432*S^6))/(583200*(1 + S^2)^3) + (Pi^2*(664663 + 508223*S^2 + 730747*S^4 + 762771*S^6))/(23328*S*(1 + S^2)) + (Pi^4*(1157758 + 887897*S^2 + 2114218*S^4 + 2139135*S^6))/(466560*S*(1 + S^2)) + (Pi^6*(318234 - 696833*S^2 + 3938539*S^4 + 1460625*S^6 + 1671323*S^8 + 354464*S^10))/(544320*S*(1 + S^2)^3) - (2*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^7)/(3*S^3*(1 + S^2)^3) - (4*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^8)/(9*S^3*(1 + S^2)^3) + ((937 + 1446*S^2 - 12693*S^4 + 11576*S^6 - 38037*S^8 - 9318*S^10 - 2951*S^12)/(324*S^3*(1 + S^2)^3) + (Pi^2*(11 + 33*S^2 + 33*S^4 + 452*S^6 - 357*S^8 - 357*S^10 - 119*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^3 - (S^3*(-167 + 144*S^2 + 144*S^4 + 48*S^6)*HPL[{2}, -S^2]^4)/(9*(1 + S^2)^3) + HPL[{1}, -S^2]^6*((Pi^2*(-140 - 420*S^2 - 420*S^4 + 851*S^6 - 303*S^8 - 303*S^10 - 101*S^12))/(81*S^3*(1 + S^2)^3) + (-35 - 146*S^2 - 889*S^4 + 460*S^6 - 889*S^8 - 146*S^10 - 35*S^12)/(18*S^3*(1 + S^2)^3) - (2*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((125 + 304*S^2 + 163*S^4 - 680*S^6 - 1007*S^8 - 836*S^10 - 205*S^12)/(36*S^3*(1 + S^2)^3) + (Pi^2*(7 + 21*S^2 + 21*S^4 - 9*S^6 - 12*S^8 - 12*S^10 - 4*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2]^2 + (2*(-14 - 42*S^2 - 42*S^4 + 19*S^6 + 66*S^8 + 66*S^10 + 22*S^12)*HPL[{4}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + (-(Pi^2*S^3*(21 + 300*S^2 + 300*S^4 + 100*S^6))/(9*(1 + S^2)^3) + (-4580 - 9792*S^2 - 12573*S^4 - 2869*S^6 + 7425*S^8 + 19341*S^10 + 5896*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{6}, -S^2] + ((20 + 303*S^2 + 330*S^4 - 1778*S^6 - 2631*S^8 - 210*S^10 + 344*S^12)*HPL[{7}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-105 - 315*S^2 - 315*S^4 + 342*S^6 + 894*S^8 + 894*S^10 + 298*S^12)*HPL[{8}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-4 - 12*S^2 - 12*S^4 - 1983*S^6 + 1419*S^8 + 1419*S^10 + 473*S^12))/(9*S^3*(1 + S^2)^3) + (10 + 2517*S^2 + 20553*S^4 - 11401*S^6 + 39237*S^8 + 8556*S^10 + 2512*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2]^2 - (4*(3 + 9*S^2 + 9*S^4 - 673*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*HPL[{3, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-104 - 193*S^2 - 923*S^4 - 977*S^6 - 841*S^8 - 266*S^10)/(108*S^3*(1 + S^2)^2) + (Pi^2*(-1 - 3*S^2 - 3*S^4 - 6*S^6 + 3*S^8 + 3*S^10 + S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 2}, -S^2] + ((-400 - 1026*S^2 - 792*S^4 - 1043*S^6 - 813*S^8 - 354*S^10 - 22*S^12)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((1609 + 1560*S^2 + 66*S^4 - 11506*S^6 - 13047*S^8 - 15018*S^10 - 3800*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(3 + 9*S^2 + 9*S^4 - 147*S^6 + 246*S^8 + 246*S^10 + 82*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{5, 1}, -S^2] + ((-793 - 2047*S^2 - 1615*S^4 - 2102*S^6 - 1765*S^8 - 823*S^10 - 79*S^12)*HPL[{5, 2}, -S^2])/(6*S^3*(1 + S^2)^3) - (2*S^3*(7 + 3*S^2 + 3*S^4 + S^6)*HPL[{5, 3}, -S^2])/(3*(1 + S^2)^3) + ((-2453 - 6351*S^2 - 4758*S^4 - 6859*S^6 - 4371*S^8 - 3219*S^10 - 779*S^12)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-2 - 6*S^2 - 6*S^4 + 18*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{6, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-51 - 153*S^2 - 153*S^4 + 31*S^6 + 570*S^8 + 570*S^10 + 190*S^12)*HPL[{7, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*S^3*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(3*(1 + S^2)^3) + ((Pi^2*(-5 - 7*S^6))/(9*S^3) + (145 - 2*S^2 - 294*S^4 - 218*S^6 - 179*S^8)/(54*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((3893 + 6072*S^2 - 50925*S^4 + 45496*S^6 - 153057*S^8 - 37848*S^10 - 11983*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(83 + 249*S^2 + 249*S^4 + 3604*S^6 - 2877*S^8 - 2877*S^10 - 959*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 2, 1}, -S^2] + ((-77 - 140*S^2 - 74*S^4 - 1198*S^6 + 1112*S^8 + 602*S^10 + 127*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-211 - 393*S^2 - 159*S^4 - 2771*S^6 + 2718*S^8 + 1530*S^10 + 338*S^12)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-35 - 105*S^2 - 105*S^4 - 5*S^6 + 186*S^8 + 186*S^10 + 62*S^12)*HPL[{3, 3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((5176 + 9681*S^2 - 74622*S^4 + 79670*S^6 - 219576*S^8 - 46623*S^10 - 15578*S^12)/(27*S^3*(1 + S^2)^3) - (8*Pi^2*(-31 - 93*S^2 - 93*S^4 - 1396*S^6 + 1095*S^8 + 1095*S^10 + 365*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 1, 1}, -S^2] + ((-868 - 1629*S^2 - 639*S^4 - 10844*S^6 + 11265*S^8 + 6369*S^10 + 1418*S^12)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-35 - 105*S^2 - 105*S^4 - 7*S^6 + 198*S^8 + 198*S^10 + 66*S^12)*HPL[{4, 1, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2788 - 5373*S^2 - 2331*S^4 - 33908*S^6 + 33261*S^8 + 18969*S^10 + 4250*S^12)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-32 - 96*S^2 - 96*S^4 - 3*S^6 + 165*S^8 + 165*S^10 + 55*S^12)*HPL[{4, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-73 - 219*S^2 - 219*S^4 - 9*S^6 + 402*S^8 + 402*S^10 + 134*S^12)*HPL[{4, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-887 - 1707*S^2 - 807*S^4 - 10996*S^6 + 11045*S^8 + 6545*S^10 + 1531*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-77 - 231*S^2 - 231*S^4 - 17*S^6 + 444*S^8 + 444*S^10 + 148*S^12)*HPL[{5, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-617 - 1851*S^2 - 1851*S^4 - 77*S^6 + 3324*S^8 + 3324*S^10 + 1108*S^12)*HPL[{5, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-400 - 1200*S^2 - 1200*S^4 - 88*S^6 + 2235*S^8 + 2235*S^10 + 745*S^12)*HPL[{6, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1139 - 7953*S^2 - 18375*S^4 + 14372*S^6 - 3465*S^8 - 783*S^10 + 391*S^12)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((4*Pi^2*(-37 - 111*S^2 - 111*S^4 - 1975*S^6 + 1470*S^8 + 1470*S^10 + 490*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-403 - 852*S^2 + 8523*S^4 - 10754*S^6 + 22869*S^8 + 3630*S^10 + 1355*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1}, -S^2] + (4*(-3341 - 23847*S^2 - 55419*S^4 + 44582*S^6 - 13059*S^8 - 4023*S^10 + 763*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-3341 - 23847*S^2 - 55419*S^4 + 44582*S^6 - 13059*S^8 - 4023*S^10 + 763*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(9 + 7*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^3) + (8*(-3379 - 23853*S^2 - 55272*S^4 + 43849*S^6 - 11727*S^8 - 3186*S^10 + 968*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(9 + 7*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^3) + (2*(-161 - 483*S^2 - 483*S^4 - 4856*S^6 + 4731*S^8 + 4731*S^10 + 1577*S^12)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-19 - 57*S^2 - 57*S^4 - 605*S^6 + 594*S^8 + 594*S^10 + 198*S^12)*HPL[{3, 3, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-6824 - 47815*S^2 - 110437*S^4 + 87380*S^6 - 23089*S^8 - 6259*S^10 + 1936*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^3) + (8*(-115 - 345*S^2 - 345*S^4 - 3632*S^6 + 3561*S^8 + 3561*S^10 + 1187*S^12)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (56*(-49 - 147*S^2 - 147*S^4 - 1556*S^6 + 1527*S^8 + 1527*S^10 + 509*S^12)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-679 - 2037*S^2 - 2037*S^4 - 21887*S^6 + 21456*S^8 + 21456*S^10 + 7152*S^12)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-16*Pi^2*(-16 - 48*S^2 - 48*S^4 - 987*S^6 + 732*S^8 + 732*S^10 + 244*S^12))/(9*S^3*(1 + S^2)^3) - (4*(-517 - 1098*S^2 + 8601*S^4 - 10304*S^6 + 23529*S^8 + 4242*S^10 + 1547*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1, 1}, -S^2] + (8*(349 + 2627*S^2 + 6191*S^4 - 5314*S^6 + 2011*S^8 + 799*S^10 + S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(349 + 2627*S^2 + 6191*S^4 - 5314*S^6 + 2011*S^8 + 799*S^10 + S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (32*(-19 - 57*S^2 - 57*S^4 - 607*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(-19 - 57*S^2 - 57*S^4 - 607*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (16*(886 + 6604*S^2 + 15472*S^4 - 13360*S^6 + 5320*S^8 + 2221*S^10 + 67*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-451 - 1353*S^2 - 1353*S^4 - 14558*S^6 + 14127*S^8 + 14127*S^10 + 4709*S^12)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (40*(-151 - 453*S^2 - 453*S^4 - 4854*S^6 + 4707*S^8 + 4707*S^10 + 1569*S^12)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-907 - 2721*S^2 - 2721*S^4 - 29126*S^6 + 28239*S^8 + 28239*S^10 + 9413*S^12)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (40*(-379 - 1137*S^2 - 1137*S^4 - 12138*S^6 + 11763*S^8 + 11763*S^10 + 3921*S^12)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-474 - 1422*S^2 - 1422*S^4 - 15191*S^6 + 14709*S^8 + 14709*S^10 + 4903*S^12)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (80*(-62 - 504*S^2 - 1233*S^4 + 1046*S^6 - 267*S^8 - 60*S^10 + 28*S^12)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (32*(-35 - 105*S^2 - 105*S^4 - 1312*S^6 + 1209*S^8 + 1209*S^10 + 403*S^12)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (320*(-2 - 6*S^2 - 6*S^4 - 87*S^6 + 81*S^8 + 81*S^10 + 27*S^12)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (-(Pi^2*S^3*(-73 + 33*S^2 + 33*S^4 + 11*S^6))/(9*(1 + S^2)^3) + (138 + 285*S^2 + 609*S^4 + 407*S^6 + 333*S^8 + 52*S^10)/(6*S*(1 + S^2)^3))*Zeta[3]^2 + HPL[{2, 2, 1}, -S^2]*((-8458 - 21799*S^2 - 22020*S^4 - 8749*S^6 + 578*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(-395 - 3744*S^2 - 9519*S^4 + 7157*S^6 - 2258*S^8 - 839*S^10 + 34*S^12))/(9*S^3*(1 + S^2)^3) + (8*(42 + 126*S^2 + 126*S^4 - 125*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1, 1}, -S^2]*((-2*(-6292 - 14260*S^2 - 8349*S^4 + 1886*S^6 + 6155*S^8))/(81*S^3*(1 + S^2)) - (2*Pi^2*(-1040 - 11049*S^2 - 29139*S^4 + 21482*S^6 - 4545*S^8 - 837*S^10 + 580*S^12))/(27*S^3*(1 + S^2)^3) + (16*(-41 - 123*S^2 - 123*S^4 + 134*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1, 1}, -S^2]*((-16837 - 41878*S^2 - 35484*S^4 - 7714*S^6 + 6185*S^8)/(54*S^3*(1 + S^2)) + (Pi^2*(-3377 - 33369*S^2 - 86037*S^4 + 64373*S^6 - 18174*S^8 - 5772*S^10 + 844*S^12))/(27*S^3*(1 + S^2)^3) + (8*(125 + 375*S^2 + 375*S^4 - 375*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4, 1}, -S^2]*((2764 - 18707*S^2 - 66630*S^4 - 66083*S^6 - 35828*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(326 + 636*S^2 + 699*S^4 + 4036*S^6 - 8775*S^8 - 6354*S^10 - 1780*S^12))/(54*S^3*(1 + S^2)^3) + (4*(-13 - 39*S^2 - 39*S^4 + 28*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(108*S^3) + (Pi^2*(-5461 - 18330*S^2 - 174867*S^4 + 108868*S^6 - 136743*S^8 - 19194*S^10 - 4705*S^12))/(1944*S^3*(1 + S^2)^3) + (Pi^4*(-8061 - 24183*S^2 - 24183*S^4 + 44045*S^6 - 12366*S^8 - 12366*S^10 - 4122*S^12))/(3240*S^3*(1 + S^2)^3) + ((-515 - 1572*S^2 - 16065*S^4 + 10304*S^6 - 16065*S^8 - 1572*S^10 - 515*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(-211 - 633*S^2 - 633*S^4 + 1260*S^6 - 447*S^8 - 447*S^10 - 149*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] - (4*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + (2*(15 + 52*S^2 + 63*S^4 - 14*S^6 + 54*S^8 + 49*S^10 + 15*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-17 - 51*S^2 - 51*S^4 + 194*S^6 - 87*S^8 - 87*S^10 - 29*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (10*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(62 + 186*S^2 + 186*S^4 - 435*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (20*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(18 + 94*S^2 + 174*S^4 - 158*S^6 + 183*S^8 + 97*S^10 + 18*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 2}, -S^2]*((429 - 1410*S^2 - 3902*S^4 - 2794*S^6 - 1595*S^8)/(72*S^3*(1 + S^2)) + (Pi^2*(554 + 1131*S^2 + 438*S^4 + 3916*S^6 - 6816*S^8 - 4323*S^10 - 1084*S^12))/(108*S^3*(1 + S^2)^3) + (2*(-19 - 57*S^2 - 57*S^4 + 44*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4}, -S^2]*((48955 + 29176*S^2 + 149658*S^4 + 380392*S^6 + 203179*S^8)/(3888*S^3*(1 + S^2)) + (Pi^4*(-115 - 345*S^2 - 345*S^4 + 944*S^6 - 1113*S^8 - 1113*S^10 - 371*S^12))/(540*S^3*(1 + S^2)^3) + (Pi^2*(59 + 4335*S^2 + 4641*S^4 + 16066*S^6 + 13245*S^8 + 15423*S^10 + 3479*S^12))/(648*S^3*(1 + S^2)^3) + ((-46 - 132*S^2 - 117*S^4 - 92*S^6 + 181*S^8 + 136*S^10 + 38*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-10 - 30*S^2 - 30*S^4 + 13*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 8*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((55 + 116*S^2 + 38*S^4 + 278*S^6 + 298*S^8 + 178*S^10 + 37*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^5*((-2*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) + (Pi^2*(-347 - 5229*S^2 - 13593*S^4 + 17678*S^6 - 10083*S^8 - 4059*S^10 - 347*S^12))/(270*S^3*(1 + S^2)^3) - (2*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(10 + 30*S^2 + 30*S^4 - 43*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3}, -S^2])/(45*S^3*(1 + S^2)^3) + (4*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(40 + 120*S^2 + 120*S^4 - 277*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*Zeta[3])/(45*S^3*(1 + S^2)^3)) + HPL[{5}, -S^2]*((1903 - 4979*S^2 + 18429*S^4 + 71719*S^6 + 39280*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(413 + 1224*S^2 + 963*S^4 + 2086*S^6 - 573*S^8 + 1254*S^10 + 737*S^12))/(108*S^3*(1 + S^2)^3) + (2*(-41 - 123*S^2 - 123*S^4 + 47*S^6 + 144*S^8 + 144*S^10 + 48*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-26 - 78*S^2 - 78*S^4 + 93*S^6 + 177*S^8 + 177*S^10 + 59*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((-25003 - 14917*S^2 - 41505*S^4 - 31837*S^6 - 23014*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-929 - 3072*S^2 + 42927*S^4 - 56668*S^6 + 78045*S^8 + 8700*S^10 + 3733*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(-193 - 579*S^2 - 579*S^4 - 20356*S^6 + 12657*S^8 + 12657*S^10 + 4219*S^12))/(540*S^3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 1346*S^6 + 1179*S^8 + 1179*S^10 + 393*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(1 + 76*S^2 + 181*S^4 - 415*S^6 + 906*S^8 + 501*S^10 + 106*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((49357 + 64930*S^2 + 41775*S^4 - 12470*S^6 + 4096*S^8)/(486*S^3*(1 + S^2)) + (Pi^4*(91 + 273*S^2 + 273*S^4 + 10416*S^6 - 5874*S^8 - 5874*S^10 - 1958*S^12))/(135*S^3*(1 + S^2)^3) + (Pi^2*(541 + 1552*S^2 - 14234*S^4 + 18764*S^6 - 26297*S^8 - 3392*S^10 - 1406*S^12))/(54*S^3*(1 + S^2)^3) + (4*(7 + 270*S^2 + 648*S^4 - 1291*S^6 + 2601*S^8 + 1467*S^10 + 322*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((3053 - 6364*S^2 - 24045*S^4 - 35740*S^6 - 9448*S^8)/(1944*S^3*(1 + S^2)) + (Pi^4*(20 + 60*S^2 + 60*S^4 + 9811*S^6 - 5676*S^8 - 5676*S^10 - 1892*S^12))/(1080*S^3*(1 + S^2)^3) + (Pi^2*(-97 - 2312*S^2 - 20705*S^4 + 13732*S^6 - 31295*S^8 - 6548*S^10 - 1879*S^12))/(432*S^3*(1 + S^2)^3) + ((-17 - 24*S^2 + 3*S^4 - 283*S^6 + 286*S^8 + 157*S^10 + 34*S^12)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^3) + ((9 + 27*S^2 + 27*S^4 - 4*S^6 - 45*S^8 - 45*S^10 - 15*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + ((1139 + 7953*S^2 + 18375*S^4 - 14372*S^6 + 3465*S^8 + 783*S^10 - 391*S^12)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + ((-39 - 117*S^2 - 117*S^4 - 1210*S^6 + 1191*S^8 + 1191*S^10 + 397*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-19 - 57*S^2 - 57*S^4 - 607*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((43 + 336*S^2 + 615*S^4 - 1129*S^6 + 2886*S^8 + 1707*S^10 + 394*S^12)*Zeta[3])/(18*S^3*(1 + S^2)^3)) + ((4158 + 5557*S^2 + 5651*S^4 + 4288*S^6)/(36*S*(1 + S^2)) + (Pi^2*(-26 - 65*S^2 + 1461*S^4 + 4540*S^6 + 3946*S^8 + 1218*S^10))/(18*S*(1 + S^2)^3))*Zeta[5] + Zeta[3]*((108754 + 42335*S^2 + 107569*S^4)/(1296*S) + (Pi^2*(3200 + 5022*S^2 + 6033*S^4 + 4175*S^6))/(216*S*(1 + S^2)) + (Pi^4*(-424 - 1060*S^2 + 10542*S^4 + 35906*S^6 + 28733*S^8 + 8481*S^10))/(1080*S*(1 + S^2)^3) - (4*S^3*(-19 + 27*S^2 + 27*S^4 + 9*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((-679141 - 964930*S^2 - 1823424*S^4 - 1719022*S^6 - 927883*S^8)/(11664*S^3*(1 + S^2)) + (Pi^2*(5789 + 13751*S^2 + 120*S^4 - 12754*S^6 - 10744*S^8))/(972*S^3*(1 + S^2)) + (Pi^4*(1148 + 32905*S^2 + 99895*S^4 - 69872*S^6 + 13437*S^8 + 2418*S^10 - 1633*S^12))/(1080*S^3*(1 + S^2)^3) + (2*(-1043 - 7869*S^2 - 18561*S^4 + 15950*S^6 - 6021*S^8 - 2385*S^10 + S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-77 - 231*S^2 - 231*S^4 + 252*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-119 - 357*S^2 - 357*S^4 + 394*S^6 + 99*S^8 + 99*S^10 + 33*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(349 + 2627*S^2 + 6191*S^4 - 5314*S^6 + 2011*S^8 + 799*S^10 + S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-19 - 57*S^2 - 57*S^4 - 607*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-75 - 225*S^2 - 225*S^4 - 3774*S^6 + 3531*S^8 + 3531*S^10 + 1177*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*S^3*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)^3) + ((-577 - 2462*S^2 - 5546*S^4 - 1568*S^6 - 2891*S^8 - 878*S^10 - 70*S^12)/(9*S^3*(1 + S^2)^3) - (2*Pi^2*(27 + 81*S^2 + 81*S^4 - 146*S^6 + 33*S^8 + 33*S^10 + 11*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] - (4*(9 + 27*S^2 + 27*S^4 - 55*S^6 + 54*S^8 + 54*S^10 + 18*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(((1 + S^2)*(27713 - 37886*S^2 + 27713*S^4))/(1944*S^3) + (Pi^2*(-4673 - 28781*S^2 - 45993*S^4 - 22715*S^6 - 1478*S^8))/(2916*S^3*(1 + S^2)) + (Pi^4*(-757 - 50388*S^2 - 146373*S^4 + 191152*S^6 - 75471*S^8 - 26754*S^10 - 757*S^12))/(3240*S^3*(1 + S^2)^3) + ((-175 - 1713*S^2 - 4101*S^4 + 5314*S^6 - 4101*S^8 - 1713*S^10 - 175*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((2*Pi^2*(4 + 12*S^2 + 12*S^4 - 13*S^6 + 21*S^8 + 21*S^10 + 7*S^12))/(27*S^3*(1 + S^2)^3) + (2*(259 + 2535*S^2 + 5361*S^4 + 4055*S^6 + 6234*S^8 + 3822*S^10 + 718*S^12))/(81*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + (2*(19 + 34*S^2 - 18*S^4 + 150*S^6 - 54*S^8 + 22*S^10 + 19*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(6 + 18*S^2 + 18*S^4 - 89*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + ((2*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(9*S^3*(1 + S^2)^3) + (2*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(85 + 1401*S^2 + 3723*S^4 - 5230*S^6 + 3777*S^8 + 1419*S^10 + 85*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(97 + 291*S^2 + 291*S^4 - 610*S^6 + 255*S^8 + 255*S^10 + 85*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (40*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (16*(578 + 1734*S^2 + 1734*S^4 - 4001*S^6 + 1743*S^8 + 1743*S^10 + 581*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (80*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(17 + 51*S^2 + 51*S^4 - 147*S^6 + 90*S^8 + 90*S^10 + 30*S^12))/(27*S^3*(1 + S^2)^3) + (2*(128 + 604*S^2 + 1406*S^4 + 415*S^6 + 1309*S^8 + 461*S^10 + 77*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-137 - 12374*S^2 - 16698*S^4 - 12374*S^6 - 137*S^8)/(486*S^3*(1 + S^2)) + (Pi^2*(-149 - 4341*S^2 - 12225*S^4 + 15326*S^6 - 8877*S^8 - 3225*S^10 - 149*S^12))/(54*S^3*(1 + S^2)^3) + (4*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(41 + 123*S^2 + 123*S^4 - 266*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + (4*(27 + 81*S^2 + 81*S^4 - 195*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((138443 + 55473*S^2 + 652524*S^4 + 723830*S^6)/(11664*S^3) + (Pi^2*(3292 + 5506*S^2 + 18801*S^4 + 28258*S^6 + 14911*S^8))/(1944*S^3*(1 + S^2)) + (Pi^4*(777 + 1729*S^2 + 37*S^4 + 2763*S^6 + 2768*S^8 + 3362*S^10 + 1224*S^12))/(1080*S^3*(1 + S^2)^3) + ((200 + 507*S^2 + 381*S^4 + 499*S^6 + 270*S^8 + 81*S^10 - 16*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-14 - 42*S^2 - 42*S^4 + 18*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-51 - 153*S^2 - 153*S^4 + 174*S^6 + 39*S^8 + 39*S^10 + 13*S^12))/(9*S^3*(1 + S^2)^3) + (-1973 - 8028*S^2 - 15525*S^4 + 500*S^6 - 1035*S^8 + 2520*S^10 + 1141*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (2*(-109 - 240*S^2 - 150*S^4 - 1073*S^6 + 975*S^8 + 579*S^10 + 134*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-17 - 51*S^2 - 51*S^4 - 2*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-14 - 42*S^2 - 42*S^4 + 3*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-16 - 14*S^2 + 31*S^4 - 263*S^6 + 426*S^8 + 267*S^10 + 65*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-39 - 117*S^2 - 117*S^4 + 126*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-121 - 363*S^2 - 363*S^4 + 388*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(39 + 117*S^2 + 117*S^4 - 132*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-1 - 3*S^2 - 3*S^4 + 36*S^6 + 87*S^8 + 87*S^10 + 29*S^12))/(9*S^3*(1 + S^2)^3) + (137 + 930*S^2 + 1929*S^4 + 3712*S^6 + 5511*S^8 + 3630*S^10 + 983*S^12)/(54*S^3*(1 + S^2)^3))*Zeta[3] + (2*(-21 - 63*S^2 - 63*S^4 + 80*S^6 + 171*S^8 + 171*S^10 + 57*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((Pi^2*(89672 + 112589*S^2 + 111930*S^4 + 118421*S^6 + 83840*S^8))/(11664*S^3*(1 + S^2)) + (2665819 + 5038276*S^2 + 5261010*S^4 + 4215892*S^6 + 2447083*S^8)/(34992*S^3*(1 + S^2)) + (Pi^6*(-1134 - 3402*S^2 - 3402*S^4 + 222663*S^6 - 76956*S^8 - 76956*S^10 - 25652*S^12))/(68040*S^3*(1 + S^2)^3) + (Pi^4*(17630 + 94290*S^2 - 397983*S^4 + 811123*S^6 - 369201*S^8 + 132891*S^10 + 19106*S^12))/(38880*S^3*(1 + S^2)^3) + ((-8 - 24*S^2 - 24*S^4 - S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-13 - 39*S^2 - 39*S^4 + 22*S^6 + 27*S^8 + 27*S^10 + 9*S^12))/(9*S^3*(1 + S^2)^3) + (-748 - 1737*S^2 - 360*S^4 + 5668*S^6 + 7974*S^8 + 6165*S^10 + 1502*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((-137 - 338*S^2 - 233*S^4 - 298*S^6 + 15*S^8 + 96*S^10 + 55*S^12)*HPL[{5}, -S^2])/(6*S^3*(1 + S^2)^3) + (2*(-30 - 90*S^2 - 90*S^4 + 33*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-19 - 57*S^2 - 57*S^4 - 607*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(7 + 21*S^2 + 21*S^4 - 1982*S^6 + 1389*S^8 + 1389*S^10 + 463*S^12))/(9*S^3*(1 + S^2)^3) + (33 + 1712*S^2 + 13637*S^4 - 7884*S^6 + 25703*S^8 + 5372*S^10 + 1587*S^12)/(18*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((34 + 51*S^2 + 3*S^4 + 566*S^6 - 581*S^8 - 317*S^10 - 68*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + ((148 + 276*S^2 + 99*S^4 + 1790*S^6 - 1897*S^8 - 1078*S^10 - 242*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-1 - 3*S^2 - 3*S^4 + 6*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-17 - 51*S^2 - 51*S^4 + 9*S^6 + 54*S^8 + 54*S^10 + 18*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(-4 - 12*S^2 - 12*S^4 - 1983*S^6 + 1419*S^8 + 1419*S^10 + 473*S^12))/(9*S^3*(1 + S^2)^3) - (2*(10 + 2517*S^2 + 20553*S^4 - 11401*S^6 + 39237*S^8 + 8556*S^10 + 2512*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (2*(-1139 - 7953*S^2 - 18375*S^4 + 14372*S^6 - 3465*S^8 - 783*S^10 + 391*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-1107 - 7925*S^2 - 18437*S^4 + 14898*S^6 - 4317*S^8 - 1317*S^10 + 261*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-1 + S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) - (2*(-1 - 3*S^2 - 3*S^4 - 2672*S^6 + 2307*S^8 + 2307*S^10 + 769*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 - 2012*S^6 + 1737*S^8 + 1737*S^10 + 579*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(349 + 2627*S^2 + 6191*S^4 - 5314*S^6 + 2011*S^8 + 799*S^10 + S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-455 - 1365*S^2 - 1365*S^4 - 15914*S^6 + 15291*S^8 + 15291*S^10 + 5097*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*S^3*(-337 + 294*S^2 + 294*S^4 + 98*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*(1 + S^2)^3) + ((-142 + 4701*S^2 + 5691*S^4 + 5627*S^6)/(162*S^3) + (Pi^2*(7 + 186*S^2 + 438*S^4 - 1084*S^6 + 3534*S^8 + 1995*S^10 + 430*S^12))/(54*S^3*(1 + S^2)^3))*Zeta[3] - (4*(-1 - 3*S^2 - 3*S^4 - 15*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((8458 + 21799*S^2 + 22020*S^4 + 8749*S^6 - 578*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(395 + 3744*S^2 + 9519*S^4 - 7157*S^6 + 2258*S^8 + 839*S^10 - 34*S^12))/(18*S^3*(1 + S^2)^3) - (4*(42 + 126*S^2 + 126*S^4 - 125*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-555 + 1834*S^2 + 5816*S^4 + 4882*S^6 + 2751*S^8)/(216*S^3*(1 + S^2)) + (Pi^2*(-148 - 318*S^2 - 165*S^4 - 1052*S^6 + 1623*S^8 + 1029*S^10 + 257*S^12))/(54*S^3*(1 + S^2)^3) + (2*(-39 - 117*S^2 - 117*S^4 + 126*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-11 - 33*S^2 - 33*S^4 + 18*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((185 + 615*S^2 + 714*S^4 + 244*S^6 + 2970*S^8 + 2088*S^10 + 554*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(104305 - 46054*S^2 + 104305*S^4))/(1944*S^3) + (Pi^2*(96481 + 5764*S^2 - 178626*S^4 + 89140*S^6 + 130393*S^8))/(23328*S^3*(1 + S^2)) + (Pi^6*(-187513 - 562539*S^2 - 562539*S^4 + 953473*S^6 - 184422*S^8 - 184422*S^10 - 61474*S^12))/(136080*S^3*(1 + S^2)^3) + (Pi^4*(-11665 + 69672*S^2 - 1554828*S^4 + 1576852*S^6 - 797703*S^8 + 32448*S^10 - 5248*S^12))/(38880*S^3*(1 + S^2)^3) + ((-2522 - 11073*S^2 - 59790*S^4 + 22802*S^6 - 59790*S^8 - 11073*S^10 - 2522*S^12)/(108*S^3*(1 + S^2)^3) + (Pi^2*(-317 - 951*S^2 - 951*S^4 + 1901*S^6 - 702*S^8 - 702*S^10 - 234*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + ((-177 - 531*S^2 - 531*S^4 + 1214*S^6 - 531*S^8 - 531*S^10 - 177*S^12)*HPL[{2}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + ((1 + 3*S^2 + 3*S^4 - 20*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-29 - 87*S^2 - 87*S^4 + 320*S^6 - 153*S^8 - 153*S^10 - 51*S^12))/(18*S^3*(1 + S^2)^3) + (-85 + 4674*S^2 + 4989*S^4 + 17452*S^6 + 9705*S^8 + 12378*S^10 + 2615*S^12)/(108*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((259 + 591*S^2 + 141*S^4 + 1238*S^6 - 453*S^8 + 393*S^10 + 259*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-9 - 27*S^2 - 27*S^4 + 219*S^6 - 192*S^8 - 192*S^10 - 64*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(313 + 939*S^2 + 939*S^4 - 1888*S^6 + 681*S^8 + 681*S^10 + 227*S^12))/(9*S^3*(1 + S^2)^3) + (668 + 2001*S^2 + 16356*S^4 - 10304*S^6 + 15774*S^8 + 1143*S^10 + 362*S^12)/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] - (2*(151 + 771*S^2 + 1383*S^4 - 1570*S^6 + 1383*S^8 + 771*S^10 + 151*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(208 + 873*S^2 + 1329*S^4 - 1120*S^6 + 1221*S^8 + 837*S^10 + 208*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-1 + S^6)*HPL[{4, 2}, -S^2])/S^3 + (4*(5 + 15*S^2 + 15*S^4 - 109*S^6 + 66*S^8 + 66*S^10 + 22*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(3*S^3*(1 + S^2)^3) - (2*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(145 + 1609*S^2 + 3975*S^4 - 5286*S^6 + 3993*S^8 + 1615*S^10 + 145*S^12)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (8*(177 + 531*S^2 + 531*S^4 - 1214*S^6 + 531*S^8 + 531*S^10 + 177*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(1079 + 3237*S^2 + 3237*S^4 - 7478*S^6 + 3273*S^8 + 3273*S^10 + 1091*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (40*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(62 + 186*S^2 + 186*S^4 - 435*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (80*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((2007 + 3077*S^2 + 1969*S^4 + 1115*S^6)/(36*S^3) + (Pi^2*(304 + 1221*S^2 + 1842*S^4 - 1174*S^6 + 2544*S^8 + 1455*S^10 + 304*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] - (2*(7 + 21*S^2 + 21*S^4 - 67*S^6 + 30*S^8 + 30*S^10 + 10*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((1243 + 3058*S^2 + 9114*S^4 + 9058*S^6 + 3919*S^8)/(108*S^3*(1 + S^2)) + (Pi^2*(431 + 1272*S^2 + 1137*S^4 + 268*S^6 + 1299*S^8 + 1326*S^10 + 431*S^12))/(54*S^3*(1 + S^2)^3) - (4*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*S^3*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((137 + 12374*S^2 + 16698*S^4 + 12374*S^6 + 137*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(149 + 4341*S^2 + 12225*S^4 - 15326*S^6 + 8877*S^8 + 3225*S^10 + 149*S^12))/(18*S^3*(1 + S^2)^3) - (4*(41 + 123*S^2 + 123*S^4 - 266*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((53453 + 52460*S^2 + 83550*S^4 + 52460*S^6 + 53453*S^8)/(1944*S^3*(1 + S^2)) + (Pi^4*(-7131 - 21393*S^2 - 21393*S^4 + 38357*S^6 - 10932*S^8 - 10932*S^10 - 3644*S^12))/(1080*S^3*(1 + S^2)^3) + (Pi^2*(-646 - 996*S^2 - 24072*S^4 + 17311*S^6 - 17577*S^8 - 615*S^10 - 325*S^12))/(108*S^3*(1 + S^2)^3) + ((151 + 771*S^2 + 1383*S^4 - 1570*S^6 + 1383*S^8 + 771*S^10 + 151*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-1 - 3*S^2 - 3*S^4 + 40*S^6 - 21*S^8 - 21*S^10 - 7*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((325 + 1725*S^2 + 3237*S^4 - 2590*S^6 + 3237*S^8 + 1725*S^10 + 325*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + ((601 + 2292*S^2 + 3273*S^4 - 1120*S^6 + 3867*S^8 + 2490*S^10 + 601*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + ((-20 - 30*S^2 + 558*S^4 + 976*S^6 + 453*S^8)*Zeta[7])/(S*(1 + S^2)^2) + HPL[{1}, -S^2]*((5*(1 + S^2)*(523277 - 119846*S^2 + 523277*S^4))/(23328*S^3) + (Pi^2*(118161 + 178096*S^2 + 87762*S^4 + 176088*S^6 + 106789*S^8))/(7776*S^3*(1 + S^2)) + (Pi^4*(354947 + 404633*S^2 + 9075*S^4 + 381827*S^6 + 325886*S^8))/(233280*S^3*(1 + S^2)) + (Pi^6*(54551 - 209714*S^2 - 954789*S^4 + 1528028*S^6 - 198555*S^8 + 42364*S^10 + 54551*S^12))/(90720*S^3*(1 + S^2)^3) + ((-187 - 2184*S^2 - 5460*S^4 + 7186*S^6 - 5460*S^8 - 2184*S^10 - 187*S^12)*HPL[{2}, -S^2]^3)/(27*S^3*(1 + S^2)^3) + ((-2 + 6*S^2 + 33*S^4 - 130*S^6 + 87*S^8 + 24*S^10 - 2*S^12)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((-2*Pi^2*(-6 - 18*S^2 - 18*S^4 - 61*S^6 + 87*S^8 + 87*S^10 + 29*S^12))/(9*S^3*(1 + S^2)^3) + (-116 + 4*S^2 + 29*S^4 + 726*S^6 + 714*S^8 + 1074*S^10 + 281*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((87 + 198*S^2 + 27*S^4 + 196*S^6 - 303*S^8 + 88*S^10 + 87*S^12)*HPL[{6}, -S^2])/(2*S^3*(1 + S^2)^3) - (2*(-78 - 234*S^2 - 234*S^4 + 39*S^6 + 435*S^8 + 435*S^10 + 145*S^12)*HPL[{7}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(25 + 75*S^2 + 75*S^4 - 167*S^6 + 60*S^8 + 60*S^10 + 20*S^12))/(9*S^3*(1 + S^2)^3) - (2*(380 + 1983*S^2 + 4917*S^4 + 175*S^6 + 4143*S^8 + 1218*S^10 + 128*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((-3989 - 27174*S^2 - 62859*S^4 - 19552*S^6 - 60555*S^8 - 28290*S^10 - 4637*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(-121 - 363*S^2 - 363*S^4 + 682*S^6 - 207*S^8 - 207*S^10 - 69*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((2 - 8*S^2 - 25*S^4 + 11*S^6 + 10*S^8 + 2*S^10)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^2) - (2*(-32 - 96*S^2 - 96*S^4 + 57*S^6 + 135*S^8 + 135*S^10 + 45*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(263 + 615*S^2 + 183*S^4 + 1498*S^6 - 735*S^8 + 309*S^10 + 263*S^12)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-47 - 141*S^2 - 141*S^4 + 81*S^6 + 204*S^8 + 204*S^10 + 68*S^12)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-159 - 477*S^2 - 477*S^4 + 459*S^6 + 498*S^8 + 498*S^10 + 166*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*Pi^2*(317 + 951*S^2 + 951*S^4 - 1901*S^6 + 702*S^8 + 702*S^10 + 234*S^12))/(9*S^3*(1 + S^2)^3) - (2*(2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((-4*Pi^2*(947 + 2841*S^2 + 2841*S^4 - 5690*S^6 + 2085*S^8 + 2085*S^10 + 695*S^12))/(9*S^3*(1 + S^2)^3) - (2*(7048 + 28149*S^2 + 168648*S^4 - 76516*S^6 + 166902*S^8 + 25575*S^10 + 6130*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (8*(187 + 2184*S^2 + 5460*S^4 - 7186*S^6 + 5460*S^8 + 2184*S^10 + 187*S^12)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(69 + 207*S^2 + 207*S^4 - 488*S^6 + 153*S^8 + 153*S^10 + 51*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(27 + 81*S^2 + 81*S^4 - 193*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(317 + 4266*S^2 + 10974*S^4 - 14822*S^6 + 11082*S^8 + 4302*S^10 + 317*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(215 + 645*S^2 + 645*S^4 - 1544*S^6 + 483*S^8 + 483*S^10 + 161*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(659 + 1977*S^2 + 1977*S^4 - 4712*S^6 + 1455*S^8 + 1455*S^10 + 485*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(327 + 981*S^2 + 981*S^4 - 2287*S^6 + 678*S^8 + 678*S^10 + 226*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(3*S^3*(1 + S^2)^3) + (4*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] + (16*(177 + 531*S^2 + 531*S^4 - 1214*S^6 + 531*S^8 + 531*S^10 + 177*S^12)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(85 + 1401*S^2 + 3723*S^4 - 5230*S^6 + 3777*S^8 + 1419*S^10 + 85*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(275 + 825*S^2 + 825*S^4 - 1888*S^6 + 825*S^8 + 825*S^10 + 275*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(275 + 825*S^2 + 825*S^4 - 1888*S^6 + 825*S^8 + 825*S^10 + 275*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(1081 + 3243*S^2 + 3243*S^4 - 7418*S^6 + 3243*S^8 + 3243*S^10 + 1081*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(6469 + 19407*S^2 + 19407*S^4 - 44314*S^6 + 19371*S^8 + 19371*S^10 + 6457*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (80*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (32*(330 + 990*S^2 + 990*S^4 - 2261*S^6 + 987*S^8 + 987*S^10 + 329*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (160*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((17551 + 24461*S^2 + 13117*S^4 + 7935*S^6)/(216*S^3) + (Pi^2*(1598 + 7554*S^2 + 14025*S^4 + 7984*S^6 + 13602*S^8 + 5106*S^10 + 731*S^12))/(108*S^3*(1 + S^2)^3) + (Pi^4*(-212 - 636*S^2 - 636*S^4 - 805*S^6 + 2697*S^8 + 2697*S^10 + 899*S^12))/(540*S^3*(1 + S^2)^3))*Zeta[3] + ((65 + 150*S^2 + 57*S^4 + 412*S^6 + 3*S^8 + 132*S^10 + 65*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((7657 + 14116*S^2 + 59910*S^4 + 76996*S^6 + 36505*S^8)/(648*S^3*(1 + S^2)) + (Pi^4*(-19 - 57*S^2 - 57*S^4 + 433*S^6 - 168*S^8 - 168*S^10 - 56*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(559 + 7368*S^2 + 13497*S^4 + 13628*S^6 + 18807*S^8 + 12696*S^10 + 2557*S^12))/(324*S^3*(1 + S^2)^3) + (2*(-17 - 51*S^2 - 51*S^4 + 33*S^6 + 66*S^8 + 66*S^10 + 22*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(151 + 771*S^2 + 1383*S^4 - 1570*S^6 + 1383*S^8 + 771*S^10 + 151*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(19 + 57*S^2 + 57*S^4 - 142*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(2 + 3*S^2 - 6*S^4 - 14*S^6 - 60*S^8 - 15*S^10 + 2*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((-1970 - 7637*S^2 - 11010*S^4 - 7637*S^6 - 1970*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-619 - 7620*S^2 - 19203*S^4 + 22720*S^6 - 14721*S^8 - 6126*S^10 - 619*S^12))/(108*S^3*(1 + S^2)^3) + (2*(9 + 27*S^2 + 27*S^4 - 61*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(177 + 531*S^2 + 531*S^4 - 1214*S^6 + 531*S^8 + 531*S^10 + 177*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(19 + 57*S^2 + 57*S^4 - 127*S^6 + 66*S^8 + 66*S^10 + 22*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((4151 + 21374*S^2 + 16698*S^4 + 3374*S^6 - 3877*S^8)/(162*S^3*(1 + S^2)) + (2*Pi^2*(94 + 3174*S^2 + 9033*S^4 - 11494*S^6 + 6711*S^8 + 2400*S^10 + 94*S^12))/(27*S^3*(1 + S^2)^3) - (8*(19 + 57*S^2 + 57*S^4 - 129*S^6 + 72*S^8 + 72*S^10 + 24*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4}, -S^2]*((4021 + 4456*S^2 + 34602*S^4 + 58960*S^6 + 31273*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(125 + 249*S^2 - 42*S^4 + 736*S^6 - 240*S^8 + 183*S^10 + 125*S^12))/(18*S^3*(1 + S^2)^3) + (2*(1 + 3*S^2 + 3*S^4 - 40*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-23 - 69*S^2 - 69*S^4 + 52*S^6 + 81*S^8 + 81*S^10 + 27*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((-137 - 12374*S^2 - 16698*S^4 - 12374*S^6 - 137*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(-149 - 4341*S^2 - 12225*S^4 + 15326*S^6 - 8877*S^8 - 3225*S^10 - 149*S^12))/(9*S^3*(1 + S^2)^3) + (8*(41 + 123*S^2 + 123*S^4 - 266*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-53453 - 52460*S^2 - 83550*S^4 - 52460*S^6 - 53453*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(646 + 996*S^2 + 24072*S^4 - 17311*S^6 + 17577*S^8 + 615*S^10 + 325*S^12))/(54*S^3*(1 + S^2)^3) + (Pi^4*(7131 + 21393*S^2 + 21393*S^4 - 38357*S^6 + 10932*S^8 + 10932*S^10 + 3644*S^12))/(540*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(325 + 1725*S^2 + 3237*S^4 - 2590*S^6 + 3237*S^8 + 1725*S^10 + 325*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + ((Pi^2*(-13 - 39*S^2 - 39*S^4 - 23*S^6 + 282*S^8 + 282*S^10 + 94*S^12))/(9*S^3*(1 + S^2)^3) + (1961 + 8760*S^2 + 15006*S^4 + 9964*S^6 + 12435*S^8 + 5040*S^10 + 602*S^12)/(18*S^3*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(4973 - 21454*S^2 - 8016*S^4 + 17678*S^6 + 22595*S^8))/(3888*S^3*(1 + S^2)) + (100439 + 167747*S^2 + 227928*S^4 + 167747*S^6 + 100439*S^8)/(1458*S^3*(1 + S^2)) + (Pi^4*(3103 - 122934*S^2 - 391305*S^4 + 479372*S^6 - 203007*S^8 - 60168*S^10 + 3103*S^12))/(6480*S^3*(1 + S^2)^3) + ((Pi^2*(25 + 75*S^2 + 75*S^4 - 167*S^6 + 60*S^8 + 60*S^10 + 20*S^12))/(9*S^3*(1 + S^2)^3) + (679 + 3750*S^2 + 9645*S^4 + 350*S^6 + 8475*S^8 + 2652*S^10 + 337*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((4 - 3*S^2 - 39*S^4 + 260*S^6 - 201*S^8 - 57*S^10 + 4*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-19 - 57*S^2 - 57*S^4 + 42*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(317 + 951*S^2 + 951*S^4 - 1901*S^6 + 702*S^8 + 702*S^10 + 234*S^12))/(9*S^3*(1 + S^2)^3) + (2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (2*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(35 + 105*S^2 + 105*S^4 - 244*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(109 + 327*S^2 + 327*S^4 - 772*S^6 + 237*S^8 + 237*S^10 + 79*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(177 + 531*S^2 + 531*S^4 - 1214*S^6 + 531*S^8 + 531*S^10 + 177*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(275 + 825*S^2 + 825*S^4 - 1888*S^6 + 825*S^8 + 825*S^10 + 275*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(27 + 81*S^2 + 81*S^4 - 277*S^6 + 192*S^8 + 192*S^10 + 64*S^12))/(9*S^3*(1 + S^2)^3) + (839 + 4512*S^2 + 11973*S^4 + 4279*S^6 + 12558*S^8 + 5061*S^10 + 1010*S^12)/(27*S^3*(1 + S^2)^3))*Zeta[3] + (2*(9 + 27*S^2 + 27*S^4 - 111*S^6 + 132*S^8 + 132*S^10 + 44*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + (10*(-2 + 7*S^6)*Zeta[7])/S^3)) + Log[T]*((-27175*(1 + S^2))/(11664*S) + (Pi^4*(1315898 + 1597087*S^2 - 1180390*S^4 - 1223115*S^6))/(233280*S*(1 + S^2)) + (Pi^2*(1104623 + 1278799*S^2 - 1100359*S^4 - 1087911*S^6))/(34992*S*(1 + S^2)) - (7*Pi^8*S^3*(70669 + 16296*S^2 + 16296*S^4 + 5432*S^6))/(291600*(1 + S^2)^3) + (Pi^6*(127178 + 1871171*S^2 - 2724285*S^4 + 28217*S^6 - 659533*S^8 - 277308*S^10))/(272160*S*(1 + S^2)^3) - (S^3*(7 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{0}, S^2]^8)/(288*(1 + S^2)^3) + (4*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^7)/(3*S^3*(1 + S^2)^3) + (8*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^8)/(9*S^3*(1 + S^2)^3) + HPL[{0}, S^2]^7*((8 + 20*S^2 - 57*S^4 - 49*S^6 - 40*S^8 - 12*S^10)/(144*S*(1 + S^2)^3) + ((4 + 12*S^2 + 12*S^4 - 13*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{1}, -S^2])/(72*S^3*(1 + S^2)^3)) + ((-153 - 351*S^2 + 58*S^4 - 58*S^6 + 351*S^8 + 153*S^10)/(18*S^3*(1 + S^2)^2) + (2*Pi^2*(-33 - 99*S^2 - 99*S^4 - 187*S^6 + 183*S^8 + 183*S^10 + 61*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^3 + (2*(14 + 42*S^2 + 42*S^4 - 187*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{2}, -S^2]^4)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^6*((35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12)/(9*S^3*(1 + S^2)^3) + (2*Pi^2*(51 + 153*S^2 + 153*S^4 - 305*S^6 + 108*S^8 + 108*S^10 + 36*S^12))/(27*S^3*(1 + S^2)^3) - (20*(-1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^6*(-(Pi^2*S^3*(74 + 51*S^2 + 51*S^4 + 17*S^6))/(216*(1 + S^2)^3) + (-80 + 331*S^2 - 1428*S^4 - 1580*S^6 - 1136*S^8 - 339*S^10)/(864*S*(1 + S^2)^3) + ((-23 + 132*S^2 + 528*S^4 - 550*S^6 - 228*S^8 - 120*S^10 - 23*S^12)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)^3) + ((23 + 69*S^2 + 69*S^4 - 70*S^6 - 15*S^8 - 15*S^10 - 5*S^12)*HPL[{1}, -S^2]^2)/(72*S^3*(1 + S^2)^3) + ((1 + 3*S^2 + 3*S^4 - 35*S^6 - 12*S^8 - 12*S^10 - 4*S^12)*HPL[{2}, -S^2])/(72*S^3*(1 + S^2)^3)) + ((Pi^2*(3 + 9*S^2 + 9*S^4 - 98*S^6 + 129*S^8 + 129*S^10 + 43*S^12))/(9*S^3*(1 + S^2)^3) + (23 + 1788*S^2 + 7125*S^4 + 4474*S^6 + 15909*S^8 + 7422*S^10 + 1859*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{3}, -S^2]^2 + (4*(1 + 3*S^2 + 3*S^4 - 11*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{4}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((480 - 692*S^2 - 1463*S^4 - 8589*S^6 - 16555*S^8 - 10007*S^10 - 2614*S^12)/(6*S^3*(1 + S^2)^3) - (2*Pi^2*(-70 - 210*S^2 - 210*S^4 - 4*S^6 + 303*S^8 + 303*S^10 + 101*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{6}, -S^2] - (2*(480 + 773*S^2 - 445*S^4 + 2871*S^6 + 5581*S^8 + 3499*S^10 + 843*S^12)*HPL[{7}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-245 - 735*S^2 - 735*S^4 + 778*S^6 + 1080*S^8 + 1080*S^10 + 360*S^12)*HPL[{8}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-1399 - 9564*S^2 - 53817*S^4 + 33976*S^6 - 53817*S^8 - 9564*S^10 - 1399*S^12)/(27*S^3*(1 + S^2)^3) - (4*Pi^2*(46 + 138*S^2 + 138*S^4 - 1195*S^6 + 321*S^8 + 321*S^10 + 107*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2]^2 + (16*(48 + 144*S^2 + 144*S^4 - 445*S^6 + 81*S^8 + 81*S^10 + 27*S^12)*HPL[{3, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((164*Pi^2*S^3*(-2 + 3*S^2 + 3*S^4 + S^6))/(9*(1 + S^2)^3) + (-54 + 315*S^2 + 1982*S^4 + 1554*S^6 + 6198*S^8 + 3011*S^10 + 786*S^12)/(6*S^3*(1 + S^2)^3))*HPL[{4, 2}, -S^2] - (2*(15 + 67*S^2 + 112*S^4 - 228*S^6 + 644*S^8 + 272*S^10 + 36*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-38 - 114*S^2 - 114*S^4 - 999*S^6 + 1425*S^8 + 1425*S^10 + 475*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-38 + 973*S^2 + 3285*S^4 + 3122*S^6 + 10267*S^8 + 4903*S^10 + 1244*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{5, 1}, -S^2] + ((-159 - 545*S^2 - 677*S^4 + 1308*S^6 - 2297*S^8 - 743*S^10 - 15*S^12)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{5, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(231 + 177*S^2 - 819*S^4 + 2016*S^6 + 4805*S^8 + 3104*S^10 + 768*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-9 - 27*S^2 - 27*S^4 - 34*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*HPL[{6, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-177 - 531*S^2 - 531*S^4 + 437*S^6 + 918*S^8 + 918*S^10 + 306*S^12)*HPL[{7, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (320*(5 + 15*S^2 + 15*S^4 - 77*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(-45 + 37*S^6))/(9*S^3) - (2*(-105 - 232*S^2 - 295*S^4 + 295*S^6 + 232*S^8 + 105*S^10))/(3*S^3*(1 + S^2)^2))*HPL[{3, 1, 2}, -S^2] + ((2*(-201 - 470*S^2 + 411*S^4 - 411*S^6 + 470*S^8 + 201*S^10))/(3*S^3*(1 + S^2)^2) + (2*Pi^2*(-219 - 657*S^2 - 657*S^4 - 1488*S^6 + 1353*S^8 + 1353*S^10 + 451*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 2, 1}, -S^2] - (2*(-180 + 249*S^2 + 1287*S^4 - 9288*S^6 + 17923*S^8 + 7261*S^10 + 840*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-53 + 39*S^2 + 289*S^4 - 2349*S^6 + 4656*S^8 + 1916*S^10 + 234*S^12)*HPL[{3, 3, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(4 + 12*S^2 + 12*S^4 - 121*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*HPL[{3, 3, 2}, -S^2])/(S^3*(1 + S^2)^3) + ((-2*(783 + 3531*S^2 + 4313*S^4 + 1960*S^6 + 7039*S^8 + 973*S^10 + 89*S^12))/(3*S^3*(1 + S^2)^3) + (4*Pi^2*(-381 - 1143*S^2 - 1143*S^4 - 1700*S^6 + 1575*S^8 + 1575*S^10 + 525*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 1, 1}, -S^2] - (2*(-657 + 329*S^2 + 3218*S^4 - 27444*S^6 + 55622*S^8 + 22853*S^10 + 2787*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(12 + 36*S^2 + 36*S^4 - 313*S^6 + 285*S^8 + 285*S^10 + 95*S^12)*HPL[{4, 1, 3}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-1917 + 1637*S^2 + 11042*S^4 - 85692*S^6 + 170750*S^8 + 70697*S^10 + 8799*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - 221*S^6 + 342*S^8 + 342*S^10 + 114*S^12)*HPL[{4, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(36 + 108*S^2 + 108*S^4 - 1039*S^6 + 1059*S^8 + 1059*S^10 + 353*S^12)*HPL[{4, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1647 + 2607*S^2 + 12219*S^4 - 87624*S^6 + 176737*S^8 + 73765*S^10 + 9375*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(54 + 162*S^2 + 162*S^4 - 1231*S^6 + 1185*S^8 + 1185*S^10 + 395*S^12)*HPL[{5, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (28*(42 + 126*S^2 + 126*S^4 - 1213*S^6 + 1275*S^8 + 1275*S^10 + 425*S^12)*HPL[{5, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(270 + 810*S^2 + 810*S^4 - 10937*S^6 + 12063*S^8 + 12063*S^10 + 4021*S^12)*HPL[{6, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-255 - 1498*S^2 - 2661*S^4 + 2661*S^6 + 1498*S^8 + 255*S^10)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + ((4*(361 + 1650*S^2 + 2497*S^4 + 980*S^6 + 3179*S^8 + 602*S^10 + 75*S^12))/(3*S^3*(1 + S^2)^3) - (16*Pi^2*(-79 - 237*S^2 - 237*S^4 - 246*S^6 + 243*S^8 + 243*S^10 + 81*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1, 1, 1}, -S^2] - (16*(-327 - 2632*S^2 - 6439*S^4 + 2100*S^6 + 1567*S^8 + 688*S^10 + 135*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-327 - 2632*S^2 - 6439*S^4 + 2100*S^6 + 1567*S^8 + 688*S^10 + 135*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(47 + 141*S^2 + 141*S^4 - 242*S^6 + 141*S^8 + 141*S^10 + 47*S^12)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-1419 - 10523*S^2 - 25355*S^4 + 4200*S^6 + 15611*S^8 + 6635*S^10 + 1035*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(47 + 141*S^2 + 141*S^4 - 242*S^6 + 141*S^8 + 141*S^10 + 47*S^12)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-535 - 1605*S^2 - 1605*S^4 + 242*S^6 + 1323*S^8 + 1323*S^10 + 441*S^12)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (1952*(-1 + S^6)*HPL[{3, 3, 1, 1}, -S^2])/S^3 - (16*(-2241 - 16253*S^2 - 38753*S^4 + 7314*S^6 + 22123*S^8 + 9361*S^10 + 1473*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-1 - 3*S^2 - 3*S^4 - 114*S^6 + 165*S^8 + 165*S^10 + 55*S^12)*HPL[{4, 1, 1, 2}, -S^2])/(S^3*(1 + S^2)^3) - (24*(-81 - 243*S^2 - 243*S^4 + 38*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{4, 1, 2, 1}, -S^2])/(S^3*(1 + S^2)^3) - (8*(-731 - 2193*S^2 - 2193*S^4 + 114*S^6 + 2031*S^8 + 2031*S^10 + 677*S^12)*HPL[{4, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (32*(-1086 - 3258*S^2 - 3258*S^4 + 511*S^6 + 2631*S^8 + 2631*S^10 + 877*S^12)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*(-143 - 381*S^2 + 722*S^4 - 722*S^6 + 381*S^8 + 143*S^10))/(3*S^3*(1 + S^2)^2) + (160*Pi^2*(-11 - 33*S^2 - 33*S^4 - 77*S^6 + 63*S^8 + 63*S^10 + 21*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (128*(8 + 81*S^2 + 203*S^4 - 175*S^6 + 203*S^8 + 81*S^10 + 8*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (384*(8 + 81*S^2 + 203*S^4 - 175*S^6 + 203*S^8 + 81*S^10 + 8*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (3904*(-1 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3) - (3904*(-1 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 - (16*(1023 + 10409*S^2 + 25799*S^4 - 26214*S^6 + 34679*S^8 + 13979*S^10 + 1473*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (7584*(-1 + S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 + (38368*(-1 + S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) + (15392*(-1 + S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^3 + (96928*(-1 + S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) + (384*(-254 - 762*S^2 - 762*S^4 + 15*S^6 + 747*S^8 + 747*S^10 + 249*S^12)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (160*(-15 - 104*S^2 - 192*S^4 + 192*S^6 + 104*S^8 + 15*S^10)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (640*(-5 - 15*S^2 - 15*S^4 + 9*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4480*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-2*Pi^2*S^3*(73 + 33*S^2 + 33*S^4 + 11*S^6))/(9*(1 + S^2)^3) + (6 + 113*S^2 - 91*S^4 + 229*S^6 + 145*S^8 + 54*S^10)/(3*S*(1 + S^2)^3))*Zeta[3]^2 + HPL[{0}, S^2]^5*((-520 - 875*S^2 - 1801*S^4 - 1338*S^6)/(864*S*(1 + S^2)) + (Pi^2*(1390 + 3475*S^2 - 9378*S^4 - 6007*S^6 - 5026*S^8 - 1530*S^10))/(2160*S*(1 + S^2)^3) + ((-200 + 1035*S^2 + 4290*S^4 - 5062*S^6 - 732*S^8 - 639*S^10 - 200*S^12)*HPL[{1}, -S^2]^2)/(360*S^3*(1 + S^2)^3) + ((275 + 825*S^2 + 825*S^4 - 1033*S^6 - 12*S^8 - 12*S^10 - 4*S^12)*HPL[{1}, -S^2]^3)/(270*S^3*(1 + S^2)^3) + ((-65 + 295*S^2 + 1075*S^4 - 2638*S^6 - 467*S^8 - 566*S^10 - 200*S^12)*HPL[{2}, -S^2])/(360*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]*((-910 - 6930*S^2 + 7395*S^4 - 23600*S^6 - 11070*S^8 - 6546*S^10 - 1195*S^12)/(2160*S^3*(1 + S^2)^3) + (Pi^2*(695 + 2085*S^2 + 2085*S^4 - 2398*S^6 - 327*S^8 - 327*S^10 - 109*S^12))/(1080*S^3*(1 + S^2)^3) + ((230 + 690*S^2 + 690*S^4 - 853*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2}, -S^2])/(180*S^3*(1 + S^2)^3)) - (S^3*HPL[{3}, -S^2])/(3*(1 + S^2)^3) + ((-115 - 345*S^2 - 345*S^4 + 156*S^6)*HPL[{2, 1}, -S^2])/(45*S^3*(1 + S^2)^3) - (S^3*(3 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(2*(1 + S^2)^3)) + HPL[{5}, -S^2]*((-7341 - 18485*S^2 - 37027*S^4 - 60707*S^6 - 30936*S^8)/(108*S^3*(1 + S^2)) + (Pi^2*(-967 - 2322*S^2 - 1269*S^4 - 152*S^6 - 15255*S^8 - 7470*S^10 - 1309*S^12))/(54*S^3*(1 + S^2)^3) - (4*(-20 - 60*S^2 - 60*S^4 + 377*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(7 + 21*S^2 + 21*S^4 + 39*S^6)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1, 1}, -S^2]*((4*(-509 - 383*S^2 + 383*S^4 + 509*S^6))/(3*S^3) + (4*Pi^2*(-459 - 3797*S^2 - 9407*S^4 + 2100*S^6 + 4535*S^8 + 1853*S^10 + 267*S^12))/(9*S^3*(1 + S^2)^3) - (320*(-10 - 30*S^2 - 30*S^4 + 77*S^6)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((-25415 + 26830*S^2 + 81162*S^4 + 26830*S^6 - 25415*S^8)/(1944*S^3*(1 + S^2)) + (Pi^4*(220 + 660*S^2 + 660*S^4 - 12053*S^6 + 3090*S^8 + 3090*S^10 + 1030*S^12))/(540*S^3*(1 + S^2)^3) + (Pi^2*(619 + 10536*S^2 + 81699*S^4 - 51592*S^6 + 86973*S^8 + 19608*S^10 + 3373*S^12))/(648*S^3*(1 + S^2)^3) + ((29 - 777*S^2 - 2109*S^4 + 7915*S^6 - 14586*S^8 - 6036*S^10 - 736*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 86*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^3) + ((-255 - 1498*S^2 - 2661*S^4 + 2661*S^6 + 1498*S^8 + 255*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (2*(-161 - 483*S^2 - 483*S^4 + 258*S^6 + 249*S^8 + 249*S^10 + 83*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (488*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((191 + 183*S^2 - 231*S^4 + 5683*S^6 - 12708*S^8 - 5076*S^10 - 574*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2, 2, 1}, -S^2]*((5571 + 12236*S^2 + 12898*S^4 + 12236*S^6 + 5571*S^8)/(27*S^3*(1 + S^2)) + (2*Pi^2*(1343 + 11847*S^2 + 29001*S^4 - 19517*S^6 + 16524*S^8 + 6588*S^10 + 578*S^12))/(27*S^3*(1 + S^2)^3) + (32*(-54 - 162*S^2 - 162*S^4 + 345*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*(((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(54*S^3) + (Pi^2*(1619 + 6333*S^2 + 36216*S^4 - 15548*S^6 + 27729*S^8 + 5235*S^10 + 1016*S^12))/(162*S^3*(1 + S^2)^3) + (Pi^4*(4460 + 13380*S^2 + 13380*S^4 - 23717*S^6 + 6639*S^8 + 6639*S^10 + 2213*S^12))/(810*S^3*(1 + S^2)^3) + ((67 + 55*S^2 + 888*S^4 - 888*S^6 - 55*S^8 - 67*S^10)/(3*S^3*(1 + S^2)^2) - (2*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (8*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) - (2*(283 + 1611*S^2 + 3147*S^4 - 6262*S^6 + 7197*S^8 + 2961*S^10 + 283*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(47 + 141*S^2 + 141*S^4 - 554*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (300*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (8*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (200*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (10*(17 + 147*S^2 + 345*S^4 - 1046*S^6 + 1155*S^8 + 417*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^5*((4*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) + (Pi^2*(109 + 1239*S^2 + 3057*S^4 - 3742*S^6 + 2247*S^8 + 969*S^10 + 109*S^12))/(27*S^3*(1 + S^2)^3) - (60*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (40*(5 + 15*S^2 + 15*S^4 - 65*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (40*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (8*(5 + 15*S^2 + 15*S^4 - 87*S^6 + 60*S^8 + 60*S^10 + 20*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1, 1}, -S^2]*((-2*(-7824 - 14291*S^2 - 5608*S^4 + 1765*S^6 + 1338*S^8))/(27*S^3*(1 + S^2)) + (2*Pi^2*(3773 + 33474*S^2 + 83163*S^4 - 42107*S^6 + 16302*S^8 + 5925*S^10 + 38*S^12))/(27*S^3*(1 + S^2)^3) + (16*(-321 - 963*S^2 - 963*S^4 + 2166*S^6 + 69*S^8 + 69*S^10 + 23*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4, 1}, -S^2]*((-1911 + 3294*S^2 + 22618*S^4 + 37106*S^6 + 19261*S^8)/(18*S^3*(1 + S^2)) + (Pi^2*(-17 + 3681*S^2 + 8496*S^4 - 45178*S^6 + 98970*S^8 + 42207*S^10 + 5653*S^12))/(27*S^3*(1 + S^2)^3) + (16*(-1 - 3*S^2 - 3*S^4 - 121*S^6 + 78*S^8 + 78*S^10 + 26*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 2}, -S^2]*((-7473 - 3794*S^2 + 25796*S^4 + 52738*S^6 + 29757*S^8)/(108*S^3*(1 + S^2)) + (Pi^2*(-466 + 819*S^2 + 3582*S^4 - 25664*S^6 + 60300*S^8 + 25641*S^10 + 3476*S^12))/(54*S^3*(1 + S^2)^3) + (4*(-1 - 3*S^2 - 3*S^4 - 124*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4}, -S^2]*((3469 - 18897*S^2 - 56139*S^4 - 52025*S^6)/(216*S^3) + (Pi^2*(2005 - 3885*S^2 - 21777*S^4 - 24178*S^6 - 94353*S^8 - 44529*S^10 - 11459*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(219 + 657*S^2 + 657*S^4 + 2078*S^6 - 2655*S^8 - 2655*S^10 - 885*S^12))/(270*S^3*(1 + S^2)^3) - (2*(-299 - 1361*S^2 - 2414*S^4 + 1604*S^6 + 190*S^8 + 235*S^10 + 121*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-3 - 9*S^2 - 9*S^4 - 161*S^6 + 234*S^8 + 234*S^10 + 78*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-1 - 3*S^2 - 3*S^4 - 106*S^6 + 165*S^8 + 165*S^10 + 55*S^12)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (2*(38 + 121*S^2 + 133*S^4 - 56*S^6 + 449*S^8 + 203*S^10 + 32*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((773 + 2166*S^2 + 16593*S^4 + 11366*S^6)/(54*S^3) + (Pi^4*(993 + 2979*S^2 + 2979*S^4 + 10096*S^6 - 4533*S^8 - 4533*S^10 - 1511*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(1115 + 4650*S^2 - 1221*S^4 + 9412*S^6 + 2337*S^8 + 18*S^10 - 55*S^12))/(54*S^3*(1 + S^2)^3) - (32*(71 + 213*S^2 + 213*S^4 - 770*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(17 + 262*S^2 + 577*S^4 - 2219*S^6 + 4368*S^8 + 1725*S^10 + 182*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((1177 + 1603*S^2 - 1603*S^4 - 1177*S^6)/(6*S^3) + (Pi^4*(-660 - 1980*S^2 - 1980*S^4 - 12377*S^6 + 5469*S^8 + 5469*S^10 + 1823*S^12))/(135*S^3*(1 + S^2)^3) + (Pi^2*(-1042 - 2058*S^2 + 32421*S^4 - 16988*S^6 + 21396*S^8 + 11622*S^10 + 2441*S^12))/(81*S^3*(1 + S^2)^3) - (8*(9 + 227*S^2 + 527*S^4 - 2100*S^6 + 4345*S^8 + 1717*S^10 + 183*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^4*((17390 + 12353*S^2 - 37562*S^4 - 31661*S^6)/(5184*S*(1 + S^2)) - (Pi^4*S^3*(11971 + 6258*S^2 + 6258*S^4 + 2086*S^6))/(6480*(1 + S^2)^3) + (Pi^2*(-376 + 3856*S^2 - 10543*S^4 - 8959*S^6 - 6825*S^8 - 2081*S^10))/(864*S*(1 + S^2)^3) + ((2 + 545*S^2 + 1614*S^4 - 1554*S^6 + 30*S^8 + 17*S^10 + 2*S^12)*HPL[{1}, -S^2]^3)/(36*S^3*(1 + S^2)^3) + ((137 + 411*S^2 + 411*S^4 - 518*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{1}, -S^2]^4)/(54*S^3*(1 + S^2)^3) + ((173 + 50*S^2 + 5630*S^4 - 8345*S^6 - 2968*S^8 - 2761*S^10 - 835*S^12)/(432*S^3*(1 + S^2)^3) + (Pi^2*(9 + 27*S^2 + 27*S^4 - 528*S^6 - 75*S^8 - 75*S^10 - 25*S^12))/(108*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((-6 - 18*S^2 - 18*S^4 - 263*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^2*((2261 + 2172*S^2 + 54867*S^4 - 42206*S^6 - 6837*S^8 - 7026*S^10 - 2311*S^12)/(1296*S^3*(1 + S^2)^3) + (Pi^2*(619 + 1857*S^2 + 1857*S^4 - 2086*S^6 - 195*S^8 - 195*S^10 - 65*S^12))/(216*S^3*(1 + S^2)^3) + ((249 + 747*S^2 + 747*S^4 - 847*S^6 - 24*S^8 - 24*S^10 - 8*S^12)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)^3)) + ((-3 + 21*S^2 + 81*S^4 - 125*S^8 - 47*S^10 - 3*S^12)*HPL[{3}, -S^2])/(24*S^3*(1 + S^2)^3) - ((-1 + S^2)*(1 + S^2 + S^4)*HPL[{4}, -S^2])/(2*S^3) + ((-103 - 3300*S^2 - 10032*S^4 + 3277*S^6 + 429*S^8 + 96*S^10 - 13*S^12)*HPL[{2, 1}, -S^2])/(108*S^3*(1 + S^2)^3) + ((-3 - 9*S^2 - 9*S^4 + 514*S^6 - 39*S^8 - 39*S^10 - 13*S^12)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + ((3 + 9*S^2 + 9*S^4 - 531*S^6 + 30*S^8 + 30*S^10 + 10*S^12)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((76 + 190*S^2 - 447*S^4 - 899*S^6 - 557*S^8 - 135*S^10)*Zeta[3])/(36*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((6685 + 12613*S^2 - 219*S^4 - 13589*S^6 - 6578*S^8)/(2592*S^3*(1 + S^2)) + (Pi^2*(-224 + 2955*S^2 + 10122*S^4 - 10162*S^6 - 2190*S^8 - 1149*S^10 - 224*S^12))/(432*S^3*(1 + S^2)^3) + ((-29 + 4452*S^2 + 13587*S^4 - 10624*S^6 - 291*S^8 - 174*S^10 - 29*S^12)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)^3) + ((5 + 15*S^2 + 15*S^4 + 3*S^6 - 18*S^8 - 18*S^10 - 6*S^12)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^3) + ((-249 - 747*S^2 - 747*S^4 + 847*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^3) + ((19 + 57*S^2 + 57*S^4 - 14*S^6 - 57*S^8 - 57*S^10 - 19*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3))) + ((4094 + 2545*S^2 - 9055*S^4 - 6426*S^6)/(27*S*(1 + S^2)) + (Pi^2*(12 + 30*S^2 + 518*S^4 - 2112*S^6 - 779*S^8 - 63*S^10))/(3*S*(1 + S^2)^3))*Zeta[5] + HPL[{0}, S^2]^3*((-335294 - 272431*S^2 - 709268*S^4 - 647715*S^6)/(23328*S*(1 + S^2)) + (Pi^2*(-7684 - 11744*S^2 - 31513*S^4 - 25617*S^6))/(3888*S*(1 + S^2)) + (Pi^4*(5348 + 13370*S^2 - 35673*S^4 - 12575*S^6 - 12513*S^8 - 4161*S^10))/(2160*S*(1 + S^2)^3) + ((16 + 882*S^2 + 2544*S^4 - 2854*S^6 + 789*S^8 + 297*S^10 + 16*S^12)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)^3) + (2*(56 + 168*S^2 + 168*S^4 - 263*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{1}, -S^2]^5)/(27*S^3*(1 + S^2)^3) + ((50 + 1611*S^2 + 3816*S^4 - 8027*S^6 + 4095*S^8 + 1854*S^10 + 293*S^12)*HPL[{2}, -S^2]^2)/(108*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^3*((-2*(-184 + 345*S^2 - 13713*S^4 + 11692*S^6 - 4182*S^8 + 129*S^10 + 5*S^12))/(243*S^3*(1 + S^2)^3) + (Pi^2*(555 + 1665*S^2 + 1665*S^4 - 2348*S^6 + 243*S^8 + 243*S^10 + 81*S^12))/(81*S^3*(1 + S^2)^3) + (4*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + ((-91 - 2178*S^2 - 1899*S^4 - 5024*S^6 - 6705*S^8 - 5382*S^10 - 1297*S^12)/(324*S^3*(1 + S^2)^3) + (Pi^2*(5 + 15*S^2 + 15*S^4 - 46*S^6 - 9*S^8 - 9*S^10 - 3*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-104 - 153*S^2 + 216*S^4 - 730*S^6 + 276*S^8 - 399*S^10 - 230*S^12)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)^3) + (2*(-5 - 15*S^2 - 15*S^4 - 30*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + ((Pi^2*(-490 - 1470*S^2 - 1470*S^4 + 813*S^6 + 33*S^8 + 33*S^10 + 11*S^12))/(27*S^3*(1 + S^2)^3) + (-286 + 698*S^2 - 10381*S^4 + 5554*S^6 - 256*S^8 + 1064*S^10 + 239*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + ((175 - 1047*S^2 - 3477*S^4 + 8657*S^6 - 3834*S^8 - 1404*S^10 - 122*S^12)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^3) + (2*S^3*(-23 + 51*S^2 + 51*S^4 + 17*S^6)*HPL[{3, 2}, -S^2])/(9*(1 + S^2)^3) + (20*(-1 - 3*S^2 - 3*S^4 - S^6 + 12*S^8 + 12*S^10 + 4*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-173 + 1074*S^2 + 3531*S^4 - 8806*S^6 + 3591*S^8 + 1278*S^10 + 97*S^12)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^3) - (4*(-246 - 738*S^2 - 738*S^4 + 471*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-748 - 2244*S^2 - 2244*S^4 + 1445*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(-260 - 780*S^2 - 780*S^4 + 501*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (-(Pi^2*S^3*(135 + 177*S^2 + 177*S^4 + 59*S^6))/(27*(1 + S^2)^3) + (-284 - 644*S^2 - 1524*S^4 - 2549*S^6 - 1622*S^8 - 405*S^10)/(27*S*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((-4241 - 2276*S^2 - 8922*S^4 - 20690*S^6 - 13691*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-368 + 1959*S^2 + 6756*S^4 - 16720*S^6 + 2190*S^8 - 420*S^10 - 503*S^12))/(324*S^3*(1 + S^2)^3) - (8*S^3*(-3 + 6*S^2 + 6*S^4 + 2*S^6)*HPL[{3}, -S^2])/(9*(1 + S^2)^3) + (2*(-246 - 738*S^2 - 738*S^4 + 471*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*S^3*(1 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3])/(9*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((-2347 - 919*S^2 + 633*S^4 - 6985*S^6 - 5542*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-56 + 933*S^2 + 3126*S^4 - 3590*S^6 + 282*S^8 - 15*S^10 - 56*S^12))/(36*S^3*(1 + S^2)^3) + ((-7 + 507*S^2 + 1575*S^4 - 1622*S^6 + 459*S^8 + 135*S^10 - 7*S^12)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 + 5*S^6)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-6 - 18*S^2 - 18*S^4 - 17*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]*((-103501 - 166036*S^2 - 127878*S^4 - 249412*S^6 - 137413*S^8)/(11664*S^3*(1 + S^2)) + (Pi^2*(-1994 - 22170*S^2 + 77037*S^4 - 117568*S^6 - 16482*S^8 - 20154*S^10 - 3605*S^12))/(1944*S^3*(1 + S^2)^3) + (Pi^4*(4011 + 12033*S^2 + 12033*S^4 - 15739*S^6 - 42*S^8 - 42*S^10 - 14*S^12))/(1620*S^3*(1 + S^2)^3) + ((131 - 576*S^2 + 8007*S^4 - 7007*S^6 + 1512*S^8 - 957*S^10 - 190*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(488 + 1464*S^2 + 1464*S^4 - 2023*S^6 + 219*S^8 + 219*S^10 + 73*S^12))/(54*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((121 + 363*S^2 + 363*S^4 - 553*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((-161 - 336*S^2 - 3*S^4 - 520*S^6 - 327*S^8 - 444*S^10 - 161*S^12)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^3) + (2*(6 + 18*S^2 + 18*S^4 - 63*S^6 + 33*S^8 + 33*S^10 + 11*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + ((7 - 507*S^2 - 1575*S^4 + 1622*S^6 - 459*S^8 - 135*S^10 + 7*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(127 + 381*S^2 + 381*S^4 - 583*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*(43 + 129*S^2 + 129*S^4 - 195*S^6 + 36*S^8 + 36*S^10 + 12*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(142 + 375*S^2 + 276*S^4 + 248*S^6 + 897*S^8 + 582*S^10 + 142*S^12)*Zeta[3])/(27*S^3*(1 + S^2)^3)) - (52*S^3*(4 + 3*S^2 + 3*S^4 + S^6)*Zeta[5])/(9*(1 + S^2)^3)) + Zeta[3]*((395734 + 326801*S^2 - 677456*S^4 - 484107*S^6)/(1944*S*(1 + S^2)) + (Pi^2*(290 - 2019*S^2 - 7194*S^4 - 4381*S^6))/(108*S*(1 + S^2)) + (Pi^4*(-462 - 1155*S^2 + 10485*S^4 - 46142*S^6 - 19838*S^8 - 2754*S^10))/(540*S*(1 + S^2)^3) - (8*S^3*(19 + 27*S^2 + 27*S^4 + 9*S^6)*Zeta[5])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((-161369 - 196361*S^2 + 196361*S^4 + 161369*S^6)/(648*S^3) + (Pi^2*(-18402 - 33544*S^2 - 6449*S^4 + 21308*S^6 + 12831*S^8))/(324*S^3*(1 + S^2)) + (Pi^4*(-14002 - 132153*S^2 - 337794*S^4 + 93343*S^6 + 104289*S^8 + 40137*S^10 + 5114*S^12))/(1620*S^3*(1 + S^2)^3) + (4*(29 + 515*S^2 + 1407*S^4 - 1400*S^6 + 1841*S^8 + 781*S^10 + 99*S^12)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^3) - (4*(507 + 1521*S^2 + 1521*S^4 - 3250*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(-137 - 411*S^2 - 411*S^4 + 824*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^3) + (64*(8 + 81*S^2 + 203*S^4 - 175*S^6 + 203*S^8 + 81*S^10 + 8*S^12)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (1952*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (32*(-51 - 153*S^2 - 153*S^4 - 770*S^6 + 453*S^8 + 453*S^10 + 151*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (640*(5 + 15*S^2 + 15*S^4 - 77*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(108 + 324*S^2 + 324*S^4 - 847*S^6 + 3*S^8 + 3*S^10 + S^12))/(9*S^3*(1 + S^2)^3) - (2*(-1532 - 7374*S^2 - 26283*S^4 + 16988*S^6 - 27534*S^8 - 2190*S^10 + 133*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + (16*(22 + 66*S^2 + 66*S^4 - 381*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((1335 + 66934*S^2 - 333469*S^4 - 1006256*S^6 - 482772*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-1096 - 10822*S^2 - 49233*S^4 - 76054*S^6 - 37195*S^8))/(972*S^3*(1 + S^2)) + (Pi^4*(-1919 - 8301*S^2 - 10677*S^4 + 56921*S^6 - 130272*S^8 - 54114*S^10 - 6554*S^12))/(1620*S^3*(1 + S^2)^3) + (2*(20 + 117*S^2 + 216*S^4 - 536*S^6 + 1890*S^8 + 900*S^10 + 155*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) + (8*S^3*(12 + 15*S^2 + 15*S^4 + 5*S^6)*HPL[{5}, -S^2])/(3*(1 + S^2)^3) + ((-2*Pi^2*(-265 - 795*S^2 - 795*S^4 + 1642*S^6 + 213*S^8 + 213*S^10 + 71*S^12))/(9*S^3*(1 + S^2)^3) - (2*(-3008 - 12243*S^2 - 34113*S^4 + 16988*S^6 - 19704*S^8 + 2679*S^10 + 1609*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (4*(-286 - 450*S^2 - 153*S^4 - 6647*S^6 + 14196*S^8 + 5925*S^10 + 767*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 250*S^6 + 249*S^8 + 249*S^10 + 83*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-3 - 9*S^2 - 9*S^4 - 14*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-84 - 104*S^2 + 31*S^4 - 2100*S^6 + 4841*S^8 + 2048*S^10 + 276*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(273 + 819*S^2 + 819*S^4 - 1754*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(821 + 2463*S^2 + 2463*S^4 - 5030*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(-66 - 198*S^2 - 198*S^4 + 385*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((577 + 708*S^2 - 1857*S^4 + 200*S^6 - 8733*S^8 - 3396*S^10 - 539*S^12)/(27*S^3*(1 + S^2)^3) - (2*Pi^2*(-5 - 15*S^2 - 15*S^4 - 112*S^6 + 63*S^8 + 63*S^10 + 21*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] - (4*(-29 - 87*S^2 - 87*S^4 - 100*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(104305 - 46054*S^2 + 104305*S^4))/(972*S^3) + (Pi^2*(208091 + 675584*S^2 + 696558*S^4 + 70424*S^6 - 73105*S^8))/(11664*S^3*(1 + S^2)) + (Pi^4*(57670 + 197979*S^2 + 1196718*S^4 - 563503*S^6 + 659832*S^8 + 103578*S^10 + 11914*S^12))/(9720*S^3*(1 + S^2)^3) + (Pi^6*(201706 + 605118*S^2 + 605118*S^4 - 958255*S^6 + 179157*S^8 + 179157*S^10 + 59719*S^12))/(68040*S^3*(1 + S^2)^3) + ((Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2089*S^6 + 771*S^8 + 771*S^10 + 257*S^12))/(9*S^3*(1 + S^2)^3) + (2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 - (62*(-1 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) + (2*(37 + 111*S^2 + 111*S^4 - 238*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-249 - 1714*S^2 - 4217*S^4 - 1660*S^6 - 6643*S^8 - 2546*S^10 - 571*S^12)/(3*S^3*(1 + S^2)^3) + (Pi^2*(-61 - 183*S^2 - 183*S^4 + 1132*S^6 - 837*S^8 - 837*S^10 - 279*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(713 + 1893*S^2 + 1425*S^4 - 2750*S^6 + 8877*S^8 + 4377*S^10 + 713*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-194 - 582*S^2 - 582*S^4 - 127*S^6 + 849*S^8 + 849*S^10 + 283*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((8*Pi^2*(-116 - 348*S^2 - 348*S^4 + 193*S^6 + 183*S^8 + 183*S^10 + 61*S^12))/(9*S^3*(1 + S^2)^3) + (2*(4 + 699*S^2 - 114*S^4 + 830*S^6 + 5544*S^8 + 1431*S^10 + 406*S^12))/(3*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (4*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(247 + 1465*S^2 + 2925*S^4 - 5946*S^6 + 6705*S^8 + 2725*S^10 + 247*S^12)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^3) + (6*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) + (16*(50 + 150*S^2 + 150*S^4 - 551*S^6 + 357*S^8 + 357*S^10 + 119*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(S^3*(1 + S^2)^2) - (8*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (8*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(121 + 1764*S^2 + 4578*S^4 - 4840*S^6 + 2553*S^8 + 1089*S^10 + 121*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (496*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 - (32*(-116 - 348*S^2 - 348*S^4 - 277*S^6 + 597*S^8 + 597*S^10 + 199*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (3600*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (32*(-71 - 213*S^2 - 213*S^4 - 277*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2400*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((7451 + 9824*S^2 - 8349*S^4 - 22198*S^6 - 7588*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(-331 - 2526*S^2 - 5703*S^4 + 17176*S^6 - 19635*S^8 - 7170*S^10 - 331*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + (8*(5 + 15*S^2 + 15*S^4 - 32*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((-3445 - 17641*S^2 - 44727*S^4 - 49663*S^6 - 18484*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(-958 - 5019*S^2 - 9330*S^4 + 19666*S^6 - 23424*S^8 - 9717*S^10 - 958*S^12))/(27*S^3*(1 + S^2)^3) + (8*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(11 + 33*S^2 + 33*S^4 - 87*S^6 + 42*S^8 + 42*S^10 + 14*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-557 - 629*S^2 + 629*S^4 + 557*S^6)/(3*S^3) + (Pi^2*(-175 - 3837*S^2 - 10473*S^4 + 5314*S^6 + 2271*S^8 + 411*S^10 - 175*S^12))/(9*S^3*(1 + S^2)^3) + (32*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((7811 + 8999*S^2 - 8999*S^4 - 7811*S^6)/(54*S^3) + (Pi^2*(8921 + 23394*S^2 + 141699*S^4 - 22802*S^6 - 22119*S^8 - 1248*S^10 - 3877*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(7200 + 21600*S^2 + 21600*S^4 - 21017*S^6 - 3411*S^8 - 3411*S^10 - 1137*S^12))/(540*S^3*(1 + S^2)^3) - (2*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(113 + 339*S^2 + 339*S^4 - 734*S^6 + 339*S^8 + 339*S^10 + 113*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(175 + 1137*S^2 + 2373*S^4 - 5314*S^6 + 5829*S^8 + 2289*S^10 + 175*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + (2*(163 - 84*S^2 - 1407*S^4 + 16904*S^6 - 19551*S^8 - 6132*S^10 + 163*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(27713 - 37886*S^2 + 27713*S^4))/(972*S^3) + (Pi^2*(21491 + 69224*S^2 + 82371*S^4 + 37202*S^6 + 6452*S^8))/(1458*S^3*(1 + S^2)) + (Pi^4*(5027 + 67896*S^2 + 172821*S^4 - 198704*S^6 + 91929*S^8 + 40932*S^10 + 5027*S^12))/(1620*S^3*(1 + S^2)^3) + (2*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((-4*Pi^2*(118 + 354*S^2 + 354*S^4 - 1703*S^6 + 1137*S^8 + 1137*S^10 + 379*S^12))/(27*S^3*(1 + S^2)^3) - (4*(1279 + 8682*S^2 + 29382*S^4 - 7666*S^6 + 54843*S^8 + 11976*S^10 + 3088*S^12))/(81*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (8*(36 + 155*S^2 + 249*S^4 - 316*S^6 + 465*S^8 + 227*S^10 + 36*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-5 - 15*S^2 - 15*S^4 - 116*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(3*S^3*(1 + S^2)^2) + (8*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] + (16*(18 - 17*S^2 - 159*S^4 - 158*S^6 + 516*S^8 + 208*S^10 + 18*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(178 + 534*S^2 + 534*S^4 - 2299*S^6 + 1479*S^8 + 1479*S^10 + 493*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (1200*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (32*(463 + 1389*S^2 + 1389*S^4 - 2419*S^6 + 714*S^8 + 714*S^10 + 238*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (800*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-4*Pi^2*(79 + 237*S^2 + 237*S^4 - 1444*S^6 + 1011*S^8 + 1011*S^10 + 337*S^12))/(27*S^3*(1 + S^2)^3) - (4*(-44 + 237*S^2 + 3789*S^4 - 5152*S^6 + 12276*S^8 + 1335*S^10 + 559*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((557 + 629*S^2 - 629*S^4 - 557*S^6)/(9*S^3) + (Pi^2*(175 + 3837*S^2 + 10473*S^4 - 5314*S^6 - 2271*S^8 - 411*S^10 + 175*S^12))/(27*S^3*(1 + S^2)^3) - (8*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (32*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) - (16*(11 + 33*S^2 + 33*S^4 - 680*S^6 + 537*S^8 + 537*S^10 + 179*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((4477 + 4597*S^2 - 4597*S^4 - 4477*S^6)/(24*S^3) + (Pi^2*(73823 + 219281*S^2 + 40581*S^4 - 192451*S^6 - 99238*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(6158 + 30114*S^2 + 533169*S^4 - 352661*S^6 + 147555*S^8 + 26019*S^10 - 8530*S^12))/(19440*S^3*(1 + S^2)^3) + (Pi^6*(-652 - 1956*S^2 - 1956*S^4 - 144378*S^6 + 20613*S^8 + 20613*S^10 + 6871*S^12))/(34020*S^3*(1 + S^2)^3) + (2*(-1 - 3*S^2 - 3*S^4 - 129*S^6 + 120*S^8 + 120*S^10 + 40*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((136 - 4545*S^2 - 20340*S^4 - 17350*S^6 - 56880*S^8 - 27945*S^10 - 7316*S^12)/(54*S^3*(1 + S^2)^3) - (4*Pi^2*(2 + 6*S^2 + 6*S^4 - 68*S^6 + 129*S^8 + 129*S^10 + 43*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((193 + 312*S^2 - 183*S^4 + 1376*S^6 - 8613*S^8 - 4644*S^10 - 977*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(20 + 60*S^2 + 60*S^4 + 61*S^6 + 138*S^8 + 138*S^10 + 46*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) - (488*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-2*Pi^2*(133 + 399*S^2 + 399*S^4 - 2390*S^6 + 519*S^8 + 519*S^10 + 173*S^12))/(9*S^3*(1 + S^2)^3) + (2*(-1631 - 7707*S^2 - 31476*S^4 + 16988*S^6 - 22341*S^8 - 1857*S^10 + 232*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (2*(-191 + 801*S^2 + 2754*S^4 - 14494*S^6 + 27708*S^8 + 11319*S^10 + 1339*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-357 + 193*S^2 + 1804*S^4 - 14226*S^6 + 29362*S^8 + 12307*S^10 + 1593*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(1 + 3*S^2 + 3*S^4 - 86*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^3) + (4*(10 + 30*S^2 + 30*S^4 - 913*S^6 + 1167*S^8 + 1167*S^10 + 389*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*Pi^2*(46 + 138*S^2 + 138*S^4 - 1195*S^6 + 321*S^8 + 321*S^10 + 107*S^12))/(9*S^3*(1 + S^2)^3) + (2*(1399 + 9564*S^2 + 53817*S^4 - 33976*S^6 + 53817*S^8 + 9564*S^10 + 1399*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] - (4*(-255 - 1498*S^2 - 2661*S^4 + 2661*S^6 + 1498*S^8 + 255*S^10)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (4*(-597 - 5051*S^2 - 12539*S^4 + 4200*S^6 + 2795*S^8 + 1163*S^10 + 213*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(13 + 39*S^2 + 39*S^4 - 86*S^6 + 39*S^8 + 39*S^10 + 13*S^12)*HPL[{3, 1, 2}, -S^2])/(S^3*(1 + S^2)^3) + (4*(185 + 555*S^2 + 555*S^4 - 2734*S^6 + 555*S^8 + 555*S^10 + 185*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(113 + 339*S^2 + 339*S^4 - 1390*S^6 + 171*S^8 + 171*S^10 + 57*S^12)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (64*(8 + 81*S^2 + 203*S^4 - 175*S^6 + 203*S^8 + 81*S^10 + 8*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (32*(-661 - 1983*S^2 - 1983*S^4 - 770*S^6 + 2283*S^8 + 2283*S^10 + 761*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (640*(5 + 15*S^2 + 15*S^4 - 77*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-78 - 1432*S^2 - 6449*S^4 - 10804*S^6 - 5493*S^8)/(54*S^3*(1 + S^2)) + (Pi^2*(-47 - 786*S^2 - 1749*S^4 + 6845*S^6 - 14538*S^8 - 5844*S^10 - 659*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + 4*S^3*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-5571 - 12236*S^2 - 12898*S^4 - 12236*S^6 - 5571*S^8)/(54*S^3*(1 + S^2)) + (Pi^2*(-1343 - 11847*S^2 - 29001*S^4 + 19517*S^6 - 16524*S^8 - 6588*S^10 - 578*S^12))/(27*S^3*(1 + S^2)^3) - (16*(-54 - 162*S^2 - 162*S^4 + 345*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((5877 + 4666*S^2 - 12898*S^4 - 29138*S^6 - 17019*S^8)/(108*S^3*(1 + S^2)) + (Pi^2*(215 + 159*S^2 - 327*S^4 + 6469*S^6 - 15552*S^8 - 6723*S^10 - 955*S^12))/(27*S^3*(1 + S^2)^3) + (4*(273 + 819*S^2 + 819*S^4 - 1754*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 58*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) - (2*(265 + 1053*S^2 + 1431*S^4 - 4951*S^6 + 13626*S^8 + 5121*S^10 + 445*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3)) + HPL[{0}, S^2]^2*((1116791 + 1303135*S^2 - 1088191*S^4 - 1087911*S^6)/(11664*S*(1 + S^2)) + (Pi^2*(56029 + 63905*S^2 - 63929*S^4 - 63381*S^6))/(3888*S*(1 + S^2)) - (Pi^6*S^3*(15415 + 5289*S^2 + 5289*S^4 + 1763*S^6))/(3888*(1 + S^2)^3) + (Pi^4*(1916 + 98324*S^2 - 161001*S^4 - 67816*S^6 - 72145*S^8 - 24498*S^10))/(6480*S*(1 + S^2)^3) + (2*(23 + 273*S^2 + 678*S^4 - 674*S^6 + 273*S^8 + 138*S^10 + 23*S^12)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)^3) + (2*(23 + 69*S^2 + 69*S^4 - 109*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{1}, -S^2]^6)/(9*S^3*(1 + S^2)^3) + ((Pi^2*(-10 - 30*S^2 - 30*S^4 - 688*S^6 + 213*S^8 + 213*S^10 + 71*S^12))/(18*S^3*(1 + S^2)^3) + (-130 + 162*S^2 + 4647*S^4 - 2936*S^6 + 5526*S^8 + 1674*S^10 + 329*S^12)/(36*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + ((-5 - 15*S^2 - 15*S^4 - 374*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2}, -S^2]^3)/(9*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^4*((Pi^2*(619 + 1857*S^2 + 1857*S^4 - 2671*S^6 + 390*S^8 + 390*S^10 + 130*S^12))/(54*S^3*(1 + S^2)^3) + (1663 + 6096*S^2 + 32427*S^4 - 10396*S^6 + 15453*S^8 + 3900*S^10 + 457*S^12)/(108*S^3*(1 + S^2)^3) + ((325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3)) + (2*(2 + 6*S^2 + 6*S^4 + 9*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((395 + 339*S^2 + 609*S^4 - 3269*S^6 - 7590*S^8 - 4278*S^10 - 1198*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(27 + 81*S^2 + 81*S^4 + 4*S^6 - 117*S^8 - 117*S^10 - 39*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] + ((-238 - 387*S^2 + 180*S^4 - 908*S^6 - 3120*S^8 - 1473*S^10 - 238*S^12)*HPL[{5}, -S^2])/(18*S^3*(1 + S^2)^3) + ((50 + 150*S^2 + 150*S^4 - 39*S^6 - 153*S^8 - 153*S^10 - 51*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-4 - 12*S^2 - 12*S^4 - 425*S^6 + 171*S^8 + 171*S^10 + 57*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(5 + 15*S^2 + 15*S^4 + 1276*S^6 - 345*S^8 - 345*S^10 - 115*S^12))/(9*S^3*(1 + S^2)^3) - (2*(-8 + 75*S^2 + 2178*S^4 - 1618*S^6 + 1800*S^8 + 447*S^10 + 70*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + ((200 + 789*S^2 + 1176*S^4 - 464*S^6 + 4242*S^8 + 2343*S^10 + 506*S^12)*HPL[{3, 2}, -S^2])/(18*S^3*(1 + S^2)^3) + ((307 + 825*S^2 + 564*S^4 - 1294*S^6 + 7122*S^8 + 3711*S^10 + 721*S^12)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + ((3 + 9*S^2 + 9*S^4 + 14*S^6 - 3*S^8 - 3*S^10 - S^12)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-14 - 42*S^2 - 42*S^4 + 23*S^6 + 99*S^8 + 99*S^10 + 33*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-2 - 6*S^2 - 6*S^4 - 1301*S^6 + 345*S^8 + 345*S^10 + 115*S^12))/(9*S^3*(1 + S^2)^3) + (245 + 2658*S^2 + 29352*S^4 - 16988*S^6 + 24465*S^8 + 6906*S^10 + 1154*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (2*(767 + 6015*S^2 + 14385*S^4 - 6917*S^6 + 1908*S^8 + 756*S^10 + 2*S^12)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-2234 - 18045*S^2 - 43632*S^4 + 19949*S^6 - 3411*S^8 - 1206*S^10 + 151*S^12)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(3 + 5*S^6)*HPL[{3, 1, 2}, -S^2])/(3*S^3) + (2*(-17 - 51*S^2 - 51*S^4 - 1488*S^6 + 747*S^8 + 747*S^10 + 249*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-21 - 63*S^2 - 63*S^4 - 2240*S^6 + 1035*S^8 + 1035*S^10 + 345*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-234 - 2012*S^2 - 4967*S^4 + 2100*S^6 + 95*S^8 + 68*S^10 + 42*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-4 - 12*S^2 - 12*S^4 - 381*S^6 + 153*S^8 + 153*S^10 + 51*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (80*(-1 - 3*S^2 - 3*S^4 - 154*S^6 + 63*S^8 + 63*S^10 + 21*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((150 - 433*S^2 - 1982*S^4 - 1327*S^6)/(36*S*(1 + S^2)) + (Pi^2*(68 + 170*S^2 - 303*S^4 - 1523*S^6 - 842*S^8 - 180*S^10))/(18*S*(1 + S^2)^3))*Zeta[3] - (2*S^3*(31 + 33*S^2 + 33*S^4 + 11*S^6)*Zeta[3]^2)/(3*(1 + S^2)^3) + HPL[{2}, -S^2]*((52309 + 213382*S^2 + 81162*S^4 - 159722*S^6 - 103139*S^8)/(3888*S^3*(1 + S^2)) + (Pi^2*(764 + 2808*S^2 + 46242*S^4 - 42023*S^6 + 15561*S^8 - 1377*S^10 - 1351*S^12))/(648*S^3*(1 + S^2)^3) + (Pi^4*(156 + 468*S^2 + 468*S^4 - 14899*S^6 + 897*S^8 + 897*S^10 + 299*S^12))/(1080*S^3*(1 + S^2)^3) + ((-37 - 153*S^2 - 234*S^4 + 169*S^6 - 1029*S^8 - 579*S^10 - 127*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((-11 - 33*S^2 - 33*S^4 - 46*S^6 - 21*S^8 - 21*S^10 - 7*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-767 - 6015*S^2 - 14385*S^4 + 6917*S^6 - 1908*S^8 - 756*S^10 - 2*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-9 - 27*S^2 - 27*S^4 - 850*S^6 + 345*S^8 + 345*S^10 + 115*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-4 - 12*S^2 - 12*S^4 - 425*S^6 + 171*S^8 + 171*S^10 + 57*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-20 - 105*S^2 - 168*S^4 + 545*S^6 - 1503*S^8 - 693*S^10 - 110*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*((201071 + 515312*S^2 + 390054*S^4 - 89848*S^6 - 80125*S^8)/(3888*S^3*(1 + S^2)) + (Pi^2*(3625 + 10230*S^2 + 76074*S^4 - 36697*S^6 + 19761*S^8 + 2337*S^10 - 470*S^12))/(324*S^3*(1 + S^2)^3) + (Pi^4*(8046 + 24138*S^2 + 24138*S^4 - 31091*S^6 + 1209*S^8 + 1209*S^10 + 403*S^12))/(1080*S^3*(1 + S^2)^3) + ((5303 + 16806*S^2 + 90777*S^4 - 22802*S^6 + 28803*S^8 + 5340*S^10 - 259*S^12)/(108*S^3*(1 + S^2)^3) + (Pi^2*(574 + 1722*S^2 + 1722*S^4 - 2195*S^6 + 177*S^8 + 177*S^10 + 59*S^12))/(18*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + ((154 + 462*S^2 + 462*S^4 - 741*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-109 - 186*S^2 + 111*S^4 + 880*S^6 - 1833*S^8 - 834*S^10 - 109*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + ((33 + 99*S^2 + 99*S^4 + 24*S^6 - 123*S^8 - 123*S^10 - 41*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-175 - 2487*S^2 - 6423*S^4 + 5314*S^6 - 1779*S^8 - 939*S^10 - 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(161 + 483*S^2 + 483*S^4 - 663*S^6 + 96*S^8 + 96*S^10 + 32*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-76 - 321*S^2 - 528*S^4 + 1486*S^6 - 2310*S^8 - 915*S^10 - 76*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-9240 - 17488*S^2 - 6449*S^4 + 5252*S^6 + 3669*S^8)/(108*S^3*(1 + S^2)) + (Pi^2*(-805 - 9336*S^2 - 24933*S^4 + 9577*S^6 + 714*S^8 + 300*S^10 + 113*S^12))/(54*S^3*(1 + S^2)^3) + (4*(8 + 24*S^2 + 24*S^4 - 77*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((1003 + 2734*S^2 - 16032*S^4 - 31394*S^6 - 16223*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(-94 + 189*S^2 + 1206*S^4 + 802*S^6 - 3438*S^8 - 1485*S^10 - 184*S^12))/(108*S^3*(1 + S^2)^3) - (2*(-1 - 3*S^2 - 3*S^4 + 102*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 8*S^6 + 3*S^8 + 3*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*((14471 + 39524*S^2 + 37011*S^4 + 7502*S^6 - 568*S^8)/(486*S^3*(1 + S^2)) + (Pi^2*(236 + 4365*S^2 + 11622*S^4 - 11402*S^6 + 2820*S^8 + 1431*S^10 + 236*S^12))/(54*S^3*(1 + S^2)^3) + ((175 + 2487*S^2 + 6423*S^4 - 5314*S^6 + 1779*S^8 + 939*S^10 + 175*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(-7 - 21*S^2 - 21*S^4 - 78*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(4 + 12*S^2 + 12*S^4 - 139*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + ((80 + 200*S^2 - 192*S^4 - 1244*S^6 - 539*S^8 - 75*S^10)*Zeta[5])/(3*S*(1 + S^2)^3) + HPL[{1}, -S^2]*((408157 + 967195*S^2 + 547413*S^4 - 454067*S^6 - 255818*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(48997 + 116887*S^2 + 73365*S^4 - 25763*S^6 - 20870*S^8))/(3888*S^3*(1 + S^2)) + (Pi^4*(490 + 72258*S^2 + 212208*S^4 - 212554*S^6 + 5847*S^8 + 3471*S^10 + 490*S^12))/(3240*S^3*(1 + S^2)^3) + ((169 + 1896*S^2 + 4677*S^4 - 4378*S^6 + 2166*S^8 + 1059*S^10 + 169*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((157 - 162*S^2 - 393*S^4 - 694*S^6 - 4353*S^8 - 1836*S^10 - 503*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(22 + 66*S^2 + 66*S^4 + 87*S^6 - 141*S^8 - 141*S^10 - 47*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((-23 + 33*S^2 + 240*S^4 + 20*S^6 - 426*S^8 - 189*S^10 - 23*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-23 - 69*S^2 - 69*S^4 - 24*S^6 + 105*S^8 + 105*S^10 + 35*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((Pi^2*(-574 - 1722*S^2 - 1722*S^4 + 2195*S^6 - 177*S^8 - 177*S^10 - 59*S^12))/(9*S^3*(1 + S^2)^3) + (-5303 - 16806*S^2 - 90777*S^4 + 22802*S^6 - 28803*S^8 - 5340*S^10 + 259*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (2*(229 + 3606*S^2 + 9465*S^4 - 7876*S^6 + 2499*S^8 + 1284*S^10 + 229*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(5 + 15*S^2 + 15*S^4 - 75*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(-3 - 9*S^2 - 9*S^4 - 474*S^6 + 411*S^8 + 411*S^10 + 137*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(175 + 2487*S^2 + 6423*S^4 - 5314*S^6 + 1779*S^8 + 939*S^10 + 175*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(154 + 462*S^2 + 462*S^4 - 741*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(469 + 1407*S^2 + 1407*S^4 - 2145*S^6 + 462*S^8 + 462*S^10 + 154*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(325 + 975*S^2 + 975*S^4 - 1348*S^6 + 201*S^8 + 201*S^10 + 67*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((91 - 90*S^2 - 1041*S^4 - 106*S^6 - 4587*S^8 - 1440*S^10 - 419*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(34 + 102*S^2 + 102*S^4 + 111*S^6 - 225*S^8 - 225*S^10 - 75*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((30749 + 79526*S^2 + 44040*S^4 - 18430*S^6 - 14989*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(496 + 11913*S^2 + 32856*S^4 - 26566*S^6 + 5046*S^8 + 2643*S^10 + 496*S^12))/(108*S^3*(1 + S^2)^3) - (2*(5 + 15*S^2 + 15*S^4 - 75*S^6 + 48*S^8 + 48*S^10 + 16*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(154 + 462*S^2 + 462*S^4 - 741*S^6 + 183*S^8 + 183*S^10 + 61*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(8 + 24*S^2 + 24*S^4 - 133*S^6 + 93*S^8 + 93*S^10 + 31*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) - (2*(-40 - 120*S^2 - 120*S^4 - 117*S^6 + 237*S^8 + 237*S^10 + 79*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3))) + HPL[{0}, S^2]*((-5*(515987 - 112556*S^2 + 523277*S^4))/(11664*S) + (Pi^2*(-483590 - 211393*S^2 - 666212*S^4 - 813993*S^6))/(23328*S*(1 + S^2)) + (Pi^4*(-38746 + 6739*S^2 - 161587*S^4 - 190980*S^6))/(38880*S*(1 + S^2)) + (Pi^6*(375026 + 937565*S^2 - 2674611*S^4 + 247744*S^6 - 306908*S^8 - 184422*S^10))/(136080*S*(1 + S^2)^3) + (14*(1 + 11*S^2 + 27*S^4 - 38*S^6 + 27*S^8 + 11*S^10 + S^12)*HPL[{1}, -S^2]^6)/(3*S^3*(1 + S^2)^3) + (32*(1 + 3*S^2 + 3*S^4 - 7*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{1}, -S^2]^7)/(9*S^3*(1 + S^2)^3) + ((-391 + 783*S^2 + 3465*S^4 - 14372*S^6 + 18375*S^8 + 7953*S^10 + 1139*S^12)*HPL[{2}, -S^2]^3)/(54*S^3*(1 + S^2)^3) + HPL[{1}, -S^2]^5*((35 + 146*S^2 + 889*S^4 - 460*S^6 + 889*S^8 + 146*S^10 + 35*S^12)/(3*S^3*(1 + S^2)^3) + (2*Pi^2*(140 + 420*S^2 + 420*S^4 - 851*S^6 + 303*S^8 + 303*S^10 + 101*S^12))/(27*S^3*(1 + S^2)^3) + (4*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^3)) + ((-18 - 60*S^2 - 75*S^4 + 12*S^6 - 19*S^8 + 20*S^10 + 12*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((407 - 52*S^2 - 694*S^4 - 3998*S^6 - 4525*S^8 - 4642*S^10 - 1192*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(-7 - 21*S^2 - 21*S^4 - 165*S^6 + 30*S^8 + 30*S^10 + 10*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((-275 - 501*S^2 + 390*S^4 - 415*S^6 + 1473*S^8 - 633*S^10 - 509*S^12)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(1 + 2*S^2)*(-25 - 25*S^2 - 25*S^4 + 21*S^6 + 30*S^8 + 12*S^10)*HPL[{7}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(1 + 799*S^2 + 2011*S^4 - 5314*S^6 + 6191*S^8 + 2627*S^10 + 349*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((Pi^2*(3 + 9*S^2 + 9*S^4 - 308*S^6 + 339*S^8 + 339*S^10 + 113*S^12))/(9*S^3*(1 + S^2)^3) + (-1051 - 480*S^2 + 8439*S^4 + 3208*S^6 + 31983*S^8 + 15360*S^10 + 3485*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((8*Pi^2*(-6 - 18*S^2 - 18*S^4 - 80*S^6 + 105*S^8 + 105*S^10 + 35*S^12))/(9*S^3*(1 + S^2)^3) + (-1484 + 2085*S^2 + 14748*S^4 + 10838*S^6 + 48804*S^8 + 26565*S^10 + 5932*S^12)/(27*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + ((-32 - 13*S^2 + 94*S^4 + 94*S^6 + 59*S^8 + 22*S^10)*HPL[{4, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*(2 + 6*S^2 + 6*S^4 + 15*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + (2*(103 + 159*S^2 - 201*S^4 + 1628*S^6 - 141*S^8 + 867*S^10 + 445*S^12)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(25 + 75*S^2 + 75*S^4 + 169*S^6 + 72*S^8 + 72*S^10 + 24*S^12)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(13 + 39*S^2 + 39*S^4 + 134*S^6 + 24*S^8 + 24*S^10 + 8*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*Pi^2*(-638 - 1914*S^2 - 1914*S^4 + 1819*S^6 + 15*S^8 + 15*S^10 + 5*S^12))/(9*S^3*(1 + S^2)^3) + (4*(2512 + 8556*S^2 + 39237*S^4 - 11401*S^6 + 20553*S^8 + 2517*S^10 + 10*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((-4*Pi^2*(-1939 - 5817*S^2 - 5817*S^4 + 5439*S^6 + 138*S^8 + 138*S^10 + 46*S^12))/(9*S^3*(1 + S^2)^3) - (2*(-15265 - 48786*S^2 - 229515*S^4 + 75166*S^6 - 108249*S^8 - 6036*S^10 + 1853*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] + (16*(1 + S^2)*(5 - 2*S^2 + 5*S^4)*HPL[{3, 1, 2}, -S^2])/(9*S^3) + (4*(-371 + 855*S^2 + 3573*S^4 - 14260*S^6 + 18483*S^8 + 8025*S^10 + 1159*S^12)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-23 - 69*S^2 - 69*S^4 - 488*S^6 + 429*S^8 + 429*S^10 + 143*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-1 - 3*S^2 - 3*S^4 - 32*S^6 + 27*S^8 + 27*S^10 + 9*S^12)*HPL[{3, 3, 1}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-419 + 760*S^2 + 3574*S^4 - 14842*S^6 + 18442*S^8 + 7780*S^10 + 1045*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-11 - 33*S^2 - 33*S^4 - 380*S^6 + 333*S^8 + 333*S^10 + 111*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-35 - 105*S^2 - 105*S^4 - 1178*S^6 + 963*S^8 + 963*S^10 + 321*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-75 - 225*S^2 - 225*S^4 - 2289*S^6 + 1878*S^8 + 1878*S^10 + 626*S^12)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*Pi^2*(-665 - 1995*S^2 - 1995*S^4 + 1806*S^6 + 123*S^8 + 123*S^10 + 41*S^12))/(9*S^3*(1 + S^2)^3) + (4*(-1547 - 4242*S^2 - 23529*S^4 + 10304*S^6 - 8601*S^8 + 1098*S^10 + 517*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] + (32*(-196 - 588*S^2 - 588*S^4 + 607*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-76 + 124*S^2 + 622*S^4 - 2648*S^6 + 3064*S^8 + 1243*S^10 + 149*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-2355 - 7065*S^2 - 7065*S^4 + 7546*S^6 + 447*S^8 + 447*S^10 + 149*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-2355 - 7065*S^2 - 7065*S^4 + 7546*S^6 + 447*S^8 + 447*S^10 + 149*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-4707 - 14121*S^2 - 14121*S^4 + 14830*S^6 + 1131*S^8 + 1131*S^10 + 377*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-3521 - 10563*S^2 - 10563*S^4 + 11081*S^6 + 876*S^8 + 876*S^10 + 292*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (80*(-28 + 60*S^2 + 267*S^4 - 1046*S^6 + 1233*S^8 + 504*S^10 + 62*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(-98 - 294*S^2 - 294*S^4 + 337*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(-98 - 294*S^2 - 294*S^4 + 337*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (160*(389 + 1167*S^2 + 1167*S^4 - 1358*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (320*(-27 - 81*S^2 - 81*S^4 + 87*S^6 + 6*S^8 + 6*S^10 + 2*S^12)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((-12166 - 6593*S^2 - 12139*S^4)/(108*S) - (373*Pi^4*S^5*(3 + 3*S^2 + S^4))/(135*(1 + S^2)^3) + (Pi^2*(-608 - 1934*S^2 - 2259*S^4 - 5516*S^6 - 2987*S^8 - 732*S^10))/(27*S*(1 + S^2)^3))*Zeta[3] - (2*(-14 - 35*S^2 + 165*S^4 - 48*S^6 + 48*S^8 + 30*S^10)*Zeta[3]^2)/(3*S*(1 + S^2)^3) + HPL[{2, 1, 1}, -S^2]*((2*(-6155 - 1886*S^2 + 8349*S^4 + 14260*S^6 + 6292*S^8))/(81*S^3*(1 + S^2)) + (2*Pi^2*(-593 + 1974*S^2 + 7536*S^4 - 24496*S^6 + 22086*S^8 + 8838*S^10 + 1027*S^12))/(27*S^3*(1 + S^2)^3) - (32*S^3*(-22 + 21*S^2 + 21*S^4 + 7*S^6)*Zeta[3])/(1 + S^2)^3) + HPL[{2, 1}, -S^2]*((4096 - 12470*S^2 + 41775*S^4 + 64930*S^6 + 49357*S^8)/(486*S^3*(1 + S^2)) + (Pi^4*(-7313 - 21939*S^2 - 21939*S^4 + 17525*S^6 + 816*S^8 + 816*S^10 + 272*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(-1833 - 3544*S^2 - 33910*S^4 + 15858*S^6 - 8857*S^8 + 2162*S^10 + 756*S^12))/(54*S^3*(1 + S^2)^3) - (8*(-391 - 1173*S^2 - 1173*S^4 + 1350*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(-98 - 294*S^2 - 294*S^4 + 337*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(106 + 485*S^2 + 863*S^4 - 433*S^6 + 212*S^8 + 86*S^10 + S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{4}, -S^2]*((-1790 - 2255*S^2 - 20316*S^4 - 36815*S^6 - 20204*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(-188 - 222*S^2 + 543*S^4 - 2140*S^6 + 477*S^8 - 918*S^10 - 512*S^12))/(54*S^3*(1 + S^2)^3) - (4*(-1 - 3*S^2 - 3*S^4 - 24*S^6 + 3*S^8 + 3*S^10 + S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-3 - 9*S^2 - 9*S^4 + 26*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((-1358 - 4901*S^2 - 30045*S^4 - 42557*S^6 - 22535*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(17 - 788*S^2 - 1301*S^4 - 1964*S^6 - 3629*S^8 - 2408*S^10 - 535*S^12))/(54*S^3*(1 + S^2)^3) + (Pi^4*(229 + 687*S^2 + 687*S^4 - 998*S^6 - 633*S^8 - 633*S^10 - 211*S^12))/(540*S^3*(1 + S^2)^3) - (8*(1 + 3*S^2 + 3*S^4 + 8*S^6)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-199 - 813*S^2 - 1290*S^4 + 781*S^6 - 105*S^8 + 30*S^10 + 44*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(-5 - 15*S^2 - 15*S^4 - 148*S^6 + 99*S^8 + 99*S^10 + 33*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(-1 - 3*S^2 - 3*S^4 - 136*S^6 + 111*S^8 + 111*S^10 + 37*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(8 + 24*S^2 + 24*S^4 + 43*S^6 + 102*S^8 + 66*S^10 + 17*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^3*(((1 + S^2)*(65 + 1354*S^2 + 65*S^4))/(27*S^3) + (Pi^4*(8061 + 24183*S^2 + 24183*S^4 - 44045*S^6 + 12366*S^8 + 12366*S^10 + 4122*S^12))/(810*S^3*(1 + S^2)^3) + (Pi^2*(5461 + 18330*S^2 + 174867*S^4 - 108868*S^6 + 136743*S^8 + 19194*S^10 + 4705*S^12))/(486*S^3*(1 + S^2)^3) + ((2*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(9*S^3*(1 + S^2)^3) + (2*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2}, -S^2] + (16*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^3) - (8*(15 + 52*S^2 + 63*S^4 - 14*S^6 + 54*S^8 + 49*S^10 + 15*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(17 + 51*S^2 + 51*S^4 - 194*S^6 + 87*S^8 + 87*S^10 + 29*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (40*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^3) - (16*(62 + 186*S^2 + 186*S^4 - 435*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (80*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(18 + 94*S^2 + 174*S^4 - 158*S^6 + 183*S^8 + 97*S^10 + 18*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((8377 - 4310*S^2 - 15024*S^4 - 18602*S^6 - 8489*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(631 - 1791*S^2 - 7209*S^4 + 24545*S^6 - 22218*S^8 - 8862*S^10 - 1016*S^12))/(27*S^3*(1 + S^2)^3) + (8*(-3 - 9*S^2 - 9*S^4 - 133*S^6 + 126*S^8 + 126*S^10 + 42*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]^4*((10*(1 + S^2)*(13 + 29*S^2 + 13*S^4))/(9*S^3) + (Pi^2*(347 + 5229*S^2 + 13593*S^4 - 17678*S^6 + 10083*S^8 + 4059*S^10 + 347*S^12))/(54*S^3*(1 + S^2)^3) + (10*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(10 + 30*S^2 + 30*S^4 - 43*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) - (20*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(40 + 120*S^2 + 120*S^4 - 277*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((-578 + 8749*S^2 + 22020*S^4 + 21799*S^6 + 8458*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(53 + 4008*S^2 + 9849*S^4 - 23969*S^6 + 22668*S^8 + 9735*S^10 + 1340*S^12))/(108*S^3*(1 + S^2)^3) + ((3 + 9*S^2 + 9*S^4 + 118*S^6 - 111*S^8 - 111*S^10 - 37*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(-196 - 588*S^2 - 588*S^4 + 607*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-4 - 12*S^2 - 12*S^4 - 129*S^6 + 129*S^8 + 129*S^10 + 43*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((-104*Pi^2*S^5*(3 + 3*S^2 + S^4))/(9*(1 + S^2)^3) + (-1202 - 3659*S^2 - 4281*S^4 - 8915*S^6 - 5141*S^8 - 1170*S^10)/(9*S*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((-927883 - 1719022*S^2 - 1823424*S^4 - 964930*S^6 - 679141*S^8)/(11664*S^3*(1 + S^2)) + (Pi^2*(-613 - 224*S^2 + 288*S^4 + 290*S^6 - 41*S^8))/(72*S^3*(1 + S^2)) + (Pi^4*(-6547 + 24219*S^2 + 91620*S^4 - 269756*S^6 + 162696*S^8 + 52914*S^10 + 1796*S^12))/(3240*S^3*(1 + S^2)^3) + ((205 + 176*S^2 - 1255*S^4 - 400*S^6 - 5305*S^8 - 2608*S^10 - 605*S^12)/(18*S^3*(1 + S^2)^3) + (Pi^2*(1 + 3*S^2 + 3*S^4 + 160*S^6 - 159*S^8 - 159*S^10 - 53*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] + ((130 + 402*S^2 + 429*S^4 - 244*S^6 - 141*S^8 - 294*S^10 - 122*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (2*(-3 - 9*S^2 - 9*S^4 - 37*S^6 + 18*S^8 + 18*S^10 + 6*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((2*Pi^2*(-638 - 1914*S^2 - 1914*S^4 + 1819*S^6 + 15*S^8 + 15*S^10 + 5*S^12))/(9*S^3*(1 + S^2)^3) - (2*(2512 + 8556*S^2 + 39237*S^4 - 11401*S^6 + 20553*S^8 + 2517*S^10 + 10*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (2*(7 + 2409*S^2 + 6045*S^4 - 15934*S^6 + 18585*S^8 + 7893*S^10 + 1051*S^12)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(-7 - 21*S^2 - 21*S^4 - 236*S^6 + 225*S^8 + 225*S^10 + 75*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-5 - 15*S^2 - 15*S^4 - 189*S^6 + 168*S^8 + 168*S^10 + 56*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(1 + 799*S^2 + 2011*S^4 - 5314*S^6 + 6191*S^8 + 2627*S^10 + 349*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(-196 - 588*S^2 - 588*S^4 + 607*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(-1175 - 3525*S^2 - 3525*S^4 + 3778*S^6 + 231*S^8 + 231*S^10 + 77*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(-98 - 294*S^2 - 294*S^4 + 337*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*S^3*(-131 + 159*S^2 + 159*S^4 + 53*S^6))/(9*(1 + S^2)^3) + (53 - 1638*S^2 - 7308*S^4 - 3854*S^6 - 16443*S^8 - 7488*S^10 - 1810*S^12)/(27*S^3*(1 + S^2)^3))*Zeta[3] - (8*S^3*(-28 + 39*S^2 + 39*S^4 + 13*S^6)*Zeta[5])/(3*(1 + S^2)^3)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(27713 - 37886*S^2 + 27713*S^4))/(648*S^3) + (Pi^2*(4673 + 28781*S^2 + 45993*S^4 + 22715*S^6 + 1478*S^8))/(972*S^3*(1 + S^2)) + (Pi^4*(757 + 50388*S^2 + 146373*S^4 - 191152*S^6 + 75471*S^8 + 26754*S^10 + 757*S^12))/(1080*S^3*(1 + S^2)^3) + ((175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(4 + 12*S^2 + 12*S^4 - 13*S^6 + 21*S^8 + 21*S^10 + 7*S^12))/(9*S^3*(1 + S^2)^3) - (2*(259 + 2535*S^2 + 5361*S^4 + 4055*S^6 + 6234*S^8 + 3822*S^10 + 718*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(19 + 34*S^2 - 18*S^4 + 150*S^6 - 54*S^8 + 22*S^10 + 19*S^12)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^3) + (4*(6 + 18*S^2 + 18*S^4 - 89*S^6 + 51*S^8 + 51*S^10 + 17*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-2*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(3*S^3*(1 + S^2)^3) - (2*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(85 + 1401*S^2 + 3723*S^4 - 5230*S^6 + 3777*S^8 + 1419*S^10 + 85*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(97 + 291*S^2 + 291*S^4 - 610*S^6 + 255*S^8 + 255*S^10 + 85*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (40*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (16*(578 + 1734*S^2 + 1734*S^4 - 4001*S^6 + 1743*S^8 + 1743*S^10 + 581*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (80*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((-4*Pi^2*(17 + 51*S^2 + 51*S^4 - 147*S^6 + 90*S^8 + 90*S^10 + 30*S^12))/(9*S^3*(1 + S^2)^3) - (2*(128 + 604*S^2 + 1406*S^4 + 415*S^6 + 1309*S^8 + 461*S^10 + 77*S^12))/(3*S^3*(1 + S^2)^3))*Zeta[3] + HPL[{2}, -S^2]*((137 + 12374*S^2 + 16698*S^4 + 12374*S^6 + 137*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(149 + 4341*S^2 + 12225*S^4 - 15326*S^6 + 8877*S^8 + 3225*S^10 + 149*S^12))/(18*S^3*(1 + S^2)^3) - (4*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(41 + 123*S^2 + 123*S^4 - 266*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) - (4*(27 + 81*S^2 + 81*S^4 - 195*S^6 + 114*S^8 + 114*S^10 + 38*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) + HPL[{1}, -S^2]*(-((1 + S^2)*(104305 - 46054*S^2 + 104305*S^4))/(972*S^3) + (Pi^2*(-96481 - 5764*S^2 + 178626*S^4 - 89140*S^6 - 130393*S^8))/(11664*S^3*(1 + S^2)) + (Pi^4*(11665 - 69672*S^2 + 1554828*S^4 - 1576852*S^6 + 797703*S^8 - 32448*S^10 + 5248*S^12))/(19440*S^3*(1 + S^2)^3) + (Pi^6*(187513 + 562539*S^2 + 562539*S^4 - 953473*S^6 + 184422*S^8 + 184422*S^10 + 61474*S^12))/(68040*S^3*(1 + S^2)^3) + ((Pi^2*(317 + 951*S^2 + 951*S^4 - 1901*S^6 + 702*S^8 + 702*S^10 + 234*S^12))/(9*S^3*(1 + S^2)^3) + (2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12)/(54*S^3*(1 + S^2)^3))*HPL[{2}, -S^2]^2 + (2*(177 + 531*S^2 + 531*S^4 - 1214*S^6 + 531*S^8 + 531*S^10 + 177*S^12)*HPL[{2}, -S^2]^3)/(9*S^3*(1 + S^2)^3) - (2*(1 + 3*S^2 + 3*S^4 - 20*S^6 + 9*S^8 + 9*S^10 + 3*S^12)*HPL[{3}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((85 - 4674*S^2 - 4989*S^4 - 17452*S^6 - 9705*S^8 - 12378*S^10 - 2615*S^12)/(54*S^3*(1 + S^2)^3) + (Pi^2*(29 + 87*S^2 + 87*S^4 - 320*S^6 + 153*S^8 + 153*S^10 + 51*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4}, -S^2] - (2*(259 + 591*S^2 + 141*S^4 + 1238*S^6 - 453*S^8 + 393*S^10 + 259*S^12)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(9 + 27*S^2 + 27*S^4 - 219*S^6 + 192*S^8 + 192*S^10 + 64*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((-4*Pi^2*(313 + 939*S^2 + 939*S^4 - 1888*S^6 + 681*S^8 + 681*S^10 + 227*S^12))/(9*S^3*(1 + S^2)^3) - (2*(668 + 2001*S^2 + 16356*S^4 - 10304*S^6 + 15774*S^8 + 1143*S^10 + 362*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3, 1}, -S^2] + (4*(151 + 771*S^2 + 1383*S^4 - 1570*S^6 + 1383*S^8 + 771*S^10 + 151*S^12)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^3) + (4*(208 + 873*S^2 + 1329*S^4 - 1120*S^6 + 1221*S^8 + 837*S^10 + 208*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(-1 + S^6)*HPL[{4, 2}, -S^2])/S^3 - (8*(5 + 15*S^2 + 15*S^4 - 109*S^6 + 66*S^8 + 66*S^10 + 22*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(211 + 633*S^2 + 633*S^4 - 1260*S^6 + 447*S^8 + 447*S^10 + 149*S^12))/(3*S^3*(1 + S^2)^3) + (4*(515 + 1572*S^2 + 16065*S^4 - 10304*S^6 + 16065*S^8 + 1572*S^10 + 515*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1}, -S^2] + (8*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(145 + 1609*S^2 + 3975*S^4 - 5286*S^6 + 3993*S^8 + 1615*S^10 + 145*S^12)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (16*(177 + 531*S^2 + 531*S^4 - 1214*S^6 + 531*S^8 + 531*S^10 + 177*S^12)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(1079 + 3237*S^2 + 3237*S^4 - 7478*S^6 + 3273*S^8 + 3273*S^10 + 1091*S^12)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (80*(17 + 282*S^2 + 750*S^4 - 1046*S^6 + 750*S^8 + 282*S^10 + 17*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(62 + 186*S^2 + 186*S^4 - 435*S^6 + 189*S^8 + 189*S^10 + 63*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (160*(25 + 75*S^2 + 75*S^4 - 174*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((-2007 - 3077*S^2 - 1969*S^4 - 1115*S^6)/(18*S^3) - (2*Pi^2*(304 + 1221*S^2 + 1842*S^4 - 1174*S^6 + 2544*S^8 + 1455*S^10 + 304*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[3] + (4*(7 + 21*S^2 + 21*S^4 - 67*S^6 + 30*S^8 + 30*S^10 + 10*S^12)*Zeta[3]^2)/(3*S^3*(1 + S^2)^3) + HPL[{3}, -S^2]*((-1243 - 3058*S^2 - 9114*S^4 - 9058*S^6 - 3919*S^8)/(54*S^3*(1 + S^2)) + (Pi^2*(-431 - 1272*S^2 - 1137*S^4 - 268*S^6 - 1299*S^8 - 1326*S^10 - 431*S^12))/(27*S^3*(1 + S^2)^3) + (8*(19 + 57*S^2 + 57*S^4 - 134*S^6 + 57*S^8 + 57*S^10 + 19*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*S^3*(-1 + 3*S^2 + 3*S^4 + S^6)*Zeta[3])/(3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-137 - 12374*S^2 - 16698*S^4 - 12374*S^6 - 137*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(-149 - 4341*S^2 - 12225*S^4 + 15326*S^6 - 8877*S^8 - 3225*S^10 - 149*S^12))/(9*S^3*(1 + S^2)^3) + (8*(41 + 123*S^2 + 123*S^4 - 266*S^6 + 123*S^8 + 123*S^10 + 41*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]*((-53453 - 52460*S^2 - 83550*S^4 - 52460*S^6 - 53453*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(646 + 996*S^2 + 24072*S^4 - 17311*S^6 + 17577*S^8 + 615*S^10 + 325*S^12))/(54*S^3*(1 + S^2)^3) + (Pi^4*(7131 + 21393*S^2 + 21393*S^4 - 38357*S^6 + 10932*S^8 + 10932*S^10 + 3644*S^12))/(540*S^3*(1 + S^2)^3) - (2*(151 + 771*S^2 + 1383*S^4 - 1570*S^6 + 1383*S^8 + 771*S^10 + 151*S^12)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^3) + (2*(1 + 3*S^2 + 3*S^4 - 40*S^6 + 21*S^8 + 21*S^10 + 7*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (2*(325 + 1725*S^2 + 3237*S^4 - 2590*S^6 + 3237*S^8 + 1725*S^10 + 325*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) - (2*(601 + 2292*S^2 + 3273*S^4 - 1120*S^6 + 3867*S^8 + 2490*S^10 + 601*S^12)*Zeta[5])/(9*S^3*(1 + S^2)^3))) + (2*(70 + 175*S^2 + 663*S^4 - 2378*S^6 - 674*S^8 + 30*S^10)*Zeta[7])/(S*(1 + S^2)^3) + HPL[{1}, -S^2]*((-5*(1 + S^2)*(523277 - 119846*S^2 + 523277*S^4))/(11664*S^3) + (Pi^2*(566897 + 1776530*S^2 + 1277940*S^4 - 1065994*S^6 - 761053*S^8))/(34992*S^3*(1 + S^2)) + (Pi^4*(664561 + 1784425*S^2 + 1582989*S^4 + 186799*S^6 - 102662*S^8))/(116640*S^3*(1 + S^2)) + (Pi^6*(66197 + 1379268*S^2 + 3711063*S^4 - 4225940*S^6 + 1155297*S^8 + 527346*S^10 + 66197*S^12))/(136080*S^3*(1 + S^2)^3) - (62*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2}, -S^2]^3)/(S*(1 + S^2)^2) + (2*(133 + 735*S^2 + 1410*S^4 - 1192*S^6 + 1410*S^8 + 735*S^10 + 133*S^12)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^3) + ((-1061 - 14034*S^2 - 26013*S^4 - 27052*S^6 - 70257*S^8 - 30918*S^10 - 7505*S^12)/(27*S^3*(1 + S^2)^3) - (4*Pi^2*(-19 - 57*S^2 - 57*S^4 - 186*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{5}, -S^2] + ((-881 - 1494*S^2 + 789*S^4 - 1624*S^6 - 7797*S^8 - 4356*S^10 - 881*S^12)*HPL[{6}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(-87 - 261*S^2 - 261*S^4 + 81*S^6 + 276*S^8 + 276*S^10 + 92*S^12)*HPL[{7}, -S^2])/(S^3*(1 + S^2)^3) - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1}, -S^2]^2)/(3*S^3*(1 + S^2)^3) + ((4*Pi^2*(108 + 324*S^2 + 324*S^4 - 1423*S^6 + 915*S^8 + 915*S^10 + 305*S^12))/(9*S^3*(1 + S^2)^3) + (4*(820 + 5073*S^2 + 20247*S^4 - 11401*S^6 + 39543*S^8 + 6000*S^10 + 1702*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 2}, -S^2] + ((2*Pi^2*(709 + 2127*S^2 + 2127*S^4 - 9670*S^6 + 6327*S^8 + 6327*S^10 + 2109*S^12))/(9*S^3*(1 + S^2)^3) + (4*(1153 + 7536*S^2 + 26478*S^4 - 8911*S^6 + 49602*S^8 + 9927*S^10 + 2599*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{4, 1}, -S^2] + (2*(133 + 753*S^2 + 1464*S^4 - 1336*S^6 + 1464*S^8 + 753*S^10 + 133*S^12)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(7 + 21*S^2 + 21*S^4 - 185*S^6 + 120*S^8 + 120*S^10 + 40*S^12)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(509 + 2133*S^2 + 3351*S^4 - 3530*S^6 + 5835*S^8 + 2961*S^10 + 509*S^12)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (8*(2 + 6*S^2 + 6*S^4 - 71*S^6 + 45*S^8 + 45*S^10 + 15*S^12)*HPL[{5, 2}, -S^2])/(S^3*(1 + S^2)^3) + (4*(-184 - 552*S^2 - 552*S^4 + 153*S^6 + 699*S^8 + 699*S^10 + 233*S^12)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((8*Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2089*S^6 + 771*S^8 + 771*S^10 + 257*S^12))/(9*S^3*(1 + S^2)^3) + (4*(2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 2, 1}, -S^2] + ((32*Pi^2*(233 + 699*S^2 + 699*S^4 - 1141*S^6 + 294*S^8 + 294*S^10 + 98*S^12))/(9*S^3*(1 + S^2)^3) + (4*(5008 + 15855*S^2 + 120606*S^4 - 53074*S^6 + 69684*S^8 + 9267*S^10 + 1390*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{3, 1, 1}, -S^2] - (1488*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (4*(443 + 1329*S^2 + 1329*S^4 - 5586*S^6 + 3561*S^8 + 3561*S^10 + 1187*S^12)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(172 + 516*S^2 + 516*S^4 - 2137*S^6 + 1353*S^8 + 1353*S^10 + 451*S^12)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(18 - 62*S^2 - 294*S^4 - 158*S^6 + 651*S^8 + 253*S^10 + 18*S^12)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (4*(1337 + 4011*S^2 + 4011*S^4 - 16838*S^6 + 10707*S^8 + 10707*S^10 + 3569*S^12)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(4253 + 12759*S^2 + 12759*S^4 - 52142*S^6 + 32847*S^8 + 32847*S^10 + 10949*S^12)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(362 + 1086*S^2 + 1086*S^4 - 4471*S^6 + 2829*S^8 + 2829*S^10 + 943*S^12)*HPL[{5, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + ((8*(-67 - 55*S^2 - 888*S^4 + 888*S^6 + 55*S^8 + 67*S^10))/(S^3*(1 + S^2)^2) + (16*Pi^2*(-275 - 825*S^2 - 825*S^4 + 674*S^6 + 237*S^8 + 237*S^10 + 79*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{2, 1, 1, 1}, -S^2] + (992*(-1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/S^3 + (32*(18 - 17*S^2 - 159*S^4 - 158*S^6 + 516*S^8 + 208*S^10 + 18*S^12)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) + (64*(191 + 573*S^2 + 573*S^4 - 674*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (64*(191 + 573*S^2 + 573*S^4 - 674*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (32*(-661 - 1983*S^2 - 1983*S^4 + 1348*S^6 + 807*S^8 + 807*S^10 + 269*S^12)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (64*(-1015 - 3045*S^2 - 3045*S^4 + 2299*S^6 + 1032*S^8 + 1032*S^10 + 344*S^12)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (7200*(-1 - 2*S^2 + 2*S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (256*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (256*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^3) - (320*(221 + 663*S^2 + 663*S^4 - 1673*S^6 + 798*S^8 + 798*S^10 + 266*S^12)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4800*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((194051 + 355040*S^2 + 83550*S^4 - 250120*S^6 - 87145*S^8)/(972*S^3*(1 + S^2)) + (Pi^4*(-231 - 693*S^2 - 693*S^4 + 10373*S^6 - 8424*S^8 - 8424*S^10 - 2808*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(179 - 564*S^2 - 8619*S^4 + 10198*S^6 - 29139*S^8 - 4110*S^10 - 1537*S^12))/(54*S^3*(1 + S^2)^3))*Zeta[3] + (2*(1 + 26*S^2 + 75*S^4 - 68*S^6 + 75*S^8 + 26*S^10 + S^12)*Zeta[3]^2)/(S^3*(1 + S^2)^3) + HPL[{4}, -S^2]*((-3425 - 7525*S^2 - 12659*S^4 - 9063*S^6)/(36*S^3) + (Pi^2*(-239 - 897*S^2 - 1254*S^4 + 1916*S^6 - 3216*S^8 - 1551*S^10 - 239*S^12))/(9*S^3*(1 + S^2)^3) + (4*(113 + 339*S^2 + 339*S^4 - 734*S^6 + 339*S^8 + 339*S^10 + 113*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(3 + 9*S^2 + 9*S^4 - 100*S^6 + 75*S^8 + 75*S^10 + 25*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1, 1}, -S^2]*((-2*(-557 - 629*S^2 + 629*S^4 + 557*S^6))/(3*S^3) + (2*Pi^2*(175 + 3837*S^2 + 10473*S^4 - 5314*S^6 - 2271*S^8 - 411*S^10 + 175*S^12))/(9*S^3*(1 + S^2)^3) - (64*(25 + 75*S^2 + 75*S^4 - 337*S^6 + 219*S^8 + 219*S^10 + 73*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3}, -S^2]*((13121 - 65416*S^2 - 434382*S^4 - 670576*S^6 - 268075*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-2087 - 17850*S^2 - 59943*S^4 + 13250*S^6 - 122745*S^8 - 29460*S^10 - 7685*S^12))/(162*S^3*(1 + S^2)^3) + (Pi^4*(-292 - 876*S^2 - 876*S^4 + 6193*S^6 - 4533*S^8 - 4533*S^10 - 1511*S^12))/(135*S^3*(1 + S^2)^3) + (4*(8 + 24*S^2 + 24*S^4 - 157*S^6 + 105*S^8 + 105*S^10 + 35*S^12)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(175 + 1155*S^2 + 2427*S^4 - 5314*S^6 + 5775*S^8 + 2271*S^10 + 175*S^12)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(103 + 309*S^2 + 309*S^4 - 1352*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (16*(103 + 309*S^2 + 309*S^4 - 1348*S^6 + 867*S^8 + 867*S^10 + 289*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (4*(104 + 489*S^2 + 822*S^4 - 1034*S^6 + 984*S^8 + 543*S^10 + 104*S^12)*Zeta[3])/(9*S^3*(1 + S^2)^3)) + HPL[{2}, -S^2]^2*((1970 + 7637*S^2 + 11010*S^4 + 7637*S^6 + 1970*S^8)/(81*S^3*(1 + S^2)) + (Pi^2*(863 + 8931*S^2 + 21657*S^4 - 24698*S^6 + 16635*S^8 + 7257*S^10 + 863*S^12))/(54*S^3*(1 + S^2)^3) - (4*(70 + 210*S^2 + 210*S^4 - 795*S^6 + 489*S^8 + 489*S^10 + 163*S^12)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^3) + (124*(-1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (4*(42 + 126*S^2 + 126*S^4 - 607*S^6 + 405*S^8 + 405*S^10 + 135*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{3, 1}, -S^2]*((2*(-55 + 318*S^2 + 2205*S^4 + 1616*S^6))/(9*S^3) + (2*Pi^2*(95 - 3912*S^2 - 12327*S^4 + 5032*S^6 + 6789*S^8 + 2460*S^10 + 95*S^12))/(27*S^3*(1 + S^2)^3) + (16*(53 + 159*S^2 + 159*S^4 - 694*S^6 + 447*S^8 + 447*S^10 + 149*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + HPL[{2, 1}, -S^2]*((-7811 - 8999*S^2 + 8999*S^4 + 7811*S^6)/(27*S^3) + (Pi^4*(-7200 - 21600*S^2 - 21600*S^4 + 21017*S^6 + 3411*S^8 + 3411*S^10 + 1137*S^12))/(270*S^3*(1 + S^2)^3) + (Pi^2*(-8921 - 23394*S^2 - 141699*S^4 + 22802*S^6 + 22119*S^8 + 1248*S^10 + 3877*S^12))/(162*S^3*(1 + S^2)^3) + (64*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(175 + 1137*S^2 + 2373*S^4 - 5314*S^6 + 5829*S^8 + 2289*S^10 + 175*S^12)*Zeta[3])/(3*S^3*(1 + S^2)^3)) + ((-2*Pi^2*(-18 - 54*S^2 - 54*S^4 - 1477*S^6 + 1311*S^8 + 1311*S^10 + 437*S^12))/(9*S^3*(1 + S^2)^3) - (2*(-2320 - 8079*S^2 - 5352*S^4 - 24341*S^6 + 37758*S^8 + 1974*S^10 + 2108*S^12))/(27*S^3*(1 + S^2)^3))*Zeta[5] + HPL[{2}, -S^2]*((73775 + 84143*S^2 - 84143*S^4 - 73775*S^6)/(324*S^3) + (Pi^2*(60827 + 143570*S^2 + 44040*S^4 - 82474*S^6 - 45067*S^8))/(1944*S^3*(1 + S^2)) + (Pi^4*(6859 + 150648*S^2 + 411261*S^4 - 252628*S^6 - 38937*S^8 + 582*S^10 + 6859*S^12))/(3240*S^3*(1 + S^2)^3) + ((-1559 - 9930*S^2 - 40305*S^4 + 22802*S^6 - 79275*S^8 - 12216*S^10 - 3485*S^12)/(27*S^3*(1 + S^2)^3) - (2*Pi^2*(108 + 324*S^2 + 324*S^4 - 1423*S^6 + 915*S^8 + 915*S^10 + 305*S^12))/(9*S^3*(1 + S^2)^3))*HPL[{3}, -S^2] - (2*(403 + 2229*S^2 + 4272*S^4 - 3748*S^6 + 4272*S^8 + 2229*S^10 + 403*S^12)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^3) - (4*(17 + 51*S^2 + 51*S^4 - 286*S^6 + 195*S^8 + 195*S^10 + 65*S^12)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-4*Pi^2*(350 + 1050*S^2 + 1050*S^4 - 2089*S^6 + 771*S^8 + 771*S^10 + 257*S^12))/(9*S^3*(1 + S^2)^3) - (2*(2522 + 11073*S^2 + 59790*S^4 - 22802*S^6 + 59790*S^8 + 11073*S^10 + 2522*S^12))/(27*S^3*(1 + S^2)^3))*HPL[{2, 1}, -S^2] - (4*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(241 + 723*S^2 + 723*S^4 - 2922*S^6 + 1839*S^8 + 1839*S^10 + 613*S^12)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^3) + (4*(727 + 2181*S^2 + 2181*S^4 - 8806*S^6 + 5529*S^8 + 5529*S^10 + 1843*S^12)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + (8*(175 + 1713*S^2 + 4101*S^4 - 5314*S^6 + 4101*S^8 + 1713*S^10 + 175*S^12)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (496*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 - (32*(191 + 573*S^2 + 573*S^4 - 674*S^6 + 15*S^8 + 15*S^10 + 5*S^12)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) - (128*(49 + 147*S^2 + 147*S^4 - 337*S^6 + 147*S^8 + 147*S^10 + 49*S^12)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^3) + ((-1685 - 10218*S^2 - 39855*S^4 + 22802*S^6 - 79725*S^8 - 11928*S^10 - 3359*S^12)/(27*S^3*(1 + S^2)^3) - (2*Pi^2*(108 + 324*S^2 + 324*S^4 - 1481*S^6 + 969*S^8 + 969*S^10 + 323*S^12))/(9*S^3*(1 + S^2)^3))*Zeta[3] - (4*(44 + 132*S^2 + 132*S^4 - 1255*S^6 + 951*S^8 + 951*S^10 + 317*S^12)*Zeta[5])/(3*S^3*(1 + S^2)^3)) - (4*(-35 - 105*S^2 - 105*S^4 - 583*S^6 + 588*S^8 + 588*S^10 + 196*S^12)*Zeta[7])/(S^3*(1 + S^2)^3))) + (3136*S^5*(3 + 3*S^2 + S^4)*Zeta[9])/(3*(1 + S^2)^3);
E5uvwT=E5uvwT0F0+T*E5uvwT1F1*(F+1/F)+T^2*(E5uvwT2F0+E5uvwT2F2*(F^2+1/F^2))+T^3*(E5uvwT3F1*(F+1/F)+E5uvwT3F3*(F^3+1/F^3));
E5vwuT0F0=(-210439*Pi^10)/8164800 - HPL[{0}, S^2]^10/3840 + HPL[{0}, S^2]^8*(-Pi^2/384 + HPL[{2}, -S^2]/96) + (8*Pi^2*HPL[{2}, -S^2]^4)/3 + (32*HPL[{2}, -S^2]^5)/5 - (31*Pi^2*HPL[{4}, -S^2]^2)/3 + 286*HPL[{5}, -S^2]^2 - 51*Pi^2*HPL[{8}, -S^2] - 3296*HPL[{10}, -S^2] + (208*Pi^2*HPL[{3, 1}, -S^2]^2)/3 + HPL[{2}, -S^2]^3*((111*Pi^4)/20 - (164*HPL[{4}, -S^2])/3 + (164*HPL[{3, 1}, -S^2])/3) - 192*HPL[{3, 2}, -S^2]^2 + 6624*HPL[{4, 1}, -S^2]^2 - (14*Pi^2*HPL[{5, 3}, -S^2])/3 - (53*Pi^2*HPL[{6, 2}, -S^2])/3 + 12*HPL[{6, 4}, -S^2] - (58*Pi^2*HPL[{7, 1}, -S^2])/3 + 148*HPL[{7, 3}, -S^2] + 292*HPL[{8, 2}, -S^2] + 732*HPL[{9, 1}, -S^2] + HPL[{2, 1}, -S^2]^2*((-2021*Pi^4)/60 + 3136*HPL[{3, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2]) + HPL[{6}, -S^2]*((-28*Pi^4)/45 + 472*HPL[{3, 1}, -S^2] - 356*HPL[{2, 1, 1}, -S^2]) + (1568*Pi^2*HPL[{2, 1, 1}, -S^2]^2)/3 + HPL[{0}, S^2]^6*((-23*Pi^4)/3456 + (23*Pi^2*HPL[{2}, -S^2])/144 + (13*HPL[{2}, -S^2]^2)/96 - HPL[{4}, -S^2]/24 - (5*HPL[{3, 1}, -S^2])/8 + (3*HPL[{2, 1, 1}, -S^2])/2) + HPL[{3}, -S^2]^2*((82*Pi^4)/45 + 20*HPL[{4}, -S^2] - 164*HPL[{3, 1}, -S^2] + 296*HPL[{2, 1, 1}, -S^2]) + HPL[{4, 2}, -S^2]*((33*Pi^4)/5 + 936*HPL[{2, 1, 1}, -S^2]) + HPL[{5, 1}, -S^2]*((1729*Pi^4)/90 + 5408*HPL[{2, 1, 1}, -S^2]) + 1376*HPL[{3, 1, 1}, -S^2]^2 - (33*Pi^4*HPL[{3, 1, 2}, -S^2])/5 + (633*Pi^4*HPL[{3, 2, 1}, -S^2])/5 + (214*Pi^2*HPL[{3, 3, 2}, -S^2])/3 + (17761*Pi^4*HPL[{4, 1, 1}, -S^2])/45 - 112*Pi^2*HPL[{4, 1, 3}, -S^2] + (190*Pi^2*HPL[{4, 2, 2}, -S^2])/3 - (1208*Pi^2*HPL[{4, 3, 1}, -S^2])/3 + 144*HPL[{4, 3, 3}, -S^2] + 444*HPL[{4, 4, 2}, -S^2] - (706*Pi^2*HPL[{5, 1, 2}, -S^2])/3 - 876*HPL[{5, 1, 4}, -S^2] - (5026*Pi^2*HPL[{5, 2, 1}, -S^2])/3 - 452*HPL[{5, 2, 3}, -S^2] + 616*HPL[{5, 3, 2}, -S^2] - 2244*HPL[{5, 4, 1}, -S^2] - (12886*Pi^2*HPL[{6, 1, 1}, -S^2])/3 - 3508*HPL[{6, 1, 3}, -S^2] - 1236*HPL[{6, 2, 2}, -S^2] - 11092*HPL[{6, 3, 1}, -S^2] - 7472*HPL[{7, 1, 2}, -S^2] - 32672*HPL[{7, 2, 1}, -S^2] - 74908*HPL[{8, 1, 1}, -S^2] - (2651*Pi^4*HPL[{3, 1, 1, 1}, -S^2])/9 + (2*Pi^2*HPL[{3, 1, 2, 2}, -S^2])/3 + (2*Pi^2*HPL[{3, 2, 1, 2}, -S^2])/3 - (4838*Pi^2*HPL[{3, 2, 2, 1}, -S^2])/3 - 4840*Pi^2*HPL[{3, 3, 1, 1}, -S^2] - 456*HPL[{3, 3, 2, 2}, -S^2] - 1888*HPL[{3, 3, 3, 1}, -S^2] + 216*Pi^2*HPL[{4, 1, 1, 2}, -S^2] - 4624*Pi^2*HPL[{4, 1, 2, 1}, -S^2] + 2052*HPL[{4, 1, 2, 3}, -S^2] + 4852*HPL[{4, 1, 3, 2}, -S^2] - 14304*Pi^2*HPL[{4, 2, 1, 1}, -S^2] + 5892*HPL[{4, 2, 1, 3}, -S^2] + 7628*HPL[{4, 2, 2, 2}, -S^2] + 3092*HPL[{4, 2, 3, 1}, -S^2] + 14356*HPL[{4, 3, 1, 2}, -S^2] + 22948*HPL[{4, 3, 2, 1}, -S^2] + 25776*HPL[{4, 4, 1, 1}, -S^2] - (84920*Pi^2*HPL[{5, 1, 1, 1}, -S^2])/3 + 11416*HPL[{5, 1, 1, 3}, -S^2] + 21132*HPL[{5, 1, 2, 2}, -S^2] + 152*HPL[{5, 1, 3, 1}, -S^2] + 45612*HPL[{5, 2, 1, 2}, -S^2] + 68652*HPL[{5, 2, 2, 1}, -S^2] + 69016*HPL[{5, 3, 1, 1}, -S^2] + 84636*HPL[{6, 1, 1, 2}, -S^2] + 113916*HPL[{6, 1, 2, 1}, -S^2] + 87516*HPL[{6, 2, 1, 1}, -S^2] + 4944*HPL[{7, 1, 1, 1}, -S^2] + (26692*Pi^4*HPL[{2, 1, 1, 1, 1}, -S^2])/45 - (9712*Pi^2*HPL[{2, 2, 1, 2, 1}, -S^2])/3 - 9712*Pi^2*HPL[{2, 2, 2, 1, 1}, -S^2] + 19208*Pi^2*HPL[{3, 1, 1, 1, 2}, -S^2] + (96472*Pi^2*HPL[{3, 1, 1, 2, 1}, -S^2])/3 + 38632*Pi^2*HPL[{3, 1, 2, 1, 1}, -S^2] - 304*HPL[{3, 1, 2, 2, 2}, -S^2] + 608*HPL[{3, 1, 3, 1, 2}, -S^2] + (242152*Pi^2*HPL[{3, 2, 1, 1, 1}, -S^2])/3 - 304*HPL[{3, 2, 1, 2, 2}, -S^2] - 608*HPL[{3, 2, 1, 3, 1}, -S^2] + 304*HPL[{3, 2, 2, 1, 2}, -S^2] + 11376*HPL[{3, 2, 2, 2, 1}, -S^2] + 33344*HPL[{3, 2, 3, 1, 1}, -S^2] + 1824*HPL[{3, 3, 1, 1, 2}, -S^2] + 34560*HPL[{3, 3, 1, 2, 1}, -S^2] + 98336*HPL[{3, 3, 2, 1, 1}, -S^2] + (727184*Pi^2*HPL[{4, 1, 1, 1, 1}, -S^2])/3 - 192576*HPL[{4, 1, 1, 1, 3}, -S^2] - 193512*HPL[{4, 1, 1, 2, 2}, -S^2] - 389504*HPL[{4, 1, 1, 3, 1}, -S^2] - 191688*HPL[{4, 1, 2, 1, 2}, -S^2] - 353448*HPL[{4, 1, 2, 2, 1}, -S^2] - 482496*HPL[{4, 1, 3, 1, 1}, -S^2] - 188040*HPL[{4, 2, 1, 1, 2}, -S^2] - 284808*HPL[{4, 2, 1, 2, 1}, -S^2] - 288456*HPL[{4, 2, 2, 1, 1}, -S^2] - 779456*HPL[{4, 3, 1, 1, 1}, -S^2] - 764592*HPL[{5, 1, 1, 1, 2}, -S^2] - 1348080*HPL[{5, 1, 1, 2, 1}, -S^2] - 1745328*HPL[{5, 1, 2, 1, 1}, -S^2] - 3119280*HPL[{5, 2, 1, 1, 1}, -S^2] - 7800672*HPL[{6, 1, 1, 1, 1}, -S^2] - 6944*Pi^2*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 25088*HPL[{3, 1, 1, 2, 2, 1}, -S^2] - 25088*HPL[{3, 1, 2, 1, 2, 1}, -S^2] + 150528*HPL[{3, 1, 3, 1, 1, 1}, -S^2] - 25088*HPL[{3, 2, 1, 1, 2, 1}, -S^2] + 125440*HPL[{3, 2, 2, 1, 1, 1}, -S^2] + 376320*HPL[{3, 3, 1, 1, 1, 1}, -S^2] + 5120*HPL[{4, 1, 1, 1, 1, 2}, -S^2] - 70144*HPL[{4, 1, 1, 1, 2, 1}, -S^2] + 5120*HPL[{4, 1, 1, 2, 1, 1}, -S^2] + 381440*HPL[{4, 1, 2, 1, 1, 1}, -S^2] + 1134080*HPL[{4, 2, 1, 1, 1, 1}, -S^2] + 2276224*HPL[{5, 1, 1, 1, 1, 1}, -S^2] + 13920*Pi^2*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] - 50176*HPL[{2, 1, 2, 1, 2, 1, 1}, -S^2] + 150528*HPL[{2, 2, 1, 1, 1, 2, 1}, -S^2] + 301056*HPL[{2, 2, 1, 1, 2, 1, 1}, -S^2] + 852992*HPL[{2, 2, 1, 2, 1, 1, 1}, -S^2] + 2257920*HPL[{2, 2, 2, 1, 1, 1, 1}, -S^2] - 4520960*HPL[{3, 1, 1, 1, 1, 1, 2}, -S^2] - 8735744*HPL[{3, 1, 1, 1, 1, 2, 1}, -S^2] - 12950528*HPL[{3, 1, 1, 1, 2, 1, 1}, -S^2] - 16362496*HPL[{3, 1, 1, 2, 1, 1, 1}, -S^2] - 18068480*HPL[{3, 1, 2, 1, 1, 1, 1}, -S^2] - 27049984*HPL[{3, 2, 1, 1, 1, 1, 1}, -S^2] - 81146112*HPL[{4, 1, 1, 1, 1, 1, 1}, -S^2] - 107520*HPL[{3, 1, 1, 1, 1, 1, 1, 1}, -S^2] + 215040*HPL[{2, 1, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2)/3 + HPL[{0}, S^2]^2 + (16*HPL[{2}, -S^2])/3)*Log[T]^8 - (4*HPL[{0}, S^2]*Log[T]^9)/3 - (4*Log[T]^10)/15 + Log[T]^6*((-23*Pi^4)/54 + (8*HPL[{0}, S^2]^4)/9 + (58*Pi^2*HPL[{2}, -S^2])/3 + HPL[{0}, S^2]^2*((37*Pi^2)/9 + (62*HPL[{2}, -S^2])/3) - 16*HPL[{4}, -S^2] - (448*HPL[{3, 1}, -S^2])/3 + (896*HPL[{2, 1, 1}, -S^2])/3 + HPL[{0}, S^2]*(-8*HPL[{3}, -S^2] + (448*HPL[{2, 1}, -S^2])/3 - 16*Zeta[3])) + HPL[{0}, S^2]^7*(HPL[{2, 1}, -S^2]/8 + Zeta[3]/6) + 112*HPL[{4, 3}, -S^2]*Zeta[3] + 388*HPL[{5, 2}, -S^2]*Zeta[3] + 564*HPL[{6, 1}, -S^2]*Zeta[3] - 204*HPL[{3, 2, 2}, -S^2]*Zeta[3] - 752*HPL[{3, 3, 1}, -S^2]*Zeta[3] - 744*HPL[{4, 1, 2}, -S^2]*Zeta[3] - 2376*HPL[{4, 2, 1}, -S^2]*Zeta[3] - 4688*HPL[{5, 1, 1}, -S^2]*Zeta[3] - 5664*HPL[{2, 2, 2, 1}, -S^2]*Zeta[3] + 17712*HPL[{3, 1, 1, 2}, -S^2]*Zeta[3] + 17712*HPL[{3, 1, 2, 1}, -S^2]*Zeta[3] + 34704*HPL[{3, 2, 1, 1}, -S^2]*Zeta[3] + 103648*HPL[{4, 1, 1, 1}, -S^2]*Zeta[3] - 12544*HPL[{2, 1, 2, 1, 1}, -S^2]*Zeta[3] - 37632*HPL[{2, 2, 1, 1, 1}, -S^2]*Zeta[3] - 63168*HPL[{3, 1, 1, 1, 1}, -S^2]*Zeta[3] - 24000*HPL[{2, 1, 1, 1, 1, 1}, -S^2]*Zeta[3] - (223*Pi^4*Zeta[3]^2)/90 + Log[T]^7*((-16*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]*((-52*Pi^2)/9 - (64*HPL[{2}, -S^2])/3) + (64*HPL[{3}, -S^2])/3 - (128*HPL[{2, 1}, -S^2])/3 + (64*Zeta[3])/3) + HPL[{7}, -S^2]*(-60*HPL[{2, 1}, -S^2] + 268*Zeta[3]) + HPL[{3, 1}, -S^2]*((-126709*Pi^6)/11340 - 468*HPL[{4, 2}, -S^2] - 2872*HPL[{5, 1}, -S^2] - (880*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 608*HPL[{3, 1, 2}, -S^2] + 1312*HPL[{3, 2, 1}, -S^2] + 6672*HPL[{4, 1, 1}, -S^2] - 2752*HPL[{3, 1, 1, 1}, -S^2] + 5312*HPL[{2, 1, 1, 1, 1}, -S^2] - 52*Zeta[3]^2) + HPL[{2}, -S^2]^2*((1049*Pi^6)/720 + 43*HPL[{3}, -S^2]^2 - (56*Pi^2*HPL[{4}, -S^2])/3 - 42*HPL[{6}, -S^2] - (605*Pi^2*HPL[{3, 1}, -S^2])/3 + 156*HPL[{4, 2}, -S^2] + 632*HPL[{5, 1}, -S^2] + (1214*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 156*HPL[{3, 1, 2}, -S^2] + 1380*HPL[{3, 2, 1}, -S^2] + 4156*HPL[{4, 1, 1}, -S^2] - 3136*HPL[{3, 1, 1, 1}, -S^2] + 6272*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-932*HPL[{2, 1}, -S^2] - 26*Zeta[3]) - 708*HPL[{2, 1}, -S^2]*Zeta[3] - 3*Zeta[3]^2) + HPL[{4}, -S^2]*((2563*Pi^6)/11340 - 580*HPL[{6}, -S^2] + 452*HPL[{2, 1}, -S^2]^2 + 122*Pi^2*HPL[{3, 1}, -S^2] + 1288*HPL[{5, 1}, -S^2] - (680*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 1312*HPL[{3, 2, 1}, -S^2] - 4176*HPL[{4, 1, 1}, -S^2] + 2736*HPL[{3, 1, 1, 1}, -S^2] - 5312*HPL[{2, 1, 1, 1, 1}, -S^2] - 112*HPL[{2, 1}, -S^2]*Zeta[3] + 4*Zeta[3]^2) + HPL[{2, 1, 1}, -S^2]*((52285*Pi^6)/2268 - 5312*HPL[{4, 1, 1}, -S^2] + 5312*HPL[{3, 1, 1, 1}, -S^2] + 160*Zeta[3]^2) + HPL[{0}, S^2]^4*((659*Pi^6)/45360 + (109*Pi^2*HPL[{2}, -S^2]^2)/72 + (5*HPL[{2}, -S^2]^3)/3 + HPL[{3}, -S^2]^2/4 - 6*HPL[{6}, -S^2] - (241*HPL[{2, 1}, -S^2]^2)/12 - (251*Pi^2*HPL[{3, 1}, -S^2])/36 + HPL[{5, 1}, -S^2]/2 + (277*Pi^2*HPL[{2, 1, 1}, -S^2])/18 + HPL[{2}, -S^2]*((2009*Pi^4)/2160 - HPL[{4}, -S^2]/2 - (39*HPL[{3, 1}, -S^2])/2 + (241*HPL[{2, 1, 1}, -S^2])/6) + 40*HPL[{3, 2, 1}, -S^2] + 125*HPL[{4, 1, 1}, -S^2] - (277*HPL[{3, 1, 1, 1}, -S^2])/3 + (568*HPL[{2, 1, 1, 1, 1}, -S^2])/3 - (9*Zeta[3]^2)/4 + HPL[{3}, -S^2]*(-HPL[{2, 1}, -S^2]/2 + (5*Zeta[3])/2)) + Log[T]^4*((659*Pi^6)/2835 + (2*HPL[{0}, S^2]^6)/9 + (196*Pi^2*HPL[{2}, -S^2]^2)/9 + (784*HPL[{2}, -S^2]^3)/9 + HPL[{0}, S^2]^4*((20*Pi^2)/9 + (71*HPL[{2}, -S^2])/9) + (172*HPL[{3}, -S^2]^2)/3 - (152*Pi^2*HPL[{4}, -S^2])/9 + 12*HPL[{6}, -S^2] - (868*Pi^2*HPL[{3, 1}, -S^2])/3 + HPL[{2}, -S^2]*((6673*Pi^4)/270 - (664*HPL[{4}, -S^2])/3 + (664*HPL[{3, 1}, -S^2])/3) + (640*HPL[{4, 2}, -S^2])/3 + (2288*HPL[{5, 1}, -S^2])/3 + 580*Pi^2*HPL[{2, 1, 1}, -S^2] + HPL[{0}, S^2]^2*((2167*Pi^4)/360 + (749*Pi^2*HPL[{2}, -S^2])/18 + (196*HPL[{2}, -S^2]^2)/3 + (28*HPL[{4}, -S^2])/3 - 308*HPL[{3, 1}, -S^2] + 620*HPL[{2, 1, 1}, -S^2]) - (640*HPL[{3, 1, 2}, -S^2])/3 + (5632*HPL[{3, 2, 1}, -S^2])/3 + 5792*HPL[{4, 1, 1}, -S^2] - 4480*HPL[{3, 1, 1, 1}, -S^2] + 8960*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((-3800*HPL[{2, 1}, -S^2])/3 - (56*Zeta[3])/3) + HPL[{0}, S^2]^3*((-32*HPL[{3}, -S^2])/9 + (730*HPL[{2, 1}, -S^2])/9 - (14*Zeta[3])/9) - 1000*HPL[{2, 1}, -S^2]*Zeta[3] - 36*Zeta[3]^2 + HPL[{0}, S^2]*((-122*Pi^2*HPL[{3}, -S^2])/9 - (32*HPL[{5}, -S^2])/3 + (2410*Pi^2*HPL[{2, 1}, -S^2])/9 + (136*HPL[{3, 2}, -S^2])/3 + 216*HPL[{4, 1}, -S^2] - 2000*HPL[{2, 2, 1}, -S^2] - 6240*HPL[{3, 1, 1}, -S^2] + 4480*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-68*HPL[{3}, -S^2])/3 + 1000*HPL[{2, 1}, -S^2] - (332*Zeta[3])/3) - (194*Pi^2*Zeta[3])/9 - (260*Zeta[5])/3)) + HPL[{2, 1, 1, 1}, -S^2]*((-3328*Pi^2*Zeta[3])/3 - 6080*Zeta[5]) - 260*Zeta[5]^2 + HPL[{0}, S^2]^5*(-(Pi^2*HPL[{3}, -S^2])/24 + (3*HPL[{5}, -S^2])/4 + (293*Pi^2*HPL[{2, 1}, -S^2])/180 + HPL[{2}, -S^2]*(HPL[{3}, -S^2]/4 + (77*HPL[{2, 1}, -S^2])/20) - HPL[{3, 2}, -S^2]/2 - HPL[{4, 1}, -S^2] - (77*HPL[{2, 2, 1}, -S^2])/10 - (241*HPL[{3, 1, 1}, -S^2])/10 + (271*HPL[{2, 1, 1, 1}, -S^2])/15 + (31*Pi^2*Zeta[3])/24 + (29*Zeta[5])/4) + HPL[{4, 1}, -S^2]*(-20560*HPL[{2, 2, 1}, -S^2] - 62768*HPL[{3, 1, 1}, -S^2] + 42944*HPL[{2, 1, 1, 1}, -S^2] + 64*Pi^2*Zeta[3] + 48*Zeta[5]) + HPL[{3, 2}, -S^2]*(192*HPL[{4, 1}, -S^2] - 6832*HPL[{2, 2, 1}, -S^2] - 19968*HPL[{3, 1, 1}, -S^2] + 12544*HPL[{2, 1, 1, 1}, -S^2] + 32*Pi^2*Zeta[3] + 144*Zeta[5]) + Log[T]^5*((-163*HPL[{0}, S^2]^5)/225 + HPL[{0}, S^2]^3*((-746*Pi^2)/135 - (146*HPL[{2}, -S^2])/9) + (364*Pi^2*HPL[{3}, -S^2])/9 + 64*HPL[{5}, -S^2] - 116*Pi^2*HPL[{2, 1}, -S^2] - 464*HPL[{3, 2}, -S^2] - 1424*HPL[{4, 1}, -S^2] + HPL[{0}, S^2]*((-14057*Pi^4)/1350 - (482*Pi^2*HPL[{2}, -S^2])/9 - 100*HPL[{2}, -S^2]^2 - 16*HPL[{4}, -S^2] + 448*HPL[{3, 1}, -S^2] - 896*HPL[{2, 1, 1}, -S^2]) + 896*HPL[{3, 1, 1}, -S^2] - 1792*HPL[{2, 1, 1, 1}, -S^2] + (124*Pi^2*Zeta[3])/3 + HPL[{0}, S^2]^2*((28*HPL[{3}, -S^2])/3 - 124*HPL[{2, 1}, -S^2] + 12*Zeta[3]) + HPL[{2}, -S^2]*((760*HPL[{3}, -S^2])/3 + 200*Zeta[3]) + 232*Zeta[5]) + HPL[{5}, -S^2]*(-80*Pi^2*HPL[{2, 1}, -S^2] - 116*HPL[{3, 2}, -S^2] - 688*HPL[{4, 1}, -S^2] + 656*HPL[{2, 2, 1}, -S^2] + 2280*HPL[{3, 1, 1}, -S^2] - 1728*HPL[{2, 1, 1, 1}, -S^2] + (82*Pi^2*Zeta[3])/3 + 356*Zeta[5]) + HPL[{2, 2, 1}, -S^2]*(12544*HPL[{3, 1, 1}, -S^2] + 25088*HPL[{2, 1, 1, 1}, -S^2] + (1724*Pi^2*Zeta[3])/3 + 2888*Zeta[5]) + HPL[{3, 1, 1}, -S^2]*(44864*HPL[{2, 1, 1, 1}, -S^2] + (5140*Pi^2*Zeta[3])/3 + 8888*Zeta[5]) + HPL[{2}, -S^2]*((13964*Pi^8)/14175 + (37*Pi^2*HPL[{3}, -S^2]^2)/3 - 18*HPL[{4}, -S^2]^2 - (67*Pi^2*HPL[{6}, -S^2])/3 - 108*HPL[{8}, -S^2] - (1214*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + 1864*HPL[{3, 1}, -S^2]^2 + 38*Pi^2*HPL[{4, 2}, -S^2] + (692*Pi^2*HPL[{5, 1}, -S^2])/3 - 24*HPL[{5, 3}, -S^2] - 60*HPL[{6, 2}, -S^2] + 108*HPL[{7, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-398*Pi^4)/15 - 6272*HPL[{2, 1, 1}, -S^2]) + HPL[{4}, -S^2]*(-7*Pi^4 + 484*HPL[{3, 1}, -S^2] - 904*HPL[{2, 1, 1}, -S^2]) + (2021*Pi^4*HPL[{2, 1, 1}, -S^2])/30 + 6272*HPL[{2, 1, 1}, -S^2]^2 + 256*Pi^2*HPL[{3, 2, 1}, -S^2] + 532*HPL[{3, 3, 2}, -S^2] + (1624*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 908*HPL[{4, 1, 3}, -S^2] + 376*HPL[{4, 2, 2}, -S^2] - 2908*HPL[{4, 3, 1}, -S^2] - 1688*HPL[{5, 1, 2}, -S^2] - 12008*HPL[{5, 2, 1}, -S^2] - 31316*HPL[{6, 1, 1}, -S^2] - (59152*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 312*HPL[{3, 1, 2, 2}, -S^2] + 312*HPL[{3, 2, 1, 2}, -S^2] + 376*HPL[{3, 2, 2, 1}, -S^2] + 192*HPL[{3, 3, 1, 1}, -S^2] + 936*HPL[{4, 1, 1, 2}, -S^2] + 1128*HPL[{4, 1, 2, 1}, -S^2] + 1512*HPL[{4, 2, 1, 1}, -S^2] + 6560*HPL[{5, 1, 1, 1}, -S^2] + (3136*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 - 5312*HPL[{4, 1, 1, 1, 1}, -S^2] + 4521152*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 104*HPL[{3, 2}, -S^2]*Zeta[3] + 424*HPL[{4, 1}, -S^2]*Zeta[3] + 2832*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 8896*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 6272*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] + (29*Pi^2*Zeta[3]^2)/3 + HPL[{5}, -S^2]*(-328*HPL[{2, 1}, -S^2] + 24*Zeta[3]) + HPL[{2, 1}, -S^2]*(3416*HPL[{3, 2}, -S^2] + 10280*HPL[{4, 1}, -S^2] - 6272*HPL[{3, 1, 1}, -S^2] - 12544*HPL[{2, 1, 1, 1}, -S^2] - (862*Pi^2*Zeta[3])/3 - 1444*Zeta[5]) + HPL[{3}, -S^2]*(56*HPL[{5}, -S^2] - (826*Pi^2*HPL[{2, 1}, -S^2])/3 - 344*HPL[{3, 2}, -S^2] - 108*HPL[{4, 1}, -S^2] + 3728*HPL[{2, 2, 1}, -S^2] - 10592*HPL[{3, 1, 1}, -S^2] - 6272*HPL[{2, 1, 1, 1}, -S^2] - (52*Pi^2*Zeta[3])/3 - 64*Zeta[5]) + 124*Zeta[3]*Zeta[5]) + HPL[{0}, S^2]^2*((109127*Pi^8)/1814400 + (335*Pi^2*HPL[{2}, -S^2]^3)/36 + 8*HPL[{2}, -S^2]^4 + (2*Pi^2*HPL[{3}, -S^2]^2)/3 - 16*HPL[{4}, -S^2]^2 - (125*Pi^2*HPL[{6}, -S^2])/12 - (479*HPL[{8}, -S^2])/2 - (211*Pi^2*HPL[{2, 1}, -S^2]^2)/2 + 380*HPL[{3, 1}, -S^2]^2 + (Pi^2*HPL[{4, 2}, -S^2])/3 - (8*Pi^2*HPL[{5, 1}, -S^2])/3 - HPL[{5, 3}, -S^2] - (25*HPL[{6, 2}, -S^2])/2 + 44*HPL[{7, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-8023*Pi^4)/360 - 1544*HPL[{2, 1, 1}, -S^2]) + HPL[{4}, -S^2]*((23*Pi^4)/40 + 24*HPL[{3, 1}, -S^2] - 16*HPL[{2, 1, 1}, -S^2]) + (8449*Pi^4*HPL[{2, 1, 1}, -S^2])/180 + 1568*HPL[{2, 1, 1}, -S^2]^2 + HPL[{2}, -S^2]^2*((6731*Pi^4)/1440 + HPL[{4}, -S^2]/2 - 213*HPL[{3, 1}, -S^2] + 430*HPL[{2, 1, 1}, -S^2]) - (Pi^2*HPL[{3, 1, 2}, -S^2])/3 + 223*Pi^2*HPL[{3, 2, 1}, -S^2] + 2*HPL[{3, 3, 2}, -S^2] + (2068*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 7*HPL[{4, 2, 2}, -S^2] + 8*HPL[{4, 3, 1}, -S^2] + 20*HPL[{5, 1, 2}, -S^2] + 20*HPL[{5, 2, 1}, -S^2] + 38*HPL[{6, 1, 1}, -S^2] - (1478*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 2*HPL[{3, 1, 2, 2}, -S^2] + 2*HPL[{3, 2, 1, 2}, -S^2] - 1702*HPL[{3, 2, 2, 1}, -S^2] - 5112*HPL[{3, 3, 1, 1}, -S^2] + 8*HPL[{4, 1, 1, 2}, -S^2] - 5104*HPL[{4, 1, 2, 1}, -S^2] - 15328*HPL[{4, 2, 1, 1}, -S^2] - 30760*HPL[{5, 1, 1, 1}, -S^2] + (2996*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 - 3440*HPL[{2, 2, 1, 2, 1}, -S^2] - 10320*HPL[{2, 2, 2, 1, 1}, -S^2] + 20632*HPL[{3, 1, 1, 1, 2}, -S^2] + 34392*HPL[{3, 1, 1, 2, 1}, -S^2] + 41272*HPL[{3, 1, 2, 1, 1}, -S^2] + 85992*HPL[{3, 2, 1, 1, 1}, -S^2] + 258224*HPL[{4, 1, 1, 1, 1}, -S^2] - 7392*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 14880*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + 6*HPL[{3, 2}, -S^2]*Zeta[3] - 20*HPL[{4, 1}, -S^2]*Zeta[3] + 156*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 492*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 328*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (11*Pi^2*Zeta[3]^2)/2 + HPL[{5}, -S^2]*(-24*HPL[{2, 1}, -S^2] + 56*Zeta[3]) + HPL[{2}, -S^2]*((39083*Pi^6)/18144 - (5*Pi^2*HPL[{4}, -S^2])/3 - (45*HPL[{6}, -S^2])/2 - 430*HPL[{2, 1}, -S^2]^2 - (310*Pi^2*HPL[{3, 1}, -S^2])/3 - 3*HPL[{4, 2}, -S^2] + 16*HPL[{5, 1}, -S^2] + 211*Pi^2*HPL[{2, 1, 1}, -S^2] + 768*HPL[{3, 2, 1}, -S^2] + 2288*HPL[{4, 1, 1}, -S^2] - 22184*HPL[{3, 1, 1, 1}, -S^2] + 3136*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-42*HPL[{2, 1}, -S^2] - 2*Zeta[3]) - 78*HPL[{2, 1}, -S^2]*Zeta[3] + 9*Zeta[3]^2) + HPL[{2, 1}, -S^2]*(84*HPL[{3, 2}, -S^2] + 268*HPL[{4, 1}, -S^2] + 1720*HPL[{2, 2, 1}, -S^2] + 4984*HPL[{3, 1, 1}, -S^2] - 3136*HPL[{2, 1, 1, 1}, -S^2] - (41*Pi^2*Zeta[3])/3 - 78*Zeta[5]) - 130*Zeta[3]*Zeta[5] + HPL[{3}, -S^2]*(31*HPL[{5}, -S^2] - (25*Pi^2*HPL[{2, 1}, -S^2])/3 - 22*HPL[{4, 1}, -S^2] + 84*HPL[{2, 2, 1}, -S^2] + 260*HPL[{3, 1, 1}, -S^2] - 176*HPL[{2, 1, 1, 1}, -S^2] + 6*Pi^2*Zeta[3] + 60*Zeta[5])) + Log[T]^2*((109127*Pi^8)/453600 + HPL[{0}, S^2]^8/64 + HPL[{0}, S^2]^6*((37*Pi^2)/144 + (3*HPL[{2}, -S^2])/4) + (607*Pi^2*HPL[{2}, -S^2]^3)/9 + (88*Pi^2*HPL[{3}, -S^2]^2)/3 - 60*HPL[{4}, -S^2]^2 + (37*Pi^2*HPL[{6}, -S^2])/3 + 346*HPL[{8}, -S^2] - (784*Pi^2*HPL[{2, 1}, -S^2]^2)/3 - 688*HPL[{3, 1}, -S^2]^2 + 108*Pi^2*HPL[{4, 2}, -S^2] + (1100*Pi^2*HPL[{5, 1}, -S^2])/3 - 52*HPL[{5, 3}, -S^2] - 162*HPL[{6, 2}, -S^2] - 408*HPL[{7, 1}, -S^2] + HPL[{4}, -S^2]*((-221*Pi^4)/90 + 1368*HPL[{3, 1}, -S^2] - 2656*HPL[{2, 1, 1}, -S^2]) + (13346*Pi^4*HPL[{2, 1, 1}, -S^2])/45 + HPL[{0}, S^2]^4*((2167*Pi^4)/1440 + (277*Pi^2*HPL[{2}, -S^2])/36 + (241*HPL[{2}, -S^2]^2)/24 + (5*HPL[{4}, -S^2])/2 - (277*HPL[{3, 1}, -S^2])/6 + (284*HPL[{2, 1, 1}, -S^2])/3) + HPL[{3, 1}, -S^2]*((-2651*Pi^4)/18 + 2656*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]^2*((2021*Pi^4)/120 - 226*HPL[{4}, -S^2] - 1568*HPL[{3, 1}, -S^2] + 3136*HPL[{2, 1, 1}, -S^2]) - 108*Pi^2*HPL[{3, 1, 2}, -S^2] + (4532*Pi^2*HPL[{3, 2, 1}, -S^2])/3 + 848*HPL[{3, 3, 2}, -S^2] + (13960*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 1344*HPL[{4, 1, 3}, -S^2] + 732*HPL[{4, 2, 2}, -S^2] - 4864*HPL[{4, 3, 1}, -S^2] - 2904*HPL[{5, 1, 2}, -S^2] - 20184*HPL[{5, 2, 1}, -S^2] - 51696*HPL[{6, 1, 1}, -S^2] - 3472*Pi^2*HPL[{3, 1, 1, 1}, -S^2] - 12544*HPL[{3, 2, 2, 1}, -S^2] - 37632*HPL[{3, 3, 1, 1}, -S^2] + 2560*HPL[{4, 1, 1, 2}, -S^2] - 35072*HPL[{4, 1, 2, 1}, -S^2] - 110336*HPL[{4, 2, 1, 1}, -S^2] - 216640*HPL[{5, 1, 1, 1}, -S^2] + 6960*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] - 25088*HPL[{2, 2, 1, 2, 1}, -S^2] - 75264*HPL[{2, 2, 2, 1, 1}, -S^2] + 147968*HPL[{3, 1, 1, 1, 2}, -S^2] + 248320*HPL[{3, 1, 1, 2, 1}, -S^2] + 298496*HPL[{3, 1, 2, 1, 1}, -S^2] + 624640*HPL[{3, 2, 1, 1, 1}, -S^2] + 1875840*HPL[{4, 1, 1, 1, 1}, -S^2] - 53760*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 107520*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + 360*HPL[{3, 2}, -S^2]*Zeta[3] + 848*HPL[{4, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 18592*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 12000*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - 22*Pi^2*Zeta[3]^2 + HPL[{0}, S^2]^5*(-HPL[{3}, -S^2]/2 + (271*HPL[{2, 1}, -S^2])/30 + (3*Zeta[3])/2) + HPL[{5}, -S^2]*(-864*HPL[{2, 1}, -S^2] + 104*Zeta[3]) + HPL[{2}, -S^2]*((52285*Pi^6)/4536 + 148*HPL[{3}, -S^2]^2 - (340*Pi^2*HPL[{4}, -S^2])/3 - 178*HPL[{6}, -S^2] - 3136*HPL[{2, 1}, -S^2]^2 - (440*Pi^2*HPL[{3, 1}, -S^2])/3 + 468*HPL[{4, 2}, -S^2] + 2704*HPL[{5, 1}, -S^2] + (1568*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 2656*HPL[{4, 1, 1}, -S^2] - 147872*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-3136*HPL[{2, 1}, -S^2] - 200*Zeta[3]) - 3136*HPL[{2, 1}, -S^2]*Zeta[3] + 80*Zeta[3]^2) + HPL[{0}, S^2]^2*((7919*Pi^6)/2520 + (211*Pi^2*HPL[{2}, -S^2]^2)/4 + (215*HPL[{2}, -S^2]^3)/3 + 2*HPL[{3}, -S^2]^2 + (29*Pi^2*HPL[{4}, -S^2])/3 + 19*HPL[{6}, -S^2] - 784*HPL[{2, 1}, -S^2]^2 - (739*Pi^2*HPL[{3, 1}, -S^2])/3 + 4*HPL[{4, 2}, -S^2] - 44*HPL[{5, 1}, -S^2] + (1498*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((8449*Pi^4)/360 - 8*HPL[{4}, -S^2] - 772*HPL[{3, 1}, -S^2] + 1568*HPL[{2, 1, 1}, -S^2]) - 4*HPL[{3, 1, 2}, -S^2] + 1716*HPL[{3, 2, 1}, -S^2] + 5272*HPL[{4, 1, 1}, -S^2] - 3696*HPL[{3, 1, 1, 1}, -S^2] + 7440*HPL[{2, 1, 1, 1, 1}, -S^2] - 164*HPL[{2, 1}, -S^2]*Zeta[3] - 12*Zeta[3]^2 + HPL[{3}, -S^2]*(-88*HPL[{2, 1}, -S^2] + 12*Zeta[3])) + HPL[{2, 1}, -S^2]*(6272*HPL[{3, 2}, -S^2] + 21472*HPL[{4, 1}, -S^2] + 12544*HPL[{2, 2, 1}, -S^2] + 22432*HPL[{3, 1, 1}, -S^2] - (1664*Pi^2*Zeta[3])/3 - 3040*Zeta[5]) - 520*Zeta[3]*Zeta[5] + HPL[{0}, S^2]^3*((-31*Pi^2*HPL[{3}, -S^2])/9 - (10*HPL[{5}, -S^2])/3 + (212*Pi^2*HPL[{2, 1}, -S^2])/3 - (22*HPL[{3, 2}, -S^2])/3 + (20*HPL[{4, 1}, -S^2])/3 - 440*HPL[{2, 2, 1}, -S^2] - (4088*HPL[{3, 1, 1}, -S^2])/3 + (2920*HPL[{2, 1, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*(4*HPL[{3}, -S^2] + 220*HPL[{2, 1}, -S^2] - (22*Zeta[3])/3) + (38*Pi^2*Zeta[3])/9 + 26*Zeta[5]) + HPL[{3}, -S^2]*(156*HPL[{5}, -S^2] - (1988*Pi^2*HPL[{2, 1}, -S^2])/3 - 584*HPL[{3, 2}, -S^2] - 544*HPL[{4, 1}, -S^2] + 6272*HPL[{2, 2, 1}, -S^2] + 20192*HPL[{3, 1, 1}, -S^2] - 15200*HPL[{2, 1, 1, 1}, -S^2] - (16*Pi^2*Zeta[3])/3 + 112*Zeta[5]) + HPL[{0}, S^2]*((-26*Pi^2*HPL[{5}, -S^2])/3 + 28*HPL[{7}, -S^2] + (46*Pi^2*HPL[{3, 2}, -S^2])/3 + (344*Pi^2*HPL[{4, 1}, -S^2])/3 + 180*HPL[{4, 3}, -S^2] + 512*HPL[{5, 2}, -S^2] + 1052*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((4061*Pi^4)/30 - 6000*HPL[{3, 1}, -S^2] - 12000*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-36*Pi^4)/5 - 84*HPL[{4}, -S^2] + 128*HPL[{3, 1}, -S^2] - 272*HPL[{2, 1, 1}, -S^2]) - 1440*Pi^2*HPL[{2, 2, 1}, -S^2] - (13448*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 608*HPL[{3, 2, 2}, -S^2] - 1472*HPL[{3, 3, 1}, -S^2] - 1456*HPL[{4, 1, 2}, -S^2] - 4048*HPL[{4, 2, 1}, -S^2] - 7904*HPL[{5, 1, 1}, -S^2] + (9640*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 12544*HPL[{2, 2, 2, 1}, -S^2] - 37088*HPL[{3, 1, 1, 2}, -S^2] - 37088*HPL[{3, 1, 2, 1}, -S^2] - 74720*HPL[{3, 2, 1, 1}, -S^2] - 223200*HPL[{4, 1, 1, 1}, -S^2] + 24000*HPL[{2, 1, 2, 1, 1}, -S^2] + 72000*HPL[{2, 2, 1, 1, 1}, -S^2] + 117120*HPL[{3, 1, 1, 1, 1}, -S^2] + 53760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^2*(-76*HPL[{3}, -S^2] + 1568*HPL[{2, 1}, -S^2] - 164*Zeta[3]) + HPL[{4}, -S^2]*(184*HPL[{2, 1}, -S^2] - 48*Zeta[3]) - (373*Pi^4*Zeta[3])/90 + 672*HPL[{3, 1}, -S^2]*Zeta[3] - 1328*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]*((-22*Pi^2*HPL[{3}, -S^2])/3 + 92*HPL[{5}, -S^2] + 720*Pi^2*HPL[{2, 1}, -S^2] + 304*HPL[{3, 2}, -S^2] + 728*HPL[{4, 1}, -S^2] - 6272*HPL[{2, 2, 1}, -S^2] + 18544*HPL[{3, 1, 1}, -S^2] + 12000*HPL[{2, 1, 1, 1}, -S^2] - (188*Pi^2*Zeta[3])/3 - 260*Zeta[5]) - (52*Pi^2*Zeta[5])/3)) + HPL[{2, 1}, -S^2]*((1652*Pi^2*HPL[{3, 2}, -S^2])/3 + (5636*Pi^2*HPL[{4, 1}, -S^2])/3 - 188*HPL[{4, 3}, -S^2] - 408*HPL[{5, 2}, -S^2] + 196*HPL[{6, 1}, -S^2] + (4856*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (10592*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 6520*HPL[{3, 2, 2}, -S^2] - 19936*HPL[{3, 3, 1}, -S^2] - 19624*HPL[{4, 1, 2}, -S^2] - 60808*HPL[{4, 2, 1}, -S^2] - 125280*HPL[{5, 1, 1}, -S^2] - (3136*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 12544*HPL[{3, 1, 1, 2}, -S^2] + 12544*HPL[{3, 1, 2, 1}, -S^2] + 12544*HPL[{3, 2, 1, 1}, -S^2] + 42944*HPL[{4, 1, 1, 1}, -S^2] + 25088*HPL[{2, 1, 2, 1, 1}, -S^2] - 75264*HPL[{2, 2, 1, 1, 1}, -S^2] - 155840*HPL[{3, 1, 1, 1, 1}, -S^2] - (1013*Pi^4*Zeta[3])/30 + 3232*HPL[{3, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 1, 1}, -S^2]*Zeta[3] - (838*Pi^2*Zeta[5])/3 - 1932*Zeta[7]) + Zeta[3]*((-260*Pi^2*Zeta[5])/3 - 600*Zeta[7]) + HPL[{0}, S^2]^3*((20*Pi^2*HPL[{5}, -S^2])/9 + (130*HPL[{7}, -S^2])/3 - (41*Pi^2*HPL[{3, 2}, -S^2])/18 - (25*Pi^2*HPL[{4, 1}, -S^2])/9 + (43*HPL[{4, 3}, -S^2])/3 + 43*HPL[{5, 2}, -S^2] + (206*HPL[{6, 1}, -S^2])/3 + HPL[{2, 1}, -S^2]*((3997*Pi^4)/540 - 220*HPL[{3, 1}, -S^2] - 440*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-161*Pi^4)/540 - (22*HPL[{4}, -S^2])/3 - 6*HPL[{3, 1}, -S^2] + 8*HPL[{2, 1, 1}, -S^2]) - (187*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (1745*Pi^2*HPL[{3, 1, 1}, -S^2])/9 - 9*HPL[{3, 2, 2}, -S^2] - (20*HPL[{3, 3, 1}, -S^2])/3 - (20*HPL[{4, 1, 2}, -S^2])/3 + (4*HPL[{4, 2, 1}, -S^2])/3 + (52*HPL[{5, 1, 1}, -S^2])/3 + (424*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 424*HPL[{2, 2, 2, 1}, -S^2] - (3860*HPL[{3, 1, 1, 2}, -S^2])/3 - (3860*HPL[{3, 1, 2, 1}, -S^2])/3 - (7676*HPL[{3, 2, 1, 1}, -S^2])/3 - (22856*HPL[{4, 1, 1, 1}, -S^2])/3 + 880*HPL[{2, 1, 2, 1, 1}, -S^2] + 2640*HPL[{2, 2, 1, 1, 1}, -S^2] + (12944*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + (5840*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + HPL[{4}, -S^2]*((34*HPL[{2, 1}, -S^2])/3 - 12*Zeta[3]) + HPL[{2}, -S^2]^2*((-7*HPL[{3}, -S^2])/6 + 53*HPL[{2, 1}, -S^2] - (3*Zeta[3])/2) + (3353*Pi^4*Zeta[3])/1080 + 10*HPL[{3, 1}, -S^2]*Zeta[3] - (44*HPL[{2, 1, 1}, -S^2]*Zeta[3])/3 + HPL[{2}, -S^2]*((7*Pi^2*HPL[{3}, -S^2])/6 + (23*HPL[{5}, -S^2])/3 + (187*Pi^2*HPL[{2, 1}, -S^2])/6 + (14*HPL[{3, 2}, -S^2])/3 + (8*HPL[{4, 1}, -S^2])/3 - 212*HPL[{2, 2, 1}, -S^2] + 644*HPL[{3, 1, 1}, -S^2] + 440*HPL[{2, 1, 1, 1}, -S^2] - (11*Pi^2*Zeta[3])/18 - (16*Zeta[5])/3) + (79*Pi^2*Zeta[5])/3 + 186*Zeta[7]) + HPL[{3}, -S^2]*((70*Pi^2*HPL[{5}, -S^2])/3 + 500*HPL[{7}, -S^2] - (146*Pi^2*HPL[{3, 2}, -S^2])/3 - (158*Pi^2*HPL[{4, 1}, -S^2])/3 - 76*HPL[{4, 3}, -S^2] - 216*HPL[{5, 2}, -S^2] - 840*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-601*Pi^4)/15 + 3136*HPL[{3, 1}, -S^2] + 6272*HPL[{2, 1, 1}, -S^2]) + (1652*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (5308*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 692*HPL[{3, 2, 2}, -S^2] + 2032*HPL[{3, 3, 1}, -S^2] - 12*HPL[{4, 1, 2}, -S^2] + 180*HPL[{4, 2, 1}, -S^2] + 888*HPL[{5, 1, 1}, -S^2] - (3976*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 7456*HPL[{2, 2, 2, 1}, -S^2] + 21200*HPL[{3, 1, 1, 2}, -S^2] + 21200*HPL[{3, 1, 2, 1}, -S^2] + 43568*HPL[{3, 2, 1, 1}, -S^2] + 323008*HPL[{4, 1, 1, 1}, -S^2] - 12544*HPL[{2, 1, 2, 1, 1}, -S^2] - 37632*HPL[{2, 2, 1, 1, 1}, -S^2] - 59968*HPL[{3, 1, 1, 1, 1}, -S^2] - 30400*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(172*HPL[{2, 1}, -S^2] - 52*Zeta[3]) + (71*Pi^4*Zeta[3])/45 + 168*HPL[{3, 1}, -S^2]*Zeta[3] - 400*HPL[{2, 1, 1}, -S^2]*Zeta[3] + (88*Pi^2*Zeta[5])/3 + 420*Zeta[7]) + Log[T]^3*(-HPL[{0}, S^2]^7/9 + HPL[{0}, S^2]^5*((-373*Pi^2)/270 - (271*HPL[{2}, -S^2])/90) + (188*Pi^2*HPL[{5}, -S^2])/3 + 88*HPL[{7}, -S^2] + HPL[{2, 1}, -S^2]*((-13346*Pi^4)/135 - (2656*HPL[{3, 1}, -S^2])/3) - (3652*Pi^2*HPL[{3, 2}, -S^2])/9 - (11320*Pi^2*HPL[{4, 1}, -S^2])/9 + 192*HPL[{4, 3}, -S^2] + 456*HPL[{5, 2}, -S^2] + (496*HPL[{6, 1}, -S^2])/3 + HPL[{0}, S^2]^3*((-2467*Pi^4)/405 - (212*Pi^2*HPL[{2}, -S^2])/9 - (110*HPL[{2}, -S^2]^2)/3 - (92*HPL[{4}, -S^2])/9 + (1448*HPL[{3, 1}, -S^2])/9 - (2920*HPL[{2, 1, 1}, -S^2])/9) + HPL[{3}, -S^2]*((3596*Pi^4)/135 - (464*HPL[{4}, -S^2])/3 - (7648*HPL[{3, 1}, -S^2])/3 + (15200*HPL[{2, 1, 1}, -S^2])/3) + (3136*Pi^2*HPL[{2, 2, 1}, -S^2])/9 + (16688*Pi^2*HPL[{3, 1, 1}, -S^2])/9 + (12544*HPL[{3, 2, 2}, -S^2])/3 + (40384*HPL[{3, 3, 1}, -S^2])/3 + (40384*HPL[{4, 1, 2}, -S^2])/3 + (123904*HPL[{4, 2, 1}, -S^2])/3 + 84800*HPL[{5, 1, 1}, -S^2] - 2320*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - (25088*HPL[{2, 2, 2, 1}, -S^2])/3 + 15808*HPL[{3, 1, 1, 2}, -S^2] + 15808*HPL[{3, 1, 2, 1}, -S^2] + 40896*HPL[{3, 2, 1, 1}, -S^2] + 122048*HPL[{4, 1, 1, 1}, -S^2] + 17920*HPL[{3, 1, 1, 1, 1}, -S^2] - 35840*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^4*(2*HPL[{3}, -S^2] - (284*HPL[{2, 1}, -S^2])/9 - (7*Zeta[3])/9) + (3353*Pi^4*Zeta[3])/135 - 2016*HPL[{3, 1}, -S^2]*Zeta[3] + 4000*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*((2656*HPL[{2, 1}, -S^2])/3 + (352*Zeta[3])/3) + HPL[{2}, -S^2]^2*((1568*HPL[{3}, -S^2])/3 - (3136*HPL[{2, 1}, -S^2])/3 + (1568*Zeta[3])/3) + HPL[{0}, S^2]*((-2863*Pi^6)/324 - 120*Pi^2*HPL[{2}, -S^2]^2 - (1568*HPL[{2}, -S^2]^3)/9 + (88*HPL[{3}, -S^2]^2)/3 - (212*Pi^2*HPL[{4}, -S^2])/9 - (292*HPL[{6}, -S^2])/3 + 2000*HPL[{2, 1}, -S^2]^2 + (4808*Pi^2*HPL[{3, 1}, -S^2])/9 + (544*HPL[{5, 1}, -S^2])/3 + HPL[{2}, -S^2]*((-4061*Pi^4)/90 - (184*HPL[{4}, -S^2])/3 + 2000*HPL[{3, 1}, -S^2] - 4000*HPL[{2, 1, 1}, -S^2]) - (9640*Pi^2*HPL[{2, 1, 1}, -S^2])/9 - (12544*HPL[{3, 2, 1}, -S^2])/3 - 12864*HPL[{4, 1, 1}, -S^2] + 8960*HPL[{3, 1, 1, 1}, -S^2] - 17920*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((272*HPL[{2, 1}, -S^2])/3 - (16*Zeta[3])/3) + (1328*HPL[{2, 1}, -S^2]*Zeta[3])/3 - 56*Zeta[3]^2) + (632*Pi^2*Zeta[5])/3 + HPL[{0}, S^2]^2*((106*Pi^2*HPL[{3}, -S^2])/9 + 28*HPL[{5}, -S^2] - (1498*Pi^2*HPL[{2, 1}, -S^2])/9 - (172*HPL[{3, 2}, -S^2])/3 - (640*HPL[{4, 1}, -S^2])/3 + (3136*HPL[{2, 2, 1}, -S^2])/3 + (9968*HPL[{3, 1, 1}, -S^2])/3 - 2480*HPL[{2, 1, 1, 1}, -S^2] + (76*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*((88*HPL[{3}, -S^2])/3 - (1568*HPL[{2, 1}, -S^2])/3 + (164*Zeta[3])/3) + 52*Zeta[5]) + HPL[{2}, -S^2]*((1988*Pi^2*HPL[{3}, -S^2])/9 + 288*HPL[{5}, -S^2] - (1568*Pi^2*HPL[{2, 1}, -S^2])/9 - (6272*HPL[{3, 2}, -S^2])/3 - (21472*HPL[{4, 1}, -S^2])/3 + (12544*HPL[{2, 2, 1}, -S^2])/3 - (22432*HPL[{3, 1, 1}, -S^2])/3 + (1664*Pi^2*Zeta[3])/9 + (3040*Zeta[5])/3) + 1488*Zeta[7]) + HPL[{0}, S^2]*((-8*HPL[{3}, -S^2]^3)/3 + (137*Pi^2*HPL[{7}, -S^2])/3 + 994*HPL[{9}, -S^2] - (3136*HPL[{2, 1}, -S^2]^3)/3 + (88*Pi^2*HPL[{4, 3}, -S^2])/3 + (257*Pi^2*HPL[{5, 2}, -S^2])/3 - 314*HPL[{5, 4}, -S^2] + (469*Pi^2*HPL[{6, 1}, -S^2])/3 - 1262*HPL[{6, 3}, -S^2] - 3124*HPL[{7, 2}, -S^2] - 6654*HPL[{8, 1}, -S^2] + HPL[{5}, -S^2]*((209*Pi^4)/180 - 156*HPL[{3, 1}, -S^2] + 184*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 2}, -S^2]*((-29*Pi^4)/18 + 608*HPL[{2, 1, 1}, -S^2]) + HPL[{4, 1}, -S^2]*((59*Pi^4)/18 + 1456*HPL[{2, 1, 1}, -S^2]) - (2155*Pi^4*HPL[{2, 2, 1}, -S^2])/18 - (11207*Pi^4*HPL[{3, 1, 1}, -S^2])/30 - (179*Pi^2*HPL[{3, 2, 2}, -S^2])/3 - (388*Pi^2*HPL[{3, 3, 1}, -S^2])/3 - 128*Pi^2*HPL[{4, 1, 2}, -S^2] - 336*Pi^2*HPL[{4, 2, 1}, -S^2] - 6*HPL[{4, 2, 3}, -S^2] - 70*HPL[{4, 3, 2}, -S^2] - 488*HPL[{4, 4, 1}, -S^2] - (1924*Pi^2*HPL[{5, 1, 1}, -S^2])/3 - 372*HPL[{5, 1, 3}, -S^2] - 570*HPL[{5, 2, 2}, -S^2] - 2196*HPL[{5, 3, 1}, -S^2] - 1858*HPL[{6, 1, 2}, -S^2] - 5778*HPL[{6, 2, 1}, -S^2] - 11704*HPL[{7, 1, 1}, -S^2] + (4061*Pi^4*HPL[{2, 1, 1, 1}, -S^2])/15 + (4408*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 - (13132*Pi^2*HPL[{3, 1, 1, 2}, -S^2])/3 - (13132*Pi^2*HPL[{3, 1, 2, 1}, -S^2])/3 - (26356*Pi^2*HPL[{3, 2, 1, 1}, -S^2])/3 + 480*HPL[{3, 2, 2, 2}, -S^2] + 1504*HPL[{3, 2, 3, 1}, -S^2] + 1504*HPL[{3, 3, 1, 2}, -S^2] + 4576*HPL[{3, 3, 2, 1}, -S^2] - (78656*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 - 8856*HPL[{4, 1, 1, 3}, -S^2] - 7364*HPL[{4, 1, 2, 2}, -S^2] - 13496*HPL[{4, 1, 3, 1}, -S^2] - 4292*HPL[{4, 2, 1, 2}, -S^2] - 4292*HPL[{4, 2, 2, 1}, -S^2] - 27288*HPL[{4, 3, 1, 1}, -S^2] - 26624*HPL[{5, 1, 1, 2}, -S^2] - 45056*HPL[{5, 1, 2, 1}, -S^2] - 109568*HPL[{5, 2, 1, 1}, -S^2] - 274376*HPL[{6, 1, 1, 1}, -S^2] + 2880*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2] + 8640*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 11328*HPL[{2, 2, 2, 2, 1}, -S^2] + (42224*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - 35200*HPL[{3, 1, 1, 2, 2}, -S^2] - 35200*HPL[{3, 1, 2, 1, 2}, -S^2] + 244480*HPL[{3, 1, 3, 1, 1}, -S^2] - 69184*HPL[{3, 2, 1, 1, 2}, -S^2] - 33984*HPL[{3, 2, 1, 2, 1}, -S^2] + 107328*HPL[{3, 2, 2, 1, 1}, -S^2] + 355968*HPL[{3, 3, 1, 1, 1}, -S^2] - 206816*HPL[{4, 1, 1, 1, 2}, -S^2] - 101216*HPL[{4, 1, 1, 2, 1}, -S^2] + 322720*HPL[{4, 1, 2, 1, 1}, -S^2] + 1068640*HPL[{4, 2, 1, 1, 1}, -S^2] + 2137664*HPL[{5, 1, 1, 1, 1}, -S^2] + (19280*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 - 25088*HPL[{2, 2, 1, 2, 1, 1}, -S^2] - 75264*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + 126528*HPL[{3, 1, 1, 1, 1, 2}, -S^2] + 277056*HPL[{3, 1, 1, 1, 2, 1}, -S^2] + 377408*HPL[{3, 1, 1, 2, 1, 1}, -S^2] + 427584*HPL[{3, 1, 2, 1, 1, 1}, -S^2] + 753728*HPL[{3, 2, 1, 1, 1, 1}, -S^2] + 2263104*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - 48000*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] - 192000*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] - 480000*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] - 1013760*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + 107520*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{6}, -S^2]*(146*HPL[{2, 1}, -S^2] - 154*Zeta[3]) + HPL[{2}, -S^2]^3*(-10*HPL[{3}, -S^2] + 236*HPL[{2, 1}, -S^2] - (82*Zeta[3])/3) + (1847*Pi^6*Zeta[3])/1134 + 328*HPL[{2, 1}, -S^2]^2*Zeta[3] - 12*HPL[{4, 2}, -S^2]*Zeta[3] + 96*HPL[{5, 1}, -S^2]*Zeta[3] - 656*HPL[{3, 2, 1}, -S^2]*Zeta[3] - 2064*HPL[{4, 1, 1}, -S^2]*Zeta[3] + 1344*HPL[{3, 1, 1, 1}, -S^2]*Zeta[3] - 2656*HPL[{2, 1, 1, 1, 1}, -S^2]*Zeta[3] + 32*Zeta[3]^3 + HPL[{3}, -S^2]^2*(-8*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + HPL[{3}, -S^2]*((-437*Pi^6)/756 - (43*Pi^2*HPL[{4}, -S^2])/3 - 160*HPL[{6}, -S^2] + 152*HPL[{2, 1}, -S^2]^2 + (14*Pi^2*HPL[{3, 1}, -S^2])/3 + 6*HPL[{4, 2}, -S^2] + 180*HPL[{5, 1}, -S^2] - (44*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 240*HPL[{3, 2, 1}, -S^2] + 8328*HPL[{4, 1, 1}, -S^2] + 256*HPL[{3, 1, 1, 1}, -S^2] - 544*HPL[{2, 1, 1, 1, 1}, -S^2] - 16*HPL[{2, 1}, -S^2]*Zeta[3]) + HPL[{2, 1}, -S^2]*((248987*Pi^6)/22680 - 720*Pi^2*HPL[{3, 1}, -S^2] - 216*HPL[{5, 1}, -S^2] - 1440*Pi^2*HPL[{2, 1, 1}, -S^2] + 5664*HPL[{3, 2, 1}, -S^2] + 17360*HPL[{4, 1, 1}, -S^2] - 12000*HPL[{3, 1, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1, 1}, -S^2] + 68*Zeta[3]^2) + HPL[{2, 1, 1}, -S^2]*(12544*HPL[{2, 2, 1}, -S^2] + 37088*HPL[{3, 1, 1}, -S^2] + 24000*HPL[{2, 1, 1, 1}, -S^2] - (376*Pi^2*Zeta[3])/3 - 520*Zeta[5]) + HPL[{4}, -S^2]*(160*HPL[{5}, -S^2] + (80*Pi^2*HPL[{2, 1}, -S^2])/3 + 20*HPL[{3, 2}, -S^2] + 208*HPL[{4, 1}, -S^2] - 32*HPL[{2, 2, 1}, -S^2] - 264*HPL[{3, 1, 1}, -S^2] + 368*HPL[{2, 1, 1, 1}, -S^2] - 16*Pi^2*Zeta[3] - 152*Zeta[5]) + HPL[{2}, -S^2]^2*((-15*Pi^2*HPL[{3}, -S^2])/2 + 2*HPL[{5}, -S^2] + (551*Pi^2*HPL[{2, 1}, -S^2])/3 + 60*HPL[{3, 2}, -S^2] + 188*HPL[{4, 1}, -S^2] - 1416*HPL[{2, 2, 1}, -S^2] - 4400*HPL[{3, 1, 1}, -S^2] + 3136*HPL[{2, 1, 1, 1}, -S^2] - (91*Pi^2*Zeta[3])/6 - 53*Zeta[5]) + (782*Pi^4*Zeta[5])/45 + HPL[{3, 1}, -S^2]*(-272*HPL[{3, 2}, -S^2] - 616*HPL[{4, 1}, -S^2] + 6272*HPL[{2, 2, 1}, -S^2] - 51840*HPL[{3, 1, 1}, -S^2] - 12000*HPL[{2, 1, 1, 1}, -S^2] + 66*Pi^2*Zeta[3] + 308*Zeta[5]) + HPL[{2}, -S^2]*((46*Pi^2*HPL[{5}, -S^2])/3 + 134*HPL[{7}, -S^2] + 30*Pi^2*HPL[{3, 2}, -S^2] + (190*Pi^2*HPL[{4, 1}, -S^2])/3 + 26*HPL[{4, 3}, -S^2] + 84*HPL[{5, 2}, -S^2] + 14*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((2155*Pi^4)/36 - 3136*HPL[{3, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((5*Pi^4)/6 - 10*HPL[{4}, -S^2] + 136*HPL[{3, 1}, -S^2] - 304*HPL[{2, 1, 1}, -S^2]) - (2204*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (6568*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 240*HPL[{3, 2, 2}, -S^2] - 752*HPL[{3, 3, 1}, -S^2] - 752*HPL[{4, 1, 2}, -S^2] - 2288*HPL[{4, 2, 1}, -S^2] - 4424*HPL[{5, 1, 1}, -S^2] + 1440*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + 5664*HPL[{2, 2, 2, 1}, -S^2] + 17600*HPL[{3, 1, 1, 2}, -S^2] + 17600*HPL[{3, 1, 2, 1}, -S^2] + 34592*HPL[{3, 2, 1, 1}, -S^2] + 103408*HPL[{4, 1, 1, 1}, -S^2] + 12544*HPL[{2, 1, 2, 1, 1}, -S^2] + 37632*HPL[{2, 2, 1, 1, 1}, -S^2] - 63264*HPL[{3, 1, 1, 1, 1}, -S^2] + 24000*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(16*HPL[{2, 1}, -S^2] - 8*Zeta[3]) - (229*Pi^4*Zeta[3])/60 + 344*HPL[{3, 1}, -S^2]*Zeta[3] - 656*HPL[{2, 1, 1}, -S^2]*Zeta[3] - 27*Pi^2*Zeta[5] - 150*Zeta[7]) + 186*Pi^2*Zeta[7] + 1568*Zeta[9]) + Log[T]*(-HPL[{0}, S^2]^9/192 + HPL[{0}, S^2]^7*((-13*Pi^2)/144 - HPL[{2}, -S^2]/8) - (8*HPL[{3}, -S^2]^3)/3 + (2*Pi^2*HPL[{7}, -S^2])/3 - 2084*HPL[{9}, -S^2] + (6272*HPL[{2, 1}, -S^2]^3)/3 + 64*Pi^2*HPL[{4, 3}, -S^2] + (490*Pi^2*HPL[{5, 2}, -S^2])/3 - 716*HPL[{5, 4}, -S^2] + 122*Pi^2*HPL[{6, 1}, -S^2] - 2908*HPL[{6, 3}, -S^2] - 7144*HPL[{7, 2}, -S^2] - 13404*HPL[{8, 1}, -S^2] + HPL[{4, 1}, -S^2]*((-10597*Pi^4)/45 - 42944*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 2}, -S^2]*((-1103*Pi^4)/15 - 12544*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]^5*((-14057*Pi^4)/21600 - (293*Pi^2*HPL[{2}, -S^2])/180 - (77*HPL[{2}, -S^2]^2)/40 - HPL[{4}, -S^2]/2 + (87*HPL[{3, 1}, -S^2])/10 - (271*HPL[{2, 1, 1}, -S^2])/15) + HPL[{5}, -S^2]*((1343*Pi^4)/90 - 968*HPL[{3, 1}, -S^2] + 1728*HPL[{2, 1, 1}, -S^2]) + (2021*Pi^4*HPL[{2, 2, 1}, -S^2])/15 + (25381*Pi^4*HPL[{3, 1, 1}, -S^2])/45 + (3302*Pi^2*HPL[{3, 2, 2}, -S^2])/3 + (10616*Pi^2*HPL[{3, 3, 1}, -S^2])/3 + (10624*Pi^2*HPL[{4, 1, 2}, -S^2])/3 + (32560*Pi^2*HPL[{4, 2, 1}, -S^2])/3 + 148*HPL[{4, 2, 3}, -S^2] + 84*HPL[{4, 3, 2}, -S^2] - 672*HPL[{4, 4, 1}, -S^2] + 22312*Pi^2*HPL[{5, 1, 1}, -S^2] - 584*HPL[{5, 1, 3}, -S^2] - 492*HPL[{5, 2, 2}, -S^2] - 3144*HPL[{5, 3, 1}, -S^2] - 2724*HPL[{6, 1, 2}, -S^2] - 8484*HPL[{6, 2, 1}, -S^2] - 16752*HPL[{7, 1, 1}, -S^2] - (26692*Pi^4*HPL[{2, 1, 1, 1}, -S^2])/45 - (9712*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 + (21832*Pi^2*HPL[{3, 1, 1, 2}, -S^2])/3 + (21832*Pi^2*HPL[{3, 1, 2, 1}, -S^2])/3 + (50968*Pi^2*HPL[{3, 2, 1, 1}, -S^2])/3 - 12736*HPL[{3, 2, 2, 2}, -S^2] - 39296*HPL[{3, 2, 3, 1}, -S^2] - 38656*HPL[{3, 3, 1, 2}, -S^2] - 119296*HPL[{3, 3, 2, 1}, -S^2] + (152176*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 + 243072*HPL[{4, 1, 1, 3}, -S^2] + 204760*HPL[{4, 1, 2, 2}, -S^2] + 365056*HPL[{4, 1, 3, 1}, -S^2] + 126040*HPL[{4, 2, 1, 2}, -S^2] + 124120*HPL[{4, 2, 2, 1}, -S^2] + 721152*HPL[{4, 3, 1, 1}, -S^2] + 734256*HPL[{5, 1, 1, 2}, -S^2] + 1210416*HPL[{5, 1, 2, 1}, -S^2] + 2882736*HPL[{5, 2, 1, 1}, -S^2] + 7200992*HPL[{6, 1, 1, 1}, -S^2] - (6272*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 6272*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 5600*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2] + 25088*HPL[{3, 1, 1, 2, 2}, -S^2] + 25088*HPL[{3, 1, 2, 1, 2}, -S^2] - 156032*HPL[{3, 1, 3, 1, 1}, -S^2] + 25088*HPL[{3, 2, 1, 1, 2}, -S^2] - 130944*HPL[{3, 2, 2, 1, 1}, -S^2] - 392832*HPL[{3, 3, 1, 1, 1}, -S^2] + 80768*HPL[{4, 1, 1, 1, 2}, -S^2] + 5504*HPL[{4, 1, 1, 2, 1}, -S^2] - 387328*HPL[{4, 1, 2, 1, 1}, -S^2] - 1172992*HPL[{4, 2, 1, 1, 1}, -S^2] - 2332800*HPL[{5, 1, 1, 1, 1}, -S^2] - 13920*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + 50176*HPL[{2, 2, 1, 2, 1, 1}, -S^2] + 150528*HPL[{2, 2, 2, 1, 1, 1}, -S^2] - 306560*HPL[{3, 1, 1, 1, 1, 2}, -S^2] - 607616*HPL[{3, 1, 1, 1, 2, 1}, -S^2] - 808320*HPL[{3, 1, 1, 2, 1, 1}, -S^2] - 908672*HPL[{3, 1, 2, 1, 1, 1}, -S^2] - 1560960*HPL[{3, 2, 1, 1, 1, 1}, -S^2] - 4686720*HPL[{4, 1, 1, 1, 1, 1}, -S^2] + 107520*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] - 215040*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]^2*(-296*HPL[{2, 1}, -S^2] - 32*Zeta[3]) + HPL[{0}, S^2]^6*(HPL[{3}, -S^2]/12 - (3*HPL[{2, 1}, -S^2])/2 - Zeta[3]/2) + (1847*Pi^6*Zeta[3])/567 - 3136*HPL[{2, 1}, -S^2]^2*Zeta[3] - 104*HPL[{4, 2}, -S^2]*Zeta[3] - 720*HPL[{5, 1}, -S^2]*Zeta[3] + 80*HPL[{3, 1, 2}, -S^2]*Zeta[3] + 5744*HPL[{3, 2, 1}, -S^2]*Zeta[3] + 17696*HPL[{4, 1, 1}, -S^2]*Zeta[3] - 12096*HPL[{3, 1, 1, 1}, -S^2]*Zeta[3] + 24000*HPL[{2, 1, 1, 1, 1}, -S^2]*Zeta[3] + 64*Zeta[3]^3 + HPL[{2}, -S^2]^3*((932*HPL[{3}, -S^2])/3 + 236*Zeta[3]) + HPL[{6}, -S^2]*(356*HPL[{2, 1}, -S^2] + 236*Zeta[3]) + HPL[{2, 1}, -S^2]*((-52285*Pi^6)/2268 + (880*Pi^2*HPL[{3, 1}, -S^2])/3 - 936*HPL[{4, 2}, -S^2] - 5408*HPL[{5, 1}, -S^2] + (3136*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 5312*HPL[{4, 1, 1}, -S^2] - 5312*HPL[{3, 1, 1, 1}, -S^2] - 160*Zeta[3]^2) + HPL[{0}, S^2]^3*((-2863*Pi^6)/1296 - (187*Pi^2*HPL[{2}, -S^2]^2)/12 - (53*HPL[{2}, -S^2]^3)/3 + (16*HPL[{3}, -S^2]^2)/3 - (38*Pi^2*HPL[{4}, -S^2])/9 + (4*HPL[{6}, -S^2])/3 + 220*HPL[{2, 1}, -S^2]^2 + (623*Pi^2*HPL[{3, 1}, -S^2])/9 + (4*HPL[{4, 2}, -S^2])/3 + (100*HPL[{5, 1}, -S^2])/3 + HPL[{2}, -S^2]*((-3997*Pi^4)/540 - (34*HPL[{4}, -S^2])/3 + 220*HPL[{3, 1}, -S^2] - 440*HPL[{2, 1, 1}, -S^2]) - (424*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - (4*HPL[{3, 1, 2}, -S^2])/3 - (1276*HPL[{3, 2, 1}, -S^2])/3 - (4000*HPL[{4, 1, 1}, -S^2])/3 + (2896*HPL[{3, 1, 1, 1}, -S^2])/3 - (5840*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + HPL[{3}, -S^2]*(-8*HPL[{2, 1}, -S^2] - 4*Zeta[3]) + (44*HPL[{2, 1}, -S^2]*Zeta[3])/3 - 14*Zeta[3]^2) + HPL[{3}, -S^2]*((30311*Pi^6)/5670 - (142*Pi^2*HPL[{4}, -S^2])/3 - 304*HPL[{6}, -S^2] - 3136*HPL[{2, 1}, -S^2]^2 - 668*Pi^2*HPL[{3, 1}, -S^2] - 156*HPL[{4, 2}, -S^2] + 344*HPL[{5, 1}, -S^2] + (3976*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 16*HPL[{3, 1, 2}, -S^2] + 7440*HPL[{3, 2, 1}, -S^2] - 220480*HPL[{4, 1, 1}, -S^2] - 15296*HPL[{3, 1, 1, 1}, -S^2] + 30400*HPL[{2, 1, 1, 1, 1}, -S^2] + 400*HPL[{2, 1}, -S^2]*Zeta[3] + 64*Zeta[3]^2) + HPL[{3, 1}, -S^2]*(6304*HPL[{3, 2}, -S^2] + 21648*HPL[{4, 1}, -S^2] - 12544*HPL[{2, 2, 1}, -S^2] + 27840*HPL[{3, 1, 1}, -S^2] - 5312*HPL[{2, 1, 1, 1}, -S^2] - 564*Pi^2*Zeta[3] - 3112*Zeta[5]) + HPL[{0}, S^2]^4*((11*Pi^2*HPL[{3}, -S^2])/12 + HPL[{5}, -S^2]/2 + HPL[{2}, -S^2]*(HPL[{3}, -S^2]/2 - (241*HPL[{2, 1}, -S^2])/6) - (277*Pi^2*HPL[{2, 1}, -S^2])/18 - HPL[{3, 2}, -S^2] - 8*HPL[{4, 1}, -S^2] + (241*HPL[{2, 2, 1}, -S^2])/3 + 253*HPL[{3, 1, 1}, -S^2] - (568*HPL[{2, 1, 1, 1}, -S^2])/3 - (97*Pi^2*Zeta[3])/36 - (65*Zeta[5])/6) + (1564*Pi^4*Zeta[5])/45 + HPL[{4}, -S^2]*(352*HPL[{5}, -S^2] + (680*Pi^2*HPL[{2, 1}, -S^2])/3 + 344*HPL[{3, 2}, -S^2] + 1272*HPL[{4, 1}, -S^2] - 1808*HPL[{2, 2, 1}, -S^2] - 6352*HPL[{3, 1, 1}, -S^2] + 5312*HPL[{2, 1, 1, 1}, -S^2] + 40*Pi^2*Zeta[3] + 336*Zeta[5]) + HPL[{2}, -S^2]^2*((413*Pi^2*HPL[{3}, -S^2])/3 + 164*HPL[{5}, -S^2] - (1214*Pi^2*HPL[{2, 1}, -S^2])/3 - 1708*HPL[{3, 2}, -S^2] - 5140*HPL[{4, 1}, -S^2] + 3136*HPL[{3, 1, 1}, -S^2] - 6272*HPL[{2, 1, 1, 1}, -S^2] + (431*Pi^2*Zeta[3])/3 + 722*Zeta[5]) + HPL[{2, 1, 1}, -S^2]*(-25088*HPL[{2, 2, 1}, -S^2] - 44864*HPL[{3, 1, 1}, -S^2] + (3328*Pi^2*Zeta[3])/3 + 6080*Zeta[5]) + HPL[{0}, S^2]^2*(8*Pi^2*HPL[{5}, -S^2] - 64*HPL[{7}, -S^2] - (49*Pi^2*HPL[{3, 2}, -S^2])/3 - (208*Pi^2*HPL[{4, 1}, -S^2])/3 + 48*HPL[{4, 3}, -S^2] + 148*HPL[{5, 2}, -S^2] + 242*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((323*Pi^4)/90 - 26*HPL[{4}, -S^2] - 92*HPL[{3, 1}, -S^2] + 176*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-8449*Pi^4)/180 + 1544*HPL[{3, 1}, -S^2] + 3136*HPL[{2, 1, 1}, -S^2]) + 422*Pi^2*HPL[{2, 2, 1}, -S^2] + (4010*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 166*HPL[{3, 2, 2}, -S^2] + 520*HPL[{3, 3, 1}, -S^2] + 528*HPL[{4, 1, 2}, -S^2] + 1584*HPL[{4, 2, 1}, -S^2] + 3336*HPL[{5, 1, 1}, -S^2] - (2996*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 3440*HPL[{2, 2, 2, 1}, -S^2] + 9976*HPL[{3, 1, 1, 2}, -S^2] + 9976*HPL[{3, 1, 2, 1}, -S^2] + 20296*HPL[{3, 2, 1, 1}, -S^2] + 60640*HPL[{4, 1, 1, 1}, -S^2] - 6272*HPL[{2, 1, 2, 1, 1}, -S^2] - 18816*HPL[{2, 2, 1, 1, 1}, -S^2] - 30240*HPL[{3, 1, 1, 1, 1}, -S^2] - 14880*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (373*Pi^4*Zeta[3])/180 - 180*HPL[{3, 1}, -S^2]*Zeta[3] + 328*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(16*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{2}, -S^2]^2*(21*HPL[{3}, -S^2] - 430*HPL[{2, 1}, -S^2] + 39*Zeta[3]) - (26*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((25*Pi^2*HPL[{3}, -S^2])/3 + 24*HPL[{5}, -S^2] - 211*Pi^2*HPL[{2, 1}, -S^2] - 84*HPL[{3, 2}, -S^2] - 268*HPL[{4, 1}, -S^2] + 1720*HPL[{2, 2, 1}, -S^2] - 4984*HPL[{3, 1, 1}, -S^2] - 3136*HPL[{2, 1, 1, 1}, -S^2] + (41*Pi^2*Zeta[3])/3 + 78*Zeta[5])) + HPL[{0}, S^2]*((-177569*Pi^8)/64800 - (551*Pi^2*HPL[{2}, -S^2]^3)/9 - 59*HPL[{2}, -S^2]^4 + (38*Pi^2*HPL[{3}, -S^2]^2)/3 - 74*HPL[{4}, -S^2]^2 - 23*Pi^2*HPL[{6}, -S^2] + 298*HPL[{8}, -S^2] + 720*Pi^2*HPL[{2, 1}, -S^2]^2 - 3008*HPL[{3, 1}, -S^2]^2 + (4*Pi^2*HPL[{4, 2}, -S^2])/3 + (236*Pi^2*HPL[{5, 1}, -S^2])/3 + 12*HPL[{5, 3}, -S^2] + 30*HPL[{6, 2}, -S^2] + 216*HPL[{7, 1}, -S^2] + HPL[{2}, -S^2]^2*((-2155*Pi^4)/72 - 8*HPL[{4}, -S^2] + 1568*HPL[{3, 1}, -S^2] - 3136*HPL[{2, 1, 1}, -S^2]) + HPL[{4}, -S^2]*((-149*Pi^4)/18 + 200*HPL[{3, 1}, -S^2] - 368*HPL[{2, 1, 1}, -S^2]) - (4061*Pi^4*HPL[{2, 1, 1}, -S^2])/15 - 12000*HPL[{2, 1, 1}, -S^2]^2 + HPL[{3, 1}, -S^2]*((12071*Pi^4)/90 + 12000*HPL[{2, 1, 1}, -S^2]) - (4*Pi^2*HPL[{3, 1, 2}, -S^2])/3 - (4412*Pi^2*HPL[{3, 2, 1}, -S^2])/3 + 64*HPL[{3, 3, 2}, -S^2] - (13648*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 152*HPL[{4, 1, 3}, -S^2] + 52*HPL[{4, 2, 2}, -S^2] - 280*HPL[{4, 3, 1}, -S^2] - 176*HPL[{5, 1, 2}, -S^2] - 1136*HPL[{5, 2, 1}, -S^2] - 3464*HPL[{6, 1, 1}, -S^2] + (9616*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + 12544*HPL[{3, 2, 2, 1}, -S^2] + 37632*HPL[{3, 3, 1, 1}, -S^2] + 37632*HPL[{4, 1, 2, 1}, -S^2] + 112896*HPL[{4, 2, 1, 1}, -S^2] + 226880*HPL[{5, 1, 1, 1}, -S^2] - (19280*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + 25088*HPL[{2, 2, 1, 2, 1}, -S^2] + 75264*HPL[{2, 2, 2, 1, 1}, -S^2] - 150528*HPL[{3, 1, 1, 1, 2}, -S^2] - 250880*HPL[{3, 1, 1, 2, 1}, -S^2] - 301056*HPL[{3, 1, 2, 1, 1}, -S^2] - 627200*HPL[{3, 2, 1, 1, 1}, -S^2] - 1883520*HPL[{4, 1, 1, 1, 1}, -S^2] + 53760*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 107520*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{5}, -S^2]*(-184*HPL[{2, 1}, -S^2] - 128*Zeta[3]) - 32*HPL[{3, 2}, -S^2]*Zeta[3] - 1312*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 3968*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 2656*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - 28*Pi^2*Zeta[3]^2 + HPL[{2}, -S^2]*((-248987*Pi^6)/22680 + 8*HPL[{3}, -S^2]^2 - (80*Pi^2*HPL[{4}, -S^2])/3 - 146*HPL[{6}, -S^2] + 3136*HPL[{2, 1}, -S^2]^2 + 720*Pi^2*HPL[{3, 1}, -S^2] + 216*HPL[{5, 1}, -S^2] - 1440*Pi^2*HPL[{2, 1, 1}, -S^2] - 5664*HPL[{3, 2, 1}, -S^2] - 17360*HPL[{4, 1, 1}, -S^2] + 162528*HPL[{3, 1, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1, 1}, -S^2] + 656*HPL[{2, 1}, -S^2]*Zeta[3] - 68*Zeta[3]^2 + HPL[{3}, -S^2]*(304*HPL[{2, 1}, -S^2] + 16*Zeta[3])) + HPL[{3}, -S^2]*(148*HPL[{5}, -S^2] + (44*Pi^2*HPL[{2, 1}, -S^2])/3 - 32*HPL[{3, 2}, -S^2] - 136*HPL[{4, 1}, -S^2] - 608*HPL[{2, 2, 1}, -S^2] - 1472*HPL[{3, 1, 1}, -S^2] + 544*HPL[{2, 1, 1, 1}, -S^2] - (16*Pi^2*Zeta[3])/3 - 96*Zeta[5]) - 336*Zeta[3]*Zeta[5] + HPL[{2, 1}, -S^2]*(-608*HPL[{3, 2}, -S^2] - 1456*HPL[{4, 1}, -S^2] - 12544*HPL[{2, 2, 1}, -S^2] - 37088*HPL[{3, 1, 1}, -S^2] + 24000*HPL[{2, 1, 1, 1}, -S^2] + (376*Pi^2*Zeta[3])/3 + 520*Zeta[5])) + 372*Pi^2*Zeta[7] + HPL[{2}, -S^2]*(80*Pi^2*HPL[{5}, -S^2] + 60*HPL[{7}, -S^2] - (1652*Pi^2*HPL[{3, 2}, -S^2])/3 - (5636*Pi^2*HPL[{4, 1}, -S^2])/3 + 188*HPL[{4, 3}, -S^2] + 408*HPL[{5, 2}, -S^2] - 196*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((601*Pi^4)/15 - 172*HPL[{4}, -S^2] - 3136*HPL[{3, 1}, -S^2] + 6272*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-2021*Pi^4)/30 + 6272*HPL[{3, 1}, -S^2] + 12544*HPL[{2, 1, 1}, -S^2]) + (4856*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (10592*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 6520*HPL[{3, 2, 2}, -S^2] + 19936*HPL[{3, 3, 1}, -S^2] + 19624*HPL[{4, 1, 2}, -S^2] + 60808*HPL[{4, 2, 1}, -S^2] + 125280*HPL[{5, 1, 1}, -S^2] - (3136*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 12544*HPL[{3, 1, 1, 2}, -S^2] - 12544*HPL[{3, 1, 2, 1}, -S^2] - 12544*HPL[{3, 2, 1, 1}, -S^2] - 42944*HPL[{4, 1, 1, 1}, -S^2] - 25088*HPL[{2, 1, 2, 1, 1}, -S^2] - 75264*HPL[{2, 2, 1, 1, 1}, -S^2] + 155840*HPL[{3, 1, 1, 1, 1}, -S^2] + (1013*Pi^4*Zeta[3])/30 - 3232*HPL[{3, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(904*HPL[{2, 1}, -S^2] + 112*Zeta[3]) + (838*Pi^2*Zeta[5])/3 + 1932*Zeta[7]) + 3136*Zeta[9]);
E5vwuT1F1=(-80*Pi^4*S)/9 - (667*Pi^6*S)/360 - (19139*Pi^8*S)/56700 - (S*HPL[{0}, S^2]^8*HPL[{1}, -S^2])/96 + ((-58*Pi^2*S)/21 - (40*(1 + S^2))/(7*S))*HPL[{1}, -S^2]^7 - (4*(1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) - (16*S*HPL[{1}, -S^2]^9)/27 - (2*(7 + 17*S^2)*HPL[{2}, -S^2]^4)/(3*S) + HPL[{0}, S^2]^7*(-S/6 - (Pi^2*S)/96 + ((-1 - S^2)*HPL[{1}, -S^2])/(12*S) - (S*HPL[{1}, -S^2]^2)/16 - (S*HPL[{2}, -S^2])/16) - (16*S*HPL[{3}, -S^2]^3)/3 - (2*(14 + 3*S^2)*HPL[{4}, -S^2]^2)/S + ((131*Pi^2*S)/3 - (8*(-5 + 112*S^2))/S)*HPL[{7}, -S^2] + (6*(35 + 52*S^2)*HPL[{8}, -S^2])/S + 918*S*HPL[{9}, -S^2] + (1568*S*HPL[{2, 1}, -S^2]^3)/3 - (4*(97 + 143*S^2)*HPL[{3, 1}, -S^2]^2)/S + (11*Pi^2*S + (38*(2 + S^2))/S)*HPL[{4, 3}, -S^2] + ((58*Pi^2*S)/3 + (16*(13 + 7*S^2))/S)*HPL[{5, 2}, -S^2] - 18*S*HPL[{5, 3}, -S^2] + 224*S*HPL[{5, 4}, -S^2] + (-75*Pi^2*S + (2*(237 + 263*S^2))/S)*HPL[{6, 1}, -S^2] - (2*(22 + 15*S^2)*HPL[{6, 2}, -S^2])/S + 868*S*HPL[{6, 3}, -S^2] + (6*(7 + 30*S^2)*HPL[{7, 1}, -S^2])/S + 2190*S*HPL[{7, 2}, -S^2] + 4212*S*HPL[{8, 1}, -S^2] - (32*(25 + 73*S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + (559*Pi^2*S + (6*(8 + 135*S^2))/S)*HPL[{3, 2, 2}, -S^2] + ((5224*Pi^2*S)/3 + (8*(8 + 327*S^2))/S)*HPL[{3, 3, 1}, -S^2] - (2*(17 + 103*S^2)*HPL[{3, 3, 2}, -S^2])/S + (1731*Pi^2*S + (2*(33 + 1273*S^2))/S)*HPL[{4, 1, 2}, -S^2] + (4*(17 + 94*S^2)*HPL[{4, 1, 3}, -S^2])/S + (5311*Pi^2*S + (2*(105 + 4033*S^2))/S)*HPL[{4, 2, 1}, -S^2] - (6*(2 + 19*S^2)*HPL[{4, 2, 2}, -S^2])/S + 88*S*HPL[{4, 2, 3}, -S^2] + (4*(43 + 308*S^2)*HPL[{4, 3, 1}, -S^2])/S - 10*S*HPL[{4, 3, 2}, -S^2] - 44*S*HPL[{4, 4, 1}, -S^2] + ((32738*Pi^2*S)/3 + (8*(52 + 2057*S^2))/S)*HPL[{5, 1, 1}, -S^2] + (2*(59 + 389*S^2)*HPL[{5, 1, 2}, -S^2])/S + 132*S*HPL[{5, 1, 3}, -S^2] + (2*(359 + 2489*S^2)*HPL[{5, 2, 1}, -S^2])/S - 4*S*HPL[{5, 2, 2}, -S^2] + 92*S*HPL[{5, 3, 1}, -S^2] + (16*(100 + 779*S^2)*HPL[{6, 1, 1}, -S^2])/S - 118*S*HPL[{6, 1, 2}, -S^2] + 762*S*HPL[{6, 2, 1}, -S^2] + 2944*S*HPL[{7, 1, 1}, -S^2] + ((-1672*Pi^2*S)/3 - (8*(-295 + 78*S^2))/S)*HPL[{2, 2, 2, 1}, -S^2] + (516*Pi^2*S + (4*(-1741 + 45*S^2))/S)*HPL[{3, 1, 1, 2}, -S^2] + (516*Pi^2*S + (4*(-1741 + 45*S^2))/S)*HPL[{3, 1, 2, 1}, -S^2] - (2*(47 + 40*S^2)*HPL[{3, 1, 2, 2}, -S^2])/S + (2188*Pi^2*S + (4*(-3511 + 513*S^2))/S)*HPL[{3, 2, 1, 1}, -S^2] - (2*(47 + 40*S^2)*HPL[{3, 2, 1, 2}, -S^2])/S + (2*(-575 + 944*S^2)*HPL[{3, 2, 2, 1}, -S^2])/S - 6208*S*HPL[{3, 2, 2, 2}, -S^2] - 19456*S*HPL[{3, 2, 3, 1}, -S^2] + (144*(-22 + 41*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S - 19152*S*HPL[{3, 3, 1, 2}, -S^2] - 59136*S*HPL[{3, 3, 2, 1}, -S^2] + ((18904*Pi^2*S)/3 + (8*(-5312 + 719*S^2))/S)*HPL[{4, 1, 1, 1}, -S^2] - (4*(-7 + 114*S^2)*HPL[{4, 1, 1, 2}, -S^2])/S + 120296*S*HPL[{4, 1, 1, 3}, -S^2] + (4*(-785 + 1362*S^2)*HPL[{4, 1, 2, 1}, -S^2])/S + 101230*S*HPL[{4, 1, 2, 2}, -S^2] + 180808*S*HPL[{4, 1, 3, 1}, -S^2] + (4*(-2369 + 4314*S^2)*HPL[{4, 2, 1, 1}, -S^2])/S + 62158*S*HPL[{4, 2, 1, 2}, -S^2] + 61246*S*HPL[{4, 2, 2, 1}, -S^2] + 357464*S*HPL[{4, 3, 1, 1}, -S^2] + (24*(-787 + 1397*S^2)*HPL[{5, 1, 1, 1}, -S^2])/S + 363284*S*HPL[{5, 1, 1, 2}, -S^2] + 599540*S*HPL[{5, 1, 2, 1}, -S^2] + 1429172*S*HPL[{5, 2, 1, 1}, -S^2] + 3570432*S*HPL[{6, 1, 1, 1}, -S^2] + ((3248*Pi^2*S)/3 + (432*(11 + 4*S^2))/S)*HPL[{2, 1, 2, 1, 1}, -S^2] + (3248*Pi^2*S + (1296*(11 + 4*S^2))/S)*HPL[{2, 2, 1, 1, 1}, -S^2] + (32*(-66 + 125*S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S + (96*(-66 + 125*S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - 6048*S*HPL[{2, 2, 2, 2, 1}, -S^2] + ((23744*Pi^2*S)/3 + (16*(1511 + 760*S^2))/S)*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(-1540 + 2967*S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S - (8*(-2596 + 4967*S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S - 5408*S*HPL[{3, 1, 1, 2, 2}, -S^2] - (8*(-3124 + 5967*S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S - 5408*S*HPL[{3, 1, 2, 1, 2}, -S^2] + 288*S*HPL[{3, 1, 2, 2, 1}, -S^2] + 49824*S*HPL[{3, 1, 3, 1, 1}, -S^2] - (8*(-6556 + 12467*S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S - 23552*S*HPL[{3, 2, 1, 1, 2}, -S^2] - 17856*S*HPL[{3, 2, 1, 2, 1}, -S^2] - 10016*S*HPL[{3, 2, 2, 1, 1}, -S^2] - 12768*S*HPL[{3, 3, 1, 1, 1}, -S^2] - (64*(-2475 + 4661*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S - 69296*S*HPL[{4, 1, 1, 1, 2}, -S^2] - 52208*S*HPL[{4, 1, 1, 2, 1}, -S^2] - 28688*S*HPL[{4, 1, 2, 1, 1}, -S^2] - 36080*S*HPL[{4, 2, 1, 1, 1}, -S^2] - 65568*S*HPL[{5, 1, 1, 1, 1}, -S^2] + ((-7328*Pi^2*S)/3 - (32*(-313 + 72*S^2))/S)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + 12544*S*HPL[{2, 2, 1, 2, 1, 1}, -S^2] + 37632*S*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + (32*(-165 + 227*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S - 89088*S*HPL[{3, 1, 1, 1, 1, 2}, -S^2] - 164352*S*HPL[{3, 1, 1, 1, 2, 1}, -S^2] - 214528*S*HPL[{3, 1, 1, 2, 1, 1}, -S^2] - 239616*S*HPL[{3, 1, 2, 1, 1, 1}, -S^2] - 402688*S*HPL[{3, 2, 1, 1, 1, 1}, -S^2] - 1213888*S*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - (1920*(-4 + 9*S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S - 24896*S*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] - 99584*S*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] - 248960*S*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] - 466176*S*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] - 53760*S*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((16*Pi^2*S)/9 + (16*S*HPL[{0}, S^2]^2)/3 + (32*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + (64*S*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*((32*S)/3 + (64*S*HPL[{1}, -S^2])/3) + (32*S*HPL[{2}, -S^2])/3)*Log[T]^7 + ((-16*S*HPL[{0}, S^2])/3 - (16*S*HPL[{1}, -S^2])/3)*Log[T]^8 + (36*S - (16*Pi^2*S)/3)*Zeta[3]^2 + 32*S*Zeta[3]^3 + HPL[{3, 1, 1, 1}, -S^2]*((8*(-161 + 227*S^2))/S + (4*Pi^2*(-188 + 513*S^2))/(3*S) - 6176*S*Zeta[3]) + HPL[{2, 1}, -S^2]^2*((4*(59 + 153*S^2))/S + (2*Pi^2*(46 + 287*S^2))/(3*S) - 1488*S*Zeta[3]) + HPL[{5, 1}, -S^2]*((Pi^2*(35 - 213*S^2))/(3*S) - (2*(-10 + 341*S^2))/S - 260*S*Zeta[3]) + HPL[{4, 2}, -S^2]*(-128*S + (Pi^2*(2 - 53*S^2))/(3*S) - 62*S*Zeta[3]) + HPL[{6}, -S^2]*((-20*Pi^2)/S + (2*(-25 + 214*S^2))/S - 142*S*HPL[{2, 1}, -S^2] - 42*S*Zeta[3]) + HPL[{3}, -S^2]^2*((-13*Pi^2*S)/3 - (3*(-3 + 13*S^2))/S + 20*S*HPL[{2, 1}, -S^2] - 30*S*Zeta[3]) + HPL[{0}, S^2]^5*((-77*S)/12 - (77*Pi^2*S)/48 - (5597*Pi^4*S)/43200 - (17*(1 + S^2)*HPL[{1}, -S^2]^3)/(12*S) - (271*S*HPL[{1}, -S^2]^4)/360 + ((-13*S)/8 - (571*Pi^2*S)/720)*HPL[{2}, -S^2] - (9*S*HPL[{2}, -S^2]^2)/10 + HPL[{1}, -S^2]^2*((-293*Pi^2*S)/360 - (29*(1 + S^2))/(12*S) - (77*S*HPL[{2}, -S^2])/40) - (S*HPL[{3}, -S^2])/8 - (5*S*HPL[{4}, -S^2])/8 + ((21 - S^2)*HPL[{2, 1}, -S^2])/(6*S) + HPL[{1}, -S^2]*((-77*(1 + S^2))/(24*S) - (15*Pi^2*(1 + S^2))/(16*S) - (7*(1 + S^2)*HPL[{2}, -S^2])/(4*S) - (S*HPL[{3}, -S^2])/4 + (77*S*HPL[{2, 1}, -S^2])/20) + (87*S*HPL[{3, 1}, -S^2])/20 - (128*S*HPL[{2, 1, 1}, -S^2])/15 - (5*S*Zeta[3])/4) + HPL[{0}, S^2]^6*(-(Pi^2*S)/16 - (5*(1 + S^2)*HPL[{1}, -S^2]^2)/(12*S) - (S*HPL[{1}, -S^2]^3)/4 - (3*S*HPL[{2}, -S^2])/8 + HPL[{1}, -S^2]*((-23*Pi^2*S)/144 - (11*(1 + S^2))/(24*S) - (13*S*HPL[{2}, -S^2])/48) + (S*HPL[{3}, -S^2])/16 - (S*HPL[{2, 1}, -S^2])/6 - (S*Zeta[3])/4) + HPL[{3, 1, 2}, -S^2]*((8*(-9 + 10*S^2))/S + (Pi^2*(-47 + 32*S^2))/(3*S) + 32*S*Zeta[3]) + HPL[{1}, -S^2]^6*((-206*(1 + S^2))/(9*S) - (50*Pi^2*(1 + S^2))/(9*S) - (26*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (380*S*HPL[{3}, -S^2])/9 + (100*S*Zeta[3])/3) + Log[T]^6*(-4*Pi^2*S - (50*S*HPL[{0}, S^2]^3)/9 + ((-58*Pi^2*S)/3 - (40*(1 + S^2))/S)*HPL[{1}, -S^2] - (112*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (448*S*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]^2*(-12*S - (62*S*HPL[{1}, -S^2])/3) - (8*(-4 + 9*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{0}, S^2]*(-40*S - 18*Pi^2*S - (112*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (224*S*HPL[{1}, -S^2]^2)/3 - (212*S*HPL[{2}, -S^2])/3) + (236*S*HPL[{3}, -S^2])/3 - (224*S*HPL[{2, 1}, -S^2])/3 + (224*S*Zeta[3])/3) + HPL[{2}, -S^2]^3*((69 - 128*S^2)/(3*S) - (2*Pi^2*(-19 + 65*S^2))/(9*S) + (422*S*HPL[{3}, -S^2])/3 + 126*S*HPL[{2, 1}, -S^2] + 122*S*Zeta[3]) + HPL[{3, 2, 1}, -S^2]*((Pi^2*(257 - 1008*S^2))/(3*S) - (16*(-30 + 59*S^2))/S + 2960*S*Zeta[3]) + HPL[{4, 1, 1}, -S^2]*((-8*(-209 + 313*S^2))/S - (2*Pi^2*(-453 + 1468*S^2))/(3*S) + 9032*S*Zeta[3]) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-1120*Pi^2*(-1 + 4*S^2))/(3*S) - (32*(-59 + 140*S^2))/S + 12224*S*Zeta[3]) + HPL[{1}, -S^2]^5*((-6673*Pi^4*S)/1350 - (1264*(1 + S^2))/(15*S) - (160*Pi^2*(1 + S^2))/(9*S) + ((-392*Pi^2*S)/45 - (132*(1 + S^2))/(5*S))*HPL[{2}, -S^2] - (784*S*HPL[{2}, -S^2]^2)/15 + (112*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (664*S*HPL[{4}, -S^2])/15 + (52*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (664*S*HPL[{3, 1}, -S^2])/15 + (24*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((-1229*Pi^4*S)/15 - (4*Pi^2*(-647 + 44*S^2))/(3*S) - (8*(-355 + 74*S^2))/S - (320*(5 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((1381*Pi^4*S)/180 - (5*Pi^2*(5 + 12*S^2))/(3*S) - (4*(15 + 121*S^2))/S - (2*(49 + 33*S^2)*HPL[{2, 1}, -S^2])/S - 276*S*HPL[{3, 1}, -S^2] + 708*S*HPL[{2, 1, 1}, -S^2] - (6*(-5 + 3*S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((-971*Pi^4*S)/30 - (14*Pi^2*(29 + 6*S^2))/S - (4*(339 + 142*S^2))/S + (16*(54 + 5*S^2)*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((-553*Pi^4*S)/30 - (2*Pi^2*(1822 + 171*S^2))/(3*S) - (4*(977 + 174*S^2))/S + (24*(107 + 14*S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((-3137*Pi^4*S)/90 - (2*Pi^2*(-9 + 106*S^2))/(3*S) - (4*(3 + 154*S^2))/S - 6536*S*HPL[{2, 1, 1}, -S^2] - (2*(1 + 22*S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((-6901*Pi^4*S)/60 + (Pi^2*(43 - 661*S^2))/(3*S) - (6*(17 + 292*S^2))/S - 20928*S*HPL[{2, 1, 1}, -S^2] - (4*(1 + 37*S^2)*Zeta[3])/S) + Log[T]^5*(12*Pi^2*S + (449*Pi^4*S)/90 + (19*S*HPL[{0}, S^2]^4)/6 + (58*Pi^2*S + (120*(1 + S^2))/S)*HPL[{1}, -S^2]^2 + (224*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (224*S*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*((112*S)/9 + (146*S*HPL[{1}, -S^2])/9) + ((340*Pi^2*S)/9 + (4*(-23 + 54*S^2))/(3*S))*HPL[{2}, -S^2] + (158*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*(36*S + (47*Pi^2*S)/3 + (44*(1 + S^2)*HPL[{1}, -S^2])/S + 62*S*HPL[{1}, -S^2]^2 + (172*S*HPL[{2}, -S^2])/3) - (4*(3 + 43*S^2)*HPL[{3}, -S^2])/(3*S) - 72*S*HPL[{4}, -S^2] + (8*(-21 + 5*S^2)*HPL[{2, 1}, -S^2])/S - 176*S*HPL[{3, 1}, -S^2] + 448*S*HPL[{2, 1, 1}, -S^2] - 40*S*Zeta[3] + HPL[{1}, -S^2]*((412*(1 + S^2))/(3*S) + (100*Pi^2*(1 + S^2))/(3*S) + (52*(1 + S^2)*HPL[{2}, -S^2])/S - (760*S*HPL[{3}, -S^2])/3 - 200*S*Zeta[3]) + HPL[{0}, S^2]*((412*S)/3 + (280*Pi^2*S)/9 + (112*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (448*S*HPL[{1}, -S^2]^3)/3 + (8*(-1 + 12*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((482*Pi^2*S)/9 + (120*(1 + S^2))/S + 200*S*HPL[{2}, -S^2]) - (44*S*HPL[{3}, -S^2])/3 + 24*S*HPL[{2, 1}, -S^2] - 48*S*Zeta[3])) + (-276*S - (43*Pi^2*S)/3 + (782*Pi^4*S)/45)*Zeta[5] + HPL[{3, 1}, -S^2]*((70*(-5 + 6*S^2))/S + (2*Pi^2*(-75 + 263*S^2))/(3*S) + (Pi^4*(-1301 + 6340*S^2))/(180*S) + 3284*S*HPL[{3, 2}, -S^2] + 10428*S*HPL[{4, 1}, -S^2] + (128*(9 + 16*S^2)*HPL[{2, 1, 1}, -S^2])/S - 3824*S*HPL[{2, 2, 1}, -S^2] - 14768*S*HPL[{3, 1, 1}, -S^2] - 7552*S*HPL[{2, 1, 1, 1}, -S^2] + (-282*Pi^2*S - (12*(8 + 35*S^2))/S)*Zeta[3] - 1436*S*Zeta[5]) + Zeta[3]*(-20*S + (46*Pi^2*S)/3 + (217*Pi^4*S)/180 + (1847*Pi^6*S)/1134 - 64*S*Zeta[5]) + HPL[{4}, -S^2]*((10*(-7 + 54*S^2))/S + (Pi^2*(-9 + 94*S^2))/(3*S) + (Pi^4*(-255 + 208*S^2))/(180*S) - 114*S*HPL[{5}, -S^2] + (15*Pi^2*S + (2*(-113 + S^2))/S)*HPL[{2, 1}, -S^2] - (6*(-8 + 35*S^2)*HPL[{3, 1}, -S^2])/S + 218*S*HPL[{3, 2}, -S^2] + 532*S*HPL[{4, 1}, -S^2] + (4*(-7 + 104*S^2)*HPL[{2, 1, 1}, -S^2])/S + 236*S*HPL[{2, 2, 1}, -S^2] + 364*S*HPL[{3, 1, 1}, -S^2] + 384*S*HPL[{2, 1, 1, 1}, -S^2] + ((19*Pi^2*S)/3 + (2*(13 + 15*S^2))/S)*Zeta[3] - 10*S*Zeta[5]) + HPL[{0}, S^2]^4*((-103*Pi^2*S)/72 - (227*Pi^4*S)/432 - (253*(1 + S^2)*HPL[{1}, -S^2]^4)/(72*S) - (71*S*HPL[{1}, -S^2]^5)/45 + ((3 - 52*S^2)*HPL[{2}, -S^2]^2)/(12*S) + HPL[{1}, -S^2]^3*((-277*Pi^2*S)/108 - (67*(1 + S^2))/(9*S) - (241*S*HPL[{2}, -S^2])/36) + ((11*Pi^2*S)/24 + (-6 - 7*S^2)/(4*S))*HPL[{3}, -S^2] + ((-6 - S^2)*HPL[{4}, -S^2])/(4*S) + (13*S*HPL[{5}, -S^2])/4 + ((-85*Pi^2*S)/72 + (248 + 23*S^2)/(12*S))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((-311*(1 + S^2))/(24*S) - (553*Pi^2*(1 + S^2))/(144*S) - (19*(1 + S^2)*HPL[{2}, -S^2])/(2*S) + (S*HPL[{3}, -S^2])/4 + (241*S*HPL[{2, 1}, -S^2])/12) + (217*S*HPL[{3, 1}, -S^2])/12 - (13*S*HPL[{4, 1}, -S^2])/4 + ((6 - 113*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*S*HPL[{2, 2, 1}, -S^2])/3 + (11*S*HPL[{3, 1, 1}, -S^2])/2 - (25*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-11*S)/4 - (97*Pi^2*S)/72)*Zeta[3] + HPL[{2}, -S^2]*((-103*S)/12 + (Pi^2*(3 - 124*S^2))/(36*S) - (S*HPL[{2, 1}, -S^2])/3 - (5*S*Zeta[3])/4) + HPL[{1}, -S^2]*((-2009*Pi^4*S)/2160 - (52*(1 + S^2))/(3*S) - (299*Pi^2*(1 + S^2))/(72*S) + ((-109*Pi^2*S)/36 - (59*(1 + S^2))/(6*S))*HPL[{2}, -S^2] - 5*S*HPL[{2}, -S^2]^2 + ((-1 - S^2)*HPL[{3}, -S^2])/S + (S*HPL[{4}, -S^2])/2 + (19*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (39*S*HPL[{3, 1}, -S^2])/2 - (241*S*HPL[{2, 1, 1}, -S^2])/6 - (5*(1 + S^2)*Zeta[3])/(4*S)) - (65*S*Zeta[5])/12) + HPL[{1}, -S^2]^4*((-835*(1 + S^2))/(3*S) - (101*Pi^2*(1 + S^2))/(2*S) - (8587*Pi^4*(1 + S^2))/(1080*S) - (196*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((497*Pi^2*S)/9 + (290*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (112*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + 72*S*HPL[{5}, -S^2] + ((392*Pi^2*S)/9 + (132*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (224*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (1568*S*HPL[{3, 2}, -S^2])/3 - (5368*S*HPL[{4, 1}, -S^2])/3 - (260*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (3136*S*HPL[{2, 2, 1}, -S^2])/3 - (5608*S*HPL[{3, 1, 1}, -S^2])/3 + ((416*Pi^2*S)/9 + (200*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-69*(1 + S^2))/S - (251*Pi^2*(1 + S^2))/(9*S) + (784*S*HPL[{3}, -S^2])/3 + (1568*S*HPL[{2, 1}, -S^2])/3 + (784*S*Zeta[3])/3) + (760*S*Zeta[5])/3) + HPL[{2}, -S^2]^2*((Pi^4*(-55 - 833*S^2))/(90*S) + (Pi^2*(-18 - 101*S^2))/(2*S) - (10*(7 + 16*S^2))/S + ((449*Pi^2*S)/6 + (21 + 116*S^2)/S)*HPL[{3}, -S^2] + ((5 + 61*S^2)*HPL[{4}, -S^2])/S + 97*S*HPL[{5}, -S^2] + ((-209*Pi^2*S)/3 + (295 - 78*S^2)/S)*HPL[{2, 1}, -S^2] + (9*(-19 + 23*S^2)*HPL[{3, 1}, -S^2])/S - 805*S*HPL[{3, 2}, -S^2] - 2591*S*HPL[{4, 1}, -S^2] - (4*(-66 + 125*S^2)*HPL[{2, 1, 1}, -S^2])/S - 756*S*HPL[{2, 2, 1}, -S^2] - 556*S*HPL[{3, 1, 1}, -S^2] - 1568*S*HPL[{2, 1, 1, 1}, -S^2] + ((409*Pi^2*S)/6 + (15*(-1 + 6*S^2))/S)*Zeta[3] + 341*S*Zeta[5]) + Log[T]^4*((-280*Pi^2*S)/9 - (227*Pi^4*S)/27 - (281*S*HPL[{0}, S^2]^5)/180 + ((-290*Pi^2*S)/3 - (200*(1 + S^2))/S)*HPL[{1}, -S^2]^3 - (280*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) - (224*S*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^4*((-58*S)/9 - (71*S*HPL[{1}, -S^2])/9) - (4*(25 + 73*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((-302*S)/9 - (328*Pi^2*S)/27 - (268*(1 + S^2)*HPL[{1}, -S^2])/(9*S) - (365*S*HPL[{1}, -S^2]^2)/9 - (349*S*HPL[{2}, -S^2])/9) + ((938*Pi^2*S)/9 + (4*(13 + 110*S^2))/(3*S))*HPL[{3}, -S^2] + (212*S*HPL[{4}, -S^2])/3 + 148*S*HPL[{5}, -S^2] + ((-916*Pi^2*S)/9 - (4*(-313 + 72*S^2))/(3*S))*HPL[{2, 1}, -S^2] + (4*(-165 + 227*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (3296*S*HPL[{3, 2}, -S^2])/3 - (10616*S*HPL[{4, 1}, -S^2])/3 - (80*(-4 + 9*S^2)*HPL[{2, 1, 1}, -S^2])/S - (3112*S*HPL[{2, 2, 1}, -S^2])/3 - 752*S*HPL[{3, 1, 1}, -S^2] - 2240*S*HPL[{2, 1, 1, 1}, -S^2] + (96*S + (310*Pi^2*S)/3)*Zeta[3] + HPL[{0}, S^2]^2*((-280*S)/3 - (251*Pi^2*S)/9 - (110*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (310*S*HPL[{1}, -S^2]^3)/3 - (10*(-2 + 29*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-749*Pi^2*S)/18 - (350*(1 + S^2))/(3*S) - (392*S*HPL[{2}, -S^2])/3) + (53*S*HPL[{3}, -S^2])/3 - (76*S*HPL[{2, 1}, -S^2])/3 + 30*S*Zeta[3]) + HPL[{1}, -S^2]^2*((-1030*(1 + S^2))/(3*S) - (250*Pi^2*(1 + S^2))/(3*S) - (130*(1 + S^2)*HPL[{2}, -S^2])/S + (1900*S*HPL[{3}, -S^2])/3 + 500*S*Zeta[3]) + HPL[{2}, -S^2]*((-140*Pi^2*(-1 + 4*S^2))/(9*S) - (4*(-59 + 140*S^2))/(3*S) + 576*S*HPL[{3}, -S^2] + (1556*S*HPL[{2, 1}, -S^2])/3 + (1528*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-6673*Pi^4*S)/270 - (1264*(1 + S^2))/(3*S) - (800*Pi^2*(1 + S^2))/(9*S) + ((-392*Pi^2*S)/9 - (132*(1 + S^2))/S)*HPL[{2}, -S^2] - (784*S*HPL[{2}, -S^2]^2)/3 + (560*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (664*S*HPL[{4}, -S^2])/3 + (260*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (664*S*HPL[{3, 1}, -S^2])/3 + (120*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]*((-1264*S)/3 - (752*Pi^2*S)/9 - (2473*Pi^4*S)/108 - (560*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (560*S*HPL[{1}, -S^2]^4)/3 + ((-1144*Pi^2*S)/9 - (10*(-3 + 74*S^2))/(3*S))*HPL[{2}, -S^2] - (767*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((-1205*Pi^2*S)/9 - (300*(1 + S^2))/S - 500*S*HPL[{2}, -S^2]) + (2*(-27 + 13*S^2)*HPL[{3}, -S^2])/(3*S) - 32*S*HPL[{4}, -S^2] + (20*(27 + S^2)*HPL[{2, 1}, -S^2])/S + (3152*S*HPL[{3, 1}, -S^2])/3 - 2120*S*HPL[{2, 1, 1}, -S^2] + (172*S*Zeta[3])/3 + HPL[{1}, -S^2]*((-1030*(1 + S^2))/(3*S) - (688*Pi^2*(1 + S^2))/(9*S) - (250*(1 + S^2)*HPL[{2}, -S^2])/S + (68*S*HPL[{3}, -S^2])/3 + 1000*S*HPL[{2, 1}, -S^2] + (332*S*Zeta[3])/3)) + 580*S*Zeta[5]) + HPL[{2, 1, 1}, -S^2]*((-80*(-7 + 16*S^2))/S - (4*Pi^2*(-59 + 296*S^2))/(3*S) - (2*Pi^4*(-269 + 1679*S^2))/(45*S) - 6272*S*HPL[{2, 2, 1}, -S^2] - 4992*S*HPL[{3, 1, 1}, -S^2] + 12448*S*HPL[{2, 1, 1, 1}, -S^2] + (560*Pi^2*S + (8*(21 + 100*S^2))/S)*Zeta[3] + 2928*S*Zeta[5]) + HPL[{1}, -S^2]^3*((-52285*Pi^6*S)/13608 - (2420*(1 + S^2))/(3*S) - (1108*Pi^2*(1 + S^2))/(9*S) - (4691*Pi^4*(1 + S^2))/(270*S) + ((-607*Pi^2*S)/9 - (134*(1 + S^2))/S)*HPL[{2}, -S^2]^2 - (148*S*HPL[{3}, -S^2]^2)/3 + ((340*Pi^2*S)/9 + (226*(1 + S^2))/(3*S))*HPL[{4}, -S^2] + (8*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (178*S*HPL[{6}, -S^2])/3 + (3136*S*HPL[{2, 1}, -S^2]^2)/3 + ((440*Pi^2*S)/9 + (448*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] - (904*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (3160*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - 156*S*HPL[{4, 2}, -S^2] - (2704*S*HPL[{5, 1}, -S^2])/3 + ((-1568*Pi^2*S)/9 - (528*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (7168*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (2656*S*HPL[{4, 1, 1}, -S^2])/3 + (1040*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (2656*S*HPL[{3, 1, 1, 1}, -S^2])/3 + ((484*(1 + S^2))/(3*S) + (196*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (80*S*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((276*(1 + S^2))/S + (1004*Pi^2*(1 + S^2))/(9*S) - (3136*S*Zeta[3])/3) + HPL[{3}, -S^2]*((632*(1 + S^2))/(3*S) + (274*Pi^2*(1 + S^2))/(9*S) - (3136*S*HPL[{2, 1}, -S^2])/3 + (200*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-2021*Pi^4*S)/180 - (452*(1 + S^2))/(3*S) - (58*Pi^2*(1 + S^2))/S + (452*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (452*S*HPL[{4}, -S^2])/3 + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (3136*S*HPL[{3, 1}, -S^2])/3 - (6272*S*HPL[{2, 1, 1}, -S^2])/3 + (448*(1 + S^2)*Zeta[3])/(3*S)) + (68*(1 + S^2)*Zeta[5])/S) + HPL[{2, 1}, -S^2]*((-68629*Pi^6*S)/22680 + (Pi^2*(753 - 8*S^2))/(3*S) + (20*(47 + S^2))/S + (Pi^4*(7891 + 121*S^2))/(180*S) + ((-976*Pi^2*S)/3 - (4*(260 + 151*S^2))/S)*HPL[{3, 1}, -S^2] + (2*(527 + 91*S^2)*HPL[{3, 2}, -S^2])/S + (4*(856 + 91*S^2)*HPL[{4, 1}, -S^2])/S + 78*S*HPL[{4, 2}, -S^2] - 4*S*HPL[{5, 1}, -S^2] + ((-1624*Pi^2*S)/3 - (216*(11 + 4*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (16*(-66 + 125*S^2)*HPL[{2, 2, 1}, -S^2])/S - (96*(-10 + 63*S^2)*HPL[{3, 1, 1}, -S^2])/S - 312*S*HPL[{3, 1, 2}, -S^2] + 2712*S*HPL[{3, 2, 1}, -S^2] + 9456*S*HPL[{4, 1, 1}, -S^2] + (64*(25 + 73*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 7552*S*HPL[{3, 1, 1, 1}, -S^2] - 12448*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-8*(59 + 16*S^2))/S - (2*Pi^2*(107 + 19*S^2))/(3*S))*Zeta[3] - 60*S*Zeta[3]^2 - (60*(3 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((2323*Pi^6*S)/945 - (10*(7 + 12*S^2))/S + (Pi^2*(9 + 76*S^2))/(3*S) + (Pi^4*(-103 + 252*S^2))/(90*S) + (-13*Pi^2*S - (2*(19 + 15*S^2))/S)*HPL[{4}, -S^2] + (2*(28 + 15*S^2)*HPL[{5}, -S^2])/S + 138*S*HPL[{6}, -S^2] - 1712*S*HPL[{2, 1}, -S^2]^2 + ((-892*Pi^2*S)/3 - (12*(-5 + 38*S^2))/S)*HPL[{3, 1}, -S^2] + (2*(5 + 71*S^2)*HPL[{3, 2}, -S^2])/S + (2*(-44 + 17*S^2)*HPL[{4, 1}, -S^2])/S - 84*S*HPL[{4, 2}, -S^2] - 40*S*HPL[{5, 1}, -S^2] + (604*Pi^2*S + (4*(-35 + 229*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (4*(283 + 65*S^2)*HPL[{2, 2, 1}, -S^2])/S + (4*(853 + 131*S^2)*HPL[{3, 1, 1}, -S^2])/S + 8*S*HPL[{3, 1, 2}, -S^2] + 3384*S*HPL[{3, 2, 1}, -S^2] - 110168*S*HPL[{4, 1, 1}, -S^2] - (48*(46 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 6848*S*HPL[{3, 1, 1, 1}, -S^2] + 13824*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((5*Pi^2*(1 + 2*S^2))/(3*S) + (4*(2 + 13*S^2))/S)*Zeta[3] + 32*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-36*(17 + S^2))/S - (17*Pi^2*(17 + S^2))/(3*S) + 64*S*Zeta[3]) - (2*(17 + 4*S^2)*Zeta[5])/S) + Log[T]^3*((200*Pi^2*S)/3 + (1523*Pi^4*S)/90 + (13364*Pi^6*S)/2835 + (19*S*HPL[{0}, S^2]^6)/36 + ((290*Pi^2*S)/3 + (200*(1 + S^2))/S)*HPL[{1}, -S^2]^4 + (224*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) + (448*S*HPL[{1}, -S^2]^6)/9 + HPL[{0}, S^2]^5*((28*S)/9 + (271*S*HPL[{1}, -S^2])/90) + ((808*Pi^2*S)/9 + (14*(5 + 14*S^2))/S)*HPL[{2}, -S^2]^2 + (784*S*HPL[{2}, -S^2]^3)/9 + HPL[{0}, S^2]^4*((73*S)/6 + (95*Pi^2*S)/18 + (253*(1 + S^2)*HPL[{1}, -S^2])/(18*S) + (142*S*HPL[{1}, -S^2]^2)/9 + (133*S*HPL[{2}, -S^2])/9) + (296*S*HPL[{3}, -S^2]^2)/3 + ((-520*Pi^2*S)/9 - (4*(6 + 115*S^2))/(3*S))*HPL[{4}, -S^2] + (4*(-1 + 3*S^2)*HPL[{5}, -S^2])/S - 24*S*HPL[{6}, -S^2] - (3160*S*HPL[{2, 1}, -S^2]^2)/3 + ((-3008*Pi^2*S)/9 - (8*(-159 + 224*S^2))/(3*S))*HPL[{3, 1}, -S^2] + (4*(-56 + 407*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (16*(-19 + 333*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (1144*S*HPL[{4, 2}, -S^2])/3 + (5168*S*HPL[{5, 1}, -S^2])/3 + ((6800*Pi^2*S)/9 + (80*(-23 + 54*S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (64*(73 + 25*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (16*(861 + 85*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (640*S*HPL[{3, 1, 2}, -S^2])/3 + (5632*S*HPL[{3, 2, 1}, -S^2])/3 + 4832*S*HPL[{4, 1, 1}, -S^2] + (160*(-21 + 5*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 3520*S*HPL[{3, 1, 1, 1}, -S^2] + 8960*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-584*S)/3 - (316*Pi^2*S)/9)*Zeta[3] - 8*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((4120*(1 + S^2))/(9*S) + (1000*Pi^2*(1 + S^2))/(9*S) + (520*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (7600*S*HPL[{3}, -S^2])/9 - (2000*S*Zeta[3])/3) + HPL[{3}, -S^2]*((-2*Pi^2*(-2 + 71*S^2))/(3*S) - (4*(37 + 237*S^2))/(3*S) - (640*S*HPL[{2, 1}, -S^2])/3 - 96*S*Zeta[3]) + HPL[{0}, S^2]^3*(78*S + (560*Pi^2*S)/27 + (536*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + (1460*S*HPL[{1}, -S^2]^3)/27 + (2*(-10 + 241*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((212*Pi^2*S)/9 + (190*(1 + S^2))/(3*S) + (220*S*HPL[{2}, -S^2])/3) - 2*S*HPL[{3}, -S^2] + (76*S*HPL[{2, 1}, -S^2])/9 - (28*S*Zeta[3])/9) + HPL[{2, 1}, -S^2]*((8*Pi^2*(-321 + 29*S^2))/(9*S) + (8*(-325 + 73*S^2))/(3*S) + (160*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((6673*Pi^4*S)/135 + (2528*(1 + S^2))/(3*S) + (1600*Pi^2*(1 + S^2))/(9*S) + ((784*Pi^2*S)/9 + (264*(1 + S^2))/S)*HPL[{2}, -S^2] + (1568*S*HPL[{2}, -S^2]^2)/3 - (1120*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (1328*S*HPL[{4}, -S^2])/3 - (520*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (1328*S*HPL[{3, 1}, -S^2])/3 - (240*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((325*Pi^4*S)/9 + (4*(-43 + 100*S^2))/S + (2*Pi^2*(-125 + 566*S^2))/(9*S) - (40*(-5 + 22*S^2)*HPL[{3}, -S^2])/(3*S) - (1096*S*HPL[{4}, -S^2])/3 - (32*(73 + 25*S^2)*HPL[{2, 1}, -S^2])/(3*S) - 832*S*HPL[{3, 1}, -S^2] + (6320*S*HPL[{2, 1, 1}, -S^2])/3 - (32*(3 + 23*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^2*(200*S + (163*Pi^2*S)/3 + (2731*Pi^4*S)/180 + (440*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (310*S*HPL[{1}, -S^2]^4)/3 + ((232*Pi^2*S)/3 + (4*(-5 + 148*S^2))/(3*S))*HPL[{2}, -S^2] + (413*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((749*Pi^2*S)/9 + (700*(1 + S^2))/(3*S) + (784*S*HPL[{2}, -S^2])/3) + (2*(21 + 2*S^2)*HPL[{3}, -S^2])/(3*S) + (20*S*HPL[{4}, -S^2])/3 - (4*(327 + 17*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (1688*S*HPL[{3, 1}, -S^2])/3 + (3440*S*HPL[{2, 1, 1}, -S^2])/3 - (16*S*Zeta[3])/3 + HPL[{1}, -S^2]*((788*(1 + S^2))/(3*S) + (583*Pi^2*(1 + S^2))/(9*S) + (614*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (88*S*HPL[{3}, -S^2])/3 - (1568*S*HPL[{2, 1}, -S^2])/3 - (164*S*Zeta[3])/3)) - (176*S*Zeta[5])/3 + HPL[{1}, -S^2]*((3340*(1 + S^2))/(3*S) + (202*Pi^2*(1 + S^2))/S + (8587*Pi^4*(1 + S^2))/(270*S) + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-1988*Pi^2*S)/9 - (1160*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (448*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - 288*S*HPL[{5}, -S^2] + ((-1568*Pi^2*S)/9 - (528*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (896*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (6272*S*HPL[{3, 2}, -S^2])/3 + (21472*S*HPL[{4, 1}, -S^2])/3 + (1040*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (12544*S*HPL[{2, 2, 1}, -S^2])/3 + (22432*S*HPL[{3, 1, 1}, -S^2])/3 + ((-1664*Pi^2*S)/9 - (800*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((276*(1 + S^2))/S + (1004*Pi^2*(1 + S^2))/(9*S) - (3136*S*HPL[{3}, -S^2])/3 - (6272*S*HPL[{2, 1}, -S^2])/3 - (3136*S*Zeta[3])/3) - (3040*S*Zeta[5])/3) + HPL[{0}, S^2]*((3340*S)/3 + (1732*Pi^2*S)/9 + (4036*Pi^4*S)/135 + (560*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + (448*S*HPL[{1}, -S^2]^5)/3 + (8*(3 + 91*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((4820*Pi^2*S)/27 + (400*(1 + S^2))/S + (2000*S*HPL[{2}, -S^2])/3) + ((-128*Pi^2*S)/9 - (4*(-29 + 7*S^2))/(3*S))*HPL[{3}, -S^2] + (4*(3 + 11*S^2)*HPL[{4}, -S^2])/(3*S) + (44*S*HPL[{5}, -S^2])/3 + ((256*Pi^2*S)/9 - (56*(59 + 4*S^2))/(3*S))*HPL[{2, 1}, -S^2] - (56*(-5 + 51*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (472*S*HPL[{3, 2}, -S^2])/3 + (1360*S*HPL[{4, 1}, -S^2])/3 + (160*(-1 + 12*S^2)*HPL[{2, 1, 1}, -S^2])/S + (272*S*HPL[{2, 2, 1}, -S^2])/3 - (64*S*HPL[{3, 1, 1}, -S^2])/3 + 480*S*HPL[{2, 1, 1, 1}, -S^2] + ((-368*S)/3 - (388*Pi^2*S)/9)*Zeta[3] + HPL[{1}, -S^2]^2*((2060*(1 + S^2))/(3*S) + (1376*Pi^2*(1 + S^2))/(9*S) + (500*(1 + S^2)*HPL[{2}, -S^2])/S - (136*S*HPL[{3}, -S^2])/3 - 2000*S*HPL[{2, 1}, -S^2] - (664*S*Zeta[3])/3) + HPL[{2}, -S^2]*((4*(3 + 401*S^2))/(3*S) + (2*Pi^2*(-40 + 601*S^2))/(9*S) - (224*S*HPL[{3}, -S^2])/3 - (136*S*HPL[{2, 1}, -S^2])/3 - (656*S*Zeta[3])/3) + HPL[{1}, -S^2]*((4061*Pi^4*S)/90 + (2528*(1 + S^2))/(3*S) + (490*Pi^2*(1 + S^2))/(3*S) + (240*Pi^2*S + (1592*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (1568*S*HPL[{2}, -S^2]^2)/3 - (80*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (184*S*HPL[{4}, -S^2])/3 - (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 2000*S*HPL[{3, 1}, -S^2] + 4000*S*HPL[{2, 1, 1}, -S^2] - (320*(1 + S^2)*Zeta[3])/(3*S)) - (520*S*Zeta[5])/3)) + HPL[{0}, S^2]^3*(-220*S - 34*Pi^2*S - (2933*Pi^4*S)/540 - (52021*Pi^6*S)/90720 - (268*(1 + S^2)*HPL[{1}, -S^2]^5)/(45*S) - (73*S*HPL[{1}, -S^2]^6)/27 + ((-541*Pi^2*S)/72 - (2*(-1 + 29*S^2))/(3*S))*HPL[{2}, -S^2]^2 - (26*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((-53*Pi^2*S)/9 - (95*(1 + S^2))/(6*S) - (55*S*HPL[{2}, -S^2])/3) + (5*S*HPL[{3}, -S^2]^2)/6 + ((-29*Pi^2*S)/9 + (2*(5 + 4*S^2))/(3*S))*HPL[{4}, -S^2] - (2*(-10 + 7*S^2)*HPL[{5}, -S^2])/(3*S) - 21*S*HPL[{6}, -S^2] + (325*S*HPL[{2, 1}, -S^2]^2)/3 + ((607*Pi^2*S)/18 + (2*(-5 + 116*S^2))/(3*S))*HPL[{3, 1}, -S^2] + ((8 + 3*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2*(13 + 10*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (2*S*HPL[{4, 2}, -S^2])/3 + (76*S*HPL[{5, 1}, -S^2])/3 + ((-482*S)/3 - (605*Pi^2*S)/9)*HPL[{2, 1, 1}, -S^2] - (8*(59 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2*(728 + 19*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (2*S*HPL[{3, 1, 2}, -S^2])/3 - (626*S*HPL[{3, 2, 1}, -S^2])/3 - (1954*S*HPL[{4, 1, 1}, -S^2])/3 + (4*(258 + 7*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (1384*S*HPL[{3, 1, 1, 1}, -S^2])/3 - (2792*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((10*S)/3 - (79*Pi^2*S)/18)*Zeta[3] + S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(156 - S^2))/(6*S) + (2*(134 + 21*S^2))/(3*S) - (2*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((-329*(1 + S^2))/(9*S) - (523*Pi^2*(1 + S^2))/(54*S) - (248*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (4*S*HPL[{3}, -S^2])/3 + (220*S*HPL[{2, 1}, -S^2])/3 + (22*S*Zeta[3])/9) + HPL[{3}, -S^2]*((Pi^2*(-10 - 11*S^2))/(18*S) - (2*(5 + 16*S^2))/(3*S) - (10*S*HPL[{2, 1}, -S^2])/3 + 4*S*Zeta[3]) + HPL[{2}, -S^2]*((-109*Pi^2*S)/9 - (959*Pi^4*S)/270 - (2*(10 + 61*S^2))/(3*S) - (2*(2 + S^2)*HPL[{3}, -S^2])/(3*S) - 2*S*HPL[{4}, -S^2] + (4*(59 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (322*S*HPL[{3, 1}, -S^2])/3 - (650*S*HPL[{2, 1, 1}, -S^2])/3 + ((-12 - S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-3997*Pi^4*S)/1080 - (72*(1 + S^2))/S - (575*Pi^2*(1 + S^2))/(36*S) + ((-187*Pi^2*S)/12 - (44*(1 + S^2))/S)*HPL[{2}, -S^2] - (53*S*HPL[{2}, -S^2]^2)/2 - (2*(1 + S^2)*HPL[{3}, -S^2])/S - (17*S*HPL[{4}, -S^2])/3 + (248*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + 110*S*HPL[{3, 1}, -S^2] - 220*S*HPL[{2, 1, 1}, -S^2] + ((-1 - S^2)*Zeta[3])/S) - (22*S*Zeta[5])/3 + HPL[{1}, -S^2]*((-110*(1 + S^2))/S - (119*Pi^2*(1 + S^2))/(6*S) - (3857*Pi^4*(1 + S^2))/(1080*S) - (39*(1 + S^2)*HPL[{2}, -S^2]^2)/(2*S) + ((-7*Pi^2*S)/6 - (14*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (2*(1 + S^2)*HPL[{4}, -S^2])/S - (23*S*HPL[{5}, -S^2])/3 + ((187*Pi^2*S)/6 + (88*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (82*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (14*S*HPL[{3, 2}, -S^2])/3 - (8*S*HPL[{4, 1}, -S^2])/3 - (496*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - 212*S*HPL[{2, 2, 1}, -S^2] - 644*S*HPL[{3, 1, 1}, -S^2] + 440*S*HPL[{2, 1, 1, 1}, -S^2] + ((11*Pi^2*S)/18 - (17*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-48*(1 + S^2))/S - (229*Pi^2*(1 + S^2))/(18*S) + (7*S*HPL[{3}, -S^2])/3 + 106*S*HPL[{2, 1}, -S^2] + 3*S*Zeta[3]) + (16*S*Zeta[5])/3)) + HPL[{0}, S^2]^2*((-80*Pi^2*S)/3 - (347*Pi^4*S)/60 - (2323*Pi^6*S)/1890 - (22*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) - (62*S*HPL[{1}, -S^2]^7)/21 - (5*(-2 + 27*S^2)*HPL[{2}, -S^2]^3)/(6*S) + HPL[{1}, -S^2]^5*((-749*Pi^2*S)/90 - (70*(1 + S^2))/(3*S) - (392*S*HPL[{2}, -S^2])/15) + ((-1 + 3*S^2)*HPL[{3}, -S^2]^2)/S + ((115*Pi^2*S)/12 + (-23 - 47*S^2)/S)*HPL[{5}, -S^2] + ((-35 + 17*S^2)*HPL[{6}, -S^2])/S + 93*S*HPL[{7}, -S^2] + (2*(-4 + 141*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-43*Pi^2*S)/6 + (7 - S^2)/(2*S))*HPL[{3, 2}, -S^2] + ((-61*Pi^2*S)/2 + (3*(15 + 8*S^2))/S)*HPL[{4, 1}, -S^2] + ((-3 + 8*S^2)*HPL[{4, 2}, -S^2])/(2*S) - 10*S*HPL[{4, 3}, -S^2] + (4*(5 + 6*S^2)*HPL[{5, 1}, -S^2])/S - (57*S*HPL[{5, 2}, -S^2])/2 - 129*S*HPL[{6, 1}, -S^2] + ((-13*Pi^2*S)/3 - (12*(52 + 3*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((35*Pi^2*S)/3 - (2*(957 + 67*S^2))/S)*HPL[{3, 1, 1}, -S^2] + ((-3 - S^2)*HPL[{3, 1, 2}, -S^2])/S + ((37 - 541*S^2)*HPL[{3, 2, 1}, -S^2])/S + 85*S*HPL[{3, 2, 2}, -S^2] + 244*S*HPL[{3, 3, 1}, -S^2] - (2*(-57 + 824*S^2)*HPL[{4, 1, 1}, -S^2])/S + 247*S*HPL[{4, 1, 2}, -S^2] + 715*S*HPL[{4, 2, 1}, -S^2] + 1478*S*HPL[{5, 1, 1}, -S^2] + (-42*Pi^2*S + (8*(167 + 14*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - 104*S*HPL[{2, 2, 2, 1}, -S^2] + (4*(-23 + 286*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + 140*S*HPL[{3, 1, 1, 2}, -S^2] + 140*S*HPL[{3, 1, 2, 1}, -S^2] + 452*S*HPL[{3, 2, 1, 1}, -S^2] + 1296*S*HPL[{4, 1, 1, 1}, -S^2] - (80*(-2 + 29*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + 136*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 408*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 1104*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 608*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (-28*S - (31*Pi^2*S)/6 - (373*Pi^4*S)/360)*Zeta[3] - 8*S*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((11 + 299*S^2)/S + (Pi^2*(-23 + 503*S^2))/(6*S) - 74*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(-39 - 20*S^2))/(12*S) + (-11 + 23*S^2)/S - 3*S*HPL[{2, 1}, -S^2] - 12*S*Zeta[3]) + HPL[{1}, -S^2]^4*((-197*(1 + S^2))/(3*S) - (583*Pi^2*(1 + S^2))/(36*S) - (307*(1 + S^2)*HPL[{2}, -S^2])/(6*S) + (22*S*HPL[{3}, -S^2])/3 + (392*S*HPL[{2, 1}, -S^2])/3 + (41*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((-5*(-1 + 30*S^2))/(2*S) - (5*Pi^2*(-2 + 49*S^2))/(12*S) + (21*S*HPL[{3}, -S^2])/2 - 13*S*HPL[{2, 1}, -S^2] + (37*S*Zeta[3])/2) + HPL[{2, 1, 1}, -S^2]*(-624*S - (4*Pi^2*(-8 + 129*S^2))/(3*S) + 152*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-134*Pi^4*S)/45 + (Pi^2*(194 + 17*S^2))/(2*S) + (2*(199 + 33*S^2))/S - 32*S*HPL[{3, 1}, -S^2] - 68*S*HPL[{2, 1, 1}, -S^2] + (2*(-7 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((133*Pi^4*S)/90 + (Pi^2*(-57 - 55*S^2))/(12*S) + (-11 - 50*S^2)/S + 4*S*HPL[{4}, -S^2] + ((-13 - 11*S^2)*HPL[{2, 1}, -S^2])/S - 36*S*HPL[{3, 1}, -S^2] + 84*S*HPL[{2, 1, 1}, -S^2] - (2*(-4 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-8449*Pi^4*S)/1080 - (476*(1 + S^2))/(3*S) - (103*Pi^2*(1 + S^2))/(3*S) + ((-211*Pi^2*S)/6 - (108*(1 + S^2))/S)*HPL[{2}, -S^2] - (215*S*HPL[{2}, -S^2]^2)/3 - (2*(1 + S^2)*HPL[{3}, -S^2])/S + (8*S*HPL[{4}, -S^2])/3 + (614*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (772*S*HPL[{3, 1}, -S^2])/3 - (1568*S*HPL[{2, 1, 1}, -S^2])/3 + (16*(1 + S^2)*Zeta[3])/(3*S)) + (-54*S - (13*Pi^2*S)/3)*Zeta[5] + HPL[{2}, -S^2]*(-160*S - (259*Pi^2*S)/6 + (Pi^4*(65 - 1601*S^2))/(180*S) + ((7*Pi^2*S)/2 + (-5 - S^2)/(2*S))*HPL[{3}, -S^2] + ((7 - 16*S^2)*HPL[{4}, -S^2])/(2*S) - (7*S*HPL[{5}, -S^2])/2 + ((13*Pi^2*S)/6 + (6*(52 + 3*S^2))/S)*HPL[{2, 1}, -S^2] + ((-7 + 281*S^2)*HPL[{3, 1}, -S^2])/S - 43*S*HPL[{3, 2}, -S^2] - 123*S*HPL[{4, 1}, -S^2] - (4*(-4 + 141*S^2)*HPL[{2, 1, 1}, -S^2])/S + 52*S*HPL[{2, 2, 1}, -S^2] - 72*S*HPL[{3, 1, 1}, -S^2] + 68*S*HPL[{2, 1, 1, 1}, -S^2] + ((23*Pi^2*S)/6 + (12 + 11*S^2)/S)*Zeta[3] + 9*S*Zeta[5]) + HPL[{1}, -S^2]^2*((-310*(1 + S^2))/S - (235*Pi^2*(1 + S^2))/(4*S) - (1837*Pi^4*(1 + S^2))/(180*S) - (149*(1 + S^2)*HPL[{2}, -S^2]^2)/(2*S) + ((25*Pi^2*S)/6 - (7*(1 + S^2))/S)*HPL[{3}, -S^2] - (23*(1 + S^2)*HPL[{4}, -S^2])/(2*S) + 12*S*HPL[{5}, -S^2] + ((211*Pi^2*S)/2 + (324*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (304*(1 + S^2)*HPL[{3, 1}, -S^2])/S - 42*S*HPL[{3, 2}, -S^2] - 134*S*HPL[{4, 1}, -S^2] - (614*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 860*S*HPL[{2, 2, 1}, -S^2] - 2492*S*HPL[{3, 1, 1}, -S^2] + 1568*S*HPL[{2, 1, 1, 1}, -S^2] + ((41*Pi^2*S)/6 + (8*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-177*(1 + S^2))/S - (535*Pi^2*(1 + S^2))/(12*S) + 21*S*HPL[{3}, -S^2] + 430*S*HPL[{2, 1}, -S^2] + 39*S*Zeta[3]) + 39*S*Zeta[5]) + HPL[{1}, -S^2]*((-39083*Pi^6*S)/18144 - (460*(1 + S^2))/S - (223*Pi^2*(1 + S^2))/(3*S) - (502*Pi^4*(1 + S^2))/(45*S) + ((-335*Pi^2*S)/12 - (153*(1 + S^2))/(2*S))*HPL[{2}, -S^2]^2 - 32*S*HPL[{2}, -S^2]^3 + ((5*Pi^2*S)/3 - (23*(1 + S^2))/(2*S))*HPL[{4}, -S^2] - (16*(1 + S^2)*HPL[{5}, -S^2])/S + (45*S*HPL[{6}, -S^2])/2 + 430*S*HPL[{2, 1}, -S^2]^2 + ((310*Pi^2*S)/3 + (320*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (12*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (13*(1 + S^2)*HPL[{4, 1}, -S^2])/S + 3*S*HPL[{4, 2}, -S^2] - 16*S*HPL[{5, 1}, -S^2] + (-211*Pi^2*S - (648*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (596*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (1800*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - 768*S*HPL[{3, 2, 1}, -S^2] - 2288*S*HPL[{4, 1, 1}, -S^2] + (1228*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 1544*S*HPL[{3, 1, 1, 1}, -S^2] - 3136*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((17*(1 + S^2))/S - (7*Pi^2*(1 + S^2))/(6*S))*Zeta[3] - 9*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((354*(1 + S^2))/S + (535*Pi^2*(1 + S^2))/(6*S) - 78*S*Zeta[3]) + HPL[{3}, -S^2]*((-16*(1 + S^2))/S - (5*Pi^2*(1 + S^2))/(2*S) - 42*S*HPL[{2, 1}, -S^2] + 2*S*Zeta[3]) + HPL[{2}, -S^2]*((-6731*Pi^4*S)/720 - (199*(1 + S^2))/S - (140*Pi^2*(1 + S^2))/(3*S) + (6*(1 + S^2)*HPL[{3}, -S^2])/S - S*HPL[{4}, -S^2] + (298*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 426*S*HPL[{3, 1}, -S^2] - 860*S*HPL[{2, 1, 1}, -S^2] + (9*(1 + S^2)*Zeta[3])/S) - (14*(1 + S^2)*Zeta[5])/S)) + (-480*S + 186*Pi^2*S)*Zeta[7] + HPL[{2}, -S^2]*((Pi^6*(479 - 6030*S^2))/(1890*S) + (Pi^4*(353 - 3561*S^2))/(180*S) - (10*Pi^2*(-7 + 32*S^2))/(3*S) - 36*S*HPL[{3}, -S^2]^2 + ((85*Pi^2*S)/3 + (10*(5 + 4*S^2))/S)*HPL[{5}, -S^2] - (2*(10 + 43*S^2)*HPL[{6}, -S^2])/S - 220*S*HPL[{7}, -S^2] + (4*(-66 + 125*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-860*Pi^2*S)/3 - (2*(23 + 213*S^2))/S)*HPL[{3, 2}, -S^2] + (-913*Pi^2*S - (2*(13 + 697*S^2))/S)*HPL[{4, 1}, -S^2] - (6*(1 + 21*S^2)*HPL[{4, 2}, -S^2])/S + 132*S*HPL[{4, 3}, -S^2] - (2*(-9 + 239*S^2)*HPL[{5, 1}, -S^2])/S + 312*S*HPL[{5, 2}, -S^2] + 322*S*HPL[{6, 1}, -S^2] + ((836*Pi^2*S)/3 + (4*(-295 + 78*S^2))/S)*HPL[{2, 2, 1}, -S^2] + (-232*Pi^2*S - (20*(-170 + S^2))/S)*HPL[{3, 1, 1}, -S^2] + (78*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (10*(37 + 101*S^2)*HPL[{3, 2, 1}, -S^2])/S + 3142*S*HPL[{3, 2, 2}, -S^2] + 9896*S*HPL[{3, 3, 1}, -S^2] - (4*(343 + 712*S^2)*HPL[{4, 1, 1}, -S^2])/S + 9818*S*HPL[{4, 1, 2}, -S^2] + 30314*S*HPL[{4, 2, 1}, -S^2] + 62196*S*HPL[{5, 1, 1}, -S^2] + ((1624*Pi^2*S)/3 + (216*(11 + 4*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + 3024*S*HPL[{2, 2, 2, 1}, -S^2] + (64*(-180 + 407*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + 2536*S*HPL[{3, 1, 1, 2}, -S^2] + 2536*S*HPL[{3, 1, 2, 1}, -S^2] + 11608*S*HPL[{3, 2, 1, 1}, -S^2] + 33504*S*HPL[{4, 1, 1, 1}, -S^2] - (64*(25 + 73*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - 6272*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 18816*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 45184*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 12448*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((2897*Pi^4*S)/180 + (Pi^2*(11 + 37*S^2))/S + (2*(43 + 140*S^2))/S)*Zeta[3] - 32*S*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((4*(84 + 137*S^2))/S + (Pi^2*(137 + 537*S^2))/(3*S) - 1528*S*Zeta[3]) + HPL[{4}, -S^2]*((44*Pi^2*S)/3 + (18*(-1 + 7*S^2))/S - 118*S*HPL[{2, 1}, -S^2] + 82*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-8*(59 + 153*S^2))/S - (4*Pi^2*(46 + 287*S^2))/(3*S) + 2976*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((971*Pi^4*S)/60 + (7*Pi^2*(29 + 6*S^2))/S + (2*(339 + 142*S^2))/S + 1912*S*HPL[{3, 1}, -S^2] + 3136*S*HPL[{2, 1, 1}, -S^2] - (8*(54 + 5*S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((1639*Pi^4*S)/90 + (2*Pi^2*(-10 + 57*S^2))/(3*S) + (2*(-5 + 164*S^2))/S - 106*S*HPL[{4}, -S^2] - (2*(283 + 65*S^2)*HPL[{2, 1}, -S^2])/S - 1728*S*HPL[{3, 1}, -S^2] + 3424*S*HPL[{2, 1, 1}, -S^2] + (2*(-1 + 11*S^2)*Zeta[3])/S) + (125*Pi^2*S + (46*(1 + 3*S^2))/S)*Zeta[5] + 756*S*Zeta[7]) + HPL[{1}, -S^2]^2*((-1960*(1 + S^2))/S - (485*Pi^2*(1 + S^2))/(2*S) - (5497*Pi^4*(1 + S^2))/(180*S) - (37673*Pi^6*(1 + S^2))/(9072*S) - (83*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - (37*(1 + S^2)*HPL[{3}, -S^2]^2)/S + (40*Pi^2*S - (8*(1 + S^2))/S)*HPL[{5}, -S^2] - (119*(1 + S^2)*HPL[{6}, -S^2])/S + 30*S*HPL[{7}, -S^2] + (784*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-826*Pi^2*S)/3 - (468*(1 + S^2))/S)*HPL[{3, 2}, -S^2] + ((-2818*Pi^2*S)/3 - (1630*(1 + S^2))/S)*HPL[{4, 1}, -S^2] - (117*(1 + S^2)*HPL[{4, 2}, -S^2])/S + 94*S*HPL[{4, 3}, -S^2] - (468*(1 + S^2)*HPL[{5, 1}, -S^2])/S + 204*S*HPL[{5, 2}, -S^2] - 98*S*HPL[{6, 1}, -S^2] + ((-2428*Pi^2*S)/3 - (1608*(1 + S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-5296*Pi^2*S)/3 - (3664*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] - (664*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + 3260*S*HPL[{3, 2, 2}, -S^2] + 9968*S*HPL[{3, 3, 1}, -S^2] - (1544*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + 9812*S*HPL[{4, 1, 2}, -S^2] + 30404*S*HPL[{4, 2, 1}, -S^2] + 62640*S*HPL[{5, 1, 1}, -S^2] + ((1568*Pi^2*S)/3 + (1584*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (896*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - 6272*S*HPL[{3, 1, 1, 2}, -S^2] - 6272*S*HPL[{3, 1, 2, 1}, -S^2] - 6272*S*HPL[{3, 2, 1, 1}, -S^2] - 21472*S*HPL[{4, 1, 1, 1}, -S^2] - (3120*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + 12544*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 37632*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 77920*S*HPL[{3, 1, 1, 1, 1}, -S^2] + ((1013*Pi^4*S)/60 + (312*(1 + S^2))/S + (36*Pi^2*(1 + S^2))/S)*Zeta[3] - (18*(1 + S^2)*Zeta[3]^2)/S + HPL[{3, 1}, -S^2]*((230*(1 + S^2))/S + (416*Pi^2*(1 + S^2))/(3*S) - 1616*S*Zeta[3]) + HPL[{4}, -S^2]*((112*(1 + S^2))/S + (89*Pi^2*(1 + S^2))/(6*S) - 452*S*HPL[{2, 1}, -S^2] + 56*S*Zeta[3]) + HPL[{2}, -S^2]^2*((-431*(1 + S^2))/(2*S) - (115*Pi^2*(1 + S^2))/(2*S) + 466*S*HPL[{3}, -S^2] + 354*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-828*(1 + S^2))/S - (1004*Pi^2*(1 + S^2))/(3*S) + 3136*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((2021*Pi^4*S)/60 + (452*(1 + S^2))/S + (174*Pi^2*(1 + S^2))/S - 3136*S*HPL[{3, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2] - (448*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((601*Pi^4*S)/30 + (344*(1 + S^2))/S + (46*Pi^2*(1 + S^2))/S - 86*S*HPL[{4}, -S^2] - (452*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 1568*S*HPL[{3, 1}, -S^2] + 3136*S*HPL[{2, 1, 1}, -S^2] + (48*(1 + S^2)*Zeta[3])/S) + ((419*Pi^2*S)/3 + (144*(1 + S^2))/S)*Zeta[5] + HPL[{2}, -S^2]*((-255*(1 + S^2))/S - (187*Pi^2*(1 + S^2))/(2*S) - (1315*Pi^4*(1 + S^2))/(72*S) + ((413*Pi^2*S)/3 + (234*(1 + S^2))/S)*HPL[{3}, -S^2] + (113*(1 + S^2)*HPL[{4}, -S^2])/S + 164*S*HPL[{5}, -S^2] + ((1214*Pi^2*S)/3 + (804*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (784*(1 + S^2)*HPL[{3, 1}, -S^2])/S - 1708*S*HPL[{3, 2}, -S^2] - 5140*S*HPL[{4, 1}, -S^2] - (1568*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + 3136*S*HPL[{3, 1, 1}, -S^2] + 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((431*Pi^2*S)/3 + (252*(1 + S^2))/S)*Zeta[3] + 722*S*Zeta[5]) + 966*S*Zeta[7]) + Log[T]^2*((-320*Pi^2*S)/3 - (261*Pi^4*S)/10 - (4646*Pi^6*S)/945 - (S*HPL[{0}, S^2]^7)/8 + (-58*Pi^2*S - (120*(1 + S^2))/S)*HPL[{1}, -S^2]^5 - (112*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) - (64*S*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^6*((-3*S)/4 - (3*S*HPL[{1}, -S^2])/4) - (2*(-66 + 125*S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^5*((-21*S)/4 - (149*Pi^2*S)/90 - (17*(1 + S^2)*HPL[{1}, -S^2])/(4*S) - (271*S*HPL[{1}, -S^2]^2)/60 - (64*S*HPL[{2}, -S^2])/15) - (4*(-1 + 16*S^2)*HPL[{3}, -S^2]^2)/S + ((259*Pi^2*S)/3 - (4*(2 + 13*S^2))/S)*HPL[{5}, -S^2] - (4*(25 + 17*S^2)*HPL[{6}, -S^2])/S + 152*S*HPL[{7}, -S^2] + (16*(25 + 73*S^2)*HPL[{2, 1}, -S^2]^2)/S + (-578*Pi^2*S - (2*(-29 + 423*S^2))/S)*HPL[{3, 2}, -S^2] + ((-5596*Pi^2*S)/3 - (4*(2 + 685*S^2))/S)*HPL[{4, 1}, -S^2] - (2*(-7 + 114*S^2)*HPL[{4, 2}, -S^2])/S + 172*S*HPL[{4, 3}, -S^2] - (12*(-5 + 79*S^2)*HPL[{5, 1}, -S^2])/S + 346*S*HPL[{5, 2}, -S^2] - 384*S*HPL[{6, 1}, -S^2] + ((-1624*Pi^2*S)/3 - (216*(11 + 4*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-1120*Pi^2*S)/3 - (8*(865 + 104*S^2))/S)*HPL[{3, 1, 1}, -S^2] + (44*(-4 + 3*S^2)*HPL[{3, 1, 2}, -S^2])/S - (4*(-220 + 467*S^2)*HPL[{3, 2, 1}, -S^2])/S + 6368*S*HPL[{3, 2, 2}, -S^2] + 19920*S*HPL[{3, 3, 1}, -S^2] - (32*(-99 + 161*S^2)*HPL[{4, 1, 1}, -S^2])/S + 19784*S*HPL[{4, 1, 2}, -S^2] + 60872*S*HPL[{4, 2, 1}, -S^2] + 125040*S*HPL[{5, 1, 1}, -S^2] + ((-3664*Pi^2*S)/3 - (16*(-313 + 72*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - 6272*S*HPL[{2, 2, 2, 1}, -S^2] + (16*(-165 + 227*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + 5632*S*HPL[{3, 1, 1, 2}, -S^2] + 5632*S*HPL[{3, 1, 2, 1}, -S^2] + 24448*S*HPL[{3, 2, 1, 1}, -S^2] + 70432*S*HPL[{4, 1, 1, 1}, -S^2] - (960*(-4 + 9*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + 12448*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 37344*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 90560*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 26880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (296*S + (148*Pi^2*S)/3 + (3353*Pi^4*S)/90)*Zeta[3] - 32*S*Zeta[3]^2 + HPL[{3, 1}, -S^2]*((4*(-161 + 227*S^2))/S + (2*Pi^2*(-188 + 513*S^2))/(3*S) - 3088*S*Zeta[3]) + HPL[{0}, S^2]^4*((-103*S)/6 - (251*Pi^2*S)/36 - (253*(1 + S^2)*HPL[{1}, -S^2]^2)/(12*S) - (142*S*HPL[{1}, -S^2]^3)/9 + ((6 - 113*S^2)*HPL[{2}, -S^2])/(6*S) + HPL[{1}, -S^2]*((-277*Pi^2*S)/36 - (67*(1 + S^2))/(3*S) - (241*S*HPL[{2}, -S^2])/12) + (7*S*HPL[{3}, -S^2])/4 - (25*S*HPL[{2, 1}, -S^2])/6 - (7*S*Zeta[3])/6) + HPL[{4}, -S^2]*((4*(2 + 71*S^2))/S + (Pi^2*(-3 + 92*S^2))/(3*S) + 192*S*HPL[{2, 1}, -S^2] + 124*S*Zeta[3]) + HPL[{1}, -S^2]^4*((-1030*(1 + S^2))/(3*S) - (250*Pi^2*(1 + S^2))/(3*S) - (130*(1 + S^2)*HPL[{2}, -S^2])/S + (1900*S*HPL[{3}, -S^2])/3 + 500*S*Zeta[3]) + HPL[{2}, -S^2]^2*((Pi^2*(-46 - 287*S^2))/(3*S) - (2*(59 + 153*S^2))/S + 856*S*HPL[{3}, -S^2] - 784*S*HPL[{2, 1}, -S^2] + 744*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-560*Pi^2*(-1 + 4*S^2))/(3*S) - (16*(-59 + 140*S^2))/S + 6112*S*Zeta[3]) + HPL[{1}, -S^2]^3*((-6673*Pi^4*S)/135 - (2528*(1 + S^2))/(3*S) - (1600*Pi^2*(1 + S^2))/(9*S) + ((-784*Pi^2*S)/9 - (264*(1 + S^2))/S)*HPL[{2}, -S^2] - (1568*S*HPL[{2}, -S^2]^2)/3 + (1120*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (1328*S*HPL[{4}, -S^2])/3 + (520*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (1328*S*HPL[{3, 1}, -S^2])/3 + (240*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-1229*Pi^4*S)/30 - (2*Pi^2*(-647 + 44*S^2))/(3*S) - (4*(-355 + 74*S^2))/S - 3776*S*HPL[{3, 1}, -S^2] - 6224*S*HPL[{2, 1, 1}, -S^2] - (160*(5 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((118*Pi^4*S)/3 + (8*(10 + 63*S^2))/S + (Pi^2*(5 + 207*S^2))/(3*S) - 172*S*HPL[{4}, -S^2] - (24*(46 + S^2)*HPL[{2, 1}, -S^2])/S - 3424*S*HPL[{3, 1}, -S^2] + 6912*S*HPL[{2, 1, 1}, -S^2] + (12*(-1 + 4*S^2)*Zeta[3])/S) + HPL[{0}, S^2]^3*((-454*S)/3 - (617*Pi^2*S)/18 - (1022*Pi^4*S)/135 - (536*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (365*S*HPL[{1}, -S^2]^4)/9 + ((-241*S)/3 - (605*Pi^2*S)/18)*HPL[{2}, -S^2] - (325*S*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((-106*Pi^2*S)/3 - (95*(1 + S^2))/S - 110*S*HPL[{2}, -S^2]) + ((-20 - 7*S^2)*HPL[{3}, -S^2])/(3*S) - (41*S*HPL[{4}, -S^2])/3 + (2*(258 + 7*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (692*S*HPL[{3, 1}, -S^2])/3 - (1396*S*HPL[{2, 1, 1}, -S^2])/3 - (8*S*Zeta[3])/3 + HPL[{1}, -S^2]*((-329*(1 + S^2))/(3*S) - (523*Pi^2*(1 + S^2))/(18*S) - (248*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - 4*S*HPL[{3}, -S^2] + 220*S*HPL[{2, 1}, -S^2] + (22*S*Zeta[3])/3)) + (44*S + 316*Pi^2*S)*Zeta[5] + HPL[{0}, S^2]^2*(-320*S - 81*Pi^2*S - (527*Pi^4*S)/30 - (110*(1 + S^2)*HPL[{1}, -S^2]^4)/S - 62*S*HPL[{1}, -S^2]^5 + ((4 - 141*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((-749*Pi^2*S)/9 - (700*(1 + S^2))/(3*S) - (784*S*HPL[{2}, -S^2])/3) + ((37*Pi^2*S)/3 + (-21 - 13*S^2)/S)*HPL[{3}, -S^2] + ((-3 - 14*S^2)*HPL[{4}, -S^2])/S + 37*S*HPL[{5}, -S^2] + (-21*Pi^2*S + (4*(167 + 14*S^2))/S)*HPL[{2, 1}, -S^2] + (2*(-23 + 286*S^2)*HPL[{3, 1}, -S^2])/S - 86*S*HPL[{3, 2}, -S^2] - 288*S*HPL[{4, 1}, -S^2] - (40*(-2 + 29*S^2)*HPL[{2, 1, 1}, -S^2])/S - 68*S*HPL[{2, 2, 1}, -S^2] + 8*S*HPL[{3, 1, 1}, -S^2] - 304*S*HPL[{2, 1, 1, 1}, -S^2] + (4*S + (38*Pi^2*S)/3)*Zeta[3] + HPL[{2}, -S^2]*(-312*S - (2*Pi^2*(-8 + 129*S^2))/(3*S) + 42*S*HPL[{3}, -S^2] + 34*S*HPL[{2, 1}, -S^2] + 76*S*Zeta[3]) + HPL[{1}, -S^2]^2*((-394*(1 + S^2))/S - (583*Pi^2*(1 + S^2))/(6*S) - (307*(1 + S^2)*HPL[{2}, -S^2])/S + 44*S*HPL[{3}, -S^2] + 784*S*HPL[{2, 1}, -S^2] + 82*S*Zeta[3]) + HPL[{1}, -S^2]*((-8449*Pi^4*S)/360 - (476*(1 + S^2))/S - (103*Pi^2*(1 + S^2))/S + ((-211*Pi^2*S)/2 - (324*(1 + S^2))/S)*HPL[{2}, -S^2] - 215*S*HPL[{2}, -S^2]^2 - (6*(1 + S^2)*HPL[{3}, -S^2])/S + 8*S*HPL[{4}, -S^2] + (614*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 772*S*HPL[{3, 1}, -S^2] - 1568*S*HPL[{2, 1, 1}, -S^2] + (16*(1 + S^2)*Zeta[3])/S) + 78*S*Zeta[5]) + HPL[{2}, -S^2]*((Pi^4*(269 - 1679*S^2))/(45*S) - (40*(-7 + 16*S^2))/S - (2*Pi^2*(-59 + 296*S^2))/(3*S) + (302*Pi^2*S + (2*(-35 + 229*S^2))/S)*HPL[{3}, -S^2] + (2*(-7 + 104*S^2)*HPL[{4}, -S^2])/S + 354*S*HPL[{5}, -S^2] + ((812*Pi^2*S)/3 + (108*(11 + 4*S^2))/S)*HPL[{2, 1}, -S^2] + (64*(9 + 16*S^2)*HPL[{3, 1}, -S^2])/S - 3268*S*HPL[{3, 2}, -S^2] - 10464*S*HPL[{4, 1}, -S^2] - (32*(25 + 73*S^2)*HPL[{2, 1, 1}, -S^2])/S + 3136*S*HPL[{2, 2, 1}, -S^2] - 2496*S*HPL[{3, 1, 1}, -S^2] + 6224*S*HPL[{2, 1, 1, 1}, -S^2] + (280*Pi^2*S + (4*(21 + 100*S^2))/S)*Zeta[3] + 1464*S*Zeta[5]) + HPL[{1}, -S^2]^2*((-1670*(1 + S^2))/S - (303*Pi^2*(1 + S^2))/S - (8587*Pi^4*(1 + S^2))/(180*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((994*Pi^2*S)/3 + (580*(1 + S^2))/S)*HPL[{3}, -S^2] + (224*(1 + S^2)*HPL[{4}, -S^2])/S + 432*S*HPL[{5}, -S^2] + ((784*Pi^2*S)/3 + (792*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (448*(1 + S^2)*HPL[{3, 1}, -S^2])/S - 3136*S*HPL[{3, 2}, -S^2] - 10736*S*HPL[{4, 1}, -S^2] - (1560*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 6272*S*HPL[{2, 2, 1}, -S^2] - 11216*S*HPL[{3, 1, 1}, -S^2] + ((832*Pi^2*S)/3 + (400*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-414*(1 + S^2))/S - (502*Pi^2*(1 + S^2))/(3*S) + 1568*S*HPL[{3}, -S^2] + 3136*S*HPL[{2, 1}, -S^2] + 1568*S*Zeta[3]) + 1520*S*Zeta[5]) + HPL[{1}, -S^2]*((-52285*Pi^6*S)/4536 - (2420*(1 + S^2))/S - (1108*Pi^2*(1 + S^2))/(3*S) - (4691*Pi^4*(1 + S^2))/(90*S) + ((-607*Pi^2*S)/3 - (402*(1 + S^2))/S)*HPL[{2}, -S^2]^2 - 148*S*HPL[{3}, -S^2]^2 + ((340*Pi^2*S)/3 + (226*(1 + S^2))/S)*HPL[{4}, -S^2] + (8*(1 + S^2)*HPL[{5}, -S^2])/S + 178*S*HPL[{6}, -S^2] + 3136*S*HPL[{2, 1}, -S^2]^2 + ((440*Pi^2*S)/3 + (448*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (904*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (3160*(1 + S^2)*HPL[{4, 1}, -S^2])/S - 468*S*HPL[{4, 2}, -S^2] - 2704*S*HPL[{5, 1}, -S^2] + ((-1568*Pi^2*S)/3 - (1584*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (7168*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + 2656*S*HPL[{4, 1, 1}, -S^2] + (3120*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 2656*S*HPL[{3, 1, 1, 1}, -S^2] + ((484*(1 + S^2))/S + (196*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - 80*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((828*(1 + S^2))/S + (1004*Pi^2*(1 + S^2))/(3*S) - 3136*S*Zeta[3]) + HPL[{3}, -S^2]*((632*(1 + S^2))/S + (274*Pi^2*(1 + S^2))/(3*S) - 3136*S*HPL[{2, 1}, -S^2] + 200*S*Zeta[3]) + HPL[{2}, -S^2]*((-2021*Pi^4*S)/60 - (452*(1 + S^2))/S - (174*Pi^2*(1 + S^2))/S + (452*(1 + S^2)*HPL[{3}, -S^2])/S + 452*S*HPL[{4}, -S^2] + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 3136*S*HPL[{3, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2] + (448*(1 + S^2)*Zeta[3])/S) + (204*(1 + S^2)*Zeta[5])/S) + HPL[{0}, S^2]*(-2420*S - 362*Pi^2*S - (199*Pi^4*S)/4 - (252431*Pi^6*S)/22680 - (112*(1 + S^2)*HPL[{1}, -S^2]^5)/S - (224*S*HPL[{1}, -S^2]^6)/3 + (-182*Pi^2*S + (-21 - 368*S^2)/S)*HPL[{2}, -S^2]^2 - (746*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((-1205*Pi^2*S)/9 - (300*(1 + S^2))/S - 500*S*HPL[{2}, -S^2]) + 24*S*HPL[{3}, -S^2]^2 + ((-89*Pi^2*S)/3 - (2*(5 + 7*S^2))/S)*HPL[{4}, -S^2] - (2*(9 + 25*S^2)*HPL[{5}, -S^2])/S - 166*S*HPL[{6}, -S^2] + ((2*Pi^2*(663 + 22*S^2))/(3*S) + (8*(223 + 24*S^2))/S)*HPL[{2, 1}, -S^2] + 3068*S*HPL[{2, 1}, -S^2]^2 + (756*Pi^2*S + (4*(-20 + 363*S^2))/S)*HPL[{3, 1}, -S^2] - (2*(-19 + 36*S^2)*HPL[{3, 2}, -S^2])/S - (4*(-47 + 45*S^2)*HPL[{4, 1}, -S^2])/S + 6*S*HPL[{4, 2}, -S^2] + 252*S*HPL[{5, 1}, -S^2] + ((-4576*Pi^2*S)/3 - (40*(-3 + 74*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (32*(95 + 7*S^2)*HPL[{2, 2, 1}, -S^2])/S - (8*(1167 + 71*S^2)*HPL[{3, 1, 1}, -S^2])/S - 24*S*HPL[{3, 1, 2}, -S^2] - 5992*S*HPL[{3, 2, 1}, -S^2] - 18288*S*HPL[{4, 1, 1}, -S^2] + (240*(27 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 12608*S*HPL[{3, 1, 1, 1}, -S^2] - 25440*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (212*S + 26*Pi^2*S)*Zeta[3] - 52*S*Zeta[3]^2 + HPL[{3}, -S^2]*((-4*(17 + 3*S^2))/S + (Pi^2*(-47 + 6*S^2))/(3*S) - 80*S*HPL[{2, 1}, -S^2] + 16*S*Zeta[3]) + HPL[{1}, -S^2]^3*((-2060*(1 + S^2))/(3*S) - (1376*Pi^2*(1 + S^2))/(9*S) - (500*(1 + S^2)*HPL[{2}, -S^2])/S + (136*S*HPL[{3}, -S^2])/3 + 2000*S*HPL[{2, 1}, -S^2] + (664*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-4061*Pi^4*S)/60 - (1264*(1 + S^2))/S - (245*Pi^2*(1 + S^2))/S + (-360*Pi^2*S - (796*(1 + S^2))/S)*HPL[{2}, -S^2] - 784*S*HPL[{2}, -S^2]^2 + (40*(1 + S^2)*HPL[{3}, -S^2])/S - 92*S*HPL[{4}, -S^2] + (1500*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 3000*S*HPL[{3, 1}, -S^2] - 6000*S*HPL[{2, 1, 1}, -S^2] + (160*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-769*Pi^4*S)/12 + (Pi^2*(15 - 611*S^2))/(3*S) - (6*(9 + 152*S^2))/S + (2*(-11 + 17*S^2)*HPL[{3}, -S^2])/S - 50*S*HPL[{4}, -S^2] + (16*(95 + 7*S^2)*HPL[{2, 1}, -S^2])/S + 3064*S*HPL[{3, 1}, -S^2] - 6136*S*HPL[{2, 1, 1}, -S^2] + (4*(-2 + 39*S^2)*Zeta[3])/S) + 152*S*Zeta[5] + HPL[{1}, -S^2]*((-1670*(1 + S^2))/S - (844*Pi^2*(1 + S^2))/(3*S) - (7801*Pi^4*(1 + S^2))/(180*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((22*Pi^2*S)/3 + (24*(1 + S^2))/S)*HPL[{3}, -S^2] - (34*(1 + S^2)*HPL[{4}, -S^2])/S - 92*S*HPL[{5}, -S^2] + (720*Pi^2*S + (1592*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (1488*(1 + S^2)*HPL[{3, 1}, -S^2])/S - 304*S*HPL[{3, 2}, -S^2] - 728*S*HPL[{4, 1}, -S^2] - (3000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 6272*S*HPL[{2, 2, 1}, -S^2] - 18544*S*HPL[{3, 1, 1}, -S^2] + 12000*S*HPL[{2, 1, 1, 1}, -S^2] + ((188*Pi^2*S)/3 + (156*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-898*(1 + S^2))/S - (623*Pi^2*(1 + S^2))/(3*S) + 152*S*HPL[{3}, -S^2] + 3136*S*HPL[{2, 1}, -S^2] + 328*S*Zeta[3]) + 260*S*Zeta[5])) + 2232*S*Zeta[7]) + HPL[{1}, -S^2]*((-13964*Pi^8*S)/14175 - (3920*(1 + S^2))/S - (355*Pi^2*(1 + S^2))/S - (118*Pi^4*(1 + S^2))/(3*S) - (15751*Pi^6*(1 + S^2))/(3240*S) + ((-32*Pi^2*S)/3 - (86*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^3 - 32*S*HPL[{2}, -S^2]^4 + ((-37*Pi^2*S)/3 - (38*(1 + S^2))/S)*HPL[{3}, -S^2]^2 + 18*S*HPL[{4}, -S^2]^2 + ((67*Pi^2*S)/3 - (172*(1 + S^2))/S)*HPL[{6}, -S^2] - (276*(1 + S^2)*HPL[{7}, -S^2])/S + 108*S*HPL[{8}, -S^2] + ((1214*Pi^2*S)/3 + (804*(1 + S^2))/S)*HPL[{2, 1}, -S^2]^2 - 1864*S*HPL[{3, 1}, -S^2]^2 + (-38*Pi^2*S - (114*(1 + S^2))/S)*HPL[{4, 2}, -S^2] + (36*(1 + S^2)*HPL[{4, 3}, -S^2])/S + ((-692*Pi^2*S)/3 - (440*(1 + S^2))/S)*HPL[{5, 1}, -S^2] + (84*(1 + S^2)*HPL[{5, 2}, -S^2])/S + 24*S*HPL[{5, 3}, -S^2] + (298*(1 + S^2)*HPL[{6, 1}, -S^2])/S + 60*S*HPL[{6, 2}, -S^2] - 108*S*HPL[{7, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2]^2 + (-256*Pi^2*S - (688*(1 + S^2))/S)*HPL[{3, 2, 1}, -S^2] + (966*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (2992*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - 532*S*HPL[{3, 3, 2}, -S^2] + ((-1624*Pi^2*S)/3 - (1612*(1 + S^2))/S)*HPL[{4, 1, 1}, -S^2] + (2914*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + 908*S*HPL[{4, 1, 3}, -S^2] + (9226*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - 376*S*HPL[{4, 2, 2}, -S^2] + 2908*S*HPL[{4, 3, 1}, -S^2] + (18952*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + 1688*S*HPL[{5, 1, 2}, -S^2] + 12008*S*HPL[{5, 2, 1}, -S^2] + 31316*S*HPL[{6, 1, 1}, -S^2] + (1328*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((880*Pi^2*S)/3 + (896*(1 + S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] - (5792*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (5792*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - 312*S*HPL[{3, 1, 2, 2}, -S^2] - (9776*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - 312*S*HPL[{3, 2, 1, 2}, -S^2] - 376*S*HPL[{3, 2, 2, 1}, -S^2] - 192*S*HPL[{3, 3, 1, 1}, -S^2] - (30224*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - 936*S*HPL[{4, 1, 1, 2}, -S^2] - 1128*S*HPL[{4, 1, 2, 1}, -S^2] - 1512*S*HPL[{4, 2, 1, 1}, -S^2] - 6560*S*HPL[{5, 1, 1, 1}, -S^2] + ((-3136*Pi^2*S)/3 - (3168*(1 + S^2))/S)*HPL[{2, 1, 1, 1, 1}, -S^2] + (6272*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (18816*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (35840*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + 5312*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (6240*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - 5312*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + ((-29*Pi^2*S)/3 - (4*(1 + S^2))/S)*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((1656*(1 + S^2))/S + (2008*Pi^2*(1 + S^2))/(3*S) - 6272*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((-1892*(1 + S^2))/S - (803*Pi^2*(1 + S^2))/(3*S) - 424*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((-556*(1 + S^2))/S - (238*Pi^2*(1 + S^2))/(3*S) - 104*S*Zeta[3]) + HPL[{5}, -S^2]*((-6*(1 + S^2))/S - (14*Pi^2*(1 + S^2))/(3*S) - 328*S*HPL[{2, 1}, -S^2] - 24*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((-1724*(1 + S^2))/S - (460*Pi^2*(1 + S^2))/S + 2832*S*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((-3908*(1 + S^2))/S - (3592*Pi^2*(1 + S^2))/(3*S) + 8896*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((398*Pi^4*S)/15 + (248*(1 + S^2))/S + (144*Pi^2*(1 + S^2))/S + 6272*S*HPL[{2, 1, 1}, -S^2] - (472*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*(7*Pi^4*S + (80*(1 + S^2))/S + (15*Pi^2*(1 + S^2))/S - (226*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 484*S*HPL[{3, 1}, -S^2] + 904*S*HPL[{2, 1, 1}, -S^2] + (10*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-333*Pi^4*S)/20 - (234*(1 + S^2))/S - (59*Pi^2*(1 + S^2))/S + (150*(1 + S^2)*HPL[{3}, -S^2])/S + 164*S*HPL[{4}, -S^2] + (166*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 164*S*HPL[{3, 1}, -S^2] + (94*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-2021*Pi^4*S)/30 - (904*(1 + S^2))/S - (348*Pi^2*(1 + S^2))/S + (896*(1 + S^2)*Zeta[3])/S) + ((196*(1 + S^2))/S + (37*Pi^2*(1 + S^2))/(3*S))*Zeta[5] + HPL[{2, 1}, -S^2]*((510*(1 + S^2))/S + (187*Pi^2*(1 + S^2))/S + (1315*Pi^4*(1 + S^2))/(36*S) - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + 3416*S*HPL[{3, 2}, -S^2] + 10280*S*HPL[{4, 1}, -S^2] - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 6272*S*HPL[{3, 1, 1}, -S^2] + 12544*S*HPL[{2, 1, 1, 1}, -S^2] + ((-862*Pi^2*S)/3 - (504*(1 + S^2))/S)*Zeta[3] - 1444*S*Zeta[5]) + Zeta[3]*((430*(1 + S^2))/S + (46*Pi^2*(1 + S^2))/S + (109*Pi^4*(1 + S^2))/(36*S) - 124*S*Zeta[5]) + HPL[{3}, -S^2]*((350*(1 + S^2))/S + (142*Pi^2*(1 + S^2))/(3*S) + (391*Pi^4*(1 + S^2))/(90*S) - (30*(1 + S^2)*HPL[{4}, -S^2])/S - 56*S*HPL[{5}, -S^2] + ((-826*Pi^2*S)/3 - (468*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (452*(1 + S^2)*HPL[{3, 1}, -S^2])/S + 344*S*HPL[{3, 2}, -S^2] + 108*S*HPL[{4, 1}, -S^2] + (904*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + 3728*S*HPL[{2, 2, 1}, -S^2] + 10592*S*HPL[{3, 1, 1}, -S^2] - 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((52*Pi^2*S)/3 + (72*(1 + S^2))/S)*Zeta[3] + 64*S*Zeta[5]) + HPL[{2}, -S^2]*((-1049*Pi^6*S)/360 - (330*(1 + S^2))/S - (104*Pi^2*(1 + S^2))/S - (3463*Pi^4*(1 + S^2))/(180*S) - 86*S*HPL[{3}, -S^2]^2 + ((112*Pi^2*S)/3 + (114*(1 + S^2))/S)*HPL[{4}, -S^2] + (54*(1 + S^2)*HPL[{5}, -S^2])/S + 84*S*HPL[{6}, -S^2] + ((1210*Pi^2*S)/3 + (812*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (522*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (1574*(1 + S^2)*HPL[{4, 1}, -S^2])/S - 312*S*HPL[{4, 2}, -S^2] - 1264*S*HPL[{5, 1}, -S^2] + ((-2428*Pi^2*S)/3 - (1608*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (664*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (2896*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + 312*S*HPL[{3, 1, 2}, -S^2] - 2760*S*HPL[{3, 2, 1}, -S^2] - 8312*S*HPL[{4, 1, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 6272*S*HPL[{3, 1, 1, 1}, -S^2] - 12544*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((294*(1 + S^2))/S + (121*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + 6*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((862*(1 + S^2))/S + (230*Pi^2*(1 + S^2))/S - 1416*S*Zeta[3]) + HPL[{3}, -S^2]*((278*(1 + S^2))/S + (119*Pi^2*(1 + S^2))/(3*S) - 1864*S*HPL[{2, 1}, -S^2] + 52*S*Zeta[3]) + (130*(1 + S^2)*Zeta[5])/S) - (60*(1 + S^2)*Zeta[7])/S) + Log[T]*((320*Pi^2*S)/3 + (2449*Pi^4*S)/90 + (12457*Pi^6*S)/2520 + (1761997*Pi^8*S)/1360800 + (S*HPL[{0}, S^2]^8)/48 + ((58*Pi^2*S)/3 + (40*(1 + S^2))/S)*HPL[{1}, -S^2]^6 + (32*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) + (16*S*HPL[{1}, -S^2]^8)/3 + HPL[{0}, S^2]^7*(S/6 + (S*HPL[{1}, -S^2])/8) + ((401*Pi^2*S)/9 + (-123 + 250*S^2)/(3*S))*HPL[{2}, -S^2]^3 + (65*S*HPL[{2}, -S^2]^4)/2 + HPL[{0}, S^2]^6*((3*S)/4 + (47*Pi^2*S)/144 + (5*(1 + S^2)*HPL[{1}, -S^2])/(6*S) + (3*S*HPL[{1}, -S^2]^2)/4 + (17*S*HPL[{2}, -S^2])/24) + ((71*Pi^2*S)/3 + (4*(1 + 18*S^2))/S)*HPL[{3}, -S^2]^2 + 16*S*HPL[{4}, -S^2]^2 + (7*Pi^2*S + (2*(65 + 9*S^2))/S)*HPL[{6}, -S^2] + (2*(95 + 372*S^2)*HPL[{7}, -S^2])/S + 836*S*HPL[{8}, -S^2] + ((-1616*Pi^2*S)/3 - (84*(5 + 14*S^2))/S)*HPL[{2, 1}, -S^2]^2 + 1592*S*HPL[{3, 1}, -S^2]^2 + (95*Pi^2*S + (2*(-7 + 121*S^2))/S)*HPL[{4, 2}, -S^2] - (16*(-1 + S^2)*HPL[{4, 3}, -S^2])/S + ((1262*Pi^2*S)/3 + (8*(-6 + 131*S^2))/S)*HPL[{5, 1}, -S^2] - (2*(-35 + 23*S^2)*HPL[{5, 2}, -S^2])/S - 44*S*HPL[{5, 3}, -S^2] - (8*(2 + 55*S^2)*HPL[{6, 1}, -S^2])/S - 126*S*HPL[{6, 2}, -S^2] - 512*S*HPL[{7, 1}, -S^2] + 6320*S*HPL[{2, 1, 1}, -S^2]^2 + (-52*Pi^2*S - (4*(-41 + 35*S^2))/S)*HPL[{3, 1, 2}, -S^2] + ((3052*Pi^2*S)/3 + (20*(-41 + 93*S^2))/S)*HPL[{3, 2, 1}, -S^2] - (6*(-19 + 274*S^2)*HPL[{3, 2, 2}, -S^2])/S - (16*(-33 + 328*S^2)*HPL[{3, 3, 1}, -S^2])/S + 928*S*HPL[{3, 3, 2}, -S^2] + ((8584*Pi^2*S)/3 + (40*(-75 + 127*S^2))/S)*HPL[{4, 1, 1}, -S^2] - (4*(-131 + 1278*S^2)*HPL[{4, 1, 2}, -S^2])/S - 1512*S*HPL[{4, 1, 3}, -S^2] - (4*(-395 + 4038*S^2)*HPL[{4, 2, 1}, -S^2])/S + 702*S*HPL[{4, 2, 2}, -S^2] - 5288*S*HPL[{4, 3, 1}, -S^2] - (24*(-131 + 1377*S^2)*HPL[{5, 1, 1}, -S^2])/S - 3132*S*HPL[{5, 1, 2}, -S^2] - 21852*S*HPL[{5, 2, 1}, -S^2] - 56304*S*HPL[{6, 1, 1}, -S^2] + (32*(-149 + 42*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((-6016*Pi^2*S)/3 - (16*(-159 + 224*S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] - (8*(-1732 + 97*S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (8*(-1732 + 97*S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + 336*S*HPL[{3, 1, 2, 2}, -S^2] - (8*(-3520 + 601*S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + 336*S*HPL[{3, 2, 1, 2}, -S^2] - 5936*S*HPL[{3, 2, 2, 1}, -S^2] - 18816*S*HPL[{3, 3, 1, 1}, -S^2] - (32*(-2663 + 423*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + 2288*S*HPL[{4, 1, 1, 2}, -S^2] - 16528*S*HPL[{4, 1, 2, 1}, -S^2] - 54160*S*HPL[{4, 2, 1, 1}, -S^2] - 102560*S*HPL[{5, 1, 1, 1}, -S^2] + ((13600*Pi^2*S)/3 + (160*(-23 + 54*S^2))/S)*HPL[{2, 1, 1, 1, 1}, -S^2] - (128*(73 + 25*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (384*(73 + 25*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - 12544*S*HPL[{2, 2, 1, 2, 1}, -S^2] - 37632*S*HPL[{2, 2, 2, 1, 1}, -S^2] - (160*(295 + 143*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + 73984*S*HPL[{3, 1, 1, 1, 2}, -S^2] + 124160*S*HPL[{3, 1, 1, 2, 1}, -S^2] + 149248*S*HPL[{3, 1, 2, 1, 1}, -S^2] + 312320*S*HPL[{3, 2, 1, 1, 1}, -S^2] + 932160*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (960*(-21 + 5*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - 21120*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 53760*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (-4*S - (2*Pi^2*S)/3)*Zeta[3]^2 + HPL[{1}, -S^2]^5*((412*(1 + S^2))/(3*S) + (100*Pi^2*(1 + S^2))/(3*S) + (52*(1 + S^2)*HPL[{2}, -S^2])/S - (760*S*HPL[{3}, -S^2])/3 - 200*S*Zeta[3]) + HPL[{0}, S^2]^5*((77*S)/12 + (35*Pi^2*S)/18 + (17*(1 + S^2)*HPL[{1}, -S^2]^2)/(4*S) + (271*S*HPL[{1}, -S^2]^3)/90 + (11*S*HPL[{2}, -S^2])/3 + HPL[{1}, -S^2]*((293*Pi^2*S)/180 + (29*(1 + S^2))/(6*S) + (77*S*HPL[{2}, -S^2])/20) - (S*HPL[{3}, -S^2])/4 + (5*S*HPL[{2, 1}, -S^2])/6 + (3*S*Zeta[3])/2) + HPL[{0}, S^2]^4*((103*S)/6 + (163*Pi^2*S)/24 + (2731*Pi^4*S)/1440 + (253*(1 + S^2)*HPL[{1}, -S^2]^3)/(18*S) + (71*S*HPL[{1}, -S^2]^4)/9 + ((521*Pi^2*S)/72 + (-4 + 71*S^2)/(4*S))*HPL[{2}, -S^2] + (61*S*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((277*Pi^2*S)/36 + (67*(1 + S^2))/(3*S) + (241*S*HPL[{2}, -S^2])/12) + ((4 + 5*S^2)*HPL[{3}, -S^2])/(4*S) + (9*S*HPL[{4}, -S^2])/4 + ((-120 - S^2)*HPL[{2, 1}, -S^2])/(3*S) + HPL[{1}, -S^2]*((311*(1 + S^2))/(12*S) + (553*Pi^2*(1 + S^2))/(72*S) + (19*(1 + S^2)*HPL[{2}, -S^2])/S - (S*HPL[{3}, -S^2])/2 - (241*S*HPL[{2, 1}, -S^2])/6) - (259*S*HPL[{3, 1}, -S^2])/6 + (266*S*HPL[{2, 1, 1}, -S^2])/3 + (43*S*Zeta[3])/6) + HPL[{5}, -S^2]*((14*(2 + 11*S^2))/S + (Pi^2*(-7 + 45*S^2))/(3*S) - 52*S*HPL[{2, 1}, -S^2] + 12*S*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((60*Pi^2*(40 + 3*S^2))/S + (16*(451 + 69*S^2))/S + 288*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((8*Pi^2*(299 + 58*S^2))/(3*S) + (8*(313 + 125*S^2))/S + 288*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((40*(-1 + 24*S^2))/S + (5*Pi^2*(-11 + 82*S^2))/(3*S) + 304*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((16*Pi^2*(-321 + 29*S^2))/(3*S) + (16*(-325 + 73*S^2))/S + 320*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((24*(4 + 125*S^2))/S + (2*Pi^2*(-61 + 660*S^2))/(3*S) + 984*S*Zeta[3]) + HPL[{1}, -S^2]^4*((6673*Pi^4*S)/270 + (1264*(1 + S^2))/(3*S) + (800*Pi^2*(1 + S^2))/(9*S) + ((392*Pi^2*S)/9 + (132*(1 + S^2))/S)*HPL[{2}, -S^2] + (784*S*HPL[{2}, -S^2]^2)/3 - (560*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (664*S*HPL[{4}, -S^2])/3 - (260*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (664*S*HPL[{3, 1}, -S^2])/3 - (120*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-33*Pi^4*S)/4 + (Pi^2*(-13 - 113*S^2))/(3*S) - (2*(-1 + 188*S^2))/S + (12*(40 + 3*S^2)*HPL[{2, 1}, -S^2])/S + 1076*S*HPL[{3, 1}, -S^2] - 2192*S*HPL[{2, 1, 1}, -S^2] - (4*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((605*Pi^4*S)/24 + (Pi^2*(33 + 194*S^2))/(2*S) + (129 + 326*S^2)/S + ((-17 - 235*S^2)*HPL[{3}, -S^2])/S - 269*S*HPL[{4}, -S^2] + (4*(-149 + 42*S^2)*HPL[{2, 1}, -S^2])/S - 628*S*HPL[{3, 1}, -S^2] + 1568*S*HPL[{2, 1, 1}, -S^2] - (28*(-1 + 6*S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((650*Pi^4*S)/3 + (24*(-43 + 100*S^2))/S + (4*Pi^2*(-125 + 566*S^2))/(3*S) - (64*(3 + 23*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-2981*Pi^4*S)/30 - (4*(-175 + 234*S^2))/S - (2*Pi^2*(-172 + 513*S^2))/(3*S) - 4992*S*HPL[{2, 1, 1}, -S^2] + (8*(13 + 96*S^2)*Zeta[3])/S) + (68*S + (32*Pi^2*S)/3)*Zeta[5] + HPL[{1}, -S^2]^3*((3340*(1 + S^2))/(3*S) + (202*Pi^2*(1 + S^2))/S + (8587*Pi^4*(1 + S^2))/(270*S) + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-1988*Pi^2*S)/9 - (1160*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (448*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - 288*S*HPL[{5}, -S^2] + ((-1568*Pi^2*S)/9 - (528*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (896*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (6272*S*HPL[{3, 2}, -S^2])/3 + (21472*S*HPL[{4, 1}, -S^2])/3 + (1040*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (12544*S*HPL[{2, 2, 1}, -S^2])/3 + (22432*S*HPL[{3, 1, 1}, -S^2])/3 + ((-1664*Pi^2*S)/9 - (800*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((276*(1 + S^2))/S + (1004*Pi^2*(1 + S^2))/(9*S) - (3136*S*HPL[{3}, -S^2])/3 - (6272*S*HPL[{2, 1}, -S^2])/3 - (3136*S*Zeta[3])/3) - (3040*S*Zeta[5])/3) + Zeta[3]*(-260*S - (134*Pi^2*S)/3 - (22*Pi^4*S)/9 - 200*S*Zeta[5]) + HPL[{3}, -S^2]*((Pi^4*(177 - 1240*S^2))/(180*S) - (10*(7 + 48*S^2))/S - (2*Pi^2*(13 + 102*S^2))/(3*S) + (2*(-4 + 13*S^2)*HPL[{4}, -S^2])/S + ((-160*Pi^2*S)/3 + (4*(269 + 5*S^2))/S)*HPL[{2, 1}, -S^2] + (4*(-61 + 225*S^2)*HPL[{3, 1}, -S^2])/S - 616*S*HPL[{3, 2}, -S^2] - 280*S*HPL[{4, 1}, -S^2] - (80*(-5 + 22*S^2)*HPL[{2, 1, 1}, -S^2])/S - 608*S*HPL[{2, 2, 1}, -S^2] - 640*S*HPL[{3, 1, 1}, -S^2] - 1280*S*HPL[{2, 1, 1, 1}, -S^2] + ((-76*Pi^2*S)/3 - (12*(-1 + 7*S^2))/S)*Zeta[3] - 56*S*Zeta[5]) + HPL[{2, 1}, -S^2]*((20*(-79 + 13*S^2))/S + (2*Pi^2*(-679 + 31*S^2))/(3*S) + (Pi^4*(-7651 + 141*S^2))/(90*S) + (64*(31 + 17*S^2)*HPL[{3, 1}, -S^2])/S - 296*S*HPL[{3, 2}, -S^2] + 368*S*HPL[{4, 1}, -S^2] + (64*(73 + 25*S^2)*HPL[{2, 1, 1}, -S^2])/S + 6272*S*HPL[{2, 2, 1}, -S^2] + 17536*S*HPL[{3, 1, 1}, -S^2] - 12640*S*HPL[{2, 1, 1, 1}, -S^2] + ((44*Pi^2*S)/3 + (8*(105 + 26*S^2))/S)*Zeta[3] - 40*S*Zeta[5]) + HPL[{0}, S^2]^3*(220*S + (368*Pi^2*S)/9 + (1009*Pi^4*S)/135 + (268*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + (146*S*HPL[{1}, -S^2]^5)/9 + ((-1 + 115*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((212*Pi^2*S)/9 + (190*(1 + S^2))/(3*S) + (220*S*HPL[{2}, -S^2])/3) + ((-4*Pi^2*S)/3 + (2*(15 + 14*S^2))/(3*S))*HPL[{3}, -S^2] + (2*(5 + 2*S^2)*HPL[{4}, -S^2])/(3*S) - 4*S*HPL[{5}, -S^2] + ((44*Pi^2*S)/9 - (2*(264 + 23*S^2))/(3*S))*HPL[{2, 1}, -S^2] - (10*(-2 + 47*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (10*S*HPL[{3, 2}, -S^2])/3 + (38*S*HPL[{4, 1}, -S^2])/3 + (4*(-10 + 241*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (28*S*HPL[{2, 2, 1}, -S^2])/3 - 40*S*HPL[{3, 1, 1}, -S^2] + (152*S*HPL[{2, 1, 1, 1}, -S^2])/3 + (-2*S + (38*Pi^2*S)/9)*Zeta[3] + HPL[{1}, -S^2]^2*((329*(1 + S^2))/(3*S) + (523*Pi^2*(1 + S^2))/(18*S) + (248*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + 4*S*HPL[{3}, -S^2] - 220*S*HPL[{2, 1}, -S^2] - (22*S*Zeta[3])/3) + HPL[{2}, -S^2]*((2*(10 + 123*S^2))/(3*S) + (Pi^2*(-10 + 461*S^2))/(18*S) - (4*S*HPL[{3}, -S^2])/3 + (14*S*HPL[{2, 1}, -S^2])/3 - (16*S*Zeta[3])/3) + HPL[{1}, -S^2]*((3997*Pi^4*S)/540 + (144*(1 + S^2))/S + (575*Pi^2*(1 + S^2))/(18*S) + ((187*Pi^2*S)/6 + (88*(1 + S^2))/S)*HPL[{2}, -S^2] + 53*S*HPL[{2}, -S^2]^2 + (4*(1 + S^2)*HPL[{3}, -S^2])/S + (34*S*HPL[{4}, -S^2])/3 - (496*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - 220*S*HPL[{3, 1}, -S^2] + 440*S*HPL[{2, 1, 1}, -S^2] + (2*(1 + S^2)*Zeta[3])/S) + 26*S*Zeta[5]) + HPL[{1}, -S^2]^2*((52285*Pi^6*S)/4536 + (2420*(1 + S^2))/S + (1108*Pi^2*(1 + S^2))/(3*S) + (4691*Pi^4*(1 + S^2))/(90*S) + ((607*Pi^2*S)/3 + (402*(1 + S^2))/S)*HPL[{2}, -S^2]^2 + 148*S*HPL[{3}, -S^2]^2 + ((-340*Pi^2*S)/3 - (226*(1 + S^2))/S)*HPL[{4}, -S^2] - (8*(1 + S^2)*HPL[{5}, -S^2])/S - 178*S*HPL[{6}, -S^2] - 3136*S*HPL[{2, 1}, -S^2]^2 + ((-440*Pi^2*S)/3 - (448*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (904*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (3160*(1 + S^2)*HPL[{4, 1}, -S^2])/S + 468*S*HPL[{4, 2}, -S^2] + 2704*S*HPL[{5, 1}, -S^2] + ((1568*Pi^2*S)/3 + (1584*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (7168*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - 2656*S*HPL[{4, 1, 1}, -S^2] - (3120*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 2656*S*HPL[{3, 1, 1, 1}, -S^2] + ((-484*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + 80*S*Zeta[3]^2 + HPL[{3}, -S^2]*((-632*(1 + S^2))/S - (274*Pi^2*(1 + S^2))/(3*S) + 3136*S*HPL[{2, 1}, -S^2] - 200*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-828*(1 + S^2))/S - (1004*Pi^2*(1 + S^2))/(3*S) + 3136*S*Zeta[3]) + HPL[{2}, -S^2]*((2021*Pi^4*S)/60 + (452*(1 + S^2))/S + (174*Pi^2*(1 + S^2))/S - (452*(1 + S^2)*HPL[{3}, -S^2])/S - 452*S*HPL[{4}, -S^2] - (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 3136*S*HPL[{3, 1}, -S^2] + 6272*S*HPL[{2, 1, 1}, -S^2] - (448*(1 + S^2)*Zeta[3])/S) - (204*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((200803*Pi^6*S)/22680 + (40*(-7 + 16*S^2))/S + (Pi^2*(-129 + 632*S^2))/(3*S) + (Pi^4*(-193 + 1361*S^2))/(36*S) + 152*S*HPL[{3}, -S^2]^2 + ((-269*Pi^2*S)/3 - (2*(1 + 115*S^2))/S)*HPL[{4}, -S^2] - (2*(5 + 21*S^2)*HPL[{5}, -S^2])/S - 26*S*HPL[{6}, -S^2] - 1568*S*HPL[{2, 1}, -S^2]^2 + ((-1444*Pi^2*S)/3 - (4*(146 + 255*S^2))/S)*HPL[{3, 1}, -S^2] + (2*(-5 + 431*S^2)*HPL[{3, 2}, -S^2])/S + (12*(-23 + 232*S^2)*HPL[{4, 1}, -S^2])/S + 546*S*HPL[{4, 2}, -S^2] + 2532*S*HPL[{5, 1}, -S^2] + ((3232*Pi^2*S)/3 + (168*(5 + 14*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (16*(-149 + 42*S^2)*HPL[{2, 2, 1}, -S^2])/S + (32*(-211 + 8*S^2)*HPL[{3, 1, 1}, -S^2])/S - 312*S*HPL[{3, 1, 2}, -S^2] + 2808*S*HPL[{3, 2, 1}, -S^2] + 7168*S*HPL[{4, 1, 1}, -S^2] - (64*(73 + 25*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 80256*S*HPL[{3, 1, 1, 1}, -S^2] + 12640*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-4*Pi^2*(7 + 51*S^2))/(3*S) - (4*(29 + 115*S^2))/S)*Zeta[3] + 48*S*Zeta[3]^2 + HPL[{3}, -S^2]*((-17*Pi^2*(-3 + 13*S^2))/(3*S) - (8*(-7 + 65*S^2))/S + 304*S*HPL[{2, 1}, -S^2] - 168*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-4*Pi^2*(299 + 58*S^2))/(3*S) - (4*(313 + 125*S^2))/S - 144*S*Zeta[3]) - (40*(2 + 5*S^2)*Zeta[5])/S) + HPL[{0}, S^2]^2*(320*S + (253*Pi^2*S)/3 + (3097*Pi^4*S)/180 + (95363*Pi^6*S)/22680 + (44*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (62*S*HPL[{1}, -S^2]^6)/3 + ((219*Pi^2*S)/4 + (3*(-1 + 48*S^2))/S)*HPL[{2}, -S^2]^2 + (205*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((749*Pi^2*S)/18 + (350*(1 + S^2))/(3*S) + (392*S*HPL[{2}, -S^2])/3) - 3*S*HPL[{3}, -S^2]^2 + ((37*Pi^2*S)/6 + (-7 + 2*S^2)/S)*HPL[{4}, -S^2] + (4*(-1 + 9*S^2)*HPL[{5}, -S^2])/S + 39*S*HPL[{6}, -S^2] - 826*S*HPL[{2, 1}, -S^2]^2 + (-227*Pi^2*S - (2*(-13 + 289*S^2))/S)*HPL[{3, 1}, -S^2] + ((1 + 3*S^2)*HPL[{3, 2}, -S^2])/S - (2*(23 + 6*S^2)*HPL[{4, 1}, -S^2])/S - S*HPL[{4, 2}, -S^2] - 30*S*HPL[{5, 1}, -S^2] + (464*Pi^2*S + (8*(-5 + 148*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (8*(153 + 8*S^2)*HPL[{2, 2, 1}, -S^2])/S + (4*(939 + 50*S^2)*HPL[{3, 1, 1}, -S^2])/S + 4*S*HPL[{3, 1, 2}, -S^2] + 1644*S*HPL[{3, 2, 1}, -S^2] + 4960*S*HPL[{4, 1, 1}, -S^2] - (8*(327 + 17*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 3376*S*HPL[{3, 1, 1, 1}, -S^2] + 6880*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (12*S + 13*Pi^2*S)*Zeta[3] + 4*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((788*(1 + S^2))/(3*S) + (583*Pi^2*(1 + S^2))/(9*S) + (614*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (88*S*HPL[{3}, -S^2])/3 - (1568*S*HPL[{2, 1}, -S^2])/3 - (164*S*Zeta[3])/3) + HPL[{3}, -S^2]*((11*(1 + 3*S^2))/S + (Pi^2*(33 + 17*S^2))/(6*S) - 4*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((Pi^2*(-567 - 19*S^2))/(3*S) - (12*(59 + 7*S^2))/S + 4*S*Zeta[3]) + HPL[{1}, -S^2]^2*((8449*Pi^4*S)/360 + (476*(1 + S^2))/S + (103*Pi^2*(1 + S^2))/S + ((211*Pi^2*S)/2 + (324*(1 + S^2))/S)*HPL[{2}, -S^2] + 215*S*HPL[{2}, -S^2]^2 + (6*(1 + S^2)*HPL[{3}, -S^2])/S - 8*S*HPL[{4}, -S^2] - (614*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 772*S*HPL[{3, 1}, -S^2] + 1568*S*HPL[{2, 1, 1}, -S^2] - (16*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*(332*S + (867*Pi^4*S)/40 + (Pi^2*(-22 + 509*S^2))/(6*S) + ((1 - S^2)*HPL[{3}, -S^2])/S + 5*S*HPL[{4}, -S^2] - (4*(153 + 8*S^2)*HPL[{2, 1}, -S^2])/S - 820*S*HPL[{3, 1}, -S^2] + 1652*S*HPL[{2, 1, 1}, -S^2] - (4*(1 + 5*S^2)*Zeta[3])/S) + 76*S*Zeta[5] + HPL[{1}, -S^2]*((620*(1 + S^2))/S + (235*Pi^2*(1 + S^2))/(2*S) + (1837*Pi^4*(1 + S^2))/(90*S) + (149*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-25*Pi^2*S)/3 + (14*(1 + S^2))/S)*HPL[{3}, -S^2] + (23*(1 + S^2)*HPL[{4}, -S^2])/S - 24*S*HPL[{5}, -S^2] + (-211*Pi^2*S - (648*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (608*(1 + S^2)*HPL[{3, 1}, -S^2])/S + 84*S*HPL[{3, 2}, -S^2] + 268*S*HPL[{4, 1}, -S^2] + (1228*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + 1720*S*HPL[{2, 2, 1}, -S^2] + 4984*S*HPL[{3, 1, 1}, -S^2] - 3136*S*HPL[{2, 1, 1, 1}, -S^2] + ((-41*Pi^2*S)/3 - (16*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((354*(1 + S^2))/S + (535*Pi^2*(1 + S^2))/(6*S) - 42*S*HPL[{3}, -S^2] - 860*S*HPL[{2, 1}, -S^2] - 78*S*Zeta[3]) - 78*S*Zeta[5])) + HPL[{0}, S^2]*(3920*S + (1495*Pi^2*S)/3 + (599*Pi^4*S)/10 + (23468*Pi^6*S)/2835 + (112*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + (64*S*HPL[{1}, -S^2]^7)/3 + (2*(-19 + 172*S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^5*((482*Pi^2*S)/9 + (120*(1 + S^2))/S + 200*S*HPL[{2}, -S^2]) - (2*(2 + 5*S^2)*HPL[{3}, -S^2]^2)/S + (-(Pi^2*S)/3 + (4*(12 + 23*S^2))/S)*HPL[{5}, -S^2] - (8*(-5 + 4*S^2)*HPL[{6}, -S^2])/S - 72*S*HPL[{7}, -S^2] - (16*(3 + 91*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((128*Pi^2*S)/3 + (6*(-5 + 13*S^2))/S)*HPL[{3, 2}, -S^2] + (126*Pi^2*S + (4*(-45 + 41*S^2))/S)*HPL[{4, 1}, -S^2] - (2*(-3 + 7*S^2)*HPL[{4, 2}, -S^2])/S + 52*S*HPL[{4, 3}, -S^2] - (4*(3 + 13*S^2)*HPL[{5, 1}, -S^2])/S + 142*S*HPL[{5, 2}, -S^2] + 260*S*HPL[{6, 1}, -S^2] + ((40*Pi^2*S)/3 + (8*(381 + 34*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-136*Pi^2*S)/3 + (8*(1172 + 95*S^2))/S)*HPL[{3, 1, 1}, -S^2] + (4*(3 + 2*S^2)*HPL[{3, 1, 2}, -S^2])/S + (4*(-73 + 690*S^2)*HPL[{3, 2, 1}, -S^2])/S - 564*S*HPL[{3, 2, 2}, -S^2] - 1600*S*HPL[{3, 3, 1}, -S^2] + (8*(-111 + 1043*S^2)*HPL[{4, 1, 1}, -S^2])/S - 1604*S*HPL[{4, 1, 2}, -S^2] - 4676*S*HPL[{4, 2, 1}, -S^2] - 9128*S*HPL[{5, 1, 1}, -S^2] + ((512*Pi^2*S)/3 - (112*(59 + 4*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + 608*S*HPL[{2, 2, 2, 1}, -S^2] - (112*(-5 + 51*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - 880*S*HPL[{3, 1, 1, 2}, -S^2] - 880*S*HPL[{3, 1, 2, 1}, -S^2] - 2704*S*HPL[{3, 2, 1, 1}, -S^2] - 8224*S*HPL[{4, 1, 1, 1}, -S^2] + (960*(-1 + 12*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - 544*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 1632*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 4480*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 2880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (-264*S - (98*Pi^2*S)/3 - (373*Pi^4*S)/90)*Zeta[3] + 32*S*Zeta[3]^2 + HPL[{2, 1, 1}, -S^2]*((8*(3 + 401*S^2))/S + (4*Pi^2*(-40 + 601*S^2))/(3*S) - 1312*S*Zeta[3]) + HPL[{2}, -S^2]^2*((Pi^2*(5 + 297*S^2))/(3*S) + (29 + 389*S^2)/S - 72*S*HPL[{3}, -S^2] + 76*S*HPL[{2, 1}, -S^2] - 160*S*Zeta[3]) + HPL[{1}, -S^2]^4*((1030*(1 + S^2))/(3*S) + (688*Pi^2*(1 + S^2))/(9*S) + (250*(1 + S^2)*HPL[{2}, -S^2])/S - (68*S*HPL[{3}, -S^2])/3 - 1000*S*HPL[{2, 1}, -S^2] - (332*S*Zeta[3])/3) + HPL[{4}, -S^2]*((-2*(-23 + 7*S^2))/S + (Pi^2*(13 + 15*S^2))/(3*S) + 68*S*HPL[{2, 1}, -S^2] + 4*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((-4*(-1 + 387*S^2))/S - (2*Pi^2*(-45 + 592*S^2))/(3*S) + 640*S*Zeta[3]) + HPL[{3}, -S^2]*(-3*Pi^4*S + (4*(29 + 20*S^2))/S + (Pi^2*(59 + 21*S^2))/(3*S) - 20*S*HPL[{4}, -S^2] + (28*(7 + 3*S^2)*HPL[{2, 1}, -S^2])/S + 224*S*HPL[{3, 1}, -S^2] - 448*S*HPL[{2, 1, 1}, -S^2] + (4*(-1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((4061*Pi^4*S)/90 + (2528*(1 + S^2))/(3*S) + (490*Pi^2*(1 + S^2))/(3*S) + (240*Pi^2*S + (1592*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (1568*S*HPL[{2}, -S^2]^2)/3 - (80*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (184*S*HPL[{4}, -S^2])/3 - (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 2000*S*HPL[{3, 1}, -S^2] + 4000*S*HPL[{2, 1, 1}, -S^2] - (320*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((76*Pi^4*S)/9 - (2*Pi^2*(677 + 51*S^2))/(3*S) - (4*(511 + 82*S^2))/S + 144*S*HPL[{3, 1}, -S^2] + 272*S*HPL[{2, 1, 1}, -S^2] + (8*(43 + 2*S^2)*Zeta[3])/S) + (-188*S - (52*Pi^2*S)/3)*Zeta[5] + HPL[{1}, -S^2]^2*((1670*(1 + S^2))/S + (844*Pi^2*(1 + S^2))/(3*S) + (7801*Pi^4*(1 + S^2))/(180*S) + (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-22*Pi^2*S)/3 - (24*(1 + S^2))/S)*HPL[{3}, -S^2] + (34*(1 + S^2)*HPL[{4}, -S^2])/S + 92*S*HPL[{5}, -S^2] + (-720*Pi^2*S - (1592*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (1488*(1 + S^2)*HPL[{3, 1}, -S^2])/S + 304*S*HPL[{3, 2}, -S^2] + 728*S*HPL[{4, 1}, -S^2] + (3000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + 6272*S*HPL[{2, 2, 1}, -S^2] + 18544*S*HPL[{3, 1, 1}, -S^2] - 12000*S*HPL[{2, 1, 1, 1}, -S^2] + ((-188*Pi^2*S)/3 - (156*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((898*(1 + S^2))/S + (623*Pi^2*(1 + S^2))/(3*S) - 152*S*HPL[{3}, -S^2] - 3136*S*HPL[{2, 1}, -S^2] - 328*S*Zeta[3]) - 260*S*Zeta[5]) + HPL[{2}, -S^2]*((10*(15 + 107*S^2))/S + (Pi^2*(23 + 647*S^2))/(3*S) + (Pi^4*(-131 + 3353*S^2))/(90*S) + (-20*Pi^2*S - (2*(-9 + 19*S^2))/S)*HPL[{3}, -S^2] + (2*(3 + 14*S^2)*HPL[{4}, -S^2])/S + 18*S*HPL[{5}, -S^2] + ((-20*Pi^2*S)/3 - (4*(381 + 34*S^2))/S)*HPL[{2, 1}, -S^2] - (4*(11 + 365*S^2)*HPL[{3, 1}, -S^2])/S + 288*S*HPL[{3, 2}, -S^2] + 796*S*HPL[{4, 1}, -S^2] + (32*(3 + 91*S^2)*HPL[{2, 1, 1}, -S^2])/S - 304*S*HPL[{2, 2, 1}, -S^2] + 464*S*HPL[{3, 1, 1}, -S^2] - 272*S*HPL[{2, 1, 1, 1}, -S^2] + (-156*S - 60*Pi^2*S)*Zeta[3] - 212*S*Zeta[5]) + HPL[{1}, -S^2]*((248987*Pi^6*S)/22680 + (2420*(1 + S^2))/S + (1064*Pi^2*(1 + S^2))/(3*S) + (1439*Pi^4*(1 + S^2))/(30*S) + ((551*Pi^2*S)/3 + (402*(1 + S^2))/S)*HPL[{2}, -S^2]^2 + 236*S*HPL[{2}, -S^2]^3 - 8*S*HPL[{3}, -S^2]^2 + ((80*Pi^2*S)/3 + (46*(1 + S^2))/S)*HPL[{4}, -S^2] + (24*(1 + S^2)*HPL[{5}, -S^2])/S + 146*S*HPL[{6}, -S^2] - 3136*S*HPL[{2, 1}, -S^2]^2 + (-720*Pi^2*S - (1560*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (152*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (388*(1 + S^2)*HPL[{4, 1}, -S^2])/S - 216*S*HPL[{5, 1}, -S^2] + (1440*Pi^2*S + (3184*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (9248*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + 5664*S*HPL[{3, 2, 1}, -S^2] + 17360*S*HPL[{4, 1, 1}, -S^2] - (6000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 12000*S*HPL[{3, 1, 1, 1}, -S^2] + 24000*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-156*(1 + S^2))/S - (74*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + 68*S*Zeta[3]^2 + HPL[{3}, -S^2]*((8*(1 + S^2))/S - (8*Pi^2*(1 + S^2))/(3*S) + 304*S*HPL[{2, 1}, -S^2] - 16*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-1796*(1 + S^2))/S - (1246*Pi^2*(1 + S^2))/(3*S) + 656*S*Zeta[3]) + HPL[{2}, -S^2]*((2155*Pi^4*S)/36 + (1076*(1 + S^2))/S + (662*Pi^2*(1 + S^2))/(3*S) - (76*(1 + S^2)*HPL[{3}, -S^2])/S + 16*S*HPL[{4}, -S^2] - (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 3136*S*HPL[{3, 1}, -S^2] + 6272*S*HPL[{2, 1, 1}, -S^2] - (164*(1 + S^2)*Zeta[3])/S) - (108*(1 + S^2)*Zeta[5])/S)) + 420*S*Zeta[7] + HPL[{1}, -S^2]*((3920*(1 + S^2))/S + (485*Pi^2*(1 + S^2))/S + (5497*Pi^4*(1 + S^2))/(90*S) + (37673*Pi^6*(1 + S^2))/(4536*S) + (166*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + (74*(1 + S^2)*HPL[{3}, -S^2]^2)/S + (-80*Pi^2*S + (16*(1 + S^2))/S)*HPL[{5}, -S^2] + (238*(1 + S^2)*HPL[{6}, -S^2])/S - 60*S*HPL[{7}, -S^2] - (1568*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((1652*Pi^2*S)/3 + (936*(1 + S^2))/S)*HPL[{3, 2}, -S^2] + ((5636*Pi^2*S)/3 + (3260*(1 + S^2))/S)*HPL[{4, 1}, -S^2] + (234*(1 + S^2)*HPL[{4, 2}, -S^2])/S - 188*S*HPL[{4, 3}, -S^2] + (936*(1 + S^2)*HPL[{5, 1}, -S^2])/S - 408*S*HPL[{5, 2}, -S^2] + 196*S*HPL[{6, 1}, -S^2] + ((4856*Pi^2*S)/3 + (3216*(1 + S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((10592*Pi^2*S)/3 + (7328*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] + (1328*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - 6520*S*HPL[{3, 2, 2}, -S^2] - 19936*S*HPL[{3, 3, 1}, -S^2] + (3088*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - 19624*S*HPL[{4, 1, 2}, -S^2] - 60808*S*HPL[{4, 2, 1}, -S^2] - 125280*S*HPL[{5, 1, 1}, -S^2] + ((-3136*Pi^2*S)/3 - (3168*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - (1792*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + 12544*S*HPL[{3, 1, 1, 2}, -S^2] + 12544*S*HPL[{3, 1, 2, 1}, -S^2] + 12544*S*HPL[{3, 2, 1, 1}, -S^2] + 42944*S*HPL[{4, 1, 1, 1}, -S^2] + (6240*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - 25088*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 75264*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 155840*S*HPL[{3, 1, 1, 1, 1}, -S^2] + ((-1013*Pi^4*S)/30 - (624*(1 + S^2))/S - (72*Pi^2*(1 + S^2))/S)*Zeta[3] + (36*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1, 1}, -S^2]*((1656*(1 + S^2))/S + (2008*Pi^2*(1 + S^2))/(3*S) - 6272*S*Zeta[3]) + HPL[{2}, -S^2]^2*((431*(1 + S^2))/S + (115*Pi^2*(1 + S^2))/S - 932*S*HPL[{3}, -S^2] - 708*S*Zeta[3]) + HPL[{4}, -S^2]*((-224*(1 + S^2))/S - (89*Pi^2*(1 + S^2))/(3*S) + 904*S*HPL[{2, 1}, -S^2] - 112*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((-460*(1 + S^2))/S - (832*Pi^2*(1 + S^2))/(3*S) + 3232*S*Zeta[3]) + HPL[{3}, -S^2]*((-601*Pi^4*S)/15 - (688*(1 + S^2))/S - (92*Pi^2*(1 + S^2))/S + 172*S*HPL[{4}, -S^2] + (904*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 3136*S*HPL[{3, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2] - (96*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-2021*Pi^4*S)/30 - (904*(1 + S^2))/S - (348*Pi^2*(1 + S^2))/S + 6272*S*HPL[{3, 1}, -S^2] + 12544*S*HPL[{2, 1, 1}, -S^2] + (896*(1 + S^2)*Zeta[3])/S) + ((-838*Pi^2*S)/3 - (288*(1 + S^2))/S)*Zeta[5] + HPL[{2}, -S^2]*((510*(1 + S^2))/S + (187*Pi^2*(1 + S^2))/S + (1315*Pi^4*(1 + S^2))/(36*S) + ((-826*Pi^2*S)/3 - (468*(1 + S^2))/S)*HPL[{3}, -S^2] - (226*(1 + S^2)*HPL[{4}, -S^2])/S - 328*S*HPL[{5}, -S^2] + ((-2428*Pi^2*S)/3 - (1608*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + 3416*S*HPL[{3, 2}, -S^2] + 10280*S*HPL[{4, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 6272*S*HPL[{3, 1, 1}, -S^2] - 12544*S*HPL[{2, 1, 1, 1}, -S^2] + ((-862*Pi^2*S)/3 - (504*(1 + S^2))/S)*Zeta[3] - 1444*S*Zeta[5]) - 1932*S*Zeta[7])) + HPL[{0}, S^2]*(-3920*S - (1265*Pi^2*S)/3 - (8137*Pi^4*S)/180 - (258557*Pi^6*S)/45360 - (2294333*Pi^8*S)/2721600 - (16*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) - (8*S*HPL[{1}, -S^2]^8)/3 + ((-529*Pi^2*S)/18 + (27 - 346*S^2)/(6*S))*HPL[{2}, -S^2]^3 - (123*S*HPL[{2}, -S^2]^4)/4 + HPL[{1}, -S^2]^6*((-241*Pi^2*S)/27 - (20*(1 + S^2))/S - (100*S*HPL[{2}, -S^2])/3) + ((17*Pi^2*S)/6 + (2*(3 + 5*S^2))/S)*HPL[{3}, -S^2]^2 + 4*S*HPL[{4}, -S^2]^2 + ((-209*Pi^2*S)/6 + (3*(25 + 47*S^2))/S)*HPL[{6}, -S^2] - (5*(-25 + 28*S^2)*HPL[{7}, -S^2])/S - 376*S*HPL[{8}, -S^2] + (364*Pi^2*S + (2*(21 + 368*S^2))/S)*HPL[{2, 1}, -S^2]^2 - 1524*S*HPL[{3, 1}, -S^2]^2 + ((7*Pi^2*S)/6 + (-3 - S^2)/S)*HPL[{4, 2}, -S^2] - (4*(-5 + 8*S^2)*HPL[{4, 3}, -S^2])/S + ((139*Pi^2*S)/3 - (4*(8 + 15*S^2))/S)*HPL[{5, 1}, -S^2] + ((59 - 91*S^2)*HPL[{5, 2}, -S^2])/S + 6*S*HPL[{5, 3}, -S^2] - (4*(-22 + 15*S^2)*HPL[{6, 1}, -S^2])/S + 9*S*HPL[{6, 2}, -S^2] + 336*S*HPL[{7, 1}, -S^2] - 6136*S*HPL[{2, 1, 1}, -S^2]^2 + ((-8*Pi^2*S)/3 - (2*(3 + S^2))/S)*HPL[{3, 1, 2}, -S^2] + (-708*Pi^2*S - (6*(-17 + 231*S^2))/S)*HPL[{3, 2, 1}, -S^2] + (11*(-5 + 8*S^2)*HPL[{3, 2, 2}, -S^2])/S + (48*(-3 + 5*S^2)*HPL[{3, 3, 1}, -S^2])/S + 64*S*HPL[{3, 3, 2}, -S^2] + ((-6526*Pi^2*S)/3 - (76*(-4 + 55*S^2))/S)*HPL[{4, 1, 1}, -S^2] + (2*(-73 + 119*S^2)*HPL[{4, 1, 2}, -S^2])/S - 140*S*HPL[{4, 1, 3}, -S^2] + (2*(-217 + 347*S^2)*HPL[{4, 2, 1}, -S^2])/S + 61*S*HPL[{4, 2, 2}, -S^2] - 268*S*HPL[{4, 3, 1}, -S^2] + (4*(-225 + 317*S^2)*HPL[{5, 1, 1}, -S^2])/S - 146*S*HPL[{5, 1, 2}, -S^2] - 1106*S*HPL[{5, 2, 1}, -S^2] - 3212*S*HPL[{6, 1, 1}, -S^2] + ((4*Pi^2*(663 + 22*S^2))/(3*S) + (16*(223 + 24*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (16*(196 + 5*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + (1512*Pi^2*S + (8*(-20 + 363*S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] - (4*(2333 + 96*S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (4*(2333 + 96*S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - 12*S*HPL[{3, 1, 2, 2}, -S^2] - (4*(4685 + 156*S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - 12*S*HPL[{3, 2, 1, 2}, -S^2] + 5988*S*HPL[{3, 2, 2, 1}, -S^2] + 18000*S*HPL[{3, 3, 1, 1}, -S^2] - (8*(7009 + 225*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + 12*S*HPL[{4, 1, 1, 2}, -S^2] + 18012*S*HPL[{4, 1, 2, 1}, -S^2] + 54012*S*HPL[{4, 2, 1, 1}, -S^2] + 108504*S*HPL[{5, 1, 1, 1}, -S^2] + ((-9152*Pi^2*S)/3 - (80*(-3 + 74*S^2))/S)*HPL[{2, 1, 1, 1, 1}, -S^2] + (64*(95 + 7*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (192*(95 + 7*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + 11936*S*HPL[{2, 2, 1, 2, 1}, -S^2] + 35808*S*HPL[{2, 2, 2, 1, 1}, -S^2] + (16*(1873 + 153*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - 71664*S*HPL[{3, 1, 1, 1, 2}, -S^2] - 119408*S*HPL[{3, 1, 1, 2, 1}, -S^2] - 143280*S*HPL[{3, 1, 2, 1, 1}, -S^2] - 298448*S*HPL[{3, 2, 1, 1, 1}, -S^2] - 895968*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (480*(27 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + 25216*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 50880*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (-38*S - (10*Pi^2*S)/3)*Zeta[3]^2 + HPL[{4}, -S^2]*((-183*Pi^4*S)/40 + (Pi^2*(5 + 3*S^2))/(2*S) + (-5 + 88*S^2)/S - (2*(2 + 13*S^2)*HPL[{2, 1}, -S^2])/S + 26*S*HPL[{3, 1}, -S^2] - 100*S*HPL[{2, 1, 1}, -S^2] - (30*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((Pi^2*(73 - 25*S^2))/(3*S) - (6*(-5 + S^2))/S - 20*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((-5*Pi^2*(-7 + 6*S^2))/(6*S) - (4*(1 + 8*S^2))/S + 4*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((-16*Pi^2*(77 + 4*S^2))/(3*S) - (24*(67 + 7*S^2))/S + 16*S*Zeta[3]) + HPL[{5}, -S^2]*((30 - 133*S^2)/S + (Pi^2*(31 - 53*S^2))/(6*S) - 10*S*HPL[{2, 1}, -S^2] + 22*S*Zeta[3]) + HPL[{1}, -S^2]^5*((-206*(1 + S^2))/(3*S) - (688*Pi^2*(1 + S^2))/(45*S) - (50*(1 + S^2)*HPL[{2}, -S^2])/S + (68*S*HPL[{3}, -S^2])/15 + 200*S*HPL[{2, 1}, -S^2] + (332*S*Zeta[3])/15) + HPL[{3, 1, 1}, -S^2]*((-10*Pi^2*(379 + 18*S^2))/(3*S) - (16*(310 + 33*S^2))/S + 80*S*Zeta[3]) + HPL[{1}, -S^2]^4*((-4061*Pi^4*S)/360 - (632*(1 + S^2))/(3*S) - (245*Pi^2*(1 + S^2))/(6*S) + (-60*Pi^2*S - (398*(1 + S^2))/(3*S))*HPL[{2}, -S^2] - (392*S*HPL[{2}, -S^2]^2)/3 + (20*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (46*S*HPL[{4}, -S^2])/3 + (250*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 500*S*HPL[{3, 1}, -S^2] - 1000*S*HPL[{2, 1, 1}, -S^2] + (80*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((-709*Pi^4*S)/48 + (Pi^2*(-13 - 600*S^2))/(12*S) + (-43 - 434*S^2)/(2*S) + ((-11 + 23*S^2)*HPL[{3}, -S^2])/(2*S) - (13*S*HPL[{4}, -S^2])/2 + (2*(196 + 5*S^2)*HPL[{2, 1}, -S^2])/S + 750*S*HPL[{3, 1}, -S^2] - 1492*S*HPL[{2, 1, 1}, -S^2] + (2*(-3 + 19*S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-769*Pi^4*S)/6 - (12*(9 + 152*S^2))/S - (2*Pi^2*(-15 + 611*S^2))/(3*S) + (8*(-2 + 39*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((255*Pi^4*S)/4 + (5*Pi^2*(-6 + 119*S^2))/(3*S) + (2*(9 + 418*S^2))/S + 6128*S*HPL[{2, 1, 1}, -S^2] - (4*(-5 + 41*S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((20*(61 + 15*S^2))/S + (2*Pi^2*(119 + 15*S^2))/S + (Pi^4*(7153 + 185*S^2))/(180*S) - (12*(127 + 9*S^2)*HPL[{3, 1}, -S^2])/S - 48*S*HPL[{3, 2}, -S^2] - 44*S*HPL[{4, 1}, -S^2] - (32*(95 + 7*S^2)*HPL[{2, 1, 1}, -S^2])/S - 5968*S*HPL[{2, 2, 1}, -S^2] - 18064*S*HPL[{3, 1, 1}, -S^2] + 12272*S*HPL[{2, 1, 1, 1}, -S^2] + ((-2*Pi^2*S)/3 + (4*(-38 + S^2))/S)*Zeta[3]) + (194*S + (16*Pi^2*S)/3)*Zeta[5] + Zeta[3]*(220*S + 21*Pi^2*S - (11*Pi^4*S)/9 - 8*S*Zeta[5]) + HPL[{3}, -S^2]*((Pi^4*(-437 - 164*S^2))/(360*S) + (Pi^2*(-27 - 35*S^2))/(3*S) - (75*(1 + 2*S^2))/S + ((-10 + 17*S^2)*HPL[{4}, -S^2])/S - 8*S*HPL[{5}, -S^2] + (-10*Pi^2*S - (2*(51 + 23*S^2))/S)*HPL[{2, 1}, -S^2] - (2*(-13 + 15*S^2)*HPL[{3, 1}, -S^2])/S - 32*S*HPL[{3, 2}, -S^2] + 44*S*HPL[{4, 1}, -S^2] + (4*(-11 + 17*S^2)*HPL[{2, 1, 1}, -S^2])/S - 48*S*HPL[{2, 2, 1}, -S^2] - 48*S*HPL[{3, 1, 1}, -S^2] - 160*S*HPL[{2, 1, 1, 1}, -S^2] + ((16*Pi^2*S)/3 - (2*(11 + 3*S^2))/S)*Zeta[3] + 28*S*Zeta[5]) + HPL[{1}, -S^2]^3*((-1670*(1 + S^2))/(3*S) - (844*Pi^2*(1 + S^2))/(9*S) - (7801*Pi^4*(1 + S^2))/(540*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((22*Pi^2*S)/9 + (8*(1 + S^2))/S)*HPL[{3}, -S^2] - (34*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (92*S*HPL[{5}, -S^2])/3 + (240*Pi^2*S + (1592*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (496*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (304*S*HPL[{3, 2}, -S^2])/3 - (728*S*HPL[{4, 1}, -S^2])/3 - (1000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (6272*S*HPL[{2, 2, 1}, -S^2])/3 - (18544*S*HPL[{3, 1, 1}, -S^2])/3 + 4000*S*HPL[{2, 1, 1, 1}, -S^2] + ((188*Pi^2*S)/9 + (52*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-898*(1 + S^2))/(3*S) - (623*Pi^2*(1 + S^2))/(9*S) + (152*S*HPL[{3}, -S^2])/3 + (3136*S*HPL[{2, 1}, -S^2])/3 + (328*S*Zeta[3])/3) + (260*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*((-248987*Pi^6*S)/45360 - (1210*(1 + S^2))/S - (532*Pi^2*(1 + S^2))/(3*S) - (1439*Pi^4*(1 + S^2))/(60*S) + ((-551*Pi^2*S)/6 - (201*(1 + S^2))/S)*HPL[{2}, -S^2]^2 - 118*S*HPL[{2}, -S^2]^3 + 4*S*HPL[{3}, -S^2]^2 + ((-40*Pi^2*S)/3 - (23*(1 + S^2))/S)*HPL[{4}, -S^2] - (12*(1 + S^2)*HPL[{5}, -S^2])/S - 73*S*HPL[{6}, -S^2] + 1568*S*HPL[{2, 1}, -S^2]^2 + (360*Pi^2*S + (780*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (76*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (194*(1 + S^2)*HPL[{4, 1}, -S^2])/S + 108*S*HPL[{5, 1}, -S^2] + (-720*Pi^2*S - (1592*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (1568*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (4624*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - 2832*S*HPL[{3, 2, 1}, -S^2] - 8680*S*HPL[{4, 1, 1}, -S^2] + (3000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 6000*S*HPL[{3, 1, 1, 1}, -S^2] - 12000*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((78*(1 + S^2))/S + (37*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - 34*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((898*(1 + S^2))/S + (623*Pi^2*(1 + S^2))/(3*S) - 328*S*Zeta[3]) + HPL[{3}, -S^2]*((-4*(1 + S^2))/S + (4*Pi^2*(1 + S^2))/(3*S) - 152*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2}, -S^2]*((-2155*Pi^4*S)/72 - (538*(1 + S^2))/S - (331*Pi^2*(1 + S^2))/(3*S) + (38*(1 + S^2)*HPL[{3}, -S^2])/S - 8*S*HPL[{4}, -S^2] + (784*(1 + S^2)*HPL[{2, 1}, -S^2])/S + 1568*S*HPL[{3, 1}, -S^2] - 3136*S*HPL[{2, 1, 1}, -S^2] + (82*(1 + S^2)*Zeta[3])/S) + (54*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((-235877*Pi^6*S)/45360 + (Pi^4*(33 - 6673*S^2))/(360*S) + (Pi^2*(-67 - 700*S^2))/(6*S) - (10*(15 + 61*S^2))/S + 8*S*HPL[{3}, -S^2]^2 + ((-37*Pi^2*S)/6 + (-13 - 21*S^2)/S)*HPL[{4}, -S^2] + ((9 - 23*S^2)*HPL[{5}, -S^2])/S + 7*S*HPL[{6}, -S^2] + 1492*S*HPL[{2, 1}, -S^2]^2 + HPL[{3}, -S^2]*(16*S + (Pi^2*(-19 + 13*S^2))/(6*S) + 24*S*HPL[{2, 1}, -S^2]) + ((1088*Pi^2*S)/3 + (6*(8 + 123*S^2))/S)*HPL[{3, 1}, -S^2] + ((23 - 45*S^2)*HPL[{3, 2}, -S^2])/S - (14*(-5 + 8*S^2)*HPL[{4, 1}, -S^2])/S - 3*S*HPL[{4, 2}, -S^2] + 18*S*HPL[{5, 1}, -S^2] + (-728*Pi^2*S - (4*(21 + 368*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (8*(196 + 5*S^2)*HPL[{2, 2, 1}, -S^2])/S + (4*(1165 + 47*S^2)*HPL[{3, 1, 1}, -S^2])/S - 2952*S*HPL[{3, 2, 1}, -S^2] - 8956*S*HPL[{4, 1, 1}, -S^2] + (32*(95 + 7*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 77744*S*HPL[{3, 1, 1, 1}, -S^2] - 12272*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((20*(-1 + 4*S^2))/S + (2*Pi^2*(-7 + 19*S^2))/(3*S))*Zeta[3] - 34*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((8*Pi^2*(77 + 4*S^2))/(3*S) + (12*(67 + 7*S^2))/S - 8*S*Zeta[3]) + (4*(-10 + 13*S^2)*Zeta[5])/S) + 210*S*Zeta[7] + HPL[{1}, -S^2]*((-1960*(1 + S^2))/S - (1495*Pi^2*(1 + S^2))/(6*S) - (5281*Pi^4*(1 + S^2))/(180*S) - (36461*Pi^6*(1 + S^2))/(9072*S) - (59*(1 + S^2)*HPL[{2}, -S^2]^3)/S + ((1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-46*Pi^2*S)/3 + (8*(1 + S^2))/S)*HPL[{5}, -S^2] - (9*(1 + S^2)*HPL[{6}, -S^2])/S - 134*S*HPL[{7}, -S^2] + (784*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + (-30*Pi^2*S - (84*(1 + S^2))/S)*HPL[{3, 2}, -S^2] + ((-190*Pi^2*S)/3 - (206*(1 + S^2))/S)*HPL[{4, 1}, -S^2] - (3*(1 + S^2)*HPL[{4, 2}, -S^2])/S - 26*S*HPL[{4, 3}, -S^2] + (20*(1 + S^2)*HPL[{5, 1}, -S^2])/S - 84*S*HPL[{5, 2}, -S^2] - 14*S*HPL[{6, 1}, -S^2] + ((-2204*Pi^2*S)/3 - (1608*(1 + S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-6568*Pi^2*S)/3 - (4776*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] - (1416*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + 240*S*HPL[{3, 2, 2}, -S^2] + 752*S*HPL[{3, 3, 1}, -S^2] - (4316*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + 752*S*HPL[{4, 1, 2}, -S^2] + 2288*S*HPL[{4, 2, 1}, -S^2] + 4424*S*HPL[{5, 1, 1}, -S^2] + (1440*Pi^2*S + (3184*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + 5664*S*HPL[{2, 2, 2, 1}, -S^2] + (2976*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - 17600*S*HPL[{3, 1, 1, 2}, -S^2] - 17600*S*HPL[{3, 1, 2, 1}, -S^2] - 34592*S*HPL[{3, 2, 1, 1}, -S^2] - 103408*S*HPL[{4, 1, 1, 1}, -S^2] - (6000*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + 12544*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 37632*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 63264*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 24000*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((229*Pi^4*S)/60 + (56*(1 + S^2))/S + (22*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (18*(1 + S^2)*Zeta[3]^2)/S + HPL[{3, 1}, -S^2]*((870*(1 + S^2))/S + (206*Pi^2*(1 + S^2))/S - 344*S*Zeta[3]) + HPL[{4}, -S^2]*((-38*(1 + S^2))/S - (29*Pi^2*(1 + S^2))/(6*S) + 16*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2}, -S^2]^2*((-431*(1 + S^2))/(2*S) - (313*Pi^2*(1 + S^2))/(6*S) + 30*S*HPL[{3}, -S^2] + 708*S*HPL[{2, 1}, -S^2] + 82*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-1796*(1 + S^2))/S - (1246*Pi^2*(1 + S^2))/(3*S) + 656*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((2155*Pi^4*S)/36 + (1076*(1 + S^2))/S + (662*Pi^2*(1 + S^2))/(3*S) - 3136*S*HPL[{3, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2] - (164*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-5*Pi^4*S)/6 - (24*(1 + S^2))/S - (8*Pi^2*(1 + S^2))/(3*S) + 10*S*HPL[{4}, -S^2] - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - 136*S*HPL[{3, 1}, -S^2] + 304*S*HPL[{2, 1, 1}, -S^2] + (4*(1 + S^2)*Zeta[3])/S) + (27*Pi^2*S + (16*(1 + S^2))/S)*Zeta[5] + HPL[{2}, -S^2]*((-685*(1 + S^2))/S - (737*Pi^2*(1 + S^2))/(6*S) - (2297*Pi^4*(1 + S^2))/(120*S) + (15*Pi^2*S + (42*(1 + S^2))/S)*HPL[{3}, -S^2] + ((-1 - S^2)*HPL[{4}, -S^2])/S - 4*S*HPL[{5}, -S^2] + ((1102*Pi^2*S)/3 + (804*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (784*(1 + S^2)*HPL[{3, 1}, -S^2])/S - 120*S*HPL[{3, 2}, -S^2] - 376*S*HPL[{4, 1}, -S^2] - (1568*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - 2832*S*HPL[{2, 2, 1}, -S^2] + 8800*S*HPL[{3, 1, 1}, -S^2] + 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((91*Pi^2*S)/3 + (76*(1 + S^2))/S)*Zeta[3] + 106*S*Zeta[5]) + 150*S*Zeta[7])) + 1568*S*Zeta[9];
E5vwuT2F0=3920 - (13964*Pi^8)/(14175*(1 + S^2)) + (2*Pi^2*(193 + 250*S^2))/3 + (11*Pi^6*(-233 + 987*S^2))/11340 + (Pi^4*(382 + 993*S^2))/90 + HPL[{0}, S^2]^9/192 + HPL[{0}, S^2]^8*((-2 - S^2)/(96*(1 + S^2)) - HPL[{1}, -S^2]/48) + ((-116*Pi^2)/21 - (8*(1 + S^2))/21)*HPL[{1}, -S^2]^7 + (8*(-1 + S^2)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)) - (32*HPL[{1}, -S^2]^9)/27 + HPL[{0}, S^2]^7*(Pi^2/24 + (-1 - S^2)/6 + ((-4 - S^2)*HPL[{1}, -S^2])/(24*(1 + S^2)) - HPL[{1}, -S^2]^2/8 - HPL[{2}, -S^2]/6) + (16*(-1 + S^2)*HPL[{2}, -S^2]^4)/(1 + S^2) - (20*HPL[{3}, -S^2]^3)/3 - (6*(8 + 11*S^2)*HPL[{4}, -S^2]^2)/(1 + S^2) + ((32*Pi^2)/3 - 4*(-50 + 227*S^2))*HPL[{7}, -S^2] + (108*HPL[{8}, -S^2])/(1 + S^2) + 4604*HPL[{9}, -S^2] + (4*(-267 + 199*S^2)*HPL[{3, 1}, -S^2]^2)/(1 + S^2) + ((-148*Pi^2)/3 + 8*(25 + 7*S^2))*HPL[{4, 3}, -S^2] + (-136*Pi^2 + 4*(146 + 43*S^2))*HPL[{5, 2}, -S^2] - (4*(17 + 23*S^2)*HPL[{5, 3}, -S^2])/(1 + S^2) + 604*HPL[{5, 4}, -S^2] + (-274*Pi^2 + 44*(26 + 11*S^2))*HPL[{6, 1}, -S^2] - (4*(31 + 46*S^2)*HPL[{6, 2}, -S^2])/(1 + S^2) + 2228*HPL[{6, 3}, -S^2] + (4*(208 + 235*S^2)*HPL[{7, 1}, -S^2])/(1 + S^2) + 5664*HPL[{7, 2}, -S^2] + 11844*HPL[{8, 1}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2) + ((1018*Pi^2)/3 + 140*S^2)*HPL[{3, 2, 2}, -S^2] + ((2888*Pi^2)/3 + 16*(7 + 29*S^2))*HPL[{3, 3, 1}, -S^2] + (4*(-15 + 118*S^2)*HPL[{3, 3, 2}, -S^2])/(1 + S^2) + ((2732*Pi^2)/3 + 4*(29 + 115*S^2))*HPL[{4, 1, 2}, -S^2] - (4*(-44 + 183*S^2)*HPL[{4, 1, 3}, -S^2])/(1 + S^2) + ((8588*Pi^2)/3 + 4*(113 + 355*S^2))*HPL[{4, 2, 1}, -S^2] + (4*(11 + 105*S^2)*HPL[{4, 2, 2}, -S^2])/(1 + S^2) + 52*HPL[{4, 2, 3}, -S^2] - (4*(-104 + 623*S^2)*HPL[{4, 3, 1}, -S^2])/(1 + S^2) - 108*HPL[{4, 3, 2}, -S^2] + 352*HPL[{4, 4, 1}, -S^2] + ((17524*Pi^2)/3 + 16*(64 + 177*S^2))*HPL[{5, 1, 1}, -S^2] - (4*(-57 + 365*S^2)*HPL[{5, 1, 2}, -S^2])/(1 + S^2) + 752*HPL[{5, 1, 3}, -S^2] - (4*(-357 + 2645*S^2)*HPL[{5, 2, 1}, -S^2])/(1 + S^2) + 396*HPL[{5, 2, 2}, -S^2] + 2480*HPL[{5, 3, 1}, -S^2] - (4*(-615 + 7214*S^2)*HPL[{6, 1, 1}, -S^2])/(1 + S^2) + 1620*HPL[{6, 1, 2}, -S^2] + 7540*HPL[{6, 2, 1}, -S^2] + 16264*HPL[{7, 1, 1}, -S^2] + ((848*Pi^2)/3 - 160*S^2)*HPL[{2, 2, 2, 1}, -S^2] + ((-4024*Pi^2)/3 + 16*(-1 + 8*S^2))*HPL[{3, 1, 1, 2}, -S^2] + ((-4024*Pi^2)/3 + 16*(-1 + 8*S^2))*HPL[{3, 1, 2, 1}, -S^2] + (156*(-1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2) + ((-6568*Pi^2)/3 + 16*(-1 + 38*S^2))*HPL[{3, 2, 1, 1}, -S^2] + (156*(-1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2) + (4*(-55 + 39*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2) - 3392*HPL[{3, 2, 2, 2}, -S^2] - 11416*HPL[{3, 2, 3, 1}, -S^2] - (192*HPL[{3, 3, 1, 1}, -S^2])/(1 + S^2) - 11088*HPL[{3, 3, 1, 2}, -S^2] - 35160*HPL[{3, 3, 2, 1}, -S^2] + ((-21040*Pi^2)/3 + 48*(-1 + 37*S^2))*HPL[{4, 1, 1, 1}, -S^2] + (4*(43 + 277*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2) + 71704*HPL[{4, 1, 1, 3}, -S^2] + (4*(-5 + 277*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2) + 60616*HPL[{4, 1, 2, 2}, -S^2] + 108432*HPL[{4, 1, 3, 1}, -S^2] + (4*(-101 + 277*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2) + 37528*HPL[{4, 2, 1, 2}, -S^2] + 36544*HPL[{4, 2, 2, 1}, -S^2] + 213184*HPL[{4, 3, 1, 1}, -S^2] + (32*(-8 + 197*S^2)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2) + 218200*HPL[{5, 1, 1, 2}, -S^2] + 358696*HPL[{5, 1, 2, 1}, -S^2] + 853384*HPL[{5, 2, 1, 1}, -S^2] + 2134384*HPL[{6, 1, 1, 1}, -S^2] + ((4736*Pi^2)/3 + 384*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2] + (4736*Pi^2 + 1152*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2] - 64*HPL[{2, 2, 1, 2, 1}, -S^2] - 192*HPL[{2, 2, 2, 1, 1}, -S^2] - 6784*HPL[{2, 2, 2, 2, 1}, -S^2] + ((28064*Pi^2)/3 + 2688*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2] - 256*HPL[{3, 1, 1, 1, 2}, -S^2] - 12656*HPL[{3, 1, 1, 2, 2}, -S^2] + 128*HPL[{3, 1, 2, 1, 1}, -S^2] - 12656*HPL[{3, 1, 2, 1, 2}, -S^2] + 656*HPL[{3, 1, 2, 2, 1}, -S^2] + 98560*HPL[{3, 1, 3, 1, 1}, -S^2] + 960*HPL[{3, 2, 1, 1, 1}, -S^2] - 33008*HPL[{3, 2, 1, 1, 2}, -S^2] - 19696*HPL[{3, 2, 1, 2, 1}, -S^2] + 24848*HPL[{3, 2, 2, 1, 1}, -S^2] + 92928*HPL[{3, 3, 1, 1, 1}, -S^2] - (32*(-135 + 31*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2) - 100448*HPL[{4, 1, 1, 1, 2}, -S^2] - 60512*HPL[{4, 1, 1, 2, 1}, -S^2] + 73120*HPL[{4, 1, 2, 1, 1}, -S^2] + 279328*HPL[{4, 2, 1, 1, 1}, -S^2] + 562496*HPL[{5, 1, 1, 1, 1}, -S^2] + ((3104*Pi^2)/3 - 960*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (64*(-19 + 64*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) - 12416*HPL[{3, 1, 1, 1, 1, 2}, -S^2] - 12416*HPL[{3, 1, 1, 1, 2, 1}, -S^2] - 12416*HPL[{3, 1, 1, 2, 1, 1}, -S^2] - 12416*HPL[{3, 1, 2, 1, 1, 1}, -S^2] - 12416*HPL[{3, 2, 1, 1, 1, 1}, -S^2] - 46976*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - 2880*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] - 24832*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] - 99328*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] - 248320*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] - 486912*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + ((104*Pi^2)/9 + (32*HPL[{0}, S^2]^2)/3 - (64*(-1 + S^2)*HPL[{1}, -S^2])/(3*(1 + S^2)) + (128*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*((-8*(-3 + 5*S^2))/(3*(1 + S^2)) + (128*HPL[{1}, -S^2])/3))*Log[T]^7 + ((8*(-1 + S^2))/(3*(1 + S^2)) - 4*HPL[{0}, S^2] - (32*HPL[{1}, -S^2])/3)*Log[T]^8 + (8*Log[T]^9)/3 + HPL[{3, 1, 1, 1}, -S^2]*((-4*Pi^2*(-159 + 61*S^2))/(3*(1 + S^2)) + (16*(-11 + 2*S^2 + 14*S^4))/S^2 - 3200*Zeta[3]) + HPL[{2, 1}, -S^2]^2*((Pi^2*(615 - 599*S^2))/(3*(1 + S^2)) - (8*(-1 - 5*S^2 + S^4))/S^2 - 736*Zeta[3]) + HPL[{6}, -S^2]*((Pi^2*(-229 - 296*S^2))/(3*(1 + S^2)) + (20*(-14 + 21*S^2 + 25*S^4))/S^2 - 1116*HPL[{2, 1}, -S^2] - 228*Zeta[3]) + HPL[{4, 2}, -S^2]*((Pi^2*(29 + 143*S^2))/(3*(1 + S^2)) - (4*(-2 + 7*S^2 + 11*S^4))/S^2 - 80*Zeta[3]) + HPL[{3}, -S^2]^2*(-2*(-2 + 3*S^2) + (Pi^2*(3 + 40*S^2))/(3*(1 + S^2)) + 188*HPL[{2, 1}, -S^2] - 24*Zeta[3]) + HPL[{3, 1, 2}, -S^2]*((-86*Pi^2)/3 + (4*(1 + 10*S^2 + 8*S^4))/S^2 - 16*Zeta[3]) + HPL[{0}, S^2]^5*((23*Pi^4)/288 + (Pi^2*(-91 - 88*S^2))/72 + (-8 - 13*S^2)/4 + ((-255 + 16*S^2)*HPL[{1}, -S^2]^3)/(90*(1 + S^2)) - (271*HPL[{1}, -S^2]^4)/180 + HPL[{1}, -S^2]^2*((-293*Pi^2)/180 + (-1 - S^2)/6 - (77*HPL[{2}, -S^2])/20) + ((-11*Pi^2)/6 + (1 + S^2)/6)*HPL[{2}, -S^2] - (13*HPL[{2}, -S^2]^2)/8 + (S^2*HPL[{3}, -S^2])/(4*(1 + S^2)) - HPL[{4}, -S^2] + ((145 - 86*S^2)*HPL[{2, 1}, -S^2])/(60*(1 + S^2)) + HPL[{1}, -S^2]*((-1 - S^2)/3 + (Pi^2*(-675 - 89*S^2))/(360*(1 + S^2)) + (7*(-10 + S^2)*HPL[{2}, -S^2])/(20*(1 + S^2)) - HPL[{3}, -S^2]/2 + (77*HPL[{2, 1}, -S^2])/10) + (15*HPL[{3, 1}, -S^2])/2 - 16*HPL[{2, 1, 1}, -S^2] - (25*Zeta[3])/4) + HPL[{0}, S^2]^6*((Pi^2*(-87 - 41*S^2))/(288*(1 + S^2)) + (6 + 17*S^2)/24 + ((-10 - S^2)*HPL[{1}, -S^2]^2)/(12*(1 + S^2)) - HPL[{1}, -S^2]^3/2 + HPL[{1}, -S^2]*((-23*Pi^2)/72 + (1 + S^2)/24 - (13*HPL[{2}, -S^2])/24) + ((-25 - 12*S^2)*HPL[{2}, -S^2])/(48*(1 + S^2)) + HPL[{3}, -S^2]/12 - HPL[{2, 1}, -S^2]/2 - (7*Zeta[3])/3) + ((-29*Pi^2)/(3*(1 + S^2)) + 4*(-1 + 21*S^2))*Zeta[3]^2 - 64*Zeta[3]^3 + HPL[{5, 1}, -S^2]*((4*Pi^2*(54 + 227*S^2))/(3*(1 + S^2)) - (4*(-22 + 9*S^2 + 54*S^4))/S^2 + 24*Zeta[3]) + Log[T]^6*(8/3 + (2*Pi^2*(-46 + 41*S^2))/(9*(1 + S^2)) - (64*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]^2*((2*(-18 + 13*S^2))/(3*(1 + S^2)) - (124*HPL[{1}, -S^2])/3) + ((-116*Pi^2)/3 - (8*(1 + S^2))/3)*HPL[{1}, -S^2] + (224*(-1 + S^2)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)) - (896*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]*((-148*Pi^2)/9 - (8*(1 + S^2))/3 + (224*(-1 + S^2)*HPL[{1}, -S^2])/(3*(1 + S^2)) - (448*HPL[{1}, -S^2]^2)/3 - (200*HPL[{2}, -S^2])/3) - 4*HPL[{2}, -S^2] + 48*HPL[{3}, -S^2] + 32*Zeta[3]) + HPL[{1}, -S^2]^6*((-4*(1 + S^2))/3 + (2*Pi^2*(-50 + 37*S^2))/(9*(1 + S^2)) - (52*HPL[{2}, -S^2])/3 + (760*HPL[{3}, -S^2])/9 + (200*Zeta[3])/3) + HPL[{2}, -S^2]^3*((-8*(-1 + S^2)*(1 + S^2))/(3*S^2) + (Pi^2*(-43 + 53*S^2))/(9*(1 + S^2)) + (212*HPL[{3}, -S^2])/3 + (424*HPL[{2, 1}, -S^2])/3 + (212*Zeta[3])/3) + HPL[{3, 2, 1}, -S^2]*((2*Pi^2*(-215 + 169*S^2))/(3*(1 + S^2)) - (4*(-17 - 10*S^2 + 8*S^4))/S^2 + 1680*Zeta[3]) + HPL[{4, 1, 1}, -S^2]*((14*Pi^2*(-83 + 33*S^2))/(3*(1 + S^2)) - (8*(-27 - 11*S^2 + 9*S^4))/S^2 + 4864*Zeta[3]) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-384*(-1 + S^2)*(1 + S^2))/S^2 + (64*Pi^2*(-31 + 18*S^2))/(3*(1 + S^2)) + 6208*Zeta[3]) + Log[T]^5*(-24 + (14057*Pi^4)/675 + (4*Pi^2*(1 + S^2))/3 + (326*HPL[{0}, S^2]^4)/45 + (116*Pi^2 + 8*(1 + S^2))*HPL[{1}, -S^2]^2 - (448*(-1 + S^2)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)) + (448*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*((-2*(-271 + 94*S^2))/(45*(1 + S^2)) + (292*HPL[{1}, -S^2])/9) + ((236*Pi^2)/9 + 8*S^2)*HPL[{2}, -S^2] + (472*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((1492*Pi^2)/45 + 4*(1 + S^2) - (4*(-22 + 9*S^2)*HPL[{1}, -S^2])/(1 + S^2) + 124*HPL[{1}, -S^2]^2 + (236*HPL[{2}, -S^2])/3) + (8*(-13 + 82*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - 96*HPL[{4}, -S^2] - 184*HPL[{2, 1}, -S^2] + 96*HPL[{3, 1}, -S^2] + HPL[{1}, -S^2]*(8*(1 + S^2) - (4*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) + 104*HPL[{2}, -S^2] - (1520*HPL[{3}, -S^2])/3 - 400*Zeta[3]) + HPL[{0}, S^2]*(8*(1 + S^2) - (2*Pi^2*(-586 + 619*S^2))/(45*(1 + S^2)) - (224*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + (896*HPL[{1}, -S^2]^3)/3 - (20*(-3 + 7*S^2)*HPL[{2}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]*((964*Pi^2)/9 + 8*(1 + S^2) + 400*HPL[{2}, -S^2]) - (16*HPL[{3}, -S^2])/3 - 400*HPL[{2, 1}, -S^2] - 48*Zeta[3]) + (200*S^2*Zeta[3])/(1 + S^2)) + HPL[{5}, -S^2]*((-97*Pi^4)/90 - (2*Pi^2*(19 + 16*S^2))/3 - (8*(30 + 8*S^2 + 55*S^4))/S^2 - (4*(111 + 29*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 280*HPL[{3, 1}, -S^2] - 280*HPL[{2, 1, 1}, -S^2] + (24*(3 + 4*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 2}, -S^2]*((-449*Pi^4)/45 - (2*Pi^2*(-5 + 26*S^2))/3 - (4*(-4 + 23*S^2 + 19*S^4))/S^2 - 4144*HPL[{2, 1, 1}, -S^2] + (4*(-11 + 15*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^5*((-6673*Pi^4)/675 - (4*Pi^2*(1 + S^2))/3 - (8*(1 + S^2)*(-2 + 3*S^2))/(5*S^2) - (784*Pi^2*HPL[{2}, -S^2])/45 - (1568*HPL[{2}, -S^2]^2)/15 - (8*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (1328*HPL[{4}, -S^2])/15 + 104*HPL[{2, 1}, -S^2] - (1328*HPL[{3, 1}, -S^2])/15 - (8*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4, 1}, -S^2]*((-2024*Pi^4)/45 - (2*Pi^2*(-33 + 82*S^2))/3 - (4*(-28 + 35*S^2 + 41*S^4))/S^2 - 11552*HPL[{2, 1, 1}, -S^2] + (4*(-19 + 87*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1, 1, 1}, -S^2]*((2144*Pi^4)/45 - (8*Pi^2*(-10 + 19*S^2))/3 - (16*(10 + 21*S^2 + 12*S^4))/S^2 + (32*(-79 + 117*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 2, 1}, -S^2]*((-2401*Pi^4)/45 - (52*Pi^2*S^2)/3 - (8*(-12 + 17*S^2 + 10*S^4))/S^2 - (8*(-169 + 185*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1, 1}, -S^2]*((-1093*Pi^4)/9 - (4*Pi^2*(10 + 11*S^2))/3 - (8*(-31 + 36*S^2 + 22*S^4))/S^2 - (8*(-499 + 613*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*((Pi^4*(-473 - 1103*S^2))/(90*(1 + S^2)) + (2*Pi^2*(3 + 8*S^2 + 12*S^4))/(3*S^2) + (4*(-26 + 21*S^2 + 115*S^4))/S^2 - 304*HPL[{5}, -S^2] + ((-412*Pi^2)/3 + 12*(5 + 3*S^2))*HPL[{2, 1}, -S^2] + (4*(21 + 142*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 192*HPL[{3, 2}, -S^2] + 136*HPL[{4, 1}, -S^2] - (4*(35 + 261*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 1376*HPL[{2, 2, 1}, -S^2] + 4320*HPL[{3, 1, 1}, -S^2] - 2752*HPL[{2, 1, 1, 1}, -S^2] + ((-68*Pi^2)/3 + 4*(29 + 10*S^2))*Zeta[3] - 408*Zeta[5]) + HPL[{3, 1}, -S^2]*((Pi^4*(1865 - 523*S^2))/(90*(1 + S^2)) + (4*(-18 + 7*S^2 + 22*S^4))/S^2 + (2*Pi^2*(-22 + 17*S^2 + 28*S^4))/(3*S^2) + 2168*HPL[{3, 2}, -S^2] + 5872*HPL[{4, 1}, -S^2] - (16*(-233 + 159*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 1376*HPL[{2, 2, 1}, -S^2] - 25152*HPL[{3, 1, 1}, -S^2] - 6208*HPL[{2, 1, 1, 1}, -S^2] + (-132*Pi^2 - 8*(11 + 10*S^2))*Zeta[3] - 136*Zeta[5]) + HPL[{0}, S^2]^4*((Pi^4*(-6673 - 2655*S^2))/(4320*(1 + S^2)) + (5*(3 + 53*S^2))/12 + (Pi^2*(19 + 69*S^2))/18 + ((-253 + 31*S^2)*HPL[{1}, -S^2]^4)/(36*(1 + S^2)) - (142*HPL[{1}, -S^2]^5)/45 + HPL[{1}, -S^2]^3*((-277*Pi^2)/54 - (5*(1 + S^2))/18 - (241*HPL[{2}, -S^2])/18) + ((-97 + 23*S^2)*HPL[{2}, -S^2]^2)/(24*(1 + S^2)) + (-2 + (5*Pi^2)/12)*HPL[{3}, -S^2] + ((-8 - 9*S^2)*HPL[{4}, -S^2])/(2*(1 + S^2)) + (9*HPL[{5}, -S^2])/2 + ((-7*Pi^2)/3 + (9 + S^2)/3)*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((Pi^2*(-553 + S^2))/(72*(1 + S^2)) + (1 + S^2)/2 + ((-228 + 13*S^2)*HPL[{2}, -S^2])/(12*(1 + S^2)) + HPL[{3}, -S^2]/2 + (241*HPL[{2, 1}, -S^2])/6) + ((109 - 8*S^2)*HPL[{3, 1}, -S^2])/(6*(1 + S^2)) + 5*HPL[{3, 2}, -S^2] + 9*HPL[{4, 1}, -S^2] + ((-209 + 32*S^2)*HPL[{2, 1, 1}, -S^2])/(6*(1 + S^2)) - 3*HPL[{2, 2, 1}, -S^2] - 9*HPL[{3, 1, 1}, -S^2] + 4*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(-146 - 37*S^2))/(36*(1 + S^2)) + (3 + 2*S^2 + S^4)/(3*S^2) - (5*HPL[{3}, -S^2])/2 + (3*HPL[{2, 1}, -S^2])/2 - 5*Zeta[3]) + HPL[{1}, -S^2]*((-2009*Pi^4)/1080 + (5*Pi^2*(1 + S^2))/36 + (3 + 7*S^2 + 4*S^4)/(3*S^2) + ((-109*Pi^2)/18 + (-1 - S^2)/3)*HPL[{2}, -S^2] - 10*HPL[{2}, -S^2]^2 + ((-4 - 5*S^2)*HPL[{3}, -S^2])/(2*(1 + S^2)) + HPL[{4}, -S^2] + ((228 - 13*S^2)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)) + 39*HPL[{3, 1}, -S^2] - (241*HPL[{2, 1, 1}, -S^2])/3 - (5*Zeta[3])/2) + ((-155*Pi^2)/12 + (7*(1 + 4*S^2))/6)*Zeta[3] - (145*Zeta[5])/2) + ((-1564*Pi^4)/45 + 4*(-85 + 27*S^2) + (2*Pi^2*(-44 + 53*S^2))/3)*Zeta[5] + HPL[{2}, -S^2]^2*(-2*(-34 + 5*S^2) + (Pi^4*(-1636 + 1361*S^2))/(180*(1 + S^2)) + (Pi^2*(-1 - 10*S^2 - 3*S^4))/(3*S^2) + ((155*Pi^2)/3 + 18*S^2)*HPL[{3}, -S^2] - (4*(-6 + 35*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 84*HPL[{5}, -S^2] + ((106*Pi^2)/3 - 20*S^2)*HPL[{2, 1}, -S^2] + (2*(-43 + 39*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 424*HPL[{3, 2}, -S^2] - 1616*HPL[{4, 1}, -S^2] + 8*HPL[{2, 1, 1}, -S^2] - 848*HPL[{2, 2, 1}, -S^2] - 1352*HPL[{3, 1, 1}, -S^2] + (33*Pi^2 + 22*S^2)*Zeta[3] + 90*Zeta[5]) + Log[T]^4*(128 - (8*Pi^2*S^2)/3 + (Pi^4*(-4018 + 2655*S^2))/(270*(1 + S^2)) - (8*HPL[{0}, S^2]^5)/3 + HPL[{0}, S^2]^4*(-71/(9*(1 + S^2)) - (142*HPL[{1}, -S^2])/9) + ((-580*Pi^2)/3 - (40*(1 + S^2))/3)*HPL[{1}, -S^2]^3 + (560*(-1 + S^2)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)) - (448*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^3*((-160*Pi^2)/9 - (4*(3 + S^2))/3 + (2*(-268 + 97*S^2)*HPL[{1}, -S^2])/(9*(1 + S^2)) - (730*HPL[{1}, -S^2]^2)/9 - 56*HPL[{2}, -S^2]) + (392*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + ((548*Pi^2)/9 + 32*S^2)*HPL[{3}, -S^2] - (4*(15 + 181*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - (8*HPL[{5}, -S^2])/3 + ((388*Pi^2)/9 - 40*S^2)*HPL[{2, 1}, -S^2] + (8*(-19 + 64*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) - (1552*HPL[{3, 2}, -S^2])/3 - (5872*HPL[{4, 1}, -S^2])/3 - 120*HPL[{2, 1, 1}, -S^2] - (3104*HPL[{2, 2, 1}, -S^2])/3 - 1664*HPL[{3, 1, 1}, -S^2] + ((388*Pi^2)/9 + 40*(-1 + S^2))*Zeta[3] + HPL[{0}, S^2]^2*(-2*(5 + 4*S^2) + (Pi^2*(-554 + 195*S^2))/(18*(1 + S^2)) + (10*(-22 + 9*S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - (620*HPL[{1}, -S^2]^3)/3 + HPL[{1}, -S^2]*((-749*Pi^2)/9 - 10*(1 + S^2) - (784*HPL[{2}, -S^2])/3) + (7*(-29 + 27*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + (8*HPL[{3}, -S^2])/3 + (388*HPL[{2, 1}, -S^2])/3 + (28*Zeta[3])/3) + HPL[{2}, -S^2]*((-16*(-1 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(-31 + 18*S^2))/(9*(1 + S^2)) + (776*HPL[{3}, -S^2])/3 + (1552*HPL[{2, 1}, -S^2])/3 + (776*Zeta[3])/3) + HPL[{1}, -S^2]^2*(-20*(1 + S^2) + (10*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) - 260*HPL[{2}, -S^2] + (3800*HPL[{3}, -S^2])/3 + 1000*Zeta[3]) + HPL[{1}, -S^2]*((-6673*Pi^4)/135 - (20*Pi^2*(1 + S^2))/3 - (8*(1 + S^2)*(-2 + 3*S^2))/S^2 - (784*Pi^2*HPL[{2}, -S^2])/9 - (1568*HPL[{2}, -S^2]^2)/3 - (40*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (1328*HPL[{4}, -S^2])/3 + 520*HPL[{2, 1}, -S^2] - (1328*HPL[{3, 1}, -S^2])/3 - (40*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]*((-2167*Pi^4)/90 - 4*(1 + 6*S^2) - (2*Pi^2*(11 + 7*S^2))/3 + (1120*(-1 + S^2)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)) - (1120*HPL[{1}, -S^2]^4)/3 + HPL[{1}, -S^2]^2*((-2410*Pi^2)/9 - 20*(1 + S^2) - 1000*HPL[{2}, -S^2]) + ((-418*Pi^2)/3 - 20*S^2)*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/3 - (4*(19 + 36*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - 16*HPL[{4}, -S^2] - (100*(-7 + 3*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (2944*HPL[{3, 1}, -S^2])/3 - 2000*HPL[{2, 1, 1}, -S^2] - (332*S^2*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(-20*(1 + S^2) + (2*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) + (500*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (136*HPL[{3}, -S^2])/3 + 2000*HPL[{2, 1}, -S^2] + (664*Zeta[3])/3)) + (520*Zeta[5])/3) + HPL[{1}, -S^2]^4*((-2*(1 + S^2)*(-36 + 23*S^2))/(3*S^2) - (Pi^2*(1 + S^2)*(-1 + 30*S^2))/(9*S^2) + (Pi^4*(-8587 + 4759*S^2))/(540*(1 + S^2)) + (392*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + ((994*Pi^2)/9 + (20*(1 + S^2))/3)*HPL[{3}, -S^2] - (8*(-28 + 55*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + 144*HPL[{5}, -S^2] + (784*Pi^2*HPL[{2, 1}, -S^2])/9 + (8*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) - (3136*HPL[{3, 2}, -S^2])/3 - (10736*HPL[{4, 1}, -S^2])/3 - 520*HPL[{2, 1, 1}, -S^2] - (6272*HPL[{2, 2, 1}, -S^2])/3 - (11216*HPL[{3, 1, 1}, -S^2])/3 + (832*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*((8*(1 + S^2))/S^2 - (2*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)) + (1568*HPL[{3}, -S^2])/3 + (3136*HPL[{2, 1}, -S^2])/3 + (1568*Zeta[3])/3) + (1520*Zeta[5])/3) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(-4244 + 1819*S^2))/(90*(1 + S^2)) + (4*(73 + 26*S^2 + S^4))/S^2 - (8*Pi^2*(-11 + 12*S^4))/(3*S^2) + 6208*HPL[{3, 1, 1}, -S^2] + 12416*HPL[{2, 1, 1, 1}, -S^2] + (272*Pi^2 + 16*(10 + 11*S^2))*Zeta[3] + 592*Zeta[5]) + Zeta[3]*((-1847*Pi^6)/567 + 2*Pi^2*(-13 + 7*S^2) + 4*(-79 + 38*S^2) + (Pi^4*(-142 + 325*S^2))/90 - (124*Zeta[5])/(1 + S^2)) + HPL[{3}, -S^2]*((1996*Pi^6)/2835 + (Pi^4*(-79 + 68*S^2))/45 + (2*Pi^2*(-1 + 18*S^2 + 2*S^4))/(3*S^2) - (4*(12 - 21*S^2 + 146*S^4))/S^2 + ((70*Pi^2)/3 - 4*(25 + 8*S^2))*HPL[{4}, -S^2] + (56*(3 + 4*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 480*HPL[{6}, -S^2] - 1192*HPL[{2, 1}, -S^2]^2 + ((-356*Pi^2)/3 - 8*(7 + 11*S^2))*HPL[{3, 1}, -S^2] - (4*(-9 + 77*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (108*(1 + 2*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 60*HPL[{4, 2}, -S^2] - 440*HPL[{5, 1}, -S^2] + (248*Pi^2 + 16*(1 + 12*S^2))*HPL[{2, 1, 1}, -S^2] - (8*(-235 + 231*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (16*(-351 + 311*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 16*HPL[{3, 1, 2}, -S^2] + 1680*HPL[{3, 2, 1}, -S^2] - 66936*HPL[{4, 1, 1}, -S^2] + (16*(-235 + 157*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 3104*HPL[{3, 1, 1, 1}, -S^2] + 6208*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((2*Pi^2*(-262 + 151*S^2))/(3*(1 + S^2)) + (32*(-1 - 2*S^2 + 2*S^4))/S^2 - 80*Zeta[3]) + ((-2*Pi^2*(-3 + 23*S^2))/(3*(1 + S^2)) + (4*(-2 + 17*S^2 + 14*S^4))/S^2)*Zeta[3] - 8*Zeta[3]^2 - (4*(21 + 37*S^2)*Zeta[5])/(1 + S^2)) + Log[T]^3*(-1480/3 + (2863*Pi^6)/162 + (4*Pi^2*(-41 + 14*S^2))/9 + (Pi^4*(322 + 351*S^2))/135 + (14*HPL[{0}, S^2]^6)/9 + ((580*Pi^2)/3 + (40*(1 + S^2))/3)*HPL[{1}, -S^2]^4 - (448*(-1 + S^2)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)) + (896*HPL[{1}, -S^2]^6)/9 + HPL[{0}, S^2]^5*((365 + 94*S^2)/(90*(1 + S^2)) + (271*HPL[{1}, -S^2])/45) + (204*Pi^2 - (8*(-5 + S^2))/3)*HPL[{2}, -S^2]^2 + HPL[{0}, S^2]^4*((373*Pi^2)/27 + (16 + 3*S^2)/9 + ((253 - 31*S^2)*HPL[{1}, -S^2])/(9*(1 + S^2)) + (284*HPL[{1}, -S^2]^2)/9 + (235*HPL[{2}, -S^2])/9) + (176*HPL[{3}, -S^2]^2)/3 + ((-704*Pi^2)/9 - 8*(1 + S^2))*HPL[{4}, -S^2] + (8*(19 + 127*S^2)*HPL[{5}, -S^2])/(3*(1 + S^2)) + (56*HPL[{6}, -S^2])/3 - (9440*HPL[{2, 1}, -S^2]^2)/3 + (-176*Pi^2 - 64*S^2)*HPL[{3, 1}, -S^2] - (16*(-11 + 381*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) - (32*(-50 + 621*S^2)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)) + 240*HPL[{4, 2}, -S^2] + (4832*HPL[{5, 1}, -S^2])/3 + ((4720*Pi^2)/9 + 160*S^2)*HPL[{2, 1, 1}, -S^2] - (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)) - (32*(-523 + 178*S^2)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)) - 1920*HPL[{4, 1, 1}, -S^2] - 3680*HPL[{2, 1, 1, 1}, -S^2] + 1920*HPL[{3, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^3*((80*(1 + S^2))/3 - (40*Pi^2*(-50 + 37*S^2))/(9*(1 + S^2)) + (1040*HPL[{2}, -S^2])/3 - (15200*HPL[{3}, -S^2])/9 - (4000*Zeta[3])/3) + HPL[{3}, -S^2]*((4*Pi^2*(-46 + 451*S^2))/(9*(1 + S^2)) - (8*(-3 + 10*S^2 + 24*S^4))/(3*S^2) + (9440*HPL[{2, 1}, -S^2])/3 - 224*Zeta[3]) + (-32*(-3 + 2*S^2) + (4*Pi^2*(11 + 427*S^2))/(9*(1 + S^2)))*Zeta[3] + 112*Zeta[3]^2 + HPL[{0}, S^2]^3*((212*Pi^2)/(9*(1 + S^2)) + (4*(23 + 3*S^2))/9 - (4*(-268 + 97*S^2)*HPL[{1}, -S^2]^2)/(9*(1 + S^2)) + (2920*HPL[{1}, -S^2]^3)/27 - (4*(-106 + 59*S^2)*HPL[{2}, -S^2])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((424*Pi^2)/9 + (8*(1 + S^2))/3 + (440*HPL[{2}, -S^2])/3) + (40*HPL[{3}, -S^2])/9 - (208*HPL[{2, 1}, -S^2])/3 + (56*Zeta[3])/9) + HPL[{2, 1}, -S^2]*(64*(1 + S^2) - (112*Pi^2*(27 + 13*S^2))/(9*(1 + S^2)) + (9440*Zeta[3])/3) + HPL[{1}, -S^2]^2*((13346*Pi^4)/135 + (40*Pi^2*(1 + S^2))/3 + (16*(1 + S^2)*(-2 + 3*S^2))/S^2 + (1568*Pi^2*HPL[{2}, -S^2])/9 + (3136*HPL[{2}, -S^2]^2)/3 + (80*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (2656*HPL[{4}, -S^2])/3 - 1040*HPL[{2, 1}, -S^2] + (2656*HPL[{3, 1}, -S^2])/3 + (80*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^2*((4934*Pi^4)/135 + (8*(2 + 7*S^2))/3 + (2*Pi^2*(31 + 18*S^2))/9 - (40*(-22 + 9*S^2)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)) + (620*HPL[{1}, -S^2]^4)/3 + ((1060*Pi^2)/9 + (56*S^2)/3)*HPL[{2}, -S^2] + (656*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((1498*Pi^2)/9 + 20*(1 + S^2) + (1568*HPL[{2}, -S^2])/3) + (4*(19 + 41*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (16*HPL[{4}, -S^2])/3 - (4*(411 + 19*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) - 768*HPL[{3, 1}, -S^2] + (4720*HPL[{2, 1, 1}, -S^2])/3 + HPL[{1}, -S^2]*((4*(1 + S^2)*(-1 + 15*S^2))/(3*S^2) - (2*Pi^2*(-583 + 166*S^2))/(9*(1 + S^2)) - (4*(-307 + 85*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) - (176*HPL[{3}, -S^2])/3 - (3136*HPL[{2, 1}, -S^2])/3 - (328*Zeta[3])/3) + (4*(11 + 52*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2}, -S^2]*((4991*Pi^4)/135 + (116*Pi^2*S^2)/9 + (8*(-22 - 9*S^2 + 14*S^4))/(3*S^2) + (8*(9 + 401*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - 144*HPL[{4}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) - (9440*HPL[{3, 1}, -S^2])/3 + (18880*HPL[{2, 1, 1}, -S^2])/3 + (16*(-33 + 163*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]*((Pi^4*(8587 - 4759*S^2))/(135*(1 + S^2)) + (8*(1 + S^2)*(-36 + 23*S^2))/(3*S^2) + (4*Pi^2*(1 + S^2)*(-1 + 30*S^2))/(9*S^2) - (1568*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + ((-3976*Pi^2)/9 - (80*(1 + S^2))/3)*HPL[{3}, -S^2] + (32*(-28 + 55*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - 576*HPL[{5}, -S^2] - (3136*Pi^2*HPL[{2, 1}, -S^2])/9 - (32*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) + (12544*HPL[{3, 2}, -S^2])/3 + (42944*HPL[{4, 1}, -S^2])/3 + 2080*HPL[{2, 1, 1}, -S^2] + (25088*HPL[{2, 2, 1}, -S^2])/3 + (44864*HPL[{3, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((-32*(1 + S^2))/S^2 + (8*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)) - (6272*HPL[{3}, -S^2])/3 - (12544*HPL[{2, 1}, -S^2])/3 - (6272*Zeta[3])/3) - (3328*Pi^2*Zeta[3])/9 - (6080*Zeta[5])/3) + HPL[{0}, S^2]*((Pi^4*(7994 - 4189*S^2))/(270*(1 + S^2)) + (8*Pi^2*(19 + 9*S^2))/9 + (8*(-25 + 23*S^2))/3 - (1120*(-1 + S^2)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)) + (896*HPL[{1}, -S^2]^5)/3 - (8*(-75 + 121*S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + HPL[{1}, -S^2]^3*((9640*Pi^2)/27 + (80*(1 + S^2))/3 + (4000*HPL[{2}, -S^2])/3) - (8*(-9 + 13*S^2)*HPL[{3}, -S^2])/3 - (4*(-33 + 13*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + (248*HPL[{5}, -S^2])/3 + ((-1208*Pi^2)/3 + 80*S^2)*HPL[{2, 1}, -S^2] + (16*(-37 + 88*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (688*HPL[{3, 2}, -S^2])/3 + (1472*HPL[{4, 1}, -S^2])/3 - (400*(-3 + 7*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (12544*HPL[{2, 2, 1}, -S^2])/3 + (37312*HPL[{3, 1, 1}, -S^2])/3 - 8000*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*(40*(1 + S^2) - (4*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) - (1000*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (272*HPL[{3}, -S^2])/3 - 4000*HPL[{2, 1}, -S^2] - (1328*Zeta[3])/3) + HPL[{2}, -S^2]*((8*(1 + S^2)*(-11 + 12*S^2))/(3*S^2) - (2*Pi^2*(-437 + 643*S^2))/(9*(1 + S^2)) - 112*HPL[{3}, -S^2] - (6272*HPL[{2, 1}, -S^2])/3 - 208*Zeta[3]) + ((-304*Pi^2)/9 - 16*(-1 + S^2))*Zeta[3] + HPL[{1}, -S^2]*((4061*Pi^4)/45 + (28*Pi^2*(1 + S^2))/3 + (16*(1 + S^2)*(-2 + 3*S^2))/S^2 + 480*Pi^2*HPL[{2}, -S^2] + (3136*HPL[{2}, -S^2]^2)/3 + (16*(-10 + 7*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (368*HPL[{4}, -S^2])/3 + (2000*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 4000*HPL[{3, 1}, -S^2] + 8000*HPL[{2, 1, 1}, -S^2] + (16*(-40 + 43*S^2)*Zeta[3])/(3*(1 + S^2))) - 208*Zeta[5]) + (32*(4 + 99*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((211*Pi^6)/540 + (Pi^4*(346 - 187*S^2))/90 - (4*Pi^2*(12 + 7*S^2 + 8*S^4))/(3*S^2) - (8*(24 + 61*S^2 + 19*S^4))/S^2 + ((-1168*Pi^2)/3 - 16*(1 + 7*S^2))*HPL[{3, 1}, -S^2] - (4*(-431 + 423*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (20*(-289 + 225*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 624*HPL[{4, 2}, -S^2] + 3528*HPL[{5, 1}, -S^2] + ((-2368*Pi^2)/3 - 192*S^2)*HPL[{2, 1, 1}, -S^2] + 32*HPL[{2, 2, 1}, -S^2] + (16*(-229 + 163*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 624*HPL[{3, 1, 2}, -S^2] + 2768*HPL[{3, 2, 1}, -S^2] + 7424*HPL[{4, 1, 1}, -S^2] - (6272*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 6208*HPL[{3, 1, 1, 1}, -S^2] - 12416*HPL[{2, 1, 1, 1, 1}, -S^2] + (-16/S^2 + (2*Pi^2*(-174 + 257*S^2))/(3*(1 + S^2)))*Zeta[3] - 32*Zeta[3]^2 + (4*(-66 + 295*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^3*((-52285*Pi^6)/6804 - (233*Pi^4*(1 + S^2))/135 - (8*Pi^2*(1 + S^2)*(-2 + 3*S^2))/(3*S^2) - (8*(1 + S^2)*(-43 + 28*S^2))/(3*S^2) + ((-1214*Pi^2)/9 - (20*(1 + S^2))/3)*HPL[{2}, -S^2]^2 - (296*HPL[{3}, -S^2]^2)/3 + (680*Pi^2*HPL[{4}, -S^2])/9 - (16*(-1 + 53*S^2)*HPL[{5}, -S^2])/(3*(1 + S^2)) + (356*HPL[{6}, -S^2])/3 + (6272*HPL[{2, 1}, -S^2]^2)/3 + (880*Pi^2*HPL[{3, 1}, -S^2])/9 + (16*(-113 + 279*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) + (16*(-395 + 947*S^2)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)) - 312*HPL[{4, 2}, -S^2] - (5408*HPL[{5, 1}, -S^2])/3 - (3136*Pi^2*HPL[{2, 1, 1}, -S^2])/9 + (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)) + (32*(-448 + 253*S^2)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)) + (5312*HPL[{4, 1, 1}, -S^2])/3 + 2080*HPL[{2, 1, 1, 1}, -S^2] - (5312*HPL[{3, 1, 1, 1}, -S^2])/3 + HPL[{2, 1}, -S^2]*((-32*(1 + S^2))/S^2 + (8*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)) - (6272*Zeta[3])/3) + ((8*(1 + S^2))/(3*S^2) - (8*Pi^2*(-49 + 159*S^2))/(9*(1 + S^2)))*Zeta[3] - (160*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((8*(1 + S^2)*(5 + 4*S^2))/(3*S^2) - (4*Pi^2*(-137 + 360*S^2))/(9*(1 + S^2)) - (6272*HPL[{2, 1}, -S^2])/3 + (400*Zeta[3])/3) + HPL[{2}, -S^2]*((-2021*Pi^4)/90 - (20*Pi^2*(1 + S^2))/9 - (8*(-16 + S^2)*(1 + S^2))/(3*S^2) - (8*(-113 + 279*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (904*HPL[{4}, -S^2])/3 - (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (6272*HPL[{3, 1}, -S^2])/3 - (12544*HPL[{2, 1, 1}, -S^2])/3 - (448*(-2 + 5*S^2)*Zeta[3])/(3*(1 + S^2))) - (8*(-51 + 329*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{0}, S^2]^3*((-659*Pi^6)/5670 + (Pi^4*(-1798 - 1669*S^2))/540 + (Pi^2*(-142 - 217*S^2))/18 - (2*(-13 + 193*S^2))/3 + (2*(-268 + 97*S^2)*HPL[{1}, -S^2]^5)/(45*(1 + S^2)) - (146*HPL[{1}, -S^2]^6)/27 + HPL[{1}, -S^2]^4*((-106*Pi^2)/9 - (2*(1 + S^2))/3 - (110*HPL[{2}, -S^2])/3) + ((-73*Pi^2)/6 + (-16 - 3*S^2)/6)*HPL[{2}, -S^2]^2 - (38*HPL[{2}, -S^2]^3)/3 - (5*HPL[{3}, -S^2]^2)/3 + ((-40*Pi^2)/9 + (16 + S^2)/3)*HPL[{4}, -S^2] + ((37 + 60*S^2)*HPL[{5}, -S^2])/(3*(1 + S^2)) - (116*HPL[{6}, -S^2])/3 + 162*HPL[{2, 1}, -S^2]^2 + ((470*Pi^2)/9 + (4*(-4 + S^2))/3)*HPL[{3, 1}, -S^2] + ((41 + 55*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) + (2*(51 + 55*S^2)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)) + (92*HPL[{5, 1}, -S^2])/3 + ((-328*Pi^2)/3 - (16*S^2)/3)*HPL[{2, 1, 1}, -S^2] + (2*(-83 + 23*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (2*(-785 + 181*S^2)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)) - 304*HPL[{3, 2, 1}, -S^2] - (2816*HPL[{4, 1, 1}, -S^2])/3 - (8*(-142 + 23*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)) + (1960*HPL[{3, 1, 1, 1}, -S^2])/3 - 1344*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((4*(-9 + S^2))/3 - (11*Pi^2*(-13 + 4*S^2))/(6*(1 + S^2)) - 20*Zeta[3]) + ((Pi^2*(-416 - 427*S^2))/(18*(1 + S^2)) - (2*(22 + 5*S^2))/3)*Zeta[3] + 18*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-19 + 2*S^2))/(18*(1 + S^2)) + (3 - S^2 + 4*S^4)/(3*S^2) - (20*HPL[{2, 1}, -S^2])/3 + 4*Zeta[3]) + HPL[{1}, -S^2]^3*((-2*(1 + S^2)*(1 + 9*S^2))/(9*S^2) + (Pi^2*(-523 + 113*S^2))/(27*(1 + S^2)) + (4*(-124 + 41*S^2)*HPL[{2}, -S^2])/(9*(1 + S^2)) - (8*HPL[{3}, -S^2])/3 + (440*HPL[{2, 1}, -S^2])/3 + (44*Zeta[3])/9) + HPL[{2}, -S^2]*((-308*Pi^4)/45 + (Pi^2*(5 + 3*S^2))/9 + (26 - 9*S^2 - 10*S^4)/(3*S^2) + ((-20 - 27*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (10*HPL[{4}, -S^2])/3 + ((83 - 23*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (476*HPL[{3, 1}, -S^2])/3 - 324*HPL[{2, 1, 1}, -S^2] + ((-50 - 59*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]^2*((-3997*Pi^4)/540 - (8*Pi^2*(1 + S^2))/9 - (4*(1 + S^2)*(-2 + 7*S^2))/(3*S^2) + ((-187*Pi^2)/6 + (-1 - S^2)/3)*HPL[{2}, -S^2] - 53*HPL[{2}, -S^2]^2 - (4*HPL[{3}, -S^2])/(1 + S^2) - (34*HPL[{4}, -S^2])/3 - (4*(-124 + 41*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + 220*HPL[{3, 1}, -S^2] - 440*HPL[{2, 1, 1}, -S^2] - (2*(3 + 14*S^2)*Zeta[3])/(3*(1 + S^2))) - (4*(95 + 99*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((7*Pi^4*(-551 + 20*S^2))/(540*(1 + S^2)) - (Pi^2*(1 + S^2)*(1 + 29*S^2))/(18*S^2) - ((1 + S^2)*(-30 + 67*S^2))/(3*S^2) + ((-39 + 14*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + ((-7*Pi^2)/3 + (4*(1 + S^2))/3)*HPL[{3}, -S^2] + (2*(-6 + 11*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - (46*HPL[{5}, -S^2])/3 + ((187*Pi^2)/3 + (2*(1 + S^2))/3)*HPL[{2, 1}, -S^2] - (4*(-41 + 14*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (28*HPL[{3, 2}, -S^2])/3 - (16*HPL[{4, 1}, -S^2])/3 + (8*(-124 + 41*S^2)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)) - 424*HPL[{2, 2, 1}, -S^2] - 1288*HPL[{3, 1, 1}, -S^2] + 880*HPL[{2, 1, 1, 1}, -S^2] + ((11*Pi^2)/9 - (26*(1 + S^2))/3)*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-11 + 4*S^2))/(3*S^2) + (Pi^2*(-458 + 103*S^2))/(18*(1 + S^2)) + (14*HPL[{3}, -S^2])/3 + 212*HPL[{2, 1}, -S^2] + 6*Zeta[3]) + (32*Zeta[5])/3)) + Log[T]^2*(1440 + (Pi^4*(-69 - 47*S^2))/30 + (Pi^2*(217 + S^2))/3 + (Pi^6*(-39083 + 13202*S^2))/(4536*(1 + S^2)) - HPL[{0}, S^2]^7/4 + HPL[{0}, S^2]^6*((-31 - 13*S^2)/(24*(1 + S^2)) - (3*HPL[{1}, -S^2])/2) + (-116*Pi^2 - 8*(1 + S^2))*HPL[{1}, -S^2]^5 + (224*(-1 + S^2)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)) - (128*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^5*((-37*Pi^2)/12 + (-7 - 4*S^2)/6 + ((-255 + 16*S^2)*HPL[{1}, -S^2])/(30*(1 + S^2)) - (271*HPL[{1}, -S^2]^2)/30 - 8*HPL[{2}, -S^2]) + (4*HPL[{2}, -S^2]^3)/3 + (2*(-3 + 71*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((-22*Pi^2)/3 - 8*(-1 + 3*S^2))*HPL[{5}, -S^2] - (2*(285 + 374*S^2)*HPL[{6}, -S^2])/(1 + S^2) - 748*HPL[{7}, -S^2] - (1568*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((-740*Pi^2)/3 - 8*(1 + 22*S^2))*HPL[{3, 2}, -S^2] + ((-2888*Pi^2)/3 - 24*(1 + 23*S^2))*HPL[{4, 1}, -S^2] + (2*(43 + 277*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) - 256*HPL[{4, 3}, -S^2] + (16*(28 + 197*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) - 700*HPL[{5, 2}, -S^2] - 1288*HPL[{6, 1}, -S^2] + ((-2368*Pi^2)/3 - 192*S^2)*HPL[{2, 2, 1}, -S^2] + ((-4912*Pi^2)/3 - 192*S^2)*HPL[{3, 1, 1}, -S^2] - 320*HPL[{3, 1, 2}, -S^2] - 288*HPL[{3, 2, 1}, -S^2] + 3848*HPL[{3, 2, 2}, -S^2] + 11392*HPL[{3, 3, 1}, -S^2] - (16*(9 + 175*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + 10832*HPL[{4, 1, 2}, -S^2] + 34448*HPL[{4, 2, 1}, -S^2] + 70816*HPL[{5, 1, 1}, -S^2] + ((1552*Pi^2)/3 - 480*S^2)*HPL[{2, 1, 1, 1}, -S^2] + (32*(-19 + 64*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - 6208*HPL[{3, 1, 1, 2}, -S^2] - 6208*HPL[{3, 1, 2, 1}, -S^2] - 6208*HPL[{3, 2, 1, 1}, -S^2] - 23488*HPL[{4, 1, 1, 1}, -S^2] - 1440*HPL[{2, 1, 1, 1, 1}, -S^2] + 12416*HPL[{2, 1, 2, 1, 1}, -S^2] + 37248*HPL[{2, 2, 1, 1, 1}, -S^2] + 79360*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-2*Pi^2*(-159 + 61*S^2))/(3*(1 + S^2)) + (8*(-11 + 2*S^2 + 14*S^4))/S^2 - 1600*Zeta[3]) + HPL[{4}, -S^2]*((-5*Pi^2*(13 + 81*S^2))/(3*(1 + S^2)) + (4*(3 + 11*S^2 + 15*S^4))/S^2 - 1376*HPL[{2, 1}, -S^2] - 112*Zeta[3]) + HPL[{0}, S^2]^4*((Pi^2*(-749 - 195*S^2))/(72*(1 + S^2)) + (7*(-2 + 3*S^2))/6 + ((-253 + 31*S^2)*HPL[{1}, -S^2]^2)/(6*(1 + S^2)) - (284*HPL[{1}, -S^2]^3)/9 + HPL[{1}, -S^2]*((-277*Pi^2)/18 - (5*(1 + S^2))/6 - (241*HPL[{2}, -S^2])/6) + ((-209 + 32*S^2)*HPL[{2}, -S^2])/(12*(1 + S^2)) + 2*HPL[{2, 1}, -S^2] - 15*Zeta[3]) + ((373*Pi^4)/45 + 24*(-9 + 4*S^2) + (4*Pi^2*(-18 + 19*S^2))/3)*Zeta[3] + (4*(-9 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2}, -S^2]^2*((Pi^2*(-615 + 599*S^2))/(6*(1 + S^2)) + (4*(-1 - 5*S^2 + S^4))/S^2 + 596*HPL[{3}, -S^2] + 368*Zeta[3]) + HPL[{1}, -S^2]^4*(-20*(1 + S^2) + (10*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) - 260*HPL[{2}, -S^2] + (3800*HPL[{3}, -S^2])/3 + 1000*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-192*(-1 + S^2)*(1 + S^2))/S^2 + (32*Pi^2*(-31 + 18*S^2))/(3*(1 + S^2)) + 3104*Zeta[3]) + HPL[{1}, -S^2]^3*((-13346*Pi^4)/135 - (40*Pi^2*(1 + S^2))/3 - (16*(1 + S^2)*(-2 + 3*S^2))/S^2 - (1568*Pi^2*HPL[{2}, -S^2])/9 - (3136*HPL[{2}, -S^2]^2)/3 - (80*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (2656*HPL[{4}, -S^2])/3 + 1040*HPL[{2, 1}, -S^2] - (2656*HPL[{3, 1}, -S^2])/3 - (80*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((869*Pi^4)/45 + (4*Pi^2*(-5 + 14*S^2))/3 + (4*(-5 + 15*S^2 + 8*S^4))/S^2 + 96*HPL[{4}, -S^2] + (8*(-235 + 157*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 1552*HPL[{3, 1}, -S^2] + 3104*HPL[{2, 1, 1}, -S^2] - (8*(4 + 29*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((1072*Pi^4)/45 - (4*Pi^2*(-10 + 19*S^2))/3 - (8*(10 + 21*S^2 + 12*S^4))/S^2 - 3104*HPL[{3, 1}, -S^2] - 6208*HPL[{2, 1, 1}, -S^2] + (16*(-79 + 117*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^3*((-2167*Pi^4)/180 + (Pi^2*(-53 - 26*S^2))/9 - (44*(1 + S^2))/3 + (4*(-268 + 97*S^2)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)) - (730*HPL[{1}, -S^2]^4)/9 + HPL[{1}, -S^2]^2*((-212*Pi^2)/3 - 4*(1 + S^2) - 220*HPL[{2}, -S^2]) + ((-164*Pi^2)/3 - (8*S^2)/3)*HPL[{2}, -S^2] - 81*HPL[{2}, -S^2]^2 - (2*(19 + 13*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (40*HPL[{4}, -S^2])/3 - (4*(-142 + 23*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (980*HPL[{3, 1}, -S^2])/3 - 672*HPL[{2, 1, 1}, -S^2] - (2*(41 + 52*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((-2*(1 + S^2)*(1 + 9*S^2))/(3*S^2) + (Pi^2*(-523 + 113*S^2))/(9*(1 + S^2)) + (4*(-124 + 41*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) - 8*HPL[{3}, -S^2] + 440*HPL[{2, 1}, -S^2] + (44*Zeta[3])/3)) + HPL[{0}, S^2]^2*(25 + S^2 - (8449*Pi^4)/(360*(1 + S^2)) + (Pi^2*(-29 + 9*S^2))/3 + (10*(-22 + 9*S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) - 124*HPL[{1}, -S^2]^5 + HPL[{1}, -S^2]^3*((-1498*Pi^2)/9 - 20*(1 + S^2) - (1568*HPL[{2}, -S^2])/3) + ((-223 + 207*S^2)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)) + ((4*Pi^2)/3 + 4*(-5 + 2*S^2))*HPL[{3}, -S^2] + ((-35 - 43*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 18*HPL[{5}, -S^2] + ((206*Pi^2)/3 - 8*(-5 + 2*S^2))*HPL[{2, 1}, -S^2] - (2*(-197 + 189*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 36*HPL[{3, 2}, -S^2] + 48*HPL[{4, 1}, -S^2] + (28*(-29 + 27*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 816*HPL[{2, 2, 1}, -S^2] - 2416*HPL[{3, 1, 1}, -S^2] + 1552*HPL[{2, 1, 1, 1}, -S^2] + ((-76*Pi^2)/3 + 4*(-3 + 4*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-412 + 221*S^2))/(6*(1 + S^2)) - (4*(-5 + 6*S^4))/S^2 - 16*HPL[{3}, -S^2] + 408*HPL[{2, 1}, -S^2] + 20*Zeta[3]) + HPL[{1}, -S^2]^2*((-2*(1 + S^2)*(-1 + 15*S^2))/S^2 + (Pi^2*(-583 + 166*S^2))/(3*(1 + S^2)) + (2*(-307 + 85*S^2)*HPL[{2}, -S^2])/(1 + S^2) + 88*HPL[{3}, -S^2] + 1568*HPL[{2, 1}, -S^2] + 164*Zeta[3]) + HPL[{1}, -S^2]*((-8449*Pi^4)/180 - (20*Pi^2*(1 + S^2))/3 - (12*(1 + S^2)*(-2 + 3*S^2))/S^2 + (-211*Pi^2 - 20*(1 + S^2))*HPL[{2}, -S^2] - 430*HPL[{2}, -S^2]^2 - (4*(3 + 25*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 16*HPL[{4}, -S^2] - (4*(-307 + 85*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 1544*HPL[{3, 1}, -S^2] - 3136*HPL[{2, 1, 1}, -S^2] - (4*(-8 + 33*S^2)*Zeta[3])/(1 + S^2)) - 156*Zeta[5]) + ((104*Pi^2)/3 + 8*(-30 + 29*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-4244 + 1819*S^2))/(180*(1 + S^2)) + (2*(73 + 26*S^2 + S^4))/S^2 - (4*Pi^2*(-11 + 12*S^4))/(3*S^2) + (124*Pi^2 + 8*(1 + 12*S^2))*HPL[{3}, -S^2] - (2*(35 + 261*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 140*HPL[{5}, -S^2] + ((1184*Pi^2)/3 + 96*S^2)*HPL[{2, 1}, -S^2] - (8*(-233 + 159*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 2072*HPL[{3, 2}, -S^2] - 5776*HPL[{4, 1}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 3104*HPL[{3, 1, 1}, -S^2] + 6208*HPL[{2, 1, 1, 1}, -S^2] + (136*Pi^2 + 8*(10 + 11*S^2))*Zeta[3] + 296*Zeta[5]) + HPL[{1}, -S^2]^2*((-4*(1 + S^2)*(-36 + 23*S^2))/S^2 - (2*Pi^2*(1 + S^2)*(-1 + 30*S^2))/(3*S^2) + (Pi^4*(-8587 + 4759*S^2))/(90*(1 + S^2)) + (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + ((1988*Pi^2)/3 + 40*(1 + S^2))*HPL[{3}, -S^2] - (16*(-28 + 55*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 864*HPL[{5}, -S^2] + (1568*Pi^2*HPL[{2, 1}, -S^2])/3 + (16*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 6272*HPL[{3, 2}, -S^2] - 21472*HPL[{4, 1}, -S^2] - 3120*HPL[{2, 1, 1}, -S^2] - 12544*HPL[{2, 2, 1}, -S^2] - 22432*HPL[{3, 1, 1}, -S^2] + (1664*Pi^2*Zeta[3])/3 + HPL[{2}, -S^2]*((48*(1 + S^2))/S^2 - (4*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)) + 3136*HPL[{3}, -S^2] + 6272*HPL[{2, 1}, -S^2] + 3136*Zeta[3]) + 3040*Zeta[5]) + HPL[{1}, -S^2]*((-52285*Pi^6)/2268 - (233*Pi^4*(1 + S^2))/45 - (8*Pi^2*(1 + S^2)*(-2 + 3*S^2))/S^2 - (8*(1 + S^2)*(-43 + 28*S^2))/S^2 + ((-1214*Pi^2)/3 - 20*(1 + S^2))*HPL[{2}, -S^2]^2 - 296*HPL[{3}, -S^2]^2 + (680*Pi^2*HPL[{4}, -S^2])/3 - (16*(-1 + 53*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 356*HPL[{6}, -S^2] + 6272*HPL[{2, 1}, -S^2]^2 + (880*Pi^2*HPL[{3, 1}, -S^2])/3 + (16*(-113 + 279*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (16*(-395 + 947*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 936*HPL[{4, 2}, -S^2] - 5408*HPL[{5, 1}, -S^2] - (3136*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (32*(-448 + 253*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 5312*HPL[{4, 1, 1}, -S^2] + 6240*HPL[{2, 1, 1, 1}, -S^2] - 5312*HPL[{3, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-96*(1 + S^2))/S^2 + (8*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)) - 6272*Zeta[3]) + ((8*(1 + S^2))/S^2 - (8*Pi^2*(-49 + 159*S^2))/(3*(1 + S^2)))*Zeta[3] - 160*Zeta[3]^2 + HPL[{3}, -S^2]*((8*(1 + S^2)*(5 + 4*S^2))/S^2 - (4*Pi^2*(-137 + 360*S^2))/(3*(1 + S^2)) - 6272*HPL[{2, 1}, -S^2] + 400*Zeta[3]) + HPL[{2}, -S^2]*((-2021*Pi^4)/30 - (20*Pi^2*(1 + S^2))/3 - (8*(-16 + S^2)*(1 + S^2))/S^2 - (8*(-113 + 279*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 904*HPL[{4}, -S^2] - (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 6272*HPL[{3, 1}, -S^2] - 12544*HPL[{2, 1, 1}, -S^2] - (448*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) - (8*(-51 + 329*S^2)*Zeta[5])/(1 + S^2)) + HPL[{0}, S^2]*((-7919*Pi^6)/630 + (Pi^4*(-646 - 397*S^2))/90 - 28*(-13 + 8*S^2) - (10*Pi^2*(5 + 8*S^2))/3 + (224*(-1 + S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) - (448*HPL[{1}, -S^2]^6)/3 + HPL[{1}, -S^2]^4*((-2410*Pi^2)/9 - 20*(1 + S^2) - 1000*HPL[{2}, -S^2]) + ((-635*Pi^2)/3 - 20*(2 + S^2))*HPL[{2}, -S^2]^2 - 236*HPL[{2}, -S^2]^3 - 20*HPL[{3}, -S^2]^2 + ((-64*Pi^2)/3 - 4*(-5 + S^2))*HPL[{4}, -S^2] + (4*(-19 + 4*S^2)*HPL[{5}, -S^2])/(1 + S^2) - 132*HPL[{6}, -S^2] + 3136*HPL[{2, 1}, -S^2]^2 + ((2452*Pi^2)/3 + 8*(-1 + 11*S^2))*HPL[{3, 1}, -S^2] + (152*(1 + 3*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (4*(109 + 291*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 40*HPL[{4, 2}, -S^2] + 232*HPL[{5, 1}, -S^2] + (-1672*Pi^2 - 240*S^2)*HPL[{2, 1, 1}, -S^2] + (32*(-121 + 75*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (16*(-745 + 414*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 16*HPL[{3, 1, 2}, -S^2] - 5680*HPL[{3, 2, 1}, -S^2] - 17184*HPL[{4, 1, 1}, -S^2] - (1200*(-7 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + 11776*HPL[{3, 1, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-8*(1 + S^2)*(-1 + 12*S^2))/S^2 - (2*Pi^2*(-809 + 271*S^2))/(3*(1 + S^2)) - 688*Zeta[3]) + (-16*(4 + S^2) - (2*Pi^2*(41 + 135*S^2))/(3*(1 + S^2)))*Zeta[3] + 48*Zeta[3]^2 + HPL[{3}, -S^2]*((-2*Pi^2*(38 + 49*S^2))/(3*(1 + S^2)) + (4*(1 + 4*S^2 + 18*S^4))/S^2 - 272*HPL[{2, 1}, -S^2] + 48*Zeta[3]) + HPL[{1}, -S^2]^3*(-40*(1 + S^2) + (4*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) + (1000*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (272*HPL[{3}, -S^2])/3 + 4000*HPL[{2, 1}, -S^2] + (1328*Zeta[3])/3) + HPL[{2}, -S^2]*((-7153*Pi^4)/90 - (38*Pi^2*S^2)/3 - (4*(-22 - 9*S^2 + 14*S^4))/S^2 - (8*(9 + 28*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 16*HPL[{4}, -S^2] - (16*(-121 + 75*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 3104*HPL[{3, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2] - (8*(-1 + 40*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-4061*Pi^4)/30 - 14*Pi^2*(1 + S^2) - (24*(1 + S^2)*(-2 + 3*S^2))/S^2 - 720*Pi^2*HPL[{2}, -S^2] - 1568*HPL[{2}, -S^2]^2 - (8*(-10 + 7*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 184*HPL[{4}, -S^2] - (3000*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 6000*HPL[{3, 1}, -S^2] - 12000*HPL[{2, 1, 1}, -S^2] - (8*(-40 + 43*S^2)*Zeta[3])/(1 + S^2)) - (52*(3 + 8*S^2)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*((-4*(1 + S^2)*(-36 + 23*S^2))/S^2 - (2*Pi^2*(1 + S^2)*(1 + 24*S^2))/(3*S^2) + (Pi^4*(-7801 + 4382*S^2))/(90*(1 + S^2)) + (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + ((44*Pi^2)/3 + 48*(1 + S^2))*HPL[{3}, -S^2] + (4*(-17 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 184*HPL[{5}, -S^2] + 1440*Pi^2*HPL[{2, 1}, -S^2] - (48*(-62 + 63*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 608*HPL[{3, 2}, -S^2] - 1456*HPL[{4, 1}, -S^2] + (6000*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 12544*HPL[{2, 2, 1}, -S^2] - 37088*HPL[{3, 1, 1}, -S^2] + 24000*HPL[{2, 1, 1, 1}, -S^2] + ((376*Pi^2)/3 - 8*(1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*((40*(1 + S^2))/S^2 + (2*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)) + 304*HPL[{3}, -S^2] + 6272*HPL[{2, 1}, -S^2] + 656*Zeta[3]) + 520*Zeta[5]))) + HPL[{0}, S^2]^2*((Pi^6*(-52285 - 13202*S^2))/(18144*(1 + S^2)) + (17*Pi^4*(13 + 115*S^2))/360 + 2*(13 + 250*S^2) + (Pi^2*(55 + 531*S^2))/12 + (2*(-22 + 9*S^2)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)) - (124*HPL[{1}, -S^2]^7)/21 + HPL[{1}, -S^2]^5*((-749*Pi^2)/45 - 2*(1 + S^2) - (784*HPL[{2}, -S^2])/15) + (4*(-11 + 13*S^2)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)) + (9*HPL[{3}, -S^2]^2)/2 + ((15*Pi^2)/2 - 2*(20 + 13*S^2))*HPL[{5}, -S^2] + ((-173 - 218*S^2)*HPL[{6}, -S^2])/(2*(1 + S^2)) + 219*HPL[{7}, -S^2] + ((223 - 207*S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + (13*Pi^2 - 4*(-3 + 2*S^2))*HPL[{3, 2}, -S^2] + (22*Pi^2 - 2*(-36 + 13*S^2))*HPL[{4, 1}, -S^2] + (3*(5 + 3*S^2)*HPL[{4, 2}, -S^2])/(2*(1 + S^2)) - 84*HPL[{4, 3}, -S^2] + (8*(13 + 15*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) - 233*HPL[{5, 2}, -S^2] - 500*HPL[{6, 1}, -S^2] + (-74*Pi^2 - 4*S^2)*HPL[{2, 2, 1}, -S^2] + ((-658*Pi^2)/3 + 4*(-10 + S^2))*HPL[{3, 1, 1}, -S^2] - 6*HPL[{3, 1, 2}, -S^2] + (2*(-179 + 205*S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + 56*HPL[{3, 2, 2}, -S^2] + 40*HPL[{3, 3, 1}, -S^2] + (2*(-563 + 581*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + 24*HPL[{4, 1, 2}, -S^2] - 24*HPL[{4, 2, 1}, -S^2] - 180*HPL[{5, 1, 1}, -S^2] + ((412*Pi^2)/3 - 16*(-5 + 2*S^2))*HPL[{2, 1, 1, 1}, -S^2] + 848*HPL[{2, 2, 2, 1}, -S^2] - (4*(-197 + 189*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - 2472*HPL[{3, 1, 1, 2}, -S^2] - 2472*HPL[{3, 1, 2, 1}, -S^2] - 5016*HPL[{3, 2, 1, 1}, -S^2] - 15168*HPL[{4, 1, 1, 1}, -S^2] + (56*(-29 + 27*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + 1632*HPL[{2, 1, 2, 1, 1}, -S^2] + 4896*HPL[{2, 2, 1, 1, 1}, -S^2] + 8224*HPL[{3, 1, 1, 1, 1}, -S^2] + 3104*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*((Pi^2*(-131 - 151*S^2))/(12*(1 + S^2)) + (3 + 5*S^2 + 9*S^4)/S^2 - 68*HPL[{2, 1}, -S^2] - 40*Zeta[3]) + ((-3353*Pi^4)/180 + 6*(-4 + 3*S^2) + (4*Pi^2*(1 + 8*S^2))/3)*Zeta[3] + ((-20 - 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((-5*Pi^2*(-83 + 41*S^2))/(6*(1 + S^2)) + (2*(-11 + 15*S^2 + 14*S^4))/S^2 + 4*Zeta[3]) + HPL[{2}, -S^2]^2*(-5 - 4*S^2 + (Pi^2*(-417 + 253*S^2))/(24*(1 + S^2)) + 6*HPL[{3}, -S^2] + 106*HPL[{2, 1}, -S^2] + 7*Zeta[3]) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(-1 + 15*S^2))/(3*S^2) + (Pi^2*(-583 + 166*S^2))/(18*(1 + S^2)) + ((-307 + 85*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + (44*HPL[{3}, -S^2])/3 + (784*HPL[{2, 1}, -S^2])/3 + (82*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-412 + 221*S^2))/(3*(1 + S^2)) - (8*(-5 + 6*S^4))/S^2 + 40*Zeta[3]) + HPL[{3}, -S^2]*((23*Pi^4)/36 + (Pi^2*(-17 + 2*S^2))/3 + (3 + 21*S^2 - 4*S^4)/S^2 + 46*HPL[{4}, -S^2] - (6*(9 + 2*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 32*HPL[{3, 1}, -S^2] - 32*HPL[{2, 1, 1}, -S^2] + (2*(7 + 6*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((29*Pi^4)/180 - (2*Pi^2*(-14 + S^2))/3 - (2*(14 - 7*S^2 + 4*S^4))/S^2 - 392*HPL[{3, 1}, -S^2] - 816*HPL[{2, 1, 1}, -S^2] + (2*(-16 + 23*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((-8449*Pi^4)/540 - (20*Pi^2*(1 + S^2))/9 - (4*(1 + S^2)*(-2 + 3*S^2))/S^2 + ((-211*Pi^2)/3 - (20*(1 + S^2))/3)*HPL[{2}, -S^2] - (430*HPL[{2}, -S^2]^2)/3 - (4*(3 + 25*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (16*HPL[{4}, -S^2])/3 - (4*(-307 + 85*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (1544*HPL[{3, 1}, -S^2])/3 - (3136*HPL[{2, 1, 1}, -S^2])/3 - (4*(-8 + 33*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^4*(-6404 + 327*S^2))/(720*(1 + S^2)) + (Pi^2*(11 + 4*S^2 - 4*S^4))/(3*S^2) + (73 + 122*S^2 + S^4)/(2*S^2) + ((-19*Pi^2)/3 + 2*(-3 + 2*S^2))*HPL[{3}, -S^2] + ((-27 - 25*S^2)*HPL[{4}, -S^2])/(2*(1 + S^2)) - 63*HPL[{5}, -S^2] + (37*Pi^2 + 2*S^2)*HPL[{2, 1}, -S^2] - (2*(-115 + 98*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 26*HPL[{3, 2}, -S^2] - 4*HPL[{4, 1}, -S^2] + (2*(-223 + 207*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 424*HPL[{2, 2, 1}, -S^2] + 1240*HPL[{3, 1, 1}, -S^2] + 816*HPL[{2, 1, 1, 1}, -S^2] + (20 - (25*Pi^2)/3)*Zeta[3] - 88*Zeta[5]) + (-158*Pi^2 + 4*(-7 + 12*S^2))*Zeta[5] + HPL[{1}, -S^2]^2*((-5*(-6 + S^2)*(1 + S^2))/S^2 - (Pi^2*(1 + S^2)*(-1 + 9*S^2))/(6*S^2) + (Pi^4*(-7348 + 1101*S^2))/(360*(1 + S^2)) + ((-149 + 66*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + (25*Pi^2*HPL[{3}, -S^2])/3 + ((-23 - 31*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 24*HPL[{5}, -S^2] + (211*Pi^2 + 20*(1 + S^2))*HPL[{2, 1}, -S^2] - (4*(-152 + 41*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 84*HPL[{3, 2}, -S^2] - 268*HPL[{4, 1}, -S^2] + (4*(-307 + 85*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 1720*HPL[{2, 2, 1}, -S^2] - 4984*HPL[{3, 1, 1}, -S^2] + 3136*HPL[{2, 1, 1, 1}, -S^2] + ((41*Pi^2)/3 - 2*(1 + S^2))*Zeta[3] + HPL[{2}, -S^2]*(-(((1 + S^2)*(-11 + 10*S^2))/S^2) + (Pi^2*(-535 + 98*S^2))/(6*(1 + S^2)) + 42*HPL[{3}, -S^2] + 860*HPL[{2, 1}, -S^2] + 78*Zeta[3]) + 78*Zeta[5]) + HPL[{1}, -S^2]*((-39083*Pi^6)/9072 - (77*Pi^4*(1 + S^2))/180 - (Pi^2*(-12 + S^2)*(1 + S^2))/(3*S^2) + (2*(1 + S^2)*(35 + 12*S^2))/S^2 + ((-335*Pi^2)/6 - 5*(1 + S^2))*HPL[{2}, -S^2]^2 - 64*HPL[{2}, -S^2]^3 + ((10*Pi^2)/3 - 4*(1 + S^2))*HPL[{4}, -S^2] - (8*(4 + 7*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 45*HPL[{6}, -S^2] + 860*HPL[{2, 1}, -S^2]^2 + ((620*Pi^2)/3 + 20*(1 + S^2))*HPL[{3, 1}, -S^2] + (12*(-2 + 5*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (2*(-13 + 121*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 6*HPL[{4, 2}, -S^2] - 32*HPL[{5, 1}, -S^2] + (-422*Pi^2 - 40*(1 + S^2))*HPL[{2, 1, 1}, -S^2] + (8*(-149 + 66*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (8*(-450 + 173*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 1536*HPL[{3, 2, 1}, -S^2] - 4576*HPL[{4, 1, 1}, -S^2] - (8*(-307 + 85*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + 3088*HPL[{3, 1, 1, 1}, -S^2] - 6272*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((Pi^2*(535 - 98*S^2))/(3*(1 + S^2)) + (2*(1 + S^2)*(-11 + 10*S^2))/S^2 - 156*Zeta[3]) + ((Pi^2*(-7 - 48*S^2))/(3*(1 + S^2)) + (2*(1 + S^2)*(1 + 9*S^2))/S^2)*Zeta[3] - 18*Zeta[3]^2 + HPL[{3}, -S^2]*((10*(1 + S^2))/S^2 - (5*Pi^2*(3 + 8*S^2))/(3*(1 + S^2)) - 84*HPL[{2, 1}, -S^2] + 4*Zeta[3]) + HPL[{2}, -S^2]*((-6731*Pi^4)/360 - (7*Pi^2*(1 + S^2))/3 - (4*(1 + S^2)*(-8 + 3*S^2))/S^2 - (6*(-2 + 5*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 2*HPL[{4}, -S^2] - (4*(-149 + 66*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 852*HPL[{3, 1}, -S^2] - 1720*HPL[{2, 1, 1}, -S^2] - (6*(-3 + 10*S^2)*Zeta[3])/(1 + S^2)) - (2*(14 + 53*S^2)*Zeta[5])/(1 + S^2)) - 1116*Zeta[7]) + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(73 + S^2))/(3*S^2) + (Pi^6*(-9212 + 229*S^2))/(3240*(1 + S^2)) + (Pi^4*(79 + 14*S^2 - 90*S^4))/(45*S^2) + (4*(71 - 82*S^2 + 250*S^4))/S^2 + (2*(-4 + 39*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((-98*Pi^2)/3 + 8*(13 + 4*S^2))*HPL[{5}, -S^2] - (12*(29 + 36*S^2)*HPL[{6}, -S^2])/(1 + S^2) - 1052*HPL[{7}, -S^2] - 8*HPL[{2, 1}, -S^2]^2 + ((-544*Pi^2)/3 - 72*S^2)*HPL[{3, 2}, -S^2] + ((-1448*Pi^2)/3 - 12*(5 + 21*S^2))*HPL[{4, 1}, -S^2] + (24*(-2 + 11*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) + 148*HPL[{4, 3}, -S^2] + (4*(39 + 355*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + 384*HPL[{5, 2}, -S^2] + 1436*HPL[{6, 1}, -S^2] + ((-424*Pi^2)/3 + 80*S^2)*HPL[{2, 2, 1}, -S^2] + (672*Pi^2 - 16*(-1 + 3*S^2))*HPL[{3, 1, 1}, -S^2] - (156*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(1 + S^2) + (1380*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + 1696*HPL[{3, 2, 2}, -S^2] + 5840*HPL[{3, 3, 1}, -S^2] + (4*(-1187 + 891*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + 5840*HPL[{4, 1, 2}, -S^2] + 18272*HPL[{4, 2, 1}, -S^2] + 37016*HPL[{5, 1, 1}, -S^2] + ((2368*Pi^2)/3 + 192*S^2)*HPL[{2, 1, 1, 1}, -S^2] + 3392*HPL[{2, 2, 2, 1}, -S^2] - (16*(-209 + 183*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) + 6032*HPL[{3, 1, 1, 2}, -S^2] + 6032*HPL[{3, 1, 2, 1}, -S^2] + 16208*HPL[{3, 2, 1, 1}, -S^2] + 49504*HPL[{4, 1, 1, 1}, -S^2] + (6272*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + 6208*HPL[{3, 1, 1, 1, 1}, -S^2] + 12416*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{3, 1}, -S^2]*(-32*(-2 + S^2) - (2*Pi^2*(-348 + 257*S^2))/(3*(1 + S^2)) - 768*Zeta[3]) + ((403*Pi^4)/90 + (2*Pi^2*(20 + 11*S^2))/3 + (16*(-1 + 7*S^2 + 2*S^4))/S^2)*Zeta[3] - (2*(4 + 7*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{4}, -S^2]*((Pi^2*(-31 - 143*S^2))/(3*(1 + S^2)) + 4*(3 + 8*S^2) - 688*HPL[{2, 1}, -S^2] + 72*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((2*Pi^2*(-615 + 599*S^2))/(3*(1 + S^2)) + (16*(-1 - 5*S^2 + S^4))/S^2 + 1472*Zeta[3]) + HPL[{3}, -S^2]*((227*Pi^4)/45 + (4*Pi^2*(-1 + 7*S^2))/3 + 4*(17 + 13*S^2) - 100*HPL[{4}, -S^2] + (4*(-235 + 231*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 1224*HPL[{3, 1}, -S^2] + 2384*HPL[{2, 1, 1}, -S^2] - (4*(-2 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((2401*Pi^4)/90 + (26*Pi^2*S^2)/3 + (4*(-12 + 17*S^2 + 10*S^4))/S^2 + 688*HPL[{3, 1}, -S^2] + (4*(-169 + 185*S^2)*Zeta[3])/(1 + S^2)) + ((-14*Pi^2)/3 + 4*(24 + 17*S^2))*Zeta[5] - 540*Zeta[7]) + (-372*Pi^2 + 60*(-7 + 5*S^2))*Zeta[7] + HPL[{1}, -S^2]^2*((-2*Pi^2*(1 + S^2)*(-33 + 14*S^2))/(3*S^2) - (20*(1 + S^2)*(-17 + 15*S^2))/S^2 - (Pi^4*(1 + S^2)*(-10 + 389*S^2))/(180*S^2) + (Pi^6*(-37673 + 14612*S^2))/(4536*(1 + S^2)) - (166*HPL[{2}, -S^2]^3)/3 + (74*(-1 + S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + (80*Pi^2 - 20*(1 + S^2))*HPL[{5}, -S^2] - (2*(119 + 208*S^2)*HPL[{6}, -S^2])/(1 + S^2) + 60*HPL[{7}, -S^2] - (1568*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((-1652*Pi^2)/3 - 40*(1 + S^2))*HPL[{3, 2}, -S^2] + ((-5636*Pi^2)/3 - 120*(1 + S^2))*HPL[{4, 1}, -S^2] + (234*(-1 + S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) + 188*HPL[{4, 3}, -S^2] + (104*(-9 + 17*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + 408*HPL[{5, 2}, -S^2] - 196*HPL[{6, 1}, -S^2] + ((-4856*Pi^2)/3 - 80*(1 + S^2))*HPL[{2, 2, 1}, -S^2] + ((-10592*Pi^2)/3 - 160*(1 + S^2))*HPL[{3, 1, 1}, -S^2] - 1328*HPL[{3, 2, 1}, -S^2] + 6520*HPL[{3, 2, 2}, -S^2] + 19936*HPL[{3, 3, 1}, -S^2] - (16*(193 + 359*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + 19624*HPL[{4, 1, 2}, -S^2] + 60808*HPL[{4, 2, 1}, -S^2] + 125280*HPL[{5, 1, 1}, -S^2] + (3136*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + (32*(56 + 139*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - 12544*HPL[{3, 1, 1, 2}, -S^2] - 12544*HPL[{3, 1, 2, 1}, -S^2] - 12544*HPL[{3, 2, 1, 1}, -S^2] - 42944*HPL[{4, 1, 1, 1}, -S^2] - 6240*HPL[{2, 1, 1, 1, 1}, -S^2] + 25088*HPL[{2, 1, 2, 1, 1}, -S^2] + 75264*HPL[{2, 2, 1, 1, 1}, -S^2] + 155840*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{3, 1}, -S^2]*((8*(-5 + S^2)*(1 + S^2))/S^2 + (8*Pi^2*(104 + 49*S^2))/(3*(1 + S^2)) - 3232*Zeta[3]) + ((1013*Pi^4)/30 - (2*Pi^2*(1 + S^2))/3)*Zeta[3] + (4*(-9 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{4}, -S^2]*((Pi^2*(89 - 251*S^2))/(3*(1 + S^2)) + (2*(1 + S^2)*(1 + 7*S^2))/S^2 - 904*HPL[{2, 1}, -S^2] + 112*Zeta[3]) + HPL[{2}, -S^2]^2*(-10*(1 + S^2) + (Pi^2*(-345 + 262*S^2))/(3*(1 + S^2)) + 932*HPL[{3}, -S^2] + 708*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((96*(1 + S^2))/S^2 - (8*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)) + 6272*Zeta[3]) + HPL[{2, 1}, -S^2]*((2021*Pi^4)/30 + (20*Pi^2*(1 + S^2))/3 + (8*(-16 + S^2)*(1 + S^2))/S^2 - 6272*HPL[{3, 1}, -S^2] - 12544*HPL[{2, 1, 1}, -S^2] + (448*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((601*Pi^4)/15 + (10*Pi^2*(1 + S^2))/3 - (4*(1 + S^2)*(-9 + 5*S^2))/S^2 - 172*HPL[{4}, -S^2] + (8*(-113 + 279*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 3136*HPL[{3, 1}, -S^2] + 6272*HPL[{2, 1, 1}, -S^2] - (8*(-12 + 13*S^2)*Zeta[3])/(1 + S^2)) + ((838*Pi^2)/3 - 8*(1 + S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-6575 - 512*S^2))/(180*(1 + S^2)) - (Pi^2*(1 + S^2)*(-23 + 10*S^2))/(3*S^2) + (2*(1 + S^2)*(62 + 13*S^2))/S^2 + ((826*Pi^2)/3 + 20*(1 + S^2))*HPL[{3}, -S^2] - (226*(-1 + S^2)*HPL[{4}, -S^2])/(1 + S^2) + 328*HPL[{5}, -S^2] + ((2428*Pi^2)/3 + 40*(1 + S^2))*HPL[{2, 1}, -S^2] - (1568*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 3416*HPL[{3, 2}, -S^2] - 10280*HPL[{4, 1}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 6272*HPL[{3, 1, 1}, -S^2] + 12544*HPL[{2, 1, 1, 1}, -S^2] + ((862*Pi^2)/3 + 40*(1 + S^2))*Zeta[3] + 1444*Zeta[5]) + 1932*Zeta[7]) + HPL[{1}, -S^2]*((-27928*Pi^8)/14175 - (95*Pi^6*(1 + S^2))/162 - (4*Pi^2*(1 + S^2)*(-39 + 8*S^2))/(3*S^2) - (Pi^4*(1 + S^2)*(-168 + 181*S^2))/(90*S^2) - (4*(1 + S^2)*(-253 + 470*S^2))/S^2 - (64*Pi^2*HPL[{2}, -S^2]^3)/3 - 64*HPL[{2}, -S^2]^4 + ((-74*Pi^2)/3 + 4*(1 + S^2))*HPL[{3}, -S^2]^2 + 36*HPL[{4}, -S^2]^2 + ((134*Pi^2)/3 - 112*(1 + S^2))*HPL[{6}, -S^2] - (12*(46 + 51*S^2)*HPL[{7}, -S^2])/(1 + S^2) + 216*HPL[{8}, -S^2] + ((2428*Pi^2)/3 + 40*(1 + S^2))*HPL[{2, 1}, -S^2]^2 - 3728*HPL[{3, 1}, -S^2]^2 - 76*Pi^2*HPL[{4, 2}, -S^2] - (4*(-18 + 29*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) + ((-1384*Pi^2)/3 + 56*(1 + S^2))*HPL[{5, 1}, -S^2] - (24*(-7 + 10*S^2)*HPL[{5, 2}, -S^2])/(1 + S^2) + 48*HPL[{5, 3}, -S^2] + (4*(149 + 198*S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) + 120*HPL[{6, 2}, -S^2] - 216*HPL[{7, 1}, -S^2] - 12544*HPL[{2, 1, 1}, -S^2]^2 - 512*Pi^2*HPL[{3, 2, 1}, -S^2] - (4*(-483 + 1147*S^2)*HPL[{3, 2, 2}, -S^2])/(1 + S^2) - (32*(-187 + 436*S^2)*HPL[{3, 3, 1}, -S^2])/(1 + S^2) - 1064*HPL[{3, 3, 2}, -S^2] - (3248*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - (4*(-1457 + 3449*S^2)*HPL[{4, 1, 2}, -S^2])/(1 + S^2) + 1816*HPL[{4, 1, 3}, -S^2] - (4*(-4613 + 10589*S^2)*HPL[{4, 2, 1}, -S^2])/(1 + S^2) - 752*HPL[{4, 2, 2}, -S^2] + 5816*HPL[{4, 3, 1}, -S^2] - (16*(-2369 + 5461*S^2)*HPL[{5, 1, 1}, -S^2])/(1 + S^2) + 3376*HPL[{5, 1, 2}, -S^2] + 24016*HPL[{5, 2, 1}, -S^2] + 62632*HPL[{6, 1, 1}, -S^2] + 2656*HPL[{2, 2, 2, 1}, -S^2] + (1760*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 + (64*(-181 + 15*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2) + (64*(-181 + 15*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2) - 624*HPL[{3, 1, 2, 2}, -S^2] - (32*(611 + 219*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2) - 624*HPL[{3, 2, 1, 2}, -S^2] - 752*HPL[{3, 2, 2, 1}, -S^2] - 384*HPL[{3, 3, 1, 1}, -S^2] - (32*(1889 + 547*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2) - 1872*HPL[{4, 1, 1, 2}, -S^2] - 2256*HPL[{4, 1, 2, 1}, -S^2] - 3024*HPL[{4, 2, 1, 1}, -S^2] - 13120*HPL[{5, 1, 1, 1}, -S^2] - (6272*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 - (12544*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2) - (37632*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2) - (320*(-224 + 263*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2) + 10624*HPL[{4, 1, 1, 1, 1}, -S^2] + 12480*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 10624*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1, 1}, -S^2]*((-192*(1 + S^2))/S^2 + (16*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)) - 12544*Zeta[3]) + HPL[{4, 1}, -S^2]*((-4*(1 + S^2)*(25 + 37*S^2))/S^2 + (2*Pi^2*(-803 + 2015*S^2))/(3*(1 + S^2)) - 848*Zeta[3]) + HPL[{3, 2}, -S^2]*((-8*(1 + S^2)*(4 + 5*S^2))/S^2 + (28*Pi^2*(-17 + 42*S^2))/(3*(1 + S^2)) - 208*Zeta[3]) + HPL[{5}, -S^2]*((8*(-3 + S^2)*(1 + S^2))/S^2 - (4*Pi^2*(7 + 67*S^2))/(3*(1 + S^2)) - 656*HPL[{2, 1}, -S^2] - 48*Zeta[3]) + ((-58*Pi^2)/3 + 48*(1 + S^2))*Zeta[3]^2 + HPL[{2, 2, 1}, -S^2]*(-80*(1 + S^2) + (8*Pi^2*(-345 + 262*S^2))/(3*(1 + S^2)) + 5664*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((-16*(1 + S^2)*(-5 + 11*S^2))/S^2 + (16*Pi^2*(-449 + 213*S^2))/(3*(1 + S^2)) + 17792*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-2021*Pi^4)/15 - (40*Pi^2*(1 + S^2))/3 - (16*(-16 + S^2)*(1 + S^2))/S^2 - (896*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*(14*Pi^4 - (4*Pi^2*(1 + S^2))/3 - (4*(1 + S^2)*(8 + 7*S^2))/S^2 + (452*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 968*HPL[{3, 1}, -S^2] + 1808*HPL[{2, 1, 1}, -S^2] - (4*(-5 + 23*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]^2*((-333*Pi^4)/10 - (10*Pi^2*(1 + S^2))/3 - (4*(1 + S^2)*(-2 + 3*S^2))/S^2 - (4*(-75 + 158*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 328*HPL[{4}, -S^2] + 332*HPL[{2, 1}, -S^2] - 328*HPL[{3, 1}, -S^2] - (4*(-47 + 130*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1}, -S^2]*((796*Pi^4)/15 + (20*Pi^2*(1 + S^2))/3 + (8*(1 + S^2)*(-13 + 11*S^2))/S^2 + 12544*HPL[{2, 1, 1}, -S^2] + (16*(-59 + 143*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((2*Pi^2*(1 + S^2)*(-23 + 10*S^2))/(3*S^2) - (4*(1 + S^2)*(62 + 13*S^2))/S^2 + (Pi^4*(6575 + 512*S^2))/(90*(1 + S^2)) + (3136*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 6832*HPL[{3, 2}, -S^2] + 20560*HPL[{4, 1}, -S^2] + (6272*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 12544*HPL[{3, 1, 1}, -S^2] + 25088*HPL[{2, 1, 1, 1}, -S^2] + ((-1724*Pi^2)/3 - 80*(1 + S^2))*Zeta[3] - 2888*Zeta[5]) + Zeta[3]*((Pi^4*(545 - 2494*S^2))/(90*(1 + S^2)) + (24*(1 + S^2)*(-1 + 3*S^2))/S^2 + (2*Pi^2*(1 + S^2)*(2 + 9*S^2))/(3*S^2) - 248*Zeta[5]) + ((4*(1 + S^2)*(4 + 7*S^2))/S^2 - (2*Pi^2*(-37 + 382*S^2))/(3*(1 + S^2)))*Zeta[5] + HPL[{3}, -S^2]*((Pi^4*(391 - 1412*S^2))/(45*(1 + S^2)) + (4*Pi^2*(1 + S^2)*(5 + 2*S^2))/(3*S^2) - (24*(1 + S^2)*(-1 + 3*S^2))/S^2 + (4*(-15 + 28*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 112*HPL[{5}, -S^2] + ((-1652*Pi^2)/3 - 40*(1 + S^2))*HPL[{2, 1}, -S^2] + (8*(-113 + 279*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 688*HPL[{3, 2}, -S^2] + 216*HPL[{4, 1}, -S^2] - (16*(-113 + 279*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 7456*HPL[{2, 2, 1}, -S^2] + 21184*HPL[{3, 1, 1}, -S^2] - 12544*HPL[{2, 1, 1, 1}, -S^2] + ((104*Pi^2)/3 + 48*(1 + S^2))*Zeta[3] + 128*Zeta[5]) + HPL[{2}, -S^2]*((-1049*Pi^6)/180 - (62*Pi^4*(1 + S^2))/45 + (40*(1 + S^2)*(5 + 4*S^2))/S^2 - (2*Pi^2*(1 + S^2)*(-32 + 7*S^2))/(3*S^2) - 172*HPL[{3}, -S^2]^2 + ((224*Pi^2)/3 - 8*(1 + S^2))*HPL[{4}, -S^2] - (4*(-27 + 55*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 168*HPL[{6}, -S^2] + ((2420*Pi^2)/3 + 40*(1 + S^2))*HPL[{3, 1}, -S^2] + (4*(-261 + 593*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (4*(-787 + 1783*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 624*HPL[{4, 2}, -S^2] - 2528*HPL[{5, 1}, -S^2] + ((-4856*Pi^2)/3 - 80*(1 + S^2))*HPL[{2, 1, 1}, -S^2] - 1328*HPL[{2, 2, 1}, -S^2] - (32*(-181 + 15*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 624*HPL[{3, 1, 2}, -S^2] - 5520*HPL[{3, 2, 1}, -S^2] - 16624*HPL[{4, 1, 1}, -S^2] - (6272*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + 12544*HPL[{3, 1, 1, 1}, -S^2] - 25088*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*(40*(1 + S^2) - (4*Pi^2*(-345 + 262*S^2))/(3*(1 + S^2)) - 2832*Zeta[3]) + ((4*(1 + S^2)*(1 + 10*S^2))/S^2 - (2*Pi^2*(-121 + 310*S^2))/(3*(1 + S^2)))*Zeta[3] + 12*Zeta[3]^2 + HPL[{3}, -S^2]*((4*(1 + S^2)*(4 + 5*S^2))/S^2 - (14*Pi^2*(-17 + 42*S^2))/(3*(1 + S^2)) - 3728*HPL[{2, 1}, -S^2] + 104*Zeta[3]) - (4*(-65 + 296*S^2)*Zeta[5])/(1 + S^2)) - (12*(10 + 171*S^2)*Zeta[7])/(1 + S^2)) + Log[T]*(-2940 + (177569*Pi^8)/32400 + (73*Pi^4*(-3 + S^2))/90 - (2*Pi^2*(239 + 42*S^2))/3 + (Pi^6*(4370 + 5259*S^2))/3780 + (3*HPL[{0}, S^2]^8)/32 + HPL[{0}, S^2]^7*((8 + 5*S^2)/(24*(1 + S^2)) + HPL[{1}, -S^2]/4) + ((116*Pi^2)/3 + (8*(1 + S^2))/3)*HPL[{1}, -S^2]^6 - (64*(-1 + S^2)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)) + (32*HPL[{1}, -S^2]^8)/3 + ((278*Pi^2)/9 + (20*S^2)/3)*HPL[{2}, -S^2]^3 + (278*HPL[{2}, -S^2]^4)/3 + HPL[{0}, S^2]^6*((91*Pi^2)/72 + (3 + S^2)/12 + ((10 + S^2)*HPL[{1}, -S^2])/(6*(1 + S^2)) + (3*HPL[{1}, -S^2]^2)/2 + (19*HPL[{2}, -S^2])/12) + (20 + (16*Pi^2)/3)*HPL[{3}, -S^2]^2 + 160*HPL[{4}, -S^2]^2 + ((134*Pi^2)/3 + 20*(2 + 3*S^2))*HPL[{6}, -S^2] + (4*(332 + 347*S^2)*HPL[{7}, -S^2])/(1 + S^2) + 3572*HPL[{8}, -S^2] + (-1224*Pi^2 + 16*(-5 + S^2))*HPL[{2, 1}, -S^2]^2 + 5344*HPL[{3, 1}, -S^2]^2 + ((164*Pi^2)/3 + 4*(1 + 11*S^2))*HPL[{4, 2}, -S^2] + (4*(16 + 63*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) + ((1100*Pi^2)/3 + 16*(1 + 8*S^2))*HPL[{5, 1}, -S^2] + (12*(3 + 37*S^2)*HPL[{5, 2}, -S^2])/(1 + S^2) + 64*HPL[{5, 3}, -S^2] - (4*(223 + 272*S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) - 92*HPL[{6, 2}, -S^2] - 2264*HPL[{7, 1}, -S^2] + 18880*HPL[{2, 1, 1}, -S^2]^2 + ((-8*Pi^2)/3 - 16*(1 + 2*S^2))*HPL[{3, 1, 2}, -S^2] + ((2216*Pi^2)/3 + 16*(-1 + 8*S^2))*HPL[{3, 2, 1}, -S^2] + (4*(-143 + 1487*S^2)*HPL[{3, 2, 2}, -S^2])/(1 + S^2) + (16*(-85 + 1161*S^2)*HPL[{3, 3, 1}, -S^2])/(1 + S^2) + 888*HPL[{3, 3, 2}, -S^2] + ((5264*Pi^2)/3 + 48*(-1 + 9*S^2))*HPL[{4, 1, 1}, -S^2] + (4*(-301 + 4605*S^2)*HPL[{4, 1, 2}, -S^2])/(1 + S^2) - 1648*HPL[{4, 1, 3}, -S^2] + (4*(-1009 + 14193*S^2)*HPL[{4, 2, 1}, -S^2])/(1 + S^2) + 424*HPL[{4, 2, 2}, -S^2] - 5200*HPL[{4, 3, 1}, -S^2] + (32*(-256 + 3659*S^2)*HPL[{5, 1, 1}, -S^2])/(1 + S^2) - 3128*HPL[{5, 1, 2}, -S^2] - 20888*HPL[{5, 2, 1}, -S^2] - 53168*HPL[{6, 1, 1}, -S^2] - 5376*HPL[{2, 2, 2, 1}, -S^2] + (-1056*Pi^2 - 384*S^2)*HPL[{3, 1, 1, 1}, -S^2] + (32*(515 + 123*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2) + (32*(515 + 123*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2) + 592*HPL[{3, 1, 2, 2}, -S^2] + (32*(1019 + 627*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2) + 592*HPL[{3, 2, 1, 2}, -S^2] + 592*HPL[{3, 2, 2, 1}, -S^2] + (704*(142 + 81*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2) + 1440*HPL[{4, 1, 1, 2}, -S^2] + 1440*HPL[{4, 1, 2, 1}, -S^2] + 1440*HPL[{4, 2, 1, 1}, -S^2] + 9664*HPL[{5, 1, 1, 1}, -S^2] + ((9440*Pi^2)/3 + 960*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + (12544*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2) + (37632*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2) + (320*(-209 + 278*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2) - 11520*HPL[{4, 1, 1, 1, 1}, -S^2] - 22080*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + 11520*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + HPL[{3, 1, 1}, -S^2]*((-4*Pi^2*(-2203 + 445*S^2))/(3*(1 + S^2)) + (16*(-3 - 10*S^2 + 12*S^4))/S^2 - 26496*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((-4*Pi^2*(-765 + 449*S^2))/(3*(1 + S^2)) + (32*(-1 + 6*S^4))/S^2 - 8384*Zeta[3]) + HPL[{1}, -S^2]^5*(8*(1 + S^2) - (4*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) + 104*HPL[{2}, -S^2] - (1520*HPL[{3}, -S^2])/3 - 400*Zeta[3]) + HPL[{5}, -S^2]*((4*Pi^2*(13 + 73*S^2))/(3*(1 + S^2)) + (4*(-10 - 19*S^2 + 4*S^4))/S^2 + 1592*HPL[{2, 1}, -S^2] - 216*Zeta[3]) + (56*Pi^2 - 72*S^2)*Zeta[3]^2 + HPL[{0}, S^2]^5*((6 + S^2)/6 + (Pi^2*(1205 + 619*S^2))/(360*(1 + S^2)) + ((255 - 16*S^2)*HPL[{1}, -S^2]^2)/(30*(1 + S^2)) + (271*HPL[{1}, -S^2]^3)/45 + (11*(25 + 4*S^2)*HPL[{2}, -S^2])/(60*(1 + S^2)) + HPL[{1}, -S^2]*((293*Pi^2)/90 + (1 + S^2)/3 + (77*HPL[{2}, -S^2])/10) + (3*HPL[{2, 1}, -S^2])/5 + 6*Zeta[3]) + HPL[{0}, S^2]^4*((14057*Pi^4)/2160 + (8 - 37*S^2)/6 + (Pi^2*(61 + 18*S^2))/36 + ((253 - 31*S^2)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)) + (142*HPL[{1}, -S^2]^4)/9 + ((130*Pi^2)/9 + (-7 + S^2)/3)*HPL[{2}, -S^2] + (77*HPL[{2}, -S^2]^2)/4 + HPL[{1}, -S^2]^2*((277*Pi^2)/18 + (5*(1 + S^2))/6 + (241*HPL[{2}, -S^2])/6) + ((4 + 5*S^2)*HPL[{3}, -S^2])/(2*(1 + S^2)) + 4*HPL[{4}, -S^2] + HPL[{1}, -S^2]*(-1 - S^2 + (Pi^2*(553 - S^2))/(36*(1 + S^2)) + ((228 - 13*S^2)*HPL[{2}, -S^2])/(6*(1 + S^2)) - HPL[{3}, -S^2] - (241*HPL[{2, 1}, -S^2])/3) + ((-247 - 6*S^2)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)) - 75*HPL[{3, 1}, -S^2] + (470*HPL[{2, 1, 1}, -S^2])/3 + (83*Zeta[3])/6) + HPL[{3, 2}, -S^2]*((-2*Pi^2*(5 + 831*S^2))/(3*(1 + S^2)) + (4*(-1 - 6*S^2 + 44*S^4))/S^2 + 272*Zeta[3]) + HPL[{4, 1}, -S^2]*((-2*Pi^2*(-99 + 2719*S^2))/(3*(1 + S^2)) + (8*(-2 + 3*S^2 + 70*S^4))/S^2 + 1440*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*(384*(1 + S^2) - (224*Pi^2*(27 + 13*S^2))/(3*(1 + S^2)) + 18880*Zeta[3]) + HPL[{1}, -S^2]^4*((6673*Pi^4)/135 + (20*Pi^2*(1 + S^2))/3 + (8*(1 + S^2)*(-2 + 3*S^2))/S^2 + (784*Pi^2*HPL[{2}, -S^2])/9 + (1568*HPL[{2}, -S^2]^2)/3 + (40*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (1328*HPL[{4}, -S^2])/3 - 520*HPL[{2, 1}, -S^2] + (1328*HPL[{3, 1}, -S^2])/3 + (40*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*((-598*Pi^4)/45 + (2*Pi^2*(-17 + 2*S^2))/3 - (4*(12 + 37*S^2 + 23*S^4))/S^2 + (4*(261 + 35*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 368*HPL[{3, 1}, -S^2] - 864*HPL[{2, 1, 1}, -S^2] + (4*(-3 + 25*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((9982*Pi^4)/45 + (232*Pi^2*S^2)/3 + (16*(-22 - 9*S^2 + 14*S^4))/S^2 + (32*(-33 + 163*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1}, -S^2]*((-457*Pi^4)/5 - (100*Pi^2*S^2)/3 - (8*(-19 - 6*S^2 + 20*S^4))/S^2 - 18880*HPL[{2, 1, 1}, -S^2] - (8*(-75 + 329*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]^2*((9587*Pi^4)/180 + (Pi^2*(20 + 7*S^2))/3 + (2*(4 - 13*S^2 + 2*S^4))/S^2 + (2*(-65 + 401*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 312*HPL[{4}, -S^2] - 672*HPL[{2, 1}, -S^2] + 312*HPL[{3, 1}, -S^2] + (2*(-19 + 335*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((Pi^4*(8587 - 4759*S^2))/(135*(1 + S^2)) + (8*(1 + S^2)*(-36 + 23*S^2))/(3*S^2) + (4*Pi^2*(1 + S^2)*(-1 + 30*S^2))/(9*S^2) - (1568*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + ((-3976*Pi^2)/9 - (80*(1 + S^2))/3)*HPL[{3}, -S^2] + (32*(-28 + 55*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - 576*HPL[{5}, -S^2] - (3136*Pi^2*HPL[{2, 1}, -S^2])/9 - (32*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) + (12544*HPL[{3, 2}, -S^2])/3 + (42944*HPL[{4, 1}, -S^2])/3 + 2080*HPL[{2, 1, 1}, -S^2] + (25088*HPL[{2, 2, 1}, -S^2])/3 + (44864*HPL[{3, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((-32*(1 + S^2))/S^2 + (8*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)) - (6272*HPL[{3}, -S^2])/3 - (12544*HPL[{2, 1}, -S^2])/3 - (6272*Zeta[3])/3) - (3328*Pi^2*Zeta[3])/9 - (6080*Zeta[5])/3) + HPL[{3}, -S^2]*((Pi^4*(-157 + 3449*S^2))/(90*(1 + S^2)) + (12*(2 - 17*S^2 + 8*S^4))/S^2 - (2*Pi^2*(-4 + 25*S^2 + 30*S^4))/(3*S^2) - (4*(15 + 58*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 392*HPL[{5}, -S^2] + ((2560*Pi^2)/3 - 16*(-4 + 7*S^2))*HPL[{2, 1}, -S^2] - (16*(3 + 199*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 608*HPL[{3, 2}, -S^2] + 160*HPL[{4, 1}, -S^2] + (16*(9 + 401*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 10144*HPL[{2, 2, 1}, -S^2] - 29728*HPL[{3, 1, 1}, -S^2] + 18880*HPL[{2, 1, 1, 1}, -S^2] + ((-208*Pi^2)/3 - 8*(1 + 13*S^2))*Zeta[3] - 480*Zeta[5]) + (-16*(-19 + 9*S^2) + (2*Pi^2*(81 + 500*S^2))/(3*(1 + S^2)))*Zeta[5] + HPL[{0}, S^2]^3*((Pi^2*(53 + 8*S^2))/9 + (7*(5 + 17*S^2))/3 + (Pi^4*(12183 + 4189*S^2))/(1080*(1 + S^2)) - (2*(-268 + 97*S^2)*HPL[{1}, -S^2]^4)/(9*(1 + S^2)) + (292*HPL[{1}, -S^2]^5)/9 + ((73 - 33*S^2)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)) + HPL[{1}, -S^2]^3*((424*Pi^2)/9 + (8*(1 + S^2))/3 + (440*HPL[{2}, -S^2])/3) + ((10*Pi^2)/9 - (2*(-20 + 3*S^2))/3)*HPL[{3}, -S^2] + (2*(21 + 4*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - (20*HPL[{5}, -S^2])/3 + ((-46*Pi^2)/3 + (4*(-1 + 3*S^2))/3)*HPL[{2, 1}, -S^2] + (10*(-41 + 25*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) + (16*HPL[{3, 2}, -S^2])/3 - (8*HPL[{4, 1}, -S^2])/3 - (8*(-106 + 59*S^2)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)) + 200*HPL[{2, 2, 1}, -S^2] + (1880*HPL[{3, 1, 1}, -S^2])/3 - 416*HPL[{2, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((Pi^2*(523 - 113*S^2))/(9*(1 + S^2)) + (2*(1 + S^2)*(1 + 9*S^2))/(3*S^2) - (4*(-124 + 41*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) + 8*HPL[{3}, -S^2] - 440*HPL[{2, 1}, -S^2] - (44*Zeta[3])/3) + ((194*Pi^2)/9 - (4*(-1 + 7*S^2))/3)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(487 - 74*S^2))/(18*(1 + S^2)) + (2*(-11 + 11*S^2 + 2*S^4))/(3*S^2) - (8*HPL[{3}, -S^2])/3 - 100*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + HPL[{1}, -S^2]*((3997*Pi^4)/270 + (16*Pi^2*(1 + S^2))/9 + (8*(1 + S^2)*(-2 + 7*S^2))/(3*S^2) + ((187*Pi^2)/3 + (2*(1 + S^2))/3)*HPL[{2}, -S^2] + 106*HPL[{2}, -S^2]^2 + (8*HPL[{3}, -S^2])/(1 + S^2) + (68*HPL[{4}, -S^2])/3 + (8*(-124 + 41*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) - 440*HPL[{3, 1}, -S^2] + 880*HPL[{2, 1, 1}, -S^2] + (4*(3 + 14*S^2)*Zeta[3])/(3*(1 + S^2))) + (260*Zeta[5])/3) + Zeta[3]*((-8*Pi^2*(-12 + 7*S^2))/3 - 4*(-79 + 25*S^2) + (Pi^4*(229 + 1242*S^2))/(30*(1 + S^2)) + 672*Zeta[5]) + HPL[{2, 1}, -S^2]*((Pi^4*(-8906 - 2843*S^2))/(90*(1 + S^2)) + (4*Pi^2*(1 + 13*S^2 + 14*S^4))/(3*S^2) + (4*(51 + 124*S^2 + 25*S^4))/S^2 - (16*(-159 + 233*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 9520*HPL[{3, 2}, -S^2] - 29568*HPL[{4, 1}, -S^2] - (6272*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 18880*HPL[{3, 1, 1}, -S^2] - 37760*HPL[{2, 1, 1, 1}, -S^2] + ((2632*Pi^2)/3 - 16*S^2)*Zeta[3] + 5184*Zeta[5]) + HPL[{0}, S^2]^2*((2863*Pi^6)/216 + (Pi^2*(12 - 23*S^2))/3 - 12*(9 + 7*S^2) + (Pi^4*(162 + 89*S^2))/45 - (4*(-22 + 9*S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) + (124*HPL[{1}, -S^2]^6)/3 + (10 + (559*Pi^2)/6 + 9*S^2)*HPL[{2}, -S^2]^2 + (278*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((749*Pi^2)/9 + 10*(1 + S^2) + (784*HPL[{2}, -S^2])/3) - 28*HPL[{3}, -S^2]^2 + ((28*Pi^2)/3 + 2*(-14 + 5*S^2))*HPL[{4}, -S^2] + (2*(7 + 19*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 120*HPL[{6}, -S^2] - 1312*HPL[{2, 1}, -S^2]^2 + (-342*Pi^2 - 52*S^2)*HPL[{3, 1}, -S^2] - (6*(9 + 23*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (2*(101 + 235*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 16*HPL[{4, 2}, -S^2] - 108*HPL[{5, 1}, -S^2] + ((2120*Pi^2)/3 + 112*S^2)*HPL[{2, 1, 1}, -S^2] - (4*(-373 + 57*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (356*(-13 + S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 8*HPL[{3, 1, 2}, -S^2] + 2216*HPL[{3, 2, 1}, -S^2] + 6704*HPL[{4, 1, 1}, -S^2] - (8*(411 + 19*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 4608*HPL[{3, 1, 1, 1}, -S^2] + 9440*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{1}, -S^2]^3*((4*(1 + S^2)*(-1 + 15*S^2))/(3*S^2) - (2*Pi^2*(-583 + 166*S^2))/(9*(1 + S^2)) - (4*(-307 + 85*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2)) - (176*HPL[{3}, -S^2])/3 - (3136*HPL[{2, 1}, -S^2])/3 - (328*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(31 + 56*S^2))/(3*(1 + S^2)) - (2*(-1 + 15*S^2 + 6*S^4))/S^2 + 200*HPL[{2, 1}, -S^2] - 40*Zeta[3]) + (-8*(-3 + S^2) + (Pi^2*(94 + 135*S^2))/(3*(1 + S^2)))*Zeta[3] + 84*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-658 - 25*S^2))/(3*(1 + S^2)) + (4*(1 + S^2 + 2*S^4))/S^2 + 272*Zeta[3]) + HPL[{1}, -S^2]^2*((8449*Pi^4)/180 + (20*Pi^2*(1 + S^2))/3 + (12*(1 + S^2)*(-2 + 3*S^2))/S^2 + (211*Pi^2 + 20*(1 + S^2))*HPL[{2}, -S^2] + 430*HPL[{2}, -S^2]^2 + (4*(3 + 25*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 16*HPL[{4}, -S^2] + (4*(-307 + 85*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 1544*HPL[{3, 1}, -S^2] + 3136*HPL[{2, 1, 1}, -S^2] + (4*(-8 + 33*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((1117*Pi^4)/30 + (2*Pi^2*(-7 + 8*S^2))/3 + (2*(-18 - 27*S^2 + 16*S^4))/S^2 + (6*(5 + 12*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 72*HPL[{4}, -S^2] + (2*(-373 + 57*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 1312*HPL[{3, 1}, -S^2] + 2624*HPL[{2, 1, 1}, -S^2] + (2*(-2 + 37*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(7348 - 1101*S^2))/(180*(1 + S^2)) + (10*(-6 + S^2)*(1 + S^2))/S^2 + (Pi^2*(1 + S^2)*(-1 + 9*S^2))/(3*S^2) - (2*(-149 + 66*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) - (50*Pi^2*HPL[{3}, -S^2])/3 + (2*(23 + 31*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 48*HPL[{5}, -S^2] + (-422*Pi^2 - 40*(1 + S^2))*HPL[{2, 1}, -S^2] + (8*(-152 + 41*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 168*HPL[{3, 2}, -S^2] + 536*HPL[{4, 1}, -S^2] - (8*(-307 + 85*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 3440*HPL[{2, 2, 1}, -S^2] + 9968*HPL[{3, 1, 1}, -S^2] - 6272*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^2*(535 - 98*S^2))/(3*(1 + S^2)) + (2*(1 + S^2)*(-11 + 10*S^2))/S^2 - 84*HPL[{3}, -S^2] - 1720*HPL[{2, 1}, -S^2] - 156*Zeta[3]) + ((-82*Pi^2)/3 + 4*(1 + S^2))*Zeta[3] - 156*Zeta[5]) + (26*(5 + 8*S^2)*Zeta[5])/(1 + S^2)) + HPL[{2}, -S^2]*((6083*Pi^6)/540 + (Pi^4*(-98 + 435*S^2))/90 + (4*Pi^2*(-20 - 18*S^2 + 15*S^4))/(3*S^2) - (8*(26 + 29*S^2 + 21*S^4))/S^2 + 156*HPL[{3}, -S^2]^2 + (-12*Pi^2 - 4*(11 + 5*S^2))*HPL[{4}, -S^2] + (4*(57 + 139*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 780*HPL[{6}, -S^2] + (-1224*Pi^2 + 32*(-2 + S^2))*HPL[{3, 1}, -S^2] - (28*(-13 + 109*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (4*(-129 + 2441*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 624*HPL[{4, 2}, -S^2] + 1528*HPL[{5, 1}, -S^2] + (2448*Pi^2 - 32*(-5 + S^2))*HPL[{2, 1, 1}, -S^2] + 2688*HPL[{2, 2, 1}, -S^2] - (16*(495 + 103*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 624*HPL[{3, 1, 2}, -S^2] + 8272*HPL[{3, 2, 1}, -S^2] + 25824*HPL[{4, 1, 1}, -S^2] + (6272*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 18880*HPL[{3, 1, 1, 1}, -S^2] + 37760*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-8*(1 + 13*S^2) + (2*Pi^2*(24 + 437*S^2))/(3*(1 + S^2)) + 5072*HPL[{2, 1}, -S^2] - 128*Zeta[3]) + ((2*Pi^2*(-68 + 363*S^2))/(3*(1 + S^2)) - (8*(-1 + 11*S^2 + 10*S^4))/S^2)*Zeta[3] + 8*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((2*Pi^2*(-765 + 449*S^2))/(3*(1 + S^2)) - (16*(-1 + 6*S^4))/S^2 + 4192*Zeta[3]) + (4*(-64 + 297*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^2*((52285*Pi^6)/2268 + (233*Pi^4*(1 + S^2))/45 + (8*Pi^2*(1 + S^2)*(-2 + 3*S^2))/S^2 + (8*(1 + S^2)*(-43 + 28*S^2))/S^2 + ((1214*Pi^2)/3 + 20*(1 + S^2))*HPL[{2}, -S^2]^2 + 296*HPL[{3}, -S^2]^2 - (680*Pi^2*HPL[{4}, -S^2])/3 + (16*(-1 + 53*S^2)*HPL[{5}, -S^2])/(1 + S^2) - 356*HPL[{6}, -S^2] - 6272*HPL[{2, 1}, -S^2]^2 - (880*Pi^2*HPL[{3, 1}, -S^2])/3 - (16*(-113 + 279*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (16*(-395 + 947*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 936*HPL[{4, 2}, -S^2] + 5408*HPL[{5, 1}, -S^2] + (3136*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (32*(-448 + 253*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 5312*HPL[{4, 1, 1}, -S^2] - 6240*HPL[{2, 1, 1, 1}, -S^2] + 5312*HPL[{3, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((-8*(1 + S^2)*(5 + 4*S^2))/S^2 + (4*Pi^2*(-137 + 360*S^2))/(3*(1 + S^2)) + 6272*HPL[{2, 1}, -S^2] - 400*Zeta[3]) + ((-8*(1 + S^2))/S^2 + (8*Pi^2*(-49 + 159*S^2))/(3*(1 + S^2)))*Zeta[3] + 160*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((96*(1 + S^2))/S^2 - (8*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)) + 6272*Zeta[3]) + HPL[{2}, -S^2]*((2021*Pi^4)/30 + (20*Pi^2*(1 + S^2))/3 + (8*(-16 + S^2)*(1 + S^2))/S^2 + (8*(-113 + 279*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 904*HPL[{4}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 6272*HPL[{3, 1}, -S^2] + 12544*HPL[{2, 1, 1}, -S^2] + (448*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + (8*(-51 + 329*S^2)*Zeta[5])/(1 + S^2)) + HPL[{0}, S^2]*((248987*Pi^6)/(22680*(1 + S^2)) + 5*Pi^2*(-1 + 11*S^2) + 20*(-43 + 30*S^2) + (Pi^4*(745 + 274*S^2))/90 - (224*(-1 + S^2)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)) + (128*HPL[{1}, -S^2]^7)/3 - (4*(-46 + 131*S^2)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)) + HPL[{1}, -S^2]^5*((964*Pi^2)/9 + 8*(1 + S^2) + 400*HPL[{2}, -S^2]) - (2*(11 + 7*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + (14*Pi^2 - 4*(-25 + 13*S^2))*HPL[{5}, -S^2] - (2*(-55 + 18*S^2)*HPL[{6}, -S^2])/(1 + S^2) - 340*HPL[{7}, -S^2] + (16*(-75 + 121*S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((188*Pi^2)/3 + 4*(-19 + 23*S^2))*HPL[{3, 2}, -S^2] + (120*Pi^2 + 8*(-25 + 41*S^2))*HPL[{4, 1}, -S^2] - 2*HPL[{4, 2}, -S^2] - 216*HPL[{4, 3}, -S^2] + (8*(-22 + 5*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) - 652*HPL[{5, 2}, -S^2] - 1400*HPL[{6, 1}, -S^2] + (-160 + (3736*Pi^2)/3)*HPL[{2, 2, 1}, -S^2] + (3736*Pi^2 - 16*(21 + 13*S^2))*HPL[{3, 1, 1}, -S^2] - 16*HPL[{3, 1, 2}, -S^2] - (16*(-91 + 263*S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) - 560*HPL[{3, 2, 2}, -S^2] - 1920*HPL[{3, 3, 1}, -S^2] - (40*(-117 + 317*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) - 1904*HPL[{4, 1, 2}, -S^2] - 6032*HPL[{4, 2, 1}, -S^2] - 11888*HPL[{5, 1, 1}, -S^2] + (-2416*Pi^2 + 480*S^2)*HPL[{2, 1, 1, 1}, -S^2] - 11328*HPL[{2, 2, 2, 1}, -S^2] + (96*(-37 + 88*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) + 35360*HPL[{3, 1, 1, 2}, -S^2] + 35360*HPL[{3, 1, 2, 1}, -S^2] + 69344*HPL[{3, 2, 1, 1}, -S^2] + 206848*HPL[{4, 1, 1, 1}, -S^2] - (2400*(-3 + 7*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) - 25088*HPL[{2, 1, 2, 1, 1}, -S^2] - 75264*HPL[{2, 2, 1, 1, 1}, -S^2] - 126080*HPL[{3, 1, 1, 1, 1}, -S^2] - 48000*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1}, -S^2]*((16*(1 + S^2)*(-11 + 12*S^2))/S^2 - (4*Pi^2*(-437 + 643*S^2))/(3*(1 + S^2)) - 1248*Zeta[3]) + HPL[{1}, -S^2]^4*(20*(1 + S^2) - (2*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) - (500*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) - (136*HPL[{3}, -S^2])/3 - 2000*HPL[{2, 1}, -S^2] - (664*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(519 - 583*S^2))/(6*(1 + S^2)) + (2*(-1 + 21*S^2 + 8*S^4))/S^2 - 68*HPL[{3}, -S^2] - 1416*HPL[{2, 1}, -S^2] - 156*Zeta[3]) + ((373*Pi^4)/45 + 48*(3 + S^2) - (8*Pi^2*(-2 + 5*S^2))/3)*Zeta[3] + (68*Zeta[3]^2)/(1 + S^2) + HPL[{4}, -S^2]*((-5*Pi^2*(-15 + S^2))/(3*(1 + S^2)) - (4*(5 - 5*S^2 + 6*S^4))/S^2 - 96*HPL[{2, 1}, -S^2] + 128*Zeta[3]) + HPL[{3, 1}, -S^2]*((2*Pi^2*(-427 + 653*S^2))/(3*(1 + S^2)) - (8*(-12 - 3*S^2 + 10*S^4))/S^2 + 592*Zeta[3]) + HPL[{3}, -S^2]*((11*Pi^4)/5 - (2*Pi^2*(-29 + 16*S^2))/3 - (4*(7 - 7*S^2 + 22*S^4))/S^2 + 104*HPL[{4}, -S^2] + (16*(28 + 9*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 416*HPL[{3, 1}, -S^2] - 672*HPL[{2, 1, 1}, -S^2] + (16*S^2*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((-3622*Pi^4)/45 + (4*Pi^2*(-1 + 18*S^2))/3 + (8*(10 + 21*S^2 + 12*S^4))/S^2 + 6336*HPL[{3, 1}, -S^2] + 12544*HPL[{2, 1, 1}, -S^2] - (16*(-40 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((4061*Pi^4)/45 + (28*Pi^2*(1 + S^2))/3 + (16*(1 + S^2)*(-2 + 3*S^2))/S^2 + 480*Pi^2*HPL[{2}, -S^2] + (3136*HPL[{2}, -S^2]^2)/3 + (16*(-10 + 7*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (368*HPL[{4}, -S^2])/3 + (2000*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 4000*HPL[{3, 1}, -S^2] + 8000*HPL[{2, 1, 1}, -S^2] + (16*(-40 + 43*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]^2*((Pi^4*(7801 - 4382*S^2))/(90*(1 + S^2)) + (4*(1 + S^2)*(-36 + 23*S^2))/S^2 + (2*Pi^2*(1 + S^2)*(1 + 24*S^2))/(3*S^2) - (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + ((-44*Pi^2)/3 - 48*(1 + S^2))*HPL[{3}, -S^2] - (4*(-17 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) + 184*HPL[{5}, -S^2] - 1440*Pi^2*HPL[{2, 1}, -S^2] + (48*(-62 + 63*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 608*HPL[{3, 2}, -S^2] + 1456*HPL[{4, 1}, -S^2] - (6000*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 12544*HPL[{2, 2, 1}, -S^2] + 37088*HPL[{3, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-40*(1 + S^2))/S^2 - (2*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)) - 304*HPL[{3}, -S^2] - 6272*HPL[{2, 1}, -S^2] - 656*Zeta[3]) + ((-376*Pi^2)/3 + 8*(1 + S^2))*Zeta[3] - 520*Zeta[5]) + HPL[{2}, -S^2]*((Pi^4*(6044 - 4731*S^2))/(180*(1 + S^2)) + (4*Pi^2*(-11 + 6*S^2 + 7*S^4))/(3*S^2) + (2*(-85 - 2*S^2 + 35*S^4))/S^2 + ((-92*Pi^2)/3 - 4*(-9 + 11*S^2))*HPL[{3}, -S^2] + (2*(31 + 23*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 100*HPL[{5}, -S^2] + (80 - (1868*Pi^2)/3)*HPL[{2, 1}, -S^2] + (32*(-37 + 61*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 272*HPL[{3, 2}, -S^2] + 912*HPL[{4, 1}, -S^2] - (32*(-75 + 121*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 5664*HPL[{2, 2, 1}, -S^2] - 17664*HPL[{3, 1, 1}, -S^2] - 12544*HPL[{2, 1, 1, 1}, -S^2] - 44*Pi^2*Zeta[3] - 120*Zeta[5]) + ((104*Pi^2)/3 - 24*(-4 + 3*S^2))*Zeta[5] + HPL[{1}, -S^2]*((248987*Pi^6)/11340 + (7*Pi^4*(1 + S^2))/2 + (4*Pi^2*(1 + S^2)*(-10 + 23*S^2))/(3*S^2) + (8*(1 + S^2)*(-43 + 28*S^2))/S^2 + ((1102*Pi^2)/3 + 20*(1 + S^2))*HPL[{2}, -S^2]^2 + 472*HPL[{2}, -S^2]^3 - 16*HPL[{3}, -S^2]^2 + ((160*Pi^2)/3 - 28*(1 + S^2))*HPL[{4}, -S^2] - (8*(-6 + 17*S^2)*HPL[{5}, -S^2])/(1 + S^2) + 292*HPL[{6}, -S^2] - 6272*HPL[{2, 1}, -S^2]^2 + (-1440*Pi^2 + 16*(1 + S^2))*HPL[{3, 1}, -S^2] - (304*(-1 + S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (8*(-97 + 85*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 432*HPL[{5, 1}, -S^2] + 2880*Pi^2*HPL[{2, 1, 1}, -S^2] - (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (32*(-578 + 581*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 11328*HPL[{3, 2, 1}, -S^2] + 34720*HPL[{4, 1, 1}, -S^2] + (12000*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) - 24000*HPL[{3, 1, 1, 1}, -S^2] + 48000*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*((-16*(1 + S^2)*(3 + 4*S^2))/S^2 + (4*Pi^2*(-4 + 7*S^2))/(3*(1 + S^2)) + 608*HPL[{2, 1}, -S^2] - 32*Zeta[3]) + ((16*(1 + S^2)*(1 + 2*S^2))/S^2 + (4*Pi^2*(-37 + 57*S^2))/(3*(1 + S^2)))*Zeta[3] + 136*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((80*(1 + S^2))/S^2 + (4*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)) + 1312*Zeta[3]) + HPL[{2}, -S^2]*((2155*Pi^4)/18 + (2*Pi^2*(1 + S^2))/3 + (8*(-16 + S^2)*(1 + S^2))/S^2 + (152*(-1 + S^2)*HPL[{3}, -S^2])/(1 + S^2) + 32*HPL[{4}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 6272*HPL[{3, 1}, -S^2] + 12544*HPL[{2, 1, 1}, -S^2] + (328*(-1 + S^2)*Zeta[3])/(1 + S^2)) + (8*(-27 + 38*S^2)*Zeta[5])/(1 + S^2))) + HPL[{1}, -S^2]*((Pi^6*(37673 - 14612*S^2))/(2268*(1 + S^2)) + (4*Pi^2*(1 + S^2)*(-33 + 14*S^2))/(3*S^2) + (40*(1 + S^2)*(-17 + 15*S^2))/S^2 + (Pi^4*(1 + S^2)*(-10 + 389*S^2))/(90*S^2) + (332*HPL[{2}, -S^2]^3)/3 - (148*(-1 + S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + (-160*Pi^2 + 40*(1 + S^2))*HPL[{5}, -S^2] + (4*(119 + 208*S^2)*HPL[{6}, -S^2])/(1 + S^2) - 120*HPL[{7}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((3304*Pi^2)/3 + 80*(1 + S^2))*HPL[{3, 2}, -S^2] + ((11272*Pi^2)/3 + 240*(1 + S^2))*HPL[{4, 1}, -S^2] - (468*(-1 + S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) - 376*HPL[{4, 3}, -S^2] - (208*(-9 + 17*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) - 816*HPL[{5, 2}, -S^2] + 392*HPL[{6, 1}, -S^2] + ((9712*Pi^2)/3 + 160*(1 + S^2))*HPL[{2, 2, 1}, -S^2] + ((21184*Pi^2)/3 + 320*(1 + S^2))*HPL[{3, 1, 1}, -S^2] + 2656*HPL[{3, 2, 1}, -S^2] - 13040*HPL[{3, 2, 2}, -S^2] - 39872*HPL[{3, 3, 1}, -S^2] + (32*(193 + 359*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) - 39248*HPL[{4, 1, 2}, -S^2] - 121616*HPL[{4, 2, 1}, -S^2] - 250560*HPL[{5, 1, 1}, -S^2] - (6272*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - (64*(56 + 139*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) + 25088*HPL[{3, 1, 1, 2}, -S^2] + 25088*HPL[{3, 1, 2, 1}, -S^2] + 25088*HPL[{3, 2, 1, 1}, -S^2] + 85888*HPL[{4, 1, 1, 1}, -S^2] + 12480*HPL[{2, 1, 1, 1, 1}, -S^2] - 50176*HPL[{2, 1, 2, 1, 1}, -S^2] - 150528*HPL[{2, 2, 1, 1, 1}, -S^2] - 311680*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1}, -S^2]*((-192*(1 + S^2))/S^2 + (16*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)) - 12544*Zeta[3]) + HPL[{2}, -S^2]^2*(20*(1 + S^2) - (2*Pi^2*(-345 + 262*S^2))/(3*(1 + S^2)) - 1864*HPL[{3}, -S^2] - 1416*Zeta[3]) + HPL[{4}, -S^2]*((-4*(1 + S^2)*(1 + 7*S^2))/S^2 + (2*Pi^2*(-89 + 251*S^2))/(3*(1 + S^2)) + 1808*HPL[{2, 1}, -S^2] - 224*Zeta[3]) + ((-1013*Pi^4)/15 + (4*Pi^2*(1 + S^2))/3)*Zeta[3] - (8*(-9 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((-16*(-5 + S^2)*(1 + S^2))/S^2 - (16*Pi^2*(104 + 49*S^2))/(3*(1 + S^2)) + 6464*Zeta[3]) + HPL[{2, 1}, -S^2]*((-2021*Pi^4)/15 - (40*Pi^2*(1 + S^2))/3 - (16*(-16 + S^2)*(1 + S^2))/S^2 + 12544*HPL[{3, 1}, -S^2] + 25088*HPL[{2, 1, 1}, -S^2] - (896*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((-1202*Pi^4)/15 - (20*Pi^2*(1 + S^2))/3 + (8*(1 + S^2)*(-9 + 5*S^2))/S^2 + 344*HPL[{4}, -S^2] - (16*(-113 + 279*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 6272*HPL[{3, 1}, -S^2] - 12544*HPL[{2, 1, 1}, -S^2] + (16*(-12 + 13*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((2*Pi^2*(1 + S^2)*(-23 + 10*S^2))/(3*S^2) - (4*(1 + S^2)*(62 + 13*S^2))/S^2 + (Pi^4*(6575 + 512*S^2))/(90*(1 + S^2)) + ((-1652*Pi^2)/3 - 40*(1 + S^2))*HPL[{3}, -S^2] + (452*(-1 + S^2)*HPL[{4}, -S^2])/(1 + S^2) - 656*HPL[{5}, -S^2] + ((-4856*Pi^2)/3 - 80*(1 + S^2))*HPL[{2, 1}, -S^2] + (3136*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 6832*HPL[{3, 2}, -S^2] + 20560*HPL[{4, 1}, -S^2] - (6272*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 12544*HPL[{3, 1, 1}, -S^2] - 25088*HPL[{2, 1, 1, 1}, -S^2] + ((-1724*Pi^2)/3 - 80*(1 + S^2))*Zeta[3] - 2888*Zeta[5]) + ((-1676*Pi^2)/3 + 16*(1 + S^2))*Zeta[5] - 3864*Zeta[7]) + (12*(25 + 186*S^2)*Zeta[7])/(1 + S^2)) + HPL[{0}, S^2]*((-109127*Pi^8)/453600 + (Pi^6*(-60622 - 55645*S^2))/22680 + (Pi^4*(-1353 - 2095*S^2))/180 - (13*Pi^2*(-9 + 34*S^2))/3 - 2*(-751 + 940*S^2) + (32*(-1 + S^2)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)) - (16*HPL[{1}, -S^2]^8)/3 + HPL[{1}, -S^2]^6*((-482*Pi^2)/27 - (4*(1 + S^2))/3 - (200*HPL[{2}, -S^2])/3) + ((-97*Pi^2)/3 - (10*S^2)/3)*HPL[{2}, -S^2]^3 - 32*HPL[{2}, -S^2]^4 + ((-10*Pi^2)/3 + 2*(5 + S^2))*HPL[{3}, -S^2]^2 + 58*HPL[{4}, -S^2]^2 + ((-149*Pi^2)/3 + 10*(16 + 13*S^2))*HPL[{6}, -S^2] + (2*(142 + 209*S^2)*HPL[{7}, -S^2])/(1 + S^2) - 1030*HPL[{8}, -S^2] + ((1270*Pi^2)/3 + 40*(2 + S^2))*HPL[{2, 1}, -S^2]^2 - 1496*HPL[{3, 1}, -S^2]^2 + ((Pi^2*(79 + 169*S^2))/(3*(1 + S^2)) - (2*(-1 + 18*S^2 + 22*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((10*Pi^2)/3 - 2*(11 + 7*S^2))*HPL[{4, 2}, -S^2] + (2*(18 + 31*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) + (50*Pi^2 - 4*(43 + 29*S^2))*HPL[{5, 1}, -S^2] + (2*(59 + 101*S^2)*HPL[{5, 2}, -S^2])/(1 + S^2) + 16*HPL[{5, 3}, -S^2] + (2*(113 + 120*S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) + 18*HPL[{6, 2}, -S^2] + 572*HPL[{7, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2]^2 + ((-4*Pi^2)/3 - 4*(-1 + S^2))*HPL[{3, 1, 2}, -S^2] + ((-2332*Pi^2)/3 - 4*(-1 + 21*S^2))*HPL[{3, 2, 1}, -S^2] - (2*(31 + 151*S^2)*HPL[{3, 2, 2}, -S^2])/(1 + S^2) - (8*(31 + 125*S^2)*HPL[{3, 3, 1}, -S^2])/(1 + S^2) + 84*HPL[{3, 3, 2}, -S^2] + ((-7112*Pi^2)/3 - 8*(-5 + 31*S^2))*HPL[{4, 1, 1}, -S^2] - (94*(3 + 11*S^2)*HPL[{4, 1, 2}, -S^2])/(1 + S^2) - 160*HPL[{4, 1, 3}, -S^2] - (2*(417 + 1561*S^2)*HPL[{4, 2, 1}, -S^2])/(1 + S^2) + 100*HPL[{4, 2, 2}, -S^2] - 304*HPL[{4, 3, 1}, -S^2] - (8*(226 + 779*S^2)*HPL[{5, 1, 1}, -S^2])/(1 + S^2) - 124*HPL[{5, 1, 2}, -S^2] - 1324*HPL[{5, 2, 1}, -S^2] - 3864*HPL[{6, 1, 1}, -S^2] - (32*(-131 + 46*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2) + ((4904*Pi^2)/3 + 16*(-1 + 11*S^2))*HPL[{3, 1, 1, 1}, -S^2] + (16*(-767 + 333*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2) + (16*(-767 + 333*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2) + 16*HPL[{3, 1, 2, 2}, -S^2] + (16*(-1553 + 609*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2) + 16*HPL[{3, 2, 1, 2}, -S^2] + 5744*HPL[{3, 2, 2, 1}, -S^2] + 17184*HPL[{3, 3, 1, 1}, -S^2] + (8*(-9323 + 3603*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2) + 80*HPL[{4, 1, 1, 2}, -S^2] + 17264*HPL[{4, 1, 2, 1}, -S^2] + 51632*HPL[{4, 2, 1, 1}, -S^2] + 103568*HPL[{5, 1, 1, 1}, -S^2] + (-3344*Pi^2 - 480*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - (64*(-121 + 75*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2) - (192*(-121 + 75*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2) + 11328*HPL[{2, 2, 1, 2, 1}, -S^2] + 33984*HPL[{2, 2, 2, 1, 1}, -S^2] - (96*(-397 + 262*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2) - 68000*HPL[{3, 1, 1, 1, 2}, -S^2] - 113312*HPL[{3, 1, 1, 2, 1}, -S^2] - 135968*HPL[{3, 1, 2, 1, 1}, -S^2] - 283232*HPL[{3, 2, 1, 1, 1}, -S^2] - 849984*HPL[{4, 1, 1, 1, 1}, -S^2] - (2400*(-7 + 3*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) + 23552*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 48000*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{2, 1, 1, 1}, -S^2]*((-16*(1 + S^2)*(-1 + 12*S^2))/S^2 - (4*Pi^2*(-809 + 271*S^2))/(3*(1 + S^2)) - 1376*Zeta[3]) + HPL[{4, 1}, -S^2]*(-4*(41 + 37*S^2) + (Pi^2*(211 + 401*S^2))/(3*(1 + S^2)) - 112*Zeta[3]) + (22*Pi^2 - 4*(8 + 11*S^2))*Zeta[3]^2 + HPL[{1}, -S^2]^5*(-4*(1 + S^2) + (2*Pi^2*(-688 + 517*S^2))/(45*(1 + S^2)) + (100*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2) + (136*HPL[{3}, -S^2])/15 + 400*HPL[{2, 1}, -S^2] + (664*Zeta[3])/15) + HPL[{5}, -S^2]*((2*Pi^2*(9 + 32*S^2))/(3*(1 + S^2)) - (2*(10 - 25*S^2 + 2*S^4))/S^2 + 116*HPL[{2, 1}, -S^2] + 84*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((2*Pi^2*(-733 + 369*S^2))/(3*(1 + S^2)) - (8*(1 - 11*S^2 + 2*S^4))/S^2 + 688*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((2*Pi^2*(-2275 + 1009*S^2))/(3*(1 + S^2)) + (8*(-2 + 37*S^2 + 12*S^4))/S^2 + 2160*Zeta[3]) + HPL[{2}, -S^2]^2*((-6751*Pi^4)/360 + (Pi^2*(-36 - 13*S^2))/6 + (4 - 33*S^2 - 8*S^4)/S^2 + ((-7 - 37*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 6*HPL[{4}, -S^2] - (4*(-131 + 46*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 716*HPL[{3, 1}, -S^2] - 1416*HPL[{2, 1, 1}, -S^2] + ((-5 - 87*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-7153*Pi^4)/45 - (76*Pi^2*S^2)/3 - (8*(-22 - 9*S^2 + 14*S^4))/S^2 - (16*(-1 + 40*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^4*((-4061*Pi^4)/180 - (7*Pi^2*(1 + S^2))/3 - (4*(1 + S^2)*(-2 + 3*S^2))/S^2 - 120*Pi^2*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/3 - (4*(-10 + 7*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (92*HPL[{4}, -S^2])/3 - (500*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 1000*HPL[{3, 1}, -S^2] - 2000*HPL[{2, 1, 1}, -S^2] - (4*(-40 + 43*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{4}, -S^2]*(7*Pi^2 - (208*Pi^4)/45 + (2*(-4 + 13*S^2 + 39*S^4))/S^2 - (2*(29 + 37*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 120*HPL[{3, 1}, -S^2] + 32*HPL[{2, 1, 1}, -S^2] - (2*(41 + 45*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1}, -S^2]*((6853*Pi^4)/90 + (2*Pi^2*(-9 + 13*S^2))/3 - (4*(23 + 30*S^2))/S^2 + 6208*HPL[{2, 1, 1}, -S^2] + (4*(1 + 87*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((Pi^4*(7738 - 3037*S^2))/(180*(1 + S^2)) - (2*Pi^2*(-1 + 29*S^2 + 10*S^4))/(3*S^2) + (2*(-63 - 100*S^2 + 11*S^4))/S^2 + (32*(-61 + 37*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 208*HPL[{3, 2}, -S^2] + 592*HPL[{4, 1}, -S^2] + (32*(-121 + 75*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 5664*HPL[{2, 2, 1}, -S^2] - 17536*HPL[{3, 1, 1}, -S^2] + 12544*HPL[{2, 1, 1, 1}, -S^2] + ((-232*Pi^2)/3 + 8*(1 + S^2))*Zeta[3] - 304*Zeta[5]) + ((Pi^2*(-419 - 500*S^2))/(3*(1 + S^2)) - 84*(2 + S^2))*Zeta[5] + HPL[{3}, -S^2]*((Pi^4*(-79 - 49*S^2))/(36*(1 + S^2)) + (2*(6 - 7*S^2 + 2*S^4))/S^2 + (Pi^2*(4 + 3*S^2 + 22*S^4))/(3*S^2) - (2*(7 + 12*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 124*HPL[{5}, -S^2] + ((-88*Pi^2)/3 + 4*(-19 + S^2))*HPL[{2, 1}, -S^2] + (8*(8 + 25*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 40*HPL[{3, 2}, -S^2] + 216*HPL[{4, 1}, -S^2] - (16*(9 + 28*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + 208*HPL[{2, 2, 1}, -S^2] + 544*HPL[{3, 1, 1}, -S^2] - 544*HPL[{2, 1, 1, 1}, -S^2] + (8*Pi^2 - 4*(10 + S^2))*Zeta[3] + 64*Zeta[5]) + HPL[{1}, -S^2]^3*((-4*(1 + S^2)*(-36 + 23*S^2))/(3*S^2) - (2*Pi^2*(1 + S^2)*(1 + 24*S^2))/(9*S^2) + (Pi^4*(-7801 + 4382*S^2))/(270*(1 + S^2)) + (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + ((44*Pi^2)/9 + 16*(1 + S^2))*HPL[{3}, -S^2] + (4*(-17 + 29*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - (184*HPL[{5}, -S^2])/3 + 480*Pi^2*HPL[{2, 1}, -S^2] - (16*(-62 + 63*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (608*HPL[{3, 2}, -S^2])/3 - (1456*HPL[{4, 1}, -S^2])/3 + (2000*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (12544*HPL[{2, 2, 1}, -S^2])/3 - (37088*HPL[{3, 1, 1}, -S^2])/3 + 8000*HPL[{2, 1, 1, 1}, -S^2] + ((376*Pi^2)/9 - (8*(1 + S^2))/3)*Zeta[3] + HPL[{2}, -S^2]*((40*(1 + S^2))/(3*S^2) + (2*Pi^2*(-623 + 457*S^2))/(9*(1 + S^2)) + (304*HPL[{3}, -S^2])/3 + (6272*HPL[{2, 1}, -S^2])/3 + (656*Zeta[3])/3) + (520*Zeta[5])/3) + Zeta[3]*((Pi^4*(-1013 - 1242*S^2))/(60*(1 + S^2)) - (2*Pi^2*(30 + 7*S^2))/3 - 10*(13 + 9*S^2) + 520*Zeta[5]) + HPL[{1}, -S^2]^2*((-248987*Pi^6)/22680 - (7*Pi^4*(1 + S^2))/4 - (2*Pi^2*(1 + S^2)*(-10 + 23*S^2))/(3*S^2) - (4*(1 + S^2)*(-43 + 28*S^2))/S^2 + ((-551*Pi^2)/3 - 10*(1 + S^2))*HPL[{2}, -S^2]^2 - 236*HPL[{2}, -S^2]^3 + 8*HPL[{3}, -S^2]^2 + ((-80*Pi^2)/3 + 14*(1 + S^2))*HPL[{4}, -S^2] + (4*(-6 + 17*S^2)*HPL[{5}, -S^2])/(1 + S^2) - 146*HPL[{6}, -S^2] + 3136*HPL[{2, 1}, -S^2]^2 + (720*Pi^2 - 8*(1 + S^2))*HPL[{3, 1}, -S^2] + (152*(-1 + S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (4*(-97 + 85*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 216*HPL[{5, 1}, -S^2] - 1440*Pi^2*HPL[{2, 1, 1}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (16*(-578 + 581*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 5664*HPL[{3, 2, 1}, -S^2] - 17360*HPL[{4, 1, 1}, -S^2] - (6000*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + 12000*HPL[{3, 1, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((-40*(1 + S^2))/S^2 - (2*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)) - 656*Zeta[3]) + ((-8*(1 + S^2)*(1 + 2*S^2))/S^2 - (2*Pi^2*(-37 + 57*S^2))/(3*(1 + S^2)))*Zeta[3] - 68*Zeta[3]^2 + HPL[{3}, -S^2]*((8*(1 + S^2)*(3 + 4*S^2))/S^2 - (2*Pi^2*(-4 + 7*S^2))/(3*(1 + S^2)) - 304*HPL[{2, 1}, -S^2] + 16*Zeta[3]) + HPL[{2}, -S^2]*((-2155*Pi^4)/36 + (Pi^2*(-1 - S^2))/3 - (4*(-16 + S^2)*(1 + S^2))/S^2 - (76*(-1 + S^2)*HPL[{3}, -S^2])/(1 + S^2) - 16*HPL[{4}, -S^2] - (1568*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + 3136*HPL[{3, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2] - (164*(-1 + S^2)*Zeta[3])/(1 + S^2)) - (4*(-27 + 38*S^2)*Zeta[5])/(1 + S^2)) + HPL[{2}, -S^2]*((-33839*Pi^6)/4536 + (Pi^4*(22 - 155*S^2))/180 - (8*Pi^2*(-2 + S^4))/S^2 - (4*(-34 + 3*S^2 + 19*S^4))/S^2 + 10*HPL[{3}, -S^2]^2 + ((14*Pi^2)/3 + 2*(-11 + S^2))*HPL[{4}, -S^2] + (2*(-1 + S^2)*HPL[{5}, -S^2])/(1 + S^2) + 142*HPL[{6}, -S^2] + 1416*HPL[{2, 1}, -S^2]^2 + ((1252*Pi^2)/3 + 4*(19 + 9*S^2))*HPL[{3, 1}, -S^2] + (30*(1 + 5*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (2*(71 + 259*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 12*HPL[{4, 2}, -S^2] - 140*HPL[{5, 1}, -S^2] + ((-2540*Pi^2)/3 - 80*(2 + S^2))*HPL[{2, 1, 1}, -S^2] + (16*(-131 + 46*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (32*(-192 + 83*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 3072*HPL[{3, 2, 1}, -S^2] - 9184*HPL[{4, 1, 1}, -S^2] - (32*(-121 + 75*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + 74176*HPL[{3, 1, 1, 1}, -S^2] - 12544*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{2, 1}, -S^2]*((Pi^2*(733 - 369*S^2))/(3*(1 + S^2)) + (4*(1 - 11*S^2 + 2*S^4))/S^2 - 344*Zeta[3]) + HPL[{3}, -S^2]*((Pi^2*(-38 - 83*S^2))/(3*(1 + S^2)) + 8*(2 + 3*S^2) - 104*HPL[{2, 1}, -S^2] - 8*Zeta[3]) + ((Pi^2*(-48 - 139*S^2))/(3*(1 + S^2)) - (4*(-1 + 11*S^2))/S^2)*Zeta[3] - 36*Zeta[3]^2 - (2*(72 + 125*S^2)*Zeta[5])/(1 + S^2)) - (6*(161 + 186*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((-20*(1 + S^2)*(-17 + 15*S^2))/S^2 - (2*Pi^2*(1 + S^2)*(-11 + 15*S^2))/S^2 - (Pi^4*(1 + S^2)*(10 + 463*S^2))/(180*S^2) + (Pi^6*(-182305 + 66682*S^2))/(22680*(1 + S^2)) + (118*(-1 + S^2)*HPL[{2}, -S^2]^3)/(1 + S^2) - (2*(-1 + 3*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((-92*Pi^2)/3 + 64*(1 + S^2))*HPL[{5}, -S^2] + (2*(-9 + 64*S^2)*HPL[{6}, -S^2])/(1 + S^2) - 268*HPL[{7}, -S^2] - (1568*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + (-60*Pi^2 - 40*(1 + S^2))*HPL[{3, 2}, -S^2] + ((-380*Pi^2)/3 - 148*(1 + S^2))*HPL[{4, 1}, -S^2] - 6*HPL[{4, 2}, -S^2] - 52*HPL[{4, 3}, -S^2] - (8*(-5 + 22*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) - 168*HPL[{5, 2}, -S^2] - 28*HPL[{6, 1}, -S^2] + ((-4408*Pi^2)/3 - 80*(1 + S^2))*HPL[{2, 2, 1}, -S^2] + ((-13136*Pi^2)/3 - 144*(1 + S^2))*HPL[{3, 1, 1}, -S^2] + (2832*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + 480*HPL[{3, 2, 2}, -S^2] + 1504*HPL[{3, 3, 1}, -S^2] + (8*(-1079 + 1091*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + 1504*HPL[{4, 1, 2}, -S^2] + 4576*HPL[{4, 2, 1}, -S^2] + 8848*HPL[{5, 1, 1}, -S^2] + 2880*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + 11328*HPL[{2, 2, 2, 1}, -S^2] - (96*(-62 + 63*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - 35200*HPL[{3, 1, 1, 2}, -S^2] - 35200*HPL[{3, 1, 2, 1}, -S^2] - 69184*HPL[{3, 2, 1, 1}, -S^2] - 206816*HPL[{4, 1, 1, 1}, -S^2] + (12000*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + 25088*HPL[{2, 1, 2, 1, 1}, -S^2] + 75264*HPL[{2, 2, 1, 1, 1}, -S^2] + 126528*HPL[{3, 1, 1, 1, 1}, -S^2] + 48000*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-24*(1 + S^2)*(2 + S^2))/S^2 - (4*Pi^2*(-103 + 77*S^2))/(1 + S^2) - 688*Zeta[3]) + ((229*Pi^4)/30 - (28*Pi^2*(1 + S^2))/3 - (16*(1 + S^2)*(1 + 5*S^2))/S^2)*Zeta[3] + (4*(-9 + 8*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{4}, -S^2]*((2*(1 + S^2)*(5 + 7*S^2))/S^2 + (Pi^2*(-29 + 51*S^2))/(3*(1 + S^2)) + 32*HPL[{2, 1}, -S^2] + 16*Zeta[3]) + HPL[{2}, -S^2]^2*(-10*(1 + S^2) + (Pi^2*(-313 + 238*S^2))/(3*(1 + S^2)) + 60*HPL[{3}, -S^2] + 1416*HPL[{2, 1}, -S^2] + 164*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((80*(1 + S^2))/S^2 + (4*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)) + 1312*Zeta[3]) + HPL[{3}, -S^2]*((-5*Pi^4)/3 + (16*Pi^2*(1 + S^2))/3 + (4*(1 + S^2)*(13 + 15*S^2))/S^2 + 20*HPL[{4}, -S^2] + (152*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - 272*HPL[{3, 1}, -S^2] + 608*HPL[{2, 1, 1}, -S^2] - (8*(-1 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((2155*Pi^4)/18 + (2*Pi^2*(1 + S^2))/3 + (8*(-16 + S^2)*(1 + S^2))/S^2 - 6272*HPL[{3, 1}, -S^2] - 12544*HPL[{2, 1, 1}, -S^2] + (328*(-1 + S^2)*Zeta[3])/(1 + S^2)) + (54*Pi^2 - 68*(1 + S^2))*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(-21 + 4*S^2))/(3*S^2) - (2*(1 + S^2)*(-74 + 23*S^2))/S^2 + (Pi^4*(-6891 + 3884*S^2))/(180*(1 + S^2)) + (30*Pi^2 + 20*(1 + S^2))*HPL[{3}, -S^2] + (2*(-1 + 7*S^2)*HPL[{4}, -S^2])/(1 + S^2) - 8*HPL[{5}, -S^2] + ((2204*Pi^2)/3 + 40*(1 + S^2))*HPL[{2, 1}, -S^2] - (1568*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 240*HPL[{3, 2}, -S^2] - 752*HPL[{4, 1}, -S^2] + (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 5664*HPL[{2, 2, 1}, -S^2] + 17600*HPL[{3, 1, 1}, -S^2] + 12544*HPL[{2, 1, 1, 1}, -S^2] + ((182*Pi^2)/3 - 4*(1 + S^2))*Zeta[3] + 212*Zeta[5]) + 300*Zeta[7])) - 3136*Zeta[9];
E5vwuT2F2=245/32 + (11*Pi^4*(211 + 1791*S^2))/1440 + (5*Pi^2*(109 + 4864*S^2))/384 + (Pi^6*(232634 + 877473*S^2))/362880 + (Pi^8*(752611*S^2 + 305763*S^4))/(907200*(1 + S^2)) + ((29*Pi^2*S^2)/21 + (23 + 106*S^2 + 83*S^4)/(21*S^2))*HPL[{1}, -S^2]^7 + ((1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^8)/(3*S^2*(1 + S^2)) + (8*S^2*HPL[{1}, -S^2]^9)/27 + HPL[{0}, S^2]^8*(S^2/(192*(1 + S^2)) + (S^2*HPL[{1}, -S^2])/192) + ((14 + 14*S^2 + 297*S^4 + 105*S^6)*HPL[{2}, -S^2]^4)/(12*S^2*(1 + S^2)) + HPL[{0}, S^2]^7*((Pi^2*S^2)/192 + (1 + 3*S^2)/48 + ((1 + S^2 + 6*S^4 + 3*S^6)*HPL[{1}, -S^2])/(48*S^2*(1 + S^2)) + (S^2*HPL[{1}, -S^2]^2)/32 + (S^2*HPL[{2}, -S^2])/32) + (8*S^2*HPL[{3}, -S^2]^3)/3 + ((14 + 14*S^2 + 9*S^4 + 27*S^6)*HPL[{4}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((-131*Pi^2*S^2)/6 + (205 + 58*S^2 + 408*S^4)/(2*S^2))*HPL[{7}, -S^2] + ((-105 - 105*S^2 - 280*S^4 - 172*S^6)*HPL[{8}, -S^2])/(2*S^2*(1 + S^2)) - 459*S^2*HPL[{9}, -S^2] - (784*S^2*HPL[{2, 1}, -S^2]^3)/3 + ((97 + 97*S^2 + 1375*S^4 + 443*S^6)*HPL[{3, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-11*Pi^2*S^2)/2 + (-10 - 52*S^2 + 175*S^4)/(4*S^2))*HPL[{4, 3}, -S^2] + ((-29*Pi^2*S^2)/3 + (-27 - 58*S^2 + 231*S^4)/(2*S^2))*HPL[{5, 2}, -S^2] + (3*S^2*(3 + 11*S^2)*HPL[{5, 3}, -S^2])/(2*(1 + S^2)) - 112*S^2*HPL[{5, 4}, -S^2] + ((75*Pi^2*S^2)/2 + (-115 - 362*S^2 + 247*S^4)/(4*S^2))*HPL[{6, 1}, -S^2] + ((22 + 22*S^2 - 7*S^4 + 53*S^6)*HPL[{6, 2}, -S^2])/(2*S^2*(1 + S^2)) - 434*S^2*HPL[{6, 3}, -S^2] - (3*(7 + 7*S^2 + 138*S^4 + 174*S^6)*HPL[{7, 1}, -S^2])/(2*S^2*(1 + S^2)) - 1095*S^2*HPL[{7, 2}, -S^2] - 2106*S^2*HPL[{8, 1}, -S^2] + (8*(25 + 25*S^2 + 614*S^4 + 222*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-559*Pi^2*S^2)/2 + (34 - 830*S^2 - 2283*S^4)/(4*S^2))*HPL[{3, 2, 2}, -S^2] + ((-2612*Pi^2*S^2)/3 + (48 - 592*S^2 - 1779*S^4)/S^2)*HPL[{3, 3, 1}, -S^2] + ((17 + 17*S^2 + 865*S^4 + 333*S^6)*HPL[{3, 3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((-1731*Pi^2*S^2)/2 + (201 - 2282*S^2 - 6927*S^4)/(4*S^2))*HPL[{4, 1, 2}, -S^2] + ((-17 - 17*S^2 - 754*S^4 - 300*S^6)*HPL[{4, 1, 3}, -S^2])/(S^2*(1 + S^2)) + ((-5311*Pi^2*S^2)/2 + (561 - 7298*S^2 - 21711*S^4)/(4*S^2))*HPL[{4, 2, 1}, -S^2] + ((6 + 6*S^2 + 571*S^4 + 195*S^6)*HPL[{4, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) - 44*S^2*HPL[{4, 2, 3}, -S^2] + ((-43 - 43*S^2 - 2444*S^4 - 990*S^6)*HPL[{4, 3, 1}, -S^2])/(S^2*(1 + S^2)) + 5*S^2*HPL[{4, 3, 2}, -S^2] + 22*S^2*HPL[{4, 4, 1}, -S^2] + ((-16369*Pi^2*S^2)/3 - (3*(-70 + 1254*S^2 + 3673*S^4))/S^2)*HPL[{5, 1, 1}, -S^2] + ((-59 - 59*S^2 - 2923*S^4 - 1235*S^6)*HPL[{5, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) - 66*S^2*HPL[{5, 1, 3}, -S^2] + ((-359 - 359*S^2 - 20023*S^4 - 8015*S^6)*HPL[{5, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 2*S^2*HPL[{5, 2, 2}, -S^2] - 46*S^2*HPL[{5, 3, 1}, -S^2] - (2*(200 + 200*S^2 + 12819*S^4 + 4990*S^6)*HPL[{6, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 59*S^2*HPL[{6, 1, 2}, -S^2] - 381*S^2*HPL[{6, 2, 1}, -S^2] - 1472*S^2*HPL[{7, 1, 1}, -S^2] + ((836*Pi^2*S^2)/3 + (-465 - 1420*S^2 + 546*S^4)/S^2)*HPL[{2, 2, 2, 1}, -S^2] + (-258*Pi^2*S^2 + (2701 + 9140*S^2 - 1095*S^4)/(2*S^2))*HPL[{3, 1, 1, 2}, -S^2] + (-258*Pi^2*S^2 + (2701 + 9140*S^2 - 1095*S^4)/(2*S^2))*HPL[{3, 1, 2, 1}, -S^2] + ((47 + 47*S^2 + 438*S^4 + 126*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) + (-1094*Pi^2*S^2 + (5491 + 17660*S^2 - 4371*S^4)/(2*S^2))*HPL[{3, 2, 1, 1}, -S^2] + ((47 + 47*S^2 + 438*S^4 + 126*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((575 + 575*S^2 - 2818*S^4 - 3194*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 3104*S^2*HPL[{3, 2, 2, 2}, -S^2] + 9728*S^2*HPL[{3, 2, 3, 1}, -S^2] - (12*(-66 - 66*S^2 + 407*S^4 + 415*S^6)*HPL[{3, 3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 9576*S^2*HPL[{3, 3, 1, 2}, -S^2] + 29568*S^2*HPL[{3, 3, 2, 1}, -S^2] + ((-9452*Pi^2*S^2)/3 + (8420 + 26880*S^2 - 6283*S^4)/S^2)*HPL[{4, 1, 1, 1}, -S^2] + ((-7 - 7*S^2 + 850*S^4 + 382*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) - 60148*S^2*HPL[{4, 1, 1, 3}, -S^2] + ((785 + 785*S^2 - 4034*S^4 - 4598*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) - 50615*S^2*HPL[{4, 1, 2, 2}, -S^2] - 90404*S^2*HPL[{4, 1, 3, 1}, -S^2] + ((2369 + 2369*S^2 - 13802*S^4 - 14558*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 31079*S^2*HPL[{4, 2, 1, 2}, -S^2] - 30623*S^2*HPL[{4, 2, 2, 1}, -S^2] - 178732*S^2*HPL[{4, 3, 1, 1}, -S^2] - (2*(-2361 - 2361*S^2 + 12541*S^4 + 14181*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 181642*S^2*HPL[{5, 1, 1, 2}, -S^2] - 299770*S^2*HPL[{5, 1, 2, 1}, -S^2] - 714586*S^2*HPL[{5, 2, 1, 1}, -S^2] - 1785216*S^2*HPL[{6, 1, 1, 1}, -S^2] + ((-1624*Pi^2*S^2)/3 - (2*(473 + 1824*S^2 + 466*S^4))/S^2)*HPL[{2, 1, 2, 1, 1}, -S^2] + (-1624*Pi^2*S^2 - (6*(473 + 1824*S^2 + 466*S^4))/S^2)*HPL[{2, 2, 1, 1, 1}, -S^2] - (8*(-66 + 413*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 - (24*(-66 + 413*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + 3024*S^2*HPL[{2, 2, 2, 2, 1}, -S^2] + ((-11872*Pi^2*S^2)/3 - (2*(2475 + 9688*S^2 + 3482*S^4))/S^2)*HPL[{3, 1, 1, 1, 1}, -S^2] + (2*(-1540 + 9799*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 + (2*(-2596 + 16407*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 + 2704*S^2*HPL[{3, 1, 1, 2, 2}, -S^2] + (2*(-3124 + 19711*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 + 2704*S^2*HPL[{3, 1, 2, 1, 2}, -S^2] - 144*S^2*HPL[{3, 1, 2, 2, 1}, -S^2] - 24912*S^2*HPL[{3, 1, 3, 1, 1}, -S^2] + (2*(-6556 + 41187*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 + 11776*S^2*HPL[{3, 2, 1, 1, 2}, -S^2] + 8928*S^2*HPL[{3, 2, 1, 2, 1}, -S^2] + 5008*S^2*HPL[{3, 2, 2, 1, 1}, -S^2] + 6384*S^2*HPL[{3, 3, 1, 1, 1}, -S^2] + (16*(-2475 - 2475*S^2 + 15239*S^4 + 15405*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 34648*S^2*HPL[{4, 1, 1, 1, 2}, -S^2] + 26104*S^2*HPL[{4, 1, 1, 2, 1}, -S^2] + 14344*S^2*HPL[{4, 1, 2, 1, 1}, -S^2] + 18040*S^2*HPL[{4, 2, 1, 1, 1}, -S^2] + 32784*S^2*HPL[{5, 1, 1, 1, 1}, -S^2] + ((3664*Pi^2*S^2)/3 + (4*(-463 - 1558*S^2 + 500*S^4))/S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 6272*S^2*HPL[{2, 2, 1, 2, 1, 1}, -S^2] - 18816*S^2*HPL[{2, 2, 2, 1, 1, 1}, -S^2] - (8*(-165 - 165*S^2 + 451*S^4 + 783*S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 44544*S^2*HPL[{3, 1, 1, 1, 1, 2}, -S^2] + 82176*S^2*HPL[{3, 1, 1, 1, 2, 1}, -S^2] + 107264*S^2*HPL[{3, 1, 1, 2, 1, 1}, -S^2] + 119808*S^2*HPL[{3, 1, 2, 1, 1, 1}, -S^2] + 201344*S^2*HPL[{3, 2, 1, 1, 1, 1}, -S^2] + 606944*S^2*HPL[{4, 1, 1, 1, 1, 1}, -S^2] + (480*(-4 + 31*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + 12448*S^2*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] + 49792*S^2*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] + 124480*S^2*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] + 233088*S^2*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + 26880*S^2*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + (-8/3 - (8*Pi^2*S^2)/9 - (8*S^2*HPL[{0}, S^2]^2)/3 - (8*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)) - (32*S^2*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*((-8*S^2*(7 + 3*S^2))/(3*(1 + S^2)) - (32*S^2*HPL[{1}, -S^2])/3) - (16*S^2*HPL[{2}, -S^2])/3)*Log[T]^7 + ((8*S^2)/(3*(1 + S^2)) + (8*S^2*HPL[{0}, S^2])/3 + (8*S^2*HPL[{1}, -S^2])/3)*Log[T]^8 + ((2 + 23*S^2)/4 + (Pi^2*(17*S^2 - 12*S^4))/(6*(1 + S^2)))*Zeta[3]^2 - 16*S^2*Zeta[3]^3 + HPL[{2, 1, 1, 1, 1}, -S^2]*((2*(-209 - 74*S^2 + 1934*S^4))/S^2 + (8*Pi^2*(-35 - 35*S^2 + 668*S^4 + 472*S^6))/(3*S^2*(1 + S^2)) - 6112*S^2*Zeta[3]) + HPL[{4, 1, 1}, -S^2]*((-690 - 835*S^2 + 4794*S^4)/(2*S^2) + (Pi^2*(-453 - 453*S^2 + 6440*S^4 + 4816*S^6))/(6*S^2*(1 + S^2)) - 4516*S^2*Zeta[3]) + HPL[{3, 2, 1}, -S^2]*((-319 - 230*S^2 + 3289*S^4)/(4*S^2) + (Pi^2*(-257 - 257*S^2 + 4818*S^4 + 3282*S^6))/(12*S^2*(1 + S^2)) - 1480*S^2*Zeta[3]) + HPL[{2}, -S^2]^3*((-225 - 164*S^2 + 1724*S^4)/(48*S^2) + (Pi^2*(-19 - 19*S^2 + 308*S^4 + 212*S^6))/(18*S^2*(1 + S^2)) - (211*S^2*HPL[{3}, -S^2])/3 - 63*S^2*HPL[{2, 1}, -S^2] - 61*S^2*Zeta[3]) + Log[T]^6*(5 + (Pi^2*(118*S^2 + 31*S^4))/(9*(1 + S^2)) + (25*S^2*HPL[{0}, S^2]^3)/9 + ((29*Pi^2*S^2)/3 + (23 + 106*S^2 + 83*S^4)/(3*S^2))*HPL[{1}, -S^2] + (28*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)) + (224*S^2*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]^2*((31*S^2*(2 + S^2))/(3*(1 + S^2)) + (31*S^2*HPL[{1}, -S^2])/3) + (2*(-4 + 31*S^4)*HPL[{2}, -S^2])/(3*S^2) + HPL[{0}, S^2]*(9*Pi^2*S^2 + (28 + 83*S^2)/3 + (28*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)) + (112*S^2*HPL[{1}, -S^2]^2)/3 + (106*S^2*HPL[{2}, -S^2])/3) - (118*S^2*HPL[{3}, -S^2])/3 + (112*S^2*HPL[{2, 1}, -S^2])/3 - (112*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^6*(((1 + S^2)*(221 + 1023*S^2))/(72*S^2) + (Pi^2*(25 + 25*S^2 + 249*S^4 + 75*S^6))/(18*S^2*(1 + S^2)) + (13*(1 + 3*S^4)*HPL[{2}, -S^2])/(6*S^2) - (190*S^2*HPL[{3}, -S^2])/9 - (50*S^2*Zeta[3])/3) + HPL[{3, 1, 2}, -S^2]*((131 + 98*S^2 - 159*S^4)/(4*S^2) + (Pi^2*(47 - 110*S^4))/(12*S^2) - 16*S^2*Zeta[3]) + HPL[{0}, S^2]^6*((3 + 92*S^2)/192 + (Pi^2*(77*S^2 + 31*S^4))/(576*(1 + S^2)) + ((5 + 5*S^2 + 33*S^4 + 15*S^6)*HPL[{1}, -S^2]^2)/(48*S^2*(1 + S^2)) + (S^2*HPL[{1}, -S^2]^3)/8 + (S^2*(44 + 31*S^2)*HPL[{2}, -S^2])/(96*(1 + S^2)) + HPL[{1}, -S^2]*((23*Pi^2*S^2)/288 + (1 + 26*S^2 + 25*S^4)/(64*S^2) + (13*S^2*HPL[{2}, -S^2])/96) - (S^2*HPL[{3}, -S^2])/32 + (S^2*HPL[{2, 1}, -S^2])/12 + (S^2*Zeta[3])/8) + HPL[{0}, S^2]^5*((5597*Pi^4*S^2)/86400 + (7*(7 + 129*S^2))/384 + (Pi^2*(90 + 299*S^2))/384 + ((255 + 255*S^2 + 1849*S^4 + 765*S^6)*HPL[{1}, -S^2]^3)/(720*S^2*(1 + S^2)) + (271*S^2*HPL[{1}, -S^2]^4)/720 + ((571*Pi^2*S^2)/1440 + (28 + 115*S^2)/64)*HPL[{2}, -S^2] + (9*S^2*HPL[{2}, -S^2]^2)/20 + HPL[{1}, -S^2]^2*((293*Pi^2*S^2)/720 + (5 + 49*S^2 + 44*S^4)/(24*S^2) + (77*S^2*HPL[{2}, -S^2])/80) - (S^2*(-3 + S^2)*HPL[{3}, -S^2])/(32*(1 + S^2)) + (5*S^2*HPL[{4}, -S^2])/16 + ((-35 - 35*S^2 - 57*S^4 + 20*S^6)*HPL[{2, 1}, -S^2])/(40*S^2*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(49 + 775*S^2))/(384*S^2) + (Pi^2*(675 + 675*S^2 + 4369*S^4 + 2025*S^6))/(2880*S^2*(1 + S^2)) + (7*(5 + 5*S^2 + 37*S^4 + 15*S^6)*HPL[{2}, -S^2])/(80*S^2*(1 + S^2)) + (S^2*HPL[{3}, -S^2])/8 - (77*S^2*HPL[{2, 1}, -S^2])/40) - (87*S^2*HPL[{3, 1}, -S^2])/40 + (64*S^2*HPL[{2, 1, 1}, -S^2])/15 + (23*S^2*Zeta[3])/16) + HPL[{3}, -S^2]^2*((Pi^2*S^2*(56 + 19*S^2))/(6*(1 + S^2)) + (51 + 164*S^2 + 177*S^4)/(16*S^2) - 10*S^2*HPL[{2, 1}, -S^2] + 15*S^2*Zeta[3]) + HPL[{6}, -S^2]*((5 - 320*S^2 + 922*S^4)/(8*S^2) + (Pi^2*(30 + 30*S^2 - 16*S^4 + 51*S^6))/(6*S^2*(1 + S^2)) + 71*S^2*HPL[{2, 1}, -S^2] + 21*S^2*Zeta[3]) + HPL[{4, 2}, -S^2]*((-35 + 163*S^2 + 273*S^4)/(4*S^2) + (Pi^2*(-2 - 2*S^2 + 413*S^4 + 185*S^6))/(12*S^2*(1 + S^2)) + 31*S^2*Zeta[3]) + HPL[{5, 1}, -S^2]*((28 + 1516*S^2 + 1731*S^4)/(8*S^2) + (Pi^2*(-35 - 35*S^2 + 2043*S^4 + 659*S^6))/(12*S^2*(1 + S^2)) + 130*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]^2*((-80 - 467*S^2 - 946*S^4)/(2*S^2) + (Pi^2*(-46 - 46*S^2 - 2109*S^4 - 895*S^6))/(6*S^2*(1 + S^2)) + 744*S^2*Zeta[3]) + HPL[{3, 1, 1, 1}, -S^2]*((657 + 816*S^2 - 3445*S^4)/(2*S^2) + (Pi^2*(188 + 188*S^2 - 2157*S^4 - 1717*S^6))/(3*S^2*(1 + S^2)) + 3088*S^2*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((971*Pi^4*S^2)/60 + (Pi^2*(971 + 3508*S^2 + 422*S^4))/(12*S^2) + (1177 + 8118*S^2 + 1718*S^4)/(8*S^2) + (4*(-54 - 54*S^2 - 347*S^4 + 7*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((1229*Pi^4*S^2)/30 + (3*(-305 - 2490*S^2 + 384*S^4))/(4*S^2) + (Pi^2*(-981 - 3340*S^2 + 482*S^4))/(6*S^2) + (16*(25 + 25*S^2 + 203*S^4 + 7*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^5*((6673*Pi^4*S^2)/2700 + ((1 + S^2)*(159 + 896*S^2))/(20*S^2) + (Pi^2*(1 + S^2)*(301 + 1115*S^2))/(90*S^2) + ((196*Pi^2*S^2)/45 + (3*(11 + 86*S^2 + 75*S^4))/(10*S^2))*HPL[{2}, -S^2] + (392*S^2*HPL[{2}, -S^2]^2)/15 - (4*(7 + 7*S^2 + 116*S^4 + 21*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (332*S^2*HPL[{4}, -S^2])/15 - (13*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 + (332*S^2*HPL[{3, 1}, -S^2])/15 - (2*(3 + 3*S^2 + 59*S^4 + 9*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{5}, -S^2]*((-1381*Pi^4*S^2)/360 + (-338 - 489*S^2 + 77*S^4)/(8*S^2) + (Pi^2*(-71 + 52*S^2 + 142*S^4))/(24*S^2) + ((49 + 49*S^2 + 435*S^4 + 107*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 138*S^2*HPL[{3, 1}, -S^2] - 354*S^2*HPL[{2, 1, 1}, -S^2] + ((-15 - 15*S^2 + 35*S^4 + 11*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((553*Pi^4*S^2)/60 + (Pi^2*(2820 + 10052*S^2 + 197*S^4))/(12*S^2) + (2813 + 22438*S^2 + 1472*S^4)/(8*S^2) - (2*(321 + 321*S^2 + 2236*S^4 + 12*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3, 2}, -S^2]*((3137*Pi^4*S^2)/180 + (Pi^2*(-17 + 164*S^2 + 507*S^4))/(12*S^2) + (-137 + 612*S^2 + 1586*S^4)/(8*S^2) + 3268*S^2*HPL[{2, 1, 1}, -S^2] + ((1 + S^2 + 232*S^4 + 128*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{4, 1}, -S^2]*((6901*Pi^4*S^2)/120 + (Pi^2*(51 + 1238*S^2 + 3263*S^4))/(24*S^2) + (441 + 5460*S^2 + 10880*S^4)/(16*S^2) + 10464*S^2*HPL[{2, 1, 1}, -S^2] + ((1 + S^2 + 423*S^4 + 211*S^6)*Zeta[3])/(S^2*(1 + S^2))) + Log[T]^5*(-103/12 - (449*Pi^4*S^2)/180 - (5*Pi^2*(30 + 37*S^2))/18 - (19*S^2*HPL[{0}, S^2]^4)/12 + (-29*Pi^2*S^2 + (-23 - 106*S^2 - 83*S^4)/S^2)*HPL[{1}, -S^2]^2 - (56*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)) - (112*S^2*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*(-(S^2*(160 + 87*S^2))/(9*(1 + S^2)) - (73*S^2*HPL[{1}, -S^2])/9) + ((-170*Pi^2*S^2)/9 + (53 + 2*S^2 - 370*S^4)/(6*S^2))*HPL[{2}, -S^2] - (79*S^2*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((-47*Pi^2*S^2)/6 + (-66 - 185*S^2)/6 + ((-11 - 11*S^2 - 95*S^4 - 33*S^6)*HPL[{1}, -S^2])/(S^2*(1 + S^2)) - 31*S^2*HPL[{1}, -S^2]^2 - (86*S^2*HPL[{2}, -S^2])/3) + ((3 + 3*S^2 + 527*S^4 + 147*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + 36*S^2*HPL[{4}, -S^2] - (2*(-21 + 23*S^4)*HPL[{2, 1}, -S^2])/S^2 + 88*S^2*HPL[{3, 1}, -S^2] - 224*S^2*HPL[{2, 1, 1}, -S^2] + (2*(73*S^2 + 23*S^4)*Zeta[3])/(1 + S^2) + HPL[{0}, S^2]*((-84 - 341*S^2)/4 + (Pi^2*(-454*S^2 - 213*S^4))/(9*(1 + S^2)) - (28*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) - (224*S^2*HPL[{1}, -S^2]^3)/3 - (2*(-1 - S^2 + 90*S^4 + 40*S^6)*HPL[{2}, -S^2])/(S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-241*Pi^2*S^2)/9 + (-23 - 106*S^2 - 83*S^4)/S^2 - 100*S^2*HPL[{2}, -S^2]) + (22*S^2*HPL[{3}, -S^2])/3 - 12*S^2*HPL[{2, 1}, -S^2] + 24*S^2*Zeta[3]) + HPL[{1}, -S^2]*(-((1 + S^2)*(221 + 1023*S^2))/(12*S^2) + (Pi^2*(-25 - 25*S^2 - 249*S^4 - 75*S^6))/(3*S^2*(1 + S^2)) - (13*(1 + 3*S^4)*HPL[{2}, -S^2])/S^2 + (380*S^2*HPL[{3}, -S^2])/3 + 100*S^2*Zeta[3])) + ((-391*Pi^4*S^2)/45 + (-414 - 295*S^2)/8 + (Pi^2*(-74 - 139*S^2))/24)*Zeta[5] + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-129 + 208*S^2 + 1956*S^4))/(6*S^2) + (-344 + 65*S^2 + 4538*S^4)/(4*S^2) + (Pi^4*(-538 - 538*S^2 + 17563*S^4 + 11500*S^6))/(180*S^2*(1 + S^2)) + 3136*S^2*HPL[{2, 2, 1}, -S^2] + 2496*S^2*HPL[{3, 1, 1}, -S^2] - 6224*S^2*HPL[{2, 1, 1, 1}, -S^2] + (-280*Pi^2*S^2 + (-55 - 224*S^2 - 518*S^4)/S^2)*Zeta[3] - 1464*S^2*Zeta[5]) + Log[T]^4*(79/6 + (Pi^2*(462 + 967*S^2))/36 + (Pi^4*(10685*S^2 + 4012*S^4))/(540*(1 + S^2)) + (281*S^2*HPL[{0}, S^2]^5)/360 + ((145*Pi^2*S^2)/3 + (5*(23 + 106*S^2 + 83*S^4))/(3*S^2))*HPL[{1}, -S^2]^3 + (70*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)) + (112*S^2*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^4*((S^2*(341 + 199*S^2))/(36*(1 + S^2)) + (71*S^2*HPL[{1}, -S^2])/18) + ((25 + 25*S^2 + 614*S^4 + 222*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + HPL[{0}, S^2]^3*((164*Pi^2*S^2)/27 + (268 + 919*S^2)/36 + ((67 + 67*S^2 + 566*S^4 + 201*S^6)*HPL[{1}, -S^2])/(9*S^2*(1 + S^2)) + (365*S^2*HPL[{1}, -S^2]^2)/18 + (349*S^2*HPL[{2}, -S^2])/18) + ((-469*Pi^2*S^2)/9 + (-55 - 284*S^2 - 576*S^4)/(6*S^2))*HPL[{3}, -S^2] - (S^2*(497 + 165*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - 74*S^2*HPL[{5}, -S^2] + ((458*Pi^2*S^2)/9 + (-463 - 1558*S^2 + 500*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + ((165 + 165*S^2 - 451*S^4 - 783*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) + (1648*S^2*HPL[{3, 2}, -S^2])/3 + (5308*S^2*HPL[{4, 1}, -S^2])/3 + (20*(-4 + 31*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (1556*S^2*HPL[{2, 2, 1}, -S^2])/3 + 376*S^2*HPL[{3, 1, 1}, -S^2] + 1120*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-155*Pi^2*S^2)/3 - (10*(9 + 25*S^2))/3)*Zeta[3] + HPL[{2}, -S^2]*((-209 - 74*S^2 + 1934*S^4)/(12*S^2) + (Pi^2*(-35 - 35*S^2 + 668*S^4 + 472*S^6))/(9*S^2*(1 + S^2)) - 288*S^2*HPL[{3}, -S^2] - (778*S^2*HPL[{2, 1}, -S^2])/3 - (764*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(221 + 1023*S^2))/(24*S^2) + (5*Pi^2*(25 + 25*S^2 + 249*S^4 + 75*S^6))/(6*S^2*(1 + S^2)) + (65*(1 + 3*S^4)*HPL[{2}, -S^2])/(2*S^2) - (950*S^2*HPL[{3}, -S^2])/3 - 250*S^2*Zeta[3]) + HPL[{0}, S^2]^2*((237 + 967*S^2)/12 + (Pi^2*(1612*S^2 + 863*S^4))/(36*(1 + S^2)) + (5*(11 + 11*S^2 + 95*S^4 + 33*S^6)*HPL[{1}, -S^2]^2)/(2*S^2*(1 + S^2)) + (155*S^2*HPL[{1}, -S^2]^3)/3 + ((-10 - 10*S^2 + 871*S^4 + 479*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((749*Pi^2*S^2)/36 + (257 + 1242*S^2 + 985*S^4)/(12*S^2) + (196*S^2*HPL[{2}, -S^2])/3) - (53*S^2*HPL[{3}, -S^2])/6 + (38*S^2*HPL[{2, 1}, -S^2])/3 - 15*S^2*Zeta[3]) + HPL[{1}, -S^2]*((6673*Pi^4*S^2)/540 + ((1 + S^2)*(159 + 896*S^2))/(4*S^2) + (Pi^2*(1 + S^2)*(301 + 1115*S^2))/(18*S^2) + ((196*Pi^2*S^2)/9 + (3*(11 + 86*S^2 + 75*S^4))/(2*S^2))*HPL[{2}, -S^2] + (392*S^2*HPL[{2}, -S^2]^2)/3 - (20*(7 + 7*S^2 + 116*S^4 + 21*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (332*S^2*HPL[{4}, -S^2])/3 - (65*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 + (332*S^2*HPL[{3, 1}, -S^2])/3 - (10*(3 + 3*S^2 + 59*S^4 + 9*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]*((2473*Pi^4*S^2)/216 + (Pi^2*(172 + 541*S^2))/9 + (345 + 1792*S^2)/8 + (140*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)) + (280*S^2*HPL[{1}, -S^2]^4)/3 + ((572*Pi^2*S^2)/9 + (-89 + 686*S^2 + 2370*S^4)/(12*S^2))*HPL[{2}, -S^2] + (767*S^2*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((1205*Pi^2*S^2)/18 + (5*(23 + 106*S^2 + 83*S^4))/(2*S^2) + 250*S^2*HPL[{2}, -S^2]) + ((27 + 27*S^2 - 133*S^4 - 65*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) + 16*S^2*HPL[{4}, -S^2] + (5*(-27 - 27*S^2 - 95*S^4 + 5*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (1576*S^2*HPL[{3, 1}, -S^2])/3 + 1060*S^2*HPL[{2, 1, 1}, -S^2] + ((-313*S^2 - 147*S^4)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((5*(1 + S^2)*(221 + 1023*S^2))/(24*S^2) + (Pi^2*(172 + 172*S^2 + 1721*S^4 + 516*S^6))/(9*S^2*(1 + S^2)) + (125*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - (34*S^2*HPL[{3}, -S^2])/3 - 500*S^2*HPL[{2, 1}, -S^2] - (166*S^2*Zeta[3])/3)) - 290*S^2*Zeta[5]) + HPL[{2}, -S^2]^2*((64 + 671*S^2 + 2169*S^4)/(16*S^2) + (Pi^2*(136 + 1340*S^2 + 3781*S^4))/(96*S^2) + (Pi^4*(110 + 110*S^2 + 11239*S^4 + 5245*S^6))/(720*S^2*(1 + S^2)) + ((-449*Pi^2*S^2)/12 + (-29 - 324*S^2 - 650*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((-5 - 5*S^2 - 517*S^4 - 189*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) - (97*S^2*HPL[{5}, -S^2])/2 + ((209*Pi^2*S^2)/6 + (-465 - 1420*S^2 + 546*S^4)/(8*S^2))*HPL[{2, 1}, -S^2] + ((171 + 171*S^2 - 385*S^4 - 713*S^6)*HPL[{3, 1}, -S^2])/(4*S^2*(1 + S^2)) + (805*S^2*HPL[{3, 2}, -S^2])/2 + (2591*S^2*HPL[{4, 1}, -S^2])/2 + ((-66 + 413*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + 378*S^2*HPL[{2, 2, 1}, -S^2] + 278*S^2*HPL[{3, 1, 1}, -S^2] + 784*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-409*Pi^2*S^2)/12 - (5*(-5 + 28*S^2 + 102*S^4))/(8*S^2))*Zeta[3] - (341*S^2*Zeta[5])/2) + HPL[{1}, -S^2]^4*(((1 + S^2)*(1195 + 7849*S^2))/(64*S^2) + (Pi^2*(1 + S^2)*(1889 + 9231*S^2))/(288*S^2) + (Pi^4*(8587 + 8587*S^2 + 79145*S^4 + 25761*S^6))/(4320*S^2*(1 + S^2)) + (49*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((-497*Pi^2*S^2)/18 - (7*(49 + 148*S^2 + 99*S^4))/(12*S^2))*HPL[{3}, -S^2] - (4*(7 + 7*S^2 + 104*S^4 + 21*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) - 36*S^2*HPL[{5}, -S^2] + ((-196*Pi^2*S^2)/9 - (3*(11 + 86*S^2 + 75*S^4))/(2*S^2))*HPL[{2, 1}, -S^2] - (4*(14 + 14*S^2 - 41*S^4 + 42*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) + (784*S^2*HPL[{3, 2}, -S^2])/3 + (2684*S^2*HPL[{4, 1}, -S^2])/3 + (65*(1 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (1568*S^2*HPL[{2, 2, 1}, -S^2])/3 + (2804*S^2*HPL[{3, 1, 1}, -S^2])/3 + ((-208*Pi^2*S^2)/9 - (2*(1 + S^2)*(22 + 65*S^2))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(75 + 1021*S^2))/(16*S^2) + (Pi^2*(251 + 251*S^2 + 1537*S^4 + 753*S^6))/(36*S^2*(1 + S^2)) - (392*S^2*HPL[{3}, -S^2])/3 - (784*S^2*HPL[{2, 1}, -S^2])/3 - (392*S^2*Zeta[3])/3) - (380*S^2*Zeta[5])/3) + HPL[{0}, S^2]^4*((-49 + 2216*S^2)/192 + (Pi^2*(354 + 4609*S^2))/1152 + (Pi^4*(4015*S^2 + 2006*S^4))/(4320*(1 + S^2)) + ((253 + 253*S^2 + 1895*S^4 + 759*S^6)*HPL[{1}, -S^2]^4)/(288*S^2*(1 + S^2)) + (71*S^2*HPL[{1}, -S^2]^5)/90 + ((-1 - S^2 + 94*S^4 + 54*S^6)*HPL[{2}, -S^2]^2)/(16*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((277*Pi^2*S^2)/216 + (36 + 241*S^2 + 205*S^4)/(36*S^2) + (241*S^2*HPL[{2}, -S^2])/72) + ((-11*Pi^2*S^2)/48 + (-2 + 24*S^2 + 19*S^4)/(32*S^2))*HPL[{3}, -S^2] + ((6 + 6*S^2 + 9*S^4 + 13*S^6)*HPL[{4}, -S^2])/(16*S^2*(1 + S^2)) - (13*S^2*HPL[{5}, -S^2])/8 + ((85*Pi^2*S^2)/144 + (-308 - 1336*S^2 + 51*S^4)/(96*S^2))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*(((1 + S^2)*(303 + 3553*S^2))/(384*S^2) + (Pi^2*(553 + 553*S^2 + 3875*S^4 + 1659*S^6))/(576*S^2*(1 + S^2)) + ((57 + 57*S^2 + 412*S^4 + 171*S^6)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)) - (S^2*HPL[{3}, -S^2])/8 - (241*S^2*HPL[{2, 1}, -S^2])/24) - (3*S^2*(131 + 79*S^2)*HPL[{3, 1}, -S^2])/(16*(1 + S^2)) + (13*S^2*HPL[{4, 1}, -S^2])/8 + ((-6 - 6*S^2 + 614*S^4 + 373*S^6)*HPL[{2, 1, 1}, -S^2])/(12*S^2*(1 + S^2)) - (S^2*HPL[{2, 2, 1}, -S^2])/3 - (11*S^2*HPL[{3, 1, 1}, -S^2])/4 + (25*S^2*HPL[{2, 1, 1, 1}, -S^2])/6 + ((97*Pi^2*S^2)/144 + (10 + 113*S^2)/32)*Zeta[3] + HPL[{2}, -S^2]*((-96 + 320*S^2 + 1665*S^4)/(192*S^2) + (Pi^2*(-3 - 3*S^2 + 637*S^4 + 419*S^6))/(144*S^2*(1 + S^2)) + (S^2*HPL[{2, 1}, -S^2])/6 + (5*S^2*Zeta[3])/8) + HPL[{1}, -S^2]*((2009*Pi^4*S^2)/4320 + (Pi^2*(189 + 2134*S^2 + 1945*S^4))/(576*S^2) + (-13 + 1975*S^2 + 1988*S^4)/(192*S^2) + ((109*Pi^2*S^2)/72 + (31 + 224*S^2 + 193*S^4)/(24*S^2))*HPL[{2}, -S^2] + (5*S^2*HPL[{2}, -S^2]^2)/2 + ((1 + S^2 + 2*S^4 + 3*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) - (S^2*HPL[{4}, -S^2])/4 + ((-57 - 57*S^2 - 412*S^4 - 171*S^6)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)) - (39*S^2*HPL[{3, 1}, -S^2])/4 + (241*S^2*HPL[{2, 1, 1}, -S^2])/12 + (5*(1 + 3*S^4)*Zeta[3])/(16*S^2)) + (65*S^2*Zeta[5])/24) + HPL[{4}, -S^2]*((Pi^2*(-87 - 310*S^2 - 182*S^4))/(48*S^2) - (21*(41 + 112*S^2 + 70*S^4))/(32*S^2) + (Pi^4*(85 + 85*S^2 - 936*S^4 - 96*S^6))/(240*S^2*(1 + S^2)) + 57*S^2*HPL[{5}, -S^2] + ((-15*Pi^2*S^2)/2 + (299 + 698*S^2 + 149*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + ((-24 - 24*S^2 + 797*S^4 + 313*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) - 109*S^2*HPL[{3, 2}, -S^2] - 266*S^2*HPL[{4, 1}, -S^2] + ((7 + 7*S^2 - 784*S^4 - 332*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 118*S^2*HPL[{2, 2, 1}, -S^2] - 182*S^2*HPL[{3, 1, 1}, -S^2] - 192*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-19*Pi^2*S^2)/6 + (-15 - 2*S^2 + 23*S^4)/(4*S^2))*Zeta[3] + 5*S^2*Zeta[5]) + HPL[{3, 1}, -S^2]*((2397 + 2728*S^2 - 16494*S^4)/(32*S^2) + (Pi^2*(197 - 33*S^2 - 1842*S^4))/(12*S^2) + (Pi^4*(1301 + 1301*S^2 - 30866*S^4 - 21314*S^6))/(720*S^2*(1 + S^2)) - 1642*S^2*HPL[{3, 2}, -S^2] - 5214*S^2*HPL[{4, 1}, -S^2] - (16*(18 + 18*S^2 + 291*S^4 + 95*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 1912*S^2*HPL[{2, 2, 1}, -S^2] + 7384*S^2*HPL[{3, 1, 1}, -S^2] + 3776*S^2*HPL[{2, 1, 1, 1}, -S^2] + (141*Pi^2*S^2 + (60 + 232*S^2 + 525*S^4)/(2*S^2))*Zeta[3] + 718*S^2*Zeta[5]) + Zeta[3]*((-1847*Pi^6*S^2)/2268 + (Pi^4*(-1090 - 1319*S^2))/1440 + (Pi^2*(-586 - 597*S^2))/48 - (33*(71 + 15*S^2))/32 - (2*(15*S^2 + 46*S^4)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^3*((52285*Pi^6*S^2)/27216 + (Pi^2*(1 + S^2)*(1579 + 9787*S^2))/(144*S^2) + (Pi^4*(1 + S^2)*(6553 + 25601*S^2))/(2160*S^2) + ((1 + S^2)*(3697 + 27105*S^2))/(96*S^2) + ((607*Pi^2*S^2)/18 + (333 + 1492*S^2 + 1159*S^4)/(12*S^2))*HPL[{2}, -S^2]^2 + (74*S^2*HPL[{3}, -S^2]^2)/3 + ((-170*Pi^2*S^2)/9 + (-377 - 860*S^2 - 483*S^4)/(12*S^2))*HPL[{4}, -S^2] - (2*(1 + S^2 + 219*S^4 + 3*S^6)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)) - (89*S^2*HPL[{6}, -S^2])/3 - (1568*S^2*HPL[{2, 1}, -S^2]^2)/3 + ((-220*Pi^2*S^2)/9 - (2*(-5 + 228*S^2 + 233*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + (2*(113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)) + (2*(395 + 395*S^2 + 6553*S^4 + 1185*S^6)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)) + 78*S^2*HPL[{4, 2}, -S^2] + (1352*S^2*HPL[{5, 1}, -S^2])/3 + ((784*Pi^2*S^2)/9 + (6*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (784*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)) + (16*(112 + 112*S^2 + 1037*S^4 + 336*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) - (1328*S^2*HPL[{4, 1, 1}, -S^2])/3 - (260*(1 + 3*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (1328*S^2*HPL[{3, 1, 1, 1}, -S^2])/3 + (-((1 + S^2)*(107 + 333*S^2))/(4*S^2) + (Pi^2*(-49 - 49*S^2 - 979*S^4 - 147*S^6))/(9*S^2*(1 + S^2)))*Zeta[3] + (40*S^2*Zeta[3]^2)/3 + HPL[{3}, -S^2]*(-((1 + S^2)*(107 + 201*S^2))/(2*S^2) + (Pi^2*(-137 - 137*S^2 - 2399*S^4 - 411*S^6))/(18*S^2*(1 + S^2)) + (1568*S^2*HPL[{2, 1}, -S^2])/3 - (100*S^2*Zeta[3])/3) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(75 + 1021*S^2))/(4*S^2) + (Pi^2*(-251 - 251*S^2 - 1537*S^4 - 753*S^6))/(9*S^2*(1 + S^2)) + (1568*S^2*Zeta[3])/3) + HPL[{2}, -S^2]*((2021*Pi^4*S^2)/360 + (7*Pi^2*(1 + S^2)*(23 + 117*S^2))/(18*S^2) + ((1 + S^2)*(101 + 3541*S^2))/(24*S^2) + ((-113 - 113*S^2 - 1907*S^4 - 339*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (226*S^2*HPL[{4}, -S^2])/3 - (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) - (1568*S^2*HPL[{3, 1}, -S^2])/3 + (3136*S^2*HPL[{2, 1, 1}, -S^2])/3 - (112*(1 + S^2 + 17*S^4 + 3*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + ((-51 - 51*S^2 - 1673*S^4 - 153*S^6)*Zeta[5])/(3*S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((68629*Pi^6*S^2)/45360 + (Pi^2*(-2131 - 15714*S^2 + 408*S^4))/(96*S^2) + (-225 - 18247*S^2 + 495*S^4)/(32*S^2) + (Pi^4*(-11489 - 40638*S^2 + 3021*S^4))/(1440*S^2) + ((488*Pi^2*S^2)/3 + (358 + 1652*S^2 + 629*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-527 - 527*S^2 - 3553*S^4 - 137*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((-856 - 856*S^2 - 5189*S^4 - 49*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - 39*S^2*HPL[{4, 2}, -S^2] + 2*S^2*HPL[{5, 1}, -S^2] + ((812*Pi^2*S^2)/3 + (473 + 1824*S^2 + 466*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(-66 + 413*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (8*(-30 - 30*S^2 + 995*S^4 + 603*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 156*S^2*HPL[{3, 1, 2}, -S^2] - 1356*S^2*HPL[{3, 2, 1}, -S^2] - 4728*S^2*HPL[{4, 1, 1}, -S^2] - (16*(25 + 25*S^2 + 614*S^4 + 222*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 3776*S^2*HPL[{3, 1, 1, 1}, -S^2] + 6224*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((2*(40 + 141*S^2 + 11*S^4))/S^2 + (Pi^2*(107 + 107*S^2 + 889*S^4 + 27*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] + 30*S^2*Zeta[3]^2 + ((45 + 45*S^2 + 723*S^4 + S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((-2323*Pi^6*S^2)/1890 + (-2717 - 4046*S^2 - 5780*S^4)/(64*S^2) + (Pi^2*(-515 - 648*S^2 - 1350*S^4))/(96*S^2) + (Pi^4*(-141 - 179*S^2 - 676*S^4))/(360*S^2) + ((13*Pi^2*S^2)/2 + (5 + 38*S^2 - 77*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((-28 - 28*S^2 - 31*S^4 - 87*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) - 69*S^2*HPL[{6}, -S^2] + 856*S^2*HPL[{2, 1}, -S^2]^2 + ((446*Pi^2*S^2)/3 + (-59 + 94*S^2 + 582*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-5 - 5*S^2 - 569*S^4 - 225*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((44 + 44*S^2 - 121*S^4 - 13*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + 42*S^2*HPL[{4, 2}, -S^2] + 20*S^2*HPL[{5, 1}, -S^2] + (-302*Pi^2*S^2 + (107 - 232*S^2 - 1175*S^4)/(2*S^2))*HPL[{2, 1, 1}, -S^2] + ((-283 - 283*S^2 - 1991*S^4 - 127*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-853 - 853*S^2 - 5489*S^4 - 193*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 4*S^2*HPL[{3, 1, 2}, -S^2] - 1692*S^2*HPL[{3, 2, 1}, -S^2] + 55084*S^2*HPL[{4, 1, 1}, -S^2] - (4*(-138 - 138*S^2 - 751*S^4 + 33*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 3424*S^2*HPL[{3, 1, 1, 1}, -S^2] - 6912*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-3*(-7 + 18*S^2 + 12*S^4))/(4*S^2) + (Pi^2*(-5 - 5*S^2 - 156*S^4 - 52*S^6))/(12*S^2*(1 + S^2)))*Zeta[3] - 16*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-3*(-85 - 202*S^2 + 3*S^4))/(2*S^2) + (Pi^2*(289 + 289*S^2 + 1611*S^4 - 41*S^6))/(12*S^2*(1 + S^2)) - 32*S^2*Zeta[3]) + ((17 + 17*S^2 - 42*S^4 + 22*S^6)*Zeta[5])/(2*S^2*(1 + S^2))) + HPL[{0}, S^2]^3*((52021*Pi^6*S^2)/181440 + (Pi^2*(332 + 4313*S^2))/288 + (521 + 5455*S^2)/96 + (Pi^4*(3857 + 13142*S^2))/4320 + ((67 + 67*S^2 + 566*S^4 + 201*S^6)*HPL[{1}, -S^2]^5)/(45*S^2*(1 + S^2)) + (73*S^2*HPL[{1}, -S^2]^6)/54 + ((541*Pi^2*S^2)/144 + (3 + 113*S^2 + 390*S^4)/(24*S^2))*HPL[{2}, -S^2]^2 + (13*S^2*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((53*Pi^2*S^2)/18 + (335 + 2048*S^2 + 1713*S^4)/(144*S^2) + (55*S^2*HPL[{2}, -S^2])/6) - (5*S^2*HPL[{3}, -S^2]^2)/12 + ((29*Pi^2*S^2)/18 + (1 + 3*S^2 + 16*S^4)/(6*S^2))*HPL[{4}, -S^2] + ((-10 - 10*S^2 + 25*S^4 + 2*S^6)*HPL[{5}, -S^2])/(6*S^2*(1 + S^2)) + (21*S^2*HPL[{6}, -S^2])/2 - (325*S^2*HPL[{2, 1}, -S^2]^2)/6 + ((-607*Pi^2*S^2)/36 + (25 - 246*S^2 - 816*S^4)/(12*S^2))*HPL[{3, 1}, -S^2] + ((-8 - 8*S^2 + 3*S^4 - 25*S^6)*HPL[{3, 2}, -S^2])/(12*S^2*(1 + S^2)) + ((-13 - 13*S^2 - 28*S^4 - 36*S^6)*HPL[{4, 1}, -S^2])/(6*S^2*(1 + S^2)) - (S^2*HPL[{4, 2}, -S^2])/3 - (38*S^2*HPL[{5, 1}, -S^2])/3 + ((605*Pi^2*S^2)/18 + (-36 + 496*S^2 + 1673*S^4)/(12*S^2))*HPL[{2, 1, 1}, -S^2] + ((118 + 118*S^2 + 301*S^4 - 17*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)) + ((728 + 728*S^2 + 1835*S^4 - 97*S^6)*HPL[{3, 1, 1}, -S^2])/(6*S^2*(1 + S^2)) + (S^2*HPL[{3, 1, 2}, -S^2])/3 + (313*S^2*HPL[{3, 2, 1}, -S^2])/3 + (977*S^2*HPL[{4, 1, 1}, -S^2])/3 + ((-258 - 258*S^2 - 611*S^4 + 49*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) - (692*S^2*HPL[{3, 1, 1, 1}, -S^2])/3 + (1396*S^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((-7 + 96*S^2)/24 + (Pi^2*(349*S^2 + 371*S^4))/(72*(1 + S^2)))*Zeta[3] - (S^2*Zeta[3]^2)/2 + HPL[{3}, -S^2]*((16 + 39*S^2 + 48*S^4)/(12*S^2) + (Pi^2*(10 + 10*S^2 + 37*S^4 - 5*S^6))/(72*S^2*(1 + S^2)) + (5*S^2*HPL[{2, 1}, -S^2])/3 - 2*S^2*Zeta[3]) + HPL[{1}, -S^2]^3*(((1 + S^2)*(411 + 3641*S^2))/(144*S^2) + (Pi^2*(523 + 523*S^2 + 4113*S^4 + 1569*S^6))/(216*S^2*(1 + S^2)) + (2*(31 + 31*S^2 + 258*S^4 + 93*S^6)*HPL[{2}, -S^2])/(9*S^2*(1 + S^2)) + (2*S^2*HPL[{3}, -S^2])/3 - (110*S^2*HPL[{2, 1}, -S^2])/3 - (11*S^2*Zeta[3])/9) + HPL[{2, 1}, -S^2]*((-182 - 1652*S^2 - 89*S^4)/(24*S^2) + (Pi^2*(-468 - 468*S^2 - 953*S^4 + 169*S^6))/(72*S^2*(1 + S^2)) + (S^2*Zeta[3])/3) + HPL[{2}, -S^2]*((959*Pi^4*S^2)/540 + (Pi^2*(-18 + 458*S^2 + 1699*S^4))/(144*S^2) + (88 + 346*S^2 + 1849*S^4)/(48*S^2) + ((2 + 2*S^2 + 7*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) + S^2*HPL[{4}, -S^2] + ((-118 - 118*S^2 - 301*S^4 + 17*S^6)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)) - (161*S^2*HPL[{3, 1}, -S^2])/3 + (325*S^2*HPL[{2, 1, 1}, -S^2])/3 + ((4 + 4*S^2 - 3*S^4 + 3*S^6)*Zeta[3])/(4*S^2*(1 + S^2))) + HPL[{1}, -S^2]^2*((3997*Pi^4*S^2)/2160 + ((1 + S^2)*(141 + 1990*S^2))/(48*S^2) + (Pi^2*(1 + S^2)*(535 + 3473*S^2))/(288*S^2) + ((187*Pi^2*S^2)/24 + (71 + 488*S^2 + 417*S^4)/(12*S^2))*HPL[{2}, -S^2] + (53*S^2*HPL[{2}, -S^2]^2)/4 + ((1 + S^2 + 7*S^4 + 3*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + (17*S^2*HPL[{4}, -S^2])/6 - (2*(31 + 31*S^2 + 258*S^4 + 93*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) - 55*S^2*HPL[{3, 1}, -S^2] + 110*S^2*HPL[{2, 1, 1}, -S^2] + ((3 + 3*S^2 - 35*S^4 + 9*S^6)*Zeta[3])/(12*S^2*(1 + S^2))) + ((115*S^2 + 131*S^4)*Zeta[5])/(6*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(164 + 1879*S^2))/(144*S^2) + ((1 + S^2)*(361 + 4575*S^2))/(96*S^2) + (7*Pi^4*(551 + 551*S^2 + 3937*S^4 + 1653*S^6))/(4320*S^2*(1 + S^2)) + ((39 + 39*S^2 + 329*S^4 + 117*S^6)*HPL[{2}, -S^2]^2)/(8*S^2*(1 + S^2)) + ((7*Pi^2*S^2)/12 + (3*(-1 + 4*S^2 + 5*S^4))/(4*S^2))*HPL[{3}, -S^2] + ((3 + 3*S^2 + 43*S^4 + 9*S^6)*HPL[{4}, -S^2])/(6*S^2*(1 + S^2)) + (23*S^2*HPL[{5}, -S^2])/6 + ((-187*Pi^2*S^2)/12 + (-71 - 488*S^2 - 417*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + ((-41 - 41*S^2 - 343*S^4 - 123*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) + (7*S^2*HPL[{3, 2}, -S^2])/3 + (4*S^2*HPL[{4, 1}, -S^2])/3 + (4*(31 + 31*S^2 + 258*S^4 + 93*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) + 106*S^2*HPL[{2, 2, 1}, -S^2] + 322*S^2*HPL[{3, 1, 1}, -S^2] - 220*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-11*Pi^2*S^2)/36 + ((1 + S^2)*(-31 + 47*S^2))/(24*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(91 + 915*S^2))/(24*S^2) + (Pi^2*(229 + 229*S^2 + 1809*S^4 + 687*S^6))/(72*S^2*(1 + S^2)) - (7*S^2*HPL[{3}, -S^2])/6 - 53*S^2*HPL[{2, 1}, -S^2] - (3*S^2*Zeta[3])/2) - (8*S^2*Zeta[5])/3)) + Log[T]^3*(-835/48 - (6682*Pi^6*S^2)/2835 + (Pi^4*(-17174 - 32027*S^2))/2160 + (Pi^2*(-1239 - 4117*S^2))/72 - (19*S^2*HPL[{0}, S^2]^6)/72 + ((-145*Pi^2*S^2)/3 - (5*(23 + 106*S^2 + 83*S^4))/(3*S^2))*HPL[{1}, -S^2]^4 - (56*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)) - (224*S^2*HPL[{1}, -S^2]^6)/9 + HPL[{0}, S^2]^5*(-(S^2*(706 + 435*S^2))/(180*(1 + S^2)) - (271*S^2*HPL[{1}, -S^2])/180) + ((-404*Pi^2*S^2)/9 + (-193 - 1160*S^2 - 1852*S^4)/(12*S^2))*HPL[{2}, -S^2]^2 - (392*S^2*HPL[{2}, -S^2]^3)/9 + HPL[{0}, S^2]^4*((-95*Pi^2*S^2)/36 + (-506 - 1737*S^2)/144 + ((-253 - 253*S^2 - 1895*S^4 - 759*S^6)*HPL[{1}, -S^2])/(72*S^2*(1 + S^2)) - (71*S^2*HPL[{1}, -S^2]^2)/9 - (133*S^2*HPL[{2}, -S^2])/18) - (148*S^2*HPL[{3}, -S^2]^2)/3 + ((260*Pi^2*S^2)/9 + (6 + 236*S^2 + 463*S^4)/(6*S^2))*HPL[{4}, -S^2] + ((3 + 3*S^2 + 449*S^4 + 17*S^6)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)) + 12*S^2*HPL[{6}, -S^2] + (1580*S^2*HPL[{2, 1}, -S^2]^2)/3 + ((1504*Pi^2*S^2)/9 + (-383 - 344*S^2 + 1618*S^4)/(3*S^2))*HPL[{3, 1}, -S^2] + ((56 + 56*S^2 - 4511*S^4 - 1375*S^6)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)) - (4*(-19 - 19*S^2 + 3803*S^4 + 1119*S^6)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)) - (572*S^2*HPL[{4, 2}, -S^2])/3 - (2584*S^2*HPL[{5, 1}, -S^2])/3 + ((-3400*Pi^2*S^2)/9 - (10*(-53 - 2*S^2 + 370*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (16*(73 + 73*S^2 + 464*S^4 + 72*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)) - (4*(861 + 861*S^2 + 2933*S^4 + 129*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) + (320*S^2*HPL[{3, 1, 2}, -S^2])/3 - (2816*S^2*HPL[{3, 2, 1}, -S^2])/3 - 2416*S^2*HPL[{4, 1, 1}, -S^2] - (40*(-21 + 23*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + 1760*S^2*HPL[{3, 1, 1, 1}, -S^2] - 4480*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((5*(80 + 161*S^2))/6 + (Pi^2*(1203*S^2 + 371*S^4))/(9*(1 + S^2)))*Zeta[3] + 4*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((643 + 3436*S^2 - 805*S^4)/(6*S^2) - (2*Pi^2*(-321 - 321*S^2 - 201*S^4 + 191*S^6))/(9*S^2*(1 + S^2)) - (80*S^2*Zeta[3])/3) + HPL[{0}, S^2]^3*((-630 - 3847*S^2)/72 + (Pi^2*(-251*S^2 - 145*S^4))/(9*(1 + S^2)) - (2*(67 + 67*S^2 + 566*S^4 + 201*S^6)*HPL[{1}, -S^2]^2)/(9*S^2*(1 + S^2)) - (730*S^2*HPL[{1}, -S^2]^3)/27 + ((10 + 10*S^2 - 1453*S^4 - 793*S^6)*HPL[{2}, -S^2])/(18*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-106*Pi^2*S^2)/9 + (-335 - 2048*S^2 - 1713*S^4)/(36*S^2) - (110*S^2*HPL[{2}, -S^2])/3) + S^2*HPL[{3}, -S^2] - (38*S^2*HPL[{2, 1}, -S^2])/9 + (14*S^2*Zeta[3])/9) + HPL[{3}, -S^2]*((307 + 1012*S^2 + 2073*S^4)/(12*S^2) + (Pi^2*(-6 - 6*S^2 + 2737*S^4 + 749*S^6))/(18*S^2*(1 + S^2)) + (320*S^2*HPL[{2, 1}, -S^2])/3 + 48*S^2*Zeta[3]) + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(221 + 1023*S^2))/(18*S^2) - (10*Pi^2*(25 + 25*S^2 + 249*S^4 + 75*S^6))/(9*S^2*(1 + S^2)) - (130*(1 + 3*S^4)*HPL[{2}, -S^2])/(3*S^2) + (3800*S^2*HPL[{3}, -S^2])/9 + (1000*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-6673*Pi^4*S^2)/270 - ((1 + S^2)*(159 + 896*S^2))/(2*S^2) - (Pi^2*(1 + S^2)*(301 + 1115*S^2))/(9*S^2) + ((-392*Pi^2*S^2)/9 - (3*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2}, -S^2] - (784*S^2*HPL[{2}, -S^2]^2)/3 + (40*(7 + 7*S^2 + 116*S^4 + 21*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + (664*S^2*HPL[{4}, -S^2])/3 + (130*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 - (664*S^2*HPL[{3, 1}, -S^2])/3 + (20*(3 + 3*S^2 + 59*S^4 + 9*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]*((-325*Pi^4*S^2)/18 + (713 + 186*S^2 - 8234*S^4)/(24*S^2) + (Pi^2*(337 - 580*S^2 - 3758*S^4))/(36*S^2) + (2*(-25 - 25*S^2 + 1156*S^4 + 372*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + (548*S^2*HPL[{4}, -S^2])/3 + (8*(73 + 73*S^2 + 464*S^4 + 72*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) + 416*S^2*HPL[{3, 1}, -S^2] - (3160*S^2*HPL[{2, 1, 1}, -S^2])/3 + (8*(3 + 3*S^2 + 273*S^4 + 77*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + HPL[{0}, S^2]^2*((-2731*Pi^4*S^2)/360 + (-724 - 4117*S^2)/24 + (Pi^2*(-1166 - 3587*S^2))/72 - (10*(11 + 11*S^2 + 95*S^4 + 33*S^6)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)) - (155*S^2*HPL[{1}, -S^2]^4)/3 + ((-116*Pi^2*S^2)/3 + (36 - 295*S^2 - 954*S^4)/(6*S^2))*HPL[{2}, -S^2] - (413*S^2*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((-749*Pi^2*S^2)/18 + (-257 - 1242*S^2 - 985*S^4)/(6*S^2) - (392*S^2*HPL[{2}, -S^2])/3) + ((-21 - 21*S^2 + 102*S^4 + 14*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) - (10*S^2*HPL[{4}, -S^2])/3 + ((327 + 327*S^2 + 747*S^4 - 37*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) + (844*S^2*HPL[{3, 1}, -S^2])/3 - (1720*S^2*HPL[{2, 1, 1}, -S^2])/3 + (2*(54*S^2 + 13*S^4)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((-49*(1 + S^2)*(4 + 21*S^2))/(6*S^2) + (Pi^2*(-583 - 583*S^2 - 4745*S^4 - 1749*S^6))/(36*S^2*(1 + S^2)) + ((-307 - 307*S^2 - 2489*S^4 - 921*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) + (44*S^2*HPL[{3}, -S^2])/3 + (784*S^2*HPL[{2, 1}, -S^2])/3 + (82*S^2*Zeta[3])/3)) + (4*(511*S^2 + 131*S^4)*Zeta[5])/(3*(1 + S^2)) + HPL[{0}, S^2]*((-1252 - 7849*S^2)/16 + (Pi^2*(-945 - 4481*S^2))/36 + (Pi^4*(-8198*S^2 - 4137*S^4))/(180*(1 + S^2)) - (140*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)) - (224*S^2*HPL[{1}, -S^2]^5)/3 - (2*(3 + 3*S^2 + 684*S^4 + 292*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((-2410*Pi^2*S^2)/27 - (10*(23 + 106*S^2 + 83*S^4))/(3*S^2) - (1000*S^2*HPL[{2}, -S^2])/3) + ((64*Pi^2*S^2)/9 + (-35 - 60*S^2 - 29*S^4)/(6*S^2))*HPL[{3}, -S^2] + ((-3 - 3*S^2 - 149*S^4 - 57*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) - (22*S^2*HPL[{5}, -S^2])/3 + ((-128*Pi^2*S^2)/9 + (639 + 2254*S^2 + 20*S^4)/(3*S^2))*HPL[{2, 1}, -S^2] + (2*(-35 - 35*S^2 + 2673*S^4 + 1173*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) - (236*S^2*HPL[{3, 2}, -S^2])/3 - (680*S^2*HPL[{4, 1}, -S^2])/3 - (40*(-1 - S^2 + 90*S^4 + 40*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (136*S^2*HPL[{2, 2, 1}, -S^2])/3 + (32*S^2*HPL[{3, 1, 1}, -S^2])/3 - 240*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((194*Pi^2*S^2)/9 + (8*(10 + 29*S^2))/3)*Zeta[3] + HPL[{2}, -S^2]*((97 - 1172*S^2 - 4867*S^4)/(12*S^2) + (Pi^2*(40 + 40*S^2 - 4153*S^4 - 1993*S^6))/(18*S^2*(1 + S^2)) + (112*S^2*HPL[{3}, -S^2])/3 + (68*S^2*HPL[{2, 1}, -S^2])/3 + (328*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(221 + 1023*S^2))/(12*S^2) - (2*Pi^2*(172 + 172*S^2 + 1721*S^4 + 516*S^6))/(9*S^2*(1 + S^2)) - (125*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(S^2*(1 + S^2)) + (68*S^2*HPL[{3}, -S^2])/3 + 1000*S^2*HPL[{2, 1}, -S^2] + (332*S^2*Zeta[3])/3) + HPL[{1}, -S^2]*((-4061*Pi^4*S^2)/180 - ((1 + S^2)*(159 + 896*S^2))/(2*S^2) - (Pi^2*(1 + S^2)*(1025 + 4203*S^2))/(36*S^2) + (-120*Pi^2*S^2 - (5*(55 + 294*S^2 + 239*S^4))/(3*S^2))*HPL[{2}, -S^2] - (784*S^2*HPL[{2}, -S^2]^2)/3 + (4*(5 + 5*S^2 + 49*S^4 + 15*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (92*S^2*HPL[{4}, -S^2])/3 + (250*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 1000*S^2*HPL[{3, 1}, -S^2] - 2000*S^2*HPL[{2, 1, 1}, -S^2] + (8*(10 + 10*S^2 + 113*S^4 + 30*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + (260*S^2*Zeta[5])/3) + HPL[{1}, -S^2]*(-((1 + S^2)*(1195 + 7849*S^2))/(16*S^2) - (Pi^2*(1 + S^2)*(1889 + 9231*S^2))/(72*S^2) + (Pi^4*(-8587 - 8587*S^2 - 79145*S^4 - 25761*S^6))/(1080*S^2*(1 + S^2)) - (196*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((994*Pi^2*S^2)/9 + (7*(49 + 148*S^2 + 99*S^4))/(3*S^2))*HPL[{3}, -S^2] + (16*(7 + 7*S^2 + 104*S^4 + 21*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) + 144*S^2*HPL[{5}, -S^2] + ((784*Pi^2*S^2)/9 + (6*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1}, -S^2] + (16*(14 + 14*S^2 - 41*S^4 + 42*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) - (3136*S^2*HPL[{3, 2}, -S^2])/3 - (10736*S^2*HPL[{4, 1}, -S^2])/3 - (260*(1 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (6272*S^2*HPL[{2, 2, 1}, -S^2])/3 - (11216*S^2*HPL[{3, 1, 1}, -S^2])/3 + ((832*Pi^2*S^2)/9 + (8*(1 + S^2)*(22 + 65*S^2))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(75 + 1021*S^2))/(4*S^2) + (Pi^2*(-251 - 251*S^2 - 1537*S^4 - 753*S^6))/(9*S^2*(1 + S^2)) + (1568*S^2*HPL[{3}, -S^2])/3 + (3136*S^2*HPL[{2, 1}, -S^2])/3 + (1568*S^2*Zeta[3])/3) + (1520*S^2*Zeta[5])/3)) + HPL[{0}, S^2]^2*((5*(-3 + 1216*S^2))/32 + (5*Pi^2*(95 + 1794*S^2))/192 + (Pi^4*(365 + 2648*S^2))/288 + (Pi^6*(402541*S^2 + 207126*S^4))/(181440*(1 + S^2)) + ((11 + 11*S^2 + 95*S^4 + 33*S^6)*HPL[{1}, -S^2]^6)/(6*S^2*(1 + S^2)) + (31*S^2*HPL[{1}, -S^2]^7)/21 + ((-10 - 10*S^2 + 819*S^4 + 435*S^6)*HPL[{2}, -S^2]^3)/(24*S^2*(1 + S^2)) + HPL[{1}, -S^2]^5*((749*Pi^2*S^2)/180 + (257 + 1242*S^2 + 985*S^4)/(60*S^2) + (196*S^2*HPL[{2}, -S^2])/15) - ((-1 + 3*S^2)*(1 + 3*S^2)*HPL[{3}, -S^2]^2)/(4*S^2) + ((-115*Pi^2*S^2)/24 + (-11 + 52*S^2 + 73*S^4)/(8*S^2))*HPL[{5}, -S^2] + ((35 + 35*S^2 - 38*S^4 + 7*S^6)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)) - (93*S^2*HPL[{7}, -S^2])/2 + ((4 + 4*S^2 - 881*S^4 - 451*S^6)*HPL[{2, 1}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((43*Pi^2*S^2)/12 - (3*(-7 - 12*S^2 + 51*S^4))/(16*S^2))*HPL[{3, 2}, -S^2] + ((61*Pi^2*S^2)/4 + (1 - 82*S^2 - 282*S^4)/(8*S^2))*HPL[{4, 1}, -S^2] - (3*(-1 - S^2 + 8*S^4 + 4*S^6)*HPL[{4, 2}, -S^2])/(8*S^2*(1 + S^2)) + 5*S^2*HPL[{4, 3}, -S^2] + ((-5 - 5*S^2 - 17*S^4 - 25*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) + (57*S^2*HPL[{5, 2}, -S^2])/4 + (129*S^2*HPL[{6, 1}, -S^2])/2 + ((13*Pi^2*S^2)/6 + (249 + 842*S^2 - 22*S^4)/(2*S^2))*HPL[{2, 2, 1}, -S^2] + ((-35*Pi^2*S^2)/6 + (1511 + 5148*S^2 - 49*S^4)/(4*S^2))*HPL[{3, 1, 1}, -S^2] + (3*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/(4*S^2) + ((-37 - 37*S^2 + 3279*S^4 + 1743*S^6)*HPL[{3, 2, 1}, -S^2])/(4*S^2*(1 + S^2)) - (85*S^2*HPL[{3, 2, 2}, -S^2])/2 - 122*S^2*HPL[{3, 3, 1}, -S^2] + ((-57 - 57*S^2 + 4956*S^4 + 2668*S^6)*HPL[{4, 1, 1}, -S^2])/(2*S^2*(1 + S^2)) - (247*S^2*HPL[{4, 1, 2}, -S^2])/2 - (715*S^2*HPL[{4, 2, 1}, -S^2])/2 - 739*S^2*HPL[{5, 1, 1}, -S^2] + (21*Pi^2*S^2 + (-259 - 891*S^2 - 9*S^4)/S^2)*HPL[{2, 1, 1, 1}, -S^2] + 52*S^2*HPL[{2, 2, 2, 1}, -S^2] + ((23 + 23*S^2 - 1706*S^4 - 934*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 70*S^2*HPL[{3, 1, 1, 2}, -S^2] - 70*S^2*HPL[{3, 1, 2, 1}, -S^2] - 226*S^2*HPL[{3, 2, 1, 1}, -S^2] - 648*S^2*HPL[{4, 1, 1, 1}, -S^2] + (4*(-10 - 10*S^2 + 871*S^4 + 479*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 68*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] - 204*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 552*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] + 304*S^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((373*Pi^4*S^2)/720 + (-167 - 21*S^2)/16 + (Pi^2*(14 + 313*S^2))/48)*Zeta[3] - (3*(-S^2 + 2*S^4)*Zeta[3]^2)/(2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-49 + 490*S^2 + 1978*S^4)/(4*S^2) + (Pi^2*(-16 - 16*S^2 + 1485*S^4 + 852*S^6))/(6*S^2*(1 + S^2)) - 76*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((-24 + 406*S^2 + 1889*S^4)/(32*S^2) + (5*Pi^2*(-2 - 2*S^2 + 289*S^4 + 155*S^6))/(48*S^2*(1 + S^2)) - (21*S^2*HPL[{3}, -S^2])/4 + (13*S^2*HPL[{2, 1}, -S^2])/2 - (37*S^2*Zeta[3])/4) + HPL[{1}, -S^2]^4*((49*(1 + S^2)*(4 + 21*S^2))/(24*S^2) + (Pi^2*(583 + 583*S^2 + 4745*S^4 + 1749*S^6))/(144*S^2*(1 + S^2)) + ((307 + 307*S^2 + 2489*S^4 + 921*S^6)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)) - (11*S^2*HPL[{3}, -S^2])/3 - (196*S^2*HPL[{2, 1}, -S^2])/3 - (41*S^2*Zeta[3])/6) + HPL[{4}, -S^2]*((-72 + 33*S^2 + 196*S^4)/(16*S^2) + (Pi^2*(39 + 39*S^2 + 96*S^4 + 136*S^6))/(48*S^2*(1 + S^2)) + (3*S^2*HPL[{2, 1}, -S^2])/2 + 6*S^2*Zeta[3]) + HPL[{3, 1}, -S^2]*((131 - 948*S^2 - 3923*S^4)/(16*S^2) + (Pi^2*(23 + 23*S^2 - 2885*S^4 - 1645*S^6))/(24*S^2*(1 + S^2)) + 37*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*((67*Pi^4*S^2)/45 + (-304 - 2061*S^2 - 186*S^4)/(8*S^2) + (Pi^2*(-826 - 3118*S^2 + 33*S^4))/(48*S^2) + 16*S^2*HPL[{3, 1}, -S^2] + 34*S^2*HPL[{2, 1, 1}, -S^2] + ((7 + 7*S^2 + 77*S^4 - S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{3}, -S^2]*((-133*Pi^4*S^2)/180 + (Pi^2*(5 + 240*S^2 + 197*S^4))/(96*S^2) + (-156 + 310*S^2 + 491*S^4)/(32*S^2) - 2*S^2*HPL[{4}, -S^2] + ((13 + 13*S^2 + 109*S^4 + 25*S^6)*HPL[{2, 1}, -S^2])/(4*S^2*(1 + S^2)) + 18*S^2*HPL[{3, 1}, -S^2] - 42*S^2*HPL[{2, 1, 1}, -S^2] + ((-4 - 4*S^2 - S^4 + S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{1}, -S^2]^3*((8449*Pi^4*S^2)/2160 + (Pi^2*(1 + S^2)*(401 + 1805*S^2))/(72*S^2) + ((1 + S^2)*(625 + 4411*S^2))/(48*S^2) + ((211*Pi^2*S^2)/12 + (223 + 1186*S^2 + 963*S^4)/(12*S^2))*HPL[{2}, -S^2] + (215*S^2*HPL[{2}, -S^2]^2)/6 + ((3 + 3*S^2 - 79*S^4 + 9*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) - (4*S^2*HPL[{4}, -S^2])/3 + ((-307 - 307*S^2 - 2489*S^4 - 921*S^6)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)) - (386*S^2*HPL[{3, 1}, -S^2])/3 + (784*S^2*HPL[{2, 1, 1}, -S^2])/3 - (2*(2 + 2*S^2 + 47*S^4 + 6*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + ((13*Pi^2*S^2)/6 + (14 + 69*S^2)/4)*Zeta[5] + HPL[{1}, -S^2]^2*(((1 + S^2)*(509 + 4939*S^2))/(32*S^2) + (Pi^2*(1 + S^2)*(1087 + 7669*S^2))/(192*S^2) + (Pi^4*(1837 + 1837*S^2 + 13960*S^4 + 5511*S^6))/(720*S^2*(1 + S^2)) + ((149 + 149*S^2 + 1307*S^4 + 447*S^6)*HPL[{2}, -S^2]^2)/(8*S^2*(1 + S^2)) + ((-25*Pi^2*S^2)/12 + (-23 + 48*S^2 + 71*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((23 + 23*S^2 + 37*S^4 + 69*S^6)*HPL[{4}, -S^2])/(8*S^2*(1 + S^2)) - 6*S^2*HPL[{5}, -S^2] + ((-211*Pi^2*S^2)/4 + (-223 - 1186*S^2 - 963*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] - (2*(38 + 38*S^2 + 307*S^4 + 114*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 21*S^2*HPL[{3, 2}, -S^2] + 67*S^2*HPL[{4, 1}, -S^2] + ((307 + 307*S^2 + 2489*S^4 + 921*S^6)*HPL[{2, 1, 1}, -S^2])/(2*S^2*(1 + S^2)) + 430*S^2*HPL[{2, 2, 1}, -S^2] + 1246*S^2*HPL[{3, 1, 1}, -S^2] - 784*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-41*Pi^2*S^2)/12 - ((1 + S^2)*(13 + 23*S^2))/(4*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(343 + 2073*S^2))/(16*S^2) + (Pi^2*(535 + 535*S^2 + 4137*S^4 + 1605*S^6))/(48*S^2*(1 + S^2)) - (21*S^2*HPL[{3}, -S^2])/2 - 215*S^2*HPL[{2, 1}, -S^2] - (39*S^2*Zeta[3])/2) - (39*S^2*Zeta[5])/2) + HPL[{2}, -S^2]*((Pi^2*(-145 + 810*S^2 + 3643*S^4))/(96*S^2) + (-216 + 1007*S^2 + 4538*S^4)/(32*S^2) + (Pi^4*(-130 - 130*S^2 + 17613*S^4 + 10882*S^6))/(1440*S^2*(1 + S^2)) + ((-7*Pi^2*S^2)/4 + (-3 - 12*S^2 + 83*S^4)/(16*S^2))*HPL[{3}, -S^2] + ((-7 - 7*S^2 + 48*S^4 + 44*S^6)*HPL[{4}, -S^2])/(8*S^2*(1 + S^2)) + (7*S^2*HPL[{5}, -S^2])/4 + ((-13*Pi^2*S^2)/12 + (-249 - 842*S^2 + 22*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + ((7 + 7*S^2 - 1747*S^4 - 895*S^6)*HPL[{3, 1}, -S^2])/(4*S^2*(1 + S^2)) + (43*S^2*HPL[{3, 2}, -S^2])/2 + (123*S^2*HPL[{4, 1}, -S^2])/2 + ((-4 - 4*S^2 + 881*S^4 + 451*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 26*S^2*HPL[{2, 2, 1}, -S^2] + 36*S^2*HPL[{3, 1, 1}, -S^2] - 34*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-23*Pi^2*S^2)/12 + (-24 - 18*S^2 - 43*S^4)/(8*S^2))*Zeta[3] - (9*S^2*Zeta[5])/2) + HPL[{1}, -S^2]*((39083*Pi^6*S^2)/36288 + (5*(1 + S^2)*(53 + 1162*S^2))/(32*S^2) + (Pi^4*(1 + S^2)*(391 + 2399*S^2))/(288*S^2) + (Pi^2*(1 + S^2)*(599 + 8387*S^2))/(192*S^2) + ((335*Pi^2*S^2)/24 + (3*(79 + 376*S^2 + 297*S^4))/(16*S^2))*HPL[{2}, -S^2]^2 + 16*S^2*HPL[{2}, -S^2]^3 + ((-5*Pi^2*S^2)/6 + (-5 + 176*S^2 + 181*S^4)/(16*S^2))*HPL[{4}, -S^2] + (4*(1 + S^2 + 3*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (45*S^2*HPL[{6}, -S^2])/4 - 215*S^2*HPL[{2, 1}, -S^2]^2 + ((-155*Pi^2*S^2)/3 + (-107 - 588*S^2 - 481*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + (3*(1 + S^2 + 17*S^4 + 3*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((13 + 13*S^2 + 575*S^4 + 39*S^6)*HPL[{4, 1}, -S^2])/(4*S^2*(1 + S^2)) - (3*S^2*HPL[{4, 2}, -S^2])/2 + 8*S^2*HPL[{5, 1}, -S^2] + ((211*Pi^2*S^2)/2 + (223 + 1186*S^2 + 963*S^4)/(2*S^2))*HPL[{2, 1, 1}, -S^2] + ((149 + 149*S^2 + 1307*S^4 + 447*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (2*(225 + 225*S^2 + 1921*S^4 + 675*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 384*S^2*HPL[{3, 2, 1}, -S^2] + 1144*S^2*HPL[{4, 1, 1}, -S^2] + ((-307 - 307*S^2 - 2489*S^4 - 921*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 772*S^2*HPL[{3, 1, 1, 1}, -S^2] + 1568*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-3*(1 + S^2)*(29 + 23*S^2))/(16*S^2) + (Pi^2*(7 + 7*S^2 - 143*S^4 + 21*S^6))/(24*S^2*(1 + S^2)))*Zeta[3] + (9*S^2*Zeta[3]^2)/2 + HPL[{3}, -S^2]*(((1 + S^2)*(-21 + 121*S^2))/(8*S^2) + (5*Pi^2*(3 + 3*S^2 - 11*S^4 + 9*S^6))/(24*S^2*(1 + S^2)) + 21*S^2*HPL[{2, 1}, -S^2] - S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(343 + 2073*S^2))/(8*S^2) + (Pi^2*(-535 - 535*S^2 - 4137*S^4 - 1605*S^6))/(24*S^2*(1 + S^2)) + 39*S^2*Zeta[3]) + HPL[{2}, -S^2]*((6731*Pi^4*S^2)/1440 + (347*Pi^2*(1 + S^2)*(1 + 5*S^2))/(48*S^2) + (3*(1 + S^2)*(177 + 1511*S^2))/(32*S^2) - (3*(1 + S^2 + 17*S^4 + 3*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + (S^2*HPL[{4}, -S^2])/2 + ((-149 - 149*S^2 - 1307*S^4 - 447*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 213*S^2*HPL[{3, 1}, -S^2] + 430*S^2*HPL[{2, 1, 1}, -S^2] - (3*(3 + 3*S^2 + 61*S^4 + 9*S^6)*Zeta[3])/(4*S^2*(1 + S^2))) + ((7 + 7*S^2 - 57*S^4 + 21*S^6)*Zeta[5])/(2*S^2*(1 + S^2)))) + (-93*Pi^2*S^2 - 15*(-1 + 4*S^2))*Zeta[7] + Log[T]^2*(605/32 + (Pi^2*(889 + 4538*S^2))/48 + (Pi^4*(10954 + 33843*S^2))/1440 + (Pi^6*(468551*S^2 + 207126*S^4))/(45360*(1 + S^2)) + (S^2*HPL[{0}, S^2]^7)/16 + (29*Pi^2*S^2 + (23 + 106*S^2 + 83*S^4)/S^2)*HPL[{1}, -S^2]^5 + (28*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)) + (32*S^2*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^6*((S^2*(49 + 31*S^2))/(48*(1 + S^2)) + (3*S^2*HPL[{1}, -S^2])/8) + ((-66 + 413*S^4)*HPL[{2}, -S^2]^3)/(6*S^2) + HPL[{0}, S^2]^5*((149*Pi^2*S^2)/180 + (34 + 131*S^2)/32 + ((255 + 255*S^2 + 1849*S^4 + 765*S^6)*HPL[{1}, -S^2])/(240*S^2*(1 + S^2)) + (271*S^2*HPL[{1}, -S^2]^2)/120 + (32*S^2*HPL[{2}, -S^2])/15) + ((-1 - S^2 + 121*S^4 + 47*S^6)*HPL[{3}, -S^2]^2)/(S^2*(1 + S^2)) + ((-259*Pi^2*S^2)/6 + (3*(-20 + 23*S^4))/(2*S^2))*HPL[{5}, -S^2] + ((25 + 25*S^2 + 6*S^4 + 95*S^6)*HPL[{6}, -S^2])/(S^2*(1 + S^2)) - 76*S^2*HPL[{7}, -S^2] - (4*(25 + 25*S^2 + 614*S^4 + 222*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + (289*Pi^2*S^2 + (-89 + 620*S^2 + 2181*S^4)/(4*S^2))*HPL[{3, 2}, -S^2] + ((2798*Pi^2*S^2)/3 + (5*(10 + 264*S^2 + 709*S^4))/(2*S^2))*HPL[{4, 1}, -S^2] + ((-7 - 7*S^2 + 850*S^4 + 382*S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) - 86*S^2*HPL[{4, 3}, -S^2] + ((-15 - 15*S^2 + 2111*S^4 + 759*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) - 173*S^2*HPL[{5, 2}, -S^2] + 192*S^2*HPL[{6, 1}, -S^2] + ((812*Pi^2*S^2)/3 + (473 + 1824*S^2 + 466*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((560*Pi^2*S^2)/3 + (1309 + 4904*S^2 + 246*S^4)/S^2)*HPL[{3, 1, 1}, -S^2] + ((44 - 113*S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((-220 + 1539*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - 3184*S^2*HPL[{3, 2, 2}, -S^2] - 9960*S^2*HPL[{3, 3, 1}, -S^2] + (8*(-99 - 99*S^2 + 371*S^4 + 537*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 9892*S^2*HPL[{4, 1, 2}, -S^2] - 30436*S^2*HPL[{4, 2, 1}, -S^2] - 62520*S^2*HPL[{5, 1, 1}, -S^2] + ((1832*Pi^2*S^2)/3 + (2*(-463 - 1558*S^2 + 500*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + 3136*S^2*HPL[{2, 2, 2, 1}, -S^2] - (4*(-165 - 165*S^2 + 451*S^4 + 783*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 2816*S^2*HPL[{3, 1, 1, 2}, -S^2] - 2816*S^2*HPL[{3, 1, 2, 1}, -S^2] - 12224*S^2*HPL[{3, 2, 1, 1}, -S^2] - 35216*S^2*HPL[{4, 1, 1, 1}, -S^2] + (240*(-4 + 31*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - 6224*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] - 18672*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 45280*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] + 13440*S^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-3353*Pi^4*S^2)/180 + (-419 - 576*S^2)/4 + (Pi^2*(-98 - 263*S^2))/6)*Zeta[3] - (4*(-7*S^2 + 3*S^4)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1, 1}, -S^2]*((-209 - 74*S^2 + 1934*S^4)/S^2 + (4*Pi^2*(-35 - 35*S^2 + 668*S^4 + 472*S^6))/(3*S^2*(1 + S^2)) - 3056*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((80 + 467*S^2 + 946*S^4)/(4*S^2) + (Pi^2*(46 + 46*S^2 + 2109*S^4 + 895*S^6))/(12*S^2*(1 + S^2)) - 428*S^2*HPL[{3}, -S^2] + 392*S^2*HPL[{2, 1}, -S^2] - 372*S^2*Zeta[3]) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(221 + 1023*S^2))/(24*S^2) + (5*Pi^2*(25 + 25*S^2 + 249*S^4 + 75*S^6))/(6*S^2*(1 + S^2)) + (65*(1 + 3*S^4)*HPL[{2}, -S^2])/(2*S^2) - (950*S^2*HPL[{3}, -S^2])/3 - 250*S^2*Zeta[3]) + HPL[{4}, -S^2]*((-15 - 343*S^2 - 378*S^4)/(4*S^2) + (Pi^2*(3 + 3*S^2 - 952*S^4 - 272*S^6))/(12*S^2*(1 + S^2)) - 96*S^2*HPL[{2, 1}, -S^2] - 62*S^2*Zeta[3]) + HPL[{0}, S^2]^4*((264 + 1849*S^2)/96 + (Pi^2*(1417*S^2 + 863*S^4))/(144*(1 + S^2)) + ((253 + 253*S^2 + 1895*S^4 + 759*S^6)*HPL[{1}, -S^2]^2)/(48*S^2*(1 + S^2)) + (71*S^2*HPL[{1}, -S^2]^3)/9 + ((-6 - 6*S^2 + 614*S^4 + 373*S^6)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((277*Pi^2*S^2)/72 + (36 + 241*S^2 + 205*S^4)/(12*S^2) + (241*S^2*HPL[{2}, -S^2])/24) - (7*S^2*HPL[{3}, -S^2])/8 + (25*S^2*HPL[{2, 1}, -S^2])/12 + (7*S^2*Zeta[3])/12) + HPL[{3, 1}, -S^2]*((657 + 816*S^2 - 3445*S^4)/(4*S^2) + (Pi^2*(188 + 188*S^2 - 2157*S^4 - 1717*S^6))/(6*S^2*(1 + S^2)) + 1544*S^2*Zeta[3]) + HPL[{3}, -S^2]*((-59*Pi^4*S^2)/3 + (-359 - 958*S^2 - 1841*S^4)/(8*S^2) + (Pi^2*(-93 - 472*S^2 - 1069*S^4))/(24*S^2) + 86*S^2*HPL[{4}, -S^2] - (2*(-138 - 138*S^2 - 751*S^4 + 33*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 1712*S^2*HPL[{3, 1}, -S^2] - 3456*S^2*HPL[{2, 1, 1}, -S^2] + ((3 + 3*S^2 - 154*S^4 - 54*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((1229*Pi^4*S^2)/60 + (3*(-305 - 2490*S^2 + 384*S^4))/(8*S^2) + (Pi^2*(-981 - 3340*S^2 + 482*S^4))/(12*S^2) + 1888*S^2*HPL[{3, 1}, -S^2] + 3112*S^2*HPL[{2, 1, 1}, -S^2] + (8*(25 + 25*S^2 + 203*S^4 + 7*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^3*((6673*Pi^4*S^2)/270 + ((1 + S^2)*(159 + 896*S^2))/(2*S^2) + (Pi^2*(1 + S^2)*(301 + 1115*S^2))/(9*S^2) + ((392*Pi^2*S^2)/9 + (3*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2}, -S^2] + (784*S^2*HPL[{2}, -S^2]^2)/3 - (40*(7 + 7*S^2 + 116*S^4 + 21*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (664*S^2*HPL[{4}, -S^2])/3 - (130*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 + (664*S^2*HPL[{3, 1}, -S^2])/3 - (20*(3 + 3*S^2 + 59*S^4 + 9*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^3*((511*Pi^4*S^2)/135 + (Pi^2*(1046 + 3803*S^2))/144 + (419 + 4111*S^2)/48 + (2*(67 + 67*S^2 + 566*S^4 + 201*S^6)*HPL[{1}, -S^2]^3)/(9*S^2*(1 + S^2)) + (365*S^2*HPL[{1}, -S^2]^4)/18 + ((605*Pi^2*S^2)/36 + (-36 + 496*S^2 + 1673*S^4)/(24*S^2))*HPL[{2}, -S^2] + (325*S^2*HPL[{2}, -S^2]^2)/12 + HPL[{1}, -S^2]^2*((53*Pi^2*S^2)/3 + (335 + 2048*S^2 + 1713*S^4)/(24*S^2) + 55*S^2*HPL[{2}, -S^2]) + ((20 + 20*S^2 + 29*S^4 + 5*S^6)*HPL[{3}, -S^2])/(12*S^2*(1 + S^2)) + (41*S^2*HPL[{4}, -S^2])/6 + ((-258 - 258*S^2 - 611*S^4 + 49*S^6)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)) - (346*S^2*HPL[{3, 1}, -S^2])/3 + (698*S^2*HPL[{2, 1, 1}, -S^2])/3 + ((2*S^2 + 13*S^4)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(411 + 3641*S^2))/(48*S^2) + (Pi^2*(523 + 523*S^2 + 4113*S^4 + 1569*S^6))/(72*S^2*(1 + S^2)) + (2*(31 + 31*S^2 + 258*S^4 + 93*S^6)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)) + 2*S^2*HPL[{3}, -S^2] - 110*S^2*HPL[{2, 1}, -S^2] - (11*S^2*Zeta[3])/3)) + (-158*Pi^2*S^2 + (-102 - 277*S^2)/2)*Zeta[5] + HPL[{1}, -S^2]^2*((3*(1 + S^2)*(1195 + 7849*S^2))/(32*S^2) + (Pi^2*(1 + S^2)*(1889 + 9231*S^2))/(48*S^2) + (Pi^4*(8587 + 8587*S^2 + 79145*S^4 + 25761*S^6))/(720*S^2*(1 + S^2)) + (98*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)) + ((-497*Pi^2*S^2)/3 - (7*(49 + 148*S^2 + 99*S^4))/(2*S^2))*HPL[{3}, -S^2] - (8*(7 + 7*S^2 + 104*S^4 + 21*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) - 216*S^2*HPL[{5}, -S^2] + ((-392*Pi^2*S^2)/3 - (9*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1}, -S^2] - (8*(14 + 14*S^2 - 41*S^4 + 42*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 1568*S^2*HPL[{3, 2}, -S^2] + 5368*S^2*HPL[{4, 1}, -S^2] + (390*(1 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + 3136*S^2*HPL[{2, 2, 1}, -S^2] + 5608*S^2*HPL[{3, 1, 1}, -S^2] + ((-416*Pi^2*S^2)/3 - (4*(1 + S^2)*(22 + 65*S^2))/S^2)*Zeta[3] + HPL[{2}, -S^2]*((3*(1 + S^2)*(75 + 1021*S^2))/(8*S^2) + (Pi^2*(251 + 251*S^2 + 1537*S^4 + 753*S^6))/(6*S^2*(1 + S^2)) - 784*S^2*HPL[{3}, -S^2] - 1568*S^2*HPL[{2, 1}, -S^2] - 784*S^2*Zeta[3]) - 760*S^2*Zeta[5]) + HPL[{2}, -S^2]*((Pi^2*(-129 + 208*S^2 + 1956*S^4))/(12*S^2) + (-344 + 65*S^2 + 4538*S^4)/(8*S^2) + (Pi^4*(-538 - 538*S^2 + 17563*S^4 + 11500*S^6))/(360*S^2*(1 + S^2)) + (-151*Pi^2*S^2 + (107 - 232*S^2 - 1175*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((7 + 7*S^2 - 784*S^4 - 332*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - 177*S^2*HPL[{5}, -S^2] + ((-406*Pi^2*S^2)/3 + (-473 - 1824*S^2 - 466*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] - (8*(18 + 18*S^2 + 291*S^4 + 95*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 1634*S^2*HPL[{3, 2}, -S^2] + 5232*S^2*HPL[{4, 1}, -S^2] + (8*(25 + 25*S^2 + 614*S^4 + 222*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 1568*S^2*HPL[{2, 2, 1}, -S^2] + 1248*S^2*HPL[{3, 1, 1}, -S^2] - 3112*S^2*HPL[{2, 1, 1, 1}, -S^2] + (-140*Pi^2*S^2 + (-55 - 224*S^2 - 518*S^4)/(2*S^2))*Zeta[3] - 732*S^2*Zeta[5]) + HPL[{0}, S^2]^2*((Pi^2*(246 + 1261*S^2))/16 + (573 + 4538*S^2)/16 + (Pi^4*(19531*S^2 + 11082*S^4))/(720*(1 + S^2)) + (5*(11 + 11*S^2 + 95*S^4 + 33*S^6)*HPL[{1}, -S^2]^4)/(2*S^2*(1 + S^2)) + 31*S^2*HPL[{1}, -S^2]^5 + ((-4 - 4*S^2 + 881*S^4 + 451*S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((749*Pi^2*S^2)/18 + (257 + 1242*S^2 + 985*S^4)/(6*S^2) + (392*S^2*HPL[{2}, -S^2])/3) + ((-37*Pi^2*S^2)/6 + (17 + 96*S^2 + 83*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((3 + 3*S^2 + 42*S^4 + 58*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) - (37*S^2*HPL[{5}, -S^2])/2 + ((21*Pi^2*S^2)/2 + (-259 - 891*S^2 - 9*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((23 + 23*S^2 - 1706*S^4 - 934*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) + 43*S^2*HPL[{3, 2}, -S^2] + 144*S^2*HPL[{4, 1}, -S^2] + (2*(-10 - 10*S^2 + 871*S^4 + 479*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 34*S^2*HPL[{2, 2, 1}, -S^2] - 4*S^2*HPL[{3, 1, 1}, -S^2] + 152*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-19*Pi^2*S^2)/3 + (-8 - 13*S^2)/2)*Zeta[3] + HPL[{1}, -S^2]^2*((49*(1 + S^2)*(4 + 21*S^2))/(4*S^2) + (Pi^2*(583 + 583*S^2 + 4745*S^4 + 1749*S^6))/(24*S^2*(1 + S^2)) + ((307 + 307*S^2 + 2489*S^4 + 921*S^6)*HPL[{2}, -S^2])/(4*S^2*(1 + S^2)) - 22*S^2*HPL[{3}, -S^2] - 392*S^2*HPL[{2, 1}, -S^2] - 41*S^2*Zeta[3]) + HPL[{2}, -S^2]*((-49 + 490*S^2 + 1978*S^4)/(8*S^2) + (Pi^2*(-16 - 16*S^2 + 1485*S^4 + 852*S^6))/(12*S^2*(1 + S^2)) - 21*S^2*HPL[{3}, -S^2] - 17*S^2*HPL[{2, 1}, -S^2] - 38*S^2*Zeta[3]) + HPL[{1}, -S^2]*((8449*Pi^4*S^2)/720 + (Pi^2*(1 + S^2)*(401 + 1805*S^2))/(24*S^2) + ((1 + S^2)*(625 + 4411*S^2))/(16*S^2) + ((211*Pi^2*S^2)/4 + (223 + 1186*S^2 + 963*S^4)/(4*S^2))*HPL[{2}, -S^2] + (215*S^2*HPL[{2}, -S^2]^2)/2 + ((3 + 3*S^2 - 79*S^4 + 9*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - 4*S^2*HPL[{4}, -S^2] + ((-307 - 307*S^2 - 2489*S^4 - 921*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 386*S^2*HPL[{3, 1}, -S^2] + 784*S^2*HPL[{2, 1, 1}, -S^2] - (2*(2 + 2*S^2 + 47*S^4 + 6*S^6)*Zeta[3])/(S^2*(1 + S^2))) - 39*S^2*Zeta[5]) + HPL[{1}, -S^2]*((52285*Pi^6*S^2)/9072 + (Pi^2*(1 + S^2)*(1579 + 9787*S^2))/(48*S^2) + (Pi^4*(1 + S^2)*(6553 + 25601*S^2))/(720*S^2) + ((1 + S^2)*(3697 + 27105*S^2))/(32*S^2) + ((607*Pi^2*S^2)/6 + (333 + 1492*S^2 + 1159*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 + 74*S^2*HPL[{3}, -S^2]^2 + ((-170*Pi^2*S^2)/3 + (-377 - 860*S^2 - 483*S^4)/(4*S^2))*HPL[{4}, -S^2] - (2*(1 + S^2 + 219*S^4 + 3*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - 89*S^2*HPL[{6}, -S^2] - 1568*S^2*HPL[{2, 1}, -S^2]^2 + ((-220*Pi^2*S^2)/3 - (2*(-5 + 228*S^2 + 233*S^4))/S^2)*HPL[{3, 1}, -S^2] + (2*(113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + (2*(395 + 395*S^2 + 6553*S^4 + 1185*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) + 234*S^2*HPL[{4, 2}, -S^2] + 1352*S^2*HPL[{5, 1}, -S^2] + ((784*Pi^2*S^2)/3 + (18*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (784*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (16*(112 + 112*S^2 + 1037*S^4 + 336*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 1328*S^2*HPL[{4, 1, 1}, -S^2] - (780*(1 + 3*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + 1328*S^2*HPL[{3, 1, 1, 1}, -S^2] + ((-3*(1 + S^2)*(107 + 333*S^2))/(4*S^2) + (Pi^2*(-49 - 49*S^2 - 979*S^4 - 147*S^6))/(3*S^2*(1 + S^2)))*Zeta[3] + 40*S^2*Zeta[3]^2 + HPL[{3}, -S^2]*((-3*(1 + S^2)*(107 + 201*S^2))/(2*S^2) + (Pi^2*(-137 - 137*S^2 - 2399*S^4 - 411*S^6))/(6*S^2*(1 + S^2)) + 1568*S^2*HPL[{2, 1}, -S^2] - 100*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*((-3*(1 + S^2)*(75 + 1021*S^2))/(4*S^2) + (Pi^2*(-251 - 251*S^2 - 1537*S^4 - 753*S^6))/(3*S^2*(1 + S^2)) + 1568*S^2*Zeta[3]) + HPL[{2}, -S^2]*((2021*Pi^4*S^2)/120 + (7*Pi^2*(1 + S^2)*(23 + 117*S^2))/(6*S^2) + ((1 + S^2)*(101 + 3541*S^2))/(8*S^2) + ((-113 - 113*S^2 - 1907*S^4 - 339*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - 226*S^2*HPL[{4}, -S^2] - (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 1568*S^2*HPL[{3, 1}, -S^2] + 3136*S^2*HPL[{2, 1, 1}, -S^2] - (112*(1 + S^2 + 17*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-51 - 51*S^2 - 1673*S^4 - 153*S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{0}, S^2]*((252431*Pi^6*S^2)/45360 + (Pi^2*(1454 + 9487*S^2))/48 + (3787 + 27105*S^2)/32 + (Pi^4*(15602 + 51761*S^2))/1440 + (28*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)) + (112*S^2*HPL[{1}, -S^2]^6)/3 + (91*Pi^2*S^2 + (55 + 784*S^2 + 2312*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 + (373*S^2*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((1205*Pi^2*S^2)/18 + (5*(23 + 106*S^2 + 83*S^4))/(2*S^2) + 250*S^2*HPL[{2}, -S^2]) - 12*S^2*HPL[{3}, -S^2]^2 + ((89*Pi^2*S^2)/6 + (-13 + 58*S^2 + 153*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((9 + 9*S^2 + 139*S^4 + 47*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) + 83*S^2*HPL[{6}, -S^2] + ((-482 - 2378*S^2 - 97*S^4)/(2*S^2) + (Pi^2*(-663 - 663*S^2 - 2036*S^4 + 124*S^6))/(6*S^2*(1 + S^2)))*HPL[{2, 1}, -S^2] - 1534*S^2*HPL[{2, 1}, -S^2]^2 + (-378*Pi^2*S^2 + (100 - 660*S^2 - 2339*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-19 - 19*S^2 + 438*S^4 + 134*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((-47 - 47*S^2 + 547*S^4 + 183*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - 3*S^2*HPL[{4, 2}, -S^2] - 126*S^2*HPL[{5, 1}, -S^2] + ((2288*Pi^2*S^2)/3 + (-89 + 686*S^2 + 2370*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (8*(95 + 95*S^2 + 394*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (2*(-1167 - 1167*S^2 - 4595*S^4 + 41*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 12*S^2*HPL[{3, 1, 2}, -S^2] + 2996*S^2*HPL[{3, 2, 1}, -S^2] + 9144*S^2*HPL[{4, 1, 1}, -S^2] + (60*(-27 - 27*S^2 - 95*S^4 + 5*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 6304*S^2*HPL[{3, 1, 1, 1}, -S^2] + 12720*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-206 - 423*S^2)/4 + (Pi^2*(-309*S^2 - 121*S^4))/(6*(1 + S^2)))*Zeta[3] + 26*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(221 + 1023*S^2))/(12*S^2) + (2*Pi^2*(172 + 172*S^2 + 1721*S^4 + 516*S^6))/(9*S^2*(1 + S^2)) + (125*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(S^2*(1 + S^2)) - (68*S^2*HPL[{3}, -S^2])/3 - 1000*S^2*HPL[{2, 1}, -S^2] - (332*S^2*Zeta[3])/3) + HPL[{3}, -S^2]*((17 + 55*S^2 + 56*S^4)/(2*S^2) + (Pi^2*(47 + 47*S^2 - 104*S^4 - 60*S^6))/(12*S^2*(1 + S^2)) + 40*S^2*HPL[{2, 1}, -S^2] - 8*S^2*Zeta[3]) + HPL[{2}, -S^2]*((769*Pi^4*S^2)/24 + (Pi^2*(-125 + 1182*S^2 + 4043*S^4))/(24*S^2) + (-55 + 2402*S^2 + 10164*S^4)/(16*S^2) + ((11 + 11*S^2 - 211*S^4 - 59*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + 25*S^2*HPL[{4}, -S^2] - (4*(95 + 95*S^2 + 394*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 1532*S^2*HPL[{3, 1}, -S^2] + 3068*S^2*HPL[{2, 1, 1}, -S^2] + ((2 + 2*S^2 - 287*S^4 - 123*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^2*((4061*Pi^4*S^2)/120 + (3*(1 + S^2)*(159 + 896*S^2))/(4*S^2) + (Pi^2*(1 + S^2)*(1025 + 4203*S^2))/(24*S^2) + (180*Pi^2*S^2 + (5*(55 + 294*S^2 + 239*S^4))/(2*S^2))*HPL[{2}, -S^2] + 392*S^2*HPL[{2}, -S^2]^2 - (2*(5 + 5*S^2 + 49*S^4 + 15*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + 46*S^2*HPL[{4}, -S^2] - (375*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 1500*S^2*HPL[{3, 1}, -S^2] + 3000*S^2*HPL[{2, 1, 1}, -S^2] - (4*(10 + 10*S^2 + 113*S^4 + 30*S^6)*Zeta[3])/(S^2*(1 + S^2))) - (2*(123*S^2 + 58*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(379 + 2189*S^2))/(12*S^2) + (3*(1 + S^2)*(1195 + 7849*S^2))/(32*S^2) + (Pi^4*(7801 + 7801*S^2 + 72135*S^4 + 23403*S^6))/(720*S^2*(1 + S^2)) + (98*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)) + ((-11*Pi^2*S^2)/3 + (2*(-15 - 8*S^2 + 7*S^4))/S^2)*HPL[{3}, -S^2] + ((17 + 17*S^2 + 235*S^4 + 51*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + 46*S^2*HPL[{5}, -S^2] + (-360*Pi^2*S^2 - (5*(55 + 294*S^2 + 239*S^4))/S^2)*HPL[{2, 1}, -S^2] - (12*(31 + 31*S^2 + 343*S^4 + 93*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 152*S^2*HPL[{3, 2}, -S^2] + 364*S^2*HPL[{4, 1}, -S^2] + (750*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 3136*S^2*HPL[{2, 2, 1}, -S^2] + 9272*S^2*HPL[{3, 1, 1}, -S^2] - 6000*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-94*Pi^2*S^2)/3 - ((1 + S^2)*(107 + 201*S^2))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((3*(1 + S^2)*(289 + 1687*S^2))/(8*S^2) + (Pi^2*(623 + 623*S^2 + 6189*S^4 + 1869*S^6))/(12*S^2*(1 + S^2)) - 76*S^2*HPL[{3}, -S^2] - 1568*S^2*HPL[{2, 1}, -S^2] - 164*S^2*Zeta[3]) - 130*S^2*Zeta[5])) - 1116*S^2*Zeta[7]) + HPL[{1}, -S^2]^2*((29*Pi^4*(1 + S^2)*(172 + 931*S^2))/(1440*S^2) + (3*(1 + S^2)*(1507 + 10940*S^2))/(64*S^2) + (Pi^2*(1 + S^2)*(5621 + 43303*S^2))/(384*S^2) + (Pi^6*(37673 + 37673*S^2 + 322159*S^4 + 113019*S^6))/(36288*S^2*(1 + S^2)) + (83*(1 + 3*S^4)*HPL[{2}, -S^2]^3)/(12*S^2) + (37*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)) + (-20*Pi^2*S^2 + (-63 - 10*S^2 + 53*S^4)/(2*S^2))*HPL[{5}, -S^2] + ((119 + 119*S^2 + S^4 + 357*S^6)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)) - 15*S^2*HPL[{7}, -S^2] - (196*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((413*Pi^2*S^2)/3 + (249 + 832*S^2 + 583*S^4)/(2*S^2))*HPL[{3, 2}, -S^2] + ((1409*Pi^2*S^2)/3 + (1871 + 5852*S^2 + 3981*S^4)/(4*S^2))*HPL[{4, 1}, -S^2] + (117*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{4, 2}, -S^2])/(4*S^2*(1 + S^2)) - 47*S^2*HPL[{4, 3}, -S^2] + (13*(9 + 9*S^2 + 131*S^4 + 27*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) - 102*S^2*HPL[{5, 2}, -S^2] + 49*S^2*HPL[{6, 1}, -S^2] + ((1214*Pi^2*S^2)/3 + (333 + 1492*S^2 + 1159*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((2648*Pi^2*S^2)/3 + (16*(41 + 215*S^2 + 174*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (166*(1 + 3*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - 1630*S^2*HPL[{3, 2, 2}, -S^2] - 4984*S^2*HPL[{3, 3, 1}, -S^2] + (2*(193 + 193*S^2 - 85*S^4 + 579*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 4906*S^2*HPL[{4, 1, 2}, -S^2] - 15202*S^2*HPL[{4, 2, 1}, -S^2] - 31320*S^2*HPL[{5, 1, 1}, -S^2] + ((-784*Pi^2*S^2)/3 - (18*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (16*(14 + 14*S^2 - 41*S^4 + 42*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 3136*S^2*HPL[{3, 1, 1, 2}, -S^2] + 3136*S^2*HPL[{3, 1, 2, 1}, -S^2] + 3136*S^2*HPL[{3, 2, 1, 1}, -S^2] + 10736*S^2*HPL[{4, 1, 1, 1}, -S^2] + (780*(1 + 3*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - 6272*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] - 18816*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 38960*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] + ((-1013*Pi^4*S^2)/120 - (Pi^2*(1 + S^2)*(101 + 283*S^2))/(12*S^2) - ((1 + S^2)*(329 + 965*S^2))/(8*S^2))*Zeta[3] + ((9 + 9*S^2 + 107*S^4 + 27*S^6)*Zeta[3]^2)/(2*S^2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((3*(1 + S^2)*(75 + 1021*S^2))/(4*S^2) + (Pi^2*(251 + 251*S^2 + 1537*S^4 + 753*S^6))/(3*S^2*(1 + S^2)) - 1568*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((3*(1 + S^2)*(351 + 1553*S^2))/(32*S^2) + (Pi^2*(345 + 345*S^2 + 3463*S^4 + 1035*S^6))/(24*S^2*(1 + S^2)) - 233*S^2*HPL[{3}, -S^2] - 177*S^2*Zeta[3]) + HPL[{4}, -S^2]*(-((1 + S^2)*(429 + 391*S^2))/(8*S^2) + (Pi^2*(-89 - 89*S^2 - 1627*S^4 - 267*S^6))/(24*S^2*(1 + S^2)) + 226*S^2*HPL[{2, 1}, -S^2] - 28*S^2*Zeta[3]) + HPL[{3, 1}, -S^2]*((-21*(1 + S^2)*(-11 + 107*S^2))/(8*S^2) - (4*Pi^2*(26 + 26*S^2 + 133*S^4 + 78*S^6))/(3*S^2*(1 + S^2)) + 808*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*((-2021*Pi^4*S^2)/120 - (7*Pi^2*(1 + S^2)*(23 + 117*S^2))/(6*S^2) - ((1 + S^2)*(101 + 3541*S^2))/(8*S^2) + 1568*S^2*HPL[{3, 1}, -S^2] + 3136*S^2*HPL[{2, 1, 1}, -S^2] + (112*(1 + S^2 + 17*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((-601*Pi^4*S^2)/60 - (Pi^2*(1 + S^2)*(183 + 311*S^2))/(12*S^2) - ((1 + S^2)*(307 + 511*S^2))/(4*S^2) + 43*S^2*HPL[{4}, -S^2] + ((113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 784*S^2*HPL[{3, 1}, -S^2] - 1568*S^2*HPL[{2, 1, 1}, -S^2] - (4*(3 + 3*S^2 + 34*S^4 + 9*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-419*Pi^2*S^2)/6 - ((1 + S^2)*(20 + 83*S^2))/S^2)*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(911 + 7209*S^2))/(96*S^2) + ((1 + S^2)*(-79 + 16995*S^2))/(64*S^2) + (Pi^4*(6575 + 6575*S^2 + 43977*S^4 + 19725*S^6))/(1440*S^2*(1 + S^2)) + ((-413*Pi^2*S^2)/6 + (-249 - 832*S^2 - 583*S^4)/(4*S^2))*HPL[{3}, -S^2] - (113*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) - 82*S^2*HPL[{5}, -S^2] + ((-607*Pi^2*S^2)/3 + (-333 - 1492*S^2 - 1159*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] - (196*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 854*S^2*HPL[{3, 2}, -S^2] + 2570*S^2*HPL[{4, 1}, -S^2] + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 1568*S^2*HPL[{3, 1, 1}, -S^2] - 3136*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-431*Pi^2*S^2)/6 - (2*(1 + S^2)*(31 + 72*S^2))/S^2)*Zeta[3] - 361*S^2*Zeta[5]) - 483*S^2*Zeta[7]) + HPL[{2}, -S^2]*((Pi^2*(-140 + 268*S^2 + 2269*S^4))/(24*S^2) + (-2432 + 885*S^2 + 24320*S^4)/(64*S^2) + (Pi^4*(-2721 + 8110*S^2 + 47857*S^4))/(2880*S^2) + (Pi^6*(-958 - 958*S^2 + 66256*S^4 + 44227*S^6))/(15120*S^2*(1 + S^2)) + (S^2*(71 + 28*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((-85*Pi^2*S^2)/6 + (15 - 70*S^2 + 124*S^4)/(4*S^2))*HPL[{5}, -S^2] + ((10 + 10*S^2 + 105*S^4 + 189*S^6)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)) + 110*S^2*HPL[{7}, -S^2] + ((66 - 413*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((430*Pi^2*S^2)/3 + (11 + 498*S^2 + 1197*S^4)/(4*S^2))*HPL[{3, 2}, -S^2] + ((913*Pi^2*S^2)/2 + (-125 + 1246*S^2 + 3751*S^4)/(4*S^2))*HPL[{4, 1}, -S^2] + (3*(1 + S^2 + 169*S^4 + 65*S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) - 66*S^2*HPL[{4, 3}, -S^2] + ((-9 - 9*S^2 + 1997*S^4 + 733*S^6)*HPL[{5, 1}, -S^2])/(2*S^2*(1 + S^2)) - 156*S^2*HPL[{5, 2}, -S^2] - 161*S^2*HPL[{6, 1}, -S^2] + ((-418*Pi^2*S^2)/3 + (465 + 1420*S^2 - 546*S^4)/(2*S^2))*HPL[{2, 2, 1}, -S^2] + (116*Pi^2*S^2 + (-1288 - 4492*S^2 + 463*S^4)/(2*S^2))*HPL[{3, 1, 1}, -S^2] - (39*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((185 + 185*S^2 + 4323*S^4 + 1563*S^6)*HPL[{3, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 1571*S^2*HPL[{3, 2, 2}, -S^2] - 4948*S^2*HPL[{3, 3, 1}, -S^2] + ((343 + 343*S^2 + 6344*S^4 + 2188*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 4909*S^2*HPL[{4, 1, 2}, -S^2] - 15157*S^2*HPL[{4, 2, 1}, -S^2] - 31098*S^2*HPL[{5, 1, 1}, -S^2] + ((-812*Pi^2*S^2)/3 + (-473 - 1824*S^2 - 466*S^4)/S^2)*HPL[{2, 1, 1, 1}, -S^2] - 1512*S^2*HPL[{2, 2, 2, 1}, -S^2] - (32*(-90 - 90*S^2 + 765*S^4 + 667*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 1268*S^2*HPL[{3, 1, 1, 2}, -S^2] - 1268*S^2*HPL[{3, 1, 2, 1}, -S^2] - 5804*S^2*HPL[{3, 2, 1, 1}, -S^2] - 16752*S^2*HPL[{4, 1, 1, 1}, -S^2] + (16*(25 + 25*S^2 + 614*S^4 + 222*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 3136*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] + 9408*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 22592*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] - 6224*S^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-2897*Pi^4*S^2)/360 + (-301 - 774*S^2 - 1896*S^4)/(16*S^2) + (Pi^2*(-79 - 242*S^2 - 561*S^4))/(24*S^2))*Zeta[3] + (3*S^2*(7 + 8*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1, 1}, -S^2]*((80 + 467*S^2 + 946*S^4)/S^2 + (Pi^2*(46 + 46*S^2 + 2109*S^4 + 895*S^6))/(3*S^2*(1 + S^2)) - 1488*S^2*Zeta[3]) + HPL[{4}, -S^2]*((-4*Pi^2*S^2*(23 + 9*S^2))/(3*(1 + S^2)) + (-13 - 294*S^2 - 341*S^4)/(8*S^2) + 59*S^2*HPL[{2, 1}, -S^2] - 41*S^2*Zeta[3]) + HPL[{3, 1}, -S^2]*((-285 - 1048*S^2 - 1706*S^4)/(4*S^2) + (Pi^2*(-137 - 137*S^2 - 4075*S^4 - 1655*S^6))/(12*S^2*(1 + S^2)) + 764*S^2*Zeta[3]) + HPL[{3}, -S^2]*((-1639*Pi^4*S^2)/180 + (265 - 522*S^2 - 1762*S^4)/(16*S^2) + (Pi^2*(26 - 61*S^2 - 273*S^4))/(12*S^2) + 53*S^2*HPL[{4}, -S^2] + ((283 + 283*S^2 + 1991*S^4 + 127*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 864*S^2*HPL[{3, 1}, -S^2] - 1712*S^2*HPL[{2, 1, 1}, -S^2] + ((1 + S^2 - 117*S^4 - 65*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-971*Pi^4*S^2)/120 + (-1177 - 8118*S^2 - 1718*S^4)/(16*S^2) + (Pi^2*(-971 - 3508*S^2 - 422*S^4))/(24*S^2) - 956*S^2*HPL[{3, 1}, -S^2] - 1568*S^2*HPL[{2, 1, 1}, -S^2] - (2*(-54 - 54*S^2 - 347*S^4 + 7*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-125*Pi^2*S^2)/2 + (-137 - 130*S^2 - 275*S^4)/(4*S^2))*Zeta[5] - 378*S^2*Zeta[7]) + HPL[{1}, -S^2]*((6982*Pi^8*S^2)/14175 + (105*(1 + S^2)*(65 + 404*S^2))/(64*S^2) + (Pi^2*(1 + S^2)*(4757 + 50345*S^2))/(384*S^2) + (Pi^4*(1 + S^2)*(7471 + 58489*S^2))/(2880*S^2) + (Pi^6*(1 + S^2)*(127813 + 566781*S^2))/(181440*S^2) + ((16*Pi^2*S^2)/3 + (43 + 326*S^2 + 283*S^4)/(12*S^2))*HPL[{2}, -S^2]^3 + 16*S^2*HPL[{2}, -S^2]^4 + ((37*Pi^2*S^2)/6 + (15*(3 + 10*S^2 + 7*S^4))/(4*S^2))*HPL[{3}, -S^2]^2 - 9*S^2*HPL[{4}, -S^2]^2 + ((-67*Pi^2*S^2)/6 + (25*(-2 + 7*S^2 + 9*S^4))/(2*S^2))*HPL[{6}, -S^2] + (3*(23 + 23*S^2 + 59*S^4 + 69*S^6)*HPL[{7}, -S^2])/(S^2*(1 + S^2)) - 54*S^2*HPL[{8}, -S^2] + ((-607*Pi^2*S^2)/3 + (-333 - 1492*S^2 - 1159*S^4)/(2*S^2))*HPL[{2, 1}, -S^2]^2 + 932*S^2*HPL[{3, 1}, -S^2]^2 + (19*Pi^2*S^2 + (3*(47 + 150*S^2 + 103*S^4))/(4*S^2))*HPL[{4, 2}, -S^2] + ((-9 - 9*S^2 - 121*S^4 - 27*S^6)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)) + ((346*Pi^2*S^2)/3 + (2*(101 + 230*S^2 + 129*S^4))/S^2)*HPL[{5, 1}, -S^2] - (3*(7 + 7*S^2 + 89*S^4 + 21*S^6)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)) - 12*S^2*HPL[{5, 3}, -S^2] + ((-149 - 149*S^2 - 251*S^4 - 447*S^6)*HPL[{6, 1}, -S^2])/(2*S^2*(1 + S^2)) - 30*S^2*HPL[{6, 2}, -S^2] + 54*S^2*HPL[{7, 1}, -S^2] + 3136*S^2*HPL[{2, 1, 1}, -S^2]^2 + (128*Pi^2*S^2 + (2*(43 + 326*S^2 + 283*S^4))/S^2)*HPL[{3, 2, 1}, -S^2] + ((-483 - 483*S^2 - 7969*S^4 - 1449*S^6)*HPL[{3, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) - (4*(187 + 187*S^2 + 3053*S^4 + 561*S^6)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)) + 266*S^2*HPL[{3, 3, 2}, -S^2] + ((812*Pi^2*S^2)/3 + (139 + 3052*S^2 + 2913*S^4)/(2*S^2))*HPL[{4, 1, 1}, -S^2] + ((-1457 - 1457*S^2 - 23995*S^4 - 4371*S^6)*HPL[{4, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) - 454*S^2*HPL[{4, 1, 3}, -S^2] + ((-4613 - 4613*S^2 - 74647*S^4 - 13839*S^6)*HPL[{4, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 188*S^2*HPL[{4, 2, 2}, -S^2] - 1454*S^2*HPL[{4, 3, 1}, -S^2] - (2*(2369 + 2369*S^2 + 38427*S^4 + 7107*S^6)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 844*S^2*HPL[{5, 1, 2}, -S^2] - 6004*S^2*HPL[{5, 2, 1}, -S^2] - 15658*S^2*HPL[{6, 1, 1}, -S^2] - (332*(1 + 3*S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((-440*Pi^2*S^2)/3 - (4*(-5 + 228*S^2 + 233*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (8*(181 + 181*S^2 + 1327*S^4 + 543*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (8*(181 + 181*S^2 + 1327*S^4 + 543*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) + 156*S^2*HPL[{3, 1, 2, 2}, -S^2] + (4*(611 + 611*S^2 + 3401*S^4 + 1833*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 156*S^2*HPL[{3, 2, 1, 2}, -S^2] + 188*S^2*HPL[{3, 2, 2, 1}, -S^2] + 96*S^2*HPL[{3, 3, 1, 1}, -S^2] + (4*(1889 + 1889*S^2 + 11035*S^4 + 5667*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 468*S^2*HPL[{4, 1, 1, 2}, -S^2] + 564*S^2*HPL[{4, 1, 2, 1}, -S^2] + 756*S^2*HPL[{4, 2, 1, 1}, -S^2] + 3280*S^2*HPL[{5, 1, 1, 1}, -S^2] + ((1568*Pi^2*S^2)/3 + (36*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - (1568*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (4704*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (160*(56 + 56*S^2 + 655*S^4 + 168*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 2656*S^2*HPL[{4, 1, 1, 1, 1}, -S^2] - (1560*(1 + 3*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + 2656*S^2*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + ((29*Pi^2*S^2)/6 + ((1 + S^2)*(1 + 45*S^2))/(2*S^2))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((15*(1 + S^2)*(125 + 771*S^2))/(4*S^2) + (2*Pi^2*(449 + 449*S^2 + 3995*S^4 + 1347*S^6))/(3*S^2*(1 + S^2)) - 4448*S^2*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((3*(1 + S^2)*(351 + 1553*S^2))/(4*S^2) + (Pi^2*(345 + 345*S^2 + 3463*S^4 + 1035*S^6))/(3*S^2*(1 + S^2)) - 1416*S^2*Zeta[3]) + HPL[{5}, -S^2]*(((1 + S^2)*(-311 + 199*S^2))/(8*S^2) + (Pi^2*(7 + 7*S^2 - 219*S^4 + 21*S^6))/(6*S^2*(1 + S^2)) + 164*S^2*HPL[{2, 1}, -S^2] + 12*S^2*Zeta[3]) + HPL[{3, 2}, -S^2]*(((1 + S^2)*(423 + 1049*S^2))/(4*S^2) + (7*Pi^2*(17 + 17*S^2 + 287*S^4 + 51*S^6))/(6*S^2*(1 + S^2)) + 52*S^2*Zeta[3]) + HPL[{4, 1}, -S^2]*(((1 + S^2)*(849 + 1769*S^2))/(2*S^2) + (Pi^2*(803 + 803*S^2 + 13681*S^4 + 2409*S^6))/(12*S^2*(1 + S^2)) + 212*S^2*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((-3*(1 + S^2)*(75 + 1021*S^2))/(2*S^2) - (2*Pi^2*(251 + 251*S^2 + 1537*S^4 + 753*S^6))/(3*S^2*(1 + S^2)) + 3136*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((333*Pi^4*S^2)/40 + (5*Pi^2*(1 + S^2)*(57 + 205*S^2))/(24*S^2) + ((1 + S^2)*(434 + 2377*S^2))/(16*S^2) + ((-75 - 75*S^2 - 1157*S^4 - 225*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - 82*S^2*HPL[{4}, -S^2] - (83*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + 82*S^2*HPL[{3, 1}, -S^2] + ((-47 - 47*S^2 - 849*S^4 - 141*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{4}, -S^2]*((-7*Pi^4*S^2)/2 - (Pi^2*(1 + S^2)*(191 + 151*S^2))/(24*S^2) - ((1 + S^2)*(553 + 417*S^2))/(8*S^2) + (113*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 242*S^2*HPL[{3, 1}, -S^2] - 452*S^2*HPL[{2, 1, 1}, -S^2] + ((-5 - 5*S^2 - 127*S^4 - 15*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((2021*Pi^4*S^2)/60 + (7*Pi^2*(1 + S^2)*(23 + 117*S^2))/(3*S^2) + ((1 + S^2)*(101 + 3541*S^2))/(4*S^2) - (224*(1 + S^2 + 17*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-199*Pi^4*S^2)/15 - (17*Pi^2*(1 + S^2)*(1 + 7*S^2))/S^2 - (5*(1 + S^2)*(-36 + 271*S^2))/(4*S^2) - 3136*S^2*HPL[{2, 1, 1}, -S^2] + (2*(59 + 59*S^2 + 985*S^4 + 177*S^6)*Zeta[3])/(S^2*(1 + S^2))) + (-((1 + S^2)*(52 + 163*S^2))/(2*S^2) + (Pi^2*(-37 - 37*S^2 - 1787*S^4 - 111*S^6))/(12*S^2*(1 + S^2)))*Zeta[5] + HPL[{3}, -S^2]*(-(Pi^2*(1 + S^2)*(171 + 241*S^2))/(12*S^2) - ((1 + S^2)*(2269 + 3583*S^2))/(32*S^2) + (Pi^4*(-391 - 391*S^2 - 8385*S^4 - 1173*S^6))/(360*S^2*(1 + S^2)) + ((15 + 15*S^2 + 217*S^4 + 45*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + 28*S^2*HPL[{5}, -S^2] + ((413*Pi^2*S^2)/3 + (249 + 832*S^2 + 583*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 172*S^2*HPL[{3, 2}, -S^2] - 54*S^2*HPL[{4, 1}, -S^2] - (2*(113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 1864*S^2*HPL[{2, 2, 1}, -S^2] - 5296*S^2*HPL[{3, 1, 1}, -S^2] + 3136*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-26*Pi^2*S^2)/3 - (2*(1 + S^2)*(9 + 7*S^2))/S^2)*Zeta[3] - 32*S^2*Zeta[5]) + Zeta[3]*(-(Pi^2*(1 + S^2)*(34 + 89*S^2))/(4*S^2) - ((1 + S^2)*(1549 + 3791*S^2))/(32*S^2) + (Pi^4*(-545 - 545*S^2 - 13791*S^4 - 1635*S^6))/(720*S^2*(1 + S^2)) + 62*S^2*Zeta[5]) + HPL[{2, 1}, -S^2]*(-(Pi^2*(1 + S^2)*(911 + 7209*S^2))/(48*S^2) - ((1 + S^2)*(-79 + 16995*S^2))/(32*S^2) + (Pi^4*(-6575 - 6575*S^2 - 43977*S^4 - 19725*S^6))/(720*S^2*(1 + S^2)) + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 1708*S^2*HPL[{3, 2}, -S^2] - 5140*S^2*HPL[{4, 1}, -S^2] + (784*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 3136*S^2*HPL[{3, 1, 1}, -S^2] - 6272*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((431*Pi^2*S^2)/3 + (4*(1 + S^2)*(31 + 72*S^2))/S^2)*Zeta[3] + 722*S^2*Zeta[5]) + HPL[{2}, -S^2]*((1049*Pi^6*S^2)/720 + (Pi^2*(1 + S^2)*(316 + 4037*S^2))/(48*S^2) + ((1 + S^2)*(-1247 + 20405*S^2))/(64*S^2) + (Pi^4*(1 + S^2)*(4271 + 21247*S^2))/(1440*S^2) + 43*S^2*HPL[{3}, -S^2]^2 + ((-56*Pi^2*S^2)/3 + (-137 - 450*S^2 - 313*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((-27 - 27*S^2 - 409*S^4 - 81*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) - 42*S^2*HPL[{6}, -S^2] + ((-605*Pi^2*S^2)/3 + (-335 - 1484*S^2 - 1149*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((261 + 261*S^2 + 4199*S^4 + 783*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((787 + 787*S^2 + 12641*S^4 + 2361*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + 156*S^2*HPL[{4, 2}, -S^2] + 632*S^2*HPL[{5, 1}, -S^2] + ((1214*Pi^2*S^2)/3 + (333 + 1492*S^2 + 1159*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (166*(1 + 3*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (4*(181 + 181*S^2 + 1327*S^4 + 543*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 156*S^2*HPL[{3, 1, 2}, -S^2] + 1380*S^2*HPL[{3, 2, 1}, -S^2] + 4156*S^2*HPL[{4, 1, 1}, -S^2] - (784*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 3136*S^2*HPL[{3, 1, 1, 1}, -S^2] + 6272*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((1 + S^2)*(461 + 1083*S^2))/(8*S^2) + (Pi^2*(-121 - 121*S^2 - 2087*S^4 - 363*S^6))/(12*S^2*(1 + S^2)))*Zeta[3] - 3*S^2*Zeta[3]^2 + HPL[{3}, -S^2]*(-((1 + S^2)*(423 + 1049*S^2))/(8*S^2) - (7*Pi^2*(17 + 17*S^2 + 287*S^4 + 51*S^6))/(12*S^2*(1 + S^2)) + 932*S^2*HPL[{2, 1}, -S^2] - 26*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*((-3*(1 + S^2)*(351 + 1553*S^2))/(8*S^2) + (Pi^2*(-345 - 345*S^2 - 3463*S^4 - 1035*S^6))/(6*S^2*(1 + S^2)) + 708*S^2*Zeta[3]) + ((-65 - 65*S^2 - 1639*S^4 - 195*S^6)*Zeta[5])/(2*S^2*(1 + S^2))) + (3*(5 + 5*S^2 - 307*S^4 + 15*S^6)*Zeta[7])/(S^2*(1 + S^2))) + HPL[{0}, S^2]*((2294333*Pi^8*S^2)/5443200 + (1957*Pi^2*(3 + 25*S^2))/384 + (105*(65 + 404*S^2))/64 + (Pi^4*(14098 + 116779*S^2))/5760 + (Pi^6*(364610 + 1191819*S^2))/362880 + (4*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)) + (4*S^2*HPL[{1}, -S^2]^8)/3 + ((529*Pi^2*S^2)/36 + (-101 + 612*S^2 + 2214*S^4)/(48*S^2))*HPL[{2}, -S^2]^3 + (123*S^2*HPL[{2}, -S^2]^4)/8 + HPL[{1}, -S^2]^6*((241*Pi^2*S^2)/54 + (23 + 106*S^2 + 83*S^4)/(6*S^2) + (50*S^2*HPL[{2}, -S^2])/3) + ((-17*Pi^2*S^2)/12 + (-7 - 3*S^2 - 24*S^4)/(4*S^2))*HPL[{3}, -S^2]^2 - 2*S^2*HPL[{4}, -S^2]^2 + ((209*Pi^2*S^2)/12 + (3*(25 + 6*S^2 + 39*S^4))/(8*S^2))*HPL[{6}, -S^2] + ((-125 - 125*S^2 + 448*S^4 + 180*S^6)*HPL[{7}, -S^2])/(4*S^2*(1 + S^2)) + 188*S^2*HPL[{8}, -S^2] + (-182*Pi^2*S^2 + (-55 - 784*S^2 - 2312*S^4)/(4*S^2))*HPL[{2, 1}, -S^2]^2 + 762*S^2*HPL[{3, 1}, -S^2]^2 + ((-7*Pi^2*S^2)/12 + (1 + 30*S^2 - 45*S^4)/(8*S^2))*HPL[{4, 2}, -S^2] + ((-5 - 5*S^2 + 28*S^4 + 15*S^6)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)) + ((-139*Pi^2*S^2)/6 + (9 - 22*S^2 - 134*S^4)/(2*S^2))*HPL[{5, 1}, -S^2] + ((-59 - 59*S^2 + 329*S^4 + 161*S^6)*HPL[{5, 2}, -S^2])/(4*S^2*(1 + S^2)) - 3*S^2*HPL[{5, 3}, -S^2] + ((-22 - 22*S^2 + 41*S^4 + 34*S^6)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)) - (9*S^2*HPL[{6, 2}, -S^2])/2 - 168*S^2*HPL[{7, 1}, -S^2] + 3068*S^2*HPL[{2, 1, 1}, -S^2]^2 + ((4*Pi^2*S^2)/3 + (1 + 12*S^2 + 21*S^4)/(4*S^2))*HPL[{3, 1, 2}, -S^2] + (354*Pi^2*S^2 + (3*(-67 + 412*S^2 + 1483*S^4))/(4*S^2))*HPL[{3, 2, 1}, -S^2] + ((55 + 55*S^2 - 882*S^4 - 402*S^6)*HPL[{3, 2, 2}, -S^2])/(4*S^2*(1 + S^2)) - (4*(-9 - 9*S^2 + 163*S^4 + 69*S^6)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)) - 32*S^2*HPL[{3, 3, 2}, -S^2] + ((3263*Pi^2*S^2)/3 + (-316 + 1894*S^2 + 6795*S^4)/(2*S^2))*HPL[{4, 1, 1}, -S^2] + ((73 + 73*S^2 - 1305*S^4 - 553*S^6)*HPL[{4, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) + 70*S^2*HPL[{4, 1, 3}, -S^2] + ((217 + 217*S^2 - 3885*S^4 - 1597*S^6)*HPL[{4, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) - (61*S^2*HPL[{4, 2, 2}, -S^2])/2 + 134*S^2*HPL[{4, 3, 1}, -S^2] + ((225 + 225*S^2 - 3731*S^4 - 1519*S^6)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 73*S^2*HPL[{5, 1, 2}, -S^2] + 553*S^2*HPL[{5, 2, 1}, -S^2] + 1606*S^2*HPL[{6, 1, 1}, -S^2] + ((-482 - 2378*S^2 - 97*S^4)/S^2 + (Pi^2*(-663 - 663*S^2 - 2036*S^4 + 124*S^6))/(3*S^2*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (4*(-196 - 196*S^2 - 685*S^4 + 23*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (-756*Pi^2*S^2 + (100 - 660*S^2 - 2339*S^4)/S^2)*HPL[{3, 1, 1, 1}, -S^2] + ((2333 + 2333*S^2 + 8658*S^4 - 142*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + ((2333 + 2333*S^2 + 8658*S^4 - 142*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) + 6*S^2*HPL[{3, 1, 2, 2}, -S^2] + ((4685 + 4685*S^2 + 16878*S^4 - 418*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 6*S^2*HPL[{3, 2, 1, 2}, -S^2] - 2994*S^2*HPL[{3, 2, 2, 1}, -S^2] - 9000*S^2*HPL[{3, 3, 1, 1}, -S^2] - (2*(-7009 - 7009*S^2 - 25207*S^4 + 645*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 6*S^2*HPL[{4, 1, 1, 2}, -S^2] - 9006*S^2*HPL[{4, 1, 2, 1}, -S^2] - 27006*S^2*HPL[{4, 2, 1, 1}, -S^2] - 54252*S^2*HPL[{5, 1, 1, 1}, -S^2] + ((4576*Pi^2*S^2)/3 + (2*(-89 + 686*S^2 + 2370*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(95 + 95*S^2 + 394*S^4 + 2*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (48*(95 + 95*S^2 + 394*S^4 + 2*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 5968*S^2*HPL[{2, 2, 1, 2, 1}, -S^2] - 17904*S^2*HPL[{2, 2, 2, 1, 1}, -S^2] - (4*(1873 + 1873*S^2 + 8013*S^4 + 105*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 35832*S^2*HPL[{3, 1, 1, 1, 2}, -S^2] + 59704*S^2*HPL[{3, 1, 1, 2, 1}, -S^2] + 71640*S^2*HPL[{3, 1, 2, 1, 1}, -S^2] + 149224*S^2*HPL[{3, 2, 1, 1, 1}, -S^2] + 447984*S^2*HPL[{4, 1, 1, 1, 1}, -S^2] + (120*(-27 - 27*S^2 - 95*S^4 + 5*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 12608*S^2*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 25440*S^2*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((5*Pi^2*S^2)/3 + (3*(6 + 19*S^2))/4)*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((701 + 3472*S^2 + 32*S^4)/S^2 + (Pi^2*(1895 + 1895*S^2 + 6430*S^4 - 138*S^6))/(6*S^2*(1 + S^2)) - 40*S^2*Zeta[3]) + HPL[{1}, -S^2]^5*(((1 + S^2)*(221 + 1023*S^2))/(24*S^2) + (Pi^2*(172 + 172*S^2 + 1721*S^4 + 516*S^6))/(45*S^2*(1 + S^2)) + (25*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - (34*S^2*HPL[{3}, -S^2])/15 - 100*S^2*HPL[{2, 1}, -S^2] - (166*S^2*Zeta[3])/15) + HPL[{5}, -S^2]*((200 + 60*S^2 + 547*S^4)/(16*S^2) + (Pi^2*(-31 - 31*S^2 + 239*S^4 + 55*S^6))/(24*S^2*(1 + S^2)) + 5*S^2*HPL[{2, 1}, -S^2] - 11*S^2*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((228 + 1139*S^2 - 8*S^4)/S^2 + (Pi^2*(308 + 308*S^2 + 1089*S^4 - 13*S^6))/(3*S^2*(1 + S^2)) - 8*S^2*Zeta[3]) + HPL[{3, 2}, -S^2]*((-47 + 134*S^2 - 139*S^4)/(8*S^2) + (Pi^2*(-35 - 35*S^2 + 444*S^4 + 84*S^6))/(24*S^2*(1 + S^2)) - 2*S^2*Zeta[3]) + HPL[{4, 1}, -S^2]*((-159 - 34*S^2 - 557*S^4)/(8*S^2) + (Pi^2*(-73 - 73*S^2 + 491*S^4 + 111*S^6))/(12*S^2*(1 + S^2)) + 10*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((709*Pi^4*S^2)/96 + (Pi^2*(67 + 1236*S^2 + 3872*S^4))/(96*S^2) + (301 + 1830*S^2 + 9598*S^4)/(64*S^2) + ((11 + 11*S^2 - 225*S^4 - 105*S^6)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)) + (13*S^2*HPL[{4}, -S^2])/4 + ((-196 - 196*S^2 - 685*S^4 + 23*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 375*S^2*HPL[{3, 1}, -S^2] + 746*S^2*HPL[{2, 1, 1}, -S^2] + ((3 + 3*S^2 - 138*S^4 - 56*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{4}, -S^2]*((183*Pi^4*S^2)/80 + (Pi^2*(-5 + 82*S^2 + 281*S^4))/(48*S^2) + (351 + 716*S^2 + 1072*S^4)/(32*S^2) + ((2 + 2*S^2 + 37*S^4 + 53*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 13*S^2*HPL[{3, 1}, -S^2] + 50*S^2*HPL[{2, 1, 1}, -S^2] + ((15 + 15*S^2 + 4*S^4 + 12*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{1}, -S^2]^4*((4061*Pi^4*S^2)/720 + ((1 + S^2)*(159 + 896*S^2))/(8*S^2) + (Pi^2*(1 + S^2)*(1025 + 4203*S^2))/(144*S^2) + (30*Pi^2*S^2 + (5*(55 + 294*S^2 + 239*S^4))/(12*S^2))*HPL[{2}, -S^2] + (196*S^2*HPL[{2}, -S^2]^2)/3 + ((-5 - 5*S^2 - 49*S^4 - 15*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + (23*S^2*HPL[{4}, -S^2])/3 - (125*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - 250*S^2*HPL[{3, 1}, -S^2] + 500*S^2*HPL[{2, 1, 1}, -S^2] - (2*(10 + 10*S^2 + 113*S^4 + 30*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-255*Pi^4*S^2)/8 + (37 - 2378*S^2 - 10122*S^4)/(16*S^2) + (Pi^2*(150 - 1152*S^2 - 3971*S^4))/(24*S^2) - 3064*S^2*HPL[{2, 1, 1}, -S^2] + ((-5 - 5*S^2 + 289*S^4 + 117*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((769*Pi^4*S^2)/12 + (Pi^2*(-125 + 1182*S^2 + 4043*S^4))/(12*S^2) + (-55 + 2402*S^2 + 10164*S^4)/(8*S^2) - (2*(-2 - 2*S^2 + 287*S^4 + 123*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-1423 - 10998*S^2 - 1317*S^4)/(16*S^2) + (Pi^2*(-332 - 2015*S^2 - 93*S^4))/(12*S^2) + (Pi^4*(-7153 - 7153*S^2 - 19471*S^4 + 2079*S^6))/(720*S^2*(1 + S^2)) + ((381 + 381*S^2 + 1581*S^4 + 13*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 24*S^2*HPL[{3, 2}, -S^2] + 22*S^2*HPL[{4, 1}, -S^2] + (8*(95 + 95*S^2 + 394*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 2984*S^2*HPL[{2, 2, 1}, -S^2] + 9032*S^2*HPL[{3, 1, 1}, -S^2] - 6136*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((Pi^2*S^2)/3 + (120 + 242*S^2 + 13*S^4)/(2*S^2))*Zeta[3]) + ((-15*(12 + 13*S^2))/8 + (Pi^2*(-8*S^2 + 73*S^4))/(6*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^2)*(379 + 2189*S^2))/(36*S^2) + ((1 + S^2)*(1195 + 7849*S^2))/(32*S^2) + (Pi^4*(7801 + 7801*S^2 + 72135*S^4 + 23403*S^6))/(2160*S^2*(1 + S^2)) + (98*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((-11*Pi^2*S^2)/9 + (2*(-15 - 8*S^2 + 7*S^4))/(3*S^2))*HPL[{3}, -S^2] + ((17 + 17*S^2 + 235*S^4 + 51*S^6)*HPL[{4}, -S^2])/(6*S^2*(1 + S^2)) + (46*S^2*HPL[{5}, -S^2])/3 + (-120*Pi^2*S^2 - (5*(55 + 294*S^2 + 239*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (4*(31 + 31*S^2 + 343*S^4 + 93*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (152*S^2*HPL[{3, 2}, -S^2])/3 + (364*S^2*HPL[{4, 1}, -S^2])/3 + (250*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3136*S^2*HPL[{2, 2, 1}, -S^2])/3 + (9272*S^2*HPL[{3, 1, 1}, -S^2])/3 - 2000*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-94*Pi^2*S^2)/9 - ((1 + S^2)*(107 + 201*S^2))/(6*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(289 + 1687*S^2))/(8*S^2) + (Pi^2*(623 + 623*S^2 + 6189*S^4 + 1869*S^6))/(36*S^2*(1 + S^2)) - (76*S^2*HPL[{3}, -S^2])/3 - (1568*S^2*HPL[{2, 1}, -S^2])/3 - (164*S^2*Zeta[3])/3) - (130*S^2*Zeta[5])/3) + HPL[{3}, -S^2]*((Pi^2*(49 + 133*S^2 + 152*S^4))/(24*S^2) + (1037 + 1584*S^2 + 2730*S^4)/(64*S^2) + (Pi^4*(437 + 437*S^2 + 250*S^4 - 350*S^6))/(1440*S^2*(1 + S^2)) + ((10 + 10*S^2 - 53*S^4 - 33*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + 4*S^2*HPL[{5}, -S^2] + (5*Pi^2*S^2 + (145 + 168*S^2 + 103*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + ((-13 - 13*S^2 + 205*S^4 + 69*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) + 16*S^2*HPL[{3, 2}, -S^2] - 22*S^2*HPL[{4, 1}, -S^2] + ((11 + 11*S^2 - 211*S^4 - 59*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 24*S^2*HPL[{2, 2, 1}, -S^2] + 24*S^2*HPL[{3, 1, 1}, -S^2] + 80*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-8*Pi^2*S^2)/3 + (-5 - 8*S^2 + 5*S^4)/(4*S^2))*Zeta[3] - 14*S^2*Zeta[5]) + Zeta[3]*((-320 - 829*S^2)/16 - (11*Pi^2*(20 + 21*S^2))/48 + (Pi^4*(110*S^2 + 797*S^4))/(360*(1 + S^2)) + 4*S^2*Zeta[5]) + HPL[{1}, -S^2]^2*((248987*Pi^6*S^2)/90720 + (Pi^2*(1 + S^2)*(309 + 2339*S^2))/(24*S^2) + (Pi^4*(1 + S^2)*(2516 + 12287*S^2))/(720*S^2) + ((1 + S^2)*(3697 + 27105*S^2))/(64*S^2) + ((551*Pi^2*S^2)/12 + (333 + 1492*S^2 + 1159*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 + 59*S^2*HPL[{2}, -S^2]^3 - 2*S^2*HPL[{3}, -S^2]^2 + ((20*Pi^2*S^2)/3 + (-19 + 160*S^2 + 179*S^4)/(8*S^2))*HPL[{4}, -S^2] + ((3 + 3*S^2 + 55*S^4 + 9*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) + (73*S^2*HPL[{6}, -S^2])/2 - 784*S^2*HPL[{2, 1}, -S^2]^2 + (-180*Pi^2*S^2 + (-273 - 1460*S^2 - 1187*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((97 + 97*S^2 + 1019*S^4 + 291*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) - 54*S^2*HPL[{5, 1}, -S^2] + (360*Pi^2*S^2 + (5*(55 + 294*S^2 + 239*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (4*(289 + 289*S^2 + 3185*S^4 + 867*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 1416*S^2*HPL[{3, 2, 1}, -S^2] + 4340*S^2*HPL[{4, 1, 1}, -S^2] - (750*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 3000*S^2*HPL[{3, 1, 1, 1}, -S^2] + 6000*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((1 + S^2)*(233 + 391*S^2))/(8*S^2) + (Pi^2*(-37 - 37*S^2 - 487*S^4 - 111*S^6))/(12*S^2*(1 + S^2)))*Zeta[3] + 17*S^2*Zeta[3]^2 + HPL[{3}, -S^2]*(((1 + S^2)*(-11 + 23*S^2))/S^2 + (Pi^2*(-1 - S^2 - 14*S^4 - 3*S^6))/(3*S^2*(1 + S^2)) + 76*S^2*HPL[{2, 1}, -S^2] - 4*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*((-3*(1 + S^2)*(289 + 1687*S^2))/(8*S^2) + (Pi^2*(-623 - 623*S^2 - 6189*S^4 - 1869*S^6))/(12*S^2*(1 + S^2)) + 164*S^2*Zeta[3]) + HPL[{2}, -S^2]*((2155*Pi^4*S^2)/144 + (Pi^2*(1 + S^2)*(417 + 2029*S^2))/(24*S^2) + ((1 + S^2)*(759 + 5471*S^2))/(16*S^2) - (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + 4*S^2*HPL[{4}, -S^2] - (196*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 784*S^2*HPL[{3, 1}, -S^2] + 1568*S^2*HPL[{2, 1, 1}, -S^2] - (41*(1 + S^2 + 11*S^4 + 3*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + ((-27 - 27*S^2 - 341*S^4 - 81*S^6)*Zeta[5])/(2*S^2*(1 + S^2))) + HPL[{2}, -S^2]*((235877*Pi^6*S^2)/90720 + (Pi^2*(297 + 3786*S^2 + 17560*S^4))/(192*S^2) + (1165 + 7413*S^2 + 24765*S^4)/(64*S^2) + (Pi^4*(-911 + 13526*S^2 + 47319*S^4))/(2880*S^2) - 4*S^2*HPL[{3}, -S^2]^2 + ((37*Pi^2*S^2)/12 + (31 - 6*S^2 + 131*S^4)/(8*S^2))*HPL[{4}, -S^2] + ((-9 - 9*S^2 + 57*S^4 + 49*S^6)*HPL[{5}, -S^2])/(4*S^2*(1 + S^2)) - (7*S^2*HPL[{6}, -S^2])/2 - 746*S^2*HPL[{2, 1}, -S^2]^2 + HPL[{3}, -S^2]*((17 - 60*S^2 + 77*S^4)/(8*S^2) + (Pi^2*(19 + 19*S^2 - 211*S^4 - 31*S^6))/(24*S^2*(1 + S^2)) - 12*S^2*HPL[{2, 1}, -S^2]) + ((-544*Pi^2*S^2)/3 + (-44 - 780*S^2 - 2317*S^4)/(4*S^2))*HPL[{3, 1}, -S^2] + ((-23 - 23*S^2 + 447*S^4 + 207*S^6)*HPL[{3, 2}, -S^2])/(4*S^2*(1 + S^2)) + ((-35 - 35*S^2 + 638*S^4 + 262*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + (3*S^2*HPL[{4, 2}, -S^2])/2 - 9*S^2*HPL[{5, 1}, -S^2] + (364*Pi^2*S^2 + (55 + 784*S^2 + 2312*S^4)/(2*S^2))*HPL[{2, 1, 1}, -S^2] - (2*(-196 - 196*S^2 - 685*S^4 + 23*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-1165 - 1165*S^2 - 4321*S^4 + 79*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 1476*S^2*HPL[{3, 2, 1}, -S^2] + 4478*S^2*HPL[{4, 1, 1}, -S^2] - (8*(95 + 95*S^2 + 394*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 38872*S^2*HPL[{3, 1, 1, 1}, -S^2] + 6136*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((16 - 102*S^2 - 195*S^4)/(4*S^2) + (Pi^2*(7 + 7*S^2 - 148*S^4 - 57*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] + 17*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-228 - 1139*S^2 + 8*S^4)/(2*S^2) + (Pi^2*(-308 - 308*S^2 - 1089*S^4 + 13*S^6))/(6*S^2*(1 + S^2)) + 4*S^2*Zeta[3]) + ((10 + 10*S^2 - 89*S^4 - 36*S^6)*Zeta[5])/(S^2*(1 + S^2))) + (15*(-7*S^2 + 3*S^4)*Zeta[7])/(2*(1 + S^2)) + HPL[{1}, -S^2]*((3*(1 + S^2)*(1507 + 10940*S^2))/(64*S^2) + (Pi^4*(1 + S^2)*(3543 + 26186*S^2))/(1440*S^2) + (Pi^2*(1 + S^2)*(5029 + 41847*S^2))/(384*S^2) + (Pi^6*(182305 + 182305*S^2 + 1542863*S^4 + 546915*S^6))/(181440*S^2*(1 + S^2)) + (59*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^3)/(4*S^2*(1 + S^2)) + ((-1 - S^2 - 19*S^4 - 3*S^6)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((23*Pi^2*S^2)/3 + (-6 + 23*S^2 + 29*S^4)/S^2)*HPL[{5}, -S^2] + ((9 + 9*S^2 + 319*S^4 + 27*S^6)*HPL[{6}, -S^2])/(4*S^2*(1 + S^2)) + 67*S^2*HPL[{7}, -S^2] - (196*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + (15*Pi^2*S^2 + (57 + 104*S^2 + 47*S^4)/(2*S^2))*HPL[{3, 2}, -S^2] + ((95*Pi^2*S^2)/3 + (361 + 464*S^2 + 103*S^4)/(4*S^2))*HPL[{4, 1}, -S^2] + (3*(1 + 3*S^4)*HPL[{4, 2}, -S^2])/(4*S^2) + 13*S^2*HPL[{4, 3}, -S^2] + ((-5 - 5*S^2 - 123*S^4 - 15*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) + 42*S^2*HPL[{5, 2}, -S^2] + 7*S^2*HPL[{6, 1}, -S^2] + ((1102*Pi^2*S^2)/3 + (333 + 1492*S^2 + 1159*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((3284*Pi^2*S^2)/3 + (939 + 4444*S^2 + 3505*S^4)/S^2)*HPL[{3, 1, 1}, -S^2] + (354*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)) - 120*S^2*HPL[{3, 2, 2}, -S^2] - 376*S^2*HPL[{3, 3, 1}, -S^2] + ((1079 + 1079*S^2 + 11917*S^4 + 3237*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 376*S^2*HPL[{4, 1, 2}, -S^2] - 1144*S^2*HPL[{4, 2, 1}, -S^2] - 2212*S^2*HPL[{5, 1, 1}, -S^2] + (-720*Pi^2*S^2 - (10*(55 + 294*S^2 + 239*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - 2832*S^2*HPL[{2, 2, 2, 1}, -S^2] - (24*(31 + 31*S^2 + 343*S^4 + 93*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 8800*S^2*HPL[{3, 1, 1, 2}, -S^2] + 8800*S^2*HPL[{3, 1, 2, 1}, -S^2] + 17296*S^2*HPL[{3, 2, 1, 1}, -S^2] + 51704*S^2*HPL[{4, 1, 1, 1}, -S^2] + (1500*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 6272*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] - 18816*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] - 31632*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] - 12000*S^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-229*Pi^4*S^2)/120 - (Pi^2*(1 + S^2)*(69 + 77*S^2))/(12*S^2) - ((1 + S^2)*(121 + 202*S^2))/(4*S^2))*Zeta[3] + ((9 + 9*S^2 + 95*S^4 + 27*S^6)*Zeta[3]^2)/(2*S^2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((3*(1 + S^2)*(289 + 1687*S^2))/(4*S^2) + (Pi^2*(623 + 623*S^2 + 6189*S^4 + 1869*S^6))/(6*S^2*(1 + S^2)) - 328*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((3*(1 + S^2)*(351 + 1553*S^2))/(32*S^2) + (Pi^2*(313 + 313*S^2 + 3143*S^4 + 939*S^6))/(24*S^2*(1 + S^2)) - 15*S^2*HPL[{3}, -S^2] - 354*S^2*HPL[{2, 1}, -S^2] - 41*S^2*Zeta[3]) + HPL[{4}, -S^2]*((3*(1 + S^2)*(2 + 21*S^2))/(2*S^2) + (Pi^2*(29 + 29*S^2 + 407*S^4 + 87*S^6))/(24*S^2*(1 + S^2)) - 8*S^2*HPL[{2, 1}, -S^2] - 4*S^2*Zeta[3]) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(877 + 5027*S^2))/(8*S^2) + (Pi^2*(-103 - 103*S^2 - 1029*S^4 - 309*S^6))/(2*S^2*(1 + S^2)) + 172*S^2*Zeta[3]) + HPL[{3}, -S^2]*((5*Pi^4*S^2)/12 + (Pi^2*(1 + S^2)*(-39 + 59*S^2))/(12*S^2) + ((1 + S^2)*(-43 + 347*S^2))/(8*S^2) - 5*S^2*HPL[{4}, -S^2] + (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 68*S^2*HPL[{3, 1}, -S^2] - 152*S^2*HPL[{2, 1, 1}, -S^2] + ((-1 - S^2 - 11*S^4 - 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-2155*Pi^4*S^2)/72 - (Pi^2*(1 + S^2)*(417 + 2029*S^2))/(12*S^2) - ((1 + S^2)*(759 + 5471*S^2))/(8*S^2) + 1568*S^2*HPL[{3, 1}, -S^2] + 3136*S^2*HPL[{2, 1, 1}, -S^2] + (41*(1 + S^2 + 11*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-27*Pi^2*S^2)/2 - (5*(1 + S^2)*(13 + 9*S^2))/(2*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(1231 + 8721*S^2))/(96*S^2) + ((1 + S^2)*(3019 + 24577*S^2))/(64*S^2) + (Pi^4*(6891 + 6891*S^2 + 63773*S^4 + 20673*S^6))/(1440*S^2*(1 + S^2)) + ((-15*Pi^2*S^2)/2 + (-57 - 104*S^2 - 47*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((1 + S^2 + 35*S^4 + 3*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + 2*S^2*HPL[{5}, -S^2] + ((-551*Pi^2*S^2)/3 + (-333 - 1492*S^2 - 1159*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] - (196*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 60*S^2*HPL[{3, 2}, -S^2] + 188*S^2*HPL[{4, 1}, -S^2] + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 1416*S^2*HPL[{2, 2, 1}, -S^2] - 4400*S^2*HPL[{3, 1, 1}, -S^2] - 3136*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-91*Pi^2*S^2)/6 - ((1 + S^2)*(55 + 107*S^2))/(2*S^2))*Zeta[3] - 53*S^2*Zeta[5]) - 75*S^2*Zeta[7])) + Log[T]*(-245/16 - (1761997*Pi^8*S^2)/2721600 + (Pi^6*(-75346 - 166299*S^2))/36288 + (Pi^4*(-4922 - 24243*S^2))/960 + (Pi^2*(-2391 - 20900*S^2))/192 - (S^2*HPL[{0}, S^2]^8)/96 + ((-29*Pi^2*S^2)/3 + (-23 - 106*S^2 - 83*S^4)/(3*S^2))*HPL[{1}, -S^2]^6 - (8*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)) - (8*S^2*HPL[{1}, -S^2]^8)/3 + HPL[{0}, S^2]^7*(-(S^2*(3 + 2*S^2))/(16*(1 + S^2)) - (S^2*HPL[{1}, -S^2])/16) + ((-401*Pi^2*S^2)/18 + (293 + 116*S^2 - 1678*S^4)/(24*S^2))*HPL[{2}, -S^2]^3 - (65*S^2*HPL[{2}, -S^2]^4)/4 + HPL[{0}, S^2]^6*((-47*Pi^2*S^2)/288 + (-20 - 77*S^2)/96 + ((-5 - 5*S^2 - 33*S^4 - 15*S^6)*HPL[{1}, -S^2])/(24*S^2*(1 + S^2)) - (3*S^2*HPL[{1}, -S^2]^2)/8 - (17*S^2*HPL[{2}, -S^2])/48) + ((-71*Pi^2*S^2)/6 + (-1 - 35*S^2 - 71*S^4)/(2*S^2))*HPL[{3}, -S^2]^2 - 8*S^2*HPL[{4}, -S^2]^2 + ((-7*Pi^2*S^2)/2 + (65 - 398*S^2 - 847*S^4)/(4*S^2))*HPL[{6}, -S^2] + ((-95 - 95*S^2 - 984*S^4 - 1044*S^6)*HPL[{7}, -S^2])/(2*S^2*(1 + S^2)) - 418*S^2*HPL[{8}, -S^2] + ((808*Pi^2*S^2)/3 + (193 + 1160*S^2 + 1852*S^4)/(2*S^2))*HPL[{2, 1}, -S^2]^2 - 796*S^2*HPL[{3, 1}, -S^2]^2 + ((-95*Pi^2*S^2)/2 + (49 - 210*S^2 - 575*S^4)/(4*S^2))*HPL[{4, 2}, -S^2] - (2*(2 + 2*S^2 - 43*S^4 + 4*S^6)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)) + ((-631*Pi^2*S^2)/3 + (-10 - 214*S^2 - 491*S^4)/S^2)*HPL[{5, 1}, -S^2] + ((-35 - 35*S^2 + 353*S^4 - 55*S^6)*HPL[{5, 2}, -S^2])/(2*S^2*(1 + S^2)) + 22*S^2*HPL[{5, 3}, -S^2] + (2*(2 + 2*S^2 + 22*S^4 + 71*S^6)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)) + 63*S^2*HPL[{6, 2}, -S^2] + 256*S^2*HPL[{7, 1}, -S^2] - 3160*S^2*HPL[{2, 1, 1}, -S^2]^2 + (26*Pi^2*S^2 + (-125 - 156*S^2 + 169*S^4)/(2*S^2))*HPL[{3, 1, 2}, -S^2] + ((-1526*Pi^2*S^2)/3 + (461 + 76*S^2 - 3187*S^4)/(2*S^2))*HPL[{3, 2, 1}, -S^2] + ((-57 - 57*S^2 + 9252*S^4 + 2732*S^6)*HPL[{3, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) + (4*(-33 - 33*S^2 + 3576*S^4 + 1084*S^6)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)) - 464*S^2*HPL[{3, 3, 2}, -S^2] + ((-4292*Pi^2*S^2)/3 + (885 + 584*S^2 - 4571*S^4)/S^2)*HPL[{4, 1, 1}, -S^2] + ((-131 - 131*S^2 + 14054*S^4 + 4242*S^6)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)) + 756*S^2*HPL[{4, 1, 3}, -S^2] + ((-395 - 395*S^2 + 43718*S^4 + 13314*S^6)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)) - 351*S^2*HPL[{4, 2, 2}, -S^2] + 2644*S^2*HPL[{4, 3, 1}, -S^2] + (2*(-393 - 393*S^2 + 44945*S^4 + 13625*S^6)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 1566*S^2*HPL[{5, 1, 2}, -S^2] + 10926*S^2*HPL[{5, 2, 1}, -S^2] + 28152*S^2*HPL[{6, 1, 1}, -S^2] - (8*(-149 + 164*S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((3008*Pi^2*S^2)/3 + (2*(-383 - 344*S^2 + 1618*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (2*(-1732 - 1732*S^2 - 2543*S^4 + 593*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (2*(-1732 - 1732*S^2 - 2543*S^4 + 593*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) - 168*S^2*HPL[{3, 1, 2, 2}, -S^2] + (2*(-3520 - 3520*S^2 - 575*S^4 + 2561*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 168*S^2*HPL[{3, 2, 1, 2}, -S^2] + 2968*S^2*HPL[{3, 2, 2, 1}, -S^2] + 9408*S^2*HPL[{3, 3, 1, 1}, -S^2] + (8*(-2663 - 2663*S^2 - 851*S^4 + 1833*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 1144*S^2*HPL[{4, 1, 1, 2}, -S^2] + 8264*S^2*HPL[{4, 1, 2, 1}, -S^2] + 27080*S^2*HPL[{4, 2, 1, 1}, -S^2] + 51280*S^2*HPL[{5, 1, 1, 1}, -S^2] + ((-6800*Pi^2*S^2)/3 - (20*(-53 - 2*S^2 + 370*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + (32*(73 + 73*S^2 + 464*S^4 + 72*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (96*(73 + 73*S^2 + 464*S^4 + 72*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 6272*S^2*HPL[{2, 2, 1, 2, 1}, -S^2] + 18816*S^2*HPL[{2, 2, 2, 1, 1}, -S^2] + (40*(295 + 295*S^2 + 2383*S^4 + 435*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 36992*S^2*HPL[{3, 1, 1, 1, 2}, -S^2] - 62080*S^2*HPL[{3, 1, 1, 2, 1}, -S^2] - 74624*S^2*HPL[{3, 1, 2, 1, 1}, -S^2] - 156160*S^2*HPL[{3, 2, 1, 1, 1}, -S^2] - 466080*S^2*HPL[{4, 1, 1, 1, 1}, -S^2] - (240*(-21 + 23*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + 10560*S^2*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 26880*S^2*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((Pi^2*S^2)/3 + (-18 - 53*S^2)/2)*Zeta[3]^2 + HPL[{4, 1}, -S^2]*((-153 - 1257*S^2 - 3214*S^4)/(2*S^2) + (Pi^2*(61 + 61*S^2 - 7896*S^4 - 2260*S^6))/(6*S^2*(1 + S^2)) - 492*S^2*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((643 + 3436*S^2 - 805*S^4)/S^2 - (4*Pi^2*(-321 - 321*S^2 - 201*S^4 + 191*S^6))/(3*S^2*(1 + S^2)) - 160*S^2*Zeta[3]) + HPL[{3, 2}, -S^2]*((43 - 618*S^2 - 1975*S^4)/(4*S^2) + (Pi^2*(55 + 55*S^2 - 4704*S^4 - 1400*S^6))/(12*S^2*(1 + S^2)) - 152*S^2*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((-2*(473 + 2630*S^2 + 138*S^4))/S^2 + (Pi^2*(-1800 - 1800*S^2 - 5387*S^4 - 91*S^6))/(3*S^2*(1 + S^2)) - 144*S^2*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((-733 - 3844*S^2 - 875*S^4)/(2*S^2) - (2*Pi^2*(299 + 299*S^2 + 1354*S^4 + 140*S^6))/(3*S^2*(1 + S^2)) - 144*S^2*Zeta[3]) + HPL[{0}, S^2]^4*((-2731*Pi^4*S^2)/2880 + (Pi^2*(-1106 - 4047*S^2))/576 + (-231 - 3977*S^2)/192 + ((-253 - 253*S^2 - 1895*S^4 - 759*S^6)*HPL[{1}, -S^2]^3)/(72*S^2*(1 + S^2)) - (71*S^2*HPL[{1}, -S^2]^4)/18 + ((-521*Pi^2*S^2)/144 + (60 - 456*S^2 - 1595*S^4)/(96*S^2))*HPL[{2}, -S^2] - (61*S^2*HPL[{2}, -S^2]^2)/12 + HPL[{1}, -S^2]^2*((-277*Pi^2*S^2)/72 + (-36 - 241*S^2 - 205*S^4)/(12*S^2) - (241*S^2*HPL[{2}, -S^2])/24) - ((2 + 3*S^2)*(2 - S^2 + S^4)*HPL[{3}, -S^2])/(16*S^2*(1 + S^2)) - (9*S^2*HPL[{4}, -S^2])/8 + ((120 + 120*S^2 + 210*S^4 - 31*S^6)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(303 + 3553*S^2))/(192*S^2) + (Pi^2*(-553 - 553*S^2 - 3875*S^4 - 1659*S^6))/(288*S^2*(1 + S^2)) + ((-57 - 57*S^2 - 412*S^4 - 171*S^6)*HPL[{2}, -S^2])/(12*S^2*(1 + S^2)) + (S^2*HPL[{3}, -S^2])/4 + (241*S^2*HPL[{2, 1}, -S^2])/12) + (259*S^2*HPL[{3, 1}, -S^2])/12 - (133*S^2*HPL[{2, 1, 1}, -S^2])/3 - (49*S^2*Zeta[3])/8) + HPL[{5}, -S^2]*((392 + 76*S^2 - 463*S^4)/(8*S^2) + (Pi^2*(7 + 7*S^2 + 433*S^4 - 47*S^6))/(12*S^2*(1 + S^2)) + 26*S^2*HPL[{2, 1}, -S^2] - 6*S^2*Zeta[3]) + HPL[{0}, S^2]^5*((-5*(16 + 171*S^2))/192 + (Pi^2*(-1651*S^2 - 1065*S^4))/(720*(1 + S^2)) + ((-255 - 255*S^2 - 1849*S^4 - 765*S^6)*HPL[{1}, -S^2]^2)/(240*S^2*(1 + S^2)) - (271*S^2*HPL[{1}, -S^2]^3)/180 - (S^2*(202 + 125*S^2)*HPL[{2}, -S^2])/(40*(1 + S^2)) + HPL[{1}, -S^2]*((-293*Pi^2*S^2)/360 + (-5 - 49*S^2 - 44*S^4)/(12*S^2) - (77*S^2*HPL[{2}, -S^2])/40) + (S^2*HPL[{3}, -S^2])/8 - (5*S^2*HPL[{2, 1}, -S^2])/12 - (3*S^2*Zeta[3])/4) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(221 + 1023*S^2))/(12*S^2) + (Pi^2*(-25 - 25*S^2 - 249*S^4 - 75*S^6))/(3*S^2*(1 + S^2)) - (13*(1 + 3*S^4)*HPL[{2}, -S^2])/S^2 + (380*S^2*HPL[{3}, -S^2])/3 + 100*S^2*Zeta[3]) + HPL[{4}, -S^2]*((33*Pi^4*S^2)/8 + (Pi^2*(19 + 178*S^2 + 315*S^4))/(24*S^2) + (181 + 1552*S^2 + 1360*S^4)/(16*S^2) + ((-120 - 120*S^2 - 459*S^4 - 7*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 538*S^2*HPL[{3, 1}, -S^2] + 1096*S^2*HPL[{2, 1, 1}, -S^2] + ((1 + S^2 + 55*S^4 - S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^4*((-6673*Pi^4*S^2)/540 - ((1 + S^2)*(159 + 896*S^2))/(4*S^2) - (Pi^2*(1 + S^2)*(301 + 1115*S^2))/(18*S^2) + ((-196*Pi^2*S^2)/9 - (3*(11 + 86*S^2 + 75*S^4))/(2*S^2))*HPL[{2}, -S^2] - (392*S^2*HPL[{2}, -S^2]^2)/3 + (20*(7 + 7*S^2 + 116*S^4 + 21*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + (332*S^2*HPL[{4}, -S^2])/3 + (65*(1 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 - (332*S^2*HPL[{3, 1}, -S^2])/3 + (10*(3 + 3*S^2 + 59*S^4 + 9*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-325*Pi^4*S^2)/3 + (713 + 186*S^2 - 8234*S^4)/(4*S^2) + (Pi^2*(337 - 580*S^2 - 3758*S^4))/(6*S^2) + (16*(3 + 3*S^2 + 273*S^4 + 77*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]^2*((-605*Pi^4*S^2)/48 + (-559 - 3126*S^2 - 7790*S^4)/(32*S^2) + (Pi^2*(-169 - 1732*S^2 - 3678*S^4))/(48*S^2) + ((17 + 17*S^2 + 2637*S^4 + 773*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) + (269*S^2*HPL[{4}, -S^2])/2 + ((149 - 164*S^4)*HPL[{2, 1}, -S^2])/S^2 + 314*S^2*HPL[{3, 1}, -S^2] - 784*S^2*HPL[{2, 1, 1}, -S^2] + ((-7 - 7*S^2 + 502*S^4 + 148*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3, 1}, -S^2]*((2981*Pi^4*S^2)/60 + (Pi^2*(-470 + 228*S^2 + 3503*S^4))/(12*S^2) + (-1179 - 1502*S^2 + 7384*S^4)/(8*S^2) + 2496*S^2*HPL[{2, 1, 1}, -S^2] - (2*(13 + 13*S^2 + 1122*S^4 + 314*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((240 + 227*S^2)/4 + (Pi^2*(492*S^2 + 73*S^4))/(3*(1 + S^2)))*Zeta[5] + HPL[{0}, S^2]^3*((-374 - 4599*S^2)/48 + (Pi^2*(-515 - 4061*S^2))/144 - (7*Pi^4*(2915*S^2 + 1773*S^4))/(2160*(1 + S^2)) + ((-67 - 67*S^2 - 566*S^4 - 201*S^6)*HPL[{1}, -S^2]^4)/(9*S^2*(1 + S^2)) - (73*S^2*HPL[{1}, -S^2]^5)/9 + ((1 + S^2 - 686*S^4 - 368*S^6)*HPL[{2}, -S^2]^2)/(12*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((-106*Pi^2*S^2)/9 + (-335 - 2048*S^2 - 1713*S^4)/(36*S^2) - (110*S^2*HPL[{2}, -S^2])/3) + ((2*Pi^2*S^2)/3 + (-13 - 52*S^2 - 54*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((-5 - 5*S^2 - 58*S^4 - 24*S^6)*HPL[{4}, -S^2])/(6*S^2*(1 + S^2)) + 2*S^2*HPL[{5}, -S^2] + ((-22*Pi^2*S^2)/9 + (320 + 1456*S^2 - 5*S^4)/(12*S^2))*HPL[{2, 1}, -S^2] + ((-10 - 10*S^2 + 1427*S^4 + 767*S^6)*HPL[{3, 1}, -S^2])/(6*S^2*(1 + S^2)) - (5*S^2*HPL[{3, 2}, -S^2])/3 - (19*S^2*HPL[{4, 1}, -S^2])/3 + ((10 + 10*S^2 - 1453*S^4 - 793*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) + (14*S^2*HPL[{2, 2, 1}, -S^2])/3 + 20*S^2*HPL[{3, 1, 1}, -S^2] - (76*S^2*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-19*Pi^2*S^2)/9 + (-6 - 101*S^2)/12)*Zeta[3] + HPL[{2}, -S^2]*((-360 - 1741*S^2)/24 + (Pi^2*(10 + 10*S^2 - 2665*S^4 - 1543*S^6))/(72*S^2*(1 + S^2)) + (2*S^2*HPL[{3}, -S^2])/3 - (7*S^2*HPL[{2, 1}, -S^2])/3 + (8*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(411 + 3641*S^2))/(48*S^2) + (Pi^2*(-523 - 523*S^2 - 4113*S^4 - 1569*S^6))/(72*S^2*(1 + S^2)) - (2*(31 + 31*S^2 + 258*S^4 + 93*S^6)*HPL[{2}, -S^2])/(3*S^2*(1 + S^2)) - 2*S^2*HPL[{3}, -S^2] + 110*S^2*HPL[{2, 1}, -S^2] + (11*S^2*Zeta[3])/3) + HPL[{1}, -S^2]*((-3997*Pi^4*S^2)/1080 - ((1 + S^2)*(141 + 1990*S^2))/(24*S^2) - (Pi^2*(1 + S^2)*(535 + 3473*S^2))/(144*S^2) + ((-187*Pi^2*S^2)/12 + (-71 - 488*S^2 - 417*S^4)/(6*S^2))*HPL[{2}, -S^2] - (53*S^2*HPL[{2}, -S^2]^2)/2 + ((-1 - S^2 - 7*S^4 - 3*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - (17*S^2*HPL[{4}, -S^2])/3 + (4*(31 + 31*S^2 + 258*S^4 + 93*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) + 110*S^2*HPL[{3, 1}, -S^2] - 220*S^2*HPL[{2, 1, 1}, -S^2] + ((-3 - 3*S^2 + 35*S^4 - 9*S^6)*Zeta[3])/(6*S^2*(1 + S^2))) - 13*S^2*Zeta[5]) + HPL[{2, 1}, -S^2]*((1297 + 16656*S^2 - 1157*S^4)/(16*S^2) + (Pi^2*(1427 + 7288*S^2 - 615*S^4))/(24*S^2) + (Pi^4*(7651 + 7651*S^2 + 8851*S^4 - 3275*S^6))/(360*S^2*(1 + S^2)) - (16*(31 + 31*S^2 + 248*S^4 + 52*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 148*S^2*HPL[{3, 2}, -S^2] - 184*S^2*HPL[{4, 1}, -S^2] - (16*(73 + 73*S^2 + 464*S^4 + 72*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 3136*S^2*HPL[{2, 2, 1}, -S^2] - 8768*S^2*HPL[{3, 1, 1}, -S^2] + 6320*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((-22*Pi^2*S^2)/3 + (-193 - 600*S^2 - 58*S^4)/S^2)*Zeta[3] + 20*S^2*Zeta[5]) + HPL[{3}, -S^2]*((Pi^2*(154 + 374*S^2 + 867*S^4))/(24*S^2) + (1629 + 3608*S^2 + 6308*S^4)/(32*S^2) + (Pi^4*(-177 - 177*S^2 + 19450*S^4 + 5026*S^6))/(720*S^2*(1 + S^2)) + ((4 + 4*S^2 - 197*S^4 - 25*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + ((80*Pi^2*S^2)/3 + (-605 - 1432*S^2 + 9*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((61 + 61*S^2 - 2307*S^4 - 739*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + 308*S^2*HPL[{3, 2}, -S^2] + 140*S^2*HPL[{4, 1}, -S^2] + (4*(-25 - 25*S^2 + 1156*S^4 + 372*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 304*S^2*HPL[{2, 2, 1}, -S^2] + 320*S^2*HPL[{3, 1, 1}, -S^2] + 640*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((38*Pi^2*S^2)/3 + (-13 + 36*S^2 + 41*S^4)/(2*S^2))*Zeta[3] + 28*S^2*Zeta[5]) + Zeta[3]*((Pi^2*(460 + 817*S^2))/24 + (1792 + 1157*S^2)/16 + (Pi^4*(3836*S^2 + 797*S^4))/(180*(1 + S^2)) + 100*S^2*Zeta[5]) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(1195 + 7849*S^2))/(16*S^2) - (Pi^2*(1 + S^2)*(1889 + 9231*S^2))/(72*S^2) + (Pi^4*(-8587 - 8587*S^2 - 79145*S^4 - 25761*S^6))/(1080*S^2*(1 + S^2)) - (196*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((994*Pi^2*S^2)/9 + (7*(49 + 148*S^2 + 99*S^4))/(3*S^2))*HPL[{3}, -S^2] + (16*(7 + 7*S^2 + 104*S^4 + 21*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) + 144*S^2*HPL[{5}, -S^2] + ((784*Pi^2*S^2)/9 + (6*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1}, -S^2] + (16*(14 + 14*S^2 - 41*S^4 + 42*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) - (3136*S^2*HPL[{3, 2}, -S^2])/3 - (10736*S^2*HPL[{4, 1}, -S^2])/3 - (260*(1 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (6272*S^2*HPL[{2, 2, 1}, -S^2])/3 - (11216*S^2*HPL[{3, 1, 1}, -S^2])/3 + ((832*Pi^2*S^2)/9 + (8*(1 + S^2)*(22 + 65*S^2))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(75 + 1021*S^2))/(4*S^2) + (Pi^2*(-251 - 251*S^2 - 1537*S^4 - 753*S^6))/(9*S^2*(1 + S^2)) + (1568*S^2*HPL[{3}, -S^2])/3 + (3136*S^2*HPL[{2, 1}, -S^2])/3 + (1568*S^2*Zeta[3])/3) + (1520*S^2*Zeta[5])/3) + HPL[{2}, -S^2]*((-200803*Pi^6*S^2)/45360 + (Pi^4*(2947 - 10398*S^2 - 45515*S^4))/(1440*S^2) + (1472 - 911*S^2 - 20900*S^4)/(32*S^2) + (Pi^2*(867 - 1698*S^2 - 16556*S^4))/(96*S^2) - 76*S^2*HPL[{3}, -S^2]^2 + ((269*Pi^2*S^2)/6 + (-25 + 202*S^2 + 477*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((5 + 5*S^2 + 383*S^4 + 55*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) + 13*S^2*HPL[{6}, -S^2] + 784*S^2*HPL[{2, 1}, -S^2]^2 + ((722*Pi^2*S^2)/3 + (312 + 1316*S^2 + 1669*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((5 + 5*S^2 - 4845*S^4 - 1429*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((69 + 69*S^2 - 7452*S^4 - 2312*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - 273*S^2*HPL[{4, 2}, -S^2] - 1266*S^2*HPL[{5, 1}, -S^2] + ((-1616*Pi^2*S^2)/3 + (-193 - 1160*S^2 - 1852*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(-149 + 164*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(-211 - 211*S^2 - 332*S^4 + 60*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 156*S^2*HPL[{3, 1, 2}, -S^2] - 1404*S^2*HPL[{3, 2, 1}, -S^2] - 3584*S^2*HPL[{4, 1, 1}, -S^2] + (16*(73 + 73*S^2 + 464*S^4 + 72*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 40128*S^2*HPL[{3, 1, 1, 1}, -S^2] - 6320*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((141 + 416*S^2 + 995*S^4)/(4*S^2) + (Pi^2*(7 + 7*S^2 + 599*S^4 + 168*S^6))/(3*S^2*(1 + S^2)))*Zeta[3] - 24*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((733 + 3844*S^2 + 875*S^4)/(4*S^2) + (Pi^2*(299 + 299*S^2 + 1354*S^4 + 140*S^6))/(3*S^2*(1 + S^2)) + 72*S^2*Zeta[3]) + HPL[{3}, -S^2]*((-87 + 260*S^2 + 1067*S^4)/(4*S^2) + (Pi^2*(-51 - 51*S^2 + 2407*S^4 + 755*S^6))/(12*S^2*(1 + S^2)) - 152*S^2*HPL[{2, 1}, -S^2] + 84*S^2*Zeta[3]) + (2*(10 + 10*S^2 + 458*S^4 + 97*S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^2*((-52285*Pi^6*S^2)/9072 - (Pi^2*(1 + S^2)*(1579 + 9787*S^2))/(48*S^2) - (Pi^4*(1 + S^2)*(6553 + 25601*S^2))/(720*S^2) - ((1 + S^2)*(3697 + 27105*S^2))/(32*S^2) + ((-607*Pi^2*S^2)/6 + (-333 - 1492*S^2 - 1159*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 - 74*S^2*HPL[{3}, -S^2]^2 + ((170*Pi^2*S^2)/3 + (377 + 860*S^2 + 483*S^4)/(4*S^2))*HPL[{4}, -S^2] + (2*(1 + S^2 + 219*S^4 + 3*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) + 89*S^2*HPL[{6}, -S^2] + 1568*S^2*HPL[{2, 1}, -S^2]^2 + ((220*Pi^2*S^2)/3 + (2*(-5 + 228*S^2 + 233*S^4))/S^2)*HPL[{3, 1}, -S^2] - (2*(113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) - (2*(395 + 395*S^2 + 6553*S^4 + 1185*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - 234*S^2*HPL[{4, 2}, -S^2] - 1352*S^2*HPL[{5, 1}, -S^2] + ((-784*Pi^2*S^2)/3 - (18*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (784*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (16*(112 + 112*S^2 + 1037*S^4 + 336*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 1328*S^2*HPL[{4, 1, 1}, -S^2] + (780*(1 + 3*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - 1328*S^2*HPL[{3, 1, 1, 1}, -S^2] + ((3*(1 + S^2)*(107 + 333*S^2))/(4*S^2) + (Pi^2*(49 + 49*S^2 + 979*S^4 + 147*S^6))/(3*S^2*(1 + S^2)))*Zeta[3] - 40*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((3*(1 + S^2)*(75 + 1021*S^2))/(4*S^2) + (Pi^2*(251 + 251*S^2 + 1537*S^4 + 753*S^6))/(3*S^2*(1 + S^2)) - 1568*S^2*Zeta[3]) + HPL[{3}, -S^2]*((3*(1 + S^2)*(107 + 201*S^2))/(2*S^2) + (Pi^2*(137 + 137*S^2 + 2399*S^4 + 411*S^6))/(6*S^2*(1 + S^2)) - 1568*S^2*HPL[{2, 1}, -S^2] + 100*S^2*Zeta[3]) + HPL[{2}, -S^2]*((-2021*Pi^4*S^2)/120 - (7*Pi^2*(1 + S^2)*(23 + 117*S^2))/(6*S^2) - ((1 + S^2)*(101 + 3541*S^2))/(8*S^2) + ((113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + 226*S^2*HPL[{4}, -S^2] + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 1568*S^2*HPL[{3, 1}, -S^2] - 3136*S^2*HPL[{2, 1, 1}, -S^2] + (112*(1 + S^2 + 17*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((51 + 51*S^2 + 1673*S^4 + 153*S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^2*((-95363*Pi^6*S^2)/45360 + (Pi^4*(-7348 - 24129*S^2))/1440 + (Pi^2*(-955 - 8094*S^2))/96 + (-389 - 5225*S^2)/16 + ((-11 - 11*S^2 - 95*S^4 - 33*S^6)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)) - (31*S^2*HPL[{1}, -S^2]^6)/3 + ((-219*Pi^2*S^2)/8 + (12 - 286*S^2 - 913*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 - (205*S^2*HPL[{2}, -S^2]^3)/6 + HPL[{1}, -S^2]^4*((-749*Pi^2*S^2)/36 + (-257 - 1242*S^2 - 985*S^4)/(12*S^2) - (196*S^2*HPL[{2}, -S^2])/3) + (3*S^2*HPL[{3}, -S^2]^2)/2 + ((-37*Pi^2*S^2)/12 + (13 - 58*S^2 - 148*S^4)/(8*S^2))*HPL[{4}, -S^2] + ((1 + S^2 - 4*S^4 - 16*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (39*S^2*HPL[{6}, -S^2])/2 + 413*S^2*HPL[{2, 1}, -S^2]^2 + ((227*Pi^2*S^2)/2 + (-87 + 572*S^2 + 1885*S^4)/(4*S^2))*HPL[{3, 1}, -S^2] + ((-1 - S^2 - 193*S^4 - 25*S^6)*HPL[{3, 2}, -S^2])/(4*S^2*(1 + S^2)) + ((23 + 23*S^2 - 290*S^4 - 22*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + (S^2*HPL[{4, 2}, -S^2])/2 + 15*S^2*HPL[{5, 1}, -S^2] + (-232*Pi^2*S^2 + (36 - 295*S^2 - 954*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (2*(-153 - 153*S^2 - 426*S^4 + 4*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-939 - 939*S^2 - 2454*S^4 + 38*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 2*S^2*HPL[{3, 1, 2}, -S^2] - 822*S^2*HPL[{3, 2, 1}, -S^2] - 2480*S^2*HPL[{4, 1, 1}, -S^2] - (2*(-327 - 327*S^2 - 747*S^4 + 37*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 1688*S^2*HPL[{3, 1, 1, 1}, -S^2] - 3440*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + ((3*(5 + S^2))/2 + (Pi^2*(-39*S^2 - 121*S^4))/(12*(1 + S^2)))*Zeta[3] - 2*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((392 + 1926*S^2 + 95*S^4)/(4*S^2) + (Pi^2*(189 + 189*S^2 + 389*S^4 - 33*S^6))/(4*S^2*(1 + S^2)) - 2*S^2*Zeta[3]) + HPL[{3}, -S^2]*((1 - 264*S^2 - 339*S^4)/(16*S^2) + (Pi^2*(-33 - 33*S^2 + 105*S^4 + 5*S^6))/(24*S^2*(1 + S^2)) + 2*S^2*Zeta[3]) + HPL[{1}, -S^2]^3*((-49*(1 + S^2)*(4 + 21*S^2))/(6*S^2) + (Pi^2*(-583 - 583*S^2 - 4745*S^4 - 1749*S^6))/(36*S^2*(1 + S^2)) + ((-307 - 307*S^2 - 2489*S^4 - 921*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) + (44*S^2*HPL[{3}, -S^2])/3 + (784*S^2*HPL[{2, 1}, -S^2])/3 + (82*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-8449*Pi^4*S^2)/720 - (Pi^2*(1 + S^2)*(401 + 1805*S^2))/(24*S^2) - ((1 + S^2)*(625 + 4411*S^2))/(16*S^2) + ((-211*Pi^2*S^2)/4 + (-223 - 1186*S^2 - 963*S^4)/(4*S^2))*HPL[{2}, -S^2] - (215*S^2*HPL[{2}, -S^2]^2)/2 + ((-3 - 3*S^2 + 79*S^4 - 9*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + 4*S^2*HPL[{4}, -S^2] + ((307 + 307*S^2 + 2489*S^4 + 921*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + 386*S^2*HPL[{3, 1}, -S^2] - 784*S^2*HPL[{2, 1, 1}, -S^2] + (2*(2 + 2*S^2 + 47*S^4 + 6*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]*((-867*Pi^4*S^2)/80 + (77 - 942*S^2 - 4161*S^4)/(16*S^2) + (Pi^2*(132 - 1046*S^2 - 3503*S^4))/(48*S^2) + ((-1 - S^2 + 95*S^4 + 11*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) - (5*S^2*HPL[{4}, -S^2])/2 + ((153 + 153*S^2 + 426*S^4 - 4*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 410*S^2*HPL[{3, 1}, -S^2] - 826*S^2*HPL[{2, 1, 1}, -S^2] + ((1 + S^2 + 53*S^4 + 14*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-19*S^2 - 58*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(509 + 4939*S^2))/(16*S^2) - (Pi^2*(1 + S^2)*(1087 + 7669*S^2))/(96*S^2) + (Pi^4*(-1837 - 1837*S^2 - 13960*S^4 - 5511*S^6))/(360*S^2*(1 + S^2)) + ((-149 - 149*S^2 - 1307*S^4 - 447*S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((25*Pi^2*S^2)/6 + (23 - 48*S^2 - 71*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((-23 - 23*S^2 - 37*S^4 - 69*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + 12*S^2*HPL[{5}, -S^2] + ((211*Pi^2*S^2)/2 + (223 + 1186*S^2 + 963*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + (4*(38 + 38*S^2 + 307*S^4 + 114*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 42*S^2*HPL[{3, 2}, -S^2] - 134*S^2*HPL[{4, 1}, -S^2] + ((-307 - 307*S^2 - 2489*S^4 - 921*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 860*S^2*HPL[{2, 2, 1}, -S^2] - 2492*S^2*HPL[{3, 1, 1}, -S^2] + 1568*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((41*Pi^2*S^2)/6 + ((1 + S^2)*(13 + 23*S^2))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(343 + 2073*S^2))/(8*S^2) + (Pi^2*(-535 - 535*S^2 - 4137*S^4 - 1605*S^6))/(24*S^2*(1 + S^2)) + 21*S^2*HPL[{3}, -S^2] + 430*S^2*HPL[{2, 1}, -S^2] + 39*S^2*Zeta[3]) + 39*S^2*Zeta[5])) + HPL[{0}, S^2]*((Pi^2*(-5252 - 41943*S^2))/192 + (Pi^4*(-954 - 5461*S^2))/144 - (3*(761 + 5470*S^2))/16 + (Pi^6*(-537029*S^2 - 288042*S^4))/(45360*(1 + S^2)) - (28*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)) - (32*S^2*HPL[{1}, -S^2]^7)/3 + ((19 + 19*S^2 - 1262*S^4 - 554*S^6)*HPL[{2}, -S^2]^3)/(6*S^2*(1 + S^2)) + HPL[{1}, -S^2]^5*((-241*Pi^2*S^2)/9 + (-23 - 106*S^2 - 83*S^4)/S^2 - 100*S^2*HPL[{2}, -S^2]) + ((2 + 2*S^2 + 29*S^4 + 21*S^6)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((Pi^2*S^2)/6 - (5*(1 + 8*S^2 + 20*S^4))/(2*S^2))*HPL[{5}, -S^2] + ((-10 - 10*S^2 - 78*S^4 - 5*S^6)*HPL[{6}, -S^2])/(S^2*(1 + S^2)) + 36*S^2*HPL[{7}, -S^2] + (4*(3 + 3*S^2 + 684*S^4 + 292*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-64*Pi^2*S^2)/3 + (61 - 92*S^2 - 3*S^4)/(4*S^2))*HPL[{3, 2}, -S^2] + (-63*Pi^2*S^2 + (87 - 18*S^2 + 53*S^4)/(2*S^2))*HPL[{4, 1}, -S^2] + ((-3 + 29*S^4)*HPL[{4, 2}, -S^2])/(2*S^2) - 26*S^2*HPL[{4, 3}, -S^2] + (3*(1 + S^2 + 65*S^4 + 29*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) - 71*S^2*HPL[{5, 2}, -S^2] - 130*S^2*HPL[{6, 1}, -S^2] + ((-20*Pi^2*S^2)/3 + (-611 - 2200*S^2 - 6*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((68*Pi^2*S^2)/3 + (-1868 - 6660*S^2 - 47*S^4)/S^2)*HPL[{3, 1, 1}, -S^2] + ((-3 - 16*S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((73 + 73*S^2 - 5064*S^4 - 2232*S^6)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)) + 282*S^2*HPL[{3, 2, 2}, -S^2] + 800*S^2*HPL[{3, 3, 1}, -S^2] - (2*(-111 - 111*S^2 + 7721*S^4 + 3381*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 802*S^2*HPL[{4, 1, 2}, -S^2] + 2338*S^2*HPL[{4, 2, 1}, -S^2] + 4564*S^2*HPL[{5, 1, 1}, -S^2] + ((-256*Pi^2*S^2)/3 + (2*(639 + 2254*S^2 + 20*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - 304*S^2*HPL[{2, 2, 2, 1}, -S^2] + (4*(-35 - 35*S^2 + 2673*S^4 + 1173*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 440*S^2*HPL[{3, 1, 1, 2}, -S^2] + 440*S^2*HPL[{3, 1, 2, 1}, -S^2] + 1352*S^2*HPL[{3, 2, 1, 1}, -S^2] + 4112*S^2*HPL[{4, 1, 1, 1}, -S^2] - (240*(-1 - S^2 + 90*S^4 + 40*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 272*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] + 816*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] + 2240*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] - 1440*S^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((373*Pi^4*S^2)/180 + (Pi^2*(74 + 131*S^2))/12 + (217 + 425*S^2)/4)*Zeta[3] - (2*(19*S^2 + 2*S^4)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((-103 + 1128*S^2 + 4835*S^4)/(4*S^2) + (5*Pi^2*(-9 - 9*S^2 + 820*S^4 + 388*S^6))/(6*S^2*(1 + S^2)) - 320*S^2*Zeta[3]) + HPL[{4}, -S^2]*((9 - 158*S^2 - 409*S^4)/(8*S^2) + (Pi^2*(-13 - 13*S^2 - 265*S^4 - 105*S^6))/(12*S^2*(1 + S^2)) - 34*S^2*HPL[{2, 1}, -S^2] - 2*S^2*Zeta[3]) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(221 + 1023*S^2))/(24*S^2) + (Pi^2*(-172 - 172*S^2 - 1721*S^4 - 516*S^6))/(9*S^2*(1 + S^2)) - (125*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) + (34*S^2*HPL[{3}, -S^2])/3 + 500*S^2*HPL[{2, 1}, -S^2] + (166*S^2*Zeta[3])/3) + HPL[{2}, -S^2]^2*((-141 - 1156*S^2 - 4691*S^4)/(16*S^2) + (Pi^2*(-5 - 5*S^2 - 2054*S^4 - 952*S^6))/(12*S^2*(1 + S^2)) + 36*S^2*HPL[{3}, -S^2] - 38*S^2*HPL[{2, 1}, -S^2] + 80*S^2*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((97 - 1172*S^2 - 4867*S^4)/(2*S^2) + (Pi^2*(40 + 40*S^2 - 4153*S^4 - 1993*S^6))/(3*S^2*(1 + S^2)) + 656*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*((-38*Pi^4*S^2)/9 + (Pi^2*(959 + 3710*S^2 + 15*S^4))/(12*S^2) + (1573 + 10058*S^2 + 778*S^4)/(8*S^2) - 72*S^2*HPL[{3, 1}, -S^2] - 136*S^2*HPL[{2, 1, 1}, -S^2] - (2*(43 + 43*S^2 + 164*S^4)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((3*Pi^4*S^2)/2 + (-83 - 334*S^2 - 432*S^4)/(8*S^2) + (Pi^2*(-61 - 164*S^2 - 137*S^4))/(24*S^2) + 10*S^2*HPL[{4}, -S^2] + ((-49 - 49*S^2 - 207*S^4 - 55*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 112*S^2*HPL[{3, 1}, -S^2] + 224*S^2*HPL[{2, 1, 1}, -S^2] + ((1 + S^2 + 9*S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^3*((-4061*Pi^4*S^2)/180 - ((1 + S^2)*(159 + 896*S^2))/(2*S^2) - (Pi^2*(1 + S^2)*(1025 + 4203*S^2))/(36*S^2) + (-120*Pi^2*S^2 - (5*(55 + 294*S^2 + 239*S^4))/(3*S^2))*HPL[{2}, -S^2] - (784*S^2*HPL[{2}, -S^2]^2)/3 + (4*(5 + 5*S^2 + 49*S^4 + 15*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (92*S^2*HPL[{4}, -S^2])/3 + (250*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 1000*S^2*HPL[{3, 1}, -S^2] - 2000*S^2*HPL[{2, 1, 1}, -S^2] + (8*(10 + 10*S^2 + 113*S^4 + 30*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + ((26*Pi^2*S^2)/3 + (54 + 145*S^2)/2)*Zeta[5] + HPL[{2}, -S^2]*((-173 - 5600*S^2 - 21943*S^4)/(32*S^2) + (Pi^2*(97 - 1892*S^2 - 8349*S^4))/(48*S^2) + (Pi^4*(131 + 131*S^2 - 22151*S^4 - 11376*S^6))/(360*S^2*(1 + S^2)) + (10*Pi^2*S^2 + (-31 + 40*S^2 - 9*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((-3 - 3*S^2 - 72*S^4 - 56*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - 9*S^2*HPL[{5}, -S^2] + ((10*Pi^2*S^2)/3 + (611 + 2200*S^2 + 6*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((11 + 11*S^2 + 2731*S^4 + 1163*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 144*S^2*HPL[{3, 2}, -S^2] - 398*S^2*HPL[{4, 1}, -S^2] - (8*(3 + 3*S^2 + 684*S^4 + 292*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 152*S^2*HPL[{2, 2, 1}, -S^2] - 232*S^2*HPL[{3, 1, 1}, -S^2] + 136*S^2*HPL[{2, 1, 1, 1}, -S^2] + (30*Pi^2*S^2 + (-10 + 82*S^2 + 201*S^4)/(2*S^2))*Zeta[3] + 106*S^2*Zeta[5]) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(379 + 2189*S^2))/(12*S^2) - (3*(1 + S^2)*(1195 + 7849*S^2))/(32*S^2) + (Pi^4*(-7801 - 7801*S^2 - 72135*S^4 - 23403*S^6))/(720*S^2*(1 + S^2)) - (98*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)) + ((11*Pi^2*S^2)/3 - (2*(-15 - 8*S^2 + 7*S^4))/S^2)*HPL[{3}, -S^2] + ((-17 - 17*S^2 - 235*S^4 - 51*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - 46*S^2*HPL[{5}, -S^2] + (360*Pi^2*S^2 + (5*(55 + 294*S^2 + 239*S^4))/S^2)*HPL[{2, 1}, -S^2] + (12*(31 + 31*S^2 + 343*S^4 + 93*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 152*S^2*HPL[{3, 2}, -S^2] - 364*S^2*HPL[{4, 1}, -S^2] - (750*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 3136*S^2*HPL[{2, 2, 1}, -S^2] - 9272*S^2*HPL[{3, 1, 1}, -S^2] + 6000*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((94*Pi^2*S^2)/3 + ((1 + S^2)*(107 + 201*S^2))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-3*(1 + S^2)*(289 + 1687*S^2))/(8*S^2) + (Pi^2*(-623 - 623*S^2 - 6189*S^4 - 1869*S^6))/(12*S^2*(1 + S^2)) + 76*S^2*HPL[{3}, -S^2] + 1568*S^2*HPL[{2, 1}, -S^2] + 164*S^2*Zeta[3]) + 130*S^2*Zeta[5]) + HPL[{1}, -S^2]*((-248987*Pi^6*S^2)/45360 - (Pi^2*(1 + S^2)*(309 + 2339*S^2))/(12*S^2) - (Pi^4*(1 + S^2)*(2516 + 12287*S^2))/(360*S^2) - ((1 + S^2)*(3697 + 27105*S^2))/(32*S^2) + ((-551*Pi^2*S^2)/6 + (-333 - 1492*S^2 - 1159*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 - 118*S^2*HPL[{2}, -S^2]^3 + 4*S^2*HPL[{3}, -S^2]^2 + ((-40*Pi^2*S^2)/3 + (19 - 160*S^2 - 179*S^4)/(4*S^2))*HPL[{4}, -S^2] - (2*(3 + 3*S^2 + 55*S^4 + 9*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - 73*S^2*HPL[{6}, -S^2] + 1568*S^2*HPL[{2, 1}, -S^2]^2 + (360*Pi^2*S^2 + (273 + 1460*S^2 + 1187*S^4)/S^2)*HPL[{3, 1}, -S^2] - (38*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((-97 - 97*S^2 - 1019*S^4 - 291*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) + 108*S^2*HPL[{5, 1}, -S^2] + (-720*Pi^2*S^2 - (10*(55 + 294*S^2 + 239*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (784*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (8*(289 + 289*S^2 + 3185*S^4 + 867*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 2832*S^2*HPL[{3, 2, 1}, -S^2] - 8680*S^2*HPL[{4, 1, 1}, -S^2] + (1500*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 6000*S^2*HPL[{3, 1, 1, 1}, -S^2] - 12000*S^2*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(233 + 391*S^2))/(4*S^2) + (Pi^2*(37 + 37*S^2 + 487*S^4 + 111*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] - 34*S^2*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((3*(1 + S^2)*(289 + 1687*S^2))/(4*S^2) + (Pi^2*(623 + 623*S^2 + 6189*S^4 + 1869*S^6))/(6*S^2*(1 + S^2)) - 328*S^2*Zeta[3]) + HPL[{3}, -S^2]*((-2*(1 + S^2)*(-11 + 23*S^2))/S^2 + (2*Pi^2*(1 + S^2 + 14*S^4 + 3*S^6))/(3*S^2*(1 + S^2)) - 152*S^2*HPL[{2, 1}, -S^2] + 8*S^2*Zeta[3]) + HPL[{2}, -S^2]*((-2155*Pi^4*S^2)/72 - (Pi^2*(1 + S^2)*(417 + 2029*S^2))/(12*S^2) - ((1 + S^2)*(759 + 5471*S^2))/(8*S^2) + (19*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - 8*S^2*HPL[{4}, -S^2] + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + 1568*S^2*HPL[{3, 1}, -S^2] - 3136*S^2*HPL[{2, 1, 1}, -S^2] + (41*(1 + S^2 + 11*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((27 + 27*S^2 + 341*S^4 + 81*S^6)*Zeta[5])/(S^2*(1 + S^2)))) + (3*(337*S^2 + 15*S^4)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((-29*Pi^4*(1 + S^2)*(172 + 931*S^2))/(720*S^2) - (3*(1 + S^2)*(1507 + 10940*S^2))/(32*S^2) - (Pi^2*(1 + S^2)*(5621 + 43303*S^2))/(192*S^2) + (Pi^6*(-37673 - 37673*S^2 - 322159*S^4 - 113019*S^6))/(18144*S^2*(1 + S^2)) - (83*(1 + 3*S^4)*HPL[{2}, -S^2]^3)/(6*S^2) - (37*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)) + (40*Pi^2*S^2 + (63 + 10*S^2 - 53*S^4)/S^2)*HPL[{5}, -S^2] + ((-119 - 119*S^2 - S^4 - 357*S^6)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)) + 30*S^2*HPL[{7}, -S^2] + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-826*Pi^2*S^2)/3 + (-249 - 832*S^2 - 583*S^4)/S^2)*HPL[{3, 2}, -S^2] + ((-2818*Pi^2*S^2)/3 + (-1871 - 5852*S^2 - 3981*S^4)/(2*S^2))*HPL[{4, 1}, -S^2] - (117*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) + 94*S^2*HPL[{4, 3}, -S^2] - (26*(9 + 9*S^2 + 131*S^4 + 27*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) + 204*S^2*HPL[{5, 2}, -S^2] - 98*S^2*HPL[{6, 1}, -S^2] + ((-2428*Pi^2*S^2)/3 - (2*(333 + 1492*S^2 + 1159*S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((-5296*Pi^2*S^2)/3 - (32*(41 + 215*S^2 + 174*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] - (332*(1 + 3*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + 3260*S^2*HPL[{3, 2, 2}, -S^2] + 9968*S^2*HPL[{3, 3, 1}, -S^2] - (4*(193 + 193*S^2 - 85*S^4 + 579*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 9812*S^2*HPL[{4, 1, 2}, -S^2] + 30404*S^2*HPL[{4, 2, 1}, -S^2] + 62640*S^2*HPL[{5, 1, 1}, -S^2] + ((1568*Pi^2*S^2)/3 + (36*(11 + 86*S^2 + 75*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (32*(14 + 14*S^2 - 41*S^4 + 42*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - 6272*S^2*HPL[{3, 1, 1, 2}, -S^2] - 6272*S^2*HPL[{3, 1, 2, 1}, -S^2] - 6272*S^2*HPL[{3, 2, 1, 1}, -S^2] - 21472*S^2*HPL[{4, 1, 1, 1}, -S^2] - (1560*(1 + 3*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + 12544*S^2*HPL[{2, 1, 2, 1, 1}, -S^2] + 37632*S^2*HPL[{2, 2, 1, 1, 1}, -S^2] + 77920*S^2*HPL[{3, 1, 1, 1, 1}, -S^2] + ((1013*Pi^4*S^2)/60 + (Pi^2*(1 + S^2)*(101 + 283*S^2))/(6*S^2) + ((1 + S^2)*(329 + 965*S^2))/(4*S^2))*Zeta[3] + ((-9 - 9*S^2 - 107*S^4 - 27*S^6)*Zeta[3]^2)/(S^2*(1 + S^2)) + HPL[{3, 1}, -S^2]*((21*(1 + S^2)*(-11 + 107*S^2))/(4*S^2) + (8*Pi^2*(26 + 26*S^2 + 133*S^4 + 78*S^6))/(3*S^2*(1 + S^2)) - 1616*S^2*Zeta[3]) + HPL[{4}, -S^2]*(((1 + S^2)*(429 + 391*S^2))/(4*S^2) + (Pi^2*(89 + 89*S^2 + 1627*S^4 + 267*S^6))/(12*S^2*(1 + S^2)) - 452*S^2*HPL[{2, 1}, -S^2] + 56*S^2*Zeta[3]) + HPL[{2}, -S^2]^2*((-3*(1 + S^2)*(351 + 1553*S^2))/(16*S^2) + (Pi^2*(-345 - 345*S^2 - 3463*S^4 - 1035*S^6))/(12*S^2*(1 + S^2)) + 466*S^2*HPL[{3}, -S^2] + 354*S^2*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-3*(1 + S^2)*(75 + 1021*S^2))/(2*S^2) - (2*Pi^2*(251 + 251*S^2 + 1537*S^4 + 753*S^6))/(3*S^2*(1 + S^2)) + 3136*S^2*Zeta[3]) + HPL[{2, 1}, -S^2]*((2021*Pi^4*S^2)/60 + (7*Pi^2*(1 + S^2)*(23 + 117*S^2))/(3*S^2) + ((1 + S^2)*(101 + 3541*S^2))/(4*S^2) - 3136*S^2*HPL[{3, 1}, -S^2] - 6272*S^2*HPL[{2, 1, 1}, -S^2] - (224*(1 + S^2 + 17*S^4 + 3*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((601*Pi^4*S^2)/30 + (Pi^2*(1 + S^2)*(183 + 311*S^2))/(6*S^2) + ((1 + S^2)*(307 + 511*S^2))/(2*S^2) - 86*S^2*HPL[{4}, -S^2] - (2*(113 + 113*S^2 + 1907*S^4 + 339*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - 1568*S^2*HPL[{3, 1}, -S^2] + 3136*S^2*HPL[{2, 1, 1}, -S^2] + (8*(3 + 3*S^2 + 34*S^4 + 9*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((419*Pi^2*S^2)/3 + (2*(1 + S^2)*(20 + 83*S^2))/S^2)*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(911 + 7209*S^2))/(48*S^2) - ((1 + S^2)*(-79 + 16995*S^2))/(32*S^2) + (Pi^4*(-6575 - 6575*S^2 - 43977*S^4 - 19725*S^6))/(720*S^2*(1 + S^2)) + ((413*Pi^2*S^2)/3 + (249 + 832*S^2 + 583*S^4)/(2*S^2))*HPL[{3}, -S^2] + (113*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + 164*S^2*HPL[{5}, -S^2] + ((1214*Pi^2*S^2)/3 + (333 + 1492*S^2 + 1159*S^4)/S^2)*HPL[{2, 1}, -S^2] + (392*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - 1708*S^2*HPL[{3, 2}, -S^2] - 5140*S^2*HPL[{4, 1}, -S^2] - (784*(1 + S^2 + 11*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + 3136*S^2*HPL[{3, 1, 1}, -S^2] + 6272*S^2*HPL[{2, 1, 1, 1}, -S^2] + ((431*Pi^2*S^2)/3 + (4*(1 + S^2)*(31 + 72*S^2))/S^2)*Zeta[3] + 722*S^2*Zeta[5]) + 966*S^2*Zeta[7])) - 784*S^2*Zeta[9];
E5vwuT3F1=(3*(-1802 + 8365*S^2))/(64*S) + (Pi^6*S*(123798 + 19685*S^2))/30240 + (Pi^4*(-2176 + 120284*S^2 - 1697*S^4))/(5760*S) + (Pi^2*(-588 + 11393*S^2 - 288*S^4))/(96*S) + (Pi^8*S*(2753669 + 2155978*S^2 + 72581*S^4))/(1360800*(1 + S^2)^2) + ((58*Pi^2*S)/21 + (19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8)/(21*S*(1 + S^2)^2))*HPL[{1}, -S^2]^7 - (2*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^8)/(3*S*(1 + S^2)^2) + (16*S*HPL[{1}, -S^2]^9)/27 + HPL[{0}, S^2]^8*(-(S^3*(5 + 4*S^2))/(192*(1 + S^2)^2) + (S*HPL[{1}, -S^2])/96) + ((-14 + 371*S^2 + 304*S^4 + 15*S^6)*HPL[{2}, -S^2]^4)/(6*S*(1 + S^2)^2) + HPL[{0}, S^2]^7*((Pi^2*S)/96 + (S*(8 + 7*S^2 + 11*S^4 + 6*S^6))/(96*(1 + S^2)^2) + ((-2 + 14*S^2 + 19*S^4 + 6*S^6)*HPL[{1}, -S^2])/(48*S*(1 + S^2)^2) + (S*HPL[{1}, -S^2]^2)/16 + (S*HPL[{2}, -S^2])/16) + (16*S*HPL[{3}, -S^2]^3)/3 + ((-14 - 26*S^2 + 35*S^4 + 38*S^6)*HPL[{4}, -S^2]^2)/(S*(1 + S^2)^2) + ((-131*Pi^2*S)/3 + (-630 - 730*S^2 + 563*S^4 + 1284*S^6 + 681*S^8)/(2*S*(1 + S^2)^2))*HPL[{7}, -S^2] + ((105 - 1186*S^2 - 2417*S^4 - 1180*S^6)*HPL[{8}, -S^2])/(S*(1 + S^2)^2) - 918*S*HPL[{9}, -S^2] - (1568*S*HPL[{2, 1}, -S^2]^3)/3 + (2*(-97 + 1760*S^2 + 1481*S^4 + 90*S^6)*HPL[{3, 1}, -S^2]^2)/(S*(1 + S^2)^2) + (-11*Pi^2*S + (36 + 200*S^2 + 353*S^4 + 74*S^6 - 21*S^8)/(S*(1 + S^2)^2))*HPL[{4, 3}, -S^2] + ((-58*Pi^2*S)/3 + (282 + 1112*S^2 + 1597*S^4 + 230*S^6 - 129*S^8)/(2*S*(1 + S^2)^2))*HPL[{5, 2}, -S^2] + (2*S*(31 + 92*S^2 + 55*S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 - 224*S*HPL[{5, 4}, -S^2] + (75*Pi^2*S + (430 - 238*S^2 - 1753*S^4 - 1252*S^6 - 363*S^8)/(2*S*(1 + S^2)^2))*HPL[{6, 1}, -S^2] + (2*(-11 + 34*S^2 + 176*S^4 + 116*S^6)*HPL[{6, 2}, -S^2])/(S*(1 + S^2)^2) - 868*S*HPL[{6, 3}, -S^2] + ((21 - 274*S^2 - 881*S^4 - 532*S^6)*HPL[{7, 1}, -S^2])/(S*(1 + S^2)^2) - 2190*S*HPL[{7, 2}, -S^2] - 4212*S*HPL[{8, 1}, -S^2] + (16*(-25 + 783*S^2 + 661*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(S*(1 + S^2)^2) + (-559*Pi^2*S + (62 - 594*S^2 + 4797*S^4 - 1172*S^6 - 105*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 2, 2}, -S^2] + ((-5224*Pi^2*S)/3 - (2*(-55 + 294*S^2 - 3914*S^4 + 808*S^6 + 87*S^8))/(S*(1 + S^2)^2))*HPL[{3, 3, 1}, -S^2] + ((-17 + 768*S^2 + 257*S^4 - 262*S^6)*HPL[{3, 3, 2}, -S^2])/(S*(1 + S^2)^2) + (-1731*Pi^2*S + (202 - 1064*S^2 + 15469*S^4 - 3234*S^6 - 345*S^8)/(2*S*(1 + S^2)^2))*HPL[{4, 1, 2}, -S^2] + (2*(17 - 718*S^2 - 352*S^4 + 156*S^6)*HPL[{4, 1, 3}, -S^2])/(S*(1 + S^2)^2) + (-5311*Pi^2*S + (718 - 3128*S^2 + 48697*S^4 - 9330*S^6 - 1065*S^8)/(2*S*(1 + S^2)^2))*HPL[{4, 2, 1}, -S^2] - (2*(3 - 214*S^2 + 33*S^4 + 156*S^6)*HPL[{4, 2, 2}, -S^2])/(S*(1 + S^2)^2) - 88*S*HPL[{4, 2, 3}, -S^2] + (2*(43 - 2158*S^2 - 810*S^4 + 664*S^6)*HPL[{4, 3, 1}, -S^2])/(S*(1 + S^2)^2) + 10*S*HPL[{4, 3, 2}, -S^2] + 44*S*HPL[{4, 4, 1}, -S^2] + ((-32738*Pi^2*S)/3 - (2*(-505 + 916*S^2 - 26107*S^4 + 4323*S^6 + 531*S^8))/(S*(1 + S^2)^2))*HPL[{5, 1, 1}, -S^2] + ((59 - 2596*S^2 - 1149*S^4 + 662*S^6)*HPL[{5, 1, 2}, -S^2])/(S*(1 + S^2)^2) - 132*S*HPL[{5, 1, 3}, -S^2] + ((359 - 17476*S^2 - 6009*S^4 + 5822*S^6)*HPL[{5, 2, 1}, -S^2])/(S*(1 + S^2)^2) + 4*S*HPL[{5, 2, 2}, -S^2] - 92*S*HPL[{5, 3, 1}, -S^2] + (2*(400 - 22324*S^2 - 6703*S^4 + 8192*S^6)*HPL[{6, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 118*S*HPL[{6, 1, 2}, -S^2] - 762*S*HPL[{6, 2, 1}, -S^2] - 2944*S*HPL[{7, 1, 1}, -S^2] + ((1672*Pi^2*S)/3 + (4*(-131 - 864*S^2 + 158*S^4 + 15*S^6))/(S*(1 + S^2)))*HPL[{2, 2, 2, 1}, -S^2] + (-516*Pi^2*S - (2*(-751 - 6015*S^2 - 1639*S^4 + 513*S^6 + 24*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1, 2}, -S^2] + (-516*Pi^2*S - (2*(-751 - 6015*S^2 - 1639*S^4 + 513*S^6 + 24*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 2, 1}, -S^2] + ((-47 + 446*S^2 + 253*S^4 - 84*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(S*(1 + S^2)^2) + (-2188*Pi^2*S - (2*(-1537 - 11985*S^2 - 5875*S^4 + 1551*S^6 + 114*S^8))/(S*(1 + S^2)^2))*HPL[{3, 2, 1, 1}, -S^2] + ((-47 + 446*S^2 + 253*S^4 - 84*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(S*(1 + S^2)^2) + ((-575 - 850*S^2 - 915*S^4 - 452*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + 6208*S*HPL[{3, 2, 2, 2}, -S^2] + 19456*S*HPL[{3, 2, 3, 1}, -S^2] - (48*(33 + 81*S^2 + 73*S^4 + 23*S^6)*HPL[{3, 3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 19152*S*HPL[{3, 3, 1, 2}, -S^2] + 59136*S*HPL[{3, 3, 2, 1}, -S^2] + ((-18904*Pi^2*S)/3 - (2*(-4428 - 35788*S^2 - 16179*S^4 + 4778*S^6 + 333*S^8))/(S*(1 + S^2)^2))*HPL[{4, 1, 1, 1}, -S^2] - (2*(-7 - 570*S^2 + 51*S^4 + 380*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(S*(1 + S^2)^2) - 120296*S*HPL[{4, 1, 1, 3}, -S^2] - (2*(785 + 1374*S^2 + 1803*S^4 + 932*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(S*(1 + S^2)^2) - 101230*S*HPL[{4, 1, 2, 2}, -S^2] - 180808*S*HPL[{4, 1, 3, 1}, -S^2] - (2*(2369 + 5262*S^2 + 5307*S^4 + 2036*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 62158*S*HPL[{4, 2, 1, 2}, -S^2] - 61246*S*HPL[{4, 2, 2, 1}, -S^2] - 357464*S*HPL[{4, 3, 1, 1}, -S^2] - (4*(2361 + 4164*S^2 + 5345*S^4 + 2722*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 363284*S*HPL[{5, 1, 1, 2}, -S^2] - 599540*S*HPL[{5, 1, 2, 1}, -S^2] - 1429172*S*HPL[{5, 2, 1, 1}, -S^2] - 3570432*S*HPL[{6, 1, 1, 1}, -S^2] + ((-3248*Pi^2*S)/3 - (8*(105 + 1070*S^2 - 509*S^4 + 112*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 2, 1, 1}, -S^2] + (-3248*Pi^2*S - (24*(105 + 1070*S^2 - 509*S^4 + 112*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{2, 2, 1, 1, 1}, -S^2] - (96*(11 + 7*S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S - (288*(11 + 7*S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S + 6048*S*HPL[{2, 2, 2, 2, 1}, -S^2] + ((-23744*Pi^2*S)/3 - (8*(439 + 5356*S^2 - 4115*S^4 + 834*S^6 + 126*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1, 1, 1}, -S^2] + (8*(770 + 551*S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S + (8*(1298 + 887*S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S + 5408*S*HPL[{3, 1, 1, 2, 2}, -S^2] + (8*(1562 + 1055*S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S + 5408*S*HPL[{3, 1, 2, 1, 2}, -S^2] - 288*S*HPL[{3, 1, 2, 2, 1}, -S^2] - 49824*S*HPL[{3, 1, 3, 1, 1}, -S^2] + (8*(3278 + 2147*S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S + 23552*S*HPL[{3, 2, 1, 1, 2}, -S^2] + 17856*S*HPL[{3, 2, 1, 2, 1}, -S^2] + 10016*S*HPL[{3, 2, 2, 1, 1}, -S^2] + 12768*S*HPL[{3, 3, 1, 1, 1}, -S^2] + (32*(2475 + 6298*S^2 + 5586*S^4 + 1680*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 69296*S*HPL[{4, 1, 1, 1, 2}, -S^2] + 52208*S*HPL[{4, 1, 1, 2, 1}, -S^2] + 28688*S*HPL[{4, 1, 2, 1, 1}, -S^2] + 36080*S*HPL[{4, 2, 1, 1, 1}, -S^2] + 65568*S*HPL[{5, 1, 1, 1, 1}, -S^2] + ((7328*Pi^2*S)/3 + (8*(-334 - 1936*S^2 + 391*S^4 + 45*S^6))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 12544*S*HPL[{2, 2, 1, 2, 1, 1}, -S^2] - 37632*S*HPL[{2, 2, 2, 1, 1, 1}, -S^2] - (16*(165 - 88*S^2 + 159*S^4 + 246*S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 89088*S*HPL[{3, 1, 1, 1, 1, 2}, -S^2] + 164352*S*HPL[{3, 1, 1, 1, 2, 1}, -S^2] + 214528*S*HPL[{3, 1, 1, 2, 1, 1}, -S^2] + 239616*S*HPL[{3, 1, 2, 1, 1, 1}, -S^2] + 402688*S*HPL[{3, 2, 1, 1, 1, 1}, -S^2] + 1213888*S*HPL[{4, 1, 1, 1, 1, 1}, -S^2] + (1920*(2 + 3*S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + 24896*S*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] + 99584*S*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] + 248960*S*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] + 466176*S*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + 53760*S*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((-16*Pi^2*S)/9 + (32*S*(-1 + S^2))/(3*(1 + S^2)^2) - (16*S*HPL[{0}, S^2]^2)/3 + (16*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^2) - (64*S*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*((32*S*(-3 - S^2 + S^4))/(3*(1 + S^2)^2) - (64*S*HPL[{1}, -S^2])/3) - (32*S*HPL[{2}, -S^2])/3)*Log[T]^7 + ((8*S*(4 + 3*S^2))/(3*(1 + S^2)^2) + (16*S*HPL[{0}, S^2])/3 + (16*S*HPL[{1}, -S^2])/3)*Log[T]^8 + (-(S*(-68 + 11*S^2))/2 - (Pi^2*S*(-72 + S^2 + 44*S^4))/(6*(1 + S^2)^2))*Zeta[3]^2 - 32*S*Zeta[3]^3 + HPL[{2, 1, 1, 1, 1}, -S^2]*((16*(-6 + 54*S^2 + 211*S^4 + 12*S^6))/S^3 + (16*Pi^2*(35 + 556*S^2 + 517*S^4 + 94*S^6))/(3*S*(1 + S^2)^2) - 12224*S*Zeta[3]) + HPL[{4, 1, 1}, -S^2]*((-108 + 827*S^2 + 5184*S^4 + 142*S^6)/(2*S^3) + (Pi^2*(453 + 5202*S^2 + 4985*S^4 + 1048*S^6))/(3*S*(1 + S^2)^2) - 9032*S*Zeta[3]) + HPL[{3, 2, 1}, -S^2]*((-68 + 151*S^2 + 2932*S^4 + 79*S^6)/(4*S^3) + (Pi^2*(257 + 4046*S^2 + 3481*S^4 + 460*S^6))/(6*S*(1 + S^2)^2) - 2960*S*Zeta[3]) + HPL[{2}, -S^2]^3*((-2 + 9*S^2 + 84*S^4 + 4*S^6)/(3*S^3) + (Pi^2*(19 + 253*S^2 + 209*S^4 + 23*S^6))/(9*S*(1 + S^2)^2) - (422*S*HPL[{3}, -S^2])/3 - 126*S*HPL[{2, 1}, -S^2] - 122*S*Zeta[3]) + Log[T]^6*(S + (Pi^2*S*(120 + 95*S^2 + 4*S^4))/(3*(1 + S^2)^2) + (50*S*HPL[{0}, S^2]^3)/9 + ((58*Pi^2*S)/3 + (19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8)/(3*S*(1 + S^2)^2))*HPL[{1}, -S^2] - (56*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)^2) + (448*S*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]^2*((S*(136 + 117*S^2 + 12*S^4))/(3*(1 + S^2)^2) + (62*S*HPL[{1}, -S^2])/3) + (8*(2 + 3*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{0}, S^2]*(18*Pi^2*S + (S*(136 - 11*S^2 + 80*S^4 + 3*S^6))/(3*(1 + S^2)^2) - (56*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2])/(3*S*(1 + S^2)^2) + (224*S*HPL[{1}, -S^2]^2)/3 + (212*S*HPL[{2}, -S^2])/3) - (236*S*HPL[{3}, -S^2])/3 + (224*S*HPL[{2, 1}, -S^2])/3 - (224*S*Zeta[3])/3) + HPL[{1}, -S^2]^6*(((1 + S^2)*(283 + 33*S^2))/(36*S) + (Pi^2*(-25 + 274*S^2 + 188*S^4 - 24*S^6))/(9*S*(1 + S^2)^2) + (13*(-1 + 6*S^2)*HPL[{2}, -S^2])/(3*S) - (380*S*HPL[{3}, -S^2])/9 - (100*S*Zeta[3])/3) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(-47 + 92*S^2))/(6*S) + (-4 - 137*S^2 + 244*S^4 - 49*S^6)/(4*S^3) - 32*S*Zeta[3]) + HPL[{0}, S^2]^6*((S*(293 + 46*S^2))/192 - (Pi^2*S*(-60 - 5*S^2 + 32*S^4))/(288*(1 + S^2)^2) + ((-5 + 38*S^2 + 46*S^4 + 12*S^6)*HPL[{1}, -S^2]^2)/(24*S*(1 + S^2)^2) + (S*HPL[{1}, -S^2]^3)/4 + (S*(108 + 151*S^2 + 56*S^4)*HPL[{2}, -S^2])/(96*(1 + S^2)^2) + HPL[{1}, -S^2]*((23*Pi^2*S)/144 + (69 + 488*S^2 + 424*S^4 + 146*S^6 - 3*S^8)/(192*S*(1 + S^2)^2) + (13*S*HPL[{2}, -S^2])/48) - (S*HPL[{3}, -S^2])/16 + (S*HPL[{2, 1}, -S^2])/6 + (S*Zeta[3])/4) + HPL[{0}, S^2]^5*((5597*Pi^4*S)/43200 - (S*(-358 + 167*S^2))/384 + (Pi^2*S*(2115 + 2264*S^2 + 1981*S^4 + 660*S^6))/(1440*(1 + S^2)^2) + ((-255 + 2104*S^2 + 2263*S^4 + 446*S^6)*HPL[{1}, -S^2]^3)/(360*S*(1 + S^2)^2) + (271*S*HPL[{1}, -S^2]^4)/360 + ((571*Pi^2*S)/720 - (S*(-395 - 493*S^2 - 247*S^4 + 5*S^6))/(80*(1 + S^2)^2))*HPL[{2}, -S^2] + (9*S*HPL[{2}, -S^2]^2)/10 + HPL[{1}, -S^2]^2*((293*Pi^2*S)/360 + (305 + 2530*S^2 + 1827*S^4 + 701*S^6 + 15*S^8)/(240*S*(1 + S^2)^2) + (77*S*HPL[{2}, -S^2])/40) + (S*(5 + 5*S^2 + S^4)*HPL[{3}, -S^2])/(8*(1 + S^2)^2) + (5*S*HPL[{4}, -S^2])/8 + (7*(30 - 52*S^2 - 29*S^4 + 20*S^6)*HPL[{2, 1}, -S^2])/(120*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(-133 + 5*S^2))/(48*S) + (Pi^2*(-675 + 5044*S^2 + 6253*S^4 + 1706*S^6))/(1440*S*(1 + S^2)^2) + (7*(-5 + 42*S^2 + 44*S^4 + 8*S^6)*HPL[{2}, -S^2])/(40*S*(1 + S^2)^2) + (S*HPL[{3}, -S^2])/4 - (77*S*HPL[{2, 1}, -S^2])/20) - (87*S*HPL[{3, 1}, -S^2])/20 + (128*S*HPL[{2, 1, 1}, -S^2])/15 + (17*S*Zeta[3])/4) + HPL[{3}, -S^2]^2*((19 - 163*S^2 + 15*S^4)/(4*S) - (Pi^2*S*(-82 + 21*S^2 + 66*S^4))/(6*(1 + S^2)^2) - 20*S*HPL[{2, 1}, -S^2] + 30*S*Zeta[3]) + HPL[{6}, -S^2]*((Pi^2*(-60 - 226*S^2 + 63*S^4 + 162*S^6))/(6*S*(1 + S^2)^2) + (140 - 905*S^2 + 1536*S^4 + 201*S^6)/(2*S^3) + 142*S*HPL[{2, 1}, -S^2] + 42*S*Zeta[3]) + HPL[{4, 2}, -S^2]*((Pi^2*(1 + 130*S^2 - 28*S^4 - 100*S^6))/(3*S*(1 + S^2)^2) + (-8 + 197*S^2 - 388*S^4 + 97*S^6)/(4*S^3) + 62*S*Zeta[3]) + HPL[{5, 1}, -S^2]*((Pi^2*(35 + 1632*S^2 - 301*S^4 - 1206*S^6))/(6*S*(1 + S^2)^2) + (-88 + 209*S^2 - 2844*S^4 + 385*S^6)/(4*S^3) + 260*S*Zeta[3]) + HPL[{2, 1}, -S^2]^2*((Pi^2*(46 - 2510*S^2 - 2123*S^4 - 174*S^6))/(3*S*(1 + S^2)^2) + (-4 + 25*S^2 - 810*S^4 + 22*S^6)/(2*S^3) + 1488*S*Zeta[3]) + HPL[{3, 1, 1, 1}, -S^2]*((44 - 559*S^2 - 1776*S^4 - 57*S^6)/S^3 - (4*Pi^2*(94 + 841*S^2 + 850*S^4 + 213*S^6))/(3*S*(1 + S^2)^2) + 6176*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((3137*Pi^4*S)/90 + (-8 - 13*S^2 - 1466*S^4 + 565*S^6)/(8*S^3) + (Pi^2*(-29 - 89*S^2 - 1558*S^4 + 193*S^6 + 39*S^8))/(6*S*(1 + S^2)^2) + 6536*S*HPL[{2, 1, 1}, -S^2] + ((-1 + 158*S^2 + 59*S^4 - 48*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2, 1, 1, 1}, -S^2]*((1229*Pi^4*S)/15 + (-10 - 1837*S^2 - 518*S^4 + 104*S^6)/S^3 + (Pi^2*(-594 - 4630*S^2 - 2029*S^4 + 496*S^6 + 57*S^8))/(3*S*(1 + S^2)^2) + (32*(-25 + 346*S^2 + 277*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{5}, -S^2]*((-1381*Pi^4*S)/180 + (-280 - 2191*S^2 - 956*S^4 - 230*S^6)/(8*S^3) + (Pi^2*(58 + 373*S^2 + 709*S^4 + 178*S^6 + 24*S^8))/(6*S*(1 + S^2)^2) + ((-49 + 824*S^2 + 975*S^4 + 266*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 276*S*HPL[{3, 1}, -S^2] - 708*S*HPL[{2, 1, 1}, -S^2] + ((15 + 88*S^2 + 71*S^4 + 10*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((971*Pi^4*S)/30 + (-20 + 1213*S^2 - 340*S^4 + 160*S^6)/(2*S^3) + (Pi^2*(426 + 4168*S^2 - 1063*S^4 + 90*S^6 + 39*S^8))/(6*S*(1 + S^2)^2) - (8*(-54 + 622*S^2 + 521*S^4 + 22*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^5*((6673*Pi^4*S)/1350 + ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(60*S^3) + (Pi^2*(281 + 4618*S^2 + 26*S^4 + 954*S^6 + 45*S^8))/(90*S*(1 + S^2)^2) + ((392*Pi^2*S)/45 + (4*(16 + 129*S^2 + 16*S^4))/(5*S*(1 + S^2)))*HPL[{2}, -S^2] + (784*S*HPL[{2}, -S^2]^2)/15 + (4*(14 - 246*S^2 - 59*S^4 + 106*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (664*S*HPL[{4}, -S^2])/15 - (26*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S + (664*S*HPL[{3, 1}, -S^2])/15 + (4*(3 - 62*S^2 - 8*S^4 + 32*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{4, 1}, -S^2]*((6901*Pi^4*S)/60 + (-8 - 722*S^2 - 4828*S^4 + 1825*S^6)/(8*S^3) + (Pi^2*(-189 - 488*S^2 - 5592*S^4 + 466*S^6 + 123*S^8))/(6*S*(1 + S^2)^2) + 20928*S*HPL[{2, 1, 1}, -S^2] - (2*(1 - 352*S^2 - 177*S^4 + 70*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3, 1, 1}, -S^2]*((553*Pi^4*S)/30 + (-34 + 8379*S^2 - 462*S^4 + 353*S^6)/(4*S^3) + (Pi^2*(1500 + 12878*S^2 + 617*S^4 - 136*S^6 + 33*S^8))/(6*S*(1 + S^2)^2) - (4*(-321 + 3902*S^2 + 3207*S^4 + 96*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + Log[T]^5*((-5*S)/2 - (449*Pi^4*S)/90 - (Pi^2*S*(706 - 183*S^2 + 164*S^4 + 9*S^6))/(18*(1 + S^2)^2) - (19*S*HPL[{0}, S^2]^4)/6 + (-58*Pi^2*S + (-19 - 336*S^2 + 54*S^4 - 80*S^6 - 3*S^8)/(S*(1 + S^2)^2))*HPL[{1}, -S^2]^2 + (112*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^2) - (224*S*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*(-(S*(340 + 315*S^2 + 48*S^4))/(9*(1 + S^2)^2) - (146*S*HPL[{1}, -S^2])/9) + ((-340*Pi^2*S)/9 + (-10 - 232*S^2 - 155*S^4 - 9*S^6)/(3*S*(1 + S^2)))*HPL[{2}, -S^2] - (158*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((-47*Pi^2*S)/3 - (S*(370 + 153*S^2 + 164*S^4 + 9*S^6))/(6*(1 + S^2)^2) - (2*(-11 + 106*S^2 + 90*S^4 + 4*S^6)*HPL[{1}, -S^2])/(S*(1 + S^2)^2) - 62*S*HPL[{1}, -S^2]^2 - (172*S*HPL[{2}, -S^2])/3) - (2*(3 - 340*S^2 + 261*S^4 + 414*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + 72*S*HPL[{4}, -S^2] + (12*(-7 + 22*S^2)*HPL[{2, 1}, -S^2])/S + 176*S*HPL[{3, 1}, -S^2] - 448*S*HPL[{2, 1, 1}, -S^2] - (4*S*(-34 + 57*S^2 + 66*S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{0}, S^2]*(-(S*(298 + 33*S^2))/6 + (Pi^2*S*(-844 - 483*S^2 + 120*S^4))/(9*(1 + S^2)^2) + (56*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^2) - (448*S*HPL[{1}, -S^2]^3)/3 + (4*(-1 - 76*S^2 - 24*S^4 + 26*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + HPL[{1}, -S^2]*((-482*Pi^2*S)/9 + (-19 - 336*S^2 + 54*S^4 - 80*S^6 - 3*S^8)/(S*(1 + S^2)^2) - 200*S*HPL[{2}, -S^2]) + (44*S*HPL[{3}, -S^2])/3 - 24*S*HPL[{2, 1}, -S^2] + 48*S*Zeta[3]) + HPL[{1}, -S^2]*(-((1 + S^2)*(283 + 33*S^2))/(6*S) + (2*Pi^2*(25 - 274*S^2 - 188*S^4 + 24*S^6))/(3*S*(1 + S^2)^2) - (26*(-1 + 6*S^2)*HPL[{2}, -S^2])/S + (760*S*HPL[{3}, -S^2])/3 + 200*S*Zeta[3])) + ((-782*Pi^4*S)/45 + (-32 + 2072*S^2 - 143*S^4)/(8*S) - (Pi^2*S*(-340 - 1669*S^2 + 506*S^4 + 159*S^6))/(12*(1 + S^2)^2))*Zeta[5] + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-44 + 407*S^2 + 1670*S^4 + 90*S^6))/(6*S^3) + (-233 + 1986*S^2 + 4881*S^4 + 106*S^6)/(4*S^3) + (Pi^4*(1076 + 33404*S^2 + 33265*S^4 + 7000*S^6))/(180*S*(1 + S^2)^2) + 6272*S*HPL[{2, 2, 1}, -S^2] + 4992*S*HPL[{3, 1, 1}, -S^2] - 12448*S*HPL[{2, 1, 1, 1}, -S^2] + (-560*Pi^2*S - (2*(-74 + 90*S^2 - 1061*S^4 + 376*S^6 + 33*S^8))/(S*(1 + S^2)^2))*Zeta[3] - 2928*S*Zeta[5]) + Log[T]^4*((3*(-4 + 9*S^2))/(4*S) + (Pi^2*S*(467 + 24*S^2))/18 + (Pi^4*S*(29270 + 25175*S^2 + 2578*S^4))/(540*(1 + S^2)^2) + (281*S*HPL[{0}, S^2]^5)/180 + ((290*Pi^2*S)/3 + (5*(19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8))/(3*S*(1 + S^2)^2))*HPL[{1}, -S^2]^3 - (140*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)^2) + (224*S*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^4*((S*(397 + 439*S^2 + 113*S^4))/(18*(1 + S^2)^2) + (71*S*HPL[{1}, -S^2])/9) + (2*(-25 + 783*S^2 + 661*S^4 + 49*S^6)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^2) + HPL[{0}, S^2]^3*((328*Pi^2*S)/27 + (S*(981 + 786*S^2 + 544*S^4 + 9*S^6))/(18*(1 + S^2)^2) + ((-134 + 1266*S^2 + 1109*S^4 + 74*S^6)*HPL[{1}, -S^2])/(9*S*(1 + S^2)^2) + (365*S*HPL[{1}, -S^2]^2)/9 + (349*S*HPL[{2}, -S^2])/9) + ((-938*Pi^2*S)/9 - (2*(-43 + 3*S^2 - 785*S^4 + 137*S^6 + 18*S^8))/(3*S*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*S*(-227 - 39*S^2 + 105*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - 148*S*HPL[{5}, -S^2] + ((916*Pi^2*S)/9 + (-334 - 1936*S^2 + 391*S^4 + 45*S^6)/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (2*(165 - 88*S^2 + 159*S^4 + 246*S^6)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^2) + (3296*S*HPL[{3, 2}, -S^2])/3 + (10616*S*HPL[{4, 1}, -S^2])/3 + (80*(2 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/S + (3112*S*HPL[{2, 2, 1}, -S^2])/3 + 752*S*HPL[{3, 1, 1}, -S^2] + 2240*S*HPL[{2, 1, 1, 1}, -S^2] + ((-310*Pi^2*S)/3 - (S*(122 - 987*S^2 + 436*S^4 + 45*S^6))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((2*(-6 + 54*S^2 + 211*S^4 + 12*S^6))/(3*S^3) + (2*Pi^2*(35 + 556*S^2 + 517*S^4 + 94*S^6))/(9*S*(1 + S^2)^2) - 576*S*HPL[{3}, -S^2] - (1556*S*HPL[{2, 1}, -S^2])/3 - (1528*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(283 + 33*S^2))/(12*S) - (5*Pi^2*(25 - 274*S^2 - 188*S^4 + 24*S^6))/(3*S*(1 + S^2)^2) + (65*(-1 + 6*S^2)*HPL[{2}, -S^2])/S - (1900*S*HPL[{3}, -S^2])/3 - 500*S*Zeta[3]) + HPL[{0}, S^2]^2*((S*(889 + 48*S^2))/12 + (Pi^2*S*(3628 + 3511*S^2 + 632*S^4))/(36*(1 + S^2)^2) + (5*(-11 + 106*S^2 + 90*S^4 + 4*S^6)*HPL[{1}, -S^2]^2)/(S*(1 + S^2)^2) + (310*S*HPL[{1}, -S^2]^3)/3 + (2*(5 + 451*S^2 + 397*S^4 + 49*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((749*Pi^2*S)/18 + (277 + 4196*S^2 + 862*S^4 + 708*S^6 + 45*S^8)/(12*S*(1 + S^2)^2) + (392*S*HPL[{2}, -S^2])/3) - (53*S*HPL[{3}, -S^2])/3 + (76*S*HPL[{2, 1}, -S^2])/3 - 30*S*Zeta[3]) + HPL[{1}, -S^2]*((6673*Pi^4*S)/270 + ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(12*S^3) + (Pi^2*(281 + 4618*S^2 + 26*S^4 + 954*S^6 + 45*S^8))/(18*S*(1 + S^2)^2) + ((392*Pi^2*S)/9 + (4*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] + (784*S*HPL[{2}, -S^2]^2)/3 + (20*(14 - 246*S^2 - 59*S^4 + 106*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (664*S*HPL[{4}, -S^2])/3 - (130*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S + (664*S*HPL[{3, 1}, -S^2])/3 + (20*(3 - 62*S^2 - 8*S^4 + 32*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]*((2473*Pi^4*S)/108 + (S*(1607 + 141*S^2))/12 + (Pi^2*S*(4002 + 1407*S^2 + 2288*S^4 + 63*S^6))/(36*(1 + S^2)^2) - (280*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^2) + (560*S*HPL[{1}, -S^2]^4)/3 + ((1144*Pi^2*S)/9 + (58 + 2054*S^2 + 263*S^4 + 1312*S^6 + 45*S^8)/(6*S*(1 + S^2)^2))*HPL[{2}, -S^2] + (767*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((1205*Pi^2*S)/9 + (5*(19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8))/(2*S*(1 + S^2)^2) + 500*S*HPL[{2}, -S^2]) + ((-27 - 100*S^2 + 51*S^4 + 90*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + 32*S*HPL[{4}, -S^2] - (10*(-27 + 148*S^2 + 127*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (3152*S*HPL[{3, 1}, -S^2])/3 + 2120*S*HPL[{2, 1, 1}, -S^2] + (2*S*(-266 - 117*S^2 + 66*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((5*(1 + S^2)*(283 + 33*S^2))/(12*S) + (Pi^2*(-344 + 3786*S^2 + 2579*S^4 - 346*S^6))/(9*S*(1 + S^2)^2) - (125*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (68*S*HPL[{3}, -S^2])/3 - 1000*S*HPL[{2, 1}, -S^2] - (332*S*Zeta[3])/3)) - 580*S*Zeta[5]) + HPL[{2}, -S^2]^2*((64 - 70*S^2 + 1698*S^4 - 85*S^6)/(16*S^3) + (Pi^2*(2 - 27*S^2 + 786*S^4 + 2*S^6))/(24*S^3) + (Pi^4*(-110 + 13183*S^2 + 11711*S^4 + 1415*S^6))/(360*S*(1 + S^2)^2) + ((-449*Pi^2*S)/6 + (28 - 222*S^2 + 1365*S^4 - 276*S^6 - 27*S^8)/(4*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((5 - 486*S^2 - 167*S^4 + 160*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) - 97*S*HPL[{5}, -S^2] + ((209*Pi^2*S)/3 + (-131 - 864*S^2 + 158*S^4 + 15*S^6)/(2*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-171 + 144*S^2 - 19*S^4 - 170*S^6)*HPL[{3, 1}, -S^2])/(2*S*(1 + S^2)^2) + 805*S*HPL[{3, 2}, -S^2] + 2591*S*HPL[{4, 1}, -S^2] + (12*(11 + 7*S^2)*HPL[{2, 1, 1}, -S^2])/S + 756*S*HPL[{2, 2, 1}, -S^2] + 556*S*HPL[{3, 1, 1}, -S^2] + 1568*S*HPL[{2, 1, 1, 1}, -S^2] + ((-409*Pi^2*S)/6 + (6 - 112*S^2 + 973*S^4 - 358*S^6 - 33*S^8)/(4*S*(1 + S^2)^2))*Zeta[3] - 341*S*Zeta[5]) + HPL[{1}, -S^2]^4*((Pi^2*(1 + S^2)*(-4 + 2891*S^2 + 269*S^4))/(144*S^3) + ((1 + S^2)*(-28 + 3449*S^2 + 335*S^4))/(48*S^3) + (Pi^4*(-8587 + 87732*S^2 + 67765*S^4 - 1862*S^6))/(2160*S*(1 + S^2)^2) - (98*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^2) + ((-497*Pi^2*S)/9 + (131 - 646*S^2 + 2836*S^4 - 202*S^6 - 15*S^8)/(6*S*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*(14 - 222*S^2 - 71*S^4 + 82*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) - 72*S*HPL[{5}, -S^2] + ((-392*Pi^2*S)/9 - (4*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (4*(-28 - 54*S^2 + 391*S^4 + 334*S^6)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^2) + (1568*S*HPL[{3, 2}, -S^2])/3 + (5368*S*HPL[{4, 1}, -S^2])/3 + (130*(-1 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/S + (3136*S*HPL[{2, 2, 1}, -S^2])/3 + (5608*S*HPL[{3, 1, 1}, -S^2])/3 + ((-416*Pi^2*S)/9 - (2*(2 + 211*S^2 - 418*S^4 + 123*S^6))/(3*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(4 - 173*S^2 + 6*S^4))/(2*S^3) + (Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(18*S*(1 + S^2)^2) - (784*S*HPL[{3}, -S^2])/3 - (1568*S*HPL[{2, 1}, -S^2])/3 - (784*S*Zeta[3])/3) - (760*S*Zeta[5])/3) + HPL[{0}, S^2]^4*((Pi^2*S*(2887 + 347*S^2))/288 + (-72 + 10360*S^2 - 867*S^4)/(384*S) - (Pi^4*S*(-7867 - 5689*S^2 + 169*S^4))/(4320*(1 + S^2)^2) + ((-253 + 2148*S^2 + 2215*S^4 + 382*S^6)*HPL[{1}, -S^2]^4)/(144*S*(1 + S^2)^2) + (71*S*HPL[{1}, -S^2]^5)/45 + ((3 + 326*S^2 + 343*S^4 + 80*S^6)*HPL[{2}, -S^2]^2)/(24*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((277*Pi^2*S)/108 + (431 + 4196*S^2 + 2388*S^4 + 910*S^6 + 15*S^8)/(144*S*(1 + S^2)^2) + (241*S*HPL[{2}, -S^2])/36) + ((-11*Pi^2*S)/24 + (5 + 36*S^2 + 47*S^4 + 14*S^6)/(8*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((1 + 2*S^2)*(-3 + 2*S^4)*HPL[{4}, -S^2])/(4*S*(1 + S^2)^2) - (13*S*HPL[{5}, -S^2])/4 + ((85*Pi^2*S)/72 + (-164 - 953*S^2 - 255*S^4 + 49*S^6 - 3*S^8)/(24*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*(((1 + S^2)*(1079 + 7*S^2))/(96*S) + (Pi^2*(-553 + 4428*S^2 + 4975*S^4 + 1102*S^6))/(288*S*(1 + S^2)^2) + ((-114 + 938*S^2 + 1013*S^4 + 202*S^6)*HPL[{2}, -S^2])/(24*S*(1 + S^2)^2) - (S*HPL[{3}, -S^2])/4 - (241*S*HPL[{2, 1}, -S^2])/12) - (S*(661 + 737*S^2 + 193*S^4)*HPL[{3, 1}, -S^2])/(12*(1 + S^2)^2) + (13*S*HPL[{4, 1}, -S^2])/4 + ((12 + 1416*S^2 + 1591*S^4 + 428*S^6)*HPL[{2, 1, 1}, -S^2])/(12*S*(1 + S^2)^2) - (2*S*HPL[{2, 2, 1}, -S^2])/3 - (11*S*HPL[{3, 1, 1}, -S^2])/2 + (25*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((97*Pi^2*S)/72 - (S*(-137 - 113*S^2 + 14*S^4))/(8*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-4 + 43*S^2 + 164*S^4 - 7*S^6)/(16*S^3) + (Pi^2*(3 + 759*S^2 + 964*S^4 + 317*S^6))/(72*S*(1 + S^2)^2) + (S*HPL[{2, 1}, -S^2])/3 + (5*S*Zeta[3])/4) + HPL[{1}, -S^2]*((2009*Pi^4*S)/2160 - ((1 + S^2)*(-6 - 1403*S^2 + 3*S^4))/(96*S^3) + (Pi^2*(733 + 5758*S^2 + 4374*S^4 + 1550*S^6 - 15*S^8))/(288*S*(1 + S^2)^2) + ((109*Pi^2*S)/36 + (103 + 977*S^2 + 606*S^4 + 217*S^6 + 3*S^8)/(24*S*(1 + S^2)^2))*HPL[{2}, -S^2] + 5*S*HPL[{2}, -S^2]^2 + ((-2 + 6*S^2 + 23*S^4 + 14*S^6)*HPL[{3}, -S^2])/(4*S*(1 + S^2)^2) - (S*HPL[{4}, -S^2])/2 + ((114 - 938*S^2 - 1013*S^4 - 202*S^6)*HPL[{2, 1}, -S^2])/(12*S*(1 + S^2)^2) - (39*S*HPL[{3, 1}, -S^2])/2 + (241*S*HPL[{2, 1, 1}, -S^2])/6 + (5*(-1 + 6*S^2)*Zeta[3])/(8*S)) + (65*S*Zeta[5])/12) + HPL[{4}, -S^2]*((-476 - 1195*S^2 + 4808*S^4 - 874*S^6)/(16*S^3) + (Pi^2*(-6 + 139*S^2 + 432*S^4 + 14*S^6))/(12*S^3) + (Pi^4*(-85 - 1052*S^2 + 251*S^4 + 798*S^6))/(120*S*(1 + S^2)^2) + 114*S*HPL[{5}, -S^2] + (-15*Pi^2*S + (-102 + 892*S^2 + 363*S^4 + 246*S^6 - 27*S^8)/(2*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-12 - 283*S^2 + 75*S^4 + 225*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 218*S*HPL[{3, 2}, -S^2] - 532*S*HPL[{4, 1}, -S^2] + (2*(-7 - 486*S^2 + 179*S^4 + 432*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 236*S*HPL[{2, 2, 1}, -S^2] - 364*S*HPL[{3, 1, 1}, -S^2] - 384*S*HPL[{2, 1, 1, 1}, -S^2] + ((-19*Pi^2*S)/3 + (22 + 76*S^2 + 101*S^4 - 24*S^6 - 15*S^8)/(S*(1 + S^2)^2))*Zeta[3] + 10*S*Zeta[5]) + HPL[{3, 1}, -S^2]*((Pi^4*(-1301 - 28562*S^2 - 29341*S^4 - 6856*S^6))/(360*S*(1 + S^2)^2) + (Pi^2*(88 - 973*S^2 - 3424*S^4 - 126*S^6))/(24*S^3) + (356 - 3317*S^2 - 9604*S^4 - 35*S^6)/(16*S^3) - 3284*S*HPL[{3, 2}, -S^2] - 10428*S*HPL[{4, 1}, -S^2] - (64*(-9 + 195*S^2 + 172*S^4 + 17*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 3824*S*HPL[{2, 2, 1}, -S^2] + 14768*S*HPL[{3, 1, 1}, -S^2] + 7552*S*HPL[{2, 1, 1, 1}, -S^2] + (282*Pi^2*S + (-81 + 114*S^2 - 1059*S^4 + 392*S^6 + 30*S^8)/(S*(1 + S^2)^2))*Zeta[3] + 1436*S*Zeta[5]) + Zeta[3]*((-1847*Pi^6*S)/1134 + (Pi^2*(-16 + 1532*S^2 - 217*S^4))/(48*S) + (-24 + 6805*S^2 - 24*S^4)/(16*S) - (Pi^4*S*(-5252 - 19161*S^2 - 778*S^4 + 975*S^6))/(720*(1 + S^2)^2) - (2*S*(-40 + 75*S^2 + 84*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((68629*Pi^6*S)/22680 + (131 - 12685*S^2 - 7075*S^4 + 24*S^6)/(16*S^3) + (Pi^2*(-8 - 3386*S^2 - 979*S^4 + 94*S^6))/(24*S^3) + (Pi^4*(-7250 - 55752*S^2 - 19665*S^4 + 5146*S^6 + 561*S^8))/(720*S*(1 + S^2)^2) + ((976*Pi^2*S)/3 + (2*(132 + 978*S^2 - 685*S^4 + 58*S^6 + 21*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((527 - 5756*S^2 - 4553*S^4 + 22*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) - (4*(-428 + 4425*S^2 + 3709*S^4 + 141*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) - 78*S*HPL[{4, 2}, -S^2] + 4*S*HPL[{5, 1}, -S^2] + ((1624*Pi^2*S)/3 + (4*(105 + 1070*S^2 - 509*S^4 + 112*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (48*(11 + 7*S^2)*HPL[{2, 2, 1}, -S^2])/S + (32*(15 + 477*S^2 + 419*S^4 + 55*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 312*S*HPL[{3, 1, 2}, -S^2] - 2712*S*HPL[{3, 2, 1}, -S^2] - 9456*S*HPL[{4, 1, 1}, -S^2] - (32*(-25 + 783*S^2 + 661*S^4 + 49*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 7552*S*HPL[{3, 1, 1, 1}, -S^2] + 12448*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((4 - 25*S^2 - 18*S^4 - 6*S^6)/S^3 + (Pi^2*(-107 + 1520*S^2 + 1206*S^4 + 10*S^6))/(3*S*(1 + S^2)^2))*Zeta[3] + 60*S*Zeta[3]^2 + (2*(-45 + 1376*S^2 + 1082*S^4 + 22*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-2323*Pi^6*S)/945 + (Pi^2*(62 + 936*S^2 + 1534*S^4 - 373*S^6))/(48*S^3) + (145 + 2088*S^2 + 1302*S^4 - 72*S^6)/(16*S^3) + (Pi^4*(741 + 2598*S^2 + 9049*S^4 - 224*S^6 - 204*S^8))/(360*S*(1 + S^2)^2) + (13*Pi^2*S + (2*(-9 - 67*S^2 - 140*S^4 - 33*S^6 + 6*S^8))/(S*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(-14 + 3*S^2 + 118*S^4 + 87*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) - 138*S*HPL[{6}, -S^2] + 1712*S*HPL[{2, 1}, -S^2]^2 + ((892*Pi^2*S)/3 + (-15 - 50*S^2 - 1404*S^4 + 232*S^6 + 33*S^8)/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((5 - 512*S^2 - 179*S^4 + 166*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + (2*(-22 - 25*S^2 + 151*S^4 + 127*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + 84*S*HPL[{4, 2}, -S^2] + 40*S*HPL[{5, 1}, -S^2] + (-604*Pi^2*S - (2*(1 - 17*S^2 - 1391*S^4 + 231*S^6 + 36*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (2*(283 - 3112*S^2 - 2413*S^4 + 50*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (2*(-853 + 8952*S^2 + 7223*S^4 + 66*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 8*S*HPL[{3, 1, 2}, -S^2] - 3384*S*HPL[{3, 2, 1}, -S^2] + 110168*S*HPL[{4, 1, 1}, -S^2] + (16*(-69 + 693*S^2 + 613*S^4 + 47*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 6848*S*HPL[{3, 1, 1, 1}, -S^2] - 13824*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((8 + 55*S^2 + 108*S^4 - 126*S^6)/(4*S^3) + (Pi^2*(5 - 150*S^2 - 55*S^4 + 48*S^6))/(6*S*(1 + S^2)^2))*Zeta[3] - 32*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((32 - 323*S^2 + 512*S^4 - 147*S^6)/(4*S^3) + (Pi^2*(-289 + 2964*S^2 + 2665*S^4 + 238*S^6))/(6*S*(1 + S^2)^2) - 64*S*Zeta[3]) + ((-17 - 62*S^2 + 87*S^4 + 100*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((52285*Pi^6*S)/13608 + (Pi^2*(1 + S^2)*(4 + 1624*S^2 + 123*S^4))/(36*S^3) + ((1 + S^2)*(-153 + 4084*S^2 + 509*S^4))/(24*S^3) + (Pi^4*(3835 + 55782*S^2 + 9289*S^4 + 11425*S^6 + 699*S^8))/(1080*S*(1 + S^2)^2) + ((607*Pi^2*S)/9 + (113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8)/(6*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (148*S*HPL[{3}, -S^2]^2)/3 + ((-340*Pi^2*S)/9 + (153 + 193*S^2 + 1605*S^4 + 237*S^6)/(3*S*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(1 - 220*S^2 + 97*S^4 + 210*S^6)*HPL[{5}, -S^2])/(3*S*(1 + S^2)^2) - (178*S*HPL[{6}, -S^2])/3 - (3136*S*HPL[{2, 1}, -S^2]^2)/3 + ((-440*Pi^2*S)/9 - (4*(122 + 803*S^2 + 1156*S^4 + 143*S^6))/(3*S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)^2) - (4*(395 - 6948*S^2 - 1661*S^4 + 2998*S^6)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)^2) + 156*S*HPL[{4, 2}, -S^2] + (2704*S*HPL[{5, 1}, -S^2])/3 + ((1568*Pi^2*S)/9 + (16*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (1568*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (16*(224 - 2298*S^2 - 1763*S^4 + 58*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)^2) - (2656*S*HPL[{4, 1, 1}, -S^2])/3 - (520*(-1 + 6*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (2656*S*HPL[{3, 1, 1, 1}, -S^2])/3 + (-((1 + S^2)*(4 - 61*S^2 + 61*S^4))/(6*S^3) + (2*Pi^2*(49 - 1028*S^2 - 123*S^4 + 538*S^6))/(9*S*(1 + S^2)^2))*Zeta[3] + (80*S*Zeta[3]^2)/3 + HPL[{3}, -S^2]*(-((1 + S^2)*(10 - 279*S^2 + 49*S^4))/(3*S^3) + (Pi^2*(137 - 2536*S^2 - 513*S^4 + 1166*S^6))/(9*S*(1 + S^2)^2) + (3136*S*HPL[{2, 1}, -S^2])/3 - (200*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((2*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 - (2*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(9*S*(1 + S^2)^2) + (3136*S*Zeta[3])/3) + HPL[{2}, -S^2]*((2021*Pi^4*S)/180 - ((1 + S^2)*(72 - 2543*S^2 + 55*S^4))/(12*S^3) + (Pi^2*(355 + 3855*S^2 + 2482*S^4 + 565*S^6 + 15*S^8))/(18*S*(1 + S^2)^2) + (2*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (452*S*HPL[{4}, -S^2])/3 + (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (3136*S*HPL[{3, 1}, -S^2])/3 + (6272*S*HPL[{2, 1, 1}, -S^2])/3 + (224*(1 - 18*S^2 - 4*S^4 + 8*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + (2*(51 - 1724*S^2 + 199*S^4 + 1214*S^6)*Zeta[5])/(3*S*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((52021*Pi^6*S)/90720 + (Pi^2*(1 + 697*S^2 - 119*S^4))/(72*S) + (-200 + 4279*S^2 + 898*S^4)/(192*S) + (Pi^4*S*(27069 + 27687*S^2 + 21613*S^4 + 5007*S^6))/(4320*(1 + S^2)^2) + ((-134 + 1266*S^2 + 1109*S^4 + 74*S^6)*HPL[{1}, -S^2]^5)/(45*S*(1 + S^2)^2) + (73*S*HPL[{1}, -S^2]^6)/27 + ((541*Pi^2*S)/72 + (-12 + 506*S^2 + 367*S^4 + 276*S^6 + 3*S^8)/(16*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (26*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((53*Pi^2*S)/9 + (198 + 2089*S^2 + 893*S^4 + 471*S^6 + 9*S^8)/(36*S*(1 + S^2)^2) + (55*S*HPL[{2}, -S^2])/3) - (5*S*HPL[{3}, -S^2]^2)/6 + ((29*Pi^2*S)/9 + (44 + 272*S^2 + 225*S^4 + 130*S^6 - 3*S^8)/(24*S*(1 + S^2)^2))*HPL[{4}, -S^2] + ((20 + 164*S^2 + 153*S^4 + 32*S^6)*HPL[{5}, -S^2])/(6*S*(1 + S^2)^2) + 21*S*HPL[{6}, -S^2] - (325*S*HPL[{2, 1}, -S^2]^2)/3 + ((-607*Pi^2*S)/18 + (-35 - 943*S^2 - 708*S^4 - 463*S^6 - 3*S^8)/(6*S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((4 + S^2 - 45*S^4 - 35*S^6)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)^2) + ((13 - 68*S^2 - 195*S^4 - 110*S^6)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)^2) - (2*S*HPL[{4, 2}, -S^2])/3 - (76*S*HPL[{5, 1}, -S^2])/3 + ((605*Pi^2*S)/9 + (16 + 932*S^2 + 743*S^4 + 493*S^6 + 6*S^8)/(3*S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(118 - 380*S^2 - 319*S^4 + 20*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (2*(364 - 1167*S^2 - 1011*S^4 + 37*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)^2) + (2*S*HPL[{3, 1, 2}, -S^2])/3 + (626*S*HPL[{3, 2, 1}, -S^2])/3 + (1954*S*HPL[{4, 1, 1}, -S^2])/3 + (4*(129 - 391*S^2 - 344*S^4 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)^2) - (1384*S*HPL[{3, 1, 1, 1}, -S^2])/3 + (2792*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + (-(S*(-94 + 85*S^2))/8 + (Pi^2*S*(546 + 1147*S^2 + 590*S^4))/(36*(1 + S^2)^2))*Zeta[3] - S*Zeta[3]^2 + HPL[{3}, -S^2]*((-12 + 240*S^2 + 616*S^4 - 19*S^6)/(48*S^3) + (Pi^2*(-10 + 102*S^2 + 129*S^4 + 38*S^6))/(36*S*(1 + S^2)^2) + (10*S*HPL[{2, 1}, -S^2])/3 - 4*S*Zeta[3]) + HPL[{1}, -S^2]^3*(((1 + S^2)*(2 + 851*S^2 + 31*S^4))/(36*S^3) + (Pi^2*(-523 + 4636*S^2 + 4481*S^4 + 594*S^6))/(108*S*(1 + S^2)^2) + (2*(-62 + 578*S^2 + 517*S^4 + 42*S^6)*HPL[{2}, -S^2])/(9*S*(1 + S^2)^2) + (4*S*HPL[{3}, -S^2])/3 - (220*S*HPL[{2, 1}, -S^2])/3 - (22*S*Zeta[3])/9) + HPL[{2, 1}, -S^2]*((-1655 - 238*S^2 - 7*S^4)/(24*S) + (Pi^2*(156 - 382*S^2 - 297*S^4 + 54*S^6))/(12*S*(1 + S^2)^2) + (2*S*Zeta[3])/3) + HPL[{2}, -S^2]*((959*Pi^4*S)/270 + (-62 + 382*S^2 + 1847*S^4 - 35*S^6)/(48*S^3) + (Pi^2*(16 + 2117*S^2 + 2222*S^4 + 1234*S^6 - 9*S^8))/(72*S*(1 + S^2)^2) + ((-4 + 47*S^4 + 36*S^6)*HPL[{3}, -S^2])/(6*S*(1 + S^2)^2) + 2*S*HPL[{4}, -S^2] + ((118 - 380*S^2 - 319*S^4 + 20*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (322*S*HPL[{3, 1}, -S^2])/3 + (650*S*HPL[{2, 1, 1}, -S^2])/3 + ((-12 - 10*S^2 + 61*S^4 + 50*S^6)*Zeta[3])/(6*S*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((3997*Pi^4*S)/1080 + ((1 + S^2)*(8 + 639*S^2 + 15*S^4))/(16*S^3) + (Pi^2*(503 + 4619*S^2 + 2720*S^4 + 1172*S^6 + 24*S^8))/(72*S*(1 + S^2)^2) + ((187*Pi^2*S)/12 + (423 + 4138*S^2 + 2058*S^4 + 986*S^6 + 3*S^8)/(24*S*(1 + S^2)^2))*HPL[{2}, -S^2] + (53*S*HPL[{2}, -S^2]^2)/2 + ((-1 + 8*S^2 + 9*S^4 + 2*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + (17*S*HPL[{4}, -S^2])/3 - (2*(-62 + 578*S^2 + 517*S^4 + 42*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) - 110*S*HPL[{3, 1}, -S^2] + 220*S*HPL[{2, 1, 1}, -S^2] + ((-3 - 32*S^2 + 55*S^4 + 62*S^6)*Zeta[3])/(6*S*(1 + S^2)^2)) + (8*S*(19 + 43*S^2 + 23*S^4)*Zeta[5])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(-2 - 2181*S^2 + 19*S^4))/(144*S^3) + ((1 + S^2)*(48 + 4779*S^2 + 215*S^4))/(96*S^3) + (7*Pi^4*(-551 + 4488*S^2 + 4919*S^4 + 1022*S^6))/(2160*S*(1 + S^2)^2) + ((-39 + 368*S^2 + 323*S^4 + 22*S^6)*HPL[{2}, -S^2]^2)/(4*S*(1 + S^2)^2) + ((7*Pi^2*S)/6 + (31 + 174*S^2 + 195*S^4 + 73*S^6 - 3*S^8)/(6*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-3 + 46*S^2 + 16*S^4 - 16*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) + (23*S*HPL[{5}, -S^2])/3 + ((-187*Pi^2*S)/6 + (-423 - 4138*S^2 - 2058*S^4 - 986*S^6 - 3*S^8)/(12*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((41 - 384*S^2 - 341*S^4 - 26*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + (14*S*HPL[{3, 2}, -S^2])/3 + (8*S*HPL[{4, 1}, -S^2])/3 + (4*(-62 + 578*S^2 + 517*S^4 + 42*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)^2) + 212*S*HPL[{2, 2, 1}, -S^2] + 644*S*HPL[{3, 1, 1}, -S^2] - 440*S*HPL[{2, 1, 1, 1}, -S^2] + ((-11*Pi^2*S)/18 + (61 + 344*S^2 + 582*S^4 + 250*S^6 + 39*S^8)/(12*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-44 + 1957*S^2 + 31*S^4))/(48*S^3) + (Pi^2*(-229 + 2038*S^2 + 1958*S^4 + 252*S^6))/(36*S*(1 + S^2)^2) - (7*S*HPL[{3}, -S^2])/3 - 106*S*HPL[{2, 1}, -S^2] - 3*S*Zeta[3]) - (16*S*Zeta[5])/3)) + Log[T]^3*((-13364*Pi^6*S)/2835 + (56 - 69*S^2)/(4*S) + (Pi^2*(4 - 2125*S^2 - 49*S^4))/(36*S) - (Pi^4*S*(46758 + 9163*S^2 + 16842*S^4 + 1053*S^6))/(1080*(1 + S^2)^2) - (19*S*HPL[{0}, S^2]^6)/36 + ((-290*Pi^2*S)/3 - (5*(19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8))/(3*S*(1 + S^2)^2))*HPL[{1}, -S^2]^4 + (112*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)^2) - (448*S*HPL[{1}, -S^2]^6)/9 + HPL[{0}, S^2]^5*(-(S*(1700 + 2045*S^2 + 616*S^4))/(180*(1 + S^2)^2) - (271*S*HPL[{1}, -S^2])/90) + ((-808*Pi^2*S)/9 + (-8 - 1182*S^2 + 15*S^4 - 376*S^6 + 3*S^8)/(3*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (784*S*HPL[{2}, -S^2]^3)/9 + HPL[{0}, S^2]^4*((-95*Pi^2*S)/18 - (S*(2134 + 2155*S^2 + 1166*S^4 + 9*S^6))/(72*(1 + S^2)^2) + ((253 - 2148*S^2 - 2215*S^4 - 382*S^6)*HPL[{1}, -S^2])/(36*S*(1 + S^2)^2) - (142*S*HPL[{1}, -S^2]^2)/9 - (133*S*HPL[{2}, -S^2])/9) - (296*S*HPL[{3}, -S^2]^2)/3 + ((520*Pi^2*S)/9 + (-12 - 456*S^2 - 2319*S^4 - 538*S^6 + 9*S^8)/(3*S*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(3 - 4*S^2 + 1063*S^4 + 854*S^6)*HPL[{5}, -S^2])/(3*S*(1 + S^2)^2) + 24*S*HPL[{6}, -S^2] + (3160*S*HPL[{2, 1}, -S^2]^2)/3 + ((3008*Pi^2*S)/9 + (4*(53 + 542*S^2 + 1251*S^4 + 448*S^6 + 18*S^8))/(3*S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(-28 - 1271*S^2 + 1462*S^4 + 1921*S^6)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)^2) + (8*(-19 - 2336*S^2 + 2095*S^4 + 3070*S^6)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)^2) - (1144*S*HPL[{4, 2}, -S^2])/3 - (5168*S*HPL[{5, 1}, -S^2])/3 + ((-6800*Pi^2*S)/9 - (20*(10 + 232*S^2 + 155*S^4 + 9*S^6))/(3*S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (32*(73 - 393*S^2 - 25*S^4 + 245*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)^2) + (8*(861 - 3016*S^2 - 1605*S^4 + 870*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)^2) + (640*S*HPL[{3, 1, 2}, -S^2])/3 - (5632*S*HPL[{3, 2, 1}, -S^2])/3 - 4832*S*HPL[{4, 1, 1}, -S^2] + (240*(-7 + 22*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 3520*S*HPL[{3, 1, 1, 1}, -S^2] - 8960*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((4*S*(-79 + 42*S^2))/3 - (52*Pi^2*S*(-21 + 38*S^2 + 43*S^4))/(9*(1 + S^2)^2))*Zeta[3] + 8*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-4*(-399 - 79*S^2 + 42*S^4))/(3*S) + (4*Pi^2*(-321 + 676*S^2 + 1335*S^4 + 534*S^6))/(9*S*(1 + S^2)^2) - (160*S*Zeta[3])/3) + HPL[{0}, S^2]^3*(-(S*(54 + S^2)) - (2*Pi^2*S*(850 + 905*S^2 + 214*S^4))/(27*(1 + S^2)^2) - (2*(-134 + 1266*S^2 + 1109*S^4 + 74*S^6)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)^2) - (1460*S*HPL[{1}, -S^2]^3)/27 - (10*(1 + 153*S^2 + 138*S^4 + 19*S^6)*HPL[{2}, -S^2])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((-212*Pi^2*S)/9 + (-198 - 2089*S^2 - 893*S^4 - 471*S^6 - 9*S^8)/(9*S*(1 + S^2)^2) - (220*S*HPL[{2}, -S^2])/3) + 2*S*HPL[{3}, -S^2] - (76*S*HPL[{2, 1}, -S^2])/9 + (28*S*Zeta[3])/9) + HPL[{3}, -S^2]*((-12 - 467*S^2 - 764*S^4 + 297*S^6)/(6*S^3) - (2*Pi^2*(-3 - 867*S^2 + 760*S^4 + 1127*S^6))/(9*S*(1 + S^2)^2) + (640*S*HPL[{2, 1}, -S^2])/3 + 96*S*Zeta[3]) + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(283 + 33*S^2))/(9*S) + (20*Pi^2*(25 - 274*S^2 - 188*S^4 + 24*S^6))/(9*S*(1 + S^2)^2) - (260*(-1 + 6*S^2)*HPL[{2}, -S^2])/(3*S) + (7600*S*HPL[{3}, -S^2])/9 + (2000*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-6673*Pi^4*S)/135 - ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(6*S^3) + (Pi^2*(-281 - 4618*S^2 - 26*S^4 - 954*S^6 - 45*S^8))/(9*S*(1 + S^2)^2) + ((-784*Pi^2*S)/9 - (8*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] - (1568*S*HPL[{2}, -S^2]^2)/3 - (40*(14 - 246*S^2 - 59*S^4 + 106*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + (1328*S*HPL[{4}, -S^2])/3 + (260*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S - (1328*S*HPL[{3, 1}, -S^2])/3 - (40*(3 - 62*S^2 - 8*S^4 + 32*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-325*Pi^4*S)/9 + (82 - 634*S^2 - 1970*S^4 - 49*S^6)/(6*S^3) + (Pi^2*(-116 - 3080*S^2 - 2935*S^4 - 1626*S^6 - 87*S^8))/(18*S*(1 + S^2)^2) - (4*(-25 - 634*S^2 + 767*S^4 + 984*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + (1096*S*HPL[{4}, -S^2])/3 - (16*(73 - 393*S^2 - 25*S^4 + 245*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) + 832*S*HPL[{3, 1}, -S^2] - (6320*S*HPL[{2, 1, 1}, -S^2])/3 - (16*(3 - 158*S^2 + 165*S^4 + 228*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((-2731*Pi^4*S)/180 + (4 - 2050*S^2 - 49*S^4)/(12*S) - (Pi^2*S*(1992 + 1460*S^2 + 993*S^4 + 27*S^6))/(18*(1 + S^2)^2) - (20*(-11 + 106*S^2 + 90*S^4 + 4*S^6)*HPL[{1}, -S^2]^3)/(3*S*(1 + S^2)^2) - (310*S*HPL[{1}, -S^2]^4)/3 + ((-232*Pi^2*S)/3 + (-33 - 935*S^2 - 500*S^4 - 403*S^6 - 21*S^8)/(3*S*(1 + S^2)^2))*HPL[{2}, -S^2] - (413*S*HPL[{2}, -S^2]^2)/3 + HPL[{1}, -S^2]^2*((-749*Pi^2*S)/9 + (-277 - 4196*S^2 - 862*S^4 - 708*S^6 - 45*S^8)/(6*S*(1 + S^2)^2) - (784*S*HPL[{2}, -S^2])/3) + ((21 + 34*S^2 - 215*S^4 - 184*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (20*S*HPL[{4}, -S^2])/3 + (2*(-327 + 992*S^2 + 1005*S^4 + 78*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) + (1688*S*HPL[{3, 1}, -S^2])/3 - (3440*S*HPL[{2, 1, 1}, -S^2])/3 - (2*S*(-36 + 133*S^2 + 128*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(-1 + 369*S^2 + 26*S^4))/(3*S^3) + (Pi^2*(583 - 5328*S^2 - 4915*S^4 - 502*S^6))/(18*S*(1 + S^2)^2) + ((307 - 2796*S^2 - 2593*S^4 - 274*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + (88*S*HPL[{3}, -S^2])/3 + (1568*S*HPL[{2, 1}, -S^2])/3 + (164*S*Zeta[3])/3)) - (304*S*(-4 + 17*S^2 + 16*S^4)*Zeta[5])/(3*(1 + S^2)^2) + HPL[{0}, S^2]*(-(Pi^2*S*(3434 + 201*S^2))/36 + (64 - 3608*S^2 - 335*S^4)/(12*S) - (Pi^4*S*(48916 + 36917*S^2 + 184*S^4))/(540*(1 + S^2)^2) + (280*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^4)/(3*S*(1 + S^2)^2) - (448*S*HPL[{1}, -S^2]^5)/3 + (4*(3 - 595*S^2 - 219*S^4 + 183*S^6)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-4820*Pi^2*S)/27 - (10*(19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8))/(3*S*(1 + S^2)^2) - (2000*S*HPL[{2}, -S^2])/3) + ((128*Pi^2*S)/9 + (-37 - 374*S^2 - 742*S^4 - 230*S^6 + 39*S^8)/(3*S*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(3 - 100*S^2 + 21*S^4 + 78*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) - (44*S*HPL[{5}, -S^2])/3 + ((-256*Pi^2*S)/9 - (2*(-342 - 3114*S^2 + 127*S^4 - 56*S^6 + 45*S^8))/(3*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(-35 - 2264*S^2 - 673*S^4 + 806*S^6)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^2) - (472*S*HPL[{3, 2}, -S^2])/3 - (1360*S*HPL[{4, 1}, -S^2])/3 + (80*(-1 - 76*S^2 - 24*S^4 + 26*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (272*S*HPL[{2, 2, 1}, -S^2])/3 + (64*S*HPL[{3, 1, 1}, -S^2])/3 - 480*S*HPL[{2, 1, 1, 1}, -S^2] + ((388*Pi^2*S)/9 + (2*S*(-18 - 435*S^2 - 76*S^4 + 9*S^6))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((44 - 375*S^2 - 1688*S^4 - 157*S^6)/(6*S^3) + (10*Pi^2*(-4 - 381*S^2 - 210*S^4 + 59*S^6))/(9*S*(1 + S^2)^2) + (224*S*HPL[{3}, -S^2])/3 + (136*S*HPL[{2, 1}, -S^2])/3 + (656*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(283 + 33*S^2))/(6*S) + (2*Pi^2*(344 - 3786*S^2 - 2579*S^4 + 346*S^6))/(9*S*(1 + S^2)^2) + (250*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (136*S*HPL[{3}, -S^2])/3 + 2000*S*HPL[{2, 1}, -S^2] + (664*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-4061*Pi^4*S)/90 - ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(6*S^3) + (Pi^2*(-681 - 9218*S^2 - 976*S^4 - 2142*S^6 - 63*S^8))/(18*S*(1 + S^2)^2) + (-240*Pi^2*S - (8*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(3*S*(1 + S^2)^2))*HPL[{2}, -S^2] - (1568*S*HPL[{2}, -S^2]^2)/3 - (8*(5 - 54*S^2 - 38*S^4 + 4*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (184*S*HPL[{4}, -S^2])/3 - (500*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 2000*S*HPL[{3, 1}, -S^2] - 4000*S*HPL[{2, 1, 1}, -S^2] - (8*(20 - 246*S^2 - 137*S^4 + 46*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + (520*S*Zeta[5])/3) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(-4 + 2891*S^2 + 269*S^4))/(36*S^3) - ((1 + S^2)*(-28 + 3449*S^2 + 335*S^4))/(12*S^3) + (Pi^4*(8587 - 87732*S^2 - 67765*S^4 + 1862*S^6))/(540*S*(1 + S^2)^2) + (392*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^2) + ((1988*Pi^2*S)/9 + (2*(-131 + 646*S^2 - 2836*S^4 + 202*S^6 + 15*S^8))/(3*S*(1 + S^2)^2))*HPL[{3}, -S^2] - (16*(14 - 222*S^2 - 71*S^4 + 82*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) + 288*S*HPL[{5}, -S^2] + ((1568*Pi^2*S)/9 + (16*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (16*(-28 - 54*S^2 + 391*S^4 + 334*S^6)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^2) - (6272*S*HPL[{3, 2}, -S^2])/3 - (21472*S*HPL[{4, 1}, -S^2])/3 - (520*(-1 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/S - (12544*S*HPL[{2, 2, 1}, -S^2])/3 - (22432*S*HPL[{3, 1, 1}, -S^2])/3 + ((1664*Pi^2*S)/9 + (8*(2 + 211*S^2 - 418*S^4 + 123*S^6))/(3*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((2*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 - (2*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(9*S*(1 + S^2)^2) + (3136*S*HPL[{3}, -S^2])/3 + (6272*S*HPL[{2, 1}, -S^2])/3 + (3136*S*Zeta[3])/3) + (3040*S*Zeta[5])/3)) + HPL[{0}, S^2]^2*((Pi^4*S*(25793 + 2803*S^2))/1440 + (Pi^2*(-160 + 15401*S^2 - 761*S^4))/(192*S) + (-264 + 10913*S^2 - 288*S^4)/(32*S) + (Pi^6*S*(169452 + 143489*S^2 + 13120*S^4))/(36288*(1 + S^2)^2) + ((-11 + 106*S^2 + 90*S^4 + 4*S^6)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)^2) + (62*S*HPL[{1}, -S^2]^7)/21 + ((5 + 419*S^2 + 343*S^4 + 25*S^6)*HPL[{2}, -S^2]^3)/(6*S*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((749*Pi^2*S)/90 + (277 + 4196*S^2 + 862*S^4 + 708*S^6 + 45*S^8)/(60*S*(1 + S^2)^2) + (392*S*HPL[{2}, -S^2])/15) + ((-1 - 12*S^2)*HPL[{3}, -S^2]^2)/(2*S) + ((-115*Pi^2*S)/12 + (-2 + 114*S^2 + 232*S^4 + 107*S^6 + 39*S^8)/(4*S*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-70 - 448*S^2 - 461*S^4 - 128*S^6)*HPL[{6}, -S^2])/(4*S*(1 + S^2)^2) - 93*S*HPL[{7}, -S^2] + ((-4 - 944*S^2 - 801*S^4 - 76*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + ((43*Pi^2*S)/6 + (-23 - 223*S^2 - 519*S^4 - 139*S^6 + 12*S^8)/(4*S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((61*Pi^2*S)/2 + (-90 - 944*S^2 - 1947*S^4 - 518*S^6 + 39*S^8)/(4*S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((-3 - 50*S^2 - 61*S^4 - 20*S^6)*HPL[{4, 2}, -S^2])/(4*S*(1 + S^2)^2) + 10*S*HPL[{4, 3}, -S^2] - (2*(-5 + 9*S^2 + 53*S^4 + 35*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) + (57*S*HPL[{5, 2}, -S^2])/2 + 129*S*HPL[{6, 1}, -S^2] + ((13*Pi^2*S)/3 + (216 + 2028*S^2 - 45*S^4 - 134*S^6 + 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-35*Pi^2*S)/3 + (698 + 6470*S^2 + 531*S^4 - 260*S^6 - 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + ((-3 - 2*S^2)*HPL[{3, 1, 2}, -S^2])/(2*S) + ((37 + 3344*S^2 + 2737*S^4 + 198*S^6)*HPL[{3, 2, 1}, -S^2])/(2*S*(1 + S^2)^2) - 85*S*HPL[{3, 2, 2}, -S^2] - 244*S*HPL[{3, 3, 1}, -S^2] + ((57 + 5066*S^2 + 4241*S^4 + 376*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 247*S*HPL[{4, 1, 2}, -S^2] - 715*S*HPL[{4, 2, 1}, -S^2] - 1478*S*HPL[{5, 1, 1}, -S^2] + (42*Pi^2*S + (4*(-65 - 590*S^2 - 121*S^4 + 15*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 104*S*HPL[{2, 2, 2, 1}, -S^2] - (2*(23 + 1770*S^2 + 1541*S^4 + 180*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 140*S*HPL[{3, 1, 1, 2}, -S^2] - 140*S*HPL[{3, 1, 2, 1}, -S^2] - 452*S*HPL[{3, 2, 1, 1}, -S^2] - 1296*S*HPL[{4, 1, 1, 1}, -S^2] + (16*(5 + 451*S^2 + 397*S^4 + 49*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 136*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 408*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 1104*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 608*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((373*Pi^4*S)/360 + (-8 + 486*S^2 - 9*S^4)/(16*S) - (Pi^2*S*(-455 - 900*S^2 - 315*S^4 + 48*S^6))/(12*(1 + S^2)^2))*Zeta[3] - (S*(-4 + 37*S^2 + 32*S^4)*Zeta[3]^2)/(2*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-20 + 191*S^2 + 826*S^4 + 42*S^6)/(2*S^3) + (Pi^2*(32 + 3220*S^2 + 3179*S^4 + 624*S^6))/(6*S*(1 + S^2)^2) - 152*S*Zeta[3]) + HPL[{2}, -S^2]^2*((-29 + 762*S^2 + 26*S^4)/(16*S) + (Pi^2*(10 + 1596*S^2 + 1487*S^4 + 236*S^6))/(24*S*(1 + S^2)^2) - (21*S*HPL[{3}, -S^2])/2 + 13*S*HPL[{2, 1}, -S^2] - (37*S*Zeta[3])/2) + HPL[{1}, -S^2]^4*(((1 + S^2)*(-1 + 369*S^2 + 26*S^4))/(12*S^3) + (Pi^2*(-583 + 5328*S^2 + 4915*S^4 + 502*S^6))/(72*S*(1 + S^2)^2) + ((-307 + 2796*S^2 + 2593*S^4 + 274*S^6)*HPL[{2}, -S^2])/(12*S*(1 + S^2)^2) - (22*S*HPL[{3}, -S^2])/3 - (392*S*HPL[{2, 1}, -S^2])/3 - (41*S*Zeta[3])/3) + HPL[{4}, -S^2]*((-12 + 161*S^2 + 576*S^4 + 106*S^6)/(16*S^3) + (Pi^2*(-39 - 34*S^2 + 149*S^4 + 124*S^6))/(24*S*(1 + S^2)^2) + 3*S*HPL[{2, 1}, -S^2] + 12*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((Pi^2*(-23 - 3092*S^2 - 3015*S^4 - 566*S^6))/(12*S*(1 + S^2)^2) + (44 - 414*S^2 - 1648*S^4 - 69*S^6)/(8*S^3) + 74*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((134*Pi^4*S)/45 + (2 - 1549*S^2 - 461*S^4 - 10*S^6)/(8*S^3) + (Pi^2*(-294 - 2133*S^2 - 497*S^4 + 79*S^6 + 3*S^8))/(12*S*(1 + S^2)^2) + 32*S*HPL[{3, 1}, -S^2] + 68*S*HPL[{2, 1, 1}, -S^2] + ((-7 + 136*S^2 + 98*S^4 - 6*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-133*Pi^4*S)/90 + (38 + 771*S^2 + 1490*S^4 - 139*S^6)/(32*S^3) + (Pi^2*(55 + 409*S^2 + 615*S^4 + 155*S^6 - 6*S^8))/(24*S*(1 + S^2)^2) - 4*S*HPL[{4}, -S^2] + ((-13 + 192*S^2 + 213*S^4 + 50*S^6)*HPL[{2, 1}, -S^2])/(2*S*(1 + S^2)^2) + 36*S*HPL[{3, 1}, -S^2] - 84*S*HPL[{2, 1, 1}, -S^2] + ((4 + 10*S^2 + 13*S^4 + 6*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((8449*Pi^4*S)/1080 + ((1 + S^2)*(-4 + 1707*S^2 + 105*S^4))/(24*S^3) + (Pi^2*(354 + 4196*S^2 + 1625*S^4 + 809*S^6 + 30*S^8))/(36*S*(1 + S^2)^2) + ((211*Pi^2*S)/6 + (163 + 2115*S^2 + 742*S^4 + 373*S^6 + 15*S^8)/(6*S*(1 + S^2)^2))*HPL[{2}, -S^2] + (215*S*HPL[{2}, -S^2]^2)/3 + ((-3 - 76*S^2 + 77*S^4 + 106*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (8*S*HPL[{4}, -S^2])/3 + ((307 - 2796*S^2 - 2593*S^4 - 274*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (772*S*HPL[{3, 1}, -S^2])/3 + (1568*S*HPL[{2, 1, 1}, -S^2])/3 + (2*(4 - 98*S^2 - 3*S^4 + 58*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + ((13*Pi^2*S)/3 - (S*(-205 - 401*S^2 - 82*S^4 + 36*S^6))/(2*(1 + S^2)^2))*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(-2 + 1817*S^2 + 59*S^4))/(48*S^3) + ((1 + S^2)*(-80 + 4427*S^2 + 283*S^4))/(32*S^3) + (Pi^4*(-3674 + 31594*S^2 + 31965*S^4 + 5146*S^6))/(720*S*(1 + S^2)^2) + ((-149 + 1456*S^2 + 1209*S^4 + 34*S^6)*HPL[{2}, -S^2]^2)/(4*S*(1 + S^2)^2) + ((-25*Pi^2*S)/6 + (29 + 152*S^2 + 266*S^4 + 55*S^6)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-23 + 60*S^2 + 269*S^4 + 170*S^6)*HPL[{4}, -S^2])/(4*S*(1 + S^2)^2) - 12*S*HPL[{5}, -S^2] + ((-211*Pi^2*S)/2 + (-163 - 2115*S^2 - 742*S^4 - 373*S^6 - 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-76 + 690*S^2 + 643*S^4 + 70*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 42*S*HPL[{3, 2}, -S^2] + 134*S*HPL[{4, 1}, -S^2] + ((-307 + 2796*S^2 + 2593*S^4 + 274*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 860*S*HPL[{2, 2, 1}, -S^2] + 2492*S*HPL[{3, 1, 1}, -S^2] - 1568*S*HPL[{2, 1, 1, 1}, -S^2] + ((-41*Pi^2*S)/6 + (19 + 12*S^2 + 320*S^4 + 2*S^6 + 3*S^8)/(4*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-44 + 1855*S^2 + 49*S^4))/(16*S^3) + (Pi^2*(-535 + 4672*S^2 + 4619*S^4 + 678*S^6))/(24*S*(1 + S^2)^2) - 21*S*HPL[{3}, -S^2] - 430*S*HPL[{2, 1}, -S^2] - 39*S*Zeta[3]) - 39*S*Zeta[5]) + HPL[{2}, -S^2]*((Pi^2*(-44 + 449*S^2 + 1810*S^4))/(48*S^3) + (-105 + 1910*S^2 + 3963*S^4 + 106*S^6)/(32*S^3) + (Pi^4*(260 + 39760*S^2 + 45085*S^4 + 12316*S^6))/(1440*S*(1 + S^2)^2) + ((-7*Pi^2*S)/2 + (7 + 111*S^2 + 273*S^4 + 79*S^6 - 6*S^8)/(4*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((7 + 90*S^2 + 149*S^4 + 68*S^6)*HPL[{4}, -S^2])/(4*S*(1 + S^2)^2) + (7*S*HPL[{5}, -S^2])/2 + ((-13*Pi^2*S)/6 + (-216 - 2028*S^2 + 45*S^4 + 134*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-7 - 1868*S^2 - 1585*S^4 - 150*S^6)*HPL[{3, 1}, -S^2])/(2*S*(1 + S^2)^2) + 43*S*HPL[{3, 2}, -S^2] + 123*S*HPL[{4, 1}, -S^2] + (2*(4 + 944*S^2 + 801*S^4 + 76*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 52*S*HPL[{2, 2, 1}, -S^2] + 72*S*HPL[{3, 1, 1}, -S^2] - 68*S*HPL[{2, 1, 1, 1}, -S^2] + ((-23*Pi^2*S)/6 + (26 + 71*S^2 + 132*S^4 + 9*S^6)/(2*S*(1 + S^2)^2))*Zeta[3] - 9*S*Zeta[5]) + HPL[{1}, -S^2]*((39083*Pi^6*S)/18144 + (Pi^2*(1 + S^2)*(8 + 4513*S^2 + 99*S^4))/(96*S^3) + ((1 + S^2)*(-173 + 6888*S^2 + 455*S^4))/(32*S^3) + (Pi^4*(6799 + 63450*S^2 + 37725*S^4 + 15101*S^6 + 231*S^8))/(1440*S*(1 + S^2)^2) + ((335*Pi^2*S)/12 + (117 + 1852*S^2 + 296*S^4 + 296*S^6 + 15*S^8)/(8*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + 32*S*HPL[{2}, -S^2]^3 + ((-5*Pi^2*S)/3 + (49 + 327*S^2 + 415*S^4 + 111*S^6 + 6*S^8)/(4*S*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(-2 + 2*S^2 + 25*S^4 + 18*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) - (45*S*HPL[{6}, -S^2])/2 - 430*S*HPL[{2, 1}, -S^2]^2 + ((-310*Pi^2*S)/3 + (-175 - 2156*S^2 - 828*S^4 - 406*S^6 - 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (6*(1 - 18*S^2 - 4*S^4 + 8*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + ((-13 + 588*S^2 - 125*S^4 - 458*S^6)*HPL[{4, 1}, -S^2])/(2*S*(1 + S^2)^2) - 3*S*HPL[{4, 2}, -S^2] + 16*S*HPL[{5, 1}, -S^2] + (211*Pi^2*S + (163 + 2115*S^2 + 742*S^4 + 373*S^6 + 15*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (2*(-149 + 1456*S^2 + 1209*S^4 + 34*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (4*(-225 + 2146*S^2 + 1852*S^4 + 104*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 768*S*HPL[{3, 2, 1}, -S^2] + 2288*S*HPL[{4, 1, 1}, -S^2] - (2*(-307 + 2796*S^2 + 2593*S^4 + 274*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 1544*S*HPL[{3, 1, 1, 1}, -S^2] + 3136*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(-2 + 133*S^2 + 13*S^4))/(4*S^3) + (Pi^2*(-7 - 136*S^2 + 159*S^4 + 206*S^6))/(12*S*(1 + S^2)^2))*Zeta[3] + 9*S*Zeta[3]^2 + HPL[{3}, -S^2]*(-((1 + S^2)*(5 - 99*S^2 + 3*S^4))/(2*S^3) + (5*Pi^2*(-3 - 8*S^2 + 43*S^4 + 38*S^6))/(12*S*(1 + S^2)^2) + 42*S*HPL[{2, 1}, -S^2] - 2*S*Zeta[3]) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(-44 + 1855*S^2 + 49*S^4))/(8*S^3) + (Pi^2*(535 - 4672*S^2 - 4619*S^4 - 678*S^6))/(12*S*(1 + S^2)^2) + 78*S*Zeta[3]) + HPL[{2}, -S^2]*((6731*Pi^4*S)/720 + ((1 + S^2)*(-28 + 1086*S^2 + 29*S^4))/(8*S^3) + (Pi^2*(369 + 4069*S^2 + 1954*S^4 + 807*S^6 + 21*S^8))/(24*S*(1 + S^2)^2) + (3*(1 - 18*S^2 - 4*S^4 + 8*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + S*HPL[{4}, -S^2] + ((149 - 1456*S^2 - 1209*S^4 - 34*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 426*S*HPL[{3, 1}, -S^2] + 860*S*HPL[{2, 1, 1}, -S^2] + (3*(3 - 64*S^2 - 7*S^4 + 34*S^6)*Zeta[3])/(2*S*(1 + S^2)^2)) + ((-7 - 50*S^2 + 116*S^4 + 120*S^6)*Zeta[5])/(S*(1 + S^2)^2))) + (-186*Pi^2*S - (3*S*(40 - 177*S^2 + 502*S^4 + 75*S^6))/(2*(1 + S^2)^2))*Zeta[7] + Log[T]^2*((3*(-27 + 40*S^2))/(2*S) + (Pi^4*S*(9501 + 602*S^2))/360 + (Pi^2*(-160 + 5203*S^2 + 106*S^4))/(48*S) + (Pi^6*S*(1232732 + 1158339*S^2 + 187032*S^4))/(45360*(1 + S^2)^2) + (S*HPL[{0}, S^2]^7)/8 + (58*Pi^2*S + (19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{1}, -S^2]^5 - (56*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)^2) + (64*S*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^6*((S*(20 + 25*S^2 + 8*S^4))/(8*(1 + S^2)^2) + (3*S*HPL[{1}, -S^2])/4) + (2*(11 + 7*S^2)*HPL[{2}, -S^2]^3)/S + HPL[{0}, S^2]^5*((149*Pi^2*S)/90 + (S*(1275 + 1529*S^2 + 826*S^4 + 30*S^6))/(120*(1 + S^2)^2) + ((-255 + 2104*S^2 + 2263*S^4 + 446*S^6)*HPL[{1}, -S^2])/(120*S*(1 + S^2)^2) + (271*S*HPL[{1}, -S^2]^2)/60 + (64*S*HPL[{2}, -S^2])/15) - (2*(-1 - 96*S^2 - 4*S^4 + 54*S^6)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^2) + ((-259*Pi^2*S)/3 + (118 + 632*S^2 + 1186*S^4 + 249*S^6 + 9*S^8)/(S*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-50 - 4*S^2 + 587*S^4 + 452*S^6)*HPL[{6}, -S^2])/(S*(1 + S^2)^2) - 152*S*HPL[{7}, -S^2] - (8*(-25 + 783*S^2 + 661*S^4 + 49*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + (578*Pi^2*S + (-35 + 45*S^2 - 2597*S^4 + 525*S^6 + 66*S^8)/(S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((5596*Pi^2*S)/3 + (-288 - 32*S^2 - 9237*S^4 + 1450*S^6 + 207*S^8)/(S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((7 + 570*S^2 - 51*S^4 - 380*S^6)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^2) - 172*S*HPL[{4, 3}, -S^2] - (2*(-15 - 1668*S^2 + 89*S^4 + 1066*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) - 346*S*HPL[{5, 2}, -S^2] + 384*S*HPL[{6, 1}, -S^2] + ((1624*Pi^2*S)/3 + (4*(105 + 1070*S^2 - 509*S^4 + 112*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((1120*Pi^2*S)/3 + (4*(401 + 3204*S^2 + 43*S^4 + 62*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (4*(-22 + 47*S^2)*HPL[{3, 1, 2}, -S^2])/S + (4*(110 + 131*S^2)*HPL[{3, 2, 1}, -S^2])/S - 6368*S*HPL[{3, 2, 2}, -S^2] - 19920*S*HPL[{3, 3, 1}, -S^2] + (16*(99 + 34*S^2 + 186*S^4 + 168*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 19784*S*HPL[{4, 1, 2}, -S^2] - 60872*S*HPL[{4, 2, 1}, -S^2] - 125040*S*HPL[{5, 1, 1}, -S^2] + ((3664*Pi^2*S)/3 + (4*(-334 - 1936*S^2 + 391*S^4 + 45*S^6))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + 6272*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(165 - 88*S^2 + 159*S^4 + 246*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 5632*S*HPL[{3, 1, 1, 2}, -S^2] - 5632*S*HPL[{3, 1, 2, 1}, -S^2] - 24448*S*HPL[{3, 2, 1, 1}, -S^2] - 70432*S*HPL[{4, 1, 1, 1}, -S^2] + (960*(2 + 3*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - 12448*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 37344*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 90560*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 26880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-3353*Pi^4*S)/90 + (-4 + 523*S^2 - 104*S^4)/(2*S) - (Pi^2*S*(34 - 1287*S^2 + 400*S^4 + 57*S^6))/(6*(1 + S^2)^2))*Zeta[3] - (8*S*(-17 - 9*S^2 + 3*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1, 1}, -S^2]*((8*(-6 + 54*S^2 + 211*S^4 + 12*S^6))/S^3 + (8*Pi^2*(35 + 556*S^2 + 517*S^4 + 94*S^6))/(3*S*(1 + S^2)^2) - 6112*S*Zeta[3]) + HPL[{2}, -S^2]^2*((4 - 25*S^2 + 810*S^4 - 22*S^6)/(4*S^3) + (Pi^2*(-46 + 2510*S^2 + 2123*S^4 + 174*S^6))/(6*S*(1 + S^2)^2) - 856*S*HPL[{3}, -S^2] + 784*S*HPL[{2, 1}, -S^2] - 744*S*Zeta[3]) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(283 + 33*S^2))/(12*S) - (5*Pi^2*(25 - 274*S^2 - 188*S^4 + 24*S^6))/(3*S*(1 + S^2)^2) + (65*(-1 + 6*S^2)*HPL[{2}, -S^2])/S - (1900*S*HPL[{3}, -S^2])/3 - 500*S*Zeta[3]) + HPL[{4}, -S^2]*((-12 + 395*S^2 + 1152*S^4 - 50*S^6)/(4*S^3) + (Pi^2*(-3 - 870*S^2 - 31*S^4 + 496*S^6))/(6*S*(1 + S^2)^2) - 192*S*HPL[{2, 1}, -S^2] - 124*S*Zeta[3]) + HPL[{0}, S^2]^4*((S*(1379 + 4*S^2))/48 + (Pi^2*S*(1694 + 2003*S^2 + 586*S^4))/(72*(1 + S^2)^2) + ((-253 + 2148*S^2 + 2215*S^4 + 382*S^6)*HPL[{1}, -S^2]^2)/(24*S*(1 + S^2)^2) + (142*S*HPL[{1}, -S^2]^3)/9 + ((12 + 1416*S^2 + 1591*S^4 + 428*S^6)*HPL[{2}, -S^2])/(24*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((277*Pi^2*S)/36 + (431 + 4196*S^2 + 2388*S^4 + 910*S^6 + 15*S^8)/(48*S*(1 + S^2)^2) + (241*S*HPL[{2}, -S^2])/12) - (7*S*HPL[{3}, -S^2])/4 + (25*S*HPL[{2, 1}, -S^2])/6 + (7*S*Zeta[3])/6) + HPL[{3, 1}, -S^2]*((44 - 559*S^2 - 1776*S^4 - 57*S^6)/(2*S^3) - (2*Pi^2*(94 + 841*S^2 + 850*S^4 + 213*S^6))/(3*S*(1 + S^2)^2) + 3088*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((1229*Pi^4*S)/30 + (-10 - 1837*S^2 - 518*S^4 + 104*S^6)/(2*S^3) + (Pi^2*(-594 - 4630*S^2 - 2029*S^4 + 496*S^6 + 57*S^8))/(6*S*(1 + S^2)^2) + 3776*S*HPL[{3, 1}, -S^2] + 6224*S*HPL[{2, 1, 1}, -S^2] + (16*(-25 + 346*S^2 + 277*S^4 + 4*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((6673*Pi^4*S)/135 + ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(6*S^3) + (Pi^2*(281 + 4618*S^2 + 26*S^4 + 954*S^6 + 45*S^8))/(9*S*(1 + S^2)^2) + ((784*Pi^2*S)/9 + (8*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] + (1568*S*HPL[{2}, -S^2]^2)/3 + (40*(14 - 246*S^2 - 59*S^4 + 106*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (1328*S*HPL[{4}, -S^2])/3 - (260*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S + (1328*S*HPL[{3, 1}, -S^2])/3 + (40*(3 - 62*S^2 - 8*S^4 + 32*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-118*Pi^4*S)/3 + (86 + 1101*S^2 + 1578*S^4 - 607*S^6)/(8*S^3) + (Pi^2*(111 + 187*S^2 + 1903*S^4 - 203*S^6 - 42*S^8))/(6*S*(1 + S^2)^2) + 172*S*HPL[{4}, -S^2] + (8*(-69 + 693*S^2 + 613*S^4 + 47*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 3424*S*HPL[{3, 1}, -S^2] - 6912*S*HPL[{2, 1, 1}, -S^2] + (2*(-3 - 170*S^2 - 81*S^4 + 36*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((1022*Pi^4*S)/135 + (8 + 3786*S^2 - 117*S^4)/(48*S) + (Pi^2*S*(2256 + 2315*S^2 + 1370*S^4 + 39*S^6))/(36*(1 + S^2)^2) + (2*(-134 + 1266*S^2 + 1109*S^4 + 74*S^6)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)^2) + (365*S*HPL[{1}, -S^2]^4)/9 + ((605*Pi^2*S)/18 + (16 + 932*S^2 + 743*S^4 + 493*S^6 + 6*S^8)/(6*S*(1 + S^2)^2))*HPL[{2}, -S^2] + (325*S*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((106*Pi^2*S)/3 + (198 + 2089*S^2 + 893*S^4 + 471*S^6 + 9*S^8)/(6*S*(1 + S^2)^2) + 110*S*HPL[{2}, -S^2]) + ((-10 + 27*S^2 + 54*S^4 + 23*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + (41*S*HPL[{4}, -S^2])/3 + (2*(129 - 391*S^2 - 344*S^4 + 11*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (692*S*HPL[{3, 1}, -S^2])/3 + (1396*S*HPL[{2, 1, 1}, -S^2])/3 + (S*(36 + 127*S^2 + 80*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(2 + 851*S^2 + 31*S^4))/(12*S^3) + (Pi^2*(-523 + 4636*S^2 + 4481*S^4 + 594*S^6))/(36*S*(1 + S^2)^2) + (2*(-62 + 578*S^2 + 517*S^4 + 42*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + 4*S*HPL[{3}, -S^2] - 220*S*HPL[{2, 1}, -S^2] - (22*S*Zeta[3])/3)) + (-316*Pi^2*S - (S*(70 - 867*S^2 + 670*S^4 + 87*S^6))/(1 + S^2)^2)*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(-4 + 2891*S^2 + 269*S^4))/(24*S^3) + ((1 + S^2)*(-28 + 3449*S^2 + 335*S^4))/(8*S^3) + (Pi^4*(-8587 + 87732*S^2 + 67765*S^4 - 1862*S^6))/(360*S*(1 + S^2)^2) - (196*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^2) + ((-994*Pi^2*S)/3 + (131 - 646*S^2 + 2836*S^4 - 202*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + (8*(14 - 222*S^2 - 71*S^4 + 82*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - 432*S*HPL[{5}, -S^2] + ((-784*Pi^2*S)/3 - (24*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] - (8*(-28 - 54*S^2 + 391*S^4 + 334*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 3136*S*HPL[{3, 2}, -S^2] + 10736*S*HPL[{4, 1}, -S^2] + (780*(-1 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/S + 6272*S*HPL[{2, 2, 1}, -S^2] + 11216*S*HPL[{3, 1, 1}, -S^2] + ((-832*Pi^2*S)/3 - (4*(2 + 211*S^2 - 418*S^4 + 123*S^6))/(S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-3*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 + (Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(3*S*(1 + S^2)^2) - 1568*S*HPL[{3}, -S^2] - 3136*S*HPL[{2, 1}, -S^2] - 1568*S*Zeta[3]) - 1520*S*Zeta[5]) + HPL[{2}, -S^2]*((Pi^2*(-44 + 407*S^2 + 1670*S^4 + 90*S^6))/(12*S^3) + (-233 + 1986*S^2 + 4881*S^4 + 106*S^6)/(8*S^3) + (Pi^4*(1076 + 33404*S^2 + 33265*S^4 + 7000*S^6))/(360*S*(1 + S^2)^2) + (-302*Pi^2*S + (-1 + 17*S^2 + 1391*S^4 - 231*S^6 - 36*S^8)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-7 - 486*S^2 + 179*S^4 + 432*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - 354*S*HPL[{5}, -S^2] + ((-812*Pi^2*S)/3 - (2*(105 + 1070*S^2 - 509*S^4 + 112*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (32*(-9 + 195*S^2 + 172*S^4 + 17*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 3268*S*HPL[{3, 2}, -S^2] + 10464*S*HPL[{4, 1}, -S^2] + (16*(-25 + 783*S^2 + 661*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 3136*S*HPL[{2, 2, 1}, -S^2] + 2496*S*HPL[{3, 1, 1}, -S^2] - 6224*S*HPL[{2, 1, 1, 1}, -S^2] + (-280*Pi^2*S + (74 - 90*S^2 + 1061*S^4 - 376*S^6 - 33*S^8)/(S*(1 + S^2)^2))*Zeta[3] - 1464*S*Zeta[5]) + HPL[{0}, S^2]^2*((Pi^2*S*(567 + 13*S^2))/6 + (-88 + 5041*S^2 + 106*S^4)/(16*S) + (Pi^4*S*(45352 + 48459*S^2 + 11556*S^4))/(720*(1 + S^2)^2) + (5*(-11 + 106*S^2 + 90*S^4 + 4*S^6)*HPL[{1}, -S^2]^4)/(S*(1 + S^2)^2) + 62*S*HPL[{1}, -S^2]^5 + ((4 + 944*S^2 + 801*S^4 + 76*S^6)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((749*Pi^2*S)/9 + (277 + 4196*S^2 + 862*S^4 + 708*S^6 + 45*S^8)/(6*S*(1 + S^2)^2) + (784*S*HPL[{2}, -S^2])/3) + ((-37*Pi^2*S)/3 + (25 + 193*S^2 + 333*S^4 + 71*S^6 - 6*S^8)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-3 + 38*S^2 + 125*S^4 + 76*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) - 37*S*HPL[{5}, -S^2] + (21*Pi^2*S + (2*(-65 - 590*S^2 - 121*S^4 + 15*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-23 - 1770*S^2 - 1541*S^4 - 180*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 86*S*HPL[{3, 2}, -S^2] + 288*S*HPL[{4, 1}, -S^2] + (8*(5 + 451*S^2 + 397*S^4 + 49*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 68*S*HPL[{2, 2, 1}, -S^2] - 8*S*HPL[{3, 1, 1}, -S^2] + 304*S*HPL[{2, 1, 1, 1}, -S^2] + ((-38*Pi^2*S)/3 - (2*S*(-22 - 75*S^2 - 9*S^4 + 3*S^6))/(1 + S^2)^2)*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(-1 + 369*S^2 + 26*S^4))/(2*S^3) + (Pi^2*(-583 + 5328*S^2 + 4915*S^4 + 502*S^6))/(12*S*(1 + S^2)^2) + ((-307 + 2796*S^2 + 2593*S^4 + 274*S^6)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^2) - 44*S*HPL[{3}, -S^2] - 784*S*HPL[{2, 1}, -S^2] - 82*S*Zeta[3]) + HPL[{2}, -S^2]*((-20 + 191*S^2 + 826*S^4 + 42*S^6)/(4*S^3) + (Pi^2*(32 + 3220*S^2 + 3179*S^4 + 624*S^6))/(12*S*(1 + S^2)^2) - 42*S*HPL[{3}, -S^2] - 34*S*HPL[{2, 1}, -S^2] - 76*S*Zeta[3]) + HPL[{1}, -S^2]*((8449*Pi^4*S)/360 + ((1 + S^2)*(-4 + 1707*S^2 + 105*S^4))/(8*S^3) + (Pi^2*(354 + 4196*S^2 + 1625*S^4 + 809*S^6 + 30*S^8))/(12*S*(1 + S^2)^2) + ((211*Pi^2*S)/2 + (163 + 2115*S^2 + 742*S^4 + 373*S^6 + 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2] + 215*S*HPL[{2}, -S^2]^2 + ((-3 - 76*S^2 + 77*S^4 + 106*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - 8*S*HPL[{4}, -S^2] + ((307 - 2796*S^2 - 2593*S^4 - 274*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 772*S*HPL[{3, 1}, -S^2] + 1568*S*HPL[{2, 1, 1}, -S^2] + (2*(4 - 98*S^2 - 3*S^4 + 58*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - 78*S*Zeta[5]) + HPL[{1}, -S^2]*((52285*Pi^6*S)/4536 + (Pi^2*(1 + S^2)*(4 + 1624*S^2 + 123*S^4))/(12*S^3) + ((1 + S^2)*(-153 + 4084*S^2 + 509*S^4))/(8*S^3) + (Pi^4*(3835 + 55782*S^2 + 9289*S^4 + 11425*S^6 + 699*S^8))/(360*S*(1 + S^2)^2) + ((607*Pi^2*S)/3 + (113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + 148*S*HPL[{3}, -S^2]^2 + ((-340*Pi^2*S)/3 + (153 + 193*S^2 + 1605*S^4 + 237*S^6)/(S*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(1 - 220*S^2 + 97*S^4 + 210*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) - 178*S*HPL[{6}, -S^2] - 3136*S*HPL[{2, 1}, -S^2]^2 + ((-440*Pi^2*S)/3 - (4*(122 + 803*S^2 + 1156*S^4 + 143*S^6))/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) - (4*(395 - 6948*S^2 - 1661*S^4 + 2998*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + 468*S*HPL[{4, 2}, -S^2] + 2704*S*HPL[{5, 1}, -S^2] + ((1568*Pi^2*S)/3 + (48*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (1568*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (16*(224 - 2298*S^2 - 1763*S^4 + 58*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 2656*S*HPL[{4, 1, 1}, -S^2] - (1560*(-1 + 6*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + 2656*S*HPL[{3, 1, 1, 1}, -S^2] + (-((1 + S^2)*(4 - 61*S^2 + 61*S^4))/(2*S^3) + (2*Pi^2*(49 - 1028*S^2 - 123*S^4 + 538*S^6))/(3*S*(1 + S^2)^2))*Zeta[3] + 80*S*Zeta[3]^2 + HPL[{3}, -S^2]*(-(((1 + S^2)*(10 - 279*S^2 + 49*S^4))/S^3) + (Pi^2*(137 - 2536*S^2 - 513*S^4 + 1166*S^6))/(3*S*(1 + S^2)^2) + 3136*S*HPL[{2, 1}, -S^2] - 200*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((6*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 - (2*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(3*S*(1 + S^2)^2) + 3136*S*Zeta[3]) + HPL[{2}, -S^2]*((2021*Pi^4*S)/60 - ((1 + S^2)*(72 - 2543*S^2 + 55*S^4))/(4*S^3) + (Pi^2*(355 + 3855*S^2 + 2482*S^4 + 565*S^6 + 15*S^8))/(6*S*(1 + S^2)^2) + (2*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - 452*S*HPL[{4}, -S^2] + (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 3136*S*HPL[{3, 1}, -S^2] + 6272*S*HPL[{2, 1, 1}, -S^2] + (224*(1 - 18*S^2 - 4*S^4 + 8*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + (2*(51 - 1724*S^2 + 199*S^4 + 1214*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]*((252431*Pi^6*S)/22680 + (Pi^2*(8 + 7000*S^2 + 165*S^4))/(48*S) + (-168 + 4324*S^2 + 509*S^4)/(8*S) + (Pi^4*S*(54302 + 37327*S^2 + 32948*S^4 + 1191*S^6))/(720*(1 + S^2)^2) - (56*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)^2) + (224*S*HPL[{1}, -S^2]^6)/3 + (182*Pi^2*S + (-37 + 897*S^2 - 78*S^4 + 571*S^6 + 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (746*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((1205*Pi^2*S)/9 + (5*(19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8))/(2*S*(1 + S^2)^2) + 500*S*HPL[{2}, -S^2]) - 24*S*HPL[{3}, -S^2]^2 + ((89*Pi^2*S)/3 + (40 + 420*S^2 + 487*S^4 + 294*S^6 + 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-9 + 216*S^2 + 229*S^4 + 50*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) + 166*S*HPL[{6}, -S^2] + ((Pi^2*(663 - 3002*S^2 - 2593*S^4 - 8*S^6))/(3*S*(1 + S^2)^2) + (-4 - 1539*S^2 - 316*S^4 + 107*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] - 3068*S*HPL[{2, 1}, -S^2]^2 + (-756*Pi^2*S + (-61 - 2040*S^2 - 230*S^4 - 1284*S^6 - 33*S^8)/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((19 + 442*S^2 + 67*S^4 - 204*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) - (2*(-47 - 508*S^2 + 35*S^4 + 314*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) - 6*S*HPL[{4, 2}, -S^2] - 252*S*HPL[{5, 1}, -S^2] + ((4576*Pi^2*S)/3 + (2*(58 + 2054*S^2 + 263*S^4 + 1312*S^6 + 45*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (16*(95 - 581*S^2 - 467*S^4 + 13*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (4*(1167 - 6872*S^2 - 5655*S^4 + 66*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 24*S*HPL[{3, 1, 2}, -S^2] + 5992*S*HPL[{3, 2, 1}, -S^2] + 18288*S*HPL[{4, 1, 1}, -S^2] - (120*(-27 + 148*S^2 + 127*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 12608*S*HPL[{3, 1, 1, 1}, -S^2] + 25440*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-(S*(-94 + 39*S^2))/2 + (2*Pi^2*S*(-115 + 5*S^2 + 73*S^4))/(3*(1 + S^2)^2))*Zeta[3] + 52*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(283 + 33*S^2))/(6*S) - (2*Pi^2*(344 - 3786*S^2 - 2579*S^4 + 346*S^6))/(9*S*(1 + S^2)^2) - (250*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (136*S*HPL[{3}, -S^2])/3 - 2000*S*HPL[{2, 1}, -S^2] - (664*S*Zeta[3])/3) + HPL[{3}, -S^2]*((-4 + 219*S^2 + 652*S^4 - 109*S^6)/(4*S^3) + (Pi^2*(-47 - 46*S^2 + 159*S^4 + 136*S^6))/(6*S*(1 + S^2)^2) + 80*S*HPL[{2, 1}, -S^2] - 16*S*Zeta[3]) + HPL[{2}, -S^2]*((769*Pi^4*S)/12 + (-66 + 484*S^2 + 1840*S^4 + 85*S^6)/(4*S^3) + (Pi^2*(30 + 1306*S^2 + 583*S^4 + 766*S^6 + 19*S^8))/(4*S*(1 + S^2)^2) + ((-11 - 220*S^2 - 27*S^4 + 106*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 50*S*HPL[{4}, -S^2] + (8*(95 - 581*S^2 - 467*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 3064*S*HPL[{3, 1}, -S^2] + 6136*S*HPL[{2, 1, 1}, -S^2] + (4*(-1 - 125*S^2 - 42*S^4 + 41*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((4061*Pi^4*S)/60 + ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(4*S^3) + (Pi^2*(681 + 9218*S^2 + 976*S^4 + 2142*S^6 + 63*S^8))/(12*S*(1 + S^2)^2) + (360*Pi^2*S + (4*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(S*(1 + S^2)^2))*HPL[{2}, -S^2] + 784*S*HPL[{2}, -S^2]^2 + (4*(5 - 54*S^2 - 38*S^4 + 4*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 92*S*HPL[{4}, -S^2] + (750*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 3000*S*HPL[{3, 1}, -S^2] + 6000*S*HPL[{2, 1, 1}, -S^2] + (4*(20 - 246*S^2 - 137*S^4 + 46*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + (2*S*(-232 - 139*S^2 + 28*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(4 + 3117*S^2 + 227*S^4))/(24*S^3) + ((1 + S^2)*(-28 + 3449*S^2 + 335*S^4))/(8*S^3) + (Pi^4*(-7801 + 79936*S^2 + 61445*S^4 - 1926*S^6))/(360*S*(1 + S^2)^2) - (196*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^2) + ((-22*Pi^2*S)/3 - (2*(-43 - 155*S^2 - 282*S^4 - 93*S^6 + 9*S^8))/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-17 + 252*S^2 + 95*S^4 - 82*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) + 92*S*HPL[{5}, -S^2] + (-720*Pi^2*S - (8*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (24*(31 - 374*S^2 - 216*S^4 + 64*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 304*S*HPL[{3, 2}, -S^2] + 728*S*HPL[{4, 1}, -S^2] - (1500*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 6272*S*HPL[{2, 2, 1}, -S^2] + 18544*S*HPL[{3, 1, 1}, -S^2] - 12000*S*HPL[{2, 1, 1, 1}, -S^2] + ((-188*Pi^2*S)/3 + (53 - 112*S^2 + 600*S^4 + 104*S^6 + 3*S^8)/(S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-20 + 977*S^2 + 25*S^4))/(2*S^3) + (Pi^2*(-623 + 6812*S^2 + 4693*S^4 - 582*S^6))/(6*S*(1 + S^2)^2) - 152*S*HPL[{3}, -S^2] - 3136*S*HPL[{2, 1}, -S^2] - 328*S*Zeta[3]) - 260*S*Zeta[5])) - 2232*S*Zeta[7]) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(-54 + 3938*S^2 + 309*S^4))/(48*S^3) + (Pi^4*(1 + S^2)*(-40 + 40563*S^2 + 3629*S^4))/(2880*S^3) + ((1 + S^2)*(-1610 + 20577*S^2 + 3797*S^4))/(64*S^3) + (Pi^6*(-37673 + 359832*S^2 + 309833*S^4 + 16898*S^6))/(18144*S*(1 + S^2)^2) + (83*(-1 + 6*S^2)*HPL[{2}, -S^2]^3)/(6*S) - (37*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3}, -S^2]^2)/(2*S*(1 + S^2)^2) + (-40*Pi^2*S + (239 + 1074*S^2 + 2144*S^4 + 460*S^6 + 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-119 + 120*S^2 + 1487*S^4 + 1070*S^6)*HPL[{6}, -S^2])/(2*S*(1 + S^2)^2) - 30*S*HPL[{7}, -S^2] + (392*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + ((826*Pi^2*S)/3 + (-51 + 768*S^2 - 2008*S^4 + 324*S^6 + 15*S^8)/(S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((2818*Pi^2*S)/3 + (-306 + 2111*S^2 - 7629*S^4 + 735*S^6 + 45*S^8)/(S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (117*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{4, 2}, -S^2])/(2*S*(1 + S^2)^2) - 94*S*HPL[{4, 3}, -S^2] - (26*(9 - 140*S^2 - 47*S^4 + 50*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) - 204*S*HPL[{5, 2}, -S^2] + 98*S*HPL[{6, 1}, -S^2] + ((2428*Pi^2*S)/3 + (2*(113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((5296*Pi^2*S)/3 + (4*(235 + 3055*S^2 + 632*S^4 + 631*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (332*(-1 + 6*S^2)*HPL[{3, 2, 1}, -S^2])/S - 3260*S*HPL[{3, 2, 2}, -S^2] - 9968*S*HPL[{3, 3, 1}, -S^2] + (4*(-193 + 108*S^2 + 2455*S^4 + 1822*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 9812*S*HPL[{4, 1, 2}, -S^2] - 30404*S*HPL[{4, 2, 1}, -S^2] - 62640*S*HPL[{5, 1, 1}, -S^2] + ((-1568*Pi^2*S)/3 - (48*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - (16*(-28 - 54*S^2 + 391*S^4 + 334*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 6272*S*HPL[{3, 1, 1, 2}, -S^2] + 6272*S*HPL[{3, 1, 2, 1}, -S^2] + 6272*S*HPL[{3, 2, 1, 1}, -S^2] + 21472*S*HPL[{4, 1, 1, 1}, -S^2] + (1560*(-1 + 6*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - 12544*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 37632*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 77920*S*HPL[{3, 1, 1, 1, 1}, -S^2] + ((-1013*Pi^4*S)/60 - ((1 + S^2)*(8 - 83*S^2 + 18*S^4))/(2*S^3) + (Pi^2*(11 - 832*S^2 + 1992*S^4 - 490*S^6 + 3*S^8))/(12*S*(1 + S^2)^2))*Zeta[3] + ((-9 + 116*S^2 + 59*S^4 - 26*S^6)*Zeta[3]^2)/(S*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-6*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 + (2*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(3*S*(1 + S^2)^2) - 3136*S*Zeta[3]) + HPL[{2}, -S^2]^2*(((1 + S^2)*(589 + 55*S^2))/(8*S) + (Pi^2*(-345 + 3808*S^2 + 2581*S^4 - 358*S^6))/(12*S*(1 + S^2)^2) - 466*S*HPL[{3}, -S^2] - 354*S*Zeta[3]) + HPL[{4}, -S^2]*(-((1 + S^2)*(4 - 1403*S^2 + 47*S^4))/(8*S^3) + (Pi^2*(89 - 1716*S^2 - 299*S^4 + 826*S^6))/(12*S*(1 + S^2)^2) + 452*S*HPL[{2, 1}, -S^2] - 56*S*Zeta[3]) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(20 - 1147*S^2 + 43*S^4))/(2*S^3) - (4*Pi^2*(-52 + 318*S^2 + 517*S^4 + 202*S^6))/(3*S*(1 + S^2)^2) + 1616*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-2021*Pi^4*S)/60 + ((1 + S^2)*(72 - 2543*S^2 + 55*S^4))/(4*S^3) + (Pi^2*(-355 - 3855*S^2 - 2482*S^4 - 565*S^6 - 15*S^8))/(6*S*(1 + S^2)^2) + 3136*S*HPL[{3, 1}, -S^2] + 6272*S*HPL[{2, 1, 1}, -S^2] - (224*(1 - 18*S^2 - 4*S^4 + 8*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-601*Pi^4*S)/30 - ((1 + S^2)*(42 - 1451*S^2 + 197*S^4))/(8*S^3) + (Pi^2*(189 - 342*S^2 + 3368*S^4 - 92*S^6 - 15*S^8))/(12*S*(1 + S^2)^2) + 86*S*HPL[{4}, -S^2] - (2*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 1568*S*HPL[{3, 1}, -S^2] - 3136*S*HPL[{2, 1, 1}, -S^2] + (4*(6 - 74*S^2 - 41*S^4 + 14*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + ((-419*Pi^2*S)/3 + (-23 - 342*S^2 + 843*S^4 - 355*S^6 + 3*S^8)/(S*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(92 - 3931*S^2 + 23*S^4))/(48*S^3) - ((1 + S^2)*(246 - 6919*S^2 + 49*S^4))/(16*S^3) + (Pi^4*(-6575 + 50552*S^2 + 60199*S^4 + 15198*S^6))/(720*S*(1 + S^2)^2) + ((-413*Pi^2*S)/3 + (51 - 768*S^2 + 2008*S^4 - 324*S^6 - 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2] + (113*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) - 164*S*HPL[{5}, -S^2] + ((-1214*Pi^2*S)/3 + (-113 - 2252*S^2 + 524*S^4 - 488*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (392*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 1708*S*HPL[{3, 2}, -S^2] + 5140*S*HPL[{4, 1}, -S^2] - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 3136*S*HPL[{3, 1, 1}, -S^2] - 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((-431*Pi^2*S)/3 + (29 - 375*S^2 + 998*S^4 - 181*S^6 - 15*S^8)/(S*(1 + S^2)^2))*Zeta[3] - 722*S*Zeta[5]) - 966*S*Zeta[7]) + HPL[{2}, -S^2]*((-478 + 7313*S^2 + 10659*S^4 - 288*S^6)/(16*S^3) + (Pi^2*(-169 + 1948*S^2 + 4422*S^4 + 106*S^6))/(48*S^3) + (Pi^4*(-316 + 3304*S^2 + 11100*S^4 + 563*S^6))/(720*S^3) + (Pi^6*(5748 + 404962*S^2 + 462245*S^4 + 129118*S^6))/(45360*S*(1 + S^2)^2) - (S*(-132 - 49*S^2 + 40*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-85*Pi^2*S)/3 - (2*(5 - 109*S^2 - 301*S^4 - 99*S^6 + 6*S^8))/(S*(1 + S^2)^2))*HPL[{5}, -S^2] + (2*(-5 + 108*S^2 + 336*S^4 + 202*S^6)*HPL[{6}, -S^2])/(S*(1 + S^2)^2) + 220*S*HPL[{7}, -S^2] - (12*(11 + 7*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((860*Pi^2*S)/3 + (-20 + 172*S^2 - 1255*S^4 + 288*S^6 + 27*S^8)/(S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + (913*Pi^2*S + (-66 + 440*S^2 - 8553*S^4 + 1410*S^6 + 189*S^8)/(2*S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (3*(1 - 154*S^2 - 51*S^4 + 52*S^6)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^2) - 132*S*HPL[{4, 3}, -S^2] + ((9 + 1480*S^2 - 227*S^4 - 1066*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) - 312*S*HPL[{5, 2}, -S^2] - 322*S*HPL[{6, 1}, -S^2] + ((-836*Pi^2*S)/3 - (2*(-131 - 864*S^2 + 158*S^4 + 15*S^6))/(S*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + (232*Pi^2*S + (2*(-394 - 2968*S^2 - 727*S^4 + 288*S^6 + 9*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (39*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 1, 2}, -S^2])/(S*(1 + S^2)^2) + ((-185 + 5468*S^2 + 4591*S^4 + 318*S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) - 3142*S*HPL[{3, 2, 2}, -S^2] - 9896*S*HPL[{3, 3, 1}, -S^2] + (2*(-343 + 8418*S^2 + 7475*S^4 + 792*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 9818*S*HPL[{4, 1, 2}, -S^2] - 30314*S*HPL[{4, 2, 1}, -S^2] - 62196*S*HPL[{5, 1, 1}, -S^2] + ((-1624*Pi^2*S)/3 - (4*(105 + 1070*S^2 - 509*S^4 + 112*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 3024*S*HPL[{2, 2, 2, 1}, -S^2] - (64*(90 + 456*S^2 + 397*S^4 + 80*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 2536*S*HPL[{3, 1, 1, 2}, -S^2] - 2536*S*HPL[{3, 1, 2, 1}, -S^2] - 11608*S*HPL[{3, 2, 1, 1}, -S^2] - 33504*S*HPL[{4, 1, 1, 1}, -S^2] + (32*(-25 + 783*S^2 + 661*S^4 + 49*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 6272*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 18816*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 45184*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 12448*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-2897*Pi^4*S)/180 - (3*(-4 - 96*S^2 - 19*S^4 + 38*S^6))/(4*S^3) + (Pi^2*(126 + 52*S^2 + 1325*S^4 - 358*S^6 - 33*S^8))/(12*S*(1 + S^2)^2))*Zeta[3] + (3*S*(12 + 29*S^2 + 16*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1, 1}, -S^2]*((4 - 25*S^2 + 810*S^4 - 22*S^6)/S^3 + (2*Pi^2*(-46 + 2510*S^2 + 2123*S^4 + 174*S^6))/(3*S*(1 + S^2)^2) - 2976*S*Zeta[3]) + HPL[{4}, -S^2]*((-151 + 584*S^2 - 65*S^4)/(4*S) + (Pi^2*S*(-99 + 82*S^2 + 125*S^4))/(3*(1 + S^2)^2) + 118*S*HPL[{2, 1}, -S^2] - 82*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((179 - 1856*S^2 + 83*S^4)/(4*S) + (Pi^2*(137 - 4988*S^2 - 4337*S^4 - 422*S^6))/(6*S*(1 + S^2)^2) + 1528*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-971*Pi^4*S)/60 + (20 - 1213*S^2 + 340*S^4 - 160*S^6)/(4*S^3) + (Pi^2*(-426 - 4168*S^2 + 1063*S^4 - 90*S^6 - 39*S^8))/(12*S*(1 + S^2)^2) - 1912*S*HPL[{3, 1}, -S^2] - 3136*S*HPL[{2, 1, 1}, -S^2] + (4*(-54 + 622*S^2 + 521*S^4 + 22*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-1639*Pi^4*S)/90 + (21 + 868*S^2 - 331*S^4)/(8*S) + (Pi^2*(3 + 64*S^2 + 832*S^4 - 76*S^6 - 21*S^8))/(6*S*(1 + S^2)^2) + 106*S*HPL[{4}, -S^2] + ((-283 + 3112*S^2 + 2413*S^4 - 50*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 1728*S*HPL[{3, 1}, -S^2] - 3424*S*HPL[{2, 1, 1}, -S^2] + ((-1 - 68*S^2 - 3*S^4 + 38*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + (-125*Pi^2*S + (226 + 360*S^2 + 1143*S^4 - 486*S^6 - 51*S^8)/(2*S*(1 + S^2)^2))*Zeta[5] - 756*S*Zeta[7]) + HPL[{1}, -S^2]*((13964*Pi^8*S)/14175 + (Pi^2*(1 + S^2)*(-163 + 5486*S^2 + 482*S^4))/(48*S^3) + (Pi^4*(1 + S^2)*(176 + 49911*S^2 + 3455*S^4))/(2880*S^3) + ((1 + S^2)*(-4410 + 30601*S^2 + 10855*S^4))/(64*S^3) + (Pi^6*(57227 + 682976*S^2 + 251017*S^4 + 158093*S^6 + 9975*S^8))/(45360*S*(1 + S^2)^2) + ((32*Pi^2*S)/3 + (2*(20 + 163*S^2 + 20*S^4))/(3*S*(1 + S^2)))*HPL[{2}, -S^2]^3 + 32*S*HPL[{2}, -S^2]^4 + ((37*Pi^2*S)/3 + (-15 + 98*S^2 - 214*S^4 - 34*S^6 - 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2]^2 - 18*S*HPL[{4}, -S^2]^2 + ((-67*Pi^2*S)/3 + (205 + 1207*S^2 + 1691*S^4 + 553*S^6 + 42*S^8)/(S*(1 + S^2)^2))*HPL[{6}, -S^2] + (6*(-23 + 82*S^2 + 258*S^4 + 148*S^6)*HPL[{7}, -S^2])/(S*(1 + S^2)^2) - 108*S*HPL[{8}, -S^2] + ((-1214*Pi^2*S)/3 + (-113 - 2252*S^2 + 524*S^4 - 488*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 + 1864*S*HPL[{3, 1}, -S^2]^2 + (38*Pi^2*S - (6*(4 - 25*S^2 + 55*S^4 + 6*S^6))/(S*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + (2*(9 - 130*S^2 - 52*S^4 + 40*S^6)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)^2) + ((692*Pi^2*S)/3 + (-333 - 478*S^2 - 3452*S^4 - 624*S^6 - 21*S^8)/(S*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + (6*(7 - 96*S^2 - 43*S^4 + 26*S^6)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)^2) - 24*S*HPL[{5, 3}, -S^2] + ((149 - 400*S^2 - 1737*S^4 - 1090*S^6)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)^2) - 60*S*HPL[{6, 2}, -S^2] + 108*S*HPL[{7, 1}, -S^2] + 6272*S*HPL[{2, 1, 1}, -S^2]^2 + (256*Pi^2*S + (16*(20 + 163*S^2 + 20*S^4))/(S*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((483 - 8452*S^2 - 2053*S^4 + 3622*S^6)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)^2) + (8*(187 - 3240*S^2 - 811*S^4 + 1370*S^6)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)^2) + 532*S*HPL[{3, 3, 2}, -S^2] + ((1624*Pi^2*S)/3 + (2*(633 + 4585*S^2 + 5997*S^4 + 717*S^6))/(S*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((1457 - 25452*S^2 - 6215*S^4 + 10882*S^6)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)^2) - 908*S*HPL[{4, 1, 3}, -S^2] + ((4613 - 79260*S^2 - 20339*S^4 + 33130*S^6)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)^2) + 376*S*HPL[{4, 2, 2}, -S^2] - 2908*S*HPL[{4, 3, 1}, -S^2] + (4*(2369 - 40796*S^2 - 10399*S^4 + 17106*S^6)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 1688*S*HPL[{5, 1, 2}, -S^2] - 12008*S*HPL[{5, 2, 1}, -S^2] - 31316*S*HPL[{6, 1, 1}, -S^2] - (664*(-1 + 6*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((-880*Pi^2*S)/3 - (8*(122 + 803*S^2 + 1156*S^4 + 143*S^6))/(S*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (16*(-181 + 1508*S^2 + 1599*S^4 + 302*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)^2) + (16*(-181 + 1508*S^2 + 1599*S^4 + 302*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)^2) + 312*S*HPL[{3, 1, 2, 2}, -S^2] + (8*(-611 + 4012*S^2 + 5937*S^4 + 2098*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 312*S*HPL[{3, 2, 1, 2}, -S^2] + 376*S*HPL[{3, 2, 2, 1}, -S^2] + 192*S*HPL[{3, 3, 1, 1}, -S^2] + (8*(-1889 + 12924*S^2 + 18095*S^4 + 5966*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 936*S*HPL[{4, 1, 1, 2}, -S^2] + 1128*S*HPL[{4, 1, 2, 1}, -S^2] + 1512*S*HPL[{4, 2, 1, 1}, -S^2] + 6560*S*HPL[{5, 1, 1, 1}, -S^2] + ((3136*Pi^2*S)/3 + (96*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] + (3136*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (9408*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (160*(112 - 1422*S^2 - 745*S^4 + 302*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 5312*S*HPL[{4, 1, 1, 1, 1}, -S^2] - (3120*(-1 + 6*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + 5312*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + ((29*Pi^2*S)/3 + (22 + 126*S^2 + 61*S^4 + 19*S^6 - 18*S^8)/(S*(1 + S^2)^2))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*(((1 + S^2)*(-20 + 2325*S^2 + 67*S^4))/S^3 + (4*Pi^2*(-449 + 4444*S^2 + 3615*S^4 + 46*S^6))/(3*S*(1 + S^2)^2) - 8896*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*(((1 + S^2)*(589 + 55*S^2))/S - (2*Pi^2*(345 - 3808*S^2 - 2581*S^4 + 358*S^6))/(3*S*(1 + S^2)^2) - 2832*S*Zeta[3]) + HPL[{5}, -S^2]*((-2*(1 + S^2)*(-3 - 126*S^2 + 2*S^4))/S^3 + (Pi^2*(-7 - 212*S^2 + 197*S^4 + 282*S^6))/(3*S*(1 + S^2)^2) + 328*S*HPL[{2, 1}, -S^2] + 24*S*Zeta[3]) + HPL[{3, 2}, -S^2]*(((1 + S^2)*(16 - 151*S^2 + 79*S^4))/(2*S^3) - (7*Pi^2*(17 - 304*S^2 - 69*S^4 + 134*S^6))/(3*S*(1 + S^2)^2) + 104*S*Zeta[3]) + HPL[{4, 1}, -S^2]*(((1 + S^2)*(100 - 2309*S^2 + 521*S^4))/(4*S^3) + (Pi^2*(-803 + 14484*S^2 + 3197*S^4 - 6454*S^6))/(6*S*(1 + S^2)^2) + 424*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((12*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 - (4*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(3*S*(1 + S^2)^2) + 6272*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((2021*Pi^4*S)/30 - ((1 + S^2)*(72 - 2543*S^2 + 55*S^4))/(2*S^3) + (Pi^2*(355 + 3855*S^2 + 2482*S^4 + 565*S^6 + 15*S^8))/(3*S*(1 + S^2)^2) + (448*(1 - 18*S^2 - 4*S^4 + 8*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{4}, -S^2]*(-7*Pi^4*S - ((1 + S^2)*(-16 - 1213*S^2 + 111*S^4))/(8*S^3) + (Pi^2*(101 + 260*S^2 + 1010*S^4 + 174*S^6 + 3*S^8))/(6*S*(1 + S^2)^2) - (113*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 484*S*HPL[{3, 1}, -S^2] - 904*S*HPL[{2, 1, 1}, -S^2] + ((5 - 132*S^2 + S^4 + 82*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((333*Pi^4*S)/20 + ((1 + S^2)*(4 + 567*S^2 + 47*S^4))/(8*S^3) + (Pi^2*(115 + 2052*S^2 - 114*S^4 + 392*S^6 + 15*S^8))/(12*S*(1 + S^2)^2) + ((75 - 1232*S^2 - 359*S^4 + 482*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - 164*S*HPL[{4}, -S^2] - (83*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S + 164*S*HPL[{3, 1}, -S^2] + ((47 - 896*S^2 - 163*S^4 + 426*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-398*Pi^4*S)/15 + ((1 + S^2)*(34 - 2585*S^2 + 103*S^4))/(4*S^3) + (Pi^2*(-419 - 3762*S^2 - 3140*S^4 - 692*S^6 - 15*S^8))/(6*S*(1 + S^2)^2) - 6272*S*HPL[{2, 1, 1}, -S^2] - (4*(59 - 1044*S^2 - 245*S^4 + 454*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + (-((1 + S^2)*(16 - 539*S^2 + 51*S^4))/(4*S^3) + (Pi^2*(37 - 1824*S^2 + 431*S^4 + 1454*S^6))/(6*S*(1 + S^2)^2))*Zeta[5] + HPL[{3}, -S^2]*(-(Pi^2*(1 + S^2)*(20 - 477*S^2 + 55*S^4))/(12*S^3) - (3*(1 + S^2)*(17 - 660*S^2 + 57*S^4))/(8*S^3) + (Pi^4*(391 - 8776*S^2 - 695*S^4 + 4866*S^6))/(180*S*(1 + S^2)^2) + ((-15 + 232*S^2 + 79*S^4 - 82*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) + 56*S*HPL[{5}, -S^2] + ((826*Pi^2*S)/3 + (-51 + 768*S^2 - 2008*S^4 + 324*S^6 + 15*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 344*S*HPL[{3, 2}, -S^2] - 108*S*HPL[{4, 1}, -S^2] + (4*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 3728*S*HPL[{2, 2, 1}, -S^2] - 10592*S*HPL[{3, 1, 1}, -S^2] + 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((-52*Pi^2*S)/3 - (2*(-15 - 11*S^2 - 111*S^4 - 6*S^6 + 9*S^8))/(S*(1 + S^2)^2))*Zeta[3] - 64*S*Zeta[5]) + Zeta[3]*(-((1 + S^2)*(26 - 489*S^2 + 26*S^4))/(4*S^3) - (Pi^2*(1 + S^2)*(8 - 327*S^2 + 35*S^4))/(24*S^3) + (Pi^4*(545 - 14336*S^2 + 83*S^4 + 8886*S^6))/(360*S*(1 + S^2)^2) + 124*S*Zeta[5]) + HPL[{2, 1}, -S^2]*((Pi^2*(1 + S^2)*(92 - 3931*S^2 + 23*S^4))/(24*S^3) + ((1 + S^2)*(246 - 6919*S^2 + 49*S^4))/(8*S^3) + (Pi^4*(6575 - 50552*S^2 - 60199*S^4 - 15198*S^6))/(360*S*(1 + S^2)^2) - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 3416*S*HPL[{3, 2}, -S^2] - 10280*S*HPL[{4, 1}, -S^2] - (1568*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 6272*S*HPL[{3, 1, 1}, -S^2] - 12544*S*HPL[{2, 1, 1, 1}, -S^2] + ((862*Pi^2*S)/3 + (2*(-29 + 375*S^2 - 998*S^4 + 181*S^6 + 15*S^8))/(S*(1 + S^2)^2))*Zeta[3] + 1444*S*Zeta[5]) + HPL[{2}, -S^2]*((1049*Pi^6*S)/360 + (Pi^2*(1 + S^2)*(-128 + 4715*S^2 + 3*S^4))/(48*S^3) + ((1 + S^2)*(-171 + 5183*S^2 + 57*S^4))/(8*S^3) + (Pi^4*(1121 + 12465*S^2 + 7275*S^4 + 2087*S^6 + 93*S^8))/(180*S*(1 + S^2)^2) + 86*S*HPL[{3}, -S^2]^2 + ((-112*Pi^2*S)/3 + (23 - 148*S^2 + 324*S^4 + 46*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{4}, -S^2] + ((27 - 436*S^2 - 133*S^4 + 166*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) - 84*S*HPL[{6}, -S^2] + ((-1210*Pi^2*S)/3 + (-109 - 2232*S^2 + 544*S^4 - 484*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-261 + 4460*S^2 + 1163*S^4 - 1850*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + ((-787 + 13428*S^2 + 3517*S^4 - 5558*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + 312*S*HPL[{4, 2}, -S^2] + 1264*S*HPL[{5, 1}, -S^2] + ((2428*Pi^2*S)/3 + (2*(113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (332*(-1 + 6*S^2)*HPL[{2, 2, 1}, -S^2])/S - (8*(-181 + 1508*S^2 + 1599*S^4 + 302*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 312*S*HPL[{3, 1, 2}, -S^2] + 2760*S*HPL[{3, 2, 1}, -S^2] + 8312*S*HPL[{4, 1, 1}, -S^2] + (1568*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 6272*S*HPL[{3, 1, 1, 1}, -S^2] + 12544*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((1 + S^2)*(4 - 221*S^2 + 121*S^4))/(4*S^3) + (Pi^2*(121 - 2208*S^2 - 469*S^4 + 998*S^6))/(6*S*(1 + S^2)^2))*Zeta[3] - 6*S*Zeta[3]^2 + HPL[{3}, -S^2]*(-((1 + S^2)*(16 - 151*S^2 + 79*S^4))/(4*S^3) + (7*Pi^2*(17 - 304*S^2 - 69*S^4 + 134*S^6))/(6*S*(1 + S^2)^2) + 1864*S*HPL[{2, 1}, -S^2] - 52*S*Zeta[3]) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(589 + 55*S^2))/(2*S) + (Pi^2*(345 - 3808*S^2 - 2581*S^4 + 358*S^6))/(3*S*(1 + S^2)^2) + 1416*S*Zeta[3]) + ((65 - 1704*S^2 + 7*S^4 + 1054*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + (6*(-5 - 302*S^2 + 216*S^4 + 352*S^6)*Zeta[7])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]*((2294333*Pi^8*S)/2721600 + (Pi^4*(80 + 75968*S^2 - 2589*S^4))/(5760*S) + (Pi^2*(-536 + 12927*S^2 + 1916*S^4))/(192*S) + (-2908 + 36581*S^2 + 10855*S^4)/(64*S) + (Pi^6*S*(1209160 + 967231*S^2 + 920954*S^4 + 166935*S^6))/(181440*(1 + S^2)^2) - (8*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^7)/(3*S*(1 + S^2)^2) + (8*S*HPL[{1}, -S^2]^8)/3 + ((529*Pi^2*S)/18 + (25 + 869*S^2 - 62*S^4 + 525*S^6 + 15*S^8)/(12*S*(1 + S^2)^2))*HPL[{2}, -S^2]^3 + (123*S*HPL[{2}, -S^2]^4)/4 + HPL[{1}, -S^2]^6*((241*Pi^2*S)/27 + (19 + 336*S^2 - 54*S^4 + 80*S^6 + 3*S^8)/(6*S*(1 + S^2)^2) + (100*S*HPL[{2}, -S^2])/3) + ((-17*Pi^2*S)/6 + (27 - 56*S^2 - 190*S^4 - 126*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{3}, -S^2]^2 - 4*S*HPL[{4}, -S^2]^2 + ((209*Pi^2*S)/6 + (-10 + 210*S^2 - 105*S^4 - 228*S^6 - 195*S^8)/(4*S*(1 + S^2)^2))*HPL[{6}, -S^2] + ((125 + 1290*S^2 + 1535*S^4 + 504*S^6)*HPL[{7}, -S^2])/(2*S*(1 + S^2)^2) + 376*S*HPL[{8}, -S^2] + (-364*Pi^2*S + (37 - 897*S^2 + 78*S^4 - 571*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 + 1524*S*HPL[{3, 1}, -S^2]^2 + ((-7*Pi^2*S)/6 + (3*(4 - 40*S^2 - 41*S^4 + 7*S^6))/(4*S*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((10 + 80*S^2 + 65*S^4 + 8*S^6)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)^2) + ((-139*Pi^2*S)/3 + (-65 - 824*S^2 - 1108*S^4 - 478*S^6 + 87*S^8)/(2*S*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + ((59 + 492*S^2 + 387*S^4 + 38*S^6)*HPL[{5, 2}, -S^2])/(2*S*(1 + S^2)^2) - 6*S*HPL[{5, 3}, -S^2] + ((44 - 8*S^2 - 183*S^4 - 124*S^6)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)^2) - 9*S*HPL[{6, 2}, -S^2] - 336*S*HPL[{7, 1}, -S^2] + 6136*S*HPL[{2, 1, 1}, -S^2]^2 + ((8*Pi^2*S)/3 + (3*(3 + 8*S^2 + S^4))/(2*S))*HPL[{3, 1, 2}, -S^2] + (708*Pi^2*S + (109 + 3518*S^2 - 188*S^4 + 2130*S^6 + 63*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] + ((-55 - 746*S^2 - 127*S^4 + 324*S^6)*HPL[{3, 2, 2}, -S^2])/(2*S*(1 + S^2)^2) + (8*(-9 - 144*S^2 - 26*S^4 + 62*S^6)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)^2) - 64*S*HPL[{3, 3, 2}, -S^2] + ((6526*Pi^2*S)/3 + (190 + 5634*S^2 + 115*S^4 + 3444*S^6 + 93*S^8)/(S*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((-73 - 1152*S^2 - 205*S^4 + 498*S^6)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)^2) + 140*S*HPL[{4, 1, 3}, -S^2] + ((-217 - 3528*S^2 - 685*S^4 + 1482*S^6)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)^2) - 61*S*HPL[{4, 2, 2}, -S^2] + 268*S*HPL[{4, 3, 1}, -S^2] + (2*(-225 - 3348*S^2 - 491*S^4 + 1526*S^6)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 146*S*HPL[{5, 1, 2}, -S^2] + 1106*S*HPL[{5, 2, 1}, -S^2] + 3212*S*HPL[{6, 1, 1}, -S^2] + ((-2*Pi^2*(-663 + 3002*S^2 + 2593*S^4 + 8*S^6))/(3*S*(1 + S^2)^2) + (-4 - 1539*S^2 - 316*S^4 + 107*S^6)/S^3)*HPL[{2, 1, 1, 1}, -S^2] - (16*(-98 + 527*S^2 + 463*S^4 + 15*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (-1512*Pi^2*S - (2*(61 + 2040*S^2 + 230*S^4 + 1284*S^6 + 33*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (2*(-2333 + 13090*S^2 + 11179*S^4 + 156*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)^2) + (2*(-2333 + 13090*S^2 + 11179*S^4 + 156*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)^2) + 12*S*HPL[{3, 1, 2, 2}, -S^2] + (2*(-4685 + 25738*S^2 + 22291*S^4 + 516*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 12*S*HPL[{3, 2, 1, 2}, -S^2] - 5988*S*HPL[{3, 2, 2, 1}, -S^2] - 18000*S*HPL[{3, 3, 1, 1}, -S^2] + (4*(-7009 + 38452*S^2 + 33301*S^4 + 766*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 12*S*HPL[{4, 1, 1, 2}, -S^2] - 18012*S*HPL[{4, 1, 2, 1}, -S^2] - 54012*S*HPL[{4, 2, 1, 1}, -S^2] - 108504*S*HPL[{5, 1, 1, 1}, -S^2] + ((9152*Pi^2*S)/3 + (4*(58 + 2054*S^2 + 263*S^4 + 1312*S^6 + 45*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (32*(95 - 581*S^2 - 467*S^4 + 13*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (96*(95 - 581*S^2 - 467*S^4 + 13*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 11936*S*HPL[{2, 2, 1, 2, 1}, -S^2] - 35808*S*HPL[{2, 2, 2, 1, 1}, -S^2] + (8*(1873 - 11720*S^2 - 9289*S^4 + 350*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 71664*S*HPL[{3, 1, 1, 1, 2}, -S^2] + 119408*S*HPL[{3, 1, 1, 2, 1}, -S^2] + 143280*S*HPL[{3, 1, 2, 1, 1}, -S^2] + 298448*S*HPL[{3, 2, 1, 1, 1}, -S^2] + 895968*S*HPL[{4, 1, 1, 1, 1}, -S^2] - (240*(-27 + 148*S^2 + 127*S^4 + 2*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 25216*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 50880*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((10*Pi^2*S)/3 + (S*(104 + 153*S^2 + 150*S^4 + 33*S^6))/(2*(1 + S^2)^2))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((Pi^2*(-1895 + 9206*S^2 + 7677*S^4 - 140*S^6))/(3*S*(1 + S^2)^2) + (4 + 2127*S^2 - 130*S^4 - 41*S^6)/S^3 - 80*S*Zeta[3]) + HPL[{1}, -S^2]^5*(((1 + S^2)*(283 + 33*S^2))/(12*S) + (Pi^2*(-344 + 3786*S^2 + 2579*S^4 - 346*S^6))/(45*S*(1 + S^2)^2) - (25*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (68*S*HPL[{3}, -S^2])/15 - 200*S*HPL[{2, 1}, -S^2] - (332*S*Zeta[3])/15) + HPL[{5}, -S^2]*((40 - 117*S^2 + 356*S^4 - 101*S^6)/(8*S^3) + (Pi^2*(31 + 544*S^2 + 535*S^4 + 114*S^6))/(12*S*(1 + S^2)^2) + 10*S*HPL[{2, 1}, -S^2] - 22*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((4 + 1345*S^2 - 304*S^4 + 9*S^6)/(2*S^3) - (2*Pi^2*(308 - 1542*S^2 - 1253*S^4 + 46*S^6))/(3*S*(1 + S^2)^2) - 16*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((Pi^2*(35 + 446*S^2 - 113*S^4 - 344*S^6))/(12*S*(1 + S^2)^2) + (-4 - 129*S^2 - 1196*S^4 + 213*S^6)/(8*S^3) - 4*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((3*(-80 - 301*S^2 + 74*S^4))/(2*S) + (Pi^2*(73 + 372*S^2 - 425*S^4 - 534*S^6))/(6*S*(1 + S^2)^2) + 20*S*Zeta[3]) + HPL[{4}, -S^2]*((183*Pi^4*S)/40 + (-72 - 216*S^2 + 656*S^4 - 383*S^6)/(16*S^3) + (Pi^2*(21 + 173*S^2 + 178*S^4 + 106*S^6))/(6*S*(1 + S^2)^2) + (2*(-1 + S^2 + 25*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 26*S*HPL[{3, 1}, -S^2] + 100*S*HPL[{2, 1, 1}, -S^2] + ((-15 - 26*S^2 + 13*S^4 + 20*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((769*Pi^4*S)/6 + (-66 + 484*S^2 + 1840*S^4 + 85*S^6)/(2*S^3) + (Pi^2*(30 + 1306*S^2 + 583*S^4 + 766*S^6 + 19*S^8))/(2*S*(1 + S^2)^2) + (8*(-1 - 125*S^2 - 42*S^4 + 41*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((4061*Pi^4*S)/360 + ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(24*S^3) + (Pi^2*(681 + 9218*S^2 + 976*S^4 + 2142*S^6 + 63*S^8))/(72*S*(1 + S^2)^2) + (60*Pi^2*S + (2*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(3*S*(1 + S^2)^2))*HPL[{2}, -S^2] + (392*S*HPL[{2}, -S^2]^2)/3 + (2*(5 - 54*S^2 - 38*S^4 + 4*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + (46*S*HPL[{4}, -S^2])/3 + (125*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 500*S*HPL[{3, 1}, -S^2] + 1000*S*HPL[{2, 1, 1}, -S^2] + (2*(20 - 246*S^2 - 137*S^4 + 46*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((709*Pi^4*S)/48 + (-12 - 292*S^2 + 1712*S^4 + 49*S^6)/(16*S^3) + (Pi^2*(-110 + 3312*S^2 + 945*S^4 + 1970*S^6 + 39*S^8))/(48*S*(1 + S^2)^2) + ((-11 - 184*S^2 - 35*S^4 + 78*S^6)*HPL[{3}, -S^2])/(4*S*(1 + S^2)^2) + (13*S*HPL[{4}, -S^2])/2 - (2*(-98 + 527*S^2 + 463*S^4 + 15*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 750*S*HPL[{3, 1}, -S^2] + 1492*S*HPL[{2, 1, 1}, -S^2] + ((-3 - 122*S^2 - 30*S^4 + 48*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-255*Pi^4*S)/4 + (138 - 1209*S^2 - 3762*S^4 - 119*S^6)/(8*S^3) + (Pi^2*(-131 - 3926*S^2 - 1646*S^4 - 2210*S^6 - 39*S^8))/(12*S*(1 + S^2)^2) - 6128*S*HPL[{2, 1, 1}, -S^2] - (2*(-5 - 268*S^2 - 91*S^4 + 86*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-2 - 1597*S^2 - 277*S^4 + 50*S^6))/(12*S^3) + (-39 - 3761*S^2 - 1063*S^4 + 103*S^6)/(8*S^3) + (Pi^4*(7153 - 27676*S^2 - 22936*S^4 + 1118*S^6))/(360*S*(1 + S^2)^2) - (2*(381 - 2328*S^2 - 1879*S^4 + 46*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 48*S*HPL[{3, 2}, -S^2] + 44*S*HPL[{4, 1}, -S^2] - (16*(95 - 581*S^2 - 467*S^4 + 13*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 5968*S*HPL[{2, 2, 1}, -S^2] + 18064*S*HPL[{3, 1, 1}, -S^2] - 12272*S*HPL[{2, 1, 1, 1}, -S^2] + ((2*Pi^2*S)/3 + (-67 + 94*S^2 - 192*S^4 - 28*S^6 - 3*S^8)/(S*(1 + S^2)^2))*Zeta[3]) + (-(S*(-54 + 199*S^2))/4 + (3*Pi^2*S*(8 + 61*S^2 + 44*S^4))/(2*(1 + S^2)^2))*Zeta[5] + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^2)*(4 + 3117*S^2 + 227*S^4))/(72*S^3) + ((1 + S^2)*(-28 + 3449*S^2 + 335*S^4))/(24*S^3) + (Pi^4*(-7801 + 79936*S^2 + 61445*S^4 - 1926*S^6))/(1080*S*(1 + S^2)^2) - (196*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^2) + ((-22*Pi^2*S)/9 - (2*(-43 - 155*S^2 - 282*S^4 - 93*S^6 + 9*S^8))/(3*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-17 + 252*S^2 + 95*S^4 - 82*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) + (92*S*HPL[{5}, -S^2])/3 + (-240*Pi^2*S - (8*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(3*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(31 - 374*S^2 - 216*S^4 + 64*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + (304*S*HPL[{3, 2}, -S^2])/3 + (728*S*HPL[{4, 1}, -S^2])/3 - (500*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (6272*S*HPL[{2, 2, 1}, -S^2])/3 + (18544*S*HPL[{3, 1, 1}, -S^2])/3 - 4000*S*HPL[{2, 1, 1, 1}, -S^2] + ((-188*Pi^2*S)/9 + (53 - 112*S^2 + 600*S^4 + 104*S^6 + 3*S^8)/(3*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-20 + 977*S^2 + 25*S^4))/(6*S^3) + (Pi^2*(-623 + 6812*S^2 + 4693*S^4 - 582*S^6))/(18*S*(1 + S^2)^2) - (152*S*HPL[{3}, -S^2])/3 - (3136*S*HPL[{2, 1}, -S^2])/3 - (328*S*Zeta[3])/3) - (260*S*Zeta[5])/3) + HPL[{3}, -S^2]*((-152 - 241*S^2 + 3824*S^4 - 715*S^6)/(32*S^3) + (Pi^2*(-16 + 459*S^2 + 1268*S^4 - 128*S^6))/(48*S^3) + (Pi^4*(-437 + 1786*S^2 + 3383*S^4 + 1460*S^6))/(720*S*(1 + S^2)^2) + ((-5 - 43*S^2 - 46*S^4 - 13*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) + 8*S*HPL[{5}, -S^2] + (10*Pi^2*S + (-107 + 126*S^2 + 62*S^4 + 130*S^6 - 3*S^8)/(2*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((13 + 212*S^2 + 45*S^4 - 86*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 32*S*HPL[{3, 2}, -S^2] - 44*S*HPL[{4, 1}, -S^2] + (2*(-11 - 220*S^2 - 27*S^4 + 106*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 48*S*HPL[{2, 2, 1}, -S^2] + 48*S*HPL[{3, 1, 1}, -S^2] + 160*S*HPL[{2, 1, 1, 1}, -S^2] + ((-16*Pi^2*S)/3 + (-4 + 46*S^2 + 135*S^4 + 72*S^6 + 3*S^8)/(2*S*(1 + S^2)^2))*Zeta[3] - 28*S*Zeta[5]) + Zeta[3]*(-(Pi^2*S*(-188 + 147*S^2))/12 - (3*(-32 + 26*S^2 + 59*S^4))/(16*S) + (Pi^4*S*(644 + 2433*S^2 + 1560*S^4))/(120*(1 + S^2)^2) + 8*S*Zeta[5]) + HPL[{2}, -S^2]*((235877*Pi^6*S)/45360 + (Pi^2*(-128 + 866*S^2 + 3687*S^4 + 50*S^6))/(48*S^3) + (-513 + 1795*S^2 + 8385*S^4 + 360*S^6)/(32*S^3) + (Pi^4*(774 + 52320*S^2 + 39607*S^4 + 31626*S^6 + 465*S^8))/(1440*S*(1 + S^2)^2) - 8*S*HPL[{3}, -S^2]^2 + ((37*Pi^2*S)/6 + (-68 + 172*S^2 + 533*S^4 + 322*S^6 - 3*S^8)/(4*S*(1 + S^2)^2))*HPL[{4}, -S^2] + ((9 + 96*S^2 + 145*S^4 + 62*S^6)*HPL[{5}, -S^2])/(2*S*(1 + S^2)^2) - 7*S*HPL[{6}, -S^2] - 1492*S*HPL[{2, 1}, -S^2]^2 + HPL[{3}, -S^2]*((79 + 680*S^2 - 105*S^4)/(8*S) + (Pi^2*(-19 - 220*S^2 + 67*S^4 + 178*S^6))/(12*S*(1 + S^2)^2) - 24*S*HPL[{2, 1}, -S^2]) + ((-1088*Pi^2*S)/3 + (57 - 1864*S^2 + 62*S^4 - 1180*S^6 - 27*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((23 + 364*S^2 + 59*S^4 - 162*S^6)*HPL[{3, 2}, -S^2])/(2*S*(1 + S^2)^2) + ((35 + 550*S^2 + 55*S^4 - 272*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + 3*S*HPL[{4, 2}, -S^2] - 18*S*HPL[{5, 1}, -S^2] + (728*Pi^2*S + (2*(-37 + 897*S^2 - 78*S^4 + 571*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(-98 + 527*S^2 + 463*S^4 + 15*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (2*(-1165 + 6544*S^2 + 5583*S^4 + 74*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 2952*S*HPL[{3, 2, 1}, -S^2] + 8956*S*HPL[{4, 1, 1}, -S^2] + (16*(95 - 581*S^2 - 467*S^4 + 13*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 77744*S*HPL[{3, 1, 1, 1}, -S^2] + 12272*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-2 - 13*S^2 + 49*S^4)/(2*S^3) + (Pi^2*(-14 - 260*S^2 - 23*S^4 + 132*S^6))/(6*S*(1 + S^2)^2))*Zeta[3] + 34*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-4 - 1345*S^2 + 304*S^4 - 9*S^6)/(4*S^3) + (Pi^2*(308 - 1542*S^2 - 1253*S^4 + 46*S^6))/(3*S*(1 + S^2)^2) + 8*S*Zeta[3]) + ((-20 - 184*S^2 - 43*S^4 + 68*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((248987*Pi^6*S)/45360 + (Pi^2*(1 + S^2)*(18 + 1729*S^2 + 93*S^4))/(24*S^3) + ((1 + S^2)*(-153 + 4084*S^2 + 509*S^4))/(16*S^3) + (Pi^4*(10761 + 118656*S^2 + 39488*S^4 + 30002*S^6 + 945*S^8))/(1440*S*(1 + S^2)^2) + ((551*Pi^2*S)/6 + (113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8)/(4*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + 118*S*HPL[{2}, -S^2]^3 - 4*S*HPL[{3}, -S^2]^2 + ((40*Pi^2*S)/3 + (113 + 662*S^2 + 476*S^4 + 274*S^6 - 21*S^8)/(4*S*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(3 - 58*S^2 - 10*S^4 + 28*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) + 73*S*HPL[{6}, -S^2] - 1568*S*HPL[{2, 1}, -S^2]^2 + (-360*Pi^2*S + (-199 - 2562*S^2 - 40*S^4 - 674*S^6 + 3*S^8)/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (38*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + ((-97 + 1116*S^2 + 703*S^4 - 146*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) - 108*S*HPL[{5, 1}, -S^2] + (720*Pi^2*S + (8*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) - (8*(289 - 3474*S^2 - 2020*S^4 + 584*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 2832*S*HPL[{3, 2, 1}, -S^2] + 8680*S*HPL[{4, 1, 1}, -S^2] + (1500*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 6000*S*HPL[{3, 1, 1, 1}, -S^2] + 12000*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(4 + 33*S^2 + 9*S^4))/(2*S^3) + (Pi^2*(37 - 524*S^2 - 219*S^4 + 154*S^6))/(6*S*(1 + S^2)^2))*Zeta[3] + 34*S*Zeta[3]^2 + HPL[{3}, -S^2]*(-((1 + S^2)*(24 - 431*S^2 + 55*S^4))/(4*S^3) + (Pi^2*(2 - 30*S^2 - 11*S^4 + 10*S^6))/(3*S*(1 + S^2)^2) + 152*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(-20 + 977*S^2 + 25*S^4))/(2*S^3) + (Pi^2*(623 - 6812*S^2 - 4693*S^4 + 582*S^6))/(6*S*(1 + S^2)^2) + 328*S*Zeta[3]) + HPL[{2}, -S^2]*((2155*Pi^4*S)/72 + ((1 + S^2)*(-40 + 2211*S^2 + 17*S^4))/(8*S^3) + (Pi^2*(823 + 9306*S^2 + 2194*S^4 + 2354*S^6 + 3*S^8))/(24*S*(1 + S^2)^2) + (19*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 8*S*HPL[{4}, -S^2] + (392*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 1568*S*HPL[{3, 1}, -S^2] + 3136*S*HPL[{2, 1, 1}, -S^2] + (41*(1 - 12*S^2 - 7*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + ((27 - 368*S^2 - 167*S^4 + 98*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + (15*S*(-14 - 3*S^2 + 6*S^4)*Zeta[7])/(1 + S^2)^2 + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(10 + 4114*S^2 + 275*S^4))/(48*S^3) + (Pi^4*(1 + S^2)*(40 + 47849*S^2 + 2291*S^4))/(2880*S^3) + ((1 + S^2)*(-1610 + 20577*S^2 + 3797*S^4))/(64*S^3) + (Pi^6*(-182305 + 1725168*S^2 + 1507381*S^4 + 97882*S^6))/(90720*S*(1 + S^2)^2) - (59*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^3)/(2*S*(1 + S^2)^2) + ((1 - 20*S^2 - 3*S^4 + 10*S^6)*HPL[{3}, -S^2]^2)/(2*S*(1 + S^2)^2) + ((46*Pi^2*S)/3 + (44 + 211*S^2 + 145*S^4 + 46*S^6 - 24*S^8)/(S*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-9 + 328*S^2 - 47*S^4 - 238*S^6)*HPL[{6}, -S^2])/(2*S*(1 + S^2)^2) + 134*S*HPL[{7}, -S^2] + (392*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + (30*Pi^2*S + (-43 - 32*S^2 - 368*S^4 - 60*S^6 + 15*S^8)/(S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((190*Pi^2*S)/3 + (-371 - 854*S^2 - 2684*S^4 - 634*S^6 + 111*S^8)/(2*S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (3*(-1 + 6*S^2)*HPL[{4, 2}, -S^2])/(2*S) + 26*S*HPL[{4, 3}, -S^2] + (2*(5 - 128*S^2 - S^4 + 78*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) + 84*S*HPL[{5, 2}, -S^2] + 14*S*HPL[{6, 1}, -S^2] + ((2204*Pi^2*S)/3 + (2*(113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((6568*Pi^2*S)/3 + (2*(425 + 7066*S^2 - 1008*S^4 + 1650*S^6 + 27*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (708*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) - 240*S*HPL[{3, 2, 2}, -S^2] - 752*S*HPL[{3, 3, 1}, -S^2] - (2*(1079 - 12996*S^2 - 7529*S^4 + 2206*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 752*S*HPL[{4, 1, 2}, -S^2] - 2288*S*HPL[{4, 2, 1}, -S^2] - 4424*S*HPL[{5, 1, 1}, -S^2] + (-1440*Pi^2*S - (16*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(S*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 5664*S*HPL[{2, 2, 2, 1}, -S^2] + (48*(31 - 374*S^2 - 216*S^4 + 64*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 17600*S*HPL[{3, 1, 1, 2}, -S^2] + 17600*S*HPL[{3, 1, 2, 1}, -S^2] + 34592*S*HPL[{3, 2, 1, 1}, -S^2] + 103408*S*HPL[{4, 1, 1, 1}, -S^2] - (3000*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 12544*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 37632*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 63264*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 24000*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-229*Pi^4*S)/60 + ((1 + S^2)*(28 + 5*S^2 + 17*S^4))/(4*S^3) + (Pi^2*(57 + 116*S^2 + 591*S^4 + 177*S^6 + 21*S^8))/(6*S*(1 + S^2)^2))*Zeta[3] + ((-9 + 104*S^2 + 65*S^4 - 14*S^6)*Zeta[3]^2)/(S*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*(((1 + S^2)*(-20 + 977*S^2 + 25*S^4))/S^3 + (Pi^2*(-623 + 6812*S^2 + 4693*S^4 - 582*S^6))/(3*S*(1 + S^2)^2) - 656*S*Zeta[3]) + HPL[{2}, -S^2]^2*(((1 + S^2)*(589 + 55*S^2))/(8*S) + (Pi^2*(-313 + 3456*S^2 + 2341*S^4 - 326*S^6))/(12*S*(1 + S^2)^2) - 30*S*HPL[{3}, -S^2] - 708*S*HPL[{2, 1}, -S^2] - 82*S*Zeta[3]) + HPL[{4}, -S^2]*((-5*(1 + S^2)*(4 - 79*S^2 + 31*S^4))/(8*S^3) + (Pi^2*(-29 + 436*S^2 + 159*S^4 - 146*S^6))/(12*S*(1 + S^2)^2) - 16*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((-6*(1 + S^2)*(-2 + 85*S^2))/S^3 + (Pi^2*(103 - 1132*S^2 - 773*S^4 + 102*S^6))/(S*(1 + S^2)^2) + 344*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-2155*Pi^4*S)/36 - ((1 + S^2)*(-40 + 2211*S^2 + 17*S^4))/(4*S^3) + (Pi^2*(-823 - 9306*S^2 - 2194*S^4 - 2354*S^6 - 3*S^8))/(12*S*(1 + S^2)^2) + 3136*S*HPL[{3, 1}, -S^2] + 6272*S*HPL[{2, 1, 1}, -S^2] - (82*(1 - 12*S^2 - 7*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((5*Pi^4*S)/6 - ((1 + S^2)*(66 - 1109*S^2 + 159*S^4))/(8*S^3) + (Pi^2*(74 + 329*S^2 + 477*S^4 + 166*S^6 - 12*S^8))/(6*S*(1 + S^2)^2) - 10*S*HPL[{4}, -S^2] - (38*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 136*S*HPL[{3, 1}, -S^2] - 304*S*HPL[{2, 1, 1}, -S^2] + (2*(1 - 12*S^2 - 7*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + (-27*Pi^2*S + (135 + 424*S^2 + 1232*S^4 + 474*S^6 + 51*S^8)/(2*S*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*(((1 + S^2)*(-142 + 4963*S^2 + 55*S^4))/(16*S^3) + (Pi^2*(1 + S^2)*(-84 + 3911*S^2 + 81*S^4))/(48*S^3) + (Pi^4*(-6891 + 70664*S^2 + 54251*S^4 - 1754*S^6))/(720*S*(1 + S^2)^2) + (-15*Pi^2*S + (43 + 32*S^2 + 368*S^4 + 60*S^6 - 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-1 + 36*S^2 - 5*S^4 - 26*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) + 4*S*HPL[{5}, -S^2] + ((-1102*Pi^2*S)/3 + (-113 - 2252*S^2 + 524*S^4 - 488*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (392*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 120*S*HPL[{3, 2}, -S^2] + 376*S*HPL[{4, 1}, -S^2] - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 2832*S*HPL[{2, 2, 1}, -S^2] - 8800*S*HPL[{3, 1, 1}, -S^2] - 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((-91*Pi^2*S)/3 + (55 - 114*S^2 + 602*S^4 + 118*S^6 + 3*S^8)/(2*S*(1 + S^2)^2))*Zeta[3] - 106*S*Zeta[5]) - 150*S*Zeta[7])) + Log[T]*((-1761997*Pi^8*S)/1360800 - (3*(-708 + 1625*S^2))/(32*S) + (Pi^4*(80 - 87564*S^2 - 353*S^4))/(2880*S) + (Pi^2*(696 - 14567*S^2 - 252*S^4))/(96*S) - (Pi^6*S*(1184824 + 642695*S^2 + 550902*S^4 + 47331*S^6))/(90720*(1 + S^2)^2) - (S*HPL[{0}, S^2]^8)/48 + ((-58*Pi^2*S)/3 + (-19 - 336*S^2 + 54*S^4 - 80*S^6 - 3*S^8)/(3*S*(1 + S^2)^2))*HPL[{1}, -S^2]^6 + (16*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^7)/(3*S*(1 + S^2)^2) - (16*S*HPL[{1}, -S^2]^8)/3 + HPL[{0}, S^2]^7*(-(S*(8 + 11*S^2 + 4*S^4))/(16*(1 + S^2)^2) - (S*HPL[{1}, -S^2])/8) + ((-401*Pi^2*S)/9 + (-29 - 440*S^2 - 318*S^4 - 15*S^6)/(6*S*(1 + S^2)))*HPL[{2}, -S^2]^3 - (65*S*HPL[{2}, -S^2]^4)/2 + HPL[{0}, S^2]^6*((-47*Pi^2*S)/144 - (S*(232 + 309*S^2 + 152*S^4 + 3*S^6))/(96*(1 + S^2)^2) + ((5 - 38*S^2 - 46*S^4 - 12*S^6)*HPL[{1}, -S^2])/(12*S*(1 + S^2)^2) - (3*S*HPL[{1}, -S^2]^2)/4 - (17*S*HPL[{2}, -S^2])/24) + ((-71*Pi^2*S)/3 + (17 + 76*S^2 + 467*S^4 + 112*S^6)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2]^2 - 16*S*HPL[{4}, -S^2]^2 + (-7*Pi^2*S + (-330 - 3590*S^2 - 5851*S^4 - 2280*S^6 - 45*S^8)/(2*S*(1 + S^2)^2))*HPL[{6}, -S^2] + ((95 - 2082*S^2 - 4599*S^4 - 2392*S^6)*HPL[{7}, -S^2])/(S*(1 + S^2)^2) - 836*S*HPL[{8}, -S^2] + ((1616*Pi^2*S)/3 - (2*(-8 - 1182*S^2 + 15*S^4 - 376*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - 1592*S*HPL[{3, 1}, -S^2]^2 + (-95*Pi^2*S + (-70 + 184*S^2 + 1637*S^4 + 414*S^6 - 33*S^8)/(2*S*(1 + S^2)^2))*HPL[{4, 2}, -S^2] - (2*(-4 - 8*S^2 + 231*S^4 + 188*S^6)*HPL[{4, 3}, -S^2])/(S*(1 + S^2)^2) + ((-1262*Pi^2*S)/3 - (2*(-50 - 814*S^2 - 2875*S^4 - 735*S^6 + 24*S^8))/(S*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + ((35 + 84*S^2 - 957*S^4 - 802*S^6)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)^2) + 44*S*HPL[{5, 3}, -S^2] + (2*(-4 + 464*S^2 + 1185*S^4 + 668*S^6)*HPL[{6, 1}, -S^2])/(S*(1 + S^2)^2) + 126*S*HPL[{6, 2}, -S^2] + 512*S*HPL[{7, 1}, -S^2] - 6320*S*HPL[{2, 1, 1}, -S^2]^2 + (52*Pi^2*S + (2*(37 - 116*S^2 - 69*S^4 + 6*S^6))/(S*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((-3052*Pi^2*S)/3 - (6*(7 + 332*S^2 + 235*S^4 + 8*S^6))/(S*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((57 + 5882*S^2 - 4707*S^4 - 7272*S^6)*HPL[{3, 2, 2}, -S^2])/(S*(1 + S^2)^2) - (8*(-33 - 2238*S^2 + 1853*S^4 + 2812*S^6)*HPL[{3, 3, 1}, -S^2])/(S*(1 + S^2)^2) - 928*S*HPL[{3, 3, 2}, -S^2] + ((-8584*Pi^2*S)/3 - (2*(186 + 3270*S^2 + 6867*S^4 + 2536*S^6 + 81*S^8))/(S*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] - (2*(-131 - 8586*S^2 + 7751*S^4 + 11300*S^6)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)^2) + 1512*S*HPL[{4, 1, 3}, -S^2] - (2*(-395 - 27354*S^2 + 22487*S^4 + 34244*S^6)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)^2) - 702*S*HPL[{4, 2, 2}, -S^2] + 5288*S*HPL[{4, 3, 1}, -S^2] - (4*(-393 - 28156*S^2 + 23167*S^4 + 35270*S^6)*HPL[{5, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 3132*S*HPL[{5, 1, 2}, -S^2] + 21852*S*HPL[{5, 2, 1}, -S^2] + 56304*S*HPL[{6, 1, 1}, -S^2] + (16*(-149 + 456*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((6016*Pi^2*S)/3 + (8*(53 + 542*S^2 + 1251*S^4 + 448*S^6 + 18*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] - (8*(-866 + 2219*S^2 + 3116*S^4 + 815*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S*(1 + S^2)^2) - (8*(-866 + 2219*S^2 + 3116*S^4 + 815*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S*(1 + S^2)^2) - 336*S*HPL[{3, 1, 2, 2}, -S^2] - (8*(-1760 + 3167*S^2 + 7694*S^4 + 3551*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 336*S*HPL[{3, 2, 1, 2}, -S^2] + 5936*S*HPL[{3, 2, 2, 1}, -S^2] + 18816*S*HPL[{3, 3, 1, 1}, -S^2] - (16*(-2663 + 5180*S^2 + 11639*S^4 + 5138*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 2288*S*HPL[{4, 1, 1, 2}, -S^2] + 16528*S*HPL[{4, 1, 2, 1}, -S^2] + 54160*S*HPL[{4, 2, 1, 1}, -S^2] + 102560*S*HPL[{5, 1, 1, 1}, -S^2] + ((-13600*Pi^2*S)/3 - (40*(10 + 232*S^2 + 155*S^4 + 9*S^6))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] - (64*(73 - 393*S^2 - 25*S^4 + 245*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (192*(73 - 393*S^2 - 25*S^4 + 245*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 12544*S*HPL[{2, 2, 1, 2, 1}, -S^2] + 37632*S*HPL[{2, 2, 2, 1, 1}, -S^2] - (80*(295 - 1912*S^2 + 161*S^4 + 1394*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 73984*S*HPL[{3, 1, 1, 1, 2}, -S^2] - 124160*S*HPL[{3, 1, 1, 2, 1}, -S^2] - 149248*S*HPL[{3, 1, 2, 1, 1}, -S^2] - 312320*S*HPL[{3, 2, 1, 1, 1}, -S^2] - 932160*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (1440*(-7 + 22*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + 21120*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 53760*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((2*Pi^2*S)/3 + (S*(-24 + 89*S^2 + 60*S^4 + 27*S^6))/(1 + S^2)^2)*Zeta[3]^2 + HPL[{4, 1}, -S^2]*((8 + 845*S^2 + 2172*S^4 - 912*S^6)/(2*S^3) + (Pi^2*(-61 - 4722*S^2 + 4829*S^4 + 6672*S^6))/(3*S*(1 + S^2)^2) - 984*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((-8*(-399 - 79*S^2 + 42*S^4))/S + (8*Pi^2*(-321 + 676*S^2 + 1335*S^4 + 534*S^6))/(3*S*(1 + S^2)^2) - 320*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((4 + 31*S^2 + 1068*S^4 - 561*S^6)/(4*S^3) + (Pi^2*(-55 - 2582*S^2 + 3261*S^4 + 4136*S^6))/(6*S*(1 + S^2)^2) - 304*S*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((12 - 4151*S^2 + 232*S^4 - 165*S^6)/S^3 + (4*Pi^2*(900 - 3027*S^2 - 2134*S^4 + 469*S^6))/(3*S*(1 + S^2)^2) - 288*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((-2*(-4 + 614*S^2 - 166*S^4 + 77*S^6))/S^3 + (4*Pi^2*(299 - 1298*S^2 - 458*S^4 + 532*S^6))/(3*S*(1 + S^2)^2) - 288*S*Zeta[3]) + HPL[{0}, S^2]^4*((-2731*Pi^4*S)/1440 + (S*(-6422 + 477*S^2))/192 - (Pi^2*S*(2807 + 3395*S^2 + 1723*S^4 + 27*S^6))/(144*(1 + S^2)^2) + ((253 - 2148*S^2 - 2215*S^4 - 382*S^6)*HPL[{1}, -S^2]^3)/(36*S*(1 + S^2)^2) - (71*S*HPL[{1}, -S^2]^4)/9 + ((-521*Pi^2*S)/72 + (-42 - 1001*S^2 - 957*S^4 - 483*S^6 - 3*S^8)/(24*S*(1 + S^2)^2))*HPL[{2}, -S^2] - (61*S*HPL[{2}, -S^2]^2)/6 + HPL[{1}, -S^2]^2*((-277*Pi^2*S)/36 + (-431 - 4196*S^2 - 2388*S^4 - 910*S^6 - 15*S^8)/(48*S*(1 + S^2)^2) - (241*S*HPL[{2}, -S^2])/12) + ((2 - 9*S^2 - 29*S^4 - 17*S^6)*HPL[{3}, -S^2])/(4*S*(1 + S^2)^2) - (9*S*HPL[{4}, -S^2])/4 + ((-240 + 460*S^2 + 435*S^4 - 24*S^6)*HPL[{2, 1}, -S^2])/(12*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(1079 + 7*S^2))/(48*S) + (Pi^2*(553 - 4428*S^2 - 4975*S^4 - 1102*S^6))/(144*S*(1 + S^2)^2) + ((114 - 938*S^2 - 1013*S^4 - 202*S^6)*HPL[{2}, -S^2])/(12*S*(1 + S^2)^2) + (S*HPL[{3}, -S^2])/2 + (241*S*HPL[{2, 1}, -S^2])/6) + (259*S*HPL[{3, 1}, -S^2])/6 - (266*S*HPL[{2, 1, 1}, -S^2])/3 - (133*S*Zeta[3])/6) + HPL[{5}, -S^2]*((Pi^2*(-7 - 184*S^2 - 1547*S^4 - 1130*S^6))/(6*S*(1 + S^2)^2) + (40 - 1293*S^2 - 1856*S^4 - 13*S^6)/(4*S^3) + 52*S*HPL[{2, 1}, -S^2] - 12*S*Zeta[3]) + HPL[{0}, S^2]^5*((-3*S*(18 + S^2))/8 - (Pi^2*S*(2110 + 2755*S^2 + 938*S^4))/(360*(1 + S^2)^2) + ((255 - 2104*S^2 - 2263*S^4 - 446*S^6)*HPL[{1}, -S^2]^2)/(120*S*(1 + S^2)^2) - (271*S*HPL[{1}, -S^2]^3)/90 - (7*S*(200 + 235*S^2 + 68*S^4)*HPL[{2}, -S^2])/(120*(1 + S^2)^2) + HPL[{1}, -S^2]*((-293*Pi^2*S)/180 + (-305 - 2530*S^2 - 1827*S^4 - 701*S^6 - 15*S^8)/(120*S*(1 + S^2)^2) - (77*S*HPL[{2}, -S^2])/20) + (S*HPL[{3}, -S^2])/4 - (5*S*HPL[{2, 1}, -S^2])/6 - (3*S*Zeta[3])/2) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(283 + 33*S^2))/(6*S) + (2*Pi^2*(25 - 274*S^2 - 188*S^4 + 24*S^6))/(3*S*(1 + S^2)^2) - (26*(-1 + 6*S^2)*HPL[{2}, -S^2])/S + (760*S*HPL[{3}, -S^2])/3 + 200*S*Zeta[3]) + HPL[{1}, -S^2]^4*((-6673*Pi^4*S)/270 - ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(12*S^3) + (Pi^2*(-281 - 4618*S^2 - 26*S^4 - 954*S^6 - 45*S^8))/(18*S*(1 + S^2)^2) + ((-392*Pi^2*S)/9 - (4*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2}, -S^2] - (784*S*HPL[{2}, -S^2]^2)/3 - (20*(14 - 246*S^2 - 59*S^4 + 106*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + (664*S*HPL[{4}, -S^2])/3 + (130*(-1 + 6*S^2)*HPL[{2, 1}, -S^2])/S - (664*S*HPL[{3, 1}, -S^2])/3 - (20*(3 - 62*S^2 - 8*S^4 + 32*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{4}, -S^2]*((33*Pi^4*S)/4 + (-24 - 1862*S^2 - 2584*S^4 + 383*S^6)/(8*S^3) + (Pi^2*(-31 - 416*S^2 - 1420*S^4 - 358*S^6 - 3*S^8))/(6*S*(1 + S^2)^2) - (4*(-60 + 435*S^2 + 485*S^4 + 103*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 1076*S*HPL[{3, 1}, -S^2] + 2192*S*HPL[{2, 1, 1}, -S^2] - (2*(1 + 16*S^2 + 169*S^4 + 126*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-650*Pi^4*S)/3 + (82 - 634*S^2 - 1970*S^4 - 49*S^6)/S^3 + (Pi^2*(-116 - 3080*S^2 - 2935*S^4 - 1626*S^6 - 87*S^8))/(3*S*(1 + S^2)^2) - (32*(3 - 158*S^2 + 165*S^4 + 228*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-605*Pi^4*S)/24 + (-28 + 71*S^2 - 1568*S^4 + 66*S^6)/(8*S^3) + (Pi^2*(-34 - 4040*S^2 - 607*S^4 - 1478*S^6 - 21*S^8))/(24*S*(1 + S^2)^2) + ((-17 + 1816*S^2 - 977*S^4 - 1878*S^6)*HPL[{3}, -S^2])/(2*S*(1 + S^2)^2) + 269*S*HPL[{4}, -S^2] + (2*(-149 + 456*S^2)*HPL[{2, 1}, -S^2])/S + 628*S*HPL[{3, 1}, -S^2] - 1568*S*HPL[{2, 1, 1}, -S^2] - (2*(-7 - 274*S^2 + 358*S^4 + 448*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((2981*Pi^4*S)/30 + (-114 + 1575*S^2 + 4066*S^4 + 81*S^6)/(4*S^3) + (Pi^2*(190 + 2982*S^2 + 3537*S^4 + 1700*S^6 + 75*S^8))/(6*S*(1 + S^2)^2) + 4992*S*HPL[{2, 1, 1}, -S^2] + (4*(13 - 674*S^2 + 633*S^4 + 916*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + (15*S*(-26 + 11*S^2) - (Pi^2*S*(-72 + 1951*S^2 + 1604*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{0}, S^2]^3*((-3*Pi^2*S*(24 + S^2))/2 + (80 - 7774*S^2 + 79*S^4)/(96*S) - (7*Pi^4*S*(3494 + 4133*S^2 + 1210*S^4))/(1080*(1 + S^2)^2) + ((134 - 1266*S^2 - 1109*S^4 - 74*S^6)*HPL[{1}, -S^2]^4)/(9*S*(1 + S^2)^2) - (146*S*HPL[{1}, -S^2]^5)/9 + ((-1 - 724*S^2 - 650*S^4 - 86*S^6)*HPL[{2}, -S^2]^2)/(6*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-212*Pi^2*S)/9 + (-198 - 2089*S^2 - 893*S^4 - 471*S^6 - 9*S^8)/(9*S*(1 + S^2)^2) - (220*S*HPL[{2}, -S^2])/3) + ((4*Pi^2*S)/3 + (-18 - 328*S^2 - 465*S^4 - 194*S^6 + 9*S^8)/(12*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((5 - 24*S^2 + 22*S^4 + 34*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) + 4*S*HPL[{5}, -S^2] + ((-44*Pi^2*S)/9 + (391 + 2274*S^2 + 572*S^4 - 9*S^8)/(6*S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (10*(1 + 149*S^2 + 130*S^4 + 15*S^6)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^2) - (10*S*HPL[{3, 2}, -S^2])/3 - (38*S*HPL[{4, 1}, -S^2])/3 - (20*(1 + 153*S^2 + 138*S^4 + 19*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)^2) + (28*S*HPL[{2, 2, 1}, -S^2])/3 + 40*S*HPL[{3, 1, 1}, -S^2] - (152*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-38*Pi^2*S)/9 + (S*(-394 - 777*S^2 - 318*S^4 + 21*S^6))/(6*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-10 - 2930*S^2 - 3025*S^4 - 666*S^6))/(36*S*(1 + S^2)^2) + (22 - 129*S^2 - 875*S^4 - 12*S^6)/(12*S^3) + (4*S*HPL[{3}, -S^2])/3 - (14*S*HPL[{2, 1}, -S^2])/3 + (16*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(2 + 851*S^2 + 31*S^4))/(12*S^3) + (Pi^2*(523 - 4636*S^2 - 4481*S^4 - 594*S^6))/(36*S*(1 + S^2)^2) - (2*(-62 + 578*S^2 + 517*S^4 + 42*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) - 4*S*HPL[{3}, -S^2] + 220*S*HPL[{2, 1}, -S^2] + (22*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-3997*Pi^4*S)/540 - ((1 + S^2)*(8 + 639*S^2 + 15*S^4))/(8*S^3) + (Pi^2*(-503 - 4619*S^2 - 2720*S^4 - 1172*S^6 - 24*S^8))/(36*S*(1 + S^2)^2) + ((-187*Pi^2*S)/6 + (-423 - 4138*S^2 - 2058*S^4 - 986*S^6 - 3*S^8)/(12*S*(1 + S^2)^2))*HPL[{2}, -S^2] - 53*S*HPL[{2}, -S^2]^2 - (2*(-1 + 8*S^2 + 9*S^4 + 2*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - (34*S*HPL[{4}, -S^2])/3 + (4*(-62 + 578*S^2 + 517*S^4 + 42*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) + 220*S*HPL[{3, 1}, -S^2] - 440*S*HPL[{2, 1, 1}, -S^2] + ((3 + 32*S^2 - 55*S^4 - 62*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) - 26*S*Zeta[5]) + HPL[{2, 1}, -S^2]*((Pi^2*(-4 + 3025*S^2 + 568*S^4 - 203*S^6))/(12*S^3) + (-13 + 4687*S^2 + 1989*S^4 - 155*S^6)/(4*S^3) + (Pi^4*(-7651 + 17148*S^2 + 26934*S^4 + 8198*S^6))/(180*S*(1 + S^2)^2) + (32*(31 - 198*S^2 + S^4 + 132*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 296*S*HPL[{3, 2}, -S^2] - 368*S*HPL[{4, 1}, -S^2] + (32*(73 - 393*S^2 - 25*S^4 + 245*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 6272*S*HPL[{2, 2, 1}, -S^2] - 17536*S*HPL[{3, 1, 1}, -S^2] + 12640*S*HPL[{2, 1, 1, 1}, -S^2] + ((-44*Pi^2*S)/3 + (2*(-16 - 660*S^2 + 935*S^4 + 14*S^6 + 3*S^8))/(S*(1 + S^2)^2))*Zeta[3] + 40*S*Zeta[5]) + HPL[{3}, -S^2]*((Pi^4*(177 + 10934*S^2 - 14723*S^4 - 18268*S^6))/(360*S*(1 + S^2)^2) + (Pi^2*(-16 - 747*S^2 - 1408*S^4 + 338*S^6))/(24*S^3) + (-408 - 4119*S^2 - 4424*S^4 + 1059*S^6)/(16*S^3) + (2*(-2 - 29*S^2 + 163*S^4 + 147*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) + ((160*Pi^2*S)/3 + (2*(52 - 785*S^2 + 617*S^4 - 93*S^6 + 21*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(-61 - 1312*S^2 + 1479*S^4 + 1946*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + 616*S*HPL[{3, 2}, -S^2] + 280*S*HPL[{4, 1}, -S^2] - (8*(-25 - 634*S^2 + 767*S^4 + 984*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 608*S*HPL[{2, 2, 1}, -S^2] + 640*S*HPL[{3, 1, 1}, -S^2] + 1280*S*HPL[{2, 1, 1, 1}, -S^2] + ((76*Pi^2*S)/3 + (15 - 46*S^2 - 358*S^4 - 58*S^6 + 39*S^8)/(S*(1 + S^2)^2))*Zeta[3] + 56*S*Zeta[5]) + Zeta[3]*((13*Pi^2*S*(-42 + 19*S^2))/12 + (24 - 1973*S^2 + 155*S^4)/(4*S) - (Pi^4*S*(-644 + 3777*S^2 + 3408*S^4))/(60*(1 + S^2)^2) + 200*S*Zeta[5]) + HPL[{1}, -S^2]^3*(-(Pi^2*(1 + S^2)*(-4 + 2891*S^2 + 269*S^4))/(36*S^3) - ((1 + S^2)*(-28 + 3449*S^2 + 335*S^4))/(12*S^3) + (Pi^4*(8587 - 87732*S^2 - 67765*S^4 + 1862*S^6))/(540*S*(1 + S^2)^2) + (392*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)^2) + ((1988*Pi^2*S)/9 + (2*(-131 + 646*S^2 - 2836*S^4 + 202*S^6 + 15*S^8))/(3*S*(1 + S^2)^2))*HPL[{3}, -S^2] - (16*(14 - 222*S^2 - 71*S^4 + 82*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) + 288*S*HPL[{5}, -S^2] + ((1568*Pi^2*S)/9 + (16*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1}, -S^2] + (16*(-28 - 54*S^2 + 391*S^4 + 334*S^6)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^2) - (6272*S*HPL[{3, 2}, -S^2])/3 - (21472*S*HPL[{4, 1}, -S^2])/3 - (520*(-1 + 6*S^2)*HPL[{2, 1, 1}, -S^2])/S - (12544*S*HPL[{2, 2, 1}, -S^2])/3 - (22432*S*HPL[{3, 1, 1}, -S^2])/3 + ((1664*Pi^2*S)/9 + (8*(2 + 211*S^2 - 418*S^4 + 123*S^6))/(3*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((2*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 - (2*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(9*S*(1 + S^2)^2) + (3136*S*HPL[{3}, -S^2])/3 + (6272*S*HPL[{2, 1}, -S^2])/3 + (3136*S*Zeta[3])/3) + (3040*S*Zeta[5])/3) + HPL[{2}, -S^2]*((-200803*Pi^6*S)/22680 + (553 - 7363*S^2 - 13885*S^4 - 252*S^6)/(16*S^3) + (Pi^2*(136 - 1201*S^2 - 3739*S^4 - 97*S^6))/(24*S^3) + (Pi^4*(-1718 - 43968*S^2 - 38535*S^4 - 21842*S^6 - 1305*S^8))/(720*S*(1 + S^2)^2) - 152*S*HPL[{3}, -S^2]^2 + ((269*Pi^2*S)/3 + (10 - 300*S^2 - 1659*S^4 - 430*S^6 + 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-5 + 48*S^2 - 709*S^4 - 598*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) + 26*S*HPL[{6}, -S^2] + 1568*S*HPL[{2, 1}, -S^2]^2 + ((1444*Pi^2*S)/3 - (2*(23 - 1254*S^2 - 141*S^4 - 426*S^6 + 6*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-5 - 3164*S^2 + 2227*S^4 + 3678*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + (2*(-69 - 4578*S^2 + 3901*S^4 + 5840*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) - 546*S*HPL[{4, 2}, -S^2] - 2532*S*HPL[{5, 1}, -S^2] + ((-3232*Pi^2*S)/3 + (4*(-8 - 1182*S^2 + 15*S^4 - 376*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(-149 + 456*S^2)*HPL[{2, 2, 1}, -S^2])/S + (16*(-211 + 554*S^2 + 761*S^4 + 192*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 312*S*HPL[{3, 1, 2}, -S^2] - 2808*S*HPL[{3, 2, 1}, -S^2] - 7168*S*HPL[{4, 1, 1}, -S^2] - (32*(73 - 393*S^2 - 25*S^4 + 245*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 80256*S*HPL[{3, 1, 1, 1}, -S^2] - 12640*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(-14 + 688*S^2 - 737*S^4 - 1008*S^6))/(3*S*(1 + S^2)^2) + (-4 - 167*S^2 - 64*S^4 + 133*S^6)/(2*S^3))*Zeta[3] - 48*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-4 + 614*S^2 - 166*S^4 + 77*S^6)/S^3 - (2*Pi^2*(299 - 1298*S^2 - 458*S^4 + 532*S^6))/(3*S*(1 + S^2)^2) + 144*S*Zeta[3]) + HPL[{3}, -S^2]*((53 - 656*S^2 + 305*S^4)/(4*S) + (Pi^2*(51 + 1292*S^2 - 1699*S^4 - 2114*S^6))/(6*S*(1 + S^2)^2) - 304*S*HPL[{2, 1}, -S^2] + 168*S*Zeta[3]) - (2*(20 - 328*S^2 + 1089*S^4 + 1076*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-52285*Pi^6*S)/4536 - (Pi^2*(1 + S^2)*(4 + 1624*S^2 + 123*S^4))/(12*S^3) - ((1 + S^2)*(-153 + 4084*S^2 + 509*S^4))/(8*S^3) + (Pi^4*(-3835 - 55782*S^2 - 9289*S^4 - 11425*S^6 - 699*S^8))/(360*S*(1 + S^2)^2) + ((-607*Pi^2*S)/3 + (-113 - 2252*S^2 + 524*S^4 - 488*S^6 - 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - 148*S*HPL[{3}, -S^2]^2 + ((340*Pi^2*S)/3 + (-153 - 193*S^2 - 1605*S^4 - 237*S^6)/(S*(1 + S^2)^2))*HPL[{4}, -S^2] - (4*(1 - 220*S^2 + 97*S^4 + 210*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) + 178*S*HPL[{6}, -S^2] + 3136*S*HPL[{2, 1}, -S^2]^2 + ((440*Pi^2*S)/3 + (4*(122 + 803*S^2 + 1156*S^4 + 143*S^6))/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + (4*(395 - 6948*S^2 - 1661*S^4 + 2998*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) - 468*S*HPL[{4, 2}, -S^2] - 2704*S*HPL[{5, 1}, -S^2] + ((-1568*Pi^2*S)/3 - (48*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (1568*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (16*(224 - 2298*S^2 - 1763*S^4 + 58*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 2656*S*HPL[{4, 1, 1}, -S^2] + (1560*(-1 + 6*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - 2656*S*HPL[{3, 1, 1, 1}, -S^2] + (((1 + S^2)*(4 - 61*S^2 + 61*S^4))/(2*S^3) - (2*Pi^2*(49 - 1028*S^2 - 123*S^4 + 538*S^6))/(3*S*(1 + S^2)^2))*Zeta[3] - 80*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-6*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 + (2*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(3*S*(1 + S^2)^2) - 3136*S*Zeta[3]) + HPL[{3}, -S^2]*(((1 + S^2)*(10 - 279*S^2 + 49*S^4))/S^3 + (Pi^2*(-137 + 2536*S^2 + 513*S^4 - 1166*S^6))/(3*S*(1 + S^2)^2) - 3136*S*HPL[{2, 1}, -S^2] + 200*S*Zeta[3]) + HPL[{2}, -S^2]*((-2021*Pi^4*S)/60 + ((1 + S^2)*(72 - 2543*S^2 + 55*S^4))/(4*S^3) + (Pi^2*(-355 - 3855*S^2 - 2482*S^4 - 565*S^6 - 15*S^8))/(6*S*(1 + S^2)^2) - (2*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 452*S*HPL[{4}, -S^2] - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 3136*S*HPL[{3, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2] - (224*(1 - 18*S^2 - 4*S^4 + 8*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - (2*(51 - 1724*S^2 + 199*S^4 + 1214*S^6)*Zeta[5])/(S*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((-95363*Pi^6*S)/22680 + (360 - 14153*S^2 - 252*S^4)/(32*S) + (Pi^2*(8 - 10522*S^2 + 379*S^4))/(96*S) - (Pi^4*S*(30433 + 30261*S^2 + 17260*S^4 + 534*S^6))/(720*(1 + S^2)^2) - (2*(-11 + 106*S^2 + 90*S^4 + 4*S^6)*HPL[{1}, -S^2]^5)/(S*(1 + S^2)^2) - (62*S*HPL[{1}, -S^2]^6)/3 + ((-219*Pi^2*S)/4 + (-18 - 1676*S^2 - 637*S^4 - 726*S^6 - 27*S^8)/(8*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (205*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((-749*Pi^2*S)/18 + (-277 - 4196*S^2 - 862*S^4 - 708*S^6 - 45*S^8)/(12*S*(1 + S^2)^2) - (392*S*HPL[{2}, -S^2])/3) + 3*S*HPL[{3}, -S^2]^2 + ((-37*Pi^2*S)/6 + (-50 - 376*S^2 - 521*S^4 - 178*S^6 - 15*S^8)/(4*S*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(1 + 47*S^2 + 121*S^4 + 69*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) - 39*S*HPL[{6}, -S^2] + 826*S*HPL[{2, 1}, -S^2]^2 + (227*Pi^2*S + (84 + 1898*S^2 + 1035*S^4 + 804*S^6 + 39*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((1 - 40*S^2 + 337*S^4 + 294*S^6)*HPL[{3, 2}, -S^2])/(2*S*(1 + S^2)^2) + ((-23 - 50*S^2 + 639*S^4 + 532*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + S*HPL[{4, 2}, -S^2] + 30*S*HPL[{5, 1}, -S^2] + (-464*Pi^2*S - (2*(33 + 935*S^2 + 500*S^4 + 403*S^6 + 21*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(153 - 512*S^2 - 408*S^4 + 42*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (2*(939 - 3038*S^2 - 2663*S^4 + 68*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 4*S*HPL[{3, 1, 2}, -S^2] - 1644*S*HPL[{3, 2, 1}, -S^2] - 4960*S*HPL[{4, 1, 1}, -S^2] + (4*(-327 + 992*S^2 + 1005*S^4 + 78*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 3376*S*HPL[{3, 1, 1, 1}, -S^2] - 6880*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((S*(-230 + 79*S^2))/4 - (Pi^2*S*(230 + 665*S^2 + 394*S^4))/(6*(1 + S^2)^2))*Zeta[3] - 4*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-4 + 1429*S^2 + 252*S^4 - 35*S^6)/(4*S^3) + (Pi^2*(-189 + 484*S^2 + 480*S^4 + 18*S^6))/(2*S*(1 + S^2)^2) - 4*S*Zeta[3]) + HPL[{3}, -S^2]*((Pi^2*(33 - 20*S^2 - 389*S^4 - 286*S^6))/(12*S*(1 + S^2)^2) + (-4 - 280*S^2 - 644*S^4 + 41*S^6)/(8*S^3) + 4*S*Zeta[3]) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(-1 + 369*S^2 + 26*S^4))/(3*S^3) + (Pi^2*(583 - 5328*S^2 - 4915*S^4 - 502*S^6))/(18*S*(1 + S^2)^2) + ((307 - 2796*S^2 - 2593*S^4 - 274*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + (88*S*HPL[{3}, -S^2])/3 + (1568*S*HPL[{2, 1}, -S^2])/3 + (164*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-867*Pi^4*S)/40 + (54 - 567*S^2 - 1769*S^4 - 48*S^6)/(8*S^3) + (Pi^2*(-75 - 1936*S^2 - 1457*S^4 - 886*S^6 - 24*S^8))/(12*S*(1 + S^2)^2) + ((1 + 24*S^2 - 165*S^4 - 146*S^6)*HPL[{3}, -S^2])/(2*S*(1 + S^2)^2) - 5*S*HPL[{4}, -S^2] - (2*(153 - 512*S^2 - 408*S^4 + 42*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 820*S*HPL[{3, 1}, -S^2] - 1652*S*HPL[{2, 1, 1}, -S^2] + ((-2 + 56*S^2 - 77*S^4 - 96*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-8449*Pi^4*S)/360 - ((1 + S^2)*(-4 + 1707*S^2 + 105*S^4))/(8*S^3) + (Pi^2*(-354 - 4196*S^2 - 1625*S^4 - 809*S^6 - 30*S^8))/(12*S*(1 + S^2)^2) + ((-211*Pi^2*S)/2 + (-163 - 2115*S^2 - 742*S^4 - 373*S^6 - 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2] - 215*S*HPL[{2}, -S^2]^2 + ((3 + 76*S^2 - 77*S^4 - 106*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) + 8*S*HPL[{4}, -S^2] + ((-307 + 2796*S^2 + 2593*S^4 + 274*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 772*S*HPL[{3, 1}, -S^2] - 1568*S*HPL[{2, 1, 1}, -S^2] - (2*(4 - 98*S^2 - 3*S^4 + 58*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - (S*(232 + 659*S^2 + 388*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(-2 + 1817*S^2 + 59*S^4))/(24*S^3) - ((1 + S^2)*(-80 + 4427*S^2 + 283*S^4))/(16*S^3) + (Pi^4*(3674 - 31594*S^2 - 31965*S^4 - 5146*S^6))/(360*S*(1 + S^2)^2) + ((149 - 1456*S^2 - 1209*S^4 - 34*S^6)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^2) + ((25*Pi^2*S)/3 + (-29 - 152*S^2 - 266*S^4 - 55*S^6)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((23 - 60*S^2 - 269*S^4 - 170*S^6)*HPL[{4}, -S^2])/(2*S*(1 + S^2)^2) + 24*S*HPL[{5}, -S^2] + (211*Pi^2*S + (163 + 2115*S^2 + 742*S^4 + 373*S^6 + 15*S^8)/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(-76 + 690*S^2 + 643*S^4 + 70*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 84*S*HPL[{3, 2}, -S^2] - 268*S*HPL[{4, 1}, -S^2] - (2*(-307 + 2796*S^2 + 2593*S^4 + 274*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 1720*S*HPL[{2, 2, 1}, -S^2] - 4984*S*HPL[{3, 1, 1}, -S^2] + 3136*S*HPL[{2, 1, 1, 1}, -S^2] + ((41*Pi^2*S)/3 + (-19 - 12*S^2 - 320*S^4 - 2*S^6 - 3*S^8)/(2*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-44 + 1855*S^2 + 49*S^4))/(8*S^3) + (Pi^2*(535 - 4672*S^2 - 4619*S^4 - 678*S^6))/(12*S*(1 + S^2)^2) + 42*S*HPL[{3}, -S^2] + 860*S*HPL[{2, 1}, -S^2] + 78*S*Zeta[3]) + 78*S*Zeta[5])) + HPL[{0}, S^2]*(-(Pi^4*S*(54150 + 4039*S^2))/1440 + (1568 - 22002*S^2 - 3797*S^4)/(32*S) + (Pi^2*(208 - 14990*S^2 - 591*S^4))/(96*S) - (Pi^6*S*(1138392 + 1031849*S^2 + 142444*S^4))/(45360*(1 + S^2)^2) + (56*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{1}, -S^2]^6)/(3*S*(1 + S^2)^2) - (64*S*HPL[{1}, -S^2]^7)/3 + ((-19 - 1070*S^2 - 313*S^4 + 384*S^6)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-482*Pi^2*S)/9 + (-19 - 336*S^2 + 54*S^4 - 80*S^6 - 3*S^8)/(S*(1 + S^2)^2) - 200*S*HPL[{2}, -S^2]) - (2*(1 - 3*S^2 + S^4 + 3*S^6)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^2) + ((Pi^2*S)/3 + (-1 - 372*S^2 - 464*S^4 - 238*S^6 + 39*S^8)/(2*S*(1 + S^2)^2))*HPL[{5}, -S^2] + ((20 + 60*S^2 + 425*S^4 + 312*S^6)*HPL[{6}, -S^2])/(S*(1 + S^2)^2) + 72*S*HPL[{7}, -S^2] - (8*(3 - 595*S^2 - 219*S^4 + 183*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + ((-128*Pi^2*S)/3 + (-51 + 338*S^2 + 1536*S^4 + 470*S^6 - 69*S^8)/(2*S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + (-126*Pi^2*S + (10 + 812*S^2 + 2383*S^4 + 730*S^6 - 123*S^8)/(S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((3 + 46*S^2)*HPL[{4, 2}, -S^2])/S - 52*S*HPL[{4, 3}, -S^2] - (6*(1 - 44*S^2 - S^4 + 26*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) - 142*S*HPL[{5, 2}, -S^2] - 260*S*HPL[{6, 1}, -S^2] + ((-40*Pi^2*S)/3 + (4*(-150 - 1355*S^2 + 446*S^4 + 83*S^6))/(S*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((136*Pi^2*S)/3 + (2*(-937 - 8504*S^2 + 1934*S^4 + 268*S^6 + 39*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (2*(-3 + 8*S^2)*HPL[{3, 1, 2}, -S^2])/S + (2*(-73 - 4282*S^2 - 1265*S^4 + 1528*S^6)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)^2) + 564*S*HPL[{3, 2, 2}, -S^2] + 1600*S*HPL[{3, 3, 1}, -S^2] + (4*(-111 - 6520*S^2 - 1857*S^4 + 2382*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 1604*S*HPL[{4, 1, 2}, -S^2] + 4676*S*HPL[{4, 2, 1}, -S^2] + 9128*S*HPL[{5, 1, 1}, -S^2] + ((-512*Pi^2*S)/3 - (4*(-342 - 3114*S^2 + 127*S^4 - 56*S^6 + 45*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 608*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(-35 - 2264*S^2 - 673*S^4 + 806*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 880*S*HPL[{3, 1, 1, 2}, -S^2] + 880*S*HPL[{3, 1, 2, 1}, -S^2] + 2704*S*HPL[{3, 2, 1, 1}, -S^2] + 8224*S*HPL[{4, 1, 1, 1}, -S^2] + (480*(-1 - 76*S^2 - 24*S^4 + 26*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 544*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 1632*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 4480*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 2880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((373*Pi^4*S)/90 + (-16 - 166*S^2 + 17*S^4)/(4*S) + (Pi^2*S*(-206 - 606*S^2 - 197*S^4 + 15*S^6))/(3*(1 + S^2)^2))*Zeta[3] + (2*S*(-24 + 37*S^2 + 44*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3, 1}, -S^2]*((Pi^2*(45 + 3754*S^2 + 1973*S^4 - 656*S^6))/(3*S*(1 + S^2)^2) + (2*(-12 + 107*S^2 + 423*S^4 + 25*S^6))/S^3 - 640*S*Zeta[3]) + HPL[{4}, -S^2]*((10 - 66*S^2 - 237*S^4 + 13*S^6)/(2*S^3) + (Pi^2*(13 - 148*S^2 + 65*S^4 + 146*S^6))/(6*S*(1 + S^2)^2) - 68*S*HPL[{2, 1}, -S^2] - 4*S*Zeta[3]) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(283 + 33*S^2))/(12*S) + (Pi^2*(344 - 3786*S^2 - 2579*S^4 + 346*S^6))/(9*S*(1 + S^2)^2) + (125*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) + (68*S*HPL[{3}, -S^2])/3 + 1000*S*HPL[{2, 1}, -S^2] + (332*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((4 + 167*S^2 - 1592*S^4 - 101*S^6)/(8*S^3) + (Pi^2*(5 - 1914*S^2 - 1088*S^4 + 280*S^6))/(6*S*(1 + S^2)^2) + 72*S*HPL[{3}, -S^2] - 76*S*HPL[{2, 1}, -S^2] + 160*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((44 - 375*S^2 - 1688*S^4 - 157*S^6)/S^3 + (20*Pi^2*(-4 - 381*S^2 - 210*S^4 + 59*S^6))/(3*S*(1 + S^2)^2) + 1312*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-76*Pi^4*S)/9 + (26 + 1687*S^2 + 388*S^4 - 68*S^6)/(2*S^3) + (Pi^2*(733 + 5388*S^2 + 445*S^4 + 56*S^6 - 54*S^8))/(6*S*(1 + S^2)^2) - 144*S*HPL[{3, 1}, -S^2] - 272*S*HPL[{2, 1, 1}, -S^2] - (4*(-43 + 242*S^2 + 203*S^4)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*(3*Pi^4*S + (18 - 293*S^2 - 1562*S^4 + 339*S^6)/(8*S^3) + (Pi^2*(-55 - 702*S^2 - 1207*S^4 - 424*S^6 + 48*S^8))/(12*S*(1 + S^2)^2) + 20*S*HPL[{4}, -S^2] - (2*(-49 + 236*S^2 + 239*S^4 + 30*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 224*S*HPL[{3, 1}, -S^2] + 448*S*HPL[{2, 1, 1}, -S^2] - (2*(1 + 17*S^4 + 14*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-4061*Pi^4*S)/90 - ((1 + S^2)*(12 + 1541*S^2 + 141*S^4))/(6*S^3) + (Pi^2*(-681 - 9218*S^2 - 976*S^4 - 2142*S^6 - 63*S^8))/(18*S*(1 + S^2)^2) + (-240*Pi^2*S - (8*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(3*S*(1 + S^2)^2))*HPL[{2}, -S^2] - (1568*S*HPL[{2}, -S^2]^2)/3 - (8*(5 - 54*S^2 - 38*S^4 + 4*S^6)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (184*S*HPL[{4}, -S^2])/3 - (500*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 2000*S*HPL[{3, 1}, -S^2] - 4000*S*HPL[{2, 1, 1}, -S^2] - (8*(20 - 246*S^2 - 137*S^4 + 46*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + ((52*Pi^2*S)/3 + (S*(-332 - 953*S^2 - 334*S^4 + 27*S^6))/(1 + S^2)^2)*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(88 - 633*S^2 - 3438*S^4 - 181*S^6))/(24*S^3) + (181 - 1060*S^2 - 3955*S^4 - 158*S^6)/(8*S^3) + (Pi^4*(-262 - 42988*S^2 - 31315*S^4 + 636*S^6))/(360*S*(1 + S^2)^2) + (20*Pi^2*S + (21 - 190*S^2 - 798*S^4 - 250*S^6 + 33*S^8)/(2*S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((3 - 38*S^2 - 45*S^4 - 12*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - 18*S*HPL[{5}, -S^2] + ((20*Pi^2*S)/3 - (2*(-150 - 1355*S^2 + 446*S^4 + 83*S^6))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(11 - 2376*S^2 - 865*S^4 + 738*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 288*S*HPL[{3, 2}, -S^2] - 796*S*HPL[{4, 1}, -S^2] + (16*(3 - 595*S^2 - 219*S^4 + 183*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 304*S*HPL[{2, 2, 1}, -S^2] - 464*S*HPL[{3, 1, 1}, -S^2] + 272*S*HPL[{2, 1, 1, 1}, -S^2] + (60*Pi^2*S - (2*(-6 - 10*S^2 + 205*S^4 + 45*S^6))/(S*(1 + S^2)^2))*Zeta[3] + 212*S*Zeta[5]) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(4 + 3117*S^2 + 227*S^4))/(24*S^3) - ((1 + S^2)*(-28 + 3449*S^2 + 335*S^4))/(8*S^3) + (Pi^4*(7801 - 79936*S^2 - 61445*S^4 + 1926*S^6))/(360*S*(1 + S^2)^2) + (196*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(S*(1 + S^2)^2) + ((22*Pi^2*S)/3 + (2*(-43 - 155*S^2 - 282*S^4 - 93*S^6 + 9*S^8))/(S*(1 + S^2)^2))*HPL[{3}, -S^2] + ((17 - 252*S^2 - 95*S^4 + 82*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - 92*S*HPL[{5}, -S^2] + (720*Pi^2*S + (8*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (24*(31 - 374*S^2 - 216*S^4 + 64*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 304*S*HPL[{3, 2}, -S^2] - 728*S*HPL[{4, 1}, -S^2] + (1500*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 6272*S*HPL[{2, 2, 1}, -S^2] - 18544*S*HPL[{3, 1, 1}, -S^2] + 12000*S*HPL[{2, 1, 1, 1}, -S^2] + ((188*Pi^2*S)/3 + (-53 + 112*S^2 - 600*S^4 - 104*S^6 - 3*S^8)/(S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-20 + 977*S^2 + 25*S^4))/(2*S^3) + (Pi^2*(623 - 6812*S^2 - 4693*S^4 + 582*S^6))/(6*S*(1 + S^2)^2) + 152*S*HPL[{3}, -S^2] + 3136*S*HPL[{2, 1}, -S^2] + 328*S*Zeta[3]) + 260*S*Zeta[5]) + HPL[{1}, -S^2]*((-248987*Pi^6*S)/22680 - (Pi^2*(1 + S^2)*(18 + 1729*S^2 + 93*S^4))/(12*S^3) - ((1 + S^2)*(-153 + 4084*S^2 + 509*S^4))/(8*S^3) + (Pi^4*(-10761 - 118656*S^2 - 39488*S^4 - 30002*S^6 - 945*S^8))/(720*S*(1 + S^2)^2) + ((-551*Pi^2*S)/3 + (-113 - 2252*S^2 + 524*S^4 - 488*S^6 - 15*S^8)/(2*S*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - 236*S*HPL[{2}, -S^2]^3 + 8*S*HPL[{3}, -S^2]^2 + ((-80*Pi^2*S)/3 + (-113 - 662*S^2 - 476*S^4 - 274*S^6 + 21*S^8)/(2*S*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(3 - 58*S^2 - 10*S^4 + 28*S^6)*HPL[{5}, -S^2])/(S*(1 + S^2)^2) - 146*S*HPL[{6}, -S^2] + 3136*S*HPL[{2, 1}, -S^2]^2 + (720*Pi^2*S - (2*(-199 - 2562*S^2 - 40*S^4 - 674*S^6 + 3*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (76*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)^2) + (2*(97 - 1116*S^2 - 703*S^4 + 146*S^6)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)^2) + 216*S*HPL[{5, 1}, -S^2] + (-1440*Pi^2*S - (16*(50 + 646*S^2 + 17*S^4 + 171*S^6))/(S*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (1568*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S*(1 + S^2)^2) + (16*(289 - 3474*S^2 - 2020*S^4 + 584*S^6)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 5664*S*HPL[{3, 2, 1}, -S^2] - 17360*S*HPL[{4, 1, 1}, -S^2] - (3000*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 12000*S*HPL[{3, 1, 1, 1}, -S^2] - 24000*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-(((1 + S^2)*(4 + 33*S^2 + 9*S^4))/S^3) + (Pi^2*(-37 + 524*S^2 + 219*S^4 - 154*S^6))/(3*S*(1 + S^2)^2))*Zeta[3] - 68*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(-20 + 977*S^2 + 25*S^4))/S^3 + (Pi^2*(-623 + 6812*S^2 + 4693*S^4 - 582*S^6))/(3*S*(1 + S^2)^2) - 656*S*Zeta[3]) + HPL[{3}, -S^2]*(((1 + S^2)*(24 - 431*S^2 + 55*S^4))/(2*S^3) - (2*Pi^2*(2 - 30*S^2 - 11*S^4 + 10*S^6))/(3*S*(1 + S^2)^2) - 304*S*HPL[{2, 1}, -S^2] + 16*S*Zeta[3]) + HPL[{2}, -S^2]*((-2155*Pi^4*S)/36 - ((1 + S^2)*(-40 + 2211*S^2 + 17*S^4))/(4*S^3) + (Pi^2*(-823 - 9306*S^2 - 2194*S^4 - 2354*S^6 - 3*S^8))/(12*S*(1 + S^2)^2) - (38*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - 16*S*HPL[{4}, -S^2] - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + 3136*S*HPL[{3, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2] - (82*(1 - 12*S^2 - 7*S^4 + 2*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - (2*(27 - 368*S^2 - 167*S^4 + 98*S^6)*Zeta[5])/(S*(1 + S^2)^2))) - (42*S*(10 + 135*S^2 + 102*S^4)*Zeta[7])/(1 + S^2)^2 + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(-54 + 3938*S^2 + 309*S^4))/(24*S^3) - (Pi^4*(1 + S^2)*(-40 + 40563*S^2 + 3629*S^4))/(1440*S^3) - ((1 + S^2)*(-1610 + 20577*S^2 + 3797*S^4))/(32*S^3) + (Pi^6*(37673 - 359832*S^2 - 309833*S^4 - 16898*S^6))/(9072*S*(1 + S^2)^2) - (83*(-1 + 6*S^2)*HPL[{2}, -S^2]^3)/(3*S) + (37*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3}, -S^2]^2)/(S*(1 + S^2)^2) + (80*Pi^2*S + (-239 - 1074*S^2 - 2144*S^4 - 460*S^6 - 15*S^8)/(S*(1 + S^2)^2))*HPL[{5}, -S^2] + ((119 - 120*S^2 - 1487*S^4 - 1070*S^6)*HPL[{6}, -S^2])/(S*(1 + S^2)^2) + 60*S*HPL[{7}, -S^2] - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + ((-1652*Pi^2*S)/3 - (2*(-51 + 768*S^2 - 2008*S^4 + 324*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-5636*Pi^2*S)/3 - (2*(-306 + 2111*S^2 - 7629*S^4 + 735*S^6 + 45*S^8))/(S*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (117*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^2) + 188*S*HPL[{4, 3}, -S^2] + (52*(9 - 140*S^2 - 47*S^4 + 50*S^6)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)^2) + 408*S*HPL[{5, 2}, -S^2] - 196*S*HPL[{6, 1}, -S^2] + ((-4856*Pi^2*S)/3 - (4*(113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-10592*Pi^2*S)/3 - (8*(235 + 3055*S^2 + 632*S^4 + 631*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (664*(-1 + 6*S^2)*HPL[{3, 2, 1}, -S^2])/S + 6520*S*HPL[{3, 2, 2}, -S^2] + 19936*S*HPL[{3, 3, 1}, -S^2] - (8*(-193 + 108*S^2 + 2455*S^4 + 1822*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 19624*S*HPL[{4, 1, 2}, -S^2] + 60808*S*HPL[{4, 2, 1}, -S^2] + 125280*S*HPL[{5, 1, 1}, -S^2] + ((3136*Pi^2*S)/3 + (96*(16 + 129*S^2 + 16*S^4))/(S*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (32*(-28 - 54*S^2 + 391*S^4 + 334*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - 12544*S*HPL[{3, 1, 1, 2}, -S^2] - 12544*S*HPL[{3, 1, 2, 1}, -S^2] - 12544*S*HPL[{3, 2, 1, 1}, -S^2] - 42944*S*HPL[{4, 1, 1, 1}, -S^2] - (3120*(-1 + 6*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + 25088*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 75264*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 155840*S*HPL[{3, 1, 1, 1, 1}, -S^2] + ((1013*Pi^4*S)/30 + ((1 + S^2)*(8 - 83*S^2 + 18*S^4))/S^3 + (Pi^2*(-11 + 832*S^2 - 1992*S^4 + 490*S^6 - 3*S^8))/(6*S*(1 + S^2)^2))*Zeta[3] + (2*(9 - 116*S^2 - 59*S^4 + 26*S^6)*Zeta[3]^2)/(S*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*(-(((1 + S^2)*(20 - 1147*S^2 + 43*S^4))/S^3) + (8*Pi^2*(-52 + 318*S^2 + 517*S^4 + 202*S^6))/(3*S*(1 + S^2)^2) - 3232*S*Zeta[3]) + HPL[{4}, -S^2]*(((1 + S^2)*(4 - 1403*S^2 + 47*S^4))/(4*S^3) + (Pi^2*(-89 + 1716*S^2 + 299*S^4 - 826*S^6))/(6*S*(1 + S^2)^2) - 904*S*HPL[{2, 1}, -S^2] + 112*S*Zeta[3]) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(589 + 55*S^2))/(4*S) + (Pi^2*(345 - 3808*S^2 - 2581*S^4 + 358*S^6))/(6*S*(1 + S^2)^2) + 932*S*HPL[{3}, -S^2] + 708*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((12*(1 + S^2)*(4 - 173*S^2 + 6*S^4))/S^3 - (4*Pi^2*(-251 + 1788*S^2 + 2369*S^4 + 722*S^6))/(3*S*(1 + S^2)^2) + 6272*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((2021*Pi^4*S)/30 - ((1 + S^2)*(72 - 2543*S^2 + 55*S^4))/(2*S^3) + (Pi^2*(355 + 3855*S^2 + 2482*S^4 + 565*S^6 + 15*S^8))/(3*S*(1 + S^2)^2) - 6272*S*HPL[{3, 1}, -S^2] - 12544*S*HPL[{2, 1, 1}, -S^2] + (448*(1 - 18*S^2 - 4*S^4 + 8*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((601*Pi^4*S)/15 + ((1 + S^2)*(42 - 1451*S^2 + 197*S^4))/(4*S^3) + (Pi^2*(-189 + 342*S^2 - 3368*S^4 + 92*S^6 + 15*S^8))/(6*S*(1 + S^2)^2) - 172*S*HPL[{4}, -S^2] + (4*(113 - 2020*S^2 - 459*S^4 + 890*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - 3136*S*HPL[{3, 1}, -S^2] + 6272*S*HPL[{2, 1, 1}, -S^2] - (8*(6 - 74*S^2 - 41*S^4 + 14*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + ((838*Pi^2*S)/3 - (2*(-23 - 342*S^2 + 843*S^4 - 355*S^6 + 3*S^8))/(S*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(92 - 3931*S^2 + 23*S^4))/(24*S^3) + ((1 + S^2)*(246 - 6919*S^2 + 49*S^4))/(8*S^3) + (Pi^4*(6575 - 50552*S^2 - 60199*S^4 - 15198*S^6))/(360*S*(1 + S^2)^2) + ((826*Pi^2*S)/3 + (-51 + 768*S^2 - 2008*S^4 + 324*S^6 + 15*S^8)/(S*(1 + S^2)^2))*HPL[{3}, -S^2] - (113*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) + 328*S*HPL[{5}, -S^2] + ((2428*Pi^2*S)/3 + (2*(113 + 2252*S^2 - 524*S^4 + 488*S^6 + 15*S^8))/(S*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (784*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - 3416*S*HPL[{3, 2}, -S^2] - 10280*S*HPL[{4, 1}, -S^2] + (1568*(1 - 12*S^2 - 7*S^4 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + 6272*S*HPL[{3, 1, 1}, -S^2] + 12544*S*HPL[{2, 1, 1, 1}, -S^2] + ((862*Pi^2*S)/3 + (2*(-29 + 375*S^2 - 998*S^4 + 181*S^6 + 15*S^8))/(S*(1 + S^2)^2))*Zeta[3] + 1444*S*Zeta[5]) + 1932*S*Zeta[7])) - 1568*S*Zeta[9];
E5vwuT3F3=(-7*(127334 + 464915*S^2))/(1259712*S) + (Pi^4*(-2602044 - 5465862*S^2 - 55270745*S^4))/(4199040*S) + (Pi^2*(-18138 - 218617*S^2 - 4038660*S^4))/(69984*S) + (Pi^6*(-265028 - 781556*S^2 - 2915727*S^4))/(1224720*S) - (Pi^8*S^3*(6390719 + 7419262*S^2 + 2369087*S^4))/(8164800*(1 + S^2)^2) + ((-58*Pi^2*S^3)/63 + (-88 - 475*S^2 - 724*S^4 - 3046*S^6 - 2020*S^8 - 655*S^10)/(189*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^7 - (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^8)/(27*S^3*(1 + S^2)^2) - (16*S^3*HPL[{1}, -S^2]^9)/81 + HPL[{0}, S^2]^8*(-(S^3*(3 + 2*S^2))/(576*(1 + S^2)^2) - (S^3*HPL[{1}, -S^2])/288) + ((-56 - 112*S^2 - 56*S^4 - 2503*S^6 - 2702*S^8 - 775*S^10)*HPL[{2}, -S^2]^4)/(108*S^3*(1 + S^2)^2) + HPL[{0}, S^2]^7*(-(Pi^2*S^3)/288 + (-24 - 36*S^2 - 241*S^4 - 281*S^6 - 106*S^8)/(2592*S*(1 + S^2)^2) + ((-4 - 8*S^2 - 4*S^4 - 49*S^6 - 62*S^8 - 22*S^10)*HPL[{1}, -S^2])/(432*S^3*(1 + S^2)^2) - (S^3*HPL[{1}, -S^2]^2)/48 - (S^3*HPL[{2}, -S^2])/48) - (16*S^3*HPL[{3}, -S^2]^3)/9 + ((-28 - 56*S^2 - 28*S^4 - 33*S^6 - 174*S^8 - 114*S^10)*HPL[{4}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((131*Pi^2*S^3)/9 + (-3790 - 8876*S^2 - 4834*S^4 - 9811*S^6 - 17282*S^8 - 6679*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{7}, -S^2] + (2*(1 + 2*S^2)*(35 + 35*S^4 + 75*S^6 + 32*S^8)*HPL[{8}, -S^2])/(3*S^3*(1 + S^2)^2) + 306*S^3*HPL[{9}, -S^2] + (1568*S^3*HPL[{2, 1}, -S^2]^3)/9 - (4*(97 + 194*S^2 + 97*S^4 + 2915*S^6 + 3034*S^8 + 818*S^10)*HPL[{3, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((11*Pi^2*S^3)/3 + (-100 + 52*S^2 + 368*S^4 - 1049*S^6 - 5662*S^8 - 2705*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4, 3}, -S^2] + ((58*Pi^2*S^3)/9 + (-17 + 254*S^2 + 505*S^4 - 1733*S^6 - 7282*S^8 - 3479*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5, 2}, -S^2] - (2*S^3*(1 + 10*S^2 + 7*S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 + (224*S^3*HPL[{5, 4}, -S^2])/3 + (-25*Pi^2*S^3 + (-75 + 816*S^2 + 1554*S^4 + 238*S^6 - 1357*S^8 - 1814*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{6, 1}, -S^2] + ((-44 - 88*S^2 - 44*S^4 + 69*S^6 - 222*S^8 - 201*S^10)*HPL[{6, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (868*S^3*HPL[{6, 3}, -S^2])/3 + (2*(7 + 14*S^2 + 7*S^4 + 273*S^6 + 654*S^8 + 354*S^10)*HPL[{7, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + 730*S^3*HPL[{7, 2}, -S^2] + 1404*S^3*HPL[{8, 1}, -S^2] - (8*(100 + 200*S^2 + 100*S^4 + 5161*S^6 + 5618*S^8 + 1633*S^10)*HPL[{2, 1, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((559*Pi^2*S^3)/3 + (-71 + 773*S^2 + 1174*S^4 + 13620*S^6 + 7971*S^8 + 4461*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3, 2, 2}, -S^2] + ((5224*Pi^2*S^3)/9 + (2*(-472 + 3193*S^2 + 4856*S^4 + 61626*S^6 + 36174*S^8 + 20595*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 3, 1}, -S^2] + ((-34 - 68*S^2 - 34*S^4 - 3635*S^6 - 4078*S^8 - 1241*S^10)*HPL[{3, 3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (577*Pi^2*S^3 + (-987 + 6057*S^2 + 9282*S^4 + 120032*S^6 + 69607*S^8 + 40121*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 2}, -S^2] + (2*(34 + 68*S^2 + 34*S^4 + 3158*S^6 + 3592*S^8 + 1115*S^10)*HPL[{4, 1, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + ((5311*Pi^2*S^3)/3 + (-2787 + 19935*S^2 + 30054*S^4 + 376004*S^6 + 220111*S^8 + 125075*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 2, 1}, -S^2] + ((-4 - 8*S^2 - 4*S^4 - 809*S^6 - 866*S^8 - 245*S^10)*HPL[{4, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (88*S^3*HPL[{4, 2, 3}, -S^2])/3 + (2*(86 + 172*S^2 + 86*S^4 + 10228*S^6 + 11732*S^8 + 3685*S^10)*HPL[{4, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (10*S^3*HPL[{4, 3, 2}, -S^2])/3 - (44*S^3*HPL[{4, 4, 1}, -S^2])/3 + ((32738*Pi^2*S^3)/9 + (2*(-2150 + 21932*S^2 + 31708*S^4 + 385076*S^6 + 221761*S^8 + 126191*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{5, 1, 1}, -S^2] + ((118 + 236*S^2 + 118*S^4 + 12181*S^6 + 14234*S^8 + 4585*S^10)*HPL[{5, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + 44*S^3*HPL[{5, 1, 3}, -S^2] + ((718 + 1436*S^2 + 718*S^4 + 83881*S^6 + 95714*S^8 + 29845*S^10)*HPL[{5, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*S^3*HPL[{5, 2, 2}, -S^2])/3 + (92*S^3*HPL[{5, 3, 1}, -S^2])/3 + (2*(800 + 1600*S^2 + 800*S^4 + 107581*S^6 + 121214*S^8 + 37120*S^10)*HPL[{6, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (118*S^3*HPL[{6, 1, 2}, -S^2])/3 + 254*S^3*HPL[{6, 2, 1}, -S^2] + (2944*S^3*HPL[{7, 1, 1}, -S^2])/3 + ((-1672*Pi^2*S^3)/9 - (4*(-1355 - 3575*S^2 - 4170*S^4 - 6519*S^6 + 3315*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 2, 2, 1}, -S^2] + (172*Pi^2*S^3 + (-15604 - 62633*S^2 - 97864*S^4 - 201384*S^6 - 79188*S^8 + 14913*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 2}, -S^2] + (172*Pi^2*S^3 + (-15604 - 62633*S^2 - 97864*S^4 - 201384*S^6 - 79188*S^8 + 14913*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 2, 1}, -S^2] + ((-94 - 188*S^2 - 94*S^4 - 1871*S^6 - 1870*S^8 - 467*S^10)*HPL[{3, 1, 2, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((2188*Pi^2*S^3)/3 + (-31864 - 121793*S^2 - 190804*S^4 - 329652*S^6 - 117636*S^8 + 54693*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 2, 1, 1}, -S^2] + ((-94 - 188*S^2 - 94*S^4 - 1871*S^6 - 1870*S^8 - 467*S^10)*HPL[{3, 2, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-1150 - 2300*S^2 - 1150*S^4 + 10321*S^6 + 22898*S^8 + 12013*S^10)*HPL[{3, 2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6208*S^3*HPL[{3, 2, 2, 2}, -S^2])/3 - (19456*S^3*HPL[{3, 2, 3, 1}, -S^2])/3 + (32*(-11 - 22*S^2 - 11*S^4 + 127*S^6 + 258*S^8 + 130*S^10)*HPL[{3, 3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - 6384*S^3*HPL[{3, 3, 1, 2}, -S^2] - 19712*S^3*HPL[{3, 3, 2, 1}, -S^2] + ((18904*Pi^2*S^3)/9 + (2*(-49220 - 187255*S^2 - 291140*S^4 - 514147*S^6 - 185150*S^8 + 79268*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 1, 1}, -S^2] - (4*(-7 - 14*S^2 - 7*S^4 + 1770*S^6 + 2136*S^8 + 717*S^10)*HPL[{4, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (120296*S^3*HPL[{4, 1, 1, 3}, -S^2])/3 + (4*(-785 - 1570*S^2 - 785*S^4 + 7374*S^6 + 16440*S^8 + 8643*S^10)*HPL[{4, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (101230*S^3*HPL[{4, 1, 2, 2}, -S^2])/3 + (180808*S^3*HPL[{4, 1, 3, 1}, -S^2])/3 + (4*(-2369 - 4738*S^2 - 2369*S^4 + 25662*S^6 + 53592*S^8 + 27363*S^10)*HPL[{4, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (62158*S^3*HPL[{4, 2, 1, 2}, -S^2])/3 + (61246*S^3*HPL[{4, 2, 2, 1}, -S^2])/3 + (357464*S^3*HPL[{4, 3, 1, 1}, -S^2])/3 + (4*(-1574 - 3148*S^2 - 1574*S^4 + 15319*S^6 + 33918*S^8 + 17779*S^10)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (363284*S^3*HPL[{5, 1, 1, 2}, -S^2])/3 + (599540*S^3*HPL[{5, 1, 2, 1}, -S^2])/3 + (1429172*S^3*HPL[{5, 2, 1, 1}, -S^2])/3 + 1190144*S^3*HPL[{6, 1, 1, 1}, -S^2] + ((3248*Pi^2*S^3)/9 + (8*(462 + 2098*S^2 + 3198*S^4 + 9795*S^6 + 4318*S^8 + 789*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((3248*Pi^2*S^3)/3 + (8*(462 + 2098*S^2 + 3198*S^4 + 9795*S^6 + 4318*S^8 + 789*S^10))/(3*S^3*(1 + S^2)^2))*HPL[{2, 2, 1, 1, 1}, -S^2] + (32*(-66 + 773*S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(9*S^3) + (32*(-66 + 773*S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(3*S^3) - 2016*S^3*HPL[{2, 2, 2, 2, 1}, -S^2] + ((23744*Pi^2*S^3)/9 + (8*(7360 + 34019*S^2 + 50956*S^4 + 170477*S^6 + 76978*S^8 + 18458*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(-1540 + 18339*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(9*S^3) - (8*(-2596 + 30707*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(9*S^3) - (5408*S^3*HPL[{3, 1, 1, 2, 2}, -S^2])/3 - (8*(-3124 + 36891*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(9*S^3) - (5408*S^3*HPL[{3, 1, 2, 1, 2}, -S^2])/3 + 96*S^3*HPL[{3, 1, 2, 2, 1}, -S^2] + 16608*S^3*HPL[{3, 1, 3, 1, 1}, -S^2] - (8*(-6556 + 77087*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(9*S^3) - (23552*S^3*HPL[{3, 2, 1, 1, 2}, -S^2])/3 - 5952*S^3*HPL[{3, 2, 1, 2, 1}, -S^2] - (10016*S^3*HPL[{3, 2, 2, 1, 1}, -S^2])/3 - 4256*S^3*HPL[{3, 3, 1, 1, 1}, -S^2] - (32*(-4950 - 9900*S^2 - 4950*S^4 + 56923*S^6 + 114842*S^8 + 57670*S^10)*HPL[{4, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (69296*S^3*HPL[{4, 1, 1, 1, 2}, -S^2])/3 - (52208*S^3*HPL[{4, 1, 1, 2, 1}, -S^2])/3 - (28688*S^3*HPL[{4, 1, 2, 1, 1}, -S^2])/3 - (36080*S^3*HPL[{4, 2, 1, 1, 1}, -S^2])/3 - 21856*S^3*HPL[{5, 1, 1, 1, 1}, -S^2] + ((-7328*Pi^2*S^3)/9 - (8*(-2602 - 7570*S^2 - 9054*S^4 - 14895*S^6 + 6723*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (12544*S^3*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/3 + 12544*S^3*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + (32*(-165 - 330*S^2 - 165*S^4 + 731*S^6 + 2458*S^8 + 1478*S^10)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 29696*S^3*HPL[{3, 1, 1, 1, 1, 2}, -S^2] - 54784*S^3*HPL[{3, 1, 1, 1, 2, 1}, -S^2] - (214528*S^3*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/3 - 79872*S^3*HPL[{3, 1, 2, 1, 1, 1}, -S^2] - (402688*S^3*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/3 - (1213888*S^3*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/3 - (320*(-8 + 117*S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (24896*S^3*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/3 - (99584*S^3*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/3 - (248960*S^3*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/3 - 155392*S^3*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] - 17920*S^3*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((16*Pi^2*S^3)/27 + (16*(2 + 3*S^2 + 18*S^4 + 5*S^6))/(27*S*(1 + S^2)^2) + (16*S^3*HPL[{0}, S^2]^2)/9 + (16*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^2) + (64*S^3*HPL[{1}, -S^2]^2)/9 + HPL[{0}, S^2]*((16*S^3*(29 + 34*S^2 + 11*S^4))/(27*(1 + S^2)^2) + (64*S^3*HPL[{1}, -S^2])/9) + (32*S^3*HPL[{2}, -S^2])/9)*Log[T]^7 + ((-8*S^3*(3 + 2*S^2))/(9*(1 + S^2)^2) - (16*S^3*HPL[{0}, S^2])/9 - (16*S^3*HPL[{1}, -S^2])/9)*Log[T]^8 + ((-4 - 115*S^2 - 159*S^4)/(27*S) + (Pi^2*S^3*(-113 + 122*S^2 + 148*S^4))/(54*(1 + S^2)^2))*Zeta[3]^2 + (32*S^3*Zeta[3]^3)/3 + HPL[{3, 1, 1, 1}, -S^2]*((-12124 - 6141*S^2 - 19956*S^4 + 134899*S^6)/(81*S^3) + (8*Pi^2*(-94 - 188*S^2 - 94*S^4 + 2106*S^6 + 3552*S^8 + 1611*S^10))/(27*S^3*(1 + S^2)^2) - (6176*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]^2*((2281 + 11115*S^2 + 31977*S^4 + 71658*S^6)/(162*S^3) + (Pi^2*(92 + 184*S^2 + 92*S^4 + 8773*S^6 + 10262*S^8 + 3310*S^10))/(27*S^3*(1 + S^2)^2) - 496*S^3*Zeta[3]) + HPL[{5, 1}, -S^2]*((-1157 - 17490*S^2 - 5025*S^4 - 12407*S^6)/(162*S^3) + (Pi^2*(70 + 140*S^2 + 70*S^4 - 8661*S^6 - 9018*S^8 - 2433*S^10))/(54*S^3*(1 + S^2)^2) - (260*S^3*Zeta[3])/3) + HPL[{4, 2}, -S^2]*((1188 - 5877*S^2 - 4608*S^4 - 13256*S^6)/(324*S^3) + (Pi^2*(2 + 4*S^2 + 2*S^4 - 863*S^6 - 1042*S^8 - 350*S^10))/(27*S^3*(1 + S^2)^2) - (62*S^3*Zeta[3])/3) + HPL[{6}, -S^2]*((5660 + 2280*S^2 - 2643*S^4 - 21752*S^6)/(162*S^3) + (Pi^2*(-40 - 80*S^2 - 40*S^4 + 48*S^6 - 172*S^8 - 153*S^10))/(18*S^3*(1 + S^2)^2) - (142*S^3*HPL[{2, 1}, -S^2])/3 - 14*S^3*Zeta[3]) + HPL[{3}, -S^2]^2*(-(Pi^2*S^3*(943 + 998*S^2 + 277*S^4))/(108*(1 + S^2)^2) + (-450 - 1213*S^2 - 826*S^4 - 839*S^6)/(216*S^3) + (20*S^3*HPL[{2, 1}, -S^2])/3 - 10*S^3*Zeta[3]) + HPL[{0}, S^2]^5*((-5597*Pi^4*S^3)/129600 + (-3588 - 14496*S^2 - 231955*S^4)/(93312*S) + (Pi^2*(-2700 - 4050*S^2 - 31561*S^4 - 38984*S^6 - 15805*S^8))/(25920*S*(1 + S^2)^2) + ((-170 - 340*S^2 - 170*S^4 - 2561*S^6 - 2954*S^8 - 935*S^10)*HPL[{1}, -S^2]^3)/(1080*S^3*(1 + S^2)^2) - (271*S^3*HPL[{1}, -S^2]^4)/1080 + ((-571*Pi^2*S^3)/2160 + (-840 - 1260*S^2 - 13031*S^4 - 17614*S^6 - 7775*S^8)/(4320*S*(1 + S^2)^2))*HPL[{2}, -S^2] - (3*S^3*HPL[{2}, -S^2]^2)/10 + HPL[{1}, -S^2]^2*((-293*Pi^2*S^3)/1080 + (-350 - 8935*S^2 - 17990*S^4 - 74654*S^6 - 67822*S^8 - 22085*S^10)/(12960*S^3*(1 + S^2)^2) - (77*S^3*HPL[{2}, -S^2])/120) + (S^3*(-11 + 2*S^2 + 7*S^4)*HPL[{3}, -S^2])/(144*(1 + S^2)^2) - (5*S^3*HPL[{4}, -S^2])/24 + ((420 + 840*S^2 + 420*S^4 + 1564*S^6 + 356*S^8 - 515*S^10)*HPL[{2, 1}, -S^2])/(1080*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(598 + 1025*S^2 + 31117*S^4))/(15552*S^3) + (Pi^2*(-450 - 900*S^2 - 450*S^4 - 5991*S^6 - 7294*S^8 - 2475*S^10))/(4320*S^3*(1 + S^2)^2) - (7*(10 + 20*S^2 + 10*S^4 + 154*S^6 + 176*S^8 + 55*S^10)*HPL[{2}, -S^2])/(360*S^3*(1 + S^2)^2) - (S^3*HPL[{3}, -S^2])/12 + (77*S^3*HPL[{2, 1}, -S^2])/60) + (29*S^3*HPL[{3, 1}, -S^2])/20 - (128*S^3*HPL[{2, 1, 1}, -S^2])/45 - (91*S^3*Zeta[3])/72) + HPL[{0}, S^2]^6*((56 - 439*S^2 - 2322*S^4)/(5184*S) - (Pi^2*S^3*(108 + 124*S^2 + 39*S^4))/(864*(1 + S^2)^2) + ((-10 - 20*S^2 - 10*S^4 - 136*S^6 - 164*S^8 - 55*S^10)*HPL[{1}, -S^2]^2)/(216*S^3*(1 + S^2)^2) - (S^3*HPL[{1}, -S^2]^3)/12 - (13*S^3*(9 + 14*S^2 + 6*S^4)*HPL[{2}, -S^2])/(288*(1 + S^2)^2) + HPL[{1}, -S^2]*((-23*Pi^2*S^3)/432 + (56 - 539*S^2 - 1348*S^4 - 5884*S^6 - 5786*S^8 - 1951*S^10)/(5184*S^3*(1 + S^2)^2) - (13*S^3*HPL[{2}, -S^2])/144) + (S^3*HPL[{3}, -S^2])/48 - (S^3*HPL[{2, 1}, -S^2])/18 - (S^3*Zeta[3])/12) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(-94 + 415*S^6))/(54*S^3) + (-3195 - 216*S^2 - 4887*S^4 + 4156*S^6)/(162*S^3) + (32*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^6*(-((1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(2916*S^3) + (Pi^2*(-50 - 100*S^2 - 50*S^4 - 1058*S^6 - 1072*S^8 - 275*S^10))/(81*S^3*(1 + S^2)^2) - (13*(2 + 11*S^6)*HPL[{2}, -S^2])/(27*S^3) + (380*S^3*HPL[{3}, -S^2])/27 + (100*S^3*Zeta[3])/9) + Log[T]^6*((-56 - 151*S^2)/(27*S) - (Pi^2*S^3*(113 + 110*S^2 + 26*S^4))/(9*(1 + S^2)^2) - (50*S^3*HPL[{0}, S^2]^3)/27 + ((-58*Pi^2*S^3)/9 + (-88 - 475*S^2 - 724*S^4 - 3046*S^6 - 2020*S^8 - 655*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] - (56*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)^2) - (448*S^3*HPL[{1}, -S^2]^3)/27 + HPL[{0}, S^2]^2*(-(S^3*(171 + 218*S^2 + 78*S^4))/(9*(1 + S^2)^2) - (62*S^3*HPL[{1}, -S^2])/9) - (4*(-8 + 117*S^6)*HPL[{2}, -S^2])/(27*S^3) + HPL[{0}, S^2]*(-6*Pi^2*S^3 + (-112 - 168*S^2 - 1513*S^4 - 1440*S^6 - 655*S^8)/(27*S*(1 + S^2)^2) - (56*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^2) - (224*S^3*HPL[{1}, -S^2]^2)/9 - (212*S^3*HPL[{2}, -S^2])/9) + (236*S^3*HPL[{3}, -S^2])/9 - (224*S^3*HPL[{2, 1}, -S^2])/9 + (224*S^3*Zeta[3])/9) + HPL[{2}, -S^2]^3*((2310 - 645*S^2 + 2784*S^4 - 32732*S^6)/(972*S^3) + (Pi^2*(76 + 152*S^2 + 76*S^4 - 2447*S^6 - 3742*S^8 - 1583*S^10))/(162*S^3*(1 + S^2)^2) + (422*S^3*HPL[{3}, -S^2])/9 + 42*S^3*HPL[{2, 1}, -S^2] + (122*S^3*Zeta[3])/3) + HPL[{3, 2, 1}, -S^2]*((6045 - 2796*S^2 + 6249*S^4 - 126772*S^6)/(162*S^3) + (Pi^2*(514 + 1028*S^2 + 514*S^4 - 19161*S^6 - 29106*S^8 - 12249*S^10))/(54*S^3*(1 + S^2)^2) + (2960*S^3*Zeta[3])/3) + HPL[{4, 1, 1}, -S^2]*((25646 + 8859*S^2 + 38244*S^4 - 378022*S^6)/(162*S^3) - (2*Pi^2*(-453 - 906*S^2 - 453*S^4 + 12655*S^6 + 20438*S^8 + 9001*S^10))/(27*S^3*(1 + S^2)^2) + (9032*S^3*Zeta[3])/3) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-8*(-1721 + 828*S^2 - 801*S^4 + 37082*S^6))/(81*S^3) - (32*Pi^2*(-35 - 70*S^2 - 35*S^4 + 1328*S^6 + 2068*S^8 + 887*S^10))/(27*S^3*(1 + S^2)^2) + (12224*S^3*Zeta[3])/3) + HPL[{3, 2}, -S^2]*((-3137*Pi^4*S^3)/270 + (9750 - 81375*S^2 - 49524*S^4 - 275639*S^6)/(1944*S^3) + (Pi^2*(216 - 2091*S^2 - 2736*S^4 - 36758*S^6 - 17908*S^8 - 11315*S^10))/(324*S^3*(1 + S^2)^2) - (6536*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((-2 - 4*S^2 - 2*S^4 - 989*S^6 - 1354*S^8 - 521*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{5}, -S^2]*((1381*Pi^4*S^3)/540 + (24123 + 18549*S^2 + 11340*S^4 - 47620*S^6)/(972*S^3) + (Pi^2*(764 + 1306*S^2 + 296*S^4 + 75*S^6 - 5688*S^8 - 1689*S^10))/(324*S^3*(1 + S^2)^2) + ((-98 - 196*S^2 - 98*S^4 - 1875*S^6 - 1782*S^8 - 399*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 92*S^3*HPL[{3, 1}, -S^2] + 236*S^3*HPL[{2, 1, 1}, -S^2] + ((10 + 20*S^2 + 10*S^4 - 45*S^6 - 42*S^8 - 9*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^5*((-6673*Pi^4*S^3)/4050 - ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(14580*S^3) + (Pi^2*(-3418 - 18833*S^2 - 28906*S^4 - 117178*S^6 - 83192*S^8 - 26485*S^10))/(2430*S^3*(1 + S^2)^2) + ((-392*Pi^2*S^3)/135 - (2*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(45*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (784*S^3*HPL[{2}, -S^2]^2)/45 + (4*(28 + 56*S^2 + 28*S^4 + 1009*S^6 + 878*S^8 + 154*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (664*S^3*HPL[{4}, -S^2])/45 + (26*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (664*S^3*HPL[{3, 1}, -S^2])/45 + (4*(2 + 4*S^2 + 2*S^4 + 86*S^6 + 72*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{3, 1, 1}, -S^2]*((-553*Pi^4*S^3)/90 + (-176930 - 203433*S^2 - 2447826*S^4 - 55029*S^6)/(972*S^3) + (Pi^2*(-16270 - 68627*S^2 - 106738*S^4 - 257193*S^6 - 105954*S^8 + 1530*S^10))/(162*S^3*(1 + S^2)^2) - (4*(-214 - 428*S^2 - 214*S^4 - 3319*S^6 - 2190*S^8 + 17*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{2, 1, 1, 1}, -S^2]*((-1229*Pi^4*S^3)/45 - (2*(-13201 - 8046*S^2 - 214461*S^4 + 30500*S^6))/(243*S^3) + (Pi^2*(5594 + 22468*S^2 + 35654*S^4 + 67387*S^6 + 27074*S^8 - 7421*S^10))/(81*S^3*(1 + S^2)^2) - (32*(50 + 100*S^2 + 50*S^4 + 901*S^6 + 626*S^8 + 19*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((-971*Pi^4*S^3)/90 + (-38559 - 55794*S^2 - 420771*S^4 - 61634*S^6)/(486*S^3) + (Pi^2*(-1898 - 8152*S^2 - 12422*S^4 - 33663*S^6 - 14130*S^8 - 1203*S^10))/(54*S^3*(1 + S^2)^2) - (8*(-108 - 216*S^2 - 108*S^4 - 1549*S^6 - 974*S^8 + 44*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{4, 1}, -S^2]*((-6901*Pi^4*S^3)/180 + (-14198 - 115624*S^2 - 69196*S^4 - 307027*S^6)/(648*S^3) + (Pi^2*(-674 - 10156*S^2 - 11816*S^4 - 127591*S^6 - 60032*S^8 - 36223*S^10))/(324*S^3*(1 + S^2)^2) - 6976*S^3*HPL[{2, 1, 1}, -S^2] - (2*(2 + 4*S^2 + 2*S^4 + 1811*S^6 + 2350*S^8 + 857*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + Log[T]^5*((449*Pi^4*S^3)/270 + (1424 + 4469*S^2)/(486*S) + (Pi^2*(200 + 300*S^2 + 2119*S^4 + 1490*S^6 + 515*S^8))/(54*S*(1 + S^2)^2) + (19*S^3*HPL[{0}, S^2]^4)/18 + ((58*Pi^2*S^3)/3 + (88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^2 + (112*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^2) + (224*S^3*HPL[{1}, -S^2]^4)/9 + HPL[{0}, S^2]^3*((S^3*(1300 + 1724*S^2 + 643*S^4))/(81*(1 + S^2)^2) + (146*S^3*HPL[{1}, -S^2])/27) + ((340*Pi^2*S^3)/27 + (-362 - 74*S^2 - 306*S^4 + 4725*S^6 + 4635*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (158*S^3*HPL[{2}, -S^2]^2)/9 + HPL[{0}, S^2]^2*((47*Pi^2*S^3)/9 + (88 + 132*S^2 + 1111*S^4 + 1210*S^6 + 515*S^8)/(18*S*(1 + S^2)^2) + (2*(22 + 44*S^2 + 22*S^4 + 400*S^6 + 428*S^8 + 121*S^10)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) + (62*S^3*HPL[{1}, -S^2]^2)/3 + (172*S^3*HPL[{2}, -S^2])/9) - (4*(3 + 6*S^2 + 3*S^4 + 1132*S^6 + 1124*S^8 + 277*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - 24*S^3*HPL[{4}, -S^2] + (28*(-6 + 13*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (176*S^3*HPL[{3, 1}, -S^2])/3 + (448*S^3*HPL[{2, 1, 1}, -S^2])/3 - (4*S^3*(316 + 332*S^2 + 91*S^4)*Zeta[3])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(486*S^3) + (2*Pi^2*(50 + 100*S^2 + 50*S^4 + 1058*S^6 + 1072*S^8 + 275*S^10))/(27*S^3*(1 + S^2)^2) + (26*(2 + 11*S^6)*HPL[{2}, -S^2])/(9*S^3) - (760*S^3*HPL[{3}, -S^2])/9 - (200*S^3*Zeta[3])/3) + HPL[{0}, S^2]*((Pi^2*S^3*(3736 + 4580*S^2 + 1567*S^4))/(81*(1 + S^2)^2) + (5*(864 + 1566*S^2 + 7291*S^4))/(486*S) + (56*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + (448*S^3*HPL[{1}, -S^2]^3)/9 + (4*(-2 - 4*S^2 - 2*S^4 + 375*S^6 + 450*S^8 + 150*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((482*Pi^2*S^3)/27 + (88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10)/(9*S^3*(1 + S^2)^2) + (200*S^3*HPL[{2}, -S^2])/3) - (44*S^3*HPL[{3}, -S^2])/9 + 8*S^3*HPL[{2, 1}, -S^2] - 16*S^3*Zeta[3])) + ((782*Pi^4*S^3)/135 + (8540 + 10334*S^2 + 15593*S^4)/(648*S) + (Pi^2*(222 + 333*S^2 + 5854*S^4 - 1111*S^6 + 688*S^8))/(162*S*(1 + S^2)^2))*Zeta[5] + HPL[{3, 1}, -S^2]*((Pi^2*(-15150 + 5814*S^2 + 13230*S^4 + 284099*S^6))/(1944*S^3) + (-300170 - 234147*S^2 - 594318*S^4 + 5763813*S^6)/(11664*S^3) + (Pi^4*(-2602 - 5204*S^2 - 2602*S^4 + 123047*S^6 + 188782*S^8 + 80063*S^10))/(3240*S^3*(1 + S^2)^2) + (3284*S^3*HPL[{3, 2}, -S^2])/3 + 3476*S^3*HPL[{4, 1}, -S^2] + (16*(72 + 144*S^2 + 72*S^4 + 2459*S^6 + 2566*S^8 + 695*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3824*S^3*HPL[{2, 2, 1}, -S^2])/3 - (14768*S^3*HPL[{3, 1, 1}, -S^2])/3 - (7552*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + (-94*Pi^2*S^3 + (-140 - 749*S^2 - 836*S^4 - 6707*S^6 - 3674*S^8 - 2042*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] - (1436*S^3*Zeta[5])/3) + HPL[{4}, -S^2]*((Pi^2*(288 + 8937*S^2 - 468*S^4 - 1183*S^6))/(1944*S^3) + (9032 + 384405*S^2 + 312234*S^4 + 126990*S^6)/(11664*S^3) + (Pi^4*(-255 - 510*S^2 - 255*S^4 + 6058*S^6 + 4556*S^8 + 388*S^10))/(1620*S^3*(1 + S^2)^2) - 38*S^3*HPL[{5}, -S^2] + (5*Pi^2*S^3 + (-1063 - 3335*S^2 - 4204*S^4 - 11464*S^6 - 6623*S^8 - 1159*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-8 - 16*S^2 - 8*S^4 + 554*S^6 + 624*S^8 + 191*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (218*S^3*HPL[{3, 2}, -S^2])/3 + (532*S^3*HPL[{4, 1}, -S^2])/3 + (4*(-7 - 14*S^2 - 7*S^4 + 1634*S^6 + 1912*S^8 + 617*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (236*S^3*HPL[{2, 2, 1}, -S^2])/3 + (364*S^3*HPL[{3, 1, 1}, -S^2])/3 + 128*S^3*HPL[{2, 1, 1, 1}, -S^2] + ((19*Pi^2*S^3)/9 + (70 + 182*S^2 + 88*S^4 - 93*S^6 - 1620*S^8 - 543*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] - (10*S^3*Zeta[5])/3) + HPL[{0}, S^2]^4*((15016 - 42866*S^2 - 1070901*S^4)/(93312*S) + (Pi^2*(-201 - 8319*S^2 - 44999*S^4))/(11664*S) - (Pi^4*S^3*(66595 + 84974*S^2 + 30433*S^4))/(77760*(1 + S^2)^2) + ((-506 - 1012*S^2 - 506*S^4 - 7895*S^6 - 8974*S^8 - 2783*S^10)*HPL[{1}, -S^2]^4)/(1296*S^3*(1 + S^2)^2) - (71*S^3*HPL[{1}, -S^2]^5)/135 + ((6 + 12*S^2 + 6*S^4 - 1139*S^6 - 1558*S^8 - 599*S^10)*HPL[{2}, -S^2]^2)/(216*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-277*Pi^2*S^3)/324 + (-1252 - 10637*S^2 - 18604*S^4 - 73036*S^6 - 63566*S^8 - 20197*S^10)/(3888*S^3*(1 + S^2)^2) - (241*S^3*HPL[{2}, -S^2])/108) + ((11*Pi^2*S^3)/72 + (12 + 3*S^2 - 42*S^4 - 124*S^6 - 134*S^8 - 34*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-6 - 12*S^2 - 6*S^4 - 19*S^6 - 50*S^8 - 28*S^10)*HPL[{4}, -S^2])/(36*S^3*(1 + S^2)^2) + (13*S^3*HPL[{5}, -S^2])/12 + ((-85*Pi^2*S^3)/216 + (1532 + 7780*S^2 + 13556*S^4 + 28937*S^6 + 11074*S^8 - 1879*S^10)/(1296*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*(-((1 + S^2)*(5242 + 10187*S^2 + 135535*S^4))/(15552*S^3) + (Pi^2*(-1106 - 2212*S^2 - 1106*S^4 - 16055*S^6 - 18814*S^8 - 6083*S^10))/(2592*S^3*(1 + S^2)^2) + ((-76 - 152*S^2 - 76*S^4 - 1141*S^6 - 1318*S^8 - 418*S^10)*HPL[{2}, -S^2])/(72*S^3*(1 + S^2)^2) + (S^3*HPL[{3}, -S^2])/12 + (241*S^3*HPL[{2, 1}, -S^2])/36) + (S^3*(4763 + 6718*S^2 + 2657*S^4)*HPL[{3, 1}, -S^2])/(216*(1 + S^2)^2) - (13*S^3*HPL[{4, 1}, -S^2])/12 + ((24 + 48*S^2 + 24*S^4 - 4961*S^6 - 7030*S^8 - 2792*S^10)*HPL[{2, 1, 1}, -S^2])/(108*S^3*(1 + S^2)^2) + (2*S^3*HPL[{2, 2, 1}, -S^2])/9 + (11*S^3*HPL[{3, 1, 1}, -S^2])/6 - (25*S^3*HPL[{2, 1, 1, 1}, -S^2])/9 + ((-97*Pi^2*S^3)/216 + (-60 - 30*S^2 - 2219*S^4 - 2069*S^6)/(432*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((972 - 1281*S^2 - 7473*S^4 - 34270*S^6)/(3888*S^3) + (Pi^2*(12 + 24*S^2 + 12*S^4 - 5113*S^6 - 7610*S^8 - 3151*S^10))/(1296*S^3*(1 + S^2)^2) - (S^3*HPL[{2, 1}, -S^2])/9 - (5*S^3*Zeta[3])/12) + HPL[{1}, -S^2]*((-2009*Pi^4*S^3)/6480 - ((1 + S^2)*(1564 + 17891*S^2 + 451267*S^4))/(46656*S^3) + (Pi^2*(-206 - 9361*S^2 - 19412*S^4 - 80648*S^6 - 75178*S^8 - 24731*S^10))/(7776*S^3*(1 + S^2)^2) + ((-109*Pi^2*S^3)/108 + (-263 - 2389*S^2 - 4295*S^4 - 16544*S^6 - 14728*S^8 - 4691*S^10)/(648*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (5*S^3*HPL[{2}, -S^2]^2)/3 + ((-4 - 8*S^2 - 4*S^4 - 13*S^6 - 38*S^8 - 22*S^10)*HPL[{3}, -S^2])/(36*S^3*(1 + S^2)^2) + (S^3*HPL[{4}, -S^2])/6 + ((76 + 152*S^2 + 76*S^4 + 1141*S^6 + 1318*S^8 + 418*S^10)*HPL[{2, 1}, -S^2])/(36*S^3*(1 + S^2)^2) + (13*S^3*HPL[{3, 1}, -S^2])/2 - (241*S^3*HPL[{2, 1, 1}, -S^2])/18 - (5*(2 + 11*S^6)*Zeta[3])/(72*S^3)) - (65*S^3*Zeta[5])/36) + HPL[{1}, -S^2]^4*(-(Pi^2*(1 + S^2)*(11160 + 15533*S^2 + 110847*S^4))/(3888*S^3) - ((1 + S^2)*(126326 + 155803*S^2 + 1865477*S^4))/(17496*S^3) + (Pi^4*(-17174 - 34348*S^2 - 17174*S^4 - 334685*S^6 - 349066*S^8 - 94457*S^10))/(19440*S^3*(1 + S^2)^2) - (98*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((497*Pi^2*S^3)/27 + (2362 + 9155*S^2 + 11686*S^4 + 53788*S^6 + 22304*S^8 + 7609*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*(28 + 56*S^2 + 28*S^4 + 901*S^6 + 806*S^8 + 154*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) + 24*S^3*HPL[{5}, -S^2] + ((392*Pi^2*S^3)/27 + (2*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (4*(56 + 112*S^2 + 56*S^4 - 439*S^6 + 118*S^8 + 308*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (1568*S^3*HPL[{3, 2}, -S^2])/9 - (5368*S^3*HPL[{4, 1}, -S^2])/9 - (130*(2 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (3136*S^3*HPL[{2, 2, 1}, -S^2])/9 - (5608*S^3*HPL[{3, 1, 1}, -S^2])/9 + ((416*Pi^2*S^3)/27 + (2*(271 + 1271*S^2 + 1837*S^4 + 9946*S^6 + 3854*S^8 + 1495*S^10))/(81*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(54*S^3) + (Pi^2*(-502 - 1004*S^2 - 502*S^4 - 6289*S^6 - 7874*S^8 - 2761*S^10))/(162*S^3*(1 + S^2)^2) + (784*S^3*HPL[{3}, -S^2])/9 + (1568*S^3*HPL[{2, 1}, -S^2])/9 + (784*S^3*Zeta[3])/9) + (760*S^3*Zeta[5])/9) + HPL[{2}, -S^2]^2*((6881 - 132705*S^2 - 380493*S^4 - 1464277*S^6)/(11664*S^3) + (Pi^2*(-456 - 6111*S^2 - 15096*S^4 - 47632*S^6))/(1296*S^3) + (Pi^4*(-440 - 880*S^2 - 440*S^4 - 92821*S^6 - 113714*S^8 - 38875*S^10))/(6480*S^3*(1 + S^2)^2) + ((449*Pi^2*S^3)/18 + (78 + 1083*S^2 + 1536*S^4 + 12553*S^6 + 7412*S^8 + 3778*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((5 + 10*S^2 + 5*S^4 + 1087*S^6 + 1190*S^8 + 349*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (97*S^3*HPL[{5}, -S^2])/3 + ((-209*Pi^2*S^3)/9 + (1355 + 3575*S^2 + 4170*S^4 + 6519*S^6 - 3315*S^8)/(54*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-114 - 228*S^2 - 114*S^4 + 405*S^6 + 1466*S^8 + 897*S^10)*HPL[{3, 1}, -S^2])/(6*S^3*(1 + S^2)^2) - (805*S^3*HPL[{3, 2}, -S^2])/3 - (2591*S^3*HPL[{4, 1}, -S^2])/3 - (4*(-66 + 773*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - 252*S^3*HPL[{2, 2, 1}, -S^2] - (556*S^3*HPL[{3, 1, 1}, -S^2])/3 - (1568*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((409*Pi^2*S^3)/18 + (-50 + 240*S^2 + 370*S^4 + 5517*S^6 + 3142*S^8 + 1953*S^10)/(36*S^3*(1 + S^2)^2))*Zeta[3] + (341*S^3*Zeta[5])/3) + Log[T]^4*((-10432 - 36973*S^2)/(2916*S) + (Pi^2*(-3867 - 8997*S^2 - 18541*S^4))/(729*S) - (Pi^4*S^3*(90490 + 100904*S^2 + 30433*S^4))/(4860*(1 + S^2)^2) - (281*S^3*HPL[{0}, S^2]^5)/540 + ((-290*Pi^2*S^3)/9 - (5*(88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^3 - (140*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)^2) - (224*S^3*HPL[{1}, -S^2]^5)/9 + HPL[{0}, S^2]^4*(-(S^3*(2779 + 3854*S^2 + 1501*S^4))/(324*(1 + S^2)^2) - (71*S^3*HPL[{1}, -S^2])/27) + ((-100 - 200*S^2 - 100*S^4 - 5161*S^6 - 5618*S^8 - 1633*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + HPL[{0}, S^2]^3*((-328*Pi^2*S^3)/81 + (-1608 - 2412*S^2 - 22141*S^4 - 26243*S^6 - 11476*S^8)/(486*S*(1 + S^2)^2) + ((-268 - 536*S^2 - 268*S^4 - 4759*S^6 - 5138*S^8 - 1474*S^10)*HPL[{1}, -S^2])/(81*S^3*(1 + S^2)^2) - (365*S^3*HPL[{1}, -S^2]^2)/27 - (349*S^3*HPL[{2}, -S^2])/27) + ((938*Pi^2*S^3)/27 + (430 + 2549*S^2 + 2986*S^4 + 23552*S^6 + 12208*S^8 + 6623*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*S^3*(1052 + 1108*S^2 + 305*S^4)*HPL[{4}, -S^2])/(27*(1 + S^2)^2) + (148*S^3*HPL[{5}, -S^2])/3 + ((-916*Pi^2*S^3)/27 + (2602 + 7570*S^2 + 9054*S^4 + 14895*S^6 - 6723*S^8)/(81*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (4*(-165 - 330*S^2 - 165*S^4 + 731*S^6 + 2458*S^8 + 1478*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (3296*S^3*HPL[{3, 2}, -S^2])/9 - (10616*S^3*HPL[{4, 1}, -S^2])/9 - (40*(-8 + 117*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (3112*S^3*HPL[{2, 2, 1}, -S^2])/9 - (752*S^3*HPL[{3, 1, 1}, -S^2])/3 - (2240*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((310*Pi^2*S^3)/9 + (120 + 180*S^2 + 2023*S^4 + 1210*S^6 + 747*S^8)/(9*S*(1 + S^2)^2))*Zeta[3] + HPL[{0}, S^2]^2*((-7908 - 15603*S^2 - 74164*S^4)/(972*S) - (Pi^2*S^3*(13253 + 17518*S^2 + 6512*S^4))/(324*(1 + S^2)^2) - (5*(22 + 44*S^2 + 22*S^4 + 400*S^6 + 428*S^8 + 121*S^10)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) - (310*S^3*HPL[{1}, -S^2]^3)/9 + ((20 + 40*S^2 + 20*S^4 - 3557*S^6 - 4762*S^8 - 1793*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-749*Pi^2*S^3)/54 + (-2876 - 16291*S^2 - 25232*S^4 - 97286*S^6 - 75484*S^8 - 23495*S^10)/(324*S^3*(1 + S^2)^2) - (392*S^3*HPL[{2}, -S^2])/9) + (53*S^3*HPL[{3}, -S^2])/9 - (76*S^3*HPL[{2, 1}, -S^2])/9 + 10*S^3*Zeta[3]) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(972*S^3) - (5*Pi^2*(50 + 100*S^2 + 50*S^4 + 1058*S^6 + 1072*S^8 + 275*S^10))/(27*S^3*(1 + S^2)^2) - (65*(2 + 11*S^6)*HPL[{2}, -S^2])/(9*S^3) + (1900*S^3*HPL[{3}, -S^2])/9 + (500*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((1721 - 828*S^2 + 801*S^4 - 37082*S^6)/(243*S^3) - (4*Pi^2*(-35 - 70*S^2 - 35*S^4 + 1328*S^6 + 2068*S^8 + 887*S^10))/(81*S^3*(1 + S^2)^2) + 192*S^3*HPL[{3}, -S^2] + (1556*S^3*HPL[{2, 1}, -S^2])/9 + (1528*S^3*Zeta[3])/9) + HPL[{1}, -S^2]*((-6673*Pi^4*S^3)/810 - ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(2916*S^3) + (Pi^2*(-3418 - 18833*S^2 - 28906*S^4 - 117178*S^6 - 83192*S^8 - 26485*S^10))/(486*S^3*(1 + S^2)^2) + ((-392*Pi^2*S^3)/27 - (2*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (784*S^3*HPL[{2}, -S^2]^2)/9 + (20*(28 + 56*S^2 + 28*S^4 + 1009*S^6 + 878*S^8 + 154*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (664*S^3*HPL[{4}, -S^2])/9 + (130*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (664*S^3*HPL[{3, 1}, -S^2])/9 + (20*(2 + 4*S^2 + 2*S^4 + 86*S^6 + 72*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((-2473*Pi^4*S^3)/324 + (-49944 - 84351*S^2 - 574261*S^4)/(2916*S) + (Pi^2*(-8256 - 12384*S^2 - 112367*S^4 - 117286*S^6 - 52427*S^8))/(972*S*(1 + S^2)^2) - (280*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^2) - (560*S^3*HPL[{1}, -S^2]^4)/9 + ((-1144*Pi^2*S^3)/27 + (726 - 2904*S^2 - 5448*S^4 - 61879*S^6 - 62216*S^8 - 29155*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (767*S^3*HPL[{2}, -S^2]^2)/9 + HPL[{1}, -S^2]^2*((-1205*Pi^2*S^3)/27 - (5*(88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10))/(18*S^3*(1 + S^2)^2) - (500*S^3*HPL[{2}, -S^2])/3) + (2*(-27 - 54*S^2 - 27*S^4 + 283*S^6 + 362*S^8 + 130*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (32*S^3*HPL[{4}, -S^2])/3 - (10*(-54 - 108*S^2 - 54*S^4 - 425*S^6 - 250*S^8 + 25*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3152*S^3*HPL[{3, 1}, -S^2])/9 - (2120*S^3*HPL[{2, 1, 1}, -S^2])/3 + (2*S^3*(1301 + 1606*S^2 + 554*S^4)*Zeta[3])/(27*(1 + S^2)^2) + HPL[{1}, -S^2]*((-5*(1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(972*S^3) + (Pi^2*(-688 - 1376*S^2 - 688*S^4 - 14629*S^6 - 14798*S^8 - 3784*S^10))/(81*S^3*(1 + S^2)^2) - (125*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (68*S^3*HPL[{3}, -S^2])/9 + (1000*S^3*HPL[{2, 1}, -S^2])/3 + (332*S^3*Zeta[3])/9)) + (580*S^3*Zeta[5])/3) + HPL[{2, 1, 1}, -S^2]*((59867 - 30486*S^2 - 43275*S^4 - 3087476*S^6)/(2916*S^3) + (Pi^2*(4603 - 8145*S^2 - 15030*S^4 - 149428*S^6))/(486*S^3) + (Pi^4*(2152 + 4304*S^2 + 2152*S^4 - 141277*S^6 - 209798*S^8 - 86710*S^10))/(1620*S^3*(1 + S^2)^2) - (6272*S^3*HPL[{2, 2, 1}, -S^2])/3 - 1664*S^3*HPL[{3, 1, 1}, -S^2] + (12448*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((560*Pi^2*S^3)/3 + (2*(390 + 2124*S^2 + 2406*S^4 + 19489*S^6 + 10730*S^8 + 6025*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + 976*S^3*Zeta[5]) + Zeta[3]*((1847*Pi^6*S^3)/3402 + (Pi^2*(54684 + 53658*S^2 + 107521*S^4))/(11664*S) + (855606 + 738021*S^2 + 206932*S^4)/(34992*S) + (Pi^4*(3270 + 4905*S^2 + 46298*S^4 - 7085*S^6 + 2954*S^8))/(9720*S*(1 + S^2)^2) + (2*S^3*(175 + 722*S^2 + 454*S^4)*Zeta[5])/(9*(1 + S^2)^2)) + HPL[{3}, -S^2]*((2323*Pi^6*S^3)/2835 + (Pi^2*(34560 + 68655*S^2 - 3336*S^4 + 96409*S^6))/(11664*S^3) + (664403 + 880116*S^2 + 711744*S^4 + 1934484*S^6)/(34992*S^3) + (Pi^4*(3053 + 9844*S^2 + 6275*S^4 + 68211*S^6 + 20280*S^8 + 16461*S^10))/(9720*S^3*(1 + S^2)^2) + ((-13*Pi^2*S^3)/3 + (25 - 49*S^2 - 146*S^4 - 66*S^6 + 1461*S^8 + 681*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(28 + 56*S^2 + 28*S^4 + 51*S^6 + 270*S^8 + 177*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + 46*S^3*HPL[{6}, -S^2] - (1712*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((-892*Pi^2*S^3)/9 + (152 - 49*S^2 - 130*S^4 - 5852*S^6 - 3420*S^8 - 2201*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((10 + 20*S^2 + 10*S^4 + 2383*S^6 + 2702*S^8 + 835*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*(-44 - 88*S^2 - 44*S^4 + 251*S^6 + 178*S^8 + 8*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 28*S^3*HPL[{4, 2}, -S^2] - (40*S^3*HPL[{5, 1}, -S^2])/3 + ((604*Pi^2*S^3)/3 + (-788 + 641*S^2 + 1300*S^4 + 35836*S^6 + 21032*S^8 + 13291*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (2*(566 + 1132*S^2 + 566*S^4 + 8797*S^6 + 6410*S^8 + 409*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*(1706 + 3412*S^2 + 1706*S^4 + 24373*S^6 + 16970*S^8 + 541*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*S^3*HPL[{3, 1, 2}, -S^2])/3 + 1128*S^3*HPL[{3, 2, 1}, -S^2] - (110168*S^3*HPL[{4, 1, 1}, -S^2])/3 + (32*(-23 - 46*S^2 - 23*S^4 - 281*S^6 - 170*S^8 + 13*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (6848*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 + 4608*S^3*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-1462 + 2520*S^2 - 90*S^4 + 1171*S^6)/(324*S^3) + (Pi^2*(10 + 20*S^2 + 10*S^4 + 677*S^6 + 730*S^8 + 209*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] + (32*S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((-1105 - 1121*S^2 - 4727*S^4 - 163*S^6)/(18*S^3) + (Pi^2*(-578 - 1156*S^2 - 578*S^4 - 7207*S^6 - 4502*S^8 + 227*S^10))/(54*S^3*(1 + S^2)^2) + (64*S^3*Zeta[3])/3) + ((-34 - 68*S^2 - 34*S^4 + 199*S^6 + 14*S^8 - 89*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-68629*Pi^6*S^3)/68040 + (303805 - 60705*S^2 + 19559241*S^4 - 206932*S^6)/(34992*S^3) + (Pi^2*(65397 + 53424*S^2 + 879489*S^4 - 31645*S^6))/(5832*S^3) + (Pi^4*(31973 + 134320*S^2 + 214844*S^4 + 434411*S^6 + 179695*S^8 - 33085*S^10))/(9720*S^3*(1 + S^2)^2) + ((-976*Pi^2*S^3)/9 + (-1922 - 10501*S^2 - 16790*S^4 - 57214*S^6 - 27440*S^8 - 6661*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((1054 + 2108*S^2 + 1054*S^4 + 15761*S^6 + 11026*S^8 + 389*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(-1712 - 3424*S^2 - 1712*S^4 - 23123*S^6 - 15406*S^8 + 7*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 26*S^3*HPL[{4, 2}, -S^2] - (4*S^3*HPL[{5, 1}, -S^2])/3 + ((-1624*Pi^2*S^3)/9 - (4*(462 + 2098*S^2 + 3198*S^4 + 9795*S^6 + 4318*S^8 + 789*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (16*(-66 + 773*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(-20 - 40*S^2 - 20*S^4 + 1335*S^6 + 1886*S^8 + 747*S^10)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - 104*S^3*HPL[{3, 1, 2}, -S^2] + 904*S^3*HPL[{3, 2, 1}, -S^2] + 3152*S^3*HPL[{4, 1, 1}, -S^2] + (16*(100 + 200*S^2 + 100*S^4 + 5161*S^6 + 5618*S^8 + 1633*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (7552*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 - (12448*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((-2281 - 4833*S^2 - 18234*S^4 - 1100*S^6)/(81*S^3) + (Pi^2*(-214 - 428*S^2 - 214*S^4 - 3953*S^6 - 2734*S^8 - 74*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] - 20*S^3*Zeta[3]^2 + (2*(-30 - 60*S^2 - 30*S^4 - 1072*S^6 - 700*S^8 + 11*S^10)*Zeta[5])/(3*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-52285*Pi^6*S^3)/40824 - (Pi^2*(1 + S^2)*(82727 + 105499*S^2 + 1056428*S^4))/(17496*S^3) - ((1 + S^2)*(772759 + 794066*S^2 + 12649645*S^4))/(52488*S^3) + (Pi^4*(-35522 - 207793*S^2 - 324908*S^4 - 1298609*S^6 - 972379*S^8 - 306863*S^10))/(29160*S^3*(1 + S^2)^2) + ((-607*Pi^2*S^3)/27 + (-664 - 3427*S^2 - 5140*S^4 - 21304*S^6 - 14056*S^8 - 4537*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (148*S^3*HPL[{3}, -S^2]^2)/9 + ((340*Pi^2*S^3)/27 + (2828 + 9271*S^2 + 10568*S^4 + 39350*S^6 + 15832*S^8 + 4511*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(2 + 4*S^2 + 2*S^4 + 983*S^6 + 670*S^8 + 11*S^10)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)^2) + (178*S^3*HPL[{6}, -S^2])/9 + (3136*S^3*HPL[{2, 1}, -S^2]^2)/9 + ((440*Pi^2*S^3)/27 + (4*(-185 + 563*S^2 + 1867*S^4 + 5062*S^6 + 9932*S^8 + 3001*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)^2) - (4*(790 + 1580*S^2 + 790*S^4 + 28501*S^6 + 24794*S^8 + 4345*S^10)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - 52*S^3*HPL[{4, 2}, -S^2] - (2704*S^3*HPL[{5, 1}, -S^2])/9 + ((-1568*Pi^2*S^3)/27 - (8*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (1568*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (16*(448 + 896*S^2 + 448*S^4 + 8773*S^6 + 9134*S^8 + 2464*S^10)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (2656*S^3*HPL[{4, 1, 1}, -S^2])/9 + (520*(2 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) - (2656*S^3*HPL[{3, 1, 1, 1}, -S^2])/9 + (((1 + S^2)*(4640 + 8971*S^2 + 32009*S^4))/(486*S^3) + (2*Pi^2*(98 + 196*S^2 + 98*S^4 + 4283*S^6 + 3574*S^8 + 539*S^10))/(81*S^3*(1 + S^2)^2))*Zeta[3] - (80*S^3*Zeta[3]^2)/9 + HPL[{2, 1}, -S^2]*((2*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(27*S^3) + (2*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(81*S^3*(1 + S^2)^2) - (3136*S^3*Zeta[3])/9) + HPL[{3}, -S^2]*(((1 + S^2)*(12118 + 14507*S^2 + 35779*S^4))/(486*S^3) + (Pi^2*(274 + 548*S^2 + 274*S^4 + 10453*S^6 + 8978*S^8 + 1507*S^10))/(81*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{2, 1}, -S^2])/9 + (200*S^3*Zeta[3])/9) + HPL[{2}, -S^2]*((-2021*Pi^4*S^3)/540 - ((1 + S^2)*(13400 + 9469*S^2 + 411947*S^4))/(2916*S^3) + (Pi^2*(-531 - 3787*S^2 - 6411*S^4 - 22680*S^6 - 21382*S^8 - 6561*S^10))/(162*S^3*(1 + S^2)^2) + (2*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (452*S^3*HPL[{4}, -S^2])/9 + (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (3136*S^3*HPL[{3, 1}, -S^2])/9 - (6272*S^3*HPL[{2, 1, 1}, -S^2])/9 + (224*(2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + (2*(34 + 68*S^2 + 34*S^4 + 2467*S^6 + 1894*S^8 + 187*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + Log[T]^3*((13364*Pi^6*S^3)/8505 + (16130 + 62867*S^2)/(4374*S) + (Pi^2*(19464 + 43269*S^2 + 157649*S^4))/(2916*S) + (Pi^4*(17174 + 25761*S^2 + 196246*S^4 + 175720*S^6 + 68137*S^8))/(4860*S*(1 + S^2)^2) + (19*S^3*HPL[{0}, S^2]^6)/108 + ((290*Pi^2*S^3)/9 + (5*(88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^4 + (112*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^5)/(27*S^3*(1 + S^2)^2) + (448*S^3*HPL[{1}, -S^2]^6)/27 + HPL[{0}, S^2]^5*((S^3*(5654 + 8056*S^2 + 3215*S^4))/(1620*(1 + S^2)^2) + (271*S^3*HPL[{1}, -S^2])/270) + ((808*Pi^2*S^3)/27 + (202 + 1329*S^2 + 1942*S^4 + 11509*S^6 + 9738*S^8 + 3748*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (784*S^3*HPL[{2}, -S^2]^3)/27 + HPL[{0}, S^2]^4*((95*Pi^2*S^3)/54 + (506 + 759*S^2 + 6953*S^4 + 8766*S^6 + 3770*S^8)/(324*S*(1 + S^2)^2) + ((506 + 1012*S^2 + 506*S^4 + 7895*S^6 + 8974*S^8 + 2783*S^10)*HPL[{1}, -S^2])/(324*S^3*(1 + S^2)^2) + (142*S^3*HPL[{1}, -S^2]^2)/27 + (133*S^3*HPL[{2}, -S^2])/27) + (296*S^3*HPL[{3}, -S^2]^2)/9 + ((-520*Pi^2*S^3)/27 + (-24 - 1419*S^2 - 2148*S^4 - 17515*S^6 - 9122*S^8 - 4312*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(2 + 4*S^2 + 2*S^4 + 681*S^6 + 498*S^8 + 33*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - 8*S^3*HPL[{6}, -S^2] - (3160*S^3*HPL[{2, 1}, -S^2]^2)/9 + ((-3008*Pi^2*S^3)/27 - (4*(-1326 - 2619*S^2 - 2874*S^4 + 4291*S^6 + 19118*S^8 + 10258*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(-56 - 112*S^2 - 56*S^4 + 9641*S^6 + 9874*S^8 + 2585*S^10)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)^2) + (8*(-38 - 76*S^2 - 38*S^4 + 16281*S^6 + 16458*S^8 + 4203*S^10)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (1144*S^3*HPL[{4, 2}, -S^2])/9 + (5168*S^3*HPL[{5, 1}, -S^2])/9 + ((6800*Pi^2*S^3)/27 + (20*(-362 - 74*S^2 - 306*S^4 + 4725*S^6 + 4635*S^8))/(81*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (16*(292 + 584*S^2 + 292*S^4 + 4051*S^6 + 3398*S^8 + 523*S^10)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (16*(861 + 1722*S^2 + 861*S^4 + 6493*S^6 + 4574*S^8 + 184*S^10)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (640*S^3*HPL[{3, 1, 2}, -S^2])/9 + (5632*S^3*HPL[{3, 2, 1}, -S^2])/9 + (4832*S^3*HPL[{4, 1, 1}, -S^2])/3 + (560*(-6 + 13*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) - (3520*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 + (8960*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((-64*Pi^2*S^3*(163 + 170*S^2 + 46*S^4))/(81*(1 + S^2)^2) - (4*(1842 + 1887*S^2 + 7400*S^4))/(243*S))*Zeta[3] - (8*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(729*S^3) + (20*Pi^2*(50 + 100*S^2 + 50*S^4 + 1058*S^6 + 1072*S^8 + 275*S^10))/(81*S^3*(1 + S^2)^2) + (260*(2 + 11*S^6)*HPL[{2}, -S^2])/(27*S^3) - (7600*S^3*HPL[{3}, -S^2])/27 - (2000*S^3*Zeta[3])/9) + HPL[{3}, -S^2]*((-7550 - 24879*S^2 - 16662*S^4 - 63141*S^6)/(486*S^3) - (2*Pi^2*(-2 - 4*S^2 - 2*S^4 + 1964*S^6 + 1940*S^8 + 473*S^10))/(27*S^3*(1 + S^2)^2) - (640*S^3*HPL[{2, 1}, -S^2])/9 - 32*S^3*Zeta[3]) + HPL[{0}, S^2]^3*((Pi^2*S^3*(6077 + 8338*S^2 + 3215*S^4))/(243*(1 + S^2)^2) + (490 + 1549*S^2 + 8263*S^4)/(162*S) + (2*(268 + 536*S^2 + 268*S^4 + 4759*S^6 + 5138*S^8 + 1474*S^10)*HPL[{1}, -S^2]^2)/(81*S^3*(1 + S^2)^2) + (1460*S^3*HPL[{1}, -S^2]^3)/81 + (2*(-10 - 20*S^2 - 10*S^4 + 2968*S^6 + 3956*S^8 + 1483*S^10)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((212*Pi^2*S^3)/27 + (265 + 1968*S^2 + 3337*S^4 + 13411*S^6 + 10878*S^8 + 3481*S^10)/(81*S^3*(1 + S^2)^2) + (220*S^3*HPL[{2}, -S^2])/9) - (2*S^3*HPL[{3}, -S^2])/3 + (76*S^3*HPL[{2, 1}, -S^2])/27 - (28*S^3*Zeta[3])/27) + HPL[{2, 1}, -S^2]*((4*(-2972 - 1899*S^2 - 31959*S^4 + 7400*S^6))/(243*S^3) + (4*Pi^2*(-642 - 1284*S^2 - 642*S^4 - 977*S^6 + 398*S^8 + 787*S^10))/(81*S^3*(1 + S^2)^2) + (160*S^3*Zeta[3])/9) + HPL[{1}, -S^2]^2*((6673*Pi^4*S^3)/405 + ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(1458*S^3) + (Pi^2*(3418 + 18833*S^2 + 28906*S^4 + 117178*S^6 + 83192*S^8 + 26485*S^10))/(243*S^3*(1 + S^2)^2) + ((784*Pi^2*S^3)/27 + (4*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (1568*S^3*HPL[{2}, -S^2]^2)/9 - (40*(28 + 56*S^2 + 28*S^4 + 1009*S^6 + 878*S^8 + 154*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (1328*S^3*HPL[{4}, -S^2])/9 - (260*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (1328*S^3*HPL[{3, 1}, -S^2])/9 - (40*(2 + 4*S^2 + 2*S^4 + 86*S^6 + 72*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((325*Pi^4*S^3)/27 + (-4334 + 2259*S^2 - 2502*S^4 + 157649*S^6)/(486*S^3) + (Pi^2*(-2408 + 254*S^2 + 2812*S^4 + 68693*S^6 + 101218*S^8 + 46787*S^10))/(486*S^3*(1 + S^2)^2) - (4*(-50 - 100*S^2 - 50*S^4 + 4927*S^6 + 5150*S^8 + 1399*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (1096*S^3*HPL[{4}, -S^2])/9 - (8*(292 + 584*S^2 + 292*S^4 + 4051*S^6 + 3398*S^8 + 523*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (832*S^3*HPL[{3, 1}, -S^2])/3 + (6320*S^3*HPL[{2, 1, 1}, -S^2])/9 - (16*(6 + 12*S^2 + 6*S^4 + 1171*S^6 + 1166*S^8 + 289*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((2731*Pi^4*S^3)/540 + (12344 + 20924*S^2 + 157649*S^4)/(972*S) + (Pi^2*(2332 + 3498*S^2 + 30571*S^4 + 35682*S^6 + 15265*S^8))/(324*S*(1 + S^2)^2) + (20*(22 + 44*S^2 + 22*S^4 + 400*S^6 + 428*S^8 + 121*S^10)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^2) + (310*S^3*HPL[{1}, -S^2]^4)/9 + ((232*Pi^2*S^3)/9 + (-299 + 1217*S^2 + 2356*S^4 + 23299*S^6 + 27209*S^8 + 11806*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (413*S^3*HPL[{2}, -S^2]^2)/9 + HPL[{1}, -S^2]^2*((749*Pi^2*S^3)/27 + (2876 + 16291*S^2 + 25232*S^4 + 97286*S^6 + 75484*S^8 + 23495*S^10)/(162*S^3*(1 + S^2)^2) + (784*S^3*HPL[{2}, -S^2])/9) - (2*(-21 - 42*S^2 - 21*S^4 + 232*S^6 + 200*S^8 + 34*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (20*S^3*HPL[{4}, -S^2])/9 + (2*(-654 - 1308*S^2 - 654*S^4 - 3319*S^6 - 1934*S^8 + 209*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (1688*S^3*HPL[{3, 1}, -S^2])/9 + (3440*S^3*HPL[{2, 1, 1}, -S^2])/9 - (2*S^3*(476 + 460*S^2 + 107*S^4)*Zeta[3])/(27*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(7210 + 9407*S^2 + 75133*S^4))/(486*S^3) + (Pi^2*(1166 + 2332*S^2 + 1166*S^4 + 19895*S^6 + 21814*S^8 + 6413*S^10))/(162*S^3*(1 + S^2)^2) + ((614 + 1228*S^2 + 614*S^4 + 10433*S^6 + 11458*S^8 + 3377*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) - (88*S^3*HPL[{3}, -S^2])/9 - (1568*S^3*HPL[{2, 1}, -S^2])/9 - (164*S^3*Zeta[3])/9)) - (16*S^3*(1136 + 1132*S^2 + 281*S^4)*Zeta[5])/(27*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(11160 + 15533*S^2 + 110847*S^4))/(972*S^3) + ((1 + S^2)*(126326 + 155803*S^2 + 1865477*S^4))/(4374*S^3) + (Pi^4*(17174 + 34348*S^2 + 17174*S^4 + 334685*S^6 + 349066*S^8 + 94457*S^10))/(4860*S^3*(1 + S^2)^2) + (392*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((-1988*Pi^2*S^3)/27 - (2*(2362 + 9155*S^2 + 11686*S^4 + 53788*S^6 + 22304*S^8 + 7609*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (16*(28 + 56*S^2 + 28*S^4 + 901*S^6 + 806*S^8 + 154*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - 96*S^3*HPL[{5}, -S^2] + ((-1568*Pi^2*S^3)/27 - (8*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (16*(56 + 112*S^2 + 56*S^4 - 439*S^6 + 118*S^8 + 308*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (6272*S^3*HPL[{3, 2}, -S^2])/9 + (21472*S^3*HPL[{4, 1}, -S^2])/9 + (520*(2 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (12544*S^3*HPL[{2, 2, 1}, -S^2])/9 + (22432*S^3*HPL[{3, 1, 1}, -S^2])/9 + ((-1664*Pi^2*S^3)/27 - (8*(271 + 1271*S^2 + 1837*S^4 + 9946*S^6 + 3854*S^8 + 1495*S^10))/(81*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((2*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(27*S^3) + (2*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(81*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{3}, -S^2])/9 - (6272*S^3*HPL[{2, 1}, -S^2])/9 - (3136*S^3*Zeta[3])/9) - (3040*S^3*Zeta[5])/9) + HPL[{0}, S^2]*((Pi^4*S^3*(201166 + 256136*S^2 + 91519*S^4))/(4860*(1 + S^2)^2) + (Pi^2*(30420 + 67032*S^2 + 331009*S^4))/(2916*S) + (130620 + 190794*S^2 + 1865477*S^4)/(4374*S) + (280*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)^2) + (448*S^3*HPL[{1}, -S^2]^5)/9 + (2*(12 + 24*S^2 + 12*S^4 + 5701*S^6 + 6698*S^8 + 2173*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((4820*Pi^2*S^3)/81 + (10*(88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10))/(27*S^3*(1 + S^2)^2) + (2000*S^3*HPL[{2}, -S^2])/9) + ((-128*Pi^2*S^3)/27 + (170 + 325*S^2 + 710*S^4 + 278*S^6 + 1396*S^8 + 449*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(6 + 12*S^2 + 6*S^4 + 643*S^6 + 734*S^8 + 229*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) + (44*S^3*HPL[{5}, -S^2])/9 + ((256*Pi^2*S^3)/27 + (2*(-3686 - 15256*S^2 - 23972*S^4 - 63733*S^6 - 23588*S^8 + 743*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(-35 - 70*S^2 - 35*S^4 + 5568*S^6 + 6636*S^8 + 2193*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (472*S^3*HPL[{3, 2}, -S^2])/9 + (1360*S^3*HPL[{4, 1}, -S^2])/9 + (80*(-2 - 4*S^2 - 2*S^4 + 375*S^6 + 450*S^8 + 150*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (272*S^3*HPL[{2, 2, 1}, -S^2])/9 - (64*S^3*HPL[{3, 1, 1}, -S^2])/9 + 160*S^3*HPL[{2, 1, 1, 1}, -S^2] + ((-388*Pi^2*S^3)/27 - (2*(480 + 720*S^2 + 6331*S^4 + 5762*S^6 + 2659*S^8))/(81*S*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(486*S^3) + (2*Pi^2*(688 + 1376*S^2 + 688*S^4 + 14629*S^6 + 14798*S^8 + 3784*S^10))/(81*S^3*(1 + S^2)^2) + (250*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) - (136*S^3*HPL[{3}, -S^2])/9 - (2000*S^3*HPL[{2, 1}, -S^2])/3 - (664*S^3*Zeta[3])/9) + HPL[{2}, -S^2]*((-2244 + 16923*S^2 + 37776*S^4 + 180337*S^6)/(486*S^3) + (2*Pi^2*(-40 - 80*S^2 - 40*S^4 + 8593*S^6 + 10706*S^8 + 3733*S^10))/(81*S^3*(1 + S^2)^2) - (224*S^3*HPL[{3}, -S^2])/9 - (136*S^3*HPL[{2, 1}, -S^2])/9 - (656*S^3*Zeta[3])/9) + HPL[{1}, -S^2]*((4061*Pi^4*S^3)/270 + ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(1458*S^3) + (Pi^2*(1850 + 11061*S^2 + 17534*S^4 + 72512*S^6 + 52056*S^8 + 16787*S^10))/(162*S^3*(1 + S^2)^2) + (80*Pi^2*S^3 + (4*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (1568*S^3*HPL[{2}, -S^2]^2)/9 - (8*(10 + 20*S^2 + 10*S^4 + 208*S^6 + 212*S^8 + 55*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (184*S^3*HPL[{4}, -S^2])/9 - (500*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2000*S^3*HPL[{3, 1}, -S^2])/3 + (4000*S^3*HPL[{2, 1, 1}, -S^2])/3 - (8*(40 + 80*S^2 + 40*S^4 + 967*S^6 + 938*S^8 + 220*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) - (520*S^3*Zeta[5])/9)) + HPL[{0}, S^2]^3*((-52021*Pi^6*S^3)/272160 + (-341634 - 228393*S^2 - 7212418*S^4)/(139968*S) + (Pi^2*(-2666 - 9651*S^2 - 117529*S^4))/(7776*S) + (Pi^4*(-46284 - 69426*S^2 - 583003*S^4 - 715850*S^6 - 299881*S^8))/(116640*S*(1 + S^2)^2) + ((-268 - 536*S^2 - 268*S^4 - 4759*S^6 - 5138*S^8 - 1474*S^10)*HPL[{1}, -S^2]^5)/(405*S^3*(1 + S^2)^2) - (73*S^3*HPL[{1}, -S^2]^6)/81 + ((-541*Pi^2*S^3)/216 + (-148 - 3068*S^2 - 4216*S^4 - 37567*S^6 - 44102*S^8 - 19279*S^10)/(1296*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (26*S^3*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((-53*Pi^2*S^3)/27 + (-265 - 1968*S^2 - 3337*S^4 - 13411*S^6 - 10878*S^8 - 3481*S^10)/(324*S^3*(1 + S^2)^2) - (55*S^3*HPL[{2}, -S^2])/9) + (5*S^3*HPL[{3}, -S^2]^2)/18 + ((-29*Pi^2*S^3)/27 + (-172 - 488*S^2 - 388*S^4 - 3743*S^6 - 4534*S^8 - 2087*S^10)/(648*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((40 + 80*S^2 + 40*S^4 - 190*S^6 - 104*S^8 + 17*S^10)*HPL[{5}, -S^2])/(54*S^3*(1 + S^2)^2) - 7*S^3*HPL[{6}, -S^2] + (325*S^3*HPL[{2, 1}, -S^2]^2)/9 + ((607*Pi^2*S^3)/54 + (-200 + 1076*S^2 + 2014*S^4 + 19967*S^6 + 23572*S^8 + 10283*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((16 + 32*S^2 + 16*S^4 - 21*S^6 + 126*S^8 + 105*S^10)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)^2) + ((26 + 52*S^2 + 26*S^4 + 101*S^6 + 250*S^8 + 137*S^10)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (2*S^3*HPL[{4, 2}, -S^2])/9 + (76*S^3*HPL[{5, 1}, -S^2])/9 + ((-605*Pi^2*S^3)/27 + (324 - 2328*S^2 - 4140*S^4 - 40645*S^6 - 48500*S^8 - 21223*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + ((-472 - 944*S^2 - 472*S^4 - 2699*S^6 - 1582*S^8 + 163*S^10)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (2*(-728 - 1456*S^2 - 728*S^4 - 4105*S^6 - 2414*S^8 + 242*S^10)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (2*S^3*HPL[{3, 1, 2}, -S^2])/9 - (626*S^3*HPL[{3, 2, 1}, -S^2])/9 - (1954*S^3*HPL[{4, 1, 1}, -S^2])/9 - (4*(-258 - 516*S^2 - 258*S^4 - 1366*S^6 - 752*S^8 + 119*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (1384*S^3*HPL[{3, 1, 1, 1}, -S^2])/9 - (2792*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/9 + ((1320 - 1146*S^2 - 13771*S^4)/(1944*S) - (Pi^2*S^3*(1373 + 2878*S^2 + 1472*S^4))/(324*(1 + S^2)^2))*Zeta[3] + (S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((4718 + 9945*S^2 + 118674*S^4 + 732*S^6)/(1944*S^3) + (Pi^2*(312 + 624*S^2 + 312*S^4 + 1432*S^6 + 620*S^8 - 251*S^10))/(108*S^3*(1 + S^2)^2) - (2*S^3*Zeta[3])/9) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(5512 + 14063*S^2 + 135913*S^4))/(5832*S^3) + (Pi^2*(-1046 - 2092*S^2 - 1046*S^4 - 17201*S^6 - 19138*S^8 - 5753*S^10))/(972*S^3*(1 + S^2)^2) - (2*(124 + 248*S^2 + 124*S^4 + 2167*S^6 + 2354*S^8 + 682*S^10)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)^2) - (4*S^3*HPL[{3}, -S^2])/9 + (220*S^3*HPL[{2, 1}, -S^2])/9 + (22*S^3*Zeta[3])/27) + HPL[{3}, -S^2]*((-2752 + 588*S^2 - 11616*S^4 - 13553*S^6)/(3888*S^3) + (Pi^2*(-20 - 40*S^2 - 20*S^4 - 139*S^6 - 26*S^8 + 50*S^10))/(324*S^3*(1 + S^2)^2) - (10*S^3*HPL[{2, 1}, -S^2])/9 + (4*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((-959*Pi^4*S^3)/810 + (-5425 - 6246*S^2 - 41949*S^4 - 218515*S^6)/(5832*S^3) + (Pi^2*(162 - 2424*S^2 - 3960*S^4 - 39869*S^6 - 50671*S^8 - 22274*S^10))/(1944*S^3*(1 + S^2)^2) + ((-8 - 16*S^2 - 8*S^4 + 5*S^6 - 74*S^8 - 58*S^10)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^2) - (2*S^3*HPL[{4}, -S^2])/3 + ((472 + 944*S^2 + 472*S^4 + 2699*S^6 + 1582*S^8 - 163*S^10)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)^2) + (322*S^3*HPL[{3, 1}, -S^2])/9 - (650*S^3*HPL[{2, 1, 1}, -S^2])/9 + ((-24 - 48*S^2 - 24*S^4 + 43*S^6 - 22*S^8 - 38*S^10)*Zeta[3])/(54*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-3997*Pi^4*S^3)/3240 - ((1 + S^2)*(6336 + 18097*S^2 + 295779*S^4))/(7776*S^3) + (Pi^2*(-1940 - 20743*S^2 - 38012*S^4 - 155120*S^6 - 133090*S^8 - 42971*S^10))/(3888*S^3*(1 + S^2)^2) + ((-187*Pi^2*S^3)/36 + (-206 - 1764*S^2 - 3134*S^4 - 12605*S^6 - 10446*S^8 - 3377*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (53*S^3*HPL[{2}, -S^2]^2)/6 + ((-2 - 4*S^2 - 2*S^4 - 29*S^6 - 34*S^8 - 11*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (17*S^3*HPL[{4}, -S^2])/9 + (2*(124 + 248*S^2 + 124*S^4 + 2167*S^6 + 2354*S^8 + 682*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (110*S^3*HPL[{3, 1}, -S^2])/3 - (220*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((-2 - 4*S^2 - 2*S^4 + 55*S^6 + 22*S^8 - 11*S^10)*Zeta[3])/(18*S^3*(1 + S^2)^2)) - (2*S^3*(245 + 538*S^2 + 281*S^4)*Zeta[5])/(27*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(1417 + 3198*S^2 + 48583*S^4))/(3888*S^3) - ((1 + S^2)*(29815 + 33908*S^2 + 998653*S^4))/(23328*S^3) - (7*Pi^4*(1102 + 2204*S^2 + 1102*S^4 + 16339*S^6 + 18974*S^8 + 6061*S^10))/(19440*S^3*(1 + S^2)^2) + ((-26 - 52*S^2 - 26*S^4 - 461*S^6 - 498*S^8 - 143*S^10)*HPL[{2}, -S^2]^2)/(12*S^3*(1 + S^2)^2) + ((-7*Pi^2*S^3)/18 + (116 + 106*S^2 - 208*S^4 - 1369*S^6 - 1541*S^8 - 586*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-2 - 4*S^2 - 2*S^4 - 62*S^6 - 56*S^8 - 11*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (23*S^3*HPL[{5}, -S^2])/9 + ((187*Pi^2*S^3)/18 + (206 + 1764*S^2 + 3134*S^4 + 12605*S^6 + 10446*S^8 + 3377*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((82 + 164*S^2 + 82*S^4 + 1441*S^6 + 1562*S^8 + 451*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (14*S^3*HPL[{3, 2}, -S^2])/9 - (8*S^3*HPL[{4, 1}, -S^2])/9 - (4*(124 + 248*S^2 + 124*S^4 + 2167*S^6 + 2354*S^8 + 682*S^10)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (212*S^3*HPL[{2, 2, 1}, -S^2])/3 - (644*S^3*HPL[{3, 1, 1}, -S^2])/3 + (440*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((11*Pi^2*S^3)/54 + (364 + 647*S^2 + 220*S^4 - 338*S^6 - 1702*S^8 - 635*S^10)/(324*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(542 + 1341*S^2 + 15281*S^4))/(432*S^3) + (Pi^2*(-458 - 916*S^2 - 458*S^4 - 7568*S^6 - 8404*S^8 - 2519*S^10))/(324*S^3*(1 + S^2)^2) + (7*S^3*HPL[{3}, -S^2])/9 + (106*S^3*HPL[{2, 1}, -S^2])/3 + S^3*Zeta[3]) + (16*S^3*Zeta[5])/9)) + HPL[{0}, S^2]^2*((-1076 - 433241*S^2 - 12115980*S^4)/(69984*S) + (Pi^2*(-139206 - 386589*S^2 - 6300179*S^4))/(139968*S) + (Pi^4*(-13550 - 66632*S^2 - 346645*S^4))/(38880*S) - (Pi^6*S^3*(1114703 + 1447746*S^2 + 528458*S^4))/(544320*(1 + S^2)^2) + ((-22 - 44*S^2 - 22*S^4 - 400*S^6 - 428*S^8 - 121*S^10)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)^2) - (62*S^3*HPL[{1}, -S^2]^7)/63 + ((5 + 10*S^2 + 5*S^4 - 837*S^6 - 1098*S^8 - 405*S^10)*HPL[{2}, -S^2]^3)/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-749*Pi^2*S^3)/270 + (-2876 - 16291*S^2 - 25232*S^4 - 97286*S^6 - 75484*S^8 - 23495*S^10)/(1620*S^3*(1 + S^2)^2) - (392*S^3*HPL[{2}, -S^2])/45) + ((-2 + 33*S^6)*HPL[{3}, -S^2]^2)/(18*S^3) + ((115*Pi^2*S^3)/36 + (214 + 191*S^2 - 254*S^4 - 1043*S^6 - 1693*S^8 - 449*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-140 - 280*S^2 - 140*S^4 + 257*S^6 - 26*S^8 - 148*S^10)*HPL[{6}, -S^2])/(36*S^3*(1 + S^2)^2) + 31*S^3*HPL[{7}, -S^2] + ((-8 - 16*S^2 - 8*S^4 + 3612*S^6 + 4644*S^8 + 1677*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-43*Pi^2*S^3)/18 + (-224 - 709*S^2 - 548*S^4 - 400*S^6 + 4924*S^8 + 2237*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-61*Pi^2*S^3)/6 + (-78 - 127*S^2 + 168*S^4 + 584*S^6 + 3258*S^8 + 1283*S^10)/(36*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((-3 - 6*S^2 - 3*S^4 + 44*S^6 + 52*S^8 + 17*S^10)*HPL[{4, 2}, -S^2])/(18*S^3*(1 + S^2)^2) - (10*S^3*HPL[{4, 3}, -S^2])/3 + ((20 + 40*S^2 + 20*S^4 + 123*S^6 + 342*S^8 + 195*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (19*S^3*HPL[{5, 2}, -S^2])/2 - 43*S^3*HPL[{6, 1}, -S^2] + ((-13*Pi^2*S^3)/9 + (-974 - 3956*S^2 - 6026*S^4 - 14073*S^6 - 5494*S^8 + 375*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((35*Pi^2*S^3)/9 + (-8814 - 35961*S^2 - 55146*S^4 - 127987*S^6 - 52646*S^8 + 2486*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + ((-6 - 11*S^6)*HPL[{3, 1, 2}, -S^2])/(18*S^3) + ((74 + 148*S^2 + 74*S^4 - 13403*S^6 - 17590*S^8 - 6491*S^10)*HPL[{3, 2, 1}, -S^2])/(18*S^3*(1 + S^2)^2) + (85*S^3*HPL[{3, 2, 2}, -S^2])/3 + (244*S^3*HPL[{3, 3, 1}, -S^2])/3 - (2*(-57 - 114*S^2 - 57*S^4 + 10121*S^6 + 13378*S^8 + 4973*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (247*S^3*HPL[{4, 1, 2}, -S^2])/3 + (715*S^3*HPL[{4, 2, 1}, -S^2])/3 + (1478*S^3*HPL[{5, 1, 1}, -S^2])/3 + (-14*Pi^2*S^3 - (2*(-1496 - 6148*S^2 - 9515*S^4 - 21719*S^6 - 9451*S^8 + 349*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (104*S^3*HPL[{2, 2, 2, 1}, -S^2])/3 + (4*(-23 - 46*S^2 - 23*S^4 + 3481*S^6 + 4646*S^8 + 1744*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (140*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 + (140*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 + (452*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 + 432*S^3*HPL[{4, 1, 1, 1}, -S^2] - (8*(-20 - 40*S^2 - 20*S^4 + 3557*S^6 + 4762*S^8 + 1793*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (136*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 136*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] + 368*S^3*HPL[{3, 1, 1, 1, 1}, -S^2] - (608*S^3*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + ((-373*Pi^4*S^3)/1080 + (14100 + 6684*S^2 - 14479*S^4)/(3888*S) + (Pi^2*(-84 - 126*S^2 - 5353*S^4 - 12824*S^6 - 6037*S^8))/(648*S*(1 + S^2)^2))*Zeta[3] + (S^3*(-7 + 94*S^2 + 74*S^4)*Zeta[3]^2)/(18*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-3026 + 11955*S^2 + 33186*S^4 + 149200*S^6)/(648*S^3) + (Pi^2*(-46 - 92*S^2 - 46*S^4 + 11725*S^6 + 16010*S^8 + 6145*S^10))/(108*S^3*(1 + S^2)^2) - (74*S^3*Zeta[3])/3) + HPL[{4}, -S^2]*((2650 + 1275*S^2 - 5772*S^4 - 17128*S^6)/(1296*S^3) + (Pi^2*(-39 - 78*S^2 - 39*S^4 - 191*S^6 - 502*S^8 - 281*S^10))/(108*S^3*(1 + S^2)^2) - S^3*HPL[{2, 1}, -S^2] - 4*S^3*Zeta[3]) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(7210 + 9407*S^2 + 75133*S^4))/(1944*S^3) + (Pi^2*(-1166 - 2332*S^2 - 1166*S^4 - 19895*S^6 - 21814*S^8 - 6413*S^10))/(648*S^3*(1 + S^2)^2) + ((-614 - 1228*S^2 - 614*S^4 - 10433*S^6 - 11458*S^8 - 3377*S^10)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)^2) + (22*S^3*HPL[{3}, -S^2])/9 + (392*S^3*HPL[{2, 1}, -S^2])/9 + (41*S^3*Zeta[3])/9) + HPL[{2}, -S^2]^2*((913 - 7218*S^2 - 13311*S^4 - 71238*S^6)/(1296*S^3) - (5*Pi^2*(-4 - 8*S^2 - 4*S^4 + 1178*S^6 + 1552*S^8 + 575*S^10))/(216*S^3*(1 + S^2)^2) + (7*S^3*HPL[{3}, -S^2])/2 - (13*S^3*HPL[{2, 1}, -S^2])/3 + (37*S^3*Zeta[3])/6) + HPL[{2, 1, 1}, -S^2]*((387 - 2163*S^2 - 5544*S^4 - 25088*S^6)/(54*S^3) + (Pi^2*(64 + 128*S^2 + 64*S^4 - 12075*S^6 - 16554*S^8 - 6378*S^10))/(54*S^3*(1 + S^2)^2) + (152*S^3*Zeta[3])/3) + HPL[{3}, -S^2]*((133*Pi^4*S^3)/270 + (14696 + 5979*S^2 - 83472*S^4 - 121957*S^6)/(7776*S^3) + (Pi^2*(240 - 285*S^2 - 1920*S^4 - 4306*S^6 - 6416*S^8 - 1705*S^10))/(1296*S^3*(1 + S^2)^2) + (4*S^3*HPL[{4}, -S^2])/3 + ((-26 - 52*S^2 - 26*S^4 - 463*S^6 - 422*S^8 - 85*S^10)*HPL[{2, 1}, -S^2])/(18*S^3*(1 + S^2)^2) - 12*S^3*HPL[{3, 1}, -S^2] + 28*S^3*HPL[{2, 1, 1}, -S^2] + ((8 + 16*S^2 + 8*S^4 + 7*S^6 + 2*S^8 - 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-134*Pi^4*S^3)/135 + (38995 + 37332*S^2 + 450567*S^4 + 29355*S^6)/(1944*S^3) + (Pi^2*(1508 + 6692*S^2 + 10862*S^4 + 24125*S^6 + 9992*S^8 - 859*S^10))/(216*S^3*(1 + S^2)^2) - (32*S^3*HPL[{3, 1}, -S^2])/3 - (68*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((-14 - 28*S^2 - 14*S^4 - 349*S^6 - 230*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-8449*Pi^4*S^3)/3240 - ((1 + S^2)*(36163 + 40790*S^2 + 482167*S^4))/(5832*S^3) + (Pi^2*(-688 - 4488*S^2 - 7306*S^4 - 28387*S^6 - 23175*S^8 - 7282*S^10))/(324*S^3*(1 + S^2)^2) + ((-211*Pi^2*S^3)/18 + (-399 - 2455*S^2 - 3957*S^4 - 15006*S^6 - 12220*S^8 - 3819*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (215*S^3*HPL[{2}, -S^2]^2)/9 + ((-2 - 4*S^2 - 2*S^4 + 121*S^6 + 66*S^8 - 11*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*S^3*HPL[{4}, -S^2])/9 + ((614 + 1228*S^2 + 614*S^4 + 10433*S^6 + 11458*S^8 + 3377*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (772*S^3*HPL[{3, 1}, -S^2])/9 - (1568*S^3*HPL[{2, 1, 1}, -S^2])/9 + (2*(8 + 16*S^2 + 8*S^4 + 413*S^6 + 334*S^8 + 44*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + ((-13*Pi^2*S^3)/9 + (-28 - 42*S^2 - 513*S^4 - 1327*S^6 - 594*S^8)/(18*S*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((73629 - 165084*S^2 - 583755*S^4 - 3087476*S^6)/(23328*S^3) + (Pi^2*(3105 - 9051*S^2 - 31578*S^4 - 143804*S^6))/(3888*S^3) + (Pi^4*(520 + 1040*S^2 + 520*S^4 - 142507*S^6 - 204242*S^8 - 81928*S^10))/(12960*S^3*(1 + S^2)^2) + ((7*Pi^2*S^3)/6 + (52 + 221*S^2 + 160*S^4 + 50*S^6 - 2672*S^8 - 1219*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((7 + 14*S^2 + 7*S^4 - 88*S^6 - 164*S^8 - 79*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - (7*S^3*HPL[{5}, -S^2])/6 + ((13*Pi^2*S^3)/18 + (974 + 3956*S^2 + 6026*S^4 + 14073*S^6 + 5494*S^8 - 375*S^10)/(36*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-14 - 28*S^2 - 14*S^4 + 7159*S^6 + 9206*S^8 + 3325*S^10)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^2) - (43*S^3*HPL[{3, 2}, -S^2])/3 - 41*S^3*HPL[{4, 1}, -S^2] - (2*(-8 - 16*S^2 - 8*S^4 + 3612*S^6 + 4644*S^8 + 1677*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (52*S^3*HPL[{2, 2, 1}, -S^2])/3 - 24*S^3*HPL[{3, 1, 1}, -S^2] + (68*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((23*Pi^2*S^3)/18 + (156 + 420*S^2 + 318*S^4 + 1565*S^6 + 448*S^8 + 341*S^10)/(108*S^3*(1 + S^2)^2))*Zeta[3] + 3*S^3*Zeta[5]) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(6554 + 9667*S^2 + 95267*S^4))/(2592*S^3) - ((1 + S^2)*(186293 + 179866*S^2 + 3186803*S^4))/(23328*S^3) + (Pi^4*(-7348 - 14696*S^2 - 7348*S^4 - 116455*S^6 - 131522*S^8 - 40414*S^10))/(6480*S^3*(1 + S^2)^2) + ((-298 - 596*S^2 - 298*S^4 - 5509*S^6 - 5858*S^8 - 1639*S^10)*HPL[{2}, -S^2]^2)/(36*S^3*(1 + S^2)^2) + ((25*Pi^2*S^3)/18 + (242 + 331*S^2 - 190*S^4 - 424*S^6 - 2630*S^8 - 901*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-46 - 92*S^2 - 46*S^4 - 109*S^6 - 410*S^8 - 253*S^10)*HPL[{4}, -S^2])/(36*S^3*(1 + S^2)^2) + 4*S^3*HPL[{5}, -S^2] + ((211*Pi^2*S^3)/6 + (399 + 2455*S^2 + 3957*S^4 + 15006*S^6 + 12220*S^8 + 3819*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(152 + 304*S^2 + 152*S^4 + 2573*S^6 + 2830*S^8 + 836*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 14*S^3*HPL[{3, 2}, -S^2] - (134*S^3*HPL[{4, 1}, -S^2])/3 + ((-614 - 1228*S^2 - 614*S^4 - 10433*S^6 - 11458*S^8 - 3377*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (860*S^3*HPL[{2, 2, 1}, -S^2])/3 - (2492*S^3*HPL[{3, 1, 1}, -S^2])/3 + (1568*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((41*Pi^2*S^3)/18 + (97 + 335*S^2 + 421*S^4 + 2014*S^6 + 569*S^8 + 214*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(4358 + 5377*S^2 + 51005*S^4))/(432*S^3) + (Pi^2*(-1070 - 2140*S^2 - 1070*S^4 - 17279*S^6 - 19366*S^8 - 5885*S^10))/(216*S^3*(1 + S^2)^2) + 7*S^3*HPL[{3}, -S^2] + (430*S^3*HPL[{2, 1}, -S^2])/3 + 13*S^3*Zeta[3]) + 13*S^3*Zeta[5]) + HPL[{1}, -S^2]*((-39083*Pi^6*S^3)/54432 - (Pi^2*(1 + S^2)*(37727 + 58681*S^2 + 933434*S^4))/(23328*S^3) - ((1 + S^2)*(363839 + 424150*S^2 + 10992389*S^4))/(69984*S^3) + (Pi^4*(-15110 - 148105*S^2 - 266210*S^4 - 1067579*S^6 - 928153*S^8 - 297953*S^10))/(38880*S^3*(1 + S^2)^2) + ((-335*Pi^2*S^3)/36 + (-456 - 2503*S^2 - 3840*S^4 - 14736*S^6 - 11308*S^8 - 3525*S^10)/(72*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (32*S^3*HPL[{2}, -S^2]^3)/3 + ((5*Pi^2*S^3)/9 + (160 - 421*S^2 - 1424*S^4 - 5042*S^6 - 7108*S^8 - 2333*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (4*(4 + 8*S^2 + 4*S^4 - 5*S^6 + 26*S^8 + 22*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (15*S^3*HPL[{6}, -S^2])/2 + (430*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((310*Pi^2*S^3)/9 + (563 + 3589*S^2 + 5855*S^4 + 22316*S^6 + 18277*S^8 + 5738*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (2*(2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + ((-26 - 52*S^2 - 26*S^4 - 2555*S^6 - 1894*S^8 - 143*S^10)*HPL[{4, 1}, -S^2])/(18*S^3*(1 + S^2)^2) + S^3*HPL[{4, 2}, -S^2] - (16*S^3*HPL[{5, 1}, -S^2])/3 + ((-211*Pi^2*S^3)/3 + (-399 - 2455*S^2 - 3957*S^4 - 15006*S^6 - 12220*S^8 - 3819*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(298 + 596*S^2 + 298*S^4 + 5509*S^6 + 5858*S^8 + 1639*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*(150 + 300*S^2 + 150*S^4 + 2694*S^6 + 2896*S^8 + 825*S^10)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - 256*S^3*HPL[{3, 2, 1}, -S^2] - (2288*S^3*HPL[{4, 1, 1}, -S^2])/3 + (2*(614 + 1228*S^2 + 614*S^4 + 10433*S^6 + 11458*S^8 + 3377*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1544*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 - (3136*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + (((1 + S^2)*(838 + 1913*S^2 + 1297*S^4))/(648*S^3) + (Pi^2*(-14 - 28*S^2 - 14*S^4 + 661*S^6 + 338*S^8 - 77*S^10))/(108*S^3*(1 + S^2)^2))*Zeta[3] - 3*S^3*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(4358 + 5377*S^2 + 51005*S^4))/(216*S^3) + (Pi^2*(1070 + 2140*S^2 + 1070*S^4 + 17279*S^6 + 19366*S^8 + 5885*S^10))/(108*S^3*(1 + S^2)^2) - 26*S^3*Zeta[3]) + HPL[{3}, -S^2]*(-((1 + S^2)*(-314 - 589*S^2 + 5005*S^4))/(324*S^3) - (5*Pi^2*(2 + 4*S^2 + 2*S^4 - 19*S^6 + 2*S^8 + 11*S^10))/(36*S^3*(1 + S^2)^2) - 14*S^3*HPL[{2, 1}, -S^2] + (2*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((-6731*Pi^4*S^3)/2160 - ((1 + S^2)*(33190 + 35993*S^2 + 506203*S^4))/(3888*S^3) + (Pi^2*(-1723 - 12143*S^2 - 20461*S^4 - 78106*S^6 - 66116*S^8 - 20839*S^10))/(648*S^3*(1 + S^2)^2) + ((2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) - (S^3*HPL[{4}, -S^2])/3 + ((298 + 596*S^2 + 298*S^4 + 5509*S^6 + 5858*S^8 + 1639*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 142*S^3*HPL[{3, 1}, -S^2] - (860*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((2 + 4*S^2 + 2*S^4 + 89*S^6 + 74*S^8 + 11*S^10)*Zeta[3])/(2*S^3*(1 + S^2)^2)) + ((-14 - 28*S^2 - 14*S^4 + 274*S^6 + 80*S^8 - 77*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2))) + (62*Pi^2*S^3 + (-120 - 180*S^2 + 4603*S^4 + 482*S^6 + 1615*S^8)/(18*S*(1 + S^2)^2))*Zeta[7] + HPL[{2}, -S^2]*((121014 + 118175*S^2 - 357177*S^4 - 4038660*S^6)/(11664*S^3) + (Pi^2*(66748 - 97785*S^2 - 313515*S^4 - 3087476*S^6))/(34992*S^3) + (Pi^4*(11533 - 27438*S^2 - 75282*S^4 - 464736*S^6))/(29160*S^3) + (Pi^6*(3832 + 7664*S^2 + 3832*S^4 - 536004*S^6 - 807660*S^8 - 337743*S^10))/(136080*S^3*(1 + S^2)^2) - (S^3*(198 + 224*S^2 + 69*S^4)*HPL[{3}, -S^2]^2)/(3*(1 + S^2)^2) + ((85*Pi^2*S^3)/9 + (-130 - 80*S^2 + 185*S^4 + 220*S^6 - 2593*S^8 - 1202*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-20 - 40*S^2 - 20*S^4 - 365*S^6 - 1234*S^8 - 743*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) - (220*S^3*HPL[{7}, -S^2])/3 + (4*(-66 + 773*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-860*Pi^2*S^3)/9 + (8 - 1523*S^2 - 2233*S^4 - 22035*S^6 - 12957*S^8 - 6996*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-913*Pi^2*S^3)/3 + (595 - 3163*S^2 - 5012*S^4 - 63854*S^6 - 37849*S^8 - 21509*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (2*(1 + 2*S^2 + S^4 + 354*S^6 + 396*S^8 + 120*S^10)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + 44*S^3*HPL[{4, 3}, -S^2] + ((18 + 36*S^2 + 18*S^4 - 8389*S^6 - 9194*S^8 - 2701*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 104*S^3*HPL[{5, 2}, -S^2] + (322*S^3*HPL[{6, 1}, -S^2])/3 + ((836*Pi^2*S^3)/9 + (2*(-1355 - 3575*S^2 - 4170*S^4 - 6519*S^6 + 3315*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((-232*Pi^2*S^3)/3 + (7342 + 30221*S^2 + 47770*S^4 + 99970*S^6 + 40256*S^8 - 6599*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (13*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + ((-370 - 740*S^2 - 370*S^4 - 18191*S^6 - 19822*S^8 - 5771*S^10)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3142*S^3*HPL[{3, 2, 2}, -S^2])/3 + (9896*S^3*HPL[{3, 3, 1}, -S^2])/3 - (4*(343 + 686*S^2 + 343*S^4 + 13384*S^6 + 14300*S^8 + 4033*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (9818*S^3*HPL[{4, 1, 2}, -S^2])/3 + (30314*S^3*HPL[{4, 2, 1}, -S^2])/3 + 20732*S^3*HPL[{5, 1, 1}, -S^2] + ((1624*Pi^2*S^3)/9 + (4*(462 + 2098*S^2 + 3198*S^4 + 9795*S^6 + 4318*S^8 + 789*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 1008*S^3*HPL[{2, 2, 2, 1}, -S^2] + (16*(-720 - 1440*S^2 - 720*S^4 + 11735*S^6 + 21118*S^8 + 9971*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2536*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 + (2536*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 + (11608*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 + 11168*S^3*HPL[{4, 1, 1, 1}, -S^2] - (16*(100 + 200*S^2 + 100*S^4 + 5161*S^6 + 5618*S^8 + 1633*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 6272*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] + (45184*S^3*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + (12448*S^3*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + ((2897*Pi^4*S^3)/540 + (12593 + 21240*S^2 + 21645*S^4 + 90355*S^6)/(972*S^3) + (Pi^2*(91 + 424*S^2 + 454*S^4 + 3509*S^6 + 1863*S^8 + 1061*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] - (S^3*(149 + 334*S^2 + 176*S^4)*Zeta[3]^2)/(9*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((5325 + 11379*S^2 + 36975*S^4 + 66931*S^6)/(162*S^3) + (Pi^2*(274 + 548*S^2 + 274*S^4 + 16995*S^6 + 19470*S^8 + 6105*S^10))/(54*S^3*(1 + S^2)^2) - (1528*S^3*Zeta[3])/3) + HPL[{4}, -S^2]*((Pi^2*S^3*(773 + 874*S^2 + 269*S^4))/(27*(1 + S^2)^2) + (45 + 324*S^2 + 219*S^4 + 293*S^6)/(18*S^3) - (118*S^3*HPL[{2, 1}, -S^2])/3 + (82*S^3*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*((-2281 - 11115*S^2 - 31977*S^4 - 71658*S^6)/(81*S^3) - (2*Pi^2*(92 + 184*S^2 + 92*S^4 + 8773*S^6 + 10262*S^8 + 3310*S^10))/(27*S^3*(1 + S^2)^2) + 992*S^3*Zeta[3]) + HPL[{2, 1}, -S^2]*((971*Pi^4*S^3)/180 + (38559 + 55794*S^2 + 420771*S^4 + 61634*S^6)/(972*S^3) + (Pi^2*(1898 + 8152*S^2 + 12422*S^4 + 33663*S^6 + 14130*S^8 + 1203*S^10))/(108*S^3*(1 + S^2)^2) + (1912*S^3*HPL[{3, 1}, -S^2])/3 + (3136*S^3*HPL[{2, 1, 1}, -S^2])/3 + (4*(-108 - 216*S^2 - 108*S^4 - 1549*S^6 - 974*S^8 + 44*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((1639*Pi^4*S^3)/270 + (-3809 + 10173*S^2 + 3324*S^4 + 37484*S^6)/(486*S^3) + (Pi^2*(-368 + 431*S^2 + 730*S^4 + 17943*S^6 + 9180*S^8 + 6036*S^10))/(324*S^3*(1 + S^2)^2) - (106*S^3*HPL[{4}, -S^2])/3 + ((-566 - 1132*S^2 - 566*S^4 - 8797*S^6 - 6410*S^8 - 409*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 576*S^3*HPL[{3, 1}, -S^2] + (3424*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((-2 - 4*S^2 - 2*S^4 + 499*S^6 + 686*S^8 + 265*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + ((125*Pi^2*S^3)/3 + (559 + 1508*S^2 + 1144*S^4 + 6654*S^6 + 1431*S^8 + 1470*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[5] + 252*S^3*Zeta[7]) + HPL[{1}, -S^2]^2*(-(Pi^4*(1 + S^2)*(175529 + 240880*S^2 + 1965665*S^4))/(116640*S^3) - (Pi^2*(1 + S^2)*(146315 + 163824*S^2 + 2305919*S^4))/(23328*S^3) - ((1 + S^2)*(11329918 + 8757449*S^2 + 179723545*S^4))/(419904*S^3) + (Pi^6*(-75346 - 150692*S^2 - 75346*S^4 - 1355533*S^6 - 1456226*S^8 - 414403*S^10))/(163296*S^3*(1 + S^2)^2) - (83*(2 + 11*S^6)*HPL[{2}, -S^2]^3)/(54*S^3) - (37*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((40*Pi^2*S^3)/3 + (1154 + 2383*S^2 + 1334*S^4 + 4448*S^6 - 5402*S^8 - 1969*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-238 - 476*S^2 - 238*S^4 + 293*S^6 - 1550*S^8 - 1309*S^10)*HPL[{6}, -S^2])/(18*S^3*(1 + S^2)^2) + 10*S^3*HPL[{7}, -S^2] + (392*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-826*Pi^2*S^3)/9 + (-552 - 2293*S^2 - 3048*S^4 - 14760*S^6 - 6244*S^8 - 2199*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-2818*Pi^2*S^3)/9 + (-12764 - 50545*S^2 - 65432*S^4 - 305030*S^6 - 128224*S^8 - 44093*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (13*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{4, 2}, -S^2])/(2*S^3*(1 + S^2)^2) + (94*S^3*HPL[{4, 3}, -S^2])/3 - (26*(6 + 12*S^2 + 6*S^4 + 189*S^6 + 170*S^8 + 33*S^10)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + 68*S^3*HPL[{5, 2}, -S^2] - (98*S^3*HPL[{6, 1}, -S^2])/3 + ((-2428*Pi^2*S^3)/9 - (2*(664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-5296*Pi^2*S^3)/9 - (4*(1807 + 10844*S^2 + 17287*S^4 + 68974*S^6 + 52100*S^8 + 16612*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (332*(2 + 11*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (3260*S^3*HPL[{3, 2, 2}, -S^2])/3 + (9968*S^3*HPL[{3, 3, 1}, -S^2])/3 - (4*(386 + 772*S^2 + 386*S^4 - 865*S^6 + 2254*S^8 + 2123*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (9812*S^3*HPL[{4, 1, 2}, -S^2])/3 + (30404*S^3*HPL[{4, 2, 1}, -S^2])/3 + 20880*S^3*HPL[{5, 1, 1}, -S^2] + ((1568*Pi^2*S^3)/9 + (8*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (16*(56 + 112*S^2 + 56*S^4 - 439*S^6 + 118*S^8 + 308*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 - (6272*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 - (6272*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 - (21472*S^3*HPL[{4, 1, 1, 1}, -S^2])/3 - (520*(2 + 11*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (12544*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 12544*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] + (77920*S^3*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + ((1013*Pi^4*S^3)/180 + ((1 + S^2)*(3467 + 7973*S^2 + 30698*S^4))/(324*S^3) + (Pi^2*(213 + 959*S^2 + 1365*S^4 + 7302*S^6 + 2759*S^8 + 1068*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] + ((-6 - 12*S^2 - 6*S^4 - 153*S^6 - 146*S^8 - 33*S^10)*Zeta[3]^2)/(3*S^3*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(-2420 - 1201*S^2 + 47521*S^4))/(162*S^3) + (4*Pi^2*(104 + 208*S^2 + 104*S^4 + 1067*S^6 + 1474*S^8 + 572*S^10))/(27*S^3*(1 + S^2)^2) - (1616*S^3*Zeta[3])/3) + HPL[{4}, -S^2]*(((1 + S^2)*(8089 + 8492*S^2 + 7027*S^4))/(324*S^3) + (Pi^2*(178 + 356*S^2 + 178*S^4 + 7099*S^6 + 6038*S^8 + 979*S^10))/(108*S^3*(1 + S^2)^2) - (452*S^3*HPL[{2, 1}, -S^2])/3 + (56*S^3*Zeta[3])/3) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(4849 + 6653*S^2 + 41650*S^4))/(324*S^3) + (Pi^2*(-230 - 460*S^2 - 230*S^4 - 4907*S^6 - 4958*S^8 - 1265*S^10))/(36*S^3*(1 + S^2)^2) + (466*S^3*HPL[{3}, -S^2])/3 + 118*S^3*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-2*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(9*S^3) - (2*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(27*S^3*(1 + S^2)^2) + (3136*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((2021*Pi^4*S^3)/180 + ((1 + S^2)*(13400 + 9469*S^2 + 411947*S^4))/(972*S^3) + (Pi^2*(531 + 3787*S^2 + 6411*S^4 + 22680*S^6 + 21382*S^8 + 6561*S^10))/(54*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{3, 1}, -S^2])/3 - (6272*S^3*HPL[{2, 1, 1}, -S^2])/3 - (224*(2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((601*Pi^4*S^3)/90 + ((1 + S^2)*(31418 + 38689*S^2 + 84815*S^4))/(972*S^3) + (Pi^2*(434 + 1581*S^2 + 1916*S^4 + 8894*S^6 + 3279*S^8 + 1118*S^10))/(54*S^3*(1 + S^2)^2) - (86*S^3*HPL[{4}, -S^2])/3 - (2*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1568*S^3*HPL[{3, 1}, -S^2])/3 + (3136*S^3*HPL[{2, 1, 1}, -S^2])/3 + (4*(4 + 8*S^2 + 4*S^4 + 97*S^6 + 94*S^8 + 22*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + ((419*Pi^2*S^3)/9 + (20 + 134*S^2 + 226*S^4 + 1805*S^6 + 393*S^8 + 220*S^10)/(3*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(6026 + 7345*S^2 + 90581*S^4))/(1296*S^3) - ((1 + S^2)*(10001 + 3776*S^2 + 483629*S^4))/(1944*S^3) + (Pi^4*(-13150 - 26300*S^2 - 13150*S^4 - 181459*S^6 - 217406*S^8 - 72325*S^10))/(6480*S^3*(1 + S^2)^2) + ((413*Pi^2*S^3)/9 + (552 + 2293*S^2 + 3048*S^4 + 14760*S^6 + 6244*S^8 + 2199*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (113*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) + (164*S^3*HPL[{5}, -S^2])/3 + ((1214*Pi^2*S^3)/9 + (664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (392*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1708*S^3*HPL[{3, 2}, -S^2])/3 - (5140*S^3*HPL[{4, 1}, -S^2])/3 - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*S^3*HPL[{3, 1, 1}, -S^2])/3 + (6272*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((431*Pi^2*S^3)/9 + (267 + 1123*S^2 + 1503*S^4 + 7332*S^6 + 3058*S^8 + 1077*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] + (722*S^3*Zeta[5])/3) + 322*S^3*Zeta[7]) + Log[T]^2*((-26669 - 111305*S^2)/(8748*S) + (Pi^2*(-246846 - 479829*S^2 - 3087476*S^4))/(34992*S) + (Pi^4*(-29066 - 69080*S^2 - 221109*S^4))/(9720*S) - (Pi^6*S^3*(1312733 + 1579766*S^2 + 528458*S^4))/(136080*(1 + S^2)^2) - (S^3*HPL[{0}, S^2]^7)/24 + ((-58*Pi^2*S^3)/3 + (-88 - 475*S^2 - 724*S^4 - 3046*S^6 - 2020*S^8 - 655*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^5 - (56*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)^2) - (64*S^3*HPL[{1}, -S^2]^7)/9 + HPL[{0}, S^2]^6*(-(S^3*(22 + 32*S^2 + 13*S^4))/(24*(1 + S^2)^2) - (S^3*HPL[{1}, -S^2])/4) - (2*(-66 + 773*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^5*((-149*Pi^2*S^3)/270 + (-340 - 510*S^2 - 4897*S^4 - 6438*S^6 - 2795*S^8)/(720*S*(1 + S^2)^2) + ((-170 - 340*S^2 - 170*S^4 - 2561*S^6 - 2954*S^8 - 935*S^10)*HPL[{1}, -S^2])/(360*S^3*(1 + S^2)^2) - (271*S^3*HPL[{1}, -S^2]^2)/180 - (64*S^3*HPL[{2}, -S^2])/45) + ((4 + 8*S^2 + 4*S^4 - 1009*S^6 - 1130*S^8 - 343*S^10)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((259*Pi^2*S^3)/9 + (550 + 1115*S^2 + 550*S^4 + 1118*S^6 - 3995*S^8 - 1240*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-100 - 200*S^2 - 100*S^4 + 31*S^6 - 1006*S^8 - 770*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) + (152*S^3*HPL[{7}, -S^2])/3 + (4*(100 + 200*S^2 + 100*S^4 + 5161*S^6 + 5618*S^8 + 1633*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-578*Pi^2*S^3)/3 + (656 - 3473*S^2 - 4924*S^4 - 73116*S^6 - 40740*S^8 - 24867*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-5596*Pi^2*S^3)/9 + (-440 - 9775*S^2 - 12320*S^4 - 129343*S^6 - 69806*S^8 - 40072*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (2*(-7 - 14*S^2 - 7*S^4 + 1770*S^6 + 2136*S^8 + 717*S^10)*HPL[{4, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (172*S^3*HPL[{4, 3}, -S^2])/3 - (2*(-10 - 20*S^2 - 10*S^4 + 2969*S^6 + 3234*S^8 + 941*S^10)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (346*S^3*HPL[{5, 2}, -S^2])/3 - 128*S^3*HPL[{6, 1}, -S^2] + ((-1624*Pi^2*S^3)/9 - (4*(462 + 2098*S^2 + 3198*S^4 + 9795*S^6 + 4318*S^8 + 789*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-1120*Pi^2*S^3)/9 - (4*(3728 + 16333*S^2 + 25796*S^4 + 64603*S^6 + 26654*S^8 + 478*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (4*(-44 + 213*S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (4*(-220 + 2879*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (6368*S^3*HPL[{3, 2, 2}, -S^2])/3 + 6640*S^3*HPL[{3, 3, 1}, -S^2] - (16*(-198 - 396*S^2 - 198*S^4 + 1267*S^6 + 3530*S^8 + 2014*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (19784*S^3*HPL[{4, 1, 2}, -S^2])/3 + (60872*S^3*HPL[{4, 2, 1}, -S^2])/3 + 41680*S^3*HPL[{5, 1, 1}, -S^2] + ((-3664*Pi^2*S^3)/9 - (4*(-2602 - 7570*S^2 - 9054*S^4 - 14895*S^6 + 6723*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - (6272*S^3*HPL[{2, 2, 2, 1}, -S^2])/3 + (16*(-165 - 330*S^2 - 165*S^4 + 731*S^6 + 2458*S^8 + 1478*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (5632*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 + (5632*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 + (24448*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 + (70432*S^3*HPL[{4, 1, 1, 1}, -S^2])/3 - (160*(-8 + 117*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (12448*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 12448*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] + (90560*S^3*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - 8960*S^3*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((3353*Pi^4*S^3)/270 + (20292 + 23487*S^2 + 61000*S^4)/(486*S) + (Pi^2*(1176 + 1764*S^2 + 19601*S^4 + 10930*S^6 + 6893*S^8))/(162*S*(1 + S^2)^2))*Zeta[3] + (4*S^3*(-53 + 14*S^2 + 37*S^4)*Zeta[3]^2)/(9*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-12124 - 6141*S^2 - 19956*S^4 + 134899*S^6)/(162*S^3) + (4*Pi^2*(-94 - 188*S^2 - 94*S^4 + 2106*S^6 + 3552*S^8 + 1611*S^10))/(27*S^3*(1 + S^2)^2) - (3088*S^3*Zeta[3])/3) + HPL[{0}, S^2]^4*((-3324 - 13521*S^2 - 75506*S^4)/(3888*S) - (Pi^2*S^3*(5749 + 8174*S^2 + 3256*S^4))/(648*(1 + S^2)^2) + ((-506 - 1012*S^2 - 506*S^4 - 7895*S^6 - 8974*S^8 - 2783*S^10)*HPL[{1}, -S^2]^2)/(216*S^3*(1 + S^2)^2) - (142*S^3*HPL[{1}, -S^2]^3)/27 + ((24 + 48*S^2 + 24*S^4 - 4961*S^6 - 7030*S^8 - 2792*S^10)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-277*Pi^2*S^3)/108 + (-1252 - 10637*S^2 - 18604*S^4 - 73036*S^6 - 63566*S^8 - 20197*S^10)/(1296*S^3*(1 + S^2)^2) - (241*S^3*HPL[{2}, -S^2])/36) + (7*S^3*HPL[{3}, -S^2])/12 - (25*S^3*HPL[{2, 1}, -S^2])/18 - (7*S^3*Zeta[3])/18) + HPL[{4}, -S^2]*((-2074 + 16599*S^2 + 4836*S^4 + 14762*S^6)/(324*S^3) + (Pi^2*(-3 - 6*S^2 - 3*S^4 + 2027*S^6 + 2014*S^8 + 497*S^10))/(27*S^3*(1 + S^2)^2) + 64*S^3*HPL[{2, 1}, -S^2] + (124*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(972*S^3) - (5*Pi^2*(50 + 100*S^2 + 50*S^4 + 1058*S^6 + 1072*S^8 + 275*S^10))/(27*S^3*(1 + S^2)^2) - (65*(2 + 11*S^6)*HPL[{2}, -S^2])/(9*S^3) + (1900*S^3*HPL[{3}, -S^2])/9 + (500*S^3*Zeta[3])/3) + HPL[{2}, -S^2]^2*((-2281 - 11115*S^2 - 31977*S^4 - 71658*S^6)/(324*S^3) + (Pi^2*(-92 - 184*S^2 - 92*S^4 - 8773*S^6 - 10262*S^8 - 3310*S^10))/(54*S^3*(1 + S^2)^2) + (856*S^3*HPL[{3}, -S^2])/3 - (784*S^3*HPL[{2, 1}, -S^2])/3 + 248*S^3*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-4*(-1721 + 828*S^2 - 801*S^4 + 37082*S^6))/(81*S^3) - (16*Pi^2*(-35 - 70*S^2 - 35*S^4 + 1328*S^6 + 2068*S^8 + 887*S^10))/(27*S^3*(1 + S^2)^2) + (6112*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^3*((-6673*Pi^4*S^3)/405 - ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(1458*S^3) + (Pi^2*(-3418 - 18833*S^2 - 28906*S^4 - 117178*S^6 - 83192*S^8 - 26485*S^10))/(243*S^3*(1 + S^2)^2) + ((-784*Pi^2*S^3)/27 - (4*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (1568*S^3*HPL[{2}, -S^2]^2)/9 + (40*(28 + 56*S^2 + 28*S^4 + 1009*S^6 + 878*S^8 + 154*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (1328*S^3*HPL[{4}, -S^2])/9 + (260*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (1328*S^3*HPL[{3, 1}, -S^2])/9 + (40*(2 + 4*S^2 + 2*S^4 + 86*S^6 + 72*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((-1229*Pi^4*S^3)/90 + (13201 + 8046*S^2 + 214461*S^4 - 30500*S^6)/(243*S^3) + (Pi^2*(5594 + 22468*S^2 + 35654*S^4 + 67387*S^6 + 27074*S^8 - 7421*S^10))/(162*S^3*(1 + S^2)^2) - (3776*S^3*HPL[{3, 1}, -S^2])/3 - (6224*S^3*HPL[{2, 1, 1}, -S^2])/3 - (16*(50 + 100*S^2 + 50*S^4 + 901*S^6 + 626*S^8 + 19*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((118*Pi^4*S^3)/9 + (54424 + 131331*S^2 + 76800*S^4 + 314775*S^6)/(1944*S^3) + (Pi^2*(812 + 4741*S^2 + 5060*S^4 + 45774*S^6 + 21216*S^8 + 12357*S^10))/(324*S^3*(1 + S^2)^2) - (172*S^3*HPL[{4}, -S^2])/3 + (16*(-23 - 46*S^2 - 23*S^4 - 281*S^6 - 170*S^8 + 13*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (3424*S^3*HPL[{3, 1}, -S^2])/3 + 2304*S^3*HPL[{2, 1, 1}, -S^2] + (2*(-2 - 4*S^2 - 2*S^4 + 221*S^6 + 242*S^8 + 71*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((-1022*Pi^4*S^3)/405 + (-30048 - 101238*S^2 - 955747*S^4)/(11664*S) + (Pi^2*(-6276 - 9414*S^2 - 88355*S^4 - 110428*S^6 - 48107*S^8))/(1944*S*(1 + S^2)^2) - (2*(268 + 536*S^2 + 268*S^4 + 4759*S^6 + 5138*S^8 + 1474*S^10)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)^2) - (365*S^3*HPL[{1}, -S^2]^4)/27 + ((-605*Pi^2*S^3)/54 + (324 - 2328*S^2 - 4140*S^4 - 40645*S^6 - 48500*S^8 - 21223*S^10)/(324*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (325*S^3*HPL[{2}, -S^2]^2)/18 + HPL[{1}, -S^2]^2*((-106*Pi^2*S^3)/9 + (-265 - 1968*S^2 - 3337*S^4 - 13411*S^6 - 10878*S^8 - 3481*S^10)/(54*S^3*(1 + S^2)^2) - (110*S^3*HPL[{2}, -S^2])/3) + ((-40 - 80*S^2 - 40*S^4 - 113*S^6 - 82*S^8 - 5*S^10)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^2) - (41*S^3*HPL[{4}, -S^2])/9 - (2*(-258 - 516*S^2 - 258*S^4 - 1366*S^6 - 752*S^8 + 119*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (692*S^3*HPL[{3, 1}, -S^2])/9 - (1396*S^3*HPL[{2, 1, 1}, -S^2])/9 - (S^3*(8 + 148*S^2 + 107*S^4)*Zeta[3])/(27*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(5512 + 14063*S^2 + 135913*S^4))/(1944*S^3) + (Pi^2*(-1046 - 2092*S^2 - 1046*S^4 - 17201*S^6 - 19138*S^8 - 5753*S^10))/(324*S^3*(1 + S^2)^2) - (2*(124 + 248*S^2 + 124*S^4 + 2167*S^6 + 2354*S^8 + 682*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) - (4*S^3*HPL[{3}, -S^2])/3 + (220*S^3*HPL[{2, 1}, -S^2])/3 + (22*S^3*Zeta[3])/9)) + ((316*Pi^2*S^3)/3 + (2*(306 + 459*S^2 + 7393*S^4 + 2870*S^6 + 2470*S^8))/(27*S*(1 + S^2)^2))*Zeta[5] + HPL[{0}, S^2]^2*((-184254 - 257991*S^2 - 3087476*S^4)/(11664*S) + (Pi^2*(-624 - 1618*S^2 - 8315*S^4))/(108*S) - (Pi^4*S^3*(53323 + 72850*S^2 + 27976*S^4))/(2160*(1 + S^2)^2) - (5*(22 + 44*S^2 + 22*S^4 + 400*S^6 + 428*S^8 + 121*S^10)*HPL[{1}, -S^2]^4)/(9*S^3*(1 + S^2)^2) - (62*S^3*HPL[{1}, -S^2]^5)/3 + ((8 + 16*S^2 + 8*S^4 - 3612*S^6 - 4644*S^8 - 1677*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-749*Pi^2*S^3)/27 + (-2876 - 16291*S^2 - 25232*S^4 - 97286*S^6 - 75484*S^8 - 23495*S^10)/(162*S^3*(1 + S^2)^2) - (784*S^3*HPL[{2}, -S^2])/9) + ((37*Pi^2*S^3)/9 + (-48 - 357*S^2 - 912*S^4 - 1330*S^6 - 3200*S^8 - 889*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-3 - 6*S^2 - 3*S^4 - 77*S^6 - 202*S^8 - 113*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (37*S^3*HPL[{5}, -S^2])/3 + (-7*Pi^2*S^3 + (1496 + 6148*S^2 + 9515*S^4 + 21719*S^6 + 9451*S^8 - 349*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(-23 - 46*S^2 - 23*S^4 + 3481*S^6 + 4646*S^8 + 1744*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (86*S^3*HPL[{3, 2}, -S^2])/3 - 96*S^3*HPL[{4, 1}, -S^2] - (4*(-20 - 40*S^2 - 20*S^4 + 3557*S^6 + 4762*S^8 + 1793*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (68*S^3*HPL[{2, 2, 1}, -S^2])/3 + (8*S^3*HPL[{3, 1, 1}, -S^2])/3 - (304*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((38*Pi^2*S^3)/9 + (48 + 72*S^2 + 697*S^4 + 20*S^6 + 85*S^8)/(27*S*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((387 - 2163*S^2 - 5544*S^4 - 25088*S^6)/(108*S^3) + (Pi^2*(64 + 128*S^2 + 64*S^4 - 12075*S^6 - 16554*S^8 - 6378*S^10))/(108*S^3*(1 + S^2)^2) + 14*S^3*HPL[{3}, -S^2] + (34*S^3*HPL[{2, 1}, -S^2])/3 + (76*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(7210 + 9407*S^2 + 75133*S^4))/(324*S^3) + (Pi^2*(-1166 - 2332*S^2 - 1166*S^4 - 19895*S^6 - 21814*S^8 - 6413*S^10))/(108*S^3*(1 + S^2)^2) + ((-614 - 1228*S^2 - 614*S^4 - 10433*S^6 - 11458*S^8 - 3377*S^10)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^2) + (44*S^3*HPL[{3}, -S^2])/3 + (784*S^3*HPL[{2, 1}, -S^2])/3 + (82*S^3*Zeta[3])/3) + HPL[{1}, -S^2]*((-8449*Pi^4*S^3)/1080 - ((1 + S^2)*(36163 + 40790*S^2 + 482167*S^4))/(1944*S^3) + (Pi^2*(-688 - 4488*S^2 - 7306*S^4 - 28387*S^6 - 23175*S^8 - 7282*S^10))/(108*S^3*(1 + S^2)^2) + ((-211*Pi^2*S^3)/6 + (-399 - 2455*S^2 - 3957*S^4 - 15006*S^6 - 12220*S^8 - 3819*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (215*S^3*HPL[{2}, -S^2]^2)/3 + ((-2 - 4*S^2 - 2*S^4 + 121*S^6 + 66*S^8 - 11*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) + (8*S^3*HPL[{4}, -S^2])/3 + ((614 + 1228*S^2 + 614*S^4 + 10433*S^6 + 11458*S^8 + 3377*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (772*S^3*HPL[{3, 1}, -S^2])/3 - (1568*S^3*HPL[{2, 1, 1}, -S^2])/3 + (2*(8 + 16*S^2 + 8*S^4 + 413*S^6 + 334*S^8 + 44*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + 26*S^3*Zeta[5]) + HPL[{2}, -S^2]*((59867 - 30486*S^2 - 43275*S^4 - 3087476*S^6)/(5832*S^3) + (Pi^2*(4603 - 8145*S^2 - 15030*S^4 - 149428*S^6))/(972*S^3) + (Pi^4*(2152 + 4304*S^2 + 2152*S^4 - 141277*S^6 - 209798*S^8 - 86710*S^10))/(3240*S^3*(1 + S^2)^2) + ((302*Pi^2*S^3)/3 + (-788 + 641*S^2 + 1300*S^4 + 35836*S^6 + 21032*S^8 + 13291*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(-7 - 14*S^2 - 7*S^4 + 1634*S^6 + 1912*S^8 + 617*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + 118*S^3*HPL[{5}, -S^2] + ((812*Pi^2*S^3)/9 + (2*(462 + 2098*S^2 + 3198*S^4 + 9795*S^6 + 4318*S^8 + 789*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(72 + 144*S^2 + 72*S^4 + 2459*S^6 + 2566*S^8 + 695*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3268*S^3*HPL[{3, 2}, -S^2])/3 - 3488*S^3*HPL[{4, 1}, -S^2] - (8*(100 + 200*S^2 + 100*S^4 + 5161*S^6 + 5618*S^8 + 1633*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*S^3*HPL[{2, 2, 1}, -S^2])/3 - 832*S^3*HPL[{3, 1, 1}, -S^2] + (6224*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((280*Pi^2*S^3)/3 + (390 + 2124*S^2 + 2406*S^4 + 19489*S^6 + 10730*S^8 + 6025*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + 488*S^3*Zeta[5]) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(11160 + 15533*S^2 + 110847*S^4))/(648*S^3) - ((1 + S^2)*(126326 + 155803*S^2 + 1865477*S^4))/(2916*S^3) + (Pi^4*(-17174 - 34348*S^2 - 17174*S^4 - 334685*S^6 - 349066*S^8 - 94457*S^10))/(3240*S^3*(1 + S^2)^2) - (196*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((994*Pi^2*S^3)/9 + (2362 + 9155*S^2 + 11686*S^4 + 53788*S^6 + 22304*S^8 + 7609*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (8*(28 + 56*S^2 + 28*S^4 + 901*S^6 + 806*S^8 + 154*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + 144*S^3*HPL[{5}, -S^2] + ((784*Pi^2*S^3)/9 + (4*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(56 + 112*S^2 + 56*S^4 - 439*S^6 + 118*S^8 + 308*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{3, 2}, -S^2])/3 - (10736*S^3*HPL[{4, 1}, -S^2])/3 - (260*(2 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (6272*S^3*HPL[{2, 2, 1}, -S^2])/3 - (11216*S^3*HPL[{3, 1, 1}, -S^2])/3 + ((832*Pi^2*S^3)/9 + (4*(271 + 1271*S^2 + 1837*S^4 + 9946*S^6 + 3854*S^8 + 1495*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(9*S^3) + (Pi^2*(-502 - 1004*S^2 - 502*S^4 - 6289*S^6 - 7874*S^8 - 2761*S^10))/(27*S^3*(1 + S^2)^2) + (1568*S^3*HPL[{3}, -S^2])/3 + (3136*S^3*HPL[{2, 1}, -S^2])/3 + (1568*S^3*Zeta[3])/3) + (1520*S^3*Zeta[5])/3) + HPL[{1}, -S^2]*((-52285*Pi^6*S^3)/13608 - (Pi^2*(1 + S^2)*(82727 + 105499*S^2 + 1056428*S^4))/(5832*S^3) - ((1 + S^2)*(772759 + 794066*S^2 + 12649645*S^4))/(17496*S^3) + (Pi^4*(-35522 - 207793*S^2 - 324908*S^4 - 1298609*S^6 - 972379*S^8 - 306863*S^10))/(9720*S^3*(1 + S^2)^2) + ((-607*Pi^2*S^3)/9 + (-664 - 3427*S^2 - 5140*S^4 - 21304*S^6 - 14056*S^8 - 4537*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (148*S^3*HPL[{3}, -S^2]^2)/3 + ((340*Pi^2*S^3)/9 + (2828 + 9271*S^2 + 10568*S^4 + 39350*S^6 + 15832*S^8 + 4511*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(2 + 4*S^2 + 2*S^4 + 983*S^6 + 670*S^8 + 11*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (178*S^3*HPL[{6}, -S^2])/3 + (3136*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((440*Pi^2*S^3)/9 + (4*(-185 + 563*S^2 + 1867*S^4 + 5062*S^6 + 9932*S^8 + 3001*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*(790 + 1580*S^2 + 790*S^4 + 28501*S^6 + 24794*S^8 + 4345*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 156*S^3*HPL[{4, 2}, -S^2] - (2704*S^3*HPL[{5, 1}, -S^2])/3 + ((-1568*Pi^2*S^3)/9 - (8*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (1568*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*(448 + 896*S^2 + 448*S^4 + 8773*S^6 + 9134*S^8 + 2464*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2656*S^3*HPL[{4, 1, 1}, -S^2])/3 + (520*(2 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) - (2656*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 + (((1 + S^2)*(4640 + 8971*S^2 + 32009*S^4))/(162*S^3) + (2*Pi^2*(98 + 196*S^2 + 98*S^4 + 4283*S^6 + 3574*S^8 + 539*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] - (80*S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((2*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(9*S^3) + (2*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(27*S^3*(1 + S^2)^2) - (3136*S^3*Zeta[3])/3) + HPL[{3}, -S^2]*(((1 + S^2)*(12118 + 14507*S^2 + 35779*S^4))/(162*S^3) + (Pi^2*(274 + 548*S^2 + 274*S^4 + 10453*S^6 + 8978*S^8 + 1507*S^10))/(27*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{2, 1}, -S^2])/3 + (200*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((-2021*Pi^4*S^3)/180 - ((1 + S^2)*(13400 + 9469*S^2 + 411947*S^4))/(972*S^3) + (Pi^2*(-531 - 3787*S^2 - 6411*S^4 - 22680*S^6 - 21382*S^8 - 6561*S^10))/(54*S^3*(1 + S^2)^2) + (2*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (452*S^3*HPL[{4}, -S^2])/3 + (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*S^3*HPL[{3, 1}, -S^2])/3 - (6272*S^3*HPL[{2, 1, 1}, -S^2])/3 + (224*(2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (2*(34 + 68*S^2 + 34*S^4 + 2467*S^6 + 1894*S^8 + 187*S^10)*Zeta[5])/(3*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((-252431*Pi^6*S^3)/68040 + (-781878 - 923061*S^2 - 12649645*S^4)/(17496*S) + (Pi^2*(-43312 - 89980*S^2 - 701423*S^4))/(3888*S) + (Pi^4*(-15602 - 23403*S^2 - 215469*S^4 - 241337*S^6 - 106767*S^8))/(3240*S*(1 + S^2)^2) - (56*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)^2) - (224*S^3*HPL[{1}, -S^2]^6)/9 + ((-182*Pi^2*S^3)/3 + (-195 - 2742*S^2 - 3723*S^4 - 32020*S^6 - 30770*S^8 - 14038*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (746*S^3*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((-1205*Pi^2*S^3)/27 - (5*(88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10))/(18*S^3*(1 + S^2)^2) - (500*S^3*HPL[{2}, -S^2])/3) + 8*S^3*HPL[{3}, -S^2]^2 + ((-89*Pi^2*S^3)/9 + (71 + 13*S^2 - 190*S^4 - 2309*S^6 - 2461*S^8 - 1112*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-18 - 36*S^2 - 18*S^4 - 563*S^6 - 574*S^8 - 149*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (166*S^3*HPL[{6}, -S^2])/3 + ((16528 + 21207*S^2 + 168816*S^4 + 2409*S^6)/(162*S^3) + (Pi^2*(1326 + 2652*S^2 + 1326*S^4 + 9107*S^6 + 5254*S^8 - 613*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (3068*S^3*HPL[{2, 1}, -S^2]^2)/3 + (252*Pi^2*S^3 + (-800 + 2675*S^2 + 5140*S^4 + 60978*S^6 + 60936*S^8 + 28623*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (19*(-2 - 4*S^2 - 2*S^4 + 99*S^6 + 102*S^8 + 27*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(-94 - 188*S^2 - 94*S^4 + 2349*S^6 + 2514*S^8 + 711*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 2*S^3*HPL[{4, 2}, -S^2] + 84*S^3*HPL[{5, 1}, -S^2] + ((-4576*Pi^2*S^3)/9 - (2*(-726 + 2904*S^2 + 5448*S^4 + 61879*S^6 + 62216*S^8 + 29155*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(-380 - 760*S^2 - 380*S^4 - 3511*S^6 - 2318*S^8 + 17*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*(-1167 - 2334*S^2 - 1167*S^4 - 10250*S^6 - 6592*S^8 + 181*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 8*S^3*HPL[{3, 1, 2}, -S^2] - (5992*S^3*HPL[{3, 2, 1}, -S^2])/3 - 6096*S^3*HPL[{4, 1, 1}, -S^2] - (40*(-54 - 108*S^2 - 54*S^4 - 425*S^6 - 250*S^8 + 25*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (12608*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 - 8480*S^3*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*S^3*(431 + 486*S^2 + 149*S^4))/(9*(1 + S^2)^2) + (4464 + 2610*S^2 + 13429*S^4)/(162*S))*Zeta[3] - (52*S^3*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((-757 + 1665*S^2 - 5733*S^4 - 5415*S^6)/(162*S^3) + (Pi^2*(-94 - 188*S^2 - 94*S^4 + 453*S^6 + 642*S^8 + 255*S^10))/(54*S^3*(1 + S^2)^2) - (80*S^3*HPL[{2, 1}, -S^2])/3 + (16*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(486*S^3) - (2*Pi^2*(688 + 1376*S^2 + 688*S^4 + 14629*S^6 + 14798*S^8 + 3784*S^10))/(81*S^3*(1 + S^2)^2) - (250*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (136*S^3*HPL[{3}, -S^2])/9 + (2000*S^3*HPL[{2, 1}, -S^2])/3 + (664*S^3*Zeta[3])/9) + HPL[{1}, -S^2]^2*((-4061*Pi^4*S^3)/180 - ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(972*S^3) + (Pi^2*(-1850 - 11061*S^2 - 17534*S^4 - 72512*S^6 - 52056*S^8 - 16787*S^10))/(108*S^3*(1 + S^2)^2) + (-120*Pi^2*S^3 - (2*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (784*S^3*HPL[{2}, -S^2]^2)/3 + (4*(10 + 20*S^2 + 10*S^4 + 208*S^6 + 212*S^8 + 55*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (92*S^3*HPL[{4}, -S^2])/3 + (250*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + 1000*S^3*HPL[{3, 1}, -S^2] - 2000*S^3*HPL[{2, 1, 1}, -S^2] + (4*(40 + 80*S^2 + 40*S^4 + 967*S^6 + 938*S^8 + 220*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-769*Pi^4*S^3)/36 + (867 - 13699*S^2 - 36169*S^4 - 188347*S^6)/(324*S^3) + (Pi^2*(525 - 2616*S^2 - 4794*S^4 - 51262*S^6 - 55358*S^8 - 25189*S^10))/(162*S^3*(1 + S^2)^2) + ((-22 - 44*S^2 - 22*S^4 + 907*S^6 + 902*S^8 + 223*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (50*S^3*HPL[{4}, -S^2])/3 - (4*(-380 - 760*S^2 - 380*S^4 - 3511*S^6 - 2318*S^8 + 17*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3064*S^3*HPL[{3, 1}, -S^2])/3 - (6136*S^3*HPL[{2, 1, 1}, -S^2])/3 + (4*(-2 - 4*S^2 - 2*S^4 + 597*S^6 + 702*S^8 + 228*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (2*S^3*(1012 + 1244*S^2 + 427*S^4)*Zeta[5])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(6143 + 10462*S^2 + 79547*S^4))/(486*S^3) - ((1 + S^2)*(126326 + 155803*S^2 + 1865477*S^4))/(2916*S^3) + (Pi^4*(-15602 - 31204*S^2 - 15602*S^4 - 305105*S^6 - 317818*S^8 - 85811*S^10))/(3240*S^3*(1 + S^2)^2) - (196*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((22*Pi^2*S^3)/9 - (2*(-85 - 207*S^2 - 133*S^4 - 232*S^6 + 66*S^8 + 83*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-34 - 68*S^2 - 34*S^4 - 1015*S^6 - 926*S^8 - 187*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (92*S^3*HPL[{5}, -S^2])/3 + (240*Pi^2*S^3 + (4*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(62 + 124*S^2 + 62*S^4 + 1466*S^6 + 1432*S^8 + 341*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (304*S^3*HPL[{3, 2}, -S^2])/3 - (728*S^3*HPL[{4, 1}, -S^2])/3 - (500*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (6272*S^3*HPL[{2, 2, 1}, -S^2])/3 - (18544*S^3*HPL[{3, 1, 1}, -S^2])/3 + 4000*S^3*HPL[{2, 1, 1, 1}, -S^2] + ((188*Pi^2*S^3)/9 + (256 + 943*S^2 + 1180*S^4 + 4204*S^6 + 2428*S^8 + 709*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(7142 + 11923*S^2 + 91373*S^4))/(162*S^3) + (Pi^2*(-1246 - 2492*S^2 - 1246*S^4 - 26293*S^6 - 26666*S^8 - 6853*S^10))/(54*S^3*(1 + S^2)^2) + (152*S^3*HPL[{3}, -S^2])/3 + (3136*S^3*HPL[{2, 1}, -S^2])/3 + (328*S^3*Zeta[3])/3) + (260*S^3*Zeta[5])/3)) + 744*S^3*Zeta[7]) + HPL[{1}, -S^2]*((-13964*Pi^8*S^3)/42525 - (Pi^4*(1 + S^2)*(136687 + 173304*S^2 + 2123545*S^4))/(116640*S^3) - (Pi^2*(1 + S^2)*(189433 + 203036*S^2 + 3940339*S^4))/(34992*S^3) - ((1 + S^2)*(55110542 + 26497639*S^2 + 667256405*S^4))/(1259712*S^3) + (Pi^6*(-299516 - 2086819*S^2 - 3425189*S^4 - 13840754*S^6 - 10970926*S^8 - 3473708*S^10))/(1224720*S^3*(1 + S^2)^2) + ((-32*Pi^2*S^3)/9 + (-86 - 764*S^2 - 789*S^4 - 4058*S^6 - 1733*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2]^3 - (32*S^3*HPL[{2}, -S^2]^4)/3 + ((-37*Pi^2*S^3)/9 + (-310 - 1235*S^2 - 1660*S^4 - 6052*S^6 - 3782*S^8 - 1129*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + 6*S^3*HPL[{4}, -S^2]^2 + ((67*Pi^2*S^3)/9 + (665 + 490*S^2 - 910*S^4 - 5320*S^6 - 9527*S^8 - 3340*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{6}, -S^2] - (2*(46 + 92*S^2 + 46*S^4 + 208*S^6 + 476*S^8 + 253*S^10)*HPL[{7}, -S^2])/(3*S^3*(1 + S^2)^2) + 36*S^3*HPL[{8}, -S^2] + ((1214*Pi^2*S^3)/9 + (664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - (1864*S^3*HPL[{3, 1}, -S^2]^2)/3 + ((-38*Pi^2*S^3)/3 + (-164 - 643*S^2 - 839*S^4 - 3071*S^6 - 1867*S^8 - 560*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + (2*(6 + 12*S^2 + 6*S^4 + 174*S^6 + 160*S^8 + 33*S^10)*HPL[{4, 3}, -S^2])/(3*S^3*(1 + S^2)^2) + ((-692*Pi^2*S^3)/9 + (-3086 - 9997*S^2 - 11366*S^4 - 41120*S^6 - 17098*S^8 - 4769*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + (2*(14 + 28*S^2 + 14*S^4 + 383*S^6 + 358*S^8 + 77*S^10)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + 8*S^3*HPL[{5, 3}, -S^2] + ((298 + 596*S^2 + 298*S^4 + 757*S^6 + 2690*S^8 + 1639*S^10)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 20*S^3*HPL[{6, 2}, -S^2] - 36*S^3*HPL[{7, 1}, -S^2] - (6272*S^3*HPL[{2, 1, 1}, -S^2]^2)/3 + ((-256*Pi^2*S^3)/3 - (8*(86 + 764*S^2 + 789*S^4 + 4058*S^6 + 1733*S^8))/(27*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((322 + 644*S^2 + 322*S^4 + 11551*S^6 + 10062*S^8 + 1771*S^10)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (8*(374 + 748*S^2 + 374*S^4 + 13271*S^6 + 11590*S^8 + 2057*S^10)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (532*S^3*HPL[{3, 3, 2}, -S^2])/3 + ((-1624*Pi^2*S^3)/9 + (764 - 11129*S^2 - 26704*S^4 - 76978*S^6 - 123152*S^8 - 37081*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((2914 + 5828*S^2 + 2914*S^4 + 104335*S^6 + 90926*S^8 + 16027*S^10)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (908*S^3*HPL[{4, 1, 3}, -S^2])/3 + ((9226 + 18452*S^2 + 9226*S^4 + 324379*S^6 + 283910*S^8 + 50743*S^10)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (376*S^3*HPL[{4, 2, 2}, -S^2])/3 + (2908*S^3*HPL[{4, 3, 1}, -S^2])/3 + (4*(4738 + 9476*S^2 + 4738*S^4 + 166999*S^6 + 146078*S^8 + 26059*S^10)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1688*S^3*HPL[{5, 1, 2}, -S^2])/3 + (12008*S^3*HPL[{5, 2, 1}, -S^2])/3 + (31316*S^3*HPL[{6, 1, 1}, -S^2])/3 + (664*(2 + 11*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + ((880*Pi^2*S^3)/9 + (8*(-185 + 563*S^2 + 1867*S^4 + 5062*S^6 + 9932*S^8 + 3001*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] - (16*(362 + 724*S^2 + 362*S^4 + 5519*S^6 + 6334*S^8 + 1991*S^10)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*(362 + 724*S^2 + 362*S^4 + 5519*S^6 + 6334*S^8 + 1991*S^10)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 104*S^3*HPL[{3, 1, 2, 2}, -S^2] - (8*(1222 + 2444*S^2 + 1222*S^4 + 13777*S^6 + 18146*S^8 + 6721*S^10)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 104*S^3*HPL[{3, 2, 1, 2}, -S^2] - (376*S^3*HPL[{3, 2, 2, 1}, -S^2])/3 - 64*S^3*HPL[{3, 3, 1, 1}, -S^2] - (8*(3778 + 7556*S^2 + 3778*S^4 + 44935*S^6 + 57662*S^8 + 20779*S^10)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 312*S^3*HPL[{4, 1, 1, 2}, -S^2] - 376*S^3*HPL[{4, 1, 2, 1}, -S^2] - 504*S^3*HPL[{4, 2, 1, 1}, -S^2] - (6560*S^3*HPL[{5, 1, 1, 1}, -S^2])/3 + ((-3136*Pi^2*S^3)/9 - (16*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] + (3136*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (160*(224 + 448*S^2 + 224*S^4 + 5615*S^6 + 5386*S^8 + 1232*S^10)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (5312*S^3*HPL[{4, 1, 1, 1, 1}, -S^2])/3 + (1040*(2 + 11*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (5312*S^3*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/3 + ((-29*Pi^2*S^3)/9 + (-4 - 179*S^2 - 418*S^4 - 1885*S^6 - 1529*S^8 - 607*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((4*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(9*S^3) + (4*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(27*S^3*(1 + S^2)^2) - (6272*S^3*Zeta[3])/3) + HPL[{4, 1}, -S^2]*(-((1 + S^2)*(32323 + 39284*S^2 + 107725*S^4))/(162*S^3) + (Pi^2*(-1606 - 3212*S^2 - 1606*S^4 - 59557*S^6 - 51482*S^8 - 8833*S^10))/(54*S^3*(1 + S^2)^2) - (424*S^3*Zeta[3])/3) + HPL[{3, 2}, -S^2]*(-((1 + S^2)*(4039 + 5132*S^2 + 16783*S^4))/(81*S^3) - (7*Pi^2*(34 + 68*S^2 + 34*S^4 + 1249*S^6 + 1082*S^8 + 187*S^10))/(27*S^3*(1 + S^2)^2) - (104*S^3*Zeta[3])/3) + HPL[{5}, -S^2]*(-((1 + S^2)*(-986 - 1031*S^2 + 2881*S^4))/(54*S^3) + (Pi^2*(-14 - 28*S^2 - 14*S^4 + 1003*S^6 + 566*S^8 - 77*S^10))/(27*S^3*(1 + S^2)^2) - (328*S^3*HPL[{2, 1}, -S^2])/3 - 8*S^3*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((-2*(1 + S^2)*(4849 + 6653*S^2 + 41650*S^4))/(81*S^3) - (2*Pi^2*(230 + 460*S^2 + 230*S^4 + 4907*S^6 + 4958*S^8 + 1265*S^10))/(9*S^3*(1 + S^2)^2) + 944*S^3*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*(-((1 + S^2)*(16976 + 25411*S^2 + 214121*S^4))/(81*S^3) - (4*Pi^2*(898 + 1796*S^2 + 898*S^4 + 16855*S^6 + 17822*S^8 + 4939*S^10))/(27*S^3*(1 + S^2)^2) + (8896*S^3*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*((-2021*Pi^4*S^3)/90 - ((1 + S^2)*(13400 + 9469*S^2 + 411947*S^4))/(486*S^3) + (Pi^2*(-531 - 3787*S^2 - 6411*S^4 - 22680*S^6 - 21382*S^8 - 6561*S^10))/(27*S^3*(1 + S^2)^2) + (448*(2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{4}, -S^2]*((7*Pi^4*S^3)/3 + ((1 + S^2)*(29021 + 24553*S^2 + 16214*S^4))/(972*S^3) + (Pi^2*(498 + 1475*S^2 + 1524*S^4 + 5718*S^6 + 1454*S^8 + 363*S^10))/(108*S^3*(1 + S^2)^2) - (113*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (484*S^3*HPL[{3, 1}, -S^2])/3 + (904*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((10 + 20*S^2 + 10*S^4 + 559*S^6 + 446*S^8 + 55*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-111*Pi^4*S^3)/20 - ((1 + S^2)*(7626 + 10435*S^2 + 85251*S^4))/(648*S^3) + (Pi^2*(-560 - 2965*S^2 - 4490*S^4 - 18020*S^6 - 12682*S^8 - 4031*S^10))/(108*S^3*(1 + S^2)^2) + ((50 + 100*S^2 + 50*S^4 + 1673*S^6 + 1482*S^8 + 275*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) + (164*S^3*HPL[{4}, -S^2])/3 + (83*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (164*S^3*HPL[{3, 1}, -S^2])/3 + ((94 + 188*S^2 + 94*S^4 + 3703*S^6 + 3158*S^8 + 517*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((398*Pi^4*S^3)/45 + ((1 + S^2)*(-4270 - 3692*S^2 + 85469*S^4))/(243*S^3) + (Pi^2*(126 + 1384*S^2 + 2574*S^4 + 9126*S^6 + 9403*S^8 + 2913*S^10))/(27*S^3*(1 + S^2)^2) + (6272*S^3*HPL[{2, 1, 1}, -S^2])/3 - (4*(118 + 236*S^2 + 118*S^4 + 4285*S^6 + 3722*S^8 + 649*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (((1 + S^2)*(-607 + 3919*S^2 + 9698*S^4))/(162*S^3) + (Pi^2*(74 + 148*S^2 + 74*S^4 + 7949*S^6 + 5842*S^8 + 407*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2, 1}, -S^2]*((Pi^2*(1 + S^2)*(6026 + 7345*S^2 + 90581*S^4))/(648*S^3) + ((1 + S^2)*(10001 + 3776*S^2 + 483629*S^4))/(972*S^3) + (Pi^4*(13150 + 26300*S^2 + 13150*S^4 + 181459*S^6 + 217406*S^8 + 72325*S^10))/(3240*S^3*(1 + S^2)^2) - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3416*S^3*HPL[{3, 2}, -S^2])/3 + (10280*S^3*HPL[{4, 1}, -S^2])/3 - (1568*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*S^3*HPL[{3, 1, 1}, -S^2])/3 + (12544*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-862*Pi^2*S^3)/9 - (2*(267 + 1123*S^2 + 1503*S^4 + 7332*S^6 + 3058*S^8 + 1077*S^10))/(9*S^3*(1 + S^2)^2))*Zeta[3] - (1444*S^3*Zeta[5])/3) + Zeta[3]*((Pi^2*(1 + S^2)*(913 + 1814*S^2 + 5551*S^4))/(324*S^3) + ((1 + S^2)*(66359 + 131740*S^2 + 544151*S^4))/(5832*S^3) + (Pi^4*(1090 + 2180*S^2 + 1090*S^4 + 60697*S^6 + 48458*S^8 + 5995*S^10))/(3240*S^3*(1 + S^2)^2) - (124*S^3*Zeta[5])/3) + HPL[{3}, -S^2]*((Pi^2*(1 + S^2)*(12746 + 15685*S^2 + 25769*S^4))/(1944*S^3) + ((1 + S^2)*(78323 + 105019*S^2 + 203108*S^4))/(2916*S^3) + (Pi^4*(782 + 1564*S^2 + 782*S^4 + 36755*S^6 + 30238*S^8 + 4301*S^10))/(1620*S^3*(1 + S^2)^2) + ((-10 - 20*S^2 - 10*S^4 - 313*S^6 - 282*S^8 - 55*S^10)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^2) - (56*S^3*HPL[{5}, -S^2])/3 + ((-826*Pi^2*S^3)/9 + (-552 - 2293*S^2 - 3048*S^4 - 14760*S^6 - 6244*S^8 - 2199*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (344*S^3*HPL[{3, 2}, -S^2])/3 + 36*S^3*HPL[{4, 1}, -S^2] + (4*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3728*S^3*HPL[{2, 2, 1}, -S^2])/3 + (10592*S^3*HPL[{3, 1, 1}, -S^2])/3 - (6272*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((52*Pi^2*S^3)/9 + (2*(13 + 44*S^2 + 45*S^4 + 169*S^6 + 71*S^8 + 16*S^10))/(3*S^3*(1 + S^2)^2))*Zeta[3] + (64*S^3*Zeta[5])/3) + HPL[{2}, -S^2]*((-1049*Pi^6*S^3)/1080 - (Pi^2*(1 + S^2)*(7765 + 7577*S^2 + 153025*S^4))/(1944*S^3) - ((1 + S^2)*(-6227 + 3719*S^2 + 1725700*S^4))/(5832*S^3) + (Pi^4*(-10562 - 74488*S^2 - 125393*S^4 - 455963*S^6 - 412825*S^8 - 127463*S^10))/(9720*S^3*(1 + S^2)^2) - (86*S^3*HPL[{3}, -S^2]^2)/3 + ((112*Pi^2*S^3)/9 + (158 + 626*S^2 + 833*S^4 + 3041*S^6 + 1883*S^8 + 563*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((18 + 36*S^2 + 18*S^4 + 591*S^6 + 526*S^8 + 99*S^10)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^2) + 28*S^3*HPL[{6}, -S^2] + ((1210*Pi^2*S^3)/9 + (2000 + 10279*S^2 + 15356*S^4 + 63668*S^6 + 41896*S^8 + 13529*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-174 - 348*S^2 - 174*S^4 - 6081*S^6 - 5330*S^8 - 957*S^10)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + ((-1574 - 3148*S^2 - 1574*S^4 - 54917*S^6 - 48154*S^8 - 8657*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 104*S^3*HPL[{4, 2}, -S^2] - (1264*S^3*HPL[{5, 1}, -S^2])/3 + ((-2428*Pi^2*S^3)/9 - (2*(664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (332*(2 + 11*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (8*(362 + 724*S^2 + 362*S^4 + 5519*S^6 + 6334*S^8 + 1991*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 104*S^3*HPL[{3, 1, 2}, -S^2] - 920*S^3*HPL[{3, 2, 1}, -S^2] - (8312*S^3*HPL[{4, 1, 1}, -S^2])/3 + (1568*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (6272*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 - (12544*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + (((1 + S^2)*(2690 + 3409*S^2 + 11429*S^4))/(108*S^3) + (Pi^2*(242 + 484*S^2 + 242*S^4 + 9089*S^6 + 7834*S^8 + 1331*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] + 2*S^3*Zeta[3]^2 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(4849 + 6653*S^2 + 41650*S^4))/(81*S^3) + (Pi^2*(230 + 460*S^2 + 230*S^4 + 4907*S^6 + 4958*S^8 + 1265*S^10))/(9*S^3*(1 + S^2)^2) - 472*S^3*Zeta[3]) + HPL[{3}, -S^2]*(((1 + S^2)*(4039 + 5132*S^2 + 16783*S^4))/(162*S^3) + (7*Pi^2*(34 + 68*S^2 + 34*S^4 + 1249*S^6 + 1082*S^8 + 187*S^10))/(54*S^3*(1 + S^2)^2) - (1864*S^3*HPL[{2, 1}, -S^2])/3 + (52*S^3*Zeta[3])/3) + ((130 + 260*S^2 + 130*S^4 + 7213*S^6 + 5762*S^8 + 715*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) - (2*(10 + 20*S^2 + 10*S^4 - 1394*S^6 - 856*S^8 + 55*S^10)*Zeta[7])/(3*S^3*(1 + S^2)^2)) + Log[T]*((1761997*Pi^8*S^3)/4082400 + (400204 + 1650115*S^2)/(209952*S) + (Pi^4*(1401684 + 3001578*S^2 + 17074121*S^4))/(699840*S) + (Pi^2*(1012050 + 1880469*S^2 + 20915332*S^4))/(209952*S) + (Pi^6*(376730 + 565095*S^2 + 4473384*S^4 + 4528427*S^6 + 1811958*S^8))/(408240*S*(1 + S^2)^2) + (S^3*HPL[{0}, S^2]^8)/144 + ((58*Pi^2*S^3)/9 + (88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^6 + (16*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)^2) + (16*S^3*HPL[{1}, -S^2]^8)/9 + HPL[{0}, S^2]^7*((S^3*(71 + 106*S^2 + 44*S^4))/(432*(1 + S^2)^2) + (S^3*HPL[{1}, -S^2])/24) + ((401*Pi^2*S^3)/27 + (-1011 - 519*S^2 - 1014*S^4 + 9713*S^6 + 10247*S^8)/(162*S^3*(1 + S^2)))*HPL[{2}, -S^2]^3 + (65*S^3*HPL[{2}, -S^2]^4)/6 + HPL[{0}, S^2]^6*((47*Pi^2*S^3)/432 + (80 + 120*S^2 + 1149*S^4 + 1568*S^6 + 675*S^8)/(864*S*(1 + S^2)^2) + ((10 + 20*S^2 + 10*S^4 + 136*S^6 + 164*S^8 + 55*S^10)*HPL[{1}, -S^2])/(108*S^3*(1 + S^2)^2) + (S^3*HPL[{1}, -S^2]^2)/4 + (17*S^3*HPL[{2}, -S^2])/72) + ((71*Pi^2*S^3)/9 + (8 + 451*S^2 + 638*S^4 + 4554*S^6 + 3000*S^8 + 1305*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + (16*S^3*HPL[{4}, -S^2]^2)/3 + ((7*Pi^2*S^3)/3 + (-455 - 16*S^2 + 1336*S^4 + 9522*S^6 + 17121*S^8 + 6894*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{6}, -S^2] + (2*(95 + 190*S^2 + 95*S^4 + 1749*S^6 + 3678*S^8 + 1884*S^10)*HPL[{7}, -S^2])/(9*S^3*(1 + S^2)^2) + (836*S^3*HPL[{8}, -S^2])/3 + ((-1616*Pi^2*S^3)/9 - (2*(202 + 1329*S^2 + 1942*S^4 + 11509*S^6 + 9738*S^8 + 3748*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 + (1592*S^3*HPL[{3, 1}, -S^2]^2)/3 + ((95*Pi^2*S^3)/3 + (-203 + 269*S^2 + 742*S^4 + 7676*S^6 + 6091*S^8 + 2897*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + (2*(8 + 16*S^2 + 8*S^4 - 377*S^6 - 190*S^8 + 46*S^10)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + ((1262*Pi^2*S^3)/9 + (2*(120 + 1599*S^2 + 2046*S^4 + 16796*S^6 + 8293*S^8 + 4232*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + ((70 + 140*S^2 + 70*S^4 - 1531*S^6 - 614*S^8 + 305*S^10)*HPL[{5, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (44*S^3*HPL[{5, 3}, -S^2])/3 - (2*(8 + 16*S^2 + 8*S^4 - 77*S^6 + 434*S^8 + 364*S^10)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 42*S^3*HPL[{6, 2}, -S^2] - (512*S^3*HPL[{7, 1}, -S^2])/3 + (6320*S^3*HPL[{2, 1, 1}, -S^2]^2)/3 + ((-52*Pi^2*S^3)/3 + (920 + 1271*S^2 + 1053*S^4 + 391*S^6 - 1715*S^8)/(27*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((3052*Pi^2*S^3)/9 + (-3124 - 805*S^2 - 3003*S^4 + 39243*S^6 + 39273*S^8)/(27*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((38 + 76*S^2 + 38*S^4 - 13193*S^6 - 13346*S^8 - 3413*S^10)*HPL[{3, 2, 2}, -S^2])/(3*S^3*(1 + S^2)^2) - (16*(-33 - 66*S^2 - 33*S^4 + 7636*S^6 + 7796*S^8 + 2029*S^10)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (928*S^3*HPL[{3, 3, 2}, -S^2])/3 + ((8584*Pi^2*S^3)/9 + (2*(-6090 - 10599*S^2 - 11346*S^4 + 34679*S^6 + 110638*S^8 + 57170*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] - (4*(-131 - 262*S^2 - 131*S^4 + 30024*S^6 + 30612*S^8 + 7947*S^10)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - 504*S^3*HPL[{4, 1, 3}, -S^2] - (4*(-395 - 790*S^2 - 395*S^4 + 93318*S^6 + 95424*S^8 + 24909*S^10)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 234*S^3*HPL[{4, 2, 2}, -S^2] - (5288*S^3*HPL[{4, 3, 1}, -S^2])/3 - (4*(-262 - 524*S^2 - 262*S^4 + 63975*S^6 + 65310*S^8 + 16995*S^10)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - 1044*S^3*HPL[{5, 1, 2}, -S^2] - 7284*S^3*HPL[{5, 2, 1}, -S^2] - 18768*S^3*HPL[{6, 1, 1}, -S^2] + (16*(-298 + 633*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + ((-6016*Pi^2*S^3)/9 - (8*(-1326 - 2619*S^2 - 2874*S^4 + 4291*S^6 + 19118*S^8 + 10258*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] - (8*(-1732 - 3464*S^2 - 1732*S^4 - 5843*S^6 - 2278*S^8 + 1213*S^10)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*(-1732 - 3464*S^2 - 1732*S^4 - 5843*S^6 - 2278*S^8 + 1213*S^10)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 112*S^3*HPL[{3, 1, 2, 2}, -S^2] - (8*(-3520 - 7040*S^2 - 3520*S^4 - 2045*S^6 + 5318*S^8 + 5011*S^10)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 112*S^3*HPL[{3, 2, 1, 2}, -S^2] - (5936*S^3*HPL[{3, 2, 2, 1}, -S^2])/3 - 6272*S^3*HPL[{3, 3, 1, 1}, -S^2] - (16*(-5326 - 10652*S^2 - 5326*S^4 - 4887*S^6 + 6330*S^8 + 7191*S^10)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2288*S^3*HPL[{4, 1, 1, 2}, -S^2])/3 - (16528*S^3*HPL[{4, 1, 2, 1}, -S^2])/3 - (54160*S^3*HPL[{4, 2, 1, 1}, -S^2])/3 - (102560*S^3*HPL[{5, 1, 1, 1}, -S^2])/3 + ((13600*Pi^2*S^3)/9 + (40*(-362 - 74*S^2 - 306*S^4 + 4725*S^6 + 4635*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] - (32*(292 + 584*S^2 + 292*S^4 + 4051*S^6 + 3398*S^8 + 523*S^10)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (32*(292 + 584*S^2 + 292*S^4 + 4051*S^6 + 3398*S^8 + 523*S^10)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (12544*S^3*HPL[{2, 2, 1, 2, 1}, -S^2])/3 - 12544*S^3*HPL[{2, 2, 2, 1, 1}, -S^2] - (160*(295 + 590*S^2 + 295*S^4 + 5183*S^6 + 4522*S^8 + 800*S^10)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (73984*S^3*HPL[{3, 1, 1, 1, 2}, -S^2])/3 + (124160*S^3*HPL[{3, 1, 1, 2, 1}, -S^2])/3 + (149248*S^3*HPL[{3, 1, 2, 1, 1}, -S^2])/3 + (312320*S^3*HPL[{3, 2, 1, 1, 1}, -S^2])/3 + 310720*S^3*HPL[{4, 1, 1, 1, 1}, -S^2] + (1120*(-6 + 13*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - 7040*S^3*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 17920*S^3*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*S^3)/9 + (2*(54 + 81*S^2 + 592*S^4 + 302*S^6 + 97*S^8))/(27*S*(1 + S^2)^2))*Zeta[3]^2 + HPL[{1}, -S^2]^5*(((1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(486*S^3) + (2*Pi^2*(50 + 100*S^2 + 50*S^4 + 1058*S^6 + 1072*S^8 + 275*S^10))/(27*S^3*(1 + S^2)^2) + (26*(2 + 11*S^6)*HPL[{2}, -S^2])/(9*S^3) - (760*S^3*HPL[{3}, -S^2])/9 - (200*S^3*Zeta[3])/3) + HPL[{0}, S^2]^5*((5*(84 + 1200*S^2 + 7001*S^4))/(7776*S) + (Pi^2*S^3*(13109 + 19186*S^2 + 7835*S^4))/(6480*(1 + S^2)^2) + ((170 + 340*S^2 + 170*S^4 + 2561*S^6 + 2954*S^8 + 935*S^10)*HPL[{1}, -S^2]^2)/(360*S^3*(1 + S^2)^2) + (271*S^3*HPL[{1}, -S^2]^3)/270 + (S^3*(4904 + 7036*S^2 + 2825*S^4)*HPL[{2}, -S^2])/(1080*(1 + S^2)^2) + HPL[{1}, -S^2]*((293*Pi^2*S^3)/540 + (350 + 8935*S^2 + 17990*S^4 + 74654*S^6 + 67822*S^8 + 22085*S^10)/(6480*S^3*(1 + S^2)^2) + (77*S^3*HPL[{2}, -S^2])/60) - (S^3*HPL[{3}, -S^2])/12 + (5*S^3*HPL[{2, 1}, -S^2])/18 + (S^3*Zeta[3])/2) + HPL[{5}, -S^2]*((-3949 - 7023*S^2 + 7791*S^4 + 16148*S^6)/(162*S^3) + (Pi^2*(-14 - 28*S^2 - 14*S^4 - 2061*S^6 - 1242*S^8 + 99*S^10))/(54*S^3*(1 + S^2)^2) - (52*S^3*HPL[{2, 1}, -S^2])/3 + 4*S^3*Zeta[3]) + HPL[{0}, S^2]^4*((2731*Pi^4*S^3)/4320 + (19356 + 87288*S^2 + 982019*S^4)/(46656*S) + (Pi^2*(2212 + 3318*S^2 + 31141*S^4 + 41052*S^6 + 17665*S^8))/(2592*S*(1 + S^2)^2) + ((506 + 1012*S^2 + 506*S^4 + 7895*S^6 + 8974*S^8 + 2783*S^10)*HPL[{1}, -S^2]^3)/(324*S^3*(1 + S^2)^2) + (71*S^3*HPL[{1}, -S^2]^4)/27 + ((521*Pi^2*S^3)/216 + (-160 + 592*S^2 + 1208*S^4 + 12413*S^6 + 15946*S^8 + 6881*S^10)/(432*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (61*S^3*HPL[{2}, -S^2]^2)/18 + HPL[{1}, -S^2]^2*((277*Pi^2*S^3)/108 + (1252 + 10637*S^2 + 18604*S^4 + 73036*S^6 + 63566*S^8 + 20197*S^10)/(1296*S^3*(1 + S^2)^2) + (241*S^3*HPL[{2}, -S^2])/36) + ((8 + 16*S^2 + 8*S^4 - 17*S^6 - 10*S^8 + S^10)*HPL[{3}, -S^2])/(72*S^3*(1 + S^2)^2) + (3*S^3*HPL[{4}, -S^2])/4 + ((-480 - 960*S^2 - 480*S^4 - 1885*S^6 - 878*S^8 + 284*S^10)*HPL[{2, 1}, -S^2])/(108*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(5242 + 10187*S^2 + 135535*S^4))/(7776*S^3) + (Pi^2*(1106 + 2212*S^2 + 1106*S^4 + 16055*S^6 + 18814*S^8 + 6083*S^10))/(1296*S^3*(1 + S^2)^2) + ((76 + 152*S^2 + 76*S^4 + 1141*S^6 + 1318*S^8 + 418*S^10)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)^2) - (S^3*HPL[{3}, -S^2])/6 - (241*S^3*HPL[{2, 1}, -S^2])/18) - (259*S^3*HPL[{3, 1}, -S^2])/18 + (266*S^3*HPL[{2, 1, 1}, -S^2])/9 + (277*S^3*Zeta[3])/54) + HPL[{3, 1, 1}, -S^2]*((36952 + 46455*S^2 + 371112*S^4 + 6711*S^6)/(81*S^3) + (16*Pi^2*(150 + 300*S^2 + 150*S^4 + 996*S^6 + 668*S^8 + 3*S^10))/(9*S^3*(1 + S^2)^2) + 96*S^3*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((2*(7417 + 11889*S^2 + 64629*S^4 + 11642*S^6))/(81*S^3) + (4*Pi^2*(598 + 1196*S^2 + 598*S^4 + 5948*S^6 + 4612*S^8 + 485*S^10))/(27*S^3*(1 + S^2)^2) + 96*S^3*Zeta[3]) + HPL[{3, 2}, -S^2]*((-539 + 16722*S^2 + 7461*S^4 + 60042*S^6)/(162*S^3) + (Pi^2*(-110 - 220*S^2 - 110*S^4 + 20143*S^6 + 20462*S^8 + 5275*S^10))/(54*S^3*(1 + S^2)^2) + (304*S^3*Zeta[3])/3) + HPL[{2, 1, 1, 1}, -S^2]*((8*(-2972 - 1899*S^2 - 31959*S^4 + 7400*S^6))/(81*S^3) + (8*Pi^2*(-642 - 1284*S^2 - 642*S^4 - 977*S^6 + 398*S^8 + 787*S^10))/(27*S^3*(1 + S^2)^2) + (320*S^3*Zeta[3])/3) + HPL[{4, 1}, -S^2]*((2350 + 22027*S^2 + 11308*S^4 + 63962*S^6)/(54*S^3) + (2*Pi^2*(-61 - 122*S^2 - 61*S^4 + 16941*S^6 + 16974*S^8 + 4260*S^10))/(27*S^3*(1 + S^2)^2) + 328*S^3*Zeta[3]) + HPL[{4}, -S^2]*((-11*Pi^4*S^3)/4 + (17926 - 111576*S^2 - 35256*S^4 - 43391*S^6)/(1944*S^3) + (Pi^2*(-106 - 1280*S^2 - 1708*S^4 - 14375*S^6 - 3772*S^8 - 2171*S^10))/(324*S^3*(1 + S^2)^2) + (2*(80 + 160*S^2 + 80*S^4 + 681*S^6 + 458*S^8 + 3*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (1076*S^3*HPL[{3, 1}, -S^2])/3 - (2192*S^3*HPL[{2, 1, 1}, -S^2])/3 + (2*(-2 - 4*S^2 - 2*S^4 - 245*S^6 - 154*S^8 + 7*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((6673*Pi^4*S^3)/810 + ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(2916*S^3) + (Pi^2*(3418 + 18833*S^2 + 28906*S^4 + 117178*S^6 + 83192*S^8 + 26485*S^10))/(486*S^3*(1 + S^2)^2) + ((392*Pi^2*S^3)/27 + (2*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (784*S^3*HPL[{2}, -S^2]^2)/9 - (20*(28 + 56*S^2 + 28*S^4 + 1009*S^6 + 878*S^8 + 154*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (664*S^3*HPL[{4}, -S^2])/9 - (130*(2 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (664*S^3*HPL[{3, 1}, -S^2])/9 - (20*(2 + 4*S^2 + 2*S^4 + 86*S^6 + 72*S^8 + 11*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((650*Pi^4*S^3)/9 + (-4334 + 2259*S^2 - 2502*S^4 + 157649*S^6)/(81*S^3) + (Pi^2*(-2408 + 254*S^2 + 2812*S^4 + 68693*S^6 + 101218*S^8 + 46787*S^10))/(81*S^3*(1 + S^2)^2) - (32*(6 + 12*S^2 + 6*S^4 + 1171*S^6 + 1166*S^8 + 289*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((605*Pi^4*S^3)/72 + (7197 + 52572*S^2 + 153345*S^4 + 449872*S^6)/(1944*S^3) + (Pi^2*(342 + 3708*S^2 + 5538*S^4 + 38417*S^6 + 36598*S^8 + 14921*S^10))/(216*S^3*(1 + S^2)^2) + ((-34 - 68*S^2 - 34*S^4 - 11279*S^6 - 11374*S^8 - 2891*S^10)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^2) - (269*S^3*HPL[{4}, -S^2])/3 + (2*(-298 + 633*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (628*S^3*HPL[{3, 1}, -S^2])/3 + (1568*S^3*HPL[{2, 1, 1}, -S^2])/3 - (2*(-14 - 28*S^2 - 14*S^4 + 2154*S^6 + 2184*S^8 + 561*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-2981*Pi^4*S^3)/90 + (56854 + 43953*S^2 + 110526*S^4 - 875259*S^6)/(972*S^3) + (Pi^2*(3370 + 3107*S^2 + 1318*S^4 - 54297*S^6 - 91662*S^8 - 43704*S^10))/(162*S^3*(1 + S^2)^2) - 1664*S^3*HPL[{2, 1, 1}, -S^2] + (4*(26 + 52*S^2 + 26*S^4 + 4809*S^6 + 4770*S^8 + 1173*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (-(Pi^2*S^3*(4468 + 3908*S^2 + 697*S^4))/(27*(1 + S^2)^2) - (4*(450 + 630*S^2 + 1711*S^4))/(81*S))*Zeta[5] + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^2)*(11160 + 15533*S^2 + 110847*S^4))/(972*S^3) + ((1 + S^2)*(126326 + 155803*S^2 + 1865477*S^4))/(4374*S^3) + (Pi^4*(17174 + 34348*S^2 + 17174*S^4 + 334685*S^6 + 349066*S^8 + 94457*S^10))/(4860*S^3*(1 + S^2)^2) + (392*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((-1988*Pi^2*S^3)/27 - (2*(2362 + 9155*S^2 + 11686*S^4 + 53788*S^6 + 22304*S^8 + 7609*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (16*(28 + 56*S^2 + 28*S^4 + 901*S^6 + 806*S^8 + 154*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - 96*S^3*HPL[{5}, -S^2] + ((-1568*Pi^2*S^3)/27 - (8*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (16*(56 + 112*S^2 + 56*S^4 - 439*S^6 + 118*S^8 + 308*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (6272*S^3*HPL[{3, 2}, -S^2])/9 + (21472*S^3*HPL[{4, 1}, -S^2])/9 + (520*(2 + 11*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (12544*S^3*HPL[{2, 2, 1}, -S^2])/9 + (22432*S^3*HPL[{3, 1, 1}, -S^2])/9 + ((-1664*Pi^2*S^3)/27 - (8*(271 + 1271*S^2 + 1837*S^4 + 9946*S^6 + 3854*S^8 + 1495*S^10))/(81*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((2*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(27*S^3) + (2*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(81*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{3}, -S^2])/9 - (6272*S^3*HPL[{2, 1}, -S^2])/9 - (3136*S^3*Zeta[3])/9) - (3040*S^3*Zeta[5])/9) + Zeta[3]*((-115830 - 134865*S^2 - 185702*S^4)/(2916*S) + (Pi^2*(-4338 - 4023*S^2 - 14002*S^4))/(486*S) - (Pi^4*S^3*(33974 + 31480*S^2 + 6623*S^4))/(1620*(1 + S^2)^2) - (200*S^3*Zeta[5])/3) + HPL[{3}, -S^2]*((-353938 - 701769*S^2 - 348726*S^4 - 1531569*S^6)/(11664*S^3) + (Pi^2*(-7606 - 26010*S^2 - 5562*S^4 - 49845*S^6))/(1944*S^3) + (Pi^4*(354 + 708*S^2 + 354*S^4 - 84425*S^6 - 82306*S^8 - 19517*S^10))/(3240*S^3*(1 + S^2)^2) + (2*(-4 - 8*S^2 - 4*S^4 + 427*S^6 + 338*S^8 + 40*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-160*Pi^2*S^3)/9 + (4100 + 13117*S^2 + 16988*S^4 + 52724*S^6 + 16432*S^8 - 97*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(-122 - 244*S^2 - 122*S^4 + 9819*S^6 + 10230*S^8 + 2763*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (616*S^3*HPL[{3, 2}, -S^2])/3 - (280*S^3*HPL[{4, 1}, -S^2])/3 - (8*(-50 - 100*S^2 - 50*S^4 + 4927*S^6 + 5150*S^8 + 1399*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (608*S^3*HPL[{2, 2, 1}, -S^2])/3 - (640*S^3*HPL[{3, 1, 1}, -S^2])/3 - (1280*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-76*Pi^2*S^3)/9 + (34 - 19*S^2 - 74*S^4 - 838*S^6 - 320*S^8 - 103*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] - (56*S^3*Zeta[5])/3) + HPL[{2, 1}, -S^2]*((Pi^2*(-27284 - 23823*S^2 - 263718*S^4 + 27113*S^6))/(972*S^3) + (-119873 - 52176*S^2 - 2881155*S^4 + 185702*S^6)/(2916*S^3) + (Pi^4*(-15302 - 30604*S^2 - 15302*S^4 - 40182*S^6 - 7608*S^8 + 14385*S^10))/(1620*S^3*(1 + S^2)^2) + (16*(124 + 248*S^2 + 124*S^4 + 2147*S^6 + 1942*S^8 + 383*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (296*S^3*HPL[{3, 2}, -S^2])/3 + (368*S^3*HPL[{4, 1}, -S^2])/3 + (16*(292 + 584*S^2 + 292*S^4 + 4051*S^6 + 3398*S^8 + 523*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (6272*S^3*HPL[{2, 2, 1}, -S^2])/3 + (17536*S^3*HPL[{3, 1, 1}, -S^2])/3 - (12640*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((44*Pi^2*S^3)/9 + (2*(1212 + 4614*S^2 + 6612*S^4 + 24503*S^6 + 7618*S^8 + 437*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] - (40*S^3*Zeta[5])/3) + HPL[{0}, S^2]^3*((Pi^4*S^3*(163465 + 231002*S^2 + 91519*S^4))/(19440*(1 + S^2)^2) + (Pi^2*(10920 + 57882*S^2 + 323759*S^4))/(11664*S) + (54624 + 122526*S^2 + 2100581*S^4)/(23328*S) + ((268 + 536*S^2 + 268*S^4 + 4759*S^6 + 5138*S^8 + 1474*S^10)*HPL[{1}, -S^2]^4)/(81*S^3*(1 + S^2)^2) + (146*S^3*HPL[{1}, -S^2]^5)/27 + ((-4 - 8*S^2 - 4*S^4 + 5599*S^6 + 7382*S^8 + 2737*S^10)*HPL[{2}, -S^2]^2)/(108*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((212*Pi^2*S^3)/27 + (265 + 1968*S^2 + 3337*S^4 + 13411*S^6 + 10878*S^8 + 3481*S^10)/(81*S^3*(1 + S^2)^2) + (220*S^3*HPL[{2}, -S^2])/9) + ((-4*Pi^2*S^3)/9 + (84 + 492*S^2 + 1020*S^4 + 3109*S^6 + 3122*S^8 + 1057*S^10)/(324*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((10 + 20*S^2 + 10*S^4 + 256*S^6 + 308*S^8 + 103*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - (4*S^3*HPL[{5}, -S^2])/3 + ((44*Pi^2*S^3)/27 + (-1560 - 8256*S^2 - 14664*S^4 - 34985*S^6 - 14176*S^8 + 961*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-10 - 20*S^2 - 10*S^4 + 2917*S^6 + 3854*S^8 + 1432*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (10*S^3*HPL[{3, 2}, -S^2])/9 + (38*S^3*HPL[{4, 1}, -S^2])/9 + (4*(-10 - 20*S^2 - 10*S^4 + 2968*S^6 + 3956*S^8 + 1483*S^10)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (28*S^3*HPL[{2, 2, 1}, -S^2])/9 - (40*S^3*HPL[{3, 1, 1}, -S^2])/3 + (152*S^3*HPL[{2, 1, 1, 1}, -S^2])/9 + ((38*Pi^2*S^3)/27 + (6 + 9*S^2 + 325*S^4 + 728*S^6 + 340*S^8)/(27*S*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(5512 + 14063*S^2 + 135913*S^4))/(1944*S^3) + (Pi^2*(1046 + 2092*S^2 + 1046*S^4 + 17201*S^6 + 19138*S^8 + 5753*S^10))/(324*S^3*(1 + S^2)^2) + (2*(124 + 248*S^2 + 124*S^4 + 2167*S^6 + 2354*S^8 + 682*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) + (4*S^3*HPL[{3}, -S^2])/3 - (220*S^3*HPL[{2, 1}, -S^2])/3 - (22*S^3*Zeta[3])/9) + HPL[{2}, -S^2]*((160 + 7002*S^2 + 30924*S^4 + 136797*S^6)/(1944*S^3) + (Pi^2*(-20 - 40*S^2 - 20*S^4 + 10840*S^6 + 14948*S^8 + 5791*S^10))/(324*S^3*(1 + S^2)^2) - (4*S^3*HPL[{3}, -S^2])/9 + (14*S^3*HPL[{2, 1}, -S^2])/9 - (16*S^3*Zeta[3])/9) + HPL[{1}, -S^2]*((3997*Pi^4*S^3)/1620 + ((1 + S^2)*(6336 + 18097*S^2 + 295779*S^4))/(3888*S^3) + (Pi^2*(1940 + 20743*S^2 + 38012*S^4 + 155120*S^6 + 133090*S^8 + 42971*S^10))/(1944*S^3*(1 + S^2)^2) + ((187*Pi^2*S^3)/18 + (206 + 1764*S^2 + 3134*S^4 + 12605*S^6 + 10446*S^8 + 3377*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (53*S^3*HPL[{2}, -S^2]^2)/3 + (2*(2 + 4*S^2 + 2*S^4 + 29*S^6 + 34*S^8 + 11*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (34*S^3*HPL[{4}, -S^2])/9 - (4*(124 + 248*S^2 + 124*S^4 + 2167*S^6 + 2354*S^8 + 682*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (220*S^3*HPL[{3, 1}, -S^2])/3 + (440*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((2 + 4*S^2 + 2*S^4 - 55*S^6 - 22*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (26*S^3*Zeta[5])/3) + HPL[{1}, -S^2]^2*((52285*Pi^6*S^3)/13608 + (Pi^2*(1 + S^2)*(82727 + 105499*S^2 + 1056428*S^4))/(5832*S^3) + ((1 + S^2)*(772759 + 794066*S^2 + 12649645*S^4))/(17496*S^3) + (Pi^4*(35522 + 207793*S^2 + 324908*S^4 + 1298609*S^6 + 972379*S^8 + 306863*S^10))/(9720*S^3*(1 + S^2)^2) + ((607*Pi^2*S^3)/9 + (664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (148*S^3*HPL[{3}, -S^2]^2)/3 + ((-340*Pi^2*S^3)/9 + (-2828 - 9271*S^2 - 10568*S^4 - 39350*S^6 - 15832*S^8 - 4511*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (4*(2 + 4*S^2 + 2*S^4 + 983*S^6 + 670*S^8 + 11*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (178*S^3*HPL[{6}, -S^2])/3 - (3136*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((-440*Pi^2*S^3)/9 - (4*(-185 + 563*S^2 + 1867*S^4 + 5062*S^6 + 9932*S^8 + 3001*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*(790 + 1580*S^2 + 790*S^4 + 28501*S^6 + 24794*S^8 + 4345*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 156*S^3*HPL[{4, 2}, -S^2] + (2704*S^3*HPL[{5, 1}, -S^2])/3 + ((1568*Pi^2*S^3)/9 + (8*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (1568*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*(448 + 896*S^2 + 448*S^4 + 8773*S^6 + 9134*S^8 + 2464*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2656*S^3*HPL[{4, 1, 1}, -S^2])/3 - (520*(2 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + (2656*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 + (-((1 + S^2)*(4640 + 8971*S^2 + 32009*S^4))/(162*S^3) - (2*Pi^2*(98 + 196*S^2 + 98*S^4 + 4283*S^6 + 3574*S^8 + 539*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + (80*S^3*Zeta[3]^2)/3 + HPL[{3}, -S^2]*(-((1 + S^2)*(12118 + 14507*S^2 + 35779*S^4))/(162*S^3) + (Pi^2*(-274 - 548*S^2 - 274*S^4 - 10453*S^6 - 8978*S^8 - 1507*S^10))/(27*S^3*(1 + S^2)^2) + (3136*S^3*HPL[{2, 1}, -S^2])/3 - (200*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-2*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(9*S^3) - (2*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(27*S^3*(1 + S^2)^2) + (3136*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((2021*Pi^4*S^3)/180 + ((1 + S^2)*(13400 + 9469*S^2 + 411947*S^4))/(972*S^3) + (Pi^2*(531 + 3787*S^2 + 6411*S^4 + 22680*S^6 + 21382*S^8 + 6561*S^10))/(54*S^3*(1 + S^2)^2) - (2*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (452*S^3*HPL[{4}, -S^2])/3 - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{3, 1}, -S^2])/3 + (6272*S^3*HPL[{2, 1, 1}, -S^2])/3 - (224*(2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) - (2*(34 + 68*S^2 + 34*S^4 + 2467*S^6 + 1894*S^8 + 187*S^10)*Zeta[5])/(3*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((200803*Pi^6*S^3)/68040 + (Pi^2*(-18807 + 38628*S^2 + 84123*S^4 + 949795*S^6))/(5832*S^3) + (-378529 + 30609*S^2 + 1193787*S^4 + 20915332*S^6)/(34992*S^3) + (Pi^4*(-10849 + 14656*S^2 + 35942*S^4 + 477515*S^6 + 645955*S^8 + 288011*S^10))/(9720*S^3*(1 + S^2)^2) + (152*S^3*HPL[{3}, -S^2]^2)/3 + ((-269*Pi^2*S^3)/9 + (115 - 421*S^2 - 794*S^4 - 6782*S^6 - 4675*S^8 - 2219*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-10 - 20*S^2 - 10*S^4 - 1671*S^6 - 1374*S^8 - 195*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (26*S^3*HPL[{6}, -S^2])/3 - (1568*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((-1444*Pi^2*S^3)/9 + (-2078 - 10057*S^2 - 13922*S^4 - 70122*S^6 - 56352*S^8 - 20397*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-10 - 20*S^2 - 10*S^4 + 20725*S^6 + 20954*S^8 + 5353*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*(-23 - 46*S^2 - 23*S^4 + 5299*S^6 + 5458*S^8 + 1444*S^10)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + 182*S^3*HPL[{4, 2}, -S^2] + 844*S^3*HPL[{5, 1}, -S^2] + ((3232*Pi^2*S^3)/9 + (4*(202 + 1329*S^2 + 1942*S^4 + 11509*S^6 + 9738*S^8 + 3748*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(-298 + 633*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (32*(-211 - 422*S^2 - 211*S^4 - 757*S^6 - 338*S^8 + 125*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 104*S^3*HPL[{3, 1, 2}, -S^2] + 936*S^3*HPL[{3, 2, 1}, -S^2] + (7168*S^3*HPL[{4, 1, 1}, -S^2])/3 - (16*(292 + 584*S^2 + 292*S^4 + 4051*S^6 + 3398*S^8 + 523*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 26752*S^3*HPL[{3, 1, 1, 1}, -S^2] + (12640*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((-3508 - 8631*S^2 - 8046*S^4 - 32087*S^6)/(162*S^3) + (Pi^2*(-28 - 56*S^2 - 28*S^4 - 5136*S^6 - 5100*S^8 - 1257*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + 16*S^3*Zeta[3]^2 + HPL[{3}, -S^2]*((1867 - 8253*S^2 - 1287*S^4 - 32099*S^6)/(162*S^3) + (Pi^2*(102 + 204*S^2 + 102*S^4 - 10279*S^6 - 10646*S^8 - 2845*S^10))/(54*S^3*(1 + S^2)^2) + (304*S^3*HPL[{2, 1}, -S^2])/3 - 56*S^3*Zeta[3]) + HPL[{2, 1}, -S^2]*((-7417 - 11889*S^2 - 64629*S^4 - 11642*S^6)/(81*S^3) - (2*Pi^2*(598 + 1196*S^2 + 598*S^4 + 5948*S^6 + 4612*S^8 + 485*S^10))/(27*S^3*(1 + S^2)^2) - 48*S^3*Zeta[3]) - (2*(40 + 80*S^2 + 40*S^4 + 3997*S^6 + 3662*S^8 + 748*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((95363*Pi^6*S^3)/68040 + (Pi^2*(93420 + 212832*S^2 + 1927913*S^4))/(23328*S) + (818490 + 1126065*S^2 + 20915332*S^4)/(69984*S) + (Pi^4*(44088 + 66132*S^2 + 593914*S^4 + 733451*S^6 + 313663*S^8))/(19440*S*(1 + S^2)^2) + (2*(22 + 44*S^2 + 22*S^4 + 400*S^6 + 428*S^8 + 121*S^10)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)^2) + (62*S^3*HPL[{1}, -S^2]^6)/9 + ((73*Pi^2*S^3)/4 + (-62 + 1050*S^2 + 1654*S^4 + 15399*S^6 + 17122*S^8 + 7425*S^10)/(72*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (205*S^3*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((749*Pi^2*S^3)/54 + (2876 + 16291*S^2 + 25232*S^4 + 97286*S^6 + 75484*S^8 + 23495*S^10)/(324*S^3*(1 + S^2)^2) + (392*S^3*HPL[{2}, -S^2])/9) - S^3*HPL[{3}, -S^2]^2 + ((37*Pi^2*S^3)/18 + (-82 + 139*S^2 + 440*S^4 + 3140*S^6 + 5350*S^8 + 2141*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-4 - 8*S^2 - 4*S^4 - 9*S^6 + 126*S^8 + 99*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + 13*S^3*HPL[{6}, -S^2] - (826*S^3*HPL[{2, 1}, -S^2]^2)/3 + ((-227*Pi^2*S^3)/3 + (718 - 2131*S^2 - 4430*S^4 - 45715*S^6 - 53426*S^8 - 23188*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((2 + 4*S^2 + 2*S^4 + 861*S^6 + 714*S^8 + 105*S^10)*HPL[{3, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + (2*(-23 - 46*S^2 - 23*S^4 + 660*S^6 + 516*S^8 + 57*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (S^3*HPL[{4, 2}, -S^2])/3 - 10*S^3*HPL[{5, 1}, -S^2] + ((464*Pi^2*S^3)/3 + (2*(-299 + 1217*S^2 + 2356*S^4 + 23299*S^6 + 27209*S^8 + 11806*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (4*(-306 - 612*S^2 - 306*S^4 - 1897*S^6 - 1214*S^8 + 38*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*(-939 - 1878*S^2 - 939*S^4 - 5459*S^6 - 3442*S^8 + 148*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*S^3*HPL[{3, 1, 2}, -S^2])/3 + 548*S^3*HPL[{3, 2, 1}, -S^2] + (4960*S^3*HPL[{4, 1, 1}, -S^2])/3 + (4*(-654 - 1308*S^2 - 654*S^4 - 3319*S^6 - 1934*S^8 + 209*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3376*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 + (6880*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((Pi^2*S^3*(26 + 216*S^2 + 149*S^4))/(18*(1 + S^2)^2) + (-218 - 83*S^2 + 266*S^4)/(54*S))*Zeta[3] + (4*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*(((1 + S^2)*(7210 + 9407*S^2 + 75133*S^4))/(486*S^3) + (Pi^2*(1166 + 2332*S^2 + 1166*S^4 + 19895*S^6 + 21814*S^8 + 6413*S^10))/(162*S^3*(1 + S^2)^2) + ((614 + 1228*S^2 + 614*S^4 + 10433*S^6 + 11458*S^8 + 3377*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) - (88*S^3*HPL[{3}, -S^2])/9 - (1568*S^3*HPL[{2, 1}, -S^2])/9 - (164*S^3*Zeta[3])/9) + HPL[{3}, -S^2]*((-56 - 1131*S^2 + 11100*S^4 + 13296*S^6)/(648*S^3) + (Pi^2*(66 + 132*S^2 + 66*S^4 - 515*S^6 - 430*S^8 - 65*S^10))/(108*S^3*(1 + S^2)^2) - (4*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-5132 - 5409*S^2 - 45294*S^4 - 829*S^6)/(108*S^3) + (Pi^2*(-1134 - 2268*S^2 - 1134*S^4 - 5204*S^6 - 2812*S^8 + 493*S^10))/(54*S^3*(1 + S^2)^2) + (4*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((289*Pi^4*S^3)/40 + (-5805 + 31851*S^2 + 91629*S^4 + 476848*S^6)/(1944*S^3) + (Pi^2*(-1078 + 4210*S^2 + 8336*S^4 + 83837*S^6 + 102256*S^8 + 44255*S^10))/(648*S^3*(1 + S^2)^2) + ((2 + 4*S^2 + 2*S^4 - 425*S^6 - 346*S^8 - 47*S^10)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^2) + (5*S^3*HPL[{4}, -S^2])/3 + (2*(-306 - 612*S^2 - 306*S^4 - 1897*S^6 - 1214*S^8 + 38*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (820*S^3*HPL[{3, 1}, -S^2])/3 + (1652*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((-4 - 8*S^2 - 4*S^4 - 452*S^6 - 436*S^8 - 101*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((8449*Pi^4*S^3)/1080 + ((1 + S^2)*(36163 + 40790*S^2 + 482167*S^4))/(1944*S^3) + (Pi^2*(688 + 4488*S^2 + 7306*S^4 + 28387*S^6 + 23175*S^8 + 7282*S^10))/(108*S^3*(1 + S^2)^2) + ((211*Pi^2*S^3)/6 + (399 + 2455*S^2 + 3957*S^4 + 15006*S^6 + 12220*S^8 + 3819*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (215*S^3*HPL[{2}, -S^2]^2)/3 + ((2 + 4*S^2 + 2*S^4 - 121*S^6 - 66*S^8 + 11*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) - (8*S^3*HPL[{4}, -S^2])/3 + ((-614 - 1228*S^2 - 614*S^4 - 10433*S^6 - 11458*S^8 - 3377*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (772*S^3*HPL[{3, 1}, -S^2])/3 + (1568*S^3*HPL[{2, 1, 1}, -S^2])/3 - (2*(8 + 16*S^2 + 8*S^4 + 413*S^6 + 334*S^8 + 44*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (S^3*(76 + 620*S^2 + 427*S^4)*Zeta[5])/(9*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(6554 + 9667*S^2 + 95267*S^4))/(1296*S^3) + ((1 + S^2)*(186293 + 179866*S^2 + 3186803*S^4))/(11664*S^3) + (Pi^4*(7348 + 14696*S^2 + 7348*S^4 + 116455*S^6 + 131522*S^8 + 40414*S^10))/(3240*S^3*(1 + S^2)^2) + ((298 + 596*S^2 + 298*S^4 + 5509*S^6 + 5858*S^8 + 1639*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((-25*Pi^2*S^3)/9 + (-242 - 331*S^2 + 190*S^4 + 424*S^6 + 2630*S^8 + 901*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((46 + 92*S^2 + 46*S^4 + 109*S^6 + 410*S^8 + 253*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - 8*S^3*HPL[{5}, -S^2] + ((-211*Pi^2*S^3)/3 + (-399 - 2455*S^2 - 3957*S^4 - 15006*S^6 - 12220*S^8 - 3819*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(152 + 304*S^2 + 152*S^4 + 2573*S^6 + 2830*S^8 + 836*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 28*S^3*HPL[{3, 2}, -S^2] + (268*S^3*HPL[{4, 1}, -S^2])/3 + (2*(614 + 1228*S^2 + 614*S^4 + 10433*S^6 + 11458*S^8 + 3377*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1720*S^3*HPL[{2, 2, 1}, -S^2])/3 + (4984*S^3*HPL[{3, 1, 1}, -S^2])/3 - (3136*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-41*Pi^2*S^3)/9 + (-97 - 335*S^2 - 421*S^4 - 2014*S^6 - 569*S^8 - 214*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(4358 + 5377*S^2 + 51005*S^4))/(216*S^3) + (Pi^2*(1070 + 2140*S^2 + 1070*S^4 + 17279*S^6 + 19366*S^8 + 5885*S^10))/(108*S^3*(1 + S^2)^2) - 14*S^3*HPL[{3}, -S^2] - (860*S^3*HPL[{2, 1}, -S^2])/3 - 26*S^3*Zeta[3]) - 26*S^3*Zeta[5])) + HPL[{0}, S^2]*((Pi^4*(14754 + 44571*S^2 + 231178*S^4))/(6480*S) + (Pi^6*S^3*(4363901 + 5739958*S^2 + 2123018*S^4))/(408240*(1 + S^2)^2) + (Pi^2*(686352 + 1130754*S^2 + 13763651*S^4))/(69984*S) + (11333964 + 9740874*S^2 + 179723545*S^4)/(209952*S) + (56*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)^2) + (64*S^3*HPL[{1}, -S^2]^7)/9 + ((-38 - 76*S^2 - 38*S^4 + 5249*S^6 + 6250*S^8 + 2063*S^10)*HPL[{2}, -S^2]^3)/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((482*Pi^2*S^3)/27 + (88 + 475*S^2 + 724*S^4 + 3046*S^6 + 2020*S^8 + 655*S^10)/(9*S^3*(1 + S^2)^2) + (200*S^3*HPL[{2}, -S^2])/3) - (2*(2 + 4*S^2 + 2*S^4 + 59*S^6 + 94*S^8 + 41*S^10)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + (-(Pi^2*S^3)/9 + (-15 + 105*S^2 + 345*S^4 + 2504*S^6 + 2569*S^8 + 1118*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((40 + 80*S^2 + 40*S^4 + 742*S^6 + 608*S^8 + 85*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) - 24*S^3*HPL[{7}, -S^2] - (4*(12 + 24*S^2 + 12*S^4 + 5701*S^6 + 6698*S^8 + 2173*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((128*Pi^2*S^3)/9 + (-158 - 57*S^2 + 118*S^4 + 1924*S^6 - 96*S^8 - 179*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + (42*Pi^2*S^3 - (2*(279 + 174*S^2 + 198*S^4 - 2368*S^6 + 1351*S^8 + 746*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((6 - 113*S^6)*HPL[{4, 2}, -S^2])/(9*S^3) + (52*S^3*HPL[{4, 3}, -S^2])/3 - (2*(6 + 12*S^2 + 6*S^4 + 845*S^6 + 1042*S^8 + 359*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (142*S^3*HPL[{5, 2}, -S^2])/3 + (260*S^3*HPL[{6, 1}, -S^2])/3 + ((40*Pi^2*S^3)/9 - (4*(-1797 - 7539*S^2 - 11697*S^4 - 31892*S^6 - 11398*S^8 + 427*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-136*Pi^2*S^3)/9 - (2*(-10952 - 45559*S^2 - 70892*S^4 - 191630*S^6 - 69784*S^8 + 2113*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (2*(6 + 67*S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) + (2*(-146 - 292*S^2 - 146*S^4 + 21063*S^6 + 25134*S^8 + 8319*S^10)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 188*S^3*HPL[{3, 2, 2}, -S^2] - (1600*S^3*HPL[{3, 3, 1}, -S^2])/3 + (4*(-222 - 444*S^2 - 222*S^4 + 32137*S^6 + 38234*S^8 + 12607*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1604*S^3*HPL[{4, 1, 2}, -S^2])/3 - (4676*S^3*HPL[{4, 2, 1}, -S^2])/3 - (9128*S^3*HPL[{5, 1, 1}, -S^2])/3 + ((512*Pi^2*S^3)/9 + (4*(-3686 - 15256*S^2 - 23972*S^4 - 63733*S^6 - 23588*S^8 + 743*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (608*S^3*HPL[{2, 2, 2, 1}, -S^2])/3 - (16*(-35 - 70*S^2 - 35*S^4 + 5568*S^6 + 6636*S^8 + 2193*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (880*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 - (880*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 - (2704*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 - (8224*S^3*HPL[{4, 1, 1, 1}, -S^2])/3 + (160*(-2 - 4*S^2 - 2*S^4 + 375*S^6 + 450*S^8 + 150*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (544*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 544*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] - (4480*S^3*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + 960*S^3*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-373*Pi^4*S^3)/270 - (5*(2004 + 1320*S^2 + 4709*S^4))/(324*S) + (Pi^2*(-444 - 666*S^2 - 4381*S^4 - 1394*S^6 - 619*S^8))/(162*S*(1 + S^2)^2))*Zeta[3] - (2*S^3*(-151 - 98*S^2 + 2*S^4)*Zeta[3]^2)/(9*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-2244 + 16923*S^2 + 37776*S^4 + 180337*S^6)/(81*S^3) + (4*Pi^2*(-40 - 80*S^2 - 40*S^4 + 8593*S^6 + 10706*S^8 + 3733*S^10))/(27*S^3*(1 + S^2)^2) - (1312*S^3*Zeta[3])/3) + HPL[{2}, -S^2]^2*((3508 + 21195*S^2 + 35532*S^4 + 173203*S^6)/(648*S^3) + (Pi^2*(20 + 40*S^2 + 20*S^4 + 17001*S^6 + 20778*S^8 + 7083*S^10))/(108*S^3*(1 + S^2)^2) - 24*S^3*HPL[{3}, -S^2] + (76*S^3*HPL[{2, 1}, -S^2])/3 - (160*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(972*S^3) + (Pi^2*(688 + 1376*S^2 + 688*S^4 + 14629*S^6 + 14798*S^8 + 3784*S^10))/(81*S^3*(1 + S^2)^2) + (125*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) - (68*S^3*HPL[{3}, -S^2])/9 - (1000*S^3*HPL[{2, 1}, -S^2])/3 - (332*S^3*Zeta[3])/9) + HPL[{4}, -S^2]*((-392 - 1122*S^2 + 7536*S^4 + 19411*S^6)/(324*S^3) + (Pi^2*(26 + 52*S^2 + 26*S^4 + 1155*S^6 + 1350*S^8 + 435*S^10))/(54*S^3*(1 + S^2)^2) + (68*S^3*HPL[{2, 1}, -S^2])/3 + (4*S^3*Zeta[3])/3) + HPL[{3, 1}, -S^2]*((2006 - 16443*S^2 - 36594*S^4 - 178983*S^6)/(162*S^3) - (10*Pi^2*(-9 - 18*S^2 - 9*S^4 + 1697*S^6 + 2098*S^8 + 725*S^10))/(27*S^3*(1 + S^2)^2) + (640*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((76*Pi^4*S^3)/27 + (-36803 - 50412*S^2 - 544935*S^4 - 31094*S^6)/(486*S^3) + (Pi^2*(-2623 - 11756*S^2 - 19318*S^4 - 49359*S^6 - 18882*S^8 + 852*S^10))/(81*S^3*(1 + S^2)^2) + 48*S^3*HPL[{3, 1}, -S^2] + (272*S^3*HPL[{2, 1, 1}, -S^2])/3 - (4*(-86 - 172*S^2 - 86*S^4 - 733*S^6 - 482*S^8 + 5*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*(-(Pi^4*S^3) + (5855 - 6870*S^2 + 47499*S^4 + 57497*S^6)/(972*S^3) + (Pi^2*(254 + 817*S^2 + 1730*S^4 + 3387*S^6 + 4518*S^8 + 1506*S^10))/(324*S^3*(1 + S^2)^2) - (20*S^3*HPL[{4}, -S^2])/3 + (2*(98 + 196*S^2 + 98*S^4 + 879*S^6 + 846*S^8 + 195*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (224*S^3*HPL[{3, 1}, -S^2])/3 - (448*S^3*HPL[{2, 1, 1}, -S^2])/3 - (2*(2 + 4*S^2 + 2*S^4 + 43*S^6 + 38*S^8 + 7*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((4061*Pi^4*S^3)/270 + ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(1458*S^3) + (Pi^2*(1850 + 11061*S^2 + 17534*S^4 + 72512*S^6 + 52056*S^8 + 16787*S^10))/(162*S^3*(1 + S^2)^2) + (80*Pi^2*S^3 + (4*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (1568*S^3*HPL[{2}, -S^2]^2)/9 - (8*(10 + 20*S^2 + 10*S^4 + 208*S^6 + 212*S^8 + 55*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (184*S^3*HPL[{4}, -S^2])/9 - (500*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2000*S^3*HPL[{3, 1}, -S^2])/3 + (4000*S^3*HPL[{2, 1, 1}, -S^2])/3 - (8*(40 + 80*S^2 + 40*S^4 + 967*S^6 + 938*S^8 + 220*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + ((-52*Pi^2*S^3)/9 - (2*(162 + 243*S^2 + 1885*S^4 + 1097*S^6 + 463*S^8))/(27*S*(1 + S^2)^2))*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(6143 + 10462*S^2 + 79547*S^4))/(486*S^3) + ((1 + S^2)*(126326 + 155803*S^2 + 1865477*S^4))/(2916*S^3) + (Pi^4*(15602 + 31204*S^2 + 15602*S^4 + 305105*S^6 + 317818*S^8 + 85811*S^10))/(3240*S^3*(1 + S^2)^2) + (196*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-22*Pi^2*S^3)/9 + (2*(-85 - 207*S^2 - 133*S^4 - 232*S^6 + 66*S^8 + 83*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((34 + 68*S^2 + 34*S^4 + 1015*S^6 + 926*S^8 + 187*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (92*S^3*HPL[{5}, -S^2])/3 + (-240*Pi^2*S^3 - (4*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(62 + 124*S^2 + 62*S^4 + 1466*S^6 + 1432*S^8 + 341*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (304*S^3*HPL[{3, 2}, -S^2])/3 + (728*S^3*HPL[{4, 1}, -S^2])/3 + (500*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (6272*S^3*HPL[{2, 2, 1}, -S^2])/3 + (18544*S^3*HPL[{3, 1, 1}, -S^2])/3 - 4000*S^3*HPL[{2, 1, 1, 1}, -S^2] + ((-188*Pi^2*S^3)/9 + (-256 - 943*S^2 - 1180*S^4 - 4204*S^6 - 2428*S^8 - 709*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(7142 + 11923*S^2 + 91373*S^4))/(162*S^3) + (Pi^2*(1246 + 2492*S^2 + 1246*S^4 + 26293*S^6 + 26666*S^8 + 6853*S^10))/(54*S^3*(1 + S^2)^2) - (152*S^3*HPL[{3}, -S^2])/3 - (3136*S^3*HPL[{2, 1}, -S^2])/3 - (328*S^3*Zeta[3])/3) - (260*S^3*Zeta[5])/3) + HPL[{2}, -S^2]*((Pi^2*(-2084 + 23925*S^2 + 68700*S^4 + 317134*S^6))/(1944*S^3) + (6492 + 228585*S^2 + 719166*S^4 + 3631627*S^6)/(5832*S^3) + (Pi^4*(-524 - 1048*S^2 - 524*S^4 + 182594*S^6 + 235888*S^8 + 85619*S^10))/(3240*S^3*(1 + S^2)^2) + ((-20*Pi^2*S^3)/3 + (234 + 93*S^2 - 126*S^4 - 2650*S^6 + 508*S^8 + 437*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((6 + 12*S^2 + 6*S^4 + 289*S^6 + 482*S^8 + 217*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + 6*S^3*HPL[{5}, -S^2] + ((-20*Pi^2*S^3)/9 + (2*(-1797 - 7539*S^2 - 11697*S^4 - 31892*S^6 - 11398*S^8 + 427*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(22 + 44*S^2 + 22*S^4 + 11377*S^6 + 13346*S^8 + 4321*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 96*S^3*HPL[{3, 2}, -S^2] + (796*S^3*HPL[{4, 1}, -S^2])/3 + (8*(12 + 24*S^2 + 12*S^4 + 5701*S^6 + 6698*S^8 + 2173*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (304*S^3*HPL[{2, 2, 1}, -S^2])/3 + (464*S^3*HPL[{3, 1, 1}, -S^2])/3 - (272*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + (-20*Pi^2*S^3 + (30 - 104*S^2 - 216*S^4 - 1957*S^6 - 1606*S^8 - 715*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] - (212*S^3*Zeta[5])/3) + HPL[{1}, -S^2]*((248987*Pi^6*S^3)/68040 + (Pi^2*(1 + S^2)*(112136 + 183709*S^2 + 2035859*S^4))/(11664*S^3) + ((1 + S^2)*(772759 + 794066*S^2 + 12649645*S^4))/(17496*S^3) + (Pi^4*(7901 + 57509*S^2 + 96719*S^4 + 401984*S^6 + 308417*S^8 + 99740*S^10))/(3240*S^3*(1 + S^2)^2) + ((551*Pi^2*S^3)/9 + (664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (236*S^3*HPL[{2}, -S^2]^3)/3 - (8*S^3*HPL[{3}, -S^2]^2)/3 + ((80*Pi^2*S^3)/9 + (-286 + 43*S^2 + 1154*S^4 + 7832*S^6 + 6100*S^8 + 2405*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(2 + 4*S^2 + 2*S^4 + 80*S^6 + 68*S^8 + 11*S^10)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^2) + (146*S^3*HPL[{6}, -S^2])/3 - (3136*S^3*HPL[{2, 1}, -S^2]^2)/3 + (-240*Pi^2*S^3 - (2*(494 + 3013*S^2 + 4874*S^4 + 20840*S^6 + 14188*S^8 + 4703*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (76*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*(194 + 388*S^2 + 194*S^4 + 4343*S^6 + 4318*S^8 + 1067*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 72*S^3*HPL[{5, 1}, -S^2] + (480*Pi^2*S^3 + (8*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (1568*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*(578 + 1156*S^2 + 578*S^4 + 13610*S^6 + 13312*S^8 + 3179*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 1888*S^3*HPL[{3, 2, 1}, -S^2] + (17360*S^3*HPL[{4, 1, 1}, -S^2])/3 - (1000*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - 4000*S^3*HPL[{3, 1, 1, 1}, -S^2] + 8000*S^3*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((1 + S^2)*(1826 + 1165*S^2 + 4025*S^4))/(54*S^3) + (Pi^2*(-74 - 148*S^2 - 74*S^4 - 2099*S^6 - 1942*S^8 - 407*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + (68*S^3*Zeta[3]^2)/3 + HPL[{3}, -S^2]*(((1 + S^2)*(-2000 - 2041*S^2 + 8305*S^4))/(162*S^3) - (2*Pi^2*(4 + 8*S^2 + 4*S^4 + 121*S^6 + 110*S^8 + 22*S^10))/(27*S^3*(1 + S^2)^2) + (304*S^3*HPL[{2, 1}, -S^2])/3 - (16*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(7142 + 11923*S^2 + 91373*S^4))/(81*S^3) + (Pi^2*(-1246 - 2492*S^2 - 1246*S^4 - 26293*S^6 - 26666*S^8 - 6853*S^10))/(27*S^3*(1 + S^2)^2) + (656*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((2155*Pi^4*S^3)/108 + ((1 + S^2)*(34202 + 57307*S^2 + 596135*S^4))/(972*S^3) + (Pi^2*(2098 + 14372*S^2 + 24112*S^4 + 100621*S^6 + 74240*S^8 + 24337*S^10))/(162*S^3*(1 + S^2)^2) - (38*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*S^3*HPL[{4}, -S^2])/3 - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{3, 1}, -S^2])/3 + (6272*S^3*HPL[{2, 1, 1}, -S^2])/3 - (82*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) - (2*(18 + 36*S^2 + 18*S^4 + 489*S^6 + 458*S^8 + 99*S^10)*Zeta[5])/(3*S^3*(1 + S^2)^2))) - (2*S^3*(1604 + 1276*S^2 + 155*S^4)*Zeta[7])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^4*(1 + S^2)*(175529 + 240880*S^2 + 1965665*S^4))/(58320*S^3) + (Pi^2*(1 + S^2)*(146315 + 163824*S^2 + 2305919*S^4))/(11664*S^3) + ((1 + S^2)*(11329918 + 8757449*S^2 + 179723545*S^4))/(209952*S^3) + (Pi^6*(75346 + 150692*S^2 + 75346*S^4 + 1355533*S^6 + 1456226*S^8 + 414403*S^10))/(81648*S^3*(1 + S^2)^2) + (83*(2 + 11*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + (37*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-80*Pi^2*S^3)/3 + (-1154 - 2383*S^2 - 1334*S^4 - 4448*S^6 + 5402*S^8 + 1969*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((238 + 476*S^2 + 238*S^4 - 293*S^6 + 1550*S^8 + 1309*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) - 20*S^3*HPL[{7}, -S^2] - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((1652*Pi^2*S^3)/9 + (2*(552 + 2293*S^2 + 3048*S^4 + 14760*S^6 + 6244*S^8 + 2199*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((5636*Pi^2*S^3)/9 + (12764 + 50545*S^2 + 65432*S^4 + 305030*S^6 + 128224*S^8 + 44093*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (13*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^2) - (188*S^3*HPL[{4, 3}, -S^2])/3 + (52*(6 + 12*S^2 + 6*S^4 + 189*S^6 + 170*S^8 + 33*S^10)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - 136*S^3*HPL[{5, 2}, -S^2] + (196*S^3*HPL[{6, 1}, -S^2])/3 + ((4856*Pi^2*S^3)/9 + (4*(664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((10592*Pi^2*S^3)/9 + (8*(1807 + 10844*S^2 + 17287*S^4 + 68974*S^6 + 52100*S^8 + 16612*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (664*(2 + 11*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (6520*S^3*HPL[{3, 2, 2}, -S^2])/3 - (19936*S^3*HPL[{3, 3, 1}, -S^2])/3 + (8*(386 + 772*S^2 + 386*S^4 - 865*S^6 + 2254*S^8 + 2123*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (19624*S^3*HPL[{4, 1, 2}, -S^2])/3 - (60808*S^3*HPL[{4, 2, 1}, -S^2])/3 - 41760*S^3*HPL[{5, 1, 1}, -S^2] + ((-3136*Pi^2*S^3)/9 - (16*(22 + 200*S^2 + 209*S^4 + 1070*S^6 + 457*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - (32*(56 + 112*S^2 + 56*S^4 - 439*S^6 + 118*S^8 + 308*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (12544*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 + (12544*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 + (12544*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 + (42944*S^3*HPL[{4, 1, 1, 1}, -S^2])/3 + (1040*(2 + 11*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) - (25088*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 25088*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] - (155840*S^3*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + ((-1013*Pi^4*S^3)/90 - ((1 + S^2)*(3467 + 7973*S^2 + 30698*S^4))/(162*S^3) + (Pi^2*(-213 - 959*S^2 - 1365*S^4 - 7302*S^6 - 2759*S^8 - 1068*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + (2*(6 + 12*S^2 + 6*S^4 + 153*S^6 + 146*S^8 + 33*S^10)*Zeta[3]^2)/(3*S^3*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((4*(1 + S^2)*(139 + 164*S^2 + 3298*S^4))/(9*S^3) + (4*Pi^2*(502 + 1004*S^2 + 502*S^4 + 6289*S^6 + 7874*S^8 + 2761*S^10))/(27*S^3*(1 + S^2)^2) - (6272*S^3*Zeta[3])/3) + HPL[{2}, -S^2]^2*(((1 + S^2)*(4849 + 6653*S^2 + 41650*S^4))/(162*S^3) + (Pi^2*(230 + 460*S^2 + 230*S^4 + 4907*S^6 + 4958*S^8 + 1265*S^10))/(18*S^3*(1 + S^2)^2) - (932*S^3*HPL[{3}, -S^2])/3 - 236*S^3*Zeta[3]) + HPL[{4}, -S^2]*(-((1 + S^2)*(8089 + 8492*S^2 + 7027*S^4))/(162*S^3) + (Pi^2*(-178 - 356*S^2 - 178*S^4 - 7099*S^6 - 6038*S^8 - 979*S^10))/(54*S^3*(1 + S^2)^2) + (904*S^3*HPL[{2, 1}, -S^2])/3 - (112*S^3*Zeta[3])/3) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(-2420 - 1201*S^2 + 47521*S^4))/(81*S^3) - (8*Pi^2*(104 + 208*S^2 + 104*S^4 + 1067*S^6 + 1474*S^8 + 572*S^10))/(27*S^3*(1 + S^2)^2) + (3232*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-2021*Pi^4*S^3)/90 - ((1 + S^2)*(13400 + 9469*S^2 + 411947*S^4))/(486*S^3) + (Pi^2*(-531 - 3787*S^2 - 6411*S^4 - 22680*S^6 - 21382*S^8 - 6561*S^10))/(27*S^3*(1 + S^2)^2) + (6272*S^3*HPL[{3, 1}, -S^2])/3 + (12544*S^3*HPL[{2, 1, 1}, -S^2])/3 + (448*(2 + 4*S^2 + 2*S^4 + 74*S^6 + 64*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-601*Pi^4*S^3)/45 - ((1 + S^2)*(31418 + 38689*S^2 + 84815*S^4))/(486*S^3) + (Pi^2*(-434 - 1581*S^2 - 1916*S^4 - 8894*S^6 - 3279*S^8 - 1118*S^10))/(27*S^3*(1 + S^2)^2) + (172*S^3*HPL[{4}, -S^2])/3 + (4*(226 + 452*S^2 + 226*S^4 + 8299*S^6 + 7190*S^8 + 1243*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*S^3*HPL[{3, 1}, -S^2])/3 - (6272*S^3*HPL[{2, 1, 1}, -S^2])/3 - (8*(4 + 8*S^2 + 4*S^4 + 97*S^6 + 94*S^8 + 22*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + ((-838*Pi^2*S^3)/9 - (2*(20 + 134*S^2 + 226*S^4 + 1805*S^6 + 393*S^8 + 220*S^10))/(3*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(6026 + 7345*S^2 + 90581*S^4))/(648*S^3) + ((1 + S^2)*(10001 + 3776*S^2 + 483629*S^4))/(972*S^3) + (Pi^4*(13150 + 26300*S^2 + 13150*S^4 + 181459*S^6 + 217406*S^8 + 72325*S^10))/(3240*S^3*(1 + S^2)^2) + ((-826*Pi^2*S^3)/9 + (-552 - 2293*S^2 - 3048*S^4 - 14760*S^6 - 6244*S^8 - 2199*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (113*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (328*S^3*HPL[{5}, -S^2])/3 + ((-2428*Pi^2*S^3)/9 - (2*(664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3416*S^3*HPL[{3, 2}, -S^2])/3 + (10280*S^3*HPL[{4, 1}, -S^2])/3 + (1568*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*S^3*HPL[{3, 1, 1}, -S^2])/3 - (12544*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-862*Pi^2*S^3)/9 - (2*(267 + 1123*S^2 + 1503*S^4 + 7332*S^6 + 3058*S^8 + 1077*S^10))/(9*S^3*(1 + S^2)^2))*Zeta[3] - (1444*S^3*Zeta[5])/3) - 644*S^3*Zeta[7])) + HPL[{0}, S^2]*((-2294333*Pi^8*S^3)/8164800 + (-54851196 - 28372179*S^2 - 667256405*S^4)/(1259712*S) + (Pi^2*(-2588658 - 2531301*S^2 - 46936544*S^4))/(419904*S) + (Pi^4*(-1131756 - 2868414*S^2 - 26892977*S^4))/(1399680*S) + (Pi^6*(-1093830 - 1640745*S^2 - 14253850*S^4 - 16197911*S^6 - 6972742*S^8))/(2449440*S*(1 + S^2)^2) - (8*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)^2) - (8*S^3*HPL[{1}, -S^2]^8)/9 + ((-529*Pi^2*S^3)/54 + (387 - 1242*S^2 - 2367*S^4 - 28403*S^6 - 28204*S^8 - 13283*S^10)/(324*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^3 - (41*S^3*HPL[{2}, -S^2]^4)/4 + HPL[{1}, -S^2]^6*((-241*Pi^2*S^3)/81 + (-88 - 475*S^2 - 724*S^4 - 3046*S^6 - 2020*S^8 - 655*S^10)/(54*S^3*(1 + S^2)^2) - (100*S^3*HPL[{2}, -S^2])/9) + ((17*Pi^2*S^3)/18 + (96 + 213*S^2 + 150*S^4 + 769*S^6 + 1262*S^8 + 670*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + (4*S^3*HPL[{4}, -S^2]^2)/3 + ((-209*Pi^2*S^3)/18 + (-175 - 368*S^2 - 202*S^4 - 1013*S^6 - 1039*S^8 - 473*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{6}, -S^2] + ((125 + 250*S^2 + 125*S^4 - 833*S^6 - 862*S^8 - 230*S^10)*HPL[{7}, -S^2])/(9*S^3*(1 + S^2)^2) - (376*S^3*HPL[{8}, -S^2])/3 + ((364*Pi^2*S^3)/3 + (195 + 2742*S^2 + 3723*S^4 + 32020*S^6 + 30770*S^8 + 14038*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - 508*S^3*HPL[{3, 1}, -S^2]^2 + ((7*Pi^2*S^3)/18 + (3 - 42*S^2 - 90*S^4 + 313*S^6 + 412*S^8)/(54*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((20 + 40*S^2 + 20*S^4 - 212*S^6 - 268*S^8 - 95*S^10)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + ((139*Pi^2*S^3)/9 + (-41 + 5*S^2 + 157*S^4 + 3495*S^6 + 4611*S^8 + 2199*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + ((118 + 236*S^2 + 118*S^4 - 1253*S^6 - 1498*S^8 - 497*S^10)*HPL[{5, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + 2*S^3*HPL[{5, 3}, -S^2] + ((88 + 176*S^2 + 88*S^4 - 294*S^6 - 504*S^8 - 231*S^10)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 3*S^3*HPL[{6, 2}, -S^2] + 112*S^3*HPL[{7, 1}, -S^2] - (6136*S^3*HPL[{2, 1, 1}, -S^2]^2)/3 + ((-8*Pi^2*S^3)/9 + (6 - 27*S^2 - 54*S^4 - 337*S^6)/(54*S^3))*HPL[{3, 1, 2}, -S^2] + (-236*Pi^2*S^3 + (518 - 1661*S^2 - 3190*S^4 - 38028*S^6 - 37848*S^8 - 17823*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] + ((-110 - 220*S^2 - 110*S^4 + 3749*S^6 + 4618*S^8 + 1589*S^10)*HPL[{3, 2, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + (8*(-6 - 12*S^2 - 6*S^4 + 232*S^6 + 276*S^8 + 91*S^10)*HPL[{3, 3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (64*S^3*HPL[{3, 3, 2}, -S^2])/3 + ((-6526*Pi^2*S^3)/9 - (2*(-1232 + 3713*S^2 + 7291*S^4 + 87518*S^6 + 87073*S^8 + 40961*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((-146 - 292*S^2 - 146*S^4 + 5575*S^6 + 6638*S^8 + 2191*S^10)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (140*S^3*HPL[{4, 1, 3}, -S^2])/3 + ((-434 - 868*S^2 - 434*S^4 + 16615*S^6 + 19502*S^8 + 6319*S^10)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (61*S^3*HPL[{4, 2, 2}, -S^2])/3 - (268*S^3*HPL[{4, 3, 1}, -S^2])/3 + (2*(-450 - 900*S^2 - 450*S^4 + 15997*S^6 + 18722*S^8 + 6043*S^10)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (146*S^3*HPL[{5, 1, 2}, -S^2])/3 - (1106*S^3*HPL[{5, 2, 1}, -S^2])/3 - (3212*S^3*HPL[{6, 1, 1}, -S^2])/3 + ((16528 + 21207*S^2 + 168816*S^4 + 2409*S^6)/(81*S^3) - (2*Pi^2*(-1326 - 2652*S^2 - 1326*S^4 - 9107*S^6 - 5254*S^8 + 613*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (16*(-196 - 392*S^2 - 196*S^4 - 1535*S^6 - 946*S^8 + 58*S^10)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (504*Pi^2*S^3 + (2*(-800 + 2675*S^2 + 5140*S^4 + 60978*S^6 + 60936*S^8 + 28623*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (2*(-4666 - 9332*S^2 - 4666*S^4 - 38721*S^6 - 24642*S^8 + 879*S^10)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*(-4666 - 9332*S^2 - 4666*S^4 - 38721*S^6 - 24642*S^8 + 879*S^10)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 4*S^3*HPL[{3, 1, 2, 2}, -S^2] + (2*(-9370 - 18740*S^2 - 9370*S^4 - 75561*S^6 - 47346*S^8 + 2271*S^10)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 4*S^3*HPL[{3, 2, 1, 2}, -S^2] + 1996*S^3*HPL[{3, 2, 2, 1}, -S^2] + 6000*S^3*HPL[{3, 3, 1, 1}, -S^2] + (4*(-14018 - 28036*S^2 - 14018*S^4 - 112869*S^6 - 70626*S^8 + 3465*S^10)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 4*S^3*HPL[{4, 1, 1, 2}, -S^2] + 6004*S^3*HPL[{4, 1, 2, 1}, -S^2] + 18004*S^3*HPL[{4, 2, 1, 1}, -S^2] + 36168*S^3*HPL[{5, 1, 1, 1}, -S^2] + ((-9152*Pi^2*S^3)/9 - (4*(-726 + 2904*S^2 + 5448*S^4 + 61879*S^6 + 62216*S^8 + 29155*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(-380 - 760*S^2 - 380*S^4 - 3511*S^6 - 2318*S^8 + 17*S^10)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*(-380 - 760*S^2 - 380*S^4 - 3511*S^6 - 2318*S^8 + 17*S^10)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (11936*S^3*HPL[{2, 2, 1, 2, 1}, -S^2])/3 + 11936*S^3*HPL[{2, 2, 2, 1, 1}, -S^2] + (16*(1873 + 3746*S^2 + 1873*S^4 + 17838*S^6 + 11952*S^8 + 45*S^10)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 23888*S^3*HPL[{3, 1, 1, 1, 2}, -S^2] - (119408*S^3*HPL[{3, 1, 1, 2, 1}, -S^2])/3 - 47760*S^3*HPL[{3, 1, 2, 1, 1}, -S^2] - (298448*S^3*HPL[{3, 2, 1, 1, 1}, -S^2])/3 - 298656*S^3*HPL[{4, 1, 1, 1, 1}, -S^2] - (80*(-54 - 108*S^2 - 54*S^4 - 425*S^6 - 250*S^8 + 25*S^10)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (25216*S^3*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/3 - 16960*S^3*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((-10*Pi^2*S^3)/9 + (-54 - 81*S^2 - 443*S^4 - 157*S^6 - 47*S^8)/(27*S*(1 + S^2)^2))*Zeta[3]^2 + HPL[{4, 1}, -S^2]*((1612 - 3422*S^2 + 4768*S^4 + 10405*S^6)/(108*S^3) + (Pi^2*(146 + 292*S^2 + 146*S^4 - 2147*S^6 - 2014*S^8 - 437*S^10))/(54*S^3*(1 + S^2)^2) - (20*S^3*Zeta[3])/3) + HPL[{3, 2}, -S^2]*((1685 - 3393*S^2 - 9*S^4 + 8161*S^6)/(324*S^3) + (Pi^2*(70 + 140*S^2 + 70*S^4 - 1923*S^6 - 1686*S^8 - 303*S^10))/(108*S^3*(1 + S^2)^2) + (4*S^3*Zeta[3])/3) + HPL[{2, 2, 1}, -S^2]*((-5296 - 8271*S^2 - 52560*S^4 + 2201*S^6)/(54*S^3) + (Pi^2*(-1232 - 2464*S^2 - 1232*S^4 - 9721*S^6 - 6218*S^8 + 197*S^10))/(27*S^3*(1 + S^2)^2) + (16*S^3*Zeta[3])/3) + HPL[{5}, -S^2]*((-1365 + 933*S^2 - 4341*S^4 - 9352*S^6)/(324*S^3) + (Pi^2*(62 + 124*S^2 + 62*S^4 - 943*S^6 - 782*S^8 - 115*S^10))/(108*S^3*(1 + S^2)^2) - (10*S^3*HPL[{2, 1}, -S^2])/3 + (22*S^3*Zeta[3])/3) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(3812 + 5557*S^2 + 36455*S^4))/(972*S^3) + (Pi^2*(-688 - 1376*S^2 - 688*S^4 - 14629*S^6 - 14798*S^8 - 3784*S^10))/(405*S^3*(1 + S^2)^2) - (25*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (68*S^3*HPL[{3}, -S^2])/45 + (200*S^3*HPL[{2, 1}, -S^2])/3 + (332*S^3*Zeta[3])/45) + HPL[{3, 1, 1}, -S^2]*((-49178 - 71109*S^2 - 484506*S^4 + 8979*S^6)/(162*S^3) + (2*Pi^2*(-1895 - 3790*S^2 - 1895*S^4 - 14355*S^6 - 9006*S^8 + 423*S^10))/(27*S^3*(1 + S^2)^2) + (80*S^3*Zeta[3])/3) + HPL[{4}, -S^2]*((-61*Pi^4*S^3)/40 + (-13094 - 15684*S^2 - 49020*S^4 - 159431*S^6)/(3888*S^3) + (Pi^2*(-10 - 154*S^2 - 256*S^4 - 2787*S^6 - 3152*S^8 - 1437*S^10))/(216*S^3*(1 + S^2)^2) - (2*(2 + 4*S^2 + 2*S^4 + 67*S^6 + 182*S^8 + 103*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (26*S^3*HPL[{3, 1}, -S^2])/3 - (100*S^3*HPL[{2, 1, 1}, -S^2])/3 - (2*(5 + 10*S^2 + 5*S^4 + 3*S^6 + 14*S^8 + 9*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((85*Pi^4*S^3)/4 + (-756 + 40653*S^2 + 108126*S^4 + 566060*S^6)/(972*S^3) + (Pi^2*(-1200 + 4827*S^2 + 9168*S^4 + 100912*S^6 + 108080*S^8 + 49189*S^10))/(324*S^3*(1 + S^2)^2) + (6128*S^3*HPL[{2, 1, 1}, -S^2])/3 - (4*(-5 - 10*S^2 - 5*S^4 + 599*S^6 + 682*S^8 + 212*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((-4061*Pi^4*S^3)/1080 - ((1 + S^2)*(46564 + 64709*S^2 + 574261*S^4))/(5832*S^3) + (Pi^2*(-1850 - 11061*S^2 - 17534*S^4 - 72512*S^6 - 52056*S^8 - 16787*S^10))/(648*S^3*(1 + S^2)^2) + (-20*Pi^2*S^3 + (-740 - 4540*S^2 - 7355*S^4 - 31403*S^6 - 21451*S^8 - 7103*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (392*S^3*HPL[{2}, -S^2]^2)/9 + (2*(10 + 20*S^2 + 10*S^4 + 208*S^6 + 212*S^8 + 55*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (46*S^3*HPL[{4}, -S^2])/9 + (125*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (500*S^3*HPL[{3, 1}, -S^2])/3 - (1000*S^3*HPL[{2, 1, 1}, -S^2])/3 + (2*(40 + 80*S^2 + 40*S^4 + 967*S^6 + 938*S^8 + 220*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-769*Pi^4*S^3)/18 + (867 - 13699*S^2 - 36169*S^4 - 188347*S^6)/(162*S^3) + (Pi^2*(525 - 2616*S^2 - 4794*S^4 - 51262*S^6 - 55358*S^8 - 25189*S^10))/(81*S^3*(1 + S^2)^2) + (8*(-2 - 4*S^2 - 2*S^4 + 597*S^6 + 702*S^8 + 228*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-709*Pi^4*S^3)/144 + (-12593 - 48738*S^2 - 75855*S^4 - 536326*S^6)/(3888*S^3) + (Pi^2*(-538 - 8552*S^2 - 11662*S^4 - 101607*S^6 - 105642*S^8 - 47355*S^10))/(1296*S^3*(1 + S^2)^2) + ((-22 - 44*S^2 - 22*S^4 + 955*S^6 + 1190*S^8 + 415*S^10)*HPL[{3}, -S^2])/(36*S^3*(1 + S^2)^2) - (13*S^3*HPL[{4}, -S^2])/6 - (2*(-196 - 392*S^2 - 196*S^4 - 1535*S^6 - 946*S^8 + 58*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 250*S^3*HPL[{3, 1}, -S^2] - (1492*S^3*HPL[{2, 1, 1}, -S^2])/3 + ((-12 - 24*S^2 - 12*S^4 + 1147*S^6 + 1310*S^8 + 409*S^10)*Zeta[3])/(18*S^3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(7082 + 10384*S^2 + 95830*S^4 + 1047*S^6))/(648*S^3) + (186232 + 250275*S^2 + 3557046*S^4 + 358449*S^6)/(5832*S^3) + (Pi^4*(14306 + 28612*S^2 + 14306*S^4 + 87157*S^6 + 45014*S^8 - 9818*S^10))/(3240*S^3*(1 + S^2)^2) + (2*(-254 - 508*S^2 - 254*S^4 - 2349*S^6 - 1562*S^8 + 3*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - 16*S^3*HPL[{3, 2}, -S^2] - (44*S^3*HPL[{4, 1}, -S^2])/3 + (8*(-380 - 760*S^2 - 380*S^4 - 3511*S^6 - 2318*S^8 + 17*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (5968*S^3*HPL[{2, 2, 1}, -S^2])/3 - (18064*S^3*HPL[{3, 1, 1}, -S^2])/3 + (12272*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-2*Pi^2*S^3)/9 + (-890 - 2632*S^2 - 3068*S^4 - 7079*S^6 - 2878*S^8 - 77*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3]) + (-(Pi^2*S^3*(-32 + 908*S^2 + 697*S^4))/(54*(1 + S^2)^2) + (2670 + 213*S^2 + 2368*S^4)/(162*S))*Zeta[5] + Zeta[3]*((Pi^2*(964 + 244*S^2 - 57*S^4))/(324*S) - (Pi^4*S^3*(440 + 9124*S^2 + 6623*S^4))/(3240*(1 + S^2)^2) + (144960 + 134970*S^2 + 411139*S^4)/(11664*S) - (8*S^3*Zeta[5])/3) + HPL[{3}, -S^2]*((-53414 + 32595*S^2 - 243630*S^4 - 342241*S^6)/(7776*S^3) + (Pi^2*(-4266 + 3918*S^2 - 23082*S^4 - 24383*S^6))/(3888*S^3) + (Pi^4*(-874 - 1748*S^2 - 874*S^4 - 715*S^6 + 2170*S^8 + 1985*S^10))/(6480*S^3*(1 + S^2)^2) + ((-10 - 20*S^2 - 10*S^4 + 98*S^6 + 136*S^8 + 53*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*S^3*HPL[{5}, -S^2])/3 + ((-10*Pi^2*S^3)/3 + (-1050 - 2763*S^2 - 2562*S^4 - 7094*S^6 - 4996*S^8 - 1487*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((26 + 52*S^2 + 26*S^4 - 885*S^6 - 954*S^8 - 273*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (32*S^3*HPL[{3, 2}, -S^2])/3 + (44*S^3*HPL[{4, 1}, -S^2])/3 + (2*(-22 - 44*S^2 - 22*S^4 + 907*S^6 + 902*S^8 + 223*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 16*S^3*HPL[{2, 2, 1}, -S^2] - 16*S^3*HPL[{3, 1, 1}, -S^2] - (160*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((16*Pi^2*S^3)/9 + (100 + 233*S^2 + 172*S^4 + 159*S^6 - 162*S^8 - 138*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] + (28*S^3*Zeta[5])/3) + HPL[{1}, -S^2]^3*(-(Pi^2*(1 + S^2)*(6143 + 10462*S^2 + 79547*S^4))/(1458*S^3) - ((1 + S^2)*(126326 + 155803*S^2 + 1865477*S^4))/(8748*S^3) + (Pi^4*(-15602 - 31204*S^2 - 15602*S^4 - 305105*S^6 - 317818*S^8 - 85811*S^10))/(9720*S^3*(1 + S^2)^2) - (196*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((22*Pi^2*S^3)/27 - (2*(-85 - 207*S^2 - 133*S^4 - 232*S^6 + 66*S^8 + 83*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-34 - 68*S^2 - 34*S^4 - 1015*S^6 - 926*S^8 - 187*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - (92*S^3*HPL[{5}, -S^2])/9 + (80*Pi^2*S^3 + (4*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (8*(62 + 124*S^2 + 62*S^4 + 1466*S^6 + 1432*S^8 + 341*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (304*S^3*HPL[{3, 2}, -S^2])/9 - (728*S^3*HPL[{4, 1}, -S^2])/9 - (500*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*S^3*HPL[{2, 2, 1}, -S^2])/9 - (18544*S^3*HPL[{3, 1, 1}, -S^2])/9 + (4000*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((188*Pi^2*S^3)/27 + (256 + 943*S^2 + 1180*S^4 + 4204*S^6 + 2428*S^8 + 709*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(7142 + 11923*S^2 + 91373*S^4))/(486*S^3) + (Pi^2*(-1246 - 2492*S^2 - 1246*S^4 - 26293*S^6 - 26666*S^8 - 6853*S^10))/(162*S^3*(1 + S^2)^2) + (152*S^3*HPL[{3}, -S^2])/9 + (3136*S^3*HPL[{2, 1}, -S^2])/9 + (328*S^3*Zeta[3])/9) + (260*S^3*Zeta[5])/9) + HPL[{1}, -S^2]^2*((-248987*Pi^6*S^3)/136080 - (Pi^2*(1 + S^2)*(112136 + 183709*S^2 + 2035859*S^4))/(23328*S^3) - ((1 + S^2)*(772759 + 794066*S^2 + 12649645*S^4))/(34992*S^3) + (Pi^4*(-7901 - 57509*S^2 - 96719*S^4 - 401984*S^6 - 308417*S^8 - 99740*S^10))/(6480*S^3*(1 + S^2)^2) + ((-551*Pi^2*S^3)/18 + (-664 - 3427*S^2 - 5140*S^4 - 21304*S^6 - 14056*S^8 - 4537*S^10)/(36*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (118*S^3*HPL[{2}, -S^2]^3)/3 + (4*S^3*HPL[{3}, -S^2]^2)/3 + ((-40*Pi^2*S^3)/9 + (286 - 43*S^2 - 1154*S^4 - 7832*S^6 - 6100*S^8 - 2405*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(2 + 4*S^2 + 2*S^4 + 80*S^6 + 68*S^8 + 11*S^10)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^2) - (73*S^3*HPL[{6}, -S^2])/3 + (1568*S^3*HPL[{2, 1}, -S^2]^2)/3 + (120*Pi^2*S^3 + (494 + 3013*S^2 + 4874*S^4 + 20840*S^6 + 14188*S^8 + 4703*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (38*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-194 - 388*S^2 - 194*S^4 - 4343*S^6 - 4318*S^8 - 1067*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + 36*S^3*HPL[{5, 1}, -S^2] + (-240*Pi^2*S^3 - (4*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*(578 + 1156*S^2 + 578*S^4 + 13610*S^6 + 13312*S^8 + 3179*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 944*S^3*HPL[{3, 2, 1}, -S^2] - (8680*S^3*HPL[{4, 1, 1}, -S^2])/3 + (500*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + 2000*S^3*HPL[{3, 1, 1, 1}, -S^2] - 4000*S^3*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(1826 + 1165*S^2 + 4025*S^4))/(108*S^3) + (Pi^2*(74 + 148*S^2 + 74*S^4 + 2099*S^6 + 1942*S^8 + 407*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] - (34*S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(7142 + 11923*S^2 + 91373*S^4))/(162*S^3) + (Pi^2*(1246 + 2492*S^2 + 1246*S^4 + 26293*S^6 + 26666*S^8 + 6853*S^10))/(54*S^3*(1 + S^2)^2) - (328*S^3*Zeta[3])/3) + HPL[{3}, -S^2]*(-((1 + S^2)*(-2000 - 2041*S^2 + 8305*S^4))/(324*S^3) + (Pi^2*(4 + 8*S^2 + 4*S^4 + 121*S^6 + 110*S^8 + 22*S^10))/(27*S^3*(1 + S^2)^2) - (152*S^3*HPL[{2, 1}, -S^2])/3 + (8*S^3*Zeta[3])/3) + HPL[{2}, -S^2]*((-2155*Pi^4*S^3)/216 - ((1 + S^2)*(34202 + 57307*S^2 + 596135*S^4))/(1944*S^3) + (Pi^2*(-2098 - 14372*S^2 - 24112*S^4 - 100621*S^6 - 74240*S^8 - 24337*S^10))/(324*S^3*(1 + S^2)^2) + (19*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*S^3*HPL[{4}, -S^2])/3 + (392*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1568*S^3*HPL[{3, 1}, -S^2])/3 - (3136*S^3*HPL[{2, 1, 1}, -S^2])/3 + (41*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + ((18 + 36*S^2 + 18*S^4 + 489*S^6 + 458*S^8 + 99*S^10)*Zeta[5])/(3*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-235877*Pi^6*S^3)/136080 + (-439311 - 1588281*S^2 - 5248131*S^4 - 24229844*S^6)/(69984*S^3) + (Pi^2*(-8249 - 53589*S^2 - 192405*S^4 - 1002071*S^6))/(11664*S^3) + (Pi^4*(4017 - 33024*S^2 - 56850*S^4 - 587465*S^6 - 678319*S^8 - 304613*S^10))/(19440*S^3*(1 + S^2)^2) + (8*S^3*HPL[{3}, -S^2]^2)/3 + ((-37*Pi^2*S^3)/18 + (-107 - 211*S^2 - 80*S^4 - 942*S^6 - 1755*S^8 - 933*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((18 + 36*S^2 + 18*S^4 - 199*S^6 - 350*S^8 - 163*S^10)*HPL[{5}, -S^2])/(18*S^3*(1 + S^2)^2) + (7*S^3*HPL[{6}, -S^2])/3 + (1492*S^3*HPL[{2, 1}, -S^2]^2)/3 + HPL[{3}, -S^2]*((-621 + 1647*S^2 - 189*S^4 - 4616*S^6)/(324*S^3) + (Pi^2*(-38 - 76*S^2 - 38*S^4 + 917*S^6 + 754*S^8 + 107*S^10))/(108*S^3*(1 + S^2)^2) + 8*S^3*HPL[{2, 1}, -S^2]) + ((1088*Pi^2*S^3)/9 + (92 + 1749*S^2 + 2432*S^4 + 21300*S^6 + 20468*S^8 + 9351*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((46 + 92*S^2 + 46*S^4 - 1899*S^6 - 2358*S^8 - 819*S^10)*HPL[{3, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + ((70 + 140*S^2 + 70*S^4 - 2731*S^6 - 3206*S^8 - 1039*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - S^3*HPL[{4, 2}, -S^2] + 6*S^3*HPL[{5, 1}, -S^2] + ((-728*Pi^2*S^3)/3 - (2*(195 + 2742*S^2 + 3723*S^4 + 32020*S^6 + 30770*S^8 + 14038*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (8*(-196 - 392*S^2 - 196*S^4 - 1535*S^6 - 946*S^8 + 58*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(-2330 - 4660*S^2 - 2330*S^4 - 19327*S^6 - 12254*S^8 + 473*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 984*S^3*HPL[{3, 2, 1}, -S^2] - (8956*S^3*HPL[{4, 1, 1}, -S^2])/3 - (8*(-380 - 760*S^2 - 380*S^4 - 3511*S^6 - 2318*S^8 + 17*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (77744*S^3*HPL[{3, 1, 1, 1}, -S^2])/3 - (12272*S^3*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((-1250 + 4314*S^2 + 3090*S^4 + 11453*S^6)/(324*S^3) + (Pi^2*(-28 - 56*S^2 - 28*S^4 + 1237*S^6 + 1382*S^8 + 418*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] - (34*S^3*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((5296 + 8271*S^2 + 52560*S^4 - 2201*S^6)/(108*S^3) + (Pi^2*(1232 + 2464*S^2 + 1232*S^4 + 9721*S^6 + 6218*S^8 - 197*S^10))/(54*S^3*(1 + S^2)^2) - (8*S^3*Zeta[3])/3) + ((-40 - 80*S^2 - 40*S^4 + 736*S^6 + 836*S^8 + 259*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) - (5*S^3*(-14 + 32*S^2 + 31*S^4)*Zeta[7])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^4*(1 + S^2)*(102683 + 198826*S^2 + 1950401*S^4))/(116640*S^3) - (Pi^2*(1 + S^2)*(342097 + 413330*S^2 + 6726913*S^4))/(69984*S^3) - ((1 + S^2)*(11329918 + 8757449*S^2 + 179723545*S^4))/(419904*S^3) + (Pi^6*(-364610 - 729220*S^2 - 364610*S^4 - 6487121*S^6 - 6998554*S^8 - 2005355*S^10))/(816480*S^3*(1 + S^2)^2) - (59*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2}, -S^2]^3)/(18*S^3*(1 + S^2)^2) + ((2 + 4*S^2 + 2*S^4 + 83*S^6 + 70*S^8 + 11*S^10)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((-46*Pi^2*S^3)/9 + (196 + 95*S^2 - 632*S^4 - 4538*S^6 - 3946*S^8 - 1595*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-6 - 12*S^2 - 6*S^4 - 471*S^6 - 358*S^8 - 33*S^10)*HPL[{6}, -S^2])/(6*S^3*(1 + S^2)^2) - (134*S^3*HPL[{7}, -S^2])/3 + (392*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + (-10*Pi^2*S^3 + (-136 - 445*S^2 - 448*S^4 - 1624*S^6 - 748*S^8 - 175*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-190*Pi^2*S^3)/9 + (-2734 - 7967*S^2 - 6910*S^4 - 21400*S^6 - 7364*S^8 - 745*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((-2 - 11*S^6)*HPL[{4, 2}, -S^2])/(6*S^3) - (26*S^3*HPL[{4, 3}, -S^2])/3 + (2*(10 + 20*S^2 + 10*S^4 + 541*S^6 + 434*S^8 + 55*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 28*S^3*HPL[{5, 2}, -S^2] - (14*S^3*HPL[{6, 1}, -S^2])/3 + ((-2204*Pi^2*S^3)/9 - (2*(664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-6568*Pi^2*S^3)/9 - (2*(1822 + 9867*S^2 + 15154*S^4 + 63448*S^6 + 42300*S^8 + 13777*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (236*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + 80*S^3*HPL[{3, 2, 2}, -S^2] + (752*S^3*HPL[{3, 3, 1}, -S^2])/3 - (2*(2158 + 4316*S^2 + 2158*S^4 + 50929*S^6 + 49778*S^8 + 11869*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (752*S^3*HPL[{4, 1, 2}, -S^2])/3 + (2288*S^3*HPL[{4, 2, 1}, -S^2])/3 + (4424*S^3*HPL[{5, 1, 1}, -S^2])/3 + (480*Pi^2*S^3 + (8*(740 + 4540*S^2 + 7355*S^4 + 31403*S^6 + 21451*S^8 + 7103*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 1888*S^3*HPL[{2, 2, 2, 1}, -S^2] + (16*(62 + 124*S^2 + 62*S^4 + 1466*S^6 + 1432*S^8 + 341*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (17600*S^3*HPL[{3, 1, 1, 2}, -S^2])/3 - (17600*S^3*HPL[{3, 1, 2, 1}, -S^2])/3 - (34592*S^3*HPL[{3, 2, 1, 1}, -S^2])/3 - (103408*S^3*HPL[{4, 1, 1, 1}, -S^2])/3 - (1000*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (12544*S^3*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 12544*S^3*HPL[{2, 2, 1, 1, 1}, -S^2] + 21088*S^3*HPL[{3, 1, 1, 1, 1}, -S^2] + 8000*S^3*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((229*Pi^4*S^3)/180 + ((1 + S^2)*(34540 + 22079*S^2 + 72673*S^4))/(1944*S^3) + (Pi^2*(566 + 1738*S^2 + 1880*S^4 + 6137*S^6 + 2791*S^8 + 746*S^10))/(162*S^3*(1 + S^2)^2))*Zeta[3] + ((-6 - 12*S^2 - 6*S^4 - 135*S^6 - 134*S^8 - 33*S^10)*Zeta[3]^2)/(3*S^3*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(2566 + 3755*S^2 + 30535*S^4))/(54*S^3) + (Pi^2*(206 + 412*S^2 + 206*S^4 + 4373*S^6 + 4426*S^8 + 1133*S^10))/(9*S^3*(1 + S^2)^2) - (344*S^3*Zeta[3])/3) + HPL[{4}, -S^2]*(-((1 + S^2)*(359 - 1112*S^2 + 11465*S^4))/(324*S^3) + (Pi^2*(-58 - 116*S^2 - 58*S^4 - 1759*S^6 - 1598*S^8 - 319*S^10))/(108*S^3*(1 + S^2)^2) + (16*S^3*HPL[{2, 1}, -S^2])/3 + (8*S^3*Zeta[3])/3) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(4849 + 6653*S^2 + 41650*S^4))/(324*S^3) + (Pi^2*(-626 - 1252*S^2 - 626*S^4 - 13361*S^6 - 13498*S^8 - 3443*S^10))/(108*S^3*(1 + S^2)^2) + 10*S^3*HPL[{3}, -S^2] + 236*S^3*HPL[{2, 1}, -S^2] + (82*S^3*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*(-((1 + S^2)*(7142 + 11923*S^2 + 91373*S^4))/(81*S^3) + (Pi^2*(-1246 - 2492*S^2 - 1246*S^4 - 26293*S^6 - 26666*S^8 - 6853*S^10))/(27*S^3*(1 + S^2)^2) + (656*S^3*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((2155*Pi^4*S^3)/108 + ((1 + S^2)*(34202 + 57307*S^2 + 596135*S^4))/(972*S^3) + (Pi^2*(2098 + 14372*S^2 + 24112*S^4 + 100621*S^6 + 74240*S^8 + 24337*S^10))/(162*S^3*(1 + S^2)^2) - (3136*S^3*HPL[{3, 1}, -S^2])/3 - (6272*S^3*HPL[{2, 1, 1}, -S^2])/3 - (82*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-5*Pi^4*S^3)/18 - ((1 + S^2)*(-2498 - 2487*S^2 + 29077*S^4))/(648*S^3) + (Pi^2*(371 + 727*S^2 + 191*S^4 - 673*S^6 - 1739*S^8 - 835*S^10))/(162*S^3*(1 + S^2)^2) + (10*S^3*HPL[{4}, -S^2])/3 - (38*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (136*S^3*HPL[{3, 1}, -S^2])/3 + (304*S^3*HPL[{2, 1, 1}, -S^2])/3 + (2*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (9*Pi^2*S^3 + (565 + 1580*S^2 + 1555*S^4 + 4300*S^6 + 1769*S^8 + 349*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(19162 + 35915*S^2 + 320275*S^4))/(3888*S^3) - ((1 + S^2)*(48181 + 71534*S^2 + 997519*S^4))/(2916*S^3) + (Pi^4*(-4594 - 9188*S^2 - 4594*S^4 - 89917*S^6 - 93634*S^8 - 25267*S^10))/(2160*S^3*(1 + S^2)^2) + (5*Pi^2*S^3 + (136 + 445*S^2 + 448*S^4 + 1624*S^6 + 748*S^8 + 175*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-2 - 4*S^2 - 2*S^4 - 155*S^6 - 118*S^8 - 11*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - (4*S^3*HPL[{5}, -S^2])/3 + ((1102*Pi^2*S^3)/9 + (664 + 3427*S^2 + 5140*S^4 + 21304*S^6 + 14056*S^8 + 4537*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (392*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 40*S^3*HPL[{3, 2}, -S^2] - (376*S^3*HPL[{4, 1}, -S^2])/3 - (784*(2 + 4*S^2 + 2*S^4 + 47*S^6 + 46*S^8 + 11*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - 944*S^3*HPL[{2, 2, 1}, -S^2] + (8800*S^3*HPL[{3, 1, 1}, -S^2])/3 + (6272*S^3*HPL[{2, 1, 1, 1}, -S^2])/3 + ((91*Pi^2*S^3)/9 + (400 + 1472*S^2 + 1858*S^4 + 6475*S^6 + 3848*S^8 + 1111*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + (106*S^3*Zeta[5])/3) + 50*S^3*Zeta[7])) + (1568*S^3*Zeta[9])/3;
E5vwuT=E5vwuT0F0+T*E5vwuT1F1*(F+1/F)+T^2*(E5vwuT2F0+E5vwuT2F2*(F^2+1/F^2))+T^3*(E5vwuT3F1*(F+1/F)+E5vwuT3F3*(F^3+1/F^3));
E5wuvT0F0=(-262799*Pi^10)/1166400 - HPL[{0}, S^2]^10/3840 + HPL[{0}, S^2]^8*((-7*Pi^2)/1152 - HPL[{2}, -S^2]/96) - (8*Pi^2*HPL[{2}, -S^2]^4)/3 - (32*HPL[{2}, -S^2]^5)/5 + (31*Pi^2*HPL[{4}, -S^2]^2)/3 - 286*HPL[{5}, -S^2]^2 + 51*Pi^2*HPL[{8}, -S^2] + 3296*HPL[{10}, -S^2] + HPL[{2}, -S^2]^3*((-111*Pi^4)/20 + (164*HPL[{4}, -S^2])/3 - (164*HPL[{3, 1}, -S^2])/3) - (208*Pi^2*HPL[{3, 1}, -S^2]^2)/3 + 192*HPL[{3, 2}, -S^2]^2 - 6624*HPL[{4, 1}, -S^2]^2 + (14*Pi^2*HPL[{5, 3}, -S^2])/3 + (53*Pi^2*HPL[{6, 2}, -S^2])/3 - 12*HPL[{6, 4}, -S^2] + (58*Pi^2*HPL[{7, 1}, -S^2])/3 - 148*HPL[{7, 3}, -S^2] - 292*HPL[{8, 2}, -S^2] - 732*HPL[{9, 1}, -S^2] + HPL[{5, 1}, -S^2]*((-1729*Pi^4)/90 - 5408*HPL[{2, 1, 1}, -S^2]) + HPL[{4, 2}, -S^2]*((-33*Pi^4)/5 - 936*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]^2*((-82*Pi^4)/45 - 20*HPL[{4}, -S^2] + 164*HPL[{3, 1}, -S^2] - 296*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]^6*((-1013*Pi^4)/17280 - (23*Pi^2*HPL[{2}, -S^2])/144 - (13*HPL[{2}, -S^2]^2)/96 + HPL[{4}, -S^2]/24 + (5*HPL[{3, 1}, -S^2])/8 - (3*HPL[{2, 1, 1}, -S^2])/2) - (1568*Pi^2*HPL[{2, 1, 1}, -S^2]^2)/3 + HPL[{6}, -S^2]*((28*Pi^4)/45 - 472*HPL[{3, 1}, -S^2] + 356*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]^2*((2021*Pi^4)/60 - 3136*HPL[{3, 1}, -S^2] + 6272*HPL[{2, 1, 1}, -S^2]) - 1376*HPL[{3, 1, 1}, -S^2]^2 + (33*Pi^4*HPL[{3, 1, 2}, -S^2])/5 - (633*Pi^4*HPL[{3, 2, 1}, -S^2])/5 - (214*Pi^2*HPL[{3, 3, 2}, -S^2])/3 - (17761*Pi^4*HPL[{4, 1, 1}, -S^2])/45 + 112*Pi^2*HPL[{4, 1, 3}, -S^2] - (190*Pi^2*HPL[{4, 2, 2}, -S^2])/3 + (1208*Pi^2*HPL[{4, 3, 1}, -S^2])/3 - 144*HPL[{4, 3, 3}, -S^2] - 444*HPL[{4, 4, 2}, -S^2] + (706*Pi^2*HPL[{5, 1, 2}, -S^2])/3 + 876*HPL[{5, 1, 4}, -S^2] + (5026*Pi^2*HPL[{5, 2, 1}, -S^2])/3 + 452*HPL[{5, 2, 3}, -S^2] - 616*HPL[{5, 3, 2}, -S^2] + 2244*HPL[{5, 4, 1}, -S^2] + (12886*Pi^2*HPL[{6, 1, 1}, -S^2])/3 + 3508*HPL[{6, 1, 3}, -S^2] + 1236*HPL[{6, 2, 2}, -S^2] + 11092*HPL[{6, 3, 1}, -S^2] + 7472*HPL[{7, 1, 2}, -S^2] + 32672*HPL[{7, 2, 1}, -S^2] + 74908*HPL[{8, 1, 1}, -S^2] + (2651*Pi^4*HPL[{3, 1, 1, 1}, -S^2])/9 - (2*Pi^2*HPL[{3, 1, 2, 2}, -S^2])/3 - (2*Pi^2*HPL[{3, 2, 1, 2}, -S^2])/3 + (4838*Pi^2*HPL[{3, 2, 2, 1}, -S^2])/3 + 4840*Pi^2*HPL[{3, 3, 1, 1}, -S^2] + 456*HPL[{3, 3, 2, 2}, -S^2] + 1888*HPL[{3, 3, 3, 1}, -S^2] - 216*Pi^2*HPL[{4, 1, 1, 2}, -S^2] + 4624*Pi^2*HPL[{4, 1, 2, 1}, -S^2] - 2052*HPL[{4, 1, 2, 3}, -S^2] - 4852*HPL[{4, 1, 3, 2}, -S^2] + 14304*Pi^2*HPL[{4, 2, 1, 1}, -S^2] - 5892*HPL[{4, 2, 1, 3}, -S^2] - 7628*HPL[{4, 2, 2, 2}, -S^2] - 3092*HPL[{4, 2, 3, 1}, -S^2] - 14356*HPL[{4, 3, 1, 2}, -S^2] - 22948*HPL[{4, 3, 2, 1}, -S^2] - 25776*HPL[{4, 4, 1, 1}, -S^2] + (84920*Pi^2*HPL[{5, 1, 1, 1}, -S^2])/3 - 11416*HPL[{5, 1, 1, 3}, -S^2] - 21132*HPL[{5, 1, 2, 2}, -S^2] - 152*HPL[{5, 1, 3, 1}, -S^2] - 45612*HPL[{5, 2, 1, 2}, -S^2] - 68652*HPL[{5, 2, 2, 1}, -S^2] - 69016*HPL[{5, 3, 1, 1}, -S^2] - 84636*HPL[{6, 1, 1, 2}, -S^2] - 113916*HPL[{6, 1, 2, 1}, -S^2] - 87516*HPL[{6, 2, 1, 1}, -S^2] - 4944*HPL[{7, 1, 1, 1}, -S^2] - (26692*Pi^4*HPL[{2, 1, 1, 1, 1}, -S^2])/45 + (9712*Pi^2*HPL[{2, 2, 1, 2, 1}, -S^2])/3 + 9712*Pi^2*HPL[{2, 2, 2, 1, 1}, -S^2] - 19208*Pi^2*HPL[{3, 1, 1, 1, 2}, -S^2] - (96472*Pi^2*HPL[{3, 1, 1, 2, 1}, -S^2])/3 - 38632*Pi^2*HPL[{3, 1, 2, 1, 1}, -S^2] + 304*HPL[{3, 1, 2, 2, 2}, -S^2] - 608*HPL[{3, 1, 3, 1, 2}, -S^2] - (242152*Pi^2*HPL[{3, 2, 1, 1, 1}, -S^2])/3 + 304*HPL[{3, 2, 1, 2, 2}, -S^2] + 608*HPL[{3, 2, 1, 3, 1}, -S^2] - 304*HPL[{3, 2, 2, 1, 2}, -S^2] - 11376*HPL[{3, 2, 2, 2, 1}, -S^2] - 33344*HPL[{3, 2, 3, 1, 1}, -S^2] - 1824*HPL[{3, 3, 1, 1, 2}, -S^2] - 34560*HPL[{3, 3, 1, 2, 1}, -S^2] - 98336*HPL[{3, 3, 2, 1, 1}, -S^2] - (727184*Pi^2*HPL[{4, 1, 1, 1, 1}, -S^2])/3 + 192576*HPL[{4, 1, 1, 1, 3}, -S^2] + 193512*HPL[{4, 1, 1, 2, 2}, -S^2] + 389504*HPL[{4, 1, 1, 3, 1}, -S^2] + 191688*HPL[{4, 1, 2, 1, 2}, -S^2] + 353448*HPL[{4, 1, 2, 2, 1}, -S^2] + 482496*HPL[{4, 1, 3, 1, 1}, -S^2] + 188040*HPL[{4, 2, 1, 1, 2}, -S^2] + 284808*HPL[{4, 2, 1, 2, 1}, -S^2] + 288456*HPL[{4, 2, 2, 1, 1}, -S^2] + 779456*HPL[{4, 3, 1, 1, 1}, -S^2] + 764592*HPL[{5, 1, 1, 1, 2}, -S^2] + 1348080*HPL[{5, 1, 1, 2, 1}, -S^2] + 1745328*HPL[{5, 1, 2, 1, 1}, -S^2] + 3119280*HPL[{5, 2, 1, 1, 1}, -S^2] + 7800672*HPL[{6, 1, 1, 1, 1}, -S^2] + 6944*Pi^2*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 25088*HPL[{3, 1, 1, 2, 2, 1}, -S^2] + 25088*HPL[{3, 1, 2, 1, 2, 1}, -S^2] - 150528*HPL[{3, 1, 3, 1, 1, 1}, -S^2] + 25088*HPL[{3, 2, 1, 1, 2, 1}, -S^2] - 125440*HPL[{3, 2, 2, 1, 1, 1}, -S^2] - 376320*HPL[{3, 3, 1, 1, 1, 1}, -S^2] - 5120*HPL[{4, 1, 1, 1, 1, 2}, -S^2] + 70144*HPL[{4, 1, 1, 1, 2, 1}, -S^2] - 5120*HPL[{4, 1, 1, 2, 1, 1}, -S^2] - 381440*HPL[{4, 1, 2, 1, 1, 1}, -S^2] - 1134080*HPL[{4, 2, 1, 1, 1, 1}, -S^2] - 2276224*HPL[{5, 1, 1, 1, 1, 1}, -S^2] - 13920*Pi^2*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + 50176*HPL[{2, 1, 2, 1, 2, 1, 1}, -S^2] - 150528*HPL[{2, 2, 1, 1, 1, 2, 1}, -S^2] - 301056*HPL[{2, 2, 1, 1, 2, 1, 1}, -S^2] - 852992*HPL[{2, 2, 1, 2, 1, 1, 1}, -S^2] - 2257920*HPL[{2, 2, 2, 1, 1, 1, 1}, -S^2] + 4520960*HPL[{3, 1, 1, 1, 1, 1, 2}, -S^2] + 8735744*HPL[{3, 1, 1, 1, 1, 2, 1}, -S^2] + 12950528*HPL[{3, 1, 1, 1, 2, 1, 1}, -S^2] + 16362496*HPL[{3, 1, 1, 2, 1, 1, 1}, -S^2] + 18068480*HPL[{3, 1, 2, 1, 1, 1, 1}, -S^2] + 27049984*HPL[{3, 2, 1, 1, 1, 1, 1}, -S^2] + 81146112*HPL[{4, 1, 1, 1, 1, 1, 1}, -S^2] + 107520*HPL[{3, 1, 1, 1, 1, 1, 1, 1}, -S^2] - 215040*HPL[{2, 1, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((-14*Pi^2)/9 - (5*HPL[{0}, S^2]^2)/3 - (16*HPL[{2}, -S^2])/3)*Log[T]^8 + (4*HPL[{0}, S^2]*Log[T]^9)/3 - (4*Log[T]^10)/15 + HPL[{7}, -S^2]*(60*HPL[{2, 1}, -S^2] - 268*Zeta[3]) + Log[T]^7*((16*HPL[{0}, S^2]^3)/9 + HPL[{0}, S^2]*((52*Pi^2)/9 + (64*HPL[{2}, -S^2])/3) - (64*HPL[{3}, -S^2])/3 + (128*HPL[{2, 1}, -S^2])/3 - (64*Zeta[3])/3) + HPL[{0}, S^2]^7*(-HPL[{2, 1}, -S^2]/8 - Zeta[3]/6) - 112*HPL[{4, 3}, -S^2]*Zeta[3] - 388*HPL[{5, 2}, -S^2]*Zeta[3] - 564*HPL[{6, 1}, -S^2]*Zeta[3] + 204*HPL[{3, 2, 2}, -S^2]*Zeta[3] + 752*HPL[{3, 3, 1}, -S^2]*Zeta[3] + 744*HPL[{4, 1, 2}, -S^2]*Zeta[3] + 2376*HPL[{4, 2, 1}, -S^2]*Zeta[3] + 4688*HPL[{5, 1, 1}, -S^2]*Zeta[3] + 5664*HPL[{2, 2, 2, 1}, -S^2]*Zeta[3] - 17712*HPL[{3, 1, 1, 2}, -S^2]*Zeta[3] - 17712*HPL[{3, 1, 2, 1}, -S^2]*Zeta[3] - 34704*HPL[{3, 2, 1, 1}, -S^2]*Zeta[3] - 103648*HPL[{4, 1, 1, 1}, -S^2]*Zeta[3] + 12544*HPL[{2, 1, 2, 1, 1}, -S^2]*Zeta[3] + 37632*HPL[{2, 2, 1, 1, 1}, -S^2]*Zeta[3] + 63168*HPL[{3, 1, 1, 1, 1}, -S^2]*Zeta[3] + 24000*HPL[{2, 1, 1, 1, 1, 1}, -S^2]*Zeta[3] - (257*Pi^4*Zeta[3]^2)/90 + HPL[{2, 1, 1}, -S^2]*((-52285*Pi^6)/2268 + 5312*HPL[{4, 1, 1}, -S^2] - 5312*HPL[{3, 1, 1, 1}, -S^2] - 160*Zeta[3]^2) + HPL[{4}, -S^2]*((-2563*Pi^6)/11340 + 580*HPL[{6}, -S^2] - 452*HPL[{2, 1}, -S^2]^2 - 122*Pi^2*HPL[{3, 1}, -S^2] - 1288*HPL[{5, 1}, -S^2] + (680*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 1312*HPL[{3, 2, 1}, -S^2] + 4176*HPL[{4, 1, 1}, -S^2] - 2736*HPL[{3, 1, 1, 1}, -S^2] + 5312*HPL[{2, 1, 1, 1, 1}, -S^2] + 112*HPL[{2, 1}, -S^2]*Zeta[3] - 4*Zeta[3]^2) + HPL[{0}, S^2]^4*((-121*Pi^6)/432 - (109*Pi^2*HPL[{2}, -S^2]^2)/72 - (5*HPL[{2}, -S^2]^3)/3 - HPL[{3}, -S^2]^2/4 + 6*HPL[{6}, -S^2] + (241*HPL[{2, 1}, -S^2]^2)/12 + (251*Pi^2*HPL[{3, 1}, -S^2])/36 - HPL[{5, 1}, -S^2]/2 + HPL[{2}, -S^2]*((-2009*Pi^4)/2160 + HPL[{4}, -S^2]/2 + (39*HPL[{3, 1}, -S^2])/2 - (241*HPL[{2, 1, 1}, -S^2])/6) - (277*Pi^2*HPL[{2, 1, 1}, -S^2])/18 - 40*HPL[{3, 2, 1}, -S^2] - 125*HPL[{4, 1, 1}, -S^2] + (277*HPL[{3, 1, 1, 1}, -S^2])/3 - (568*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + HPL[{3}, -S^2]*(HPL[{2, 1}, -S^2]/2 - (5*Zeta[3])/2) - (7*Zeta[3]^2)/4) + HPL[{3, 1}, -S^2]*((126709*Pi^6)/11340 + 468*HPL[{4, 2}, -S^2] + 2872*HPL[{5, 1}, -S^2] + (880*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 608*HPL[{3, 1, 2}, -S^2] - 1312*HPL[{3, 2, 1}, -S^2] - 6672*HPL[{4, 1, 1}, -S^2] + 2752*HPL[{3, 1, 1, 1}, -S^2] - 5312*HPL[{2, 1, 1, 1, 1}, -S^2] + 52*Zeta[3]^2) + Log[T]^6*((-1013*Pi^4)/270 - (11*HPL[{0}, S^2]^4)/9 + HPL[{0}, S^2]^2*((-19*Pi^2)/3 - (62*HPL[{2}, -S^2])/3) - (58*Pi^2*HPL[{2}, -S^2])/3 + 16*HPL[{4}, -S^2] + (448*HPL[{3, 1}, -S^2])/3 - (896*HPL[{2, 1, 1}, -S^2])/3 + HPL[{0}, S^2]*(8*HPL[{3}, -S^2] - (448*HPL[{2, 1}, -S^2])/3 + 16*Zeta[3])) + HPL[{2}, -S^2]^2*((-1049*Pi^6)/720 - 43*HPL[{3}, -S^2]^2 + (56*Pi^2*HPL[{4}, -S^2])/3 + 42*HPL[{6}, -S^2] + (605*Pi^2*HPL[{3, 1}, -S^2])/3 - 156*HPL[{4, 2}, -S^2] - 632*HPL[{5, 1}, -S^2] - (1214*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 156*HPL[{3, 1, 2}, -S^2] - 1380*HPL[{3, 2, 1}, -S^2] - 4156*HPL[{4, 1, 1}, -S^2] + 3136*HPL[{3, 1, 1, 1}, -S^2] - 6272*HPL[{2, 1, 1, 1, 1}, -S^2] + 708*HPL[{2, 1}, -S^2]*Zeta[3] + 3*Zeta[3]^2 + HPL[{3}, -S^2]*(932*HPL[{2, 1}, -S^2] + 26*Zeta[3])) + HPL[{3, 1, 1}, -S^2]*(-44864*HPL[{2, 1, 1, 1}, -S^2] - (5140*Pi^2*Zeta[3])/3 - 8888*Zeta[5]) + HPL[{2, 2, 1}, -S^2]*(-12544*HPL[{3, 1, 1}, -S^2] - 25088*HPL[{2, 1, 1, 1}, -S^2] - (1724*Pi^2*Zeta[3])/3 - 2888*Zeta[5]) + HPL[{5}, -S^2]*(80*Pi^2*HPL[{2, 1}, -S^2] + 116*HPL[{3, 2}, -S^2] + 688*HPL[{4, 1}, -S^2] - 656*HPL[{2, 2, 1}, -S^2] - 2280*HPL[{3, 1, 1}, -S^2] + 1728*HPL[{2, 1, 1, 1}, -S^2] - (82*Pi^2*Zeta[3])/3 - 356*Zeta[5]) + Log[T]^5*((163*HPL[{0}, S^2]^5)/225 + HPL[{0}, S^2]^3*((746*Pi^2)/135 + (146*HPL[{2}, -S^2])/9) - (364*Pi^2*HPL[{3}, -S^2])/9 - 64*HPL[{5}, -S^2] + 116*Pi^2*HPL[{2, 1}, -S^2] + 464*HPL[{3, 2}, -S^2] + 1424*HPL[{4, 1}, -S^2] + HPL[{0}, S^2]*((14057*Pi^4)/1350 + (482*Pi^2*HPL[{2}, -S^2])/9 + 100*HPL[{2}, -S^2]^2 + 16*HPL[{4}, -S^2] - 448*HPL[{3, 1}, -S^2] + 896*HPL[{2, 1, 1}, -S^2]) - 896*HPL[{3, 1, 1}, -S^2] + 1792*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-760*HPL[{3}, -S^2])/3 - 200*Zeta[3]) + HPL[{0}, S^2]^2*((-28*HPL[{3}, -S^2])/3 + 124*HPL[{2, 1}, -S^2] - 12*Zeta[3]) - (124*Pi^2*Zeta[3])/3 - 232*Zeta[5]) + HPL[{3, 2}, -S^2]*(-192*HPL[{4, 1}, -S^2] + 6832*HPL[{2, 2, 1}, -S^2] + 19968*HPL[{3, 1, 1}, -S^2] - 12544*HPL[{2, 1, 1, 1}, -S^2] - 32*Pi^2*Zeta[3] - 144*Zeta[5]) + HPL[{4, 1}, -S^2]*(20560*HPL[{2, 2, 1}, -S^2] + 62768*HPL[{3, 1, 1}, -S^2] - 42944*HPL[{2, 1, 1, 1}, -S^2] - 64*Pi^2*Zeta[3] - 48*Zeta[5]) + HPL[{0}, S^2]^5*((Pi^2*HPL[{3}, -S^2])/24 - (3*HPL[{5}, -S^2])/4 + HPL[{2}, -S^2]*(-HPL[{3}, -S^2]/4 - (77*HPL[{2, 1}, -S^2])/20) - (293*Pi^2*HPL[{2, 1}, -S^2])/180 + HPL[{3, 2}, -S^2]/2 + HPL[{4, 1}, -S^2] + (77*HPL[{2, 2, 1}, -S^2])/10 + (241*HPL[{3, 1, 1}, -S^2])/10 - (271*HPL[{2, 1, 1, 1}, -S^2])/15 - (31*Pi^2*Zeta[3])/24 - (29*Zeta[5])/4) + 260*Zeta[5]^2 + HPL[{2, 1, 1, 1}, -S^2]*((3328*Pi^2*Zeta[3])/3 + 6080*Zeta[5]) + HPL[{0}, S^2]^2*((-456659*Pi^8)/777600 - (335*Pi^2*HPL[{2}, -S^2]^3)/36 - 8*HPL[{2}, -S^2]^4 - (2*Pi^2*HPL[{3}, -S^2]^2)/3 + 16*HPL[{4}, -S^2]^2 + (125*Pi^2*HPL[{6}, -S^2])/12 + (479*HPL[{8}, -S^2])/2 + (211*Pi^2*HPL[{2, 1}, -S^2]^2)/2 - 380*HPL[{3, 1}, -S^2]^2 - (Pi^2*HPL[{4, 2}, -S^2])/3 + (8*Pi^2*HPL[{5, 1}, -S^2])/3 + HPL[{5, 3}, -S^2] + (25*HPL[{6, 2}, -S^2])/2 - 44*HPL[{7, 1}, -S^2] + HPL[{2}, -S^2]^2*((-6731*Pi^4)/1440 - HPL[{4}, -S^2]/2 + 213*HPL[{3, 1}, -S^2] - 430*HPL[{2, 1, 1}, -S^2]) - (8449*Pi^4*HPL[{2, 1, 1}, -S^2])/180 - 1568*HPL[{2, 1, 1}, -S^2]^2 + HPL[{4}, -S^2]*((-23*Pi^4)/40 - 24*HPL[{3, 1}, -S^2] + 16*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 1}, -S^2]*((8023*Pi^4)/360 + 1544*HPL[{2, 1, 1}, -S^2]) + (Pi^2*HPL[{3, 1, 2}, -S^2])/3 - 223*Pi^2*HPL[{3, 2, 1}, -S^2] - 2*HPL[{3, 3, 2}, -S^2] - (2068*Pi^2*HPL[{4, 1, 1}, -S^2])/3 - 7*HPL[{4, 2, 2}, -S^2] - 8*HPL[{4, 3, 1}, -S^2] - 20*HPL[{5, 1, 2}, -S^2] - 20*HPL[{5, 2, 1}, -S^2] - 38*HPL[{6, 1, 1}, -S^2] + (1478*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 - 2*HPL[{3, 1, 2, 2}, -S^2] - 2*HPL[{3, 2, 1, 2}, -S^2] + 1702*HPL[{3, 2, 2, 1}, -S^2] + 5112*HPL[{3, 3, 1, 1}, -S^2] - 8*HPL[{4, 1, 1, 2}, -S^2] + 5104*HPL[{4, 1, 2, 1}, -S^2] + 15328*HPL[{4, 2, 1, 1}, -S^2] + 30760*HPL[{5, 1, 1, 1}, -S^2] - (2996*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + 3440*HPL[{2, 2, 1, 2, 1}, -S^2] + 10320*HPL[{2, 2, 2, 1, 1}, -S^2] - 20632*HPL[{3, 1, 1, 1, 2}, -S^2] - 34392*HPL[{3, 1, 1, 2, 1}, -S^2] - 41272*HPL[{3, 1, 2, 1, 1}, -S^2] - 85992*HPL[{3, 2, 1, 1, 1}, -S^2] - 258224*HPL[{4, 1, 1, 1, 1}, -S^2] + 7392*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 14880*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{5}, -S^2]*(24*HPL[{2, 1}, -S^2] - 56*Zeta[3]) - 6*HPL[{3, 2}, -S^2]*Zeta[3] + 20*HPL[{4, 1}, -S^2]*Zeta[3] - 156*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 492*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 328*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (31*Pi^2*Zeta[3]^2)/6 + HPL[{2}, -S^2]*((-39083*Pi^6)/18144 + (5*Pi^2*HPL[{4}, -S^2])/3 + (45*HPL[{6}, -S^2])/2 + 430*HPL[{2, 1}, -S^2]^2 + (310*Pi^2*HPL[{3, 1}, -S^2])/3 + 3*HPL[{4, 2}, -S^2] - 16*HPL[{5, 1}, -S^2] - 211*Pi^2*HPL[{2, 1, 1}, -S^2] - 768*HPL[{3, 2, 1}, -S^2] - 2288*HPL[{4, 1, 1}, -S^2] + 22184*HPL[{3, 1, 1, 1}, -S^2] - 3136*HPL[{2, 1, 1, 1, 1}, -S^2] + 78*HPL[{2, 1}, -S^2]*Zeta[3] - 9*Zeta[3]^2 + HPL[{3}, -S^2]*(42*HPL[{2, 1}, -S^2] + 2*Zeta[3])) + HPL[{3}, -S^2]*(-31*HPL[{5}, -S^2] + (25*Pi^2*HPL[{2, 1}, -S^2])/3 + 22*HPL[{4, 1}, -S^2] - 84*HPL[{2, 2, 1}, -S^2] - 260*HPL[{3, 1, 1}, -S^2] + 176*HPL[{2, 1, 1, 1}, -S^2] - 6*Pi^2*Zeta[3] - 60*Zeta[5]) - 30*Zeta[3]*Zeta[5] + HPL[{2, 1}, -S^2]*(-84*HPL[{3, 2}, -S^2] - 268*HPL[{4, 1}, -S^2] - 1720*HPL[{2, 2, 1}, -S^2] - 4984*HPL[{3, 1, 1}, -S^2] + 3136*HPL[{2, 1, 1, 1}, -S^2] + (41*Pi^2*Zeta[3])/3 + 78*Zeta[5])) + Log[T]^4*((-121*Pi^6)/27 - (11*HPL[{0}, S^2]^6)/36 + HPL[{0}, S^2]^4*((-55*Pi^2)/18 - (71*HPL[{2}, -S^2])/9) - (196*Pi^2*HPL[{2}, -S^2]^2)/9 - (784*HPL[{2}, -S^2]^3)/9 - (172*HPL[{3}, -S^2]^2)/3 + (152*Pi^2*HPL[{4}, -S^2])/9 - 12*HPL[{6}, -S^2] + HPL[{2}, -S^2]*((-6673*Pi^4)/270 + (664*HPL[{4}, -S^2])/3 - (664*HPL[{3, 1}, -S^2])/3) + (868*Pi^2*HPL[{3, 1}, -S^2])/3 - (640*HPL[{4, 2}, -S^2])/3 - (2288*HPL[{5, 1}, -S^2])/3 + HPL[{0}, S^2]^2*((-659*Pi^4)/72 - (749*Pi^2*HPL[{2}, -S^2])/18 - (196*HPL[{2}, -S^2]^2)/3 - (28*HPL[{4}, -S^2])/3 + 308*HPL[{3, 1}, -S^2] - 620*HPL[{2, 1, 1}, -S^2]) - 580*Pi^2*HPL[{2, 1, 1}, -S^2] + (640*HPL[{3, 1, 2}, -S^2])/3 - (5632*HPL[{3, 2, 1}, -S^2])/3 - 5792*HPL[{4, 1, 1}, -S^2] + 4480*HPL[{3, 1, 1, 1}, -S^2] - 8960*HPL[{2, 1, 1, 1, 1}, -S^2] + 1000*HPL[{2, 1}, -S^2]*Zeta[3] - 28*Zeta[3]^2 + HPL[{0}, S^2]^3*((32*HPL[{3}, -S^2])/9 - (730*HPL[{2, 1}, -S^2])/9 + (14*Zeta[3])/9) + HPL[{3}, -S^2]*((3800*HPL[{2, 1}, -S^2])/3 + (56*Zeta[3])/3) + HPL[{0}, S^2]*((122*Pi^2*HPL[{3}, -S^2])/9 + (32*HPL[{5}, -S^2])/3 - (2410*Pi^2*HPL[{2, 1}, -S^2])/9 - (136*HPL[{3, 2}, -S^2])/3 - 216*HPL[{4, 1}, -S^2] + 2000*HPL[{2, 2, 1}, -S^2] + 6240*HPL[{3, 1, 1}, -S^2] - 4480*HPL[{2, 1, 1, 1}, -S^2] + (194*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*((68*HPL[{3}, -S^2])/3 - 1000*HPL[{2, 1}, -S^2] + (332*Zeta[3])/3) + (260*Zeta[5])/3)) + HPL[{2}, -S^2]*((-13964*Pi^8)/14175 - (37*Pi^2*HPL[{3}, -S^2]^2)/3 + 18*HPL[{4}, -S^2]^2 + (67*Pi^2*HPL[{6}, -S^2])/3 + 108*HPL[{8}, -S^2] + (1214*Pi^2*HPL[{2, 1}, -S^2]^2)/3 - 1864*HPL[{3, 1}, -S^2]^2 - 38*Pi^2*HPL[{4, 2}, -S^2] - (692*Pi^2*HPL[{5, 1}, -S^2])/3 + 24*HPL[{5, 3}, -S^2] + 60*HPL[{6, 2}, -S^2] - 108*HPL[{7, 1}, -S^2] - (2021*Pi^4*HPL[{2, 1, 1}, -S^2])/30 - 6272*HPL[{2, 1, 1}, -S^2]^2 + HPL[{4}, -S^2]*(7*Pi^4 - 484*HPL[{3, 1}, -S^2] + 904*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 1}, -S^2]*((398*Pi^4)/15 + 6272*HPL[{2, 1, 1}, -S^2]) - 256*Pi^2*HPL[{3, 2, 1}, -S^2] - 532*HPL[{3, 3, 2}, -S^2] - (1624*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 908*HPL[{4, 1, 3}, -S^2] - 376*HPL[{4, 2, 2}, -S^2] + 2908*HPL[{4, 3, 1}, -S^2] + 1688*HPL[{5, 1, 2}, -S^2] + 12008*HPL[{5, 2, 1}, -S^2] + 31316*HPL[{6, 1, 1}, -S^2] + (59152*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 - 312*HPL[{3, 1, 2, 2}, -S^2] - 312*HPL[{3, 2, 1, 2}, -S^2] - 376*HPL[{3, 2, 2, 1}, -S^2] - 192*HPL[{3, 3, 1, 1}, -S^2] - 936*HPL[{4, 1, 1, 2}, -S^2] - 1128*HPL[{4, 1, 2, 1}, -S^2] - 1512*HPL[{4, 2, 1, 1}, -S^2] - 6560*HPL[{5, 1, 1, 1}, -S^2] - (3136*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + 5312*HPL[{4, 1, 1, 1, 1}, -S^2] - 4521152*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + HPL[{5}, -S^2]*(328*HPL[{2, 1}, -S^2] - 24*Zeta[3]) - 104*HPL[{3, 2}, -S^2]*Zeta[3] - 424*HPL[{4, 1}, -S^2]*Zeta[3] - 2832*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 8896*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 6272*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (29*Pi^2*Zeta[3]^2)/3 - 124*Zeta[3]*Zeta[5] + HPL[{3}, -S^2]*(-56*HPL[{5}, -S^2] + (826*Pi^2*HPL[{2, 1}, -S^2])/3 + 344*HPL[{3, 2}, -S^2] + 108*HPL[{4, 1}, -S^2] - 3728*HPL[{2, 2, 1}, -S^2] + 10592*HPL[{3, 1, 1}, -S^2] + 6272*HPL[{2, 1, 1, 1}, -S^2] + (52*Pi^2*Zeta[3])/3 + 64*Zeta[5]) + HPL[{2, 1}, -S^2]*(-3416*HPL[{3, 2}, -S^2] - 10280*HPL[{4, 1}, -S^2] + 6272*HPL[{3, 1, 1}, -S^2] + 12544*HPL[{2, 1, 1, 1}, -S^2] + (862*Pi^2*Zeta[3])/3 + 1444*Zeta[5])) + Log[T]^2*((-456659*Pi^8)/194400 - (5*HPL[{0}, S^2]^8)/192 + HPL[{0}, S^2]^6*((-19*Pi^2)/48 - (3*HPL[{2}, -S^2])/4) - (607*Pi^2*HPL[{2}, -S^2]^3)/9 - (88*Pi^2*HPL[{3}, -S^2]^2)/3 + 60*HPL[{4}, -S^2]^2 - (37*Pi^2*HPL[{6}, -S^2])/3 - 346*HPL[{8}, -S^2] + (784*Pi^2*HPL[{2, 1}, -S^2]^2)/3 + 688*HPL[{3, 1}, -S^2]^2 - 108*Pi^2*HPL[{4, 2}, -S^2] - (1100*Pi^2*HPL[{5, 1}, -S^2])/3 + 52*HPL[{5, 3}, -S^2] + 162*HPL[{6, 2}, -S^2] + 408*HPL[{7, 1}, -S^2] + HPL[{2}, -S^2]^2*((-2021*Pi^4)/120 + 226*HPL[{4}, -S^2] + 1568*HPL[{3, 1}, -S^2] - 3136*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 1}, -S^2]*((2651*Pi^4)/18 - 2656*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]^4*((-659*Pi^4)/288 - (277*Pi^2*HPL[{2}, -S^2])/36 - (241*HPL[{2}, -S^2]^2)/24 - (5*HPL[{4}, -S^2])/2 + (277*HPL[{3, 1}, -S^2])/6 - (284*HPL[{2, 1, 1}, -S^2])/3) - (13346*Pi^4*HPL[{2, 1, 1}, -S^2])/45 + HPL[{4}, -S^2]*((221*Pi^4)/90 - 1368*HPL[{3, 1}, -S^2] + 2656*HPL[{2, 1, 1}, -S^2]) + 108*Pi^2*HPL[{3, 1, 2}, -S^2] - (4532*Pi^2*HPL[{3, 2, 1}, -S^2])/3 - 848*HPL[{3, 3, 2}, -S^2] - (13960*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 1344*HPL[{4, 1, 3}, -S^2] - 732*HPL[{4, 2, 2}, -S^2] + 4864*HPL[{4, 3, 1}, -S^2] + 2904*HPL[{5, 1, 2}, -S^2] + 20184*HPL[{5, 2, 1}, -S^2] + 51696*HPL[{6, 1, 1}, -S^2] + 3472*Pi^2*HPL[{3, 1, 1, 1}, -S^2] + 12544*HPL[{3, 2, 2, 1}, -S^2] + 37632*HPL[{3, 3, 1, 1}, -S^2] - 2560*HPL[{4, 1, 1, 2}, -S^2] + 35072*HPL[{4, 1, 2, 1}, -S^2] + 110336*HPL[{4, 2, 1, 1}, -S^2] + 216640*HPL[{5, 1, 1, 1}, -S^2] - 6960*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2] + 25088*HPL[{2, 2, 1, 2, 1}, -S^2] + 75264*HPL[{2, 2, 2, 1, 1}, -S^2] - 147968*HPL[{3, 1, 1, 1, 2}, -S^2] - 248320*HPL[{3, 1, 1, 2, 1}, -S^2] - 298496*HPL[{3, 1, 2, 1, 1}, -S^2] - 624640*HPL[{3, 2, 1, 1, 1}, -S^2] - 1875840*HPL[{4, 1, 1, 1, 1}, -S^2] + 53760*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 107520*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{5}, -S^2]*(864*HPL[{2, 1}, -S^2] - 104*Zeta[3]) + HPL[{0}, S^2]^5*(HPL[{3}, -S^2]/2 - (271*HPL[{2, 1}, -S^2])/30 - (3*Zeta[3])/2) - 360*HPL[{3, 2}, -S^2]*Zeta[3] - 848*HPL[{4, 1}, -S^2]*Zeta[3] - 6272*HPL[{2, 2, 1}, -S^2]*Zeta[3] - 18592*HPL[{3, 1, 1}, -S^2]*Zeta[3] + 12000*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] - (62*Pi^2*Zeta[3]^2)/3 + HPL[{0}, S^2]^2*((-3413*Pi^6)/648 - (211*Pi^2*HPL[{2}, -S^2]^2)/4 - (215*HPL[{2}, -S^2]^3)/3 - 2*HPL[{3}, -S^2]^2 - (29*Pi^2*HPL[{4}, -S^2])/3 - 19*HPL[{6}, -S^2] + 784*HPL[{2, 1}, -S^2]^2 + (739*Pi^2*HPL[{3, 1}, -S^2])/3 - 4*HPL[{4, 2}, -S^2] + 44*HPL[{5, 1}, -S^2] + HPL[{2}, -S^2]*((-8449*Pi^4)/360 + 8*HPL[{4}, -S^2] + 772*HPL[{3, 1}, -S^2] - 1568*HPL[{2, 1, 1}, -S^2]) - (1498*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 4*HPL[{3, 1, 2}, -S^2] - 1716*HPL[{3, 2, 1}, -S^2] - 5272*HPL[{4, 1, 1}, -S^2] + 3696*HPL[{3, 1, 1, 1}, -S^2] - 7440*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(88*HPL[{2, 1}, -S^2] - 12*Zeta[3]) + 164*HPL[{2, 1}, -S^2]*Zeta[3] - 20*Zeta[3]^2) + HPL[{2}, -S^2]*((-52285*Pi^6)/4536 - 148*HPL[{3}, -S^2]^2 + (340*Pi^2*HPL[{4}, -S^2])/3 + 178*HPL[{6}, -S^2] + 3136*HPL[{2, 1}, -S^2]^2 + (440*Pi^2*HPL[{3, 1}, -S^2])/3 - 468*HPL[{4, 2}, -S^2] - 2704*HPL[{5, 1}, -S^2] - (1568*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 2656*HPL[{4, 1, 1}, -S^2] + 147872*HPL[{3, 1, 1, 1}, -S^2] + 3136*HPL[{2, 1}, -S^2]*Zeta[3] - 80*Zeta[3]^2 + HPL[{3}, -S^2]*(3136*HPL[{2, 1}, -S^2] + 200*Zeta[3])) + HPL[{3}, -S^2]*(-156*HPL[{5}, -S^2] + (1988*Pi^2*HPL[{2, 1}, -S^2])/3 + 584*HPL[{3, 2}, -S^2] + 544*HPL[{4, 1}, -S^2] - 6272*HPL[{2, 2, 1}, -S^2] - 20192*HPL[{3, 1, 1}, -S^2] + 15200*HPL[{2, 1, 1, 1}, -S^2] + (16*Pi^2*Zeta[3])/3 - 112*Zeta[5]) + HPL[{0}, S^2]^3*((31*Pi^2*HPL[{3}, -S^2])/9 + (10*HPL[{5}, -S^2])/3 - (212*Pi^2*HPL[{2, 1}, -S^2])/3 + (22*HPL[{3, 2}, -S^2])/3 - (20*HPL[{4, 1}, -S^2])/3 + 440*HPL[{2, 2, 1}, -S^2] + (4088*HPL[{3, 1, 1}, -S^2])/3 - (2920*HPL[{2, 1, 1, 1}, -S^2])/3 - (38*Pi^2*Zeta[3])/9 + HPL[{2}, -S^2]*(-4*HPL[{3}, -S^2] - 220*HPL[{2, 1}, -S^2] + (22*Zeta[3])/3) - 26*Zeta[5]) - 120*Zeta[3]*Zeta[5] + HPL[{2, 1}, -S^2]*(-6272*HPL[{3, 2}, -S^2] - 21472*HPL[{4, 1}, -S^2] - 12544*HPL[{2, 2, 1}, -S^2] - 22432*HPL[{3, 1, 1}, -S^2] + (1664*Pi^2*Zeta[3])/3 + 3040*Zeta[5]) + HPL[{0}, S^2]*((26*Pi^2*HPL[{5}, -S^2])/3 - 28*HPL[{7}, -S^2] - (46*Pi^2*HPL[{3, 2}, -S^2])/3 - (344*Pi^2*HPL[{4, 1}, -S^2])/3 - 180*HPL[{4, 3}, -S^2] - 512*HPL[{5, 2}, -S^2] - 1052*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((36*Pi^4)/5 + 84*HPL[{4}, -S^2] - 128*HPL[{3, 1}, -S^2] + 272*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-4061*Pi^4)/30 + 6000*HPL[{3, 1}, -S^2] + 12000*HPL[{2, 1, 1}, -S^2]) + 1440*Pi^2*HPL[{2, 2, 1}, -S^2] + (13448*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 608*HPL[{3, 2, 2}, -S^2] + 1472*HPL[{3, 3, 1}, -S^2] + 1456*HPL[{4, 1, 2}, -S^2] + 4048*HPL[{4, 2, 1}, -S^2] + 7904*HPL[{5, 1, 1}, -S^2] - (9640*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 12544*HPL[{2, 2, 2, 1}, -S^2] + 37088*HPL[{3, 1, 1, 2}, -S^2] + 37088*HPL[{3, 1, 2, 1}, -S^2] + 74720*HPL[{3, 2, 1, 1}, -S^2] + 223200*HPL[{4, 1, 1, 1}, -S^2] - 24000*HPL[{2, 1, 2, 1, 1}, -S^2] - 72000*HPL[{2, 2, 1, 1, 1}, -S^2] - 117120*HPL[{3, 1, 1, 1, 1}, -S^2] - 53760*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (373*Pi^4*Zeta[3])/90 - 672*HPL[{3, 1}, -S^2]*Zeta[3] + 1328*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-184*HPL[{2, 1}, -S^2] + 48*Zeta[3]) + HPL[{2}, -S^2]^2*(76*HPL[{3}, -S^2] - 1568*HPL[{2, 1}, -S^2] + 164*Zeta[3]) + (52*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((22*Pi^2*HPL[{3}, -S^2])/3 - 92*HPL[{5}, -S^2] - 720*Pi^2*HPL[{2, 1}, -S^2] - 304*HPL[{3, 2}, -S^2] - 728*HPL[{4, 1}, -S^2] + 6272*HPL[{2, 2, 1}, -S^2] - 18544*HPL[{3, 1, 1}, -S^2] - 12000*HPL[{2, 1, 1, 1}, -S^2] + (188*Pi^2*Zeta[3])/3 + 260*Zeta[5]))) + Log[T]^3*(HPL[{0}, S^2]^7/9 + HPL[{0}, S^2]^5*((373*Pi^2)/270 + (271*HPL[{2}, -S^2])/90) - (188*Pi^2*HPL[{5}, -S^2])/3 - 88*HPL[{7}, -S^2] + HPL[{2, 1}, -S^2]*((13346*Pi^4)/135 + (2656*HPL[{3, 1}, -S^2])/3) + (3652*Pi^2*HPL[{3, 2}, -S^2])/9 + (11320*Pi^2*HPL[{4, 1}, -S^2])/9 - 192*HPL[{4, 3}, -S^2] - 456*HPL[{5, 2}, -S^2] - (496*HPL[{6, 1}, -S^2])/3 + HPL[{3}, -S^2]*((-3596*Pi^4)/135 + (464*HPL[{4}, -S^2])/3 + (7648*HPL[{3, 1}, -S^2])/3 - (15200*HPL[{2, 1, 1}, -S^2])/3) + HPL[{0}, S^2]^3*((2467*Pi^4)/405 + (212*Pi^2*HPL[{2}, -S^2])/9 + (110*HPL[{2}, -S^2]^2)/3 + (92*HPL[{4}, -S^2])/9 - (1448*HPL[{3, 1}, -S^2])/9 + (2920*HPL[{2, 1, 1}, -S^2])/9) - (3136*Pi^2*HPL[{2, 2, 1}, -S^2])/9 - (16688*Pi^2*HPL[{3, 1, 1}, -S^2])/9 - (12544*HPL[{3, 2, 2}, -S^2])/3 - (40384*HPL[{3, 3, 1}, -S^2])/3 - (40384*HPL[{4, 1, 2}, -S^2])/3 - (123904*HPL[{4, 2, 1}, -S^2])/3 - 84800*HPL[{5, 1, 1}, -S^2] + 2320*Pi^2*HPL[{2, 1, 1, 1}, -S^2] + (25088*HPL[{2, 2, 2, 1}, -S^2])/3 - 15808*HPL[{3, 1, 1, 2}, -S^2] - 15808*HPL[{3, 1, 2, 1}, -S^2] - 40896*HPL[{3, 2, 1, 1}, -S^2] - 122048*HPL[{4, 1, 1, 1}, -S^2] - 17920*HPL[{3, 1, 1, 1, 1}, -S^2] + 35840*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^2*((-1568*HPL[{3}, -S^2])/3 + (3136*HPL[{2, 1}, -S^2])/3 - (1568*Zeta[3])/3) + HPL[{4}, -S^2]*((-2656*HPL[{2, 1}, -S^2])/3 - (352*Zeta[3])/3) + HPL[{0}, S^2]^4*(-2*HPL[{3}, -S^2] + (284*HPL[{2, 1}, -S^2])/9 + (7*Zeta[3])/9) - (3353*Pi^4*Zeta[3])/135 + 2016*HPL[{3, 1}, -S^2]*Zeta[3] - 4000*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{0}, S^2]*((2863*Pi^6)/324 + 120*Pi^2*HPL[{2}, -S^2]^2 + (1568*HPL[{2}, -S^2]^3)/9 - (88*HPL[{3}, -S^2]^2)/3 + (212*Pi^2*HPL[{4}, -S^2])/9 + (292*HPL[{6}, -S^2])/3 - 2000*HPL[{2, 1}, -S^2]^2 - (4808*Pi^2*HPL[{3, 1}, -S^2])/9 - (544*HPL[{5, 1}, -S^2])/3 + (9640*Pi^2*HPL[{2, 1, 1}, -S^2])/9 + HPL[{2}, -S^2]*((4061*Pi^4)/90 + (184*HPL[{4}, -S^2])/3 - 2000*HPL[{3, 1}, -S^2] + 4000*HPL[{2, 1, 1}, -S^2]) + (12544*HPL[{3, 2, 1}, -S^2])/3 + 12864*HPL[{4, 1, 1}, -S^2] - 8960*HPL[{3, 1, 1, 1}, -S^2] + 17920*HPL[{2, 1, 1, 1, 1}, -S^2] - (1328*HPL[{2, 1}, -S^2]*Zeta[3])/3 + 56*Zeta[3]^2 + HPL[{3}, -S^2]*((-272*HPL[{2, 1}, -S^2])/3 + (16*Zeta[3])/3)) + HPL[{2}, -S^2]*((-1988*Pi^2*HPL[{3}, -S^2])/9 - 288*HPL[{5}, -S^2] + (1568*Pi^2*HPL[{2, 1}, -S^2])/9 + (6272*HPL[{3, 2}, -S^2])/3 + (21472*HPL[{4, 1}, -S^2])/3 - (12544*HPL[{2, 2, 1}, -S^2])/3 + (22432*HPL[{3, 1, 1}, -S^2])/3 - (1664*Pi^2*Zeta[3])/9 - (3040*Zeta[5])/3) + HPL[{0}, S^2]^2*((-106*Pi^2*HPL[{3}, -S^2])/9 - 28*HPL[{5}, -S^2] + (1498*Pi^2*HPL[{2, 1}, -S^2])/9 + (172*HPL[{3, 2}, -S^2])/3 + (640*HPL[{4, 1}, -S^2])/3 - (3136*HPL[{2, 2, 1}, -S^2])/3 - (9968*HPL[{3, 1, 1}, -S^2])/3 + 2480*HPL[{2, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-88*HPL[{3}, -S^2])/3 + (1568*HPL[{2, 1}, -S^2])/3 - (164*Zeta[3])/3) - (76*Pi^2*Zeta[3])/9 - 52*Zeta[5]) - (632*Pi^2*Zeta[5])/3 - 1488*Zeta[7]) + HPL[{3}, -S^2]*((-70*Pi^2*HPL[{5}, -S^2])/3 - 500*HPL[{7}, -S^2] + (146*Pi^2*HPL[{3, 2}, -S^2])/3 + (158*Pi^2*HPL[{4, 1}, -S^2])/3 + 76*HPL[{4, 3}, -S^2] + 216*HPL[{5, 2}, -S^2] + 840*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((601*Pi^4)/15 - 3136*HPL[{3, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2]) - (1652*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (5308*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 692*HPL[{3, 2, 2}, -S^2] - 2032*HPL[{3, 3, 1}, -S^2] + 12*HPL[{4, 1, 2}, -S^2] - 180*HPL[{4, 2, 1}, -S^2] - 888*HPL[{5, 1, 1}, -S^2] + (3976*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 7456*HPL[{2, 2, 2, 1}, -S^2] - 21200*HPL[{3, 1, 1, 2}, -S^2] - 21200*HPL[{3, 1, 2, 1}, -S^2] - 43568*HPL[{3, 2, 1, 1}, -S^2] - 323008*HPL[{4, 1, 1, 1}, -S^2] + 12544*HPL[{2, 1, 2, 1, 1}, -S^2] + 37632*HPL[{2, 2, 1, 1, 1}, -S^2] + 59968*HPL[{3, 1, 1, 1, 1}, -S^2] + 30400*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (71*Pi^4*Zeta[3])/45 - 168*HPL[{3, 1}, -S^2]*Zeta[3] + 400*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-172*HPL[{2, 1}, -S^2] + 52*Zeta[3]) - (88*Pi^2*Zeta[5])/3 - 420*Zeta[7]) + HPL[{0}, S^2]^3*((-20*Pi^2*HPL[{5}, -S^2])/9 - (130*HPL[{7}, -S^2])/3 + (41*Pi^2*HPL[{3, 2}, -S^2])/18 + (25*Pi^2*HPL[{4, 1}, -S^2])/9 - (43*HPL[{4, 3}, -S^2])/3 - 43*HPL[{5, 2}, -S^2] - (206*HPL[{6, 1}, -S^2])/3 + HPL[{3}, -S^2]*((161*Pi^4)/540 + (22*HPL[{4}, -S^2])/3 + 6*HPL[{3, 1}, -S^2] - 8*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-3997*Pi^4)/540 + 220*HPL[{3, 1}, -S^2] + 440*HPL[{2, 1, 1}, -S^2]) + (187*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (1745*Pi^2*HPL[{3, 1, 1}, -S^2])/9 + 9*HPL[{3, 2, 2}, -S^2] + (20*HPL[{3, 3, 1}, -S^2])/3 + (20*HPL[{4, 1, 2}, -S^2])/3 - (4*HPL[{4, 2, 1}, -S^2])/3 - (52*HPL[{5, 1, 1}, -S^2])/3 - (424*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 424*HPL[{2, 2, 2, 1}, -S^2] + (3860*HPL[{3, 1, 1, 2}, -S^2])/3 + (3860*HPL[{3, 1, 2, 1}, -S^2])/3 + (7676*HPL[{3, 2, 1, 1}, -S^2])/3 + (22856*HPL[{4, 1, 1, 1}, -S^2])/3 - 880*HPL[{2, 1, 2, 1, 1}, -S^2] - 2640*HPL[{2, 2, 1, 1, 1}, -S^2] - (12944*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - (5840*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 - (3353*Pi^4*Zeta[3])/1080 - 10*HPL[{3, 1}, -S^2]*Zeta[3] + (44*HPL[{2, 1, 1}, -S^2]*Zeta[3])/3 + HPL[{2}, -S^2]^2*((7*HPL[{3}, -S^2])/6 - 53*HPL[{2, 1}, -S^2] + (3*Zeta[3])/2) + HPL[{4}, -S^2]*((-34*HPL[{2, 1}, -S^2])/3 + 12*Zeta[3]) - (79*Pi^2*Zeta[5])/3 + HPL[{2}, -S^2]*((-7*Pi^2*HPL[{3}, -S^2])/6 - (23*HPL[{5}, -S^2])/3 - (187*Pi^2*HPL[{2, 1}, -S^2])/6 - (14*HPL[{3, 2}, -S^2])/3 - (8*HPL[{4, 1}, -S^2])/3 + 212*HPL[{2, 2, 1}, -S^2] - 644*HPL[{3, 1, 1}, -S^2] - 440*HPL[{2, 1, 1, 1}, -S^2] + (11*Pi^2*Zeta[3])/18 + (16*Zeta[5])/3) - 186*Zeta[7]) + Zeta[3]*(-20*Pi^2*Zeta[5] + 600*Zeta[7]) + HPL[{2, 1}, -S^2]*((-1652*Pi^2*HPL[{3, 2}, -S^2])/3 - (5636*Pi^2*HPL[{4, 1}, -S^2])/3 + 188*HPL[{4, 3}, -S^2] + 408*HPL[{5, 2}, -S^2] - 196*HPL[{6, 1}, -S^2] - (4856*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (10592*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 6520*HPL[{3, 2, 2}, -S^2] + 19936*HPL[{3, 3, 1}, -S^2] + 19624*HPL[{4, 1, 2}, -S^2] + 60808*HPL[{4, 2, 1}, -S^2] + 125280*HPL[{5, 1, 1}, -S^2] + (3136*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 - 12544*HPL[{3, 1, 1, 2}, -S^2] - 12544*HPL[{3, 1, 2, 1}, -S^2] - 12544*HPL[{3, 2, 1, 1}, -S^2] - 42944*HPL[{4, 1, 1, 1}, -S^2] - 25088*HPL[{2, 1, 2, 1, 1}, -S^2] + 75264*HPL[{2, 2, 1, 1, 1}, -S^2] + 155840*HPL[{3, 1, 1, 1, 1}, -S^2] + (1013*Pi^4*Zeta[3])/30 - 3232*HPL[{3, 1}, -S^2]*Zeta[3] - 6272*HPL[{2, 1, 1}, -S^2]*Zeta[3] + (838*Pi^2*Zeta[5])/3 + 1932*Zeta[7]) + Log[T]*(HPL[{0}, S^2]^9/192 + HPL[{0}, S^2]^7*((13*Pi^2)/144 + HPL[{2}, -S^2]/8) + (8*HPL[{3}, -S^2]^3)/3 - (2*Pi^2*HPL[{7}, -S^2])/3 + 2084*HPL[{9}, -S^2] - (6272*HPL[{2, 1}, -S^2]^3)/3 - 64*Pi^2*HPL[{4, 3}, -S^2] - (490*Pi^2*HPL[{5, 2}, -S^2])/3 + 716*HPL[{5, 4}, -S^2] - 122*Pi^2*HPL[{6, 1}, -S^2] + 2908*HPL[{6, 3}, -S^2] + 7144*HPL[{7, 2}, -S^2] + 13404*HPL[{8, 1}, -S^2] + HPL[{5}, -S^2]*((-1343*Pi^4)/90 + 968*HPL[{3, 1}, -S^2] - 1728*HPL[{2, 1, 1}, -S^2]) + HPL[{0}, S^2]^5*((14057*Pi^4)/21600 + (293*Pi^2*HPL[{2}, -S^2])/180 + (77*HPL[{2}, -S^2]^2)/40 + HPL[{4}, -S^2]/2 - (87*HPL[{3, 1}, -S^2])/10 + (271*HPL[{2, 1, 1}, -S^2])/15) + HPL[{3, 2}, -S^2]*((1103*Pi^4)/15 + 12544*HPL[{2, 1, 1}, -S^2]) + HPL[{4, 1}, -S^2]*((10597*Pi^4)/45 + 42944*HPL[{2, 1, 1}, -S^2]) - (2021*Pi^4*HPL[{2, 2, 1}, -S^2])/15 - (25381*Pi^4*HPL[{3, 1, 1}, -S^2])/45 - (3302*Pi^2*HPL[{3, 2, 2}, -S^2])/3 - (10616*Pi^2*HPL[{3, 3, 1}, -S^2])/3 - (10624*Pi^2*HPL[{4, 1, 2}, -S^2])/3 - (32560*Pi^2*HPL[{4, 2, 1}, -S^2])/3 - 148*HPL[{4, 2, 3}, -S^2] - 84*HPL[{4, 3, 2}, -S^2] + 672*HPL[{4, 4, 1}, -S^2] - 22312*Pi^2*HPL[{5, 1, 1}, -S^2] + 584*HPL[{5, 1, 3}, -S^2] + 492*HPL[{5, 2, 2}, -S^2] + 3144*HPL[{5, 3, 1}, -S^2] + 2724*HPL[{6, 1, 2}, -S^2] + 8484*HPL[{6, 2, 1}, -S^2] + 16752*HPL[{7, 1, 1}, -S^2] + (26692*Pi^4*HPL[{2, 1, 1, 1}, -S^2])/45 + (9712*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 - (21832*Pi^2*HPL[{3, 1, 1, 2}, -S^2])/3 - (21832*Pi^2*HPL[{3, 1, 2, 1}, -S^2])/3 - (50968*Pi^2*HPL[{3, 2, 1, 1}, -S^2])/3 + 12736*HPL[{3, 2, 2, 2}, -S^2] + 39296*HPL[{3, 2, 3, 1}, -S^2] + 38656*HPL[{3, 3, 1, 2}, -S^2] + 119296*HPL[{3, 3, 2, 1}, -S^2] - (152176*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 - 243072*HPL[{4, 1, 1, 3}, -S^2] - 204760*HPL[{4, 1, 2, 2}, -S^2] - 365056*HPL[{4, 1, 3, 1}, -S^2] - 126040*HPL[{4, 2, 1, 2}, -S^2] - 124120*HPL[{4, 2, 2, 1}, -S^2] - 721152*HPL[{4, 3, 1, 1}, -S^2] - 734256*HPL[{5, 1, 1, 2}, -S^2] - 1210416*HPL[{5, 1, 2, 1}, -S^2] - 2882736*HPL[{5, 2, 1, 1}, -S^2] - 7200992*HPL[{6, 1, 1, 1}, -S^2] + (6272*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 6272*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] + 5600*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2] - 25088*HPL[{3, 1, 1, 2, 2}, -S^2] - 25088*HPL[{3, 1, 2, 1, 2}, -S^2] + 156032*HPL[{3, 1, 3, 1, 1}, -S^2] - 25088*HPL[{3, 2, 1, 1, 2}, -S^2] + 130944*HPL[{3, 2, 2, 1, 1}, -S^2] + 392832*HPL[{3, 3, 1, 1, 1}, -S^2] - 80768*HPL[{4, 1, 1, 1, 2}, -S^2] - 5504*HPL[{4, 1, 1, 2, 1}, -S^2] + 387328*HPL[{4, 1, 2, 1, 1}, -S^2] + 1172992*HPL[{4, 2, 1, 1, 1}, -S^2] + 2332800*HPL[{5, 1, 1, 1, 1}, -S^2] + 13920*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - 50176*HPL[{2, 2, 1, 2, 1, 1}, -S^2] - 150528*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + 306560*HPL[{3, 1, 1, 1, 1, 2}, -S^2] + 607616*HPL[{3, 1, 1, 1, 2, 1}, -S^2] + 808320*HPL[{3, 1, 1, 2, 1, 1}, -S^2] + 908672*HPL[{3, 1, 2, 1, 1, 1}, -S^2] + 1560960*HPL[{3, 2, 1, 1, 1, 1}, -S^2] + 4686720*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - 107520*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + 215040*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^3*((-932*HPL[{3}, -S^2])/3 - 236*Zeta[3]) + HPL[{6}, -S^2]*(-356*HPL[{2, 1}, -S^2] - 236*Zeta[3]) + HPL[{0}, S^2]^6*(-HPL[{3}, -S^2]/12 + (3*HPL[{2, 1}, -S^2])/2 + Zeta[3]/2) - (1847*Pi^6*Zeta[3])/567 + 3136*HPL[{2, 1}, -S^2]^2*Zeta[3] + 104*HPL[{4, 2}, -S^2]*Zeta[3] + 720*HPL[{5, 1}, -S^2]*Zeta[3] - 80*HPL[{3, 1, 2}, -S^2]*Zeta[3] - 5744*HPL[{3, 2, 1}, -S^2]*Zeta[3] - 17696*HPL[{4, 1, 1}, -S^2]*Zeta[3] + 12096*HPL[{3, 1, 1, 1}, -S^2]*Zeta[3] - 24000*HPL[{2, 1, 1, 1, 1}, -S^2]*Zeta[3] - 64*Zeta[3]^3 + HPL[{3}, -S^2]^2*(296*HPL[{2, 1}, -S^2] + 32*Zeta[3]) + HPL[{3}, -S^2]*((-30311*Pi^6)/5670 + (142*Pi^2*HPL[{4}, -S^2])/3 + 304*HPL[{6}, -S^2] + 3136*HPL[{2, 1}, -S^2]^2 + 668*Pi^2*HPL[{3, 1}, -S^2] + 156*HPL[{4, 2}, -S^2] - 344*HPL[{5, 1}, -S^2] - (3976*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 16*HPL[{3, 1, 2}, -S^2] - 7440*HPL[{3, 2, 1}, -S^2] + 220480*HPL[{4, 1, 1}, -S^2] + 15296*HPL[{3, 1, 1, 1}, -S^2] - 30400*HPL[{2, 1, 1, 1, 1}, -S^2] - 400*HPL[{2, 1}, -S^2]*Zeta[3] - 64*Zeta[3]^2) + HPL[{2, 1}, -S^2]*((52285*Pi^6)/2268 - (880*Pi^2*HPL[{3, 1}, -S^2])/3 + 936*HPL[{4, 2}, -S^2] + 5408*HPL[{5, 1}, -S^2] - (3136*Pi^2*HPL[{2, 1, 1}, -S^2])/3 - 5312*HPL[{4, 1, 1}, -S^2] + 5312*HPL[{3, 1, 1, 1}, -S^2] + 160*Zeta[3]^2) + HPL[{0}, S^2]^3*((2863*Pi^6)/1296 + (187*Pi^2*HPL[{2}, -S^2]^2)/12 + (53*HPL[{2}, -S^2]^3)/3 - (16*HPL[{3}, -S^2]^2)/3 + (38*Pi^2*HPL[{4}, -S^2])/9 - (4*HPL[{6}, -S^2])/3 - 220*HPL[{2, 1}, -S^2]^2 - (623*Pi^2*HPL[{3, 1}, -S^2])/9 - (4*HPL[{4, 2}, -S^2])/3 - (100*HPL[{5, 1}, -S^2])/3 + (424*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + HPL[{2}, -S^2]*((3997*Pi^4)/540 + (34*HPL[{4}, -S^2])/3 - 220*HPL[{3, 1}, -S^2] + 440*HPL[{2, 1, 1}, -S^2]) + (4*HPL[{3, 1, 2}, -S^2])/3 + (1276*HPL[{3, 2, 1}, -S^2])/3 + (4000*HPL[{4, 1, 1}, -S^2])/3 - (2896*HPL[{3, 1, 1, 1}, -S^2])/3 + (5840*HPL[{2, 1, 1, 1, 1}, -S^2])/3 - (44*HPL[{2, 1}, -S^2]*Zeta[3])/3 + 14*Zeta[3]^2 + HPL[{3}, -S^2]*(8*HPL[{2, 1}, -S^2] + 4*Zeta[3])) + HPL[{2, 1, 1}, -S^2]*(25088*HPL[{2, 2, 1}, -S^2] + 44864*HPL[{3, 1, 1}, -S^2] - (3328*Pi^2*Zeta[3])/3 - 6080*Zeta[5]) + HPL[{2}, -S^2]^2*((-413*Pi^2*HPL[{3}, -S^2])/3 - 164*HPL[{5}, -S^2] + (1214*Pi^2*HPL[{2, 1}, -S^2])/3 + 1708*HPL[{3, 2}, -S^2] + 5140*HPL[{4, 1}, -S^2] - 3136*HPL[{3, 1, 1}, -S^2] + 6272*HPL[{2, 1, 1, 1}, -S^2] - (431*Pi^2*Zeta[3])/3 - 722*Zeta[5]) + HPL[{4}, -S^2]*(-352*HPL[{5}, -S^2] - (680*Pi^2*HPL[{2, 1}, -S^2])/3 - 344*HPL[{3, 2}, -S^2] - 1272*HPL[{4, 1}, -S^2] + 1808*HPL[{2, 2, 1}, -S^2] + 6352*HPL[{3, 1, 1}, -S^2] - 5312*HPL[{2, 1, 1, 1}, -S^2] - 40*Pi^2*Zeta[3] - 336*Zeta[5]) - (1564*Pi^4*Zeta[5])/45 + HPL[{0}, S^2]^4*((-11*Pi^2*HPL[{3}, -S^2])/12 - HPL[{5}, -S^2]/2 + (277*Pi^2*HPL[{2, 1}, -S^2])/18 + HPL[{2}, -S^2]*(-HPL[{3}, -S^2]/2 + (241*HPL[{2, 1}, -S^2])/6) + HPL[{3, 2}, -S^2] + 8*HPL[{4, 1}, -S^2] - (241*HPL[{2, 2, 1}, -S^2])/3 - 253*HPL[{3, 1, 1}, -S^2] + (568*HPL[{2, 1, 1, 1}, -S^2])/3 + (97*Pi^2*Zeta[3])/36 + (65*Zeta[5])/6) + HPL[{3, 1}, -S^2]*(-6304*HPL[{3, 2}, -S^2] - 21648*HPL[{4, 1}, -S^2] + 12544*HPL[{2, 2, 1}, -S^2] - 27840*HPL[{3, 1, 1}, -S^2] + 5312*HPL[{2, 1, 1, 1}, -S^2] + 564*Pi^2*Zeta[3] + 3112*Zeta[5]) + HPL[{0}, S^2]^2*(-8*Pi^2*HPL[{5}, -S^2] + 64*HPL[{7}, -S^2] + (49*Pi^2*HPL[{3, 2}, -S^2])/3 + (208*Pi^2*HPL[{4, 1}, -S^2])/3 - 48*HPL[{4, 3}, -S^2] - 148*HPL[{5, 2}, -S^2] - 242*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((8449*Pi^4)/180 - 1544*HPL[{3, 1}, -S^2] - 3136*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-323*Pi^4)/90 + 26*HPL[{4}, -S^2] + 92*HPL[{3, 1}, -S^2] - 176*HPL[{2, 1, 1}, -S^2]) - 422*Pi^2*HPL[{2, 2, 1}, -S^2] - (4010*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 166*HPL[{3, 2, 2}, -S^2] - 520*HPL[{3, 3, 1}, -S^2] - 528*HPL[{4, 1, 2}, -S^2] - 1584*HPL[{4, 2, 1}, -S^2] - 3336*HPL[{5, 1, 1}, -S^2] + (2996*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 3440*HPL[{2, 2, 2, 1}, -S^2] - 9976*HPL[{3, 1, 1, 2}, -S^2] - 9976*HPL[{3, 1, 2, 1}, -S^2] - 20296*HPL[{3, 2, 1, 1}, -S^2] - 60640*HPL[{4, 1, 1, 1}, -S^2] + 6272*HPL[{2, 1, 2, 1, 1}, -S^2] + 18816*HPL[{2, 2, 1, 1, 1}, -S^2] + 30240*HPL[{3, 1, 1, 1, 1}, -S^2] + 14880*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{2}, -S^2]^2*(-21*HPL[{3}, -S^2] + 430*HPL[{2, 1}, -S^2] - 39*Zeta[3]) + HPL[{4}, -S^2]*(-16*HPL[{2, 1}, -S^2] - 32*Zeta[3]) + (373*Pi^4*Zeta[3])/180 + 180*HPL[{3, 1}, -S^2]*Zeta[3] - 328*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{2}, -S^2]*((-25*Pi^2*HPL[{3}, -S^2])/3 - 24*HPL[{5}, -S^2] + 211*Pi^2*HPL[{2, 1}, -S^2] + 84*HPL[{3, 2}, -S^2] + 268*HPL[{4, 1}, -S^2] - 1720*HPL[{2, 2, 1}, -S^2] + 4984*HPL[{3, 1, 1}, -S^2] + 3136*HPL[{2, 1, 1, 1}, -S^2] - (41*Pi^2*Zeta[3])/3 - 78*Zeta[5]) + (26*Pi^2*Zeta[5])/3) + HPL[{0}, S^2]*((177569*Pi^8)/64800 + (551*Pi^2*HPL[{2}, -S^2]^3)/9 + 59*HPL[{2}, -S^2]^4 - (38*Pi^2*HPL[{3}, -S^2]^2)/3 + 74*HPL[{4}, -S^2]^2 + 23*Pi^2*HPL[{6}, -S^2] - 298*HPL[{8}, -S^2] - 720*Pi^2*HPL[{2, 1}, -S^2]^2 + 3008*HPL[{3, 1}, -S^2]^2 - (4*Pi^2*HPL[{4, 2}, -S^2])/3 - (236*Pi^2*HPL[{5, 1}, -S^2])/3 - 12*HPL[{5, 3}, -S^2] - 30*HPL[{6, 2}, -S^2] - 216*HPL[{7, 1}, -S^2] + HPL[{3, 1}, -S^2]*((-12071*Pi^4)/90 - 12000*HPL[{2, 1, 1}, -S^2]) + (4061*Pi^4*HPL[{2, 1, 1}, -S^2])/15 + 12000*HPL[{2, 1, 1}, -S^2]^2 + HPL[{4}, -S^2]*((149*Pi^4)/18 - 200*HPL[{3, 1}, -S^2] + 368*HPL[{2, 1, 1}, -S^2]) + HPL[{2}, -S^2]^2*((2155*Pi^4)/72 + 8*HPL[{4}, -S^2] - 1568*HPL[{3, 1}, -S^2] + 3136*HPL[{2, 1, 1}, -S^2]) + (4*Pi^2*HPL[{3, 1, 2}, -S^2])/3 + (4412*Pi^2*HPL[{3, 2, 1}, -S^2])/3 - 64*HPL[{3, 3, 2}, -S^2] + (13648*Pi^2*HPL[{4, 1, 1}, -S^2])/3 + 152*HPL[{4, 1, 3}, -S^2] - 52*HPL[{4, 2, 2}, -S^2] + 280*HPL[{4, 3, 1}, -S^2] + 176*HPL[{5, 1, 2}, -S^2] + 1136*HPL[{5, 2, 1}, -S^2] + 3464*HPL[{6, 1, 1}, -S^2] - (9616*Pi^2*HPL[{3, 1, 1, 1}, -S^2])/3 - 12544*HPL[{3, 2, 2, 1}, -S^2] - 37632*HPL[{3, 3, 1, 1}, -S^2] - 37632*HPL[{4, 1, 2, 1}, -S^2] - 112896*HPL[{4, 2, 1, 1}, -S^2] - 226880*HPL[{5, 1, 1, 1}, -S^2] + (19280*Pi^2*HPL[{2, 1, 1, 1, 1}, -S^2])/3 - 25088*HPL[{2, 2, 1, 2, 1}, -S^2] - 75264*HPL[{2, 2, 2, 1, 1}, -S^2] + 150528*HPL[{3, 1, 1, 1, 2}, -S^2] + 250880*HPL[{3, 1, 1, 2, 1}, -S^2] + 301056*HPL[{3, 1, 2, 1, 1}, -S^2] + 627200*HPL[{3, 2, 1, 1, 1}, -S^2] + 1883520*HPL[{4, 1, 1, 1, 1}, -S^2] - 53760*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 107520*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + 32*HPL[{3, 2}, -S^2]*Zeta[3] + 1312*HPL[{2, 2, 1}, -S^2]*Zeta[3] + 3968*HPL[{3, 1, 1}, -S^2]*Zeta[3] - 2656*HPL[{2, 1, 1, 1}, -S^2]*Zeta[3] + 28*Pi^2*Zeta[3]^2 + HPL[{5}, -S^2]*(184*HPL[{2, 1}, -S^2] + 128*Zeta[3]) + HPL[{2}, -S^2]*((248987*Pi^6)/22680 - 8*HPL[{3}, -S^2]^2 + (80*Pi^2*HPL[{4}, -S^2])/3 + 146*HPL[{6}, -S^2] - 3136*HPL[{2, 1}, -S^2]^2 - 720*Pi^2*HPL[{3, 1}, -S^2] - 216*HPL[{5, 1}, -S^2] + 1440*Pi^2*HPL[{2, 1, 1}, -S^2] + 5664*HPL[{3, 2, 1}, -S^2] + 17360*HPL[{4, 1, 1}, -S^2] - 162528*HPL[{3, 1, 1, 1}, -S^2] + 24000*HPL[{2, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]*(-304*HPL[{2, 1}, -S^2] - 16*Zeta[3]) - 656*HPL[{2, 1}, -S^2]*Zeta[3] + 68*Zeta[3]^2) + HPL[{2, 1}, -S^2]*(608*HPL[{3, 2}, -S^2] + 1456*HPL[{4, 1}, -S^2] + 12544*HPL[{2, 2, 1}, -S^2] + 37088*HPL[{3, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1}, -S^2] - (376*Pi^2*Zeta[3])/3 - 520*Zeta[5]) + 336*Zeta[3]*Zeta[5] + HPL[{3}, -S^2]*(-148*HPL[{5}, -S^2] - (44*Pi^2*HPL[{2, 1}, -S^2])/3 + 32*HPL[{3, 2}, -S^2] + 136*HPL[{4, 1}, -S^2] + 608*HPL[{2, 2, 1}, -S^2] + 1472*HPL[{3, 1, 1}, -S^2] - 544*HPL[{2, 1, 1, 1}, -S^2] + (16*Pi^2*Zeta[3])/3 + 96*Zeta[5])) + HPL[{2}, -S^2]*(-80*Pi^2*HPL[{5}, -S^2] - 60*HPL[{7}, -S^2] + (1652*Pi^2*HPL[{3, 2}, -S^2])/3 + (5636*Pi^2*HPL[{4, 1}, -S^2])/3 - 188*HPL[{4, 3}, -S^2] - 408*HPL[{5, 2}, -S^2] + 196*HPL[{6, 1}, -S^2] + HPL[{2, 1}, -S^2]*((2021*Pi^4)/30 - 6272*HPL[{3, 1}, -S^2] - 12544*HPL[{2, 1, 1}, -S^2]) + HPL[{3}, -S^2]*((-601*Pi^4)/15 + 172*HPL[{4}, -S^2] + 3136*HPL[{3, 1}, -S^2] - 6272*HPL[{2, 1, 1}, -S^2]) - (4856*Pi^2*HPL[{2, 2, 1}, -S^2])/3 + (10592*Pi^2*HPL[{3, 1, 1}, -S^2])/3 - 6520*HPL[{3, 2, 2}, -S^2] - 19936*HPL[{3, 3, 1}, -S^2] - 19624*HPL[{4, 1, 2}, -S^2] - 60808*HPL[{4, 2, 1}, -S^2] - 125280*HPL[{5, 1, 1}, -S^2] + (3136*Pi^2*HPL[{2, 1, 1, 1}, -S^2])/3 + 12544*HPL[{3, 1, 1, 2}, -S^2] + 12544*HPL[{3, 1, 2, 1}, -S^2] + 12544*HPL[{3, 2, 1, 1}, -S^2] + 42944*HPL[{4, 1, 1, 1}, -S^2] + 25088*HPL[{2, 1, 2, 1, 1}, -S^2] + 75264*HPL[{2, 2, 1, 1, 1}, -S^2] - 155840*HPL[{3, 1, 1, 1, 1}, -S^2] + HPL[{4}, -S^2]*(-904*HPL[{2, 1}, -S^2] - 112*Zeta[3]) - (1013*Pi^4*Zeta[3])/30 + 3232*HPL[{3, 1}, -S^2]*Zeta[3] - 6272*HPL[{2, 1, 1}, -S^2]*Zeta[3] - (838*Pi^2*Zeta[5])/3 - 1932*Zeta[7]) - 372*Pi^2*Zeta[7] - 3136*Zeta[9]) + HPL[{0}, S^2]*((8*HPL[{3}, -S^2]^3)/3 - (137*Pi^2*HPL[{7}, -S^2])/3 - 994*HPL[{9}, -S^2] + (3136*HPL[{2, 1}, -S^2]^3)/3 - (88*Pi^2*HPL[{4, 3}, -S^2])/3 - (257*Pi^2*HPL[{5, 2}, -S^2])/3 + 314*HPL[{5, 4}, -S^2] - (469*Pi^2*HPL[{6, 1}, -S^2])/3 + 1262*HPL[{6, 3}, -S^2] + 3124*HPL[{7, 2}, -S^2] + 6654*HPL[{8, 1}, -S^2] + HPL[{4, 1}, -S^2]*((-59*Pi^4)/18 - 1456*HPL[{2, 1, 1}, -S^2]) + HPL[{3, 2}, -S^2]*((29*Pi^4)/18 - 608*HPL[{2, 1, 1}, -S^2]) + HPL[{5}, -S^2]*((-209*Pi^4)/180 + 156*HPL[{3, 1}, -S^2] - 184*HPL[{2, 1, 1}, -S^2]) + (2155*Pi^4*HPL[{2, 2, 1}, -S^2])/18 + (11207*Pi^4*HPL[{3, 1, 1}, -S^2])/30 + (179*Pi^2*HPL[{3, 2, 2}, -S^2])/3 + (388*Pi^2*HPL[{3, 3, 1}, -S^2])/3 + 128*Pi^2*HPL[{4, 1, 2}, -S^2] + 336*Pi^2*HPL[{4, 2, 1}, -S^2] + 6*HPL[{4, 2, 3}, -S^2] + 70*HPL[{4, 3, 2}, -S^2] + 488*HPL[{4, 4, 1}, -S^2] + (1924*Pi^2*HPL[{5, 1, 1}, -S^2])/3 + 372*HPL[{5, 1, 3}, -S^2] + 570*HPL[{5, 2, 2}, -S^2] + 2196*HPL[{5, 3, 1}, -S^2] + 1858*HPL[{6, 1, 2}, -S^2] + 5778*HPL[{6, 2, 1}, -S^2] + 11704*HPL[{7, 1, 1}, -S^2] - (4061*Pi^4*HPL[{2, 1, 1, 1}, -S^2])/15 - (4408*Pi^2*HPL[{2, 2, 2, 1}, -S^2])/3 + (13132*Pi^2*HPL[{3, 1, 1, 2}, -S^2])/3 + (13132*Pi^2*HPL[{3, 1, 2, 1}, -S^2])/3 + (26356*Pi^2*HPL[{3, 2, 1, 1}, -S^2])/3 - 480*HPL[{3, 2, 2, 2}, -S^2] - 1504*HPL[{3, 2, 3, 1}, -S^2] - 1504*HPL[{3, 3, 1, 2}, -S^2] - 4576*HPL[{3, 3, 2, 1}, -S^2] + (78656*Pi^2*HPL[{4, 1, 1, 1}, -S^2])/3 + 8856*HPL[{4, 1, 1, 3}, -S^2] + 7364*HPL[{4, 1, 2, 2}, -S^2] + 13496*HPL[{4, 1, 3, 1}, -S^2] + 4292*HPL[{4, 2, 1, 2}, -S^2] + 4292*HPL[{4, 2, 2, 1}, -S^2] + 27288*HPL[{4, 3, 1, 1}, -S^2] + 26624*HPL[{5, 1, 1, 2}, -S^2] + 45056*HPL[{5, 1, 2, 1}, -S^2] + 109568*HPL[{5, 2, 1, 1}, -S^2] + 274376*HPL[{6, 1, 1, 1}, -S^2] - 2880*Pi^2*HPL[{2, 1, 2, 1, 1}, -S^2] - 8640*Pi^2*HPL[{2, 2, 1, 1, 1}, -S^2] + 11328*HPL[{2, 2, 2, 2, 1}, -S^2] - (42224*Pi^2*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + 35200*HPL[{3, 1, 1, 2, 2}, -S^2] + 35200*HPL[{3, 1, 2, 1, 2}, -S^2] - 244480*HPL[{3, 1, 3, 1, 1}, -S^2] + 69184*HPL[{3, 2, 1, 1, 2}, -S^2] + 33984*HPL[{3, 2, 1, 2, 1}, -S^2] - 107328*HPL[{3, 2, 2, 1, 1}, -S^2] - 355968*HPL[{3, 3, 1, 1, 1}, -S^2] + 206816*HPL[{4, 1, 1, 1, 2}, -S^2] + 101216*HPL[{4, 1, 1, 2, 1}, -S^2] - 322720*HPL[{4, 1, 2, 1, 1}, -S^2] - 1068640*HPL[{4, 2, 1, 1, 1}, -S^2] - 2137664*HPL[{5, 1, 1, 1, 1}, -S^2] - (19280*Pi^2*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + 25088*HPL[{2, 2, 1, 2, 1, 1}, -S^2] + 75264*HPL[{2, 2, 2, 1, 1, 1}, -S^2] - 126528*HPL[{3, 1, 1, 1, 1, 2}, -S^2] - 277056*HPL[{3, 1, 1, 1, 2, 1}, -S^2] - 377408*HPL[{3, 1, 1, 2, 1, 1}, -S^2] - 427584*HPL[{3, 1, 2, 1, 1, 1}, -S^2] - 753728*HPL[{3, 2, 1, 1, 1, 1}, -S^2] - 2263104*HPL[{4, 1, 1, 1, 1, 1}, -S^2] + 48000*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] + 192000*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] + 480000*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] + 1013760*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] - 107520*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + HPL[{3}, -S^2]^2*(8*HPL[{2, 1}, -S^2] - 8*Zeta[3]) - (1847*Pi^6*Zeta[3])/1134 - 328*HPL[{2, 1}, -S^2]^2*Zeta[3] + 12*HPL[{4, 2}, -S^2]*Zeta[3] - 96*HPL[{5, 1}, -S^2]*Zeta[3] + 656*HPL[{3, 2, 1}, -S^2]*Zeta[3] + 2064*HPL[{4, 1, 1}, -S^2]*Zeta[3] - 1344*HPL[{3, 1, 1, 1}, -S^2]*Zeta[3] + 2656*HPL[{2, 1, 1, 1, 1}, -S^2]*Zeta[3] - 32*Zeta[3]^3 + HPL[{2}, -S^2]^3*(10*HPL[{3}, -S^2] - 236*HPL[{2, 1}, -S^2] + (82*Zeta[3])/3) + HPL[{6}, -S^2]*(-146*HPL[{2, 1}, -S^2] + 154*Zeta[3]) + HPL[{3}, -S^2]*((437*Pi^6)/756 + (43*Pi^2*HPL[{4}, -S^2])/3 + 160*HPL[{6}, -S^2] - 152*HPL[{2, 1}, -S^2]^2 - (14*Pi^2*HPL[{3, 1}, -S^2])/3 - 6*HPL[{4, 2}, -S^2] - 180*HPL[{5, 1}, -S^2] + (44*Pi^2*HPL[{2, 1, 1}, -S^2])/3 + 240*HPL[{3, 2, 1}, -S^2] - 8328*HPL[{4, 1, 1}, -S^2] - 256*HPL[{3, 1, 1, 1}, -S^2] + 544*HPL[{2, 1, 1, 1, 1}, -S^2] + 16*HPL[{2, 1}, -S^2]*Zeta[3]) + HPL[{2, 1}, -S^2]*((-248987*Pi^6)/22680 + 720*Pi^2*HPL[{3, 1}, -S^2] + 216*HPL[{5, 1}, -S^2] + 1440*Pi^2*HPL[{2, 1, 1}, -S^2] - 5664*HPL[{3, 2, 1}, -S^2] - 17360*HPL[{4, 1, 1}, -S^2] + 12000*HPL[{3, 1, 1, 1}, -S^2] + 24000*HPL[{2, 1, 1, 1, 1}, -S^2] - 68*Zeta[3]^2) + HPL[{3, 1}, -S^2]*(272*HPL[{3, 2}, -S^2] + 616*HPL[{4, 1}, -S^2] - 6272*HPL[{2, 2, 1}, -S^2] + 51840*HPL[{3, 1, 1}, -S^2] + 12000*HPL[{2, 1, 1, 1}, -S^2] - 66*Pi^2*Zeta[3] - 308*Zeta[5]) - (782*Pi^4*Zeta[5])/45 + HPL[{2}, -S^2]^2*((15*Pi^2*HPL[{3}, -S^2])/2 - 2*HPL[{5}, -S^2] - (551*Pi^2*HPL[{2, 1}, -S^2])/3 - 60*HPL[{3, 2}, -S^2] - 188*HPL[{4, 1}, -S^2] + 1416*HPL[{2, 2, 1}, -S^2] + 4400*HPL[{3, 1, 1}, -S^2] - 3136*HPL[{2, 1, 1, 1}, -S^2] + (91*Pi^2*Zeta[3])/6 + 53*Zeta[5]) + HPL[{4}, -S^2]*(-160*HPL[{5}, -S^2] - (80*Pi^2*HPL[{2, 1}, -S^2])/3 - 20*HPL[{3, 2}, -S^2] - 208*HPL[{4, 1}, -S^2] + 32*HPL[{2, 2, 1}, -S^2] + 264*HPL[{3, 1, 1}, -S^2] - 368*HPL[{2, 1, 1, 1}, -S^2] + 16*Pi^2*Zeta[3] + 152*Zeta[5]) + HPL[{2, 1, 1}, -S^2]*(-12544*HPL[{2, 2, 1}, -S^2] - 37088*HPL[{3, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1}, -S^2] + (376*Pi^2*Zeta[3])/3 + 520*Zeta[5]) - 186*Pi^2*Zeta[7] + HPL[{2}, -S^2]*((-46*Pi^2*HPL[{5}, -S^2])/3 - 134*HPL[{7}, -S^2] - 30*Pi^2*HPL[{3, 2}, -S^2] - (190*Pi^2*HPL[{4, 1}, -S^2])/3 - 26*HPL[{4, 3}, -S^2] - 84*HPL[{5, 2}, -S^2] - 14*HPL[{6, 1}, -S^2] + HPL[{3}, -S^2]*((-5*Pi^4)/6 + 10*HPL[{4}, -S^2] - 136*HPL[{3, 1}, -S^2] + 304*HPL[{2, 1, 1}, -S^2]) + HPL[{2, 1}, -S^2]*((-2155*Pi^4)/36 + 3136*HPL[{3, 1}, -S^2] + 6272*HPL[{2, 1, 1}, -S^2]) + (2204*Pi^2*HPL[{2, 2, 1}, -S^2])/3 - (6568*Pi^2*HPL[{3, 1, 1}, -S^2])/3 + 240*HPL[{3, 2, 2}, -S^2] + 752*HPL[{3, 3, 1}, -S^2] + 752*HPL[{4, 1, 2}, -S^2] + 2288*HPL[{4, 2, 1}, -S^2] + 4424*HPL[{5, 1, 1}, -S^2] - 1440*Pi^2*HPL[{2, 1, 1, 1}, -S^2] - 5664*HPL[{2, 2, 2, 1}, -S^2] - 17600*HPL[{3, 1, 1, 2}, -S^2] - 17600*HPL[{3, 1, 2, 1}, -S^2] - 34592*HPL[{3, 2, 1, 1}, -S^2] - 103408*HPL[{4, 1, 1, 1}, -S^2] - 12544*HPL[{2, 1, 2, 1, 1}, -S^2] - 37632*HPL[{2, 2, 1, 1, 1}, -S^2] + 63264*HPL[{3, 1, 1, 1, 1}, -S^2] - 24000*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (229*Pi^4*Zeta[3])/60 - 344*HPL[{3, 1}, -S^2]*Zeta[3] + 656*HPL[{2, 1, 1}, -S^2]*Zeta[3] + HPL[{4}, -S^2]*(-16*HPL[{2, 1}, -S^2] + 8*Zeta[3]) + 27*Pi^2*Zeta[5] + 150*Zeta[7]) - 1568*Zeta[9]);
E5wuvT1F1=(-35*Pi^4*S)/9 - (479*Pi^6*S)/1080 - (199*Pi^8*S)/9450 - (HPL[{0}, S^2]^8*HPL[{1}, -S^2])/(96*S) + ((-58*Pi^2)/(21*S) - (40*(1 + S^2))/(7*S))*HPL[{1}, -S^2]^7 - (4*(1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) - (16*HPL[{1}, -S^2]^9)/(27*S) + HPL[{0}, S^2]^7*(S/24 + ((1 + S^2)*HPL[{1}, -S^2])/(48*S) - HPL[{1}, -S^2]^2/(16*S)) - (2*(17 + 7*S^2)*HPL[{2}, -S^2]^4)/(3*S) - (4*HPL[{3}, -S^2]^3)/S + (2*(21 + 11*S^2)*HPL[{4}, -S^2]^2)/S + ((130*Pi^2)/(3*S) + (4*(-65 + 163*S^2))/S)*HPL[{7}, -S^2] + (20*(-21 + S^2)*HPL[{8}, -S^2])/S + (1960*HPL[{9}, -S^2])/S - (1568*HPL[{2, 1}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^6*((5*Pi^2*S)/288 + ((1 + S^2)*HPL[{1}, -S^2]^2)/(24*S) - HPL[{1}, -S^2]^3/(4*S) + (5*S*HPL[{2}, -S^2])/48 + HPL[{1}, -S^2]*((-23*Pi^2)/(144*S) + (-1 - S^2)/(48*S) - (13*HPL[{2}, -S^2])/(48*S)) + HPL[{3}, -S^2]/(48*S) + (7*HPL[{2, 1}, -S^2])/(12*S)) - (4*(182 + 53*S^2)*HPL[{3, 1}, -S^2]^2)/S + ((-21*Pi^2)/S + (66*(-2 + S^2))/S)*HPL[{4, 3}, -S^2] + ((-187*Pi^2)/(3*S) + (2*(-178 + 59*S^2))/S)*HPL[{5, 2}, -S^2] + (2*(1 + 17*S^2)*HPL[{5, 3}, -S^2])/S + (582*HPL[{5, 4}, -S^2])/S + ((-136*Pi^2)/S - (4*(203 + 128*S^2))/S)*HPL[{6, 1}, -S^2] + (2*(31 + 33*S^2)*HPL[{6, 2}, -S^2])/S + (2322*HPL[{6, 3}, -S^2])/S - (4*(2 + 75*S^2)*HPL[{7, 1}, -S^2])/S + (5762*HPL[{7, 2}, -S^2])/S + (10914*HPL[{8, 1}, -S^2])/S - (32*(73 + 25*S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((26*Pi^2)/(3*S) + (2*(93 + 1204*S^2))/S)*HPL[{3, 2, 2}, -S^2] + ((-28*Pi^2)/S + (16*(21 + 463*S^2))/S)*HPL[{3, 3, 1}, -S^2] - (2*(49 + 124*S^2)*HPL[{3, 3, 2}, -S^2])/S + ((-119*Pi^2)/(3*S) + (38*(7 + 195*S^2))/S)*HPL[{4, 1, 2}, -S^2] + (40*(5 + 9*S^2)*HPL[{4, 1, 3}, -S^2])/S + ((-347*Pi^2)/(3*S) + (2*(409 + 11253*S^2))/S)*HPL[{4, 2, 1}, -S^2] - (2*(31 + 109*S^2)*HPL[{4, 2, 2}, -S^2])/S + (14*HPL[{4, 2, 3}, -S^2])/S + (8*(54 + 173*S^2)*HPL[{4, 3, 1}, -S^2])/S - (52*HPL[{4, 3, 2}, -S^2])/S + (292*HPL[{4, 4, 1}, -S^2])/S + ((-730*Pi^2)/(3*S) + (4*(439 + 11543*S^2))/S)*HPL[{5, 1, 1}, -S^2] + (6*(33 + 130*S^2)*HPL[{5, 1, 2}, -S^2])/S + (424*HPL[{5, 1, 3}, -S^2])/S + (6*(293 + 970*S^2)*HPL[{5, 2, 1}, -S^2])/S + (242*HPL[{5, 2, 2}, -S^2])/S + (1664*HPL[{5, 3, 1}, -S^2])/S + (4*(1216 + 3891*S^2)*HPL[{6, 1, 1}, -S^2])/S + (1244*HPL[{6, 1, 2}, -S^2])/S + (5004*HPL[{6, 2, 1}, -S^2])/S + (11320*HPL[{7, 1, 1}, -S^2])/S + ((3184*Pi^2)/(3*S) - (8*(-78 + 295*S^2))/S)*HPL[{2, 2, 2, 1}, -S^2] + ((-9368*Pi^2)/(3*S) + (4*(-477 + 553*S^2))/S)*HPL[{3, 1, 1, 2}, -S^2] + ((-9368*Pi^2)/(3*S) + (4*(-477 + 553*S^2))/S)*HPL[{3, 1, 2, 1}, -S^2] - (2*(40 + 47*S^2)*HPL[{3, 1, 2, 2}, -S^2])/S + ((-18920*Pi^2)/(3*S) + (4*(-945 + 2323*S^2))/S)*HPL[{3, 2, 1, 1}, -S^2] - (2*(40 + 47*S^2)*HPL[{3, 2, 1, 2}, -S^2])/S + (2*(-1056 + 481*S^2)*HPL[{3, 2, 2, 1}, -S^2])/S + (160*HPL[{3, 2, 2, 2}, -S^2])/S + (192*HPL[{3, 2, 3, 1}, -S^2])/S + (48*(-127 + 66*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (176*HPL[{3, 3, 1, 2}, -S^2])/S + (512*HPL[{3, 3, 2, 1}, -S^2])/S + ((-57184*Pi^2)/(3*S) + (8*(-1527 + 3362*S^2))/S)*HPL[{4, 1, 1, 1}, -S^2] - (4*(-18 + 169*S^2)*HPL[{4, 1, 1, 2}, -S^2])/S - (1240*HPL[{4, 1, 1, 3}, -S^2])/S + (4*(-1506 + 623*S^2)*HPL[{4, 1, 2, 1}, -S^2])/S - (1150*HPL[{4, 1, 2, 2}, -S^2])/S - (1720*HPL[{4, 1, 3, 1}, -S^2])/S + (4*(-4554 + 2207*S^2)*HPL[{4, 2, 1, 1}, -S^2])/S - (862*HPL[{4, 2, 1, 2}, -S^2])/S - (814*HPL[{4, 2, 2, 1}, -S^2])/S - (3112*HPL[{4, 3, 1, 1}, -S^2])/S + (8*(-4642 + 1943*S^2)*HPL[{5, 1, 1, 1}, -S^2])/S - (3844*HPL[{5, 1, 1, 2}, -S^2])/S - (5668*HPL[{5, 1, 2, 1}, -S^2])/S - (12196*HPL[{5, 2, 1, 1}, -S^2])/S - (30064*HPL[{6, 1, 1, 1}, -S^2])/S + ((2128*Pi^2)/S + (432*(4 + 11*S^2))/S)*HPL[{2, 1, 2, 1, 1}, -S^2] + ((6384*Pi^2)/S + (1296*(4 + 11*S^2))/S)*HPL[{2, 2, 1, 1, 1}, -S^2] + (32*(-125 + 66*S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S + (96*(-125 + 66*S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (6048*HPL[{2, 2, 2, 2, 1}, -S^2])/S + ((32144*Pi^2)/(3*S) + (16*(616 + 2137*S^2))/S)*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(-2967 + 1540*S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S - (8*(-4967 + 2596*S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S - (17952*HPL[{3, 1, 1, 2, 2}, -S^2])/S - (8*(-5967 + 3124*S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S - (17952*HPL[{3, 1, 2, 1, 2}, -S^2])/S + (288*HPL[{3, 1, 2, 2, 1}, -S^2])/S + (127840*HPL[{3, 1, 3, 1, 1}, -S^2])/S - (8*(-12467 + 6556*S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S - (36096*HPL[{3, 2, 1, 1, 2}, -S^2])/S - (17856*HPL[{3, 2, 1, 2, 1}, -S^2])/S + (55456*HPL[{3, 2, 2, 1, 1}, -S^2])/S + (183648*HPL[{3, 3, 1, 1, 1}, -S^2])/S - (384*(-784 + 405*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S - (109680*HPL[{4, 1, 1, 1, 2}, -S^2])/S - (54960*HPL[{4, 1, 1, 2, 1}, -S^2])/S + (164976*HPL[{4, 1, 2, 1, 1}, -S^2])/S + (550416*HPL[{4, 2, 1, 1, 1}, -S^2])/S + (1100832*HPL[{5, 1, 1, 1, 1}, -S^2])/S + ((13552*Pi^2)/(3*S) - (32*(-72 + 313*S^2))/S)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (12544*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/S - (37632*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S + (32*(-313 + 75*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + (64192*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/S + (139456*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/S + (189632*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/S + (214720*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/S + (377792*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/S + (1129472*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S - (1920*(-9 + 4*S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S - (24896*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S - (99584*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S - (248960*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S - (519936*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S + (53760*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((-16*Pi^2*S)/9 + ((-58*Pi^2)/(3*S) - (40*(1 + S^2))/S)*HPL[{1}, -S^2] - (112*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (448*HPL[{1}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^2*((-16*S)/3 - (62*HPL[{1}, -S^2])/(3*S)) - (8*(-9 + 4*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{0}, S^2]*(-40*S - (112*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (224*HPL[{1}, -S^2]^2)/(3*S) + (4*HPL[{2}, -S^2])/S) + (4*HPL[{3}, -S^2])/S + (224*HPL[{2, 1}, -S^2])/(3*S))*Log[T]^6 + ((32*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + (64*HPL[{1}, -S^2]^2)/(3*S) + HPL[{0}, S^2]*((32*S)/3 + (64*HPL[{1}, -S^2])/(3*S)) - (32*HPL[{2}, -S^2])/(3*S))*Log[T]^7 - (16*HPL[{1}, -S^2]*Log[T]^8)/(3*S) + (-20*S + (11*Pi^2*S)/3)*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((9659*Pi^4)/(45*S) - (8*Pi^2*(-76 + 175*S^2))/(3*S) - (8*(-74 + 355*S^2))/S - (4352*Zeta[3])/S) + HPL[{6}, -S^2]*((-2*(82 + 3*S^2))/S + (Pi^2*(58 + 63*S^2))/(3*S) - (320*HPL[{2, 1}, -S^2])/S - (160*Zeta[3])/S) + HPL[{3, 1, 1, 1}, -S^2]*((32*Pi^2*(-13 + 8*S^2))/S + (24*(-111 + 25*S^2))/S - (128*Zeta[3])/S) + HPL[{3}, -S^2]^2*((-2*Pi^2*(-1 + 11*S^2))/(3*S) - (5*(3 + 11*S^2))/S + (168*HPL[{2, 1}, -S^2])/S - (14*Zeta[3])/S) + HPL[{4, 2}, -S^2]*((-4*Pi^2*(-1 + 7*S^2))/S - (16*(-2 + 9*S^2))/S - (10*Zeta[3])/S) + HPL[{3, 1, 2}, -S^2]*((8*(-10 + 9*S^2))/S + (Pi^2*(-11 + 13*S^2))/S - (8*Zeta[3])/S) + HPL[{2}, -S^2]^3*((128 - 69*S^2)/(3*S) - (2*Pi^2*(-31 + 33*S^2))/(9*S) - (44*HPL[{3}, -S^2])/(3*S) + (126*HPL[{2, 1}, -S^2])/S + (4*Zeta[3])/S) + HPL[{1}, -S^2]^6*((-206*(1 + S^2))/(9*S) - (37*Pi^2*(1 + S^2))/(9*S) + (26*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (380*HPL[{3}, -S^2])/(9*S) + (100*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]^2*((4*Pi^2*(81 + 56*S^2))/(3*S) + (4*(153 + 59*S^2))/S + (80*Zeta[3])/S) + HPL[{3, 2, 1}, -S^2]*((Pi^2*(463 - 489*S^2))/(3*S) - (16*(-59 + 30*S^2))/S + (88*Zeta[3])/S) + HPL[{5, 1}, -S^2]*((-6*(23 + 122*S^2))/S - (2*Pi^2*(49 + 229*S^2))/(3*S) + (100*Zeta[3])/S) + HPL[{4, 1, 1}, -S^2]*((-8*(-419 + 123*S^2))/S - (2*Pi^2*(-818 + 597*S^2))/(3*S) + (184*Zeta[3])/S) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-32*(-140 + 59*S^2))/S - (32*Pi^2*(-67 + 60*S^2))/(3*S) + (224*Zeta[3])/S) + HPL[{0}, S^2]^5*((-8*S)/5 + (23*Pi^2*S)/90 - (4*(1 + S^2)*HPL[{1}, -S^2]^3)/(45*S) - (271*HPL[{1}, -S^2]^4)/(360*S) + (Pi^2/(48*S) + (-5 - 6*S^2)/(20*S))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(16*S) + HPL[{1}, -S^2]^2*((-293*Pi^2)/(360*S) - (17*(1 + S^2))/(40*S) - (77*HPL[{2}, -S^2])/(40*S)) - HPL[{3}, -S^2]/(8*S) - (3*HPL[{4}, -S^2])/(8*S) + ((6 + 25*S^2)*HPL[{2, 1}, -S^2])/(60*S) + HPL[{1}, -S^2]*((-4*(1 + S^2))/(5*S) + (89*Pi^2*(1 + S^2))/(720*S) - (7*(1 + S^2)*HPL[{2}, -S^2])/(40*S) - HPL[{3}, -S^2]/(4*S) + (77*HPL[{2, 1}, -S^2])/(20*S)) + HPL[{2, 1, 1}, -S^2]/(2*S) + (5*S*Zeta[3])/4) + HPL[{1}, -S^2]^5*((-6673*Pi^4)/(1350*S) - (1264*(1 + S^2))/(15*S) - (602*Pi^2*(1 + S^2))/(45*S) + ((-392*Pi^2)/(45*S) + (132*(1 + S^2))/(5*S))*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(15*S) + (268*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (664*HPL[{4}, -S^2])/(15*S) - (52*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (664*HPL[{3, 1}, -S^2])/(15*S) + (76*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((19*Pi^4)/(90*S) + (Pi^2*(39 + 158*S^2))/(3*S) + (2*(-66 + 163*S^2))/S + (4*(-70 + 29*S^2)*HPL[{2, 1}, -S^2])/S + (208*HPL[{3, 1}, -S^2])/S - (156*HPL[{2, 1, 1}, -S^2])/S + (4*(-15 + 4*S^2)*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((-1496*Pi^4)/(15*S) - (4*Pi^2*(102 + 157*S^2))/(3*S) - (4*(142 + 339*S^2))/S - (32*(-65 + 6*S^2)*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((-2704*Pi^4)/(9*S) - (2*Pi^2*(515 + 231*S^2))/(3*S) - (4*(322 + 267*S^2))/S - (8*(-797 + 43*S^2)*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((86*Pi^4)/(45*S) + (Pi^2*(-4 - 645*S^2))/(3*S) - (48*(-1 + 28*S^2))/S - (264*HPL[{2, 1, 1}, -S^2])/S - (2*(-27 + 47*S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((491*Pi^4)/(180*S) + (Pi^2*(-167 - 2095*S^2))/(3*S) - (2*(120 + 2207*S^2))/S + (544*HPL[{2, 1, 1}, -S^2])/S - (4*(-16 + 79*S^2)*Zeta[3])/S) + Log[T]^5*((46*Pi^2*S)/9 + ((58*Pi^2)/S + (120*(1 + S^2))/S)*HPL[{1}, -S^2]^2 + (224*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (224*HPL[{1}, -S^2]^4)/(3*S) + HPL[{0}, S^2]^3*(4*S + (146*HPL[{1}, -S^2])/(9*S)) + ((-182*Pi^2)/(9*S) + (4*(-54 + 23*S^2))/(3*S))*HPL[{2}, -S^2] + (158*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^2*((46*S)/3 + (18*(1 + S^2)*HPL[{1}, -S^2])/S + (62*HPL[{1}, -S^2]^2)/S - (14*HPL[{2}, -S^2])/(3*S)) - (4*(13 + 129*S^2)*HPL[{3}, -S^2])/(3*S) - (24*HPL[{4}, -S^2])/S + (8*(-5 + 21*S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*((412*S)/3 + (68*Pi^2*S)/3 + (112*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (448*HPL[{1}, -S^2]^3)/(3*S) + (4*(1 + 27*S^2)*HPL[{2}, -S^2])/S + HPL[{1}, -S^2]*((482*Pi^2)/(9*S) + (120*(1 + S^2))/S + (200*HPL[{2}, -S^2])/S) + (28*HPL[{3}, -S^2])/(3*S) - (424*HPL[{2, 1}, -S^2])/S) + (272*HPL[{3, 1}, -S^2])/S - (448*HPL[{2, 1, 1}, -S^2])/S - 168*S*Zeta[3] + HPL[{1}, -S^2]*((412*(1 + S^2))/(3*S) + (74*Pi^2*(1 + S^2))/(3*S) - (52*(1 + S^2)*HPL[{2}, -S^2])/S - (760*HPL[{3}, -S^2])/(3*S) - (200*Zeta[3])/S)) + HPL[{0}, S^2]^4*(-(Pi^2*S)/4 + (221*Pi^4*S)/2160 - (31*(1 + S^2)*HPL[{1}, -S^2]^4)/(72*S) - (71*HPL[{1}, -S^2]^5)/(45*S) + ((-3 - 8*S^2)*HPL[{2}, -S^2]^2)/(12*S) + HPL[{1}, -S^2]^3*((-277*Pi^2)/(108*S) - (59*(1 + S^2))/(36*S) - (241*HPL[{2}, -S^2])/(36*S)) + ((7 + 8*S^2)*HPL[{3}, -S^2])/(4*S) + ((7 + 2*S^2)*HPL[{4}, -S^2])/(4*S) + (3*HPL[{5}, -S^2])/S + ((469*Pi^2)/(72*S) + (-3 - 11*S^2)/(6*S))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*((Pi^2*(-1 - S^2))/(144*S) - (17*(1 + S^2))/(4*S) - (13*(1 + S^2)*HPL[{2}, -S^2])/(24*S) + HPL[{3}, -S^2]/(4*S) + (241*HPL[{2, 1}, -S^2])/(12*S)) + ((-3 + 20*S^2)*HPL[{3, 1}, -S^2])/(12*S) + HPL[{3, 2}, -S^2]/(2*S) + (3*HPL[{4, 1}, -S^2])/(4*S) + ((-4 - 5*S^2)*HPL[{2, 1, 1}, -S^2])/(2*S) - (79*HPL[{2, 2, 1}, -S^2])/(2*S) - (121*HPL[{3, 1, 1}, -S^2])/S + (259*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (5*S*Zeta[3])/2 + HPL[{2}, -S^2]*((-3*S)/2 + (Pi^2*(-1 + 5*S^2))/(12*S) - HPL[{3}, -S^2]/(4*S) + (79*HPL[{2, 1}, -S^2])/(4*S) - (5*Zeta[3])/(4*S)) + HPL[{1}, -S^2]*((-2009*Pi^4)/(2160*S) - (7*(1 + S^2))/S - (37*Pi^2*(1 + S^2))/(72*S) + ((-109*Pi^2)/(36*S) + (-1 - S^2)/(4*S))*HPL[{2}, -S^2] - (5*HPL[{2}, -S^2]^2)/S + (5*(1 + S^2)*HPL[{3}, -S^2])/(4*S) + HPL[{4}, -S^2]/(2*S) + (13*(1 + S^2)*HPL[{2, 1}, -S^2])/(12*S) + (39*HPL[{3, 1}, -S^2])/(2*S) - (241*HPL[{2, 1, 1}, -S^2])/(6*S) + (5*(1 + S^2)*Zeta[3])/(4*S))) + Log[T]^4*((-118*Pi^2*S)/9 - (151*Pi^4*S)/54 + ((-290*Pi^2)/(3*S) - (200*(1 + S^2))/S)*HPL[{1}, -S^2]^3 - (280*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) - (224*HPL[{1}, -S^2]^5)/(3*S) + HPL[{0}, S^2]^4*((-5*S)/18 - (71*HPL[{1}, -S^2])/(9*S)) - (4*(73 + 25*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((-37*S)/3 - (97*(1 + S^2)*HPL[{1}, -S^2])/(9*S) - (365*HPL[{1}, -S^2]^2)/(9*S) + (16*HPL[{2}, -S^2])/(9*S)) + ((28*Pi^2)/(9*S) + (8*(19 + 163*S^2))/(3*S))*HPL[{3}, -S^2] + (4*(11 + 30*S^2)*HPL[{4}, -S^2])/S - (12*HPL[{5}, -S^2])/S + ((1694*Pi^2)/(9*S) - (4*(-72 + 313*S^2))/(3*S))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-118*S)/3 - (65*Pi^2*S)/9 - (45*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (310*HPL[{1}, -S^2]^3)/(3*S) - (2*(1 + 60*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((-749*Pi^2)/(18*S) - (152*(1 + S^2))/(3*S) - (392*HPL[{2}, -S^2])/(3*S)) - (17*HPL[{3}, -S^2])/(3*S) + (854*HPL[{2, 1}, -S^2])/(3*S)) + (4*(-313 + 75*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (184*HPL[{3, 2}, -S^2])/(3*S) + (64*HPL[{4, 1}, -S^2])/(3*S) - (80*(-9 + 4*S^2)*HPL[{2, 1, 1}, -S^2])/S - (3112*HPL[{2, 2, 1}, -S^2])/(3*S) - (2992*HPL[{3, 1, 1}, -S^2])/S + (2240*HPL[{2, 1, 1, 1}, -S^2])/S + (1252*S*Zeta[3])/3 + HPL[{2}, -S^2]*((-4*(-140 + 59*S^2))/(3*S) - (4*Pi^2*(-67 + 60*S^2))/(9*S) - (172*HPL[{3}, -S^2])/(3*S) + (1556*HPL[{2, 1}, -S^2])/(3*S) + (28*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-1030*(1 + S^2))/(3*S) - (185*Pi^2*(1 + S^2))/(3*S) + (130*(1 + S^2)*HPL[{2}, -S^2])/S + (1900*HPL[{3}, -S^2])/(3*S) + (500*Zeta[3])/S) + HPL[{1}, -S^2]*((-6673*Pi^4)/(270*S) - (1264*(1 + S^2))/(3*S) - (602*Pi^2*(1 + S^2))/(9*S) + ((-392*Pi^2)/(9*S) + (132*(1 + S^2))/S)*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(3*S) + (1340*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (664*HPL[{4}, -S^2])/(3*S) - (260*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (664*HPL[{3, 1}, -S^2])/(3*S) + (380*(1 + S^2)*Zeta[3])/S) + HPL[{0}, S^2]*((-1264*S)/3 - (187*Pi^2*S)/3 - (560*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (560*HPL[{1}, -S^2]^4)/(3*S) + ((61*Pi^2)/(9*S) - (14*(4 + 59*S^2))/(3*S))*HPL[{2}, -S^2] - (17*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^2*((-1205*Pi^2)/(9*S) - (300*(1 + S^2))/S - (500*HPL[{2}, -S^2])/S) + (2*(1 + 37*S^2)*HPL[{3}, -S^2])/(3*S) + (8*HPL[{4}, -S^2])/S - (40*(-12 + S^2)*HPL[{2, 1}, -S^2])/S - (208*HPL[{3, 1}, -S^2])/(3*S) + (120*HPL[{2, 1, 1}, -S^2])/S + 60*S*Zeta[3] + HPL[{1}, -S^2]*((-1030*(1 + S^2))/(3*S) - (517*Pi^2*(1 + S^2))/(9*S) - (250*(1 + S^2)*HPL[{2}, -S^2])/S + (68*HPL[{3}, -S^2])/(3*S) + (1000*HPL[{2, 1}, -S^2])/S + (332*Zeta[3])/(3*S)))) + (912*S + 145*Pi^2*S)*Zeta[5] + HPL[{4}, -S^2]*((10*(-10 + 21*S^2))/S + (Pi^2*(53 + 92*S^2))/(3*S) + (Pi^4*(506 + 813*S^2))/(180*S) - (290*HPL[{5}, -S^2])/S + ((-295*Pi^2)/(3*S) + (2*(-171 + 35*S^2))/S)*HPL[{2, 1}, -S^2] - (2*(-13 + 174*S^2)*HPL[{3, 1}, -S^2])/S + (46*HPL[{3, 2}, -S^2])/S - (104*HPL[{4, 1}, -S^2])/S + (4*(-40 + 169*S^2)*HPL[{2, 1, 1}, -S^2])/S + (1140*HPL[{2, 2, 1}, -S^2])/S + (3540*HPL[{3, 1, 1}, -S^2])/S - (2272*HPL[{2, 1, 1, 1}, -S^2])/S + ((-41*Pi^2)/(3*S) + (6*(-7 + 3*S^2))/S)*Zeta[3] - (178*Zeta[5])/S) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(622 - 763*S^2))/(30*S) - (80*(-16 + 7*S^2))/S - (4*Pi^2*(-143 + 118*S^2))/(3*S) + (6272*HPL[{2, 2, 1}, -S^2])/S + (17440*HPL[{3, 1, 1}, -S^2])/S + (12448*HPL[{2, 1, 1, 1}, -S^2])/S + ((16*Pi^2)/(3*S) + (32*(2 + 69*S^2))/S)*Zeta[3] - (112*Zeta[5])/S) + HPL[{2}, -S^2]^2*((Pi^4*(-644 - 577*S^2))/(180*S) + (Pi^2*(-175 - 123*S^2))/(6*S) - (10*(16 + 7*S^2))/S + ((6*Pi^2)/S + (2*(19 + 158*S^2))/S)*HPL[{3}, -S^2] + ((25 + 73*S^2)*HPL[{4}, -S^2])/S + (15*HPL[{5}, -S^2])/S + ((398*Pi^2)/(3*S) + (78 - 295*S^2)/S)*HPL[{2, 1}, -S^2] + ((-293 + 93*S^2)*HPL[{3, 1}, -S^2])/S + (49*HPL[{3, 2}, -S^2])/S - (21*HPL[{4, 1}, -S^2])/S - (4*(-125 + 66*S^2)*HPL[{2, 1, 1}, -S^2])/S - (756*HPL[{2, 2, 1}, -S^2])/S - (2124*HPL[{3, 1, 1}, -S^2])/S + (1568*HPL[{2, 1, 1, 1}, -S^2])/S + ((-11*Pi^2)/(3*S) + (4*(3 + 70*S^2))/S)*Zeta[3] - (20*Zeta[5])/S) + HPL[{3, 1}, -S^2]*((10*Pi^2*(-36 + 19*S^2))/(3*S) + (10*(-86 + 21*S^2))/S + (Pi^4*(-2302 + 1967*S^2))/(180*S) + (132*HPL[{3, 2}, -S^2])/S - (396*HPL[{4, 1}, -S^2])/S + (64*(41 + 7*S^2)*HPL[{2, 1, 1}, -S^2])/S + (2448*HPL[{2, 2, 1}, -S^2])/S - (28688*HPL[{3, 1, 1}, -S^2])/S - (4896*HPL[{2, 1, 1, 1}, -S^2])/S - (20*(1 + 55*S^2)*Zeta[3])/S + (120*Zeta[5])/S) + HPL[{1}, -S^2]^4*((-835*(1 + S^2))/(3*S) - (39*Pi^2*(1 + S^2))/S - (4759*Pi^4*(1 + S^2))/(1080*S) - (196*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((497*Pi^2)/(9*S) + (686*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (220*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (72*HPL[{5}, -S^2])/S + ((392*Pi^2)/(9*S) - (132*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (556*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (1568*HPL[{3, 2}, -S^2])/(3*S) - (5368*HPL[{4, 1}, -S^2])/(3*S) + (260*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (3136*HPL[{2, 2, 1}, -S^2])/(3*S) - (5608*HPL[{3, 1, 1}, -S^2])/(3*S) + ((416*Pi^2)/(9*S) + (596*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((69*(1 + S^2))/S + (55*Pi^2*(1 + S^2))/(9*S) + (784*HPL[{3}, -S^2])/(3*S) + (1568*HPL[{2, 1}, -S^2])/(3*S) + (784*Zeta[3])/(3*S)) + (760*Zeta[5])/(3*S)) + Zeta[3]*(940*S + (412*Pi^2*S)/3 + (2819*Pi^4*S)/180 + 104*S*Zeta[5]) + HPL[{1}, -S^2]^3*((-52285*Pi^6)/(13608*S) - (2420*(1 + S^2))/(3*S) - (98*Pi^2*(1 + S^2))/S - (5363*Pi^4*(1 + S^2))/(540*S) + ((-607*Pi^2)/(9*S) - (134*(1 + S^2))/S)*HPL[{2}, -S^2]^2 - (148*HPL[{3}, -S^2]^2)/(3*S) + ((340*Pi^2)/(9*S) + (154*(1 + S^2))/S)*HPL[{4}, -S^2] + (424*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (178*HPL[{6}, -S^2])/(3*S) + (3136*HPL[{2, 1}, -S^2]^2)/(3*S) + ((440*Pi^2)/(9*S) - (1136*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] - (744*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (7576*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (156*HPL[{4, 2}, -S^2])/S - (2704*HPL[{5, 1}, -S^2])/(3*S) + ((-1568*Pi^2)/(9*S) + (528*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4048*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (2656*HPL[{4, 1, 1}, -S^2])/(3*S) - (1040*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (2656*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + ((1312*(1 + S^2))/(3*S) + (212*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (80*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((-276*(1 + S^2))/S - (220*Pi^2*(1 + S^2))/(9*S) - (3136*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((1460*(1 + S^2))/(3*S) + (80*Pi^2*(1 + S^2))/S - (3136*HPL[{2, 1}, -S^2])/(3*S) + (200*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((-2021*Pi^4)/(180*S) + (452*(1 + S^2))/(3*S) + (40*Pi^2*(1 + S^2))/(3*S) + (372*(1 + S^2)*HPL[{3}, -S^2])/S + (452*HPL[{4}, -S^2])/(3*S) + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (3136*HPL[{3, 1}, -S^2])/(3*S) - (6272*HPL[{2, 1, 1}, -S^2])/(3*S) + (1120*(1 + S^2)*Zeta[3])/(3*S)) + (1316*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2, 1}, -S^2]*((48199*Pi^6)/(5670*S) + (Pi^4*(230 - 591*S^2))/(36*S) - (20*(1 + 47*S^2))/S - (2*Pi^2*(-25 + 69*S^2))/S + ((-472*Pi^2)/S - (4*(65 + 334*S^2))/S)*HPL[{3, 1}, -S^2] - (2*(-1091 + S^2)*HPL[{3, 2}, -S^2])/S - (4*(-1735 + 112*S^2)*HPL[{4, 1}, -S^2])/S + (546*HPL[{4, 2}, -S^2])/S + (2700*HPL[{5, 1}, -S^2])/S + ((-1064*Pi^2)/S - (216*(4 + 11*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (16*(-125 + 66*S^2)*HPL[{2, 2, 1}, -S^2])/S - (32*(-43 + 80*S^2)*HPL[{3, 1, 1}, -S^2])/S - (312*HPL[{3, 1, 2}, -S^2])/S + (2712*HPL[{3, 2, 1}, -S^2])/S + (6800*HPL[{4, 1, 1}, -S^2])/S + (64*(73 + 25*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (4896*HPL[{3, 1, 1, 1}, -S^2])/S - (12448*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (-1096/S - (2*Pi^2*(303 + 2*S^2))/(3*S))*Zeta[3] + (20*Zeta[3]^2)/S - (4*(300 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((-487*Pi^6)/(2268*S) + (14*Pi^2*(5 + 31*S^2))/(3*S) + (10*(-10 + 87*S^2))/S + (Pi^4*(192 + 949*S^2))/(60*S) + ((32*Pi^2)/(3*S) - (4*(-17 + 16*S^2))/S)*HPL[{4}, -S^2] - (4*(21 + 19*S^2)*HPL[{5}, -S^2])/S + (290*HPL[{6}, -S^2])/S - (144*HPL[{2, 1}, -S^2]^2)/S + ((110*Pi^2)/(3*S) - (4*(-15 + 313*S^2))/S)*HPL[{3, 1}, -S^2] + (6*(8 + 27*S^2)*HPL[{3, 2}, -S^2])/S + (2*(-41 + 68*S^2)*HPL[{4, 1}, -S^2])/S - (6*HPL[{4, 2}, -S^2])/S - (212*HPL[{5, 1}, -S^2])/S + ((-176*Pi^2)/(3*S) + (4*(-13 + 629*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (4*(565 + 19*S^2)*HPL[{2, 2, 1}, -S^2])/S - (4*(-1709 + 27*S^2)*HPL[{3, 1, 1}, -S^2])/S + (16*HPL[{3, 1, 2}, -S^2])/S - (336*HPL[{3, 2, 1}, -S^2])/S + (72*HPL[{4, 1, 1}, -S^2])/S + (16*(-289 + 38*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (800*HPL[{3, 1, 1, 1}, -S^2])/S - (1376*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((4*(2 + 5*S^2))/S + (Pi^2*(8 + 33*S^2))/(3*S))*Zeta[3] + HPL[{2, 1}, -S^2]*((5*Pi^2*(-121 + 17*S^2))/(3*S) + (4*(-297 + 35*S^2))/S - (136*Zeta[3])/S) + (2*(8 + 41*S^2)*Zeta[5])/S) + Log[T]^3*((86*Pi^2*S)/3 + (53*Pi^4*S)/10 + ((290*Pi^2)/(3*S) + (200*(1 + S^2))/S)*HPL[{1}, -S^2]^4 + (224*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) + (448*HPL[{1}, -S^2]^6)/(9*S) + HPL[{0}, S^2]^5*(-S/10 + (271*HPL[{1}, -S^2])/(90*S)) + ((416*Pi^2)/(9*S) + (14*(14 + 5*S^2))/S)*HPL[{2}, -S^2]^2 - (784*HPL[{2}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^4*((23*S)/18 + (31*(1 + S^2)*HPL[{1}, -S^2])/(18*S) + (142*HPL[{1}, -S^2]^2)/(9*S) - HPL[{2}, -S^2]/S) - (16*HPL[{3}, -S^2]^2)/S + ((-24*Pi^2)/S - (4*(69 + 170*S^2))/(3*S))*HPL[{4}, -S^2] - (4*(24 + 203*S^2)*HPL[{5}, -S^2])/(3*S) - (48*HPL[{6}, -S^2])/S - (3160*HPL[{2, 1}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*(34*S + 3*Pi^2*S + (194*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + (1460*HPL[{1}, -S^2]^3)/(27*S) + (2*(16 + 83*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((212*Pi^2)/(9*S) + (254*(1 + S^2))/(9*S) + (220*HPL[{2}, -S^2])/(3*S)) + (46*HPL[{3}, -S^2])/(9*S) - (1384*HPL[{2, 1}, -S^2])/(9*S)) + ((2200*Pi^2)/(9*S) - (8*(-316 + 71*S^2))/(3*S))*HPL[{3, 1}, -S^2] + (4*(-7 + 1224*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (16*(47 + 971*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (136*HPL[{4, 2}, -S^2])/(3*S) + (592*HPL[{5, 1}, -S^2])/(3*S) + ((-3640*Pi^2)/(9*S) + (80*(-54 + 23*S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (64*(25 + 73*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (16*(235 + 231*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (640*HPL[{3, 1, 2}, -S^2])/(3*S) - (5632*HPL[{3, 2, 1}, -S^2])/(3*S) - (6752*HPL[{4, 1, 1}, -S^2])/S + (160*(-5 + 21*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (5440*HPL[{3, 1, 1, 1}, -S^2])/S - (8960*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-2600*S)/3 - (1400*Pi^2*S)/9)*Zeta[3] + HPL[{1}, -S^2]^3*((4120*(1 + S^2))/(9*S) + (740*Pi^2*(1 + S^2))/(9*S) - (520*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (7600*HPL[{3}, -S^2])/(9*S) - (2000*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-8*Pi^2*(21 + 172*S^2))/(9*S) - (4*(91 + 687*S^2))/(3*S) + (2320*HPL[{2, 1}, -S^2])/S - (176*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((8*Pi^2*(-79 + 175*S^2))/(9*S) + (8*(-73 + 325*S^2))/(3*S) + (6160*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((6673*Pi^4)/(135*S) + (2528*(1 + S^2))/(3*S) + (1204*Pi^2*(1 + S^2))/(9*S) + ((784*Pi^2)/(9*S) - (264*(1 + S^2))/S)*HPL[{2}, -S^2] + (1568*HPL[{2}, -S^2]^2)/(3*S) - (2680*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (1328*HPL[{4}, -S^2])/(3*S) + (520*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (1328*HPL[{3, 1}, -S^2])/(3*S) - (760*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-1798*Pi^4)/(135*S) + (4*(-100 + 43*S^2))/S + (4*Pi^2*(-136 + 115*S^2))/(9*S) - (8*(-10 + 317*S^2)*HPL[{3}, -S^2])/(3*S) + (232*HPL[{4}, -S^2])/(3*S) - (32*(25 + 73*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (3824*HPL[{3, 1}, -S^2])/(3*S) + (6320*HPL[{2, 1, 1}, -S^2])/(3*S) - (64*(1 + 35*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^2*(86*S + (46*Pi^2*S)/3 + (60*(1 + S^2)*HPL[{1}, -S^2]^3)/S + (310*HPL[{1}, -S^2]^4)/(3*S) + ((-53*Pi^2)/(9*S) + (2*(-2 + 115*S^2))/(3*S))*HPL[{2}, -S^2] + (7*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^2*((749*Pi^2)/(9*S) + (304*(1 + S^2))/(3*S) + (784*HPL[{2}, -S^2])/(3*S)) - (2*(19 + 43*S^2)*HPL[{3}, -S^2])/(3*S) - (12*HPL[{4}, -S^2])/S + (4*(-83 + 35*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (160*HPL[{3, 1}, -S^2])/(3*S) - (280*HPL[{2, 1, 1}, -S^2])/(3*S) - (140*S*Zeta[3])/3 + HPL[{1}, -S^2]*((374*(1 + S^2))/(3*S) + (166*Pi^2*(1 + S^2))/(9*S) + (170*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (88*HPL[{3}, -S^2])/(3*S) - (1568*HPL[{2, 1}, -S^2])/(3*S) - (164*Zeta[3])/(3*S))) + HPL[{0}, S^2]*((3340*S)/3 + (1336*Pi^2*S)/9 + (1387*Pi^4*S)/90 + (560*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + (448*HPL[{1}, -S^2]^5)/(3*S) + (8*(7 + 95*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((4820*Pi^2)/(27*S) + (400*(1 + S^2))/S + (2000*HPL[{2}, -S^2])/(3*S)) + ((116*Pi^2)/(9*S) - (4*(-9 + 31*S^2))/(3*S))*HPL[{3}, -S^2] + (4*(4 + 5*S^2)*HPL[{4}, -S^2])/S + (36*HPL[{5}, -S^2])/S + ((-4564*Pi^2)/(9*S) + (40*(-74 + 3*S^2))/(3*S))*HPL[{2, 1}, -S^2] - (8*(15 + 403*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (200*HPL[{3, 2}, -S^2])/(3*S) + (64*HPL[{4, 1}, -S^2])/(3*S) + (80*(1 + 27*S^2)*HPL[{2, 1, 1}, -S^2])/S + (12272*HPL[{2, 2, 1}, -S^2])/(3*S) + (37376*HPL[{3, 1, 1}, -S^2])/(3*S) - (8480*HPL[{2, 1, 1, 1}, -S^2])/S - (352*S*Zeta[3])/3 + HPL[{1}, -S^2]^2*((2060*(1 + S^2))/(3*S) + (1034*Pi^2*(1 + S^2))/(9*S) + (500*(1 + S^2)*HPL[{2}, -S^2])/S - (136*HPL[{3}, -S^2])/(3*S) - (2000*HPL[{2, 1}, -S^2])/S - (664*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((8*(24 + 223*S^2))/(3*S) + (2*Pi^2*(31 + 488*S^2))/(9*S) - (88*HPL[{3}, -S^2])/(3*S) - (6136*HPL[{2, 1}, -S^2])/(3*S) + (8*Zeta[3])/(3*S)) + HPL[{1}, -S^2]*((4061*Pi^4)/(90*S) + (2528*(1 + S^2))/(3*S) + (1154*Pi^2*(1 + S^2))/(9*S) + ((240*Pi^2)/S + (1592*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (1568*HPL[{2}, -S^2]^2)/(3*S) - (56*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (184*HPL[{4}, -S^2])/(3*S) - (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2000*HPL[{3, 1}, -S^2])/S + (4000*HPL[{2, 1, 1}, -S^2])/S - (344*(1 + S^2)*Zeta[3])/(3*S))) - (2720*S*Zeta[5])/3 + HPL[{1}, -S^2]*((3340*(1 + S^2))/(3*S) + (156*Pi^2*(1 + S^2))/S + (4759*Pi^4*(1 + S^2))/(270*S) + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-1988*Pi^2)/(9*S) - (2744*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (880*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (288*HPL[{5}, -S^2])/S + ((-1568*Pi^2)/(9*S) + (528*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (2224*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (6272*HPL[{3, 2}, -S^2])/(3*S) + (21472*HPL[{4, 1}, -S^2])/(3*S) - (1040*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (12544*HPL[{2, 2, 1}, -S^2])/(3*S) + (22432*HPL[{3, 1, 1}, -S^2])/(3*S) + ((-1664*Pi^2)/(9*S) - (2384*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-276*(1 + S^2))/S - (220*Pi^2*(1 + S^2))/(9*S) - (3136*HPL[{3}, -S^2])/(3*S) - (6272*HPL[{2, 1}, -S^2])/(3*S) - (3136*Zeta[3])/(3*S)) - (3040*Zeta[5])/(3*S))) + HPL[{0}, S^2]^3*(-135*S - (143*Pi^2*S)/12 - (Pi^4*S)/720 - (97*(1 + S^2)*HPL[{1}, -S^2]^5)/(45*S) - (73*HPL[{1}, -S^2]^6)/(27*S) + ((5*Pi^2)/(18*S) + (-16 - 73*S^2)/(12*S))*HPL[{2}, -S^2]^2 + HPL[{2}, -S^2]^3/(6*S) + HPL[{1}, -S^2]^4*((-53*Pi^2)/(9*S) - (127*(1 + S^2))/(18*S) - (55*HPL[{2}, -S^2])/(3*S)) - (11*HPL[{3}, -S^2]^2)/(6*S) + ((-10*Pi^2)/(9*S) + (-23 - 21*S^2)/(3*S))*HPL[{4}, -S^2] + ((-55 - 4*S^2)*HPL[{5}, -S^2])/(6*S) - (65*HPL[{6}, -S^2])/(3*S) - (5*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-8*Pi^2)/(9*S) + (32 + 103*S^2)/(3*S))*HPL[{3, 1}, -S^2] + ((-11 - 42*S^2)*HPL[{3, 2}, -S^2])/(6*S) + ((-3 - 52*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (26*HPL[{5, 1}, -S^2])/(3*S) + ((31*Pi^2)/(9*S) - (8*(5 + 24*S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] - (2*(73 + 5*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2*(213 + 7*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (4*HPL[{3, 2, 1}, -S^2])/S + (46*HPL[{4, 1, 1}, -S^2])/(3*S) - (4*(-66 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (64*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (128*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (3*S + 5*Pi^2*S)*Zeta[3] + HPL[{2, 1}, -S^2]*((4*Pi^2*(3 + S^2))/(3*S) + (107 + 13*S^2)/(3*S) - (8*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-178*(1 + S^2))/(9*S) - (113*Pi^2*(1 + S^2))/(54*S) - (82*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (4*HPL[{3}, -S^2])/(3*S) + (220*HPL[{2, 1}, -S^2])/(3*S) + (22*Zeta[3])/(9*S)) + HPL[{3}, -S^2]*((2*(-7 + 3*S^2))/(3*S) + (Pi^2*(-9 + 8*S^2))/(36*S) + (2*HPL[{2, 1}, -S^2])/(3*S) + (6*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-3997*Pi^4)/(1080*S) - (131*(1 + S^2))/(3*S) - (89*Pi^2*(1 + S^2))/(18*S) + ((-187*Pi^2)/(12*S) - (16*(1 + S^2))/S)*HPL[{2}, -S^2] - (53*HPL[{2}, -S^2]^2)/(2*S) - (17*HPL[{4}, -S^2])/(3*S) + (82*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (110*HPL[{3, 1}, -S^2])/S - (220*HPL[{2, 1, 1}, -S^2])/S + (14*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((161*Pi^4)/(1080*S) + (Pi^2*(-25 - 66*S^2))/(18*S) - (7*(8 + 25*S^2))/(6*S) + ((3 + 10*S^2)*HPL[{3}, -S^2])/(3*S) + (11*HPL[{4}, -S^2])/(3*S) + ((73 + 5*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*HPL[{3, 1}, -S^2])/(3*S) + (10*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(6 + 5*S^2)*Zeta[3])/(3*S)) + (38*S*Zeta[5])/3 + HPL[{1}, -S^2]*((-135*(1 + S^2))/(2*S) - (137*Pi^2*(1 + S^2))/(18*S) - (7*Pi^4*(1 + S^2))/(54*S) - (7*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-7*Pi^2)/(6*S) - (7*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (11*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (23*HPL[{5}, -S^2])/(3*S) + ((187*Pi^2)/(6*S) + (32*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (28*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (14*HPL[{3, 2}, -S^2])/(3*S) - (8*HPL[{4, 1}, -S^2])/(3*S) - (164*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (212*HPL[{2, 2, 1}, -S^2])/S - (644*HPL[{3, 1, 1}, -S^2])/S + (440*HPL[{2, 1, 1, 1}, -S^2])/S + ((11*Pi^2)/(18*S) + (10*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-45*(1 + S^2))/(2*S) - (103*Pi^2*(1 + S^2))/(36*S) + (7*HPL[{3}, -S^2])/(3*S) + (106*HPL[{2, 1}, -S^2])/S + (3*Zeta[3])/S) + (16*Zeta[5])/(3*S))) + HPL[{0}, S^2]^2*((-35*Pi^2*S)/3 - (533*Pi^4*S)/360 + (233*Pi^6*S)/3360 - (3*(1 + S^2)*HPL[{1}, -S^2]^6)/S - (62*HPL[{1}, -S^2]^7)/(21*S) + ((-1 - 66*S^2)*HPL[{2}, -S^2]^3)/(6*S) + HPL[{1}, -S^2]^5*((-749*Pi^2)/(90*S) - (152*(1 + S^2))/(15*S) - (392*HPL[{2}, -S^2])/(15*S)) + ((-3 - 2*S^2)*HPL[{3}, -S^2]^2)/(2*S) + ((67*Pi^2)/(12*S) + (53 + 95*S^2)/(2*S))*HPL[{5}, -S^2] + (5*(14 + 3*S^2)*HPL[{6}, -S^2])/(2*S) + (125*HPL[{7}, -S^2])/S + (4*(8 + 31*S^2)*HPL[{2, 1}, -S^2]^2)/S + (Pi^2/S + (1 - 73*S^2)/(2*S))*HPL[{3, 2}, -S^2] + ((25*Pi^2)/(6*S) + (-44 - 147*S^2)/S)*HPL[{4, 1}, -S^2] + ((6 + S^2)*HPL[{4, 2}, -S^2])/(2*S) - (34*HPL[{4, 3}, -S^2])/S + ((-28 - 25*S^2)*HPL[{5, 1}, -S^2])/S - (205*HPL[{5, 2}, -S^2])/(2*S) - (250*HPL[{6, 1}, -S^2])/S + ((-646*Pi^2)/(3*S) - (2*(96 + 17*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-1970*Pi^2)/(3*S) + (2*(-267 + 8*S^2))/S)*HPL[{3, 1, 1}, -S^2] - 5*S*HPL[{3, 1, 2}, -S^2] + ((-4 - 269*S^2)*HPL[{3, 2, 1}, -S^2])/S + (2*HPL[{3, 2, 2}, -S^2])/S - (16*HPL[{3, 3, 1}, -S^2])/S - (2*(-2 + 381*S^2)*HPL[{4, 1, 1}, -S^2])/S - (17*HPL[{4, 1, 2}, -S^2])/S - (77*HPL[{4, 2, 1}, -S^2])/S - (190*HPL[{5, 1, 1}, -S^2])/S + ((1372*Pi^2)/(3*S) - (4*(-80 + 37*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (1616*HPL[{2, 2, 2, 1}, -S^2])/S + (4*(1 + 117*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (4848*HPL[{3, 1, 1, 2}, -S^2])/S - (4848*HPL[{3, 1, 2, 1}, -S^2])/S - (9696*HPL[{3, 2, 1, 1}, -S^2])/S - (29024*HPL[{4, 1, 1, 1}, -S^2])/S - (16*(1 + 60*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (3272*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (9816*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (16224*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (6832*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (57*S + (67*Pi^2*S)/6)*Zeta[3] + S*Zeta[3]^2 + HPL[{4}, -S^2]*((2*(9 + 4*S^2))/S + (Pi^2*(50 + 27*S^2))/(12*S) - (11*HPL[{2, 1}, -S^2])/S - (28*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-14 - 135*S^2))/(3*S) - (4*(-3 + 59*S^2))/S - (12*Zeta[3])/S) + HPL[{2}, -S^2]^2*((Pi^2*(-11 - 39*S^2))/(6*S) + (-11 - 32*S^2)/S + (202*HPL[{2, 1}, -S^2])/S - Zeta[3]/S) + HPL[{1}, -S^2]^4*((-187*(1 + S^2))/(6*S) - (83*Pi^2*(1 + S^2))/(18*S) - (85*(1 + S^2)*HPL[{2}, -S^2])/(6*S) + (22*HPL[{3}, -S^2])/(3*S) + (392*HPL[{2, 1}, -S^2])/(3*S) + (41*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((-27 + 115*S^2)/S + (Pi^2*(-2 + 137*S^2))/(6*S) + (16*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-8449*Pi^4)/(1080*S) - (250*(1 + S^2))/(3*S) - (211*Pi^2*(1 + S^2))/(18*S) + ((-211*Pi^2)/(6*S) - (26*(1 + S^2))/S)*HPL[{2}, -S^2] - (215*HPL[{2}, -S^2]^2)/(3*S) + (50*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (8*HPL[{4}, -S^2])/(3*S) + (170*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (772*HPL[{3, 1}, -S^2])/(3*S) - (1568*HPL[{2, 1, 1}, -S^2])/(3*S) + (22*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((2459*Pi^4)/(120*S) + (Pi^2*(74 - 59*S^2))/(6*S) + (76 - 59*S^2)/S - (804*HPL[{3, 1}, -S^2])/S - (1636*HPL[{2, 1, 1}, -S^2])/S - (2*(31 + 2*S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-19*Pi^4)/(60*S) + (18 + 59*S^2)/S + (Pi^2*(63 + 107*S^2))/(12*S) + (17*HPL[{4}, -S^2])/S + (9*(-3 + S^2)*HPL[{2, 1}, -S^2])/S + (10*HPL[{3, 1}, -S^2])/S - (4*HPL[{2, 1, 1}, -S^2])/S + ((-9 + 4*S^2)*Zeta[3])/S) + 82*S*Zeta[5] + HPL[{2}, -S^2]*(-70*S + (Pi^4*(-134 - 453*S^2))/(720*S) + (Pi^2*(3 - 77*S^2))/(6*S) + ((-2*Pi^2)/(3*S) + (-1 + 35*S^2)/(2*S))*HPL[{3}, -S^2] + (7*S*HPL[{4}, -S^2])/2 - (31*HPL[{5}, -S^2])/(2*S) + ((323*Pi^2)/(3*S) + (96 + 17*S^2)/S)*HPL[{2, 1}, -S^2] + ((29 + 123*S^2)*HPL[{3, 1}, -S^2])/S - HPL[{3, 2}, -S^2]/S + (11*HPL[{4, 1}, -S^2])/S - (8*(8 + 31*S^2)*HPL[{2, 1, 1}, -S^2])/S - (808*HPL[{2, 2, 1}, -S^2])/S + (2420*HPL[{3, 1, 1}, -S^2])/S + (1636*HPL[{2, 1, 1, 1}, -S^2])/S + ((-3*Pi^2)/S + (3*(-4 + 9*S^2))/S)*Zeta[3] - (30*Zeta[5])/S) + HPL[{1}, -S^2]^2*((-365*(1 + S^2))/(2*S) - (289*Pi^2*(1 + S^2))/(12*S) - (367*Pi^4*(1 + S^2))/(240*S) - (33*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((25*Pi^2)/(6*S) + (32*(1 + S^2))/S)*HPL[{3}, -S^2] + (31*(1 + S^2)*HPL[{4}, -S^2])/(2*S) + (12*HPL[{5}, -S^2])/S + ((211*Pi^2)/(2*S) + (78*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (82*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (42*HPL[{3, 2}, -S^2])/S - (134*HPL[{4, 1}, -S^2])/S - (170*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (860*HPL[{2, 2, 1}, -S^2])/S - (2492*HPL[{3, 1, 1}, -S^2])/S + (1568*HPL[{2, 1, 1, 1}, -S^2])/S + ((41*Pi^2)/(6*S) + (37*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-77*(1 + S^2))/(2*S) - (49*Pi^2*(1 + S^2))/(6*S) + (21*HPL[{3}, -S^2])/S + (430*HPL[{2, 1}, -S^2])/S + (39*Zeta[3])/S) + (39*Zeta[5])/S) + HPL[{1}, -S^2]*((-39083*Pi^6)/(18144*S) - (295*(1 + S^2))/S - (209*Pi^2*(1 + S^2))/(6*S) - (1883*Pi^4*(1 + S^2))/(720*S) + ((-335*Pi^2)/(12*S) - (67*(1 + S^2))/(2*S))*HPL[{2}, -S^2]^2 - (32*HPL[{2}, -S^2]^3)/S + ((5*Pi^2)/(3*S) + (55*(1 + S^2))/(2*S))*HPL[{4}, -S^2] + (28*(1 + S^2)*HPL[{5}, -S^2])/S + (45*HPL[{6}, -S^2])/(2*S) + (430*HPL[{2, 1}, -S^2]^2)/S + ((310*Pi^2)/(3*S) + (70*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (30*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (121*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (3*HPL[{4, 2}, -S^2])/S - (16*HPL[{5, 1}, -S^2])/S + ((-211*Pi^2)/S - (156*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (264*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (692*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (768*HPL[{3, 2, 1}, -S^2])/S - (2288*HPL[{4, 1, 1}, -S^2])/S + (340*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (1544*HPL[{3, 1, 1, 1}, -S^2])/S - (3136*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((35*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/S)*Zeta[3] - (9*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((77*(1 + S^2))/S + (49*Pi^2*(1 + S^2))/(3*S) - (78*Zeta[3])/S) + HPL[{3}, -S^2]*((46*(1 + S^2))/S + (20*Pi^2*(1 + S^2))/(3*S) - (42*HPL[{2, 1}, -S^2])/S + (2*Zeta[3])/S) + HPL[{2}, -S^2]*((-6731*Pi^4)/(720*S) - (35*(1 + S^2))/S - (7*Pi^2*(1 + S^2))/S + (15*(1 + S^2)*HPL[{3}, -S^2])/S - HPL[{4}, -S^2]/S + (132*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (426*HPL[{3, 1}, -S^2])/S - (860*HPL[{2, 1, 1}, -S^2])/S + (30*(1 + S^2)*Zeta[3])/S) + (53*(1 + S^2)*Zeta[5])/S)) + Log[T]^2*((-140*Pi^2*S)/3 - (358*Pi^4*S)/45 - (6841*Pi^6*S)/7560 + ((-58*Pi^2)/S - (120*(1 + S^2))/S)*HPL[{1}, -S^2]^5 - (112*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) - (64*HPL[{1}, -S^2]^7)/(3*S) + HPL[{0}, S^2]^6*((5*S)/24 - (3*HPL[{1}, -S^2])/(4*S)) - (2*(-125 + 66*S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{0}, S^2]^5*((-13*S)/30 - (4*(1 + S^2)*HPL[{1}, -S^2])/(15*S) - (271*HPL[{1}, -S^2]^2)/(60*S) + HPL[{2}, -S^2]/(4*S)) - (14*(-1 + 6*S^2)*HPL[{3}, -S^2]^2)/S + ((-23*Pi^2)/(3*S) + (2*(25 + 221*S^2))/S)*HPL[{5}, -S^2] + (2*(46 + 111*S^2)*HPL[{6}, -S^2])/S + (20*HPL[{7}, -S^2])/S + (16*(73 + 25*S^2)*HPL[{2, 1}, -S^2]^2)/S + HPL[{0}, S^2]^4*(-3*S + (65*Pi^2*S)/72 - (31*(1 + S^2)*HPL[{1}, -S^2]^2)/(12*S) - (142*HPL[{1}, -S^2]^3)/(9*S) + ((-4 - 5*S^2)*HPL[{2}, -S^2])/(4*S) + HPL[{1}, -S^2]*((-277*Pi^2)/(36*S) - (59*(1 + S^2))/(12*S) - (241*HPL[{2}, -S^2])/(12*S)) - (5*HPL[{3}, -S^2])/(4*S) + (259*HPL[{2, 1}, -S^2])/(6*S)) + ((92*Pi^2)/(3*S) - (2*(9 + 1217*S^2))/S)*HPL[{3, 2}, -S^2] + ((64*Pi^2)/(3*S) - (4*(123 + 1948*S^2))/S)*HPL[{4, 1}, -S^2] - (2*(-18 + 169*S^2)*HPL[{4, 2}, -S^2])/S - (116*HPL[{4, 3}, -S^2])/S - (4*(70 + 433*S^2)*HPL[{5, 1}, -S^2])/S - (338*HPL[{5, 2}, -S^2])/S - (632*HPL[{6, 1}, -S^2])/S + ((-1064*Pi^2)/S - (216*(4 + 11*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-9464*Pi^2)/(3*S) - (8*(248 + 239*S^2))/S)*HPL[{3, 1, 1}, -S^2] + (44*(-3 + 4*S^2)*HPL[{3, 1, 2}, -S^2])/S - (4*(-467 + 220*S^2)*HPL[{3, 2, 1}, -S^2])/S + (96*HPL[{3, 2, 2}, -S^2])/S - (272*HPL[{3, 3, 1}, -S^2])/S - (192*(-34 + 9*S^2)*HPL[{4, 1, 1}, -S^2])/S - (408*HPL[{4, 1, 2}, -S^2])/S - (1080*HPL[{4, 2, 1}, -S^2])/S - (2160*HPL[{5, 1, 1}, -S^2])/S + ((6776*Pi^2)/(3*S) - (16*(-72 + 313*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (6272*HPL[{2, 2, 2, 1}, -S^2])/S + (16*(-313 + 75*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (18080*HPL[{3, 1, 1, 2}, -S^2])/S - (18080*HPL[{3, 1, 2, 1}, -S^2])/S - (36896*HPL[{3, 2, 1, 1}, -S^2])/S - (112640*HPL[{4, 1, 1, 1}, -S^2])/S - (960*(-9 + 4*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (12448*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (37344*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (63680*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (26880*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (1420*S + (700*Pi^2*S)/3)*Zeta[3] + 40*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((9659*Pi^4)/(90*S) - (4*Pi^2*(-76 + 175*S^2))/(3*S) - (4*(-74 + 355*S^2))/S - (2448*HPL[{3, 1}, -S^2])/S - (6224*HPL[{2, 1, 1}, -S^2])/S - (2176*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((16*Pi^2*(-13 + 8*S^2))/S + (12*(-111 + 25*S^2))/S - (64*Zeta[3])/S) + HPL[{4}, -S^2]*((28*(5 + 12*S^2))/S + (Pi^2*(74 + 195*S^2))/(3*S) - (1136*HPL[{2, 1}, -S^2])/S - (52*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-2*Pi^2*(81 + 56*S^2))/(3*S) - (2*(153 + 59*S^2))/S + (72*HPL[{3}, -S^2])/S + (784*HPL[{2, 1}, -S^2])/S - (40*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-16*(-140 + 59*S^2))/S - (16*Pi^2*(-67 + 60*S^2))/(3*S) + (112*Zeta[3])/S) + HPL[{1}, -S^2]^4*((-1030*(1 + S^2))/(3*S) - (185*Pi^2*(1 + S^2))/(3*S) + (130*(1 + S^2)*HPL[{2}, -S^2])/S + (1900*HPL[{3}, -S^2])/(3*S) + (500*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-6673*Pi^4)/(135*S) - (2528*(1 + S^2))/(3*S) - (1204*Pi^2*(1 + S^2))/(9*S) + ((-784*Pi^2)/(9*S) + (264*(1 + S^2))/S)*HPL[{2}, -S^2] - (1568*HPL[{2}, -S^2]^2)/(3*S) + (2680*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (1328*HPL[{4}, -S^2])/(3*S) - (520*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (1328*HPL[{3, 1}, -S^2])/(3*S) + (760*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-28*Pi^4)/(45*S) + (4*(52 + 375*S^2))/S + (Pi^2*(97 + 711*S^2))/(3*S) + (60*HPL[{4}, -S^2])/S + (8*(-289 + 38*S^2)*HPL[{2, 1}, -S^2])/S + (400*HPL[{3, 1}, -S^2])/S - (688*HPL[{2, 1, 1}, -S^2])/S + (4*(17 + 29*S^2)*Zeta[3])/S) + HPL[{0}, S^2]^3*(-79*S - (137*Pi^2*S)/18 - (194*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (365*HPL[{1}, -S^2]^4)/(9*S) + ((31*Pi^2)/(18*S) - (4*(5 + 24*S^2))/(3*S))*HPL[{2}, -S^2] + (5*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^2*((-106*Pi^2)/(3*S) - (127*(1 + S^2))/(3*S) - (110*HPL[{2}, -S^2])/S) + (2*(3 + 4*S^2)*HPL[{3}, -S^2])/(3*S) + (5*HPL[{4}, -S^2])/(3*S) - (2*(-66 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (32*HPL[{3, 1}, -S^2])/(3*S) + (64*HPL[{2, 1, 1}, -S^2])/(3*S) + 10*S*Zeta[3] + HPL[{1}, -S^2]*((-178*(1 + S^2))/(3*S) - (113*Pi^2*(1 + S^2))/(18*S) - (82*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (4*HPL[{3}, -S^2])/S + (220*HPL[{2, 1}, -S^2])/S + (22*Zeta[3])/(3*S))) + HPL[{0}, S^2]^2*(-140*S - (77*Pi^2*S)/3 - (403*Pi^4*S)/360 - (45*(1 + S^2)*HPL[{1}, -S^2]^4)/S - (62*HPL[{1}, -S^2]^5)/S - (2*(8 + 31*S^2)*HPL[{2}, -S^2]^2)/S + HPL[{1}, -S^2]^3*((-749*Pi^2)/(9*S) - (304*(1 + S^2))/(3*S) - (784*HPL[{2}, -S^2])/(3*S)) + ((-16*Pi^2)/(3*S) + (21 + 59*S^2)/S)*HPL[{3}, -S^2] + ((8 + 15*S^2)*HPL[{4}, -S^2])/S - (5*HPL[{5}, -S^2])/S + ((686*Pi^2)/(3*S) - (2*(-80 + 37*S^2))/S)*HPL[{2, 1}, -S^2] + (2*(1 + 117*S^2)*HPL[{3, 1}, -S^2])/S + (32*HPL[{4, 1}, -S^2])/S - (8*(1 + 60*S^2)*HPL[{2, 1, 1}, -S^2])/S - (1636*HPL[{2, 2, 1}, -S^2])/S - (4976*HPL[{3, 1, 1}, -S^2])/S + (3416*HPL[{2, 1, 1, 1}, -S^2])/S + 74*S*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-14 - 135*S^2))/(6*S) - (2*(-3 + 59*S^2))/S - (2*HPL[{3}, -S^2])/S + (818*HPL[{2, 1}, -S^2])/S - (6*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-187*(1 + S^2))/S - (83*Pi^2*(1 + S^2))/(3*S) - (85*(1 + S^2)*HPL[{2}, -S^2])/S + (44*HPL[{3}, -S^2])/S + (784*HPL[{2, 1}, -S^2])/S + (82*Zeta[3])/S) + HPL[{1}, -S^2]*((-8449*Pi^4)/(360*S) - (250*(1 + S^2))/S - (211*Pi^2*(1 + S^2))/(6*S) + ((-211*Pi^2)/(2*S) - (78*(1 + S^2))/S)*HPL[{2}, -S^2] - (215*HPL[{2}, -S^2]^2)/S + (50*(1 + S^2)*HPL[{3}, -S^2])/S + (8*HPL[{4}, -S^2])/S + (170*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (772*HPL[{3, 1}, -S^2])/S - (1568*HPL[{2, 1, 1}, -S^2])/S + (66*(1 + S^2)*Zeta[3])/S)) + 1412*S*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(622 - 763*S^2))/(60*S) - (40*(-16 + 7*S^2))/S - (2*Pi^2*(-143 + 118*S^2))/(3*S) + ((-88*Pi^2)/(3*S) + (2*(-13 + 629*S^2))/S)*HPL[{3}, -S^2] + (2*(-40 + 169*S^2)*HPL[{4}, -S^2])/S - (78*HPL[{5}, -S^2])/S + ((532*Pi^2)/S + (108*(4 + 11*S^2))/S)*HPL[{2, 1}, -S^2] + (32*(41 + 7*S^2)*HPL[{3, 1}, -S^2])/S - (132*HPL[{3, 2}, -S^2])/S + (272*HPL[{4, 1}, -S^2])/S - (32*(73 + 25*S^2)*HPL[{2, 1, 1}, -S^2])/S - (3136*HPL[{2, 2, 1}, -S^2])/S + (8720*HPL[{3, 1, 1}, -S^2])/S + (6224*HPL[{2, 1, 1, 1}, -S^2])/S + ((8*Pi^2)/(3*S) + (16*(2 + 69*S^2))/S)*Zeta[3] - (56*Zeta[5])/S) + HPL[{1}, -S^2]^2*((-1670*(1 + S^2))/S - (234*Pi^2*(1 + S^2))/S - (4759*Pi^4*(1 + S^2))/(180*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((994*Pi^2)/(3*S) + (1372*(1 + S^2))/S)*HPL[{3}, -S^2] + (440*(1 + S^2)*HPL[{4}, -S^2])/S + (432*HPL[{5}, -S^2])/S + ((784*Pi^2)/(3*S) - (792*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (1112*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (3136*HPL[{3, 2}, -S^2])/S - (10736*HPL[{4, 1}, -S^2])/S + (1560*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (6272*HPL[{2, 2, 1}, -S^2])/S - (11216*HPL[{3, 1, 1}, -S^2])/S + ((832*Pi^2)/(3*S) + (1192*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((414*(1 + S^2))/S + (110*Pi^2*(1 + S^2))/(3*S) + (1568*HPL[{3}, -S^2])/S + (3136*HPL[{2, 1}, -S^2])/S + (1568*Zeta[3])/S) + (1520*Zeta[5])/S) + HPL[{1}, -S^2]*((-52285*Pi^6)/(4536*S) - (2420*(1 + S^2))/S - (294*Pi^2*(1 + S^2))/S - (5363*Pi^4*(1 + S^2))/(180*S) + ((-607*Pi^2)/(3*S) - (402*(1 + S^2))/S)*HPL[{2}, -S^2]^2 - (148*HPL[{3}, -S^2]^2)/S + ((340*Pi^2)/(3*S) + (462*(1 + S^2))/S)*HPL[{4}, -S^2] + (424*(1 + S^2)*HPL[{5}, -S^2])/S + (178*HPL[{6}, -S^2])/S + (3136*HPL[{2, 1}, -S^2]^2)/S + ((440*Pi^2)/(3*S) - (1136*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (2232*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (7576*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (468*HPL[{4, 2}, -S^2])/S - (2704*HPL[{5, 1}, -S^2])/S + ((-1568*Pi^2)/(3*S) + (1584*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (4048*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (2656*HPL[{4, 1, 1}, -S^2])/S - (3120*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (2656*HPL[{3, 1, 1, 1}, -S^2])/S + ((1312*(1 + S^2))/S + (212*Pi^2*(1 + S^2))/S)*Zeta[3] - (80*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((-828*(1 + S^2))/S - (220*Pi^2*(1 + S^2))/(3*S) - (3136*Zeta[3])/S) + HPL[{3}, -S^2]*((1460*(1 + S^2))/S + (240*Pi^2*(1 + S^2))/S - (3136*HPL[{2, 1}, -S^2])/S + (200*Zeta[3])/S) + HPL[{2}, -S^2]*((-2021*Pi^4)/(60*S) + (452*(1 + S^2))/S + (40*Pi^2*(1 + S^2))/S + (1116*(1 + S^2)*HPL[{3}, -S^2])/S + (452*HPL[{4}, -S^2])/S + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (3136*HPL[{3, 1}, -S^2])/S - (6272*HPL[{2, 1, 1}, -S^2])/S + (1120*(1 + S^2)*Zeta[3])/S) + (1316*(1 + S^2)*Zeta[5])/S) + HPL[{0}, S^2]*(-2420*S - (869*Pi^2*S)/3 - (829*Pi^4*S)/30 - (112*(1 + S^2)*HPL[{1}, -S^2]^5)/S - (224*HPL[{1}, -S^2]^6)/(3*S) + ((-2*Pi^2)/S + (-34 - 381*S^2)/S)*HPL[{2}, -S^2]^2 + (38*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^4*((-1205*Pi^2)/(9*S) - (300*(1 + S^2))/S - (500*HPL[{2}, -S^2])/S) - (20*HPL[{3}, -S^2]^2)/S + ((17*Pi^2)/(3*S) - (2*(23 + 39*S^2))/S)*HPL[{4}, -S^2] + (6*(-3 + 2*S^2)*HPL[{5}, -S^2])/S - (20*HPL[{6}, -S^2])/S + (68*HPL[{2, 1}, -S^2]^2)/S + ((-136*Pi^2)/(3*S) + (4*(29 + 416*S^2))/S)*HPL[{3, 1}, -S^2] - (10*(8 + 21*S^2)*HPL[{3, 2}, -S^2])/S - (4*(40 + 139*S^2)*HPL[{4, 1}, -S^2])/S + (6*HPL[{4, 2}, -S^2])/S - (20*HPL[{5, 1}, -S^2])/S + ((244*Pi^2)/(3*S) - (56*(4 + 59*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (32*(91 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/S + (8*(-1091 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (24*HPL[{3, 1, 2}, -S^2])/S + (280*HPL[{3, 2, 1}, -S^2])/S + (1008*HPL[{4, 1, 1}, -S^2])/S - (480*(-12 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (832*HPL[{3, 1, 1, 1}, -S^2])/S + (1440*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (172*S + 40*Pi^2*S)*Zeta[3] + HPL[{2, 1}, -S^2]*((4*(401 + 3*S^2))/S - (2*Pi^2*(-426 + 31*S^2))/(3*S) - (664*Zeta[3])/S) + HPL[{3}, -S^2]*((4*(-13 + 11*S^2))/S + (Pi^2*(7 + 45*S^2))/(3*S) - (216*HPL[{2, 1}, -S^2])/S + (24*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-2060*(1 + S^2))/(3*S) - (1034*Pi^2*(1 + S^2))/(9*S) - (500*(1 + S^2)*HPL[{2}, -S^2])/S + (136*HPL[{3}, -S^2])/(3*S) + (2000*HPL[{2, 1}, -S^2])/S + (664*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-4061*Pi^4)/(60*S) - (1264*(1 + S^2))/S - (577*Pi^2*(1 + S^2))/(3*S) + ((-360*Pi^2)/S - (796*(1 + S^2))/S)*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/S + (28*(1 + S^2)*HPL[{3}, -S^2])/S - (92*HPL[{4}, -S^2])/S + (1500*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (3000*HPL[{3, 1}, -S^2])/S - (6000*HPL[{2, 1, 1}, -S^2])/S + (172*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((18*Pi^4)/(5*S) + (Pi^2*(-48 - 509*S^2))/(3*S) - (2*(82 + 511*S^2))/S + (2*(19 + 51*S^2)*HPL[{3}, -S^2])/S + (42*HPL[{4}, -S^2])/S + (16*(91 + 3*S^2)*HPL[{2, 1}, -S^2])/S + (64*HPL[{3, 1}, -S^2])/S - (136*HPL[{2, 1, 1}, -S^2])/S + (12*(1 + 14*S^2)*Zeta[3])/S) + 100*S*Zeta[5] + HPL[{1}, -S^2]*((-1670*(1 + S^2))/S - (231*Pi^2*(1 + S^2))/S - (2191*Pi^4*(1 + S^2))/(90*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((22*Pi^2)/(3*S) - (8*(1 + S^2))/S)*HPL[{3}, -S^2] - (58*(1 + S^2)*HPL[{4}, -S^2])/S - (92*HPL[{5}, -S^2])/S + ((720*Pi^2)/S + (1592*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (1512*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (304*HPL[{3, 2}, -S^2])/S - (728*HPL[{4, 1}, -S^2])/S - (3000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (6272*HPL[{2, 2, 1}, -S^2])/S - (18544*HPL[{3, 1, 1}, -S^2])/S + (12000*HPL[{2, 1, 1, 1}, -S^2])/S + ((188*Pi^2)/(3*S) + (188*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-898*(1 + S^2))/S - (457*Pi^2*(1 + S^2))/(3*S) + (152*HPL[{3}, -S^2])/S + (3136*HPL[{2, 1}, -S^2])/S + (328*Zeta[3])/S) + (260*Zeta[5])/S))) + 1176*S*Zeta[7] + HPL[{2}, -S^2]*((Pi^6*(4682 - 4507*S^2))/(7560*S) + (Pi^4*(1082 - 1069*S^2))/(180*S) - (20*Pi^2*(-8 + 7*S^2))/(3*S) + ((-11 - 39*S^2)*HPL[{3}, -S^2]^2)/S + ((-35*Pi^2)/(3*S) + (2*(-50 + 71*S^2))/S)*HPL[{5}, -S^2] + (38*(1 + 4*S^2)*HPL[{6}, -S^2])/S - (250*HPL[{7}, -S^2])/S + (4*(-125 + 66*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-34*Pi^2)/(3*S) - (2*(57 + 613*S^2))/S)*HPL[{3, 2}, -S^2] + ((79*Pi^2)/(3*S) - (2*(57 + 1931*S^2))/S)*HPL[{4, 1}, -S^2] - (30*(1 + 5*S^2)*HPL[{4, 2}, -S^2])/S + (38*HPL[{4, 3}, -S^2])/S - (12*(-1 + 68*S^2)*HPL[{5, 1}, -S^2])/S + (108*HPL[{5, 2}, -S^2])/S + (420*HPL[{6, 1}, -S^2])/S + ((-1592*Pi^2)/(3*S) + (4*(-78 + 295*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((4600*Pi^2)/(3*S) - (4*(-221 + 256*S^2))/S)*HPL[{3, 1, 1}, -S^2] + (78*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (10*(101 + 37*S^2)*HPL[{3, 2, 1}, -S^2])/S - (118*HPL[{3, 2, 2}, -S^2])/S - (72*HPL[{3, 3, 1}, -S^2])/S - (4*(856 + 167*S^2)*HPL[{4, 1, 1}, -S^2])/S + (6*HPL[{4, 1, 2}, -S^2])/S - (90*HPL[{4, 2, 1}, -S^2])/S - (444*HPL[{5, 1, 1}, -S^2])/S + ((1064*Pi^2)/S + (216*(4 + 11*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (3024*HPL[{2, 2, 2, 1}, -S^2])/S + (64*(-334 + 205*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (8808*HPL[{3, 1, 1, 2}, -S^2])/S + (8808*HPL[{3, 1, 2, 1}, -S^2])/S + (17880*HPL[{3, 2, 1, 1}, -S^2])/S + (54976*HPL[{4, 1, 1, 1}, -S^2])/S - (64*(73 + 25*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (6272*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (18816*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (32736*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (12448*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((-71*Pi^4)/(90*S) + (4*(1 + 148*S^2))/S + (Pi^2*(-4 + 303*S^2))/(3*S))*Zeta[3] + (2*(12 + 7*S^2)*Zeta[3]^2)/S + HPL[{2, 1, 1}, -S^2]*((-8*Pi^2*(81 + 56*S^2))/(3*S) - (8*(153 + 59*S^2))/S - (160*Zeta[3])/S) + HPL[{4}, -S^2]*((4*Pi^2*(-5 + 22*S^2))/(3*S) + (2*(-1 + 91*S^2))/S - (570*HPL[{2, 1}, -S^2])/S + (26*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((4*(169 + 34*S^2))/S + (Pi^2*(357 + 179*S^2))/(3*S) + (88*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((748*Pi^4)/(15*S) + (2*Pi^2*(102 + 157*S^2))/(3*S) + (2*(142 + 339*S^2))/S - (1224*HPL[{3, 1}, -S^2])/S - (3136*HPL[{2, 1, 1}, -S^2])/S + (16*(-65 + 6*S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-82*Pi^4)/(45*S) + (4*(-11 + 172*S^2))/S + (Pi^2*(-7 + 332*S^2))/(3*S) - (20*HPL[{4}, -S^2])/S - (2*(565 + 19*S^2)*HPL[{2, 1}, -S^2])/S - (160*HPL[{3, 1}, -S^2])/S + (288*HPL[{2, 1, 1}, -S^2])/S + (2*(-13 + 29*S^2)*Zeta[3])/S) + ((-44*Pi^2)/(3*S) + (2*(-16 + 271*S^2))/S)*Zeta[5] - (210*Zeta[7])/S) + HPL[{1}, -S^2]^2*((-1960*(1 + S^2))/S - (200*Pi^2*(1 + S^2))/S - (2207*Pi^4*(1 + S^2))/(120*S) - (3653*Pi^6*(1 + S^2))/(2268*S) + (83*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - (37*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((40*Pi^2)/S + (226*(1 + S^2))/S)*HPL[{5}, -S^2] + (208*(1 + S^2)*HPL[{6}, -S^2])/S + (30*HPL[{7}, -S^2])/S + (784*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-826*Pi^2)/(3*S) - (1140*(1 + S^2))/S)*HPL[{3, 2}, -S^2] + ((-2818*Pi^2)/(3*S) - (3882*(1 + S^2))/S)*HPL[{4, 1}, -S^2] - (117*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (94*HPL[{4, 3}, -S^2])/S - (884*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (204*HPL[{5, 2}, -S^2])/S - (98*HPL[{6, 1}, -S^2])/S + ((-2428*Pi^2)/(3*S) - (1608*(1 + S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-5296*Pi^2)/(3*S) - (2080*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] + (664*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (3260*HPL[{3, 2, 2}, -S^2])/S + (9968*HPL[{3, 3, 1}, -S^2])/S + (2872*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (9812*HPL[{4, 1, 2}, -S^2])/S + (30404*HPL[{4, 2, 1}, -S^2])/S + (62640*HPL[{5, 1, 1}, -S^2])/S + ((1568*Pi^2)/(3*S) - (1584*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - (2224*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (6272*HPL[{3, 1, 1, 2}, -S^2])/S - (6272*HPL[{3, 1, 2, 1}, -S^2])/S - (6272*HPL[{3, 2, 1, 1}, -S^2])/S - (21472*HPL[{4, 1, 1, 1}, -S^2])/S + (3120*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (12544*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (37632*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (77920*HPL[{3, 1, 1, 1, 1}, -S^2])/S + ((1013*Pi^4)/(60*S) + (764*(1 + S^2))/S + (335*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (22*(1 + S^2)*Zeta[3]^2)/S + HPL[{3, 1}, -S^2]*((-598*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/(3*S) - (1616*Zeta[3])/S) + HPL[{4}, -S^2]*((256*(1 + S^2))/S + (251*Pi^2*(1 + S^2))/(6*S) - (452*HPL[{2, 1}, -S^2])/S + (56*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-431*(1 + S^2))/(2*S) - (131*Pi^2*(1 + S^2))/(3*S) + (466*HPL[{3}, -S^2])/S + (354*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((828*(1 + S^2))/S + (220*Pi^2*(1 + S^2))/(3*S) + (3136*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((2021*Pi^4)/(60*S) - (452*(1 + S^2))/S - (40*Pi^2*(1 + S^2))/S - (3136*HPL[{3, 1}, -S^2])/S - (6272*HPL[{2, 1, 1}, -S^2])/S - (1120*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((601*Pi^4)/(30*S) + (796*(1 + S^2))/S + (125*Pi^2*(1 + S^2))/S - (86*HPL[{4}, -S^2])/S - (1116*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (1568*HPL[{3, 1}, -S^2])/S + (3136*HPL[{2, 1, 1}, -S^2])/S + (52*(1 + S^2)*Zeta[3])/S) + ((419*Pi^2)/(3*S) + (718*(1 + S^2))/S)*Zeta[5] + HPL[{2}, -S^2]*((255*(1 + S^2))/S + (65*Pi^2*(1 + S^2))/(3*S) + (64*Pi^4*(1 + S^2))/(45*S) + ((413*Pi^2)/(3*S) + (570*(1 + S^2))/S)*HPL[{3}, -S^2] + (113*(1 + S^2)*HPL[{4}, -S^2])/S + (164*HPL[{5}, -S^2])/S + ((1214*Pi^2)/(3*S) + (804*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (784*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (1708*HPL[{3, 2}, -S^2])/S - (5140*HPL[{4, 1}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (3136*HPL[{3, 1, 1}, -S^2])/S + (6272*HPL[{2, 1, 1, 1}, -S^2])/S + ((431*Pi^2)/(3*S) + (552*(1 + S^2))/S)*Zeta[3] + (722*Zeta[5])/S) + (966*Zeta[7])/S) + HPL[{1}, -S^2]*((-13964*Pi^8)/(14175*S) - (3920*(1 + S^2))/S - (300*Pi^2*(1 + S^2))/S - (149*Pi^4*(1 + S^2))/(6*S) - (6499*Pi^6*(1 + S^2))/(3240*S) + ((-32*Pi^2)/(3*S) + (86*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^3 - (32*HPL[{2}, -S^2]^4)/S + ((-37*Pi^2)/(3*S) - (46*(1 + S^2))/S)*HPL[{3}, -S^2]^2 + (18*HPL[{4}, -S^2]^2)/S + ((67*Pi^2)/(3*S) + (302*(1 + S^2))/S)*HPL[{6}, -S^2] + (306*(1 + S^2)*HPL[{7}, -S^2])/S + (108*HPL[{8}, -S^2])/S + ((1214*Pi^2)/(3*S) + (804*(1 + S^2))/S)*HPL[{2, 1}, -S^2]^2 - (1864*HPL[{3, 1}, -S^2]^2)/S + ((-38*Pi^2)/S - (114*(1 + S^2))/S)*HPL[{4, 2}, -S^2] + (58*(1 + S^2)*HPL[{4, 3}, -S^2])/S + ((-692*Pi^2)/(3*S) - (940*(1 + S^2))/S)*HPL[{5, 1}, -S^2] + (120*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (24*HPL[{5, 3}, -S^2])/S - (396*(1 + S^2)*HPL[{6, 1}, -S^2])/S + (60*HPL[{6, 2}, -S^2])/S - (108*HPL[{7, 1}, -S^2])/S - (6272*HPL[{2, 1, 1}, -S^2]^2)/S + ((-256*Pi^2)/S + (688*(1 + S^2))/S)*HPL[{3, 2, 1}, -S^2] + (2294*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (6976*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (532*HPL[{3, 3, 2}, -S^2])/S + ((-1624*Pi^2)/(3*S) + (2988*(1 + S^2))/S)*HPL[{4, 1, 1}, -S^2] + (6898*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (908*HPL[{4, 1, 3}, -S^2])/S + (21178*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (376*HPL[{4, 2, 2}, -S^2])/S + (2908*HPL[{4, 3, 1}, -S^2])/S + (43688*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + (1688*HPL[{5, 1, 2}, -S^2])/S + (12008*HPL[{5, 2, 1}, -S^2])/S + (31316*HPL[{6, 1, 1}, -S^2])/S - (1328*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((880*Pi^2)/(3*S) - (2272*(1 + S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] - (480*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (480*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (312*HPL[{3, 1, 2, 2}, -S^2])/S + (3504*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (312*HPL[{3, 2, 1, 2}, -S^2])/S - (376*HPL[{3, 2, 2, 1}, -S^2])/S - (192*HPL[{3, 3, 1, 1}, -S^2])/S + (8752*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (936*HPL[{4, 1, 1, 2}, -S^2])/S - (1128*HPL[{4, 1, 2, 1}, -S^2])/S - (1512*HPL[{4, 2, 1, 1}, -S^2])/S - (6560*HPL[{5, 1, 1, 1}, -S^2])/S + ((-3136*Pi^2)/(3*S) + (3168*(1 + S^2))/S)*HPL[{2, 1, 1, 1, 1}, -S^2] + (6272*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (18816*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (42080*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (5312*HPL[{4, 1, 1, 1, 1}, -S^2])/S - (6240*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - (5312*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + ((-29*Pi^2)/(3*S) - (34*(1 + S^2))/S)*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((-1656*(1 + S^2))/S - (440*Pi^2*(1 + S^2))/(3*S) - (6272*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((-4016*(1 + S^2))/S - (2015*Pi^2*(1 + S^2))/(3*S) - (424*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((-1168*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/S - (104*Zeta[3])/S) + HPL[{5}, -S^2]*((210*(1 + S^2))/S + (134*Pi^2*(1 + S^2))/(3*S) - (328*HPL[{2, 1}, -S^2])/S - (24*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((-1724*(1 + S^2))/S - (1048*Pi^2*(1 + S^2))/(3*S) + (2832*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((-2252*(1 + S^2))/S - (568*Pi^2*(1 + S^2))/S + (8896*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((398*Pi^4)/(15*S) - (656*(1 + S^2))/S - (214*Pi^2*(1 + S^2))/(3*S) + (6272*HPL[{2, 1, 1}, -S^2])/S - (1144*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((7*Pi^4)/S + (328*(1 + S^2))/S + (143*Pi^2*(1 + S^2))/(3*S) - (226*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (484*HPL[{3, 1}, -S^2])/S + (904*HPL[{2, 1, 1}, -S^2])/S + (46*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-333*Pi^4)/(20*S) - (234*(1 + S^2))/S - (134*Pi^2*(1 + S^2))/(3*S) + (316*(1 + S^2)*HPL[{3}, -S^2])/S + (164*HPL[{4}, -S^2])/S - (166*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (164*HPL[{3, 1}, -S^2])/S + (260*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-2021*Pi^4)/(30*S) + (904*(1 + S^2))/S + (80*Pi^2*(1 + S^2))/S + (2240*(1 + S^2)*Zeta[3])/S) + ((862*(1 + S^2))/S + (382*Pi^2*(1 + S^2))/(3*S))*Zeta[5] + HPL[{2, 1}, -S^2]*((-510*(1 + S^2))/S - (130*Pi^2*(1 + S^2))/(3*S) - (128*Pi^4*(1 + S^2))/(45*S) - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (3416*HPL[{3, 2}, -S^2])/S + (10280*HPL[{4, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (6272*HPL[{3, 1, 1}, -S^2])/S + (12544*HPL[{2, 1, 1, 1}, -S^2])/S + ((-862*Pi^2)/(3*S) - (1104*(1 + S^2))/S)*Zeta[3] - (1444*Zeta[5])/S) + Zeta[3]*((940*(1 + S^2))/S + (121*Pi^2*(1 + S^2))/S + (1247*Pi^4*(1 + S^2))/(90*S) - (124*Zeta[5])/S) + HPL[{3}, -S^2]*((860*(1 + S^2))/S + (137*Pi^2*(1 + S^2))/S + (706*Pi^4*(1 + S^2))/(45*S) - (56*(1 + S^2)*HPL[{4}, -S^2])/S - (56*HPL[{5}, -S^2])/S + ((-826*Pi^2)/(3*S) - (1140*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (1116*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (344*HPL[{3, 2}, -S^2])/S + (108*HPL[{4, 1}, -S^2])/S + (2232*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (3728*HPL[{2, 2, 1}, -S^2])/S + (10592*HPL[{3, 1, 1}, -S^2])/S - (6272*HPL[{2, 1, 1, 1}, -S^2])/S + ((52*Pi^2)/(3*S) + (20*(1 + S^2))/S)*Zeta[3] + (64*Zeta[5])/S) + HPL[{2}, -S^2]*((-1049*Pi^6)/(360*S) + (330*(1 + S^2))/S + (26*Pi^2*(1 + S^2))/S + (21*Pi^4*(1 + S^2))/(10*S) - (86*HPL[{3}, -S^2]^2)/S + ((112*Pi^2)/(3*S) + (130*(1 + S^2))/S)*HPL[{4}, -S^2] + (110*(1 + S^2)*HPL[{5}, -S^2])/S + (84*HPL[{6}, -S^2])/S + ((1210*Pi^2)/(3*S) + (796*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (1186*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (3566*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (312*HPL[{4, 2}, -S^2])/S - (1264*HPL[{5, 1}, -S^2])/S + ((-2428*Pi^2)/(3*S) - (1608*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (664*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (240*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (312*HPL[{3, 1, 2}, -S^2])/S - (2760*HPL[{3, 2, 1}, -S^2])/S - (8312*HPL[{4, 1, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (6272*HPL[{3, 1, 1, 1}, -S^2])/S - (12544*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((568*(1 + S^2))/S + (310*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (6*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((862*(1 + S^2))/S + (524*Pi^2*(1 + S^2))/(3*S) - (1416*Zeta[3])/S) + HPL[{3}, -S^2]*((584*(1 + S^2))/S + (98*Pi^2*(1 + S^2))/S - (1864*HPL[{2, 1}, -S^2])/S + (52*Zeta[3])/S) + (592*(1 + S^2)*Zeta[5])/S) + (1026*(1 + S^2)*Zeta[7])/S) + Log[T]*((140*Pi^2*S)/3 + (257*Pi^4*S)/30 + (243*Pi^6*S)/280 + ((58*Pi^2)/(3*S) + (40*(1 + S^2))/S)*HPL[{1}, -S^2]^6 + (32*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) + (16*HPL[{1}, -S^2]^8)/(3*S) + HPL[{0}, S^2]^7*(-S/24 + HPL[{1}, -S^2]/(8*S)) + ((-206*Pi^2)/(9*S) + (-250 + 123*S^2)/(3*S))*HPL[{2}, -S^2]^3 + (65*HPL[{2}, -S^2]^4)/(2*S) + HPL[{0}, S^2]^6*((-5*S)/24 + ((-1 - S^2)*HPL[{1}, -S^2])/(12*S) + (3*HPL[{1}, -S^2]^2)/(4*S) - HPL[{2}, -S^2]/(24*S)) + ((-17*Pi^2)/(3*S) + (2*(-7 + 43*S^2))/S)*HPL[{3}, -S^2]^2 + (76*HPL[{4}, -S^2]^2)/S + ((-16*Pi^2)/(3*S) - (8*(19 + 29*S^2))/S)*HPL[{6}, -S^2] - (4*(55 + 184*S^2)*HPL[{7}, -S^2])/S + (490*HPL[{8}, -S^2])/S + ((-832*Pi^2)/(3*S) - (84*(14 + 5*S^2))/S)*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*((8*S)/5 - (19*Pi^2*S)/60 + (4*(1 + S^2)*HPL[{1}, -S^2]^2)/(15*S) + (271*HPL[{1}, -S^2]^3)/(90*S) + ((15 - 4*S^2)*HPL[{2}, -S^2])/(60*S) + HPL[{1}, -S^2]*((293*Pi^2)/(180*S) + (17*(1 + S^2))/(20*S) + (77*HPL[{2}, -S^2])/(20*S)) + HPL[{3}, -S^2]/(4*S) - (41*HPL[{2, 1}, -S^2])/(5*S)) + (2280*HPL[{3, 1}, -S^2]^2)/S + ((-13*Pi^2)/S + (2*(-19 + 157*S^2))/S)*HPL[{4, 2}, -S^2] - (8*(-3 + 25*S^2)*HPL[{4, 3}, -S^2])/S + ((54*Pi^2)/S + (4*(79 + 407*S^2))/S)*HPL[{5, 1}, -S^2] - (2*(-13 + 214*S^2)*HPL[{5, 2}, -S^2])/S + (8*HPL[{5, 3}, -S^2])/S + (4*(82 + 97*S^2)*HPL[{6, 1}, -S^2])/S + (36*HPL[{6, 2}, -S^2])/S - (104*HPL[{7, 1}, -S^2])/S + (6320*HPL[{2, 1, 1}, -S^2]^2)/S + ((56*Pi^2)/S - (4*(-35 + 41*S^2))/S)*HPL[{3, 1, 2}, -S^2] + ((-1480*Pi^2)/(3*S) + (20*(-93 + 41*S^2))/S)*HPL[{3, 2, 1}, -S^2] - (2*(150 + 2327*S^2)*HPL[{3, 2, 2}, -S^2])/S - (16*(37 + 905*S^2)*HPL[{3, 3, 1}, -S^2])/S + (80*HPL[{3, 3, 2}, -S^2])/S + ((-1792*Pi^2)/S + (8*(-819 + 199*S^2))/S)*HPL[{4, 1, 1}, -S^2] - (12*(38 + 1207*S^2)*HPL[{4, 1, 2}, -S^2])/S - (168*HPL[{4, 1, 3}, -S^2])/S - (156*(10 + 283*S^2)*HPL[{4, 2, 1}, -S^2])/S - (30*HPL[{4, 2, 2}, -S^2])/S - (424*HPL[{4, 3, 1}, -S^2])/S - (8*(438 + 11327*S^2)*HPL[{5, 1, 1}, -S^2])/S - (228*HPL[{5, 1, 2}, -S^2])/S - (1668*HPL[{5, 2, 1}, -S^2])/S - (4608*HPL[{6, 1, 1}, -S^2])/S + (32*(-42 + 149*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((4400*Pi^2)/(3*S) - (16*(-316 + 71*S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] - (8*(-497 + 564*S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (8*(-497 + 564*S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (336*HPL[{3, 1, 2, 2}, -S^2])/S - (56*(-143 + 336*S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (336*HPL[{3, 2, 1, 2}, -S^2])/S + (6608*HPL[{3, 2, 2, 1}, -S^2])/S + (18816*HPL[{3, 3, 1, 1}, -S^2])/S - (32*(-803 + 1711*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (272*HPL[{4, 1, 1, 2}, -S^2])/S + (18544*HPL[{4, 1, 2, 1}, -S^2])/S + (56176*HPL[{4, 2, 1, 1}, -S^2])/S + (114080*HPL[{5, 1, 1, 1}, -S^2])/S + ((-7280*Pi^2)/(3*S) + (160*(-54 + 23*S^2))/S)*HPL[{2, 1, 1, 1, 1}, -S^2] - (128*(25 + 73*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (384*(25 + 73*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (12544*HPL[{2, 2, 1, 2, 1}, -S^2])/S + (37632*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (160*(113 + 421*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (73984*HPL[{3, 1, 1, 1, 2}, -S^2])/S - (124160*HPL[{3, 1, 1, 2, 1}, -S^2])/S - (149248*HPL[{3, 1, 2, 1, 1}, -S^2])/S - (312320*HPL[{3, 2, 1, 1, 1}, -S^2])/S - (943680*HPL[{4, 1, 1, 1, 1}, -S^2])/S + (960*(-5 + 21*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (32640*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S - (53760*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (-1580*S - (734*Pi^2*S)/3 - (2827*Pi^4*S)/90)*Zeta[3] - 8*S*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((16*Pi^2*(129 + 53*S^2))/(3*S) + (32*(71 + 63*S^2))/S - (18304*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((400*Pi^2*(2 + 3*S^2))/(3*S) + (8*(125 + 313*S^2))/S - (5984*Zeta[3])/S) + HPL[{1}, -S^2]^5*((412*(1 + S^2))/(3*S) + (74*Pi^2*(1 + S^2))/(3*S) - (52*(1 + S^2)*HPL[{2}, -S^2])/S - (760*HPL[{3}, -S^2])/(3*S) - (200*Zeta[3])/S) + HPL[{5}, -S^2]*((-2*Pi^2*(17 + 125*S^2))/(3*S) - (2*(43 + 242*S^2))/S + (812*HPL[{2, 1}, -S^2])/S - (92*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((8*(5 + 318*S^2))/S + (Pi^2*(-1 + 1307*S^2))/(3*S) - (56*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((8*(78 + 1025*S^2))/S + (2*Pi^2*(126 + 2075*S^2))/(3*S) + (136*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((16*Pi^2*(-79 + 175*S^2))/(3*S) + (16*(-73 + 325*S^2))/S + (12320*Zeta[3])/S) + HPL[{2}, -S^2]^2*((251*Pi^4)/(30*S) + (Pi^2*(166 + 111*S^2))/(3*S) + (326 + 129*S^2)/S + ((-67 - 613*S^2)*HPL[{3}, -S^2])/S - (43*HPL[{4}, -S^2])/S + (4*(-42 + 149*S^2)*HPL[{2, 1}, -S^2])/S + (940*HPL[{3, 1}, -S^2])/S - (1568*HPL[{2, 1, 1}, -S^2])/S - 568*S*Zeta[3]) + HPL[{4}, -S^2]*((-1043*Pi^4)/(180*S) + (Pi^2*(-77 - 183*S^2))/(3*S) - (2*(76 + 185*S^2))/S - (4*(-153 + 56*S^2)*HPL[{2, 1}, -S^2])/S - (292*HPL[{3, 1}, -S^2])/S + (464*HPL[{2, 1, 1}, -S^2])/S - 124*S*Zeta[3]) + HPL[{0}, S^2]^4*(3*S - (13*Pi^2*S)/18 + (31*(1 + S^2)*HPL[{1}, -S^2]^3)/(18*S) + (71*HPL[{1}, -S^2]^4)/(9*S) + ((-11*Pi^2)/(24*S) + (3 + 7*S^2)/(3*S))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(8*S) + HPL[{1}, -S^2]^2*((277*Pi^2)/(36*S) + (59*(1 + S^2))/(12*S) + (241*HPL[{2}, -S^2])/(12*S)) + ((-5 - 6*S^2)*HPL[{3}, -S^2])/(4*S) - HPL[{4}, -S^2]/(4*S) + ((-1 + 2*S^2)*HPL[{2, 1}, -S^2])/(6*S) + HPL[{1}, -S^2]*((17*(1 + S^2))/(2*S) + (Pi^2*(1 + S^2))/(72*S) + (13*(1 + S^2)*HPL[{2}, -S^2])/(12*S) - HPL[{3}, -S^2]/(2*S) - (241*HPL[{2, 1}, -S^2])/(6*S)) + (3*HPL[{3, 1}, -S^2])/S - (6*HPL[{2, 1, 1}, -S^2])/S - (20*S*Zeta[3])/3) + HPL[{1}, -S^2]^4*((6673*Pi^4)/(270*S) + (1264*(1 + S^2))/(3*S) + (602*Pi^2*(1 + S^2))/(9*S) + ((392*Pi^2)/(9*S) - (132*(1 + S^2))/S)*HPL[{2}, -S^2] + (784*HPL[{2}, -S^2]^2)/(3*S) - (1340*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (664*HPL[{4}, -S^2])/(3*S) + (260*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (664*HPL[{3, 1}, -S^2])/(3*S) - (380*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-3596*Pi^4)/(45*S) + (24*(-100 + 43*S^2))/S + (8*Pi^2*(-136 + 115*S^2))/(3*S) - (128*(1 + 35*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((2156*Pi^4)/(45*S) - (2*Pi^2*(-107 + 61*S^2))/S - (4*(-366 + 83*S^2))/S - (7648*HPL[{2, 1, 1}, -S^2])/S + (8*(9 + 281*S^2)*Zeta[3])/S) + HPL[{0}, S^2]^3*(135*S + (83*Pi^2*S)/6 - (67*Pi^4*S)/1080 + (97*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + (146*HPL[{1}, -S^2]^5)/(9*S) + ((11 + 79*S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^3*((212*Pi^2)/(9*S) + (254*(1 + S^2))/(9*S) + (220*HPL[{2}, -S^2])/(3*S)) + ((19*Pi^2)/(9*S) - (2*(1 + 8*S^2))/(3*S))*HPL[{3}, -S^2] + (7*(1 + 2*S^2)*HPL[{4}, -S^2])/(3*S) - (2*HPL[{5}, -S^2])/(3*S) + (-152/(3*S) - (592*Pi^2)/(9*S))*HPL[{2, 1}, -S^2] - (2*(17 + 87*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (32*HPL[{3, 2}, -S^2])/(3*S) + (6*HPL[{4, 1}, -S^2])/S + (4*(16 + 83*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (1292*HPL[{2, 2, 1}, -S^2])/(3*S) + (3968*HPL[{3, 1, 1}, -S^2])/(3*S) - (2768*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (22*S*Zeta[3])/3 + HPL[{1}, -S^2]^2*((178*(1 + S^2))/(3*S) + (113*Pi^2*(1 + S^2))/(18*S) + (82*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (4*HPL[{3}, -S^2])/S - (220*HPL[{2, 1}, -S^2])/S - (22*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((2*(14 + 61*S^2))/(3*S) + (Pi^2*(31 + 79*S^2))/(18*S) - (16*HPL[{3}, -S^2])/(3*S) - (646*HPL[{2, 1}, -S^2])/(3*S) + (2*Zeta[3])/S) + HPL[{1}, -S^2]*((3997*Pi^4)/(540*S) + (262*(1 + S^2))/(3*S) + (89*Pi^2*(1 + S^2))/(9*S) + ((187*Pi^2)/(6*S) + (32*(1 + S^2))/S)*HPL[{2}, -S^2] + (53*HPL[{2}, -S^2]^2)/S + (34*HPL[{4}, -S^2])/(3*S) - (164*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (220*HPL[{3, 1}, -S^2])/S + (440*HPL[{2, 1, 1}, -S^2])/S - (28*(1 + S^2)*Zeta[3])/(3*S))) + (-1484*S - (812*Pi^2*S)/3)*Zeta[5] + HPL[{1}, -S^2]^3*((3340*(1 + S^2))/(3*S) + (156*Pi^2*(1 + S^2))/S + (4759*Pi^4*(1 + S^2))/(270*S) + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-1988*Pi^2)/(9*S) - (2744*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (880*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (288*HPL[{5}, -S^2])/S + ((-1568*Pi^2)/(9*S) + (528*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (2224*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (6272*HPL[{3, 2}, -S^2])/(3*S) + (21472*HPL[{4, 1}, -S^2])/(3*S) - (1040*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (12544*HPL[{2, 2, 1}, -S^2])/(3*S) + (22432*HPL[{3, 1, 1}, -S^2])/(3*S) + ((-1664*Pi^2)/(9*S) - (2384*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-276*(1 + S^2))/S - (220*Pi^2*(1 + S^2))/(9*S) - (3136*HPL[{3}, -S^2])/(3*S) - (6272*HPL[{2, 1}, -S^2])/(3*S) - (3136*Zeta[3])/(3*S)) - (3040*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((Pi^4*(-770 - 5307*S^2))/(180*S) - (110*(2 + 15*S^2))/S - (2*Pi^2*(56 + 383*S^2))/(3*S) + (14*(-1 + 12*S^2)*HPL[{4}, -S^2])/S - (156*HPL[{5}, -S^2])/S + ((1828*Pi^2)/(3*S) - (4*(-583 + 59*S^2))/S)*HPL[{2, 1}, -S^2] + (28*(-3 + 89*S^2)*HPL[{3, 1}, -S^2])/S - (32*HPL[{3, 2}, -S^2])/S + (264*HPL[{4, 1}, -S^2])/S - (16*(-10 + 317*S^2)*HPL[{2, 1, 1}, -S^2])/S - (6880*HPL[{2, 2, 1}, -S^2])/S - (20832*HPL[{3, 1, 1}, -S^2])/S + (13920*HPL[{2, 1, 1, 1}, -S^2])/S + ((-20*Pi^2)/S - (4*(17 + 15*S^2))/S)*Zeta[3] - (168*Zeta[5])/S) + HPL[{2, 1}, -S^2]*((4*Pi^2*(-26 + 61*S^2))/S + (20*(-13 + 79*S^2))/S + (Pi^4*(-1354 + 2801*S^2))/(90*S) + (128*(4 + 21*S^2)*HPL[{3, 1}, -S^2])/S - (6568*HPL[{3, 2}, -S^2])/S - (21104*HPL[{4, 1}, -S^2])/S + (64*(25 + 73*S^2)*HPL[{2, 1, 1}, -S^2])/S - (6272*HPL[{2, 2, 1}, -S^2])/S - (4896*HPL[{3, 1, 1}, -S^2])/S - (12640*HPL[{2, 1, 1, 1}, -S^2])/S + (2144/S + (1708*Pi^2)/(3*S))*Zeta[3] + (3000*Zeta[5])/S) + HPL[{1}, -S^2]^2*((52285*Pi^6)/(4536*S) + (2420*(1 + S^2))/S + (294*Pi^2*(1 + S^2))/S + (5363*Pi^4*(1 + S^2))/(180*S) + ((607*Pi^2)/(3*S) + (402*(1 + S^2))/S)*HPL[{2}, -S^2]^2 + (148*HPL[{3}, -S^2]^2)/S + ((-340*Pi^2)/(3*S) - (462*(1 + S^2))/S)*HPL[{4}, -S^2] - (424*(1 + S^2)*HPL[{5}, -S^2])/S - (178*HPL[{6}, -S^2])/S - (3136*HPL[{2, 1}, -S^2]^2)/S + ((-440*Pi^2)/(3*S) + (1136*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (2232*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (7576*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (468*HPL[{4, 2}, -S^2])/S + (2704*HPL[{5, 1}, -S^2])/S + ((1568*Pi^2)/(3*S) - (1584*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (4048*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (2656*HPL[{4, 1, 1}, -S^2])/S + (3120*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (2656*HPL[{3, 1, 1, 1}, -S^2])/S + ((-1312*(1 + S^2))/S - (212*Pi^2*(1 + S^2))/S)*Zeta[3] + (80*Zeta[3]^2)/S + HPL[{3}, -S^2]*((-1460*(1 + S^2))/S - (240*Pi^2*(1 + S^2))/S + (3136*HPL[{2, 1}, -S^2])/S - (200*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((828*(1 + S^2))/S + (220*Pi^2*(1 + S^2))/(3*S) + (3136*Zeta[3])/S) + HPL[{2}, -S^2]*((2021*Pi^4)/(60*S) - (452*(1 + S^2))/S - (40*Pi^2*(1 + S^2))/S - (1116*(1 + S^2)*HPL[{3}, -S^2])/S - (452*HPL[{4}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (3136*HPL[{3, 1}, -S^2])/S + (6272*HPL[{2, 1, 1}, -S^2])/S - (1120*(1 + S^2)*Zeta[3])/S) - (1316*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((-30311*Pi^6)/(11340*S) + (40*(-16 + 7*S^2))/S + (2*Pi^2*(-51 + 43*S^2))/S + (Pi^4*(-1906 + 2199*S^2))/(180*S) + (4*HPL[{3}, -S^2]^2)/S + ((71*Pi^2)/(3*S) - (2*(-41 + 165*S^2))/S)*HPL[{4}, -S^2] - (12*(-5 + 28*S^2)*HPL[{5}, -S^2])/S + (152*HPL[{6}, -S^2])/S + (1568*HPL[{2, 1}, -S^2]^2)/S + ((-1004*Pi^2)/(3*S) - (4*(333 + 64*S^2))/S)*HPL[{3, 1}, -S^2] + (2*(95 + 1187*S^2)*HPL[{3, 2}, -S^2])/S + (4*(48 + 1895*S^2)*HPL[{4, 1}, -S^2])/S + (78*HPL[{4, 2}, -S^2])/S - (172*HPL[{5, 1}, -S^2])/S + ((1664*Pi^2)/(3*S) + (168*(14 + 5*S^2))/S)*HPL[{2, 1, 1}, -S^2] - (16*(-42 + 149*S^2)*HPL[{2, 2, 1}, -S^2])/S + (32*(-58 + 65*S^2)*HPL[{3, 1, 1}, -S^2])/S - (312*HPL[{3, 1, 2}, -S^2])/S + (2808*HPL[{3, 2, 1}, -S^2])/S + (9824*HPL[{4, 1, 1}, -S^2])/S - (64*(25 + 73*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (67616*HPL[{3, 1, 1, 1}, -S^2])/S + (12640*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-14*Pi^2*(1 + 44*S^2))/(3*S) - (8*(5 + 142*S^2))/S)*Zeta[3] - (32*Zeta[3]^2)/S + HPL[{3}, -S^2]*((Pi^2*(17 - 673*S^2))/(3*S) - (4*(-5 + 327*S^2))/S + (3440*HPL[{2, 1}, -S^2])/S + (32*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-200*Pi^2*(2 + 3*S^2))/(3*S) - (4*(125 + 313*S^2))/S + (2992*Zeta[3])/S) - (4*(-4 + 295*S^2)*Zeta[5])/S) + HPL[{0}, S^2]^2*(140*S + (55*Pi^2*S)/2 + (29*Pi^4*S)/20 + (18*(1 + S^2)*HPL[{1}, -S^2]^5)/S + (62*HPL[{1}, -S^2]^6)/(3*S) + ((2*Pi^2)/S + (38 + 117*S^2)/(2*S))*HPL[{2}, -S^2]^2 - (10*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^4*((749*Pi^2)/(18*S) + (152*(1 + S^2))/(3*S) + (392*HPL[{2}, -S^2])/(3*S)) - (5*HPL[{3}, -S^2]^2)/S + ((-7*Pi^2)/(2*S) + (-8 - 13*S^2)/S)*HPL[{4}, -S^2] + ((-10 - 47*S^2)*HPL[{5}, -S^2])/S + (20*HPL[{6}, -S^2])/S - (42*HPL[{2, 1}, -S^2]^2)/S + ((58*Pi^2)/(3*S) - (2*(-5 + 112*S^2))/S)*HPL[{3, 1}, -S^2] + ((6 + 83*S^2)*HPL[{3, 2}, -S^2])/S + (2*(32 + 133*S^2)*HPL[{4, 1}, -S^2])/S - (5*HPL[{4, 2}, -S^2])/S + (14*HPL[{5, 1}, -S^2])/S + ((-106*Pi^2)/(3*S) + (4*(-2 + 115*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (16*(25 + 2*S^2)*HPL[{2, 2, 1}, -S^2])/S - (4*(-281 + 19*S^2)*HPL[{3, 1, 1}, -S^2])/S + (8*HPL[{3, 1, 2}, -S^2])/S - (72*HPL[{3, 2, 1}, -S^2])/S - (312*HPL[{4, 1, 1}, -S^2])/S + (8*(-83 + 35*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (320*HPL[{3, 1, 1, 1}, -S^2])/S - (560*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (-84*S - 25*Pi^2*S)*Zeta[3] + HPL[{1}, -S^2]^3*((374*(1 + S^2))/(3*S) + (166*Pi^2*(1 + S^2))/(9*S) + (170*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (88*HPL[{3}, -S^2])/(3*S) - (1568*HPL[{2, 1}, -S^2])/(3*S) - (164*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-21 - 79*S^2)/S + (Pi^2*(-34 - 61*S^2))/(6*S) + (88*HPL[{2, 1}, -S^2])/S - (16*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((Pi^2*(-84 + 37*S^2))/(3*S) + (2*(-83 + 41*S^2))/S + (168*Zeta[3])/S) + HPL[{1}, -S^2]^2*((8449*Pi^4)/(360*S) + (250*(1 + S^2))/S + (211*Pi^2*(1 + S^2))/(6*S) + ((211*Pi^2)/(2*S) + (78*(1 + S^2))/S)*HPL[{2}, -S^2] + (215*HPL[{2}, -S^2]^2)/S - (50*(1 + S^2)*HPL[{3}, -S^2])/S - (8*HPL[{4}, -S^2])/S - (170*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (772*HPL[{3, 1}, -S^2])/S + (1568*HPL[{2, 1, 1}, -S^2])/S - (66*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-323*Pi^4)/(180*S) + (3*(-2 + 43*S^2))/S + (Pi^2*(10 + 143*S^2))/(6*S) - (3*(1 + 13*S^2)*HPL[{3}, -S^2])/S + (13*HPL[{4}, -S^2])/S - (8*(25 + 2*S^2)*HPL[{2, 1}, -S^2])/S - (48*HPL[{3, 1}, -S^2])/S + (84*HPL[{2, 1, 1}, -S^2])/S - (2*(-1 + 28*S^2)*Zeta[3])/S) - 132*S*Zeta[5] + HPL[{1}, -S^2]*((365*(1 + S^2))/S + (289*Pi^2*(1 + S^2))/(6*S) + (367*Pi^4*(1 + S^2))/(120*S) + (66*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-25*Pi^2)/(3*S) - (64*(1 + S^2))/S)*HPL[{3}, -S^2] - (31*(1 + S^2)*HPL[{4}, -S^2])/S - (24*HPL[{5}, -S^2])/S + ((-211*Pi^2)/S - (156*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (164*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (84*HPL[{3, 2}, -S^2])/S + (268*HPL[{4, 1}, -S^2])/S + (340*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (1720*HPL[{2, 2, 1}, -S^2])/S + (4984*HPL[{3, 1, 1}, -S^2])/S - (3136*HPL[{2, 1, 1, 1}, -S^2])/S + ((-41*Pi^2)/(3*S) - (74*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((77*(1 + S^2))/S + (49*Pi^2*(1 + S^2))/(3*S) - (42*HPL[{3}, -S^2])/S - (860*HPL[{2, 1}, -S^2])/S - (78*Zeta[3])/S) - (78*Zeta[5])/S)) + HPL[{0}, S^2]*(3920*S + (1240*Pi^2*S)/3 + (6611*Pi^4*S)/180 + (4391*Pi^6*S)/1620 + (112*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + (64*HPL[{1}, -S^2]^7)/(3*S) + (2*(5 + 196*S^2)*HPL[{2}, -S^2]^3)/(3*S) + HPL[{1}, -S^2]^5*((482*Pi^2)/(9*S) + (120*(1 + S^2))/S + (200*HPL[{2}, -S^2])/S) - (2*(-2 + 3*S^2)*HPL[{3}, -S^2]^2)/S + ((25*Pi^2)/(3*S) + (2*(25 + 9*S^2))/S)*HPL[{5}, -S^2] + (10*(4 + 9*S^2)*HPL[{6}, -S^2])/S - (100*HPL[{7}, -S^2])/S - (16*(7 + 95*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((82*Pi^2)/(3*S) + (2*(43 + 93*S^2))/S)*HPL[{3, 2}, -S^2] + ((34*Pi^2)/(3*S) + (4*(31 + 119*S^2))/S)*HPL[{4, 1}, -S^2] + (2*(2 + 9*S^2)*HPL[{4, 2}, -S^2])/S - (128*HPL[{4, 3}, -S^2])/S - (4*(13 + 10*S^2)*HPL[{5, 1}, -S^2])/S - (370*HPL[{5, 2}, -S^2])/S - (792*HPL[{6, 1}, -S^2])/S + ((4360*Pi^2)/(3*S) + (8*(368 + 21*S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((13312*Pi^2)/(3*S) + (8*(1113 + 32*S^2))/S)*HPL[{3, 1, 1}, -S^2] + (4*(2 + 3*S^2)*HPL[{3, 1, 2}, -S^2])/S + (4*(22 + 787*S^2)*HPL[{3, 2, 1}, -S^2])/S + (44*HPL[{3, 2, 2}, -S^2])/S - (128*HPL[{3, 3, 1}, -S^2])/S + (24*(14 + 397*S^2)*HPL[{4, 1, 1}, -S^2])/S - (148*HPL[{4, 1, 2}, -S^2])/S - (628*HPL[{4, 2, 1}, -S^2])/S - (1224*HPL[{5, 1, 1}, -S^2])/S + ((-9128*Pi^2)/(3*S) + (80*(-74 + 3*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] - (11936*HPL[{2, 2, 2, 1}, -S^2])/S - (16*(15 + 403*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (36208*HPL[{3, 1, 1, 2}, -S^2])/S + (36208*HPL[{3, 1, 2, 1}, -S^2])/S + (72016*HPL[{3, 2, 1, 1}, -S^2])/S + (214976*HPL[{4, 1, 1, 1}, -S^2])/S + (480*(1 + 27*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (24544*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (73632*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (121600*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (50880*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (-184*S - (110*Pi^2*S)/3)*Zeta[3] + 40*S*Zeta[3]^2 + HPL[{1}, -S^2]^4*((1030*(1 + S^2))/(3*S) + (517*Pi^2*(1 + S^2))/(9*S) + (250*(1 + S^2)*HPL[{2}, -S^2])/S - (68*HPL[{3}, -S^2])/(3*S) - (1000*HPL[{2, 1}, -S^2])/S - (332*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((-96*(2 + 19*S^2))/S - (4*Pi^2*(16 + 245*S^2))/(3*S) - (32*Zeta[3])/S) + HPL[{2}, -S^2]^2*((6*(7 + 67*S^2))/S + (Pi^2*(13 + 153*S^2))/(2*S) + (4*HPL[{3}, -S^2])/S - (1492*HPL[{2, 1}, -S^2])/S + (4*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((16*(24 + 223*S^2))/S + (4*Pi^2*(31 + 488*S^2))/(3*S) + (16*Zeta[3])/S) + HPL[{4}, -S^2]*((Pi^2*(19 + 29*S^2))/(3*S) + (2*(45 + 67*S^2))/S - (116*HPL[{2, 1}, -S^2])/S + (52*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-11423*Pi^4)/(90*S) - (12*(152 + 9*S^2))/S + (2*Pi^2*(-446 + 15*S^2))/(3*S) + (6144*HPL[{3, 1}, -S^2])/S + (12272*HPL[{2, 1, 1}, -S^2])/S - (8*(-38 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((4061*Pi^4)/(90*S) + (2528*(1 + S^2))/(3*S) + (1154*Pi^2*(1 + S^2))/(9*S) + ((240*Pi^2)/S + (1592*(1 + S^2))/(3*S))*HPL[{2}, -S^2] + (1568*HPL[{2}, -S^2]^2)/(3*S) - (56*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (184*HPL[{4}, -S^2])/(3*S) - (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2000*HPL[{3, 1}, -S^2])/S + (4000*HPL[{2, 1, 1}, -S^2])/S - (344*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((21*Pi^4)/(5*S) + (Pi^2*(7 - 47*S^2))/(3*S) + (4*(30 + S^2))/S + (64*HPL[{4}, -S^2])/S - (4*(-19 + 13*S^2)*HPL[{2, 1}, -S^2])/S + (96*HPL[{3, 1}, -S^2])/S - (176*HPL[{2, 1, 1}, -S^2])/S - (4*(-1 + 5*S^2)*Zeta[3])/S) - 108*S*Zeta[5] + HPL[{1}, -S^2]^2*((1670*(1 + S^2))/S + (231*Pi^2*(1 + S^2))/S + (2191*Pi^4*(1 + S^2))/(90*S) + (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-22*Pi^2)/(3*S) + (8*(1 + S^2))/S)*HPL[{3}, -S^2] + (58*(1 + S^2)*HPL[{4}, -S^2])/S + (92*HPL[{5}, -S^2])/S + ((-720*Pi^2)/S - (1592*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (1512*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (304*HPL[{3, 2}, -S^2])/S + (728*HPL[{4, 1}, -S^2])/S + (3000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (6272*HPL[{2, 2, 1}, -S^2])/S + (18544*HPL[{3, 1, 1}, -S^2])/S - (12000*HPL[{2, 1, 1, 1}, -S^2])/S + ((-188*Pi^2)/(3*S) - (188*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((898*(1 + S^2))/S + (457*Pi^2*(1 + S^2))/(3*S) - (152*HPL[{3}, -S^2])/S - (3136*HPL[{2, 1}, -S^2])/S - (328*Zeta[3])/S) - (260*Zeta[5])/S) + HPL[{2}, -S^2]*((71*Pi^4*(6 + 55*S^2))/(180*S) + (20*(15 + 61*S^2))/S + (4*Pi^2*(19 + 142*S^2))/(3*S) + ((-38*Pi^2)/(3*S) - (6*(7 + 15*S^2))/S)*HPL[{3}, -S^2] - (6*(2 + S^2)*HPL[{4}, -S^2])/S - (74*HPL[{5}, -S^2])/S + ((-2180*Pi^2)/(3*S) - (4*(368 + 21*S^2))/S)*HPL[{2, 1}, -S^2] - (4*(29 + 379*S^2)*HPL[{3, 1}, -S^2])/S - (16*HPL[{3, 2}, -S^2])/S + (68*HPL[{4, 1}, -S^2])/S + (32*(7 + 95*S^2)*HPL[{2, 1, 1}, -S^2])/S + (5968*HPL[{2, 2, 1}, -S^2])/S - (18080*HPL[{3, 1, 1}, -S^2])/S - (12272*HPL[{2, 1, 1, 1}, -S^2])/S + ((8*Pi^2)/(3*S) - 164*S)*Zeta[3] + (48*Zeta[5])/S) + HPL[{1}, -S^2]*((248987*Pi^6)/(22680*S) + (2420*(1 + S^2))/S + (298*Pi^2*(1 + S^2))/S + (1057*Pi^4*(1 + S^2))/(36*S) + ((551*Pi^2)/(3*S) + (402*(1 + S^2))/S)*HPL[{2}, -S^2]^2 + (236*HPL[{2}, -S^2]^3)/S - (8*HPL[{3}, -S^2]^2)/S + ((80*Pi^2)/(3*S) + (110*(1 + S^2))/S)*HPL[{4}, -S^2] + (68*(1 + S^2)*HPL[{5}, -S^2])/S + (146*HPL[{6}, -S^2])/S - (3136*HPL[{2, 1}, -S^2]^2)/S + ((-720*Pi^2)/S - (1624*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (152*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (340*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (216*HPL[{5, 1}, -S^2])/S + ((1440*Pi^2)/S + (3184*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (9296*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (5664*HPL[{3, 2, 1}, -S^2])/S + (17360*HPL[{4, 1, 1}, -S^2])/S - (6000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (12000*HPL[{3, 1, 1, 1}, -S^2])/S + (24000*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-212*(1 + S^2))/S - (38*Pi^2*(1 + S^2))/S)*Zeta[3] + (68*Zeta[3]^2)/S + HPL[{3}, -S^2]*((64*(1 + S^2))/S - (14*Pi^2*(1 + S^2))/(3*S) + (304*HPL[{2, 1}, -S^2])/S - (16*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-1796*(1 + S^2))/S - (914*Pi^2*(1 + S^2))/(3*S) + (656*Zeta[3])/S) + HPL[{2}, -S^2]*((2155*Pi^4)/(36*S) + (1076*(1 + S^2))/S + (494*Pi^2*(1 + S^2))/(3*S) - (76*(1 + S^2)*HPL[{3}, -S^2])/S + (16*HPL[{4}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (3136*HPL[{3, 1}, -S^2])/S + (6272*HPL[{2, 1, 1}, -S^2])/S - (164*(1 + S^2)*Zeta[3])/S) - (152*(1 + S^2)*Zeta[5])/S)) - 1812*S*Zeta[7] + HPL[{1}, -S^2]*((3920*(1 + S^2))/S + (400*Pi^2*(1 + S^2))/S + (2207*Pi^4*(1 + S^2))/(60*S) + (3653*Pi^6*(1 + S^2))/(1134*S) - (166*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + (74*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-80*Pi^2)/S - (452*(1 + S^2))/S)*HPL[{5}, -S^2] - (416*(1 + S^2)*HPL[{6}, -S^2])/S - (60*HPL[{7}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((1652*Pi^2)/(3*S) + (2280*(1 + S^2))/S)*HPL[{3, 2}, -S^2] + ((5636*Pi^2)/(3*S) + (7764*(1 + S^2))/S)*HPL[{4, 1}, -S^2] + (234*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (188*HPL[{4, 3}, -S^2])/S + (1768*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (408*HPL[{5, 2}, -S^2])/S + (196*HPL[{6, 1}, -S^2])/S + ((4856*Pi^2)/(3*S) + (3216*(1 + S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((10592*Pi^2)/(3*S) + (4160*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] - (1328*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (6520*HPL[{3, 2, 2}, -S^2])/S - (19936*HPL[{3, 3, 1}, -S^2])/S - (5744*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (19624*HPL[{4, 1, 2}, -S^2])/S - (60808*HPL[{4, 2, 1}, -S^2])/S - (125280*HPL[{5, 1, 1}, -S^2])/S + ((-3136*Pi^2)/(3*S) + (3168*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (4448*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (12544*HPL[{3, 1, 1, 2}, -S^2])/S + (12544*HPL[{3, 1, 2, 1}, -S^2])/S + (12544*HPL[{3, 2, 1, 1}, -S^2])/S + (42944*HPL[{4, 1, 1, 1}, -S^2])/S - (6240*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (25088*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (75264*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (155840*HPL[{3, 1, 1, 1, 1}, -S^2])/S + ((-1013*Pi^4)/(30*S) - (1528*(1 + S^2))/S - (670*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (44*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1, 1}, -S^2]*((-1656*(1 + S^2))/S - (440*Pi^2*(1 + S^2))/(3*S) - (6272*Zeta[3])/S) + HPL[{2}, -S^2]^2*((431*(1 + S^2))/S + (262*Pi^2*(1 + S^2))/(3*S) - (932*HPL[{3}, -S^2])/S - (708*Zeta[3])/S) + HPL[{4}, -S^2]*((-512*(1 + S^2))/S - (251*Pi^2*(1 + S^2))/(3*S) + (904*HPL[{2, 1}, -S^2])/S - (112*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((1196*(1 + S^2))/S + (392*Pi^2*(1 + S^2))/(3*S) + (3232*Zeta[3])/S) + HPL[{3}, -S^2]*((-601*Pi^4)/(15*S) - (1592*(1 + S^2))/S - (250*Pi^2*(1 + S^2))/S + (172*HPL[{4}, -S^2])/S + (2232*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (3136*HPL[{3, 1}, -S^2])/S - (6272*HPL[{2, 1, 1}, -S^2])/S - (104*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-2021*Pi^4)/(30*S) + (904*(1 + S^2))/S + (80*Pi^2*(1 + S^2))/S + (6272*HPL[{3, 1}, -S^2])/S + (12544*HPL[{2, 1, 1}, -S^2])/S + (2240*(1 + S^2)*Zeta[3])/S) + ((-838*Pi^2)/(3*S) - (1436*(1 + S^2))/S)*Zeta[5] + HPL[{2}, -S^2]*((-510*(1 + S^2))/S - (130*Pi^2*(1 + S^2))/(3*S) - (128*Pi^4*(1 + S^2))/(45*S) + ((-826*Pi^2)/(3*S) - (1140*(1 + S^2))/S)*HPL[{3}, -S^2] - (226*(1 + S^2)*HPL[{4}, -S^2])/S - (328*HPL[{5}, -S^2])/S + ((-2428*Pi^2)/(3*S) - (1608*(1 + S^2))/S)*HPL[{2, 1}, -S^2] - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (3416*HPL[{3, 2}, -S^2])/S + (10280*HPL[{4, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (6272*HPL[{3, 1, 1}, -S^2])/S - (12544*HPL[{2, 1, 1, 1}, -S^2])/S + ((-862*Pi^2)/(3*S) - (1104*(1 + S^2))/S)*Zeta[3] - (1444*Zeta[5])/S) - (1932*Zeta[7])/S)) + HPL[{0}, S^2]*(-3920*S - (1010*Pi^2*S)/3 - (4861*Pi^4*S)/180 - (81827*Pi^6*S)/45360 - (16*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) - (8*HPL[{1}, -S^2]^8)/(3*S) + ((11*Pi^2)/(9*S) + (-18 - 391*S^2)/(6*S))*HPL[{2}, -S^2]^3 - (5*HPL[{2}, -S^2]^4)/(4*S) + HPL[{1}, -S^2]^6*((-241*Pi^2)/(27*S) - (20*(1 + S^2))/S - (100*HPL[{2}, -S^2])/(3*S)) + ((-7*Pi^2)/(2*S) + (-13 - 5*S^2)/S)*HPL[{3}, -S^2]^2 + (41*HPL[{4}, -S^2]^2)/S + ((-70*Pi^2)/(3*S) - (10*(12 + 17*S^2))/S)*HPL[{6}, -S^2] + (2*(-75 + 11*S^2)*HPL[{7}, -S^2])/S - (525*HPL[{8}, -S^2])/S + ((4*Pi^2)/S + (2*(34 + 381*S^2))/S)*HPL[{2, 1}, -S^2]^2 - (20*HPL[{3, 1}, -S^2]^2)/S + (Pi^2/(2*S) + (-7 - 3*S^2)/S)*HPL[{4, 2}, -S^2] + (2*(-29 + 9*S^2)*HPL[{4, 3}, -S^2])/S + ((7*Pi^2)/S + (2*(43 + 75*S^2))/S)*HPL[{5, 1}, -S^2] + ((-181 + 42*S^2)*HPL[{5, 2}, -S^2])/S + (2*(-136 + 19*S^2)*HPL[{6, 1}, -S^2])/S - (6*HPL[{6, 2}, -S^2])/S + (228*HPL[{7, 1}, -S^2])/S - (136*HPL[{2, 1, 1}, -S^2]^2)/S + ((-2*Pi^2)/S - (2*(1 + 3*S^2))/S)*HPL[{3, 1, 2}, -S^2] + ((82*Pi^2)/(3*S) - (2*(37 + 785*S^2))/S)*HPL[{3, 2, 1}, -S^2] + (7*(2 + 25*S^2)*HPL[{3, 2, 2}, -S^2])/S + (16*(5 + 34*S^2)*HPL[{3, 3, 1}, -S^2])/S + (32*HPL[{3, 3, 2}, -S^2])/S + ((298*Pi^2)/(3*S) - (4*(77 + 1212*S^2))/S)*HPL[{4, 1, 1}, -S^2] + (2*(42 + 281*S^2)*HPL[{4, 1, 2}, -S^2])/S - (64*HPL[{4, 1, 3}, -S^2])/S + (2*(138 + 821*S^2)*HPL[{4, 2, 1}, -S^2])/S + (35*HPL[{4, 2, 2}, -S^2])/S - (128*HPL[{4, 3, 1}, -S^2])/S + (12*(45 + 272*S^2)*HPL[{5, 1, 1}, -S^2])/S - (58*HPL[{5, 1, 2}, -S^2])/S - (538*HPL[{5, 2, 1}, -S^2])/S - (1480*HPL[{6, 1, 1}, -S^2])/S - (16*(-172 + 19*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((-272*Pi^2)/(3*S) + (8*(29 + 416*S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] + (4*(-2104 + 123*S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (4*(-2104 + 123*S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (12*HPL[{3, 1, 2, 2}, -S^2])/S + (4*(-4168 + 351*S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (12*HPL[{3, 2, 1, 2}, -S^2])/S - (284*HPL[{3, 2, 2, 1}, -S^2])/S - (816*HPL[{3, 3, 1, 1}, -S^2])/S + (8*(-6232 + 545*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (12*HPL[{4, 1, 1, 2}, -S^2])/S - (804*HPL[{4, 1, 2, 1}, -S^2])/S - (2436*HPL[{4, 2, 1, 1}, -S^2])/S - (4936*HPL[{5, 1, 1, 1}, -S^2])/S + ((488*Pi^2)/(3*S) - (112*(4 + 59*S^2))/S)*HPL[{2, 1, 1, 1, 1}, -S^2] + (64*(91 + 3*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (192*(91 + 3*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (608*HPL[{2, 2, 1, 2, 1}, -S^2])/S - (1824*HPL[{2, 2, 2, 1, 1}, -S^2])/S + (16*(1821 + 97*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (3600*HPL[{3, 1, 1, 1, 2}, -S^2])/S + (6032*HPL[{3, 1, 1, 2, 1}, -S^2])/S + (7248*HPL[{3, 1, 2, 1, 1}, -S^2])/S + (15152*HPL[{3, 2, 1, 1, 1}, -S^2])/S + (45792*HPL[{4, 1, 1, 1, 1}, -S^2])/S - (960*(-12 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - (1664*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + (2880*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (70*S + (52*Pi^2*S)/3 + (51*Pi^4*S)/10)*Zeta[3] + 2*S*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((8*(401 + 3*S^2))/S - (4*Pi^2*(-426 + 31*S^2))/(3*S) - (1328*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((Pi^2*(-43 - 191*S^2))/(3*S) - (2*(-37 + 141*S^2))/S - (20*Zeta[3])/S) + HPL[{3, 2}, -S^2]*((Pi^2*(-17 - 49*S^2))/(2*S) - (4*(2 + 29*S^2))/S + (20*Zeta[3])/S) + HPL[{1}, -S^2]^5*((-206*(1 + S^2))/(3*S) - (517*Pi^2*(1 + S^2))/(45*S) - (50*(1 + S^2)*HPL[{2}, -S^2])/S + (68*HPL[{3}, -S^2])/(15*S) + (200*HPL[{2, 1}, -S^2])/S + (332*Zeta[3])/(15*S)) + HPL[{5}, -S^2]*((-105 - 38*S^2)/S + (Pi^2*(-32 + S^2))/(3*S) + (82*HPL[{2, 1}, -S^2])/S + (86*Zeta[3])/S) + HPL[{2, 2, 1}, -S^2]*((-2*Pi^2*(437 + 17*S^2))/(3*S) - (4*(389 + 29*S^2))/S + (672*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((-4*Pi^2*(652 + 3*S^2))/(3*S) - (4*(1193 + 65*S^2))/S + (2064*Zeta[3])/S) + HPL[{1}, -S^2]^4*((-4061*Pi^4)/(360*S) - (632*(1 + S^2))/(3*S) - (577*Pi^2*(1 + S^2))/(18*S) + ((-60*Pi^2)/S - (398*(1 + S^2))/(3*S))*HPL[{2}, -S^2] - (392*HPL[{2}, -S^2]^2)/(3*S) + (14*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (46*HPL[{4}, -S^2])/(3*S) + (250*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (500*HPL[{3, 1}, -S^2])/S - (1000*HPL[{2, 1, 1}, -S^2])/S + (86*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((-157*Pi^4)/(360*S) + (-120 - 131*S^2)/S + (Pi^2*(-23 - 27*S^2))/(2*S) + (2*(13 + 10*S^2)*HPL[{2, 1}, -S^2])/S - (74*HPL[{3, 1}, -S^2])/S + (84*HPL[{2, 1, 1}, -S^2])/S + (2*(17 + 5*S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((7*Pi^4)/(36*S) + (Pi^2*(-25 - 227*S^2))/(6*S) - (17*(2 + 25*S^2))/(2*S) + (3*(1 + 15*S^2)*HPL[{3}, -S^2])/(2*S) - (5*HPL[{4}, -S^2])/(2*S) - (2*(-172 + 19*S^2)*HPL[{2, 1}, -S^2])/S - (34*HPL[{3, 1}, -S^2])/S + (76*HPL[{2, 1, 1}, -S^2])/S + (5*(1 + 9*S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((36*Pi^4)/(5*S) - (2*Pi^2*(48 + 509*S^2))/(3*S) - (4*(82 + 511*S^2))/S + (24*(1 + 14*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-149*Pi^4)/(45*S) + (Pi^2*(61 + 519*S^2))/(3*S) + (2*(90 + 539*S^2))/S + (128*HPL[{2, 1, 1}, -S^2])/S - (8*(4 + 21*S^2)*Zeta[3])/S) + (4*S + 21*Pi^2*S)*Zeta[5] + HPL[{2, 1}, -S^2]*((-7*Pi^4*(-494 + 3*S^2))/(180*S) + (4*Pi^2*(127 + 4*S^2))/(3*S) + (10*(107 + 15*S^2))/S - (4*(363 + 13*S^2)*HPL[{3, 1}, -S^2])/S + (256*HPL[{3, 2}, -S^2])/S + (684*HPL[{4, 1}, -S^2])/S - (32*(91 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/S + (304*HPL[{2, 2, 1}, -S^2])/S + (480*HPL[{3, 1, 1}, -S^2])/S + (272*HPL[{2, 1, 1, 1}, -S^2])/S + ((-190*Pi^2)/(3*S) - (4*(42 + S^2))/S)*Zeta[3] - (260*Zeta[5])/S) + HPL[{3}, -S^2]*((-75*(2 + S^2))/S + (Pi^2*(-27 + 17*S^2))/(3*S) + (Pi^4*(-70 + 339*S^2))/(360*S) + ((29 - 16*S^2)*HPL[{4}, -S^2])/S - (82*HPL[{5}, -S^2])/S + ((-52*Pi^2)/(3*S) + (2*(-13 + 11*S^2))/S)*HPL[{2, 1}, -S^2] - (2*(13 + 45*S^2)*HPL[{3, 1}, -S^2])/S - (16*HPL[{3, 2}, -S^2])/S + (112*HPL[{4, 1}, -S^2])/S + (4*(19 + 51*S^2)*HPL[{2, 1, 1}, -S^2])/S + (256*HPL[{2, 2, 1}, -S^2])/S + (688*HPL[{3, 1, 1}, -S^2])/S - (432*HPL[{2, 1, 1, 1}, -S^2])/S + ((8*Pi^2)/S + (2*(11 + 5*S^2))/S)*Zeta[3] + (76*Zeta[5])/S) + HPL[{1}, -S^2]^3*((-1670*(1 + S^2))/(3*S) - (77*Pi^2*(1 + S^2))/S - (2191*Pi^4*(1 + S^2))/(270*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((22*Pi^2)/(9*S) - (8*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (58*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (92*HPL[{5}, -S^2])/(3*S) + ((240*Pi^2)/S + (1592*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (504*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (304*HPL[{3, 2}, -S^2])/(3*S) - (728*HPL[{4, 1}, -S^2])/(3*S) - (1000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (6272*HPL[{2, 2, 1}, -S^2])/(3*S) - (18544*HPL[{3, 1, 1}, -S^2])/(3*S) + (4000*HPL[{2, 1, 1, 1}, -S^2])/S + ((188*Pi^2)/(9*S) + (188*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-898*(1 + S^2))/(3*S) - (457*Pi^2*(1 + S^2))/(9*S) + (152*HPL[{3}, -S^2])/(3*S) + (3136*HPL[{2, 1}, -S^2])/(3*S) + (328*Zeta[3])/(3*S)) + (260*Zeta[5])/(3*S)) + HPL[{1}, -S^2]^2*((-248987*Pi^6)/(45360*S) - (1210*(1 + S^2))/S - (149*Pi^2*(1 + S^2))/S - (1057*Pi^4*(1 + S^2))/(72*S) + ((-551*Pi^2)/(6*S) - (201*(1 + S^2))/S)*HPL[{2}, -S^2]^2 - (118*HPL[{2}, -S^2]^3)/S + (4*HPL[{3}, -S^2]^2)/S + ((-40*Pi^2)/(3*S) - (55*(1 + S^2))/S)*HPL[{4}, -S^2] - (34*(1 + S^2)*HPL[{5}, -S^2])/S - (73*HPL[{6}, -S^2])/S + (1568*HPL[{2, 1}, -S^2]^2)/S + ((360*Pi^2)/S + (812*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (76*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (170*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (108*HPL[{5, 1}, -S^2])/S + ((-720*Pi^2)/S - (1592*(1 + S^2))/S)*HPL[{2, 1, 1}, -S^2] - (1568*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (4648*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (2832*HPL[{3, 2, 1}, -S^2])/S - (8680*HPL[{4, 1, 1}, -S^2])/S + (3000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (6000*HPL[{3, 1, 1, 1}, -S^2])/S - (12000*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((106*(1 + S^2))/S + (19*Pi^2*(1 + S^2))/S)*Zeta[3] - (34*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((898*(1 + S^2))/S + (457*Pi^2*(1 + S^2))/(3*S) - (328*Zeta[3])/S) + HPL[{3}, -S^2]*((-32*(1 + S^2))/S + (7*Pi^2*(1 + S^2))/(3*S) - (152*HPL[{2, 1}, -S^2])/S + (8*Zeta[3])/S) + HPL[{2}, -S^2]*((-2155*Pi^4)/(72*S) - (538*(1 + S^2))/S - (247*Pi^2*(1 + S^2))/(3*S) + (38*(1 + S^2)*HPL[{3}, -S^2])/S - (8*HPL[{4}, -S^2])/S + (784*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (1568*HPL[{3, 1}, -S^2])/S - (3136*HPL[{2, 1, 1}, -S^2])/S + (82*(1 + S^2)*Zeta[3])/S) + (76*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((437*Pi^6)/(1512*S) + (Pi^4*(-718 - 4427*S^2))/(360*S) + (Pi^2*(-69 - 343*S^2))/(3*S) - (20*(15 + 38*S^2))/S + (4*HPL[{3}, -S^2]^2)/S + ((43*Pi^2)/(6*S) + (33 + 17*S^2)/S)*HPL[{4}, -S^2] + (2*(-11 + 16*S^2)*HPL[{5}, -S^2])/S + (80*HPL[{6}, -S^2])/S - (76*HPL[{2, 1}, -S^2]^2)/S + ((8*Pi^2)/(3*S) + (2*(31 + 380*S^2))/S)*HPL[{3, 1}, -S^2] - (7*(1 + 13*S^2)*HPL[{3, 2}, -S^2])/S - (2*(22 + 145*S^2)*HPL[{4, 1}, -S^2])/S - (3*HPL[{4, 2}, -S^2])/S - (90*HPL[{5, 1}, -S^2])/S + ((-8*Pi^2)/S - (4*(34 + 381*S^2))/S)*HPL[{2, 1, 1}, -S^2] + (8*(-172 + 19*S^2)*HPL[{2, 2, 1}, -S^2])/S - (4*(-1051 + 63*S^2)*HPL[{3, 1, 1}, -S^2])/S - (120*HPL[{3, 2, 1}, -S^2])/S - (276*HPL[{4, 1, 1}, -S^2])/S + (32*(91 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (3520*HPL[{3, 1, 1, 1}, -S^2])/S - (272*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((16*(1 + 5*S^2))/S + (Pi^2*(15 + 52*S^2))/(3*S))*Zeta[3] + HPL[{2, 1}, -S^2]*((Pi^2*(437 + 17*S^2))/(3*S) + (2*(389 + 29*S^2))/S - (336*Zeta[3])/S) + HPL[{3}, -S^2]*((4*(1 + 14*S^2))/S + (Pi^2*(25 + 71*S^2))/(6*S) - (128*HPL[{2, 1}, -S^2])/S - (8*Zeta[3])/S) + (2*(20 + 27*S^2)*Zeta[5])/S) - 60*S*Zeta[7] + HPL[{1}, -S^2]*((-1960*(1 + S^2))/S - (620*Pi^2*(1 + S^2))/(3*S) - (2287*Pi^4*(1 + S^2))/(120*S) - (4763*Pi^6*(1 + S^2))/(3240*S) - (59*(1 + S^2)*HPL[{2}, -S^2]^3)/S + (3*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-46*Pi^2)/(3*S) - (122*(1 + S^2))/S)*HPL[{5}, -S^2] - (64*(1 + S^2)*HPL[{6}, -S^2])/S - (134*HPL[{7}, -S^2])/S + (784*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-30*Pi^2)/S - (68*(1 + S^2))/S)*HPL[{3, 2}, -S^2] + ((-190*Pi^2)/(3*S) - (94*(1 + S^2))/S)*HPL[{4, 1}, -S^2] + (3*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (26*HPL[{4, 3}, -S^2])/S + (88*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (84*HPL[{5, 2}, -S^2])/S - (14*HPL[{6, 1}, -S^2])/S + ((-2204*Pi^2)/(3*S) - (1608*(1 + S^2))/S)*HPL[{2, 2, 1}, -S^2] + ((-6568*Pi^2)/(3*S) - (4840*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] - (1416*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (240*HPL[{3, 2, 2}, -S^2])/S + (752*HPL[{3, 3, 1}, -S^2])/S - (4364*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (752*HPL[{4, 1, 2}, -S^2])/S + (2288*HPL[{4, 2, 1}, -S^2])/S + (4424*HPL[{5, 1, 1}, -S^2])/S + ((1440*Pi^2)/S + (3184*(1 + S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (5664*HPL[{2, 2, 2, 1}, -S^2])/S + (3024*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (17600*HPL[{3, 1, 1, 2}, -S^2])/S - (17600*HPL[{3, 1, 2, 1}, -S^2])/S - (34592*HPL[{3, 2, 1, 1}, -S^2])/S - (103408*HPL[{4, 1, 1, 1}, -S^2])/S - (6000*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (12544*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (37632*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (63264*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (24000*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((229*Pi^4)/(60*S) + (148*(1 + S^2))/S + (77*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (16*(1 + S^2)*Zeta[3]^2)/S + HPL[{3, 1}, -S^2]*((926*(1 + S^2))/S + (154*Pi^2*(1 + S^2))/S - (344*Zeta[3])/S) + HPL[{4}, -S^2]*((-94*(1 + S^2))/S - (17*Pi^2*(1 + S^2))/(2*S) + (16*HPL[{2, 1}, -S^2])/S + (8*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-431*(1 + S^2))/(2*S) - (119*Pi^2*(1 + S^2))/(3*S) + (30*HPL[{3}, -S^2])/S + (708*HPL[{2, 1}, -S^2])/S + (82*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-1796*(1 + S^2))/S - (914*Pi^2*(1 + S^2))/(3*S) + (656*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((2155*Pi^4)/(36*S) + (1076*(1 + S^2))/S + (494*Pi^2*(1 + S^2))/(3*S) - (3136*HPL[{3, 1}, -S^2])/S - (6272*HPL[{2, 1, 1}, -S^2])/S - (164*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-5*Pi^4)/(6*S) - (116*(1 + S^2))/S - (3*Pi^2*(1 + S^2))/S + (10*HPL[{4}, -S^2])/S - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (136*HPL[{3, 1}, -S^2])/S + (304*HPL[{2, 1, 1}, -S^2])/S + (4*(1 + S^2)*Zeta[3])/S) + ((27*Pi^2)/S + (138*(1 + S^2))/S)*Zeta[5] + HPL[{2}, -S^2]*((-685*(1 + S^2))/S - (292*Pi^2*(1 + S^2))/(3*S) - (971*Pi^4*(1 + S^2))/(90*S) + ((15*Pi^2)/S + (34*(1 + S^2))/S)*HPL[{3}, -S^2] - (7*(1 + S^2)*HPL[{4}, -S^2])/S - (4*HPL[{5}, -S^2])/S + ((1102*Pi^2)/(3*S) + (804*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (784*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (120*HPL[{3, 2}, -S^2])/S - (376*HPL[{4, 1}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (2832*HPL[{2, 2, 1}, -S^2])/S + (8800*HPL[{3, 1, 1}, -S^2])/S + (6272*HPL[{2, 1, 1, 1}, -S^2])/S + ((91*Pi^2)/(3*S) + (84*(1 + S^2))/S)*Zeta[3] + (106*Zeta[5])/S) + (150*Zeta[7])/S));
E5wuvT2F0=3920 + (Pi^6*(-19825 - 1851*S^2))/11340 + (Pi^4*(-118 - 349*S^2))/90 + (Pi^8*(46931 - 36853*S^2))/(85050*(1 + S^2)) - (2*Pi^2*(-275 + 71*S^2))/3 - (S^2*HPL[{0}, S^2]^8)/(96*(1 + S^2)) - (8*(1 + S^2)*HPL[{1}, -S^2]^7)/(21*S^2) - (8*(-1 + S^2)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)) + HPL[{0}, S^2]^7*(5/24 + ((4 + S^2)*HPL[{1}, -S^2])/(24*(1 + S^2))) + ((Pi^2*(43 - 53*S^2))/(9*(1 + S^2)) - (8*(-1 + S^2)*(1 + S^2))/(3*S^2))*HPL[{2}, -S^2]^3 - (16*(-1 + S^2)*HPL[{2}, -S^2]^4)/(1 + S^2) + HPL[{1}, -S^2]^6*((-4*(1 + S^2))/(3*S^2) - (2*Pi^2*(-50 + 37*S^2))/(9*(1 + S^2)) + (52*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^6*((Pi^2*(29 - 17*S^2))/(288*(1 + S^2)) + (-13 + 5*S^2)/24 + ((-1 - S^2)*HPL[{1}, -S^2])/(24*S^2) + ((10 + S^2)*HPL[{1}, -S^2]^2)/(12*(1 + S^2)) + ((29 + 16*S^2)*HPL[{2}, -S^2])/(48*(1 + S^2))) + ((Pi^2*(-1 - 38*S^2))/(3*(1 + S^2)) + (2*(1 - 20*S^2 + 3*S^4))/S^2)*HPL[{3}, -S^2]^2 + (6*(8 + 11*S^2)*HPL[{4}, -S^2]^2)/(1 + S^2) + ((Pi^2*(173 + 240*S^2))/(3*(1 + S^2)) - (4*(170 + 180*S^2 + 3*S^4))/S^2)*HPL[{6}, -S^2] - (4*(350 + 23*S^2)*HPL[{7}, -S^2])/S^2 - (108*HPL[{8}, -S^2])/(1 + S^2) + ((Pi^2*(-595 + 619*S^2))/(3*(1 + S^2)) + (8*(-1 + 5*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2]^2 - (4*(-267 + 199*S^2)*HPL[{3, 1}, -S^2]^2)/(1 + S^2) + ((Pi^2*(-29 - 143*S^2))/(3*(1 + S^2)) + (4*(5 + 13*S^2 + 4*S^4))/S^2)*HPL[{4, 2}, -S^2] + (4*(3 + 23*S^2)*HPL[{4, 3}, -S^2])/S^2 + ((-4*Pi^2*(47 + 220*S^2))/(3*(1 + S^2)) + (4*(68 + 71*S^2 + 35*S^4))/S^2)*HPL[{5, 1}, -S^2] + (4*(13 + 71*S^2)*HPL[{5, 2}, -S^2])/S^2 + (4*(17 + 23*S^2)*HPL[{5, 3}, -S^2])/(1 + S^2) + (4*(156 + 181*S^2)*HPL[{6, 1}, -S^2])/S^2 + (4*(31 + 46*S^2)*HPL[{6, 2}, -S^2])/(1 + S^2) - (4*(208 + 235*S^2)*HPL[{7, 1}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2) + HPL[{1}, -S^2]^4*((Pi^4*(8587 - 4759*S^2))/(540*(1 + S^2)) - (Pi^2*(1 + S^2)*(30 + 11*S^2))/(9*S^2) + (2*(1 + S^2)*(-23 + 36*S^2))/(3*S^2) + (-8*(1 + S^2) + (2*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)))*HPL[{2}, -S^2] - (392*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + (20*(1 + S^2)*HPL[{3}, -S^2])/(3*S^2) + (8*(-28 + 55*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - (8*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) + 520*HPL[{2, 1, 1}, -S^2]) + ((86*Pi^2)/3 - (4*(8 + 10*S^2 + S^4))/S^2)*HPL[{3, 1, 2}, -S^2] + ((-2*Pi^2*(-215 + 169*S^2))/(3*(1 + S^2)) - (4*(-8 + 10*S^2 + 17*S^4))/S^2)*HPL[{3, 2, 1}, -S^2] - (20*HPL[{3, 2, 2}, -S^2])/S^2 + (16*(-1 + 5*S^2)*HPL[{3, 3, 1}, -S^2])/S^2 - (4*(-15 + 118*S^2)*HPL[{3, 3, 2}, -S^2])/(1 + S^2) + ((-14*Pi^2*(-83 + 33*S^2))/(3*(1 + S^2)) - (8*(-1 + 19*S^2 + 31*S^4))/S^2)*HPL[{4, 1, 1}, -S^2] + (4*(-5 + 21*S^2)*HPL[{4, 1, 2}, -S^2])/S^2 + (4*(-44 + 183*S^2)*HPL[{4, 1, 3}, -S^2])/(1 + S^2) + (4*(-5 + 81*S^2)*HPL[{4, 2, 1}, -S^2])/S^2 - (4*(11 + 105*S^2)*HPL[{4, 2, 2}, -S^2])/(1 + S^2) + (4*(-104 + 623*S^2)*HPL[{4, 3, 1}, -S^2])/(1 + S^2) + (64*(-5 + 11*S^2)*HPL[{5, 1, 1}, -S^2])/S^2 + (4*(-57 + 365*S^2)*HPL[{5, 1, 2}, -S^2])/(1 + S^2) + (4*(-357 + 2645*S^2)*HPL[{5, 2, 1}, -S^2])/(1 + S^2) + (4*(-615 + 7214*S^2)*HPL[{6, 1, 1}, -S^2])/(1 + S^2) + (160*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((4*Pi^2*(-159 + 61*S^2))/(3*(1 + S^2)) + (16*(-10 + 2*S^2 + 13*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (16*(-32 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (16*(-32 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (156*(-1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2) + (16*(-62 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (156*(-1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2) - (4*(-55 + 39*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2) + (192*HPL[{3, 3, 1, 1}, -S^2])/(1 + S^2) + (48*(-57 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (4*(43 + 277*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2) - (4*(-5 + 277*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2) - (4*(-101 + 277*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2) - (32*(-8 + 197*S^2)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2) + ((-384*(-1 + S^2)*(1 + S^2))/S^2 - (64*Pi^2*(-31 + 18*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] + (384*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (1152*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + 64*HPL[{2, 2, 1, 2, 1}, -S^2] + 192*HPL[{2, 2, 2, 1, 1}, -S^2] + (1728*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + 256*HPL[{3, 1, 1, 1, 2}, -S^2] - 128*HPL[{3, 1, 2, 1, 1}, -S^2] - 960*HPL[{3, 2, 1, 1, 1}, -S^2] + (32*(-135 + 31*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2) + (960*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 - (64*(-19 + 64*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) + 2880*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (8/3 - (2*Pi^2*(-44 + 43*S^2))/(9*(1 + S^2)) - (2*(-16 + 15*S^2)*HPL[{0}, S^2]^2)/(3*(1 + S^2)) - (8*(1 + S^2)*HPL[{1}, -S^2])/(3*S^2) - (224*(-1 + S^2)*HPL[{0}, S^2]*HPL[{1}, -S^2])/(3*(1 + S^2)) - (224*(-1 + S^2)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)) + 4*HPL[{2}, -S^2])*Log[T]^6 + ((8*(-3 + 5*S^2)*HPL[{0}, S^2])/(3*(1 + S^2)) + (64*(-1 + S^2)*HPL[{1}, -S^2])/(3*(1 + S^2)))*Log[T]^7 - (8*(-1 + S^2)*Log[T]^8)/(3*(1 + S^2)) + ((29*Pi^2)/(3*(1 + S^2)) + 4*(14 + 11*S^2))*Zeta[3]^2 + HPL[{0}, S^2]^5*((55*Pi^2)/36 + (57 - 50*S^2)/30 + ((-1 - S^2)*HPL[{1}, -S^2]^2)/(4*S^2) + ((255 - 16*S^2)*HPL[{1}, -S^2]^3)/(90*(1 + S^2)) + ((3 - 5*S^2)*HPL[{2}, -S^2])/(12*S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(3 + 5*S^2))/(12*S^2) + (Pi^2*(675 + 89*S^2))/(360*(1 + S^2)) - (7*(-10 + S^2)*HPL[{2}, -S^2])/(20*(1 + S^2))) - (S^2*HPL[{3}, -S^2])/(4*(1 + S^2)) + ((-45 + 32*S^2)*HPL[{2, 1}, -S^2])/(20*(1 + S^2)) + (29*Zeta[3])/4) + HPL[{2}, -S^2]^2*((2*(-5 + 34*S^2))/S^2 - (3*Pi^4*(-56 + 55*S^2))/(20*(1 + S^2)) + (Pi^2*(1 - 10*S^2 - 5*S^4))/(3*S^2) - (2*HPL[{3}, -S^2])/S^2 + (4*(-6 + 35*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (20*HPL[{2, 1}, -S^2])/S^2 - (2*(-43 + 39*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - 8*HPL[{2, 1, 1}, -S^2] + (2*Zeta[3])/S^2) + HPL[{5}, -S^2]*((2*Pi^2*(-40 + 11*S^2))/(3*S^2) - (8*(70 + 11*S^2 + 13*S^4))/S^2 + (4*(111 + 29*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (24*(2 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1}, -S^2]*((Pi^4*(-1717 + 671*S^2))/(90*(1 + S^2)) + (2*Pi^2*(-24 + 11*S^2 + 25*S^4))/(3*S^2) + (4*(23 + 33*S^2 + 55*S^4))/S^2 + (16*(-233 + 159*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (8*(-2 + 9*S^2)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(4144 - 1919*S^2))/(90*(1 + S^2)) - (8*Pi^2*(-13 + 5*S^2 + 12*S^4))/(3*S^2) - (4*(1 + 26*S^2 + 73*S^4))/S^2 - (16*(-1 + 10*S^2)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^4*(73 + 199*S^2))/(18*(1 + S^2)) - (2*Pi^2*(19 + 14*S^2 + 3*S^4))/(3*S^2) - (4*(160 + 61*S^2 + 11*S^4))/S^2 + (4*(1 + 7*S^2)*HPL[{2, 1}, -S^2])/S^2 - (4*(21 + 142*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (4*(35 + 261*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (4*(2 + 11*S^2)*Zeta[3])/S^2) + HPL[{1}, -S^2]^5*((-4*Pi^2*(1 + S^2))/(3*S^2) + (8*(1 + S^2)*(-3 + 2*S^2))/(5*S^2) + (8*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - 104*HPL[{2, 1}, -S^2] + (8*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + Log[T]^5*(-24 + (4*Pi^2)/3 + (2*(-271 + 94*S^2)*HPL[{0}, S^2]^3)/(45*(1 + S^2)) + (8*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 + (448*(-1 + S^2)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)) + HPL[{0}, S^2]^2*(4 + (4*(-22 + 9*S^2)*HPL[{1}, -S^2])/(1 + S^2)) + HPL[{1}, -S^2]*((8*(1 + S^2))/S^2 + (4*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) - 104*HPL[{2}, -S^2]) - (8*HPL[{2}, -S^2])/S^2 + HPL[{0}, S^2]*((2*Pi^2*(-586 + 619*S^2))/(45*(1 + S^2)) + (8*(1 + S^2)*HPL[{1}, -S^2])/S^2 + (224*(-1 + S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) + (20*(-3 + 7*S^2)*HPL[{2}, -S^2])/(1 + S^2)) - (8*(-13 + 82*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + 184*HPL[{2, 1}, -S^2] - (8*(-2 + 23*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 2}, -S^2]*((-2*Pi^2*(3 + 5*S^2))/(3*S^2) + (4*(-1 - 11*S^2 + 20*S^4))/S^2 - (4*(9 + 35*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 2, 1}, -S^2]*((-92*Pi^2)/(3*S^2) + (8*(-10 - 17*S^2 + 12*S^4))/S^2 + (24*(-63 + 55*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1, 1, 1}, -S^2]*((-8*Pi^2*(-31 + 10*S^2))/(3*S^2) + (16*(12 + 21*S^2 + 10*S^4))/S^2 - (32*(-79 + 117*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4, 1}, -S^2]*((-2*Pi^2*(-20 + 19*S^2))/(3*S^2) + (4*(37 + 25*S^2 + 56*S^4))/S^2 - (4*(41 + 147*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1, 1}, -S^2]*((4*Pi^2*(-83 + 10*S^2))/(3*S^2) + (8*(-46 - 78*S^2 + 11*S^4))/S^2 + (8*(-539 + 573*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^4*((Pi^4*(3385 - 633*S^2))/(4320*(1 + S^2)) + (-13 + 5*S^2)/4 + (Pi^2*(-107 + 34*S^2))/36 - (5*(1 + S^2)*HPL[{1}, -S^2]^3)/(6*S^2) + ((253 - 31*S^2)*HPL[{1}, -S^2]^4)/(36*(1 + S^2)) + ((Pi^2*(166 + 57*S^2))/(36*(1 + S^2)) + (6 + 5*S^2 - 6*S^4)/(6*S^2))*HPL[{2}, -S^2] + ((31 - 9*S^2)*HPL[{2}, -S^2]^2)/(8*(1 + S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(553 - S^2))/(72*(1 + S^2)) - ((1 + S^2)*(15 + 7*S^2))/(12*S^2) + ((228 - 13*S^2)*HPL[{2}, -S^2])/(12*(1 + S^2))) + ((-1 + 4*S^2)*HPL[{3}, -S^2])/(2*S^2) + ((4 + 5*S^2)*HPL[{4}, -S^2])/(2*(1 + S^2)) + ((15 - 7*S^2)*HPL[{2, 1}, -S^2])/(6*S^2) + ((-35 + 4*S^2)*HPL[{3, 1}, -S^2])/(2*(1 + S^2)) + ((229 - 12*S^2)*HPL[{2, 1, 1}, -S^2])/(6*(1 + S^2)) - (14*Zeta[3])/3 + HPL[{1}, -S^2]*((-5*Pi^2*(1 + S^2))/(12*S^2) + (-9 - 5*S^2 + 4*S^4)/(6*S^2) + ((4 + 5*S^2)*HPL[{3}, -S^2])/(2*(1 + S^2)) + ((-228 + 13*S^2)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)) + (5*Zeta[3])/2)) + Log[T]^4*(128 - (8*Pi^2*S^2)/3 + (Pi^4*(3646 - 3027*S^2))/(270*(1 + S^2)) + ((68 - 3*S^2)*HPL[{0}, S^2]^4)/(9*(1 + S^2)) - (40*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S^2) - (560*(-1 + S^2)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)) + HPL[{0}, S^2]^3*(2/3 - (2*(-268 + 97*S^2)*HPL[{1}, -S^2])/(9*(1 + S^2))) + ((-16*(-1 + S^2)*(1 + S^2))/S^2 - (8*Pi^2*(-31 + 18*S^2))/(9*(1 + S^2)))*HPL[{2}, -S^2] - (392*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + HPL[{1}, -S^2]^2*((-20*(1 + S^2))/S^2 - (10*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) + 260*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*((Pi^2*(512 - 237*S^2))/(18*(1 + S^2)) - 2*(5 + 4*S^2) - (10*(1 + S^2)*HPL[{1}, -S^2])/S^2 - (10*(-22 + 9*S^2)*HPL[{1}, -S^2]^2)/(1 + S^2) - (7*(-29 + 27*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) - (8*HPL[{3}, -S^2])/S^2 + (4*(15 + 181*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + (40*HPL[{2, 1}, -S^2])/S^2 - (8*(-19 + 64*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) + 120*HPL[{2, 1, 1}, -S^2] - 40*Zeta[3] + HPL[{0}, S^2]*((2*Pi^2)/3 + 4*(-1 + 4*S^2) - (20*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 - (1120*(-1 + S^2)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)) + (20*HPL[{2}, -S^2])/S^2 + HPL[{1}, -S^2]*((-20*(1 + S^2))/S^2 - (2*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) - (500*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) + (4*(19 + 36*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (100*(-7 + 3*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (332*S^2*Zeta[3])/(3*(1 + S^2))) + HPL[{1}, -S^2]*((-20*Pi^2*(1 + S^2))/(3*S^2) + (8*(1 + S^2)*(-3 + 2*S^2))/S^2 + (40*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - 520*HPL[{2, 1}, -S^2] + (40*(-6 + 19*S^2)*Zeta[3])/(1 + S^2))) + ((-106*Pi^2)/3 - 4*(133 + 2*S^2))*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^6*(37673 - 14612*S^2))/(4536*(1 + S^2)) + (Pi^2*(1 + S^2)*(-41 + 4*S^2))/(3*S^2) + (20*(1 + S^2)*(-15 + 17*S^2))/S^2 - (Pi^4*(1 + S^2)*(416 + 279*S^2))/(180*S^2) + ((Pi^2*(345 - 262*S^2))/(3*(1 + S^2)) - (10*(1 + S^2))/S^2)*HPL[{2}, -S^2]^2 + (166*HPL[{2}, -S^2]^3)/3 - (74*(-1 + S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((-6*(1 + S^2)*(5 + 3*S^2))/S^2 + (Pi^2*(-89 + 251*S^2))/(3*(1 + S^2)))*HPL[{4}, -S^2] - (20*(1 + S^2)*HPL[{5}, -S^2])/S^2 + (2*(119 + 208*S^2)*HPL[{6}, -S^2])/(1 + S^2) + (1568*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((8*(1 + S^2)*(1 + 7*S^2))/S^2 - (8*Pi^2*(104 + 49*S^2))/(3*(1 + S^2)))*HPL[{3, 1}, -S^2] - (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S^2 - (120*(1 + S^2)*HPL[{4, 1}, -S^2])/S^2 - (234*(-1 + S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) - (104*(-9 + 17*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + (-96*(1 + S^2) + (8*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((-23*Pi^2*(1 + S^2))/3 - (2*(1 + S^2)*(13 + 62*S^2))/S^2 + (Pi^4*(6575 + 512*S^2))/(180*(1 + S^2)) + (20*(1 + S^2)*HPL[{3}, -S^2])/S^2 + (226*(-1 + S^2)*HPL[{4}, -S^2])/(1 + S^2) + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (1568*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)) - (80*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (160*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + 1328*HPL[{3, 2, 1}, -S^2] + (16*(193 + 359*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) - (32*(56 + 139*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) + 6240*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*(1 + S^2))/(3*S^2) - (8*(1 + S^2)*(-1 + 16*S^2))/S^2)*Zeta[3] - (4*(-9 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1}, -S^2]*((8*(1 + S^2)*(-1 + 16*S^2))/S^2 - (448*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((20*Pi^2*(1 + S^2))/(3*S^2) - (4*(1 + S^2)*(3 + 23*S^2))/S^2 - (8*(-113 + 279*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (8*(-12 + 13*S^2)*Zeta[3])/(1 + S^2)) - (8*(1 + S^2)*Zeta[5])/S^2) + Zeta[3]*((-65*Pi^4)/18 + (2*Pi^2*(-57 + 2*S^2))/3 - 12*(67 + 16*S^2) - (4*(-29 + 2*S^2)*Zeta[5])/(1 + S^2)) + HPL[{2}, -S^2]*((Pi^6*(8768 - 673*S^2))/(3240*(1 + S^2)) + (Pi^2*(-11 - 6*S^2 - 73*S^4))/(3*S^2) + (Pi^4*(62 - 25*S^2 - 68*S^4))/(30*S^2) - (4*(250 - 82*S^2 + 71*S^4))/S^2 - (2*(-4 + 39*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((Pi^2*(27 + 139*S^2))/(3*(1 + S^2)) - (4*(4 - 15*S^2 + 4*S^4))/S^2)*HPL[{4}, -S^2] + (4*(-1 + 7*S^2)*HPL[{5}, -S^2])/S^2 + (12*(29 + 36*S^2)*HPL[{6}, -S^2])/(1 + S^2) + 8*HPL[{2, 1}, -S^2]^2 + ((2*Pi^2*(-338 + 267*S^2))/(3*(1 + S^2)) + (16*(1 + S^2 + S^4))/S^2)*HPL[{3, 1}, -S^2] + (8*HPL[{3, 2}, -S^2])/S^2 - (4*(-5 + 7*S^2)*HPL[{4, 1}, -S^2])/S^2 - (24*(-2 + 11*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) - (4*(39 + 355*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + ((-2*Pi^2*(-595 + 619*S^2))/(3*(1 + S^2)) - (16*(-1 + 5*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (80*HPL[{2, 2, 1}, -S^2])/S^2 - (16*(-15 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + (156*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(1 + S^2) - (1380*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) - (4*(-1187 + 891*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + (192*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (16*(-209 + 183*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - (6272*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + ((-2*Pi^2*(-2 + 9*S^2))/(3*S^2) - (4*(-2 + 11*S^2 + 8*S^4))/S^2)*Zeta[3] + (6*(8 + 9*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3}, -S^2]*((4*Pi^2)/3 - (12*(1 + 4*S^4))/S^2 - (4*(-235 + 231*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(8 + 21*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((46*Pi^2)/(3*S^2) - (4*(-10 - 17*S^2 + 12*S^4))/S^2 - (12*(-63 + 55*S^2)*Zeta[3])/(1 + S^2)) - (4*(-4 + 13*S^2)*Zeta[5])/S^2) + HPL[{3}, -S^2]*((Pi^4*(-41 + 79*S^2))/(45*S^2) - (2*Pi^2*(18 + 7*S^2 + 17*S^4))/(3*S^2) - (4*(184 + 101*S^2 + 60*S^4))/S^2 - (4*(1 + 10*S^2)*HPL[{4}, -S^2])/S^2 - (56*(3 + 4*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((-14*Pi^2*(-36 + 23*S^2))/(3*(1 + S^2)) + (16*(-3 - S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (8*(1 + 5*S^2)*HPL[{3, 1}, -S^2])/S^2 + (4*(-9 + 77*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (108*(1 + 2*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - 16*HPL[{2, 1, 1}, -S^2] + (8*(-235 + 231*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (16*(-351 + 311*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - (16*(-235 + 157*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((2*Pi^2*(19 + 45*S^2))/(3*(1 + S^2)) + (4*(2 + 11*S^2 + 5*S^4))/S^2)*Zeta[3] + (4*(49 + 65*S^2)*Zeta[5])/(1 + S^2)) + Log[T]^3*(-1480/3 + (131*Pi^4)/45 + (8*Pi^2*(-16 + 11*S^2))/9 + ((-375 - 104*S^2)*HPL[{0}, S^2]^5)/(90*(1 + S^2)) + (40*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S^2) + (448*(-1 + S^2)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)) + HPL[{0}, S^2]^4*(1 + ((-253 + 31*S^2)*HPL[{1}, -S^2])/(9*(1 + S^2))) + HPL[{1}, -S^2]^3*((80*(1 + S^2))/(3*S^2) + (40*Pi^2*(-50 + 37*S^2))/(9*(1 + S^2)) - (1040*HPL[{2}, -S^2])/3) + (8*(-1 + 5*S^2)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^3*((4*(-2 + S^2))/3 - (2*Pi^2*(323 + 5*S^2))/(27*(1 + S^2)) + (56*(1 + S^2)*HPL[{1}, -S^2])/(9*S^2) + (4*(-268 + 97*S^2)*HPL[{1}, -S^2]^2)/(9*(1 + S^2)) + (4*(-38 + 17*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) + ((8*(14 + 3*S^2))/3 - (28*Pi^2*(-8 + 63*S^2))/(9*(1 + S^2)))*HPL[{3}, -S^2] + (8*(-3 + S^2)*HPL[{4}, -S^2])/S^2 - (8*(19 + 127*S^2)*HPL[{5}, -S^2])/(3*(1 + S^2)) + ((-64*(1 + S^2))/S^2 + (112*Pi^2*(27 + 13*S^2))/(9*(1 + S^2)))*HPL[{2, 1}, -S^2] + (96*HPL[{3, 1}, -S^2])/S^2 + (16*(-11 + 381*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) + (32*(-50 + 621*S^2)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((4*Pi^2*(1 + S^2)*(30 + 11*S^2))/(9*S^2) - (8*(1 + S^2)*(-23 + 36*S^2))/(3*S^2) + (Pi^4*(-8587 + 4759*S^2))/(135*(1 + S^2)) + (32*(1 + S^2) - (8*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)))*HPL[{2}, -S^2] + (1568*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) - (80*(1 + S^2)*HPL[{3}, -S^2])/(3*S^2) - (32*(-28 + 55*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + (32*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) - 2080*HPL[{2, 1, 1}, -S^2]) - (160*HPL[{2, 1, 1}, -S^2])/S^2 + (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)) + (32*(-523 + 178*S^2)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)) + 3680*HPL[{2, 1, 1, 1}, -S^2] + (160 - (4*Pi^2*(-25 + 391*S^2))/(9*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((40*Pi^2*(1 + S^2))/(3*S^2) - (16*(1 + S^2)*(-3 + 2*S^2))/S^2 - (80*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + 1040*HPL[{2, 1}, -S^2] - (80*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^2*((16*Pi^2)/3 + (4*(13 + 22*S^2))/3 + (20*(1 + S^2)*HPL[{1}, -S^2]^2)/S^2 + (40*(-22 + 9*S^2)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)) + (8*(-8 + 5*S^2)*HPL[{2}, -S^2])/(3*S^2) + HPL[{1}, -S^2]*((4*(1 + S^2)*(15 + 11*S^2))/(3*S^2) + (2*Pi^2*(-583 + 166*S^2))/(9*(1 + S^2)) + (4*(-307 + 85*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) - (4*(9 + 31*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (4*(411 + 19*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) - (4*(5 + 46*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2}, -S^2]*((4*Pi^2*(-31 + 10*S^2))/(9*S^2) + (8*(-14 + 9*S^2 + 22*S^4))/(3*S^2) - (8*(9 + 401*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) - (16*(-33 + 163*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{0}, S^2]*((4*Pi^2*(-2 + S^2))/3 - 32*(-1 + 3*S^2) + (Pi^4*(-2672 + 1389*S^2))/(90*(1 + S^2)) + (80*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S^2) + (1120*(-1 + S^2)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)) + ((8*(-12 + S^2)*(1 + S^2))/(3*S^2) + (2*Pi^2*(-151 + 209*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] + (8*(-75 + 121*S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + HPL[{1}, -S^2]^2*((40*(1 + S^2))/S^2 + (4*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) + (1000*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) - (8*(-9 + 19*S^2)*HPL[{3}, -S^2])/(3*S^2) + (4*(-45 + S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) - (80*HPL[{2, 1}, -S^2])/S^2 - (16*(-37 + 88*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (400*(-3 + 7*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 16*Zeta[3] + HPL[{1}, -S^2]*((116*Pi^2*(1 + S^2))/(9*S^2) - (16*(1 + S^2)*(-3 + 2*S^2))/S^2 - (16*(-10 + 7*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (2000*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (16*(-40 + 43*S^2)*Zeta[3])/(3*(1 + S^2)))) - (32*(-11 + 84*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{0}, S^2]^3*((1999*Pi^4)/540 + (Pi^2*(124 - 103*S^2))/18 + (2*(-38 + 7*S^2))/3 - (14*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S^2) - (2*(-268 + 97*S^2)*HPL[{1}, -S^2]^5)/(45*(1 + S^2)) + ((1 + 6*S^2)*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^3*((Pi^2*(523 - 113*S^2))/(27*(1 + S^2)) - (2*(1 + S^2)*(13 + S^2))/(9*S^2) - (4*(-124 + 41*S^2)*HPL[{2}, -S^2])/(9*(1 + S^2))) + ((Pi^2*(11 - 10*S^2))/(18*(1 + S^2)) + (-6 + S^2 + 4*S^4)/(3*S^2))*HPL[{3}, -S^2] + ((15 - 4*S^2)*HPL[{4}, -S^2])/(3*S^2) + ((-5 - 28*S^2)*HPL[{5}, -S^2])/(3*(1 + S^2)) + ((Pi^2*(-403 + 158*S^2))/(18*(1 + S^2)) - (4*(-2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (4*(9 + S^2)*HPL[{3, 1}, -S^2])/(3*S^2) + ((-33 - 47*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) - (2*(47 + 51*S^2)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)) - (8*(-7 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + HPL[{1}, -S^2]*((-4*(1 + S^2)*(7 + 2*S^2))/(3*S^2) - (Pi^2*(1 + S^2)*(14 + 13*S^2))/(9*S^2) - (7*Pi^4*(-551 + 20*S^2))/(540*(1 + S^2)) + ((Pi^2*(458 - 103*S^2))/(18*(1 + S^2)) + ((1 + S^2)*(-4 + 3*S^2))/(3*S^2))*HPL[{2}, -S^2] + ((39 - 14*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S^2) - (2*(-6 + 11*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + (2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(-41 + 14*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (8*(-124 + 41*S^2)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2))) - (2*(-83 + 23*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (2*(-769 + 197*S^2)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)) + (8*(-134 + 31*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)) + ((-2*(-16 + 21*S^2))/3 + (Pi^2*(478 + 489*S^2))/(18*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(29 - 27*S^2))/(18*S^2) + (2*(-7 + S^2))/3 + ((16 + 23*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + ((-83 + 23*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + ((8 + 11*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-29*Pi^2*(1 + S^2))/(18*S^2) + (2*(-8 + S^2)*(1 + S^2))/(3*S^2) + ((-1 - S^2)*HPL[{2}, -S^2])/(3*S^2) + (4*HPL[{3}, -S^2])/(1 + S^2) + (4*(-124 + 41*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (2*(3 + 14*S^2)*Zeta[3])/(3*(1 + S^2))) + (4*(101 + 105*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((Pi^4*(426 - 269*S^2))/(90*S^2) + (2*Pi^2*(26 + 31*S^2 + 12*S^4))/(3*S^2) + (8*(19 + 61*S^2 + 24*S^4))/S^2 + (16*(-5 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (4*(-431 + 423*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (20*(-289 + 225*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - (192*HPL[{2, 1, 1}, -S^2])/S^2 - 32*HPL[{2, 2, 1}, -S^2] - (16*(-229 + 163*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + (6272*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((-16*(-1 + 5*S^2))/S^2 - (2*Pi^2*(-174 + 257*S^2))/(3*(1 + S^2)))*Zeta[3] - (4*(-66 + 295*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^3*((-208*Pi^4*(1 + S^2))/(135*S^2) - (4*Pi^2*(1 + S^2)*(17 + 4*S^2))/(9*S^2) + (8*(1 + S^2)*(-28 + 43*S^2))/(3*S^2) - (20*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-8*(1 + S^2)*(-4 + 7*S^2))/(3*S^2) + (4*Pi^2*(-137 + 360*S^2))/(9*(1 + S^2)))*HPL[{3}, -S^2] + (16*(-1 + 53*S^2)*HPL[{5}, -S^2])/(3*(1 + S^2)) + (32*(1 + S^2) - (8*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)))*HPL[{2, 1}, -S^2] - (16*(-113 + 279*S^2)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)) - (16*(-395 + 947*S^2)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)) - (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)) - (32*(-448 + 253*S^2)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)) - 2080*HPL[{2, 1, 1, 1}, -S^2] + ((-88*(1 + S^2))/3 + (8*Pi^2*(-49 + 159*S^2))/(9*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-8*(1 + S^2)*(-1 + 16*S^2))/(3*S^2) + (8*(-113 + 279*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (448*(-2 + 5*S^2)*Zeta[3])/(3*(1 + S^2))) + (8*(-51 + 329*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{0}, S^2]^2*((Pi^2*(-79 - 43*S^2))/12 + (Pi^6*(150597 - 44818*S^2))/(90720*(1 + S^2)) - 2*(-95 + 71*S^2) + (Pi^4*(-1788 + 287*S^2))/360 - (2*(1 + S^2)*HPL[{1}, -S^2]^5)/S^2 - (2*(-22 + 9*S^2)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)) + (-5 - 4*S^2 + (Pi^2*(389 - 281*S^2))/(24*(1 + S^2)))*HPL[{2}, -S^2]^2 - (4*(-11 + 13*S^2)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(583 - 166*S^2))/(18*(1 + S^2)) - ((1 + S^2)*(15 + 11*S^2))/(3*S^2) + ((307 - 85*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) - (5*HPL[{3}, -S^2]^2)/2 + ((Pi^2*(83 + 103*S^2))/(12*(1 + S^2)) + (-15 - 9*S^2 + S^4)/S^2)*HPL[{4}, -S^2] + (8*(-5 + 3*S^2)*HPL[{5}, -S^2])/S^2 + ((61 + 106*S^2)*HPL[{6}, -S^2])/(2*(1 + S^2)) + ((-203 + 227*S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((Pi^2*(-407 + 213*S^2))/(6*(1 + S^2)) + (2*(-14 + 9*S^2 + 12*S^4))/S^2)*HPL[{3, 1}, -S^2] - (2*(1 + 6*S^2)*HPL[{3, 2}, -S^2])/S^2 - (22*(-1 + 2*S^2)*HPL[{4, 1}, -S^2])/S^2 - (3*(5 + 3*S^2)*HPL[{4, 2}, -S^2])/(2*(1 + S^2)) - (4*(19 + 23*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + ((Pi^2*(144 - 67*S^2))/(1 + S^2) - (8*(-7 + 5*S^2 + 6*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (44*HPL[{2, 2, 1}, -S^2])/S^2 + (4*(-41 + 10*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 + 6*HPL[{3, 1, 2}, -S^2] - (2*(-179 + 205*S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) - (2*(-563 + 581*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) - (16*(-8 + 5*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (4*(-197 + 189*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - (56*(-29 + 27*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + ((-32*Pi^2)/3 + 6*(-3 + 4*S^2))*Zeta[3] - (9*S^2*Zeta[3]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((Pi^4*(7348 - 1101*S^2))/(360*(1 + S^2)) - (Pi^2*(1 + S^2)*(5 + 3*S^2))/S^2 - (2*(1 + S^2)*(9 + 16*S^2))/S^2 + ((Pi^2*(535 - 98*S^2))/(6*(1 + S^2)) - 11*(1 + S^2))*HPL[{2}, -S^2] + ((149 - 66*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + (10*(1 + S^2)*HPL[{3}, -S^2])/S^2 + ((23 + 31*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (4*(-152 + 41*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (4*(-307 + 85*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (2*(1 + S^2)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^4*(6928 + 197*S^2))/(720*(1 + S^2)) + (-21 + 14*S^2 - 73*S^4)/(2*S^2) + (Pi^2*(13 - 12*S^4))/(3*S^2) + 6*HPL[{3}, -S^2] + ((19 + 17*S^2)*HPL[{4}, -S^2])/(2*(1 + S^2)) + (22*HPL[{2, 1}, -S^2])/S^2 + (6*(-35 + 36*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (2*(-203 + 227*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (2*(1 + S^2)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^2*(-7 + 17*S^2))/(3*S^2) + (-20 + 13*S^2 - 9*S^4)/S^2 - (2*(-17 + 4*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (2*(5 + 6*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(31 - 17*S^2))/(3*S^2) + (4*(7 + 5*S^2 + S^4))/S^2 - (2*(-16 + 23*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((-10*Pi^2*(1 + S^2))/(3*S^2) - (8*(1 + S^2)*(4 + 5*S^2))/(3*S^2) + (4*(3 + 25*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (4*(-307 + 85*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (4*(-8 + 33*S^2)*Zeta[3])/(3*(1 + S^2))) - 48*Zeta[5] + HPL[{1}, -S^2]*((-52*Pi^4*(1 + S^2))/(45*S^2) - (Pi^2*(1 + S^2)*(17 + 6*S^2))/(3*S^2) - (2*(1 + S^2)*(28 + 15*S^2))/S^2 - (5*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + ((-2*(1 + S^2)*(-5 + 2*S^2))/S^2 + (5*Pi^2*(3 + 8*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] + (8*(4 + 7*S^2)*HPL[{5}, -S^2])/(1 + S^2) + (22*(1 + S^2) + (Pi^2*(-535 + 98*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (12*(-2 + 5*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (2*(-13 + 121*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - (8*(-149 + 66*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (8*(-450 + 173*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + (8*(-307 + 85*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((-4*(1 + S^2))/S^2 + (Pi^2*(7 + 48*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*(-24*(1 + S^2) + (6*(-2 + 5*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (4*(-149 + 66*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (6*(-3 + 10*S^2)*Zeta[3])/(1 + S^2)) + (2*(14 + 53*S^2)*Zeta[5])/(1 + S^2))) + Log[T]^2*(1440 + (Pi^4*(-362 - 289*S^2))/90 + (Pi^2*(191 - 73*S^2))/3 + (Pi^6*(162979 - 98446*S^2))/(22680*(1 + S^2)) + ((29 + 11*S^2)*HPL[{0}, S^2]^6)/(24*(1 + S^2)) - (8*(1 + S^2)*HPL[{1}, -S^2]^5)/S^2 - (224*(-1 + S^2)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)) + HPL[{0}, S^2]^5*(5/6 + ((255 - 16*S^2)*HPL[{1}, -S^2])/(30*(1 + S^2))) + ((Pi^2*(595 - 619*S^2))/(6*(1 + S^2)) - (4*(-1 + 5*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 - (4*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((-20*(1 + S^2))/S^2 - (10*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) + 260*HPL[{2}, -S^2]) + HPL[{0}, S^2]^4*((-19 - 7*S^2)/6 + (Pi^2*(707 + 153*S^2))/(72*(1 + S^2)) - (5*(1 + S^2)*HPL[{1}, -S^2])/(2*S^2) + ((253 - 31*S^2)*HPL[{1}, -S^2]^2)/(6*(1 + S^2)) + ((229 - 12*S^2)*HPL[{2}, -S^2])/(12*(1 + S^2))) - (2*(-3 + 71*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((5*Pi^2*(13 + 81*S^2))/(3*(1 + S^2)) - (4*(23 + 19*S^2 + 7*S^4))/S^2)*HPL[{4}, -S^2] - (8*(20 + S^2)*HPL[{5}, -S^2])/S^2 + (2*(285 + 374*S^2)*HPL[{6}, -S^2])/(1 + S^2) + (1568*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((2*Pi^2*(-159 + 61*S^2))/(3*(1 + S^2)) + (8*(-10 + 2*S^2 + 13*S^4))/S^2)*HPL[{3, 1}, -S^2] + (8*(-2 + S^2)*HPL[{3, 2}, -S^2])/S^2 + (24*(3 + S^2)*HPL[{4, 1}, -S^2])/S^2 - (2*(43 + 277*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) - (16*(28 + 197*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + ((-192*(-1 + S^2)*(1 + S^2))/S^2 - (32*Pi^2*(-31 + 18*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + HPL[{1}, -S^2]^2*((Pi^4*(8587 - 4759*S^2))/(90*(1 + S^2)) - (2*Pi^2*(1 + S^2)*(30 + 11*S^2))/(3*S^2) + (4*(1 + S^2)*(-23 + 36*S^2))/S^2 + (-48*(1 + S^2) + (4*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] - (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + (40*(1 + S^2)*HPL[{3}, -S^2])/S^2 + (16*(-28 + 55*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (16*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + 3120*HPL[{2, 1, 1}, -S^2]) - (192*HPL[{2, 2, 1}, -S^2])/S^2 - (672*HPL[{3, 1, 1}, -S^2])/S^2 + 320*HPL[{3, 1, 2}, -S^2] + 288*HPL[{3, 2, 1}, -S^2] + (16*(9 + 175*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + (480*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (32*(-19 + 64*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) + 1440*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-76*Pi^2)/3 - 16*(24 + 5*S^2))*Zeta[3] + (4*(29 + 9*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2}, -S^2]*((Pi^4*(4144 - 1919*S^2))/(180*(1 + S^2)) - (4*Pi^2*(-13 + 5*S^2 + 12*S^4))/(3*S^2) - (2*(1 + 26*S^2 + 73*S^4))/S^2 - 8*HPL[{3}, -S^2] + (2*(35 + 261*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (96*HPL[{2, 1}, -S^2])/S^2 + (8*(-233 + 159*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (8*(-1 + 10*S^2)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((-40*Pi^2*(1 + S^2))/(3*S^2) + (16*(1 + S^2)*(-3 + 2*S^2))/S^2 + (80*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - 1040*HPL[{2, 1}, -S^2] + (80*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((4*Pi^2*(-7 + 5*S^2))/(3*S^2) - (4*(16 + 27*S^2 + 25*S^4))/S^2 - (8*(-235 + 157*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (8*(14 + 39*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^3*((28*Pi^2)/9 - (2*(-10 + 3*S^2))/3 - (28*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S^2) - (4*(-268 + 97*S^2)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)) - (4*(-7 + S^2)*HPL[{2}, -S^2])/(3*S^2) + HPL[{1}, -S^2]*((Pi^2*(523 - 113*S^2))/(9*(1 + S^2)) - (2*(1 + S^2)*(13 + S^2))/(3*S^2) - (4*(-124 + 41*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) + (2*(11 + 5*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (4*(-134 + 31*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) + (2*(43 + 54*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-4*Pi^2*(-31 + 10*S^2))/(3*S^2) + (8*(12 + 21*S^2 + 10*S^4))/S^2 - (16*(-79 + 117*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^2*(-1 - 73*S^2 + (Pi^2*(-34 - 19*S^2))/3 + (Pi^4*(7677 - 772*S^2))/(360*(1 + S^2)) - (20*(1 + S^2)*HPL[{1}, -S^2]^3)/S^2 - (10*(-22 + 9*S^2)*HPL[{1}, -S^2]^4)/(1 + S^2) + ((Pi^2*(144 - 67*S^2))/(2*(1 + S^2)) - (4*(-7 + 5*S^2 + 6*S^4))/S^2)*HPL[{2}, -S^2] + ((203 - 227*S^2)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(583 - 166*S^2))/(3*(1 + S^2)) - (2*(1 + S^2)*(15 + 11*S^2))/S^2 - (2*(-307 + 85*S^2)*HPL[{2}, -S^2])/(1 + S^2)) + (4*(-4 + 5*S^2)*HPL[{3}, -S^2])/S^2 + ((35 + 43*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (8*(-8 + 5*S^2)*HPL[{2, 1}, -S^2])/S^2 + (2*(-197 + 189*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (28*(-29 + 27*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - 16*Zeta[3] + HPL[{1}, -S^2]*((-10*Pi^2*(1 + S^2))/S^2 - (8*(1 + S^2)*(4 + 5*S^2))/S^2 + (4*(3 + 25*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (4*(-307 + 85*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(-8 + 33*S^2)*Zeta[3])/(1 + S^2))) - 232*Zeta[5] + HPL[{0}, S^2]*((241*Pi^4)/90 + (2*Pi^2*(7 + 9*S^2))/3 + 4*(-61 + 86*S^2) - (20*(1 + S^2)*HPL[{1}, -S^2]^4)/S^2 - (224*(-1 + S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) + 20*HPL[{2}, -S^2]^2 + HPL[{1}, -S^2]^3*((-40*(1 + S^2))/S^2 - (4*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) - (1000*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) + ((2*Pi^2*(30 + 41*S^2))/(3*(1 + S^2)) + (4*(-6 + 16*S^2 + 9*S^4))/S^2)*HPL[{3}, -S^2] + (4*(13 + S^2)*HPL[{4}, -S^2])/S^2 + (92*HPL[{5}, -S^2])/(1 + S^2) + ((-8*(1 + S^2)*(-12 + 11*S^2))/S^2 + (2*Pi^2*(-793 + 287*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(-17 + S^2)*HPL[{3, 1}, -S^2])/S^2 - (8*(21 + 59*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (4*(121 + 303*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + (240*HPL[{2, 1, 1}, -S^2])/S^2 - (32*(-121 + 75*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (16*(-745 + 414*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + (1200*(-7 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (-8*(-6 + S^2) + (2*Pi^2*(43 + 137*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]*((Pi^4*(7801 - 4382*S^2))/(90*(1 + S^2)) - (2*Pi^2*(1 + S^2)*(28 + S^2))/(3*S^2) + (4*(1 + S^2)*(-23 + 36*S^2))/S^2 + (40*(1 + S^2) - (2*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] - (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) + (32*(1 + S^2)*HPL[{3}, -S^2])/S^2 - (4*(-17 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (48*(-62 + 63*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (6000*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (8*(1 + S^2)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-2*Pi^2*(-29 + 2*S^2))/(3*S^2) + (4*(12 + 21*S^2 + 10*S^4))/S^2 + (8*(11 + 30*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (16*(-121 + 75*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (8*(-3 + 38*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^2*((-58*Pi^2*(1 + S^2))/(3*S^2) + (24*(1 + S^2)*(-3 + 2*S^2))/S^2 + (8*(-10 + 7*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (3000*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (8*(-40 + 43*S^2)*Zeta[3])/(1 + S^2)) + (4*(37 + 102*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]*((-208*Pi^4*(1 + S^2))/(45*S^2) - (4*Pi^2*(1 + S^2)*(17 + 4*S^2))/(3*S^2) + (8*(1 + S^2)*(-28 + 43*S^2))/S^2 - (20*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + ((-8*(1 + S^2)*(-4 + 7*S^2))/S^2 + (4*Pi^2*(-137 + 360*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] + (16*(-1 + 53*S^2)*HPL[{5}, -S^2])/(1 + S^2) + (96*(1 + S^2) - (8*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (16*(-113 + 279*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (16*(-395 + 947*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (32*(-448 + 253*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - 6240*HPL[{2, 1, 1, 1}, -S^2] + (-88*(1 + S^2) + (8*Pi^2*(-49 + 159*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-8*(1 + S^2)*(-1 + 16*S^2))/S^2 + (8*(-113 + 279*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (448*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + (8*(-51 + 329*S^2)*Zeta[5])/(1 + S^2))) - 300*Zeta[7] + Log[T]*(-2940 + (6239*Pi^6)/3780 + (2*Pi^2*(-181 + 52*S^2))/3 + (Pi^4*(79 + 118*S^2))/18 + ((-8 - 5*S^2)*HPL[{0}, S^2]^7)/(24*(1 + S^2)) + (8*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S^2) + (64*(-1 + S^2)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)) + HPL[{0}, S^2]^6*(-1/12 + ((-10 - S^2)*HPL[{1}, -S^2])/(6*(1 + S^2))) + HPL[{1}, -S^2]^5*((8*(1 + S^2))/S^2 + (4*Pi^2*(-50 + 37*S^2))/(3*(1 + S^2)) - 104*HPL[{2}, -S^2]) - (20*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^5*(-1/2 + (Pi^2*(-1215 - 629*S^2))/(360*(1 + S^2)) + ((1 + S^2)*HPL[{1}, -S^2])/(2*S^2) + ((-255 + 16*S^2)*HPL[{1}, -S^2]^2)/(30*(1 + S^2)) + ((-95 - 18*S^2)*HPL[{2}, -S^2])/(20*(1 + S^2))) + 12*HPL[{3}, -S^2]^2 + ((-8*Pi^2*(3 + 13*S^2))/(1 + S^2) + (4*(20 + 17*S^2 + 5*S^4))/S^2)*HPL[{5}, -S^2] + (20*(-14 + S^2)*HPL[{6}, -S^2])/S^2 - (4*(332 + 347*S^2)*HPL[{7}, -S^2])/(1 + S^2) - (16*(-1 + 5*S^2)*HPL[{2, 1}, -S^2]^2)/S^2 + ((2*Pi^2*(-15 + 811*S^2))/(3*(1 + S^2)) - (4*(-4 - 6*S^2 + 7*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((2*Pi^2*(-159 + 2659*S^2))/(3*(1 + S^2)) - (8*(-2 + 11*S^2 + 14*S^4))/S^2)*HPL[{4, 1}, -S^2] - (4*(5 + 7*S^2)*HPL[{4, 2}, -S^2])/S^2 - (4*(16 + 63*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) - (16*(-9 + 7*S^2)*HPL[{5, 1}, -S^2])/S^2 - (12*(3 + 37*S^2)*HPL[{5, 2}, -S^2])/(1 + S^2) + (4*(223 + 272*S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) + HPL[{1}, -S^2]^3*((4*Pi^2*(1 + S^2)*(30 + 11*S^2))/(9*S^2) - (8*(1 + S^2)*(-23 + 36*S^2))/(3*S^2) + (Pi^4*(-8587 + 4759*S^2))/(135*(1 + S^2)) + (32*(1 + S^2) - (8*Pi^2*(251 + 55*S^2))/(9*(1 + S^2)))*HPL[{2}, -S^2] + (1568*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) - (80*(1 + S^2)*HPL[{3}, -S^2])/(3*S^2) - (32*(-28 + 55*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + (32*(56 + 139*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) - 2080*HPL[{2, 1, 1}, -S^2]) + ((4*Pi^2*(-785 + 429*S^2))/(3*(1 + S^2)) - (32*(-6 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((4*Pi^2*(-2243 + 405*S^2))/(3*(1 + S^2)) - (16*(-36 - 14*S^2 + 3*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (16*(2 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 + (16*(-8 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 - (4*(-143 + 1487*S^2)*HPL[{3, 2, 2}, -S^2])/(1 + S^2) - (16*(-85 + 1161*S^2)*HPL[{3, 3, 1}, -S^2])/(1 + S^2) + (48*(-13 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 - (4*(-301 + 4605*S^2)*HPL[{4, 1, 2}, -S^2])/(1 + S^2) - (4*(-1009 + 14193*S^2)*HPL[{4, 2, 1}, -S^2])/(1 + S^2) - (32*(-256 + 3659*S^2)*HPL[{5, 1, 1}, -S^2])/(1 + S^2) + ((-384*(1 + S^2))/S^2 + (224*Pi^2*(27 + 13*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + 5376*HPL[{2, 2, 2, 1}, -S^2] + (576*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (32*(515 + 123*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2) - (32*(515 + 123*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2) - (32*(1019 + 627*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2) - (704*(142 + 81*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2) - (960*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (12544*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2) - (37632*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2) - (320*(-209 + 278*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2) + 22080*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + HPL[{0}, S^2]^4*(-Pi^2/6 + (14 + 11*S^2)/3 + (5*(1 + S^2)*HPL[{1}, -S^2]^2)/(2*S^2) + ((-253 + 31*S^2)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)) + ((-15 + 7*S^2)*HPL[{2}, -S^2])/(6*S^2) + HPL[{1}, -S^2]*((Pi^2*(-553 + S^2))/(36*(1 + S^2)) + ((1 + S^2)*(15 + 7*S^2))/(6*S^2) + ((-228 + 13*S^2)*HPL[{2}, -S^2])/(6*(1 + S^2))) + ((-4 - 5*S^2)*HPL[{3}, -S^2])/(2*(1 + S^2)) + ((227 - 14*S^2)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)) - (29*Zeta[3])/2) + ((Pi^4*(-127 - 1140*S^2))/(30*(1 + S^2)) + (4*Pi^2*(37 + 3*S^2))/3 + 4*(203 + 51*S^2))*Zeta[3] - 88*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^4*(3002 + 981*S^2))/(30*(1 + S^2)) + (4*Pi^2*(-26 - 13*S^2 + S^4))/(3*S^2) - (4*(25 + 124*S^2 + 51*S^4))/S^2 + (16*(-159 + 233*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (6272*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (16*(-1 + 10*S^2)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^4*(257 - 3349*S^2))/(90*(1 + S^2)) + (2*Pi^2*(4 + 9*S^2 + 3*S^4))/(3*S^2) + (4*(49 + 73*S^2 + 57*S^4))/S^2 + (4*(15 + 58*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (16*(5 + 6*S^2)*HPL[{2, 1}, -S^2])/S^2 + (16*(3 + 199*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (16*(9 + 401*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (8*(1 + 11*S^2)*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*((20*Pi^2*(1 + S^2))/(3*S^2) - (8*(1 + S^2)*(-3 + 2*S^2))/S^2 - (40*(-28 + 67*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + 520*HPL[{2, 1}, -S^2] - (40*(-6 + 19*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*((2*Pi^2*(-20 + 7*S^2))/(3*S^2) + (4*(47 + 49*S^2 + 24*S^4))/S^2 - (4*(261 + 35*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(-3 + 25*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((8*Pi^2*(-31 + 10*S^2))/(3*S^2) + (16*(-14 + 9*S^2 + 22*S^4))/S^2 - (32*(-33 + 163*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1}, -S^2]*((-4*Pi^2*(-37 + 10*S^2))/(3*S^2) - (8*(-8 + 12*S^2 + 25*S^4))/S^2 + (8*(-75 + 329*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(-3 + 20*S^2))/(3*S^2) + (2*(2 - 13*S^2 + 4*S^4))/S^2 - (2*(-65 + 401*S^2)*HPL[{3}, -S^2])/(1 + S^2) + 672*HPL[{2, 1}, -S^2] - (2*(1 + 355*S^2)*Zeta[3])/(1 + S^2)) + HPL[{0}, S^2]^3*(-13 - 3*S^2 + (Pi^2*(-7 + S^2))/3 + (Pi^4*(-12283 - 4289*S^2))/(1080*(1 + S^2)) + (56*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S^2) + (2*(-268 + 97*S^2)*HPL[{1}, -S^2]^4)/(9*(1 + S^2)) + ((Pi^2*(-171 + 16*S^2))/(6*(1 + S^2)) + (2*(-8 + S^2 + 3*S^4))/(3*S^2))*HPL[{2}, -S^2] + ((-73 + 33*S^2)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)) + HPL[{1}, -S^2]^2*((2*(1 + S^2)*(13 + S^2))/(3*S^2) + (Pi^2*(-523 + 113*S^2))/(9*(1 + S^2)) + (4*(-124 + 41*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) - (2*(-3 + 4*S^2)*HPL[{3}, -S^2])/S^2 + (2*(-13 + 4*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + (4*(-15 + S^2)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(-221 + 109*S^2)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)) + (8*(-38 + 17*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (4*Zeta[3])/3 + HPL[{1}, -S^2]*((29*Pi^2*(1 + S^2))/(9*S^2) - (4*(-8 + S^2)*(1 + S^2))/(3*S^2) + (2*(1 + S^2)*HPL[{2}, -S^2])/(3*S^2) - (8*HPL[{3}, -S^2])/(1 + S^2) - (8*(-124 + 41*S^2)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)) - (4*(3 + 14*S^2)*Zeta[3])/(3*(1 + S^2)))) + (648 - (2*Pi^2*(-3 + 416*S^2))/(3*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]*((-2*Pi^2*(1 + S^2)*(-41 + 4*S^2))/(3*S^2) - (40*(1 + S^2)*(-15 + 17*S^2))/S^2 + (Pi^4*(1 + S^2)*(416 + 279*S^2))/(90*S^2) + (Pi^6*(-37673 + 14612*S^2))/(2268*(1 + S^2)) + ((20*(1 + S^2))/S^2 + (2*Pi^2*(-345 + 262*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2]^2 - (332*HPL[{2}, -S^2]^3)/3 + (148*(-1 + S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((12*(1 + S^2)*(5 + 3*S^2))/S^2 - (2*Pi^2*(-89 + 251*S^2))/(3*(1 + S^2)))*HPL[{4}, -S^2] + (40*(1 + S^2)*HPL[{5}, -S^2])/S^2 - (4*(119 + 208*S^2)*HPL[{6}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((-16*(1 + S^2)*(1 + 7*S^2))/S^2 + (16*Pi^2*(104 + 49*S^2))/(3*(1 + S^2)))*HPL[{3, 1}, -S^2] + (80*(1 + S^2)*HPL[{3, 2}, -S^2])/S^2 + (240*(1 + S^2)*HPL[{4, 1}, -S^2])/S^2 + (468*(-1 + S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) + (208*(-9 + 17*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + (192*(1 + S^2) - (16*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + HPL[{2}, -S^2]*((Pi^4*(-6575 - 512*S^2))/(90*(1 + S^2)) + (46*Pi^2*(1 + S^2))/3 + (4*(1 + S^2)*(13 + 62*S^2))/S^2 - (40*(1 + S^2)*HPL[{3}, -S^2])/S^2 - (452*(-1 + S^2)*HPL[{4}, -S^2])/(1 + S^2) - (80*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (3136*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (6272*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)) + (160*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (320*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - 2656*HPL[{3, 2, 1}, -S^2] - (32*(193 + 359*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + (64*(56 + 139*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - 12480*HPL[{2, 1, 1, 1, 1}, -S^2] + ((4*Pi^2*(1 + S^2))/(3*S^2) + (16*(1 + S^2)*(-1 + 16*S^2))/S^2)*Zeta[3] + (8*(-9 + 11*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1}, -S^2]*((-16*(1 + S^2)*(-1 + 16*S^2))/S^2 + (896*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((-40*Pi^2*(1 + S^2))/(3*S^2) + (8*(1 + S^2)*(3 + 23*S^2))/S^2 + (16*(-113 + 279*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (16*(-12 + 13*S^2)*Zeta[3])/(1 + S^2)) + (16*(1 + S^2)*Zeta[5])/S^2) + HPL[{0}, S^2]^2*((127*Pi^4)/90 + 8*(1 + 13*S^2) + (Pi^2*(41 + 44*S^2))/3 + (10*(1 + S^2)*HPL[{1}, -S^2]^4)/S^2 + (4*(-22 + 9*S^2)*HPL[{1}, -S^2]^5)/(1 + S^2) + ((-1 + 10*S^2)*HPL[{2}, -S^2]^2)/S^2 + HPL[{1}, -S^2]^3*((4*(1 + S^2)*(15 + 11*S^2))/(3*S^2) + (2*Pi^2*(-583 + 166*S^2))/(9*(1 + S^2)) + (4*(-307 + 85*S^2)*HPL[{2}, -S^2])/(3*(1 + S^2))) + ((Pi^2*(-21 - 46*S^2))/(3*(1 + S^2)) - (2*(-4 + 5*S^2))/S^2)*HPL[{3}, -S^2] + (2*(-11 + 4*S^2)*HPL[{4}, -S^2])/S^2 - (2*(17 + 29*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((Pi^2*(638 + 5*S^2))/(3*(1 + S^2)) + (4*(-14 - S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (4*(-19 + 10*S^2)*HPL[{3, 1}, -S^2])/S^2 + (14*(1 + 7*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (2*(41 + 175*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + (16*(-8 + 5*S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(-393 + 37*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (28*(-171 + 7*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + (8*(411 + 19*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((Pi^2*(-92 - 133*S^2))/(3*(1 + S^2)) + 4*(7 + 3*S^2))*Zeta[3] + HPL[{1}, -S^2]*((2*Pi^2*(1 + S^2)*(5 + 3*S^2))/S^2 + (4*(1 + S^2)*(9 + 16*S^2))/S^2 + (Pi^4*(-7348 + 1101*S^2))/(180*(1 + S^2)) + (22*(1 + S^2) + (Pi^2*(-535 + 98*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] + (2*(-149 + 66*S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) - (20*(1 + S^2)*HPL[{3}, -S^2])/S^2 - (2*(23 + 31*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (8*(-152 + 41*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (8*(-307 + 85*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (4*(1 + S^2)*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*((10*Pi^2*(1 + S^2))/S^2 + (8*(1 + S^2)*(4 + 5*S^2))/S^2 - (4*(3 + 25*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (4*(-307 + 85*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (4*(-8 + 33*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((Pi^2*(-31 + 17*S^2))/(3*S^2) + (4*(-7 + 7*S^2 + 11*S^4))/S^2 - (2*(5 + 26*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (2*(-393 + 37*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (2*(-2 + 37*S^2)*Zeta[3])/(1 + S^2)) - (2*(41 + 80*S^2)*Zeta[5])/(1 + S^2)) + HPL[{2}, -S^2]*((Pi^4*(-426 + 269*S^2))/(90*S^2) + (8*(21 + 29*S^2 + 26*S^4))/S^2 + (2*Pi^2*(-28 + 23*S^2 + 44*S^4))/(3*S^2) + ((-14*Pi^2*(2 + 61*S^2))/(3*(1 + S^2)) + (8*(1 + S^2 + 2*S^4))/S^2)*HPL[{3}, -S^2] - (12*(-1 + S^2)*HPL[{4}, -S^2])/S^2 - (4*(57 + 139*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((-2*Pi^2*(-785 + 429*S^2))/(3*(1 + S^2)) + (16*(-6 + S^4))/S^2)*HPL[{2, 1}, -S^2] - 96*HPL[{3, 1}, -S^2] + (28*(-13 + 109*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (4*(-129 + 2441*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + (32*(-1 + 5*S^2)*HPL[{2, 1, 1}, -S^2])/S^2 - 2688*HPL[{2, 2, 1}, -S^2] + (16*(495 + 103*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - (6272*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((-2*Pi^2*(-68 + 363*S^2))/(3*(1 + S^2)) + (8*(-2 + 11*S^2 + S^4))/S^2)*Zeta[3] - (4*(-64 + 297*S^2)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^2*((208*Pi^4*(1 + S^2))/(45*S^2) + (4*Pi^2*(1 + S^2)*(17 + 4*S^2))/(3*S^2) - (8*(1 + S^2)*(-28 + 43*S^2))/S^2 + (20*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + ((8*(1 + S^2)*(-4 + 7*S^2))/S^2 - (4*Pi^2*(-137 + 360*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] - (16*(-1 + 53*S^2)*HPL[{5}, -S^2])/(1 + S^2) + (-96*(1 + S^2) + (8*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (16*(-113 + 279*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (16*(-395 + 947*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (32*(-448 + 253*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + 6240*HPL[{2, 1, 1, 1}, -S^2] + (88*(1 + S^2) - (8*Pi^2*(-49 + 159*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((8*(1 + S^2)*(-1 + 16*S^2))/S^2 - (8*(-113 + 279*S^2)*HPL[{3}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (448*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) - (8*(-51 + 329*S^2)*Zeta[5])/(1 + S^2)) + HPL[{0}, S^2]*(Pi^2*(-5 - 27*S^2) + (Pi^6*(-249449 - 462*S^2))/(22680*(1 + S^2)) + (Pi^4*(-103 + 10*S^2))/30 - 20*(-39 + 34*S^2) + (8*(1 + S^2)*HPL[{1}, -S^2]^5)/S^2 + (224*(-1 + S^2)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)) + ((Pi^2*(-519 + 583*S^2))/(6*(1 + S^2)) + (2*(2 - 11*S^2 + S^4))/S^2)*HPL[{2}, -S^2]^2 + (4*(-46 + 131*S^2)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)) + HPL[{1}, -S^2]^4*((20*(1 + S^2))/S^2 + (2*Pi^2*(-688 + 517*S^2))/(9*(1 + S^2)) + (500*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) + (2*(15 + 11*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((Pi^2*(-71 + 9*S^2))/(3*(1 + S^2)) + (4*(9 + 5*S^2 + S^4))/S^2)*HPL[{4}, -S^2] - (8*(-15 + 13*S^2)*HPL[{5}, -S^2])/S^2 + (2*(-45 + 28*S^2)*HPL[{6}, -S^2])/(1 + S^2) - (16*(-75 + 121*S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((-2*Pi^2*(-443 + 637*S^2))/(3*(1 + S^2)) - (8*(-8 - 7*S^2 + 2*S^4))/S^2)*HPL[{3, 1}, -S^2] + (4*(3 + 41*S^2)*HPL[{3, 2}, -S^2])/S^2 + (8*(-11 + 61*S^2)*HPL[{4, 1}, -S^2])/S^2 + 34*HPL[{4, 2}, -S^2] + (8*(38 + 11*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + ((16*(-12 + S^2)*(1 + S^2))/S^2 + (4*Pi^2*(-151 + 209*S^2))/(1 + S^2))*HPL[{2, 1, 1}, -S^2] + (160*(1 + 2*S^2)*HPL[{2, 2, 1}, -S^2])/S^2 + (16*(39 + 41*S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - 16*HPL[{3, 1, 2}, -S^2] + (48*(-31 + 87*S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) + (8*(-597 + 1573*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) - (480*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (96*(-37 + 88*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) + (2400*(-3 + 7*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + ((-8*Pi^2)/3 + 24*(-5 + S^2))*Zeta[3] - (4*(19 + 2*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{1}, -S^2]^2*((2*Pi^2*(1 + S^2)*(28 + S^2))/(3*S^2) - (4*(1 + S^2)*(-23 + 36*S^2))/S^2 + (Pi^4*(-7801 + 4382*S^2))/(90*(1 + S^2)) + (-40*(1 + S^2) + (2*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)))*HPL[{2}, -S^2] + (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(1 + S^2) - (32*(1 + S^2)*HPL[{3}, -S^2])/S^2 + (4*(-17 + 29*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (48*(-62 + 63*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (6000*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (8*(1 + S^2)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^4*(-6226 + 4549*S^2))/(180*(1 + S^2)) + (4*Pi^2*(-10 - 5*S^2 + 2*S^4))/(3*S^2) - (2*(-11 + 100*S^2 + 63*S^4))/S^2 - (4*(1 + 21*S^2)*HPL[{3}, -S^2])/S^2 - (2*(47 + 39*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (80*(1 + 2*S^2)*HPL[{2, 1}, -S^2])/S^2 - (64*(-19 + 30*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (32*(-75 + 121*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (16*(1 + S^2)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-2*Pi^2*(-18 + 31*S^2))/(3*S^2) - (4*(-20 + 21*S^2 + 17*S^4))/S^2 - (16*(30 + 11*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (16*(1 + 2*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1}, -S^2]*((4*Pi^2*(-30 + S^2))/(3*S^2) + (8*(-14 + 9*S^2 + 22*S^4))/S^2 + (16*(-38 + 3*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^3*((116*Pi^2*(1 + S^2))/(9*S^2) - (16*(1 + S^2)*(-3 + 2*S^2))/S^2 - (16*(-10 + 7*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) - (2000*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (16*(-40 + 43*S^2)*Zeta[3])/(3*(1 + S^2))) - 88*Zeta[5] + HPL[{1}, -S^2]*((203*Pi^4*(1 + S^2))/(45*S^2) - (4*Pi^2*(1 + S^2)*(-17 + 7*S^2))/(3*S^2) - (8*(1 + S^2)*(-28 + 43*S^2))/S^2 + (20*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + ((-16*(1 + S^2)*(1 + 2*S^2))/S^2 - (4*Pi^2*(-4 + 7*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] + (4*(1 + S^2)*HPL[{4}, -S^2])/S^2 + (8*(-6 + 17*S^2)*HPL[{5}, -S^2])/(1 + S^2) + (80*(1 + S^2) - (4*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 + (304*(-1 + S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) + (8*(-97 + 85*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + (6272*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (32*(-578 + 581*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) - (12000*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((-16*(1 + S^2))/S^2 - (4*Pi^2*(-37 + 57*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S^2) - (8*(1 + S^2)*(-1 + 16*S^2))/S^2 - (152*(-1 + S^2)*HPL[{3}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) - (328*(-1 + S^2)*Zeta[3])/(1 + S^2)) - (8*(-27 + 38*S^2)*Zeta[5])/(1 + S^2))) - (12*(-45 + 116*S^2)*Zeta[7])/(1 + S^2)) + HPL[{0}, S^2]*((18983*Pi^6)/7560 + (Pi^4*(993 - 538*S^2))/180 + (Pi^2*(-137 + 100*S^2))/3 + 2*(-1185 + 506*S^2) - (4*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S^2) - (32*(-1 + S^2)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)) + (10*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^5*((-4*(1 + S^2))/S^2 - (2*Pi^2*(-688 + 517*S^2))/(45*(1 + S^2)) - (100*(-1 + S^2)*HPL[{2}, -S^2])/(1 + S^2)) - 8*HPL[{3}, -S^2]^2 + ((-2*Pi^2*(-9 + 14*S^2))/(3*(1 + S^2)) + 2*(-3 + 17*S^2))*HPL[{5}, -S^2] - (50*(-2 + S^2)*HPL[{6}, -S^2])/S^2 - (2*(-4 + 63*S^2)*HPL[{7}, -S^2])/(1 + S^2) - 40*HPL[{2, 1}, -S^2]^2 + ((-5*Pi^2*(5 + 11*S^2))/(1 + S^2) - (2*(2 + 66*S^2 + 11*S^4))/S^2)*HPL[{3, 2}, -S^2] + ((-5*Pi^2*(43 + 81*S^2))/(3*(1 + S^2)) - (4*(-2 + 81*S^2 + 16*S^4))/S^2)*HPL[{4, 1}, -S^2] + (2*(5 + 7*S^2)*HPL[{4, 2}, -S^2])/S^2 + (2*(36 + 23*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) + (16*(-5 + 3*S^2)*HPL[{5, 1}, -S^2])/S^2 + (14*(13 + 7*S^2)*HPL[{5, 2}, -S^2])/(1 + S^2) + (2*(97 + 90*S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) + ((-2*Pi^2*(-733 + 369*S^2))/(3*(1 + S^2)) + (8*(-8 - 21*S^2 + S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((-2*Pi^2*(-2259 + 1025*S^2))/(3*(1 + S^2)) + (8*(-30 - 47*S^2 + 12*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (4*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/S^2 + (4*(19 + S^2)*HPL[{3, 2, 1}, -S^2])/S^2 + (2*(31 + 151*S^2)*HPL[{3, 2, 2}, -S^2])/(1 + S^2) + (8*(35 + 129*S^2)*HPL[{3, 3, 1}, -S^2])/(1 + S^2) + (8*(43 + S^2)*HPL[{4, 1, 1}, -S^2])/S^2 + (2*(157 + 533*S^2)*HPL[{4, 1, 2}, -S^2])/(1 + S^2) + (26*(37 + 125*S^2)*HPL[{4, 2, 1}, -S^2])/(1 + S^2) + (56*(38 + 117*S^2)*HPL[{5, 1, 1}, -S^2])/(1 + S^2) + ((-16*(1 + S^2)*(-12 + 11*S^2))/S^2 + (4*Pi^2*(-793 + 287*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (32*(-131 + 46*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2) + (16*(-17 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (80*(-153 + 67*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2) - (80*(-153 + 67*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2) - (752*(-33 + 13*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2) - (8*(-9311 + 3615*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2) + (480*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (64*(-121 + 75*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2) + (192*(-121 + 75*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2) + (96*(-397 + 262*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2) + (2400*(-7 + 3*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2) + ((-44*Pi^2*(-1 + S^2))/3 - 2*(-25 + 37*S^2) + (Pi^4*(3383 + 4070*S^2))/(180*(1 + S^2)))*Zeta[3] + 44*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^4*(-7556 + 3219*S^2))/(180*(1 + S^2)) - (2*Pi^2*(-24 - S^2 + 17*S^4))/(3*S^2) - (2*(-35 + 2*S^2 + 85*S^4))/S^2 - (64*(-30 + 19*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (32*(-121 + 75*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (8*(1 + S^2)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((Pi^4*(7801 - 4382*S^2))/(270*(1 + S^2)) - (2*Pi^2*(1 + S^2)*(28 + S^2))/(9*S^2) + (4*(1 + S^2)*(-23 + 36*S^2))/(3*S^2) + ((40*(1 + S^2))/3 - (2*Pi^2*(-623 + 457*S^2))/(9*(1 + S^2)))*HPL[{2}, -S^2] - (784*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)) + (32*(1 + S^2)*HPL[{3}, -S^2])/(3*S^2) - (4*(-17 + 29*S^2)*HPL[{4}, -S^2])/(3*(1 + S^2)) + (16*(-62 + 63*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (2000*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (8*(1 + S^2)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^4*(21 + 11*S^2))/(12*(1 + S^2)) + (Pi^2*(-12 + 17*S^2 + 13*S^4))/(3*S^2) + (2*(-29 - S^2 + 55*S^4))/S^2 - (2*(23 + 18*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (4*(-9 + 11*S^2)*HPL[{2, 1}, -S^2])/S^2 - (8*(10 + 27*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (16*(11 + 30*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (4*(1 + 2*S^2)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(28 - 3*S^2))/(3*S^2) - (2*(3 + 29*S^2 + 24*S^4))/S^2 + (2*(45 + 53*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (2*(17 + 21*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-4*Pi^2*(-29 + 2*S^2))/(3*S^2) + (8*(12 + 21*S^2 + 10*S^4))/S^2 + (16*(-3 + 38*S^2)*Zeta[3])/(1 + S^2)) + HPL[{1}, -S^2]^4*((-29*Pi^2*(1 + S^2))/(9*S^2) + (4*(1 + S^2)*(-3 + 2*S^2))/S^2 + (4*(-10 + 7*S^2)*HPL[{3}, -S^2])/(3*(1 + S^2)) + (500*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(-40 + 43*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-2*Pi^2*(35 + S^2))/(3*S^2) - (4*(6 + 20*S^2 + 9*S^4))/S^2 - (4*(-3 + 83*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(1 + 16*S^2))/(6*S^2) + (-4 + 29*S^2 + 4*S^4)/S^2 + ((7 + 37*S^2)*HPL[{3}, -S^2])/(1 + S^2) + (4*(-131 + 46*S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + ((5 + 87*S^2)*Zeta[3])/(1 + S^2)) + (-20*(-2 + 3*S^2) + (3*Pi^2*(49 + 58*S^2))/(1 + S^2))*Zeta[5] + HPL[{1}, -S^2]*((Pi^6*(182305 - 66682*S^2))/(22680*(1 + S^2)) + (20*(1 + S^2)*(-15 + 17*S^2))/S^2 + (Pi^2*(1 + S^2)*(-51 + 28*S^2))/(3*S^2) - (Pi^4*(1 + S^2)*(396 + 161*S^2))/(180*S^2) + ((Pi^2*(313 - 238*S^2))/(3*(1 + S^2)) - (10*(1 + S^2))/S^2)*HPL[{2}, -S^2]^2 - (118*(-1 + S^2)*HPL[{2}, -S^2]^3)/(1 + S^2) + (2*(-1 + 3*S^2)*HPL[{3}, -S^2]^2)/(1 + S^2) + ((Pi^2*(29 - 51*S^2))/(3*(1 + S^2)) - (2*(1 + S^2)*(17 + 3*S^2))/S^2)*HPL[{4}, -S^2] - (12*(1 + S^2)*HPL[{5}, -S^2])/S^2 - (2*(-9 + 64*S^2)*HPL[{6}, -S^2])/(1 + S^2) + (1568*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(1 + S^2) + ((-8*(1 + S^2)*(-3 + 4*S^2))/S^2 + (4*Pi^2*(-103 + 77*S^2))/(1 + S^2))*HPL[{3, 1}, -S^2] - (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S^2 - (116*(1 + S^2)*HPL[{4, 1}, -S^2])/S^2 + 6*HPL[{4, 2}, -S^2] + (8*(-5 + 22*S^2)*HPL[{5, 1}, -S^2])/(1 + S^2) + (80*(1 + S^2) - (4*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (80*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S^2 - (176*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S^2 - (2832*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(1 + S^2) - (8*(-1079 + 1091*S^2)*HPL[{4, 1, 1}, -S^2])/(1 + S^2) + (96*(-62 + 63*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2) - (12000*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2) + (-8*(1 + S^2) + (2*Pi^2*(1 + S^2))/(3*S^2))*Zeta[3] - (4*(-9 + 8*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1}, -S^2]*((2*Pi^2*(1 + S^2))/(3*S^2) - (8*(1 + S^2)*(-1 + 16*S^2))/S^2 - (328*(-1 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{3}, -S^2]*((16*Pi^2*(1 + S^2))/(3*S^2) + (4*(1 + S^2)*(-5 + 11*S^2))/S^2 - (152*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (8*(-1 + S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]*((Pi^4*(6891 - 3884*S^2))/(180*(1 + S^2)) + (Pi^2*(1 + S^2)*(-4 + 13*S^2))/(3*S^2) + (2*(1 + S^2)*(-23 + 74*S^2))/S^2 + (20*(1 + S^2)*HPL[{3}, -S^2])/S^2 - (2*(-1 + 7*S^2)*HPL[{4}, -S^2])/(1 + S^2) + (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 + (1568*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) - (4*(1 + S^2)*Zeta[3])/S^2) + (8*(1 + S^2)*Zeta[5])/S^2) + HPL[{1}, -S^2]^2*((-203*Pi^4*(1 + S^2))/(90*S^2) + (2*Pi^2*(1 + S^2)*(-17 + 7*S^2))/(3*S^2) + (4*(1 + S^2)*(-28 + 43*S^2))/S^2 - (10*(1 + S^2)*HPL[{2}, -S^2]^2)/S^2 + ((8*(1 + S^2)*(1 + 2*S^2))/S^2 + (2*Pi^2*(-4 + 7*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] - (2*(1 + S^2)*HPL[{4}, -S^2])/S^2 - (4*(-6 + 17*S^2)*HPL[{5}, -S^2])/(1 + S^2) + (-40*(1 + S^2) + (2*Pi^2*(-623 + 457*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - (152*(-1 + S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (4*(-97 + 85*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - (3136*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) - (16*(-578 + 581*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + (6000*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((8*(1 + S^2))/S^2 + (2*Pi^2*(-37 + 57*S^2))/(3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-1 - S^2))/(3*S^2) + (4*(1 + S^2)*(-1 + 16*S^2))/S^2 + (76*(-1 + S^2)*HPL[{3}, -S^2])/(1 + S^2) + (1568*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (164*(-1 + S^2)*Zeta[3])/(1 + S^2)) + (4*(-27 + 38*S^2)*Zeta[5])/(1 + S^2)) + HPL[{2}, -S^2]*((Pi^4*(406 - 171*S^2))/(180*S^2) + (Pi^2*(12 + 7*S^2 + 12*S^4))/(3*S^2) + (4*(-21 + 29*S^2 + 32*S^4))/S^2 + ((Pi^2*(38 + 83*S^2))/(3*(1 + S^2)) + (4*(1 + 16*S^2 + 3*S^4))/S^2)*HPL[{3}, -S^2] + (2*(-1 + 11*S^2)*HPL[{4}, -S^2])/S^2 + (2*(39 + 37*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((Pi^2*(-733 + 369*S^2))/(3*(1 + S^2)) - (4*(-8 - 21*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] - (4*(1 + 11*S^2)*HPL[{3, 1}, -S^2])/S^2 - (30*(1 + 5*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (2*(87 + 275*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) + 80*HPL[{2, 1, 1}, -S^2] - (16*(-131 + 46*S^2)*HPL[{2, 2, 1}, -S^2])/(1 + S^2) + (32*(-191 + 84*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + (32*(-121 + 75*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + ((Pi^2*(18 + 109*S^2))/(3*(1 + S^2)) - (4*(6 + 5*S^2 + S^4))/S^2)*Zeta[3] + (2*(34 + 87*S^2)*Zeta[5])/(1 + S^2)) + (6*(141 + 166*S^2)*Zeta[7])/(1 + S^2)) + HPL[{1}, -S^2]*((-182*Pi^6*(1 + S^2))/(405*S^2) + (56*Pi^2*(-2 + S^2)*(1 + S^2))/(3*S^2) - (Pi^4*(1 + S^2)*(23 + 15*S^2))/(9*S^2) + (4*(1 + S^2)*(-470 + 253*S^2))/S^2 + (4*(1 + S^2)*HPL[{3}, -S^2]^2)/S^2 + ((-4*(1 + S^2)*(31 + 13*S^2))/S^2 + (4*Pi^2*(7 + 67*S^2))/(3*(1 + S^2)))*HPL[{5}, -S^2] - (112*(1 + S^2)*HPL[{6}, -S^2])/S^2 + (12*(46 + 51*S^2)*HPL[{7}, -S^2])/(1 + S^2) + (40*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S^2 + ((8*(1 + S^2)*(-5 + 4*S^2))/S^2 - (28*Pi^2*(-17 + 42*S^2))/(3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((12*(1 + S^2)*(-5 + 11*S^2))/S^2 - (2*Pi^2*(-803 + 2015*S^2))/(3*(1 + S^2)))*HPL[{4, 1}, -S^2] + (4*(-18 + 29*S^2)*HPL[{4, 3}, -S^2])/(1 + S^2) + (56*(1 + S^2)*HPL[{5, 1}, -S^2])/S^2 + (24*(-7 + 10*S^2)*HPL[{5, 2}, -S^2])/(1 + S^2) - (4*(149 + 198*S^2)*HPL[{6, 1}, -S^2])/(1 + S^2) + HPL[{2, 1}, -S^2]*((Pi^4*(-6575 - 512*S^2))/(90*(1 + S^2)) + (46*Pi^2*(1 + S^2))/3 + (4*(1 + S^2)*(13 + 62*S^2))/S^2 - (3136*(-1 + S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) - (6272*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)) + ((-80*(1 + S^2))/S^2 - (8*Pi^2*(-345 + 262*S^2))/(3*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((-16*(1 + S^2)*(11 + 7*S^2))/S^2 - (16*Pi^2*(-449 + 213*S^2))/(3*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + (4*(-483 + 1147*S^2)*HPL[{3, 2, 2}, -S^2])/(1 + S^2) + (32*(-187 + 436*S^2)*HPL[{3, 3, 1}, -S^2])/(1 + S^2) + (4*(-1457 + 3449*S^2)*HPL[{4, 1, 2}, -S^2])/(1 + S^2) + (4*(-4613 + 10589*S^2)*HPL[{4, 2, 1}, -S^2])/(1 + S^2) + (16*(-2369 + 5461*S^2)*HPL[{5, 1, 1}, -S^2])/(1 + S^2) + (192*(1 + S^2) - (16*Pi^2*(251 + 55*S^2))/(3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - 2656*HPL[{2, 2, 2, 1}, -S^2] - (64*(-181 + 15*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2) - (64*(-181 + 15*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2) + (32*(611 + 219*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2) + (32*(1889 + 547*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2) + (12544*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2) + (37632*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2) + (320*(-224 + 263*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2) - 12480*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*(1 + S^2)*(2 + 11*S^2))/(3*S^2) - (4*(1 + S^2)*(-5 + 68*S^2))/S^2 + (Pi^4*(-545 + 2494*S^2))/(90*(1 + S^2)))*Zeta[3] + (8*(1 + S^2)*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((-6*Pi^2*(-1 + S^2)*(1 + S^2))/S^2 - (4*(1 + S^2)*(31 + 56*S^2))/S^2 + (Pi^4*(-391 + 1412*S^2))/(45*(1 + S^2)) - (4*(-15 + 28*S^2)*HPL[{4}, -S^2])/(1 + S^2) - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S^2 - (8*(-113 + 279*S^2)*HPL[{3, 1}, -S^2])/(1 + S^2) + (16*(-113 + 279*S^2)*HPL[{2, 1, 1}, -S^2])/(1 + S^2) + (8*(1 + S^2)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((-16*(1 + S^2)*(-1 + 16*S^2))/S^2 + (896*(-2 + 5*S^2)*Zeta[3])/(1 + S^2)) + HPL[{4}, -S^2]*((-4*(1 + S^2)*(33 + 4*S^2))/S^2 - (452*(-1 + S^2)*HPL[{2, 1}, -S^2])/(1 + S^2) + (4*(-5 + 23*S^2)*Zeta[3])/(1 + S^2)) + HPL[{2}, -S^2]^2*((-10*Pi^2*(1 + S^2))/(3*S^2) + (4*(1 + S^2)*(-3 + 2*S^2))/S^2 + (4*(-75 + 158*S^2)*HPL[{3}, -S^2])/(1 + S^2) - 332*HPL[{2, 1}, -S^2] + (4*(-47 + 130*S^2)*Zeta[3])/(1 + S^2)) + HPL[{3, 1}, -S^2]*((8*(1 + S^2)*(9 + 19*S^2))/S^2 - (16*(-59 + 143*S^2)*Zeta[3])/(1 + S^2)) + ((-4*(1 + S^2)*(4 + 17*S^2))/S^2 + (2*Pi^2*(-37 + 382*S^2))/(3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((-40*(1 + S^2)*(4 + 5*S^2))/S^2 - (2*Pi^2*(1 + S^2)*(-1 + 28*S^2))/(3*S^2) + ((-4*(1 + S^2)*(-5 + 4*S^2))/S^2 + (14*Pi^2*(-17 + 42*S^2))/(3*(1 + S^2)))*HPL[{3}, -S^2] - (8*(1 + S^2)*HPL[{4}, -S^2])/S^2 + (4*(-27 + 55*S^2)*HPL[{5}, -S^2])/(1 + S^2) + ((40*(1 + S^2))/S^2 + (4*Pi^2*(-345 + 262*S^2))/(3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (40*(1 + S^2)*HPL[{3, 1}, -S^2])/S^2 - (4*(-261 + 593*S^2)*HPL[{3, 2}, -S^2])/(1 + S^2) - (4*(-787 + 1783*S^2)*HPL[{4, 1}, -S^2])/(1 + S^2) - (80*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S^2 + 1328*HPL[{2, 2, 1}, -S^2] + (32*(-181 + 15*S^2)*HPL[{3, 1, 1}, -S^2])/(1 + S^2) + (6272*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2) + (-4*(1 + S^2) + (2*Pi^2*(-121 + 310*S^2))/(3*(1 + S^2)))*Zeta[3] + (4*(-65 + 296*S^2)*Zeta[5])/(1 + S^2)) + (12*(10 + 171*S^2)*Zeta[7])/(1 + S^2));
E5wuvT2F2=245/32 + (Pi^2*(-85 + 608*S^2))/96 + (Pi^4*(1459 + 3184*S^2))/2880 + (Pi^6*(120230 + 14727*S^2))/362880 + (Pi^8*(55856 + 597*S^2 + 597*S^4))/(113400*(1 + S^2)) + ((29*Pi^2)/(21*S^2) + (83 + 106*S^2 + 23*S^4)/(21*S^2))*HPL[{1}, -S^2]^7 + ((3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^8)/(3*S^2*(1 + S^2)) + (8*HPL[{1}, -S^2]^9)/(27*S^2) + HPL[{0}, S^2]^8*(1/(192*(1 + S^2)) + HPL[{1}, -S^2]/(192*S^2)) + HPL[{0}, S^2]^7*((-3 - S^2)/192 + ((-3 + 9*S^2 - S^4 - S^6)*HPL[{1}, -S^2])/(192*S^2*(1 + S^2)) + HPL[{1}, -S^2]^2/(32*S^2)) + ((105 + 297*S^2 + 14*S^4 + 14*S^6)*HPL[{2}, -S^2]^4)/(12*S^2*(1 + S^2)) + (2*HPL[{3}, -S^2]^3)/S^2 + ((59 + 41*S^2 - 11*S^4 - 11*S^6)*HPL[{4}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((-65*Pi^2)/(3*S^2) + (-135 - 289*S^2 - 215*S^4)/(2*S^2))*HPL[{7}, -S^2] + ((945 + 891*S^2 - 5*S^4 - 5*S^6)*HPL[{8}, -S^2])/(S^2*(1 + S^2)) - (980*HPL[{9}, -S^2])/S^2 + (784*HPL[{2, 1}, -S^2]^3)/(3*S^2) + HPL[{0}, S^2]^6*((7 - 40*S^2)/384 + (Pi^2*(92 - 5*S^2 - 5*S^4))/(1152*(1 + S^2)) + ((-3 + 33*S^2 - S^4 - S^6)*HPL[{1}, -S^2]^2)/(96*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3/(8*S^2) + ((26 - 5*S^2 - 5*S^4)*HPL[{2}, -S^2])/(192*(1 + S^2)) + HPL[{1}, -S^2]*((23*Pi^2)/(288*S^2) + (11 - 8*S^2 - 19*S^4)/(384*S^2) + (13*HPL[{2}, -S^2])/(96*S^2)) - HPL[{3}, -S^2]/(96*S^2) - (7*HPL[{2, 1}, -S^2])/(24*S^2)) + ((586 + 1518*S^2 + 53*S^4 + 53*S^6)*HPL[{3, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((21*Pi^2)/(2*S^2) + (-78 - 266*S^2 - 127*S^4)/(4*S^2))*HPL[{4, 3}, -S^2] + ((187*Pi^2)/(6*S^2) + (-264 - 608*S^2 - 261*S^4)/(4*S^2))*HPL[{5, 2}, -S^2] + ((-3 - 27*S^2 - 17*S^4 - 17*S^6)*HPL[{5, 3}, -S^2])/(2*S^2*(1 + S^2)) - (291*HPL[{5, 4}, -S^2])/S^2 + ((68*Pi^2)/S^2 + (-219 + 142*S^2 + 158*S^4)/(2*S^2))*HPL[{6, 1}, -S^2] + ((-77 - 137*S^2 - 33*S^4 - 33*S^6)*HPL[{6, 2}, -S^2])/(2*S^2*(1 + S^2)) - (1161*HPL[{6, 3}, -S^2])/S^2 + (3*(-91 - 73*S^2 + 25*S^4 + 25*S^6)*HPL[{7, 1}, -S^2])/(S^2*(1 + S^2)) - (2881*HPL[{7, 2}, -S^2])/S^2 - (5457*HPL[{8, 1}, -S^2])/S^2 + (8*(222 + 614*S^2 + 25*S^4 + 25*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-13*Pi^2)/(3*S^2) + (-99 - 6510*S^2 - 1826*S^4)/(4*S^2))*HPL[{3, 2, 2}, -S^2] + ((14*Pi^2)/S^2 - (4*(-4 + 1260*S^2 + 363*S^4))/S^2)*HPL[{3, 3, 1}, -S^2] + ((13 + 545*S^2 + 124*S^4 + 124*S^6)*HPL[{3, 3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((119*Pi^2)/(6*S^2) + (253 - 20074*S^2 - 5799*S^4)/(4*S^2))*HPL[{4, 1, 2}, -S^2] - (2*(8 + 235*S^2 + 45*S^4 + 45*S^6)*HPL[{4, 1, 3}, -S^2])/(S^2*(1 + S^2)) + ((347*Pi^2)/(6*S^2) + (457 - 61426*S^2 - 17859*S^4)/(4*S^2))*HPL[{4, 2, 1}, -S^2] + ((-41 + 335*S^2 + 109*S^4 + 109*S^6)*HPL[{4, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) - (7*HPL[{4, 2, 3}, -S^2])/S^2 - (2*(25 + 752*S^2 + 173*S^4 + 173*S^6)*HPL[{4, 3, 1}, -S^2])/(S^2*(1 + S^2)) + (26*HPL[{4, 3, 2}, -S^2])/S^2 - (146*HPL[{4, 4, 1}, -S^2])/S^2 + ((365*Pi^2)/(3*S^2) + (351 - 63136*S^2 - 18527*S^4)/(2*S^2))*HPL[{5, 1, 1}, -S^2] + ((-27 - 1715*S^2 - 390*S^4 - 390*S^6)*HPL[{5, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) - (212*HPL[{5, 1, 3}, -S^2])/S^2 + ((-327 - 12335*S^2 - 2910*S^4 - 2910*S^6)*HPL[{5, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) - (121*HPL[{5, 2, 2}, -S^2])/S^2 - (832*HPL[{5, 3, 1}, -S^2])/S^2 + ((-568 - 16226*S^2 - 3891*S^4 - 3891*S^6)*HPL[{6, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (622*HPL[{6, 1, 2}, -S^2])/S^2 - (2502*HPL[{6, 2, 1}, -S^2])/S^2 - (5660*HPL[{7, 1, 1}, -S^2])/S^2 + ((-1592*Pi^2)/(3*S^2) + (-546 + 1420*S^2 + 465*S^4)/S^2)*HPL[{2, 2, 2, 1}, -S^2] + ((4684*Pi^2)/(3*S^2) + (2959 - 1844*S^2 - 809*S^4)/(2*S^2))*HPL[{3, 1, 1, 2}, -S^2] + ((4684*Pi^2)/(3*S^2) + (2959 - 1844*S^2 - 809*S^4)/(2*S^2))*HPL[{3, 1, 2, 1}, -S^2] + ((126 + 438*S^2 + 47*S^4 + 47*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((9460*Pi^2)/(3*S^2) + (6235 - 10364*S^2 - 3599*S^4)/(2*S^2))*HPL[{3, 2, 1, 1}, -S^2] + ((126 + 438*S^2 + 47*S^4 + 47*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((3414 + 3790*S^2 - 481*S^4 - 481*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) - (80*HPL[{3, 2, 2, 2}, -S^2])/S^2 - (96*HPL[{3, 2, 3, 1}, -S^2])/S^2 - (12*(-411 - 419*S^2 + 66*S^4 + 66*S^6)*HPL[{3, 3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (88*HPL[{3, 3, 1, 2}, -S^2])/S^2 - (256*HPL[{3, 3, 2, 1}, -S^2])/S^2 + ((28592*Pi^2)/(3*S^2) + (9823 - 14728*S^2 - 5182*S^4)/S^2)*HPL[{4, 1, 1, 1}, -S^2] + ((-70 + 398*S^2 + 169*S^4 + 169*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (620*HPL[{4, 1, 1, 3}, -S^2])/S^2 + ((4862 + 5426*S^2 - 623*S^4 - 623*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (575*HPL[{4, 1, 2, 2}, -S^2])/S^2 + (860*HPL[{4, 1, 3, 1}, -S^2])/S^2 + ((14726 + 15482*S^2 - 2207*S^4 - 2207*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (431*HPL[{4, 2, 1, 2}, -S^2])/S^2 + (407*HPL[{4, 2, 2, 1}, -S^2])/S^2 + (1556*HPL[{4, 3, 1, 1}, -S^2])/S^2 - (2*(-15036 - 16676*S^2 + 1943*S^4 + 1943*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (1922*HPL[{5, 1, 1, 2}, -S^2])/S^2 + (2834*HPL[{5, 1, 2, 1}, -S^2])/S^2 + (6098*HPL[{5, 2, 1, 1}, -S^2])/S^2 + (15032*HPL[{6, 1, 1, 1}, -S^2])/S^2 + ((-1064*Pi^2)/S^2 - (2*(466 + 1824*S^2 + 473*S^4))/S^2)*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-3192*Pi^2)/S^2 - (6*(466 + 1824*S^2 + 473*S^4))/S^2)*HPL[{2, 2, 1, 1, 1}, -S^2] - (8*(-413 + 66*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 - (24*(-413 + 66*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (3024*HPL[{2, 2, 2, 2, 1}, -S^2])/S^2 + ((-16072*Pi^2)/(3*S^2) - (2*(2482 + 12804*S^2 + 3401*S^4))/S^2)*HPL[{3, 1, 1, 1, 1}, -S^2] + (2*(-9799 + 1540*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 + (2*(-16407 + 2596*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 + (8976*HPL[{3, 1, 1, 2, 2}, -S^2])/S^2 + (2*(-19711 + 3124*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 + (8976*HPL[{3, 1, 2, 1, 2}, -S^2])/S^2 - (144*HPL[{3, 1, 2, 2, 1}, -S^2])/S^2 - (63920*HPL[{3, 1, 3, 1, 1}, -S^2])/S^2 + (2*(-41187 + 6556*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 + (18048*HPL[{3, 2, 1, 1, 2}, -S^2])/S^2 + (8928*HPL[{3, 2, 1, 2, 1}, -S^2])/S^2 - (27728*HPL[{3, 2, 2, 1, 1}, -S^2])/S^2 - (91824*HPL[{3, 3, 1, 1, 1}, -S^2])/S^2 + (32*(-7776 - 7859*S^2 + 1215*S^4 + 1215*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (54840*HPL[{4, 1, 1, 1, 2}, -S^2])/S^2 + (27480*HPL[{4, 1, 1, 2, 1}, -S^2])/S^2 - (82488*HPL[{4, 1, 2, 1, 1}, -S^2])/S^2 - (275208*HPL[{4, 2, 1, 1, 1}, -S^2])/S^2 - (550416*HPL[{5, 1, 1, 1, 1}, -S^2])/S^2 + ((-6776*Pi^2)/(3*S^2) + (4*(-500 + 1558*S^2 + 463*S^4))/S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (6272*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/S^2 + (18816*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S^2 - (8*(-1077 - 1409*S^2 + 75*S^4 + 75*S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (32096*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/S^2 - (69728*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/S^2 - (94816*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/S^2 - (107360*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/S^2 - (188896*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/S^2 - (564736*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S^2 + (480*(-31 + 4*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (12448*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S^2 + (49792*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S^2 + (124480*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (259968*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 - (26880*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (5 + (Pi^2*(87 + 4*S^2 + 4*S^4))/(9*(1 + S^2)) + ((29*Pi^2)/(3*S^2) + (83 + 106*S^2 + 23*S^4)/(3*S^2))*HPL[{1}, -S^2] + (28*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(3*S^2*(1 + S^2)) + (224*HPL[{1}, -S^2]^3)/(9*S^2) + HPL[{0}, S^2]^2*((31 + 4*S^2 + 4*S^4)/(3*(1 + S^2)) + (31*HPL[{1}, -S^2])/(3*S^2)) + (2*(-31 + 4*S^4)*HPL[{2}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((78 + 23*S^2)/3 + (28*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)) + (112*HPL[{1}, -S^2]^2)/(3*S^2) - (2*HPL[{2}, -S^2])/S^2) - (2*HPL[{3}, -S^2])/S^2 - (112*HPL[{2, 1}, -S^2])/(3*S^2))*Log[T]^6 + (-8/3 - (8*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(3*S^2*(1 + S^2)) - (32*HPL[{1}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]*((-8*(4 + S^2 + S^4))/(3*(1 + S^2)) - (32*HPL[{1}, -S^2])/(3*S^2)) + (16*HPL[{2}, -S^2])/(3*S^2))*Log[T]^7 + (8/(3*(1 + S^2)) + (8*HPL[{1}, -S^2])/(3*S^2))*Log[T]^8 + ((83 + 5*S^2)/4 + (Pi^2*(58 - 11*S^2 - 11*S^4))/(12*(1 + S^2)))*Zeta[3]^2 + HPL[{2, 1, 1, 1, 1}, -S^2]*((2*(-1934 + 74*S^2 + 209*S^4))/S^2 + (16*Pi^2*(-125 - 27*S^2 + 30*S^4 + 30*S^6))/(3*S^2*(1 + S^2)) - (112*Zeta[3])/S^2) + HPL[{4, 1, 1}, -S^2]*((-5640 - 501*S^2 + 212*S^4)/(2*S^2) + (Pi^2*(-2870 - 1246*S^2 + 597*S^4 + 597*S^6))/(6*S^2*(1 + S^2)) - (92*Zeta[3])/S^2) + HPL[{5, 1}, -S^2]*((909 + 4500*S^2 + 2326*S^4)/(8*S^2) + (Pi^2*(121 + 813*S^2 + 229*S^4 + 229*S^6))/(6*S^2*(1 + S^2)) - (50*Zeta[3])/S^2) + HPL[{3, 2, 1}, -S^2]*((-3289 + 230*S^2 + 319*S^4)/(4*S^2) + (Pi^2*(-531 - 19*S^2 + 163*S^4 + 163*S^6))/(4*S^2*(1 + S^2)) - (44*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]^2*((-946 - 467*S^2 - 80*S^4)/(2*S^2) + (Pi^2*(-241 - 848*S^2 - 56*S^4 - 56*S^6))/(3*S^2*(1 + S^2)) - (40*Zeta[3])/S^2) + HPL[{1}, -S^2]^6*(((1 + S^2)*(1023 + 221*S^2))/(72*S^2) + (Pi^2*(111 + 459*S^2 + 37*S^4 + 37*S^6))/(36*S^2*(1 + S^2)) - (13*(3 + S^4)*HPL[{2}, -S^2])/(6*S^2) - (190*HPL[{3}, -S^2])/(9*S^2) - (50*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^3*((-1724 + 164*S^2 + 225*S^4)/(48*S^2) + (Pi^2*(-107 - 11*S^2 + 33*S^4 + 33*S^6))/(18*S^2*(1 + S^2)) + (22*HPL[{3}, -S^2])/(3*S^2) - (63*HPL[{2, 1}, -S^2])/S^2 - (2*Zeta[3])/S^2) + HPL[{3, 1, 2}, -S^2]*((159 - 98*S^2 - 131*S^4)/(4*S^2) + (Pi^2*(119 - 39*S^4))/(12*S^2) + (4*Zeta[3])/S^2) + HPL[{4, 2}, -S^2]*((-45 + 359*S^2 + 227*S^4)/(4*S^2) + (Pi^2*(-11 + 46*S^2 + 21*S^4 + 21*S^6))/(3*S^2*(1 + S^2)) + (5*Zeta[3])/S^2) + HPL[{3}, -S^2]^2*((-249 + 424*S^2 + 289*S^4)/(16*S^2) + (Pi^2*(-39 + 35*S^2 + 22*S^4 + 22*S^6))/(12*S^2*(1 + S^2)) - (84*HPL[{2, 1}, -S^2])/S^2 + (7*Zeta[3])/S^2) + HPL[{3, 1, 1, 1}, -S^2]*((4291 + 520*S^2 - 179*S^4)/(2*S^2) - (4*Pi^2*(-289 - 179*S^2 + 48*S^4 + 48*S^6))/(3*S^2*(1 + S^2)) + (64*Zeta[3])/S^2) + HPL[{6}, -S^2]*((-310 - 626*S^2 - 689*S^4)/(8*S^2) + (Pi^2*(46 - 88*S^2 - 63*S^4 - 63*S^6))/(12*S^2*(1 + S^2)) + (160*HPL[{2, 1}, -S^2])/S^2 + (80*Zeta[3])/S^2) + HPL[{0}, S^2]^5*((Pi^2*(-99 - 64*S^2))/960 - (3*(-5 + 7*S^2))/80 + ((12 + 283*S^2 + 4*S^4 + 4*S^6)*HPL[{1}, -S^2]^3)/(180*S^2*(1 + S^2)) + (271*HPL[{1}, -S^2]^4)/(720*S^2) + (-Pi^2/(96*S^2) + (-15 + 33*S^2 - 82*S^4)/(480*S^2))*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/(32*S^2) + HPL[{1}, -S^2]^2*((293*Pi^2)/(720*S^2) + (137 + 88*S^2 - 49*S^4)/(960*S^2) + (77*HPL[{2}, -S^2])/(80*S^2)) + ((-1 + 3*S^2)*HPL[{3}, -S^2])/(32*S^2*(1 + S^2)) + (3*HPL[{4}, -S^2])/(16*S^2) + ((-78 - 540*S^2 - 25*S^4 - 25*S^6)*HPL[{2, 1}, -S^2])/(240*S^2*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(-15 + 13*S^2))/(240*S^2) + (Pi^2*(-267 + 2077*S^2 - 89*S^4 - 89*S^6))/(2880*S^2*(1 + S^2)) + (7*(3 + 47*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(160*S^2*(1 + S^2)) + HPL[{3}, -S^2]/(8*S^2) - (77*HPL[{2, 1}, -S^2])/(40*S^2)) - HPL[{2, 1, 1}, -S^2]/(4*S^2) - (5*S^2*Zeta[3])/16) + HPL[{2, 1, 1, 1}, -S^2]*((-9659*Pi^4)/(90*S^2) + (2*Pi^2*(-237 + 379*S^2 + 127*S^4))/(3*S^2) + (3*(-384 + 2490*S^2 + 305*S^4))/(4*S^2) + (16*(215 + 411*S^2)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^5*((6673*Pi^4)/(2700*S^2) + ((1 + S^2)*(896 + 159*S^2))/(20*S^2) + (Pi^2*(1 + S^2)*(1555 + 503*S^2))/(180*S^2) + ((196*Pi^2)/(45*S^2) - (3*(75 + 86*S^2 + 11*S^4))/(10*S^2))*HPL[{2}, -S^2] + (392*HPL[{2}, -S^2]^2)/(15*S^2) + ((-201 - 581*S^2 - 67*S^4 - 67*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (332*HPL[{4}, -S^2])/(15*S^2) + (13*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (332*HPL[{3, 1}, -S^2])/(15*S^2) + ((-57 - 157*S^2 - 19*S^4 - 19*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{5}, -S^2]*((-19*Pi^4)/(180*S^2) + (-22 - 2070*S^2 - 695*S^4)/(16*S^2) + (Pi^2*(87 - 640*S^2 - 268*S^4))/(24*S^2) + ((258 + 422*S^2 - 29*S^4 - 29*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (104*HPL[{3, 1}, -S^2])/S^2 + (78*HPL[{2, 1, 1}, -S^2])/S^2 + ((-45 - 33*S^2 - 4*S^4 - 4*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((748*Pi^4)/(15*S^2) + (Pi^2*(484 + 1044*S^2 + 253*S^4))/(6*S^2) + (1718 + 8118*S^2 + 1177*S^4)/(8*S^2) + (8*(-203 - 380*S^2 + 6*S^4 + 6*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((1352*Pi^4)/(9*S^2) + (Pi^2*(2725 + 2372*S^2 + 391*S^4))/(12*S^2) + (3776 + 7498*S^2 + 983*S^4)/(8*S^2) + (2*(-2511 - 4735*S^2 + 43*S^4 + 43*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3, 2}, -S^2]*((-43*Pi^4)/(45*S^2) + (3*(22 + 1251*S^2 + 219*S^4))/(4*S^2) + (Pi^2*(-164 + 3516*S^2 + 1091*S^4))/(24*S^2) + (132*HPL[{2, 1, 1}, -S^2])/S^2 + ((-45 + 59*S^2 + 47*S^4 + 47*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{4, 1}, -S^2]*((-491*Pi^4)/(360*S^2) + (Pi^2*(5 + 11406*S^2 + 3513*S^4))/(24*S^2) + (2676 + 48320*S^2 + 8445*S^4)/(16*S^2) - (272*HPL[{2, 1, 1}, -S^2])/S^2 + ((58 + 270*S^2 + 79*S^4 + 79*S^6)*Zeta[3])/(S^2*(1 + S^2))) + Log[T]^5*(-103/12 + (Pi^2*(-302 - 53*S^2))/36 + ((-29*Pi^2)/S^2 + (-83 - 106*S^2 - 23*S^4)/S^2)*HPL[{1}, -S^2]^2 - (56*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)) - (112*HPL[{1}, -S^2]^4)/(3*S^2) + HPL[{0}, S^2]^3*((-73 - 9*S^2 - 9*S^4)/(9*(1 + S^2)) - (73*HPL[{1}, -S^2])/(9*S^2)) + ((91*Pi^2)/(9*S^2) + (370 - 2*S^2 - 53*S^4)/(6*S^2))*HPL[{2}, -S^2] - (79*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^2*((-134 - 53*S^2)/12 + ((-27 - 151*S^2 - 9*S^4 - 9*S^6)*HPL[{1}, -S^2])/(2*S^2*(1 + S^2)) - (31*HPL[{1}, -S^2]^2)/S^2 + (7*HPL[{2}, -S^2])/(3*S^2)) + ((9 + 389*S^2 + 129*S^4 + 129*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + (12*HPL[{4}, -S^2])/S^2 - (2*(-23 + 21*S^4)*HPL[{2, 1}, -S^2])/S^2 + HPL[{0}, S^2]*((-992 - 221*S^2)/12 + (Pi^2*(-241 - 51*S^2 - 51*S^4))/(9*(1 + S^2)) - (28*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^2)/(S^2*(1 + S^2)) - (224*HPL[{1}, -S^2]^3)/(3*S^2) + ((5 - 95*S^2 - 27*S^4 - 27*S^6)*HPL[{2}, -S^2])/(S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-241*Pi^2)/(9*S^2) + (-83 - 106*S^2 - 23*S^4)/S^2 - (100*HPL[{2}, -S^2])/S^2) - (14*HPL[{3}, -S^2])/(3*S^2) + (212*HPL[{2, 1}, -S^2])/S^2) - (136*HPL[{3, 1}, -S^2])/S^2 + (224*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(50 + 21*S^2 + 21*S^4)*Zeta[3])/(1 + S^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(1023 + 221*S^2))/(12*S^2) + (Pi^2*(-111 - 459*S^2 - 37*S^4 - 37*S^6))/(6*S^2*(1 + S^2)) + (13*(3 + S^4)*HPL[{2}, -S^2])/S^2 + (380*HPL[{3}, -S^2])/(3*S^2) + (100*Zeta[3])/S^2)) + HPL[{0}, S^2]^4*((Pi^2*(119 - 332*S^2))/576 + (21 + 8*S^2)/64 + (Pi^4*(4018 - 221*S^2 - 221*S^4))/(8640*(1 + S^2)) + ((93 + 1229*S^2 + 31*S^4 + 31*S^6)*HPL[{1}, -S^2]^4)/(288*S^2*(1 + S^2)) + (71*HPL[{1}, -S^2]^5)/(90*S^2) + ((3 + 33*S^2 + 2*S^4 + 2*S^6)*HPL[{2}, -S^2]^2)/(12*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((277*Pi^2)/(216*S^2) + (121 + 180*S^2 + 59*S^4)/(288*S^2) + (241*HPL[{2}, -S^2])/(72*S^2)) + ((9 - 10*S^2 - 8*S^4)*HPL[{3}, -S^2])/(32*S^2) + ((1 - 3*S^2 - 2*S^4 - 2*S^6)*HPL[{4}, -S^2])/(16*S^2*(1 + S^2)) - (3*HPL[{5}, -S^2])/(2*S^2) + ((-469*Pi^2)/(144*S^2) + (-25 - 5*S^2 - 19*S^4)/(48*S^2))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*(((1 + S^2)*(105 + 59*S^2))/(192*S^2) + (Pi^2*(3 + 2219*S^2 + S^4 + S^6))/(576*S^2*(1 + S^2)) + ((39 + 1003*S^2 + 13*S^4 + 13*S^6)*HPL[{2}, -S^2])/(96*S^2*(1 + S^2)) - HPL[{3}, -S^2]/(8*S^2) - (241*HPL[{2, 1}, -S^2])/(24*S^2)) + ((33 - 435*S^2 - 20*S^4 - 20*S^6)*HPL[{3, 1}, -S^2])/(48*S^2*(1 + S^2)) - HPL[{3, 2}, -S^2]/(4*S^2) - (3*HPL[{4, 1}, -S^2])/(8*S^2) + ((-24 + 458*S^2 + 15*S^4 + 15*S^6)*HPL[{2, 1, 1}, -S^2])/(24*S^2*(1 + S^2)) + (79*HPL[{2, 2, 1}, -S^2])/(4*S^2) + (121*HPL[{3, 1, 1}, -S^2])/(2*S^2) - (259*HPL[{2, 1, 1, 1}, -S^2])/(6*S^2) - (5*(3 + 23*S^2)*Zeta[3])/48 + HPL[{2}, -S^2]*((48 + 25*S^2 - 12*S^4)/(96*S^2) + (Pi^2*(-6 + 212*S^2 - 15*S^4 - 15*S^6))/(144*S^2*(1 + S^2)) + HPL[{3}, -S^2]/(8*S^2) - (79*HPL[{2, 1}, -S^2])/(8*S^2) + (5*Zeta[3])/(8*S^2)) + HPL[{1}, -S^2]*((2009*Pi^4)/(4320*S^2) + (Pi^2*(143 + 30*S^2 - 113*S^4))/(576*S^2) + (63 + 88*S^2 + 25*S^4)/(64*S^2) + ((109*Pi^2)/(72*S^2) + (37 + 50*S^2 + 13*S^4)/(96*S^2))*HPL[{2}, -S^2] + (5*HPL[{2}, -S^2]^2)/(2*S^2) + ((-15 - 19*S^2 - 5*S^4 - 5*S^6)*HPL[{3}, -S^2])/(16*S^2*(1 + S^2)) - HPL[{4}, -S^2]/(4*S^2) + ((-39 - 1003*S^2 - 13*S^4 - 13*S^6)*HPL[{2, 1}, -S^2])/(48*S^2*(1 + S^2)) - (39*HPL[{3, 1}, -S^2])/(4*S^2) + (241*HPL[{2, 1, 1}, -S^2])/(12*S^2) - (5*(3 + S^4)*Zeta[3])/(16*S^2))) + Log[T]^4*(79/6 + (Pi^2*(998 + 209*S^2))/72 + (Pi^4*(13346 + 755*S^2 + 755*S^4))/(1080*(1 + S^2)) + ((145*Pi^2)/(3*S^2) + (5*(83 + 106*S^2 + 23*S^4))/(3*S^2))*HPL[{1}, -S^2]^3 + (70*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)) + (112*HPL[{1}, -S^2]^5)/(3*S^2) + HPL[{0}, S^2]^4*((284 + 5*S^2 + 5*S^4)/(72*(1 + S^2)) + (71*HPL[{1}, -S^2])/(18*S^2)) + ((222 + 614*S^2 + 25*S^4 + 25*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + HPL[{0}, S^2]^3*((518 + 117*S^2)/72 + ((291 + 1751*S^2 + 97*S^4 + 97*S^6)*HPL[{1}, -S^2])/(36*S^2*(1 + S^2)) + (365*HPL[{1}, -S^2]^2)/(18*S^2) - (8*HPL[{2}, -S^2])/(9*S^2)) + ((-14*Pi^2)/(9*S^2) + (-38 - 921*S^2 - 259*S^4)/(3*S^2))*HPL[{3}, -S^2] + ((-129 - 461*S^2 - 90*S^4 - 90*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) + (6*HPL[{5}, -S^2])/S^2 + ((-847*Pi^2)/(9*S^2) + (-500 + 1558*S^2 + 463*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((548 + 209*S^2)/24 + (Pi^2*(749 + 65*S^2 + 65*S^4))/(36*(1 + S^2)) + (5*(27 + 151*S^2 + 9*S^4 + 9*S^6)*HPL[{1}, -S^2]^2)/(4*S^2*(1 + S^2)) + (155*HPL[{1}, -S^2]^3)/(3*S^2) + ((-35 + 357*S^2 + 60*S^4 + 60*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((749*Pi^2)/(36*S^2) + (155 + 234*S^2 + 79*S^4)/(6*S^2) + (196*HPL[{2}, -S^2])/(3*S^2)) + (17*HPL[{3}, -S^2])/(6*S^2) - (427*HPL[{2, 1}, -S^2])/(3*S^2)) + ((1077 + 1409*S^2 - 75*S^4 - 75*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) - (92*HPL[{3, 2}, -S^2])/(3*S^2) - (32*HPL[{4, 1}, -S^2])/(3*S^2) + (20*(-31 + 4*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (1556*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (1496*HPL[{3, 1, 1}, -S^2])/S^2 - (1120*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-1738 - 463*S^2)*Zeta[3])/6 + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(1023 + 221*S^2))/(24*S^2) + (5*Pi^2*(111 + 459*S^2 + 37*S^4 + 37*S^6))/(12*S^2*(1 + S^2)) - (65*(3 + S^4)*HPL[{2}, -S^2])/(2*S^2) - (950*HPL[{3}, -S^2])/(3*S^2) - (250*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-1934 + 74*S^2 + 209*S^4)/(12*S^2) + (2*Pi^2*(-125 - 27*S^2 + 30*S^4 + 30*S^6))/(9*S^2*(1 + S^2)) + (86*HPL[{3}, -S^2])/(3*S^2) - (778*HPL[{2, 1}, -S^2])/(3*S^2) - (14*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]*((6673*Pi^4)/(540*S^2) + ((1 + S^2)*(896 + 159*S^2))/(4*S^2) + (Pi^2*(1 + S^2)*(1555 + 503*S^2))/(36*S^2) + ((196*Pi^2)/(9*S^2) - (3*(75 + 86*S^2 + 11*S^4))/(2*S^2))*HPL[{2}, -S^2] + (392*HPL[{2}, -S^2]^2)/(3*S^2) - (5*(201 + 581*S^2 + 67*S^4 + 67*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (332*HPL[{4}, -S^2])/(3*S^2) + (65*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (332*HPL[{3, 1}, -S^2])/(3*S^2) - (5*(57 + 157*S^2 + 19*S^4 + 19*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]*((1765 + 318*S^2)/8 + (Pi^2*(2858 + 807*S^2))/72 + (140*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)) + (280*HPL[{1}, -S^2]^4)/(3*S^2) + ((-61*Pi^2)/(18*S^2) + (20 + 2254*S^2 + 639*S^4)/(12*S^2))*HPL[{2}, -S^2] + (17*HPL[{2}, -S^2]^2)/(6*S^2) + HPL[{1}, -S^2]^2*((1205*Pi^2)/(18*S^2) + (5*(83 + 106*S^2 + 23*S^4))/(2*S^2) + (250*HPL[{2}, -S^2])/S^2) + ((59 - 9*S^2 - 37*S^4 - 37*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) - (4*HPL[{4}, -S^2])/S^2 + (10*(-40 - 90*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (104*HPL[{3, 1}, -S^2])/(3*S^2) - (60*HPL[{2, 1, 1}, -S^2])/S^2 + ((-166 - 45*S^2 - 45*S^4)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((5*(1 + S^2)*(1023 + 221*S^2))/(24*S^2) + (Pi^2*(1551 + 6371*S^2 + 517*S^4 + 517*S^6))/(36*S^2*(1 + S^2)) + (125*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - (34*HPL[{3}, -S^2])/(3*S^2) - (500*HPL[{2, 1}, -S^2])/S^2 - (166*Zeta[3])/(3*S^2)))) + ((Pi^2*(-2116 - 609*S^2))/24 + (-4811 - 14*S^2)/8)*Zeta[5] + HPL[{1}, -S^2]^4*((Pi^2*(1 + S^2)*(771 + 208*S^2))/(36*S^2) + ((1 + S^2)*(7849 + 1195*S^2))/(64*S^2) + (Pi^4*(14277 + 67661*S^2 + 4759*S^4 + 4759*S^6))/(4320*S^2*(1 + S^2)) + (49*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((-497*Pi^2)/(18*S^2) + (-2043 - 2584*S^2 - 541*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((-165 - 497*S^2 - 55*S^4 - 55*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) - (36*HPL[{5}, -S^2])/S^2 + ((-196*Pi^2)/(9*S^2) + (3*(75 + 86*S^2 + 11*S^4))/(2*S^2))*HPL[{2, 1}, -S^2] + ((417 + 749*S^2 + 139*S^4 + 139*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) + (784*HPL[{3, 2}, -S^2])/(3*S^2) + (2684*HPL[{4, 1}, -S^2])/(3*S^2) - (65*(3 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (1568*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (2804*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((-208*Pi^2)/(9*S^2) - (187*(1 + S^2)*(5 + S^2))/(6*S^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(1021 + 75*S^2))/(16*S^2) + (Pi^2*(-165 + 619*S^2 - 55*S^4 - 55*S^6))/(36*S^2*(1 + S^2)) - (392*HPL[{3}, -S^2])/(3*S^2) - (784*HPL[{2, 1}, -S^2])/(3*S^2) - (392*Zeta[3])/(3*S^2)) - (380*Zeta[5])/(3*S^2)) + HPL[{3, 1}, -S^2]*((19810 + 3248*S^2 - 355*S^4)/(32*S^2) + (Pi^2*(2221 - 152*S^2 - 288*S^4))/(24*S^2) + (Pi^4*(9340 - 212*S^2 - 1967*S^4 - 1967*S^6))/(720*S^2*(1 + S^2)) - (66*HPL[{3, 2}, -S^2])/S^2 + (198*HPL[{4, 1}, -S^2])/S^2 - (16*(127 + 323*S^2 + 7*S^4 + 7*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (1224*HPL[{2, 2, 1}, -S^2])/S^2 + (14344*HPL[{3, 1, 1}, -S^2])/S^2 + (2448*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-39 + 1624*S^2 + 413*S^4)*Zeta[3])/(2*S^2) - (60*Zeta[5])/S^2) + HPL[{2}, -S^2]^2*((2169 + 671*S^2 + 64*S^4)/(16*S^2) + (Pi^2*(2057 + 1504*S^2 + 361*S^4))/(96*S^2) + (Pi^4*(1908 + 7902*S^2 + 577*S^4 + 577*S^6))/(720*S^2*(1 + S^2)) + ((-3*Pi^2)/S^2 + (-52 - 872*S^2 - 247*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((-37 - 365*S^2 - 73*S^4 - 73*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) - (15*HPL[{5}, -S^2])/(2*S^2) + ((-199*Pi^2)/(3*S^2) + (-546 + 1420*S^2 + 465*S^4)/(8*S^2))*HPL[{2, 1}, -S^2] + ((939 + 1267*S^2 - 93*S^4 - 93*S^6)*HPL[{3, 1}, -S^2])/(4*S^2*(1 + S^2)) - (49*HPL[{3, 2}, -S^2])/(2*S^2) + (21*HPL[{4, 1}, -S^2])/(2*S^2) + ((-413 + 66*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (378*HPL[{2, 2, 1}, -S^2])/S^2 + (1062*HPL[{3, 1, 1}, -S^2])/S^2 - (784*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((11*Pi^2)/(6*S^2) + (9 - 390*S^2 - 110*S^4)/(2*S^2))*Zeta[3] + (10*Zeta[5])/S^2) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-1010 + 259*S^2 + 209*S^4))/(6*S^2) + (-4538 - 65*S^2 + 344*S^4)/(4*S^2) + (Pi^4*(-2662 + 1380*S^2 + 763*S^4 + 763*S^6))/(120*S^2*(1 + S^2)) - (3136*HPL[{2, 2, 1}, -S^2])/S^2 - (8720*HPL[{3, 1, 1}, -S^2])/S^2 - (6224*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-8*Pi^2)/(3*S^2) - (2*(-26 + 800*S^2 + 209*S^4))/S^2)*Zeta[3] + (56*Zeta[5])/S^2) + HPL[{4}, -S^2]*((-1846 - 3624*S^2 - 1181*S^4)/(32*S^2) + (Pi^2*(-139 - 374*S^2 - 172*S^4))/(16*S^2) + (Pi^4*(-1630 - 4150*S^2 - 813*S^4 - 813*S^6))/(720*S^2*(1 + S^2)) + (145*HPL[{5}, -S^2])/S^2 + ((295*Pi^2)/(6*S^2) + (801 + 10*S^2 - 161*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + ((-221 + 263*S^2 + 174*S^4 + 174*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) - (23*HPL[{3, 2}, -S^2])/S^2 + (52*HPL[{4, 1}, -S^2])/S^2 + ((180 - 272*S^2 - 169*S^4 - 169*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (570*HPL[{2, 2, 1}, -S^2])/S^2 - (1770*HPL[{3, 1, 1}, -S^2])/S^2 + (1136*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((41*Pi^2)/(6*S^2) + (-17 - 182*S^2 - 51*S^4)/(4*S^2))*Zeta[3] + (89*Zeta[5])/S^2) + Zeta[3]*((Pi^4*(-14396 - 5321*S^2))/1440 + (Pi^2*(-4407 - 550*S^2))/48 - (5*(4118 + 45*S^2))/32 - (2*(-31 + 13*S^2 + 13*S^4)*Zeta[5])/(1 + S^2)) + HPL[{1}, -S^2]^3*((52285*Pi^6)/(27216*S^2) + (Pi^2*(1 + S^2)*(3123 + 739*S^2))/(72*S^2) + ((1 + S^2)*(27105 + 3697*S^2))/(96*S^2) + (Pi^4*(1 + S^2)*(24861 + 9187*S^2))/(4320*S^2) + ((607*Pi^2)/(18*S^2) + (1159 + 1492*S^2 + 333*S^4)/(12*S^2))*HPL[{2}, -S^2]^2 + (74*HPL[{3}, -S^2]^2)/(3*S^2) + ((-170*Pi^2)/(9*S^2) + (-1189 - 1684*S^2 - 495*S^4)/(12*S^2))*HPL[{4}, -S^2] - (2*(159 + 375*S^2 + 53*S^4 + 53*S^6)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)) - (89*HPL[{6}, -S^2])/(3*S^2) - (1568*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-220*Pi^2)/(9*S^2) + (52*(17 + 21*S^2 + 4*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + (2*(837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)) + (2*(2841 + 8209*S^2 + 947*S^4 + 947*S^6)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)) + (78*HPL[{4, 2}, -S^2])/S^2 + (1352*HPL[{5, 1}, -S^2])/(3*S^2) + ((784*Pi^2)/(9*S^2) - (6*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (784*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)) + (4*(759 + 3563*S^2 + 253*S^4 + 253*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) - (1328*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (260*(3 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (1328*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (-((1 + S^2)*(677 + 91*S^2))/(2*S^2) + (Pi^2*(-477 - 1309*S^2 - 159*S^4 - 159*S^6))/(9*S^2*(1 + S^2)))*Zeta[3] + (40*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*(-((1 + S^2)*(1423 + 289*S^2))/(4*S^2) - (2*Pi^2*(270 + 767*S^2 + 90*S^4 + 90*S^6))/(9*S^2*(1 + S^2)) + (1568*HPL[{2, 1}, -S^2])/(3*S^2) - (100*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(1021 + 75*S^2))/(4*S^2) + (Pi^2*(165 - 619*S^2 + 55*S^4 + 55*S^6))/(9*S^2*(1 + S^2)) + (1568*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((2021*Pi^4)/(360*S^2) + (Pi^2*(1 + S^2)*(-479 + 11*S^2))/(36*S^2) - ((1 + S^2)*(3541 + 101*S^2))/(24*S^2) + ((-837 - 2405*S^2 - 279*S^4 - 279*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (226*HPL[{4}, -S^2])/(3*S^2) - (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) - (1568*HPL[{3, 1}, -S^2])/(3*S^2) + (3136*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (56*(15 + 43*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + ((-987 - 2507*S^2 - 329*S^4 - 329*S^6)*Zeta[5])/(3*S^2*(1 + S^2))) + HPL[{3}, -S^2]*((487*Pi^6)/(4536*S^2) + (Pi^4*(-308 - 14784*S^2 - 4471*S^4))/(1440*S^2) + (-4790 - 40540*S^2 - 3167*S^4)/(64*S^2) + (Pi^2*(-317 - 4473*S^2 - 730*S^4))/(48*S^2) + ((-16*Pi^2)/(3*S^2) + (9*(1 + 6*S^2 + 3*S^4))/S^2)*HPL[{4}, -S^2] + ((-59 - 31*S^2 + 19*S^4 + 19*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (145*HPL[{6}, -S^2])/S^2 + (72*HPL[{2, 1}, -S^2]^2)/S^2 + ((-55*Pi^2)/(3*S^2) + (-121 + 1702*S^2 + 511*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-2 - 346*S^2 - 81*S^4 - 81*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((177 + 69*S^2 - 68*S^4 - 68*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + (3*HPL[{4, 2}, -S^2])/S^2 + (106*HPL[{5, 1}, -S^2])/S^2 + ((88*Pi^2)/(3*S^2) + (243 - 3416*S^2 - 1053*S^4)/(2*S^2))*HPL[{2, 1, 1}, -S^2] + ((-1779 - 3643*S^2 - 19*S^4 - 19*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-5435 - 10731*S^2 + 27*S^4 + 27*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (8*HPL[{3, 1, 2}, -S^2])/S^2 + (168*HPL[{3, 2, 1}, -S^2])/S^2 - (36*HPL[{4, 1, 1}, -S^2])/S^2 - (4*(-921 - 1705*S^2 + 38*S^4 + 38*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (400*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (688*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-143 - 8*S^2 - 50*S^4)/(4*S^2) + (Pi^2*(-102 - 206*S^2 - 33*S^4 - 33*S^6))/(12*S^2*(1 + S^2)))*Zeta[3] + HPL[{2, 1}, -S^2]*((1901 + 328*S^2 - 95*S^4)/(2*S^2) + (Pi^2*(1959 + 3611*S^2 - 85*S^4 - 85*S^6))/(12*S^2*(1 + S^2)) + (68*Zeta[3])/S^2) + ((-194 - 258*S^2 - 41*S^4 - 41*S^6)*Zeta[5])/(2*S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-48199*Pi^6)/(11340*S^2) + (-495 + 18247*S^2 + 225*S^4)/(32*S^2) + (Pi^2*(-1063 + 3798*S^2 + 477*S^4))/(48*S^2) + (Pi^4*(-7578 + 11488*S^2 + 3641*S^4))/(1440*S^2) + ((236*Pi^2)/S^2 + (303 + 1996*S^2 + 588*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-3441 - 6857*S^2 + S^4 + S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((-5517 - 10657*S^2 + 112*S^4 + 112*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - (273*HPL[{4, 2}, -S^2])/S^2 - (1350*HPL[{5, 1}, -S^2])/S^2 + ((532*Pi^2)/S^2 + (466 + 1824*S^2 + 473*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(-413 + 66*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (8*(-159 + 233*S^2 + 80*S^4 + 80*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (156*HPL[{3, 1, 2}, -S^2])/S^2 - (1356*HPL[{3, 2, 1}, -S^2])/S^2 - (3400*HPL[{4, 1, 1}, -S^2])/S^2 - (16*(222 + 614*S^2 + 25*S^4 + 25*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (2448*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (6224*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((924 + 185*S^2)/S^2 + (Pi^2*(967 + 1829*S^2 + 2*S^4 + 2*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] - (10*Zeta[3]^2)/S^2 + ((980 + 1702*S^2 + S^4 + S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^3*((Pi^4*(392 - 2459*S^2))/17280 + (Pi^2*(3156 - 733*S^2))/1152 + (5*(1285 + 151*S^2))/384 + ((291 + 1751*S^2 + 97*S^4 + 97*S^6)*HPL[{1}, -S^2]^5)/(180*S^2*(1 + S^2)) + (73*HPL[{1}, -S^2]^6)/(54*S^2) + ((-5*Pi^2)/(36*S^2) + (4 + 464*S^2 + 131*S^4)/(96*S^2))*HPL[{2}, -S^2]^2 - HPL[{2}, -S^2]^3/(12*S^2) + HPL[{1}, -S^2]^4*((53*Pi^2)/(18*S^2) + (531 + 692*S^2 + 161*S^4)/(144*S^2) + (55*HPL[{2}, -S^2])/(6*S^2)) + (11*HPL[{3}, -S^2]^2)/(12*S^2) + ((5*Pi^2)/(9*S^2) + (-37 + 22*S^2 + 5*S^4)/(24*S^2))*HPL[{4}, -S^2] + ((-65 + 27*S^2 + 4*S^4 + 4*S^6)*HPL[{5}, -S^2])/(24*S^2*(1 + S^2)) + (65*HPL[{6}, -S^2])/(6*S^2) + (5*HPL[{2, 1}, -S^2]^2)/(6*S^2) + ((4*Pi^2)/(9*S^2) + (-32 - 472*S^2 - 129*S^4)/(24*S^2))*HPL[{3, 1}, -S^2] + ((99 + 155*S^2 + 42*S^4 + 42*S^6)*HPL[{3, 2}, -S^2])/(24*S^2*(1 + S^2)) + ((91 + 107*S^2 + 52*S^4 + 52*S^6)*HPL[{4, 1}, -S^2])/(12*S^2*(1 + S^2)) - (13*HPL[{5, 1}, -S^2])/(3*S^2) + ((-31*Pi^2)/(18*S^2) + (2*(4 + 59*S^2 + 14*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + ((257 + 893*S^2 + 5*S^4 + 5*S^6)*HPL[{2, 2, 1}, -S^2])/(6*S^2*(1 + S^2)) + (7*(113 + 389*S^2 + S^4 + S^6)*HPL[{3, 1, 1}, -S^2])/(6*S^2*(1 + S^2)) - (2*HPL[{3, 2, 1}, -S^2])/S^2 - (23*HPL[{4, 1, 1}, -S^2])/(3*S^2) + ((-272 - 932*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) + (32*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (64*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((-248 - 195*S^2)/48 + (Pi^2*(-11 - 45*S^2 - 45*S^4))/(36*(1 + S^2)))*Zeta[3] + HPL[{3}, -S^2]*((-23 + 19*S^2 - 33*S^4)/(24*S^2) + (Pi^2*(5 + 89*S^2 - 8*S^4 - 8*S^6))/(144*S^2*(1 + S^2)) - HPL[{2, 1}, -S^2]/(3*S^2) - (3*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*(((1 + S^2)*(557 + 145*S^2))/(72*S^2) + (Pi^2*(339 + 2883*S^2 + 113*S^4 + 113*S^6))/(216*S^2*(1 + S^2)) + ((123 + 783*S^2 + 41*S^4 + 41*S^6)*HPL[{2}, -S^2])/(18*S^2*(1 + S^2)) + (2*HPL[{3}, -S^2])/(3*S^2) - (110*HPL[{2, 1}, -S^2])/(3*S^2) - (11*Zeta[3])/(9*S^2)) + HPL[{2, 1}, -S^2]*((-1031 - 276*S^2 - 3*S^4)/(48*S^2) + (Pi^2*(-175 - 736*S^2 - 12*S^4 - 12*S^6))/(36*S^2*(1 + S^2)) + (4*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-161*Pi^4)/(2160*S^2) + (Pi^2*(1 + 269*S^2 - 26*S^4))/(144*S^2) + (-184 + 1966*S^2 + 273*S^4)/(192*S^2) + ((-25 - 39*S^2 - 10*S^4 - 10*S^6)*HPL[{3}, -S^2])/(12*S^2*(1 + S^2)) - (11*HPL[{4}, -S^2])/(6*S^2) + ((-257 - 893*S^2 - 5*S^4 - 5*S^6)*HPL[{2, 1}, -S^2])/(12*S^2*(1 + S^2)) + (4*HPL[{3, 1}, -S^2])/(3*S^2) - (5*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-9 - 5*S^2 - 5*S^4)*Zeta[3])/(6*(1 + S^2))) + HPL[{1}, -S^2]^2*((3997*Pi^4)/(2160*S^2) + (Pi^2*(1 + S^2)*(167 + 28*S^2))/(72*S^2) + ((1 + S^2)*(1187 + 297*S^2))/(96*S^2) + ((187*Pi^2)/(24*S^2) + (129 + 158*S^2 + 29*S^4)/(12*S^2))*HPL[{2}, -S^2] + (53*HPL[{2}, -S^2]^2)/(4*S^2) + (2*HPL[{3}, -S^2])/(1 + S^2) + (17*HPL[{4}, -S^2])/(6*S^2) + ((-123 - 783*S^2 - 41*S^4 - 41*S^6)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)) - (55*HPL[{3, 1}, -S^2])/S^2 + (110*HPL[{2, 1, 1}, -S^2])/S^2 + ((-21 - 43*S^2 - 7*S^4 - 7*S^6)*Zeta[3])/(6*S^2*(1 + S^2))) + ((-16 - 19*S^2 - 19*S^4)*Zeta[5])/(6*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(617 + 93*S^2))/(288*S^2) + ((1 + S^2)*(4633 + 1267*S^2))/(384*S^2) + (7*Pi^4*(15 + 586*S^2 + 5*S^4 + 5*S^6))/(1080*S^2*(1 + S^2)) + ((21 + 127*S^2 + 7*S^4 + 7*S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((7*Pi^2)/(12*S^2) + (11 + 4*S^2 - 7*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((33 + 101*S^2 + 11*S^4 + 11*S^6)*HPL[{4}, -S^2])/(12*S^2*(1 + S^2)) + (23*HPL[{5}, -S^2])/(6*S^2) + ((-187*Pi^2)/(12*S^2) + (-129 - 158*S^2 - 29*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + ((-21 - 131*S^2 - 7*S^4 - 7*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (7*HPL[{3, 2}, -S^2])/(3*S^2) + (4*HPL[{4, 1}, -S^2])/(3*S^2) + ((123 + 783*S^2 + 41*S^4 + 41*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) + (106*HPL[{2, 2, 1}, -S^2])/S^2 + (322*HPL[{3, 1, 1}, -S^2])/S^2 - (220*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-11*Pi^2)/(36*S^2) - (13*(1 + S^2)^2)/(6*S^2))*Zeta[3] + HPL[{2}, -S^2]*((157*(1 + S^2)*(7 + S^2))/(96*S^2) + (Pi^2*(309 + 2553*S^2 + 103*S^4 + 103*S^6))/(144*S^2*(1 + S^2)) - (7*HPL[{3}, -S^2])/(6*S^2) - (53*HPL[{2, 1}, -S^2])/S^2 - (3*Zeta[3])/(2*S^2)) - (8*Zeta[5])/(3*S^2))) + Log[T]^3*(-835/48 + (Pi^2*(-2664 - 713*S^2))/144 + (Pi^4*(-2834 - 651*S^2))/432 + ((-145*Pi^2)/(3*S^2) - (5*(83 + 106*S^2 + 23*S^4))/(3*S^2))*HPL[{1}, -S^2]^4 - (56*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^5)/(3*S^2*(1 + S^2)) - (224*HPL[{1}, -S^2]^6)/(9*S^2) + HPL[{0}, S^2]^5*((-542 + 9*S^2 + 9*S^4)/(360*(1 + S^2)) - (271*HPL[{1}, -S^2])/(180*S^2)) + ((-208*Pi^2)/(9*S^2) + (-1852 - 1160*S^2 - 193*S^4)/(12*S^2))*HPL[{2}, -S^2]^2 + (392*HPL[{2}, -S^2]^3)/(9*S^2) + HPL[{0}, S^2]^4*((-114 + 37*S^2)/144 + ((-93 - 1229*S^2 - 31*S^4 - 31*S^6)*HPL[{1}, -S^2])/(72*S^2*(1 + S^2)) - (71*HPL[{1}, -S^2]^2)/(9*S^2) + HPL[{2}, -S^2]/(2*S^2)) + (8*HPL[{3}, -S^2]^2)/S^2 + ((12*Pi^2)/S^2 + (465 + 1100*S^2 + 466*S^4)/(6*S^2))*HPL[{4}, -S^2] + ((-30 + 402*S^2 + 203*S^4 + 203*S^6)*HPL[{5}, -S^2])/(3*S^2*(1 + S^2)) + (24*HPL[{6}, -S^2])/S^2 + (1580*HPL[{2, 1}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^3*((-1142 - 155*S^2)/72 + (Pi^2*(-424 - 27*S^2 - 27*S^4))/(36*(1 + S^2)) + ((-291 - 1751*S^2 - 97*S^4 - 97*S^6)*HPL[{1}, -S^2]^2)/(18*S^2*(1 + S^2)) - (730*HPL[{1}, -S^2]^3)/(27*S^2) + ((26 - 634*S^2 - 83*S^4 - 83*S^6)*HPL[{2}, -S^2])/(18*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-106*Pi^2)/(9*S^2) + (-531 - 692*S^2 - 161*S^4)/(36*S^2) - (110*HPL[{2}, -S^2])/(3*S^2)) - (23*HPL[{3}, -S^2])/(9*S^2) + (692*HPL[{2, 1}, -S^2])/(9*S^2)) + ((-1100*Pi^2)/(9*S^2) + (-694 - 108*S^2 + 49*S^4)/S^2)*HPL[{3, 1}, -S^2] + ((223 - 2913*S^2 - 1224*S^4 - 1224*S^6)*HPL[{3, 2}, -S^2])/(3*S^2*(1 + S^2)) - (4*(-51 + 2633*S^2 + 971*S^4 + 971*S^6)*HPL[{4, 1}, -S^2])/(3*S^2*(1 + S^2)) + (68*HPL[{4, 2}, -S^2])/(3*S^2) - (296*HPL[{5, 1}, -S^2])/(3*S^2) + ((1820*Pi^2)/(9*S^2) - (10*(-370 + 2*S^2 + 53*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (16*(72 + 464*S^2 + 73*S^4 + 73*S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^2*(1 + S^2)) - (4*(819 + 3623*S^2 + 231*S^4 + 231*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) - (320*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (2816*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (3376*HPL[{4, 1, 1}, -S^2])/S^2 - (40*(-23 + 21*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (2720*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (4480*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((3836 + 643*S^2)/6 + (2*Pi^2*(416 + 175*S^2 + 175*S^4))/(9*(1 + S^2)))*Zeta[3] + HPL[{2, 1}, -S^2]*((805 - 3436*S^2 - 643*S^4)/(6*S^2) - (2*Pi^2*(-335 - 727*S^2 + 175*S^4 + 175*S^6))/(9*S^2*(1 + S^2)) - (3080*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((463 + 7884*S^2 + 1593*S^4)/(12*S^2) + (2*Pi^2*(10 + 507*S^2 + 172*S^4 + 172*S^6))/(9*S^2*(1 + S^2)) - (1160*HPL[{2, 1}, -S^2])/S^2 + (88*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(1023 + 221*S^2))/(18*S^2) - (5*Pi^2*(111 + 459*S^2 + 37*S^4 + 37*S^6))/(9*S^2*(1 + S^2)) + (130*(3 + S^4)*HPL[{2}, -S^2])/(3*S^2) + (3800*HPL[{3}, -S^2])/(9*S^2) + (1000*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((-6673*Pi^4)/(270*S^2) - ((1 + S^2)*(896 + 159*S^2))/(2*S^2) - (Pi^2*(1 + S^2)*(1555 + 503*S^2))/(18*S^2) + ((-392*Pi^2)/(9*S^2) + (3*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(3*S^2) + (10*(201 + 581*S^2 + 67*S^4 + 67*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + (664*HPL[{4}, -S^2])/(3*S^2) - (130*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (664*HPL[{3, 1}, -S^2])/(3*S^2) + (10*(57 + 157*S^2 + 19*S^4 + 19*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]*((899*Pi^4)/(135*S^2) + (8234 - 186*S^2 - 713*S^4)/(24*S^2) + (Pi^2*(953 - 290*S^2 - 265*S^4))/(18*S^2) + (2*(-84 + 700*S^2 + 317*S^4 + 317*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (116*HPL[{4}, -S^2])/(3*S^2) + (8*(72 + 464*S^2 + 73*S^4 + 73*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) + (1912*HPL[{3, 1}, -S^2])/(3*S^2) - (3160*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (8*(-5 + 191*S^2 + 70*S^4 + 70*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + HPL[{0}, S^2]^2*((-1634 - 713*S^2)/48 + (Pi^2*(-196 - 57*S^2))/18 - (5*(27 + 151*S^2 + 9*S^4 + 9*S^6)*HPL[{1}, -S^2]^3)/(3*S^2*(1 + S^2)) - (155*HPL[{1}, -S^2]^4)/(3*S^2) + ((53*Pi^2)/(18*S^2) + (56 - 570*S^2 - 265*S^4)/(12*S^2))*HPL[{2}, -S^2] - (7*HPL[{2}, -S^2]^2)/(2*S^2) + HPL[{1}, -S^2]^2*((-749*Pi^2)/(18*S^2) + (-155 - 234*S^2 - 79*S^4)/(3*S^2) - (392*HPL[{2}, -S^2])/(3*S^2)) + ((-5 + 83*S^2 + 43*S^4 + 43*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) + (6*HPL[{4}, -S^2])/S^2 + ((325 + 1109*S^2 - 35*S^4 - 35*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) - (80*HPL[{3, 1}, -S^2])/(3*S^2) + (140*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((82 + 35*S^2 + 35*S^4)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((-13*(1 + S^2)*(81 + 43*S^2))/(24*S^2) + (Pi^2*(-249 - 1747*S^2 - 83*S^4 - 83*S^6))/(18*S^2*(1 + S^2)) + ((-255 - 1823*S^2 - 85*S^4 - 85*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) + (44*HPL[{3}, -S^2])/(3*S^2) + (784*HPL[{2, 1}, -S^2])/(3*S^2) + (82*Zeta[3])/(3*S^2))) + HPL[{0}, S^2]*((-7792 - 1195*S^2)/16 + (Pi^2*(-339 - 70*S^2))/4 + (Pi^4*(-8122 - 1387*S^2 - 1387*S^4))/(360*(1 + S^2)) - (140*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^4)/(3*S^2*(1 + S^2)) - (224*HPL[{1}, -S^2]^5)/(3*S^2) - (2*(2 + 394*S^2 + 95*S^4 + 95*S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((-2410*Pi^2)/(27*S^2) - (10*(83 + 106*S^2 + 23*S^4))/(3*S^2) - (1000*HPL[{2}, -S^2])/(3*S^2)) + ((-58*Pi^2)/(9*S^2) + (-89 + 72*S^2 + 133*S^4)/(6*S^2))*HPL[{3}, -S^2] + ((30 - 62*S^2 - 15*S^4 - 15*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) - (18*HPL[{5}, -S^2])/S^2 + ((2282*Pi^2)/(9*S^2) + (2370 + 686*S^2 - 89*S^4)/(3*S^2))*HPL[{2, 1}, -S^2] + (2*(-93 + 1407*S^2 + 403*S^4 + 403*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) - (100*HPL[{3, 2}, -S^2])/(3*S^2) - (32*HPL[{4, 1}, -S^2])/(3*S^2) - (20*(-5 + 95*S^2 + 27*S^4 + 27*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (6136*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (18688*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (4240*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (2*(127 + 59*S^2)*Zeta[3])/3 + HPL[{2}, -S^2]*((-97 - 2378*S^2 - 482*S^4)/(6*S^2) + (Pi^2*(101 - 2059*S^2 - 488*S^4 - 488*S^6))/(18*S^2*(1 + S^2)) + (44*HPL[{3}, -S^2])/(3*S^2) + (3068*HPL[{2, 1}, -S^2])/(3*S^2) - (4*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(1023 + 221*S^2))/(12*S^2) + (Pi^2*(-1551 - 6371*S^2 - 517*S^4 - 517*S^6))/(18*S^2*(1 + S^2)) - (125*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(S^2*(1 + S^2)) + (68*HPL[{3}, -S^2])/(3*S^2) + (1000*HPL[{2, 1}, -S^2])/S^2 + (332*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]*((-4061*Pi^4)/(180*S^2) - ((1 + S^2)*(896 + 159*S^2))/(2*S^2) - (Pi^2*(1 + S^2)*(3021 + 851*S^2))/(36*S^2) + ((-120*Pi^2)/S^2 - (5*(239 + 294*S^2 + 55*S^4))/(3*S^2))*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(3*S^2) + (2*(21 + 89*S^2 + 7*S^4 + 7*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (92*HPL[{4}, -S^2])/(3*S^2) + (250*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (1000*HPL[{3, 1}, -S^2])/S^2 - (2000*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(129 + 461*S^2 + 43*S^4 + 43*S^6)*Zeta[3])/(3*S^2*(1 + S^2)))) + (40*(38 + 17*S^2 + 17*S^4)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(771 + 208*S^2))/(9*S^2) - ((1 + S^2)*(7849 + 1195*S^2))/(16*S^2) + (Pi^4*(-14277 - 67661*S^2 - 4759*S^4 - 4759*S^6))/(1080*S^2*(1 + S^2)) - (196*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((994*Pi^2)/(9*S^2) + (2043 + 2584*S^2 + 541*S^4)/(3*S^2))*HPL[{3}, -S^2] + (4*(165 + 497*S^2 + 55*S^4 + 55*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) + (144*HPL[{5}, -S^2])/S^2 + ((784*Pi^2)/(9*S^2) - (6*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1}, -S^2] - (4*(417 + 749*S^2 + 139*S^4 + 139*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) - (3136*HPL[{3, 2}, -S^2])/(3*S^2) - (10736*HPL[{4, 1}, -S^2])/(3*S^2) + (260*(3 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (6272*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (11216*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((832*Pi^2)/(9*S^2) + (374*(1 + S^2)*(5 + S^2))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(1021 + 75*S^2))/(4*S^2) + (Pi^2*(165 - 619*S^2 + 55*S^4 + 55*S^6))/(9*S^2*(1 + S^2)) + (1568*HPL[{3}, -S^2])/(3*S^2) + (3136*HPL[{2, 1}, -S^2])/(3*S^2) + (1568*Zeta[3])/(3*S^2)) + (1520*Zeta[5])/(3*S^2))) + HPL[{0}, S^2]^2*((Pi^4*(5353 - 2993*S^2))/5760 + (Pi^2*(317 + 196*S^2))/96 + (-945 + 2432*S^2)/128 + (Pi^6*(390830 - 6291*S^2 - 6291*S^4))/(362880*(1 + S^2)) + ((27 + 151*S^2 + 9*S^4 + 9*S^6)*HPL[{1}, -S^2]^6)/(12*S^2*(1 + S^2)) + (31*HPL[{1}, -S^2]^7)/(21*S^2) + ((-5 + 123*S^2 + 22*S^4 + 22*S^6)*HPL[{2}, -S^2]^3)/(8*S^2*(1 + S^2)) + HPL[{1}, -S^2]^5*((749*Pi^2)/(180*S^2) + (155 + 234*S^2 + 79*S^4)/(30*S^2) + (196*HPL[{2}, -S^2])/(15*S^2)) + ((-29 + 2*S^4)*HPL[{3}, -S^2]^2)/(8*S^2) + ((-67*Pi^2)/(24*S^2) + (129 - 172*S^2 - 99*S^4)/(16*S^2))*HPL[{5}, -S^2] - (15*(-14 - 8*S^2 + S^4 + S^6)*HPL[{6}, -S^2])/(8*S^2*(1 + S^2)) - (125*HPL[{7}, -S^2])/(2*S^2) + ((-19 - 234*S^2 - 31*S^4 - 31*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + (-Pi^2/(2*S^2) + (-11 + 356*S^2 + 201*S^4)/(16*S^2))*HPL[{3, 2}, -S^2] + ((-25*Pi^2)/(12*S^2) + (10 + 574*S^2 + 325*S^4)/(8*S^2))*HPL[{4, 1}, -S^2] + ((-18 - 30*S^2 - S^4 - S^6)*HPL[{4, 2}, -S^2])/(8*S^2*(1 + S^2)) + (17*HPL[{4, 3}, -S^2])/S^2 + ((2 + 34*S^2 + 25*S^4 + 25*S^6)*HPL[{5, 1}, -S^2])/(4*S^2*(1 + S^2)) + (205*HPL[{5, 2}, -S^2])/(4*S^2) + (125*HPL[{6, 1}, -S^2])/S^2 + ((323*Pi^2)/(3*S^2) + (502 + 264*S^2 + 33*S^4)/(4*S^2))*HPL[{2, 2, 1}, -S^2] + ((985*Pi^2)/(3*S^2) + (1479 + 584*S^2 + 8*S^4)/(4*S^2))*HPL[{3, 1, 1}, -S^2] + ((6 + 5*S^4)*HPL[{3, 1, 2}, -S^2])/(4*S^2) + ((-54 + 1482*S^2 + 269*S^4 + 269*S^6)*HPL[{3, 2, 1}, -S^2])/(4*S^2*(1 + S^2)) - HPL[{3, 2, 2}, -S^2]/S^2 + (8*HPL[{3, 3, 1}, -S^2])/S^2 + ((-134 + 2154*S^2 + 381*S^4 + 381*S^6)*HPL[{4, 1, 1}, -S^2])/(2*S^2*(1 + S^2)) + (17*HPL[{4, 1, 2}, -S^2])/(2*S^2) + (77*HPL[{4, 2, 1}, -S^2])/(2*S^2) + (95*HPL[{5, 1, 1}, -S^2])/S^2 + ((-686*Pi^2)/(3*S^2) + (-448 - 42*S^2 + 45*S^4)/(2*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (808*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((79 - 693*S^2 - 117*S^4 - 117*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (2424*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (2424*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (4848*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (14512*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (4*(-35 + 357*S^2 + 60*S^4 + 60*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (1636*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (4908*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (8112*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (3416*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-216 - 301*S^2))/48 + (-506 - 185*S^2)/32)*Zeta[3] + ((18 - S^2 - S^4)*Zeta[3]^2)/(4*(1 + S^2)) + HPL[{3, 1}, -S^2]*((151 - 824*S^2 - 397*S^4)/(16*S^2) + (Pi^2*(112 - 1128*S^2 - 137*S^4 - 137*S^6))/(24*S^2*(1 + S^2)) - (8*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*((13*(1 + S^2)*(81 + 43*S^2))/(96*S^2) + (Pi^2*(249 + 1747*S^2 + 83*S^4 + 83*S^6))/(72*S^2*(1 + S^2)) + ((255 + 1823*S^2 + 85*S^4 + 85*S^6)*HPL[{2}, -S^2])/(24*S^2*(1 + S^2)) - (11*HPL[{3}, -S^2])/(3*S^2) - (196*HPL[{2, 1}, -S^2])/(3*S^2) - (41*Zeta[3])/(6*S^2)) + HPL[{2}, -S^2]^2*((3*(55 + 190*S^2 + 67*S^4))/(32*S^2) + (Pi^2*(31 + 366*S^2 + 39*S^4 + 39*S^6))/(24*S^2*(1 + S^2)) - (101*HPL[{2, 1}, -S^2])/S^2 + Zeta[3]/(2*S^2)) + HPL[{2, 1, 1}, -S^2]*((-86 + 444*S^2 + 209*S^4)/(4*S^2) + (Pi^2*(-94 + 1172*S^2 + 135*S^4 + 135*S^6))/(12*S^2*(1 + S^2)) + (6*Zeta[3])/S^2) + HPL[{4}, -S^2]*((51 - 129*S^2 - 53*S^4)/(16*S^2) + (Pi^2*(-38 - 78*S^2 - 27*S^4 - 27*S^6))/(48*S^2*(1 + S^2)) + (11*HPL[{2, 1}, -S^2])/(2*S^2) + (14*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((8449*Pi^4)/(2160*S^2) + (Pi^2*(1 + S^2)*(247 + 125*S^2))/(48*S^2) + ((1 + S^2)*(435 + 262*S^2))/(24*S^2) + ((211*Pi^2)/(12*S^2) + (98 + 153*S^2 + 55*S^4)/(6*S^2))*HPL[{2}, -S^2] + (215*HPL[{2}, -S^2]^2)/(6*S^2) + ((-75 - 163*S^2 - 25*S^4 - 25*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) - (4*HPL[{4}, -S^2])/(3*S^2) + ((-255 - 1823*S^2 - 85*S^4 - 85*S^6)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)) - (386*HPL[{3, 1}, -S^2])/(3*S^2) + (784*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-99 - 263*S^2 - 33*S^4 - 33*S^6)*Zeta[3])/(6*S^2*(1 + S^2))) + HPL[{3}, -S^2]*((19*Pi^4)/(120*S^2) + (55 - 518*S^2 - 186*S^4)/(32*S^2) + (Pi^2*(27 - 268*S^2 - 139*S^4))/(96*S^2) - (17*HPL[{4}, -S^2])/(2*S^2) - (3*(-39 - 67*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(4*S^2*(1 + S^2)) - (5*HPL[{3, 1}, -S^2])/S^2 + (2*HPL[{2, 1, 1}, -S^2])/S^2 + ((-27 - 31*S^2 - 4*S^4 - 4*S^6)*Zeta[3])/(4*S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-2459*Pi^4)/(240*S^2) + (Pi^2*(-498 - 52*S^2 + 7*S^4))/(48*S^2) + (-974 + 126*S^2 + 39*S^4)/(32*S^2) + (402*HPL[{3, 1}, -S^2])/S^2 + (818*HPL[{2, 1, 1}, -S^2])/S^2 + ((107 + 185*S^2 + 2*S^4 + 2*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + ((-99 - 92*S^2)*Zeta[5])/4 + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(1263 + 677*S^2))/(192*S^2) + ((1 + S^2)*(2761 + 2115*S^2))/(128*S^2) + (Pi^4*(3303 + 37099*S^2 + 1101*S^4 + 1101*S^6))/(2880*S^2*(1 + S^2)) + ((99 + 529*S^2 + 33*S^4 + 33*S^6)*HPL[{2}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((-25*Pi^2)/(12*S^2) + (-30 - 43*S^2 - 13*S^4)/(2*S^2))*HPL[{3}, -S^2] + ((-93 - 125*S^2 - 31*S^4 - 31*S^6)*HPL[{4}, -S^2])/(8*S^2*(1 + S^2)) - (6*HPL[{5}, -S^2])/S^2 + ((-211*Pi^2)/(4*S^2) + (-98 - 153*S^2 - 55*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((-123 - 895*S^2 - 41*S^4 - 41*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) + (21*HPL[{3, 2}, -S^2])/S^2 + (67*HPL[{4, 1}, -S^2])/S^2 + ((255 + 1823*S^2 + 85*S^4 + 85*S^6)*HPL[{2, 1, 1}, -S^2])/(2*S^2*(1 + S^2)) + (430*HPL[{2, 2, 1}, -S^2])/S^2 + (1246*HPL[{3, 1, 1}, -S^2])/S^2 - (784*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-41*Pi^2)/(12*S^2) - ((1 + S^2)*(201 + 55*S^2))/(8*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(513 + 367*S^2))/(32*S^2) + (Pi^2*(147 + 1413*S^2 + 49*S^4 + 49*S^6))/(24*S^2*(1 + S^2)) - (21*HPL[{3}, -S^2])/(2*S^2) - (215*HPL[{2, 1}, -S^2])/S^2 - (39*Zeta[3])/(2*S^2)) - (39*Zeta[5])/(2*S^2)) + HPL[{2}, -S^2]*((Pi^2*(10 + 494*S^2 + 185*S^4))/(96*S^2) + (-200 + 335*S^2 + 344*S^4)/(32*S^2) + (Pi^4*(-970 + 12492*S^2 + 453*S^4 + 453*S^6))/(2880*S^2*(1 + S^2)) + (Pi^2/(3*S^2) + (7 - 168*S^2 - 99*S^4)/(16*S^2))*HPL[{3}, -S^2] + ((76 + 80*S^2 - 7*S^4 - 7*S^6)*HPL[{4}, -S^2])/(8*S^2*(1 + S^2)) + (31*HPL[{5}, -S^2])/(4*S^2) + ((-323*Pi^2)/(6*S^2) + (-502 - 264*S^2 - 33*S^4)/(8*S^2))*HPL[{2, 1}, -S^2] - (3*(29 + 313*S^2 + 41*S^4 + 41*S^6)*HPL[{3, 1}, -S^2])/(4*S^2*(1 + S^2)) + HPL[{3, 2}, -S^2]/(2*S^2) - (11*HPL[{4, 1}, -S^2])/(2*S^2) + (2*(19 + 234*S^2 + 31*S^4 + 31*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (404*HPL[{2, 2, 1}, -S^2])/S^2 - (1210*HPL[{3, 1, 1}, -S^2])/S^2 - (818*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((3*Pi^2)/(2*S^2) + (24 - 172*S^2 - 51*S^4)/(8*S^2))*Zeta[3] + (15*Zeta[5])/S^2) + HPL[{1}, -S^2]*((39083*Pi^6)/(36288*S^2) + (Pi^2*(1 + S^2)*(624 + 337*S^2))/(96*S^2) + (3*(1 + S^2)*(945 + 769*S^2))/(128*S^2) + (Pi^4*(1 + S^2)*(6381 + 1147*S^2))/(5760*S^2) + ((335*Pi^2)/(24*S^2) + (325 + 476*S^2 + 151*S^4)/(16*S^2))*HPL[{2}, -S^2]^2 + (16*HPL[{2}, -S^2]^3)/S^2 + ((-5*Pi^2)/(6*S^2) - (3*(39 + 64*S^2 + 25*S^4))/(16*S^2))*HPL[{4}, -S^2] + ((-21 - 33*S^2 - 7*S^4 - 7*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (45*HPL[{6}, -S^2])/(4*S^2) - (215*HPL[{2, 1}, -S^2]^2)/S^2 + ((-155*Pi^2)/(3*S^2) + (-205 - 304*S^2 - 99*S^4)/(4*S^2))*HPL[{3, 1}, -S^2] + (3*(15 + 43*S^2 + 5*S^4 + 5*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((363 + 899*S^2 + 121*S^4 + 121*S^6)*HPL[{4, 1}, -S^2])/(4*S^2*(1 + S^2)) - (3*HPL[{4, 2}, -S^2])/(2*S^2) + (8*HPL[{5, 1}, -S^2])/S^2 + ((211*Pi^2)/(2*S^2) + (98 + 153*S^2 + 55*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (2*(99 + 529*S^2 + 33*S^4 + 33*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((519 + 3011*S^2 + 173*S^4 + 173*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (384*HPL[{3, 2, 1}, -S^2])/S^2 + (1144*HPL[{4, 1, 1}, -S^2])/S^2 + ((-255 - 1823*S^2 - 85*S^4 - 85*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (772*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (1568*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-3*(1 + S^2)*(139 + 41*S^2))/(16*S^2) + (Pi^2*(-36 - 77*S^2 - 12*S^4 - 12*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] + (9*Zeta[3]^2)/(2*S^2) + HPL[{3}, -S^2]*((-49*(1 + S^2)*(3 + S^2))/(8*S^2) - (5*Pi^2*(6 + 11*S^2 + 2*S^4 + 2*S^6))/(6*S^2*(1 + S^2)) + (21*HPL[{2, 1}, -S^2])/S^2 - Zeta[3]/S^2) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(513 + 367*S^2))/(16*S^2) + (Pi^2*(-147 - 1413*S^2 - 49*S^4 - 49*S^6))/(12*S^2*(1 + S^2)) + (39*Zeta[3])/S^2) + HPL[{2}, -S^2]*((6731*Pi^4)/(1440*S^2) + (Pi^2*(1 + S^2)*(233 + 123*S^2))/(48*S^2) + ((1 + S^2)*(221 + 337*S^2))/(32*S^2) - (3*(15 + 43*S^2 + 5*S^4 + 5*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) + HPL[{4}, -S^2]/(2*S^2) + ((-99 - 529*S^2 - 33*S^4 - 33*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (213*HPL[{3, 1}, -S^2])/S^2 + (430*HPL[{2, 1, 1}, -S^2])/S^2 - (3*(15 + 41*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + ((-159 - 315*S^2 - 53*S^4 - 53*S^6)*Zeta[5])/(4*S^2*(1 + S^2)))) + Log[T]^2*(605/32 + (Pi^2*(103 + 43*S^2))/6 + (Pi^4*(9337 + 2230*S^2))/1440 + (Pi^6*(522850 + 20523*S^2 + 20523*S^4))/(90720*(1 + S^2)) + ((29*Pi^2)/S^2 + (83 + 106*S^2 + 23*S^4)/S^2)*HPL[{1}, -S^2]^5 + (28*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)) + (32*HPL[{1}, -S^2]^7)/(3*S^2) + HPL[{0}, S^2]^6*((36 - 5*S^2 - 5*S^4)/(96*(1 + S^2)) + (3*HPL[{1}, -S^2])/(8*S^2)) + ((-413 + 66*S^4)*HPL[{2}, -S^2]^3)/(6*S^2) + HPL[{0}, S^2]^5*((6 - 29*S^2)/80 + ((12 + 283*S^2 + 4*S^4 + 4*S^6)*HPL[{1}, -S^2])/(60*S^2*(1 + S^2)) + (271*HPL[{1}, -S^2]^2)/(120*S^2) - HPL[{2}, -S^2]/(8*S^2)) + ((-49 + 99*S^2 + 42*S^4 + 42*S^6)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((23*Pi^2)/(6*S^2) + (45 - 1108*S^2 - 437*S^4)/(4*S^2))*HPL[{5}, -S^2] + ((-118 - 296*S^2 - 111*S^4 - 111*S^6)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)) - (10*HPL[{7}, -S^2])/S^2 - (4*(222 + 614*S^2 + 25*S^4 + 25*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + HPL[{0}, S^2]^4*((133 - 64*S^2)/96 + (Pi^2*(1108 - 65*S^2 - 65*S^4))/(288*(1 + S^2)) + ((93 + 1229*S^2 + 31*S^4 + 31*S^6)*HPL[{1}, -S^2]^2)/(48*S^2*(1 + S^2)) + (71*HPL[{1}, -S^2]^3)/(9*S^2) + ((-24 + 458*S^2 + 15*S^4 + 15*S^6)*HPL[{2}, -S^2])/(48*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((277*Pi^2)/(72*S^2) + (121 + 180*S^2 + 59*S^4)/(96*S^2) + (241*HPL[{2}, -S^2])/(24*S^2)) + (5*HPL[{3}, -S^2])/(8*S^2) - (259*HPL[{2, 1}, -S^2])/(12*S^2)) + ((-46*Pi^2)/(3*S^2) + (-317 + 6676*S^2 + 1981*S^4)/(4*S^2))*HPL[{3, 2}, -S^2] + ((-32*Pi^2)/(3*S^2) + (-5 + 10832*S^2 + 3188*S^4)/(2*S^2))*HPL[{4, 1}, -S^2] + ((-70 + 398*S^2 + 169*S^4 + 169*S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) + (58*HPL[{4, 3}, -S^2])/S^2 + ((240 + 1592*S^2 + 433*S^4 + 433*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) + (169*HPL[{5, 2}, -S^2])/S^2 + (316*HPL[{6, 1}, -S^2])/S^2 + ((532*Pi^2)/S^2 + (466 + 1824*S^2 + 473*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((4732*Pi^2)/(3*S^2) + (1246 + 1788*S^2 + 383*S^4)/S^2)*HPL[{3, 1, 1}, -S^2] + ((113 - 44*S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((-1539 + 220*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (48*HPL[{3, 2, 2}, -S^2])/S^2 + (136*HPL[{3, 3, 1}, -S^2])/S^2 + (16*(-342 - 425*S^2 + 27*S^4 + 27*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (204*HPL[{4, 1, 2}, -S^2])/S^2 + (540*HPL[{4, 2, 1}, -S^2])/S^2 + (1080*HPL[{5, 1, 1}, -S^2])/S^2 + ((-3388*Pi^2)/(3*S^2) + (2*(-500 + 1558*S^2 + 463*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (3136*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (4*(-1077 - 1409*S^2 + 75*S^4 + 75*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (9040*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (9040*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (18448*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (56320*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (240*(-31 + 4*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (6224*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (18672*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (31840*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (13440*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-8308 - 915*S^2)/8 + (Pi^2*(-962 - 267*S^2))/6)*Zeta[3] - (10*(-4 + S^2 + S^4)*Zeta[3]^2)/(1 + S^2) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(1023 + 221*S^2))/(24*S^2) + (5*Pi^2*(111 + 459*S^2 + 37*S^4 + 37*S^6))/(12*S^2*(1 + S^2)) - (65*(3 + S^4)*HPL[{2}, -S^2])/(2*S^2) - (950*HPL[{3}, -S^2])/(3*S^2) - (250*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((-1934 + 74*S^2 + 209*S^4)/S^2 + (8*Pi^2*(-125 - 27*S^2 + 30*S^4 + 30*S^6))/(3*S^2*(1 + S^2)) - (56*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((946 + 467*S^2 + 80*S^4)/(4*S^2) + (Pi^2*(241 + 848*S^2 + 56*S^4 + 56*S^6))/(6*S^2*(1 + S^2)) - (36*HPL[{3}, -S^2])/S^2 - (392*HPL[{2, 1}, -S^2])/S^2 + (20*Zeta[3])/S^2) + HPL[{4}, -S^2]*((-468 - 993*S^2 - 463*S^4)/(4*S^2) + (Pi^2*(-302 - 982*S^2 - 195*S^4 - 195*S^6))/(12*S^2*(1 + S^2)) + (568*HPL[{2, 1}, -S^2])/S^2 + (26*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((4291 + 520*S^2 - 179*S^4)/(4*S^2) - (2*Pi^2*(-289 - 179*S^2 + 48*S^4 + 48*S^6))/(3*S^2*(1 + S^2)) + (32*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-9659*Pi^4)/(180*S^2) + (Pi^2*(-237 + 379*S^2 + 127*S^4))/(3*S^2) + (3*(-384 + 2490*S^2 + 305*S^4))/(8*S^2) + (1224*HPL[{3, 1}, -S^2])/S^2 + (3112*HPL[{2, 1, 1}, -S^2])/S^2 + (8*(215 + 411*S^2)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((14*Pi^4)/(45*S^2) + (-689 - 8428*S^2 - 1274*S^4)/(8*S^2) + (Pi^2*(-179 - 3892*S^2 - 1127*S^4))/(24*S^2) - (30*HPL[{4}, -S^2])/S^2 - (2*(-921 - 1705*S^2 + 38*S^4 + 38*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (200*HPL[{3, 1}, -S^2])/S^2 + (344*HPL[{2, 1, 1}, -S^2])/S^2 + ((-75 - 175*S^2 - 29*S^4 - 29*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^3*((6673*Pi^4)/(270*S^2) + ((1 + S^2)*(896 + 159*S^2))/(2*S^2) + (Pi^2*(1 + S^2)*(1555 + 503*S^2))/(18*S^2) + ((392*Pi^2)/(9*S^2) - (3*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2}, -S^2] + (784*HPL[{2}, -S^2]^2)/(3*S^2) - (10*(201 + 581*S^2 + 67*S^4 + 67*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (664*HPL[{4}, -S^2])/(3*S^2) + (130*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (664*HPL[{3, 1}, -S^2])/(3*S^2) - (10*(57 + 157*S^2 + 19*S^4 + 19*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^3*((Pi^2*(554 - 57*S^2))/144 + (2436 + 275*S^2)/96 + ((291 + 1751*S^2 + 97*S^4 + 97*S^6)*HPL[{1}, -S^2]^3)/(18*S^2*(1 + S^2)) + (365*HPL[{1}, -S^2]^4)/(18*S^2) + ((-31*Pi^2)/(36*S^2) + (4 + 59*S^2 + 14*S^4)/(3*S^2))*HPL[{2}, -S^2] - (5*HPL[{2}, -S^2]^2)/(12*S^2) + HPL[{1}, -S^2]^2*((53*Pi^2)/(3*S^2) + (531 + 692*S^2 + 161*S^4)/(24*S^2) + (55*HPL[{2}, -S^2])/S^2) + ((5 + 11*S^2 - 2*S^4 - 2*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (5*HPL[{4}, -S^2])/(6*S^2) + ((-272 - 932*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(6*S^2*(1 + S^2)) + (16*HPL[{3, 1}, -S^2])/(3*S^2) - (32*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-22 - 15*S^2 - 15*S^4)*Zeta[3])/(6*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(557 + 145*S^2))/(24*S^2) + (Pi^2*(339 + 2883*S^2 + 113*S^4 + 113*S^6))/(72*S^2*(1 + S^2)) + ((123 + 783*S^2 + 41*S^4 + 41*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) + (2*HPL[{3}, -S^2])/S^2 - (110*HPL[{2, 1}, -S^2])/S^2 - (11*Zeta[3])/(3*S^2))) + HPL[{0}, S^2]^2*((127 + 86*S^2)/4 + (Pi^2*(681 + 145*S^2))/48 + (Pi^4*(16898 + 403*S^2 + 403*S^4))/(1440*(1 + S^2)) + (5*(27 + 151*S^2 + 9*S^4 + 9*S^6)*HPL[{1}, -S^2]^4)/(4*S^2*(1 + S^2)) + (31*HPL[{1}, -S^2]^5)/S^2 + ((19 + 234*S^2 + 31*S^4 + 31*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((749*Pi^2)/(18*S^2) + (155 + 234*S^2 + 79*S^4)/(3*S^2) + (392*HPL[{2}, -S^2])/(3*S^2)) + ((8*Pi^2)/(3*S^2) + (-27 - 208*S^2 - 91*S^4)/(8*S^2))*HPL[{3}, -S^2] + ((-44 - 60*S^2 - 15*S^4 - 15*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + (5*HPL[{5}, -S^2])/(2*S^2) + ((-343*Pi^2)/(3*S^2) + (-448 - 42*S^2 + 45*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + ((79 - 693*S^2 - 117*S^4 - 117*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) - (16*HPL[{4, 1}, -S^2])/S^2 + (2*(-35 + 357*S^2 + 60*S^4 + 60*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (818*HPL[{2, 2, 1}, -S^2])/S^2 + (2488*HPL[{3, 1, 1}, -S^2])/S^2 - (1708*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-186 - 71*S^2)*Zeta[3])/4 + HPL[{1}, -S^2]^2*((13*(1 + S^2)*(81 + 43*S^2))/(16*S^2) + (Pi^2*(249 + 1747*S^2 + 83*S^4 + 83*S^6))/(12*S^2*(1 + S^2)) + ((255 + 1823*S^2 + 85*S^4 + 85*S^6)*HPL[{2}, -S^2])/(4*S^2*(1 + S^2)) - (22*HPL[{3}, -S^2])/S^2 - (392*HPL[{2, 1}, -S^2])/S^2 - (41*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-86 + 444*S^2 + 209*S^4)/(8*S^2) + (Pi^2*(-94 + 1172*S^2 + 135*S^4 + 135*S^6))/(24*S^2*(1 + S^2)) + HPL[{3}, -S^2]/S^2 - (409*HPL[{2, 1}, -S^2])/S^2 + (3*Zeta[3])/S^2) + HPL[{1}, -S^2]*((8449*Pi^4)/(720*S^2) + (Pi^2*(1 + S^2)*(247 + 125*S^2))/(16*S^2) + ((1 + S^2)*(435 + 262*S^2))/(8*S^2) + ((211*Pi^2)/(4*S^2) + (98 + 153*S^2 + 55*S^4)/(2*S^2))*HPL[{2}, -S^2] + (215*HPL[{2}, -S^2]^2)/(2*S^2) + ((-75 - 163*S^2 - 25*S^4 - 25*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - (4*HPL[{4}, -S^2])/S^2 + ((-255 - 1823*S^2 - 85*S^4 - 85*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - (386*HPL[{3, 1}, -S^2])/S^2 + (784*HPL[{2, 1, 1}, -S^2])/S^2 + ((-99 - 263*S^2 - 33*S^4 - 33*S^6)*Zeta[3])/(2*S^2*(1 + S^2)))) + ((-1918 - 425*S^2)*Zeta[5])/2 + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(771 + 208*S^2))/(6*S^2) + (3*(1 + S^2)*(7849 + 1195*S^2))/(32*S^2) + (Pi^4*(14277 + 67661*S^2 + 4759*S^4 + 4759*S^6))/(720*S^2*(1 + S^2)) + (98*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)) + ((-497*Pi^2)/(3*S^2) + (-2043 - 2584*S^2 - 541*S^4)/(2*S^2))*HPL[{3}, -S^2] - (2*(165 + 497*S^2 + 55*S^4 + 55*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) - (216*HPL[{5}, -S^2])/S^2 + ((-392*Pi^2)/(3*S^2) + (9*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1}, -S^2] + (2*(417 + 749*S^2 + 139*S^4 + 139*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (1568*HPL[{3, 2}, -S^2])/S^2 + (5368*HPL[{4, 1}, -S^2])/S^2 - (390*(3 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (3136*HPL[{2, 2, 1}, -S^2])/S^2 + (5608*HPL[{3, 1, 1}, -S^2])/S^2 + ((-416*Pi^2)/(3*S^2) - (187*(1 + S^2)*(5 + S^2))/S^2)*Zeta[3] + HPL[{2}, -S^2]*((-3*(1 + S^2)*(1021 + 75*S^2))/(8*S^2) + (Pi^2*(-165 + 619*S^2 - 55*S^4 - 55*S^6))/(6*S^2*(1 + S^2)) - (784*HPL[{3}, -S^2])/S^2 - (1568*HPL[{2, 1}, -S^2])/S^2 - (784*Zeta[3])/S^2) - (760*Zeta[5])/S^2) + HPL[{2}, -S^2]*((Pi^2*(-1010 + 259*S^2 + 209*S^4))/(12*S^2) + (-4538 - 65*S^2 + 344*S^4)/(8*S^2) + (Pi^4*(-2662 + 1380*S^2 + 763*S^4 + 763*S^6))/(240*S^2*(1 + S^2)) + ((44*Pi^2)/(3*S^2) + (243 - 3416*S^2 - 1053*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((180 - 272*S^2 - 169*S^4 - 169*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + (39*HPL[{5}, -S^2])/S^2 + ((-266*Pi^2)/S^2 + (-466 - 1824*S^2 - 473*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] - (8*(127 + 323*S^2 + 7*S^4 + 7*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (66*HPL[{3, 2}, -S^2])/S^2 - (136*HPL[{4, 1}, -S^2])/S^2 + (8*(222 + 614*S^2 + 25*S^4 + 25*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (1568*HPL[{2, 2, 1}, -S^2])/S^2 - (4360*HPL[{3, 1, 1}, -S^2])/S^2 - (3112*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-4*Pi^2)/(3*S^2) + (26 - 800*S^2 - 209*S^4)/S^2)*Zeta[3] + (28*Zeta[5])/S^2) + HPL[{1}, -S^2]*((52285*Pi^6)/(9072*S^2) + (Pi^2*(1 + S^2)*(3123 + 739*S^2))/(24*S^2) + ((1 + S^2)*(27105 + 3697*S^2))/(32*S^2) + (Pi^4*(1 + S^2)*(24861 + 9187*S^2))/(1440*S^2) + ((607*Pi^2)/(6*S^2) + (1159 + 1492*S^2 + 333*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 + (74*HPL[{3}, -S^2]^2)/S^2 + ((-170*Pi^2)/(3*S^2) + (-1189 - 1684*S^2 - 495*S^4)/(4*S^2))*HPL[{4}, -S^2] - (2*(159 + 375*S^2 + 53*S^4 + 53*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (89*HPL[{6}, -S^2])/S^2 - (1568*HPL[{2, 1}, -S^2]^2)/S^2 + ((-220*Pi^2)/(3*S^2) + (52*(17 + 21*S^2 + 4*S^4))/S^2)*HPL[{3, 1}, -S^2] + (2*(837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + (2*(2841 + 8209*S^2 + 947*S^4 + 947*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) + (234*HPL[{4, 2}, -S^2])/S^2 + (1352*HPL[{5, 1}, -S^2])/S^2 + ((784*Pi^2)/(3*S^2) - (18*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (784*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (4*(759 + 3563*S^2 + 253*S^4 + 253*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (1328*HPL[{4, 1, 1}, -S^2])/S^2 + (780*(3 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (1328*HPL[{3, 1, 1, 1}, -S^2])/S^2 + ((-3*(1 + S^2)*(677 + 91*S^2))/(2*S^2) + (Pi^2*(-477 - 1309*S^2 - 159*S^4 - 159*S^6))/(3*S^2*(1 + S^2)))*Zeta[3] + (40*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((-3*(1 + S^2)*(1423 + 289*S^2))/(4*S^2) - (2*Pi^2*(270 + 767*S^2 + 90*S^4 + 90*S^6))/(3*S^2*(1 + S^2)) + (1568*HPL[{2, 1}, -S^2])/S^2 - (100*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((3*(1 + S^2)*(1021 + 75*S^2))/(4*S^2) + (Pi^2*(165 - 619*S^2 + 55*S^4 + 55*S^6))/(3*S^2*(1 + S^2)) + (1568*Zeta[3])/S^2) + HPL[{2}, -S^2]*((2021*Pi^4)/(120*S^2) + (Pi^2*(1 + S^2)*(-479 + 11*S^2))/(12*S^2) - ((1 + S^2)*(3541 + 101*S^2))/(8*S^2) + ((-837 - 2405*S^2 - 279*S^4 - 279*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - (226*HPL[{4}, -S^2])/S^2 - (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (1568*HPL[{3, 1}, -S^2])/S^2 + (3136*HPL[{2, 1, 1}, -S^2])/S^2 - (56*(15 + 43*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-987 - 2507*S^2 - 329*S^4 - 329*S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{0}, S^2]*((Pi^2*(13026 + 2183*S^2))/96 + (Pi^4*(11850 + 2669*S^2))/720 + (27015 + 3697*S^2)/32 + (28*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^5)/(S^2*(1 + S^2)) + (112*HPL[{1}, -S^2]^6)/(3*S^2) + (Pi^2/S^2 + (6 + 2200*S^2 + 611*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 - (19*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^4*((1205*Pi^2)/(18*S^2) + (5*(83 + 106*S^2 + 23*S^4))/(2*S^2) + (250*HPL[{2}, -S^2])/S^2) + (10*HPL[{3}, -S^2]^2)/S^2 + ((-17*Pi^2)/(6*S^2) + (29 + 114*S^2 - 31*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((33 + 125*S^2 - 6*S^4 - 6*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) + (10*HPL[{6}, -S^2])/S^2 - (34*HPL[{2, 1}, -S^2]^2)/S^2 + ((68*Pi^2)/(3*S^2) + (-5 - 2248*S^2 - 632*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((146 + 450*S^2 + 105*S^4 + 105*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((78 + 442*S^2 + 139*S^4 + 139*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - (3*HPL[{4, 2}, -S^2])/S^2 + (10*HPL[{5, 1}, -S^2])/S^2 + ((-122*Pi^2)/(3*S^2) + (20 + 2254*S^2 + 639*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (8*(292 + 684*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (2*(-3563 - 8199*S^2 + S^4 + S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (12*HPL[{3, 1, 2}, -S^2])/S^2 - (140*HPL[{3, 2, 1}, -S^2])/S^2 - (504*HPL[{4, 1, 1}, -S^2])/S^2 + (120*(-40 - 90*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (416*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (720*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-462 - 239*S^2)/4 - (2*Pi^2*(47 + 15*S^2 + 15*S^4))/(3*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(1023 + 221*S^2))/(12*S^2) + (Pi^2*(1551 + 6371*S^2 + 517*S^4 + 517*S^6))/(18*S^2*(1 + S^2)) + (125*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(S^2*(1 + S^2)) - (68*HPL[{3}, -S^2])/(3*S^2) - (1000*HPL[{2, 1}, -S^2])/S^2 - (332*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((52 + 15*S^2 - 58*S^4)/(2*S^2) + (Pi^2*(79 + 35*S^2 - 45*S^4 - 45*S^6))/(12*S^2*(1 + S^2)) + (108*HPL[{2, 1}, -S^2])/S^2 - (12*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-4867 - 1172*S^2 + 97*S^4)/(4*S^2) + (Pi^2*(-1472 - 3632*S^2 + 31*S^4 + 31*S^6))/(6*S^2*(1 + S^2)) + (332*Zeta[3])/S^2) + HPL[{1}, -S^2]^2*((4061*Pi^4)/(120*S^2) + (3*(1 + S^2)*(896 + 159*S^2))/(4*S^2) + (Pi^2*(1 + S^2)*(3021 + 851*S^2))/(24*S^2) + ((180*Pi^2)/S^2 + (5*(239 + 294*S^2 + 55*S^4))/(2*S^2))*HPL[{2}, -S^2] + (392*HPL[{2}, -S^2]^2)/S^2 + ((-21 - 89*S^2 - 7*S^4 - 7*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (46*HPL[{4}, -S^2])/S^2 - (375*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (1500*HPL[{3, 1}, -S^2])/S^2 + (3000*HPL[{2, 1, 1}, -S^2])/S^2 + ((-129 - 461*S^2 - 43*S^4 - 43*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]*((-9*Pi^4)/(5*S^2) + (Pi^2*(52 + 2726*S^2 + 751*S^4))/(24*S^2) + (778 + 10058*S^2 + 1573*S^4)/(16*S^2) + ((-65 - 217*S^2 - 51*S^4 - 51*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) - (21*HPL[{4}, -S^2])/S^2 - (4*(292 + 684*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (32*HPL[{3, 1}, -S^2])/S^2 + (68*HPL[{2, 1, 1}, -S^2])/S^2 + ((5 - 159*S^2 - 42*S^4 - 42*S^6)*Zeta[3])/(S^2*(1 + S^2))) - (5*(26 + 5*S^2 + 5*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*((3*(1 + S^2)*(7849 + 1195*S^2))/(32*S^2) + (Pi^2*(1 + S^2)*(6229 + 1395*S^2))/(48*S^2) + (Pi^4*(6573 + 30939*S^2 + 2191*S^4 + 2191*S^6))/(360*S^2*(1 + S^2)) + (98*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)) + ((-11*Pi^2)/(3*S^2) - (2*(-11 + 3*S^2 + 14*S^4))/S^2)*HPL[{3}, -S^2] + ((87 + 271*S^2 + 29*S^4 + 29*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + (46*HPL[{5}, -S^2])/S^2 + ((-360*Pi^2)/S^2 - (5*(239 + 294*S^2 + 55*S^4))/S^2)*HPL[{2, 1}, -S^2] - (6*(189 + 689*S^2 + 63*S^4 + 63*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (152*HPL[{3, 2}, -S^2])/S^2 + (364*HPL[{4, 1}, -S^2])/S^2 + (750*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3136*HPL[{2, 2, 1}, -S^2])/S^2 + (9272*HPL[{3, 1, 1}, -S^2])/S^2 - (6000*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-94*Pi^2)/(3*S^2) - ((1 + S^2)*(217 + 111*S^2))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((3*(1 + S^2)*(1687 + 289*S^2))/(8*S^2) + (Pi^2*(1371 + 5691*S^2 + 457*S^4 + 457*S^6))/(12*S^2*(1 + S^2)) - (76*HPL[{3}, -S^2])/S^2 - (1568*HPL[{2, 1}, -S^2])/S^2 - (164*Zeta[3])/S^2) - (130*Zeta[5])/S^2))) - (3*(443 + 68*S^2)*Zeta[7])/2 + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(6577 + 1425*S^2))/(96*S^2) + (3*(1 + S^2)*(10940 + 1507*S^2))/(64*S^2) + (Pi^4*(1 + S^2)*(47125 + 15279*S^2))/(5760*S^2) + (Pi^6*(10959 + 63244*S^2 + 3653*S^4 + 3653*S^6))/(9072*S^2*(1 + S^2)) - (83*(3 + S^4)*HPL[{2}, -S^2]^3)/(12*S^2) + (37*(3 + 11*S^2 + S^4 + S^6)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((-20*Pi^2)/S^2 + (-557 - 800*S^2 - 243*S^4)/(4*S^2))*HPL[{5}, -S^2] + ((-156 - 245*S^2 - 52*S^4 - 52*S^6)*HPL[{6}, -S^2])/(S^2*(1 + S^2)) - (15*HPL[{7}, -S^2])/S^2 - (196*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((413*Pi^2)/(3*S^2) + (1735 + 2152*S^2 + 417*S^4)/(2*S^2))*HPL[{3, 2}, -S^2] + ((1409*Pi^2)/(3*S^2) + (11599 + 14596*S^2 + 2997*S^4)/(4*S^2))*HPL[{4, 1}, -S^2] + (117*(3 + 11*S^2 + S^4 + S^6)*HPL[{4, 2}, -S^2])/(4*S^2*(1 + S^2)) - (47*HPL[{4, 3}, -S^2])/S^2 + (13*(51 + 155*S^2 + 17*S^4 + 17*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) - (102*HPL[{5, 2}, -S^2])/S^2 + (49*HPL[{6, 1}, -S^2])/S^2 + ((1214*Pi^2)/(3*S^2) + (1159 + 1492*S^2 + 333*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((2648*Pi^2)/(3*S^2) + (2*(717 + 946*S^2 + 229*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] - (166*(3 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (1630*HPL[{3, 2, 2}, -S^2])/S^2 - (4984*HPL[{3, 3, 1}, -S^2])/S^2 - (2*(1077 + 1741*S^2 + 359*S^4 + 359*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (4906*HPL[{4, 1, 2}, -S^2])/S^2 - (15202*HPL[{4, 2, 1}, -S^2])/S^2 - (31320*HPL[{5, 1, 1}, -S^2])/S^2 + ((-784*Pi^2)/(3*S^2) + (18*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (4*(417 + 749*S^2 + 139*S^4 + 139*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3136*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (3136*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (3136*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (10736*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (780*(3 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (6272*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (18816*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (38960*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + ((-1013*Pi^4)/(120*S^2) - ((1 + S^2)*(2253 + 215*S^2))/(4*S^2) - (Pi^2*(1 + S^2)*(2071 + 429*S^2))/(24*S^2))*Zeta[3] + ((33 + 113*S^2 + 11*S^4 + 11*S^6)*Zeta[3]^2)/(2*S^2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-3*(1 + S^2)*(1021 + 75*S^2))/(4*S^2) + (Pi^2*(-165 + 619*S^2 - 55*S^4 - 55*S^6))/(3*S^2*(1 + S^2)) - (1568*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((3*(1 + S^2)*(1553 + 351*S^2))/(32*S^2) + (Pi^2*(393 + 1607*S^2 + 131*S^4 + 131*S^6))/(12*S^2*(1 + S^2)) - (233*HPL[{3}, -S^2])/S^2 - (177*Zeta[3])/S^2) + HPL[{4}, -S^2]*(-((1 + S^2)*(1241 + 483*S^2))/(8*S^2) + (Pi^2*(-753 - 2113*S^2 - 251*S^4 - 251*S^6))/(24*S^2*(1 + S^2)) + (226*HPL[{2, 1}, -S^2])/S^2 - (28*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((3*(1 + S^2)*(1293 + 227*S^2))/(8*S^2) + (Pi^2*(147 - 73*S^2 + 49*S^4 + 49*S^6))/(3*S^2*(1 + S^2)) + (808*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-601*Pi^4)/(60*S^2) - (13*(1 + S^2)*(351 + 55*S^2))/(8*S^2) - (Pi^2*(1 + S^2)*(2163 + 593*S^2))/(24*S^2) + (43*HPL[{4}, -S^2])/S^2 + ((837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (784*HPL[{3, 1}, -S^2])/S^2 - (1568*HPL[{2, 1, 1}, -S^2])/S^2 + ((-39 - 139*S^2 - 13*S^4 - 13*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-2021*Pi^4)/(120*S^2) - (Pi^2*(1 + S^2)*(-479 + 11*S^2))/(12*S^2) + ((1 + S^2)*(3541 + 101*S^2))/(8*S^2) + (1568*HPL[{3, 1}, -S^2])/S^2 + (3136*HPL[{2, 1, 1}, -S^2])/S^2 + (56*(15 + 43*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-419*Pi^2)/(6*S^2) - ((1 + S^2)*(2233 + 367*S^2))/(4*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(-1275 + 71*S^2))/(48*S^2) + ((1 + S^2)*(-16995 + 79*S^2))/(64*S^2) + (Pi^4*(-384 + 5679*S^2 - 128*S^4 - 128*S^6))/(360*S^2*(1 + S^2)) + ((-413*Pi^2)/(6*S^2) + (-1735 - 2152*S^2 - 417*S^4)/(4*S^2))*HPL[{3}, -S^2] - (113*(3 + 11*S^2 + S^4 + S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) - (82*HPL[{5}, -S^2])/S^2 + ((-607*Pi^2)/(3*S^2) + (-1159 - 1492*S^2 - 333*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] - (196*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (854*HPL[{3, 2}, -S^2])/S^2 + (2570*HPL[{4, 1}, -S^2])/S^2 + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (1568*HPL[{3, 1, 1}, -S^2])/S^2 - (3136*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-431*Pi^2)/(6*S^2) - ((1 + S^2)*(871 + 209*S^2))/(2*S^2))*Zeta[3] - (361*Zeta[5])/S^2) - (483*Zeta[7])/S^2) + HPL[{2}, -S^2]*((Pi^2*(-2369 + 135*S^2 + 344*S^4))/(48*S^2) + (-24320 - 885*S^2 + 2432*S^4)/(64*S^2) + (Pi^4*(-14666 + 4324*S^2 + 3685*S^4))/(2880*S^2) + (Pi^6*(-23766 + 20292*S^2 + 4507*S^4 + 4507*S^6))/(30240*S^2*(1 + S^2)) + ((-3 + 169*S^2 + 39*S^4 + 39*S^6)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((35*Pi^2)/(6*S^2) + (4 - 406*S^2 - 237*S^4)/(4*S^2))*HPL[{5}, -S^2] + ((177 + 93*S^2 - 76*S^4 - 76*S^6)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)) + (125*HPL[{7}, -S^2])/S^2 + ((413 - 66*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((17*Pi^2)/(3*S^2) + (105 + 3338*S^2 + 941*S^4)/(4*S^2))*HPL[{3, 2}, -S^2] + ((-79*Pi^2)/(6*S^2) + (-177 + 10454*S^2 + 3125*S^4)/(4*S^2))*HPL[{4, 1}, -S^2] + (3*(13 + 117*S^2 + 25*S^4 + 25*S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) - (19*HPL[{4, 3}, -S^2])/S^2 + ((-101 + 531*S^2 + 204*S^4 + 204*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) - (54*HPL[{5, 2}, -S^2])/S^2 - (210*HPL[{6, 1}, -S^2])/S^2 + ((796*Pi^2)/(3*S^2) + (546 - 1420*S^2 - 465*S^4)/(2*S^2))*HPL[{2, 2, 1}, -S^2] + ((-2300*Pi^2)/(3*S^2) + (-1395 + 844*S^2 + 342*S^4)/(2*S^2))*HPL[{3, 1, 1}, -S^2] - (39*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((1563 + 4323*S^2 + 185*S^4 + 185*S^6)*HPL[{3, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (59*HPL[{3, 2, 2}, -S^2])/S^2 + (36*HPL[{3, 3, 1}, -S^2])/S^2 + ((2700 + 6856*S^2 + 167*S^4 + 167*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (3*HPL[{4, 1, 2}, -S^2])/S^2 + (45*HPL[{4, 2, 1}, -S^2])/S^2 + (222*HPL[{5, 1, 1}, -S^2])/S^2 + ((-532*Pi^2)/S^2 + (-466 - 1824*S^2 - 473*S^4)/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (1512*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (16*(-1112 - 916*S^2 + 205*S^4 + 205*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (4404*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (4404*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (8940*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (27488*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (16*(222 + 614*S^2 + 25*S^4 + 25*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (3136*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (9408*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (16368*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (6224*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((71*Pi^4)/(180*S^2) + (Pi^2*(76 - 1772*S^2 - 469*S^4))/(24*S^2) + (89 - 3672*S^2 - 438*S^4)/(8*S^2))*Zeta[3] + ((-28 - 34*S^2 - 7*S^4 - 7*S^6)*Zeta[3]^2)/(2*S^2*(1 + S^2)) + HPL[{3, 1}, -S^2]*((-2078 - 820*S^2 - 35*S^4)/(4*S^2) + (Pi^2*(-1103 - 3523*S^2 - 179*S^4 - 179*S^6))/(12*S^2*(1 + S^2)) - (44*Zeta[3])/S^2) + HPL[{4}, -S^2]*((403 - 750*S^2 - 513*S^4)/(8*S^2) - (2*Pi^2*(-16 + 12*S^2 + 11*S^4 + 11*S^6))/(3*S^2*(1 + S^2)) + (285*HPL[{2, 1}, -S^2])/S^2 - (13*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((946 + 467*S^2 + 80*S^4)/S^2 + (2*Pi^2*(241 + 848*S^2 + 56*S^4 + 56*S^6))/(3*S^2*(1 + S^2)) + (80*Zeta[3])/S^2) + HPL[{3}, -S^2]*((41*Pi^4)/(45*S^2) + (22 - 3798*S^2 - 721*S^4)/(8*S^2) + (Pi^2*(125 - 1792*S^2 - 576*S^4))/(24*S^2) + (10*HPL[{4}, -S^2])/S^2 + ((1779 + 3643*S^2 + 19*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (80*HPL[{3, 1}, -S^2])/S^2 - (144*HPL[{2, 1, 1}, -S^2])/S^2 + ((19 - 33*S^2 - 29*S^4 - 29*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-374*Pi^4)/(15*S^2) + (-1718 - 8118*S^2 - 1177*S^4)/(16*S^2) + (Pi^2*(-484 - 1044*S^2 - 253*S^4))/(12*S^2) + (612*HPL[{3, 1}, -S^2])/S^2 + (1568*HPL[{2, 1, 1}, -S^2])/S^2 - (4*(-203 - 380*S^2 + 6*S^4 + 6*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((22*Pi^2)/(3*S^2) + (160 - 1696*S^2 - 405*S^4)/(4*S^2))*Zeta[5] + (105*Zeta[7])/S^2) + HPL[{1}, -S^2]*((6982*Pi^8)/(14175*S^2) + (105*(1 + S^2)*(404 + 65*S^2))/(64*S^2) + (Pi^2*(1 + S^2)*(7485 + 1501*S^2))/(96*S^2) + (Pi^4*(1 + S^2)*(23565 + 7024*S^2))/(2880*S^2) + (Pi^6*(1 + S^2)*(183231 + 66157*S^2))/(181440*S^2) + ((16*Pi^2)/(3*S^2) + (-283 - 326*S^2 - 43*S^4)/(12*S^2))*HPL[{2}, -S^2]^3 + (16*HPL[{2}, -S^2]^4)/S^2 + ((37*Pi^2)/(6*S^2) + (85 + 134*S^2 + 49*S^4)/(4*S^2))*HPL[{3}, -S^2]^2 - (9*HPL[{4}, -S^2]^2)/S^2 + ((-67*Pi^2)/(6*S^2) + (-327 - 664*S^2 - 337*S^4)/(4*S^2))*HPL[{6}, -S^2] - (3*(153 + 173*S^2 + 51*S^4 + 51*S^6)*HPL[{7}, -S^2])/(2*S^2*(1 + S^2)) - (54*HPL[{8}, -S^2])/S^2 + ((-607*Pi^2)/(3*S^2) + (-1159 - 1492*S^2 - 333*S^4)/(2*S^2))*HPL[{2, 1}, -S^2]^2 + (932*HPL[{3, 1}, -S^2]^2)/S^2 + ((19*Pi^2)/S^2 + (3*(103 + 150*S^2 + 47*S^4))/(4*S^2))*HPL[{4, 2}, -S^2] + ((-87 - 275*S^2 - 29*S^4 - 29*S^6)*HPL[{4, 3}, -S^2])/(2*S^2*(1 + S^2)) + ((346*Pi^2)/(3*S^2) + (1139 + 1668*S^2 + 529*S^4)/(2*S^2))*HPL[{5, 1}, -S^2] - (6*(15 + 49*S^2 + 5*S^4 + 5*S^6)*HPL[{5, 2}, -S^2])/(S^2*(1 + S^2)) - (12*HPL[{5, 3}, -S^2])/S^2 + ((297 + 395*S^2 + 99*S^4 + 99*S^6)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)) - (30*HPL[{6, 2}, -S^2])/S^2 + (54*HPL[{7, 1}, -S^2])/S^2 + (3136*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((128*Pi^2)/S^2 - (2*(283 + 326*S^2 + 43*S^4))/S^2)*HPL[{3, 2, 1}, -S^2] + ((-3441 - 9961*S^2 - 1147*S^4 - 1147*S^6)*HPL[{3, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) - (16*(327 + 950*S^2 + 109*S^4 + 109*S^6)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)) + (266*HPL[{3, 3, 2}, -S^2])/S^2 + ((812*Pi^2)/(3*S^2) + (-4585 - 5596*S^2 - 1011*S^4)/(2*S^2))*HPL[{4, 1, 1}, -S^2] + ((-10347 - 29971*S^2 - 3449*S^4 - 3449*S^6)*HPL[{4, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) - (454*HPL[{4, 1, 3}, -S^2])/S^2 + ((-31767 - 92575*S^2 - 10589*S^4 - 10589*S^6)*HPL[{4, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (188*HPL[{4, 2, 2}, -S^2])/S^2 - (1454*HPL[{4, 3, 1}, -S^2])/S^2 - (2*(16383 + 47703*S^2 + 5461*S^4 + 5461*S^6)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (844*HPL[{5, 1, 2}, -S^2])/S^2 - (6004*HPL[{5, 2, 1}, -S^2])/S^2 - (15658*HPL[{6, 1, 1}, -S^2])/S^2 + (332*(3 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((-440*Pi^2)/(3*S^2) + (104*(17 + 21*S^2 + 4*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (8*(45 + 829*S^2 + 15*S^4 + 15*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (8*(45 + 829*S^2 + 15*S^4 + 15*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (156*HPL[{3, 1, 2, 2}, -S^2])/S^2 - (4*(657 - 911*S^2 + 219*S^4 + 219*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (156*HPL[{3, 2, 1, 2}, -S^2])/S^2 + (188*HPL[{3, 2, 2, 1}, -S^2])/S^2 + (96*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (4*(1641 - 3727*S^2 + 547*S^4 + 547*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (468*HPL[{4, 1, 1, 2}, -S^2])/S^2 + (564*HPL[{4, 1, 2, 1}, -S^2])/S^2 + (756*HPL[{4, 2, 1, 1}, -S^2])/S^2 + (3280*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((1568*Pi^2)/(3*S^2) - (36*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - (1568*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (4704*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (40*(789 + 2737*S^2 + 263*S^4 + 263*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (2656*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + (1560*(3 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (2656*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((29*Pi^2)/(6*S^2) - ((1 + S^2)*(-139 + 3*S^2))/(4*S^2))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((3*(1 + S^2)*(1813 + 475*S^2))/(4*S^2) + (2*Pi^2*(639 + 3287*S^2 + 213*S^4 + 213*S^6))/(3*S^2*(1 + S^2)) - (4448*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((3*(1 + S^2)*(1553 + 351*S^2))/(4*S^2) + (2*Pi^2*(393 + 1607*S^2 + 131*S^4 + 131*S^6))/(3*S^2*(1 + S^2)) - (1416*Zeta[3])/S^2) + HPL[{5}, -S^2]*(-((1 + S^2)*(1347 + 437*S^2))/(8*S^2) + (Pi^2*(-201 - 441*S^2 - 67*S^4 - 67*S^6))/(6*S^2*(1 + S^2)) + (164*HPL[{2, 1}, -S^2])/S^2 + (12*Zeta[3])/S^2) + HPL[{3, 2}, -S^2]*((5*(1 + S^2)*(361 + 63*S^2))/(2*S^2) + (7*Pi^2*(63 + 181*S^2 + 21*S^4 + 21*S^6))/(3*S^2*(1 + S^2)) + (52*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*(((1 + S^2)*(12071 + 2373*S^2))/(4*S^2) + (Pi^2*(6045 + 17317*S^2 + 2015*S^4 + 2015*S^6))/(12*S^2*(1 + S^2)) + (212*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((3*(1 + S^2)*(1021 + 75*S^2))/(2*S^2) + (2*Pi^2*(165 - 619*S^2 + 55*S^4 + 55*S^6))/(3*S^2*(1 + S^2)) + (3136*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((333*Pi^4)/(40*S^2) + (Pi^2*(1 + S^2)*(371 + 121*S^2))/(12*S^2) + ((1 + S^2)*(2377 + 434*S^2))/(16*S^2) + ((-237 - 703*S^2 - 79*S^4 - 79*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - (82*HPL[{4}, -S^2])/S^2 + (83*(3 + S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + (82*HPL[{3, 1}, -S^2])/S^2 + ((-195 - 549*S^2 - 65*S^4 - 65*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{4}, -S^2]*((-7*Pi^4)/(2*S^2) - (3*(1 + S^2)*(415 + 123*S^2))/(8*S^2) - (Pi^2*(1 + S^2)*(653 + 285*S^2))/(24*S^2) + (113*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (242*HPL[{3, 1}, -S^2])/S^2 - (452*HPL[{2, 1, 1}, -S^2])/S^2 + ((-69 - 181*S^2 - 23*S^4 - 23*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((2021*Pi^4)/(60*S^2) + (Pi^2*(1 + S^2)*(-479 + 11*S^2))/(6*S^2) - ((1 + S^2)*(3541 + 101*S^2))/(4*S^2) - (112*(15 + 43*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-199*Pi^4)/(15*S^2) + (Pi^2*(1 + S^2)*(679 + 109*S^2))/(12*S^2) + ((1 + S^2)*(2186 + 281*S^2))/(4*S^2) - (3136*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(429 + 1237*S^2 + 143*S^4 + 143*S^6)*Zeta[3])/(S^2*(1 + S^2))) + (-((1 + S^2)*(5067 + 505*S^2))/(8*S^2) + (Pi^2*(-573 - 1411*S^2 - 191*S^4 - 191*S^6))/(6*S^2*(1 + S^2)))*Zeta[5] + HPL[{3}, -S^2]*(-(Pi^2*(1 + S^2)*(4563 + 965*S^2))/(48*S^2) - ((1 + S^2)*(10289 + 1095*S^2))/(16*S^2) + (Pi^4*(-1059 - 2862*S^2 - 353*S^4 - 353*S^6))/(90*S^2*(1 + S^2)) + (2*(21 + 64*S^2 + 7*S^4 + 7*S^6)*HPL[{4}, -S^2])/(S^2*(1 + S^2)) + (28*HPL[{5}, -S^2])/S^2 + ((413*Pi^2)/(3*S^2) + (1735 + 2152*S^2 + 417*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (172*HPL[{3, 2}, -S^2])/S^2 - (54*HPL[{4, 1}, -S^2])/S^2 - (2*(837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (1864*HPL[{2, 2, 1}, -S^2])/S^2 - (5296*HPL[{3, 1, 1}, -S^2])/S^2 + (3136*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-26*Pi^2)/(3*S^2) - (11*(1 + S^2)*(5 + 3*S^2))/(2*S^2))*Zeta[3] - (32*Zeta[5])/S^2) + Zeta[3]*(-(Pi^2*(1 + S^2)*(1493 + 223*S^2))/(16*S^2) - ((1 + S^2)*(10393 + 735*S^2))/(16*S^2) + (Pi^4*(-3741 - 9819*S^2 - 1247*S^4 - 1247*S^6))/(360*S^2*(1 + S^2)) + (62*Zeta[5])/S^2) + HPL[{2, 1}, -S^2]*(-(Pi^2*(1 + S^2)*(-1275 + 71*S^2))/(24*S^2) - ((1 + S^2)*(-16995 + 79*S^2))/(32*S^2) + (Pi^4*(384 - 5679*S^2 + 128*S^4 + 128*S^6))/(180*S^2*(1 + S^2)) + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (1708*HPL[{3, 2}, -S^2])/S^2 - (5140*HPL[{4, 1}, -S^2])/S^2 + (784*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3136*HPL[{3, 1, 1}, -S^2])/S^2 - (6272*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((431*Pi^2)/(3*S^2) + ((1 + S^2)*(871 + 209*S^2))/S^2)*Zeta[3] + (722*Zeta[5])/S^2) + HPL[{2}, -S^2]*((1049*Pi^6)/(720*S^2) + (Pi^2*(1 + S^2)*(-830 + 59*S^2))/(24*S^2) + (Pi^4*(1 + S^2)*(-1655 + 339*S^2))/(720*S^2) + ((1 + S^2)*(-20405 + 1247*S^2))/(64*S^2) + (43*HPL[{3}, -S^2]^2)/S^2 + ((-56*Pi^2)/(3*S^2) + (-273 - 418*S^2 - 145*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((-165 - 493*S^2 - 55*S^4 - 55*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) - (42*HPL[{6}, -S^2])/S^2 + ((-605*Pi^2)/(3*S^2) + (-1169 - 1500*S^2 - 331*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((1779 + 5195*S^2 + 593*S^4 + 593*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((5349 + 15629*S^2 + 1783*S^4 + 1783*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + (156*HPL[{4, 2}, -S^2])/S^2 + (632*HPL[{5, 1}, -S^2])/S^2 + ((1214*Pi^2)/(3*S^2) + (1159 + 1492*S^2 + 333*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] - (166*(3 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (4*(45 + 829*S^2 + 15*S^4 + 15*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (156*HPL[{3, 1, 2}, -S^2])/S^2 + (1380*HPL[{3, 2, 1}, -S^2])/S^2 + (4156*HPL[{4, 1, 1}, -S^2])/S^2 - (784*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (3136*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (6272*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (-(((1 + S^2)*(447 + 74*S^2))/S^2) + (Pi^2*(-465 - 1327*S^2 - 155*S^4 - 155*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] - (3*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((-5*(1 + S^2)*(361 + 63*S^2))/(4*S^2) - (7*Pi^2*(63 + 181*S^2 + 21*S^4 + 21*S^6))/(6*S^2*(1 + S^2)) + (932*HPL[{2, 1}, -S^2])/S^2 - (26*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-3*(1 + S^2)*(1553 + 351*S^2))/(8*S^2) + (Pi^2*(-393 - 1607*S^2 - 131*S^4 - 131*S^6))/(3*S^2*(1 + S^2)) + (708*Zeta[3])/S^2) - (2*(222 + 583*S^2 + 74*S^4 + 74*S^6)*Zeta[5])/(S^2*(1 + S^2))) - (3*(513 + 1157*S^2 + 171*S^4 + 171*S^6)*Zeta[7])/(2*S^2*(1 + S^2))) + HPL[{0}, S^2]*((105*(404 + 65*S^2))/64 + (Pi^2*(8360 + 1113*S^2))/96 + (Pi^4*(58041 + 5845*S^2))/5760 + (Pi^6*(347652 + 58829*S^2))/362880 + (4*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)) + (4*HPL[{1}, -S^2]^8)/(3*S^2) + ((-11*Pi^2)/(18*S^2) + (-10 + 2148*S^2 + 657*S^4)/(48*S^2))*HPL[{2}, -S^2]^3 + (5*HPL[{2}, -S^2]^4)/(8*S^2) + HPL[{1}, -S^2]^6*((241*Pi^2)/(54*S^2) + (83 + 106*S^2 + 23*S^4)/(6*S^2) + (50*HPL[{2}, -S^2])/(3*S^2)) + ((7*Pi^2)/(4*S^2) + (7 - 38*S^2 + 23*S^4)/(8*S^2))*HPL[{3}, -S^2]^2 - (41*HPL[{4}, -S^2]^2)/(2*S^2) + ((35*Pi^2)/(3*S^2) + (-180 + 32*S^2 + 29*S^4)/(4*S^2))*HPL[{6}, -S^2] + ((-250 - 116*S^2 - 11*S^4 - 11*S^6)*HPL[{7}, -S^2])/(2*S^2*(1 + S^2)) + (525*HPL[{8}, -S^2])/(2*S^2) + ((-2*Pi^2)/S^2 + (-6 - 2200*S^2 - 611*S^4)/(4*S^2))*HPL[{2, 1}, -S^2]^2 + (10*HPL[{3, 1}, -S^2]^2)/S^2 + (-Pi^2/(4*S^2) + (9 + 18*S^2 + 49*S^4)/(8*S^2))*HPL[{4, 2}, -S^2] + ((-103 - 77*S^2 - 9*S^4 - 9*S^6)*HPL[{4, 3}, -S^2])/(2*S^2*(1 + S^2)) + ((-7*Pi^2)/(2*S^2) + (19 - 108*S^2 + 113*S^4)/(4*S^2))*HPL[{5, 1}, -S^2] + ((-611 - 443*S^2 - 42*S^4 - 42*S^6)*HPL[{5, 2}, -S^2])/(4*S^2*(1 + S^2)) + ((-532 - 518*S^2 - 19*S^4 - 19*S^6)*HPL[{6, 1}, -S^2])/(2*S^2*(1 + S^2)) + (3*HPL[{6, 2}, -S^2])/S^2 - (114*HPL[{7, 1}, -S^2])/S^2 + (68*HPL[{2, 1, 1}, -S^2]^2)/S^2 + (Pi^2/S^2 + (21 + 12*S^2 + S^4)/(4*S^2))*HPL[{3, 1, 2}, -S^2] + ((-41*Pi^2)/(3*S^2) + (1 + 4308*S^2 + 1315*S^4)/(4*S^2))*HPL[{3, 2, 1}, -S^2] - (5*(4 + 100*S^2 + 35*S^4 + 35*S^6)*HPL[{3, 2, 2}, -S^2])/(4*S^2*(1 + S^2)) - (4*(25 + 119*S^2 + 34*S^4 + 34*S^6)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)) - (16*HPL[{3, 3, 2}, -S^2])/S^2 + ((-149*Pi^2)/(3*S^2) + (-1 + 6558*S^2 + 1940*S^4)/(2*S^2))*HPL[{4, 1, 1}, -S^2] + ((-208 - 960*S^2 - 281*S^4 - 281*S^6)*HPL[{4, 1, 2}, -S^2])/(2*S^2*(1 + S^2)) + (32*HPL[{4, 1, 3}, -S^2])/S^2 + ((-760 - 3048*S^2 - 821*S^4 - 821*S^6)*HPL[{4, 2, 1}, -S^2])/(2*S^2*(1 + S^2)) - (35*HPL[{4, 2, 2}, -S^2])/(2*S^2) + (64*HPL[{4, 3, 1}, -S^2])/S^2 + ((-795 - 3007*S^2 - 816*S^4 - 816*S^6)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (29*HPL[{5, 1, 2}, -S^2])/S^2 + (269*HPL[{5, 2, 1}, -S^2])/S^2 + (740*HPL[{6, 1, 1}, -S^2])/S^2 + (4*(-554 - 1262*S^2 + 19*S^4 + 19*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((136*Pi^2)/(3*S^2) + (-5 - 2248*S^2 - 632*S^4)/S^2)*HPL[{3, 1, 1, 1}, -S^2] + ((6794 + 15594*S^2 - 123*S^4 - 123*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + ((6794 + 15594*S^2 - 123*S^4 - 123*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (6*HPL[{3, 1, 2, 2}, -S^2])/S^2 + ((13442 + 30738*S^2 - 351*S^4 - 351*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (6*HPL[{3, 2, 1, 2}, -S^2])/S^2 + (142*HPL[{3, 2, 2, 1}, -S^2])/S^2 + (408*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (2*(-20022 - 45874*S^2 + 545*S^4 + 545*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (6*HPL[{4, 1, 1, 2}, -S^2])/S^2 + (402*HPL[{4, 1, 2, 1}, -S^2])/S^2 + (1218*HPL[{4, 2, 1, 1}, -S^2])/S^2 + (2468*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((-244*Pi^2)/(3*S^2) + (2*(20 + 2254*S^2 + 639*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(292 + 684*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (48*(292 + 684*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (304*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (912*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 - (4*(5781 + 13689*S^2 + 97*S^4 + 97*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (1800*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 - (3016*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 - (3624*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 - (7576*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 - (22896*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + (240*(-40 - 90*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (832*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 - (1440*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-2348 - 1021*S^2)/32 + (Pi^2*(-355 - 217*S^2))/24 + (Pi^4*(-229 - 153*S^2 - 153*S^4))/(120*(1 + S^2)))*Zeta[3] + ((48 + S^2)*Zeta[3]^2)/4 + HPL[{3, 1, 1}, -S^2]*((14281 + 3528*S^2 + 191*S^4)/(4*S^2) + (Pi^2*(2177 + 5461*S^2 + 3*S^4 + 3*S^6))/(3*S^2*(1 + S^2)) - (1032*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((4691 + 1156*S^2 + 141*S^4)/(4*S^2) + (Pi^2*(1425 + 3629*S^2 + 17*S^4 + 17*S^6))/(6*S^2*(1 + S^2)) - (336*Zeta[3])/S^2) + HPL[{5}, -S^2]*((-187 + 668*S^2 - 158*S^4)/(16*S^2) + (Pi^2*(-16 + 76*S^2 - S^4 - S^6))/(12*S^2*(1 + S^2)) - (41*HPL[{2, 1}, -S^2])/S^2 - (43*Zeta[3])/S^2) + HPL[{1}, -S^2]^5*(((1 + S^2)*(1023 + 221*S^2))/(24*S^2) + (Pi^2*(1551 + 6371*S^2 + 517*S^4 + 517*S^6))/(180*S^2*(1 + S^2)) + (25*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) - (34*HPL[{3}, -S^2])/(15*S^2) - (100*HPL[{2, 1}, -S^2])/S^2 - (166*Zeta[3])/(15*S^2)) + HPL[{3, 2}, -S^2]*((249 + 158*S^2 + 289*S^4)/(8*S^2) + (Pi^2*(245 + 605*S^2 + 147*S^4 + 147*S^6))/(24*S^2*(1 + S^2)) - (10*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((255 + 182*S^2 + 813*S^4)/(8*S^2) + (Pi^2*(169 + 549*S^2 + 191*S^4 + 191*S^6))/(12*S^2*(1 + S^2)) + (10*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((-4867 - 1172*S^2 + 97*S^4)/(2*S^2) + (Pi^2*(-1472 - 3632*S^2 + 31*S^4 + 31*S^6))/(3*S^2*(1 + S^2)) + (664*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((-7*Pi^4)/(72*S^2) + (Pi^2*(5 + 1332*S^2 + 371*S^4))/(48*S^2) + (-90 + 9414*S^2 + 1435*S^4)/(64*S^2) - (5*(1 + 25*S^2 + 9*S^4 + 9*S^6)*HPL[{3}, -S^2])/(8*S^2*(1 + S^2)) + (5*HPL[{4}, -S^2])/(4*S^2) + ((-554 - 1262*S^2 + 19*S^4 + 19*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (17*HPL[{3, 1}, -S^2])/S^2 - (38*HPL[{2, 1, 1}, -S^2])/S^2 + ((-1 - 165*S^2 - 45*S^4 - 45*S^6)*Zeta[3])/(4*S^2*(1 + S^2))) + HPL[{1}, -S^2]^4*((4061*Pi^4)/(720*S^2) + ((1 + S^2)*(896 + 159*S^2))/(8*S^2) + (Pi^2*(1 + S^2)*(3021 + 851*S^2))/(144*S^2) + ((30*Pi^2)/S^2 + (5*(239 + 294*S^2 + 55*S^4))/(12*S^2))*HPL[{2}, -S^2] + (196*HPL[{2}, -S^2]^2)/(3*S^2) + ((-21 - 89*S^2 - 7*S^4 - 7*S^6)*HPL[{3}, -S^2])/(6*S^2*(1 + S^2)) + (23*HPL[{4}, -S^2])/(3*S^2) - (125*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) - (250*HPL[{3, 1}, -S^2])/S^2 + (500*HPL[{2, 1, 1}, -S^2])/S^2 + ((-129 - 461*S^2 - 43*S^4 - 43*S^6)*Zeta[3])/(6*S^2*(1 + S^2))) + HPL[{4}, -S^2]*((157*Pi^4)/(720*S^2) + (28 + 924*S^2 - 75*S^4)/(32*S^2) + (Pi^2*(-45 + 158*S^2 - 21*S^4))/(48*S^2) + ((-85 - 101*S^2 - 10*S^4 - 10*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (37*HPL[{3, 1}, -S^2])/S^2 - (42*HPL[{2, 1, 1}, -S^2])/S^2 + ((39 + 31*S^2 - 5*S^4 - 5*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{3, 1}, -S^2]*((149*Pi^4)/(90*S^2) + (-782 - 10034*S^2 - 1545*S^4)/(16*S^2) + (Pi^2*(-37 - 2720*S^2 - 761*S^4))/(24*S^2) - (64*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(-7 + 79*S^2 + 21*S^4 + 21*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-18*Pi^4)/(5*S^2) + (Pi^2*(52 + 2726*S^2 + 751*S^4))/(12*S^2) + (778 + 10058*S^2 + 1573*S^4)/(8*S^2) - (2*(-5 + 159*S^2 + 42*S^4 + 42*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-219 - 145*S^2)/4 - (3*Pi^2*(18 + 7*S^2 + 7*S^4))/(4*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^3*(((1 + S^2)*(7849 + 1195*S^2))/(32*S^2) + (Pi^2*(1 + S^2)*(6229 + 1395*S^2))/(144*S^2) + (Pi^4*(6573 + 30939*S^2 + 2191*S^4 + 2191*S^6))/(1080*S^2*(1 + S^2)) + (98*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((-11*Pi^2)/(9*S^2) - (2*(-11 + 3*S^2 + 14*S^4))/(3*S^2))*HPL[{3}, -S^2] + ((87 + 271*S^2 + 29*S^4 + 29*S^6)*HPL[{4}, -S^2])/(6*S^2*(1 + S^2)) + (46*HPL[{5}, -S^2])/(3*S^2) + ((-120*Pi^2)/S^2 - (5*(239 + 294*S^2 + 55*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(189 + 689*S^2 + 63*S^4 + 63*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (152*HPL[{3, 2}, -S^2])/(3*S^2) + (364*HPL[{4, 1}, -S^2])/(3*S^2) + (250*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3136*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (9272*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (2000*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-94*Pi^2)/(9*S^2) - ((1 + S^2)*(217 + 111*S^2))/(6*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(1687 + 289*S^2))/(8*S^2) + (Pi^2*(1371 + 5691*S^2 + 457*S^4 + 457*S^6))/(36*S^2*(1 + S^2)) - (76*HPL[{3}, -S^2])/(3*S^2) - (1568*HPL[{2, 1}, -S^2])/(3*S^2) - (164*Zeta[3])/(3*S^2)) - (130*Zeta[5])/(3*S^2)) + HPL[{3}, -S^2]*((1002 + 3368*S^2 - 435*S^4)/(64*S^2) + (Pi^2*(29 + 34*S^2 - 91*S^4))/(24*S^2) + (Pi^4*(812 + 1412*S^2 - 339*S^4 - 339*S^6))/(1440*S^2*(1 + S^2)) + ((103 + 83*S^2 + 16*S^4 + 16*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + (41*HPL[{5}, -S^2])/S^2 + ((26*Pi^2)/(3*S^2) + (41 + 64*S^2 - 61*S^4)/(4*S^2))*HPL[{2, 1}, -S^2] + ((87 + 223*S^2 + 45*S^4 + 45*S^6)*HPL[{3, 1}, -S^2])/(2*S^2*(1 + S^2)) + (8*HPL[{3, 2}, -S^2])/S^2 - (56*HPL[{4, 1}, -S^2])/S^2 + ((-65 - 217*S^2 - 51*S^4 - 51*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (128*HPL[{2, 2, 1}, -S^2])/S^2 - (344*HPL[{3, 1, 1}, -S^2])/S^2 + (216*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-4*Pi^2)/S^2 + (23 - 29*S^4)/(4*S^2))*Zeta[3] - (38*Zeta[5])/S^2) + HPL[{2, 1}, -S^2]*((-21943 - 5600*S^2 - 173*S^4)/(32*S^2) + (Pi^2*(-2949 - 724*S^2 + 47*S^4))/(24*S^2) + (Pi^4*(-12742 - 34292*S^2 + 21*S^4 + 21*S^6))/(720*S^2*(1 + S^2)) + ((1173 + 2741*S^2 + 13*S^4 + 13*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (128*HPL[{3, 2}, -S^2])/S^2 - (342*HPL[{4, 1}, -S^2])/S^2 + (8*(292 + 684*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (152*HPL[{2, 2, 1}, -S^2])/S^2 - (240*HPL[{3, 1, 1}, -S^2])/S^2 - (136*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((95*Pi^2)/(3*S^2) + (176 + 70*S^2 + 5*S^4)/(2*S^2))*Zeta[3] + (130*Zeta[5])/S^2) + HPL[{2}, -S^2]*((-437*Pi^6)/(3024*S^2) + (Pi^2*(297 + 6012*S^2 + 923*S^4))/(96*S^2) + (3370 + 24749*S^2 + 2862*S^4)/(64*S^2) + (Pi^4*(378 + 22488*S^2 + 4697*S^4))/(2880*S^2) - (2*HPL[{3}, -S^2]^2)/S^2 + ((-43*Pi^2)/(12*S^2) + (-39 + 54*S^2 - 83*S^4)/(8*S^2))*HPL[{4}, -S^2] + ((-59 - 55*S^2 - 16*S^4 - 16*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) - (40*HPL[{6}, -S^2])/S^2 + (38*HPL[{2, 1}, -S^2]^2)/S^2 + ((-4*Pi^2)/(3*S^2) + (-31 - 2212*S^2 - 596*S^4)/(4*S^2))*HPL[{3, 1}, -S^2] + ((13 + 253*S^2 + 91*S^4 + 91*S^6)*HPL[{3, 2}, -S^2])/(4*S^2*(1 + S^2)) + ((100 + 476*S^2 + 145*S^4 + 145*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + (3*HPL[{4, 2}, -S^2])/(2*S^2) + (45*HPL[{5, 1}, -S^2])/S^2 + ((4*Pi^2)/S^2 + (6 + 2200*S^2 + 611*S^4)/(2*S^2))*HPL[{2, 1, 1}, -S^2] - (2*(-554 - 1262*S^2 + 19*S^4 + 19*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-3389 - 7789*S^2 + 63*S^4 + 63*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (60*HPL[{3, 2, 1}, -S^2])/S^2 + (138*HPL[{4, 1, 1}, -S^2])/S^2 - (8*(292 + 684*S^2 + 3*S^4 + 3*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (1760*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (136*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-9 - 216*S^2 - 109*S^4)/(4*S^2) + (Pi^2*(5 - 177*S^2 - 52*S^4 - 52*S^6))/(12*S^2*(1 + S^2)))*Zeta[3] + HPL[{3}, -S^2]*((-117 - 72*S^2 - 151*S^4)/(8*S^2) + (Pi^2*(-115 - 295*S^2 - 71*S^4 - 71*S^6))/(24*S^2*(1 + S^2)) + (64*HPL[{2, 1}, -S^2])/S^2 + (4*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-4691 - 1156*S^2 - 141*S^4)/(8*S^2) + (Pi^2*(-1425 - 3629*S^2 - 17*S^4 - 17*S^6))/(12*S^2*(1 + S^2)) + (168*Zeta[3])/S^2) + ((20 - 86*S^2 - 27*S^4 - 27*S^6)*Zeta[5])/(2*S^2*(1 + S^2))) + HPL[{1}, -S^2]^2*((248987*Pi^6)/(90720*S^2) + (Pi^2*(1 + S^2)*(6563 + 1251*S^2))/(96*S^2) + ((1 + S^2)*(27105 + 3697*S^2))/(64*S^2) + (Pi^4*(1 + S^2)*(25775 + 6533*S^2))/(2880*S^2) + ((551*Pi^2)/(12*S^2) + (1159 + 1492*S^2 + 333*S^4)/(8*S^2))*HPL[{2}, -S^2]^2 + (59*HPL[{2}, -S^2]^3)/S^2 - (2*HPL[{3}, -S^2]^2)/S^2 + ((20*Pi^2)/(3*S^2) - (3*(-81 - 80*S^2 + S^4))/(8*S^2))*HPL[{4}, -S^2] + ((51 + 143*S^2 + 17*S^4 + 17*S^6)*HPL[{5}, -S^2])/(2*S^2*(1 + S^2)) + (73*HPL[{6}, -S^2])/(2*S^2) - (784*HPL[{2, 1}, -S^2]^2)/S^2 + ((-180*Pi^2)/S^2 + (-1203 - 1480*S^2 - 277*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((255 + 983*S^2 + 85*S^4 + 85*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) - (54*HPL[{5, 1}, -S^2])/S^2 + ((360*Pi^2)/S^2 + (5*(239 + 294*S^2 + 55*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (2*(1743 + 6379*S^2 + 581*S^4 + 581*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (1416*HPL[{3, 2, 1}, -S^2])/S^2 + (4340*HPL[{4, 1, 1}, -S^2])/S^2 - (750*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (3000*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (6000*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (-((1 + S^2)*(425 + 223*S^2))/(8*S^2) + (Pi^2*(-171 - 547*S^2 - 57*S^4 - 57*S^6))/(12*S^2*(1 + S^2)))*Zeta[3] + (17*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*(-((1 + S^2)*(-109 + 49*S^2))/(4*S^2) + (Pi^2*(-21 - 65*S^2 - 7*S^4 - 7*S^6))/(12*S^2*(1 + S^2)) + (76*HPL[{2, 1}, -S^2])/S^2 - (4*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-3*(1 + S^2)*(1687 + 289*S^2))/(8*S^2) + (Pi^2*(-1371 - 5691*S^2 - 457*S^4 - 457*S^6))/(12*S^2*(1 + S^2)) + (164*Zeta[3])/S^2) + HPL[{2}, -S^2]*((2155*Pi^4)/(144*S^2) + (Pi^2*(1 + S^2)*(1453 + 333*S^2))/(24*S^2) + ((1 + S^2)*(5471 + 759*S^2))/(16*S^2) - (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + (4*HPL[{4}, -S^2])/S^2 - (196*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (784*HPL[{3, 1}, -S^2])/S^2 + (1568*HPL[{2, 1, 1}, -S^2])/S^2 - (41*(3 + 11*S^2 + S^4 + S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + ((-57 - 187*S^2 - 19*S^4 - 19*S^6)*Zeta[5])/(S^2*(1 + S^2))) + (15*(-5 + S^2 + S^4)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(7045 + 1213*S^2))/(96*S^2) + (3*(1 + S^2)*(10940 + 1507*S^2))/(64*S^2) + (Pi^4*(1 + S^2)*(52781 + 10639*S^2))/(5760*S^2) + (Pi^6*(100023 + 597997*S^2 + 33341*S^4 + 33341*S^6))/(90720*S^2*(1 + S^2)) + (59*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^3)/(4*S^2*(1 + S^2)) + ((-9 - 25*S^2 - 3*S^4 - 3*S^6)*HPL[{3}, -S^2]^2)/(4*S^2*(1 + S^2)) + ((23*Pi^2)/(3*S^2) + (113 + 116*S^2 + 3*S^4)/(4*S^2))*HPL[{5}, -S^2] + ((48 + 121*S^2 + 16*S^4 + 16*S^6)*HPL[{6}, -S^2])/(S^2*(1 + S^2)) + (67*HPL[{7}, -S^2])/S^2 - (196*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((15*Pi^2)/S^2 + (67 + 120*S^2 + 53*S^4)/(2*S^2))*HPL[{3, 2}, -S^2] + ((95*Pi^2)/(3*S^2) + (3*(53 + 160*S^2 + 107*S^4))/(4*S^2))*HPL[{4, 1}, -S^2] - (3*(3 + S^4)*HPL[{4, 2}, -S^2])/(4*S^2) + (13*HPL[{4, 3}, -S^2])/S^2 - (2*(33 + 87*S^2 + 11*S^4 + 11*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) + (42*HPL[{5, 2}, -S^2])/S^2 + (7*HPL[{6, 1}, -S^2])/S^2 + ((1102*Pi^2)/(3*S^2) + (1159 + 1492*S^2 + 333*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((3284*Pi^2)/(3*S^2) + (3521 + 4464*S^2 + 943*S^4)/S^2)*HPL[{3, 1, 1}, -S^2] + (354*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (120*HPL[{3, 2, 2}, -S^2])/S^2 - (376*HPL[{3, 3, 1}, -S^2])/S^2 + ((3273 + 11953*S^2 + 1091*S^4 + 1091*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (376*HPL[{4, 1, 2}, -S^2])/S^2 - (1144*HPL[{4, 2, 1}, -S^2])/S^2 - (2212*HPL[{5, 1, 1}, -S^2])/S^2 + ((-720*Pi^2)/S^2 - (10*(239 + 294*S^2 + 55*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (2832*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (12*(189 + 689*S^2 + 63*S^4 + 63*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (8800*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (8800*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (17296*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (51704*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (1500*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (6272*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (18816*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (31632*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (12000*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-229*Pi^4)/(120*S^2) - (Pi^2*(1 + S^2)*(269 + 163*S^2))/(24*S^2) - ((1 + S^2)*(427 + 219*S^2))/(8*S^2))*Zeta[3] + (2*(6 + 23*S^2 + 2*S^4 + 2*S^6)*Zeta[3]^2)/(S^2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((3*(1 + S^2)*(1687 + 289*S^2))/(4*S^2) + (Pi^2*(1371 + 5691*S^2 + 457*S^4 + 457*S^6))/(6*S^2*(1 + S^2)) - (328*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((3*(1 + S^2)*(1553 + 351*S^2))/(32*S^2) + (Pi^2*(357 + 1459*S^2 + 119*S^4 + 119*S^6))/(12*S^2*(1 + S^2)) - (15*HPL[{3}, -S^2])/S^2 - (354*HPL[{2, 1}, -S^2])/S^2 - (41*Zeta[3])/S^2) + HPL[{4}, -S^2]*(((1 + S^2)*(80 + S^2))/(2*S^2) + (Pi^2*(153 + 473*S^2 + 51*S^4 + 51*S^6))/(24*S^2*(1 + S^2)) - (8*HPL[{2, 1}, -S^2])/S^2 - (4*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(5095 + 857*S^2))/(8*S^2) + (Pi^2*(-231 - 951*S^2 - 77*S^4 - 77*S^6))/(2*S^2*(1 + S^2)) + (172*Zeta[3])/S^2) + HPL[{3}, -S^2]*((5*Pi^4)/(12*S^2) - (77*Pi^2*(-1 + S^2)*(1 + S^2))/(24*S^2) - ((1 + S^2)*(-185 + 33*S^2))/(4*S^2) - (5*HPL[{4}, -S^2])/S^2 + (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (68*HPL[{3, 1}, -S^2])/S^2 - (152*HPL[{2, 1, 1}, -S^2])/S^2 + ((-3 - 11*S^2 - S^4 - S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-2155*Pi^4)/(72*S^2) - (Pi^2*(1 + S^2)*(1453 + 333*S^2))/(12*S^2) - ((1 + S^2)*(5471 + 759*S^2))/(8*S^2) + (1568*HPL[{3, 1}, -S^2])/S^2 + (3136*HPL[{2, 1, 1}, -S^2])/S^2 + (41*(3 + 11*S^2 + S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((-27*Pi^2)/(2*S^2) - ((1 + S^2)*(107 + 153*S^2))/(4*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(385 + 64*S^2))/(6*S^2) + ((1 + S^2)*(24577 + 3019*S^2))/(64*S^2) + (Pi^4*(2913 + 13688*S^2 + 971*S^4 + 971*S^6))/(360*S^2*(1 + S^2)) + ((-15*Pi^2)/(2*S^2) + (-67 - 120*S^2 - 53*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((21 + 53*S^2 + 7*S^4 + 7*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + (2*HPL[{5}, -S^2])/S^2 + ((-551*Pi^2)/(3*S^2) + (-1159 - 1492*S^2 - 333*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] - (196*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (60*HPL[{3, 2}, -S^2])/S^2 + (188*HPL[{4, 1}, -S^2])/S^2 + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (1416*HPL[{2, 2, 1}, -S^2])/S^2 - (4400*HPL[{3, 1, 1}, -S^2])/S^2 - (3136*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-91*Pi^2)/(6*S^2) - ((1 + S^2)*(97 + 57*S^2))/(2*S^2))*Zeta[3] - (53*Zeta[5])/S^2) - (75*Zeta[7])/S^2)) + Log[T]*(-245/16 + (Pi^6*(-195872 - 37557*S^2))/181440 + (Pi^4*(-10497 - 3817*S^2))/2880 + (Pi^2*(-185 - 184*S^2))/24 + ((-29*Pi^2)/(3*S^2) + (-83 - 106*S^2 - 23*S^4)/(3*S^2))*HPL[{1}, -S^2]^6 - (8*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^7)/(3*S^2*(1 + S^2)) - (8*HPL[{1}, -S^2]^8)/(3*S^2) + HPL[{0}, S^2]^7*(((-2 + S^2)*(3 + S^2))/(96*(1 + S^2)) - HPL[{1}, -S^2]/(16*S^2)) + ((103*Pi^2)/(9*S^2) + (1678 - 116*S^2 - 293*S^4)/(24*S^2))*HPL[{2}, -S^2]^3 - (65*HPL[{2}, -S^2]^4)/(4*S^2) + HPL[{0}, S^2]^6*((16 + 25*S^2)/192 + ((3 - 33*S^2 + S^4 + S^6)*HPL[{1}, -S^2])/(48*S^2*(1 + S^2)) - (3*HPL[{1}, -S^2]^2)/(8*S^2) + HPL[{2}, -S^2]/(48*S^2)) + ((17*Pi^2)/(6*S^2) + (55 - 226*S^2 - 115*S^4)/(4*S^2))*HPL[{3}, -S^2]^2 - (38*HPL[{4}, -S^2]^2)/S^2 + ((8*Pi^2)/(3*S^2) + (83 + 196*S^2 + 142*S^4)/S^2)*HPL[{6}, -S^2] + (2*(130 + 145*S^2 + 92*S^4 + 92*S^6)*HPL[{7}, -S^2])/(S^2*(1 + S^2)) - (245*HPL[{8}, -S^2])/S^2 + ((416*Pi^2)/(3*S^2) + (1852 + 1160*S^2 + 193*S^4)/(2*S^2))*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*((-167 + 252*S^2)/480 + (Pi^2*(-586 + 57*S^2 + 57*S^4))/(720*(1 + S^2)) + ((-12 - 283*S^2 - 4*S^4 - 4*S^6)*HPL[{1}, -S^2]^2)/(60*S^2*(1 + S^2)) - (271*HPL[{1}, -S^2]^3)/(180*S^2) + ((15 - 447*S^2 + 4*S^4 + 4*S^6)*HPL[{2}, -S^2])/(240*S^2*(1 + S^2)) + HPL[{1}, -S^2]*((-293*Pi^2)/(360*S^2) + (-137 - 88*S^2 + 49*S^4)/(480*S^2) - (77*HPL[{2}, -S^2])/(40*S^2)) - HPL[{3}, -S^2]/(8*S^2) + (41*HPL[{2, 1}, -S^2])/(10*S^2)) - (1140*HPL[{3, 1}, -S^2]^2)/S^2 + ((13*Pi^2)/(2*S^2) + (101 - 834*S^2 - 451*S^4)/(4*S^2))*HPL[{4, 2}, -S^2] + (2*(-62 - 15*S^2 + 25*S^4 + 25*S^6)*HPL[{4, 3}, -S^2])/(S^2*(1 + S^2)) + ((-27*Pi^2)/S^2 + (-469 - 2440*S^2 - 1163*S^4)/(2*S^2))*HPL[{5, 1}, -S^2] + ((-685 - 277*S^2 + 214*S^4 + 214*S^6)*HPL[{5, 2}, -S^2])/(2*S^2*(1 + S^2)) - (4*HPL[{5, 3}, -S^2])/S^2 + ((-846 - 944*S^2 - 97*S^4 - 97*S^6)*HPL[{6, 1}, -S^2])/(S^2*(1 + S^2)) - (18*HPL[{6, 2}, -S^2])/S^2 + (52*HPL[{7, 1}, -S^2])/S^2 - (3160*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((-28*Pi^2)/S^2 + (-169 + 156*S^2 + 125*S^4)/(2*S^2))*HPL[{3, 1, 2}, -S^2] + ((740*Pi^2)/(3*S^2) + (3187 - 76*S^2 - 461*S^4)/(2*S^2))*HPL[{3, 2, 1}, -S^2] + ((108 + 6628*S^2 + 2327*S^4 + 2327*S^6)*HPL[{3, 2, 2}, -S^2])/(2*S^2*(1 + S^2)) + (4*(-43 + 2449*S^2 + 905*S^4 + 905*S^6)*HPL[{3, 3, 1}, -S^2])/(S^2*(1 + S^2)) - (40*HPL[{3, 3, 2}, -S^2])/S^2 + ((896*Pi^2)/S^2 + (5499 + 752*S^2 - 413*S^4)/S^2)*HPL[{4, 1, 1}, -S^2] + ((-266 + 9546*S^2 + 3621*S^4 + 3621*S^6)*HPL[{4, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (84*HPL[{4, 1, 3}, -S^2])/S^2 + ((-782 + 29622*S^2 + 11037*S^4 + 11037*S^6)*HPL[{4, 2, 1}, -S^2])/(S^2*(1 + S^2)) + (15*HPL[{4, 2, 2}, -S^2])/S^2 + (212*HPL[{4, 3, 1}, -S^2])/S^2 + (2*(-804 + 30516*S^2 + 11327*S^4 + 11327*S^6)*HPL[{5, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (114*HPL[{5, 1, 2}, -S^2])/S^2 + (834*HPL[{5, 2, 1}, -S^2])/S^2 + (2304*HPL[{6, 1, 1}, -S^2])/S^2 - (8*(-164 + 149*S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((-2200*Pi^2)/(3*S^2) + (6*(-694 - 108*S^2 + 49*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (2*(-1745 - 4881*S^2 + 564*S^4 + 564*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(S^2*(1 + S^2)) + (2*(-1745 - 4881*S^2 + 564*S^4 + 564*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (168*HPL[{3, 1, 2, 2}, -S^2])/S^2 + (2*(-3713 - 6849*S^2 + 2352*S^4 + 2352*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (168*HPL[{3, 2, 1, 2}, -S^2])/S^2 - (3304*HPL[{3, 2, 2, 1}, -S^2])/S^2 - (9408*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (8*(-2901 - 5585*S^2 + 1711*S^4 + 1711*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (136*HPL[{4, 1, 1, 2}, -S^2])/S^2 - (9272*HPL[{4, 1, 2, 1}, -S^2])/S^2 - (28088*HPL[{4, 2, 1, 1}, -S^2])/S^2 - (57040*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((3640*Pi^2)/(3*S^2) - (20*(-370 + 2*S^2 + 53*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + (32*(72 + 464*S^2 + 73*S^4 + 73*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (96*(72 + 464*S^2 + 73*S^4 + 73*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (6272*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 - (18816*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (40*(297 + 2245*S^2 + 421*S^4 + 421*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (36992*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 + (62080*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 + (74624*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 + (156160*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 + (471840*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 - (240*(-23 + 21*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 - (16320*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + (26880*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(4234 + 775*S^2))/24 + (18448 + 1297*S^2)/16 + (Pi^4*(6078 + 2827*S^2 + 2827*S^4))/(360*(1 + S^2)))*Zeta[3] + (-17 + 12*S^2)*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((805 - 3436*S^2 - 643*S^4)/S^2 - (4*Pi^2*(-335 - 727*S^2 + 175*S^4 + 175*S^6))/(3*S^2*(1 + S^2)) - (6160*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((-197 - 11483*S^2 - 2480*S^4)/(2*S^2) + (Pi^2*(134 - 5502*S^2 - 2075*S^4 - 2075*S^6))/(6*S^2*(1 + S^2)) - (68*Zeta[3])/S^2) + HPL[{3, 2}, -S^2]*((225 - 7070*S^2 - 1509*S^4)/(4*S^2) + (Pi^2*(271 - 3033*S^2 - 1307*S^4 - 1307*S^6))/(12*S^2*(1 + S^2)) + (28*Zeta[3])/S^2) + HPL[{5}, -S^2]*((55 + 2524*S^2 + 918*S^4)/(8*S^2) + (Pi^2*(3 + 243*S^2 + 125*S^4 + 125*S^6))/(6*S^2*(1 + S^2)) - (406*HPL[{2, 1}, -S^2])/S^2 + (46*Zeta[3])/S^2) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(1023 + 221*S^2))/(12*S^2) + (Pi^2*(-111 - 459*S^2 - 37*S^4 - 37*S^6))/(6*S^2*(1 + S^2)) + (13*(3 + S^4)*HPL[{2}, -S^2])/S^2 + (380*HPL[{3}, -S^2])/(3*S^2) + (100*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((-875 - 3844*S^2 - 733*S^4)/(2*S^2) - (4*Pi^2*(152 + 759*S^2 + 75*S^4 + 75*S^6))/(3*S^2*(1 + S^2)) + (2992*Zeta[3])/S^2) + HPL[{3, 1, 1}, -S^2]*((-1081 - 1824*S^2 - 303*S^4)/S^2 - (4*Pi^2*(446 + 1770*S^2 + 53*S^4 + 53*S^6))/(3*S^2*(1 + S^2)) + (9152*Zeta[3])/S^2) + HPL[{0}, S^2]^4*((-33 + 16*S^2)/32 + (Pi^2*(63 + 206*S^2))/288 + ((-93 - 1229*S^2 - 31*S^4 - 31*S^6)*HPL[{1}, -S^2]^3)/(72*S^2*(1 + S^2)) - (71*HPL[{1}, -S^2]^4)/(18*S^2) + ((11*Pi^2)/(48*S^2) + (-4 - 15*S^2 + 2*S^4)/(16*S^2))*HPL[{2}, -S^2] - HPL[{2}, -S^2]^2/(16*S^2) + HPL[{1}, -S^2]^2*((-277*Pi^2)/(72*S^2) + (-121 - 180*S^2 - 59*S^4)/(96*S^2) - (241*HPL[{2}, -S^2])/(24*S^2)) + ((3 + 7*S^2 + 6*S^4 + 6*S^6)*HPL[{3}, -S^2])/(16*S^2*(1 + S^2)) + HPL[{4}, -S^2]/(8*S^2) + ((63 + 545*S^2 - 2*S^4 - 2*S^6)*HPL[{2, 1}, -S^2])/(24*S^2*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(105 + 59*S^2))/(96*S^2) + (Pi^2*(-3 - 2219*S^2 - S^4 - S^6))/(288*S^2*(1 + S^2)) + ((-39 - 1003*S^2 - 13*S^4 - 13*S^6)*HPL[{2}, -S^2])/(48*S^2*(1 + S^2)) + HPL[{3}, -S^2]/(4*S^2) + (241*HPL[{2, 1}, -S^2])/(12*S^2)) - (3*HPL[{3, 1}, -S^2])/(2*S^2) + (3*HPL[{2, 1, 1}, -S^2])/S^2 + (5*S^2*Zeta[3])/3) + HPL[{1}, -S^2]^4*((-6673*Pi^4)/(540*S^2) - ((1 + S^2)*(896 + 159*S^2))/(4*S^2) - (Pi^2*(1 + S^2)*(1555 + 503*S^2))/(36*S^2) + ((-196*Pi^2)/(9*S^2) + (3*(75 + 86*S^2 + 11*S^4))/(2*S^2))*HPL[{2}, -S^2] - (392*HPL[{2}, -S^2]^2)/(3*S^2) + (5*(201 + 581*S^2 + 67*S^4 + 67*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) + (332*HPL[{4}, -S^2])/(3*S^2) - (65*(3 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (332*HPL[{3, 1}, -S^2])/(3*S^2) + (5*(57 + 157*S^2 + 19*S^4 + 19*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{4}, -S^2]*((1043*Pi^4)/(360*S^2) + (Pi^2*(551 + 1222*S^2 + 513*S^4))/(24*S^2) + (2040 + 3712*S^2 + 1683*S^4)/(16*S^2) + ((-519 - 971*S^2 + 56*S^4 + 56*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (146*HPL[{3, 1}, -S^2])/S^2 - (232*HPL[{2, 1, 1}, -S^2])/S^2 + ((-46 + 10*S^2 + 31*S^4 + 31*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((1798*Pi^4)/(45*S^2) + (8234 - 186*S^2 - 713*S^4)/(4*S^2) + (Pi^2*(953 - 290*S^2 - 265*S^4))/(3*S^2) + (16*(-5 + 191*S^2 + 70*S^4 + 70*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{2}, -S^2]^2*((-251*Pi^4)/(60*S^2) + (-7790 - 3126*S^2 - 559*S^4)/(32*S^2) + (Pi^2*(-1000 - 924*S^2 - 231*S^4))/(24*S^2) + ((117 + 1981*S^2 + 613*S^4 + 613*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) + (43*HPL[{4}, -S^2])/(2*S^2) + ((164 - 149*S^4)*HPL[{2, 1}, -S^2])/S^2 - (470*HPL[{3, 1}, -S^2])/S^2 + (784*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(-8 + 169*S^2 + 71*S^4 + 71*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-1078*Pi^4)/(45*S^2) + (-9084 - 1130*S^2 + 247*S^4)/(8*S^2) + (Pi^2*(-2147 + 228*S^2 + 403*S^4))/(12*S^2) + (3824*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(-29 + 779*S^2 + 281*S^4 + 281*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^3*((-5372 - 659*S^2)/192 + (Pi^2*(-1476 + 349*S^2))/288 + (Pi^4*(-15988 + 67*S^2 + 67*S^4))/(4320*(1 + S^2)) + ((-291 - 1751*S^2 - 97*S^4 - 97*S^6)*HPL[{1}, -S^2]^4)/(36*S^2*(1 + S^2)) - (73*HPL[{1}, -S^2]^5)/(9*S^2) + ((5 - 631*S^2 - 79*S^4 - 79*S^6)*HPL[{2}, -S^2]^2)/(24*S^2*(1 + S^2)) + HPL[{1}, -S^2]^3*((-106*Pi^2)/(9*S^2) + (-531 - 692*S^2 - 161*S^4)/(36*S^2) - (110*HPL[{2}, -S^2])/(3*S^2)) + ((-19*Pi^2)/(18*S^2) + (-19 - 8*S^2 + 20*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((-7 - 75*S^2 - 14*S^4 - 14*S^6)*HPL[{4}, -S^2])/(12*S^2*(1 + S^2)) + HPL[{5}, -S^2]/(3*S^2) + ((296*Pi^2)/(9*S^2) + (121 + 40*S^2 + S^4)/(3*S^2))*HPL[{2, 1}, -S^2] + ((-25 + 635*S^2 + 87*S^4 + 87*S^6)*HPL[{3, 1}, -S^2])/(6*S^2*(1 + S^2)) - (16*HPL[{3, 2}, -S^2])/(3*S^2) - (3*HPL[{4, 1}, -S^2])/S^2 + ((26 - 634*S^2 - 83*S^4 - 83*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^2*(1 + S^2)) - (646*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (1984*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (1384*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((24 + 31*S^2)*Zeta[3])/4 + HPL[{2}, -S^2]*((-34 - 490*S^2 - 77*S^4)/(24*S^2) + (Pi^2*(41 - 1081*S^2 - 79*S^4 - 79*S^6))/(72*S^2*(1 + S^2)) + (8*HPL[{3}, -S^2])/(3*S^2) + (323*HPL[{2, 1}, -S^2])/(3*S^2) - Zeta[3]/S^2) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(557 + 145*S^2))/(24*S^2) + (Pi^2*(-339 - 2883*S^2 - 113*S^4 - 113*S^6))/(72*S^2*(1 + S^2)) + ((-123 - 783*S^2 - 41*S^4 - 41*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) - (2*HPL[{3}, -S^2])/S^2 + (110*HPL[{2, 1}, -S^2])/S^2 + (11*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]*((-3997*Pi^4)/(1080*S^2) - (Pi^2*(1 + S^2)*(167 + 28*S^2))/(36*S^2) - ((1 + S^2)*(1187 + 297*S^2))/(48*S^2) + ((-187*Pi^2)/(12*S^2) + (-129 - 158*S^2 - 29*S^4)/(6*S^2))*HPL[{2}, -S^2] - (53*HPL[{2}, -S^2]^2)/(2*S^2) - (4*HPL[{3}, -S^2])/(1 + S^2) - (17*HPL[{4}, -S^2])/(3*S^2) + ((123 + 783*S^2 + 41*S^4 + 41*S^6)*HPL[{2, 1}, -S^2])/(3*S^2*(1 + S^2)) + (110*HPL[{3, 1}, -S^2])/S^2 - (220*HPL[{2, 1, 1}, -S^2])/S^2 + ((21 + 43*S^2 + 7*S^4 + 7*S^6)*Zeta[3])/(3*S^2*(1 + S^2)))) + ((4434 + 509*S^2)/4 + (Pi^2*(419 + 203*S^2 + 203*S^4))/(3*(1 + S^2)))*Zeta[5] + HPL[{2, 1}, -S^2]*((1157 - 16656*S^2 - 1297*S^4)/(16*S^2) + (Pi^2*(745 - 1722*S^2 - 347*S^4))/(12*S^2) + (Pi^4*(6450 + 18576*S^2 - 2801*S^4 - 2801*S^6))/(360*S^2*(1 + S^2)) - (32*(10 + 108*S^2 + 21*S^4 + 21*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (3284*HPL[{3, 2}, -S^2])/S^2 + (10552*HPL[{4, 1}, -S^2])/S^2 - (16*(72 + 464*S^2 + 73*S^4 + 73*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3136*HPL[{2, 2, 1}, -S^2])/S^2 + (2448*HPL[{3, 1, 1}, -S^2])/S^2 + (6320*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-854*Pi^2)/(3*S^2) - (2*(897 + 280*S^2))/S^2)*Zeta[3] - (1500*Zeta[5])/S^2) + HPL[{3}, -S^2]*((Pi^2*(285 + 4176*S^2 + 892*S^4))/(24*S^2) + (3994 + 36920*S^2 + 4223*S^4)/(32*S^2) + (Pi^4*(-28 + 14396*S^2 + 5307*S^4 + 5307*S^6))/(720*S^2*(1 + S^2)) + ((127 - 45*S^2 - 84*S^4 - 84*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + (78*HPL[{5}, -S^2])/S^2 + ((-914*Pi^2)/(3*S^2) + (-3713 - 888*S^2 + 219*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] - (7*(-29 + 195*S^2 + 89*S^4 + 89*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (16*HPL[{3, 2}, -S^2])/S^2 - (132*HPL[{4, 1}, -S^2])/S^2 + (4*(-84 + 700*S^2 + 317*S^4 + 317*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3440*HPL[{2, 2, 1}, -S^2])/S^2 + (10416*HPL[{3, 1, 1}, -S^2])/S^2 - (6960*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((10*Pi^2)/S^2 + (113 + 112*S^2 + 93*S^4)/(2*S^2))*Zeta[3] + (84*Zeta[5])/S^2) + HPL[{1}, -S^2]^3*(-(Pi^2*(1 + S^2)*(771 + 208*S^2))/(9*S^2) - ((1 + S^2)*(7849 + 1195*S^2))/(16*S^2) + (Pi^4*(-14277 - 67661*S^2 - 4759*S^4 - 4759*S^6))/(1080*S^2*(1 + S^2)) - (196*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(3*S^2*(1 + S^2)) + ((994*Pi^2)/(9*S^2) + (2043 + 2584*S^2 + 541*S^4)/(3*S^2))*HPL[{3}, -S^2] + (4*(165 + 497*S^2 + 55*S^4 + 55*S^6)*HPL[{4}, -S^2])/(3*S^2*(1 + S^2)) + (144*HPL[{5}, -S^2])/S^2 + ((784*Pi^2)/(9*S^2) - (6*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1}, -S^2] - (4*(417 + 749*S^2 + 139*S^4 + 139*S^6)*HPL[{3, 1}, -S^2])/(3*S^2*(1 + S^2)) - (3136*HPL[{3, 2}, -S^2])/(3*S^2) - (10736*HPL[{4, 1}, -S^2])/(3*S^2) + (260*(3 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (6272*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (11216*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((832*Pi^2)/(9*S^2) + (374*(1 + S^2)*(5 + S^2))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(1021 + 75*S^2))/(4*S^2) + (Pi^2*(165 - 619*S^2 + 55*S^4 + 55*S^6))/(9*S^2*(1 + S^2)) + (1568*HPL[{3}, -S^2])/(3*S^2) + (3136*HPL[{2, 1}, -S^2])/(3*S^2) + (1568*Zeta[3])/(3*S^2)) + (1520*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((30311*Pi^6)/(22680*S^2) + (Pi^4*(14198 - 6224*S^2 - 4997*S^4))/(1440*S^2) + (20900 + 911*S^2 - 1472*S^4)/(32*S^2) + (Pi^2*(4383 - 714*S^2 - 713*S^4))/(48*S^2) - (2*HPL[{3}, -S^2]^2)/S^2 + ((-71*Pi^2)/(6*S^2) + (-255 + 826*S^2 + 451*S^4)/(4*S^2))*HPL[{4}, -S^2] + ((-93 + 71*S^2 + 84*S^4 + 84*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (76*HPL[{6}, -S^2])/S^2 - (784*HPL[{2, 1}, -S^2]^2)/S^2 + ((502*Pi^2)/(3*S^2) + (2035 + 1004*S^2 + 74*S^4)/(2*S^2))*HPL[{3, 1}, -S^2] + ((-117 - 3533*S^2 - 1187*S^4 - 1187*S^6)*HPL[{3, 2}, -S^2])/(2*S^2*(1 + S^2)) + ((168 - 4972*S^2 - 1895*S^4 - 1895*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - (39*HPL[{4, 2}, -S^2])/S^2 + (86*HPL[{5, 1}, -S^2])/S^2 + ((-832*Pi^2)/(3*S^2) + (-1852 - 1160*S^2 - 193*S^4)/S^2)*HPL[{2, 1, 1}, -S^2] + (4*(-164 + 149*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(-204 - 596*S^2 + 65*S^4 + 65*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (156*HPL[{3, 1, 2}, -S^2])/S^2 - (1404*HPL[{3, 2, 1}, -S^2])/S^2 - (4912*HPL[{4, 1, 1}, -S^2])/S^2 + (16*(72 + 464*S^2 + 73*S^4 + 73*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (33808*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (6320*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-30 + 857*S^2 + 148*S^4)/S^2 + (Pi^2*(-37 + 825*S^2 + 308*S^4 + 308*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] + (16*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((875 + 3844*S^2 + 733*S^4)/(4*S^2) + (2*Pi^2*(152 + 759*S^2 + 75*S^4 + 75*S^6))/(3*S^2*(1 + S^2)) - (1496*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-48 + 896*S^2 + 205*S^4)/S^2 + (Pi^2*(-195 + 1457*S^2 + 673*S^4 + 673*S^6))/(12*S^2*(1 + S^2)) - (1720*HPL[{2, 1}, -S^2])/S^2 - (16*Zeta[3])/S^2) + ((-92 + 630*S^2 + 295*S^4 + 295*S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^2*((-52285*Pi^6)/(9072*S^2) - (Pi^2*(1 + S^2)*(3123 + 739*S^2))/(24*S^2) - ((1 + S^2)*(27105 + 3697*S^2))/(32*S^2) - (Pi^4*(1 + S^2)*(24861 + 9187*S^2))/(1440*S^2) + ((-607*Pi^2)/(6*S^2) + (-1159 - 1492*S^2 - 333*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 - (74*HPL[{3}, -S^2]^2)/S^2 + ((170*Pi^2)/(3*S^2) + (1189 + 1684*S^2 + 495*S^4)/(4*S^2))*HPL[{4}, -S^2] + (2*(159 + 375*S^2 + 53*S^4 + 53*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) + (89*HPL[{6}, -S^2])/S^2 + (1568*HPL[{2, 1}, -S^2]^2)/S^2 + ((220*Pi^2)/(3*S^2) - (52*(17 + 21*S^2 + 4*S^4))/S^2)*HPL[{3, 1}, -S^2] - (2*(837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) - (2*(2841 + 8209*S^2 + 947*S^4 + 947*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) - (234*HPL[{4, 2}, -S^2])/S^2 - (1352*HPL[{5, 1}, -S^2])/S^2 + ((-784*Pi^2)/(3*S^2) + (18*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (784*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (4*(759 + 3563*S^2 + 253*S^4 + 253*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (1328*HPL[{4, 1, 1}, -S^2])/S^2 - (780*(3 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (1328*HPL[{3, 1, 1, 1}, -S^2])/S^2 + ((3*(1 + S^2)*(677 + 91*S^2))/(2*S^2) + (Pi^2*(477 + 1309*S^2 + 159*S^4 + 159*S^6))/(3*S^2*(1 + S^2)))*Zeta[3] - (40*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((-3*(1 + S^2)*(1021 + 75*S^2))/(4*S^2) + (Pi^2*(-165 + 619*S^2 - 55*S^4 - 55*S^6))/(3*S^2*(1 + S^2)) - (1568*Zeta[3])/S^2) + HPL[{3}, -S^2]*((3*(1 + S^2)*(1423 + 289*S^2))/(4*S^2) + (2*Pi^2*(270 + 767*S^2 + 90*S^4 + 90*S^6))/(3*S^2*(1 + S^2)) - (1568*HPL[{2, 1}, -S^2])/S^2 + (100*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-2021*Pi^4)/(120*S^2) - (Pi^2*(1 + S^2)*(-479 + 11*S^2))/(12*S^2) + ((1 + S^2)*(3541 + 101*S^2))/(8*S^2) + ((837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) + (226*HPL[{4}, -S^2])/S^2 + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (1568*HPL[{3, 1}, -S^2])/S^2 - (3136*HPL[{2, 1, 1}, -S^2])/S^2 + (56*(15 + 43*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((987 + 2507*S^2 + 329*S^4 + 329*S^6)*Zeta[5])/(S^2*(1 + S^2))) + HPL[{0}, S^2]^2*((-645 - 1472*S^2)/64 + (Pi^2*(-2030 - 521*S^2))/192 + (Pi^4*(-2011 + 504*S^2))/1440 + ((-27 - 151*S^2 - 9*S^4 - 9*S^6)*HPL[{1}, -S^2]^5)/(2*S^2*(1 + S^2)) - (31*HPL[{1}, -S^2]^6)/(3*S^2) + (-(Pi^2/S^2) + (-148 - 688*S^2 - 269*S^4)/(16*S^2))*HPL[{2}, -S^2]^2 + (5*HPL[{2}, -S^2]^3)/(3*S^2) + HPL[{1}, -S^2]^4*((-749*Pi^2)/(36*S^2) + (-155 - 234*S^2 - 79*S^4)/(6*S^2) - (196*HPL[{2}, -S^2])/(3*S^2)) + (5*HPL[{3}, -S^2]^2)/(2*S^2) + ((7*Pi^2)/(4*S^2) + (86 + 122*S^2 + 47*S^4)/(8*S^2))*HPL[{4}, -S^2] + ((36 + 84*S^2 + 47*S^4 + 47*S^6)*HPL[{5}, -S^2])/(4*S^2*(1 + S^2)) - (10*HPL[{6}, -S^2])/S^2 + (21*HPL[{2, 1}, -S^2]^2)/S^2 + ((-29*Pi^2)/(3*S^2) + (-65 + 552*S^2 + 256*S^4)/(4*S^2))*HPL[{3, 1}, -S^2] + ((48 - 120*S^2 - 83*S^4 - 83*S^6)*HPL[{3, 2}, -S^2])/(4*S^2*(1 + S^2)) + ((32 - 236*S^2 - 133*S^4 - 133*S^6)*HPL[{4, 1}, -S^2])/(2*S^2*(1 + S^2)) + (5*HPL[{4, 2}, -S^2])/(2*S^2) - (7*HPL[{5, 1}, -S^2])/S^2 + ((53*Pi^2)/(3*S^2) + (56 - 570*S^2 - 265*S^4)/(2*S^2))*HPL[{2, 1, 1}, -S^2] - (4*(80 + 295*S^2 + 2*S^4 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) + ((-965 - 3457*S^2 + 19*S^4 + 19*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (4*HPL[{3, 1, 2}, -S^2])/S^2 + (36*HPL[{3, 2, 1}, -S^2])/S^2 + (156*HPL[{4, 1, 1}, -S^2])/S^2 - (2*(-325 - 1109*S^2 + 35*S^4 + 35*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (160*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (280*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((199 + 66*S^2)/4 + (Pi^2*(82 + 75*S^2 + 75*S^4))/(12*(1 + S^2)))*Zeta[3] + HPL[{2, 1}, -S^2]*((685 - 8*S^2 - 51*S^4)/(8*S^2) + (Pi^2*(388 + 1654*S^2 - 37*S^4 - 37*S^6))/(12*S^2*(1 + S^2)) - (84*Zeta[3])/S^2) + HPL[{3}, -S^2]*((107 + 468*S^2 + 191*S^4)/(16*S^2) + (Pi^2*(4 + 104*S^2 + 61*S^4 + 61*S^6))/(24*S^2*(1 + S^2)) - (44*HPL[{2, 1}, -S^2])/S^2 + (8*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((-13*(1 + S^2)*(81 + 43*S^2))/(24*S^2) + (Pi^2*(-249 - 1747*S^2 - 83*S^4 - 83*S^6))/(18*S^2*(1 + S^2)) + ((-255 - 1823*S^2 - 85*S^4 - 85*S^6)*HPL[{2}, -S^2])/(6*S^2*(1 + S^2)) + (44*HPL[{3}, -S^2])/(3*S^2) + (784*HPL[{2, 1}, -S^2])/(3*S^2) + (82*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((323*Pi^4)/(360*S^2) + (532 - 1242*S^2 - 713*S^4)/(32*S^2) + (Pi^2*(32 - 660*S^2 - 253*S^4))/(48*S^2) + (3*(-9 + 19*S^2 + 13*S^4 + 13*S^6)*HPL[{3}, -S^2])/(4*S^2*(1 + S^2)) - (13*HPL[{4}, -S^2])/(2*S^2) + (2*(80 + 295*S^2 + 2*S^4 + 2*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (24*HPL[{3, 1}, -S^2])/S^2 - (42*HPL[{2, 1, 1}, -S^2])/S^2 + ((-17 + 61*S^2 + 28*S^4 + 28*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + HPL[{1}, -S^2]^2*((-8449*Pi^4)/(720*S^2) - (Pi^2*(1 + S^2)*(247 + 125*S^2))/(16*S^2) - ((1 + S^2)*(435 + 262*S^2))/(8*S^2) + ((-211*Pi^2)/(4*S^2) + (-98 - 153*S^2 - 55*S^4)/(2*S^2))*HPL[{2}, -S^2] - (215*HPL[{2}, -S^2]^2)/(2*S^2) + ((75 + 163*S^2 + 25*S^4 + 25*S^6)*HPL[{3}, -S^2])/(2*S^2*(1 + S^2)) + (4*HPL[{4}, -S^2])/S^2 + ((255 + 1823*S^2 + 85*S^4 + 85*S^6)*HPL[{2, 1}, -S^2])/(2*S^2*(1 + S^2)) + (386*HPL[{3, 1}, -S^2])/S^2 - (784*HPL[{2, 1, 1}, -S^2])/S^2 + ((99 + 263*S^2 + 33*S^4 + 33*S^6)*Zeta[3])/(2*S^2*(1 + S^2))) + (3*(13 + 11*S^2 + 11*S^4)*Zeta[5])/(1 + S^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(1263 + 677*S^2))/(96*S^2) - ((1 + S^2)*(2761 + 2115*S^2))/(64*S^2) + (Pi^4*(-3303 - 37099*S^2 - 1101*S^4 - 1101*S^6))/(1440*S^2*(1 + S^2)) + ((-99 - 529*S^2 - 33*S^4 - 33*S^6)*HPL[{2}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((25*Pi^2)/(6*S^2) + (30 + 43*S^2 + 13*S^4)/S^2)*HPL[{3}, -S^2] + ((93 + 125*S^2 + 31*S^4 + 31*S^6)*HPL[{4}, -S^2])/(4*S^2*(1 + S^2)) + (12*HPL[{5}, -S^2])/S^2 + ((211*Pi^2)/(2*S^2) + (98 + 153*S^2 + 55*S^4)/S^2)*HPL[{2, 1}, -S^2] + ((123 + 895*S^2 + 41*S^4 + 41*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (42*HPL[{3, 2}, -S^2])/S^2 - (134*HPL[{4, 1}, -S^2])/S^2 + ((-255 - 1823*S^2 - 85*S^4 - 85*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (860*HPL[{2, 2, 1}, -S^2])/S^2 - (2492*HPL[{3, 1, 1}, -S^2])/S^2 + (1568*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((41*Pi^2)/(6*S^2) + ((1 + S^2)*(201 + 55*S^2))/(4*S^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(513 + 367*S^2))/(16*S^2) + (Pi^2*(-147 - 1413*S^2 - 49*S^4 - 49*S^6))/(12*S^2*(1 + S^2)) + (21*HPL[{3}, -S^2])/S^2 + (430*HPL[{2, 1}, -S^2])/S^2 + (39*Zeta[3])/S^2) + (39*Zeta[5])/S^2)) + HPL[{0}, S^2]*((Pi^4*(-17746 - 2291*S^2))/960 + (Pi^2*(-7187 - 1061*S^2))/48 - (3*(10925 + 1507*S^2))/32 + (Pi^6*(-248987 - 30737*S^2 - 30737*S^4))/(45360*(1 + S^2)) - (28*(3 + 11*S^2 + S^4 + S^6)*HPL[{1}, -S^2]^6)/(3*S^2*(1 + S^2)) - (32*HPL[{1}, -S^2]^7)/(3*S^2) + ((23 - 685*S^2 - 196*S^4 - 196*S^6)*HPL[{2}, -S^2]^3)/(6*S^2*(1 + S^2)) + HPL[{1}, -S^2]^5*((-241*Pi^2)/(9*S^2) + (-83 - 106*S^2 - 23*S^4)/S^2 - (100*HPL[{2}, -S^2])/S^2) + ((-32 - 24*S^2 + 3*S^4 + 3*S^6)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((-25*Pi^2)/(6*S^2) + (-131 - 112*S^2 + 75*S^4)/(4*S^2))*HPL[{5}, -S^2] + ((-100 - 246*S^2 - 45*S^4 - 45*S^6)*HPL[{6}, -S^2])/(2*S^2*(1 + S^2)) + (50*HPL[{7}, -S^2])/S^2 + (4*(2 + 394*S^2 + 95*S^4 + 95*S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-41*Pi^2)/(3*S^2) + (-207 - 364*S^2 - 335*S^4)/(4*S^2))*HPL[{3, 2}, -S^2] + ((-17*Pi^2)/(3*S^2) + (-65 - 402*S^2 - 473*S^4)/(2*S^2))*HPL[{4, 1}, -S^2] + ((8 - 9*S^4)*HPL[{4, 2}, -S^2])/(2*S^2) + (64*HPL[{4, 3}, -S^2])/S^2 + ((5 + 113*S^2 + 10*S^4 + 10*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) + (185*HPL[{5, 2}, -S^2])/S^2 + (396*HPL[{6, 1}, -S^2])/S^2 + ((-2180*Pi^2)/(3*S^2) + (-2312 - 784*S^2 - 55*S^4)/S^2)*HPL[{2, 2, 1}, -S^2] + ((-6656*Pi^2)/(3*S^2) + (-7025 - 2280*S^2 - 32*S^4)/S^2)*HPL[{3, 1, 1}, -S^2] + ((-16 - 3*S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((76 - 2756*S^2 - 787*S^4 - 787*S^6)*HPL[{3, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (22*HPL[{3, 2, 2}, -S^2])/S^2 + (64*HPL[{3, 3, 1}, -S^2])/S^2 - (2*(-168 + 4172*S^2 + 1191*S^4 + 1191*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (74*HPL[{4, 1, 2}, -S^2])/S^2 + (314*HPL[{4, 2, 1}, -S^2])/S^2 + (612*HPL[{5, 1, 1}, -S^2])/S^2 + ((4564*Pi^2)/(3*S^2) - (2*(-2370 - 686*S^2 + 89*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (5968*HPL[{2, 2, 2, 1}, -S^2])/S^2 + (4*(-93 + 1407*S^2 + 403*S^4 + 403*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (18104*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (18104*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (36008*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (107488*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (120*(-5 + 95*S^2 + 27*S^4 + 27*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (12272*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (36816*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (60800*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (25440*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(326 + 211*S^2))/12 + (441 + 233*S^2)/4)*Zeta[3] - (2*(17 + 5*S^2 + 5*S^4)*Zeta[3]^2)/(1 + S^2) + HPL[{4}, -S^2]*((-193 - 398*S^2 + 85*S^4)/(8*S^2) + (Pi^2*(23 - 137*S^2 - 29*S^4 - 29*S^6))/(12*S^2*(1 + S^2)) + (58*HPL[{2, 1}, -S^2])/S^2 - (26*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((-97 - 2378*S^2 - 482*S^4)/S^2 + (Pi^2*(101 - 2059*S^2 - 488*S^4 - 488*S^6))/(3*S^2*(1 + S^2)) - (8*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((8 - 1139*S^2 - 228*S^4)/(4*S^2) + (Pi^2*(-3 - 2207*S^2 - 459*S^4 - 459*S^6))/(24*S^2*(1 + S^2)) - (2*HPL[{3}, -S^2])/S^2 + (746*HPL[{2, 1}, -S^2])/S^2 - (2*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((49 + 1184*S^2 + 237*S^4)/S^2 + (Pi^2*(-59 + 1021*S^2 + 245*S^4 + 245*S^6))/(3*S^2*(1 + S^2)) + (16*Zeta[3])/S^2) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(1023 + 221*S^2))/(24*S^2) + (Pi^2*(-1551 - 6371*S^2 - 517*S^4 - 517*S^6))/(36*S^2*(1 + S^2)) - (125*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2])/(2*S^2*(1 + S^2)) + (34*HPL[{3}, -S^2])/(3*S^2) + (500*HPL[{2, 1}, -S^2])/S^2 + (166*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((11423*Pi^4)/(180*S^2) + (Pi^2*(2854 + 846*S^2 - 85*S^4))/(12*S^2) + (10164 + 2402*S^2 - 55*S^4)/(8*S^2) - (3072*HPL[{3, 1}, -S^2])/S^2 - (6136*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(-128 - 292*S^2 + S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((-21*Pi^4)/(10*S^2) + (Pi^2*(-127 + 56*S^2 + 173*S^4))/(24*S^2) + (-304 - 298*S^2 + 187*S^4)/(8*S^2) - (32*HPL[{4}, -S^2])/S^2 + ((-49 - 201*S^2 + 13*S^4 + 13*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (48*HPL[{3, 1}, -S^2])/S^2 + (88*HPL[{2, 1, 1}, -S^2])/S^2 + ((21 + 29*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{1}, -S^2]^3*((-4061*Pi^4)/(180*S^2) - ((1 + S^2)*(896 + 159*S^2))/(2*S^2) - (Pi^2*(1 + S^2)*(3021 + 851*S^2))/(36*S^2) + ((-120*Pi^2)/S^2 - (5*(239 + 294*S^2 + 55*S^4))/(3*S^2))*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(3*S^2) + (2*(21 + 89*S^2 + 7*S^4 + 7*S^6)*HPL[{3}, -S^2])/(3*S^2*(1 + S^2)) - (92*HPL[{4}, -S^2])/(3*S^2) + (250*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (1000*HPL[{3, 1}, -S^2])/S^2 - (2000*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(129 + 461*S^2 + 43*S^4 + 43*S^6)*Zeta[3])/(3*S^2*(1 + S^2))) + ((180 + 133*S^2)*Zeta[5])/2 + HPL[{2}, -S^2]*((-1317 - 10998*S^2 - 1423*S^4)/(16*S^2) + (Pi^2*(-131 - 2868*S^2 - 559*S^4))/(24*S^2) + (Pi^4*(218 - 4092*S^2 - 781*S^4 - 781*S^6))/(144*S^2*(1 + S^2)) + ((19*Pi^2)/(3*S^2) + (93 + 176*S^2 + 167*S^4)/(4*S^2))*HPL[{3}, -S^2] + ((64 + 48*S^2 + 3*S^4 + 3*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + (37*HPL[{5}, -S^2])/S^2 + ((1090*Pi^2)/(3*S^2) + (2312 + 784*S^2 + 55*S^4)/(2*S^2))*HPL[{2, 1}, -S^2] + ((3 + 1571*S^2 + 379*S^4 + 379*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) + (8*HPL[{3, 2}, -S^2])/S^2 - (34*HPL[{4, 1}, -S^2])/S^2 - (8*(2 + 394*S^2 + 95*S^4 + 95*S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (2984*HPL[{2, 2, 1}, -S^2])/S^2 + (9040*HPL[{3, 1, 1}, -S^2])/S^2 + (6136*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-4*Pi^2)/(3*S^2) + (18 + 238*S^2 + 109*S^4)/(2*S^2))*Zeta[3] - (24*Zeta[5])/S^2) + HPL[{1}, -S^2]^2*((-3*(1 + S^2)*(7849 + 1195*S^2))/(32*S^2) - (Pi^2*(1 + S^2)*(6229 + 1395*S^2))/(48*S^2) + (Pi^4*(-6573 - 30939*S^2 - 2191*S^4 - 2191*S^6))/(360*S^2*(1 + S^2)) - (98*(3 + 11*S^2 + S^4 + S^6)*HPL[{2}, -S^2]^2)/(S^2*(1 + S^2)) + ((11*Pi^2)/(3*S^2) + (2*(-11 + 3*S^2 + 14*S^4))/S^2)*HPL[{3}, -S^2] + ((-87 - 271*S^2 - 29*S^4 - 29*S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) - (46*HPL[{5}, -S^2])/S^2 + ((360*Pi^2)/S^2 + (5*(239 + 294*S^2 + 55*S^4))/S^2)*HPL[{2, 1}, -S^2] + (6*(189 + 689*S^2 + 63*S^4 + 63*S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (152*HPL[{3, 2}, -S^2])/S^2 - (364*HPL[{4, 1}, -S^2])/S^2 - (750*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (3136*HPL[{2, 2, 1}, -S^2])/S^2 - (9272*HPL[{3, 1, 1}, -S^2])/S^2 + (6000*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((94*Pi^2)/(3*S^2) + ((1 + S^2)*(217 + 111*S^2))/(2*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-3*(1 + S^2)*(1687 + 289*S^2))/(8*S^2) + (Pi^2*(-1371 - 5691*S^2 - 457*S^4 - 457*S^6))/(12*S^2*(1 + S^2)) + (76*HPL[{3}, -S^2])/S^2 + (1568*HPL[{2, 1}, -S^2])/S^2 + (164*Zeta[3])/S^2) + (130*Zeta[5])/S^2) + HPL[{1}, -S^2]*((-248987*Pi^6)/(45360*S^2) - (Pi^2*(1 + S^2)*(6563 + 1251*S^2))/(48*S^2) - ((1 + S^2)*(27105 + 3697*S^2))/(32*S^2) - (Pi^4*(1 + S^2)*(25775 + 6533*S^2))/(1440*S^2) + ((-551*Pi^2)/(6*S^2) + (-1159 - 1492*S^2 - 333*S^4)/(4*S^2))*HPL[{2}, -S^2]^2 - (118*HPL[{2}, -S^2]^3)/S^2 + (4*HPL[{3}, -S^2]^2)/S^2 + ((-40*Pi^2)/(3*S^2) + (3*(-81 - 80*S^2 + S^4))/(4*S^2))*HPL[{4}, -S^2] + ((-51 - 143*S^2 - 17*S^4 - 17*S^6)*HPL[{5}, -S^2])/(S^2*(1 + S^2)) - (73*HPL[{6}, -S^2])/S^2 + (1568*HPL[{2, 1}, -S^2]^2)/S^2 + ((360*Pi^2)/S^2 + (1203 + 1480*S^2 + 277*S^4)/S^2)*HPL[{3, 1}, -S^2] - (38*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 2}, -S^2])/(S^2*(1 + S^2)) + ((-255 - 983*S^2 - 85*S^4 - 85*S^6)*HPL[{4, 1}, -S^2])/(S^2*(1 + S^2)) + (108*HPL[{5, 1}, -S^2])/S^2 + ((-720*Pi^2)/S^2 - (10*(239 + 294*S^2 + 55*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (784*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 2, 1}, -S^2])/(S^2*(1 + S^2)) - (4*(1743 + 6379*S^2 + 581*S^4 + 581*S^6)*HPL[{3, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (2832*HPL[{3, 2, 1}, -S^2])/S^2 - (8680*HPL[{4, 1, 1}, -S^2])/S^2 + (1500*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (6000*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (12000*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (((1 + S^2)*(425 + 223*S^2))/(4*S^2) + (Pi^2*(171 + 547*S^2 + 57*S^4 + 57*S^6))/(6*S^2*(1 + S^2)))*Zeta[3] - (34*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((3*(1 + S^2)*(1687 + 289*S^2))/(4*S^2) + (Pi^2*(1371 + 5691*S^2 + 457*S^4 + 457*S^6))/(6*S^2*(1 + S^2)) - (328*Zeta[3])/S^2) + HPL[{3}, -S^2]*(((1 + S^2)*(-109 + 49*S^2))/(2*S^2) + (Pi^2*(21 + 65*S^2 + 7*S^4 + 7*S^6))/(6*S^2*(1 + S^2)) - (152*HPL[{2, 1}, -S^2])/S^2 + (8*Zeta[3])/S^2) + HPL[{2}, -S^2]*((-2155*Pi^4)/(72*S^2) - (Pi^2*(1 + S^2)*(1453 + 333*S^2))/(12*S^2) - ((1 + S^2)*(5471 + 759*S^2))/(8*S^2) + (19*(3 + 11*S^2 + S^4 + S^6)*HPL[{3}, -S^2])/(S^2*(1 + S^2)) - (8*HPL[{4}, -S^2])/S^2 + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) + (1568*HPL[{3, 1}, -S^2])/S^2 - (3136*HPL[{2, 1, 1}, -S^2])/S^2 + (41*(3 + 11*S^2 + S^4 + S^6)*Zeta[3])/(S^2*(1 + S^2))) + (2*(57 + 187*S^2 + 19*S^4 + 19*S^6)*Zeta[5])/(S^2*(1 + S^2)))) + (3*(322 + 151*S^2 + 151*S^4)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(6577 + 1425*S^2))/(48*S^2) - (3*(1 + S^2)*(10940 + 1507*S^2))/(32*S^2) - (Pi^4*(1 + S^2)*(47125 + 15279*S^2))/(2880*S^2) + (Pi^6*(-10959 - 63244*S^2 - 3653*S^4 - 3653*S^6))/(4536*S^2*(1 + S^2)) + (83*(3 + S^4)*HPL[{2}, -S^2]^3)/(6*S^2) - (37*(3 + 11*S^2 + S^4 + S^6)*HPL[{3}, -S^2]^2)/(2*S^2*(1 + S^2)) + ((40*Pi^2)/S^2 + (557 + 800*S^2 + 243*S^4)/(2*S^2))*HPL[{5}, -S^2] + (2*(156 + 245*S^2 + 52*S^4 + 52*S^6)*HPL[{6}, -S^2])/(S^2*(1 + S^2)) + (30*HPL[{7}, -S^2])/S^2 + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1}, -S^2]^2)/(S^2*(1 + S^2)) + ((-826*Pi^2)/(3*S^2) + (-1735 - 2152*S^2 - 417*S^4)/S^2)*HPL[{3, 2}, -S^2] + ((-2818*Pi^2)/(3*S^2) + (-11599 - 14596*S^2 - 2997*S^4)/(2*S^2))*HPL[{4, 1}, -S^2] - (117*(3 + 11*S^2 + S^4 + S^6)*HPL[{4, 2}, -S^2])/(2*S^2*(1 + S^2)) + (94*HPL[{4, 3}, -S^2])/S^2 - (26*(51 + 155*S^2 + 17*S^4 + 17*S^6)*HPL[{5, 1}, -S^2])/(S^2*(1 + S^2)) + (204*HPL[{5, 2}, -S^2])/S^2 - (98*HPL[{6, 1}, -S^2])/S^2 + ((-2428*Pi^2)/(3*S^2) - (2*(1159 + 1492*S^2 + 333*S^4))/S^2)*HPL[{2, 2, 1}, -S^2] + ((-5296*Pi^2)/(3*S^2) - (4*(717 + 946*S^2 + 229*S^4))/S^2)*HPL[{3, 1, 1}, -S^2] + (332*(3 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (3260*HPL[{3, 2, 2}, -S^2])/S^2 + (9968*HPL[{3, 3, 1}, -S^2])/S^2 + (4*(1077 + 1741*S^2 + 359*S^4 + 359*S^6)*HPL[{4, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (9812*HPL[{4, 1, 2}, -S^2])/S^2 + (30404*HPL[{4, 2, 1}, -S^2])/S^2 + (62640*HPL[{5, 1, 1}, -S^2])/S^2 + ((1568*Pi^2)/(3*S^2) - (36*(75 + 86*S^2 + 11*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (8*(417 + 749*S^2 + 139*S^4 + 139*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S^2*(1 + S^2)) - (6272*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (6272*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (6272*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (21472*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (1560*(3 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (12544*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (37632*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (77920*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + ((1013*Pi^4)/(60*S^2) + ((1 + S^2)*(2253 + 215*S^2))/(2*S^2) + (Pi^2*(1 + S^2)*(2071 + 429*S^2))/(12*S^2))*Zeta[3] + ((-33 - 113*S^2 - 11*S^4 - 11*S^6)*Zeta[3]^2)/(S^2*(1 + S^2)) + HPL[{3, 1}, -S^2]*((-3*(1 + S^2)*(1293 + 227*S^2))/(4*S^2) - (2*Pi^2*(147 - 73*S^2 + 49*S^4 + 49*S^6))/(3*S^2*(1 + S^2)) - (1616*Zeta[3])/S^2) + HPL[{4}, -S^2]*(((1 + S^2)*(1241 + 483*S^2))/(4*S^2) + (Pi^2*(753 + 2113*S^2 + 251*S^4 + 251*S^6))/(12*S^2*(1 + S^2)) - (452*HPL[{2, 1}, -S^2])/S^2 + (56*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((-3*(1 + S^2)*(1553 + 351*S^2))/(16*S^2) + (Pi^2*(-393 - 1607*S^2 - 131*S^4 - 131*S^6))/(6*S^2*(1 + S^2)) + (466*HPL[{3}, -S^2])/S^2 + (354*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((3*(1 + S^2)*(1021 + 75*S^2))/(2*S^2) + (2*Pi^2*(165 - 619*S^2 + 55*S^4 + 55*S^6))/(3*S^2*(1 + S^2)) + (3136*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((2021*Pi^4)/(60*S^2) + (Pi^2*(1 + S^2)*(-479 + 11*S^2))/(6*S^2) - ((1 + S^2)*(3541 + 101*S^2))/(4*S^2) - (3136*HPL[{3, 1}, -S^2])/S^2 - (6272*HPL[{2, 1, 1}, -S^2])/S^2 - (112*(15 + 43*S^2 + 5*S^4 + 5*S^6)*Zeta[3])/(S^2*(1 + S^2))) + HPL[{3}, -S^2]*((601*Pi^4)/(30*S^2) + (13*(1 + S^2)*(351 + 55*S^2))/(4*S^2) + (Pi^2*(1 + S^2)*(2163 + 593*S^2))/(12*S^2) - (86*HPL[{4}, -S^2])/S^2 - (2*(837 + 2405*S^2 + 279*S^4 + 279*S^6)*HPL[{2, 1}, -S^2])/(S^2*(1 + S^2)) - (1568*HPL[{3, 1}, -S^2])/S^2 + (3136*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(39 + 139*S^2 + 13*S^4 + 13*S^6)*Zeta[3])/(S^2*(1 + S^2))) + ((419*Pi^2)/(3*S^2) + ((1 + S^2)*(2233 + 367*S^2))/(2*S^2))*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(-1275 + 71*S^2))/(24*S^2) - ((1 + S^2)*(-16995 + 79*S^2))/(32*S^2) + (Pi^4*(384 - 5679*S^2 + 128*S^4 + 128*S^6))/(180*S^2*(1 + S^2)) + ((413*Pi^2)/(3*S^2) + (1735 + 2152*S^2 + 417*S^4)/(2*S^2))*HPL[{3}, -S^2] + (113*(3 + 11*S^2 + S^4 + S^6)*HPL[{4}, -S^2])/(2*S^2*(1 + S^2)) + (164*HPL[{5}, -S^2])/S^2 + ((1214*Pi^2)/(3*S^2) + (1159 + 1492*S^2 + 333*S^4)/S^2)*HPL[{2, 1}, -S^2] + (392*(3 + 11*S^2 + S^4 + S^6)*HPL[{3, 1}, -S^2])/(S^2*(1 + S^2)) - (1708*HPL[{3, 2}, -S^2])/S^2 - (5140*HPL[{4, 1}, -S^2])/S^2 - (784*(3 + 11*S^2 + S^4 + S^6)*HPL[{2, 1, 1}, -S^2])/(S^2*(1 + S^2)) + (3136*HPL[{3, 1, 1}, -S^2])/S^2 + (6272*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((431*Pi^2)/(3*S^2) + ((1 + S^2)*(871 + 209*S^2))/S^2)*Zeta[3] + (722*Zeta[5])/S^2) + (966*Zeta[7])/S^2));
E5wuvT3F1=(-3*(-8365 + 1802*S^2))/(64*S) + (Pi^2*(734 - 861*S^2 + 478*S^4))/(96*S) + (Pi^8*S*(-27331 + 1194*S^2 + 597*S^4))/(56700*(1 + S^2)^2) + (Pi^4*(1075 + 1349*S^2 + 2147*S^4))/(1440*S) + (Pi^6*(10192 - 21189*S^2 + 2468*S^4))/(60480*S) - (S*HPL[{0}, S^2]^8)/(192*(1 + S^2)^2) + ((3 + 40*S^2 - 174*S^4 + 216*S^6 - 21*S^8)*HPL[{1}, -S^2]^7)/(21*S^3*(1 + S^2)^2) + (2*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^8)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^7*((S*(-17 - 4*S^2 + S^4))/(192*(1 + S^2)^2) - (S*(7 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(96*(1 + S^2)^2)) + ((Pi^2*S*(-5 + 22*S^2 + 11*S^4))/(3*(1 + S^2)^2) + (-4 - 10*S^2 - 3*S^4 + 2*S^6)/(3*S^3))*HPL[{2}, -S^2]^3 + (S*(-41 + 14*S^2 + 7*S^4)*HPL[{2}, -S^2]^4)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^6*(((1 + S^2)*(33 + 35*S^2))/(36*S^3) + (Pi^2*S*(-137 + 74*S^2 + 37*S^4))/(18*(1 + S^2)^2) - (13*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^6*((6 - 31*S^2 - 20*S^4)/(384*S) - (Pi^2*S*(51 + 10*S^2 + 5*S^4))/(576*(1 + S^2)^2) + ((3 + 64*S^2 - 110*S^4 - 58*S^6 - 31*S^8)*HPL[{1}, -S^2])/(192*S^3*(1 + S^2)^2) - (S*(19 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(48*(1 + S^2)^2) - (S*(18 + 10*S^2 + 5*S^4)*HPL[{2}, -S^2])/(96*(1 + S^2)^2)) + ((Pi^2*S*(-15 + 44*S^2 + 22*S^4))/(6*(1 + S^2)^2) + (1 - 42*S^2 + 197*S^4 - 12*S^6)/(8*S^3))*HPL[{3}, -S^2]^2 - (S*(2 + 22*S^2 + 11*S^4)*HPL[{4}, -S^2]^2)/(1 + S^2)^2 + (-(Pi^2*S*(-4 + 126*S^2 + 63*S^4))/(6*(1 + S^2)^2) + (-320 - 18*S^2 - 115*S^4 + 3*S^6)/S^3)*HPL[{6}, -S^2] + ((525 + 845*S^2 - 251*S^4 - 663*S^6 - 62*S^8)*HPL[{7}, -S^2])/(S^3*(1 + S^2)^2) - (2*S*(-22 + 10*S^2 + 5*S^4)*HPL[{8}, -S^2])/(1 + S^2)^2 + (-(Pi^2*S*(-495 + 224*S^2 + 112*S^4))/(3*(1 + S^2)^2) + (22 - 138*S^2 + 49*S^4 - 4*S^6)/(2*S^3))*HPL[{2, 1}, -S^2]^2 + (2*S*(-413 + 106*S^2 + 53*S^4)*HPL[{3, 1}, -S^2]^2)/(1 + S^2)^2 + ((Pi^2*S*(-5 + 28*S^2 + 14*S^4))/(1 + S^2)^2 + (-1 - 36*S^2 + 251*S^4 - 16*S^6)/(4*S^3))*HPL[{4, 2}, -S^2] + ((-9 - 26*S^2 - 67*S^4 - 256*S^6 - 18*S^8)*HPL[{4, 3}, -S^2])/(2*S^3*(1 + S^2)^2) + ((Pi^2*S*(-117 + 458*S^2 + 229*S^4))/(3*(1 + S^2)^2) + (237 + 156*S^2 + 756*S^4 - 70*S^6)/(2*S^3))*HPL[{5, 1}, -S^2] + ((-39 - 60*S^2 - 53*S^4 - 430*S^6 + 10*S^8)*HPL[{5, 2}, -S^2])/(2*S^3*(1 + S^2)^2) - (S*(5 + 34*S^2 + 17*S^4)*HPL[{5, 3}, -S^2])/(1 + S^2)^2 + ((-234 - 475*S^2 + 268*S^4 + 837*S^6 + 230*S^8)*HPL[{6, 1}, -S^2])/(S^3*(1 + S^2)^2) - (3*S*(1 + 22*S^2 + 11*S^4)*HPL[{6, 2}, -S^2])/(1 + S^2)^2 + (6*S*(16 + 50*S^2 + 25*S^4)*HPL[{7, 1}, -S^2])/(1 + S^2)^2 + (16*S*(-171 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(1 + S^2)^2 + ((-13*Pi^2*S)/2 + (49 + 12*S^2 - 119*S^4 + 4*S^6)/(4*S^3))*HPL[{3, 1, 2}, -S^2] + ((Pi^2*S*(-93 + 326*S^2 + 163*S^4))/(2*(1 + S^2)^2) + (-79 - 308*S^2 - 215*S^4 + 68*S^6)/(4*S^3))*HPL[{3, 2, 1}, -S^2] + ((15 + 8*S^2 + 745*S^4 - 4750*S^6 + 1018*S^8)*HPL[{3, 2, 2}, -S^2])/(2*S^3*(1 + S^2)^2) + (2*(3 + 4*S^2 + 504*S^4 - 3746*S^6 + 735*S^8)*HPL[{3, 3, 1}, -S^2])/(S^3*(1 + S^2)^2) + (2*S*(-71 + 124*S^2 + 62*S^4)*HPL[{3, 3, 2}, -S^2])/(1 + S^2)^2 + ((Pi^2*S*(-215 + 1194*S^2 + 597*S^4))/(3*(1 + S^2)^2) + (-298 - 752*S^2 - 591*S^4 + 124*S^6)/(2*S^3))*HPL[{4, 1, 1}, -S^2] + ((15 + 10*S^2 + 1865*S^4 - 14788*S^6 + 2966*S^8)*HPL[{4, 1, 2}, -S^2])/(2*S^3*(1 + S^2)^2) - (2*S*(-137 + 180*S^2 + 90*S^4)*HPL[{4, 1, 3}, -S^2])/(1 + S^2)^2 + ((15 + 34*S^2 + 6077*S^4 - 46060*S^6 + 8690*S^8)*HPL[{4, 2, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(-79 + 218*S^2 + 109*S^4)*HPL[{4, 2, 2}, -S^2])/(1 + S^2)^2 - (2*S*(-381 + 692*S^2 + 346*S^4)*HPL[{4, 3, 1}, -S^2])/(1 + S^2)^2 + (2*(60 + 196*S^2 + 3143*S^4 - 24047*S^6 + 4266*S^8)*HPL[{5, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (2*S*(-227 + 390*S^2 + 195*S^4)*HPL[{5, 1, 2}, -S^2])/(1 + S^2)^2 - (2*S*(-1547 + 2910*S^2 + 1455*S^4)*HPL[{5, 2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-3938 + 7782*S^2 + 3891*S^4)*HPL[{6, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(15 + 202*S^2 - 558*S^4 + 131*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(S^3*(1 + S^2)) + ((-8*Pi^2*S*(-7 + 96*S^2 + 48*S^4))/(3*(1 + S^2)^2) + (135 + 296*S^2 + 201*S^4 - 52*S^6)/S^3)*HPL[{3, 1, 1, 1}, -S^2] + (2*(96 + 1295*S^2 - 2369*S^4 - 125*S^6 + 307*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(S^3*(1 + S^2)^2) + (2*(96 + 1295*S^2 - 2369*S^4 - 125*S^6 + 307*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-109 + 94*S^2 + 47*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(1 + S^2)^2 + (2*(186 + 2597*S^2 - 4505*S^4 - 2687*S^6 + 1093*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-109 + 94*S^2 + 47*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(1 + S^2)^2 - (S*(669 + 962*S^2 + 481*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(1 + S^2)^2 - (48*S*(35 + 66*S^2 + 33*S^4)*HPL[{3, 3, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(513 + 7646*S^2 - 14003*S^4 - 7112*S^6 + 3288*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (26*S*(-5 + 26*S^2 + 13*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (2*S*(905 + 1246*S^2 + 623*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(2585 + 4414*S^2 + 2207*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*S*(2763 + 3886*S^2 + 1943*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((32*Pi^2*S*(-19 + 60*S^2 + 30*S^4))/(3*(1 + S^2)^2) + (48*(-4 - 9*S^2 - 6*S^4 + 2*S^6))/S^3)*HPL[{2, 1, 1, 1, 1}, -S^2] + (8*(-18 - 220*S^2 + 515*S^4 - 734*S^6 + 117*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (24*(-18 - 220*S^2 + 515*S^4 - 734*S^6 + 117*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - 1056*S*HPL[{2, 2, 1, 2, 1}, -S^2] - 3168*S*HPL[{2, 2, 2, 1, 1}, -S^2] + (8*(-81 - 1054*S^2 + 2876*S^4 - 5046*S^6 + 845*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + 6160*S*HPL[{3, 1, 1, 1, 2}, -S^2] + 10384*S*HPL[{3, 1, 1, 2, 1}, -S^2] + 12496*S*HPL[{3, 1, 2, 1, 1}, -S^2] + 26224*S*HPL[{3, 2, 1, 1, 1}, -S^2] + (32*S*(2513 + 4860*S^2 + 2430*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (8*(45 + 479*S^2 - 1180*S^4 + 334*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - (16*S*(241 + 150*S^2 + 75*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 3840*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (S^(-1) + (Pi^2*S*(-79 + 16*S^2 + 8*S^4))/(9*(1 + S^2)^2) + (S*(-23 + 16*S^2 + 8*S^4)*HPL[{0}, S^2]^2)/(3*(1 + S^2)^2) + ((3 + 40*S^2 - 174*S^4 + 216*S^6 - 21*S^8)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) + (56*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{0}, S^2]*(-(S*(83 - 120*S^2 + 21*S^4))/(3*(1 + S^2)^2) + (56*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2)) + (16*S*HPL[{2}, -S^2])/3)*Log[T]^6 + ((-32*S*(-1 + S^2))/(3*(1 + S^2)^2) - (16*S*(-1 + 2*S^2 + S^4)*HPL[{0}, S^2])/(3*(1 + S^2)^2) - (16*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(3*(1 + S^2)^2))*Log[T]^7 - (8*S*Log[T]^8)/(3*(1 + S^2)^2) + ((-12 + 47*S^2 - 44*S^4)/(4*S) - (Pi^2*S*(40 + 22*S^2 + 11*S^4))/(6*(1 + S^2)^2))*Zeta[3]^2 + HPL[{0}, S^2]^5*((75 - 1967*S^2 - 100*S^4)/(960*S) - (Pi^2*S*(1555 + 484*S^2 + 101*S^4))/(1440*(1 + S^2)^2) + ((45 + 660*S^2 - 1490*S^4 - 114*S^6 - 177*S^8)*HPL[{1}, -S^2]^2)/(480*S^3*(1 + S^2)^2) + (S*(-263 + 16*S^2 + 8*S^4)*HPL[{1}, -S^2]^3)/(180*(1 + S^2)^2) + ((-15 - 30*S^2 - 395*S^4 - 176*S^6 - 104*S^8)*HPL[{2}, -S^2])/(160*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(33 - 137*S^2 + 20*S^4))/(192*S^3) - (Pi^2*S*(1261 + 178*S^2 + 89*S^4))/(1440*(1 + S^2)^2) + (7*S*(-21 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(80*(1 + S^2)^2)) - (S*HPL[{3}, -S^2])/(8*(1 + S^2)^2) - (S*(-206 + 50*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(120*(1 + S^2)^2) - (5*S*Zeta[3])/8) + HPL[{2, 1, 1, 1}, -S^2]*((-104 + 22*S^2 + 117*S^4 + 10*S^6)/S^3 + (Pi^2*(-93 - 1024*S^2 + 1671*S^4 + 650*S^6 - 384*S^8))/(3*S^3*(1 + S^2)^2) - (3136*S*Zeta[3])/(1 + S^2)^2) + HPL[{5}, -S^2]*((-120 + 337*S^2 - 598*S^4 + 14*S^6)/(4*S^3) + (Pi^2*(60 + 162*S^2 + 3*S^4 - 353*S^6 - 14*S^8))/(6*S^3*(1 + S^2)^2) - (2*S*(111 + 58*S^2 + 29*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(5 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 2, 1}, -S^2]*((160 + 12*S^2 + 277*S^4 - 20*S^6)/(2*S^3) + (Pi^2*(69 + 868*S^2 - 1987*S^4 + 1858*S^6 - 212*S^8))/(6*S^3*(1 + S^2)^2) + (24*S*(63 + 8*S^2 + 4*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^5*(((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(60*S^3) + (Pi^2*(45 + 554*S^2 - 2338*S^4 + 2254*S^6 - 119*S^8))/(90*S^3*(1 + S^2)^2) + (4*(16 - 65*S^2 + 16*S^4)*HPL[{2}, -S^2])/(5*S*(1 + S^2)) - (2*S*(-123 + 134*S^2 + 67*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + 26*S*HPL[{2, 1}, -S^2] - (2*S*(-31 + 38*S^2 + 19*S^4)*Zeta[3])/(1 + S^2)^2) + Log[T]^5*(-5/(2*S) - (Pi^2*S*(-275 + 252*S^2 + 5*S^4))/(9*(1 + S^2)^2) - (S*(-55 + 36*S^2 + 18*S^4)*HPL[{0}, S^2]^3)/(9*(1 + S^2)^2) + ((-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^2)/(S^3*(1 + S^2)^2) - (112*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^2*(-(S*(-107 + 84*S^2 + 5*S^4))/(3*(1 + S^2)^2) - (S*(-53 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2])/(1 + S^2)^2) + ((9 + 19*S^2 + 76*S^4 - 10*S^6)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(33 + 35*S^2))/(6*S^3) - (Pi^2*S*(-137 + 74*S^2 + 37*S^4))/(3*(1 + S^2)^2) + 26*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]*((-18 - 35*S^2)/(6*S) - (Pi^2*S*(-139 + 204*S^2 + 102*S^4))/(9*(1 + S^2)^2) + ((-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2])/(S^3*(1 + S^2)^2) - (56*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^2)/(1 + S^2)^2 - (2*S*(-23 + 54*S^2 + 27*S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (2*S*(-61 + 258*S^2 + 129*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 84*S*HPL[{2, 1}, -S^2] + (4*S*(-4 + 42*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1, 1}, -S^2]*((769 - 166*S^2 + 695*S^4 - 74*S^6)/(4*S^3) + (Pi^2*(249 + 2790*S^2 - 5361*S^4 + 2576*S^6 - 114*S^8))/(6*S^3*(1 + S^2)^2) + (4*S*(1155 + 86*S^2 + 43*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 2}, -S^2]*((75 + 106*S^2 + 1089*S^4 - 72*S^6)/(8*S^3) + (Pi^2*(9 - 18*S^2 - 227*S^4 + 2648*S^6 - 456*S^8))/(12*S^3*(1 + S^2)^2) + (S*(-5 + 94*S^2 + 47*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4, 1}, -S^2]*((411 + 404*S^2 + 3146*S^4 - 336*S^6)/(8*S^3) + (Pi^2*(-30 - 164*S^2 - 581*S^4 + 4516*S^6 - 673*S^8))/(6*S^3*(1 + S^2)^2) + (2*S*(-27 + 158*S^2 + 79*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(-335 - 713*S^2 + 28*S^4))/(48*S^3) + (Pi^2*(1 + S^2)*(341 + 79*S^2 + 44*S^4))/(144*S^3) + (Pi^4*S*(-21933 + 9518*S^2 + 4759*S^4))/(2160*(1 + S^2)^2) + (((1 + S^2)*(6 - 27*S^2 + 4*S^4))/(2*S^3) - (Pi^2*S*(447 + 110*S^2 + 55*S^4))/(18*(1 + S^2)^2))*HPL[{2}, -S^2] + (98*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + ((-15 - 70*S^2 + 904*S^4 - 2578*S^6 + 263*S^8)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^2) - (2*S*(-111 + 110*S^2 + 55*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (4*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (2*S*(-27 + 278*S^2 + 139*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - 130*S*HPL[{2, 1, 1}, -S^2] + (2*(-23 + 136*S^2 - 493*S^4 + 98*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*(-(Pi^4*S*(-2809 + 3934*S^2 + 1967*S^4))/(360*(1 + S^2)^2) + (389 + 1152*S^2 + 1011*S^4 - 576*S^6)/(16*S^3) + (Pi^2*(288 + 316*S^2 + 345*S^4 - 100*S^6))/(24*S^3) - (224*S*(-13 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((6 - 22*S^2 - 305*S^4 + 1040*S^6 - 299*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + HPL[{4}, -S^2]*(-(Pi^4*S*(-149 + 542*S^2 + 271*S^4))/(120*(1 + S^2)^2) + (Pi^2*(-62 - 66*S^2 - 129*S^4 + 6*S^6))/(12*S^3) + (520 + 1340*S^2 + 781*S^4 + 696*S^6)/(16*S^3) + ((-3 + 42*S^2 - 785*S^4 - 8*S^6 - 82*S^8)*HPL[{2, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + (2*S*(-34 + 174*S^2 + 87*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-57 + 338*S^2 + 169*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((3 + 14*S^2 + 5*S^4 - 50*S^6 + 12*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((Pi^4*S*(-2420 + 1154*S^2 + 577*S^4))/(360*(1 + S^2)^2) + (Pi^2*(-14 + 94*S^2 - 51*S^4 + 10*S^6))/(24*S^3) + (-85 + 322*S^2 - 150*S^4 + 64*S^6)/(16*S^3) + ((3 - 6*S^2 + 277*S^4 - 1336*S^6 + 242*S^8)*HPL[{3}, -S^2])/(4*S^3*(1 + S^2)^2) - (S*(-91 + 146*S^2 + 73*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((-15 - 202*S^2 + 558*S^4 - 131*S^6)*HPL[{2, 1}, -S^2])/(2*S^3*(1 + S^2)) - (S*(257 + 186*S^2 + 93*S^4)*HPL[{3, 1}, -S^2])/(2*(1 + S^2)^2) + 132*S*HPL[{2, 1, 1}, -S^2] + ((-3 - 12*S^2 + 73*S^4 - 1078*S^6 + 256*S^8)*Zeta[3])/(4*S^3*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^4*S*(-1258 + 1526*S^2 + 763*S^4))/(60*(1 + S^2)^2) + (2*Pi^2*(-28 - 27*S^2 - 36*S^4 + 12*S^6))/(3*S^3) + (-106 - 465*S^2 - 162*S^4 + 233*S^6)/(4*S^3) + (2*(-3 + 24*S^2 + 269*S^4 - 1042*S^6 + 284*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^4*((Pi^2*(45 - 224*S^2 - 68*S^4))/(288*S) + (27 + 204*S^2 + 119*S^4)/(64*S) - (Pi^4*S*(2230 + 442*S^2 + 221*S^4))/(4320*(1 + S^2)^2) + ((45 + 548*S^2 - 1514*S^4 + 234*S^6 - 21*S^8)*HPL[{1}, -S^2]^3)/(144*S^3*(1 + S^2)^2) + (S*(-537 + 62*S^2 + 31*S^4)*HPL[{1}, -S^2]^4)/(144*(1 + S^2)^2) + (-(Pi^2*S*(124 + 30*S^2 + 15*S^4))/(72*(1 + S^2)^2) + (-12 + 9*S^2 - 50*S^4 + 6*S^6)/(24*S^3))*HPL[{2}, -S^2] + (S*(-13 + 4*S^2 + 2*S^4)*HPL[{2}, -S^2]^2)/(6*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((Pi^2*S*(-1107 + 2*S^2 + S^4))/(288*(1 + S^2)^2) + ((1 + S^2)*(165 - 237*S^2 + 28*S^4))/(192*S^3) + (S*(-469 + 26*S^2 + 13*S^4)*HPL[{2}, -S^2])/(48*(1 + S^2)^2)) - ((-1 + S^2)*(3 + 21*S^2 + 22*S^4 + 2*S^6)*HPL[{3}, -S^2])/(16*S^3*(1 + S^2)^2) - (S^3*(2 + S^2)*HPL[{4}, -S^2])/(4*(1 + S^2)^2) + ((-45 - 486*S^2 + 439*S^4 - 168*S^6 - 84*S^8)*HPL[{2, 1}, -S^2])/(48*S^3*(1 + S^2)^2) - (S*(-107 + 20*S^2 + 10*S^4)*HPL[{3, 1}, -S^2])/(12*(1 + S^2)^2) + (S*(-226 + 30*S^2 + 15*S^4)*HPL[{2, 1, 1}, -S^2])/(12*(1 + S^2)^2) - (5*S*(6 + 5*S^2)*Zeta[3])/(4*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(141 - 7*S^2 + 96*S^4))/(192*S^3) + (Pi^2*(45 + 754*S^2 - 1582*S^4 - 318*S^6 - 243*S^8))/(288*S^3*(1 + S^2)^2) + ((105 - 350*S^2 + 27*S^4)*HPL[{2}, -S^2])/(24*S*(1 + S^2)^2) - (S*(3 + 10*S^2 + 5*S^4)*HPL[{3}, -S^2])/(8*(1 + S^2)^2) - (S*(-469 + 26*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(24*(1 + S^2)^2) - (5*S*Zeta[3])/8)) + Log[T]^4*((-3*(-9 + 4*S^2))/(4*S) + (Pi^2*(15 - 12*S^2 + 4*S^4))/(6*S) + (Pi^4*S*(-5918 + 1510*S^2 + 755*S^4))/(540*(1 + S^2)^2) + (S*(-137 + 10*S^2 + 5*S^4)*HPL[{0}, S^2]^4)/(36*(1 + S^2)^2) - (5*(-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^2) + (140*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^3*(-(S*(1039 - 292*S^2 + 129*S^4))/(36*(1 + S^2)^2) + (S*(-633 + 194*S^2 + 97*S^4)*HPL[{1}, -S^2])/(18*(1 + S^2)^2)) + ((4*Pi^2*S*(-19 + 60*S^2 + 30*S^4))/(9*(1 + S^2)^2) + (2*(-4 - 9*S^2 - 6*S^4 + 2*S^6))/S^3)*HPL[{2}, -S^2] + (2*S*(-9 + 5*S^2)*(19 + 5*S^2)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(33 + 35*S^2))/(12*S^3) + (5*Pi^2*S*(-137 + 74*S^2 + 37*S^4))/(6*(1 + S^2)^2) - 65*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^2*((15 - 24*S^2 + 8*S^4)/(4*S) + (Pi^2*S*(-619 + 260*S^2 + 130*S^4))/(36*(1 + S^2)^2) + ((45 + 508*S^2 - 2066*S^4 + 1268*S^6 + 77*S^8)*HPL[{1}, -S^2])/(12*S^3*(1 + S^2)^2) + (5*S*(-53 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^2)/(2*(1 + S^2)^2) + (4*S*(-34 + 30*S^2 + 15*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((9 + 46*S^2 + 301*S^4 - 1376*S^6 + 260*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*S*(-38 + 90*S^2 + 45*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + ((-45 - 479*S^2 + 1180*S^4 - 334*S^6)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (2*S*(241 + 150*S^2 + 75*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + 160*S*HPL[{2, 1, 1}, -S^2] + (2*S*(55 - 528*S^2 + 167*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(12*S^3) + (Pi^2*(45 + 554*S^2 - 2338*S^4 + 2254*S^6 - 119*S^8))/(18*S^3*(1 + S^2)^2) + (4*(16 - 65*S^2 + 16*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) - (10*S*(-123 + 134*S^2 + 67*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + 130*S*HPL[{2, 1}, -S^2] - (10*S*(-31 + 38*S^2 + 19*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]*((75 + 257*S^2 + 12*S^4)/(12*S) - (Pi^2*S*(571 - 523*S^2 + 111*S^4))/(9*(1 + S^2)^2) - (5*(-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^2)/(2*S^3*(1 + S^2)^2) + (280*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + ((-45 - 48*S^2 - 1019*S^4 + 1642*S^6 - 342*S^8)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((5*(1 + S^2)*(33 + 35*S^2))/(12*S^3) + (Pi^2*S*(-1893 + 1034*S^2 + 517*S^4))/(18*(1 + S^2)^2) + (125*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) - (S*(3 + 74*S^2 + 37*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (20*S*(26 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-38 + 90*S^2 + 45*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + ((40 + 257*S^2 - 2*S^4)/(4*S) + (Pi^2*S*(-61 - 696*S^2 + 203*S^4))/(6*(1 + S^2)^2))*Zeta[5] + HPL[{2, 1}, -S^2]*((-24 + 35*S^2 - 115*S^4 - 131*S^6)/(16*S^3) + (Pi^2*(-254 + 151*S^2 + 109*S^4 + 28*S^6))/(24*S^3) + (Pi^4*(-639 - 6331*S^2 + 9932*S^4 + 1537*S^6 - 1961*S^8))/(360*S^3*(1 + S^2)^2) - (2*(-15 - 208*S^2 + 417*S^4 - 868*S^6 + 90*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) + (S*(1709 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*S*(1341 + 112*S^2 + 56*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (4*(-18 - 220*S^2 + 515*S^4 - 734*S^6 + 117*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + 528*S*HPL[{2, 2, 1}, -S^2] + (64*S*(-29 + 40*S^2 + 20*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (32*S*(-171 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((4*(-4 + 27*S^2))/S^3 + (Pi^2*S*(-429 + 4*S^2 + 2*S^4))/(3*(1 + S^2)^2))*Zeta[3] + (2*S*(-360 + 2*S^2 + S^4)*Zeta[5])/(1 + S^2)^2) + Log[T]^3*((-69 + 56*S^2)/(4*S) + (Pi^2*(-155 + 150*S^2 - 82*S^4))/(36*S) - (Pi^4*S*(-15781 + 11141*S^2 + 230*S^4))/(540*(1 + S^2)^2) + (S*(280 + 18*S^2 + 9*S^4)*HPL[{0}, S^2]^5)/(180*(1 + S^2)^2) + (5*(-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^4)/(3*S^3*(1 + S^2)^2) - (112*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^4*((S*(549 + 37*S^2 + 56*S^4))/(36*(1 + S^2)^2) - (S*(-537 + 62*S^2 + 31*S^4)*HPL[{1}, -S^2])/(36*(1 + S^2)^2)) + ((3 - 32*S^2 + 717*S^4 - 810*S^6 + 6*S^8)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(33 + 35*S^2))/(9*S^3) - (10*Pi^2*S*(-137 + 74*S^2 + 37*S^4))/(9*(1 + S^2)^2) + (260*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^3*((-42 + 77*S^2 - 6*S^4)/(18*S) - (Pi^2*S*(-185 + 54*S^2 + 27*S^4))/(18*(1 + S^2)^2) + ((-21 - 269*S^2 + 805*S^4 - 367*S^6 + 40*S^8)*HPL[{1}, -S^2])/(9*S^3*(1 + S^2)^2) - (S*(-633 + 194*S^2 + 97*S^4)*HPL[{1}, -S^2]^2)/(9*(1 + S^2)^2) - (S*(-247 + 166*S^2 + 83*S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2)) + ((2*Pi^2*S*(-153 + 688*S^2 + 344*S^4))/(9*(1 + S^2)^2) + (-39 + 100*S^2 + 461*S^4 - 12*S^6)/(6*S^3))*HPL[{3}, -S^2] + ((27 + 54*S^2 + 115*S^4 + 1628*S^6 + 212*S^8)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^2) + (2*S*(-13 + 406*S^2 + 203*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + ((-4*(-14 + 3*S^2 + 11*S^4))/S^3 - (28*Pi^2*S*(53 + 50*S^2 + 25*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(27 + 84*S^2 + 114*S^4 + 392*S^6 + 3*S^8)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (16*S*(-43 + 306*S^2 + 153*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) - (8*S*(-371 + 1942*S^2 + 971*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) - (20*(-9 - 19*S^2 - 76*S^4 + 10*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (32*S*(-123 + 146*S^2 + 73*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) - (8*S*(-1171 + 462*S^2 + 231*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) - 1680*S*HPL[{2, 1, 1, 1}, -S^2] + (44*S + (4*Pi^2*S*(-33 + 350*S^2 + 175*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((49 + 258*S^2 + 146*S^4 - 82*S^6)/(6*S^3) + (Pi^2*(93 + 210*S^2 + 1437*S^4 - 348*S^6 - 100*S^8))/(18*S^3*(1 + S^2)^2) + (4*S*(-75 + 634*S^2 + 317*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (16*S*(-123 + 146*S^2 + 73*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (224*S*(-2 + 10*S^2 + 5*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(6*S^3) + (Pi^2*(-45 - 554*S^2 + 2338*S^4 - 2254*S^6 + 119*S^8))/(9*S^3*(1 + S^2)^2) - (8*(16 - 65*S^2 + 16*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) + (20*S*(-123 + 134*S^2 + 67*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 260*S*HPL[{2, 1}, -S^2] + (20*S*(-31 + 38*S^2 + 19*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^2*((-40 + 75*S^2 - 41*S^4)/(6*S) + (Pi^2*S*(1084 - 383*S^2 + 31*S^4))/(18*(1 + S^2)^2) + ((-45 - 508*S^2 + 2066*S^4 - 1268*S^6 - 77*S^8)*HPL[{1}, -S^2]^2)/(6*S^3*(1 + S^2)^2) - (10*S*(-53 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^3)/(3*(1 + S^2)^2) + ((24 + 35*S^2 + 481*S^4 - 339*S^6 - 25*S^8)*HPL[{2}, -S^2])/(3*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(44 - 24*S^2 + 11*S^4))/(3*S^3) - (Pi^2*S*(-666 + 166*S^2 + 83*S^4))/(9*(1 + S^2)^2) - (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + (S*(-1 + 86*S^2 + 43*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (14*S*(61 + 10*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (2*S*(-6 + 70*S^2 + 35*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(-335 - 713*S^2 + 28*S^4))/(12*S^3) - (Pi^2*(1 + S^2)*(341 + 79*S^2 + 44*S^4))/(36*S^3) - (Pi^4*S*(-21933 + 9518*S^2 + 4759*S^4))/(540*(1 + S^2)^2) + ((-2*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 + (2*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] - (392*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (2*(-15 - 70*S^2 + 904*S^4 - 2578*S^6 + 263*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) + (8*S*(-111 + 110*S^2 + 55*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (16*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (8*S*(-27 + 278*S^2 + 139*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + 520*S*HPL[{2, 1, 1}, -S^2] - (8*(-23 + 136*S^2 - 493*S^4 + 98*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + HPL[{0}, S^2]*((Pi^2*(-58 - 7*S^2 - 4*S^4))/(12*S) + (-176 - 749*S^2 + 28*S^4)/(12*S) - (Pi^4*S*(-2674 + 2774*S^2 + 1387*S^4))/(180*(1 + S^2)^2) + (10*(-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^3)/(3*S^3*(1 + S^2)^2) - (280*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^4)/(3*(1 + S^2)^2) + ((-8*Pi^2*S*(-74 + 122*S^2 + 61*S^4))/(9*(1 + S^2)^2) + (107 - 44*S^2 - 83*S^4 - 4*S^6)/(6*S^3))*HPL[{2}, -S^2] - (4*S*(-101 + 190*S^2 + 95*S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(33 + 35*S^2))/(6*S^3) - (Pi^2*S*(-1893 + 1034*S^2 + 517*S^4))/(9*(1 + S^2)^2) - (250*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + ((-27 - 106*S^2 - 32*S^4 + 290*S^6 + 107*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) - (2*S*(-31 + 30*S^2 + 15*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) - (2*(-45 - 616*S^2 + 1245*S^4 - 1126*S^6 + 58*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (4*S*(-347 + 806*S^2 + 403*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) - (40*S*(-23 + 54*S^2 + 27*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (8*S*(-5 + 92*S^2 + 14*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(6*S^3) + (Pi^2*(-87 - 1138*S^2 + 4220*S^4 - 3974*S^6 + 395*S^8))/(18*S^3*(1 + S^2)^2) + (8*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + (4*S*(-27 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (500*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*S*(-123 + 86*S^2 + 43*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + (80*S*(-2 + 34*S^2 + 17*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((Pi^2*(270 - 4161*S^2 - 110*S^4))/(576*S) + (436 - 447*S^2 + 115*S^4)/(192*S) - (7*Pi^4*S*(2495 + 496*S^2 + 285*S^4))/(4320*(1 + S^2)^2) + ((21 + 269*S^2 - 805*S^4 + 367*S^6 - 40*S^8)*HPL[{1}, -S^2]^4)/(36*S^3*(1 + S^2)^2) + (S*(-633 + 194*S^2 + 97*S^4)*HPL[{1}, -S^2]^5)/(90*(1 + S^2)^2) + ((-3 - 34*S^2 - 891*S^4 + 360*S^6 - 52*S^8)*HPL[{2}, -S^2]^2)/(48*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*(((1 + S^2)*(36 + 2*S^2 + S^4))/(18*S^3) + (Pi^2*S*(-1159 + 226*S^2 + 113*S^4))/(108*(1 + S^2)^2) + (S*(-289 + 82*S^2 + 41*S^4)*HPL[{2}, -S^2])/(9*(1 + S^2)^2)) + (-(Pi^2*S*(25 + 8*S^2 + 4*S^4))/(36*(1 + S^2)^2) + (135 - 100*S^2 - 84*S^4 - 16*S^6)/(48*S^3))*HPL[{3}, -S^2] + ((-45 - 94*S^2 - 137*S^4 + 12*S^6 - 36*S^8)*HPL[{4}, -S^2])/(24*S^3*(1 + S^2)^2) + (S*(-21 + 4*S^2 + 2*S^4)*HPL[{5}, -S^2])/(6*(1 + S^2)^2) + (-(Pi^2*S*(-179 + 16*S^2 + 8*S^4))/(12*(1 + S^2)^2) + (-84 - 31*S^2 - 41*S^4 + 12*S^6)/(12*S^3))*HPL[{2, 1}, -S^2] + ((27 + 40*S^2 + 460*S^4 - 168*S^6 + 45*S^8)*HPL[{3, 1}, -S^2])/(6*S^3*(1 + S^2)^2) + (7*S*(1 + 6*S^2 + 3*S^4)*HPL[{3, 2}, -S^2])/(6*(1 + S^2)^2) + (2*S*(11 + 26*S^2 + 13*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + ((-21 - 32*S^2 - 474*S^4 + 143*S^6 - 54*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (S*(-313 + 10*S^2 + 5*S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) + (7*S*(-137 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) + (2*S*(331 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((S*(-397 + 84*S^2))/24 - (Pi^2*S*(79 + 180*S^2 + 90*S^4))/(36*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^2*(((1 + S^2)*(95 + 57*S^2 + 30*S^4))/(48*S^3) + (Pi^2*(87 + 1198*S^2 - 3100*S^4 + 620*S^6 - 257*S^8))/(144*S^3*(1 + S^2)^2) + ((3 + 466*S^2 - 1486*S^4 + 594*S^6 - 97*S^8)*HPL[{2}, -S^2])/(24*S^3*(1 + S^2)^2) - (2*S*HPL[{3}, -S^2])/(1 + S^2)^2 - (S*(-289 + 82*S^2 + 41*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (S*(-4 + 14*S^2 + 7*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-17 - 133*S^2 - 25*S^4 + 50*S^6)/(48*S^3) + (Pi^2*(-87 - 154*S^2 - 2133*S^4 - 242*S^6 - 420*S^8))/(144*S^3*(1 + S^2)^2) - (S*(3 + 20*S^2 + 10*S^4)*HPL[{3}, -S^2])/(6*(1 + S^2)^2) - (S*(-313 + 10*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(6*(1 + S^2)^2) - (S*(1 + 20*S^2 + 10*S^4)*Zeta[3])/(6*(1 + S^2)^2)) + HPL[{1}, -S^2]*((7*Pi^4*S*(-561 + 20*S^2 + 10*S^4))/(1080*(1 + S^2)^2) + ((1 + S^2)*(81 - 76*S^2 + 20*S^4))/(48*S^3) + (Pi^2*(1 + S^2)*(309 - 677*S^2 + 104*S^4))/(288*S^3) + (-((1 + S^2)*(-79 + 27*S^2 + 12*S^4))/(48*S^3) + (Pi^2*S*(-1019 + 206*S^2 + 103*S^4))/(72*(1 + S^2)^2))*HPL[{2}, -S^2] + (S*(-46 + 14*S^2 + 7*S^4)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)^2) + ((-6 + 14*S^2 - 6*S^4 - 21*S^6 - 19*S^8)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^2) + (S*(-23 + 22*S^2 + 11*S^4)*HPL[{4}, -S^2])/(6*(1 + S^2)^2) + ((-3 - 466*S^2 + 1486*S^4 - 594*S^6 + 97*S^8)*HPL[{2, 1}, -S^2])/(12*S^3*(1 + S^2)^2) - (2*S*(-48 + 14*S^2 + 7*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (2*S*(-289 + 82*S^2 + 41*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + ((12 - 25*S^2 - 105*S^4 - 24*S^6)*Zeta[3])/(6*S*(1 + S^2)^2)) - (S*(11 + 38*S^2 + 19*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + Zeta[3]*((Pi^2*(10 - 18*S^2 + 25*S^4))/(12*S) + (-270 + 91*S^2 + 131*S^4)/(16*S) + (Pi^4*S*(-929 - 6674*S^2 + 333*S^4))/(360*(1 + S^2)^2) - (2*S*(57 + 52*S^2 + 26*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{3}, -S^2]*((Pi^2*(-99 - 218*S^2 - 698*S^4 + 14*S^6))/(48*S^3) + (3*(-16 + 209*S^2 - 439*S^4 + 92*S^6))/(16*S^3) + (Pi^4*(123 + 735*S^2 + 1089*S^4 - 5815*S^6 + 920*S^8))/(360*S^3*(1 + S^2)^2) + ((3 + 10*S^2 + 57*S^4 + 252*S^6 + 30*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)^2) + (2*S*(5 + 38*S^2 + 19*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (-(Pi^2*S*(911 + 170*S^2 + 85*S^4))/(6*(1 + S^2)^2) + (59 + 440*S^2 - 177*S^4 - 16*S^6)/(4*S^3))*HPL[{2, 1}, -S^2] + ((3 - 8*S^2 - 74*S^4 + 1270*S^6 - 235*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) - (S*(-91 + 162*S^2 + 81*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (2*S*(7 + 68*S^2 + 34*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (2*(9 + 61*S^2 - 1295*S^4 + 221*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (2*S*(-913 + 38*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(2675 + 54*S^2 + 27*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (16*S*(215 + 38*S^2 + 19*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-(Pi^2*S*(-19 + 66*S^2 + 33*S^4))/(6*(1 + S^2)^2) + (-32 - 56*S^2 + 13*S^4 - 20*S^6)/(4*S^3))*Zeta[3] - (S*(9 + 82*S^2 + 41*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^2)*(301 + 161*S^2 + 80*S^4))/(72*S^3) - ((1 + S^2)*(-509 - 1204*S^2 + 153*S^4))/(24*S^3) + (Pi^4*(624 + 6826*S^2 - 26844*S^4 + 19799*S^6 - 539*S^8))/(1080*S^3*(1 + S^2)^2) + ((15 + 252*S^2 - 1232*S^4 + 1544*S^6 - 123*S^8)*HPL[{2}, -S^2]^2)/(6*S^3*(1 + S^2)^2) + (((1 + S^2)*(-13 - 155*S^2 + 14*S^4))/(3*S^3) - (2*Pi^2*S*(-317 + 360*S^2 + 180*S^4))/(9*(1 + S^2)^2))*HPL[{3}, -S^2] + ((29 + 353*S^2 - 1059*S^4 - 55*S^6)*HPL[{4}, -S^2])/(3*S*(1 + S^2)^2) - (4*S*(-55 + 106*S^2 + 53*S^4)*HPL[{5}, -S^2])/(3*(1 + S^2)^2) + ((-2*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 + (2*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(9*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(91 - 164*S^2 - 517*S^4 + 70*S^6)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)^2) + (4*S*(-505 + 558*S^2 + 279*S^4)*HPL[{3, 2}, -S^2])/(3*(1 + S^2)^2) + (4*S*(-1737 + 1894*S^2 + 947*S^4)*HPL[{4, 1}, -S^2])/(3*(1 + S^2)^2) + (16*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (1568*S*(-3 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*(1 + S^2)^2) + (8*S*(-1149 + 506*S^2 + 253*S^4)*HPL[{3, 1, 1}, -S^2])/(3*(1 + S^2)^2) + 520*S*HPL[{2, 1, 1, 1}, -S^2] + (((1 + S^2)*(11 - 271*S^2 + 44*S^4))/(6*S^3) - (2*Pi^2*S*(-257 + 318*S^2 + 159*S^4))/(9*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(55 - 335*S^2 + 72*S^4))/(12*S^3) + (Pi^2*(407 - 1554*S^2 - 151*S^4 + 242*S^6))/(18*S*(1 + S^2)^2) - (2*S*(-505 + 558*S^2 + 279*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (112*S*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(3*(1 + S^2)^2)) - (2*S*(-431 + 658*S^2 + 329*S^4)*Zeta[5])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((Pi^6*S*(-17522 + 9014*S^2 + 4507*S^4))/(15120*(1 + S^2)^2) + (Pi^4*(-184 - 75*S^2 - 406*S^4 + 102*S^6))/(180*S^3) + (Pi^2*(-191 - 196*S^2 - 194*S^4 + 233*S^6))/(48*S^3) + (288 + 2141*S^2 - 273*S^4 + 478*S^6)/(16*S^3) + (S*(-47 + 78*S^2 + 39*S^4)*HPL[{3}, -S^2]^2)/(2*(1 + S^2)^2) + ((-4*Pi^2*S*(-3 + 22*S^2 + 11*S^4))/(3*(1 + S^2)^2) + (13 + 96*S^2 - 341*S^4 + 16*S^6)/(4*S^3))*HPL[{4}, -S^2] + ((3 - 30*S^2 - 219*S^4 - 632*S^6 - 118*S^8)*HPL[{5}, -S^2])/(2*S^3*(1 + S^2)^2) - (2*S*(17 + 76*S^2 + 38*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - 132*S*HPL[{2, 1}, -S^2]^2 + (-(Pi^2*S*(-1031 + 358*S^2 + 179*S^4))/(6*(1 + S^2)^2) + (5 - 280*S^2 + 225*S^4 - 16*S^6)/(4*S^3))*HPL[{3, 1}, -S^2] + ((-3 + 2*S^2 - 215*S^4 + 1238*S^6 - 250*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)^2) + ((-15 - 6*S^2 - 877*S^4 + 8024*S^6 - 1370*S^8)*HPL[{4, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + (3*S*(-27 + 50*S^2 + 25*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (8*S*(-28 + 102*S^2 + 51*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((2*Pi^2*S*(-495 + 224*S^2 + 112*S^4))/(3*(1 + S^2)^2) + (-22 + 138*S^2 - 49*S^4 + 4*S^6)/S^3)*HPL[{2, 1, 1}, -S^2] + (2*(15 + 202*S^2 - 558*S^4 + 131*S^6)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)) - (2*(45 + 642*S^2 - 1129*S^4 + 14*S^6 + 172*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (39*S*(-3 + 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(1 + S^2)^2 + (5*S*(-239 + 74*S^2 + 37*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(-1911 + 334*S^2 + 167*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (4*(-18 - 220*S^2 + 515*S^4 - 734*S^6 + 117*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (32*S*(107 + 410*S^2 + 205*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (32*S*(-171 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-46 + 107*S^2 - 125*S^4 + 8*S^6)/(4*S^3) + (Pi^2*(-3 + 15*S^2 + 140*S^4 - 593*S^6 + 147*S^8))/(6*S^3*(1 + S^2)^2))*Zeta[3] - (S*(4 + 14*S^2 + 7*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((-160 - 12*S^2 - 277*S^4 + 20*S^6)/(4*S^3) + (Pi^2*(-69 - 868*S^2 + 1987*S^4 - 1858*S^6 + 212*S^8))/(12*S^3*(1 + S^2)^2) - (12*S*(63 + 8*S^2 + 4*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((11 - 92*S^2 - 655*S^4 + 40*S^6)/(8*S^3) + (Pi^2*(8 + 27*S^2 - 704*S^4 + 103*S^6))/(6*S*(1 + S^2)^2) + (S*(-913 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (S*(3 + 58*S^2 + 29*S^4)*Zeta[3])/(1 + S^2)^2) + ((-6 + 41*S^2 + 139*S^4 - 445*S^6 + 185*S^8)*Zeta[5])/(S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(667 + 573*S^2 + 138*S^4))/(96*S^3) + (Pi^4*(1 + S^2)*(781 - 447*S^2 + 186*S^4))/(480*S^3) - ((1 + S^2)*(-3797 - 9057*S^2 + 1610*S^4))/(64*S^3) + (Pi^6*S*(-44979 + 14612*S^2 + 7306*S^4))/(9072*(1 + S^2)^2) + (((1 + S^2)*(55 + 81*S^2))/(8*S^3) + (Pi^2*S*(-476 + 262*S^2 + 131*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (83*S*HPL[{2}, -S^2]^3)/6 + (37*S*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(2*(1 + S^2)^2) + (((1 + S^2)*(-9 - 563*S^2 + 36*S^4))/(8*S^3) - (Pi^2*S*(-429 + 502*S^2 + 251*S^4))/(12*(1 + S^2)^2))*HPL[{4}, -S^2] + ((15 + 154*S^2 + 30*S^4 - 1040*S^6 - 67*S^8)*HPL[{5}, -S^2])/(2*S^3*(1 + S^2)^2) - (S*(15 + 208*S^2 + 104*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (392*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + (-((1 + S^2)*(29 - 229*S^2 + 28*S^4))/(2*S^3) + (2*Pi^2*S*(159 + 98*S^2 + 49*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((15 + 88*S^2 - 732*S^4 + 2044*S^6 - 287*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)^2) + ((45 + 235*S^2 - 2549*S^4 + 7191*S^6 - 806*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^2) + (117*S*(-3 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(2*(1 + S^2)^2) + (26*S*(-35 + 34*S^2 + 17*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((6*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 - (2*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (4*(-15 - 343*S^2 + 1396*S^4 - 1027*S^6 + 53*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - 332*S*HPL[{3, 2, 1}, -S^2] - (4*S*(27 + 718*S^2 + 359*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (48*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (8*S*(-27 + 278*S^2 + 139*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 1560*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (((1 + S^2)*(19 - 329*S^2 + 56*S^4))/(4*S^3) + (Pi^2*(3 - 88*S^2 + 586*S^4 - 2238*S^6 + 413*S^8))/(12*S^3*(1 + S^2)^2))*Zeta[3] + (S*(-29 + 22*S^2 + 11*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(55 - 335*S^2 + 72*S^4))/(4*S^3) + (Pi^2*(-407 + 1554*S^2 + 151*S^4 - 242*S^6))/(6*S*(1 + S^2)^2) + (112*S*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*(((1 + S^2)*(-87 - 691*S^2 + 102*S^4))/(8*S^3) + (Pi^2*(-15 - 31*S^2 + 444*S^4 - 1396*S^6 + 132*S^8))/(6*S^3*(1 + S^2)^2) + (2*S*(-505 + 558*S^2 + 279*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-37 + 26*S^2 + 13*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(133 - 497*S^2 + 92*S^4))/(48*S^3) + ((1 + S^2)*(49 - 663*S^2 + 246*S^4))/(16*S^3) - (Pi^4*S*(6319 + 512*S^2 + 256*S^4))/(360*(1 + S^2)^2) + ((-15 - 88*S^2 + 732*S^4 - 2044*S^6 + 287*S^8)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^2) - (113*S*(-3 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (392*S*(-3 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-23 + 378*S^2 - 1025*S^4 + 142*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + ((3 - 42*S^2 + 132*S^4 - 1053*S^6 + 290*S^8)*Zeta[5])/(S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((Pi^4*(2496 - 8825*S^2 - 1148*S^4))/(5760*S) + (254 - 537*S^2 + 478*S^4)/(32*S) + (Pi^2*(322 + 974*S^2 + 947*S^4))/(192*S) - (Pi^6*S*(201706 + 12582*S^2 + 6291*S^4))/(181440*(1 + S^2)^2) + ((45 + 508*S^2 - 2066*S^4 + 1268*S^6 + 77*S^8)*HPL[{1}, -S^2]^5)/(60*S^3*(1 + S^2)^2) + (S*(-53 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^6)/(6*(1 + S^2)^2) + ((Pi^2*S*(-257 + 156*S^2 + 78*S^4))/(24*(1 + S^2)^2) + (-6 + 50*S^2 - 53*S^4 + 16*S^6)/(16*S^3))*HPL[{2}, -S^2]^2 + (S*(-21 + 22*S^2 + 11*S^4)*HPL[{2}, -S^2]^3)/(2*(1 + S^2)^2) + HPL[{1}, -S^2]^4*(((1 + S^2)*(44 - 24*S^2 + 11*S^4))/(12*S^3) + (Pi^2*S*(-666 + 166*S^2 + 83*S^4))/(36*(1 + S^2)^2) + (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2}, -S^2])/(12*(1 + S^2)^2)) + (S*HPL[{3}, -S^2]^2)/2 + (-(Pi^2*S*(7 + 54*S^2 + 27*S^4))/(24*(1 + S^2)^2) + (-142 + 8*S^2 - 69*S^4 - 4*S^6)/(16*S^3))*HPL[{4}, -S^2] + ((60 + 146*S^2 + 22*S^4 - 113*S^6 - S^8)*HPL[{5}, -S^2])/(4*S^3*(1 + S^2)^2) - (15*S*(-2 + 2*S^2 + S^4)*HPL[{6}, -S^2])/(4*(1 + S^2)^2) - (S*(-153 + 124*S^2 + 62*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + (-(Pi^2*S*(-483 + 274*S^2 + 137*S^4))/(12*(1 + S^2)^2) + (153 + 20*S^2 + 144*S^4 - 48*S^6)/(8*S^3))*HPL[{3, 1}, -S^2] + ((3 - 11*S^2 + 6*S^4 + 211*S^6 + 23*S^8)*HPL[{3, 2}, -S^2])/(4*S^3*(1 + S^2)^2) + ((-33 - 162*S^2 + 25*S^4 + 772*S^6 + 82*S^8)*HPL[{4, 1}, -S^2])/(4*S^3*(1 + S^2)^2) - (S*(-5 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(4*(1 + S^2)^2) + (S*(9 + 50*S^2 + 25*S^4)*HPL[{5, 1}, -S^2])/(2*(1 + S^2)^2) + ((Pi^2*S*(-166 + 90*S^2 + 45*S^4))/(2*(1 + S^2)^2) + (4*(-8 - 9*S^4 + 3*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + ((33 + 428*S^2 - 957*S^4 + 390*S^6 + 22*S^8)*HPL[{2, 2, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + ((123 + 1378*S^2 - 2873*S^4 + 924*S^6 + 68*S^8)*HPL[{3, 1, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + (5*S*HPL[{3, 1, 2}, -S^2])/2 + (S*(-499 + 538*S^2 + 269*S^4)*HPL[{3, 2, 1}, -S^2])/(2*(1 + S^2)^2) + (S*(-763 + 762*S^2 + 381*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(24 + 250*S^2 - 485*S^4 + 98*S^6 + 25*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (2*S*(-269 + 234*S^2 + 117*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (32*S*(-34 + 30*S^2 + 15*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((5*(3 + 17*S^2 + 12*S^4))/(8*S) - (Pi^2*S*(195 + 428*S^2 + 151*S^4))/(12*(1 + S^2)^2))*Zeta[3] - (S*(10 + 2*S^2 + S^4)*Zeta[3]^2)/(2*(1 + S^2)^2) + HPL[{2, 1}, -S^2]*((-150 + 129*S^2 - 8*S^4 + 18*S^6)/(8*S^3) + (Pi^2*(-93 - 986*S^2 + 1409*S^4 - 364*S^6 - 134*S^8))/(24*S^3*(1 + S^2)^2) + (S*(-37 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((-7 - 198*S^2 - 429*S^4 - 18*S^6)/(32*S^3) + (Pi^2*(21 + 101*S^2 + 2*S^4 - 183*S^6 - 5*S^8))/(24*S^3*(1 + S^2)^2) - (3*S*(17 + 6*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(2*(1 + S^2)^2) - (S*(1 + 4*S^2 + 2*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*(((1 + S^2)*(40 - 21*S^2 + 17*S^4))/(6*S^3) + (Pi^2*(45 + 528*S^2 - 1790*S^4 + 751*S^6 + 28*S^8))/(36*S^3*(1 + S^2)^2) + ((215 - 966*S^2 + 437*S^4 + 50*S^6)*HPL[{2}, -S^2])/(6*S*(1 + S^2)^2) - (S*(-19 + 50*S^2 + 25*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (S*(-49 + 66*S^2 + 33*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((Pi^4*S*(-6278 + 906*S^2 + 453*S^4))/(1440*(1 + S^2)^2) + (Pi^2*(-28 + 9*S^2 - 68*S^4 + 12*S^6))/(12*S^3) + (-276 + 73*S^2 - 226*S^4 + 233*S^6)/(32*S^3) + ((7 - 7*S^2 - 113*S^4 - 15*S^6)*HPL[{3}, -S^2])/(4*S*(1 + S^2)^2) - (S*(9 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(4*(1 + S^2)^2) + ((-33 - 428*S^2 + 957*S^4 - 390*S^6 - 22*S^8)*HPL[{2, 1}, -S^2])/(4*S^3*(1 + S^2)^2) - (3*S*(-101 + 82*S^2 + 41*S^4)*HPL[{3, 1}, -S^2])/(2*(1 + S^2)^2) + (2*S*(-153 + 124*S^2 + 62*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-3 + 6*S^2 + 11*S^4 - 144*S^6 + 10*S^8)*Zeta[3])/(4*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(341 - 333*S^2 + 72*S^4))/(96*S^3) + ((1 + S^2)*(166 - 70*S^2 + 83*S^4))/(16*S^3) + (Pi^4*S*(-15797 + 2202*S^2 + 1101*S^4))/(1440*(1 + S^2)^2) + (((1 + S^2)*(61 - 173*S^2 + 44*S^4))/(16*S^3) + (Pi^2*S*(-584 + 98*S^2 + 49*S^4))/(12*(1 + S^2)^2))*HPL[{2}, -S^2] + (S*(-182 + 66*S^2 + 33*S^4)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)^2) + ((-15 + 8*S^2 - 16*S^4 - 214*S^6 + S^8)*HPL[{3}, -S^2])/(4*S^3*(1 + S^2)^2) - (S*(15 + 62*S^2 + 31*S^4)*HPL[{4}, -S^2])/(4*(1 + S^2)^2) + ((-215 + 966*S^2 - 437*S^4 - 50*S^6)*HPL[{2, 1}, -S^2])/(2*S*(1 + S^2)^2) - (S*(-345 + 82*S^2 + 41*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((3 + 4*S^2 + 42*S^4 - 266*S^6 + 21*S^8)*Zeta[3])/(4*S^3*(1 + S^2)^2)) - (S*(103 + 233*S^2 + 52*S^4)*Zeta[5])/(2*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(301 - 91*S^2 + 164*S^4))/(96*S^3) + ((1 + S^2)*(341 + 42*S^2 + 169*S^4))/(32*S^3) + (Pi^4*(624 + 8218*S^2 - 21912*S^4 + 3027*S^6 - 1263*S^8))/(1440*S^3*(1 + S^2)^2) + ((15 + 212*S^2 - 940*S^4 + 616*S^6 + 33*S^8)*HPL[{2}, -S^2]^2)/(8*S^3*(1 + S^2)^2) + (((1 + S^2)*(-15 - 41*S^2 + 4*S^4))/(4*S^3) - (5*Pi^2*S*(-1 + 8*S^2 + 4*S^4))/(6*(1 + S^2)^2))*HPL[{3}, -S^2] + ((31 - 81*S^2 - 157*S^4 - 13*S^6)*HPL[{4}, -S^2])/(4*S*(1 + S^2)^2) - (2*S*(1 + 14*S^2 + 7*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (-((1 + S^2)*(61 - 173*S^2 + 44*S^4))/(8*S^3) - (Pi^2*S*(-584 + 98*S^2 + 49*S^4))/(6*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-110 + 478*S^2 - 201*S^4 - 17*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + (3*S*(-9 + 10*S^2 + 5*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (S*(-147 + 242*S^2 + 121*S^4)*HPL[{4, 1}, -S^2])/(2*(1 + S^2)^2) + ((215 - 966*S^2 + 437*S^4 + 50*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-182 + 66*S^2 + 33*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(-1073 + 346*S^2 + 173*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-699 + 170*S^2 + 85*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (-((1 + S^2)*(-21 + 113*S^2))/(8*S^3) - (Pi^2*S*(-17 + 48*S^2 + 24*S^4))/(6*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(18 - 103*S^2 + 32*S^4))/(8*S^3) + (Pi^2*(425 - 1666*S^2 + 491*S^4 + 50*S^6))/(24*S*(1 + S^2)^2) - (3*S*(-9 + 10*S^2 + 5*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) - (2*S*(-182 + 66*S^2 + 33*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (3*S*(-8 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) - (S*(-25 + 106*S^2 + 53*S^4)*Zeta[5])/(2*(1 + S^2)^2))) + Log[T]^2*((-3*(-40 + 27*S^2))/(2*S) + (Pi^2*(322 - 322*S^2 + 233*S^4))/(48*S) + (Pi^4*(2496 - 5009*S^2 + 1156*S^4))/(1440*S) + (Pi^6*S*(-240902 + 41046*S^2 + 20523*S^4))/(45360*(1 + S^2)^2) - (S*(23 + 10*S^2 + 5*S^4)*HPL[{0}, S^2]^6)/(48*(1 + S^2)^2) + ((3 + 40*S^2 - 174*S^4 + 216*S^6 - 21*S^8)*HPL[{1}, -S^2]^5)/(S^3*(1 + S^2)^2) + (56*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^5*(-(S*(1325 + 548*S^2 + 307*S^4))/(240*(1 + S^2)^2) + (S*(-263 + 16*S^2 + 8*S^4)*HPL[{1}, -S^2])/(60*(1 + S^2)^2)) + ((Pi^2*S*(-495 + 224*S^2 + 112*S^4))/(6*(1 + S^2)^2) + (-22 + 138*S^2 - 49*S^4 + 4*S^6)/(4*S^3))*HPL[{2}, -S^2]^2 + 22*S*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(33 + 35*S^2))/(12*S^3) + (5*Pi^2*S*(-137 + 74*S^2 + 37*S^4))/(6*(1 + S^2)^2) - 65*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^4*((90 - 431*S^2 + 28*S^4)/(96*S) - (Pi^2*S*(619 + 130*S^2 + 65*S^4))/(144*(1 + S^2)^2) + ((45 + 548*S^2 - 1514*S^4 + 234*S^6 - 21*S^8)*HPL[{1}, -S^2])/(48*S^3*(1 + S^2)^2) + (S*(-537 + 62*S^2 + 31*S^4)*HPL[{1}, -S^2]^2)/(24*(1 + S^2)^2) + (S*(-226 + 30*S^2 + 15*S^4)*HPL[{2}, -S^2])/(24*(1 + S^2)^2)) + (2*S*(-16 + 42*S^2 + 21*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + ((-5*Pi^2*S*(-29 + 78*S^2 + 39*S^4))/(6*(1 + S^2)^2) + (-106 - 272*S^2 - 447*S^4 + 28*S^6)/(4*S^3))*HPL[{4}, -S^2] + ((60 + 178*S^2 - 16*S^4 - 593*S^6 - 27*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)^2) - (S*(22 + 222*S^2 + 111*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (8*S*(-171 + 50*S^2 + 25*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((-4*Pi^2*S*(-7 + 96*S^2 + 48*S^4))/(3*(1 + S^2)^2) + (135 + 296*S^2 + 201*S^4 - 52*S^6)/(2*S^3))*HPL[{3, 1}, -S^2] + ((6 - 7*S^2 - 233*S^4 + 2437*S^6 - 479*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)^2) + ((-27 - 166*S^2 - 1187*S^4 + 8260*S^6 - 1428*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^2) + (13*S*(-5 + 26*S^2 + 13*S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 + (2*S*(-243 + 866*S^2 + 433*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((16*Pi^2*S*(-19 + 60*S^2 + 30*S^4))/(3*(1 + S^2)^2) + (24*(-4 - 9*S^2 - 6*S^4 + 2*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (4*(-18 - 220*S^2 + 515*S^4 - 734*S^6 + 117*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (4*(-63 - 706*S^2 + 1244*S^4 - 826*S^6 + 91*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - 88*S*HPL[{3, 1, 2}, -S^2] + 440*S*HPL[{3, 2, 1}, -S^2] + (16*S*(137 + 108*S^2 + 54*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(45 + 479*S^2 - 1180*S^4 + 334*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) - (8*S*(241 + 150*S^2 + 75*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 1920*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((5 - 121*S^2 - 10*S^4)/(2*S) + (2*Pi^2*S*(20 - 313*S^2 + 83*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (20*S*(3 + 2*S^2 + S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((-104 + 22*S^2 + 117*S^4 + 10*S^6)/(2*S^3) + (Pi^2*(-93 - 1024*S^2 + 1671*S^4 + 650*S^6 - 384*S^8))/(6*S^3*(1 + S^2)^2) - (1568*S*Zeta[3])/(1 + S^2)^2) + HPL[{0}, S^2]^3*((120 - 227*S^2 + 90*S^4)/(48*S) - (Pi^2*S*(591 + 64*S^2 + 109*S^4))/(18*(1 + S^2)^2) + ((21 + 269*S^2 - 805*S^4 + 367*S^6 - 40*S^8)*HPL[{1}, -S^2]^2)/(6*S^3*(1 + S^2)^2) + (S*(-633 + 194*S^2 + 97*S^4)*HPL[{1}, -S^2]^3)/(9*(1 + S^2)^2) + ((-21 - 32*S^2 - 474*S^4 + 143*S^6 - 54*S^8)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(36 + 2*S^2 + S^4))/(6*S^3) + (Pi^2*S*(-1159 + 226*S^2 + 113*S^4))/(36*(1 + S^2)^2) + (S*(-289 + 82*S^2 + 41*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) - (2*S*(5 + 4*S^2 + 2*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (S*(331 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) - (S*(4 + 30*S^2 + 15*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*(((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(6*S^3) + (Pi^2*(45 + 554*S^2 - 2338*S^4 + 2254*S^6 - 119*S^8))/(9*S^3*(1 + S^2)^2) + (8*(16 - 65*S^2 + 16*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) - (20*S*(-123 + 134*S^2 + 67*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + 260*S*HPL[{2, 1}, -S^2] - (20*S*(-31 + 38*S^2 + 19*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((-191 - 238*S^2 - 967*S^4 + 46*S^6)/(8*S^3) + (Pi^2*(21 + 93*S^2 + 300*S^4 - 1499*S^6 + 261*S^8))/(6*S^3*(1 + S^2)^2) - (8*S*(215 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-21 + 58*S^2 + 29*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(-335 - 713*S^2 + 28*S^4))/(8*S^3) + (Pi^2*(1 + S^2)*(341 + 79*S^2 + 44*S^4))/(24*S^3) + (Pi^4*S*(-21933 + 9518*S^2 + 4759*S^4))/(360*(1 + S^2)^2) + ((3*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 - (Pi^2*S*(447 + 110*S^2 + 55*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2] + (196*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((-15 - 70*S^2 + 904*S^4 - 2578*S^6 + 263*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) - (4*S*(-111 + 110*S^2 + 55*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (24*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4*S*(-27 + 278*S^2 + 139*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - 780*S*HPL[{2, 1, 1}, -S^2] + (4*(-23 + 136*S^2 - 493*S^4 + 98*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{2}, -S^2]*((Pi^4*S*(-1258 + 1526*S^2 + 763*S^4))/(120*(1 + S^2)^2) + (Pi^2*(-28 - 27*S^2 - 36*S^4 + 12*S^6))/(3*S^3) + (-106 - 465*S^2 - 162*S^4 + 233*S^6)/(8*S^3) + ((9 + 61*S^2 - 1295*S^4 + 221*S^6)*HPL[{3}, -S^2])/(S*(1 + S^2)^2) - (S*(-57 + 338*S^2 + 169*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(-18 - 220*S^2 + 515*S^4 - 734*S^6 + 117*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (112*S*(-13 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*S*(-171 + 50*S^2 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-3 + 24*S^2 + 269*S^4 - 1042*S^6 + 284*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((Pi^2*(180 - 575*S^2 + 76*S^4))/(48*S) + (160 - 250*S^2 + 233*S^4)/(16*S) + (Pi^4*S*(-8046 + 806*S^2 + 403*S^4))/(720*(1 + S^2)^2) + ((45 + 508*S^2 - 2066*S^4 + 1268*S^6 + 77*S^8)*HPL[{1}, -S^2]^3)/(6*S^3*(1 + S^2)^2) + (5*S*(-53 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^4)/(2*(1 + S^2)^2) + ((Pi^2*S*(-166 + 90*S^2 + 45*S^4))/(4*(1 + S^2)^2) + (2*(-8 - 9*S^4 + 3*S^6))/S^3)*HPL[{2}, -S^2] + (S*(-153 + 124*S^2 + 62*S^4)*HPL[{2}, -S^2]^2)/(2*(1 + S^2)^2) + HPL[{1}, -S^2]^2*(((1 + S^2)*(44 - 24*S^2 + 11*S^4))/(2*S^3) + (Pi^2*S*(-666 + 166*S^2 + 83*S^4))/(6*(1 + S^2)^2) + (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2}, -S^2])/(2*(1 + S^2)^2)) + ((12 + 47*S^2 - S^4 - 123*S^6 + S^8)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^2) - (S*(7 + 30*S^2 + 15*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((-24 - 250*S^2 + 485*S^4 - 98*S^6 - 25*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (S*(-269 + 234*S^2 + 117*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*S*(-34 + 30*S^2 + 15*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (S*(15 + 98*S^2 + S^4)*Zeta[3])/(1 + S^2)^2 + HPL[{1}, -S^2]*(((1 + S^2)*(40 - 21*S^2 + 17*S^4))/(2*S^3) + (Pi^2*(45 + 528*S^2 - 1790*S^4 + 751*S^6 + 28*S^8))/(12*S^3*(1 + S^2)^2) + ((215 - 966*S^2 + 437*S^4 + 50*S^6)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^2) - (S*(-19 + 50*S^2 + 25*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (S*(-49 + 66*S^2 + 33*S^4)*Zeta[3])/(1 + S^2)^2)) + (2*S*(42 - 463*S^2 + 255*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{0}, S^2]*((269 + 1219*S^2 - 153*S^4)/(8*S) + (Pi^2*(270 + 287*S^2 + 114*S^4))/(48*S) - (Pi^4*S*(7465 - 3187*S^2 + 1531*S^4))/(180*(1 + S^2)^2) - (5*(-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^4)/(2*S^3*(1 + S^2)^2) + (56*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 + ((-15 - 608*S^2 + 827*S^4 - 148*S^6)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(33 + 35*S^2))/(6*S^3) + (Pi^2*S*(-1893 + 1034*S^2 + 517*S^4))/(9*(1 + S^2)^2) + (250*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (-(Pi^2*S*(23 + 90*S^2 + 45*S^4))/(6*(1 + S^2)^2) + (113 - 84*S^2 - 71*S^4 - 36*S^6)/(4*S^3))*HPL[{3}, -S^2] + ((-39 - 46*S^2 - 151*S^4 - 84*S^6 - 124*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)^2) - (2*S*(26 + 6*S^2 + 3*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((Pi^2*S*(1111 + 62*S^2 + 31*S^4))/(3*(1 + S^2)^2) + (-157 - 224*S^2 - 95*S^4 + 44*S^6)/(2*S^3))*HPL[{2, 1}, -S^2] + ((51 + 60*S^2 + 1016*S^4 - 1644*S^6 + 349*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-47 + 210*S^2 + 105*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (2*S*(-43 + 278*S^2 + 139*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (2*(45 + 48*S^2 + 1019*S^4 - 1642*S^6 + 342*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (16*S*(-193 + 6*S^2 + 3*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(2319 + 2*S^2 + S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (240*S*(26 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-6 - 57*S^2 + 4*S^4)/(2*S) - (2*Pi^2*S*(-17 + 60*S^2 + 30*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-68 + 52*S^2 + 127*S^4 + 26*S^6)/(4*S^3) + (Pi^2*(-87 - 112*S^2 - 1967*S^4 + 1928*S^6 - 450*S^8))/(12*S^3*(1 + S^2)^2) - (S*(-25 + 102*S^2 + 51*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (8*S*(-193 + 6*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-20 + 42*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*(((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(4*S^3) + (Pi^2*(87 + 1138*S^2 - 4220*S^4 + 3974*S^6 - 395*S^8))/(12*S^3*(1 + S^2)^2) - (4*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2}, -S^2])/(S*(1 + S^2)^2) - (2*S*(-27 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (750*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-123 + 86*S^2 + 43*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(309 + 183*S^2 + 4*S^4))/(24*S^3) - ((1 + S^2)*(-335 - 713*S^2 + 28*S^4))/(8*S^3) + (Pi^4*S*(-9992 + 4382*S^2 + 2191*S^4))/(180*(1 + S^2)^2) + (-((1 + S^2)*(-25 - 109*S^2 + 20*S^4))/(2*S^3) + (Pi^2*S*(-1703 + 914*S^2 + 457*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2] + (196*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 - (2*(6 - 19*S^2 - 58*S^4 + 75*S^6 + 40*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-63 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (8*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) - (12*S*(-187 + 126*S^2 + 63*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (1500*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-3 - 16*S^2 + 244*S^4 - 456*S^6 - 49*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) - (10*S*(-8 + 10*S^2 + 5*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(301 + 161*S^2 + 80*S^4))/(24*S^3) - ((1 + S^2)*(-509 - 1204*S^2 + 153*S^4))/(8*S^3) + (Pi^4*(624 + 6826*S^2 - 26844*S^4 + 19799*S^6 - 539*S^8))/(360*S^3*(1 + S^2)^2) + ((15 + 252*S^2 - 1232*S^4 + 1544*S^6 - 123*S^8)*HPL[{2}, -S^2]^2)/(2*S^3*(1 + S^2)^2) + (((1 + S^2)*(-13 - 155*S^2 + 14*S^4))/S^3 - (2*Pi^2*S*(-317 + 360*S^2 + 180*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((29 + 353*S^2 - 1059*S^4 - 55*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) - (4*S*(-55 + 106*S^2 + 53*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((-6*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 + (2*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(91 - 164*S^2 - 517*S^4 + 70*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-505 + 558*S^2 + 279*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (4*S*(-1737 + 1894*S^2 + 947*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (48*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + (1568*S*(-3 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (8*S*(-1149 + 506*S^2 + 253*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + 1560*S*HPL[{2, 1, 1, 1}, -S^2] + (((1 + S^2)*(11 - 271*S^2 + 44*S^4))/(2*S^3) - (2*Pi^2*S*(-257 + 318*S^2 + 159*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(55 - 335*S^2 + 72*S^4))/(4*S^3) + (Pi^2*(407 - 1554*S^2 - 151*S^4 + 242*S^6))/(6*S*(1 + S^2)^2) - (2*S*(-505 + 558*S^2 + 279*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (112*S*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) - (2*S*(-431 + 658*S^2 + 329*S^4)*Zeta[5])/(1 + S^2)^2)) + (6*S*(5 - 73*S^2 + 83*S^4)*Zeta[7])/(1 + S^2)^2 + HPL[{0}, S^2]*((4875 + 29099*S^2 - 4410*S^4)/(64*S) + (Pi^2*(974 + 1991*S^2 - 191*S^4))/(192*S) + (Pi^4*(1930 - 11023*S^2 - 58*S^4))/(2880*S) - (Pi^6*S*(374505 - 60002*S^2 + 63467*S^4))/(90720*(1 + S^2)^2) + ((3 + 40*S^2 - 174*S^4 + 216*S^6 - 21*S^8)*HPL[{1}, -S^2]^6)/(6*S^3*(1 + S^2)^2) + (8*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^2) + ((-15 - 17*S^2 - 440*S^4 + 851*S^6 - 127*S^8)*HPL[{2}, -S^2]^3)/(12*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*(((1 + S^2)*(33 + 35*S^2))/(12*S^3) + (Pi^2*S*(-1893 + 1034*S^2 + 517*S^4))/(90*(1 + S^2)^2) + (25*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + ((4 + 30*S^2 + 45*S^4 + 27*S^6)*HPL[{3}, -S^2]^2)/(2*S*(1 + S^2)^2) + (-(Pi^2*S*(47 + 2*S^2 + S^4))/(6*(1 + S^2)^2) + (125 + 22*S^2 - 16*S^4 - 34*S^6)/(4*S^3))*HPL[{5}, -S^2] + ((-75 - 155*S^2 - 151*S^4 + 43*S^6 - 32*S^8)*HPL[{6}, -S^2])/(2*S^3*(1 + S^2)^2) - (S*(78 + 22*S^2 + 11*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 + ((15 + 608*S^2 - 827*S^4 + 148*S^6)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)^2) + ((Pi^2*S*(-11 + 98*S^2 + 49*S^4))/(4*(1 + S^2)^2) + (45 + 116*S^2 + 223*S^4 + 44*S^6)/(8*S^3))*HPL[{3, 2}, -S^2] + ((Pi^2*S*(1 + 382*S^2 + 191*S^4))/(6*(1 + S^2)^2) + (-65 + 113*S^2 + 201*S^4 + 32*S^6)/(2*S^3))*HPL[{4, 1}, -S^2] + ((-15 + S^2 + 68*S^4 + 64*S^6)*HPL[{4, 2}, -S^2])/(4*S^3*(1 + S^2)) - (S*(22 + 18*S^2 + 9*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + ((30 + 36*S^2 + 137*S^4 + 157*S^6 + 134*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)^2) - (21*S*(3 + 2*S^2 + S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (S*(26 + 38*S^2 + 19*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((Pi^2*S*(-1085 + 34*S^2 + 17*S^4))/(3*(1 + S^2)^2) + (101 + 288*S^2 + 113*S^4 - 4*S^6)/(2*S^3))*HPL[{2, 2, 1}, -S^2] + ((2*Pi^2*S*(-1639 + 6*S^2 + 3*S^4))/(3*(1 + S^2)^2) - (2*(-104 - 195*S^2 - 67*S^4 + 12*S^6))/S^3)*HPL[{3, 1, 1}, -S^2] + ((3 + 4*S^2 - 11*S^4)*HPL[{3, 1, 2}, -S^2])/(2*S^3) + ((-57 - 58*S^2 - 1760*S^4 + 3386*S^6 - 519*S^8)*HPL[{3, 2, 1}, -S^2])/(2*S^3*(1 + S^2)^2) - (5*S*(-13 + 70*S^2 + 35*S^4)*HPL[{3, 2, 2}, -S^2])/(2*(1 + S^2)^2) - (8*S*(-13 + 68*S^2 + 34*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + ((-129 - 148*S^2 - 2791*S^4 + 5022*S^6 - 886*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (S*(-95 + 562*S^2 + 281*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 - (S*(-323 + 1642*S^2 + 821*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-145 + 816*S^2 + 408*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((2*Pi^2*S*(1111 + 62*S^2 + 31*S^4))/(3*(1 + S^2)^2) + (-157 - 224*S^2 - 95*S^4 + 44*S^6)/S^3)*HPL[{2, 1, 1, 1}, -S^2] + (8*S*(373 + 38*S^2 + 19*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(1 + S^2)^2 + (2*(51 + 60*S^2 + 1016*S^4 - 1644*S^6 + 349*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (2*S*(4523 + 246*S^2 + 123*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 - (2*S*(4523 + 246*S^2 + 123*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(8999 + 702*S^2 + 351*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (4*S*(13471 + 1090*S^2 + 545*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(45 + 48*S^2 + 1019*S^4 - 1642*S^6 + 342*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (32*S*(-193 + 6*S^2 + 3*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (96*S*(-193 + 6*S^2 + 3*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (8*S*(-3857 + 194*S^2 + 97*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (480*S*(26 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((Pi^2*(-3 - 227*S^2 + 44*S^4))/(12*S) + (-80 - 783*S^2 + 110*S^4)/(16*S) - (Pi^4*S*(77 + 612*S^2 + 306*S^4))/(120*(1 + S^2)^2))*Zeta[3] - (S*(29 + 14*S^2 + 19*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{4}, -S^2]*((31 + 328*S^2 - 664*S^4 - 16*S^6)/(16*S^3) + (Pi^2*(-21 - 35*S^2 - 72*S^4 - 18*S^6 - 40*S^8))/(6*S^3*(1 + S^2)^2) - (2*S*(1 + 10*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (S*(1 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((23 - 94*S^2 - 275*S^4 - 82*S^6)/(8*S^3) + (Pi^2*(105 + 140*S^2 + 1936*S^4 - 1980*S^6 + 439*S^8))/(12*S^3*(1 + S^2)^2) + (4*S*(-22 + 42*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-68 + 52*S^2 + 127*S^4 + 26*S^6)/(2*S^3) + (Pi^2*(-87 - 112*S^2 - 1967*S^4 + 1928*S^6 - 450*S^8))/(6*S^3*(1 + S^2)^2) - (8*S*(-20 + 42*S^2 + 21*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*(((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(24*S^3) + (Pi^2*(87 + 1138*S^2 - 4220*S^4 + 3974*S^6 - 395*S^8))/(72*S^3*(1 + S^2)^2) - (2*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) - (S*(-27 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - (125*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (S*(-123 + 86*S^2 + 43*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((45 - 52*S^2 + 50*S^4 + 20*S^6)/(16*S^3) + (Pi^2*(-3 - 64*S^2 - 2107*S^4 + 2014*S^6 - 348*S^8))/(48*S^3*(1 + S^2)^2) - (15*S*(-1 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(4*(1 + S^2)^2) + (S*(373 + 38*S^2 + 19*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (S*(-37 + 90*S^2 + 45*S^4)*Zeta[3])/(2*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^2)*(309 + 183*S^2 + 4*S^4))/(72*S^3) - ((1 + S^2)*(-335 - 713*S^2 + 28*S^4))/(24*S^3) + (Pi^4*S*(-9992 + 4382*S^2 + 2191*S^4))/(540*(1 + S^2)^2) + (-((1 + S^2)*(-25 - 109*S^2 + 20*S^4))/(6*S^3) + (Pi^2*S*(-1703 + 914*S^2 + 457*S^4))/(18*(1 + S^2)^2))*HPL[{2}, -S^2] + (196*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (2*(6 - 19*S^2 - 58*S^4 + 75*S^6 + 40*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) + (S*(-63 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (8*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)^2) - (4*S*(-187 + 126*S^2 + 63*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (500*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-3 - 16*S^2 + 244*S^4 - 456*S^6 - 49*S^8)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*(-(Pi^4*S*(213 + 226*S^2 + 113*S^4))/(240*(1 + S^2)^2) + (593 + 600*S^2 + 1371*S^4 - 64*S^6)/(32*S^3) + (Pi^2*(248 - 184*S^2 - 155*S^4 - 52*S^6))/(48*S^3) + (S*(13 + 16*S^2 + 8*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + ((27 + 6*S^2 - 342*S^4 - 86*S^6 - 69*S^8)*HPL[{2, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(-23 + 90*S^2 + 45*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-25 + 102*S^2 + 51*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((3 + 16*S^2 - 5*S^4 - 74*S^6 - 40*S^8)*Zeta[3])/(2*S^3*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((Pi^4*S*(10796 + 42*S^2 + 21*S^4))/(360*(1 + S^2)^2) + (Pi^2*(-325 - 286*S^2 - 177*S^4 + 68*S^6))/(24*S^3) + (-158 - 707*S^2 - 404*S^4 + 181*S^6)/(8*S^3) + (2*S*(-771 + 26*S^2 + 13*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (16*S*(-193 + 6*S^2 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((3 + 8*S^2 - 228*S^4 + 110*S^6 + 15*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + ((-3*Pi^2*S*(-2 + 14*S^2 + 7*S^4))/(2*(1 + S^2)^2) + (-12 - 169*S^2 + 60*S^4)/(4*S))*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(118 + 151*S^2 + 21*S^4))/(24*S^3) - ((1 + S^2)*(-509 - 1204*S^2 + 153*S^4))/(16*S^3) + (Pi^4*(609 + 7596*S^2 - 23580*S^4 + 15731*S^6 - 2434*S^8))/(720*S^3*(1 + S^2)^2) + ((15 + 252*S^2 - 1232*S^4 + 1544*S^6 - 123*S^8)*HPL[{2}, -S^2]^2)/(4*S^3*(1 + S^2)^2) + (-(Pi^2*S*(-15 + 14*S^2 + 7*S^4))/(6*(1 + S^2)^2) - ((1 + S^2)*(5 + 23*S^2 + 16*S^4))/(4*S^3))*HPL[{3}, -S^2] + ((3 + 110*S^2 - 32*S^4 + 106*S^6 - 123*S^8)*HPL[{4}, -S^2])/(4*S^3*(1 + S^2)^2) + (S*(-29 + 34*S^2 + 17*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (((1 + S^2)*(-25 - 109*S^2 + 20*S^4))/(2*S^3) - (Pi^2*S*(-1703 + 914*S^2 + 457*S^4))/(6*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-3 - 290*S^2 + 1116*S^4 - 1394*S^6 + 203*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) + (38*S*(-3 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (S*(-279 + 170*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (8*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (4*S*(-1737 + 1162*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (1500*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-4*(1 + S^2)*(2 + S^2))/S^3 - (Pi^2*S*(-131 + 114*S^2 + 57*S^4))/(6*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-17 - 323*S^2 + 40*S^4))/(8*S^3) + (Pi^2*(3 + 1034*S^2 - 3750*S^4 + 3362*S^6 - 497*S^8))/(24*S^3*(1 + S^2)^2) - (19*S*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 - (392*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (41*S*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) - (2*S*(-46 + 38*S^2 + 19*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]*((84 + 1575*S^2 + 1357*S^4 - 91*S^6)/(32*S^3) + (Pi^2*(-85 - 81*S^2 + 102*S^4 + 76*S^6))/(48*S^3) + (Pi^4*(-609 - 923*S^2 - 13170*S^4 + 5581*S^6 - 3113*S^8))/(720*S^3*(1 + S^2)^2) + (-(Pi^2*S*(-19 + 142*S^2 + 71*S^4))/(12*(1 + S^2)^2) + (-21 - 24*S^2 - 145*S^4 - 24*S^6)/(8*S^3))*HPL[{3}, -S^2] + ((3 - 22*S^2 - 177*S^4 - 264*S^6 - 144*S^8)*HPL[{4}, -S^2])/(4*S^3*(1 + S^2)^2) - (2*S*(9 + 16*S^2 + 8*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (-(Pi^2*S*(-1085 + 34*S^2 + 17*S^4))/(6*(1 + S^2)^2) + (-101 - 288*S^2 - 113*S^4 + 4*S^6)/(4*S^3))*HPL[{2, 1}, -S^2] + ((3 + 28*S^2 + 1222*S^4 - 1616*S^6 + 323*S^8)*HPL[{3, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(-29 + 182*S^2 + 91*S^4)*HPL[{3, 2}, -S^2])/(2*(1 + S^2)^2) + (S*(-43 + 290*S^2 + 145*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (2*(15 + 608*S^2 - 827*S^4 + 148*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (4*S*(373 + 38*S^2 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(2263 + 126*S^2 + 63*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (16*S*(-193 + 6*S^2 + 3*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-13*Pi^2*S*(-3 + 8*S^2 + 4*S^4))/(6*(1 + S^2)^2) + (39 - 58*S^2 - 57*S^4 + 4*S^6)/(4*S^3))*Zeta[3] - (S*(-26 + 54*S^2 + 27*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(497 + 561*S^2 + 12*S^4))/(96*S^3) + (Pi^4*(1 + S^2)*(2183 - 1405*S^2 + 322*S^4))/(1440*S^3) - ((1 + S^2)*(-3797 - 9057*S^2 + 1610*S^4))/(64*S^3) + (Pi^6*S*(-215646 + 66682*S^2 + 33341*S^4))/(45360*(1 + S^2)^2) + (((1 + S^2)*(55 + 81*S^2))/(8*S^3) + (Pi^2*S*(-432 + 238*S^2 + 119*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (59*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^3)/(2*(1 + S^2)^2) - (S*(-5 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2]^2)/(2*(1 + S^2)^2) + (((1 + S^2)*(45 - 157*S^2 + 12*S^4))/(8*S^3) + (Pi^2*S*(-109 + 102*S^2 + 51*S^4))/(12*(1 + S^2)^2))*HPL[{4}, -S^2] + ((9 + 110*S^2 + 70*S^4 + 88*S^6 - 65*S^8)*HPL[{5}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(-41 + 64*S^2 + 32*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 - (392*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + (((1 + S^2)*(-25 - 29*S^2 + 8*S^4))/S^3 - (Pi^2*S*(-283 + 154*S^2 + 77*S^4))/(1 + S^2)^2)*HPL[{3, 1}, -S^2] + ((15 + 8*S^2 - 148*S^4 + 188*S^6 + 25*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)^2) + ((87 - 62*S^2 - 856*S^4 + 1022*S^6 + 273*S^8)*HPL[{4, 1}, -S^2])/(2*S^3*(1 + S^2)^2) - (3*S*HPL[{4, 2}, -S^2])/2 - (4*S*(-16 + 22*S^2 + 11*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + (-(((1 + S^2)*(-25 - 109*S^2 + 20*S^4))/S^3) + (Pi^2*S*(-1703 + 914*S^2 + 457*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (2*(-33 - 794*S^2 + 3580*S^4 - 4482*S^6 + 449*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (708*S*(-3 + 2*S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(-3249 + 2182*S^2 + 1091*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (16*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (24*S*(-187 + 126*S^2 + 63*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (3000*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (((1 + S^2)*(-65 - 59*S^2 + 10*S^4))/(4*S^3) + (Pi^2*(-3 + 8*S^2 + 194*S^4 - 666*S^6 - 97*S^8))/(12*S^3*(1 + S^2)^2))*Zeta[3] + (2*S*(-13 + 8*S^2 + 4*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{3}, -S^2]*((-5*(1 + S^2)*(-1 - 17*S^2 + 6*S^4))/(8*S^3) + (Pi^2*(-12 + 33*S^2 + 52*S^4 - 96*S^6 - 59*S^8))/(6*S^3*(1 + S^2)^2) + (38*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(-17 - 323*S^2 + 40*S^4))/(4*S^3) + (Pi^2*(-3 - 1034*S^2 + 3750*S^4 - 3362*S^6 + 497*S^8))/(12*S^3*(1 + S^2)^2) + (82*S*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(-129 - 191*S^2 + 52*S^4))/(48*S^3) - ((1 + S^2)*(-55 - 1043*S^2 + 142*S^4))/(16*S^3) + (Pi^4*S*(-8833 + 3884*S^2 + 1942*S^4))/(360*(1 + S^2)^2) + ((-15 - 8*S^2 + 148*S^4 - 188*S^6 - 25*S^8)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(-9 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (392*S*(-3 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((3 - 2*S^2 + 258*S^4 - 458*S^6 - 65*S^8)*Zeta[3])/(2*S^3*(1 + S^2)^2)) + ((-3 + 8*S^2 + 58*S^4 - 289*S^6 - 76*S^8)*Zeta[5])/(S^3*(1 + S^2)^2)) + (15*S*(7 + 4*S^2 + 2*S^4)*Zeta[7])/(1 + S^2)^2) + Log[T]*((3*(-1625 + 708*S^2))/(32*S) + (Pi^2*(-682 + 1019*S^2 - 553*S^4))/(96*S) + (Pi^4*(-426 + 1173*S^2 - 386*S^4))/(288*S) + (Pi^6*S*(368915 - 149312*S^2 + 4623*S^4))/(45360*(1 + S^2)^2) + (S*(4 + 2*S^2 + S^4)*HPL[{0}, S^2]^7)/(48*(1 + S^2)^2) + ((-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^6)/(3*S^3*(1 + S^2)^2) - (16*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^7)/(3*(1 + S^2)^2) + HPL[{0}, S^2]^6*((S*(57 + 35*S^2 + 14*S^4))/(48*(1 + S^2)^2) + (S*(19 + 2*S^2 + S^4)*HPL[{1}, -S^2])/(24*(1 + S^2)^2)) + ((15 + 42*S^2 + 106*S^4 - 29*S^6)*HPL[{2}, -S^2]^3)/(6*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(33 + 35*S^2))/(6*S^3) - (Pi^2*S*(-137 + 74*S^2 + 37*S^4))/(3*(1 + S^2)^2) + 26*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^5*((3*(-1 + 8*S^2))/(16*S) + (Pi^2*S*(350 + 114*S^2 + 57*S^4))/(360*(1 + S^2)^2) + ((-45 - 660*S^2 + 1490*S^4 + 114*S^6 + 177*S^8)*HPL[{1}, -S^2])/(240*S^3*(1 + S^2)^2) - (S*(-263 + 16*S^2 + 8*S^4)*HPL[{1}, -S^2]^2)/(60*(1 + S^2)^2) + (S*(235 + 8*S^2 + 4*S^4)*HPL[{2}, -S^2])/(120*(1 + S^2)^2)) + ((2 + 17*S^2 - 338*S^4 - 57*S^6)*HPL[{3}, -S^2]^2)/(2*S*(1 + S^2)^2) + ((5*Pi^2*S*(1 + 50*S^2 + 25*S^4))/(3*(1 + S^2)^2) + (-285 + 94*S^2 + 466*S^4 - 10*S^6)/(2*S^3))*HPL[{5}, -S^2] + ((105 + 115*S^2 + 631*S^4 + 1145*S^6 + 346*S^8)*HPL[{6}, -S^2])/(S^3*(1 + S^2)^2) + (2*S*(169 + 368*S^2 + 184*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 - (2*(3 - 32*S^2 + 717*S^4 - 810*S^6 + 6*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)^2) + (-(Pi^2*S*(-345 + 2614*S^2 + 1307*S^4))/(6*(1 + S^2)^2) + (-55 + 36*S^2 - 879*S^4 + 28*S^6)/(4*S^3))*HPL[{3, 2}, -S^2] + (-(Pi^2*S*(-743 + 4150*S^2 + 2075*S^4))/(3*(1 + S^2)^2) + (88 - 228*S^2 - 1577*S^4 + 56*S^6)/(2*S^3))*HPL[{4, 1}, -S^2] + ((15 + 2*S^2 - 111*S^4 - 1260*S^6 - 226*S^8)*HPL[{4, 2}, -S^2])/(2*S^3*(1 + S^2)^2) + (2*S*(3 + 100*S^2 + 50*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 - (2*(27 + 26*S^2 + 199*S^4 + 1849*S^6 + 297*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)^2) + (2*S*(5 + 214*S^2 + 107*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 - (2*S*(48 + 194*S^2 + 97*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + ((-4*Pi^2*S*(-457 + 300*S^2 + 150*S^4))/(3*(1 + S^2)^2) + (2*(-77 + 2*S^2 - 130*S^4 + 4*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + ((-8*Pi^2*S*(-609 + 106*S^2 + 53*S^4))/(3*(1 + S^2)^2) + (-501 + 112*S^2 - 319*S^4 + 12*S^6)/S^3)*HPL[{3, 1, 1}, -S^2] + (2*(-6 - 5*S^2 + 116*S^4 + 37*S^6)*HPL[{3, 1, 2}, -S^2])/(S^3*(1 + S^2)) - (2*(-24 - 79*S^2 - 328*S^4 + 21*S^6)*HPL[{3, 2, 1}, -S^2])/(S^3*(1 + S^2)) + (S*(-933 + 4654*S^2 + 2327*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 + (8*S*(-341 + 1810*S^2 + 905*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (2*(117 + 396*S^2 + 1003*S^4 + 2090*S^6 + 38*S^8)*HPL[{4, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (2*S*(-1285 + 7242*S^2 + 3621*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 + (2*S*(-4165 + 22074*S^2 + 11037*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 + (4*S*(-4333 + 22654*S^2 + 11327*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((-24*(-14 + 3*S^2 + 11*S^4))/S^3 - (56*Pi^2*S*(53 + 50*S^2 + 25*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - 2384*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(27 + 84*S^2 + 114*S^4 + 392*S^6 + 3*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (16*S*(533 + 282*S^2 + 141*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (16*S*(533 + 282*S^2 + 141*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 + (3136*S*(5 + 6*S^2 + 3*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (16*S*(3053 + 3422*S^2 + 1711*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (40*(-9 - 19*S^2 - 76*S^4 + 10*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (64*S*(-123 + 146*S^2 + 73*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 + (192*S*(-123 + 146*S^2 + 73*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (80*S*(-553 + 842*S^2 + 421*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 - 10080*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((16 + 279*S^2 - 13*S^4)/(4*S) + (Pi^2*(-1 + 50*S^2 - 2*S^4))/(2*S) + (Pi^4*S*(-212 + 5654*S^2 + 2827*S^4))/(180*(1 + S^2)^2))*Zeta[3] + (2*S*(18 - 19*S^2 + 3*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{0}, S^2]^4*((-25 + 165*S^2 - 22*S^4)/(32*S) + (Pi^2*S*(702 + 281*S^2 + 133*S^4))/(72*(1 + S^2)^2) + ((-45 - 548*S^2 + 1514*S^4 - 234*S^6 + 21*S^8)*HPL[{1}, -S^2]^2)/(48*S^3*(1 + S^2)^2) - (S*(-537 + 62*S^2 + 31*S^4)*HPL[{1}, -S^2]^3)/(36*(1 + S^2)^2) + ((45 + 66*S^2 + 961*S^4 + 60*S^6 + 84*S^8)*HPL[{2}, -S^2])/(48*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*S*(-1107 + 2*S^2 + S^4))/(144*(1 + S^2)^2) - ((1 + S^2)*(165 - 237*S^2 + 28*S^4))/(96*S^3) - (S*(-469 + 26*S^2 + 13*S^4)*HPL[{2}, -S^2])/(24*(1 + S^2)^2)) + (S*(2 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2])/(4*(1 + S^2)^2) - (S*(243 + 4*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(12*(1 + S^2)^2) + (10*S*Zeta[3])/3) + HPL[{2, 1, 1}, -S^2]*((49 + 258*S^2 + 146*S^4 - 82*S^6)/S^3 + (Pi^2*(93 + 210*S^2 + 1437*S^4 - 348*S^6 - 100*S^8))/(3*S^3*(1 + S^2)^2) + (448*S*(-2 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(12*S^3) + (Pi^2*(-45 - 554*S^2 + 2338*S^4 - 2254*S^6 + 119*S^8))/(18*S^3*(1 + S^2)^2) - (4*(16 - 65*S^2 + 16*S^4)*HPL[{2}, -S^2])/(S*(1 + S^2)) + (10*S*(-123 + 134*S^2 + 67*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) - 130*S*HPL[{2, 1}, -S^2] + (10*S*(-31 + 38*S^2 + 19*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*((-315 + 800*S^2 + 1002*S^4 - 176*S^6)/(8*S^3) + (Pi^2*(30 + 56*S^2 + 147*S^4 + 924*S^6 + 123*S^8))/(6*S^3*(1 + S^2)^2) + (4*S*(141 + 56*S^2 + 28*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(3 + 62*S^2 + 31*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*((66 - 272*S^2 + 79*S^4 - 28*S^6)/(8*S^3) + (Pi^2*(9 - 60*S^2 + 2357*S^4 - 2462*S^6 - 32*S^8))/(24*S^3*(1 + S^2)^2) + (S*(-319 + 1226*S^2 + 613*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) - 298*S*HPL[{2, 1}, -S^2] + (2*S*(-35 + 284*S^2 + 142*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-115 - 774*S^2 - 369*S^4 + 214*S^6)/(4*S^3) + (Pi^2*(-111 - 250*S^2 - 1181*S^4 - 124*S^6 + 38*S^8))/(6*S^3*(1 + S^2)^2) - (4*S*(-123 + 562*S^2 + 281*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*(((1 + S^2)*(-335 - 713*S^2 + 28*S^4))/(12*S^3) - (Pi^2*(1 + S^2)*(341 + 79*S^2 + 44*S^4))/(36*S^3) - (Pi^4*S*(-21933 + 9518*S^2 + 4759*S^4))/(540*(1 + S^2)^2) + ((-2*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 + (2*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(9*(1 + S^2)^2))*HPL[{2}, -S^2] - (392*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(3*(1 + S^2)^2) - (2*(-15 - 70*S^2 + 904*S^4 - 2578*S^6 + 263*S^8)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) + (8*S*(-111 + 110*S^2 + 55*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + (16*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (8*S*(-27 + 278*S^2 + 139*S^4)*HPL[{3, 1}, -S^2])/(3*(1 + S^2)^2) + 520*S*HPL[{2, 1, 1}, -S^2] - (8*(-23 + 136*S^2 - 493*S^4 + 98*S^6)*Zeta[3])/(3*S*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*(-(Pi^4*S*(8864 + 5602*S^2 + 2801*S^4))/(180*(1 + S^2)^2) + (Pi^2*(357 - 148*S^2 - 117*S^4 - 4*S^6))/(12*S^3) + (155 - 149*S^2 - 255*S^4 + 13*S^6)/(4*S^3) - (448*S*(-4 + 6*S^2 + 3*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (32*S*(-123 + 146*S^2 + 73*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(-3 + 70*S^2 - 487*S^4 + 1008*S^6)*Zeta[3])/(S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((Pi^4*S*(-635 + 3538*S^2 + 1769*S^4))/(120*(1 + S^2)^2) + (439 + 1036*S^2 + 1797*S^4 - 460*S^6)/(16*S^3) + (Pi^2*(-120 + 204*S^2 + 571*S^4 - 12*S^6))/(24*S^3) - (2*S*(-1 + 84*S^2 + 42*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(-15 - 97*S^2 + 671*S^4 - 749*S^6 + 66*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (14*S*(-23 + 178*S^2 + 89*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (8*S*(-75 + 634*S^2 + 317*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((3 + 6*S^2 + 12*S^4 + 278*S^6 + 69*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((-240 - 163*S^2 - 378*S^4)/(96*S) + (Pi^2*(-87 + 437*S^2 - 6*S^4))/(72*S) + (Pi^4*S*(8061 + 134*S^2 + 67*S^4))/(2160*(1 + S^2)^2) + ((-21 - 269*S^2 + 805*S^4 - 367*S^6 + 40*S^8)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) - (S*(-633 + 194*S^2 + 97*S^4)*HPL[{1}, -S^2]^4)/(18*(1 + S^2)^2) + (-(Pi^2*S*(-482 + 158*S^2 + 79*S^4))/(36*(1 + S^2)^2) + (89 + 10*S^2 + 121*S^4 - 12*S^6)/(24*S^3))*HPL[{2}, -S^2] - (S*(-239 + 158*S^2 + 79*S^4)*HPL[{2}, -S^2]^2)/(12*(1 + S^2)^2) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(36 + 2*S^2 + S^4))/(6*S^3) - (Pi^2*S*(-1159 + 226*S^2 + 113*S^4))/(36*(1 + S^2)^2) - (S*(-289 + 82*S^2 + 41*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((-27 - 102*S^2 - 5*S^4 + 60*S^6 + 38*S^8)*HPL[{3}, -S^2])/(12*S^3*(1 + S^2)^2) - (S*(-10 + 14*S^2 + 7*S^4)*HPL[{4}, -S^2])/(3*(1 + S^2)^2) + ((45 + 530*S^2 - 538*S^4 + 308*S^6 + 11*S^8)*HPL[{2, 1}, -S^2])/(6*S^3*(1 + S^2)^2) + (S*(-81 + 58*S^2 + 29*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-247 + 166*S^2 + 83*S^4)*HPL[{2, 1, 1}, -S^2])/(3*(1 + S^2)^2) + (S*(80 + 165*S^2 + 63*S^4)*Zeta[3])/(3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(95 + 57*S^2 + 30*S^4))/(24*S^3) + (Pi^2*(-87 - 1198*S^2 + 3100*S^4 - 620*S^6 + 257*S^8))/(72*S^3*(1 + S^2)^2) + ((-3 - 466*S^2 + 1486*S^4 - 594*S^6 + 97*S^8)*HPL[{2}, -S^2])/(12*S^3*(1 + S^2)^2) + (4*S*HPL[{3}, -S^2])/(1 + S^2)^2 + (2*S*(-289 + 82*S^2 + 41*S^4)*HPL[{2, 1}, -S^2])/(3*(1 + S^2)^2) + (2*S*(-4 + 14*S^2 + 7*S^4)*Zeta[3])/(3*(1 + S^2)^2))) + ((-12 + 205*S^2)/(2*S) + (Pi^2*S*(-13 + 812*S^2 + 406*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{0}, S^2]^2*((-268 + 683*S^2 - 553*S^4)/(32*S) + (Pi^2*(-155 + 645*S^2 - 148*S^4))/(48*S) + (Pi^4*S*(15964 + 789*S^2 + 1723*S^4))/(720*(1 + S^2)^2) + ((-45 - 508*S^2 + 2066*S^4 - 1268*S^6 - 77*S^8)*HPL[{1}, -S^2]^4)/(12*S^3*(1 + S^2)^2) - (S*(-53 + 18*S^2 + 9*S^4)*HPL[{1}, -S^2]^5)/(1 + S^2)^2 + ((3 + 4*S^2 + 923*S^4 - 842*S^6 - 44*S^8)*HPL[{2}, -S^2]^2)/(8*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(44 - 24*S^2 + 11*S^4))/(3*S^3) - (Pi^2*S*(-666 + 166*S^2 + 83*S^4))/(9*(1 + S^2)^2) - (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2}, -S^2])/(3*(1 + S^2)^2)) + ((Pi^2*S*(11 + 122*S^2 + 61*S^4))/(12*(1 + S^2)^2) + (-81 + 104*S^2 + 110*S^4)/(8*S^3))*HPL[{3}, -S^2] + ((33 + 58*S^2 + 179*S^4 + 220*S^6 + 34*S^8)*HPL[{4}, -S^2])/(4*S^3*(1 + S^2)^2) + (S*(23 + 94*S^2 + 47*S^4)*HPL[{5}, -S^2])/(2*(1 + S^2)^2) + (-(Pi^2*S*(670 + 74*S^2 + 37*S^4))/(6*(1 + S^2)^2) + (189 - 112*S^2 + 15*S^4 - 4*S^6)/(4*S^3))*HPL[{2, 1}, -S^2] + ((-57 - 82*S^2 - 953*S^4 + 660*S^6 + 44*S^8)*HPL[{3, 1}, -S^2])/(2*S^3*(1 + S^2)^2) - (S*(-1 + 166*S^2 + 83*S^4)*HPL[{3, 2}, -S^2])/(2*(1 + S^2)^2) - (S*(-1 + 266*S^2 + 133*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (2*(-24 - 35*S^2 - 481*S^4 + 339*S^6 + 25*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (4*S*(-211 + 8*S^2 + 4*S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(1265 + 38*S^2 + 19*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (28*S*(61 + 10*S^2 + 5*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((-3*(1 - 28*S^2 + 2*S^4))/(2*S) + (Pi^2*S*(34 + 150*S^2 + 75*S^4))/(6*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((114 + 41*S^2 + 150*S^4 - 82*S^6)/(8*S^3) + (Pi^2*(93 + 136*S^2 + 1923*S^4 - 618*S^6 + 34*S^8))/(24*S^3*(1 + S^2)^2) + (3*S*(-1 + 26*S^2 + 13*S^4)*HPL[{3}, -S^2])/(2*(1 + S^2)^2) + (2*S*(-211 + 8*S^2 + 4*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (S*(-11 + 56*S^2 + 28*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(40 - 21*S^2 + 17*S^4))/(2*S^3) + (Pi^2*(-45 - 528*S^2 + 1790*S^4 - 751*S^6 - 28*S^8))/(12*S^3*(1 + S^2)^2) + ((-215 + 966*S^2 - 437*S^4 - 50*S^6)*HPL[{2}, -S^2])/(2*S*(1 + S^2)^2) + (S*(-19 + 50*S^2 + 25*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (S*(-699 + 170*S^2 + 85*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (S*(-49 + 66*S^2 + 33*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(341 - 333*S^2 + 72*S^4))/(48*S^3) - ((1 + S^2)*(166 - 70*S^2 + 83*S^4))/(8*S^3) - (Pi^4*S*(-15797 + 2202*S^2 + 1101*S^4))/(720*(1 + S^2)^2) + (-((1 + S^2)*(61 - 173*S^2 + 44*S^4))/(8*S^3) - (Pi^2*S*(-584 + 98*S^2 + 49*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2] - (S*(-182 + 66*S^2 + 33*S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + ((15 - 8*S^2 + 16*S^4 + 214*S^6 - S^8)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(15 + 62*S^2 + 31*S^4)*HPL[{4}, -S^2])/(2*(1 + S^2)^2) + ((215 - 966*S^2 + 437*S^4 + 50*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (2*S*(-345 + 82*S^2 + 41*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (2*S*(-699 + 170*S^2 + 85*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-3 - 4*S^2 - 42*S^4 + 266*S^6 - 21*S^8)*Zeta[3])/(2*S^3*(1 + S^2)^2)) + (3*S*(9 + 44*S^2 + 22*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{2}, -S^2]*((252 + 1085*S^2 + 323*S^4 - 553*S^6)/(16*S^3) + (Pi^2*(163 + 299*S^2 + 296*S^4 - 164*S^6))/(24*S^3) + (Pi^4*(639 + 1203*S^2 + 10720*S^4 - 2389*S^6 - 419*S^8))/(360*S^3*(1 + S^2)^2) + ((Pi^2*S*(-153 + 1346*S^2 + 673*S^4))/(6*(1 + S^2)^2) + (3 - 24*S^2 + 499*S^4 - 16*S^6)/(4*S^3))*HPL[{3}, -S^2] + ((-9 - 2*S^2 + 97*S^4 + 1208*S^6 + 214*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)^2) + (4*S*(1 + 84*S^2 + 42*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((2*Pi^2*S*(-457 + 300*S^2 + 150*S^4))/(3*(1 + S^2)^2) + (77 - 2*S^2 + 130*S^4 - 4*S^6)/S^3)*HPL[{2, 1}, -S^2] - (2*(-40 + 819*S^2 - 672*S^4 + 37*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - (S*(-521 + 2374*S^2 + 1187*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (10*S*(-135 + 758*S^2 + 379*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (4*(3 - 32*S^2 + 717*S^4 - 810*S^6 + 6*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + 1192*S*HPL[{2, 2, 1}, -S^2] - (16*S*(261 + 130*S^2 + 65*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (32*S*(-123 + 146*S^2 + 73*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((Pi^2*S*(-123 + 616*S^2 + 308*S^4))/(3*(1 + S^2)^2) + (21 - 76*S^2 + 147*S^4 - 4*S^6)/(2*S^3))*Zeta[3] + (2*S*(-66 + 590*S^2 + 295*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(301 + 161*S^2 + 80*S^4))/(24*S^3) + ((1 + S^2)*(-509 - 1204*S^2 + 153*S^4))/(8*S^3) + (Pi^4*(-624 - 6826*S^2 + 26844*S^4 - 19799*S^6 + 539*S^8))/(360*S^3*(1 + S^2)^2) + ((-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2}, -S^2]^2)/(2*S^3*(1 + S^2)^2) + (-(((1 + S^2)*(-13 - 155*S^2 + 14*S^4))/S^3) + (2*Pi^2*S*(-317 + 360*S^2 + 180*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-29 - 353*S^2 + 1059*S^4 + 55*S^6)*HPL[{4}, -S^2])/(S*(1 + S^2)^2) + (4*S*(-55 + 106*S^2 + 53*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + ((6*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 - (2*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(91 - 164*S^2 - 517*S^4 + 70*S^6)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)^2) - (4*S*(-505 + 558*S^2 + 279*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (4*S*(-1737 + 1894*S^2 + 947*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (48*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (1568*S*(-3 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (8*S*(-1149 + 506*S^2 + 253*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - 1560*S*HPL[{2, 1, 1, 1}, -S^2] + (-((1 + S^2)*(11 - 271*S^2 + 44*S^4))/(2*S^3) + (2*Pi^2*S*(-257 + 318*S^2 + 159*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(55 - 335*S^2 + 72*S^4))/(4*S^3) + (Pi^2*(-407 + 1554*S^2 + 151*S^4 - 242*S^6))/(6*S*(1 + S^2)^2) + (2*S*(-505 + 558*S^2 + 279*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (112*S*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + (2*S*(-431 + 658*S^2 + 329*S^4)*Zeta[5])/(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(667 + 573*S^2 + 138*S^4))/(48*S^3) - (Pi^4*(1 + S^2)*(781 - 447*S^2 + 186*S^4))/(240*S^3) + ((1 + S^2)*(-3797 - 9057*S^2 + 1610*S^4))/(32*S^3) - (Pi^6*S*(-44979 + 14612*S^2 + 7306*S^4))/(4536*(1 + S^2)^2) + (-((1 + S^2)*(55 + 81*S^2))/(4*S^3) - (Pi^2*S*(-476 + 262*S^2 + 131*S^4))/(3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (83*S*HPL[{2}, -S^2]^3)/3 - (37*S*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + (-((1 + S^2)*(-9 - 563*S^2 + 36*S^4))/(4*S^3) + (Pi^2*S*(-429 + 502*S^2 + 251*S^4))/(6*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-15 - 154*S^2 - 30*S^4 + 1040*S^6 + 67*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)^2) + (2*S*(15 + 208*S^2 + 104*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + (((1 + S^2)*(29 - 229*S^2 + 28*S^4))/S^3 - (4*Pi^2*S*(159 + 98*S^2 + 49*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (2*(-15 - 88*S^2 + 732*S^4 - 2044*S^6 + 287*S^8)*HPL[{3, 2}, -S^2])/(S^3*(1 + S^2)^2) + (2*(-45 - 235*S^2 + 2549*S^4 - 7191*S^6 + 806*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^2) - (117*S*(-3 + 2*S^2 + S^4)*HPL[{4, 2}, -S^2])/(1 + S^2)^2 - (52*S*(-35 + 34*S^2 + 17*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-12*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 + (4*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)^2) + (8*(-15 - 343*S^2 + 1396*S^4 - 1027*S^6 + 53*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + 664*S*HPL[{3, 2, 1}, -S^2] + (8*S*(27 + 718*S^2 + 359*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 + (96*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (16*S*(-27 + 278*S^2 + 139*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 3120*S*HPL[{2, 1, 1, 1, 1}, -S^2] + (-((1 + S^2)*(19 - 329*S^2 + 56*S^4))/(2*S^3) + (Pi^2*(-3 + 88*S^2 - 586*S^4 + 2238*S^6 - 413*S^8))/(6*S^3*(1 + S^2)^2))*Zeta[3] - (2*S*(-29 + 22*S^2 + 11*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(55 - 335*S^2 + 72*S^4))/(2*S^3) + (Pi^2*(407 - 1554*S^2 - 151*S^4 + 242*S^6))/(3*S*(1 + S^2)^2) - (224*S*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*(-((1 + S^2)*(-87 - 691*S^2 + 102*S^4))/(4*S^3) + (Pi^2*(15 + 31*S^2 - 444*S^4 + 1396*S^6 - 132*S^8))/(3*S^3*(1 + S^2)^2) - (4*S*(-505 + 558*S^2 + 279*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*S*(-37 + 26*S^2 + 13*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(133 - 497*S^2 + 92*S^4))/(24*S^3) - ((1 + S^2)*(49 - 663*S^2 + 246*S^4))/(8*S^3) + (Pi^4*S*(6319 + 512*S^2 + 256*S^4))/(180*(1 + S^2)^2) + ((15 + 88*S^2 - 732*S^4 + 2044*S^6 - 287*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) + (113*S*(-3 + 2*S^2 + S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (2*(-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) + (784*S*(-3 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (1568*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(-23 + 378*S^2 - 1025*S^4 + 142*S^6)*Zeta[3])/(S*(1 + S^2)^2)) - (2*(3 - 42*S^2 + 132*S^4 - 1053*S^6 + 290*S^8)*Zeta[5])/(S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((Pi^2*(-592 - 1661*S^2 - 322*S^4))/(96*S) + (Pi^4*(-2436 + 4603*S^2 - 120*S^4))/(1440*S) + (-2372 - 9015*S^2 + 1610*S^4)/(32*S) - (Pi^6*S*(-187513 + 122948*S^2 + 61474*S^4))/(45360*(1 + S^2)^2) + ((-3 - 40*S^2 + 174*S^4 - 216*S^6 + 21*S^8)*HPL[{1}, -S^2]^5)/(S^3*(1 + S^2)^2) - (56*S*(-3 + 2*S^2 + S^4)*HPL[{1}, -S^2]^6)/(3*(1 + S^2)^2) + (-(Pi^2*S*(-643 + 918*S^2 + 459*S^4))/(12*(1 + S^2)^2) + (-9 + 16*S^2 - 49*S^4 - 4*S^6)/(8*S^3))*HPL[{2}, -S^2]^2 - (2*S*(-79 + 196*S^2 + 98*S^4)*HPL[{2}, -S^2]^3)/(3*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(33 + 35*S^2))/(12*S^3) - (Pi^2*S*(-1893 + 1034*S^2 + 517*S^4))/(18*(1 + S^2)^2) - (125*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(1 + S^2)^2) + (S*(-1 + 6*S^2 + 3*S^4)*HPL[{3}, -S^2]^2)/(1 + S^2)^2 + (-(Pi^2*S*(-51 + 58*S^2 + 29*S^4))/(6*(1 + S^2)^2) + (74 - 21*S^2 + 89*S^4 - 2*S^6)/(2*S^3))*HPL[{4}, -S^2] + ((-45 - 126*S^2 - 33*S^4 + 13*S^6 + 57*S^8)*HPL[{5}, -S^2])/(S^3*(1 + S^2)^2) - (S*(-28 + 90*S^2 + 45*S^4)*HPL[{6}, -S^2])/(1 + S^2)^2 + (8*S*(-101 + 190*S^2 + 95*S^4)*HPL[{2, 1}, -S^2]^2)/(1 + S^2)^2 + ((10*Pi^2*S*(-59 + 98*S^2 + 49*S^4))/(3*(1 + S^2)^2) + (-57 + 6*S^2 + 21*S^4 + 4*S^6)/S^3)*HPL[{3, 1}, -S^2] + ((-9 - 30*S^2 - 92*S^4 - 906*S^6 - 227*S^8)*HPL[{3, 2}, -S^2])/(2*S^3*(1 + S^2)^2) + ((33 + 126*S^2 - 19*S^4 - 1196*S^6 - 356*S^8)*HPL[{4, 1}, -S^2])/(S^3*(1 + S^2)^2) - 9*S*HPL[{4, 2}, -S^2] + (4*S*(-22 + 10*S^2 + 5*S^4)*HPL[{5, 1}, -S^2])/(1 + S^2)^2 + ((-16*Pi^2*S*(-74 + 122*S^2 + 61*S^4))/(3*(1 + S^2)^2) + (107 - 44*S^2 - 83*S^4 - 4*S^6)/S^3)*HPL[{2, 1, 1}, -S^2] - (4*(15 + 267*S^2 - 624*S^4 + 717*S^6 + 25*S^8)*HPL[{2, 2, 1}, -S^2])/(S^3*(1 + S^2)^2) - (2*(117 + 1708*S^2 - 3712*S^4 + 4012*S^6 + 43*S^8)*HPL[{3, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - 6*S*HPL[{3, 1, 2}, -S^2] - (2*S*(-629 + 1574*S^2 + 787*S^4)*HPL[{3, 2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-979 + 2382*S^2 + 1191*S^4)*HPL[{4, 1, 1}, -S^2])/(1 + S^2)^2 - (4*(-45 - 616*S^2 + 1245*S^4 - 1126*S^6 + 58*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) + (8*S*(-347 + 806*S^2 + 403*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (240*S*(-23 + 54*S^2 + 27*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((40 + 93*S^2 - 50*S^4)/(4*S) + (Pi^2*S*(70 + 349*S^2 + 91*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (2*S*(-7 + 20*S^2 + 10*S^4)*Zeta[3]^2)/(1 + S^2)^2 + HPL[{2, 1}, -S^2]*((85 + 288*S^2 + 156*S^4 - 66*S^6)/(2*S^3) + (Pi^2*(90 + 1146*S^2 - 1783*S^4 + 1434*S^6 - 47*S^8))/(6*S^3*(1 + S^2)^2) + (4*S*(83 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3}, -S^2]*((-123 + 18*S^2 + 65*S^4 + 102*S^6)/(8*S^3) + (Pi^2*(-54 - 208*S^2 - 37*S^4 + 350*S^6 + 145*S^8))/(12*S^3*(1 + S^2)^2) + (2*S*(89 + 26*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (2*S*(1 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(141 + 245*S^2 + 12*S^4))/(6*S^3) + (Pi^2*(-87 - 1138*S^2 + 4220*S^4 - 3974*S^6 + 395*S^8))/(18*S^3*(1 + S^2)^2) + (8*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2}, -S^2])/(3*S*(1 + S^2)^2) + (4*S*(-27 + 14*S^2 + 7*S^4)*HPL[{3}, -S^2])/(3*(1 + S^2)^2) + (500*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (4*S*(-123 + 86*S^2 + 43*S^4)*Zeta[3])/(3*(1 + S^2)^2)) + HPL[{2}, -S^2]*(-(Pi^4*S*(-1374 + 1562*S^2 + 781*S^4))/(72*(1 + S^2)^2) + (103 - 391*S^2 - 497*S^4 - 39*S^6)/(8*S^3) + (Pi^2*(98 - 17*S^2 + 19*S^4 - 8*S^6))/(12*S^3) + ((3 + 10*S^2 + 46*S^4 + 462*S^6 + 119*S^8)*HPL[{3}, -S^2])/(2*S^3*(1 + S^2)^2) + (S*(11 + 6*S^2 + 3*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + (2*(15 + 267*S^2 - 624*S^4 + 717*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) + (2*S*(-405 + 758*S^2 + 379*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (16*S*(-101 + 190*S^2 + 95*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + (2*(-3 - 3*S^2 - 15*S^4 + 174*S^6 + 25*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(309 + 183*S^2 + 4*S^4))/(24*S^3) + ((1 + S^2)*(-335 - 713*S^2 + 28*S^4))/(8*S^3) - (Pi^4*S*(-9992 + 4382*S^2 + 2191*S^4))/(180*(1 + S^2)^2) + (((1 + S^2)*(-25 - 109*S^2 + 20*S^4))/(2*S^3) - (Pi^2*S*(-1703 + 914*S^2 + 457*S^4))/(6*(1 + S^2)^2))*HPL[{2}, -S^2] - (196*S*(-3 + 2*S^2 + S^4)*HPL[{2}, -S^2]^2)/(1 + S^2)^2 + (2*(6 - 19*S^2 - 58*S^4 + 75*S^6 + 40*S^8)*HPL[{3}, -S^2])/(S^3*(1 + S^2)^2) - (S*(-63 + 58*S^2 + 29*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 - (8*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)^2) + (12*S*(-187 + 126*S^2 + 63*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (1500*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((3 + 16*S^2 - 244*S^4 + 456*S^6 + 49*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + (2*S*(55 + 268*S^2 + 83*S^4)*Zeta[5])/(1 + S^2)^2 + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(118 + 151*S^2 + 21*S^4))/(12*S^3) + ((1 + S^2)*(-509 - 1204*S^2 + 153*S^4))/(8*S^3) + (Pi^4*(-609 - 7596*S^2 + 23580*S^4 - 15731*S^6 + 2434*S^8))/(360*S^3*(1 + S^2)^2) + ((-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2}, -S^2]^2)/(2*S^3*(1 + S^2)^2) + ((Pi^2*S*(-15 + 14*S^2 + 7*S^4))/(3*(1 + S^2)^2) + ((1 + S^2)*(5 + 23*S^2 + 16*S^4))/(2*S^3))*HPL[{3}, -S^2] + ((-3 - 110*S^2 + 32*S^4 - 106*S^6 + 123*S^8)*HPL[{4}, -S^2])/(2*S^3*(1 + S^2)^2) - (2*S*(-29 + 34*S^2 + 17*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (-(((1 + S^2)*(-25 - 109*S^2 + 20*S^4))/S^3) + (Pi^2*S*(-1703 + 914*S^2 + 457*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-3 - 290*S^2 + 1116*S^4 - 1394*S^6 + 203*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) - (76*S*(-3 + 2*S^2 + S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 - (2*S*(-279 + 170*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 + (16*(-71 + 283*S^2 - 346*S^4 + 50*S^6)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (1568*S*(-3 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(1 + S^2)^2 - (8*S*(-1737 + 1162*S^2 + 581*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 + (3000*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + ((8*(1 + S^2)*(2 + S^2))/S^3 + (Pi^2*S*(-131 + 114*S^2 + 57*S^4))/(3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-17 - 323*S^2 + 40*S^4))/(4*S^3) + (Pi^2*(-3 - 1034*S^2 + 3750*S^4 - 3362*S^6 + 497*S^8))/(12*S^3*(1 + S^2)^2) + (38*S*(-3 + 2*S^2 + S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + (784*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 + (82*S*(-3 + 2*S^2 + S^4)*Zeta[3])/(1 + S^2)^2) + (4*S*(-46 + 38*S^2 + 19*S^4)*Zeta[5])/(1 + S^2)^2)) + (6*S*(-10 + 302*S^2 + 151*S^4)*Zeta[7])/(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(425 + 623*S^2 + 8*S^4))/(48*S^3) + (Pi^4*(1 + S^2)*(2055 - 463*S^2 + 1030*S^4))/(1440*S^3) - ((1 + S^2)*(-10855 - 30601*S^2 + 4410*S^4))/(64*S^3) + (Pi^6*(7644 + 84422*S^2 - 293918*S^4 + 142703*S^6 - 9451*S^8))/(45360*S^3*(1 + S^2)^2) + (2*(20 - 83*S^2 + 20*S^4)*HPL[{2}, -S^2]^3)/(3*S*(1 + S^2)) + ((-3 + 6*S^2 - 110*S^4 + 202*S^6 + 25*S^8)*HPL[{3}, -S^2]^2)/(2*S^3*(1 + S^2)^2) + (((1 + S^2)*(-7 - 501*S^2 + 52*S^4))/(4*S^3) - (Pi^2*S*(-53 + 134*S^2 + 67*S^4))/(3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((42 + 205*S^2 - 187*S^4 - 671*S^6 - 143*S^8)*HPL[{6}, -S^2])/(S^3*(1 + S^2)^2) - (3*S*(41 + 102*S^2 + 51*S^4)*HPL[{7}, -S^2])/(1 + S^2)^2 + ((-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 1}, -S^2]^2)/(S^3*(1 + S^2)^2) + (-((1 + S^2)*(-31 - 177*S^2 + 16*S^4))/(2*S^3) + (14*Pi^2*S*(-38 + 42*S^2 + 21*S^4))/(3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + (-((1 + S^2)*(-195 - 1625*S^2 + 132*S^4))/(4*S^3) + (Pi^2*S*(-3621 + 4030*S^2 + 2015*S^4))/(6*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (6*(2 - 31*S^2 + 49*S^4 + 4*S^6)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)^2) - (S*(-65 + 58*S^2 + 29*S^4)*HPL[{4, 3}, -S^2])/(1 + S^2)^2 + ((-21 - 110*S^2 - 746*S^4 + 2228*S^6 + 181*S^8)*HPL[{5, 1}, -S^2])/(S^3*(1 + S^2)^2) - (12*S*(-12 + 10*S^2 + 5*S^4)*HPL[{5, 2}, -S^2])/(1 + S^2)^2 + (2*S*(50 + 198*S^2 + 99*S^4)*HPL[{6, 1}, -S^2])/(1 + S^2)^2 + (((1 + S^2)*(55 + 81*S^2))/S^3 + (4*Pi^2*S*(-476 + 262*S^2 + 131*S^4))/(3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + (((1 + S^2)*(139 - 67*S^2 + 28*S^4))/S^3 + (4*Pi^2*S*(-1111 + 426*S^2 + 213*S^4))/(3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (16*(20 - 83*S^2 + 20*S^4)*HPL[{3, 2, 1}, -S^2])/(S*(1 + S^2)) - (S*(-2113 + 2294*S^2 + 1147*S^4)*HPL[{3, 2, 2}, -S^2])/(1 + S^2)^2 - (16*S*(-405 + 436*S^2 + 218*S^4)*HPL[{3, 3, 1}, -S^2])/(1 + S^2)^2 + (2*(509 - 1159*S^2 - 2571*S^4 + 425*S^6)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)^2) - (S*(-6363 + 6898*S^2 + 3449*S^4)*HPL[{4, 1, 2}, -S^2])/(1 + S^2)^2 - (S*(-19815 + 21178*S^2 + 10589*S^4)*HPL[{4, 2, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-10199 + 10922*S^2 + 5461*S^4)*HPL[{5, 1, 1}, -S^2])/(1 + S^2)^2 + ((-12*(1 + S^2)*(6 - 27*S^2 + 4*S^4))/S^3 + (4*Pi^2*S*(447 + 110*S^2 + 55*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + 664*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(91 - 164*S^2 - 517*S^4 + 70*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(S*(1 + S^2)^2) + (16*S*(-377 + 30*S^2 + 15*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(1 + S^2)^2 + (16*S*(-377 + 30*S^2 + 15*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(1 + S^2)^2 - (8*S*(1003 + 438*S^2 + 219*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (8*S*(3231 + 1094*S^2 + 547*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (96*(16 - 65*S^2 + 16*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (3136*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(1 + S^2)^2 - (9408*S*(-3 + 2*S^2 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(1 + S^2)^2 - (80*S*(-711 + 526*S^2 + 263*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(1 + S^2)^2 + 3120*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((Pi^2*(1 + S^2)*(8 - 96*S^2 + 11*S^4))/(6*S^3) + ((1 + S^2)*(-3 - 853*S^2 + 194*S^4))/(8*S^3) - (Pi^4*S*(-1792 + 2494*S^2 + 1247*S^4))/(180*(1 + S^2)^2))*Zeta[3] + ((-3 + 18*S^2 - 6*S^4 + 29*S^6 - 24*S^8)*Zeta[3]^2)/(S^3*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*(((1 + S^2)*(55 - 335*S^2 + 72*S^4))/(2*S^3) + (Pi^2*(407 - 1554*S^2 - 151*S^4 + 242*S^6))/(3*S*(1 + S^2)^2) - (224*S*(-9 + 10*S^2 + 5*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{4}, -S^2]*(((1 + S^2)*(-81 - 245*S^2 + 136*S^4))/(8*S^3) + (Pi^2*(15 + 68*S^2 - 304*S^4 - 17*S^6))/(3*S*(1 + S^2)^2) + (113*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/(1 + S^2)^2 - (S*(-33 + 46*S^2 + 23*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2}, -S^2]^2*(((1 + S^2)*(47 + 95*S^2 + 4*S^4))/(8*S^3) + (Pi^2*(15 + 232*S^2 - 1086*S^4 + 1080*S^6 - 45*S^8))/(12*S^3*(1 + S^2)^2) - (2*S*(-154 + 158*S^2 + 79*S^4)*HPL[{3}, -S^2])/(1 + S^2)^2 + 83*S*HPL[{2, 1}, -S^2] - (2*S*(-112 + 130*S^2 + 65*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(7 - 501*S^2 + 110*S^4))/(4*S^3) + (Pi^2*(-201 + 642*S^2 + 316*S^4 - 87*S^6))/(3*S*(1 + S^2)^2) + (4*S*(-261 + 286*S^2 + 143*S^4)*Zeta[3])/(1 + S^2)^2) + HPL[{2, 1}, -S^2]*(-(Pi^2*(1 + S^2)*(133 - 497*S^2 + 92*S^4))/(24*S^3) - ((1 + S^2)*(49 - 663*S^2 + 246*S^4))/(8*S^3) + (Pi^4*S*(6319 + 512*S^2 + 256*S^4))/(180*(1 + S^2)^2) + (784*S*(-3 + 2*S^2 + S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 + (1568*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 - (2*(-23 + 378*S^2 - 1025*S^4 + 142*S^6)*Zeta[3])/(S*(1 + S^2)^2)) + HPL[{3}, -S^2]*((Pi^2*(1 + S^2)*(-14 - 98*S^2 + 9*S^4))/(6*S^3) + ((1 + S^2)*(-122 - 747*S^2 + 195*S^4))/(8*S^3) - (Pi^4*S*(-1097 + 1412*S^2 + 706*S^4))/(90*(1 + S^2)^2) + (2*S*(-29 + 28*S^2 + 14*S^4)*HPL[{4}, -S^2])/(1 + S^2)^2 + ((15 + 88*S^2 - 732*S^4 + 2044*S^6 - 287*S^8)*HPL[{2, 1}, -S^2])/(S^3*(1 + S^2)^2) + (2*S*(-505 + 558*S^2 + 279*S^4)*HPL[{3, 1}, -S^2])/(1 + S^2)^2 - (4*S*(-505 + 558*S^2 + 279*S^4)*HPL[{2, 1, 1}, -S^2])/(1 + S^2)^2 + ((-3 + 14*S^2 + 110*S^4 - 120*S^6 - 13*S^8)*Zeta[3])/(S^3*(1 + S^2)^2)) + (((1 + S^2)*(16 - 125*S^2 + 17*S^4))/S^3 - (Pi^2*S*(-228 + 382*S^2 + 191*S^4))/(3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(91 - 541*S^2 + 136*S^4))/(48*S^3) + ((1 + S^2)*(-57 - 223*S^2 + 171*S^4))/(8*S^3) + (Pi^4*(1282 - 5163*S^2 + 213*S^4 + 595*S^6))/(180*S*(1 + S^2)^2) + (((1 + S^2)*(-31 - 177*S^2 + 16*S^4))/(4*S^3) - (7*Pi^2*S*(-38 + 42*S^2 + 21*S^4))/(3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((3 - 10*S^2 + 172*S^4 - 300*S^6 - 33*S^8)*HPL[{4}, -S^2])/(S^3*(1 + S^2)^2) - (S*(-109 + 110*S^2 + 55*S^4)*HPL[{5}, -S^2])/(1 + S^2)^2 + (-((1 + S^2)*(55 + 81*S^2))/(2*S^3) - (2*Pi^2*S*(-476 + 262*S^2 + 131*S^4))/(3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-15 - 248*S^2 + 1236*S^4 - 1540*S^6 + 127*S^8)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) + (S*(-1115 + 1186*S^2 + 593*S^4)*HPL[{3, 2}, -S^2])/(1 + S^2)^2 + (S*(-3357 + 3566*S^2 + 1783*S^4)*HPL[{4, 1}, -S^2])/(1 + S^2)^2 - (2*(-15 - 252*S^2 + 1232*S^4 - 1544*S^6 + 123*S^8)*HPL[{2, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - 332*S*HPL[{2, 2, 1}, -S^2] - (8*S*(-377 + 30*S^2 + 15*S^4)*HPL[{3, 1, 1}, -S^2])/(1 + S^2)^2 - (1568*S*(-3 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(1 + S^2)^2 + (((1 + S^2)*(11 - 151*S^2 + 4*S^4))/(4*S^3) - (Pi^2*S*(-276 + 310*S^2 + 155*S^4))/(3*(1 + S^2)^2))*Zeta[3] - (2*S*(-213 + 296*S^2 + 148*S^4)*Zeta[5])/(1 + S^2)^2) - (3*S*(-151 + 342*S^2 + 171*S^4)*Zeta[7])/(1 + S^2)^2);
E5wuvT3F3=(-7*(464915 + 127334*S^2))/(1259712*S) + (Pi^2*(138560 - 136313*S^2 - 121014*S^4))/(69984*S) + (Pi^4*(-41688 - 317178*S^2 - 23257*S^4))/(524880*S) + (Pi^6*(-1375202 - 616727*S^2 + 93308*S^4))/(4898880*S) + (Pi^8*(-27928 - 41892*S^2 - 199*S^4 - 398*S^6 - 199*S^8))/(85050*S*(1 + S^2)^2) + ((-58*Pi^2)/(63*S^3) + (-655 - 2020*S^2 - 3046*S^4 - 724*S^6 - 475*S^8 - 88*S^10)/(189*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^7 - (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^8)/(27*S^3*(1 + S^2)^2) - (16*HPL[{1}, -S^2]^9)/(81*S^3) + HPL[{0}, S^2]^8*((-2 - 3*S^2)/(576*S*(1 + S^2)^2) - HPL[{1}, -S^2]/(288*S^3)) + HPL[{0}, S^2]^7*((66 - 9*S^2 + 62*S^4 + 37*S^6 + 8*S^8)/(5184*S*(1 + S^2)^2) + ((11 - 14*S^2 - 43*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(864*S^3*(1 + S^2)^2) - HPL[{1}, -S^2]^2/(48*S^3)) + ((-775 - 2702*S^2 - 2503*S^4 - 56*S^6 - 112*S^8 - 56*S^10)*HPL[{2}, -S^2]^4)/(108*S^3*(1 + S^2)^2) - (4*HPL[{3}, -S^2]^3)/(3*S^3) + ((-318 - 582*S^2 - 237*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*HPL[{4}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((130*Pi^2)/(9*S^3) + (8245 + 19649*S^2 + 13051*S^4 + 3721*S^6 + 3464*S^8 + 1120*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{7}, -S^2] + (2*(-3990 - 7818*S^2 - 3747*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{8}, -S^2])/(9*S^3*(1 + S^2)^2) + (1960*HPL[{9}, -S^2])/(3*S^3) - (1568*HPL[{2, 1}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^6*((-296 + 331*S^2 + 540*S^4)/(10368*S) + (Pi^2*(-138 - 207*S^2 + 5*S^4 + 10*S^6 + 5*S^8))/(2592*S*(1 + S^2)^2) + ((11 - 86*S^2 - 151*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)^2) - HPL[{1}, -S^2]^3/(12*S^3) + ((-78 - 117*S^2 + 10*S^4 + 20*S^6 + 10*S^8)*HPL[{2}, -S^2])/(864*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((-23*Pi^2)/(432*S^3) + (-92 + 47*S^2 - 497*S^4 + 124*S^6 + 200*S^8 + 88*S^10)/(2592*S^3*(1 + S^2)^2) - (13*HPL[{2}, -S^2])/(144*S^3)) + HPL[{3}, -S^2]/(144*S^3) + (7*HPL[{2, 1}, -S^2])/(36*S^3)) - (4*(1091 + 3580*S^2 + 3188*S^4 + 53*S^6 + 106*S^8 + 53*S^10)*HPL[{3, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-7*Pi^2)/S^3 + (-337 + 216*S^2 + 1643*S^4 + 1124*S^6 + 924*S^8 + 326*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{4, 3}, -S^2] + ((-187*Pi^2)/(9*S^3) + (-1490 + 44*S^2 + 5197*S^4 + 3763*S^6 + 2963*S^8 + 1027*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5, 2}, -S^2] + ((11 + 94*S^2 + 119*S^4 + 34*S^6 + 68*S^8 + 34*S^10)*HPL[{5, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + (194*HPL[{5, 4}, -S^2])/S^3 + ((-136*Pi^2)/(3*S^3) - (2*(2557 + 6419*S^2 + 4411*S^4 + 1030*S^6 + 1313*S^8 + 391*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{6, 1}, -S^2] + ((269 + 718*S^2 + 539*S^4 + 66*S^6 + 132*S^8 + 66*S^10)*HPL[{6, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (774*HPL[{6, 3}, -S^2])/S^3 + ((2467 + 4610*S^2 + 1981*S^4 - 300*S^6 - 600*S^8 - 300*S^10)*HPL[{7, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (5762*HPL[{7, 2}, -S^2])/(3*S^3) + (3638*HPL[{8, 1}, -S^2])/S^3 - (8*(1633 + 5618*S^2 + 5161*S^4 + 100*S^6 + 200*S^8 + 100*S^10)*HPL[{2, 1, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((26*Pi^2)/(9*S^3) + (123 + 36729*S^2 + 83616*S^4 + 34502*S^6 + 22039*S^8 + 5207*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 2, 2}, -S^2] + ((-28*Pi^2)/(3*S^3) + (4*(-717 + 26829*S^2 + 63714*S^4 + 26899*S^6 + 17378*S^8 + 4219*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 3, 1}, -S^2] - (2*(-32 + 734*S^2 + 1165*S^4 + 124*S^6 + 248*S^8 + 124*S^10)*HPL[{3, 3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-119*Pi^2)/(9*S^3) + (-3937 + 104575*S^2 + 251636*S^4 + 107166*S^6 + 69183*S^8 + 16833*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 2}, -S^2] + (2*(-53 + 1256*S^2 + 1990*S^4 + 180*S^6 + 360*S^8 + 180*S^10)*HPL[{4, 1, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-347*Pi^2)/(9*S^3) + (-11377 + 321535*S^2 + 774152*S^4 + 328650*S^6 + 213279*S^8 + 52233*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 2, 1}, -S^2] - (2*(-131 + 302*S^2 + 715*S^4 + 109*S^6 + 218*S^8 + 109*S^10)*HPL[{4, 2, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (14*HPL[{4, 2, 3}, -S^2])/(3*S^3) + (2*(-45 + 4272*S^2 + 6498*S^4 + 692*S^6 + 1384*S^8 + 692*S^10)*HPL[{4, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (52*HPL[{4, 3, 2}, -S^2])/(3*S^3) + (292*HPL[{4, 4, 1}, -S^2])/(3*S^3) + ((-730*Pi^2)/(9*S^3) + (-23867 + 660338*S^2 + 1592218*S^4 + 677252*S^6 + 442027*S^8 + 109028*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5, 1, 1}, -S^2] + (2*(-21 + 802*S^2 + 1245*S^4 + 130*S^6 + 260*S^8 + 130*S^10)*HPL[{5, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (424*HPL[{5, 1, 3}, -S^2])/(3*S^3) + (2*(-121 + 5762*S^2 + 8885*S^4 + 970*S^6 + 1940*S^8 + 970*S^10)*HPL[{5, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (242*HPL[{5, 2, 2}, -S^2])/(3*S^3) + (1664*HPL[{5, 3, 1}, -S^2])/(3*S^3) + (2*(-484 + 46006*S^2 + 69977*S^4 + 7782*S^6 + 15564*S^8 + 7782*S^10)*HPL[{6, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1244*HPL[{6, 1, 2}, -S^2])/(3*S^3) + (1668*HPL[{6, 2, 1}, -S^2])/S^3 + (11320*HPL[{7, 1, 1}, -S^2])/(3*S^3) + ((3184*Pi^2)/(9*S^3) - (4*(-3315 + 6519*S^2 + 4170*S^4 + 3575*S^6 + 1355*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 2, 2, 1}, -S^2] + ((-9368*Pi^2)/(9*S^3) + (-33849 - 24444*S^2 - 33696*S^4 + 21112*S^6 + 12281*S^8 + 4516*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 2}, -S^2] + ((-9368*Pi^2)/(9*S^3) + (-33849 - 24444*S^2 - 33696*S^4 + 21112*S^6 + 12281*S^8 + 4516*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 2, 1}, -S^2] + ((-467 - 1870*S^2 - 1871*S^4 - 94*S^6 - 188*S^8 - 94*S^10)*HPL[{3, 1, 2, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-18920*Pi^2)/(9*S^3) + (-73629 + 14004*S^2 + 94572*S^4 + 114052*S^6 + 71441*S^8 + 20776*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 2, 1, 1}, -S^2] + ((-467 - 1870*S^2 - 1871*S^4 - 94*S^6 - 188*S^8 - 94*S^10)*HPL[{3, 2, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-12723 - 26574*S^2 - 14415*S^4 + 962*S^6 + 1924*S^8 + 962*S^10)*HPL[{3, 2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (160*HPL[{3, 2, 2, 2}, -S^2])/(3*S^3) + (64*HPL[{3, 2, 3, 1}, -S^2])/S^3 + (32*(-383 - 772*S^2 - 392*S^4 + 33*S^6 + 66*S^8 + 33*S^10)*HPL[{3, 3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (176*HPL[{3, 3, 1, 2}, -S^2])/(3*S^3) + (512*HPL[{3, 3, 2, 1}, -S^2])/(3*S^3) + ((-57184*Pi^2)/(9*S^3) + (2*(-114828 + 2982*S^2 + 112395*S^4 + 162380*S^6 + 100999*S^8 + 29828*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 1, 1}, -S^2] - (4*(-135 + 432*S^2 + 918*S^4 + 169*S^6 + 338*S^8 + 169*S^10)*HPL[{4, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (1240*HPL[{4, 1, 1, 3}, -S^2])/(3*S^3) + (4*(-9057 - 18960*S^2 - 10326*S^4 + 623*S^6 + 1246*S^8 + 623*S^10)*HPL[{4, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1150*HPL[{4, 1, 2, 2}, -S^2])/(3*S^3) - (1720*HPL[{4, 1, 3, 1}, -S^2])/(3*S^3) + (4*(-27441 - 56016*S^2 - 29142*S^4 + 2207*S^6 + 4414*S^8 + 2207*S^10)*HPL[{4, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (862*HPL[{4, 2, 1, 2}, -S^2])/(3*S^3) - (814*HPL[{4, 2, 2, 1}, -S^2])/(3*S^3) - (3112*HPL[{4, 3, 1, 1}, -S^2])/(3*S^3) + (4*(-56057 - 117034*S^2 - 63437*S^4 + 3886*S^6 + 7772*S^8 + 3886*S^10)*HPL[{5, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3844*HPL[{5, 1, 1, 2}, -S^2])/(3*S^3) - (5668*HPL[{5, 1, 2, 1}, -S^2])/(3*S^3) - (12196*HPL[{5, 2, 1, 1}, -S^2])/(3*S^3) - (30064*HPL[{6, 1, 1, 1}, -S^2])/(3*S^3) + ((2128*Pi^2)/(3*S^3) + (8*(789 + 4318*S^2 + 9795*S^4 + 3198*S^6 + 2098*S^8 + 462*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((2128*Pi^2)/S^3 + (8*(789 + 4318*S^2 + 9795*S^4 + 3198*S^6 + 2098*S^8 + 462*S^10))/(3*S^3*(1 + S^2)^2))*HPL[{2, 2, 1, 1, 1}, -S^2] + (32*(-773 + 66*S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(9*S^3) + (32*(-773 + 66*S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(3*S^3) - (2016*HPL[{2, 2, 2, 2, 1}, -S^2])/S^3 + ((32144*Pi^2)/(9*S^3) + (8*(11735 + 85150*S^2 + 194426*S^4 + 67580*S^6 + 44191*S^8 + 9962*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(-18339 + 1540*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(9*S^3) - (8*(-30707 + 2596*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(9*S^3) - (5984*HPL[{3, 1, 1, 2, 2}, -S^2])/S^3 - (8*(-36891 + 3124*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(9*S^3) - (5984*HPL[{3, 1, 2, 1, 2}, -S^2])/S^3 + (96*HPL[{3, 1, 2, 2, 1}, -S^2])/S^3 + (127840*HPL[{3, 1, 3, 1, 1}, -S^2])/(3*S^3) - (8*(-77087 + 6556*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(9*S^3) - (12032*HPL[{3, 2, 1, 1, 2}, -S^2])/S^3 - (5952*HPL[{3, 2, 1, 2, 1}, -S^2])/S^3 + (55456*HPL[{3, 2, 2, 1, 1}, -S^2])/(3*S^3) + (61216*HPL[{3, 3, 1, 1, 1}, -S^2])/S^3 - (32*(-19408 - 38982*S^2 - 19657*S^4 + 1620*S^6 + 3240*S^8 + 1620*S^10)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (36560*HPL[{4, 1, 1, 1, 2}, -S^2])/S^3 - (18320*HPL[{4, 1, 1, 2, 1}, -S^2])/S^3 + (54992*HPL[{4, 1, 2, 1, 1}, -S^2])/S^3 + (183472*HPL[{4, 2, 1, 1, 1}, -S^2])/S^3 + (366944*HPL[{5, 1, 1, 1, 1}, -S^2])/S^3 + ((13552*Pi^2)/(9*S^3) - (8*(-6723 + 14895*S^2 + 9054*S^4 + 7570*S^6 + 2602*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (12544*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (12544*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S^3 + (32*(-2032 - 4562*S^2 - 2779*S^4 + 75*S^6 + 150*S^8 + 75*S^10)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (64192*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(3*S^3) + (139456*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(3*S^3) + (189632*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(3*S^3) + (214720*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(3*S^3) + (377792*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (1129472*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (320*(-117 + 8*S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (24896*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(3*S^3) - (99584*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(3*S^3) - (248960*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (173312*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + (17920*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-151 - 56*S^2)/(27*S) + (Pi^2*(-522 - 783*S^2 - 16*S^4 - 32*S^6 - 16*S^8))/(81*S*(1 + S^2)^2) + ((-58*Pi^2)/(9*S^3) + (-655 - 2020*S^2 - 3046*S^4 - 724*S^6 - 475*S^8 - 88*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2] - (56*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)^2) - (448*HPL[{1}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^2*((-186 - 279*S^2 - 16*S^4 - 32*S^6 - 16*S^8)/(27*S*(1 + S^2)^2) - (62*HPL[{1}, -S^2])/(9*S^3)) - (4*(-117 + 8*S^6)*HPL[{2}, -S^2])/(27*S^3) + HPL[{0}, S^2]*((-580 - 1533*S^2 - 556*S^4 - 363*S^6 - 88*S^8)/(27*S*(1 + S^2)^2) - (56*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^2) - (224*HPL[{1}, -S^2]^2)/(9*S^3) + (4*HPL[{2}, -S^2])/(3*S^3)) + (4*HPL[{3}, -S^2])/(3*S^3) + (224*HPL[{2, 1}, -S^2])/(9*S^3))*Log[T]^6 + ((16*(5 + 18*S^2 + 3*S^4 + 2*S^6))/(27*S*(1 + S^2)^2) + (16*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)^2) + (64*HPL[{1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]*((32*(6 + 9*S^2 + S^4 + 2*S^6 + S^8))/(27*S*(1 + S^2)^2) + (64*HPL[{1}, -S^2])/(9*S^3)) - (32*HPL[{2}, -S^2])/(9*S^3))*Log[T]^7 + ((-8*(2 + 3*S^2))/(9*S*(1 + S^2)^2) - (16*HPL[{1}, -S^2])/(9*S^3))*Log[T]^8 + ((-5970 + 249*S^2 - 260*S^4)/(324*S) + (Pi^2*(-174 - 261*S^2 + 22*S^4 + 44*S^6 + 22*S^8))/(54*S*(1 + S^2)^2))*Zeta[3]^2 + HPL[{6}, -S^2]*((3520 + 14280*S^2 + 11301*S^4 + 17814*S^6)/(324*S^3) + (Pi^2*(-352 - 302*S^2 + 251*S^4 + 126*S^6 + 252*S^8 + 126*S^10))/(54*S^3*(1 + S^2)^2) - (320*HPL[{2, 1}, -S^2])/(3*S^3) - (160*Zeta[3])/(3*S^3)) + HPL[{3, 1, 1, 1}, -S^2]*((-53919 - 4516*S^2 - 4255*S^4 + 548*S^6)/(27*S^3) + (4*Pi^2*(-737 - 1254*S^2 - 407*S^4 + 64*S^6 + 128*S^8 + 64*S^10))/(9*S^3*(1 + S^2)^2) - (128*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]^2*((8079 - 12696*S^2 - 4263*S^4 - 7136*S^6)/(648*S^3) + (Pi^2*(341 + 238*S^2 - 325*S^4 - 88*S^6 - 176*S^8 - 88*S^10))/(108*S^3*(1 + S^2)^2) + (56*HPL[{2, 1}, -S^2])/S^3 - (14*Zeta[3])/(3*S^3)) + HPL[{4, 2}, -S^2]*((3368 - 24156*S^2 - 6741*S^4 - 11592*S^6)/(324*S^3) + (Pi^2*(28 - 58*S^2 - 143*S^4 - 28*S^6 - 56*S^8 - 28*S^10))/(9*S^3*(1 + S^2)^2) - (10*Zeta[3])/(3*S^3)) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(-151 + 26*S^6))/(18*S^3) + (-4156 + 4887*S^2 + 216*S^4 + 3195*S^6)/(162*S^3) - (8*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^3*((32732 - 2784*S^2 + 645*S^4 - 2310*S^6)/(972*S^3) - (2*Pi^2*(-202 - 260*S^2 + 14*S^4 + 33*S^6 + 66*S^8 + 33*S^10))/(81*S^3*(1 + S^2)^2) - (44*HPL[{3}, -S^2])/(9*S^3) + (42*HPL[{2, 1}, -S^2])/S^3 + (4*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^6*(-((1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(2916*S^3) + (Pi^2*(-407 - 1858*S^2 - 1973*S^4 - 74*S^6 - 148*S^8 - 74*S^10))/(162*S^3*(1 + S^2)^2) + (13*(11 + 2*S^6)*HPL[{2}, -S^2])/(27*S^3) + (380*HPL[{3}, -S^2])/(27*S^3) + (100*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]^2*((71658 + 31977*S^2 + 11115*S^4 + 2281*S^6)/(162*S^3) + (Pi^2*(1764 + 7170*S^2 + 7227*S^4 + 224*S^6 + 448*S^8 + 224*S^10))/(27*S^3*(1 + S^2)^2) + (80*Zeta[3])/(3*S^3)) + HPL[{3, 2, 1}, -S^2]*((126772 - 6249*S^2 + 2796*S^4 - 6045*S^6)/(162*S^3) + (Pi^2*(6011 + 7414*S^2 - 901*S^4 - 978*S^6 - 1956*S^8 - 978*S^10))/(54*S^3*(1 + S^2)^2) + (88*Zeta[3])/(3*S^3)) + HPL[{5, 1}, -S^2]*((-6017 - 23426*S^2 - 7577*S^4 - 10304*S^6)/(54*S^3) - (2*Pi^2*(211 + 1460*S^2 + 1768*S^4 + 229*S^6 + 458*S^8 + 229*S^10))/(27*S^3*(1 + S^2)^2) + (100*Zeta[3])/(3*S^3)) + HPL[{4, 1, 1}, -S^2]*((431738 + 28764*S^2 + 28953*S^4 - 4686*S^6)/(162*S^3) - (2*Pi^2*(-5435 - 8434*S^2 - 1781*S^4 + 597*S^6 + 1194*S^8 + 597*S^10))/(27*S^3*(1 + S^2)^2) + (184*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-8*(-37082 + 801*S^2 - 828*S^4 + 1721*S^6))/(81*S^3) - (8*Pi^2*(-1915 - 2654*S^2 - 151*S^4 + 240*S^6 + 480*S^8 + 240*S^10))/(27*S^3*(1 + S^2)^2) + (224*Zeta[3])/(3*S^3)) + HPL[{0}, S^2]^5*((-5115 + 843*S^2 + 26188*S^4)/(77760*S) + (Pi^2*(3207 - 5670*S^2 + 3941*S^4 + 3538*S^6 + 1268*S^8))/(38880*S*(1 + S^2)^2) + ((-88 - 1802*S^2 - 2527*S^4 - 16*S^6 - 32*S^8 - 16*S^10)*HPL[{1}, -S^2]^3)/(1620*S^3*(1 + S^2)^2) - (271*HPL[{1}, -S^2]^4)/(1080*S^3) + (Pi^2/(144*S^3) + (185 + 88*S^2 - 2965*S^4 + 354*S^6 + 1002*S^8 + 552*S^10)/(4320*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(48*S^3) + HPL[{1}, -S^2]^2*((-293*Pi^2)/(1080*S^3) + (-355 - 201*S^2 - 3157*S^4 - 16*S^6 + 159*S^8 + 116*S^10)/(2160*S^3*(1 + S^2)^2) - (77*HPL[{2}, -S^2])/(120*S^3)) + ((7 + 2*S^2 - 11*S^4)*HPL[{3}, -S^2])/(144*S^3*(1 + S^2)^2) - HPL[{4}, -S^2]/(8*S^3) + ((336 + 2058*S^2 + 2415*S^4 + 50*S^6 + 100*S^8 + 50*S^10)*HPL[{2, 1}, -S^2])/(1080*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(-835 - 1853*S^2 + 3644*S^4))/(25920*S^3) + (Pi^2*(979 - 5074*S^2 - 9569*S^4 + 178*S^6 + 356*S^8 + 178*S^10))/(12960*S^3*(1 + S^2)^2) - (7*(11 + 154*S^2 + 209*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(720*S^3*(1 + S^2)^2) - HPL[{3}, -S^2]/(12*S^3) + (77*HPL[{2, 1}, -S^2])/(60*S^3)) + HPL[{2, 1, 1}, -S^2]/(6*S^3) + (5*S^3*Zeta[3])/36) + HPL[{2, 1, 1, 1}, -S^2]*((9659*Pi^4)/(135*S^3) - (2*(-30500 + 214461*S^2 + 8046*S^4 + 13201*S^6))/(243*S^3) + (Pi^2*(12155 - 1166*S^2 - 8617*S^4 - 16466*S^6 - 9880*S^8 - 2822*S^10))/(81*S^3*(1 + S^2)^2) - (16*(1595 + 4366*S^2 + 3359*S^4)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3, 2}, -S^2]*((86*Pi^4)/(135*S^3) + (9701 - 544520*S^2 - 47267*S^4 - 54662*S^6)/(648*S^3) + (Pi^2*(3611 - 32144*S^2 - 84814*S^4 - 38238*S^6 - 25509*S^8 - 6594*S^10))/(324*S^3*(1 + S^2)^2) - (88*HPL[{2, 1, 1}, -S^2])/S^3 + ((135 - 42*S^2 - 333*S^4 - 94*S^6 - 188*S^8 - 94*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{5}, -S^2]*((19*Pi^4)/(270*S^3) + (-21432 + 272592*S^2 + 36477*S^4 + 81502*S^6)/(1944*S^3) + (Pi^2*(-843 + 5790*S^2 + 14268*S^4 + 7382*S^6 + 5689*S^8 + 1622*S^10))/(324*S^3*(1 + S^2)^2) + (4*(-493 - 1232*S^2 - 862*S^4 + 29*S^6 + 58*S^8 + 29*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (208*HPL[{3, 1}, -S^2])/(3*S^3) - (52*HPL[{2, 1, 1}, -S^2])/S^3 + (4*(120 + 222*S^2 + 93*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2, 2, 1}, -S^2]*((-1496*Pi^4)/(45*S^3) + (-61634 - 420771*S^2 - 55794*S^4 - 38559*S^6)/(486*S^3) + (Pi^2*(-10239 - 35982*S^2 - 79611*S^4 - 21776*S^6 - 14596*S^8 - 2984*S^10))/(162*S^3*(1 + S^2)^2) - (8*(-1502 - 4066*S^2 - 3095*S^4 + 24*S^6 + 48*S^8 + 24*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^5*((-6673*Pi^4)/(4050*S^3) - ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(14580*S^3) + (Pi^2*(-18259 - 55706*S^2 - 94156*S^4 - 21544*S^6 - 14837*S^8 - 3022*S^10))/(2430*S^3*(1 + S^2)^2) + ((-392*Pi^2)/(135*S^3) + (2*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(45*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(45*S^3) + (2*(737 + 2614*S^2 + 2447*S^4 + 134*S^6 + 268*S^8 + 134*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (664*HPL[{4}, -S^2])/(45*S^3) - (26*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (664*HPL[{3, 1}, -S^2])/(45*S^3) + (2*(209 + 718*S^2 + 659*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3, 1, 1}, -S^2]*((-2704*Pi^4)/(27*S^3) + (-299029 - 732138*S^2 - 139065*S^4 - 71322*S^6)/(972*S^3) + (Pi^2*(-31094 - 64690*S^2 - 138545*S^4 - 23712*S^6 - 16455*S^8 - 2364*S^10))/(162*S^3*(1 + S^2)^2) - (4*(-9307 - 25286*S^2 - 19315*S^4 + 86*S^6 + 172*S^8 + 86*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{4, 1}, -S^2]*((491*Pi^4)/(540*S^3) + (-96555 - 5214072*S^2 - 530364*S^4 - 540554*S^6)/(1944*S^3) + (Pi^2*(5857 - 116776*S^2 - 285959*S^4 - 123796*S^6 - 83060*S^8 - 21142*S^10))/(324*S^3*(1 + S^2)^2) + (544*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(301 + 1238*S^2 + 1255*S^4 + 158*S^6 + 316*S^8 + 158*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + Log[T]^5*((4469 + 1424*S^2)/(486*S) + (Pi^2*(2025 + 7326*S^2 + 1540*S^4 + 1118*S^6 + 181*S^8))/(243*S*(1 + S^2)^2) + ((58*Pi^2)/(3*S^3) + (655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^2 + (112*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^2) + (224*HPL[{1}, -S^2]^4)/(9*S^3) + HPL[{0}, S^2]^3*((146 + 219*S^2 + 12*S^4 + 24*S^6 + 12*S^8)/(27*S*(1 + S^2)^2) + (146*HPL[{1}, -S^2])/(27*S^3)) + ((-182*Pi^2)/(27*S^3) + (-4635 - 4725*S^2 + 306*S^4 + 74*S^6 + 362*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (158*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^2*((765 + 2790*S^2 + 784*S^4 + 614*S^6 + 181*S^8)/(81*S*(1 + S^2)^2) + ((33 + 190*S^2 + 219*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{1}, -S^2])/(3*S^3*(1 + S^2)^2) + (62*HPL[{1}, -S^2]^2)/(3*S^3) - (14*HPL[{2}, -S^2])/(9*S^3)) - (4*(4 + 578*S^2 + 859*S^4 + 129*S^6 + 258*S^8 + 129*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (8*HPL[{4}, -S^2])/S^3 + (28*(-13 + 6*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + HPL[{0}, S^2]*((34182 + 5049*S^2 + 3812*S^4)/(486*S) + (Pi^2*(482 + 723*S^2 + 68*S^4 + 136*S^6 + 68*S^8))/(27*S*(1 + S^2)^2) + (56*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + (448*HPL[{1}, -S^2]^3)/(9*S^3) + (2*(-25 + 250*S^2 + 425*S^4 + 54*S^6 + 108*S^8 + 54*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((482*Pi^2)/(27*S^3) + (655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10)/(9*S^3*(1 + S^2)^2) + (200*HPL[{2}, -S^2])/(3*S^3)) + (28*HPL[{3}, -S^2])/(9*S^3) - (424*HPL[{2, 1}, -S^2])/(3*S^3)) + (272*HPL[{3, 1}, -S^2])/(3*S^3) - (448*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(50 + 75*S^2 + 14*S^4 + 28*S^6 + 14*S^8)*Zeta[3])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(486*S^3) + (Pi^2*(407 + 1858*S^2 + 1973*S^4 + 74*S^6 + 148*S^8 + 74*S^10))/(27*S^3*(1 + S^2)^2) - (26*(11 + 2*S^6)*HPL[{2}, -S^2])/(9*S^3) - (760*HPL[{3}, -S^2])/(9*S^3) - (200*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]^4*((Pi^2*(-1723 + 1121*S^2 + 2691*S^4))/(7776*S) + (-4441 - 2668*S^2 + 10287*S^4)/(15552*S) + (Pi^4*(-12054 - 18081*S^2 + 442*S^4 + 884*S^6 + 442*S^8))/(38880*S*(1 + S^2)^2) + ((-341 - 4090*S^2 - 5453*S^4 - 62*S^6 - 124*S^8 - 62*S^10)*HPL[{1}, -S^2]^4)/(1296*S^3*(1 + S^2)^2) - (71*HPL[{1}, -S^2]^5)/(135*S^3) + ((-93 - 906*S^2 - 1173*S^4 - 32*S^6 - 64*S^8 - 32*S^10)*HPL[{2}, -S^2]^2)/(432*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-277*Pi^2)/(324*S^3) + (-757 - 635*S^2 - 10477*S^4 - 928*S^6 - 671*S^8 - 118*S^10)/(1944*S^3*(1 + S^2)^2) - (241*HPL[{2}, -S^2])/(108*S^3)) + ((-125 - 28*S^2 + 163*S^4 + 122*S^6 + 124*S^8 + 32*S^10)*HPL[{3}, -S^2])/(432*S^3*(1 + S^2)^2) + ((-11 - 16*S^2 - 2*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{4}, -S^2])/(36*S^3*(1 + S^2)^2) + HPL[{5}, -S^2]/S^3 + ((469*Pi^2)/(216*S^3) + (795 - 2124*S^2 + 5727*S^4 + 542*S^6 + 1024*S^8 + 452*S^10)/(1296*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + HPL[{1}, -S^2]^2*(((1 + S^2)*(-1397 - 1467*S^2 + 508*S^4))/(5184*S^3) + (Pi^2*(-11 - 6670*S^2 - 9983*S^4 - 2*S^6 - 4*S^8 - 2*S^10))/(2592*S^3*(1 + S^2)^2) + ((-143 - 3178*S^2 - 4481*S^4 - 26*S^6 - 52*S^8 - 26*S^10)*HPL[{2}, -S^2])/(432*S^3*(1 + S^2)^2) + HPL[{3}, -S^2]/(12*S^3) + (241*HPL[{2, 1}, -S^2])/(36*S^3)) + ((-141 + 1122*S^2 + 1965*S^4 + 40*S^6 + 80*S^8 + 40*S^10)*HPL[{3, 1}, -S^2])/(216*S^3*(1 + S^2)^2) + HPL[{3, 2}, -S^2]/(6*S^3) + HPL[{4, 1}, -S^2]/(4*S^3) + ((46 - 390*S^2 - 677*S^4 - 10*S^6 - 20*S^8 - 10*S^10)*HPL[{2, 1, 1}, -S^2])/(36*S^3*(1 + S^2)^2) - (79*HPL[{2, 2, 1}, -S^2])/(6*S^3) - (121*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (259*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + (5*(15 + 3*S^2 + 70*S^4 + 64*S^6)*Zeta[3])/(216*S*(1 + S^2)) + HPL[{2}, -S^2]*((-108 - 160*S^2 - 9*S^4 + 177*S^6)/(432*S^3) + (Pi^2*(23 - 390*S^2 - 631*S^4 + 20*S^6 + 40*S^8 + 20*S^10))/(432*S^3*(1 + S^2)^2) - HPL[{3}, -S^2]/(12*S^3) + (79*HPL[{2, 1}, -S^2])/(12*S^3) - (5*Zeta[3])/(12*S^3)) + HPL[{1}, -S^2]*((-2009*Pi^4)/(6480*S^3) + ((1 + S^2)*(-6853 - 2987*S^2 + 2510*S^4))/(15552*S^3) + (Pi^2*(-2137 + 70*S^2 - 17932*S^4 + 932*S^6 + 2329*S^8 + 1202*S^10))/(7776*S^3*(1 + S^2)^2) + ((-109*Pi^2)/(108*S^3) + (-68 + 93*S^2 - 1325*S^4 - 92*S^6 - 69*S^8 - 17*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (5*HPL[{2}, -S^2]^2)/(3*S^3) + ((55 + 122*S^2 + 73*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{3}, -S^2])/(72*S^3*(1 + S^2)^2) + HPL[{4}, -S^2]/(6*S^3) + ((143 + 3178*S^2 + 4481*S^4 + 26*S^6 + 52*S^8 + 26*S^10)*HPL[{2, 1}, -S^2])/(216*S^3*(1 + S^2)^2) + (13*HPL[{3, 1}, -S^2])/(2*S^3) - (241*HPL[{2, 1, 1}, -S^2])/(18*S^3) + (5*(11 + 2*S^6)*Zeta[3])/(72*S^3))) + Log[T]^4*((-36973 - 10432*S^2)/(2916*S) + (Pi^2*(-18795 - 6906*S^2 - 1721*S^4))/(1458*S) + (Pi^4*(-40038 - 60057*S^2 - 1510*S^4 - 3020*S^6 - 1510*S^8))/(4860*S*(1 + S^2)^2) + ((-290*Pi^2)/(9*S^3) - (5*(655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^3 - (140*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)^2) - (224*HPL[{1}, -S^2]^5)/(9*S^3) + HPL[{0}, S^2]^4*((-426 - 639*S^2 - 5*S^4 - 10*S^6 - 5*S^8)/(162*S*(1 + S^2)^2) - (71*HPL[{1}, -S^2])/(27*S^3)) + ((-1633 - 5618*S^2 - 5161*S^4 - 100*S^6 - 200*S^8 - 100*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + HPL[{0}, S^2]^3*((-1942 - 7245*S^2 - 1720*S^4 - 963*S^6 - 166*S^8)/(324*S*(1 + S^2)^2) + ((-1067 - 6514*S^2 - 7637*S^4 - 194*S^6 - 388*S^8 - 194*S^10)*HPL[{1}, -S^2])/(162*S^3*(1 + S^2)^2) - (365*HPL[{1}, -S^2]^2)/(27*S^3) + (16*HPL[{2}, -S^2])/(27*S^3)) + ((28*Pi^2)/(27*S^3) + (-100 + 20380*S^2 + 47501*S^4 + 19610*S^6 + 12721*S^8 + 3032*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*(83 + 332*S^2 + 332*S^4 + 30*S^6 + 60*S^8 + 30*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*HPL[{5}, -S^2])/S^3 + ((1694*Pi^2)/(27*S^3) + (6723 - 14895*S^2 - 9054*S^4 - 7570*S^6 - 2602*S^8)/(81*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + HPL[{0}, S^2]^2*((-17205 - 6252*S^2 - 3442*S^4)/(972*S) + (Pi^2*(-4494 - 6741*S^2 - 260*S^4 - 520*S^6 - 260*S^8))/(324*S*(1 + S^2)^2) - (5*(33 + 190*S^2 + 219*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{1}, -S^2]^2)/(6*S^3*(1 + S^2)^2) - (310*HPL[{1}, -S^2]^3)/(9*S^3) - (4*(-40 + 214*S^2 + 401*S^4 + 30*S^6 + 60*S^8 + 30*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-749*Pi^2)/(54*S^3) + (-7043 - 20512*S^2 - 51242*S^4 - 10508*S^6 - 8299*S^8 - 2084*S^10)/(324*S^3*(1 + S^2)^2) - (392*HPL[{2}, -S^2])/(9*S^3)) - (17*HPL[{3}, -S^2])/(9*S^3) + (854*HPL[{2, 1}, -S^2])/(9*S^3)) + (4*(-2032 - 4562*S^2 - 2779*S^4 + 75*S^6 + 150*S^8 + 75*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (184*HPL[{3, 2}, -S^2])/(9*S^3) + (64*HPL[{4, 1}, -S^2])/(9*S^3) - (40*(-117 + 8*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (3112*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (2992*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (2240*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + (2*(9531 + 21078*S^2 + 9122*S^4 + 5626*S^6 + 1301*S^8)*Zeta[3])/(81*S*(1 + S^2)^2) + HPL[{2}, -S^2]*((37082 - 801*S^2 + 828*S^4 - 1721*S^6)/(243*S^3) + (Pi^2*(1915 + 2654*S^2 + 151*S^4 - 240*S^6 - 480*S^8 - 240*S^10))/(81*S^3*(1 + S^2)^2) - (172*HPL[{3}, -S^2])/(9*S^3) + (1556*HPL[{2, 1}, -S^2])/(9*S^3) + (28*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(972*S^3) - (5*Pi^2*(407 + 1858*S^2 + 1973*S^4 + 74*S^6 + 148*S^8 + 74*S^10))/(54*S^3*(1 + S^2)^2) + (65*(11 + 2*S^6)*HPL[{2}, -S^2])/(9*S^3) + (1900*HPL[{3}, -S^2])/(9*S^3) + (500*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((-6673*Pi^4)/(810*S^3) - ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(2916*S^3) + (Pi^2*(-18259 - 55706*S^2 - 94156*S^4 - 21544*S^6 - 14837*S^8 - 3022*S^10))/(486*S^3*(1 + S^2)^2) + ((-392*Pi^2)/(27*S^3) + (2*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(9*S^3) + (10*(737 + 2614*S^2 + 2447*S^4 + 134*S^6 + 268*S^8 + 134*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (664*HPL[{4}, -S^2])/(9*S^3) - (130*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (664*HPL[{3, 1}, -S^2])/(9*S^3) + (10*(209 + 718*S^2 + 659*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((-554619 - 61329*S^2 - 46564*S^4)/(2916*S) + (Pi^2*(-5321 - 15120*S^2 - 5030*S^4 - 3204*S^6 - 743*S^8))/(162*S*(1 + S^2)^2) - (280*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)^2) - (560*HPL[{1}, -S^2]^4)/(9*S^3) + ((61*Pi^2)/(27*S^3) + (743 - 23588*S^2 - 63733*S^4 - 23972*S^6 - 15256*S^8 - 3686*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (17*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{1}, -S^2]^2*((-1205*Pi^2)/(27*S^3) - (5*(655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10))/(18*S^3*(1 + S^2)^2) - (500*HPL[{2}, -S^2])/(3*S^3)) + (2*(-134 - 166*S^2 + 19*S^4 + 37*S^6 + 74*S^8 + 37*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (8*HPL[{4}, -S^2])/(3*S^3) - (20*(-150 - 450*S^2 - 375*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (208*HPL[{3, 1}, -S^2])/(9*S^3) + (40*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(166 + 249*S^2 + 30*S^4 + 60*S^6 + 30*S^8)*Zeta[3])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((-5*(1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(972*S^3) + (Pi^2*(-5687 - 25834*S^2 - 27377*S^4 - 1034*S^6 - 2068*S^8 - 1034*S^10))/(162*S^3*(1 + S^2)^2) - (125*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (68*HPL[{3}, -S^2])/(9*S^3) + (1000*HPL[{2, 1}, -S^2])/(3*S^3) + (332*Zeta[3])/(9*S^3)))) + ((180310 + 10147*S^2 + 1186*S^4)/(324*S) + (Pi^2*(3938 + 8355*S^2 + 3725*S^4 + 2373*S^6 + 551*S^8))/(54*S*(1 + S^2)^2))*Zeta[5] + HPL[{4}, -S^2]*((Pi^2*(20431 + 33906*S^2 + 12162*S^4 + 12994*S^6))/(1944*S^3) + (695288 + 1049502*S^2 + 205833*S^4 + 351840*S^6)/(11664*S^3) + (Pi^4*(3035 + 9850*S^2 + 8705*S^4 + 813*S^6 + 1626*S^8 + 813*S^10))/(1620*S^3*(1 + S^2)^2) - (290*HPL[{5}, -S^2])/(3*S^3) + ((-295*Pi^2)/(9*S^3) + (-5013 - 9687*S^2 - 8352*S^4 + 592*S^6 + 839*S^8 + 637*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-481 - 236*S^2 + 608*S^4 + 174*S^6 + 348*S^8 + 174*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (46*HPL[{3, 2}, -S^2])/(3*S^3) - (104*HPL[{4, 1}, -S^2])/(3*S^3) + (4*(-355 - 32*S^2 + 662*S^4 + 169*S^6 + 338*S^8 + 169*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (380*HPL[{2, 2, 1}, -S^2])/S^3 + (1180*HPL[{3, 1, 1}, -S^2])/S^3 - (2272*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-41*Pi^2)/(9*S^3) + (-235 + 180*S^2 + 1103*S^4 + 684*S^6 + 470*S^8 + 138*S^10)/(18*S^3*(1 + S^2)^2))*Zeta[3] - (178*Zeta[5])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((3087476 + 43275*S^2 + 30486*S^4 - 59867*S^6)/(2916*S^3) + (Pi^2*(77770 - 16947*S^2 - 2970*S^4 - 6884*S^6))/(486*S^3) + (Pi^4*(10424 + 8722*S^2 - 7765*S^4 - 1526*S^6 - 3052*S^8 - 1526*S^10))/(540*S^3*(1 + S^2)^2) + (6272*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (17440*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (12448*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((16*Pi^2)/(9*S^3) + (2*(-1291 + 15178*S^2 + 39281*S^4 + 16782*S^6 + 10464*S^8 + 2382*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] - (112*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]^2*((Pi^2*(-77432 - 50856*S^2 - 17043*S^4 - 5988*S^6))/(3888*S^3) + (-1464277 - 380493*S^2 - 132705*S^4 + 6881*S^6)/(11664*S^3) + (Pi^4*(-6976 - 31934*S^2 - 33949*S^4 - 1154*S^6 - 2308*S^8 - 1154*S^10))/(3240*S^3*(1 + S^2)^2) + ((2*Pi^2)/S^3 + (463 + 10616*S^2 + 23242*S^4 + 9281*S^6 + 6013*S^8 + 1433*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((52 + 596*S^2 + 790*S^4 + 73*S^6 + 146*S^8 + 73*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (5*HPL[{5}, -S^2])/S^3 + ((398*Pi^2)/(9*S^3) + (3315 - 6519*S^2 - 4170*S^4 - 3575*S^6 - 1355*S^8)/(54*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-3493 - 7970*S^2 - 4969*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^2) + (49*HPL[{3, 2}, -S^2])/(3*S^3) - (7*HPL[{4, 1}, -S^2])/S^3 - (4*(-773 + 66*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (252*HPL[{2, 2, 1}, -S^2])/S^3 - (708*HPL[{3, 1, 1}, -S^2])/S^3 + (1568*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-11*Pi^2)/(9*S^3) + (-771 + 15834*S^2 + 37929*S^4 + 16600*S^6 + 10580*S^8 + 2560*S^10)/(108*S^3*(1 + S^2)^2))*Zeta[3] - (20*Zeta[5])/(3*S^3)) + HPL[{3, 1}, -S^2]*((-6586091 - 767418*S^2 - 356091*S^4 - 60702*S^6)/(11664*S^3) + (Pi^2*(-169155 + 16842*S^2 - 4632*S^4 + 8126*S^6))/(1944*S^3) + (Pi^4*(-36275 - 43894*S^2 + 6709*S^4 + 3934*S^6 + 7868*S^8 + 3934*S^10))/(3240*S^3*(1 + S^2)^2) + (44*HPL[{3, 2}, -S^2])/S^3 - (132*HPL[{4, 1}, -S^2])/S^3 + (224*(67 + 218*S^2 + 193*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (816*HPL[{2, 2, 1}, -S^2])/S^3 - (28688*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (1632*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((1402 - 15262*S^2 - 40025*S^4 - 16958*S^6 - 10483*S^8 - 2342*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2) + (40*Zeta[5])/S^3) + HPL[{1}, -S^2]^4*(-(Pi^2*(1 + S^2)*(71271 + 13565*S^2 + 9492*S^4))/(3888*S^3) - ((1 + S^2)*(1865477 + 155803*S^2 + 126326*S^4))/(17496*S^3) + (Pi^4*(-52349 - 264850*S^2 - 292577*S^4 - 9518*S^6 - 19036*S^8 - 9518*S^10))/(19440*S^3*(1 + S^2)^2) - (98*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((497*Pi^2)/(27*S^3) + (24061 + 77276*S^2 + 99832*S^4 + 26410*S^6 + 17147*S^8 + 3154*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(605 + 2206*S^2 + 2099*S^4 + 110*S^6 + 220*S^8 + 110*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) + (24*HPL[{5}, -S^2])/S^3 + ((392*Pi^2)/(27*S^3) - (2*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (2*(1529 + 4054*S^2 + 3023*S^4 + 278*S^6 + 556*S^8 + 278*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (1568*HPL[{3, 2}, -S^2])/(9*S^3) - (5368*HPL[{4, 1}, -S^2])/(9*S^3) + (130*(11 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (3136*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (5608*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((416*Pi^2)/(27*S^3) + (2*(5608 + 17597*S^2 + 21457*S^4 + 5518*S^6 + 3269*S^8 + 469*S^10))/(81*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(54*S^3) + (Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(162*S^3*(1 + S^2)^2) + (784*HPL[{3}, -S^2])/(9*S^3) + (1568*HPL[{2, 1}, -S^2])/(9*S^3) + (784*Zeta[3])/(9*S^3)) + (760*Zeta[5])/(9*S^3)) + Zeta[3]*((Pi^2*(243216 + 21501*S^2 + 18811*S^4))/(2916*S) + (20297262 + 794901*S^2 + 303805*S^4)/(34992*S) + (Pi^4*(79746 + 173682*S^2 + 81679*S^4 + 59342*S^6 + 16897*S^8))/(9720*S*(1 + S^2)^2) + (2*(-186 - 279*S^2 + 52*S^4 + 104*S^6 + 52*S^8)*Zeta[5])/(9*S*(1 + S^2)^2)) + HPL[{2, 1}, -S^2]*((48199*Pi^6)/(17010*S^3) + (206932 - 19559241*S^2 + 60705*S^4 - 303805*S^6)/(34992*S^3) + (Pi^2*(31093 - 152906*S^2 + 790*S^4 - 8946*S^6))/(1944*S^3) + (Pi^4*(50837 - 14942*S^2 + 6503*S^4 - 60693*S^6 - 32838*S^8 - 8997*S^10))/(9720*S^3*(1 + S^2)^2) + ((-472*Pi^2)/(3*S^3) + (-2807 - 24376*S^2 - 60326*S^4 - 21586*S^6 - 14675*S^8 - 3622*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((12757 + 35762*S^2 + 28129*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(-20489 - 56398*S^2 - 43619*S^4 + 224*S^6 + 448*S^8 + 224*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (182*HPL[{4, 2}, -S^2])/S^3 + (900*HPL[{5, 1}, -S^2])/S^3 + ((-1064*Pi^2)/(3*S^3) - (4*(789 + 4318*S^2 + 9795*S^4 + 3198*S^6 + 2098*S^8 + 462*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (16*(-773 + 66*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (64*(-152 - 10*S^2 + 289*S^4 + 40*S^6 + 80*S^8 + 40*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (104*HPL[{3, 1, 2}, -S^2])/S^3 + (904*HPL[{3, 2, 1}, -S^2])/S^3 + (6800*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (16*(1633 + 5618*S^2 + 5161*S^4 + 100*S^6 + 200*S^8 + 100*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1632*HPL[{3, 1, 1, 1}, -S^2])/S^3 - (12448*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-70558 - 13743*S^2 - 6282*S^4)/(81*S^3) + (Pi^2*(-3594 - 9774*S^2 - 7473*S^4 - 4*S^6 - 8*S^8 - 4*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + (20*Zeta[3]^2)/(3*S^3) - (2*(3660 + 9486*S^2 + 6909*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-487*Pi^6)/(6804*S^3) + (Pi^2*(17777 + 475164*S^2 + 52299*S^4 + 46861*S^6))/(5832*S^3) + (1727552 + 20270985*S^2 + 819411*S^4 + 968208*S^6)/(34992*S^3) + (Pi^4*(-891 + 12448*S^2 + 30708*S^4 + 13255*S^6 + 8871*S^8 + 2167*S^10))/(1620*S^3*(1 + S^2)^2) + ((32*Pi^2)/(9*S^3) - (2*(-133 + 295*S^2 + 1127*S^4 + 689*S^6 + 580*S^8 + 203*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (4*(-159 - 276*S^2 - 96*S^4 + 19*S^6 + 38*S^8 + 19*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (290*HPL[{6}, -S^2])/(3*S^3) - (48*HPL[{2, 1}, -S^2]^2)/S^3 + ((110*Pi^2)/(9*S^3) - (2*(-1083 + 7464*S^2 + 20301*S^4 + 9176*S^6 + 5995*S^8 + 1517*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-17 + 310*S^2 + 499*S^4 + 54*S^6 + 108*S^8 + 54*S^10)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (2*(-347 - 532*S^2 - 104*S^4 + 68*S^6 + 136*S^8 + 68*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*HPL[{4, 2}, -S^2])/S^3 - (212*HPL[{5, 1}, -S^2])/(3*S^3) + ((-176*Pi^2)/(9*S^3) + (-3823 + 30784*S^2 + 81704*S^4 + 37076*S^6 + 24535*S^8 + 6332*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (2*(6593 + 18778*S^2 + 14981*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(-20185 - 56258*S^2 - 44017*S^4 + 54*S^6 + 108*S^8 + 54*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*HPL[{3, 1, 2}, -S^2])/(3*S^3) - (112*HPL[{3, 2, 1}, -S^2])/S^3 + (24*HPL[{4, 1, 1}, -S^2])/S^3 + (16*(-1711 - 4598*S^2 - 3475*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (800*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (1376*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((10301 + 1842*S^2 + 2742*S^4 + 3518*S^6)/(324*S^3) + (Pi^2*(439 + 1190*S^2 + 907*S^4 + 66*S^6 + 132*S^8 + 66*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2, 1}, -S^2]*((-141849 - 21411*S^2 - 12141*S^4 + 5383*S^6)/(162*S^3) + (Pi^2*(-7303 - 19562*S^2 - 14737*S^4 + 170*S^6 + 340*S^8 + 170*S^10))/(54*S^3*(1 + S^2)^2) - (136*Zeta[3])/(3*S^3)) + ((853 + 1898*S^2 + 1141*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-52285*Pi^6)/(40824*S^3) - (Pi^2*(1 + S^2)*(71609 + 10670*S^2 + 7703*S^4))/(1944*S^3) - ((1 + S^2)*(12649645 + 794066*S^2 + 772759*S^4))/(52488*S^3) + (Pi^4*(-292577 - 870982*S^2 - 1697756*S^4 - 362300*S^6 - 259729*S^8 - 55868*S^10))/(58320*S^3*(1 + S^2)^2) + ((-607*Pi^2)/(27*S^3) + (-4537 - 14056*S^2 - 21304*S^4 - 5140*S^6 - 3427*S^8 - 664*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (148*HPL[{3}, -S^2]^2)/(9*S^3) + ((340*Pi^2)/(27*S^3) + (4427 + 15048*S^2 + 21278*S^4 + 6152*S^6 + 4563*S^8 + 1100*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(583 + 1814*S^2 + 1555*S^4 + 106*S^6 + 212*S^8 + 106*S^10)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)^2) + (178*HPL[{6}, -S^2])/(9*S^3) + (3136*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((440*Pi^2)/(27*S^3) - (4*(5225 + 17554*S^2 + 17960*S^4 + 5495*S^6 + 3433*S^8 + 581*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*(10417 + 36938*S^2 + 34573*S^4 + 1894*S^6 + 3788*S^8 + 1894*S^10)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (52*HPL[{4, 2}, -S^2])/S^3 - (2704*HPL[{5, 1}, -S^2])/(9*S^3) + ((-1568*Pi^2)/(27*S^3) + (8*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (1568*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (8*(2783 + 13978*S^2 + 15401*S^4 + 506*S^6 + 1012*S^8 + 506*S^10)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (2656*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (520*(11 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) - (2656*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (((1 + S^2)*(150737 + 14875*S^2 + 9644*S^4))/(486*S^3) + (2*Pi^2*(583 + 1998*S^2 + 1831*S^4 + 106*S^6 + 212*S^8 + 106*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] - (80*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*((-2*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(27*S^3) - (2*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(81*S^3*(1 + S^2)^2) - (3136*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*(((1 + S^2)*(154507 + 20411*S^2 + 17122*S^4))/(486*S^3) + (2*Pi^2*(660 + 2314*S^2 + 2151*S^4 + 120*S^6 + 240*S^8 + 120*S^10))/(27*S^3*(1 + S^2)^2) - (3136*HPL[{2, 1}, -S^2])/(9*S^3) + (200*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((-2021*Pi^4)/(540*S^3) + ((1 + S^2)*(411947 + 9469*S^2 + 13400*S^4))/(2916*S^3) + (Pi^2*(2024 + 7326*S^2 + 1376*S^4 + 1271*S^6 + 360*S^8 - 133*S^10))/(162*S^3*(1 + S^2)^2) + (2*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (452*HPL[{4}, -S^2])/(9*S^3) + (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (3136*HPL[{3, 1}, -S^2])/(9*S^3) - (6272*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (112*(55 + 194*S^2 + 181*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + (2*(3619 + 11798*S^2 + 10459*S^4 + 658*S^6 + 1316*S^8 + 658*S^10)*Zeta[5])/(27*S^3*(1 + S^2)^2)) + Log[T]^3*((62867 + 16130*S^2)/(4374*S) + (Pi^2*(45771 + 17205*S^2 + 4334*S^4))/(2916*S) + (Pi^4*(61546 + 241683*S^2 + 49890*S^4 + 37285*S^6 + 7380*S^8))/(9720*S*(1 + S^2)^2) + ((290*Pi^2)/(9*S^3) + (5*(655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^4 + (112*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^5)/(27*S^3*(1 + S^2)^2) + (448*HPL[{1}, -S^2]^6)/(27*S^3) + HPL[{0}, S^2]^5*((542 + 813*S^2 - 6*S^4 - 12*S^6 - 6*S^8)/(540*S*(1 + S^2)^2) + (271*HPL[{1}, -S^2])/(270*S^3)) + ((416*Pi^2)/(27*S^3) + (3748 + 9738*S^2 + 11509*S^4 + 1942*S^6 + 1329*S^8 + 202*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (784*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^4*((1398 + 12159*S^2 + 578*S^4 - 407*S^6 - 448*S^8)/(1944*S*(1 + S^2)^2) + ((341 + 4090*S^2 + 5453*S^4 + 62*S^6 + 124*S^8 + 62*S^10)*HPL[{1}, -S^2])/(324*S^3*(1 + S^2)^2) + (142*HPL[{1}, -S^2]^2)/(27*S^3) - HPL[{2}, -S^2]/(3*S^3)) - (16*HPL[{3}, -S^2]^2)/(3*S^3) + ((-8*Pi^2)/S^3 + (-6324 - 25134*S^2 - 36537*S^4 - 13244*S^6 - 10813*S^8 - 3344*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(-195 + 906*S^2 + 1749*S^4 + 406*S^6 + 812*S^8 + 406*S^10)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)^2) - (16*HPL[{6}, -S^2])/S^3 - (3160*HPL[{2, 1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^3*((6280 + 925*S^2 - 63*S^4)/(486*S) + (Pi^2*(212 + 318*S^2 + 9*S^4 + 18*S^6 + 9*S^8))/(27*S*(1 + S^2)^2) + ((1067 + 6514*S^2 + 7637*S^4 + 194*S^6 + 388*S^8 + 194*S^10)*HPL[{1}, -S^2]^2)/(81*S^3*(1 + S^2)^2) + (1460*HPL[{1}, -S^2]^3)/(81*S^3) + ((-157 + 1666*S^2 + 2813*S^4 + 166*S^6 + 332*S^8 + 166*S^10)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((212*Pi^2)/(27*S^3) + (3197 + 8476*S^2 + 20027*S^4 + 3521*S^6 + 2320*S^8 + 407*S^10)/(243*S^3*(1 + S^2)^2) + (220*HPL[{2}, -S^2])/(9*S^3)) + (46*HPL[{3}, -S^2])/(27*S^3) - (1384*HPL[{2, 1}, -S^2])/(27*S^3)) + ((2200*Pi^2)/(27*S^3) - (4*(-12917 - 27682*S^2 - 17804*S^4 - 974*S^6 - 439*S^8 + 484*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(-493 + 3718*S^2 + 6563*S^4 + 1224*S^6 + 2448*S^8 + 1224*S^10)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)^2) + (8*(-347 + 7358*S^2 + 11731*S^4 + 1942*S^6 + 3884*S^8 + 1942*S^10)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (136*HPL[{4, 2}, -S^2])/(9*S^3) + (592*HPL[{5, 1}, -S^2])/(9*S^3) + ((-3640*Pi^2)/(27*S^3) + (20*(-4635 - 4725*S^2 + 306*S^4 + 74*S^6 + 362*S^8))/(81*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (16*(523 + 3398*S^2 + 4051*S^4 + 292*S^6 + 584*S^8 + 292*S^10)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (16*(1549 + 7304*S^2 + 7858*S^4 + 231*S^6 + 462*S^8 + 231*S^10)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (640*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (5632*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (6752*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (560*(-13 + 6*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + (5440*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (8960*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*(33846 + 3741*S^2 + 2972*S^4))/(243*S) - (8*Pi^2*(624 + 936*S^2 + 175*S^4 + 350*S^6 + 175*S^8))/(81*S*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(729*S^3) + (10*Pi^2*(407 + 1858*S^2 + 1973*S^4 + 74*S^6 + 148*S^8 + 74*S^10))/(81*S^3*(1 + S^2)^2) - (260*(11 + 2*S^6)*HPL[{2}, -S^2])/(27*S^3) - (7600*HPL[{3}, -S^2])/(27*S^3) - (2000*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((-3941 - 272334*S^2 - 40071*S^4 - 31326*S^6)/(486*S^3) - (2*Pi^2*(-15 + 2952*S^2 + 4458*S^4 + 688*S^6 + 1376*S^8 + 688*S^10))/(81*S^3*(1 + S^2)^2) + (2320*HPL[{2, 1}, -S^2])/(3*S^3) - (176*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((4*(-7400 + 31959*S^2 + 1899*S^4 + 2972*S^6))/(243*S^3) + (8*Pi^2*(-655 - 1898*S^2 - 1537*S^4 + 175*S^6 + 350*S^8 + 175*S^10))/(81*S^3*(1 + S^2)^2) + (6160*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((6673*Pi^4)/(405*S^3) + ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(1458*S^3) + (Pi^2*(18259 + 55706*S^2 + 94156*S^4 + 21544*S^6 + 14837*S^8 + 3022*S^10))/(243*S^3*(1 + S^2)^2) + ((784*Pi^2)/(27*S^3) - (4*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (1568*HPL[{2}, -S^2]^2)/(9*S^3) - (20*(737 + 2614*S^2 + 2447*S^4 + 134*S^6 + 268*S^8 + 134*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (1328*HPL[{4}, -S^2])/(9*S^3) + (260*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (1328*HPL[{3, 1}, -S^2])/(9*S^3) - (20*(209 + 718*S^2 + 659*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((-1798*Pi^4)/(405*S^3) + (-157649 + 2502*S^2 - 2259*S^4 + 4334*S^6)/(486*S^3) + (Pi^2*(-24299 - 42790*S^2 + 361*S^4 + 8840*S^6 + 7720*S^8 + 3620*S^10))/(486*S^3*(1 + S^2)^2) - (4*(-353 + 1646*S^2 + 3175*S^4 + 634*S^6 + 1268*S^8 + 634*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (232*HPL[{4}, -S^2])/(9*S^3) - (8*(523 + 3398*S^2 + 4051*S^4 + 292*S^6 + 584*S^8 + 292*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (3824*HPL[{3, 1}, -S^2])/(9*S^3) + (6320*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (8*(-55 + 1066*S^2 + 1709*S^4 + 280*S^6 + 560*S^8 + 280*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((23426 + 10085*S^2 + 4334*S^4)/(972*S) + (Pi^2*(3016 + 13353*S^2 + 2806*S^4 + 1911*S^6 + 454*S^8))/(324*S*(1 + S^2)^2) + (10*(33 + 190*S^2 + 219*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{1}, -S^2]^3)/(9*S^3*(1 + S^2)^2) + (310*HPL[{1}, -S^2]^4)/(9*S^3) + ((-53*Pi^2)/(27*S^3) + (-562 + 2005*S^2 + 11228*S^4 + 3470*S^6 + 2770*S^8 + 905*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (7*HPL[{2}, -S^2]^2)/(3*S^3) + HPL[{1}, -S^2]^2*((749*Pi^2)/(27*S^3) + (7043 + 20512*S^2 + 51242*S^4 + 10508*S^6 + 8299*S^8 + 2084*S^10)/(162*S^3*(1 + S^2)^2) + (784*HPL[{2}, -S^2])/(9*S^3)) - (2*(-35 + 62*S^2 + 163*S^4 + 43*S^6 + 86*S^8 + 43*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (4*HPL[{4}, -S^2])/S^3 + (2*(-1255 - 4862*S^2 - 4783*S^4 + 70*S^6 + 140*S^8 + 70*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (160*HPL[{3, 1}, -S^2])/(9*S^3) - (280*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(246 + 369*S^2 + 70*S^4 + 140*S^6 + 70*S^8)*Zeta[3])/(27*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(((1 + S^2)*(15769 + 6455*S^2 + 4708*S^4))/(486*S^3) + (Pi^2*(913 + 6320*S^2 + 7654*S^4 + 166*S^6 + 332*S^8 + 166*S^10))/(81*S^3*(1 + S^2)^2) + ((935 + 6574*S^2 + 7991*S^4 + 170*S^6 + 340*S^8 + 170*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) - (88*HPL[{3}, -S^2])/(9*S^3) - (1568*HPL[{2, 1}, -S^2])/(9*S^3) - (164*Zeta[3])/(9*S^3))) + HPL[{0}, S^2]*((Pi^2*(208590 + 30795*S^2 + 18682*S^4))/(2916*S) + (1830486 + 151509*S^2 + 126326*S^4)/(4374*S) + (Pi^4*(24366 + 36549*S^2 + 2774*S^4 + 5548*S^6 + 2774*S^8))/(1620*S*(1 + S^2)^2) + (280*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)^2) + (448*HPL[{1}, -S^2]^5)/(9*S^3) + (2*(-17 + 2318*S^2 + 3511*S^4 + 380*S^6 + 760*S^8 + 380*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((4820*Pi^2)/(81*S^3) + (10*(655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10))/(27*S^3*(1 + S^2)^2) + (2000*HPL[{2}, -S^2])/(9*S^3)) + ((116*Pi^2)/(27*S^3) + (1611 + 1956*S^2 - 1260*S^4 - 1690*S^6 - 2351*S^8 - 1042*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(-55 - 18*S^2 + 83*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (12*HPL[{5}, -S^2])/S^3 + ((-4564*Pi^2)/(27*S^3) + (2*(-29155 - 62216*S^2 - 61879*S^4 - 5448*S^6 - 2904*S^8 + 726*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (8*(-228 + 1794*S^2 + 3147*S^4 + 403*S^6 + 806*S^8 + 403*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (200*HPL[{3, 2}, -S^2])/(9*S^3) + (64*HPL[{4, 1}, -S^2])/(9*S^3) + (40*(-25 + 250*S^2 + 425*S^4 + 54*S^6 + 108*S^8 + 54*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (12272*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (37376*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (8480*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) - (4*(1401 + 3591*S^2 + 1564*S^4 + 1289*S^6 + 421*S^8)*Zeta[3])/(81*S*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(486*S^3) + (Pi^2*(5687 + 25834*S^2 + 27377*S^4 + 1034*S^6 + 2068*S^8 + 1034*S^10))/(81*S^3*(1 + S^2)^2) + (250*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) - (136*HPL[{3}, -S^2])/(9*S^3) - (2000*HPL[{2, 1}, -S^2])/(3*S^3) - (664*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((2409 + 168816*S^2 + 21207*S^4 + 16528*S^6)/(486*S^3) + (4*Pi^2*(-133 + 1354*S^2 + 2297*S^4 + 244*S^6 + 488*S^8 + 244*S^10))/(81*S^3*(1 + S^2)^2) - (88*HPL[{3}, -S^2])/(9*S^3) - (6136*HPL[{2, 1}, -S^2])/(9*S^3) + (8*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((4061*Pi^4)/(270*S^3) + ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(1458*S^3) + (Pi^2*(35869 + 107852*S^2 + 177124*S^4 + 39622*S^6 + 26015*S^8 + 4774*S^10))/(486*S^3*(1 + S^2)^2) + ((80*Pi^2)/S^3 + (4*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (1568*HPL[{2}, -S^2]^2)/(9*S^3) - (4*(77 + 358*S^2 + 383*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (184*HPL[{4}, -S^2])/(9*S^3) - (500*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2000*HPL[{3, 1}, -S^2])/(3*S^3) + (4000*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(473 + 1942*S^2 + 1967*S^4 + 86*S^6 + 172*S^8 + 86*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2))) - (80*(114 + 171*S^2 + 34*S^4 + 68*S^6 + 34*S^8)*Zeta[5])/(27*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(71271 + 13565*S^2 + 9492*S^4))/(972*S^3) + ((1 + S^2)*(1865477 + 155803*S^2 + 126326*S^4))/(4374*S^3) + (Pi^4*(52349 + 264850*S^2 + 292577*S^4 + 9518*S^6 + 19036*S^8 + 9518*S^10))/(4860*S^3*(1 + S^2)^2) + (392*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((-1988*Pi^2)/(27*S^3) - (2*(24061 + 77276*S^2 + 99832*S^4 + 26410*S^6 + 17147*S^8 + 3154*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (8*(605 + 2206*S^2 + 2099*S^4 + 110*S^6 + 220*S^8 + 110*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - (96*HPL[{5}, -S^2])/S^3 + ((-1568*Pi^2)/(27*S^3) + (8*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(1529 + 4054*S^2 + 3023*S^4 + 278*S^6 + 556*S^8 + 278*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (6272*HPL[{3, 2}, -S^2])/(9*S^3) + (21472*HPL[{4, 1}, -S^2])/(9*S^3) - (520*(11 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (12544*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (22432*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((-1664*Pi^2)/(27*S^3) - (8*(5608 + 17597*S^2 + 21457*S^4 + 5518*S^6 + 3269*S^8 + 469*S^10))/(81*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-2*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(27*S^3) - (2*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(81*S^3*(1 + S^2)^2) - (3136*HPL[{3}, -S^2])/(9*S^3) - (6272*HPL[{2, 1}, -S^2])/(9*S^3) - (3136*Zeta[3])/(9*S^3)) - (3040*Zeta[5])/(9*S^3))) + HPL[{0}, S^2]^3*((-579946 - 45469*S^2 + 9677*S^4)/(46656*S) + (Pi^2*(-90916 - 7975*S^2 + 57076*S^4))/(46656*S) + (Pi^4*(-1148 - 49203*S^2 + 3103*S^4 + 6885*S^6 + 3691*S^8))/(38880*S*(1 + S^2)^2) + ((-1067 - 6514*S^2 - 7637*S^4 - 194*S^6 - 388*S^8 - 194*S^10)*HPL[{1}, -S^2]^5)/(810*S^3*(1 + S^2)^2) - (73*HPL[{1}, -S^2]^6)/(81*S^3) + ((5*Pi^2)/(54*S^3) + (539 - 4178*S^2 - 18667*S^4 - 4990*S^6 - 3302*S^8 - 814*S^10)/(1296*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + HPL[{2}, -S^2]^3/(18*S^3) + HPL[{1}, -S^2]^4*((-53*Pi^2)/(27*S^3) + (-3197 - 8476*S^2 - 20027*S^4 - 3521*S^6 - 2320*S^8 - 407*S^10)/(972*S^3*(1 + S^2)^2) - (55*HPL[{2}, -S^2])/(9*S^3)) - (11*HPL[{3}, -S^2]^2)/(18*S^3) + ((-10*Pi^2)/(27*S^3) + (491 + 322*S^2 - 1525*S^4 - 276*S^6 - 24*S^8 + 120*S^10)/(648*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((215 + 292*S^2 + 8*S^4 - 4*S^6 - 8*S^8 - 4*S^10)*HPL[{5}, -S^2])/(54*S^3*(1 + S^2)^2) - (65*HPL[{6}, -S^2])/(9*S^3) - (5*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-8*Pi^2)/(27*S^3) + (-17 + 2594*S^2 + 9829*S^4 + 2447*S^6 + 1492*S^8 + 323*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-209 - 502*S^2 - 335*S^4 - 42*S^6 - 84*S^8 - 42*S^10)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)^2) + ((-201 - 426*S^2 - 237*S^4 - 52*S^6 - 104*S^8 - 52*S^10)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (26*HPL[{5, 1}, -S^2])/(9*S^3) + ((31*Pi^2)/(27*S^3) + (118 - 4996*S^2 - 19565*S^4 - 4776*S^6 - 2733*S^8 - 528*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (2*(487 + 1928*S^2 + 1918*S^4 + 5*S^6 + 10*S^8 + 5*S^10)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + ((-3027 - 11850*S^2 - 11721*S^4 - 14*S^6 - 28*S^8 - 14*S^10)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (4*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (46*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (2*(-1059 - 4098*S^2 - 4029*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (64*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (128*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((328 + 96*S^2 + 491*S^4)/(108*S) + (Pi^2*(22 + 33*S^2 + 60*S^4 + 120*S^6 + 60*S^8))/(108*S*(1 + S^2)^2))*Zeta[3] + HPL[{2, 1}, -S^2]*((38278 + 8766*S^2 + 3609*S^4 + 1274*S^6)/(1944*S^3) + (Pi^2*(465 + 2052*S^2 + 2148*S^4 + 16*S^6 + 32*S^8 + 16*S^10))/(108*S^3*(1 + S^2)^2) - (8*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(38351 + 6589*S^2 + 3368*S^4))/(5832*S^3) + (Pi^2*(-1243 - 10118*S^2 - 12691*S^4 - 226*S^6 - 452*S^8 - 226*S^10))/(972*S^3*(1 + S^2)^2) + ((-451 - 2882*S^2 - 3421*S^4 - 82*S^6 - 164*S^8 - 82*S^10)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)^2) - (4*HPL[{3}, -S^2])/(9*S^3) + (220*HPL[{2, 1}, -S^2])/(9*S^3) + (22*Zeta[3])/(27*S^3)) + HPL[{3}, -S^2]*((217 - 3252*S^2 + 978*S^4 + 2472*S^6)/(3888*S^3) + (Pi^2*(-126 - 189*S^2 + 8*S^4 + 16*S^6 + 8*S^8))/(324*S*(1 + S^2)^2) + (2*HPL[{2, 1}, -S^2])/(9*S^3) + (2*Zeta[3])/S^3) + HPL[{1}, -S^2]^2*((-3997*Pi^4)/(3240*S^3) - ((1 + S^2)*(246553 + 30851*S^2 + 14776*S^4))/(23328*S^3) + (Pi^2*(-4262 - 9079*S^2 - 29498*S^4 - 3569*S^6 - 1843*S^8 - 59*S^10))/(1944*S^3*(1 + S^2)^2) + ((-187*Pi^2)/(36*S^3) + (-1039 - 2634*S^2 - 6061*S^4 - 1042*S^6 - 630*S^8 - 94*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (53*HPL[{2}, -S^2]^2)/(6*S^3) - (2*(2 + 3*S^2)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) - (17*HPL[{4}, -S^2])/(9*S^3) + ((451 + 2882*S^2 + 3421*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (110*HPL[{3, 1}, -S^2])/(3*S^3) - (220*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((77 + 220*S^2 + 176*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((161*Pi^4)/(3240*S^3) + (8615 - 112851*S^2 - 6705*S^4 + 3541*S^6)/(11664*S^3) + (Pi^2*(673 - 4732*S^2 - 28460*S^4 - 3714*S^6 + 273*S^8 + 1128*S^10))/(3888*S^3*(1 + S^2)^2) + ((105 + 252*S^2 + 168*S^4 + 20*S^6 + 40*S^8 + 20*S^10)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^2) + (11*HPL[{4}, -S^2])/(9*S^3) + ((487 + 1928*S^2 + 1918*S^4 + 5*S^6 + 10*S^8 + 5*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (8*HPL[{3, 1}, -S^2])/(9*S^3) + (10*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-30 - 6*S^2 + 51*S^4 + 20*S^6 + 40*S^8 + 20*S^10)*Zeta[3])/(54*S^3*(1 + S^2)^2)) + (2*(24 + 36*S^2 + 19*S^4 + 38*S^6 + 19*S^8)*Zeta[5])/(27*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(-10214 - 3037*S^2 + 1891*S^4))/(5832*S^3) - ((1 + S^2)*(250581 + 26252*S^2 + 14187*S^4))/(23328*S^3) - (7*Pi^4*(110 + 3646*S^2 + 5249*S^4 + 20*S^6 + 40*S^8 + 20*S^10))/(9720*S^3*(1 + S^2)^2) + ((-77 - 472*S^2 - 554*S^4 - 14*S^6 - 28*S^8 - 14*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((-7*Pi^2)/(18*S^3) + (-559 - 1010*S^2 - 964*S^4 + 116*S^6 + 421*S^8 + 224*S^10)/(324*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-121 - 446*S^2 - 427*S^4 - 22*S^6 - 44*S^8 - 22*S^10)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)^2) - (23*HPL[{5}, -S^2])/(9*S^3) + ((187*Pi^2)/(18*S^3) + (1039 + 2634*S^2 + 6061*S^4 + 1042*S^6 + 630*S^8 + 94*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(77 + 484*S^2 + 572*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (14*HPL[{3, 2}, -S^2])/(9*S^3) - (8*HPL[{4, 1}, -S^2])/(9*S^3) - (2*(451 + 2882*S^2 + 3421*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (212*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (644*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (440*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((11*Pi^2)/(54*S^3) + (86 + 387*S^2 + 515*S^4 + 209*S^6 + 180*S^8 + 53*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(4229 + 665*S^2 + 182*S^4))/(432*S^3) + (Pi^2*(-1133 - 8998*S^2 - 11231*S^4 - 206*S^6 - 412*S^8 - 206*S^10))/(648*S^3*(1 + S^2)^2) + (7*HPL[{3}, -S^2])/(9*S^3) + (106*HPL[{2, 1}, -S^2])/(3*S^3) + Zeta[3]/S^3) + (16*Zeta[5])/(9*S^3))) + HPL[{0}, S^2]^2*((638290 - 355601*S^2 - 363042*S^4)/(69984*S) + (Pi^2*(-294654 - 201792*S^2 + 125299*S^4))/(139968*S) + (Pi^4*(-358590 - 9633*S^2 + 196528*S^4))/(466560*S) + (Pi^6*(-390830 - 586245*S^2 + 4194*S^4 + 8388*S^6 + 4194*S^8))/(544320*S*(1 + S^2)^2) + ((-33 - 190*S^2 - 219*S^4 - 6*S^6 - 12*S^8 - 6*S^10)*HPL[{1}, -S^2]^6)/(18*S^3*(1 + S^2)^2) - (62*HPL[{1}, -S^2]^7)/(63*S^3) + ((35 - 506*S^2 - 829*S^4 - 66*S^6 - 132*S^8 - 66*S^10)*HPL[{2}, -S^2]^3)/(54*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((-749*Pi^2)/(270*S^3) + (-7043 - 20512*S^2 - 51242*S^4 - 10508*S^6 - 8299*S^8 - 2084*S^10)/(1620*S^3*(1 + S^2)^2) - (392*HPL[{2}, -S^2])/(45*S^3)) + ((69 - 2*S^6)*HPL[{3}, -S^2]^2)/(18*S^3) + ((67*Pi^2)/(36*S^3) + (-139 + 2122*S^2 + 3866*S^4 + 1964*S^6 + 1639*S^8 + 416*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + (5*(-224 - 394*S^2 - 143*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{6}, -S^2])/(36*S^3*(1 + S^2)^2) + (125*HPL[{7}, -S^2])/(3*S^3) + ((131 + 1552*S^2 + 2066*S^4 + 124*S^6 + 248*S^8 + 124*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + (Pi^2/(3*S^3) + (1291 - 1396*S^2 - 7664*S^4 - 4648*S^6 - 4139*S^8 - 1444*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((25*Pi^2)/(18*S^3) + (1345 - 4414*S^2 - 13550*S^4 - 7356*S^6 - 6579*S^8 - 2190*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((33 + 84*S^2 + 60*S^4 + S^6 + 2*S^8 + S^10)*HPL[{4, 2}, -S^2])/(18*S^3*(1 + S^2)^2) - (34*HPL[{4, 3}, -S^2])/(3*S^3) + ((61 + 26*S^2 - 83*S^4 - 50*S^6 - 100*S^8 - 50*S^10)*HPL[{5, 1}, -S^2])/(18*S^3*(1 + S^2)^2) - (205*HPL[{5, 2}, -S^2])/(6*S^3) - (250*HPL[{6, 1}, -S^2])/(3*S^3) + ((-646*Pi^2)/(9*S^3) + (-5505 - 10074*S^2 - 20841*S^4 - 2588*S^6 - 2008*S^8 - 212*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-1970*Pi^2)/(9*S^3) + (-16692 - 27726*S^2 - 57237*S^4 - 5368*S^6 - 4133*S^8 - 112*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + ((-27 - 10*S^6)*HPL[{3, 1, 2}, -S^2])/(18*S^3) + ((253 - 4102*S^2 - 6659*S^4 - 538*S^6 - 1076*S^8 - 538*S^10)*HPL[{3, 2, 1}, -S^2])/(18*S^3*(1 + S^2)^2) + (2*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (16*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (2*(-299 + 2834*S^2 + 4849*S^4 + 381*S^6 + 762*S^8 + 381*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (17*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (77*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (190*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((1372*Pi^2)/(9*S^3) - (2*(-2716 - 3503*S^2 - 7666*S^4 - 79*S^6 - 146*S^8 + 110*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (1616*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) + (4*(-179 + 800*S^2 + 1558*S^4 + 117*S^6 + 234*S^8 + 117*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1616*HPL[{3, 1, 1, 2}, -S^2])/S^3 - (1616*HPL[{3, 1, 2, 1}, -S^2])/S^3 - (3232*HPL[{3, 2, 1, 1}, -S^2])/S^3 - (29024*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (32*(-40 + 214*S^2 + 401*S^4 + 30*S^6 + 60*S^8 + 30*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3272*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (3272*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (5408*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 + (6832*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((11341 + 2206*S^2 + 3740*S^4)/(648*S) + (Pi^2*(1260 + 2547*S^2 + 2159*S^4 + 2797*S^6 + 1187*S^8))/(324*S*(1 + S^2)^2))*Zeta[3] + ((-54 - 81*S^2 + 2*S^4 + 4*S^6 + 2*S^8)*Zeta[3]^2)/(18*S*(1 + S^2)^2) + HPL[{4}, -S^2]*((1908 + 5640*S^2 + 3111*S^4 + 2954*S^6)/(1296*S^3) + (Pi^2*(23 + 106*S^2 + 113*S^4 + 27*S^6 + 54*S^8 + 27*S^10))/(108*S^3*(1 + S^2)^2) - (11*HPL[{2, 1}, -S^2])/(3*S^3) - (28*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((3606 - 15345*S^2 - 4626*S^4 - 3442*S^6)/(162*S^3) + (Pi^2*(458 - 2882*S^2 - 5239*S^4 - 270*S^6 - 540*S^8 - 270*S^10))/(54*S^3*(1 + S^2)^2) - (4*Zeta[3])/S^3) + HPL[{2}, -S^2]^2*((-5774 - 18879*S^2 - 5928*S^4 - 3707*S^6)/(1296*S^3) + (Pi^2*(-224 - 2458*S^2 - 3239*S^4 - 156*S^6 - 312*S^8 - 156*S^10))/(216*S^3*(1 + S^2)^2) + (202*HPL[{2, 1}, -S^2])/(3*S^3) - Zeta[3]/(3*S^3)) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(15769 + 6455*S^2 + 4708*S^4))/(1944*S^3) + (Pi^2*(-913 - 6320*S^2 - 7654*S^4 - 166*S^6 - 332*S^8 - 166*S^10))/(324*S^3*(1 + S^2)^2) + ((-935 - 6574*S^2 - 7991*S^4 - 170*S^6 - 340*S^8 - 170*S^10)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)^2) + (22*HPL[{3}, -S^2])/(9*S^3) + (392*HPL[{2, 1}, -S^2])/(9*S^3) + (41*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((-7398 + 30390*S^2 + 8133*S^4 + 6482*S^6)/(648*S^3) + (Pi^2*(-499 + 2722*S^2 + 5081*S^4 + 274*S^6 + 548*S^8 + 274*S^10))/(108*S^3*(1 + S^2)^2) + (16*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((2459*Pi^4)/(360*S^3) + (32279 - 29796*S^2 + 18462*S^4 - 436*S^6)/(1944*S^3) + (Pi^2*(6227 + 4882*S^2 + 21059*S^4 + 700*S^6 + 1316*S^8 + 232*S^10))/(648*S^3*(1 + S^2)^2) - (268*HPL[{3, 1}, -S^2])/S^3 - (1636*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-404 - 1042*S^2 - 755*S^4 - 4*S^6 - 8*S^8 - 4*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-19*Pi^4)/(180*S^3) + (333 + 108168*S^2 + 13497*S^4 + 27412*S^6)/(7776*S^3) + (Pi^2*(-927 + 2328*S^2 + 6264*S^4 + 3128*S^6 + 2635*S^8 + 716*S^10))/(1296*S^3*(1 + S^2)^2) + (17*HPL[{4}, -S^2])/(3*S^3) + ((-51 - 130*S^2 - 93*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(2*S^3*(1 + S^2)^2) + (10*HPL[{3, 1}, -S^2])/(3*S^3) - (4*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((72 + 150*S^2 + 81*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-8449*Pi^4)/(3240*S^3) - ((1 + S^2)*(70220 + 31321*S^2 + 22763*S^4))/(5832*S^3) + (Pi^2*(-8557 - 21782*S^2 - 72196*S^4 - 12364*S^6 - 9641*S^8 - 2320*S^10))/(1944*S^3*(1 + S^2)^2) + ((-211*Pi^2)/(18*S^3) + (-718 - 1836*S^2 - 6298*S^4 - 1183*S^6 - 972*S^8 - 265*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (215*HPL[{2}, -S^2]^2)/(9*S^3) + ((275 + 814*S^2 + 671*S^4 + 50*S^6 + 100*S^8 + 50*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (8*HPL[{4}, -S^2])/(9*S^3) + ((935 + 6574*S^2 + 7991*S^4 + 170*S^6 + 340*S^8 + 170*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (772*HPL[{3, 1}, -S^2])/(9*S^3) - (1568*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((121 + 406*S^2 + 367*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + ((2418 + 4761*S^2 + 3028*S^4 + 3335*S^6 + 1246*S^8)*Zeta[5])/(108*S*(1 + S^2)^2) + HPL[{2}, -S^2]*((158922 - 177231*S^2 - 100326*S^4 - 59867*S^6)/(23328*S^3) + (Pi^2*(1662 - 18225*S^2 - 4788*S^4 - 256*S^6))/(3888*S^3) + (Pi^4*(4700 - 30986*S^2 - 55879*S^4 - 906*S^6 - 1812*S^8 - 906*S^10))/(12960*S^3*(1 + S^2)^2) + ((-2*Pi^2)/(9*S^3) + (-643 + 640*S^2 + 3704*S^4 + 2228*S^6 + 2035*S^8 + 716*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-171 - 348*S^2 - 180*S^4 + 7*S^6 + 14*S^8 + 7*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - (31*HPL[{5}, -S^2])/(6*S^3) + ((323*Pi^2)/(9*S^3) + (5505 + 10074*S^2 + 20841*S^4 + 2588*S^6 + 2008*S^8 + 212*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((319 + 3194*S^2 + 4153*S^4 + 246*S^6 + 492*S^8 + 246*S^10)*HPL[{3, 1}, -S^2])/(18*S^3*(1 + S^2)^2) - HPL[{3, 2}, -S^2]/(3*S^3) + (11*HPL[{4, 1}, -S^2])/(3*S^3) - (2*(131 + 1552*S^2 + 2066*S^4 + 124*S^6 + 248*S^8 + 124*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (808*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (2420*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (1636*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + (-(Pi^2/S^3) + (-175 + 286*S^2 + 1241*S^4 + 624*S^6 + 420*S^8 + 108*S^10)/(36*S^3*(1 + S^2)^2))*Zeta[3] - (10*Zeta[5])/S^3) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(35729 + 17311*S^2 + 7892*S^4))/(7776*S^3) - ((1 + S^2)*(285029 + 157210*S^2 + 126287*S^4))/(23328*S^3) + (Pi^4*(-4037 - 41870*S^2 - 54731*S^4 - 734*S^6 - 1468*S^8 - 734*S^10))/(4320*S^3*(1 + S^2)^2) + ((-121 - 672*S^2 - 766*S^4 - 22*S^6 - 44*S^8 - 22*S^10)*HPL[{2}, -S^2]^2)/(6*S^3*(1 + S^2)^2) + ((25*Pi^2)/(18*S^3) + (694 + 2543*S^2 + 3034*S^4 + 928*S^6 + 689*S^8 + 154*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((341 + 778*S^2 + 485*S^4 + 62*S^6 + 124*S^8 + 62*S^10)*HPL[{4}, -S^2])/(36*S^3*(1 + S^2)^2) + (4*HPL[{5}, -S^2])/S^3 + ((211*Pi^2)/(6*S^3) + (718 + 1836*S^2 + 6298*S^4 + 1183*S^6 + 972*S^8 + 265*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((451 + 3218*S^2 + 3925*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (14*HPL[{3, 2}, -S^2])/S^3 - (134*HPL[{4, 1}, -S^2])/(3*S^3) + ((-935 - 6574*S^2 - 7991*S^4 - 170*S^6 - 340*S^8 - 170*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (860*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (2492*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (1568*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((41*Pi^2)/(18*S^3) + (2389 + 7694*S^2 + 9490*S^4 + 2614*S^6 + 1691*S^8 + 310*S^10)/(108*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(13585 + 10481*S^2 + 6322*S^4))/(1296*S^3) + (Pi^2*(-539 - 4876*S^2 - 6236*S^4 - 98*S^6 - 196*S^8 - 98*S^10))/(108*S^3*(1 + S^2)^2) + (7*HPL[{3}, -S^2])/S^3 + (430*HPL[{2, 1}, -S^2])/(3*S^3) + (13*Zeta[3])/S^3) + (13*Zeta[5])/S^3) + HPL[{1}, -S^2]*((-39083*Pi^6)/(54432*S^3) - (Pi^2*(1 + S^2)*(90779 + 40282*S^2 + 15233*S^4))/(23328*S^3) - ((1 + S^2)*(638189 + 401836*S^2 + 401201*S^4))/(69984*S^3) + (Pi^4*(-79757 - 134854*S^2 - 697724*S^4 - 68660*S^6 - 35269*S^8 - 908*S^10))/(77760*S^3*(1 + S^2)^2) + ((-335*Pi^2)/(36*S^3) + (-3643 - 10760*S^2 - 24820*S^4 - 5308*S^6 - 4109*S^8 - 1024*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (32*HPL[{2}, -S^2]^3)/(3*S^3) + ((5*Pi^2)/(9*S^3) + (1561 + 5972*S^2 + 5818*S^4 + 2128*S^6 + 1697*S^8 + 400*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(77 + 190*S^2 + 131*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (15*HPL[{6}, -S^2])/(2*S^3) + (430*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((310*Pi^2)/(9*S^3) + (2255 + 5674*S^2 + 18752*S^4 + 3452*S^6 + 2731*S^8 + 716*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-55 - 194*S^2 - 181*S^4 - 10*S^6 - 20*S^8 - 10*S^10)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + ((-1331 - 4270*S^2 - 3743*S^4 - 242*S^6 - 484*S^8 - 242*S^10)*HPL[{4, 1}, -S^2])/(18*S^3*(1 + S^2)^2) + HPL[{4, 2}, -S^2]/S^3 - (16*HPL[{5, 1}, -S^2])/(3*S^3) + ((-211*Pi^2)/(3*S^3) + (-718 - 1836*S^2 - 6298*S^4 - 1183*S^6 - 972*S^8 - 265*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (4*(121 + 672*S^2 + 766*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (2*(1903 + 11282*S^2 + 13117*S^4 + 346*S^6 + 692*S^8 + 346*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (256*HPL[{3, 2, 1}, -S^2])/S^3 - (2288*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (2*(935 + 6574*S^2 + 7991*S^4 + 170*S^6 + 340*S^8 + 170*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1544*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (3136*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (((1 + S^2)*(15355 + 1721*S^2 + 2584*S^4))/(648*S^3) + (Pi^2*(88 + 258*S^2 + 211*S^4 + 16*S^6 + 32*S^8 + 16*S^10))/(18*S^3*(1 + S^2)^2))*Zeta[3] - (3*Zeta[3]^2)/S^3 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(13585 + 10481*S^2 + 6322*S^4))/(648*S^3) + (Pi^2*(539 + 4876*S^2 + 6236*S^4 + 98*S^6 + 196*S^8 + 98*S^10))/(54*S^3*(1 + S^2)^2) - (26*Zeta[3])/S^3) + HPL[{3}, -S^2]*(((1 + S^2)*(9971 + 961*S^2 + 2384*S^4))/(648*S^3) + (5*Pi^2*(44 + 118*S^2 + 89*S^4 + 8*S^6 + 16*S^8 + 8*S^10))/(54*S^3*(1 + S^2)^2) - (14*HPL[{2, 1}, -S^2])/S^3 + (2*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-6731*Pi^4)/(2160*S^3) - ((1 + S^2)*(5303 + 26617*S^2 + 12566*S^4))/(3888*S^3) + (Pi^2*(-854 - 1650*S^2 - 8948*S^4 - 1367*S^6 - 1110*S^8 - 299*S^10))/(216*S^3*(1 + S^2)^2) + ((55 + 194*S^2 + 181*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^2) - HPL[{4}, -S^2]/(3*S^3) + (2*(121 + 672*S^2 + 766*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (142*HPL[{3, 1}, -S^2])/S^3 - (860*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((55 + 188*S^2 + 172*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + ((583 + 1634*S^2 + 1285*S^4 + 106*S^6 + 212*S^8 + 106*S^10)*Zeta[5])/(18*S^3*(1 + S^2)^2))) + Log[T]^2*((-111305 - 26669*S^2)/(8748*S) + (Pi^2*(-436554 - 216360*S^2 - 59867*S^4))/(34992*S) + (Pi^4*(-653862 - 274269*S^2 - 40760*S^4))/(116640*S) + (Pi^6*(-522850 - 784275*S^2 - 13682*S^4 - 27364*S^6 - 13682*S^8))/(136080*S*(1 + S^2)^2) + ((-58*Pi^2)/(3*S^3) + (-655 - 2020*S^2 - 3046*S^4 - 724*S^6 - 475*S^8 - 88*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^5 - (56*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)^2) - (64*HPL[{1}, -S^2]^7)/(9*S^3) + HPL[{0}, S^2]^6*((-54 - 81*S^2 + 5*S^4 + 10*S^6 + 5*S^8)/(216*S*(1 + S^2)^2) - HPL[{1}, -S^2]/(4*S^3)) - (2*(-773 + 66*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^5*((-516 - 10395*S^2 + 1372*S^4 + 3191*S^6 + 1696*S^8)/(6480*S*(1 + S^2)^2) + ((-88 - 1802*S^2 - 2527*S^4 - 16*S^6 - 32*S^8 - 16*S^10)*HPL[{1}, -S^2])/(540*S^3*(1 + S^2)^2) - (271*HPL[{1}, -S^2]^2)/(180*S^3) + HPL[{2}, -S^2]/(12*S^3)) + ((203 - 38*S^2 - 463*S^4 - 84*S^6 - 168*S^8 - 84*S^10)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-23*Pi^2)/(9*S^3) + (-1547 + 9458*S^2 + 24670*S^4 + 12800*S^6 + 9739*S^8 + 2828*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((416 + 1366*S^2 + 1217*S^4 + 222*S^6 + 444*S^8 + 222*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) + (20*HPL[{7}, -S^2])/(3*S^3) + (4*(1633 + 5618*S^2 + 5161*S^4 + 100*S^6 + 200*S^8 + 100*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + HPL[{0}, S^2]^4*((-2452 - 481*S^2 + 2664*S^4)/(2592*S) + (Pi^2*(-1662 - 2493*S^2 + 65*S^4 + 130*S^6 + 65*S^8))/(648*S*(1 + S^2)^2) + ((-341 - 4090*S^2 - 5453*S^4 - 62*S^6 - 124*S^8 - 62*S^10)*HPL[{1}, -S^2]^2)/(216*S^3*(1 + S^2)^2) - (142*HPL[{1}, -S^2]^3)/(27*S^3) + ((46 - 390*S^2 - 677*S^4 - 10*S^6 - 20*S^8 - 10*S^10)*HPL[{2}, -S^2])/(72*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((-277*Pi^2)/(108*S^3) + (-757 - 635*S^2 - 10477*S^4 - 928*S^6 - 671*S^8 - 118*S^10)/(648*S^3*(1 + S^2)^2) - (241*HPL[{2}, -S^2])/(36*S^3)) - (5*HPL[{3}, -S^2])/(12*S^3) + (259*HPL[{2, 1}, -S^2])/(18*S^3)) + ((92*Pi^2)/(9*S^3) + (5931 - 62892*S^2 - 161964*S^4 - 71828*S^6 - 46879*S^8 - 11744*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((64*Pi^2)/(9*S^3) + (4512 - 112362*S^2 - 272409*S^4 - 116440*S^6 - 76481*S^8 - 18952*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (2*(-135 + 432*S^2 + 918*S^4 + 169*S^6 + 338*S^8 + 169*S^10)*HPL[{4, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (116*HPL[{4, 3}, -S^2])/(3*S^3) - (2*(905 + 5866*S^2 + 6989*S^4 + 866*S^6 + 1732*S^8 + 866*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (338*HPL[{5, 2}, -S^2])/(3*S^3) - (632*HPL[{6, 1}, -S^2])/(3*S^3) + ((-1064*Pi^2)/(3*S^3) - (4*(789 + 4318*S^2 + 9795*S^4 + 3198*S^6 + 2098*S^8 + 462*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-9464*Pi^2)/(9*S^3) - (4*(7201 + 18482*S^2 + 40654*S^4 + 9172*S^6 + 6161*S^8 + 1126*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (4*(-213 + 44*S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (4*(-2879 + 220*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (32*HPL[{3, 2, 2}, -S^2])/S^3 - (272*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (16*(-856 - 1878*S^2 - 1105*S^4 + 36*S^6 + 72*S^8 + 36*S^10)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (136*HPL[{4, 1, 2}, -S^2])/S^3 - (360*HPL[{4, 2, 1}, -S^2])/S^3 - (720*HPL[{5, 1, 1}, -S^2])/S^3 + ((6776*Pi^2)/(9*S^3) - (4*(-6723 + 14895*S^2 + 9054*S^4 + 7570*S^6 + 2602*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (6272*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) + (16*(-2032 - 4562*S^2 - 2779*S^4 + 75*S^6 + 150*S^8 + 75*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (18080*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (18080*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (36896*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (112640*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (160*(-117 + 8*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (12448*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (12448*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (63680*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + (8960*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((452409 + 36384*S^2 + 26402*S^4)/(486*S) + (Pi^2*(10566 + 23355*S^2 + 10186*S^4 + 6413*S^6 + 1528*S^8))/(81*S*(1 + S^2)^2))*Zeta[3] + (40*(-6 - 9*S^2 + S^4 + 2*S^6 + S^8)*Zeta[3]^2)/(9*S*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*((-53919 - 4516*S^2 - 4255*S^4 + 548*S^6)/(54*S^3) + (2*Pi^2*(-737 - 1254*S^2 - 407*S^4 + 64*S^6 + 128*S^8 + 64*S^10))/(9*S^3*(1 + S^2)^2) - (64*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((38954 + 62172*S^2 + 21213*S^4 + 23034*S^6)/(324*S^3) + (Pi^2*(587 + 2194*S^2 + 2117*S^4 + 195*S^6 + 390*S^8 + 195*S^10))/(27*S^3*(1 + S^2)^2) - (1136*HPL[{2, 1}, -S^2])/(3*S^3) - (52*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((-71658 - 31977*S^2 - 11115*S^4 - 2281*S^6)/(324*S^3) + (Pi^2*(-1764 - 7170*S^2 - 7227*S^4 - 224*S^6 - 448*S^8 - 224*S^10))/(54*S^3*(1 + S^2)^2) + (24*HPL[{3}, -S^2])/S^3 + (784*HPL[{2, 1}, -S^2])/(3*S^3) - (40*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((-4*(-37082 + 801*S^2 - 828*S^4 + 1721*S^6))/(81*S^3) - (4*Pi^2*(-1915 - 2654*S^2 - 151*S^4 + 240*S^6 + 480*S^8 + 240*S^10))/(27*S^3*(1 + S^2)^2) + (112*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(972*S^3) - (5*Pi^2*(407 + 1858*S^2 + 1973*S^4 + 74*S^6 + 148*S^8 + 74*S^10))/(54*S^3*(1 + S^2)^2) + (65*(11 + 2*S^6)*HPL[{2}, -S^2])/(9*S^3) + (1900*HPL[{3}, -S^2])/(9*S^3) + (500*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((9659*Pi^4)/(270*S^3) + (30500 - 214461*S^2 - 8046*S^4 - 13201*S^6)/(243*S^3) + (Pi^2*(12155 - 1166*S^2 - 8617*S^4 - 16466*S^6 - 9880*S^8 - 2822*S^10))/(162*S^3*(1 + S^2)^2) - (816*HPL[{3, 1}, -S^2])/S^3 - (6224*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (8*(1595 + 4366*S^2 + 3359*S^4)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((-6673*Pi^4)/(405*S^3) - ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(1458*S^3) + (Pi^2*(-18259 - 55706*S^2 - 94156*S^4 - 21544*S^6 - 14837*S^8 - 3022*S^10))/(243*S^3*(1 + S^2)^2) + ((-784*Pi^2)/(27*S^3) + (4*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (1568*HPL[{2}, -S^2]^2)/(9*S^3) + (20*(737 + 2614*S^2 + 2447*S^4 + 134*S^6 + 268*S^8 + 134*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (1328*HPL[{4}, -S^2])/(9*S^3) - (260*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (1328*HPL[{3, 1}, -S^2])/(9*S^3) + (20*(209 + 718*S^2 + 659*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-28*Pi^4)/(135*S^3) + (70775 + 1792488*S^2 + 195699*S^4 + 160032*S^6)/(1944*S^3) + (Pi^2*(-377 + 43256*S^2 + 100288*S^4 + 41616*S^6 + 27333*S^8 + 6588*S^10))/(324*S^3*(1 + S^2)^2) + (20*HPL[{4}, -S^2])/S^3 + (8*(-1711 - 4598*S^2 - 3475*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (400*HPL[{3, 1}, -S^2])/(3*S^3) - (688*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(295 + 890*S^2 + 745*S^4 + 58*S^6 + 116*S^8 + 58*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((-80686 - 9661*S^2 + 4700*S^4)/(3888*S) + (Pi^2*(-3171 - 16065*S^2 - 1894*S^4 + 151*S^6 + 599*S^8))/(972*S*(1 + S^2)^2) + ((-1067 - 6514*S^2 - 7637*S^4 - 194*S^6 - 388*S^8 - 194*S^10)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)^2) - (365*HPL[{1}, -S^2]^4)/(27*S^3) + ((31*Pi^2)/(54*S^3) + (118 - 4996*S^2 - 19565*S^4 - 4776*S^6 - 2733*S^8 - 528*S^10)/(324*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (5*HPL[{2}, -S^2]^2)/(18*S^3) + HPL[{1}, -S^2]^2*((-106*Pi^2)/(9*S^3) + (-3197 - 8476*S^2 - 20027*S^4 - 3521*S^6 - 2320*S^8 - 407*S^10)/(162*S^3*(1 + S^2)^2) - (110*HPL[{2}, -S^2])/(3*S^3)) + ((-105 - 282*S^2 - 213*S^4 + 16*S^6 + 32*S^8 + 16*S^10)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)^2) + (5*HPL[{4}, -S^2])/(9*S^3) + ((1059 + 4098*S^2 + 4029*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (32*HPL[{3, 1}, -S^2])/(9*S^3) + (64*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((22 + 33*S^2 + 10*S^4 + 20*S^6 + 10*S^8)*Zeta[3])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(38351 + 6589*S^2 + 3368*S^4))/(1944*S^3) + (Pi^2*(-1243 - 10118*S^2 - 12691*S^4 - 226*S^6 - 452*S^8 - 226*S^10))/(324*S^3*(1 + S^2)^2) + ((-451 - 2882*S^2 - 3421*S^4 - 82*S^6 - 164*S^8 - 82*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) - (4*HPL[{3}, -S^2])/(3*S^3) + (220*HPL[{2, 1}, -S^2])/(3*S^3) + (22*Zeta[3])/(9*S^3))) + HPL[{0}, S^2]^2*((-214716 - 153768*S^2 - 59867*S^4)/(11664*S) + (Pi^2*(-41766 - 13947*S^2 + 1108*S^4))/(3888*S) + (Pi^4*(-50694 - 76041*S^2 - 806*S^4 - 1612*S^6 - 806*S^8))/(6480*S*(1 + S^2)^2) - (5*(33 + 190*S^2 + 219*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{1}, -S^2]^4)/(6*S^3*(1 + S^2)^2) - (62*HPL[{1}, -S^2]^5)/(3*S^3) + ((-131 - 1552*S^2 - 2066*S^4 - 124*S^6 - 248*S^8 - 124*S^10)*HPL[{2}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((-749*Pi^2)/(27*S^3) + (-7043 - 20512*S^2 - 51242*S^4 - 10508*S^6 - 8299*S^8 - 2084*S^10)/(162*S^3*(1 + S^2)^2) - (784*HPL[{2}, -S^2])/(9*S^3)) + ((-16*Pi^2)/(9*S^3) + (-177 + 2496*S^2 + 5286*S^4 + 2396*S^6 + 1891*S^8 + 524*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((89 + 202*S^2 + 125*S^4 + 15*S^6 + 30*S^8 + 15*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (5*HPL[{5}, -S^2])/(3*S^3) + ((686*Pi^2)/(9*S^3) + (2716 + 3503*S^2 + 7666*S^4 + 79*S^6 + 146*S^8 - 110*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (2*(-179 + 800*S^2 + 1558*S^4 + 117*S^6 + 234*S^8 + 117*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (32*HPL[{4, 1}, -S^2])/(3*S^3) - (16*(-40 + 214*S^2 + 401*S^4 + 30*S^6 + 60*S^8 + 30*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1636*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (4976*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (3416*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((1035 + 2277*S^2 + 1064*S^4 + 787*S^6 + 227*S^8)*Zeta[3])/(27*S*(1 + S^2)^2) + HPL[{2}, -S^2]*((3606 - 15345*S^2 - 4626*S^4 - 3442*S^6)/(324*S^3) + (Pi^2*(458 - 2882*S^2 - 5239*S^4 - 270*S^6 - 540*S^8 - 270*S^10))/(108*S^3*(1 + S^2)^2) - (2*HPL[{3}, -S^2])/(3*S^3) + (818*HPL[{2, 1}, -S^2])/(3*S^3) - (2*Zeta[3])/S^3) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(15769 + 6455*S^2 + 4708*S^4))/(324*S^3) + (Pi^2*(-913 - 6320*S^2 - 7654*S^4 - 166*S^6 - 332*S^8 - 166*S^10))/(54*S^3*(1 + S^2)^2) + ((-935 - 6574*S^2 - 7991*S^4 - 170*S^6 - 340*S^8 - 170*S^10)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)^2) + (44*HPL[{3}, -S^2])/(3*S^3) + (784*HPL[{2, 1}, -S^2])/(3*S^3) + (82*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((-8449*Pi^4)/(1080*S^3) - ((1 + S^2)*(70220 + 31321*S^2 + 22763*S^4))/(1944*S^3) + (Pi^2*(-8557 - 21782*S^2 - 72196*S^4 - 12364*S^6 - 9641*S^8 - 2320*S^10))/(648*S^3*(1 + S^2)^2) + ((-211*Pi^2)/(6*S^3) + (-718 - 1836*S^2 - 6298*S^4 - 1183*S^6 - 972*S^8 - 265*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (215*HPL[{2}, -S^2]^2)/(3*S^3) + ((275 + 814*S^2 + 671*S^4 + 50*S^6 + 100*S^8 + 50*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*HPL[{4}, -S^2])/(3*S^3) + ((935 + 6574*S^2 + 7991*S^4 + 170*S^6 + 340*S^8 + 170*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (772*HPL[{3, 1}, -S^2])/(3*S^3) - (1568*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((121 + 406*S^2 + 367*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2))) + ((21210 + 45369*S^2 + 19322*S^4 + 10903*S^6 + 2060*S^8)*Zeta[5])/(27*S*(1 + S^2)^2) + HPL[{2}, -S^2]*((3087476 + 43275*S^2 + 30486*S^4 - 59867*S^6)/(5832*S^3) + (Pi^2*(77770 - 16947*S^2 - 2970*S^4 - 6884*S^6))/(972*S^3) + (Pi^4*(10424 + 8722*S^2 - 7765*S^4 - 1526*S^6 - 3052*S^8 - 1526*S^10))/(1080*S^3*(1 + S^2)^2) + ((-88*Pi^2)/(9*S^3) + (-3823 + 30784*S^2 + 81704*S^4 + 37076*S^6 + 24535*S^8 + 6332*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (2*(-355 - 32*S^2 + 662*S^4 + 169*S^6 + 338*S^8 + 169*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (26*HPL[{5}, -S^2])/S^3 + ((532*Pi^2)/(3*S^3) + (2*(789 + 4318*S^2 + 9795*S^4 + 3198*S^6 + 2098*S^8 + 462*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (112*(67 + 218*S^2 + 193*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (44*HPL[{3, 2}, -S^2])/S^3 + (272*HPL[{4, 1}, -S^2])/(3*S^3) - (8*(1633 + 5618*S^2 + 5161*S^4 + 100*S^6 + 200*S^8 + 100*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3136*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (8720*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (6224*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((8*Pi^2)/(9*S^3) + (-1291 + 15178*S^2 + 39281*S^4 + 16782*S^6 + 10464*S^8 + 2382*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] - (56*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]^2*(-(Pi^2*(1 + S^2)*(71271 + 13565*S^2 + 9492*S^4))/(648*S^3) - ((1 + S^2)*(1865477 + 155803*S^2 + 126326*S^4))/(2916*S^3) + (Pi^4*(-52349 - 264850*S^2 - 292577*S^4 - 9518*S^6 - 19036*S^8 - 9518*S^10))/(3240*S^3*(1 + S^2)^2) - (196*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((994*Pi^2)/(9*S^3) + (24061 + 77276*S^2 + 99832*S^4 + 26410*S^6 + 17147*S^8 + 3154*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (4*(605 + 2206*S^2 + 2099*S^4 + 110*S^6 + 220*S^8 + 110*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (144*HPL[{5}, -S^2])/S^3 + ((784*Pi^2)/(9*S^3) - (4*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (4*(1529 + 4054*S^2 + 3023*S^4 + 278*S^6 + 556*S^8 + 278*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3136*HPL[{3, 2}, -S^2])/(3*S^3) - (10736*HPL[{4, 1}, -S^2])/(3*S^3) + (260*(11 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (6272*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (11216*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((832*Pi^2)/(9*S^3) + (4*(5608 + 17597*S^2 + 21457*S^4 + 5518*S^6 + 3269*S^8 + 469*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(9*S^3) + (Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(27*S^3*(1 + S^2)^2) + (1568*HPL[{3}, -S^2])/(3*S^3) + (3136*HPL[{2, 1}, -S^2])/(3*S^3) + (1568*Zeta[3])/(3*S^3)) + (1520*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]*((-52285*Pi^6)/(13608*S^3) - (Pi^2*(1 + S^2)*(71609 + 10670*S^2 + 7703*S^4))/(648*S^3) - ((1 + S^2)*(12649645 + 794066*S^2 + 772759*S^4))/(17496*S^3) + (Pi^4*(-292577 - 870982*S^2 - 1697756*S^4 - 362300*S^6 - 259729*S^8 - 55868*S^10))/(19440*S^3*(1 + S^2)^2) + ((-607*Pi^2)/(9*S^3) + (-4537 - 14056*S^2 - 21304*S^4 - 5140*S^6 - 3427*S^8 - 664*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (148*HPL[{3}, -S^2]^2)/(3*S^3) + ((340*Pi^2)/(9*S^3) + (4427 + 15048*S^2 + 21278*S^4 + 6152*S^6 + 4563*S^8 + 1100*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (4*(583 + 1814*S^2 + 1555*S^4 + 106*S^6 + 212*S^8 + 106*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (178*HPL[{6}, -S^2])/(3*S^3) + (3136*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((440*Pi^2)/(9*S^3) - (4*(5225 + 17554*S^2 + 17960*S^4 + 5495*S^6 + 3433*S^8 + 581*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (4*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^2) - (4*(10417 + 36938*S^2 + 34573*S^4 + 1894*S^6 + 3788*S^8 + 1894*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (156*HPL[{4, 2}, -S^2])/S^3 - (2704*HPL[{5, 1}, -S^2])/(3*S^3) + ((-1568*Pi^2)/(9*S^3) + (8*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (1568*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*(2783 + 13978*S^2 + 15401*S^4 + 506*S^6 + 1012*S^8 + 506*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2656*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (520*(11 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) - (2656*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (((1 + S^2)*(150737 + 14875*S^2 + 9644*S^4))/(162*S^3) + (2*Pi^2*(583 + 1998*S^2 + 1831*S^4 + 106*S^6 + 212*S^8 + 106*S^10))/(9*S^3*(1 + S^2)^2))*Zeta[3] - (80*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*((-2*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(9*S^3) - (2*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(27*S^3*(1 + S^2)^2) - (3136*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*(((1 + S^2)*(154507 + 20411*S^2 + 17122*S^4))/(162*S^3) + (2*Pi^2*(660 + 2314*S^2 + 2151*S^4 + 120*S^6 + 240*S^8 + 120*S^10))/(9*S^3*(1 + S^2)^2) - (3136*HPL[{2, 1}, -S^2])/(3*S^3) + (200*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-2021*Pi^4)/(180*S^3) + ((1 + S^2)*(411947 + 9469*S^2 + 13400*S^4))/(972*S^3) + (Pi^2*(2024 + 7326*S^2 + 1376*S^4 + 1271*S^6 + 360*S^8 - 133*S^10))/(54*S^3*(1 + S^2)^2) + (2*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) + (452*HPL[{4}, -S^2])/(3*S^3) + (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*HPL[{3, 1}, -S^2])/(3*S^3) - (6272*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (112*(55 + 194*S^2 + 181*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (2*(3619 + 11798*S^2 + 10459*S^4 + 658*S^6 + 1316*S^8 + 658*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]*((-12520650 - 784947*S^2 - 772759*S^4)/(17496*S) + (Pi^2*(-1351296 - 151641*S^2 - 79028*S^4))/(11664*S) + (Pi^4*(-44314 - 138597*S^2 - 39412*S^4 - 22089*S^6 - 3862*S^8))/(3240*S*(1 + S^2)^2) - (56*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)^2) - (224*HPL[{1}, -S^2]^6)/(9*S^3) + ((-2*Pi^2)/(3*S^3) + (427 - 11398*S^2 - 31892*S^4 - 11697*S^6 - 7539*S^8 - 1797*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (38*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{1}, -S^2]^4*((-1205*Pi^2)/(27*S^3) - (5*(655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10))/(18*S^3*(1 + S^2)^2) - (500*HPL[{2}, -S^2])/(3*S^3)) - (20*HPL[{3}, -S^2]^2)/(3*S^3) + ((17*Pi^2)/(9*S^3) + (80 - 473*S^2 - 1657*S^4 - 276*S^6 + 237*S^8 + 237*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(-21 - 88*S^2 - 90*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^2) - (20*HPL[{6}, -S^2])/(3*S^3) + (68*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-136*Pi^2)/(9*S^3) + (-1081 + 22984*S^2 + 63404*S^4 + 23840*S^6 + 15109*S^8 + 3608*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-557 - 2026*S^2 - 1925*S^4 - 210*S^6 - 420*S^8 - 210*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(251 + 1594*S^2 + 1889*S^4 + 278*S^6 + 556*S^8 + 278*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*HPL[{4, 2}, -S^2])/S^3 - (20*HPL[{5, 1}, -S^2])/(3*S^3) + ((244*Pi^2)/(9*S^3) - (2*(-743 + 23588*S^2 + 63733*S^4 + 23972*S^6 + 15256*S^8 + 3686*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(2173 + 6698*S^2 + 5701*S^4 + 12*S^6 + 24*S^8 + 12*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*(-6653 - 20260*S^2 - 17084*S^4 + S^6 + 2*S^8 + S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*HPL[{3, 1, 2}, -S^2])/S^3 + (280*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (336*HPL[{4, 1, 1}, -S^2])/S^3 - (80*(-150 - 450*S^2 - 375*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (832*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (480*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((14142 + 4989*S^2 + 5240*S^4)/(162*S) + (2*Pi^2*(94 + 141*S^2 + 20*S^4 + 40*S^6 + 20*S^8))/(9*S*(1 + S^2)^2))*Zeta[3] + HPL[{2, 1}, -S^2]*((180337 + 37776*S^2 + 16923*S^4 - 2244*S^6)/(162*S^3) + (Pi^2*(5559 + 17598*S^2 + 15279*S^4 - 62*S^6 - 124*S^8 - 62*S^10))/(27*S^3*(1 + S^2)^2) - (664*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((-4244 - 1713*S^2 + 1896*S^4 + 2995*S^6)/(162*S^3) + (Pi^2*(-373 - 614*S^2 - 175*S^4 + 90*S^6 + 180*S^8 + 90*S^10))/(54*S^3*(1 + S^2)^2) - (72*HPL[{2, 1}, -S^2])/S^3 + (8*Zeta[3])/S^3) + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(486*S^3) + (Pi^2*(-5687 - 25834*S^2 - 27377*S^4 - 1034*S^6 - 2068*S^8 - 1034*S^10))/(81*S^3*(1 + S^2)^2) - (250*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (136*HPL[{3}, -S^2])/(9*S^3) + (2000*HPL[{2, 1}, -S^2])/(3*S^3) + (664*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((6*Pi^4)/(5*S^3) + (-31094 - 544935*S^2 - 50412*S^4 - 36803*S^6)/(972*S^3) + (Pi^2*(861 - 28584*S^2 - 83298*S^4 - 28748*S^6 - 17989*S^8 - 4214*S^10))/(324*S^3*(1 + S^2)^2) + ((245 + 946*S^2 + 929*S^4 + 102*S^6 + 204*S^8 + 102*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (14*HPL[{4}, -S^2])/S^3 + (4*(2173 + 6698*S^2 + 5701*S^4 + 12*S^6 + 24*S^8 + 12*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (64*HPL[{3, 1}, -S^2])/(3*S^3) - (136*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(-5 + 72*S^2 + 118*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((-4061*Pi^4)/(180*S^3) - ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(972*S^3) + (Pi^2*(-35869 - 107852*S^2 - 177124*S^4 - 39622*S^6 - 26015*S^8 - 4774*S^10))/(324*S^3*(1 + S^2)^2) + ((-120*Pi^2)/S^3 - (2*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (784*HPL[{2}, -S^2]^2)/(3*S^3) + (2*(77 + 358*S^2 + 383*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (92*HPL[{4}, -S^2])/(3*S^3) + (250*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (1000*HPL[{3, 1}, -S^2])/S^3 - (2000*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(473 + 1942*S^2 + 1967*S^4 + 86*S^6 + 172*S^8 + 86*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (10*(78 + 117*S^2 + 10*S^4 + 20*S^6 + 10*S^8)*Zeta[5])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^2*(1 + S^2)*(36771 + 5729*S^2 + 3738*S^4))/(324*S^3) - ((1 + S^2)*(1865477 + 155803*S^2 + 126326*S^4))/(2916*S^3) + (Pi^4*(-24101 - 121300*S^2 - 133748*S^4 - 4382*S^6 - 8764*S^8 - 4382*S^10))/(1620*S^3*(1 + S^2)^2) - (196*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((22*Pi^2)/(9*S^3) + (2*(-346 - 536*S^2 + 410*S^4 + 311*S^6 + 580*S^8 + 257*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-319 - 1190*S^2 - 1147*S^4 - 58*S^6 - 116*S^8 - 58*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (92*HPL[{5}, -S^2])/(3*S^3) + ((240*Pi^2)/S^3 + (4*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(231 + 962*S^2 + 981*S^4 + 42*S^6 + 84*S^8 + 42*S^10)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) - (304*HPL[{3, 2}, -S^2])/(3*S^3) - (728*HPL[{4, 1}, -S^2])/(3*S^3) - (500*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (6272*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (18544*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (4000*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((188*Pi^2)/(9*S^3) + (2321 + 7960*S^2 + 13184*S^4 + 3716*S^6 + 2911*S^8 + 764*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(91373 + 11923*S^2 + 7142*S^4))/(162*S^3) + (Pi^2*(-5027 - 23014*S^2 - 24467*S^4 - 914*S^6 - 1828*S^8 - 914*S^10))/(54*S^3*(1 + S^2)^2) + (152*HPL[{3}, -S^2])/(3*S^3) + (3136*HPL[{2, 1}, -S^2])/(3*S^3) + (328*Zeta[3])/(3*S^3)) + (260*Zeta[5])/(3*S^3)))) + ((5013 + 10260*S^2 + 4109*S^4 + 1882*S^6 + 122*S^8)*Zeta[7])/(9*S*(1 + S^2)^2) + HPL[{2}, -S^2]*((4038660 + 357177*S^2 - 118175*S^4 - 121014*S^6)/(11664*S^3) + (Pi^2*(1623199 - 66978*S^2 - 34920*S^4 - 59867*S^6))/(34992*S^3) + (Pi^4*(292364 - 72990*S^2 - 22419*S^4 - 19594*S^6))/(58320*S^3) + (Pi^6*(95242 + 58310*S^2 - 103019*S^4 - 9014*S^6 - 18028*S^8 - 9014*S^10))/(136080*S^3*(1 + S^2)^2) + ((41 - 434*S^2 - 733*S^4 - 78*S^6 - 156*S^8 - 78*S^10)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((-35*Pi^2)/(9*S^3) + (-388 + 1345*S^2 + 4373*S^4 + 2716*S^6 + 2441*S^8 + 889*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + (2*(-422 - 718*S^2 - 233*S^4 + 76*S^6 + 152*S^8 + 76*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) - (250*HPL[{7}, -S^2])/(3*S^3) + (4*(-773 + 66*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-34*Pi^2)/(9*S^3) + (-366 - 19365*S^2 - 43413*S^4 - 17723*S^6 - 11383*S^8 - 2702*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((79*Pi^2)/(9*S^3) + (2235 - 54009*S^2 - 131100*S^4 - 56278*S^6 - 36917*S^8 - 9235*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (2*(23 + 202*S^2 + 257*S^4 + 25*S^6 + 50*S^8 + 25*S^10)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (38*HPL[{4, 3}, -S^2])/(3*S^3) - (2*(-149 + 334*S^2 + 799*S^4 + 136*S^6 + 272*S^8 + 136*S^10)*HPL[{5, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (36*HPL[{5, 2}, -S^2])/S^3 + (140*HPL[{6, 1}, -S^2])/S^3 + ((-1592*Pi^2)/(9*S^3) + (2*(-3315 + 6519*S^2 + 4170*S^4 + 3575*S^6 + 1355*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((4600*Pi^2)/(9*S^3) + (16067 + 11560*S^2 + 17570*S^4 - 9394*S^6 - 5045*S^8 - 1798*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (13*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + ((-5771 - 19822*S^2 - 18191*S^4 - 370*S^6 - 740*S^8 - 370*S^10)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (118*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (24*HPL[{3, 3, 1}, -S^2])/S^3 - (4*(5005 + 16244*S^2 + 14356*S^4 + 167*S^6 + 334*S^8 + 167*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*HPL[{4, 1, 2}, -S^2])/S^3 - (30*HPL[{4, 2, 1}, -S^2])/S^3 - (148*HPL[{5, 1, 1}, -S^2])/S^3 + ((1064*Pi^2)/(3*S^3) + (4*(789 + 4318*S^2 + 9795*S^4 + 3198*S^6 + 2098*S^8 + 462*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (1008*HPL[{2, 2, 2, 1}, -S^2])/S^3 + (32*(-4169 - 7750*S^2 - 3287*S^4 + 410*S^6 + 820*S^8 + 410*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (2936*HPL[{3, 1, 1, 2}, -S^2])/S^3 + (2936*HPL[{3, 1, 2, 1}, -S^2])/S^3 + (5960*HPL[{3, 2, 1, 1}, -S^2])/S^3 + (54976*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (16*(1633 + 5618*S^2 + 5161*S^4 + 100*S^6 + 200*S^8 + 100*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (6272*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (6272*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (10912*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 + (12448*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-71*Pi^4)/(270*S^3) + (-28721 + 399126*S^2 + 34554*S^4 + 25966*S^6)/(972*S^3) + (Pi^2*(-908 + 8018*S^2 + 21502*S^4 + 9327*S^6 + 5862*S^8 + 1353*S^10))/(162*S^3*(1 + S^2)^2))*Zeta[3] + ((96 + 210*S^2 + 123*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*Zeta[3]^2)/(9*S^3*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-71658 - 31977*S^2 - 11115*S^4 - 2281*S^6)/(81*S^3) - (2*Pi^2*(1764 + 7170*S^2 + 7227*S^4 + 224*S^6 + 448*S^8 + 224*S^10))/(27*S^3*(1 + S^2)^2) - (160*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-6817 + 11967*S^2 + 3444*S^4 + 6493*S^6)/(162*S^3) + (Pi^2*(-263 - 190*S^2 + 241*S^4 + 88*S^6 + 176*S^8 + 88*S^10))/(27*S^3*(1 + S^2)^2) - (190*HPL[{2, 1}, -S^2])/S^3 + (26*Zeta[3])/(3*S^3)) + HPL[{3, 1}, -S^2]*((76385 + 26979*S^2 + 10851*S^4 - 763*S^6)/(162*S^3) + (Pi^2*(4071 + 15402*S^2 + 14961*S^4 + 358*S^6 + 716*S^8 + 358*S^10))/(54*S^3*(1 + S^2)^2) + (88*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((748*Pi^4)/(45*S^3) + (61634 + 420771*S^2 + 55794*S^4 + 38559*S^6)/(972*S^3) + (Pi^2*(10239 + 35982*S^2 + 79611*S^4 + 21776*S^6 + 14596*S^8 + 2984*S^10))/(324*S^3*(1 + S^2)^2) - (408*HPL[{3, 1}, -S^2])/S^3 - (3136*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(-1502 - 4066*S^2 - 3095*S^4 + 24*S^6 + 48*S^8 + 24*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-82*Pi^4)/(135*S^3) + (-13334 + 414123*S^2 + 35448*S^4 + 46177*S^6)/(972*S^3) + (Pi^2*(-2233 + 15712*S^2 + 42704*S^4 + 19652*S^6 + 13285*S^8 + 3524*S^10))/(324*S^3*(1 + S^2)^2) - (20*HPL[{4}, -S^2])/(3*S^3) + ((-6593 - 18778*S^2 - 14981*S^4 - 38*S^6 - 76*S^8 - 38*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (160*HPL[{3, 1}, -S^2])/(3*S^3) + (96*HPL[{2, 1, 1}, -S^2])/S^3 + ((-53 + 50*S^2 + 181*S^4 + 58*S^6 + 116*S^8 + 58*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + ((-44*Pi^2)/(9*S^3) + (-1823 + 5762*S^2 + 18697*S^4 + 8777*S^6 + 5308*S^8 + 1145*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[5] - (70*Zeta[7])/S^3) + HPL[{1}, -S^2]^2*((-7*Pi^4*(1 + S^2)*(37529 + 9173*S^2 + 5540*S^4))/(38880*S^3) - (Pi^2*(1 + S^2)*(1338661 + 156272*S^2 + 126313*S^4))/(23328*S^3) - ((1 + S^2)*(179723545 + 8757449*S^2 + 11329918*S^4))/(419904*S^3) + (Pi^6*(-80366 - 474442*S^2 - 550931*S^4 - 14612*S^6 - 29224*S^8 - 14612*S^10))/(81648*S^3*(1 + S^2)^2) + (83*(11 + 2*S^6)*HPL[{2}, -S^2]^3)/(54*S^3) - (37*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)^2) + ((40*Pi^2)/(3*S^3) + (3169 + 11183*S^2 + 13807*S^4 + 4411*S^6 + 3317*S^8 + 811*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((1144 + 2822*S^2 + 1945*S^4 + 208*S^6 + 416*S^8 + 208*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) + (10*HPL[{7}, -S^2])/S^3 + (392*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-826*Pi^2)/(9*S^3) + (-6875 - 21868*S^2 - 27848*S^4 - 7232*S^6 - 4561*S^8 - 776*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-2818*Pi^2)/(9*S^3) + (-45677 - 146256*S^2 - 188366*S^4 - 49544*S^6 - 31929*S^8 - 5756*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] - (13*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{4, 2}, -S^2])/(2*S^3*(1 + S^2)^2) + (94*HPL[{4, 3}, -S^2])/(3*S^3) - (26*(187 + 686*S^2 + 655*S^4 + 34*S^6 + 68*S^8 + 34*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (68*HPL[{5, 2}, -S^2])/S^3 - (98*HPL[{6, 1}, -S^2])/(3*S^3) + ((-2428*Pi^2)/(9*S^3) - (2*(4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-5296*Pi^2)/(9*S^3) - (4*(8386 + 24614*S^2 + 45952*S^4 + 9925*S^6 + 6848*S^8 + 1411*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (332*(11 + 2*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (3260*HPL[{3, 2, 2}, -S^2])/(3*S^3) + (9968*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (4*(3949 + 9890*S^2 + 6937*S^4 + 718*S^6 + 1436*S^8 + 718*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (9812*HPL[{4, 1, 2}, -S^2])/(3*S^3) + (30404*HPL[{4, 2, 1}, -S^2])/(3*S^3) + (20880*HPL[{5, 1, 1}, -S^2])/S^3 + ((1568*Pi^2)/(9*S^3) - (8*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - (8*(1529 + 4054*S^2 + 3023*S^4 + 278*S^6 + 556*S^8 + 278*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (6272*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (6272*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (21472*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (520*(11 + 2*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (12544*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (12544*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (77920*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((1013*Pi^4)/(180*S^3) + ((1 + S^2)*(504041 + 33388*S^2 + 23801*S^4))/(972*S^3) + (Pi^2*(24821 + 78082*S^2 + 95318*S^4 + 24686*S^6 + 14767*S^8 + 2186*S^10))/(324*S^3*(1 + S^2)^2))*Zeta[3] + ((-121 - 482*S^2 - 481*S^4 - 22*S^6 - 44*S^8 - 22*S^10)*Zeta[3]^2)/(9*S^3*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*(-((1 + S^2)*(71207 + 7105*S^2 + 7424*S^4))/(162*S^3) - (2*Pi^2*(539 + 418*S^2 - 451*S^4 + 98*S^6 + 196*S^8 + 98*S^10))/(27*S^3*(1 + S^2)^2) - (1616*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*(((1 + S^2)*(40345 + 8120*S^2 + 11599*S^4))/(324*S^3) + (Pi^2*(2761 + 9602*S^2 + 8881*S^4 + 502*S^6 + 1004*S^8 + 502*S^10))/(108*S^3*(1 + S^2)^2) - (452*HPL[{2, 1}, -S^2])/(3*S^3) + (56*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(41650 + 6653*S^2 + 4849*S^4))/(324*S^3) + (Pi^2*(-1441 - 6524*S^2 - 6904*S^4 - 262*S^6 - 524*S^8 - 262*S^10))/(54*S^3*(1 + S^2)^2) + (466*HPL[{3}, -S^2])/(3*S^3) + (118*Zeta[3])/S^3) + HPL[{2, 1, 1}, -S^2]*((2*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(9*S^3) + (2*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(27*S^3*(1 + S^2)^2) + (3136*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((2021*Pi^4)/(180*S^3) - ((1 + S^2)*(411947 + 9469*S^2 + 13400*S^4))/(972*S^3) + (Pi^2*(-2024 - 7326*S^2 - 1376*S^4 - 1271*S^6 - 360*S^8 + 133*S^10))/(54*S^3*(1 + S^2)^2) - (3136*HPL[{3, 1}, -S^2])/(3*S^3) - (6272*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (112*(55 + 194*S^2 + 181*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((601*Pi^4)/(90*S^3) + ((1 + S^2)*(248381 + 24079*S^2 + 22409*S^4))/(486*S^3) + (Pi^2*(8483 + 27454*S^2 + 35300*S^4 + 9422*S^6 + 6175*S^8 + 1154*S^10))/(108*S^3*(1 + S^2)^2) - (86*HPL[{4}, -S^2])/(3*S^3) - (2*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (1568*HPL[{3, 1}, -S^2])/(3*S^3) + (3136*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(143 + 586*S^2 + 593*S^4 + 26*S^6 + 52*S^8 + 26*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + ((419*Pi^2)/(9*S^3) + (27221 + 84802*S^2 + 97556*S^4 + 24908*S^6 + 13801*S^8 + 1508*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(-105143 + 4577*S^2 + 1318*S^4))/(3888*S^3) + ((1 + S^2)*(483629 + 3776*S^2 + 10001*S^4))/(1944*S^3) + (Pi^4*(2816 - 30746*S^2 - 51751*S^4 + 512*S^6 + 1024*S^8 + 512*S^10))/(3240*S^3*(1 + S^2)^2) + ((413*Pi^2)/(9*S^3) + (6875 + 21868*S^2 + 27848*S^4 + 7232*S^6 + 4561*S^8 + 776*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + (113*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) + (164*HPL[{5}, -S^2])/(3*S^3) + ((1214*Pi^2)/(9*S^3) + (4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (392*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (1708*HPL[{3, 2}, -S^2])/(3*S^3) - (5140*HPL[{4, 1}, -S^2])/(3*S^3) - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (6272*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((431*Pi^2)/(9*S^3) + (3460 + 10998*S^2 + 13972*S^4 + 3637*S^6 + 2304*S^8 + 397*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] + (722*Zeta[5])/(3*S^3)) + (322*Zeta[7])/S^3) + HPL[{1}, -S^2]*((-13964*Pi^8)/(42525*S^3) - (Pi^4*(1 + S^2)*(378284 + 73645*S^2 + 44648*S^4))/(58320*S^3) - (Pi^2*(1 + S^2)*(738213 + 66439*S^2 + 65220*S^4))/(11664*S^3) - ((1 + S^2)*(667256405 + 26497639*S^2 + 55110542*S^4))/(1259712*S^3) + (Pi^6*(-2226637 - 6144098*S^2 - 14464180*S^4 - 2612440*S^6 - 1844969*S^8 - 367948*S^10))/(2449440*S^3*(1 + S^2)^2) + ((-32*Pi^2)/(9*S^3) + (1733 + 4058*S^2 + 789*S^4 + 764*S^6 + 86*S^8)/(81*S^3*(1 + S^2)))*HPL[{2}, -S^2]^3 - (32*HPL[{2}, -S^2]^4)/(3*S^3) + ((-37*Pi^2)/(9*S^3) + (-965 - 3238*S^2 - 5564*S^4 - 1532*S^6 - 1231*S^8 - 326*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + (6*HPL[{4}, -S^2]^2)/S^3 + ((67*Pi^2)/(9*S^3) + (2102 + 8692*S^2 + 9653*S^4 + 4127*S^6 + 3805*S^8 + 1139*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{6}, -S^2] + ((187 + 394*S^2 + 217*S^4 + 34*S^6 + 68*S^8 + 34*S^10)*HPL[{7}, -S^2])/(S^3*(1 + S^2)^2) + (36*HPL[{8}, -S^2])/S^3 + ((1214*Pi^2)/(9*S^3) + (4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - (1864*HPL[{3, 1}, -S^2]^2)/(3*S^3) + ((-38*Pi^2)/(3*S^3) + (-560 - 1867*S^2 - 3071*S^4 - 839*S^6 - 643*S^8 - 164*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{4, 2}, -S^2] + ((319 + 1202*S^2 + 1165*S^4 + 58*S^6 + 116*S^8 + 58*S^10)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-692*Pi^2)/(9*S^3) - (2*(6374 + 21889*S^2 + 31655*S^4 + 9299*S^6 + 7120*S^8 + 1793*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + (4*(55 + 212*S^2 + 208*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{5, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (8*HPL[{5, 3}, -S^2])/S^3 - (2*(363 + 824*S^2 + 510*S^4 + 66*S^6 + 132*S^8 + 66*S^10)*HPL[{6, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (20*HPL[{6, 2}, -S^2])/S^3 - (36*HPL[{7, 1}, -S^2])/S^3 - (6272*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((-256*Pi^2)/(3*S^3) + (8*(1733 + 4058*S^2 + 789*S^4 + 764*S^6 + 86*S^8))/(27*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((12617 + 44794*S^2 + 41957*S^4 + 2294*S^6 + 4588*S^8 + 2294*S^10)*HPL[{3, 2, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*(2398 + 8534*S^2 + 8005*S^4 + 436*S^6 + 872*S^8 + 436*S^10)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (532*HPL[{3, 3, 2}, -S^2])/(3*S^3) + ((-1624*Pi^2)/(9*S^3) + (18291 + 61376*S^2 + 60054*S^4 + 18576*S^6 + 11363*S^8 + 1788*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((37939 + 134750*S^2 + 126247*S^4 + 6898*S^6 + 13796*S^8 + 6898*S^10)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (908*HPL[{4, 1, 3}, -S^2])/(3*S^3) + ((116479 + 415382*S^2 + 390115*S^4 + 21178*S^6 + 42356*S^8 + 21178*S^10)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (376*HPL[{4, 2, 2}, -S^2])/(3*S^3) + (2908*HPL[{4, 3, 1}, -S^2])/(3*S^3) + (4*(60071 + 214102*S^2 + 201011*S^4 + 10922*S^6 + 21844*S^8 + 10922*S^10)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1688*HPL[{5, 1, 2}, -S^2])/(3*S^3) + (12008*HPL[{5, 2, 1}, -S^2])/(3*S^3) + (31316*HPL[{6, 1, 1}, -S^2])/(3*S^3) - (664*(11 + 2*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + ((880*Pi^2)/(9*S^3) - (8*(5225 + 17554*S^2 + 17960*S^4 + 5495*S^6 + 3433*S^8 + 581*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] - (16*(55 + 894*S^2 + 1231*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^2) - (16*(55 + 894*S^2 + 1231*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (104*HPL[{3, 1, 2, 2}, -S^2])/S^3 + (8*(803 + 38*S^2 - 1549*S^4 + 146*S^6 + 292*S^8 + 146*S^10)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (104*HPL[{3, 2, 1, 2}, -S^2])/S^3 - (376*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3) - (64*HPL[{3, 3, 1, 1}, -S^2])/S^3 + (8*(6017 - 4070*S^2 - 18139*S^4 + 1094*S^6 + 2188*S^8 + 1094*S^10)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (312*HPL[{4, 1, 1, 2}, -S^2])/S^3 - (376*HPL[{4, 1, 2, 1}, -S^2])/S^3 - (504*HPL[{4, 2, 1, 1}, -S^2])/S^3 - (6560*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((-3136*Pi^2)/(9*S^3) + (16*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] + (3136*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3136*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (80*(2893 + 11630*S^2 + 11659*S^4 + 526*S^6 + 1052*S^8 + 526*S^10)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (5312*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3) - (1040*(11 + 2*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (5312*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-29*Pi^2)/(9*S^3) + (-1571 - 4378*S^2 - 5000*S^4 - 1112*S^6 - 247*S^8 + 112*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((-4*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(9*S^3) - (4*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(27*S^3*(1 + S^2)^2) - (6272*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*(-((1 + S^2)*(439447 + 57164*S^2 + 45553*S^4))/(162*S^3) + (Pi^2*(-22165 - 78146*S^2 - 72889*S^4 - 4030*S^6 - 8060*S^8 - 4030*S^10))/(54*S^3*(1 + S^2)^2) - (424*Zeta[3])/(3*S^3)) + HPL[{3, 2}, -S^2]*(-((1 + S^2)*(66517 + 8174*S^2 + 5659*S^4))/(81*S^3) - (14*Pi^2*(77 + 272*S^2 + 254*S^4 + 14*S^6 + 28*S^8 + 14*S^10))/(9*S^3*(1 + S^2)^2) - (104*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*(((1 + S^2)*(7358 + 905*S^2 + 2153*S^4))/(54*S^3) + (Pi^2*(737 + 2194*S^2 + 1817*S^4 + 134*S^6 + 268*S^8 + 134*S^10))/(27*S^3*(1 + S^2)^2) - (328*HPL[{2, 1}, -S^2])/(3*S^3) - (8*Zeta[3])/S^3) + HPL[{2, 2, 1}, -S^2]*((-2*(1 + S^2)*(41650 + 6653*S^2 + 4849*S^4))/(81*S^3) - (4*Pi^2*(1441 + 6524*S^2 + 6904*S^4 + 262*S^6 + 524*S^8 + 262*S^10))/(27*S^3*(1 + S^2)^2) + (944*Zeta[3])/S^3) + HPL[{3, 1, 1}, -S^2]*(-((1 + S^2)*(95393 + 19507*S^2 + 11972*S^4))/(81*S^3) - (4*Pi^2*(781 + 4210*S^2 + 4753*S^4 + 142*S^6 + 284*S^8 + 142*S^10))/(9*S^3*(1 + S^2)^2) + (8896*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((-2021*Pi^4)/(90*S^3) + ((1 + S^2)*(411947 + 9469*S^2 + 13400*S^4))/(486*S^3) + (Pi^2*(2024 + 7326*S^2 + 1376*S^4 + 1271*S^6 + 360*S^8 - 133*S^10))/(27*S^3*(1 + S^2)^2) + (224*(55 + 194*S^2 + 181*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{4}, -S^2]*((7*Pi^4)/(3*S^3) + ((1 + S^2)*(123928 + 23921*S^2 + 31939*S^4))/(972*S^3) + (Pi^2*(7421 + 25558*S^2 + 34826*S^4 + 10292*S^6 + 7693*S^8 + 1850*S^10))/(324*S^3*(1 + S^2)^2) - (113*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (484*HPL[{3, 1}, -S^2])/(3*S^3) + (904*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((253 + 842*S^2 + 757*S^4 + 46*S^6 + 92*S^8 + 46*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((-111*Pi^4)/(20*S^3) - ((1 + S^2)*(85251 + 10435*S^2 + 7626*S^4))/(648*S^3) + (Pi^2*(-8627 - 26464*S^2 - 44366*S^4 - 10364*S^6 - 7195*S^8 - 1508*S^10))/(324*S^3*(1 + S^2)^2) + (2*(869 + 3136*S^2 + 2966*S^4 + 158*S^6 + 316*S^8 + 158*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (164*HPL[{4}, -S^2])/(3*S^3) - (83*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (164*HPL[{3, 1}, -S^2])/(3*S^3) + (2*(715 + 2492*S^2 + 2308*S^4 + 130*S^6 + 260*S^8 + 130*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((398*Pi^4)/(45*S^3) - ((1 + S^2)*(241009 + 16853*S^2 + 21940*S^4))/(486*S^3) + (Pi^2*(-8195 - 29434*S^2 - 17168*S^4 - 7538*S^6 - 4135*S^8 - 446*S^10))/(162*S^3*(1 + S^2)^2) + (6272*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(1573 + 5570*S^2 + 5209*S^4 + 286*S^6 + 572*S^8 + 286*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (((1 + S^2)*(95351 + 6595*S^2 + 4532*S^4))/(162*S^3) + (Pi^2*(2101 + 6716*S^2 + 5872*S^4 + 382*S^6 + 764*S^8 + 382*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2, 1}, -S^2]*((Pi^2*(1 + S^2)*(-105143 + 4577*S^2 + 1318*S^4))/(1944*S^3) - ((1 + S^2)*(483629 + 3776*S^2 + 10001*S^4))/(972*S^3) + (Pi^4*(-2816 + 30746*S^2 + 51751*S^4 - 512*S^6 - 1024*S^8 - 512*S^10))/(1620*S^3*(1 + S^2)^2) - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3416*HPL[{3, 2}, -S^2])/(3*S^3) + (10280*HPL[{4, 1}, -S^2])/(3*S^3) - (1568*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (12544*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-862*Pi^2)/(9*S^3) - (2*(3460 + 10998*S^2 + 13972*S^4 + 3637*S^6 + 2304*S^8 + 397*S^10))/(9*S^3*(1 + S^2)^2))*Zeta[3] - (1444*Zeta[5])/(3*S^3)) + Zeta[3]*((Pi^2*(1 + S^2)*(13841 + 1383*S^2 + 1019*S^4))/(162*S^3) + ((1 + S^2)*(3445925 + 154396*S^2 + 126365*S^4))/(5832*S^3) + (Pi^4*(13717 + 45668*S^2 + 41068*S^4 + 2494*S^6 + 4988*S^8 + 2494*S^10))/(1620*S^3*(1 + S^2)^2) - (124*Zeta[5])/(3*S^3)) + HPL[{3}, -S^2]*((Pi^2*(1 + S^2)*(27413 + 3562*S^2 + 3251*S^4))/(324*S^3) + ((1 + S^2)*(1653995 + 116347*S^2 + 108326*S^4))/(2916*S^3) + (Pi^4*(7766 + 26350*S^2 + 23993*S^4 + 1412*S^6 + 2824*S^8 + 1412*S^10))/(810*S^3*(1 + S^2)^2) - (2*(154 + 566*S^2 + 541*S^4 + 28*S^6 + 56*S^8 + 28*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (56*HPL[{5}, -S^2])/(3*S^3) + ((-826*Pi^2)/(9*S^3) + (-6875 - 21868*S^2 - 27848*S^4 - 7232*S^6 - 4561*S^8 - 776*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (344*HPL[{3, 2}, -S^2])/(3*S^3) + (36*HPL[{4, 1}, -S^2])/S^3 + (4*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (3728*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (10592*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (6272*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((52*Pi^2)/(9*S^3) + (587 + 2206*S^2 + 3818*S^4 + 1064*S^6 + 937*S^8 + 272*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + (64*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((-1049*Pi^6)/(1080*S^3) + (Pi^2*(1 + S^2)*(67774 - 2858*S^2 + 139*S^4))/(1944*S^3) - ((1 + S^2)*(-1725700 - 3719*S^2 + 6227*S^4))/(5832*S^3) + (Pi^4*(7167 + 28582*S^2 - 12642*S^4 + 2616*S^6 - 1037*S^8 - 1332*S^10))/(3240*S^3*(1 + S^2)^2) - (86*HPL[{3}, -S^2]^2)/(3*S^3) + ((112*Pi^2)/(9*S^3) + (1525 + 5105*S^2 + 8635*S^4 + 2371*S^6 + 1874*S^8 + 490*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((605 + 2194*S^2 + 2081*S^4 + 110*S^6 + 220*S^8 + 110*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (28*HPL[{6}, -S^2])/S^3 + ((1210*Pi^2)/(9*S^3) + (13693 + 42440*S^2 + 64156*S^4 + 15484*S^6 + 10283*S^8 + 1984*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-6523 - 23294*S^2 - 21895*S^4 - 1186*S^6 - 2372*S^8 - 1186*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-19613 - 70066*S^2 - 65873*S^4 - 3566*S^6 - 7132*S^8 - 3566*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (104*HPL[{4, 2}, -S^2])/S^3 - (1264*HPL[{5, 1}, -S^2])/(3*S^3) + ((-2428*Pi^2)/(9*S^3) - (2*(4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (332*(11 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (8*(55 + 894*S^2 + 1231*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (104*HPL[{3, 1, 2}, -S^2])/S^3 - (920*HPL[{3, 2, 1}, -S^2])/S^3 - (8312*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (1568*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (6272*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (12544*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + (((1 + S^2)*(132313 + 16385*S^2 + 11326*S^4))/(324*S^3) + (Pi^2*(1705 + 5996*S^2 + 5584*S^4 + 310*S^6 + 620*S^8 + 310*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] + (2*Zeta[3]^2)/S^3 + HPL[{2, 1}, -S^2]*(((1 + S^2)*(41650 + 6653*S^2 + 4849*S^4))/(81*S^3) + (2*Pi^2*(1441 + 6524*S^2 + 6904*S^4 + 262*S^6 + 524*S^8 + 262*S^10))/(27*S^3*(1 + S^2)^2) - (472*Zeta[3])/S^3) + HPL[{3}, -S^2]*(((1 + S^2)*(66517 + 8174*S^2 + 5659*S^4))/(162*S^3) + (7*Pi^2*(77 + 272*S^2 + 254*S^4 + 14*S^6 + 28*S^8 + 14*S^10))/(9*S^3*(1 + S^2)^2) - (1864*HPL[{2, 1}, -S^2])/(3*S^3) + (52*Zeta[3])/(3*S^3)) + (2*(1628 + 5422*S^2 + 4877*S^4 + 296*S^6 + 592*S^8 + 296*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + ((627 + 1898*S^2 + 1593*S^4 + 114*S^6 + 228*S^8 + 114*S^10)*Zeta[7])/(S^3*(1 + S^2)^2)) + Log[T]*((1650115 + 400204*S^2)/(209952*S) + (Pi^4*(298698 + 183945*S^2 - 9544*S^4))/(116640*S) + (Pi^2*(686682 + 981441*S^2 + 378529*S^4))/(209952*S) + (Pi^6*(439928 + 2137509*S^2 + 333741*S^4 + 244643*S^6 + 39933*S^8))/(408240*S*(1 + S^2)^2) + ((58*Pi^2)/(9*S^3) + (655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{1}, -S^2]^6 + (16*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)^2) + (16*HPL[{1}, -S^2]^8)/(9*S^3) + HPL[{0}, S^2]^7*(-((-2 + S^2)*(9 + 18*S^2 + 8*S^4 + 2*S^6))/(432*S*(1 + S^2)^2) + HPL[{1}, -S^2]/(24*S^3)) + ((-206*Pi^2)/(27*S^3) + (-10247 - 9713*S^2 + 1014*S^4 + 519*S^6 + 1011*S^8)/(162*S^3*(1 + S^2)))*HPL[{2}, -S^2]^3 + (65*HPL[{2}, -S^2]^4)/(6*S^3) + HPL[{0}, S^2]^6*((-168 + 387*S^2 - 344*S^4 - 451*S^6 - 200*S^8)/(2592*S*(1 + S^2)^2) + ((-11 + 86*S^2 + 151*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^2/(4*S^3) - HPL[{2}, -S^2]/(72*S^3)) + ((-17*Pi^2)/(9*S^3) + (-581 + 86*S^2 + 2623*S^4 + 1427*S^6 + 1213*S^8 + 410*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + (76*HPL[{4}, -S^2]^2)/(3*S^3) + ((-16*Pi^2)/(9*S^3) - (2*(265 + 3098*S^2 + 4567*S^4 + 2897*S^6 + 3097*S^8 + 1133*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{6}, -S^2] + ((-2065 - 4310*S^2 - 2335*S^4 - 736*S^6 - 1472*S^8 - 736*S^10)*HPL[{7}, -S^2])/(9*S^3*(1 + S^2)^2) + (490*HPL[{8}, -S^2])/(3*S^3) + ((-832*Pi^2)/(9*S^3) - (2*(3748 + 9738*S^2 + 11509*S^4 + 1942*S^6 + 1329*S^8 + 202*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 + HPL[{0}, S^2]^5*((2040 - 657*S^2 - 3172*S^4)/(6480*S) + (Pi^2*(586 + 879*S^2 - 38*S^4 - 76*S^6 - 38*S^8))/(1080*S*(1 + S^2)^2) + ((88 + 1802*S^2 + 2527*S^4 + 16*S^6 + 32*S^8 + 16*S^10)*HPL[{1}, -S^2]^2)/(540*S^3*(1 + S^2)^2) + (271*HPL[{1}, -S^2]^3)/(270*S^3) + ((-105 + 1176*S^2 + 1974*S^4 - 8*S^6 - 16*S^8 - 8*S^10)*HPL[{2}, -S^2])/(1080*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*((293*Pi^2)/(540*S^3) + (355 + 201*S^2 + 3157*S^4 + 16*S^6 - 159*S^8 - 116*S^10)/(1080*S^3*(1 + S^2)^2) + (77*HPL[{2}, -S^2])/(60*S^3)) + HPL[{3}, -S^2]/(12*S^3) - (41*HPL[{2, 1}, -S^2])/(15*S^3)) + (760*HPL[{3, 1}, -S^2]^2)/S^3 + ((-13*Pi^2)/(3*S^3) + (-533 + 3443*S^2 + 10564*S^4 + 5390*S^6 + 4651*S^8 + 1637*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4, 2}, -S^2] - (2*(-543 - 804*S^2 - 120*S^4 + 100*S^6 + 200*S^8 + 100*S^10)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + ((18*Pi^2)/S^3 + (5491 + 38426*S^2 + 70426*S^4 + 30392*S^6 + 25669*S^8 + 8432*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] - (2*(-1525 - 2438*S^2 - 607*S^4 + 214*S^6 + 428*S^8 + 214*S^10)*HPL[{5, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*HPL[{5, 3}, -S^2])/(3*S^3) + (2*(3602 + 7498*S^2 + 4043*S^4 + 194*S^6 + 388*S^8 + 194*S^10)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (12*HPL[{6, 2}, -S^2])/S^3 - (104*HPL[{7, 1}, -S^2])/(3*S^3) + (6320*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((56*Pi^2)/(3*S^3) + (1715 - 391*S^2 - 1053*S^4 - 1271*S^6 - 920*S^8)/(27*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((-1480*Pi^2)/(9*S^3) + (-39273 - 39243*S^2 + 3003*S^4 + 805*S^6 + 3124*S^8)/(27*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((-111 - 19782*S^2 - 29451*S^4 - 4654*S^6 - 9308*S^8 - 4654*S^10)*HPL[{3, 2, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*(-143 + 3452*S^2 + 5464*S^4 + 905*S^6 + 1810*S^8 + 905*S^10)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (80*HPL[{3, 3, 2}, -S^2])/(3*S^3) + ((-1792*Pi^2)/(3*S^3) + (2*(-67806 - 144894*S^2 - 88731*S^4 - 4046*S^6 - 1633*S^8 + 2722*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] - (4*(-247 + 4412*S^2 + 7112*S^4 + 1207*S^6 + 2414*S^8 + 1207*S^10)*HPL[{4, 1, 2}, -S^2])/(3*S^3*(1 + S^2)^2) - (56*HPL[{4, 1, 3}, -S^2])/S^3 - (4*(-749 + 13704*S^2 + 22054*S^4 + 3679*S^6 + 7358*S^8 + 3679*S^10)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (10*HPL[{4, 2, 2}, -S^2])/S^3 - (424*HPL[{4, 3, 1}, -S^2])/(3*S^3) - (4*(-4713 + 84534*S^2 + 136227*S^4 + 22654*S^6 + 45308*S^8 + 22654*S^10)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (76*HPL[{5, 1, 2}, -S^2])/S^3 - (556*HPL[{5, 2, 1}, -S^2])/S^3 - (1536*HPL[{6, 1, 1}, -S^2])/S^3 + (16*(-633 + 298*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + ((4400*Pi^2)/(9*S^3) - (8*(-12917 - 27682*S^2 - 17804*S^4 - 974*S^6 - 439*S^8 + 484*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] - (8*(-3305 - 11314*S^2 - 10361*S^4 + 564*S^6 + 1128*S^8 + 564*S^10)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*(-3305 - 11314*S^2 - 10361*S^4 + 564*S^6 + 1128*S^8 + 564*S^10)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (112*HPL[{3, 1, 2, 2}, -S^2])/S^3 - (8*(-7103 - 18910*S^2 - 14159*S^4 + 2352*S^6 + 4704*S^8 + 2352*S^10)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (112*HPL[{3, 2, 1, 2}, -S^2])/S^3 + (6608*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3) + (6272*HPL[{3, 3, 1, 1}, -S^2])/S^3 - (16*(-11047 - 30146*S^2 - 23125*S^4 + 3422*S^6 + 6844*S^8 + 3422*S^10)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (272*HPL[{4, 1, 1, 2}, -S^2])/(3*S^3) + (18544*HPL[{4, 1, 2, 1}, -S^2])/(3*S^3) + (56176*HPL[{4, 2, 1, 1}, -S^2])/(3*S^3) + (114080*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((-7280*Pi^2)/(9*S^3) + (40*(-4635 - 4725*S^2 + 306*S^4 + 74*S^6 + 362*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1, 1}, -S^2] - (32*(523 + 3398*S^2 + 4051*S^4 + 292*S^6 + 584*S^8 + 292*S^10)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (32*(523 + 3398*S^2 + 4051*S^4 + 292*S^6 + 584*S^8 + 292*S^10)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (12544*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3) + (12544*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 - (160*(527 + 3976*S^2 + 4910*S^4 + 421*S^6 + 842*S^8 + 421*S^10)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (73984*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^3) - (124160*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) - (149248*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^3) - (312320*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) - (314560*HPL[{4, 1, 1, 1, 1}, -S^2])/S^3 + (1120*(-13 + 6*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + (10880*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^3 - (17920*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-3016020 - 168006*S^2 - 119873*S^4)/(2916*S) + (Pi^2*(-148782 - 17211*S^2 - 15914*S^4))/(972*S) + (Pi^4*(-18234 - 27351*S^2 - 5654*S^4 - 11308*S^6 - 5654*S^8))/(1620*S*(1 + S^2)^2))*Zeta[3] + ((438 + 1305*S^2 + 100*S^4 - 253*S^6 - 206*S^8)*Zeta[3]^2)/(27*S*(1 + S^2)^2) + HPL[{3, 1, 1}, -S^2]*((65911 + 115440*S^2 + 31263*S^4 + 13176*S^6)/(81*S^3) + (4*Pi^2*(3369 + 14682*S^2 + 15285*S^4 + 212*S^6 + 424*S^8 + 212*S^10))/(27*S^3*(1 + S^2)^2) - (18304*Zeta[3])/(3*S^3)) + HPL[{2, 2, 1}, -S^2]*((2*(11642 + 64629*S^2 + 11889*S^4 + 7417*S^6))/(81*S^3) + (4*Pi^2*(1118 + 5878*S^2 + 6581*S^4 + 300*S^6 + 600*S^8 + 300*S^10))/(27*S^3*(1 + S^2)^2) - (5984*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^5*(((1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(486*S^3) + (Pi^2*(407 + 1858*S^2 + 1973*S^4 + 74*S^6 + 148*S^8 + 74*S^10))/(27*S^3*(1 + S^2)^2) - (26*(11 + 2*S^6)*HPL[{2}, -S^2])/(9*S^3) - (760*HPL[{3}, -S^2])/(9*S^3) - (200*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*((2101 - 18474*S^2 - 5190*S^4 - 6271*S^6)/(81*S^3) + (Pi^2*(29 - 662*S^2 - 1051*S^4 - 250*S^6 - 500*S^8 - 250*S^10))/(27*S^3*(1 + S^2)^2) + (812*HPL[{2, 1}, -S^2])/(3*S^3) - (92*Zeta[3])/(3*S^3)) + HPL[{3, 2}, -S^2]*((-13474 + 251055*S^2 + 30834*S^4 + 30207*S^6)/(162*S^3) + (Pi^2*(-1217 + 7478*S^2 + 13651*S^4 + 2614*S^6 + 5228*S^8 + 2614*S^10))/(54*S^3*(1 + S^2)^2) - (56*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*((-11154 + 802584*S^2 + 111375*S^4 + 100370*S^6)/(162*S^3) + (2*Pi^2*(-459 + 7536*S^2 + 12222*S^4 + 2075*S^6 + 4150*S^8 + 2075*S^10))/(27*S^3*(1 + S^2)^2) + (136*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1, 1}, -S^2]*((8*(-7400 + 31959*S^2 + 1899*S^4 + 2972*S^6))/(81*S^3) + (16*Pi^2*(-655 - 1898*S^2 - 1537*S^4 + 175*S^6 + 350*S^8 + 175*S^10))/(27*S^3*(1 + S^2)^2) + (12320*Zeta[3])/(3*S^3)) + HPL[{0}, S^2]^4*((1187 + 615*S^2 - 3624*S^4)/(2592*S) + (Pi^2*(-561 + 8982*S^2 - 2291*S^4 - 3586*S^6 - 1724*S^8))/(3888*S*(1 + S^2)^2) + ((341 + 4090*S^2 + 5453*S^4 + 62*S^6 + 124*S^8 + 62*S^10)*HPL[{1}, -S^2]^3)/(324*S^3*(1 + S^2)^2) + (71*HPL[{1}, -S^2]^4)/(27*S^3) + ((-11*Pi^2)/(72*S^3) + (21 + 1008*S^2 + 10173*S^4 + 562*S^6 - 196*S^8 - 248*S^10)/(1296*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + HPL[{2}, -S^2]^2/(24*S^3) + HPL[{1}, -S^2]^2*((277*Pi^2)/(108*S^3) + (757 + 635*S^2 + 10477*S^4 + 928*S^6 + 671*S^8 + 118*S^10)/(648*S^3*(1 + S^2)^2) + (241*HPL[{2}, -S^2])/(36*S^3)) + ((-1 - 14*S^2 - 19*S^4 - 12*S^6 - 24*S^8 - 12*S^10)*HPL[{3}, -S^2])/(72*S^3*(1 + S^2)^2) - HPL[{4}, -S^2]/(12*S^3) + ((-281 - 2008*S^2 - 2450*S^4 + 4*S^6 + 8*S^8 + 4*S^10)*HPL[{2, 1}, -S^2])/(108*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]*(-((1 + S^2)*(-1397 - 1467*S^2 + 508*S^4))/(2592*S^3) + (Pi^2*(11 + 6670*S^2 + 9983*S^4 + 2*S^6 + 4*S^8 + 2*S^10))/(1296*S^3*(1 + S^2)^2) + ((143 + 3178*S^2 + 4481*S^4 + 26*S^6 + 52*S^8 + 26*S^10)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)^2) - HPL[{3}, -S^2]/(6*S^3) - (241*HPL[{2, 1}, -S^2])/(18*S^3)) + HPL[{3, 1}, -S^2]/S^3 - (2*HPL[{2, 1, 1}, -S^2])/S^3 - (20*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^4*((6673*Pi^4)/(810*S^3) + ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(2916*S^3) + (Pi^2*(18259 + 55706*S^2 + 94156*S^4 + 21544*S^6 + 14837*S^8 + 3022*S^10))/(486*S^3*(1 + S^2)^2) + ((392*Pi^2)/(27*S^3) - (2*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (784*HPL[{2}, -S^2]^2)/(9*S^3) - (10*(737 + 2614*S^2 + 2447*S^4 + 134*S^6 + 268*S^8 + 134*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (664*HPL[{4}, -S^2])/(9*S^3) + (130*(11 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (664*HPL[{3, 1}, -S^2])/(9*S^3) - (10*(209 + 718*S^2 + 659*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{4}, -S^2]*((-1043*Pi^4)/(540*S^3) + (-239149 - 346800*S^2 - 118452*S^4 - 141326*S^6)/(1944*S^3) + (Pi^2*(-7301 - 28612*S^2 - 39917*S^4 - 14700*S^6 - 12036*S^8 - 3702*S^10))/(324*S^3*(1 + S^2)^2) - (2*(-1953 - 5262*S^2 - 3987*S^4 + 112*S^6 + 224*S^8 + 112*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (292*HPL[{3, 1}, -S^2])/(3*S^3) + (464*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(-207 - 246*S^2 + 45*S^4 + 62*S^6 + 124*S^8 + 62*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((-3596*Pi^4)/(135*S^3) + (-157649 + 2502*S^2 - 2259*S^4 + 4334*S^6)/(81*S^3) + (Pi^2*(-24299 - 42790*S^2 + 361*S^4 + 8840*S^6 + 7720*S^8 + 3620*S^10))/(81*S^3*(1 + S^2)^2) - (16*(-55 + 1066*S^2 + 1709*S^4 + 280*S^6 + 560*S^8 + 280*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((251*Pi^4)/(90*S^3) + (449872 + 153345*S^2 + 52572*S^4 + 7197*S^6)/(1944*S^3) + (Pi^2*(24269 + 69874*S^2 + 97853*S^4 + 19680*S^6 + 14184*S^8 + 3048*S^10))/(648*S^3*(1 + S^2)^2) + ((-359 - 6310*S^2 - 8747*S^4 - 1226*S^6 - 2452*S^8 - 1226*S^10)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)^2) - (43*HPL[{4}, -S^2])/(3*S^3) + (2*(-633 + 298*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (940*HPL[{3, 1}, -S^2])/(3*S^3) - (1568*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(-72 + 918*S^2 + 1521*S^4 + 284*S^6 + 568*S^8 + 284*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((2156*Pi^4)/(135*S^3) + (1016529 + 80502*S^2 + 71061*S^4 + 4846*S^6)/(972*S^3) + (Pi^2*(9002 + 17198*S^2 + 4553*S^4 - 1588*S^6 - 1489*S^8 - 904*S^10))/(54*S^3*(1 + S^2)^2) - (7648*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(-153 + 2118*S^2 + 3483*S^4 + 562*S^6 + 1124*S^8 + 562*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^3*((535502 + 52841*S^2 - 29460*S^4)/(23328*S) + (Pi^2*(8320 + 268*S^2 - 3235*S^4))/(1944*S) + (Pi^4*(23982 + 35973*S^2 - 67*S^4 - 134*S^6 - 67*S^8))/(9720*S*(1 + S^2)^2) + ((1067 + 6514*S^2 + 7637*S^4 + 194*S^6 + 388*S^8 + 194*S^10)*HPL[{1}, -S^2]^4)/(162*S^3*(1 + S^2)^2) + (146*HPL[{1}, -S^2]^5)/(27*S^3) + ((-25 + 904*S^2 + 1406*S^4 + 79*S^6 + 158*S^8 + 79*S^10)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^3*((212*Pi^2)/(27*S^3) + (3197 + 8476*S^2 + 20027*S^4 + 3521*S^6 + 2320*S^8 + 407*S^10)/(243*S^3*(1 + S^2)^2) + (220*HPL[{2}, -S^2])/(9*S^3)) + ((19*Pi^2)/(27*S^3) + (613 + 1010*S^2 + 937*S^4 - 136*S^6 - 524*S^8 - 280*S^10)/(324*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((7 + 116*S^2 + 160*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - (2*HPL[{5}, -S^2])/(9*S^3) + ((-592*Pi^2)/(27*S^3) + (-6352 - 10808*S^2 - 16801*S^4 - 1476*S^6 - 1047*S^8 - 36*S^10)/(162*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((155 - 1670*S^2 - 2815*S^4 - 174*S^6 - 348*S^8 - 174*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (32*HPL[{3, 2}, -S^2])/(9*S^3) + (2*HPL[{4, 1}, -S^2])/S^3 + (2*(-157 + 1666*S^2 + 2813*S^4 + 166*S^6 + 332*S^8 + 166*S^10)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (1292*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (3968*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (2768*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-816 - 1593*S^2 - 1430*S^4 - 1831*S^6 - 782*S^8)*Zeta[3])/(162*S*(1 + S^2)^2) + HPL[{1}, -S^2]^2*(((1 + S^2)*(38351 + 6589*S^2 + 3368*S^4))/(1944*S^3) + (Pi^2*(1243 + 10118*S^2 + 12691*S^4 + 226*S^6 + 452*S^8 + 226*S^10))/(324*S^3*(1 + S^2)^2) + ((451 + 2882*S^2 + 3421*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) + (4*HPL[{3}, -S^2])/(3*S^3) - (220*HPL[{2, 1}, -S^2])/(3*S^3) - (22*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((-217 + 35280*S^2 + 4014*S^4 + 364*S^6)/(1944*S^3) + (Pi^2*(-262 + 2842*S^2 + 4787*S^4 + 158*S^6 + 316*S^8 + 158*S^10))/(324*S^3*(1 + S^2)^2) - (16*HPL[{3}, -S^2])/(9*S^3) - (646*HPL[{2, 1}, -S^2])/(9*S^3) + (2*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]*((3997*Pi^4)/(1620*S^3) + ((1 + S^2)*(246553 + 30851*S^2 + 14776*S^4))/(11664*S^3) + (Pi^2*(4262 + 9079*S^2 + 29498*S^4 + 3569*S^6 + 1843*S^8 + 59*S^10))/(972*S^3*(1 + S^2)^2) + ((187*Pi^2)/(18*S^3) + (1039 + 2634*S^2 + 6061*S^4 + 1042*S^6 + 630*S^8 + 94*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (53*HPL[{2}, -S^2]^2)/(3*S^3) + (4*(2 + 3*S^2)*HPL[{3}, -S^2])/(3*S*(1 + S^2)^2) + (34*HPL[{4}, -S^2])/(9*S^3) - (2*(451 + 2882*S^2 + 3421*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)^2) - (220*HPL[{3, 1}, -S^2])/(3*S^3) + (440*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(77 + 220*S^2 + 176*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2))) + ((-157854 - 13215*S^2 - 8944*S^4)/(162*S) + (Pi^2*(-2514 - 3771*S^2 - 812*S^4 - 1624*S^6 - 812*S^8))/(27*S*(1 + S^2)^2))*Zeta[5] + HPL[{1}, -S^2]^3*((Pi^2*(1 + S^2)*(71271 + 13565*S^2 + 9492*S^4))/(972*S^3) + ((1 + S^2)*(1865477 + 155803*S^2 + 126326*S^4))/(4374*S^3) + (Pi^4*(52349 + 264850*S^2 + 292577*S^4 + 9518*S^6 + 19036*S^8 + 9518*S^10))/(4860*S^3*(1 + S^2)^2) + (392*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((-1988*Pi^2)/(27*S^3) - (2*(24061 + 77276*S^2 + 99832*S^4 + 26410*S^6 + 17147*S^8 + 3154*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (8*(605 + 2206*S^2 + 2099*S^4 + 110*S^6 + 220*S^8 + 110*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - (96*HPL[{5}, -S^2])/S^3 + ((-1568*Pi^2)/(27*S^3) + (8*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(9*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (8*(1529 + 4054*S^2 + 3023*S^4 + 278*S^6 + 556*S^8 + 278*S^10)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)^2) + (6272*HPL[{3, 2}, -S^2])/(9*S^3) + (21472*HPL[{4, 1}, -S^2])/(9*S^3) - (520*(11 + 2*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (12544*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (22432*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((-1664*Pi^2)/(27*S^3) - (8*(5608 + 17597*S^2 + 21457*S^4 + 5518*S^6 + 3269*S^8 + 469*S^10))/(81*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*((-2*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(27*S^3) - (2*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(81*S^3*(1 + S^2)^2) - (3136*HPL[{3}, -S^2])/(9*S^3) - (6272*HPL[{2, 1}, -S^2])/(9*S^3) - (3136*Zeta[3])/(9*S^3)) - (3040*Zeta[5])/(9*S^3)) + HPL[{3}, -S^2]*((-788761 - 11873346*S^2 - 910473*S^4 - 833430*S^6)/(11664*S^3) + (Pi^2*(-4937 - 286830*S^2 - 43038*S^4 - 35162*S^6))/(1944*S^3) + (Pi^4*(2051 - 39170*S^2 - 62857*S^4 - 10614*S^6 - 21228*S^8 - 10614*S^10))/(3240*S^3*(1 + S^2)^2) + (2*(-277 - 296*S^2 + 110*S^4 + 84*S^6 + 168*S^8 + 84*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (52*HPL[{5}, -S^2])/S^3 + ((1828*Pi^2)/(9*S^3) + (45073 + 100424*S^2 + 85384*S^4 + 6316*S^6 + 2831*S^8 - 1676*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (14*(-123 + 426*S^2 + 885*S^4 + 178*S^6 + 356*S^8 + 178*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (32*HPL[{3, 2}, -S^2])/(3*S^3) + (88*HPL[{4, 1}, -S^2])/S^3 - (8*(-353 + 1646*S^2 + 3175*S^4 + 634*S^6 + 1268*S^8 + 634*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6880*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (6944*HPL[{3, 1, 1}, -S^2])/S^3 + (4640*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-20*Pi^2)/(3*S^3) + (-1805 - 4984*S^2 - 5540*S^4 - 1770*S^6 - 1971*S^8 - 762*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] - (56*Zeta[5])/S^3) + HPL[{2, 1}, -S^2]*((Pi^2*(-16799 + 44820*S^2 + 15*S^4 + 4150*S^6))/(324*S^3) + (-185702 + 2881155*S^2 + 52176*S^4 + 119873*S^6)/(2916*S^3) + (Pi^4*(-25640 - 87658*S^2 - 80207*S^4 + 5602*S^6 + 11204*S^8 + 5602*S^10))/(1620*S^3*(1 + S^2)^2) + (448*(5 + 52*S^2 + 68*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6568*HPL[{3, 2}, -S^2])/(3*S^3) - (21104*HPL[{4, 1}, -S^2])/(3*S^3) + (16*(523 + 3398*S^2 + 4051*S^4 + 292*S^6 + 584*S^8 + 292*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (1632*HPL[{3, 1, 1}, -S^2])/S^3 - (12640*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((1708*Pi^2)/(9*S^3) + (2*(22051 + 50810*S^2 + 44551*S^4 + 5040*S^6 + 3360*S^8))/(27*S^3*(1 + S^2)^2))*Zeta[3] + (1000*Zeta[5])/S^3) + HPL[{2}, -S^2]*((-30311*Pi^6)/(34020*S^3) + (Pi^2*(-166641 + 23074*S^2 + 4648*S^4 + 8668*S^6))/(1944*S^3) + (-20915332 - 1193787*S^2 - 30609*S^4 + 378529*S^6)/(34992*S^3) + (Pi^4*(-93839 - 156550*S^2 + 69349*S^4 + 44997*S^6 + 39060*S^8 + 16989*S^10))/(9720*S^3*(1 + S^2)^2) + (4*HPL[{3}, -S^2]^2)/(3*S^3) + ((71*Pi^2)/(9*S^3) + (1963 - 523*S^2 - 8918*S^4 - 5334*S^6 - 4587*S^8 - 1617*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (2*(-127 - 90*S^2 + 119*S^4 + 56*S^6 + 112*S^8 + 56*S^10)*HPL[{5}, -S^2])/(3*S^3*(1 + S^2)^2) + (152*HPL[{6}, -S^2])/(3*S^3) + (1568*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-1004*Pi^2)/(9*S^3) + (-24579 - 60504*S^2 - 67986*S^4 - 9382*S^6 - 5891*S^8 - 346*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((289 + 10826*S^2 + 15661*S^4 + 2374*S^6 + 4748*S^8 + 2374*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*(-438 + 6834*S^2 + 11127*S^4 + 1895*S^6 + 3790*S^8 + 1895*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (26*HPL[{4, 2}, -S^2])/S^3 - (172*HPL[{5, 1}, -S^2])/(3*S^3) + ((1664*Pi^2)/(9*S^3) + (4*(3748 + 9738*S^2 + 11509*S^4 + 1942*S^6 + 1329*S^8 + 202*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (8*(-633 + 298*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (16*(-773 - 2722*S^2 - 2537*S^4 + 130*S^6 + 260*S^8 + 130*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (104*HPL[{3, 1, 2}, -S^2])/S^3 + (936*HPL[{3, 2, 1}, -S^2])/S^3 + (9824*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (16*(523 + 3398*S^2 + 4051*S^4 + 292*S^6 + 584*S^8 + 292*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (67616*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (12640*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((8803 - 121212*S^2 - 15147*S^4 - 11326*S^6)/(162*S^3) + (Pi^2*(184 - 2218*S^2 - 3695*S^4 - 616*S^6 - 1232*S^8 - 616*S^10))/(27*S^3*(1 + S^2)^2))*Zeta[3] - (32*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*((8815 - 127971*S^2 - 15525*S^4 - 16701*S^6)/(162*S^3) + (Pi^2*(835 - 3286*S^2 - 6599*S^4 - 1346*S^6 - 2692*S^8 - 1346*S^10))/(54*S^3*(1 + S^2)^2) + (3440*HPL[{2, 1}, -S^2])/(3*S^3) + (32*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-11642 - 64629*S^2 - 11889*S^4 - 7417*S^6)/(81*S^3) - (2*Pi^2*(1118 + 5878*S^2 + 6581*S^4 + 300*S^6 + 600*S^8 + 300*S^10))/(27*S^3*(1 + S^2)^2) + (2992*Zeta[3])/(3*S^3)) - (2*(-404 + 1358*S^2 + 2845*S^4 + 590*S^6 + 1180*S^8 + 590*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((52285*Pi^6)/(13608*S^3) + (Pi^2*(1 + S^2)*(71609 + 10670*S^2 + 7703*S^4))/(648*S^3) + ((1 + S^2)*(12649645 + 794066*S^2 + 772759*S^4))/(17496*S^3) + (Pi^4*(292577 + 870982*S^2 + 1697756*S^4 + 362300*S^6 + 259729*S^8 + 55868*S^10))/(19440*S^3*(1 + S^2)^2) + ((607*Pi^2)/(9*S^3) + (4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (148*HPL[{3}, -S^2]^2)/(3*S^3) + ((-340*Pi^2)/(9*S^3) + (-4427 - 15048*S^2 - 21278*S^4 - 6152*S^6 - 4563*S^8 - 1100*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] - (4*(583 + 1814*S^2 + 1555*S^4 + 106*S^6 + 212*S^8 + 106*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (178*HPL[{6}, -S^2])/(3*S^3) - (3136*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-440*Pi^2)/(9*S^3) + (4*(5225 + 17554*S^2 + 17960*S^4 + 5495*S^6 + 3433*S^8 + 581*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (4*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3, 2}, -S^2])/(3*S^3*(1 + S^2)^2) + (4*(10417 + 36938*S^2 + 34573*S^4 + 1894*S^6 + 3788*S^8 + 1894*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (156*HPL[{4, 2}, -S^2])/S^3 + (2704*HPL[{5, 1}, -S^2])/(3*S^3) + ((1568*Pi^2)/(9*S^3) - (8*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (1568*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*(2783 + 13978*S^2 + 15401*S^4 + 506*S^6 + 1012*S^8 + 506*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2656*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (520*(11 + 2*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + (2656*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (-((1 + S^2)*(150737 + 14875*S^2 + 9644*S^4))/(162*S^3) - (2*Pi^2*(583 + 1998*S^2 + 1831*S^4 + 106*S^6 + 212*S^8 + 106*S^10))/(9*S^3*(1 + S^2)^2))*Zeta[3] + (80*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*(-((1 + S^2)*(154507 + 20411*S^2 + 17122*S^4))/(162*S^3) - (2*Pi^2*(660 + 2314*S^2 + 2151*S^4 + 120*S^6 + 240*S^8 + 120*S^10))/(9*S^3*(1 + S^2)^2) + (3136*HPL[{2, 1}, -S^2])/(3*S^3) - (200*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((2*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(9*S^3) + (2*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(27*S^3*(1 + S^2)^2) + (3136*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((2021*Pi^4)/(180*S^3) - ((1 + S^2)*(411947 + 9469*S^2 + 13400*S^4))/(972*S^3) + (Pi^2*(-2024 - 7326*S^2 - 1376*S^4 - 1271*S^6 - 360*S^8 + 133*S^10))/(54*S^3*(1 + S^2)^2) - (2*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)^2) - (452*HPL[{4}, -S^2])/(3*S^3) - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3136*HPL[{3, 1}, -S^2])/(3*S^3) + (6272*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (112*(55 + 194*S^2 + 181*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) - (2*(3619 + 11798*S^2 + 10459*S^4 + 658*S^6 + 1316*S^8 + 658*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{0}, S^2]^2*((Pi^2*(26987 + 11930*S^2 - 6538*S^4))/(3888*S) + (-67722 + 787881*S^2 + 378529*S^4)/(69984*S) + (Pi^4*(5490 + 41385*S^2 + 2724*S^4 - 673*S^6 - 1298*S^8))/(4320*S*(1 + S^2)^2) + ((33 + 190*S^2 + 219*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{1}, -S^2]^5)/(3*S^3*(1 + S^2)^2) + (62*HPL[{1}, -S^2]^6)/(9*S^3) + ((2*Pi^2)/(3*S^3) + (1781 + 11446*S^2 + 28799*S^4 + 8028*S^6 + 6210*S^8 + 1836*S^10)/(216*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (10*HPL[{2}, -S^2]^3)/(9*S^3) + HPL[{1}, -S^2]^4*((749*Pi^2)/(54*S^3) + (7043 + 20512*S^2 + 51242*S^4 + 10508*S^6 + 8299*S^8 + 2084*S^10)/(324*S^3*(1 + S^2)^2) + (392*HPL[{2}, -S^2])/(9*S^3)) - (5*HPL[{3}, -S^2]^2)/(3*S^3) + ((-7*Pi^2)/(6*S^3) + (-977 - 3478*S^2 - 3380*S^4 - 1456*S^6 - 1223*S^8 - 358*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-137 - 418*S^2 - 353*S^4 - 94*S^6 - 188*S^8 - 94*S^10)*HPL[{5}, -S^2])/(18*S^3*(1 + S^2)^2) + (20*HPL[{6}, -S^2])/(3*S^3) - (14*HPL[{2, 1}, -S^2]^2)/S^3 + ((58*Pi^2)/(9*S^3) + (1172 - 3770*S^2 - 21949*S^4 - 6712*S^6 - 5345*S^8 - 1744*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-231 + 42*S^2 + 525*S^4 + 166*S^6 + 332*S^8 + 166*S^10)*HPL[{3, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + (2*(-112 + 178*S^2 + 491*S^4 + 133*S^6 + 266*S^8 + 133*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (5*HPL[{4, 2}, -S^2])/(3*S^3) + (14*HPL[{5, 1}, -S^2])/(3*S^3) + ((-106*Pi^2)/(9*S^3) + (2*(-562 + 2005*S^2 + 11228*S^4 + 3470*S^6 + 2770*S^8 + 905*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(595 + 2480*S^2 + 2530*S^4 + 8*S^6 + 16*S^8 + 8*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*(-1820 - 7378*S^2 - 7427*S^4 + 19*S^6 + 38*S^8 + 19*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*HPL[{3, 1, 2}, -S^2])/(3*S^3) - (24*HPL[{3, 2, 1}, -S^2])/S^3 - (104*HPL[{4, 1, 1}, -S^2])/S^3 + (4*(-1255 - 4862*S^2 - 4783*S^4 + 70*S^6 + 140*S^8 + 70*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (320*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (560*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-4466 - 749*S^2 - 1342*S^4)/(108*S) + (Pi^2*(-82 - 123*S^2 - 50*S^4 - 100*S^6 - 50*S^8))/(18*S*(1 + S^2)^2))*Zeta[3] + HPL[{1}, -S^2]^3*(((1 + S^2)*(15769 + 6455*S^2 + 4708*S^4))/(486*S^3) + (Pi^2*(913 + 6320*S^2 + 7654*S^4 + 166*S^6 + 332*S^8 + 166*S^10))/(81*S^3*(1 + S^2)^2) + ((935 + 6574*S^2 + 7991*S^4 + 170*S^6 + 340*S^8 + 170*S^10)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)^2) - (88*HPL[{3}, -S^2])/(9*S^3) - (1568*HPL[{2, 1}, -S^2])/(9*S^3) - (164*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((-996 - 14496*S^2 - 2967*S^4 - 3836*S^6)/(648*S^3) + (Pi^2*(67 - 166*S^2 - 383*S^4 - 122*S^6 - 244*S^8 - 122*S^10))/(108*S^3*(1 + S^2)^2) + (88*HPL[{2, 1}, -S^2])/(3*S^3) - (16*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-20797 + 6624*S^2 - 7551*S^4 + 562*S^6)/(324*S^3) + (Pi^2*(-1536 - 6870*S^2 - 7233*S^4 + 74*S^6 + 148*S^8 + 74*S^10))/(54*S^3*(1 + S^2)^2) + (56*Zeta[3])/S^3) + HPL[{2}, -S^2]*((-323*Pi^4)/(540*S^3) + (-8992 + 20572*S^2 + 6907*S^4 + 4334*S^6)/(648*S^3) + (Pi^2*(-1103 + 5018*S^2 + 32629*S^4 + 7502*S^6 + 5344*S^8 + 1562*S^10))/(648*S^3*(1 + S^2)^2) + ((43 + 2*S^2 - 83*S^4 - 26*S^6 - 52*S^8 - 26*S^10)*HPL[{3}, -S^2])/(6*S^3*(1 + S^2)^2) + (13*HPL[{4}, -S^2])/(3*S^3) - (2*(595 + 2480*S^2 + 2530*S^4 + 8*S^6 + 16*S^8 + 8*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*HPL[{3, 1}, -S^2])/S^3 + (28*HPL[{2, 1, 1}, -S^2])/S^3 + ((74 - 86*S^2 - 277*S^4 - 56*S^6 - 112*S^8 - 56*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^2*((8449*Pi^4)/(1080*S^3) + ((1 + S^2)*(70220 + 31321*S^2 + 22763*S^4))/(1944*S^3) + (Pi^2*(8557 + 21782*S^2 + 72196*S^4 + 12364*S^6 + 9641*S^8 + 2320*S^10))/(648*S^3*(1 + S^2)^2) + ((211*Pi^2)/(6*S^3) + (718 + 1836*S^2 + 6298*S^4 + 1183*S^6 + 972*S^8 + 265*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (215*HPL[{2}, -S^2]^2)/(3*S^3) + ((-275 - 814*S^2 - 671*S^4 - 50*S^6 - 100*S^8 - 50*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*HPL[{4}, -S^2])/(3*S^3) + ((-935 - 6574*S^2 - 7991*S^4 - 170*S^6 - 340*S^8 - 170*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (772*HPL[{3, 1}, -S^2])/(3*S^3) + (1568*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-121 - 406*S^2 - 367*S^4 - 22*S^6 - 44*S^8 - 22*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + ((-78 - 117*S^2 - 44*S^4 - 88*S^6 - 44*S^8)*Zeta[5])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((Pi^2*(1 + S^2)*(35729 + 17311*S^2 + 7892*S^4))/(3888*S^3) + ((1 + S^2)*(285029 + 157210*S^2 + 126287*S^4))/(11664*S^3) + (Pi^4*(4037 + 41870*S^2 + 54731*S^4 + 734*S^6 + 1468*S^8 + 734*S^10))/(2160*S^3*(1 + S^2)^2) + ((121 + 672*S^2 + 766*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*HPL[{2}, -S^2]^2)/(3*S^3*(1 + S^2)^2) + ((-25*Pi^2)/(9*S^3) + (-694 - 2543*S^2 - 3034*S^4 - 928*S^6 - 689*S^8 - 154*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-341 - 778*S^2 - 485*S^4 - 62*S^6 - 124*S^8 - 62*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - (8*HPL[{5}, -S^2])/S^3 + ((-211*Pi^2)/(3*S^3) + (-718 - 1836*S^2 - 6298*S^4 - 1183*S^6 - 972*S^8 - 265*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(451 + 3218*S^2 + 3925*S^4 + 82*S^6 + 164*S^8 + 82*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (28*HPL[{3, 2}, -S^2])/S^3 + (268*HPL[{4, 1}, -S^2])/(3*S^3) + (2*(935 + 6574*S^2 + 7991*S^4 + 170*S^6 + 340*S^8 + 170*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1720*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (4984*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (3136*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-41*Pi^2)/(9*S^3) + (-2389 - 7694*S^2 - 9490*S^4 - 2614*S^6 - 1691*S^8 - 310*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(13585 + 10481*S^2 + 6322*S^4))/(648*S^3) + (Pi^2*(539 + 4876*S^2 + 6236*S^4 + 98*S^6 + 196*S^8 + 98*S^10))/(54*S^3*(1 + S^2)^2) - (14*HPL[{3}, -S^2])/S^3 - (860*HPL[{2, 1}, -S^2])/(3*S^3) - (26*Zeta[3])/S^3) - (26*Zeta[5])/S^3)) + HPL[{0}, S^2]*((Pi^4*(1817418 + 216633*S^2 + 13432*S^4))/(116640*S) + (Pi^2*(8928450 + 764559*S^2 + 416924*S^4))/(69984*S) + (178740120 + 8753403*S^2 + 11329918*S^4)/(209952*S) + (Pi^6*(1493922 + 2240883*S^2 + 122948*S^4 + 245896*S^6 + 122948*S^8))/(408240*S*(1 + S^2)^2) + (56*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)^2) + (64*HPL[{1}, -S^2]^7)/(9*S^3) + (2*(-58 + 946*S^2 + 1535*S^4 + 196*S^6 + 392*S^8 + 196*S^10)*HPL[{2}, -S^2]^3)/(27*S^3*(1 + S^2)^2) + HPL[{1}, -S^2]^5*((482*Pi^2)/(27*S^3) + (655 + 2020*S^2 + 3046*S^4 + 724*S^6 + 475*S^8 + 88*S^10)/(9*S^3*(1 + S^2)^2) + (200*HPL[{2}, -S^2])/(3*S^3)) + ((139 + 254*S^2 + 103*S^4 - 6*S^6 - 12*S^8 - 6*S^10)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((25*Pi^2)/(9*S^3) + (1027 + 3218*S^2 + 4348*S^4 + 288*S^6 - 933*S^8 - 720*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((400 + 1238*S^2 + 1057*S^4 + 90*S^6 + 180*S^8 + 90*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) - (100*HPL[{7}, -S^2])/(3*S^3) - (4*(-17 + 2318*S^2 + 3511*S^4 + 380*S^6 + 760*S^8 + 380*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((82*Pi^2)/(9*S^3) + (3403 + 11264*S^2 + 15220*S^4 + 5826*S^6 + 6489*S^8 + 2550*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((34*Pi^2)/(9*S^3) + (2*(629 + 3973*S^2 + 7658*S^4 + 3640*S^6 + 4433*S^8 + 1831*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((-41 + 18*S^6)*HPL[{4, 2}, -S^2])/(9*S^3) - (128*HPL[{4, 3}, -S^2])/(3*S^3) - (4*(-5 + 152*S^2 + 238*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (370*HPL[{5, 2}, -S^2])/(3*S^3) - (264*HPL[{6, 1}, -S^2])/S^3 + ((4360*Pi^2)/(9*S^3) + (4*(14038 + 30770*S^2 + 32020*S^4 + 3723*S^6 + 2742*S^8 + 195*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((13312*Pi^2)/(9*S^3) + (2*(85839 + 186576*S^2 + 190860*S^4 + 20648*S^6 + 14101*S^8 + 128*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] + (2*(67 + 6*S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) + (2*(-397 + 7702*S^2 + 12347*S^4 + 1574*S^6 + 3148*S^8 + 1574*S^10)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (44*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (128*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (4*(-287 + 3766*S^2 + 6223*S^4 + 794*S^6 + 1588*S^8 + 794*S^10)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (148*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (628*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (408*HPL[{5, 1, 1}, -S^2])/S^3 + ((-9128*Pi^2)/(9*S^3) + (4*(-29155 - 62216*S^2 - 61879*S^4 - 5448*S^6 - 2904*S^8 + 726*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] - (11936*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) - (16*(-228 + 1794*S^2 + 3147*S^4 + 403*S^6 + 806*S^8 + 403*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (36208*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (36208*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (72016*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (214976*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (80*(-25 + 250*S^2 + 425*S^4 + 54*S^6 + 108*S^8 + 54*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (24544*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (24544*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (121600*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) - (16960*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-75714 - 27447*S^2 - 30850*S^4)/(972*S) + (Pi^2*(-3618 - 8775*S^2 - 4558*S^4 - 4409*S^6 - 1624*S^8))/(162*S*(1 + S^2)^2))*Zeta[3] + (2*(102 + 153*S^2 + 20*S^4 + 40*S^6 + 20*S^8)*Zeta[3]^2)/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(972*S^3) + (Pi^2*(5687 + 25834*S^2 + 27377*S^4 + 1034*S^6 + 2068*S^8 + 1034*S^10))/(162*S^3*(1 + S^2)^2) + (125*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) - (68*HPL[{3}, -S^2])/(9*S^3) - (1000*HPL[{2, 1}, -S^2])/(3*S^3) - (332*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((-197 - 56162*S^2 - 6977*S^4 - 5218*S^6)/(54*S^3) + (Pi^2*(611 - 5258*S^2 - 9109*S^4 - 980*S^6 - 1960*S^8 - 980*S^10))/(27*S^3*(1 + S^2)^2) - (32*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((-2201 + 52560*S^2 + 8271*S^4 + 5296*S^6)/(216*S^3) + (Pi^2*(-14 + 1074*S^2 + 1639*S^4 + 153*S^6 + 306*S^8 + 153*S^10))/(18*S^3*(1 + S^2)^2) + (4*HPL[{3}, -S^2])/(3*S^3) - (1492*HPL[{2, 1}, -S^2])/(3*S^3) + (4*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((2409 + 168816*S^2 + 21207*S^4 + 16528*S^6)/(81*S^3) + (8*Pi^2*(-133 + 1354*S^2 + 2297*S^4 + 244*S^6 + 488*S^8 + 244*S^10))/(27*S^3*(1 + S^2)^2) + (16*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((2673 + 14172*S^2 - 894*S^4 - 5044*S^6)/(324*S^3) + (Pi^2*(-151 + 178*S^2 + 569*S^4 + 58*S^6 + 116*S^8 + 58*S^10))/(54*S^3*(1 + S^2)^2) - (116*HPL[{2, 1}, -S^2])/(3*S^3) + (52*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-11423*Pi^4)/(270*S^3) + (-188347 - 36169*S^2 - 13699*S^4 + 867*S^6)/(162*S^3) + (Pi^2*(-35507 - 73024*S^2 - 78680*S^4 - 6924*S^6 - 3951*S^8 + 690*S^10))/(162*S^3*(1 + S^2)^2) + (2048*HPL[{3, 1}, -S^2])/S^3 + (12272*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(-481 - 1454*S^2 - 1219*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((7*Pi^4)/(5*S^3) + (27696 + 33033*S^2 - 7197*S^4 - 17039*S^6)/(972*S^3) + (Pi^2*(2224 + 2966*S^2 - 323*S^4 - 1826*S^6 - 2875*S^8 - 1322*S^10))/(324*S^3*(1 + S^2)^2) + (64*HPL[{4}, -S^2])/(3*S^3) - (2*(-173 - 802*S^2 - 857*S^4 + 26*S^6 + 52*S^8 + 26*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (32*HPL[{3, 1}, -S^2])/S^3 - (176*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(97 + 218*S^2 + 133*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^3*((4061*Pi^4)/(270*S^3) + ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(1458*S^3) + (Pi^2*(35869 + 107852*S^2 + 177124*S^4 + 39622*S^6 + 26015*S^8 + 4774*S^10))/(486*S^3*(1 + S^2)^2) + ((80*Pi^2)/S^3 + (4*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] + (1568*HPL[{2}, -S^2]^2)/(9*S^3) - (4*(77 + 358*S^2 + 383*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) + (184*HPL[{4}, -S^2])/(9*S^3) - (500*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2000*HPL[{3, 1}, -S^2])/(3*S^3) + (4000*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(473 + 1942*S^2 + 1967*S^4 + 86*S^6 + 172*S^8 + 86*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) - (2*(346 + 891*S^2 + 447*S^4 + 469*S^6 + 177*S^8)*Zeta[5])/(9*S*(1 + S^2)^2) + HPL[{1}, -S^2]^2*((Pi^2*(1 + S^2)*(36771 + 5729*S^2 + 3738*S^4))/(324*S^3) + ((1 + S^2)*(1865477 + 155803*S^2 + 126326*S^4))/(2916*S^3) + (Pi^4*(24101 + 121300*S^2 + 133748*S^4 + 4382*S^6 + 8764*S^8 + 4382*S^10))/(1620*S^3*(1 + S^2)^2) + (196*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-22*Pi^2)/(9*S^3) - (2*(-346 - 536*S^2 + 410*S^4 + 311*S^6 + 580*S^8 + 257*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((319 + 1190*S^2 + 1147*S^4 + 58*S^6 + 116*S^8 + 58*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) + (92*HPL[{5}, -S^2])/(3*S^3) + ((-240*Pi^2)/S^3 - (4*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (4*(231 + 962*S^2 + 981*S^4 + 42*S^6 + 84*S^8 + 42*S^10)*HPL[{3, 1}, -S^2])/(S^3*(1 + S^2)^2) + (304*HPL[{3, 2}, -S^2])/(3*S^3) + (728*HPL[{4, 1}, -S^2])/(3*S^3) + (500*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (6272*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (18544*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (4000*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-188*Pi^2)/(9*S^3) + (-2321 - 7960*S^2 - 13184*S^4 - 3716*S^6 - 2911*S^8 - 764*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(91373 + 11923*S^2 + 7142*S^4))/(162*S^3) + (Pi^2*(5027 + 23014*S^2 + 24467*S^4 + 914*S^6 + 1828*S^8 + 914*S^10))/(54*S^3*(1 + S^2)^2) - (152*HPL[{3}, -S^2])/(3*S^3) - (3136*HPL[{2, 1}, -S^2])/(3*S^3) - (328*Zeta[3])/(3*S^3)) - (260*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((Pi^2*(2192 + 204096*S^2 + 25221*S^4 + 16892*S^6))/(1944*S^3) + (358449 + 3557046*S^2 + 250275*S^4 + 186232*S^6)/(5832*S^3) + (Pi^4*(-1194 + 10542*S^2 + 18201*S^4 + 1562*S^6 + 3124*S^8 + 1562*S^10))/(648*S^3*(1 + S^2)^2) + ((-38*Pi^2)/(9*S^3) + (-511 - 1756*S^2 - 2458*S^4 - 954*S^6 - 1079*S^8 - 426*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-91 - 166*S^2 - 67*S^4 - 2*S^6 - 4*S^8 - 2*S^10)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)^2) - (74*HPL[{5}, -S^2])/(3*S^3) + ((-2180*Pi^2)/(9*S^3) - (2*(14038 + 30770*S^2 + 32020*S^4 + 3723*S^6 + 2742*S^8 + 195*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (2*(-59 + 4586*S^2 + 6997*S^4 + 758*S^6 + 1516*S^8 + 758*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*HPL[{3, 2}, -S^2])/(3*S^3) + (68*HPL[{4, 1}, -S^2])/(3*S^3) + (8*(-17 + 2318*S^2 + 3511*S^4 + 380*S^6 + 760*S^8 + 380*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (5968*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (18080*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (12272*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((8*Pi^2)/(9*S^3) + (-54 - 2742*S^2 - 6939*S^4 - 2918*S^6 - 2395*S^8 - 776*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] + (16*Zeta[5])/S^3) + HPL[{1}, -S^2]*((248987*Pi^6)/(68040*S^3) + (Pi^2*(1 + S^2)*(465025 + 53423*S^2 + 35968*S^4))/(3888*S^3) + ((1 + S^2)*(12649645 + 794066*S^2 + 772759*S^4))/(17496*S^3) + (Pi^4*(311507 + 892918*S^2 + 1610936*S^4 + 323144*S^6 + 203167*S^8 + 32372*S^10))/(19440*S^3*(1 + S^2)^2) + ((551*Pi^2)/(9*S^3) + (4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10)/(18*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 + (236*HPL[{2}, -S^2]^3)/(3*S^3) - (8*HPL[{3}, -S^2]^2)/(3*S^3) + ((80*Pi^2)/(9*S^3) + (3181 + 8804*S^2 + 10120*S^4 + 1858*S^6 + 371*S^8 - 302*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + (2*(187 + 650*S^2 + 601*S^4 + 34*S^6 + 68*S^8 + 34*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (146*HPL[{6}, -S^2])/(3*S^3) - (3136*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-240*Pi^2)/S^3 - (2*(14303 + 43240*S^2 + 63092*S^4 + 14798*S^6 + 9121*S^8 + 1478*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + (76*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*(935 + 4054*S^2 + 4211*S^4 + 170*S^6 + 340*S^8 + 170*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (72*HPL[{5, 1}, -S^2])/S^3 + ((480*Pi^2)/S^3 + (8*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (1568*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (8*(6391 + 26690*S^2 + 27253*S^4 + 1162*S^6 + 2324*S^8 + 1162*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1888*HPL[{3, 2, 1}, -S^2])/S^3 + (17360*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (1000*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (4000*HPL[{3, 1, 1, 1}, -S^2])/S^3 + (8000*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + (-((1 + S^2)*(11611 + 4811*S^2 + 4366*S^4))/(162*S^3) + (Pi^2*(-209 - 794*S^2 - 773*S^4 - 38*S^6 - 76*S^8 - 38*S^10))/(9*S^3*(1 + S^2)^2))*Zeta[3] + (68*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*(-((1 + S^2)*(-7841 + 725*S^2 + 3112*S^4))/(162*S^3) + (Pi^2*(-77 - 286*S^2 - 275*S^4 - 14*S^6 - 28*S^8 - 14*S^10))/(27*S^3*(1 + S^2)^2) + (304*HPL[{2, 1}, -S^2])/(3*S^3) - (16*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(91373 + 11923*S^2 + 7142*S^4))/(81*S^3) + (Pi^2*(-5027 - 23014*S^2 - 24467*S^4 - 914*S^6 - 1828*S^8 - 914*S^10))/(27*S^3*(1 + S^2)^2) + (656*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((2155*Pi^4)/(108*S^3) + ((1 + S^2)*(596135 + 57307*S^2 + 34202*S^4))/(972*S^3) + (Pi^2*(17323 + 50804*S^2 + 80989*S^4 + 17836*S^6 + 10970*S^8 + 1762*S^10))/(162*S^3*(1 + S^2)^2) - (38*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*HPL[{4}, -S^2])/(3*S^3) - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3136*HPL[{3, 1}, -S^2])/(3*S^3) + (6272*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (82*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) - (4*(209 + 808*S^2 + 794*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2))) - (2*(966 + 1449*S^2 + 302*S^4 + 604*S^6 + 302*S^8)*Zeta[7])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*((7*Pi^4*(1 + S^2)*(37529 + 9173*S^2 + 5540*S^4))/(19440*S^3) + (Pi^2*(1 + S^2)*(1338661 + 156272*S^2 + 126313*S^4))/(11664*S^3) + ((1 + S^2)*(179723545 + 8757449*S^2 + 11329918*S^4))/(209952*S^3) + (Pi^6*(80366 + 474442*S^2 + 550931*S^4 + 14612*S^6 + 29224*S^8 + 14612*S^10))/(40824*S^3*(1 + S^2)^2) - (83*(11 + 2*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + (37*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-80*Pi^2)/(3*S^3) - (2*(3169 + 11183*S^2 + 13807*S^4 + 4411*S^6 + 3317*S^8 + 811*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] - (2*(1144 + 2822*S^2 + 1945*S^4 + 208*S^6 + 416*S^8 + 208*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) - (20*HPL[{7}, -S^2])/S^3 - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((1652*Pi^2)/(9*S^3) + (2*(6875 + 21868*S^2 + 27848*S^4 + 7232*S^6 + 4561*S^8 + 776*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((5636*Pi^2)/(9*S^3) + (45677 + 146256*S^2 + 188366*S^4 + 49544*S^6 + 31929*S^8 + 5756*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + (13*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{4, 2}, -S^2])/(S^3*(1 + S^2)^2) - (188*HPL[{4, 3}, -S^2])/(3*S^3) + (52*(187 + 686*S^2 + 655*S^4 + 34*S^6 + 68*S^8 + 34*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (136*HPL[{5, 2}, -S^2])/S^3 + (196*HPL[{6, 1}, -S^2])/(3*S^3) + ((4856*Pi^2)/(9*S^3) + (4*(4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((10592*Pi^2)/(9*S^3) + (8*(8386 + 24614*S^2 + 45952*S^4 + 9925*S^6 + 6848*S^8 + 1411*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (664*(11 + 2*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (6520*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (19936*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (8*(3949 + 9890*S^2 + 6937*S^4 + 718*S^6 + 1436*S^8 + 718*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (19624*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (60808*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (41760*HPL[{5, 1, 1}, -S^2])/S^3 + ((-3136*Pi^2)/(9*S^3) + (16*(457 + 1070*S^2 + 209*S^4 + 200*S^6 + 22*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (16*(1529 + 4054*S^2 + 3023*S^4 + 278*S^6 + 556*S^8 + 278*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (12544*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (12544*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (12544*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (42944*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (1040*(11 + 2*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) - (25088*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (25088*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (155840*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-1013*Pi^4)/(90*S^3) - ((1 + S^2)*(504041 + 33388*S^2 + 23801*S^4))/(486*S^3) + (Pi^2*(-24821 - 78082*S^2 - 95318*S^4 - 24686*S^6 - 14767*S^8 - 2186*S^10))/(162*S^3*(1 + S^2)^2))*Zeta[3] + (2*(121 + 482*S^2 + 481*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*Zeta[3]^2)/(9*S^3*(1 + S^2)^2) + HPL[{2, 1, 1}, -S^2]*((-4*(1 + S^2)*(3298 + 164*S^2 + 139*S^4))/(9*S^3) - (4*Pi^2*(605 - 1142*S^2 - 2923*S^4 + 110*S^6 + 220*S^8 + 110*S^10))/(27*S^3*(1 + S^2)^2) - (6272*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(((1 + S^2)*(41650 + 6653*S^2 + 4849*S^4))/(162*S^3) + (Pi^2*(1441 + 6524*S^2 + 6904*S^4 + 262*S^6 + 524*S^8 + 262*S^10))/(27*S^3*(1 + S^2)^2) - (932*HPL[{3}, -S^2])/(3*S^3) - (236*Zeta[3])/S^3) + HPL[{4}, -S^2]*(-((1 + S^2)*(40345 + 8120*S^2 + 11599*S^4))/(162*S^3) + (Pi^2*(-2761 - 9602*S^2 - 8881*S^4 - 502*S^6 - 1004*S^8 - 502*S^10))/(54*S^3*(1 + S^2)^2) + (904*HPL[{2, 1}, -S^2])/(3*S^3) - (112*Zeta[3])/(3*S^3)) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(71207 + 7105*S^2 + 7424*S^4))/(81*S^3) + (4*Pi^2*(539 + 418*S^2 - 451*S^4 + 98*S^6 + 196*S^8 + 98*S^10))/(27*S^3*(1 + S^2)^2) + (3232*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((-2021*Pi^4)/(90*S^3) + ((1 + S^2)*(411947 + 9469*S^2 + 13400*S^4))/(486*S^3) + (Pi^2*(2024 + 7326*S^2 + 1376*S^4 + 1271*S^6 + 360*S^8 - 133*S^10))/(27*S^3*(1 + S^2)^2) + (6272*HPL[{3, 1}, -S^2])/(3*S^3) + (12544*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (224*(55 + 194*S^2 + 181*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-601*Pi^4)/(45*S^3) - ((1 + S^2)*(248381 + 24079*S^2 + 22409*S^4))/(243*S^3) + (Pi^2*(-8483 - 27454*S^2 - 35300*S^4 - 9422*S^6 - 6175*S^8 - 1154*S^10))/(54*S^3*(1 + S^2)^2) + (172*HPL[{4}, -S^2])/(3*S^3) + (4*(1023 + 3614*S^2 + 3375*S^4 + 186*S^6 + 372*S^8 + 186*S^10)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (3136*HPL[{3, 1}, -S^2])/(3*S^3) - (6272*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(143 + 586*S^2 + 593*S^4 + 26*S^6 + 52*S^8 + 26*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + ((-838*Pi^2)/(9*S^3) + (-27221 - 84802*S^2 - 97556*S^4 - 24908*S^6 - 13801*S^8 - 1508*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(1 + S^2)*(-105143 + 4577*S^2 + 1318*S^4))/(1944*S^3) - ((1 + S^2)*(483629 + 3776*S^2 + 10001*S^4))/(972*S^3) + (Pi^4*(-2816 + 30746*S^2 + 51751*S^4 - 512*S^6 - 1024*S^8 - 512*S^10))/(1620*S^3*(1 + S^2)^2) + ((-826*Pi^2)/(9*S^3) + (-6875 - 21868*S^2 - 27848*S^4 - 7232*S^6 - 4561*S^8 - 776*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] - (113*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (328*HPL[{5}, -S^2])/(3*S^3) + ((-2428*Pi^2)/(9*S^3) - (2*(4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (3416*HPL[{3, 2}, -S^2])/(3*S^3) + (10280*HPL[{4, 1}, -S^2])/(3*S^3) + (1568*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (12544*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-862*Pi^2)/(9*S^3) - (2*(3460 + 10998*S^2 + 13972*S^4 + 3637*S^6 + 2304*S^8 + 397*S^10))/(9*S^3*(1 + S^2)^2))*Zeta[3] - (1444*Zeta[5])/(3*S^3)) - (644*Zeta[7])/S^3)) + HPL[{0}, S^2]*((-665381865 - 26756985*S^2 - 55110542*S^4)/(1259712*S) + (Pi^2*(-30260814 - 1979115*S^2 - 1458425*S^4))/(419904*S) + (Pi^4*(-5832954 - 581157*S^2 + 217568*S^4))/(699840*S) + (Pi^6*(-1964526 - 7369560*S^2 - 1624597*S^4 - 761492*S^6 - 60163*S^8))/(2449440*S*(1 + S^2)^2) - (8*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)^2) - (8*HPL[{1}, -S^2]^8)/(9*S^3) + ((11*Pi^2)/(27*S^3) + (279 - 11448*S^2 - 30393*S^4 - 11645*S^6 - 7702*S^8 - 1979*S^10)/(324*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^3 - (5*HPL[{2}, -S^2]^4)/(12*S^3) + HPL[{1}, -S^2]^6*((-241*Pi^2)/(81*S^3) + (-655 - 2020*S^2 - 3046*S^4 - 724*S^6 - 475*S^8 - 88*S^10)/(54*S^3*(1 + S^2)^2) - (100*HPL[{2}, -S^2])/(9*S^3)) + ((-7*Pi^2)/(6*S^3) + (-547 - 734*S^2 + 191*S^4 + 160*S^6 - 256*S^8 - 182*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{3}, -S^2]^2 + (41*HPL[{4}, -S^2]^2)/(3*S^3) + ((-70*Pi^2)/(9*S^3) + (150 - 36*S^2 - 831*S^4 - 62*S^6 + 8*S^8 + 82*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{6}, -S^2] + ((2625 + 4446*S^2 + 1419*S^4 + 44*S^6 + 88*S^8 + 44*S^10)*HPL[{7}, -S^2])/(18*S^3*(1 + S^2)^2) - (175*HPL[{8}, -S^2])/S^3 + ((4*Pi^2)/(3*S^3) + (-427 + 11398*S^2 + 31892*S^4 + 11697*S^6 + 7539*S^8 + 1797*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2]^2 - (20*HPL[{3, 1}, -S^2]^2)/(3*S^3) + (Pi^2/(6*S^3) + (-32 - 41*S^2 - 72*S^4 - 222*S^6 - 213*S^8)/(54*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((536 + 994*S^2 + 419*S^4 + 18*S^6 + 36*S^8 + 18*S^10)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)^2) + ((7*Pi^2)/(3*S^3) + (271 + 1934*S^2 + 4006*S^4 - 420*S^6 - 2211*S^8 - 1392*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{5, 1}, -S^2] + ((1601 + 2950*S^2 + 1223*S^4 + 42*S^6 + 84*S^8 + 42*S^10)*HPL[{5, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((2734 + 5426*S^2 + 2671*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*HPL[{6, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*HPL[{6, 2}, -S^2])/S^3 + (76*HPL[{7, 1}, -S^2])/S^3 - (136*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((-2*Pi^2)/(3*S^3) + (-337 - 54*S^2 - 27*S^4 + 6*S^6)/(54*S^3))*HPL[{3, 1, 2}, -S^2] + ((82*Pi^2)/(9*S^3) + (779 - 46520*S^2 - 122044*S^4 - 46682*S^6 - 30823*S^8 - 7910*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 2, 1}, -S^2] + (5*(11 + 310*S^2 + 443*S^4 + 70*S^6 + 140*S^8 + 70*S^10)*HPL[{3, 2, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + (8*(100 + 482*S^2 + 523*S^4 + 68*S^6 + 136*S^8 + 68*S^10)*HPL[{3, 3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (32*HPL[{3, 3, 2}, -S^2])/(3*S^3) + ((298*Pi^2)/(9*S^3) - (2*(-917 + 34817*S^2 + 92836*S^4 + 35211*S^6 + 22869*S^8 + 5700*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{4, 1, 1}, -S^2] + ((831 + 3918*S^2 + 4215*S^4 + 562*S^6 + 1124*S^8 + 562*S^10)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) - (64*HPL[{4, 1, 3}, -S^2])/(3*S^3) + ((3075 + 13014*S^2 + 13371*S^4 + 1642*S^6 + 3284*S^8 + 1642*S^10)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (35*HPL[{4, 2, 2}, -S^2])/(3*S^3) - (128*HPL[{4, 3, 1}, -S^2])/(3*S^3) + (4*(540 + 2186*S^2 + 2199*S^4 + 272*S^6 + 544*S^8 + 272*S^10)*HPL[{5, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (58*HPL[{5, 1, 2}, -S^2])/(3*S^3) - (538*HPL[{5, 2, 1}, -S^2])/(3*S^3) - (1480*HPL[{6, 1, 1}, -S^2])/(3*S^3) - (8*(-2063 - 6250*S^2 - 5249*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-272*Pi^2)/(9*S^3) + (2*(-1081 + 22984*S^2 + 63404*S^4 + 23840*S^6 + 15109*S^8 + 3608*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1, 1}, -S^2] + (2*(-25313 - 77026*S^2 - 64913*S^4 + 246*S^6 + 492*S^8 + 246*S^10)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + (2*(-25313 - 77026*S^2 - 64913*S^4 + 246*S^6 + 492*S^8 + 246*S^10)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*HPL[{3, 1, 2, 2}, -S^2])/S^3 + (2*(-50069 - 152026*S^2 - 127901*S^4 + 702*S^6 + 1404*S^8 + 702*S^10)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*HPL[{3, 2, 1, 2}, -S^2])/S^3 - (284*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3) - (272*HPL[{3, 3, 1, 1}, -S^2])/S^3 + (4*(-74519 - 226594*S^2 - 190853*S^4 + 1090*S^6 + 2180*S^8 + 1090*S^10)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (4*HPL[{4, 1, 1, 2}, -S^2])/S^3 - (268*HPL[{4, 1, 2, 1}, -S^2])/S^3 - (812*HPL[{4, 2, 1, 1}, -S^2])/S^3 - (4936*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((488*Pi^2)/(9*S^3) - (4*(-743 + 23588*S^2 + 63733*S^4 + 23972*S^6 + 15256*S^8 + 3686*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (16*(2173 + 6698*S^2 + 5701*S^4 + 12*S^6 + 24*S^8 + 12*S^10)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (16*(2173 + 6698*S^2 + 5701*S^4 + 12*S^6 + 24*S^8 + 12*S^10)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (608*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3) - (608*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 + (16*(10731 + 33324*S^2 + 28524*S^4 + 97*S^6 + 194*S^8 + 97*S^10)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1200*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 + (6032*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) + (2416*HPL[{3, 1, 2, 1, 1}, -S^2])/S^3 + (15152*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) + (15264*HPL[{4, 1, 1, 1, 1}, -S^2])/S^3 - (160*(-150 - 450*S^2 - 375*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (1664*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + (960*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((Pi^2*(20046 + 6717*S^2 + 14078*S^4))/(1944*S) + (545898 + 150159*S^2 + 180436*S^4)/(11664*S) + (Pi^4*(458 + 687*S^2 + 204*S^4 + 408*S^6 + 204*S^8))/(360*S*(1 + S^2)^2))*Zeta[3] + ((-264 - 702*S^2 - 223*S^4 - 98*S^6 - 7*S^8)*Zeta[3]^2)/(27*S*(1 + S^2)^2) + HPL[{2, 1, 1, 1}, -S^2]*((180337 + 37776*S^2 + 16923*S^4 - 2244*S^6)/(81*S^3) - (2*Pi^2*(-5559 - 17598*S^2 - 15279*S^4 + 62*S^6 + 124*S^8 + 62*S^10))/(27*S^3*(1 + S^2)^2) - (1328*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*((-6157 - 5952*S^2 - 11316*S^4 - 22980*S^6)/(324*S^3) + (Pi^2*(-653 - 2446*S^2 - 2363*S^4 - 382*S^6 - 764*S^8 - 382*S^10))/(54*S^3*(1 + S^2)^2) - (20*Zeta[3])/(3*S^3)) + HPL[{3, 2}, -S^2]*((-9257 - 5685*S^2 - 3939*S^4 - 7655*S^6)/(324*S^3) + (Pi^2*(-325 - 1010*S^2 - 865*S^4 - 98*S^6 - 196*S^8 - 98*S^10))/(36*S^3*(1 + S^2)^2) + (20*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^5*(-((1 + S^2)*(36455 + 5557*S^2 + 3812*S^4))/(972*S^3) + (Pi^2*(-5687 - 25834*S^2 - 27377*S^4 - 1034*S^6 - 2068*S^8 - 1034*S^10))/(810*S^3*(1 + S^2)^2) - (25*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)^2) + (68*HPL[{3}, -S^2])/(45*S^3) + (200*HPL[{2, 1}, -S^2])/(3*S^3) + (332*Zeta[3])/(45*S^3)) + HPL[{5}, -S^2]*((-1830 - 4368*S^2 + 204*S^4 + 1319*S^6)/(162*S^3) + (Pi^2*(76 + 14*S^2 - 131*S^4 + S^6 + 2*S^8 + S^10))/(27*S^3*(1 + S^2)^2) + (82*HPL[{2, 1}, -S^2])/(3*S^3) + (86*Zeta[3])/(3*S^3)) + HPL[{2, 2, 1}, -S^2]*((-173203 - 35532*S^2 - 21195*S^4 - 3508*S^6)/(162*S^3) - (2*Pi^2*(2660 + 8626*S^2 + 7619*S^4 + 17*S^6 + 34*S^8 + 17*S^10))/(27*S^3*(1 + S^2)^2) + (224*Zeta[3])/S^3) + HPL[{3, 1, 1}, -S^2]*((-528097 - 110022*S^2 - 59793*S^4 - 4534*S^6)/(162*S^3) + (Pi^2*(-16333 - 52370*S^2 - 45889*S^4 - 12*S^6 - 24*S^8 - 12*S^10))/(27*S^3*(1 + S^2)^2) + (688*Zeta[3])/S^3) + HPL[{4}, -S^2]*((-157*Pi^4)/(1080*S^3) + (-23295 - 87456*S^2 - 5718*S^4 + 32230*S^6)/(3888*S^3) + (Pi^2*(217 - 208*S^2 - 1613*S^4 - 276*S^6 + 150*S^8 + 198*S^10))/(216*S^3*(1 + S^2)^2) + (2*(175 + 374*S^2 + 211*S^4 + 10*S^6 + 20*S^8 + 10*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (74*HPL[{3, 1}, -S^2])/(3*S^3) + (28*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(-109 - 206*S^2 - 91*S^4 + 5*S^6 + 10*S^8 + 5*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{2, 1, 1}, -S^2]*((12*Pi^4)/(5*S^3) + (-31094 - 544935*S^2 - 50412*S^4 - 36803*S^6)/(486*S^3) + (Pi^2*(861 - 28584*S^2 - 83298*S^4 - 28748*S^6 - 17989*S^8 - 4214*S^10))/(162*S^3*(1 + S^2)^2) + (8*(-5 + 72*S^2 + 118*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*Zeta[3])/(3*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]^2*((7*Pi^4)/(108*S^3) + (24820 - 498261*S^2 - 59628*S^4 - 33163*S^6)/(3888*S^3) + (Pi^2*(1393 - 26974*S^2 - 82451*S^4 - 28384*S^6 - 18380*S^8 - 4408*S^10))/(1296*S^3*(1 + S^2)^2) + (5*(1 + 26*S^2 + 37*S^4 + 6*S^6 + 12*S^8 + 6*S^10)*HPL[{3}, -S^2])/(12*S^3*(1 + S^2)^2) - (5*HPL[{4}, -S^2])/(6*S^3) + ((2063 + 6250*S^2 + 5249*S^4 - 38*S^6 - 76*S^8 - 38*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (34*HPL[{3, 1}, -S^2])/(3*S^3) + (76*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-4 + 238*S^2 + 365*S^4 + 45*S^6 + 90*S^8 + 45*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3, 1}, -S^2]*((-149*Pi^4)/(135*S^3) + (29511 + 544110*S^2 + 48066*S^4 + 34588*S^6)/(972*S^3) + (Pi^2*(-1115 + 28172*S^2 + 83062*S^4 + 28734*S^6 + 18093*S^8 + 4254*S^10))/(324*S^3*(1 + S^2)^2) + (128*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(-83 + 350*S^2 + 691*S^4 + 84*S^6 + 168*S^8 + 84*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{1}, -S^2]^4*((-4061*Pi^4)/(1080*S^3) - ((1 + S^2)*(574261 + 64709*S^2 + 46564*S^4))/(5832*S^3) + (Pi^2*(-35869 - 107852*S^2 - 177124*S^4 - 39622*S^6 - 26015*S^8 - 4774*S^10))/(1944*S^3*(1 + S^2)^2) + ((-20*Pi^2)/S^3 + (-7103 - 21451*S^2 - 31403*S^4 - 7355*S^6 - 4540*S^8 - 740*S^10)/(81*S^3*(1 + S^2)^2))*HPL[{2}, -S^2] - (392*HPL[{2}, -S^2]^2)/(9*S^3) + ((77 + 358*S^2 + 383*S^4 + 14*S^6 + 28*S^8 + 14*S^10)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)^2) - (46*HPL[{4}, -S^2])/(9*S^3) + (125*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (500*HPL[{3, 1}, -S^2])/(3*S^3) - (1000*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((473 + 1942*S^2 + 1967*S^4 + 86*S^6 + 172*S^8 + 86*S^10)*Zeta[3])/(27*S^3*(1 + S^2)^2)) + ((8874 + 5841*S^2 + 8368*S^4)/(324*S) + (Pi^2*(54 + 81*S^2 + 14*S^4 + 28*S^6 + 14*S^8))/(6*S*(1 + S^2)^2))*Zeta[5] + HPL[{2, 1}, -S^2]*((Pi^2*(218615 + 46542*S^2 + 20532*S^4 - 970*S^6))/(1944*S^3) + (3631627 + 719166*S^2 + 228585*S^4 + 6492*S^6)/(5832*S^3) + (Pi^4*(48694 + 162038*S^2 + 145669*S^4 - 42*S^6 - 84*S^8 - 42*S^10))/(3240*S^3*(1 + S^2)^2) - (2*(4371 + 13446*S^2 + 11427*S^4 + 26*S^6 + 52*S^8 + 26*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (256*HPL[{3, 2}, -S^2])/(3*S^3) + (228*HPL[{4, 1}, -S^2])/S^3 - (8*(2173 + 6698*S^2 + 5701*S^4 + 12*S^6 + 24*S^8 + 12*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (304*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (160*HPL[{3, 1, 1}, -S^2])/S^3 + (272*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-190*Pi^2)/(9*S^3) + (-2004 - 4410*S^2 - 5523*S^4 - 670*S^6 - 545*S^8 - 40*S^10)/(27*S^3*(1 + S^2)^2))*Zeta[3] - (260*Zeta[5])/(3*S^3)) + HPL[{3}, -S^2]*((Pi^2*(-8271 - 6678*S^2 + 4770*S^4 + 8462*S^6))/(3888*S^3) + (-115765 - 289798*S^2 - 4561*S^4 + 53506*S^6)/(7776*S^3) + (Pi^4*(-3479 - 8758*S^2 - 6179*S^4 + 678*S^6 + 1356*S^8 + 678*S^10))/(6480*S^3*(1 + S^2)^2) + ((-268 - 506*S^2 - 223*S^4 - 16*S^6 - 32*S^8 - 16*S^10)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)^2) - (82*HPL[{5}, -S^2])/(3*S^3) + ((-52*Pi^2)/(9*S^3) + (155 - 308*S^2 - 3346*S^4 - 82*S^6 + 559*S^8 + 494*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + ((-359 - 1126*S^2 - 971*S^4 - 90*S^6 - 180*S^8 - 90*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (16*HPL[{3, 2}, -S^2])/(3*S^3) + (112*HPL[{4, 1}, -S^2])/(3*S^3) + (2*(245 + 946*S^2 + 929*S^4 + 102*S^6 + 204*S^8 + 102*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (256*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (688*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (144*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((8*Pi^2)/(3*S^3) + (80 + 166*S^2 + 215*S^4 + 236*S^6 + 487*S^8 + 236*S^10)/(54*S^3*(1 + S^2)^2))*Zeta[3] + (76*Zeta[5])/(3*S^3)) + HPL[{1}, -S^2]^3*(-(Pi^2*(1 + S^2)*(36771 + 5729*S^2 + 3738*S^4))/(972*S^3) - ((1 + S^2)*(1865477 + 155803*S^2 + 126326*S^4))/(8748*S^3) + (Pi^4*(-24101 - 121300*S^2 - 133748*S^4 - 4382*S^6 - 8764*S^8 - 4382*S^10))/(4860*S^3*(1 + S^2)^2) - (196*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)^2) + ((22*Pi^2)/(27*S^3) + (2*(-346 - 536*S^2 + 410*S^4 + 311*S^6 + 580*S^8 + 257*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-319 - 1190*S^2 - 1147*S^4 - 58*S^6 - 116*S^8 - 58*S^10)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)^2) - (92*HPL[{5}, -S^2])/(9*S^3) + ((80*Pi^2)/S^3 + (4*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(81*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (4*(231 + 962*S^2 + 981*S^4 + 42*S^6 + 84*S^8 + 42*S^10)*HPL[{3, 1}, -S^2])/(3*S^3*(1 + S^2)^2) - (304*HPL[{3, 2}, -S^2])/(9*S^3) - (728*HPL[{4, 1}, -S^2])/(9*S^3) - (500*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (6272*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (18544*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (4000*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((188*Pi^2)/(27*S^3) + (2321 + 7960*S^2 + 13184*S^4 + 3716*S^6 + 2911*S^8 + 764*S^10)/(81*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(91373 + 11923*S^2 + 7142*S^4))/(486*S^3) + (Pi^2*(-5027 - 23014*S^2 - 24467*S^4 - 914*S^6 - 1828*S^8 - 914*S^10))/(162*S^3*(1 + S^2)^2) + (152*HPL[{3}, -S^2])/(9*S^3) + (3136*HPL[{2, 1}, -S^2])/(9*S^3) + (328*Zeta[3])/(9*S^3)) + (260*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]^2*((-248987*Pi^6)/(136080*S^3) - (Pi^2*(1 + S^2)*(465025 + 53423*S^2 + 35968*S^4))/(7776*S^3) - ((1 + S^2)*(12649645 + 794066*S^2 + 772759*S^4))/(34992*S^3) + (Pi^4*(-311507 - 892918*S^2 - 1610936*S^4 - 323144*S^6 - 203167*S^8 - 32372*S^10))/(38880*S^3*(1 + S^2)^2) + ((-551*Pi^2)/(18*S^3) + (-4537 - 14056*S^2 - 21304*S^4 - 5140*S^6 - 3427*S^8 - 664*S^10)/(36*S^3*(1 + S^2)^2))*HPL[{2}, -S^2]^2 - (118*HPL[{2}, -S^2]^3)/(3*S^3) + (4*HPL[{3}, -S^2]^2)/(3*S^3) + ((-40*Pi^2)/(9*S^3) + (-3181 - 8804*S^2 - 10120*S^4 - 1858*S^6 - 371*S^8 + 302*S^10)/(108*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((-187 - 650*S^2 - 601*S^4 - 34*S^6 - 68*S^8 - 34*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) - (73*HPL[{6}, -S^2])/(3*S^3) + (1568*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((120*Pi^2)/S^3 + (14303 + 43240*S^2 + 63092*S^4 + 14798*S^6 + 9121*S^8 + 1478*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] - (38*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)^2) + ((-935 - 4054*S^2 - 4211*S^4 - 170*S^6 - 340*S^8 - 170*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (36*HPL[{5, 1}, -S^2])/S^3 + ((-240*Pi^2)/S^3 - (4*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (4*(6391 + 26690*S^2 + 27253*S^4 + 1162*S^6 + 2324*S^8 + 1162*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (944*HPL[{3, 2, 1}, -S^2])/S^3 - (8680*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (500*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (2000*HPL[{3, 1, 1, 1}, -S^2])/S^3 - (4000*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + (((1 + S^2)*(11611 + 4811*S^2 + 4366*S^4))/(324*S^3) + (Pi^2*(209 + 794*S^2 + 773*S^4 + 38*S^6 + 76*S^8 + 38*S^10))/(18*S^3*(1 + S^2)^2))*Zeta[3] - (34*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(91373 + 11923*S^2 + 7142*S^4))/(162*S^3) + (Pi^2*(5027 + 23014*S^2 + 24467*S^4 + 914*S^6 + 1828*S^8 + 914*S^10))/(54*S^3*(1 + S^2)^2) - (328*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*(((1 + S^2)*(-7841 + 725*S^2 + 3112*S^4))/(324*S^3) + (Pi^2*(77 + 286*S^2 + 275*S^4 + 14*S^6 + 28*S^8 + 14*S^10))/(54*S^3*(1 + S^2)^2) - (152*HPL[{2, 1}, -S^2])/(3*S^3) + (8*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-2155*Pi^4)/(216*S^3) - ((1 + S^2)*(596135 + 57307*S^2 + 34202*S^4))/(1944*S^3) + (Pi^2*(-17323 - 50804*S^2 - 80989*S^4 - 17836*S^6 - 10970*S^8 - 1762*S^10))/(324*S^3*(1 + S^2)^2) + (19*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)^2) - (8*HPL[{4}, -S^2])/(3*S^3) + (392*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (1568*HPL[{3, 1}, -S^2])/(3*S^3) - (3136*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (41*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + (2*(209 + 808*S^2 + 794*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) + HPL[{2}, -S^2]*((437*Pi^6)/(4536*S^3) + (-3107580 - 23613585*S^2 - 1496967*S^4 - 1121645*S^6)/(69984*S^3) + (Pi^2*(-22479 - 657786*S^2 - 57117*S^4 - 33262*S^6))/(11664*S^3) + (Pi^4*(6169 - 112738*S^2 - 374189*S^4 - 111265*S^6 - 60002*S^8 - 10069*S^10))/(19440*S^3*(1 + S^2)^2) + (4*HPL[{3}, -S^2]^2)/(3*S^3) + ((43*Pi^2)/(18*S^3) + (669 + 1035*S^2 + 66*S^4 + 88*S^6 + 575*S^8 + 331*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4}, -S^2] + ((293 + 574*S^2 + 275*S^4 + 32*S^6 + 64*S^8 + 32*S^10)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)^2) + (80*HPL[{6}, -S^2])/(3*S^3) - (76*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((8*Pi^2)/(9*S^3) + (-713 + 23204*S^2 + 64132*S^4 + 23372*S^6 + 14845*S^8 + 3464*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3, 1}, -S^2] + ((-41 - 802*S^2 - 1121*S^4 - 182*S^6 - 364*S^8 - 182*S^10)*HPL[{3, 2}, -S^2])/(18*S^3*(1 + S^2)^2) + ((-395 - 1918*S^2 - 2087*S^4 - 290*S^6 - 580*S^8 - 290*S^10)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - HPL[{4, 2}, -S^2]/S^3 - (30*HPL[{5, 1}, -S^2])/S^3 + ((-8*Pi^2)/(3*S^3) - (2*(-427 + 11398*S^2 + 31892*S^4 + 11697*S^6 + 7539*S^8 + 1797*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1}, -S^2] + (4*(-2063 - 6250*S^2 - 5249*S^4 + 38*S^6 + 76*S^8 + 38*S^10)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (2*(-12623 - 38446*S^2 - 32423*S^4 + 126*S^6 + 252*S^8 + 126*S^10)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (40*HPL[{3, 2, 1}, -S^2])/S^3 - (92*HPL[{4, 1, 1}, -S^2])/S^3 + (8*(2173 + 6698*S^2 + 5701*S^4 + 12*S^6 + 24*S^8 + 12*S^10)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (3520*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (272*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((1999 + 13086*S^2 + 4842*S^4 + 4838*S^6)/(324*S^3) + (Pi^2*(-60 + 426*S^2 + 759*S^4 + 104*S^6 + 208*S^8 + 104*S^10))/(54*S^3*(1 + S^2)^2))*Zeta[3] + HPL[{2, 1}, -S^2]*((173203 + 35532*S^2 + 21195*S^4 + 3508*S^6)/(324*S^3) + (Pi^2*(2660 + 8626*S^2 + 7619*S^4 + 17*S^6 + 34*S^8 + 17*S^10))/(27*S^3*(1 + S^2)^2) - (112*Zeta[3])/S^3) + HPL[{3}, -S^2]*((4093 + 2649*S^2 + 1920*S^4 + 4049*S^6)/(324*S^3) + (Pi^2*(455 + 1450*S^2 + 1265*S^4 + 142*S^6 + 284*S^8 + 142*S^10))/(108*S^3*(1 + S^2)^2) - (128*HPL[{2, 1}, -S^2])/(3*S^3) - (8*Zeta[3])/(3*S^3)) + ((-140 + 38*S^2 + 337*S^4 + 54*S^6 + 108*S^8 + 54*S^10)*Zeta[5])/(9*S^3*(1 + S^2)^2)) - (5*(-30 - 45*S^2 + 4*S^4 + 8*S^6 + 4*S^8)*Zeta[7])/(3*S*(1 + S^2)^2) + HPL[{1}, -S^2]*(-(Pi^4*(1 + S^2)*(309865 + 51693*S^2 + 16636*S^4))/(38880*S^3) - (Pi^2*(1 + S^2)*(4482697 + 390362*S^2 + 295213*S^4))/(69984*S^3) - ((1 + S^2)*(179723545 + 8757449*S^2 + 11329918*S^4))/(419904*S^3) + (Pi^6*(-366751 - 2227424*S^2 - 2607634*S^4 - 66682*S^6 - 133364*S^8 - 66682*S^10))/(408240*S^3*(1 + S^2)^2) - (59*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2}, -S^2]^3)/(18*S^3*(1 + S^2)^2) + ((11 + 38*S^2 + 35*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3}, -S^2]^2)/(6*S^3*(1 + S^2)^2) + ((-46*Pi^2)/(9*S^3) + (-842 - 2257*S^2 - 2507*S^4 - 383*S^6 + 20*S^8 + 139*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{5}, -S^2] + ((-352 - 1142*S^2 - 1009*S^4 - 64*S^6 - 128*S^8 - 64*S^10)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)^2) - (134*HPL[{7}, -S^2])/(3*S^3) + (392*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)^2) + ((-10*Pi^2)/S^3 + (-689 - 2788*S^2 - 5360*S^4 - 1472*S^6 - 1339*S^8 - 392*S^10)/(27*S^3*(1 + S^2)^2))*HPL[{3, 2}, -S^2] + ((-190*Pi^2)/(9*S^3) + (-953 - 7924*S^2 - 22040*S^4 - 6974*S^6 - 7663*S^8 - 2654*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{4, 1}, -S^2] + ((11 + 2*S^6)*HPL[{4, 2}, -S^2])/(6*S^3) - (26*HPL[{4, 3}, -S^2])/(3*S^3) + (4*(121 + 404*S^2 + 364*S^4 + 22*S^6 + 44*S^8 + 22*S^10)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (28*HPL[{5, 2}, -S^2])/S^3 - (14*HPL[{6, 1}, -S^2])/(3*S^3) + ((-2204*Pi^2)/(9*S^3) - (2*(4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10))/(9*S^3*(1 + S^2)^2))*HPL[{2, 2, 1}, -S^2] + ((-6568*Pi^2)/(9*S^3) - (2*(41525 + 127576*S^2 + 190916*S^4 + 45638*S^6 + 29683*S^8 + 5462*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{3, 1, 1}, -S^2] - (236*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 2, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (80*HPL[{3, 2, 2}, -S^2])/S^3 + (752*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (2*(12001 + 50042*S^2 + 51061*S^4 + 2182*S^6 + 4364*S^8 + 2182*S^10)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) + (752*HPL[{4, 1, 2}, -S^2])/(3*S^3) + (2288*HPL[{4, 2, 1}, -S^2])/(3*S^3) + (4424*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((480*Pi^2)/S^3 + (8*(7103 + 21451*S^2 + 31403*S^4 + 7355*S^6 + 4540*S^8 + 740*S^10))/(27*S^3*(1 + S^2)^2))*HPL[{2, 1, 1, 1}, -S^2] + (1888*HPL[{2, 2, 2, 1}, -S^2])/S^3 + (8*(231 + 962*S^2 + 981*S^4 + 42*S^6 + 84*S^8 + 42*S^10)*HPL[{3, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)^2) - (17600*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (17600*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (34592*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (103408*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (1000*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)^2) + (12544*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (12544*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (21088*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 + (8000*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((229*Pi^4)/(180*S^3) + ((1 + S^2)*(67469 + 26395*S^2 + 26420*S^4))/(1944*S^3) + (Pi^2*(2837 + 10282*S^2 + 16274*S^4 + 4970*S^6 + 3991*S^8 + 1082*S^10))/(324*S^3*(1 + S^2)^2))*Zeta[3] - (2*(44 + 190*S^2 + 197*S^4 + 8*S^6 + 16*S^8 + 8*S^10)*Zeta[3]^2)/(9*S^3*(1 + S^2)^2) + HPL[{3, 1}, -S^2]*(((1 + S^2)*(91141 + 12581*S^2 + 6586*S^4))/(162*S^3) + (Pi^2*(847 + 3854*S^2 + 4087*S^4 + 154*S^6 + 308*S^8 + 154*S^10))/(9*S^3*(1 + S^2)^2) - (344*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*(((1 + S^2)*(-10537 - 1520*S^2 + 1865*S^4))/(324*S^3) + (Pi^2*(-187 - 694*S^2 - 667*S^4 - 34*S^6 - 68*S^8 - 34*S^10))/(36*S^3*(1 + S^2)^2) + (16*HPL[{2, 1}, -S^2])/(3*S^3) + (8*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(41650 + 6653*S^2 + 4849*S^4))/(324*S^3) + (Pi^2*(-1309 - 5924*S^2 - 6268*S^4 - 238*S^6 - 476*S^8 - 238*S^10))/(54*S^3*(1 + S^2)^2) + (10*HPL[{3}, -S^2])/S^3 + (236*HPL[{2, 1}, -S^2])/S^3 + (82*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*(-((1 + S^2)*(91373 + 11923*S^2 + 7142*S^4))/(81*S^3) + (Pi^2*(-5027 - 23014*S^2 - 24467*S^4 - 914*S^6 - 1828*S^8 - 914*S^10))/(27*S^3*(1 + S^2)^2) + (656*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((2155*Pi^4)/(108*S^3) + ((1 + S^2)*(596135 + 57307*S^2 + 34202*S^4))/(972*S^3) + (Pi^2*(17323 + 50804*S^2 + 80989*S^4 + 17836*S^6 + 10970*S^8 + 1762*S^10))/(162*S^3*(1 + S^2)^2) - (3136*HPL[{3, 1}, -S^2])/(3*S^3) - (6272*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (82*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + HPL[{3}, -S^2]*((-5*Pi^4)/(18*S^3) + ((1 + S^2)*(-82027 + 3145*S^2 + 15614*S^4))/(1944*S^3) + (Pi^2*(-417 - 694*S^2 - 48*S^4 + 246*S^6 + 527*S^8 + 246*S^10))/(108*S^3*(1 + S^2)^2) + (10*HPL[{4}, -S^2])/(3*S^3) - (38*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (136*HPL[{3, 1}, -S^2])/(3*S^3) + (304*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*Zeta[3])/(9*S^3*(1 + S^2)^2)) + ((9*Pi^2)/S^3 + (317 + 1550*S^2 + 3188*S^4 + 1124*S^6 + 1073*S^8 + 344*S^10)/(18*S^3*(1 + S^2)^2))*Zeta[5] + HPL[{2}, -S^2]*(-(Pi^2*(1 + S^2)*(220807 + 29831*S^2 + 15922*S^4))/(3888*S^3) - ((1 + S^2)*(997519 + 71534*S^2 + 48181*S^4))/(2916*S^3) + (Pi^4*(-21362 - 107374*S^2 - 118337*S^4 - 3884*S^6 - 7768*S^8 - 3884*S^10))/(3240*S^3*(1 + S^2)^2) + ((5*Pi^2)/S^3 + (689 + 2788*S^2 + 5360*S^4 + 1472*S^6 + 1339*S^8 + 392*S^10)/(54*S^3*(1 + S^2)^2))*HPL[{3}, -S^2] + ((-77 - 250*S^2 - 221*S^4 - 14*S^6 - 28*S^8 - 14*S^10)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)^2) - (4*HPL[{5}, -S^2])/(3*S^3) + ((1102*Pi^2)/(9*S^3) + (4537 + 14056*S^2 + 21304*S^4 + 5140*S^6 + 3427*S^8 + 664*S^10)/(9*S^3*(1 + S^2)^2))*HPL[{2, 1}, -S^2] + (392*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (40*HPL[{3, 2}, -S^2])/S^3 - (376*HPL[{4, 1}, -S^2])/(3*S^3) - (784*(11 + 46*S^2 + 47*S^4 + 2*S^6 + 4*S^8 + 2*S^10)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)^2) - (944*HPL[{2, 2, 1}, -S^2])/S^3 + (8800*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (6272*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((91*Pi^2)/(9*S^3) + (343 + 1192*S^2 + 2077*S^4 + 598*S^6 + 490*S^8 + 136*S^10)/(9*S^3*(1 + S^2)^2))*Zeta[3] + (106*Zeta[5])/(3*S^3)) + (50*Zeta[7])/S^3));
E5wuvT=E5wuvT0F0+T*E5wuvT1F1*(F+1/F)+T^2*(E5wuvT2F0+E5wuvT2F2*(F^2+1/F^2))+T^3*(E5wuvT3F1*(F+1/F)+E5wuvT3F3*(F^3+1/F^3));
Et5uvwT1F1=(490*Pi^2*S)/3 + (3286*Pi^4*S)/135 + (17497*Pi^6*S)/5670 + (4301*Pi^8*S)/8100 + HPL[{0}, S^2]^8*(S/48 + ((1 + S^2)*HPL[{1}, -S^2])/(96*S)) + (20*(-1 + S^2)*HPL[{2}, -S^2]^4)/(9*S) + HPL[{0}, S^2]^7*((5*Pi^2*S)/864 + (5*(1 + S^2)*HPL[{1}, -S^2])/(144*S) + (5*(1 + S^2)*HPL[{1}, -S^2]^2)/(144*S) + (5*S*HPL[{2}, -S^2])/144) + HPL[{1}, -S^2]^7*((10*Pi^2*(1 + S^2))/(63*S) + (40*(1 + S^2)*HPL[{2}, -S^2])/(21*S)) - (4*(19 + 21*S^2)*HPL[{3}, -S^2]^3)/(9*S) + (2*(61 + 40*S^2)*HPL[{4}, -S^2]^2)/(3*S) + ((4*(375 + 233*S^2))/(3*S) + (Pi^2*(420 + 649*S^2))/(9*S))*HPL[{7}, -S^2] + (2*(1785 + 1954*S^2)*HPL[{8}, -S^2])/(3*S) + (2*(4116 + 3253*S^2)*HPL[{9}, -S^2])/(3*S) + (896*(1 + S^2)*HPL[{2, 1}, -S^2]^3)/(9*S) + (4*(-83 + 92*S^2)*HPL[{3, 1}, -S^2]^2)/(3*S) + ((Pi^2*(-151 - 33*S^2))/(9*S) - (4*(7 + 6*S^2))/S)*HPL[{4, 3}, -S^2] + ((Pi^2*(-431 - 152*S^2))/(9*S) - (2*(106 + 143*S^2))/(3*S))*HPL[{5, 2}, -S^2] + (2*(-17 + 8*S^2)*HPL[{5, 3}, -S^2])/(3*S) + (2*(295 + 396*S^2)*HPL[{5, 4}, -S^2])/(3*S) + ((-7*Pi^2*(160 + 133*S^2))/(9*S) - (2*(663 + 919*S^2))/(3*S))*HPL[{6, 1}, -S^2] - (10*(5 + 6*S^2)*HPL[{6, 2}, -S^2])/(3*S) + (2*(1173 + 1654*S^2)*HPL[{6, 3}, -S^2])/(3*S) - (2*(961 + 1176*S^2)*HPL[{7, 1}, -S^2])/(3*S) + (2*(2973 + 4117*S^2)*HPL[{7, 2}, -S^2])/(3*S) + (2*(1327 + 1874*S^2)*HPL[{8, 1}, -S^2])/S + (512*(-1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((5*Pi^2*(32 + 169*S^2))/(9*S) + (2*(159 + 949*S^2))/(3*S))*HPL[{3, 2, 2}, -S^2] + ((4*Pi^2*(69 + 632*S^2))/(9*S) + (8*(106 + 703*S^2))/(3*S))*HPL[{3, 3, 1}, -S^2] - (2*(62 + 51*S^2)*HPL[{3, 3, 2}, -S^2])/(3*S) + ((8*(98 + 711*S^2))/(3*S) + (Pi^2*(233 + 2575*S^2))/(9*S))*HPL[{4, 1, 2}, -S^2] + (4*(63 + 26*S^2)*HPL[{4, 1, 3}, -S^2])/(3*S) + ((104*(23 + 162*S^2))/(3*S) + (Pi^2*(605 + 7603*S^2))/(9*S))*HPL[{4, 2, 1}, -S^2] - (2*(55 + 82*S^2)*HPL[{4, 2, 2}, -S^2])/(3*S) + (10*(-1 + 4*S^2)*HPL[{4, 2, 3}, -S^2])/(3*S) + (4*(107 + 80*S^2)*HPL[{4, 3, 1}, -S^2])/(3*S) - (2*(330 + 307*S^2)*HPL[{4, 3, 2}, -S^2])/(3*S) - (4*(211 + 237*S^2)*HPL[{4, 4, 1}, -S^2])/(3*S) + ((2*Pi^2*(583 + 7825*S^2))/(9*S) + (4*(1379 + 8669*S^2))/(3*S))*HPL[{5, 1, 1}, -S^2] + (2*(70 + 31*S^2)*HPL[{5, 1, 2}, -S^2])/(3*S) + (4*(116 + 67*S^2)*HPL[{5, 1, 3}, -S^2])/(3*S) + (2*(910 + 811*S^2)*HPL[{5, 2, 1}, -S^2])/(3*S) - (2*(727 + 806*S^2)*HPL[{5, 2, 2}, -S^2])/(3*S) - (4*(382 + 563*S^2)*HPL[{5, 3, 1}, -S^2])/(3*S) + (4*(1596 + 1555*S^2)*HPL[{6, 1, 1}, -S^2])/(3*S) - (2*(1054 + 1301*S^2)*HPL[{6, 1, 2}, -S^2])/(3*S) - (2*(294 + 1181*S^2)*HPL[{6, 2, 1}, -S^2])/(3*S) + (80*(72 + 47*S^2)*HPL[{7, 1, 1}, -S^2])/(3*S) + ((-2216*(1 + S^2))/(3*S) - (8*Pi^2*(218 + 135*S^2))/(9*S))*HPL[{2, 2, 2, 1}, -S^2] + ((16*(389 + 176*S^2))/(3*S) + (4*Pi^2*(1301 + 352*S^2))/(9*S))*HPL[{3, 1, 1, 2}, -S^2] + ((16*(389 + 176*S^2))/(3*S) + (4*Pi^2*(1301 + 352*S^2))/(9*S))*HPL[{3, 1, 2, 1}, -S^2] - (14*(-1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/(3*S) + ((4*Pi^2*(2609 + 1162*S^2))/(9*S) + (8*(1609 + 1183*S^2))/(3*S))*HPL[{3, 2, 1, 1}, -S^2] - (14*(-1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/(3*S) - (2*(721 + 703*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(3*S) - (8*(39 + 371*S^2)*HPL[{3, 2, 2, 2}, -S^2])/(3*S) - (8*(194 + 1175*S^2)*HPL[{3, 2, 3, 1}, -S^2])/(3*S) - (16*(91 + 87*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S - (16*(95 + 588*S^2)*HPL[{3, 3, 1, 2}, -S^2])/(3*S) - (56*(94 + 513*S^2)*HPL[{3, 3, 2, 1}, -S^2])/(3*S) + ((8*Pi^2*(3869 + 1714*S^2))/(9*S) + (8*(4697 + 3435*S^2))/(3*S))*HPL[{4, 1, 1, 1}, -S^2] - (4*(-35 + 31*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(3*S) + (8*(1367 + 7286*S^2)*HPL[{4, 1, 1, 3}, -S^2])/(3*S) - (4*(1057 + 1075*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(3*S) + (2*(4693 + 24425*S^2)*HPL[{4, 1, 2, 2}, -S^2])/(3*S) + (8*(703 + 3647*S^2)*HPL[{4, 1, 3, 1}, -S^2])/S - (4*(3241 + 3163*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(3*S) + (2*(2869 + 14753*S^2)*HPL[{4, 2, 1, 2}, -S^2])/(3*S) + (2*(2821 + 14765*S^2)*HPL[{4, 2, 2, 1}, -S^2])/(3*S) + (8*(4139 + 21785*S^2)*HPL[{4, 3, 1, 1}, -S^2])/(3*S) - (8*(3415 + 3382*S^2)*HPL[{5, 1, 1, 1}, -S^2])/(3*S) + (4*(2769 + 14539*S^2)*HPL[{5, 1, 1, 2}, -S^2])/S + (4*(4609 + 24207*S^2)*HPL[{5, 1, 2, 1}, -S^2])/S + (4*(11073 + 58039*S^2)*HPL[{5, 2, 1, 1}, -S^2])/S + (16*(20727 + 108601*S^2)*HPL[{6, 1, 1, 1}, -S^2])/(3*S) + ((1136*(-1 + S^2))/S + (16*Pi^2*(-209 + 97*S^2))/(9*S))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((3408*(-1 + S^2))/S + (16*Pi^2*(-209 + 97*S^2))/(3*S))*HPL[{2, 2, 1, 1, 1}, -S^2] - (2848*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S) - (2848*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (2656*(-1 + S^2)*HPL[{2, 2, 2, 2, 1}, -S^2])/(3*S) + ((16*Pi^2*(-1017 + 722*S^2))/(9*S) + (16*(-943 + 1605*S^2))/(3*S))*HPL[{3, 1, 1, 1, 1}, -S^2] + (17080*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S) + (28472*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S) - (8*(-1117 + 221*S^2)*HPL[{3, 1, 1, 2, 2}, -S^2])/(3*S) + (34168*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S) - (8*(-1117 + 221*S^2)*HPL[{3, 1, 2, 1, 2}, -S^2])/(3*S) - (40*(-1 + S^2)*HPL[{3, 1, 2, 2, 1}, -S^2])/(3*S) + (32*(-1907 + 565*S^2)*HPL[{3, 1, 3, 1, 1}, -S^2])/(3*S) + (71192*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S) - (8*(-2113 + 1217*S^2)*HPL[{3, 2, 1, 1, 2}, -S^2])/(3*S) - (8008*(-1 + S^2)*HPL[{3, 2, 1, 2, 1}, -S^2])/(3*S) - (104*(271 + 73*S^2)*HPL[{3, 2, 2, 1, 1}, -S^2])/(3*S) - (32*(965 + 153*S^2)*HPL[{3, 3, 1, 1, 1}, -S^2])/S + (64*(3363 + 3365*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S) - (64*(-781 + 446*S^2)*HPL[{4, 1, 1, 1, 2}, -S^2])/(3*S) - (64*(-364 + 365*S^2)*HPL[{4, 1, 1, 2, 1}, -S^2])/(3*S) - (32*(2665 + 691*S^2)*HPL[{4, 1, 2, 1, 1}, -S^2])/(3*S) - (8704*(32 + 5*S^2)*HPL[{4, 2, 1, 1, 1}, -S^2])/(3*S) - (32*(17397 + 2623*S^2)*HPL[{5, 1, 1, 1, 1}, -S^2])/(3*S) + ((-10592*(1 + S^2))/(3*S) - (16*Pi^2*(473 + 278*S^2))/(9*S))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (7168*(1 + S^2)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(3*S) + (7168*(1 + S^2)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S - (64*(119 + 121*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S) - (64*(574 + 769*S^2)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(3*S) - (64*(1246 + 1441*S^2)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(3*S) - (64*(1694 + 1889*S^2)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(3*S) - (64*(1918 + 2113*S^2)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(3*S) - (64*(3374 + 3569*S^2)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(3*S) - (64*(3382 + 3577*S^2)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S + (5120*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S - (4160*(-1 + S^2)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S - (16640*(-1 + S^2)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S - (41600*(-1 + S^2)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S - (1280*(-69 + 61*S^2)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S - (10240*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((-8*Pi^2*S)/27 - (8*S*HPL[{0}, S^2]^2)/9 - (16*(1 + S^2)*HPL[{2}, -S^2])/(9*S))*Log[T]^7 + ((-116*S)/3 + (17*Pi^2*S)/3)*Zeta[3]^2 + 32*S*Zeta[3]^3 + HPL[{0}, S^2]^6*((37*S)/72 + (67*Pi^2*S)/288 + (5*(1 + S^2)*HPL[{1}, -S^2]^2)/(24*S) + (7*(1 + S^2)*HPL[{1}, -S^2]^3)/(54*S) + ((2 + 7*S^2)*HPL[{2}, -S^2])/(48*S) + HPL[{1}, -S^2]*((37*(1 + S^2))/(144*S) + (7*Pi^2*(1 + S^2))/(54*S) + (25*(1 + S^2)*HPL[{2}, -S^2])/(144*S)) + ((1 + S^2)*HPL[{3}, -S^2])/(48*S) - (11*HPL[{2, 1}, -S^2])/(36*S) + (25*S*Zeta[3])/36) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(-2 - 9*S^2))/(9*S) - (4*(1 + S^2))/S + (40*S*Zeta[3])/3) + Log[T]^6*((32*Pi^2*S)/27 + (26*S*HPL[{0}, S^2]^3)/27 + HPL[{0}, S^2]^2*((32*S)/9 + (10*(1 + S^2)*HPL[{1}, -S^2])/(3*S)) + (64*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{0}, S^2]*((26*Pi^2*S)/27 - (4*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + HPL[{1}, -S^2]*((10*Pi^2*(1 + S^2))/(9*S) + (40*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + (4*(3 + 29*S^2)*HPL[{3}, -S^2])/(9*S) - (128*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (128*S*Zeta[3])/9) + HPL[{2, 1, 1, 1}, -S^2]*((-4760*(1 + S^2))/(3*S) - (319*Pi^4*(19 + 7*S^2))/(135*S) - (4*Pi^2*(655 + 442*S^2))/(9*S) + (128*(-23 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^6*((17*Pi^2*(1 + S^2))/(27*S) + (68*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (20*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (20*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^5*((106*Pi^2*(1 + S^2))/(45*S) + (749*Pi^4*(1 + S^2))/(1350*S) + ((424*(1 + S^2))/(15*S) + (236*Pi^2*(1 + S^2))/(45*S))*HPL[{2}, -S^2] + (68*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{4}, -S^2])/(5*S) - (136*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (40*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (80*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (68*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{4, 2}, -S^2]*((Pi^2*(26 - 15*S^2))/(9*S) - (4*(-5 + 3*S^2))/S - (2*(9 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]^2*((-512*(-1 + S^2))/(3*S) - (2*Pi^2*(-111 + 200*S^2))/(9*S) - (112*(1 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{2, 2, 1}, -S^2]*((Pi^4*(5760 - 1327*S^2))/(270*S) - (1180*(-1 + S^2))/(3*S) - (2*Pi^2*(-491 + 214*S^2))/(9*S) + (16*(81 + 8*S^2)*Zeta[3])/(3*S)) + HPL[{5, 1}, -S^2]*((Pi^2*(-235 - 403*S^2))/(9*S) - (2*(321 + 517*S^2))/(3*S) + (4*(59 + 13*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1}, -S^2]*((Pi^4*(17698 - 71*S^2))/(270*S) + (20*(237 + S^2))/(3*S) + (2*Pi^2*(1651 + 16*S^2))/(9*S) + (8*(504 + 23*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]^2*((Pi^2*(1 - 14*S^2))/(9*S) - (2*(33 + 16*S^2))/(3*S) + (52*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(19 + 29*S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((Pi^4*(96 - 593*S^2))/(90*S) + (Pi^2*(-38 - 547*S^2))/(9*S) - (20*(1 + 60*S^2))/(3*S) - (16*(29 + 195*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(28 + 55*S^2)*Zeta[3])/(3*S)) + HPL[{3, 2, 1}, -S^2]*((1132*(1 + S^2))/(3*S) + (Pi^2*(414 + 727*S^2))/(9*S) + (8*(4 + 61*S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((Pi^4*(535 - 11581*S^2))/(540*S) - (4*Pi^2*(89 + 463*S^2))/(9*S) - (2*(159 + 749*S^2))/S - (16*(61 + 613*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*(23 + 84*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^3*((143*(1 + S^2))/(9*S) + (4*Pi^2*(13 + 23*S^2))/(27*S) + (2*(12 + 95*S^2)*HPL[{3}, -S^2])/(9*S) + (166*(-1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (2*(6 + 89*S^2)*Zeta[3])/(9*S)) + HPL[{5}, -S^2]*((2*Pi^2*(97 + 116*S^2))/(9*S) + (2*(528 + 233*S^2))/(3*S) + (Pi^4*(-74 + 1539*S^2))/(540*S) + (2*(-109 + 73*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(-68 + 19*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (4*(-67 + 141*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (2*(31 + 89*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1, 1}, -S^2]*((-16*(205 + 209*S^2))/(3*S) - (4*Pi^2*(296 + 493*S^2))/(9*S) - (32*(3 + 100*S^2)*Zeta[3])/(3*S)) + HPL[{6}, -S^2]*((2*(201 + 233*S^2))/S + (Pi^2*(338 + 395*S^2))/(9*S) - (2*(152 + 43*S^2)*HPL[{2, 1}, -S^2])/S - (2*(200 + 187*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1, 1, 1}, -S^2]*((2208*(1 + S^2))/S + (64*Pi^2*(37 + 61*S^2))/(9*S) + (32*(7 + 202*S^2)*Zeta[3])/(3*S)) + HPL[{4, 1, 1}, -S^2]*((8*(537 + 545*S^2))/(3*S) + (2*Pi^2*(779 + 1285*S^2))/(9*S) + (8*(19 + 563*S^2)*Zeta[3])/(3*S)) + Log[T]^5*((-122*Pi^2*S)/27 - (4459*Pi^4*S)/4050 - (277*S*HPL[{0}, S^2]^4)/270 + HPL[{0}, S^2]^3*((-76*S)/27 - (26*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + ((-244*(1 + S^2))/(9*S) - (2*Pi^2*(47 + 86*S^2))/(27*S))*HPL[{2}, -S^2] - (26*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^2*((-10*Pi^2*(1 + S^2))/(3*S) - (40*(1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^2*((-122*S)/9 - (487*Pi^2*S)/135 - (34*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (10*(1 + S^2)*HPL[{1}, -S^2]^2)/S - (2*(5 + 44*S^2)*HPL[{2}, -S^2])/(9*S)) - (16*(4 + 23*S^2)*HPL[{3}, -S^2])/(9*S) - (136*(1 + S^2)*HPL[{4}, -S^2])/(15*S) + (48*(1 + S^2)*HPL[{2, 1}, -S^2])/S + HPL[{0}, S^2]*((-76*Pi^2*S)/27 - (26*Pi^2*(1 + S^2)*HPL[{1}, -S^2])/(9*S) + (4*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (8*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S)) + (112*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (224*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - 48*S*Zeta[3] + HPL[{1}, -S^2]*((-34*Pi^2*(1 + S^2))/(9*S) - (136*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (40*(1 + S^2)*HPL[{3}, -S^2])/S + (80*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (40*(1 + S^2)*Zeta[3])/S)) + HPL[{0}, S^2]^5*((83*Pi^2*S)/720 + (7873*Pi^4*S)/129600 + (269*(1 + S^2)*HPL[{1}, -S^2]^3)/(540*S) + (31*(1 + S^2)*HPL[{1}, -S^2]^4)/(120*S) + ((83*S)/120 + (Pi^2*(15 + 779*S^2))/(2160*S))*HPL[{2}, -S^2] + ((5 + 68*S^2)*HPL[{2}, -S^2]^2)/(240*S) + HPL[{1}, -S^2]^2*((269*(1 + S^2))/(360*S) + (67*Pi^2*(1 + S^2))/(180*S) + (229*(1 + S^2)*HPL[{2}, -S^2])/(360*S)) + ((-3 - S^2)*HPL[{3}, -S^2])/(24*S) + ((-1 - S^2)*HPL[{4}, -S^2])/(8*S) + ((-68 + 5*S^2)*HPL[{2, 1}, -S^2])/(60*S) - (21*S*HPL[{3, 1}, -S^2])/20 + ((15 + 254*S^2)*HPL[{2, 1, 1}, -S^2])/(90*S) + (S*Zeta[3])/6 + HPL[{1}, -S^2]*((289*(1 + S^2))/(360*S) + (397*Pi^2*(1 + S^2))/(1080*S) + (73*(1 + S^2)*HPL[{2}, -S^2])/(120*S) + ((-1 - S^2)*HPL[{3}, -S^2])/(12*S) - (229*(1 + S^2)*HPL[{2, 1}, -S^2])/(180*S) + (2*(1 + S^2)*Zeta[3])/(3*S))) + (888*S + (262*Pi^2*S)/3 + (782*Pi^4*S)/45)*Zeta[5] + HPL[{0}, S^2]^4*((188*S)/9 + (791*Pi^2*S)/216 + (541*Pi^4*S)/540 + (23*(1 + S^2)*HPL[{1}, -S^2]^4)/(18*S) + (22*(1 + S^2)*HPL[{1}, -S^2]^5)/(45*S) + ((-1 + 17*S^2)*HPL[{2}, -S^2]^2)/(12*S) + HPL[{1}, -S^2]^3*((37*(1 + S^2))/(12*S) + (19*Pi^2*(1 + S^2))/(18*S) + (257*(1 + S^2)*HPL[{2}, -S^2])/(108*S)) + ((19*(1 + S^2))/(12*S) + (Pi^2*(10 + 11*S^2))/(72*S))*HPL[{3}, -S^2] + ((17 + 23*S^2)*HPL[{4}, -S^2])/(12*S) + ((16 + 23*S^2)*HPL[{5}, -S^2])/(12*S) + ((-296 - 115*S^2)/(36*S) + (Pi^2*(-563 - 11*S^2))/(216*S))*HPL[{2, 1}, -S^2] + ((-23 - 93*S^2)*HPL[{3, 1}, -S^2])/(12*S) + (3*HPL[{3, 2}, -S^2])/(2*S) - (23*(-1 + S^2)*HPL[{4, 1}, -S^2])/(12*S) + ((18 + 83*S^2)*HPL[{2, 1, 1}, -S^2])/(6*S) + (5*(47 + 4*S^2)*HPL[{2, 2, 1}, -S^2])/(18*S) + ((80 + 9*S^2)*HPL[{3, 1, 1}, -S^2])/(2*S) + ((-233 - 11*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(9*S) + ((47*S)/12 + (833*Pi^2*S)/216)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(12 + 47*S^2))/(36*S) + (114 + 199*S^2)/(36*S) - (3*HPL[{3}, -S^2])/(4*S) - (5*(47 + 4*S^2)*HPL[{2, 1}, -S^2])/(36*S) + (5*(-1 + S^2)*Zeta[3])/(12*S)) + HPL[{1}, -S^2]*((94*(1 + S^2))/(9*S) + (37*Pi^2*(1 + S^2))/(18*S) + (1303*Pi^4*(1 + S^2))/(2160*S) + ((205*(1 + S^2))/(36*S) + (79*Pi^2*(1 + S^2))/(54*S))*HPL[{2}, -S^2] + (13*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) + (7*(1 + S^2)*HPL[{3}, -S^2])/(4*S) + (11*(1 + S^2)*HPL[{4}, -S^2])/(6*S) - (33*(1 + S^2)*HPL[{2, 1}, -S^2])/(4*S) - (137*(1 + S^2)*HPL[{3, 1}, -S^2])/(18*S) + (257*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(18*S) + (2*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((473*(1 + S^2))/(72*S) + (121*Pi^2*(1 + S^2))/(72*S) + (33*(1 + S^2)*HPL[{2}, -S^2])/(8*S) + (11*(1 + S^2)*HPL[{3}, -S^2])/(12*S) - (257*(1 + S^2)*HPL[{2, 1}, -S^2])/(36*S) + (19*(1 + S^2)*Zeta[3])/(9*S)) + (805*S*Zeta[5])/36) + Zeta[3]*(980*S + (752*Pi^2*S)/9 + (2071*Pi^4*S)/270 + (1847*Pi^6*S)/1134 + (344*S*Zeta[5])/3) + Log[T]^4*((46*Pi^2*S)/3 + (857*Pi^4*S)/270 + (289*S*HPL[{0}, S^2]^5)/540 + HPL[{0}, S^2]^4*((47*S)/18 + (22*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + (64*(-1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((50*Pi^2*(1 + S^2))/(9*S) + (200*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]^3*((209*S)/27 + (242*Pi^2*S)/81 + (65*(1 + S^2)*HPL[{1}, -S^2])/(9*S) + (65*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + ((4 + 61*S^2)*HPL[{2}, -S^2])/(9*S)) + ((2*Pi^2*(28 + 237*S^2))/(27*S) + (4*(61 + 270*S^2))/(9*S))*HPL[{3}, -S^2] + (4*(51 + 55*S^2)*HPL[{4}, -S^2])/(9*S) + (4*(3 + 107*S^2)*HPL[{5}, -S^2])/(9*S) + ((-1324*(1 + S^2))/(9*S) - (2*Pi^2*(473 + 278*S^2))/(27*S))*HPL[{2, 1}, -S^2] - (8*(119 + 121*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (8*(14 + 209*S^2)*HPL[{3, 2}, -S^2])/(9*S) - (8*(22 + 217*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (640*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (520*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (80*(-21 + 5*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (1280*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((1324*S)/9 + (542*Pi^2*S)/27)*Zeta[3] + HPL[{0}, S^2]^2*(46*S + (29*Pi^2*S)/3 + (85*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (50*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (8*(7 + 31*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((106*(1 + S^2))/(3*S) + (163*Pi^2*(1 + S^2))/(18*S) + (86*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((11 + 39*S^2)*HPL[{3}, -S^2])/(9*S) - (2*(233 + 38*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (62*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((85*Pi^2*(1 + S^2))/(9*S) + (340*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (100*(1 + S^2)*HPL[{3}, -S^2])/S - (200*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (100*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]*((106*Pi^2*(1 + S^2))/(9*S) + (749*Pi^4*(1 + S^2))/(270*S) + ((424*(1 + S^2))/(3*S) + (236*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (340*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{4}, -S^2])/S - (680*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (200*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (400*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (340*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((92*(1 + S^2))/S + (8*Pi^2*(37 + 61*S^2))/(27*S) + (20*(1 + 14*S^2)*HPL[{3}, -S^2])/(3*S) + (260*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(7 + 202*S^2)*Zeta[3])/(9*S)) + HPL[{0}, S^2]*((209*Pi^2*S)/27 + (4021*Pi^4*S)/1620 + (65*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + ((-26*(1 + S^2))/(9*S) + (Pi^2*(-1 + 56*S^2))/(9*S))*HPL[{2}, -S^2] - (17*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) - (4*(1 + 3*S^2)*HPL[{3}, -S^2])/(9*S) + (8*(2 + S^2)*HPL[{4}, -S^2])/(3*S) - (20*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (40*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*S*Zeta[3])/9 + HPL[{1}, -S^2]*((65*Pi^2*(1 + S^2))/(9*S) - (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (4*(1 + S^2)*Zeta[3])/(3*S))) + (1220*S*Zeta[5])/9) + HPL[{1}, -S^2]^4*((47*Pi^2*(1 + S^2))/(6*S) + (97*Pi^4*(1 + S^2))/(60*S) + ((212*(1 + S^2))/(3*S) + (29*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (56*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (92*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-424*(1 + S^2))/(3*S) - (236*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (340*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (248*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (280*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (680*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (200*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (400*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((212*(1 + S^2))/(3*S) + (86*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((94*(1 + S^2))/S + (46*Pi^2*(1 + S^2))/(3*S) + (124*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (128*(1 + S^2)*Zeta[3])/(3*S)) + (224*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]^3*((590*Pi^2*(1 + S^2))/(27*S) + (751*Pi^4*(1 + S^2))/(180*S) + (47329*Pi^6*(1 + S^2))/(68040*S) + (31*Pi^2*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) + (124*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + ((476*(1 + S^2))/(9*S) + (218*Pi^2*(1 + S^2))/(27*S))*HPL[{4}, -S^2] + (224*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (106*(1 + S^2)*HPL[{6}, -S^2])/S + ((-848*(1 + S^2))/(3*S) - (472*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] - (544*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (624*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (368*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((1696*(1 + S^2))/(3*S) + (944*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (1360*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (992*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (1120*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (2720*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (800*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (1600*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((188*(1 + S^2))/S + (196*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2, 1}, -S^2]*((-376*(1 + S^2))/S - (184*Pi^2*(1 + S^2))/(3*S) - (512*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((188*(1 + S^2))/S + (626*Pi^2*(1 + S^2))/(27*S) - (496*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((2360*(1 + S^2))/(9*S) + (1058*Pi^2*(1 + S^2))/(27*S) + (2779*Pi^4*(1 + S^2))/(540*S) + (824*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (256*(1 + S^2)*Zeta[3])/(3*S)) + (176*(1 + S^2)*Zeta[5])/S) + HPL[{2, 1}, -S^2]*((Pi^6*(-46812 - 8377*S^2))/(22680*S) + (Pi^4*(-8917 - 4728*S^2))/(540*S) - (980*(1 + S^2))/S - (5*Pi^2*(237 + 178*S^2))/(9*S) + ((-4*Pi^2*(-71 + 31*S^2))/(3*S) - (4*(-73 + 69*S^2))/S)*HPL[{3, 1}, -S^2] + (8*(171 + 7*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(-1067 + 15*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (2*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (4*(-171 + 37*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-568*(-1 + S^2))/S - (8*Pi^2*(-209 + 97*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (1424*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (64*(7 + 23*S^2)*HPL[{3, 1, 1}, -S^2])/S + (1328*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (16*(-275 + 277*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (1024*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (32*(-97 + 98*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (2080*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((16*(-63 + S^2))/(3*S) + (2*Pi^2*(-208 + 5*S^2))/(9*S))*Zeta[3] - (4*(3 + 5*S^2)*Zeta[3]^2)/(3*S) - (4*(277 + 8*S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]^2*((50*(-1 + S^2))/S + (143*Pi^2*(-1 + 2*S^2))/(18*S) + (Pi^4*(-482 + 1389*S^2))/(540*S) + ((Pi^2*(38 + 213*S^2))/(18*S) + (39 + 238*S^2)/(3*S))*HPL[{3}, -S^2] + (8*(4 + 3*S^2)*HPL[{4}, -S^2])/(3*S) + (7*(13 + 17*S^2)*HPL[{5}, -S^2])/(3*S) + ((Pi^2*(-218 - 135*S^2))/(9*S) - (277*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (2*(91 + 87*S^2)*HPL[{3, 1}, -S^2])/(3*S) + ((-43 - 375*S^2)*HPL[{3, 2}, -S^2])/(3*S) + ((-209 - 1205*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (356*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (332*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(-139 + 27*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (896*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((65 + 212*S^2)/(3*S) + (Pi^2*(50 + 239*S^2))/(18*S))*Zeta[3] + (11*(4 + 25*S^2)*Zeta[5])/(3*S)) + HPL[{3, 1}, -S^2]*((Pi^4*(-3201 - 7165*S^2))/(540*S) - (292*Pi^2*(2 + 3*S^2))/(9*S) - (10*(175 + 177*S^2))/(3*S) + (4*(115 + 427*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(233 + 1273*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (32*(-47 + 49*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (1792*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(-795 + 349*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (32*(-97 + 98*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-2*Pi^2*(-2 + 73*S^2))/(3*S) - (4*(1 + 210*S^2))/(3*S))*Zeta[3] - (20*(-16 + 43*S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((490*(1 + S^2))/S + (295*Pi^2*(1 + 2*S^2))/(9*S) + (Pi^4*(1306 + 3175*S^2))/(540*S) + (Pi^6*(-260 + 5559*S^2))/(11340*S) + ((Pi^2*(76 - S^2))/(9*S) + (2*(7 + S^2))/S)*HPL[{4}, -S^2] - (2*(114 + 97*S^2)*HPL[{5}, -S^2])/(3*S) + (2*(145 + 119*S^2)*HPL[{6}, -S^2])/(3*S) - (4*(29 + 195*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-2*Pi^2*(-7 + 206*S^2))/(9*S) - (4*(28 + 227*S^2))/(3*S))*HPL[{3, 1}, -S^2] + (2*(35 + 26*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2*(1 + 17*S^2)*HPL[{4, 1}, -S^2])/S - (10*(-1 + 2*S^2)*HPL[{4, 2}, -S^2])/(3*S) - (4*(57 + 10*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((4*Pi^2*(5 + 228*S^2))/(9*S) + (8*(29 + 242*S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (8*(171 + 7*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (8*(172 + 3*S^2)*HPL[{3, 1, 1}, -S^2])/S + (8*(-3 + 2*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (8*(7 + 64*S^2)*HPL[{3, 2, 1}, -S^2])/S - (104*(101 + 516*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (16*(-61 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (16*(19 + 203*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (160*(1 + 14*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((Pi^2*(11 - 57*S^2))/(9*S) - (20*(-1 + 10*S^2))/(3*S))*Zeta[3] + (4*(3 + 13*S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((32*(-31 + S^2))/(3*S) + (2*Pi^2*(-212 + 17*S^2))/(9*S) + (8*(12 + 13*S^2)*Zeta[3])/(3*S)) - (2*(-33 + 59*S^2)*Zeta[5])/(3*S)) + HPL[{4}, -S^2]*((2*Pi^2*(114 + 121*S^2))/(9*S) + (2*(597 + 607*S^2))/(3*S) + (Pi^4*(1169 + 1445*S^2))/(540*S) - (10*(29 + 39*S^2)*HPL[{5}, -S^2])/(3*S) + ((4*(-23 + 11*S^2))/(3*S) + (Pi^2*(-131 + 31*S^2))/(9*S))*HPL[{2, 1}, -S^2] - (2*(23 + 81*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(155 + 191*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(98 + 171*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (4*(-41 + 57*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (260*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(233 + 129*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (32*(-13 + 14*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((Pi^2*(-53 - 7*S^2))/(9*S) - (16*(3 + 2*S^2))/(3*S))*Zeta[3] - (2*(189 + 79*S^2)*Zeta[5])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((3520*(1 + S^2))/(3*S) + (128*Pi^2*(9 + 13*S^2))/(9*S) + (Pi^4*(3058 + 6895*S^2))/(270*S) - (3584*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (32*(107 + 42*S^2)*HPL[{3, 1, 1}, -S^2])/S + (2080*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((16*Pi^2*(1 + 56*S^2))/(9*S) + (8*(7 + 220*S^2))/(3*S))*Zeta[3] + (16*(-7 + 132*S^2)*Zeta[5])/(3*S)) + Log[T]^3*((-130*Pi^2*S)/3 - (3311*Pi^4*S)/405 - (8431*Pi^6*S)/5670 - (31*S*HPL[{0}, S^2]^6)/108 + HPL[{0}, S^2]^5*((-269*S)/270 - (31*(1 + S^2)*HPL[{1}, -S^2])/(30*S)) + ((-142*(-1 + S^2))/(3*S) - (4*Pi^2*(-58 + 95*S^2))/(27*S))*HPL[{2}, -S^2]^2 - (296*(1 + S^2)*HPL[{2}, -S^2]^3)/(27*S) + HPL[{0}, S^2]^4*((-166*S)/27 - (371*Pi^2*S)/162 - (46*(1 + S^2)*HPL[{1}, -S^2])/(9*S) - (44*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + ((-4 - 41*S^2)*HPL[{2}, -S^2])/(9*S)) + HPL[{1}, -S^2]^4*((-50*Pi^2*(1 + S^2))/(9*S) - (200*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + (8*(-5 + 4*S^2)*HPL[{3}, -S^2]^2)/(9*S) + ((-4*Pi^2*(69 + 77*S^2))/(27*S) - (4*(123 + 139*S^2))/(9*S))*HPL[{4}, -S^2] - (4*(51 + 242*S^2)*HPL[{5}, -S^2])/(9*S) - (16*(54 + 71*S^2)*HPL[{6}, -S^2])/(9*S) + (520*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((8*Pi^2*(117 + 214*S^2))/(27*S) + (8*(301 + 309*S^2))/(9*S))*HPL[{3, 1}, -S^2] + (4*(85 + 853*S^2)*HPL[{3, 2}, -S^2])/(9*S) + (32*(51 + 337*S^2)*HPL[{4, 1}, -S^2])/(9*S) + (16*(-7 + 11*S^2)*HPL[{4, 2}, -S^2])/(9*S) + (16*(61 + 119*S^2)*HPL[{5, 1}, -S^2])/(9*S) + ((-4880*(1 + S^2))/(9*S) - (40*Pi^2*(47 + 86*S^2))/(27*S))*HPL[{2, 1, 1}, -S^2] + (1024*(-1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (64*(-164 + 29*S^2)*HPL[{3, 1, 1}, -S^2])/(9*S) - (32*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(9*S) - (800*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (2912*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (960*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (2240*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (4480*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (-384*S - (1228*Pi^2*S)/27)*Zeta[3] + (8*S*Zeta[3]^2)/3 + HPL[{0}, S^2]^3*((-56*S)/3 - (17*Pi^2*S)/3 - (130*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) - (260*(1 + S^2)*HPL[{1}, -S^2]^3)/(27*S) - (8*(7 + 45*S^2)*HPL[{2}, -S^2])/(27*S) + HPL[{1}, -S^2]*((-436*(1 + S^2))/(27*S) - (158*Pi^2*(1 + S^2))/(27*S) - (124*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) - (2*(-1 + S^2)*HPL[{3}, -S^2])/(9*S) + (4*(58 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (28*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((-212*Pi^2*(1 + S^2))/(9*S) - (749*Pi^4*(1 + S^2))/(135*S) + ((-848*(1 + S^2))/(3*S) - (472*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (680*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (64*(1 + S^2)*HPL[{4}, -S^2])/S + (1360*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (400*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (800*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (680*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((-340*Pi^2*(1 + S^2))/(27*S) - (1360*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (400*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (800*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (400*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-16*(5 + 19*S^2))/S - (2*Pi^2*(108 + 533*S^2))/(27*S) - (16*(-57 + 8*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (16*(14 + S^2)*Zeta[3])/(9*S)) + HPL[{2, 1}, -S^2]*((384*(1 + S^2))/S + (16*Pi^2*(133 + 85*S^2))/(27*S) - (80*(-37 + 2*S^2)*Zeta[3])/(9*S)) + HPL[{2}, -S^2]*((-260*(1 + S^2))/S - (2*Pi^2*(403 + 616*S^2))/(27*S) - (2*Pi^4*(569 + 1526*S^2))/(405*S) - (8*(23 + 215*S^2)*HPL[{3}, -S^2])/(9*S) - (16*(-13 + 14*S^2)*HPL[{4}, -S^2])/(9*S) - (512*(-1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (16*(-97 + 98*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (1040*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (64*(1 + 25*S^2)*Zeta[3])/(9*S)) + HPL[{0}, S^2]^2*(-130*S - (637*Pi^2*S)/27 - (8159*Pi^4*S)/1620 - (340*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (50*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + ((Pi^2*(-49 - 466*S^2))/(27*S) - (2*(98 + 311*S^2))/(9*S))*HPL[{2}, -S^2] - (37*(-1 + 5*S^2)*HPL[{2}, -S^2]^2)/(9*S) + HPL[{1}, -S^2]^2*((-212*(1 + S^2))/(3*S) - (163*Pi^2*(1 + S^2))/(9*S) - (172*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (2*(28 + 73*S^2)*HPL[{3}, -S^2])/(9*S) - (8*(9 + 13*S^2)*HPL[{4}, -S^2])/(9*S) + (8*(131 + 35*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (8*(12 + 109*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (40*(5 + 44*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) - (148*S*Zeta[3])/9 + HPL[{1}, -S^2]*((-94*(1 + S^2))/S - (59*Pi^2*(1 + S^2))/(3*S) - (212*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (44*(1 + S^2)*Zeta[3])/(3*S))) - 336*S*Zeta[5] + HPL[{0}, S^2]*((-56*Pi^2*S)/3 - (1289*Pi^4*S)/270 - (260*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^3)/(27*S) + (32*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) + ((32*S)/9 + (4*Pi^2*(4 + S^2))/(27*S))*HPL[{3}, -S^2] + (4*(-15 + 4*S^2)*HPL[{4}, -S^2])/(9*S) - (4*(-7 + S^2)*HPL[{5}, -S^2])/(3*S) + ((104*(1 + S^2))/(9*S) + (4*Pi^2*(21 + 2*S^2))/(3*S))*HPL[{2, 1}, -S^2] - (32*(5 + 4*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (16*(11 + 10*S^2)*HPL[{3, 2}, -S^2])/(9*S) + (16*(6 + 5*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (80*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (272*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) - (736*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(9*S) + (160*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-32*S)/9 - (28*Pi^2*S)/9)*Zeta[3] + HPL[{1}, -S^2]^2*((-130*Pi^2*(1 + S^2))/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]*((-436*Pi^2*(1 + S^2))/(27*S) - (1313*Pi^4*(1 + S^2))/(270*S) - (124*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((4*(1 + S^2))/S - (2*Pi^2*(13 + 165*S^2))/(27*S) - (8*(4 + 3*S^2)*HPL[{3}, -S^2])/(3*S) + (136*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (8*(-1 + 2*S^2)*Zeta[3])/(9*S)) + (104*S*Zeta[5])/9) + HPL[{1}, -S^2]*((-94*Pi^2*(1 + S^2))/(3*S) - (97*Pi^4*(1 + S^2))/(15*S) + ((-848*(1 + S^2))/(3*S) - (116*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (224*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (368*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((1696*(1 + S^2))/(3*S) + (944*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (1360*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (992*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (1120*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (2720*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (800*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (1600*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-848*(1 + S^2))/(3*S) - (344*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-376*(1 + S^2))/S - (184*Pi^2*(1 + S^2))/(3*S) - (496*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (512*(1 + S^2)*Zeta[3])/(3*S)) - (896*(1 + S^2)*Zeta[5])/(3*S))) + HPL[{0}, S^2]^3*((295*Pi^2*S)/108 + (4049*Pi^4*S)/6480 + (2033*Pi^6*S)/10080 + (13*(1 + S^2)*HPL[{1}, -S^2]^5)/(9*S) + (13*(1 + S^2)*HPL[{1}, -S^2]^6)/(27*S) + ((-6 + 193*S^2)/(36*S) + (Pi^2*(12 + 367*S^2))/(216*S))*HPL[{2}, -S^2]^2 + ((-1 + 24*S^2)*HPL[{2}, -S^2]^3)/(18*S) + HPL[{1}, -S^2]^4*((109*(1 + S^2))/(27*S) + (79*Pi^2*(1 + S^2))/(54*S) + (31*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((-35 - 31*S^2)*HPL[{3}, -S^2]^2)/(18*S) + ((Pi^2*(-9 - 8*S^2))/(27*S) - (8*(4 + S^2))/(9*S))*HPL[{4}, -S^2] + ((-107 - 116*S^2)*HPL[{5}, -S^2])/(18*S) + ((-25 - 29*S^2)*HPL[{6}, -S^2])/(3*S) + ((3 - 163*S^2)*HPL[{2, 1}, -S^2]^2)/(9*S) + ((Pi^2*(-12 - 361*S^2))/(54*S) + (-34 - 185*S^2)/(9*S))*HPL[{3, 1}, -S^2] + ((5 - 48*S^2)*HPL[{3, 2}, -S^2])/(18*S) + ((27 - 32*S^2)*HPL[{4, 1}, -S^2])/(9*S) + (2*S*HPL[{4, 2}, -S^2])/9 + (10*(3 + 4*S^2)*HPL[{5, 1}, -S^2])/(9*S) + ((2*(44 + 201*S^2))/(9*S) + (Pi^2*(27 + 437*S^2))/(27*S))*HPL[{2, 1, 1}, -S^2] + (2*(171 + 7*S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) + (2*(171 + 14*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (2*S*HPL[{3, 1, 2}, -S^2])/9 + (2*(-6 + 143*S^2)*HPL[{3, 2, 1}, -S^2])/(9*S) + (2*(-9 + 445*S^2)*HPL[{4, 1, 1}, -S^2])/(9*S) - (8*(89 + 13*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(9*S) - (16*(3 + 43*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(9*S) + (8*(4 + 61*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + ((11*S)/9 + (5*Pi^2*S)/6)*Zeta[3] - (S*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((263*(1 + S^2))/(27*S) + (232*Pi^2*(1 + S^2))/(81*S) + (206*(1 + S^2)*HPL[{2}, -S^2])/(27*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (124*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (46*(1 + S^2)*Zeta[3])/(27*S)) + HPL[{1}, -S^2]^2*((155*(1 + S^2))/(9*S) + (487*Pi^2*(1 + S^2))/(108*S) + (805*Pi^4*(1 + S^2))/(648*S) + ((124*(1 + S^2))/(9*S) + (415*Pi^2*(1 + S^2))/(108*S))*HPL[{2}, -S^2] + (83*(1 + S^2)*HPL[{2}, -S^2]^2)/(18*S) + (16*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (5*(1 + S^2)*HPL[{4}, -S^2])/(9*S) - (206*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (178*(1 + S^2)*HPL[{3, 1}, -S^2])/(9*S) + (124*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (7*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((Pi^2*(-15 + 2*S^2))/(36*S) + (-32 + 9*S^2)/(9*S) + (2*(13 + 19*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (2*(1 + 2*S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((295*S)/18 + (Pi^2*(22 + 225*S^2))/(54*S) + (Pi^4*(19 + 432*S^2))/(360*S) + ((-1 + 12*S^2)*HPL[{3}, -S^2])/(9*S) + (5*(7 + 6*S^2)*HPL[{4}, -S^2])/(9*S) + ((-171 - 7*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (2*(10 + 91*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (2*(-3 + 163*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + ((4 + 17*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-229 - 29*S^2)/(9*S) + (Pi^2*(-382 - 11*S^2))/(54*S) - (2*(40 + 23*S^2)*Zeta[3])/(9*S)) + (4*S*Zeta[5])/3 + HPL[{1}, -S^2]*((325*(1 + S^2))/(18*S) + (46*Pi^2*(1 + S^2))/(9*S) + (265*Pi^4*(1 + S^2))/(216*S) + (85*(1 + S^2)*HPL[{2}, -S^2]^2)/(18*S) + ((Pi^2*(-1 - S^2))/(6*S) + (5*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (11*(1 + S^2)*HPL[{4}, -S^2])/(9*S) - (59*(1 + S^2)*HPL[{5}, -S^2])/(9*S) + ((-248*(1 + S^2))/(9*S) - (415*Pi^2*(1 + S^2))/(54*S))*HPL[{2, 1}, -S^2] - (202*(1 + S^2)*HPL[{3, 1}, -S^2])/(9*S) + (10*(1 + S^2)*HPL[{3, 2}, -S^2])/(9*S) + (40*(1 + S^2)*HPL[{4, 1}, -S^2])/(9*S) + (412*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (332*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) + (340*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (248*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((29*(1 + S^2))/(9*S) + (143*Pi^2*(1 + S^2))/(54*S))*Zeta[3] + HPL[{2}, -S^2]*((91*(1 + S^2))/(6*S) + (425*Pi^2*(1 + S^2))/(108*S) - (5*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (166*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (37*(1 + S^2)*Zeta[3])/(9*S)) + (32*(1 + S^2)*Zeta[5])/(3*S))) + (892*S + 186*Pi^2*S)*Zeta[7] + HPL[{0}, S^2]^2*(490*S + (596*Pi^2*S)/9 + (1481*Pi^4*S)/180 + (5699*Pi^6*S)/3360 + (17*(1 + S^2)*HPL[{1}, -S^2]^6)/(9*S) + (10*(1 + S^2)*HPL[{1}, -S^2]^7)/(21*S) + (5*(3 + 19*S^2)*HPL[{2}, -S^2]^3)/(18*S) + HPL[{1}, -S^2]^5*((106*(1 + S^2))/(15*S) + (163*Pi^2*(1 + S^2))/(90*S) + (86*(1 + S^2)*HPL[{2}, -S^2])/(15*S)) + ((-1 - 16*S^2)*HPL[{3}, -S^2]^2)/(6*S) + ((23*Pi^2*(5 + 9*S^2))/(36*S) + (5*(43 + 33*S^2))/(6*S))*HPL[{5}, -S^2] + (5*(68 + 81*S^2)*HPL[{6}, -S^2])/(6*S) + ((270 + 269*S^2)*HPL[{7}, -S^2])/(3*S) - (2*(-15 + 104*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((15 - 68*S^2)/(3*S) - (5*Pi^2*(-15 + 8*S^2))/(18*S))*HPL[{3, 2}, -S^2] + ((-67 - 301*S^2)/(3*S) + (Pi^2*(91 - 199*S^2))/(18*S))*HPL[{4, 1}, -S^2] + ((17 + S^2)*HPL[{4, 2}, -S^2])/(6*S) - (2*(57 + 37*S^2)*HPL[{4, 3}, -S^2])/(3*S) + ((-32 - 51*S^2)*HPL[{5, 1}, -S^2])/S + ((-673 - 469*S^2)*HPL[{5, 2}, -S^2])/(6*S) - (11*(74 + 63*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((-2*(-278 + S^2))/(3*S) + (Pi^2*(458 + 21*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((10*(178 + 23*S^2))/(3*S) + (Pi^2*(1400 + 123*S^2))/(9*S))*HPL[{3, 1, 1}, -S^2] + ((-1 - 8*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + ((59 + 372*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + ((39 + 70*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (4*(-8 + 39*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) + (2*(143 + 641*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + ((-39 + 167*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + ((-243 + 419*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (2*(-287 + 447*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((-4*(108 + 37*S^2))/S - (2*Pi^2*(466 + 49*S^2))/(9*S))*HPL[{2, 1, 1, 1}, -S^2] - (8*(106 + 23*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) - (4*(58 + 251*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (4*(657 + 98*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (4*(657 + 98*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (4*(1293 + 236*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (8*(1919 + 349*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) + (64*(7 + 31*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) - (8*(223 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) - (8*(223 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (16*(-552 + 17*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) - (16*(233 + 38*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S) + ((157*S)/3 + 11*Pi^2*S + (2111*Pi^4*S)/360)*Zeta[3] + 23*S*Zeta[3]^2 + HPL[{3}, -S^2]*((145*(1 + S^2))/(3*S) + (Pi^2*(85 + 116*S^2))/(18*S) + (Pi^4*(271 + 459*S^2))/(1080*S) + ((57 + 32*S^2)*HPL[{4}, -S^2])/(3*S) + (2*(-29 + 8*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(-26 + 3*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (8*(-5 + 9*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + ((-7 - 32*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((2*(20 + 21*S^2))/S + (Pi^2*(155 + 209*S^2))/(36*S) + ((-79 - 25*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (12*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^4*((47*(1 + S^2))/(2*S) + (59*Pi^2*(1 + S^2))/(12*S) + (53*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/S - (86*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (11*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((590*(1 + S^2))/(9*S) + (217*Pi^2*(1 + S^2))/(18*S) + (7643*Pi^4*(1 + S^2))/(3240*S) + ((422*(1 + S^2))/(9*S) + (515*Pi^2*(1 + S^2))/(54*S))*HPL[{2}, -S^2] + (31*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (116*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (74*(1 + S^2)*HPL[{4}, -S^2])/(9*S) - (212*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (172*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (26*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((Pi^4*(-6615 - 368*S^2))/(1080*S) + (Pi^2*(-310 - 113*S^2))/(9*S) - (295*(2 + S^2))/(3*S) + (4*(116 + 5*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (4*(223 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (2*(8 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((Pi^2*(-127 - 530*S^2))/(18*S) - (2*(87 + 229*S^2))/(3*S) - (2*(-12 + 19*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((4*(81 + 209*S^2))/(3*S) + (Pi^2*(110 + 497*S^2))/(9*S) + (4*(-3 + 22*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((-15 + 158*S^2)/(6*S) + (Pi^2*(-21 + 206*S^2))/(36*S) + (3*(1 + 2*S^2)*HPL[{3}, -S^2])/(2*S) + ((-106 - 23*S^2)*HPL[{2, 1}, -S^2])/(3*S) + ((22 + 43*S^2)*Zeta[3])/(6*S)) + ((268*S)/3 + (461*Pi^2*S)/9)*Zeta[5] + HPL[{1}, -S^2]^2*((295*(1 + S^2))/(2*S) + (224*Pi^2*(1 + S^2))/(9*S) + (187*Pi^4*(1 + S^2))/(48*S) + (103*(1 + S^2)*HPL[{2}, -S^2]^2)/(6*S) + ((91*(1 + S^2))/(3*S) + (23*Pi^2*(1 + S^2))/(6*S))*HPL[{3}, -S^2] + (53*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (58*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-422*(1 + S^2))/(3*S) - (515*Pi^2*(1 + S^2))/(18*S))*HPL[{2, 1}, -S^2] - (322*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (22*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (140*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (212*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (124*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (420*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((19*(1 + S^2))/S + (109*Pi^2*(1 + S^2))/(18*S))*Zeta[3] + HPL[{2}, -S^2]*((589*(1 + S^2))/(6*S) + (205*Pi^2*(1 + S^2))/(12*S) + (11*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (62*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (23*(1 + S^2)*Zeta[3])/(3*S)) + (119*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]*((245*(1 + S^2))/S + (671*Pi^2*(1 + S^2))/(18*S) + (2129*Pi^4*(1 + S^2))/(432*S) + (10607*Pi^6*(1 + S^2))/(10080*S) + ((21*(1 + S^2))/S + (197*Pi^2*(1 + S^2))/(36*S))*HPL[{2}, -S^2]^2 + (53*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) - (11*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((33*(1 + S^2))/S + (103*Pi^2*(1 + S^2))/(18*S))*HPL[{4}, -S^2] + (30*(1 + S^2)*HPL[{5}, -S^2])/S + (123*(1 + S^2)*HPL[{6}, -S^2])/(2*S) - (62*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-434*(1 + S^2))/(3*S) - (266*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] - (40*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (232*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (160*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((844*(1 + S^2))/(3*S) + (515*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (412*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (1468*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (424*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (1420*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (424*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((74*(1 + S^2))/(3*S) + (37*Pi^2*(1 + S^2))/(6*S))*Zeta[3] + (17*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((-589*(1 + S^2))/(3*S) - (205*Pi^2*(1 + S^2))/(6*S) - (46*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((54*(1 + S^2))/S + (121*Pi^2*(1 + S^2))/(18*S) - (22*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (22*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((440*(1 + S^2))/(3*S) + (208*Pi^2*(1 + S^2))/(9*S) + (7573*Pi^4*(1 + S^2))/(2160*S) + (7*(1 + S^2)*HPL[{3}, -S^2])/S + (22*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (206*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (190*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (124*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (9*(1 + S^2)*Zeta[3])/S) + (143*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((10*(29 + 44*S^2))/(3*S) + (Pi^2*(65 + 136*S^2))/(6*S) + (Pi^4*(1874 + 7171*S^2))/(2160*S) + ((2*(-3 + 17*S^2))/(3*S) + (Pi^2*(-37 + 18*S^2))/(18*S))*HPL[{3}, -S^2] + ((-7 + 39*S^2)*HPL[{4}, -S^2])/(6*S) + ((-123 - 35*S^2)*HPL[{5}, -S^2])/(6*S) + ((Pi^2*(-458 - 21*S^2))/(18*S) + (-278 + S^2)/(3*S))*HPL[{2, 1}, -S^2] - (2*(-14 + 103*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (6*(1 + 2*S^2)*HPL[{3, 2}, -S^2])/S + ((25 - 83*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (4*(-15 + 104*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*(106 + 23*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4*(328 + 51*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (4*(223 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((4*(-1 + 4*S^2))/(3*S) + (Pi^2*(-18 + 37*S^2))/(18*S))*Zeta[3] + ((-30 + 37*S^2)*Zeta[5])/(3*S)) + 372*S*Zeta[7]) + Log[T]^2*((880*Pi^2*S)/9 + (2359*Pi^4*S)/135 + (60551*Pi^6*S)/22680 + (5*S*HPL[{0}, S^2]^7)/72 + HPL[{0}, S^2]^6*((11*S)/24 + (7*(1 + S^2)*HPL[{1}, -S^2])/(18*S)) + (178*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{1}, -S^2]^5*((10*Pi^2*(1 + S^2))/(3*S) + (40*(1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^5*((83*S)/60 + (407*Pi^2*S)/540 + (269*(1 + S^2)*HPL[{1}, -S^2])/(180*S) + (31*(1 + S^2)*HPL[{1}, -S^2]^2)/(20*S) + ((15 + 254*S^2)*HPL[{2}, -S^2])/(180*S)) - (2*(-1 + 4*S^2)*HPL[{3}, -S^2]^2)/S + ((Pi^2*(25 + 283*S^2))/(9*S) + (2*(173 + 299*S^2))/(3*S))*HPL[{5}, -S^2] + (14*(48 + 55*S^2)*HPL[{6}, -S^2])/(3*S) + (40*(15 + 38*S^2)*HPL[{7}, -S^2])/(3*S) - (256*(-1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-2*Pi^2*(7 + 458*S^2))/(9*S) - (4*(53 + 479*S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((-4*Pi^2*(55 + 716*S^2))/(9*S) - (4*(289 + 1551*S^2))/(3*S))*HPL[{4, 1}, -S^2] - (2*(-35 + 31*S^2)*HPL[{4, 2}, -S^2])/(3*S) + (4*(-37 + 41*S^2)*HPL[{4, 3}, -S^2])/(3*S) - (4*(139 + 250*S^2)*HPL[{5, 1}, -S^2])/(3*S) + (2*(-63 + 55*S^2)*HPL[{5, 2}, -S^2])/S - (136*(9 + 7*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((-568*(-1 + S^2))/S - (8*Pi^2*(-209 + 97*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((-8*Pi^2*(-655 + 54*S^2))/(9*S) - (8*(-761 + 99*S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] - (4*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (1420*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (4*(121 + 775*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (16*(77 + 593*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) + (32*(159 + 161*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (32*(34 + 301*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + (64*(53 + 449*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (16*(435 + 3689*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((-5296*(1 + S^2))/(3*S) - (8*Pi^2*(473 + 278*S^2))/(9*S))*HPL[{2, 1, 1, 1}, -S^2] - (3584*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) - (32*(119 + 121*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (32*(322 + 127*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (32*(322 + 127*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (32*(658 + 463*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (2080*(10 + 7*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (2560*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (2080*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (6240*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (320*(-31 + 47*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (5120*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((2380*S)/3 + (776*Pi^2*S)/9 + (869*Pi^4*S)/90)*Zeta[3] - 24*S*Zeta[3]^2 + HPL[{0}, S^2]^4*((118*S)/9 + (259*Pi^2*S)/72 + (23*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + (44*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + ((18 + 83*S^2)*HPL[{2}, -S^2])/(12*S) + HPL[{1}, -S^2]*((37*(1 + S^2))/(4*S) + (19*Pi^2*(1 + S^2))/(6*S) + (257*(1 + S^2)*HPL[{2}, -S^2])/(36*S)) + ((5 + 7*S^2)*HPL[{3}, -S^2])/(12*S) + ((-233 - 11*S^2)*HPL[{2, 1}, -S^2])/(18*S) + (83*S*Zeta[3])/18) + HPL[{2, 1}, -S^2]*((-2380*(1 + S^2))/(3*S) - (319*Pi^4*(19 + 7*S^2))/(270*S) - (2*Pi^2*(655 + 442*S^2))/(9*S) - (16*(-97 + 98*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (1040*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (64*(-23 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^4*((85*Pi^2*(1 + S^2))/(9*S) + (340*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (100*(1 + S^2)*HPL[{3}, -S^2])/S - (200*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (100*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((212*Pi^2*(1 + S^2))/(9*S) + (749*Pi^4*(1 + S^2))/(135*S) + ((848*(1 + S^2))/(3*S) + (472*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (680*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (64*(1 + S^2)*HPL[{4}, -S^2])/S - (1360*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (400*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (800*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (680*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((256*(-1 + S^2))/(3*S) + (Pi^2*(-111 + 200*S^2))/(9*S) + (2*(29 + 195*S^2)*HPL[{3}, -S^2])/(3*S) - (448*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (56*(1 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((20*(30 + 89*S^2))/(3*S) + (2*Pi^2*(89 + 329*S^2))/(9*S) + (Pi^4*(209 + 1955*S^2))/(270*S) - (4*(-19 + 33*S^2)*HPL[{4}, -S^2])/(3*S) + (8*(-61 + 3*S^2)*HPL[{2, 1}, -S^2])/S - (8*(19 + 203*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (80*(1 + 14*S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(-18 + 25*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((16*(27 + 29*S^2))/(3*S) + (Pi^2*(155 + 181*S^2))/(9*S) + (16*(-13 + 14*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-17 + 29*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((-8*(205 + 209*S^2))/(3*S) - (2*Pi^2*(296 + 493*S^2))/(9*S) - (16*(3 + 100*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((1104*(1 + S^2))/S + (32*Pi^2*(37 + 61*S^2))/(9*S) + (16*(7 + 202*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^3*((295*S)/9 + (229*Pi^2*S)/27 + (821*Pi^4*S)/324 + (130*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + (65*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + ((44 + 201*S^2)/(9*S) + (Pi^2*(27 + 437*S^2))/(54*S))*HPL[{2}, -S^2] + ((-3 + 163*S^2)*HPL[{2}, -S^2]^2)/(18*S) + HPL[{1}, -S^2]^2*((218*(1 + S^2))/(9*S) + (79*Pi^2*(1 + S^2))/(9*S) + (62*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + (7*S*HPL[{3}, -S^2])/3 + ((9 + 13*S^2)*HPL[{4}, -S^2])/(9*S) - (4*(89 + 13*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (8*(3 + 43*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (4*(4 + 61*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (10*S*Zeta[3])/3 + HPL[{1}, -S^2]*((263*(1 + S^2))/(9*S) + (232*Pi^2*(1 + S^2))/(27*S) + (206*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (124*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (46*(1 + S^2)*Zeta[3])/(9*S))) + ((2072*S)/3 + (844*Pi^2*S)/9)*Zeta[5] + HPL[{0}, S^2]^2*((880*S)/3 + (443*Pi^2*S)/9 + (8801*Pi^4*S)/1080 + (85*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + (10*(1 + S^2)*HPL[{1}, -S^2]^5)/S + ((-15 + 104*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((212*(1 + S^2))/(3*S) + (163*Pi^2*(1 + S^2))/(9*S) + (172*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((Pi^2*(13 + 30*S^2))/(9*S) + (2*(28 + 59*S^2))/(3*S))*HPL[{3}, -S^2] + ((53 + 71*S^2)*HPL[{4}, -S^2])/(3*S) + ((19 + 69*S^2)*HPL[{5}, -S^2])/(3*S) + ((Pi^2*(-466 - 49*S^2))/(9*S) - (2*(108 + 37*S^2))/S)*HPL[{2, 1}, -S^2] - (2*(58 + 251*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (2*(-21 + 40*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(-11 + 65*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (32*(7 + 31*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*(223 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (8*(340 + 21*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (8*(233 + 38*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (38*S + (38*Pi^2*S)/3)*Zeta[3] + HPL[{1}, -S^2]^2*((141*(1 + S^2))/S + (59*Pi^2*(1 + S^2))/(2*S) + (106*(1 + S^2)*HPL[{2}, -S^2])/S + (24*(1 + S^2)*HPL[{3}, -S^2])/S - (172*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (22*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]*((590*(1 + S^2))/(3*S) + (217*Pi^2*(1 + S^2))/(6*S) + (7643*Pi^4*(1 + S^2))/(1080*S) + ((422*(1 + S^2))/(3*S) + (515*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2] + (31*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (116*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (74*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (212*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (172*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (26*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((2*(81 + 209*S^2))/(3*S) + (Pi^2*(110 + 497*S^2))/(18*S) + (4*(-5 + 9*S^2)*HPL[{3}, -S^2])/(3*S) - (2*(223 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-3 + 22*S^2)*Zeta[3])/(3*S)) + 78*S*Zeta[5]) + HPL[{1}, -S^2]^2*((47*Pi^2*(1 + S^2))/S + (97*Pi^4*(1 + S^2))/(10*S) + ((424*(1 + S^2))/S + (58*Pi^2*(1 + S^2))/S)*HPL[{3}, -S^2] + (112*(1 + S^2)*HPL[{4}, -S^2])/S + (184*(1 + S^2)*HPL[{5}, -S^2])/S + ((-848*(1 + S^2))/S - (472*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (680*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (496*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (1680*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (1360*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (1200*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (2400*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((424*(1 + S^2))/S + (172*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((564*(1 + S^2))/S + (92*Pi^2*(1 + S^2))/S + (248*(1 + S^2)*HPL[{3}, -S^2])/S + (256*(1 + S^2)*Zeta[3])/S) + (448*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]*((590*Pi^2*(1 + S^2))/(9*S) + (751*Pi^4*(1 + S^2))/(60*S) + (47329*Pi^6*(1 + S^2))/(22680*S) + (31*Pi^2*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (124*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + ((476*(1 + S^2))/(3*S) + (218*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + (224*(1 + S^2)*HPL[{5}, -S^2])/S + (318*(1 + S^2)*HPL[{6}, -S^2])/S + ((-848*(1 + S^2))/S - (472*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] - (544*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (1872*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (368*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((1696*(1 + S^2))/S + (944*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (1360*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (992*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (3360*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (2720*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (2400*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (4800*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((564*(1 + S^2))/S + (196*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2, 1}, -S^2]*((-1128*(1 + S^2))/S - (184*Pi^2*(1 + S^2))/S - (512*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((564*(1 + S^2))/S + (626*Pi^2*(1 + S^2))/(9*S) - (496*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((2360*(1 + S^2))/(3*S) + (1058*Pi^2*(1 + S^2))/(9*S) + (2779*Pi^4*(1 + S^2))/(180*S) + (824*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (256*(1 + S^2)*Zeta[3])/S) + (528*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((1760*(1 + S^2))/(3*S) + (64*Pi^2*(9 + 13*S^2))/(9*S) + (Pi^4*(3058 + 6895*S^2))/(540*S) + ((2*Pi^2*(5 + 228*S^2))/(9*S) + (4*(29 + 242*S^2))/(3*S))*HPL[{3}, -S^2] + (2*(-41 + 57*S^2)*HPL[{4}, -S^2])/(3*S) + (2*(-67 + 141*S^2)*HPL[{5}, -S^2])/(3*S) + ((284*(-1 + S^2))/S + (4*Pi^2*(-209 + 97*S^2))/(9*S))*HPL[{2, 1}, -S^2] - (16*(-47 + 49*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(29 + 195*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (8*(61 + 613*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (512*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (1792*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(107 + 42*S^2)*HPL[{3, 1, 1}, -S^2])/S + (1040*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((8*Pi^2*(1 + 56*S^2))/(9*S) + (4*(7 + 220*S^2))/(3*S))*Zeta[3] + (8*(-7 + 132*S^2)*Zeta[5])/(3*S)) + HPL[{0}, S^2]*((295*Pi^2*S)/9 + (3953*Pi^4*S)/540 + (43007*Pi^6*S)/22680 + (65*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + ((-13*(1 + S^2))/(3*S) + (Pi^2*(-10 + 73*S^2))/(9*S))*HPL[{2}, -S^2]^2 - (38*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) - (4*(7 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-4*(-1 + 12*S^2))/(3*S) + (Pi^2*(33 + 25*S^2))/(9*S))*HPL[{4}, -S^2] - (10*(2 + S^2)*HPL[{5}, -S^2])/S - (2*(-10 + 17*S^2)*HPL[{6}, -S^2])/(3*S) + (68*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((4*(21 + 13*S^2))/(3*S) - (4*Pi^2*(-3 + 77*S^2))/(9*S))*HPL[{3, 1}, -S^2] - (2*(23 + 17*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(-15 + 2*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (14*(-1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) - (20*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-104*(1 + S^2))/(3*S) + (4*Pi^2*(-1 + 56*S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (128*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (16*(23 + 21*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (16*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (32*(9 + 10*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (16*(15 + 17*S^2)*HPL[{4, 1, 1}, -S^2])/S - (80*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (96*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (160*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((16*S)/3 + (34*Pi^2*S)/9)*Zeta[3] - 12*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((130*Pi^2*(1 + S^2))/(9*S) - (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((218*Pi^2*(1 + S^2))/(9*S) + (1313*Pi^4*(1 + S^2))/(180*S) + (62*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (4*(1 + S^2)*HPL[{3}, -S^2])/S - (8*(1 + S^2)*HPL[{4}, -S^2])/S + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-12*(1 + S^2))/S - (2*Pi^2*(193 + 41*S^2))/(9*S) + (8*(-1 + 2*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-4*(1 + 5*S^2))/(3*S) + (Pi^2*(-2 + 15*S^2))/(9*S) + (8*(4 + 3*S^2)*HPL[{2, 1}, -S^2])/S + (8*(4 + 3*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((-10*(1 + S^2))/(3*S) + (Pi^2*(31 + 188*S^2))/(9*S) + (Pi^4*(284 + 3703*S^2))/(540*S) + (4*(3 + S^2)*HPL[{3}, -S^2])/S + (2*(25 + 13*S^2)*HPL[{4}, -S^2])/(3*S) - (64*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(7 + 10*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*(-1 + 5*S^2)*Zeta[3])/(3*S)) - 12*S*Zeta[5] + HPL[{1}, -S^2]*((263*Pi^2*(1 + S^2))/(9*S) + (3917*Pi^4*(1 + S^2))/(540*S) + (206*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + ((-16*(1 + S^2))/(3*S) + (2*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (16*(1 + S^2)*HPL[{4}, -S^2])/S - (44*(1 + S^2)*HPL[{5}, -S^2])/(3*S) - (124*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((16*(1 + S^2))/(3*S) + (52*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (44*(1 + S^2)*Zeta[5])/(3*S))) + 744*S*Zeta[7]) + HPL[{1}, -S^2]^2*((295*Pi^2*(1 + S^2))/(6*S) + (9533*Pi^4*(1 + S^2))/(1080*S) + (58141*Pi^6*(1 + S^2))/(45360*S) + (206*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) - (4*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((490*(1 + S^2))/(3*S) + (196*Pi^2*(1 + S^2))/(9*S))*HPL[{5}, -S^2] + (637*(1 + S^2)*HPL[{6}, -S^2])/(3*S) + (358*(1 + S^2)*HPL[{7}, -S^2])/S + ((-976*(1 + S^2))/(3*S) - (394*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((-3452*(1 + S^2))/(3*S) - (1400*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1}, -S^2] + (16*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) + (22*(1 + S^2)*HPL[{4, 3}, -S^2])/S - (208*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (52*(1 + S^2)*HPL[{5, 2}, -S^2])/S - (278*(1 + S^2)*HPL[{6, 1}, -S^2])/S + (124*Pi^2*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + ((848*(1 + S^2))/S + (240*Pi^2*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (544*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (496*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (1488*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (1872*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (1488*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (4464*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S + (9296*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((-1696*(1 + S^2))/S - (944*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] - (992*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S - (1360*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (1984*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (1984*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (4960*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (14496*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (2720*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (2400*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (4800*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((1180*(1 + S^2))/(3*S) + (125*Pi^2*(1 + S^2))/(3*S) + (859*Pi^4*(1 + S^2))/(180*S))*Zeta[3] - (40*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{3, 1}, -S^2]*((-564*(1 + S^2))/S - (832*Pi^2*(1 + S^2))/(9*S) - (256*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-2360*(1 + S^2))/(3*S) - (1058*Pi^2*(1 + S^2))/(9*S) - (2779*Pi^4*(1 + S^2))/(180*S) - (256*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((1180*(1 + S^2))/(3*S) + (409*Pi^2*(1 + S^2))/(9*S) + (1219*Pi^4*(1 + S^2))/(270*S) - (18*(1 + S^2)*HPL[{4}, -S^2])/S - (824*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (248*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (496*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (12*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((144*(1 + S^2))/S + (137*Pi^2*(1 + S^2))/(9*S) + (44*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((103*Pi^2*(1 + S^2))/(18*S) + (62*(1 + S^2)*HPL[{3}, -S^2])/S - (124*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (62*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((1128*(1 + S^2))/S + (184*Pi^2*(1 + S^2))/S + (512*(1 + S^2)*Zeta[3])/S) + ((1046*(1 + S^2))/(3*S) + (455*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2}, -S^2]*((590*(1 + S^2))/S + (1435*Pi^2*(1 + S^2))/(18*S) + (3367*Pi^4*(1 + S^2))/(360*S) + ((496*(1 + S^2))/(3*S) + (197*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (32*(1 + S^2)*HPL[{5}, -S^2])/S - (62*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (248*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (744*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (496*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (992*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((428*(1 + S^2))/(3*S) + (215*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (182*(1 + S^2)*Zeta[5])/S) + (462*(1 + S^2)*Zeta[7])/S) + HPL[{1}, -S^2]*((245*Pi^2*(1 + S^2))/(3*S) + (3661*Pi^4*(1 + S^2))/(270*S) + (20507*Pi^6*(1 + S^2))/(11340*S) + (13367*Pi^8*(1 + S^2))/(42525*S) + ((28*(1 + S^2))/S + (146*Pi^2*(1 + S^2))/(27*S))*HPL[{2}, -S^2]^3 + ((-16*(1 + S^2))/(3*S) - (11*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2]^2 + (34*(1 + S^2)*HPL[{4}, -S^2]^2)/S + ((1094*(1 + S^2))/(3*S) + (47*Pi^2*(1 + S^2))/S)*HPL[{6}, -S^2] + (1274*(1 + S^2)*HPL[{7}, -S^2])/(3*S) + (1228*(1 + S^2)*HPL[{8}, -S^2])/S - (62*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + (32*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) + (2*(1 + S^2)*HPL[{4, 3}, -S^2])/(3*S) + ((-916*(1 + S^2))/(3*S) - (436*Pi^2*(1 + S^2))/(9*S))*HPL[{5, 1}, -S^2] - (8*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (8*(1 + S^2)*HPL[{5, 3}, -S^2])/S - (1394*(1 + S^2)*HPL[{6, 1}, -S^2])/(3*S) + (20*(1 + S^2)*HPL[{6, 2}, -S^2])/S - (876*(1 + S^2)*HPL[{7, 1}, -S^2])/S - (32*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + ((1984*(1 + S^2))/(3*S) + (1168*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2, 1}, -S^2] + (1648*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (4912*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) - (84*(1 + S^2)*HPL[{3, 3, 2}, -S^2])/S + ((7000*(1 + S^2))/(3*S) + (3940*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1, 1}, -S^2] + (4912*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + (140*(1 + S^2)*HPL[{4, 1, 3}, -S^2])/S + (14704*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) - (104*(1 + S^2)*HPL[{4, 2, 2}, -S^2])/S + (284*(1 + S^2)*HPL[{4, 3, 1}, -S^2])/S + (10240*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + (88*(1 + S^2)*HPL[{5, 1, 2}, -S^2])/S + (1288*(1 + S^2)*HPL[{5, 2, 1}, -S^2])/S + (4236*(1 + S^2)*HPL[{6, 1, 1}, -S^2])/S - (3296*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + ((-1696*(1 + S^2))/S - (944*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1, 1}, -S^2] + (2208*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (2208*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (5504*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (992*(1 + S^2)*HPL[{3, 2, 2, 1}, -S^2])/S - (2976*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (16032*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (2976*(1 + S^2)*HPL[{4, 1, 2, 1}, -S^2])/S - (8928*(1 + S^2)*HPL[{4, 2, 1, 1}, -S^2])/S - (18592*(1 + S^2)*HPL[{5, 1, 1, 1}, -S^2])/S + ((3392*(1 + S^2))/S + (1888*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1, 1}, -S^2] - (1984*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S - (5952*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S + (2720*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (11904*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S + (19840*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S + (23808*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S + (49600*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S + (149568*(1 + S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S - (5440*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - (4800*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + (9600*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((-70*(1 + S^2))/(3*S) + (17*Pi^2*(1 + S^2))/(3*S))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((-2256*(1 + S^2))/S - (368*Pi^2*(1 + S^2))/S - (1024*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-2360*(1 + S^2))/(3*S) - (1070*Pi^2*(1 + S^2))/(9*S) - (2126*Pi^4*(1 + S^2))/(135*S) - (752*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{5}, -S^2]*((752*(1 + S^2))/(3*S) + (86*Pi^2*(1 + S^2))/(3*S) - (64*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (48*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((904*(1 + S^2))/(3*S) + (218*Pi^2*(1 + S^2))/(9*S) + (389*Pi^4*(1 + S^2))/(135*S) - (28*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (28*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((-1076*(1 + S^2))/(3*S) - (448*Pi^2*(1 + S^2))/(9*S) + (40*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((7*Pi^2*(1 + S^2))/S + (907*Pi^4*(1 + S^2))/(540*S) + (206*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{4}, -S^2])/S - (412*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (124*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (248*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (206*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{4, 1}, -S^2]*((-1380*(1 + S^2))/S - (1636*Pi^2*(1 + S^2))/(9*S) + (272*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 2, 1}, -S^2]*((412*Pi^2*(1 + S^2))/(9*S) + (496*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((4720*(1 + S^2))/(3*S) + (2116*Pi^2*(1 + S^2))/(9*S) + (2779*Pi^4*(1 + S^2))/(90*S) + (512*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((1128*(1 + S^2))/S + (2488*Pi^2*(1 + S^2))/(9*S) + (1504*(1 + S^2)*Zeta[3])/S) + ((1610*(1 + S^2))/(3*S) + (539*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2, 1}, -S^2]*((-1180*(1 + S^2))/S - (1435*Pi^2*(1 + S^2))/(9*S) - (3367*Pi^4*(1 + S^2))/(180*S) + (496*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (1488*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (992*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (1984*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((-856*(1 + S^2))/(3*S) - (430*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (364*(1 + S^2)*Zeta[5])/S) + HPL[{3}, -S^2]*((590*(1 + S^2))/S + (65*Pi^2*(1 + S^2))/S + (319*Pi^4*(1 + S^2))/(54*S) - (22*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (80*(1 + S^2)*HPL[{5}, -S^2])/S + ((-992*(1 + S^2))/(3*S) - (394*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (808*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (40*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (28*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (1648*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (496*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (1488*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (992*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-100*(1 + S^2))/(3*S) - (16*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (16*(1 + S^2)*Zeta[5])/S) + Zeta[3]*((590*(1 + S^2))/S + (497*Pi^2*(1 + S^2))/(9*S) + (961*Pi^4*(1 + S^2))/(180*S) + (332*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((980*(1 + S^2))/S + (1030*Pi^2*(1 + S^2))/(9*S) + (449*Pi^4*(1 + S^2))/(36*S) + (35*Pi^6*(1 + S^2))/(24*S) - (10*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((16*(1 + S^2))/(3*S) + (22*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + (56*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (100*(1 + S^2)*HPL[{6}, -S^2])/S - (248*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-16*(1 + S^2))/(3*S) - (190*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] - (824*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (824*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (8*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (72*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (124*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (1648*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (3296*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (11904*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + ((514*(1 + S^2))/(3*S) + (73*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (22*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((-206*Pi^2*(1 + S^2))/(9*S) - (248*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((182*(1 + S^2))/S + (227*Pi^2*(1 + S^2))/(9*S) - (248*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (20*(1 + S^2)*Zeta[3])/S) + (562*(1 + S^2)*Zeta[5])/(3*S)) + (602*(1 + S^2)*Zeta[7])/S) + HPL[{2}, -S^2]*((980*(1 + S^2))/S + (10*Pi^2*(73 + 88*S^2))/(9*S) + (Pi^4*(3613 + 6028*S^2))/(540*S) + (Pi^6*(12202 + 31121*S^2))/(22680*S) + ((-21 - 13*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((2*(-39 + 35*S^2))/(3*S) + (Pi^2*(-95 + 53*S^2))/(9*S))*HPL[{5}, -S^2] + (6*(9 + 19*S^2)*HPL[{6}, -S^2])/S + (2*(-205 + 86*S^2)*HPL[{7}, -S^2])/(3*S) - (356*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-2*Pi^2*(38 + 213*S^2))/(9*S) - (4*(39 + 238*S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((Pi^2*(-97 - 1309*S^2))/(9*S) - (4*(94 + 725*S^2))/(3*S))*HPL[{4, 1}, -S^2] - (8*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (2*(155 + 166*S^2)*HPL[{4, 3}, -S^2])/(3*S) - (2*(21 + 187*S^2)*HPL[{5, 1}, -S^2])/(3*S) + (4*(223 + 232*S^2)*HPL[{5, 2}, -S^2])/(3*S) + (2*(1106 + 759*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((1108*(1 + S^2))/(3*S) + (4*Pi^2*(218 + 135*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((-236*Pi^2*(11 + 3*S^2))/(9*S) - (4*(773 + 347*S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + (640*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (2*(81 + 745*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (8*(31 + 197*S^2)*HPL[{3, 3, 1}, -S^2])/S + (4*(-521 + 537*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (2*(391 + 2383*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + (2*(1279 + 7255*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (4*(1265 + 7449*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((568*(-1 + S^2))/S + (8*Pi^2*(-209 + 97*S^2))/(9*S))*HPL[{2, 1, 1, 1}, -S^2] + (1328*(-1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) - (32*(487 + 583*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (32*(-139 + 27*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (32*(-139 + 27*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (16*(-527 + 303*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (16*(-1555 + 881*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) + (1024*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (3584*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) - (3584*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (160*(115 + 154*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) + (2080*(-1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((10*(1 + 60*S^2))/(3*S) + (Pi^2*(3 + 236*S^2))/(9*S) + (Pi^4*(-142 + 1807*S^2))/(540*S))*Zeta[3] - (2*(-4 + 25*S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1, 1}, -S^2]*((1024*(-1 + S^2))/(3*S) + (4*Pi^2*(-111 + 200*S^2))/(9*S) + (224*(1 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((590*(-1 + S^2))/(3*S) + (Pi^2*(-491 + 214*S^2))/(9*S) + (Pi^4*(-5760 + 1327*S^2))/(540*S) + (896*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (1792*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(81 + 8*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((23*Pi^2*(1 + 12*S^2))/(9*S) + (10*(1 + 60*S^2))/(3*S) + (Pi^4*(-144 + 877*S^2))/(270*S) - (26*(6 + 7*S^2)*HPL[{4}, -S^2])/(3*S) - (4*(171 + 7*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(25 + 108*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (8*(29 + 195*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(8 + 13*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((-2*Pi^2*(-36 + 67*S^2))/(3*S) - (4*(-105 + 151*S^2))/(3*S) - (16*(3 + 17*S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((8*Pi^2*(-1 + 2*S^2))/(3*S) + (8*(11 + 12*S^2))/(3*S) - (130*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(41 + 59*S^2)*Zeta[3])/(3*S)) + ((2*(17 + 278*S^2))/(3*S) + (Pi^2*(-44 + 301*S^2))/(9*S))*Zeta[5] + (2*(-35 + 146*S^2)*Zeta[7])/S) + Log[T]*((-490*Pi^2*S)/3 - (7297*Pi^4*S)/270 - (4547*Pi^6*S)/1260 - (942223*Pi^8*S)/1360800 - (S*HPL[{0}, S^2]^8)/48 + HPL[{0}, S^2]^7*((-5*S)/72 - (5*(1 + S^2)*HPL[{1}, -S^2])/(72*S)) + ((Pi^2*(-74 - 157*S^2))/(27*S) - (227*(1 + S^2))/(9*S))*HPL[{2}, -S^2]^3 - (83*(-1 + S^2)*HPL[{2}, -S^2]^4)/(18*S) + HPL[{0}, S^2]^6*((-37*S)/72 - (115*Pi^2*S)/432 - (5*(1 + S^2)*HPL[{1}, -S^2])/(12*S) - (7*(1 + S^2)*HPL[{1}, -S^2]^2)/(18*S) + ((-3 - 25*S^2)*HPL[{2}, -S^2])/(72*S)) + HPL[{1}, -S^2]^6*((-10*Pi^2*(1 + S^2))/(9*S) - (40*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((10*(1 + S^2))/(3*S) + (Pi^2*(-23 + 15*S^2))/(9*S))*HPL[{3}, -S^2]^2 + (68*HPL[{4}, -S^2]^2)/(3*S) + ((Pi^2*(-296 - 425*S^2))/(9*S) - (2*(461 + 585*S^2))/(3*S))*HPL[{6}, -S^2] - (10*(61 + 168*S^2)*HPL[{7}, -S^2])/(3*S) - (2*(735 + 1858*S^2)*HPL[{8}, -S^2])/(3*S) + ((284*(-1 + S^2))/S + (8*Pi^2*(-58 + 95*S^2))/(9*S))*HPL[{2, 1}, -S^2]^2 - (8*(-93 + 91*S^2)*HPL[{3, 1}, -S^2]^2)/(3*S) + ((16*(-2 + S^2))/S + (Pi^2*(-39 + 43*S^2))/(9*S))*HPL[{4, 2}, -S^2] - (8*(-3 + 5*S^2)*HPL[{4, 3}, -S^2])/S + ((4*(167 + 313*S^2))/(3*S) + (2*Pi^2*(157 + 319*S^2))/(9*S))*HPL[{5, 1}, -S^2] - (2*(-68 + 101*S^2)*HPL[{5, 2}, -S^2])/(3*S) - (4*(-8 + 17*S^2)*HPL[{5, 3}, -S^2])/(3*S) + (4*(226 + 347*S^2)*HPL[{6, 1}, -S^2])/(3*S) - (2*(18 + 17*S^2)*HPL[{6, 2}, -S^2])/(3*S) + (16*(82 + 185*S^2)*HPL[{7, 1}, -S^2])/(3*S) - (1040*(-1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((8*(1 + S^2))/S + (4*Pi^2*(-3 + 2*S^2))/(9*S))*HPL[{3, 1, 2}, -S^2] + ((-1792*(1 + S^2))/(3*S) - (4*Pi^2*(151 + 312*S^2))/(9*S))*HPL[{3, 2, 1}, -S^2] - (2*(287 + 1585*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) - (16*(98 + 605*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) + (8*(-2 + 13*S^2)*HPL[{3, 3, 2}, -S^2])/(3*S) + ((-32*(201 + 205*S^2))/(3*S) - (8*Pi^2*(291 + 548*S^2))/(9*S))*HPL[{4, 1, 1}, -S^2] - (4*(357 + 2455*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) - (8*(-3 + S^2)*HPL[{4, 1, 3}, -S^2])/(3*S) - (4*(1113 + 7327*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (2*(-19 + 105*S^2)*HPL[{4, 2, 2}, -S^2])/(3*S) - (8*(-19 + 45*S^2)*HPL[{4, 3, 1}, -S^2])/(3*S) - (40*(237 + 1510*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) - (4*(-51 + 7*S^2)*HPL[{5, 1, 2}, -S^2])/(3*S) - (4*(-171 + 487*S^2)*HPL[{5, 2, 1}, -S^2])/(3*S) - (32*(9 + 251*S^2)*HPL[{6, 1, 1}, -S^2])/(3*S) + (1248*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((16*Pi^2*(117 + 214*S^2))/(9*S) + (16*(301 + 309*S^2))/(3*S))*HPL[{3, 1, 1, 1}, -S^2] - (8*(1319 + 551*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) - (8*(1319 + 551*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (40*(-1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/(3*S) - (8*(2723 + 1955*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (40*(-1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/(3*S) + (8*(291 + 301*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(3*S) + (2368*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S - (128*(501 + 358*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) + (32*(-7 + 11*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(3*S) + (32*(215 + 233*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(3*S) + (32*(659 + 677*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(3*S) + (32*(1393 + 1451*S^2)*HPL[{5, 1, 1, 1}, -S^2])/(3*S) + ((-9760*(1 + S^2))/(3*S) - (80*Pi^2*(47 + 86*S^2))/(9*S))*HPL[{2, 1, 1, 1, 1}, -S^2] - (2048*(-1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (6144*(-1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (4736*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S) + (4736*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (640*(-44 + 71*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) - (28480*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S) - (15808*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S - (56896*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S) - (39488*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S - (119488*(1 + S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S + (5760*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (4480*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S - (8960*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (52*S - (14*Pi^2*S)/3)*Zeta[3]^2 + HPL[{0}, S^2]^5*((-83*S)/60 - (397*Pi^2*S)/540 - (269*(1 + S^2)*HPL[{1}, -S^2]^2)/(180*S) - (31*(1 + S^2)*HPL[{1}, -S^2]^3)/(30*S) + ((-5 - 78*S^2)*HPL[{2}, -S^2])/(60*S) + HPL[{1}, -S^2]*((-269*(1 + S^2))/(180*S) - (67*Pi^2*(1 + S^2))/(90*S) - (229*(1 + S^2)*HPL[{2}, -S^2])/(180*S)) + ((1 + S^2)*HPL[{3}, -S^2])/(12*S) + ((214 - 25*S^2)*HPL[{2, 1}, -S^2])/(90*S) - (3*S*Zeta[3])/2) + HPL[{1}, -S^2]^4*((-106*Pi^2*(1 + S^2))/(9*S) - (749*Pi^4*(1 + S^2))/(270*S) + ((-424*(1 + S^2))/(3*S) - (236*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (340*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (32*(1 + S^2)*HPL[{4}, -S^2])/S + (680*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (200*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (400*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (340*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^5*((-34*Pi^2*(1 + S^2))/(9*S) - (136*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (40*(1 + S^2)*HPL[{3}, -S^2])/S + (80*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (40*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((2304*(1 + S^2))/S + (32*Pi^2*(133 + 85*S^2))/(9*S) - (160*(-37 + 2*S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((4*(45 + 557*S^2))/(3*S) + (Pi^2*(50 + 973*S^2))/(9*S) - (8*(2 + 3*S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((Pi^2*(-101 - 329*S^2))/(9*S) - (2*(387 + 427*S^2))/(3*S) - (4*(-163 + 45*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(37 + 3*S^2)*Zeta[3])/(3*S)) + HPL[{2, 2, 1}, -S^2]*((2048*(-1 + S^2))/(3*S) + (8*Pi^2*(-214 + 97*S^2))/(9*S) + (32*(-79 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1}, -S^2]*((32*(-79 + 7*S^2))/S + (4*Pi^2*(-1392 + 49*S^2))/(9*S) + (32*(-251 + 14*S^2)*Zeta[3])/(3*S)) + HPL[{4, 1}, -S^2]*((8*(183 + 943*S^2))/(3*S) + (2*Pi^2*(209 + 1557*S^2))/(9*S) - (8*(-21 + 19*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((Pi^4*(-1919 - 2055*S^2))/(540*S) - (914*(1 + S^2))/(3*S) - (2*Pi^2*(109 + 120*S^2))/(9*S) - (4*(-41 + 57*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-61 + 43*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (32*(-13 + 14*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(-11 + 20*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((-1560*(1 + S^2))/S - (4*Pi^2*(403 + 616*S^2))/(9*S) - (4*Pi^4*(569 + 1526*S^2))/(135*S) - (128*(1 + 25*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((Pi^4*(2132 - 4955*S^2))/(1080*S) + (Pi^2*(239 - 466*S^2))/(18*S) - (295*(-1 + S^2))/(3*S) - (2*(35 + 199*S^2)*HPL[{3}, -S^2])/(3*S) - (31*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (156*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (296*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (592*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(22 + 95*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((780*(1 + S^2))/S + (2*Pi^2*(401 + 626*S^2))/(9*S) + (Pi^4*(2326 + 5921*S^2))/(270*S) + (32*(-97 + 98*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*(8 + 197*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^4*((-188*S)/9 - (887*Pi^2*S)/216 - (16537*Pi^4*S)/12960 - (46*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (22*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + ((-114 - 295*S^2)/(36*S) - (23*Pi^2*(1 + 9*S^2))/(72*S))*HPL[{2}, -S^2] + ((27 - 188*S^2)*HPL[{2}, -S^2]^2)/(72*S) + HPL[{1}, -S^2]^2*((-37*(1 + S^2))/(4*S) - (19*Pi^2*(1 + S^2))/(6*S) - (257*(1 + S^2)*HPL[{2}, -S^2])/(36*S)) + ((-15 - 17*S^2)*HPL[{3}, -S^2])/(12*S) + ((-13 - 21*S^2)*HPL[{4}, -S^2])/(12*S) + ((81 + 16*S^2)*HPL[{2, 1}, -S^2])/(6*S) + ((24 + 233*S^2)*HPL[{3, 1}, -S^2])/(18*S) - (2*(4 + 41*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (23*S*Zeta[3])/6 + HPL[{1}, -S^2]*((-473*(1 + S^2))/(36*S) - (121*Pi^2*(1 + S^2))/(36*S) - (33*(1 + S^2)*HPL[{2}, -S^2])/(4*S) - (11*(1 + S^2)*HPL[{3}, -S^2])/(6*S) + (257*(1 + S^2)*HPL[{2, 1}, -S^2])/(18*S) - (38*(1 + S^2)*Zeta[3])/(9*S))) + (-1048*S - (340*Pi^2*S)/3)*Zeta[5] + Zeta[3]*((-3560*S)/3 - (1048*Pi^2*S)/9 - (2891*Pi^4*S)/270 - (232*S*Zeta[5])/3) + HPL[{0}, S^2]^3*((-295*S)/9 - (167*Pi^2*S)/18 - (7939*Pi^4*S)/3240 - (65*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) - (26*(1 + S^2)*HPL[{1}, -S^2]^5)/(9*S) + ((1 - 163*S^2)*HPL[{2}, -S^2]^2)/(18*S) + HPL[{1}, -S^2]^3*((-436*(1 + S^2))/(27*S) - (158*Pi^2*(1 + S^2))/(27*S) - (124*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((Pi^2*(3 + 2*S^2))/(9*S) - (2*(-5 + 19*S^2))/(9*S))*HPL[{3}, -S^2] + ((1 - 18*S^2)*HPL[{4}, -S^2])/(9*S) + (2*(3 + 4*S^2)*HPL[{5}, -S^2])/(3*S) + ((-2*Pi^2*(-194 + 11*S^2))/(27*S) + (2*(204 + 47*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (2*(31 + 174*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (2*(16 + 29*S^2)*HPL[{3, 2}, -S^2])/(9*S) + (2*(29 + 61*S^2)*HPL[{4, 1}, -S^2])/(9*S) - (16*(7 + 45*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) - (4*(169 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) - (16*(42 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (8*(58 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-44*S)/9 - (52*Pi^2*S)/9)*Zeta[3] + HPL[{1}, -S^2]^2*((-263*(1 + S^2))/(9*S) - (232*Pi^2*(1 + S^2))/(27*S) - (206*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (124*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (46*(1 + S^2)*Zeta[3])/(9*S)) + HPL[{1}, -S^2]*((-310*(1 + S^2))/(9*S) - (487*Pi^2*(1 + S^2))/(54*S) - (805*Pi^4*(1 + S^2))/(324*S) + ((-248*(1 + S^2))/(9*S) - (415*Pi^2*(1 + S^2))/(54*S))*HPL[{2}, -S^2] - (83*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) - (32*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (10*(1 + S^2)*HPL[{4}, -S^2])/(9*S) + (412*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (356*(1 + S^2)*HPL[{3, 1}, -S^2])/(9*S) - (248*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (14*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((Pi^2*(-43 - 414*S^2))/(54*S) - (4*(11 + 61*S^2))/(9*S) - (4*(4 + 7*S^2)*HPL[{3}, -S^2])/(9*S) + (2*(169 + 3*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (2*(-3 + 14*S^2)*Zeta[3])/(9*S)) - (182*S*Zeta[5])/9) + HPL[{1}, -S^2]^2*((-590*Pi^2*(1 + S^2))/(9*S) - (751*Pi^4*(1 + S^2))/(60*S) - (47329*Pi^6*(1 + S^2))/(22680*S) - (31*Pi^2*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (124*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + ((-476*(1 + S^2))/(3*S) - (218*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] - (224*(1 + S^2)*HPL[{5}, -S^2])/S - (318*(1 + S^2)*HPL[{6}, -S^2])/S + ((848*(1 + S^2))/S + (472*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] + (544*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (1872*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (368*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-1696*(1 + S^2))/S - (944*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] - (1360*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (992*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (3360*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (2720*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (2400*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (4800*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-564*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-2360*(1 + S^2))/(3*S) - (1058*Pi^2*(1 + S^2))/(9*S) - (2779*Pi^4*(1 + S^2))/(180*S) - (824*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (256*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-564*(1 + S^2))/S - (626*Pi^2*(1 + S^2))/(9*S) + (496*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((1128*(1 + S^2))/S + (184*Pi^2*(1 + S^2))/S + (512*(1 + S^2)*Zeta[3])/S) - (528*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^3*((-94*Pi^2*(1 + S^2))/(3*S) - (97*Pi^4*(1 + S^2))/(15*S) + ((-848*(1 + S^2))/(3*S) - (116*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (224*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (368*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((1696*(1 + S^2))/(3*S) + (944*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (1360*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (992*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (1120*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (2720*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (800*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (1600*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-848*(1 + S^2))/(3*S) - (344*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-376*(1 + S^2))/S - (184*Pi^2*(1 + S^2))/(3*S) - (496*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (512*(1 + S^2)*Zeta[3])/(3*S)) - (896*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((Pi^4*(-1251 - 4771*S^2))/(540*S) - (10*(119 + 237*S^2))/(3*S) - (2*Pi^2*(150 + 433*S^2))/(9*S) + (2*(-19 + 55*S^2)*HPL[{4}, -S^2])/(3*S) + (4*(-39 + 20*S^2)*HPL[{5}, -S^2])/(3*S) + ((8*(73 + 2*S^2))/S - (4*Pi^2*(-192 + 31*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (8*(28 + 207*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(1 + 6*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (8*(-9 + 13*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (16*(23 + 215*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (16*(-157 + 9*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (16*(-481 + 35*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (32*(-57 + 8*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-8*Pi^2*(10 + S^2))/(9*S) + (8*(-7 + 24*S^2))/(3*S))*Zeta[3] - (16*(25 + 9*S^2)*Zeta[5])/(3*S)) + HPL[{2, 1}, -S^2]*((3560*(1 + S^2))/(3*S) + (2*Pi^2*(859 + 603*S^2))/(9*S) + (Pi^4*(7043 + 3206*S^2))/(270*S) + (32*(-47 + 49*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (16*(-157 + 9*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (16*(-497 + 55*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (1024*(-1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (2368*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (32*(17 + 82*S^2)*HPL[{3, 1, 1}, -S^2])/S + (2080*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-8*(-69 + 2*S^2))/S - (4*Pi^2*(-211 + 9*S^2))/(9*S))*Zeta[3] + (8*(287 + 9*S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((Pi^6*(-19338 - 57773*S^2))/(22680*S) + (Pi^4*(-4553 - 8742*S^2))/(540*S) - (980*(1 + S^2))/S - (5*Pi^2*(175 + 234*S^2))/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(29 - 25*S^2))/(3*S) - (4*(-15 + 19*S^2))/(3*S))*HPL[{4}, -S^2] - (2*(-53 + 129*S^2)*HPL[{5}, -S^2])/(3*S) - (2*(-52 + 57*S^2)*HPL[{6}, -S^2])/S + (592*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((8*Pi^2*(-59 + 94*S^2))/(9*S) + (4*(-211 + 215*S^2))/(3*S))*HPL[{3, 1}, -S^2] + (8*(35 + 199*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(169 + 1251*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (18*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (4*(-63 + 145*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-568*(-1 + S^2))/S - (16*Pi^2*(-58 + 95*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (624*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (128*(41 + 17*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (1328*(-1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (16*(-275 + 277*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (1024*(-1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (32*(791 + 986*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (2080*(-1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-2*Pi^2*(11 + 224*S^2))/(9*S) - (4*(5 + 261*S^2))/(3*S))*Zeta[3] - (8*(4 + 3*S^2)*Zeta[3]^2)/(3*S) + HPL[{3}, -S^2]*((-2*Pi^2*(15 + 244*S^2))/(9*S) - (4*(25 + 281*S^2))/(3*S) - (8*(-157 + 9*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(3 + 2*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-1024*(-1 + S^2))/(3*S) - (4*Pi^2*(-214 + 97*S^2))/(9*S) - (16*(-79 + 5*S^2)*Zeta[3])/(3*S)) - (4*(4 + 273*S^2)*Zeta[5])/(3*S)) + HPL[{0}, S^2]^2*(-490*S - (1337*Pi^2*S)/18 - (1327*Pi^4*S)/135 - (4363*Pi^6*S)/1890 - (34*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) - (10*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + ((Pi^2*(64 - 373*S^2))/(36*S) + (26 - 253*S^2)/(6*S))*HPL[{2}, -S^2]^2 - (83*S*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((-106*(1 + S^2))/(3*S) - (163*Pi^2*(1 + S^2))/(18*S) - (86*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-13 + 7*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-95 - 101*S^2)/(3*S) - (5*Pi^2*(15 + 23*S^2))/(18*S))*HPL[{4}, -S^2] + ((-50 - 87*S^2)*HPL[{5}, -S^2])/(3*S) + ((-80 - 141*S^2)*HPL[{6}, -S^2])/(3*S) + (74*(-1 + 5*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((2*(100 + 317*S^2))/(3*S) + (Pi^2*(48 + 451*S^2))/(9*S))*HPL[{3, 1}, -S^2] + (5*(-7 + 24*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2*(5 + 209*S^2)*HPL[{4, 1}, -S^2])/(3*S) + ((-11 - S^2)*HPL[{4, 2}, -S^2])/(3*S) + (2*(35 + 81*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-4*(98 + 311*S^2))/(3*S) - (2*Pi^2*(49 + 466*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (8*(-118 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4*(736 + 67*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (4*(-1 + 4*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (4*(1 + 162*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (8*(18 + 275*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (16*(131 + 35*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (16*(12 + 109*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (80*(5 + 44*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + ((-184*S)/3 - (106*Pi^2*S)/9)*Zeta[3] - 16*S*Zeta[3]^2 + HPL[{1}, -S^2]^2*((-590*(1 + S^2))/(3*S) - (217*Pi^2*(1 + S^2))/(6*S) - (7643*Pi^4*(1 + S^2))/(1080*S) + ((-422*(1 + S^2))/(3*S) - (515*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2] - (31*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (116*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (74*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (212*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (172*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (344*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (26*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-94*(1 + S^2))/S - (59*Pi^2*(1 + S^2))/(3*S) - (212*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3}, -S^2])/S + (344*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (44*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((Pi^2*(-73 - 124*S^2))/(18*S) - (2*(60 + 91*S^2))/(3*S) - (28*(-3 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(6 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((Pi^2*(505 + 118*S^2))/(9*S) + (2*(427 + 171*S^2))/(3*S) + (4*(26 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((Pi^4*(-958 - 7205*S^2))/(1080*S) + (Pi^2*(-106 - 303*S^2))/(9*S) - (5*(58 + 117*S^2))/(3*S) - (2*(-8 + 29*S^2)*HPL[{3}, -S^2])/(3*S) + ((35 - 19*S^2)*HPL[{4}, -S^2])/(3*S) - (4*(-118 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-7 + 30*S^2)*HPL[{3, 1}, -S^2])/S - (148*(-1 + 5*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (2*(1 + 8*S^2)*Zeta[3])/S) - 88*S*Zeta[5] + HPL[{1}, -S^2]*((-295*(1 + S^2))/S - (448*Pi^2*(1 + S^2))/(9*S) - (187*Pi^4*(1 + S^2))/(24*S) - (103*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-182*(1 + S^2))/(3*S) - (23*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (106*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (116*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((844*(1 + S^2))/(3*S) + (515*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (644*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (44*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (280*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (424*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (248*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (840*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (688*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-38*(1 + S^2))/S - (109*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-589*(1 + S^2))/(3*S) - (205*Pi^2*(1 + S^2))/(6*S) - (22*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (124*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (46*(1 + S^2)*Zeta[3])/(3*S)) - (238*(1 + S^2)*Zeta[5])/(3*S))) + HPL[{0}, S^2]*((-295*Pi^2*S)/9 - (487*Pi^4*S)/60 - (20891*Pi^6*S)/11340 - (26*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^5)/(9*S) + (28*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) - (4*(-3 + 2*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(13 + 7*S^2))/(3*S) + (2*(19 + 33*S^2))/(3*S))*HPL[{5}, -S^2] + (2*(-40 + S^2)*HPL[{6}, -S^2])/(3*S) + 56*S*HPL[{7}, -S^2] - (64*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((4*(7 + S^2))/(3*S) + (2*Pi^2*(38 + 49*S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((26*Pi^2*(5 + 7*S^2))/(9*S) - (8*(-6 + 11*S^2))/(3*S))*HPL[{4, 1}, -S^2] - (10*(1 + 4*S^2)*HPL[{4, 2}, -S^2])/(3*S) - (20*(8 + S^2)*HPL[{4, 3}, -S^2])/(3*S) - (4*(-16 + 35*S^2)*HPL[{5, 1}, -S^2])/(3*S) - (2*(235 + 23*S^2)*HPL[{5, 2}, -S^2])/(3*S) - (4*(250 + 33*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((-104*(1 + S^2))/(3*S) - (8*Pi^2*(93 + 10*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((-8*Pi^2*(275 + 29*S^2))/(9*S) - (8*(39 + 31*S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + (4*(-5 + 13*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (4*(17 + 23*S^2)*HPL[{3, 2, 1}, -S^2])/S - (8*(6 + S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) - (64*(5 + 2*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) + (8*(69 + 88*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (4*(81 + 43*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) - (4*(297 + 115*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) - (8*(101 + 37*S^2)*HPL[{5, 1, 1}, -S^2])/S + ((208*(1 + S^2))/(3*S) + (8*Pi^2*(21 + 2*S^2))/S)*HPL[{2, 1, 1, 1}, -S^2] + (608*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) - (64*(5 + 4*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (32*(46 + 47*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) - (32*(46 + 47*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) - (32*(103 + 104*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) - (32*(108 + 109*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (160*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (544*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) + (544*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (960*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (320*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((-52*Pi^2*S)/9 - (373*Pi^4*S)/90)*Zeta[3] + 8*S*Zeta[3]^2 + HPL[{2}, -S^2]^2*((Pi^2*(17 - 147*S^2))/(18*S) + (3*(1 + S^2))/S - (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (76*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-436*Pi^2*(1 + S^2))/(27*S) - (1313*Pi^4*(1 + S^2))/(270*S) - (124*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((20*(1 + S^2))/(3*S) - (10*Pi^2*(-1 + 3*S^2))/(9*S) + (Pi^4*(149 + 59*S^2))/(270*S) + (20*(4 + S^2)*HPL[{4}, -S^2])/(3*S) - (8*(3 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(17 + 5*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (16*(4 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/S - (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^4*((-65*Pi^2*(1 + S^2))/(9*S) + (4*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (4*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((24*(1 + S^2))/S - (4*Pi^2*(13 + 165*S^2))/(9*S) - (16*(-1 + 2*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((-4*(19 + 11*S^2))/(3*S) + (2*Pi^2*(11 + 158*S^2))/(9*S) + (16*(1 + 2*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((Pi^4*(3203 - 216*S^2))/(270*S) + (20*(1 + S^2))/(3*S) + (2*Pi^2*(217 + 60*S^2))/(9*S) - (16*(7 + 10*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (272*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(-1 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((-14*Pi^2*(1 + S^2))/(9*S) + (4*(3 + 16*S^2))/(3*S) - (4*(31 + 19*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(-7 + 11*S^2)*Zeta[3])/(3*S)) + ((-16*S)/3 - (52*Pi^2*S)/3)*Zeta[5] + HPL[{1}, -S^2]*((-310*Pi^2*(1 + S^2))/(9*S) - (4207*Pi^4*(1 + S^2))/(540*S) - (42013*Pi^6*(1 + S^2))/(22680*S) - (83*Pi^2*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) - (4*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((80*(1 + S^2))/(3*S) + (22*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + HPL[{2}, -S^2]*((-248*Pi^2*(1 + S^2))/(9*S) - (3487*Pi^4*(1 + S^2))/(540*S) + (4*(1 + S^2)*HPL[{4}, -S^2])/S) + (20*(1 + S^2)*HPL[{5}, -S^2])/S + (110*(1 + S^2)*HPL[{6}, -S^2])/(3*S) + (412*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + ((-32*(1 + S^2))/(3*S) + (344*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (32*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (4*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (136*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) - (248*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (32*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (32*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + ((-8*(1 + S^2))/S - (16*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (4*(1 + S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((8*(1 + S^2))/S - (26*Pi^2*(1 + S^2))/(9*S) - (16*(1 + S^2)*Zeta[3])/(3*S)) - (52*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]^2*((-263*Pi^2*(1 + S^2))/(9*S) - (3917*Pi^4*(1 + S^2))/(540*S) - (206*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + ((16*(1 + S^2))/(3*S) - (2*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (16*(1 + S^2)*HPL[{4}, -S^2])/S + (44*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + (124*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((-16*(1 + S^2))/(3*S) - (52*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (44*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((Pi^4*(-384 - 3509*S^2))/(540*S) + (10*(1 + S^2))/(3*S) - (5*Pi^2*(7 + 47*S^2))/(9*S) + ((4*(-9 + S^2))/(3*S) - (2*Pi^2*(20 + 23*S^2))/(9*S))*HPL[{3}, -S^2] + (2*(-13 + 11*S^2)*HPL[{4}, -S^2])/(3*S) - (2*(43 + 21*S^2)*HPL[{5}, -S^2])/(3*S) + ((52*(1 + S^2))/(3*S) + (4*Pi^2*(93 + 10*S^2))/(9*S))*HPL[{2, 1}, -S^2] - (8*(5 + 11*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (4*(37 + 25*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (128*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (304*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (16*(15 + 16*S^2)*HPL[{3, 1, 1}, -S^2])/S + (272*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-8*(-2 + 3*S^2))/(3*S) - (8*Pi^2*(-1 + 4*S^2))/(9*S))*Zeta[3] + (4*(12 + S^2)*Zeta[5])/(3*S))) - 1024*S*Zeta[7] + HPL[{1}, -S^2]*((-295*Pi^2*(1 + S^2))/(3*S) - (9533*Pi^4*(1 + S^2))/(540*S) - (58141*Pi^6*(1 + S^2))/(22680*S) - (412*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-980*(1 + S^2))/(3*S) - (392*Pi^2*(1 + S^2))/(9*S))*HPL[{5}, -S^2] - (1274*(1 + S^2)*HPL[{6}, -S^2])/(3*S) - (716*(1 + S^2)*HPL[{7}, -S^2])/S + ((1952*(1 + S^2))/(3*S) + (788*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((6904*(1 + S^2))/(3*S) + (2800*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1}, -S^2] - (32*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) - (44*(1 + S^2)*HPL[{4, 3}, -S^2])/S + (416*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (104*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (556*(1 + S^2)*HPL[{6, 1}, -S^2])/S - (248*Pi^2*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + ((-1696*(1 + S^2))/S - (480*Pi^2*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] + (32*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (1088*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (992*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (2976*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (3744*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (2976*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (8928*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (18592*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((3392*(1 + S^2))/S + (1888*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] + (1984*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + (2720*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (3968*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (3968*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (9920*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (28992*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (5440*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (4800*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (9600*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((-2360*(1 + S^2))/(3*S) - (250*Pi^2*(1 + S^2))/(3*S) - (859*Pi^4*(1 + S^2))/(90*S))*Zeta[3] + (80*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1, 1}, -S^2]*((-2256*(1 + S^2))/S - (368*Pi^2*(1 + S^2))/S - (1024*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-103*Pi^2*(1 + S^2))/(9*S) - (124*(1 + S^2)*HPL[{3}, -S^2])/S + (248*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (124*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-288*(1 + S^2))/S - (274*Pi^2*(1 + S^2))/(9*S) - (88*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-2360*(1 + S^2))/(3*S) - (818*Pi^2*(1 + S^2))/(9*S) - (1219*Pi^4*(1 + S^2))/(135*S) + (36*(1 + S^2)*HPL[{4}, -S^2])/S + (1648*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (496*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (992*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (24*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((1128*(1 + S^2))/S + (1664*Pi^2*(1 + S^2))/(9*S) + (512*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((4720*(1 + S^2))/(3*S) + (2116*Pi^2*(1 + S^2))/(9*S) + (2779*Pi^4*(1 + S^2))/(90*S) + (512*(1 + S^2)*Zeta[3])/S) + ((-2092*(1 + S^2))/(3*S) - (910*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2}, -S^2]*((-1180*(1 + S^2))/S - (1435*Pi^2*(1 + S^2))/(9*S) - (3367*Pi^4*(1 + S^2))/(180*S) + ((-992*(1 + S^2))/(3*S) - (394*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (64*(1 + S^2)*HPL[{5}, -S^2])/S + (124*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (496*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (1488*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (992*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (1984*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + ((-856*(1 + S^2))/(3*S) - (430*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (364*(1 + S^2)*Zeta[5])/S) - (924*(1 + S^2)*Zeta[7])/S)) + HPL[{0}, S^2]*((295*Pi^4*S)/108 + (1711*Pi^6*S)/3240 + (15181*Pi^8*S)/100800 + (13*Pi^2*(1 + S^2)*HPL[{1}, -S^2]^6)/(27*S) + ((-25*(1 + S^2))/(18*S) + (Pi^2*(-22 + 53*S^2))/(54*S))*HPL[{2}, -S^2]^3 - (5*(1 + S^2)*HPL[{2}, -S^2]^4)/(12*S) + ((Pi^2*(-49 - 33*S^2))/(18*S) + (-3 + S^2)/S)*HPL[{3}, -S^2]^2 + ((97 + 84*S^2)*HPL[{4}, -S^2]^2)/(3*S) + ((Pi^2*(-140 - 191*S^2))/(18*S) + (-25 - 17*S^2)/S)*HPL[{6}, -S^2] + ((-125 - 174*S^2)*HPL[{7}, -S^2])/S + ((-315 - 272*S^2)*HPL[{8}, -S^2])/S + ((26*(1 + S^2))/(3*S) - (2*Pi^2*(-10 + 73*S^2))/(9*S))*HPL[{2, 1}, -S^2]^2 - (4*(-1 + 11*S^2)*HPL[{3, 1}, -S^2]^2)/(3*S) + ((38*S)/3 + (Pi^2*(7 - 3*S^2))/(18*S))*HPL[{4, 2}, -S^2] - (2*(23 + 67*S^2)*HPL[{4, 3}, -S^2])/(3*S) + ((5*Pi^2*(3 + 5*S^2))/(9*S) + (2*(17 + 91*S^2))/(3*S))*HPL[{5, 1}, -S^2] + ((-150 - 377*S^2)*HPL[{5, 2}, -S^2])/(3*S) - (10*S*HPL[{5, 3}, -S^2])/3 - (2*(40 + 231*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((-14 - 29*S^2)*HPL[{6, 2}, -S^2])/(3*S) + (8*(54 + 53*S^2)*HPL[{7, 1}, -S^2])/(3*S) - (136*(1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/(3*S) + ((12*(1 + S^2))/S + (2*Pi^2*(187 + 23*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((-2*Pi^2*(-2 + 3*S^2))/(9*S) - (4*(-3 + 11*S^2))/(3*S))*HPL[{3, 1, 2}, -S^2] + ((-8*(11 + 18*S^2))/(3*S) + (2*Pi^2*(-42 + 103*S^2))/(9*S))*HPL[{3, 2, 1}, -S^2] + ((-11 + 7*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (16*S*HPL[{3, 3, 1}, -S^2])/3 + (4*(43 + 46*S^2)*HPL[{3, 3, 2}, -S^2])/(3*S) + ((-4*(73 + 99*S^2))/(3*S) + (2*Pi^2*(-99 + 343*S^2))/(9*S))*HPL[{4, 1, 1}, -S^2] + (2*(1 + 6*S^2)*HPL[{4, 1, 2}, -S^2])/S - (4*(86 + 97*S^2)*HPL[{4, 1, 3}, -S^2])/(3*S) + (6*(3 + 2*S^2)*HPL[{4, 2, 1}, -S^2])/S + ((163 + 159*S^2)*HPL[{4, 2, 2}, -S^2])/(3*S) - (4*(178 + 201*S^2)*HPL[{4, 3, 1}, -S^2])/(3*S) - (4*(-2 + 5*S^2)*HPL[{5, 1, 1}, -S^2])/S - (2*(183 + 223*S^2)*HPL[{5, 1, 2}, -S^2])/(3*S) - (2*(1503 + 1663*S^2)*HPL[{5, 2, 1}, -S^2])/(3*S) - (4*(1970 + 2177*S^2)*HPL[{6, 1, 1}, -S^2])/(3*S) - (224*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + ((8*(21 + 13*S^2))/(3*S) - (8*Pi^2*(-3 + 77*S^2))/(9*S))*HPL[{3, 1, 1, 1}, -S^2] + (4*(145 + 151*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (4*(145 + 151*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) - (8*(-3 + 2*S^2)*HPL[{3, 1, 2, 2}, -S^2])/(3*S) + (4*(313 + 319*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) - (8*(-3 + 2*S^2)*HPL[{3, 2, 1, 2}, -S^2])/(3*S) + (40*(9 + 8*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(3*S) + (336*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (8*(489 + 506*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) - (28*(-1 + S^2)*HPL[{4, 1, 1, 2}, -S^2])/(3*S) + (28*(37 + 35*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(3*S) + (28*(109 + 107*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(3*S) + (1976*(1 + S^2)*HPL[{5, 1, 1, 1}, -S^2])/S + ((-208*(1 + S^2))/(3*S) + (8*Pi^2*(-1 + 56*S^2))/(3*S))*HPL[{2, 1, 1, 1, 1}, -S^2] - (256*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) - (256*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (608*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S) + (608*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (32*(41 + 43*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) - (32*(113 + 115*S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S) - (32*(189 + 191*S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S) - (32*(227 + 229*S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S) - (64*(237 + 238*S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S) - (32*(471 + 473*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S - (160*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (192*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S - (320*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (-8*S - (4*Pi^2*S)/3)*Zeta[3]^2 + HPL[{1}, -S^2]^5*((13*Pi^2*(1 + S^2))/(9*S) - (4*(1 + S^2)*HPL[{3}, -S^2])/(15*S) + (4*(1 + S^2)*Zeta[3])/(15*S)) + HPL[{1}, -S^2]^4*((109*Pi^2*(1 + S^2))/(27*S) + (1313*Pi^4*(1 + S^2))/(1080*S) + (31*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (4*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (4*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1, 1}, -S^2]*((-24*(1 + S^2))/S - (4*Pi^2*(193 + 41*S^2))/(9*S) + (16*(-1 + 2*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1}, -S^2]*((4*(25 + 17*S^2))/(3*S) + (2*Pi^2*(559 + 84*S^2))/(9*S) + (16*(4 + 3*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((-20*(1 + S^2))/(3*S) + (2*Pi^2*(31 + 188*S^2))/(9*S) + (Pi^4*(284 + 3703*S^2))/(270*S) + (8*(-1 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((Pi^2*(-18 - 65*S^2))/(18*S) + (2*(-1 + 53*S^2))/(3*S) + (8*(4 + 5*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((Pi^4*(-210 - 3037*S^2))/(540*S) + (Pi^2*(-13 - 172*S^2))/(9*S) + (10*(1 + S^2))/S + (16*(7 + 10*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(9 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((Pi^2*(-31 - 20*S^2))/(9*S) - (5*(1 + S^2))/S + (Pi^4*(303 + 163*S^2))/(1080*S) + (2*(31 + 7*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(77 + 41*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (4*(25 + 13*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (14*(4 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((-5*(1 + S^2))/(6*S) + (Pi^2*(-19 + 180*S^2))/(36*S) + (Pi^4*(60 + 3067*S^2))/(2160*S) + ((-5 - S^2)*HPL[{3}, -S^2])/(3*S) + ((-41 - 47*S^2)*HPL[{4}, -S^2])/(6*S) - (28*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (44*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (76*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + ((11 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{4, 1}, -S^2]*((-2*Pi^2*(-2 + 5*S^2))/(3*S) + (4*(3 + 92*S^2))/(3*S) + (4*(7 + 13*S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((-45 - 157*S^2)/(3*S) + (Pi^2*(-137 - 131*S^2))/(18*S) + (2*(123 + 101*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(95 + 107*S^2)*Zeta[3])/(3*S)) + ((58*S)/3 + (Pi^2*S)/3)*Zeta[5] + Zeta[3]*((10*S)/3 + (5*Pi^2*S)/3 + (5*Pi^4*S)/6 - (208*S*Zeta[5])/3) + HPL[{1}, -S^2]^3*((263*Pi^2*(1 + S^2))/(27*S) + (3917*Pi^4*(1 + S^2))/(1620*S) + (206*Pi^2*(1 + S^2)*HPL[{2}, -S^2])/(27*S) + ((-16*(1 + S^2))/(9*S) + (2*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (16*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (44*(1 + S^2)*HPL[{5}, -S^2])/(9*S) - (124*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + ((16*(1 + S^2))/(9*S) + (52*Pi^2*(1 + S^2))/(27*S))*Zeta[3] + (44*(1 + S^2)*Zeta[5])/(9*S)) + HPL[{1}, -S^2]^2*((155*Pi^2*(1 + S^2))/(9*S) + (4207*Pi^4*(1 + S^2))/(1080*S) + (42013*Pi^6*(1 + S^2))/(45360*S) + (83*Pi^2*(1 + S^2)*HPL[{2}, -S^2]^2)/(18*S) + (2*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-40*(1 + S^2))/(3*S) - (11*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + HPL[{2}, -S^2]*((124*Pi^2*(1 + S^2))/(9*S) + (3487*Pi^4*(1 + S^2))/(1080*S) - (2*(1 + S^2)*HPL[{4}, -S^2])/S) - (10*(1 + S^2)*HPL[{5}, -S^2])/S - (55*(1 + S^2)*HPL[{6}, -S^2])/(3*S) - (206*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + ((16*(1 + S^2))/(3*S) - (172*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (2*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (68*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + (124*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (16*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + ((4*(1 + S^2))/S + (8*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (2*(1 + S^2)*Zeta[3]^2)/S + HPL[{3}, -S^2]*((-4*(1 + S^2))/S + (13*Pi^2*(1 + S^2))/(9*S) + (8*(1 + S^2)*Zeta[3])/(3*S)) + (26*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((Pi^2*(-33 + 4*S^2))/(9*S) - (5*(3 + 5*S^2))/(3*S) + (Pi^4*(-425 + 31*S^2))/(1080*S) + ((19 + 67*S^2)*HPL[{4}, -S^2])/(3*S) - (2*(97 + 80*S^2)*HPL[{5}, -S^2])/(3*S) + ((4*(13 + 3*S^2))/(3*S) + (2*Pi^2*(25 + 28*S^2))/(9*S))*HPL[{2, 1}, -S^2] - (4*(7 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(21 + 23*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(28 + 23*S^2)*HPL[{4, 1}, -S^2])/S + (8*(3 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (56*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(35 + 23*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (16*(4 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((4*(8 + 7*S^2))/(3*S) + (2*Pi^2*(13 + 21*S^2))/(9*S))*Zeta[3] + (40*(4 + 5*S^2)*Zeta[5])/(3*S)) + HPL[{2, 1}, -S^2]*((Pi^4*(-3281 - 156*S^2))/(540*S) - (10*(1 + S^2))/(3*S) - (2*Pi^2*(119 + 19*S^2))/(9*S) + (8*(5 + 11*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (52*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(67 + 55*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (128*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (304*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(15 + 16*S^2)*HPL[{3, 1, 1}, -S^2])/S + (272*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((8*(-4 + S^2))/(3*S) - (2*Pi^2*(41 + 21*S^2))/(9*S))*Zeta[3] - (4*(47 + 36*S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((5*Pi^2*(-1 + 58*S^2))/(18*S) + (Pi^4*(421 + 3854*S^2))/(1080*S) + (Pi^6*(5882 + 44423*S^2))/(45360*S) + (2*(10 + 11*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-2*(-11 + 9*S^2))/(3*S) + (Pi^2*(95 + 73*S^2))/(18*S))*HPL[{4}, -S^2] + ((-13 - 79*S^2)*HPL[{5}, -S^2])/(3*S) + (5*(40 + 29*S^2)*HPL[{6}, -S^2])/(3*S) + ((Pi^2*(-187 - 23*S^2))/(9*S) - (6*(1 + S^2))/S)*HPL[{2, 1}, -S^2] + (76*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((2*(-1 + 19*S^2))/(3*S) - (2*Pi^2*(1 + 27*S^2))/(3*S))*HPL[{3, 1}, -S^2] - (2*(-7 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + ((1 + 7*S^2)*HPL[{4, 2}, -S^2])/(3*S) - (2*(79 + 45*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-52*(1 + S^2))/(3*S) + (4*Pi^2*(-10 + 73*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (112*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(11 + 13*S^2)*HPL[{3, 1, 1}, -S^2])/S - (4*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (124*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (4*(65 + 77*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (128*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (16*(235 + 238*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (272*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + ((4*(3 + 20*S^2))/(3*S) + (Pi^2*(11 + 56*S^2))/(9*S))*Zeta[3] - (2*(4 + 3*S^2)*Zeta[3]^2)/(3*S) + HPL[{3}, -S^2]*((-4*(-3 + 14*S^2))/(3*S) + (Pi^2*(8 + 15*S^2))/(9*S) + (28*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (52*(1 + S^2)*Zeta[3])/(3*S)) + (2*(12 + 49*S^2)*Zeta[5])/(3*S)) - 10*S*Zeta[7] + HPL[{1}, -S^2]*((325*Pi^2*(1 + S^2))/(18*S) + (1607*Pi^4*(1 + S^2))/(360*S) + (4651*Pi^6*(1 + S^2))/(5040*S) + (2*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-70*(1 + S^2))/(3*S) - (70*Pi^2*(1 + S^2))/(9*S))*HPL[{5}, -S^2] - (15*(1 + S^2)*HPL[{6}, -S^2])/S - (446*(1 + S^2)*HPL[{7}, -S^2])/(3*S) + ((-248*Pi^2*(1 + S^2))/(9*S) - (3487*Pi^4*(1 + S^2))/(540*S))*HPL[{2, 1}, -S^2] + HPL[{3}, -S^2]*((-20*(1 + S^2))/(3*S) + (11*Pi^2*(1 + S^2))/(9*S) - (37*Pi^4*(1 + S^2))/(270*S) + (26*(1 + S^2)*HPL[{4}, -S^2])/S + (16*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S)) + ((32*(1 + S^2))/(3*S) + (10*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((128*(1 + S^2))/(3*S) + (52*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1}, -S^2] + (22*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) - (154*(1 + S^2)*HPL[{4, 3}, -S^2])/(3*S) + (44*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (460*(1 + S^2)*HPL[{5, 2}, -S^2])/(3*S) - (650*(1 + S^2)*HPL[{6, 1}, -S^2])/(3*S) + (412*Pi^2*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (332*Pi^2*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) + ((-32*(1 + S^2))/(3*S) + (112*Pi^2*(1 + S^2))/S)*HPL[{3, 1, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (16*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (12*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (112*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) - (32*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (36*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (116*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (808*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) - (248*Pi^2*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (16*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (32*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (32*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + ((20*(1 + S^2))/(3*S) + (11*Pi^2*(1 + S^2))/(3*S) + (1111*Pi^4*(1 + S^2))/(540*S))*Zeta[3] - (10*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{3, 1}, -S^2]*((8*(1 + S^2))/S - (196*Pi^2*(1 + S^2))/(9*S) - (40*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((85*Pi^2*(1 + S^2))/(18*S) - (2*(1 + S^2)*HPL[{3}, -S^2])/S + (2*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-16*(1 + S^2))/S - (23*Pi^2*(1 + S^2))/(9*S) + (4*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (100*(1 + S^2)*Zeta[3])/(3*S)) + ((18*(1 + S^2))/S + (107*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2}, -S^2]*((91*Pi^2*(1 + S^2))/(6*S) + (733*Pi^4*(1 + S^2))/(216*S) + ((-8*(1 + S^2))/(3*S) - (5*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (6*(1 + S^2)*HPL[{4}, -S^2])/S - (80*(1 + S^2)*HPL[{5}, -S^2])/(3*S) - (166*Pi^2*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (20*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (20*(1 + S^2)*HPL[{4, 1}, -S^2])/S + ((8*(1 + S^2))/(3*S) + (37*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (70*(1 + S^2)*Zeta[5])/(3*S)) + (90*(1 + S^2)*Zeta[7])/S)) + 1568*S*Zeta[9];
Et5uvwT2F2=(Pi^8*(-427744 - 609595*S^2))/2721600 + (Pi^4*(-33919 - 68826*S^2))/8640 + (Pi^6*(-21079 - 55626*S^2))/45360 - (245*Pi^2*(131 + 199*S^2))/1152 + ((1 - S^4)*HPL[{1}, -S^2]^8)/(9*S^2) + HPL[{0}, S^2]^8*((-1 - S^2)/192 + ((-1 - S^4)*HPL[{1}, -S^2])/(192*S^2)) - (19*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^4)/(12*S^2) + HPL[{0}, S^2]^7*((-5*Pi^2*S^2)/1728 + (3 - 16*S^2)/192 - ((1 + S^2)*(-9 + 29*S^2)*HPL[{1}, -S^2])/(576*S^2) - (5*(1 + S^4)*HPL[{1}, -S^2]^2)/(288*S^2) - (5*S^2*HPL[{2}, -S^2])/288) + HPL[{1}, -S^2]^7*((-46*(-1 + S^4))/(63*S^2) - (5*Pi^2*(1 + S^4))/(63*S^2) - (20*(1 + S^4)*HPL[{2}, -S^2])/(21*S^2)) + (2*(19 + 21*S^4)*HPL[{3}, -S^2]^3)/(9*S^2) + ((75 + 2*S^2 - 28*S^4)*HPL[{4}, -S^2]^2)/(6*S^2) + ((1970 - 633*S^2 - 3443*S^4)/(6*S^2) + (Pi^2*(-420 - 649*S^4))/(18*S^2))*HPL[{7}, -S^2] + ((4767 - 3684*S^2 - 5818*S^4)*HPL[{8}, -S^2])/(6*S^2) + ((-4116 - 3253*S^4)*HPL[{9}, -S^2])/(3*S^2) - (448*(1 + S^4)*HPL[{2, 1}, -S^2]^3)/(9*S^2) + ((235 + 8*S^2 - 268*S^4)*HPL[{3, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(151 + 33*S^4))/(18*S^2) + (-55 - 157*S^2 + 74*S^4)/(6*S^2))*HPL[{4, 3}, -S^2] + ((Pi^2*(431 + 152*S^4))/(18*S^2) + (-298 - 1104*S^2 + 847*S^4)/(12*S^2))*HPL[{5, 2}, -S^2] + ((19 - 24*S^2 - 148*S^4)*HPL[{5, 3}, -S^2])/(6*S^2) + ((-295 - 396*S^4)*HPL[{5, 4}, -S^2])/(3*S^2) + ((7*Pi^2*(160 + 133*S^4))/(18*S^2) + (-2559 - 358*S^2 + 6529*S^4)/(12*S^2))*HPL[{6, 1}, -S^2] + ((39 - 60*S^2 - 212*S^4)*HPL[{6, 2}, -S^2])/(6*S^2) + ((-1173 - 1654*S^4)*HPL[{6, 3}, -S^2])/(3*S^2) + ((-1789 + 2628*S^2 + 4200*S^4)*HPL[{7, 1}, -S^2])/(6*S^2) + ((-2973 - 4117*S^4)*HPL[{7, 2}, -S^2])/(3*S^2) + ((-1327 - 1874*S^4)*HPL[{8, 1}, -S^2])/S^2 - (1112*(-1 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^2) + ((-459 - 4528*S^2 - 1409*S^4)/(12*S^2) - (5*Pi^2*(32 + 169*S^4))/(18*S^2))*HPL[{3, 2, 2}, -S^2] + ((-420 - 3352*S^2 - 1117*S^4)/(3*S^2) - (2*Pi^2*(69 + 632*S^4))/(9*S^2))*HPL[{3, 3, 1}, -S^2] + ((-394 + 252*S^2 + 441*S^4)*HPL[{3, 3, 2}, -S^2])/(6*S^2) + ((Pi^2*(-233 - 2575*S^4))/(18*S^2) + (-389 - 3352*S^2 - 1148*S^4)/(3*S^2))*HPL[{4, 1, 2}, -S^2] + ((395 - 210*S^2 - 352*S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^2) + ((Pi^2*(-605 - 7603*S^4))/(18*S^2) + (-1274 - 10012*S^2 - 3473*S^4)/(3*S^2))*HPL[{4, 2, 1}, -S^2] + ((-381 + 312*S^2 + 500*S^4)*HPL[{4, 2, 2}, -S^2])/(6*S^2) - (5*(-1 + 2*S^2)*(1 + 2*S^2)*HPL[{4, 2, 3}, -S^2])/(3*S^2) + ((831 - 426*S^2 - 946*S^4)*HPL[{4, 3, 1}, -S^2])/(3*S^2) + ((330 + 307*S^4)*HPL[{4, 3, 2}, -S^2])/(3*S^2) + (2*(211 + 237*S^4)*HPL[{4, 4, 1}, -S^2])/(3*S^2) + ((-4465 - 41244*S^2 - 15825*S^4)/(6*S^2) + (Pi^2*(-583 - 7825*S^4))/(9*S^2))*HPL[{5, 1, 1}, -S^2] + ((814 - 264*S^2 - 1005*S^4)*HPL[{5, 1, 2}, -S^2])/(6*S^2) - (2*(116 + 67*S^4)*HPL[{5, 1, 3}, -S^2])/(3*S^2) + ((6934 - 3864*S^2 - 8385*S^4)*HPL[{5, 2, 1}, -S^2])/(6*S^2) + ((727 + 806*S^4)*HPL[{5, 2, 2}, -S^2])/(3*S^2) + (2*(382 + 563*S^4)*HPL[{5, 3, 1}, -S^2])/(3*S^2) + ((9032 - 6354*S^2 - 12555*S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^2) + ((1054 + 1301*S^4)*HPL[{6, 1, 2}, -S^2])/(3*S^2) + ((294 + 1181*S^4)*HPL[{6, 2, 1}, -S^2])/(3*S^2) - (40*(72 + 47*S^4)*HPL[{7, 1, 1}, -S^2])/(3*S^2) + ((4*Pi^2*(218 + 135*S^4))/(9*S^2) + (467 + 2264*S^2 + 467*S^4)/(3*S^2))*HPL[{2, 2, 2, 1}, -S^2] + ((-1145 - 4572*S^2 - 587*S^4)/(3*S^2) - (2*Pi^2*(1301 + 352*S^4))/(9*S^2))*HPL[{3, 1, 1, 2}, -S^2] + ((-1145 - 4572*S^2 - 587*S^4)/(3*S^2) - (2*Pi^2*(1301 + 352*S^4))/(9*S^2))*HPL[{3, 1, 2, 1}, -S^2] + (65*(-1 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/(6*S^2) + ((-2*(1273 + 5682*S^2 + 994*S^4))/(3*S^2) - (2*Pi^2*(2609 + 1162*S^4))/(9*S^2))*HPL[{3, 2, 1, 1}, -S^2] + (65*(-1 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/(6*S^2) + ((1271 + 2976*S^2 + 2041*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(6*S^2) + (4*(39 + 371*S^4)*HPL[{3, 2, 2, 2}, -S^2])/(3*S^2) + (4*(194 + 1175*S^4)*HPL[{3, 2, 3, 1}, -S^2])/(3*S^2) + (4*(167 + 372*S^2 + 247*S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (8*(95 + 588*S^4)*HPL[{3, 3, 1, 2}, -S^2])/(3*S^2) + (28*(94 + 513*S^4)*HPL[{3, 3, 2, 1}, -S^2])/(3*S^2) + ((-7881 - 33280*S^2 - 5407*S^4)/(3*S^2) - (4*Pi^2*(3869 + 1714*S^4))/(9*S^2))*HPL[{4, 1, 1, 1}, -S^2] + ((-11 + 295*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^2) - (4*(1367 + 7286*S^4)*HPL[{4, 1, 1, 3}, -S^2])/(3*S^2) + ((1993 + 4464*S^2 + 3259*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^2) + ((-4693 - 24425*S^4)*HPL[{4, 1, 2, 2}, -S^2])/(3*S^2) - (4*(703 + 3647*S^4)*HPL[{4, 1, 3, 1}, -S^2])/S^2 + ((6001 + 13392*S^2 + 9187*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^2) + ((-2869 - 14753*S^4)*HPL[{4, 2, 1, 2}, -S^2])/(3*S^2) + ((-2821 - 14765*S^4)*HPL[{4, 2, 2, 1}, -S^2])/(3*S^2) - (4*(4139 + 21785*S^4)*HPL[{4, 3, 1, 1}, -S^2])/(3*S^2) + (2*(6197 + 13944*S^2 + 10064*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^2) - (2*(2769 + 14539*S^4)*HPL[{5, 1, 1, 2}, -S^2])/S^2 - (2*(4609 + 24207*S^4)*HPL[{5, 1, 2, 1}, -S^2])/S^2 - (2*(11073 + 58039*S^4)*HPL[{5, 2, 1, 1}, -S^2])/S^2 - (8*(20727 + 108601*S^4)*HPL[{6, 1, 1, 1}, -S^2])/(3*S^2) + ((-186*(-1 + S^4))/S^2 - (8*Pi^2*(-209 + 97*S^4))/(9*S^2))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-558*(-1 + S^4))/S^2 - (8*Pi^2*(-209 + 97*S^4))/(3*S^2))*HPL[{2, 2, 1, 1, 1}, -S^2] + (8*(69 + 124*S^2 + 69*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (24*(69 + 124*S^2 + 69*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (1328*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 2, 2, 1}, -S^2])/(3*S^2) + ((-8*Pi^2*(-1017 + 722*S^4))/(9*S^2) - (2*(-1361 + 2796*S^2 + 2387*S^4))/(3*S^2))*HPL[{3, 1, 1, 1, 1}, -S^2] - (2*(5039 + 8928*S^2 + 5039*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^2) - (2*(8351 + 14880*S^2 + 8351*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^2) + (4*(-1117 + 221*S^4)*HPL[{3, 1, 1, 2, 2}, -S^2])/(3*S^2) - (2*(10007 + 17856*S^2 + 10007*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^2) + (4*(-1117 + 221*S^4)*HPL[{3, 1, 2, 1, 2}, -S^2])/(3*S^2) + (20*(-1 + S^4)*HPL[{3, 1, 2, 2, 1}, -S^2])/(3*S^2) - (16*(-1907 + 565*S^4)*HPL[{3, 1, 3, 1, 1}, -S^2])/(3*S^2) - (2*(20771 + 37200*S^2 + 20771*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^2) + (4*(-2113 + 1217*S^4)*HPL[{3, 2, 1, 1, 2}, -S^2])/(3*S^2) + (4004*(-1 + S^4)*HPL[{3, 2, 1, 2, 1}, -S^2])/(3*S^2) + (52*(271 + 73*S^4)*HPL[{3, 2, 2, 1, 1}, -S^2])/(3*S^2) + (16*(965 + 153*S^4)*HPL[{3, 3, 1, 1, 1}, -S^2])/S^2 - (32*(3912 + 7011*S^2 + 3941*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^2) + (32*(-781 + 446*S^4)*HPL[{4, 1, 1, 1, 2}, -S^2])/(3*S^2) + (32*(-364 + 365*S^4)*HPL[{4, 1, 1, 2, 1}, -S^2])/(3*S^2) + (16*(2665 + 691*S^4)*HPL[{4, 1, 2, 1, 1}, -S^2])/(3*S^2) + (4352*(32 + 5*S^4)*HPL[{4, 2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(17397 + 2623*S^4)*HPL[{5, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((4*(171 + 932*S^2 + 171*S^4))/S^2 + (8*Pi^2*(473 + 278*S^4))/(9*S^2))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (3584*(1 + S^4)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(3*S^2) - (3584*(1 + S^4)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S^2 + (16*(271 + 450*S^2 + 329*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) + (32*(574 + 769*S^4)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(3*S^2) + (32*(1246 + 1441*S^4)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(3*S^2) + (32*(1694 + 1889*S^4)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(3*S^2) + (32*(1918 + 2113*S^4)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(3*S^2) + (32*(3374 + 3569*S^4)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (32*(3382 + 3577*S^4)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S^2 - (1600*(2 + 3*S^2 + 2*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (2080*(-1 + S^4)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S^2 + (8320*(-1 + S^4)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S^2 + (20800*(-1 + S^4)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (640*(-69 + 61*S^4)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (5120*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((4*Pi^2*S^2)/27 + (8*S^2*HPL[{0}, S^2])/9 + (4*S^2*HPL[{0}, S^2]^2)/9 + (8*(-1 + S^4)*HPL[{1}, -S^2])/(9*S^2) + (8*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2))*Log[T]^7 + ((Pi^2*(-34 + 11*S^2))/12 + (77 + 185*S^2)/12)*Zeta[3]^2 - 16*S^2*Zeta[3]^3 + Log[T]^6*((-5*Pi^2*(3 + 4*S^2))/27 - (13*S^2*HPL[{0}, S^2]^3)/27 - (28*(-1 + S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + HPL[{0}, S^2]^2*((-5*(3 + 4*S^2))/9 - (5*(1 + S^4)*HPL[{1}, -S^2])/(3*S^2)) - (20*(2 + 3*S^2 + 2*S^4)*HPL[{2}, -S^2])/(9*S^2) + HPL[{1}, -S^2]*((-46*(-1 + S^4))/(9*S^2) - (5*Pi^2*(1 + S^4))/(9*S^2) - (20*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]*((-13*Pi^2*S^2)/27 - (2*(-15 + 23*S^2))/9 - (28*(-1 + S^4)*HPL[{1}, -S^2])/(9*S^2) + (2*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) - (2*(3 + 29*S^4)*HPL[{3}, -S^2])/(9*S^2) + (64*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (64*S^2*Zeta[3])/9) + HPL[{3, 1, 2}, -S^2]*((-151 + 340*S^2 - 151*S^4)/(12*S^2) + (Pi^2*(-88 - 4*S^2 - 65*S^4))/(36*S^2) - (20*S^2*Zeta[3])/3) + HPL[{0}, S^2]^6*((Pi^2*(-224 - 277*S^2))/3456 + (-15 - 277*S^2)/1152 + ((-5 - 60*S^2 - 47*S^4)*HPL[{1}, -S^2]^2)/(288*S^2) - (7*(1 + S^4)*HPL[{1}, -S^2]^3)/(108*S^2) + ((-6 - 50*S^2 - 97*S^4)*HPL[{2}, -S^2])/(576*S^2) + HPL[{1}, -S^2]*((9 - 276*S^2 - 221*S^4)/(1152*S^2) - (7*Pi^2*(1 + S^4))/(108*S^2) - (25*(1 + S^4)*HPL[{2}, -S^2])/(288*S^2)) + ((-1 - S^4)*HPL[{3}, -S^2])/(96*S^2) + (11*HPL[{2, 1}, -S^2])/(72*S^2) - (25*S^2*Zeta[3])/72) + HPL[{4, 1}, -S^2]*((Pi^2*(103 + 1990*S^2 + 1059*S^4))/(18*S^2) + (3995 + 50140*S^2 + 11073*S^4)/(48*S^2) + (Pi^4*(-535 + 11581*S^4))/(1080*S^2) + (8*(61 + 613*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((179 - 116*S^2 - 90*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^3*((-1487 - 824*S^2 - 1487*S^4)/(144*S^2) + (Pi^2*(-51 - 146*S^2 - 108*S^4))/(54*S^2) + ((-12 - 95*S^4)*HPL[{3}, -S^2])/(9*S^2) - (83*(-1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + ((-6 - 89*S^4)*Zeta[3])/(9*S^2)) + HPL[{3, 2}, -S^2]*((Pi^4*(-96 + 593*S^4))/(180*S^2) + (813 + 7406*S^2 + 758*S^4)/(24*S^2) + (Pi^2*(230 + 2304*S^2 + 1107*S^4))/(72*S^2) + (8*(29 + 195*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((26 - 116*S^2 - 81*S^4)*Zeta[3])/(6*S^2)) + HPL[{1}, -S^2]^5*((Pi^2*(473 - 1014*S^2 - 1487*S^4))/(540*S^2) - (2449*(-1 + S^4))/(180*S^2) - (749*Pi^4*(1 + S^4))/(2700*S^2) + ((-118*Pi^2*(1 + S^4))/(45*S^2) - (169*(1 + 2*S^2 + S^4))/(15*S^2))*HPL[{2}, -S^2] + ((-179 - 300*S^2 - 121*S^4)*HPL[{3}, -S^2])/(15*S^2) - (16*(1 + S^4)*HPL[{4}, -S^2])/(5*S^2) + (20*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-137 - 180*S^2 - 43*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]^6*((Pi^2*(31 - 180*S^2 - 211*S^4))/(324*S^2) - (125*(-1 + S^4))/(36*S^2) - (10*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(3*S^2) - (10*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (20*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (10*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1, 1}, -S^2]*((319*Pi^4*(19 + 7*S^4))/(270*S^2) + (Pi^2*(1081 + 4304*S^2 + 802*S^4))/(18*S^2) + (2913 + 19292*S^2 + 2913*S^4)/(12*S^2) - (16*(-135 - 96*S^2 + 4*S^4)*Zeta[3])/(3*S^2)) + HPL[{4, 2}, -S^2]*((Pi^2*(-14 + 4*S^2 + 167*S^4))/(36*S^2) + (1 - 340*S^2 + 301*S^4)/(12*S^2) + ((9 + 5*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]^2*((863*(-1 + S^4))/(6*S^2) + (Pi^2*(-329 + 186*S^2 + 536*S^4))/(18*S^2) + (56*(1 + 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{5}, -S^2]*((2002 - 4076*S^2 - 7781*S^4)/(48*S^2) + (Pi^4*(74 - 1539*S^4))/(1080*S^2) + (Pi^2*(158 - 164*S^2 - 369*S^4))/(18*S^2) + ((41 + 348*S^2 - 223*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (2*(-68 + 19*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (2*(-67 + 141*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (11*(-23 + 4*S^2 + 9*S^4)*Zeta[3])/(6*S^2)) + HPL[{5, 1}, -S^2]*((Pi^2*(151 + 804*S^2 + 1585*S^4))/(36*S^2) + (-529 + 784*S^2 + 6843*S^4)/(24*S^2) - (2*(59 + 13*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 2, 1}, -S^2]*((-55*(-1 + S^4))/(24*S^2) + (Pi^2*(-781 - 1132*S^2 + 314*S^4))/(36*S^2) + (Pi^4*(-5760 + 1327*S^4))/(540*S^2) + (4*(-227 - 186*S^2 + 20*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]^2*((Pi^2*(-72 + 14*S^2 + 75*S^4))/(36*S^2) + (-11 - 258*S^2 + 166*S^4)/(24*S^2) - (26*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((19 + 29*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 2, 1}, -S^2]*((-3125 - 1308*S^2 - 3125*S^4)/(12*S^2) + (Pi^2*(-904 - 2340*S^2 - 1793*S^4))/(36*S^2) - (4*(4 + 61*S^4)*Zeta[3])/S^2) + HPL[{3, 1, 1}, -S^2]*((-951 - 19292*S^2 - 4875*S^4)/(24*S^2) + (Pi^2*(-2379 - 6552*S^2 - 478*S^4))/(36*S^2) + (Pi^4*(-17698 + 71*S^4))/(540*S^2) + (2*(-1454 - 1132*S^2 + 83*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1, 1, 1}, -S^2]*((2*(808 + 598*S^2 + 1091*S^4))/(3*S^2) + (Pi^2*(584 + 1412*S^2 + 1273*S^4))/(9*S^2) + (16*(3 + 100*S^4)*Zeta[3])/(3*S^2)) + HPL[{6}, -S^2]*((1105 - 1998*S^2 - 5811*S^4)/(24*S^2) + (Pi^2*(66 - 726*S^2 - 1081*S^4))/(36*S^2) + ((152 + 43*S^4)*HPL[{2, 1}, -S^2])/S^2 + ((200 + 187*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-8*Pi^2*(165 + 354*S^2 + 304*S^4))/(9*S^2) - (2*(1899 + 1196*S^2 + 1899*S^4))/(3*S^2) - (16*(7 + 202*S^4)*Zeta[3])/(3*S^2)) + HPL[{4, 1, 1}, -S^2]*((-4721 - 2794*S^2 - 5853*S^4)/(6*S^2) + (Pi^2*(-1539 - 3932*S^2 - 3261*S^4))/(18*S^2) - (4*(19 + 563*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^5*((-7873*Pi^4*S^2)/259200 + (Pi^2*(1916 - 13059*S^2))/17280 + (707 - 1712*S^2)/1152 + ((43 - 1216*S^2 - 1059*S^4)*HPL[{1}, -S^2]^3)/(2160*S^2) - (31*(1 + S^4)*HPL[{1}, -S^2]^4)/(240*S^2) + ((120 - 214*S^2 - 2259*S^4)/(2880*S^2) + (Pi^2*(-15 - 779*S^4))/(4320*S^2))*HPL[{2}, -S^2] + ((-5 - 68*S^4)*HPL[{2}, -S^2]^2)/(480*S^2) + HPL[{1}, -S^2]^2*((707 - 2172*S^2 - 2479*S^4)/(2880*S^2) - (67*Pi^2*(1 + S^4))/(360*S^2) - (229*(1 + S^4)*HPL[{2}, -S^2])/(720*S^2)) - ((-5 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(96*S^2) + ((1 + S^4)*HPL[{4}, -S^2])/(16*S^2) + ((-28 + 558*S^2 - 145*S^4)*HPL[{2, 1}, -S^2])/(720*S^2) + (21*S^2*HPL[{3, 1}, -S^2])/40 + ((-15 - 254*S^4)*HPL[{2, 1, 1}, -S^2])/(180*S^2) + ((-2 - 13*S^2)*Zeta[3])/6 + HPL[{1}, -S^2]*((2635 - 2984*S^2 - 5619*S^4)/(5760*S^2) + (Pi^2*(247 - 829*S^2 - 1026*S^4))/(2160*S^2) + ((43 - 1016*S^2 - 859*S^4)*HPL[{2}, -S^2])/(1440*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(24*S^2) + (229*(1 + S^4)*HPL[{2, 1}, -S^2])/(360*S^2) + ((-1 - S^4)*Zeta[3])/(3*S^2))) + Log[T]^5*((4459*Pi^4*S^2)/8100 + (Pi^2*(42 + 101*S^2))/36 + (277*S^2*HPL[{0}, S^2]^4)/540 + (56*(-1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + HPL[{0}, S^2]^3*((65 + 124*S^2)/45 + (13*(1 + S^4)*HPL[{1}, -S^2])/(9*S^2)) + ((Pi^2*(47 + 86*S^4))/(27*S^2) + (101 + 84*S^2 + 101*S^4)/(6*S^2))*HPL[{2}, -S^2] + (13*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{1}, -S^2]^2*((46*(-1 + S^4))/(3*S^2) + (5*Pi^2*(1 + S^4))/(3*S^2) + (20*(1 + S^4)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^2*((487*Pi^2*S^2)/270 + (42 + 101*S^2)/12 + ((53 + 180*S^2 + 127*S^4)*HPL[{1}, -S^2])/(18*S^2) + (5*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + ((5 + 44*S^4)*HPL[{2}, -S^2])/(9*S^2)) + (4*(-2 + 75*S^2 + 52*S^4)*HPL[{3}, -S^2])/(15*S^2) + (68*(1 + S^4)*HPL[{4}, -S^2])/(15*S^2) - (40*(1 + 3*S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + HPL[{0}, S^2]*((Pi^2*(65 + 194*S^2))/45 + (-314 + 375*S^2)/18 + ((46*(-1 + S^4))/(3*S^2) + (13*Pi^2*(1 + S^4))/(9*S^2))*HPL[{1}, -S^2] + (28*(-1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + ((-17 + 77*S^4)*HPL[{2}, -S^2])/(9*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) - (4*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2)) - (56*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (112*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (20*(3 + 2*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((125*(-1 + S^4))/(6*S^2) + (Pi^2*(-31 + 180*S^2 + 211*S^4))/(54*S^2) + (20*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (20*(1 + S^4)*Zeta[3])/S^2)) + ((-391*Pi^4*S^2)/45 + (-7369 - 3538*S^2)/24 + (Pi^2*(-1235 - 607*S^2))/36)*Zeta[5] + Log[T]^4*((Pi^4*(-4494 - 6557*S^2))/3240 + (Pi^2*(-598 - 1899*S^2))/216 - (289*S^2*HPL[{0}, S^2]^5)/1080 - (70*(-1 + S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + HPL[{0}, S^2]^4*((-264 - 443*S^2)/216 - (11*(1 + S^4)*HPL[{1}, -S^2])/(9*S^2)) - (139*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S^2) + HPL[{0}, S^2]^3*((-121*Pi^2*S^2)/81 + (-114 - 1859*S^2)/216 + ((-11 - 276*S^2 - 233*S^4)*HPL[{1}, -S^2])/(36*S^2) - (65*(1 + S^4)*HPL[{1}, -S^2]^2)/(18*S^2) + ((-4 - 61*S^4)*HPL[{2}, -S^2])/(18*S^2)) + HPL[{1}, -S^2]^3*((-230*(-1 + S^4))/(9*S^2) - (25*Pi^2*(1 + S^4))/(9*S^2) - (100*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-17 - 1398*S^2 - 496*S^4)/(18*S^2) + (Pi^2*(-28 - 237*S^4))/(27*S^2))*HPL[{3}, -S^2] + ((-123 - 144*S^2 - 239*S^4)*HPL[{4}, -S^2])/(9*S^2) - (2*(3 + 107*S^4)*HPL[{5}, -S^2])/(9*S^2) + ((171 + 932*S^2 + 171*S^4)/(6*S^2) + (Pi^2*(473 + 278*S^4))/(27*S^2))*HPL[{2, 1}, -S^2] + (2*(271 + 450*S^2 + 329*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (4*(14 + 209*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) + (4*(22 + 217*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (200*(2 + 3*S^2 + 2*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (260*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (40*(-21 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (640*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-271*Pi^2*S^2)/27 + (-466 - 171*S^2)/6)*Zeta[3] + HPL[{0}, S^2]^2*((-598 - 1899*S^2)/72 + (Pi^2*(-489 - 743*S^2))/108 - (5*(53 + 180*S^2 + 127*S^4)*HPL[{1}, -S^2]^2)/(36*S^2) - (25*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + ((-15 - 129*S^2 - 154*S^4)*HPL[{2}, -S^2])/(9*S^2) + HPL[{1}, -S^2]*((-217 - 1014*S^2 - 797*S^4)/(36*S^2) - (163*Pi^2*(1 + S^4))/(36*S^2) - (43*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-11 - 39*S^4)*HPL[{3}, -S^2])/(18*S^2) + ((233 + 38*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (31*S^2*Zeta[3])/9) + HPL[{1}, -S^2]^2*((-625*(-1 + S^4))/(12*S^2) - (5*Pi^2*(-31 + 180*S^2 + 211*S^4))/(108*S^2) - (50*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 - (50*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (100*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (50*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((Pi^2*(473 - 1014*S^2 - 1487*S^4))/(108*S^2) - (2449*(-1 + S^4))/(36*S^2) - (749*Pi^4*(1 + S^4))/(540*S^2) + ((-118*Pi^2*(1 + S^4))/(9*S^2) - (169*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2}, -S^2] - ((1 + S^2)*(179 + 121*S^2)*HPL[{3}, -S^2])/(3*S^2) - (16*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (100*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (100*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (200*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (5*(137 + 180*S^2 + 43*S^4)*Zeta[3])/(9*S^2)) + HPL[{2}, -S^2]*((-1899 - 1196*S^2 - 1899*S^4)/(36*S^2) + (Pi^2*(-165 - 354*S^2 - 304*S^4))/(27*S^2) - (10*(1 + 14*S^4)*HPL[{3}, -S^2])/(3*S^2) - (130*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(7 + 202*S^4)*Zeta[3])/(9*S^2)) + HPL[{0}, S^2]*((-4021*Pi^4*S^2)/3240 + (Pi^2*(786 - 3239*S^2))/216 + (2242 - 2449*S^2)/36 + ((-115*(-1 + S^4))/(3*S^2) - (65*Pi^2*(1 + S^4))/(18*S^2))*HPL[{1}, -S^2]^2 - (140*(-1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + ((299 + 768*S^2 - 1301*S^4)/(36*S^2) + (Pi^2*(1 - 56*S^4))/(18*S^2))*HPL[{2}, -S^2] + (17*(1 + S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + ((41 + 30*S^2 - 49*S^4)*HPL[{3}, -S^2])/(9*S^2) - (4*(2 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (5*(-77 + 17*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (4*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(3 + 29*S^2)*Zeta[3])/9 + HPL[{1}, -S^2]*((Pi^2*(129 - 276*S^2 - 373*S^4))/(36*S^2) - (625*(-1 + S^4))/(12*S^2) - (235*(-1 + S^4)*HPL[{2}, -S^2])/(9*S^2) + (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (2*(1 + S^4)*Zeta[3])/(3*S^2))) - (610*S^2*Zeta[5])/9) + HPL[{0}, S^2]^4*((Pi^4*(-7818 - 10879*S^2))/25920 + (Pi^2*(-592 - 6583*S^2))/3456 + (-1574 - 3893*S^2)/576 + ((-33 - 186*S^2 - 133*S^4)*HPL[{1}, -S^2]^4)/(144*S^2) - (11*(1 + S^4)*HPL[{1}, -S^2]^5)/(45*S^2) + ((24 - 104*S^2 - 143*S^4)*HPL[{2}, -S^2]^2)/(144*S^2) + HPL[{1}, -S^2]^3*((-223 - 2300*S^2 - 1885*S^4)/(864*S^2) - (19*Pi^2*(1 + S^4))/(36*S^2) - (257*(1 + S^4)*HPL[{2}, -S^2])/(216*S^2)) + ((-19 - 18*S^2 - 67*S^4)/(96*S^2) + (Pi^2*(-10 - 11*S^4))/(144*S^2))*HPL[{3}, -S^2] + ((-13 - 28*S^2 - 31*S^4)*HPL[{4}, -S^2])/(48*S^2) + ((-16 - 23*S^4)*HPL[{5}, -S^2])/(24*S^2) + ((Pi^2*(563 + 11*S^4))/(432*S^2) + (232 + 1450*S^2 + 181*S^4)/(288*S^2))*HPL[{2, 1}, -S^2] + ((39 + 500*S^2 + 713*S^4)*HPL[{3, 1}, -S^2])/(144*S^2) - (3*HPL[{3, 2}, -S^2])/(4*S^2) + (23*(-1 + S^4)*HPL[{4, 1}, -S^2])/(24*S^2) + ((-42 - 514*S^2 - 777*S^4)*HPL[{2, 1, 1}, -S^2])/(72*S^2) - (5*(47 + 4*S^4)*HPL[{2, 2, 1}, -S^2])/(36*S^2) + ((-80 - 9*S^4)*HPL[{3, 1, 1}, -S^2])/(4*S^2) + ((233 + 11*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(18*S^2) + ((-833*Pi^2*S^2)/432 + (32 - 639*S^2)/288)*Zeta[3] + HPL[{1}, -S^2]*((-662 - 3691*S^2 - 2837*S^4)/(576*S^2) + (Pi^2*(-11 - 805*S^2 - 650*S^4))/(432*S^2) - (1303*Pi^4*(1 + S^4))/(4320*S^2) + ((-185 - 1066*S^2 - 1009*S^4)/(288*S^2) - (79*Pi^2*(1 + S^4))/(108*S^2))*HPL[{2}, -S^2] - (13*(1 + S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + ((-27 - 28*S^2 - 33*S^4)*HPL[{3}, -S^2])/(48*S^2) - (11*(1 + S^4)*HPL[{4}, -S^2])/(12*S^2) + ((275 + 1032*S^2 + 749*S^4)*HPL[{2, 1}, -S^2])/(144*S^2) + (137*(1 + S^4)*HPL[{3, 1}, -S^2])/(36*S^2) - (257*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(36*S^2) + ((-7 - 202*S^2 - 95*S^4)*Zeta[3])/(72*S^2)) + HPL[{2}, -S^2]*((-258 - 778*S^2 - 2151*S^4)/(576*S^2) + (Pi^2*(-33 - 316*S^2 - 558*S^4))/(432*S^2) + (3*HPL[{3}, -S^2])/(8*S^2) + (5*(47 + 4*S^4)*HPL[{2, 1}, -S^2])/(72*S^2) - (5*(-1 + S^4)*Zeta[3])/(24*S^2)) + HPL[{1}, -S^2]^2*((-645 - 5288*S^2 - 4451*S^4)/(1152*S^2) + (Pi^2*(-29 - 243*S^2 - 184*S^4))/(144*S^2) + ((-275 - 1032*S^2 - 749*S^4)*HPL[{2}, -S^2])/(288*S^2) - (11*(1 + S^4)*HPL[{3}, -S^2])/(24*S^2) + (257*(1 + S^4)*HPL[{2, 1}, -S^2])/(72*S^2) - (19*(1 + S^4)*Zeta[3])/(18*S^2)) - (805*S^2*Zeta[5])/72) + Zeta[3]*((-1847*Pi^6*S^2)/2268 + (-33469 - 14687*S^2)/96 + (Pi^4*(-5815 - 5073*S^2))/2160 + (Pi^2*(-5129 - 2196*S^2))/144 + (2*(-83 + 63*S^2)*Zeta[5])/3) + HPL[{3}, -S^2]*((-4467 - 66938*S^2 - 24907*S^4)/(192*S^2) + (Pi^4*(-404 - 13500*S^2 - 7879*S^4))/(4320*S^2) + (Pi^6*(260 - 5559*S^4))/(22680*S^2) + (Pi^2*(-917 - 11098*S^2 - 4222*S^4))/(288*S^2) + ((Pi^2*(-76 + S^4))/(18*S^2) + (43 + 166*S^2 + 37*S^4)/(12*S^2))*HPL[{4}, -S^2] + ((-158 + 28*S^2 + 209*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-145 - 119*S^4)*HPL[{6}, -S^2])/(3*S^2) + (2*(29 + 195*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(-7 + 206*S^4))/(9*S^2) + (210 + 1088*S^2 + 393*S^4)/(6*S^2))*HPL[{3, 1}, -S^2] + ((187 - 116*S^2 - 240*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((-251 + 204*S^2 + 81*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + (5*(-1 + 2*S^4)*HPL[{4, 2}, -S^2])/(3*S^2) + (2*(57 + 10*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-182 - 1072*S^2 - 461*S^4)/(3*S^2) - (2*Pi^2*(5 + 228*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] - (4*(187 + 186*S^2 + 20*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(1171 + 1124*S^2 + 38*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (4*(-3 + 2*S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) - (4*(7 + 64*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (52*(101 + 516*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (4*(-459 - 376*S^2 + 97*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (8*(19 + 203*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (80*(1 + 14*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-145 - 8*S^2 - 53*S^4))/(36*S^2) + (-243 + 162*S^2 + 130*S^4)/(12*S^2))*Zeta[3] - (2*(3 + 13*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(529 + 402*S^2 - 148*S^4))/(18*S^2) + (765 + 313*S^2 - 98*S^4)/(3*S^2) - (4*(12 + 13*S^4)*Zeta[3])/(3*S^2)) + ((-451 - 103*S^4)*Zeta[5])/(6*S^2)) + HPL[{2, 1}, -S^2]*((Pi^4*(4909 + 16326*S^2 + 2828*S^4))/(1440*S^2) + (Pi^2*(5767 + 29726*S^2 + 5822*S^4))/(288*S^2) + (Pi^6*(46812 + 8377*S^4))/(45360*S^2) + (14687 + 66938*S^2 + 14687*S^4)/(96*S^2) + ((2*Pi^2*(-71 + 31*S^4))/(3*S^2) + (-103 - 120*S^2 + 455*S^4)/(6*S^2))*HPL[{3, 1}, -S^2] + ((-769 - 744*S^2 - 59*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-2381 - 2248*S^2 + 105*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (2*(-171 + 37*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((93*(-1 + S^4))/S^2 + (4*Pi^2*(-209 + 97*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] - (4*(69 + 124*S^2 + 69*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(81 + 370*S^2 + 359*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (664*(-1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (8*(-275 + 277*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (2224*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(-97 + 98*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (1040*(-1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((832 + 103*S^2 - 31*S^4)/(3*S^2) + (Pi^2*(560 + 422*S^2 + 27*S^4))/(18*S^2))*Zeta[3] + (2*(3 + 5*S^4)*Zeta[3]^2)/(3*S^2) + ((917 + 542*S^2 - 18*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]^4*((Pi^4*(-449 - 4455*S^2 - 4084*S^4))/(3240*S^2) + (Pi^2*(933 - 1640*S^2 - 2573*S^4))/(288*S^2) - (12859*(-1 + S^4))/(288*S^2) - (37*(-1 + S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((-346 - 507*S^2 - 161*S^4)/(9*S^2) - (29*Pi^2*(1 + S^4))/(6*S^2))*HPL[{3}, -S^2] - (2*(4 + 75*S^2 + 65*S^4)*HPL[{4}, -S^2])/(9*S^2) - (46*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((118*Pi^2*(1 + S^4))/(9*S^2) + (169*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + ((389 + 900*S^2 + 511*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (124*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (140*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (100*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (100*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (200*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-907 - 1014*S^2 - 107*S^4)/(18*S^2) - (43*Pi^2*(1 + S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-323 - 696*S^2 - 397*S^4))/(54*S^2) - (205*(1 + 2*S^2 + S^4))/(6*S^2) - (62*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (64*(1 + S^4)*Zeta[3])/(3*S^2)) - (112*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(1951 - 412*S^2 - 3438*S^4))/(288*S^2) + (Pi^4*(789 - 907*S^2 - 1768*S^4))/(1080*S^2) - (779*(-1 + S^4))/(16*S^2) + ((-85 - 1132*S^2 - 382*S^4)/(24*S^2) + (Pi^2*(-38 - 213*S^4))/(36*S^2))*HPL[{3}, -S^2] + ((19 - 24*S^2 - 42*S^4)*HPL[{4}, -S^2])/(3*S^2) - (7*(13 + 17*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((Pi^2*(218 + 135*S^4))/(18*S^2) + (467 + 2264*S^2 + 467*S^4)/(24*S^2))*HPL[{2, 1}, -S^2] + ((73 + 186*S^2 + 134*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((43 + 375*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((209 + 1205*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((-69 - 124*S^2 - 69*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (166*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (4*(-139 + 27*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (448*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-223 - 1132*S^2 - 244*S^4)/(24*S^2) + (Pi^2*(-50 - 239*S^4))/(36*S^2))*Zeta[3] - (11*(4 + 25*S^4)*Zeta[5])/(6*S^2)) + HPL[{3, 1}, -S^2]*((Pi^2*(850 + 1071*S^2 + 2148*S^4))/(36*S^2) + (Pi^4*(6199 + 16536*S^2 + 17003*S^4))/(2160*S^2) + (19545 + 17432*S^2 + 31087*S^4)/(96*S^2) - (2*(115 + 427*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(233 + 1273*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (16*(-63 - S^2 + 76*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (896*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(-795 + 349*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (16*(-97 + 98*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(-2 + 73*S^4))/(3*S^2) + (-51 + 1304*S^2 + 180*S^4)/(6*S^2))*Zeta[3] + (10*(-16 + 43*S^4)*Zeta[5])/(3*S^2)) + HPL[{4}, -S^2]*((-453 - 11880*S^2 - 11995*S^4)/(96*S^2) + (Pi^4*(-2933 - 2640*S^2 - 3629*S^4))/(2160*S^2) + (Pi^2*(-172 - 302*S^2 - 1081*S^4))/(72*S^2) + (5*(29 + 39*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-161 + 120*S^2 - 191*S^4)/(6*S^2) + (Pi^2*(131 - 31*S^4))/(18*S^2))*HPL[{2, 1}, -S^2] + ((-209 - 36*S^2 + 321*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + ((-155 - 191*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(98 + 171*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((137 + 16*S^2 - 345*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (130*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(233 + 129*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (16*(-13 + 14*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(53 + 7*S^4))/(18*S^2) + (-1 - 33*S^2 + 12*S^4)/S^2)*Zeta[3] + ((189 + 79*S^4)*Zeta[5])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(-6206 - 16674*S^2 - 17655*S^4))/(1080*S^2) + (-6329 - 4358*S^2 - 6329*S^4)/(12*S^2) + (Pi^2*(-1067 - 1093*S^2 - 1930*S^4))/(18*S^2) + (1792*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (16*(107 + 42*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (1040*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((55 - 1288*S^2 - 224*S^4)/(3*S^2) - (8*Pi^2*(1 + 56*S^4))/(9*S^2))*Zeta[3] - (8*(-7 + 132*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]^3*((Pi^4*(831 - 40652*S^2 - 42443*S^4))/(12960*S^2) + (Pi^2*(1207 - 2102*S^2 - 3309*S^4))/(144*S^2) - (2903*(-1 + S^4))/(24*S^2) - (47329*Pi^6*(1 + S^4))/(136080*S^2) + ((-283*(-1 + S^4))/(18*S^2) - (31*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2]^2 - (62*(1 + S^4)*HPL[{2}, -S^2]^3)/(9*S^2) + ((39 - 314*S^2 - 353*S^4)/(9*S^2) - (109*Pi^2*(1 + S^4))/(27*S^2))*HPL[{4}, -S^2] - (8*(7 + 70*S^2 + 61*S^4)*HPL[{5}, -S^2])/(9*S^2) - (53*(1 + S^4)*HPL[{6}, -S^2])/S^2 + ((236*Pi^2*(1 + S^4))/(9*S^2) + (2*(409 + 1014*S^2 + 605*S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + (4*(259 + 374*S^2 + 111*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) + (8*(394 + 633*S^2 + 233*S^4)*HPL[{4, 1}, -S^2])/(9*S^2) + (184*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-472*Pi^2*(1 + S^4))/(9*S^2) - (676*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (592*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) - (4*(31 + 300*S^2 + 269*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (496*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (560*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (400*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (400*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (800*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-375 - 518*S^2 - 139*S^4))/(27*S^2) + (-1567 - 1640*S^2 - 73*S^4)/(12*S^2))*Zeta[3] + HPL[{3}, -S^2]*((-3511 - 4920*S^2 - 1409*S^4)/(36*S^2) + (Pi^2*(-601 - 1016*S^2 - 471*S^4))/(54*S^2) + (248*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((410*(1 + 2*S^2 + S^4))/(3*S^2) + (2*Pi^2*(323 + 696*S^2 + 397*S^4))/(27*S^2) + (256*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-1375 - 3220*S^2 - 1941*S^4))/(108*S^2) - (2779*Pi^4*(1 + S^4))/(1080*S^2) - (1051*(1 + 2*S^2 + S^4))/(12*S^2) - (8*(65 + 93*S^2 + 28*S^4)*HPL[{3}, -S^2])/(9*S^2) + (296*(-1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (4*(127 + 204*S^2 + 53*S^4)*Zeta[3])/(9*S^2)) - (2*(537 + 670*S^2 + 137*S^4)*Zeta[5])/(9*S^2)) + HPL[{0}, S^2]^3*((-2033*Pi^6*S^2)/20160 + (Pi^4*(14444 - 119579*S^2))/51840 + (26503 - 45056*S^2)/1152 + (Pi^2*(3268 - 9571*S^2))/1152 + ((-11 - 276*S^2 - 233*S^4)*HPL[{1}, -S^2]^5)/(180*S^2) - (13*(1 + S^4)*HPL[{1}, -S^2]^6)/(54*S^2) + ((-18 - 140*S^2 - 1447*S^4)/(288*S^2) + (Pi^2*(-12 - 367*S^4))/(432*S^2))*HPL[{2}, -S^2]^2 + ((1 - 24*S^4)*HPL[{2}, -S^2]^3)/(36*S^2) + HPL[{1}, -S^2]^4*((72 - 401*S^2 - 433*S^4)/(108*S^2) - (79*Pi^2*(1 + S^4))/(108*S^2) - (31*(1 + S^4)*HPL[{2}, -S^2])/(18*S^2)) + ((35 + 31*S^4)*HPL[{3}, -S^2]^2)/(36*S^2) + ((5 - 77*S^2 - 80*S^4)/(36*S^2) + (Pi^2*(9 + 8*S^4))/(54*S^2))*HPL[{4}, -S^2] + (5*(7 + 24*S^2)*HPL[{5}, -S^2])/(72*S^2) + ((25 + 29*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((-3 + 163*S^4)*HPL[{2, 1}, -S^2]^2)/(18*S^2) + ((Pi^2*(12 + 361*S^4))/(108*S^2) + (26 + 492*S^2 + 1631*S^4)/(72*S^2))*HPL[{3, 1}, -S^2] + ((275 - 100*S^2 + 196*S^4)*HPL[{3, 2}, -S^2])/(72*S^2) + ((229 - 148*S^2 + 292*S^4)*HPL[{4, 1}, -S^2])/(36*S^2) - (S^2*HPL[{4, 2}, -S^2])/9 - (5*(3 + 4*S^4)*HPL[{5, 1}, -S^2])/(9*S^2) + ((32 - 304*S^2 - 1677*S^4)/(36*S^2) + (Pi^2*(-27 - 437*S^4))/(54*S^2))*HPL[{2, 1, 1}, -S^2] + ((-51 - 368*S^2 - 13*S^4)*HPL[{2, 2, 1}, -S^2])/(18*S^2) + ((-99 - 1084*S^2 - 110*S^4)*HPL[{3, 1, 1}, -S^2])/(18*S^2) + (S^2*HPL[{3, 1, 2}, -S^2])/9 + ((6 - 143*S^4)*HPL[{3, 2, 1}, -S^2])/(9*S^2) + ((9 - 445*S^4)*HPL[{4, 1, 1}, -S^2])/(9*S^2) + (2*(18 + 188*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^2) + (8*(3 + 43*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^2) - (4*(4 + 61*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(-286 - 1737*S^2))/216 + (658 - 1371*S^2)/144)*Zeta[3] + (S^2*Zeta[3]^2)/6 + HPL[{2}, -S^2]*((Pi^2*(76 - 259*S^2 - 1968*S^4))/(432*S^2) + (Pi^4*(-19 - 432*S^4))/(720*S^2) - (7*(-256 + 86*S^2 + 1487*S^4))/(576*S^2) + ((-69 + 26*S^2 - 48*S^4)*HPL[{3}, -S^2])/(36*S^2) - (5*(7 + 6*S^4)*HPL[{4}, -S^2])/(18*S^2) + ((51 + 368*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(36*S^2) + ((10 + 91*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + ((3 - 163*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + ((-26 - 107*S^2)*Zeta[3])/36) + HPL[{1}, -S^2]^2*((2063 - 3586*S^2 - 5393*S^4)/(288*S^2) + (Pi^2*(995 - 3776*S^2 - 4211*S^4))/(864*S^2) - (805*Pi^4*(1 + S^4))/(1296*S^2) + ((63 - 410*S^2 - 473*S^4)/(36*S^2) - (415*Pi^2*(1 + S^4))/(216*S^2))*HPL[{2}, -S^2] - (83*(1 + S^4)*HPL[{2}, -S^2]^2)/(36*S^2) + ((11 - S^2 - 22*S^4)*HPL[{3}, -S^2])/(9*S^2) + (5*(1 + S^4)*HPL[{4}, -S^2])/(18*S^2) + ((23 + 372*S^2 + 349*S^4)*HPL[{2, 1}, -S^2])/(18*S^2) + (89*(1 + S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (62*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((79 - 108*S^2 - 155*S^4)*Zeta[3])/(36*S^2)) + HPL[{3}, -S^2]*((222 - 330*S^2 - 581*S^4)/(144*S^2) + (Pi^2*(129 + 80*S^2 - 86*S^4))/(432*S^2) + ((-13 - 19*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + ((-1 - 2*S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((1159 - 3336*S^2 - 4239*S^4)/(432*S^2) + (Pi^2*(5 - 1022*S^2 - 879*S^4))/(324*S^2) + ((-23 - 372*S^2 - 349*S^4)*HPL[{2}, -S^2])/(54*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) + (62*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (23*(1 + S^4)*Zeta[3])/(27*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(8 + 934*S^2 - 119*S^4))/(216*S^2) + (-875 + 3780*S^2 + 867*S^4)/(144*S^2) + ((40 + 23*S^4)*Zeta[3])/(9*S^2)) + ((-48 - 403*S^2)*Zeta[5])/9 + HPL[{1}, -S^2]*((15623 - 12884*S^2 - 28507*S^4)/(1152*S^2) + (Pi^4*(3953 - 16816*S^2 - 19337*S^4))/(12960*S^2) + (Pi^2*(1897 - 3160*S^2 - 4929*S^4))/(864*S^2) + ((-49 - 344*S^2 - 271*S^4)*HPL[{2}, -S^2]^2)/(72*S^2) + ((75 - 220*S^2 - 263*S^4)/(72*S^2) + (Pi^2*(1 + S^4))/(12*S^2))*HPL[{3}, -S^2] + ((105 + 8*S^2 - 73*S^4)*HPL[{4}, -S^2])/(36*S^2) + (59*(1 + S^4)*HPL[{5}, -S^2])/(18*S^2) + ((415*Pi^2*(1 + S^4))/(108*S^2) + (-63 + 410*S^2 + 473*S^4)/(18*S^2))*HPL[{2, 1}, -S^2] + ((5 + 348*S^2 + 359*S^4)*HPL[{3, 1}, -S^2])/(18*S^2) - (5*(1 + S^4)*HPL[{3, 2}, -S^2])/(9*S^2) - (20*(1 + S^4)*HPL[{4, 1}, -S^2])/(9*S^2) + ((-23 - 372*S^2 - 349*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) - (166*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) - (170*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (124*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((401 + 172*S^2 - 437*S^4)/(72*S^2) - (143*Pi^2*(1 + S^4))/(108*S^2))*Zeta[3] + HPL[{2}, -S^2]*((1211 - 4144*S^2 - 4971*S^4)/(288*S^2) + (Pi^2*(-3 - 1760*S^2 - 1557*S^4))/(432*S^2) + (5*(1 + S^4)*HPL[{3}, -S^2])/(18*S^2) + (83*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (37*(1 + S^4)*Zeta[3])/(18*S^2)) - (16*(1 + S^4)*Zeta[5])/(3*S^2))) + Log[T]^3*((8431*Pi^6*S^2)/11340 + (Pi^4*(1058 + 2695*S^2))/540 + (Pi^2*(2966 + 9699*S^2))/432 + (31*S^2*HPL[{0}, S^2]^6)/216 + (56*(-1 + S^4)*HPL[{1}, -S^2]^5)/(9*S^2) + HPL[{0}, S^2]^5*((558 + 1219*S^2)/1080 + (31*(1 + S^4)*HPL[{1}, -S^2])/(60*S^2)) + ((1411*(-1 + S^4))/(36*S^2) + (2*Pi^2*(-58 + 95*S^4))/(27*S^2))*HPL[{2}, -S^2]^2 + (148*(1 + S^4)*HPL[{2}, -S^2]^3)/(27*S^2) + HPL[{1}, -S^2]^4*((230*(-1 + S^4))/(9*S^2) + (25*Pi^2*(1 + S^4))/(9*S^2) + (100*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]^4*((371*Pi^2*S^2)/324 + (82 + 351*S^2)/72 + ((33 + 186*S^2 + 133*S^4)*HPL[{1}, -S^2])/(36*S^2) + (22*(1 + S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + ((4 + 41*S^4)*HPL[{2}, -S^2])/(18*S^2)) - (4*(-5 + 4*S^4)*HPL[{3}, -S^2]^2)/(9*S^2) + ((2*Pi^2*(69 + 77*S^4))/(27*S^2) + (137 + 72*S^2 + 393*S^4)/(6*S^2))*HPL[{4}, -S^2] + ((-327 + 552*S^2 + 692*S^4)*HPL[{5}, -S^2])/(9*S^2) + (8*(54 + 71*S^4)*HPL[{6}, -S^2])/(9*S^2) - (260*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-441 - 420*S^2 - 569*S^4)/(3*S^2) - (4*Pi^2*(117 + 214*S^4))/(27*S^2))*HPL[{3, 1}, -S^2] + ((-165 - 1488*S^2 - 1205*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) - (16*(19 + 315*S^2 + 246*S^4)*HPL[{4, 1}, -S^2])/(9*S^2) - (8*(-7 + 11*S^4)*HPL[{4, 2}, -S^2])/(9*S^2) - (8*(61 + 119*S^4)*HPL[{5, 1}, -S^2])/(9*S^2) + ((20*Pi^2*(47 + 86*S^4))/(27*S^2) + (10*(101 + 84*S^2 + 101*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (1040*(-1 + S^2)*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(9*S^2) - (16*(-63 - 75*S^2 + 13*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (16*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/(9*S^2) + (400*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (1456*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (800*(1 + 3*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (1120*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (2240*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(172 + 125*S^2))/9 + (1862 + 561*S^2)/9)*Zeta[3] - (4*S^2*Zeta[3]^2)/3 + HPL[{0}, S^2]^3*((Pi^2*(948 + 1963*S^2))/324 + (-280 + 2267*S^2)/108 + ((11 + 276*S^2 + 233*S^4)*HPL[{1}, -S^2]^2)/(18*S^2) + (130*(1 + S^4)*HPL[{1}, -S^2]^3)/(27*S^2) + ((5 + 184*S^2 + 336*S^4)*HPL[{2}, -S^2])/(27*S^2) + HPL[{1}, -S^2]*((79*Pi^2*(1 + S^4))/(27*S^2) + (-72 + 401*S^2 + 433*S^4)/(27*S^2) + (62*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((-1 + S^2)*(1 + S^2)*HPL[{3}, -S^2])/(9*S^2) - (2*(58 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (14*S^2*Zeta[3])/9) + HPL[{1}, -S^2]^3*((625*(-1 + S^4))/(9*S^2) + (5*Pi^2*(-31 + 180*S^2 + 211*S^4))/(81*S^2) + (200*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/(3*S^2) + (200*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (400*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (200*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-40 + 992*S^2 + 741*S^4))/(54*S^2) + (169 + 3724*S^2 + 953*S^4)/(18*S^2) + (8*(-57 + 8*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (8*(14 + S^4)*Zeta[3])/(9*S^2)) + HPL[{2, 1}, -S^2]*((-561 - 3724*S^2 - 561*S^4)/(9*S^2) - (4*Pi^2*(158 + 342*S^2 + 93*S^4))/(27*S^2) + (40*(-37 + 2*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]^2*((2449*(-1 + S^4))/(18*S^2) + (749*Pi^4*(1 + S^4))/(270*S^2) + (Pi^2*(-473 + 1014*S^2 + 1487*S^4))/(54*S^2) + ((236*Pi^2*(1 + S^4))/(9*S^2) + (338*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2}, -S^2] + (2*(179 + 300*S^2 + 121*S^4)*HPL[{3}, -S^2])/(3*S^2) + (32*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (200*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (200*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (400*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (10*(137 + 180*S^2 + 43*S^4)*Zeta[3])/(9*S^2)) + HPL[{2}, -S^2]*((Pi^4*(569 + 1526*S^4))/(405*S^2) + (Pi^2*(1669 + 2136*S^2 + 3080*S^4))/(108*S^2) + (9699 + 5932*S^2 + 9699*S^4)/(72*S^2) + (2*(61 + 368*S^2 + 321*S^4)*HPL[{3}, -S^2])/(9*S^2) + (8*(-13 + 14*S^4)*HPL[{4}, -S^2])/(9*S^2) + (520*(-1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (8*(-97 + 98*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (520*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (8*(-8 + 108*S^2 + 57*S^4)*Zeta[3])/(9*S^2)) + HPL[{0}, S^2]^2*((8159*Pi^4*S^2)/3240 + (17*Pi^2*(22 + 71*S^2))/72 + (2966 + 9699*S^2)/144 + (5*(53 + 180*S^2 + 127*S^4)*HPL[{1}, -S^2]^3)/(27*S^2) + (25*(1 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + ((Pi^2*(49 + 466*S^4))/(54*S^2) + (154 + 876*S^2 + 1565*S^4)/(36*S^2))*HPL[{2}, -S^2] + (37*(-1 + 5*S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + HPL[{1}, -S^2]^2*((163*Pi^2*(1 + S^4))/(18*S^2) + (217 + 1014*S^2 + 797*S^4)/(18*S^2) + (86*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-16 + 92*S^2 + 117*S^4)*HPL[{3}, -S^2])/(18*S^2) + (4*(9 + 13*S^4)*HPL[{4}, -S^2])/(9*S^2) - (4*(83 + 117*S^2 + 18*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (4*(12 + 109*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (20*(5 + 44*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + ((22 + 25*S^2)*Zeta[3])/3 + HPL[{1}, -S^2]*((317 + 1640*S^2 + 1323*S^4)/(24*S^2) + (Pi^2*(463 + 2016*S^2 + 1433*S^4))/(108*S^2) + (4*(49 + 123*S^2 + 86*S^4)*HPL[{2}, -S^2])/(9*S^2) + (8*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (22*(1 + S^4)*Zeta[3])/(3*S^2))) + (4*(336 + 145*S^2)*Zeta[5])/9 + HPL[{0}, S^2]*((Pi^2*(-925 + 2071*S^2))/54 + (Pi^4*(2626 + 6783*S^2))/1080 + (-12274 + 12859*S^2)/72 + ((460*(-1 + S^4))/(9*S^2) + (130*Pi^2*(1 + S^4))/(27*S^2))*HPL[{1}, -S^2]^3 + (140*(-1 + S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + (4*(2 - 6*S^2 + 39*S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((-2*Pi^2*(4 + S^4))/(27*S^2) + (-75 - 34*S^2 + 163*S^4)/(9*S^2))*HPL[{3}, -S^2] + ((33 - 12*S^2 + 154*S^4)*HPL[{4}, -S^2])/(9*S^2) + (2*(-7 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((1301 - 768*S^2 - 299*S^4)/(9*S^2) - (2*Pi^2*(21 + 2*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (8*(-22 - 3*S^2 + 94*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (8*(11 + 10*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) - (8*(6 + 5*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (20*(-17 + 77*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (136*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) + (368*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^2) - (80*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((14*Pi^2*S^2)/9 + (2*(-19 + 32*S^2))/3)*Zeta[3] + HPL[{1}, -S^2]^2*((625*(-1 + S^4))/(6*S^2) + (Pi^2*(-129 + 276*S^2 + 373*S^4))/(18*S^2) + (470*(-1 + S^4)*HPL[{2}, -S^2])/(9*S^2) - (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-75 + 368*S^2 + 1057*S^4))/(54*S^2) + (-903 - 2528*S^2 + 3579*S^4)/(36*S^2) + (4*(4 + 3*S^4)*HPL[{3}, -S^2])/(3*S^2) - (68*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (4*(-1 + 2*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]*((2449*(-1 + S^4))/(18*S^2) + (1313*Pi^4*(1 + S^4))/(540*S^2) + (Pi^2*(-417 + 401*S^2 + 778*S^4))/(27*S^2) + ((800*(-1 + S^4))/(9*S^2) + (62*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] + (2*(1 + S^2)*(-31 + 27*S^2)*HPL[{3}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (940*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S^2) + (8*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(-55 + 12*S^2 + 67*S^4)*Zeta[3])/(9*S^2)) - (52*S^2*Zeta[5])/9) + HPL[{1}, -S^2]*((12859*(-1 + S^4))/(72*S^2) + (Pi^2*(-933 + 1640*S^2 + 2573*S^4))/(72*S^2) + (Pi^4*(449 + 4455*S^2 + 4084*S^4))/(810*S^2) + (148*(-1 + S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((58*Pi^2*(1 + S^4))/(3*S^2) + (4*(346 + 507*S^2 + 161*S^4))/(9*S^2))*HPL[{3}, -S^2] + (8*(4 + 75*S^2 + 65*S^4)*HPL[{4}, -S^2])/(9*S^2) + (184*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-472*Pi^2*(1 + S^4))/(9*S^2) - (676*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (4*(389 + 900*S^2 + 511*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (496*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (560*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (400*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (400*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (800*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((172*Pi^2*(1 + S^4))/(9*S^2) + (2*(907 + 1014*S^2 + 107*S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((410*(1 + 2*S^2 + S^4))/(3*S^2) + (2*Pi^2*(323 + 696*S^2 + 397*S^4))/(27*S^2) + (248*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (256*(1 + S^4)*Zeta[3])/(3*S^2)) + (448*(1 + S^4)*Zeta[5])/(3*S^2))) + (-93*Pi^2*S^2 + (-673 - 243*S^2)/2)*Zeta[7] + Log[T]^2*((Pi^4*(-13253 - 39550*S^2))/4320 + (Pi^2*(-2179 - 6329*S^2))/144 - (47*Pi^6*(2014 + 3257*S^2))/90720 - (5*S^2*HPL[{0}, S^2]^7)/144 - (28*(-1 + S^4)*HPL[{1}, -S^2]^6)/(9*S^2) + HPL[{0}, S^2]^6*((-56 - 109*S^2)/288 - (7*(1 + S^4)*HPL[{1}, -S^2])/(36*S^2)) + ((-69 - 124*S^2 - 69*S^4)*HPL[{2}, -S^2]^3)/(6*S^2) + HPL[{0}, S^2]^5*((-407*Pi^2*S^2)/1080 + (26 - 2979*S^2)/1440 + ((43 - 1216*S^2 - 1059*S^4)*HPL[{1}, -S^2])/(720*S^2) - (31*(1 + S^4)*HPL[{1}, -S^2]^2)/(40*S^2) + ((-15 - 254*S^4)*HPL[{2}, -S^2])/(360*S^2)) + HPL[{1}, -S^2]^5*((-46*(-1 + S^4))/(3*S^2) - (5*Pi^2*(1 + S^4))/(3*S^2) - (20*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((-49 - 8*S^2 + 82*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((845 - 1284*S^2 - 1875*S^4)/(12*S^2) + (Pi^2*(-25 - 283*S^4))/(18*S^2))*HPL[{5}, -S^2] + ((-148 - 954*S^2 - 1485*S^4)*HPL[{6}, -S^2])/(6*S^2) - (20*(15 + 38*S^4)*HPL[{7}, -S^2])/(3*S^2) + (556*(-1 + S^2)*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((128 + 1110*S^2 + 407*S^4)/(3*S^2) + (Pi^2*(7 + 458*S^4))/(9*S^2))*HPL[{3, 2}, -S^2] + ((2*Pi^2*(55 + 716*S^4))/(9*S^2) + (525 + 7472*S^2 + 2999*S^4)/(6*S^2))*HPL[{4, 1}, -S^2] + ((-11 + 295*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) - (2*(-37 + 41*S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((185 + 552*S^2 + 1172*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((63 - 55*S^4)*HPL[{5, 2}, -S^2])/S^2 + (68*(9 + 7*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((93*(-1 + S^4))/S^2 + (4*Pi^2*(-209 + 97*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((-871 - 2796*S^2 - 155*S^4)/(3*S^2) + (4*Pi^2*(-655 + 54*S^4))/(9*S^2))*HPL[{3, 1, 1}, -S^2] - (71*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) - (31*(29 + 48*S^2 + 29*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (2*(121 + 775*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) - (8*(77 + 593*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) - (16*(186 + 315*S^2 + 215*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (16*(34 + 301*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) - (32*(53 + 449*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) - (8*(435 + 3689*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((2*(171 + 932*S^2 + 171*S^4))/S^2 + (4*Pi^2*(473 + 278*S^4))/(9*S^2))*HPL[{2, 1, 1, 1}, -S^2] + (1792*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) + (8*(271 + 450*S^2 + 329*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (16*(322 + 127*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) - (16*(322 + 127*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (16*(658 + 463*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (1040*(10 + 7*S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (800*(2 + 3*S^2 + 2*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (1040*(-1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (3120*(-1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (160*(-31 + 47*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (2560*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-869*Pi^4*S^2)/180 + (-9646 - 2913*S^2)/24 + (Pi^2*(-379 - 173*S^2))/9)*Zeta[3] + 14*S^2*Zeta[3]^2 + HPL[{0}, S^2]^4*((Pi^2*(-1368 - 2521*S^2))/864 + (-367 - 2428*S^2)/288 + ((-33 - 186*S^2 - 133*S^4)*HPL[{1}, -S^2]^2)/(24*S^2) - (22*(1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + ((-42 - 514*S^2 - 777*S^4)*HPL[{2}, -S^2])/(144*S^2) + HPL[{1}, -S^2]*((-223 - 2300*S^2 - 1885*S^4)/(288*S^2) - (19*Pi^2*(1 + S^4))/(12*S^2) - (257*(1 + S^4)*HPL[{2}, -S^2])/(72*S^2)) + ((-5 - 7*S^4)*HPL[{3}, -S^2])/(24*S^2) + ((233 + 11*S^4)*HPL[{2, 1}, -S^2])/(36*S^2) - (83*S^2*Zeta[3])/36) + HPL[{3}, -S^2]*((-558 - 9646*S^2 - 2355*S^4)/(24*S^2) + (Pi^4*(-209 - 1955*S^4))/(540*S^2) + (Pi^2*(-9 - 789*S^2 - 355*S^4))/(18*S^2) + (2*(-19 + 33*S^4)*HPL[{4}, -S^2])/(3*S^2) - (2*(-459 - 376*S^2 + 97*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(19 + 203*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (40*(1 + 14*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-92 - 16*S^2 - 37*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^4*((-625*(-1 + S^4))/(12*S^2) - (5*Pi^2*(-31 + 180*S^2 + 211*S^4))/(108*S^2) - (50*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 - (50*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (100*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (50*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((319*Pi^4*(19 + 7*S^4))/(540*S^2) + (Pi^2*(1081 + 4304*S^2 + 802*S^4))/(36*S^2) + (2913 + 19292*S^2 + 2913*S^4)/(24*S^2) + (8*(-97 + 98*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (520*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (8*(-135 - 96*S^2 + 4*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(329 - 186*S^2 - 536*S^4))/(36*S^2) - (863*(-1 + S^4))/(12*S^2) + ((-29 - 195*S^4)*HPL[{3}, -S^2])/(3*S^2) + (224*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (28*(1 + 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((-130 - 161*S^2 - 696*S^4)/(6*S^2) + (Pi^2*(-315 - 428*S^2 - 669*S^4))/(36*S^2) - (8*(-13 + 14*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(-17 + 29*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((Pi^2*(473 - 1014*S^2 - 1487*S^4))/(54*S^2) - (2449*(-1 + S^4))/(18*S^2) - (749*Pi^4*(1 + S^4))/(270*S^2) + ((-236*Pi^2*(1 + S^4))/(9*S^2) - (338*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2}, -S^2] - (2*(179 + 300*S^2 + 121*S^4)*HPL[{3}, -S^2])/(3*S^2) - (32*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (200*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (200*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (400*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (10*(137 + 180*S^2 + 43*S^4)*Zeta[3])/(9*S^2)) + HPL[{3, 1}, -S^2]*((808 + 598*S^2 + 1091*S^4)/(3*S^2) + (Pi^2*(584 + 1412*S^2 + 1273*S^4))/(18*S^2) + (8*(3 + 100*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((-1899 - 1196*S^2 - 1899*S^4)/(3*S^2) - (4*Pi^2*(165 + 354*S^2 + 304*S^4))/(9*S^2) - (8*(7 + 202*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^3*((-821*Pi^4*S^2)/648 + (2734 - 11593*S^2)/288 + (Pi^2*(-44 - 2419*S^2))/216 + ((-11 - 276*S^2 - 233*S^4)*HPL[{1}, -S^2]^3)/(18*S^2) - (65*(1 + S^4)*HPL[{1}, -S^2]^4)/(18*S^2) + ((32 - 304*S^2 - 1677*S^4)/(72*S^2) + (Pi^2*(-27 - 437*S^4))/(108*S^2))*HPL[{2}, -S^2] + ((3 - 163*S^4)*HPL[{2}, -S^2]^2)/(36*S^2) + HPL[{1}, -S^2]^2*((72 - 401*S^2 - 433*S^4)/(18*S^2) - (79*Pi^2*(1 + S^4))/(18*S^2) - (31*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((54 + 20*S^2 - 71*S^4)*HPL[{3}, -S^2])/(36*S^2) + ((-9 - 13*S^4)*HPL[{4}, -S^2])/(18*S^2) + ((18 + 188*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (4*(3 + 43*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (2*(4 + 61*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-46 - 177*S^2)*Zeta[3])/18 + HPL[{1}, -S^2]*((1159 - 3336*S^2 - 4239*S^4)/(144*S^2) + (Pi^2*(5 - 1022*S^2 - 879*S^4))/(108*S^2) + ((-23 - 372*S^2 - 349*S^4)*HPL[{2}, -S^2])/(18*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (62*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (23*(1 + S^4)*Zeta[3])/(9*S^2))) + ((-422*Pi^2*S^2)/9 - (2*(523 + 162*S^2))/3)*Zeta[5] + HPL[{0}, S^2]^2*((Pi^4*(-15286 - 26253*S^2))/4320 + (-2179 - 6329*S^2)/48 + (Pi^2*(-965 - 4327*S^2))/144 - (5*(53 + 180*S^2 + 127*S^4)*HPL[{1}, -S^2]^4)/(36*S^2) - (5*(1 + S^4)*HPL[{1}, -S^2]^5)/S^2 + ((17 - 62*S^2 - 86*S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + HPL[{1}, -S^2]^3*((-217 - 1014*S^2 - 797*S^4)/(18*S^2) - (163*Pi^2*(1 + S^4))/(18*S^2) - (86*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-1 - 180*S^2 - 214*S^4)/(12*S^2) + (Pi^2*(-13 - 30*S^4))/(18*S^2))*HPL[{3}, -S^2] + ((-69 - 140*S^2 - 191*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((-19 - 69*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((Pi^2*(466 + 49*S^4))/(18*S^2) + (568 + 1508*S^2 + 289*S^4)/(12*S^2))*HPL[{2, 1}, -S^2] + ((42 + 512*S^2 + 615*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + ((-21 + 40*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (2*(-11 + 65*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (4*(15 + 129*S^2 + 154*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(223 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (4*(340 + 21*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (4*(233 + 38*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-19*Pi^2*S^2)/3 + (-118 - 179*S^2)/12)*Zeta[3] + HPL[{1}, -S^2]*((-1277 - 6306*S^2 - 5029*S^4)/(48*S^2) + (Pi^2*(-657 - 4328*S^2 - 3479*S^4))/(144*S^2) - (7643*Pi^4*(1 + S^4))/(2160*S^2) + ((-361 - 1192*S^2 - 927*S^4)/(12*S^2) - (515*Pi^2*(1 + S^4))/(36*S^2))*HPL[{2}, -S^2] - (31*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) - (2*(16 + 29*S^2 + 27*S^4)*HPL[{3}, -S^2])/(3*S^2) - (37*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (4*(49 + 123*S^2 + 86*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (86*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-65 - 136*S^2 - 63*S^4)*Zeta[3])/(6*S^2)) + HPL[{2}, -S^2]*((-235 - 990*S^2 - 1961*S^4)/(24*S^2) + (Pi^2*(-102 - 1030*S^2 - 1393*S^4))/(72*S^2) - (2*(-5 + 9*S^4)*HPL[{3}, -S^2])/(3*S^2) + ((223 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((3 - 22*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(-463 - 2016*S^2 - 1433*S^4))/(72*S^2) + (-317 - 1640*S^2 - 1323*S^4)/(16*S^2) - (2*(49 + 123*S^2 + 86*S^4)*HPL[{2}, -S^2])/(3*S^2) - (12*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (86*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (11*(1 + S^4)*Zeta[3])/S^2) - 39*S^2*Zeta[5]) + HPL[{1}, -S^2]^2*((Pi^4*(-449 - 4455*S^2 - 4084*S^4))/(540*S^2) + (Pi^2*(933 - 1640*S^2 - 2573*S^4))/(48*S^2) - (12859*(-1 + S^4))/(48*S^2) - (74*(-1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-29*Pi^2*(1 + S^4))/S^2 - (2*(346 + 507*S^2 + 161*S^4))/(3*S^2))*HPL[{3}, -S^2] - (4*(4 + 75*S^2 + 65*S^4)*HPL[{4}, -S^2])/(3*S^2) - (92*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((236*Pi^2*(1 + S^4))/(3*S^2) + (338*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1}, -S^2] + (2*(389 + 900*S^2 + 511*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (248*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (840*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (600*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (600*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (1200*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-907 - 1014*S^2 - 107*S^4)/(3*S^2) - (86*Pi^2*(1 + S^4))/(3*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-323 - 696*S^2 - 397*S^4))/(9*S^2) - (205*(1 + 2*S^2 + S^4))/S^2 - (124*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (128*(1 + S^4)*Zeta[3])/S^2) - (224*(1 + S^4)*Zeta[5])/S^2) + HPL[{2}, -S^2]*((Pi^4*(-6206 - 16674*S^2 - 17655*S^4))/(2160*S^2) + (-6329 - 4358*S^2 - 6329*S^4)/(24*S^2) + (Pi^2*(-1067 - 1093*S^2 - 1930*S^4))/(36*S^2) + ((-182 - 1072*S^2 - 461*S^4)/(6*S^2) + (Pi^2*(-5 - 228*S^4))/(9*S^2))*HPL[{3}, -S^2] + ((137 + 16*S^2 - 345*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((67 - 141*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-93*(-1 + S^4))/(2*S^2) - (2*Pi^2*(-209 + 97*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + (8*(-63 - S^2 + 76*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(29 + 195*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (4*(61 + 613*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (1112*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (896*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(107 + 42*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (520*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((55 - 1288*S^2 - 224*S^4)/(6*S^2) - (4*Pi^2*(1 + 56*S^4))/(9*S^2))*Zeta[3] - (4*(-7 + 132*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]*((Pi^4*(831 - 40652*S^2 - 42443*S^4))/(4320*S^2) + (Pi^2*(1207 - 2102*S^2 - 3309*S^4))/(48*S^2) - (2903*(-1 + S^4))/(8*S^2) - (47329*Pi^6*(1 + S^4))/(45360*S^2) + ((-283*(-1 + S^4))/(6*S^2) - (31*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2}, -S^2]^2 - (62*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + ((39 - 314*S^2 - 353*S^4)/(3*S^2) - (109*Pi^2*(1 + S^4))/(9*S^2))*HPL[{4}, -S^2] - (8*(7 + 70*S^2 + 61*S^4)*HPL[{5}, -S^2])/(3*S^2) - (159*(1 + S^4)*HPL[{6}, -S^2])/S^2 + ((236*Pi^2*(1 + S^4))/(3*S^2) + (2*(409 + 1014*S^2 + 605*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + (4*(259 + 374*S^2 + 111*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (8*(394 + 633*S^2 + 233*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (184*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-472*Pi^2*(1 + S^4))/(3*S^2) - (676*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (592*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (4*(31 + 300*S^2 + 269*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (496*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (1680*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (1200*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (1200*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (2400*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-375 - 518*S^2 - 139*S^4))/(9*S^2) + (-1567 - 1640*S^2 - 73*S^4)/(4*S^2))*Zeta[3] + HPL[{3}, -S^2]*((-3511 - 4920*S^2 - 1409*S^4)/(12*S^2) + (Pi^2*(-601 - 1016*S^2 - 471*S^4))/(18*S^2) + (248*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((410*(1 + 2*S^2 + S^4))/S^2 + (2*Pi^2*(323 + 696*S^2 + 397*S^4))/(9*S^2) + (256*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((Pi^2*(-1375 - 3220*S^2 - 1941*S^4))/(36*S^2) - (2779*Pi^4*(1 + S^4))/(360*S^2) - (1051*(1 + 2*S^2 + S^4))/(4*S^2) - (8*(65 + 93*S^2 + 28*S^4)*HPL[{3}, -S^2])/(3*S^2) + (296*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(127 + 204*S^2 + 53*S^4)*Zeta[3])/(3*S^2)) - (2*(537 + 670*S^2 + 137*S^4)*Zeta[5])/(3*S^2)) + HPL[{0}, S^2]*((-43007*Pi^6*S^2)/45360 + (Pi^4*(6982 - 52943*S^2))/4320 + (Pi^2*(11702 - 21389*S^2))/288 + (8489 - 8709*S^2)/24 + ((-115*(-1 + S^4))/(3*S^2) - (65*Pi^2*(1 + S^4))/(18*S^2))*HPL[{1}, -S^2]^4 - (28*(-1 + S^4)*HPL[{1}, -S^2]^5)/(3*S^2) + ((-5 + 904*S^2 - 1137*S^4)/(24*S^2) + (Pi^2*(10 - 73*S^4))/(18*S^2))*HPL[{2}, -S^2]^2 + (19*(1 + S^4)*HPL[{2}, -S^2]^3)/(9*S^2) + (2*(7 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((-1 + 24*S^2 - 192*S^4)/(6*S^2) + (Pi^2*(-33 - 25*S^4))/(18*S^2))*HPL[{4}, -S^2] + ((130 + 68*S^2 - 139*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-10 + 17*S^4)*HPL[{6}, -S^2])/(3*S^2) - (34*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((2*Pi^2*(-3 + 77*S^4))/(9*S^2) + (-277 - 700*S^2 + 1315*S^4)/(6*S^2))*HPL[{3, 1}, -S^2] + ((209 - 88*S^2 + 271*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((101 - 156*S^2 + 372*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (7*(-1 + S^2)*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S^2) + (10*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((299 + 768*S^2 - 1301*S^4)/(3*S^2) - (2*Pi^2*(-1 + 56*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (16*(39 - 6*S^2 + 2*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (4*(-509 + 42*S^2 + 25*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (8*(-1 + S^2)*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (16*(9 + 10*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (8*(15 + 17*S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (20*(-77 + 17*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (48*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (80*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((208 - 283*S^2)/6 + (Pi^2*(-52 - 235*S^2))/18)*Zeta[3] + 6*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^2*((Pi^2*(417 - 401*S^2 - 778*S^4))/(18*S^2) - (2449*(-1 + S^4))/(12*S^2) - (1313*Pi^4*(1 + S^4))/(360*S^2) + ((-400*(-1 + S^4))/(3*S^2) - (31*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2}, -S^2] + ((31 + 4*S^2 - 27*S^4)*HPL[{3}, -S^2])/S^2 + (4*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (470*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + ((55 - 12*S^2 - 67*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((2651 + 6680*S^2 - 9437*S^4)/(48*S^2) + (Pi^4*(-284 - 3703*S^4))/(1080*S^2) + (Pi^2*(331 + 464*S^2 - 2978*S^4))/(72*S^2) - (2*(28 - 12*S^2 + 33*S^4)*HPL[{3}, -S^2])/(3*S^2) + ((-25 - 13*S^4)*HPL[{4}, -S^2])/(3*S^2) - (8*(39 - 6*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(7 + 10*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (68*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((13 + 4*S^2 - 65*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((Pi^2*(129 - 276*S^2 - 373*S^4))/(18*S^2) - (625*(-1 + S^4))/(6*S^2) - (470*(-1 + S^4)*HPL[{2}, -S^2])/(9*S^2) + (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-349 + 376*S^2 + 111*S^4))/(18*S^2) + (-3579 + 2528*S^2 + 903*S^4)/(12*S^2) - (4*(-1 + 2*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((149 - 8*S^2 - 475*S^4)/(12*S^2) + (Pi^2*(136 + 80*S^2 - 169*S^4))/(36*S^2) - (4*(4 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(4 + 3*S^4)*Zeta[3])/(3*S^2)) + ((-22 - 177*S^2)*Zeta[5])/3 + HPL[{1}, -S^2]*((Pi^4*(4059 - 16840*S^2 - 18731*S^4))/(2160*S^2) + (Pi^2*(4909 - 3336*S^2 - 7989*S^4))/(144*S^2) - (12859*(-1 + S^4))/(48*S^2) + ((-747*(-1 + S^4))/(4*S^2) - (2*Pi^2*(-53 + 93*S^2 + 146*S^4))/(9*S^2))*HPL[{2}, -S^2] - (74*(-1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((Pi^2*(-1 - S^4))/(3*S^2) - (2*(-54 + 17*S^2 + 63*S^4))/(3*S^2))*HPL[{3}, -S^2] + ((101 + 12*S^2 - 65*S^4)*HPL[{4}, -S^2])/(3*S^2) + (22*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((800*(-1 + S^4))/(3*S^2) + (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (2*(-241 - 12*S^2 + 229*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (940*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((107 + 34*S^2 - 89*S^4)/(3*S^2) - (26*Pi^2*(1 + S^4))/(9*S^2))*Zeta[3] - (22*(1 + S^4)*Zeta[5])/(3*S^2))) - 372*S^2*Zeta[7]) + HPL[{0}, S^2]^2*((Pi^6*(-63642 - 94051*S^2))/120960 + (Pi^4*(-13443 - 71474*S^2))/17280 + (Pi^2*(-5327 - 14115*S^2))/576 - (245*(131 + 199*S^2))/384 + ((-53 - 180*S^2 - 127*S^4)*HPL[{1}, -S^2]^6)/(108*S^2) - (5*(1 + S^4)*HPL[{1}, -S^2]^7)/(21*S^2) + ((3 - 212*S^2 - 225*S^4)*HPL[{2}, -S^2]^3)/(72*S^2) + HPL[{1}, -S^2]^5*((-217 - 1014*S^2 - 797*S^4)/(180*S^2) - (163*Pi^2*(1 + S^4))/(180*S^2) - (43*(1 + S^4)*HPL[{2}, -S^2])/(15*S^2)) + ((-95 + 36*S^2 + 68*S^4)*HPL[{3}, -S^2]^2)/(24*S^2) + ((419 - 28*S^2 - 1077*S^4)/(48*S^2) - (23*Pi^2*(5 + 9*S^4))/(72*S^2))*HPL[{5}, -S^2] + ((280 - 498*S^2 - 677*S^4)*HPL[{6}, -S^2])/(24*S^2) + ((-270 - 269*S^4)*HPL[{7}, -S^2])/(6*S^2) + ((-17 + 62*S^2 + 86*S^4)*HPL[{2, 1}, -S^2]^2)/(2*S^2) + ((5*Pi^2*(-15 + 8*S^4))/(36*S^2) + (-26 + 84*S^2 + 293*S^4)/(24*S^2))*HPL[{3, 2}, -S^2] + ((Pi^2*(-91 + 199*S^4))/(36*S^2) + (-113 + 488*S^2 + 1237*S^4)/(24*S^2))*HPL[{4, 1}, -S^2] + ((-17 + 8*S^2 + 39*S^4)*HPL[{4, 2}, -S^2])/(24*S^2) + ((57 + 37*S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((-34 + 252*S^2 + 413*S^4)*HPL[{5, 1}, -S^2])/(12*S^2) + ((673 + 469*S^4)*HPL[{5, 2}, -S^2])/(12*S^2) + (11*(74 + 63*S^4)*HPL[{6, 1}, -S^2])/(6*S^2) + ((Pi^2*(-458 - 21*S^4))/(18*S^2) + (-502 - 1132*S^2 + 35*S^4)/(12*S^2))*HPL[{2, 2, 1}, -S^2] + ((-1508 - 3756*S^2 - 323*S^4)/(12*S^2) + (Pi^2*(-1400 - 123*S^4))/(18*S^2))*HPL[{3, 1, 1}, -S^2] + ((-17 - 4*S^2 + 6*S^4)*HPL[{3, 1, 2}, -S^2])/(12*S^2) + ((-5 - 852*S^2 - 894*S^4)*HPL[{3, 2, 1}, -S^2])/(12*S^2) + ((-39 - 70*S^4)*HPL[{3, 2, 2}, -S^2])/(6*S^2) - (2*(-8 + 39*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + ((-51 - 1412*S^2 - 1541*S^4)*HPL[{4, 1, 1}, -S^2])/(6*S^2) + ((39 - 167*S^4)*HPL[{4, 1, 2}, -S^2])/(6*S^2) + ((243 - 419*S^4)*HPL[{4, 2, 1}, -S^2])/(6*S^2) + ((287 - 447*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(466 + 49*S^4))/(9*S^2) + (568 + 1508*S^2 + 289*S^4)/(6*S^2))*HPL[{2, 1, 1, 1}, -S^2] + (4*(106 + 23*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) + ((42 + 512*S^2 + 615*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (2*(657 + 98*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) - (2*(657 + 98*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (2*(1293 + 236*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (4*(1919 + 349*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) - (8*(15 + 129*S^2 + 154*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (4*(223 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (4*(223 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (8*(-552 + 17*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) + (8*(233 + 38*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((-2111*Pi^4*S^2)/720 + (Pi^2*(-43 - 409*S^2))/72 - (17*(12 + 29*S^2))/32)*Zeta[3] + ((-34 - 3*S^2)*Zeta[3]^2)/4 + HPL[{1}, -S^2]^3*((-1277 - 6306*S^2 - 5029*S^4)/(144*S^2) + (Pi^2*(-657 - 4328*S^2 - 3479*S^4))/(432*S^2) - (7643*Pi^4*(1 + S^4))/(6480*S^2) + ((-361 - 1192*S^2 - 927*S^4)/(36*S^2) - (515*Pi^2*(1 + S^4))/(108*S^2))*HPL[{2}, -S^2] - (31*(1 + S^4)*HPL[{2}, -S^2]^2)/(6*S^2) - (2*(16 + 29*S^2 + 27*S^4)*HPL[{3}, -S^2])/(9*S^2) - (37*(1 + S^4)*HPL[{4}, -S^2])/(9*S^2) + (4*(49 + 123*S^2 + 86*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (86*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (172*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-65 - 136*S^2 - 63*S^4)*Zeta[3])/(18*S^2)) + HPL[{2}, -S^2]^2*((225 - 412*S^2 - 1712*S^4)/(96*S^2) + (Pi^2*(99 - 394*S^2 - 544*S^4))/(144*S^2) - (3*(1 + 2*S^4)*HPL[{3}, -S^2])/(4*S^2) + ((106 + 23*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((-22 - 43*S^4)*Zeta[3])/(12*S^2)) + HPL[{3}, -S^2]*((-359 - 1452*S^2 - 1867*S^4)/(96*S^2) + (Pi^4*(-271 - 459*S^4))/(2160*S^2) + (Pi^2*(-58 - 234*S^2 - 415*S^4))/(144*S^2) + ((-57 - 32*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((70 + 26*S^2 - 51*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((-26 + 3*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (4*(-5 + 9*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-53 + 8*S^2 - 16*S^4)*Zeta[3])/(12*S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(-463 - 2016*S^2 - 1433*S^4))/(432*S^2) + (-317 - 1640*S^2 - 1323*S^4)/(96*S^2) + ((-49 - 123*S^2 - 86*S^4)*HPL[{2}, -S^2])/(9*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (43*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (11*(1 + S^4)*Zeta[3])/(6*S^2)) + HPL[{4}, -S^2]*((-42 - 141*S^2 - 385*S^4)/(24*S^2) + (Pi^2*(-147 - 308*S^2 - 377*S^4))/(144*S^2) + ((79 + 25*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (6*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((42 + 473*S^2 + 1057*S^4)/(12*S^2) + (Pi^2*(81 + 1012*S^2 + 1328*S^4))/(72*S^2) + ((-12 + 19*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((-235 - 990*S^2 - 1961*S^4)/(12*S^2) + (Pi^2*(-102 - 1030*S^2 - 1393*S^4))/(36*S^2) - (2*(-3 + 22*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(400 + 1479*S^2 + 235*S^4))/(72*S^2) + (Pi^4*(6615 + 368*S^4))/(2160*S^2) + (2854 + 10434*S^2 + 2909*S^4)/(96*S^2) - (2*(116 + 5*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (2*(223 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((20 + 38*S^2 + 43*S^4)*Zeta[3])/(6*S^2)) + ((-461*Pi^2*S^2)/18 + (-189 - 283*S^2)/12)*Zeta[5] + HPL[{1}, -S^2]*((Pi^4*(-7231 - 70704*S^2 - 56369*S^4))/(17280*S^2) + (-13919 - 48850*S^2 - 34931*S^4)/(384*S^2) + (Pi^2*(-2601 - 13688*S^2 - 10703*S^4))/(576*S^2) - (10607*Pi^6*(1 + S^4))/(20160*S^2) + ((-37 - 203*S^2 - 166*S^4)/(12*S^2) - (197*Pi^2*(1 + S^4))/(72*S^2))*HPL[{2}, -S^2]^2 - (53*(1 + S^4)*HPL[{2}, -S^2]^3)/(18*S^2) + (11*(1 + S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((-4 - 39*S^2 - 51*S^4)/(3*S^2) - (103*Pi^2*(1 + S^4))/(36*S^2))*HPL[{4}, -S^2] + ((-39 - 98*S^2 - 95*S^4)*HPL[{5}, -S^2])/(6*S^2) - (123*(1 + S^4)*HPL[{6}, -S^2])/(4*S^2) + (31*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((133*Pi^2*(1 + S^4))/(9*S^2) + (297 + 1208*S^2 + 1007*S^4)/(12*S^2))*HPL[{3, 1}, -S^2] + ((17 + 15*S^2 + 12*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((161 + 220*S^2 + 179*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + (80*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-361 - 1192*S^2 - 927*S^4)/(6*S^2) - (515*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2, 1, 1}, -S^2] + ((-41 - 124*S^2 - 83*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + ((-433 - 1232*S^2 - 855*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (212*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (710*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (8*(49 + 123*S^2 + 86*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (172*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-79 - 540*S^2 - 253*S^4))/(72*S^2) + (-211 - 520*S^2 - 149*S^4)/(24*S^2))*Zeta[3] - (17*(1 + S^4)*Zeta[3]^2)/(2*S^2) + HPL[{2}, -S^2]*((-1141 - 3957*S^2 - 3200*S^4)/(48*S^2) + (Pi^2*(-273 - 1129*S^2 - 968*S^4))/(72*S^2) - (7573*Pi^4*(1 + S^4))/(4320*S^2) + ((-35 - 28*S^2 - 25*S^4)*HPL[{3}, -S^2])/(12*S^2) - (11*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + ((41 + 124*S^2 + 83*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + (95*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (62*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((1 - 88*S^2 - 97*S^4)*Zeta[3])/(12*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-145 - 200*S^2 - 207*S^4))/(72*S^2) + (-49 - 139*S^2 - 130*S^4)/(6*S^2) + (11*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (11*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(667 + 2016*S^2 + 1437*S^4))/(72*S^2) + (1657 + 6128*S^2 + 4855*S^4)/(48*S^2) + (23*(1 + S^4)*Zeta[3])/(3*S^2)) + ((-249 - 532*S^2 - 171*S^4)*Zeta[5])/(12*S^2)) + HPL[{2}, -S^2]*((Pi^4*(-2022 - 15146*S^2 - 23823*S^4))/(8640*S^2) + (-1655 - 4180*S^2 - 6329*S^4)/(96*S^2) + (Pi^2*(-493 - 1768*S^2 - 4112*S^4))/(288*S^2) + ((1 - 30*S^2 - 159*S^4)/(24*S^2) + (Pi^2*(37 - 18*S^4))/(36*S^2))*HPL[{3}, -S^2] + ((199 - 72*S^2 - 167*S^4)*HPL[{4}, -S^2])/(24*S^2) + ((123 + 35*S^4)*HPL[{5}, -S^2])/(12*S^2) + ((502 + 1132*S^2 - 35*S^4)/(24*S^2) + (Pi^2*(458 + 21*S^4))/(36*S^2))*HPL[{2, 1}, -S^2] + ((-73 + 186*S^2 + 276*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + (3*(1 + 2*S^4)*HPL[{3, 2}, -S^2])/S^2 + ((-25 + 83*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((17 - 62*S^2 - 86*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(106 + 23*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (2*(328 + 51*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (2*(223 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((10 - 115*S^2 - 54*S^4)/(12*S^2) + (Pi^2*(18 - 37*S^4))/(36*S^2))*Zeta[3] + ((30 - 37*S^4)*Zeta[5])/(6*S^2)) + HPL[{1}, -S^2]^2*((-7945 - 34004*S^2 - 26059*S^4)/(384*S^2) + (Pi^4*(-5685 - 31820*S^2 - 23639*S^4))/(8640*S^2) + (Pi^2*(-399 - 2552*S^2 - 2105*S^4))/(144*S^2) + ((-41 - 124*S^2 - 83*S^4)*HPL[{2}, -S^2]^2)/(8*S^2) + ((-149 - 396*S^2 - 343*S^4)/(24*S^2) - (23*Pi^2*(1 + S^4))/(12*S^2))*HPL[{3}, -S^2] - (2*(7 + 17*S^2 + 13*S^4)*HPL[{4}, -S^2])/(3*S^2) - (29*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((515*Pi^2*(1 + S^4))/(36*S^2) + (361 + 1192*S^2 + 927*S^4)/(12*S^2))*HPL[{2, 1}, -S^2] + ((187 + 488*S^2 + 357*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + (11*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (70*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (4*(49 + 123*S^2 + 86*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (62*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (210*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-155 - 288*S^2 - 133*S^4)/(24*S^2) - (109*Pi^2*(1 + S^4))/(36*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-1657 - 6128*S^2 - 4855*S^4)/(96*S^2) + (Pi^2*(-667 - 2016*S^2 - 1437*S^4))/(144*S^2) - (11*(1 + S^4)*HPL[{3}, -S^2])/(6*S^2) + (31*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (23*(1 + S^4)*Zeta[3])/(6*S^2)) - (119*(1 + S^4)*Zeta[5])/(6*S^2)) - 186*S^2*Zeta[7]) + HPL[{1}, -S^2]*((Pi^6*(-16500 - 107943*S^2 - 98611*S^4))/(90720*S^2) + (Pi^2*(20917 - 48850*S^2 - 69767*S^4))/(1152*S^2) + (Pi^4*(-1782 - 67015*S^2 - 68497*S^4))/(8640*S^2) - (1330*(-1 + S^4))/(3*S^2) - (13367*Pi^8*(1 + S^4))/(85050*S^2) + ((-73*Pi^2*(1 + S^4))/(27*S^2) - (203*(1 + 2*S^2 + S^4))/(18*S^2))*HPL[{2}, -S^2]^3 + ((11*Pi^2*(1 + S^4))/(18*S^2) + (2*(-10 + S^2 + 11*S^4))/(3*S^2))*HPL[{3}, -S^2]^2 - (17*(1 + S^4)*HPL[{4}, -S^2]^2)/S^2 + ((1031 - 2274*S^2 - 3305*S^4)/(12*S^2) - (47*Pi^2*(1 + S^4))/(2*S^2))*HPL[{6}, -S^2] + ((1117 - 2440*S^2 - 2973*S^4)*HPL[{7}, -S^2])/(6*S^2) - (614*(1 + S^4)*HPL[{8}, -S^2])/S^2 + ((283*(-1 + S^4))/(3*S^2) + (31*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2]^2 + (2*(-7 - 4*S^2 + 3*S^4)*HPL[{4, 2}, -S^2])/S^2 + ((113 - 240*S^2 - 137*S^4)*HPL[{4, 3}, -S^2])/(6*S^2) + ((218*Pi^2*(1 + S^4))/(9*S^2) + (-549 + 1100*S^2 + 1649*S^4)/(6*S^2))*HPL[{5, 1}, -S^2] - (2*(-29 + 51*S^2 + 30*S^4)*HPL[{5, 2}, -S^2])/S^2 - (4*(1 + S^4)*HPL[{5, 3}, -S^2])/S^2 + ((155 + 416*S^2 + 541*S^4)*HPL[{6, 1}, -S^2])/(2*S^2) - (10*(1 + S^4)*HPL[{6, 2}, -S^2])/S^2 + (438*(1 + S^4)*HPL[{7, 1}, -S^2])/S^2 + (4*(1 + 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((-584*Pi^2*(1 + S^4))/(9*S^2) - (800*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{3, 2, 1}, -S^2] + ((-955 - 1488*S^2 - 533*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) - (4*(711 + 1120*S^2 + 401*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + (42*(1 + S^4)*HPL[{3, 3, 2}, -S^2])/S^2 + ((-1970*Pi^2*(1 + S^4))/(9*S^2) - (2*(1179 + 2750*S^2 + 1571*S^4))/(3*S^2))*HPL[{4, 1, 1}, -S^2] + ((-2865 - 4480*S^2 - 1583*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) - (70*(1 + S^4)*HPL[{4, 1, 3}, -S^2])/S^2 + ((-8469 - 13456*S^2 - 4859*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) + (52*(1 + S^4)*HPL[{4, 2, 2}, -S^2])/S^2 - (142*(1 + S^4)*HPL[{4, 3, 1}, -S^2])/S^2 - (4*(4231 + 7012*S^2 + 2701*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) - (44*(1 + S^4)*HPL[{5, 1, 2}, -S^2])/S^2 - (644*(1 + S^4)*HPL[{5, 2, 1}, -S^2])/S^2 - (2118*(1 + S^4)*HPL[{6, 1, 1}, -S^2])/S^2 + (496*(1 + 2*S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((472*Pi^2*(1 + S^4))/(3*S^2) + (4*(409 + 1014*S^2 + 605*S^4))/(3*S^2))*HPL[{3, 1, 1, 1}, -S^2] - (8*(299 + 742*S^2 + 447*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) - (8*(299 + 742*S^2 + 447*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (8*(857 + 1858*S^2 + 1005*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (496*(1 + S^4)*HPL[{3, 2, 2, 1}, -S^2])/S^2 + (1488*(1 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (16*(1280 + 2715*S^2 + 1441*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) + (1488*(1 + S^4)*HPL[{4, 1, 2, 1}, -S^2])/S^2 + (4464*(1 + S^4)*HPL[{4, 2, 1, 1}, -S^2])/S^2 + (9296*(1 + S^4)*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((-944*Pi^2*(1 + S^4))/(3*S^2) - (1352*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + (1184*(-1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (1184*(-1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (992*(1 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 + (2976*(1 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (8*(-1277 - 900*S^2 + 377*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) - (5952*(1 + S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 - (9920*(1 + S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 - (11904*(1 + S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 - (24800*(1 + S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 - (74784*(1 + S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 - (4800*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-17*Pi^2*(1 + S^4))/(6*S^2) + (133 + 36*S^2 + 95*S^4)/(12*S^2))*Zeta[3]^2 + HPL[{2}, -S^2]^2*((Pi^2*(209 - 406*S^2 - 615*S^4))/(72*S^2) - (2059*(-1 + S^4))/(48*S^2) - (907*Pi^4*(1 + S^4))/(1080*S^2) + ((-223 - 372*S^2 - 149*S^4)*HPL[{3}, -S^2])/(6*S^2) - (8*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (62*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (62*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (124*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-271 - 372*S^2 - 101*S^4)*Zeta[3])/(6*S^2)) + HPL[{3, 1, 1}, -S^2]*((643 - 2460*S^2 - 3103*S^4)/(3*S^2) - (2*Pi^2*(263 + 1066*S^2 + 831*S^4))/(9*S^2) - (752*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((Pi^2*(25 - 372*S^2 - 397*S^4))/(9*S^2) - (533*(-1 + S^4))/(2*S^2) - (248*(1 + S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((Pi^2*(1737 + 2752*S^2 + 1111*S^4))/(18*S^2) + (10225 + 14008*S^2 + 2823*S^4)/(12*S^2) - (136*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 2}, -S^2]*((Pi^2*(276 + 389*S^2 + 123*S^4))/(9*S^2) + (3451 + 4024*S^2 + 253*S^4)/(12*S^2) - (20*(1 + S^4)*Zeta[3])/S^2) + HPL[{5}, -S^2]*((Pi^2*(-67 - 378*S^2 - 339*S^4))/(18*S^2) - (2*(-49 + 251*S^2 + 260*S^4))/(3*S^2) + (32*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (24*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((820*(1 + 2*S^2 + S^4))/S^2 + (4*Pi^2*(323 + 696*S^2 + 397*S^4))/(9*S^2) + (512*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((61 - 671*S^2 - 828*S^4)/(6*S^2) + (Pi^2*(23 - 470*S^2 - 557*S^4))/(36*S^2) - (389*Pi^4*(1 + S^4))/(270*S^2) + (67*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (14*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (2*(5 + 28*S^2 + 11*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((1063*Pi^4*(1 + S^4))/(135*S^2) + (1132 + 3153*S^2 + 2021*S^4)/(6*S^2) + (Pi^2*(1115 + 3236*S^2 + 2217*S^4))/(36*S^2) + (8*(62 + 103*S^2 + 27*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-1375 - 3220*S^2 - 1941*S^4))/(18*S^2) - (2779*Pi^4*(1 + S^4))/(180*S^2) - (1051*(1 + 2*S^2 + S^4))/(2*S^2) - (8*(127 + 204*S^2 + 53*S^4)*Zeta[3])/(3*S^2)) + ((-7431 - 7752*S^2 - 641*S^4)/(24*S^2) + (Pi^2*(-1323 - 1872*S^2 - 445*S^4))/(36*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-15023 - 37866*S^2 - 25851*S^4))/(4320*S^2) + (Pi^2*(-4294 - 10263*S^2 - 6353*S^4))/(144*S^2) - (35*Pi^6*(1 + S^4))/(48*S^2) - (24425*(1 + 2*S^2 + S^4))/(96*S^2) + (5*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-11*Pi^2*(1 + S^4))/(9*S^2) - (8*(-7 - S^2 + 6*S^4))/(3*S^2))*HPL[{4}, -S^2] + ((19 - 136*S^2 - 75*S^4)*HPL[{5}, -S^2])/(3*S^2) - (50*(1 + S^4)*HPL[{6}, -S^2])/S^2 + (124*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((95*Pi^2*(1 + S^4))/(9*S^2) + (-287 - 8*S^2 + 279*S^4)/(3*S^2))*HPL[{3, 1}, -S^2] + ((467 + 744*S^2 + 277*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((1405 + 2232*S^2 + 827*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (4*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (36*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-566*(-1 + S^4))/(3*S^2) - (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (248*(1 + 2*S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (8*(149 + 372*S^2 + 223*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (592*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (5952*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-507 - 904*S^2 - 309*S^4))/(36*S^2) + (-3263 - 3712*S^2 - 65*S^4)/(24*S^2))*Zeta[3] - (11*(1 + S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*((-3479 - 4144*S^2 - 281*S^4)/(24*S^2) + (Pi^2*(-555 - 772*S^2 - 249*S^4))/(36*S^2) + (124*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (10*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((533*(-1 + S^4))/(4*S^2) + (Pi^2*(-25 + 372*S^2 + 397*S^4))/(18*S^2) + (124*(1 + S^4)*Zeta[3])/S^2) + ((-717 - 1160*S^2 - 307*S^4)*Zeta[5])/(6*S^2)) + Zeta[3]*((Pi^4*(-6099 - 10952*S^2 - 3565*S^4))/(2160*S^2) + (Pi^2*(-5123 - 5960*S^2 - 517*S^4))/(144*S^2) + (-33663 - 34004*S^2 - 341*S^4)/(96*S^2) - (166*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{3}, -S^2]*((-20655 - 34004*S^2 - 13349*S^4)/(96*S^2) + (Pi^2*(-3903 - 6032*S^2 - 2449*S^4))/(144*S^2) + (Pi^4*(-2839 - 4520*S^2 - 2393*S^4))/(1080*S^2) + ((-49 + 168*S^2 + 97*S^4)*HPL[{4}, -S^2])/(6*S^2) + (40*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((197*Pi^2*(1 + S^4))/(9*S^2) + (693 + 820*S^2 + 127*S^4)/(3*S^2))*HPL[{2, 1}, -S^2] + (8*(61 + 94*S^2 + 31*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (20*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (14*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (16*(65 + 93*S^2 + 28*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (744*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (496*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((8*Pi^2*(1 + S^4))/(9*S^2) + (53 - 8*S^2 + 35*S^4)/(6*S^2))*Zeta[3] + (8*(1 + S^4)*Zeta[5])/S^2) + HPL[{2, 1}, -S^2]*((8501*(1 + 2*S^2 + S^4))/(24*S^2) + (Pi^2*(6577 + 15968*S^2 + 9775*S^4))/(144*S^2) + (Pi^4*(14313 + 32320*S^2 + 20063*S^4))/(2160*S^2) - (296*(-1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (744*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (592*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (496*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (992*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((215*Pi^2*(1 + S^4))/(9*S^2) + (653 + 836*S^2 + 87*S^4)/(3*S^2))*Zeta[3] + (182*(1 + S^4)*Zeta[5])/S^2) + ((-743 - 884*S^2 - 221*S^4)*Zeta[7])/(2*S^2)) + HPL[{2}, -S^2]*((Pi^6*(-26698 - 66150*S^2 - 89403*S^4))/(90720*S^2) + (Pi^4*(-20189 - 30350*S^2 - 53232*S^4))/(8640*S^2) + (Pi^2*(-3992 - 4269*S^2 - 6329*S^4))/(144*S^2) - (245*(199 + 262*S^2 + 199*S^4))/(192*S^2) + ((-85 + 56*S^2 + 117*S^4)*HPL[{3}, -S^2]^2)/(12*S^2) + ((-83 + 40*S^2 - 489*S^4)/(12*S^2) + (Pi^2*(95 - 53*S^4))/(18*S^2))*HPL[{5}, -S^2] + ((155 - 68*S^2 - 597*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((205 - 86*S^4)*HPL[{7}, -S^2])/(3*S^2) + ((69 + 124*S^2 + 69*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((Pi^2*(38 + 213*S^4))/(9*S^2) + (105 + 1132*S^2 + 362*S^4)/(6*S^2))*HPL[{3, 2}, -S^2] + ((Pi^2*(97 + 1309*S^4))/(18*S^2) + (416 + 3276*S^2 + 1337*S^4)/(6*S^2))*HPL[{4, 1}, -S^2] + (2*(1 + 2*S^2 + 8*S^4)*HPL[{4, 2}, -S^2])/S^2 + ((-155 - 166*S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((-139 + 84*S^2 + 865*S^4)*HPL[{5, 1}, -S^2])/(6*S^2) - (2*(223 + 232*S^4)*HPL[{5, 2}, -S^2])/(3*S^2) + ((-1106 - 759*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((-467 - 2264*S^2 - 467*S^4)/(6*S^2) - (2*Pi^2*(218 + 135*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((118*Pi^2*(11 + 3*S^4))/(9*S^2) + (1037 + 4648*S^2 + 479*S^4)/(6*S^2))*HPL[{3, 1, 1}, -S^2] - (7*(-1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 - (159*(-1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + ((-81 - 745*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) - (4*(31 + 197*S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + ((1505 + 16*S^2 - 1713*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + ((-391 - 2383*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) + ((-1279 - 7255*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) - (2*(1265 + 7449*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((-93*(-1 + S^4))/S^2 - (4*Pi^2*(-209 + 97*S^4))/(9*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (664*(-1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) + (16*(558 + 1115*S^2 + 697*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (16*(-139 + 27*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) - (16*(-139 + 27*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (8*(-527 + 303*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (8*(-1555 + 881*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) - (2224*(-1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (1792*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (1792*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (80*(115 + 154*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) - (1040*(-1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^4*(142 - 1807*S^4))/(1080*S^2) + (Pi^2*(75 - 1518*S^2 - 332*S^4))/(72*S^2) + (-59 - 8858*S^2 - 4*S^4)/(48*S^2))*Zeta[3] + ((-16 - 30*S^2 - 11*S^4)*Zeta[3]^2)/(6*S^2) + HPL[{4}, -S^2]*((18 + 214*S^2 - 171*S^4)/(6*S^2) + (Pi^2*(42 - 7*S^2 - 64*S^4))/(9*S^2) + (65*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((-41 - 59*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((-943 - 7282*S^2 - 888*S^4)/(48*S^2) + (Pi^4*(144 - 877*S^4))/(540*S^2) + (Pi^2*(-181 - 1102*S^2 - 620*S^4))/(72*S^2) + (13*(6 + 7*S^4)*HPL[{4}, -S^2])/(3*S^2) + (2*(187 + 186*S^2 + 20*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(25 + 108*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (4*(29 + 195*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-3 + 10*S^2 + 4*S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(329 - 186*S^2 - 536*S^4))/(9*S^2) - (863*(-1 + S^4))/(3*S^2) - (112*(1 + 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((Pi^2*(-325 + 182*S^2 + 580*S^4))/(18*S^2) + (-1573 - 428*S^2 + 1879*S^4)/(12*S^2) + (8*(3 + 17*S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((Pi^4*(5760 - 1327*S^4))/(1080*S^2) + (Pi^2*(781 + 1132*S^2 - 314*S^4))/(72*S^2) + (55*(-1 + S^4))/(48*S^2) - (448*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (896*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(-227 - 186*S^2 + 20*S^4)*Zeta[3])/(3*S^2)) + ((Pi^2*(44 - 301*S^4))/(18*S^2) + (177 - 2026*S^2 - 274*S^4)/(12*S^2))*Zeta[5] + ((35 - 146*S^4)*Zeta[7])/S^2) + HPL[{1}, -S^2]^2*((Pi^6*(-30097 - 185480*S^2 - 163055*S^4))/(181440*S^2) + (Pi^4*(2585 - 100712*S^2 - 106561*S^4))/(17280*S^2) + (Pi^2*(17773 - 34004*S^2 - 51777*S^4))/(1152*S^2) - (25445*(-1 + S^4))/(96*S^2) - (31*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + ((-21 - 4*S^2 + 25*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((133 - 1276*S^2 - 1409*S^4)/(12*S^2) - (98*Pi^2*(1 + S^4))/(9*S^2))*HPL[{5}, -S^2] + ((135 - 1888*S^2 - 2063*S^4)*HPL[{6}, -S^2])/(12*S^2) - (179*(1 + S^4)*HPL[{7}, -S^2])/S^2 + (148*(-1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((197*Pi^2*(1 + S^4))/(9*S^2) + (687 + 808*S^2 + 121*S^4)/(3*S^2))*HPL[{3, 2}, -S^2] + ((700*Pi^2*(1 + S^4))/(9*S^2) + (2*(1020 + 1387*S^2 + 367*S^4))/(3*S^2))*HPL[{4, 1}, -S^2] + ((-71 + 16*S^2 + 55*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) - (11*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + (2*(-43 + 292*S^2 + 303*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) - (26*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 + (139*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((-566*(-1 + S^4))/(3*S^2) - (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 2, 1}, -S^2] + ((-120*Pi^2*(1 + S^4))/S^2 - (2*(-157 + 1014*S^2 + 1171*S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] + (4*(1 - 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) - (4*(185 + 374*S^2 + 185*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 - (744*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 - (8*(283 + 633*S^2 + 344*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (744*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 - (2232*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 - (4648*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((472*Pi^2*(1 + S^4))/(3*S^2) + (676*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (496*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + (4*(389 + 900*S^2 + 511*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (992*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (992*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (2480*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (7248*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (1200*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (1200*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-1969 - 2316*S^2 - 347*S^4))/(72*S^2) + (-6175 - 6306*S^2 - 131*S^4)/(24*S^2) - (859*Pi^4*(1 + S^4))/(360*S^2))*Zeta[3] + ((15 - 22*S^2 + 7*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*((-1441 - 2102*S^2 - 661*S^4)/(8*S^2) + (Pi^2*(-511 - 808*S^2 - 329*S^4))/(24*S^2) - (1219*Pi^4*(1 + S^4))/(540*S^2) + (9*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (8*(65 + 93*S^2 + 28*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (124*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (248*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((23 - 40*S^2 - 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((-410*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(323 + 696*S^2 + 397*S^4))/(9*S^2) - (256*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((Pi^2*(25 - 372*S^2 - 397*S^4))/(72*S^2) - (533*(-1 + S^4))/(16*S^2) - (31*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (62*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (31*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((53 - 394*S^2 - 495*S^4)/(6*S^2) + (Pi^2*(-18 - 109*S^2 - 91*S^4))/(9*S^2) - (22*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((2*Pi^2*(144 + 347*S^2 + 217*S^4))/(9*S^2) + (2*(239 + 615*S^2 + 376*S^4))/(3*S^2) + (128*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((2779*Pi^4*(1 + S^4))/(360*S^2) + (1051*(1 + 2*S^2 + S^4))/(4*S^2) + (Pi^2*(1375 + 3220*S^2 + 1941*S^4))/(36*S^2) + (4*(127 + 204*S^2 + 53*S^4)*Zeta[3])/(3*S^2)) + ((-455*Pi^2*(1 + S^4))/(18*S^2) - (5*(561 + 628*S^2 + 67*S^4))/(12*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-14313 - 32320*S^2 - 20063*S^4))/(4320*S^2) + (Pi^2*(-6577 - 15968*S^2 - 9775*S^4))/(288*S^2) - (8501*(1 + 2*S^2 + S^4))/(48*S^2) + ((-693 - 820*S^2 - 127*S^4)/(6*S^2) - (197*Pi^2*(1 + S^4))/(18*S^2))*HPL[{3}, -S^2] - (67*(-1 + S^4)*HPL[{4}, -S^2])/(6*S^2) - (16*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((283*(-1 + S^4))/(3*S^2) + (31*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (148*(-1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (124*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (372*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (296*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (496*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((-653 - 836*S^2 - 87*S^4)/(6*S^2) - (215*Pi^2*(1 + S^4))/(18*S^2))*Zeta[3] - (91*(1 + S^4)*Zeta[5])/S^2) - (231*(1 + S^4)*Zeta[7])/S^2) + HPL[{0}, S^2]*((-15181*Pi^8*S^2)/201600 + (Pi^6*(65041 - 360157*S^2))/181440 + (Pi^2*(60459 - 79892*S^2))/1152 - (35*(-2411 + 2432*S^2))/192 - (7*Pi^4*(-12013 + 24309*S^2))/17280 + ((-23*(-1 + S^4))/(9*S^2) - (13*Pi^2*(1 + S^4))/(54*S^2))*HPL[{1}, -S^2]^6 - (4*(-1 + S^4)*HPL[{1}, -S^2]^7)/(9*S^2) + ((271 + 640*S^2 - 961*S^4)/(144*S^2) + (Pi^2*(22 - 53*S^4))/(108*S^2))*HPL[{2}, -S^2]^3 + (5*(1 + S^4)*HPL[{2}, -S^2]^4)/(24*S^2) + ((Pi^2*(49 + 33*S^4))/(36*S^2) + (-1 - 176*S^2 + 105*S^4)/(24*S^2))*HPL[{3}, -S^2]^2 + ((-97 - 84*S^4)*HPL[{4}, -S^2]^2)/(6*S^2) + ((-915 - 1678*S^2 - 235*S^4)/(24*S^2) + (Pi^2*(140 + 191*S^4))/(36*S^2))*HPL[{6}, -S^2] + ((-145 + 164*S^2 + 118*S^4)*HPL[{7}, -S^2])/(4*S^2) + ((315 + 272*S^4)*HPL[{8}, -S^2])/(2*S^2) + ((Pi^2*(-10 + 73*S^4))/(9*S^2) + (5 - 904*S^2 + 1137*S^4)/(12*S^2))*HPL[{2, 1}, -S^2]^2 + (2*(-1 + 11*S^4)*HPL[{3, 1}, -S^2]^2)/(3*S^2) + ((-8 - 54*S^2 - 43*S^4)/(12*S^2) + (Pi^2*(-7 + 3*S^4))/(36*S^2))*HPL[{4, 2}, -S^2] + ((-285 + 98*S^2 + 61*S^4)*HPL[{4, 3}, -S^2])/(6*S^2) + ((-5*Pi^2*(3 + 5*S^4))/(18*S^2) + (239 + 204*S^2 + 287*S^4)/(12*S^2))*HPL[{5, 1}, -S^2] + ((-1694 + 584*S^2 + 407*S^4)*HPL[{5, 2}, -S^2])/(12*S^2) + (5*S^2*HPL[{5, 3}, -S^2])/3 + ((-1656 + 370*S^2 + 477*S^4)*HPL[{6, 1}, -S^2])/(6*S^2) + ((14 + 29*S^4)*HPL[{6, 2}, -S^2])/(6*S^2) - (4*(54 + 53*S^4)*HPL[{7, 1}, -S^2])/(3*S^2) + (68*(1 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^2) + ((3139 - 2888*S^2 - 59*S^4)/(12*S^2) + (Pi^2*(261 - 416*S^2 + 3*S^4))/(18*S^2))*HPL[{2, 2, 1}, -S^2] + ((Pi^2*(-2 + 3*S^4))/(9*S^2) + (2*(1 + 6*S^2 + 5*S^4))/(3*S^2))*HPL[{3, 1, 2}, -S^2] + ((275 + 664*S^2 - 941*S^4)/(6*S^2) + (Pi^2*(42 - 103*S^4))/(9*S^2))*HPL[{3, 2, 1}, -S^2] + ((-243 + 200*S^2 + 11*S^4)*HPL[{3, 2, 2}, -S^2])/(12*S^2) - (4*(74 - 38*S^2 + 15*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) - (2*(43 + 46*S^4)*HPL[{3, 3, 2}, -S^2])/(3*S^2) + ((811 + 1968*S^2 - 3267*S^4)/(6*S^2) + (Pi^2*(99 - 343*S^4))/(9*S^2))*HPL[{4, 1, 1}, -S^2] + ((-609 + 312*S^2 - 160*S^4)*HPL[{4, 1, 2}, -S^2])/(6*S^2) + (2*(86 + 97*S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^2) + ((-2049 + 936*S^2 - 496*S^4)*HPL[{4, 2, 1}, -S^2])/(6*S^2) + ((-163 - 159*S^4)*HPL[{4, 2, 2}, -S^2])/(6*S^2) + (2*(178 + 201*S^4)*HPL[{4, 3, 1}, -S^2])/(3*S^2) + ((-2030 + 1004*S^2 - 643*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((183 + 223*S^4)*HPL[{5, 1, 2}, -S^2])/(3*S^2) + ((1503 + 1663*S^4)*HPL[{5, 2, 1}, -S^2])/(3*S^2) + (2*(1970 + 2177*S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^2) + (8*(-53 + 32*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) + ((4*Pi^2*(-3 + 77*S^4))/(9*S^2) + (-277 - 700*S^2 + 1315*S^4)/(3*S^2))*HPL[{3, 1, 1, 1}, -S^2] + ((1481 - 88*S^2 - 497*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + ((1481 - 88*S^2 - 497*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + (4*(-3 + 2*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^2) + ((2753 - 88*S^2 - 1265*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (4*(-3 + 2*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^2) - (20*(9 + 8*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^2) - (168*(1 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (2*(-3917 + 156*S^2 + 1932*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) + (14*(-1 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^2) - (14*(37 + 35*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^2) - (14*(109 + 107*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^2) - (988*(1 + S^4)*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((-4*Pi^2*(-1 + 56*S^4))/(3*S^2) - (2*(-299 - 768*S^2 + 1301*S^4))/(3*S^2))*HPL[{2, 1, 1, 1, 1}, -S^2] - (32*(39 - 6*S^2 + 2*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) - (32*(39 - 6*S^2 + 2*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (304*(1 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^2) - (304*(1 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 - (8*(739 - 150*S^2 + 89*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) + (16*(113 + 115*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^2) + (16*(189 + 191*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^2) + (16*(227 + 229*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^2) + (32*(237 + 238*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(471 + 473*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + (40*(-77 + 17*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) - (96*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + (160*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((2*Pi^2*S^2)/3 + (113 - 154*S^2)/6)*Zeta[3]^2 + HPL[{4}, -S^2]*((513 - 4112*S^2 - 3407*S^4)/(96*S^2) + (Pi^2*(9 - 130*S^2 - 352*S^4))/(72*S^2) + (Pi^4*(-303 - 163*S^4))/(2160*S^2) + ((-159 + 20*S^2 - 103*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((77 + 41*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (2*(25 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((104 - 48*S^2 - 113*S^4)*Zeta[3])/(6*S^2)) + HPL[{2}, -S^2]^2*((251 + 8320*S^2 - 7985*S^4)/(192*S^2) + (Pi^4*(-60 - 3067*S^4))/(4320*S^2) + (Pi^2*(-23 + 764*S^2 - 2584*S^4))/(288*S^2) + ((-12 + 12*S^2 + S^4)*HPL[{3}, -S^2])/(6*S^2) + ((41 + 47*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((-53 + 32*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (22*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (38*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((13 - 109*S^4)*Zeta[3])/(12*S^2)) + HPL[{5}, -S^2]*((-115 - 744*S^2 - 571*S^4)/(16*S^2) + (Pi^2*(165 + 188*S^2 - 139*S^4))/(72*S^2) + ((-123 - 101*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((-95 - 107*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(417 - 401*S^2 - 778*S^4))/(108*S^2) - (2449*(-1 + S^4))/(72*S^2) - (1313*Pi^4*(1 + S^4))/(2160*S^2) + ((-200*(-1 + S^4))/(9*S^2) - (31*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2] + ((31 + 4*S^2 - 27*S^4)*HPL[{3}, -S^2])/(6*S^2) + (2*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (235*(-1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (2*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((55 - 12*S^2 - 67*S^4)*Zeta[3])/(18*S^2)) + HPL[{1}, -S^2]^5*((Pi^2*(129 - 276*S^2 - 373*S^4))/(180*S^2) - (125*(-1 + S^4))/(12*S^2) - (47*(-1 + S^4)*HPL[{2}, -S^2])/(9*S^2) + (2*(1 + S^4)*HPL[{3}, -S^2])/(15*S^2) - (2*(1 + S^4)*Zeta[3])/(15*S^2)) + HPL[{2, 1, 1, 1}, -S^2]*((Pi^2*(-349 + 376*S^2 + 111*S^4))/(9*S^2) + (-3579 + 2528*S^2 + 903*S^4)/(6*S^2) - (8*(-1 + 2*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1, 1}, -S^2]*((9715 - 8680*S^2 - 1127*S^4)/(12*S^2) + (Pi^2*(919 - 1168*S^2 - 160*S^4))/(18*S^2) - (8*(4 + 3*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 2}, -S^2]*((Pi^2*(484 - 188*S^2 + 467*S^4))/(72*S^2) + (339 - 512*S^2 + 497*S^4)/(24*S^2) - (4*(4 + 5*S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((Pi^2*(165 - 152*S^2 + 332*S^4))/(18*S^2) + (231 - 256*S^2 + 1040*S^4)/(12*S^2) - (2*(7 + 13*S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((2651 + 6680*S^2 - 9437*S^4)/(24*S^2) + (Pi^4*(-284 - 3703*S^4))/(540*S^2) + (Pi^2*(331 + 464*S^2 - 2978*S^4))/(36*S^2) - (2*(-13 - 4*S^2 + 65*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((Pi^2*(-251 - 208*S^2 + 2946*S^4))/(72*S^2) + (Pi^4*(210 + 3037*S^4))/(1080*S^2) + (-1977 - 4456*S^2 + 9963*S^4)/(48*S^2) - (8*(7 + 10*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-17 + 16*S^2 + 73*S^4)*Zeta[3])/(3*S^2)) + ((1658 - 2503*S^2)/24 + (Pi^2*(-214 - 1789*S^2))/36)*Zeta[5] + Zeta[3]*((Pi^4*(-1111 - 6566*S^2))/1080 + (4636 - 5771*S^2)/96 + (Pi^2*(1074 - 1937*S^2))/144 + (104*S^2*Zeta[5])/3) + HPL[{2}, -S^2]*((Pi^4*(3629 + 1926*S^2 - 45602*S^4))/(8640*S^2) + (Pi^6*(-5882 - 44423*S^4))/(90720*S^2) + (Pi^2*(4443 + 6078*S^2 - 19846*S^4))/(576*S^2) + (3648 + 4522*S^2 - 8517*S^4)/(48*S^2) + ((-10 - 11*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((-21 + 218*S^2 - 109*S^4)/(12*S^2) + (Pi^2*(-95 - 73*S^4))/(36*S^2))*HPL[{4}, -S^2] + ((-307 + 124*S^2 - 23*S^4)*HPL[{5}, -S^2])/(12*S^2) - (5*(40 + 29*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((Pi^2*(-261 + 416*S^2 - 3*S^4))/(36*S^2) + (-3139 + 2888*S^2 + 59*S^4)/(24*S^2))*HPL[{2, 1}, -S^2] - (38*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(1 + 27*S^4))/(3*S^2) + (-3 - 920*S^2 + 1129*S^4)/(12*S^2))*HPL[{3, 1}, -S^2] - (2*(-13 + 12*S^2)*HPL[{3, 2}, -S^2])/(3*S^2) + ((303 - 164*S^2 + 91*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((-1 - 7*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) + ((79 + 45*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-5 + 904*S^2 - 1137*S^4)/(6*S^2) - (2*Pi^2*(-10 + 73*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] - (4*(-53 + 32*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (4*(-187 + 12*S^2 + 63*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (2*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (62*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (2*(65 + 77*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (16*(39 - 6*S^2 + 2*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (8*(235 + 238*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (136*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((63 + 214*S^2 - 216*S^4)/(12*S^2) + (Pi^2*(13 - 22*S^2 - 172*S^4))/(36*S^2))*Zeta[3] + ((4 + 3*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*((-91 + 98*S^2 - 132*S^4)/(12*S^2) + (Pi^2*(-125 + 50*S^2 - 114*S^4))/(36*S^2) - (14*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (26*(1 + S^4)*Zeta[3])/(3*S^2)) + ((112 + 2*S^2 - 251*S^4)*Zeta[5])/(6*S^2)) + HPL[{1}, -S^2]^2*((Pi^4*(21017 - 31004*S^2 - 48005*S^4))/(8640*S^2) + (Pi^2*(6961 - 3586*S^2 - 10291*S^4))/(288*S^2) - (2903*(-1 + S^4))/(16*S^2) - (42013*Pi^6*(1 + S^4))/(90720*S^2) + ((-283*(-1 + S^4))/(12*S^2) - (83*Pi^2*(1 + S^4))/(36*S^2))*HPL[{2}, -S^2]^2 + ((-1 - S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((223 - 64*S^2 - 223*S^4)/(12*S^2) + (11*Pi^2*(1 + S^4))/(18*S^2))*HPL[{4}, -S^2] + ((141 + 36*S^2 - 89*S^4)*HPL[{5}, -S^2])/(6*S^2) + (55*(1 + S^4)*HPL[{6}, -S^2])/(6*S^2) + ((747*(-1 + S^4))/(4*S^2) + (2*Pi^2*(-53 + 93*S^2 + 146*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((86*Pi^2*(1 + S^4))/(9*S^2) + (-391 + 34*S^2 + 409*S^4)/(3*S^2))*HPL[{3, 1}, -S^2] + (4*(-6 + S^2 + 5*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-167 - 12*S^2 + 131*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((-1 - S^4)*HPL[{4, 2}, -S^2])/S^2 - (34*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-800*(-1 + S^4))/(3*S^2) - (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (296*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(-179 - 4*S^2 + 175*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (8*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (940*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(67 - 60*S^2 - 111*S^4))/(18*S^2) + (84 + 47*S^2 - 53*S^4)/(3*S^2))*Zeta[3] + ((1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2}, -S^2]*((Pi^2*(463 - 410*S^2 - 873*S^4))/(36*S^2) - (1511*(-1 + S^4))/(12*S^2) - (3487*Pi^4*(1 + S^4))/(2160*S^2) - (11*(-1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + ((1 + S^4)*HPL[{4}, -S^2])/S^2 + (148*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (11*(-1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((259 - 188*S^2 - 383*S^4)/(12*S^2) + (Pi^2*(137 + 8*S^2 - 169*S^4))/(36*S^2) - (4*(1 + S^4)*Zeta[3])/(3*S^2)) + ((179 - 40*S^2 - 227*S^4)*Zeta[5])/(6*S^2)) + HPL[{1}, -S^2]^3*((Pi^4*(4059 - 16840*S^2 - 18731*S^4))/(6480*S^2) + (Pi^2*(4909 - 3336*S^2 - 7989*S^4))/(432*S^2) - (12859*(-1 + S^4))/(144*S^2) + ((-249*(-1 + S^4))/(4*S^2) - (2*Pi^2*(-53 + 93*S^2 + 146*S^4))/(27*S^2))*HPL[{2}, -S^2] - (74*(-1 + S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((Pi^2*(-1 - S^4))/(9*S^2) - (2*(-54 + 17*S^2 + 63*S^4))/(9*S^2))*HPL[{3}, -S^2] + ((101 + 12*S^2 - 65*S^4)*HPL[{4}, -S^2])/(9*S^2) + (22*(1 + S^4)*HPL[{5}, -S^2])/(9*S^2) + ((800*(-1 + S^4))/(9*S^2) + (62*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + (2*(-241 - 12*S^2 + 229*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (8*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (940*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (8*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((107 + 34*S^2 - 89*S^4)/(9*S^2) - (26*Pi^2*(1 + S^4))/(27*S^2))*Zeta[3] - (22*(1 + S^4)*Zeta[5])/(9*S^2)) + HPL[{3}, -S^2]*((3297 - 5112*S^2 - 11177*S^4)/(192*S^2) + (Pi^4*(2711 + 1168*S^2 - 2253*S^4))/(4320*S^2) + (Pi^2*(371 - 338*S^2 - 1056*S^4))/(144*S^2) + ((289 - 108*S^2 - 35*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((97 + 80*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-67 + 70*S^2 - 42*S^4)/(3*S^2) + (Pi^2*(-25 - 28*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + (2*(48 - 14*S^2 + 15*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(21 + 23*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(28 + 23*S^4)*HPL[{4, 1}, -S^2])/S^2 - (4*(28 - 12*S^2 + 33*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (28*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (4*(35 + 23*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (8*(4 + 3*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((47 + 60*S^2 - 58*S^4)/(6*S^2) + (Pi^2*(-13 - 21*S^4))/(9*S^2))*Zeta[3] - (20*(4 + 5*S^4)*Zeta[5])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^4*(-3963 + 7618*S^2 - 440*S^4))/(2160*S^2) + (Pi^2*(-2227 + 3154*S^2 + 885*S^4))/(72*S^2) + (-24975 + 16572*S^2 + 8347*S^4)/(96*S^2) + (4*(81 - 12*S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (26*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (2*(67 + 55*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (16*(39 - 6*S^2 + 2*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (152*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(15 + 16*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (136*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((2*(-46 + 15*S^2 + 2*S^4))/(3*S^2) + (Pi^2*(41 + 21*S^4))/(9*S^2))*Zeta[3] + (2*(47 + 36*S^4)*Zeta[5])/(3*S^2)) + ((-90 - 649*S^2)*Zeta[7])/2 + HPL[{1}, -S^2]*((Pi^6*(76805 - 175304*S^2 - 237605*S^4))/(181440*S^2) + (Pi^4*(68413 - 52616*S^2 - 118469*S^4))/(17280*S^2) + (Pi^2*(41341 - 12884*S^2 - 54225*S^4))/(1152*S^2) - (25445*(-1 + S^4))/(96*S^2) - (85*(-1 + S^4)*HPL[{2}, -S^2]^3)/(18*S^2) + ((-3 - S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((123 - 484*S^2 - 303*S^4)/(12*S^2) + (35*Pi^2*(1 + S^4))/(9*S^2))*HPL[{5}, -S^2] + ((401 + 240*S^2 - 201*S^4)*HPL[{6}, -S^2])/(12*S^2) + (223*(1 + S^4)*HPL[{7}, -S^2])/(3*S^2) + (148*(-1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-5*Pi^2*(1 + S^4))/(9*S^2) + (-27 - 4*S^2 + 23*S^4)/(3*S^2))*HPL[{3, 2}, -S^2] + ((-26*Pi^2*(1 + S^4))/(9*S^2) + (-349 + 112*S^2 + 397*S^4)/(6*S^2))*HPL[{4, 1}, -S^2] + ((-7 + 2*S^2 - 7*S^4)*HPL[{4, 2}, -S^2])/(3*S^2) + (77*(1 + S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((-169 - 36*S^2 + 69*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + (230*(1 + S^4)*HPL[{5, 2}, -S^2])/(3*S^2) + (325*(1 + S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((-747*(-1 + S^4))/(2*S^2) - (4*Pi^2*(-53 + 93*S^2 + 146*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + ((-566*(-1 + S^4))/(3*S^2) - (166*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((-56*Pi^2*(1 + S^4))/S^2 - (2*(-957 + 34*S^2 + 975*S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] + (4*(1 - 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) - (8*(-43 + S^2 + 42*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (6*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (56*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) - (2*(-611 - 12*S^2 + 575*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (18*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (58*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (404*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((1600*(-1 + S^4))/(3*S^2) + (124*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] + (4*(-241 - 12*S^2 + 229*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (16*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (1880*(-1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (16*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + ((1189 + 1112*S^2 - 589*S^4)/(24*S^2) - (1111*Pi^4*(1 + S^4))/(1080*S^2) - (5*Pi^2*(-41 - 16*S^2 + 41*S^4))/(24*S^2))*Zeta[3] + ((105 + 16*S^2 - 97*S^4)*Zeta[3]^2)/(6*S^2) + HPL[{2}, -S^2]^2*((Pi^2*(99 - 344*S^2 - 419*S^4))/(72*S^2) - (533*(-1 + S^4))/(16*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/S^2 + ((-1 - S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((1511*(-1 + S^4))/(6*S^2) + (3487*Pi^4*(1 + S^4))/(1080*S^2) + (Pi^2*(-463 + 410*S^2 + 873*S^4))/(18*S^2) + (22*(-1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((111 - 98*S^2 - 193*S^4)/(6*S^2) + (Pi^2*(103 + 10*S^2 - 69*S^4))/(18*S^2) - (2*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (50*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((2*Pi^2*(-59 + 84*S^2 + 147*S^4))/(9*S^2) + (-2117 + 376*S^2 + 2365*S^4)/(12*S^2) + (20*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((663 - 1112*S^2 - 1263*S^4)/(24*S^2) + (Pi^2*(291 - 288*S^2 - 515*S^4))/(72*S^2) + (37*Pi^4*(1 + S^4))/(540*S^2) - (13*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (22*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(-1 - 8*S^2 + S^4)*Zeta[3])/(3*S^2)) + ((925 + 492*S^2 - 737*S^4)/(12*S^2) - (107*Pi^2*(1 + S^4))/(18*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(4331 - 14552*S^2 - 17675*S^4))/(4320*S^2) + (Pi^2*(5693 - 4144*S^2 - 9453*S^4))/(288*S^2) - (16661*(-1 + S^4))/(96*S^2) + ((21 - 8*S^2 - 29*S^4)/(6*S^2) + (5*Pi^2*(1 + S^4))/(18*S^2))*HPL[{3}, -S^2] + (4*(2 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (40*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((283*(-1 + S^4))/(3*S^2) + (83*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + (148*(-1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (10*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (10*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (296*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-37*Pi^2*(1 + S^4))/(18*S^2) - (2*(-25 - 2*S^2 + 23*S^4))/(3*S^2))*Zeta[3] - (35*(1 + S^4)*Zeta[5])/(3*S^2)) - (45*(1 + S^4)*Zeta[7])/S^2)) + Log[T]*((942223*Pi^8*S^2)/2721600 + (Pi^2*(15381 + 34163*S^2))/576 + (Pi^4*(38785 + 101529*S^2))/8640 + (Pi^6*(68773 + 188539*S^2))/90720 + (S^2*HPL[{0}, S^2]^8)/96 + (8*(-1 + S^4)*HPL[{1}, -S^2]^7)/(9*S^2) + HPL[{0}, S^2]^7*((10 + 29*S^2)/288 + (5*(1 + S^4)*HPL[{1}, -S^2])/(144*S^2)) + ((Pi^2*(74 + 157*S^4))/(54*S^2) + (1157 + 984*S^2 + 1157*S^4)/(72*S^2))*HPL[{2}, -S^2]^3 + (83*(-1 + S^2)*(1 + S^2)*HPL[{2}, -S^2]^4)/(36*S^2) + HPL[{1}, -S^2]^6*((46*(-1 + S^4))/(9*S^2) + (5*Pi^2*(1 + S^4))/(9*S^2) + (20*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]^6*((115*Pi^2*S^2)/864 + (32 + 269*S^2)/576 + ((5 + 60*S^2 + 47*S^4)*HPL[{1}, -S^2])/(144*S^2) + (7*(1 + S^4)*HPL[{1}, -S^2]^2)/(36*S^2) + ((3 + 25*S^4)*HPL[{2}, -S^2])/(144*S^2)) + ((35 + 28*S^2 - 187*S^4)/(12*S^2) + (Pi^2*(23 - 15*S^4))/(18*S^2))*HPL[{3}, -S^2]^2 - (34*HPL[{4}, -S^2]^2)/(3*S^2) + ((Pi^2*(296 + 425*S^4))/(18*S^2) + (467 + 1186*S^2 + 4231*S^4)/(12*S^2))*HPL[{6}, -S^2] + ((-565 + 2148*S^2 + 3760*S^4)*HPL[{7}, -S^2])/(6*S^2) + ((735 + 1858*S^4)*HPL[{8}, -S^2])/(3*S^2) + ((-1411*(-1 + S^4))/(6*S^2) - (4*Pi^2*(-58 + 95*S^4))/(9*S^2))*HPL[{2, 1}, -S^2]^2 + (4*(-93 + 91*S^4)*HPL[{3, 1}, -S^2]^2)/(3*S^2) + ((-3 + 124*S^2 - 165*S^4)/(3*S^2) + (Pi^2*(39 - 43*S^4))/(18*S^2))*HPL[{4, 2}, -S^2] + (2*(-1 + S^2)*(26 + 15*S^2)*HPL[{4, 3}, -S^2])/S^2 + ((Pi^2*(-157 - 319*S^4))/(9*S^2) - (5*(57 + 44*S^2 + 577*S^4))/(6*S^2))*HPL[{5, 1}, -S^2] + ((-952 + 312*S^2 + 199*S^4)*HPL[{5, 2}, -S^2])/(6*S^2) + (2*(-8 + 17*S^4)*HPL[{5, 3}, -S^2])/(3*S^2) + ((-682 - 834*S^2 - 1403*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((18 + 17*S^4)*HPL[{6, 2}, -S^2])/(3*S^2) - (8*(82 + 185*S^4)*HPL[{7, 1}, -S^2])/(3*S^2) + (520*(-1 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((-2*Pi^2*(-3 + 2*S^4))/(9*S^2) + (4*(21 - 31*S^2 + 21*S^4))/(3*S^2))*HPL[{3, 1, 2}, -S^2] + ((2*Pi^2*(151 + 312*S^4))/(9*S^2) + (1241 + 860*S^2 + 1241*S^4)/(3*S^2))*HPL[{3, 2, 1}, -S^2] + ((725 + 2976*S^2 + 1915*S^4)*HPL[{3, 2, 2}, -S^2])/(6*S^2) + (4*(230 + 1116*S^2 + 785*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) - (4*(-2 + 13*S^4)*HPL[{3, 3, 2}, -S^2])/(3*S^2) + ((4*Pi^2*(291 + 548*S^4))/(9*S^2) + (2*(647 + 528*S^2 + 775*S^4))/S^2)*HPL[{4, 1, 1}, -S^2] + ((853 + 4464*S^2 + 3207*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) + (4*(-3 + S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^2) + ((2497 + 13392*S^2 + 9783*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) + ((19 - 105*S^4)*HPL[{4, 2, 2}, -S^2])/(3*S^2) + (4*(-19 + 45*S^4)*HPL[{4, 3, 1}, -S^2])/(3*S^2) + (2*(2139 + 13944*S^2 + 10556*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + (2*(-51 + 7*S^4)*HPL[{5, 1, 2}, -S^2])/(3*S^2) + (2*(-171 + 487*S^4)*HPL[{5, 2, 1}, -S^2])/(3*S^2) + (16*(9 + 251*S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^2) - (8*(55 + 124*S^2 + 55*S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((-8*Pi^2*(117 + 214*S^4))/(9*S^2) - (2*(441 + 420*S^2 + 569*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (2*(1815 + 2976*S^2 + 775*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + (2*(1815 + 2976*S^2 + 775*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (20*(-1 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^2) + (10*(759 + 1488*S^2 + 551*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (20*(-1 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^2) - (4*(291 + 301*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^2) - (1184*(1 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (16*(1447 + 2718*S^2 + 993*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) - (16*(-7 + 11*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^2) - (16*(215 + 233*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^2) - (16*(659 + 677*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^2) - (16*(1393 + 1451*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^2) + ((40*Pi^2*(47 + 86*S^4))/(9*S^2) + (20*(101 + 84*S^2 + 101*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] + (2080*(-1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (2080*(-1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (2368*(1 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^2) - (2368*(1 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (32*(-331 + 225*S^2 + 481*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) + (14240*(1 + S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^2) + (7904*(1 + S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 + (28448*(1 + S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^2) + (19744*(1 + S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 + (59744*(1 + S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 - (1600*(1 + 3*S^2 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 - (2240*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + (4480*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((7*Pi^2*S^2)/3 + (-28 - 103*S^2)/6)*Zeta[3]^2 + HPL[{0}, S^2]^5*((Pi^2*(201 + 533*S^2))/540 + (-1594 + 6779*S^2)/2880 + ((-43 + 1216*S^2 + 1059*S^4)*HPL[{1}, -S^2]^2)/(720*S^2) + (31*(1 + S^4)*HPL[{1}, -S^2]^3)/(60*S^2) + ((-15 + 458*S^2 + 1004*S^4)*HPL[{2}, -S^2])/(720*S^2) + HPL[{1}, -S^2]*((67*Pi^2*(1 + S^4))/(180*S^2) + (-707 + 2172*S^2 + 2479*S^4)/(1440*S^2) + (229*(1 + S^4)*HPL[{2}, -S^2])/(360*S^2)) + ((-1 - S^4)*HPL[{3}, -S^2])/(24*S^2) + ((-214 + 25*S^4)*HPL[{2, 1}, -S^2])/(180*S^2) + (3*S^2*Zeta[3])/4) + HPL[{1}, -S^2]^5*((125*(-1 + S^4))/(6*S^2) + (Pi^2*(-31 + 180*S^2 + 211*S^4))/(54*S^2) + (20*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2])/S^2 + (20*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (40*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (20*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((-8*Pi^2*(158 + 342*S^2 + 93*S^4))/(9*S^2) - (2*(561 + 3724*S^2 + 561*S^4))/(3*S^2) + (80*(-37 + 2*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 2}, -S^2]*((Pi^2*(-4 - 1500*S^2 - 1511*S^4))/(36*S^2) + (-631 - 5884*S^2 - 1139*S^4)/(12*S^2) + (4*(2 + 3*S^4)*Zeta[3])/S^2) + HPL[{5}, -S^2]*((Pi^2*(-363 + 764*S^2 + 919*S^4))/(36*S^2) + (-1483 + 3496*S^2 + 4957*S^4)/(24*S^2) + (2*(-163 + 45*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(37 + 3*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 2, 1}, -S^2]*((-127*(-1 + S^4))/(3*S^2) - (2*Pi^2*(-304 - 186*S^2 + 139*S^4))/(9*S^2) - (16*(-79 + 5*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(1784 + 2108*S^2 - 93*S^4))/(9*S^2) + (2*(275 + 1862*S^2 + 286*S^4))/(3*S^2) - (16*(-251 + 14*S^4)*Zeta[3])/(3*S^2)) + HPL[{4, 1}, -S^2]*((-785 - 9930*S^2 - 2607*S^4)/(6*S^2) + (Pi^2*(15 - 2664*S^2 - 2441*S^4))/(18*S^2) + (4*(-21 + 19*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^4*((2449*(-1 + S^4))/(36*S^2) + (749*Pi^4*(1 + S^4))/(540*S^2) + (Pi^2*(-473 + 1014*S^2 + 1487*S^4))/(108*S^2) + ((118*Pi^2*(1 + S^4))/(9*S^2) + (169*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2}, -S^2] + ((179 + 300*S^2 + 121*S^4)*HPL[{3}, -S^2])/(3*S^2) + (16*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (100*(1 + 2*S^2 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (100*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (200*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (5*(137 + 180*S^2 + 43*S^4)*Zeta[3])/(9*S^2)) + HPL[{2, 1, 1}, -S^2]*((2*Pi^4*(569 + 1526*S^4))/(135*S^2) + (Pi^2*(1669 + 2136*S^2 + 3080*S^4))/(18*S^2) + (9699 + 5932*S^2 + 9699*S^4)/(12*S^2) + (16*(-8 + 108*S^2 + 57*S^4)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((Pi^2*(291 + 266*S^2 + 856*S^4))/(36*S^2) + (Pi^4*(1919 + 2055*S^4))/(1080*S^2) + (687 + 4288*S^2 + 7503*S^4)/(48*S^2) + ((-3 - 16*S^2 + 211*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(-61 + 43*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (16*(-13 + 14*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-105 + 48*S^2 + 62*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((2727*(-1 + S^4))/(32*S^2) + (Pi^2*(-1617 + 492*S^2 + 2774*S^4))/(144*S^2) + (Pi^4*(-2132 + 4955*S^4))/(2160*S^2) + ((12 + 62*S^2 + 43*S^4)*HPL[{3}, -S^2])/S^2 + (31*(1 + S^4)*HPL[{4}, -S^2])/(6*S^2) + ((-55 - 124*S^2 - 55*S^4)*HPL[{2, 1}, -S^2])/S^2 - (148*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (296*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((44 + 186*S^2 + 121*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((-7995 - 5932*S^2 - 11403*S^4)/(24*S^2) + (Pi^4*(-2326 - 5921*S^4))/(540*S^2) + (Pi^2*(-1413 - 2184*S^2 - 3328*S^4))/(36*S^2) - (16*(-97 + 98*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(-50 + 436*S^2 + 219*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^4*((16537*Pi^4*S^2)/25920 + (447 + 1982*S^2)/192 + (Pi^2*(324 + 2047*S^2))/576 + ((33 + 186*S^2 + 133*S^4)*HPL[{1}, -S^2]^3)/(36*S^2) + (11*(1 + S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + ((23*Pi^2*(1 + 9*S^4))/(144*S^2) + (138 + 682*S^2 + 1837*S^4)/(288*S^2))*HPL[{2}, -S^2] + ((-27 + 188*S^4)*HPL[{2}, -S^2]^2)/(144*S^2) + HPL[{1}, -S^2]^2*((19*Pi^2*(1 + S^4))/(12*S^2) + (223 + 2300*S^2 + 1885*S^4)/(288*S^2) + (257*(1 + S^4)*HPL[{2}, -S^2])/(72*S^2)) + ((1 + S^2)*(9 + 19*S^2)*HPL[{3}, -S^2])/(48*S^2) + ((13 + 21*S^4)*HPL[{4}, -S^2])/(24*S^2) + ((-233 - 518*S^2 + 28*S^4)*HPL[{2, 1}, -S^2])/(72*S^2) + ((-24 - 233*S^4)*HPL[{3, 1}, -S^2])/(36*S^2) + ((4 + 41*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((152 + 353*S^2)*Zeta[3])/72 + HPL[{1}, -S^2]*((Pi^2*(29 + 243*S^2 + 184*S^4))/(72*S^2) + (645 + 5288*S^2 + 4451*S^4)/(576*S^2) + ((275 + 1032*S^2 + 749*S^4)*HPL[{2}, -S^2])/(144*S^2) + (11*(1 + S^4)*HPL[{3}, -S^2])/(12*S^2) - (257*(1 + S^4)*HPL[{2, 1}, -S^2])/(36*S^2) + (19*(1 + S^4)*Zeta[3])/(9*S^2))) + ((5*Pi^2*(91 + 60*S^2))/9 + (2805 + 1048*S^2)/6)*Zeta[5] + HPL[{0}, S^2]^3*((Pi^2*(-718 + 3771*S^2))/288 + (-11836 + 31337*S^2)/576 + (Pi^4*(16100 + 41333*S^2))/12960 + ((11 + 276*S^2 + 233*S^4)*HPL[{1}, -S^2]^4)/(36*S^2) + (13*(1 + S^4)*HPL[{1}, -S^2]^5)/(9*S^2) + ((47 + 320*S^2 + 529*S^4)*HPL[{2}, -S^2]^2)/(72*S^2) + HPL[{1}, -S^2]^3*((79*Pi^2*(1 + S^4))/(27*S^2) + (-72 + 401*S^2 + 433*S^4)/(27*S^2) + (62*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((Pi^2*(-3 - 2*S^4))/(18*S^2) + (-79 + 44*S^2 + 171*S^4)/(36*S^2))*HPL[{3}, -S^2] + ((-25 - 24*S^2 + 142*S^4)*HPL[{4}, -S^2])/(36*S^2) + ((-3 - 4*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((220 - 1336*S^2 - 215*S^4)/(36*S^2) + (Pi^2*(-194 + 11*S^4))/(27*S^2))*HPL[{2, 1}, -S^2] + ((-13 - 348*S^2 - 634*S^4)*HPL[{3, 1}, -S^2])/(18*S^2) + ((-16 - 29*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) + ((-29 - 61*S^4)*HPL[{4, 1}, -S^2])/(9*S^2) + (2*(5 + 184*S^2 + 336*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (2*(169 + 3*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) + (8*(42 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (4*(58 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((26*Pi^2*S^2)/9 + (-85 + 218*S^2)/18)*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-5 + 1022*S^2 + 879*S^4))/(108*S^2) + (-1159 + 3336*S^2 + 4239*S^4)/(144*S^2) + ((23 + 372*S^2 + 349*S^4)*HPL[{2}, -S^2])/(18*S^2) + (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (62*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (23*(1 + S^4)*Zeta[3])/(9*S^2)) + HPL[{2}, -S^2]*((-84 + 91*S^2 + 1026*S^4)/(36*S^2) + (Pi^2*(-5 + 826*S^2 + 1676*S^4))/(216*S^2) + (2*(4 + 7*S^4)*HPL[{3}, -S^2])/(9*S^2) + ((-169 - 3*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + ((-3 + 14*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]*((805*Pi^4*(1 + S^4))/(648*S^2) + (Pi^2*(-995 + 3776*S^2 + 4211*S^4))/(432*S^2) + (-2063 + 3586*S^2 + 5393*S^4)/(144*S^2) + ((415*Pi^2*(1 + S^4))/(108*S^2) + (-63 + 410*S^2 + 473*S^4)/(18*S^2))*HPL[{2}, -S^2] + (83*(1 + S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + (2*(-11 + S^2 + 22*S^4)*HPL[{3}, -S^2])/(9*S^2) - (5*(1 + S^4)*HPL[{4}, -S^2])/(9*S^2) - ((1 + S^2)*(23 + 349*S^2)*HPL[{2, 1}, -S^2])/(9*S^2) - (178*(1 + S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (124*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-79 + 108*S^2 + 155*S^4)*Zeta[3])/(18*S^2)) + (91*S^2*Zeta[5])/9) + Zeta[3]*((Pi^2*(2023 + 811*S^2))/36 + (3161 + 1086*S^2)/6 + (Pi^4*(5154 + 5189*S^2))/1080 + (116*S^2*Zeta[5])/3) + HPL[{1}, -S^2]^3*((12859*(-1 + S^4))/(72*S^2) + (Pi^2*(-933 + 1640*S^2 + 2573*S^4))/(72*S^2) + (Pi^4*(449 + 4455*S^2 + 4084*S^4))/(810*S^2) + (148*(-1 + S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((58*Pi^2*(1 + S^4))/(3*S^2) + (4*(346 + 507*S^2 + 161*S^4))/(9*S^2))*HPL[{3}, -S^2] + (8*(4 + 75*S^2 + 65*S^4)*HPL[{4}, -S^2])/(9*S^2) + (184*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-472*Pi^2*(1 + S^4))/(9*S^2) - (676*(1 + 2*S^2 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (4*(389 + 900*S^2 + 511*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (496*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (560*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (400*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (400*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (800*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((172*Pi^2*(1 + S^4))/(9*S^2) + (2*(907 + 1014*S^2 + 107*S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((410*(1 + 2*S^2 + S^4))/(3*S^2) + (2*Pi^2*(323 + 696*S^2 + 397*S^4))/(27*S^2) + (248*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (256*(1 + S^4)*Zeta[3])/(3*S^2)) + (448*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(252 + 4302*S^2 + 1591*S^4))/(72*S^2) + (Pi^4*(-1155 + 8800*S^2 + 6713*S^4))/(2160*S^2) + (3069 + 50576*S^2 + 14307*S^4)/(96*S^2) + ((155 - 108*S^2 - 179*S^4)*HPL[{4}, -S^2])/(6*S^2) - (2*(-39 + 20*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((2*Pi^2*(-192 + 31*S^4))/(9*S^2) + (-1204 - 568*S^2 + 207*S^4)/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(65 + 372*S^2 + 290*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(1 + 6*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (4*(-9 + 13*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (4*(61 + 368*S^2 + 321*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (8*(-157 + 9*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (8*(-481 + 35*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (16*(-57 + 8*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((28 - 26*S^2 - S^4)/S^2 + (4*Pi^2*(10 + S^4))/(9*S^2))*Zeta[3] + (8*(25 + 9*S^4)*Zeta[5])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^4*(-8107 - 15646*S^2 - 2408*S^4))/(1080*S^2) + (Pi^2*(-2309 - 11596*S^2 - 2055*S^4))/(72*S^2) + (-543 - 3161*S^2 - 543*S^4)/(3*S^2) - (16*(-26 - S^2 + 39*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (8*(-157 + 9*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (8*(-497 + 55*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (1040*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (1184*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (16*(17 + 82*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (1040*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((2*Pi^2*(-211 + 9*S^4))/(9*S^2) + (-1361 - 384*S^2 + 50*S^4)/(3*S^2))*Zeta[3] - (4*(287 + 9*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]^2*((2903*(-1 + S^4))/(8*S^2) + (47329*Pi^6*(1 + S^4))/(45360*S^2) + (Pi^2*(-1207 + 2102*S^2 + 3309*S^4))/(48*S^2) + (Pi^4*(-831 + 40652*S^2 + 42443*S^4))/(4320*S^2) + ((283*(-1 + S^4))/(6*S^2) + (31*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2}, -S^2]^2 + (62*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + ((109*Pi^2*(1 + S^4))/(9*S^2) + (-39 + 314*S^2 + 353*S^4)/(3*S^2))*HPL[{4}, -S^2] + (8*(7 + 70*S^2 + 61*S^4)*HPL[{5}, -S^2])/(3*S^2) + (159*(1 + S^4)*HPL[{6}, -S^2])/S^2 + ((-236*Pi^2*(1 + S^4))/(3*S^2) - (2*(409 + 1014*S^2 + 605*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] - (4*(259 + 374*S^2 + 111*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (8*(394 + 633*S^2 + 233*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (184*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((472*Pi^2*(1 + S^4))/(3*S^2) + (676*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (592*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (4*(31 + 300*S^2 + 269*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (496*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (1680*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (1200*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (1200*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((1567 + 1640*S^2 + 73*S^4)/(4*S^2) + (Pi^2*(375 + 518*S^2 + 139*S^4))/(9*S^2))*Zeta[3] + HPL[{2, 1}, -S^2]*((-410*(1 + 2*S^2 + S^4))/S^2 - (2*Pi^2*(323 + 696*S^2 + 397*S^4))/(9*S^2) - (256*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^2*(601 + 1016*S^2 + 471*S^4))/(18*S^2) + (3511 + 4920*S^2 + 1409*S^4)/(12*S^2) - (248*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (4*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((2779*Pi^4*(1 + S^4))/(360*S^2) + (1051*(1 + 2*S^2 + S^4))/(4*S^2) + (Pi^2*(1375 + 3220*S^2 + 1941*S^4))/(36*S^2) + (8*(65 + 93*S^2 + 28*S^4)*HPL[{3}, -S^2])/(3*S^2) - (296*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(127 + 204*S^2 + 53*S^4)*Zeta[3])/(3*S^2)) + (2*(537 + 670*S^2 + 137*S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(11409 + 11326*S^2 + 19590*S^4))/(288*S^2) + (34163 + 30762*S^2 + 34163*S^4)/(96*S^2) + (Pi^4*(15319 + 26754*S^2 + 43218*S^4))/(4320*S^2) + (Pi^6*(19338 + 57773*S^4))/(45360*S^2) - (4*(1 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((Pi^2*(-29 + 25*S^4))/(6*S^2) + (-63 - 152*S^2 + 383*S^4)/(6*S^2))*HPL[{4}, -S^2] + ((-117 + 196*S^2 + 523*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-52 + 57*S^4)*HPL[{6}, -S^2])/S^2 - (296*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((1251 + 152*S^2 - 1571*S^4)/(6*S^2) - (4*Pi^2*(-59 + 94*S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + ((-55 - 248*S^2 - 165*S^4)*HPL[{3, 2}, -S^2])/S^2 + ((-429 - 2216*S^2 - 1759*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (9*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (2*(-63 + 145*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((1411*(-1 + S^4))/(3*S^2) + (8*Pi^2*(-58 + 95*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + (4*(55 + 124*S^2 + 55*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(217 + 374*S^2 + 87*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (664*(-1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (8*(-275 + 277*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (1040*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (16*(791 + 986*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (1040*(-1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-65 + 3300*S^2 + 189*S^4)/(12*S^2) + (Pi^2*(-53 + 482*S^2 + 282*S^4))/(18*S^2))*Zeta[3] + (4*(4 + 3*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*((Pi^2*(26 + 370*S^2 + 397*S^4))/(18*S^2) + (419 + 2892*S^2 + 673*S^4)/(12*S^2) + (4*(-157 + 9*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(3 + 2*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((127*(-1 + S^4))/(6*S^2) + (Pi^2*(-304 - 186*S^2 + 139*S^4))/(9*S^2) + (8*(-79 + 5*S^4)*Zeta[3])/(3*S^2)) + ((-200 + 618*S^2 + 325*S^4)*Zeta[5])/(3*S^2)) + HPL[{0}, S^2]^2*((4363*Pi^6*S^2)/3780 + (Pi^2*(5648 + 21591*S^2))/576 + (Pi^4*(7601 + 31857*S^2))/4320 + (15381 + 34163*S^2)/192 + ((53 + 180*S^2 + 127*S^4)*HPL[{1}, -S^2]^5)/(18*S^2) + (5*(1 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + ((Pi^2*(-64 + 373*S^4))/(72*S^2) + (-206 + 492*S^2 + 1363*S^4)/(48*S^2))*HPL[{2}, -S^2]^2 + (83*S^2*HPL[{2}, -S^2]^3)/18 + HPL[{1}, -S^2]^4*((163*Pi^2*(1 + S^4))/(36*S^2) + (217 + 1014*S^2 + 797*S^4)/(36*S^2) + (43*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((13 - 7*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((5*Pi^2*(15 + 23*S^4))/(36*S^2) + (171 + 316*S^2 + 533*S^4)/(24*S^2))*HPL[{4}, -S^2] + ((-36 + 212*S^2 + 227*S^4)*HPL[{5}, -S^2])/(12*S^2) + ((80 + 141*S^4)*HPL[{6}, -S^2])/(6*S^2) - (37*(-1 + 5*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-90 - 924*S^2 - 1621*S^4)/(12*S^2) + (Pi^2*(-48 - 451*S^4))/(18*S^2))*HPL[{3, 1}, -S^2] + ((161 - 12*S^2 - 306*S^4)*HPL[{3, 2}, -S^2])/(12*S^2) + ((167 - 144*S^2 - 473*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((11 + S^4)*HPL[{4, 2}, -S^2])/(6*S^2) + ((-35 - 81*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((Pi^2*(49 + 466*S^4))/(9*S^2) + (154 + 876*S^2 + 1565*S^4)/(6*S^2))*HPL[{2, 1, 1}, -S^2] - (2*(-58 - 62*S^2 + 3*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + ((1028 + 1208*S^2 + 63*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (2*(-1 + 4*S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (2*(1 + 162*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (4*(18 + 275*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (8*(83 + 117*S^2 + 18*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (8*(12 + 109*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (40*(5 + 44*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(109 + 214*S^2))/18 + (161 + 250*S^2)/12)*Zeta[3] + 8*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^3*((317 + 1640*S^2 + 1323*S^4)/(24*S^2) + (Pi^2*(463 + 2016*S^2 + 1433*S^4))/(108*S^2) + (4*(49 + 123*S^2 + 86*S^4)*HPL[{2}, -S^2])/(9*S^2) + (8*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (172*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (22*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(11 + 176*S^2 + 174*S^4))/(72*S^2) + (83 + 578*S^2 + 638*S^4)/(24*S^2) + (14*(-3 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(6 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((-1187 - 4148*S^2 - 933*S^4)/(24*S^2) + (Pi^2*(-565 - 986*S^2 - 44*S^4))/(36*S^2) - (2*(26 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(146 + 779*S^2 + 1701*S^4))/(72*S^2) + (570 + 1798*S^2 + 3297*S^4)/(32*S^2) + (Pi^4*(958 + 7205*S^4))/(2160*S^2) + ((-35 + 2*S^2 + 76*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-35 + 19*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((-58 - 62*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/S^2 - (2*(-7 + 30*S^4)*HPL[{3, 1}, -S^2])/S^2 + (74*(-1 + 5*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-21 + 50*S^2 + 54*S^4)*Zeta[3])/(6*S^2)) + HPL[{1}, -S^2]^2*((7643*Pi^4*(1 + S^4))/(2160*S^2) + (Pi^2*(657 + 4328*S^2 + 3479*S^4))/(144*S^2) + (1277 + 6306*S^2 + 5029*S^4)/(48*S^2) + ((515*Pi^2*(1 + S^4))/(36*S^2) + (361 + 1192*S^2 + 927*S^4)/(12*S^2))*HPL[{2}, -S^2] + (31*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + (2*(16 + 29*S^2 + 27*S^4)*HPL[{3}, -S^2])/(3*S^2) + (37*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (4*(49 + 123*S^2 + 86*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (86*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (172*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((65 + 136*S^2 + 63*S^4)*Zeta[3])/(6*S^2)) + ((119 + 155*S^2)*Zeta[5])/3 + HPL[{1}, -S^2]*((Pi^2*(399 + 2552*S^2 + 2105*S^4))/(72*S^2) + (Pi^4*(5685 + 31820*S^2 + 23639*S^4))/(4320*S^2) + (7945 + 34004*S^2 + 26059*S^4)/(192*S^2) + ((41 + 124*S^2 + 83*S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + ((23*Pi^2*(1 + S^4))/(6*S^2) + (149 + 396*S^2 + 343*S^4)/(12*S^2))*HPL[{3}, -S^2] + (4*(7 + 17*S^2 + 13*S^4)*HPL[{4}, -S^2])/(3*S^2) + (58*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-361 - 1192*S^2 - 927*S^4)/(6*S^2) - (515*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2, 1}, -S^2] + ((-187 - 488*S^2 - 357*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (22*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (140*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (8*(49 + 123*S^2 + 86*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (124*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (420*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (344*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((109*Pi^2*(1 + S^4))/(18*S^2) + (155 + 288*S^2 + 133*S^4)/(12*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(667 + 2016*S^2 + 1437*S^4))/(72*S^2) + (1657 + 6128*S^2 + 4855*S^4)/(48*S^2) + (11*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (62*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (23*(1 + S^4)*Zeta[3])/(3*S^2)) + (119*(1 + S^4)*Zeta[5])/(3*S^2))) + HPL[{0}, S^2]*((35*(-1433 + 1454*S^2))/96 + (Pi^2*(-36384 + 57055*S^2))/576 + (Pi^6*(42013 + 126597*S^2))/45360 + (Pi^4*(-45890 + 130067*S^2))/8640 + ((46*(-1 + S^4))/(3*S^2) + (13*Pi^2*(1 + S^4))/(9*S^2))*HPL[{1}, -S^2]^5 + (28*(-1 + S^4)*HPL[{1}, -S^2]^6)/(9*S^2) + ((-32 + 53*S^4)*HPL[{2}, -S^2]^3)/(9*S^2) - (2*(15 - S^2 + 7*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((Pi^2*(-13 - 7*S^4))/(6*S^2) + (-311 + 76*S^2 + 561*S^4)/(12*S^2))*HPL[{5}, -S^2] + ((-100 - 150*S^2 + 189*S^4)*HPL[{6}, -S^2])/(6*S^2) - 28*S^2*HPL[{7}, -S^2] - (8*(2 - 6*S^2 + 39*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(-38 - 49*S^4))/(9*S^2) - (2*(41 - 68*S^2 + 70*S^4))/(3*S^2))*HPL[{3, 2}, -S^2] + ((-52 + 284*S^2 - 457*S^4)/(3*S^2) - (13*Pi^2*(5 + 7*S^4))/(9*S^2))*HPL[{4, 1}, -S^2] + ((7 + 8*S^2 - 18*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) + (10*(8 + S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((4 + 60*S^2 - 219*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((235 + 23*S^4)*HPL[{5, 2}, -S^2])/(3*S^2) + (2*(250 + 33*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((-1137 + 904*S^2 - 5*S^4)/(3*S^2) + (4*Pi^2*(93 + 10*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((4*Pi^2*(275 + 29*S^4))/(9*S^2) + (-3561 + 2644*S^2 + 311*S^4)/(3*S^2))*HPL[{3, 1, 1}, -S^2] + ((7 + 8*S^2 - 15*S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + ((-249 + 8*S^2 + 409*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (4*(6 + S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) + (32*(5 + 2*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + (2*(-351 - 12*S^2 + 790*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (2*(81 + 43*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) + (2*(297 + 115*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) + (4*(101 + 37*S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((-4*Pi^2*(21 + 2*S^4))/S^2 - (2*(-1301 + 768*S^2 + 299*S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (304*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) - (16*(-22 - 3*S^2 + 94*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (16*(46 + 47*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + (16*(46 + 47*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + (16*(103 + 104*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (16*(108 + 109*S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (40*(-17 + 77*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) - (272*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) - (272*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (480*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (160*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((373*Pi^4*S^2)/180 + (Pi^2*(-71 + 157*S^2))/9 + (-182 + 213*S^2)/3)*Zeta[3] + 2*(-1 + 5*S^2)*Zeta[3]^2 + HPL[{1}, -S^2]^4*((625*(-1 + S^4))/(12*S^2) + (Pi^2*(-129 + 276*S^2 + 373*S^4))/(36*S^2) + (235*(-1 + S^4)*HPL[{2}, -S^2])/(9*S^2) - (2*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (2*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(63 + 272*S^2 + 841*S^4))/(72*S^2) + (-59 - 2888*S^2 + 3139*S^4)/(48*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (38*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((9437 - 6680*S^2 - 2651*S^4)/(24*S^2) + (Pi^2*(1521 - 2104*S^2 - 514*S^4))/(36*S^2) + (Pi^4*(-3203 + 216*S^4))/(540*S^2) + (8*(7 + 10*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (136*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(-53 + 4*S^2 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-75 + 368*S^2 + 1057*S^4))/(9*S^2) + (-903 - 2528*S^2 + 3579*S^4)/(6*S^2) + (8*(-1 + 2*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((797 + 2152*S^2 - 3721*S^4)/(12*S^2) + (Pi^2*(75 - 336*S^2 - 1010*S^4))/(18*S^2) - (8*(1 + 2*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^4*(-149 - 59*S^4))/(540*S^2) + (Pi^2*(-77 + 5*S^2 + 167*S^4))/(18*S^2) + (-463 + 292*S^2 + 1537*S^4)/(24*S^2) - (10*(4 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (4*(39 - 12*S^2 + 22*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(17 + 5*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (8*(4 + 3*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (8*(1 + 2*S^2 + 4*S^4)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((Pi^2*(2 - 9*S^2 + 74*S^4))/(9*S^2) + (-129 + 60*S^2 + 524*S^4)/(12*S^2) + (2*(31 + 19*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(-7 + 11*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((2449*(-1 + S^4))/(18*S^2) + (1313*Pi^4*(1 + S^4))/(540*S^2) + (Pi^2*(-417 + 401*S^2 + 778*S^4))/(27*S^2) + ((800*(-1 + S^4))/(9*S^2) + (62*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] + (2*(-31 - 4*S^2 + 27*S^4)*HPL[{3}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (940*(-1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (8*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(-55 + 12*S^2 + 67*S^4)*Zeta[3])/(9*S^2)) + ((26*Pi^2*S^2)/3 + (7*(-29 + 44*S^2))/3)*Zeta[5] + HPL[{1}, -S^2]^2*((12859*(-1 + S^4))/(48*S^2) + (Pi^2*(-4909 + 3336*S^2 + 7989*S^4))/(144*S^2) + (Pi^4*(-4059 + 16840*S^2 + 18731*S^4))/(2160*S^2) + ((747*(-1 + S^4))/(4*S^2) + (2*Pi^2*(-53 + 93*S^2 + 146*S^4))/(9*S^2))*HPL[{2}, -S^2] + (74*(-1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((Pi^2*(1 + S^4))/(3*S^2) + (2*(-54 + 17*S^2 + 63*S^4))/(3*S^2))*HPL[{3}, -S^2] + ((-101 - 12*S^2 + 65*S^4)*HPL[{4}, -S^2])/(3*S^2) - (22*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-800*(-1 + S^4))/(3*S^2) - (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(-241 - 12*S^2 + 229*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (8*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (940*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (8*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((26*Pi^2*(1 + S^4))/(9*S^2) + (-107 - 34*S^2 + 89*S^4)/(3*S^2))*Zeta[3] + (22*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-1239 - 2164*S^2 + 7683*S^4))/(144*S^2) + (Pi^4*(-368 + 6934*S^2 + 18115*S^4))/(2160*S^2) + (-8347 - 16572*S^2 + 24975*S^4)/(96*S^2) + ((Pi^2*(20 + 23*S^4))/(9*S^2) + (46 - 62*S^2 + 71*S^4)/(3*S^2))*HPL[{3}, -S^2] + ((127 - 20*S^2 + 87*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((43 + 21*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((1137 - 904*S^2 + 5*S^4)/(6*S^2) - (2*Pi^2*(93 + 10*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] - (4*(7 - 12*S^2 + 75*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (2*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (2*(37 + 25*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (16*(2 - 6*S^2 + 39*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (152*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (8*(15 + 16*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (136*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((4*Pi^2*(-1 + 4*S^4))/(9*S^2) + (2*(-4 - 19*S^2 + 44*S^4))/(3*S^2))*Zeta[3] - (2*(12 + S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]*((2903*(-1 + S^4))/(8*S^2) + (42013*Pi^6*(1 + S^4))/(45360*S^2) + (Pi^2*(-6961 + 3586*S^2 + 10291*S^4))/(144*S^2) + (Pi^4*(-21017 + 31004*S^2 + 48005*S^4))/(4320*S^2) + ((283*(-1 + S^4))/(6*S^2) + (83*Pi^2*(1 + S^4))/(18*S^2))*HPL[{2}, -S^2]^2 + (2*(1 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((-11*Pi^2*(1 + S^4))/(9*S^2) + (-223 + 64*S^2 + 223*S^4)/(6*S^2))*HPL[{4}, -S^2] + ((-141 - 36*S^2 + 89*S^4)*HPL[{5}, -S^2])/(3*S^2) - (55*(1 + S^4)*HPL[{6}, -S^2])/(3*S^2) + ((-747*(-1 + S^4))/(2*S^2) - (4*Pi^2*(-53 + 93*S^2 + 146*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((-172*Pi^2*(1 + S^4))/(9*S^2) - (2*(-391 + 34*S^2 + 409*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] - (8*(-6 + S^2 + 5*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(-167 - 12*S^2 + 131*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (2*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (68*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((1600*(-1 + S^4))/(3*S^2) + (124*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (592*(-1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (4*(-179 - 4*S^2 + 175*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (16*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (1880*(-1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + ((2*(-84 - 47*S^2 + 53*S^4))/(3*S^2) + (Pi^2*(-67 + 60*S^2 + 111*S^4))/(9*S^2))*Zeta[3] - (2*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2}, -S^2]*((1511*(-1 + S^4))/(6*S^2) + (3487*Pi^4*(1 + S^4))/(1080*S^2) + (Pi^2*(-463 + 410*S^2 + 873*S^4))/(18*S^2) + (22*(-1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (2*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (296*(-1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (22*(-1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^2*(-137 - 8*S^2 + 169*S^4))/(18*S^2) + (-259 + 188*S^2 + 383*S^4)/(6*S^2) + (8*(1 + S^4)*Zeta[3])/(3*S^2)) + ((-179 + 40*S^2 + 227*S^4)*Zeta[5])/(3*S^2))) + 2*(231 + 83*S^2)*Zeta[7] + HPL[{1}, -S^2]*((25445*(-1 + S^4))/(48*S^2) + (Pi^2*(-17773 + 34004*S^2 + 51777*S^4))/(576*S^2) + (Pi^4*(-2585 + 100712*S^2 + 106561*S^4))/(8640*S^2) + (Pi^6*(30097 + 185480*S^2 + 163055*S^4))/(90720*S^2) + (62*(1 + 2*S^2 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + ((21 + 4*S^2 - 25*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((196*Pi^2*(1 + S^4))/(9*S^2) + (-133 + 1276*S^2 + 1409*S^4)/(6*S^2))*HPL[{5}, -S^2] + ((-135 + 1888*S^2 + 2063*S^4)*HPL[{6}, -S^2])/(6*S^2) + (358*(1 + S^4)*HPL[{7}, -S^2])/S^2 - (296*(-1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-394*Pi^2*(1 + S^4))/(9*S^2) - (2*(687 + 808*S^2 + 121*S^4))/(3*S^2))*HPL[{3, 2}, -S^2] + ((-1400*Pi^2*(1 + S^4))/(9*S^2) - (4*(1020 + 1387*S^2 + 367*S^4))/(3*S^2))*HPL[{4, 1}, -S^2] + ((71 - 16*S^2 - 55*S^4)*HPL[{4, 2}, -S^2])/(3*S^2) + (22*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 - (4*(-43 + 292*S^2 + 303*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + (52*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 - (278*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((1132*(-1 + S^4))/(3*S^2) + (124*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 2, 1}, -S^2] + ((240*Pi^2*(1 + S^4))/S^2 + (4*(-157 + 1014*S^2 + 1171*S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] - (8*(1 - 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (8*(185 + 374*S^2 + 185*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (496*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (1488*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + (16*(283 + 633*S^2 + 344*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (1488*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (4464*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (9296*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((-944*Pi^2*(1 + S^4))/(3*S^2) - (1352*(1 + 2*S^2 + S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (992*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (8*(389 + 900*S^2 + 511*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (1984*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (1984*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (4960*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (14496*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + 2*S^2 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (4800*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((859*Pi^4*(1 + S^4))/(180*S^2) + (6175 + 6306*S^2 + 131*S^4)/(12*S^2) + (Pi^2*(1969 + 2316*S^2 + 347*S^4))/(36*S^2))*Zeta[3] - (2*(15 - 22*S^2 + 7*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3, 1}, -S^2]*((-4*Pi^2*(144 + 347*S^2 + 217*S^4))/(9*S^2) - (4*(239 + 615*S^2 + 376*S^4))/(3*S^2) - (256*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((2*Pi^2*(18 + 109*S^2 + 91*S^4))/(9*S^2) + (-53 + 394*S^2 + 495*S^4)/(3*S^2) + (44*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((533*(-1 + S^4))/(8*S^2) + (Pi^2*(-25 + 372*S^2 + 397*S^4))/(36*S^2) + (62*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (124*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (62*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((820*(1 + 2*S^2 + S^4))/S^2 + (4*Pi^2*(323 + 696*S^2 + 397*S^4))/(9*S^2) + (512*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((1219*Pi^4*(1 + S^4))/(270*S^2) + (Pi^2*(511 + 808*S^2 + 329*S^4))/(12*S^2) + (1441 + 2102*S^2 + 661*S^4)/(4*S^2) - (18*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (16*(65 + 93*S^2 + 28*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (496*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(-23 + 40*S^2 + 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-1375 - 3220*S^2 - 1941*S^4))/(18*S^2) - (2779*Pi^4*(1 + S^4))/(180*S^2) - (1051*(1 + 2*S^2 + S^4))/(2*S^2) - (8*(127 + 204*S^2 + 53*S^4)*Zeta[3])/(3*S^2)) + ((455*Pi^2*(1 + S^4))/(9*S^2) + (5*(561 + 628*S^2 + 67*S^4))/(6*S^2))*Zeta[5] + HPL[{2}, -S^2]*((8501*(1 + 2*S^2 + S^4))/(24*S^2) + (Pi^2*(6577 + 15968*S^2 + 9775*S^4))/(144*S^2) + (Pi^4*(14313 + 32320*S^2 + 20063*S^4))/(2160*S^2) + ((197*Pi^2*(1 + S^4))/(9*S^2) + (693 + 820*S^2 + 127*S^4)/(3*S^2))*HPL[{3}, -S^2] + (67*(-1 + S^2)*(1 + S^2)*HPL[{4}, -S^2])/(3*S^2) + (32*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-566*(-1 + S^4))/(3*S^2) - (62*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (296*(-1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (744*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (592*(-1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (496*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (992*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + ((215*Pi^2*(1 + S^4))/(9*S^2) + (653 + 836*S^2 + 87*S^4)/(3*S^2))*Zeta[3] + (182*(1 + S^4)*Zeta[5])/S^2) + (462*(1 + S^4)*Zeta[7])/S^2)) - 784*S^2*Zeta[9];
Et5uvwT3F1=(-38155*(-1 + S^2))/(192*S) - (Pi^8*S*(476511 + 262639*S^2))/(1360800*(1 + S^2)) + (Pi^2*(2000 - 9536*S^2 - 133*S^4))/(144*S) + (Pi^6*(10192 - 397431*S^2 - 411939*S^4 - 11484*S^6))/(181440*S*(1 + S^2)) + (Pi^4*(21532 - 189052*S^2 - 206249*S^4 + 1071*S^6))/(17280*S*(1 + S^2)) + ((-1 - 3*S^2)*HPL[{1}, -S^2]^8)/(9*S) + HPL[{0}, S^2]^8*(-S/(192*(1 + S^2)) - (S*HPL[{1}, -S^2])/96) + ((3 - 34*S^2)*HPL[{2}, -S^2]^4)/(18*S) + HPL[{1}, -S^2]^7*((-10*Pi^2*S)/63 + (3 - 61*S^2 - 67*S^4 - 3*S^6)/(63*S^3) - (40*S*HPL[{2}, -S^2])/21) + HPL[{0}, S^2]^7*((-5*Pi^2*S)/864 - (S*(103 + 12*S^2))/576 + ((-12 - 53*S^2 - 31*S^4)*HPL[{1}, -S^2])/(288*S*(1 + S^2)) - (5*S*HPL[{1}, -S^2]^2)/144 - (5*S*HPL[{2}, -S^2])/144) + (28*S*HPL[{3}, -S^2]^3)/3 + ((10 - 74*S^2 - 33*S^4)*HPL[{4}, -S^2]^2)/(3*S*(1 + S^2)) + ((-649*Pi^2*S)/9 + (1050 - 6102*S^2 - 16586*S^4 - 10407*S^6 - 681*S^8)/(6*S^3*(1 + S^2)))*HPL[{7}, -S^2] + ((-2331 - 10163*S^2 - 5990*S^4)*HPL[{8}, -S^2])/(3*S*(1 + S^2)) - (6506*S*HPL[{9}, -S^2])/3 - (896*S*HPL[{2, 1}, -S^2]^3)/9 - (2*(-11 + 59*S^2)*HPL[{3, 1}, -S^2]^2)/S + ((11*Pi^2*S)/3 + (-9 + 253*S^2 + 666*S^4 + 338*S^6 + 42*S^8)/(6*S^3*(1 + S^2)))*HPL[{4, 3}, -S^2] + ((152*Pi^2*S)/9 + (-39 + 617*S^2 + 2272*S^4 + 1445*S^6 + 129*S^8)/(6*S^3*(1 + S^2)))*HPL[{5, 2}, -S^2] + ((-2 - 201*S^2 - 187*S^4)*HPL[{5, 3}, -S^2])/(3*S*(1 + S^2)) - 264*S*HPL[{5, 4}, -S^2] + ((931*Pi^2*S)/9 + (-468 + 4500*S^2 + 13642*S^4 + 8617*S^6 + 363*S^8)/(6*S^3*(1 + S^2)))*HPL[{6, 1}, -S^2] + ((-52 - 403*S^2 - 321*S^4)*HPL[{6, 2}, -S^2])/(3*S*(1 + S^2)) - (3308*S*HPL[{6, 3}, -S^2])/3 + ((1121 + 6729*S^2 + 4294*S^4)*HPL[{7, 1}, -S^2])/(3*S*(1 + S^2)) - (8234*S*HPL[{7, 2}, -S^2])/3 - 3748*S*HPL[{8, 1}, -S^2] - (16*(-4 + 87*S^2)*HPL[{2, 1, 1}, -S^2]^2)/(3*S) + ((-845*Pi^2*S)/9 + (15 - 146*S^2 - 414*S^4 + 105*S^6)/(6*S^3))*HPL[{3, 2, 2}, -S^2] + ((-2528*Pi^2*S)/9 + (2*(3 + 74*S^2 - 216*S^4 - 208*S^6 + 87*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 3, 1}, -S^2] + ((193 + 911*S^2 + 592*S^4)*HPL[{3, 3, 2}, -S^2])/(3*S*(1 + S^2)) + ((-2575*Pi^2*S)/9 + (15 + 465*S^2 - 856*S^4 - 993*S^6 + 345*S^8)/(6*S^3*(1 + S^2)))*HPL[{4, 1, 2}, -S^2] - (2*(195 + 824*S^2 + 524*S^4)*HPL[{4, 1, 3}, -S^2])/(3*S*(1 + S^2)) + ((-7603*Pi^2*S)/9 + (15 + 1629*S^2 - 2056*S^4 - 2733*S^6 + 1065*S^8)/(6*S^3*(1 + S^2)))*HPL[{4, 2, 1}, -S^2] + ((176 + 953*S^2 + 621*S^4)*HPL[{4, 2, 2}, -S^2])/(3*S*(1 + S^2)) - (40*S*HPL[{4, 2, 3}, -S^2])/3 - (2*(397 + 1894*S^2 + 1284*S^4)*HPL[{4, 3, 1}, -S^2])/(3*S*(1 + S^2)) + (614*S*HPL[{4, 3, 2}, -S^2])/3 + 316*S*HPL[{4, 4, 1}, -S^2] + ((-15650*Pi^2*S)/9 + (2*(60 + 479*S^2 - 2276*S^4 - 2244*S^6 + 531*S^8))/(3*S^3*(1 + S^2)))*HPL[{5, 1, 1}, -S^2] + ((-347 - 1941*S^2 - 1462*S^4)*HPL[{5, 1, 2}, -S^2])/(3*S*(1 + S^2)) - (268*S*HPL[{5, 1, 3}, -S^2])/3 + ((-3287 - 16401*S^2 - 11182*S^4)*HPL[{5, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (1612*S*HPL[{5, 2, 2}, -S^2])/3 + (2252*S*HPL[{5, 3, 1}, -S^2])/3 - (2*(1530 + 7940*S^2 + 5351*S^4)*HPL[{6, 1, 1}, -S^2])/(S*(1 + S^2)) + (2602*S*HPL[{6, 1, 2}, -S^2])/3 + (2362*S*HPL[{6, 2, 1}, -S^2])/3 - (3760*S*HPL[{7, 1, 1}, -S^2])/3 + (120*Pi^2*S - (4*(15 - 346*S^2 - 88*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 2, 2, 1}, -S^2] + ((-1408*Pi^2*S)/9 + (4*(48 - 1095*S^2 - 1284*S^4 - 125*S^6 + 12*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 1, 1, 2}, -S^2] + ((-1408*Pi^2*S)/9 + (4*(48 - 1095*S^2 - 1284*S^4 - 125*S^6 + 12*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 1, 2, 1}, -S^2] + (5*(5 + 13*S^2)*HPL[{3, 1, 2, 2}, -S^2])/(3*S) + ((-4648*Pi^2*S)/9 + (4*(93 - 2088*S^2 - 2586*S^4 - 344*S^6 + 57*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2, 1, 1}, -S^2] + (5*(5 + 13*S^2)*HPL[{3, 2, 1, 2}, -S^2])/(3*S) + ((329 + 3466*S^2 + 1649*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2968*S*HPL[{3, 2, 2, 2}, -S^2])/3 + (9400*S*HPL[{3, 2, 3, 1}, -S^2])/3 + (16*(19 + 211*S^2 + 99*S^4)*HPL[{3, 3, 1, 1}, -S^2])/(S*(1 + S^2)) + 3136*S*HPL[{3, 3, 1, 2}, -S^2] + 9576*S*HPL[{3, 3, 2, 1}, -S^2] + ((-13712*Pi^2*S)/9 + (2*(513 - 11947*S^2 - 14368*S^4 - 1551*S^6 + 333*S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 1, 1, 1}, -S^2] + (2*(-31 + 317*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(3*S) - (58288*S*HPL[{4, 1, 1, 3}, -S^2])/3 + (2*(425 + 5350*S^2 + 2693*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (48850*S*HPL[{4, 1, 2, 2}, -S^2])/3 - 29176*S*HPL[{4, 1, 3, 1}, -S^2] + (2*(1337 + 15478*S^2 + 7445*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (29506*S*HPL[{4, 2, 1, 2}, -S^2])/3 - (29530*S*HPL[{4, 2, 2, 1}, -S^2])/3 - (174280*S*HPL[{4, 3, 1, 1}, -S^2])/3 + (4*(1445 + 16648*S^2 + 8231*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 58156*S*HPL[{5, 1, 1, 2}, -S^2] - 96828*S*HPL[{5, 1, 2, 1}, -S^2] - 232156*S*HPL[{5, 2, 1, 1}, -S^2] - (1737616*S*HPL[{6, 1, 1, 1}, -S^2])/3 + ((-1552*Pi^2*S)/9 + (8*(-6 + 135*S^2 - 17*S^4 + 6*S^6))/S^3)*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-1552*Pi^2*S)/3 + (24*(-6 + 135*S^2 - 17*S^4 + 6*S^6))/S^3)*HPL[{2, 2, 1, 1, 1}, -S^2] + (16*(19 + 342*S^2 + 137*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (16*(19 + 342*S^2 + 137*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (2656*S*HPL[{2, 2, 2, 2, 1}, -S^2])/3 + ((-11552*Pi^2*S)/9 + (8*(-81 + 1955*S^2 - 459*S^4 + 126*S^6))/(3*S^3))*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(212 + 4135*S^2 + 1691*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) - (8*(364 + 6871*S^2 + 2787*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (1768*S*HPL[{3, 1, 1, 2, 2}, -S^2])/3 - (8*(440 + 8239*S^2 + 3335*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (1768*S*HPL[{3, 1, 2, 1, 2}, -S^2])/3 + (40*S*HPL[{3, 1, 2, 2, 1}, -S^2])/3 - (18080*S*HPL[{3, 1, 3, 1, 1}, -S^2])/3 - (8*(934 + 17131*S^2 + 6897*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (9736*S*HPL[{3, 2, 1, 1, 2}, -S^2])/3 + (8008*S*HPL[{3, 2, 1, 2, 1}, -S^2])/3 + (7592*S*HPL[{3, 2, 2, 1, 1}, -S^2])/3 + 4896*S*HPL[{3, 3, 1, 1, 1}, -S^2] - (16*(479 + 8650*S^2 + 3497*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (28544*S*HPL[{4, 1, 1, 1, 2}, -S^2])/3 + (23360*S*HPL[{4, 1, 1, 2, 1}, -S^2])/3 + (22112*S*HPL[{4, 1, 2, 1, 1}, -S^2])/3 + (43520*S*HPL[{4, 2, 1, 1, 1}, -S^2])/3 + (83936*S*HPL[{5, 1, 1, 1, 1}, -S^2])/3 + ((4448*Pi^2*S)/9 - (8*(45 - 818*S^2 - 118*S^4 + 45*S^6))/(3*S^3))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (7168*S*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/3 - 7168*S*HPL[{2, 2, 2, 1, 1, 1}, -S^2] + (16*(65 + 986*S^2 + 471*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (49216*S*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/3 + (92224*S*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/3 + (120896*S*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/3 + (135232*S*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/3 + (228416*S*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/3 + 228928*S*HPL[{4, 1, 1, 1, 1, 1}, -S^2] - (320*(1 + 29*S^2 + 13*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 4160*S*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] + 16640*S*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] + 41600*S*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] + 78080*S*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + 10240*S*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((8*Pi^2*S)/27 + (8*S*HPL[{0}, S^2])/3 + (8*S*HPL[{0}, S^2]^2)/9 + (8*(1 + 3*S^2)*HPL[{1}, -S^2])/(9*S) + (16*S*HPL[{2}, -S^2])/9)*Log[T]^7 + ((Pi^2*S*(22 + 39*S^2))/(6*(1 + S^2)) + (-12 - 71*S^2 - 221*S^4 - 66*S^6)/(12*S*(1 + S^2)))*Zeta[3]^2 - 32*S*Zeta[3]^3 + HPL[{2, 1, 1, 1, 1}, -S^2]*((-16*Pi^2*(11 + 381*S^2 + 193*S^4))/(9*S*(1 + S^2)) + (8*(9 - 171*S^2 - 563*S^4 + 9*S^6))/(3*S^3) - (6464*S*Zeta[3])/3) + HPL[{4, 1, 1}, -S^2]*((Pi^2*(-189 - 4382*S^2 - 2223*S^4))/(9*S*(1 + S^2)) + (90 - 2693*S^2 - 7369*S^4 + 102*S^6)/(6*S^3) - (4504*S*Zeta[3])/3) + HPL[{3, 2, 1}, -S^2]*((Pi^2*(-65 - 2440*S^2 - 1207*S^4))/(18*S*(1 + S^2)) + (81 - 479*S^2 - 3535*S^4 + 81*S^6)/(12*S^3) - 488*S*Zeta[3]) + HPL[{2}, -S^2]^3*((Pi^2*(-13 - 296*S^2 - 137*S^4))/(54*S*(1 + S^2)) + (3 - 41*S^2 - 209*S^4 + 3*S^6)/(18*S^3) - (190*S*HPL[{3}, -S^2])/9 - (166*S*HPL[{2, 1}, -S^2])/9 - (178*S*Zeta[3])/9) + HPL[{5, 1}, -S^2]*((Pi^2*(115 + 2055*S^2 + 1504*S^4))/(18*S*(1 + S^2)) + (162 + 4099*S^2 + 6096*S^4 - 225*S^6)/(12*S^3) - (52*S*Zeta[3])/3) + Log[T]^6*((1 - S^2)/(3*S) - (Pi^2*S*(41 + 26*S^2))/(27*(1 + S^2)) - (26*S*HPL[{0}, S^2]^3)/27 - (28*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(9*S) + HPL[{0}, S^2]^2*(-(S*(41 + 26*S^2))/(9*(1 + S^2)) - (10*S*HPL[{1}, -S^2])/3) - (4*(1 + 29*S^2 + 13*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((-10*Pi^2*S)/9 + (3 - 61*S^2 - 67*S^4 - 3*S^6)/(9*S^3) - (40*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]*((-26*Pi^2*S)/27 - (S*(67 + 3*S^2))/9 - (28*(1 + 3*S^2)*HPL[{1}, -S^2])/(9*S) + (4*S*HPL[{2}, -S^2])/9) - (116*S*HPL[{3}, -S^2])/9 + (128*S*HPL[{2, 1}, -S^2])/9 - (128*S*Zeta[3])/9) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(13 - 37*S^2))/(6*S) + (33 + 177*S^2 - 191*S^4 + 33*S^6)/(12*S^3) - (40*S*Zeta[3])/3) + HPL[{1}, -S^2]^6*((Pi^2*(-80 - 371*S^2 - 201*S^4))/(162*S*(1 + S^2)) - ((1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(108*S^3) + ((-13 - 86*S^2 - 13*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - (20*S*HPL[{3}, -S^2])/3 + (40*S*HPL[{2, 1}, -S^2])/3 - (20*S*Zeta[3])/3) + HPL[{0}, S^2]^6*(-(Pi^2*S*(195 + 83*S^2))/(1728*(1 + S^2)) + (6 - 665*S^2 - 763*S^4 - 60*S^6)/(1152*S*(1 + S^2)) + ((-18 - 81*S^2 - 35*S^4)*HPL[{1}, -S^2]^2)/(144*S*(1 + S^2)) - (7*S*HPL[{1}, -S^2]^3)/54 - (S*(108 + 83*S^2)*HPL[{2}, -S^2])/(288*(1 + S^2)) + HPL[{1}, -S^2]*((-7*Pi^2*S)/54 + (3 - 236*S^2 - 434*S^4 - 204*S^6 + 7*S^8)/(576*S^3*(1 + S^2)) - (25*S*HPL[{2}, -S^2])/144) - (S*HPL[{3}, -S^2])/48 - (25*S*Zeta[3])/36) + HPL[{4, 2}, -S^2]*((Pi^2*(-3 + 32*S^2))/(3*S) + (3 - 111*S^2 + 413*S^4 - 69*S^6)/(12*S^3) + (10*S*Zeta[3])/3) + HPL[{3}, -S^2]^2*((Pi^2*(13 + 119*S^2 + 95*S^4))/(18*S*(1 + S^2)) + (-9 - 284*S^2 + 275*S^4 - 36*S^6)/(24*S^3) - (52*S*HPL[{2, 1}, -S^2])/3 + (58*S*Zeta[3])/3) + HPL[{6}, -S^2]*((Pi^2*(-50 - 532*S^2 - 341*S^4))/(6*S*(1 + S^2)) + (-120 - 1427*S^2 - 1263*S^4 - 61*S^6)/(2*S^3) + 86*S*HPL[{2, 1}, -S^2] + (374*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]^2*((Pi^2*(-5 + 424*S^2 + 336*S^4))/(9*S*(1 + S^2)) + (12 - 71*S^2 + 1071*S^4 - 12*S^6)/(6*S^3) + (784*S*Zeta[3])/3) + HPL[{3, 1, 1, 1}, -S^2]*((8*Pi^2*(22 + 412*S^2 + 213*S^4))/(9*S*(1 + S^2)) + (-33 + 1135*S^2 + 2681*S^4 - 39*S^6)/(3*S^3) + (3200*S*Zeta[3])/3) + HPL[{3, 2}, -S^2]*((593*Pi^4*S)/90 + (107 - 678*S^2 - 1110*S^4 - 930*S^6 - 925*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(9 - 327*S^2 + 134*S^4 + 372*S^6 - 78*S^8))/(36*S^3*(1 + S^2)) + 1040*S*HPL[{2, 1, 1}, -S^2] + ((-35 - 176*S^2 - 81*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((2233*Pi^4*S)/135 + (-252 + 2629*S^2 + 685*S^4 - 252*S^6)/(3*S^3) + (Pi^2*(-93 + 1533*S^2 + 1906*S^4 + 175*S^6 - 57*S^8))/(9*S^3*(1 + S^2)) + (64*(2 + 27*S^2 + S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((71*Pi^4*S)/270 + (1539 - 16385*S^2 - 3139*S^4 - 531*S^6)/(12*S^3) + (Pi^2*(249 - 4701*S^2 - 5208*S^4 - 235*S^6 - 33*S^8))/(18*S^3*(1 + S^2)) + (4*(-21 - 200*S^2 + 9*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((1327*Pi^4*S)/270 + (258 - 2379*S^2 - 77*S^4 - 258*S^6)/(6*S^3) + (Pi^2*(69 - 1566*S^2 + 178*S^4 - 39*S^6))/(18*S^3) + (8*(-11 - 92*S^2 + 12*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^5*((-749*Pi^4*S)/1350 - ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(60*S^3) + (Pi^2*(45 - 919*S^2 - 955*S^4 - 15*S^6))/(270*S^3) + ((-236*Pi^2*S)/45 + (2*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(15*S^3))*HPL[{2}, -S^2] + (2*(-18 - 157*S^2 + 11*S^4)*HPL[{3}, -S^2])/(15*S*(1 + S^2)) - (32*S*HPL[{4}, -S^2])/5 + (2*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 40*S*HPL[{3, 1}, -S^2] - 80*S*HPL[{2, 1, 1}, -S^2] + (2*(4 - 35*S^2 + 51*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{4, 1}, -S^2]*((11581*Pi^4*S)/540 + (391 + 4107*S^2 + 8944*S^4 + 3495*S^6 - 2693*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-30 - 48*S^2 + 1166*S^4 + 1013*S^6 - 123*S^8))/(18*S^3*(1 + S^2)) + (9808*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(55 + 222*S^2 + 99*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{5}, -S^2]*((-57*Pi^4*S)/20 + (-240 - 8989*S^2 - 17209*S^4 - 8958*S^6 - 178*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(60 - 303*S^2 - 1164*S^4 - 811*S^6 - 24*S^8))/(18*S^3*(1 + S^2)) + ((251 + 139*S^2 - 208*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (76*S*HPL[{3, 1}, -S^2])/3 - 188*S*HPL[{2, 1, 1}, -S^2] + ((47 + 265*S^2 + 146*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^5*((-7873*Pi^4*S)/129600 - (Pi^2*S*(1317 + 1459*S^2 + 132*S^4))/(864*(1 + S^2)) + (450 - 14526*S^2 + 455*S^4)/(5760*S) + ((-445 - 1899*S^2 - 896*S^4)*HPL[{1}, -S^2]^3)/(1080*S*(1 + S^2)) - (31*S*HPL[{1}, -S^2]^4)/120 + ((-779*Pi^2*S)/2160 + (3 - 39*S^2 - 358*S^4 - 330*S^6 + 6*S^8)/(288*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (17*S*HPL[{2}, -S^2]^2)/60 + HPL[{1}, -S^2]^2*((-67*Pi^2*S)/180 + (9 - 393*S^2 - 735*S^4 - 387*S^6 - 14*S^8)/(288*S^3*(1 + S^2)) - (229*S*HPL[{2}, -S^2])/360) + ((-1 - 2*S^2 - 2*S^4)*HPL[{3}, -S^2])/(24*S*(1 + S^2)) + (S*HPL[{4}, -S^2])/8 + ((340 + 414*S^2 - 155*S^4)*HPL[{2, 1}, -S^2])/(360*S*(1 + S^2)) + (21*S*HPL[{3, 1}, -S^2])/20 - (127*S*HPL[{2, 1, 1}, -S^2])/45 - (S*(143 + 135*S^2)*Zeta[3])/(24*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-1705 - 7464*S^2 - 4151*S^4))/(4320*S*(1 + S^2)) + (39 - 823*S^2 - 1621*S^4 - 865*S^6 - 26*S^8)/(576*S^3*(1 + S^2)) + ((-370 - 1549*S^2 - 721*S^4)*HPL[{2}, -S^2])/(720*S*(1 + S^2)) + (S*HPL[{3}, -S^2])/12 + (229*S*HPL[{2, 1}, -S^2])/180 - (2*S*Zeta[3])/3)) + Log[T]^5*((4459*Pi^4*S)/4050 + (5*(-1 + S^2))/(2*S) - (Pi^2*S*(-974 + 15*S^2))/270 + (277*S*HPL[{0}, S^2]^4)/270 + (56*(1 + 3*S^2)*HPL[{1}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^3*((S*(277 + 212*S^2))/(45*(1 + S^2)) + (26*S*HPL[{1}, -S^2])/9) + ((172*Pi^2*S)/27 + (-15 + 274*S^2 + 974*S^4 - 15*S^6)/(45*S^3))*HPL[{2}, -S^2] + (26*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((487*Pi^2*S)/135 - (S*(-974 + 15*S^2))/90 + ((38 + 203*S^2 + 75*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) + 10*S*HPL[{1}, -S^2]^2 + (88*S*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]^2*((10*Pi^2*S)/3 + (-3 + 61*S^2 + 67*S^4 + 3*S^6)/(3*S^3) + 40*S*HPL[{2}, -S^2]) - (2*(-3 - 32*S^2 + 21*S^4)*HPL[{3}, -S^2])/(5*S*(1 + S^2)) + (136*S*HPL[{4}, -S^2])/15 + (4*(-11 - 28*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + HPL[{0}, S^2]*((Pi^2*S*(487 + 422*S^2))/(45*(1 + S^2)) + (-18 + 509*S^2 + 39*S^4)/(18*S) + ((26*Pi^2*S)/9 + (-3 + 61*S^2 + 67*S^4 + 3*S^6)/(3*S^3))*HPL[{1}, -S^2] + (28*(1 + 3*S^2)*HPL[{1}, -S^2]^2)/(3*S) + (2*(10 + 129*S^2)*HPL[{2}, -S^2])/(9*S) - (4*S*HPL[{3}, -S^2])/9 - (8*S*HPL[{2, 1}, -S^2])/3) - (112*S*HPL[{3, 1}, -S^2])/3 + (224*S*HPL[{2, 1, 1}, -S^2])/3 - (4*S*(-2 + 13*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(18*S^3) + (Pi^2*(80 + 371*S^2 + 201*S^4))/(27*S*(1 + S^2)) + (2*(13 + 86*S^2 + 13*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + 40*S*HPL[{3}, -S^2] - 80*S*HPL[{2, 1}, -S^2] + 40*S*Zeta[3])) + ((-782*Pi^4*S)/45 + (Pi^2*S*(-1602 - 1495*S^2 + 159*S^4))/(36*(1 + S^2)) + (48 - 6032*S^2 - 5397*S^4 + 523*S^6)/(24*S*(1 + S^2)))*Zeta[5] + HPL[{2, 1, 1}, -S^2]*((Pi^4*(-410 - 20114*S^2 - 11367*S^4))/(540*S*(1 + S^2)) + (6 - 751*S^2 - 1911*S^4 + 6*S^6)/(3*S^3) + (Pi^2*(24 - 589*S^2 - 2977*S^4 - 2280*S^6 + 36*S^8))/(18*S^3*(1 + S^2)) + (3584*S*HPL[{2, 2, 1}, -S^2])/3 + 1344*S*HPL[{3, 1, 1}, -S^2] - 2080*S*HPL[{2, 1, 1, 1}, -S^2] + ((-896*Pi^2*S)/9 + (2*(-3 - 13*S^2 + 34*S^4 + 29*S^6 + 33*S^8))/(3*S^3*(1 + S^2)))*Zeta[3] - 704*S*Zeta[5]) + Log[T]^4*((-133*(-1 + S^2))/(12*S) - (Pi^4*S*(6572 + 4325*S^2))/(1620*(1 + S^2)) + (Pi^2*(45 - 608*S^2 + 9*S^4))/(54*S) - (289*S*HPL[{0}, S^2]^5)/540 - (70*(1 + 3*S^2)*HPL[{1}, -S^2]^4)/(9*S) + HPL[{0}, S^2]^4*(-(S*(449 + 317*S^2))/(108*(1 + S^2)) - (22*S*HPL[{1}, -S^2])/9) - (2*(-4 + 87*S^2)*HPL[{2}, -S^2]^2)/(9*S) + HPL[{1}, -S^2]^3*((-50*Pi^2*S)/9 - (5*(-3 + 61*S^2 + 67*S^4 + 3*S^6))/(9*S^3) - (200*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^3*((-242*Pi^2*S)/81 - (S*(1247 + 1313*S^2 + 18*S^4))/(108*(1 + S^2)) + ((-92 - 409*S^2 - 187*S^4)*HPL[{1}, -S^2])/(18*S*(1 + S^2)) - (65*S*HPL[{1}, -S^2]^2)/9 - (61*S*HPL[{2}, -S^2])/9) + ((-158*Pi^2*S)/9 + (9 - 70*S^2 - 204*S^4 + 36*S^6)/(9*S^3))*HPL[{3}, -S^2] - (8*(1 + 25*S^2 + 18*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (428*S*HPL[{5}, -S^2])/9 + ((556*Pi^2*S)/27 + (-45 + 818*S^2 + 118*S^4 - 45*S^6)/(9*S^3))*HPL[{2, 1}, -S^2] + (2*(65 + 986*S^2 + 471*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (1672*S*HPL[{3, 2}, -S^2])/9 + (1736*S*HPL[{4, 1}, -S^2])/3 - (40*(1 + 29*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (520*S*HPL[{2, 2, 1}, -S^2])/3 + (400*S*HPL[{3, 1, 1}, -S^2])/3 + (1280*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-542*Pi^2*S)/27 + (S*(-118 + 45*S^2))/9)*Zeta[3] + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(36*S^3) - (5*Pi^2*(80 + 371*S^2 + 201*S^4))/(54*S*(1 + S^2)) - (5*(13 + 86*S^2 + 13*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - 100*S*HPL[{3}, -S^2] + 200*S*HPL[{2, 1}, -S^2] - 100*S*Zeta[3]) + HPL[{2}, -S^2]*((-2*Pi^2*(11 + 381*S^2 + 193*S^4))/(27*S*(1 + S^2)) + (9 - 171*S^2 - 563*S^4 + 9*S^6)/(9*S^3) - (280*S*HPL[{3}, -S^2])/3 - (260*S*HPL[{2, 1}, -S^2])/3 - (808*S*Zeta[3])/9) + HPL[{0}, S^2]^2*(-(Pi^2*S*(1513 + 1024*S^2))/(108*(1 + S^2)) + (45 - 1171*S^2 + 18*S^4)/(36*S) - (5*(38 + 203*S^2 + 75*S^4)*HPL[{1}, -S^2]^2)/(18*S*(1 + S^2)) - (50*S*HPL[{1}, -S^2]^3)/3 + ((-7 - 327*S^2 - 191*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((-163*Pi^2*S)/18 + (45 - 923*S^2 - 905*S^4 + 15*S^6)/(36*S^3) - (86*S*HPL[{2}, -S^2])/3) - (13*S*HPL[{3}, -S^2])/3 + (76*S*HPL[{2, 1}, -S^2])/9 - (62*S*Zeta[3])/9) + HPL[{1}, -S^2]*((-749*Pi^4*S)/270 - ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(12*S^3) + (Pi^2*(45 - 919*S^2 - 955*S^4 - 15*S^6))/(54*S^3) + ((-236*Pi^2*S)/9 + (2*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2}, -S^2] + (2*(-18 - 157*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 32*S*HPL[{4}, -S^2] + (10*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 200*S*HPL[{3, 1}, -S^2] - 400*S*HPL[{2, 1, 1}, -S^2] + (10*(4 - 35*S^2 + 51*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{0}, S^2]*((-4021*Pi^4*S)/1620 + (75 - 1138*S^2 - 109*S^4)/(12*S) - (Pi^2*S*(2252 + 2363*S^2 + 63*S^4))/(108*(1 + S^2)) + ((-65*Pi^2*S)/9 - (5*(-3 + 61*S^2 + 67*S^4 + 3*S^6))/(6*S^3))*HPL[{1}, -S^2]^2 - (140*(1 + 3*S^2)*HPL[{1}, -S^2]^3)/(9*S) + ((-56*Pi^2*S)/9 + (15 - 266*S^2 - 1074*S^4 - 45*S^6)/(18*S^3))*HPL[{2}, -S^2] + (17*S*HPL[{2}, -S^2]^2)/9 + ((-13 - 158*S^2 - 151*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (8*S*HPL[{4}, -S^2])/3 + (10*(37 + 12*S^2)*HPL[{2, 1}, -S^2])/(9*S) - 8*S*HPL[{3, 1}, -S^2] + (40*S*HPL[{2, 1, 1}, -S^2])/3 - (2*S*(28 + 27*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-162 - 689*S^2 - 397*S^4))/(18*S*(1 + S^2)) - (5*(1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(36*S^3) - (235*(1 + 3*S^2)*HPL[{2}, -S^2])/(9*S) + (4*S*HPL[{3}, -S^2])/3 - (4*S*Zeta[3])/3)) - (1220*S*Zeta[5])/9) + HPL[{2}, -S^2]^2*((Pi^4*(-26 - 3189*S^2 - 2256*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(-6 + 67*S^2 - 1045*S^4 + 12*S^6))/(72*S^3) + (-15 + 466*S^2 - 2786*S^4 + 15*S^6)/(48*S^3) + ((-71*Pi^2*S)/6 + (1 - 22*S^2 - 38*S^4 + 9*S^6)/(4*S^3))*HPL[{3}, -S^2] + ((-55 - 314*S^2 - 211*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - (119*S*HPL[{5}, -S^2])/3 + (15*Pi^2*S + (-15 + 346*S^2 + 88*S^4 - 15*S^6)/(6*S^3))*HPL[{2, 1}, -S^2] + ((97 + 928*S^2 + 459*S^4)*HPL[{3, 1}, -S^2])/(6*S*(1 + S^2)) + 125*S*HPL[{3, 2}, -S^2] + (1205*S*HPL[{4, 1}, -S^2])/3 - (2*(19 + 342*S^2 + 137*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (332*S*HPL[{2, 2, 1}, -S^2])/3 + 72*S*HPL[{3, 1, 1}, -S^2] + (896*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-239*Pi^2*S)/18 + (-3 + 54*S^2 - 26*S^4 + 33*S^6)/(12*S^3))*Zeta[3] - (275*S*Zeta[5])/3) + HPL[{1}, -S^2]^4*((Pi^4*(-5471 - 27356*S^2 - 12897*S^4))/(6480*S*(1 + S^2)) - ((1 + S^2)*(-1039 + 9360*S^2 + 1039*S^4))/(144*S^3) + (Pi^2*(393 - 4355*S^2 - 4861*S^4 - 177*S^6))/(432*S^3) - (37*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(9*S) + ((-29*Pi^2*S)/3 + (19 - 345*S^2 - 307*S^4 + 41*S^6)/(18*S^3))*HPL[{3}, -S^2] - (2*(47 + 221*S^2 + 102*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) - (92*S*HPL[{5}, -S^2])/3 + ((236*Pi^2*S)/9 - (2*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (2*(128 + 767*S^2 + 189*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (248*S*HPL[{3, 2}, -S^2])/3 + 280*S*HPL[{4, 1}, -S^2] - (10*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 200*S*HPL[{3, 1, 1}, -S^2] + 400*S*HPL[{2, 1, 1, 1}, -S^2] + ((-86*Pi^2*S)/9 + (2*(-2 + 25*S^2 + 15*S^4))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-89 - 581*S^2 - 138*S^4))/(27*S*(1 + S^2)) + ((1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 - (124*S*HPL[{3}, -S^2])/3 - (128*S*Zeta[3])/3) - (224*S*Zeta[5])/3) + HPL[{0}, S^2]^4*(-(Pi^4*S*(8596 + 4687*S^2))/(12960*(1 + S^2)) + (Pi^2*(15 - 1105*S^2 - 1239*S^4 - 71*S^6))/(288*S*(1 + S^2)) + (798 - 10636*S^2 - 11497*S^4 + 129*S^6)/(1152*S*(1 + S^2)) + ((-97 - 450*S^2 - 177*S^4)*HPL[{1}, -S^2]^4)/(144*S*(1 + S^2)) - (22*S*HPL[{1}, -S^2]^5)/45 + ((-3 - 154*S^2 - 99*S^4)*HPL[{2}, -S^2]^2)/(72*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((-19*Pi^2*S)/18 + (45 - 1356*S^2 - 2546*S^4 - 1252*S^6 + 13*S^8)/(432*S^3*(1 + S^2)) - (257*S*HPL[{2}, -S^2])/108) + ((-11*Pi^2*S)/72 + (3 + S^2 - 70*S^4 - 52*S^6)/(48*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((2 - 17*S^2 - 8*S^4)*HPL[{4}, -S^2])/(12*S*(1 + S^2)) - (23*S*HPL[{5}, -S^2])/12 + ((11*Pi^2*S)/216 + (-45 + 1009*S^2 + 1066*S^4 + 22*S^6 + 6*S^8)/(144*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((3 + 380*S^2 + 240*S^4)*HPL[{3, 1}, -S^2])/(36*S*(1 + S^2)) + (23*S*HPL[{4, 1}, -S^2])/12 + ((-12 - 820*S^2 - 551*S^4)*HPL[{2, 1, 1}, -S^2])/(36*S*(1 + S^2)) - (10*S*HPL[{2, 2, 1}, -S^2])/9 - (9*S*HPL[{3, 1, 1}, -S^2])/2 + (11*S*HPL[{2, 1, 1, 1}, -S^2])/9 + ((-833*Pi^2*S)/216 + (S*(-299 - 303*S^2 + 21*S^4))/(36*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-277 - 1260*S^2 - 527*S^4))/(288*S*(1 + S^2)) + (195 - 2837*S^2 - 5819*S^4 - 2995*S^6 - 16*S^8)/(576*S^3*(1 + S^2)) + ((-228 - 1203*S^2 - 461*S^4)*HPL[{2}, -S^2])/(144*S*(1 + S^2)) - (11*S*HPL[{3}, -S^2])/12 + (257*S*HPL[{2, 1}, -S^2])/36 - (19*S*Zeta[3])/9) + HPL[{2}, -S^2]*((Pi^2*(-3 - 610*S^2 - 449*S^4))/(216*S*(1 + S^2)) + (9 - 69*S^2 - 799*S^4 - 662*S^6 + 27*S^8)/(144*S^3*(1 + S^2)) + (5*S*HPL[{2, 1}, -S^2])/9 - (5*S*Zeta[3])/12) + HPL[{1}, -S^2]*((-1303*Pi^4*S)/2160 + (327 - 3413*S^2 - 7729*S^4 - 4247*S^6 - 162*S^8)/(576*S^3*(1 + S^2)) + (Pi^2*(45 - 2448*S^2 - 4528*S^4 - 2156*S^6 + 59*S^8))/(864*S^3*(1 + S^2)) + ((-79*Pi^2*S)/54 + (15 - 277*S^2 - 618*S^4 - 325*S^6 + 3*S^8)/(72*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (13*S*HPL[{2}, -S^2]^2)/9 + ((2 - 37*S^2 - 17*S^4)*HPL[{3}, -S^2])/(24*S*(1 + S^2)) - (11*S*HPL[{4}, -S^2])/6 + ((228 + 1203*S^2 + 461*S^4)*HPL[{2, 1}, -S^2])/(72*S*(1 + S^2)) + (137*S*HPL[{3, 1}, -S^2])/18 - (257*S*HPL[{2, 1, 1}, -S^2])/18 + ((-109 - 358*S^2 - 97*S^4)*Zeta[3])/(72*S*(1 + S^2))) - (805*S*Zeta[5])/36) + HPL[{4}, -S^2]*((Pi^4*(301 - 3848*S^2 - 2593*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(-638 - 1691*S^2 - 1024*S^4 - 3*S^6))/(36*S*(1 + S^2)) + (192 - 14519*S^2 - 26552*S^4 - 11451*S^6 + 6*S^8)/(48*S^3*(1 + S^2)) + 130*S*HPL[{5}, -S^2] + ((-31*Pi^2*S)/9 + (-3 + 710*S^2 - 238*S^4 + 27*S^6)/(6*S^3))*HPL[{2, 1}, -S^2] + (2*(-4 + 63*S^2 + 60*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (382*S*HPL[{3, 2}, -S^2])/3 - 228*S*HPL[{4, 1}, -S^2] - (2*(-23 + 369*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (260*S*HPL[{2, 2, 1}, -S^2])/3 - 172*S*HPL[{3, 1, 1}, -S^2] - (448*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((7*Pi^2*S)/9 + (3 - 2*S^2 + 124*S^4 + 132*S^6 + 15*S^8)/(3*S^3*(1 + S^2)))*Zeta[3] + (158*S*Zeta[5])/3) + HPL[{3, 1}, -S^2]*((Pi^4*(483 + 19674*S^2 + 10687*S^4))/(1080*S*(1 + S^2)) + (-141 + 10099*S^2 + 20765*S^4 + 45*S^6)/(48*S^3) + (Pi^2*(-48 + 1759*S^2 + 7326*S^4 + 5345*S^6 - 78*S^8))/(72*S^3*(1 + S^2)) - (1708*S*HPL[{3, 2}, -S^2])/3 - (5092*S*HPL[{4, 1}, -S^2])/3 + (8*(-23 + 209*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (1792*S*HPL[{2, 2, 1}, -S^2])/3 + (5584*S*HPL[{3, 1, 1}, -S^2])/3 + (3136*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((146*Pi^2*S)/3 + (6 - 17*S^2 - 128*S^4 - 79*S^6 - 30*S^8)/(3*S^3*(1 + S^2)))*Zeta[3] + (860*S*Zeta[5])/3) + Zeta[3]*((-1847*Pi^6*S)/1134 + (Pi^4*S*(-11534 - 11203*S^2 + 975*S^4))/(2160*(1 + S^2)) + (-498 - 9602*S^2 + 1585*S^4)/(48*S) + (Pi^2*(24 - 3270*S^2 - 3121*S^4 + 333*S^6))/(144*S*(1 + S^2)) + (2*S*(207 + 290*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{3}, -S^2]*((-1853*Pi^6*S)/3780 + (449 - 12351*S^2 - 11957*S^4 + 1136*S^6)/(48*S^3) + (Pi^4*(123 - 339*S^2 - 3102*S^4 - 2080*S^6 + 204*S^8))/(1080*S^3*(1 + S^2)) + (Pi^2*(87 - 1569*S^2 - 4438*S^4 - 2015*S^6 + 607*S^8))/(144*S^3*(1 + S^2)) + ((Pi^2*S)/9 + (3 - 129*S^2 - 226*S^4 - 58*S^6 - 24*S^8)/(6*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(-11 + 174*S^2 + 125*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (238*S*HPL[{6}, -S^2])/3 + 260*S*HPL[{2, 1}, -S^2]^2 + ((412*Pi^2*S)/9 + (3 - 160*S^2 - 80*S^4 + 58*S^6 - 33*S^8)/(3*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-31 - 160*S^2 - 109*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (2*(104 + 220*S^2 + 95*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (20*S*HPL[{4, 2}, -S^2])/3 + (40*S*HPL[{5, 1}, -S^2])/3 + ((-304*Pi^2*S)/3 + (4*(64 - 79*S^2 + 18*S^4))/(3*S))*HPL[{2, 1, 1}, -S^2] - (2*(121 + 680*S^2 + 187*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (2*(363 + 1832*S^2 + 353*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{3, 1, 2}, -S^2])/3 - 512*S*HPL[{3, 2, 1}, -S^2] + 17888*S*HPL[{4, 1, 1}, -S^2] - (16*(-7 - 26*S^2 + 12*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (3248*S*HPL[{3, 1, 1, 1}, -S^2])/3 - 2240*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(5 - 46*S^2 - 67*S^4))/(18*S*(1 + S^2)) + (-24 - 217*S^2 + 182*S^4 + 297*S^6 + 18*S^8)/(12*S^3*(1 + S^2)))*Zeta[3] - (52*S*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((Pi^2*(79 + 212*S^2 - 261*S^4))/(18*S*(1 + S^2)) + (-9 + 779*S^2 - 753*S^4 + 39*S^6)/(12*S^3) - (104*S*Zeta[3])/3) + ((75 + 44*S^2 - 55*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((8377*Pi^6*S)/22680 - (5*(317 - 3876*S^2 - 2020*S^4 + 317*S^6))/(48*S^3) + (Pi^4*(-1278 + 20482*S^2 + 24362*S^4 + 1013*S^6 - 561*S^8))/(2160*S^3*(1 + S^2)) + (Pi^2*(-552 + 4521*S^2 + 6647*S^4 + 1184*S^6 - 294*S^8))/(72*S^3*(1 + S^2)) + ((124*Pi^2*S)/3 - (2*(-15 + 474*S^2 - 70*S^4 + 21*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] + ((-221 - 1276*S^2 - 311*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (4*(193 + 847*S^2 + 96*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 2*S*HPL[{4, 2}, -S^2] + (148*S*HPL[{5, 1}, -S^2])/3 + ((776*Pi^2*S)/9 - (4*(-6 + 135*S^2 - 17*S^4 + 6*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (8*(19 + 342*S^2 + 137*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(5 + 290*S^2 + 161*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - (1328*S*HPL[{3, 2, 1}, -S^2])/3 - (4432*S*HPL[{4, 1, 1}, -S^2])/3 + (32*(-4 + 87*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (3136*S*HPL[{3, 1, 1, 1}, -S^2])/3 + 2080*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(45 + 328*S^2 + 68*S^4))/(9*S*(1 + S^2)) + (-12 + 59*S^2 - 41*S^4 - 64*S^6)/(3*S^3*(1 + S^2)))*Zeta[3] + (20*S*Zeta[3]^2)/3 - (2*(27 - 193*S^2 + 53*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-47329*Pi^6*S)/68040 - (2*(1 + S^2)*(-101 + 880*S^2 + 101*S^4))/(9*S^3) + (Pi^2*(645 - 5632*S^2 - 6589*S^4 - 344*S^6))/(216*S^3) + (Pi^4*(624 - 12677*S^2 - 26903*S^4 - 13411*S^6 + 35*S^8))/(3240*S^3*(1 + S^2)) + ((-31*Pi^2*S)/9 + (17 - 347*S^2 - 397*S^4 - 17*S^6)/(18*S^3))*HPL[{2}, -S^2]^2 - (124*S*HPL[{2}, -S^2]^3)/9 + ((-218*Pi^2*S)/27 - (8*(-3 + 74*S^2 + 154*S^4 + 80*S^6))/(9*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (8*(41 + 203*S^2 + 93*S^4)*HPL[{5}, -S^2])/(9*S*(1 + S^2)) - 106*S*HPL[{6}, -S^2] + ((472*Pi^2*S)/9 - (8*(9 - 173*S^2 - 176*S^4 + 6*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (4*(-11 - 242*S^2 + 141*S^4)*HPL[{3, 2}, -S^2])/(9*S*(1 + S^2)) - (4*(-121 - 1168*S^2 + 213*S^4)*HPL[{4, 1}, -S^2])/(9*S*(1 + S^2)) + (368*S*HPL[{5, 1}, -S^2])/3 + ((-944*Pi^2*S)/9 + (8*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (592*(1 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) - (8*(92 + 453*S^2 + 211*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (992*S*HPL[{3, 2, 1}, -S^2])/3 - 1120*S*HPL[{4, 1, 1}, -S^2] + (40*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 800*S*HPL[{3, 1, 1, 1}, -S^2] - 1600*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((2*Pi^2*(1 - 44*S^2 + 41*S^4))/(9*S*(1 + S^2)) + (3 + 135*S^2 + 409*S^4 + 213*S^6)/(18*S^3))*Zeta[3] + HPL[{3}, -S^2]*((Pi^2*(-65 - 615*S^2 - 28*S^4))/(27*S*(1 + S^2)) + (2*(12 - 215*S^2 - 181*S^4 + 42*S^6))/(9*S^3) + (496*S*HPL[{2, 1}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-4*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 + (4*Pi^2*(89 + 581*S^2 + 138*S^4))/(27*S*(1 + S^2)) + (512*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-2779*Pi^4*S)/540 + ((1 + S^2)*(301 - 3818*S^2 + 301*S^4))/(36*S^3) + (Pi^2*(60 - 966*S^2 - 2173*S^4 - 1056*S^6 + 43*S^8))/(54*S^3*(1 + S^2)) + (2*(-9 - 242*S^2 + 139*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (296*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (4*(-17 - 128*S^2 + 81*S^4)*Zeta[3])/(9*S*(1 + S^2))) + (2*(21 - 50*S^2 + 153*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^3*((-2033*Pi^6*S)/10080 + (2688 - 42518*S^2 - 2545*S^4)/(576*S) - (Pi^4*S*(57188 + 62911*S^2 + 5007*S^4))/(12960*(1 + S^2)) + (Pi^2*(870 - 21693*S^2 - 22377*S^4 + 314*S^6))/(1728*S*(1 + S^2)) + ((-92 - 409*S^2 - 187*S^4)*HPL[{1}, -S^2]^5)/(90*S*(1 + S^2)) - (13*S*HPL[{1}, -S^2]^6)/27 + ((-367*Pi^2*S)/216 + (1 + 3*S^2 - 882*S^4 - 917*S^6 - 9*S^8)/(144*S^3*(1 + S^2)))*HPL[{2}, -S^2]^2 - (4*S*HPL[{2}, -S^2]^3)/3 + HPL[{1}, -S^2]^4*((-79*Pi^2*S)/54 + (21 - 554*S^2 - 1088*S^4 - 574*S^6 - 13*S^8)/(108*S^3*(1 + S^2)) - (31*S*HPL[{2}, -S^2])/9) + (31*S*HPL[{3}, -S^2]^2)/18 + ((8*Pi^2*S)/27 + (3 - 179*S^2 - 424*S^4 - 263*S^6 + 3*S^8)/(72*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-21 - 3*S^2 - 41*S^4)*HPL[{5}, -S^2])/(18*S*(1 + S^2)) + (29*S*HPL[{6}, -S^2])/3 + (163*S*HPL[{2, 1}, -S^2]^2)/9 + ((361*Pi^2*S)/54 + (-9 + 104*S^2 + 663*S^4 + 545*S^6 + 3*S^8)/(18*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + (5*(-1 + S^2)*(11 + 12*S^2)*HPL[{3, 2}, -S^2])/(18*S*(1 + S^2)) + ((-46 + 61*S^2 + 127*S^4)*HPL[{4, 1}, -S^2])/(9*S*(1 + S^2)) - (2*S*HPL[{4, 2}, -S^2])/9 - (40*S*HPL[{5, 1}, -S^2])/9 + ((-437*Pi^2*S)/27 + (9 - 94*S^2 - 569*S^4 - 6*S^6)/(9*S^3))*HPL[{2, 1, 1}, -S^2] + ((-222 - 393*S^2 - 5*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S*(1 + S^2)) + ((-226 - 431*S^2 - 35*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2*S*HPL[{3, 1, 2}, -S^2])/9 - (286*S*HPL[{3, 2, 1}, -S^2])/9 - (890*S*HPL[{4, 1, 1}, -S^2])/9 + (2*(76 + 143*S^2 + 5*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (688*S*HPL[{3, 1, 1, 1}, -S^2])/9 - (488*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + (-(Pi^2*S*(2383 + 2240*S^2))/(108*(1 + S^2)) + (S*(-1117 - 878*S^2 + 135*S^4))/(72*(1 + S^2)))*Zeta[3] + (S*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((Pi^2*(-7 - 29*S^2 - 25*S^4))/(36*S*(1 + S^2)) + (111 - 463*S^2 - 1472*S^4 - 939*S^6 - 9*S^8)/(144*S^3*(1 + S^2)) - (38*S*HPL[{2, 1}, -S^2])/9 - 4*S*Zeta[3]) + HPL[{1}, -S^2]^3*((Pi^2*(-721 - 3126*S^2 - 1457*S^4))/(324*S*(1 + S^2)) + (87 - 1243*S^2 - 2643*S^4 - 1441*S^6 - 48*S^8)/(108*S^3*(1 + S^2)) + ((-123 - 595*S^2 - 286*S^4)*HPL[{2}, -S^2])/(27*S*(1 + S^2)) - (4*S*HPL[{3}, -S^2])/9 + (124*S*HPL[{2, 1}, -S^2])/9 - (46*S*Zeta[3])/27) + HPL[{2, 1}, -S^2]*((Pi^2*(568 + 843*S^2 - 140*S^4))/(108*S*(1 + S^2)) + (-180 + 2335*S^2 + 662*S^4 + 51*S^6)/(72*S^3) + (46*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((-805*Pi^4*S)/648 + (279 - 3238*S^2 - 7268*S^4 - 4058*S^6 - 179*S^8)/(144*S^3*(1 + S^2)) + (Pi^2*(87 - 3073*S^2 - 5851*S^4 - 3083*S^6 - 96*S^8))/(432*S^3*(1 + S^2)) + ((-415*Pi^2*S)/108 + (63 - 1131*S^2 - 1265*S^4 - 23*S^6)/(72*S^3))*HPL[{2}, -S^2] - (83*S*HPL[{2}, -S^2]^2)/18 + ((-13 - 75*S^2 - 56*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (5*S*HPL[{4}, -S^2])/9 + ((123 + 595*S^2 + 286*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (178*S*HPL[{3, 1}, -S^2])/9 - (124*S*HPL[{2, 1, 1}, -S^2])/3 + ((-75 - 297*S^2 - 176*S^4)*Zeta[3])/(18*S*(1 + S^2))) + HPL[{2}, -S^2]*((-6*Pi^4*S)/5 + (115 - 1108*S^2 - 4703*S^4 - 3637*S^6 - 61*S^8)/(144*S^3*(1 + S^2)) + (Pi^2*(33 - 365*S^2 - 3116*S^4 - 2800*S^6 + 18*S^8))/(432*S^3*(1 + S^2)) + ((28 + 3*S^2 - 30*S^4)*HPL[{3}, -S^2])/(18*S*(1 + S^2)) - (10*S*HPL[{4}, -S^2])/3 + ((222 + 393*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(18*S*(1 + S^2)) + (182*S*HPL[{3, 1}, -S^2])/9 - (326*S*HPL[{2, 1, 1}, -S^2])/9 + ((12 - 145*S^2 - 120*S^4)*Zeta[3])/(18*S*(1 + S^2))) - (S*(1157 + 1109*S^2)*Zeta[5])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(-8039 - 35057*S^2 - 18968*S^4))/(6480*S*(1 + S^2)) + (880 - 9023*S^2 - 21127*S^4 - 12177*S^6 - 697*S^8)/(288*S^3*(1 + S^2)) + (Pi^2*(369 - 6601*S^2 - 13391*S^4 - 7207*S^6 - 226*S^8))/(864*S^3*(1 + S^2)) + ((-99 - 463*S^2 - 198*S^4)*HPL[{2}, -S^2]^2)/(36*S*(1 + S^2)) + ((Pi^2*S)/6 + (11 - 85*S^2 - 235*S^4 - 119*S^6)/(18*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-48 - 163*S^2 - 125*S^4)*HPL[{4}, -S^2])/(18*S*(1 + S^2)) + (59*S*HPL[{5}, -S^2])/9 + ((415*Pi^2*S)/54 + (-63 + 1131*S^2 + 1265*S^4 + 23*S^6)/(36*S^3))*HPL[{2, 1}, -S^2] + ((125 + 613*S^2 + 310*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - (10*S*HPL[{3, 2}, -S^2])/9 - (40*S*HPL[{4, 1}, -S^2])/9 - (2*(123 + 595*S^2 + 286*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) - (332*S*HPL[{2, 2, 1}, -S^2])/9 - (340*S*HPL[{3, 1, 1}, -S^2])/3 + (248*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-143*Pi^2*S)/54 + (-271 - 597*S^2 - 409*S^4 - 51*S^6)/(36*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-616 - 2739*S^2 - 1293*S^4))/(216*S*(1 + S^2)) + (231 - 3077*S^2 - 3359*S^4 - 83*S^6)/(144*S^3) + (5*S*HPL[{3}, -S^2])/9 + (166*S*HPL[{2, 1}, -S^2])/9 - (37*S*Zeta[3])/9) - (32*S*Zeta[5])/3)) + Log[T]^3*((8431*Pi^6*S)/5670 + (433*(-1 + S^2))/(12*S) + (Pi^2*(-447 + 3279*S^2 - 49*S^4))/(108*S) - (Pi^4*S*(-22100 - 21529*S^2 + 415*S^4))/(3240*(1 + S^2)) + (31*S*HPL[{0}, S^2]^6)/108 + (56*(1 + 3*S^2)*HPL[{1}, -S^2]^5)/(9*S) + HPL[{0}, S^2]^5*((S*(1390 + 1111*S^2))/(540*(1 + S^2)) + (31*S*HPL[{1}, -S^2])/30) + ((380*Pi^2*S)/27 + (1 - 58*S^2 + 448*S^4 - S^6)/(9*S^3))*HPL[{2}, -S^2]^2 + (296*S*HPL[{2}, -S^2]^3)/27 + HPL[{0}, S^2]^4*((371*Pi^2*S)/162 - (S*(-1488 - 1529*S^2 + 19*S^4))/(216*(1 + S^2)) + ((97 + 450*S^2 + 177*S^4)*HPL[{1}, -S^2])/(36*S*(1 + S^2)) + (44*S*HPL[{1}, -S^2]^2)/9 + (41*S*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]^4*((50*Pi^2*S)/9 + (5*(-3 + 61*S^2 + 67*S^4 + 3*S^6))/(9*S^3) + (200*S*HPL[{2}, -S^2])/3) - (32*S*HPL[{3}, -S^2]^2)/9 + ((308*Pi^2*S)/27 + (-21 + 447*S^2 + 1388*S^4 + 935*S^6 - 9*S^8)/(9*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(159 + 928*S^2 + 493*S^4)*HPL[{5}, -S^2])/(9*S*(1 + S^2)) + (1136*S*HPL[{6}, -S^2])/9 - (520*S*HPL[{2, 1}, -S^2]^2)/3 + ((-1712*Pi^2*S)/27 + (4*(9 - 217*S^2 - 551*S^4 + 6*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] + (4*(46 - 141*S^2 + 185*S^4)*HPL[{3, 2}, -S^2])/(9*S*(1 + S^2)) + (8*(17 - 400*S^2 + 213*S^4)*HPL[{4, 1}, -S^2])/(9*S*(1 + S^2)) - (176*S*HPL[{4, 2}, -S^2])/9 - (1904*S*HPL[{5, 1}, -S^2])/9 + ((3440*Pi^2*S)/27 - (4*(15 - 274*S^2 - 974*S^4 + 15*S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] + (32*(41 + 24*S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) + (8*(173 + 356*S^2 + 33*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (32*S*HPL[{3, 1, 2}, -S^2])/9 + (800*S*HPL[{3, 2, 1}, -S^2])/3 + (2912*S*HPL[{4, 1, 1}, -S^2])/3 + (80*(-11 - 28*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (2240*S*HPL[{3, 1, 1, 1}, -S^2])/3 + (4480*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((-4*S*(-103 + 45*S^2))/9 - (4*Pi^2*S*(-47 + 82*S^2))/(27*(1 + S^2)))*Zeta[3] - (8*S*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((-2*Pi^2*(-16 - 215*S^2 + 62*S^4))/(27*S*(1 + S^2)) + (-39 + 443*S^2 + 909*S^4 - 321*S^6)/(18*S^3) + (128*S*HPL[{2, 1}, -S^2])/3 + (16*S*Zeta[3])/9) + HPL[{0}, S^2]^3*((Pi^2*S*(2221 + 1747*S^2))/(162*(1 + S^2)) + (-42 + 1442*S^2 + 1551*S^4 + 27*S^6)/(54*S*(1 + S^2)) + ((92 + 409*S^2 + 187*S^4)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)) + (260*S*HPL[{1}, -S^2]^3)/27 + ((18 + 761*S^2 + 557*S^4)*HPL[{2}, -S^2])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((158*Pi^2*S)/27 + (-21 + 554*S^2 + 1088*S^4 + 574*S^6 + 13*S^8)/(27*S^3*(1 + S^2)) + (124*S*HPL[{2}, -S^2])/9) + (2*S*HPL[{3}, -S^2])/9 - (4*S*HPL[{2, 1}, -S^2])/9 + (28*S*Zeta[3])/9) + HPL[{2, 1}, -S^2]*((8*Pi^2*(-78 - 200*S^2 + 55*S^4))/(27*S*(1 + S^2)) + (4*(45 - 495*S^2 - 103*S^4 + 45*S^6))/(9*S^3) + (160*S*Zeta[3])/9) + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(27*S^3) + (10*Pi^2*(80 + 371*S^2 + 201*S^4))/(81*S*(1 + S^2)) + (20*(13 + 86*S^2 + 13*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (400*S*HPL[{3}, -S^2])/3 - (800*S*HPL[{2, 1}, -S^2])/3 + (400*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((749*Pi^4*S)/135 + ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(6*S^3) + (Pi^2*(-45 + 919*S^2 + 955*S^4 + 15*S^6))/(27*S^3) + ((472*Pi^2*S)/9 - (4*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2}, -S^2] - (4*(-18 - 157*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + 64*S*HPL[{4}, -S^2] - (20*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 400*S*HPL[{3, 1}, -S^2] + 800*S*HPL[{2, 1, 1}, -S^2] - (20*(4 - 35*S^2 + 51*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{2}, -S^2]*((3052*Pi^4*S)/405 + (-49 + 888*S^2 + 2832*S^4 - 49*S^6)/(18*S^3) + (Pi^2*(-27 + 399*S^2 + 2440*S^4 + 1937*S^6 - 29*S^8))/(54*S^3*(1 + S^2)) - (4*(33 - 86*S^2 + 67*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (224*S*HPL[{4}, -S^2])/9 - (16*(41 + 24*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (1568*S*HPL[{3, 1}, -S^2])/9 + (1040*S*HPL[{2, 1, 1}, -S^2])/3 - (8*(-9 - 20*S^2 + 85*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{0}, S^2]^2*((8159*Pi^4*S)/1620 + (-222 + 3054*S^2 - 49*S^4)/(36*S) - (Pi^2*S*(-1231 - 1244*S^2 + 17*S^4))/(54*(1 + S^2)) + (10*(38 + 203*S^2 + 75*S^4)*HPL[{1}, -S^2]^3)/(27*S*(1 + S^2)) + (50*S*HPL[{1}, -S^2]^4)/3 + ((466*Pi^2*S)/27 + (-6 + 70*S^2 + 596*S^4 + 489*S^6 - 7*S^8)/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (185*S*HPL[{2}, -S^2]^2)/9 + HPL[{1}, -S^2]^2*((163*Pi^2*S)/9 + (-45 + 923*S^2 + 905*S^4 - 15*S^6)/(18*S^3) + (172*S*HPL[{2}, -S^2])/3) + ((5 + 142*S^2 + 65*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (104*S*HPL[{4}, -S^2])/9 + (2*(-147 - 380*S^2 + 25*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (872*S*HPL[{3, 1}, -S^2])/9 + (1760*S*HPL[{2, 1, 1}, -S^2])/9 + (2*S*(64 + 31*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(481 + 2365*S^2 + 906*S^4))/(54*S*(1 + S^2)) + (-99 + 1055*S^2 + 1113*S^4 - 9*S^6)/(18*S^3) + ((161 + 1034*S^2 + 357*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + 16*S*HPL[{3}, -S^2] - (344*S*HPL[{2, 1}, -S^2])/3 + (44*S*Zeta[3])/3)) - (32*S*(5 + 47*S^2)*Zeta[5])/(9*(1 + S^2)) + HPL[{0}, S^2]*((Pi^4*S*(24526 + 20587*S^2))/(1620*(1 + S^2)) + (-828 + 9571*S^2 + 1039*S^4)/(36*S) + (Pi^2*(-174 + 5339*S^2 + 5842*S^4 + 249*S^6))/(108*S*(1 + S^2)) + ((260*Pi^2*S)/27 + (10*(-3 + 61*S^2 + 67*S^4 + 3*S^6))/(9*S^3))*HPL[{1}, -S^2]^3 + (140*(1 + 3*S^2)*HPL[{1}, -S^2]^4)/(9*S) + (2*(-9 + 263*S^2)*HPL[{2}, -S^2]^2)/(9*S) + ((-4*Pi^2*S)/27 + (-27 + 141*S^2 + 355*S^4 + 5*S^6)/(9*S^3))*HPL[{3}, -S^2] + (2*(7 + 68*S^2 + 65*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (4*S*HPL[{5}, -S^2])/3 + ((-8*Pi^2*S)/3 - (2*(-45 + 810*S^2 + 218*S^4 + 15*S^6))/(9*S^3))*HPL[{2, 1}, -S^2] - (4*(53 + 680*S^2 + 633*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - (160*S*HPL[{3, 2}, -S^2])/9 - (80*S*HPL[{4, 1}, -S^2])/3 + (40*(10 + 129*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (272*S*HPL[{2, 2, 1}, -S^2])/9 + (736*S*HPL[{3, 1, 1}, -S^2])/9 - (160*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((28*Pi^2*S)/9 + (2*S*(128 + 3*S^2))/9)*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2*(34 + 728*S^2 + 601*S^4))/(27*S*(1 + S^2)) + (-11 + 273*S^2 + 887*S^4 + 59*S^6)/(6*S^3) + 8*S*HPL[{3}, -S^2] - (136*S*HPL[{2, 1}, -S^2])/9 + (16*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(18*S^3) + (Pi^2*(162 + 689*S^2 + 397*S^4))/(9*S*(1 + S^2)) + (470*(1 + 3*S^2)*HPL[{2}, -S^2])/(9*S) - (8*S*HPL[{3}, -S^2])/3 + (8*S*Zeta[3])/3) + HPL[{1}, -S^2]*((1313*Pi^4*S)/270 + ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(6*S^3) + (Pi^2*(-87 + 1978*S^2 + 4096*S^4 + 2198*S^6 + 71*S^8))/(54*S^3*(1 + S^2)) + ((124*Pi^2*S)/9 + (4*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(9*S^3))*HPL[{2}, -S^2] + (4*(14 + 55*S^2 + 43*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{4}, -S^2])/3 - (940*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (16*S*HPL[{3, 1}, -S^2])/3 + (4*(32 + 131*S^2 + 93*S^4)*Zeta[3])/(9*S*(1 + S^2))) - (104*S*Zeta[5])/9) + HPL[{1}, -S^2]*(((1 + S^2)*(-1039 + 9360*S^2 + 1039*S^4))/(36*S^3) + (Pi^4*(5471 + 27356*S^2 + 12897*S^4))/(1620*S*(1 + S^2)) + (Pi^2*(-393 + 4355*S^2 + 4861*S^4 + 177*S^6))/(108*S^3) + (148*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(9*S) + ((116*Pi^2*S)/3 - (2*(19 - 345*S^2 - 307*S^4 + 41*S^6))/(9*S^3))*HPL[{3}, -S^2] + (8*(47 + 221*S^2 + 102*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) + (368*S*HPL[{5}, -S^2])/3 + ((-944*Pi^2*S)/9 + (8*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (8*(128 + 767*S^2 + 189*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - (992*S*HPL[{3, 2}, -S^2])/3 - 1120*S*HPL[{4, 1}, -S^2] + (40*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 800*S*HPL[{3, 1, 1}, -S^2] - 1600*S*HPL[{2, 1, 1, 1}, -S^2] + ((344*Pi^2*S)/9 - (8*(-2 + 25*S^2 + 15*S^4))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-4*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 + (4*Pi^2*(89 + 581*S^2 + 138*S^4))/(27*S*(1 + S^2)) + (496*S*HPL[{3}, -S^2])/3 + (512*S*Zeta[3])/3) + (896*S*Zeta[5])/3)) + (-186*Pi^2*S + (S*(-674 - 559*S^2 + 75*S^4))/(2*(1 + S^2)))*Zeta[7] + Log[T]^2*((-2147*(-1 + S^2))/(24*S) - (Pi^6*S*(148496 + 101167*S^2))/(45360*(1 + S^2)) + (Pi^2*(259 - 1533*S^2 + 4*S^4))/(24*S) + (Pi^4*(2496 - 51059*S^2 - 52235*S^4 + 840*S^6))/(4320*S*(1 + S^2)) - (5*S*HPL[{0}, S^2]^7)/72 - (28*(1 + 3*S^2)*HPL[{1}, -S^2]^6)/(9*S) + HPL[{0}, S^2]^6*(-(S*(111 + 83*S^2))/(144*(1 + S^2)) - (7*S*HPL[{1}, -S^2])/18) + ((-19 - 342*S^2 - 137*S^4)*HPL[{2}, -S^2]^3)/(9*S*(1 + S^2)) + HPL[{1}, -S^2]^5*((-10*Pi^2*S)/3 + (3 - 61*S^2 - 67*S^4 - 3*S^6)/(3*S^3) - 40*S*HPL[{2}, -S^2]) + HPL[{0}, S^2]^5*((-407*Pi^2*S)/540 - (S*(471 + 503*S^2 + 12*S^4))/(144*(1 + S^2)) + ((-445 - 1899*S^2 - 896*S^4)*HPL[{1}, -S^2])/(360*S*(1 + S^2)) - (31*S*HPL[{1}, -S^2]^2)/20 - (127*S*HPL[{2}, -S^2])/90) + (104*S*HPL[{3}, -S^2]^2)/3 + ((-283*Pi^2*S)/9 + (60 - 394*S^2 - 1376*S^4 - 939*S^6 - 9*S^8)/(3*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-60 - 710*S^2 - 491*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) - (1520*S*HPL[{7}, -S^2])/3 + (8*(-4 + 87*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((916*Pi^2*S)/9 - (2*(-3 + 102*S^2 - 18*S^4 - 94*S^6 + 33*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((2864*Pi^2*S)/9 + (-27 - 31*S^2 + 1256*S^4 + 1077*S^6 - 207*S^8)/(3*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-31 + 317*S^2)*HPL[{4, 2}, -S^2])/(3*S) - (164*S*HPL[{4, 3}, -S^2])/3 + (2*(77 + 1456*S^2 + 1103*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - 110*S*HPL[{5, 2}, -S^2] + (952*S*HPL[{6, 1}, -S^2])/3 + ((776*Pi^2*S)/9 - (4*(-6 + 135*S^2 - 17*S^4 + 6*S^6))/S^3)*HPL[{2, 2, 1}, -S^2] + (48*Pi^2*S - (4*(-63 + 1285*S^2 + 51*S^4 + 18*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] - (4*(-16 + 47*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (4*(22 + 715*S^2 + 321*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (3100*S*HPL[{3, 2, 2}, -S^2])/3 - (9488*S*HPL[{3, 3, 1}, -S^2])/3 - (8*(23 + 442*S^2 + 209*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (9632*S*HPL[{4, 1, 2}, -S^2])/3 - (28736*S*HPL[{4, 2, 1}, -S^2])/3 - (59024*S*HPL[{5, 1, 1}, -S^2])/3 + ((2224*Pi^2*S)/9 - (4*(45 - 818*S^2 - 118*S^4 + 45*S^6))/(3*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (3584*S*HPL[{2, 2, 2, 1}, -S^2])/3 + (8*(65 + 986*S^2 + 471*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4064*S*HPL[{3, 1, 1, 2}, -S^2])/3 - (4064*S*HPL[{3, 1, 2, 1}, -S^2])/3 - (14816*S*HPL[{3, 2, 1, 1}, -S^2])/3 - 14560*S*HPL[{4, 1, 1, 1}, -S^2] - (160*(1 + 29*S^2 + 13*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 2080*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 6240*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 15040*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 5120*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-869*Pi^4*S)/90 + (Pi^2*S*(-294 - 241*S^2 + 57*S^4))/(18*(1 + S^2)) + (-3 - 682*S^2 + 252*S^4)/(6*S))*Zeta[3] + 40*S*Zeta[3]^2 + HPL[{2, 1, 1}, -S^2]*((-8*Pi^2*(11 + 381*S^2 + 193*S^4))/(9*S*(1 + S^2)) + (4*(9 - 171*S^2 - 563*S^4 + 9*S^6))/(3*S^3) - (3232*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(5 - 424*S^2 - 336*S^4))/(18*S*(1 + S^2)) + (-12 + 71*S^2 - 1071*S^4 + 12*S^6)/(12*S^3) - 130*S*HPL[{3}, -S^2] + (448*S*HPL[{2, 1}, -S^2])/3 - (392*S*Zeta[3])/3) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(36*S^3) - (5*Pi^2*(80 + 371*S^2 + 201*S^4))/(54*S*(1 + S^2)) - (5*(13 + 86*S^2 + 13*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - 100*S*HPL[{3}, -S^2] + 200*S*HPL[{2, 1}, -S^2] - 100*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(-33 - 830*S^2 - 579*S^4))/(18*S*(1 + S^2)) + (18 - 1709*S^2 - 2353*S^4 + 30*S^6)/(12*S^3) - (224*S*HPL[{2, 1}, -S^2])/3 - (116*S*Zeta[3])/3) + HPL[{0}, S^2]^4*(-(Pi^2*S*(2563 + 1879*S^2))/(432*(1 + S^2)) + (30 - 1095*S^2 - 1141*S^4 + 16*S^6)/(96*S*(1 + S^2)) + ((-97 - 450*S^2 - 177*S^4)*HPL[{1}, -S^2]^2)/(24*S*(1 + S^2)) - (44*S*HPL[{1}, -S^2]^3)/9 + ((-12 - 820*S^2 - 551*S^4)*HPL[{2}, -S^2])/(72*S*(1 + S^2)) + HPL[{1}, -S^2]*((-19*Pi^2*S)/6 + (45 - 1356*S^2 - 2546*S^4 - 1252*S^6 + 13*S^8)/(144*S^3*(1 + S^2)) - (257*S*HPL[{2}, -S^2])/36) - (7*S*HPL[{3}, -S^2])/12 + (11*S*HPL[{2, 1}, -S^2])/18 - (83*S*Zeta[3])/18) + HPL[{3, 1}, -S^2]*((4*Pi^2*(22 + 412*S^2 + 213*S^4))/(9*S*(1 + S^2)) + (-33 + 1135*S^2 + 2681*S^4 - 39*S^6)/(6*S^3) + (1600*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((2233*Pi^4*S)/270 + (-252 + 2629*S^2 + 685*S^4 - 252*S^6)/(6*S^3) + (Pi^2*(-93 + 1533*S^2 + 1906*S^4 + 175*S^6 - 57*S^8))/(18*S^3*(1 + S^2)) + (1568*S*HPL[{3, 1}, -S^2])/3 + 1040*S*HPL[{2, 1, 1}, -S^2] + (32*(2 + 27*S^2 + S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((-391*Pi^4*S)/54 + (-9 - 2111*S^2 - 2677*S^4 + 1017*S^6)/(24*S^3) + (Pi^2*(21 - 105*S^2 - 522*S^4 - 326*S^6 + 42*S^8))/(18*S^3*(1 + S^2)) + 44*S*HPL[{4}, -S^2] - (8*(-7 - 26*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (1624*S*HPL[{3, 1}, -S^2])/3 - 1120*S*HPL[{2, 1, 1}, -S^2] - (2*(-1 + 16*S^2 + 15*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-749*Pi^4*S)/135 - ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(6*S^3) + (Pi^2*(45 - 919*S^2 - 955*S^4 - 15*S^6))/(27*S^3) + ((-472*Pi^2*S)/9 + (4*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2}, -S^2] + (4*(-18 - 157*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 64*S*HPL[{4}, -S^2] + (20*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 400*S*HPL[{3, 1}, -S^2] - 800*S*HPL[{2, 1, 1}, -S^2] + (20*(4 - 35*S^2 + 51*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{0}, S^2]^3*((-821*Pi^4*S)/324 - (Pi^2*S*(1801 + 1914*S^2 + 39*S^4))/(108*(1 + S^2)) + (420 - 7617*S^2 - 8306*S^4 - 141*S^6)/(144*S*(1 + S^2)) + ((-92 - 409*S^2 - 187*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) - (65*S*HPL[{1}, -S^2]^4)/9 + ((-437*Pi^2*S)/54 + (9 - 94*S^2 - 569*S^4 - 6*S^6)/(18*S^3))*HPL[{2}, -S^2] - (163*S*HPL[{2}, -S^2]^2)/18 + HPL[{1}, -S^2]^2*((-79*Pi^2*S)/9 + (21 - 554*S^2 - 1088*S^4 - 574*S^6 - 13*S^8)/(18*S^3*(1 + S^2)) - (62*S*HPL[{2}, -S^2])/3) + ((-2 - 19*S^2 - 15*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (13*S*HPL[{4}, -S^2])/9 + ((76 + 143*S^2 + 5*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (344*S*HPL[{3, 1}, -S^2])/9 - (244*S*HPL[{2, 1, 1}, -S^2])/3 - (S*(238 + 215*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-721 - 3126*S^2 - 1457*S^4))/(108*S*(1 + S^2)) + (87 - 1243*S^2 - 2643*S^4 - 1441*S^6 - 48*S^8)/(36*S^3*(1 + S^2)) + ((-123 - 595*S^2 - 286*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - (4*S*HPL[{3}, -S^2])/3 + (124*S*HPL[{2, 1}, -S^2])/3 - (46*S*Zeta[3])/9)) + ((-844*Pi^2*S)/9 + (S*(-234 - 143*S^2 + 87*S^4))/(3*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^4*(-5471 - 27356*S^2 - 12897*S^4))/(1080*S*(1 + S^2)) - ((1 + S^2)*(-1039 + 9360*S^2 + 1039*S^4))/(24*S^3) + (Pi^2*(393 - 4355*S^2 - 4861*S^4 - 177*S^6))/(72*S^3) - (74*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(3*S) + (-58*Pi^2*S + (19 - 345*S^2 - 307*S^4 + 41*S^6)/(3*S^3))*HPL[{3}, -S^2] - (4*(47 + 221*S^2 + 102*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - 184*S*HPL[{5}, -S^2] + ((472*Pi^2*S)/3 - (4*(5 - 91*S^2 - 91*S^4 + 5*S^6))/S^3)*HPL[{2, 1}, -S^2] + (4*(128 + 767*S^2 + 189*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 496*S*HPL[{3, 2}, -S^2] + 1680*S*HPL[{4, 1}, -S^2] - (20*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - 1200*S*HPL[{3, 1, 1}, -S^2] + 2400*S*HPL[{2, 1, 1, 1}, -S^2] + ((-172*Pi^2*S)/3 + (4*(-2 + 25*S^2 + 15*S^4))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((6*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 - (2*Pi^2*(89 + 581*S^2 + 138*S^4))/(9*S*(1 + S^2)) - 248*S*HPL[{3}, -S^2] - 256*S*Zeta[3]) - 448*S*Zeta[5]) + HPL[{2}, -S^2]*((Pi^4*(-410 - 20114*S^2 - 11367*S^4))/(1080*S*(1 + S^2)) + (6 - 751*S^2 - 1911*S^4 + 6*S^6)/(6*S^3) + (Pi^2*(24 - 589*S^2 - 2977*S^4 - 2280*S^6 + 36*S^8))/(36*S^3*(1 + S^2)) + ((-152*Pi^2*S)/3 + (2*(64 - 79*S^2 + 18*S^4))/(3*S))*HPL[{3}, -S^2] + ((23 - 369*S^2)*HPL[{4}, -S^2])/(3*S) - 94*S*HPL[{5}, -S^2] + ((-388*Pi^2*S)/9 + (2*(-6 + 135*S^2 - 17*S^4 + 6*S^6))/S^3)*HPL[{2, 1}, -S^2] + (4*(-23 + 209*S^2)*HPL[{3, 1}, -S^2])/(3*S) + 520*S*HPL[{3, 2}, -S^2] + (4904*S*HPL[{4, 1}, -S^2])/3 - (16*(-4 + 87*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (1792*S*HPL[{2, 2, 1}, -S^2])/3 + 672*S*HPL[{3, 1, 1}, -S^2] - 1040*S*HPL[{2, 1, 1, 1}, -S^2] + ((-448*Pi^2*S)/9 + (-3 - 13*S^2 + 34*S^4 + 29*S^6 + 33*S^8)/(3*S^3*(1 + S^2)))*Zeta[3] - 352*S*Zeta[5]) + HPL[{0}, S^2]^2*(-(Pi^4*S*(26304 + 18661*S^2))/(2160*(1 + S^2)) + (63 - 700*S^2 + 2*S^4)/(4*S) + (Pi^2*(180 - 5537*S^2 - 5729*S^4 + 84*S^6))/(144*S*(1 + S^2)) - (5*(38 + 203*S^2 + 75*S^4)*HPL[{1}, -S^2]^4)/(18*S*(1 + S^2)) - 10*S*HPL[{1}, -S^2]^5 + ((-1 - 86*S^2 - 54*S^4)*HPL[{2}, -S^2]^2)/(2*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((-163*Pi^2*S)/9 + (45 - 923*S^2 - 905*S^4 + 15*S^6)/(18*S^3) - (172*S*HPL[{2}, -S^2])/3) + ((-10*Pi^2*S)/3 + (6 - 22*S^2 - 124*S^4 - 79*S^6 + 3*S^8)/(3*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-9 - 230*S^2 - 147*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - 23*S*HPL[{5}, -S^2] + ((49*Pi^2*S)/9 + (-24 + 380*S^2 + 485*S^4 + 51*S^6 - 6*S^8)/(3*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((23 + 662*S^2 + 381*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (80*S*HPL[{3, 2}, -S^2])/3 + (260*S*HPL[{4, 1}, -S^2])/3 - (4*(7 + 327*S^2 + 191*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{2, 2, 1}, -S^2])/3 - 56*S*HPL[{3, 1, 1}, -S^2] + (304*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-38*Pi^2*S)/3 + (2*S*(-44 - 42*S^2 + 3*S^4))/(3*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-481 - 2365*S^2 - 906*S^4))/(36*S*(1 + S^2)) + (99 - 1055*S^2 - 1113*S^4 + 9*S^6)/(12*S^3) + ((-161 - 1034*S^2 - 357*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) - 24*S*HPL[{3}, -S^2] + 172*S*HPL[{2, 1}, -S^2] - 22*S*Zeta[3]) + HPL[{2}, -S^2]*((Pi^2*(-26 - 1474*S^2 - 933*S^4))/(36*S*(1 + S^2)) + (6 - 265*S^2 - 1509*S^4 - 1172*S^6 + 18*S^8)/(12*S^3*(1 + S^2)) - 12*S*HPL[{3}, -S^2] + (2*S*HPL[{2, 1}, -S^2])/3 - (44*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-7643*Pi^4*S)/1080 + (318 - 2647*S^2 - 2950*S^4 - 17*S^6)/(24*S^3) + (Pi^2*(45 - 1117*S^2 - 2187*S^4 - 1071*S^6 + 14*S^8))/(36*S^3*(1 + S^2)) + ((-515*Pi^2*S)/18 + (30 - 450*S^2 - 1081*S^4 - 540*S^6 + 13*S^8)/(6*S^3*(1 + S^2)))*HPL[{2}, -S^2] - 31*S*HPL[{2}, -S^2]^2 + ((-11 - 144*S^2 - 61*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (74*S*HPL[{4}, -S^2])/3 + ((161 + 1034*S^2 + 357*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 172*S*HPL[{3, 1}, -S^2] - 344*S*HPL[{2, 1, 1}, -S^2] + ((-14 - 89*S^2 - 9*S^4)*Zeta[3])/(3*S*(1 + S^2))) - 78*S*Zeta[5]) + HPL[{1}, -S^2]*((-47329*Pi^6*S)/22680 - (2*(1 + S^2)*(-101 + 880*S^2 + 101*S^4))/(3*S^3) + (Pi^2*(645 - 5632*S^2 - 6589*S^4 - 344*S^6))/(72*S^3) + (Pi^4*(624 - 12677*S^2 - 26903*S^4 - 13411*S^6 + 35*S^8))/(1080*S^3*(1 + S^2)) + ((-31*Pi^2*S)/3 + (17 - 347*S^2 - 397*S^4 - 17*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 - (124*S*HPL[{2}, -S^2]^3)/3 + ((-218*Pi^2*S)/9 - (8*(-3 + 74*S^2 + 154*S^4 + 80*S^6))/(3*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (8*(41 + 203*S^2 + 93*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - 318*S*HPL[{6}, -S^2] + ((472*Pi^2*S)/3 - (8*(9 - 173*S^2 - 176*S^4 + 6*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] - (4*(-11 - 242*S^2 + 141*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (4*(-121 - 1168*S^2 + 213*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 368*S*HPL[{5, 1}, -S^2] + ((-944*Pi^2*S)/3 + (8*(5 - 91*S^2 - 91*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (592*(1 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(92 + 453*S^2 + 211*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - 992*S*HPL[{3, 2, 1}, -S^2] - 3360*S*HPL[{4, 1, 1}, -S^2] + (40*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 2400*S*HPL[{3, 1, 1, 1}, -S^2] - 4800*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((2*Pi^2*(1 - 44*S^2 + 41*S^4))/(3*S*(1 + S^2)) + (3 + 135*S^2 + 409*S^4 + 213*S^6)/(6*S^3))*Zeta[3] + HPL[{3}, -S^2]*((Pi^2*(-65 - 615*S^2 - 28*S^4))/(9*S*(1 + S^2)) + (2*(12 - 215*S^2 - 181*S^4 + 42*S^6))/(3*S^3) + 496*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-12*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 + (4*Pi^2*(89 + 581*S^2 + 138*S^4))/(9*S*(1 + S^2)) + 512*S*Zeta[3]) + HPL[{2}, -S^2]*((-2779*Pi^4*S)/180 + ((1 + S^2)*(301 - 3818*S^2 + 301*S^4))/(12*S^3) + (Pi^2*(60 - 966*S^2 - 2173*S^4 - 1056*S^6 + 43*S^8))/(18*S^3*(1 + S^2)) + (2*(-9 - 242*S^2 + 139*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (296*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-17 - 128*S^2 + 81*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (2*(21 - 50*S^2 + 153*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{0}, S^2]*((-43007*Pi^6*S)/22680 + (1401 - 14295*S^2 - 1616*S^4)/(24*S) - (Pi^4*S*(39550 + 41825*S^2 + 1191*S^4))/(2160*(1 + S^2)) + (Pi^2*(870 - 13995*S^2 - 15788*S^4 - 795*S^6))/(144*S*(1 + S^2)) + ((-65*Pi^2*S)/9 - (5*(-3 + 61*S^2 + 67*S^4 + 3*S^6))/(6*S^3))*HPL[{1}, -S^2]^4 - (28*(1 + 3*S^2)*HPL[{1}, -S^2]^5)/(3*S) + ((-73*Pi^2*S)/9 + (2 + 2*S^2 - 437*S^4 - 15*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 + (38*S*HPL[{2}, -S^2]^3)/9 + (4*S*HPL[{3}, -S^2]^2)/3 + ((-25*Pi^2*S)/9 + (9 - 187*S^2 - 616*S^4 - 447*S^6 - 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-35 - 207*S^2 - 194*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (34*S*HPL[{6}, -S^2])/3 - (68*S*HPL[{2, 1}, -S^2]^2)/3 + ((308*Pi^2*S)/9 + (-21 + 323*S^2 + 1071*S^4 + 33*S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + ((-65 + 267*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2*(-43 + 386*S^2 + 441*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (14*S*HPL[{4, 2}, -S^2])/3 + 20*S*HPL[{5, 1}, -S^2] + ((-224*Pi^2*S)/3 - (2*(-15 + 266*S^2 + 1074*S^4 + 45*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (8*(-83 + 41*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(-511 - 410*S^2 + 95*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (16*S*HPL[{3, 1, 2}, -S^2])/3 + (320*S*HPL[{3, 2, 1}, -S^2])/3 + 272*S*HPL[{4, 1, 1}, -S^2] + (40*(37 + 12*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - 96*S*HPL[{3, 1, 1, 1}, -S^2] + 160*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*S*(161 + 148*S^2))/(9*(1 + S^2)) + (-6 - 457*S^2 - 432*S^4 + 3*S^6)/(6*S*(1 + S^2)))*Zeta[3] + 12*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-25 - 272*S^2 - 241*S^4))/(18*S*(1 + S^2)) + (105 - 342*S^2 - 1326*S^4 - 902*S^6 + 9*S^8)/(12*S^3*(1 + S^2)) - 24*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((Pi^2*(413 + 674*S^2 + 75*S^4))/(9*S*(1 + S^2)) + (-177 + 2115*S^2 + 821*S^4 + 33*S^6)/(6*S^3) - (16*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((Pi^2*(-162 - 689*S^2 - 397*S^4))/(9*S*(1 + S^2)) - (5*(1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(18*S^3) - (470*(1 + 3*S^2)*HPL[{2}, -S^2])/(9*S) + (8*S*HPL[{3}, -S^2])/3 - (8*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-3703*Pi^4*S)/540 + (58 - 1226*S^2 - 3521*S^4 - 261*S^6)/(12*S^3) + (Pi^2*(33 - 454*S^2 - 2212*S^4 - 57*S^6))/(36*S^3) + ((37 - 135*S^2)*HPL[{3}, -S^2])/(3*S) - (26*S*HPL[{4}, -S^2])/3 - (4*(-83 + 41*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (80*S*HPL[{3, 1}, -S^2])/3 + (136*S*HPL[{2, 1, 1}, -S^2])/3 - (4*(1 + 45*S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-1313*Pi^4*S)/180 - ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(4*S^3) + (Pi^2*(87 - 1978*S^2 - 4096*S^4 - 2198*S^6 - 71*S^8))/(36*S^3*(1 + S^2)) + ((-62*Pi^2*S)/3 - (2*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(3*S^3))*HPL[{2}, -S^2] - (2*(14 + 55*S^2 + 43*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + 8*S*HPL[{4}, -S^2] + (470*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) - 8*S*HPL[{3, 1}, -S^2] - (2*(32 + 131*S^2 + 93*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (2*S*(310 + 299*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(-7949 - 34087*S^2 - 18260*S^4))/(1080*S*(1 + S^2)) - ((1 + S^2)*(-1039 + 9360*S^2 + 1039*S^4))/(24*S^3) + (Pi^2*(369 - 4536*S^2 - 10166*S^4 - 5712*S^6 - 291*S^8))/(72*S^3*(1 + S^2)) + ((Pi^2*(-481 - 2130*S^2 - 1277*S^4))/(18*S*(1 + S^2)) + (105 - 1467*S^2 - 1741*S^4 - 105*S^6)/(6*S^3))*HPL[{2}, -S^2] - (74*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-2*Pi^2*S)/3 - (2*(-11 + 117*S^2 + 138*S^4 + 2*S^6))/(3*S^3))*HPL[{3}, -S^2] + ((-89 - 296*S^2 - 231*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (44*S*HPL[{5}, -S^2])/3 + ((124*Pi^2*S)/3 + (4*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (4*(116 + 461*S^2 + 351*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - 16*S*HPL[{4, 1}, -S^2] - (940*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + 16*S*HPL[{3, 1, 1}, -S^2] + ((-52*Pi^2*S)/9 + (-3 - 103*S^2 - 131*S^4 - 15*S^6)/(3*S^3))*Zeta[3] - (44*S*Zeta[5])/3)) - 744*S*Zeta[7]) + HPL[{1}, -S^2]^2*((Pi^6*(-50539 - 266051*S^2 - 120854*S^4))/(90720*S*(1 + S^2)) - (5*(1 + S^2)*(-663 + 6272*S^2 + 663*S^4))/(64*S^3) + (Pi^2*(1949 - 15390*S^2 - 18525*S^4 - 1250*S^6))/(288*S^3) + (Pi^4*(5438 - 55601*S^2 - 128685*S^4 - 67847*S^6 - 1161*S^8))/(8640*S^3*(1 + S^2)) + ((-83 - 538*S^2 - 83*S^4)*HPL[{2}, -S^2]^3)/(18*S*(1 + S^2)) + ((19 + 73*S^2)*HPL[{3}, -S^2]^2)/(6*S) + ((-196*Pi^2*S)/9 + (69 - 1160*S^2 - 2536*S^4 - 1332*S^6 - 9*S^8)/(6*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-703 - 3479*S^2 - 1822*S^4)*HPL[{6}, -S^2])/(6*S*(1 + S^2)) - 358*S*HPL[{7}, -S^2] + (148*(1 + 3*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((394*Pi^2*S)/9 + (-1 + 32*S^2 + 8*S^4 - 52*S^6 - 35*S^8)/(3*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((1400*Pi^2*S)/9 + (-33 + 688*S^2 + 1292*S^4 + 484*S^6 - 111*S^8)/(3*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((79 + 173*S^2)*HPL[{4, 2}, -S^2])/(6*S) - 22*S*HPL[{4, 3}, -S^2] + (2*(241 + 1072*S^2 + 555*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - 52*S*HPL[{5, 2}, -S^2] + 278*S*HPL[{6, 1}, -S^2] + ((-124*Pi^2*S)/3 - (2*(-17 + 347*S^2 + 397*S^4 + 17*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + (-240*Pi^2*S - (4*(-35 + 693*S^2 + 749*S^4 + 5*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] + (8*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (4*(85 + 538*S^2 + 81*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - 496*S*HPL[{3, 2, 2}, -S^2] - 1488*S*HPL[{3, 3, 1}, -S^2] - (4*(343 + 2056*S^2 + 453*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 1488*S*HPL[{4, 1, 2}, -S^2] - 4464*S*HPL[{4, 2, 1}, -S^2] - 9296*S*HPL[{5, 1, 1}, -S^2] + ((944*Pi^2*S)/3 - (8*(5 - 91*S^2 - 91*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] + 992*S*HPL[{2, 2, 2, 1}, -S^2] + (8*(128 + 767*S^2 + 189*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 1984*S*HPL[{3, 1, 1, 2}, -S^2] - 1984*S*HPL[{3, 1, 2, 1}, -S^2] - 4960*S*HPL[{3, 2, 1, 1}, -S^2] - 14496*S*HPL[{4, 1, 1, 1}, -S^2] - (40*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 2400*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 4800*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-859*Pi^4*S)/180 + (-9 + 338*S^2 + 689*S^4 + 310*S^6)/(12*S^3) + (Pi^2*(3 - 166*S^2 - 192*S^4 + 38*S^6 + 69*S^8))/(36*S^3*(1 + S^2)))*Zeta[3] + ((-25 + 11*S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1, 1}, -S^2]*((12*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 - (4*Pi^2*(89 + 581*S^2 + 138*S^4))/(9*S*(1 + S^2)) - 512*S*Zeta[3]) + HPL[{2}, -S^2]^2*((Pi^2*(-147 - 691*S^2 - 358*S^4))/(36*S*(1 + S^2)) - ((1 + S^2)*(-23 + 324*S^2 + 23*S^4))/(8*S^3) - 62*S*HPL[{3}, -S^2] + 124*S*HPL[{2, 1}, -S^2] - 62*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(-227 - 1182*S^2 - 519*S^4))/(36*S*(1 + S^2)) + (71 - 3495*S^2 - 3695*S^4 - S^6)/(24*S^3) - (44*S*Zeta[3])/3) + HPL[{3, 1}, -S^2]*((2*Pi^2*(106 + 653*S^2 + 193*S^4))/(9*S*(1 + S^2)) + (-117 + 1763*S^2 + 1765*S^4 - 99*S^6)/(6*S^3) + 256*S*Zeta[3]) + HPL[{3}, -S^2]*((-1219*Pi^4*S)/270 + (105 - 2721*S^2 - 2393*S^4 + 497*S^6)/(24*S^3) + (Pi^2*(38 - 491*S^2 - 1163*S^4 - 529*S^6 + 49*S^8))/(36*S^3*(1 + S^2)) + 18*S*HPL[{4}, -S^2] - (2*(-9 - 242*S^2 + 139*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 248*S*HPL[{3, 1}, -S^2] - 496*S*HPL[{2, 1, 1}, -S^2] - (2*(22 + 37*S^2 + 9*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((2779*Pi^4*S)/180 - ((1 + S^2)*(301 - 3818*S^2 + 301*S^4))/(12*S^3) + (Pi^2*(-60 + 966*S^2 + 2173*S^4 + 1056*S^6 - 43*S^8))/(18*S^3*(1 + S^2)) - (4*(-17 - 128*S^2 + 81*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-455*Pi^2*S)/9 + (3 - 72*S^2 - 68*S^4 + 68*S^6 + 57*S^8)/(3*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-1489 - 9837*S^2 - 2790*S^4))/(720*S*(1 + S^2)) + ((1 + S^2)*(233 - 3618*S^2 + 233*S^4))/(16*S^3) + (Pi^2*(143 - 1586*S^2 - 3632*S^4 - 1742*S^6 + 97*S^8))/(48*S^3*(1 + S^2)) + ((-197*Pi^2*S)/9 + (3 - 35*S^2 + 15*S^4 + 37*S^6)/(6*S^3))*HPL[{3}, -S^2] - (67*(1 + 3*S^2)*HPL[{4}, -S^2])/(6*S) - 32*S*HPL[{5}, -S^2] + ((62*Pi^2*S)/3 + (-17 + 347*S^2 + 397*S^4 + 17*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + (148*(1 + 3*S^2)*HPL[{3, 1}, -S^2])/(3*S) + 248*S*HPL[{3, 2}, -S^2] + 744*S*HPL[{4, 1}, -S^2] - (296*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - 496*S*HPL[{2, 2, 1}, -S^2] + 992*S*HPL[{3, 1, 1}, -S^2] + ((-215*Pi^2*S)/9 + (-66 - 11*S^2 + 24*S^4 + 17*S^6)/(3*S*(1 + S^2)))*Zeta[3] - 182*S*Zeta[5]) - 462*S*Zeta[7]) + HPL[{0}, S^2]^2*(-(Pi^6*S*(229336 + 133873*S^2))/(181440*(1 + S^2)) + (1853 - 16925*S^2 - 266*S^4)/(96*S) + (Pi^4*(832 - 42729*S^2 - 46633*S^4 - 1888*S^6))/(5760*S*(1 + S^2)) + (Pi^2*(1554 - 18280*S^2 - 19873*S^4 + 153*S^6))/(576*S*(1 + S^2)) + ((-38 - 203*S^2 - 75*S^4)*HPL[{1}, -S^2]^6)/(54*S*(1 + S^2)) - (10*S*HPL[{1}, -S^2]^7)/21 + ((-7 - 250*S^2 - 137*S^4)*HPL[{2}, -S^2]^3)/(36*S*(1 + S^2)) + HPL[{1}, -S^2]^5*((-163*Pi^2*S)/90 + (45 - 923*S^2 - 905*S^4 + 15*S^6)/(180*S^3) - (86*S*HPL[{2}, -S^2])/15) + ((13 + 67*S^2 + 43*S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((-23*Pi^2*S)/4 + (60 - 212*S^2 - 952*S^4 - 683*S^6 - 39*S^8)/(12*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-40 - 354*S^2 - 191*S^4)*HPL[{6}, -S^2])/(4*S*(1 + S^2)) - (269*S*HPL[{7}, -S^2])/3 + ((1 + 86*S^2 + 54*S^4)*HPL[{2, 1}, -S^2]^2)/(S*(1 + S^2)) + ((20*Pi^2*S)/9 + (3 - 123*S^2 + 98*S^4 + 184*S^6 - 12*S^8)/(12*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((199*Pi^2*S)/18 + (-33 - 65*S^2 + 1076*S^4 + 949*S^6 - 39*S^8)/(12*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-5 + 67*S^2)*HPL[{4, 2}, -S^2])/(12*S) + (74*S*HPL[{4, 3}, -S^2])/3 + ((38 + 599*S^2 + 401*S^4)*HPL[{5, 1}, -S^2])/(6*S*(1 + S^2)) + (469*S*HPL[{5, 2}, -S^2])/6 + 231*S*HPL[{6, 1}, -S^2] + ((-7*Pi^2*S)/3 + (33 - 756*S^2 + 76*S^4 - 3*S^6)/(6*S^3))*HPL[{2, 2, 1}, -S^2] + ((-41*Pi^2*S)/3 + (123 - 2257*S^2 - 2536*S^4 - 97*S^6 + 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + ((7 - 17*S^2)*HPL[{3, 1, 2}, -S^2])/(6*S) + ((-21 - 1010*S^2 - 565*S^4)*HPL[{3, 2, 1}, -S^2])/(6*S*(1 + S^2)) - (70*S*HPL[{3, 2, 2}, -S^2])/3 - 52*S*HPL[{3, 3, 1}, -S^2] + ((-51 - 1730*S^2 - 969*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (167*S*HPL[{4, 1, 2}, -S^2])/3 - (419*S*HPL[{4, 2, 1}, -S^2])/3 - 298*S*HPL[{5, 1, 1}, -S^2] + ((98*Pi^2*S)/9 - (2*(24 - 380*S^2 - 485*S^4 - 51*S^6 + 6*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (184*S*HPL[{2, 2, 2, 1}, -S^2])/3 + (2*(23 + 662*S^2 + 381*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (392*S*HPL[{3, 1, 1, 2}, -S^2])/3 - (392*S*HPL[{3, 1, 2, 1}, -S^2])/3 - (944*S*HPL[{3, 2, 1, 1}, -S^2])/3 - (2792*S*HPL[{4, 1, 1, 1}, -S^2])/3 - (8*(7 + 327*S^2 + 191*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (8*S*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 8*S*HPL[{2, 2, 1, 1, 1}, -S^2] - (272*S*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + (608*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + ((-2111*Pi^4*S)/360 + (Pi^2*S*(-343 - 345*S^2 + 24*S^4))/(18*(1 + S^2)) + (30 - 1900*S^2 - 2261*S^4 - 171*S^6)/(48*S*(1 + S^2)))*Zeta[3] + (S*(2 + 19*S^2)*Zeta[3]^2)/(2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-26 - 1474*S^2 - 933*S^4))/(18*S*(1 + S^2)) + (6 - 265*S^2 - 1509*S^4 - 1172*S^6 + 18*S^8)/(6*S^3*(1 + S^2)) - (88*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(-9 - 566*S^2 - 360*S^4))/(72*S*(1 + S^2)) + (63 - 1019*S^2 + 12*S^4)/(48*S) - 3*S*HPL[{3}, -S^2] + (23*S*HPL[{2, 1}, -S^2])/3 - (43*S*Zeta[3])/6) + HPL[{1}, -S^2]^4*((Pi^2*(-481 - 2365*S^2 - 906*S^4))/(216*S*(1 + S^2)) + (99 - 1055*S^2 - 1113*S^4 + 9*S^6)/(72*S^3) + ((-161 - 1034*S^2 - 357*S^4)*HPL[{2}, -S^2])/(36*S*(1 + S^2)) - 4*S*HPL[{3}, -S^2] + (86*S*HPL[{2, 1}, -S^2])/3 - (11*S*Zeta[3])/3) + HPL[{4}, -S^2]*((Pi^2*(15 - 434*S^2 - 243*S^4))/(72*S*(1 + S^2)) + (-18 - 861*S^2 - 2702*S^4 - 1773*S^6 - 42*S^8)/(48*S^3*(1 + S^2)) + (25*S*HPL[{2, 1}, -S^2])/3 + 12*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((Pi^2*(29 + 1422*S^2 + 861*S^4))/(36*S*(1 + S^2)) + (-5 + 219*S^2 + 1170*S^4 + 901*S^6 - 13*S^8)/(8*S^3*(1 + S^2)) + (38*S*Zeta[3])/3) + HPL[{3}, -S^2]*((-17*Pi^4*S)/40 + (Pi^2*(21 - 41*S^2 - 458*S^4 - 314*S^6 + 6*S^8))/(72*S^3*(1 + S^2)) + (183 - 1018*S^2 - 4088*S^4 - 2370*S^6 + 197*S^8)/(96*S^3*(1 + S^2)) - (32*S*HPL[{4}, -S^2])/3 + ((-5 - 100*S^2 - 117*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) + 2*S*HPL[{3, 1}, -S^2] - 24*S*HPL[{2, 1, 1}, -S^2] + ((1 + S^2 - 11*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-7643*Pi^4*S)/3240 + (318 - 2647*S^2 - 2950*S^4 - 17*S^6)/(72*S^3) + (Pi^2*(45 - 1117*S^2 - 2187*S^4 - 1071*S^6 + 14*S^8))/(108*S^3*(1 + S^2)) + ((-515*Pi^2*S)/54 + (30 - 450*S^2 - 1081*S^4 - 540*S^6 + 13*S^8)/(18*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (31*S*HPL[{2}, -S^2]^2)/3 + ((-11 - 144*S^2 - 61*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (74*S*HPL[{4}, -S^2])/9 + ((161 + 1034*S^2 + 357*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (172*S*HPL[{3, 1}, -S^2])/3 - (344*S*HPL[{2, 1, 1}, -S^2])/3 + ((-14 - 89*S^2 - 9*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((46*Pi^4*S)/135 + (-300 + 2144*S^2 + 3333*S^4 + 751*S^6 - 42*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-93 + 1769*S^2 + 2036*S^4 + 124*S^6 - 6*S^8))/(72*S^3*(1 + S^2)) - (20*S*HPL[{3, 1}, -S^2])/3 - (4*S*HPL[{2, 1, 1}, -S^2])/3 + ((29 + 112*S^2 + 60*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-461*Pi^2*S)/9 + (2*S*(-171 - 169*S^2 + 9*S^4))/(3*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^4*(-8236 - 39487*S^2 - 15965*S^4))/(4320*S*(1 + S^2)) + (910 - 7069*S^2 - 8126*S^4 - 211*S^6)/(96*S^3) + (Pi^2*(393 - 4749*S^2 - 10155*S^4 - 5203*S^6 + 2*S^8))/(288*S^3*(1 + S^2)) + ((-73 - 395*S^2 - 136*S^4)*HPL[{2}, -S^2]^2)/(12*S*(1 + S^2)) + ((-23*Pi^2*S)/6 + (19 - 165*S^2 - 511*S^4 - 263*S^6 + 8*S^8)/(12*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-39 - 298*S^2 - 111*S^4)*HPL[{4}, -S^2])/(12*S*(1 + S^2)) - (58*S*HPL[{5}, -S^2])/3 + ((515*Pi^2*S)/18 + (-30 + 450*S^2 + 1081*S^4 + 540*S^6 - 13*S^8)/(6*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((84 + 539*S^2 + 197*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (22*S*HPL[{3, 2}, -S^2])/3 + (140*S*HPL[{4, 1}, -S^2])/3 + ((-161 - 1034*S^2 - 357*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 124*S*HPL[{2, 2, 1}, -S^2] - 420*S*HPL[{3, 1, 1}, -S^2] + 344*S*HPL[{2, 1, 1, 1}, -S^2] + ((-109*Pi^2*S)/18 + (3 - 158*S^2 - 284*S^4 - 122*S^6 + 9*S^8)/(12*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-389 - 2237*S^2 - 818*S^4))/(72*S*(1 + S^2)) + (71 - 770*S^2 - 1856*S^4 - 926*S^6 + 25*S^8)/(16*S^3*(1 + S^2)) - (11*S*HPL[{3}, -S^2])/3 + 62*S*HPL[{2, 1}, -S^2] - (23*S*Zeta[3])/3) - (119*S*Zeta[5])/3) + HPL[{2}, -S^2]*((Pi^4*(-218 - 25518*S^2 - 17727*S^4))/(4320*S*(1 + S^2)) + (-3 - 1220*S^2 - 5412*S^4 - 3991*S^6 + 12*S^8)/(48*S^3*(1 + S^2)) + (Pi^2*(24 - 403*S^2 - 3107*S^4 - 2496*S^6 + 72*S^8))/(144*S^3*(1 + S^2)) + (-(Pi^2*S) + (35 - 29*S^2 - 53*S^4 + 3*S^6)/(6*S*(1 + S^2)))*HPL[{3}, -S^2] + ((-43 - 294*S^2 - 207*S^4)*HPL[{4}, -S^2])/(12*S*(1 + S^2)) + (35*S*HPL[{5}, -S^2])/6 + ((7*Pi^2*S)/6 + (-33 + 756*S^2 - 76*S^4 + 3*S^6)/(12*S^3))*HPL[{2, 1}, -S^2] + ((19 + 600*S^2 + 391*S^4)*HPL[{3, 1}, -S^2])/(6*S*(1 + S^2)) + 12*S*HPL[{3, 2}, -S^2] + (83*S*HPL[{4, 1}, -S^2])/3 - (2*(1 + 86*S^2 + 54*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (92*S*HPL[{2, 2, 1}, -S^2])/3 + 68*S*HPL[{3, 1, 1}, -S^2] + (4*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-37*Pi^2*S)/18 + (-3 - 17*S^2 - 136*S^4 - 118*S^6)/(12*S^3*(1 + S^2)))*Zeta[3] - (37*S*Zeta[5])/3) + HPL[{1}, -S^2]*((-10607*Pi^6*S)/10080 - ((1 + S^2)*(-616 + 5475*S^2 + 282*S^4))/(48*S^3) + (Pi^2*(645 - 5742*S^2 - 13326*S^4 - 7214*S^6 - 179*S^8))/(288*S^3*(1 + S^2)) + (Pi^4*(624 - 23015*S^2 - 44065*S^4 - 21113*S^6 + 561*S^8))/(4320*S^3*(1 + S^2)) + ((-197*Pi^2*S)/36 + (17 - 355*S^2 - 369*S^4 + 3*S^6)/(24*S^3))*HPL[{2}, -S^2]^2 - (53*S*HPL[{2}, -S^2]^3)/9 + (11*S*HPL[{3}, -S^2]^2)/3 + ((-103*Pi^2*S)/18 + (6 - 65*S^2 - 177*S^4 - 99*S^6 + S^8)/(3*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(8 + 68*S^2 + 31*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (123*S*HPL[{6}, -S^2])/2 + 62*S*HPL[{2, 1}, -S^2]^2 + ((266*Pi^2*S)/9 + (-36 + 503*S^2 + 1235*S^4 + 629*S^6 - 11*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-5 + 21*S^2 + 4*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + ((3 + 424*S^2 + 141*S^4)*HPL[{4, 1}, -S^2])/(6*S*(1 + S^2)) + (160*S*HPL[{5, 1}, -S^2])/3 + ((-515*Pi^2*S)/9 + (30 - 450*S^2 - 1081*S^4 - 540*S^6 + 13*S^8)/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (2*(73 + 395*S^2 + 136*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (2*(230 + 1329*S^2 + 469*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (424*S*HPL[{3, 2, 1}, -S^2])/3 - (1420*S*HPL[{4, 1, 1}, -S^2])/3 + (2*(161 + 1034*S^2 + 357*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 344*S*HPL[{3, 1, 1, 1}, -S^2] - 688*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(-123 - 447*S^2 - 106*S^4))/(36*S*(1 + S^2)) + (21 - 406*S^2 - 321*S^4 - 30*S^6)/(24*S^3))*Zeta[3] - 17*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-5 - 255*S^2 - 112*S^4))/(36*S*(1 + S^2)) + (24 - 269*S^2 - 737*S^4 - 379*S^6 + 17*S^8)/(12*S^3*(1 + S^2)) + (22*S*HPL[{2, 1}, -S^2])/3 + (22*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((Pi^2*(389 + 2237*S^2 + 818*S^4))/(36*S*(1 + S^2)) + (-71 + 770*S^2 + 1856*S^4 + 926*S^6 - 25*S^8)/(8*S^3*(1 + S^2)) + (46*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-7573*Pi^4*S)/2160 + (Pi^2*(60 - 1004*S^2 - 2317*S^4 - 1190*S^6 + 19*S^8))/(72*S^3*(1 + S^2)) + (155 - 1477*S^2 - 3631*S^4 - 1859*S^6 + 44*S^8)/(24*S^3*(1 + S^2)) + ((6 - 21*S^2 - 5*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) - (22*S*HPL[{4}, -S^2])/3 + ((73 + 395*S^2 + 136*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (190*S*HPL[{3, 1}, -S^2])/3 - 124*S*HPL[{2, 1, 1}, -S^2] + ((-33 - 165*S^2 - 86*S^4)*Zeta[3])/(6*S*(1 + S^2))) + ((-42 - 227*S^2 + 53*S^4)*Zeta[5])/(6*S*(1 + S^2))) - 372*S*Zeta[7]) + HPL[{2}, -S^2]*((Pi^6*(-126 - 31744*S^2 - 20593*S^4))/(15120*S*(1 + S^2)) - ((1 + S^2)*(133 + 7403*S^2 + 133*S^4))/(24*S^3) + (Pi^2*(9 - 2710*S^2 - 10736*S^4 - 7801*S^6 + 24*S^8))/(144*S^3*(1 + S^2)) + (Pi^4*(102 - 1710*S^2 - 10369*S^4 - 7986*S^6 + 195*S^8))/(1080*S^3*(1 + S^2)) + ((44 + 239*S^2 + 165*S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((-53*Pi^2*S)/9 + (3 + 293*S^2 - 54*S^4 - 400*S^6 + 24*S^8)/(6*S^3*(1 + S^2)))*HPL[{5}, -S^2] - (2*(-43 + 368*S^2 + 336*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) - (172*S*HPL[{7}, -S^2])/3 + (2*(19 + 342*S^2 + 137*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((142*Pi^2*S)/3 + (-3 + 46*S^2 + 102*S^4 - 27*S^6)/(3*S^3))*HPL[{3, 2}, -S^2] + ((1309*Pi^2*S)/9 + (-15 - 314*S^2 + 922*S^4 - 189*S^6)/(6*S^3))*HPL[{4, 1}, -S^2] + ((3 + 42*S^2 + 35*S^4)*HPL[{4, 2}, -S^2])/(S*(1 + S^2)) - (332*S*HPL[{4, 3}, -S^2])/3 + ((-25 + 313*S^2 + 302*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) - (928*S*HPL[{5, 2}, -S^2])/3 - 506*S*HPL[{6, 1}, -S^2] + (-60*Pi^2*S + (2*(15 - 346*S^2 - 88*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + ((236*Pi^2*S)/3 - (2*(45 - 1166*S^2 - 106*S^4 + 9*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] - (7*(1 + 3*S^2)*HPL[{3, 1, 2}, -S^2])/S + ((27 - 607*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (1490*S*HPL[{3, 2, 2}, -S^2])/3 - 1576*S*HPL[{3, 3, 1}, -S^2] - (10*(-19 + 237*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (4766*S*HPL[{4, 1, 2}, -S^2])/3 - (14510*S*HPL[{4, 2, 1}, -S^2])/3 - 9932*S*HPL[{5, 1, 1}, -S^2] + ((-776*Pi^2*S)/9 + (4*(-6 + 135*S^2 - 17*S^4 + 6*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] - (1328*S*HPL[{2, 2, 2, 1}, -S^2])/3 + (8*(205 + 4290*S^2 + 1853*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 288*S*HPL[{3, 1, 1, 2}, -S^2] - 288*S*HPL[{3, 1, 2, 1}, -S^2] - 1616*S*HPL[{3, 2, 1, 1}, -S^2] - (14096*S*HPL[{4, 1, 1, 1}, -S^2])/3 - (32*(-4 + 87*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (3584*S*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 3584*S*HPL[{2, 2, 1, 1, 1}, -S^2] - (24640*S*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - 2080*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-1807*Pi^4*S)/540 + (Pi^2*(-6 - 30*S^2 - 102*S^4 - 89*S^6 + 33*S^8))/(36*S^3*(1 + S^2)) + (-48 - 233*S^2 + 19*S^4 + 318*S^6 + 210*S^8)/(12*S^3*(1 + S^2)))*Zeta[3] + ((-6 - 24*S^2 - 7*S^4)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-2*Pi^2*(-5 + 424*S^2 + 336*S^4))/(9*S*(1 + S^2)) + (-12 + 71*S^2 - 1071*S^4 + 12*S^6)/(3*S^3) - (1568*S*Zeta[3])/3) + HPL[{4}, -S^2]*((Pi^2*(-5 - 160*S^2 - 144*S^4))/(9*S*(1 + S^2)) + (15 + 463*S^2 - 565*S^4 + 63*S^6)/(12*S^3) + (130*S*HPL[{2, 1}, -S^2])/3 - (118*S*Zeta[3])/3) + HPL[{3, 1}, -S^2]*((Pi^2*(-27 + 972*S^2 + 809*S^4))/(18*S*(1 + S^2)) + (-15 - 451*S^2 + 2425*S^4 - 63*S^6)/(12*S^3) + 272*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-1327*Pi^4*S)/540 + (Pi^2*(-69 + 1566*S^2 - 178*S^4 + 39*S^6))/(36*S^3) + (-258 + 2379*S^2 + 77*S^4 + 258*S^6)/(12*S^3) - (896*S*HPL[{3, 1}, -S^2])/3 - (1792*S*HPL[{2, 1, 1}, -S^2])/3 - (4*(-11 - 92*S^2 + 12*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((-877*Pi^4*S)/270 + (Pi^2*(99 - 44*S^2 - 114*S^4 + 21*S^6))/(18*S*(1 + S^2)) + (-1 + 486*S^2 + 728*S^4 + 564*S^6 + 515*S^8)/(24*S^3*(1 + S^2)) + (182*S*HPL[{4}, -S^2])/3 + ((121 + 680*S^2 + 187*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 288*S*HPL[{3, 1}, -S^2] - 520*S*HPL[{2, 1, 1}, -S^2] + ((19 + 80*S^2 + 31*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-301*Pi^2*S)/9 + (-12 - 28*S^2 - 82*S^4 - 83*S^6 + 51*S^8)/(6*S^3*(1 + S^2)))*Zeta[5] - 292*S*Zeta[7]) + HPL[{1}, -S^2]*((-13367*Pi^8*S)/42525 - (Pi^2*(1 + S^2)*(-1424 + 12515*S^2 + 1090*S^4))/(144*S^3) - (5*(1 + S^2)*(-3299 + 37632*S^2 + 3299*S^4))/(192*S^3) + (Pi^4*(8966 - 67671*S^2 - 169637*S^4 - 95005*S^6 - 3637*S^8))/(8640*S^3*(1 + S^2)) + (Pi^6*(1274 - 33551*S^2 - 71154*S^4 - 34347*S^6 + 1023*S^8))/(22680*S^3*(1 + S^2)) + ((-146*Pi^2*S)/27 + (5 - 103*S^2 - 103*S^4 + 5*S^6)/(9*S^3))*HPL[{2}, -S^2]^3 + ((11*Pi^2*S)/9 + (-2 + 47*S^2 + 92*S^4 + 39*S^6)/(3*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 - 34*S*HPL[{4}, -S^2]^2 + (-47*Pi^2*S - (2*(-51 + 855*S^2 + 1849*S^4 + 949*S^6 + 11*S^8))/(3*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((-1314 - 5455*S^2 - 3067*S^4)*HPL[{7}, -S^2])/(3*S*(1 + S^2)) - 1228*S*HPL[{8}, -S^2] + ((62*Pi^2*S)/3 + (-17 + 347*S^2 + 397*S^4 + 17*S^6)/(3*S^3))*HPL[{2, 1}, -S^2]^2 + (4*(1 + 15*S^2 + 18*S^4 + 9*S^6 + S^8)*HPL[{4, 2}, -S^2])/(3*S^3*(1 + S^2)) + ((-122 - 327*S^2 - 139*S^4)*HPL[{4, 3}, -S^2])/(3*S*(1 + S^2)) + ((436*Pi^2*S)/9 + (-61 + 1508*S^2 + 3064*S^4 + 1584*S^6 + 25*S^8)/(3*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] - (2*(56 + 147*S^2 + 65*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) - 8*S*HPL[{5, 3}, -S^2] + ((253 + 2339*S^2 + 1252*S^4)*HPL[{6, 1}, -S^2])/(3*S*(1 + S^2)) - 20*S*HPL[{6, 2}, -S^2] + 876*S*HPL[{7, 1}, -S^2] - (4*(1 - 6*S^4 + S^8)*HPL[{3, 1, 2}, -S^2])/(3*S^3*(1 + S^2)) + ((-1168*Pi^2*S)/9 + (4*(9 - 196*S^2 - 406*S^4 - 196*S^6 + 9*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((-121 - 1308*S^2 + 301*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S*(1 + S^2)) + (8*(-49 - 497*S^2 + 110*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S*(1 + S^2)) + 84*S*HPL[{3, 3, 2}, -S^2] + ((-3940*Pi^2*S)/9 + (8*(21 - 442*S^2 - 926*S^4 - 454*S^6 + 15*S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((-371 - 3892*S^2 + 943*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S*(1 + S^2)) - 140*S*HPL[{4, 1, 3}, -S^2] + ((-1247 - 12148*S^2 + 2491*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S*(1 + S^2)) + 104*S*HPL[{4, 2, 2}, -S^2] - 284*S*HPL[{4, 3, 1}, -S^2] + (4*(-821 - 7004*S^2 + 789*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 88*S*HPL[{5, 1, 2}, -S^2] - 1288*S*HPL[{5, 2, 1}, -S^2] - 4236*S*HPL[{6, 1, 1}, -S^2] + (8*(83 + 538*S^2 + 83*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + ((944*Pi^2*S)/3 - (16*(9 - 173*S^2 - 176*S^4 + 6*S^6))/(3*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (16*(119 + 686*S^2 + 195*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) - (16*(119 + 686*S^2 + 195*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(487 + 2986*S^2 + 639*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 992*S*HPL[{3, 2, 2, 1}, -S^2] + 2976*S*HPL[{3, 3, 1, 1}, -S^2] - (8*(1373 + 8516*S^2 + 1707*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 2976*S*HPL[{4, 1, 2, 1}, -S^2] + 8928*S*HPL[{4, 2, 1, 1}, -S^2] + 18592*S*HPL[{5, 1, 1, 1}, -S^2] + ((-1888*Pi^2*S)/3 + (16*(5 - 91*S^2 - 91*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1, 1}, -S^2] + (1184*(1 + 3*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) + (1184*(1 + 3*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + 1984*S*HPL[{2, 2, 1, 2, 1}, -S^2] + 5952*S*HPL[{2, 2, 2, 1, 1}, -S^2] + (16*(316 + 1009*S^2 + 1143*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 11904*S*HPL[{3, 1, 1, 1, 2}, -S^2] - 19840*S*HPL[{3, 1, 1, 2, 1}, -S^2] - 23808*S*HPL[{3, 1, 2, 1, 1}, -S^2] - 49600*S*HPL[{3, 2, 1, 1, 1}, -S^2] - 149568*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (80*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 4800*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 9600*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((-17*Pi^2*S)/3 + (-3 - 69*S^2 - 57*S^4 - 35*S^6)/(3*S^3*(1 + S^2)))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((-4*Pi^2*(253 + 1344*S^2 + 551*S^4))/(9*S*(1 + S^2)) + (255 - 3569*S^2 - 3847*S^4 - 39*S^6)/(3*S^3) - 1504*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*(-(((1 + S^2)*(-23 + 324*S^2 + 23*S^4))/S^3) - (2*Pi^2*(147 + 691*S^2 + 358*S^4))/(9*S*(1 + S^2)) - 496*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((-5*Pi^2*(-49 - 552*S^2 + 57*S^4))/(18*S*(1 + S^2)) + (-101 + 4257*S^2 + 2477*S^4 - 857*S^6)/(12*S^3) - (272*S*Zeta[3])/3) + HPL[{3, 2}, -S^2]*((Pi^2*(6 + 263*S^2 - 137*S^4))/(9*S*(1 + S^2)) + (1 + 109*S^2 - 189*S^4 - 137*S^6)/(6*S^3) - 40*S*Zeta[3]) + HPL[{5}, -S^2]*((-2*Pi^2*(49 + 271*S^2 + 124*S^4))/(9*S*(1 + S^2)) + (111 - 4290*S^2 - 3987*S^4 - 58*S^6)/(12*S^3) + 64*S*HPL[{2, 1}, -S^2] + 48*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((-24*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 + (8*Pi^2*(89 + 581*S^2 + 138*S^4))/(9*S*(1 + S^2)) + 1024*S*Zeta[3]) + HPL[{4}, -S^2]*((-389*Pi^4*S)/135 + (Pi^2*(12 - 225*S^2 - 260*S^4 + S^6))/(9*S^3) + (13 - 6100*S^2 - 12778*S^4 - 6564*S^6 - 91*S^8)/(24*S^3*(1 + S^2)) + (67*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) + 28*S*HPL[{3, 1}, -S^2] + ((-27 - 86*S^2 - 15*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((2126*Pi^4*S)/135 + (-327 + 4979*S^2 + 4967*S^4 - 275*S^6)/(12*S^3) + (Pi^2*(-72 + 1159*S^2 + 2631*S^4 + 1309*S^6 - 35*S^8))/(18*S^3*(1 + S^2)) - (4*(-21 - 136*S^2 + 77*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-2779*Pi^4*S)/90 + ((1 + S^2)*(301 - 3818*S^2 + 301*S^4))/(6*S^3) + (Pi^2*(60 - 966*S^2 - 2173*S^4 - 1056*S^6 + 43*S^8))/(9*S^3*(1 + S^2)) + (8*(-17 - 128*S^2 + 81*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]^2*((-907*Pi^4*S)/540 + (111 - 1129*S^2 - 1287*S^4 - 111*S^6)/(24*S^3) + (Pi^2*(17 - 351*S^2 - 383*S^4 - 7*S^6))/(36*S^3) + ((-23 - 195*S^2 + 14*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 16*S*HPL[{4}, -S^2] + ((83 + 538*S^2 + 83*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 124*S*HPL[{3, 1}, -S^2] - 248*S*HPL[{2, 1, 1}, -S^2] + ((1 - 99*S^2 + 86*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((Pi^2*(21 - 377*S^2 + 512*S^4))/(18*S*(1 + S^2)) + (48 + 41*S^2 + 192*S^4 + 319*S^6)/(12*S^3))*Zeta[5] + Zeta[3]*((Pi^4*(-221 - 1523*S^2 + 416*S^4))/(360*S*(1 + S^2)) + (Pi^2*(24 - 271*S^2 + 88*S^4 + 183*S^6))/(72*S^3) + (-129 + 1252*S^2 + 2273*S^4 + 828*S^6)/(24*S^3) - (332*S*Zeta[5])/3) + HPL[{3}, -S^2]*((Pi^4*(-221 - 3013*S^2 - 354*S^4))/(540*S*(1 + S^2)) + ((1 + S^2)*(33 - 1833*S^2 + 200*S^4))/(8*S^3) + (Pi^2*(48 - 675*S^2 - 1529*S^4 - 657*S^6 + 101*S^8))/(36*S^3*(1 + S^2)) + ((73 + 213*S^2 + 86*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + 80*S*HPL[{5}, -S^2] + ((394*Pi^2*S)/9 + (-3 + 35*S^2 - 15*S^4 - 37*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(-27 - 298*S^2 + 101*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - 40*S*HPL[{3, 2}, -S^2] + 28*S*HPL[{4, 1}, -S^2] + (4*(-9 - 242*S^2 + 139*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 496*S*HPL[{2, 2, 1}, -S^2] - 1488*S*HPL[{3, 1, 1}, -S^2] + 992*S*HPL[{2, 1, 1, 1}, -S^2] + ((16*Pi^2*S)/9 + (-3 - 43*S^2 + 27*S^4 + 7*S^6 - 4*S^8)/(3*S^3*(1 + S^2)))*Zeta[3] + 16*S*Zeta[5]) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(233 - 3618*S^2 + 233*S^4))/(8*S^3) + (Pi^4*(1489 + 9837*S^2 + 2790*S^4))/(360*S*(1 + S^2)) + (Pi^2*(-143 + 1586*S^2 + 3632*S^4 + 1742*S^6 - 97*S^8))/(24*S^3*(1 + S^2)) - (296*(1 + 3*S^2)*HPL[{3, 1}, -S^2])/(3*S) - 496*S*HPL[{3, 2}, -S^2] - 1488*S*HPL[{4, 1}, -S^2] - (592*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - 992*S*HPL[{2, 2, 1}, -S^2] - 1984*S*HPL[{3, 1, 1}, -S^2] + ((430*Pi^2*S)/9 - (2*(-66 - 11*S^2 + 24*S^4 + 17*S^6))/(3*S*(1 + S^2)))*Zeta[3] + 364*S*Zeta[5]) + HPL[{2}, -S^2]*((-35*Pi^6*S)/24 + ((1 + S^2)*(167 - 4115*S^2 + 167*S^4))/(12*S^3) + (Pi^4*(416 - 6327*S^2 - 14839*S^4 - 7317*S^6 + 265*S^8))/(1080*S^3*(1 + S^2)) + (Pi^2*(611 - 6170*S^2 - 14296*S^4 - 6934*S^6 + 389*S^8))/(144*S^3*(1 + S^2)) + 10*S*HPL[{3}, -S^2]^2 + ((-22*Pi^2*S)/9 - (2*(-1 + 58*S^2 + 44*S^4 + S^6))/(3*S^3))*HPL[{4}, -S^2] + ((-101 - 312*S^2 - 115*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - 100*S*HPL[{6}, -S^2] + 248*S*HPL[{2, 1}, -S^2]^2 + ((190*Pi^2*S)/9 + (-17 + 377*S^2 + 427*S^4 + 17*S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + ((71 + 696*S^2 - 119*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + ((209 + 2072*S^2 - 369*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 8*S*HPL[{4, 2}, -S^2] + 72*S*HPL[{5, 1}, -S^2] + ((-124*Pi^2*S)/3 - (2*(-17 + 347*S^2 + 397*S^4 + 17*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(83 + 538*S^2 + 83*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (16*(60 + 343*S^2 + 97*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (592*(1 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + 11904*S*HPL[{3, 1, 1, 1}, -S^2] + ((Pi^2*(-67 - 421*S^2 + 76*S^4))/(18*S*(1 + S^2)) + (1 - 46*S^2 + 80*S^4 + 110*S^6 + 47*S^8)/(4*S^3*(1 + S^2)))*Zeta[3] - (22*S*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((Pi^2*(-3 - 263*S^2 + 134*S^4))/(18*S*(1 + S^2)) + (5 - 127*S^2 + 203*S^4 + 143*S^6)/(12*S^3) + 248*S*HPL[{2, 1}, -S^2] + 20*S*Zeta[3]) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(-23 + 324*S^2 + 23*S^4))/(2*S^3) + (Pi^2*(147 + 691*S^2 + 358*S^4))/(9*S*(1 + S^2)) + 248*S*Zeta[3]) + ((-47 - 367*S^2 + 226*S^4)*Zeta[5])/(3*S*(1 + S^2))) + ((60 - 121*S^2 + 281*S^4)*Zeta[7])/(S*(1 + S^2))) + HPL[{0}, S^2]*((-15181*Pi^8*S)/100800 + (15561 - 189094*S^2 - 16495*S^4)/(192*S) + (Pi^2*(5490 - 71108*S^2 - 5777*S^4))/(576*S) - (Pi^6*S*(676262 + 739159*S^2 + 55645*S^4))/(181440*(1 + S^2)) + (Pi^4*(12180 - 255768*S^2 - 277003*S^4 - 7775*S^6))/(17280*S*(1 + S^2)) + ((-13*Pi^2*S)/27 + (3 - 61*S^2 - 67*S^4 - 3*S^6)/(18*S^3))*HPL[{1}, -S^2]^6 - (4*(1 + 3*S^2)*HPL[{1}, -S^2]^7)/(9*S) + ((-53*Pi^2*S)/54 + (5 - 58*S^2 - 352*S^4 - 15*S^6)/(36*S^3))*HPL[{2}, -S^2]^3 + (5*S*HPL[{2}, -S^2]^4)/12 + ((11*Pi^2*S)/6 + (-2 + 31*S^2 + 169*S^4 + 147*S^6 + 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 - 28*S*HPL[{4}, -S^2]^2 + ((191*Pi^2*S)/18 + (5*(18 - 110*S^2 - 82*S^4 + 89*S^6 + 39*S^8))/(12*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((5 + 665*S^2 + 214*S^4)*HPL[{7}, -S^2])/(6*S*(1 + S^2)) + 272*S*HPL[{8}, -S^2] + ((146*Pi^2*S)/9 + (-2 - 2*S^2 + 437*S^4 + 15*S^6)/(3*S^3))*HPL[{2, 1}, -S^2]^2 + (44*S*HPL[{3, 1}, -S^2]^2)/3 + ((Pi^2*S)/6 + (1 - 43*S^2 - 136*S^4 - 81*S^6 - 21*S^8)/(12*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((70 + 248*S^2 + 101*S^4)*HPL[{4, 3}, -S^2])/(3*S*(1 + S^2)) + ((-25*Pi^2*S)/9 + (-20 + 211*S^2 + 413*S^4 + 159*S^6 - 87*S^8)/(6*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((417 + 1523*S^2 + 646*S^4)*HPL[{5, 2}, -S^2])/(6*S*(1 + S^2)) + (10*S*HPL[{5, 3}, -S^2])/3 + ((418 + 1528*S^2 + 785*S^4)*HPL[{6, 1}, -S^2])/(3*S*(1 + S^2)) + (29*S*HPL[{6, 2}, -S^2])/3 - (424*S*HPL[{7, 1}, -S^2])/3 + (136*S*HPL[{2, 1, 1}, -S^2]^2)/3 + ((Pi^2*(-388 - 477*S^2 + 77*S^4))/(9*S*(1 + S^2)) + (117 - 1805*S^2 - 7*S^4 - 21*S^6)/(6*S^3))*HPL[{2, 2, 1}, -S^2] + ((2*Pi^2*S)/3 + (-5 + 38*S^2 + 32*S^4 - 30*S^6 - 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((-206*Pi^2*S)/9 + (15 - 174*S^2 - 1608*S^4 - 1498*S^6 - 63*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((133 + 244*S^2 + 75*S^4)*HPL[{3, 2, 2}, -S^2])/(6*S*(1 + S^2)) - (8*(-30 - 35*S^2 + 2*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S*(1 + S^2)) - (184*S*HPL[{3, 3, 2}, -S^2])/3 + ((-686*Pi^2*S)/9 + (39 - 505*S^2 - 3076*S^4 - 2649*S^6 - 93*S^8)/(3*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((83 + 88*S^2 - 13*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + (388*S*HPL[{4, 1, 3}, -S^2])/3 + ((259 + 252*S^2 - 65*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) - 53*S*HPL[{4, 2, 2}, -S^2] + 268*S*HPL[{4, 3, 1}, -S^2] - (2*(-757 - 531*S^2 + 428*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (446*S*HPL[{5, 1, 2}, -S^2])/3 + (3326*S*HPL[{5, 2, 1}, -S^2])/3 + (8708*S*HPL[{6, 1, 1}, -S^2])/3 + (8*(65 + 32*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + ((616*Pi^2*S)/9 + (2*(-21 + 323*S^2 + 1071*S^4 + 33*S^6))/(3*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (26*(65 + 9*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) - (26*(65 + 9*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (16*S*HPL[{3, 1, 2, 2}, -S^2])/3 - (2*(1625 + 501*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (16*S*HPL[{3, 2, 1, 2}, -S^2])/3 - (320*S*HPL[{3, 2, 2, 1}, -S^2])/3 - 336*S*HPL[{3, 3, 1, 1}, -S^2] - (4*(2383 + 3106*S^2 + 711*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (28*S*HPL[{4, 1, 1, 2}, -S^2])/3 - (980*S*HPL[{4, 1, 2, 1}, -S^2])/3 - (2996*S*HPL[{4, 2, 1, 1}, -S^2])/3 - 1976*S*HPL[{5, 1, 1, 1}, -S^2] + ((-448*Pi^2*S)/3 - (4*(-15 + 266*S^2 + 1074*S^4 + 45*S^6))/(3*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(-83 + 41*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) - (16*(-83 + 41*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (608*S*HPL[{2, 2, 1, 2, 1}, -S^2])/3 - 608*S*HPL[{2, 2, 2, 1, 1}, -S^2] - (8*(-817 - 262*S^2 + 561*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (3680*S*HPL[{3, 1, 1, 1, 2}, -S^2])/3 + (6112*S*HPL[{3, 1, 1, 2, 1}, -S^2])/3 + (7328*S*HPL[{3, 1, 2, 1, 1}, -S^2])/3 + (15232*S*HPL[{3, 2, 1, 1, 1}, -S^2])/3 + 15136*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (80*(37 + 12*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S) - 192*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 320*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((4*Pi^2*S)/3 - (S*(266 + 295*S^2 + 33*S^4))/(6*(1 + S^2)))*Zeta[3]^2 + HPL[{5}, -S^2]*((Pi^2*(-77 - 213*S^2 - 276*S^4))/(36*S*(1 + S^2)) + (210 - 1965*S^2 - 3151*S^4 - 1151*S^6 + 129*S^8)/(24*S^3*(1 + S^2)) - (202*S*HPL[{2, 1}, -S^2])/3 - (214*S*Zeta[3])/3) + HPL[{4, 1}, -S^2]*((Pi^2*(-135 + 508*S^2 + 695*S^4))/(18*S*(1 + S^2)) + (-49 + 247*S^2 + 951*S^4 + 621*S^6 - 66*S^8)/(6*S^3*(1 + S^2)) - 52*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((Pi^2*(-175 + 192*S^2 + 387*S^4))/(36*S*(1 + S^2)) + (37 - 159*S^2 + 519*S^4 - 21*S^6)/(24*S^3) - 40*S*Zeta[3]) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(-1189 - 1703*S^2 - 10*S^4))/(9*S*(1 + S^2)) + (228 - 2703*S^2 - 3381*S^4 - 493*S^6 - 27*S^8)/(3*S^3*(1 + S^2)) - 16*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((2*Pi^2*(413 + 674*S^2 + 75*S^4))/(9*S*(1 + S^2)) + (-177 + 2115*S^2 + 821*S^4 + 33*S^6)/(3*S^3) - (32*S*Zeta[3])/3) + HPL[{1}, -S^2]^5*((Pi^2*(-162 - 689*S^2 - 397*S^4))/(90*S*(1 + S^2)) - ((1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(36*S^3) - (47*(1 + 3*S^2)*HPL[{2}, -S^2])/(9*S) + (4*S*HPL[{3}, -S^2])/15 - (4*S*Zeta[3])/15) + HPL[{2, 1, 1}, -S^2]*((-3703*Pi^4*S)/270 + (58 - 1226*S^2 - 3521*S^4 - 261*S^6)/(6*S^3) + (Pi^2*(33 - 454*S^2 - 2212*S^4 - 57*S^6))/(18*S^3) - (8*(1 + 45*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((-3067*Pi^4*S)/2160 + (51 + 238*S^2 - 2424*S^4 - 171*S^6)/(48*S^3) + (Pi^2*(5 + 11*S^2 - 1752*S^4 - 1821*S^6 - 39*S^8))/(144*S^3*(1 + S^2)) + ((29 + 64*S^2 + 23*S^4)*HPL[{3}, -S^2])/(12*S*(1 + S^2)) + (47*S*HPL[{4}, -S^2])/6 + ((65 + 32*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (44*S*HPL[{3, 1}, -S^2])/3 + (76*S*HPL[{2, 1, 1}, -S^2])/3 + ((-10 - 161*S^2 - 145*S^4)*Zeta[3])/(6*S*(1 + S^2))) + HPL[{4}, -S^2]*((-163*Pi^4*S)/1080 + (Pi^2*(6 - 183*S^2 - 520*S^4 - 355*S^6))/(36*S^3*(1 + S^2)) + (-81 - 5187*S^2 - 8568*S^4 - 2955*S^6 + 571*S^8)/(48*S^3*(1 + S^2)) - (2*(-7 + 10*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (82*S*HPL[{3, 1}, -S^2])/3 - (52*S*HPL[{2, 1, 1}, -S^2])/3 + ((-27 - 212*S^2 - 135*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^4*((-1313*Pi^4*S)/1080 - ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(24*S^3) + (Pi^2*(87 - 1978*S^2 - 4096*S^4 - 2198*S^6 - 71*S^8))/(216*S^3*(1 + S^2)) + ((-31*Pi^2*S)/9 + (15 - 269*S^2 - 323*S^4 - 15*S^6)/(9*S^3))*HPL[{2}, -S^2] + ((-14 - 55*S^2 - 43*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (4*S*HPL[{4}, -S^2])/3 + (235*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (4*S*HPL[{3, 1}, -S^2])/3 + ((-32 - 131*S^2 - 93*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((3037*Pi^4*S)/540 + (Pi^2*(-39 + 510*S^2 + 2720*S^4 + 2194*S^6 + 39*S^8))/(36*S^3*(1 + S^2)) + (-243 + 2964*S^2 + 10502*S^4 + 7864*S^6 + 441*S^8)/(24*S^3*(1 + S^2)) - (160*S*HPL[{2, 1, 1}, -S^2])/3 + (2*(5 + 113*S^2 + 98*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (-(Pi^2*S*(2624 + 2517*S^2))/(18*(1 + S^2)) + (-12 - 2277*S^2 - 2086*S^4 + 27*S^6)/(12*S*(1 + S^2)))*Zeta[5] + HPL[{3}, -S^2]*((Pi^4*(-773 - 4138*S^2 - 3513*S^4))/(2160*S*(1 + S^2)) + (Pi^2*(216 - 805*S^2 - 2798*S^4 - 1841*S^6))/(144*S^3*(1 + S^2)) + (891 - 10366*S^2 - 21144*S^4 - 10746*S^6 + 165*S^8)/(96*S^3*(1 + S^2)) + ((-37 - 115*S^2 - 39*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (160*S*HPL[{5}, -S^2])/3 + ((-56*Pi^2*S)/9 + (-9 + 111*S^2 - 221*S^4 + 3*S^6)/(6*S^3))*HPL[{2, 1}, -S^2] + ((-59 - 18*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (92*S*HPL[{3, 2}, -S^2])/3 - 92*S*HPL[{4, 1}, -S^2] - (2*(-37 + 135*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (56*S*HPL[{2, 2, 1}, -S^2])/3 + (184*S*HPL[{3, 1, 1}, -S^2])/3 - 48*S*HPL[{2, 1, 1, 1}, -S^2] + ((-14*Pi^2*S)/3 + (3 - 57*S^2 - 228*S^4 - 187*S^6 - 3*S^8)/(6*S^3*(1 + S^2)))*Zeta[3] - (200*S*Zeta[5])/3) + HPL[{1}, -S^2]^3*((Pi^4*(-7949 - 34087*S^2 - 18260*S^4))/(3240*S*(1 + S^2)) - ((1 + S^2)*(-1039 + 9360*S^2 + 1039*S^4))/(72*S^3) + (Pi^2*(369 - 4536*S^2 - 10166*S^4 - 5712*S^6 - 291*S^8))/(216*S^3*(1 + S^2)) + ((Pi^2*(-481 - 2130*S^2 - 1277*S^4))/(54*S*(1 + S^2)) + (105 - 1467*S^2 - 1741*S^4 - 105*S^6)/(18*S^3))*HPL[{2}, -S^2] - (74*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(9*S) + ((-2*Pi^2*S)/9 - (2*(-11 + 117*S^2 + 138*S^4 + 2*S^6))/(9*S^3))*HPL[{3}, -S^2] + ((-89 - 296*S^2 - 231*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) + (44*S*HPL[{5}, -S^2])/9 + ((124*Pi^2*S)/9 + (4*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(9*S^3))*HPL[{2, 1}, -S^2] + (4*(116 + 461*S^2 + 351*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - (16*S*HPL[{4, 1}, -S^2])/3 - (940*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + (16*S*HPL[{3, 1, 1}, -S^2])/3 + ((-52*Pi^2*S)/27 + (-3 - 103*S^2 - 131*S^4 - 15*S^6)/(9*S^3))*Zeta[3] - (44*S*Zeta[5])/9) + HPL[{2, 1}, -S^2]*((Pi^4*(6455 + 9435*S^2 - 507*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(-357 + 4450*S^2 + 1483*S^4 + 84*S^6))/(72*S^3) + (-804 + 8403*S^2 + 4784*S^4 + 153*S^6)/(24*S^3) + (2*(-167 + 71*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (52*S*HPL[{3, 2}, -S^2])/3 + (220*S*HPL[{4, 1}, -S^2])/3 + (8*(-83 + 41*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (304*S*HPL[{2, 2, 1}, -S^2])/3 + 256*S*HPL[{3, 1, 1}, -S^2] - (272*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((14*Pi^2*S)/3 + (3 + 129*S^2 + 65*S^4 + 3*S^6)/(3*S^3))*Zeta[3] + 48*S*Zeta[5]) + Zeta[3]*(-(Pi^4*S*(18163 + 17052*S^2))/(1080*(1 + S^2)) + (24 - 5941*S^2 - 5546*S^4 - 93*S^6)/(48*S*(1 + S^2)) + (Pi^2*(-3 - 787*S^2 - 655*S^4 + 69*S^6))/(36*S*(1 + S^2)) + (208*S*Zeta[5])/3) + HPL[{2}, -S^2]*((-44423*Pi^6*S)/45360 + (519 - 17696*S^2 - 29848*S^4 - 2353*S^6)/(96*S^3) + (Pi^4*(446 - 6030*S^2 - 40298*S^4 - 34891*S^6 - 465*S^8))/(4320*S^3*(1 + S^2)) + (Pi^2*(173 - 2276*S^2 - 9450*S^4 - 7419*S^6 - 322*S^8))/(144*S^3*(1 + S^2)) - (22*S*HPL[{3}, -S^2]^2)/3 + ((-73*Pi^2*S)/18 + (-1 - 9*S^2 - 260*S^4 - 273*S^6 + 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((81 + 187*S^2 + 26*S^4)*HPL[{5}, -S^2])/(6*S*(1 + S^2)) - (145*S*HPL[{6}, -S^2])/3 + ((Pi^2*(388 + 477*S^2 - 77*S^4))/(18*S*(1 + S^2)) + (-117 + 1805*S^2 + 7*S^4 + 21*S^6)/(12*S^3))*HPL[{2, 1}, -S^2] - (76*S*HPL[{2, 1}, -S^2]^2)/3 + (18*Pi^2*S + (-1 + 5*S^2 + 925*S^4 + 27*S^6)/(6*S^3))*HPL[{3, 1}, -S^2] + ((-61 - 122*S^2 - 41*S^4)*HPL[{3, 2}, -S^2])/(6*S*(1 + S^2)) + ((-43 - 44*S^2 + 9*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - (7*S*HPL[{4, 2}, -S^2])/3 + 30*S*HPL[{5, 1}, -S^2] + ((-292*Pi^2*S)/9 - (2*(-2 - 2*S^2 + 437*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(65 + 32*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (2*(427 + 57*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (4*S*HPL[{3, 1, 2}, -S^2])/3 + (124*S*HPL[{3, 2, 1}, -S^2])/3 + (308*S*HPL[{4, 1, 1}, -S^2])/3 - (8*(-83 + 41*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (3808*S*HPL[{3, 1, 1, 1}, -S^2])/3 + (272*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((39 - 50*S^2 - 377*S^4)/(12*S^3) + (Pi^2*(10 - 237*S^2 - 210*S^4))/(18*S*(1 + S^2)))*Zeta[3] + 2*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(93 - 92*S^2 - 195*S^4))/(36*S*(1 + S^2)) + (-17 + 117*S^2 - 293*S^4 + 21*S^6)/(24*S^3) - (28*S*HPL[{2, 1}, -S^2])/3 + (52*S*Zeta[3])/3) + ((-26 - 434*S^2 - 373*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^2*((-42013*Pi^6*S)/45360 - ((1 + S^2)*(-101 + 880*S^2 + 101*S^4))/(3*S^3) + (Pi^4*(1218 - 33021*S^2 - 66581*S^4 - 35863*S^6 - 1353*S^8))/(4320*S^3*(1 + S^2)) + (Pi^2*(303 - 2948*S^2 - 6946*S^4 - 4012*S^6 - 253*S^8))/(72*S^3*(1 + S^2)) + ((-83*Pi^2*S)/18 + (17 - 347*S^2 - 397*S^4 - 17*S^6)/(12*S^3))*HPL[{2}, -S^2]^2 - (2*S*HPL[{3}, -S^2]^2)/3 + ((11*Pi^2*S)/9 + (51 - 466*S^2 - 1016*S^4 - 550*S^6 - 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-56 - 197*S^2 - 163*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (55*S*HPL[{6}, -S^2])/3 + ((Pi^2*(481 + 2130*S^2 + 1277*S^4))/(18*S*(1 + S^2)) + (-105 + 1467*S^2 + 1741*S^4 + 105*S^6)/(6*S^3))*HPL[{2, 1}, -S^2] + ((172*Pi^2*S)/9 + (-39 + 581*S^2 + 673*S^4 + 21*S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + (2*(13 + 31*S^2)*HPL[{3, 2}, -S^2])/(3*S) + ((155 + 560*S^2 + 429*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - 2*S*HPL[{4, 2}, -S^2] - (68*S*HPL[{5, 1}, -S^2])/3 + ((-124*Pi^2*S)/3 - (4*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (296*(1 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4*(88 + 351*S^2 + 265*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + 16*S*HPL[{4, 1, 1}, -S^2] + (940*(1 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - 16*S*HPL[{3, 1, 1, 1}, -S^2] + ((Pi^2*(-107 - 428*S^2 - 269*S^4))/(18*S*(1 + S^2)) + (-12 - 149*S^2 - 323*S^4 - 191*S^6 - 21*S^8)/(6*S^3*(1 + S^2)))*Zeta[3] + 2*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-68 - 315*S^2 - 241*S^4))/(18*S*(1 + S^2)) + (69 - 652*S^2 - 1482*S^4 - 796*S^6 - 3*S^8)/(12*S^3*(1 + S^2)) - (8*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-3487*Pi^4*S)/1080 + (319 - 4193*S^2 - 4895*S^4 - 319*S^6)/(24*S^3) + (Pi^2*(123 - 2207*S^2 - 2557*S^4 - 83*S^6))/(72*S^3) - (11*(1 + 3*S^2)*HPL[{3}, -S^2])/(3*S) + 2*S*HPL[{4}, -S^2] + (148*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (11*(1 + 3*S^2)*Zeta[3])/S) + ((-105 - 439*S^2 - 312*S^4)*Zeta[5])/(3*S*(1 + S^2))) - (S*(1031 + 986*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((Pi^6*(-101499 - 436977*S^2 - 251452*S^4))/(90720*S*(1 + S^2)) - (5*(1 + S^2)*(-663 + 6272*S^2 + 663*S^4))/(64*S^3) + (Pi^4*(5198 - 73719*S^2 - 160307*S^4 - 89873*S^6 - 4467*S^8))/(8640*S^3*(1 + S^2)) + (Pi^2*(1919 - 16305*S^2 - 39847*S^4 - 23615*S^6 - 1736*S^8))/(288*S^3*(1 + S^2)) - (85*(1 + 3*S^2)*HPL[{2}, -S^2]^3)/(18*S) + ((5 + 2*S^2 + S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((70*Pi^2*S)/9 + (63 - 333*S^2 - 701*S^4 - 291*S^6 + 30*S^8)/(6*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-113 - 437*S^2 - 434*S^4)*HPL[{6}, -S^2])/(6*S*(1 + S^2)) + (446*S*HPL[{7}, -S^2])/3 + (148*(1 + 3*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-10*Pi^2*S)/9 + (-1 + 16*S^2 + 48*S^4 + 44*S^6 + 5*S^8)/(3*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-52*Pi^2*S)/9 + (-69 + 562*S^2 + 1376*S^4 + 814*S^6 + 21*S^8)/(6*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((13 - 18*S^2 - 19*S^4)*HPL[{4, 2}, -S^2])/(6*S*(1 + S^2)) + (154*S*HPL[{4, 3}, -S^2])/3 + (2*(67 + 187*S^2 + 154*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + (460*S*HPL[{5, 2}, -S^2])/3 + (650*S*HPL[{6, 1}, -S^2])/3 + ((Pi^2*(-481 - 2130*S^2 - 1277*S^4))/(9*S*(1 + S^2)) + (105 - 1467*S^2 - 1741*S^4 - 105*S^6)/(3*S^3))*HPL[{2, 1, 1}, -S^2] + ((-332*Pi^2*S)/9 - (2*(-17 + 347*S^2 + 397*S^4 + 17*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + (-112*Pi^2*S - (2*(-73 + 1275*S^2 + 1467*S^4 + 55*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] + (8*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (4*(87 + 253*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + 12*S*HPL[{3, 2, 2}, -S^2] + (112*S*HPL[{3, 3, 1}, -S^2])/3 - (2*(599 + 2336*S^2 + 1761*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 36*S*HPL[{4, 1, 2}, -S^2] + 116*S*HPL[{4, 2, 1}, -S^2] + (808*S*HPL[{5, 1, 1}, -S^2])/3 + ((248*Pi^2*S)/3 + (8*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (8*(116 + 461*S^2 + 351*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 32*S*HPL[{4, 1, 1, 1}, -S^2] - (1880*(1 + 3*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + 32*S*HPL[{3, 1, 1, 1, 1}, -S^2] + ((-1111*Pi^4*S)/540 + (Pi^2*(-3 - 377*S^2 - 831*S^4 - 555*S^6 - 66*S^8))/(36*S^3*(1 + S^2)) + (-39 - 318*S^2 - 872*S^4 - 594*S^6 - 65*S^8)/(12*S^3*(1 + S^2)))*Zeta[3] + ((-49 - 197*S^2 - 154*S^4)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{4}, -S^2]*((Pi^2*(-185 - 622*S^2 - 481*S^4))/(36*S*(1 + S^2)) + (101 - 1798*S^2 - 3568*S^4 - 1706*S^6 + 91*S^8)/(24*S^3*(1 + S^2)) - 4*S*HPL[{2, 1}, -S^2] - (100*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(-173 - 759*S^2 - 420*S^4))/(36*S*(1 + S^2)) - ((1 + S^2)*(-23 + 324*S^2 + 23*S^4))/(8*S^3) + 2*S*HPL[{3}, -S^2] - 2*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((Pi^2*(241 + 1074*S^2 + 661*S^4))/(9*S*(1 + S^2)) + (-69 + 743*S^2 + 1713*S^4 + 953*S^6 + 36*S^8)/(3*S^3*(1 + S^2)) + (40*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((3487*Pi^4*S)/540 + (Pi^2*(-123 + 2207*S^2 + 2557*S^4 + 83*S^6))/(36*S^3) + (-319 + 4193*S^2 + 4895*S^4 + 319*S^6)/(12*S^3) + (22*(1 + 3*S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((37*Pi^4*S)/270 + (Pi^2*(22 - 191*S^2 - 490*S^4 - 259*S^6 - 2*S^8))/(18*S^3*(1 + S^2)) + (201 - 2638*S^2 - 5424*S^4 - 2706*S^6 + 7*S^8)/(24*S^3*(1 + S^2)) - 26*S*HPL[{4}, -S^2] + (22*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (16*S*HPL[{3, 1}, -S^2])/3 + (2*(-3 + 7*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-107*Pi^2*S)/9 + (-6 - 367*S^2 - 987*S^4 - 709*S^6 - 91*S^8)/(6*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-7307 - 31987*S^2 - 17706*S^4))/(2160*S*(1 + S^2)) + (957 - 12659*S^2 - 14701*S^4 - 957*S^6)/(48*S^3) + (Pi^2*(441 - 6011*S^2 - 6841*S^4 - 293*S^6))/(144*S^3) + ((5*Pi^2*S)/9 + (3 - 19*S^2 - 41*S^4 - 3*S^6)/(6*S^3))*HPL[{3}, -S^2] + ((-13 + 2*S^2 + 3*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) + (80*S*HPL[{5}, -S^2])/3 + ((166*Pi^2*S)/9 + (-17 + 347*S^2 + 397*S^4 + 17*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + (148*(1 + 3*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (20*S*HPL[{3, 2}, -S^2])/3 - 20*S*HPL[{4, 1}, -S^2] - (296*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + ((-37*Pi^2*S)/9 - ((1 + S^2)*(-1 + 58*S^2 + S^4))/(2*S^3))*Zeta[3] - (70*S*Zeta[5])/3) - 90*S*Zeta[7])) + Log[T]*((942223*Pi^8*S)/1360800 + (5187*(-1 + S^2))/(32*S) + (Pi^2*(-4902 + 26386*S^2 + 249*S^4))/(288*S) - (Pi^6*S*(-302282 - 292739*S^2 + 5707*S^4))/(90720*(1 + S^2)) + (Pi^4*(-12420 + 129992*S^2 + 136853*S^4 - 3927*S^6))/(8640*S*(1 + S^2)) + (S*HPL[{0}, S^2]^8)/48 + (8*(1 + 3*S^2)*HPL[{1}, -S^2]^7)/(9*S) + HPL[{0}, S^2]^7*((S*(36 + 31*S^2))/(144*(1 + S^2)) + (5*S*HPL[{1}, -S^2])/72) + ((157*Pi^2*S)/27 + (-5 + 66*S^2 + 324*S^4 - 5*S^6)/(18*S^3))*HPL[{2}, -S^2]^3 + (83*S*HPL[{2}, -S^2]^4)/18 + HPL[{0}, S^2]^6*((115*Pi^2*S)/432 - (S*(-244 - 251*S^2 + S^4))/(288*(1 + S^2)) + ((18 + 81*S^2 + 35*S^4)*HPL[{1}, -S^2])/(72*S*(1 + S^2)) + (7*S*HPL[{1}, -S^2]^2)/18 + (25*S*HPL[{2}, -S^2])/72) + HPL[{1}, -S^2]^6*((10*Pi^2*S)/9 + (-3 + 61*S^2 + 67*S^4 + 3*S^6)/(9*S^3) + (40*S*HPL[{2}, -S^2])/3) + ((-5*Pi^2*S)/3 + (2 + 35*S^2 - 108*S^4 - 127*S^6 + 6*S^8)/(6*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + ((425*Pi^2*S)/9 - (5*(6 - 398*S^2 - 1242*S^4 - 827*S^6 + 7*S^8))/(6*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((735 + 5533*S^2 + 3724*S^4)*HPL[{7}, -S^2])/(3*S*(1 + S^2)) + (3716*S*HPL[{8}, -S^2])/3 + ((-760*Pi^2*S)/9 + (2*(-1 + 58*S^2 - 448*S^4 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2]^2 + (728*S*HPL[{3, 1}, -S^2]^2)/3 + ((-43*Pi^2*S)/9 + (-1 + 193*S^2 - 264*S^4 - 473*S^6 + 17*S^8)/(6*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + (2*(14 + 89*S^2 + 42*S^4)*HPL[{4, 3}, -S^2])/(3*S*(1 + S^2)) + ((-638*Pi^2*S)/9 + (2*(13 - 369*S^2 - 1524*S^4 - 1154*S^6 + 20*S^8))/(3*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((141 + 239*S^2 - 58*S^4)*HPL[{5, 2}, -S^2])/(3*S*(1 + S^2)) + (68*S*HPL[{5, 3}, -S^2])/3 - (2*(158 + 2014*S^2 + 1439*S^4)*HPL[{6, 1}, -S^2])/(3*S*(1 + S^2)) + (34*S*HPL[{6, 2}, -S^2])/3 - (2960*S*HPL[{7, 1}, -S^2])/3 + 1040*S*HPL[{2, 1, 1}, -S^2]^2 + ((-8*Pi^2*S)/9 - (4*(1 + 26*S^2 - 28*S^6 + S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((416*Pi^2*S)/3 - (4*(6 - 35*S^2 - 390*S^4 - 347*S^6 + 6*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((-183 + 142*S^2 - 1163*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S*(1 + S^2)) - (8*(73 - 120*S^2 + 365*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S*(1 + S^2)) - (104*S*HPL[{3, 3, 2}, -S^2])/3 + ((4384*Pi^2*S)/9 - (2*(51 - 813*S^2 - 3728*S^4 - 2849*S^6 + 39*S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] - (2*(307 - 470*S^2 + 1455*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S*(1 + S^2)) + (8*S*HPL[{4, 1, 3}, -S^2])/3 - (2*(883 - 1814*S^2 + 3999*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S*(1 + S^2)) - 70*S*HPL[{4, 2, 2}, -S^2] + 120*S*HPL[{4, 3, 1}, -S^2] - (4*(705 - 2944*S^2 + 3323*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (28*S*HPL[{5, 1, 2}, -S^2])/3 + (1948*S*HPL[{5, 2, 1}, -S^2])/3 + (8032*S*HPL[{6, 1, 1}, -S^2])/3 + (32*(-32 - 98*S^2 + 27*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + ((-3424*Pi^2*S)/9 + (8*(9 - 217*S^2 - 551*S^4 + 6*S^6))/(3*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (8*(-430 - 1035*S^2 + 139*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) - (8*(-430 - 1035*S^2 + 139*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (40*S*HPL[{3, 1, 2, 2}, -S^2])/3 - (8*(-814 - 2211*S^2 + 463*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (40*S*HPL[{3, 2, 1, 2}, -S^2])/3 - (2408*S*HPL[{3, 2, 2, 1}, -S^2])/3 - 2368*S*HPL[{3, 3, 1, 1}, -S^2] - (16*(-1169 - 3128*S^2 + 759*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (352*S*HPL[{4, 1, 1, 2}, -S^2])/3 - (7456*S*HPL[{4, 1, 2, 1}, -S^2])/3 - (21664*S*HPL[{4, 2, 1, 1}, -S^2])/3 - (46432*S*HPL[{5, 1, 1, 1}, -S^2])/3 + ((6880*Pi^2*S)/9 - (8*(15 - 274*S^2 - 974*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (64*(41 + 24*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) - (64*(41 + 24*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (4736*S*HPL[{2, 2, 1, 2, 1}, -S^2])/3 - 4736*S*HPL[{2, 2, 2, 1, 1}, -S^2] - (16*(793 + 1012*S^2 + 669*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (28480*S*HPL[{3, 1, 1, 1, 2}, -S^2])/3 + 15808*S*HPL[{3, 1, 1, 2, 1}, -S^2] + (56896*S*HPL[{3, 1, 2, 1, 1}, -S^2])/3 + 39488*S*HPL[{3, 2, 1, 1, 1}, -S^2] + 119488*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (160*(-11 - 28*S^2 + 13*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 4480*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 8960*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((14*Pi^2*S)/3 + (S*(-28 + 25*S^2 + 9*S^4))/(3*(1 + S^2)))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((16*Pi^2*(118 + 254*S^2 + S^4))/(9*S*(1 + S^2)) + (-525 + 6287*S^2 + 729*S^4 + 165*S^6)/(3*S^3) - (448*S*Zeta[3])/3) + HPL[{2, 2, 1}, -S^2]*((4*Pi^2*(152 + 267*S^2 + 22*S^4))/(9*S*(1 + S^2)) + (2*(-81 + 974*S^2 - 30*S^4 + 81*S^6))/(3*S^3) - (160*S*Zeta[3])/3) + HPL[{0}, S^2]^5*((Pi^2*S*(2585 + 2183*S^2))/(1080*(1 + S^2)) + (-9 + 517*S^2 + 565*S^4 + 19*S^6)/(144*S*(1 + S^2)) + ((445 + 1899*S^2 + 896*S^4)*HPL[{1}, -S^2]^2)/(360*S*(1 + S^2)) + (31*S*HPL[{1}, -S^2]^3)/30 + ((30 + 1135*S^2 + 876*S^4)*HPL[{2}, -S^2])/(360*S*(1 + S^2)) + HPL[{1}, -S^2]*((67*Pi^2*S)/90 + (-9 + 393*S^2 + 735*S^4 + 387*S^6 + 14*S^8)/(144*S^3*(1 + S^2)) + (229*S*HPL[{2}, -S^2])/180) - (S*HPL[{3}, -S^2])/12 + (5*S*HPL[{2, 1}, -S^2])/18 + (3*S*Zeta[3])/2) + HPL[{5}, -S^2]*((Pi^2*(201 + 1245*S^2 + 652*S^4))/(18*S*(1 + S^2)) + (-450 + 2481*S^2 + 4748*S^4 + 53*S^6)/(12*S^3) + 60*S*HPL[{2, 1}, -S^2] + 4*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((Pi^2*(95 - 556*S^2 + 137*S^4))/(18*S*(1 + S^2)) + (-55 + 945*S^2 - 559*S^4 + 593*S^6)/(12*S^3) + 24*S*Zeta[3]) + HPL[{1}, -S^2]^5*(((1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(18*S^3) + (Pi^2*(80 + 371*S^2 + 201*S^4))/(27*S*(1 + S^2)) + (2*(13 + 86*S^2 + 13*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + 40*S*HPL[{3}, -S^2] - 80*S*HPL[{2, 1}, -S^2] + 40*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((Pi^2*(25 - 1294*S^2 + 81*S^4))/(9*S*(1 + S^2)) + (56 - 211*S^2 - 2383*S^4 + 944*S^6)/(6*S^3) + (152*S*Zeta[3])/3) + HPL[{2, 1, 1, 1}, -S^2]*((16*Pi^2*(-78 - 200*S^2 + 55*S^4))/(9*S*(1 + S^2)) + (8*(45 - 495*S^2 - 103*S^4 + 45*S^6))/(3*S^3) + (320*S*Zeta[3])/3) + HPL[{4}, -S^2]*((137*Pi^4*S)/36 + (Pi^2*(-18 + 324*S^2 + 714*S^4 - 7*S^6))/(18*S^3) + (-411 + 5177*S^2 + 12244*S^4 + 6249*S^6 - 215*S^8)/(24*S^3*(1 + S^2)) + (4*(-15 + 28*S^2)*HPL[{2, 1}, -S^2])/S - (172*S*HPL[{3, 1}, -S^2])/3 + (448*S*HPL[{2, 1, 1}, -S^2])/3 + (2*(25 + 68*S^2 + 21*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^4*((749*Pi^4*S)/270 + ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(12*S^3) + (Pi^2*(-45 + 919*S^2 + 955*S^4 + 15*S^6))/(54*S^3) + ((236*Pi^2*S)/9 - (2*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2}, -S^2] - (2*(-18 - 157*S^2 + 11*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + 32*S*HPL[{4}, -S^2] - (10*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 200*S*HPL[{3, 1}, -S^2] + 400*S*HPL[{2, 1, 1}, -S^2] - (10*(4 - 35*S^2 + 51*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{2}, -S^2]^2*((991*Pi^4*S)/216 + (36 - 121*S^2 + 2497*S^4 - 36*S^6)/(24*S^3) + (Pi^2*(1 - 162*S^2 + 1710*S^4 - 11*S^6))/(72*S^3) + ((-29 + 100*S^2 - 243*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) + (31*S*HPL[{4}, -S^2])/3 + (4*(-32 - 98*S^2 + 27*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (296*S*HPL[{3, 1}, -S^2])/3 + (592*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(12 - 7*S^2 + 74*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((6104*Pi^4*S)/135 + (-49 + 888*S^2 + 2832*S^4 - 49*S^6)/(3*S^3) + (Pi^2*(-27 + 399*S^2 + 2440*S^4 + 1937*S^6 - 29*S^8))/(9*S^3*(1 + S^2)) - (16*(-9 - 20*S^2 + 85*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-5921*Pi^4*S)/270 + (147 - 3089*S^2 - 7103*S^4 + 49*S^6)/(12*S^3) + (Pi^2*(33 - 611*S^2 - 2830*S^4 - 2105*S^6 + 25*S^8))/(18*S^3*(1 + S^2)) - (3136*S*HPL[{2, 1, 1}, -S^2])/3 + (4*(-23 - 40*S^2 + 175*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^4*((16537*Pi^4*S)/12960 - (Pi^2*S*(-2574 - 2647*S^2 + 17*S^4))/(432*(1 + S^2)) + (-450 + 7760*S^2 + 7909*S^4 - 397*S^6)/(576*S*(1 + S^2)) + ((97 + 450*S^2 + 177*S^4)*HPL[{1}, -S^2]^3)/(36*S*(1 + S^2)) + (22*S*HPL[{1}, -S^2]^4)/9 + ((23*Pi^2*S)/8 + (-15 + 99*S^2 + 1406*S^4 + 1278*S^6 - 18*S^8)/(144*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (47*S*HPL[{2}, -S^2]^2)/18 + HPL[{1}, -S^2]^2*((19*Pi^2*S)/6 + (-45 + 1356*S^2 + 2546*S^4 + 1252*S^6 - 13*S^8)/(144*S^3*(1 + S^2)) + (257*S*HPL[{2}, -S^2])/36) + ((-1 + 13*S^2 + 3*S^4)*HPL[{3}, -S^2])/(12*S*(1 + S^2)) + (7*S*HPL[{4}, -S^2])/4 + ((-216 - 383*S^2 + 90*S^4)*HPL[{2, 1}, -S^2])/(36*S*(1 + S^2)) - (233*S*HPL[{3, 1}, -S^2])/18 + (82*S*HPL[{2, 1, 1}, -S^2])/3 + (S*(100 + 81*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(277 + 1260*S^2 + 527*S^4))/(144*S*(1 + S^2)) + (-195 + 2837*S^2 + 5819*S^4 + 2995*S^6 + 16*S^8)/(288*S^3*(1 + S^2)) + ((228 + 1203*S^2 + 461*S^4)*HPL[{2}, -S^2])/(72*S*(1 + S^2)) + (11*S*HPL[{3}, -S^2])/6 - (257*S*HPL[{2, 1}, -S^2])/18 + (38*S*Zeta[3])/9)) + ((-13*Pi^2*S*(-19 + 16*S^2))/(9*(1 + S^2)) + (-12 + 1287*S^2 - 322*S^4)/(6*S))*Zeta[5] + HPL[{2, 1}, -S^2]*((Pi^4*(-4057 - 9397*S^2 + 2997*S^4))/(540*S*(1 + S^2)) + (675 - 7151*S^2 - 2511*S^4 + 675*S^6)/(12*S^3) + (Pi^2*(381 - 3580*S^2 - 4942*S^4 - 666*S^6 + 219*S^8))/(36*S^3*(1 + S^2)) + (8*(97 + 13*S^2)*HPL[{3, 1}, -S^2])/(3*S) - 48*S*HPL[{3, 2}, -S^2] - (880*S*HPL[{4, 1}, -S^2])/3 + (32*(41 + 24*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2368*S*HPL[{2, 2, 1}, -S^2])/3 + 2624*S*HPL[{3, 1, 1}, -S^2] - 2080*S*HPL[{2, 1, 1, 1}, -S^2] + (4*Pi^2*S + (2*(3 - 119*S^2 - 56*S^4 + 19*S^6 + S^8))/(3*S^3*(1 + S^2)))*Zeta[3] - 24*S*Zeta[5]) + HPL[{0}, S^2]^3*((Pi^4*S*(49621 + 41571*S^2))/(6480*(1 + S^2)) + (Pi^2*(-87 + 4027*S^2 + 4376*S^4 + 122*S^6))/(216*S*(1 + S^2)) + (-1536 + 22423*S^2 + 25138*S^4 + 923*S^6)/(288*S*(1 + S^2)) + ((92 + 409*S^2 + 187*S^4)*HPL[{1}, -S^2]^4)/(18*S*(1 + S^2)) + (26*S*HPL[{1}, -S^2]^5)/9 + ((-24 + 533*S^2 + 391*S^4)*HPL[{2}, -S^2]^2)/(36*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((158*Pi^2*S)/27 + (-21 + 554*S^2 + 1088*S^4 + 574*S^6 + 13*S^8)/(27*S^3*(1 + S^2)) + (124*S*HPL[{2}, -S^2])/9) + ((-2*Pi^2*S)/9 + (-27 + 129*S^2 + 496*S^4 + 303*S^6 + 3*S^8)/(36*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((10 + 93*S^2 + 88*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) - (8*S*HPL[{5}, -S^2])/3 + ((22*Pi^2*S)/27 + (45 - 943*S^2 - 127*S^4 - 11*S^6)/(18*S^3))*HPL[{2, 1}, -S^2] + ((-16 - 719*S^2 - 525*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - (58*S*HPL[{3, 2}, -S^2])/9 - (122*S*HPL[{4, 1}, -S^2])/9 + (2*(18 + 761*S^2 + 557*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) + (4*S*HPL[{2, 2, 1}, -S^2])/3 + (16*S*HPL[{3, 1, 1}, -S^2])/3 - (8*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((52*Pi^2*S)/9 - (S*(-356 - 363*S^2 + 9*S^4))/(18*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(48 + 1896*S^2 + 1433*S^4))/(108*S*(1 + S^2)) + (-51 + 742*S^2 + 2697*S^4 + 32*S^6)/(72*S^3) + (28*S*HPL[{3}, -S^2])/9 - (2*S*HPL[{2, 1}, -S^2])/3 + (28*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((Pi^2*(721 + 3126*S^2 + 1457*S^4))/(108*S*(1 + S^2)) + (-87 + 1243*S^2 + 2643*S^4 + 1441*S^6 + 48*S^8)/(36*S^3*(1 + S^2)) + ((123 + 595*S^2 + 286*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (4*S*HPL[{3}, -S^2])/3 - (124*S*HPL[{2, 1}, -S^2])/3 + (46*S*Zeta[3])/9) + HPL[{1}, -S^2]*((805*Pi^4*S)/324 + (Pi^2*(-87 + 3073*S^2 + 5851*S^4 + 3083*S^6 + 96*S^8))/(216*S^3*(1 + S^2)) + (-279 + 3238*S^2 + 7268*S^4 + 4058*S^6 + 179*S^8)/(72*S^3*(1 + S^2)) + ((415*Pi^2*S)/54 + (-63 + 1131*S^2 + 1265*S^4 + 23*S^6)/(36*S^3))*HPL[{2}, -S^2] + (83*S*HPL[{2}, -S^2]^2)/9 + (2*(13 + 75*S^2 + 56*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (10*S*HPL[{4}, -S^2])/9 - (2*(123 + 595*S^2 + 286*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (356*S*HPL[{3, 1}, -S^2])/9 + (248*S*HPL[{2, 1, 1}, -S^2])/3 + ((75 + 297*S^2 + 176*S^4)*Zeta[3])/(9*S*(1 + S^2))) + (182*S*Zeta[5])/9) + HPL[{3}, -S^2]*((Pi^4*(505 + 5134*S^2 - 247*S^4))/(1080*S*(1 + S^2)) + (-195 + 9637*S^2 + 9975*S^4 - 2505*S^6)/(48*S^3) + (Pi^2*(-120 + 697*S^2 + 2702*S^4 + 1415*S^6 - 374*S^8))/(72*S^3*(1 + S^2)) - (2*(6 + 88*S^2 + 55*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (80*S*HPL[{5}, -S^2])/3 + ((124*Pi^2*S)/9 + (2*(3 - 163*S^2 + 173*S^4 + S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (2*(67 - 124*S^2 + 181*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 16*S*HPL[{3, 2}, -S^2] + (104*S*HPL[{4, 1}, -S^2])/3 - (8*(33 - 86*S^2 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 48*S*HPL[{2, 2, 1}, -S^2] - (560*S*HPL[{3, 1, 1}, -S^2])/3 + 256*S*HPL[{2, 1, 1, 1}, -S^2] + ((8*Pi^2*S)/9 + (3 + 52*S^2 + 46*S^4 + 58*S^6 + 5*S^8)/(3*S^3*(1 + S^2)))*Zeta[3] + 48*S*Zeta[5]) + Zeta[3]*((Pi^4*S*(3518 + 941*S^2))/(540*(1 + S^2)) + (Pi^2*(-6 + 896*S^2 - 231*S^4))/(36*S) - (3*(-8 - 271*S^2 + 75*S^4))/(4*S) + (232*S*Zeta[5])/3) + HPL[{1}, -S^2]^3*(((1 + S^2)*(-1039 + 9360*S^2 + 1039*S^4))/(36*S^3) + (Pi^4*(5471 + 27356*S^2 + 12897*S^4))/(1620*S*(1 + S^2)) + (Pi^2*(-393 + 4355*S^2 + 4861*S^4 + 177*S^6))/(108*S^3) + (148*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(9*S) + ((116*Pi^2*S)/3 - (2*(19 - 345*S^2 - 307*S^4 + 41*S^6))/(9*S^3))*HPL[{3}, -S^2] + (8*(47 + 221*S^2 + 102*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) + (368*S*HPL[{5}, -S^2])/3 + ((-944*Pi^2*S)/9 + (8*(5 - 91*S^2 - 91*S^4 + 5*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (8*(128 + 767*S^2 + 189*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - (992*S*HPL[{3, 2}, -S^2])/3 - 1120*S*HPL[{4, 1}, -S^2] + (40*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 800*S*HPL[{3, 1, 1}, -S^2] - 1600*S*HPL[{2, 1, 1, 1}, -S^2] + ((344*Pi^2*S)/9 - (8*(-2 + 25*S^2 + 15*S^4))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-4*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 + (4*Pi^2*(89 + 581*S^2 + 138*S^4))/(27*S*(1 + S^2)) + (496*S*HPL[{3}, -S^2])/3 + (512*S*Zeta[3])/3) + (896*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*((47329*Pi^6*S)/22680 + (2*(1 + S^2)*(-101 + 880*S^2 + 101*S^4))/(3*S^3) + (Pi^2*(-645 + 5632*S^2 + 6589*S^4 + 344*S^6))/(72*S^3) + (Pi^4*(-624 + 12677*S^2 + 26903*S^4 + 13411*S^6 - 35*S^8))/(1080*S^3*(1 + S^2)) + ((31*Pi^2*S)/3 + (-17 + 347*S^2 + 397*S^4 + 17*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 + (124*S*HPL[{2}, -S^2]^3)/3 + ((218*Pi^2*S)/9 + (8*(-3 + 74*S^2 + 154*S^4 + 80*S^6))/(3*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (8*(41 + 203*S^2 + 93*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + 318*S*HPL[{6}, -S^2] + ((-472*Pi^2*S)/3 + (8*(9 - 173*S^2 - 176*S^4 + 6*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] + (4*(-11 - 242*S^2 + 141*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (4*(-121 - 1168*S^2 + 213*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - 368*S*HPL[{5, 1}, -S^2] + ((944*Pi^2*S)/3 - (8*(5 - 91*S^2 - 91*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (592*(1 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (8*(92 + 453*S^2 + 211*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + 992*S*HPL[{3, 2, 1}, -S^2] + 3360*S*HPL[{4, 1, 1}, -S^2] - (40*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 2400*S*HPL[{3, 1, 1, 1}, -S^2] + 4800*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-2*Pi^2*(1 - 44*S^2 + 41*S^4))/(3*S*(1 + S^2)) + (-3 - 135*S^2 - 409*S^4 - 213*S^6)/(6*S^3))*Zeta[3] + HPL[{2, 1}, -S^2]*((12*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 - (4*Pi^2*(89 + 581*S^2 + 138*S^4))/(9*S*(1 + S^2)) - 512*S*Zeta[3]) + HPL[{3}, -S^2]*((Pi^2*(65 + 615*S^2 + 28*S^4))/(9*S*(1 + S^2)) - (2*(12 - 215*S^2 - 181*S^4 + 42*S^6))/(3*S^3) - 496*S*HPL[{2, 1}, -S^2] + 8*S*Zeta[3]) + HPL[{2}, -S^2]*((2779*Pi^4*S)/180 - ((1 + S^2)*(301 - 3818*S^2 + 301*S^4))/(12*S^3) + (Pi^2*(-60 + 966*S^2 + 2173*S^4 + 1056*S^6 - 43*S^8))/(18*S^3*(1 + S^2)) - (2*(-9 - 242*S^2 + 139*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (296*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(-17 - 128*S^2 + 81*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (2*(21 - 50*S^2 + 153*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{2}, -S^2]*((57773*Pi^6*S)/22680 + (249 + 12204*S^2 + 21484*S^4 + 249*S^6)/(48*S^3) + (Pi^4*(-386 + 4826*S^2 + 34994*S^4 + 28255*S^6 - 499*S^8))/(2160*S^3*(1 + S^2)) + (Pi^2*(-59 + 1649*S^2 + 7649*S^4 + 5750*S^6 - 95*S^8))/(72*S^3*(1 + S^2)) - (8*S*HPL[{3}, -S^2]^2)/3 + ((25*Pi^2*S)/3 + (-5 - 246*S^2 + 590*S^4 - 19*S^6)/(6*S^3))*HPL[{4}, -S^2] + ((-49 + 485*S^2 + 438*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + 114*S*HPL[{6}, -S^2] - (592*S*HPL[{2, 1}, -S^2]^2)/3 + ((-752*Pi^2*S)/9 + (2*(2 + 97*S^2 - 497*S^4 + 4*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] + ((79 - 116*S^2 + 549*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (2*(59 - 126*S^2 + 187*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - 18*S*HPL[{4, 2}, -S^2] - (580*S*HPL[{5, 1}, -S^2])/3 + ((1520*Pi^2*S)/9 - (4*(-1 + 58*S^2 - 448*S^4 + S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (16*(-32 - 98*S^2 + 27*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(-225 - 502*S^2 + 95*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (1328*S*HPL[{3, 2, 1}, -S^2])/3 + (4432*S*HPL[{4, 1, 1}, -S^2])/3 - (32*(41 + 24*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (31552*S*HPL[{3, 1, 1, 1}, -S^2])/3 + 2080*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(22 + 93*S^2 - 144*S^4))/(9*S*(1 + S^2)) + (21 + 20*S^2 - 158*S^4 - 202*S^6 - 141*S^8)/(6*S^3*(1 + S^2)))*Zeta[3] + 8*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-73 + 314*S^2 - 7*S^4))/(18*S*(1 + S^2)) + (-1 - 525*S^2 + 347*S^4 - 325*S^6)/(12*S^3) + 24*S*HPL[{2, 1}, -S^2] - (16*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-2*Pi^2*(152 + 267*S^2 + 22*S^4))/(9*S*(1 + S^2)) + (81 - 974*S^2 + 30*S^4 - 81*S^6)/(3*S^3) + (80*S*Zeta[3])/3) - (2*(-74 - 174*S^2 + 173*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^2*((4363*Pi^6*S)/1890 - (Pi^4*S*(-8481 - 8603*S^2 + 86*S^4))/(720*(1 + S^2)) + (-2304 + 23788*S^2 + 249*S^4)/(96*S) + (Pi^2*(-894 + 13424*S^2 + 13919*S^4 - 495*S^6))/(288*S*(1 + S^2)) + ((38 + 203*S^2 + 75*S^4)*HPL[{1}, -S^2]^5)/(9*S*(1 + S^2)) + (10*S*HPL[{1}, -S^2]^6)/3 + ((373*Pi^2*S)/36 + (-1 - 46*S^2 + 814*S^4 - 9*S^6)/(24*S^3))*HPL[{2}, -S^2]^2 + (83*S*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((163*Pi^2*S)/18 + (-45 + 923*S^2 + 905*S^4 - 15*S^6)/(36*S^3) + (86*S*HPL[{2}, -S^2])/3) - (7*S*HPL[{3}, -S^2]^2)/3 + ((115*Pi^2*S)/18 + (-15 + 165*S^2 + 688*S^4 + 479*S^6 - 5*S^8)/(12*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((42 + 317*S^2 + 159*S^4)*HPL[{5}, -S^2])/(6*S*(1 + S^2)) + 47*S*HPL[{6}, -S^2] - (370*S*HPL[{2, 1}, -S^2]^2)/3 + ((-451*Pi^2*S)/9 + (15 - 195*S^2 - 1294*S^4 - 1015*S^6 + 13*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((3 - 274*S^2 - 233*S^4)*HPL[{3, 2}, -S^2])/(6*S*(1 + S^2)) + ((-9 - 494*S^2 - 345*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (S*HPL[{4, 2}, -S^2])/3 - 54*S*HPL[{5, 1}, -S^2] + ((932*Pi^2*S)/9 - (2*(6 - 70*S^2 - 596*S^4 - 489*S^6 + 7*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (4*(-70 - 137*S^2 + 26*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (2*(-425 - 964*S^2 + 91*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{3, 1, 2}, -S^2])/3 + 216*S*HPL[{3, 2, 1}, -S^2] + (2200*S*HPL[{4, 1, 1}, -S^2])/3 + (4*(-147 - 380*S^2 + 25*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (1744*S*HPL[{3, 1, 1, 1}, -S^2])/3 + (3520*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((Pi^2*S*(464 + 355*S^2))/(18*(1 + S^2)) + (-6 + 484*S^2 - 51*S^4)/(12*S))*Zeta[3] + 16*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(-363 - 763*S^2 + 115*S^4))/(18*S*(1 + S^2)) + (201 - 1780*S^2 - 2550*S^4 - 434*S^6 + 39*S^8)/(12*S^3*(1 + S^2)) - (4*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(-1 + 220*S^2 + 83*S^4))/(36*S*(1 + S^2)) + (-81 + 293*S^2 + 1350*S^4 + 827*S^6 - 53*S^8)/(24*S^3*(1 + S^2)) + (28*S*HPL[{2, 1}, -S^2])/3 + (4*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((Pi^2*(481 + 2365*S^2 + 906*S^4))/(54*S*(1 + S^2)) + (-99 + 1055*S^2 + 1113*S^4 - 9*S^6)/(18*S^3) + ((161 + 1034*S^2 + 357*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + 16*S*HPL[{3}, -S^2] - (344*S*HPL[{2, 1}, -S^2])/3 + (44*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((7643*Pi^4*S)/1080 + (-318 + 2647*S^2 + 2950*S^4 + 17*S^6)/(24*S^3) + (Pi^2*(-45 + 1117*S^2 + 2187*S^4 + 1071*S^6 - 14*S^8))/(36*S^3*(1 + S^2)) + ((515*Pi^2*S)/18 + (-30 + 450*S^2 + 1081*S^4 + 540*S^6 - 13*S^8)/(6*S^3*(1 + S^2)))*HPL[{2}, -S^2] + 31*S*HPL[{2}, -S^2]^2 + ((11 + 144*S^2 + 61*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (74*S*HPL[{4}, -S^2])/3 + ((-161 - 1034*S^2 - 357*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 172*S*HPL[{3, 1}, -S^2] + 344*S*HPL[{2, 1, 1}, -S^2] + ((14 + 89*S^2 + 9*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]*((1441*Pi^4*S)/216 + (-10 + 810*S^2 + 3929*S^4 + 2967*S^6 - 46*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-27 + 239*S^2 + 2598*S^4 + 2256*S^6 - 32*S^8))/(72*S^3*(1 + S^2)) + ((-7 + 142*S^2 + 127*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) + (19*S*HPL[{4}, -S^2])/3 + (2*(-70 - 137*S^2 + 26*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 120*S*HPL[{3, 1}, -S^2] + (740*S*HPL[{2, 1, 1}, -S^2])/3 + ((4 + 53*S^2 + 26*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (7*S*(41 + 24*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(8236 + 39487*S^2 + 15965*S^4))/(2160*S*(1 + S^2)) + (-910 + 7069*S^2 + 8126*S^4 + 211*S^6)/(48*S^3) + (Pi^2*(-393 + 4749*S^2 + 10155*S^4 + 5203*S^6 - 2*S^8))/(144*S^3*(1 + S^2)) + ((73 + 395*S^2 + 136*S^4)*HPL[{2}, -S^2]^2)/(6*S*(1 + S^2)) + ((23*Pi^2*S)/3 + (-19 + 165*S^2 + 511*S^4 + 263*S^6 - 8*S^8)/(6*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((39 + 298*S^2 + 111*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) + (116*S*HPL[{5}, -S^2])/3 + ((-515*Pi^2*S)/9 + (30 - 450*S^2 - 1081*S^4 - 540*S^6 + 13*S^8)/(3*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (2*(84 + 539*S^2 + 197*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (44*S*HPL[{3, 2}, -S^2])/3 - (280*S*HPL[{4, 1}, -S^2])/3 + (2*(161 + 1034*S^2 + 357*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 248*S*HPL[{2, 2, 1}, -S^2] + 840*S*HPL[{3, 1, 1}, -S^2] - 688*S*HPL[{2, 1, 1, 1}, -S^2] + ((109*Pi^2*S)/9 + (-3 + 158*S^2 + 284*S^4 + 122*S^6 - 9*S^8)/(6*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(389 + 2237*S^2 + 818*S^4))/(36*S*(1 + S^2)) + (-71 + 770*S^2 + 1856*S^4 + 926*S^6 - 25*S^8)/(8*S^3*(1 + S^2)) + (22*S*HPL[{3}, -S^2])/3 - 124*S*HPL[{2, 1}, -S^2] + (46*S*Zeta[3])/3) + (238*S*Zeta[5])/3)) + HPL[{0}, S^2]*((Pi^6*S*(314899 + 272886*S^2))/(45360*(1 + S^2)) + (-9176 + 94849*S^2 + 9945*S^4)/(96*S) + (Pi^2*(-3192 + 39909*S^2 + 46358*S^4 + 3001*S^6))/(288*S*(1 + S^2)) + (Pi^4*(-2436 + 91831*S^2 + 100742*S^4 + 4467*S^6))/(4320*S*(1 + S^2)) + ((26*Pi^2*S)/9 + (-3 + 61*S^2 + 67*S^4 + 3*S^6)/(3*S^3))*HPL[{1}, -S^2]^5 + (28*(1 + 3*S^2)*HPL[{1}, -S^2]^6)/(9*S) + ((20 + 223*S^2)*HPL[{2}, -S^2]^3)/(9*S) + ((10 - 25*S^2 - 37*S^4)*HPL[{3}, -S^2]^2)/(3*S*(1 + S^2)) + ((-7*Pi^2*S)/3 + (-90 + 305*S^2 + 1015*S^4 + 633*S^6 - 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((30 + 274*S^2 + 299*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) - 56*S*HPL[{7}, -S^2] - (4*(-9 + 263*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-98*Pi^2*S)/9 + (-9 + 102*S^2 - 444*S^4 - 582*S^6 - 11*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-182*Pi^2*S)/9 + (33 - 69*S^2 - 1090*S^4 - 1021*S^6 - 9*S^8)/(3*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((5 - 11*S^4)*HPL[{4, 2}, -S^2])/(3*S*(1 + S^2)) + (20*S*HPL[{4, 3}, -S^2])/3 - (2*(21 + 269*S^2 + 282*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + (46*S*HPL[{5, 2}, -S^2])/3 + 44*S*HPL[{6, 1}, -S^2] + ((80*Pi^2*S)/9 + (4*(-15 + 349*S^2 - 40*S^4 + 2*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + ((232*Pi^2*S)/9 + (2*(-117 + 2235*S^2 + 115*S^4 + 17*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] - (2*(1 + 5*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (2*(79 + 887*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (8*S*HPL[{3, 2, 2}, -S^2])/3 + (128*S*HPL[{3, 3, 1}, -S^2])/3 + (4*(47 + 554*S^2 + 511*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (172*S*HPL[{4, 1, 2}, -S^2])/3 + (460*S*HPL[{4, 2, 1}, -S^2])/3 + 296*S*HPL[{5, 1, 1}, -S^2] + (-16*Pi^2*S - (4*(-45 + 810*S^2 + 218*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (608*S*HPL[{2, 2, 2, 1}, -S^2])/3 - (8*(53 + 680*S^2 + 633*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (1504*S*HPL[{3, 1, 1, 2}, -S^2])/3 + (1504*S*HPL[{3, 1, 2, 1}, -S^2])/3 + (3328*S*HPL[{3, 2, 1, 1}, -S^2])/3 + 3488*S*HPL[{4, 1, 1, 1}, -S^2] + (80*(10 + 129*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) - (544*S*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 544*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 960*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 320*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((373*Pi^4*S)/90 - (Pi^2*S*(-242 - 247*S^2 + 3*S^4))/(9*(1 + S^2)) + (24 + 1551*S^2 + 1512*S^4 + 49*S^6)/(12*S*(1 + S^2)))*Zeta[3] + (2*S*(21 + 22*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((Pi^2*(-69 - 1399*S^2 - 1158*S^4))/(9*S*(1 + S^2)) + (27 - 471*S^2 - 1857*S^4 - 1441*S^6 - 66*S^8)/(3*S^3*(1 + S^2)) - (32*S*Zeta[3])/3) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(-39 + 488*S^2 + 39*S^4))/(36*S^3) + (Pi^2*(162 + 689*S^2 + 397*S^4))/(18*S*(1 + S^2)) + (235*(1 + 3*S^2)*HPL[{2}, -S^2])/(9*S) - (4*S*HPL[{3}, -S^2])/3 + (4*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(-42 + 1041*S^2 + 917*S^4))/(36*S*(1 + S^2)) + (-21 + S^2 + 2075*S^4 + 117*S^6)/(24*S^3) + (2*S*HPL[{3}, -S^2])/3 - (76*S*HPL[{2, 1}, -S^2])/3 + 4*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((4*Pi^2*(34 + 728*S^2 + 601*S^4))/(9*S*(1 + S^2)) + (-11 + 273*S^2 + 887*S^4 + 59*S^6)/S^3 + (32*S*Zeta[3])/3) + HPL[{4}, -S^2]*((Pi^2*(41 + 390*S^2 + 371*S^4))/(18*S*(1 + S^2)) + (24 + 502*S^2 + 1097*S^4 + 640*S^6 - 11*S^8)/(6*S^3*(1 + S^2)) + (76*S*HPL[{2, 1}, -S^2])/3 + (44*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((4*Pi^4*S)/5 + (261 - 2967*S^2 - 1374*S^4 - 58*S^6)/(6*S^3) + (Pi^2*(90 - 1753*S^2 - 345*S^4 - 26*S^6))/(18*S^3) + (160*S*HPL[{3, 1}, -S^2])/3 + (272*S*HPL[{2, 1, 1}, -S^2])/3 - (4*(31 + 9*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-59*Pi^4*S)/270 + (-261 + 1734*S^2 + 4718*S^4 + 2738*S^6 - 113*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-54 + 243*S^2 + 992*S^4 + 663*S^6 + 8*S^8))/(36*S^3*(1 + S^2)) - (20*S*HPL[{4}, -S^2])/3 + (2*(-59 + 69*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (40*S*HPL[{3, 1}, -S^2])/3 + 48*S*HPL[{2, 1, 1}, -S^2] + (2*(11 + 48*S^2 + 33*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((1313*Pi^4*S)/270 + ((1 + S^2)*(-109 + 1104*S^2 + 109*S^4))/(6*S^3) + (Pi^2*(-87 + 1978*S^2 + 4096*S^4 + 2198*S^6 + 71*S^8))/(54*S^3*(1 + S^2)) + ((124*Pi^2*S)/9 + (4*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(9*S^3))*HPL[{2}, -S^2] + (4*(14 + 55*S^2 + 43*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{4}, -S^2])/3 - (940*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (16*S*HPL[{3, 1}, -S^2])/3 + (4*(32 + 131*S^2 + 93*S^4)*Zeta[3])/(9*S*(1 + S^2))) + ((52*Pi^2*S)/3 + (S*(462 + 471*S^2 + 13*S^4))/(3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(852 + 22552*S^2 + 18213*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(-84 + 1561*S^2 + 5358*S^4 + 209*S^6))/(72*S^3) + (-153 + 4256*S^2 + 9917*S^4 + 804*S^6)/(24*S^3) + ((46*Pi^2*S)/9 + (3 - 73*S^2 + 303*S^4 + 3*S^6)/(6*S^3))*HPL[{3}, -S^2] + ((-29 + 58*S^2 + 93*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + 14*S*HPL[{5}, -S^2] + ((-40*Pi^2*S)/9 - (2*(-15 + 349*S^2 - 40*S^4 + 2*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(-19 + 515*S^2)*HPL[{3, 1}, -S^2])/(3*S) - 4*S*HPL[{3, 2}, -S^2] - (100*S*HPL[{4, 1}, -S^2])/3 + (8*(-9 + 263*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (304*S*HPL[{2, 2, 1}, -S^2])/3 - 256*S*HPL[{3, 1, 1}, -S^2] - (272*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((32*Pi^2*S)/9 + (2*(-3 + 21*S^2 + 56*S^4))/(3*S^3))*Zeta[3] - (4*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*(((1 + S^2)*(-1039 + 9360*S^2 + 1039*S^4))/(24*S^3) + (Pi^4*(7949 + 34087*S^2 + 18260*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(-369 + 4536*S^2 + 10166*S^4 + 5712*S^6 + 291*S^8))/(72*S^3*(1 + S^2)) + ((Pi^2*(481 + 2130*S^2 + 1277*S^4))/(18*S*(1 + S^2)) + (-105 + 1467*S^2 + 1741*S^4 + 105*S^6)/(6*S^3))*HPL[{2}, -S^2] + (74*(1 + 3*S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((2*Pi^2*S)/3 + (2*(-11 + 117*S^2 + 138*S^4 + 2*S^6))/(3*S^3))*HPL[{3}, -S^2] + ((89 + 296*S^2 + 231*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (44*S*HPL[{5}, -S^2])/3 + ((-124*Pi^2*S)/3 - (4*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (4*(116 + 461*S^2 + 351*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 16*S*HPL[{4, 1}, -S^2] + (940*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - 16*S*HPL[{3, 1, 1}, -S^2] + ((52*Pi^2*S)/9 + (3 + 103*S^2 + 131*S^4 + 15*S^6)/(3*S^3))*Zeta[3] + (44*S*Zeta[5])/3) + HPL[{1}, -S^2]*((42013*Pi^6*S)/22680 + (2*(1 + S^2)*(-101 + 880*S^2 + 101*S^4))/(3*S^3) + (Pi^2*(-303 + 2948*S^2 + 6946*S^4 + 4012*S^6 + 253*S^8))/(36*S^3*(1 + S^2)) + (Pi^4*(-1218 + 33021*S^2 + 66581*S^4 + 35863*S^6 + 1353*S^8))/(2160*S^3*(1 + S^2)) + ((83*Pi^2*S)/9 + (-17 + 347*S^2 + 397*S^4 + 17*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 + (4*S*HPL[{3}, -S^2]^2)/3 + ((-22*Pi^2*S)/9 + (-51 + 466*S^2 + 1016*S^4 + 550*S^6 + 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(56 + 197*S^2 + 163*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (110*S*HPL[{6}, -S^2])/3 + ((Pi^2*(-481 - 2130*S^2 - 1277*S^4))/(9*S*(1 + S^2)) + (105 - 1467*S^2 - 1741*S^4 - 105*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] + ((-344*Pi^2*S)/9 - (2*(-39 + 581*S^2 + 673*S^4 + 21*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] - (4*(13 + 31*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2*(155 + 560*S^2 + 429*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 4*S*HPL[{4, 2}, -S^2] + (136*S*HPL[{5, 1}, -S^2])/3 + ((248*Pi^2*S)/3 + (8*(-15 + 269*S^2 + 323*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (592*(1 + 3*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (8*(88 + 351*S^2 + 265*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - 32*S*HPL[{4, 1, 1}, -S^2] - (1880*(1 + 3*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + 32*S*HPL[{3, 1, 1, 1}, -S^2] + ((Pi^2*(107 + 428*S^2 + 269*S^4))/(9*S*(1 + S^2)) + (12 + 149*S^2 + 323*S^4 + 191*S^6 + 21*S^8)/(3*S^3*(1 + S^2)))*Zeta[3] - 4*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(68 + 315*S^2 + 241*S^4))/(9*S*(1 + S^2)) + (-69 + 652*S^2 + 1482*S^4 + 796*S^6 + 3*S^8)/(6*S^3*(1 + S^2)) + (16*S*Zeta[3])/3) + HPL[{2}, -S^2]*((3487*Pi^4*S)/540 + (Pi^2*(-123 + 2207*S^2 + 2557*S^4 + 83*S^6))/(36*S^3) + (-319 + 4193*S^2 + 4895*S^4 + 319*S^6)/(12*S^3) + (22*(1 + 3*S^2)*HPL[{3}, -S^2])/(3*S) - 4*S*HPL[{4}, -S^2] - (296*(1 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (22*(1 + 3*S^2)*Zeta[3])/S) + (2*(105 + 439*S^2 + 312*S^4)*Zeta[5])/(3*S*(1 + S^2)))) - (2*S*(10 + 241*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((5*(1 + S^2)*(-663 + 6272*S^2 + 663*S^4))/(32*S^3) + (Pi^6*(50539 + 266051*S^2 + 120854*S^4))/(45360*S*(1 + S^2)) + (Pi^2*(-1949 + 15390*S^2 + 18525*S^4 + 1250*S^6))/(144*S^3) + (Pi^4*(-5438 + 55601*S^2 + 128685*S^4 + 67847*S^6 + 1161*S^8))/(4320*S^3*(1 + S^2)) + ((83 + 538*S^2 + 83*S^4)*HPL[{2}, -S^2]^3)/(9*S*(1 + S^2)) + ((-19 - 73*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((392*Pi^2*S)/9 + (-69 + 1160*S^2 + 2536*S^4 + 1332*S^6 + 9*S^8)/(3*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((703 + 3479*S^2 + 1822*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) + 716*S*HPL[{7}, -S^2] - (296*(1 + 3*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-788*Pi^2*S)/9 + (2*(1 - 32*S^2 - 8*S^4 + 52*S^6 + 35*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-2800*Pi^2*S)/9 + (2*(33 - 688*S^2 - 1292*S^4 - 484*S^6 + 111*S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-79 - 173*S^2)*HPL[{4, 2}, -S^2])/(3*S) + 44*S*HPL[{4, 3}, -S^2] - (4*(241 + 1072*S^2 + 555*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + 104*S*HPL[{5, 2}, -S^2] - 556*S*HPL[{6, 1}, -S^2] + ((248*Pi^2*S)/3 + (4*(-17 + 347*S^2 + 397*S^4 + 17*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + (480*Pi^2*S + (8*(-35 + 693*S^2 + 749*S^4 + 5*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] - (16*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (8*(85 + 538*S^2 + 81*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) + 992*S*HPL[{3, 2, 2}, -S^2] + 2976*S*HPL[{3, 3, 1}, -S^2] + (8*(343 + 2056*S^2 + 453*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 2976*S*HPL[{4, 1, 2}, -S^2] + 8928*S*HPL[{4, 2, 1}, -S^2] + 18592*S*HPL[{5, 1, 1}, -S^2] + ((-1888*Pi^2*S)/3 + (16*(5 - 91*S^2 - 91*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] - 1984*S*HPL[{2, 2, 2, 1}, -S^2] - (16*(128 + 767*S^2 + 189*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 3968*S*HPL[{3, 1, 1, 2}, -S^2] + 3968*S*HPL[{3, 1, 2, 1}, -S^2] + 9920*S*HPL[{3, 2, 1, 1}, -S^2] + 28992*S*HPL[{4, 1, 1, 1}, -S^2] + (80*(13 + 86*S^2 + 13*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 4800*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 9600*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((859*Pi^4*S)/90 + (9 - 338*S^2 - 689*S^4 - 310*S^6)/(6*S^3) + (Pi^2*(-3 + 166*S^2 + 192*S^4 - 38*S^6 - 69*S^8))/(18*S^3*(1 + S^2)))*Zeta[3] - (2*(-25 + 11*S^2)*Zeta[3]^2)/(3*S) + HPL[{3, 1}, -S^2]*((-4*Pi^2*(106 + 653*S^2 + 193*S^4))/(9*S*(1 + S^2)) + (117 - 1763*S^2 - 1765*S^4 + 99*S^6)/(3*S^3) - 512*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(227 + 1182*S^2 + 519*S^4))/(18*S*(1 + S^2)) + (-71 + 3495*S^2 + 3695*S^4 + S^6)/(12*S^3) + (88*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*(((1 + S^2)*(-23 + 324*S^2 + 23*S^4))/(4*S^3) + (Pi^2*(147 + 691*S^2 + 358*S^4))/(18*S*(1 + S^2)) + 124*S*HPL[{3}, -S^2] - 248*S*HPL[{2, 1}, -S^2] + 124*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-24*(1 + S^2)*(3 - 40*S^2 + 3*S^4))/S^3 + (8*Pi^2*(89 + 581*S^2 + 138*S^4))/(9*S*(1 + S^2)) + 1024*S*Zeta[3]) + HPL[{3}, -S^2]*((1219*Pi^4*S)/135 + (-105 + 2721*S^2 + 2393*S^4 - 497*S^6)/(12*S^3) + (Pi^2*(-38 + 491*S^2 + 1163*S^4 + 529*S^6 - 49*S^8))/(18*S^3*(1 + S^2)) - 36*S*HPL[{4}, -S^2] + (4*(-9 - 242*S^2 + 139*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 496*S*HPL[{3, 1}, -S^2] + 992*S*HPL[{2, 1, 1}, -S^2] + (4*(22 + 37*S^2 + 9*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-2779*Pi^4*S)/90 + ((1 + S^2)*(301 - 3818*S^2 + 301*S^4))/(6*S^3) + (Pi^2*(60 - 966*S^2 - 2173*S^4 - 1056*S^6 + 43*S^8))/(9*S^3*(1 + S^2)) + (8*(-17 - 128*S^2 + 81*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((910*Pi^2*S)/9 - (2*(3 - 72*S^2 - 68*S^4 + 68*S^6 + 57*S^8))/(3*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*(-((1 + S^2)*(233 - 3618*S^2 + 233*S^4))/(8*S^3) + (Pi^4*(1489 + 9837*S^2 + 2790*S^4))/(360*S*(1 + S^2)) + (Pi^2*(-143 + 1586*S^2 + 3632*S^4 + 1742*S^6 - 97*S^8))/(24*S^3*(1 + S^2)) + ((394*Pi^2*S)/9 + (-3 + 35*S^2 - 15*S^4 - 37*S^6)/(3*S^3))*HPL[{3}, -S^2] + (67*(1 + 3*S^2)*HPL[{4}, -S^2])/(3*S) + 64*S*HPL[{5}, -S^2] + ((-124*Pi^2*S)/3 - (2*(-17 + 347*S^2 + 397*S^4 + 17*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (296*(1 + 3*S^2)*HPL[{3, 1}, -S^2])/(3*S) - 496*S*HPL[{3, 2}, -S^2] - 1488*S*HPL[{4, 1}, -S^2] + (592*(1 + 3*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + 992*S*HPL[{2, 2, 1}, -S^2] - 1984*S*HPL[{3, 1, 1}, -S^2] + ((430*Pi^2*S)/9 - (2*(-66 - 11*S^2 + 24*S^4 + 17*S^6))/(3*S*(1 + S^2)))*Zeta[3] + 364*S*Zeta[5]) + 924*S*Zeta[7])) - 1568*S*Zeta[9];
Et5uvwT3F3=(731275*(-1 + S^2))/(419904*S) + (Pi^2*(7262766 - 12021*S^2 + 12334051*S^4))/(314928*S) + (Pi^8*(855488 + 427744*S^2 + 2082133*S^4 + 1226645*S^6))/(8164800*S*(1 + S^2)) + (Pi^6*(5331570 + 6841137*S^2 + 23160143*S^4 + 21069968*S^6))/(14696640*S*(1 + S^2)) + (Pi^4*(42853980 + 42625698*S^2 + 99301091*S^4 + 97149917*S^6))/(12597120*S*(1 + S^2)) + ((-1 + S^6)*HPL[{1}, -S^2]^8)/(9*S^3) + HPL[{0}, S^2]^8*((6 + 3*S^2 + 10*S^4 + 4*S^6)/(1728*S*(1 + S^2)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(288*S^3)) + (413*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^4)/(324*S^3) + HPL[{0}, S^2]^7*((5*Pi^2*S^3)/2592 + (-106 + 113*S^2 + 324*S^4)/(5184*S) + ((-53 + 7*S^2 + 30*S^4 + 178*S^6 + 118*S^8)*HPL[{1}, -S^2])/(2592*S^3*(1 + S^2)) + (5*(1 + S^6)*HPL[{1}, -S^2]^2)/(432*S^3) + (5*S^3*HPL[{2}, -S^2])/432) + HPL[{1}, -S^2]^7*((131*(-1 + S^2)*(1 + S^2)^2)/(189*S^3) + (10*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(189*S^3) + (40*(1 + S^6)*HPL[{2}, -S^2])/(63*S^3)) - (4*(19 + 21*S^6)*HPL[{3}, -S^2]^3)/(27*S^3) + ((-490 - 340*S^2 - 159*S^4 + 176*S^6 + 26*S^8)*HPL[{4}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((Pi^2*(420 + 649*S^6))/(27*S^3) + (8148 - 26166*S^2 + 25728*S^4 + 147253*S^6 + 95095*S^8)/(162*S^3*(1 + S^2)))*HPL[{7}, -S^2] + (2*(-12957 - 7431*S^2 + 2763*S^4 + 16174*S^6 + 10648*S^8)*HPL[{8}, -S^2])/(27*S^3*(1 + S^2)) + (2*(4116 + 3253*S^6)*HPL[{9}, -S^2])/(9*S^3) + (896*(1 + S^6)*HPL[{2, 1}, -S^2]^3)/(27*S^3) + (4*(-425 - 6*S^2 - 6*S^4 + 488*S^6)*HPL[{3, 1}, -S^2]^2)/(27*S^3) + ((Pi^2*(-151 - 33*S^6))/(27*S^3) + (-851 - 271*S^2 + 1424*S^4 - 341*S^6 - 213*S^8)/(54*S^3*(1 + S^2)))*HPL[{4, 3}, -S^2] + ((Pi^2*(-431 - 152*S^6))/(27*S^3) + (-4163 - 1472*S^2 + 6525*S^4 - 4543*S^6 - 4327*S^8)/(81*S^3*(1 + S^2)))*HPL[{5, 2}, -S^2] + ((-43 + 29*S^2 + 36*S^4 + 718*S^6 + 646*S^8)*HPL[{5, 3}, -S^2])/(27*S^3*(1 + S^2)) + (2*(295 + 396*S^6)*HPL[{5, 4}, -S^2])/(9*S^3) + ((-7*Pi^2*(160 + 133*S^6))/(27*S^3) + (-7005 + 5301*S^2 - 1794*S^4 - 66086*S^6 - 46316*S^8)/(81*S^3*(1 + S^2)))*HPL[{6, 1}, -S^2] + ((-113 + 67*S^2 + 90*S^4 + 1209*S^6 + 1029*S^8)*HPL[{6, 2}, -S^2])/(27*S^3*(1 + S^2)) + (2*(1173 + 1654*S^6)*HPL[{6, 3}, -S^2])/(9*S^3) + ((10453 + 2569*S^2 - 3942*S^4 - 23844*S^6 - 15960*S^8)*HPL[{7, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(2973 + 4117*S^6)*HPL[{7, 2}, -S^2])/(9*S^3) + (2*(1327 + 1874*S^6)*HPL[{8, 1}, -S^2])/(3*S^3) + (2696*(-1 + S^6)*HPL[{2, 1, 1}, -S^2]^2)/(9*S^3) + ((5*Pi^2*(32 + 169*S^6))/(27*S^3) + (4359 + 21999*S^2 + 3585*S^4 + 6209*S^6)/(81*S^3))*HPL[{3, 2, 2}, -S^2] + ((4*Pi^2*(69 + 632*S^6))/(27*S^3) + (2*(5608 + 39031*S^2 + 38181*S^4 + 14995*S^6 + 10453*S^8))/(81*S^3*(1 + S^2)))*HPL[{3, 3, 1}, -S^2] + ((1928 + 1172*S^2 - 378*S^4 - 2613*S^6 - 1857*S^8)*HPL[{3, 3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((Pi^2*(233 + 2575*S^6))/(27*S^3) + (10108 + 77647*S^2 + 76362*S^4 + 30405*S^6 + 22014*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1, 2}, -S^2] + (2*(-1935 - 1305*S^2 + 315*S^4 + 2149*S^6 + 1519*S^8)*HPL[{4, 1, 3}, -S^2])/(27*S^3*(1 + S^2)) + ((Pi^2*(605 + 7603*S^6))/(27*S^3) + (29860 + 230833*S^2 + 228696*S^4 + 92919*S^6 + 66924*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 2, 1}, -S^2] + ((1852 + 916*S^2 - 468*S^4 - 2981*S^6 - 2045*S^8)*HPL[{4, 2, 2}, -S^2])/(27*S^3*(1 + S^2)) + (10*(-1 + 4*S^6)*HPL[{4, 2, 3}, -S^2])/(9*S^3) + (2*(-4007 - 2729*S^2 + 639*S^4 + 5335*S^6 + 4057*S^8)*HPL[{4, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(330 + 307*S^6)*HPL[{4, 3, 2}, -S^2])/(9*S^3) - (4*(211 + 237*S^6)*HPL[{4, 4, 1}, -S^2])/(9*S^3) + ((2*Pi^2*(583 + 7825*S^6))/(27*S^3) + (48833 + 449405*S^2 + 473229*S^4 + 230327*S^6 + 161990*S^8)/(81*S^3*(1 + S^2)))*HPL[{5, 1, 1}, -S^2] + ((-3838 - 3046*S^2 + 396*S^4 + 5237*S^6 + 4445*S^8)*HPL[{5, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + (4*(116 + 67*S^6)*HPL[{5, 1, 3}, -S^2])/(9*S^3) + ((-33478 - 21886*S^2 + 5796*S^4 + 47297*S^6 + 35705*S^8)*HPL[{5, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(727 + 806*S^6)*HPL[{5, 2, 2}, -S^2])/(9*S^3) - (4*(382 + 563*S^6)*HPL[{5, 3, 1}, -S^2])/(9*S^3) + (2*(-44634 - 25572*S^2 + 9531*S^4 + 71672*S^6 + 52610*S^8)*HPL[{6, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(1054 + 1301*S^6)*HPL[{6, 1, 2}, -S^2])/(9*S^3) - (2*(294 + 1181*S^6)*HPL[{6, 2, 1}, -S^2])/(9*S^3) + (80*(72 + 47*S^6)*HPL[{7, 1, 1}, -S^2])/(9*S^3) + ((-8*Pi^2*(218 + 135*S^6))/(27*S^3) - (8*(1321 + 3198*S^2 + 3198*S^4 + 1321*S^6))/(81*S^3))*HPL[{2, 2, 2, 1}, -S^2] + ((4*Pi^2*(1301 + 352*S^6))/(27*S^3) + (28319 + 56966*S^2 + 102726*S^4 + 88046*S^6 + 13535*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 1, 1, 2}, -S^2] + ((4*Pi^2*(1301 + 352*S^6))/(27*S^3) + (28319 + 56966*S^2 + 102726*S^4 + 88046*S^6 + 13535*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 1, 2, 1}, -S^2] - (275*(-1 + S^6)*HPL[{3, 1, 2, 2}, -S^2])/(27*S^3) + ((4*Pi^2*(2609 + 1162*S^6))/(27*S^3) + (60023 + 165422*S^2 + 256230*S^4 + 196502*S^6 + 45239*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2, 1, 1}, -S^2] - (275*(-1 + S^6)*HPL[{3, 2, 1, 2}, -S^2])/(27*S^3) + ((-3917 - 12845*S^2 - 4464*S^4 - 16355*S^6 - 7427*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(39 + 371*S^6)*HPL[{3, 2, 2, 2}, -S^2])/(9*S^3) - (8*(194 + 1175*S^6)*HPL[{3, 2, 3, 1}, -S^2])/(9*S^3) - (16*(262 + 820*S^2 + 279*S^4 + 1005*S^6 + 447*S^8)*HPL[{3, 3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(95 + 588*S^6)*HPL[{3, 3, 1, 2}, -S^2])/(9*S^3) - (56*(94 + 513*S^6)*HPL[{3, 3, 2, 1}, -S^2])/(9*S^3) + ((8*Pi^2*(3869 + 1714*S^6))/(27*S^3) + (2*(93182 + 251519*S^2 + 375030*S^4 + 277719*S^6 + 60378*S^8))/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1, 1}, -S^2] - (4*(19 + 625*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(27*S^3) + (8*(1367 + 7286*S^6)*HPL[{4, 1, 1, 3}, -S^2])/(9*S^3) - (4*(3163 + 9859*S^2 + 3348*S^4 + 12685*S^6 + 5989*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(4693 + 24425*S^6)*HPL[{4, 1, 2, 2}, -S^2])/(9*S^3) + (8*(703 + 3647*S^6)*HPL[{4, 1, 3, 1}, -S^2])/(3*S^3) - (4*(9451 + 29539*S^2 + 10044*S^4 + 36805*S^6 + 16717*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(2869 + 14753*S^6)*HPL[{4, 2, 1, 2}, -S^2])/(9*S^3) + (2*(2821 + 14765*S^6)*HPL[{4, 2, 2, 1}, -S^2])/(9*S^3) + (8*(4139 + 21785*S^6)*HPL[{4, 3, 1, 1}, -S^2])/(9*S^3) - (4*(19349 + 61181*S^2 + 20916*S^4 + 78665*S^6 + 36833*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(2769 + 14539*S^6)*HPL[{5, 1, 1, 2}, -S^2])/(3*S^3) + (4*(4609 + 24207*S^6)*HPL[{5, 1, 2, 1}, -S^2])/(3*S^3) + (4*(11073 + 58039*S^6)*HPL[{5, 2, 1, 1}, -S^2])/(3*S^3) + (16*(20727 + 108601*S^6)*HPL[{6, 1, 1, 1}, -S^2])/(9*S^3) + ((56*(-88 + 273*S^2 - 273*S^4 + 88*S^6))/(27*S^3) + (16*Pi^2*(-209 + 97*S^6))/(27*S^3))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((56*(-88 + 273*S^2 - 273*S^4 + 88*S^6))/(9*S^3) + (16*Pi^2*(-209 + 97*S^6))/(9*S^3))*HPL[{2, 2, 1, 1, 1}, -S^2] - (16*(709 + 1825*S^2 + 558*S^4 + 1825*S^6 + 709*S^8)*HPL[{2, 2, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(709 + 1825*S^2 + 558*S^4 + 1825*S^6 + 709*S^8)*HPL[{2, 2, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2656*(-1 + S^6)*HPL[{2, 2, 2, 2, 1}, -S^2])/(9*S^3) + ((16*Pi^2*(-1017 + 722*S^6))/(27*S^3) + (8*(-10202 + 40986*S^2 - 25362*S^4 + 14631*S^6))/(81*S^3))*HPL[{3, 1, 1, 1, 1}, -S^2] + (8*(8669 + 22061*S^2 + 6696*S^4 + 22061*S^6 + 8669*S^8)*HPL[{3, 1, 1, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + (8*(14341 + 36661*S^2 + 11160*S^4 + 36661*S^6 + 14341*S^8)*HPL[{3, 1, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-1117 + 221*S^6)*HPL[{3, 1, 1, 2, 2}, -S^2])/(9*S^3) + (8*(17177 + 43961*S^2 + 13392*S^4 + 43961*S^6 + 17177*S^8)*HPL[{3, 1, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-1117 + 221*S^6)*HPL[{3, 1, 2, 1, 2}, -S^2])/(9*S^3) - (40*(-1 + S^6)*HPL[{3, 1, 2, 2, 1}, -S^2])/(9*S^3) + (32*(-1907 + 565*S^6)*HPL[{3, 1, 3, 1, 1}, -S^2])/(9*S^3) + (8*(35611 + 91411*S^2 + 27900*S^4 + 91411*S^6 + 35611*S^8)*HPL[{3, 2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-2113 + 1217*S^6)*HPL[{3, 2, 1, 1, 2}, -S^2])/(9*S^3) - (8008*(-1 + S^6)*HPL[{3, 2, 1, 2, 1}, -S^2])/(9*S^3) - (104*(271 + 73*S^6)*HPL[{3, 2, 2, 1, 1}, -S^2])/(9*S^3) - (32*(965 + 153*S^6)*HPL[{3, 3, 1, 1, 1}, -S^2])/(3*S^3) + (16*(53601 + 137733*S^2 + 42066*S^4 + 138245*S^6 + 54113*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (64*(-781 + 446*S^6)*HPL[{4, 1, 1, 1, 2}, -S^2])/(9*S^3) - (64*(-364 + 365*S^6)*HPL[{4, 1, 1, 2, 1}, -S^2])/(9*S^3) - (32*(2665 + 691*S^6)*HPL[{4, 1, 2, 1, 1}, -S^2])/(9*S^3) - (8704*(32 + 5*S^6)*HPL[{4, 2, 1, 1, 1}, -S^2])/(9*S^3) - (32*(17397 + 2623*S^6)*HPL[{5, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-16*Pi^2*(473 + 278*S^6))/(27*S^3) - (8*(4429 + 15624*S^2 + 15624*S^4 + 4429*S^6))/(81*S^3))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (7168*(1 + S^6)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(9*S^3) + (7168*(1 + S^6)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/(3*S^3) - (32*(922 + 2272*S^2 + 675*S^4 + 2528*S^6 + 1178*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (64*(574 + 769*S^6)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(9*S^3) - (64*(1246 + 1441*S^6)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(9*S^3) - (64*(1694 + 1889*S^6)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(9*S^3) - (64*(1918 + 2113*S^6)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(9*S^3) - (64*(3374 + 3569*S^6)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(9*S^3) - (64*(3382 + 3577*S^6)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + (1600*(14 + 32*S^2 + 9*S^4 + 32*S^6 + 14*S^8)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4160*(-1 + S^6)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(3*S^3) - (16640*(-1 + S^6)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(3*S^3) - (41600*(-1 + S^6)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (1280*(-69 + 61*S^6)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (10240*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-8*Pi^2*S^3)/81 - (8*(-1 + S^2))/(27*S) - (8*S^3*HPL[{0}, S^2])/9 - (8*S^3*HPL[{0}, S^2]^2)/27 - (8*(-1 + S^6)*HPL[{1}, -S^2])/(9*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(27*S^3))*Log[T]^7 + ((Pi^2*(102 + 51*S^2 + 10*S^4 - 92*S^6))/(54*S*(1 + S^2)) + (798 + 2919*S^2 - 5039*S^4 + 616*S^6)/(972*S*(1 + S^2)))*Zeta[3]^2 + (32*S^3*Zeta[3]^3)/3 + HPL[{0}, S^2]^6*((Pi^2*(28 + 14*S^2 + 59*S^4 + 31*S^6))/(648*S*(1 + S^2)) + (3372 + 5727*S^2 + 34735*S^4 + 34972*S^6)/(93312*S*(1 + S^2)) + ((-5 + 53*S^2 + 32*S^4 + 116*S^6 + 58*S^8)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)) + (7*(1 + S^6)*HPL[{1}, -S^2]^3)/(162*S^3) + ((4 + 54*S^2 + 25*S^4 + 178*S^6 + 128*S^8)*HPL[{2}, -S^2])/(864*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((7*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (382 + 421*S^2 + 3633*S^4 + 6883*S^6 + 3721*S^8)/(15552*S^3*(1 + S^2)) + (25*(1 + S^6)*HPL[{2}, -S^2])/(432*S^3)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(144*S^3) - (11*HPL[{2, 1}, -S^2])/(108*S^3) + (25*S^3*Zeta[3])/108) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(401 + 6*S^2 + 6*S^4 + 315*S^6))/(162*S^3) + (2*(727 - 511*S^2 - 511*S^4 + 727*S^6))/(81*S^3) + (40*S^3*Zeta[3])/9) + Log[T]^6*((77*(-1 + S^2))/(81*S) + (5*Pi^2*(18 + 9*S^2 + 46*S^4 + 28*S^6))/(243*S*(1 + S^2)) + (26*S^3*HPL[{0}, S^2]^3)/81 + (28*(-1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^2*((5*(18 + 9*S^2 + 46*S^4 + 28*S^6))/(81*S*(1 + S^2)) + (10*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3)) + (20*(14 + 32*S^2 + 9*S^4 + 32*S^6 + 14*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + HPL[{0}, S^2]*((26*Pi^2*S^3)/81 + (-88 + 43*S^2 + 131*S^4)/(27*S) + (28*(-1 + S^6)*HPL[{1}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(27*S^3)) + HPL[{1}, -S^2]*((10*Pi^2*(1 + S^6))/(27*S^3) + (131*(-1 - S^2 + S^4 + S^6))/(27*S^3) + (40*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + (4*(3 + 29*S^6)*HPL[{3}, -S^2])/(27*S^3) - (128*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(27*S^3) + (128*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^6*((1033*(-1 + S^2)*(1 + S^2)^2)/(324*S^3) + (Pi^2*(-89 + 91*S^2 + 90*S^4 + 454*S^6 + 274*S^8))/(486*S^3*(1 + S^2)) + (5*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + (20*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (40*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{4, 2}, -S^2]*((8 + 4097*S^2 + 4079*S^4 - 11640*S^6)/(324*S^3) + (Pi^2*(-1 - 3*S^2 - 3*S^4 - 357*S^6))/(81*S^3) - (2*(9 + 5*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]^2*((67408 + 4959*S^2 - 4959*S^4 - 67408*S^6)/(486*S^3) + (Pi^2*(1203 + 645*S^2 - 279*S^4 - 2470*S^6 - 1912*S^8))/(81*S^3*(1 + S^2)) - (112*(1 + 7*S^6)*Zeta[3])/(9*S^3)) + HPL[{5, 1}, -S^2]*((-21291 + 36120*S^2 - 57363*S^4 - 169225*S^6)/(486*S^3) + (Pi^2*(-92 - 2606*S^2 - 1104*S^4 - 8639*S^6 - 6125*S^8))/(162*S^3*(1 + S^2)) + (4*(59 + 13*S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]^2*((1965 + 3651*S^2 + 1725*S^4 - 18841*S^6)/(1944*S^3) + (Pi^2*(643 + 535*S^2 - 18*S^4 - 713*S^6 - 605*S^8))/(324*S^3*(1 + S^2)) + (52*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (2*(19 + 29*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 2, 1}, -S^2]*((2*(1 + S^2)*(29879 - 21899*S^2 + 29879*S^4))/(243*S^3) + (Pi^2*(3033 + 10047*S^2 + 3516*S^4 + 13265*S^6 + 6251*S^8))/(162*S^3*(1 + S^2)) + (8*(4 + 61*S^6)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^3*(((1 + S^2)*(27698 - 18185*S^2 + 27698*S^4))/(2916*S^3) + (Pi^2*(329 + 1205*S^2 + 438*S^4 + 1618*S^6 + 742*S^8))/(486*S^3*(1 + S^2)) + (2*(12 + 95*S^6)*HPL[{3}, -S^2])/(27*S^3) + (166*(-1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (2*(6 + 89*S^6)*Zeta[3])/(27*S^3)) + HPL[{3, 1, 1, 1}, -S^2]*((-126193 - 30015*S^2 - 73737*S^4 - 165479*S^6)/(243*S^3) - (4*Pi^2*(944 + 3065*S^2 + 1056*S^4 + 4369*S^6 + 2248*S^8))/(81*S^3*(1 + S^2)) - (32*(3 + 100*S^6)*Zeta[3])/(9*S^3)) + HPL[{6}, -S^2]*((24360 - 15280*S^2 + 50969*S^4 + 105160*S^6)/(324*S^3) + (Pi^2*(-1142 + 1216*S^2 + 909*S^4 + 6235*S^6 + 3877*S^8))/(162*S^3*(1 + S^2)) - (2*(152 + 43*S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (2*(200 + 187*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1, 1, 1}, -S^2]*((8*(1 + S^2)*(4051 - 2610*S^2 + 4051*S^4))/(27*S^3) + (8*Pi^2*(1115 + 3239*S^2 + 1062*S^4 + 4250*S^6 + 2126*S^8))/(81*S^3*(1 + S^2)) + (32*(7 + 202*S^6)*Zeta[3])/(9*S^3)) + HPL[{4, 1, 1}, -S^2]*((382866 + 84687*S^2 + 172131*S^4 + 461438*S^6)/(486*S^3) + (2*Pi^2*(2489 + 8393*S^2 + 2943*S^4 + 11635*S^6 + 5731*S^8))/(81*S^3*(1 + S^2)) + (8*(19 + 563*S^6)*Zeta[3])/(9*S^3)) + HPL[{5}, -S^2]*((Pi^4*(-74 + 1539*S^6))/(1620*S^3) + (Pi^2*(-5857 - 6187*S^2 + 9537*S^4 + 30748*S^6 + 20125*S^8))/(972*S^3*(1 + S^2)) + (-143562 - 147492*S^2 + 700503*S^4 + 1682087*S^6 + 1055414*S^8)/(5832*S^3*(1 + S^2)) + ((88 - 722*S^2 - 756*S^4 + 11*S^6 + 821*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-68 + 19*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (4*(-67 + 141*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((1216 + 934*S^2 + 84*S^4 - 505*S^6 - 223*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^5*((59017*(-1 + S^2)*(1 + S^2)^2)/(4860*S^3) + (749*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(4050*S^3) + (Pi^2*(-2269 - 2145*S^2 + 6489*S^4 + 6149*S^6))/(2430*S^3) + ((236*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + (8*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(405*S^3))*HPL[{2}, -S^2] + (2*(593 + 1493*S^2 + 450*S^4 + 1232*S^6 + 332*S^8)*HPL[{3}, -S^2])/(135*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{4}, -S^2])/(15*S^3) - (10*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (40*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (80*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(163 + 343*S^2 + 90*S^4 + 202*S^6 + 22*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*(-((1 + S^2)*(158849 + 373024*S^2 + 158849*S^4))/(729*S^3) - (319*Pi^4*(19 + 7*S^6))/(405*S^3) + (Pi^2*(-10405 - 28963*S^2 - 47286*S^4 - 36733*S^6 - 6709*S^8))/(243*S^3*(1 + S^2)) + (16*(-985 - 1561*S^2 - 288*S^4 - 550*S^6 + 26*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((33437 - 441711*S^2 + 441711*S^4 - 33437*S^6)/(1458*S^3) + (Pi^2*(9749 - 10830*S^2 + 23622*S^4 - 4465*S^6))/(486*S^3) + (Pi^4*(5760 - 1327*S^6))/(810*S^3) - (8*(-819 - 1377*S^2 - 279*S^4 - 448*S^6 + 110*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{4, 1}, -S^2]*((Pi^4*(535 - 11581*S^6))/(1620*S^3) + (-122289 - 1785543*S^2 - 1900740*S^4 - 677807*S^6 - 518081*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(2221 - 74261*S^2 - 89388*S^4 - 67159*S^6 - 51661*S^8))/(972*S^3*(1 + S^2)) - (16*(61 + 613*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(-863 - 485*S^2 + 144*S^4 + 573*S^6 + 195*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 2}, -S^2]*((Pi^4*(96 - 593*S^6))/(270*S^3) + (-123757 - 1786204*S^2 - 1635810*S^4 - 153108*S^6 - 257505*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(289 - 25232*S^2 - 25680*S^4 - 14002*S^6 - 13303*S^8))/(972*S^3*(1 + S^2)) - (16*(29 + 195*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-187 + 167*S^2 + 168*S^4 + 581*S^6 + 227*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((Pi^4*(17698 - 71*S^6))/(810*S^3) + (254913 - 900585*S^2 + 3028077*S^4 + 380483*S^6)/(2916*S^3) + (Pi^2*(26998 + 20893*S^2 + 72588*S^4 + 82357*S^6 + 2152*S^8))/(486*S^3*(1 + S^2)) - (4*(-5283 - 8673*S^2 - 1704*S^4 - 2959*S^6 + 431*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + Log[T]^5*((-4459*Pi^4*S^3)/12150 - (1027*(-1 + S^2))/(486*S) + (Pi^2*(-450 - 9990*S^2 - 18851*S^4))/(7290*S) - (277*S^3*HPL[{0}, S^2]^4)/810 - (56*(-1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + HPL[{0}, S^2]^3*((-13*(90 + 45*S^2 + 311*S^4 + 221*S^6))/(1215*S*(1 + S^2)) - (26*(1 + S^6)*HPL[{1}, -S^2])/(27*S^3)) + ((-18851 - 10440*S^2 - 10440*S^4 - 18851*S^6)/(1215*S^3) - (2*Pi^2*(47 + 86*S^6))/(81*S^3))*HPL[{2}, -S^2] - (26*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{1}, -S^2]^2*((-10*Pi^2*(1 + S^6))/(9*S^3) - (131*(-1 - S^2 + S^4 + S^6))/(9*S^3) - (40*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^2*((-487*Pi^2*S^3)/405 + (-4230 - 6210*S^2 - 18851*S^4)/(2430*S) + ((-37 - 217*S^2 - 90*S^4 - 328*S^6 - 148*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) - (10*(1 + S^6)*HPL[{1}, -S^2]^2)/(3*S^3) - (2*(5 + 44*S^6)*HPL[{2}, -S^2])/(27*S^3)) - (4*(-154 + 1196*S^2 + 675*S^4 + 2179*S^6 + 829*S^8)*HPL[{3}, -S^2])/(405*S^3*(1 + S^2)) - (136*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(45*S^3) + (20*(1 + 5*S^2 + 2*S^4 + 5*S^6 + S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + HPL[{0}, S^2]*(-((1 + S^2)*(-886 + 1033*S^2))/(54*S) + (Pi^2*(-1170 - 585*S^2 - 5933*S^4 - 4763*S^6))/(1215*S*(1 + S^2)) + ((-26*Pi^2*(1 + S^6))/(27*S^3) - (131*(-1 - S^2 + S^4 + S^6))/(9*S^3))*HPL[{1}, -S^2] - (28*(-1 + S^6)*HPL[{1}, -S^2]^2)/(3*S^3) - (2*(-23 + 118*S^6)*HPL[{2}, -S^2])/(27*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(27*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3)) + (112*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (224*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (20*(2 + S^2 + 3*S^4 + S^6)*Zeta[3])/(3*S*(1 + S^2)) + HPL[{1}, -S^2]*((-1033*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^2*(89 - 91*S^2 - 90*S^4 - 454*S^6 - 274*S^8))/(81*S^3*(1 + S^2)) - (10*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(3*S^3) + (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]^5*((7873*Pi^4*S^3)/388800 + (-210710 - 23024*S^2 + 730215*S^4)/(466560*S) + (Pi^2*(-12682 + 3652*S^2 + 63181*S^4 + 47747*S^6))/(77760*S*(1 + S^2)) + ((-866 + 2632*S^2 + 1974*S^4 + 7591*S^6 + 4093*S^8)*HPL[{1}, -S^2]^3)/(9720*S^3*(1 + S^2)) + (31*(1 + S^6)*HPL[{1}, -S^2]^4)/(360*S^3) + ((Pi^2*(15 + 779*S^6))/(6480*S^3) + (-405 - 1437*S^2 + 2982*S^4 + 14411*S^6 + 11297*S^8)/(12960*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((5 + 68*S^6)*HPL[{2}, -S^2]^2)/(720*S^3) + HPL[{1}, -S^2]^2*((67*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + (-8860 - 16171*S^2 + 33789*S^4 + 68231*S^6 + 32531*S^8)/(38880*S^3*(1 + S^2)) + (229*(1 + S^6)*HPL[{2}, -S^2])/(1080*S^3)) + ((-15 - 27*S^2 - 6*S^4 - 5*S^6 + 7*S^8)*HPL[{3}, -S^2])/(432*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(24*S^3) + ((212 - 296*S^2 - 329*S^4 - 303*S^6 + 205*S^8)*HPL[{2, 1}, -S^2])/(1080*S^3*(1 + S^2)) - (7*S^3*HPL[{3, 1}, -S^2])/20 + ((15 + 254*S^6)*HPL[{2, 1, 1}, -S^2])/(270*S^3) + ((48 + 24*S^2 + 511*S^4 + 463*S^6)*Zeta[3])/(216*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-6431 + 3367*S^2 + 5124*S^4 + 26281*S^6 + 16483*S^8))/(38880*S^3*(1 + S^2)) + (-80245 - 183514*S^2 + 172164*S^4 + 473450*S^6 + 230417*S^8)/(233280*S^3*(1 + S^2)) + ((-247 + 719*S^2 + 558*S^4 + 2072*S^6 + 1106*S^8)*HPL[{2}, -S^2])/(2160*S^3*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(36*S^3) - (229*(1 + S^6)*HPL[{2, 1}, -S^2])/(540*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + ((782*Pi^4*S^3)/135 + (Pi^2*(4342 + 4913*S^2 + 4638*S^4 + 4301*S^6))/(162*S*(1 + S^2)) + (569572 + 568994*S^2 + 290191*S^4 + 277809*S^6)/(1944*S*(1 + S^2)))*Zeta[5] + HPL[{0}, S^2]^4*((Pi^4*(15636 + 7818*S^2 + 37453*S^4 + 21817*S^6))/(77760*S*(1 + S^2)) + (Pi^2*(17721 + 32499*S^2 + 188357*S^4 + 185243*S^6))/(69984*S*(1 + S^2)) + (2137074 + 2083566*S^2 + 5770579*S^4 + 5964055*S^6)/(839808*S*(1 + S^2)) + ((67 + 1153*S^2 + 588*S^4 + 2053*S^6 + 967*S^8)*HPL[{1}, -S^2]^4)/(1296*S^3*(1 + S^2)) + (22*(1 + S^6)*HPL[{1}, -S^2]^5)/(135*S^3) + ((-67 + 141*S^2 + 104*S^4 + 552*S^6 + 344*S^8)*HPL[{2}, -S^2]^2)/(432*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((19*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (280 + 545*S^2 + 3589*S^4 + 5727*S^6 + 2763*S^8)/(1296*S^3*(1 + S^2)) + (257*(1 + S^6)*HPL[{2}, -S^2])/(324*S^3)) + ((Pi^2*(10 + 11*S^6))/(216*S^3) + (139 + 343*S^2 + 156*S^4 + 982*S^6 + 598*S^8)/(1296*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((8 + 62*S^2 + 9*S^4 + 95*S^6 + 41*S^8)*HPL[{4}, -S^2])/(108*S^3*(1 + S^2)) + ((16 + 23*S^6)*HPL[{5}, -S^2])/(36*S^3) + ((Pi^2*(-563 - 11*S^6))/(648*S^3) + (-2867 - 3395*S^2 - 17256*S^4 - 15739*S^6 + 881*S^8)/(3888*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-1 - 525*S^2 - 226*S^4 - 1361*S^6 - 837*S^8)*HPL[{3, 1}, -S^2])/(216*S^3*(1 + S^2)) + HPL[{3, 2}, -S^2]/(2*S^3) - (23*(-1 + S^6)*HPL[{4, 1}, -S^2])/(36*S^3) + ((18 + 532*S^2 + 257*S^4 + 1472*S^6 + 958*S^8)*HPL[{2, 1, 1}, -S^2])/(108*S^3*(1 + S^2)) + (5*(47 + 4*S^6)*HPL[{2, 2, 1}, -S^2])/(54*S^3) + ((80 + 9*S^6)*HPL[{3, 1, 1}, -S^2])/(6*S^3) + ((-233 - 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3) + ((833*Pi^2*S^3)/648 + (-414 + 960*S^2 + 7577*S^4 + 7103*S^6)/(1296*S*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-83 + 2743*S^2 + 1548*S^4 + 5533*S^6 + 2707*S^8))/(2592*S^3*(1 + S^2)) + (36553 + 59314*S^2 + 218448*S^4 + 360454*S^6 + 180319*S^8)/(46656*S^3*(1 + S^2)) + ((165 + 1195*S^2 + 518*S^4 + 1906*S^6 + 876*S^8)*HPL[{2}, -S^2])/(432*S^3*(1 + S^2)) + (11*(1 + S^6)*HPL[{3}, -S^2])/(36*S^3) - (257*(1 + S^6)*HPL[{2, 1}, -S^2])/(108*S^3) + (19*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) + HPL[{2}, -S^2]*((Pi^2*(39 + 671*S^2 + 316*S^4 + 2071*S^6 + 1439*S^8))/(1296*S^3*(1 + S^2)) + (3507 + 9801*S^2 + 14307*S^4 + 55960*S^6 + 45355*S^8)/(11664*S^3*(1 + S^2)) - HPL[{3}, -S^2]/(4*S^3) - (5*(47 + 4*S^6)*HPL[{2, 1}, -S^2])/(108*S^3) + (5*(-1 + S^6)*Zeta[3])/(36*S^3)) + HPL[{1}, -S^2]*((1303*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(6480*S^3) + (Pi^2*(1375 + 1870*S^2 + 14466*S^4 + 25798*S^6 + 13447*S^8))/(7776*S^3*(1 + S^2)) + (226507 + 420940*S^2 + 833430*S^4 + 1275076*S^6 + 659407*S^8)/(139968*S^3*(1 + S^2)) + ((79*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (493 + 964*S^2 + 3615*S^4 + 6148*S^6 + 3031*S^8)/(972*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (13*(1 + S^6)*HPL[{2}, -S^2]^2)/(27*S^3) + ((23 + 59*S^2 + 6*S^4 + 68*S^6 + 32*S^8)*HPL[{3}, -S^2])/(72*S^3*(1 + S^2)) + (11*(1 + S^6)*HPL[{4}, -S^2])/(18*S^3) + ((-165 - 1195*S^2 - 518*S^4 - 1906*S^6 - 876*S^8)*HPL[{2, 1}, -S^2])/(216*S^3*(1 + S^2)) - (137*(1 + S^6)*HPL[{3, 1}, -S^2])/(54*S^3) + (257*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(54*S^3) + ((-13 + 105*S^2 + 84*S^4 + 193*S^6 + 75*S^8)*Zeta[3])/(72*S^3*(1 + S^2))) + (805*S^3*Zeta[5])/108) + Log[T]^4*((1199*(-1 + S^2))/(324*S) + (Pi^2*(297 + 1144*S^2 + 4051*S^4))/(486*S) + (7*Pi^4*(642 + 321*S^2 + 1741*S^4 + 1099*S^6))/(4860*S*(1 + S^2)) + (289*S^3*HPL[{0}, S^2]^5)/1620 + (70*(-1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + HPL[{0}, S^2]^4*((264 + 132*S^2 + 811*S^4 + 547*S^6)/(324*S*(1 + S^2)) + (22*(1 + S^6)*HPL[{1}, -S^2])/(27*S^3)) + (337*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^2)/(27*S^3) + HPL[{1}, -S^2]^3*((50*Pi^2*(1 + S^6))/(27*S^3) + (655*(-1 - S^2 + S^4 + S^6))/(27*S^3) + (200*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]^3*((242*Pi^2*S^3)/243 + (-1602 + 6759*S^2 + 31103*S^4 + 24038*S^6)/(2916*S*(1 + S^2)) + ((-113 + 691*S^2 + 438*S^4 + 1690*S^6 + 886*S^8)*HPL[{1}, -S^2])/(162*S^3*(1 + S^2)) + (65*(1 + S^6)*HPL[{1}, -S^2]^2)/(27*S^3) + ((4 + 61*S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((2*Pi^2*(28 + 237*S^6))/(81*S^3) + (-962 + 12321*S^2 + 3303*S^4 + 5391*S^6)/(243*S^3))*HPL[{3}, -S^2] + (4*(213 + 429*S^2 + 108*S^4 + 685*S^6 + 469*S^8)*HPL[{4}, -S^2])/(81*S^3*(1 + S^2)) + (4*(3 + 107*S^6)*HPL[{5}, -S^2])/(27*S^3) + ((-4429 - 15624*S^2 - 15624*S^4 - 4429*S^6)/(243*S^3) - (2*Pi^2*(473 + 278*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] - (4*(922 + 2272*S^2 + 675*S^4 + 2528*S^6 + 1178*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) - (8*(14 + 209*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) - (8*(22 + 217*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (200*(14 + 32*S^2 + 9*S^4 + 32*S^6 + 14*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (520*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (80*(-21 + 5*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (1280*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((542*Pi^2*S^3)/81 + (14922 + 702*S^2 + 4429*S^4)/(243*S))*Zeta[3] + HPL[{0}, S^2]^2*((1749 + 1133*S^2 + 8102*S^4)/(324*S) + (Pi^2*(326 + 163*S^2 + 924*S^4 + 598*S^6))/(108*S*(1 + S^2)) + (5*(37 + 217*S^2 + 90*S^4 + 328*S^6 + 148*S^8)*HPL[{1}, -S^2]^2)/(54*S^3*(1 + S^2)) + (50*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((65 + 839*S^2 + 387*S^4 + 1850*S^6 + 1076*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((163*Pi^2*(1 + S^6))/(54*S^3) + (1357 + 1605*S^2 + 7083*S^4 + 6403*S^6)/(324*S^3) + (86*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((11 + 39*S^6)*HPL[{3}, -S^2])/(27*S^3) - (2*(233 + 38*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (62*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^2*((5165*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (5*Pi^2*(-89 + 91*S^2 + 90*S^4 + 454*S^6 + 274*S^8))/(162*S^3*(1 + S^2)) + (25*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (100*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (200*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (100*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*(((1 + S^2)*(4051 - 2610*S^2 + 4051*S^4))/(81*S^3) + (Pi^2*(1115 + 3239*S^2 + 1062*S^4 + 4250*S^6 + 2126*S^8))/(243*S^3*(1 + S^2)) + (20*(1 + 14*S^6)*HPL[{3}, -S^2])/(9*S^3) + (260*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(7 + 202*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]*((59017*(-1 + S^2)*(1 + S^2)^2)/(972*S^3) + (749*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(-2269 - 2145*S^2 + 6489*S^4 + 6149*S^6))/(486*S^3) + ((236*Pi^2*(1 + S^6))/(27*S^3) + (8*(485 + 543*S^2 + 543*S^4 + 485*S^6))/(81*S^3))*HPL[{2}, -S^2] + (2*(593 + 1493*S^2 + 450*S^4 + 1232*S^6 + 332*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (50*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (200*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (400*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (10*(163 + 343*S^2 + 90*S^4 + 202*S^6 + 22*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]*((4021*Pi^4*S^3)/4860 + ((1 + S^2)*(-54935 + 59017*S^2))/(972*S) + (Pi^2*(-13482 + 684*S^2 + 54593*S^4 + 41723*S^6))/(2916*S*(1 + S^2)) + ((655*(-1 + S^2)*(1 + S^2)^2)/(18*S^3) + (65*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3))*HPL[{1}, -S^2]^2 + (140*(-1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((Pi^2*(-1 + 56*S^6))/(27*S^3) + (-2905 - 12060*S^2 + 6876*S^4 + 17327*S^6)/(486*S^3))*HPL[{2}, -S^2] - (17*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^2)/(27*S^3) + (2*(-182 - 236*S^2 - 81*S^4 + 174*S^6 + 228*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (8*(2 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (10*(-118 + 23*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^3) - (40*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(18 + 9*S^2 + 274*S^4 + 256*S^6)*Zeta[3])/(81*S*(1 + S^2)) + HPL[{1}, -S^2]*((5165*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(-743 + 61*S^2 + 438*S^4 + 2320*S^6 + 1516*S^8))/(162*S^3*(1 + S^2)) + (235*(-1 + S^6)*HPL[{2}, -S^2])/(9*S^3) - (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + (1220*S^3*Zeta[5])/27) + HPL[{1}, -S^2]^4*((4195*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(-11553 - 11541*S^2 + 32381*S^4 + 31793*S^6))/(3888*S^3) + (Pi^4*(-557 + 5409*S^2 + 2944*S^4 + 12679*S^6 + 6713*S^8))/(6480*S^3*(1 + S^2)) + (37*(-1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((29*Pi^2*(1 + S^6))/(9*S^3) + (5401 + 5793*S^2 + 2895*S^4 + 2359*S^6)/(162*S^3))*HPL[{3}, -S^2] + (2*(-23 + 124*S^2 + 78*S^4 + 307*S^6 + 160*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (92*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-236*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (8*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(81*S^3))*HPL[{2, 1}, -S^2] - (2*(371 + 1271*S^2 + 450*S^4 + 1454*S^6 + 554*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (248*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (280*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (50*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (200*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (400*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((86*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2*(1813 + 1875*S^2 + 297*S^4 + 127*S^6))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*((5*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(81*S^3) + (Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(27*S^3*(1 + S^2)) + (124*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (128*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (224*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]^2*((Pi^2*(-77050 + 5715*S^2 + 13311*S^4 + 132446*S^6))/(11664*S^3) + (-269479 + 3243*S^2 - 3243*S^4 + 269479*S^6)/(5832*S^3) + (Pi^4*(-11792 - 908*S^2 + 5442*S^4 + 35763*S^6 + 24879*S^8))/(19440*S^3*(1 + S^2)) + ((Pi^2*(38 + 213*S^6))/(54*S^3) + (435 + 2598*S^2 + 600*S^4 + 886*S^6)/(81*S^3))*HPL[{3}, -S^2] + ((-211 - 67*S^2 + 72*S^4 + 492*S^6 + 348*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (7*(13 + 17*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-1321 - 3198*S^2 - 3198*S^4 - 1321*S^6)/(81*S^3) + (Pi^2*(-218 - 135*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((-859 - 3091*S^2 - 1116*S^4 - 4209*S^6 - 1977*S^8)*HPL[{3, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((-43 - 375*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + ((-209 - 1205*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (2*(709 + 1825*S^2 + 558*S^4 + 1825*S^6 + 709*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (332*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (8*(-139 + 27*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (896*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((Pi^2*(50 + 239*S^6))/(54*S^3) + (2357 + 12102*S^2 + 690*S^4 + 2927*S^6)/(324*S^3))*Zeta[3] + (11*(4 + 25*S^6)*Zeta[5])/(9*S^3)) + HPL[{3, 1}, -S^2]*((-6766237 - 1023135*S^2 - 4646913*S^4 - 10362219*S^6)/(34992*S^3) + (Pi^2*(-131869 - 191041*S^2 - 181110*S^4 - 454287*S^6 - 324573*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(-19893 - 70209*S^2 - 24096*S^4 - 108917*S^6 - 58601*S^8))/(9720*S^3*(1 + S^2)) + (4*(115 + 427*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (4*(233 + 1273*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (8*(-899 - 6*S^2 - 6*S^4 + 1123*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (1792*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(-795 + 349*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (32*(-97 + 98*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-2*Pi^2*(-2 + 73*S^6))/(9*S^3) + (2174 - 10513*S^2 - 15492*S^4 - 2601*S^6 - 1308*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (20*(-16 + 43*S^6)*Zeta[5])/(9*S^3)) + HPL[{4}, -S^2]*((Pi^4*(5138 + 9452*S^2 + 1626*S^4 + 10673*S^6 + 6359*S^8))/(4860*S^3*(1 + S^2)) + (Pi^2*(35079 + 24186*S^2 + 30009*S^4 + 145141*S^6 + 99055*S^8))/(5832*S^3*(1 + S^2)) + (932316 + 1081917*S^2 + 3643044*S^4 + 8301677*S^6 + 4528298*S^8)/(34992*S^3*(1 + S^2)) - (10*(29 + 39*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((Pi^2*(-131 + 31*S^6))/(27*S^3) + (88 + 1863*S^2 - 2817*S^4 + 3266*S^6)/(81*S^3))*HPL[{2, 1}, -S^2] - (2*(-499 - 463*S^2 - 117*S^4 + 657*S^6 + 621*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(155 + 191*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (4*(98 + 171*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(-257 - 12*S^2 - 12*S^4 + 705*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + (260*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (4*(233 + 129*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (32*(-13 + 14*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((Pi^2*(-53 - 7*S^6))/(27*S^3) + (-1869 + 111*S^2 + 3312*S^4 - 73*S^6 - 757*S^8)/(162*S^3*(1 + S^2)))*Zeta[3] - (2*(189 + 79*S^6)*Zeta[5])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*(((1 + S^2)*(2141057 - 1432301*S^2 + 2141057*S^4))/(4374*S^3) + (Pi^4*(20282 + 70304*S^2 + 25011*S^4 + 112232*S^6 + 62210*S^8))/(4860*S^3*(1 + S^2)) + (Pi^2*(80478 + 124359*S^2 + 88833*S^4 + 196726*S^6 + 147886*S^8))/(1458*S^3*(1 + S^2)) - (3584*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (32*(107 + 42*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (2080*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((16*Pi^2*(1 + 56*S^6))/(27*S^3) + (2*(-1547 + 11143*S^2 + 15210*S^4 + 3373*S^6 + 2149*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] + (16*(-7 + 132*S^6)*Zeta[5])/(9*S^3)) + Zeta[3]*((1847*Pi^6*S^3)/3402 + (11273112 + 54924*S^2 + 4997759*S^4)/(34992*S) + (Pi^4*(58158 + 77724*S^2 + 116239*S^4 + 105367*S^6))/(29160*S*(1 + S^2)) + (Pi^2*(1198248 + 1215300*S^2 + 557465*S^4 + 579293*S^6))/(34992*S*(1 + S^2)) - (2*(-498 - 249*S^2 + 284*S^4 + 782*S^6)*Zeta[5])/(27*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((448081*(-1 + S^2)*(1 + S^2)^2)/(4374*S^3) + (47329*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(204120*S^3) + (Pi^2*(-371417 - 380862*S^2 + 1081809*S^4 + 1083478*S^6))/(52488*S^3) + (Pi^4*(-4229 - 8963*S^2 + 57227*S^4 + 122195*S^6 + 59298*S^8))/(19440*S^3*(1 + S^2)) + ((31*Pi^2*(1 + S^6))/(27*S^3) + (-779 - 755*S^2 + 755*S^4 + 779*S^6)/(54*S^3))*HPL[{2}, -S^2]^2 + (124*(1 + S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + ((218*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + (241 - 1604*S^2 + 17190*S^4 + 37564*S^6 + 19825*S^8)/(486*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (8*(-14 + 125*S^2 + 71*S^4 + 287*S^6 + 148*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (106*(1 + S^6)*HPL[{6}, -S^2])/(3*S^3) + ((-472*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (16*(1 + S^2)*(383 + 58*S^2 + 587*S^4))/(81*S^3))*HPL[{3, 1}, -S^2] - (4*(607 + 1353*S^2 + 376*S^4 + 909*S^6 + 163*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (4*(593 + 1435*S^2 + 424*S^4 + 1113*S^6 + 271*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (368*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((944*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (32*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(81*S^3))*HPL[{2, 1, 1}, -S^2] + (592*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (8*(-73 + 827*S^2 + 450*S^4 + 1898*S^6 + 998*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (992*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (1120*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (200*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (800*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (1600*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((19437 + 19449*S^2 + 1391*S^4 + 803*S^6)/(162*S^3) + (2*Pi^2*(440 + 957*S^2 + 260*S^4 + 603*S^6 + 86*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] + HPL[{2, 1}, -S^2]*((-20*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(81*S^3) - (4*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(27*S^3*(1 + S^2)) - (512*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((14329 + 14557*S^2 + 6283*S^4 + 5911*S^6)/(162*S^3) + (Pi^2*(1922 + 5012*S^2 + 1482*S^4 + 4427*S^6 + 1337*S^8))/(243*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((2779*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + ((1 + S^2)*(712061 - 11114*S^2 + 712061*S^4))/(8748*S^3) + (Pi^2*(15436 + 32824*S^2 + 40275*S^4 + 46630*S^6 + 22447*S^8))/(1458*S^3*(1 + S^2)) + (2*(1825 + 4057*S^2 + 1116*S^4 + 2725*S^6 + 493*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) - (296*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(301 + 697*S^2 + 216*S^4 + 475*S^6 + 79*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + (2*(1281 + 2623*S^2 + 668*S^4 + 1423*S^6 + 81*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(4997759 + 6330277*S^2 + 4997759*S^4))/(34992*S^3) + (Pi^6*(-46812 - 8377*S^6))/(68040*S^3) + (Pi^2*(-340320 - 960804*S^2 - 1659351*S^4 - 1369078*S^6 - 306883*S^8))/(17496*S^3*(1 + S^2)) + (Pi^4*(-36574 - 78439*S^2 - 133779*S^4 - 110250*S^6 - 11397*S^8))/(14580*S^3*(1 + S^2)) + ((673 - 3663*S^2 + 3981*S^4 - 1791*S^6)/(27*S^3) - (4*Pi^2*(-71 + 31*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] + ((5211 + 9675*S^2 + 2232*S^4 + 4925*S^6 + 461*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-8047 - 14767*S^2 - 3396*S^4 - 6285*S^6 + 435*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/(3*S^3) - (4*(-171 + 37*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-28*(-88 + 273*S^2 - 273*S^4 + 88*S^6))/(27*S^3) - (8*Pi^2*(-209 + 97*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (8*(709 + 1825*S^2 + 558*S^4 + 1825*S^6 + 709*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(173 + 915*S^2 + 368*S^4 + 1589*S^6 + 847*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1328*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (16*(-275 + 277*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (5392*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) - (32*(-97 + 98*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (2080*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(-2000 - 3278*S^2 - 621*S^4 - 1412*S^6 - 134*S^8))/(81*S^3*(1 + S^2)) + (-65358 - 73353*S^2 - 14919*S^4 - 986*S^6 + 2050*S^8)/(243*S^3*(1 + S^2)))*Zeta[3] - (4*(3 + 5*S^6)*Zeta[3]^2)/(9*S^3) + (2*(-3434 - 5066*S^2 - 807*S^4 - 1531*S^6 + 101*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^6*(-260 + 5559*S^6))/(34020*S^3) + (760447 + 7329267*S^2 + 3998769*S^4 + 4237312*S^6)/(34992*S^3) + (Pi^4*(-9925 + 46007*S^2 + 71760*S^4 + 68789*S^6 + 43349*S^8))/(29160*S^3*(1 + S^2)) + (Pi^2*(68350 + 1022815*S^2 + 1244991*S^4 + 838499*S^6 + 509093*S^8))/(34992*S^3*(1 + S^2)) + ((Pi^2*(76 - S^6))/(27*S^3) + (233 + 73*S^2 - 425*S^4 - 260*S^6 - 265*S^8)/(27*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(-498 - 297*S^2 - 138*S^4 + 550*S^6 + 349*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (2*(145 + 119*S^6)*HPL[{6}, -S^2])/(9*S^3) - (4*(29 + 195*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-2*Pi^2*(-7 + 206*S^6))/(27*S^3) + (-1552 - 13399*S^2 - 12597*S^4 - 4475*S^6 - 3941*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-929 - 575*S^2 + 168*S^4 + 1369*S^6 + 1015*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-187 - 115*S^2 + 81*S^4 + 154*S^6 + 82*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (10*(-1 + 2*S^6)*HPL[{4, 2}, -S^2])/(9*S^3) - (4*(57 + 10*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(5 + 228*S^6))/(27*S^3) + (3265 + 23781*S^2 + 849*S^4 + 10657*S^6)/(81*S^3))*HPL[{2, 1, 1}, -S^2] + (2*(2511 + 4743*S^2 + 1116*S^4 + 2557*S^6 + 325*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(2653 + 4893*S^2 + 1132*S^4 + 2339*S^6 + 99*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(-3 + 2*S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) + (8*(7 + 64*S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (104*(101 + 516*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (16*(-268 - 455*S^2 - 95*S^4 - 118*S^6 + 69*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(19 + 203*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (160*(1 + 14*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((19727 + 2765*S^2 - 11658*S^4 - 6089*S^6 - 3617*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(625 + 589*S^2 + 72*S^4 + 345*S^6 + 381*S^8))/(162*S^3*(1 + S^2)))*Zeta[3] + (4*(3 + 13*S^6)*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*((-114223 - 28395*S^2 - 18477*S^4 + 20593*S^6)/(486*S^3) + (Pi^2*(-3701 - 6089*S^2 - 1230*S^4 - 1141*S^6 + 1247*S^8))/(162*S^3*(1 + S^2)) + (8*(12 + 13*S^6)*Zeta[3])/(9*S^3)) + ((1947 + 1875*S^2 + 72*S^4 + 539*S^6 + 611*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + Log[T]^3*((-8431*Pi^6*S^3)/17010 - (2495*(-1 + S^2))/(486*S) + (Pi^2*(-10811 - 7975*S^2 - 61468*S^4))/(2916*S) + (Pi^4*(-51858 - 206793*S^2 - 578197*S^4 - 419050*S^6))/(87480*S*(1 + S^2)) - (31*S^3*HPL[{0}, S^2]^6)/324 - (56*(-1 + S^6)*HPL[{1}, -S^2]^5)/(9*S^3) + HPL[{0}, S^2]^5*((-1674 - 837*S^2 - 6487*S^4 - 4813*S^6)/(4860*S*(1 + S^2)) - (31*(1 + S^6)*HPL[{1}, -S^2])/(90*S^3)) + ((2953 + 354*S^2 - 354*S^4 - 2953*S^6)/(81*S^3) - (4*Pi^2*(-58 + 95*S^6))/(81*S^3))*HPL[{2}, -S^2]^2 - (296*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(81*S^3) + HPL[{0}, S^2]^4*((-371*Pi^2*S^3)/486 + (-2070 - 11295*S^2 - 36941*S^4 - 29336*S^6)/(5832*S*(1 + S^2)) + ((-67 - 1153*S^2 - 588*S^4 - 2053*S^6 - 967*S^8)*HPL[{1}, -S^2])/(324*S^3*(1 + S^2)) - (44*(1 + S^6)*HPL[{1}, -S^2]^2)/(27*S^3) + ((-4 - 41*S^6)*HPL[{2}, -S^2])/(27*S^3)) + HPL[{1}, -S^2]^4*((-655*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) - (50*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (200*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + (8*(-5 + 4*S^6)*HPL[{3}, -S^2]^2)/(27*S^3) + ((-4*Pi^2*(69 + 77*S^6))/(81*S^3) + (-8106 - 5685*S^2 - 5598*S^4 - 24433*S^6 - 17062*S^8)/(243*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(-1599 + 57*S^2 + 828*S^4 + 4165*S^6 + 2509*S^8)*HPL[{5}, -S^2])/(81*S^3*(1 + S^2)) - (16*(54 + 71*S^6)*HPL[{6}, -S^2])/(27*S^3) + (520*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((8*Pi^2*(117 + 214*S^6))/(81*S^3) + (4*(8306 + 3996*S^2 + 6444*S^4 + 10545*S^6))/(243*S^3))*HPL[{3, 1}, -S^2] + (4*(265 + 2497*S^2 + 1116*S^4 + 3877*S^6 + 1645*S^8)*HPL[{3, 2}, -S^2])/(81*S^3*(1 + S^2)) + (8*(87 + 3867*S^2 + 1890*S^4 + 6523*S^6 + 2743*S^8)*HPL[{4, 1}, -S^2])/(81*S^3*(1 + S^2)) + (16*(-7 + 11*S^6)*HPL[{4, 2}, -S^2])/(27*S^3) + (16*(61 + 119*S^6)*HPL[{5, 1}, -S^2])/(27*S^3) + ((-40*Pi^2*(47 + 86*S^6))/(81*S^3) - (4*(18851 + 10440*S^2 + 10440*S^4 + 18851*S^6))/(243*S^3))*HPL[{2, 1, 1}, -S^2] + (1840*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) + (16*(-881 - 2231*S^2 - 675*S^4 - 1144*S^6 + 206*S^8)*HPL[{3, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) - (32*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/(27*S^3) - (800*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (2912*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (400*(1 + 5*S^2 + 2*S^4 + 5*S^6 + S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (2240*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (4480*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-4*(3630 + 139*S^2 + 1009*S^4))/(81*S) - (4*Pi^2*(774 + 387*S^2 + 1234*S^4 + 460*S^6))/(243*S*(1 + S^2)))*Zeta[3] + (8*S^3*Zeta[3]^2)/9 + HPL[{0}, S^2]^3*((5182 + 443*S^2 - 33470*S^4 - 29811*S^6)/(1458*S*(1 + S^2)) + (Pi^2*(-158 - 79*S^2 - 585*S^4 - 427*S^6))/(81*S*(1 + S^2)) + ((113 - 691*S^2 - 438*S^4 - 1690*S^6 - 886*S^8)*HPL[{1}, -S^2]^2)/(81*S^3*(1 + S^2)) - (260*(1 + S^6)*HPL[{1}, -S^2]^3)/(81*S^3) + ((25 - 1085*S^2 - 546*S^4 - 3684*S^6 - 2574*S^8)*HPL[{2}, -S^2])/(243*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-158*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) - (2*(-1231 - 1957*S^2 + 5865*S^4 + 11273*S^6 + 5330*S^8))/(729*S^3*(1 + S^2)) - (124*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) - (2*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3}, -S^2])/(27*S^3) + (4*(58 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (28*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^3*((-5165*(-1 + S^2)*(1 + S^2)^2)/(81*S^3) - (10*Pi^2*(-89 + 91*S^2 + 90*S^4 + 454*S^6 + 274*S^8))/(243*S^3*(1 + S^2)) - (100*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) - (400*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (800*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (400*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((343 - 24677*S^2 - 5475*S^4 - 8415*S^6)/(162*S^3) - (2*Pi^2*(-225 + 1302*S^2 + 705*S^4 + 2528*S^6 + 1001*S^8))/(243*S^3*(1 + S^2)) - (16*(-57 + 8*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (16*(14 + S^6)*Zeta[3])/(27*S^3)) + HPL[{2, 1}, -S^2]*((4*(1 + S^2)*(1009 + 2760*S^2 + 1009*S^4))/(81*S^3) + (4*Pi^2*(757 + 2845*S^2 + 990*S^4 + 2500*S^6 + 412*S^8))/(243*S^3*(1 + S^2)) - (80*(-37 + 2*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]^2*((-59017*(-1 + S^2)*(1 + S^2)^2)/(486*S^3) - (749*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (Pi^2*(2269 + 2145*S^2 - 6489*S^4 - 6149*S^6))/(243*S^3) + ((-472*Pi^2*(1 + S^6))/(27*S^3) - (16*(485 + 543*S^2 + 543*S^4 + 485*S^6))/(81*S^3))*HPL[{2}, -S^2] - (4*(593 + 1493*S^2 + 450*S^4 + 1232*S^6 + 332*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (64*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + (100*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (400*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (800*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (20*(163 + 343*S^2 + 90*S^4 + 202*S^6 + 22*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]*(-((1 + S^2)*(30734 - 21341*S^2 + 30734*S^4))/(243*S^3) - (2*Pi^4*(569 + 1526*S^6))/(1215*S^3) + (Pi^2*(-20467 - 36685*S^2 - 33264*S^4 - 56527*S^6 - 38185*S^8))/(1458*S^3*(1 + S^2)) - (4*(217 + 1327*S^2 + 546*S^4 + 2017*S^6 + 907*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) - (16*(-13 + 14*S^6)*HPL[{4}, -S^2])/(27*S^3) - (920*(-1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (16*(-97 + 98*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (1040*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (8*(-82 + 530*S^2 + 360*S^4 + 875*S^6 + 263*S^8)*Zeta[3])/(81*S^3*(1 + S^2))) + HPL[{0}, S^2]^2*((-8159*Pi^4*S^3)/4860 + (-7973 - 1420*S^2 - 30734*S^4)/(486*S) + (Pi^2*(-6300 - 21735*S^2 - 62002*S^4 - 48187*S^6))/(2916*S*(1 + S^2)) - (10*(37 + 217*S^2 + 90*S^4 + 328*S^6 + 148*S^8)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)) - (50*(1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + ((Pi^2*(-49 - 466*S^6))/(81*S^3) + (-808 - 3697*S^2 - 6192*S^4 - 13618*S^6 - 9667*S^8)/(243*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (37*(-1 + 5*S^6)*HPL[{2}, -S^2]^2)/(27*S^3) + HPL[{1}, -S^2]^2*((-1357 - 1605*S^2 - 7083*S^4 - 6403*S^6)/(162*S^3) - (163*Pi^2*(1 + S^6))/(27*S^3) - (172*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) - (2*(-71 + 106*S^2 + 30*S^4 + 349*S^6 + 172*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) - (8*(9 + 13*S^6)*HPL[{4}, -S^2])/(27*S^3) + (2*(839 + 2315*S^2 + 630*S^4 + 1625*S^6 + 149*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) + (8*(12 + 109*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (40*(5 + 44*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (2*(198 + 99*S^2 + 443*S^4 + 245*S^6)*Zeta[3])/(81*S*(1 + S^2)) + HPL[{1}, -S^2]*((-1971 - 1977*S^2 - 8443*S^4 - 8149*S^6)/(162*S^3) + (Pi^2*(-84 - 746*S^2 - 346*S^4 - 1231*S^6 - 569*S^8))/(54*S^3*(1 + S^2)) + ((-323 - 1331*S^2 - 468*S^4 - 1775*S^6 - 767*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) - (16*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (344*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (44*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) - (32*(28 + 14*S^2 + 33*S^4 + 5*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{0}, S^2]*(-((1 + S^2)*(-36419 + 37755*S^2))/(243*S) + (Pi^2*(50234 + 34141*S^2 - 120040*S^4 - 106107*S^6))/(2916*S*(1 + S^2)) + (Pi^4*(-7878 - 3939*S^2 - 35179*S^4 - 27301*S^6))/(4860*S*(1 + S^2)) + ((-260*Pi^2*(1 + S^6))/(81*S^3) - (1310*(-1 - S^2 + S^4 + S^6))/(27*S^3))*HPL[{1}, -S^2]^3 - (140*(-1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) - (4*(28 - 18*S^2 - 18*S^4 + 361*S^6)*HPL[{2}, -S^2]^2)/(81*S^3) + ((1971 + 3315*S^2 - 2031*S^4 - 4657*S^6)/(243*S^3) + (4*Pi^2*(4 + S^6))/(81*S^3))*HPL[{3}, -S^2] - (2*(111 + 57*S^2 + 649*S^6 + 703*S^8)*HPL[{4}, -S^2])/(81*S^3*(1 + S^2)) - (4*(-7 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((4*Pi^2*(21 + 2*S^6))/(9*S^3) + (2*(-17327 - 6876*S^2 + 12060*S^4 + 2905*S^6))/(243*S^3))*HPL[{2, 1}, -S^2] + (8*(-173 - 191*S^2 - 9*S^4 + 848*S^6 + 866*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) + (16*(11 + 10*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) + (16*(6 + 5*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (40*(-23 + 118*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (272*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(27*S^3) - (736*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(27*S^3) + (160*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-28*Pi^2*S^3)/27 - (2*(-1566 + 882*S^2 + 2239*S^4))/(243*S))*Zeta[3] + HPL[{1}, -S^2]^2*((-5165*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^2*(743 - 61*S^2 - 438*S^4 - 2320*S^6 - 1516*S^8))/(81*S^3*(1 + S^2)) - (470*(-1 + S^6)*HPL[{2}, -S^2])/(9*S^3) + (8*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((3233 + 13685*S^2 - 4373*S^4 - 15401*S^6)/(162*S^3) - (2*Pi^2*(-185 + 370*S^2 + 273*S^4 + 2727*S^6 + 2172*S^8))/(243*S^3*(1 + S^2)) - (8*(4 + 3*S^6)*HPL[{3}, -S^2])/(9*S^3) + (136*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (8*(-1 + 2*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]*((-59017*(-1 + S^2)*(1 + S^2)^2)/(486*S^3) - (1313*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(22609 + 43198*S^2 - 23460*S^4 - 80462*S^6 - 39005*S^8))/(1458*S^3*(1 + S^2)) + ((-124*Pi^2*(1 + S^6))/(27*S^3) - (8*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(27*S^3))*HPL[{2}, -S^2] - (4*(-137 - 149*S^2 - 6*S^4 + 112*S^6 + 124*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (940*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (16*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (4*(-85 - 73*S^2 + 6*S^4 + 110*S^6 + 98*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + (104*S^3*Zeta[5])/27) + HPL[{1}, -S^2]*((-4195*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) + (Pi^2*(11553 + 11541*S^2 - 32381*S^4 - 31793*S^6))/(972*S^3) + (Pi^4*(557 - 5409*S^2 - 2944*S^4 - 12679*S^6 - 6713*S^8))/(1620*S^3*(1 + S^2)) - (148*(-1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((-116*Pi^2*(1 + S^6))/(9*S^3) - (2*(5401 + 5793*S^2 + 2895*S^4 + 2359*S^6))/(81*S^3))*HPL[{3}, -S^2] - (8*(-23 + 124*S^2 + 78*S^4 + 307*S^6 + 160*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (368*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((944*Pi^2*(1 + S^6))/(27*S^3) + (32*(485 + 543*S^2 + 543*S^4 + 485*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] + (8*(371 + 1271*S^2 + 450*S^4 + 1454*S^6 + 554*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (992*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) + (1120*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (200*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (800*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (1600*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-344*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (8*(1813 + 1875*S^2 + 297*S^4 + 127*S^6))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-20*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(81*S^3) - (4*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(27*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (512*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (896*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + HPL[{0}, S^2]^3*((2033*Pi^6*S^3)/30240 + (-7347280 + 76166*S^2 + 14230809*S^4)/(419904*S) + (Pi^4*(-160200 + 72783*S^2 + 904183*S^4 + 690532*S^6))/(349920*S*(1 + S^2)) + (Pi^2*(-951588 - 932643*S^2 + 3504199*S^4 + 3516358*S^6))/(419904*S*(1 + S^2)) + ((-113 + 691*S^2 + 438*S^4 + 1690*S^6 + 886*S^8)*HPL[{1}, -S^2]^5)/(810*S^3*(1 + S^2)) + (13*(1 + S^6)*HPL[{1}, -S^2]^6)/(81*S^3) + ((Pi^2*(12 + 367*S^6))/(648*S^3) + (1389 + 1131*S^2 + 5730*S^4 + 22555*S^6 + 17215*S^8)/(3888*S^3*(1 + S^2)))*HPL[{2}, -S^2]^2 + ((-1 + 24*S^6)*HPL[{2}, -S^2]^3)/(54*S^3) + HPL[{1}, -S^2]^4*((79*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (-1231 - 1957*S^2 + 5865*S^4 + 11273*S^6 + 5330*S^8)/(1458*S^3*(1 + S^2)) + (31*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((-35 - 31*S^6)*HPL[{3}, -S^2]^2)/(54*S^3) + ((Pi^2*(-9 - 8*S^6))/(81*S^3) + (-427 - 2197*S^2 + 1608*S^4 + 7247*S^6 + 4517*S^8)/(1944*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((55 - 212*S^2 - 3*S^4 - 122*S^6 + 145*S^8)*HPL[{5}, -S^2])/(162*S^3*(1 + S^2)) + ((-25 - 29*S^6)*HPL[{6}, -S^2])/(9*S^3) + ((3 - 163*S^6)*HPL[{2, 1}, -S^2]^2)/(27*S^3) + ((Pi^2*(-12 - 361*S^6))/(162*S^3) + (-221 - 17*S^2 - 3858*S^4 - 14458*S^6 - 10180*S^8)/(486*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-625 - 520*S^2 + 120*S^4 - 276*S^6 - 381*S^8)*HPL[{3, 2}, -S^2])/(162*S^3*(1 + S^2)) + ((-549 - 378*S^2 + 162*S^4 - 446*S^6 - 617*S^8)*HPL[{4, 1}, -S^2])/(81*S^3*(1 + S^2)) + (2*S^3*HPL[{4, 2}, -S^2])/27 + (10*(3 + 4*S^6)*HPL[{5, 1}, -S^2])/(27*S^3) + ((Pi^2*(27 + 437*S^6))/(81*S^3) + (-130 - 840*S^2 + 7971*S^4 + 21513*S^6)/(486*S^3))*HPL[{2, 1, 1}, -S^2] + ((-198 + 852*S^2 + 606*S^4 + 1091*S^6 + 41*S^8)*HPL[{2, 2, 1}, -S^2])/(81*S^3*(1 + S^2)) + ((-279 + 773*S^2 + 574*S^4 + 1182*S^6 + 130*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*S^3*HPL[{3, 1, 2}, -S^2])/27 + (2*(-6 + 143*S^6)*HPL[{3, 2, 1}, -S^2])/(27*S^3) + (2*(-9 + 445*S^6)*HPL[{4, 1, 1}, -S^2])/(27*S^3) - (2*(-283 + 839*S^2 + 570*S^4 + 1174*S^6 + 52*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) - (16*(3 + 43*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3) + (8*(4 + 61*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((Pi^2*(286 + 143*S^2 + 2854*S^4 + 2568*S^6))/(324*S*(1 + S^2)) + (-25440 - 28074*S^2 + 62209*S^4 + 56419*S^6)/(5832*S*(1 + S^2)))*Zeta[3] - (S^3*Zeta[3]^2)/9 + HPL[{1}, -S^2]^3*((Pi^2*(-1205 + 4705*S^2 + 3288*S^4 + 12661*S^6 + 6751*S^8))/(2916*S^3*(1 + S^2)) + (-45659 - 84080*S^2 + 140562*S^4 + 323512*S^6 + 157489*S^8)/(17496*S^3*(1 + S^2)) + ((-154 + 962*S^2 + 558*S^4 + 2429*S^6 + 1313*S^8)*HPL[{2}, -S^2])/(243*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) - (124*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (46*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(81*S^3)) + HPL[{3}, -S^2]*((Pi^2*(-78 - 107*S^2 - 31*S^4 + 33*S^6 + 62*S^8))/(324*S^3*(1 + S^2)) + (-16001 - 25799*S^2 + 17682*S^4 + 68799*S^6 + 43911*S^8)/(11664*S^3*(1 + S^2)) + (2*(13 + 19*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (2*(1 + 2*S^6)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((38416 + 7101*S^2 - 137781*S^4 - 22534*S^6)/(5832*S^3) + (Pi^2*(919 - 1727*S^2 - 1557*S^4 - 2083*S^6 + 563*S^8))/(972*S^3*(1 + S^2)) - (2*(40 + 23*S^6)*Zeta[3])/(27*S^3)) + HPL[{2}, -S^2]*((Pi^4*(19 + 432*S^6))/(1080*S^3) + (Pi^2*(-1345 - 5281*S^2 + 16077*S^4 + 72717*S^6 + 55404*S^8))/(11664*S^3*(1 + S^2)) + (-78003 - 232860*S^2 + 40746*S^4 + 765512*S^6 + 593237*S^8)/(34992*S^3*(1 + S^2)) + ((313 + 259*S^2 - 63*S^4 + 132*S^6 + 186*S^8)*HPL[{3}, -S^2])/(162*S^3*(1 + S^2)) + (5*(7 + 6*S^6)*HPL[{4}, -S^2])/(27*S^3) + ((198 - 852*S^2 - 606*S^4 - 1091*S^6 - 41*S^8)*HPL[{2, 1}, -S^2])/(162*S^3*(1 + S^2)) - (2*(10 + 91*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (2*(-3 + 163*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + ((-10 + 40*S^2 - 11*S^4 + 168*S^6 + 118*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) + HPL[{1}, -S^2]^2*((805*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1944*S^3) + (Pi^2*(-13784 - 23999*S^2 + 57249*S^4 + 113323*S^6 + 53851*S^8))/(11664*S^3*(1 + S^2)) + (-441431 - 846890*S^2 + 847764*S^4 + 2361610*S^6 + 1170595*S^8)/(69984*S^3*(1 + S^2)) + ((415*Pi^2*(1 + S^6))/(324*S^3) + (-2339 - 1110*S^2 + 11796*S^4 + 11215*S^6)/(972*S^3))*HPL[{2}, -S^2] + (83*(1 + S^6)*HPL[{2}, -S^2]^2)/(54*S^3) + ((-119 - 98*S^2 - 12*S^4 + 199*S^6 + 178*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) - (5*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) + ((154 - 962*S^2 - 558*S^4 - 2429*S^6 - 1313*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) - (178*(1 + S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (124*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-136 - 36*S^2 + 62*S^4 + 315*S^6 + 215*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) + (4*(24 + 12*S^2 + 325*S^4 + 301*S^6)*Zeta[5])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(-9242 + 7216*S^2 + 8766*S^4 + 42151*S^6 + 25693*S^8))/(19440*S^3*(1 + S^2)) + (Pi^2*(-20984 - 44599*S^2 + 52121*S^4 + 132827*S^6 + 64651*S^8))/(11664*S^3*(1 + S^2)) + (-1179784 - 2363893*S^2 + 1171329*S^4 + 4528577*S^6 + 2266451*S^8)/(104976*S^3*(1 + S^2)) + ((8 + 1022*S^2 + 534*S^4 + 2021*S^6 + 1007*S^8)*HPL[{2}, -S^2]^2)/(324*S^3*(1 + S^2)) + (-(Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3) + (-427 - 693*S^2 + 305*S^4 + 2061*S^6 + 1130*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-445 - 487*S^2 + 6*S^4 + 314*S^6 + 356*S^8)*HPL[{4}, -S^2])/(162*S^3*(1 + S^2)) - (59*(1 + S^6)*HPL[{5}, -S^2])/(27*S^3) + ((2339 + 1110*S^2 - 11796*S^4 - 11215*S^6)/(486*S^3) - (415*Pi^2*(1 + S^6))/(162*S^3))*HPL[{2, 1}, -S^2] + ((230 - 826*S^2 - 510*S^4 - 2419*S^6 - 1363*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) + (10*(1 + S^6)*HPL[{3, 2}, -S^2])/(27*S^3) + (40*(1 + S^6)*HPL[{4, 1}, -S^2])/(27*S^3) + (2*(-154 + 962*S^2 + 558*S^4 + 2429*S^6 + 1313*S^8)*HPL[{2, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) + (332*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) + (340*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (248*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((143*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (-4708 - 10201*S^2 + 1029*S^4 + 10265*S^6 + 4607*S^8)/(972*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-15511 - 10855*S^2 + 61223*S^4 + 60887*S^6)/(3888*S^3) + (Pi^2*(-1049 + 4081*S^2 + 2790*S^4 + 11074*S^6 + 5944*S^8))/(1944*S^3*(1 + S^2)) - (5*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) - (166*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (37*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) + (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + (62*Pi^2*S^3 + (14286 + 14784*S^2 + 9833*S^4 + 8255*S^6)/(54*S*(1 + S^2)))*Zeta[7] + HPL[{0}, S^2]^2*((14811135 - 309645*S^2 + 24668102*S^4)/(209952*S) + (Pi^6*(21214 + 10607*S^2 + 53992*S^4 + 32778*S^6))/(60480*S*(1 + S^2)) + (Pi^4*(346622 + 551863*S^2 + 2534265*S^4 + 2424928*S^6))/(466560*S*(1 + S^2)) + (Pi^2*(3521766 + 3501078*S^2 + 10085513*S^4 + 10246169*S^6))/(419904*S*(1 + S^2)) + ((37 + 217*S^2 + 90*S^4 + 328*S^6 + 148*S^8)*HPL[{1}, -S^2]^6)/(162*S^3*(1 + S^2)) + (10*(1 + S^6)*HPL[{1}, -S^2]^7)/(63*S^3) + ((-51 + 585*S^2 + 318*S^4 + 1411*S^6 + 775*S^8)*HPL[{2}, -S^2]^3)/(324*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((163*Pi^2*(1 + S^6))/(270*S^3) + (1357 + 1605*S^2 + 7083*S^4 + 6403*S^6)/(1620*S^3) + (86*(1 + S^6)*HPL[{2}, -S^2])/(45*S^3)) + ((215 + 155*S^2 - 21*S^4 - 193*S^6 - 133*S^8)*HPL[{3}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((23*Pi^2*(5 + 9*S^6))/(108*S^3) + (-1291 - 2221*S^2 + 2847*S^4 + 18711*S^6 + 12990*S^8)/(648*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-2110 - 256*S^2 + 387*S^4 + 3888*S^6 + 2034*S^8)*HPL[{6}, -S^2])/(108*S^3*(1 + S^2)) + ((270 + 269*S^6)*HPL[{7}, -S^2])/(9*S^3) + ((192 - 366*S^2 - 279*S^4 - 1459*S^6 - 901*S^8)*HPL[{2, 1}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((-5*Pi^2*(-15 + 8*S^6))/(54*S^3) + (3963 + 1026*S^2 - 582*S^4 - 7594*S^6 - 8437*S^8)/(648*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((Pi^2*(91 - 199*S^6))/(54*S^3) + (4151 - 412*S^2 - 3906*S^4 - 19510*S^6 - 16927*S^8)/(324*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((17 - 6*S^2 - 6*S^4 - 89*S^6)*HPL[{4, 2}, -S^2])/(54*S^3) - (2*(57 + 37*S^6)*HPL[{4, 3}, -S^2])/(9*S^3) + ((131 - 155*S^2 - 92*S^4 - 778*S^6 - 492*S^8)*HPL[{5, 1}, -S^2])/(18*S^3*(1 + S^2)) + ((-673 - 469*S^6)*HPL[{5, 2}, -S^2])/(18*S^3) - (11*(74 + 63*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((6053 + 636*S^2 + 12156*S^4 - 769*S^6)/(162*S^3) + (Pi^2*(458 + 21*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((Pi^2*(1400 + 123*S^6))/(27*S^3) + (17834 + 21485*S^2 + 41340*S^4 + 41659*S^6 + 2458*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + ((79 + 6*S^2 + 6*S^4 - 7*S^6)*HPL[{3, 1, 2}, -S^2])/(54*S^3) + ((-125 + 2425*S^2 + 1284*S^4 + 5643*S^6 + 3093*S^8)*HPL[{3, 2, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((39 + 70*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) + (4*(-8 + 39*S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) + (2*(-64 + 2060*S^2 + 1053*S^4 + 4790*S^6 + 2666*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-39 + 167*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) + ((-243 + 419*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) + (2*(-287 + 447*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((-2*Pi^2*(466 + 49*S^6))/(27*S^3) - (2*(996 + 1485*S^2 + 2673*S^4 + 2780*S^6 + 380*S^8))/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - (8*(106 + 23*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) - (4*(22 + 793*S^2 + 381*S^4 + 1841*S^6 + 1070*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(657 + 98*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) + (4*(657 + 98*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) + (4*(1293 + 236*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) + (8*(1919 + 349*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3) + (8*(65 + 839*S^2 + 387*S^4 + 1850*S^6 + 1076*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(223 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3) - (8*(223 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3) + (16*(-552 + 17*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3) - (16*(233 + 38*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((2111*Pi^4*S^3)/1080 + (Pi^2*(-20 + 512*S^2 + 2935*S^4 + 2715*S^6))/(216*S*(1 + S^2)) + (146670 + 151554*S^2 + 227599*S^4 + 261595*S^6)/(11664*S*(1 + S^2)))*Zeta[3] + ((102 + 51*S^2 + 58*S^4 - 44*S^6)*Zeta[3]^2)/(18*S*(1 + S^2)) + HPL[{4}, -S^2]*((Pi^2*(137 + 677*S^2 + 153*S^4 + 1127*S^6 + 587*S^8))/(324*S^3*(1 + S^2)) + (6556 + 9117*S^2 + 10504*S^4 + 34415*S^6 + 23016*S^8)/(1296*S^3*(1 + S^2)) + ((-79 - 25*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{1}, -S^2]^4*((1971 + 1977*S^2 + 8443*S^4 + 8149*S^6)/(648*S^3) + (Pi^2*(84 + 746*S^2 + 346*S^4 + 1231*S^6 + 569*S^8))/(216*S^3*(1 + S^2)) + ((323 + 1331*S^2 + 468*S^4 + 1775*S^6 + 767*S^8)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (86*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (11*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((-5676 - 34833*S^2 - 77358*S^4 - 215071*S^6 - 159094*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-47 - 3161*S^2 - 1440*S^4 - 7765*S^6 - 4651*S^8))/(324*S^3*(1 + S^2)) - (2*(-12 + 19*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(184 + 3274*S^2 + 1545*S^4 + 8116*S^6 + 5026*S^8))/(162*S^3*(1 + S^2)) + (7560 + 25503*S^2 + 36957*S^4 + 97870*S^6 + 74968*S^8)/(486*S^3*(1 + S^2)) + (4*(-3 + 22*S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((-4821 + 5337*S^2 + 4176*S^4 + 32519*S^6)/(1944*S^3) + (Pi^2*(-393 + 789*S^2 + 591*S^4 + 3115*S^6 + 1933*S^8))/(648*S^3*(1 + S^2)) + ((1 + 2*S^6)*HPL[{3}, -S^2])/(2*S^3) + ((-106 - 23*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + ((22 + 43*S^6)*Zeta[3])/(18*S^3)) + HPL[{2, 1}, -S^2]*((Pi^4*(-6615 - 368*S^6))/(3240*S^3) + (-181471 - 270082*S^2 - 595605*S^4 - 678356*S^6 - 148034*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(-8843 - 12305*S^2 - 33294*S^4 - 32419*S^6 - 1399*S^8))/(1944*S^3*(1 + S^2)) + (4*(116 + 5*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (4*(223 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-10 - 52*S^2 - 15*S^4 - 104*S^6 - 62*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((7643*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(9720*S^3) + (159736 + 150291*S^2 + 550656*S^4 + 552325*S^6)/(17496*S^3) + (Pi^2*(2197 + 4597*S^2 + 19455*S^4 + 30667*S^6 + 14692*S^8))/(1944*S^3*(1 + S^2)) + ((515*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (3796 + 8152*S^2 + 14211*S^4 + 21958*S^6 + 10807*S^8)/(486*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (31*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((143 + 533*S^2 + 132*S^4 + 731*S^6 + 341*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (74*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) + ((-323 - 1331*S^2 - 468*S^4 - 1775*S^6 - 767*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (172*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (344*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((65 + 199*S^2 + 70*S^4 + 196*S^6 + 62*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^4*(271 + 459*S^6))/(3240*S^3) + (Pi^2*(509 + 3476*S^2 + 3900*S^4 + 13390*S^6 + 8353*S^8))/(3888*S^3*(1 + S^2)) + (82409 + 241658*S^2 + 362490*S^4 + 718082*S^6 + 437081*S^8)/(23328*S^3*(1 + S^2)) + ((57 + 32*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-485 - 629*S^2 - 90*S^4 + 275*S^6 + 419*S^8)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)) - (2*(-26 + 3*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (8*(-5 + 9*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((128 + 89*S^2 + 21*S^4 + 37*S^6 + 76*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((461*Pi^2*S^3)/27 + (3498 + 6267*S^2 + 21427*S^4 + 20170*S^6)/(324*S*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^2*((255191 + 237440*S^2 + 693695*S^4 + 703670*S^6)/(11664*S^3) + (Pi^4*(1515 + 32711*S^2 + 16534*S^4 + 59642*S^6 + 28446*S^8))/(12960*S^3*(1 + S^2)) + (Pi^2*(72031 + 130378*S^2 + 406008*S^4 + 659110*S^6 + 327001*S^8))/(23328*S^3*(1 + S^2)) + ((296 + 1412*S^2 + 558*S^4 + 1979*S^6 + 863*S^8)*HPL[{2}, -S^2]^2)/(108*S^3*(1 + S^2)) + ((23*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3) + (1840 + 3601*S^2 + 3513*S^4 + 7363*S^6 + 4099*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((239 + 1091*S^2 + 372*S^4 + 1523*S^6 + 671*S^8)*HPL[{4}, -S^2])/(108*S^3*(1 + S^2)) + (58*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-515*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (-3796 - 8152*S^2 - 14211*S^4 - 21958*S^6 - 10807*S^8)/(162*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-439 - 1945*S^2 - 690*S^4 - 2710*S^6 - 1204*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (22*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (140*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + ((323 + 1331*S^2 + 468*S^4 + 1775*S^6 + 767*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (124*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (140*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 - (344*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((109*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (871 + 1423*S^2 + 1293*S^4 + 1441*S^6 + 772*S^8)/(108*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(488 + 2526*S^2 + 986*S^4 + 3681*S^6 + 1643*S^8))/(216*S^3*(1 + S^2)) + (60179 + 119612*S^2 + 220854*S^4 + 354692*S^6 + 177719*S^8)/(3888*S^3*(1 + S^2)) + (11*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (62*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (23*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (119*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*((Pi^2*(4858 + 15035*S^2 + 21857*S^4 + 69930*S^6 + 55226*S^8))/(3888*S^3*(1 + S^2)) + (Pi^4*(4414 + 49852*S^2 + 22719*S^4 + 134714*S^6 + 89276*S^8))/(38880*S^3*(1 + S^2)) + (524183 + 1247141*S^2 + 1286490*S^4 + 2844557*S^6 + 2141057*S^8)/(34992*S^3*(1 + S^2)) + ((Pi^2*(-37 + 18*S^6))/(54*S^3) + (-1659 - 234*S^2 + 42*S^4 + 3992*S^6 + 4511*S^8)/(648*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-439 - 319*S^2 + 42*S^4 + 447*S^6 + 327*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) + ((-123 - 35*S^6)*HPL[{5}, -S^2])/(18*S^3) + ((Pi^2*(-458 - 21*S^6))/(54*S^3) + (-6053 - 636*S^2 - 12156*S^4 + 769*S^6)/(324*S^3))*HPL[{2, 1}, -S^2] + ((587 - 541*S^2 - 546*S^4 - 3097*S^6 - 1969*S^8)*HPL[{3, 1}, -S^2])/(54*S^3*(1 + S^2)) - (2*(1 + 2*S^6)*HPL[{3, 2}, -S^2])/S^3 + ((25 - 83*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (2*(-192 + 366*S^2 + 279*S^4 + 1459*S^6 + 901*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(106 + 23*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (4*(328 + 51*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (4*(223 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((Pi^2*(-18 + 37*S^6))/(54*S^3) + (-835 + 11*S^2 + 1962*S^4 + 2827*S^6 + 1603*S^8)/(324*S^3*(1 + S^2)))*Zeta[3] + ((-30 + 37*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((10607*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(30240*S^3) + ((1 + S^2)*(1347308 - 48191*S^2 + 2778269*S^4))/(34992*S^3) + (Pi^4*(127315 + 210853*S^2 + 936927*S^4 + 1602163*S^6 + 816166*S^8))/(233280*S^3*(1 + S^2)) + (Pi^2*(386243 + 730967*S^2 + 1534377*S^4 + 2378057*S^6 + 1211732*S^8))/(69984*S^3*(1 + S^2)) + ((197*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(108*S^3) + ((1 + S^2)*(471 + 248*S^2 + 2577*S^4))/(216*S^3))*HPL[{2}, -S^2]^2 + (53*(1 + S^6)*HPL[{2}, -S^2]^3)/(27*S^3) - (11*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((103*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (1059 + 1516*S^2 + 2474*S^4 + 6076*S^6 + 3627*S^8)/(216*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((21 + 128*S^2 + 40*S^4 + 212*S^6 + 105*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (41*(1 + S^6)*HPL[{6}, -S^2])/(2*S^3) - (62*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-266*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-3253 - 7171*S^2 - 14145*S^4 - 23569*S^6 - 11830*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-103 - 214*S^2 - 24*S^4 - 169*S^6 - 58*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((-869 - 2369*S^2 - 480*S^4 - 2531*S^6 - 1031*S^8)*HPL[{4, 1}, -S^2])/(54*S^3*(1 + S^2)) - (160*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((515*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (3796 + 8152*S^2 + 14211*S^4 + 21958*S^6 + 10807*S^8)/(81*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (2*(296 + 1412*S^2 + 558*S^4 + 1979*S^6 + 863*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(1031 + 4769*S^2 + 1806*S^4 + 6668*S^6 + 2930*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (424*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (1420*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (2*(323 + 1331*S^2 + 468*S^4 + 1775*S^6 + 767*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (344*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (688*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((28015 + 22785*S^2 + 12021*S^4 + 19195*S^6)/(1944*S^3) + (Pi^2*(26 + 514*S^2 + 322*S^4 + 775*S^6 + 287*S^8))/(108*S^3*(1 + S^2)))*Zeta[3] + (17*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*((-60179 - 119612*S^2 - 220854*S^4 - 354692*S^6 - 177719*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-488 - 2526*S^2 - 986*S^4 - 3681*S^6 - 1643*S^8))/(108*S^3*(1 + S^2)) - (46*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((Pi^2*(350 + 1064*S^2 + 186*S^4 + 1343*S^6 + 629*S^8))/(324*S^3*(1 + S^2)) + (4629 + 8675*S^2 + 12805*S^4 + 24149*S^6 + 12798*S^8)/(648*S^3*(1 + S^2)) - (22*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (22*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((7573*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(6480*S^3) + (Pi^2*(5768 + 12008*S^2 + 28671*S^4 + 46550*S^6 + 22931*S^8))/(1944*S^3*(1 + S^2)) + (266051 + 497714*S^2 + 878352*S^4 + 1405526*S^6 + 712181*S^8)/(11664*S^3*(1 + S^2)) + ((35 + 71*S^2 + 6*S^4 + 56*S^6 + 20*S^8)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)) + (22*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-296 - 1412*S^2 - 558*S^4 - 1979*S^6 - 863*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (190*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (124*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-8 + 22*S^2 + 14*S^4 + 71*S^6 + 41*S^8)*Zeta[3])/(6*S^3*(1 + S^2))) + ((763 + 2275*S^2 + 882*S^4 + 1924*S^6 + 412*S^8)*Zeta[5])/(54*S^3*(1 + S^2))) + 124*S^3*Zeta[7]) + Log[T]^2*((95201*(-1 + S^2))/(17496*S) + (Pi^2*(595227 + 113529*S^2 + 2141057*S^4))/(52488*S) + (Pi^6*(283974 + 141987*S^2 + 821452*S^4 + 537478*S^6))/(408240*S*(1 + S^2)) + (Pi^4*(592074 + 1091853*S^2 + 3742403*S^4 + 3203744*S^6))/(349920*S*(1 + S^2)) + (5*S^3*HPL[{0}, S^2]^7)/216 + (28*(-1 + S^6)*HPL[{1}, -S^2]^6)/(9*S^3) + HPL[{0}, S^2]^6*((14 + 7*S^2 + 48*S^4 + 34*S^6)/(108*S*(1 + S^2)) + (7*(1 + S^6)*HPL[{1}, -S^2])/(54*S^3)) + ((709 + 1825*S^2 + 558*S^4 + 1825*S^6 + 709*S^8)*HPL[{2}, -S^2]^3)/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((10*Pi^2*(1 + S^6))/(9*S^3) + (131*(-1 - S^2 + S^4 + S^6))/(9*S^3) + (40*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^5*((407*Pi^2*S^3)/1620 + (-1552 + 2917*S^2 + 17296*S^4 + 13727*S^6)/(6480*S*(1 + S^2)) + ((-866 + 2632*S^2 + 1974*S^4 + 7591*S^6 + 4093*S^8)*HPL[{1}, -S^2])/(3240*S^3*(1 + S^2)) + (31*(1 + S^6)*HPL[{1}, -S^2]^2)/(60*S^3) + ((15 + 254*S^6)*HPL[{2}, -S^2])/(540*S^3)) + ((71 + 4*S^2 + 4*S^4 - 113*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((Pi^2*(25 + 283*S^6))/(27*S^3) + (-10423 - 10153*S^2 + 16227*S^4 + 42785*S^6 + 27260*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-174 + 2688*S^2 + 1431*S^4 + 8582*S^6 + 5720*S^8)*HPL[{6}, -S^2])/(27*S^3*(1 + S^2)) + (40*(15 + 38*S^6)*HPL[{7}, -S^2])/(9*S^3) - (1348*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-2*Pi^2*(7 + 458*S^6))/(27*S^3) + (-3385 - 51490*S^2 - 50778*S^4 - 20410*S^6 - 18169*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-4*Pi^2*(55 + 716*S^6))/(27*S^3) + (-1930 - 73849*S^2 - 85482*S^4 - 47649*S^6 - 34734*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] - (2*(19 + 625*S^6)*HPL[{4, 2}, -S^2])/(27*S^3) + (4*(-37 + 41*S^6)*HPL[{4, 3}, -S^2])/(9*S^3) - (2*(485 + 2141*S^2 + 828*S^4 + 6305*S^6 + 4649*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-63 + 55*S^6)*HPL[{5, 2}, -S^2])/(3*S^3) - (136*(9 + 7*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((-28*(-88 + 273*S^2 - 273*S^4 + 88*S^6))/(27*S^3) - (8*Pi^2*(-209 + 97*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((-8*Pi^2*(-655 + 54*S^6))/(27*S^3) - (4*(-4582 + 4878*S^2 - 20502*S^4 + 153*S^6))/(81*S^3))*HPL[{3, 1, 1}, -S^2] + (644*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/(27*S^3) + (4*(1579 + 3811*S^2 + 1116*S^4 + 3811*S^6 + 1579*S^8)*HPL[{3, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(121 + 775*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) + (16*(77 + 593*S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) + (8*(2553 + 6333*S^2 + 1890*S^4 + 6845*S^6 + 3065*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(34 + 301*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) + (64*(53 + 449*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) + (16*(435 + 3689*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((-8*Pi^2*(473 + 278*S^6))/(27*S^3) - (4*(4429 + 15624*S^2 + 15624*S^4 + 4429*S^6))/(81*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (3584*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) - (16*(922 + 2272*S^2 + 675*S^4 + 2528*S^6 + 1178*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(322 + 127*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) + (32*(322 + 127*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) + (32*(658 + 463*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) + (2080*(10 + 7*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (800*(14 + 32*S^2 + 9*S^4 + 32*S^6 + 14*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2080*(-1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (2080*(-1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (320*(-31 + 47*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) - (5120*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((869*Pi^4*S^3)/270 + (525789 + 6084*S^2 + 158849*S^4)/(1458*S) + (Pi^2*(15984 + 17352*S^2 + 8815*S^4 + 7555*S^6))/(486*S*(1 + S^2)))*Zeta[3] - (32*S^3*Zeta[3]^2)/3 + HPL[{0}, S^2]^4*((Pi^2*(684 + 342*S^2 + 2251*S^4 + 1567*S^6))/(648*S*(1 + S^2)) + (20304 + 44091*S^2 + 232403*S^4 + 216392*S^6)/(23328*S*(1 + S^2)) + ((67 + 1153*S^2 + 588*S^4 + 2053*S^6 + 967*S^8)*HPL[{1}, -S^2]^2)/(216*S^3*(1 + S^2)) + (44*(1 + S^6)*HPL[{1}, -S^2]^3)/(27*S^3) + ((18 + 532*S^2 + 257*S^4 + 1472*S^6 + 958*S^8)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((19*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3) + (280 + 545*S^2 + 3589*S^4 + 5727*S^6 + 2763*S^8)/(432*S^3*(1 + S^2)) + (257*(1 + S^6)*HPL[{2}, -S^2])/(108*S^3)) + ((5 + 7*S^6)*HPL[{3}, -S^2])/(36*S^3) + ((-233 - 11*S^6)*HPL[{2, 1}, -S^2])/(54*S^3) + (83*S^3*Zeta[3])/54) + HPL[{1}, -S^2]^4*((5165*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (5*Pi^2*(-89 + 91*S^2 + 90*S^4 + 454*S^6 + 274*S^8))/(162*S^3*(1 + S^2)) + (25*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (100*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (200*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (100*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((-67408 - 4959*S^2 + 4959*S^4 + 67408*S^6)/(972*S^3) + (Pi^2*(-1203 - 645*S^2 + 279*S^4 + 2470*S^6 + 1912*S^8))/(162*S^3*(1 + S^2)) + (2*(29 + 195*S^6)*HPL[{3}, -S^2])/(9*S^3) - (448*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (56*(1 + 7*S^6)*Zeta[3])/(9*S^3)) + HPL[{4}, -S^2]*((50490 - 29469*S^2 + 57975*S^4 + 129062*S^6)/(972*S^3) + (Pi^2*(515 + 1163*S^2 + 315*S^4 + 1927*S^6 + 1279*S^8))/(81*S^3*(1 + S^2)) + (16*(-13 + 14*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(-17 + 29*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((-126193 - 30015*S^2 - 73737*S^4 - 165479*S^6)/(486*S^3) - (2*Pi^2*(944 + 3065*S^2 + 1056*S^4 + 4369*S^6 + 2248*S^8))/(81*S^3*(1 + S^2)) - (16*(3 + 100*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((4*(1 + S^2)*(4051 - 2610*S^2 + 4051*S^4))/(27*S^3) + (4*Pi^2*(1115 + 3239*S^2 + 1062*S^4 + 4250*S^6 + 2126*S^8))/(81*S^3*(1 + S^2)) + (16*(7 + 202*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^3*((59017*(-1 + S^2)*(1 + S^2)^2)/(486*S^3) + (749*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (Pi^2*(-2269 - 2145*S^2 + 6489*S^4 + 6149*S^6))/(243*S^3) + ((472*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (16*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(81*S^3))*HPL[{2}, -S^2] + (4*(593 + 1493*S^2 + 450*S^4 + 1232*S^6 + 332*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (64*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (100*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (400*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (800*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (20*(163 + 343*S^2 + 90*S^4 + 202*S^6 + 22*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(158849 + 373024*S^2 + 158849*S^4))/(1458*S^3) - (319*Pi^4*(19 + 7*S^6))/(810*S^3) + (Pi^2*(-10405 - 28963*S^2 - 47286*S^4 - 36733*S^6 - 6709*S^8))/(486*S^3*(1 + S^2)) - (16*(-97 + 98*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (1040*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (8*(-985 - 1561*S^2 - 288*S^4 - 550*S^6 + 26*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^4*(209 + 1955*S^6))/(810*S^3) + (54291 + 1749681*S^2 + 377811*S^4 + 581105*S^6)/(5832*S^3) + (Pi^2*(-2249 + 24136*S^2 + 34212*S^4 + 24886*S^6 + 15547*S^8))/(972*S^3*(1 + S^2)) - (4*(-19 + 33*S^6)*HPL[{4}, -S^2])/(9*S^3) + (8*(-268 - 455*S^2 - 95*S^4 - 118*S^6 + 69*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(19 + 203*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (80*(1 + 14*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(369 + 411*S^2 + 30*S^4 + 271*S^6 + 229*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^3*((821*Pi^4*S^3)/972 + (Pi^2*(-6258 + 15510*S^2 + 82991*S^4 + 65219*S^6))/(5832*S*(1 + S^2)) + (-319458 - 231441*S^2 + 1382626*S^4 + 1325713*S^6)/(34992*S*(1 + S^2)) + ((-113 + 691*S^2 + 438*S^4 + 1690*S^6 + 886*S^8)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)) + (65*(1 + S^6)*HPL[{1}, -S^2]^4)/(27*S^3) + ((Pi^2*(27 + 437*S^6))/(162*S^3) + (-130 - 840*S^2 + 7971*S^4 + 21513*S^6)/(972*S^3))*HPL[{2}, -S^2] + ((-3 + 163*S^6)*HPL[{2}, -S^2]^2)/(54*S^3) + HPL[{1}, -S^2]^2*((79*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-1231 - 1957*S^2 + 5865*S^4 + 11273*S^6 + 5330*S^8)/(243*S^3*(1 + S^2)) + (62*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-81 - 79*S^2 - 32*S^4 + 91*S^6 + 89*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) + ((9 + 13*S^6)*HPL[{4}, -S^2])/(27*S^3) + ((283 - 839*S^2 - 570*S^4 - 1174*S^6 - 52*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) - (8*(3 + 43*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (4*(4 + 61*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (23*(2 + S^2 + 13*S^4 + 11*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-1205 + 4705*S^2 + 3288*S^4 + 12661*S^6 + 6751*S^8))/(972*S^3*(1 + S^2)) + (-45659 - 84080*S^2 + 140562*S^4 + 323512*S^6 + 157489*S^8)/(5832*S^3*(1 + S^2)) + ((-154 + 962*S^2 + 558*S^4 + 2429*S^6 + 1313*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (124*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (46*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3))) + ((844*Pi^2*S^3)/27 + (22554 + 23211*S^2 + 6401*S^4 + 5636*S^6)/(81*S*(1 + S^2)))*Zeta[5] + HPL[{0}, S^2]^2*((692346 + 16410*S^2 + 2141057*S^4)/(17496*S) + (Pi^4*(45858 + 22929*S^2 + 141994*S^4 + 96136*S^6))/(19440*S*(1 + S^2)) + (Pi^2*(51786 + 95967*S^2 + 398633*S^4 + 362228*S^6))/(11664*S*(1 + S^2)) + (5*(37 + 217*S^2 + 90*S^4 + 328*S^6 + 148*S^8)*HPL[{1}, -S^2]^4)/(54*S^3*(1 + S^2)) + (10*(1 + S^6)*HPL[{1}, -S^2]^5)/(3*S^3) + ((-192 + 366*S^2 + 279*S^4 + 1459*S^6 + 901*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((163*Pi^2*(1 + S^6))/(27*S^3) + (1357 + 1605*S^2 + 7083*S^4 + 6403*S^6)/(162*S^3) + (172*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((Pi^2*(13 + 30*S^6))/(27*S^3) + (-325 + 1418*S^2 + 2964*S^4 + 7498*S^6 + 4765*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((89 + 305*S^2 + 99*S^4 + 557*S^6 + 341*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + ((19 + 69*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((Pi^2*(-466 - 49*S^6))/(27*S^3) + (-996 - 1485*S^2 - 2673*S^4 - 2780*S^6 - 380*S^8)/(27*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (2*(22 + 793*S^2 + 381*S^4 + 1841*S^6 + 1070*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-21 + 40*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (4*(-11 + 65*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(65 + 839*S^2 + 387*S^4 + 1850*S^6 + 1076*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(223 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (8*(340 + 21*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (8*(233 + 38*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((38*Pi^2*S^3)/9 + (177 + 288*S^2 + 614*S^4 + 521*S^6)/(27*S*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((1971 + 1977*S^2 + 8443*S^4 + 8149*S^6)/(108*S^3) + (Pi^2*(84 + 746*S^2 + 346*S^4 + 1231*S^6 + 569*S^8))/(36*S^3*(1 + S^2)) + ((323 + 1331*S^2 + 468*S^4 + 1775*S^6 + 767*S^8)*HPL[{2}, -S^2])/(18*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{3}, -S^2])/S^3 - (172*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (22*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((Pi^2*(184 + 3274*S^2 + 1545*S^4 + 8116*S^6 + 5026*S^8))/(324*S^3*(1 + S^2)) + (7560 + 25503*S^2 + 36957*S^4 + 97870*S^6 + 74968*S^8)/(972*S^3*(1 + S^2)) + (4*(-5 + 9*S^6)*HPL[{3}, -S^2])/(9*S^3) - (2*(223 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(-3 + 22*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((7643*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(3240*S^3) + (159736 + 150291*S^2 + 550656*S^4 + 552325*S^6)/(5832*S^3) + (Pi^2*(2197 + 4597*S^2 + 19455*S^4 + 30667*S^6 + 14692*S^8))/(648*S^3*(1 + S^2)) + ((515*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (3796 + 8152*S^2 + 14211*S^4 + 21958*S^6 + 10807*S^8)/(162*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (31*(1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + ((143 + 533*S^2 + 132*S^4 + 731*S^6 + 341*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (74*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-323 - 1331*S^2 - 468*S^4 - 1775*S^6 - 767*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (172*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (344*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((65 + 199*S^2 + 70*S^4 + 196*S^6 + 62*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + 26*S^3*Zeta[5]) + HPL[{1}, -S^2]^2*((4195*(-1 + S^2)*(1 + S^2)^2)/(18*S^3) + (Pi^2*(-11553 - 11541*S^2 + 32381*S^4 + 31793*S^6))/(648*S^3) + (Pi^4*(-557 + 5409*S^2 + 2944*S^4 + 12679*S^6 + 6713*S^8))/(1080*S^3*(1 + S^2)) + (74*(-1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + ((58*Pi^2*(1 + S^6))/(3*S^3) + (5401 + 5793*S^2 + 2895*S^4 + 2359*S^6)/(27*S^3))*HPL[{3}, -S^2] + (4*(-23 + 124*S^2 + 78*S^4 + 307*S^6 + 160*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (184*(1 + S^6)*HPL[{5}, -S^2])/(3*S^3) + ((-472*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (16*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(27*S^3))*HPL[{2, 1}, -S^2] - (4*(371 + 1271*S^2 + 450*S^4 + 1454*S^6 + 554*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) - (560*(1 + S^6)*HPL[{4, 1}, -S^2])/S^3 + (100*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (400*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 - (800*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((172*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (4*(1813 + 1875*S^2 + 297*S^4 + 127*S^6))/(27*S^3))*Zeta[3] + HPL[{2}, -S^2]*((10*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(27*S^3) + (2*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(9*S^3*(1 + S^2)) + (248*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (256*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + (448*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*(((1 + S^2)*(2141057 - 1432301*S^2 + 2141057*S^4))/(8748*S^3) + (Pi^4*(20282 + 70304*S^2 + 25011*S^4 + 112232*S^6 + 62210*S^8))/(9720*S^3*(1 + S^2)) + (Pi^2*(80478 + 124359*S^2 + 88833*S^4 + 196726*S^6 + 147886*S^8))/(2916*S^3*(1 + S^2)) + ((2*Pi^2*(5 + 228*S^6))/(27*S^3) + (3265 + 23781*S^2 + 849*S^4 + 10657*S^6)/(162*S^3))*HPL[{3}, -S^2] + (2*(-257 - 12*S^2 - 12*S^4 + 705*S^6)*HPL[{4}, -S^2])/(27*S^3) + (2*(-67 + 141*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((14*(-88 + 273*S^2 - 273*S^4 + 88*S^6))/(27*S^3) + (4*Pi^2*(-209 + 97*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (4*(-899 - 6*S^2 - 6*S^4 + 1123*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (8*(29 + 195*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (8*(61 + 613*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (2696*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (1792*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(107 + 42*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (1040*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((8*Pi^2*(1 + 56*S^6))/(27*S^3) + (-1547 + 11143*S^2 + 15210*S^4 + 3373*S^6 + 2149*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] + (8*(-7 + 132*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((448081*(-1 + S^2)*(1 + S^2)^2)/(1458*S^3) + (47329*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(68040*S^3) + (Pi^2*(-371417 - 380862*S^2 + 1081809*S^4 + 1083478*S^6))/(17496*S^3) + (Pi^4*(-4229 - 8963*S^2 + 57227*S^4 + 122195*S^6 + 59298*S^8))/(6480*S^3*(1 + S^2)) + ((31*Pi^2*(1 + S^6))/(9*S^3) + (-779 - 755*S^2 + 755*S^4 + 779*S^6)/(18*S^3))*HPL[{2}, -S^2]^2 + (124*(1 + S^6)*HPL[{2}, -S^2]^3)/(9*S^3) + ((218*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (241 - 1604*S^2 + 17190*S^4 + 37564*S^6 + 19825*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (8*(-14 + 125*S^2 + 71*S^4 + 287*S^6 + 148*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (106*(1 + S^6)*HPL[{6}, -S^2])/S^3 + ((-472*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (16*(1 + S^2)*(383 + 58*S^2 + 587*S^4))/(27*S^3))*HPL[{3, 1}, -S^2] - (4*(607 + 1353*S^2 + 376*S^4 + 909*S^6 + 163*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(593 + 1435*S^2 + 424*S^4 + 1113*S^6 + 271*S^8)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)) - (368*(1 + S^6)*HPL[{5, 1}, -S^2])/(3*S^3) + ((944*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (32*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (592*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (8*(-73 + 827*S^2 + 450*S^4 + 1898*S^6 + 998*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (992*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (1120*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/S^3 - (200*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (800*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/S^3 + (1600*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((19437 + 19449*S^2 + 1391*S^4 + 803*S^6)/(54*S^3) + (2*Pi^2*(440 + 957*S^2 + 260*S^4 + 603*S^6 + 86*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + HPL[{2, 1}, -S^2]*((-20*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(27*S^3) - (4*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(9*S^3*(1 + S^2)) - (512*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((14329 + 14557*S^2 + 6283*S^4 + 5911*S^6)/(54*S^3) + (Pi^2*(1922 + 5012*S^2 + 1482*S^4 + 4427*S^6 + 1337*S^8))/(81*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((2779*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + ((1 + S^2)*(712061 - 11114*S^2 + 712061*S^4))/(2916*S^3) + (Pi^2*(15436 + 32824*S^2 + 40275*S^4 + 46630*S^6 + 22447*S^8))/(486*S^3*(1 + S^2)) + (2*(1825 + 4057*S^2 + 1116*S^4 + 2725*S^6 + 493*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (296*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (4*(301 + 697*S^2 + 216*S^4 + 475*S^6 + 79*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + (2*(1281 + 2623*S^2 + 668*S^4 + 1423*S^6 + 81*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]*((43007*Pi^6*S^3)/68040 + ((1 + S^2)*(-879703 + 896162*S^2))/(2916*S) + (Pi^4*(-79062 + 37527*S^2 + 451780*S^4 + 349825*S^6))/(29160*S*(1 + S^2)) + (Pi^2*(-1308288 - 1146795*S^2 + 2518408*S^4 + 2388019*S^6))/(34992*S*(1 + S^2)) + ((65*Pi^2*(1 + S^6))/(27*S^3) + (655*(-1 - S^2 + S^4 + S^6))/(18*S^3))*HPL[{1}, -S^2]^4 + (28*(-1 + S^6)*HPL[{1}, -S^2]^5)/(3*S^3) + ((Pi^2*(-10 + 73*S^6))/(27*S^3) + (532 - 5076*S^2 + 1719*S^4 + 7543*S^6)/(162*S^3))*HPL[{2}, -S^2]^2 - (38*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^3)/(27*S^3) - (4*(7 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((Pi^2*(33 + 25*S^6))/(27*S^3) + (481 - 1034*S^2 - 114*S^4 + 4404*S^6 + 3327*S^8)/(81*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-170 - 226*S^2 - 46*S^4 + 165*S^6 + 221*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (2*(-10 + 17*S^6)*HPL[{6}, -S^2])/(9*S^3) + (68*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((2217 + 11937*S^2 - 6999*S^4 - 17597*S^6)/(81*S^3) - (4*Pi^2*(-3 + 77*S^6))/(27*S^3))*HPL[{3, 1}, -S^2] + ((-883 + 132*S^2 + 132*S^4 - 1177*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) - (2*(417 + 147*S^2 - 432*S^4 + 1409*S^6 + 1679*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) - (14*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{4, 2}, -S^2])/(9*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 1}, -S^2])/(3*S^3) + ((4*Pi^2*(-1 + 56*S^6))/(9*S^3) + (2*(-2905 - 12060*S^2 + 6876*S^4 + 17327*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] - (16*(361 - 18*S^2 - 18*S^4 + 28*S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) + (8*(-2348 - 2294*S^2 + 135*S^4 + 114*S^6 + 60*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (32*(9 + 10*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (16*(15 + 17*S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (40*(-118 + 23*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + (32*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/S^3 - (160*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(156 + 78*S^2 + 1171*S^4 + 1015*S^6))/(81*S*(1 + S^2)) + (-17850 - 15135*S^2 + 23654*S^4 + 19643*S^6)/(486*S*(1 + S^2)))*Zeta[3] - 4*S^3*Zeta[3]^2 + HPL[{1}, -S^2]^3*((5165*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^2*(-743 + 61*S^2 + 438*S^4 + 2320*S^6 + 1516*S^8))/(81*S^3*(1 + S^2)) + (470*(-1 + S^6)*HPL[{2}, -S^2])/(9*S^3) - (8*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((15401 + 4373*S^2 - 13685*S^4 - 3233*S^6)/(54*S^3) + (Pi^2*(2053 + 931*S^2 - 570*S^4 - 1519*S^6 - 397*S^8))/(81*S^3*(1 + S^2)) + (8*(-1 + 2*S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((Pi^2*(-607 - 709*S^2 - 258*S^4 + 621*S^6 + 723*S^8))/(162*S^3*(1 + S^2)) + (-5192 - 16193*S^2 + 1461*S^4 + 32303*S^6 + 21137*S^8)/(486*S^3*(1 + S^2)) + (8*(4 + 3*S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(4 + 3*S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((Pi^4*(284 + 3703*S^6))/(1620*S^3) + (Pi^2*(-3035 - 12900*S^2 + 14847*S^4 + 38840*S^6))/(972*S^3) + (-137677 - 512370*S^2 + 149571*S^4 + 532040*S^6)/(2916*S^3) + ((153 - 24*S^2 - 24*S^4 + 193*S^6)*HPL[{3}, -S^2])/(9*S^3) + (2*(25 + 13*S^6)*HPL[{4}, -S^2])/(9*S^3) + (8*(361 - 18*S^2 - 18*S^4 + 28*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (8*(7 + 10*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(-28 - 3*S^2 - 3*S^4 + 140*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]^2*((59017*(-1 + S^2)*(1 + S^2)^2)/(324*S^3) + (1313*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + (Pi^2*(-22609 - 43198*S^2 + 23460*S^4 + 80462*S^6 + 39005*S^8))/(972*S^3*(1 + S^2)) + ((62*Pi^2*(1 + S^6))/(9*S^3) + (4*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(9*S^3))*HPL[{2}, -S^2] + (2*(-137 - 149*S^2 - 6*S^4 + 112*S^6 + 124*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (470*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (2*(-85 - 73*S^2 + 6*S^4 + 110*S^6 + 98*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + (2*(22 + 11*S^2 + 295*S^4 + 273*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((4195*(-1 + S^2)*(1 + S^2)^2)/(18*S^3) + (Pi^4*(-28058 + 20836*S^2 + 26886*S^4 + 123391*S^6 + 74497*S^8))/(9720*S^3*(1 + S^2)) + (Pi^2*(-92557 - 181495*S^2 + 70281*S^4 + 301211*S^6 + 148472*S^8))/(2916*S^3*(1 + S^2)) + ((-9317 - 9029*S^2 + 9029*S^4 + 9317*S^6)/(54*S^3) + (Pi^2*(-2423 - 191*S^2 + 1116*S^4 + 6973*S^6 + 4741*S^8))/(162*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (74*(-1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + ((2*Pi^2*(1 + S^6))/(9*S^3) + (2*(-1313 - 1275*S^2 + 1398*S^4 + 1792*S^6))/(81*S^3))*HPL[{3}, -S^2] + ((-283 - 319*S^2 + 179*S^6 + 215*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(9*S^3) + ((-124*Pi^2*(1 + S^6))/(9*S^3) - (8*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(9*S^3))*HPL[{2, 1}, -S^2] - (4*(-359 - 371*S^2 - 6*S^4 + 334*S^6 + 346*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (16*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 1}, -S^2])/(3*S^3) + (940*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (16*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((52*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(-2927 + 356*S^2 + 1969*S^4))/(81*S^3))*Zeta[3] + (44*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + 248*S^3*Zeta[7]) + HPL[{1}, -S^2]^2*((30260371*(-1 + S^2)*(1 + S^2)^2)/(139968*S^3) + (Pi^2*(-424399 - 442150*S^2 + 1373285*S^4 + 1383260*S^6))/(34992*S^3) + (Pi^6*(-9916 + 552278*S^2 + 272466*S^4 + 1150589*S^6 + 588395*S^8))/(816480*S^3*(1 + S^2)) + (Pi^4*(-14059 - 112078*S^2 + 1902132*S^4 + 4057370*S^6 + 2018339*S^8))/(349920*S^3*(1 + S^2)) + ((1159 + 3391*S^2 + 1116*S^4 + 3391*S^6 + 1159*S^8)*HPL[{2}, -S^2]^3)/(162*S^3*(1 + S^2)) + ((199 + 12*S^2 + 12*S^4 - 215*S^6)*HPL[{3}, -S^2]^2)/(54*S^3) + ((196*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (1106 + 107*S^2 + 16317*S^4 + 36305*S^6 + 19421*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-2200 + 3494*S^2 + 2802*S^4 + 13385*S^6 + 7691*S^8)*HPL[{6}, -S^2])/(54*S^3*(1 + S^2)) + (358*(1 + S^6)*HPL[{7}, -S^2])/(3*S^3) - (148*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-394*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-15781 - 33160*S^2 - 21384*S^4 - 5548*S^6 - 1759*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-1400*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-95563 - 198604*S^2 - 145422*S^4 - 72100*S^6 - 31015*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((599 - 48*S^2 - 48*S^4 - 535*S^6)*HPL[{4, 2}, -S^2])/(54*S^3) + (22*(1 + S^6)*HPL[{4, 3}, -S^2])/(3*S^3) - (2*(-259 + 309*S^2 + 308*S^4 + 1347*S^6 + 779*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) + (52*(1 + S^6)*HPL[{5, 2}, -S^2])/(3*S^3) - (278*(1 + S^6)*HPL[{6, 1}, -S^2])/(3*S^3) + ((124*Pi^2*(1 + S^6))/(9*S^3) + (2*(-779 - 755*S^2 + 755*S^4 + 779*S^6))/(9*S^3))*HPL[{2, 2, 1}, -S^2] + ((80*Pi^2*(1 + S^6))/S^3 + (4*(-805 - 501*S^2 + 4845*S^4 + 4685*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] - (8*(1 + S^2)*(2 - 5*S^2 + 2*S^4)*HPL[{3, 1, 2}, -S^2])/(27*S^3) + (4*(385 + 1131*S^2 + 376*S^4 + 1131*S^6 + 385*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (496*(1 + S^6)*HPL[{3, 2, 2}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{3, 3, 1}, -S^2])/S^3 + (4*(371 + 1213*S^2 + 424*S^4 + 1335*S^6 + 493*S^8)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (496*(1 + S^6)*HPL[{4, 1, 2}, -S^2])/S^3 + (1488*(1 + S^6)*HPL[{4, 2, 1}, -S^2])/S^3 + (9296*(1 + S^6)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((-944*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (32*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (992*(1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) - (8*(371 + 1271*S^2 + 450*S^4 + 1454*S^6 + 554*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1984*(1 + S^6)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) + (1984*(1 + S^6)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) + (4960*(1 + S^6)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) + (4832*(1 + S^6)*HPL[{4, 1, 1, 1}, -S^2])/S^3 + (200*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (800*(1 + S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 - (1600*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((859*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + (690889 + 681444*S^2 + 19503*S^4 + 21172*S^6)/(2916*S^3) + (Pi^2*(8123 + 16175*S^2 + 9981*S^4 + 3137*S^6 + 1280*S^8))/(324*S^3*(1 + S^2)))*Zeta[3] + ((-85 + 66*S^2 + 66*S^4 - 13*S^6)*Zeta[3]^2)/(27*S^3) + HPL[{3, 1}, -S^2]*((-7799 - 8027*S^2 - 12813*S^4 - 12441*S^6)/(54*S^3) - (2*Pi^2*(776 + 2879*S^2 + 1020*S^4 + 3536*S^6 + 1433*S^8))/(81*S^3*(1 + S^2)) - (256*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((1149 - 3661*S^2 + 25055*S^4 + 29001*S^6)/(324*S^3) + (Pi^2*(-37 + 2579*S^2 + 1308*S^4 + 5207*S^6 + 2591*S^8))/(324*S^3*(1 + S^2)) + (44*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((3265*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(-370 + 746*S^2 + 558*S^4 + 2645*S^6 + 1529*S^8))/(324*S^3*(1 + S^2)) + (62*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (124*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (62*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((20*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(27*S^3) + (4*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(9*S^3*(1 + S^2)) + (512*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((1219*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (484177 + 482508*S^2 + 218439*S^4 + 227884*S^6)/(2916*S^3) + (Pi^2*(18043 + 37183*S^2 + 29577*S^4 + 23125*S^6 + 11176*S^8))/(972*S^3*(1 + S^2)) - (6*(1 + S^6)*HPL[{4}, -S^2])/S^3 - (2*(1825 + 4057*S^2 + 1116*S^4 + 2725*S^6 + 493*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (248*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(-27 - S^2 + 34*S^4 + 44*S^6 + 18*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-2779*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) - ((1 + S^2)*(712061 - 11114*S^2 + 712061*S^4))/(2916*S^3) + (Pi^2*(-15436 - 32824*S^2 - 40275*S^4 - 46630*S^6 - 22447*S^8))/(486*S^3*(1 + S^2)) - (4*(301 + 697*S^2 + 216*S^4 + 475*S^6 + 79*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((455*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (35725 + 70501*S^2 + 39303*S^4 + 8707*S^6 + 3964*S^8)/(162*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*(((1 + S^2)*(958861 - 27726*S^2 + 958861*S^4))/(5832*S^3) + (Pi^4*(13052 + 45886*S^2 + 15646*S^4 + 54511*S^6 + 21677*S^8))/(6480*S^3*(1 + S^2)) + (Pi^2*(242339 + 489332*S^2 + 595974*S^4 + 724412*S^6 + 359879*S^8))/(11664*S^3*(1 + S^2)) + ((197*Pi^2*(1 + S^6))/(27*S^3) + (15887 + 17481*S^2 + 3891*S^4 + 1865*S^6)/(162*S^3))*HPL[{3}, -S^2] + (67*(-1 + S^6)*HPL[{4}, -S^2])/(6*S^3) + (32*(1 + S^6)*HPL[{5}, -S^2])/(3*S^3) + ((779 + 755*S^2 - 755*S^4 - 779*S^6)/(9*S^3) - (62*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2] - (148*(-1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (248*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) - (248*(1 + S^6)*HPL[{4, 1}, -S^2])/S^3 + (296*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (992*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((215*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (7844 + 16520*S^2 + 11853*S^4 + 2714*S^6 + 833*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] + (182*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + (154*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3) + HPL[{2}, -S^2]*(((1 + S^2)*(12334051 - 5083306*S^2 + 12334051*S^4))/(52488*S^3) + (Pi^6*(89636 + 288086*S^2 + 99225*S^4 + 522961*S^6 + 324511*S^8))/(408240*S^3*(1 + S^2)) + (Pi^4*(185021 + 339407*S^2 + 283959*S^4 + 681854*S^6 + 521825*S^8))/(87480*S^3*(1 + S^2)) + (Pi^2*(1332620 + 2048477*S^2 + 1352001*S^4 + 2847185*S^6 + 2141057*S^8))/(52488*S^3*(1 + S^2)) + ((435 + 261*S^2 - 78*S^4 - 668*S^6 - 494*S^8)*HPL[{3}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((Pi^2*(-95 + 53*S^6))/(27*S^3) + (-447 - 99*S^2 + 1002*S^4 + 4018*S^6 + 4444*S^8)/(81*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-300 - 116*S^2 - 82*S^4 + 937*S^6 + 753*S^8)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)) + (2*(-205 + 86*S^6)*HPL[{7}, -S^2])/(9*S^3) - (2*(709 + 1825*S^2 + 558*S^4 + 1825*S^6 + 709*S^8)*HPL[{2, 1}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((-2*Pi^2*(38 + 213*S^6))/(27*S^3) - (4*(507 + 2697*S^2 + 501*S^4 + 814*S^6))/(81*S^3))*HPL[{3, 2}, -S^2] + ((-5308 - 33039*S^2 - 4383*S^4 - 13898*S^6)/(81*S^3) + (Pi^2*(-97 - 1309*S^6))/(27*S^3))*HPL[{4, 1}, -S^2] - (2*(4 + 16*S^2 + 6*S^4 + 79*S^6 + 67*S^8)*HPL[{4, 2}, -S^2])/(9*S^3*(1 + S^2)) + (2*(155 + 166*S^6)*HPL[{4, 3}, -S^2])/(9*S^3) + ((678 + 228*S^2 + 72*S^4 - 3875*S^6 - 3425*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(223 + 232*S^6)*HPL[{5, 2}, -S^2])/(9*S^3) + (2*(1106 + 759*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(218 + 135*S^6))/(27*S^3) + (4*(1321 + 3198*S^2 + 3198*S^4 + 1321*S^6))/(81*S^3))*HPL[{2, 2, 1}, -S^2] + ((-12587 - 14595*S^2 - 37527*S^4 - 5195*S^6)/(81*S^3) - (236*Pi^2*(11 + 3*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + (7*(-1 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 + (3493*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(27*S^3) + (2*(81 + 745*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) + (8*(31 + 197*S^6)*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (4*(-2735 - 12*S^2 - 12*S^4 + 3183*S^6)*HPL[{4, 1, 1}, -S^2])/(27*S^3) + (2*(391 + 2383*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) + (2*(1279 + 7255*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) + (4*(1265 + 7449*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((28*(-88 + 273*S^2 - 273*S^4 + 88*S^6))/(27*S^3) + (8*Pi^2*(-209 + 97*S^6))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (1328*(-1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) - (8*(7609 + 20995*S^2 + 6684*S^4 + 23017*S^6 + 9631*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(-139 + 27*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) + (32*(-139 + 27*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) + (16*(-527 + 303*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) + (16*(-1555 + 881*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3) + (5392*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) - (3584*(1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3) - (3584*(1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3) + (160*(115 + 154*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3) + (2080*(-1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^4*(-142 + 1807*S^6))/(1620*S^3) + (Pi^2*(-1191 + 5577*S^2 + 8586*S^4 + 3100*S^6 + 1876*S^8))/(486*S^3*(1 + S^2)) + (-22622 + 420640*S^2 + 468141*S^4 + 12366*S^6 + 10815*S^8)/(2916*S^3*(1 + S^2)))*Zeta[3] + ((62 + 140*S^2 + 57*S^4 + 190*S^6 + 112*S^8)*Zeta[3]^2)/(27*S^3*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-67408 - 4959*S^2 + 4959*S^4 + 67408*S^6)/(243*S^3) + (2*Pi^2*(-1203 - 645*S^2 + 279*S^4 + 2470*S^6 + 1912*S^8))/(81*S^3*(1 + S^2)) + (224*(1 + 7*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((58827 + 9369*S^2 - 549*S^4 - 75989*S^6)/(486*S^3) + (Pi^2*(795 + 423*S^2 - 174*S^4 - 1777*S^6 - 1405*S^8))/(54*S^3*(1 + S^2)) - (16*(3 + 17*S^6)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-3199 - 2601*S^2 - 6219*S^4 + 20361*S^6)/(486*S^3) + (Pi^2*(-116 - 98*S^2 + 3*S^4 + 190*S^6 + 172*S^8))/(27*S^3*(1 + S^2)) - (130*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(41 + 59*S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((Pi^4*(-144 + 877*S^6))/(810*S^3) + (Pi^2*(803 + 13406*S^2 + 12336*S^4 + 7749*S^6 + 7584*S^8))/(972*S^3*(1 + S^2)) + (43717 + 454681*S^2 + 403545*S^4 + 46407*S^6 + 77154*S^8)/(2916*S^3*(1 + S^2)) - (26*(6 + 7*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-2511 - 4743*S^2 - 1116*S^4 - 2557*S^6 - 325*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(25 + 108*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (8*(29 + 195*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((121 - 59*S^2 - 90*S^4 - 223*S^6 - 43*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((Pi^4*(-5760 + 1327*S^6))/(1620*S^3) + (Pi^2*(-9749 + 10830*S^2 - 23622*S^4 + 4465*S^6))/(972*S^3) + (-33437 + 441711*S^2 - 441711*S^4 + 33437*S^6)/(2916*S^3) + (896*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (1792*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(-819 - 1377*S^2 - 279*S^4 - 448*S^6 + 110*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((Pi^2*(-44 + 301*S^6))/(27*S^3) + (-3206 + 6106*S^2 + 11316*S^4 + 3415*S^6 + 2329*S^8)/(81*S^3*(1 + S^2)))*Zeta[5] + (2*(-35 + 146*S^6)*Zeta[7])/(3*S^3)) + HPL[{1}, -S^2]*((21815*(-1 + S^2)*(1 + S^2)^2)/(64*S^3) + (13367*Pi^8*(1 + S^2)*(1 - S^2 + S^4))/(127575*S^3) + (Pi^2*(1 + S^2)*(-1341178 - 48191*S^2 + 5466755*S^4))/(104976*S^3) + (Pi^6*(369499 + 486901*S^2 + 2674785*S^4 + 5412223*S^6 + 2751268*S^8))/(2449440*S^3*(1 + S^2)) + (Pi^4*(646357 + 936916*S^2 + 7486170*S^4 + 15005572*S^6 + 7611673*S^8))/(1049760*S^3*(1 + S^2)) + ((146*Pi^2*(1 + S^6))/(81*S^3) + (2*(381 + 443*S^2 + 443*S^4 + 381*S^6))/(81*S^3))*HPL[{2}, -S^2]^3 + ((-11*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (281 + 887*S^2 + 60*S^4 - 1309*S^6 - 655*S^8)/(81*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + (34*(1 + S^6)*HPL[{4}, -S^2]^2)/(3*S^3) + ((47*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (1085 - 4867*S^2 + 13692*S^4 + 45245*S^6 + 25331*S^8)/(81*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((-6619 + 263*S^2 + 4098*S^4 + 18668*S^6 + 11786*S^8)*HPL[{7}, -S^2])/(27*S^3*(1 + S^2)) + (1228*(1 + S^6)*HPL[{8}, -S^2])/(3*S^3) + ((779 + 755*S^2 - 755*S^4 - 779*S^6)/(9*S^3) - (62*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2, 1}, -S^2]^2 - (4*(-269 - 617*S^2 + 6*S^4 + 409*S^6 + 163*S^8)*HPL[{4, 2}, -S^2])/(81*S^3*(1 + S^2)) + ((-511 + 47*S^2 + 522*S^4 + 1172*S^6 + 614*S^8)*HPL[{4, 3}, -S^2])/(27*S^3*(1 + S^2)) + ((-436*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (3170 + 10577*S^2 - 16173*S^4 - 45349*S^6 - 23497*S^8)/(81*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + (2*(-256 - 25*S^2 + 228*S^4 + 506*S^6 + 275*S^8)*HPL[{5, 2}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{5, 3}, -S^2])/(3*S^3) + ((-350 - 4724*S^2 - 1242*S^4 - 9935*S^6 - 5561*S^8)*HPL[{6, 1}, -S^2])/(27*S^3*(1 + S^2)) + (20*(1 + S^6)*HPL[{6, 2}, -S^2])/(3*S^3) - (292*(1 + S^6)*HPL[{7, 1}, -S^2])/S^3 - (4*(53 + 104*S^2 - 6*S^4 + 104*S^6 + 53*S^8)*HPL[{3, 1, 2}, -S^2])/(81*S^3*(1 + S^2)) + ((1168*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (4*(4519 + 9784*S^2 + 10638*S^4 + 9784*S^6 + 4519*S^8))/(81*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((6535 + 15463*S^2 + 4464*S^4 + 11665*S^6 + 2737*S^8)*HPL[{3, 2, 2}, -S^2])/(27*S^3*(1 + S^2)) + (8*(2432 + 5786*S^2 + 1686*S^4 + 4391*S^6 + 1037*S^8)*HPL[{3, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (28*(1 + S^6)*HPL[{3, 3, 2}, -S^2])/S^3 + ((3940*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (55105 + 117052*S^2 + 144774*S^4 + 156220*S^6 + 74689*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((19645 + 46477*S^2 + 13488*S^4 + 34939*S^6 + 8107*S^8)*HPL[{4, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + (140*(1 + S^6)*HPL[{4, 1, 3}, -S^2])/(3*S^3) + ((57841 + 138385*S^2 + 40560*S^4 + 105895*S^6 + 25351*S^8)*HPL[{4, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (104*(1 + S^6)*HPL[{4, 2, 2}, -S^2])/(3*S^3) + (284*(1 + S^6)*HPL[{4, 3, 1}, -S^2])/(3*S^3) + (4*(9493 + 23477*S^2 + 7052*S^4 + 18887*S^6 + 4903*S^8)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (88*(1 + S^6)*HPL[{5, 1, 2}, -S^2])/(3*S^3) + (1288*(1 + S^6)*HPL[{5, 2, 1}, -S^2])/(3*S^3) + (1412*(1 + S^6)*HPL[{6, 1, 1}, -S^2])/S^3 - (8*(1159 + 3391*S^2 + 1116*S^4 + 3391*S^6 + 1159*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-944*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (32*(1 + S^2)*(383 + 58*S^2 + 587*S^4))/(27*S^3))*HPL[{3, 1, 1, 1}, -S^2] + (16*(276 + 1019*S^2 + 370*S^4 + 1241*S^6 + 498*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) + (16*(276 + 1019*S^2 + 370*S^4 + 1241*S^6 + 498*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1711 + 5429*S^2 + 1856*S^4 + 5873*S^6 + 2155*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (992*(1 + S^6)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3) - (992*(1 + S^6)*HPL[{3, 3, 1, 1}, -S^2])/S^3 + (8*(1725 + 5347*S^2 + 1808*S^4 + 5669*S^6 + 2047*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (992*(1 + S^6)*HPL[{4, 1, 2, 1}, -S^2])/S^3 - (2976*(1 + S^6)*HPL[{4, 2, 1, 1}, -S^2])/S^3 - (18592*(1 + S^6)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((1888*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (64*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(27*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (1184*(-1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (1184*(-1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (1984*(1 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3) - (1984*(1 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 - (16*(-1703 - 2603*S^2 - 450*S^4 - 122*S^6 + 778*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (3968*(1 + S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 + (19840*(1 + S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) + (7936*(1 + S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^3 + (49600*(1 + S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) + (49856*(1 + S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^3 - (400*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1600*(1 + S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^3 + (3200*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((17*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (-455 - 845*S^2 + 1389*S^4 - 179*S^6 + 418*S^8)/(162*S^3*(1 + S^2)))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((-40*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(27*S^3) - (8*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(9*S^3*(1 + S^2)) - (1024*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*((3565 - 10674*S^2 + 82881*S^4 + 90964*S^6)/(486*S^3) + (Pi^2*(-7 + 378*S^2 + 182*S^4 + 786*S^6 + 401*S^8))/(27*S^3*(1 + S^2)) - (64*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{3, 2}, -S^2]*((-2*(1 + S^2)*(31534 + 1604*S^2 + 2149*S^4))/(243*S^3) + (Pi^2*(-1924 - 4273*S^2 - 1152*S^4 - 2896*S^6 - 547*S^8))/(81*S^3*(1 + S^2)) + (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*((-127983 - 130661*S^2 - 41837*S^4 - 38295*S^6)/(162*S^3) + (Pi^2*(-11543 - 28199*S^2 - 8112*S^4 - 22565*S^6 - 5909*S^8))/(162*S^3*(1 + S^2)) + (272*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 2, 1}, -S^2]*((6530*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) + (2*Pi^2*(-370 + 746*S^2 + 558*S^4 + 2645*S^6 + 1529*S^8))/(81*S^3*(1 + S^2)) + (496*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 1, 1}, -S^2]*((-5261 - 5033*S^2 + 25873*S^4 + 25501*S^6)/(27*S^3) + (4*Pi^2*(406 + 3625*S^2 + 1578*S^4 + 6181*S^6 + 2962*S^8))/(81*S^3*(1 + S^2)) + (1504*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((2779*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + ((1 + S^2)*(712061 - 11114*S^2 + 712061*S^4))/(1458*S^3) + (Pi^2*(15436 + 32824*S^2 + 40275*S^4 + 46630*S^6 + 22447*S^8))/(243*S^3*(1 + S^2)) + (8*(301 + 697*S^2 + 216*S^4 + 475*S^6 + 79*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{4}, -S^2]*((389*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (Pi^2*(1709 - 237*S^2 + 12543*S^4 + 15353*S^6))/(972*S^3) + (30175 - 830*S^2 + 309888*S^4 + 774070*S^6 + 409849*S^8)/(2916*S^3*(1 + S^2)) - (67*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (28*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + ((55 + 355*S^2 + 204*S^4 + 463*S^6 + 163*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]^2*((907*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (Pi^2*(-933 - 773*S^2 + 2545*S^4 + 2457*S^6))/(324*S^3) + (-24785 - 25649*S^2 + 25649*S^4 + 24785*S^6)/(648*S^3) + ((746 + 1862*S^2 + 558*S^4 + 1529*S^6 + 413*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + ((-1159 - 3391*S^2 - 1116*S^4 - 3391*S^6 - 1159*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (124*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (248*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((962 + 2078*S^2 + 558*S^4 + 1313*S^6 + 197*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-2126*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (-261112 - 251667*S^2 - 449280*S^4 - 450949*S^6)/(1458*S^3) + (Pi^2*(-12445 - 26947*S^2 - 40209*S^4 - 53137*S^6 - 25918*S^8))/(486*S^3*(1 + S^2)) - (4*(881 + 2075*S^2 + 660*S^4 + 1445*S^6 + 251*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((146995 + 140718*S^2 + 10461*S^4 + 15118*S^6)/(486*S^3) + (Pi^2*(4606 + 10144*S^2 + 2886*S^4 + 6193*S^6 + 655*S^8))/(162*S^3*(1 + S^2)))*Zeta[5] + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(958861 - 27726*S^2 + 958861*S^4))/(2916*S^3) + (Pi^2*(-242339 - 489332*S^2 - 595974*S^4 - 724412*S^6 - 359879*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(-13052 - 45886*S^2 - 15646*S^4 - 54511*S^6 - 21677*S^8))/(3240*S^3*(1 + S^2)) + (296*(-1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{4, 1}, -S^2])/S^3 + (592*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (992*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (1984*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((-430*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (2*(7844 + 16520*S^2 + 11853*S^4 + 2714*S^6 + 833*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] - (364*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{3}, -S^2]*(((1 + S^2)*(584648 - 13863*S^2 + 374213*S^4))/(2916*S^3) + (Pi^4*(8788 + 22882*S^2 + 6246*S^4 + 20875*S^6 + 6781*S^8))/(4860*S^3*(1 + S^2)) + (Pi^2*(47616 + 95333*S^2 + 75325*S^4 + 60731*S^6 + 30531*S^8))/(1944*S^3*(1 + S^2)) + ((248 - 166*S^2 - 342*S^4 - 823*S^6 - 409*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (80*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/(3*S^3) + ((-15887 - 17481*S^2 - 3891*S^4 - 1865*S^6)/(81*S^3) - (394*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (2*(1691 + 3935*S^2 + 1140*S^4 + 2855*S^6 + 611*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (40*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) - (28*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (4*(1825 + 4057*S^2 + 1116*S^4 + 2725*S^6 + 493*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (496*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 - (992*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-16*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-703 - 1099*S^2 + 1287*S^4 - 73*S^6 - 244*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + Zeta[3]*((Pi^2*(101474 + 98913*S^2 + 12270*S^4 + 13211*S^6))/(2916*S^3) + (934781 + 917030*S^2 + 14105*S^4 + 24080*S^6)/(2916*S^3) + (Pi^4*(6746 + 17376*S^2 + 5798*S^4 + 13575*S^6 + 2945*S^8))/(3240*S^3*(1 + S^2)) + (332*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*((35*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(72*S^3) + ((1 + S^2)*(4125577 - 96382*S^2 + 4125577*S^4))/(17496*S^3) + (Pi^4*(27998 + 57736*S^2 + 77569*S^4 + 102598*S^6 + 50141*S^8))/(9720*S^3*(1 + S^2)) + (Pi^2*(489056 + 955361*S^2 + 1140123*S^4 + 1409267*S^6 + 712121*S^8))/(17496*S^3*(1 + S^2)) - (10*(1 + S^6)*HPL[{3}, -S^2]^2)/(3*S^3) + ((22*Pi^2*(1 + S^6))/(27*S^3) + (2*(-478 - 855*S^2 + 801*S^4 + 746*S^6))/(81*S^3))*HPL[{4}, -S^2] + ((-241 + 455*S^2 + 528*S^4 + 1301*S^6 + 605*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (100*(1 + S^6)*HPL[{6}, -S^2])/(3*S^3) - (248*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((6743 + 6849*S^2 - 6741*S^4 - 7279*S^6)/(81*S^3) - (190*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3, 1}, -S^2] + ((-3173 - 7637*S^2 - 2232*S^4 - 5927*S^6 - 1463*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((-3185 - 7649*S^2 - 2232*S^4 - 5915*S^6 - 1451*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{4, 2}, -S^2])/(3*S^3) - (24*(1 + S^6)*HPL[{5, 1}, -S^2])/S^3 + ((124*Pi^2*(1 + S^6))/(9*S^3) + (2*(-779 - 755*S^2 + 755*S^4 + 779*S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(1159 + 3391*S^2 + 1116*S^4 + 3391*S^6 + 1159*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(413 + 1529*S^2 + 558*S^4 + 1862*S^6 + 746*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (592*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) - (3968*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/S^3 + ((Pi^2*(578 + 1460*S^2 + 474*S^4 + 1163*S^6 + 281*S^8))/(54*S^3*(1 + S^2)) + (121981 + 250108*S^2 + 154266*S^4 + 15028*S^6 + 4441*S^8)/(972*S^3*(1 + S^2)))*Zeta[3] + (22*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*((-3265*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) + (Pi^2*(370 - 746*S^2 - 558*S^4 - 2645*S^6 - 1529*S^8))/(81*S^3*(1 + S^2)) - (248*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*(((1 + S^2)*(21139 + 1248*S^2 + 1549*S^4))/(162*S^3) + (Pi^2*(1930 + 4270*S^2 + 1134*S^4 + 2893*S^6 + 553*S^8))/(162*S^3*(1 + S^2)) - (248*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + ((2524 + 5902*S^2 + 1842*S^4 + 4057*S^6 + 679*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + ((2591 + 5303*S^2 + 1266*S^4 + 2954*S^6 + 242*S^8)*Zeta[7])/(9*S^3*(1 + S^2))) + Log[T]*((-942223*Pi^8*S^3)/4082400 - (286583*(-1 + S^2))/(69984*S) + (Pi^2*(-4667040 - 121704*S^2 - 11504549*S^4))/(209952*S) + (Pi^4*(-7348596 - 8214798*S^2 - 25540169*S^4 - 24277391*S^6))/(2099520*S*(1 + S^2)) + (Pi^6*(-106112 - 360283*S^2 - 1144952*S^4 - 873519*S^6))/(408240*S*(1 + S^2)) - (S^3*HPL[{0}, S^2]^8)/144 - (8*(-1 + S^6)*HPL[{1}, -S^2]^7)/(9*S^3) + HPL[{0}, S^2]^7*((-30 - 15*S^2 - 148*S^4 - 118*S^6)/(1296*S*(1 + S^2)) - (5*(1 + S^6)*HPL[{1}, -S^2])/(216*S^3)) + ((-3251 - 2118*S^2 - 2118*S^4 - 3251*S^6)/(243*S^3) + (Pi^2*(-74 - 157*S^6))/(81*S^3))*HPL[{2}, -S^2]^3 - (83*(-1 + S^2)*(1 + S^2 + S^4)*HPL[{2}, -S^2]^4)/(54*S^3) + HPL[{0}, S^2]^6*((-115*Pi^2*S^3)/1296 + (72 - 1071*S^2 - 5134*S^4 - 4207*S^6)/(7776*S*(1 + S^2)) + ((5 - 53*S^2 - 32*S^4 - 116*S^6 - 58*S^8)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)) - (7*(1 + S^6)*HPL[{1}, -S^2]^2)/(54*S^3) + ((-3 - 25*S^6)*HPL[{2}, -S^2])/(216*S^3)) + HPL[{1}, -S^2]^6*((-131*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) - (10*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (40*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((Pi^2*(-23 + 15*S^6))/(27*S^3) + (-1312 - 2281*S^2 - 435*S^4 + 3767*S^6 + 3017*S^8)/(162*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + (68*HPL[{4}, -S^2]^2)/(9*S^3) + ((Pi^2*(-296 - 425*S^6))/(27*S^3) + (-4675 + 1043*S^2 - 10110*S^4 - 48984*S^6 - 32886*S^8)/(81*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((3305 - 3139*S^2 - 3222*S^4 - 21264*S^6 - 14820*S^8)*HPL[{7}, -S^2])/(27*S^3*(1 + S^2)) - (2*(735 + 1858*S^6)*HPL[{8}, -S^2])/(9*S^3) + ((8*Pi^2*(-58 + 95*S^6))/(27*S^3) + (2*(-2953 - 354*S^2 + 354*S^4 + 2953*S^6))/(27*S^3))*HPL[{2, 1}, -S^2]^2 - (8*(-93 + 91*S^6)*HPL[{3, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(-39 + 43*S^6))/(27*S^3) + (28 - 595*S^2 - 490*S^4 + 1775*S^6 + 1786*S^8)/(27*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] - (2*(-219 - 153*S^2 + 33*S^4 + 176*S^6 + 110*S^8)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)) + ((2*Pi^2*(157 + 319*S^6))/(27*S^3) + (5915 - 2995*S^2 + 9657*S^4 + 60319*S^6 + 43480*S^8)/(81*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((4114 + 3178*S^2 - 468*S^4 - 1579*S^6 - 643*S^8)*HPL[{5, 2}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-8 + 17*S^6)*HPL[{5, 3}, -S^2])/(9*S^3) + (2*(2504 + 5006*S^2 + 1251*S^4 + 7948*S^6 + 5446*S^8)*HPL[{6, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(18 + 17*S^6)*HPL[{6, 2}, -S^2])/(9*S^3) + (16*(82 + 185*S^6)*HPL[{7, 1}, -S^2])/(9*S^3) - (1040*(-1 + S^6)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((4*Pi^2*(-3 + 2*S^6))/(27*S^3) + (-907 - 590*S^2 + 490*S^4 - 590*S^6 - 907*S^8)/(27*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((-4*Pi^2*(151 + 312*S^6))/(27*S^3) + (-28729 - 44722*S^2 - 32418*S^4 - 44722*S^6 - 28729*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((-2545 - 11473*S^2 - 4464*S^4 - 13583*S^6 - 4655*S^8)*HPL[{3, 2, 2}, -S^2])/(27*S^3*(1 + S^2)) - (16*(395 + 2069*S^2 + 837*S^4 + 2684*S^6 + 1010*S^8)*HPL[{3, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-2 + 13*S^6)*HPL[{3, 3, 2}, -S^2])/(9*S^3) + ((-8*Pi^2*(291 + 548*S^6))/(27*S^3) - (2*(47118 + 70113*S^2 + 56430*S^4 + 88861*S^6 + 56074*S^8))/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] - (4*(1473 + 8169*S^2 + 3348*S^4 + 10843*S^6 + 4147*S^8)*HPL[{4, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-3 + S^6)*HPL[{4, 1, 3}, -S^2])/(9*S^3) - (4*(4227 + 24315*S^2 + 10044*S^4 + 32941*S^6 + 12853*S^8)*HPL[{4, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-19 + 105*S^6)*HPL[{4, 2, 2}, -S^2])/(9*S^3) - (8*(-19 + 45*S^6)*HPL[{4, 3, 1}, -S^2])/(9*S^3) - (4*(6663 + 48495*S^2 + 20916*S^4 + 70459*S^6 + 28627*S^8)*HPL[{5, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-51 + 7*S^6)*HPL[{5, 1, 2}, -S^2])/(9*S^3) - (4*(-171 + 487*S^6)*HPL[{5, 2, 1}, -S^2])/(9*S^3) - (32*(9 + 251*S^6)*HPL[{6, 1, 1}, -S^2])/(9*S^3) + (32*(25 + 87*S^2 + 31*S^4 + 87*S^6 + 25*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)) + ((16*Pi^2*(117 + 214*S^6))/(27*S^3) + (8*(8306 + 3996*S^2 + 6444*S^4 + 10545*S^6))/(81*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (8*(2435 + 6899*S^2 + 2232*S^4 + 5519*S^6 + 1055*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) - (8*(2435 + 6899*S^2 + 2232*S^4 + 5519*S^6 + 1055*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (40*(-1 + S^6)*HPL[{3, 1, 2, 2}, -S^2])/(9*S^3) - (40*(1027 + 3259*S^2 + 1116*S^4 + 2983*S^6 + 751*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (40*(-1 + S^6)*HPL[{3, 2, 1, 2}, -S^2])/(9*S^3) + (8*(291 + 301*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(9*S^3) + (2368*(1 + S^6)*HPL[{3, 3, 1, 1}, -S^2])/(3*S^3) - (16*(8013 + 24321*S^2 + 8154*S^4 + 21665*S^6 + 5357*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(-7 + 11*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(9*S^3) + (32*(215 + 233*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(9*S^3) + (32*(659 + 677*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(9*S^3) + (32*(1393 + 1451*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(9*S^3) + ((-80*Pi^2*(47 + 86*S^6))/(27*S^3) - (8*(18851 + 10440*S^2 + 10440*S^4 + 18851*S^6))/(81*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (3680*(-1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3) - (3680*(-1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3) + (4736*(1 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(9*S^3) + (4736*(1 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(3*S^3) - (32*(-1879 - 529*S^2 + 675*S^4 + 3904*S^6 + 2554*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (28480*(1 + S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(9*S^3) - (15808*(1 + S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) - (56896*(1 + S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(9*S^3) - (39488*(1 + S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) - (119488*(1 + S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3) + (800*(1 + 5*S^2 + 2*S^4 + 5*S^6 + S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S^3*(1 + S^2)) + (4480*(1 + S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (8960*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-14*Pi^2*S^3)/9 + (74 - 119*S^2 + 471*S^4 + 268*S^6)/(27*S*(1 + S^2)))*Zeta[3]^2 + HPL[{0}, S^2]^5*((20060 + 7276*S^2 - 109223*S^4 - 101839*S^6)/(38880*S*(1 + S^2)) + (Pi^2*(-4824 - 2412*S^2 - 22027*S^4 - 17203*S^6))/(19440*S*(1 + S^2)) + ((866 - 2632*S^2 - 1974*S^4 - 7591*S^6 - 4093*S^8)*HPL[{1}, -S^2]^2)/(3240*S^3*(1 + S^2)) - (31*(1 + S^6)*HPL[{1}, -S^2]^3)/(90*S^3) + ((35 - 423*S^2 - 229*S^4 - 1769*S^6 - 1311*S^8)*HPL[{2}, -S^2])/(1080*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-67*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (8860 + 16171*S^2 - 33789*S^4 - 68231*S^6 - 32531*S^8)/(19440*S^3*(1 + S^2)) - (229*(1 + S^6)*HPL[{2}, -S^2])/(540*S^3)) + ((1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(36*S^3) + ((214 - 25*S^6)*HPL[{2, 1}, -S^2])/(270*S^3) - (S^3*Zeta[3])/2) + HPL[{1}, -S^2]^5*((-1033*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^2*(89 - 91*S^2 - 90*S^4 - 454*S^6 - 274*S^8))/(81*S^3*(1 + S^2)) - (10*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) - (40*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (80*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1, 1}, -S^2]*((8*(1 + S^2)*(1009 + 2760*S^2 + 1009*S^4))/(27*S^3) + (8*Pi^2*(757 + 2845*S^2 + 990*S^4 + 2500*S^6 + 412*S^8))/(81*S^3*(1 + S^2)) - (160*(-37 + 2*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 2}, -S^2]*((7551 + 107223*S^2 - 399*S^4 + 24827*S^6)/(243*S^3) + (Pi^2*(-107 + 4507*S^2 + 2136*S^4 + 8981*S^6 + 4367*S^8))/(162*S^3*(1 + S^2)) - (8*(2 + 3*S^6)*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*((33858 - 4917*S^2 - 63822*S^4 - 119068*S^6)/(486*S^3) + (Pi^2*(1886 - 436*S^2 - 1116*S^4 - 5635*S^6 - 3313*S^8))/(162*S^3*(1 + S^2)) - (4*(-163 + 45*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(37 + 3*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 2, 1}, -S^2]*((2*(-8638 + 53811*S^2 - 53811*S^4 + 8638*S^6))/(243*S^3) + (4*Pi^2*(-833 - 1391*S^2 - 279*S^4 - 175*S^6 + 383*S^8))/(81*S^3*(1 + S^2)) + (32*(-79 + 5*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1, 1}, -S^2]*((-16247 + 33591*S^2 - 124047*S^4 - 7969*S^6)/(81*S^3) + (4*Pi^2*(-2274 - 5475*S^2 - 1542*S^4 - 3053*S^6 + 148*S^8))/(81*S^3*(1 + S^2)) + (32*(-251 + 14*S^6)*Zeta[3])/(9*S^3)) + HPL[{4, 1}, -S^2]*((32070 + 643065*S^2 + 82185*S^4 + 224266*S^6)/(486*S^3) + (2*Pi^2*(-295 + 3803*S^2 + 1896*S^4 + 7644*S^6 + 3546*S^8))/(81*S^3*(1 + S^2)) - (8*(-21 + 19*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^4*((-59017*(-1 + S^2)*(1 + S^2)^2)/(972*S^3) - (749*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(2269 + 2145*S^2 - 6489*S^4 - 6149*S^6))/(486*S^3) + ((-236*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (8*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(81*S^3))*HPL[{2}, -S^2] - (2*(593 + 1493*S^2 + 450*S^4 + 1232*S^6 + 332*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (32*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + (50*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (200*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (400*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (10*(163 + 343*S^2 + 90*S^4 + 202*S^6 + 22*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{4}, -S^2]*((Pi^2*(-10457 + 1338*S^2 - 10578*S^4 - 24549*S^6))/(972*S^3) + (Pi^4*(-1919 - 2055*S^6))/(1620*S^3) + (-278437 - 96223*S^2 - 379872*S^4 - 1619743*S^6 - 1011001*S^8)/(5832*S^3*(1 + S^2)) - (2*(89 - 24*S^2 - 24*S^4 + 807*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (4*(-61 + 43*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (32*(-13 + 14*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(-445 - 307*S^2 + 78*S^4 + 367*S^6 + 229*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-2*(1 + S^2)*(30734 - 21341*S^2 + 30734*S^4))/(81*S^3) - (4*Pi^4*(569 + 1526*S^6))/(405*S^3) + (Pi^2*(-20467 - 36685*S^2 - 33264*S^4 - 56527*S^6 - 38185*S^8))/(243*S^3*(1 + S^2)) - (16*(-82 + 530*S^2 + 360*S^4 + 875*S^6 + 263*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]^2*((479567 + 19971*S^2 - 19971*S^4 - 479567*S^6)/(5832*S^3) + (Pi^2*(20945 - 1554*S^2 - 6918*S^4 - 33949*S^6))/(1944*S^3) + (Pi^4*(2132 - 4955*S^6))/(3240*S^3) + ((-473 - 2705*S^2 - 1116*S^4 - 3559*S^6 - 1327*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) - (31*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + (4*(25 + 87*S^2 + 31*S^4 + 87*S^6 + 25*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (296*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (592*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(143 + 701*S^2 + 279*S^4 + 865*S^6 + 307*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((Pi^4*(2326 + 5921*S^6))/(810*S^3) + (102587 + 15601*S^2 + 59543*S^4 + 143285*S^6)/(324*S^3) + (Pi^2*(17390 + 30839*S^2 + 33414*S^4 + 62231*S^6 + 40754*S^8))/(486*S^3*(1 + S^2)) + (32*(-97 + 98*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(-245 + 985*S^2 + 732*S^4 + 1723*S^6 + 493*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^4*((-16537*Pi^4*S^3)/38880 + (-310578 - 300738*S^2 - 1526945*S^4 - 1560113*S^6)/(139968*S*(1 + S^2)) + (Pi^2*(-990 - 27360*S^2 - 113951*S^4 - 92441*S^6))/(23328*S*(1 + S^2)) + ((-67 - 1153*S^2 - 588*S^4 - 2053*S^6 - 967*S^8)*HPL[{1}, -S^2]^3)/(324*S^3*(1 + S^2)) - (22*(1 + S^6)*HPL[{1}, -S^2]^4)/(27*S^3) + ((-23*Pi^2*(1 + 9*S^6))/(216*S^3) + (-1077 - 4317*S^2 - 11664*S^4 - 33445*S^6 - 25129*S^8)/(3888*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((27 - 188*S^6)*HPL[{2}, -S^2]^2)/(216*S^3) + HPL[{1}, -S^2]^2*((-19*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3) + (-280 - 545*S^2 - 3589*S^4 - 5727*S^6 - 2763*S^8)/(432*S^3*(1 + S^2)) - (257*(1 + S^6)*HPL[{2}, -S^2])/(108*S^3)) + ((-3 - 111*S^2 - 18*S^4 - 151*S^6 - 43*S^8)*HPL[{3}, -S^2])/(216*S^3*(1 + S^2)) + ((-13 - 21*S^6)*HPL[{4}, -S^2])/(36*S^3) + ((147 + 663*S^2 + 261*S^4 + 434*S^6 - 82*S^8)*HPL[{2, 1}, -S^2])/(108*S^3*(1 + S^2)) + ((24 + 233*S^6)*HPL[{3, 1}, -S^2])/(54*S^3) - (2*(4 + 41*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-38 - 19*S^2 - 156*S^4 - 118*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((-36553 - 59314*S^2 - 218448*S^4 - 360454*S^6 - 180319*S^8)/(23328*S^3*(1 + S^2)) + (Pi^2*(83 - 2743*S^2 - 1548*S^4 - 5533*S^6 - 2707*S^8))/(1296*S^3*(1 + S^2)) + ((-165 - 1195*S^2 - 518*S^4 - 1906*S^6 - 876*S^8)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)) - (11*(1 + S^6)*HPL[{3}, -S^2])/(18*S^3) + (257*(1 + S^6)*HPL[{2, 1}, -S^2])/(54*S^3) - (38*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3))) + ((-67730 - 1169*S^2 - 23768*S^4)/(162*S) - (5*Pi^2*(182 + 91*S^2 + 277*S^4 + 95*S^6))/(27*S*(1 + S^2)))*Zeta[5] + Zeta[3]*((-2090550 + 5901*S^2 - 735526*S^4)/(4374*S) + (Pi^2*(-145278 - 3699*S^2 - 63412*S^4))/(2916*S) + (Pi^4*(-15462 - 7731*S^2 - 31585*S^4 - 16123*S^6))/(4860*S*(1 + S^2)) - (232*S^3*Zeta[5])/9) + HPL[{0}, S^2]^3*((3572166 + 3217569*S^2 - 10467338*S^4 - 10299365*S^6)/(209952*S*(1 + S^2)) + (Pi^4*(-48300 - 24150*S^2 - 214451*S^4 - 166151*S^6))/(58320*S*(1 + S^2)) + (Pi^2*(30424 + 8162*S^2 - 176163*S^4 - 161461*S^6))/(11664*S*(1 + S^2)) + ((113 - 691*S^2 - 438*S^4 - 1690*S^6 - 886*S^8)*HPL[{1}, -S^2]^4)/(162*S^3*(1 + S^2)) - (26*(1 + S^6)*HPL[{1}, -S^2]^5)/(27*S^3) + ((-214 - 1192*S^2 - 462*S^4 - 2951*S^6 - 1973*S^8)*HPL[{2}, -S^2]^2)/(324*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-158*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) - (2*(-1231 - 1957*S^2 + 5865*S^4 + 11273*S^6 + 5330*S^8))/(729*S^3*(1 + S^2)) - (124*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((Pi^2*(3 + 2*S^6))/(27*S^3) + (1615 + 3061*S^2 + 156*S^4 - 6005*S^6 - 3635*S^8)/(972*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((55 + 88*S^2 + 21*S^4 - 264*S^6 - 297*S^8)*HPL[{4}, -S^2])/(81*S^3*(1 + S^2)) + (2*(3 + 4*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-2*Pi^2*(-194 + 11*S^6))/(81*S^3) + (-4548 - 1380*S^2 + 15621*S^4 + 917*S^6)/(486*S^3))*HPL[{2, 1}, -S^2] + ((-19 + 1037*S^2 + 510*S^4 + 3474*S^6 + 2418*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) + (2*(16 + 29*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) + (2*(29 + 61*S^6)*HPL[{4, 1}, -S^2])/(27*S^3) - (2*(-25 + 1085*S^2 + 546*S^4 + 3684*S^6 + 2574*S^8)*HPL[{2, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) - (4*(169 + 3*S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) - (16*(42 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (8*(58 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-52*Pi^2*S^3)/27 + (2556 + 333*S^2 - 9061*S^4 - 7270*S^6)/(486*S*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((45659 + 84080*S^2 - 140562*S^4 - 323512*S^6 - 157489*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(1205 - 4705*S^2 - 3288*S^4 - 12661*S^6 - 6751*S^8))/(972*S^3*(1 + S^2)) + ((154 - 962*S^2 - 558*S^4 - 2429*S^6 - 1313*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (124*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (46*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) + HPL[{2}, -S^2]*((8117 + 25464*S^2 - 45888*S^4 - 160127*S^6)/(5832*S^3) + (Pi^2*(130 - 2354*S^2 - 1233*S^4 - 8991*S^6 - 6507*S^8))/(972*S^3*(1 + S^2)) - (4*(4 + 7*S^6)*HPL[{3}, -S^2])/(27*S^3) + (2*(169 + 3*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (2*(-3 + 14*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]*((-805*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(972*S^3) + (441431 + 846890*S^2 - 847764*S^4 - 2361610*S^6 - 1170595*S^8)/(34992*S^3*(1 + S^2)) + (Pi^2*(13784 + 23999*S^2 - 57249*S^4 - 113323*S^6 - 53851*S^8))/(5832*S^3*(1 + S^2)) + ((2339 + 1110*S^2 - 11796*S^4 - 11215*S^6)/(486*S^3) - (415*Pi^2*(1 + S^6))/(162*S^3))*HPL[{2}, -S^2] - (83*(1 + S^6)*HPL[{2}, -S^2]^2)/(27*S^3) - (2*(-119 - 98*S^2 - 12*S^4 + 199*S^6 + 178*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (10*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) + (2*(-154 + 962*S^2 + 558*S^4 + 2429*S^6 + 1313*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) + (356*(1 + S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (248*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((136 + 36*S^2 - 62*S^4 - 315*S^6 - 215*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) - (182*S^3*Zeta[5])/27) + HPL[{1}, -S^2]^3*((-4195*(-1 + S^2)*(1 + S^2)^2)/(27*S^3) + (Pi^2*(11553 + 11541*S^2 - 32381*S^4 - 31793*S^6))/(972*S^3) + (Pi^4*(557 - 5409*S^2 - 2944*S^4 - 12679*S^6 - 6713*S^8))/(1620*S^3*(1 + S^2)) - (148*(-1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((-116*Pi^2*(1 + S^6))/(9*S^3) - (2*(5401 + 5793*S^2 + 2895*S^4 + 2359*S^6))/(81*S^3))*HPL[{3}, -S^2] - (8*(-23 + 124*S^2 + 78*S^4 + 307*S^6 + 160*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (368*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((944*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (32*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(81*S^3))*HPL[{2, 1}, -S^2] + (8*(371 + 1271*S^2 + 450*S^4 + 1454*S^6 + 554*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (992*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (1120*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (200*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (800*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (1600*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-344*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (8*(1813 + 1875*S^2 + 297*S^4 + 127*S^6))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-20*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(81*S^3) - (4*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(27*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (512*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (896*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{3}, -S^2]*((-797819 - 12753537*S^2 - 3923655*S^4 - 5086389*S^6)/(34992*S^3) + (Pi^2*(273 - 238287*S^2 - 308892*S^4 - 201613*S^6 - 123505*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(8325 - 19503*S^2 - 11772*S^4 - 46109*S^6 - 18281*S^8))/(9720*S^3*(1 + S^2)) + (2*(-325 - 163*S^2 + 81*S^4 + 496*S^6 + 334*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-39 + 20*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((9503 + 3727*S^2 + 2311*S^4 - 2309*S^6)/(27*S^3) - (4*Pi^2*(-192 + 31*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + (2*(445 + 2677*S^2 + 1116*S^4 + 3807*S^6 + 1575*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(1 + 6*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (8*(-9 + 13*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (8*(217 + 1327*S^2 + 546*S^4 + 2017*S^6 + 907*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(-157 + 9*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (16*(-481 + 35*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (32*(-57 + 8*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-8*Pi^2*(10 + S^6))/(27*S^3) + (-3125 - 1748*S^2 + 126*S^4 - 870*S^6 - 1131*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (16*(25 + 9*S^6)*Zeta[5])/(9*S^3)) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(735526 + 1349123*S^2 + 735526*S^4))/(4374*S^3) + (Pi^4*(18874 + 67354*S^2 + 21927*S^4 + 51301*S^6 + 2821*S^8))/(4860*S^3*(1 + S^2)) + (Pi^2*(81383 + 240614*S^2 + 418308*S^4 + 330960*S^6 + 64107*S^8))/(2916*S^3*(1 + S^2)) + (8*(-233 - 6*S^2 - 6*S^4 + 457*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (16*(-157 + 9*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (16*(-497 + 55*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (1840*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2368*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (32*(17 + 82*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (2080*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*(-211 + 9*S^6))/(27*S^3) - (2*(-5745 - 7299*S^2 - 2832*S^4 - 685*S^6 + 161*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + (8*(287 + 9*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]^2*((-448081*(-1 + S^2)*(1 + S^2)^2)/(1458*S^3) - (47329*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(68040*S^3) + (Pi^2*(371417 + 380862*S^2 - 1081809*S^4 - 1083478*S^6))/(17496*S^3) + (Pi^4*(4229 + 8963*S^2 - 57227*S^4 - 122195*S^6 - 59298*S^8))/(6480*S^3*(1 + S^2)) + ((779 + 755*S^2 - 755*S^4 - 779*S^6)/(18*S^3) - (31*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2}, -S^2]^2 - (124*(1 + S^6)*HPL[{2}, -S^2]^3)/(9*S^3) + ((-218*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-241 + 1604*S^2 - 17190*S^4 - 37564*S^6 - 19825*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (8*(-14 + 125*S^2 + 71*S^4 + 287*S^6 + 148*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (106*(1 + S^6)*HPL[{6}, -S^2])/S^3 + ((472*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (16*(1 + S^2)*(383 + 58*S^2 + 587*S^4))/(27*S^3))*HPL[{3, 1}, -S^2] + (4*(607 + 1353*S^2 + 376*S^4 + 909*S^6 + 163*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + (4*(593 + 1435*S^2 + 424*S^4 + 1113*S^6 + 271*S^8)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)) + (368*(1 + S^6)*HPL[{5, 1}, -S^2])/(3*S^3) + ((-944*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (32*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (592*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (8*(-73 + 827*S^2 + 450*S^4 + 1898*S^6 + 998*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (992*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (1120*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/S^3 + (200*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (800*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/S^3 - (1600*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-19437 - 19449*S^2 - 1391*S^4 - 803*S^6)/(54*S^3) - (2*Pi^2*(440 + 957*S^2 + 260*S^4 + 603*S^6 + 86*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + HPL[{3}, -S^2]*((-14329 - 14557*S^2 - 6283*S^4 - 5911*S^6)/(54*S^3) + (Pi^2*(-1922 - 5012*S^2 - 1482*S^4 - 4427*S^6 - 1337*S^8))/(81*S^3*(1 + S^2)) + (496*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((20*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(27*S^3) + (4*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(9*S^3*(1 + S^2)) + (512*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-2779*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) - ((1 + S^2)*(712061 - 11114*S^2 + 712061*S^4))/(2916*S^3) + (Pi^2*(-15436 - 32824*S^2 - 40275*S^4 - 46630*S^6 - 22447*S^8))/(486*S^3*(1 + S^2)) - (2*(1825 + 4057*S^2 + 1116*S^4 + 2725*S^6 + 493*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (296*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (4*(301 + 697*S^2 + 216*S^4 + 475*S^6 + 79*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) - (2*(1281 + 2623*S^2 + 668*S^4 + 1423*S^6 + 81*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*(-((1 + S^2)*(11504549 - 6715805*S^2 + 11504549*S^4))/(34992*S^3) + (Pi^6*(-19338 - 57773*S^6))/(68040*S^3) + (Pi^2*(-637792 - 949918*S^2 - 620895*S^4 - 1449456*S^6 - 1117359*S^8))/(17496*S^3*(1 + S^2)) + (Pi^4*(-47420 - 94769*S^2 - 98928*S^4 - 197544*S^6 - 139026*S^8))/(14580*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2]^2)/(9*S^3) + ((1824 + 1557*S^2 - 387*S^4 - 6250*S^6)/(81*S^3) + (Pi^2*(29 - 25*S^6))/(9*S^3))*HPL[{4}, -S^2] + ((394 - 188*S^2 - 300*S^4 - 2613*S^6 - 2031*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-52 + 57*S^6)*HPL[{6}, -S^2])/(3*S^3) + (592*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((8*Pi^2*(-59 + 94*S^6))/(27*S^3) + (-15505 - 2709*S^2 + 1539*S^4 + 19931*S^6)/(81*S^3))*HPL[{3, 1}, -S^2] + ((1135 + 5599*S^2 + 2232*S^4 + 6929*S^6 + 2465*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + (8*(377 + 2045*S^2 + 825*S^4 + 2865*S^6 + 1197*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + (6*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 2}, -S^2])/S^3 + (4*(-63 + 145*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-16*Pi^2*(-58 + 95*S^6))/(27*S^3) - (4*(-2953 - 354*S^2 + 354*S^4 + 2953*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (16*(25 + 87*S^2 + 31*S^4 + 87*S^6 + 25*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (8*(1133 + 3371*S^2 + 1128*S^4 + 2681*S^6 + 443*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (1328*(-1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (16*(-275 + 277*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (1840*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + (32*(791 + 986*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (2080*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((8735 - 103402*S^2 - 124428*S^4 - 13056*S^6 - 8541*S^8)/(486*S^3*(1 + S^2)) + (Pi^2*(266 - 1102*S^2 - 801*S^4 - 2077*S^6 - 709*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] - (8*(4 + 3*S^6)*Zeta[3]^2)/(9*S^3) + HPL[{3}, -S^2]*((-12611 - 105927*S^2 + 1695*S^4 - 29887*S^6)/(486*S^3) + (Pi^2*(-159 - 2451*S^2 - 1038*S^4 - 4645*S^6 - 2353*S^8))/(162*S^3*(1 + S^2)) - (8*(-157 + 9*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(3 + 2*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((8638 - 53811*S^2 + 53811*S^4 - 8638*S^6)/(243*S^3) - (2*Pi^2*(-833 - 1391*S^2 - 279*S^4 - 175*S^6 + 383*S^8))/(81*S^3*(1 + S^2)) - (16*(-79 + 5*S^6)*Zeta[3])/(9*S^3)) - (2*(-910 + 836*S^2 + 1035*S^4 + 2526*S^6 + 780*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^2*((-4363*Pi^6*S^3)/5670 + (-4936500 + 147756*S^2 - 11504549*S^4)/(69984*S) + (Pi^2*(-597606 - 638886*S^2 - 2684489*S^4 - 2666537*S^6))/(69984*S*(1 + S^2)) + (Pi^4*(-61758 - 325881*S^2 - 1153379*S^4 - 922952*S^6))/(116640*S*(1 + S^2)) + ((-37 - 217*S^2 - 90*S^4 - 328*S^6 - 148*S^8)*HPL[{1}, -S^2]^5)/(27*S^3*(1 + S^2)) - (10*(1 + S^6)*HPL[{1}, -S^2]^6)/(9*S^3) + ((3227 - 3678*S^2 - 4794*S^4 - 16231*S^6)/(648*S^3) + (Pi^2*(64 - 373*S^6))/(108*S^3))*HPL[{2}, -S^2]^2 - (83*S^3*HPL[{2}, -S^2]^3)/27 + HPL[{1}, -S^2]^4*((-1357 - 1605*S^2 - 7083*S^4 - 6403*S^6)/(324*S^3) - (163*Pi^2*(1 + S^6))/(54*S^3) - (86*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-13 + 7*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((-5*Pi^2*(15 + 23*S^6))/(54*S^3) + (-2351 - 3434*S^2 - 3642*S^4 - 10694*S^6 - 7487*S^8)/(324*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((287 - 379*S^2 - 288*S^4 - 1470*S^6 - 804*S^8)*HPL[{5}, -S^2])/(54*S^3*(1 + S^2)) + ((-80 - 141*S^6)*HPL[{6}, -S^2])/(9*S^3) + (74*(-1 + 5*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(48 + 451*S^6))/(27*S^3) + (778 + 6235*S^2 + 12534*S^4 + 28253*S^6 + 19664*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-637 - 487*S^2 - 96*S^4 + 1227*S^6 + 1077*S^8)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)) + (2*(-382 - 64*S^2 + 6*S^4 + 1121*S^6 + 803*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-11 - S^6)*HPL[{4, 2}, -S^2])/(9*S^3) + (2*(35 + 81*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-2*Pi^2*(49 + 466*S^6))/(27*S^3) - (2*(808 + 3697*S^2 + 6192*S^4 + 13618*S^6 + 9667*S^8))/(81*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (4*(-488 - 1046*S^2 - 279*S^4 - 520*S^6 + 38*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(1393 + 3244*S^2 + 867*S^4 + 1909*S^6 + 58*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-1 + 4*S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (4*(1 + 162*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (8*(18 + 275*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (4*(839 + 2315*S^2 + 630*S^4 + 1625*S^6 + 149*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(12 + 109*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (80*(5 + 44*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-14598 + 1305*S^2 - 27088*S^4)/(972*S) + (Pi^2*(-654 - 327*S^2 - 2315*S^4 - 1661*S^6))/(162*S*(1 + S^2)))*Zeta[3] - (16*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((-1971 - 1977*S^2 - 8443*S^4 - 8149*S^6)/(162*S^3) + (Pi^2*(-84 - 746*S^2 - 346*S^4 - 1231*S^6 - 569*S^8))/(54*S^3*(1 + S^2)) + ((-323 - 1331*S^2 - 468*S^4 - 1775*S^6 - 767*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) - (16*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (344*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (44*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((-2814 - 19281*S^2 - 37524*S^4 - 76603*S^6 - 47770*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(133 - 545*S^2 - 114*S^4 - 1151*S^6 - 473*S^8))/(324*S^3*(1 + S^2)) - (28*(-3 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(6 + S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((Pi^2*(1280 + 4304*S^2 + 1413*S^4 + 2927*S^6 - 97*S^8))/(162*S^3*(1 + S^2)) + (45059 + 68606*S^2 + 146940*S^4 + 158952*S^6 + 27783*S^8)/(972*S^3*(1 + S^2)) + (4*(26 + S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((-7643*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(3240*S^3) + (-159736 - 150291*S^2 - 550656*S^4 - 552325*S^6)/(5832*S^3) + (Pi^2*(-2197 - 4597*S^2 - 19455*S^4 - 30667*S^6 - 14692*S^8))/(648*S^3*(1 + S^2)) + ((-515*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (-3796 - 8152*S^2 - 14211*S^4 - 21958*S^6 - 10807*S^8)/(162*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (31*(1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + ((-143 - 533*S^2 - 132*S^4 - 731*S^6 - 341*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (74*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + ((323 + 1331*S^2 + 468*S^4 + 1775*S^6 + 767*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (172*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (344*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-65 - 199*S^2 - 70*S^4 - 196*S^6 - 62*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^4*(-958 - 7205*S^6))/(3240*S^3) + (-84580 - 227632*S^2 - 282747*S^4 - 727170*S^6 - 564147*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(-2693 - 11711*S^2 - 24048*S^4 - 60681*S^6 - 44463*S^8))/(1944*S^3*(1 + S^2)) + ((275 + 203*S^2 + 54*S^4 - 611*S^6 - 539*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) + ((35 - 19*S^6)*HPL[{4}, -S^2])/(9*S^3) - (2*(-488 - 1046*S^2 - 279*S^4 - 520*S^6 + 38*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-7 + 30*S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (148*(-1 + 5*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((34 - 14*S^2 - 27*S^4 - 109*S^6 - 61*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((-238 - 119*S^2 - 593*S^4 - 355*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((-255191 - 237440*S^2 - 693695*S^4 - 703670*S^6)/(5832*S^3) + (Pi^2*(-72031 - 130378*S^2 - 406008*S^4 - 659110*S^6 - 327001*S^8))/(11664*S^3*(1 + S^2)) + (Pi^4*(-1515 - 32711*S^2 - 16534*S^4 - 59642*S^6 - 28446*S^8))/(6480*S^3*(1 + S^2)) + ((-296 - 1412*S^2 - 558*S^4 - 1979*S^6 - 863*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((-23*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (-1840 - 3601*S^2 - 3513*S^4 - 7363*S^6 - 4099*S^8)/(162*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-239 - 1091*S^2 - 372*S^4 - 1523*S^6 - 671*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) - (116*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((515*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (3796 + 8152*S^2 + 14211*S^4 + 21958*S^6 + 10807*S^8)/(81*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (2*(439 + 1945*S^2 + 690*S^4 + 2710*S^6 + 1204*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (44*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (280*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (2*(323 + 1331*S^2 + 468*S^4 + 1775*S^6 + 767*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (248*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (280*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 + (688*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-109*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-871 - 1423*S^2 - 1293*S^4 - 1441*S^6 - 772*S^8)/(54*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-60179 - 119612*S^2 - 220854*S^4 - 354692*S^6 - 177719*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(-488 - 2526*S^2 - 986*S^4 - 3681*S^6 - 1643*S^8))/(108*S^3*(1 + S^2)) - (22*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (124*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (46*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (238*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + HPL[{0}, S^2]*(-((1 + S^2)*(-29970128 + 30260371*S^2))/(69984*S) + (Pi^2*(11438670 + 10795497*S^2 - 18910994*S^4 - 18454445*S^6))/(209952*S*(1 + S^2)) + (Pi^4*(623686 + 369077*S^2 - 1958549*S^4 - 1758156*S^6))/(116640*S*(1 + S^2)) + (Pi^6*(-252078 - 126039*S^2 - 1286996*S^4 - 1034918*S^6))/(408240*S*(1 + S^2)) + ((-131*(-1 + S^2)*(1 + S^2)^2)/(9*S^3) - (26*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3))*HPL[{1}, -S^2]^5 - (28*(-1 + S^6)*HPL[{1}, -S^2]^6)/(9*S^3) + ((253 - 512*S^6)*HPL[{2}, -S^2]^3)/(81*S^3) + ((255 + 243*S^2 - 6*S^4 + 124*S^6 + 136*S^8)*HPL[{3}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((Pi^2*(13 + 7*S^6))/(9*S^3) + (1687 + 5359*S^2 + 153*S^4 - 11667*S^6 - 8580*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((550 + 940*S^2 + 285*S^4 - 463*S^6 - 853*S^8)*HPL[{6}, -S^2])/(27*S^3*(1 + S^2)) + (56*S^3*HPL[{7}, -S^2])/3 + (8*(28 - 18*S^2 - 18*S^4 + 361*S^6)*HPL[{2, 1}, -S^2]^2)/(27*S^3) + ((2*Pi^2*(38 + 49*S^6))/(27*S^3) + (6131 + 2714*S^2 - 4548*S^4 + 7670*S^6 + 9233*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((26*Pi^2*(5 + 7*S^6))/(27*S^3) + (2*(1806 - 1788*S^2 - 2787*S^4 + 7990*S^6 + 7507*S^8))/(81*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-19 - 49*S^2 - 6*S^4 + 101*S^6 + 131*S^8)*HPL[{4, 2}, -S^2])/(27*S^3*(1 + S^2)) - (20*(2 + S^2)*(4 - 2*S^2 + S^4)*HPL[{4, 3}, -S^2])/(9*S^3) + (2*(-58 - 250*S^2 - 78*S^4 + 881*S^6 + 1073*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(235 + 23*S^6)*HPL[{5, 2}, -S^2])/(9*S^3) - (4*(250 + 33*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((-8*Pi^2*(93 + 10*S^6))/(27*S^3) + (4*(7543 + 1719*S^2 - 5076*S^4 + 532*S^6))/(81*S^3))*HPL[{2, 2, 1}, -S^2] + ((-8*Pi^2*(275 + 29*S^6))/(27*S^3) - (2*(-47229 - 13629*S^2 + 32487*S^4 + 1465*S^6))/(81*S^3))*HPL[{3, 1, 1}, -S^2] + (2*(-19 - 12*S^2 - 12*S^4 + 35*S^6)*HPL[{3, 1, 2}, -S^2])/(27*S^3) - (2*(-331 + 4*S^2 + 4*S^4 + 671*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (8*(6 + S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) - (64*(5 + 2*S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) - (4*(-1407 - 1461*S^2 + 3721*S^6 + 3775*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(81 + 43*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) - (4*(297 + 115*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) - (8*(101 + 37*S^6)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((8*Pi^2*(21 + 2*S^6))/(3*S^3) + (4*(-17327 - 6876*S^2 + 12060*S^4 + 2905*S^6))/(81*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (608*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + (16*(-173 - 191*S^2 - 9*S^4 + 848*S^6 + 866*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (32*(46 + 47*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) - (32*(46 + 47*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) - (32*(103 + 104*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) - (32*(108 + 109*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (80*(-23 + 118*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + (544*(1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3) + (544*(1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3) + (320*(1 + S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 + (320*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-373*Pi^4*S^3)/270 + (19334 + 18425*S^2 - 22986*S^4 - 20349*S^6)/(324*S*(1 + S^2)) + (Pi^2*(4122 + 1017*S^2 - 12182*S^4 - 9509*S^6))/(486*S*(1 + S^2)))*Zeta[3] - (2*(-6 - 3*S^2 + 44*S^4 + 50*S^6)*Zeta[3]^2)/(9*S*(1 + S^2)) + HPL[{2}, -S^2]^2*((-5*(1 + S^2)*(103 - 2460*S^2 + 2715*S^4))/(216*S^3) + (Pi^2*(-326 - 1232*S^2 - 318*S^4 - 4323*S^6 - 3417*S^8))/(324*S^3*(1 + S^2)) - (2*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3}, -S^2])/(9*S^3) + (76*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^4*((-5165*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(743 - 61*S^2 - 438*S^4 - 2320*S^6 - 1516*S^8))/(162*S^3*(1 + S^2)) - (235*(-1 + S^6)*HPL[{2}, -S^2])/(9*S^3) + (4*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((3233 + 13685*S^2 - 4373*S^4 - 15401*S^6)/(27*S^3) - (4*Pi^2*(-185 + 370*S^2 + 273*S^4 + 2727*S^6 + 2172*S^8))/(81*S^3*(1 + S^2)) - (16*(-1 + 2*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((Pi^2*(-365 + 655*S^2 + 492*S^4 + 5170*S^6 + 4150*S^8))/(81*S^3*(1 + S^2)) + (-20555 - 138488*S^2 - 70104*S^4 + 189896*S^6 + 144659*S^8)/(486*S^3*(1 + S^2)) + (16*(1 + 2*S^6)*Zeta[3])/(9*S^3)) + HPL[{4}, -S^2]*((1605 + 23613*S^2 - 7284*S^4 - 83279*S^6 - 59171*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-1 + 119*S^2 + 42*S^4 - 1177*S^6 - 1297*S^8))/(162*S^3*(1 + S^2)) - (4*(31 + 19*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(-7 + 11*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((Pi^4*(3203 - 216*S^6))/(810*S^3) + (Pi^2*(-21875 - 8256*S^2 + 27681*S^4 + 3822*S^6))/(486*S^3) + (-532040 - 149571*S^2 + 512370*S^4 + 137677*S^6)/(1458*S^3) - (16*(7 + 10*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (272*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(-241 + 6*S^2 + 6*S^4 + 17*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]^3*((-59017*(-1 + S^2)*(1 + S^2)^2)/(486*S^3) - (1313*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(22609 + 43198*S^2 - 23460*S^4 - 80462*S^6 - 39005*S^8))/(1458*S^3*(1 + S^2)) + ((-124*Pi^2*(1 + S^6))/(27*S^3) - (8*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(27*S^3))*HPL[{2}, -S^2] - (4*(-137 - 149*S^2 - 6*S^4 + 112*S^6 + 124*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (940*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (16*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (4*(-85 - 73*S^2 + 6*S^4 + 110*S^6 + 98*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^4*(149 + 59*S^6))/(810*S^3) + (36917 + 119900*S^2 - 49719*S^4 - 310516*S^6 - 193366*S^8)/(2916*S^3*(1 + S^2)) + (Pi^2*(3586 + 8347*S^2 + 1440*S^4 - 12693*S^6 - 8292*S^8))/(972*S^3*(1 + S^2)) + (20*(4 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (2*(219 - 24*S^2 - 24*S^4 + 127*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(17 + 5*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (16*(4 + 3*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(31 + 67*S^2 + 36*S^4 + 175*S^6 + 139*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((-52*Pi^2*S^3)/9 - (2*(-2730 - 1239*S^2 + 5423*S^4 + 3878*S^6))/(81*S*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^2*((-4195*(-1 + S^2)*(1 + S^2)^2)/(18*S^3) + (Pi^2*(92557 + 181495*S^2 - 70281*S^4 - 301211*S^6 - 148472*S^8))/(2916*S^3*(1 + S^2)) + (Pi^4*(28058 - 20836*S^2 - 26886*S^4 - 123391*S^6 - 74497*S^8))/(9720*S^3*(1 + S^2)) + ((9317 + 9029*S^2 - 9029*S^4 - 9317*S^6)/(54*S^3) + (Pi^2*(2423 + 191*S^2 - 1116*S^4 - 6973*S^6 - 4741*S^8))/(162*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (74*(-1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + ((-2*Pi^2*(1 + S^6))/(9*S^3) - (2*(-1313 - 1275*S^2 + 1398*S^4 + 1792*S^6))/(81*S^3))*HPL[{3}, -S^2] + ((283 + 319*S^2 - 179*S^6 - 215*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (44*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((124*Pi^2*(1 + S^6))/(9*S^3) + (8*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(9*S^3))*HPL[{2, 1}, -S^2] + (4*(-359 - 371*S^2 - 6*S^4 + 334*S^6 + 346*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (940*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (16*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((-52*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(-2927 + 356*S^2 + 1969*S^4))/(81*S^3))*Zeta[3] - (44*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*((663286 + 2042334*S^2 - 666441*S^4 - 2068817*S^6)/(8748*S^3) + (Pi^2*(37214 + 148629*S^2 - 85245*S^4 - 298736*S^6))/(5832*S^3) + (Pi^4*(2616 - 18246*S^2 - 10341*S^4 - 93607*S^6 - 72745*S^8))/(9720*S^3*(1 + S^2)) + ((-3069 + 1575*S^2 + 711*S^4 - 4825*S^6)/(162*S^3) - (2*Pi^2*(20 + 23*S^6))/(27*S^3))*HPL[{3}, -S^2] + ((-539 - 491*S^2 + 42*S^4 - 371*S^6 - 419*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (2*(43 + 21*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((4*Pi^2*(93 + 10*S^6))/(27*S^3) - (2*(7543 + 1719*S^2 - 5076*S^4 + 532*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] + (2*(151 - 72*S^2 - 72*S^4 + 1405*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (4*(37 + 25*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (16*(28 - 18*S^2 - 18*S^4 + 361*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (304*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (16*(15 + 16*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (272*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((70 + 1584*S^2 - 999*S^4 - 2283*S^6)/(81*S^3) - (8*Pi^2*(-1 + 4*S^6))/(27*S^3))*Zeta[3] + (4*(12 + S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((-448081*(-1 + S^2)*(1 + S^2)^2)/(1458*S^3) - (42013*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(68040*S^3) + (Pi^2*(1503737 + 2971502*S^2 - 847764*S^4 - 4486222*S^6 - 2232901*S^8))/(34992*S^3*(1 + S^2)) + (Pi^4*(285419 + 531731*S^2 - 467883*S^4 - 1264327*S^6 - 608668*S^8))/(58320*S^3*(1 + S^2)) + ((779 + 755*S^2 - 755*S^4 - 779*S^6)/(18*S^3) - (83*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2]^2 - (4*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((22*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (4633 + 10126*S^2 - 1056*S^4 - 12446*S^6 - 7193*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(-199 - 239*S^2 - 14*S^4 + 106*S^6 + 146*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (110*(1 + S^6)*HPL[{6}, -S^2])/(9*S^3) + ((-9317 - 9029*S^2 + 9029*S^4 + 9317*S^6)/(27*S^3) + (Pi^2*(-2423 - 191*S^2 + 1116*S^4 + 6973*S^6 + 4741*S^8))/(81*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((344*Pi^2*(1 + S^6))/(27*S^3) + (2*(-9637 - 9345*S^2 + 9591*S^4 + 10595*S^6))/(81*S^3))*HPL[{3, 1}, -S^2] + (4*(-103 + 6*S^2 + 6*S^4 + 95*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) + (2*(-481 - 517*S^2 + 377*S^6 + 413*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{4, 2}, -S^2])/(3*S^3) - (136*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-248*Pi^2*(1 + S^6))/(9*S^3) - (16*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] - (592*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (8*(-803 - 815*S^2 - 6*S^4 + 778*S^6 + 790*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (1880*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) - (32*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + ((9395 + 18426*S^2 + 4568*S^4 - 9858*S^6 - 4531*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(221 + 109*S^2 - 68*S^4 - 425*S^6 - 313*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*((5929 + 11574*S^2 - 4568*S^4 - 20142*S^6 - 10793*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(649 + 643*S^2 + 42*S^4 - 734*S^6 - 728*S^8))/(81*S^3*(1 + S^2)) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((74413 + 73549*S^2 - 73549*S^4 - 74413*S^6)/(324*S^3) + (Pi^2*(12455 + 10578*S^2 - 21264*S^4 - 21331*S^6))/(486*S^3) - (3487*Pi^4*(1 + S^6))/(1620*S^3) - (22*(-1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (4*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + (296*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (22*(-1 + S^6)*Zeta[3])/S^3) - (2*(-838 - 712*S^2 + 54*S^4 + 1115*S^6 + 989*S^8)*Zeta[5])/(27*S^3*(1 + S^2)))) - (2*(1386 + 693*S^2 + 1493*S^4 + 107*S^6)*Zeta[7])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((-30260371*(-1 + S^2)*(1 + S^2)^2)/(69984*S^3) + (Pi^2*(424399 + 442150*S^2 - 1373285*S^4 - 1383260*S^6))/(17496*S^3) + (Pi^4*(14059 + 112078*S^2 - 1902132*S^4 - 4057370*S^6 - 2018339*S^8))/(174960*S^3*(1 + S^2)) + (Pi^6*(9916 - 552278*S^2 - 272466*S^4 - 1150589*S^6 - 588395*S^8))/(408240*S^3*(1 + S^2)) + ((-1159 - 3391*S^2 - 1116*S^4 - 3391*S^6 - 1159*S^8)*HPL[{2}, -S^2]^3)/(81*S^3*(1 + S^2)) + ((-199 - 12*S^2 - 12*S^4 + 215*S^6)*HPL[{3}, -S^2]^2)/(27*S^3) + ((-392*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-1106 - 107*S^2 - 16317*S^4 - 36305*S^6 - 19421*S^8)/(81*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((2200 - 3494*S^2 - 2802*S^4 - 13385*S^6 - 7691*S^8)*HPL[{6}, -S^2])/(27*S^3*(1 + S^2)) - (716*(1 + S^6)*HPL[{7}, -S^2])/(3*S^3) + (296*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((788*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2*(15781 + 33160*S^2 + 21384*S^4 + 5548*S^6 + 1759*S^8))/(81*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((2800*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (95563 + 198604*S^2 + 145422*S^4 + 72100*S^6 + 31015*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-599 + 48*S^2 + 48*S^4 + 535*S^6)*HPL[{4, 2}, -S^2])/(27*S^3) - (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4, 3}, -S^2])/(3*S^3) + (4*(-259 + 309*S^2 + 308*S^4 + 1347*S^6 + 779*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (104*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/(3*S^3) + (556*(1 + S^6)*HPL[{6, 1}, -S^2])/(3*S^3) + ((-248*Pi^2*(1 + S^6))/(9*S^3) - (4*(-779 - 755*S^2 + 755*S^4 + 779*S^6))/(9*S^3))*HPL[{2, 2, 1}, -S^2] + ((-160*Pi^2*(1 + S^6))/S^3 - (8*(-805 - 501*S^2 + 4845*S^4 + 4685*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + (16*(1 + S^2)*(2 - 5*S^2 + 2*S^4)*HPL[{3, 1, 2}, -S^2])/(27*S^3) - (8*(385 + 1131*S^2 + 376*S^4 + 1131*S^6 + 385*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (992*(1 + S^6)*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (992*(1 + S^6)*HPL[{3, 3, 1}, -S^2])/S^3 - (8*(371 + 1213*S^2 + 424*S^4 + 1335*S^6 + 493*S^8)*HPL[{4, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (992*(1 + S^6)*HPL[{4, 1, 2}, -S^2])/S^3 - (2976*(1 + S^6)*HPL[{4, 2, 1}, -S^2])/S^3 - (18592*(1 + S^6)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((1888*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (64*(1 + S^2)*(485 + 58*S^2 + 485*S^4))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (1984*(1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) + (16*(371 + 1271*S^2 + 450*S^4 + 1454*S^6 + 554*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (3968*(1 + S^6)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (3968*(1 + S^6)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (9920*(1 + S^6)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (9664*(1 + S^6)*HPL[{4, 1, 1, 1}, -S^2])/S^3 - (400*(37 + 109*S^2 + 36*S^4 + 109*S^6 + 37*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1600*(1 + S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^3 + (3200*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-859*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + (-690889 - 681444*S^2 - 19503*S^4 - 21172*S^6)/(1458*S^3) + (Pi^2*(-8123 - 16175*S^2 - 9981*S^4 - 3137*S^6 - 1280*S^8))/(162*S^3*(1 + S^2)))*Zeta[3] + (2*(85 - 66*S^2 - 66*S^4 + 13*S^6)*Zeta[3]^2)/(27*S^3) + HPL[{2, 1, 1}, -S^2]*((-40*(1 + S^2)*(506 + 15*S^2 + 506*S^4))/(27*S^3) - (8*Pi^2*(104 + 338*S^2 + 114*S^4 + 375*S^6 + 141*S^8))/(9*S^3*(1 + S^2)) - (1024*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((-3265*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^2*(370 - 746*S^2 - 558*S^4 - 2645*S^6 - 1529*S^8))/(162*S^3*(1 + S^2)) - (124*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (248*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (124*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-1149 + 3661*S^2 - 25055*S^4 - 29001*S^6)/(162*S^3) + (Pi^2*(37 - 2579*S^2 - 1308*S^4 - 5207*S^6 - 2591*S^8))/(162*S^3*(1 + S^2)) - (88*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((7799 + 8027*S^2 + 12813*S^4 + 12441*S^6)/(27*S^3) + (4*Pi^2*(776 + 2879*S^2 + 1020*S^4 + 3536*S^6 + 1433*S^8))/(81*S^3*(1 + S^2)) + (512*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((-1219*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (-484177 - 482508*S^2 - 218439*S^4 - 227884*S^6)/(1458*S^3) + (Pi^2*(-18043 - 37183*S^2 - 29577*S^4 - 23125*S^6 - 11176*S^8))/(486*S^3*(1 + S^2)) + (12*(1 + S^6)*HPL[{4}, -S^2])/S^3 + (4*(1825 + 4057*S^2 + 1116*S^4 + 2725*S^6 + 493*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (496*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (992*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(-27 - S^2 + 34*S^4 + 44*S^6 + 18*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((2779*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + ((1 + S^2)*(712061 - 11114*S^2 + 712061*S^4))/(1458*S^3) + (Pi^2*(15436 + 32824*S^2 + 40275*S^4 + 46630*S^6 + 22447*S^8))/(243*S^3*(1 + S^2)) + (8*(301 + 697*S^2 + 216*S^4 + 475*S^6 + 79*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((-910*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-35725 - 70501*S^2 - 39303*S^4 - 8707*S^6 - 3964*S^8)/(81*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*(-((1 + S^2)*(958861 - 27726*S^2 + 958861*S^4))/(2916*S^3) + (Pi^2*(-242339 - 489332*S^2 - 595974*S^4 - 724412*S^6 - 359879*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(-13052 - 45886*S^2 - 15646*S^4 - 54511*S^6 - 21677*S^8))/(3240*S^3*(1 + S^2)) + ((-15887 - 17481*S^2 - 3891*S^4 - 1865*S^6)/(81*S^3) - (394*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3}, -S^2] - (67*(-1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (64*(1 + S^6)*HPL[{5}, -S^2])/(3*S^3) + ((124*Pi^2*(1 + S^6))/(9*S^3) + (2*(-779 - 755*S^2 + 755*S^4 + 779*S^6))/(9*S^3))*HPL[{2, 1}, -S^2] + (296*(-1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (496*(1 + S^6)*HPL[{4, 1}, -S^2])/S^3 - (592*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (992*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (1984*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + ((-430*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (2*(7844 + 16520*S^2 + 11853*S^4 + 2714*S^6 + 833*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] - (364*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) - (308*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3)) + HPL[{0}, S^2]*((15181*Pi^8*S^3)/302400 + ((1 + S^2)*(-47471743 + 47709405*S^2))/(139968*S) + (Pi^2*(-17903716 + 273674*S^2 + 24984753*S^4))/(419904*S) + (Pi^6*(-1244934 + 192870*S^2 + 5606551*S^4 + 4266649*S^6))/(2449440*S*(1 + S^2)) + (Pi^4*(-17818812 - 16307154*S^2 + 40581481*S^4 + 39380863*S^6))/(4199040*S*(1 + S^2)) + ((131*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (13*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3))*HPL[{1}, -S^2]^6 + (4*(-1 + S^6)*HPL[{1}, -S^2]^7)/(9*S^3) + ((Pi^2*(-22 + 53*S^6))/(162*S^3) + (-961 - 2358*S^2 + 1278*S^4 + 2891*S^6)/(486*S^3))*HPL[{2}, -S^2]^3 - (5*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2]^4)/(36*S^3) + ((Pi^2*(-49 - 33*S^6))/(54*S^3) + (-423 - 84*S^2 + 339*S^4 - 626*S^6 - 698*S^8)/(108*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + ((97 + 84*S^6)*HPL[{4}, -S^2]^2)/(9*S^3) + ((Pi^2*(-140 - 191*S^6))/(54*S^3) + (1255 + 1333*S^2 + 1254*S^4 + 2399*S^6 + 1133*S^8)/(54*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((965 + 273*S^2 - 46*S^4 - 788*S^6 - 96*S^8)*HPL[{7}, -S^2])/(18*S^3*(1 + S^2)) + ((-315 - 272*S^6)*HPL[{8}, -S^2])/(3*S^3) + ((-532 + 5076*S^2 - 1719*S^4 - 7543*S^6)/(81*S^3) - (2*Pi^2*(-10 + 73*S^6))/(27*S^3))*HPL[{2, 1}, -S^2]^2 - (4*(-1 + 11*S^6)*HPL[{3, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(7 - 3*S^6))/(54*S^3) + (117 + 456*S^2 + 210*S^4 - 80*S^6 - 383*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((1340 + 962*S^2 - 63*S^4 - 485*S^6 - 107*S^8)*HPL[{4, 3}, -S^2])/(27*S^3*(1 + S^2)) + ((5*Pi^2*(3 + 5*S^6))/(27*S^3) + (-2353 + 1091*S^2 - 969*S^4 - 11843*S^6 - 9158*S^8)/(162*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((7998 + 5742*S^2 - 372*S^4 - 3145*S^6 - 889*S^8)*HPL[{5, 2}, -S^2])/(54*S^3*(1 + S^2)) - (10*S^3*HPL[{5, 3}, -S^2])/9 + ((7552 + 6022*S^2 - 135*S^4 - 3099*S^6 - 1569*S^8)*HPL[{6, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-14 - 29*S^6)*HPL[{6, 2}, -S^2])/(9*S^3) + (8*(54 + 53*S^6)*HPL[{7, 1}, -S^2])/(9*S^3) - (136*(1 + S^6)*HPL[{2, 1, 1}, -S^2]^2)/(9*S^3) + ((-5*(1 + S^2)*(2715 - 2460*S^2 + 103*S^4))/(54*S^3) + (Pi^2*(-1642 - 520*S^2 + 750*S^4 + 1051*S^6 - 71*S^8))/(81*S^3*(1 + S^2)))*HPL[{2, 2, 1}, -S^2] + ((-2*Pi^2*(-2 + 3*S^6))/(27*S^3) + (-417 - 558*S^2 + 24*S^4 - 274*S^6 - 7*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((2*Pi^2*(-42 + 103*S^6))/(27*S^3) + (-8105 - 27110*S^2 - 8616*S^4 + 33078*S^6 + 23121*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((1121 + 713*S^2 - 492*S^4 - 475*S^6 - 67*S^8)*HPL[{3, 2, 2}, -S^2])/(54*S^3*(1 + S^2)) + (8*(333 + 255*S^2 - 93*S^4 - 13*S^6 + 65*S^8)*HPL[{3, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(43 + 46*S^6)*HPL[{3, 3, 2}, -S^2])/(9*S^3) + ((2*Pi^2*(-99 + 343*S^6))/(27*S^3) + (2*(-5285 - 20948*S^2 - 6594*S^4 + 29418*S^6 + 20673*S^8))/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((911 + 701*S^2 - 258*S^4 + 15*S^6 + 225*S^8)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(86 + 97*S^6)*HPL[{4, 1, 3}, -S^2])/(9*S^3) + ((1017 + 803*S^2 - 254*S^4 + 29*S^6 + 243*S^8)*HPL[{4, 2, 1}, -S^2])/(3*S^3*(1 + S^2)) + ((163 + 159*S^6)*HPL[{4, 2, 2}, -S^2])/(9*S^3) - (4*(178 + 201*S^6)*HPL[{4, 3, 1}, -S^2])/(9*S^3) + (2*(3040 + 2336*S^2 - 802*S^4 + 273*S^6 + 977*S^8)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2*(183 + 223*S^6)*HPL[{5, 1, 2}, -S^2])/(9*S^3) - (2*(1503 + 1663*S^6)*HPL[{5, 2, 1}, -S^2])/(9*S^3) - (4*(1970 + 2177*S^6)*HPL[{6, 1, 1}, -S^2])/(9*S^3) - (8*(-512 + 253*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(27*S^3) + ((-8*Pi^2*(-3 + 77*S^6))/(27*S^3) - (2*(-2217 - 11937*S^2 + 6999*S^4 + 17597*S^6))/(81*S^3))*HPL[{3, 1, 1, 1}, -S^2] + (2*(-7027 + 132*S^2 + 132*S^4 + 1859*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(27*S^3) + (2*(-7027 + 132*S^2 + 132*S^4 + 1859*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(27*S^3) - (8*(-3 + 2*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(9*S^3) + (2*(-13171 + 132*S^2 + 132*S^4 + 4895*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(27*S^3) - (8*(-3 + 2*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(9*S^3) + (40*(9 + 8*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(9*S^3) + (112*(1 + S^6)*HPL[{3, 3, 1, 1}, -S^2])/S^3 + (4*(-18849 - 18579*S^2 + 432*S^4 + 7699*S^6 + 7429*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (28*(-1 + S^6)*HPL[{4, 1, 1, 2}, -S^2])/(9*S^3) + (28*(37 + 35*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(9*S^3) + (28*(109 + 107*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(9*S^3) + (1976*(1 + S^6)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((8*Pi^2*(-1 + 56*S^6))/(9*S^3) + (4*(-2905 - 12060*S^2 + 6876*S^4 + 17327*S^6))/(81*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] + (32*(361 - 18*S^2 - 18*S^4 + 28*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(27*S^3) + (32*(361 - 18*S^2 - 18*S^4 + 28*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(9*S^3) + (608*(1 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(9*S^3) + (608*(1 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(3*S^3) + (16*(3428 + 3194*S^2 - 441*S^4 + 274*S^6 + 508*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (32*(113 + 115*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(9*S^3) - (32*(189 + 191*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(9*S^3) - (32*(227 + 229*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(9*S^3) - (64*(237 + 238*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(9*S^3) - (32*(471 + 473*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3) - (80*(-118 + 23*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3) + (64*(1 + S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^3 - (320*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-4*Pi^2*S^3)/9 + (2*(-242 - 136*S^2 + 291*S^4 + 176*S^6))/(27*S*(1 + S^2)))*Zeta[3]^2 + HPL[{1}, -S^2]^5*((1033*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(-743 + 61*S^2 + 438*S^4 + 2320*S^6 + 1516*S^8))/(810*S^3*(1 + S^2)) + (47*(-1 + S^6)*HPL[{2}, -S^2])/(9*S^3) - (4*(1 + S^6)*HPL[{3}, -S^2])/(45*S^3) + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(45*S^3)) + HPL[{2, 1, 1, 1}, -S^2]*((15401 + 4373*S^2 - 13685*S^4 - 3233*S^6)/(27*S^3) - (2*Pi^2*(-2053 - 931*S^2 + 570*S^4 + 1519*S^6 + 397*S^8))/(81*S^3*(1 + S^2)) + (16*(-1 + 2*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(-5533 - 2269*S^2 + 1992*S^4 + 3774*S^6 + 510*S^8))/(81*S^3*(1 + S^2)) + (-376909 - 433336*S^2 + 286692*S^4 + 368896*S^6 + 28369*S^8)/(486*S^3*(1 + S^2)) + (16*(4 + 3*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 2}, -S^2]*((-14345 + 15633*S^2 + 7497*S^4 - 25613*S^6)/(972*S^3) + (Pi^2*(-2133 - 1791*S^2 + 504*S^4 - 1597*S^6 - 1939*S^8))/(324*S^3*(1 + S^2)) + (8*(4 + 5*S^6)*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*((-12633 + 44943*S^2 + 32478*S^4 - 123769*S^6 - 103855*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-505 - 301*S^2 + 252*S^4 - 767*S^6 - 971*S^8))/(54*S^3*(1 + S^2)) + (4*(7 + 13*S^6)*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*((Pi^2*(-400 - 1102*S^2 - 144*S^4 + 251*S^6 + 953*S^8))/(324*S^3*(1 + S^2)) + (-5850 - 19785*S^2 + 29343*S^4 + 74222*S^6 + 43256*S^8)/(972*S^3*(1 + S^2)) + (2*(123 + 101*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(95 + 107*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(284 + 3703*S^6))/(810*S^3) + (Pi^2*(-3035 - 12900*S^2 + 14847*S^4 + 38840*S^6))/(486*S^3) + (-137677 - 512370*S^2 + 149571*S^4 + 532040*S^6)/(1458*S^3) + (8*(-28 - 3*S^2 - 3*S^4 + 140*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]^4*((59017*(-1 + S^2)*(1 + S^2)^2)/(1944*S^3) + (1313*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(3240*S^3) + (Pi^2*(-22609 - 43198*S^2 + 23460*S^4 + 80462*S^6 + 39005*S^8))/(5832*S^3*(1 + S^2)) + ((31*Pi^2*(1 + S^6))/(27*S^3) + (2*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(27*S^3))*HPL[{2}, -S^2] + ((-137 - 149*S^2 - 6*S^4 + 112*S^6 + 124*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (235*(-1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + ((-85 - 73*S^2 + 6*S^4 + 110*S^6 + 98*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{4}, -S^2]*((Pi^4*(303 + 163*S^6))/(3240*S^3) + (Pi^2*(535 - 4265*S^2 + 1380*S^4 + 16055*S^6 + 11171*S^8))/(1944*S^3*(1 + S^2)) + (-36413 - 91323*S^2 + 74542*S^4 + 303333*S^6 + 179065*S^8)/(3888*S^3*(1 + S^2)) + (2*(319 + 313*S^2 - 39*S^4 + 217*S^6 + 223*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(77 + 41*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (4*(25 + 13*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(-269 - 158*S^2 - 3*S^4 + 304*S^6 + 193*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((Pi^4*(-210 - 3037*S^6))/(1620*S^3) + (31225 + 188018*S^2 + 87713*S^4 - 253678*S^6 - 189782*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(1775 + 14120*S^2 - 2778*S^4 - 53512*S^6 - 37957*S^8))/(972*S^3*(1 + S^2)) + (16*(7 + 10*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(-99 - 45*S^2 + 18*S^4 + 370*S^6 + 316*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]^2*((Pi^4*(60 + 3067*S^6))/(6480*S^3) + (11687 - 437211*S^2 + 24471*S^4 + 457817*S^6)/(11664*S^3) + (Pi^2*(2453 - 7957*S^2 - 984*S^4 + 41079*S^6 + 32301*S^8))/(3888*S^3*(1 + S^2)) + ((241 + 133*S^2 - 108*S^4 - 121*S^6 - 13*S^8)*HPL[{3}, -S^2])/(108*S^3*(1 + S^2)) + ((-41 - 47*S^6)*HPL[{4}, -S^2])/(18*S^3) + ((512 - 253*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (44*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1}, -S^2])/(9*S^3) - (76*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-86 - 68*S^2 - 18*S^4 + 491*S^6 + 473*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) + ((Pi^2*(214 + 107*S^2 + 2895*S^4 + 2681*S^6))/(54*S*(1 + S^2)) + (-71118 - 64557*S^2 + 94561*S^4 + 75688*S^6)/(972*S*(1 + S^2)))*Zeta[5] + Zeta[3]*((Pi^4*(2222 + 1111*S^2 + 21545*S^4 + 19323*S^6))/(3240*S*(1 + S^2)) + (Pi^2*(-14430 - 14403*S^2 + 28621*S^4 + 25354*S^6))/(1944*S*(1 + S^2)) + (-1647282 - 1855923*S^2 + 1962598*S^4 + 1797991*S^6)/(34992*S*(1 + S^2)) - (208*S^3*Zeta[5])/9) + HPL[{1}, -S^2]^3*((4195*(-1 + S^2)*(1 + S^2)^2)/(54*S^3) + (Pi^4*(-28058 + 20836*S^2 + 26886*S^4 + 123391*S^6 + 74497*S^8))/(29160*S^3*(1 + S^2)) + (Pi^2*(-92557 - 181495*S^2 + 70281*S^4 + 301211*S^6 + 148472*S^8))/(8748*S^3*(1 + S^2)) + ((-9317 - 9029*S^2 + 9029*S^4 + 9317*S^6)/(162*S^3) + (Pi^2*(-2423 - 191*S^2 + 1116*S^4 + 6973*S^6 + 4741*S^8))/(486*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (74*(-1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((2*Pi^2*(1 + S^6))/(27*S^3) + (2*(-1313 - 1275*S^2 + 1398*S^4 + 1792*S^6))/(243*S^3))*HPL[{3}, -S^2] + ((-283 - 319*S^2 + 179*S^6 + 215*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (44*(1 + S^6)*HPL[{5}, -S^2])/(27*S^3) + ((-124*Pi^2*(1 + S^6))/(27*S^3) - (8*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (4*(-359 - 371*S^2 - 6*S^4 + 334*S^6 + 346*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (940*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (16*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + ((52*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + ((1 + S^2)*(-2927 + 356*S^2 + 1969*S^4))/(243*S^3))*Zeta[3] + (44*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(27*S^3)) + HPL[{3}, -S^2]*((Pi^4*(-11137 - 13333*S^2 - 3060*S^4 + 7865*S^6 + 10061*S^8))/(19440*S^3*(1 + S^2)) + (Pi^2*(-26385 - 58185*S^2 + 20604*S^4 + 133405*S^6 + 86185*S^8))/(11664*S^3*(1 + S^2)) + (-920505 - 2703588*S^2 + 1866432*S^4 + 6789724*S^6 + 3886705*S^8)/(69984*S^3*(1 + S^2)) + ((-674 - 476*S^2 + 45*S^4 + 193*S^6 - 5*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (2*(97 + 80*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((2*Pi^2*(25 + 28*S^6))/(27*S^3) + (4991 - 729*S^2 - 1773*S^4 + 3975*S^6)/(162*S^3))*HPL[{2, 1}, -S^2] + ((-829 - 721*S^2 + 144*S^4 - 157*S^6 - 265*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(21 + 23*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (4*(28 + 23*S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (2*(153 - 24*S^2 - 24*S^4 + 193*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (56*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (8*(35 + 23*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (16*(4 + 3*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((2*Pi^2*(13 + 21*S^6))/(27*S^3) + (-386 - 1031*S^2 - 210*S^4 + 2435*S^6 + 2432*S^8)/(162*S^3*(1 + S^2)))*Zeta[3] + (40*(4 + 5*S^6)*Zeta[5])/(9*S^3)) + HPL[{2, 1}, -S^2]*((2068817 + 666441*S^2 - 2042334*S^4 - 663286*S^6)/(8748*S^3) + (Pi^2*(177025 + 46458*S^2 - 260946*S^4 - 51631*S^6))/(5832*S^3) + (Pi^4*(26036 + 4148*S^2 - 12393*S^4 - 19518*S^6 + 2370*S^8))/(9720*S^3*(1 + S^2)) - (2*(1483 - 72*S^2 - 72*S^4 + 73*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(9*S^3) - (4*(67 + 55*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (16*(361 - 18*S^2 - 18*S^4 + 28*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (304*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(15 + 16*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (272*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((2200 + 1008*S^2 - 1485*S^4 - 523*S^6)/(81*S^3) - (2*Pi^2*(41 + 21*S^6))/(27*S^3))*Zeta[3] - (4*(47 + 36*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]^2*((448081*(-1 + S^2)*(1 + S^2)^2)/(2916*S^3) + (42013*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(136080*S^3) + (Pi^4*(-285419 - 531731*S^2 + 467883*S^4 + 1264327*S^6 + 608668*S^8))/(116640*S^3*(1 + S^2)) + (Pi^2*(-1503737 - 2971502*S^2 + 847764*S^4 + 4486222*S^6 + 2232901*S^8))/(69984*S^3*(1 + S^2)) + ((83*Pi^2*(1 + S^6))/(54*S^3) + (-779 - 755*S^2 + 755*S^4 + 779*S^6)/(36*S^3))*HPL[{2}, -S^2]^2 + (2*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((-11*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-4633 - 10126*S^2 + 1056*S^4 + 12446*S^6 + 7193*S^8)/(324*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-199 - 239*S^2 - 14*S^4 + 106*S^6 + 146*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (55*(1 + S^6)*HPL[{6}, -S^2])/(9*S^3) + ((9317 + 9029*S^2 - 9029*S^4 - 9317*S^6)/(54*S^3) + (Pi^2*(2423 + 191*S^2 - 1116*S^4 - 6973*S^6 - 4741*S^8))/(162*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((9637 + 9345*S^2 - 9591*S^4 - 10595*S^6)/(81*S^3) - (172*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3, 1}, -S^2] - (2*(-103 + 6*S^2 + 6*S^4 + 95*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) + ((481 + 517*S^2 - 377*S^6 - 413*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{4, 2}, -S^2])/(3*S^3) + (68*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((124*Pi^2*(1 + S^6))/(9*S^3) + (8*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] + (296*(-1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (4*(-803 - 815*S^2 - 6*S^4 + 778*S^6 + 790*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (16*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (940*(-1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + (16*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(-221 - 109*S^2 + 68*S^4 + 425*S^6 + 313*S^8))/(54*S^3*(1 + S^2)) + (-9395 - 18426*S^2 - 4568*S^4 + 9858*S^6 + 4531*S^8)/(324*S^3*(1 + S^2)))*Zeta[3] - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*((Pi^2*(-649 - 643*S^2 - 42*S^4 + 734*S^6 + 728*S^8))/(162*S^3*(1 + S^2)) + (-5929 - 11574*S^2 + 4568*S^4 + 20142*S^6 + 10793*S^8)/(324*S^3*(1 + S^2)) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((3487*Pi^4*(1 + S^6))/(3240*S^3) + (Pi^2*(-12455 - 10578*S^2 + 21264*S^4 + 21331*S^6))/(972*S^3) + (-74413 - 73549*S^2 + 73549*S^4 + 74413*S^6)/(648*S^3) + (11*(-1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (2*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (148*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (11*(-1 + S^6)*Zeta[3])/S^3) + ((-838 - 712*S^2 + 54*S^4 + 1115*S^6 + 989*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]*(((1 + S^2)*(-1546209 - 2174347*S^2 + 3715139*S^4))/(23328*S^3) + (Pi^6*(5882 + 44423*S^6))/(136080*S^3) + (Pi^4*(-6653 - 41738*S^2 + 22440*S^4 + 210599*S^6 + 157151*S^8))/(29160*S^3*(1 + S^2)) + (Pi^2*(-215680 - 882907*S^2 - 322053*S^4 + 1447123*S^6 + 1125277*S^8))/(34992*S^3*(1 + S^2)) + (2*(10 + 11*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((Pi^2*(95 + 73*S^6))/(54*S^3) + (1448 + 209*S^2 - 1308*S^4 + 2145*S^6 + 2538*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((1414 + 988*S^2 - 132*S^4 - 125*S^6 + 301*S^8)*HPL[{5}, -S^2])/(54*S^3*(1 + S^2)) + (5*(40 + 29*S^6)*HPL[{6}, -S^2])/(9*S^3) + ((5*(1 + S^2)*(2715 - 2460*S^2 + 103*S^4))/(108*S^3) + (Pi^2*(1642 + 520*S^2 - 750*S^4 - 1051*S^6 + 71*S^8))/(162*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (76*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-1147 + 10161*S^2 - 3339*S^4 - 15539*S^6)/(162*S^3) - (2*Pi^2*(1 + 27*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] + ((-503 - 299*S^2 + 228*S^4 + 209*S^6 + 5*S^8)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)) + ((-1361 - 1025*S^2 + 402*S^4 - 71*S^6 - 407*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((1 + 7*S^6)*HPL[{4, 2}, -S^2])/(9*S^3) - (2*(79 + 45*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(-10 + 73*S^6))/(27*S^3) + (2*(532 - 5076*S^2 + 1719*S^4 + 7543*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(-512 + 253*S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) - (2*(-1177 + 24*S^2 + 24*S^4 + 313*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (4*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (124*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (4*(65 + 77*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (16*(361 - 18*S^2 - 18*S^4 + 28*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3) + (16*(235 + 238*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (272*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((597 - 14436*S^2 + 5616*S^4 + 16565*S^6)/(972*S^3) + (Pi^2*(-86 + 58*S^2 - 45*S^4 + 778*S^6 + 634*S^8))/(162*S^3*(1 + S^2)))*Zeta[3] - (2*(4 + 3*S^6)*Zeta[3]^2)/(9*S^3) + HPL[{3}, -S^2]*((6411 - 6135*S^2 - 3660*S^4 + 14266*S^6)/(972*S^3) + (Pi^2*(1085 + 905*S^2 - 270*S^4 + 771*S^6 + 951*S^8))/(324*S^3*(1 + S^2)) + (28*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) - (52*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + ((-534 - 432*S^2 - 111*S^4 + 1109*S^6 + 1007*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + ((270 + 135*S^2 + 3203*S^4 + 2933*S^6)*Zeta[7])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((30260371*(-1 + S^2)*(1 + S^2)^2)/(139968*S^3) + (Pi^6*(-50030 + 7196*S^2 + 30426*S^4 + 164401*S^6 + 107175*S^8))/(90720*S^3*(1 + S^2)) + (Pi^4*(-412441 - 822840*S^2 + 421880*S^4 + 1528488*S^6 + 750425*S^8))/(116640*S^3*(1 + S^2)) + (Pi^2*(-3218554 - 6441433*S^2 + 1171329*S^4 + 8606117*S^6 + 4305221*S^8))/(104976*S^3*(1 + S^2)) + (85*(-1 + S^6)*HPL[{2}, -S^2]^3)/(18*S^3) + ((13 + 17*S^2 - 4*S^4 + 5*S^6 + S^8)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)) + ((-70*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-1652 - 3305*S^2 + 2589*S^4 + 8809*S^6 + 4999*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-564 - 794*S^2 - 130*S^4 + 109*S^6 + 339*S^8)*HPL[{6}, -S^2])/(18*S^3*(1 + S^2)) - (446*(1 + S^6)*HPL[{7}, -S^2])/(9*S^3) - (148*(-1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((10*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (1067 + 1592*S^2 - 120*S^4 - 748*S^6 - 319*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((52*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (10399 + 18430*S^2 - 1704*S^4 - 18182*S^6 - 9743*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((71 + 95*S^2 - 60*S^4 + 95*S^6 + 71*S^8)*HPL[{4, 2}, -S^2])/(54*S^3*(1 + S^2)) - (154*(1 + S^6)*HPL[{4, 3}, -S^2])/(9*S^3) - (2*(-226 - 278*S^2 - 2*S^4 + 79*S^6 + 131*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (460*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5, 2}, -S^2])/(9*S^3) - (650*(1 + S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((-9317 - 9029*S^2 + 9029*S^4 + 9317*S^6)/(27*S^3) + (Pi^2*(-2423 - 191*S^2 + 1116*S^4 + 6973*S^6 + 4741*S^8))/(81*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + ((332*Pi^2*(1 + S^6))/(27*S^3) + (2*(-779 - 755*S^2 + 755*S^4 + 779*S^6))/(9*S^3))*HPL[{2, 2, 1}, -S^2] + ((112*Pi^2*(1 + S^6))/(3*S^3) + (2*(-23659 - 22935*S^2 + 23181*S^4 + 24617*S^6))/(81*S^3))*HPL[{3, 1, 1}, -S^2] - (8*(1 + S^2)*(2 - 5*S^2 + 2*S^4)*HPL[{3, 1, 2}, -S^2])/(27*S^3) + (4*(-769 + 6*S^2 + 6*S^4 + 761*S^6)*HPL[{3, 2, 1}, -S^2])/(27*S^3) - (4*(1 + S^6)*HPL[{3, 2, 2}, -S^2])/S^3 - (112*(1 + S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) + (2*(-1813 - 1849*S^2 + 1709*S^6 + 1745*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (12*(1 + S^6)*HPL[{4, 1, 2}, -S^2])/S^3 - (116*(1 + S^6)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (808*(1 + S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((-248*Pi^2*(1 + S^6))/(9*S^3) - (16*(-281 - 263*S^2 + 263*S^4 + 281*S^6))/(9*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (8*(-359 - 371*S^2 - 6*S^4 + 334*S^6 + 346*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (1880*(-1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) - (32*(1 + S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((1111*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (Pi^2*(-2545 - 5233*S^2 + 261*S^4 + 4853*S^6 + 2192*S^8))/(324*S^3*(1 + S^2)) + (-271145 - 552866*S^2 - 199320*S^4 + 222034*S^6 + 108529*S^8)/(5832*S^3*(1 + S^2)))*Zeta[3] + ((-460 - 502*S^2 - 30*S^4 + 407*S^6 + 449*S^8)*Zeta[3]^2)/(27*S^3*(1 + S^2)) + HPL[{3, 1}, -S^2]*((25519 + 50754*S^2 - 4568*S^4 - 59322*S^6 - 30383*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(1307 + 287*S^2 - 492*S^4 - 3421*S^6 - 2401*S^8))/(81*S^3*(1 + S^2)) - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((3265*(-1 + S^2)*(1 + S^2)^2)/(108*S^3) + (Pi^2*(-658 + 356*S^2 + 534*S^4 + 2687*S^6 + 1673*S^8))/(324*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((Pi^2*(-1739 - 1931*S^2 + 12*S^4 + 1165*S^6 + 1357*S^8))/(324*S^3*(1 + S^2)) + (-4573 - 11702*S^2 + 5596*S^4 + 23902*S^6 + 12905*S^8)/(324*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (100*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((74413 + 73549*S^2 - 73549*S^4 - 74413*S^6)/(324*S^3) + (Pi^2*(12455 + 10578*S^2 - 21264*S^4 - 21331*S^6))/(486*S^3) - (3487*Pi^4*(1 + S^6))/(1620*S^3) - (22*(-1 + S^6)*Zeta[3])/S^3) + HPL[{3}, -S^2]*((-37*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(-3907 - 7255*S^2 + 1161*S^4 + 12563*S^6 + 6974*S^8))/(972*S^3*(1 + S^2)) + (-142279 - 258430*S^2 + 199320*S^4 + 589262*S^6 + 304895*S^8)/(5832*S^3*(1 + S^2)) + (26*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (22*(-1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (16*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (2*(-1 - 5*S^2 - 4*S^4 - 3*S^6 + S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + ((107*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-3843 - 7289*S^2 - 823*S^4 + 5173*S^6 + 2478*S^8)/(54*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((-101189 - 100325*S^2 + 100325*S^4 + 101189*S^6)/(648*S^3) + (Pi^2*(-71413 - 65029*S^2 + 115397*S^4 + 116789*S^6))/(3888*S^3) + (Pi^4*(-28652 + 14098*S^2 + 22734*S^4 + 113125*S^6 + 70375*S^8))/(19440*S^3*(1 + S^2)) + ((-5*Pi^2*(1 + S^6))/(27*S^3) + (-961 - 423*S^2 + 531*S^4 + 425*S^6)/(162*S^3))*HPL[{3}, -S^2] + ((-11 - 15*S^2 + 4*S^4 - 7*S^6 - 3*S^8)*HPL[{4}, -S^2])/(6*S^3*(1 + S^2)) - (80*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((779 + 755*S^2 - 755*S^4 - 779*S^6)/(9*S^3) - (166*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (148*(-1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (20*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (20*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (296*(-1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((37*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(-1135 - 161*S^2 + 1403*S^4))/(81*S^3))*Zeta[3] + (70*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + (30*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3)) + (1568*S^3*Zeta[9])/3;
Et5uvwT=T*Et5uvwT1F1*(F-1/F)+T^2*(Et5uvwT2F2*(F^2-1/F^2))+T^3*(Et5uvwT3F1*(F-1/F)+Et5uvwT3F3*(F^3-1/F^3));
Et5vwuT1F1=(-490*Pi^2*S)/3 - (3533*Pi^4*S)/135 - (2425*Pi^6*S)/648 - (55259*Pi^8*S)/85050 - (4*(1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) - (8*(1 + S^2)*HPL[{1}, -S^2]^9)/(27*S) + HPL[{0}, S^2]^8*(-S/48 + ((-1 - S^2)*HPL[{1}, -S^2])/(96*S)) - (2*(31 + 41*S^2)*HPL[{2}, -S^2]^4)/(9*S) + HPL[{0}, S^2]^7*((-7*Pi^2*S)/864 - (7*(1 + S^2)*HPL[{1}, -S^2])/(144*S) - (7*(1 + S^2)*HPL[{1}, -S^2]^2)/(144*S) - (7*S*HPL[{2}, -S^2])/144) + HPL[{1}, -S^2]^7*((-16*(1 + S^2))/(3*S) - (92*Pi^2*(1 + S^2))/(63*S) - (20*(1 + S^2)*HPL[{2}, -S^2])/(21*S)) + (2*(10 + 9*S^2)*HPL[{3}, -S^2]^3)/(9*S) - (2*(-19 + 47*S^2)*HPL[{4}, -S^2]^2)/(3*S) + ((Pi^2*(-15 - 128*S^2))/(9*S) + (4*(105 + 242*S^2))/(3*S))*HPL[{7}, -S^2] - (3556*S*HPL[{8}, -S^2])/3 - (28*(42 + 67*S^2)*HPL[{9}, -S^2])/(3*S) + (112*(-25 + 17*S^2)*HPL[{2, 1}, -S^2]^3)/(9*S) - (4*(374 + 343*S^2)*HPL[{3, 1}, -S^2]^2)/(3*S) + ((-2*(44 + 21*S^2))/S + (Pi^2*(-19 + 66*S^2))/(9*S))*HPL[{4, 3}, -S^2] + ((Pi^2*(-65 + 163*S^2))/(9*S) - (2*(400 + 233*S^2))/(3*S))*HPL[{5, 2}, -S^2] + (2*(1 + 17*S^2)*HPL[{5, 3}, -S^2])/(3*S) - (2*(-289 + 30*S^2)*HPL[{5, 4}, -S^2])/(3*S) + ((4*Pi^2*(-13 + 32*S^2))/(9*S) - (8*(207 + 214*S^2))/(3*S))*HPL[{6, 1}, -S^2] + (2*(-13 + 81*S^2)*HPL[{6, 2}, -S^2])/(3*S) - (22*(-105 + 16*S^2)*HPL[{6, 3}, -S^2])/(3*S) + (4*(19 + 483*S^2)*HPL[{7, 1}, -S^2])/(3*S) - (2*(-2835 + 416*S^2)*HPL[{7, 2}, -S^2])/(3*S) + (2*(2065 + 116*S^2)*HPL[{8, 1}, -S^2])/S - (32*(41 + 57*S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((2*(-9 + 1954*S^2))/(3*S) + (Pi^2*(-41 + 2093*S^2))/(9*S))*HPL[{3, 2, 2}, -S^2] + ((80*(-8 + 151*S^2))/(3*S) + (4*Pi^2*(-66 + 1643*S^2))/(9*S))*HPL[{3, 3, 1}, -S^2] - (2*(83 + 300*S^2)*HPL[{3, 3, 2}, -S^2])/(3*S) + ((2*(-355 + 5973*S^2))/(3*S) + (Pi^2*(-295 + 6502*S^2))/(9*S))*HPL[{4, 1, 2}, -S^2] + (16*(21 + 62*S^2)*HPL[{4, 1, 3}, -S^2])/(3*S) + ((2*(-1135 + 18393*S^2))/(3*S) + (Pi^2*(-823 + 20098*S^2))/(9*S))*HPL[{4, 2, 1}, -S^2] - (2*(43 + 193*S^2)*HPL[{4, 2, 2}, -S^2])/(3*S) + (2*(13 + 56*S^2)*HPL[{4, 2, 3}, -S^2])/(3*S) + (8*(97 + 460*S^2)*HPL[{4, 3, 1}, -S^2])/(3*S) + (4*(63 + 73*S^2)*HPL[{4, 3, 2}, -S^2])/(3*S) + (4*(215 + 102*S^2)*HPL[{4, 4, 1}, -S^2])/(3*S) + ((4*(-1201 + 18887*S^2))/(3*S) + (2*Pi^2*(-839 + 20641*S^2))/(9*S))*HPL[{5, 1, 1}, -S^2] + (2*(217 + 1138*S^2)*HPL[{5, 1, 2}, -S^2])/(3*S) + (4*(101 + 16*S^2)*HPL[{5, 1, 3}, -S^2])/(3*S) + (2*(1597 + 7498*S^2)*HPL[{5, 2, 1}, -S^2])/(3*S) + (10*(109 + 80*S^2)*HPL[{5, 2, 2}, -S^2])/(3*S) + (4*(815 + 316*S^2)*HPL[{5, 3, 1}, -S^2])/(3*S) + (4*(2016 + 9343*S^2)*HPL[{6, 1, 1}, -S^2])/(3*S) + (4*(730 + 281*S^2)*HPL[{6, 1, 2}, -S^2])/(3*S) + (4*(1950 + 581*S^2)*HPL[{6, 2, 1}, -S^2])/(3*S) + (4*(3525 + 634*S^2)*HPL[{7, 1, 1}, -S^2])/(3*S) + ((-16*Pi^2*(-353 + 123*S^2))/(9*S) - (8*(-728 + 451*S^2))/(3*S))*HPL[{2, 2, 2, 1}, -S^2] + ((4*(-4159 + 743*S^2))/(3*S) + (2*Pi^2*(-8327 + 809*S^2))/(9*S))*HPL[{3, 1, 1, 2}, -S^2] + ((4*(-4159 + 743*S^2))/(3*S) + (2*Pi^2*(-8327 + 809*S^2))/(9*S))*HPL[{3, 1, 2, 1}, -S^2] - (2*(134 + 127*S^2)*HPL[{3, 1, 2, 2}, -S^2])/(3*S) + ((4*(-8527 + 3449*S^2))/(3*S) + (2*Pi^2*(-16799 + 3761*S^2))/(9*S))*HPL[{3, 2, 1, 1}, -S^2] - (2*(134 + 127*S^2)*HPL[{3, 2, 1, 2}, -S^2])/(3*S) + (2*(-2206 + 2609*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(3*S) - (4*(-99 + 1957*S^2)*HPL[{3, 2, 2, 2}, -S^2])/(3*S) - (4*(-266 + 6121*S^2)*HPL[{3, 2, 3, 1}, -S^2])/(3*S) + (16*(-259 + 342*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S - (8*(-128 + 3003*S^2)*HPL[{3, 3, 1, 2}, -S^2])/(3*S) - (20*(-170 + 3717*S^2)*HPL[{3, 3, 2, 1}, -S^2])/(3*S) + ((8*(-12949 + 4926*S^2))/(3*S) + (4*Pi^2*(-25313 + 5375*S^2))/(9*S))*HPL[{4, 1, 1, 1}, -S^2] - (4*(-32 + 421*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(3*S) + (4*(-1832 + 37825*S^2)*HPL[{4, 1, 1, 3}, -S^2])/(3*S) + (4*(-3076 + 3683*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(3*S) + (2*(-3209 + 63710*S^2)*HPL[{4, 1, 2, 2}, -S^2])/(3*S) + (216*(-17 + 351*S^2)*HPL[{4, 1, 3, 1}, -S^2])/S + (92*(-404 + 517*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(3*S) + (2*(-2081 + 39242*S^2)*HPL[{4, 2, 1, 2}, -S^2])/(3*S) + (2*(-2021 + 38552*S^2)*HPL[{4, 2, 2, 1}, -S^2])/(3*S) + (8*(-2653 + 56132*S^2)*HPL[{4, 3, 1, 1}, -S^2])/(3*S) + (8*(-9364 + 11459*S^2)*HPL[{5, 1, 1, 1}, -S^2])/(3*S) + (4*(-1865 + 38141*S^2)*HPL[{5, 1, 1, 2}, -S^2])/S + (4*(-3013 + 62839*S^2)*HPL[{5, 1, 2, 1}, -S^2])/S + (4*(-7061 + 149627*S^2)*HPL[{5, 2, 1, 1}, -S^2])/S + (8*(-26364 + 560855*S^2)*HPL[{6, 1, 1, 1}, -S^2])/(3*S) + ((16*(226 + 155*S^2))/S + (16*Pi^2*(703 + 256*S^2))/(9*S))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((48*(226 + 155*S^2))/S + (16*Pi^2*(703 + 256*S^2))/(3*S))*HPL[{2, 2, 1, 1, 1}, -S^2] + (32*(-257 + 346*S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S) + (32*(-257 + 346*S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (32*(325 + 242*S^2)*HPL[{2, 2, 2, 2, 1}, -S^2])/(3*S) + ((16*Pi^2*(3522 + 1865*S^2))/(9*S) + (16*(3410 + 3381*S^2))/(3*S))*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(-6047 + 8182*S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S) - (8*(-10159 + 13718*S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S) - (4*(7849 + 1807*S^2)*HPL[{3, 1, 1, 2, 2}, -S^2])/(3*S) - (8*(-12215 + 16486*S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S) - (4*(7849 + 1807*S^2)*HPL[{3, 1, 2, 1, 2}, -S^2])/(3*S) + (4*(103 + 113*S^2)*HPL[{3, 1, 2, 2, 1}, -S^2])/(3*S) + (32*(6946 + 2053*S^2)*HPL[{3, 1, 3, 1, 1}, -S^2])/(3*S) - (8*(-25579 + 34478*S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S) - (4*(15649 + 7615*S^2)*HPL[{3, 2, 1, 1, 2}, -S^2])/(3*S) - (4*(7697 + 5695*S^2)*HPL[{3, 2, 1, 2, 1}, -S^2])/(3*S) - (4*(-24319 + 2807*S^2)*HPL[{3, 2, 2, 1, 1}, -S^2])/(3*S) - (32*(-3352 + 123*S^2)*HPL[{3, 3, 1, 1, 1}, -S^2])/S - (128*(-4827 + 6443*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S) - (8*(23689 + 11209*S^2)*HPL[{4, 1, 1, 1, 2}, -S^2])/(3*S) - (8*(11761 + 8329*S^2)*HPL[{4, 1, 1, 2, 1}, -S^2])/(3*S) - (8*(-36263 + 3997*S^2)*HPL[{4, 1, 2, 1, 1}, -S^2])/(3*S) - (8*(-120611 + 4045*S^2)*HPL[{4, 2, 1, 1, 1}, -S^2])/(3*S) - (64*(-30150 + 881*S^2)*HPL[{5, 1, 1, 1, 1}, -S^2])/(3*S) + ((-2192*Pi^2*(-11 + 4*S^2))/(9*S) - (32*(-788 + 457*S^2))/(3*S))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (896*(-25 + 17*S^2)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(3*S) + (896*(-25 + 17*S^2)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S + (32*(-643 + 619*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S) - (32*(-3583 + 3407*S^2)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(3*S) - (32*(-7783 + 6263*S^2)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(3*S) - (32*(-10583 + 8167*S^2)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(3*S) - (32*(-11983 + 9119*S^2)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(3*S) - (32*(-21083 + 15307*S^2)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(3*S) - (960*(-701 + 513*S^2)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S - (640*(-17 + 25*S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S - (64*(227 + 162*S^2)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S - (256*(227 + 162*S^2)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S - (640*(227 + 162*S^2)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S - (512*(594 + 379*S^2)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S - (1280*(-25 + 17*S^2)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((28*Pi^2*S)/27 + (28*S*HPL[{0}, S^2]^2)/9 + (32*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + HPL[{0}, S^2]*((32*S)/3 + (32*(1 + S^2)*HPL[{1}, -S^2])/(3*S)) + (8*(-5 + 7*S^2)*HPL[{2}, -S^2])/(9*S))*Log[T]^7 + ((-8*S*HPL[{0}, S^2])/3 - (8*(1 + S^2)*HPL[{1}, -S^2])/(3*S))*Log[T]^8 + ((-32*S)/3 - (23*Pi^2*S)/3)*Zeta[3]^2 + HPL[{0}, S^2]^6*((-47*S)/72 - (71*Pi^2*S)/288 - (7*(1 + S^2)*HPL[{1}, -S^2]^2)/(24*S) - (41*(1 + S^2)*HPL[{1}, -S^2]^3)/(216*S) - (11*S*HPL[{2}, -S^2])/48 + HPL[{1}, -S^2]*((-47*(1 + S^2))/(144*S) - (125*Pi^2*(1 + S^2))/(864*S) - (2*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + (S*HPL[{3}, -S^2])/48 + ((16 - 3*S^2)*HPL[{2, 1}, -S^2])/(36*S) - (17*S*Zeta[3])/36) + Log[T]^6*((-100*Pi^2*S)/27 - (88*S*HPL[{0}, S^2]^3)/27 - (112*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (224*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^2*((-100*S)/9 - (12*(1 + S^2)*HPL[{1}, -S^2])/S) - (8*(-17 + 25*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((-112*(1 + S^2))/(3*S) - (92*Pi^2*(1 + S^2))/(9*S) - (20*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]*((-112*S)/3 - (256*Pi^2*S)/27 - (112*(1 + S^2)*HPL[{1}, -S^2])/(3*S) - (112*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (4*(-5 + 79*S^2)*HPL[{2}, -S^2])/(9*S)) + (4*(3 + 74*S^2)*HPL[{3}, -S^2])/(9*S) - (16*(-25 + 17*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (272*S*Zeta[3])/9) + HPL[{1}, -S^2]^6*((-170*(1 + S^2))/(9*S) - (139*Pi^2*(1 + S^2))/(27*S) - (34*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (160*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (20*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (40*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^5*((-176*(1 + S^2))/(3*S) - (706*Pi^2*(1 + S^2))/(45*S) - (1237*Pi^4*(1 + S^2))/(450*S) + ((-212*(1 + S^2))/(15*S) - (314*Pi^2*(1 + S^2))/(45*S))*HPL[{2}, -S^2] - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/(15*S) + (52*(1 + S^2)*HPL[{3}, -S^2])/S + (284*(1 + S^2)*HPL[{4}, -S^2])/(15*S) + (68*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (32*(1 + S^2)*HPL[{3, 1}, -S^2])/(15*S) - (40*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (116*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1, 1}, -S^2]*((Pi^4*(17519 - 4414*S^2))/(135*S) - (80*Pi^2*(-79 + 23*S^2))/(9*S) - (40*(-184 + 65*S^2))/(3*S) - (64*(121 + 4*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 2}, -S^2]*((8*Pi^2*(-16 + 15*S^2))/(9*S) + (4*(-19 + 20*S^2))/S + (4*(-3 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]^2*((-3 - 65*S^2)/(3*S) + (Pi^2*(-2 - 41*S^2))/(9*S) + (2*(113 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(1 + 8*S^2)*Zeta[3])/(3*S)) + HPL[{5, 1}, -S^2]*((Pi^2*(-61 - 721*S^2))/(9*S) - (2*(93 + 574*S^2))/(3*S) - (32*(-1 + 13*S^2)*Zeta[3])/(3*S)) + HPL[{2, 2, 1}, -S^2]*((Pi^4*(-8172 - 1853*S^2))/(135*S) - (20*(124 + 65*S^2))/(3*S) - (4*Pi^2*(710 + 239*S^2))/(9*S) - (16*(-243 + 22*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1}, -S^2]*((Pi^4*(-49409 - 2453*S^2))/(270*S) - (20*(378 + 11*S^2))/(3*S) - (2*Pi^2*(4277 + 347*S^2))/(9*S) - (16*(-735 + 29*S^2)*Zeta[3])/(3*S)) + HPL[{6}, -S^2]*((Pi^2*(8 - 283*S^2))/(9*S) - (2*(-56 + 207*S^2))/S - (4*(2 + 7*S^2)*HPL[{2, 1}, -S^2])/S + (4*(-10 + 31*S^2)*Zeta[3])/(3*S)) + HPL[{4, 2}, -S^2]*((Pi^2*(17 - 207*S^2))/(9*S) - (4*(-2 + 33*S^2))/S - (2*(3 + 44*S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((Pi^2*(115 - 988*S^2))/(9*S) + (Pi^4*(19 - 636*S^2))/(45*S) - (40*(-7 + 39*S^2))/(3*S) - (4*(41 + 2061*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(-17 + 70*S^2)*Zeta[3])/(3*S)) + HPL[{5}, -S^2]*((14*(18 + 83*S^2))/(3*S) + (Pi^2*(2 + 199*S^2))/(9*S) + (Pi^4*(47 + 651*S^2))/(270*S) - (2*(199 + 29*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(-22 + 47*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (20*(-5 + 39*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(-43 + 79*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]^2*((4*(215 + 343*S^2))/(3*S) + (2*Pi^2*(249 + 706*S^2))/(9*S) - (16*(-11 + 115*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^3*((230 - 373*S^2)/(9*S) - (8*Pi^2*(-17 + 44*S^2))/(27*S) + (2*(-39 + 269*S^2)*HPL[{3}, -S^2])/(9*S) + (2*(325 + 242*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (4*(3 + 115*S^2)*Zeta[3])/(9*S)) + HPL[{4, 1}, -S^2]*((Pi^4*(469 - 25264*S^2))/(540*S) + (Pi^2*(199 - 3259*S^2))/(9*S) - (2*(-72 + 923*S^2))/S - (8*(-163 + 3311*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(-23 + 228*S^2)*Zeta[3])/(3*S)) + HPL[{3, 2, 1}, -S^2]*((-8*Pi^2*(-120 + 337*S^2))/(9*S) - (4*(-403 + 686*S^2))/(3*S) + (4*(7 + 309*S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-32*(-68 + 137*S^2))/S - (32*Pi^2*(-134 + 379*S^2))/(9*S) + (32*(7 + 472*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1, 1}, -S^2]*((8*(-533 + 701*S^2))/(3*S) + (4*Pi^2*(-677 + 1379*S^2))/(9*S) - (16*(9 + 479*S^2)*Zeta[3])/(3*S)) + HPL[{4, 1, 1}, -S^2]*((-40*(-141 + 200*S^2))/(3*S) - (2*Pi^2*(-1700 + 3923*S^2))/(9*S) + (8*(25 + 1412*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^5*((-43*Pi^2*S)/180 - (3083*Pi^4*S)/32400 - (541*(1 + S^2)*HPL[{1}, -S^2]^3)/(540*S) - (91*(1 + S^2)*HPL[{1}, -S^2]^4)/(180*S) + ((-43*S)/30 + (Pi^2*(15 - 1246*S^2))/(2160*S))*HPL[{2}, -S^2] + ((5 - 142*S^2)*HPL[{2}, -S^2]^2)/(240*S) + HPL[{1}, -S^2]^2*((-139*(1 + S^2))/(90*S) - (427*Pi^2*(1 + S^2))/(720*S) - (461*(1 + S^2)*HPL[{2}, -S^2])/(360*S)) + ((-3 + 2*S^2)*HPL[{3}, -S^2])/(24*S) + ((-1 - 2*S^2)*HPL[{4}, -S^2])/(8*S) + ((157 - 10*S^2)*HPL[{2, 1}, -S^2])/(60*S) + (27*S*HPL[{3, 1}, -S^2])/10 + ((15 - 511*S^2)*HPL[{2, 1, 1}, -S^2])/(90*S) - (S*Zeta[3])/12 + HPL[{1}, -S^2]*((-149*(1 + S^2))/(90*S) - (319*Pi^2*(1 + S^2))/(540*S) - (19*(1 + S^2)*HPL[{2}, -S^2])/(15*S) + ((-1 - S^2)*HPL[{3}, -S^2])/(12*S) + (461*(1 + S^2)*HPL[{2, 1}, -S^2])/(180*S) + ((-1 - S^2)*Zeta[3])/(3*S))) + Log[T]^5*((310*Pi^2*S)/27 + (6166*Pi^4*S)/2025 + (283*S*HPL[{0}, S^2]^4)/135 + (224*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (112*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + HPL[{0}, S^2]^3*((260*S)/27 + (86*(1 + S^2)*HPL[{1}, -S^2])/(9*S)) + ((4*(-94 + 155*S^2))/(9*S) + (2*Pi^2*(-113 + 298*S^2))/(27*S))*HPL[{2}, -S^2] + (2*(33 + 46*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^2*((112*(1 + S^2))/S + (92*Pi^2*(1 + S^2))/(3*S) + (20*(1 + S^2)*HPL[{2}, -S^2])/S) + HPL[{0}, S^2]^2*((310*S)/9 + (1301*Pi^2*S)/135 + (110*(1 + S^2)*HPL[{1}, -S^2])/(3*S) + (36*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (2*(-8 + 151*S^2)*HPL[{2}, -S^2])/(9*S)) - (4*(7 + 221*S^2)*HPL[{3}, -S^2])/(9*S) - (8*(14 + 59*S^2)*HPL[{4}, -S^2])/(15*S) + (8*(-17 + 11*S^2)*HPL[{2, 1}, -S^2])/S - (32*(-11 + 10*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (112*(-5 + 7*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - 88*S*Zeta[3] + HPL[{0}, S^2]*((340*S)/3 + (764*Pi^2*S)/27 + (112*(1 + S^2)*HPL[{1}, -S^2]^2)/S + (224*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) + (4*(-5 + 79*S^2)*HPL[{2}, -S^2])/(3*S) + HPL[{1}, -S^2]*((112*(1 + S^2))/S + (254*Pi^2*(1 + S^2))/(9*S) + (100*(1 + S^2)*HPL[{2}, -S^2])/S) - (4*(-10 + 17*S^2)*HPL[{3}, -S^2])/(9*S) + (32*(-20 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - 24*S*Zeta[3]) + HPL[{1}, -S^2]*((340*(1 + S^2))/(3*S) + (278*Pi^2*(1 + S^2))/(9*S) + (68*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (320*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (80*(1 + S^2)*Zeta[3])/S)) + (56*S + 35*Pi^2*S)*Zeta[5] + Zeta[3]*((344*Pi^2*S)/9 + (595*Pi^4*S)/108 - (352*S*Zeta[5])/3) + HPL[{0}, S^2]^4*((-214*S)/9 - (521*Pi^2*S)/108 - (821*Pi^4*S)/720 - (47*(1 + S^2)*HPL[{1}, -S^2]^4)/(18*S) - (31*(1 + S^2)*HPL[{1}, -S^2]^5)/(30*S) + ((1 - 20*S^2)*HPL[{2}, -S^2]^2)/(6*S) + HPL[{1}, -S^2]^3*((-67*(1 + S^2))/(12*S) - (391*Pi^2*(1 + S^2))/(216*S) - (245*(1 + S^2)*HPL[{2}, -S^2])/(54*S)) + ((-5 + 4*S^2)/(12*S) + (Pi^2*(-5 + 11*S^2))/(72*S))*HPL[{3}, -S^2] + ((5 - 22*S^2)*HPL[{4}, -S^2])/(12*S) + ((5 + 4*S^2)*HPL[{5}, -S^2])/(6*S) + ((Pi^2*(985 - 122*S^2))/(216*S) + (251 - 2*S^2)/(18*S))*HPL[{2, 1}, -S^2] + (5*(-1 + 36*S^2)*HPL[{3, 1}, -S^2])/(12*S) - HPL[{3, 2}, -S^2]/(2*S) + ((-7 - 8*S^2)*HPL[{4, 1}, -S^2])/(12*S) - (57*S*HPL[{2, 1, 1}, -S^2])/2 + ((-473 - 4*S^2)*HPL[{2, 2, 1}, -S^2])/(18*S) + ((-161 + S^2)*HPL[{3, 1, 1}, -S^2])/(2*S) + ((505 - 32*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(9*S) + ((-11*S)/6 - (281*Pi^2*S)/108)*Zeta[3] + HPL[{1}, -S^2]*((-107*(1 + S^2))/(9*S) - (109*Pi^2*(1 + S^2))/(36*S) - (23*Pi^4*(1 + S^2))/(30*S) + ((-133*(1 + S^2))/(18*S) - (485*Pi^2*(1 + S^2))/(216*S))*HPL[{2}, -S^2] - (29*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) - (3*(1 + S^2)*HPL[{3}, -S^2])/(4*S) - (2*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (85*(1 + S^2)*HPL[{2, 1}, -S^2])/(6*S) + (122*(1 + S^2)*HPL[{3, 1}, -S^2])/(9*S) - (245*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) + ((-1 - S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-347*(1 + S^2))/(36*S) - (199*Pi^2*(1 + S^2))/(72*S) - (85*(1 + S^2)*HPL[{2}, -S^2])/(12*S) + ((-1 - S^2)*HPL[{3}, -S^2])/(3*S) + (245*(1 + S^2)*HPL[{2, 1}, -S^2])/(18*S) - (19*(1 + S^2)*Zeta[3])/(18*S)) + HPL[{2}, -S^2]*((-7*Pi^2*S)/3 - (5*(3 + 29*S^2))/(18*S) + HPL[{3}, -S^2]/(4*S) + ((473 + 4*S^2)*HPL[{2, 1}, -S^2])/(36*S) - (5*(1 + 2*S^2)*Zeta[3])/(12*S)) - (125*S*Zeta[5])/9) + Log[T]^4*((-274*Pi^2*S)/9 - (233*Pi^4*S)/30 - (283*S*HPL[{0}, S^2]^5)/270 - (280*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) - (112*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) + HPL[{0}, S^2]^4*((-31*S)/6 - (31*(1 + S^2)*HPL[{1}, -S^2])/(6*S)) - (4*(41 + 57*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((-661*S)/27 - (613*Pi^2*S)/81 - (215*(1 + S^2)*HPL[{1}, -S^2])/(9*S) - (215*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + ((6 - 205*S^2)*HPL[{2}, -S^2])/(9*S)) + HPL[{1}, -S^2]^3*((-560*(1 + S^2))/(3*S) - (460*Pi^2*(1 + S^2))/(9*S) - (100*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((8*(5 + 264*S^2))/(9*S) + (2*Pi^2*(7 + 585*S^2))/(27*S))*HPL[{3}, -S^2] + (4*(33 + 178*S^2)*HPL[{4}, -S^2])/(9*S) + (4*(-15 + 113*S^2)*HPL[{5}, -S^2])/(9*S) + ((-274*Pi^2*(-11 + 4*S^2))/(27*S) - (4*(-788 + 457*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (4*(-643 + 619*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (4*(-83 + 1027*S^2)*HPL[{3, 2}, -S^2])/(9*S) - (40*(-1 + 37*S^2)*HPL[{4, 1}, -S^2])/S - (80*(-17 + 25*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(227 + 162*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(333 + 58*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (160*(-25 + 17*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((1828*S)/9 + (1124*Pi^2*S)/27)*Zeta[3] + HPL[{0}, S^2]^2*((-274*S)/3 - (218*Pi^2*S)/9 - (275*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (60*(1 + S^2)*HPL[{1}, -S^2]^3)/S - (2*(-13 + 383*S^2)*HPL[{2}, -S^2])/(9*S) + HPL[{1}, -S^2]*((-286*(1 + S^2))/(3*S) - (76*Pi^2*(1 + S^2))/(3*S) - (239*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-31 + 60*S^2)*HPL[{3}, -S^2])/(9*S) - (2*(-757 + 38*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (104*S*Zeta[3])/9) + HPL[{1}, -S^2]*((-880*(1 + S^2))/(3*S) - (706*Pi^2*(1 + S^2))/(9*S) - (1237*Pi^4*(1 + S^2))/(90*S) + ((-212*(1 + S^2))/(3*S) - (314*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (260*(1 + S^2)*HPL[{3}, -S^2])/S + (284*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (340*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (32*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (200*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (580*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-850*(1 + S^2))/(3*S) - (695*Pi^2*(1 + S^2))/(9*S) - (170*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (800*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (100*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (200*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-4*(-68 + 137*S^2))/(3*S) - (4*Pi^2*(-134 + 379*S^2))/(27*S) + (4*(-24 + 181*S^2)*HPL[{3}, -S^2])/(3*S) + (4*(227 + 162*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(7 + 472*S^2)*Zeta[3])/(9*S)) + HPL[{0}, S^2]*((-880*S)/3 - (1921*Pi^2*S)/27 - (10279*Pi^4*S)/810 - (560*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (280*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + ((Pi^2*(31 - 600*S^2))/(9*S) - (2*(-68 + 1177*S^2))/(9*S))*HPL[{2}, -S^2] + ((-17 - 1142*S^2)*HPL[{2}, -S^2]^2)/(9*S) + HPL[{1}, -S^2]^2*((-280*(1 + S^2))/S - (635*Pi^2*(1 + S^2))/(9*S) - (250*(1 + S^2)*HPL[{2}, -S^2])/S) + (2*(-47 + 87*S^2)*HPL[{3}, -S^2])/(9*S) - (4*(-1 + 13*S^2)*HPL[{4}, -S^2])/(3*S) - (80*(-20 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-29 + 391*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (40*(-5 + 79*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (524*S*Zeta[3])/9 + HPL[{1}, -S^2]*((-850*(1 + S^2))/(3*S) - (635*Pi^2*(1 + S^2))/(9*S) - (250*(1 + S^2)*HPL[{2}, -S^2])/S + (12*(1 + S^2)*HPL[{3}, -S^2])/S + (500*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (164*(1 + S^2)*Zeta[3])/(3*S))) + (2000*S*Zeta[5])/9) + HPL[{1}, -S^2]^4*((-155*(1 + S^2))/S - (122*Pi^2*(1 + S^2))/(3*S) - (3773*Pi^4*(1 + S^2))/(540*S) - (196*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((362*(1 + S^2))/(3*S) + (205*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (46*(1 + S^2)*HPL[{4}, -S^2])/S + (62*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((212*(1 + S^2))/(3*S) + (314*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (4*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (220*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (2264*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (340*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (1568*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (3104*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (200*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((268*(1 + S^2))/(3*S) + (55*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-47*(1 + S^2))/S - (167*Pi^2*(1 + S^2))/(9*S) + (110*(1 + S^2)*HPL[{3}, -S^2])/S + (784*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (328*(1 + S^2)*Zeta[3])/(3*S)) + (268*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]^3*((-980*(1 + S^2))/(3*S) - (2350*Pi^2*(1 + S^2))/(27*S) - (1579*Pi^4*(1 + S^2))/(108*S) - (17153*Pi^6*(1 + S^2))/(7560*S) + ((-382*(1 + S^2))/(3*S) - (319*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2]^2 - (62*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) - (74*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((794*(1 + S^2))/(9*S) + (401*Pi^2*(1 + S^2))/(27*S))*HPL[{4}, -S^2] + (104*(1 + S^2)*HPL[{5}, -S^2])/(3*S) - (70*(1 + S^2)*HPL[{6}, -S^2])/(3*S) + (1568*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((80*(1 + S^2))/(3*S) + (152*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1}, -S^2] - (432*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (4432*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (78*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (1168*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-848*(1 + S^2))/(3*S) - (1256*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2096*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (496*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (352*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (1360*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (128*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (800*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((472*(1 + S^2))/(3*S) + (106*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (40*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((188*(1 + S^2))/S + (668*Pi^2*(1 + S^2))/(9*S) - (1312*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((644*(1 + S^2))/(3*S) + (1178*Pi^2*(1 + S^2))/(27*S) - (440*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (32*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-1180*(1 + S^2))/(9*S) - (1102*Pi^2*(1 + S^2))/(27*S) - (4421*Pi^4*(1 + S^2))/(540*S) + (1940*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (226*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (656*(1 + S^2)*Zeta[3])/(3*S)) + (496*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2, 1}, -S^2]*(980/S + (Pi^6*(59902 - 15063*S^2))/(11340*S) + (Pi^4*(18422 - 3297*S^2))/(540*S) - (10*Pi^2*(-180 + 29*S^2))/(9*S) + ((-4*(187 + 196*S^2))/S - (2*Pi^2*(425 + 213*S^2))/(3*S))*HPL[{3, 1}, -S^2] + (2*(2145 + 61*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(-3443 + 114*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (2*(137 + 20*S^2)*HPL[{4, 2}, -S^2])/S + (4*(927 + 17*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-8*(226 + 155*S^2))/S - (8*Pi^2*(703 + 256*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (16*(-257 + 346*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(-69 + 325*S^2)*HPL[{3, 1, 1}, -S^2])/S - (156*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (4*(1183 + 851*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (16*(775 + 748*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (64*(41 + 57*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (32*(278 + 305*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (32*(227 + 162*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-8*(213 + 4*S^2))/(3*S) - (2*Pi^2*(529 + 16*S^2))/(9*S))*Zeta[3] - (4*(-9 + 20*S^2)*Zeta[3]^2)/(3*S) + (4*(-403 + 4*S^2)*Zeta[5])/(3*S)) + HPL[{4}, -S^2]*((Pi^2*(15 + 14*S^2))/(9*S) - (14*(-12 + 53*S^2))/(3*S) + (Pi^4*(266 + 335*S^2))/(540*S) + (2*(-145 + 12*S^2)*HPL[{5}, -S^2])/(3*S) + ((13*Pi^2*(-29 + 4*S^2))/(9*S) - (2*(451 + 5*S^2))/(3*S))*HPL[{2, 1}, -S^2] - (2*(-31 + 342*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(-43 + 68*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (8*(-44 + 57*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (4*(-50 + 381*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*(395 + 56*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(1211 + 72*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (32*(-100 + 11*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((2*(-45 + 11*S^2))/(3*S) + (Pi^2*(-35 + 32*S^2))/(9*S))*Zeta[3] + (2*(-39 + 32*S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*(490*S + (50*Pi^2*(-1 + 10*S^2))/(9*S) + (Pi^4*(-410 + 3913*S^2))/(540*S) + (Pi^6*(-725 + 7439*S^2))/(7560*S) + ((4*(11 + S^2))/S - (2*Pi^2*(-5 + 29*S^2))/(9*S))*HPL[{4}, -S^2] + (2*(-39 + 89*S^2)*HPL[{5}, -S^2])/(3*S) + (2*(145 + 44*S^2)*HPL[{6}, -S^2])/(3*S) - (2*(79 + 1089*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-4*(-107 + 503*S^2))/(3*S) - (2*Pi^2*(-79 + 566*S^2))/(9*S))*HPL[{3, 1}, -S^2] + (2*(35 + 206*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (6*(-11 + 8*S^2)*HPL[{4, 1}, -S^2])/S - (2*(7 + 58*S^2)*HPL[{4, 2}, -S^2])/(3*S) - (4*(51 + 10*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((4*(-167 + 1039*S^2))/(3*S) + (2*Pi^2*(-137 + 1131*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (4*(1131 + 89*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (12*(379 + 7*S^2)*HPL[{3, 1, 1}, -S^2])/S + (4*(9 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (4*(-49 + 359*S^2)*HPL[{3, 2, 1}, -S^2])/S - (20*(-268 + 6921*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (16*(-188 + 21*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (8*(-169 + 1081*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (32*(-24 + 181*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((8*(-8 + 29*S^2))/(3*S) + (Pi^2*(-4 + 111*S^2))/(9*S))*Zeta[3] + (2*(-3 + 11*S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((4*(-497 + 59*S^2))/(3*S) + (Pi^2*(-1159 + 115*S^2))/(9*S) + (4*(-63 + 11*S^2)*Zeta[3])/(3*S)) + (2*(-54 + 109*S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]^2*((Pi^2*(-209 - 725*S^2))/(18*S) - (10*(6 + 11*S^2))/S - (7*Pi^4*(116 + 591*S^2))/(540*S) + ((14*(3 + 38*S^2))/(3*S) + (7*Pi^2*(5 + 81*S^2))/(18*S))*HPL[{3}, -S^2] + ((35 + 183*S^2)*HPL[{4}, -S^2])/(3*S) + ((-23 + 86*S^2)*HPL[{5}, -S^2])/(3*S) + ((728 - 451*S^2)/(3*S) - (2*Pi^2*(-353 + 123*S^2))/(9*S))*HPL[{2, 1}, -S^2] + ((-635 + 567*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (5*(-19 + 204*S^2)*HPL[{3, 2}, -S^2])/(3*S) + ((73 - 3284*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (4*(-257 + 346*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(325 + 242*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2*(1871 + 363*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (112*(-25 + 17*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((4*(-16 + 113*S^2))/(3*S) + (Pi^2*(-29 + 247*S^2))/(9*S))*Zeta[3] + (2*(-26 + 187*S^2)*Zeta[5])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(3790 - 17861*S^2))/(270*S) - (880*(-1 + 5*S^2))/(3*S) - (4*Pi^2*(-195 + 826*S^2))/(9*S) - (448*(-25 + 17*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (32*(-326 + 57*S^2)*HPL[{3, 1, 1}, -S^2])/S + (32*(227 + 162*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((16*(2 + 227*S^2))/(3*S) + (8*Pi^2*(2 + 259*S^2))/(9*S))*Zeta[3] + (8*(-14 + 417*S^2)*Zeta[5])/(3*S)) + HPL[{3, 1}, -S^2]*((10*(-76 + 189*S^2))/(3*S) + (8*Pi^2*(-67 + 195*S^2))/(9*S) + (Pi^4*(-4902 + 17141*S^2))/(540*S) + (8*(-4 + 509*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(-265 + 3274*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (16*(307 + 283*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(-571 + 605*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(3087 + 1210*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (32*(278 + 305*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-2*Pi^2*(1 + 175*S^2))/(3*S) - (4*(7 + 459*S^2))/(3*S))*Zeta[3] - (4*(-5 + 431*S^2)*Zeta[5])/(3*S)) + Log[T]^3*((610*Pi^2*S)/9 + (13247*Pi^4*S)/810 + (35159*Pi^6*S)/11340 + (11*S*HPL[{0}, S^2]^6)/27 + (224*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) + (224*(1 + S^2)*HPL[{1}, -S^2]^6)/(9*S) + HPL[{0}, S^2]^5*((541*S)/270 + (91*(1 + S^2)*HPL[{1}, -S^2])/(45*S)) + ((2*(156 + 227*S^2))/(3*S) + (2*Pi^2*(254 + 701*S^2))/(27*S))*HPL[{2}, -S^2]^2 + (4*(-257 + 331*S^2)*HPL[{2}, -S^2]^3)/(27*S) + HPL[{1}, -S^2]^4*((560*(1 + S^2))/(3*S) + (460*Pi^2*(1 + S^2))/(9*S) + (100*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + HPL[{0}, S^2]^4*((583*S)/54 + (613*Pi^2*S)/162 + (94*(1 + S^2)*HPL[{1}, -S^2])/(9*S) + (31*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) + ((-5 + 174*S^2)*HPL[{2}, -S^2])/(18*S)) + (4*(-13 + 107*S^2)*HPL[{3}, -S^2]^2)/(9*S) + ((-2*Pi^2*(93 + 313*S^2))/(27*S) - (4*(51 + 322*S^2))/(9*S))*HPL[{4}, -S^2] - (20*(-6 + 43*S^2)*HPL[{5}, -S^2])/(9*S) + (4*(54 + 115*S^2)*HPL[{6}, -S^2])/(9*S) - (40*(33 + 46*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + HPL[{0}, S^2]^3*((154*S)/3 + (397*Pi^2*S)/27 + (430*(1 + S^2)*HPL[{1}, -S^2]^2)/(9*S) + (860*(1 + S^2)*HPL[{1}, -S^2]^3)/(27*S) + (2*(-7 + 606*S^2)*HPL[{2}, -S^2])/(27*S) + HPL[{1}, -S^2]*((1334*(1 + S^2))/(27*S) + (397*Pi^2*(1 + S^2))/(27*S) + (392*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) - (2*(-11 + 4*S^2)*HPL[{3}, -S^2])/(9*S) + (4*(-202 + 9*S^2)*HPL[{2, 1}, -S^2])/(9*S)) + ((-8*(-598 + 651*S^2))/(9*S) - (8*Pi^2*(-354 + 671*S^2))/(27*S))*HPL[{3, 1}, -S^2] + (4*(-191 + 2074*S^2)*HPL[{3, 2}, -S^2])/(9*S) + (112*(-9 + 239*S^2)*HPL[{4, 1}, -S^2])/(9*S) + (148*(-1 + 11*S^2)*HPL[{4, 2}, -S^2])/(9*S) + (400*(1 + 17*S^2)*HPL[{5, 1}, -S^2])/(9*S) + ((80*(-94 + 155*S^2))/(9*S) + (40*Pi^2*(-113 + 298*S^2))/(27*S))*HPL[{2, 1, 1}, -S^2] + (64*(57 + 41*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (16*(2017 + 371*S^2)*HPL[{3, 1, 1}, -S^2])/(9*S) - (16*(-61 + 59*S^2)*HPL[{3, 1, 2}, -S^2])/(9*S) + (16*(-151 + 201*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (32*(-271 + 272*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (160*(-17 + 11*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (640*(-11 + 10*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (2240*(-5 + 7*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + ((-1064*S)/3 - (2176*Pi^2*S)/27)*Zeta[3] - (16*S*Zeta[3]^2)/3 + HPL[{1}, -S^2]^2*((1760*(1 + S^2))/(3*S) + (1412*Pi^2*(1 + S^2))/(9*S) + (1237*Pi^4*(1 + S^2))/(45*S) + ((424*(1 + S^2))/(3*S) + (628*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (520*(1 + S^2)*HPL[{3}, -S^2])/S - (568*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (680*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (64*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (400*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (1160*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^3*((3400*(1 + S^2))/(9*S) + (2780*Pi^2*(1 + S^2))/(27*S) + (680*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (3200*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (400*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (800*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((8*(-277 + 133*S^2))/(3*S) + (8*Pi^2*(-769 + 257*S^2))/(27*S) + (80*(97 + 4*S^2)*Zeta[3])/(9*S)) + HPL[{3}, -S^2]*((-4*(1 + 327*S^2))/(3*S) - (2*Pi^2*(3 + 1145*S^2))/(27*S) - (16*(-189 + 16*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*(19 + 53*S^2)*Zeta[3])/(9*S)) + HPL[{2}, -S^2]*((20*(-22 + 61*S^2))/(3*S) + (4*Pi^2*(-239 + 781*S^2))/(27*S) + (Pi^4*(-4256 + 17677*S^2))/(810*S) - (8*(-79 + 548*S^2)*HPL[{3}, -S^2])/(9*S) - (4*(-61 + 383*S^2)*HPL[{4}, -S^2])/(9*S) - (32*(57 + 41*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (16*(310 + 283*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (80*(33 + 46*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (32*(2 + 119*S^2)*Zeta[3])/(9*S)) + HPL[{0}, S^2]^2*((610*S)/3 + (1358*Pi^2*S)/27 + (16369*Pi^4*S)/1620 + (1100*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + (60*(1 + S^2)*HPL[{1}, -S^2]^4)/S + ((2*(-8 + 787*S^2))/(9*S) + (Pi^2*(-55 + 1277*S^2))/(27*S))*HPL[{2}, -S^2] + ((13 + 712*S^2)*HPL[{2}, -S^2]^2)/(9*S) + HPL[{1}, -S^2]^2*((572*(1 + S^2))/(3*S) + (152*Pi^2*(1 + S^2))/(3*S) + (478*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) - (16*(-4 + 5*S^2)*HPL[{3}, -S^2])/(9*S) + (2*(-9 + 41*S^2)*HPL[{4}, -S^2])/(9*S) + (4*(-773 + 19*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (8*(-24 + 371*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (40*(-8 + 151*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) - (196*S*Zeta[3])/9 + HPL[{1}, -S^2]*((614*(1 + S^2))/(3*S) + (463*Pi^2*(1 + S^2))/(9*S) + (166*(1 + S^2)*HPL[{2}, -S^2])/S - (20*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (956*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (20*(1 + S^2)*Zeta[3])/S)) - (1184*S*Zeta[5])/3 + HPL[{0}, S^2]*(620*S + (1312*Pi^2*S)/9 + (6761*Pi^4*S)/270 + (560*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) + (224*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) + (16*(2 + 143*S^2)*HPL[{2}, -S^2]^2)/(9*S) + HPL[{1}, -S^2]^3*((1120*(1 + S^2))/(3*S) + (2540*Pi^2*(1 + S^2))/(27*S) + (1000*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-68*(-3 + 5*S^2))/(9*S) - (2*Pi^2*(-83 + 97*S^2))/(27*S))*HPL[{3}, -S^2] + (4*(3 + 64*S^2)*HPL[{4}, -S^2])/(9*S) + (8*(5 + 3*S^2)*HPL[{5}, -S^2])/(3*S) + ((40*(-238 + 11*S^2))/(9*S) + (4*Pi^2*(-602 + 29*S^2))/(9*S))*HPL[{2, 1}, -S^2] - (8*(-85 + 1177*S^2)*HPL[{3, 1}, -S^2])/(9*S) + (4*(53 + 157*S^2)*HPL[{3, 2}, -S^2])/(9*S) + (16*(-1 + 40*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (80*(-5 + 79*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (16*(1159 + 34*S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) + (16*(3527 + 17*S^2)*HPL[{3, 1, 1}, -S^2])/(9*S) + (640*(-20 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-992*S)/9 - 20*Pi^2*S)*Zeta[3] + HPL[{1}, -S^2]^2*((1700*(1 + S^2))/(3*S) + (1270*Pi^2*(1 + S^2))/(9*S) + (500*(1 + S^2)*HPL[{2}, -S^2])/S - (24*(1 + S^2)*HPL[{3}, -S^2])/S - (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (328*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]*((1760*(1 + S^2))/(3*S) + (3854*Pi^2*(1 + S^2))/(27*S) + (3374*Pi^4*(1 + S^2))/(135*S) + ((1496*(1 + S^2))/(3*S) + (1142*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (24*(1 + S^2)*HPL[{3}, -S^2])/S + (28*(1 + S^2)*HPL[{4}, -S^2])/S - (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2992*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (328*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((8*(-9 + 196*S^2))/(3*S) + (2*Pi^2*(-82 + 1791*S^2))/(27*S) - (4*(7 + 25*S^2)*HPL[{3}, -S^2])/(3*S) - (8*(1159 + 34*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (8*(-1 + 122*S^2)*Zeta[3])/(9*S)) - (832*S*Zeta[5])/9) + HPL[{1}, -S^2]*((620*(1 + S^2))/S + (488*Pi^2*(1 + S^2))/(3*S) + (3773*Pi^4*(1 + S^2))/(135*S) + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-1448*(1 + S^2))/(3*S) - (820*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (184*(1 + S^2)*HPL[{4}, -S^2])/S - (248*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-848*(1 + S^2))/(3*S) - (1256*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (880*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (9056*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (1360*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (6272*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (12416*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (800*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-1072*(1 + S^2))/(3*S) - (220*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((188*(1 + S^2))/S + (668*Pi^2*(1 + S^2))/(9*S) - (440*(1 + S^2)*HPL[{3}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (1312*(1 + S^2)*Zeta[3])/(3*S)) - (1072*(1 + S^2)*Zeta[5])/(3*S))) + HPL[{0}, S^2]^3*((-725*Pi^2*S)/108 - (10519*Pi^4*S)/6480 - (35159*Pi^6*S)/90720 - (43*(1 + S^2)*HPL[{1}, -S^2]^5)/(9*S) - (43*(1 + S^2)*HPL[{1}, -S^2]^6)/(27*S) + ((Pi^2*(24 - 995*S^2))/(216*S) + (30 - 557*S^2)/(36*S))*HPL[{2}, -S^2]^2 + ((1 - 45*S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{1}, -S^2]^4*((-667*(1 + S^2))/(54*S) - (397*Pi^2*(1 + S^2))/(108*S) - (98*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((1 + 23*S^2)*HPL[{3}, -S^2]^2)/(18*S) + ((Pi^2*(-21 - 79*S^2))/(54*S) + (-20 - 71*S^2)/(9*S))*HPL[{4}, -S^2] + ((-80 + 121*S^2)*HPL[{5}, -S^2])/(18*S) + ((-20 - 17*S^2)*HPL[{6}, -S^2])/(3*S) + ((-9 + 569*S^2)*HPL[{2, 1}, -S^2]^2)/(9*S) + ((13*(2 + 49*S^2))/(9*S) + (Pi^2*(-18 + 1091*S^2))/(54*S))*HPL[{3, 1}, -S^2] + ((2 - 27*S^2)*HPL[{3, 2}, -S^2])/(18*S) + ((60 - 71*S^2)*HPL[{4, 1}, -S^2])/(9*S) + (2*S*HPL[{4, 2}, -S^2])/9 + (2*(12 + 47*S^2)*HPL[{5, 1}, -S^2])/(9*S) + ((Pi^2*(33 - 1126*S^2))/(27*S) - (4*(2 + 309*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (4*(-285 + 2*S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) + (2*(-581 + 5*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (2*S*HPL[{3, 1, 2}, -S^2])/9 - (2*(-12 + 541*S^2)*HPL[{3, 2, 1}, -S^2])/(9*S) - (2*(-39 + 1688*S^2)*HPL[{4, 1, 1}, -S^2])/(9*S) - (4*(-605 + 8*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(9*S) + (4*(-18 + 605*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(9*S) - (8*(-6 + 205*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + ((41*S)/9 - (Pi^2*S)/9)*Zeta[3] + (2*S*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((4*(-5 + 3*S^2))/(9*S) + (Pi^2*(-26 + 11*S^2))/(36*S) - (2*(5 + 17*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (2*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-712*(1 + S^2))/(27*S) - (593*Pi^2*(1 + S^2))/(81*S) - (598*(1 + S^2)*HPL[{2}, -S^2])/(27*S) - (8*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (392*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (10*(1 + S^2)*Zeta[3])/(27*S)) + HPL[{1}, -S^2]^2*((-385*(1 + S^2))/(9*S) - (1223*Pi^2*(1 + S^2))/(108*S) - (1001*Pi^4*(1 + S^2))/(405*S) + ((-311*(1 + S^2))/(9*S) - (1049*Pi^2*(1 + S^2))/(108*S))*HPL[{2}, -S^2] - (140*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) - (17*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (23*(1 + S^2)*HPL[{4}, -S^2])/(9*S) + (598*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (584*(1 + S^2)*HPL[{3, 1}, -S^2])/(9*S) - (392*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((-725*S)/18 + (Pi^4*(26 - 1283*S^2))/(540*S) + (Pi^2*(-2 - 567*S^2))/(54*S) + ((-1 + 6*S^2)*HPL[{3}, -S^2])/(9*S) + ((-1 - 24*S^2)*HPL[{4}, -S^2])/(9*S) - (2*(-285 + 2*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (2*(-1 + 287*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (2*(-9 + 569*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) - (2*(-2 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((Pi^2*(538 - 19*S^2))/(27*S) + (641 - 5*S^2)/(9*S) + (4*(1 + 5*S^2)*Zeta[3])/(9*S)) + 2*S*Zeta[5] + HPL[{1}, -S^2]*((-815*(1 + S^2))/(18*S) - (109*Pi^2*(1 + S^2))/(9*S) - (887*Pi^4*(1 + S^2))/(360*S) - (281*(1 + S^2)*HPL[{2}, -S^2]^2)/(18*S) + ((Pi^2*(-1 - S^2))/(2*S) - (13*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (20*(1 + S^2)*HPL[{4}, -S^2])/(9*S) - (5*(1 + S^2)*HPL[{5}, -S^2])/(9*S) + ((622*(1 + S^2))/(9*S) + (1049*Pi^2*(1 + S^2))/(54*S))*HPL[{2, 1}, -S^2] + (596*(1 + S^2)*HPL[{3, 1}, -S^2])/(9*S) - (26*(1 + S^2)*HPL[{3, 2}, -S^2])/(9*S) - (32*(1 + S^2)*HPL[{4, 1}, -S^2])/(9*S) - (1196*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) - (1120*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) - (1136*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (784*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((41*(1 + S^2))/(9*S) - (55*Pi^2*(1 + S^2))/(54*S))*Zeta[3] + HPL[{2}, -S^2]*((-215*(1 + S^2))/(6*S) - (527*Pi^2*(1 + S^2))/(54*S) + (13*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (560*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (5*(1 + S^2)*Zeta[3])/(9*S)) - (8*(1 + S^2)*Zeta[5])/(3*S))) + 112*S*Zeta[7] + HPL[{0}, S^2]^2*(-490*S - (703*Pi^2*S)/9 - (2029*Pi^4*S)/180 - (190627*Pi^6*S)/90720 - (55*(1 + S^2)*HPL[{1}, -S^2]^6)/(9*S) - (12*(1 + S^2)*HPL[{1}, -S^2]^7)/(7*S) + ((15 - 358*S^2)*HPL[{2}, -S^2]^3)/(18*S) + HPL[{1}, -S^2]^5*((-286*(1 + S^2))/(15*S) - (76*Pi^2*(1 + S^2))/(15*S) - (239*(1 + S^2)*HPL[{2}, -S^2])/(15*S)) + ((-13 + 20*S^2)*HPL[{3}, -S^2]^2)/(6*S) + ((Pi^2*(43 + 69*S^2))/(36*S) + (35 + 141*S^2)/(6*S))*HPL[{5}, -S^2] + ((70 - 369*S^2)*HPL[{6}, -S^2])/(6*S) + (5*(21 + 2*S^2)*HPL[{7}, -S^2])/(6*S) + (2*(3 + 364*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((Pi^2*(-57 - 89*S^2))/(36*S) + (21 - 13*S^2)/(6*S))*HPL[{3, 2}, -S^2] + ((Pi^2*(-8 - 175*S^2))/(18*S) + (44 - 67*S^2)/(3*S))*HPL[{4, 1}, -S^2] + ((2 + 7*S^2)*HPL[{4, 2}, -S^2])/(6*S) + (2*(3 + 11*S^2)*HPL[{4, 3}, -S^2])/(3*S) + ((-7 + 44*S^2)*HPL[{5, 1}, -S^2])/S + ((29 + 149*S^2)*HPL[{5, 2}, -S^2])/(6*S) + ((32 + 153*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((-2*(742 + 13*S^2))/(3*S) - (2*Pi^2*(599 + 15*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((Pi^2*(-3655 - 9*S^2))/(9*S) - (2*(2263 + 8*S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + ((-7 - 2*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + ((53 - 1434*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + ((-33 + 185*S^2)*HPL[{3, 2, 2}, -S^2])/(6*S) + (8*(-1 + 36*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) - (2*(-92 + 2203*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + ((-6 + 287*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + ((6 + 863*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (2*(1 + 885*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((-4*(-264 + S^2))/S - (4*Pi^2*(-631 + 35*S^2))/(9*S))*HPL[{2, 1, 1, 1}, -S^2] - (32*(-89 + 2*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + (8*(-17 + 380*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (2*(-4293 + 7*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (2*(-4293 + 7*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (2*(-8565 + 103*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (4*(-12803 + 137*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) - (16*(-13 + 383*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + (8*(725 + 26*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) + (8*(725 + 26*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (16*(1797 + 95*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) - (16*(-757 + 38*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S) + ((19*S)/3 - (3*Pi^2*S)/2 - (69*Pi^4*S)/20)*Zeta[3] - 25*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^4*(14373 - 1424*S^2))/(1080*S) + (Pi^2*(1294 - 7*S^2))/(18*S) + (5*(176 + 7*S^2))/(3*S) - (2*(719 + 29*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(725 + 26*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (30*Zeta[3])/S) + HPL[{4}, -S^2]*(-35*S + (Pi^2*(32 - 187*S^2))/(36*S) + ((23 + 8*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (8*Zeta[3])/S) + HPL[{1}, -S^2]^4*((-307*(1 + S^2))/(6*S) - (463*Pi^2*(1 + S^2))/(36*S) - (83*(1 + S^2)*HPL[{2}, -S^2])/(2*S) + (5*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (239*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (5*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-1030*(1 + S^2))/(9*S) - (487*Pi^2*(1 + S^2))/(18*S) - (3299*Pi^4*(1 + S^2))/(648*S) + ((-784*(1 + S^2))/(9*S) - (1207*Pi^2*(1 + S^2))/(54*S))*HPL[{2}, -S^2] - (41*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (8*(1 + S^2)*HPL[{3}, -S^2])/(9*S) - (25*(1 + S^2)*HPL[{4}, -S^2])/(9*S) + (166*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (472*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (956*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (28*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((Pi^2*(9 - 604*S^2))/(36*S) + (3 - 191*S^2)/(3*S) + (3*(-1 + 5*S^2)*HPL[{3}, -S^2])/(4*S) - (4*(-89 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) + ((-7 + 17*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((-3 + 859*S^2)/(3*S) + (Pi^2*(-49 + 1300*S^2))/(18*S) - (4*(-3 + 23*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((5*(-7 + 8*S^2))/(3*S) + (Pi^2*(-67 + 55*S^2))/(36*S) + (Pi^4*(-613 + 1137*S^2))/(2160*S) + ((-3 - 10*S^2)*HPL[{4}, -S^2])/(3*S) + ((-31 - 11*S^2)*HPL[{2, 1}, -S^2])/(3*S) + ((-11 - 51*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(7 + 45*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + ((-16 + 37*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(26 - 1279*S^2))/(9*S) - (4*(9 + 415*S^2))/(3*S) + (4*(-3 + 46*S^2)*Zeta[3])/(3*S)) + ((-62*S)/3 - (250*Pi^2*S)/9)*Zeta[5] + HPL[{1}, -S^2]^2*((-405*(1 + S^2))/(2*S) - (1615*Pi^2*(1 + S^2))/(36*S) - (5627*Pi^4*(1 + S^2))/(720*S) - (187*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-8*(1 + S^2))/(3*S) + (Pi^2*(1 + S^2))/(6*S))*HPL[{3}, -S^2] - (41*(1 + S^2)*HPL[{4}, -S^2])/(6*S) - (11*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((784*(1 + S^2))/(3*S) + (1207*Pi^2*(1 + S^2))/(18*S))*HPL[{2, 1}, -S^2] + (740*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (52*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (131*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) - (498*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (492*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (1456*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (956*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((13*(1 + S^2))/S + (7*Pi^2*(1 + S^2))/(18*S))*Zeta[3] + HPL[{2}, -S^2]*((-851*(1 + S^2))/(6*S) - (419*Pi^2*(1 + S^2))/(12*S) + (26*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (246*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (47*(1 + S^2)*Zeta[3])/(3*S)) + ((-1 - S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]*((-245*(1 + S^2))/S - (943*Pi^2*(1 + S^2))/(18*S) - (18383*Pi^4*(1 + S^2))/(2160*S) - (20777*Pi^6*(1 + S^2))/(12960*S) + ((-125*(1 + S^2))/(2*S) - (601*Pi^2*(1 + S^2))/(36*S))*HPL[{2}, -S^2]^2 - (341*(1 + S^2)*HPL[{2}, -S^2]^3)/(18*S) + (11*(1 + S^2)*HPL[{3}, -S^2]^2)/(6*S) + ((-9*(1 + S^2))/(2*S) - (73*Pi^2*(1 + S^2))/(36*S))*HPL[{4}, -S^2] - (9*(1 + S^2)*HPL[{5}, -S^2])/S - (39*(1 + S^2)*HPL[{6}, -S^2])/(2*S) + (246*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((766*(1 + S^2))/(3*S) + (598*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] - (43*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (85*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (3*(1 + S^2)*HPL[{4, 2}, -S^2])/(2*S) + (56*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-1568*(1 + S^2))/(3*S) - (1207*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (1496*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4472*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (1364*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (4142*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (996*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (944*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (1912*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((41*(1 + S^2))/(3*S) + (Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (13*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((851*(1 + S^2))/(3*S) + (419*Pi^2*(1 + S^2))/(6*S) - (94*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-12*(1 + S^2))/S - (23*Pi^2*(1 + S^2))/(18*S) - (52*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (14*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((-475*(1 + S^2))/(3*S) - (329*Pi^2*(1 + S^2))/(9*S) - (13883*Pi^4*(1 + S^2))/(2160*S) + (7*(1 + S^2)*HPL[{3}, -S^2])/S - (25*(1 + S^2)*HPL[{4}, -S^2])/(6*S) + (748*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (734*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (492*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (15*(1 + S^2)*Zeta[3])/S) - (13*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((Pi^4*(158 - 14777*S^2))/(2160*S) + (Pi^2*(-13 - 235*S^2))/(6*S) - (10*(7 + 55*S^2))/(3*S) + ((5*(-3 + S^2))/(6*S) + (5*Pi^2*(5 + 9*S^2))/(36*S))*HPL[{3}, -S^2] + ((26 - 45*S^2)*HPL[{4}, -S^2])/(6*S) + ((15 + 7*S^2)*HPL[{5}, -S^2])/(6*S) + ((742 + 13*S^2)/(3*S) + (Pi^2*(599 + 15*S^2))/(9*S))*HPL[{2, 1}, -S^2] + ((1 + 727*S^2)*HPL[{3, 1}, -S^2])/(3*S) + ((5 - 31*S^2)*HPL[{3, 2}, -S^2])/(2*S) + ((4 - 143*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (4*(3 + 364*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (16*(-89 + 2*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (2*(-2143 + 3*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (4*(725 + 26*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((Pi^2*(-9 + 8*S^2))/(9*S) + (-16 + 31*S^2)/(3*S))*Zeta[3] - (5*(6 + S^2)*Zeta[5])/(3*S)) - 186*S*Zeta[7]) + Log[T]^2*((-1100*Pi^2*S)/9 - (7381*Pi^4*S)/270 - (109189*Pi^6*S)/22680 - (7*S*HPL[{0}, S^2]^7)/72 - (112*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) - (32*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) + HPL[{0}, S^2]^6*((-5*S)/8 - (41*(1 + S^2)*HPL[{1}, -S^2])/(72*S)) - (2*(-257 + 346*S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{0}, S^2]^5*((-43*S)/15 - (1301*Pi^2*S)/1080 - (541*(1 + S^2)*HPL[{1}, -S^2])/(180*S) - (91*(1 + S^2)*HPL[{1}, -S^2]^2)/(30*S) + ((15 - 511*S^2)*HPL[{2}, -S^2])/(180*S)) + HPL[{1}, -S^2]^5*((-112*(1 + S^2))/S - (92*Pi^2*(1 + S^2))/(3*S) - (20*(1 + S^2)*HPL[{2}, -S^2])/S) - (2*(-3 + 34*S^2)*HPL[{3}, -S^2]^2)/S + ((Pi^2*(-47 + 247*S^2))/(9*S) + (2*(-31 + 257*S^2))/(3*S))*HPL[{5}, -S^2] - (2*(54 + 197*S^2)*HPL[{6}, -S^2])/(3*S) - (2*(135 + 266*S^2)*HPL[{7}, -S^2])/(3*S) + (16*(41 + 57*S^2)*HPL[{2, 1}, -S^2]^2)/S + ((Pi^2*(145 - 2143*S^2))/(9*S) - (2*(-209 + 1963*S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((-4*(-155 + 3192*S^2))/(3*S) - (2*Pi^2*(-103 + 3481*S^2))/(9*S))*HPL[{4, 1}, -S^2] - (2*(-32 + 421*S^2)*HPL[{4, 2}, -S^2])/(3*S) + (4*(-25 + 44*S^2)*HPL[{4, 3}, -S^2])/(3*S) - (4*(40 + 853*S^2)*HPL[{5, 1}, -S^2])/(3*S) + (2*(-53 + 59*S^2)*HPL[{5, 2}, -S^2])/S - (4*(84 + 25*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((-8*(226 + 155*S^2))/S - (8*Pi^2*(703 + 256*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((-8*Pi^2*(2102 + 183*S^2))/(9*S) - (8*(2014 + 339*S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + (4*(-121 + 122*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (4*(-907 + 1262*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (2*(-49 + 4001*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (16*(-64 + 1571*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) - (64*(-201 + 215*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (4*(-289 + 6215*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + (4*(-829 + 19235*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (32*(-210 + 4939*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((-1096*Pi^2*(-11 + 4*S^2))/(9*S) - (16*(-788 + 457*S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] - (448*(-25 + 17*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + (16*(-643 + 619*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (16*(-2017 + 401*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (16*(-2017 + 401*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (16*(-4117 + 1829*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (96*(-695 + 291*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (320*(-17 + 25*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (32*(227 + 162*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (96*(227 + 162*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (320*(115 + 118*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (640*(-25 + 17*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((1300*S)/3 + (992*Pi^2*S)/9 + (69*Pi^4*S)/5)*Zeta[3] + 8*S*Zeta[3]^2 + HPL[{0}, S^2]^4*((-337*S)/18 - (137*Pi^2*S)/24 - (47*(1 + S^2)*HPL[{1}, -S^2]^2)/(3*S) - (31*(1 + S^2)*HPL[{1}, -S^2]^3)/(3*S) - (57*S*HPL[{2}, -S^2])/4 + HPL[{1}, -S^2]*((-67*(1 + S^2))/(4*S) - (391*Pi^2*(1 + S^2))/(72*S) - (245*(1 + S^2)*HPL[{2}, -S^2])/(18*S)) + ((-10 + 7*S^2)*HPL[{3}, -S^2])/(12*S) + ((505 - 32*S^2)*HPL[{2, 1}, -S^2])/(18*S) - (26*S*Zeta[3])/9) + HPL[{1}, -S^2]^4*((-850*(1 + S^2))/(3*S) - (695*Pi^2*(1 + S^2))/(9*S) - (170*(1 + S^2)*HPL[{2}, -S^2])/(3*S) + (800*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (100*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (200*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((-1760*(1 + S^2))/(3*S) - (1412*Pi^2*(1 + S^2))/(9*S) - (1237*Pi^4*(1 + S^2))/(45*S) + ((-424*(1 + S^2))/(3*S) - (628*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] - (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (520*(1 + S^2)*HPL[{3}, -S^2])/S + (568*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (680*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (64*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (400*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (1160*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((Pi^4*(17519 - 4414*S^2))/(270*S) - (40*Pi^2*(-79 + 23*S^2))/(9*S) - (20*(-184 + 65*S^2))/(3*S) - (16*(278 + 305*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (16*(227 + 162*S^2)*HPL[{2, 1, 1}, -S^2])/S - (32*(121 + 4*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((4*(15 + 119*S^2))/(3*S) + (Pi^2*(68 + 301*S^2))/(9*S) + (16*(-100 + 11*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-11 + 32*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((20*(-3 + 92*S^2))/(3*S) + (Pi^2*(-17 + 1087*S^2))/(9*S) + (Pi^4*(-377 + 8665*S^2))/(540*S) - (4*(-13 + 48*S^2)*HPL[{4}, -S^2])/(3*S) + (8*(-188 + 21*S^2)*HPL[{2, 1}, -S^2])/S - (4*(-169 + 1081*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (16*(-24 + 181*S^2)*HPL[{2, 1, 1}, -S^2])/S + (8*(6 + 37*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((Pi^2*(-249 - 706*S^2))/(9*S) - (2*(215 + 343*S^2))/(3*S) + ((79 + 1089*S^2)*HPL[{3}, -S^2])/(3*S) - (56*(-25 + 17*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(-11 + 115*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((-16*(-68 + 137*S^2))/S - (16*Pi^2*(-134 + 379*S^2))/(9*S) + (16*(7 + 472*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((4*(-533 + 701*S^2))/(3*S) + (2*Pi^2*(-677 + 1379*S^2))/(9*S) - (8*(9 + 479*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^3*((-725*S)/9 - (1177*Pi^2*S)/54 - (16369*Pi^4*S)/3240 - (430*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) - (215*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + ((Pi^2*(33 - 1126*S^2))/(54*S) - (2*(2 + 309*S^2))/(9*S))*HPL[{2}, -S^2] + ((9 - 569*S^2)*HPL[{2}, -S^2]^2)/(18*S) + HPL[{1}, -S^2]^2*((-667*(1 + S^2))/(9*S) - (397*Pi^2*(1 + S^2))/(18*S) - (196*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-11 + S^2)*HPL[{3}, -S^2])/(3*S) + ((3 - 68*S^2)*HPL[{4}, -S^2])/(9*S) - (2*(-605 + 8*S^2)*HPL[{2, 1}, -S^2])/(9*S) + (2*(-18 + 605*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (4*(-6 + 205*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + 2*S*Zeta[3] + HPL[{1}, -S^2]*((-712*(1 + S^2))/(9*S) - (593*Pi^2*(1 + S^2))/(27*S) - (598*(1 + S^2)*HPL[{2}, -S^2])/(9*S) - (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (392*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (10*(1 + S^2)*Zeta[3])/(9*S))) + HPL[{0}, S^2]^2*((-1100*S)/3 - (748*Pi^2*S)/9 - (3299*Pi^4*S)/216 - (275*(1 + S^2)*HPL[{1}, -S^2]^4)/(3*S) - (36*(1 + S^2)*HPL[{1}, -S^2]^5)/S + ((-3 - 364*S^2)*HPL[{2}, -S^2]^2)/(3*S) + HPL[{1}, -S^2]^3*((-572*(1 + S^2))/(3*S) - (152*Pi^2*(1 + S^2))/(3*S) - (478*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-37 + 31*S^2)/(3*S) + (Pi^2*(-61 + 81*S^2))/(18*S))*HPL[{3}, -S^2] + ((2 - 55*S^2)*HPL[{4}, -S^2])/(3*S) + ((-17 + 21*S^2)*HPL[{5}, -S^2])/(3*S) + ((-2*(-264 + S^2))/S - (2*Pi^2*(-631 + 35*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (4*(-17 + 380*S^2)*HPL[{3, 1}, -S^2])/(3*S) + ((-21 - 89*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2*(-13 + 151*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (8*(-13 + 383*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(725 + 26*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(1103 + 9*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (8*(-757 + 38*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + 26*S*Zeta[3] + HPL[{1}, -S^2]*((-1030*(1 + S^2))/(3*S) - (487*Pi^2*(1 + S^2))/(6*S) - (3299*Pi^4*(1 + S^2))/(216*S) + ((-784*(1 + S^2))/(3*S) - (1207*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2] - (123*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (25*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (498*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (472*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (956*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (28*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^2*((-307*(1 + S^2))/S - (463*Pi^2*(1 + S^2))/(6*S) - (249*(1 + S^2)*HPL[{2}, -S^2])/S + (10*(1 + S^2)*HPL[{3}, -S^2])/S + (478*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (30*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((Pi^2*(26 - 1279*S^2))/(18*S) - (2*(9 + 415*S^2))/(3*S) + ((7 + 45*S^2)*HPL[{3}, -S^2])/(3*S) + (2*(725 + 26*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-3 + 46*S^2)*Zeta[3])/(3*S))) + ((1508*S)/3 + (1000*Pi^2*S)/9)*Zeta[5] + HPL[{1}, -S^2]*((-980*(1 + S^2))/S - (2350*Pi^2*(1 + S^2))/(9*S) - (1579*Pi^4*(1 + S^2))/(36*S) - (17153*Pi^6*(1 + S^2))/(2520*S) + ((-382*(1 + S^2))/S - (319*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 - (62*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) - (74*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((794*(1 + S^2))/(3*S) + (401*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + (104*(1 + S^2)*HPL[{5}, -S^2])/S - (70*(1 + S^2)*HPL[{6}, -S^2])/S + (1568*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((80*(1 + S^2))/S + (152*Pi^2*(1 + S^2))/S)*HPL[{3, 1}, -S^2] - (1296*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (4432*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (234*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (1168*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-848*(1 + S^2))/S - (1256*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (6288*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (496*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (352*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (1360*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (128*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (2400*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((472*(1 + S^2))/S + (106*Pi^2*(1 + S^2))/S)*Zeta[3] - (40*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((564*(1 + S^2))/S + (668*Pi^2*(1 + S^2))/(3*S) - (1312*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((644*(1 + S^2))/S + (1178*Pi^2*(1 + S^2))/(9*S) - (1320*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (96*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]*((-1180*(1 + S^2))/(3*S) - (1102*Pi^2*(1 + S^2))/(9*S) - (4421*Pi^4*(1 + S^2))/(180*S) + (1940*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (226*(1 + S^2)*HPL[{4}, -S^2])/S + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (656*(1 + S^2)*Zeta[3])/S) + (496*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^2*((-930*(1 + S^2))/S - (244*Pi^2*(1 + S^2))/S - (3773*Pi^4*(1 + S^2))/(90*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((724*(1 + S^2))/S + (410*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (276*(1 + S^2)*HPL[{4}, -S^2])/S + (124*(1 + S^2)*HPL[{5}, -S^2])/S + ((424*(1 + S^2))/S + (628*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (1320*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (4528*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (680*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (6208*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (1200*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((536*(1 + S^2))/S + (110*Pi^2*(1 + S^2))/S)*Zeta[3] + HPL[{2}, -S^2]*((-282*(1 + S^2))/S - (334*Pi^2*(1 + S^2))/(3*S) + (660*(1 + S^2)*HPL[{3}, -S^2])/S + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (656*(1 + S^2)*Zeta[3])/S) + (536*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((Pi^4*(3790 - 17861*S^2))/(540*S) - (440*(-1 + 5*S^2))/(3*S) - (2*Pi^2*(-195 + 826*S^2))/(9*S) + ((2*(-167 + 1039*S^2))/(3*S) + (Pi^2*(-137 + 1131*S^2))/(9*S))*HPL[{3}, -S^2] + (2*(-50 + 381*S^2)*HPL[{4}, -S^2])/(3*S) + (10*(-5 + 39*S^2)*HPL[{5}, -S^2])/(3*S) + ((4*(226 + 155*S^2))/S + (4*Pi^2*(703 + 256*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (8*(307 + 283*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (2*(41 + 2061*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(-163 + 3311*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (32*(41 + 57*S^2)*HPL[{2, 1, 1}, -S^2])/S + (224*(-25 + 17*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (16*(-326 + 57*S^2)*HPL[{3, 1, 1}, -S^2])/S + (16*(227 + 162*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((8*(2 + 227*S^2))/(3*S) + (4*Pi^2*(2 + 259*S^2))/(9*S))*Zeta[3] + (4*(-14 + 417*S^2)*Zeta[5])/(3*S)) + HPL[{0}, S^2]*(-980*S - (2045*Pi^2*S)/9 - (10199*Pi^4*S)/270 - (147719*Pi^6*S)/22680 - (112*(1 + S^2)*HPL[{1}, -S^2]^5)/S - (112*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + ((Pi^2*(-8 - 1711*S^2))/(18*S) + (-10 - 1123*S^2)/(3*S))*HPL[{2}, -S^2]^2 - (4*(-19 + 275*S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{1}, -S^2]^4*((-280*(1 + S^2))/S - (635*Pi^2*(1 + S^2))/(9*S) - (250*(1 + S^2)*HPL[{2}, -S^2])/S) + (2*(-8 + 19*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(9 - 146*S^2))/(9*S) - (2*(19 + 87*S^2))/(3*S))*HPL[{4}, -S^2] + (2*(-13 + 2*S^2)*HPL[{5}, -S^2])/S - (8*(5 + 29*S^2)*HPL[{6}, -S^2])/(3*S) + (4*(17 + 1142*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((14*Pi^2*(-15 + 254*S^2))/(9*S) + (4*(-69 + 1180*S^2))/(3*S))*HPL[{3, 1}, -S^2] - (2*(32 + 191*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (4*(-27 + 286*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (2*(1 + 8*S^2)*HPL[{4, 2}, -S^2])/(3*S) + 136*S*HPL[{5, 1}, -S^2] + ((-4*Pi^2*(-31 + 600*S^2))/(3*S) - (8*(-68 + 1177*S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] - (64*(145 + 4*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (8*(3527 + 9*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (4*(11 + 7*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (4*(-141 + 2207*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (16*(-39 + 563*S^2)*HPL[{4, 1, 1}, -S^2])/S - (320*(-20 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (16*(-29 + 391*S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (160*(-5 + 79*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((484*S)/3 + (280*Pi^2*S)/9)*Zeta[3] - 20*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((-1700*(1 + S^2))/(3*S) - (1270*Pi^2*(1 + S^2))/(9*S) - (500*(1 + S^2)*HPL[{2}, -S^2])/S + (24*(1 + S^2)*HPL[{3}, -S^2])/S + (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (328*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((-880*(1 + S^2))/S - (1927*Pi^2*(1 + S^2))/(9*S) - (1687*Pi^4*(1 + S^2))/(45*S) + ((-748*(1 + S^2))/S - (571*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2] - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + (36*(1 + S^2)*HPL[{3}, -S^2])/S - (42*(1 + S^2)*HPL[{4}, -S^2])/S + (1500*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (1496*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (3000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (164*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-20*(-79 + 3*S^2))/S - (2*Pi^2*(-1805 + 68*S^2))/(9*S) - (8*(124 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((10*Pi^2*(-8 + 9*S^2))/(9*S) + (4*(-31 + 40*S^2))/(3*S) - (4*(31 + 13*S^2)*HPL[{2, 1}, -S^2])/S + (4*(5 + 3*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((Pi^4*(415 - 9577*S^2))/(270*S) + (Pi^2*(64 - 1795*S^2))/(9*S) - (10*(-8 + 241*S^2))/(3*S) + (2*(3 + 31*S^2)*HPL[{3}, -S^2])/S - (2*(-19 + 44*S^2)*HPL[{4}, -S^2])/(3*S) + (32*(145 + 4*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (68*(1 + 67*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(17 + 1142*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (4*(2 + 119*S^2)*Zeta[3])/(3*S)) + 132*S*Zeta[5] + HPL[{1}, -S^2]*((-930*(1 + S^2))/S - (1987*Pi^2*(1 + S^2))/(9*S) - (20233*Pi^4*(1 + S^2))/(540*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((56*(1 + S^2))/(3*S) + (10*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] - (38*(1 + S^2)*HPL[{4}, -S^2])/S - (116*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((1496*(1 + S^2))/S + (1142*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (1496*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (152*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (372*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (3000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (9264*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (6000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((508*(1 + S^2))/(3*S) + (256*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((-754*(1 + S^2))/S - (1723*Pi^2*(1 + S^2))/(9*S) + (76*(1 + S^2)*HPL[{3}, -S^2])/S + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (164*(1 + S^2)*Zeta[3])/S) + (368*(1 + S^2)*Zeta[5])/(3*S))) + 744*S*Zeta[7]) + HPL[{1}, -S^2]*((-490*Pi^2*(1 + S^2))/(3*S) - (7493*Pi^4*(1 + S^2))/(270*S) - (45229*Pi^6*(1 + S^2))/(11340*S) - (55259*Pi^8*(1 + S^2))/(85050*S) + ((-14*(1 + S^2))/S - (217*Pi^2*(1 + S^2))/(27*S))*HPL[{2}, -S^2]^3 - (16*(1 + S^2)*HPL[{2}, -S^2]^4)/S + ((-130*(1 + S^2))/(3*S) - (50*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2]^2 - (8*(1 + S^2)*HPL[{4}, -S^2]^2)/S + ((-16*(1 + S^2))/(3*S) - (37*Pi^2*(1 + S^2))/(3*S))*HPL[{6}, -S^2] - (592*(1 + S^2)*HPL[{7}, -S^2])/(3*S) - (560*(1 + S^2)*HPL[{8}, -S^2])/S + ((764*(1 + S^2))/S + (638*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2]^2 - (932*(1 + S^2)*HPL[{3, 1}, -S^2]^2)/S + ((-358*(1 + S^2))/(3*S) - (19*Pi^2*(1 + S^2))/S)*HPL[{4, 2}, -S^2] + (140*(1 + S^2)*HPL[{4, 3}, -S^2])/(3*S) + ((-1780*(1 + S^2))/(3*S) - (820*Pi^2*(1 + S^2))/(9*S))*HPL[{5, 1}, -S^2] + (106*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (8*(1 + S^2)*HPL[{5, 3}, -S^2])/S + (550*(1 + S^2)*HPL[{6, 1}, -S^2])/(3*S) + (20*(1 + S^2)*HPL[{6, 2}, -S^2])/S + (384*(1 + S^2)*HPL[{7, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + (16*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + ((-992*(1 + S^2))/(3*S) - (1736*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2, 1}, -S^2] + (4066*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (12496*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) - (224*(1 + S^2)*HPL[{3, 3, 2}, -S^2])/S + ((-1436*(1 + S^2))/(3*S) - (4406*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1, 1}, -S^2] + (12262*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + (384*(1 + S^2)*HPL[{4, 1, 3}, -S^2])/S + (38254*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) - (136*(1 + S^2)*HPL[{4, 2, 2}, -S^2])/S + (1312*(1 + S^2)*HPL[{4, 3, 1}, -S^2])/S + (26200*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + (800*(1 + S^2)*HPL[{5, 1, 2}, -S^2])/S + (5360*(1 + S^2)*HPL[{5, 2, 1}, -S^2])/S + (13540*(1 + S^2)*HPL[{6, 1, 1}, -S^2])/S + (1648*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + ((160*(1 + S^2))/S + (304*Pi^2*(1 + S^2))/S)*HPL[{3, 1, 1, 1}, -S^2] - (4240*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (4240*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (156*(1 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/S - (5888*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (156*(1 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/S + (308*(1 + S^2)*HPL[{3, 2, 2, 1}, -S^2])/S + (1392*(1 + S^2)*HPL[{3, 3, 1, 1}, -S^2])/S - (18752*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (468*(1 + S^2)*HPL[{4, 1, 1, 2}, -S^2])/S + (924*(1 + S^2)*HPL[{4, 1, 2, 1}, -S^2])/S + (3708*(1 + S^2)*HPL[{4, 2, 1, 1}, -S^2])/S + (6016*(1 + S^2)*HPL[{5, 1, 1, 1}, -S^2])/S + ((-1696*(1 + S^2))/S - (2512*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1, 1}, -S^2] + (6272*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (18816*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (992*(1 + S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/S + (2976*(1 + S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S + (37600*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (5952*(1 + S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/S - (9920*(1 + S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S - (11904*(1 + S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/S - (24800*(1 + S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S - (72128*(1 + S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S + (2720*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - (256*(1 + S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S - (4800*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + ((-46*(1 + S^2))/(3*S) - (23*Pi^2*(1 + S^2))/(3*S))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((1128*(1 + S^2))/S + (1336*Pi^2*(1 + S^2))/(3*S) - (2624*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((400*(1 + S^2))/(3*S) + (826*Pi^2*(1 + S^2))/(9*S) + (2854*Pi^4*(1 + S^2))/(135*S) + (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (2048*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{4, 1}, -S^2]*((-1904*(1 + S^2))/S - (3409*Pi^2*(1 + S^2))/(9*S) - (772*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((-1688*(1 + S^2))/(3*S) - (1015*Pi^2*(1 + S^2))/(9*S) - (72*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((110*(1 + S^2))/(3*S) + (17*Pi^2*(1 + S^2))/(3*S) - (132*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (12*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((328*(1 + S^2))/(3*S) + (185*Pi^2*(1 + S^2))/(9*S) + (278*Pi^4*(1 + S^2))/(135*S) - (226*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (228*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (452*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (70*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((-170*(1 + S^2))/S - (158*Pi^2*(1 + S^2))/(3*S) - (4949*Pi^4*(1 + S^2))/(540*S) + (596*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (74*(1 + S^2)*HPL[{4}, -S^2])/S + (206*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (20*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (124*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (428*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 2, 1}, -S^2]*((-1484*(1 + S^2))/S - (3848*Pi^2*(1 + S^2))/(9*S) + (1168*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-2360*(1 + S^2))/(3*S) - (2204*Pi^2*(1 + S^2))/(9*S) - (4421*Pi^4*(1 + S^2))/(90*S) + (1312*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1, 1}, -S^2]*((-3164*(1 + S^2))/S - (9188*Pi^2*(1 + S^2))/(9*S) + (3696*(1 + S^2)*Zeta[3])/S) + ((494*(1 + S^2))/(3*S) + (359*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2, 1}, -S^2]*((590*(1 + S^2))/S + (1274*Pi^2*(1 + S^2))/(9*S) + (943*Pi^4*(1 + S^2))/(36*S) - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (1460*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (4396*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (496*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (4128*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (6272*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-1864*(1 + S^2))/(3*S) - (1078*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (540*(1 + S^2)*Zeta[5])/S) + Zeta[3]*((120*(1 + S^2))/S + (395*Pi^2*(1 + S^2))/(9*S) + (1039*Pi^4*(1 + S^2))/(180*S) - (352*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((200*(1 + S^2))/S + (149*Pi^2*(1 + S^2))/(3*S) + (1907*Pi^4*(1 + S^2))/(270*S) - (118*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (12*(1 + S^2)*HPL[{5}, -S^2])/S + ((-1796*(1 + S^2))/(3*S) - (1042*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (1948*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (152*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (68*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (3880*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (1616*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (4552*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (2640*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((164*(1 + S^2))/(3*S) + (86*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (40*(1 + S^2)*Zeta[5])/S) + HPL[{2}, -S^2]*((-490*(1 + S^2))/S - (770*Pi^2*(1 + S^2))/(9*S) - (2561*Pi^4*(1 + S^2))/(180*S) - (787*Pi^6*(1 + S^2))/(360*S) - (38*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((382*(1 + S^2))/(3*S) + (157*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + (218*(1 + S^2)*HPL[{5}, -S^2])/(3*S) - (8*(1 + S^2)*HPL[{6}, -S^2])/S + (124*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((2300*(1 + S^2))/(3*S) + (1910*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] - (2150*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2158*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (152*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (596*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((-1528*(1 + S^2))/S - (1276*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] - (824*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (6352*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (156*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (1380*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (4156*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (9088*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (6272*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((856*(1 + S^2))/(3*S) + (179*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (2*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((742*(1 + S^2))/S + (1924*Pi^2*(1 + S^2))/(9*S) - (584*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((280*(1 + S^2))/S + (506*Pi^2*(1 + S^2))/(9*S) - (808*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (36*(1 + S^2)*Zeta[3])/S) + (802*(1 + S^2)*Zeta[5])/(3*S)) + (182*(1 + S^2)*Zeta[7])/S) + HPL[{1}, -S^2]^2*((-490*(1 + S^2))/S - (145*Pi^2*(1 + S^2))/S - (25753*Pi^4*(1 + S^2))/(1080*S) - (53261*Pi^6*(1 + S^2))/(15120*S) - (103*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) - (109*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((142*(1 + S^2))/(3*S) + (82*Pi^2*(1 + S^2))/(9*S))*HPL[{5}, -S^2] - (185*(1 + S^2)*HPL[{6}, -S^2])/(3*S) - (164*(1 + S^2)*HPL[{7}, -S^2])/S + (784*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-1804*(1 + S^2))/(3*S) - (1042*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((-6182*(1 + S^2))/(3*S) - (3527*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1}, -S^2] - (359*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) + (36*(1 + S^2)*HPL[{4, 3}, -S^2])/S - (572*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (76*(1 + S^2)*HPL[{5, 2}, -S^2])/S + (90*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((-1528*(1 + S^2))/S - (1276*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((-3136*(1 + S^2))/S - (3008*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (272*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (1382*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (4240*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S - (272*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (4162*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (12970*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S + (26672*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((848*(1 + S^2))/S + (1256*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] + (496*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + (16*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (4128*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (4128*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (5616*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (17984*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (1360*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (6272*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (18816*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (37760*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (2400*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((580*(1 + S^2))/(3*S) + (49*Pi^2*(1 + S^2))/S + (109*Pi^4*(1 + S^2))/(18*S))*Zeta[3] - (40*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{3, 1}, -S^2]*((98*(1 + S^2))/S + (746*Pi^2*(1 + S^2))/(9*S) - (680*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((1180*(1 + S^2))/(3*S) + (1102*Pi^2*(1 + S^2))/(9*S) + (4421*Pi^4*(1 + S^2))/(180*S) - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (656*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((112*(1 + S^2))/S + (373*Pi^2*(1 + S^2))/(18*S) - (226*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (62*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((820*(1 + S^2))/(3*S) + (535*Pi^2*(1 + S^2))/(9*S) + (419*Pi^4*(1 + S^2))/(54*S) - (34*(1 + S^2)*HPL[{4}, -S^2])/S - (1940*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (660*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (1320*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (56*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-371*(1 + S^2))/(2*S) - (481*Pi^2*(1 + S^2))/(9*S) + (202*(1 + S^2)*HPL[{3}, -S^2])/S + (62*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (146*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-564*(1 + S^2))/S - (668*Pi^2*(1 + S^2))/(3*S) + (1312*(1 + S^2)*Zeta[3])/S) + ((674*(1 + S^2))/(3*S) + (401*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2}, -S^2]*((-295*(1 + S^2))/S - (637*Pi^2*(1 + S^2))/(9*S) - (943*Pi^4*(1 + S^2))/(72*S) + ((898*(1 + S^2))/(3*S) + (521*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + (113*(1 + S^2)*HPL[{4}, -S^2])/S + (66*(1 + S^2)*HPL[{5}, -S^2])/S + ((764*(1 + S^2))/S + (638*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] + (784*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (730*(1 + S^2)*HPL[{3, 2}, -S^2])/S - (2198*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (248*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (2064*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((932*(1 + S^2))/(3*S) + (539*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (270*(1 + S^2)*Zeta[5])/S) + (252*(1 + S^2)*Zeta[7])/S) + HPL[{2}, -S^2]*(-980*S + (Pi^6*(2586 - 20821*S^2))/(7560*S) + (Pi^4*(904 - 9965*S^2))/(540*S) - (20*Pi^2*(-2 + 55*S^2))/(9*S) - (4*(3 + 25*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((2*(-63 + 44*S^2))/(3*S) + (Pi^2*(-5 + 101*S^2))/(9*S))*HPL[{5}, -S^2] - (2*(-19 + 40*S^2)*HPL[{6}, -S^2])/S - (2*(85 + 208*S^2)*HPL[{7}, -S^2])/(3*S) + (4*(-257 + 346*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((Pi^2*(-13 - 1077*S^2))/(9*S) - (2*(27 + 1007*S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((Pi^2*(167 - 3454*S^2))/(9*S) - (2*(-199 + 3187*S^2))/(3*S))*HPL[{4, 1}, -S^2] - (2*(7 + 67*S^2)*HPL[{4, 2}, -S^2])/S + (2*(-49 + 16*S^2)*HPL[{4, 3}, -S^2])/(3*S) - (2*(9 + 835*S^2)*HPL[{5, 1}, -S^2])/(3*S) + (4*(-71 + S^2)*HPL[{5, 2}, -S^2])/(3*S) - (4*(119 + 69*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((8*Pi^2*(-353 + 123*S^2))/(9*S) + (4*(-728 + 451*S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((-4*(-2017 + 314*S^2))/(3*S) - (2*Pi^2*(-4099 + 345*S^2))/(9*S))*HPL[{3, 1, 1}, -S^2] + (78*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S - (10*(175 + 239*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (2*(-129 + 1984*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (160*(-1 + 26*S^2)*HPL[{3, 3, 1}, -S^2])/S - (4*(1538 + 1587*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (2*(-191 + 6172*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) + (2*(-707 + 19108*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (188*(-17 + 417*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((8*(226 + 155*S^2))/S + (8*Pi^2*(703 + 256*S^2))/(9*S))*HPL[{2, 1, 1, 1}, -S^2] + (16*(325 + 242*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + (16*(-2777 + 4435*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (4*(3859 + 843*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (4*(3859 + 843*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (4*(7759 + 3747*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (8*(11863 + 5401*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) - (64*(41 + 57*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (448*(-25 + 17*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) - (448*(-25 + 17*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (32*(-1822 + 1733*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) + (32*(227 + 162*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((80*(-1 + 9*S^2))/(3*S) + (Pi^2*(-12 + 485*S^2))/(9*S) + (Pi^4*(-71 + 1721*S^2))/(270*S))*Zeta[3] + (10*(2 + S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((10*(124 + 65*S^2))/(3*S) + (2*Pi^2*(710 + 239*S^2))/(9*S) + (Pi^4*(8172 + 1853*S^2))/(270*S) + (4*(-571 + 605*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (224*(-25 + 17*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*(-243 + 22*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((4*Pi^2*(-1 + 14*S^2))/(3*S) + (2*(-13 + 147*S^2))/(3*S) - (2*(395 + 56*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-1 + 32*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((40*(-5 + 21*S^2))/(3*S) + (Pi^2*(-91 + 522*S^2))/(9*S) + (Pi^4*(-87 + 1010*S^2))/(135*S) - (4*(-12 + 17*S^2)*HPL[{4}, -S^2])/(3*S) - (2*(1131 + 89*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (20*(7 + 108*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (4*(79 + 1089*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(-19 + 79*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((-8*(215 + 343*S^2))/(3*S) - (4*Pi^2*(249 + 706*S^2))/(9*S) + (32*(-11 + 115*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((4*(267 + 314*S^2))/(3*S) + (Pi^2*(205 + 431*S^2))/(3*S) - (4*(-17 + 157*S^2)*Zeta[3])/S) + ((4*Pi^2*(-11 + 103*S^2))/(9*S) + (2*(-70 + 347*S^2))/(3*S))*Zeta[5] + (2*(-35 + 116*S^2)*Zeta[7])/S) + Log[T]*((490*Pi^2*S)/3 + (8891*Pi^4*S)/270 + (5701*Pi^6*S)/1080 + (135211*Pi^8*S)/136080 + (S*HPL[{0}, S^2]^8)/48 + (32*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) + (8*(1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) + HPL[{0}, S^2]^7*((7*S)/72 + (7*(1 + S^2)*HPL[{1}, -S^2])/(72*S)) + ((136*Pi^2*(-2 + 5*S^2))/(27*S) + (-476 + 703*S^2)/(9*S))*HPL[{2}, -S^2]^3 + ((251 + 334*S^2)*HPL[{2}, -S^2]^4)/(18*S) + HPL[{0}, S^2]^6*((47*S)/72 + (8*Pi^2*S)/27 + (7*(1 + S^2)*HPL[{1}, -S^2])/(12*S) + (41*(1 + S^2)*HPL[{1}, -S^2]^2)/(72*S) + (19*S*HPL[{2}, -S^2])/36) + HPL[{1}, -S^2]^6*((112*(1 + S^2))/(3*S) + (92*Pi^2*(1 + S^2))/(9*S) + (20*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((Pi^2*(-14 + 99*S^2))/(9*S) + (2*(-19 + 101*S^2))/(3*S))*HPL[{3}, -S^2]^2 + (8*(10 + 3*S^2)*HPL[{4}, -S^2]^2)/(3*S) + ((4*Pi^2*(31 + 61*S^2))/(9*S) + (4*(77 + 156*S^2))/(3*S))*HPL[{6}, -S^2] + (8*(70 + 69*S^2)*HPL[{7}, -S^2])/(3*S) + (2*(735 + 1556*S^2)*HPL[{8}, -S^2])/(3*S) + ((-4*(156 + 227*S^2))/S - (4*Pi^2*(254 + 701*S^2))/(9*S))*HPL[{2, 1}, -S^2]^2 + (8*(381 + 344*S^2)*HPL[{3, 1}, -S^2]^2)/(3*S) + ((2*(-9 + 139*S^2))/S + (Pi^2*(-39 + 406*S^2))/(9*S))*HPL[{4, 2}, -S^2] - (8*(3 + 7*S^2)*HPL[{4, 3}, -S^2])/S + ((4*(11 + 787*S^2))/(3*S) + (2*Pi^2*(43 + 787*S^2))/(9*S))*HPL[{5, 1}, -S^2] - (2*(97 + 170*S^2)*HPL[{5, 2}, -S^2])/(3*S) - (4*(1 + 8*S^2)*HPL[{5, 3}, -S^2])/(3*S) + (4*(-206 + 17*S^2)*HPL[{6, 1}, -S^2])/(3*S) - (4*(-18 + 43*S^2)*HPL[{6, 2}, -S^2])/(3*S) - (4*(203 + 562*S^2)*HPL[{7, 1}, -S^2])/(3*S) + (80*(33 + 46*S^2)*HPL[{2, 1, 1}, -S^2]^2)/S + ((-4*(-39 + 41*S^2))/S - (2*Pi^2*(-129 + 119*S^2))/(9*S))*HPL[{3, 1, 2}, -S^2] + ((4*(-835 + 1283*S^2))/(3*S) + (2*Pi^2*(-959 + 2601*S^2))/(9*S))*HPL[{3, 2, 1}, -S^2] - (2*(-124 + 4051*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) - (16*(-85 + 1589*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) + (4*(32 + 335*S^2)*HPL[{3, 3, 2}, -S^2])/(3*S) + ((8*(-1479 + 1787*S^2))/(3*S) + (4*Pi^2*(-1725 + 3767*S^2))/(9*S))*HPL[{4, 1, 1}, -S^2] - (4*(-372 + 6289*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) - (8*(33 + 283*S^2)*HPL[{4, 1, 3}, -S^2])/(3*S) - (4*(-1056 + 19441*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) + (2*(-13 + 474*S^2)*HPL[{4, 2, 2}, -S^2])/(3*S) - (8*(89 + 969*S^2)*HPL[{4, 3, 1}, -S^2])/(3*S) - (88*(-96 + 1813*S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) - (4*(111 + 1171*S^2)*HPL[{5, 1, 2}, -S^2])/(3*S) - (4*(711 + 7951*S^2)*HPL[{5, 2, 1}, -S^2])/(3*S) - (8*(846 + 10055*S^2)*HPL[{6, 1, 1}, -S^2])/(3*S) + (96*(-40 + 27*S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + ((-16*(-598 + 651*S^2))/(3*S) - (16*Pi^2*(-354 + 671*S^2))/(9*S))*HPL[{3, 1, 1, 1}, -S^2] - (8*(-4129 + 842*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) - (8*(-4129 + 842*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) + (4*(131 + 121*S^2)*HPL[{3, 1, 2, 2}, -S^2])/(3*S) - (8*(-8449 + 3758*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) + (4*(131 + 121*S^2)*HPL[{3, 2, 1, 2}, -S^2])/(3*S) - (4*(-2187 + 2527*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(3*S) - (32*(-257 + 331*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S - (32*(-6417 + 2701*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) + (296*(-1 + 11*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(3*S) - (8*(-3047 + 3565*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(3*S) - (8*(-9215 + 11509*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(3*S) - (32*(-4651 + 5533*S^2)*HPL[{5, 1, 1, 1}, -S^2])/(3*S) + ((160*(-94 + 155*S^2))/(3*S) + (80*Pi^2*(-113 + 298*S^2))/(9*S))*HPL[{2, 1, 1, 1, 1}, -S^2] - (128*(57 + 41*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (384*(57 + 41*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (64*(-257 + 331*S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S) - (64*(-257 + 331*S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S - (160*(691 + 713*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) + (32*(-3023 + 3913*S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S) + (32*(-1693 + 2187*S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/S + (32*(-6107 + 7885*S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S) + (32*(-4263 + 5497*S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/S + (64*(-6439 + 8216*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S + (960*(-17 + 11*S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S - (1280*(-11 + 10*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S + (4480*(-5 + 7*S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (-24*S + 2*Pi^2*S)*Zeta[3]^2 + HPL[{0}, S^2]^5*((43*S)/15 + (319*Pi^2*S)/270 + (541*(1 + S^2)*HPL[{1}, -S^2]^2)/(180*S) + (91*(1 + S^2)*HPL[{1}, -S^2]^3)/(45*S) + ((-5 + 162*S^2)*HPL[{2}, -S^2])/(60*S) + HPL[{1}, -S^2]*((139*(1 + S^2))/(45*S) + (427*Pi^2*(1 + S^2))/(360*S) + (461*(1 + S^2)*HPL[{2}, -S^2])/(180*S)) + ((1 - 2*S^2)*HPL[{3}, -S^2])/(12*S) + ((-238 + 25*S^2)*HPL[{2, 1}, -S^2])/(45*S) + (3*S*Zeta[3])/2) + HPL[{1}, -S^2]^4*((880*(1 + S^2))/(3*S) + (706*Pi^2*(1 + S^2))/(9*S) + (1237*Pi^4*(1 + S^2))/(90*S) + ((212*(1 + S^2))/(3*S) + (314*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (392*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (260*(1 + S^2)*HPL[{3}, -S^2])/S - (284*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (340*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (200*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (580*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^5*((340*(1 + S^2))/(3*S) + (278*Pi^2*(1 + S^2))/(9*S) + (68*(1 + S^2)*HPL[{2}, -S^2])/(3*S) - (320*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (40*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (80*(1 + S^2)*Zeta[3])/S) + HPL[{5}, -S^2]*((Pi^2*(79 - 233*S^2))/(9*S) - (14*(-15 + 46*S^2))/(3*S) + (4*(223 + 3*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (8*(-8 + 3*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1, 1}, -S^2]*((16*(-277 + 133*S^2))/S + (16*Pi^2*(-769 + 257*S^2))/(9*S) + (160*(97 + 4*S^2)*Zeta[3])/(3*S)) + HPL[{2, 2, 1}, -S^2]*((8*Pi^2*(713 + 256*S^2))/(9*S) + (8*(683 + 427*S^2))/(3*S) + (32*(-241 + 11*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1}, -S^2]*((16*(341 + 50*S^2))/S + (4*Pi^2*(4275 + 391*S^2))/(9*S) + (16*(-1465 + 13*S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((20*Pi^2*(-8 + 107*S^2))/(9*S) + (4*(-93 + 902*S^2))/(3*S) + (4*(-5 + 41*S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((Pi^2*(-23 - 243*S^2))/(9*S) + (Pi^4*(-121 - 240*S^2))/(108*S) - (2*(-56 + 79*S^2))/(3*S) - (4*(-389 + 42*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(-79 + 382*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(-61 + 383*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(1 + 44*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((40*(-22 + 61*S^2))/S + (8*Pi^2*(-239 + 781*S^2))/(9*S) + (Pi^4*(-4256 + 17677*S^2))/(135*S) - (64*(2 + 119*S^2)*Zeta[3])/(3*S)) + HPL[{4, 1}, -S^2]*((16*(-39 + 743*S^2))/(3*S) + (2*Pi^2*(-136 + 3453*S^2))/(9*S) + (8*(15 + 194*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((5*(80 + 139*S^2))/(3*S) + (Pi^2*(238 + 709*S^2))/(9*S) + (Pi^4*(1726 + 8045*S^2))/(540*S) + ((-61 - 1103*S^2)*HPL[{3}, -S^2])/(3*S) + ((-49 - 388*S^2)*HPL[{4}, -S^2])/(3*S) + (12*(-40 + 27*S^2)*HPL[{2, 1}, -S^2])/S - (2*(-631 + 545*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (8*(-257 + 331*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(-29 + 236*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((Pi^4*(1061 - 3275*S^2))/(54*S) - (20*(-30 + 53*S^2))/S - (2*Pi^2*(-611 + 1435*S^2))/(9*S) - (32*(310 + 283*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (16*(7 + 241*S^2)*Zeta[3])/(3*S)) + HPL[{0}, S^2]^4*((214*S)/9 + (161*Pi^2*S)/27 + (10279*Pi^4*S)/6480 + (94*(1 + S^2)*HPL[{1}, -S^2]^3)/(9*S) + (31*(1 + S^2)*HPL[{1}, -S^2]^4)/(6*S) + ((15 + 268*S^2)/(18*S) + (Pi^2*(-5 + 364*S^2))/(72*S))*HPL[{2}, -S^2] + ((-9 + 460*S^2)*HPL[{2}, -S^2]^2)/(72*S) + HPL[{1}, -S^2]^2*((67*(1 + S^2))/(4*S) + (391*Pi^2*(1 + S^2))/(72*S) + (245*(1 + S^2)*HPL[{2}, -S^2])/(18*S)) + ((15 - 2*S^2)*HPL[{3}, -S^2])/(12*S) + ((5 + 24*S^2)*HPL[{4}, -S^2])/(12*S) + ((-170 + S^2)*HPL[{2, 1}, -S^2])/(6*S) - (5*(-3 + 101*S^2)*HPL[{3, 1}, -S^2])/(18*S) + ((-5 + 174*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (5*S*Zeta[3])/3 + HPL[{1}, -S^2]*((347*(1 + S^2))/(18*S) + (199*Pi^2*(1 + S^2))/(36*S) + (85*(1 + S^2)*HPL[{2}, -S^2])/(6*S) + (2*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (245*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) + (19*(1 + S^2)*Zeta[3])/(9*S))) + (-372*S - 100*Pi^2*S)*Zeta[5] + Zeta[3]*((-860*S)/3 - (862*Pi^2*S)/9 - (3617*Pi^4*S)/270 - (184*S*Zeta[5])/3) + HPL[{0}, S^2]^3*((725*S)/9 + (403*Pi^2*S)/18 + (15977*Pi^4*S)/3240 + (215*(1 + S^2)*HPL[{1}, -S^2]^4)/(9*S) + (86*(1 + S^2)*HPL[{1}, -S^2]^5)/(9*S) + ((-4 + 283*S^2)*HPL[{2}, -S^2]^2)/(9*S) + HPL[{1}, -S^2]^3*((1334*(1 + S^2))/(27*S) + (397*Pi^2*(1 + S^2))/(27*S) + (392*(1 + S^2)*HPL[{2}, -S^2])/(9*S)) + ((Pi^2*(8 - 7*S^2))/(9*S) - (2*(-11 + S^2))/(9*S))*HPL[{3}, -S^2] + ((-14 + 75*S^2)*HPL[{4}, -S^2])/(9*S) - (2*(2 + 5*S^2)*HPL[{5}, -S^2])/(3*S) + ((-4*(309 + 2*S^2))/(9*S) + (Pi^2*(-1082 + 77*S^2))/(27*S))*HPL[{2, 1}, -S^2] - (2*(-7 + 603*S^2)*HPL[{3, 1}, -S^2])/(9*S) - (2*(-16 + 7*S^2)*HPL[{3, 2}, -S^2])/(9*S) - (2*(1 + 2*S^2)*HPL[{4, 1}, -S^2])/(9*S) + (4*(-7 + 606*S^2)*HPL[{2, 1, 1}, -S^2])/(9*S) - (4*(-569 + 9*S^2)*HPL[{2, 2, 1}, -S^2])/(9*S) - (4*(-580 + 13*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) + (8*(-202 + 9*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-2*S)/9 + 5*Pi^2*S)*Zeta[3] + HPL[{1}, -S^2]*((770*(1 + S^2))/(9*S) + (1223*Pi^2*(1 + S^2))/(54*S) + (2002*Pi^4*(1 + S^2))/(405*S) + ((622*(1 + S^2))/(9*S) + (1049*Pi^2*(1 + S^2))/(54*S))*HPL[{2}, -S^2] + (280*(1 + S^2)*HPL[{2}, -S^2]^2)/(9*S) + (34*(1 + S^2)*HPL[{3}, -S^2])/(9*S) + (46*(1 + S^2)*HPL[{4}, -S^2])/(9*S) - (1196*(1 + S^2)*HPL[{2, 1}, -S^2])/(9*S) - (1168*(1 + S^2)*HPL[{3, 1}, -S^2])/(9*S) + (784*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^2*((712*(1 + S^2))/(9*S) + (593*Pi^2*(1 + S^2))/(27*S) + (598*(1 + S^2)*HPL[{2}, -S^2])/(9*S) + (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (392*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (10*(1 + S^2)*Zeta[3])/(9*S)) + HPL[{2}, -S^2]*((2*(2 + 325*S^2))/(9*S) + (Pi^2*(-11 + 546*S^2))/(27*S) + (8*(-2 + S^2)*HPL[{3}, -S^2])/(9*S) + (2*(-569 + 9*S^2)*HPL[{2, 1}, -S^2])/(9*S) - (2*(-3 + 5*S^2)*Zeta[3])/(9*S)) + (208*S*Zeta[5])/9) + HPL[{1}, -S^2]^2*((980*(1 + S^2))/S + (2350*Pi^2*(1 + S^2))/(9*S) + (1579*Pi^4*(1 + S^2))/(36*S) + (17153*Pi^6*(1 + S^2))/(2520*S) + ((382*(1 + S^2))/S + (319*Pi^2*(1 + S^2))/(3*S))*HPL[{2}, -S^2]^2 + (62*(1 + S^2)*HPL[{2}, -S^2]^3)/(3*S) + (74*(1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-794*(1 + S^2))/(3*S) - (401*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] - (104*(1 + S^2)*HPL[{5}, -S^2])/S + (70*(1 + S^2)*HPL[{6}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-80*(1 + S^2))/S - (152*Pi^2*(1 + S^2))/S)*HPL[{3, 1}, -S^2] + (1296*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (4432*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (234*(1 + S^2)*HPL[{4, 2}, -S^2])/S + (1168*(1 + S^2)*HPL[{5, 1}, -S^2])/S + ((848*(1 + S^2))/S + (1256*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (6288*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (496*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (352*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (1360*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (128*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (2400*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-472*(1 + S^2))/S - (106*Pi^2*(1 + S^2))/S)*Zeta[3] + (40*(1 + S^2)*Zeta[3]^2)/S + HPL[{2}, -S^2]*((1180*(1 + S^2))/(3*S) + (1102*Pi^2*(1 + S^2))/(9*S) + (4421*Pi^4*(1 + S^2))/(180*S) - (1940*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (226*(1 + S^2)*HPL[{4}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (656*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-644*(1 + S^2))/S - (1178*Pi^2*(1 + S^2))/(9*S) + (1320*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (96*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1}, -S^2]*((-564*(1 + S^2))/S - (668*Pi^2*(1 + S^2))/(3*S) + (1312*(1 + S^2)*Zeta[3])/S) - (496*(1 + S^2)*Zeta[5])/S) + HPL[{1}, -S^2]^3*((620*(1 + S^2))/S + (488*Pi^2*(1 + S^2))/(3*S) + (3773*Pi^4*(1 + S^2))/(135*S) + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((-1448*(1 + S^2))/(3*S) - (820*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (184*(1 + S^2)*HPL[{4}, -S^2])/S - (248*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-848*(1 + S^2))/(3*S) - (1256*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (880*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (9056*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (1360*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (6272*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (12416*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (800*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-1072*(1 + S^2))/(3*S) - (220*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((188*(1 + S^2))/S + (668*Pi^2*(1 + S^2))/(9*S) - (440*(1 + S^2)*HPL[{3}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (1312*(1 + S^2)*Zeta[3])/(3*S)) - (1072*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((Pi^4*(522 - 8221*S^2))/(540*S) - (10*(-28 + 177*S^2))/(3*S) - (4*Pi^2*(-15 + 251*S^2))/(9*S) + (2*(17 + 94*S^2)*HPL[{4}, -S^2])/(3*S) - (4*(39 + 10*S^2)*HPL[{5}, -S^2])/(3*S) + ((-4*(-355 + 47*S^2))/S - (2*Pi^2*(-1179 + 89*S^2))/(9*S))*HPL[{2, 1}, -S^2] + (4*(-175 + 1089*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(11 + 225*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (8*(-45 + 46*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (16*(-79 + 548*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(1133 + 123*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (40*(685 + 31*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (32*(-189 + 16*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-10*Pi^2*(5 + 11*S^2))/(9*S) - (4*(11 + 75*S^2))/(3*S))*Zeta[3] - (4*(13 + 3*S^2)*Zeta[5])/(3*S)) + HPL[{2, 1}, -S^2]*((20*(-221 + 43*S^2))/(3*S) + (4*Pi^2*(-832 + 189*S^2))/(9*S) + (Pi^4*(-17935 + 3716*S^2))/(270*S) + (16*(281 + 305*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(2149 + 129*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (16*(-1730 + 7*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (64*(57 + 41*S^2)*HPL[{2, 1, 1}, -S^2])/S + (32*(-257 + 331*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (32*(-68 + 315*S^2)*HPL[{3, 1, 1}, -S^2])/S - (160*(33 + 46*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((16*(77 + 2*S^2))/S + (4*Pi^2*(535 + 21*S^2))/(9*S))*Zeta[3] - (8*(-419 + 12*S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*(980*S + (10*Pi^2*(-26 + 183*S^2))/(9*S) + (Pi^4*(-3056 + 18663*S^2))/(540*S) + (Pi^6*(-10321 + 64644*S^2))/(11340*S) + (2*(1 + 112*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(21 - 122*S^2))/(3*S) - (2*(-69 + 377*S^2))/(3*S))*HPL[{4}, -S^2] - (2*(19 + 189*S^2)*HPL[{5}, -S^2])/(3*S) + (4*(6 + 11*S^2)*HPL[{6}, -S^2])/S - (8*(-257 + 331*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((-4*(589 + 562*S^2))/(3*S) - (2*Pi^2*(635 + 1271*S^2))/(9*S))*HPL[{3, 1}, -S^2] + (2*(5 + 2089*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(-206 + 3351*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (6*(5 + 44*S^2)*HPL[{4, 2}, -S^2])/S + (4*(-33 + 877*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((8*(156 + 227*S^2))/S + (8*Pi^2*(254 + 701*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] - (48*(-40 + 27*S^2)*HPL[{2, 2, 1}, -S^2])/S + (16*(-1001 + 181*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (156*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/S + (4*(887 + 1219*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (8*(1567 + 1621*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (64*(57 + 41*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (32*(-2774 + 4255*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (160*(33 + 46*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-8*(1 + 210*S^2))/(3*S) - (2*Pi^2*(8 + 521*S^2))/(9*S))*Zeta[3] + (4*(-8 + 21*S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((-4*Pi^2*(713 + 256*S^2))/(9*S) - (4*(683 + 427*S^2))/(3*S) - (16*(-241 + 11*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-49*Pi^2*(-3 + 23*S^2))/(9*S) - (4*(-77 + 479*S^2))/(3*S) + (4*(1133 + 123*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(-9 + 65*S^2)*Zeta[3])/(3*S)) - (4*(-2 + 405*S^2)*Zeta[5])/(3*S)) + HPL[{0}, S^2]^2*(490*S + (1771*Pi^2*S)/18 + (8693*Pi^4*S)/540 + (147719*Pi^6*S)/45360 + (110*(1 + S^2)*HPL[{1}, -S^2]^5)/(3*S) + (12*(1 + S^2)*HPL[{1}, -S^2]^6)/S + ((Pi^2*(1 + 293*S^2))/(9*S) + (8 + 737*S^2)/(6*S))*HPL[{2}, -S^2]^2 + ((-15 + 349*S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{1}, -S^2]^4*((286*(1 + S^2))/(3*S) + (76*Pi^2*(1 + S^2))/(3*S) + (239*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-1 - 8*S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((28 + 79*S^2)/(3*S) + (Pi^2*(6 + 113*S^2))/(18*S))*HPL[{4}, -S^2] + ((49 - 18*S^2)*HPL[{5}, -S^2])/(3*S) + ((70 + 129*S^2)*HPL[{6}, -S^2])/(3*S) - (2*(13 + 712*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((Pi^2*(63 - 1247*S^2))/(9*S) - (2*(-13 + 784*S^2))/(3*S))*HPL[{3, 1}, -S^2] + ((31 + 66*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (2*(-10 + 107*S^2)*HPL[{4, 1}, -S^2])/(3*S) + ((-2 - S^2)*HPL[{4, 2}, -S^2])/(3*S) - (14*(1 + 9*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((4*(-8 + 787*S^2))/(3*S) + (2*Pi^2*(-55 + 1277*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (8*(371 + 10*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (8*(1129 + 10*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (2*(-7 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (2*(-53 + 1395*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (4*(-99 + 2135*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (8*(-773 + 19*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) - (16*(-24 + 371*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) + (80*(-8 + 151*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + ((-64*S)/3 - (19*Pi^2*S)/9)*Zeta[3] + 10*S*Zeta[3]^2 + HPL[{2}, -S^2]*((5*(14 + 183*S^2))/(3*S) + (Pi^2*(22 + 1323*S^2))/(18*S) + (Pi^4*(-490 + 15307*S^2))/(1080*S) + ((-11 - 31*S^2)*HPL[{3}, -S^2])/(3*S) + ((2 + 17*S^2)*HPL[{4}, -S^2])/(3*S) - (4*(371 + 10*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (10*(1 + 47*S^2)*HPL[{3, 1}, -S^2])/S + (4*(13 + 712*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - 30*S*Zeta[3]) + HPL[{1}, -S^2]^2*((1030*(1 + S^2))/(3*S) + (487*Pi^2*(1 + S^2))/(6*S) + (3299*Pi^4*(1 + S^2))/(216*S) + ((784*(1 + S^2))/(3*S) + (1207*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2] + (123*(1 + S^2)*HPL[{2}, -S^2]^2)/S - (8*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (25*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (498*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (472*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (956*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (28*(1 + S^2)*Zeta[3])/S) + HPL[{1}, -S^2]^3*((614*(1 + S^2))/(3*S) + (463*Pi^2*(1 + S^2))/(9*S) + (166*(1 + S^2)*HPL[{2}, -S^2])/S - (20*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (956*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) - (20*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((Pi^2*(77 - 46*S^2))/(18*S) + (63 - 23*S^2)/(3*S) + (2*(45 + 7*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (4*(3 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-14*(119 + 3*S^2))/(3*S) + (Pi^2*(-1283 + 22*S^2))/(9*S) + (4*(50 + S^2)*Zeta[3])/(3*S)) - 4*S*Zeta[5] + HPL[{1}, -S^2]*((405*(1 + S^2))/S + (1615*Pi^2*(1 + S^2))/(18*S) + (5627*Pi^4*(1 + S^2))/(360*S) + (374*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((Pi^2*(-1 - S^2))/(3*S) + (16*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (41*(1 + S^2)*HPL[{4}, -S^2])/(3*S) + (22*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-1568*(1 + S^2))/(3*S) - (1207*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] - (1480*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (104*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (262*(1 + S^2)*HPL[{4, 1}, -S^2])/(3*S) + (996*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (984*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (2912*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (1912*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-26*(1 + S^2))/S - (7*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((851*(1 + S^2))/(3*S) + (419*Pi^2*(1 + S^2))/(6*S) - (52*(1 + S^2)*HPL[{3}, -S^2])/(3*S) - (492*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (94*(1 + S^2)*Zeta[3])/(3*S)) + (2*(1 + S^2)*Zeta[5])/(3*S))) + HPL[{0}, S^2]*(980*S + (2120*Pi^2*S)/9 + (7037*Pi^4*S)/180 + (2425*Pi^6*S)/378 + (112*(1 + S^2)*HPL[{1}, -S^2]^6)/(3*S) + (32*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) + (2*(-43 + 560*S^2)*HPL[{2}, -S^2]^3)/(9*S) + HPL[{1}, -S^2]^5*((112*(1 + S^2))/S + (254*Pi^2*(1 + S^2))/(9*S) + (100*(1 + S^2)*HPL[{2}, -S^2])/S) - (26*S*HPL[{3}, -S^2]^2)/3 + ((-2*Pi^2*(-3 + 2*S^2))/(3*S) - (8*(-7 + 6*S^2))/(3*S))*HPL[{5}, -S^2] + (2*(-10 + 133*S^2)*HPL[{6}, -S^2])/(3*S) - (2*(25 + 32*S^2)*HPL[{7}, -S^2])/S - (32*(2 + 143*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((Pi^2*(85 + 143*S^2))/(9*S) + (2*(41 + 179*S^2))/(3*S))*HPL[{3, 2}, -S^2] + ((14*Pi^2*(-1 + 34*S^2))/(9*S) + (4*(-21 + 275*S^2))/(3*S))*HPL[{4, 1}, -S^2] + (2*(1 + 22*S^2)*HPL[{4, 2}, -S^2])/(3*S) + (8*(-14 + 11*S^2)*HPL[{4, 3}, -S^2])/(3*S) - (4*(-1 + 50*S^2)*HPL[{5, 1}, -S^2])/(3*S) + (4*(-80 + 59*S^2)*HPL[{5, 2}, -S^2])/(3*S) + (8*(-86 + 57*S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((8*(1136 + 23*S^2))/(3*S) + (4*Pi^2*(1728 + 25*S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((-8*(-3459 + 16*S^2))/(3*S) - (4*Pi^2*(-5267 + 22*S^2))/(9*S))*HPL[{3, 1, 1}, -S^2] + (4*(10 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (36*(-6 + 83*S^2)*HPL[{3, 2, 1}, -S^2])/S - (2*(-45 + 421*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) - (32*(1 + 73*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) + (8*(-255 + 3424*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) - (20*(3 + 116*S^2)*HPL[{4, 1, 2}, -S^2])/(3*S) - (4*(87 + 1696*S^2)*HPL[{4, 2, 1}, -S^2])/(3*S) - (16*(13 + 276*S^2)*HPL[{5, 1, 1}, -S^2])/S + ((80*(-238 + 11*S^2))/(3*S) + (8*Pi^2*(-602 + 29*S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] + (32*(-569 + 19*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) - (16*(-85 + 1177*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (8*(-6881 + 71*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) - (8*(-6881 + 71*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) - (8*(-13709 + 299*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) - (32*(-3413 + 74*S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (160*(-5 + 79*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (32*(1159 + 34*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) - (32*(1159 + 34*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (160*(383 + 17*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (1280*(-20 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (-160*S - (250*Pi^2*S)/9)*Zeta[3] + 32*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((1760*(1 + S^2))/(3*S) + (3854*Pi^2*(1 + S^2))/(27*S) + (3374*Pi^4*(1 + S^2))/(135*S) + ((1496*(1 + S^2))/(3*S) + (1142*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2] + (784*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) - (24*(1 + S^2)*HPL[{3}, -S^2])/S + (28*(1 + S^2)*HPL[{4}, -S^2])/S - (1000*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (2992*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (328*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{1}, -S^2]^4*((850*(1 + S^2))/(3*S) + (635*Pi^2*(1 + S^2))/(9*S) + (250*(1 + S^2)*HPL[{2}, -S^2])/S - (12*(1 + S^2)*HPL[{3}, -S^2])/S - (500*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (164*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((20*(-242 + 7*S^2))/(3*S) + (2*Pi^2*(-1808 + 51*S^2))/(9*S) + (8*Pi^4*(-1171 + 78*S^2))/(135*S) + (8*(1159 + 37*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (16*(1159 + 34*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (8*(121 + 4*S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((Pi^4*(985 - 869*S^2))/(540*S) + (Pi^2*(73 - 87*S^2))/(9*S) - (20*(-7 + 8*S^2))/(3*S) - (8*(-7 + 5*S^2)*HPL[{4}, -S^2])/(3*S) + (28*(5 + S^2)*HPL[{2, 1}, -S^2])/S + (4*(19 + 79*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(7 + 25*S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(-1 + 5*S^2)*Zeta[3])/(3*S)) + HPL[{4}, -S^2]*((Pi^2*(-11 + 139*S^2))/(9*S) + (2*(27 + 149*S^2))/(3*S) + (28*(-4 + 5*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (4*(16 + 7*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((2*(1 + 183*S^2))/S + (Pi^2*(4 + 855*S^2))/(9*S) + ((7 - 107*S^2)*HPL[{3}, -S^2])/(3*S) + (4*(-569 + 19*S^2)*HPL[{2, 1}, -S^2])/(3*S) - (2*(-2 + 39*S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-8*Pi^2*(-23 + 445*S^2))/(9*S) - (8*(-22 + 595*S^2))/(3*S) + (8*(-7 + 118*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((16*(-9 + 196*S^2))/S + (4*Pi^2*(-82 + 1791*S^2))/(9*S) - (16*(-1 + 122*S^2)*Zeta[3])/(3*S)) - (316*S*Zeta[5])/3 + HPL[{1}, -S^2]^2*((930*(1 + S^2))/S + (1987*Pi^2*(1 + S^2))/(9*S) + (20233*Pi^4*(1 + S^2))/(540*S) + (392*(1 + S^2)*HPL[{2}, -S^2]^2)/S + ((-56*(1 + S^2))/(3*S) - (10*Pi^2*(1 + S^2))/(3*S))*HPL[{3}, -S^2] + (38*(1 + S^2)*HPL[{4}, -S^2])/S + (116*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((-1496*(1 + S^2))/S - (1142*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (1496*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (152*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (372*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (3000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (9264*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (6000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-508*(1 + S^2))/(3*S) - (256*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((754*(1 + S^2))/S + (1723*Pi^2*(1 + S^2))/(9*S) - (76*(1 + S^2)*HPL[{3}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (164*(1 + S^2)*Zeta[3])/S) - (368*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{1}, -S^2]*((980*(1 + S^2))/S + (2090*Pi^2*(1 + S^2))/(9*S) + (10393*Pi^4*(1 + S^2))/(270*S) + (2425*Pi^6*(1 + S^2))/(378*S) + ((382*(1 + S^2))/S + (868*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2]^2 + (118*(1 + S^2)*HPL[{2}, -S^2]^3)/S - (10*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((170*(1 + S^2))/(3*S) + (109*Pi^2*(1 + S^2))/(9*S))*HPL[{4}, -S^2] + (36*(1 + S^2)*HPL[{5}, -S^2])/S + (164*(1 + S^2)*HPL[{6}, -S^2])/(3*S) - (1568*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-4472*(1 + S^2))/(3*S) - (3412*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] + (464*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) + (380*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (2*(1 + S^2)*HPL[{4, 2}, -S^2])/S - (256*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((2992*(1 + S^2))/S + (2284*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] + (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (9264*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (2832*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S + (8664*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (6000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S - (5984*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (12000*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((-180*(1 + S^2))/S - (86*Pi^2*(1 + S^2))/(3*S))*Zeta[3] + (32*(1 + S^2)*Zeta[3]^2)/S + HPL[{2}, -S^2]*((780*(1 + S^2))/S + (1744*Pi^2*(1 + S^2))/(9*S) + (8953*Pi^4*(1 + S^2))/(270*S) - (76*(1 + S^2)*HPL[{3}, -S^2])/S + (6*(1 + S^2)*HPL[{4}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (164*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((8*(1 + S^2))/S - (20*Pi^2*(1 + S^2))/(9*S) + (152*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (16*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-1508*(1 + S^2))/S - (3446*Pi^2*(1 + S^2))/(9*S) + (328*(1 + S^2)*Zeta[3])/S) - (364*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*((80*(-1 + 32*S^2))/(3*S) + (2*Pi^2*(-25 + 913*S^2))/(9*S) + (Pi^4*(-660 + 18769*S^2))/(540*S) + ((Pi^2*(-37 - 67*S^2))/(9*S) - (2*(15 + 91*S^2))/(3*S))*HPL[{3}, -S^2] + (2*(-4 + 17*S^2)*HPL[{4}, -S^2])/(3*S) + (4*(-17 + 12*S^2)*HPL[{5}, -S^2])/(3*S) + ((-4*(1136 + 23*S^2))/(3*S) - (2*Pi^2*(1728 + 25*S^2))/(9*S))*HPL[{2, 1}, -S^2] - (4*(19 + 1141*S^2)*HPL[{3, 1}, -S^2])/(3*S) + (2*(-5 + 71*S^2)*HPL[{3, 2}, -S^2])/S + (4*(7 + 286*S^2)*HPL[{4, 1}, -S^2])/(3*S) + (64*(2 + 143*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (16*(-569 + 19*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (8*(-1145 + 13*S^2)*HPL[{3, 1, 1}, -S^2])/S - (16*(1159 + 34*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-4*(2 + 117*S^2))/(3*S) - (2*Pi^2*(-4 + 127*S^2))/(9*S))*Zeta[3] - (16*(-3 + 20*S^2)*Zeta[5])/(3*S))) - 604*S*Zeta[7] + HPL[{1}, -S^2]*((980*(1 + S^2))/S + (290*Pi^2*(1 + S^2))/S + (25753*Pi^4*(1 + S^2))/(540*S) + (53261*Pi^6*(1 + S^2))/(7560*S) + (206*(1 + S^2)*HPL[{2}, -S^2]^3)/(9*S) + (218*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-284*(1 + S^2))/(3*S) - (164*Pi^2*(1 + S^2))/(9*S))*HPL[{5}, -S^2] + (370*(1 + S^2)*HPL[{6}, -S^2])/(3*S) + (328*(1 + S^2)*HPL[{7}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((3608*(1 + S^2))/(3*S) + (2084*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((12364*(1 + S^2))/(3*S) + (7054*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1}, -S^2] + (718*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) - (72*(1 + S^2)*HPL[{4, 3}, -S^2])/S + (1144*(1 + S^2)*HPL[{5, 1}, -S^2])/S - (152*(1 + S^2)*HPL[{5, 2}, -S^2])/S - (180*(1 + S^2)*HPL[{6, 1}, -S^2])/S + ((3056*(1 + S^2))/S + (2552*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((6272*(1 + S^2))/S + (6016*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] - (16*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (544*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (2764*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S - (8480*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/S + (544*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S - (8324*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S - (25940*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S - (53344*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/S + ((-1696*(1 + S^2))/S - (2512*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] - (992*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S - (32*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S + (8256*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S + (8256*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S + (11232*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S + (35968*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S + (2720*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S - (12544*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S - (37632*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S - (75520*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S - (4800*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((-1160*(1 + S^2))/(3*S) - (98*Pi^2*(1 + S^2))/S - (109*Pi^4*(1 + S^2))/(9*S))*Zeta[3] + (80*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1, 1}, -S^2]*((1128*(1 + S^2))/S + (1336*Pi^2*(1 + S^2))/(3*S) - (2624*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((371*(1 + S^2))/S + (962*Pi^2*(1 + S^2))/(9*S) - (404*(1 + S^2)*HPL[{3}, -S^2])/S - (124*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (292*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-1640*(1 + S^2))/(3*S) - (1070*Pi^2*(1 + S^2))/(9*S) - (419*Pi^4*(1 + S^2))/(27*S) + (68*(1 + S^2)*HPL[{4}, -S^2])/S + (3880*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (1320*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (2640*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (112*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-224*(1 + S^2))/S - (373*Pi^2*(1 + S^2))/(9*S) + (452*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (124*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((-2360*(1 + S^2))/(3*S) - (2204*Pi^2*(1 + S^2))/(9*S) - (4421*Pi^4*(1 + S^2))/(90*S) + (3136*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (6272*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (1312*(1 + S^2)*Zeta[3])/S) + HPL[{3, 1}, -S^2]*((-196*(1 + S^2))/S - (1492*Pi^2*(1 + S^2))/(9*S) + (1360*(1 + S^2)*Zeta[3])/S) + ((-1348*(1 + S^2))/(3*S) - (802*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2}, -S^2]*((590*(1 + S^2))/S + (1274*Pi^2*(1 + S^2))/(9*S) + (943*Pi^4*(1 + S^2))/(36*S) + ((-1796*(1 + S^2))/(3*S) - (1042*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (226*(1 + S^2)*HPL[{4}, -S^2])/S - (132*(1 + S^2)*HPL[{5}, -S^2])/S + ((-1528*(1 + S^2))/S - (1276*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1}, -S^2] - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S + (1460*(1 + S^2)*HPL[{3, 2}, -S^2])/S + (4396*(1 + S^2)*HPL[{4, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (496*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (4128*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (6272*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((-1864*(1 + S^2))/(3*S) - (1078*Pi^2*(1 + S^2))/(9*S))*Zeta[3] - (540*(1 + S^2)*Zeta[5])/S) - (504*(1 + S^2)*Zeta[7])/S)) + HPL[{0}, S^2]*((-245*Pi^2*S)/3 - (1829*Pi^4*S)/108 - (122389*Pi^6*S)/45360 - (135211*Pi^8*S)/272160 - (16*(1 + S^2)*HPL[{1}, -S^2]^7)/(3*S) - (4*(1 + S^2)*HPL[{1}, -S^2]^8)/(3*S) + ((80 - 1099*S^2)/(18*S) - (2*Pi^2*(-11 + 205*S^2))/(27*S))*HPL[{2}, -S^2]^3 + ((-5 - 182*S^2)*HPL[{2}, -S^2]^4)/(12*S) + HPL[{1}, -S^2]^6*((-56*(1 + S^2))/(3*S) - (127*Pi^2*(1 + S^2))/(27*S) - (50*(1 + S^2)*HPL[{2}, -S^2])/(3*S)) + ((-7 - S^2)/S + (7*Pi^2*(-1 + 6*S^2))/(18*S))*HPL[{3}, -S^2]^2 + ((13 - 36*S^2)*HPL[{4}, -S^2]^2)/(3*S) + ((Pi^2*(-70 - 109*S^2))/(9*S) - (2*(45 + 73*S^2))/S)*HPL[{6}, -S^2] + (2*(-50 + 89*S^2)*HPL[{7}, -S^2])/S + ((-105 - 52*S^2)*HPL[{8}, -S^2])/S + ((2*(10 + 1123*S^2))/(3*S) + (Pi^2*(8 + 1711*S^2))/(9*S))*HPL[{2, 1}, -S^2]^2 - (8*(4 + 283*S^2)*HPL[{3, 1}, -S^2]^2)/(3*S) + ((-9 - 37*S^2)/(3*S) + (Pi^2*(1 + 12*S^2))/(18*S))*HPL[{4, 2}, -S^2] + (2*(-35 + 41*S^2)*HPL[{4, 3}, -S^2])/(3*S) + ((4*Pi^2*(6 + 49*S^2))/(9*S) + (4*(37 + 65*S^2))/(3*S))*HPL[{5, 1}, -S^2] + ((-225 + 232*S^2)*HPL[{5, 2}, -S^2])/(3*S) + (14*S*HPL[{5, 3}, -S^2])/3 + (2*(-118 + 99*S^2)*HPL[{6, 1}, -S^2])/(3*S) + (2*(-1 + 14*S^2)*HPL[{6, 2}, -S^2])/(3*S) + (2*(63 + 146*S^2)*HPL[{7, 1}, -S^2])/(3*S) - (8*(17 + 1142*S^2)*HPL[{2, 1, 1}, -S^2]^2)/(3*S) + ((Pi^2*(-11 - 9*S^2))/(9*S) + (2*(-3 + 11*S^2))/(3*S))*HPL[{3, 1, 2}, -S^2] + ((-11*Pi^2*(-15 + 299*S^2))/(9*S) - (2*(-157 + 2187*S^2))/(3*S))*HPL[{3, 2, 1}, -S^2] + (5*(-16 + 83*S^2)*HPL[{3, 2, 2}, -S^2])/(3*S) + (16*(-9 + 76*S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) + (2*(-19 + 2*S^2)*HPL[{3, 3, 2}, -S^2])/(3*S) + ((-4*(-221 + 3384*S^2))/(3*S) - (2*Pi^2*(-273 + 5066*S^2))/(9*S))*HPL[{4, 1, 1}, -S^2] + (2*(-21 + 202*S^2)*HPL[{4, 1, 2}, -S^2])/S - (4*(-19 + 4*S^2)*HPL[{4, 1, 3}, -S^2])/(3*S) + (2*(-61 + 598*S^2)*HPL[{4, 2, 1}, -S^2])/S + ((-29 + 12*S^2)*HPL[{4, 2, 2}, -S^2])/(3*S) + (164*HPL[{4, 3, 1}, -S^2])/(3*S) + (4*(-73 + 596*S^2)*HPL[{5, 1, 1}, -S^2])/S + (4*(24 + S^2)*HPL[{5, 1, 2}, -S^2])/(3*S) + (4*(174 + S^2)*HPL[{5, 2, 1}, -S^2])/(3*S) - (8*(-215 + 58*S^2)*HPL[{6, 1, 1}, -S^2])/(3*S) - (16*(-574 + 29*S^2)*HPL[{2, 2, 2, 1}, -S^2])/(3*S) + ((28*Pi^2*(-15 + 254*S^2))/(9*S) + (8*(-69 + 1180*S^2))/(3*S))*HPL[{3, 1, 1, 1}, -S^2] + (4*(-6920 + 157*S^2)*HPL[{3, 1, 1, 2}, -S^2])/(3*S) + (4*(-6920 + 157*S^2)*HPL[{3, 1, 2, 1}, -S^2])/(3*S) - (10*(3 + S^2)*HPL[{3, 1, 2, 2}, -S^2])/(3*S) + (4*(-13808 + 505*S^2)*HPL[{3, 2, 1, 1}, -S^2])/(3*S) - (10*(3 + S^2)*HPL[{3, 2, 1, 2}, -S^2])/(3*S) + (2*(-303 + 4411*S^2)*HPL[{3, 2, 2, 1}, -S^2])/(3*S) + (192*(-3 + 46*S^2)*HPL[{3, 3, 1, 1}, -S^2])/S + (8*(-20637 + 758*S^2)*HPL[{4, 1, 1, 1}, -S^2])/(3*S) + (4*(1 + 8*S^2)*HPL[{4, 1, 1, 2}, -S^2])/(3*S) + (4*(-431 + 6632*S^2)*HPL[{4, 1, 2, 1}, -S^2])/(3*S) + (140*(-37 + 568*S^2)*HPL[{4, 2, 1, 1}, -S^2])/(3*S) + (16*(-216 + 3329*S^2)*HPL[{5, 1, 1, 1}, -S^2])/S + ((-8*Pi^2*(-31 + 600*S^2))/(3*S) - (16*(-68 + 1177*S^2))/(3*S))*HPL[{2, 1, 1, 1, 1}, -S^2] + (128*(145 + 4*S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S) + (128*(145 + 4*S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (64*(-19 + 275*S^2)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S) + (64*(-19 + 275*S^2)*HPL[{2, 2, 2, 1, 1}, -S^2])/S + (16*(5753 + 247*S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S) - (8*(-901 + 13207*S^2)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S) - (8*(-1509 + 22007*S^2)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S) - (8*(-1813 + 26407*S^2)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S) - (8*(-3789 + 55007*S^2)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S) - (32*(-951 + 13763*S^2)*HPL[{4, 1, 1, 1, 1}, -S^2])/S - (640*(-20 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + (32*(-29 + 391*S^2)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S - (320*(-5 + 79*S^2)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S + (6*S - Pi^2*S)*Zeta[3]^2 + HPL[{1}, -S^2]^5*((-170*(1 + S^2))/(3*S) - (127*Pi^2*(1 + S^2))/(9*S) - (50*(1 + S^2)*HPL[{2}, -S^2])/S + (12*(1 + S^2)*HPL[{3}, -S^2])/(5*S) + (100*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (164*(1 + S^2)*Zeta[3])/(15*S)) + HPL[{1}, -S^2]^4*((-440*(1 + S^2))/(3*S) - (1927*Pi^2*(1 + S^2))/(54*S) - (1687*Pi^4*(1 + S^2))/(270*S) + ((-374*(1 + S^2))/(3*S) - (571*Pi^2*(1 + S^2))/(18*S))*HPL[{2}, -S^2] - (196*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + (6*(1 + S^2)*HPL[{3}, -S^2])/S - (7*(1 + S^2)*HPL[{4}, -S^2])/S + (250*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (748*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (500*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (82*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 2, 1}, -S^2]*((-4*(369 + 5*S^2))/S - (4*Pi^2*(865 + 14*S^2))/(9*S) + (8*(42 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1, 1}, -S^2]*((-40*(-79 + 3*S^2))/S - (4*Pi^2*(-1805 + 68*S^2))/(9*S) - (16*(124 + S^2)*Zeta[3])/(3*S)) + HPL[{3, 2}, -S^2]*((Pi^2*(-15 - 109*S^2))/(9*S) - (2*(-11 + 130*S^2))/(3*S) - (6*(1 + 3*S^2)*Zeta[3])/S) + HPL[{4, 1}, -S^2]*((Pi^2*(29 - 119*S^2))/(3*S) - (2*(-147 + 419*S^2))/(3*S) - (12*(2 + 3*S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((Pi^4*(-387 - 2552*S^2))/(1080*S) + (Pi^2*(-59 - 229*S^2))/(18*S) - (15*(4 + 9*S^2))/S - (14*(-1 + 2*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(-17 + 40*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (4*(-19 + 44*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (8*(-4 + 11*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1, 1}, -S^2]*((4*Pi^2*(-2635 + 3*S^2))/(9*S) + (4*(-3383 + 35*S^2))/(3*S) + (8*(383 + 12*S^2)*Zeta[3])/(3*S)) + HPL[{5}, -S^2]*((Pi^2*(-119 + 127*S^2))/(18*S) + (-225 + 182*S^2)/(3*S) - (116*S*HPL[{2, 1}, -S^2])/3 - (2*(-17 + 37*S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]^2*((Pi^4*(90 - 8743*S^2))/(1080*S) - (5*Pi^2*(-1 + 84*S^2))/(9*S) - (5*(-8 + 211*S^2))/(6*S) + ((-13 + 109*S^2)*HPL[{3}, -S^2])/(6*S) + ((13 + 4*S^2)*HPL[{4}, -S^2])/(6*S) - (2*(-574 + 29*S^2)*HPL[{2, 1}, -S^2])/(3*S) + ((-73 + 1103*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (8*(-19 + 275*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) + (2*(-2 + 59*S^2)*Zeta[3])/(3*S)) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(415 - 9577*S^2))/(135*S) - (20*(-8 + 241*S^2))/(3*S) - (2*Pi^2*(-64 + 1795*S^2))/(9*S) + (8*(2 + 119*S^2)*Zeta[3])/(3*S)) + HPL[{3, 1}, -S^2]*((10*(2 + 85*S^2))/S + (Pi^2*(-43 + 1817*S^2))/(9*S) + (Pi^4*(-789 + 18731*S^2))/(540*S) + (136*(1 + 67*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (4*(3 + 119*S^2)*Zeta[3])/(3*S)) + ((232*S)/3 + 13*Pi^2*S)*Zeta[5] + Zeta[3]*((310*S)/3 + 18*Pi^2*S + (137*Pi^4*S)/90 + (92*S*Zeta[5])/3) + HPL[{1}, -S^2]^3*((-310*(1 + S^2))/S - (1987*Pi^2*(1 + S^2))/(27*S) - (20233*Pi^4*(1 + S^2))/(1620*S) - (392*(1 + S^2)*HPL[{2}, -S^2]^2)/(3*S) + ((56*(1 + S^2))/(9*S) + (10*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] - (38*(1 + S^2)*HPL[{4}, -S^2])/(3*S) - (116*(1 + S^2)*HPL[{5}, -S^2])/(9*S) + ((1496*(1 + S^2))/(3*S) + (1142*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (1496*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) - (152*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (124*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (1000*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (3088*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (2000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((508*(1 + S^2))/(9*S) + (256*Pi^2*(1 + S^2))/(27*S))*Zeta[3] + HPL[{2}, -S^2]*((-754*(1 + S^2))/(3*S) - (1723*Pi^2*(1 + S^2))/(27*S) + (76*(1 + S^2)*HPL[{3}, -S^2])/(3*S) + (1568*(1 + S^2)*HPL[{2, 1}, -S^2])/(3*S) + (164*(1 + S^2)*Zeta[3])/(3*S)) + (368*(1 + S^2)*Zeta[5])/(9*S)) + HPL[{1}, -S^2]^2*((-490*(1 + S^2))/S - (1045*Pi^2*(1 + S^2))/(9*S) - (10393*Pi^4*(1 + S^2))/(540*S) - (2425*Pi^6*(1 + S^2))/(756*S) + ((-191*(1 + S^2))/S - (434*Pi^2*(1 + S^2))/(9*S))*HPL[{2}, -S^2]^2 - (59*(1 + S^2)*HPL[{2}, -S^2]^3)/S + (5*(1 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((-85*(1 + S^2))/(3*S) - (109*Pi^2*(1 + S^2))/(18*S))*HPL[{4}, -S^2] - (18*(1 + S^2)*HPL[{5}, -S^2])/S - (82*(1 + S^2)*HPL[{6}, -S^2])/(3*S) + (784*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((2236*(1 + S^2))/(3*S) + (1706*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 1}, -S^2] - (232*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (190*(1 + S^2)*HPL[{4, 1}, -S^2])/S + ((-1 - S^2)*HPL[{4, 2}, -S^2])/S + (128*(1 + S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-1496*(1 + S^2))/S - (1142*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1}, -S^2] - (1568*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S - (4632*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S - (1416*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/S - (4332*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (3000*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + (2992*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (6000*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + ((90*(1 + S^2))/S + (43*Pi^2*(1 + S^2))/(3*S))*Zeta[3] - (16*(1 + S^2)*Zeta[3]^2)/S + HPL[{2, 1}, -S^2]*((754*(1 + S^2))/S + (1723*Pi^2*(1 + S^2))/(9*S) - (164*(1 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((-4*(1 + S^2))/S + (10*Pi^2*(1 + S^2))/(9*S) - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (8*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2}, -S^2]*((-390*(1 + S^2))/S - (872*Pi^2*(1 + S^2))/(9*S) - (8953*Pi^4*(1 + S^2))/(540*S) + (38*(1 + S^2)*HPL[{3}, -S^2])/S - (3*(1 + S^2)*HPL[{4}, -S^2])/S + (784*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (784*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (82*(1 + S^2)*Zeta[3])/S) + (182*(1 + S^2)*Zeta[5])/(3*S)) + HPL[{2, 1}, -S^2]*((Pi^4*(18655 - 774*S^2))/(540*S) - (10*(-257 + 7*S^2))/(3*S) - (2*Pi^2*(-913 + 25*S^2))/(9*S) - (4*(1157 + 35*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (2*(-205 + 23*S^2)*HPL[{3, 2}, -S^2])/(3*S) + (4*(290 + 11*S^2)*HPL[{4, 1}, -S^2])/(3*S) - (64*(145 + 4*S^2)*HPL[{2, 1, 1}, -S^2])/(3*S) - (32*(-19 + 275*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (24*(-15 + 371*S^2)*HPL[{3, 1, 1}, -S^2])/S + (16*(17 + 1142*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + ((-4*(122 + 7*S^2))/(3*S) + (2*Pi^2*(-122 + 9*S^2))/(9*S))*Zeta[3] + (8*(-37 + 9*S^2)*Zeta[5])/(3*S)) + HPL[{3}, -S^2]*((5*(-36 + 25*S^2))/(3*S) + (Pi^2*(-51 + 52*S^2))/(9*S) + (Pi^4*(-1142 + 841*S^2))/(1080*S) + ((37 - 50*S^2)*HPL[{4}, -S^2])/(3*S) + (2*(-13 + 34*S^2)*HPL[{5}, -S^2])/(3*S) + ((Pi^2*(-103 - 73*S^2))/(9*S) - (2*(91 + 15*S^2))/(3*S))*HPL[{2, 1}, -S^2] - (2*(-7 + 89*S^2)*HPL[{3, 1}, -S^2])/(3*S) - (2*(-9 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - 24*S*HPL[{4, 1}, -S^2] + (4*(3 + 31*S^2)*HPL[{2, 1, 1}, -S^2])/S - (4*(-103 + 11*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) + (4*(293 + 5*S^2)*HPL[{3, 1, 1}, -S^2])/(3*S) - (8*(31 + 13*S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((Pi^2*(23 + 3*S^2))/(9*S) + (2*(19 + 23*S^2))/(3*S))*Zeta[3] - (2*(-17 + 29*S^2)*Zeta[5])/(3*S)) + HPL[{2}, -S^2]*(-490*S + (Pi^6*(1807 - 70075*S^2))/(22680*S) + (Pi^4*(364 - 19171*S^2))/(1080*S) - (5*Pi^2*(-4 + 193*S^2))/(9*S) + ((-4 + S^2)*HPL[{3}, -S^2]^2)/(3*S) + ((Pi^2*(17 - 92*S^2))/(18*S) + (7*(7 + 3*S^2))/(3*S))*HPL[{4}, -S^2] + ((-31 + 71*S^2)*HPL[{5}, -S^2])/(3*S) - (2*(-10 + 31*S^2)*HPL[{6}, -S^2])/(3*S) + (8*(-19 + 275*S^2)*HPL[{2, 1}, -S^2]^2)/(3*S) + ((Pi^2*(5 + 571*S^2))/(3*S) + (2*(11 + 1114*S^2))/(3*S))*HPL[{3, 1}, -S^2] + ((29 - 215*S^2)*HPL[{3, 2}, -S^2])/(3*S) - (2*(-32 + 313*S^2)*HPL[{4, 1}, -S^2])/(3*S) + ((-5 - 8*S^2)*HPL[{4, 2}, -S^2])/(3*S) + (8*(-7 + 9*S^2)*HPL[{5, 1}, -S^2])/(3*S) + ((-4*(10 + 1123*S^2))/(3*S) - (2*Pi^2*(8 + 1711*S^2))/(9*S))*HPL[{2, 1, 1}, -S^2] + (8*(-574 + 29*S^2)*HPL[{2, 2, 1}, -S^2])/(3*S) - (4*(-1151 + 27*S^2)*HPL[{3, 1, 1}, -S^2])/S + (2*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (118*(1 + 37*S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) - (4*(71 + 3320*S^2)*HPL[{4, 1, 1}, -S^2])/(3*S) + (64*(145 + 4*S^2)*HPL[{2, 1, 1, 1}, -S^2])/(3*S) + (8*(-895 + 14339*S^2)*HPL[{3, 1, 1, 1}, -S^2])/(3*S) - (16*(17 + 1142*S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S) + ((4*(9 + 41*S^2))/(3*S) + (Pi^2*(14 + 89*S^2))/(9*S))*Zeta[3] - (4*(-1 + 12*S^2)*Zeta[3]^2)/(3*S) + HPL[{2, 1}, -S^2]*((2*(369 + 5*S^2))/S + (2*Pi^2*(865 + 14*S^2))/(9*S) - (4*(42 + S^2)*Zeta[3])/S) + HPL[{3}, -S^2]*((7*Pi^2*(1 + 15*S^2))/(18*S) + (4*(-3 + 34*S^2))/(3*S) + (2*(-103 + 11*S^2)*HPL[{2, 1}, -S^2])/(3*S) + (2*(7 + 13*S^2)*Zeta[3])/(3*S)) + (2*(18 + 31*S^2)*Zeta[5])/(3*S)) + 80*S*Zeta[7] + HPL[{1}, -S^2]*((-490*(1 + S^2))/S - (1105*Pi^2*(1 + S^2))/(9*S) - (7319*Pi^4*(1 + S^2))/(360*S) - (145423*Pi^6*(1 + S^2))/(45360*S) - (59*(1 + S^2)*HPL[{2}, -S^2]^3)/S + ((1 + S^2)*HPL[{3}, -S^2]^2)/S + ((-172*(1 + S^2))/(3*S) - (34*Pi^2*(1 + S^2))/(9*S))*HPL[{5}, -S^2] - (29*(1 + S^2)*HPL[{6}, -S^2])/S + (22*(1 + S^2)*HPL[{7}, -S^2])/(3*S) + (784*(1 + S^2)*HPL[{2, 1}, -S^2]^2)/S + ((-220*(1 + S^2))/(3*S) - (140*Pi^2*(1 + S^2))/(9*S))*HPL[{3, 2}, -S^2] + ((-466*(1 + S^2))/(3*S) - (311*Pi^2*(1 + S^2))/(9*S))*HPL[{4, 1}, -S^2] - (11*(1 + S^2)*HPL[{4, 2}, -S^2])/(3*S) + (38*(1 + S^2)*HPL[{4, 3}, -S^2])/(3*S) + (32*(1 + S^2)*HPL[{5, 1}, -S^2])/S + (104*(1 + S^2)*HPL[{5, 2}, -S^2])/(3*S) + (304*(1 + S^2)*HPL[{6, 1}, -S^2])/(3*S) + ((-1528*(1 + S^2))/S - (3472*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 2, 1}, -S^2] + ((-13640*(1 + S^2))/(3*S) - (3452*Pi^2*(1 + S^2))/(3*S))*HPL[{3, 1, 1}, -S^2] + (8*(1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (4240*(1 + S^2)*HPL[{3, 2, 1}, -S^2])/(3*S) + (126*(1 + S^2)*HPL[{3, 2, 2}, -S^2])/S + (1184*(1 + S^2)*HPL[{3, 3, 1}, -S^2])/(3*S) - (4324*(1 + S^2)*HPL[{4, 1, 1}, -S^2])/S + (394*(1 + S^2)*HPL[{4, 1, 2}, -S^2])/S + (1202*(1 + S^2)*HPL[{4, 2, 1}, -S^2])/S + (7040*(1 + S^2)*HPL[{5, 1, 1}, -S^2])/(3*S) + ((2992*(1 + S^2))/S + (2284*Pi^2*(1 + S^2))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] + (2832*(1 + S^2)*HPL[{2, 2, 2, 1}, -S^2])/S + (2992*(1 + S^2)*HPL[{3, 1, 1, 1}, -S^2])/S - (8800*(1 + S^2)*HPL[{3, 1, 1, 2}, -S^2])/S - (8800*(1 + S^2)*HPL[{3, 1, 2, 1}, -S^2])/S - (17296*(1 + S^2)*HPL[{3, 2, 1, 1}, -S^2])/S - (51720*(1 + S^2)*HPL[{4, 1, 1, 1}, -S^2])/S - (6000*(1 + S^2)*HPL[{2, 1, 1, 1, 1}, -S^2])/S + (6272*(1 + S^2)*HPL[{2, 1, 2, 1, 1}, -S^2])/S + (18816*(1 + S^2)*HPL[{2, 2, 1, 1, 1}, -S^2])/S + (31648*(1 + S^2)*HPL[{3, 1, 1, 1, 1}, -S^2])/S + (12000*(1 + S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S + ((380*(1 + S^2))/(3*S) + (56*Pi^2*(1 + S^2))/(3*S) + (95*Pi^4*(1 + S^2))/(108*S))*Zeta[3] - (46*(1 + S^2)*Zeta[3]^2)/(3*S) + HPL[{3, 1}, -S^2]*((750*(1 + S^2))/S + (1718*Pi^2*(1 + S^2))/(9*S) - (496*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{2, 1}, -S^2]*((780*(1 + S^2))/S + (1744*Pi^2*(1 + S^2))/(9*S) + (8953*Pi^4*(1 + S^2))/(270*S) - (1568*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (3136*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (164*(1 + S^2)*Zeta[3])/S) + HPL[{4}, -S^2]*((-46*(1 + S^2))/S - (97*Pi^2*(1 + S^2))/(18*S) + (6*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (38*(1 + S^2)*Zeta[3])/(3*S)) + HPL[{3}, -S^2]*((-140*(1 + S^2))/(3*S) - (25*Pi^2*(1 + S^2))/(9*S) - (47*Pi^4*(1 + S^2))/(135*S) - (8*(1 + S^2)*HPL[{4}, -S^2])/S - (76*(1 + S^2)*HPL[{2, 1}, -S^2])/S - (212*(1 + S^2)*HPL[{3, 1}, -S^2])/(3*S) + (152*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S + (4*(1 + S^2)*Zeta[3])/S) + HPL[{2}, -S^2]^2*((-371*(1 + S^2))/(2*S) - (869*Pi^2*(1 + S^2))/(18*S) + (16*(1 + S^2)*HPL[{3}, -S^2])/S + (354*(1 + S^2)*HPL[{2, 1}, -S^2])/S + (40*(1 + S^2)*Zeta[3])/S) + HPL[{2, 1, 1}, -S^2]*((-1508*(1 + S^2))/S - (3446*Pi^2*(1 + S^2))/(9*S) + (328*(1 + S^2)*Zeta[3])/S) + ((100*(1 + S^2))/S + (68*Pi^2*(1 + S^2))/(9*S))*Zeta[5] + HPL[{2}, -S^2]*((-415*(1 + S^2))/S - (296*Pi^2*(1 + S^2))/(3*S) - (3599*Pi^4*(1 + S^2))/(216*S) + ((106*(1 + S^2))/(3*S) + (70*Pi^2*(1 + S^2))/(9*S))*HPL[{3}, -S^2] + ((-1 - S^2)*HPL[{4}, -S^2])/S + (34*(1 + S^2)*HPL[{5}, -S^2])/(3*S) + ((764*(1 + S^2))/S + (1736*Pi^2*(1 + S^2))/(9*S))*HPL[{2, 1}, -S^2] + (784*(1 + S^2)*HPL[{3, 1}, -S^2])/S - (190*(1 + S^2)*HPL[{3, 2}, -S^2])/(3*S) - (198*(1 + S^2)*HPL[{4, 1}, -S^2])/S - (1568*(1 + S^2)*HPL[{2, 1, 1}, -S^2])/S - (1416*(1 + S^2)*HPL[{2, 2, 1}, -S^2])/S + (4400*(1 + S^2)*HPL[{3, 1, 1}, -S^2])/S + (3136*(1 + S^2)*HPL[{2, 1, 1, 1}, -S^2])/S + ((248*(1 + S^2))/(3*S) + (118*Pi^2*(1 + S^2))/(9*S))*Zeta[3] + (124*(1 + S^2)*Zeta[5])/(3*S)) + (30*(1 + S^2)*Zeta[7])/S));
Et5vwuT2F2=(35*Pi^2*(538 + 1673*S^2))/1152 + (Pi^4*(25799 + 92388*S^2))/8640 + (Pi^8*(442072 + 455019*S^2))/1360800 + (Pi^6*(244900 + 661413*S^2))/362880 + ((11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^8)/(18*S^2) + (4*(1 + S^4)*HPL[{1}, -S^2]^9)/(27*S^2) + HPL[{0}, S^2]^8*((1 + S^2)/192 + ((1 + S^4)*HPL[{1}, -S^2])/(192*S^2)) + ((50 + 96*S^2 + 69*S^4)*HPL[{2}, -S^2]^4)/(12*S^2) + HPL[{0}, S^2]^7*((7*Pi^2*S^2)/1728 + (-1 + 16*S^2)/192 + ((1 + S^2)*(-3 + 31*S^2)*HPL[{1}, -S^2])/(576*S^2) + (7*(1 + S^4)*HPL[{1}, -S^2]^2)/(288*S^2) + (7*S^2*HPL[{2}, -S^2])/288) + HPL[{1}, -S^2]^7*((46*Pi^2*(1 + S^4))/(63*S^2) + (2*(68 + 159*S^2 + 91*S^4))/(63*S^2) + (10*(1 + S^4)*HPL[{2}, -S^2])/(21*S^2)) + ((-10 - 9*S^4)*HPL[{3}, -S^2]^3)/(9*S^2) + ((33 - 28*S^2 + 77*S^4)*HPL[{4}, -S^2]^2)/(6*S^2) + ((Pi^2*(15 + 128*S^4))/(18*S^2) + (-355 - 30*S^2 + 2311*S^4)/(6*S^2))*HPL[{7}, -S^2] + ((-378 + 840*S^2 + 1843*S^4)*HPL[{8}, -S^2])/(3*S^2) + (14*(42 + 67*S^4)*HPL[{9}, -S^2])/(3*S^2) - (56*(-25 + 17*S^4)*HPL[{2, 1}, -S^2]^3)/(9*S^2) + ((904 + 1394*S^2 + 881*S^4)*HPL[{3, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(19 - 66*S^4))/(18*S^2) + (-68 - 320*S^2 + 151*S^4)/(12*S^2))*HPL[{4, 3}, -S^2] + ((Pi^2*(65 - 163*S^4))/(18*S^2) + (-316 - 534*S^2 + 295*S^4)/(12*S^2))*HPL[{5, 2}, -S^2] + ((-5 - 24*S^2 + 89*S^4)*HPL[{5, 3}, -S^2])/(6*S^2) + ((-289 + 30*S^4)*HPL[{5, 4}, -S^2])/(3*S^2) + ((31 - 805*S^2)/6 - (2*Pi^2*(-13 + 32*S^4))/(9*S^2))*HPL[{6, 1}, -S^2] + ((-63 - 60*S^2 + 97*S^4)*HPL[{6, 2}, -S^2])/(6*S^2) + (11*(-105 + 16*S^4)*HPL[{6, 3}, -S^2])/(3*S^2) + ((256 - 576*S^2 - 1563*S^4)*HPL[{7, 1}, -S^2])/(3*S^2) + ((-2835 + 416*S^4)*HPL[{7, 2}, -S^2])/(3*S^2) + ((-2065 - 116*S^4)*HPL[{8, 1}, -S^2])/S^2 + (8*(301 + 588*S^2 + 440*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^2) + ((363 - 8746*S^2 - 5588*S^4)/(12*S^2) + (Pi^2*(41 - 2093*S^4))/(18*S^2))*HPL[{3, 2, 2}, -S^2] + ((-2*Pi^2*(-66 + 1643*S^4))/(9*S^2) - (2*(-243 + 3386*S^2 + 2180*S^4))/(3*S^2))*HPL[{3, 3, 1}, -S^2] + ((257 + 672*S^2 + 450*S^4)*HPL[{3, 3, 2}, -S^2])/(6*S^2) + ((2203 - 26830*S^2 - 17057*S^4)/(12*S^2) + (Pi^2*(295 - 6502*S^4))/(18*S^2))*HPL[{4, 1, 2}, -S^2] - (2*(131 + 288*S^2 + 197*S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^2) + ((6295 - 83062*S^2 - 53141*S^4)/(12*S^2) + (Pi^2*(823 - 20098*S^4))/(18*S^2))*HPL[{4, 2, 1}, -S^2] + ((153 + 408*S^2 + 191*S^4)*HPL[{4, 2, 2}, -S^2])/(6*S^2) + ((-13 - 56*S^4)*HPL[{4, 2, 3}, -S^2])/(3*S^2) - (2*(288 + 984*S^2 + 755*S^4)*HPL[{4, 3, 1}, -S^2])/(3*S^2) - (2*(63 + 73*S^4)*HPL[{4, 3, 2}, -S^2])/(3*S^2) - (2*(215 + 102*S^4)*HPL[{4, 4, 1}, -S^2])/(3*S^2) + ((5855 - 85368*S^2 - 53655*S^4)/(6*S^2) + (Pi^2*(839 - 20641*S^4))/(9*S^2))*HPL[{5, 1, 1}, -S^2] + ((-551 - 2400*S^2 - 1920*S^4)*HPL[{5, 1, 2}, -S^2])/(6*S^2) - (2*(101 + 16*S^4)*HPL[{5, 1, 3}, -S^2])/(3*S^2) + ((-4691 - 16080*S^2 - 12000*S^4)*HPL[{5, 2, 1}, -S^2])/(6*S^2) - (5*(109 + 80*S^4)*HPL[{5, 2, 2}, -S^2])/(3*S^2) - (2*(815 + 316*S^4)*HPL[{5, 3, 1}, -S^2])/(3*S^2) + ((-6358 - 20310*S^2 - 14139*S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^2) - (2*(730 + 281*S^4)*HPL[{6, 1, 2}, -S^2])/(3*S^2) - (2*(1950 + 581*S^4)*HPL[{6, 2, 1}, -S^2])/(3*S^2) - (2*(3525 + 634*S^4)*HPL[{7, 1, 1}, -S^2])/(3*S^2) + ((8*Pi^2*(-353 + 123*S^4))/(9*S^2) + (-1840 - 1132*S^2 + 1373*S^4)/(3*S^2))*HPL[{2, 2, 2, 1}, -S^2] + ((9941 + 15516*S^2 - 2719*S^4)/(6*S^2) + (Pi^2*(8327 - 809*S^4))/(9*S^2))*HPL[{3, 1, 1, 2}, -S^2] + ((9941 + 15516*S^2 - 2719*S^4)/(6*S^2) + (Pi^2*(8327 - 809*S^4))/(9*S^2))*HPL[{3, 1, 2, 1}, -S^2] + ((292 + 468*S^2 + 227*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(6*S^2) + ((20981 + 22308*S^2 - 10957*S^4)/(6*S^2) + (Pi^2*(16799 - 3761*S^4))/(9*S^2))*HPL[{3, 2, 1, 1}, -S^2] + ((292 + 468*S^2 + 227*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(6*S^2) + ((5468 - 924*S^2 - 6653*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(6*S^2) + (2*(-99 + 1957*S^4)*HPL[{3, 2, 2, 2}, -S^2])/(3*S^2) + (2*(-266 + 6121*S^4)*HPL[{3, 2, 3, 1}, -S^2])/(3*S^2) - (4*(-647 + 174*S^2 + 860*S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (4*(-128 + 3003*S^4)*HPL[{3, 3, 1, 2}, -S^2])/(3*S^2) + (10*(-170 + 3717*S^4)*HPL[{3, 3, 2, 1}, -S^2])/(3*S^2) + ((32475 + 34868*S^2 - 15916*S^4)/(3*S^2) - (2*Pi^2*(-25313 + 5375*S^4))/(9*S^2))*HPL[{4, 1, 1, 1}, -S^2] + ((-122 + 702*S^2 + 691*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^2) - (2*(-1832 + 37825*S^4)*HPL[{4, 1, 1, 3}, -S^2])/(3*S^2) + ((7642 - 1386*S^2 - 9629*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^2) + ((3209 - 63710*S^4)*HPL[{4, 1, 2, 2}, -S^2])/(3*S^2) - (108*(-17 + 351*S^4)*HPL[{4, 1, 3, 1}, -S^2])/S^2 + ((23170 - 5562*S^2 - 30269*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^2) + ((2081 - 39242*S^4)*HPL[{4, 2, 1, 2}, -S^2])/(3*S^2) + ((2021 - 38552*S^4)*HPL[{4, 2, 2, 1}, -S^2])/(3*S^2) - (4*(-2653 + 56132*S^4)*HPL[{4, 3, 1, 1}, -S^2])/(3*S^2) - (2*(-23564 + 4512*S^2 + 29785*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^2) - (2*(-1865 + 38141*S^4)*HPL[{5, 1, 1, 2}, -S^2])/S^2 - (2*(-3013 + 62839*S^4)*HPL[{5, 1, 2, 1}, -S^2])/S^2 - (2*(-7061 + 149627*S^4)*HPL[{5, 2, 1, 1}, -S^2])/S^2 - (4*(-26364 + 560855*S^4)*HPL[{6, 1, 1, 1}, -S^2])/(3*S^2) + ((-6*(168 + 608*S^2 + 137*S^4))/S^2 - (8*Pi^2*(703 + 256*S^4))/(9*S^2))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-18*(168 + 608*S^2 + 137*S^4))/S^2 - (8*Pi^2*(703 + 256*S^4))/(3*S^2))*HPL[{2, 2, 1, 1, 1}, -S^2] - (8*(-210 + 62*S^2 + 279*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 - (24*(-210 + 62*S^2 + 279*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (16*(325 + 242*S^4)*HPL[{2, 2, 2, 2, 1}, -S^2])/(3*S^2) + ((-8*Pi^2*(3522 + 1865*S^4))/(9*S^2) - (2*(7756 + 32340*S^2 + 9041*S^4))/(3*S^2))*HPL[{3, 1, 1, 1, 1}, -S^2] + (2*(-14843 + 4464*S^2 + 19882*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^2) + (2*(-24923 + 7440*S^2 + 33274*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^2) + (2*(7849 + 1807*S^4)*HPL[{3, 1, 1, 2, 2}, -S^2])/(3*S^2) + (2*(-29963 + 8928*S^2 + 39970*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^2) + (2*(7849 + 1807*S^4)*HPL[{3, 1, 2, 1, 2}, -S^2])/(3*S^2) - (2*(103 + 113*S^4)*HPL[{3, 1, 2, 2, 1}, -S^2])/(3*S^2) - (16*(6946 + 2053*S^4)*HPL[{3, 1, 3, 1, 1}, -S^2])/(3*S^2) + (2*(-62723 + 18600*S^2 + 83494*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^2) + (2*(15649 + 7615*S^4)*HPL[{3, 2, 1, 1, 2}, -S^2])/(3*S^2) + (2*(7697 + 5695*S^4)*HPL[{3, 2, 1, 2, 1}, -S^2])/(3*S^2) + (2*(-24319 + 2807*S^4)*HPL[{3, 2, 2, 1, 1}, -S^2])/(3*S^2) + (16*(-3352 + 123*S^4)*HPL[{3, 3, 1, 1, 1}, -S^2])/S^2 + (8*(-47391 + 13524*S^2 + 62521*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^2) + (4*(23689 + 11209*S^4)*HPL[{4, 1, 1, 1, 2}, -S^2])/(3*S^2) + (4*(11761 + 8329*S^4)*HPL[{4, 1, 1, 2, 1}, -S^2])/(3*S^2) + (4*(-36263 + 3997*S^4)*HPL[{4, 1, 2, 1, 1}, -S^2])/(3*S^2) + (4*(-120611 + 4045*S^4)*HPL[{4, 2, 1, 1, 1}, -S^2])/(3*S^2) + (32*(-30150 + 881*S^4)*HPL[{5, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((1096*Pi^2*(-11 + 4*S^4))/(9*S^2) + (4*(-612 - 466*S^2 + 441*S^4))/S^2)*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (448*(-25 + 17*S^4)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(3*S^2) - (448*(-25 + 17*S^4)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/S^2 - (8*(-1637 - 48*S^2 + 1661*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) + (16*(-3583 + 3407*S^4)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(3*S^2) + (16*(-7783 + 6263*S^4)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(3*S^2) + (16*(-10583 + 8167*S^4)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(3*S^2) + (16*(-11983 + 9119*S^4)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(-21083 + 15307*S^4)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (480*(-701 + 513*S^4)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S^2 + (160*(-44 + 15*S^2 + 64*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (32*(227 + 162*S^4)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/S^2 + (128*(227 + 162*S^4)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/S^2 + (320*(227 + 162*S^4)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (256*(594 + 379*S^4)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (640*(-25 + 17*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (-8/3 - (14*Pi^2*S^2)/27 - (14*S^2*HPL[{0}, S^2]^2)/9 - (4*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2])/(9*S^2) - (16*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]*((-4*(12 + 13*S^2))/9 - (16*(1 + S^4)*HPL[{1}, -S^2])/(3*S^2)) - (4*(-5 + 7*S^4)*HPL[{2}, -S^2])/(9*S^2))*Log[T]^7 + (4/3 + (4*S^2*HPL[{0}, S^2])/3 + (4*(1 + S^4)*HPL[{1}, -S^2])/(3*S^2))*Log[T]^8 + ((101 - 46*S^2)/12 + (Pi^2*(46 - 11*S^2))/12)*Zeta[3]^2 + Log[T]^6*(14/3 + (2*Pi^2*(69 + 32*S^2))/27 + (44*S^2*HPL[{0}, S^2]^3)/27 + (14*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^2)/(9*S^2) + (112*(1 + S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + HPL[{0}, S^2]^2*((2*(27 + 32*S^2))/9 + (6*(1 + S^4)*HPL[{1}, -S^2])/S^2) + (2*(-44 + 15*S^2 + 64*S^4)*HPL[{2}, -S^2])/(9*S^2) + HPL[{1}, -S^2]*((46*Pi^2*(1 + S^4))/(9*S^2) + (2*(68 + 159*S^2 + 91*S^4))/(9*S^2) + (10*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]*((128*Pi^2*S^2)/27 + (2*(72 + 91*S^2))/9 + (14*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2])/(9*S^2) + (56*(1 + S^4)*HPL[{1}, -S^2]^2)/(3*S^2) + (2*(-5 + 79*S^4)*HPL[{2}, -S^2])/(9*S^2)) - (2*(3 + 74*S^4)*HPL[{3}, -S^2])/(9*S^2) + (8*(-25 + 17*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (136*S^2*Zeta[3])/9) + HPL[{0}, S^2]^6*((Pi^2*(250 + 317*S^2))/3456 + (21 + 347*S^2)/1152 + ((13 + 84*S^2 + 67*S^4)*HPL[{1}, -S^2]^2)/(288*S^2) + (41*(1 + S^4)*HPL[{1}, -S^2]^3)/(432*S^2) + ((64 + 137*S^2)*HPL[{2}, -S^2])/576 + HPL[{1}, -S^2]*((125*Pi^2*(1 + S^4))/(1728*S^2) + (21 + 360*S^2 + 307*S^4)/(1152*S^2) + ((1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) - (S^2*HPL[{3}, -S^2])/96 + ((-16 + 3*S^4)*HPL[{2, 1}, -S^2])/(72*S^2) + (17*S^2*Zeta[3])/72) + HPL[{5}, -S^2]*((Pi^4*(-47 - 651*S^4))/(540*S^2) + (Pi^2*(-58 - 554*S^2 + 513*S^4))/(72*S^2) + (-566 - 2522*S^2 + 2875*S^4)/(48*S^2) + ((797 + 318*S^2 + 215*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (4*(-22 + 47*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (10*(-5 + 39*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((5 + 14*S^2 - 81*S^4)*Zeta[3])/(6*S^2)) + HPL[{1}, -S^2]^6*((5*(97 + 244*S^2 + 147*S^4))/(72*S^2) + (Pi^2*(709 + 1656*S^2 + 947*S^4))/(324*S^2) + ((-3 + 20*S^2 + 23*S^4)*HPL[{2}, -S^2])/(6*S^2) - (80*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) - (10*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (20*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1, 2}, -S^2]*((530 - 170*S^2 - 379*S^4)/(12*S^2) + (Pi^2*(151 + S^2 - 100*S^4))/(18*S^2) - (2*(-3 + 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]^2*((Pi^2*(-9 + 52*S^2 + 24*S^4))/(18*S^2) + (-385 + 1164*S^2 + 383*S^4)/(48*S^2) + ((-113 - 2*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((1 + 8*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1, 1}, -S^2]*((Pi^2*(-1816 - 2444*S^2 + 659*S^4))/(9*S^2) + (-5106 - 9646*S^2 + 2193*S^4)/(12*S^2) + (Pi^4*(-17519 + 4414*S^4))/(270*S^2) + (16*(297 + 246*S^2 + 8*S^4)*Zeta[3])/(3*S^2)) + HPL[{5, 1}, -S^2]*((Pi^2*(319 + 1674*S^2 + 799*S^4))/(36*S^2) + (1307 + 8800*S^2 + 2568*S^4)/(24*S^2) + (16*(-1 + 13*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 2, 1}, -S^2]*((Pi^2*(1642 + 4480*S^2 + 565*S^4))/(18*S^2) + (5*(752 + 4722*S^2 + 763*S^4))/(24*S^2) + (Pi^4*(8172 + 1853*S^4))/(270*S^2) + (8*(-292 - 219*S^2 + 13*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(9699 + 21912*S^2 + 683*S^4))/(36*S^2) + (Pi^4*(49409 + 2453*S^4))/(540*S^2) + (9732 + 53158*S^2 + 4395*S^4)/(24*S^2) + (4*(-1783 - 1385*S^2 + 25*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^5*((1237*Pi^4*(1 + S^4))/(900*S^2) + (Pi^2*(2999 + 7842*S^2 + 4843*S^4))/(540*S^2) + (3316 + 9081*S^2 + 5765*S^4)/(180*S^2) + ((157*Pi^2*(1 + S^4))/(45*S^2) + (-119 + 338*S^2 + 457*S^4)/(30*S^2))*HPL[{2}, -S^2] + (196*(1 + S^4)*HPL[{2}, -S^2]^2)/(15*S^2) + ((-483 - 800*S^2 - 317*S^4)*HPL[{3}, -S^2])/(15*S^2) - (142*(1 + S^4)*HPL[{4}, -S^2])/(15*S^2) + ((3 - 20*S^2 - 23*S^4)*HPL[{2, 1}, -S^2])/S^2 + (16*(1 + S^4)*HPL[{3, 1}, -S^2])/(15*S^2) + (20*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (5*(43 + 72*S^2 + 29*S^4)*Zeta[3])/(9*S^2)) + HPL[{6}, -S^2]*((Pi^2*(-54 + 162*S^2 + 779*S^4))/(36*S^2) + (-200 - 756*S^2 + 3099*S^4)/(24*S^2) + (2*(2 + 7*S^4)*HPL[{2, 1}, -S^2])/S^2 - (2*(-10 + 31*S^4)*Zeta[3])/(3*S^2)) + HPL[{4, 2}, -S^2]*((Pi^2*(-71 + 340*S^2 + 329*S^4))/(36*S^2) + (-140 + 953*S^2 + 619*S^4)/(12*S^2) + ((3 + 44*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]^2*((-1127 - 1371*S^2 - 1990*S^4)/(6*S^2) + (Pi^2*(-310 - 957*S^2 - 893*S^4))/(9*S^2) + (8*(-11 + 115*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^3*((Pi^2*(-339 + 434*S^2 + 855*S^4))/(108*S^2) + (-2234 + 412*S^2 + 3721*S^4)/(144*S^2) + ((39 - 269*S^4)*HPL[{3}, -S^2])/(9*S^2) + ((-325 - 242*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (2*(3 + 115*S^4)*Zeta[3])/(9*S^2)) + HPL[{3, 2}, -S^2]*((Pi^4*(-19 + 636*S^4))/(90*S^2) + (-300 + 4051*S^2 + 1801*S^4)/(12*S^2) + (Pi^2*(-535 + 4614*S^2 + 2634*S^4))/(72*S^2) + (2*(41 + 2061*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-44 + 107*S^2 + 156*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 2, 1}, -S^2]*((Pi^2*(-1205 + 1737*S^2 + 3320*S^4))/(18*S^2) + (-3938 + 654*S^2 + 7063*S^4)/(12*S^2) - (2*(7 + 309*S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1, 1}, -S^2]*((8*Pi^2*(-363 + 471*S^2 + 968*S^4))/(9*S^2) + (2*(-2346 + 598*S^2 + 4245*S^4))/(3*S^2) - (16*(7 + 472*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1, 1, 1}, -S^2]*((5935 + 808*S^2 - 7813*S^4)/(6*S^2) + (Pi^2*(1799 - 1366*S^2 - 3575*S^4))/(9*S^2) + (8*(9 + 479*S^4)*Zeta[3])/(3*S^2)) + HPL[{4, 1}, -S^2]*((Pi^2*(-659 + 14986*S^2 + 8283*S^4))/(72*S^2) + (644 + 53176*S^2 + 22419*S^4)/(48*S^2) + (Pi^4*(-469 + 25264*S^4))/(1080*S^2) + (4*(-163 + 3311*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-13 + 376*S^2 + 492*S^4)*Zeta[3])/(3*S^2)) + HPL[{4, 1, 1}, -S^2]*((Pi^2*(-4398 + 4402*S^2 + 9933*S^4))/(18*S^2) + (-7256 - 607*S^2 + 10623*S^4)/(6*S^2) - (4*(25 + 1412*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^5*((3083*Pi^4*S^2)/64800 + (-113 + 1064*S^2)/576 + (Pi^2*(88 + 7203*S^2))/8640 + ((433 + 2234*S^2 + 1701*S^4)*HPL[{1}, -S^2]^3)/(2160*S^2) + (91*(1 + S^4)*HPL[{1}, -S^2]^4)/(360*S^2) + ((Pi^2*(-15 + 1246*S^4))/(4320*S^2) + (-120 + 418*S^2 + 1803*S^4)/(1440*S^2))*HPL[{2}, -S^2] + ((-5 + 142*S^4)*HPL[{2}, -S^2]^2)/(480*S^2) + HPL[{1}, -S^2]^2*((427*Pi^2*(1 + S^4))/(1440*S^2) + (76 + 2079*S^2 + 1903*S^4)/(1440*S^2) + (461*(1 + S^4)*HPL[{2}, -S^2])/(720*S^2)) - ((-1 + 2*S^2)^2*HPL[{3}, -S^2])/(96*S^2) + ((1 + 2*S^4)*HPL[{4}, -S^2])/(16*S^2) + ((-463 - 972*S^2 + 260*S^4)*HPL[{2, 1}, -S^2])/(720*S^2) - (27*S^2*HPL[{3, 1}, -S^2])/20 + ((-15 + 511*S^4)*HPL[{2, 1, 1}, -S^2])/(180*S^2) + ((8 + 79*S^2)*Zeta[3])/48 + HPL[{1}, -S^2]*((Pi^2*(59 + 2587*S^2 + 2478*S^4))/(4320*S^2) + (-475 + 3668*S^2 + 4143*S^4)/(2880*S^2) + ((194 + 947*S^2 + 703*S^4)*HPL[{2}, -S^2])/(720*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(24*S^2) - (461*(1 + S^4)*HPL[{2, 1}, -S^2])/(360*S^2) + ((1 + S^4)*Zeta[3])/(6*S^2))) + Log[T]^5*(-85/12 - (3083*Pi^4*S^2)/2025 + (Pi^2*(-322 - 271*S^2))/36 - (283*S^2*HPL[{0}, S^2]^4)/270 - (28*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) - (56*(1 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + HPL[{0}, S^2]^3*((-215 - 302*S^2)/45 - (43*(1 + S^4)*HPL[{1}, -S^2])/(9*S^2)) + ((Pi^2*(113 - 298*S^4))/(27*S^2) + (170 - 42*S^2 - 271*S^4)/(6*S^2))*HPL[{2}, -S^2] + ((-33 - 46*S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^2*((-1301*Pi^2*S^2)/270 + (-154 - 271*S^2)/12 + ((-247 - 648*S^2 - 401*S^4)*HPL[{1}, -S^2])/(18*S^2) - (18*(1 + S^4)*HPL[{1}, -S^2]^2)/S^2 + ((8 - 151*S^4)*HPL[{2}, -S^2])/(9*S^2)) + HPL[{1}, -S^2]^2*((-46*Pi^2*(1 + S^4))/(3*S^2) - (2*(68 + 159*S^2 + 91*S^4))/(3*S^2) - (10*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((19 + 800*S^2 + 601*S^4)*HPL[{3}, -S^2])/(15*S^2) + (4*(14 + 59*S^4)*HPL[{4}, -S^2])/(15*S^2) - (2*(-79 - 30*S^2 + 59*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (16*(-11 + 10*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (56*(-5 + 7*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(60 + 59*S^2)*Zeta[3])/3 + HPL[{0}, S^2]*((-1516 - 2205*S^2)/36 + (Pi^2*(-635 - 757*S^2))/45 - (14*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^2)/(3*S^2) - (112*(1 + S^4)*HPL[{1}, -S^2]^3)/(3*S^2) + ((49 - 450*S^2 - 529*S^4)*HPL[{2}, -S^2])/(9*S^2) + HPL[{1}, -S^2]*((-127*Pi^2*(1 + S^4))/(9*S^2) - (2*(68 + 159*S^2 + 91*S^4))/(3*S^2) - (50*(1 + S^4)*HPL[{2}, -S^2])/S^2) + (2*(-10 + 17*S^4)*HPL[{3}, -S^2])/(9*S^2) - (16*(-20 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + 12*S^2*Zeta[3]) + HPL[{1}, -S^2]*((Pi^2*(-709 - 1656*S^2 - 947*S^4))/(54*S^2) - (5*(97 + 244*S^2 + 147*S^4))/(12*S^2) + ((3 - 20*S^2 - 23*S^4)*HPL[{2}, -S^2])/S^2 + (160*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (20*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (40*(1 + S^4)*Zeta[3])/S^2)) + ((5*(-725 + 28*S^2))/24 - (25*Pi^2*(82 + 35*S^2))/72)*Zeta[5] + Log[T]^4*(55/6 + (Pi^2*(3038 + 4245*S^2))/216 + (Pi^4*(22266 + 16915*S^2))/3240 + (283*S^2*HPL[{0}, S^2]^5)/540 + (35*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^4)/(9*S^2) + (56*(1 + S^4)*HPL[{1}, -S^2]^5)/(3*S^2) + HPL[{0}, S^2]^4*((558 + 853*S^2)/216 + (31*(1 + S^4)*HPL[{1}, -S^2])/(12*S^2)) + ((301 + 588*S^2 + 440*S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + HPL[{1}, -S^2]^3*((230*Pi^2*(1 + S^4))/(9*S^2) + (10*(68 + 159*S^2 + 91*S^4))/(9*S^2) + (50*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + HPL[{0}, S^2]^3*((613*Pi^2*S^2)/162 + (1638 + 3907*S^2)/216 + ((285 + 868*S^2 + 567*S^4)*HPL[{1}, -S^2])/(36*S^2) + (215*(1 + S^4)*HPL[{1}, -S^2]^2)/(18*S^2) + ((-6 + 205*S^4)*HPL[{2}, -S^2])/(18*S^2)) + ((-49 - 1245*S^2 - 719*S^4)/(9*S^2) + (Pi^2*(-7 - 585*S^4))/(27*S^2))*HPL[{3}, -S^2] + ((-141 - 426*S^2 - 254*S^4)*HPL[{4}, -S^2])/(9*S^2) - (2*(-15 + 113*S^4)*HPL[{5}, -S^2])/(9*S^2) + ((137*Pi^2*(-11 + 4*S^4))/(27*S^2) + (-612 - 466*S^2 + 441*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + ((1637 + 48*S^2 - 1661*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (2*(-83 + 1027*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) + (20*(-1 + 37*S^4)*HPL[{4, 1}, -S^2])/S^2 + (20*(-44 + 15*S^2 + 64*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (4*(227 + 162*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(333 + 58*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (80*(-25 + 17*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-562*Pi^2*S^2)/27 + (-242 - 147*S^2)/2)*Zeta[3] + HPL[{0}, S^2]^2*((Pi^2*(1368 + 1813*S^2))/108 + (1778 + 4245*S^2)/72 + (5*(247 + 648*S^2 + 401*S^4)*HPL[{1}, -S^2]^2)/(36*S^2) + (30*(1 + S^4)*HPL[{1}, -S^2]^3)/S^2 + ((-66 + 717*S^2 + 976*S^4)*HPL[{2}, -S^2])/(18*S^2) + HPL[{1}, -S^2]*((38*Pi^2*(1 + S^4))/(3*S^2) + (959 + 3072*S^2 + 2113*S^4)/(36*S^2) + (239*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((31 - 60*S^4)*HPL[{3}, -S^2])/(18*S^2) + ((-757 + 38*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (52*S^2*Zeta[3])/9) + HPL[{1}, -S^2]^2*((25*(97 + 244*S^2 + 147*S^4))/(24*S^2) + (5*Pi^2*(709 + 1656*S^2 + 947*S^4))/(108*S^2) + (5*(-3 + 20*S^2 + 23*S^4)*HPL[{2}, -S^2])/(2*S^2) - (400*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (50*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (100*(1 + S^4)*Zeta[3])/S^2) + HPL[{1}, -S^2]*((1237*Pi^4*(1 + S^4))/(180*S^2) + (Pi^2*(2999 + 7842*S^2 + 4843*S^4))/(108*S^2) + (3316 + 9081*S^2 + 5765*S^4)/(36*S^2) + ((157*Pi^2*(1 + S^4))/(9*S^2) + (-119 + 338*S^2 + 457*S^4)/(6*S^2))*HPL[{2}, -S^2] + (196*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-483 - 800*S^2 - 317*S^4)*HPL[{3}, -S^2])/(3*S^2) - (142*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (5*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/S^2 + (16*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (100*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (25*(43 + 72*S^2 + 29*S^4)*Zeta[3])/(9*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-363 + 471*S^2 + 968*S^4))/(27*S^2) + (-2346 + 598*S^2 + 4245*S^4)/(36*S^2) - (2*(-24 + 181*S^4)*HPL[{3}, -S^2])/(3*S^2) - (2*(227 + 162*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(7 + 472*S^4)*Zeta[3])/(9*S^2)) + HPL[{0}, S^2]*((10279*Pi^4*S^2)/1620 + (Pi^2*(5958 + 9367*S^2))/216 + (6839 + 11530*S^2)/72 + (70*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^3)/(9*S^2) + (140*(1 + S^4)*HPL[{1}, -S^2]^4)/(3*S^2) + ((Pi^2*(-31 + 600*S^4))/(18*S^2) + (-388 + 4026*S^2 + 5299*S^4)/(36*S^2))*HPL[{2}, -S^2] + ((17 + 1142*S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + HPL[{1}, -S^2]^2*((635*Pi^2*(1 + S^4))/(18*S^2) + (5*(68 + 159*S^2 + 91*S^4))/(3*S^2) + (125*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((97 - 132*S^2 - 113*S^4)*HPL[{3}, -S^2])/(18*S^2) + (2*(-1 + 13*S^4)*HPL[{4}, -S^2])/(3*S^2) + (10*(-226 - 225*S^2 + 16*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (2*(-29 + 391*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (20*(-5 + 79*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-246 - 259*S^2)*Zeta[3])/9 + HPL[{1}, -S^2]*((25*(97 + 244*S^2 + 147*S^4))/(24*S^2) + (Pi^2*(1055 + 2548*S^2 + 1477*S^4))/(36*S^2) + (5*(403 + 900*S^2 + 497*S^4)*HPL[{2}, -S^2])/(18*S^2) - (6*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (250*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (82*(1 + S^4)*Zeta[3])/(3*S^2))) - (1000*S^2*Zeta[5])/9) + HPL[{0}, S^2]^4*((5*Pi^2*(104 + 917*S^2))/1728 + (961 + 4969*S^2)/576 + (Pi^4*(4968 + 6949*S^2))/12960 + ((103 + 377*S^2 + 264*S^4)*HPL[{1}, -S^2]^4)/(144*S^2) + (31*(1 + S^4)*HPL[{1}, -S^2]^5)/(60*S^2) + ((-3 + 232*S^2 + 331*S^4)*HPL[{2}, -S^2]^2)/(144*S^2) + HPL[{1}, -S^2]^3*((391*Pi^2*(1 + S^4))/(432*S^2) + (725 + 4312*S^2 + 3491*S^4)/(864*S^2) + (245*(1 + S^4)*HPL[{2}, -S^2])/(108*S^2)) + ((Pi^2*(5 - 11*S^4))/(144*S^2) + (35 + 30*S^2 + 38*S^4)/(96*S^2))*HPL[{3}, -S^2] + ((5 + 8*S^2 + 44*S^4)*HPL[{4}, -S^2])/(48*S^2) + ((-5 - 4*S^4)*HPL[{5}, -S^2])/(12*S^2) + ((-349 - 1372*S^2 + 23*S^4)/(144*S^2) + (Pi^2*(-985 + 122*S^4))/(432*S^2))*HPL[{2, 1}, -S^2] + ((75 - 952*S^2 - 1498*S^4)*HPL[{3, 1}, -S^2])/(144*S^2) + HPL[{3, 2}, -S^2]/(4*S^2) + ((7 + 8*S^4)*HPL[{4, 1}, -S^2])/(24*S^2) + ((-60 + 980*S^2 + 1557*S^4)*HPL[{2, 1, 1}, -S^2])/(72*S^2) + ((473 + 4*S^4)*HPL[{2, 2, 1}, -S^2])/(36*S^2) + ((161 - S^4)*HPL[{3, 1, 1}, -S^2])/(4*S^2) + ((-505 + 32*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(18*S^2) + ((281*Pi^2*S^2)/216 + (-2 + 57*S^2)/36)*Zeta[3] + HPL[{1}, -S^2]^2*((33 + 272*S^2 + 236*S^4)/(36*S^2) + (Pi^2*(168 + 797*S^2 + 599*S^4))/(288*S^2) + ((269 + 981*S^2 + 710*S^4)*HPL[{2}, -S^2])/(144*S^2) + ((1 + S^4)*HPL[{3}, -S^2])/(6*S^2) - (245*(1 + S^4)*HPL[{2, 1}, -S^2])/(36*S^2) + (19*(1 + S^4)*Zeta[3])/(36*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-15 + 485*S^2 + 903*S^4))/(432*S^2) + (105 + 454*S^2 + 1809*S^4)/(288*S^2) - HPL[{3}, -S^2]/(8*S^2) + ((-473 - 4*S^4)*HPL[{2, 1}, -S^2])/(72*S^2) + (5*(1 + 2*S^4)*Zeta[3])/(24*S^2)) + HPL[{1}, -S^2]*((23*Pi^4*(1 + S^4))/(60*S^2) + (Pi^2*(65 + 607*S^2 + 506*S^4))/(216*S^2) + (721 + 5114*S^2 + 4297*S^4)/(576*S^2) + ((485*Pi^2*(1 + S^4))/(432*S^2) + (167 + 976*S^2 + 841*S^4)/(144*S^2))*HPL[{2}, -S^2] + (29*(1 + S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + ((-3 + 8*S^2 + 27*S^4)*HPL[{3}, -S^2])/(48*S^2) + ((1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + ((-269 - 981*S^2 - 710*S^4)*HPL[{2, 1}, -S^2])/(72*S^2) - (61*(1 + S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (245*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(18*S^2) + ((-19 + 101*S^2 + 70*S^4)*Zeta[3])/(72*S^2)) + (125*S^2*Zeta[5])/18) + Zeta[3]*((Pi^4*(-17414 - 6363*S^2))/4320 + (Pi^2*(-4529 - 1056*S^2))/144 + (-3283 + 652*S^2)/24 - (4*(-44 + 45*S^2)*Zeta[5])/3) + HPL[{2}, -S^2]^2*((747 + 639*S^2 + 1526*S^4)/(16*S^2) + (Pi^2*(2359 + 4376*S^2 + 8031*S^4))/(288*S^2) + (Pi^4*(2160 + 9898*S^2 + 10579*S^4))/(2160*S^2) + ((-50 - 1268*S^2 - 779*S^4)/(12*S^2) - (7*Pi^2*(5 + 81*S^4))/(36*S^2))*HPL[{3}, -S^2] + ((-107 - 444*S^2 - 303*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((23 - 86*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((Pi^2*(-353 + 123*S^4))/(9*S^2) + (-1840 - 1132*S^2 + 1373*S^4)/(24*S^2))*HPL[{2, 1}, -S^2] + ((1549 + 120*S^2 - 1507*S^4)*HPL[{3, 1}, -S^2])/(12*S^2) + (5*(-19 + 204*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((-73 + 3284*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((-210 + 62*S^2 + 279*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(325 + 242*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + ((1871 + 363*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (56*(-25 + 17*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((65 - 496*S^2 - 334*S^4)/(6*S^2) + (Pi^2*(29 - 247*S^4))/(18*S^2))*Zeta[3] + ((26 - 187*S^4)*Zeta[5])/(3*S^2)) + HPL[{4}, -S^2]*((Pi^2*(-401 - 1870*S^2 + 124*S^4))/(144*S^2) + (Pi^4*(-1070 - 2460*S^2 + 637*S^4))/(2160*S^2) + (-1596 - 3768*S^2 + 1079*S^4)/(96*S^2) + ((145 - 12*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-13*Pi^2*(-29 + 4*S^4))/(18*S^2) + (1859 + 942*S^2 + 221*S^4)/(12*S^2))*HPL[{2, 1}, -S^2] + ((-227 + 744*S^2 + 534*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + ((43 - 68*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (4*(-44 + 57*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((212 - 686*S^2 - 579*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(395 + 56*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(1211 + 72*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (16*(-100 + 11*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-1 - 26*S^2 - 37*S^4)/(4*S^2) + (Pi^2*(35 - 32*S^4))/(18*S^2))*Zeta[3] + ((39 - 32*S^4)*Zeta[5])/(3*S^2)) + HPL[{2, 1}, -S^2]*((-12079 - 33469*S^2 - 2608*S^4)/(96*S^2) + (Pi^2*(-4942 - 13334*S^2 + 151*S^4))/(144*S^2) + (Pi^4*(-12726 - 22738*S^2 + 2991*S^4))/(1440*S^2) + (Pi^6*(-59902 + 15063*S^4))/(22680*S^2) + ((Pi^2*(425 + 213*S^4))/(3*S^2) + (1007 + 5532*S^2 + 1562*S^4)/(6*S^2))*HPL[{3, 1}, -S^2] + ((-5243 - 4380*S^2 - 85*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((-8459 - 6586*S^2 + 132*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((-137 - 20*S^4)*HPL[{4, 2}, -S^2])/S^2 - (2*(927 + 17*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((3*(168 + 608*S^2 + 137*S^4))/S^2 + (4*Pi^2*(703 + 256*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + (4*(-210 + 62*S^2 + 279*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (8*(-258 + 773*S^2 + 1219*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (78*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 - (2*(1183 + 851*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (8*(775 + 748*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (16*(301 + 588*S^2 + 440*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(278 + 305*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (16*(227 + 162*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(1349 + 1082*S^2 + 12*S^4))/(18*S^2) + (2*(560 + 317*S^2 + 19*S^4))/(3*S^2))*Zeta[3] + (2*(-9 + 20*S^4)*Zeta[3]^2)/(3*S^2) + ((1103 + 812*S^2 - 12*S^4)*Zeta[5])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^4*(346 - 16500*S^2 - 7729*S^4))/(4320*S^2) + (Pi^6*(725 - 7439*S^4))/(15120*S^2) + (-3144 - 29960*S^2 - 2395*S^4)/(192*S^2) + (Pi^2*(-193 - 4187*S^2 - 1127*S^4))/(144*S^2) + ((17 + 149*S^2 - 25*S^4)/(6*S^2) + (Pi^2*(-5 + 29*S^4))/(9*S^2))*HPL[{4}, -S^2] + ((-65 + 70*S^2 - 253*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-145 - 44*S^4)*HPL[{6}, -S^2])/(3*S^2) + ((79 + 1089*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(-79 + 566*S^4))/(9*S^2) + (-441 + 2150*S^2 + 1449*S^4)/(6*S^2))*HPL[{3, 1}, -S^2] + ((-113 - 458*S^2 - 330*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((427 - 264*S^2 - 132*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((7 + 58*S^4)*HPL[{4, 2}, -S^2])/(3*S^2) + (2*(51 + 10*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((833 - 4400*S^2 - 2935*S^4)/(6*S^2) + (Pi^2*(137 - 1131*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + ((-2749 - 2424*S^2 - 149*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + ((-8345 - 6820*S^2 - 127*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (2*(9 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) - (2*(-49 + 359*S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (10*(-268 + 6921*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (4*(-1374 - 988*S^2 + 73*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (4*(-169 + 1081*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (16*(-24 + 181*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-75 - 162*S^2 - 203*S^4)/(12*S^2) + (Pi^2*(-70 - 152*S^2 - 119*S^4))/(36*S^2))*Zeta[3] + ((3 - 11*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(2873 + 2076*S^2 - 71*S^4))/(36*S^2) + (1257 + 529*S^2 - 32*S^4)/(3*S^2) - (2*(-63 + 11*S^4)*Zeta[3])/(3*S^2)) + ((-16 - 96*S^2 - S^4)*Zeta[5])/(6*S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(1739 + 5052*S^2 + 3313*S^4))/(144*S^2) + (11*(2269 + 6876*S^2 + 4607*S^4))/(576*S^2) + (Pi^4*(17597 + 44493*S^2 + 26974*S^4))/(6480*S^2) + ((551 + 1176*S^2 + 625*S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + ((-2887 - 4416*S^2 - 1529*S^4)/(36*S^2) - (205*Pi^2*(1 + S^4))/(18*S^2))*HPL[{3}, -S^2] + ((-571 - 846*S^2 - 287*S^4)*HPL[{4}, -S^2])/(18*S^2) - (31*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((119 - 338*S^2 - 457*S^4)/(6*S^2) - (157*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((347 + 48*S^2 - 299*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (110*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (1132*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (5*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (784*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (1552*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (100*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-1081 - 1698*S^2 - 617*S^4)/(18*S^2) - (55*Pi^2*(1 + S^4))/(6*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(113 + 468*S^2 + 361*S^4))/(27*S^2) + (5*(-115 + 328*S^2 + 443*S^4))/(48*S^2) - (55*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (392*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (164*(1 + S^4)*Zeta[3])/(3*S^2)) - (134*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]^3*((17153*Pi^6*(1 + S^4))/(15120*S^2) + (Pi^2*(786 + 2543*S^2 + 1757*S^4))/(36*S^2) + (8061 + 27734*S^2 + 19673*S^4)/(96*S^2) + (Pi^4*(11307 + 33572*S^2 + 22361*S^4))/(2592*S^2) + ((319*Pi^2*(1 + S^4))/(18*S^2) + (1955 + 4476*S^2 + 2521*S^4)/(36*S^2))*HPL[{2}, -S^2]^2 + (31*(1 + S^4)*HPL[{2}, -S^2]^3)/(9*S^2) + (37*(1 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((-2427 - 3188*S^2 - 761*S^4)/(36*S^2) - (401*Pi^2*(1 + S^4))/(54*S^2))*HPL[{4}, -S^2] + (4*(-113 - 92*S^2 + 19*S^4)*HPL[{5}, -S^2])/(9*S^2) + (35*(1 + S^4)*HPL[{6}, -S^2])/(3*S^2) - (784*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-76*Pi^2*(1 + S^4))/(3*S^2) - (4*(-233 + 15*S^2 + 248*S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + (4*(583 + 989*S^2 + 408*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) + (4*(2033 + 3393*S^2 + 1366*S^4)*HPL[{4, 1}, -S^2])/(9*S^2) + (39*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (584*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((628*Pi^2*(1 + S^4))/(9*S^2) + (2*(-119 + 338*S^2 + 457*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (8*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) + (4*(619 + 1552*S^2 + 933*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (248*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (176*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (20*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (64*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (400*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-1203 - 1978*S^2 - 779*S^4))/(54*S^2) + (-343 - 524*S^2 - 181*S^4)/(3*S^2))*Zeta[3] + (20*(1 + S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*((-5515 - 7896*S^2 - 2381*S^4)/(36*S^2) + (Pi^2*(-1525 - 2474*S^2 - 921*S^4))/(54*S^2) + (220*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (16*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-4*Pi^2*(113 + 468*S^2 + 361*S^4))/(27*S^2) - (5*(-115 + 328*S^2 + 443*S^4))/(12*S^2) + (656*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((4421*Pi^4*(1 + S^4))/(1080*S^2) + (Pi^2*(113 + 962*S^2 + 861*S^4))/(27*S^2) + (-575 + 2102*S^2 + 2677*S^4)/(24*S^2) - (5*(233 + 396*S^2 + 163*S^4)*HPL[{3}, -S^2])/(9*S^2) - (113*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (784*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (2*(587 + 972*S^2 + 409*S^4)*Zeta[3])/(9*S^2)) - (2*(510 + 805*S^2 + 293*S^4)*Zeta[5])/(9*S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-1226 + 1232*S^2 + 4283*S^4))/(18*S^2) + (-3902 + 2179*S^2 + 10231*S^4)/(12*S^2) + (Pi^4*(-11396 + 26526*S^2 + 47667*S^4))/(1080*S^2) + (224*(-25 + 17*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (16*(-326 + 57*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (16*(227 + 162*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-4*Pi^2*(2 + 259*S^4))/(9*S^2) - (4*(-10 + 523*S^2 + 332*S^4))/(3*S^2))*Zeta[3] - (4*(-14 + 417*S^4)*Zeta[5])/(3*S^2)) + HPL[{3, 1}, -S^2]*((Pi^4*(13960 - 22596*S^2 - 44521*S^4))/(2160*S^2) + (21864 + 992*S^2 - 40439*S^4)/(96*S^2) + (Pi^2*(3155 - 1362*S^2 - 8289*S^4))/(72*S^2) - (4*(-4 + 509*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(-265 + 3274*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (8*(372 + 587*S^2 + 382*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (4*(-571 + 605*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(3087 + 1210*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (16*(278 + 305*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(1 + 175*S^4))/(3*S^2) + (-9 + 2132*S^2 + 1341*S^4)/(6*S^2))*Zeta[3] + (2*(-5 + 431*S^4)*Zeta[5])/(3*S^2)) + HPL[{0}, S^2]^3*((35159*Pi^6*S^2)/181440 + (Pi^2*(292 + 13161*S^2))/1152 + (-3365 + 54016*S^2)/1152 + (Pi^4*(16508 + 148021*S^2))/51840 + ((285 + 868*S^2 + 567*S^4)*HPL[{1}, -S^2]^5)/(180*S^2) + (43*(1 + S^4)*HPL[{1}, -S^2]^6)/(54*S^2) + ((Pi^2*(-24 + 995*S^4))/(432*S^2) + (-18 + 1444*S^2 + 3335*S^4)/(288*S^2))*HPL[{2}, -S^2]^2 + ((-1 + 45*S^4)*HPL[{2}, -S^2]^3)/(18*S^2) + HPL[{1}, -S^2]^4*((397*Pi^2*(1 + S^4))/(216*S^2) + (1155 + 4912*S^2 + 3677*S^4)/(432*S^2) + (49*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((-1 - 23*S^4)*HPL[{3}, -S^2]^2)/(36*S^2) + ((Pi^2*(21 + 79*S^4))/(108*S^2) + (-116 + 128*S^2 + 239*S^4)/(72*S^2))*HPL[{4}, -S^2] + ((-64 + 78*S^2 - 93*S^4)*HPL[{5}, -S^2])/(72*S^2) + ((20 + 17*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((9 - 569*S^4)*HPL[{2, 1}, -S^2]^2)/(18*S^2) + ((98 - 1692*S^2 - 3571*S^4)/(72*S^2) + (Pi^2*(18 - 1091*S^4))/(108*S^2))*HPL[{3, 1}, -S^2] + ((-10 + 134*S^2 - 113*S^4)*HPL[{3, 2}, -S^2])/(72*S^2) + ((-56 + 98*S^2 - 137*S^4)*HPL[{4, 1}, -S^2])/(36*S^2) - (S^2*HPL[{4, 2}, -S^2])/9 + ((-12 - 47*S^4)*HPL[{5, 1}, -S^2])/(9*S^2) + ((Pi^2*(-33 + 1126*S^4))/(54*S^2) + (-50 + 802*S^2 + 1809*S^4)/(18*S^2))*HPL[{2, 1, 1}, -S^2] + ((393 + 569*S^2 - 29*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) + ((2403 + 3440*S^2 - 155*S^4)*HPL[{3, 1, 1}, -S^2])/(18*S^2) + (S^2*HPL[{3, 1, 2}, -S^2])/9 + ((-12 + 541*S^4)*HPL[{3, 2, 1}, -S^2])/(9*S^2) + ((-39 + 1688*S^4)*HPL[{4, 1, 1}, -S^2])/(9*S^2) + ((-843 - 1178*S^2 + 92*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^2) - (2*(-18 + 605*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^2) + (4*(-6 + 205*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((5*Pi^2*(11 + 129*S^2))/108 + (-794 + 807*S^2)/144)*Zeta[3] - (S^2*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((Pi^2*(30 + 86*S^2 - 41*S^4))/(432*S^2) + (-45 + 114*S^2 + 106*S^4)/(36*S^2) + ((5 + 17*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - Zeta[3]/S^2) + HPL[{2}, -S^2]*((Pi^4*(-26 + 1283*S^4))/(1080*S^2) + (Pi^2*(-85 + 610*S^2 + 1806*S^4))/(216*S^2) + (-1280 + 4930*S^2 + 16699*S^4)/(576*S^2) + ((3 - 34*S^2 + 30*S^4)*HPL[{3}, -S^2])/(36*S^2) + ((1 + 24*S^4)*HPL[{4}, -S^2])/(18*S^2) + ((-393 - 569*S^2 + 29*S^4)*HPL[{2, 1}, -S^2])/(18*S^2) + ((1 - 287*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + ((-9 + 569*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (7*(-1 + 5*S^2)*Zeta[3])/18) + HPL[{1}, -S^2]^3*((Pi^2*(644 + 2419*S^2 + 1701*S^4))/(324*S^2) + (403 + 2403*S^2 + 1968*S^4)/(108*S^2) + ((191 + 588*S^2 + 397*S^4)*HPL[{2}, -S^2])/(27*S^2) + (4*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) - (196*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (5*(1 + S^4)*Zeta[3])/(27*S^2)) + HPL[{2, 1}, -S^2]*((-1709 - 7176*S^2 - 465*S^4)/(144*S^2) + (Pi^2*(-653 - 1075*S^2 + 176*S^4))/(108*S^2) - (2*(1 + 5*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]^2*((1001*Pi^4*(1 + S^4))/(810*S^2) + (Pi^2*(1307 + 9070*S^2 + 7483*S^4))/(864*S^2) + (1007 + 9884*S^2 + 8749*S^4)/(288*S^2) + ((1049*Pi^2*(1 + S^4))/(216*S^2) + (537 + 2348*S^2 + 1811*S^4)/(72*S^2))*HPL[{2}, -S^2] + (70*(1 + S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((-13 + 38*S^2 + 71*S^4)*HPL[{3}, -S^2])/(36*S^2) + (23*(1 + S^4)*HPL[{4}, -S^2])/(18*S^2) + ((-191 - 588*S^2 - 397*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) - (292*(1 + S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (196*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-49 - 6*S^2 + 35*S^4)*Zeta[3])/(18*S^2)) + ((24 + 571*S^2)*Zeta[5])/18 + HPL[{1}, -S^2]*((Pi^2*(331 + 8474*S^2 + 8079*S^4))/(864*S^2) + (Pi^4*(4439 + 32390*S^2 + 27235*S^4))/(12960*S^2) + (-325 + 40564*S^2 + 40889*S^4)/(1152*S^2) + ((389 + 1126*S^2 + 725*S^4)*HPL[{2}, -S^2]^2)/(72*S^2) + ((Pi^2*(1 + S^4))/(4*S^2) + (-15 + 236*S^2 + 235*S^4)/(72*S^2))*HPL[{3}, -S^2] + ((3 + 49*S^2 + 40*S^4)*HPL[{4}, -S^2])/(18*S^2) + (5*(1 + S^4)*HPL[{5}, -S^2])/(18*S^2) + ((-537 - 2348*S^2 - 1811*S^4)/(36*S^2) - (1049*Pi^2*(1 + S^4))/(108*S^2))*HPL[{2, 1}, -S^2] - (2*(94 + 291*S^2 + 199*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (13*(1 + S^4)*HPL[{3, 2}, -S^2])/(9*S^2) + (16*(1 + S^4)*HPL[{4, 1}, -S^2])/(9*S^2) + (2*(191 + 588*S^2 + 397*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (560*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) + (568*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (392*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((55*Pi^2*(1 + S^4))/(108*S^2) + (-325 - 218*S^2 + 211*S^4)/(72*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(576 + 2123*S^2 + 1497*S^4))/(216*S^2) + (1529 + 9824*S^2 + 8103*S^4)/(288*S^2) - (13*(1 + S^4)*HPL[{3}, -S^2])/(18*S^2) - (280*(1 + S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (5*(1 + S^4)*Zeta[3])/(18*S^2)) + (4*(1 + S^4)*Zeta[5])/(3*S^2))) + Log[T]^3*(-155/16 - (35159*Pi^6*S^2)/22680 + (Pi^4*(-17788 - 23967*S^2))/2160 - (5*Pi^2*(1676 + 3651*S^2))/432 - (11*S^2*HPL[{0}, S^2]^6)/54 - (28*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^5)/(9*S^2) - (112*(1 + S^4)*HPL[{1}, -S^2]^6)/(9*S^2) + HPL[{0}, S^2]^5*((-1092 - 1901*S^2)/1080 - (91*(1 + S^4)*HPL[{1}, -S^2])/(90*S^2)) + ((-2398 - 3480*S^2 - 3809*S^4)/(36*S^2) + (Pi^2*(-254 - 701*S^4))/(27*S^2))*HPL[{2}, -S^2]^2 - (2*(-257 + 331*S^4)*HPL[{2}, -S^2]^3)/(27*S^2) + HPL[{0}, S^2]^4*((-613*Pi^2*S^2)/324 + (-392 - 1255*S^2)/144 + ((-103 - 377*S^2 - 264*S^4)*HPL[{1}, -S^2])/(36*S^2) - (31*(1 + S^4)*HPL[{1}, -S^2]^2)/(6*S^2) + ((5 - 174*S^4)*HPL[{2}, -S^2])/(36*S^2)) + HPL[{1}, -S^2]^4*((-230*Pi^2*(1 + S^4))/(9*S^2) - (10*(68 + 159*S^2 + 91*S^4))/(9*S^2) - (50*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) - (2*(-13 + 107*S^4)*HPL[{3}, -S^2]^2)/(9*S^2) + ((191 + 632*S^2 + 256*S^4)/(6*S^2) + (Pi^2*(93 + 313*S^4))/(27*S^2))*HPL[{4}, -S^2] + ((78 + 372*S^2 + 29*S^4)*HPL[{5}, -S^2])/(9*S^2) - (2*(54 + 115*S^4)*HPL[{6}, -S^2])/(9*S^2) + (20*(33 + 46*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + HPL[{0}, S^2]^3*((-2258 - 8255*S^2)/216 + (Pi^2*(-2382 - 3713*S^2))/324 + ((-285 - 868*S^2 - 567*S^4)*HPL[{1}, -S^2]^2)/(18*S^2) - (430*(1 + S^4)*HPL[{1}, -S^2]^3)/(27*S^2) + ((79 - 1174*S^2 - 1680*S^4)*HPL[{2}, -S^2])/(54*S^2) + HPL[{1}, -S^2]*((-1155 - 4912*S^2 - 3677*S^4)/(108*S^2) - (397*Pi^2*(1 + S^4))/(54*S^2) - (196*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((-11 + 4*S^4)*HPL[{3}, -S^2])/(9*S^2) - (2*(-202 + 9*S^4)*HPL[{2, 1}, -S^2])/(9*S^2)) + ((4*Pi^2*(-354 + 671*S^4))/(27*S^2) + (-1060 - 124*S^2 + 1209*S^4)/(3*S^2))*HPL[{3, 1}, -S^2] - (5*(-111 + 792*S^2 + 670*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) - (4*(-197 + 3396*S^2 + 2697*S^4)*HPL[{4, 1}, -S^2])/(9*S^2) - (74*(-1 + 11*S^4)*HPL[{4, 2}, -S^2])/(9*S^2) - (200*(1 + 17*S^4)*HPL[{5, 1}, -S^2])/(9*S^2) + ((-10*(-170 + 42*S^2 + 271*S^4))/(3*S^2) - (20*Pi^2*(-113 + 298*S^4))/(27*S^2))*HPL[{2, 1, 1}, -S^2] - (16*(250 + 588*S^2 + 185*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) - (4*(981 + 1552*S^2 + 139*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (8*(-61 + 59*S^4)*HPL[{3, 1, 2}, -S^2])/(9*S^2) - (8*(-151 + 201*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (16*(-271 + 272*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (40*(-79 - 30*S^2 + 59*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (320*(-11 + 10*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (1120*(-5 + 7*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((2*Pi^2*(165 + 158*S^2))/9 + (5*(884 + 369*S^2))/18)*Zeta[3] + (8*S^2*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((-25*(97 + 244*S^2 + 147*S^4))/(18*S^2) - (5*Pi^2*(709 + 1656*S^2 + 947*S^4))/(81*S^2) - (10*(-3 + 20*S^2 + 23*S^4)*HPL[{2}, -S^2])/(3*S^2) + (1600*(1 + S^4)*HPL[{3}, -S^2])/(9*S^2) + (200*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (400*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((2967 + 3724*S^2 - 1845*S^4)/(18*S^2) - (4*Pi^2*(-589 - 465*S^2 + 246*S^4))/(27*S^2) - (40*(97 + 4*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]^2*((-3316 - 9081*S^2 - 5765*S^4)/(18*S^2) + (Pi^2*(-2999 - 7842*S^2 - 4843*S^4))/(54*S^2) - (1237*Pi^4*(1 + S^4))/(90*S^2) + ((119 - 338*S^2 - 457*S^4)/(3*S^2) - (314*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] - (392*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (2*(483 + 800*S^2 + 317*S^4)*HPL[{3}, -S^2])/(3*S^2) + (284*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (10*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/S^2 - (32*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (200*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (50*(43 + 72*S^2 + 29*S^4)*Zeta[3])/(9*S^2)) + HPL[{3}, -S^2]*((Pi^2*(11 + 2486*S^2 + 1845*S^4))/(54*S^2) + (587 + 9500*S^2 + 4615*S^4)/(36*S^2) + (8*(-189 + 16*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (4*(19 + 53*S^4)*Zeta[3])/(9*S^2)) + HPL[{2}, -S^2]*((8556 - 2966*S^2 - 18255*S^4)/(72*S^2) + (Pi^4*(4256 - 17677*S^4))/(1620*S^2) + (Pi^2*(1364 - 1404*S^2 - 4103*S^4))/(54*S^2) + (2*(-209 + 992*S^2 + 888*S^4)*HPL[{3}, -S^2])/(9*S^2) + (2*(-61 + 383*S^4)*HPL[{4}, -S^2])/(9*S^2) + (8*(250 + 588*S^2 + 185*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (8*(310 + 283*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (40*(33 + 46*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (4*(-7 + 480*S^2 + 393*S^4)*Zeta[3])/(9*S^2)) + HPL[{0}, S^2]^2*((-16369*Pi^4*S^2)/3240 + (Pi^2*(-581 - 1305*S^2))/36 - (5*(1166 + 3651*S^2))/144 - (5*(247 + 648*S^2 + 401*S^4)*HPL[{1}, -S^2]^3)/(27*S^2) - (30*(1 + S^4)*HPL[{1}, -S^2]^4)/S^2 + ((178 - 2178*S^2 - 4141*S^4)/(36*S^2) + (Pi^2*(55 - 1277*S^4))/(54*S^2))*HPL[{2}, -S^2] + ((-13 - 712*S^4)*HPL[{2}, -S^2]^2)/(18*S^2) + HPL[{1}, -S^2]^2*((-959 - 3072*S^2 - 2113*S^4)/(18*S^2) - (76*Pi^2*(1 + S^4))/(3*S^2) - (239*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-23 + 43*S^2 + 21*S^4)*HPL[{3}, -S^2])/(9*S^2) + ((9 - 41*S^4)*HPL[{4}, -S^2])/(9*S^2) + ((1171 + 1410*S^2 - 99*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (4*(-24 + 371*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (20*(-8 + 151*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (10 + 7*S^2)*Zeta[3] + HPL[{1}, -S^2]*((Pi^2*(-1853 - 5502*S^2 - 3589*S^4))/(108*S^2) - (13*(81 + 308*S^2 + 227*S^4))/(24*S^2) + ((-1039 - 2844*S^2 - 1853*S^4)*HPL[{2}, -S^2])/(18*S^2) + (10*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (478*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (10*(1 + S^4)*Zeta[3])/S^2)) + (8*(201 + 212*S^2)*Zeta[5])/9 + HPL[{0}, S^2]*((-25544 - 50677*S^2)/144 + (Pi^4*(-13496 - 17883*S^2))/1080 + (Pi^2*(-4919 - 9640*S^2))/108 - (70*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^4)/(9*S^2) - (112*(1 + S^4)*HPL[{1}, -S^2]^5)/(3*S^2) + ((-1 - 1164*S^2 - 1257*S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + HPL[{1}, -S^2]^3*((-1270*Pi^2*(1 + S^4))/(27*S^2) - (20*(68 + 159*S^2 + 91*S^4))/(9*S^2) - (500*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-147 + 52*S^2 + 11*S^4)/(18*S^2) + (Pi^2*(-83 + 97*S^4))/(27*S^2))*HPL[{3}, -S^2] + ((51 - 132*S^2 - 212*S^4)*HPL[{4}, -S^2])/(9*S^2) - (4*(5 + 3*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((3998 + 4794*S^2 - 89*S^4)/(9*S^2) - (2*Pi^2*(-602 + 29*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + (2*(-281 + 2244*S^2 + 2597*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (2*(53 + 157*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) - (8*(-1 + 40*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (20*(-49 + 450*S^2 + 529*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) - (8*(1159 + 34*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) - (8*(3527 + 17*S^4)*HPL[{3, 1, 1}, -S^2])/(9*S^2) - (320*(-20 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (10*Pi^2*S^2 + (2*(93 + 73*S^2))/3)*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(-1055 - 2548*S^2 - 1477*S^4))/(18*S^2) - (25*(97 + 244*S^2 + 147*S^4))/(12*S^2) - (5*(403 + 900*S^2 + 497*S^4)*HPL[{2}, -S^2])/(9*S^2) + (12*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (500*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (164*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((288 - 3742*S^2 - 5331*S^4)/(18*S^2) + (Pi^2*(324 - 3424*S^2 - 4325*S^4))/(54*S^2) + (2*(7 + 25*S^4)*HPL[{3}, -S^2])/(3*S^2) + (4*(1159 + 34*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (4*(-1 + 122*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]*((Pi^2*(-5235 - 14452*S^2 - 9137*S^4))/(108*S^2) + (-3316 - 9081*S^2 - 5765*S^4)/(18*S^2) - (1687*Pi^4*(1 + S^4))/(135*S^2) + ((-571*Pi^2*(1 + S^4))/(9*S^2) - (5*(361 + 882*S^2 + 521*S^4))/(9*S^2))*HPL[{2}, -S^2] - (392*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (2*(31 + 36*S^2 + 5*S^4)*HPL[{3}, -S^2])/(3*S^2) - (14*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (10*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (1496*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (1000*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(281 + 492*S^2 + 211*S^4)*Zeta[3])/(9*S^2)) + (416*S^2*Zeta[5])/9) + HPL[{1}, -S^2]*((Pi^4*(-17597 - 44493*S^2 - 26974*S^4))/(1620*S^2) + (Pi^2*(-1739 - 5052*S^2 - 3313*S^4))/(36*S^2) - (11*(2269 + 6876*S^2 + 4607*S^4))/(144*S^2) - (2*(551 + 1176*S^2 + 625*S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((410*Pi^2*(1 + S^4))/(9*S^2) + (2887 + 4416*S^2 + 1529*S^4)/(9*S^2))*HPL[{3}, -S^2] + (2*(571 + 846*S^2 + 287*S^4)*HPL[{4}, -S^2])/(9*S^2) + (124*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((628*Pi^2*(1 + S^4))/(9*S^2) + (2*(-119 + 338*S^2 + 457*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (4*(-347 - 48*S^2 + 299*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (440*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (4528*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (20*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (3136*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (6208*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (400*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((110*Pi^2*(1 + S^4))/(3*S^2) + (2*(1081 + 1698*S^2 + 617*S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-4*Pi^2*(113 + 468*S^2 + 361*S^4))/(27*S^2) - (5*(-115 + 328*S^2 + 443*S^4))/(12*S^2) + (220*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (1568*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (656*(1 + S^4)*Zeta[3])/(3*S^2)) + (536*(1 + S^4)*Zeta[5])/(3*S^2))) + ((-313 - 198*S^2)*Zeta[7])/2 + Log[T]^2*(245/32 + (Pi^2*(3278 + 10231*S^2))/144 + (Pi^4*(35251 + 75209*S^2))/4320 + (Pi^6*(308754 + 306827*S^2))/90720 + (7*S^2*HPL[{0}, S^2]^7)/144 + (14*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^6)/(9*S^2) + (16*(1 + S^4)*HPL[{1}, -S^2]^7)/(3*S^2) + HPL[{0}, S^2]^6*((82 + 149*S^2)/288 + (41*(1 + S^4)*HPL[{1}, -S^2])/(144*S^2)) + ((-210 + 62*S^2 + 279*S^4)*HPL[{2}, -S^2]^3)/(6*S^2) + HPL[{1}, -S^2]^5*((46*Pi^2*(1 + S^4))/(3*S^2) + (2*(68 + 159*S^2 + 91*S^4))/(3*S^2) + (10*(1 + S^4)*HPL[{2}, -S^2])/S^2) + HPL[{0}, S^2]^5*((1301*Pi^2*S^2)/2160 + (403 + 2163*S^2)/720 + ((433 + 2234*S^2 + 1701*S^4)*HPL[{1}, -S^2])/(720*S^2) + (91*(1 + S^4)*HPL[{1}, -S^2]^2)/(60*S^2) + ((-15 + 511*S^4)*HPL[{2}, -S^2])/(360*S^2)) + ((-49 + 226*S^2 + 160*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((Pi^2*(47 - 247*S^4))/(18*S^2) + (-283 - 1020*S^2 + 471*S^4)/(12*S^2))*HPL[{5}, -S^2] + ((-148 + 210*S^2 + 981*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((135 + 266*S^4)*HPL[{7}, -S^2])/(3*S^2) - (4*(301 + 588*S^2 + 440*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(-145 + 2143*S^4))/(18*S^2) + (-1099 + 8724*S^2 + 5519*S^4)/(12*S^2))*HPL[{3, 2}, -S^2] + ((Pi^2*(-103 + 3481*S^4))/(9*S^2) + (-645 + 14492*S^2 + 8798*S^4)/(6*S^2))*HPL[{4, 1}, -S^2] + ((-122 + 702*S^2 + 691*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) - (2*(-25 + 44*S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((272 + 1752*S^2 + 1175*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((53 - 59*S^4)*HPL[{5, 2}, -S^2])/S^2 + (2*(84 + 25*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((3*(168 + 608*S^2 + 137*S^4))/S^2 + (4*Pi^2*(703 + 256*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((4*Pi^2*(2102 + 183*S^4))/(9*S^2) + (4340 + 11436*S^2 + 823*S^4)/(3*S^2))*HPL[{3, 1, 1}, -S^2] + ((277 - 206*S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + ((-2243 + 744*S^2 + 3142*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + ((49 - 4001*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) - (8*(-64 + 1571*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + (4*(-2031 + 132*S^2 + 2257*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (2*(-289 + 6215*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) - (2*(-829 + 19235*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) - (16*(-210 + 4939*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((548*Pi^2*(-11 + 4*S^4))/(9*S^2) + (2*(-612 - 466*S^2 + 441*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (224*(-25 + 17*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) - (4*(-1637 - 48*S^2 + 1661*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (8*(-2017 + 401*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) - (8*(-2017 + 401*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (8*(-4117 + 1829*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (48*(-695 + 291*S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (80*(-44 + 15*S^2 + 64*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (16*(227 + 162*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (48*(227 + 162*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (160*(115 + 118*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (320*(-25 + 17*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-69*Pi^4*S^2)/10 + (-8392 - 2193*S^2)/24 + (Pi^2*(-1211 - 703*S^2))/18)*Zeta[3] - 4*(-5 + 4*S^2)*Zeta[3]^2 + HPL[{0}, S^2]^4*((5*(145 + 793*S^2))/288 + (Pi^2*(2346 + 3941*S^2))/864 + ((103 + 377*S^2 + 264*S^4)*HPL[{1}, -S^2]^2)/(24*S^2) + (31*(1 + S^4)*HPL[{1}, -S^2]^3)/(6*S^2) + ((-60 + 980*S^2 + 1557*S^4)*HPL[{2}, -S^2])/(144*S^2) + HPL[{1}, -S^2]*((391*Pi^2*(1 + S^4))/(144*S^2) + (725 + 4312*S^2 + 3491*S^4)/(288*S^2) + (245*(1 + S^4)*HPL[{2}, -S^2])/(36*S^2)) + ((10 - 7*S^4)*HPL[{3}, -S^2])/(24*S^2) + ((-505 + 32*S^4)*HPL[{2, 1}, -S^2])/(36*S^2) + (13*S^2*Zeta[3])/9) + HPL[{1}, -S^2]^4*((25*(97 + 244*S^2 + 147*S^4))/(24*S^2) + (5*Pi^2*(709 + 1656*S^2 + 947*S^4))/(108*S^2) + (5*(-3 + 20*S^2 + 23*S^4)*HPL[{2}, -S^2])/(2*S^2) - (400*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (50*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (100*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((Pi^2*(-1816 - 2444*S^2 + 659*S^4))/(18*S^2) + (-5106 - 9646*S^2 + 2193*S^4)/(24*S^2) + (Pi^4*(-17519 + 4414*S^4))/(540*S^2) + (8*(278 + 305*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (8*(227 + 162*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (8*(297 + 246*S^2 + 8*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((1237*Pi^4*(1 + S^4))/(90*S^2) + (Pi^2*(2999 + 7842*S^2 + 4843*S^4))/(54*S^2) + (3316 + 9081*S^2 + 5765*S^4)/(18*S^2) + ((314*Pi^2*(1 + S^4))/(9*S^2) + (-119 + 338*S^2 + 457*S^4)/(3*S^2))*HPL[{2}, -S^2] + (392*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) - (2*(483 + 800*S^2 + 317*S^4)*HPL[{3}, -S^2])/(3*S^2) - (284*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) - (10*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/S^2 + (32*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (200*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (50*(43 + 72*S^2 + 29*S^4)*Zeta[3])/(9*S^2)) + HPL[{4}, -S^2]*((-554 - 1843*S^2 - 540*S^4)/(12*S^2) + (Pi^2*(-330 - 806*S^2 - 327*S^4))/(36*S^2) - (8*(-100 + 11*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(-11 + 32*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^4*(377 - 8665*S^4))/(1080*S^2) + (-774 - 8836*S^2 - 3525*S^4)/(24*S^2) + (Pi^2*(-153 - 4968*S^2 - 2707*S^4))/(72*S^2) + (2*(-13 + 48*S^4)*HPL[{4}, -S^2])/(3*S^2) - (2*(-1374 - 988*S^2 + 73*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(-169 + 1081*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (8*(-24 + 181*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(31 + 71*S^2 + 53*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(310 + 957*S^2 + 893*S^4))/(18*S^2) + (1127 + 1371*S^2 + 1990*S^4)/(12*S^2) + ((-79 - 1089*S^4)*HPL[{3}, -S^2])/(6*S^2) + (28*(-25 + 17*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(-11 + 115*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((4*Pi^2*(-363 + 471*S^2 + 968*S^4))/(9*S^2) + (-2346 + 598*S^2 + 4245*S^4)/(3*S^2) - (8*(7 + 472*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((5935 + 808*S^2 - 7813*S^4)/(12*S^2) + (Pi^2*(1799 - 1366*S^2 - 3575*S^4))/(18*S^2) + (4*(9 + 479*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^2*((Pi^2*(2503 + 8210*S^2))/144 + (2618 + 10231*S^2)/48 + (Pi^4*(32990 + 48981*S^2))/4320 + (5*(247 + 648*S^2 + 401*S^4)*HPL[{1}, -S^2]^4)/(36*S^2) + (18*(1 + S^4)*HPL[{1}, -S^2]^5)/S^2 + ((3 + 123*S^2 + 151*S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + HPL[{1}, -S^2]^3*((76*Pi^2*(1 + S^4))/(3*S^2) + (959 + 3072*S^2 + 2113*S^4)/(18*S^2) + (239*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((Pi^2*(61 - 81*S^4))/(36*S^2) + (43 + 12*S^2 + 169*S^4)/(24*S^2))*HPL[{3}, -S^2] + ((-48 + 46*S^2 + 181*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((17 - 21*S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-1796 - 3490*S^2 - 5*S^4)/(12*S^2) + (Pi^2*(-631 + 35*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((81 - 707*S^2 - 957*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((21 + 89*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((-13 + 151*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (2*(-66 + 717*S^2 + 976*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(725 + 26*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (4*(1103 + 9*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (4*(-757 + 38*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-244 - 83*S^2)*Zeta[3])/12 + HPL[{2}, -S^2]*((Pi^2*(-192 + 2414*S^2 + 3509*S^4))/(72*S^2) + (-106 + 1866*S^2 + 4321*S^4)/(24*S^2) + ((-7 - 45*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-725 - 26*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((3 - 46*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]*((3299*Pi^4*(1 + S^4))/(432*S^2) + (1400 + 6177*S^2 + 4777*S^4)/(24*S^2) + (Pi^2*(2643 + 10456*S^2 + 7717*S^4))/(144*S^2) + ((1207*Pi^2*(1 + S^4))/(36*S^2) + (809 + 2834*S^2 + 2073*S^4)/(12*S^2))*HPL[{2}, -S^2] + (123*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((-38 - 37*S^2 + 15*S^4)*HPL[{3}, -S^2])/(3*S^2) + (25*(1 + S^4)*HPL[{4}, -S^2])/(6*S^2) + ((-1039 - 2844*S^2 - 1853*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) - (236*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (478*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-64 - 89*S^2 - 27*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((13*(81 + 308*S^2 + 227*S^4))/(16*S^2) + (Pi^2*(1853 + 5502*S^2 + 3589*S^4))/(72*S^2) + ((1039 + 2844*S^2 + 1853*S^4)*HPL[{2}, -S^2])/(12*S^2) - (5*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (239*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (15*(1 + S^4)*Zeta[3])/S^2)) + HPL[{0}, S^2]^3*((16369*Pi^4*S^2)/6480 + (Pi^2*(2444 + 8233*S^2))/432 + (3136 + 18203*S^2)/288 + ((285 + 868*S^2 + 567*S^4)*HPL[{1}, -S^2]^3)/(18*S^2) + (215*(1 + S^4)*HPL[{1}, -S^2]^4)/(18*S^2) + ((Pi^2*(-33 + 1126*S^4))/(108*S^2) + (-50 + 802*S^2 + 1809*S^4)/(36*S^2))*HPL[{2}, -S^2] + ((-9 + 569*S^4)*HPL[{2}, -S^2]^2)/(36*S^2) + HPL[{1}, -S^2]^2*((397*Pi^2*(1 + S^4))/(36*S^2) + (1155 + 4912*S^2 + 3677*S^4)/(72*S^2) + (98*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((45 + 26*S^2 + 19*S^4)*HPL[{3}, -S^2])/(36*S^2) + ((-3 + 68*S^4)*HPL[{4}, -S^2])/(18*S^2) + ((-843 - 1178*S^2 + 92*S^4)*HPL[{2, 1}, -S^2])/(18*S^2) + ((18 - 605*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (2*(-6 + 205*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (5*(-2 + 21*S^2)*Zeta[3])/18 + HPL[{1}, -S^2]*((Pi^2*(644 + 2419*S^2 + 1701*S^4))/(108*S^2) + (403 + 2403*S^2 + 1968*S^4)/(36*S^2) + ((1 + S^2)*(191 + 397*S^2)*HPL[{2}, -S^2])/(9*S^2) + (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (196*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (5*(1 + S^4)*Zeta[3])/(9*S^2))) + ((-500*Pi^2*S^2)/9 + (-1984 - 999*S^2)/6)*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^2*(1739 + 5052*S^2 + 3313*S^4))/(24*S^2) + (11*(2269 + 6876*S^2 + 4607*S^4))/(96*S^2) + (Pi^4*(17597 + 44493*S^2 + 26974*S^4))/(1080*S^2) + ((551 + 1176*S^2 + 625*S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-2887 - 4416*S^2 - 1529*S^4)/(6*S^2) - (205*Pi^2*(1 + S^4))/(3*S^2))*HPL[{3}, -S^2] + ((-571 - 846*S^2 - 287*S^4)*HPL[{4}, -S^2])/(3*S^2) - (62*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((119 - 338*S^2 - 457*S^4)/S^2 - (314*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(-347 - 48*S^2 + 299*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (660*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (2264*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (30*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (1568*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (3104*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (600*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-1081 - 1698*S^2 - 617*S^4)/(3*S^2) - (55*Pi^2*(1 + S^4))/S^2)*Zeta[3] + HPL[{2}, -S^2]*((2*Pi^2*(113 + 468*S^2 + 361*S^4))/(9*S^2) + (5*(-115 + 328*S^2 + 443*S^4))/(8*S^2) - (330*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (784*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (328*(1 + S^4)*Zeta[3])/S^2) - (268*(1 + S^4)*Zeta[5])/S^2) + HPL[{1}, -S^2]*((17153*Pi^6*(1 + S^4))/(5040*S^2) + (Pi^2*(786 + 2543*S^2 + 1757*S^4))/(12*S^2) + (8061 + 27734*S^2 + 19673*S^4)/(32*S^2) + (Pi^4*(11307 + 33572*S^2 + 22361*S^4))/(864*S^2) + ((319*Pi^2*(1 + S^4))/(6*S^2) + (1955 + 4476*S^2 + 2521*S^4)/(12*S^2))*HPL[{2}, -S^2]^2 + (31*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) + (37*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-2427 - 3188*S^2 - 761*S^4)/(12*S^2) - (401*Pi^2*(1 + S^4))/(18*S^2))*HPL[{4}, -S^2] + (4*(-113 - 92*S^2 + 19*S^4)*HPL[{5}, -S^2])/(3*S^2) + (35*(1 + S^4)*HPL[{6}, -S^2])/S^2 - (784*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-76*Pi^2*(1 + S^4))/S^2 - (4*(-233 + 15*S^2 + 248*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] + (4*(583 + 989*S^2 + 408*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (4*(2033 + 3393*S^2 + 1366*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (117*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (584*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((628*Pi^2*(1 + S^4))/(3*S^2) + (2*(-119 + 338*S^2 + 457*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] + (8*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (4*(619 + 1552*S^2 + 933*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (248*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (176*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (60*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + (64*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (1200*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-1203 - 1978*S^2 - 779*S^4))/(18*S^2) + (-343 - 524*S^2 - 181*S^4)/S^2)*Zeta[3] + (20*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{3}, -S^2]*((-5515 - 7896*S^2 - 2381*S^4)/(12*S^2) + (Pi^2*(-1525 - 2474*S^2 - 921*S^4))/(18*S^2) + (660*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (48*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-4*Pi^2*(113 + 468*S^2 + 361*S^4))/(9*S^2) - (5*(-115 + 328*S^2 + 443*S^4))/(4*S^2) + (656*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((4421*Pi^4*(1 + S^4))/(360*S^2) + (Pi^2*(113 + 962*S^2 + 861*S^4))/(9*S^2) + (-575 + 2102*S^2 + 2677*S^4)/(8*S^2) - (5*(233 + 396*S^2 + 163*S^4)*HPL[{3}, -S^2])/(3*S^2) - (113*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (784*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(587 + 972*S^2 + 409*S^4)*Zeta[3])/(3*S^2)) - (2*(510 + 805*S^2 + 293*S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-1226 + 1232*S^2 + 4283*S^4))/(36*S^2) + (-3902 + 2179*S^2 + 10231*S^4)/(24*S^2) + (Pi^4*(-11396 + 26526*S^2 + 47667*S^4))/(2160*S^2) + ((833 - 4400*S^2 - 2935*S^4)/(12*S^2) + (Pi^2*(137 - 1131*S^4))/(18*S^2))*HPL[{3}, -S^2] + ((212 - 686*S^2 - 579*S^4)*HPL[{4}, -S^2])/(6*S^2) - (5*(-5 + 39*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-3*(168 + 608*S^2 + 137*S^4))/(2*S^2) - (2*Pi^2*(703 + 256*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] - (4*(372 + 587*S^2 + 382*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((41 + 2061*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (2*(-163 + 3311*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (8*(301 + 588*S^2 + 440*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (112*(-25 + 17*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (8*(-326 + 57*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (8*(227 + 162*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-2*Pi^2*(2 + 259*S^4))/(9*S^2) - (2*(-10 + 523*S^2 + 332*S^4))/(3*S^2))*Zeta[3] - (2*(-14 + 417*S^4)*Zeta[5])/(3*S^2)) + HPL[{0}, S^2]*((147719*Pi^6*S^2)/45360 + (Pi^2*(16814 + 41263*S^2))/288 + (Pi^4*(27731 + 56828*S^2))/2160 + (24623 + 59019*S^2)/96 + (14*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^5)/(3*S^2) + (56*(1 + S^4)*HPL[{1}, -S^2]^6)/(3*S^2) + ((Pi^2*(8 + 1711*S^4))/(36*S^2) + (-14 + 4024*S^2 + 5061*S^4)/(24*S^2))*HPL[{2}, -S^2]^2 + (2*(-19 + 275*S^4)*HPL[{2}, -S^2]^3)/(9*S^2) + HPL[{1}, -S^2]^4*((635*Pi^2*(1 + S^4))/(18*S^2) + (5*(68 + 159*S^2 + 91*S^4))/(3*S^2) + (125*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((8 - 19*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((Pi^2*(-9 + 146*S^4))/(18*S^2) + (-65 + 234*S^2 + 447*S^4)/(12*S^2))*HPL[{4}, -S^2] + ((25 + 104*S^2 + 104*S^4)*HPL[{5}, -S^2])/(6*S^2) + (4*(5 + 29*S^4)*HPL[{6}, -S^2])/(3*S^2) - (2*(17 + 1142*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((425 - 4012*S^2 - 5240*S^4)/(6*S^2) - (7*Pi^2*(-15 + 254*S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + ((98 + 500*S^2 + 211*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((-13 + 624*S^2 + 306*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((-1 - 8*S^4)*HPL[{4, 2}, -S^2])/(3*S^2) - 68*S^2*HPL[{5, 1}, -S^2] + ((2*Pi^2*(-31 + 600*S^4))/(3*S^2) + (-388 + 4026*S^2 + 5299*S^4)/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (4*(-1101 - 1188*S^2 + 7*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(-6703 - 6996*S^2 + 155*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (2*(11 + 7*S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (2*(-141 + 2207*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (8*(-39 + 563*S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (40*(-226 - 225*S^2 + 16*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (8*(-29 + 391*S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (80*(-5 + 79*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-1210 - 677*S^2)/12 + (Pi^2*(-128 - 77*S^2))/9)*Zeta[3] + 10*S^2*Zeta[3]^2 + HPL[{2}, -S^2]*((Pi^2*(-488 + 5630*S^2 + 8917*S^4))/(72*S^2) + (Pi^4*(-415 + 9577*S^4))/(540*S^2) + (-892 + 14582*S^2 + 22207*S^4)/(48*S^2) + ((-31 - 252*S^2 - 93*S^4)*HPL[{3}, -S^2])/(6*S^2) + ((-19 + 44*S^4)*HPL[{4}, -S^2])/(3*S^2) + (2*(-1101 - 1188*S^2 + 7*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (34*(1 + 67*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(17 + 1142*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((4 - 248*S^2 - 215*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((1687*Pi^4*(1 + S^4))/(90*S^2) + (3316 + 9081*S^2 + 5765*S^4)/(12*S^2) + (Pi^2*(5235 + 14452*S^2 + 9137*S^4))/(72*S^2) + ((571*Pi^2*(1 + S^4))/(6*S^2) + (5*(361 + 882*S^2 + 521*S^4))/(6*S^2))*HPL[{2}, -S^2] + (196*(1 + S^4)*HPL[{2}, -S^2]^2)/S^2 + ((-31 - 36*S^2 - 5*S^4)*HPL[{3}, -S^2])/S^2 + (21*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (5*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (748*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (1500*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-281 - 492*S^2 - 211*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((25*(97 + 244*S^2 + 147*S^4))/(12*S^2) + (Pi^2*(1055 + 2548*S^2 + 1477*S^4))/(18*S^2) + (5*(403 + 900*S^2 + 497*S^4)*HPL[{2}, -S^2])/(9*S^2) - (12*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (500*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (164*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((-7083 - 10012*S^2 - 327*S^4)/(12*S^2) + (Pi^2*(-3103 - 3428*S^2 + 252*S^4))/(18*S^2) + (4*(124 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(71 - 53*S^2 - 47*S^4))/(18*S^2) + (116 + 202*S^2 + 203*S^4)/(12*S^2) + (2*(31 + 13*S^4)*HPL[{2, 1}, -S^2])/S^2 - (2*(5 + 3*S^4)*Zeta[3])/(3*S^2)) + ((-184 - 123*S^2)*Zeta[5])/3 + HPL[{1}, -S^2]*((11*(2269 + 6876*S^2 + 4607*S^4))/(96*S^2) + (Pi^2*(8887 + 27912*S^2 + 18897*S^4))/(144*S^2) + (Pi^4*(29391 + 81518*S^2 + 51043*S^4))/(2160*S^2) + ((551 + 1176*S^2 + 625*S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-5*Pi^2*(1 + S^4))/(3*S^2) + (2*(-33 - 8*S^2 + 21*S^4))/(3*S^2))*HPL[{3}, -S^2] + ((55 + 264*S^2 + 185*S^4)*HPL[{4}, -S^2])/(6*S^2) + (58*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-571*Pi^2*(1 + S^4))/(3*S^2) - (5*(361 + 882*S^2 + 521*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(1009 + 2244*S^2 + 1235*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (76*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (186*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (10*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (1568*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (4632*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (3000*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-593 - 988*S^2 - 379*S^4)/(6*S^2) - (128*Pi^2*(1 + S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((9*(241 + 648*S^2 + 407*S^4))/(8*S^2) + (Pi^2*(2779 + 6852*S^2 + 4073*S^4))/(36*S^2) - (38*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (784*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (82*(1 + S^4)*Zeta[3])/S^2) - (184*(1 + S^4)*Zeta[5])/(3*S^2))) - 372*S^2*Zeta[7]) + HPL[{0}, S^2]^2*((35*(517 + 1673*S^2))/384 + (Pi^2*(4540 + 20169*S^2))/576 + (Pi^4*(23889 + 110980*S^2))/17280 + (Pi^6*(290878 + 406141*S^2))/362880 + ((247 + 648*S^2 + 401*S^4)*HPL[{1}, -S^2]^6)/(108*S^2) + (6*(1 + S^4)*HPL[{1}, -S^2]^7)/(7*S^2) + ((-48 + 682*S^2 + 873*S^4)*HPL[{2}, -S^2]^3)/(72*S^2) + HPL[{1}, -S^2]^5*((38*Pi^2*(1 + S^4))/(15*S^2) + (959 + 3072*S^2 + 2113*S^4)/(180*S^2) + (239*(1 + S^4)*HPL[{2}, -S^2])/(30*S^2)) + ((13 - 18*S^2 - 64*S^4)*HPL[{3}, -S^2]^2)/(24*S^2) + ((Pi^2*(-43 - 69*S^4))/(72*S^2) + (167 - 88*S^2 + 555*S^4)/(48*S^2))*HPL[{5}, -S^2] + ((40 + 114*S^2 + 577*S^4)*HPL[{6}, -S^2])/(24*S^2) - (5*(21 + 2*S^4)*HPL[{7}, -S^2])/(12*S^2) + ((-3 - 123*S^2 - 151*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((29 + 504*S^2 - 251*S^4)/(48*S^2) + (Pi^2*(57 + 89*S^4))/(72*S^2))*HPL[{3, 2}, -S^2] + ((-14 + 494*S^2 - 515*S^4)/(24*S^2) + (Pi^2*(8 + 175*S^4))/(36*S^2))*HPL[{4, 1}, -S^2] + ((-20 - 22*S^2 - 33*S^4)*HPL[{4, 2}, -S^2])/(24*S^2) + ((-3 - 11*S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((47 - 78*S^2 - 376*S^4)*HPL[{5, 1}, -S^2])/(12*S^2) + ((-29 - 149*S^4)*HPL[{5, 2}, -S^2])/(12*S^2) + ((-32 - 153*S^4)*HPL[{6, 1}, -S^2])/(6*S^2) + ((1772 + 3488*S^2 - 103*S^4)/(12*S^2) + (Pi^2*(599 + 15*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((5359 + 10476*S^2 - 140*S^4)/(12*S^2) + (Pi^2*(3655 + 9*S^4))/(18*S^2))*HPL[{3, 1, 1}, -S^2] + ((25 + 2*S^2 + 6*S^4)*HPL[{3, 1, 2}, -S^2])/(12*S^2) + ((-167 + 2730*S^2 + 3498*S^4)*HPL[{3, 2, 1}, -S^2])/(12*S^2) + ((33 - 185*S^4)*HPL[{3, 2, 2}, -S^2])/(12*S^2) - (4*(-1 + 36*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + ((-336 + 4138*S^2 + 5419*S^4)*HPL[{4, 1, 1}, -S^2])/(6*S^2) + ((6 - 287*S^4)*HPL[{4, 1, 2}, -S^2])/(6*S^2) + ((-6 - 863*S^4)*HPL[{4, 2, 1}, -S^2])/(6*S^2) + ((-1 - 885*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((-1796 - 3490*S^2 - 5*S^4)/(6*S^2) + (2*Pi^2*(-631 + 35*S^4))/(9*S^2))*HPL[{2, 1, 1, 1}, -S^2] + (16*(-89 + 2*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) - (2*(-81 + 707*S^2 + 957*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + ((4293 - 7*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + ((4293 - 7*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + ((8565 - 103*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (2*(-12803 + 137*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) + (4*(-66 + 717*S^2 + 976*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) - (4*(725 + 26*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) - (4*(725 + 26*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (8*(1797 + 95*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) + (8*(-757 + 38*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((69*Pi^4*S^2)/40 + (3*(-74 + 9*S^2))/32 + (Pi^2*(-260 + 373*S^2))/144)*Zeta[3] + ((26 + 5*S^2)*Zeta[3]^2)/4 + HPL[{4}, -S^2]*((Pi^2*(-18 + 94*S^2 + 445*S^4))/(144*S^2) + (153 - 27*S^2 + 664*S^4)/(48*S^2) + ((-23 - 8*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (4*Zeta[3])/S^2) + HPL[{1}, -S^2]^3*((3299*Pi^4*(1 + S^4))/(1296*S^2) + (1400 + 6177*S^2 + 4777*S^4)/(72*S^2) + (Pi^2*(2643 + 10456*S^2 + 7717*S^4))/(432*S^2) + ((1207*Pi^2*(1 + S^4))/(108*S^2) + (809 + 2834*S^2 + 2073*S^4)/(36*S^2))*HPL[{2}, -S^2] + (41*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((-38 - 37*S^2 + 15*S^4)*HPL[{3}, -S^2])/(9*S^2) + (25*(1 + S^4)*HPL[{4}, -S^2])/(18*S^2) + ((-1039 - 2844*S^2 - 1853*S^4)*HPL[{2, 1}, -S^2])/(18*S^2) - (236*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (478*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-64 - 89*S^2 - 27*S^4)*Zeta[3])/(9*S^2)) + HPL[{2, 1}, -S^2]*((-4778 - 17022*S^2 - 1891*S^4)/(96*S^2) + (Pi^2*(-2494 - 6234*S^2 + 41*S^4))/(144*S^2) + (Pi^4*(-14373 + 1424*S^4))/(2160*S^2) + ((719 + 29*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(725 + 26*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((161 + 98*S^2 - 20*S^4)*Zeta[3])/(6*S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(6 + 601*S^2 + 784*S^4))/(72*S^2) + (105 + 1634*S^2 + 4051*S^4)/(96*S^2) - (3*(-1 + 5*S^4)*HPL[{3}, -S^2])/(8*S^2) + (2*(-89 + 2*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((7 - 17*S^4)*Zeta[3])/(6*S^2)) + HPL[{3}, -S^2]*((Pi^4*(613 - 1137*S^4))/(4320*S^2) + (Pi^2*(253 + 192*S^2 + 397*S^4))/(288*S^2) + (388 + 462*S^2 + 1271*S^4)/(96*S^2) + ((3 + 10*S^4)*HPL[{4}, -S^2])/(6*S^2) + (25*(5 + 4*S^2 + 3*S^4)*HPL[{2, 1}, -S^2])/(12*S^2) + ((11 + 51*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + ((-7 - 45*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-8 - 10*S^2 - 13*S^4)*Zeta[3])/(12*S^2)) + HPL[{1}, -S^2]^4*((13*(81 + 308*S^2 + 227*S^4))/(96*S^2) + (Pi^2*(1853 + 5502*S^2 + 3589*S^4))/(432*S^2) + ((1039 + 2844*S^2 + 1853*S^4)*HPL[{2}, -S^2])/(72*S^2) - (5*(1 + S^4)*HPL[{3}, -S^2])/(6*S^2) - (239*(1 + S^4)*HPL[{2, 1}, -S^2])/(6*S^2) - (5*(1 + S^4)*Zeta[3])/(2*S^2)) + HPL[{3, 1}, -S^2]*((375 - 3532*S^2 - 8765*S^4)/(48*S^2) + (Pi^2*(237 - 2366*S^2 - 3412*S^4))/(72*S^2) + (2*(-3 + 23*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-192 + 2414*S^2 + 3509*S^4))/(36*S^2) + (-106 + 1866*S^2 + 4321*S^4)/(12*S^2) - (2*(-3 + 46*S^4)*Zeta[3])/(3*S^2)) + ((125*Pi^2*S^2)/9 + (-33 + 62*S^2)/12)*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^2*(4215 + 20716*S^2 + 16405*S^4))/(576*S^2) + (11075 + 54196*S^2 + 43121*S^4)/(384*S^2) + (Pi^4*(18819 + 66604*S^2 + 46537*S^4))/(8640*S^2) + ((97 + 246*S^2 + 149*S^4)*HPL[{2}, -S^2]^2)/(4*S^2) + ((Pi^2*(-1 - S^4))/(12*S^2) + (-35 + 3*S^2 + 50*S^4)/(6*S^2))*HPL[{3}, -S^2] + ((-49 + 88*S^2 + 161*S^4)*HPL[{4}, -S^2])/(24*S^2) + (11*(1 + S^4)*HPL[{5}, -S^2])/(6*S^2) + ((-809 - 2834*S^2 - 2073*S^4)/(12*S^2) - (1207*Pi^2*(1 + S^4))/(36*S^2))*HPL[{2, 1}, -S^2] + ((-253 - 701*S^2 - 462*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (26*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (131*(1 + S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((1039 + 2844*S^2 + 1853*S^4)*HPL[{2, 1, 1}, -S^2])/(6*S^2) + (246*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (728*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (478*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-263 - 348*S^2 - 85*S^4)/(24*S^2) - (7*Pi^2*(1 + S^4))/(36*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1577 + 4806*S^2 + 3273*S^4))/(144*S^2) + (2615 + 11512*S^2 + 9089*S^4)/(96*S^2) - (13*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (123*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (47*(1 + S^4)*Zeta[3])/(6*S^2)) + ((1 + S^4)*Zeta[5])/(6*S^2)) + HPL[{2}, -S^2]*((Pi^2*(104 + 2774*S^2 + 7939*S^4))/(288*S^2) + (580 + 4007*S^2 + 10231*S^4)/(96*S^2) + (Pi^4*(-1740 + 27766*S^2 + 46143*S^4))/(8640*S^2) + ((-5*Pi^2*(5 + 9*S^4))/(72*S^2) + (17 - 240*S^2 + 147*S^4)/(48*S^2))*HPL[{3}, -S^2] + ((-8 + 42*S^2 + 151*S^4)*HPL[{4}, -S^2])/(24*S^2) + ((-15 - 7*S^4)*HPL[{5}, -S^2])/(12*S^2) + ((Pi^2*(-599 - 15*S^4))/(18*S^2) + (-1772 - 3488*S^2 + 103*S^4)/(24*S^2))*HPL[{2, 1}, -S^2] + ((-29 - 1464*S^2 - 1821*S^4)*HPL[{3, 1}, -S^2])/(12*S^2) + ((-5 + 31*S^4)*HPL[{3, 2}, -S^2])/(4*S^2) + ((-4 + 143*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + (2*(3 + 123*S^2 + 151*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (8*(-89 + 2*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + ((-2143 + 3*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (2*(725 + 26*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((8 - 170*S^2 - 69*S^4)/(24*S^2) + (Pi^2*(9 - 8*S^4))/(18*S^2))*Zeta[3] + (5*(6 + S^4)*Zeta[5])/(6*S^2)) + HPL[{1}, -S^2]*((20777*Pi^6*(1 + S^4))/(25920*S^2) + (Pi^2*(2121 + 11291*S^2 + 9074*S^4))/(288*S^2) + (14383 + 65642*S^2 + 51259*S^4)/(384*S^2) + (Pi^4*(24917 + 130344*S^2 + 101875*S^4))/(17280*S^2) + ((601*Pi^2*(1 + S^4))/(72*S^2) + (917 + 2812*S^2 + 1895*S^4)/(48*S^2))*HPL[{2}, -S^2]^2 + (341*(1 + S^4)*HPL[{2}, -S^2]^3)/(36*S^2) - (11*(1 + S^4)*HPL[{3}, -S^2]^2)/(12*S^2) + ((73*Pi^2*(1 + S^4))/(72*S^2) + (-151 + 288*S^2 + 567*S^4)/(48*S^2))*HPL[{4}, -S^2] + ((-63 + 26*S^2 + 125*S^4)*HPL[{5}, -S^2])/(12*S^2) + (39*(1 + S^4)*HPL[{6}, -S^2])/(4*S^2) - (123*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-777 - 2824*S^2 - 2095*S^4)/(12*S^2) - (299*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + ((119 + 222*S^2 + 75*S^4)*HPL[{3, 2}, -S^2])/(12*S^2) + ((403 + 584*S^2 + 61*S^4)*HPL[{4, 1}, -S^2])/(12*S^2) - (3*(1 + S^4)*HPL[{4, 2}, -S^2])/(4*S^2) - (28*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((1207*Pi^2*(1 + S^4))/(18*S^2) + (809 + 2834*S^2 + 2073*S^4)/(6*S^2))*HPL[{2, 1, 1}, -S^2] + (2*(97 + 246*S^2 + 149*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (2*(835 + 2177*S^2 + 1356*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (682*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (2071*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + ((-1039 - 2844*S^2 - 1853*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (472*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (956*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-509 - 524*S^2 - 175*S^4)/(48*S^2) + (Pi^2*(-83 + 12*S^2 + 43*S^4))/(36*S^2))*Zeta[3] + (13*(1 + S^4)*Zeta[3]^2)/(2*S^2) + HPL[{2}, -S^2]*((13883*Pi^4*(1 + S^4))/(4320*S^2) + (Pi^2*(1143 + 4786*S^2 + 3755*S^4))/(144*S^2) + (2329 + 12114*S^2 + 10169*S^4)/(96*S^2) + ((-59 - 112*S^2 - 37*S^4)*HPL[{3}, -S^2])/(12*S^2) + (25*(1 + S^4)*HPL[{4}, -S^2])/(12*S^2) + ((-97 - 246*S^2 - 149*S^4)*HPL[{2, 1}, -S^2])/S^2 - (367*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (246*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-149 - 190*S^2 - 37*S^4)*Zeta[3])/(12*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-85 - 50*S^2 + 111*S^4))/(72*S^2) + (-74 + 67*S^2 + 181*S^4)/(12*S^2) + (26*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (7*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((-2615 - 11512*S^2 - 9089*S^4)/(48*S^2) + (Pi^2*(-1577 - 4806*S^2 - 3273*S^4))/(72*S^2) + (47*(1 + S^4)*Zeta[3])/(3*S^2)) + ((-93 + 32*S^2 + 69*S^4)*Zeta[5])/(12*S^2)) + 93*S^2*Zeta[7]) + HPL[{2}, -S^2]*((245*(-40 + 131*S^2 + 239*S^4))/(192*S^2) + (Pi^2*(-1661 + 3093*S^2 + 10231*S^4))/(144*S^2) + (Pi^4*(-16208 + 33202*S^2 + 105999*S^4))/(8640*S^2) + (Pi^6*(-29136 + 99162*S^2 + 188105*S^4))/(90720*S^2) + ((22 + 115*S^2 + 81*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((Pi^2*(5 - 101*S^4))/(18*S^2) + (85 - 734*S^2 + 180*S^4)/(12*S^2))*HPL[{5}, -S^2] + ((119 - 92*S^2 + 552*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((85 + 208*S^4)*HPL[{7}, -S^2])/(3*S^2) + ((210 - 62*S^2 - 279*S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((Pi^2*(13 + 1077*S^4))/(18*S^2) + (-45 + 4622*S^2 + 2911*S^4)/(12*S^2))*HPL[{3, 2}, -S^2] + ((Pi^2*(-167 + 3454*S^4))/(18*S^2) + (-1259 + 14274*S^2 + 9127*S^4)/(12*S^2))*HPL[{4, 1}, -S^2] + ((19 + 152*S^2 + 119*S^4)*HPL[{4, 2}, -S^2])/(2*S^2) - ((-7 + 4*S^2)*(7 + 4*S^2)*HPL[{4, 3}, -S^2])/(3*S^2) + ((-205 + 1854*S^2 + 1237*S^4)*HPL[{5, 1}, -S^2])/(6*S^2) - (2*(-71 + S^4)*HPL[{5, 2}, -S^2])/(3*S^2) + (2*(119 + 69*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((1840 + 1132*S^2 - 1373*S^4)/(6*S^2) - (4*Pi^2*(-353 + 123*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((Pi^2*(-4099 + 345*S^4))/(9*S^2) + (-4687 - 7796*S^2 + 1184*S^4)/(6*S^2))*HPL[{3, 1, 1}, -S^2] + ((-85 - 156*S^2 - 71*S^4)*HPL[{3, 1, 2}, -S^2])/(2*S^2) + ((715 + 1380*S^2 + 1033*S^4)*HPL[{3, 2, 1}, -S^2])/(2*S^2) + ((129 - 1984*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) - (80*(-1 + 26*S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + ((3812 + 6226*S^2 + 4389*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + ((191 - 6172*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) + ((707 - 19108*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) - (94*(-17 + 417*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((-3*(168 + 608*S^2 + 137*S^4))/S^2 - (4*Pi^2*(703 + 256*S^4))/(9*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (8*(325 + 242*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) - (8*(-3408 + 1703*S^2 + 5404*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (2*(3859 + 843*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) - (2*(3859 + 843*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (2*(7759 + 3747*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (4*(11863 + 5401*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) + (16*(301 + 588*S^2 + 440*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (224*(-25 + 17*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (224*(-25 + 17*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (16*(-1822 + 1733*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) - (16*(227 + 162*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^4*(71 - 1721*S^4))/(540*S^2) + (Pi^2*(48 - 2262*S^2 - 1397*S^4))/(72*S^2) + (82 - 1844*S^2 - 1021*S^4)/(12*S^2))*Zeta[3] + ((-28 + 6*S^2 + 61*S^4)*Zeta[3]^2)/(6*S^2) + HPL[{3}, -S^2]*((583 - 4082*S^2 - 2019*S^4)/(24*S^2) + (Pi^2*(425 - 2320*S^2 - 1394*S^4))/(72*S^2) + (Pi^4*(87 - 1010*S^4))/(270*S^2) + (2*(-12 + 17*S^4)*HPL[{4}, -S^2])/(3*S^2) + ((2749 + 2424*S^2 + 149*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (10*(7 + 108*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (2*(79 + 1089*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((15 - 36*S^2 - 53*S^4)*Zeta[3])/(2*S^2)) + HPL[{4}, -S^2]*((693 - 2018*S^2 - 783*S^4)/(24*S^2) + (Pi^2*(51 - 161*S^2 - 107*S^4))/(18*S^2) + ((395 + 56*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((1 - 32*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^4*(-8172 - 1853*S^4))/(540*S^2) + (Pi^2*(-1642 - 4480*S^2 - 565*S^4))/(36*S^2) - (5*(752 + 4722*S^2 + 763*S^4))/(48*S^2) - (2*(-571 + 605*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (112*(-25 + 17*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (4*(-292 - 219*S^2 + 13*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((2*Pi^2*(310 + 957*S^2 + 893*S^4))/(9*S^2) + (1127 + 1371*S^2 + 1990*S^4)/(3*S^2) - (16*(-11 + 115*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((-2794 - 2528*S^2 - 3593*S^4)/(12*S^2) + (Pi^2*(-1517 - 3812*S^2 - 3349*S^4))/(36*S^2) + (2*(-17 + 157*S^4)*Zeta[3])/S^2) + ((66 - 1726*S^2 - 907*S^4)/(12*S^2) - (2*Pi^2*(-11 + 103*S^4))/(9*S^2))*Zeta[5] + ((35 - 116*S^4)*Zeta[7])/S^2) + HPL[{1}, -S^2]*((55259*Pi^8*(1 + S^4))/(170100*S^2) + (70*(4 + 27*S^2 + 23*S^4))/(3*S^2) + (Pi^2*(19283 + 74422*S^2 + 55139*S^4))/(576*S^2) + (Pi^4*(46347 + 171647*S^2 + 126932*S^4))/(8640*S^2) + (Pi^6*(86011 + 289967*S^2 + 207540*S^4))/(90720*S^2) + ((217*Pi^2*(1 + S^4))/(54*S^2) + (-157 + 406*S^2 + 563*S^4)/(36*S^2))*HPL[{2}, -S^2]^3 + (8*(1 + S^4)*HPL[{2}, -S^2]^4)/S^2 + ((25*Pi^2*(1 + S^4))/(9*S^2) + (235 + 422*S^2 + 187*S^4)/(12*S^2))*HPL[{3}, -S^2]^2 + (4*(1 + S^4)*HPL[{4}, -S^2]^2)/S^2 + ((37*Pi^2*(1 + S^4))/(6*S^2) + (-578 + 333*S^2 + 911*S^4)/(6*S^2))*HPL[{6}, -S^2] + ((-520 + 565*S^2 + 939*S^4)*HPL[{7}, -S^2])/(3*S^2) + (280*(1 + S^4)*HPL[{8}, -S^2])/S^2 + ((-1955 - 4476*S^2 - 2521*S^4)/(6*S^2) - (319*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2]^2 + (466*(1 + S^4)*HPL[{3, 1}, -S^2]^2)/S^2 + ((19*Pi^2*(1 + S^4))/(2*S^2) + (253 + 466*S^2 + 213*S^4)/(4*S^2))*HPL[{4, 2}, -S^2] + ((-107 - 81*S^2 - 28*S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((410*Pi^2*(1 + S^4))/(9*S^2) + (2589 + 3332*S^2 + 743*S^4)/(6*S^2))*HPL[{5, 1}, -S^2] + ((-169 - 102*S^2 - 33*S^4)*HPL[{5, 2}, -S^2])/(2*S^2) - (4*(1 + S^4)*HPL[{5, 3}, -S^2])/S^2 - (5*(-29 + 22*S^2 + 79*S^4)*HPL[{6, 1}, -S^2])/(2*S^2) - (10*(1 + S^4)*HPL[{6, 2}, -S^2])/S^2 - (192*(1 + S^4)*HPL[{7, 1}, -S^2])/S^2 + (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2]^2)/S^2 - (2*(1 + 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + ((868*Pi^2*(1 + S^4))/(9*S^2) + (160*(-2 + 5*S^2 + 7*S^4))/(3*S^2))*HPL[{3, 2, 1}, -S^2] + ((-4931 - 8292*S^2 - 3361*S^4)*HPL[{3, 2, 2}, -S^2])/(6*S^2) - (4*(1887 + 3178*S^2 + 1295*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + (112*(1 + S^4)*HPL[{3, 3, 2}, -S^2])/S^2 + ((2203*Pi^2*(1 + S^4))/(9*S^2) + (-4311 + 1684*S^2 + 5995*S^4)/(6*S^2))*HPL[{4, 1, 1}, -S^2] + ((-14841 - 24956*S^2 - 10147*S^4)*HPL[{4, 1, 2}, -S^2])/(6*S^2) - (192*(1 + S^4)*HPL[{4, 1, 3}, -S^2])/S^2 + ((-46101 - 77756*S^2 - 31783*S^4)*HPL[{4, 2, 1}, -S^2])/(6*S^2) + (68*(1 + S^4)*HPL[{4, 2, 2}, -S^2])/S^2 - (656*(1 + S^4)*HPL[{4, 3, 1}, -S^2])/S^2 - (2*(23897 + 39968*S^2 + 16151*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) - (400*(1 + S^4)*HPL[{5, 1, 2}, -S^2])/S^2 - (2680*(1 + S^4)*HPL[{5, 2, 1}, -S^2])/S^2 - (6770*(1 + S^4)*HPL[{6, 1, 1}, -S^2])/S^2 - (4*(-21 + 124*S^2 + 145*S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((-152*Pi^2*(1 + S^4))/S^2 - (8*(-233 + 15*S^2 + 248*S^4))/(3*S^2))*HPL[{3, 1, 1, 1}, -S^2] + (4*(977 + 3094*S^2 + 2121*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + (4*(977 + 3094*S^2 + 2121*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + (78*(1 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/S^2 + (8*(394 + 2105*S^2 + 1713*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (78*(1 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/S^2 - (154*(1 + S^4)*HPL[{3, 2, 2, 1}, -S^2])/S^2 - (696*(1 + S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (8*(1466 + 6741*S^2 + 5281*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) + (234*(1 + S^4)*HPL[{4, 1, 1, 2}, -S^2])/S^2 - (462*(1 + S^4)*HPL[{4, 1, 2, 1}, -S^2])/S^2 - (1854*(1 + S^4)*HPL[{4, 2, 1, 1}, -S^2])/S^2 - (3008*(1 + S^4)*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((1256*Pi^2*(1 + S^4))/(3*S^2) + (4*(-119 + 338*S^2 + 457*S^4))/S^2)*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) - (16*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (496*(1 + S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/S^2 - (1488*(1 + S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 - (8*(6959 + 14160*S^2 + 7201*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) + (2976*(1 + S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^2 + (4960*(1 + S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 + (5952*(1 + S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^2 + (12400*(1 + S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 + (36064*(1 + S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 - (120*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (128*(1 + S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((23*Pi^2*(1 + S^4))/(6*S^2) + (145 + 324*S^2 + 83*S^4)/(12*S^2))*Zeta[3]^2 + HPL[{4}, -S^2]*((Pi^2*(-1289 - 1450*S^2 - 97*S^4))/(72*S^2) - (139*Pi^4*(1 + S^4))/(135*S^2) + (-2537 - 2486*S^2 + 243*S^4)/(24*S^2) + ((745 + 1356*S^2 + 611*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (114*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (226*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-101 - 112*S^2 - 35*S^4)*Zeta[3])/(6*S^2)) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(3527 + 9010*S^2 + 5511*S^4))/(9*S^2) + (9517 + 34896*S^2 + 25379*S^4)/(12*S^2) - (1848*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 2, 1}, -S^2]*((4*Pi^2*(421 + 957*S^2 + 536*S^4))/(9*S^2) + (2283 + 5632*S^2 + 3349*S^4)/(4*S^2) - (584*(1 + S^4)*Zeta[3])/S^2) + HPL[{5}, -S^2]*((Pi^2*(-515 - 342*S^2 + 201*S^4))/(36*S^2) + (-2819 - 956*S^2 + 1543*S^4)/(24*S^2) + (66*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (6*(1 + S^4)*Zeta[3])/S^2) + HPL[{3, 2}, -S^2]*((1060 + 1609*S^2 + 589*S^4)/(3*S^2) + (Pi^2*(2451 + 4178*S^2 + 1707*S^4))/(36*S^2) + (36*(1 + S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((Pi^2*(8535 + 14156*S^2 + 5525*S^4))/(36*S^2) + (15241 + 22156*S^2 + 7395*S^4)/(12*S^2) + (386*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1, 1}, -S^2]*((-8*Pi^2*(113 + 468*S^2 + 361*S^4))/(9*S^2) - (5*(-115 + 328*S^2 + 443*S^4))/(2*S^2) + (1312*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((4949*Pi^4*(1 + S^4))/(1080*S^2) + (Pi^2*(359 + 911*S^2 + 552*S^4))/(18*S^2) + (3049 + 8157*S^2 + 5108*S^4)/(48*S^2) - (2*(178 + 303*S^2 + 125*S^4)*HPL[{3}, -S^2])/(3*S^2) - (37*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((21 - 124*S^2 - 145*S^4)*HPL[{2, 1}, -S^2])/(2*S^2) + (10*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (62*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(130 + 219*S^2 + 89*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((2264 - 1239*S^2 - 3503*S^4)/(12*S^2) + (Pi^2*(155 - 2884*S^2 - 3087*S^4))/(36*S^2) - (1427*Pi^4*(1 + S^4))/(135*S^2) - (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(304 + 503*S^2 + 213*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((4421*Pi^4*(1 + S^4))/(180*S^2) + (2*Pi^2*(113 + 962*S^2 + 861*S^4))/(9*S^2) + (-575 + 2102*S^2 + 2677*S^4)/(4*S^2) - (4*(587 + 972*S^2 + 409*S^4)*Zeta[3])/(3*S^2)) + ((Pi^2*(-1113 - 1578*S^2 - 517*S^4))/(36*S^2) - (5*(801 + 1116*S^2 + 283*S^4))/(24*S^2))*Zeta[5] + HPL[{2}, -S^2]*((787*Pi^6*(1 + S^4))/(720*S^2) + (Pi^2*(151 + 4605*S^2 + 4550*S^4))/(72*S^2) + (5*(-389 + 9770*S^2 + 10159*S^4))/(192*S^2) + (Pi^4*(8953 + 53262*S^2 + 45813*S^4))/(4320*S^2) + (19*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((-727 - 1318*S^2 - 591*S^4)/(12*S^2) - (157*Pi^2*(1 + S^4))/(18*S^2))*HPL[{4}, -S^2] + ((-307 - 356*S^2 - 129*S^4)*HPL[{5}, -S^2])/(6*S^2) + (4*(1 + S^4)*HPL[{6}, -S^2])/S^2 - (62*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-1969 - 4468*S^2 - 2499*S^4)/(6*S^2) - (955*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + ((2593 + 4380*S^2 + 1787*S^4)*HPL[{3, 2}, -S^2])/(6*S^2) + ((7799 + 13188*S^2 + 5389*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + (76*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 + (298*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((638*Pi^2*(1 + S^4))/(3*S^2) + (1955 + 4476*S^2 + 2521*S^4)/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (2*(-21 + 124*S^2 + 145*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (16*(122 + 387*S^2 + 265*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (78*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 + (690*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (2078*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (8*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (4544*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (3136*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-1323 - 2134*S^2 - 855*S^4))/(36*S^2) + (-1085 - 1648*S^2 - 611*S^4)/(6*S^2))*Zeta[3] + ((1 + S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*((-2113 - 3188*S^2 - 1171*S^4)/(12*S^2) + (Pi^2*(-306 - 523*S^2 - 213*S^4))/(9*S^2) + (404*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (18*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1}, -S^2]*((-2283 - 5632*S^2 - 3349*S^4)/(8*S^2) - (2*Pi^2*(421 + 957*S^2 + 536*S^4))/(9*S^2) + (292*(1 + S^4)*Zeta[3])/S^2) + ((-1071 - 1586*S^2 - 583*S^4)*Zeta[5])/(6*S^2)) + HPL[{3}, -S^2]*((Pi^4*(-5521 - 8558*S^2 - 2681*S^4))/(1080*S^2) + (Pi^2*(-5811 - 7628*S^2 - 1657*S^4))/(144*S^2) + (-5481 - 6128*S^2 - 647*S^4)/(24*S^2) + ((173 + 174*S^2 + 61*S^4)*HPL[{4}, -S^2])/(6*S^2) - (6*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((521*Pi^2*(1 + S^4))/(9*S^2) + (2283 + 3656*S^2 + 1373*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + ((1181 + 1976*S^2 + 803*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (76*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (34*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (10*(233 + 396*S^2 + 163*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (808*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (2276*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (1320*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-163 - 224*S^2 - 109*S^4)/(6*S^2) - (43*Pi^2*(1 + S^4))/(9*S^2))*Zeta[3] - (20*(1 + S^4)*Zeta[5])/S^2) + Zeta[3]*((Pi^4*(-8991 - 12758*S^2 - 4411*S^4))/(2160*S^2) + (Pi^2*(-4625 - 6812*S^2 - 2347*S^4))/(144*S^2) + (-3471 - 5360*S^2 - 1889*S^4)/(24*S^2) + (176*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{2, 1}, -S^2]*((5987 - 34004*S^2 - 39991*S^4)/(96*S^2) + (Pi^4*(-14715 - 52538*S^2 - 38851*S^4))/(2160*S^2) + (Pi^2*(-445 - 8216*S^2 - 7867*S^4))/(72*S^2) + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (730*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (2198*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (8*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (248*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (2064*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (3136*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((539*Pi^2*(1 + S^4))/(9*S^2) + (2*(583 + 910*S^2 + 351*S^4))/(3*S^2))*Zeta[3] + (270*(1 + S^4)*Zeta[5])/S^2) + ((-383 - 524*S^2 - 101*S^4)*Zeta[7])/(2*S^2)) + HPL[{1}, -S^2]^2*((35*(1309 + 5526*S^2 + 4217*S^4))/(384*S^2) + (Pi^2*(18017 + 64916*S^2 + 46899*S^4))/(576*S^2) + (Pi^4*(96707 + 328636*S^2 + 233561*S^4))/(17280*S^2) + (Pi^6*(218821 + 615590*S^2 + 400605*S^4))/(181440*S^2) + ((-21 + 124*S^2 + 145*S^4)*HPL[{2}, -S^2]^3)/(12*S^2) + ((243 + 448*S^2 + 197*S^4)*HPL[{3}, -S^2]^2)/(12*S^2) + ((-41*Pi^2*(1 + S^4))/(9*S^2) + (-1091 - 592*S^2 + 499*S^4)/(12*S^2))*HPL[{5}, -S^2] + (5*(-165 + 82*S^2 + 251*S^4)*HPL[{6}, -S^2])/(12*S^2) + (82*(1 + S^4)*HPL[{7}, -S^2])/S^2 - (2*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((521*Pi^2*(1 + S^4))/(9*S^2) + (7*(327 + 524*S^2 + 197*S^4))/(6*S^2))*HPL[{3, 2}, -S^2] + ((3527*Pi^2*(1 + S^4))/(18*S^2) + (16125 + 25124*S^2 + 8999*S^4)/(12*S^2))*HPL[{4, 1}, -S^2] + ((773 + 1388*S^2 + 647*S^4)*HPL[{4, 2}, -S^2])/(12*S^2) - (18*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 + ((1213 + 1736*S^2 + 555*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) - (38*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 - (45*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((638*Pi^2*(1 + S^4))/(3*S^2) + (1955 + 4476*S^2 + 2521*S^4)/(3*S^2))*HPL[{2, 2, 1}, -S^2] + ((1504*Pi^2*(1 + S^4))/(3*S^2) + (2*(1489 + 4506*S^2 + 3017*S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] - (2*(1 - 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (4*(-32 + 187*S^2 + 217*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (691*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 - (2120*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 + (4*(-380 + 135*S^2 + 509*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (2081*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 - (6485*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 - (13336*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((-628*Pi^2*(1 + S^4))/(3*S^2) - (2*(-119 + 338*S^2 + 457*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] - (248*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (4*(-347 - 48*S^2 + 299*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (2064*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (2064*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (2808*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (8992*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (60*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 - (3136*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (9408*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (18880*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (1200*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-2425 - 3744*S^2 - 1319*S^4))/(72*S^2) + (-479 - 726*S^2 - 247*S^4)/(3*S^2) - (109*Pi^4*(1 + S^4))/(36*S^2))*Zeta[3] + ((24 + 71*S^2 + 25*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{2, 1, 1}, -S^2]*((4*Pi^2*(113 + 468*S^2 + 361*S^4))/(9*S^2) + (5*(-115 + 328*S^2 + 443*S^4))/(4*S^2) - (656*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((Pi^2*(421 + 957*S^2 + 536*S^4))/(18*S^2) + (2283 + 5632*S^2 + 3349*S^4)/(32*S^2) - (101*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (31*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (73*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(-1191 - 1604*S^2 - 413*S^4))/(72*S^2) + (-2563 - 3028*S^2 - 369*S^4)/(24*S^2) + (113*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (31*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((4181 - 1104*S^2 - 5285*S^4)/(24*S^2) + (Pi^2*(-159 - 1354*S^2 - 1223*S^4))/(18*S^2) + (340*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((-1771 - 2306*S^2 - 535*S^4)/(8*S^2) + (Pi^2*(-1009 - 1468*S^2 - 443*S^4))/(24*S^2) - (419*Pi^4*(1 + S^4))/(108*S^2) + (17*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (5*(233 + 396*S^2 + 163*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (330*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (660*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (2*(44 + 65*S^2 + 35*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((575 - 2102*S^2 - 2677*S^4)/(8*S^2) + (Pi^2*(-113 - 962*S^2 - 861*S^4))/(9*S^2) - (4421*Pi^4*(1 + S^4))/(360*S^2) + (784*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(587 + 972*S^2 + 409*S^4)*Zeta[3])/(3*S^2)) + ((-2067 - 2948*S^2 - 881*S^4)/(12*S^2) - (401*Pi^2*(1 + S^4))/(18*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(445 + 8216*S^2 + 7867*S^4))/(144*S^2) + (Pi^4*(14715 + 52538*S^2 + 38851*S^4))/(4320*S^2) + (-5987 + 34004*S^2 + 39991*S^4)/(192*S^2) + ((-2283 - 3656*S^2 - 1373*S^4)/(12*S^2) - (521*Pi^2*(1 + S^4))/(18*S^2))*HPL[{3}, -S^2] + ((-745 - 1356*S^2 - 611*S^4)*HPL[{4}, -S^2])/(12*S^2) - (33*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((-1955 - 4476*S^2 - 2521*S^4)/(6*S^2) - (319*Pi^2*(1 + S^4))/(3*S^2))*HPL[{2, 1}, -S^2] - (2*(551 + 1176*S^2 + 625*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (365*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 + (1099*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (124*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (1032*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (1568*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-583 - 910*S^2 - 351*S^4)/(3*S^2) - (539*Pi^2*(1 + S^4))/(18*S^2))*Zeta[3] - (135*(1 + S^4)*Zeta[5])/S^2) - (126*(1 + S^4)*Zeta[7])/S^2) + HPL[{0}, S^2]*((135211*Pi^8*S^2)/544320 + (35*(1045 + 5888*S^2))/384 + (Pi^2*(21258 + 113035*S^2))/1152 + (Pi^4*(58039 + 265929*S^2))/17280 + (Pi^6*(291090 + 1047869*S^2))/362880 + (2*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^7)/(9*S^2) + (2*(1 + S^4)*HPL[{1}, -S^2]^8)/(3*S^2) + ((Pi^2*(-11 + 205*S^4))/(27*S^2) + (-392 + 3820*S^2 + 4877*S^4)/(144*S^2))*HPL[{2}, -S^2]^3 + ((5 + 182*S^4)*HPL[{2}, -S^2]^4)/(24*S^2) + HPL[{1}, -S^2]^6*((127*Pi^2*(1 + S^4))/(54*S^2) + (68 + 159*S^2 + 91*S^4)/(9*S^2) + (25*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((-1 + 22*S^2 - 99*S^4)/(24*S^2) - (7*Pi^2*(-1 + 6*S^4))/(36*S^2))*HPL[{3}, -S^2]^2 + ((-13 + 36*S^4)*HPL[{4}, -S^2]^2)/(6*S^2) + ((Pi^2*(70 + 109*S^4))/(18*S^2) + (-165 + 481*S^2 + 280*S^4)/(12*S^2))*HPL[{6}, -S^2] + ((-45 + 26*S^2 - 65*S^4)*HPL[{7}, -S^2])/(2*S^2) + ((105 + 52*S^4)*HPL[{8}, -S^2])/(2*S^2) + ((14 - 4024*S^2 - 5061*S^4)/(12*S^2) + (Pi^2*(-8 - 1711*S^4))/(18*S^2))*HPL[{2, 1}, -S^2]^2 + (4*(4 + 283*S^4)*HPL[{3, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(-1 - 12*S^4))/(36*S^2) + (-7 + 126*S^2 + 73*S^4)/(24*S^2))*HPL[{4, 2}, -S^2] + ((-9 - 10*S^2 - 17*S^4)*HPL[{4, 3}, -S^2])/(6*S^2) + ((31 - 165*S^2 - 224*S^4)/(6*S^2) - (2*Pi^2*(6 + 49*S^4))/(9*S^2))*HPL[{5, 1}, -S^2] + ((-41 - 40*S^2 - 142*S^4)*HPL[{5, 2}, -S^2])/(12*S^2) - (7*S^2*HPL[{5, 3}, -S^2])/3 + ((-36 - 164*S^2 - 165*S^4)*HPL[{6, 1}, -S^2])/(6*S^2) + ((1 - 14*S^4)*HPL[{6, 2}, -S^2])/(3*S^2) + ((-63 - 146*S^4)*HPL[{7, 1}, -S^2])/(3*S^2) + (4*(17 + 1142*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(11 + 9*S^4))/(18*S^2) + (35 + 12*S^2 + 19*S^4)/(12*S^2))*HPL[{3, 1, 2}, -S^2] + ((11*Pi^2*(-15 + 299*S^4))/(18*S^2) + (-749 + 7652*S^2 + 9773*S^4)/(12*S^2))*HPL[{3, 2, 1}, -S^2] + ((198 - 820*S^2 - 895*S^4)*HPL[{3, 2, 2}, -S^2])/(12*S^2) - (8*(-8 + 80*S^2 + 75*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + ((19 - 2*S^4)*HPL[{3, 3, 2}, -S^2])/(3*S^2) + ((Pi^2*(-273 + 5066*S^4))/(9*S^2) + (-1241 + 11694*S^2 + 15078*S^4)/(6*S^2))*HPL[{4, 1, 1}, -S^2] + ((117 - 1284*S^2 - 1186*S^4)*HPL[{4, 1, 2}, -S^2])/(6*S^2) + (2*(-19 + 4*S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^2) + ((261 - 3900*S^2 - 3430*S^4)*HPL[{4, 2, 1}, -S^2])/(6*S^2) + ((29 - 12*S^4)*HPL[{4, 2, 2}, -S^2])/(6*S^2) - (82*HPL[{4, 3, 1}, -S^2])/(3*S^2) + ((241 - 3820*S^2 - 3262*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) - (2*(24 + S^4)*HPL[{5, 1, 2}, -S^2])/(3*S^2) - (2*(174 + S^4)*HPL[{5, 2, 1}, -S^2])/(3*S^2) + (4*(-215 + 58*S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^2) + (4*(-1087 - 1062*S^2 + 46*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) + ((425 - 4012*S^2 - 5240*S^4)/(3*S^2) - (14*Pi^2*(-15 + 254*S^4))/(9*S^2))*HPL[{3, 1, 1, 1}, -S^2] + ((13142 + 13244*S^2 - 341*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + ((13142 + 13244*S^2 - 341*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + (5*(3 + S^4)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^2) + ((26186 + 25988*S^2 - 893*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (5*(3 + S^4)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^2) + ((303 - 4411*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^2) - (96*(-3 + 46*S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 - (2*(-39119 - 38856*S^2 + 1350*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) - (2*(1 + 8*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^2) - (2*(-431 + 6632*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^2) - (70*(-37 + 568*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^2) - (8*(-216 + 3329*S^4)*HPL[{5, 1, 1, 1}, -S^2])/S^2 + ((4*Pi^2*(-31 + 600*S^4))/(3*S^2) + (2*(-388 + 4026*S^2 + 5299*S^4))/(3*S^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (8*(-1101 - 1188*S^2 + 7*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (8*(-1101 - 1188*S^2 + 7*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (32*(-19 + 275*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^2) - (32*(-19 + 275*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 - (4*(10913 + 12012*S^2 + 43*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) + (4*(-901 + 13207*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^2) + (4*(-1509 + 22007*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^2) + (4*(-1813 + 26407*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^2) + (4*(-3789 + 55007*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(-951 + 13763*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 + (80*(-226 - 225*S^2 + 16*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^2) - (16*(-29 + 391*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 + (160*(-5 + 79*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*S^2)/2 + (-14 + 271*S^2)/12)*Zeta[3]^2 + HPL[{1}, -S^2]^4*((1687*Pi^4*(1 + S^4))/(540*S^2) + (3316 + 9081*S^2 + 5765*S^4)/(72*S^2) + (Pi^2*(5235 + 14452*S^2 + 9137*S^4))/(432*S^2) + ((571*Pi^2*(1 + S^4))/(36*S^2) + (5*(361 + 882*S^2 + 521*S^4))/(36*S^2))*HPL[{2}, -S^2] + (98*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((-31 - 36*S^2 - 5*S^4)*HPL[{3}, -S^2])/(6*S^2) + (7*(1 + S^4)*HPL[{4}, -S^2])/(2*S^2) - (5*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1}, -S^2])/(18*S^2) - (374*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (250*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-281 - 492*S^2 - 211*S^4)*Zeta[3])/(18*S^2)) + HPL[{2}, -S^2]^2*((Pi^2*(-8 + 1367*S^2 + 2099*S^4))/(72*S^2) + (Pi^4*(-90 + 8743*S^4))/(2160*S^2) + (-328 + 12154*S^2 + 20509*S^4)/(192*S^2) + ((39 - 204*S^2 - 233*S^4)*HPL[{3}, -S^2])/(24*S^2) + ((-13 - 4*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((-1087 - 1062*S^2 + 46*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((73 - 1103*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + (4*(-19 + 275*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-1 - 123*S^2 - 89*S^4)*Zeta[3])/(6*S^2)) + HPL[{1}, -S^2]^5*((5*(97 + 244*S^2 + 147*S^4))/(24*S^2) + (Pi^2*(1055 + 2548*S^2 + 1477*S^4))/(180*S^2) + ((403 + 900*S^2 + 497*S^4)*HPL[{2}, -S^2])/(18*S^2) - (6*(1 + S^4)*HPL[{3}, -S^2])/(5*S^2) - (50*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (82*(1 + S^4)*Zeta[3])/(15*S^2)) + HPL[{2, 2, 1}, -S^2]*((6961 + 9892*S^2 - 53*S^4)/(12*S^2) + (Pi^2*(1494 + 1757*S^2 - 36*S^4))/(9*S^2) - (4*(42 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1, 1}, -S^2]*((-7083 - 10012*S^2 - 327*S^4)/(6*S^2) + (Pi^2*(-3103 - 3428*S^2 + 252*S^4))/(9*S^2) + (8*(124 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 2}, -S^2]*((192 + 670*S^2 - 73*S^4)/(24*S^2) + (Pi^2*(44 + 317*S^2 + 49*S^4))/(36*S^2) + (3*(1 + 3*S^4)*Zeta[3])/S^2) + HPL[{4, 1}, -S^2]*((-5*(-15 - 86*S^2 + 127*S^4))/(24*S^2) + (Pi^2*(-69 + 722*S^2 + 169*S^4))/(36*S^2) + (6*(2 + 3*S^4)*Zeta[3])/S^2) + HPL[{3, 1, 1}, -S^2]*((Pi^2*(4553 + 5218*S^2 - 155*S^4))/(9*S^2) + (21115 + 30080*S^2 + 247*S^4)/(12*S^2) - (4*(383 + 12*S^4)*Zeta[3])/(3*S^2)) + HPL[{5}, -S^2]*((Pi^2*(-39 + 182*S^2 + 11*S^4))/(72*S^2) + (-107 + 760*S^2 + 444*S^4)/(16*S^2) + (58*S^2*HPL[{2, 1}, -S^2])/3 + ((-17 + 37*S^4)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((Pi^2*(-297 + 490*S^2 + 925*S^4))/(144*S^2) + (Pi^4*(387 + 2552*S^4))/(2160*S^2) + (-744 + 3676*S^2 + 3331*S^4)/(96*S^2) + ((-51 - 34*S^2 + 122*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + ((17 - 40*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(-19 + 44*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((1 + 6*S^2 + 47*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((462 - 15574*S^2 - 22485*S^4)/(48*S^2) + (Pi^4*(789 - 18731*S^4))/(1080*S^2) + (Pi^2*(523 - 5704*S^2 - 8811*S^4))/(72*S^2) - (68*(1 + 67*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-17 + 250*S^2 + 199*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-488 + 5630*S^2 + 8917*S^4))/(36*S^2) + (Pi^4*(-415 + 9577*S^4))/(270*S^2) + (-892 + 14582*S^2 + 22207*S^4)/(24*S^2) - (2*(-4 + 248*S^2 + 215*S^4)*Zeta[3])/(3*S^2)) + ((-926 + 379*S^2)/12 + (Pi^2*(-136 + 1019*S^2))/36)*Zeta[5] + Zeta[3]*((-7172 - 485*S^2)/96 + (Pi^2*(-1002 + 65*S^2))/72 + (Pi^4*(-95 + 758*S^2))/216 - (46*S^2*Zeta[5])/3) + HPL[{1}, -S^2]^2*((2425*Pi^6*(1 + S^4))/(1512*S^2) + (8061 + 27734*S^2 + 19673*S^4)/(64*S^2) + (Pi^2*(7639 + 28046*S^2 + 20279*S^4))/(288*S^2) + (Pi^4*(21625 + 76391*S^2 + 53762*S^4))/(4320*S^2) + ((217*Pi^2*(1 + S^4))/(9*S^2) + (1955 + 4476*S^2 + 2521*S^4)/(24*S^2))*HPL[{2}, -S^2]^2 + (59*(1 + S^4)*HPL[{2}, -S^2]^3)/(2*S^2) - (5*(1 + S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((109*Pi^2*(1 + S^4))/(36*S^2) + (113 + 664*S^2 + 487*S^4)/(24*S^2))*HPL[{4}, -S^2] + ((15 + 120*S^2 + 97*S^4)*HPL[{5}, -S^2])/(6*S^2) + (41*(1 + S^4)*HPL[{6}, -S^2])/(3*S^2) - (392*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((-1823 - 4444*S^2 - 2605*S^4)/(6*S^2) - (853*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3, 1}, -S^2] + (2*(63 + 113*S^2 + 52*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((695 + 1104*S^2 + 433*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((1 + S^4)*HPL[{4, 2}, -S^2])/(2*S^2) - (64*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((571*Pi^2*(1 + S^4))/(3*S^2) + (5*(361 + 882*S^2 + 521*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (6*(357 + 772*S^2 + 415*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (708*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 + (2166*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 - (10*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (1496*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 + (3000*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-1323 - 2096*S^2 - 709*S^4)/(24*S^2) + (Pi^2*(-379 - 504*S^2 - 141*S^4))/(36*S^2))*Zeta[3] + (8*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2}, -S^2]*((8953*Pi^4*(1 + S^4))/(1080*S^2) + (Pi^2*(1171 + 3379*S^2 + 2208*S^4))/(36*S^2) + (5939 + 17922*S^2 + 11983*S^4)/(48*S^2) + ((-125 - 228*S^2 - 103*S^4)*HPL[{3}, -S^2])/(6*S^2) + (3*(1 + S^4)*HPL[{4}, -S^2])/(2*S^2) - (2*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (392*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (784*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-93 - 164*S^2 - 71*S^4)*Zeta[3])/(2*S^2)) + HPL[{3}, -S^2]*((Pi^2*(-53 - 35*S^2 + 28*S^4))/(18*S^2) + (-19 + 122*S^2 + 125*S^4)/(6*S^2) + (38*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (4*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-2779 - 6852*S^2 - 4073*S^4))/(36*S^2) - (9*(241 + 648*S^2 + 407*S^4))/(8*S^2) + (82*(1 + S^4)*Zeta[3])/S^2) + ((-301 - 370*S^2 - 65*S^4)*Zeta[5])/(6*S^2)) + HPL[{1}, -S^2]^3*((11*(2269 + 6876*S^2 + 4607*S^4))/(288*S^2) + (Pi^2*(8887 + 27912*S^2 + 18897*S^4))/(432*S^2) + (Pi^4*(29391 + 81518*S^2 + 51043*S^4))/(6480*S^2) + ((551 + 1176*S^2 + 625*S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((-5*Pi^2*(1 + S^4))/(9*S^2) + (2*(-33 - 8*S^2 + 21*S^4))/(9*S^2))*HPL[{3}, -S^2] + ((55 + 264*S^2 + 185*S^4)*HPL[{4}, -S^2])/(18*S^2) + (58*(1 + S^4)*HPL[{5}, -S^2])/(9*S^2) + ((-571*Pi^2*(1 + S^4))/(9*S^2) - (5*(361 + 882*S^2 + 521*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] - (2*(1009 + 2244*S^2 + 1235*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) + (76*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (62*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (10*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (1568*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (1544*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (1000*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-593 - 988*S^2 - 379*S^4)/(18*S^2) - (128*Pi^2*(1 + S^4))/(27*S^2))*Zeta[3] + HPL[{2}, -S^2]*((3*(241 + 648*S^2 + 407*S^4))/(8*S^2) + (Pi^2*(2779 + 6852*S^2 + 4073*S^4))/(108*S^2) - (38*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) - (784*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (82*(1 + S^4)*Zeta[3])/(3*S^2)) - (184*(1 + S^4)*Zeta[5])/(9*S^2)) + HPL[{2}, -S^2]*((Pi^2*(-1086 + 9756*S^2 + 19453*S^4))/(288*S^2) + (-4224 + 32941*S^2 + 55947*S^4)/(192*S^2) + (Pi^6*(-1807 + 70075*S^4))/(45360*S^2) + (Pi^4*(-5788 + 53058*S^2 + 104239*S^4))/(8640*S^2) - ((-2 + S^2)*(2 + S^2)*HPL[{3}, -S^2]^2)/(6*S^2) + ((Pi^2*(-17 + 92*S^4))/(36*S^2) + (-9 - 146*S^2 + 199*S^4)/(24*S^2))*HPL[{4}, -S^2] + ((-19 - 50*S^2 + 19*S^4)*HPL[{5}, -S^2])/(12*S^2) + ((-10 + 31*S^4)*HPL[{6}, -S^2])/(3*S^2) - (4*(-19 + 275*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-3 - 4028*S^2 - 5042*S^4)/(12*S^2) + (Pi^2*(-5 - 571*S^4))/(6*S^2))*HPL[{3, 1}, -S^2] + ((-79 + 408*S^2 + 459*S^4)*HPL[{3, 2}, -S^2])/(12*S^2) + ((-66 + 646*S^2 + 577*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((5 + 8*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) - (4*(-7 + 9*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((Pi^2*(8 + 1711*S^4))/(9*S^2) + (-14 + 4024*S^2 + 5061*S^4)/(6*S^2))*HPL[{2, 1, 1}, -S^2] - (2*(-1087 - 1062*S^2 + 46*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + ((-6553 - 6624*S^2 + 183*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((-1 - S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (59*(1 + 37*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (2*(71 + 3320*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (4*(-1101 - 1188*S^2 + 7*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) - (4*(-895 + 14339*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (8*(17 + 1142*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((-9 - 295*S^2 - 171*S^4)/(6*S^2) + (Pi^2*(4 - 262*S^2 - 145*S^4))/(36*S^2))*Zeta[3] + (2*(-1 + 12*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3}, -S^2]*((Pi^2*(-25 - 320*S^2 - 33*S^4))/(72*S^2) + (-95 - 284*S^2 + 39*S^4)/(24*S^2) + ((103 - 11*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((-7 - 13*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(-1494 - 1757*S^2 + 36*S^4))/(18*S^2) + (-6961 - 9892*S^2 + 53*S^4)/(24*S^2) + (2*(42 + S^4)*Zeta[3])/S^2) + ((-20 - 160*S^2 + S^4)*Zeta[5])/(6*S^2)) + HPL[{2, 1}, -S^2]*((-23505 - 46728*S^2 - 6623*S^4)/(96*S^2) + (Pi^2*(-2198 - 4297*S^2 - 198*S^4))/(36*S^2) + (Pi^4*(-28959 - 36134*S^2 + 4468*S^4))/(2160*S^2) + ((2205 + 2376*S^2 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((-205 + 23*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (2*(290 + 11*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (4*(-1101 - 1188*S^2 + 7*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (16*(-19 + 275*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (12*(-15 + 371*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (8*(17 + 1142*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(122 - 9*S^4))/(9*S^2) + (536 + 438*S^2 + 23*S^4)/(6*S^2))*Zeta[3] - (4*(-37 + 9*S^4)*Zeta[5])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^4*(1112 + 316*S^2 - 501*S^4))/(4320*S^2) + (Pi^2*(-64 + 658*S^2 + 627*S^4))/(144*S^2) + (-744 + 9192*S^2 + 8353*S^4)/(192*S^2) + ((7 + 24*S^2 + 10*S^4)*HPL[{4}, -S^2])/(12*S^2) + ((13 - 34*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((Pi^2*(103 + 73*S^4))/(18*S^2) + (395 + 208*S^2 + 165*S^4)/(12*S^2))*HPL[{2, 1}, -S^2] + ((15 + 232*S^2 + 141*S^4)*HPL[{3, 1}, -S^2])/(6*S^2) + ((-3 + S^2)*(3 + S^2)*HPL[{3, 2}, -S^2])/(3*S^2) + 12*S^2*HPL[{4, 1}, -S^2] + ((-31 - 252*S^2 - 93*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(-103 + 11*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (2*(293 + 5*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (4*(31 + 13*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(-23 - 3*S^4))/(18*S^2) + (-29 - 72*S^2 + 13*S^4)/(12*S^2))*Zeta[3] + ((-17 + 29*S^4)*Zeta[5])/(3*S^2)) + (-15 + 181*S^2)*Zeta[7] + HPL[{1}, -S^2]*((35*(1309 + 5526*S^2 + 4217*S^4))/(384*S^2) + (Pi^2*(12317 + 58100*S^2 + 45783*S^4))/(576*S^2) + (Pi^4*(62071 + 291028*S^2 + 227677*S^4))/(17280*S^2) + (Pi^6*(152773 + 585626*S^2 + 425601*S^4))/(181440*S^2) + ((977 + 2124*S^2 + 1147*S^4)*HPL[{2}, -S^2]^3)/(36*S^2) + ((-9 - 24*S^2 - 7*S^4)*HPL[{3}, -S^2]^2)/(12*S^2) + ((17*Pi^2*(1 + S^4))/(9*S^2) + (36 + 277*S^2 + 165*S^4)/(6*S^2))*HPL[{5}, -S^2] + ((101 + 318*S^2 + 237*S^4)*HPL[{6}, -S^2])/(12*S^2) - (11*(1 + S^4)*HPL[{7}, -S^2])/(3*S^2) - (2*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((70*Pi^2*(1 + S^4))/(9*S^2) + (213 + 340*S^2 + 127*S^4)/(6*S^2))*HPL[{3, 2}, -S^2] + ((311*Pi^2*(1 + S^4))/(18*S^2) + (1129 + 1304*S^2 + 239*S^4)/(12*S^2))*HPL[{4, 1}, -S^2] + ((5 - 4*S^2 + 23*S^4)*HPL[{4, 2}, -S^2])/(12*S^2) - (19*(1 + S^4)*HPL[{4, 3}, -S^2])/(3*S^2) - (2*(11 + 72*S^2 + 45*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) - (52*(1 + S^4)*HPL[{5, 2}, -S^2])/(3*S^2) - (152*(1 + S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((1736*Pi^2*(1 + S^4))/(9*S^2) + (1955 + 4476*S^2 + 2521*S^4)/(3*S^2))*HPL[{2, 2, 1}, -S^2] + ((1726*Pi^2*(1 + S^4))/(3*S^2) + (5733 + 13396*S^2 + 7647*S^4)/(3*S^2))*HPL[{3, 1, 1}, -S^2] - (2*(1 - 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + (4*(488 + 1063*S^2 + 573*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (63*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 - (592*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) + ((5917 + 13008*S^2 + 7067*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (197*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 - (601*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 - (3520*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + ((-1142*Pi^2*(1 + S^4))/(3*S^2) - (10*(361 + 882*S^2 + 521*S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (1416*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 - (4*(1009 + 2244*S^2 + 1235*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (4400*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 + (4400*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 + (8648*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 + (25860*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 + (20*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) - (3136*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 - (9408*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 - (15824*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (6000*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((-1571 - 2470*S^2 - 643*S^4)/(24*S^2) + (Pi^2*(-153 - 201*S^2 - 28*S^4))/(12*S^2) - (95*Pi^4*(1 + S^4))/(216*S^2))*Zeta[3] + ((-3 + 94*S^2 + 101*S^4)*Zeta[3]^2)/(6*S^2) + HPL[{3}, -S^2]*((47*Pi^4*(1 + S^4))/(270*S^2) + (Pi^2*(-147 + 204*S^2 + 319*S^4))/(72*S^2) + (45 + 680*S^2 + 507*S^4)/(12*S^2) + (4*(1 + S^4)*HPL[{4}, -S^2])/S^2 + ((125 + 228*S^2 + 103*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (106*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (76*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((-5 - 4*S^2 - 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((9*(241 + 648*S^2 + 407*S^4))/(4*S^2) + (Pi^2*(2779 + 6852*S^2 + 4073*S^4))/(18*S^2) - (164*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]^2*((Pi^2*(1491 + 3478*S^2 + 1975*S^4))/(72*S^2) + (2283 + 5632*S^2 + 3349*S^4)/(32*S^2) - (8*(1 + S^4)*HPL[{3}, -S^2])/S^2 - (177*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 - (20*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((Pi^2*(67 + 460*S^2 + 345*S^4))/(72*S^2) + (141 + 536*S^2 + 379*S^4)/(12*S^2) - (3*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (19*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1}, -S^2]*((-6697 - 17872*S^2 - 11047*S^4)/(24*S^2) + (Pi^2*(-1385 - 3408*S^2 - 2031*S^4))/(18*S^2) + (248*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((-5939 - 17922*S^2 - 11983*S^4)/(24*S^2) + (Pi^2*(-1171 - 3379*S^2 - 2208*S^4))/(18*S^2) - (8953*Pi^4*(1 + S^4))/(540*S^2) + (784*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((93 + 164*S^2 + 71*S^4)*Zeta[3])/S^2) + ((-34*Pi^2*(1 + S^4))/(9*S^2) + (-409 - 483*S^2 + 2*S^4)/(6*S^2))*Zeta[5] + HPL[{2}, -S^2]*((Pi^2*(2009 + 6830*S^2 + 4773*S^4))/(72*S^2) + (Pi^4*(25649 + 71926*S^2 + 45673*S^4))/(4320*S^2) + (21781 + 76884*S^2 + 55103*S^4)/(192*S^2) + ((-207 - 328*S^2 - 121*S^4)/(12*S^2) - (35*Pi^2*(1 + S^4))/(9*S^2))*HPL[{3}, -S^2] + ((17 + 48*S^2 + 7*S^4)*HPL[{4}, -S^2])/(12*S^2) - (17*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((-1955 - 4476*S^2 - 2521*S^4)/(6*S^2) - (868*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2, 1}, -S^2] - (2*(551 + 1176*S^2 + 625*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (95*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (99*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (708*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (2200*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (1568*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-139 - 239*S^2 - 100*S^4)/(3*S^2) - (59*Pi^2*(1 + S^4))/(9*S^2))*Zeta[3] - (62*(1 + S^4)*Zeta[5])/(3*S^2)) - (15*(1 + S^4)*Zeta[7])/S^2)) + Log[T]*(-245/64 - (135211*Pi^8*S^2)/272160 + (Pi^6*(-355074 - 661765*S^2))/181440 + (Pi^4*(-53387 - 164349*S^2))/8640 + (Pi^2*(-13002 - 48187*S^2))/576 - (S^2*HPL[{0}, S^2]^8)/96 - (4*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^7)/(9*S^2) - (4*(1 + S^4)*HPL[{1}, -S^2]^8)/(3*S^2) + HPL[{0}, S^2]^7*((-14 - 31*S^2)/288 - (7*(1 + S^4)*HPL[{1}, -S^2])/(144*S^2)) + ((2468 - 492*S^2 - 3625*S^4)/(72*S^2) - (68*Pi^2*(-2 + 5*S^4))/(27*S^2))*HPL[{2}, -S^2]^3 + ((-251 - 334*S^4)*HPL[{2}, -S^2]^4)/(36*S^2) + HPL[{0}, S^2]^6*((-4*Pi^2*S^2)/27 + (-52 - 355*S^2)/576 + ((-13 - 84*S^2 - 67*S^4)*HPL[{1}, -S^2])/(144*S^2) - (41*(1 + S^4)*HPL[{1}, -S^2]^2)/(144*S^2) - (19*S^2*HPL[{2}, -S^2])/72) + HPL[{1}, -S^2]^6*((-46*Pi^2*(1 + S^4))/(9*S^2) - (2*(68 + 159*S^2 + 91*S^4))/(9*S^2) - (10*(1 + S^4)*HPL[{2}, -S^2])/(3*S^2)) + ((71 - 458*S^2 - 265*S^4)/(12*S^2) + (Pi^2*(14 - 99*S^4))/(18*S^2))*HPL[{3}, -S^2]^2 - (4*(10 + 3*S^4)*HPL[{4}, -S^2]^2)/(3*S^2) + ((391 - 7*S^2 - 1417*S^4)/(6*S^2) - (2*Pi^2*(31 + 61*S^4))/(9*S^2))*HPL[{6}, -S^2] + ((385 - 492*S^2 - 1372*S^4)*HPL[{7}, -S^2])/(3*S^2) + ((-735 - 1556*S^4)*HPL[{8}, -S^2])/(3*S^2) + ((2*Pi^2*(254 + 701*S^4))/(9*S^2) + (2398 + 3480*S^2 + 3809*S^4)/(6*S^2))*HPL[{2, 1}, -S^2]^2 - (4*(381 + 344*S^4)*HPL[{3, 1}, -S^2]^2)/(3*S^2) + ((267 - 1814*S^2 - 1245*S^4)/(12*S^2) + (Pi^2*(39 - 406*S^4))/(18*S^2))*HPL[{4, 2}, -S^2] - (2*(15 - 18*S^2 + S^4)*HPL[{4, 3}, -S^2])/S^2 + ((-705 - 4192*S^2 - 1727*S^4)/(6*S^2) + (Pi^2*(-43 - 787*S^4))/(9*S^2))*HPL[{5, 1}, -S^2] + ((-469 + 456*S^2 + 4*S^4)*HPL[{5, 2}, -S^2])/(6*S^2) + (2*(1 + 8*S^4)*HPL[{5, 3}, -S^2])/(3*S^2) + ((-712 + 270*S^2 + 559*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + (2*(-18 + 43*S^4)*HPL[{6, 2}, -S^2])/(3*S^2) + (2*(203 + 562*S^4)*HPL[{7, 1}, -S^2])/(3*S^2) - (40*(33 + 46*S^4)*HPL[{2, 1, 1}, -S^2]^2)/S^2 + ((Pi^2*(-129 + 119*S^4))/(9*S^2) + (-543 + 124*S^2 + 375*S^4)/(6*S^2))*HPL[{3, 1, 2}, -S^2] + ((4393 - 860*S^2 - 6875*S^4)/(6*S^2) + (Pi^2*(959 - 2601*S^4))/(9*S^2))*HPL[{3, 2, 1}, -S^2] + ((-406 + 8292*S^2 + 6751*S^4)*HPL[{3, 2, 2}, -S^2])/(6*S^2) + (4*(-271 + 3180*S^2 + 2633*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) - (2*(32 + 335*S^4)*HPL[{3, 3, 2}, -S^2])/(3*S^2) + ((2659 + 140*S^2 - 3369*S^4)/S^2 - (2*Pi^2*(-1725 + 3767*S^4))/(9*S^2))*HPL[{4, 1, 1}, -S^2] + ((-1190 + 12486*S^2 + 10359*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) + (4*(33 + 283*S^4)*HPL[{4, 1, 3}, -S^2])/(3*S^2) + ((-3506 + 38910*S^2 + 32127*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) + ((13 - 474*S^4)*HPL[{4, 2, 2}, -S^2])/(3*S^2) + (4*(89 + 969*S^4)*HPL[{4, 3, 1}, -S^2])/(3*S^2) + (2*(-3396 + 40008*S^2 + 32681*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S^2) + (2*(111 + 1171*S^4)*HPL[{5, 1, 2}, -S^2])/(3*S^2) + (2*(711 + 7951*S^4)*HPL[{5, 2, 1}, -S^2])/(3*S^2) + (4*(846 + 10055*S^4)*HPL[{6, 1, 1}, -S^2])/(3*S^2) - (8*(-189 - 62*S^2 + 134*S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + ((8*Pi^2*(-354 + 671*S^4))/(9*S^2) + (2*(-1060 - 124*S^2 + 1209*S^4))/S^2)*HPL[{3, 1, 1, 1}, -S^2] + (2*(-6249 - 6192*S^2 + 1474*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + (2*(-6249 - 6192*S^2 + 1474*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) - (2*(131 + 121*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(3*S^2) + (2*(-13053 - 8424*S^2 + 6298*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) - (2*(131 + 121*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(3*S^2) + (2*(-2187 + 2527*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^2) + (16*(-257 + 331*S^4)*HPL[{3, 3, 1, 1}, -S^2])/S^2 + (8*(-10009 - 6744*S^2 + 4539*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^2) - (148*(-1 + 11*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S^2) + (4*(-3047 + 3565*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S^2) + (4*(-9215 + 11509*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S^2) + (16*(-4651 + 5533*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^2) + ((-20*(-170 + 42*S^2 + 271*S^4))/S^2 - (40*Pi^2*(-113 + 298*S^4))/(9*S^2))*HPL[{2, 1, 1, 1, 1}, -S^2] + (32*(250 + 588*S^2 + 185*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (32*(250 + 588*S^2 + 185*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (32*(-257 + 331*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^2) + (32*(-257 + 331*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^2 + (8*(5057 + 14160*S^2 + 5503*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^2) - (16*(-3023 + 3913*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S^2) - (16*(-1693 + 2187*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/S^2 - (16*(-6107 + 7885*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S^2) - (16*(-4263 + 5497*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/S^2 - (32*(-6439 + 8216*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/S^2 - (80*(-79 - 30*S^2 + 59*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + (640*(-11 + 10*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/S^2 - (2240*(-5 + 7*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^2 + (-(Pi^2*S^2) + (-32 - 5*S^2)/3)*Zeta[3]^2 + HPL[{0}, S^2]^5*((-62 - 4583*S^2)/1440 + (Pi^2*(-1281 - 2578*S^2))/2160 + ((-433 - 2234*S^2 - 1701*S^4)*HPL[{1}, -S^2]^2)/(720*S^2) - (91*(1 + S^4)*HPL[{1}, -S^2]^3)/(90*S^2) + ((75 - 922*S^2 - 1666*S^4)*HPL[{2}, -S^2])/(720*S^2) + HPL[{1}, -S^2]*((-76 - 2079*S^2 - 1903*S^4)/(720*S^2) - (427*Pi^2*(1 + S^4))/(720*S^2) - (461*(1 + S^4)*HPL[{2}, -S^2])/(360*S^2)) + ((-1 + 2*S^4)*HPL[{3}, -S^2])/(24*S^2) + ((238 - 25*S^4)*HPL[{2, 1}, -S^2])/(90*S^2) - (3*S^2*Zeta[3])/4) + HPL[{1}, -S^2]^5*((Pi^2*(-709 - 1656*S^2 - 947*S^4))/(54*S^2) - (5*(97 + 244*S^2 + 147*S^4))/(12*S^2) + ((3 - 20*S^2 - 23*S^4)*HPL[{2}, -S^2])/S^2 + (160*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (20*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (40*(1 + S^4)*Zeta[3])/S^2) + HPL[{5}, -S^2]*((1097 + 2272*S^2 - 1688*S^4)/(24*S^2) + (Pi^2*(111 + 338*S^2 - 65*S^4))/(36*S^2) - (2*(223 + 3*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (4*(-8 + 3*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1, 1}, -S^2]*((2967 + 3724*S^2 - 1845*S^4)/(3*S^2) - (8*Pi^2*(-589 - 465*S^2 + 246*S^4))/(9*S^2) - (80*(97 + 4*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 2, 1}, -S^2]*((-2341 - 11412*S^2 - 2087*S^4)/(6*S^2) - (4*Pi^2*(532 + 957*S^2 + 179*S^4))/(9*S^2) - (16*(-241 + 11*S^4)*Zeta[3])/(3*S^2)) + HPL[{3, 1, 1}, -S^2]*((-3218 - 12368*S^2 - 823*S^4)/(3*S^2) + (Pi^2*(-6373 - 8998*S^2 - 303*S^4))/(9*S^2) - (8*(-1465 + 13*S^4)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((Pi^4*(121 + 240*S^4))/(216*S^2) + (Pi^2*(687 + 1834*S^2 + 275*S^4))/(72*S^2) + (2508 + 5752*S^2 + 837*S^4)/(48*S^2) + ((-957 - 670*S^2 - 32*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(-79 + 382*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(-61 + 383*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-21 + 60*S^2 + 20*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^4*((-3316 - 9081*S^2 - 5765*S^4)/(36*S^2) + (Pi^2*(-2999 - 7842*S^2 - 4843*S^4))/(108*S^2) - (1237*Pi^4*(1 + S^4))/(180*S^2) + ((119 - 338*S^2 - 457*S^4)/(6*S^2) - (157*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2] - (196*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((483 + 800*S^2 + 317*S^4)*HPL[{3}, -S^2])/(3*S^2) + (142*(1 + S^4)*HPL[{4}, -S^2])/(3*S^2) + (5*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1}, -S^2])/S^2 - (16*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (100*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (25*(43 + 72*S^2 + 29*S^4)*Zeta[3])/(9*S^2)) + HPL[{3, 2}, -S^2]*((1046 - 8470*S^2 - 4589*S^4)/(12*S^2) + (Pi^2*(271 - 2103*S^2 - 1678*S^4))/(18*S^2) - (2*(-5 + 41*S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((Pi^4*(-1061 + 3275*S^4))/(108*S^2) + (Pi^2*(-3441 + 1776*S^2 + 7751*S^4))/(36*S^2) + (-11268 - 982*S^2 + 17247*S^4)/(24*S^2) + (16*(310 + 283*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (28*(-1 + 71*S^2 + 57*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((Pi^4*(-1726 - 8045*S^4))/(1080*S^2) + (-2812 - 3006*S^2 - 5539*S^4)/(32*S^2) + (Pi^2*(-1230 - 2808*S^2 - 3851*S^4))/(72*S^2) + ((33 + 808*S^2 + 617*S^4)*HPL[{3}, -S^2])/(4*S^2) + ((49 + 388*S^4)*HPL[{4}, -S^2])/(6*S^2) + ((189 + 62*S^2 - 134*S^4)*HPL[{2, 1}, -S^2])/S^2 + ((-631 + 545*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (4*(-257 + 331*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(-32 + 219*S^2 + 191*S^4)*Zeta[3])/(3*S^2)) + HPL[{4, 1}, -S^2]*((397 - 13965*S^2 - 7239*S^4)/(6*S^2) + (Pi^2*(414 - 7122*S^2 - 5411*S^4))/(18*S^2) - (4*(15 + 194*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((8556 - 2966*S^2 - 18255*S^4)/(12*S^2) + (Pi^4*(4256 - 17677*S^4))/(270*S^2) + (Pi^2*(1364 - 1404*S^2 - 4103*S^4))/(9*S^2) + (8*(-7 + 480*S^2 + 393*S^4)*Zeta[3])/(3*S^2)) + HPL[{0}, S^2]^4*((-10279*Pi^4*S^2)/12960 + (Pi^2*(-326 - 1515*S^2))/288 + (-216 - 1451*S^2)/96 + ((-103 - 377*S^2 - 264*S^4)*HPL[{1}, -S^2]^3)/(36*S^2) - (31*(1 + S^4)*HPL[{1}, -S^2]^4)/(12*S^2) + ((Pi^2*(5 - 364*S^4))/(144*S^2) - (5*(-3 + 116*S^2 + 341*S^4))/(144*S^2))*HPL[{2}, -S^2] + ((9 - 460*S^4)*HPL[{2}, -S^2]^2)/(144*S^2) + HPL[{1}, -S^2]^2*((-725 - 4312*S^2 - 3491*S^4)/(288*S^2) - (391*Pi^2*(1 + S^4))/(144*S^2) - (245*(1 + S^4)*HPL[{2}, -S^2])/(36*S^2)) + ((-15 - 8*S^2 + 4*S^4)*HPL[{3}, -S^2])/(48*S^2) + ((-5 - 24*S^4)*HPL[{4}, -S^2])/(24*S^2) + ((598 + 982*S^2 - 137*S^4)*HPL[{2, 1}, -S^2])/(72*S^2) + (5*(-3 + 101*S^4)*HPL[{3, 1}, -S^2])/(36*S^2) + ((5 - 174*S^4)*HPL[{2, 1, 1}, -S^2])/(6*S^2) + ((-19 - 82*S^2)*Zeta[3])/18 + HPL[{1}, -S^2]*((Pi^2*(-168 - 797*S^2 - 599*S^4))/(144*S^2) + (-33 - 272*S^2 - 236*S^4)/(18*S^2) + ((-269 - 981*S^2 - 710*S^4)*HPL[{2}, -S^2])/(72*S^2) + ((-1 - S^4)*HPL[{3}, -S^2])/(3*S^2) + (245*(1 + S^4)*HPL[{2, 1}, -S^2])/(18*S^2) - (19*(1 + S^4)*Zeta[3])/(18*S^2))) + ((Pi^2*(401 + 324*S^2))/9 + (4110 + 533*S^2)/12)*Zeta[5] + HPL[{0}, S^2]^3*((-2908 - 42619*S^2)/576 + (Pi^2*(-794 - 5807*S^2))/288 - (7*Pi^4*(4576 + 8257*S^2))/12960 + ((-285 - 868*S^2 - 567*S^4)*HPL[{1}, -S^2]^4)/(36*S^2) - (43*(1 + S^4)*HPL[{1}, -S^2]^5)/(9*S^2) + ((4 - 557*S^2 - 754*S^4)*HPL[{2}, -S^2]^2)/(36*S^2) + HPL[{1}, -S^2]^3*((-1155 - 4912*S^2 - 3677*S^4)/(108*S^2) - (397*Pi^2*(1 + S^4))/(54*S^2) - (196*(1 + S^4)*HPL[{2}, -S^2])/(9*S^2)) + ((-25 - 112*S^2 - 117*S^4)/(36*S^2) + (Pi^2*(-8 + 7*S^4))/(18*S^2))*HPL[{3}, -S^2] + ((26 - 90*S^2 - 203*S^4)*HPL[{4}, -S^2])/(36*S^2) + ((2 + 5*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((Pi^2*(1082 - 77*S^4))/(54*S^2) + (587 + 1546*S^2 + 2*S^4)/(18*S^2))*HPL[{2, 1}, -S^2] + ((-79 + 1164*S^2 + 1631*S^4)*HPL[{3, 1}, -S^2])/(18*S^2) + ((-16 + 7*S^4)*HPL[{3, 2}, -S^2])/(9*S^2) + ((1 + 2*S^4)*HPL[{4, 1}, -S^2])/(9*S^2) + ((79 - 1174*S^2 - 1680*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S^2) + (2*(-569 + 9*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S^2) + (2*(-580 + 13*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) - (4*(-202 + 9*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((-5*Pi^2*S^2)/2 + (184 - 221*S^2)/36)*Zeta[3] + HPL[{1}, -S^2]*((-1007 - 9884*S^2 - 8749*S^4)/(144*S^2) + (Pi^2*(-1307 - 9070*S^2 - 7483*S^4))/(432*S^2) - (1001*Pi^4*(1 + S^4))/(405*S^2) + ((-537 - 2348*S^2 - 1811*S^4)/(36*S^2) - (1049*Pi^2*(1 + S^4))/(108*S^2))*HPL[{2}, -S^2] - (140*(1 + S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((13 - 38*S^2 - 71*S^4)*HPL[{3}, -S^2])/(18*S^2) - (23*(1 + S^4)*HPL[{4}, -S^2])/(9*S^2) + (2*(191 + 588*S^2 + 397*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (584*(1 + S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (392*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((49 + 6*S^2 - 35*S^4)*Zeta[3])/(9*S^2)) + HPL[{1}, -S^2]^2*((-403 - 2403*S^2 - 1968*S^4)/(36*S^2) + (Pi^2*(-644 - 2419*S^2 - 1701*S^4))/(108*S^2) + ((-191 - 588*S^2 - 397*S^4)*HPL[{2}, -S^2])/(9*S^2) - (4*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (196*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (5*(1 + S^4)*Zeta[3])/(9*S^2)) + HPL[{2}, -S^2]*((90 - 1324*S^2 - 3819*S^4)/(72*S^2) + (Pi^2*(77 - 1048*S^2 - 1673*S^4))/(108*S^2) - (4*(-2 + S^4)*HPL[{3}, -S^2])/(9*S^2) + ((569 - 9*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + ((-3 + 5*S^4)*Zeta[3])/(9*S^2)) - (104*S^2*Zeta[5])/9) + Zeta[3]*((15544 + 933*S^2)/48 + (Pi^2*(4946 + 1847*S^2))/72 + (Pi^4*(6540 + 4529*S^2))/1080 + (92*S^2*Zeta[5])/3) + HPL[{1}, -S^2]^3*((Pi^4*(-17597 - 44493*S^2 - 26974*S^4))/(1620*S^2) + (Pi^2*(-1739 - 5052*S^2 - 3313*S^4))/(36*S^2) - (11*(2269 + 6876*S^2 + 4607*S^4))/(144*S^2) - (2*(551 + 1176*S^2 + 625*S^4)*HPL[{2}, -S^2]^2)/(9*S^2) + ((410*Pi^2*(1 + S^4))/(9*S^2) + (2887 + 4416*S^2 + 1529*S^4)/(9*S^2))*HPL[{3}, -S^2] + (2*(571 + 846*S^2 + 287*S^4)*HPL[{4}, -S^2])/(9*S^2) + (124*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((628*Pi^2*(1 + S^4))/(9*S^2) + (2*(-119 + 338*S^2 + 457*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (4*(-347 - 48*S^2 + 299*S^4)*HPL[{3, 1}, -S^2])/(9*S^2) - (440*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (4528*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (20*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (3136*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (6208*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (400*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((110*Pi^2*(1 + S^4))/(3*S^2) + (2*(1081 + 1698*S^2 + 617*S^4))/(9*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-4*Pi^2*(113 + 468*S^2 + 361*S^4))/(27*S^2) - (5*(-115 + 328*S^2 + 443*S^4))/(12*S^2) + (220*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (1568*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (656*(1 + S^4)*Zeta[3])/(3*S^2)) + (536*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{3}, -S^2]*((Pi^2*(297 + 4614*S^2 + 1915*S^4))/(72*S^2) + (4056 + 32696*S^2 + 8991*S^4)/(96*S^2) + (Pi^4*(-516 + 17236*S^2 + 12929*S^4))/(2160*S^2) + ((95 - 204*S^2 - 50*S^4)*HPL[{4}, -S^2])/(6*S^2) + (2*(39 + 10*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((Pi^2*(-1179 + 89*S^4))/(9*S^2) + (-5399 - 2912*S^2 + 189*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + ((485 - 1980*S^2 - 1777*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(11 + 225*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + (4*(-45 + 46*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + (4*(-209 + 992*S^2 + 888*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (4*(1133 + 123*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) + (20*(685 + 31*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (16*(-189 + 16*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((5*Pi^2*(5 + 11*S^4))/(9*S^2) + (25 + 100*S^2 + 71*S^4)/(2*S^2))*Zeta[3] + (2*(13 + 3*S^4)*Zeta[5])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^4*(26111 + 26012*S^2 - 8816*S^4))/(1080*S^2) + (9621 + 25288*S^2 - 933*S^4)/(48*S^2) + (Pi^2*(2897 + 5752*S^2 - 699*S^4))/(36*S^2) - (8*(179 + 589*S^2 + 243*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (2*(2149 + 129*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (8*(-1730 + 7*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (16*(250 + 588*S^2 + 185*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (16*(-257 + 331*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (16*(-68 + 315*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (80*(33 + 46*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((-4*(593 + 387*S^2 + 19*S^4))/(3*S^2) - (2*Pi^2*(535 + 21*S^4))/(9*S^2))*Zeta[3] + (4*(-419 + 12*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]^2*((Pi^4*(-11307 - 33572*S^2 - 22361*S^4))/(864*S^2) + (-8061 - 27734*S^2 - 19673*S^4)/(32*S^2) + (Pi^2*(-786 - 2543*S^2 - 1757*S^4))/(12*S^2) - (17153*Pi^6*(1 + S^4))/(5040*S^2) + ((-1955 - 4476*S^2 - 2521*S^4)/(12*S^2) - (319*Pi^2*(1 + S^4))/(6*S^2))*HPL[{2}, -S^2]^2 - (31*(1 + S^4)*HPL[{2}, -S^2]^3)/(3*S^2) - (37*(1 + S^4)*HPL[{3}, -S^2]^2)/S^2 + ((401*Pi^2*(1 + S^4))/(18*S^2) + (2427 + 3188*S^2 + 761*S^4)/(12*S^2))*HPL[{4}, -S^2] - (4*(-113 - 92*S^2 + 19*S^4)*HPL[{5}, -S^2])/(3*S^2) - (35*(1 + S^4)*HPL[{6}, -S^2])/S^2 + (784*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((76*Pi^2*(1 + S^4))/S^2 + (4*(-233 + 15*S^2 + 248*S^4))/(3*S^2))*HPL[{3, 1}, -S^2] - (4*(583 + 989*S^2 + 408*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (4*(2033 + 3393*S^2 + 1366*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (117*(1 + S^4)*HPL[{4, 2}, -S^2])/S^2 - (584*(1 + S^4)*HPL[{5, 1}, -S^2])/S^2 + ((-628*Pi^2*(1 + S^4))/(3*S^2) - (2*(-119 + 338*S^2 + 457*S^4))/S^2)*HPL[{2, 1, 1}, -S^2] - (8*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (4*(619 + 1552*S^2 + 933*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (248*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (176*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (60*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 - (64*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (1200*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((343 + 524*S^2 + 181*S^4)/S^2 + (Pi^2*(1203 + 1978*S^2 + 779*S^4))/(18*S^2))*Zeta[3] - (20*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((4*Pi^2*(113 + 468*S^2 + 361*S^4))/(9*S^2) + (5*(-115 + 328*S^2 + 443*S^4))/(4*S^2) - (656*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((Pi^2*(1525 + 2474*S^2 + 921*S^4))/(18*S^2) + (5515 + 7896*S^2 + 2381*S^4)/(12*S^2) - (660*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (48*(1 + S^4)*Zeta[3])/S^2) + HPL[{2}, -S^2]*((575 - 2102*S^2 - 2677*S^4)/(8*S^2) + (Pi^2*(-113 - 962*S^2 - 861*S^4))/(9*S^2) - (4421*Pi^4*(1 + S^4))/(360*S^2) + (5*(233 + 396*S^2 + 163*S^4)*HPL[{3}, -S^2])/(3*S^2) + (113*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (784*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(587 + 972*S^2 + 409*S^4)*Zeta[3])/(3*S^2)) + (2*(510 + 805*S^2 + 293*S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^4*(20272 - 38310*S^2 - 100599*S^4))/(4320*S^2) + (Pi^6*(10321 - 64644*S^4))/(22680*S^2) + (14024 - 15381*S^2 - 48187*S^4)/(96*S^2) + (Pi^2*(4338 - 5086*S^2 - 18351*S^4))/(144*S^2) + ((-1 - 112*S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((Pi^2*(-21 + 122*S^4))/(6*S^2) + (-405 + 1694*S^2 + 961*S^4)/(12*S^2))*HPL[{4}, -S^2] + ((-183 + 394*S^2 + 43*S^4)*HPL[{5}, -S^2])/(6*S^2) - (2*(6 + 11*S^4)*HPL[{6}, -S^2])/S^2 + (4*(-257 + 331*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(635 + 1271*S^4))/(9*S^2) + (2931 + 3404*S^2 + 3436*S^4)/(6*S^2))*HPL[{3, 1}, -S^2] + ((19 - 1460*S^2 - 1163*S^4)*HPL[{3, 2}, -S^2])/(2*S^2) + ((660 - 6602*S^2 - 5521*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (3*(5 + 44*S^4)*HPL[{4, 2}, -S^2])/S^2 - (2*(-33 + 877*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-2398 - 3480*S^2 - 3809*S^4)/(3*S^2) - (4*Pi^2*(254 + 701*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + (4*(-189 - 62*S^2 + 134*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (8*(-746 - 775*S^2 + 159*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + (78*(1 + S^4)*HPL[{3, 1, 2}, -S^2])/S^2 - (2*(887 + 1219*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (4*(1567 + 1621*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (16*(250 + 588*S^2 + 185*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (16*(-2774 + 4255*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (80*(33 + 46*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((-35 + 1014*S^2 + 573*S^4)/(3*S^2) + (Pi^2*(-26 + 1052*S^2 + 843*S^4))/(18*S^2))*Zeta[3] - (2*(-8 + 21*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{2, 1}, -S^2]*((2*Pi^2*(532 + 957*S^2 + 179*S^4))/(9*S^2) + (2341 + 11412*S^2 + 2087*S^4)/(12*S^2) + (8*(-241 + 11*S^4)*Zeta[3])/(3*S^2)) + HPL[{3}, -S^2]*((-401 + 2130*S^2 + 1235*S^4)/(6*S^2) + (Pi^2*(-425 + 2108*S^2 + 1775*S^4))/(36*S^2) - (2*(1133 + 123*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(-9 + 65*S^4)*Zeta[3])/(3*S^2)) + ((-32 + 774*S^2 + 595*S^4)*Zeta[5])/(3*S^2)) + HPL[{0}, S^2]^2*((-147719*Pi^6*S^2)/90720 + (Pi^4*(-17839 - 54372*S^2))/4320 + (-11607 - 48187*S^2)/192 + (Pi^2*(-8422 - 35667*S^2))/576 + ((-247 - 648*S^2 - 401*S^4)*HPL[{1}, -S^2]^5)/(18*S^2) - (6*(1 + S^4)*HPL[{1}, -S^2]^6)/S^2 + ((-62 - 2136*S^2 - 3893*S^4)/(48*S^2) + (Pi^2*(-1 - 293*S^4))/(18*S^2))*HPL[{2}, -S^2]^2 + ((15 - 349*S^4)*HPL[{2}, -S^2]^3)/(18*S^2) + HPL[{1}, -S^2]^4*((-959 - 3072*S^2 - 2113*S^4)/(36*S^2) - (38*Pi^2*(1 + S^4))/(3*S^2) - (239*(1 + S^4)*HPL[{2}, -S^2])/(6*S^2)) + ((1 + 8*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((114 - 62*S^2 - 493*S^4)/(24*S^2) + (Pi^2*(-6 - 113*S^4))/(36*S^2))*HPL[{4}, -S^2] + ((33 - 34*S^2 - 94*S^4)*HPL[{5}, -S^2])/(12*S^2) + ((-70 - 129*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((13 + 712*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((Pi^2*(-63 + 1247*S^4))/(18*S^2) + (-261 + 2148*S^2 + 4124*S^4)/(12*S^2))*HPL[{3, 1}, -S^2] + ((-13 - 246*S^2 - 6*S^4)*HPL[{3, 2}, -S^2])/(12*S^2) + ((20 - 330*S^2 - 17*S^4)*HPL[{4, 1}, -S^2])/(6*S^2) + ((2 + S^4)*HPL[{4, 2}, -S^2])/(6*S^2) + (7*(1 + 9*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((178 - 2178*S^2 - 4141*S^4)/(6*S^2) + (Pi^2*(55 - 1277*S^4))/(9*S^2))*HPL[{2, 1, 1}, -S^2] + (4*(-94 - 123*S^2 + 2*S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (2*(-1715 - 2171*S^2 + 57*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S^2) + ((-7 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + ((53 - 1395*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) - (2*(-99 + 2135*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) - (2*(-1171 - 1410*S^2 + 99*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (8*(-24 + 371*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (40*(-8 + 151*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(14 - 265*S^2))/36 + (263 + S^2)/12)*Zeta[3] - 5*S^2*Zeta[3]^2 + HPL[{1}, -S^2]^3*((Pi^2*(-1853 - 5502*S^2 - 3589*S^4))/(108*S^2) - (13*(81 + 308*S^2 + 227*S^4))/(24*S^2) + ((-1039 - 2844*S^2 - 1853*S^4)*HPL[{2}, -S^2])/(18*S^2) + (10*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (478*(1 + S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (10*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((7 - 272*S^2 - 785*S^4)/(48*S^2) + (Pi^2*(-91 + 62*S^2 + 54*S^4))/(72*S^2) + ((-45 - 7*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (2*(3 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(1769 + 2392*S^2 - 236*S^4))/(36*S^2) + (2827 + 7780*S^2 + 447*S^4)/(24*S^2) - (2*(50 + S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^2*((Pi^2*(-2643 - 10456*S^2 - 7717*S^4))/(144*S^2) + (-1400 - 6177*S^2 - 4777*S^4)/(24*S^2) - (3299*Pi^4*(1 + S^4))/(432*S^2) + ((-809 - 2834*S^2 - 2073*S^4)/(12*S^2) - (1207*Pi^2*(1 + S^4))/(36*S^2))*HPL[{2}, -S^2] - (123*(1 + S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((38 + 37*S^2 - 15*S^4)*HPL[{3}, -S^2])/(3*S^2) - (25*(1 + S^4)*HPL[{4}, -S^2])/(6*S^2) + ((1039 + 2844*S^2 + 1853*S^4)*HPL[{2, 1}, -S^2])/(6*S^2) + (236*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (478*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((64 + 89*S^2 + 27*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^4*(490 - 15307*S^4))/(2160*S^2) + (Pi^2*(208 - 3338*S^2 - 7551*S^4))/(144*S^2) + (40 - 2402*S^2 - 6149*S^4)/(32*S^2) + ((-7 + 124*S^2 - S^4)*HPL[{3}, -S^2])/(12*S^2) + ((-2 - 17*S^4)*HPL[{4}, -S^2])/(6*S^2) - (2*(-94 - 123*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/S^2 + (5*(1 + 47*S^4)*HPL[{3, 1}, -S^2])/S^2 - (2*(13 + 712*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + ((-12 + 92*S^2 + 57*S^4)*Zeta[3])/(6*S^2)) + ((-1 - 100*S^2)*Zeta[5])/3 + HPL[{1}, -S^2]*((Pi^4*(-18819 - 66604*S^2 - 46537*S^4))/(4320*S^2) + (-11075 - 54196*S^2 - 43121*S^4)/(192*S^2) + (Pi^2*(-4215 - 20716*S^2 - 16405*S^4))/(288*S^2) + ((-97 - 246*S^2 - 149*S^4)*HPL[{2}, -S^2]^2)/(2*S^2) + ((35 - 3*S^2 - 50*S^4)/(3*S^2) + (Pi^2*(1 + S^4))/(6*S^2))*HPL[{3}, -S^2] + ((49 - 88*S^2 - 161*S^4)*HPL[{4}, -S^2])/(12*S^2) - (11*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((1207*Pi^2*(1 + S^4))/(18*S^2) + (809 + 2834*S^2 + 2073*S^4)/(6*S^2))*HPL[{2, 1}, -S^2] + (2*(253 + 701*S^2 + 462*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (52*(1 + S^4)*HPL[{3, 2}, -S^2])/(3*S^2) - (131*(1 + S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((-1039 - 2844*S^2 - 1853*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (492*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (1456*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (956*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((7*Pi^2*(1 + S^4))/(18*S^2) + (263 + 348*S^2 + 85*S^4)/(12*S^2))*Zeta[3] + HPL[{2}, -S^2]*((-2615 - 11512*S^2 - 9089*S^4)/(48*S^2) + (Pi^2*(-1577 - 4806*S^2 - 3273*S^4))/(72*S^2) + (26*(1 + S^4)*HPL[{3}, -S^2])/(3*S^2) + (246*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (47*(1 + S^4)*Zeta[3])/(3*S^2)) + ((-1 - S^4)*Zeta[5])/(3*S^2))) + HPL[{0}, S^2]*((Pi^4*(-81140 - 237859*S^2))/8640 + (Pi^6*(-36375 - 55672*S^2))/11340 + (Pi^2*(-7113 - 23324*S^2))/144 - (35*(1330 + 4217*S^2))/192 - (14*(11 + 24*S^2 + 13*S^4)*HPL[{1}, -S^2]^6)/(9*S^2) - (16*(1 + S^4)*HPL[{1}, -S^2]^7)/(3*S^2) + ((110 - 1062*S^2 - 1193*S^4)*HPL[{2}, -S^2]^3)/(18*S^2) + HPL[{1}, -S^2]^5*((-127*Pi^2*(1 + S^4))/(9*S^2) - (2*(68 + 159*S^2 + 91*S^4))/(3*S^2) - (50*(1 + S^4)*HPL[{2}, -S^2])/S^2) + ((-18 + 10*S^2 + 53*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((-82 - 163*S^2 - 207*S^4)/(6*S^2) + (Pi^2*(-3 + 2*S^4))/(3*S^2))*HPL[{5}, -S^2] + ((-40 - 144*S^2 - 267*S^4)*HPL[{6}, -S^2])/(6*S^2) + ((25 + 32*S^4)*HPL[{7}, -S^2])/S^2 + (2*(1 + 1164*S^2 + 1257*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-97 - 956*S^2 - 197*S^4)/(12*S^2) + (Pi^2*(-85 - 143*S^4))/(18*S^2))*HPL[{3, 2}, -S^2] + ((121 - 914*S^2 - 191*S^4)/(6*S^2) - (7*Pi^2*(-1 + 34*S^4))/(9*S^2))*HPL[{4, 1}, -S^2] + ((13 - 4*S^2 + 30*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) - (4*(-14 + 11*S^4)*HPL[{4, 3}, -S^2])/(3*S^2) + ((-23 + 132*S^2 + 288*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) - (2*(-80 + 59*S^4)*HPL[{5, 2}, -S^2])/(3*S^2) - (4*(-86 + 57*S^4)*HPL[{6, 1}, -S^2])/(3*S^2) + ((-3924 - 4928*S^2 + 19*S^4)/(3*S^2) - (2*Pi^2*(1728 + 25*S^4))/(9*S^2))*HPL[{2, 2, 1}, -S^2] + ((2*Pi^2*(-5267 + 22*S^4))/(9*S^2) + (-11919 - 14732*S^2 + 68*S^4)/(3*S^2))*HPL[{3, 1, 1}, -S^2] + ((-32 - 4*S^2 - 21*S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) + ((408 - 4252*S^2 - 4793*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + ((-45 + 421*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S^2) + (16*(1 + 73*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S^2) - (2*(-711 + 6504*S^2 + 7370*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (10*(3 + 116*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S^2) + (2*(87 + 1696*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S^2) + (8*(13 + 276*S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((-4*Pi^2*(-602 + 29*S^4))/(3*S^2) - (2*(-3998 - 4794*S^2 + 89*S^4))/(3*S^2))*HPL[{2, 1, 1, 1}, -S^2] - (16*(-569 + 19*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^2) + (4*(-281 + 2244*S^2 + 2597*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) + (4*(-6881 + 71*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^2) + (4*(-6881 + 71*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^2) + (4*(-13709 + 299*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^2) + (16*(-3413 + 74*S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (40*(-49 + 450*S^2 + 529*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^2) + (16*(1159 + 34*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^2) + (16*(1159 + 34*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (80*(383 + 17*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 - (640*(-20 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((7*Pi^2*(106 + 31*S^2))/36 + (7*(193 + 72*S^2))/12)*Zeta[3] - 4*(4 + 3*S^2)*Zeta[3]^2 + HPL[{3}, -S^2]*((-247 - 1010*S^2 - 1040*S^4)/(24*S^2) + (Pi^2*(-197 - 172*S^2 - 223*S^4))/(72*S^2) + (Pi^4*(-985 + 869*S^4))/(1080*S^2) + (4*(-7 + 5*S^4)*HPL[{4}, -S^2])/(3*S^2) + ((-219 - 204*S^2 - 113*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(19 + 79*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + (4*(7 + 25*S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((29 + 4*S^2 - 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^4*((Pi^2*(-1055 - 2548*S^2 - 1477*S^4))/(36*S^2) - (25*(97 + 244*S^2 + 147*S^4))/(24*S^2) - (5*(403 + 900*S^2 + 497*S^4)*HPL[{2}, -S^2])/(18*S^2) + (6*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (250*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (82*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((Pi^2*(5172 + 7886*S^2 - 85*S^4))/(36*S^2) - (4*Pi^4*(-1171 + 78*S^4))/(135*S^2) + (12770 + 21262*S^2 + 1759*S^4)/(24*S^2) - (4*(1159 + 37*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (8*(1159 + 34*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (2*(-283 - 244*S^2 + 2*S^4)*Zeta[3])/(3*S^2)) + HPL[{4}, -S^2]*((-69 - 870*S^2 - 1115*S^4)/(24*S^2) + (Pi^2*(77 - 222*S^2 - 415*S^4))/(36*S^2) - (14*(-4 + 5*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (2*(16 + 7*S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((28 - 1751*S^2 - 2525*S^4)/(12*S^2) + (Pi^2*(3 - 1721*S^2 - 2011*S^4))/(36*S^2) + ((-7 + 107*S^4)*HPL[{3}, -S^2])/(6*S^2) - (2*(-569 + 19*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + ((-2 + 39*S^4)*Zeta[3])/S^2) + HPL[{3, 1}, -S^2]*((2*Pi^2*(-90 + 852*S^2 + 1057*S^4))/(9*S^2) + (-248 + 3788*S^2 + 5347*S^4)/(6*S^2) - (4*(-7 + 118*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1, 1}, -S^2]*((288 - 3742*S^2 - 5331*S^4)/(3*S^2) + (Pi^2*(324 - 3424*S^2 - 4325*S^4))/(9*S^2) + (8*(-1 + 122*S^4)*Zeta[3])/(3*S^2)) + HPL[{1}, -S^2]^3*((Pi^2*(-5235 - 14452*S^2 - 9137*S^4))/(108*S^2) + (-3316 - 9081*S^2 - 5765*S^4)/(18*S^2) - (1687*Pi^4*(1 + S^4))/(135*S^2) + ((-571*Pi^2*(1 + S^4))/(9*S^2) - (5*(361 + 882*S^2 + 521*S^4))/(9*S^2))*HPL[{2}, -S^2] - (392*(1 + S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + (2*(31 + 36*S^2 + 5*S^4)*HPL[{3}, -S^2])/(3*S^2) - (14*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (10*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1}, -S^2])/(9*S^2) + (1496*(1 + S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (1000*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (2*(281 + 492*S^2 + 211*S^4)*Zeta[3])/(9*S^2)) + ((554 + 139*S^2)*Zeta[5])/6 + HPL[{1}, -S^2]^2*((Pi^4*(-29391 - 81518*S^2 - 51043*S^4))/(2160*S^2) + (Pi^2*(-8887 - 27912*S^2 - 18897*S^4))/(144*S^2) - (11*(2269 + 6876*S^2 + 4607*S^4))/(96*S^2) + ((-551 - 1176*S^2 - 625*S^4)*HPL[{2}, -S^2]^2)/(3*S^2) + ((5*Pi^2*(1 + S^4))/(3*S^2) - (2*(-33 - 8*S^2 + 21*S^4))/(3*S^2))*HPL[{3}, -S^2] + ((-55 - 264*S^2 - 185*S^4)*HPL[{4}, -S^2])/(6*S^2) - (58*(1 + S^4)*HPL[{5}, -S^2])/(3*S^2) + ((571*Pi^2*(1 + S^4))/(3*S^2) + (5*(361 + 882*S^2 + 521*S^4))/(3*S^2))*HPL[{2, 1}, -S^2] + (2*(1009 + 2244*S^2 + 1235*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (76*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (186*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (10*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (1568*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 - (4632*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (3000*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((128*Pi^2*(1 + S^4))/(9*S^2) + (593 + 988*S^2 + 379*S^4)/(6*S^2))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-2779 - 6852*S^2 - 4073*S^4))/(36*S^2) - (9*(241 + 648*S^2 + 407*S^4))/(8*S^2) + (38*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (784*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (82*(1 + S^4)*Zeta[3])/S^2) + (184*(1 + S^4)*Zeta[5])/(3*S^2)) + HPL[{2}, -S^2]*((Pi^4*(3310 - 35792*S^2 - 50141*S^4))/(2160*S^2) + (431 - 7539*S^2 - 12120*S^4)/(24*S^2) + (Pi^2*(189 - 2533*S^2 - 4575*S^4))/(36*S^2) + ((Pi^2*(37 + 67*S^4))/(18*S^2) + (19 + 448*S^2 + 77*S^4)/(12*S^2))*HPL[{3}, -S^2] + ((34 - 14*S^2 - 129*S^4)*HPL[{4}, -S^2])/(6*S^2) - (2*(-17 + 12*S^4)*HPL[{5}, -S^2])/(3*S^2) + ((3924 + 4928*S^2 - 19*S^4)/(6*S^2) + (Pi^2*(1728 + 25*S^4))/(9*S^2))*HPL[{2, 1}, -S^2] + ((-1 + 2328*S^2 + 2499*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) + ((5 - 71*S^4)*HPL[{3, 2}, -S^2])/S^2 - (2*(7 + 286*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) - (4*(1 + 1164*S^2 + 1257*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) + (8*(-569 + 19*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (4*(-1145 + 13*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (8*(1159 + 34*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + ((Pi^2*(-4 + 127*S^4))/(9*S^2) + (20 + 518*S^2 + 377*S^4)/(6*S^2))*Zeta[3] + (8*(-3 + 20*S^4)*Zeta[5])/(3*S^2)) + HPL[{1}, -S^2]*((Pi^4*(-21625 - 76391*S^2 - 53762*S^4))/(2160*S^2) + (Pi^2*(-7639 - 28046*S^2 - 20279*S^4))/(144*S^2) + (-8061 - 27734*S^2 - 19673*S^4)/(32*S^2) - (2425*Pi^6*(1 + S^4))/(756*S^2) + ((-1955 - 4476*S^2 - 2521*S^4)/(12*S^2) - (434*Pi^2*(1 + S^4))/(9*S^2))*HPL[{2}, -S^2]^2 - (59*(1 + S^4)*HPL[{2}, -S^2]^3)/S^2 + (5*(1 + S^4)*HPL[{3}, -S^2]^2)/(3*S^2) + ((-113 - 664*S^2 - 487*S^4)/(12*S^2) - (109*Pi^2*(1 + S^4))/(18*S^2))*HPL[{4}, -S^2] + ((-15 - 120*S^2 - 97*S^4)*HPL[{5}, -S^2])/(3*S^2) - (82*(1 + S^4)*HPL[{6}, -S^2])/(3*S^2) + (784*(1 + S^4)*HPL[{2, 1}, -S^2]^2)/S^2 + ((1706*Pi^2*(1 + S^4))/(9*S^2) + (1823 + 4444*S^2 + 2605*S^4)/(3*S^2))*HPL[{3, 1}, -S^2] - (4*(63 + 113*S^2 + 52*S^4)*HPL[{3, 2}, -S^2])/(3*S^2) + ((-695 - 1104*S^2 - 433*S^4)*HPL[{4, 1}, -S^2])/(3*S^2) + ((-1 - S^4)*HPL[{4, 2}, -S^2])/S^2 + (128*(1 + S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + ((-1142*Pi^2*(1 + S^4))/(3*S^2) - (10*(361 + 882*S^2 + 521*S^4))/(3*S^2))*HPL[{2, 1, 1}, -S^2] - (8*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S^2) - (12*(357 + 772*S^2 + 415*S^4)*HPL[{3, 1, 1}, -S^2])/S^2 - (1416*(1 + S^4)*HPL[{3, 2, 1}, -S^2])/S^2 - (4332*(1 + S^4)*HPL[{4, 1, 1}, -S^2])/S^2 + (20*(403 + 900*S^2 + 497*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^2) + (2992*(1 + S^4)*HPL[{3, 1, 1, 1}, -S^2])/S^2 - (6000*(1 + S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + ((Pi^2*(379 + 504*S^2 + 141*S^4))/(18*S^2) + (1323 + 2096*S^2 + 709*S^4)/(12*S^2))*Zeta[3] - (16*(1 + S^4)*Zeta[3]^2)/S^2 + HPL[{2, 1}, -S^2]*((9*(241 + 648*S^2 + 407*S^4))/(4*S^2) + (Pi^2*(2779 + 6852*S^2 + 4073*S^4))/(18*S^2) - (164*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((19 - 122*S^2 - 125*S^4)/(3*S^2) + (Pi^2*(53 + 35*S^2 - 28*S^4))/(9*S^2) - (76*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (8*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]*((-5939 - 17922*S^2 - 11983*S^4)/(24*S^2) + (Pi^2*(-1171 - 3379*S^2 - 2208*S^4))/(18*S^2) - (8953*Pi^4*(1 + S^4))/(540*S^2) + ((125 + 228*S^2 + 103*S^4)*HPL[{3}, -S^2])/(3*S^2) - (3*(1 + S^4)*HPL[{4}, -S^2])/S^2 + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) + (784*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (1568*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + ((93 + 164*S^2 + 71*S^4)*Zeta[3])/S^2) + ((301 + 370*S^2 + 65*S^4)*Zeta[5])/(3*S^2))) + (252 + 271*S^2)*Zeta[7] + HPL[{1}, -S^2]*((Pi^6*(-218821 - 615590*S^2 - 400605*S^4))/(90720*S^2) + (Pi^4*(-96707 - 328636*S^2 - 233561*S^4))/(8640*S^2) + (Pi^2*(-18017 - 64916*S^2 - 46899*S^4))/(288*S^2) - (35*(1309 + 5526*S^2 + 4217*S^4))/(192*S^2) + ((21 - 124*S^2 - 145*S^4)*HPL[{2}, -S^2]^3)/(6*S^2) + ((-243 - 448*S^2 - 197*S^4)*HPL[{3}, -S^2]^2)/(6*S^2) + ((1091 + 592*S^2 - 499*S^4)/(6*S^2) + (82*Pi^2*(1 + S^4))/(9*S^2))*HPL[{5}, -S^2] - (5*(-165 + 82*S^2 + 251*S^4)*HPL[{6}, -S^2])/(6*S^2) - (164*(1 + S^4)*HPL[{7}, -S^2])/S^2 + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S^2) + ((-1042*Pi^2*(1 + S^4))/(9*S^2) - (7*(327 + 524*S^2 + 197*S^4))/(3*S^2))*HPL[{3, 2}, -S^2] + ((-16125 - 25124*S^2 - 8999*S^4)/(6*S^2) - (3527*Pi^2*(1 + S^4))/(9*S^2))*HPL[{4, 1}, -S^2] + ((-773 - 1388*S^2 - 647*S^4)*HPL[{4, 2}, -S^2])/(6*S^2) + (36*(1 + S^4)*HPL[{4, 3}, -S^2])/S^2 - (2*(1213 + 1736*S^2 + 555*S^4)*HPL[{5, 1}, -S^2])/(3*S^2) + (76*(1 + S^4)*HPL[{5, 2}, -S^2])/S^2 + (90*(1 + S^4)*HPL[{6, 1}, -S^2])/S^2 + ((-1276*Pi^2*(1 + S^4))/(3*S^2) - (2*(1955 + 4476*S^2 + 2521*S^4))/(3*S^2))*HPL[{2, 2, 1}, -S^2] + ((-3008*Pi^2*(1 + S^4))/(3*S^2) - (4*(1489 + 4506*S^2 + 3017*S^4))/(3*S^2))*HPL[{3, 1, 1}, -S^2] + (4*(1 - 2*S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/(3*S^2) - (8*(-32 + 187*S^2 + 217*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S^2) + (1382*(1 + S^4)*HPL[{3, 2, 2}, -S^2])/S^2 + (4240*(1 + S^4)*HPL[{3, 3, 1}, -S^2])/S^2 - (8*(-380 + 135*S^2 + 509*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S^2) + (4162*(1 + S^4)*HPL[{4, 1, 2}, -S^2])/S^2 + (12970*(1 + S^4)*HPL[{4, 2, 1}, -S^2])/S^2 + (26672*(1 + S^4)*HPL[{5, 1, 1}, -S^2])/S^2 + ((1256*Pi^2*(1 + S^4))/(3*S^2) + (4*(-119 + 338*S^2 + 457*S^4))/S^2)*HPL[{2, 1, 1, 1}, -S^2] + (496*(1 + S^4)*HPL[{2, 2, 2, 1}, -S^2])/S^2 + (8*(-347 - 48*S^2 + 299*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^2) - (4128*(1 + S^4)*HPL[{3, 1, 1, 2}, -S^2])/S^2 - (4128*(1 + S^4)*HPL[{3, 1, 2, 1}, -S^2])/S^2 - (5616*(1 + S^4)*HPL[{3, 2, 1, 1}, -S^2])/S^2 - (17984*(1 + S^4)*HPL[{4, 1, 1, 1}, -S^2])/S^2 - (120*(-3 + 20*S^2 + 23*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^2 + (6272*(1 + S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/S^2 + (18816*(1 + S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^2 + (37760*(1 + S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/S^2 + (2400*(1 + S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^2 + ((109*Pi^4*(1 + S^4))/(18*S^2) + (2*(479 + 726*S^2 + 247*S^4))/(3*S^2) + (Pi^2*(2425 + 3744*S^2 + 1319*S^4))/(36*S^2))*Zeta[3] - (2*(24 + 71*S^2 + 25*S^4)*Zeta[3]^2)/(3*S^2) + HPL[{3, 1}, -S^2]*((Pi^2*(159 + 1354*S^2 + 1223*S^4))/(9*S^2) + (-4181 + 1104*S^2 + 5285*S^4)/(12*S^2) - (680*(1 + S^4)*Zeta[3])/S^2) + HPL[{4}, -S^2]*((2563 + 3028*S^2 + 369*S^4)/(12*S^2) + (Pi^2*(1191 + 1604*S^2 + 413*S^4))/(36*S^2) - (226*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (62*(1 + S^4)*Zeta[3])/(3*S^2)) + HPL[{2}, -S^2]^2*((-2283 - 5632*S^2 - 3349*S^4)/(16*S^2) + (Pi^2*(-421 - 957*S^2 - 536*S^4))/(9*S^2) + (202*(1 + S^4)*HPL[{3}, -S^2])/S^2 + (62*(1 + S^4)*HPL[{2, 1}, -S^2])/S^2 + (146*(1 + S^4)*Zeta[3])/S^2) + HPL[{2, 1, 1}, -S^2]*((-8*Pi^2*(113 + 468*S^2 + 361*S^4))/(9*S^2) - (5*(-115 + 328*S^2 + 443*S^4))/(2*S^2) + (1312*(1 + S^4)*Zeta[3])/S^2) + HPL[{3}, -S^2]*((419*Pi^4*(1 + S^4))/(54*S^2) + (Pi^2*(1009 + 1468*S^2 + 443*S^4))/(12*S^2) + (1771 + 2306*S^2 + 535*S^4)/(4*S^2) - (34*(1 + S^4)*HPL[{4}, -S^2])/S^2 - (10*(233 + 396*S^2 + 163*S^4)*HPL[{2, 1}, -S^2])/(3*S^2) - (660*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 + (1320*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 + (4*(44 + 65*S^2 + 35*S^4)*Zeta[3])/(3*S^2)) + HPL[{2, 1}, -S^2]*((4421*Pi^4*(1 + S^4))/(180*S^2) + (2*Pi^2*(113 + 962*S^2 + 861*S^4))/(9*S^2) + (-575 + 2102*S^2 + 2677*S^4)/(4*S^2) - (1568*(1 + S^4)*HPL[{3, 1}, -S^2])/S^2 - (3136*(1 + S^4)*HPL[{2, 1, 1}, -S^2])/S^2 - (4*(587 + 972*S^2 + 409*S^4)*Zeta[3])/(3*S^2)) + ((401*Pi^2*(1 + S^4))/(9*S^2) + (2067 + 2948*S^2 + 881*S^4)/(6*S^2))*Zeta[5] + HPL[{2}, -S^2]*((5987 - 34004*S^2 - 39991*S^4)/(96*S^2) + (Pi^4*(-14715 - 52538*S^2 - 38851*S^4))/(2160*S^2) + (Pi^2*(-445 - 8216*S^2 - 7867*S^4))/(72*S^2) + ((521*Pi^2*(1 + S^4))/(9*S^2) + (2283 + 3656*S^2 + 1373*S^4)/(6*S^2))*HPL[{3}, -S^2] + ((1 + S^2)*(745 + 611*S^2)*HPL[{4}, -S^2])/(6*S^2) + (66*(1 + S^4)*HPL[{5}, -S^2])/S^2 + ((638*Pi^2*(1 + S^4))/(3*S^2) + (1955 + 4476*S^2 + 2521*S^4)/(3*S^2))*HPL[{2, 1}, -S^2] + (4*(551 + 1176*S^2 + 625*S^4)*HPL[{3, 1}, -S^2])/(3*S^2) - (730*(1 + S^4)*HPL[{3, 2}, -S^2])/S^2 - (2198*(1 + S^4)*HPL[{4, 1}, -S^2])/S^2 - (8*(551 + 1176*S^2 + 625*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S^2) - (248*(1 + S^4)*HPL[{2, 2, 1}, -S^2])/S^2 + (2064*(1 + S^4)*HPL[{3, 1, 1}, -S^2])/S^2 + (3136*(1 + S^4)*HPL[{2, 1, 1, 1}, -S^2])/S^2 + ((539*Pi^2*(1 + S^4))/(9*S^2) + (2*(583 + 910*S^2 + 351*S^4))/(3*S^2))*Zeta[3] + (270*(1 + S^4)*Zeta[5])/S^2) + (252*(1 + S^4)*Zeta[7])/S^2));
Et5vwuT3F1=(5*(3407 + 11038*S^2))/(192*S) + (Pi^8*S*(455019 + 233983*S^2))/(680400*(1 + S^2)) + (Pi^2*(-683 + 5570*S^2 - 788*S^4))/(288*S) + (Pi^6*S*(384133 + 396110*S^2 + 15561*S^4))/(181440*(1 + S^2)) + (Pi^4*(-2968 + 77824*S^2 + 78731*S^4 - 1245*S^6))/(8640*S*(1 + S^2)) + ((7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^8)/(18*S*(1 + S^2)) + (8*S*HPL[{1}, -S^2]^9)/27 + HPL[{0}, S^2]^8*(S/(192*(1 + S^2)) + (S*HPL[{1}, -S^2])/96) + ((39 + 532*S^2 + 205*S^4)*HPL[{2}, -S^2]^4)/(36*S*(1 + S^2)) + HPL[{0}, S^2]^7*((7*Pi^2*S)/864 + (S*(101 + 12*S^2))/576 + ((12 + 55*S^2 + 29*S^4)*HPL[{1}, -S^2])/(288*S*(1 + S^2)) + (7*S*HPL[{1}, -S^2]^2)/144 + (7*S*HPL[{2}, -S^2])/144) + HPL[{1}, -S^2]^7*((92*Pi^2*S)/63 + (155 + 158*S^2 + 3*S^4)/(63*S) + (20*S*HPL[{2}, -S^2])/21) - 2*S*HPL[{3}, -S^2]^3 + (2*(8 + 65*S^2 + 51*S^4)*HPL[{4}, -S^2]^2)/(3*S*(1 + S^2)) + ((128*Pi^2*S)/9 + (2676 + 9484*S^2 + 7635*S^4 + 681*S^6)/(6*S*(1 + S^2)))*HPL[{7}, -S^2] + (8*(126 + 641*S^2 + 410*S^4)*HPL[{8}, -S^2])/(3*S*(1 + S^2)) + (1876*S*HPL[{9}, -S^2])/3 - (1904*S*HPL[{2, 1}, -S^2]^3)/9 + (2*(43 + 432*S^2 + 156*S^4)*HPL[{3, 1}, -S^2]^2)/(S*(1 + S^2)) + ((-22*Pi^2*S)/3 + (-275 - 114*S^2 + 173*S^4 - 42*S^6)/(6*S*(1 + S^2)))*HPL[{4, 3}, -S^2] + ((-163*Pi^2*S)/9 + (-670 - 521*S^2 + 170*S^4 - 129*S^6)/(6*S*(1 + S^2)))*HPL[{5, 2}, -S^2] + ((1 + 153*S^2 + 164*S^4)*HPL[{5, 3}, -S^2])/(3*S*(1 + S^2)) + 20*S*HPL[{5, 4}, -S^2] + ((-128*Pi^2*S)/9 + (-3192 - 6542*S^2 - 3503*S^4 - 363*S^6)/(6*S*(1 + S^2)))*HPL[{6, 1}, -S^2] + ((59 + 311*S^2 + 282*S^4)*HPL[{6, 2}, -S^2])/(3*S*(1 + S^2)) + (352*S*HPL[{6, 3}, -S^2])/3 - (2*(296 + 2187*S^2 + 1603*S^4)*HPL[{7, 1}, -S^2])/(3*S*(1 + S^2)) + (832*S*HPL[{7, 2}, -S^2])/3 - 232*S*HPL[{8, 1}, -S^2] + (8*(71 + 1118*S^2 + 459*S^4)*HPL[{2, 1, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((-2093*Pi^2*S)/9 + (-119 - 1341*S^2 - 105*S^4)/(6*S))*HPL[{3, 2, 2}, -S^2] + ((-6572*Pi^2*S)/9 - (2*(127 + 1143*S^2 + 1099*S^4 + 87*S^6))/(3*S*(1 + S^2)))*HPL[{3, 3, 1}, -S^2] + ((-71 + 104*S^2 - 161*S^4)*HPL[{3, 3, 2}, -S^2])/(3*S*(1 + S^2)) + ((-6502*Pi^2*S)/9 + (-618 - 4462*S^2 - 4173*S^4 - 345*S^6)/(6*S*(1 + S^2)))*HPL[{4, 1, 2}, -S^2] + (2*(72 - 95*S^2 + 121*S^4)*HPL[{4, 1, 3}, -S^2])/(3*S*(1 + S^2)) + ((-20098*Pi^2*S)/9 + (-1866 - 13906*S^2 - 13041*S^4 - 1065*S^6)/(6*S*(1 + S^2)))*HPL[{4, 2, 1}, -S^2] + ((-79 - 193*S^2 - 318*S^4)*HPL[{4, 2, 2}, -S^2])/(3*S*(1 + S^2)) - (112*S*HPL[{4, 2, 3}, -S^2])/3 + (2*(134 - 727*S^2 + 123*S^4)*HPL[{4, 3, 1}, -S^2])/(3*S*(1 + S^2)) - (292*S*HPL[{4, 3, 2}, -S^2])/3 - 136*S*HPL[{4, 4, 1}, -S^2] + ((-41282*Pi^2*S)/9 - (2*(625 + 6185*S^2 + 6051*S^4 + 531*S^6))/(3*S*(1 + S^2)))*HPL[{5, 1, 1}, -S^2] + ((85 - 1116*S^2 - S^4)*HPL[{5, 1, 2}, -S^2])/(3*S*(1 + S^2)) - (64*S*HPL[{5, 1, 3}, -S^2])/3 + ((1105 - 5316*S^2 + 1619*S^4)*HPL[{5, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (800*S*HPL[{5, 2, 2}, -S^2])/3 - (1264*S*HPL[{5, 3, 1}, -S^2])/3 + (10*(113 - 325*S^2 + 239*S^4)*HPL[{6, 1, 1}, -S^2])/(S*(1 + S^2)) - (1124*S*HPL[{6, 1, 2}, -S^2])/3 - (2324*S*HPL[{6, 2, 1}, -S^2])/3 - (2536*S*HPL[{7, 1, 1}, -S^2])/3 + ((656*Pi^2*S)/3 + (4*(-818 + 202*S^2 + 15*S^4))/(3*S))*HPL[{2, 2, 2, 1}, -S^2] + ((-1618*Pi^2*S)/9 - (8*(-1245 - 1095*S^2 + 157*S^4 + 6*S^6))/(3*S*(1 + S^2)))*HPL[{3, 1, 1, 2}, -S^2] + ((-1618*Pi^2*S)/9 - (8*(-1245 - 1095*S^2 + 157*S^4 + 6*S^6))/(3*S*(1 + S^2)))*HPL[{3, 1, 2, 1}, -S^2] + ((58 + 345*S^2 + 53*S^4)*HPL[{3, 1, 2, 2}, -S^2])/(3*S*(1 + S^2)) + ((-7522*Pi^2*S)/9 - (4*(-4944 - 4038*S^2 + 965*S^4 + 57*S^6))/(3*S*(1 + S^2)))*HPL[{3, 2, 1, 1}, -S^2] + ((58 + 345*S^2 + 53*S^4)*HPL[{3, 2, 1, 2}, -S^2])/(3*S*(1 + S^2)) + ((698 - 3671*S^2 - 3907*S^4)*HPL[{3, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (7828*S*HPL[{3, 2, 2, 2}, -S^2])/3 + (24484*S*HPL[{3, 2, 3, 1}, -S^2])/3 - (8*(-80 + 502*S^2 + 495*S^4)*HPL[{3, 3, 1, 1}, -S^2])/(S*(1 + S^2)) + 8008*S*HPL[{3, 3, 1, 2}, -S^2] + 24780*S*HPL[{3, 3, 2, 1}, -S^2] + ((-21500*Pi^2*S)/9 - (2*(-29378 - 23828*S^2 + 5895*S^4 + 333*S^6))/(3*S*(1 + S^2)))*HPL[{4, 1, 1, 1}, -S^2] + (2*(5 + 412*S^2 + 56*S^4)*HPL[{4, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) - (151300*S*HPL[{4, 1, 1, 3}, -S^2])/3 - (2*(-965 + 5612*S^2 + 5884*S^4)*HPL[{4, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (127420*S*HPL[{4, 1, 2, 2}, -S^2])/3 - 75816*S*HPL[{4, 1, 3, 1}, -S^2] - (2*(-2885 + 17660*S^2 + 17764*S^4)*HPL[{4, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (78484*S*HPL[{4, 2, 1, 2}, -S^2])/3 - (77104*S*HPL[{4, 2, 2, 1}, -S^2])/3 - (449056*S*HPL[{4, 3, 1, 1}, -S^2])/3 - (4*(-2819 + 17513*S^2 + 18076*S^4)*HPL[{5, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 152564*S*HPL[{5, 1, 1, 2}, -S^2] - 251356*S*HPL[{5, 1, 2, 1}, -S^2] - 598508*S*HPL[{5, 2, 1, 1}, -S^2] - (4486840*S*HPL[{6, 1, 1, 1}, -S^2])/3 + ((-4096*Pi^2*S)/9 - (8*(291 + 26*S^2 + 6*S^4))/S)*HPL[{2, 1, 2, 1, 1}, -S^2] + ((-4096*Pi^2*S)/3 - (24*(291 + 26*S^2 + 6*S^4))/S)*HPL[{2, 2, 1, 1, 1}, -S^2] - (8*(-179 + 924*S^2 + 917*S^4)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(-179 + 924*S^2 + 917*S^4)*HPL[{2, 2, 2, 1, 1}, -S^2])/(S*(1 + S^2)) + (7744*S*HPL[{2, 2, 2, 2, 1}, -S^2])/3 + ((-29840*Pi^2*S)/9 - (8*(4333 + 675*S^2 + 126*S^4))/(3*S))*HPL[{3, 1, 1, 1, 1}, -S^2] + (8*(-1049 + 5558*S^2 + 5491*S^4)*HPL[{3, 1, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) + (8*(-1765 + 9254*S^2 + 9159*S^4)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (7228*S*HPL[{3, 1, 1, 2, 2}, -S^2])/3 + (8*(-2123 + 11102*S^2 + 10993*S^4)*HPL[{3, 1, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (7228*S*HPL[{3, 1, 2, 1, 2}, -S^2])/3 - (452*S*HPL[{3, 1, 2, 2, 1}, -S^2])/3 - (65696*S*HPL[{3, 1, 3, 1, 1}, -S^2])/3 + (16*(-2225 + 11557*S^2 + 11457*S^4)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (30460*S*HPL[{3, 2, 1, 1, 2}, -S^2])/3 + (22780*S*HPL[{3, 2, 1, 2, 1}, -S^2])/3 + (11228*S*HPL[{3, 2, 2, 1, 1}, -S^2])/3 + 3936*S*HPL[{3, 3, 1, 1, 1}, -S^2] + (8*(-4471 + 22986*S^2 + 22949*S^4)*HPL[{4, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (89672*S*HPL[{4, 1, 1, 1, 2}, -S^2])/3 + (66632*S*HPL[{4, 1, 1, 2, 1}, -S^2])/3 + (31976*S*HPL[{4, 1, 2, 1, 1}, -S^2])/3 + (32360*S*HPL[{4, 2, 1, 1, 1}, -S^2])/3 + (56384*S*HPL[{5, 1, 1, 1, 1}, -S^2])/3 + ((8768*Pi^2*S)/9 + (8*(-1861 + 439*S^2 + 45*S^4))/(3*S))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] - (15232*S*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/3 - 15232*S*HPL[{2, 2, 2, 1, 1, 1}, -S^2] - (16*(-215 + 793*S^2 + 1032*S^4)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (109024*S*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/3 + (200416*S*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/3 + (261344*S*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/3 + (291808*S*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/3 + (489824*S*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/3 + 492480*S*HPL[{4, 1, 1, 1, 1, 1}, -S^2] + (160*(-11 + 77*S^2 + 73*S^4)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 10368*S*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2] + 41472*S*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2] + 103680*S*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2] + 194048*S*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2] + 21760*S*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2] + ((-28*Pi^2*S)/27 - (28*S*HPL[{0}, S^2]^2)/9 - (4*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) - (32*S*HPL[{1}, -S^2]^2)/3 + HPL[{0}, S^2]*((-4*S*(7 + 3*S^2))/(3*(1 + S^2)) - (32*S*HPL[{1}, -S^2])/3) - (56*S*HPL[{2}, -S^2])/9)*Log[T]^7 + ((4*S)/(3*(1 + S^2)) + (8*S*HPL[{0}, S^2])/3 + (8*S*HPL[{1}, -S^2])/3)*Log[T]^8 + (-(Pi^2*S*(11 + 34*S^2))/(6*(1 + S^2)) - (S*(5 - 19*S^2 + 24*S^4))/(12*(1 + S^2)))*Zeta[3]^2 + HPL[{2, 1, 1, 1, 1}, -S^2]*((8*Pi^2*(-94 + 1464*S^2 + 1087*S^4))/(9*S*(1 + S^2)) + (4*(-45 + 27*S^2 + 2027*S^4 + 27*S^6))/(3*S^3) - (15104*S*Zeta[3])/3) + HPL[{4, 1, 1}, -S^2]*((Pi^2*(-585 + 7354*S^2 + 5736*S^4))/(9*S*(1 + S^2)) + (-216 - 524*S^2 + 10793*S^4 + 42*S^6)/(6*S^3) - (11296*S*Zeta[3])/3) + HPL[{3, 2, 1}, -S^2]*((Pi^2*(-353 + 5051*S^2 + 3668*S^4))/(18*S*(1 + S^2)) + (-108 - 875*S^2 + 6602*S^4 + 27*S^6)/(12*S^3) - 1236*S*Zeta[3]) + HPL[{2}, -S^2]^3*((Pi^2*(-101 + 1250*S^2 + 917*S^4))/(108*S*(1 + S^2)) + (-15 - 115*S^2 + 845*S^4 + 9*S^6)/(36*S^3) - (538*S*HPL[{3}, -S^2])/9 - (484*S*HPL[{2, 1}, -S^2])/9 - (460*S*Zeta[3])/9) + HPL[{6}, -S^2]*((Pi^2*(55 + 369*S^2 + 277*S^4))/(6*S*(1 + S^2)) + (60 + 820*S^2 + 1053*S^4 + 22*S^6)/(4*S^3) + 28*S*HPL[{2, 1}, -S^2] - (124*S*Zeta[3])/3) + Log[T]^6*(S/3 + (Pi^2*S*(211 + 73*S^2))/(27*(1 + S^2)) + (88*S*HPL[{0}, S^2]^3)/27 + (14*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)) + (224*S*HPL[{1}, -S^2]^3)/9 + HPL[{0}, S^2]^2*((S*(127 + 73*S^2))/(9*(1 + S^2)) + 12*S*HPL[{1}, -S^2]) + (2*(-11 + 77*S^2 + 73*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((92*Pi^2*S)/9 + (155 + 158*S^2 + 3*S^4)/(9*S) + (20*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]*((256*Pi^2*S)/27 + (S*(158 + 3*S^2))/9 + (14*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) + (112*S*HPL[{1}, -S^2]^2)/3 + (316*S*HPL[{2}, -S^2])/9) - (296*S*HPL[{3}, -S^2])/9 + (272*S*HPL[{2, 1}, -S^2])/9 - (272*S*Zeta[3])/9) + HPL[{1}, -S^2]^6*(((1 + S^2)*(3 + 967*S^2 + 42*S^4))/(108*S^3) + (Pi^2*(265 + 1477*S^2 + 384*S^4))/(162*S*(1 + S^2)) + ((26 + 121*S^2 + 65*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - (160*S*HPL[{3}, -S^2])/9 - (20*S*HPL[{2, 1}, -S^2])/3 - (40*S*Zeta[3])/3) + HPL[{3, 1, 2}, -S^2]*((17*Pi^2)/(6*S) + (12 + 45*S^2 - 158*S^4 - 45*S^6)/(12*S^3) - (28*S*Zeta[3])/3) + HPL[{0}, S^2]^6*((Pi^2*S*(234 + 109*S^2))/(1728*(1 + S^2)) + (S*(499 + 545*S^2 + 30*S^4))/(1152*(1 + S^2)) + ((24 + 114*S^2 + 49*S^4)*HPL[{1}, -S^2]^2)/(144*S*(1 + S^2)) + (41*S*HPL[{1}, -S^2]^3)/216 + (S*(141 + 109*S^2)*HPL[{2}, -S^2])/(288*(1 + S^2)) + HPL[{1}, -S^2]*((125*Pi^2*S)/864 + (265 + 505*S^2 + 243*S^4 - 5*S^6)/(576*S*(1 + S^2)) + (2*S*HPL[{2}, -S^2])/9) - (S*HPL[{3}, -S^2])/48 + (S*HPL[{2, 1}, -S^2])/12 + (17*S*Zeta[3])/36) + HPL[{3}, -S^2]^2*((Pi^2*(-13 - 26*S^2 - 113*S^4))/(36*S*(1 + S^2)) + (3 + 100*S^2 - 226*S^4 + 27*S^6)/(24*S^3) - (4*S*HPL[{2, 1}, -S^2])/3 + (16*S*Zeta[3])/3) + HPL[{4, 2}, -S^2]*((Pi^2*(2 + 59*S^2))/(6*S*(1 + S^2)) + (-12 + 156*S^2 + 209*S^4 + 81*S^6)/(12*S^3) + (88*S*Zeta[3])/3) + HPL[{5, 1}, -S^2]*((Pi^2*(-55 + 21*S^2 - 334*S^4))/(9*S*(1 + S^2)) + (12 - 1421*S^2 - 1590*S^4 + 345*S^6)/(12*S^3) + (416*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]^2*((Pi^2*(-133 - 3943*S^2 - 1896*S^4))/(18*S*(1 + S^2)) + (3 - 248*S^2 - 1959*S^4 + 15*S^6)/(6*S^3) + (1840*S*Zeta[3])/3) + HPL[{3, 1, 1, 1}, -S^2]*((-2*Pi^2*(-238 + 2525*S^2 + 2079*S^4))/(9*S*(1 + S^2)) + (108 - 23*S^2 - 4012*S^4 - 33*S^6)/(3*S^3) + (7664*S*Zeta[3])/3) + HPL[{1}, -S^2]^5*((1237*Pi^4*S)/450 + (Pi^2*(1072 + 1081*S^2 + 15*S^4))/(135*S) + ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(60*S^3) + ((314*Pi^2*S)/45 + (-5 + 283*S^2 + 283*S^4 - 5*S^6)/(15*S^3))*HPL[{2}, -S^2] + (392*S*HPL[{2}, -S^2]^2)/15 + (2*(-61 - 439*S^2 + 22*S^4)*HPL[{3}, -S^2])/(15*S*(1 + S^2)) - (284*S*HPL[{4}, -S^2])/15 - (2*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (32*S*HPL[{3, 1}, -S^2])/15 + 40*S*HPL[{2, 1, 1}, -S^2] + (2*(-29 - 203*S^2 + 6*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((2453*Pi^4*S)/270 + (Pi^2*(10611 + 10062*S^2 - 544*S^4 + 33*S^6))/(18*S*(1 + S^2)) + (-84 + 23521*S^2 + 1160*S^4 + 519*S^6)/(12*S^3) + (24*(-25 - 95*S^2 + 7*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((4414*Pi^4*S)/135 + (Pi^2*(-3723 - 3218*S^2 + 586*S^4 + 57*S^6))/(9*S*(1 + S^2)) + (18 - 3959*S^2 + 202*S^4 + 234*S^6)/(3*S^3) - (16*(-71 - 309*S^2 + 8*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((1853*Pi^4*S)/135 + (Pi^2*(3453 - 89*S^2 + 39*S^4))/(18*S) + (-12 + 3852*S^2 + 361*S^4 + 246*S^6)/(6*S^3) + (4*(-151 - 529*S^2 + 60*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{5}, -S^2]*((-217*Pi^4*S)/90 + (Pi^2*(567 + 1536*S^2 + 1003*S^4 + 48*S^6))/(36*S*(1 + S^2)) + (30 + 1018*S^2 + 3823*S^4 + 3042*S^6 + 127*S^8)/(12*S^3*(1 + S^2)) + (2*(-26 + 224*S^2 + 151*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (376*S*HPL[{3, 1}, -S^2])/3 - 260*S*HPL[{2, 1, 1}, -S^2] - (2*(23 + 115*S^2 + 83*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3, 2}, -S^2]*((212*Pi^4*S)/15 + (Pi^2*(93 + 485*S^2 + 480*S^4 + 78*S^6))/(36*S*(1 + S^2)) + (-4 + 819*S^2 + 2805*S^4 + 2703*S^6 + 881*S^8)/(24*S^3*(1 + S^2)) + 2748*S*HPL[{2, 1, 1}, -S^2] + ((19 + 325*S^2 + 198*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{4, 1}, -S^2]*((6316*Pi^4*S)/135 + (Pi^2*(-351 + 532*S^2 + 1177*S^4 + 246*S^6))/(36*S*(1 + S^2)) + (4 + 459*S^2 + 4792*S^4 + 6402*S^6 + 2545*S^8)/(24*S^3*(1 + S^2)) + (26488*S*HPL[{2, 1, 1}, -S^2])/3 + (2*(29 + 546*S^2 + 324*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^5*((3083*Pi^4*S)/32400 + (-90 + 18939*S^2 - 325*S^4)/(5760*S) + (Pi^2*S*(2745 + 3019*S^2 + 264*S^4))/(1728*(1 + S^2)) + ((605 + 2886*S^2 + 1189*S^4)*HPL[{1}, -S^2]^3)/(1080*S*(1 + S^2)) + (91*S*HPL[{1}, -S^2]^4)/180 + ((623*Pi^2*S)/1080 + (-6 + 15*S^2 + 494*S^4 + 477*S^6 - 6*S^8)/(288*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (71*S*HPL[{2}, -S^2]^2)/120 + HPL[{1}, -S^2]^2*((427*Pi^2*S)/720 + (525 + 1014*S^2 + 519*S^4 + 10*S^6)/(288*S*(1 + S^2)) + (461*S*HPL[{2}, -S^2])/360) + ((1 + 2*S^2 - S^4)*HPL[{3}, -S^2])/(48*S*(1 + S^2)) + (S*HPL[{4}, -S^2])/4 + ((-485 - 681*S^2 + 265*S^4)*HPL[{2, 1}, -S^2])/(360*S*(1 + S^2)) - (27*S*HPL[{3, 1}, -S^2])/10 + (511*S*HPL[{2, 1, 1}, -S^2])/90 + (S*(25 + 24*S^2)*Zeta[3])/(6*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1865 + 8661*S^2 + 4234*S^4))/(4320*S*(1 + S^2)) + (3 + 1106*S^2 + 2138*S^4 + 1094*S^6 + 19*S^8)/(576*S^3*(1 + S^2)) + ((500 + 2381*S^2 + 959*S^4)*HPL[{2}, -S^2])/(720*S*(1 + S^2)) + (S*HPL[{3}, -S^2])/12 - (461*S*HPL[{2, 1}, -S^2])/180 + (S*Zeta[3])/3)) + Log[T]^5*((-6166*Pi^4*S)/2025 + (1 - 4*S^2)/(2*S) - (Pi^2*S*(2137 + 15*S^2))/270 - (283*S*HPL[{0}, S^2]^4)/135 - (28*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) - (112*S*HPL[{1}, -S^2]^4)/3 + HPL[{0}, S^2]^3*(-(S*(576 + 361*S^2))/(45*(1 + S^2)) - (86*S*HPL[{1}, -S^2])/9) + ((-596*Pi^2*S)/27 + (30 + 163*S^2 - 2137*S^4 - 15*S^6)/(45*S^3))*HPL[{2}, -S^2] - (92*S*HPL[{2}, -S^2]^2)/3 + HPL[{0}, S^2]^2*((-1301*Pi^2*S)/135 - (S*(2137 + 15*S^2))/90 + ((-118 - 637*S^2 - 195*S^4)*HPL[{1}, -S^2])/(9*S*(1 + S^2)) - 36*S*HPL[{1}, -S^2]^2 - (302*S*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]^2*((-92*Pi^2*S)/3 + (-155 - 158*S^2 - 3*S^4)/(3*S) - 20*S*HPL[{2}, -S^2]) - (2*(-3 - 397*S^2 + 6*S^4)*HPL[{3}, -S^2])/(15*S*(1 + S^2)) + (472*S*HPL[{4}, -S^2])/15 - (4*(-37 - 44*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (320*S*HPL[{3, 1}, -S^2])/3 - (784*S*HPL[{2, 1, 1}, -S^2])/3 + (8*S*(19 + 4*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{0}, S^2]*(-(S*(991 + 42*S^2))/18 - (Pi^2*S*(1311 + 676*S^2))/(45*(1 + S^2)) - (14*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^2)/(3*S*(1 + S^2)) - (224*S*HPL[{1}, -S^2]^3)/3 - (2*(-4 + 434*S^2 + 213*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((-254*Pi^2*S)/9 + (-155 - 158*S^2 - 3*S^4)/(3*S) - 100*S*HPL[{2}, -S^2]) + (68*S*HPL[{3}, -S^2])/9 - (32*S*HPL[{2, 1}, -S^2])/3 + 24*S*Zeta[3]) + HPL[{1}, -S^2]*((Pi^2*(-265 - 1477*S^2 - 384*S^4))/(27*S*(1 + S^2)) - ((1 + S^2)*(3 + 967*S^2 + 42*S^4))/(18*S^3) - (2*(26 + 121*S^2 + 65*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + (320*S*HPL[{3}, -S^2])/3 + 40*S*HPL[{2, 1}, -S^2] + 80*S*Zeta[3])) + (-(Pi^2*S*(-282 - 149*S^2 + 159*S^4))/(36*(1 + S^2)) - (S*(-1789 - 1254*S^2 + 455*S^4))/(24*(1 + S^2)))*Zeta[5] + HPL[{2, 1, 1}, -S^2]*((Pi^4*(-1409 + 40150*S^2 + 28296*S^4))/(540*S*(1 + S^2)) + (-249 + 3031*S^2 + 18657*S^4 + 201*S^6)/(24*S^3) + (Pi^2*(-90 + 197*S^2 + 4412*S^4 + 4152*S^6 + 51*S^8))/(18*S^3*(1 + S^2)) + (7616*S*HPL[{2, 2, 1}, -S^2])/3 + 1824*S*HPL[{3, 1, 1}, -S^2] - 5184*S*HPL[{2, 1, 1, 1}, -S^2] + ((-2072*Pi^2*S)/9 - (2*(1 + 374*S^2 + 382*S^4 + 33*S^6))/(3*S*(1 + S^2)))*Zeta[3] - 1112*S*Zeta[5]) + Log[T]^4*((7*(-5 + 14*S^2))/(12*S) + (Pi^2*S*(2117 + 27*S^2))/108 + (Pi^4*S*(21496 + 10363*S^2))/(1620*(1 + S^2)) + (283*S*HPL[{0}, S^2]^5)/270 + (35*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^4)/(9*S*(1 + S^2)) + (112*S*HPL[{1}, -S^2]^5)/3 + HPL[{0}, S^2]^4*((S*(853 + 574*S^2))/(108*(1 + S^2)) + (31*S*HPL[{1}, -S^2])/6) + ((71 + 1118*S^2 + 459*S^4)*HPL[{2}, -S^2]^2)/(9*S*(1 + S^2)) + HPL[{0}, S^2]^3*((613*Pi^2*S)/81 + (S*(2215 + 2257*S^2 + 18*S^4))/(108*(1 + S^2)) + ((180 + 923*S^2 + 313*S^4)*HPL[{1}, -S^2])/(18*S*(1 + S^2)) + (215*S*HPL[{1}, -S^2]^2)/9 + (205*S*HPL[{2}, -S^2])/9) + HPL[{1}, -S^2]^3*((460*Pi^2*S)/9 + (5*(155 + 158*S^2 + 3*S^4))/(9*S) + (100*S*HPL[{2}, -S^2])/3) + ((-130*Pi^2*S)/3 + (32 - 285*S^2 - 36*S^4)/(9*S))*HPL[{3}, -S^2] + (2*(2 - 57*S^2 + 12*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (452*S*HPL[{5}, -S^2])/9 + ((1096*Pi^2*S)/27 + (-1861 + 439*S^2 + 45*S^4)/(9*S))*HPL[{2, 1}, -S^2] - (2*(-215 + 793*S^2 + 1032*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (4108*S*HPL[{3, 2}, -S^2])/9 + 1480*S*HPL[{4, 1}, -S^2] + (20*(-11 + 77*S^2 + 73*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 432*S*HPL[{2, 2, 1}, -S^2] + (928*S*HPL[{3, 1, 1}, -S^2])/3 + (2720*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-1124*Pi^2*S)/27 - (S*(439 + 45*S^2))/9)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-94 + 1464*S^2 + 1087*S^4))/(27*S*(1 + S^2)) + (-45 + 27*S^2 + 2027*S^4 + 27*S^6)/(18*S^3) - (724*S*HPL[{3}, -S^2])/3 - 216*S*HPL[{2, 1}, -S^2] - (1888*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(3 + 967*S^2 + 42*S^4))/(36*S^3) + (5*Pi^2*(265 + 1477*S^2 + 384*S^4))/(54*S*(1 + S^2)) + (5*(26 + 121*S^2 + 65*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (800*S*HPL[{3}, -S^2])/3 - 100*S*HPL[{2, 1}, -S^2] - 200*S*Zeta[3]) + HPL[{0}, S^2]^2*((S*(2072 + 27*S^2))/36 + (Pi^2*S*(3611 + 2243*S^2))/(108*(1 + S^2)) + (5*(118 + 637*S^2 + 195*S^4)*HPL[{1}, -S^2]^2)/(18*S*(1 + S^2)) + 60*S*HPL[{1}, -S^2]^3 + ((-23 + 1773*S^2 + 1079*S^4)*HPL[{2}, -S^2])/(18*S*(1 + S^2)) + HPL[{1}, -S^2]*((76*Pi^2*S)/3 + (1963 + 1954*S^2 + 15*S^4)/(36*S) + (239*S*HPL[{2}, -S^2])/3) - (20*S*HPL[{3}, -S^2])/3 + (76*S*HPL[{2, 1}, -S^2])/9 - (104*S*Zeta[3])/9) + HPL[{1}, -S^2]*((1237*Pi^4*S)/90 + (Pi^2*(1072 + 1081*S^2 + 15*S^4))/(27*S) + ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(12*S^3) + ((314*Pi^2*S)/9 + (-5 + 283*S^2 + 283*S^4 - 5*S^6)/(3*S^3))*HPL[{2}, -S^2] + (392*S*HPL[{2}, -S^2]^2)/3 + (2*(-61 - 439*S^2 + 22*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (284*S*HPL[{4}, -S^2])/3 - (10*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (32*S*HPL[{3, 1}, -S^2])/3 + 200*S*HPL[{2, 1, 1}, -S^2] + (10*(-29 - 203*S^2 + 6*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{0}, S^2]*((10279*Pi^4*S)/810 + (Pi^2*S*(4585 + 4672*S^2 + 63*S^4))/(108*(1 + S^2)) + (-15 + 1931*S^2 + 104*S^4)/(12*S) + (70*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + (280*S*HPL[{1}, -S^2]^4)/3 + ((200*Pi^2*S)/3 + (-30 + 199*S^2 + 2553*S^4 + 45*S^6)/(18*S^3))*HPL[{2}, -S^2] + (1142*S*HPL[{2}, -S^2]^2)/9 + HPL[{1}, -S^2]^2*((635*Pi^2*S)/9 + (5*(155 + 158*S^2 + 3*S^4))/(6*S) + 250*S*HPL[{2}, -S^2]) + ((47 + 19*S^2 + 26*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (52*S*HPL[{4}, -S^2])/3 + (50*(-28 - 67*S^2 + 6*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (1564*S*HPL[{3, 1}, -S^2])/3 + (3160*S*HPL[{2, 1, 1}, -S^2])/3 - (2*S*(62 + 21*S^2)*Zeta[3])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((5*(1 + S^2)*(3 + 967*S^2 + 42*S^4))/(36*S^3) + (Pi^2*(425 + 2323*S^2 + 628*S^4))/(18*S*(1 + S^2)) + (5*(136 + 769*S^2 + 183*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - 12*S*HPL[{3}, -S^2] - 500*S*HPL[{2, 1}, -S^2] - (164*S*Zeta[3])/3)) - (2000*S*Zeta[5])/9) + HPL[{2}, -S^2]^2*((151 + 4537*S^2 - 15*S^4)/(48*S) + (Pi^2*(-3 + 85*S^2 + 1937*S^4))/(72*S^3) + (Pi^4*(178 + 11130*S^2 + 6003*S^4))/(1080*S*(1 + S^2)) + ((-63*Pi^2*S)/2 + (-21 - 127*S^2 - 9*S^4)/(4*S))*HPL[{3}, -S^2] + ((20 - 173*S^2 + 29*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - (86*S*HPL[{5}, -S^2])/3 + ((82*Pi^2*S)/3 + (-818 + 202*S^2 + 15*S^4)/(6*S))*HPL[{2, 1}, -S^2] + ((208 - 695*S^2 - 963*S^4)*HPL[{3, 1}, -S^2])/(6*S*(1 + S^2)) + 340*S*HPL[{3, 2}, -S^2] + (3284*S*HPL[{4, 1}, -S^2])/3 + ((-179 + 924*S^2 + 917*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (968*S*HPL[{2, 2, 1}, -S^2])/3 + 242*S*HPL[{3, 1, 1}, -S^2] + (1904*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-247*Pi^2*S)/9 + (-39 - 401*S^2 - 33*S^4)/(12*S))*Zeta[3] - (374*S*Zeta[5])/3) + HPL[{1}, -S^2]^4*(((1 + S^2)*(-104 + 14397*S^2 + 935*S^4))/(144*S^3) + (Pi^4*(15616 + 85219*S^2 + 25071*S^4))/(6480*S*(1 + S^2)) + (Pi^2*(30 + 8797*S^2 + 9014*S^4 + 279*S^6))/(432*S^3) + ((331 + 1912*S^2 + 405*S^4)*HPL[{2}, -S^2]^2)/(18*S*(1 + S^2)) + ((-205*Pi^2*S)/9 + (-17 - 204*S^2 - 223*S^4 - 28*S^6)/(18*S^3))*HPL[{3}, -S^2] + ((-37 - 364*S^2 + 99*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) - (62*S*HPL[{5}, -S^2])/3 + ((-314*Pi^2*S)/9 + (5 - 283*S^2 - 283*S^4 + 5*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(148 + 595*S^2 + 471*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + 220*S*HPL[{3, 2}, -S^2] + (2264*S*HPL[{4, 1}, -S^2])/3 + (10*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (1568*S*HPL[{2, 2, 1}, -S^2])/3 + (3104*S*HPL[{3, 1, 1}, -S^2])/3 - 200*S*HPL[{2, 1, 1, 1}, -S^2] + ((-55*Pi^2*S)/3 + (-181 - 208*S^2 - 15*S^4)/(9*S))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(2 - 105*S^2 + 4*S^4))/(2*S^3) + (Pi^2*(931 + 4762*S^2 + 1947*S^4))/(108*S*(1 + S^2)) - 110*S*HPL[{3}, -S^2] - (784*S*HPL[{2, 1}, -S^2])/3 - (328*S*Zeta[3])/3) - (268*S*Zeta[5])/3) + HPL[{4}, -S^2]*((Pi^4*(232 + 1297*S^2 + 2177*S^4))/(1080*S*(1 + S^2)) + (270 + 4966*S^2 + 3451*S^4 - 2361*S^6 - 924*S^8)/(48*S^3*(1 + S^2)) + (Pi^2*(-36 + 707*S^2 + 1823*S^4 + 1033*S^6 - 15*S^8))/(72*S^3*(1 + S^2)) - 8*S*HPL[{5}, -S^2] + ((-52*Pi^2*S)/9 + (14 + 296*S^2 - 27*S^4)/(6*S))*HPL[{2, 1}, -S^2] - (2*(4 - 29*S^2 + 24*S^4)*HPL[{3, 1}, -S^2])/(S*(1 + S^2)) - (136*S*HPL[{3, 2}, -S^2])/3 - 152*S*HPL[{4, 1}, -S^2] + (2*(-1 - 268*S^2 + 72*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (224*S*HPL[{2, 2, 1}, -S^2])/3 - 96*S*HPL[{3, 1, 1}, -S^2] - (352*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-32*Pi^2*S)/9 + (-1 - 64*S^2 - 81*S^4 - 30*S^6)/(6*S*(1 + S^2)))*Zeta[3] - (64*S*Zeta[5])/3) + HPL[{0}, S^2]^4*((Pi^4*S*(23215 + 13279*S^2))/(25920*(1 + S^2)) + (Pi^2*S*(1999 + 2115*S^2 + 68*S^4))/(576*(1 + S^2)) + (-210 + 6161*S^2 + 5744*S^4 - 723*S^6)/(1152*S*(1 + S^2)) + ((175 + 873*S^2 + 326*S^4)*HPL[{1}, -S^2]^4)/(144*S*(1 + S^2)) + (31*S*HPL[{1}, -S^2]^5)/30 + ((-6 + 655*S^2 + 429*S^4)*HPL[{2}, -S^2]^2)/(144*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((391*Pi^2*S)/216 + (2091 + 4039*S^2 + 2009*S^4 + S^6)/(432*S*(1 + S^2)) + (245*S*HPL[{2}, -S^2])/54) + ((-11*Pi^2*S)/72 + (40 + 83*S^2 + 35*S^4)/(48*S*(1 + S^2)))*HPL[{3}, -S^2] + ((7 + 50*S^2 + 35*S^4)*HPL[{4}, -S^2])/(24*S*(1 + S^2)) - (2*S*HPL[{5}, -S^2])/3 + ((61*Pi^2*S)/108 + (-1805 - 1634*S^2 + 163*S^4 - 6*S^6)/(144*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-3 - 1490*S^2 - 999*S^4)*HPL[{3, 1}, -S^2])/(72*S*(1 + S^2)) + (2*S*HPL[{4, 1}, -S^2])/3 + ((-12 + 1517*S^2 + 1039*S^4)*HPL[{2, 1, 1}, -S^2])/(36*S*(1 + S^2)) + (2*S*HPL[{2, 2, 1}, -S^2])/9 - (S*HPL[{3, 1, 1}, -S^2])/2 + (32*S*HPL[{2, 1, 1, 1}, -S^2])/9 + ((281*Pi^2*S)/108 - (S*(-805 - 771*S^2 + 84*S^4))/(144*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-6 + 1816*S^2 + 1337*S^4))/(432*S*(1 + S^2)) + (-45 + 168*S^2 + 2260*S^4 + 1979*S^6 - 36*S^8)/(288*S^3*(1 + S^2)) - (S*HPL[{2, 1}, -S^2])/9 + (5*S*Zeta[3])/6) + HPL[{1}, -S^2]^2*((Pi^2*(415 + 2013*S^2 + 816*S^4))/(288*S*(1 + S^2)) + (15 + 4240*S^2 + 8218*S^4 + 4100*S^6 + 11*S^8)/(576*S^3*(1 + S^2)) + ((456 + 2331*S^2 + 895*S^4)*HPL[{2}, -S^2])/(144*S*(1 + S^2)) + (S*HPL[{3}, -S^2])/3 - (245*S*HPL[{2, 1}, -S^2])/18 + (19*S*Zeta[3])/18) + HPL[{1}, -S^2]*((23*Pi^4*S)/30 + (Pi^2*(3033 + 5807*S^2 + 2827*S^4 - 37*S^6))/(864*S*(1 + S^2)) + (-15 + 4789*S^2 + 9587*S^4 + 4915*S^6 + 84*S^8)/(576*S^3*(1 + S^2)) + ((485*Pi^2*S)/216 + (-15 + 907*S^2 + 1881*S^4 + 961*S^6)/(144*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (29*S*HPL[{2}, -S^2]^2)/9 + ((5 + 41*S^2 + 28*S^4)*HPL[{3}, -S^2])/(24*S*(1 + S^2)) + (2*S*HPL[{4}, -S^2])/3 + ((-456 - 2331*S^2 - 895*S^4)*HPL[{2, 1}, -S^2])/(72*S*(1 + S^2)) - (122*S*HPL[{3, 1}, -S^2])/9 + (245*S*HPL[{2, 1, 1}, -S^2])/9 + ((77 + 269*S^2 + 116*S^4)*Zeta[3])/(72*S*(1 + S^2))) + (125*S*Zeta[5])/9) + HPL[{3, 1}, -S^2]*((Pi^4*(1710 - 36381*S^2 - 26675*S^4))/(1080*S*(1 + S^2)) + (573 - 2324*S^2 - 19843*S^4 + 30*S^6)/(48*S^3) + (Pi^2*(216 - 524*S^2 - 9255*S^4 - 8539*S^6 - 72*S^8))/(72*S^3*(1 + S^2)) - (4072*S*HPL[{3, 2}, -S^2])/3 - (13096*S*HPL[{4, 1}, -S^2])/3 - (4*(193 + 2238*S^2 + 869*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (4840*S*HPL[{2, 2, 1}, -S^2])/3 + (19360*S*HPL[{3, 1, 1}, -S^2])/3 + (9760*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((350*Pi^2*S)/3 + (10 + 391*S^2 + 383*S^4 + 30*S^6)/(3*S*(1 + S^2)))*Zeta[3] + (1724*S*Zeta[5])/3) + Zeta[3]*(-(S*(-2191 + 977*S^2))/48 - (Pi^2*S*(-213 + 4*S^2 + 297*S^4))/(144*(1 + S^2)) - (Pi^4*S*(-3316 - 2663*S^2 + 975*S^4))/(2160*(1 + S^2)) - (8*S*(45 + 67*S^2)*Zeta[5])/(3*(1 + S^2))) + HPL[{3}, -S^2]*((-7439*Pi^6*S)/7560 + (236 + 4371*S^2 + 8533*S^4 - 292*S^6)/(48*S^3) + (Pi^4*(660 + 852*S^2 + S^4 - 102*S^6))/(540*S*(1 + S^2)) + (Pi^2*(-12 + 621*S^2 + 1136*S^4 - 146*S^6 - 569*S^8))/(144*S^3*(1 + S^2)) + ((58*Pi^2*S)/9 + (69 + S^2 - 71*S^4 + 12*S^6)/(3*S*(1 + S^2)))*HPL[{4}, -S^2] + ((-31 - 414*S^2 - 365*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (88*S*HPL[{6}, -S^2])/3 + 726*S*HPL[{2, 1}, -S^2]^2 + ((1132*Pi^2*S)/9 + (41 + 343*S^2 + 331*S^4 + 33*S^6)/(3*S*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((13 - 41*S^2 + 22*S^4)*HPL[{3, 2}, -S^2])/(S*(1 + S^2)) + (2*(-19 - 50*S^2 + 20*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (116*S*HPL[{4, 2}, -S^2])/3 + (40*S*HPL[{5, 1}, -S^2])/3 + ((-754*Pi^2*S)/3 - (4*(11 + 160*S^2 + 18*S^4))/(3*S))*HPL[{2, 1, 1}, -S^2] + (2*(-364 - 1433*S^2 + 143*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(-1098 - 4145*S^2 + 367*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{3, 1, 2}, -S^2])/3 - 1436*S*HPL[{3, 2, 1}, -S^2] + 46140*S*HPL[{4, 1, 1}, -S^2] - (8*(-62 - 219*S^2 + 8*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (8648*S*HPL[{3, 1, 1, 1}, -S^2])/3 - 5792*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(-10 - 175*S^2 - 79*S^4))/(18*S*(1 + S^2)) + (92 - 211*S^2 - 339*S^4 - 84*S^6)/(12*S*(1 + S^2)))*Zeta[3] - (22*S*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((Pi^2*(394 + 1481*S^2 + 45*S^4))/(18*S*(1 + S^2)) + (54 + 1085*S^2 + 516*S^4 - 105*S^6)/(12*S^3) - (44*S*Zeta[3])/3) + ((-12 - 127*S^2 - 55*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((5021*Pi^6*S)/3780 + (Pi^4*(-46346 - 40672*S^2 + 6749*S^4 + 561*S^6))/(2160*S*(1 + S^2)) + (608 - 18291*S^2 - 2689*S^4 + 977*S^6)/(48*S^3) + (Pi^2*(18 - 3909*S^2 - 4025*S^4 + 61*S^6 + 135*S^8))/(36*S^3*(1 + S^2)) + (142*Pi^2*S + (2*(840 + 118*S^2 + 21*S^4))/(3*S))*HPL[{3, 1}, -S^2] + ((-680 - 2557*S^2 + 313*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (2*(-1091 - 4031*S^2 + 357*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - 40*S*HPL[{4, 2}, -S^2] - (68*S*HPL[{5, 1}, -S^2])/3 + ((2048*Pi^2*S)/9 + (4*(291 + 26*S^2 + 6*S^4))/S)*HPL[{2, 1, 1}, -S^2] + (4*(-179 + 924*S^2 + 917*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (4*(-55 + 1362*S^2 + 901*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + 156*S*HPL[{3, 1, 2}, -S^2] - (3404*S*HPL[{3, 2, 1}, -S^2])/3 - (11968*S*HPL[{4, 1, 1}, -S^2])/3 - (16*(71 + 1118*S^2 + 459*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (9760*S*HPL[{3, 1, 1, 1}, -S^2])/3 + 5184*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(138 + 631*S^2 - 46*S^4))/(9*S*(1 + S^2)) + (233 + 304*S^2 + 44*S^4 - 3*S^6)/(3*S*(1 + S^2)))*Zeta[3] + (80*S*Zeta[3]^2)/3 + (2*(81 + 502*S^2 + 16*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((17153*Pi^6*S)/7560 + ((1 + S^2)*(-133 + 20894*S^2 + 1483*S^4))/(72*S^3) + (Pi^2*(-15 + 4984*S^2 + 5200*S^4 + 209*S^6))/(108*S^3) + (Pi^4*(26491 + 53170*S^2 + 26933*S^4 + 332*S^6))/(3240*S*(1 + S^2)) + ((319*Pi^2*S)/9 + (-1 + 1003*S^2 + 1028*S^4 + 16*S^6)/(18*S^3))*HPL[{2}, -S^2]^2 + (62*S*HPL[{2}, -S^2]^3)/9 + (74*S*HPL[{3}, -S^2]^2)/3 + ((-401*Pi^2*S)/27 + (-12 + 197*S^2 + 418*S^4 + 221*S^6)/(9*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(79 + 232*S^2 + 339*S^4)*HPL[{5}, -S^2])/(9*S*(1 + S^2)) + (70*S*HPL[{6}, -S^2])/3 - (1568*S*HPL[{2, 1}, -S^2]^2)/3 + ((-152*Pi^2*S)/3 + (2*(18 - 799*S^2 - 805*S^4 + 12*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (4*(-164 - 1145*S^2 + 9*S^4)*HPL[{3, 2}, -S^2])/(9*S*(1 + S^2)) - (4*(-532 - 3799*S^2 + 129*S^4)*HPL[{4, 1}, -S^2])/(9*S*(1 + S^2)) + 78*S*HPL[{4, 2}, -S^2] + (1168*S*HPL[{5, 1}, -S^2])/3 + ((1256*Pi^2*S)/9 - (4*(5 - 283*S^2 - 283*S^4 + 5*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (8*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S*(1 + S^2)) + (8*(270 + 1473*S^2 + 427*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (496*S*HPL[{3, 2, 1}, -S^2])/3 + (352*S*HPL[{4, 1, 1}, -S^2])/3 - (40*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (128*S*HPL[{3, 1, 1, 1}, -S^2])/3 + 800*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-903 - 1076*S^2 - 141*S^4)/(18*S) + (10*Pi^2*(-5 - 36*S^2 + 2*S^4))/(9*S*(1 + S^2)))*Zeta[3] + (40*S*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((Pi^2*(-173 - 1260*S^2 + 143*S^4))/(27*S*(1 + S^2)) + (-45 - 239*S^2 - 343*S^4 - 141*S^6)/(18*S^3) + 440*S*HPL[{2, 1}, -S^2] - 32*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((Pi^2*(-931 - 4762*S^2 - 1947*S^4))/(27*S*(1 + S^2)) + (2*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 + (1312*S*Zeta[3])/3) + HPL[{2}, -S^2]*((4421*Pi^4*S)/540 - ((1 + S^2)*(104 - 4309*S^2 + 197*S^4))/(36*S^3) + (Pi^2*(-30 + 1797*S^2 + 3722*S^4 + 1857*S^6 - 14*S^8))/(54*S^3*(1 + S^2)) + (10*(-33 - 229*S^2 + 2*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (226*S*HPL[{4}, -S^2])/3 - (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (1568*S*HPL[{3, 1}, -S^2])/3 + (3136*S*HPL[{2, 1, 1}, -S^2])/3 + (2*(-151 - 1132*S^2 + 3*S^4)*Zeta[3])/(9*S*(1 + S^2))) + (2*(-36 - 267*S^2 + 37*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^3*((35159*Pi^6*S)/90720 + (-696 + 57139*S^2 + 3359*S^4)/(576*S) + (Pi^4*S*(63664 + 69029*S^2 + 5007*S^4))/(12960*(1 + S^2)) + (Pi^2*(-180 + 29709*S^2 + 29763*S^4 - 190*S^6))/(1728*S*(1 + S^2)) + ((180 + 923*S^2 + 313*S^4)*HPL[{1}, -S^2]^5)/(90*S*(1 + S^2)) + (43*S*HPL[{1}, -S^2]^6)/27 + ((995*Pi^2*S)/216 + (-2 - 69*S^2 + 1692*S^4 + 1780*S^6 + 9*S^8)/(144*S^3*(1 + S^2)))*HPL[{2}, -S^2]^2 + 5*S*HPL[{2}, -S^2]^3 + HPL[{1}, -S^2]^4*((397*Pi^2*S)/108 + (1000 + 1963*S^2 + 998*S^4 + 11*S^6)/(108*S*(1 + S^2)) + (98*S*HPL[{2}, -S^2])/9) - (23*S*HPL[{3}, -S^2]^2)/18 + ((79*Pi^2*S)/54 + (-24 - 23*S^2 + 386*S^4 + 394*S^6 - 3*S^8)/(72*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-39 - 96*S^2 - 67*S^4)*HPL[{5}, -S^2])/(36*S*(1 + S^2)) + (17*S*HPL[{6}, -S^2])/3 - (569*S*HPL[{2, 1}, -S^2]^2)/9 + HPL[{3}, -S^2]*((Pi^2*(17 + 48*S^2 + 13*S^4))/(72*S*(1 + S^2)) + (12 + 563*S^2 + 1300*S^4 + 756*S^6 - 9*S^8)/(144*S^3*(1 + S^2)) + (34*S*HPL[{2, 1}, -S^2])/9) + ((-1091*Pi^2*S)/54 + (18 - 43*S^2 - 1074*S^4 - 1012*S^6 - 3*S^8)/(18*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((31 - 4*S^2 - 87*S^4)*HPL[{3, 2}, -S^2])/(36*S*(1 + S^2)) + ((7 - 106*S^2 - 145*S^4)*HPL[{4, 1}, -S^2])/(18*S*(1 + S^2)) - (2*S*HPL[{4, 2}, -S^2])/9 - (94*S*HPL[{5, 1}, -S^2])/9 + ((1126*Pi^2*S)/27 + (-15 + 65*S^2 + 1021*S^4 + 6*S^6)/(9*S^3))*HPL[{2, 1, 1}, -S^2] + ((465 + 948*S^2 - 77*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S*(1 + S^2)) + ((477 + 986*S^2 - 59*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2*S*HPL[{3, 1, 2}, -S^2])/9 + (1082*S*HPL[{3, 2, 1}, -S^2])/9 + (3376*S*HPL[{4, 1, 1}, -S^2])/9 + (2*(-167 - 333*S^2 + 30*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (2420*S*HPL[{3, 1, 1, 1}, -S^2])/9 + (1640*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((5*Pi^2*S*(331 + 320*S^2))/(108*(1 + S^2)) - (S*(-587 - 382*S^2 + 153*S^4))/(72*(1 + S^2)))*Zeta[3] - (2*S*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((Pi^2*(-986 - 1680*S^2 + 355*S^4))/(108*S*(1 + S^2)) + (-18 - 3698*S^2 - 421*S^4 - 21*S^6)/(72*S^3) - (20*S*Zeta[3])/9) + HPL[{1}, -S^2]^3*((Pi^2*(1145 + 5655*S^2 + 2128*S^4))/(324*S*(1 + S^2)) + (15 + 4270*S^2 + 8436*S^4 + 4354*S^6 + 93*S^8)/(216*S^3*(1 + S^2)) + ((495 + 2578*S^2 + 907*S^4)*HPL[{2}, -S^2])/(54*S*(1 + S^2)) + (8*S*HPL[{3}, -S^2])/9 - (392*S*HPL[{2, 1}, -S^2])/9 - (10*S*Zeta[3])/27) + HPL[{1}, -S^2]^2*((1001*Pi^4*S)/405 + (Pi^2*(4625 + 8996*S^2 + 4591*S^4 + 72*S^6))/(432*S*(1 + S^2)) + (-15 + 5090*S^2 + 10276*S^4 + 5398*S^6 + 163*S^8)/(144*S^3*(1 + S^2)) + ((1049*Pi^2*S)/108 + (-30 + 1965*S^2 + 2032*S^4 + 13*S^6)/(72*S^3))*HPL[{2}, -S^2] + (140*S*HPL[{2}, -S^2]^2)/9 + ((11 + 60*S^2 + 37*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (23*S*HPL[{4}, -S^2])/9 + ((-495 - 2578*S^2 - 907*S^4)*HPL[{2, 1}, -S^2])/(18*S*(1 + S^2)) - (584*S*HPL[{3, 1}, -S^2])/9 + (392*S*HPL[{2, 1, 1}, -S^2])/3 + ((21 + 75*S^2 + 59*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{2}, -S^2]*((1283*Pi^4*S)/540 + (Pi^2*(-60 + 175*S^2 + 4642*S^4 + 4439*S^6 - 18*S^8))/(432*S^3*(1 + S^2)) + (-86 + 1193*S^2 + 6070*S^4 + 4892*S^6 + 53*S^8)/(144*S^3*(1 + S^2)) + ((-8 + 3*S^2 + 24*S^4)*HPL[{3}, -S^2])/(18*S*(1 + S^2)) + (8*S*HPL[{4}, -S^2])/3 + ((-465 - 948*S^2 + 77*S^4)*HPL[{2, 1}, -S^2])/(18*S*(1 + S^2)) - (574*S*HPL[{3, 1}, -S^2])/9 + (1138*S*HPL[{2, 1, 1}, -S^2])/9 + ((12 + 143*S^2 + 126*S^4)*Zeta[3])/(18*S*(1 + S^2))) + (S*(757 + 745*S^2)*Zeta[5])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(9805 + 46666*S^2 + 20845*S^4))/(6480*S*(1 + S^2)) + (Pi^2*(15 + 4900*S^2 + 9563*S^4 + 4912*S^6 + 94*S^8))/(432*S^3*(1 + S^2)) + (-52 + 6611*S^2 + 13624*S^4 + 7335*S^6 + 310*S^8)/(144*S^3*(1 + S^2)) + ((225 + 1172*S^2 + 387*S^4)*HPL[{2}, -S^2]^2)/(36*S*(1 + S^2)) + ((Pi^2*S)/2 + (-17 + 208*S^2 + 496*S^4 + 248*S^6 - 3*S^8)/(36*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((33 + 143*S^2 + 64*S^4)*HPL[{4}, -S^2])/(18*S*(1 + S^2)) + (5*S*HPL[{5}, -S^2])/9 + ((-1049*Pi^2*S)/54 + (30 - 1965*S^2 - 2032*S^4 - 13*S^6)/(36*S^3))*HPL[{2, 1}, -S^2] + ((-247 - 1292*S^2 - 461*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (26*S*HPL[{3, 2}, -S^2])/9 + (32*S*HPL[{4, 1}, -S^2])/9 + ((495 + 2578*S^2 + 907*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) + (1120*S*HPL[{2, 2, 1}, -S^2])/9 + (1136*S*HPL[{3, 1, 1}, -S^2])/3 - (784*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((55*Pi^2*S)/54 + (194 + 435*S^2 + 302*S^4 + 45*S^6)/(36*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(995 + 4959*S^2 + 1866*S^4))/(216*S*(1 + S^2)) + (-72 + 4471*S^2 + 4588*S^4 + 61*S^6)/(144*S^3) - (13*S*HPL[{3}, -S^2])/9 - (560*S*HPL[{2, 1}, -S^2])/9 + (5*S*Zeta[3])/9) + (8*S*Zeta[5])/3)) + Log[T]^3*((-35159*Pi^6*S)/11340 + (116 - 317*S^2)/(12*S) + (Pi^2*(90 - 4671*S^2 - 37*S^4))/(108*S) - (Pi^4*S*(40768 + 41009*S^2 + 319*S^4))/(3240*(1 + S^2)) - (11*S*HPL[{0}, S^2]^6)/27 - (28*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^5)/(9*S*(1 + S^2)) - (224*S*HPL[{1}, -S^2]^6)/9 + HPL[{0}, S^2]^5*(-(S*(1985 + 1439*S^2))/(540*(1 + S^2)) - (91*S*HPL[{1}, -S^2])/45) + ((-1402*Pi^2*S)/27 + (1 - 130*S^2 - 950*S^4 + 2*S^6)/(9*S^3))*HPL[{2}, -S^2]^2 - (1324*S*HPL[{2}, -S^2]^3)/27 + HPL[{1}, -S^2]^4*((-460*Pi^2*S)/9 - (5*(155 + 158*S^2 + 3*S^4))/(9*S) - (100*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^4*((-613*Pi^2*S)/162 + (S*(-2334 - 2359*S^2 + 5*S^4))/(216*(1 + S^2)) + ((-175 - 873*S^2 - 326*S^4)*HPL[{1}, -S^2])/(36*S*(1 + S^2)) - (31*S*HPL[{1}, -S^2]^2)/3 - (29*S*HPL[{2}, -S^2])/3) - (428*S*HPL[{3}, -S^2]^2)/9 + ((626*Pi^2*S)/27 + (24 - 192*S^2 - 436*S^4 - 223*S^6 + 9*S^8)/(9*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(75 + 413*S^2 + 524*S^4)*HPL[{5}, -S^2])/(9*S*(1 + S^2)) - (460*S*HPL[{6}, -S^2])/9 + (1840*S*HPL[{2, 1}, -S^2]^2)/3 + HPL[{0}, S^2]^3*(-(Pi^2*S*(3713 + 2522*S^2))/(162*(1 + S^2)) - (S*(4559 + 4662*S^2 + 63*S^4))/(108*(1 + S^2)) + ((-180 - 923*S^2 - 313*S^4)*HPL[{1}, -S^2]^2)/(9*S*(1 + S^2)) - (860*S*HPL[{1}, -S^2]^3)/27 + ((6 - 1579*S^2 - 997*S^4)*HPL[{2}, -S^2])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((-397*Pi^2*S)/27 + (-1000 - 1963*S^2 - 998*S^4 - 11*S^6)/(27*S*(1 + S^2)) - (392*S*HPL[{2}, -S^2])/9) + (8*S*HPL[{3}, -S^2])/9 - 4*S*HPL[{2, 1}, -S^2]) + ((5368*Pi^2*S)/27 + (8*(-9 - 53*S^2 + 506*S^4 + 3*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] - (4*(-19 + 990*S^2 + 19*S^4)*HPL[{3, 2}, -S^2])/(9*S*(1 + S^2)) + (8*(20 - 1657*S^2 + 21*S^4)*HPL[{4, 1}, -S^2])/(9*S*(1 + S^2)) - (1628*S*HPL[{4, 2}, -S^2])/9 - (6800*S*HPL[{5, 1}, -S^2])/9 + ((-11920*Pi^2*S)/27 - (4*(-30 - 163*S^2 + 2137*S^4 + 15*S^6))/(9*S^3))*HPL[{2, 1, 1}, -S^2] + (32*(-130 - 397*S^2 + 27*S^4)*HPL[{2, 2, 1}, -S^2])/(9*S*(1 + S^2)) + (8*(-517 - 1191*S^2 + 102*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (944*S*HPL[{3, 1, 2}, -S^2])/9 - 1072*S*HPL[{3, 2, 1}, -S^2] - (8704*S*HPL[{4, 1, 1}, -S^2])/3 - (80*(-37 - 44*S^2 + 8*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (6400*S*HPL[{3, 1, 1, 1}, -S^2])/3 - (15680*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((22*Pi^2*S*(53 + 8*S^2))/(27*(1 + S^2)) + (22*S*(19 + 9*S^2))/9)*Zeta[3] + (16*S*Zeta[3]^2)/3 + HPL[{2, 1}, -S^2]*((-2*Pi^2*(-1119 - 1834*S^2 + 227*S^4))/(27*S*(1 + S^2)) - (2*(-9 - 1827*S^2 + 209*S^4 + 99*S^6))/(9*S^3) - (320*S*Zeta[3])/9) + HPL[{3}, -S^2]*((Pi^2*(-25 + 1102*S^2 - 103*S^4))/(27*S*(1 + S^2)) + (-12 + 5*S^2 + 780*S^4 + 345*S^6)/(18*S^3) + (256*S*HPL[{2, 1}, -S^2])/3 + (424*S*Zeta[3])/9) + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(3 + 967*S^2 + 42*S^4))/(27*S^3) - (10*Pi^2*(265 + 1477*S^2 + 384*S^4))/(81*S*(1 + S^2)) - (20*(26 + 121*S^2 + 65*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (3200*S*HPL[{3}, -S^2])/9 + (400*S*HPL[{2, 1}, -S^2])/3 + (800*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((-1237*Pi^4*S)/45 - (2*Pi^2*(1072 + 1081*S^2 + 15*S^4))/(27*S) - ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(6*S^3) + ((-628*Pi^2*S)/9 + (2*(5 - 283*S^2 - 283*S^4 + 5*S^6))/(3*S^3))*HPL[{2}, -S^2] - (784*S*HPL[{2}, -S^2]^2)/3 - (4*(-61 - 439*S^2 + 22*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (568*S*HPL[{4}, -S^2])/3 + (20*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (64*S*HPL[{3, 1}, -S^2])/3 - 400*S*HPL[{2, 1, 1}, -S^2] - (20*(-29 - 203*S^2 + 6*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{2}, -S^2]*((-17677*Pi^4*S)/810 + (86 - 246*S^2 - 4314*S^4 - 37*S^6)/(18*S^3) + (Pi^2*(60 + 129*S^2 - 4226*S^4 - 4300*S^6 - 29*S^8))/(54*S^3*(1 + S^2)) + (4*(-21 + 488*S^2 + 14*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (1532*S*HPL[{4}, -S^2])/9 - (16*(-130 - 397*S^2 + 27*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (4528*S*HPL[{3, 1}, -S^2])/9 - (3680*S*HPL[{2, 1, 1}, -S^2])/3 + (4*(9 + 514*S^2 + 13*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{0}, S^2]^2*((-16369*Pi^4*S)/1620 + (45 - 4491*S^2 - 37*S^4)/(36*S) - (Pi^2*S*(4471 + 4511*S^2 + 10*S^4))/(108*(1 + S^2)) - (10*(118 + 637*S^2 + 195*S^4)*HPL[{1}, -S^2]^3)/(27*S*(1 + S^2)) - 60*S*HPL[{1}, -S^2]^4 + ((-1277*Pi^2*S)/27 + (15 - 32*S^2 - 1126*S^4 - 1074*S^6 - 7*S^8)/(9*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (712*S*HPL[{2}, -S^2]^2)/9 + HPL[{1}, -S^2]^2*((-152*Pi^2*S)/3 + (-1963 - 1954*S^2 - 15*S^4)/(18*S) - (478*S*HPL[{2}, -S^2])/3) + ((-34 - 89*S^2 - 85*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (82*S*HPL[{4}, -S^2])/9 - (2*(-564 - 1174*S^2 + 107*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (2968*S*HPL[{3, 1}, -S^2])/9 - (6040*S*HPL[{2, 1, 1}, -S^2])/9 - (2*S*(-13 + 32*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-1115 - 5804*S^2 - 1953*S^4))/(54*S*(1 + S^2)) + (-15 - 3947*S^2 - 3969*S^4 - 69*S^6)/(36*S^3) + ((-541 - 2947*S^2 - 972*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (20*S*HPL[{3}, -S^2])/3 + (956*S*HPL[{2, 1}, -S^2])/3 + 20*S*Zeta[3])) + (8*S*(238 + 37*S^2)*Zeta[5])/(9*(1 + S^2)) + HPL[{0}, S^2]*(-(Pi^4*S*(24769 + 14647*S^2))/(810*(1 + S^2)) + (210 - 14714*S^2 - 935*S^4)/(36*S) - (Pi^2*S*(9514 + 9827*S^2 + 273*S^4))/(108*(1 + S^2)) - (70*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^4)/(9*S*(1 + S^2)) - (224*S*HPL[{1}, -S^2]^5)/3 + ((-9 - 2132*S^2 - 947*S^4)*HPL[{2}, -S^2]^2)/(9*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((-2540*Pi^2*S)/27 - (10*(155 + 158*S^2 + 3*S^4))/(9*S) - (1000*S*HPL[{2}, -S^2])/3) + ((194*Pi^2*S)/27 + (-237 - 248*S^2 + 17*S^4)/(9*S))*HPL[{3}, -S^2] - (2*(5 + 60*S^2 + 34*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - 8*S*HPL[{5}, -S^2] + ((-116*Pi^2*S)/9 - (2*(-2223 + 23*S^2 + 15*S^4))/(9*S))*HPL[{2, 1}, -S^2] + (4*(-26 + 2107*S^2 + 1011*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - (628*S*HPL[{3, 2}, -S^2])/9 - (640*S*HPL[{4, 1}, -S^2])/3 - (40*(-4 + 434*S^2 + 213*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) - (544*S*HPL[{2, 2, 1}, -S^2])/9 - (272*S*HPL[{3, 1, 1}, -S^2])/9 - (640*S*HPL[{2, 1, 1, 1}, -S^2])/3 + (20*Pi^2*S + (2*S*(113 + 3*S^2))/9)*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(26 - 3749*S^2 - 2062*S^4))/(27*S*(1 + S^2)) + (30 - 319*S^2 - 1710*S^4 - 65*S^6)/(6*S^3) + (100*S*HPL[{3}, -S^2])/3 + (272*S*HPL[{2, 1}, -S^2])/9 + (976*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((Pi^2*(-425 - 2323*S^2 - 628*S^4))/(9*S*(1 + S^2)) - (5*(1 + S^2)*(3 + 967*S^2 + 42*S^4))/(18*S^3) - (10*(136 + 769*S^2 + 183*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + 24*S*HPL[{3}, -S^2] + 1000*S*HPL[{2, 1}, -S^2] + (328*S*Zeta[3])/3) + HPL[{1}, -S^2]*((-3374*Pi^4*S)/135 - ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(6*S^3) + (Pi^2*(-4325 - 8621*S^2 - 4411*S^4 - 67*S^6))/(54*S*(1 + S^2)) + ((-1142*Pi^2*S)/9 - (2*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(9*S^3))*HPL[{2}, -S^2] - (784*S*HPL[{2}, -S^2]^2)/3 - (4*(2 - S^2 + 15*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 28*S*HPL[{4}, -S^2] + (20*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (2992*S*HPL[{3, 1}, -S^2])/3 - 2000*S*HPL[{2, 1, 1}, -S^2] + (4*(44 + 299*S^2 + 9*S^4)*Zeta[3])/(9*S*(1 + S^2))) + (832*S*Zeta[5])/9) + HPL[{1}, -S^2]*((Pi^4*(-15616 - 85219*S^2 - 25071*S^4))/(1620*S*(1 + S^2)) - ((1 + S^2)*(-104 + 14397*S^2 + 935*S^4))/(36*S^3) + (Pi^2*(-30 - 8797*S^2 - 9014*S^4 - 279*S^6))/(108*S^3) - (2*(331 + 1912*S^2 + 405*S^4)*HPL[{2}, -S^2]^2)/(9*S*(1 + S^2)) + ((820*Pi^2*S)/9 + (2*(17 + 204*S^2 + 223*S^4 + 28*S^6))/(9*S^3))*HPL[{3}, -S^2] - (4*(-37 - 364*S^2 + 99*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) + (248*S*HPL[{5}, -S^2])/3 + ((1256*Pi^2*S)/9 - (4*(5 - 283*S^2 - 283*S^4 + 5*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (8*(148 + 595*S^2 + 471*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - 880*S*HPL[{3, 2}, -S^2] - (9056*S*HPL[{4, 1}, -S^2])/3 - (40*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (6272*S*HPL[{2, 2, 1}, -S^2])/3 - (12416*S*HPL[{3, 1, 1}, -S^2])/3 + 800*S*HPL[{2, 1, 1, 1}, -S^2] + ((220*Pi^2*S)/3 + (4*(181 + 208*S^2 + 15*S^4))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-931 - 4762*S^2 - 1947*S^4))/(27*S*(1 + S^2)) + (2*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 + 440*S*HPL[{3}, -S^2] + (3136*S*HPL[{2, 1}, -S^2])/3 + (1312*S*Zeta[3])/3) + (1072*S*Zeta[5])/3)) - (S*(53 + 148*S^2 + 75*S^4)*Zeta[7])/(2*(1 + S^2)) + Log[T]^2*((-683 + 3611*S^2)/(48*S) + (Pi^6*S*(355061 + 200684*S^2))/(45360*(1 + S^2)) + (Pi^2*(-280 + 6975*S^2 + 67*S^4))/(96*S) + (Pi^4*S*(78433 + 79303*S^2 + 1110*S^4))/(4320*(1 + S^2)) + (7*S*HPL[{0}, S^2]^7)/72 + (14*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^6)/(9*S*(1 + S^2)) + (32*S*HPL[{1}, -S^2]^7)/3 + HPL[{0}, S^2]^6*((S*(150 + 109*S^2))/(144*(1 + S^2)) + (41*S*HPL[{1}, -S^2])/72) + ((-179 + 924*S^2 + 917*S^4)*HPL[{2}, -S^2]^3)/(18*S*(1 + S^2)) + HPL[{0}, S^2]^5*((1301*Pi^2*S)/1080 + (S*(312 + 323*S^2 + 6*S^4))/(72*(1 + S^2)) + ((605 + 2886*S^2 + 1189*S^4)*HPL[{1}, -S^2])/(360*S*(1 + S^2)) + (91*S*HPL[{1}, -S^2]^2)/30 + (511*S*HPL[{2}, -S^2])/180) + HPL[{1}, -S^2]^5*((92*Pi^2*S)/3 + (155 + 158*S^2 + 3*S^4)/(3*S) + 20*S*HPL[{2}, -S^2]) + ((-3 + 77*S^2 - 31*S^4)*HPL[{3}, -S^2]^2)/(3*S*(1 + S^2)) + ((-247*Pi^2*S)/9 + (311 + 898*S^2 + 600*S^4 + 9*S^6)/(3*S*(1 + S^2)))*HPL[{5}, -S^2] + (5*(11 + 95*S^2 + 77*S^4)*HPL[{6}, -S^2])/(S*(1 + S^2)) + (532*S*HPL[{7}, -S^2])/3 - (4*(71 + 1118*S^2 + 459*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((2143*Pi^2*S)/9 + (2*(36 + 342*S^2 + 337*S^4 + 33*S^6))/(3*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((6962*Pi^2*S)/9 + (-70 + 1652*S^2 + 1917*S^4 + 207*S^6)/(3*S*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((5 + 412*S^2 + 56*S^4)*HPL[{4, 2}, -S^2])/(3*S*(1 + S^2)) - (176*S*HPL[{4, 3}, -S^2])/3 - (2*(61 - 559*S^2 + 256*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - 118*S*HPL[{5, 2}, -S^2] + (100*S*HPL[{6, 1}, -S^2])/3 + ((2048*Pi^2*S)/9 + (4*(291 + 26*S^2 + 6*S^4))/S)*HPL[{2, 2, 1}, -S^2] + ((488*Pi^2*S)/3 + (4*(2651 - 51*S^2 + 18*S^4))/(3*S))*HPL[{3, 1, 1}, -S^2] - (4*(-25 + 11*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (8*(-77 + 469*S^2 + 453*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (8002*S*HPL[{3, 2, 2}, -S^2])/3 - (25136*S*HPL[{3, 3, 1}, -S^2])/3 + (4*(-175 + 810*S^2 + 941*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) - (24860*S*HPL[{4, 1, 2}, -S^2])/3 - (76940*S*HPL[{4, 2, 1}, -S^2])/3 - (158048*S*HPL[{5, 1, 1}, -S^2])/3 + ((4384*Pi^2*S)/9 + (4*(-1861 + 439*S^2 + 45*S^4))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] + (7616*S*HPL[{2, 2, 2, 1}, -S^2])/3 - (8*(-215 + 793*S^2 + 1032*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (6416*S*HPL[{3, 1, 1, 2}, -S^2])/3 - (6416*S*HPL[{3, 1, 2, 1}, -S^2])/3 - (29264*S*HPL[{3, 2, 1, 1}, -S^2])/3 - 27936*S*HPL[{4, 1, 1, 1}, -S^2] + (80*(-11 + 77*S^2 + 73*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 5184*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 15552*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 37760*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 10880*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-69*Pi^4*S)/5 - (S*(205 + 234*S^2))/6 - (Pi^2*S*(390 + 445*S^2 + 57*S^4))/(18*(1 + S^2)))*Zeta[3] - (2*S*(17 + 27*S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{2, 1, 1}, -S^2]*((4*Pi^2*(-94 + 1464*S^2 + 1087*S^4))/(9*S*(1 + S^2)) + (2*(-45 + 27*S^2 + 2027*S^4 + 27*S^6))/(3*S^3) - (7552*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(133 + 3943*S^2 + 1896*S^4))/(36*S*(1 + S^2)) + (-3 + 248*S^2 + 1959*S^4 - 15*S^6)/(12*S^3) - 363*S*HPL[{3}, -S^2] + (952*S*HPL[{2, 1}, -S^2])/3 - (920*S*Zeta[3])/3) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(3 + 967*S^2 + 42*S^4))/(36*S^3) + (5*Pi^2*(265 + 1477*S^2 + 384*S^4))/(54*S*(1 + S^2)) + (5*(26 + 121*S^2 + 65*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) - (800*S*HPL[{3}, -S^2])/3 - 100*S*HPL[{2, 1}, -S^2] - 200*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(21 - 146*S^2 + 234*S^4))/(18*S*(1 + S^2)) + (-36 + 856*S^2 + 653*S^4 - 66*S^6)/(12*S^3) - (176*S*HPL[{2, 1}, -S^2])/3 - (128*S*Zeta[3])/3) + HPL[{0}, S^2]^4*((23*Pi^2*S*(172 + 121*S^2))/(432*(1 + S^2)) - (S*(-1503 - 1505*S^2 + 14*S^4))/(96*(1 + S^2)) + ((175 + 873*S^2 + 326*S^4)*HPL[{1}, -S^2]^2)/(24*S*(1 + S^2)) + (31*S*HPL[{1}, -S^2]^3)/3 + ((-12 + 1517*S^2 + 1039*S^4)*HPL[{2}, -S^2])/(72*S*(1 + S^2)) + HPL[{1}, -S^2]*((391*Pi^2*S)/72 + (2091 + 4039*S^2 + 2009*S^4 + S^6)/(144*S*(1 + S^2)) + (245*S*HPL[{2}, -S^2])/18) - (7*S*HPL[{3}, -S^2])/12 + (16*S*HPL[{2, 1}, -S^2])/9 + (26*S*Zeta[3])/9) + HPL[{3, 1}, -S^2]*((Pi^2*(238 - 2525*S^2 - 2079*S^4))/(9*S*(1 + S^2)) + (108 - 23*S^2 - 4012*S^4 - 33*S^6)/(6*S^3) + (3832*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((1237*Pi^4*S)/45 + (2*Pi^2*(1072 + 1081*S^2 + 15*S^4))/(27*S) + ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(6*S^3) + ((628*Pi^2*S)/9 - (2*(5 - 283*S^2 - 283*S^4 + 5*S^6))/(3*S^3))*HPL[{2}, -S^2] + (784*S*HPL[{2}, -S^2]^2)/3 + (4*(-61 - 439*S^2 + 22*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (568*S*HPL[{4}, -S^2])/3 - (20*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (64*S*HPL[{3, 1}, -S^2])/3 + 400*S*HPL[{2, 1, 1}, -S^2] + (20*(-29 - 203*S^2 + 6*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((2207*Pi^4*S)/135 + (Pi^2*(-3723 - 3218*S^2 + 586*S^4 + 57*S^6))/(18*S*(1 + S^2)) + (18 - 3959*S^2 + 202*S^4 + 234*S^6)/(6*S^3) + (4880*S*HPL[{3, 1}, -S^2])/3 + 2592*S*HPL[{2, 1, 1}, -S^2] - (8*(-71 - 309*S^2 + 8*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((-1733*Pi^4*S)/108 + (-12 + 409*S^2 - 1006*S^4 - 957*S^6)/(24*S^3) + (Pi^2*(126 - 15*S^2 - 197*S^4 - 42*S^6))/(18*S*(1 + S^2)) + 64*S*HPL[{4}, -S^2] - (4*(-62 - 219*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) + (4324*S*HPL[{3, 1}, -S^2])/3 - 2896*S*HPL[{2, 1, 1}, -S^2] - (2*(-1 + 41*S^2 + 18*S^4)*Zeta[3])/(S*(1 + S^2))) + HPL[{0}, S^2]^3*((16369*Pi^4*S)/3240 + (Pi^2*S*(5335 + 5487*S^2 + 78*S^4))/(216*(1 + S^2)) + (-90 + 10860*S^2 + 11149*S^4 + 135*S^6)/(144*S*(1 + S^2)) + ((180 + 923*S^2 + 313*S^4)*HPL[{1}, -S^2]^3)/(9*S*(1 + S^2)) + (215*S*HPL[{1}, -S^2]^4)/9 + ((563*Pi^2*S)/27 + (-15 + 65*S^2 + 1021*S^4 + 6*S^6)/(18*S^3))*HPL[{2}, -S^2] + (569*S*HPL[{2}, -S^2]^2)/18 + HPL[{1}, -S^2]^2*((397*Pi^2*S)/18 + (1000 + 1963*S^2 + 998*S^4 + 11*S^6)/(18*S*(1 + S^2)) + (196*S*HPL[{2}, -S^2])/3) + ((6 + 19*S^2 + 9*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (68*S*HPL[{4}, -S^2])/9 + ((-167 - 333*S^2 + 30*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (1210*S*HPL[{3, 1}, -S^2])/9 + (820*S*HPL[{2, 1, 1}, -S^2])/3 + (5*S*(31 + 32*S^2)*Zeta[3])/(9*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(1145 + 5655*S^2 + 2128*S^4))/(108*S*(1 + S^2)) + (15 + 4270*S^2 + 8436*S^4 + 4354*S^6 + 93*S^8)/(72*S^3*(1 + S^2)) + ((495 + 2578*S^2 + 907*S^4)*HPL[{2}, -S^2])/(18*S*(1 + S^2)) + (8*S*HPL[{3}, -S^2])/3 - (392*S*HPL[{2, 1}, -S^2])/3 - (10*S*Zeta[3])/9)) + HPL[{0}, S^2]^2*((Pi^4*S*(48981 + 32486*S^2))/(2160*(1 + S^2)) + (Pi^2*S*(8653 + 8713*S^2 + 12*S^4))/(144*(1 + S^2)) + (-140 + 6583*S^2 + 67*S^4)/(32*S) + (5*(118 + 637*S^2 + 195*S^4)*HPL[{1}, -S^2]^4)/(18*S*(1 + S^2)) + 36*S*HPL[{1}, -S^2]^5 + ((-3 + 569*S^2 + 326*S^4)*HPL[{2}, -S^2]^2)/(4*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((152*Pi^2*S)/3 + (1963 + 1954*S^2 + 15*S^4)/(18*S) + (478*S*HPL[{2}, -S^2])/3) + ((-9*Pi^2*S)/2 + (47 + 119*S^2 + 62*S^4 - 3*S^6)/(3*S*(1 + S^2)))*HPL[{3}, -S^2] + ((9 + 196*S^2 + 162*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - 7*S*HPL[{5}, -S^2] + ((70*Pi^2*S)/9 + (-931 - 898*S^2 + 51*S^4 + 6*S^6)/(3*S*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((23 - 1732*S^2 - 1047*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (89*S*HPL[{3, 2}, -S^2])/3 + (302*S*HPL[{4, 1}, -S^2])/3 + (2*(-23 + 1773*S^2 + 1079*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (104*S*HPL[{2, 2, 1}, -S^2])/3 + 24*S*HPL[{3, 1, 1}, -S^2] + (304*S*HPL[{2, 1, 1, 1}, -S^2])/3 - (S*(-49 - 39*S^2 + 12*S^4)*Zeta[3])/(6*(1 + S^2)) + HPL[{2}, -S^2]*((Pi^2*(-35 + 3290*S^2 + 2118*S^4))/(36*S*(1 + S^2)) + (-45 + 215*S^2 + 2358*S^4 + 2098*S^6 + 24*S^8)/(12*S^3*(1 + S^2)) - 15*S*HPL[{3}, -S^2] - (52*S*HPL[{2, 1}, -S^2])/3 - (92*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((Pi^2*(1115 + 5804*S^2 + 1953*S^4))/(36*S*(1 + S^2)) + (15 + 3947*S^2 + 3969*S^4 + 69*S^6)/(24*S^3) + ((541 + 2947*S^2 + 972*S^4)*HPL[{2}, -S^2])/(6*S*(1 + S^2)) - 10*S*HPL[{3}, -S^2] - 478*S*HPL[{2, 1}, -S^2] - 30*S*Zeta[3]) + HPL[{1}, -S^2]*((3299*Pi^4*S)/216 + (Pi^2*(2027 + 3978*S^2 + 1989*S^4 + 8*S^6))/(36*S*(1 + S^2)) + (-15 + 4322*S^2 + 4427*S^4 + 106*S^6)/(24*S^3) + ((1207*Pi^2*S)/18 + (-15 + 963*S^2 + 2024*S^4 + 1023*S^6 + S^8)/(6*S^3*(1 + S^2)))*HPL[{2}, -S^2] + 123*S*HPL[{2}, -S^2]^2 + ((10 + 57*S^2 + 77*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (25*S*HPL[{4}, -S^2])/3 + ((-541 - 2947*S^2 - 972*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 472*S*HPL[{3, 1}, -S^2] + 956*S*HPL[{2, 1, 1}, -S^2] + (5*(-1 - 13*S^2 + 6*S^4)*Zeta[3])/(3*S*(1 + S^2)))) + ((-1000*Pi^2*S)/9 - (S*(360 + 449*S^2 + 87*S^4))/(3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-1409 + 40150*S^2 + 28296*S^4))/(1080*S*(1 + S^2)) + (-249 + 3031*S^2 + 18657*S^4 + 201*S^6)/(48*S^3) + (Pi^2*(-90 + 197*S^2 + 4412*S^4 + 4152*S^6 + 51*S^8))/(36*S^3*(1 + S^2)) + ((-377*Pi^2*S)/3 - (2*(11 + 160*S^2 + 18*S^4))/(3*S))*HPL[{3}, -S^2] + ((-1 - 268*S^2 + 72*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - 130*S*HPL[{5}, -S^2] + ((-1024*Pi^2*S)/9 - (2*(291 + 26*S^2 + 6*S^4))/S)*HPL[{2, 1}, -S^2] - (2*(193 + 2238*S^2 + 869*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 1374*S*HPL[{3, 2}, -S^2] + (13244*S*HPL[{4, 1}, -S^2])/3 + (8*(71 + 1118*S^2 + 459*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (3808*S*HPL[{2, 2, 1}, -S^2])/3 + 912*S*HPL[{3, 1, 1}, -S^2] - 2592*S*HPL[{2, 1, 1, 1}, -S^2] + ((-1036*Pi^2*S)/9 + (-1 - 374*S^2 - 382*S^4 - 33*S^6)/(3*S*(1 + S^2)))*Zeta[3] - 556*S*Zeta[5]) + HPL[{1}, -S^2]^2*(((1 + S^2)*(-104 + 14397*S^2 + 935*S^4))/(24*S^3) + (Pi^4*(15616 + 85219*S^2 + 25071*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(30 + 8797*S^2 + 9014*S^4 + 279*S^6))/(72*S^3) + ((331 + 1912*S^2 + 405*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + ((-410*Pi^2*S)/3 + (-17 - 204*S^2 - 223*S^4 - 28*S^6)/(3*S^3))*HPL[{3}, -S^2] + (2*(-37 - 364*S^2 + 99*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - 124*S*HPL[{5}, -S^2] + ((-628*Pi^2*S)/3 + (2*(5 - 283*S^2 - 283*S^4 + 5*S^6))/S^3)*HPL[{2, 1}, -S^2] - (4*(148 + 595*S^2 + 471*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 1320*S*HPL[{3, 2}, -S^2] + 4528*S*HPL[{4, 1}, -S^2] + (20*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) + 3136*S*HPL[{2, 2, 1}, -S^2] + 6208*S*HPL[{3, 1, 1}, -S^2] - 1200*S*HPL[{2, 1, 1, 1}, -S^2] + (-110*Pi^2*S - (2*(181 + 208*S^2 + 15*S^4))/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((-3*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 + (Pi^2*(931 + 4762*S^2 + 1947*S^4))/(18*S*(1 + S^2)) - 660*S*HPL[{3}, -S^2] - 1568*S*HPL[{2, 1}, -S^2] - 656*S*Zeta[3]) - 536*S*Zeta[5]) + HPL[{1}, -S^2]*((17153*Pi^6*S)/2520 + ((1 + S^2)*(-133 + 20894*S^2 + 1483*S^4))/(24*S^3) + (Pi^2*(-15 + 4984*S^2 + 5200*S^4 + 209*S^6))/(36*S^3) + (Pi^4*(26491 + 53170*S^2 + 26933*S^4 + 332*S^6))/(1080*S*(1 + S^2)) + ((319*Pi^2*S)/3 + (-1 + 1003*S^2 + 1028*S^4 + 16*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 + (62*S*HPL[{2}, -S^2]^3)/3 + 74*S*HPL[{3}, -S^2]^2 + ((-401*Pi^2*S)/9 + (-12 + 197*S^2 + 418*S^4 + 221*S^6)/(3*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(79 + 232*S^2 + 339*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + 70*S*HPL[{6}, -S^2] - 1568*S*HPL[{2, 1}, -S^2]^2 + (-152*Pi^2*S + (2*(18 - 799*S^2 - 805*S^4 + 12*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] - (4*(-164 - 1145*S^2 + 9*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (4*(-532 - 3799*S^2 + 129*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 234*S*HPL[{4, 2}, -S^2] + 1168*S*HPL[{5, 1}, -S^2] + ((1256*Pi^2*S)/3 - (4*(5 - 283*S^2 - 283*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] + (8*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(270 + 1473*S^2 + 427*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + 496*S*HPL[{3, 2, 1}, -S^2] + 352*S*HPL[{4, 1, 1}, -S^2] - (40*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 128*S*HPL[{3, 1, 1, 1}, -S^2] + 2400*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-903 - 1076*S^2 - 141*S^4)/(6*S) + (10*Pi^2*(-5 - 36*S^2 + 2*S^4))/(3*S*(1 + S^2)))*Zeta[3] + 40*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-173 - 1260*S^2 + 143*S^4))/(9*S*(1 + S^2)) + (-45 - 239*S^2 - 343*S^4 - 141*S^6)/(6*S^3) + 1320*S*HPL[{2, 1}, -S^2] - 96*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((Pi^2*(-931 - 4762*S^2 - 1947*S^4))/(9*S*(1 + S^2)) + (6*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 + 1312*S*Zeta[3]) + HPL[{2}, -S^2]*((4421*Pi^4*S)/180 - ((1 + S^2)*(104 - 4309*S^2 + 197*S^4))/(12*S^3) + (Pi^2*(-30 + 1797*S^2 + 3722*S^4 + 1857*S^6 - 14*S^8))/(18*S^3*(1 + S^2)) + (10*(-33 - 229*S^2 + 2*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 226*S*HPL[{4}, -S^2] - (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 1568*S*HPL[{3, 1}, -S^2] + 3136*S*HPL[{2, 1, 1}, -S^2] + (2*(-151 - 1132*S^2 + 3*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (2*(-36 - 267*S^2 + 37*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{0}, S^2]*((147719*Pi^6*S)/22680 + (Pi^4*S*(64832 + 66565*S^2 + 1191*S^4))/(2160*(1 + S^2)) + (-348 + 21324*S^2 + 1483*S^4)/(24*S) + (Pi^2*(-180 + 22356*S^2 + 23359*S^4 + 759*S^6))/(144*S*(1 + S^2)) + (14*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^5)/(3*S*(1 + S^2)) + (112*S*HPL[{1}, -S^2]^6)/3 + ((1711*Pi^2*S)/18 + (-1 + 2*S^2 + 1126*S^4 + 15*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 + (1100*S*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((635*Pi^2*S)/9 + (5*(155 + 158*S^2 + 3*S^4))/(6*S) + 250*S*HPL[{2}, -S^2]) - (38*S*HPL[{3}, -S^2]^2)/3 + ((146*Pi^2*S)/9 + (-24 + 140*S^2 + 590*S^4 + 441*S^6 + 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((31 + 180*S^2 + 91*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (232*S*HPL[{6}, -S^2])/3 - (4568*S*HPL[{2, 1}, -S^2]^2)/3 + ((-3556*Pi^2*S)/9 + (36 - 217*S^2 - 2490*S^4 - 33*S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + ((4 + 241*S^2 + 9*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (2*(49 - 182*S^2 + 48*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - (16*S*HPL[{4, 2}, -S^2])/3 - 136*S*HPL[{5, 1}, -S^2] + (800*Pi^2*S + (2*(-30 + 199*S^2 + 2553*S^4 + 45*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(-653 - 1692*S^2 + 137*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(-2006 - 5095*S^2 + 385*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (28*S*HPL[{3, 1, 2}, -S^2])/3 + (8828*S*HPL[{3, 2, 1}, -S^2])/3 + 9008*S*HPL[{4, 1, 1}, -S^2] + (200*(-28 - 67*S^2 + 6*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 6256*S*HPL[{3, 1, 1, 1}, -S^2] + 12640*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*S*(-31 + 97*S^2))/(9*(1 + S^2)) - (S*(28 + 57*S^2 + 21*S^4))/(6*(1 + S^2)))*Zeta[3] + 20*S*Zeta[3]^2 + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(3 + 967*S^2 + 42*S^4))/(18*S^3) + (Pi^2*(425 + 2323*S^2 + 628*S^4))/(9*S*(1 + S^2)) + (10*(136 + 769*S^2 + 183*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - 24*S*HPL[{3}, -S^2] - 1000*S*HPL[{2, 1}, -S^2] - (328*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(83 + 133*S^2 + 80*S^4))/(18*S*(1 + S^2)) + (12 + 573*S^2 + 1437*S^4 + 817*S^6 - 75*S^8)/(12*S^3*(1 + S^2)) + 52*S*HPL[{2, 1}, -S^2] - 4*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((Pi^2*(-1201 - 2674*S^2 + 240*S^4))/(9*S*(1 + S^2)) + (-18 - 4557*S^2 - 658*S^4 + 57*S^6)/(6*S^3) + (8*S*Zeta[3])/3) + HPL[{1}, -S^2]^2*((1687*Pi^4*S)/45 + ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(4*S^3) + (Pi^2*(4325 + 8621*S^2 + 4411*S^4 + 67*S^6))/(36*S*(1 + S^2)) + ((571*Pi^2*S)/3 + (-15 + 1211*S^2 + 1265*S^4 + 15*S^6)/(3*S^3))*HPL[{2}, -S^2] + 392*S*HPL[{2}, -S^2]^2 + (2*(2 - S^2 + 15*S^4)*HPL[{3}, -S^2])/(S*(1 + S^2)) + 42*S*HPL[{4}, -S^2] - (10*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 1496*S*HPL[{3, 1}, -S^2] + 3000*S*HPL[{2, 1, 1}, -S^2] - (2*(44 + 299*S^2 + 9*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]*((9577*Pi^4*S)/270 + (Pi^2*(-60 + 329*S^2 + 4595*S^4 + 57*S^6))/(36*S^3) + (-86 + 1570*S^2 + 5860*S^4 + 243*S^6)/(12*S^3) + ((-2 - 107*S^2 + 9*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (88*S*HPL[{4}, -S^2])/3 + (2*(-653 - 1692*S^2 + 137*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (4556*S*HPL[{3, 1}, -S^2])/3 + (9136*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(-4 + 140*S^2 + 21*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (2*S*(-13 + 79*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(-104 + 14397*S^2 + 935*S^4))/(24*S^3) + (Pi^4*(3919 + 20531*S^2 + 6490*S^4))/(270*S*(1 + S^2)) + (Pi^2*(30 + 9135*S^2 + 18331*S^4 + 9609*S^6 + 303*S^8))/(72*S^3*(1 + S^2)) + ((331 + 1912*S^2 + 405*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + ((-10*Pi^2*S)/3 + (-17 + 225*S^2 + 243*S^4 - 7*S^6)/(3*S^3))*HPL[{3}, -S^2] + ((70 + 319*S^2 + 123*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (116*S*HPL[{5}, -S^2])/3 + ((-1142*Pi^2*S)/3 - (2*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (4*(337 + 1909*S^2 + 450*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 152*S*HPL[{3, 2}, -S^2] + 372*S*HPL[{4, 1}, -S^2] + (20*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 3136*S*HPL[{2, 2, 1}, -S^2] + 9264*S*HPL[{3, 1, 1}, -S^2] - 6000*S*HPL[{2, 1, 1, 1}, -S^2] + ((-256*Pi^2*S)/9 + (-67 - 50*S^2 + 9*S^4)/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1175 + 6423*S^2 + 1822*S^4))/(18*S*(1 + S^2)) + (-36 + 2757*S^2 + 2894*S^4 + 69*S^6)/(6*S^3) - 76*S*HPL[{3}, -S^2] - 1568*S*HPL[{2, 1}, -S^2] - 164*S*Zeta[3]) - (368*S*Zeta[5])/3)) - 744*S*Zeta[7]) + HPL[{1}, -S^2]^2*(((1 + S^2)*(127 + 45531*S^2 + 3442*S^4))/(64*S^3) + (Pi^6*(59726 + 320234*S^2 + 106131*S^4))/(45360*S*(1 + S^2)) + (Pi^2*(-208 + 24081*S^2 + 25542*S^4 + 1285*S^6))/(288*S^3) + (Pi^4*(416 + 107611*S^2 + 217071*S^4 + 112489*S^6 + 3093*S^8))/(8640*S^3*(1 + S^2)) + ((166 + 767*S^2 + 415*S^4)*HPL[{2}, -S^2]^3)/(18*S*(1 + S^2)) + ((46 + 287*S^2 + 19*S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((-82*Pi^2*S)/9 + (-27 + 787*S^2 + 1667*S^4 + 873*S^6 + 12*S^8)/(6*S^3*(1 + S^2)))*HPL[{5}, -S^2] + (5*(53 + 232*S^2 + 158*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) + 164*S*HPL[{7}, -S^2] - (2*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((1042*Pi^2*S)/9 + (8 + 329*S^2 + 671*S^4 + 371*S^6 + 25*S^8)/(3*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((3527*Pi^2*S)/9 + (39 + 790*S^2 + 1577*S^4 + 892*S^6 + 78*S^8)/(3*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((136 + 927*S^2 + 89*S^4)*HPL[{4, 2}, -S^2])/(6*S*(1 + S^2)) - 36*S*HPL[{4, 3}, -S^2] - (2*(-55 - 673*S^2 + 258*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - 76*S*HPL[{5, 2}, -S^2] - 90*S*HPL[{6, 1}, -S^2] + ((1276*Pi^2*S)/3 + (2*(-1 + 1003*S^2 + 1028*S^4 + 16*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + ((3008*Pi^2*S)/3 + (2*(-20 + 2805*S^2 + 2861*S^4 + 20*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] - (4*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (4*(167 + 767*S^2 + 414*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - 1382*S*HPL[{3, 2, 2}, -S^2] - 4240*S*HPL[{3, 3, 1}, -S^2] + (4*(461 + 1937*S^2 + 1344*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 4162*S*HPL[{4, 1, 2}, -S^2] - 12970*S*HPL[{4, 2, 1}, -S^2] - 26672*S*HPL[{5, 1, 1}, -S^2] + ((-1256*Pi^2*S)/3 + (4*(5 - 283*S^2 - 283*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] - 496*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(148 + 595*S^2 + 471*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 4128*S*HPL[{3, 1, 1, 2}, -S^2] + 4128*S*HPL[{3, 1, 2, 1}, -S^2] + 5616*S*HPL[{3, 2, 1, 1}, -S^2] + 17984*S*HPL[{4, 1, 1, 1}, -S^2] + (40*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 6272*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 18816*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 37760*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 2400*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-109*Pi^4*S)/18 + (-662 - 773*S^2 - 103*S^4)/(6*S) + (Pi^2*(-313 - 699*S^2 - 415*S^4 - 33*S^6))/(36*S*(1 + S^2)))*Zeta[3] + ((26 + 91*S^2 + 5*S^4)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((-6*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 + (Pi^2*(931 + 4762*S^2 + 1947*S^4))/(9*S*(1 + S^2)) - 1312*S*Zeta[3]) + HPL[{2}, -S^2]^2*(((1 + S^2)*(1 + 679*S^2 + 24*S^4))/(8*S^3) + (Pi^2*(591 + 3326*S^2 + 821*S^4))/(36*S*(1 + S^2)) - 202*S*HPL[{3}, -S^2] - 62*S*HPL[{2, 1}, -S^2] - 146*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(-20 - 453*S^2 + 369*S^4))/(36*S*(1 + S^2)) + (-10 + 1329*S^2 + 1366*S^4 - 37*S^6)/(24*S^3) + 226*S*HPL[{2, 1}, -S^2] - (62*S*Zeta[3])/3) + HPL[{3, 1}, -S^2]*((-2*Pi^2*(209 + 1033*S^2 + 482*S^4))/(9*S*(1 + S^2)) + (42 - 1801*S^2 - 1766*S^4 + 69*S^6)/(6*S^3) + 680*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((-4421*Pi^4*S)/180 + ((1 + S^2)*(104 - 4309*S^2 + 197*S^4))/(12*S^3) + (Pi^2*(30 - 1797*S^2 - 3722*S^4 - 1857*S^6 + 14*S^8))/(18*S^3*(1 + S^2)) + 1568*S*HPL[{3, 1}, -S^2] + 3136*S*HPL[{2, 1, 1}, -S^2] - (2*(-151 - 1132*S^2 + 3*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((-419*Pi^4*S)/54 + (-105 + 30*S^2 - 227*S^4 - 394*S^6)/(24*S^3) + (Pi^2*(-17 - 31*S^2 + 2*S^4 - 14*S^6 - 16*S^8))/(18*S^3*(1 + S^2)) + 34*S*HPL[{4}, -S^2] - (10*(-33 - 229*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 660*S*HPL[{3, 1}, -S^2] - 1320*S*HPL[{2, 1, 1}, -S^2] - (2*(7 + 91*S^2 + 12*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-401*Pi^2*S)/9 + (-114 - 269*S^2 - 184*S^4 - 27*S^6)/(3*S*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*(-((1 + S^2)*(81 - 3449*S^2 + 152*S^4))/(16*S^3) + (Pi^4*(2016 + 10550*S^2 + 4113*S^4))/(360*S*(1 + S^2)) + (Pi^2*(-48 + 2579*S^2 + 5319*S^4 + 2613*S^6 - 47*S^8))/(48*S^3*(1 + S^2)) + ((-521*Pi^2*S)/9 + (-9 - 320*S^2 - 345*S^4 - 26*S^6)/(6*S^3))*HPL[{3}, -S^2] + ((-136 - 883*S^2 - 69*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - 66*S*HPL[{5}, -S^2] + ((-638*Pi^2*S)/3 + (1 - 1003*S^2 - 1028*S^4 - 16*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(331 + 1912*S^2 + 405*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 730*S*HPL[{3, 2}, -S^2] + 2198*S*HPL[{4, 1}, -S^2] + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 248*S*HPL[{2, 2, 1}, -S^2] - 2064*S*HPL[{3, 1, 1}, -S^2] - 3136*S*HPL[{2, 1, 1, 1}, -S^2] + ((-539*Pi^2*S)/9 + (-129 - 326*S^2 - 189*S^4 - 16*S^6)/(3*S*(1 + S^2)))*Zeta[3] - 270*S*Zeta[5]) - 252*S*Zeta[7]) + HPL[{2}, -S^2]*((Pi^6*(-895 + 56850*S^2 + 41218*S^4))/(15120*S*(1 + S^2)) + (1054 + 12819*S^2 + 2253*S^4 - 788*S^6)/(48*S^3) + (Pi^2*(-249 + 3160*S^2 + 22544*S^4 + 19144*S^6 + 201*S^8))/(288*S^3*(1 + S^2)) + (Pi^4*(-1272 + 4812*S^2 + 59786*S^4 + 53547*S^6 + 597*S^8))/(4320*S^3*(1 + S^2)) + ((-22 + 53*S^2 - 39*S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((-101*Pi^2*S)/9 + (-277 + 186*S^2 + 479*S^4 - 24*S^6)/(6*S*(1 + S^2)))*HPL[{5}, -S^2] + (4*(-7 + 188*S^2 + 192*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) + (416*S*HPL[{7}, -S^2])/3 + ((179 - 924*S^2 - 917*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((359*Pi^2*S)/3 + (43 + 357*S^2 + 27*S^4)/(3*S))*HPL[{3, 2}, -S^2] + ((3454*Pi^2*S)/9 + (364 + 1990*S^2 + 189*S^4)/(6*S))*HPL[{4, 1}, -S^2] + (S*(93 + 17*S^2)*HPL[{4, 2}, -S^2])/(1 + S^2) - (32*S*HPL[{4, 3}, -S^2])/3 - (2*(-4 - 103*S^2 + 50*S^4)*HPL[{5, 1}, -S^2])/(S*(1 + S^2)) - (4*S*HPL[{5, 2}, -S^2])/3 + 92*S*HPL[{6, 1}, -S^2] + ((-328*Pi^2*S)/3 - (2*(-818 + 202*S^2 + 15*S^4))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((230*Pi^2*S)/3 + (2*(-2476 + 286*S^2 + 9*S^4))/(3*S))*HPL[{3, 1, 1}, -S^2] + ((-16 - 103*S^2 - 9*S^4)*HPL[{3, 1, 2}, -S^2])/(S*(1 + S^2)) + ((264 + 3947*S^2 + 1613*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (3968*S*HPL[{3, 2, 2}, -S^2])/3 - 4160*S*HPL[{3, 3, 1}, -S^2] + (2*(467 + 6116*S^2 + 2532*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (12344*S*HPL[{4, 1, 2}, -S^2])/3 - (38216*S*HPL[{4, 2, 1}, -S^2])/3 - 26132*S*HPL[{5, 1, 1}, -S^2] + ((-2048*Pi^2*S)/9 - (4*(291 + 26*S^2 + 6*S^4))/S)*HPL[{2, 1, 1, 1}, -S^2] - (3872*S*HPL[{2, 2, 2, 1}, -S^2])/3 - (4*(-1955 + 13326*S^2 + 11873*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 1124*S*HPL[{3, 1, 1, 2}, -S^2] - 1124*S*HPL[{3, 1, 2, 1}, -S^2] - 4996*S*HPL[{3, 2, 1, 1}, -S^2] - (43208*S*HPL[{4, 1, 1, 1}, -S^2])/3 + (16*(71 + 1118*S^2 + 459*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (7616*S*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 7616*S*HPL[{2, 2, 1, 1, 1}, -S^2] - (55456*S*HPL[{3, 1, 1, 1, 1}, -S^2])/3 - 5184*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-1721*Pi^4*S)/270 + (32 - 268*S^2 - 375*S^4 - 99*S^6)/(6*S*(1 + S^2)) + (Pi^2*(-24 - 288*S^2 - 275*S^4 - 33*S^6))/(36*S*(1 + S^2)))*Zeta[3] + ((3 + 36*S^2 + 32*S^4)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(133 + 3943*S^2 + 1896*S^4))/(9*S*(1 + S^2)) + (-3 + 248*S^2 + 1959*S^4 - 15*S^6)/(3*S^3) - (3680*S*Zeta[3])/3) + HPL[{4}, -S^2]*((Pi^2*(5 - 17*S^2 + 135*S^4))/(18*S*(1 + S^2)) + (3 - 227*S^2 + 272*S^4 - 60*S^6)/(12*S^3) + (112*S*HPL[{2, 1}, -S^2])/3 - (64*S*Zeta[3])/3) + HPL[{3, 1}, -S^2]*((Pi^2*(-192 - 3981*S^2 - 1879*S^4))/(18*S*(1 + S^2)) + (6 - 625*S^2 - 3896*S^4 + 69*S^6)/(12*S^3) + 628*S*Zeta[3]) + HPL[{3}, -S^2]*((-202*Pi^4*S)/27 + (Pi^2*(-18 - 116*S^2 - 123*S^4 - 21*S^6))/(18*S*(1 + S^2)) + (2 - 393*S^2 - 1609*S^4 - 1611*S^6 - 493*S^8)/(24*S^3*(1 + S^2)) + (68*S*HPL[{4}, -S^2])/3 + ((364 + 1433*S^2 - 143*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 720*S*HPL[{3, 1}, -S^2] - 1452*S*HPL[{2, 1, 1}, -S^2] + ((-8 - 163*S^2 - 101*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-1853*Pi^4*S)/270 + (Pi^2*(-3453 + 89*S^2 - 39*S^4))/(36*S) + (12 - 3852*S^2 - 361*S^4 - 246*S^6)/(12*S^3) - (2420*S*HPL[{3, 1}, -S^2])/3 - (3808*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(-151 - 529*S^2 + 60*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-412*Pi^2*S)/9 + (98 + 8*S^2 - 107*S^4 - 51*S^6)/(6*S*(1 + S^2)))*Zeta[5] - 232*S*Zeta[7]) + HPL[{0}, S^2]^2*((Pi^6*S*(357907 + 212468*S^2))/(181440*(1 + S^2)) + (-683 + 7529*S^2 - 1576*S^4)/(192*S) + (Pi^4*S*(44195 + 45959*S^2 + 1172*S^4))/(5760*(1 + S^2)) + (Pi^2*(-840 + 31651*S^2 + 31438*S^4 - 1245*S^6))/(1152*S*(1 + S^2)) + ((118 + 637*S^2 + 195*S^4)*HPL[{1}, -S^2]^6)/(54*S*(1 + S^2)) + (12*S*HPL[{1}, -S^2]^7)/7 + ((-23 + 1576*S^2 + 917*S^4)*HPL[{2}, -S^2]^3)/(72*S*(1 + S^2)) + HPL[{1}, -S^2]^5*((76*Pi^2*S)/15 + (1963 + 1954*S^2 + 15*S^4)/(180*S) + (239*S*HPL[{2}, -S^2])/15) + ((-10 - 103*S^2 - 82*S^4)*HPL[{3}, -S^2]^2)/(12*S*(1 + S^2)) + ((-23*Pi^2*S)/12 + (256 + 638*S^2 + 403*S^4 + 39*S^6)/(12*S*(1 + S^2)))*HPL[{5}, -S^2] + ((55 + 263*S^2 + 169*S^4)*HPL[{6}, -S^2])/(4*S*(1 + S^2)) - (5*S*HPL[{7}, -S^2])/3 + ((3 - 569*S^2 - 326*S^4)*HPL[{2, 1}, -S^2]^2)/(2*S*(1 + S^2)) + HPL[{4}, -S^2]*((Pi^2*(51 + 496*S^2 + 372*S^4))/(72*S*(1 + S^2)) + (-36 + 594*S^2 + 2137*S^4 + 1479*S^6 + 36*S^8)/(48*S^3*(1 + S^2)) - (8*S*HPL[{2, 1}, -S^2])/3) + ((89*Pi^2*S)/36 + (21 - 199*S^2 - 194*S^4 + 12*S^6)/(12*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((175*Pi^2*S)/18 + (-281 - 1120*S^2 - 740*S^4 + 39*S^6)/(12*S*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((7 - 58*S^2 - 56*S^4)*HPL[{4, 2}, -S^2])/(12*S*(1 + S^2)) - (22*S*HPL[{4, 3}, -S^2])/3 + ((-49 - 517*S^2 - 412*S^4)*HPL[{5, 1}, -S^2])/(6*S*(1 + S^2)) - (149*S*HPL[{5, 2}, -S^2])/6 - 51*S*HPL[{6, 1}, -S^2] + ((10*Pi^2*S)/3 + (1707 - 245*S^2 + 3*S^4)/(6*S))*HPL[{2, 2, 1}, -S^2] + (Pi^2*S + (5309 + 4862*S^2 - 478*S^4 - 3*S^6)/(6*S*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + ((1 + 22*S^2)*HPL[{3, 1, 2}, -S^2])/(6*S) + ((-45 + 3175*S^2 + 1856*S^4)*HPL[{3, 2, 1}, -S^2])/(6*S*(1 + S^2)) - (185*S*HPL[{3, 2, 2}, -S^2])/6 - 96*S*HPL[{3, 3, 1}, -S^2] + ((-60 + 4924*S^2 + 2913*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (287*S*HPL[{4, 1, 2}, -S^2])/3 - (863*S*HPL[{4, 2, 1}, -S^2])/3 - 590*S*HPL[{5, 1, 1}, -S^2] + ((140*Pi^2*S)/9 + (2*(-931 - 898*S^2 + 51*S^4 + 6*S^6))/(3*S*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] + (64*S*HPL[{2, 2, 2, 1}, -S^2])/3 - (2*(-23 + 1732*S^2 + 1047*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (14*S*HPL[{3, 1, 1, 2}, -S^2])/3 - (14*S*HPL[{3, 1, 2, 1}, -S^2])/3 - (206*S*HPL[{3, 2, 1, 1}, -S^2])/3 - (548*S*HPL[{4, 1, 1, 1}, -S^2])/3 + (4*(-23 + 1773*S^2 + 1079*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (208*S*HPL[{2, 1, 2, 1, 1}, -S^2])/3 - 208*S*HPL[{2, 2, 1, 1, 1}, -S^2] - (1520*S*HPL[{3, 1, 1, 1, 1}, -S^2])/3 + (608*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/3 + ((69*Pi^4*S)/20 - (Pi^2*S*(-427 - 405*S^2 + 48*S^4))/(36*(1 + S^2)) + (S*(623 + 874*S^2 + 171*S^4))/(48*(1 + S^2)))*Zeta[3] - (S*(-6 + 7*S^2)*Zeta[3]^2)/(2*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(-35 + 3290*S^2 + 2118*S^4))/(18*S*(1 + S^2)) + (-45 + 215*S^2 + 2358*S^4 + 2098*S^6 + 24*S^8)/(6*S^3*(1 + S^2)) - (184*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(-21 + 3017*S^2 + 1836*S^4))/(144*S*(1 + S^2)) + (-3 - 78*S^2 + 1915*S^4 + 15*S^6)/(48*S^3) - (15*S*HPL[{3}, -S^2])/4 + (8*S*HPL[{2, 1}, -S^2])/3 - (17*S*Zeta[3])/3) + HPL[{1}, -S^2]^4*((Pi^2*(1115 + 5804*S^2 + 1953*S^4))/(216*S*(1 + S^2)) + (15 + 3947*S^2 + 3969*S^4 + 69*S^6)/(144*S^3) + ((541 + 2947*S^2 + 972*S^4)*HPL[{2}, -S^2])/(36*S*(1 + S^2)) - (5*S*HPL[{3}, -S^2])/3 - (239*S*HPL[{2, 1}, -S^2])/3 - 5*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((Pi^2*(10 - 1611*S^2 - 1023*S^4))/(18*S*(1 + S^2)) + (36 - 203*S^2 - 1740*S^4 - 1498*S^6 - 13*S^8)/(8*S^3*(1 + S^2)) + (92*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((178*Pi^4*S)/135 + (Pi^2*(-3667 - 3430*S^2 + 265*S^4 + 6*S^6))/(72*S*(1 + S^2)) + (18 - 3877*S^2 - 4293*S^4 - 314*S^6 + 36*S^8)/(24*S^3*(1 + S^2)) + (58*S*HPL[{3, 1}, -S^2])/3 + (104*S*HPL[{2, 1, 1}, -S^2])/3 + ((-4 + 13*S^2 - 30*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((-379*Pi^4*S)/720 + (Pi^2*(214 + 487*S^2 + 229*S^4 - 6*S^6))/(72*S*(1 + S^2)) + (-12 + 845*S^2 + 2869*S^4 + 1671*S^6 - 181*S^8)/(96*S^3*(1 + S^2)) + (10*S*HPL[{4}, -S^2])/3 + ((22 + 167*S^2 + 93*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) + 17*S*HPL[{3, 1}, -S^2] - 30*S*HPL[{2, 1, 1}, -S^2] + ((-13 - 52*S^2 - 25*S^4)*Zeta[3])/(6*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((3299*Pi^4*S)/648 + (Pi^2*(2027 + 3978*S^2 + 1989*S^4 + 8*S^6))/(108*S*(1 + S^2)) + (-15 + 4322*S^2 + 4427*S^4 + 106*S^6)/(72*S^3) + ((1207*Pi^2*S)/54 + (-15 + 963*S^2 + 2024*S^4 + 1023*S^6 + S^8)/(18*S^3*(1 + S^2)))*HPL[{2}, -S^2] + 41*S*HPL[{2}, -S^2]^2 + ((10 + 57*S^2 + 77*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) + (25*S*HPL[{4}, -S^2])/9 + ((-541 - 2947*S^2 - 972*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (472*S*HPL[{3, 1}, -S^2])/3 + (956*S*HPL[{2, 1, 1}, -S^2])/3 + (5*(-1 - 13*S^2 + 6*S^4)*Zeta[3])/(9*S*(1 + S^2))) + ((250*Pi^2*S)/9 - (S*(-321 - 299*S^2 + 36*S^4))/(6*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^2*((Pi^4*(3028 + 15301*S^2 + 5675*S^4))/(864*S*(1 + S^2)) + (-52 + 4894*S^2 + 5105*S^4 + 175*S^6)/(48*S^3) + (Pi^2*(15 + 4101*S^2 + 8067*S^4 + 4069*S^6 + 40*S^8))/(144*S^3*(1 + S^2)) + ((130 + 707*S^2 + 208*S^4)*HPL[{2}, -S^2]^2)/(6*S*(1 + S^2)) + (-(Pi^2*S)/6 + (-17 + 159*S^2 + 431*S^4 + 223*S^6 - 4*S^8)/(12*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((54 + 275*S^2 + 171*S^4)*HPL[{4}, -S^2])/(12*S*(1 + S^2)) + (11*S*HPL[{5}, -S^2])/3 + ((-1207*Pi^2*S)/18 + (15 - 963*S^2 - 2024*S^4 - 1023*S^6 - S^8)/(6*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-270 - 1471*S^2 - 493*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (52*S*HPL[{3, 2}, -S^2])/3 + (131*S*HPL[{4, 1}, -S^2])/3 + ((541 + 2947*S^2 + 972*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 492*S*HPL[{2, 2, 1}, -S^2] + 1456*S*HPL[{3, 1, 1}, -S^2] - 956*S*HPL[{2, 1, 1, 1}, -S^2] + ((-7*Pi^2*S)/18 + (49 + 79*S^2 + 31*S^4 - 3*S^6)/(12*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(997 + 5278*S^2 + 1867*S^4))/(72*S*(1 + S^2)) + (-24 + 1367*S^2 + 2871*S^4 + 1449*S^6 + S^8)/(16*S^3*(1 + S^2)) - (26*S*HPL[{3}, -S^2])/3 - 246*S*HPL[{2, 1}, -S^2] - (47*S*Zeta[3])/3) + (S*Zeta[5])/3) + HPL[{2}, -S^2]*((Pi^4*(-281 + 44790*S^2 + 31188*S^4))/(4320*S*(1 + S^2)) + (Pi^2*(-90 + 383*S^2 + 4618*S^4 + 4077*S^6 - 12*S^8))/(144*S^3*(1 + S^2)) + (-249 + 3538*S^2 + 23400*S^4 + 19430*S^6 + 201*S^8)/(192*S^3*(1 + S^2)) + ((-5*Pi^2*S)/4 + (-7 + 55*S^2 + 55*S^4 - 3*S^6)/(6*S*(1 + S^2)))*HPL[{3}, -S^2] + ((11 + 234*S^2 + 198*S^4)*HPL[{4}, -S^2])/(12*S*(1 + S^2)) - (7*S*HPL[{5}, -S^2])/6 + ((-5*Pi^2*S)/3 + (-1707 + 245*S^2 - 3*S^4)/(12*S))*HPL[{2, 1}, -S^2] + ((1 - 1743*S^2 - 1010*S^4)*HPL[{3, 1}, -S^2])/(6*S*(1 + S^2)) + (31*S*HPL[{3, 2}, -S^2])/2 + (143*S*HPL[{4, 1}, -S^2])/3 + ((-3 + 569*S^2 + 326*S^4)*HPL[{2, 1, 1}, -S^2])/(S*(1 + S^2)) - (32*S*HPL[{2, 2, 1}, -S^2])/3 + 2*S*HPL[{3, 1, 1}, -S^2] - (104*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((-8*Pi^2*S)/9 + (-23 + 86*S^2 + 107*S^4)/(12*S*(1 + S^2)))*Zeta[3] + (5*S*Zeta[5])/3) + HPL[{1}, -S^2]*((20777*Pi^6*S)/12960 + ((1 + S^2)*(-133 + 12234*S^2 + 639*S^4))/(96*S^3) + (Pi^4*(32542 + 63281*S^2 + 31198*S^4 - 165*S^6))/(4320*S*(1 + S^2)) + (Pi^2*(-15 + 4548*S^2 + 9168*S^4 + 4724*S^6 + 95*S^8))/(144*S^3*(1 + S^2)) + ((601*Pi^2*S)/36 + (-1 + 833*S^2 + 840*S^4 + 6*S^6)/(24*S^3))*HPL[{2}, -S^2]^2 + (341*S*HPL[{2}, -S^2]^3)/18 - (11*S*HPL[{3}, -S^2]^2)/6 + ((73*Pi^2*S)/36 + (-12 + 196*S^2 + 489*S^4 + 270*S^6 + S^8)/(12*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((20 + 107*S^2 + 76*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (39*S*HPL[{6}, -S^2])/2 - 246*S*HPL[{2, 1}, -S^2]^2 + ((-598*Pi^2*S)/9 + (18 - 991*S^2 - 2104*S^4 - 1069*S^6 - 2*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((23 + 114*S^2 - 13*S^4)*HPL[{3, 2}, -S^2])/(6*S*(1 + S^2)) + ((18 + 67*S^2 - 213*S^4)*HPL[{4, 1}, -S^2])/(6*S*(1 + S^2)) - (3*S*HPL[{4, 2}, -S^2])/2 - (56*S*HPL[{5, 1}, -S^2])/3 + ((1207*Pi^2*S)/9 + (-15 + 963*S^2 + 2024*S^4 + 1023*S^6 + S^8)/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (4*(130 + 707*S^2 + 208*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(790 + 4299*S^2 + 1325*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (1364*S*HPL[{3, 2, 1}, -S^2])/3 + (4142*S*HPL[{4, 1, 1}, -S^2])/3 - (2*(541 + 2947*S^2 + 972*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 944*S*HPL[{3, 1, 1, 1}, -S^2] + 1912*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-41 - 72*S^2 + 3*S^4)/(12*S) + (Pi^2*(36 + 102*S^2 + 73*S^4))/(18*S*(1 + S^2)))*Zeta[3] + 13*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(25 + 180*S^2 + 161*S^4))/(36*S*(1 + S^2)) + (-45 + 512*S^2 + 1280*S^4 + 652*S^6 - 23*S^8)/(24*S^3*(1 + S^2)) + (52*S*HPL[{2, 1}, -S^2])/3 - (14*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((Pi^2*(-997 - 5278*S^2 - 1867*S^4))/(36*S*(1 + S^2)) + (24 - 1367*S^2 - 2871*S^4 - 1449*S^6 - S^8)/(8*S^3*(1 + S^2)) + (94*S*Zeta[3])/3) + HPL[{2}, -S^2]*((13883*Pi^4*S)/2160 + (Pi^2*(-30 + 1870*S^2 + 3905*S^4 + 1984*S^6 + S^8))/(72*S^3*(1 + S^2)) + (-52 + 2213*S^2 + 4712*S^4 + 2401*S^6 + 2*S^8)/(24*S^3*(1 + S^2)) + ((-12 - 57*S^2 + 7*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) + (25*S*HPL[{4}, -S^2])/6 - (2*(130 + 707*S^2 + 208*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (734*S*HPL[{3, 1}, -S^2])/3 + 492*S*HPL[{2, 1, 1}, -S^2] + ((3 - 30*S^2 + 61*S^4)*Zeta[3])/(6*S*(1 + S^2))) + ((42 + 139*S^2 + 95*S^4)*Zeta[5])/(6*S*(1 + S^2))) + 186*S*Zeta[7]) + HPL[{1}, -S^2]*((55259*Pi^8*S)/85050 + (Pi^2*(1 + S^2)*(-133 + 16564*S^2 + 1061*S^4))/(144*S^3) + ((1 + S^2)*(7435 + 318033*S^2 + 23930*S^4))/(192*S^3) + (Pi^6*(225201 + 454187*S^2 + 228347*S^4 + 1279*S^6))/(90720*S*(1 + S^2)) + (Pi^4*(-212 + 60375*S^2 + 124784*S^4 + 66247*S^6 + 2458*S^8))/(4320*S^3*(1 + S^2)) + ((217*Pi^2*S)/27 + (-5 + 343*S^2 + 343*S^4 - 5*S^6)/(18*S^3))*HPL[{2}, -S^2]^3 + 16*S*HPL[{2}, -S^2]^4 + ((50*Pi^2*S)/9 + (1 + 56*S^2 + 122*S^4 + 72*S^6 - 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + 8*S*HPL[{4}, -S^2]^2 + ((37*Pi^2*S)/3 + (-30 + 1113*S^2 + 2323*S^4 + 1207*S^6 + 32*S^8)/(3*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((864 + 3533*S^2 + 2177*S^4)*HPL[{7}, -S^2])/(3*S*(1 + S^2)) + 560*S*HPL[{8}, -S^2] + ((-638*Pi^2*S)/3 + (1 - 1003*S^2 - 1028*S^4 - 16*S^6)/(3*S^3))*HPL[{2, 1}, -S^2]^2 + 932*S*HPL[{3, 1}, -S^2]^2 + (19*Pi^2*S - (2*(1 - 30*S^2 - 72*S^4 - 36*S^6 + S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((34 - 15*S^2 + 59*S^4)*HPL[{4, 3}, -S^2])/(3*S*(1 + S^2)) + ((820*Pi^2*S)/9 + (20 - 571*S^2 - 1145*S^4 - 609*S^6 - 23*S^8)/(3*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((35 + 12*S^2 + 53*S^4)*HPL[{5, 2}, -S^2])/(S*(1 + S^2)) - 8*S*HPL[{5, 3}, -S^2] - (10*(35 + 199*S^2 + 137*S^4)*HPL[{6, 1}, -S^2])/(3*S*(1 + S^2)) - 20*S*HPL[{6, 2}, -S^2] - 384*S*HPL[{7, 1}, -S^2] + 3136*S*HPL[{2, 1, 1}, -S^2]^2 + (2*(1 - 6*S^4 + S^8)*HPL[{3, 1, 2}, -S^2])/(3*S^3*(1 + S^2)) + ((1736*Pi^2*S)/9 - (2*(9 - 676*S^2 - 1366*S^4 - 676*S^6 + 9*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((-664 - 4689*S^2 + 121*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S*(1 + S^2)) + (16*(-128 - 904*S^2 + 19*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S*(1 + S^2)) + 224*S*HPL[{3, 3, 2}, -S^2] + ((4406*Pi^2*S)/9 - (2*(42 - 2225*S^2 - 4534*S^4 - 2249*S^6 + 30*S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((-2000 - 14155*S^2 + 331*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S*(1 + S^2)) - 384*S*HPL[{4, 1, 3}, -S^2] + ((-6296 - 44407*S^2 + 799*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S*(1 + S^2)) + 136*S*HPL[{4, 2, 2}, -S^2] - 1312*S*HPL[{4, 3, 1}, -S^2] + (4*(-3143 - 22457*S^2 + 690*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 800*S*HPL[{5, 1, 2}, -S^2] - 5360*S*HPL[{5, 2, 1}, -S^2] - 13540*S*HPL[{6, 1, 1}, -S^2] - (8*(166 + 767*S^2 + 415*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (-304*Pi^2*S + (4*(18 - 799*S^2 - 805*S^4 + 12*S^6))/(3*S^3))*HPL[{3, 1, 1, 1}, -S^2] + (16*(331 + 1723*S^2 + 618*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) + (16*(331 + 1723*S^2 + 618*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) + 156*S*HPL[{3, 1, 2, 2}, -S^2] + (8*(1160 + 5747*S^2 + 2481*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 156*S*HPL[{3, 2, 1, 2}, -S^2] - 308*S*HPL[{3, 2, 2, 1}, -S^2] - 1392*S*HPL[{3, 3, 1, 1}, -S^2] + (8*(3520 + 17605*S^2 + 7341*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 468*S*HPL[{4, 1, 1, 2}, -S^2] - 924*S*HPL[{4, 1, 2, 1}, -S^2] - 3708*S*HPL[{4, 2, 1, 1}, -S^2] - 6016*S*HPL[{5, 1, 1, 1}, -S^2] + ((2512*Pi^2*S)/3 - (8*(5 - 283*S^2 - 283*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1, 1}, -S^2] - (16*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (16*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 992*S*HPL[{2, 2, 1, 2, 1}, -S^2] - 2976*S*HPL[{2, 2, 2, 1, 1}, -S^2] - (16*(1838 + 10877*S^2 + 1959*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 5952*S*HPL[{3, 1, 1, 1, 2}, -S^2] + 9920*S*HPL[{3, 1, 1, 2, 1}, -S^2] + 11904*S*HPL[{3, 1, 2, 1, 1}, -S^2] + 24800*S*HPL[{3, 2, 1, 1, 1}, -S^2] + 72128*S*HPL[{4, 1, 1, 1, 1}, -S^2] - (80*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 256*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 4800*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + ((23*Pi^2*S)/3 + (78 + 111*S^2 + 46*S^4 - 9*S^6)/(3*S*(1 + S^2)))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((4*Pi^2*(800 + 4359*S^2 + 1303*S^4))/(9*S*(1 + S^2)) + (-36 + 5881*S^2 + 5984*S^4 + 75*S^6)/(3*S^3) - 3696*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*(((1 + S^2)*(1 + 679*S^2 + 24*S^4))/S^3 + (2*Pi^2*(591 + 3326*S^2 + 821*S^4))/(9*S*(1 + S^2)) - 1168*S*Zeta[3]) + HPL[{5}, -S^2]*((Pi^2*(119 + 446*S^2 + 491*S^4))/(18*S*(1 + S^2)) + (3 + 2085*S^2 + 1863*S^4 + 17*S^6)/(12*S^3) + 132*S*HPL[{2, 1}, -S^2] - 12*S*Zeta[3]) + HPL[{3, 2}, -S^2]*((Pi^2*(351 + 2404*S^2 - 31*S^4))/(18*S*(1 + S^2)) + (25 + 652*S^2 + 825*S^4 + 118*S^6)/(6*S^3) + 72*S*Zeta[3]) + HPL[{4, 1}, -S^2]*((Pi^2*(1082 + 7665*S^2 - 471*S^4))/(18*S*(1 + S^2)) + (178 + 2529*S^2 + 3626*S^4 + 763*S^6)/(12*S^3) + (772*S*Zeta[3])/3) + HPL[{2, 1, 1, 1}, -S^2]*((12*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 - (2*Pi^2*(931 + 4762*S^2 + 1947*S^4))/(9*S*(1 + S^2)) + 2624*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((-2854*Pi^4*S)/135 + (117 - 4288*S^2 - 4189*S^4 + 184*S^6)/(12*S^3) + (Pi^2*(18 - 886*S^2 - 1854*S^4 - 931*S^6 + 5*S^8))/(9*S^3*(1 + S^2)) - 3136*S*HPL[{2, 1, 1}, -S^2] + (4*(78 + 589*S^2 + S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((4421*Pi^4*S)/90 - ((1 + S^2)*(104 - 4309*S^2 + 197*S^4))/(6*S^3) + (Pi^2*(-30 + 1797*S^2 + 3722*S^4 + 1857*S^6 - 14*S^8))/(9*S^3*(1 + S^2)) + (4*(-151 - 1132*S^2 + 3*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]^2*((4949*Pi^4*S)/540 + (Pi^2*(-1 + 918*S^2 + 934*S^4 + 11*S^6))/(36*S^3) + (-6 + 2129*S^2 + 2208*S^4 + 105*S^6)/(24*S^3) + ((-101 - 702*S^2 + 5*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 74*S*HPL[{4}, -S^2] + ((-166 - 767*S^2 - 415*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 20*S*HPL[{3, 1}, -S^2] + 124*S*HPL[{2, 1, 1}, -S^2] + ((-71 - 498*S^2 + 11*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{4}, -S^2]*((-278*Pi^4*S)/135 + (Pi^2*(-24 + 417*S^2 + 490*S^4 + S^6))/(36*S^3) + (49 + 2249*S^2 + 4565*S^4 + 2259*S^6 - 10*S^8)/(24*S^3*(1 + S^2)) + ((136 + 883*S^2 + 69*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 228*S*HPL[{3, 1}, -S^2] - 452*S*HPL[{2, 1, 1}, -S^2] + ((6 - 29*S^2 + 27*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((-889 - 1044*S^2 - 215*S^4)/(12*S) + (Pi^2*(-33 - 331*S^2 + 103*S^4))/(9*S*(1 + S^2)))*Zeta[5] + HPL[{3}, -S^2]*(-((1 + S^2)*(36 - 357*S^2 + 155*S^4))/(8*S^3) + (Pi^4*(-238 - 1772*S^2 + 561*S^4))/(270*S*(1 + S^2)) + (Pi^2*(-45 + 114*S^2 + 349*S^4 + 84*S^6 - 82*S^8))/(36*S^3*(1 + S^2)) - (2*(7 - 24*S^2 + 20*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - 12*S*HPL[{5}, -S^2] + ((1042*Pi^2*S)/9 + (9 + 320*S^2 + 345*S^4 + 26*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(-156 - 1117*S^2 + 29*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - 152*S*HPL[{3, 2}, -S^2] - 68*S*HPL[{4, 1}, -S^2] + (20*(-33 - 229*S^2 + 2*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 1616*S*HPL[{2, 2, 1}, -S^2] - 4552*S*HPL[{3, 1, 1}, -S^2] + 2640*S*HPL[{2, 1, 1, 1}, -S^2] + ((-86*Pi^2*S)/9 + (35 + 9*S^2 - 5*S^4 - 7*S^6)/(3*S*(1 + S^2)))*Zeta[3] - 40*S*Zeta[5]) + Zeta[3]*((-4505 - 5122*S^2 - 585*S^4)/(24*S) - (5*Pi^2*(197 + 244*S^2 + 27*S^4))/(72*S) + (Pi^4*(-81 - 924*S^2 + 247*S^4))/(180*S*(1 + S^2)) + (352*S*Zeta[5])/3) + HPL[{2, 1}, -S^2]*((Pi^4*(-2016 - 10550*S^2 - 4113*S^4))/(180*S*(1 + S^2)) + ((1 + S^2)*(81 - 3449*S^2 + 152*S^4))/(8*S^3) + (Pi^2*(48 - 2579*S^2 - 5319*S^4 - 2613*S^6 + 47*S^8))/(24*S^3*(1 + S^2)) + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - 1460*S*HPL[{3, 2}, -S^2] - 4396*S*HPL[{4, 1}, -S^2] + (8*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 496*S*HPL[{2, 2, 1}, -S^2] + 4128*S*HPL[{3, 1, 1}, -S^2] - 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((1078*Pi^2*S)/9 + (2*(129 + 326*S^2 + 189*S^4 + 16*S^6))/(3*S*(1 + S^2)))*Zeta[3] + 540*S*Zeta[5]) + HPL[{2}, -S^2]*((787*Pi^6*S)/360 - ((1 + S^2)*(104 - 6275*S^2 + 230*S^4))/(24*S^3) + (Pi^2*(-208 + 8527*S^2 + 17741*S^4 + 8717*S^6 - 193*S^8))/(144*S^3*(1 + S^2)) + (Pi^4*(-416 + 23109*S^2 + 48589*S^4 + 24471*S^6 - 79*S^8))/(2160*S^3*(1 + S^2)) + 38*S*HPL[{3}, -S^2]^2 + ((-157*Pi^2*S)/9 + (1 - 97*S^2 - 125*S^4 + 5*S^6)/(6*S^3))*HPL[{4}, -S^2] + ((10 - 129*S^2 + 59*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + 8*S*HPL[{6}, -S^2] - 124*S*HPL[{2, 1}, -S^2]^2 + ((-1910*Pi^2*S)/9 + (1 - 1006*S^2 - 1031*S^4 - 16*S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + ((356 + 2499*S^2 - 47*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + ((1076 + 7541*S^2 - 129*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + 152*S*HPL[{4, 2}, -S^2] + 596*S*HPL[{5, 1}, -S^2] + ((1276*Pi^2*S)/3 + (2*(-1 + 1003*S^2 + 1028*S^4 + 16*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(166 + 767*S^2 + 415*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(663 + 3446*S^2 + 1235*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 156*S*HPL[{3, 1, 2}, -S^2] + 1380*S*HPL[{3, 2, 1}, -S^2] + 4156*S*HPL[{4, 1, 1}, -S^2] - (8*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 9088*S*HPL[{3, 1, 1, 1}, -S^2] + 6272*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(-74 - 581*S^2 + 32*S^4))/(9*S*(1 + S^2)) + (-155 - 423*S^2 - 285*S^4 - 49*S^6)/(4*S*(1 + S^2)))*Zeta[3] + (2*S*Zeta[3]^2)/3 + HPL[{3}, -S^2]*((Pi^2*(-177 - 1202*S^2 + 17*S^4))/(18*S*(1 + S^2)) + (-28 - 643*S^2 - 832*S^4 - 121*S^6)/(12*S^3) + 808*S*HPL[{2, 1}, -S^2] - 36*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((Pi^2*(-591 - 3326*S^2 - 821*S^4))/(9*S*(1 + S^2)) - ((1 + S^2)*(1 + 679*S^2 + 24*S^4))/(2*S^3) + 584*S*Zeta[3]) + (2*(-37 - 374*S^2 + 68*S^4)*Zeta[5])/(3*S*(1 + S^2))) + ((-15 - 121*S^2 + 146*S^4)*Zeta[7])/(S*(1 + S^2))) + HPL[{0}, S^2]*((135211*Pi^8*S)/272160 + (Pi^2*(-1392 + 99787*S^2 + 6325*S^4))/(576*S) + (63 + 326339*S^2 + 23930*S^4)/(192*S) + (Pi^6*S*(807480 + 866751*S^2 + 55645*S^4))/(181440*(1 + S^2)) + (Pi^4*(-2496 + 359799*S^2 + 371222*S^4 + 8287*S^6))/(17280*S*(1 + S^2)) + (2*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^7)/(9*S*(1 + S^2)) + (4*S*HPL[{1}, -S^2]^8)/3 + ((410*Pi^2*S)/27 + (-10 + 38*S^2 + 1076*S^4 + 15*S^6)/(36*S^3))*HPL[{2}, -S^2]^3 + (91*S*HPL[{2}, -S^2]^4)/6 + HPL[{1}, -S^2]^6*((127*Pi^2*S)/27 + (155 + 158*S^2 + 3*S^4)/(18*S) + (50*S*HPL[{2}, -S^2])/3) + ((-7*Pi^2*S)/3 + (1 - 20*S^2 - 104*S^4 - 90*S^6 - 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + 12*S*HPL[{4}, -S^2]^2 + ((109*Pi^2*S)/9 - (5*(24 - 10*S^2 - 20*S^4 + 55*S^6 + 39*S^8))/(12*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((-95 - 281*S^2 - 175*S^4)*HPL[{7}, -S^2])/(3*S*(1 + S^2)) + 52*S*HPL[{8}, -S^2] + ((-1711*Pi^2*S)/9 + (1 - 2*S^2 - 1126*S^4 - 15*S^6)/(3*S^3))*HPL[{2, 1}, -S^2]^2 + (2264*S*HPL[{3, 1}, -S^2]^2)/3 + ((-2*Pi^2*S)/3 + (-8 + 56*S^2 + 122*S^4 + 63*S^6 + 21*S^8)/(12*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((-50 - 184*S^2 - 115*S^4)*HPL[{4, 3}, -S^2])/(3*S*(1 + S^2)) + ((-196*Pi^2*S)/9 + (40 - 140*S^2 - 535*S^4 - 300*S^6 + 87*S^8)/(6*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((-297 - 1090*S^2 - 689*S^4)*HPL[{5, 2}, -S^2])/(6*S*(1 + S^2)) - (14*S*HPL[{5, 3}, -S^2])/3 + ((-275 - 1091*S^2 - 664*S^4)*HPL[{6, 1}, -S^2])/(3*S*(1 + S^2)) - (28*S*HPL[{6, 2}, -S^2])/3 - (292*S*HPL[{7, 1}, -S^2])/3 + (9136*S*HPL[{2, 1, 1}, -S^2]^2)/3 + (Pi^2*S + (4 - 7*S^2 + 29*S^4 + 51*S^6 + 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((3289*Pi^2*S)/9 + (-36 + 105*S^2 + 4485*S^4 + 4415*S^6 + 63*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((16 - 749*S^2 - 387*S^4)*HPL[{3, 2, 2}, -S^2])/(6*S*(1 + S^2)) - (4*(3 + 281*S^2 + 130*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{3, 3, 2}, -S^2])/3 + ((10132*Pi^2*S)/9 + (-84 + 308*S^2 + 7274*S^4 + 6987*S^6 + 93*S^8)/(3*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((-5 - 378*S^2 - 176*S^4)*HPL[{4, 1, 2}, -S^2])/(S*(1 + S^2)) + (16*S*HPL[{4, 1, 3}, -S^2])/3 + ((-21 - 1114*S^2 - 492*S^4)*HPL[{4, 2, 1}, -S^2])/(S*(1 + S^2)) - 4*S*HPL[{4, 2, 2}, -S^2] - (2*(41 + 3132*S^2 + 1331*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (4*S*HPL[{5, 1, 2}, -S^2])/3 - (4*S*HPL[{5, 2, 1}, -S^2])/3 + (464*S*HPL[{6, 1, 1}, -S^2])/3 + (4*(-653 - 1606*S^2 + 109*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + ((-7112*Pi^2*S)/9 - (2*(-36 + 217*S^2 + 2490*S^4 + 33*S^6))/(3*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (2*(-3922 - 9877*S^2 + 645*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) - (2*(-3922 - 9877*S^2 + 645*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (10*S*HPL[{3, 1, 2, 2}, -S^2])/3 - (2*(-7840 - 19513*S^2 + 1299*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (10*S*HPL[{3, 2, 1, 2}, -S^2])/3 - (8822*S*HPL[{3, 2, 2, 1}, -S^2])/3 - 8832*S*HPL[{3, 3, 1, 1}, -S^2] - (20*(-2341 - 5818*S^2 + 402*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (32*S*HPL[{4, 1, 1, 2}, -S^2])/3 - (26528*S*HPL[{4, 1, 2, 1}, -S^2])/3 - (79520*S*HPL[{4, 2, 1, 1}, -S^2])/3 - 53264*S*HPL[{5, 1, 1, 1}, -S^2] + (1600*Pi^2*S + (4*(-30 + 199*S^2 + 2553*S^4 + 45*S^6))/(3*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] + (8*(-653 - 1692*S^2 + 137*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (8*(-653 - 1692*S^2 + 137*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - (17600*S*HPL[{2, 2, 1, 2, 1}, -S^2])/3 - 17600*S*HPL[{2, 2, 2, 1, 1}, -S^2] + (8*(-3218 - 8441*S^2 + 711*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (105656*S*HPL[{3, 1, 1, 1, 2}, -S^2])/3 + (176056*S*HPL[{3, 1, 1, 2, 1}, -S^2])/3 + (211256*S*HPL[{3, 1, 2, 1, 1}, -S^2])/3 + (440056*S*HPL[{3, 2, 1, 1, 1}, -S^2])/3 + 440416*S*HPL[{4, 1, 1, 1, 1}, -S^2] + (400*(-28 - 67*S^2 + 6*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 12512*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] + 25280*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (Pi^2*S + (S*(256 + 287*S^2 + 33*S^4))/(6*(1 + S^2)))*Zeta[3]^2 + HPL[{3, 1, 1}, -S^2]*((Pi^2*(3437 + 8053*S^2 - 562*S^4))/(9*S*(1 + S^2)) + (24 + 6381*S^2 + 6465*S^4 + 101*S^6 - 15*S^8)/(3*S^3*(1 + S^2)) - 32*S*Zeta[3]) + HPL[{1}, -S^2]^5*(((1 + S^2)*(3 + 967*S^2 + 42*S^4))/(36*S^3) + (Pi^2*(425 + 2323*S^2 + 628*S^4))/(90*S*(1 + S^2)) + ((136 + 769*S^2 + 183*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) - (12*S*HPL[{3}, -S^2])/5 - 100*S*HPL[{2, 1}, -S^2] - (164*S*Zeta[3])/15) + HPL[{2, 2, 1}, -S^2]*((-2*Pi^2*(-559 - 1320*S^2 + 107*S^4))/(9*S*(1 + S^2)) + (12 + 4051*S^2 - 220*S^4 + 15*S^6)/(6*S^3) - 8*S*Zeta[3]) + HPL[{2, 1, 1, 1}, -S^2]*((2*Pi^2*(-1201 - 2674*S^2 + 240*S^4))/(9*S*(1 + S^2)) + (-18 - 4557*S^2 - 658*S^4 + 57*S^6)/(3*S^3) + (16*S*Zeta[3])/3) + HPL[{3, 2}, -S^2]*((Pi^2*(35 + 237*S^2 - 78*S^4))/(36*S*(1 + S^2)) + (4 + 117*S^2 - 462*S^4 + 141*S^6)/(24*S^3) + 18*S*Zeta[3]) + HPL[{5}, -S^2]*((Pi^2*(-2 + 21*S^2 + 6*S^4))/(9*S*(1 + S^2)) + (60 + 1659*S^2 + 2729*S^4 + 1207*S^6 - 75*S^8)/(24*S^3*(1 + S^2)) + (116*S*HPL[{2, 1}, -S^2])/3 + (74*S*Zeta[3])/3) + HPL[{4, 1}, -S^2]*((Pi^2*(-42 + 76*S^2 - 193*S^4))/(18*S*(1 + S^2)) + (-20 - 733*S^2 - 2016*S^4 - 1041*S^6 + 294*S^8)/(12*S^3*(1 + S^2)) + 36*S*Zeta[3]) + HPL[{1}, -S^2]^4*((1687*Pi^4*S)/270 + ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(24*S^3) + (Pi^2*(4325 + 8621*S^2 + 4411*S^4 + 67*S^6))/(216*S*(1 + S^2)) + ((571*Pi^2*S)/18 + (-15 + 1211*S^2 + 1265*S^4 + 15*S^6)/(18*S^3))*HPL[{2}, -S^2] + (196*S*HPL[{2}, -S^2]^2)/3 + ((2 - S^2 + 15*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + 7*S*HPL[{4}, -S^2] - (5*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) - (748*S*HPL[{3, 1}, -S^2])/3 + 500*S*HPL[{2, 1, 1}, -S^2] + ((-44 - 299*S^2 - 9*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{3, 1}, -S^2]*((-18731*Pi^4*S)/540 + (198 - 3345*S^2 - 15337*S^4 - 12263*S^6 - 405*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(72 - 267*S^2 - 4855*S^4 - 4547*S^6 - 39*S^8))/(36*S^3*(1 + S^2)) - (9112*S*HPL[{2, 1, 1}, -S^2])/3 + (2*(-10 + 119*S^2 + 5*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]^2*((8743*Pi^4*S)/1080 + (-47 + 4473*S^2 + 159*S^4)/(48*S) + (Pi^2*(-4 - 67*S^2 + 3948*S^4 + 4062*S^6 + 39*S^8))/(144*S^3*(1 + S^2)) + ((2 - 203*S^2 - 109*S^4)*HPL[{3}, -S^2])/(12*S*(1 + S^2)) - (2*S*HPL[{4}, -S^2])/3 + ((-653 - 1606*S^2 + 109*S^4)*HPL[{2, 1}, -S^2])/(6*S*(1 + S^2)) - (1103*S*HPL[{3, 1}, -S^2])/3 + (2200*S*HPL[{2, 1, 1}, -S^2])/3 + ((7 - 43*S^2 + 10*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((9577*Pi^4*S)/135 + (Pi^2*(-60 + 329*S^2 + 4595*S^4 + 57*S^6))/(18*S^3) + (-86 + 1570*S^2 + 5860*S^4 + 243*S^6)/(6*S^3) - (4*(-4 + 140*S^2 + 21*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{4}, -S^2]*((319*Pi^4*S)/135 + (Pi^2*(-48 + 117*S^2 + 976*S^4 + 835*S^6))/(72*S^3*(1 + S^2)) + (114 + 4515*S^2 + 8040*S^4 + 3084*S^6 - 587*S^8)/(48*S^3*(1 + S^2)) + (3*(-2 + 5*S^2 + 8*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (80*S*HPL[{3, 1}, -S^2])/3 + (176*S*HPL[{2, 1, 1}, -S^2])/3 + ((36 + 184*S^2 + 129*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((Pi^2*S*(1501 + 1569*S^2))/(18*(1 + S^2)) - (S*(-1281 - 1118*S^2 + 87*S^4))/(12*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^3*(((1 + S^2)*(-104 + 14397*S^2 + 935*S^4))/(72*S^3) + (Pi^4*(3919 + 20531*S^2 + 6490*S^4))/(810*S*(1 + S^2)) + (Pi^2*(30 + 9135*S^2 + 18331*S^4 + 9609*S^6 + 303*S^8))/(216*S^3*(1 + S^2)) + ((331 + 1912*S^2 + 405*S^4)*HPL[{2}, -S^2]^2)/(9*S*(1 + S^2)) + ((-10*Pi^2*S)/9 + (-17 + 225*S^2 + 243*S^4 - 7*S^6)/(9*S^3))*HPL[{3}, -S^2] + ((70 + 319*S^2 + 123*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) + (116*S*HPL[{5}, -S^2])/9 + ((-1142*Pi^2*S)/9 - (2*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(9*S^3))*HPL[{2, 1}, -S^2] - (4*(337 + 1909*S^2 + 450*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (152*S*HPL[{3, 2}, -S^2])/3 + 124*S*HPL[{4, 1}, -S^2] + (20*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) + (3136*S*HPL[{2, 2, 1}, -S^2])/3 + 3088*S*HPL[{3, 1, 1}, -S^2] - 2000*S*HPL[{2, 1, 1, 1}, -S^2] + ((-256*Pi^2*S)/27 + (-67 - 50*S^2 + 9*S^4)/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1175 + 6423*S^2 + 1822*S^4))/(54*S*(1 + S^2)) + (-36 + 2757*S^2 + 2894*S^4 + 69*S^6)/(18*S^3) - (76*S*HPL[{3}, -S^2])/3 - (1568*S*HPL[{2, 1}, -S^2])/3 - (164*S*Zeta[3])/3) - (368*S*Zeta[5])/9) + Zeta[3]*((Pi^4*S*(2188 + 2283*S^2))/(216*(1 + S^2)) - (Pi^2*S*(-559 - 325*S^2 + 174*S^4))/(72*(1 + S^2)) - (S*(-1418 - 931*S^2 + 231*S^4))/(48*(1 + S^2)) - (92*S*Zeta[5])/3) + HPL[{2, 1}, -S^2]*((Pi^4*(-13957 - 27642*S^2 + 4221*S^4))/(1080*S*(1 + S^2)) + (237 - 26187*S^2 - 11369*S^4 - 57*S^6)/(48*S^3) + (Pi^2*(-36 - 8255*S^2 - 1079*S^4 + 36*S^6))/(72*S^3) - (2*(-655 - 1713*S^2 + 118*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (46*S*HPL[{3, 2}, -S^2])/3 - (44*S*HPL[{4, 1}, -S^2])/3 - (4*(-653 - 1692*S^2 + 137*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (8800*S*HPL[{2, 2, 1}, -S^2])/3 + 8904*S*HPL[{3, 1, 1}, -S^2] - (18272*S*HPL[{2, 1, 1, 1}, -S^2])/3 + (-2*Pi^2*S + (45 - 34*S^2 - 3*S^4)/(3*S))*Zeta[3] - 24*S*Zeta[5]) + HPL[{3}, -S^2]*((Pi^4*(1042 + 2651*S^2 + 1233*S^4))/(2160*S*(1 + S^2)) + (141 + 11705*S^2 + 23445*S^4 + 12303*S^6 - 90*S^8)/(96*S^3*(1 + S^2)) + (Pi^2*(24 + 1136*S^2 + 2737*S^4 + 1573*S^6 - 84*S^8))/(144*S^3*(1 + S^2)) + (2*(13 + 46*S^2 + 27*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (68*S*HPL[{5}, -S^2])/3 + ((73*Pi^2*S)/9 + (18 - 57*S^2 + 124*S^4 - 3*S^6)/(6*S^3))*HPL[{2, 1}, -S^2] + ((10 + 165*S^2 + 49*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (2*S*HPL[{3, 2}, -S^2])/3 + 24*S*HPL[{4, 1}, -S^2] + (2*(-2 - 107*S^2 + 9*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (44*S*HPL[{2, 2, 1}, -S^2])/3 - (20*S*HPL[{3, 1, 1}, -S^2])/3 + 104*S*HPL[{2, 1, 1, 1}, -S^2] + (-(Pi^2*S)/3 + (81 + 126*S^2 + 56*S^4 + 3*S^6)/(6*S*(1 + S^2)))*Zeta[3] + (58*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*((2425*Pi^6*S)/756 + ((1 + S^2)*(-133 + 20894*S^2 + 1483*S^4))/(48*S^3) + (Pi^4*(58074 + 115063*S^2 + 59222*S^4 + 1149*S^6))/(4320*S*(1 + S^2)) + (Pi^2*(-30 + 10721*S^2 + 21895*S^4 + 11683*S^6 + 475*S^8))/(144*S^3*(1 + S^2)) + ((434*Pi^2*S)/9 + (-1 + 1003*S^2 + 1028*S^4 + 16*S^6)/(12*S^3))*HPL[{2}, -S^2]^2 + 59*S*HPL[{2}, -S^2]^3 - (5*S*HPL[{3}, -S^2]^2)/3 + ((109*Pi^2*S)/18 + (-24 + 479*S^2 + 985*S^4 + 497*S^6 - 9*S^8)/(12*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((37 + 169*S^2 + 74*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (82*S*HPL[{6}, -S^2])/3 - 784*S*HPL[{2, 1}, -S^2]^2 + ((-1706*Pi^2*S)/9 + (18 - 1228*S^2 - 1271*S^4 - 9*S^6)/(3*S^3))*HPL[{3, 1}, -S^2] + (2*(22 + 149*S^2 + 13*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + ((68 + 575*S^2 - 51*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + S*HPL[{4, 2}, -S^2] - (128*S*HPL[{5, 1}, -S^2])/3 + ((1142*Pi^2*S)/3 + (2*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (12*(111 + 637*S^2 + 140*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) + 1416*S*HPL[{3, 2, 1}, -S^2] + 4332*S*HPL[{4, 1, 1}, -S^2] - (20*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 2992*S*HPL[{3, 1, 1, 1}, -S^2] + 6000*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(-2 - 149*S^2 + 109*S^4))/(18*S*(1 + S^2)) + (-65 - 95*S^2 - 23*S^4 + 15*S^6)/(6*S*(1 + S^2)))*Zeta[3] + 16*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(28 + 117*S^2 + 119*S^4))/(18*S*(1 + S^2)) + (-45 + 749*S^2 + 1587*S^4 + 779*S^6 - 30*S^8)/(12*S^3*(1 + S^2)) + 76*S*HPL[{2, 1}, -S^2] - (8*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((Pi^2*(-1175 - 6423*S^2 - 1822*S^4))/(18*S*(1 + S^2)) + (36 - 2757*S^2 - 2894*S^4 - 69*S^6)/(6*S^3) + 164*S*Zeta[3]) + HPL[{2}, -S^2]*((8953*Pi^4*S)/540 + (Pi^2*(-60 + 4387*S^2 + 4562*S^4 + 43*S^6))/(72*S^3) + (-104 + 6853*S^2 + 7204*S^4 + 215*S^6)/(24*S^3) + ((-23 - 149*S^2 - 12*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + 3*S*HPL[{4}, -S^2] - (2*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 784*S*HPL[{3, 1}, -S^2] + 1568*S*HPL[{2, 1, 1}, -S^2] + ((-15 - 101*S^2 - 4*S^4)*Zeta[3])/(S*(1 + S^2))) + (4*(3 - 10*S^2 + 33*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]*((14015*Pi^6*S)/4536 + (192 + 23713*S^2 + 40499*S^4 + 1745*S^6)/(96*S^3) + (Pi^2*(-172 + 2677*S^2 + 13500*S^4 + 10995*S^6 + 296*S^8))/(144*S^3*(1 + S^2)) + (Pi^4*(-832 + 3516*S^2 + 63538*S^4 + 59957*S^6 + 465*S^8))/(4320*S^3*(1 + S^2)) - (S*HPL[{3}, -S^2]^2)/3 + ((46*Pi^2*S)/9 + (2 - 6*S^2 + 142*S^4 + 159*S^6 - 3*S^8)/(12*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-27 - 94*S^2 - 50*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) + (62*S*HPL[{6}, -S^2])/3 - (2200*S*HPL[{2, 1}, -S^2]^2)/3 + ((-571*Pi^2*S)/3 + (2 - 19*S^2 - 2276*S^4 - 27*S^6)/(6*S^3))*HPL[{3, 1}, -S^2] + ((-4 + 397*S^2 + 211*S^4)*HPL[{3, 2}, -S^2])/(6*S*(1 + S^2)) + ((4 + 188*S^2 + 85*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) + (8*S*HPL[{4, 2}, -S^2])/3 - 24*S*HPL[{5, 1}, -S^2] + ((3422*Pi^2*S)/9 + (2*(-1 + 2*S^2 + 1126*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (2*(-653 - 1606*S^2 + 109*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(-1961 - 4925*S^2 + 336*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (2*S*HPL[{3, 1, 2}, -S^2])/3 + (4366*S*HPL[{3, 2, 1}, -S^2])/3 + (13280*S*HPL[{4, 1, 1}, -S^2])/3 + (4*(-653 - 1692*S^2 + 137*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (114712*S*HPL[{3, 1, 1, 1}, -S^2])/3 + (18272*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((73 + 49*S^2)/(12*S) + (Pi^2*(16 + 3*S^2 + 105*S^4))/(18*S*(1 + S^2)))*Zeta[3] + 16*S*Zeta[3]^2 + HPL[{3}, -S^2]*((Pi^2*(-18 - 101*S^2 + 57*S^4))/(36*S*(1 + S^2)) + (-2 - 39*S^2 + 274*S^4 - 75*S^6)/(24*S^3) - (22*S*HPL[{2, 1}, -S^2])/3 - (26*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((Pi^2*(-559 - 1320*S^2 + 107*S^4))/(9*S*(1 + S^2)) + (-12 - 4051*S^2 + 220*S^4 - 15*S^6)/(12*S^3) + 4*S*Zeta[3]) + ((43 + 196*S^2 + 215*S^4)*Zeta[5])/(3*S*(1 + S^2))) + (S*(568 + 583*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*(((1 + S^2)*(127 + 45531*S^2 + 3442*S^4))/(64*S^3) + (Pi^6*(70951 + 353796*S^2 + 137345*S^4))/(45360*S*(1 + S^2)) + (Pi^2*(-208 + 27411*S^2 + 56873*S^4 + 30937*S^6 + 1555*S^8))/(288*S^3*(1 + S^2)) + (Pi^4*(416 + 124425*S^2 + 248359*S^4 + 130711*S^6 + 4353*S^8))/(8640*S^3*(1 + S^2)) + ((308 + 1763*S^2 + 393*S^4)*HPL[{2}, -S^2]^3)/(18*S*(1 + S^2)) + ((-4 - 13*S^2 + S^4)*HPL[{3}, -S^2]^2)/(6*S*(1 + S^2)) + ((34*Pi^2*S)/9 + (-27 + 375*S^2 + 730*S^4 + 297*S^6 - 39*S^8)/(6*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((35 + 191*S^2 + 74*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) - (22*S*HPL[{7}, -S^2])/3 - (2*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((140*Pi^2*S)/9 + (8 - 11*S^2 - 45*S^4 - 25*S^6 + 5*S^8)/(3*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((311*Pi^2*S)/9 + (78 - 545*S^2 - 1291*S^4 - 647*S^6 + 45*S^8)/(6*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-2 + 27*S^2 + 23*S^4)*HPL[{4, 2}, -S^2])/(6*S*(1 + S^2)) - (38*S*HPL[{4, 3}, -S^2])/3 - (2*(41 + 164*S^2 + 59*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - (104*S*HPL[{5, 2}, -S^2])/3 - (304*S*HPL[{6, 1}, -S^2])/3 + ((3472*Pi^2*S)/9 + (2*(-1 + 1003*S^2 + 1028*S^4 + 16*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + ((3452*Pi^2*S)/3 + (2*(-20 + 3234*S^2 + 3327*S^4 + 41*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] - (4*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) + (4*(309 + 1763*S^2 + 392*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) - 126*S*HPL[{3, 2, 2}, -S^2] - (1184*S*HPL[{3, 3, 1}, -S^2])/3 + (2*(1918 + 10897*S^2 + 2481*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 394*S*HPL[{4, 1, 2}, -S^2] - 1202*S*HPL[{4, 2, 1}, -S^2] - (7040*S*HPL[{5, 1, 1}, -S^2])/3 + ((-2284*Pi^2*S)/3 - (4*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1, 1}, -S^2] - 2832*S*HPL[{2, 2, 2, 1}, -S^2] - (8*(337 + 1909*S^2 + 450*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 8800*S*HPL[{3, 1, 1, 2}, -S^2] + 8800*S*HPL[{3, 1, 2, 1}, -S^2] + 17296*S*HPL[{3, 2, 1, 1}, -S^2] + 51720*S*HPL[{4, 1, 1, 1}, -S^2] + (40*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 6272*S*HPL[{2, 1, 2, 1, 1}, -S^2] - 18816*S*HPL[{2, 2, 1, 1, 1}, -S^2] - 31648*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 12000*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((-95*Pi^4*S)/108 + (-54 - 59*S^2 + 13*S^6)/(3*S*(1 + S^2)) + (Pi^2*(127 + 318*S^2 + 261*S^4 + 54*S^6))/(36*S*(1 + S^2)))*Zeta[3] + (2*(19 + 89*S^2 + 46*S^4)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((Pi^2*(1175 + 6423*S^2 + 1822*S^4))/(9*S*(1 + S^2)) + (-36 + 2757*S^2 + 2894*S^4 + 69*S^6)/(3*S^3) - 328*S*Zeta[3]) + HPL[{2}, -S^2]^2*(((1 + S^2)*(1 + 679*S^2 + 24*S^4))/(8*S^3) + (Pi^2*(139 + 771*S^2 + 198*S^4))/(9*S*(1 + S^2)) - 16*S*HPL[{3}, -S^2] - 354*S*HPL[{2, 1}, -S^2] - 40*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(136 + 605*S^2 + 251*S^4))/(36*S*(1 + S^2)) + (-10 + 1907*S^2 + 3635*S^4 + 1693*S^6 - 89*S^8)/(24*S^3*(1 + S^2)) - 6*S*HPL[{2, 1}, -S^2] + (38*S*Zeta[3])/3) + HPL[{3, 1}, -S^2]*((Pi^2*(-584 - 3201*S^2 - 911*S^4))/(9*S*(1 + S^2)) + (21 - 1396*S^2 - 2868*S^4 - 1480*S^6 - 21*S^8)/(3*S^3*(1 + S^2)) + (496*S*Zeta[3])/3) + HPL[{3}, -S^2]*((47*Pi^4*S)/135 + (-105 + 3005*S^2 + 6015*S^4 + 2883*S^6 - 86*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(-17 + 208*S^2 + 482*S^4 + 242*S^6 - 5*S^8))/(18*S^3*(1 + S^2)) + 8*S*HPL[{4}, -S^2] + (2*(23 + 149*S^2 + 12*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (212*S*HPL[{3, 1}, -S^2])/3 - 152*S*HPL[{2, 1, 1}, -S^2] - (2*S*(9 + 5*S^2)*Zeta[3])/(3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-8953*Pi^4*S)/270 + (104 - 6853*S^2 - 7204*S^4 - 215*S^6)/(12*S^3) + (Pi^2*(60 - 4387*S^2 - 4562*S^4 - 43*S^6))/(36*S^3) + 1568*S*HPL[{3, 1}, -S^2] + 3136*S*HPL[{2, 1, 1}, -S^2] + (2*(15 + 101*S^2 + 4*S^4)*Zeta[3])/(S*(1 + S^2))) + ((-68*Pi^2*S)/9 + (158 + 477*S^2 + 386*S^4 + 71*S^6)/(6*S*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(6995 + 36751*S^2 + 11850*S^4))/(1080*S*(1 + S^2)) + (Pi^2*(-144 + 9985*S^2 + 10376*S^4 + 199*S^6))/(144*S^3) + (-243 + 19114*S^2 + 20135*S^4 + 714*S^6)/(48*S^3) + ((-70*Pi^2*S)/9 + (-9 + 20*S^2 + 31*S^4 - 6*S^6)/(6*S^3))*HPL[{3}, -S^2] + ((8 + 17*S^2 - 9*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - (34*S*HPL[{5}, -S^2])/3 + ((-1736*Pi^2*S)/9 + (1 - 1003*S^2 - 1028*S^4 - 16*S^6)/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(331 + 1912*S^2 + 405*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + (190*S*HPL[{3, 2}, -S^2])/3 + 198*S*HPL[{4, 1}, -S^2] + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 1416*S*HPL[{2, 2, 1}, -S^2] - 4400*S*HPL[{3, 1, 1}, -S^2] - 3136*S*HPL[{2, 1, 1, 1}, -S^2] + ((-118*Pi^2*S)/9 + ((-11 + S^2)*(1 + S^2))/(2*S))*Zeta[3] - (124*S*Zeta[5])/3) - 30*S*Zeta[7])) + Log[T]*((-135211*Pi^8*S)/136080 - (21*(1 + 248*S^2))/(32*S) + (Pi^2*(1392 - 25001*S^2 - 57*S^4))/(288*S) - (Pi^6*S*(434284 + 437401*S^2 + 5035*S^4))/(90720*(1 + S^2)) + (Pi^4*(2496 - 171523*S^2 - 171898*S^4 + 1305*S^6))/(8640*S*(1 + S^2)) - (S*HPL[{0}, S^2]^8)/48 - (4*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^7)/(9*S*(1 + S^2)) - (8*S*HPL[{1}, -S^2]^8)/3 + HPL[{0}, S^2]^7*(-(S*(36 + 29*S^2))/(144*(1 + S^2)) - (7*S*HPL[{1}, -S^2])/72) + ((-680*Pi^2*S)/27 + (10 + 132*S^2 - 888*S^4 - 5*S^6)/(18*S^3))*HPL[{2}, -S^2]^3 - (167*S*HPL[{2}, -S^2]^4)/9 + HPL[{1}, -S^2]^6*((-92*Pi^2*S)/9 + (-155 - 158*S^2 - 3*S^4)/(9*S) - (20*S*HPL[{2}, -S^2])/3) + HPL[{0}, S^2]^6*((-8*Pi^2*S)/27 - (S*(269 + 274*S^2 + S^4))/(288*(1 + S^2)) + ((-24 - 114*S^2 - 49*S^4)*HPL[{1}, -S^2])/(72*S*(1 + S^2)) - (41*S*HPL[{1}, -S^2]^2)/72 - (19*S*HPL[{2}, -S^2])/36) + (-11*Pi^2*S + (-1 - 34*S^2 - 21*S^4 + 5*S^6 - 3*S^8)/(6*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 - 8*S*HPL[{4}, -S^2]^2 + ((-244*Pi^2*S)/9 - (5*(-24 + 250*S^2 + 930*S^4 + 655*S^6 + S^8))/(6*S^3*(1 + S^2)))*HPL[{6}, -S^2] - (2*(255 + 2248*S^2 + 1747*S^4)*HPL[{7}, -S^2])/(3*S*(1 + S^2)) - (3112*S*HPL[{8}, -S^2])/3 + ((2804*Pi^2*S)/9 - (2*(1 - 130*S^2 - 950*S^4 + 2*S^6))/(3*S^3))*HPL[{2, 1}, -S^2]^2 - (2752*S*HPL[{3, 1}, -S^2]^2)/3 + ((-406*Pi^2*S)/9 + (8 - 110*S^2 - 294*S^4 - 185*S^6 - 25*S^8)/(6*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] - (2*(13 + 85*S^2 + 126*S^4)*HPL[{4, 3}, -S^2])/(3*S*(1 + S^2)) + ((-1574*Pi^2*S)/9 - (4*(10 - 111*S^2 - 282*S^4 - 158*S^6 + 11*S^8))/(3*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((-123 - 376*S^2 - 481*S^4)*HPL[{5, 2}, -S^2])/(3*S*(1 + S^2)) + (32*S*HPL[{5, 3}, -S^2])/3 + (10*(17 + 217*S^2 + 173*S^4)*HPL[{6, 1}, -S^2])/(3*S*(1 + S^2)) + (172*S*HPL[{6, 2}, -S^2])/3 + (2248*S*HPL[{7, 1}, -S^2])/3 - 3680*S*HPL[{2, 1, 1}, -S^2]^2 + ((238*Pi^2*S)/9 + (4*(-1 - 14*S^2 + 6*S^4 + 19*S^6 + 2*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + (-578*Pi^2*S - (4*(-9 - 128*S^2 + 750*S^4 + 874*S^6 + 3*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((6 + 4537*S^2 + 385*S^4)*HPL[{3, 2, 2}, -S^2])/(3*S*(1 + S^2)) + (8*(-13 + 1698*S^2 + 121*S^4)*HPL[{3, 3, 1}, -S^2])/(3*S*(1 + S^2)) - (1340*S*HPL[{3, 3, 2}, -S^2])/3 + ((-15068*Pi^2*S)/9 - (2*(-84 - 660*S^2 + 4972*S^4 + 5581*S^6 + 21*S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + (2*(-43 + 6608*S^2 + 408*S^4)*HPL[{4, 1, 2}, -S^2])/(3*S*(1 + S^2)) + (2264*S*HPL[{4, 1, 3}, -S^2])/3 + (2*(-151 + 20588*S^2 + 1284*S^4)*HPL[{4, 2, 1}, -S^2])/(3*S*(1 + S^2)) - 316*S*HPL[{4, 2, 2}, -S^2] + 2584*S*HPL[{4, 3, 1}, -S^2] + (4*(-237 + 20557*S^2 + 790*S^4)*HPL[{5, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (4684*S*HPL[{5, 1, 2}, -S^2])/3 + (31804*S*HPL[{5, 2, 1}, -S^2])/3 + (80440*S*HPL[{6, 1, 1}, -S^2])/3 - (8*(-511 - 610*S^2 + 87*S^4)*HPL[{2, 2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + ((10736*Pi^2*S)/9 + (16*(-9 - 53*S^2 + 506*S^4 + 3*S^6))/(3*S^3))*HPL[{3, 1, 1, 1}, -S^2] + (16*(-757 - 1410*S^2 + 121*S^4)*HPL[{3, 1, 1, 2}, -S^2])/(3*S*(1 + S^2)) + (16*(-757 - 1410*S^2 + 121*S^4)*HPL[{3, 1, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (484*S*HPL[{3, 1, 2, 2}, -S^2])/3 + (8*(-3047 - 4650*S^2 + 503*S^4)*HPL[{3, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (484*S*HPL[{3, 2, 1, 2}, -S^2])/3 + (10108*S*HPL[{3, 2, 2, 1}, -S^2])/3 + 10592*S*HPL[{3, 3, 1, 1}, -S^2] + (16*(-4579 - 7147*S^2 + 804*S^4)*HPL[{4, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (3256*S*HPL[{4, 1, 1, 2}, -S^2])/3 + (28520*S*HPL[{4, 1, 2, 1}, -S^2])/3 + (92072*S*HPL[{4, 2, 1, 1}, -S^2])/3 + (177056*S*HPL[{5, 1, 1, 1}, -S^2])/3 + ((-23840*Pi^2*S)/9 - (8*(-30 - 163*S^2 + 2137*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (64*(-130 - 397*S^2 + 27*S^4)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (64*(-130 - 397*S^2 + 27*S^4)*HPL[{2, 2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + (21184*S*HPL[{2, 2, 1, 2, 1}, -S^2])/3 + 21184*S*HPL[{2, 2, 2, 1, 1}, -S^2] - (16*(-2609 - 9131*S^2 + 558*S^4)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (125216*S*HPL[{3, 1, 1, 1, 2}, -S^2])/3 - 69984*S*HPL[{3, 1, 1, 2, 1}, -S^2] - (252320*S*HPL[{3, 1, 2, 1, 1}, -S^2])/3 - 175904*S*HPL[{3, 2, 1, 1, 1}, -S^2] - 525824*S*HPL[{4, 1, 1, 1, 1}, -S^2] - (160*(-37 - 44*S^2 + 8*S^4)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 12800*S*HPL[{3, 1, 1, 1, 1, 1}, -S^2] - 31360*S*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2] + (-2*Pi^2*S + (S*(20 + 7*S^2 + 9*S^4))/(3*(1 + S^2)))*Zeta[3]^2 + HPL[{4, 1}, -S^2]*((Pi^2*(79 - 3076*S^2 + 372*S^4))/(9*S*(1 + S^2)) + (20 - 130*S^2 - 2731*S^4 - 1012*S^6)/(6*S^3) - (1552*S*Zeta[3])/3) + HPL[{2, 1, 1, 1}, -S^2]*((-4*Pi^2*(-1119 - 1834*S^2 + 227*S^4))/(9*S*(1 + S^2)) - (4*(-9 - 1827*S^2 + 209*S^4 + 99*S^6))/(3*S^3) - (640*S*Zeta[3])/3) + HPL[{3, 2}, -S^2]*((Pi^2*(35 - 1897*S^2 + 152*S^4))/(18*S*(1 + S^2)) + (-4 - 483*S^2 - 2110*S^4 - 637*S^6)/(12*S^3) - 164*S*Zeta[3]) + HPL[{2, 2, 1}, -S^2]*((2*Pi^2*(-1049 - 2709*S^2 + 254*S^4))/(9*S*(1 + S^2)) - (2*(6 + 1792*S^2 + 150*S^4 + 87*S^6))/(3*S^3) - (352*S*Zeta[3])/3) + HPL[{3, 1, 1}, -S^2]*((2*Pi^2*(-3172 - 7025*S^2 + 659*S^4))/(9*S*(1 + S^2)) + (-48 - 10747*S^2 - 120*S^4 - 177*S^6)/(3*S^3) - (208*S*Zeta[3])/3) + HPL[{5}, -S^2]*((Pi^2*(-45 - 321*S^2 - 358*S^4))/(9*S*(1 + S^2)) + (-60 - 1533*S^2 - 2956*S^4 - 61*S^6)/(12*S^3) - 4*S*HPL[{2, 1}, -S^2] - 8*S*Zeta[3]) + HPL[{0}, S^2]^5*(-(Pi^2*S*(5765 + 4484*S^2))/(2160*(1 + S^2)) - (S*(1306 + 1369*S^2 + 43*S^4))/(288*(1 + S^2)) + ((-605 - 2886*S^2 - 1189*S^4)*HPL[{1}, -S^2]^2)/(360*S*(1 + S^2)) - (91*S*HPL[{1}, -S^2]^3)/45 + ((-15 - 1700*S^2 - 1224*S^4)*HPL[{2}, -S^2])/(360*S*(1 + S^2)) + HPL[{1}, -S^2]*((-427*Pi^2*S)/360 + (-525 - 1014*S^2 - 519*S^4 - 10*S^6)/(144*S*(1 + S^2)) - (461*S*HPL[{2}, -S^2])/180) + (S*HPL[{3}, -S^2])/6 - (5*S*HPL[{2, 1}, -S^2])/9 - (3*S*Zeta[3])/2) + HPL[{1}, -S^2]^5*((Pi^2*(-265 - 1477*S^2 - 384*S^4))/(27*S*(1 + S^2)) - ((1 + S^2)*(3 + 967*S^2 + 42*S^4))/(18*S^3) - (2*(26 + 121*S^2 + 65*S^4)*HPL[{2}, -S^2])/(3*S*(1 + S^2)) + (320*S*HPL[{3}, -S^2])/3 + 40*S*HPL[{2, 1}, -S^2] + 80*S*Zeta[3]) + HPL[{3, 1}, -S^2]*((3275*Pi^4*S)/54 + (-198 + 463*S^2 + 8662*S^4 + 97*S^6)/(12*S^3) + (Pi^2*(-72 - 161*S^2 + 4082*S^4 + 4168*S^6 + 25*S^8))/(18*S^3*(1 + S^2)) + (9056*S*HPL[{2, 1, 1}, -S^2])/3 - (8*(4 + 263*S^2 + 4*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^4*((-1237*Pi^4*S)/90 + (Pi^2*(-1072 - 1081*S^2 - 15*S^4))/(27*S) - ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(12*S^3) + ((-314*Pi^2*S)/9 + (5 - 283*S^2 - 283*S^4 + 5*S^6)/(3*S^3))*HPL[{2}, -S^2] - (392*S*HPL[{2}, -S^2]^2)/3 - (2*(-61 - 439*S^2 + 22*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + (284*S*HPL[{4}, -S^2])/3 + (10*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (32*S*HPL[{3, 1}, -S^2])/3 - 200*S*HPL[{2, 1, 1}, -S^2] - (10*(-29 - 203*S^2 + 6*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-17677*Pi^4*S)/135 + (86 - 246*S^2 - 4314*S^4 - 37*S^6)/(3*S^3) + (Pi^2*(60 + 129*S^2 - 4226*S^4 - 4300*S^6 - 29*S^8))/(9*S^3*(1 + S^2)) + (8*(9 + 514*S^2 + 13*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{2}, -S^2]^2*((-1609*Pi^4*S)/108 + (-406 - 4055*S^2 + 36*S^4)/(24*S) + (Pi^2*(4 - 219*S^2 - 3825*S^4 - 5*S^6))/(72*S^3) + ((40 + 1375*S^2 + 123*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) + (388*S*HPL[{4}, -S^2])/3 + ((511 + 610*S^2 - 87*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + (1090*S*HPL[{3, 1}, -S^2])/3 - (2648*S*HPL[{2, 1, 1}, -S^2])/3 + ((-9 + 467*S^2 + 38*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{4}, -S^2]*((20*Pi^4*S)/9 + (Pi^2*(48 - 267*S^2 - 687*S^4 + 4*S^6))/(36*S^3) + (-114 - 2599*S^2 - 4268*S^4 - 1254*S^6 + 433*S^8)/(24*S^3*(1 + S^2)) - (2*(45 + 205*S^2 + 47*S^4)*HPL[{2, 1}, -S^2])/(S*(1 + S^2)) - (1528*S*HPL[{3, 1}, -S^2])/3 + (3064*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(11 + 28*S^2 + 48*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^4*((-10279*Pi^4*S)/6480 - (Pi^2*S*(6369 + 6469*S^2 + 10*S^4))/(864*(1 + S^2)) + (90 - 9415*S^2 - 8990*S^4 + 563*S^6)/(576*S*(1 + S^2)) + ((-175 - 873*S^2 - 326*S^4)*HPL[{1}, -S^2]^3)/(36*S*(1 + S^2)) - (31*S*HPL[{1}, -S^2]^4)/6 + ((-91*Pi^2*S)/18 + (30 - 9*S^2 - 2128*S^4 - 2085*S^6 + 6*S^8)/(144*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (115*S*HPL[{2}, -S^2]^2)/18 + HPL[{1}, -S^2]^2*((-391*Pi^2*S)/72 + (-2091 - 4039*S^2 - 2009*S^4 - S^6)/(144*S*(1 + S^2)) - (245*S*HPL[{2}, -S^2])/18) + ((-5 - 22*S^2 - 9*S^4)*HPL[{3}, -S^2])/(24*S*(1 + S^2)) - 2*S*HPL[{4}, -S^2] + ((234 + 407*S^2 - 72*S^4)*HPL[{2, 1}, -S^2])/(18*S*(1 + S^2)) + (505*S*HPL[{3, 1}, -S^2])/18 - 58*S*HPL[{2, 1, 1}, -S^2] - (S*(401 + 363*S^2)*Zeta[3])/(36*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(-415 - 2013*S^2 - 816*S^4))/(144*S*(1 + S^2)) + (-15 - 4240*S^2 - 8218*S^4 - 4100*S^6 - 11*S^8)/(288*S^3*(1 + S^2)) + ((-456 - 2331*S^2 - 895*S^4)*HPL[{2}, -S^2])/(72*S*(1 + S^2)) - (2*S*HPL[{3}, -S^2])/3 + (245*S*HPL[{2, 1}, -S^2])/9 - (19*S*Zeta[3])/9)) + (-(Pi^2*S*(-166 + 235*S^2))/(9*(1 + S^2)) + (S*(-489 + 362*S^2))/6)*Zeta[5] + HPL[{0}, S^2]^3*(-(Pi^4*S*(30955 + 22947*S^2))/(3240*(1 + S^2)) - (Pi^2*S*(11089 + 11507*S^2 + 278*S^4))/(432*(1 + S^2)) + (420 - 28604*S^2 - 30245*S^4 - 1093*S^6)/(288*S*(1 + S^2)) + ((-180 - 923*S^2 - 313*S^4)*HPL[{1}, -S^2]^4)/(18*S*(1 + S^2)) - (86*S*HPL[{1}, -S^2]^5)/9 + ((15 - 1396*S^2 - 851*S^4)*HPL[{2}, -S^2]^2)/(36*S*(1 + S^2)) + HPL[{1}, -S^2]^3*((-397*Pi^2*S)/27 + (-1000 - 1963*S^2 - 998*S^4 - 11*S^6)/(27*S*(1 + S^2)) - (392*S*HPL[{2}, -S^2])/9) + ((7*Pi^2*S)/9 + (-261 - 536*S^2 - 252*S^4 + 3*S^6)/(36*S*(1 + S^2)))*HPL[{3}, -S^2] + ((-25 - 198*S^2 - 127*S^4)*HPL[{4}, -S^2])/(18*S*(1 + S^2)) + (10*S*HPL[{5}, -S^2])/3 + ((-77*Pi^2*S)/27 + (1835 - 10*S^2 + S^4)/(18*S))*HPL[{2, 1}, -S^2] + ((-7 + 1522*S^2 + 945*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) + (14*S*HPL[{3, 2}, -S^2])/9 + (4*S*HPL[{4, 1}, -S^2])/9 - (2*(-6 + 1579*S^2 + 997*S^4)*HPL[{2, 1, 1}, -S^2])/(9*S*(1 + S^2)) + 4*S*HPL[{2, 2, 1}, -S^2] + (52*S*HPL[{3, 1, 1}, -S^2])/3 - 24*S*HPL[{2, 1, 1, 1}, -S^2] + (-5*Pi^2*S + (S*(-271 - 264*S^2 + 15*S^4))/(18*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-9 - 3279*S^2 - 2221*S^4))/(108*S*(1 + S^2)) + (90 - 773*S^2 - 4167*S^4 - 40*S^6)/(72*S^3) - (8*S*HPL[{3}, -S^2])/9 - 2*S*HPL[{2, 1}, -S^2] + (10*S*Zeta[3])/9) + HPL[{1}, -S^2]^2*((Pi^2*(-1145 - 5655*S^2 - 2128*S^4))/(108*S*(1 + S^2)) + (-15 - 4270*S^2 - 8436*S^4 - 4354*S^6 - 93*S^8)/(72*S^3*(1 + S^2)) + ((-495 - 2578*S^2 - 907*S^4)*HPL[{2}, -S^2])/(18*S*(1 + S^2)) - (8*S*HPL[{3}, -S^2])/3 + (392*S*HPL[{2, 1}, -S^2])/3 + (10*S*Zeta[3])/9) + HPL[{1}, -S^2]*((-2002*Pi^4*S)/405 + (Pi^2*(-4625 - 8996*S^2 - 4591*S^4 - 72*S^6))/(216*S*(1 + S^2)) + (15 - 5090*S^2 - 10276*S^4 - 5398*S^6 - 163*S^8)/(72*S^3*(1 + S^2)) + ((-1049*Pi^2*S)/54 + (30 - 1965*S^2 - 2032*S^4 - 13*S^6)/(36*S^3))*HPL[{2}, -S^2] - (280*S*HPL[{2}, -S^2]^2)/9 - (2*(11 + 60*S^2 + 37*S^4)*HPL[{3}, -S^2])/(9*S*(1 + S^2)) - (46*S*HPL[{4}, -S^2])/9 + ((495 + 2578*S^2 + 907*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (1168*S*HPL[{3, 1}, -S^2])/9 - (784*S*HPL[{2, 1, 1}, -S^2])/3 - (2*(21 + 75*S^2 + 59*S^4)*Zeta[3])/(9*S*(1 + S^2))) - (208*S*Zeta[5])/9) + HPL[{3}, -S^2]*((Pi^4*(-518 + 6037*S^2 - 1825*S^4))/(1080*S*(1 + S^2)) + (-141 - 2132*S^2 - 729*S^4 + 1890*S^6)/(48*S^3) + (Pi^2*(-24 - 260*S^2 - 229*S^4 + 455*S^6 + 400*S^8))/(72*S^3*(1 + S^2)) + (2*(6 + 38*S^2 + 83*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + (40*S*HPL[{5}, -S^2])/3 + ((178*Pi^2*S)/9 + (2*(-9 - 298*S^2 - 25*S^4 + 10*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] - (2*(-58 + 955*S^2 + 23*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 300*S*HPL[{3, 2}, -S^2] + (368*S*HPL[{4, 1}, -S^2])/3 + (8*(-21 + 488*S^2 + 14*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 328*S*HPL[{2, 2, 1}, -S^2] + (1240*S*HPL[{3, 1, 1}, -S^2])/3 + 512*S*HPL[{2, 1, 1, 1}, -S^2] + ((110*Pi^2*S)/9 + (-41 + 31*S^2 + 61*S^4 + 17*S^6)/(3*S*(1 + S^2)))*Zeta[3] + 4*S*Zeta[5]) + HPL[{2, 1}, -S^2]*((Pi^4*(13505 + 23150*S^2 - 3618*S^4))/(540*S*(1 + S^2)) + (-237 + 17177*S^2 + 1125*S^4 - 1113*S^6)/(24*S^3) + (Pi^2*(36 + 7343*S^2 + 7133*S^4 - 465*S^6 - 243*S^8))/(36*S^3*(1 + S^2)) + (4*(-469 - 1586*S^2 + 59*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) + 172*S*HPL[{3, 2}, -S^2] - (112*S*HPL[{4, 1}, -S^2])/3 + (32*(-130 - 397*S^2 + 27*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (10592*S*HPL[{2, 2, 1}, -S^2])/3 - 10080*S*HPL[{3, 1, 1}, -S^2] + 7360*S*HPL[{2, 1, 1, 1}, -S^2] + ((-28*Pi^2*S)/3 + (2*(-257 - 278*S^2 + 4*S^4 + S^6))/(3*S*(1 + S^2)))*Zeta[3] + 32*S*Zeta[5]) + Zeta[3]*((Pi^2*S*(191 + 255*S^2))/36 + (S*(-327 + 371*S^2))/8 - (Pi^4*S*(-1169 + 2101*S^2))/(540*(1 + S^2)) + (184*S*Zeta[5])/3) + HPL[{1}, -S^2]^3*((Pi^4*(-15616 - 85219*S^2 - 25071*S^4))/(1620*S*(1 + S^2)) - ((1 + S^2)*(-104 + 14397*S^2 + 935*S^4))/(36*S^3) + (Pi^2*(-30 - 8797*S^2 - 9014*S^4 - 279*S^6))/(108*S^3) - (2*(331 + 1912*S^2 + 405*S^4)*HPL[{2}, -S^2]^2)/(9*S*(1 + S^2)) + ((820*Pi^2*S)/9 + (2*(17 + 204*S^2 + 223*S^4 + 28*S^6))/(9*S^3))*HPL[{3}, -S^2] - (4*(-37 - 364*S^2 + 99*S^4)*HPL[{4}, -S^2])/(9*S*(1 + S^2)) + (248*S*HPL[{5}, -S^2])/3 + ((1256*Pi^2*S)/9 - (4*(5 - 283*S^2 - 283*S^4 + 5*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (8*(148 + 595*S^2 + 471*S^4)*HPL[{3, 1}, -S^2])/(9*S*(1 + S^2)) - 880*S*HPL[{3, 2}, -S^2] - (9056*S*HPL[{4, 1}, -S^2])/3 - (40*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - (6272*S*HPL[{2, 2, 1}, -S^2])/3 - (12416*S*HPL[{3, 1, 1}, -S^2])/3 + 800*S*HPL[{2, 1, 1, 1}, -S^2] + ((220*Pi^2*S)/3 + (4*(181 + 208*S^2 + 15*S^4))/(9*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-931 - 4762*S^2 - 1947*S^4))/(27*S*(1 + S^2)) + (2*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 + 440*S*HPL[{3}, -S^2] + (3136*S*HPL[{2, 1}, -S^2])/3 + (1312*S*Zeta[3])/3) + (1072*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*((-17153*Pi^6*S)/2520 - ((1 + S^2)*(-133 + 20894*S^2 + 1483*S^4))/(24*S^3) + (Pi^4*(-26491 - 53170*S^2 - 26933*S^4 - 332*S^6))/(1080*S*(1 + S^2)) + (Pi^2*(15 - 4984*S^2 - 5200*S^4 - 209*S^6))/(36*S^3) + ((-319*Pi^2*S)/3 + (1 - 1003*S^2 - 1028*S^4 - 16*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 - (62*S*HPL[{2}, -S^2]^3)/3 - 74*S*HPL[{3}, -S^2]^2 + ((401*Pi^2*S)/9 + (12 - 197*S^2 - 418*S^4 - 221*S^6)/(3*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(79 + 232*S^2 + 339*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - 70*S*HPL[{6}, -S^2] + 1568*S*HPL[{2, 1}, -S^2]^2 + (152*Pi^2*S - (2*(18 - 799*S^2 - 805*S^4 + 12*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] + (4*(-164 - 1145*S^2 + 9*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (4*(-532 - 3799*S^2 + 129*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - 234*S*HPL[{4, 2}, -S^2] - 1168*S*HPL[{5, 1}, -S^2] + ((-1256*Pi^2*S)/3 + (4*(5 - 283*S^2 - 283*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1}, -S^2] - (8*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (8*(270 + 1473*S^2 + 427*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - 496*S*HPL[{3, 2, 1}, -S^2] - 352*S*HPL[{4, 1, 1}, -S^2] + (40*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(S*(1 + S^2)) - 128*S*HPL[{3, 1, 1, 1}, -S^2] - 2400*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((-10*Pi^2*(-5 - 36*S^2 + 2*S^4))/(3*S*(1 + S^2)) + (903 + 1076*S^2 + 141*S^4)/(6*S))*Zeta[3] - 40*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((-6*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 + (Pi^2*(931 + 4762*S^2 + 1947*S^4))/(9*S*(1 + S^2)) - 1312*S*Zeta[3]) + HPL[{3}, -S^2]*((Pi^2*(173 + 1260*S^2 - 143*S^4))/(9*S*(1 + S^2)) + (45 + 239*S^2 + 343*S^4 + 141*S^6)/(6*S^3) - 1320*S*HPL[{2, 1}, -S^2] + 96*S*Zeta[3]) + HPL[{2}, -S^2]*((-4421*Pi^4*S)/180 + ((1 + S^2)*(104 - 4309*S^2 + 197*S^4))/(12*S^3) + (Pi^2*(30 - 1797*S^2 - 3722*S^4 - 1857*S^6 + 14*S^8))/(18*S^3*(1 + S^2)) - (10*(-33 - 229*S^2 + 2*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) + 226*S*HPL[{4}, -S^2] + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 1568*S*HPL[{3, 1}, -S^2] - 3136*S*HPL[{2, 1, 1}, -S^2] - (2*(-151 - 1132*S^2 + 3*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (2*(-36 - 267*S^2 + 37*S^4)*Zeta[5])/(S*(1 + S^2))) + HPL[{2}, -S^2]*((-5387*Pi^6*S)/945 + (-192 - 6393*S^2 - 21491*S^4 - 57*S^6)/(48*S^3) + (Pi^4*(832 + 128*S^2 - 56506*S^4 - 55691*S^6 - 403*S^8))/(2160*S^3*(1 + S^2)) + (Pi^2*(172 - 709*S^2 - 9691*S^4 - 8839*S^6 - 77*S^8))/(72*S^3*(1 + S^2)) - (224*S*HPL[{3}, -S^2]^2)/3 + ((122*Pi^2*S)/3 + (-2 + 180*S^2 - 46*S^4 + 17*S^6)/(6*S^3))*HPL[{4}, -S^2] - (2*(-16 + 95*S^2 + 210*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - 44*S*HPL[{6}, -S^2] + (2648*S*HPL[{2, 1}, -S^2]^2)/3 + ((2542*Pi^2*S)/9 - (2*(1 - 166*S^2 - 913*S^4 + 5*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] + ((-32 - 2441*S^2 - 219*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) - (2*(-5 + 1170*S^2 + 76*S^4)*HPL[{4, 1}, -S^2])/(S*(1 + S^2)) - 264*S*HPL[{4, 2}, -S^2] - (3508*S*HPL[{5, 1}, -S^2])/3 + ((-5608*Pi^2*S)/9 + (4*(1 - 130*S^2 - 950*S^4 + 2*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(-511 - 610*S^2 + 87*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (4*(-1491 - 2806*S^2 + 233*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 156*S*HPL[{3, 1, 2}, -S^2] - (4876*S*HPL[{3, 2, 1}, -S^2])/3 - (12968*S*HPL[{4, 1, 1}, -S^2])/3 - (32*(-130 - 397*S^2 + 27*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (136160*S*HPL[{3, 1, 1, 1}, -S^2])/3 - 7360*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(10 + 531*S^2 - 18*S^4))/(9*S*(1 + S^2)) + (-1 + 661*S^2 + 767*S^4 + 153*S^6)/(6*S*(1 + S^2)))*Zeta[3] - 28*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(1049 + 2709*S^2 - 254*S^4))/(9*S*(1 + S^2)) + (6 + 1792*S^2 + 150*S^4 + 87*S^6)/(3*S^3) + (176*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(-40 + 923*S^2 - 79*S^4))/(18*S*(1 + S^2)) + (2 + 201*S^2 + 1148*S^4 + 347*S^6)/(12*S^3) - 164*S*HPL[{2, 1}, -S^2] + (260*S*Zeta[3])/3) - (2*(7 - 246*S^2 + 152*S^4)*Zeta[5])/(3*S*(1 + S^2))) + HPL[{0}, S^2]^2*((-147719*Pi^6*S)/45360 + (696 - 23099*S^2 - 57*S^4)/(96*S) - (Pi^4*S*(5907 + 5982*S^2 + 23*S^4))/(360*(1 + S^2)) + (Pi^2*(180 - 18307*S^2 - 18046*S^4 + 489*S^6))/(288*S*(1 + S^2)) + ((-118 - 637*S^2 - 195*S^4)*HPL[{1}, -S^2]^5)/(9*S*(1 + S^2)) - 12*S*HPL[{1}, -S^2]^6 + ((-293*Pi^2*S)/9 + (2 + 41*S^2 - 1925*S^4 - 9*S^6)/(24*S^3))*HPL[{2}, -S^2]^2 - (349*S*HPL[{2}, -S^2]^3)/9 + HPL[{1}, -S^2]^4*((-76*Pi^2*S)/3 + (-1963 - 1954*S^2 - 15*S^4)/(36*S) - (239*S*HPL[{2}, -S^2])/3) + (8*S*HPL[{3}, -S^2]^2)/3 + ((-113*Pi^2*S)/18 + (24 - 27*S^2 - 518*S^4 - 460*S^6 - 5*S^8)/(12*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-15 - 229*S^2 - 192*S^4)*HPL[{5}, -S^2])/(6*S*(1 + S^2)) - 43*S*HPL[{6}, -S^2] + (1424*S*HPL[{2, 1}, -S^2]^2)/3 + ((1247*Pi^2*S)/9 + (-36 + 87*S^2 + 2270*S^4 + 2132*S^6 + 13*S^8)/(6*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-3 + 83*S^2 + 190*S^4)*HPL[{3, 2}, -S^2])/(6*S*(1 + S^2)) + ((39 + 238*S^2 + 330*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) + (S*HPL[{4, 2}, -S^2])/3 + 42*S*HPL[{5, 1}, -S^2] + ((-2554*Pi^2*S)/9 - (2*(-15 + 32*S^2 + 1126*S^4 + 1074*S^6 + 7*S^8))/(3*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] + (2*(-529 - 1121*S^2 + 146*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (2*(-1621 - 3452*S^2 + 353*S^4)*HPL[{3, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (2*S*HPL[{3, 1, 2}, -S^2])/3 - 930*S*HPL[{3, 2, 1}, -S^2] - (8540*S*HPL[{4, 1, 1}, -S^2])/3 - (4*(-564 - 1174*S^2 + 107*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (5936*S*HPL[{3, 1, 1, 1}, -S^2])/3 - (12080*S*HPL[{2, 1, 1, 1, 1}, -S^2])/3 + ((S*(-227 + 57*S^2))/12 - (Pi^2*S*(388 + 395*S^2))/(18*(1 + S^2)))*Zeta[3] - 10*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(1032 + 1988*S^2 - 251*S^4))/(18*S*(1 + S^2)) + (18 + 3671*S^2 + 3897*S^4 + 151*S^6 - 45*S^8)/(12*S^3*(1 + S^2)) - (4*S*Zeta[3])/3) + HPL[{3}, -S^2]*((Pi^2*(-49 - 155*S^2 - 112*S^4))/(36*S*(1 + S^2)) + (-12 - 253*S^2 - 1014*S^4 - 670*S^6 + 55*S^8)/(24*S^3*(1 + S^2)) - (14*S*HPL[{2, 1}, -S^2])/3 + (4*S*Zeta[3])/3) + HPL[{1}, -S^2]^3*((Pi^2*(-1115 - 5804*S^2 - 1953*S^4))/(54*S*(1 + S^2)) + (-15 - 3947*S^2 - 3969*S^4 - 69*S^6)/(36*S^3) + ((-541 - 2947*S^2 - 972*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + (20*S*HPL[{3}, -S^2])/3 + (956*S*HPL[{2, 1}, -S^2])/3 + 20*S*Zeta[3]) + HPL[{2}, -S^2]*((-15307*Pi^4*S)/1080 + (86 - 549*S^2 - 5131*S^4 - 4488*S^6 - 40*S^8)/(24*S^3*(1 + S^2)) + (Pi^2*(60 - 73*S^2 - 4380*S^4 - 4233*S^6 - 8*S^8))/(72*S^3*(1 + S^2)) + ((2 - 53*S^2 - 107*S^4)*HPL[{3}, -S^2])/(6*S*(1 + S^2)) - (17*S*HPL[{4}, -S^2])/3 + ((529 + 1121*S^2 - 146*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 470*S*HPL[{3, 1}, -S^2] - (2848*S*HPL[{2, 1, 1}, -S^2])/3 + ((1 + 17*S^2 - 31*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^2*((-3299*Pi^4*S)/216 + (15 - 4322*S^2 - 4427*S^4 - 106*S^6)/(24*S^3) + (Pi^2*(-2027 - 3978*S^2 - 1989*S^4 - 8*S^6))/(36*S*(1 + S^2)) + ((-1207*Pi^2*S)/18 + (15 - 963*S^2 - 2024*S^4 - 1023*S^6 - S^8)/(6*S^3*(1 + S^2)))*HPL[{2}, -S^2] - 123*S*HPL[{2}, -S^2]^2 + ((-10 - 57*S^2 - 77*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - (25*S*HPL[{4}, -S^2])/3 + ((541 + 2947*S^2 + 972*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 472*S*HPL[{3, 1}, -S^2] - 956*S*HPL[{2, 1, 1}, -S^2] - (5*(-1 - 13*S^2 + 6*S^4)*Zeta[3])/(3*S*(1 + S^2))) - (S*(310 + 309*S^2)*Zeta[5])/(3*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^4*(-3028 - 15301*S^2 - 5675*S^4))/(432*S*(1 + S^2)) + (52 - 4894*S^2 - 5105*S^4 - 175*S^6)/(24*S^3) + (Pi^2*(-15 - 4101*S^2 - 8067*S^4 - 4069*S^6 - 40*S^8))/(72*S^3*(1 + S^2)) + ((-130 - 707*S^2 - 208*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + ((Pi^2*S)/3 + (17 - 159*S^2 - 431*S^4 - 223*S^6 + 4*S^8)/(6*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-54 - 275*S^2 - 171*S^4)*HPL[{4}, -S^2])/(6*S*(1 + S^2)) - (22*S*HPL[{5}, -S^2])/3 + ((1207*Pi^2*S)/9 + (-15 + 963*S^2 + 2024*S^4 + 1023*S^6 + S^8)/(3*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + (2*(270 + 1471*S^2 + 493*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - (104*S*HPL[{3, 2}, -S^2])/3 - (262*S*HPL[{4, 1}, -S^2])/3 - (2*(541 + 2947*S^2 + 972*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 984*S*HPL[{2, 2, 1}, -S^2] - 2912*S*HPL[{3, 1, 1}, -S^2] + 1912*S*HPL[{2, 1, 1, 1}, -S^2] + ((7*Pi^2*S)/9 + (-49 - 79*S^2 - 31*S^4 + 3*S^6)/(6*S*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-997 - 5278*S^2 - 1867*S^4))/(36*S*(1 + S^2)) + (24 - 1367*S^2 - 2871*S^4 - 1449*S^6 - S^8)/(8*S^3*(1 + S^2)) + (52*S*HPL[{3}, -S^2])/3 + 492*S*HPL[{2, 1}, -S^2] + (94*S*Zeta[3])/3) - (2*S*Zeta[5])/3)) + HPL[{0}, S^2]*(-(Pi^6*S*(111344 + 74969*S^2))/(11340*(1 + S^2)) + (1366 - 139109*S^2 - 10326*S^4)/(96*S) - (Pi^4*S*(135689 + 141658*S^2 + 4965*S^4))/(4320*(1 + S^2)) + (Pi^2*(840 - 57612*S^2 - 61543*S^4 - 2963*S^6))/(288*S*(1 + S^2)) - (14*(7 + 40*S^2 + 9*S^4)*HPL[{1}, -S^2]^6)/(9*S*(1 + S^2)) - (32*S*HPL[{1}, -S^2]^7)/3 + ((37 - 1920*S^2 - 895*S^4)*HPL[{2}, -S^2]^3)/(18*S*(1 + S^2)) + HPL[{1}, -S^2]^5*((-254*Pi^2*S)/9 + (-155 - 158*S^2 - 3*S^4)/(3*S) - 100*S*HPL[{2}, -S^2]) + ((-2 + 32*S^2 + 29*S^4)*HPL[{3}, -S^2]^2)/(3*S*(1 + S^2)) + ((4*Pi^2*S)/3 + (-466 - 869*S^2 - 390*S^4 + 21*S^6)/(6*S*(1 + S^2)))*HPL[{5}, -S^2] + ((-45 - 191*S^2 - 64*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) + 64*S*HPL[{7}, -S^2] + (2*(9 + 2132*S^2 + 947*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((-143*Pi^2*S)/9 + (-27 + 285*S^2 + 291*S^4 - 29*S^6)/(6*S*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-476*Pi^2*S)/9 + (288 + 902*S^2 + 569*S^4 - 57*S^6)/(3*S*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-1 + 2*S^2)*(7 + 8*S^2)*HPL[{4, 2}, -S^2])/(3*S*(1 + S^2)) - (88*S*HPL[{4, 3}, -S^2])/3 + (2*(15 + 214*S^2 + 135*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) - (236*S*HPL[{5, 2}, -S^2])/3 - 152*S*HPL[{6, 1}, -S^2] + ((-100*Pi^2*S)/9 - (4*(1001 - 98*S^2 + S^4))/(3*S))*HPL[{2, 2, 1}, -S^2] + ((88*Pi^2*S)/9 + (2*(-6243 + 340*S^2 + 11*S^4))/(3*S))*HPL[{3, 1, 1}, -S^2] - (2*(4 + 23*S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (2*(-70 + 3867*S^2 + 1813*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) + (842*S*HPL[{3, 2, 2}, -S^2])/3 + (2336*S*HPL[{3, 3, 1}, -S^2])/3 - (4*(-32 + 1980*S^2 + 929*S^4)*HPL[{4, 1, 1}, -S^2])/(S*(1 + S^2)) + (2320*S*HPL[{4, 1, 2}, -S^2])/3 + (6784*S*HPL[{4, 2, 1}, -S^2])/3 + 4416*S*HPL[{5, 1, 1}, -S^2] + ((-232*Pi^2*S)/3 - (4*(-2223 + 23*S^2 + 15*S^4))/(3*S))*HPL[{2, 1, 1, 1}, -S^2] - (608*S*HPL[{2, 2, 2, 1}, -S^2])/3 + (8*(-26 + 2107*S^2 + 1011*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (568*S*HPL[{3, 1, 1, 2}, -S^2])/3 + (568*S*HPL[{3, 1, 2, 1}, -S^2])/3 + (2392*S*HPL[{3, 2, 1, 1}, -S^2])/3 + 2368*S*HPL[{4, 1, 1, 1}, -S^2] - (80*(-4 + 434*S^2 + 213*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (1088*S*HPL[{2, 1, 2, 1, 1}, -S^2])/3 + 1088*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 2720*S*HPL[{3, 1, 1, 1, 1}, -S^2] - 1280*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((Pi^2*S*(-79 - 74*S^2 + 9*S^4))/(9*(1 + S^2)) - (S*(90 + 81*S^2 + 23*S^4))/(12*(1 + S^2)))*Zeta[3] - (8*S*(3 + S^2)*Zeta[3]^2)/(1 + S^2) + HPL[{3, 1}, -S^2]*((Pi^2*(-33 + 3629*S^2 + 1956*S^4))/(9*S*(1 + S^2)) + (2*(-27 + 237*S^2 + 1551*S^4 + 1327*S^6 + 36*S^8))/(3*S^3*(1 + S^2)) - (944*S*Zeta[3])/3) + HPL[{4}, -S^2]*((Pi^2*(-40 - 378*S^2 - 229*S^4))/(18*S*(1 + S^2)) + (36 - 1051*S^2 - 2324*S^4 - 1249*S^6 + 20*S^8)/(12*S^3*(1 + S^2)) - (140*S*HPL[{2, 1}, -S^2])/3 - (28*S*Zeta[3])/3) + HPL[{1}, -S^2]^4*((Pi^2*(-425 - 2323*S^2 - 628*S^4))/(18*S*(1 + S^2)) - (5*(1 + S^2)*(3 + 967*S^2 + 42*S^4))/(36*S^3) - (5*(136 + 769*S^2 + 183*S^4)*HPL[{2}, -S^2])/(9*S*(1 + S^2)) + 12*S*HPL[{3}, -S^2] + 500*S*HPL[{2, 1}, -S^2] + (164*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(3 - 1764*S^2 - 899*S^4))/(18*S*(1 + S^2)) + (6 - 29*S^2 - 4438*S^4 - 129*S^6)/(24*S^3) + (107*S*HPL[{3}, -S^2])/3 - (76*S*HPL[{2, 1}, -S^2])/3 + 78*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((-2*Pi^2*(-26 + 3749*S^2 + 2062*S^4))/(9*S*(1 + S^2)) + (30 - 319*S^2 - 1710*S^4 - 65*S^6)/S^3 + (1952*S*Zeta[3])/3) + HPL[{2, 1}, -S^2]*((-208*Pi^4*S)/45 + (Pi^2*(4058 - 33*S^2 - 14*S^4))/(18*S) + (-18 + 5283*S^2 + 1344*S^4 - 28*S^6)/(6*S^3) - (296*S*HPL[{3, 1}, -S^2])/3 - (544*S*HPL[{2, 1, 1}, -S^2])/3 + (4*(-49 - 163*S^2 + 9*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{1}, -S^2]^3*((-3374*Pi^4*S)/135 - ((1 + S^2)*(-5 + 1887*S^2 + 104*S^4))/(6*S^3) + (Pi^2*(-4325 - 8621*S^2 - 4411*S^4 - 67*S^6))/(54*S*(1 + S^2)) + ((-1142*Pi^2*S)/9 - (2*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(9*S^3))*HPL[{2}, -S^2] - (784*S*HPL[{2}, -S^2]^2)/3 - (4*(2 - S^2 + 15*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 28*S*HPL[{4}, -S^2] + (20*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1}, -S^2])/(9*S*(1 + S^2)) + (2992*S*HPL[{3, 1}, -S^2])/3 - 2000*S*HPL[{2, 1, 1}, -S^2] + (4*(44 + 299*S^2 + 9*S^4)*Zeta[3])/(9*S*(1 + S^2))) + HPL[{3}, -S^2]*((869*Pi^4*S)/540 + (Pi^2*(-498 - 1021*S^2 - 483*S^4 + 20*S^6))/(36*S*(1 + S^2)) + (12 - 2571*S^2 - 5545*S^4 - 2767*S^6 + 259*S^8)/(24*S^3*(1 + S^2)) + (40*S*HPL[{4}, -S^2])/3 - (2*(44 + 191*S^2 + 33*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - (316*S*HPL[{3, 1}, -S^2])/3 + 200*S*HPL[{2, 1, 1}, -S^2] - (2*(4 + 15*S^2 + 15*S^4)*Zeta[3])/(3*S*(1 + S^2))) + (S*(-114 - 105*S^2 + 7*S^4)*Zeta[5])/(3*(1 + S^2)) + HPL[{2}, -S^2]*((Pi^4*(-33 - 45860*S^2 - 27921*S^4))/(1080*S*(1 + S^2)) + (249 - 12041*S^2 - 28901*S^4 - 1371*S^6)/(48*S^3) + (Pi^2*(180 - 1730*S^2 - 9297*S^4 - 235*S^6))/(72*S^3) + ((67*Pi^2*S)/9 + (17 - 186*S^2 + 15*S^4)/(6*S))*HPL[{3}, -S^2] + ((10 - 62*S^2 - 63*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - 16*S*HPL[{5}, -S^2] + ((50*Pi^2*S)/9 + (2*(1001 - 98*S^2 + S^4))/(3*S))*HPL[{2, 1}, -S^2] + (2*(7 + 2111*S^2 + 928*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - 142*S*HPL[{3, 2}, -S^2] - (1144*S*HPL[{4, 1}, -S^2])/3 - (4*(9 + 2132*S^2 + 947*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) + (304*S*HPL[{2, 2, 1}, -S^2])/3 - 104*S*HPL[{3, 1, 1}, -S^2] + (544*S*HPL[{2, 1, 1, 1}, -S^2])/3 + ((254*Pi^2*S)/9 + (4*(-3 + 16*S^2))/(3*S))*Zeta[3] + (320*S*Zeta[5])/3) + HPL[{1}, -S^2]^2*((Pi^4*(-3919 - 20531*S^2 - 6490*S^4))/(270*S*(1 + S^2)) - ((1 + S^2)*(-104 + 14397*S^2 + 935*S^4))/(24*S^3) + (Pi^2*(-30 - 9135*S^2 - 18331*S^4 - 9609*S^6 - 303*S^8))/(72*S^3*(1 + S^2)) + ((-331 - 1912*S^2 - 405*S^4)*HPL[{2}, -S^2]^2)/(3*S*(1 + S^2)) + ((10*Pi^2*S)/3 + (17 - 225*S^2 - 243*S^4 + 7*S^6)/(3*S^3))*HPL[{3}, -S^2] + ((-70 - 319*S^2 - 123*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) - (116*S*HPL[{5}, -S^2])/3 + ((1142*Pi^2*S)/3 + (2*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (4*(337 + 1909*S^2 + 450*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - 152*S*HPL[{3, 2}, -S^2] - 372*S*HPL[{4, 1}, -S^2] - (20*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 3136*S*HPL[{2, 2, 1}, -S^2] - 9264*S*HPL[{3, 1, 1}, -S^2] + 6000*S*HPL[{2, 1, 1, 1}, -S^2] + ((256*Pi^2*S)/9 + (67 + 50*S^2 - 9*S^4)/(3*S))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(-1175 - 6423*S^2 - 1822*S^4))/(18*S*(1 + S^2)) + (36 - 2757*S^2 - 2894*S^4 - 69*S^6)/(6*S^3) + 76*S*HPL[{3}, -S^2] + 1568*S*HPL[{2, 1}, -S^2] + 164*S*Zeta[3]) + (368*S*Zeta[5])/3) + HPL[{1}, -S^2]*((-2425*Pi^6*S)/378 - ((1 + S^2)*(-133 + 20894*S^2 + 1483*S^4))/(24*S^3) + (Pi^4*(-58074 - 115063*S^2 - 59222*S^4 - 1149*S^6))/(2160*S*(1 + S^2)) + (Pi^2*(30 - 10721*S^2 - 21895*S^4 - 11683*S^6 - 475*S^8))/(72*S^3*(1 + S^2)) + ((-868*Pi^2*S)/9 + (1 - 1003*S^2 - 1028*S^4 - 16*S^6)/(6*S^3))*HPL[{2}, -S^2]^2 - 118*S*HPL[{2}, -S^2]^3 + (10*S*HPL[{3}, -S^2]^2)/3 + ((-109*Pi^2*S)/9 + (24 - 479*S^2 - 985*S^4 - 497*S^6 + 9*S^8)/(6*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(37 + 169*S^2 + 74*S^4)*HPL[{5}, -S^2])/(3*S*(1 + S^2)) - (164*S*HPL[{6}, -S^2])/3 + 1568*S*HPL[{2, 1}, -S^2]^2 + ((3412*Pi^2*S)/9 + (2*(-18 + 1228*S^2 + 1271*S^4 + 9*S^6))/(3*S^3))*HPL[{3, 1}, -S^2] - (4*(22 + 149*S^2 + 13*S^4)*HPL[{3, 2}, -S^2])/(3*S*(1 + S^2)) + (2*(-68 - 575*S^2 + 51*S^4)*HPL[{4, 1}, -S^2])/(3*S*(1 + S^2)) - 2*S*HPL[{4, 2}, -S^2] + (256*S*HPL[{5, 1}, -S^2])/3 + ((-2284*Pi^2*S)/3 - (4*(-15 + 1211*S^2 + 1265*S^4 + 15*S^6))/(3*S^3))*HPL[{2, 1, 1}, -S^2] - (8*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 2, 1}, -S^2])/(3*S*(1 + S^2)) - (24*(111 + 637*S^2 + 140*S^4)*HPL[{3, 1, 1}, -S^2])/(S*(1 + S^2)) - 2832*S*HPL[{3, 2, 1}, -S^2] - 8664*S*HPL[{4, 1, 1}, -S^2] + (40*(136 + 769*S^2 + 183*S^4)*HPL[{2, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 5984*S*HPL[{3, 1, 1, 1}, -S^2] - 12000*S*HPL[{2, 1, 1, 1, 1}, -S^2] + ((Pi^2*(2 + 149*S^2 - 109*S^4))/(9*S*(1 + S^2)) + (65 + 95*S^2 + 23*S^4 - 15*S^6)/(3*S*(1 + S^2)))*Zeta[3] - 32*S*Zeta[3]^2 + HPL[{2, 1}, -S^2]*((Pi^2*(1175 + 6423*S^2 + 1822*S^4))/(9*S*(1 + S^2)) + (-36 + 2757*S^2 + 2894*S^4 + 69*S^6)/(3*S^3) - 328*S*Zeta[3]) + HPL[{3}, -S^2]*((Pi^2*(-28 - 117*S^2 - 119*S^4))/(9*S*(1 + S^2)) + (45 - 749*S^2 - 1587*S^4 - 779*S^6 + 30*S^8)/(6*S^3*(1 + S^2)) - 152*S*HPL[{2, 1}, -S^2] + (16*S*Zeta[3])/3) + HPL[{2}, -S^2]*((-8953*Pi^4*S)/270 + (104 - 6853*S^2 - 7204*S^4 - 215*S^6)/(12*S^3) + (Pi^2*(60 - 4387*S^2 - 4562*S^4 - 43*S^6))/(36*S^3) + (2*(23 + 149*S^2 + 12*S^4)*HPL[{3}, -S^2])/(3*S*(1 + S^2)) - 6*S*HPL[{4}, -S^2] + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) + 1568*S*HPL[{3, 1}, -S^2] - 3136*S*HPL[{2, 1, 1}, -S^2] + (2*(15 + 101*S^2 + 4*S^4)*Zeta[3])/(S*(1 + S^2))) - (8*(3 - 10*S^2 + 33*S^4)*Zeta[5])/(3*S*(1 + S^2)))) - (2*S*(-65 + 61*S^2)*Zeta[7])/(1 + S^2) + HPL[{1}, -S^2]*((Pi^6*(-59726 - 320234*S^2 - 106131*S^4))/(22680*S*(1 + S^2)) - ((1 + S^2)*(127 + 45531*S^2 + 3442*S^4))/(32*S^3) + (Pi^2*(208 - 24081*S^2 - 25542*S^4 - 1285*S^6))/(144*S^3) + (Pi^4*(-416 - 107611*S^2 - 217071*S^4 - 112489*S^6 - 3093*S^8))/(4320*S^3*(1 + S^2)) + ((-166 - 767*S^2 - 415*S^4)*HPL[{2}, -S^2]^3)/(9*S*(1 + S^2)) + ((-46 - 287*S^2 - 19*S^4)*HPL[{3}, -S^2]^2)/(3*S*(1 + S^2)) + ((164*Pi^2*S)/9 + (27 - 787*S^2 - 1667*S^4 - 873*S^6 - 12*S^8)/(3*S^3*(1 + S^2)))*HPL[{5}, -S^2] - (10*(53 + 232*S^2 + 158*S^4)*HPL[{6}, -S^2])/(3*S*(1 + S^2)) - 328*S*HPL[{7}, -S^2] + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1}, -S^2]^2)/(3*S*(1 + S^2)) + ((-2084*Pi^2*S)/9 - (2*(8 + 329*S^2 + 671*S^4 + 371*S^6 + 25*S^8))/(3*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-7054*Pi^2*S)/9 - (2*(39 + 790*S^2 + 1577*S^4 + 892*S^6 + 78*S^8))/(3*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-136 - 927*S^2 - 89*S^4)*HPL[{4, 2}, -S^2])/(3*S*(1 + S^2)) + 72*S*HPL[{4, 3}, -S^2] + (4*(-55 - 673*S^2 + 258*S^4)*HPL[{5, 1}, -S^2])/(3*S*(1 + S^2)) + 152*S*HPL[{5, 2}, -S^2] + 180*S*HPL[{6, 1}, -S^2] + ((-2552*Pi^2*S)/3 - (4*(-1 + 1003*S^2 + 1028*S^4 + 16*S^6))/(3*S^3))*HPL[{2, 2, 1}, -S^2] + ((-6016*Pi^2*S)/3 - (4*(-20 + 2805*S^2 + 2861*S^4 + 20*S^6))/(3*S^3))*HPL[{3, 1, 1}, -S^2] + (8*(-1 + S^2)*HPL[{3, 1, 2}, -S^2])/(3*S) - (8*(167 + 767*S^2 + 414*S^4)*HPL[{3, 2, 1}, -S^2])/(3*S*(1 + S^2)) + 2764*S*HPL[{3, 2, 2}, -S^2] + 8480*S*HPL[{3, 3, 1}, -S^2] - (8*(461 + 1937*S^2 + 1344*S^4)*HPL[{4, 1, 1}, -S^2])/(3*S*(1 + S^2)) + 8324*S*HPL[{4, 1, 2}, -S^2] + 25940*S*HPL[{4, 2, 1}, -S^2] + 53344*S*HPL[{5, 1, 1}, -S^2] + ((2512*Pi^2*S)/3 - (8*(5 - 283*S^2 - 283*S^4 + 5*S^6))/S^3)*HPL[{2, 1, 1, 1}, -S^2] + 992*S*HPL[{2, 2, 2, 1}, -S^2] + (16*(148 + 595*S^2 + 471*S^4)*HPL[{3, 1, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 8256*S*HPL[{3, 1, 1, 2}, -S^2] - 8256*S*HPL[{3, 1, 2, 1}, -S^2] - 11232*S*HPL[{3, 2, 1, 1}, -S^2] - 35968*S*HPL[{4, 1, 1, 1}, -S^2] - (80*(26 + 121*S^2 + 65*S^4)*HPL[{2, 1, 1, 1, 1}, -S^2])/(S*(1 + S^2)) + 12544*S*HPL[{2, 1, 2, 1, 1}, -S^2] + 37632*S*HPL[{2, 2, 1, 1, 1}, -S^2] + 75520*S*HPL[{3, 1, 1, 1, 1}, -S^2] + 4800*S*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + ((109*Pi^4*S)/9 + (662 + 773*S^2 + 103*S^4)/(3*S) + (Pi^2*(313 + 699*S^2 + 415*S^4 + 33*S^6))/(18*S*(1 + S^2)))*Zeta[3] - (2*(26 + 91*S^2 + 5*S^4)*Zeta[3]^2)/(3*S*(1 + S^2)) + HPL[{3, 1}, -S^2]*((4*Pi^2*(209 + 1033*S^2 + 482*S^4))/(9*S*(1 + S^2)) + (-42 + 1801*S^2 + 1766*S^4 - 69*S^6)/(3*S^3) - 1360*S*Zeta[3]) + HPL[{4}, -S^2]*((Pi^2*(20 + 453*S^2 - 369*S^4))/(18*S*(1 + S^2)) + (10 - 1329*S^2 - 1366*S^4 + 37*S^6)/(12*S^3) - 452*S*HPL[{2, 1}, -S^2] + (124*S*Zeta[3])/3) + HPL[{2}, -S^2]^2*((Pi^2*(-591 - 3326*S^2 - 821*S^4))/(18*S*(1 + S^2)) - ((1 + S^2)*(1 + 679*S^2 + 24*S^4))/(4*S^3) + 404*S*HPL[{3}, -S^2] + 124*S*HPL[{2, 1}, -S^2] + 292*S*Zeta[3]) + HPL[{2, 1, 1}, -S^2]*((12*(1 + S^2)*(2 - 105*S^2 + 4*S^4))/S^3 - (2*Pi^2*(931 + 4762*S^2 + 1947*S^4))/(9*S*(1 + S^2)) + 2624*S*Zeta[3]) + HPL[{2, 1}, -S^2]*((4421*Pi^4*S)/90 - ((1 + S^2)*(104 - 4309*S^2 + 197*S^4))/(6*S^3) + (Pi^2*(-30 + 1797*S^2 + 3722*S^4 + 1857*S^6 - 14*S^8))/(9*S^3*(1 + S^2)) - 3136*S*HPL[{3, 1}, -S^2] - 6272*S*HPL[{2, 1, 1}, -S^2] + (4*(-151 - 1132*S^2 + 3*S^4)*Zeta[3])/(3*S*(1 + S^2))) + HPL[{3}, -S^2]*((419*Pi^4*S)/27 + (105 - 30*S^2 + 227*S^4 + 394*S^6)/(12*S^3) + (Pi^2*(17 + 31*S^2 - 2*S^4 + 14*S^6 + 16*S^8))/(9*S^3*(1 + S^2)) - 68*S*HPL[{4}, -S^2] + (20*(-33 - 229*S^2 + 2*S^4)*HPL[{2, 1}, -S^2])/(3*S*(1 + S^2)) - 1320*S*HPL[{3, 1}, -S^2] + 2640*S*HPL[{2, 1, 1}, -S^2] + (4*(7 + 91*S^2 + 12*S^4)*Zeta[3])/(3*S*(1 + S^2))) + ((802*Pi^2*S)/9 + (2*(114 + 269*S^2 + 184*S^4 + 27*S^6))/(3*S*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((Pi^4*(-2016 - 10550*S^2 - 4113*S^4))/(180*S*(1 + S^2)) + ((1 + S^2)*(81 - 3449*S^2 + 152*S^4))/(8*S^3) + (Pi^2*(48 - 2579*S^2 - 5319*S^4 - 2613*S^6 + 47*S^8))/(24*S^3*(1 + S^2)) + ((1042*Pi^2*S)/9 + (9 + 320*S^2 + 345*S^4 + 26*S^6)/(3*S^3))*HPL[{3}, -S^2] + ((136 + 883*S^2 + 69*S^4)*HPL[{4}, -S^2])/(3*S*(1 + S^2)) + 132*S*HPL[{5}, -S^2] + ((1276*Pi^2*S)/3 + (2*(-1 + 1003*S^2 + 1028*S^4 + 16*S^6))/(3*S^3))*HPL[{2, 1}, -S^2] + (4*(331 + 1912*S^2 + 405*S^4)*HPL[{3, 1}, -S^2])/(3*S*(1 + S^2)) - 1460*S*HPL[{3, 2}, -S^2] - 4396*S*HPL[{4, 1}, -S^2] - (8*(331 + 1912*S^2 + 405*S^4)*HPL[{2, 1, 1}, -S^2])/(3*S*(1 + S^2)) - 496*S*HPL[{2, 2, 1}, -S^2] + 4128*S*HPL[{3, 1, 1}, -S^2] + 6272*S*HPL[{2, 1, 1, 1}, -S^2] + ((1078*Pi^2*S)/9 + (2*(129 + 326*S^2 + 189*S^4 + 16*S^6))/(3*S*(1 + S^2)))*Zeta[3] + 540*S*Zeta[5]) + 504*S*Zeta[7]));
Et5vwuT3F3=(-5*(22707 + 168962*S^2))/(419904*S) + (Pi^2*(-7623423 - 1435800*S^2 - 30054476*S^4))/(629856*S) + (Pi^4*(-13429380 - 18942702*S^2 - 71260847*S^4 - 65152661*S^6))/(6298560*S*(1 + S^2)) + (Pi^6*(-3135606 - 6296439*S^2 - 17661293*S^4 - 14355308*S^6))/(7348320*S*(1 + S^2)) + (Pi^8*(-2652432 - 1326216*S^2 - 5642423*S^4 - 2989991*S^6))/(12247200*S*(1 + S^2)) + ((-23 - 71*S^2 - 24*S^4 - 77*S^6 - 29*S^8)*HPL[{1}, -S^2]^8)/(54*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{1}, -S^2]^9)/(81*S^3) + HPL[{0}, S^2]^8*((-6 - 3*S^2 - 10*S^4 - 4*S^6)/(1728*S*(1 + S^2)) - ((1 + S^2)*(1 - S^2 + S^4)*HPL[{1}, -S^2])/(288*S^3)) + ((-1040 - 2768*S^2 - 864*S^4 - 3181*S^6 - 1453*S^8)*HPL[{2}, -S^2]^4)/(324*S^3*(1 + S^2)) + HPL[{0}, S^2]^7*((-7*Pi^2*S^3)/2592 + (62 - 115*S^2 - 324*S^4)/(5184*S) + ((31 - 53*S^2 - 42*S^4 - 206*S^6 - 122*S^8)*HPL[{1}, -S^2])/(2592*S^3*(1 + S^2)) - (7*(1 + S^6)*HPL[{1}, -S^2]^2)/(432*S^3) - (7*S^3*HPL[{2}, -S^2])/432) + HPL[{1}, -S^2]^7*((-92*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(189*S^3) - ((1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(567*S^3) - (20*(1 + S^6)*HPL[{2}, -S^2])/(63*S^3)) + (2*(10 + 9*S^6)*HPL[{3}, -S^2]^3)/(27*S^3) + ((-196 - 190*S^2 + 120*S^4 - 223*S^6 - 229*S^8)*HPL[{4}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((Pi^2*(-15 - 128*S^6))/(27*S^3) + (1776 + 26466*S^2 - 7545*S^4 - 92399*S^6 - 64106*S^8)/(162*S^3*(1 + S^2)))*HPL[{7}, -S^2] - (2*(-1701 + 819*S^2 + 1260*S^4 + 8591*S^6 + 6071*S^8)*HPL[{8}, -S^2])/(27*S^3*(1 + S^2)) - (28*(42 + 67*S^6)*HPL[{9}, -S^2])/(9*S^3) + (112*(-25 + 17*S^6)*HPL[{2, 1}, -S^2]^3)/(27*S^3) - (2*(3133 + 7321*S^2 + 2085*S^4 + 7295*S^6 + 3107*S^8)*HPL[{3, 1}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((Pi^2*(-19 + 66*S^6))/(27*S^3) + (28 + 1199*S^2 + 1031*S^4 - 605*S^6 - 951*S^8)/(54*S^3*(1 + S^2)))*HPL[{4, 3}, -S^2] + ((Pi^2*(-65 + 163*S^6))/(27*S^3) + (1244 + 8489*S^2 + 5166*S^4 - 2426*S^6 - 4397*S^8)/(162*S^3*(1 + S^2)))*HPL[{5, 2}, -S^2] + ((20 + 92*S^2 + 36*S^4 - 371*S^6 - 443*S^8)*HPL[{5, 3}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-289 + 30*S^6)*HPL[{5, 4}, -S^2])/(9*S^3) + ((4*Pi^2*(-13 + 32*S^6))/(27*S^3) + (18 - 17220*S^2 + 489*S^4 + 61265*S^6 + 37868*S^8)/(162*S^3*(1 + S^2)))*HPL[{6, 1}, -S^2] + ((316 + 496*S^2 + 90*S^4 - 459*S^6 - 639*S^8)*HPL[{6, 2}, -S^2])/(27*S^3*(1 + S^2)) - (22*(-105 + 16*S^6)*HPL[{6, 3}, -S^2])/(9*S^3) + ((-2399 + 1057*S^2 + 1728*S^4 + 15108*S^6 + 11652*S^8)*HPL[{7, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-2835 + 416*S^6)*HPL[{7, 2}, -S^2])/(9*S^3) + (2*(2065 + 116*S^6)*HPL[{8, 1}, -S^2])/(3*S^3) - (8*(698 + 1874*S^2 + 588*S^4 + 2211*S^6 + 1035*S^8)*HPL[{2, 1, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((Pi^2*(-41 + 2093*S^6))/(27*S^3) + (-6183 + 95685*S^2 + 22731*S^4 + 50647*S^6)/(162*S^3))*HPL[{3, 2, 2}, -S^2] + ((4*Pi^2*(-66 + 1643*S^6))/(27*S^3) + (2*(-6773 + 67510*S^2 + 91200*S^4 + 56086*S^6 + 39061*S^8))/(81*S^3*(1 + S^2)))*HPL[{3, 3, 1}, -S^2] + ((-949 - 2965*S^2 - 1008*S^4 - 3291*S^6 - 1275*S^8)*HPL[{3, 3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((Pi^2*(-295 + 6502*S^6))/(27*S^3) + (-29536 + 264365*S^2 + 359724*S^4 + 217839*S^6 + 151584*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 1, 2}, -S^2] + (2*(969 + 2697*S^2 + 864*S^4 + 2881*S^6 + 1153*S^8)*HPL[{4, 1, 3}, -S^2])/(27*S^3*(1 + S^2)) + ((Pi^2*(-823 + 20098*S^6))/(27*S^3) + (-85792 + 822629*S^2 + 1117020*S^4 + 683535*S^6 + 473208*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 2, 1}, -S^2] + ((-581 - 1805*S^2 - 612*S^4 - 1601*S^6 - 377*S^8)*HPL[{4, 2, 2}, -S^2])/(27*S^3*(1 + S^2)) + (2*(13 + 56*S^6)*HPL[{4, 2, 3}, -S^2])/(9*S^3) + (2*(2107 + 8011*S^2 + 2952*S^4 + 10399*S^6 + 4495*S^8)*HPL[{4, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(63 + 73*S^6)*HPL[{4, 3, 2}, -S^2])/(9*S^3) + (4*(215 + 102*S^6)*HPL[{4, 4, 1}, -S^2])/(9*S^3) + ((2*Pi^2*(-839 + 20641*S^6))/(27*S^3) + (-82231 + 858287*S^2 + 1148283*S^4 + 678845*S^6 + 468920*S^8)/(81*S^3*(1 + S^2)))*HPL[{5, 1, 1}, -S^2] + ((1937 + 9137*S^2 + 3600*S^4 + 12995*S^6 + 5795*S^8)*HPL[{5, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + (4*(101 + 16*S^6)*HPL[{5, 1, 3}, -S^2])/(9*S^3) + ((17117 + 65357*S^2 + 24120*S^4 + 83495*S^6 + 35255*S^8)*HPL[{5, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (10*(109 + 80*S^6)*HPL[{5, 2, 2}, -S^2])/(9*S^3) + (4*(815 + 316*S^6)*HPL[{5, 3, 1}, -S^2])/(9*S^3) + (2*(23571 + 84501*S^2 + 30465*S^4 + 101198*S^6 + 40268*S^8)*HPL[{6, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(730 + 281*S^6)*HPL[{6, 1, 2}, -S^2])/(9*S^3) + (4*(1950 + 581*S^6)*HPL[{6, 2, 1}, -S^2])/(9*S^3) + (4*(3525 + 634*S^6)*HPL[{7, 1, 1}, -S^2])/(9*S^3) + ((-16*Pi^2*(-353 + 123*S^6))/(27*S^3) - (4*(-8656 + 8223*S^2 - 14619*S^4 + 6014*S^6))/(81*S^3))*HPL[{2, 2, 2, 1}, -S^2] + ((2*Pi^2*(-8327 + 809*S^6))/(27*S^3) + (-90823 - 87403*S^2 - 192267*S^4 - 170467*S^6 + 25436*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 1, 1, 2}, -S^2] + ((2*Pi^2*(-8327 + 809*S^6))/(27*S^3) + (-90823 - 87403*S^2 - 192267*S^4 - 170467*S^6 + 25436*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 1, 2, 1}, -S^2] + ((-979 - 2383*S^2 - 702*S^4 - 2108*S^6 - 704*S^8)*HPL[{3, 1, 2, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((2*Pi^2*(-16799 + 3761*S^6))/(27*S^3) + (-194695 - 92599*S^2 - 269019*S^4 - 273727*S^6 + 97604*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2, 1, 1}, -S^2] + ((-979 - 2383*S^2 - 702*S^4 - 2108*S^6 - 704*S^8)*HPL[{3, 2, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((-19091 - 16319*S^2 + 1386*S^4 + 26188*S^6 + 23416*S^8)*HPL[{3, 2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-99 + 1957*S^6)*HPL[{3, 2, 2, 2}, -S^2])/(9*S^3) - (4*(-266 + 6121*S^6)*HPL[{3, 2, 3, 1}, -S^2])/(9*S^3) + (8*(-2264 - 1742*S^2 + 261*S^4 + 3537*S^6 + 3015*S^8)*HPL[{3, 3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(-128 + 3003*S^6)*HPL[{3, 3, 1, 2}, -S^2])/(9*S^3) - (20*(-170 + 3717*S^6)*HPL[{3, 3, 2, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(-25313 + 5375*S^6))/(27*S^3) + (2*(-301483 - 164917*S^2 - 425295*S^4 - 418542*S^6 + 143643*S^8))/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1, 1}, -S^2] - (2*(-469 + 1637*S^2 + 1053*S^4 + 4163*S^6 + 2057*S^8)*HPL[{4, 1, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-1832 + 37825*S^6)*HPL[{4, 1, 1, 3}, -S^2])/(9*S^3) + (2*(-26699 - 22541*S^2 + 2079*S^4 + 38281*S^6 + 34123*S^8)*HPL[{4, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-3209 + 63710*S^6)*HPL[{4, 1, 2, 2}, -S^2])/(9*S^3) + (72*(-17 + 351*S^6)*HPL[{4, 1, 3, 1}, -S^2])/S^3 + (2*(-81035 - 64349*S^2 + 8343*S^4 + 123169*S^6 + 106483*S^8)*HPL[{4, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-2081 + 39242*S^6)*HPL[{4, 2, 1, 2}, -S^2])/(9*S^3) + (2*(-2021 + 38552*S^6)*HPL[{4, 2, 2, 1}, -S^2])/(9*S^3) + (8*(-2653 + 56132*S^6)*HPL[{4, 3, 1, 1}, -S^2])/(9*S^3) + (4*(-82628 - 69092*S^2 + 6768*S^4 + 118921*S^6 + 105385*S^8)*HPL[{5, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-1865 + 38141*S^6)*HPL[{5, 1, 1, 2}, -S^2])/(3*S^3) + (4*(-3013 + 62839*S^6)*HPL[{5, 1, 2, 1}, -S^2])/(3*S^3) + (4*(-7061 + 149627*S^6)*HPL[{5, 2, 1, 1}, -S^2])/(3*S^3) + (8*(-26364 + 560855*S^6)*HPL[{6, 1, 1, 1}, -S^2])/(9*S^3) + ((16*Pi^2*(703 + 256*S^6))/(27*S^3) + (4*(4321 + 9831*S^2 + 13653*S^4 + 3089*S^6))/(27*S^3))*HPL[{2, 1, 2, 1, 1}, -S^2] + ((16*Pi^2*(703 + 256*S^6))/(9*S^3) + (4*(4321 + 9831*S^2 + 13653*S^4 + 3089*S^6))/(9*S^3))*HPL[{2, 2, 1, 1, 1}, -S^2] + (8*(-4385 - 3269*S^2 + 558*S^4 + 6919*S^6 + 5803*S^8)*HPL[{2, 2, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-4385 - 3269*S^2 + 558*S^4 + 6919*S^6 + 5803*S^8)*HPL[{2, 2, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (32*(325 + 242*S^6)*HPL[{2, 2, 2, 2, 1}, -S^2])/(9*S^3) + ((16*Pi^2*(3522 + 1865*S^6))/(27*S^3) + (4*(65507 + 201951*S^2 + 218349*S^4 + 70629*S^6))/(81*S^3))*HPL[{3, 1, 1, 1, 1}, -S^2] - (8*(-25838 - 19142*S^2 + 3348*S^4 + 41203*S^6 + 34507*S^8)*HPL[{3, 1, 1, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-43378 - 32218*S^2 + 5580*S^4 + 68879*S^6 + 57719*S^8)*HPL[{3, 1, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(7849 + 1807*S^6)*HPL[{3, 1, 1, 2, 2}, -S^2])/(9*S^3) - (8*(-52148 - 38756*S^2 + 6696*S^4 + 82717*S^6 + 69325*S^8)*HPL[{3, 1, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(7849 + 1807*S^6)*HPL[{3, 1, 2, 1, 2}, -S^2])/(9*S^3) + (4*(103 + 113*S^6)*HPL[{3, 1, 2, 2, 1}, -S^2])/(9*S^3) + (32*(6946 + 2053*S^6)*HPL[{3, 1, 3, 1, 1}, -S^2])/(9*S^3) - (8*(-109153 - 81253*S^2 + 13950*S^4 + 172664*S^6 + 144764*S^8)*HPL[{3, 2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(15649 + 7615*S^6)*HPL[{3, 2, 1, 1, 2}, -S^2])/(9*S^3) - (4*(7697 + 5695*S^6)*HPL[{3, 2, 1, 2, 1}, -S^2])/(9*S^3) - (4*(-24319 + 2807*S^6)*HPL[{3, 2, 2, 1, 1}, -S^2])/(9*S^3) - (32*(-3352 + 123*S^6)*HPL[{3, 3, 1, 1, 1}, -S^2])/(3*S^3) - (8*(-329979 - 248835*S^2 + 40572*S^4 + 514973*S^6 + 433829*S^8)*HPL[{4, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(23689 + 11209*S^6)*HPL[{4, 1, 1, 1, 2}, -S^2])/(9*S^3) - (8*(11761 + 8329*S^6)*HPL[{4, 1, 1, 2, 1}, -S^2])/(9*S^3) - (8*(-36263 + 3997*S^6)*HPL[{4, 1, 2, 1, 1}, -S^2])/(9*S^3) - (8*(-120611 + 4045*S^6)*HPL[{4, 2, 1, 1, 1}, -S^2])/(9*S^3) - (64*(-30150 + 881*S^6)*HPL[{5, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-2192*Pi^2*(-11 + 4*S^6))/(27*S^3) - (8*(-17192 + 17163*S^2 - 32787*S^4 + 12763*S^6))/(81*S^3))*HPL[{2, 1, 1, 1, 1, 1}, -S^2] + (896*(-25 + 17*S^6)*HPL[{2, 2, 1, 2, 1, 1}, -S^2])/(9*S^3) + (896*(-25 + 17*S^6)*HPL[{2, 2, 2, 1, 1, 1}, -S^2])/(3*S^3) + (16*(-5759 - 5903*S^2 - 72*S^4 + 5783*S^6 + 5927*S^8)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (32*(-3583 + 3407*S^6)*HPL[{3, 1, 1, 1, 1, 2}, -S^2])/(9*S^3) - (32*(-7783 + 6263*S^6)*HPL[{3, 1, 1, 1, 2, 1}, -S^2])/(9*S^3) - (32*(-10583 + 8167*S^6)*HPL[{3, 1, 1, 2, 1, 1}, -S^2])/(9*S^3) - (32*(-11983 + 9119*S^6)*HPL[{3, 1, 2, 1, 1, 1}, -S^2])/(9*S^3) - (32*(-21083 + 15307*S^6)*HPL[{3, 2, 1, 1, 1, 1}, -S^2])/(9*S^3) - (320*(-701 + 513*S^6)*HPL[{4, 1, 1, 1, 1, 1}, -S^2])/S^3 - (160*(-311 - 221*S^2 + 45*S^4 + 541*S^6 + 451*S^8)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (64*(227 + 162*S^6)*HPL[{2, 1, 1, 2, 1, 1, 1}, -S^2])/(3*S^3) - (256*(227 + 162*S^6)*HPL[{2, 1, 2, 1, 1, 1, 1}, -S^2])/(3*S^3) - (640*(227 + 162*S^6)*HPL[{2, 2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (512*(594 + 379*S^6)*HPL[{3, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (1280*(-25 + 17*S^6)*HPL[{2, 1, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((28*Pi^2*S^3)/81 + (4*(13 + 15*S^2))/(27*S) + (28*S^3*HPL[{0}, S^2]^2)/27 + (4*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]*((4*(24 + 12*S^2 + 53*S^4 + 29*S^6))/(27*S*(1 + S^2)) + (32*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3)) + (8*(-5 + 7*S^6)*HPL[{2}, -S^2])/(27*S^3))*Log[T]^7 + ((-4*(2 + S^2 + 2*S^4))/(9*S*(1 + S^2)) - (8*S^3*HPL[{0}, S^2])/9 - (8*(1 + S^6)*HPL[{1}, -S^2])/(9*S^3))*Log[T]^8 + ((-9498 - 12327*S^2 - 3713*S^4 - 4772*S^6)/(972*S*(1 + S^2)) + (Pi^2*(-138 - 69*S^2 - 31*S^4 + 107*S^6))/(54*S*(1 + S^2)))*Zeta[3]^2 + HPL[{0}, S^2]^6*((-2478 - 6081*S^2 - 40769*S^4 - 38462*S^6)/(93312*S*(1 + S^2)) + (Pi^2*(-250 - 125*S^2 - 548*S^4 - 298*S^6))/(5184*S*(1 + S^2)) + ((-2 - 85*S^2 - 43*S^4 - 166*S^6 - 83*S^8)*HPL[{1}, -S^2]^2)/(432*S^3*(1 + S^2)) - (41*(1 + S^6)*HPL[{1}, -S^2]^3)/(648*S^3) + ((-32 - 16*S^2 - 121*S^4 - 89*S^6)*HPL[{2}, -S^2])/(432*S*(1 + S^2)) + HPL[{1}, -S^2]*((-125*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(2592*S^3) + (-413 - 716*S^2 - 4854*S^4 - 8888*S^6 - 4553*S^8)/(15552*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + (S^3*HPL[{3}, -S^2])/144 + ((16 - 3*S^6)*HPL[{2, 1}, -S^2])/(108*S^3) - (17*S^3*Zeta[3])/108) + Log[T]^6*((-270 - 347*S^2)/(81*S) + (Pi^2*(-828 - 414*S^2 - 1279*S^4 - 451*S^6))/(243*S*(1 + S^2)) - (88*S^3*HPL[{0}, S^2]^3)/81 - (14*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^2)/(27*S^3*(1 + S^2)) - (224*(1 + S^6)*HPL[{1}, -S^2]^3)/(27*S^3) + HPL[{0}, S^2]^2*((-324 - 162*S^2 - 775*S^4 - 451*S^6)/(81*S*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2])/S^3) - (2*(-311 - 221*S^2 + 45*S^4 + 541*S^6 + 451*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-928 - 1317*S^2 - 1710*S^4 - 1321*S^6)/(81*S^3) - (92*Pi^2*(1 + S^6))/(27*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]*((-256*Pi^2*S^3)/81 + (-906 - 540*S^2 - 1321*S^4)/(81*S) - (14*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) - (112*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) - (4*(-5 + 79*S^6)*HPL[{2}, -S^2])/(27*S^3)) + (4*(3 + 74*S^6)*HPL[{3}, -S^2])/(27*S^3) - (16*(-25 + 17*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (272*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^6*(-((1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(2916*S^3) + (Pi^2*(-716 - 2372*S^2 - 828*S^4 - 2729*S^6 - 1073*S^8))/(486*S^3*(1 + S^2)) + ((83 - 97*S^2 - 90*S^4 - 448*S^6 - 268*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) + (160*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) + (20*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3, 1, 2}, -S^2]*((Pi^2*(-1039 - 3*S^2 - 3*S^4 + 600*S^6))/(162*S^3) + (-10357 + 6715*S^2 - 2627*S^4 + 4541*S^6)/(324*S^3) + (4*(-3 + 7*S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]^2*((11271 - 26400*S^2 - 11046*S^4 - 2257*S^6)/(1944*S^3) + (Pi^2*(172 - 440*S^2 - 324*S^4 - 839*S^6 - 227*S^8))/(324*S^3*(1 + S^2)) + (2*(113 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (2*(1 + 8*S^6)*Zeta[3])/(9*S^3)) + HPL[{5, 1}, -S^2]*((-40137 - 299928*S^2 - 26409*S^4 + 45466*S^6)/(972*S^3) + (Pi^2*(-1283 - 6254*S^2 - 2562*S^4 - 6764*S^6 - 1793*S^8))/(162*S^3*(1 + S^2)) - (32*(-1 + 13*S^6)*Zeta[3])/(9*S^3)) + HPL[{6}, -S^2]*((-2000 + 17396*S^2 - 22141*S^4 - 70341*S^6)/(324*S^3) + (Pi^2*(223 - 353*S^2 - 153*S^4 - 3374*S^6 - 2798*S^8))/(162*S^3*(1 + S^2)) - (4*(2 + 7*S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (4*(-10 + 31*S^6)*Zeta[3])/(9*S^3)) + HPL[{4, 2}, -S^2]*((2372 - 17065*S^2 - 7714*S^4 - 6702*S^6)/(324*S^3) + (Pi^2*(277 - 746*S^2 - 507*S^4 - 1986*S^6 - 963*S^8))/(162*S^3*(1 + S^2)) - (2*(3 + 44*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]^2*((158591 + 123957*S^2 + 133875*S^4 + 293407*S^6)/(972*S^3) + (Pi^2*(4335 + 15819*S^2 + 5742*S^4 + 24028*S^6 + 12544*S^8))/(162*S^3*(1 + S^2)) - (16*(-11 + 115*S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^3*((39656 - 9900*S^2 + 387*S^4 - 67354*S^6)/(2916*S^3) + (Pi^2*(2371 - 233*S^2 - 1302*S^4 - 8539*S^6 - 5935*S^8))/(972*S^3*(1 + S^2)) + (2*(-39 + 269*S^6)*HPL[{3}, -S^2])/(27*S^3) + (2*(325 + 242*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (4*(3 + 115*S^6)*Zeta[3])/(27*S^3)) + HPL[{3, 2, 1}, -S^2]*((286177 - 59055*S^2 - 4785*S^4 - 525209*S^6)/(972*S^3) + (Pi^2*(8445 - 1974*S^2 - 5214*S^4 - 33559*S^6 - 23140*S^8))/(162*S^3*(1 + S^2)) + (4*(7 + 309*S^6)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1, 1, 1}, -S^2]*((-8*(-13796 + 2976*S^2 + 1347*S^4 + 25949*S^6))/(81*S^3) - (8*Pi^2*(-2597 + 229*S^2 + 1413*S^4 + 9643*S^6 + 6817*S^8))/(81*S^3*(1 + S^2)) + (32*(7 + 472*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1, 1, 1}, -S^2]*((-203587 - 14526*S^2 - 12213*S^4 + 292996*S^6)/(243*S^3) + (2*Pi^2*(-6403 - 2302*S^2 + 2046*S^4 + 16741*S^6 + 12640*S^8))/(81*S^3*(1 + S^2)) - (16*(9 + 479*S^6)*Zeta[3])/(9*S^3)) + HPL[{4, 1, 1}, -S^2]*((509241 + 14091*S^2 + 14730*S^4 - 818539*S^6)/(486*S^3) + (Pi^2*(15541 + 2329*S^2 - 6597*S^4 - 48103*S^6 - 34891*S^8))/(81*S^3*(1 + S^2)) + (8*(25 + 1412*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 2}, -S^2]*((Pi^4*(19 - 636*S^6))/(135*S^3) + (152018 - 1568857*S^2 - 2016861*S^4 - 834471*S^6 - 499605*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(6328 - 43745*S^2 - 61392*S^4 - 31651*S^6 - 20602*S^8))/(972*S^3*(1 + S^2)) - (4*(41 + 2061*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((311 - 334*S^2 - 318*S^4 - 1699*S^6 - 1054*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1, 1, 1}, -S^2]*((454955 - 694629*S^2 + 1758375*S^4 - 137257*S^6)/(1458*S^3) + (Pi^4*(17519 - 4414*S^6))/(405*S^3) + (Pi^2*(33338 + 21323*S^2 + 58869*S^4 + 57866*S^6 - 13666*S^8))/(243*S^3*(1 + S^2)) - (32*(1034 + 1772*S^2 + 369*S^4 + 764*S^6 + 26*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^5*((-1237*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1350*S^3) - ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(14580*S^3) - (2*Pi^2*(2456 + 3630*S^2 + 5688*S^4 + 4487*S^6))/(1215*S^3) + ((-314*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - ((1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(405*S^3))*HPL[{2}, -S^2] - (392*(1 + S^6)*HPL[{2}, -S^2]^2)/(45*S^3) + (2*(562 + 1362*S^2 + 400*S^4 + 1113*S^6 + 313*S^8)*HPL[{3}, -S^2])/(45*S^3*(1 + S^2)) + (284*(1 + S^6)*HPL[{4}, -S^2])/(45*S^3) + (2*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (32*(1 + S^6)*HPL[{3, 1}, -S^2])/(45*S^3) - (40*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (10*(50 + 122*S^2 + 36*S^4 + 101*S^6 + 29*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 1, 1}, -S^2]*((-807597 - 941886*S^2 - 5359221*S^4 - 278170*S^6)/(2916*S^3) + (Pi^4*(-49409 - 2453*S^6))/(810*S^3) + (Pi^2*(-86543 - 141374*S^2 - 275289*S^4 - 220919*S^6 + 295*S^8))/(486*S^3*(1 + S^2)) - (4*(-12372 - 20685*S^2 - 4152*S^4 - 8233*S^6 + 80*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 2, 1}, -S^2]*((-151273 - 487836*S^2 - 929547*S^4 - 117836*S^6)/(1458*S^3) + (Pi^2*(-28864 - 37443*S^2 - 77511*S^4 - 7087*S^6))/(486*S^3) + (Pi^4*(-8172 - 1853*S^6))/(405*S^3) - (4*(-4041 - 6669*S^2 - 1314*S^4 - 2504*S^6 + 124*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{5}, -S^2]*((Pi^4*(47 + 651*S^6))/(810*S^3) + (62766 + 509610*S^2 + 203667*S^4 - 755215*S^6 - 550918*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(314 + 11360*S^2 + 6315*S^4 - 15788*S^6 - 10679*S^8))/(972*S^3*(1 + S^2)) + ((-3089 - 4160*S^2 - 360*S^4 - 1966*S^6 - 895*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-22 + 47*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (20*(-5 + 39*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((85 + 118*S^2 - 96*S^4 + 200*S^6 + 167*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{4, 1}, -S^2]*((Pi^4*(469 - 25264*S^6))/(1620*S^3) + (32886 - 1889355*S^2 - 2172510*S^4 - 745646*S^6 - 456497*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(10462 - 157244*S^2 - 203796*S^4 - 96889*S^6 - 62095*S^8))/(972*S^3*(1 + S^2)) - (8*(-163 + 3311*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(-1 + 1142*S^2 + 549*S^4 + 2787*S^6 + 1644*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + Log[T]^5*((6166*Pi^4*S^3)/6075 + (2325 + 3352*S^2)/(486*S) + (Pi^2*(44100 + 47385*S^2 + 47893*S^4))/(7290*S) + (283*S^3*HPL[{0}, S^2]^4)/405 + (28*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) + (112*(1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + HPL[{0}, S^2]^3*((3870 + 1935*S^2 + 10399*S^4 + 6529*S^6)/(1215*S*(1 + S^2)) + (86*(1 + S^6)*HPL[{1}, -S^2])/(27*S^3)) + ((2*Pi^2*(-113 + 298*S^6))/(81*S^3) + (-29042 + 6705*S^2 + 3735*S^4 + 47893*S^6)/(1215*S^3))*HPL[{2}, -S^2] + (2*(33 + 46*S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + HPL[{1}, -S^2]^2*((92*Pi^2*(1 + S^6))/(9*S^3) + (928 + 1317*S^2 + 1710*S^4 + 1321*S^6)/(27*S^3) + (20*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + HPL[{0}, S^2]^2*((1301*Pi^2*S^3)/405 + (19530 + 19035*S^2 + 47893*S^4)/(2430*S) + ((233 + 881*S^2 + 324*S^4 + 1112*S^6 + 464*S^8)*HPL[{1}, -S^2])/(27*S^3*(1 + S^2)) + (12*(1 + S^6)*HPL[{1}, -S^2]^2)/S^3 + (2*(-8 + 151*S^6)*HPL[{2}, -S^2])/(27*S^3)) - (2*(169 + 7369*S^2 + 3600*S^4 + 12551*S^6 + 5351*S^8)*HPL[{3}, -S^2])/(405*S^3*(1 + S^2)) - (8*(14 + 59*S^6)*HPL[{4}, -S^2])/(45*S^3) + (4*(-76 - 106*S^2 - 15*S^4 + 31*S^6 + 61*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (32*(-11 + 10*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (112*(-5 + 7*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (4*(60 + 30*S^2 + 121*S^4 + 61*S^6)*Zeta[3])/(9*S*(1 + S^2)) + HPL[{0}, S^2]*((15228 + 7065*S^2 + 24854*S^4)/(486*S) + (Pi^2*(11430 + 5715*S^2 + 27094*S^4 + 15664*S^6))/(1215*S*(1 + S^2)) + (14*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^2)/(9*S^3*(1 + S^2)) + (224*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + (2*(-61 + 389*S^2 + 225*S^4 + 1046*S^6 + 596*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((254*Pi^2*(1 + S^6))/(27*S^3) + (928 + 1317*S^2 + 1710*S^4 + 1321*S^6)/(27*S^3) + (100*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2}, -S^2])/(3*S^3)) - (4*(-10 + 17*S^6)*HPL[{3}, -S^2])/(27*S^3) + (32*(-20 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - 8*S^3*Zeta[3]) + HPL[{1}, -S^2]*(((1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(486*S^3) + (Pi^2*(716 + 2372*S^2 + 828*S^4 + 2729*S^6 + 1073*S^8))/(81*S^3*(1 + S^2)) + (2*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) - (320*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (40*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (80*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) + HPL[{0}, S^2]^5*((-3083*Pi^4*S^3)/97200 + (84280 - 18959*S^2 - 888165*S^4)/(466560*S) + (Pi^2*(5498 - 12728*S^2 - 71039*S^4 - 53263*S^6))/(77760*S*(1 + S^2)) + ((-596 - 7223*S^2 - 3426*S^4 - 12929*S^6 - 6302*S^8)*HPL[{1}, -S^2]^3)/(9720*S^3*(1 + S^2)) - (91*(1 + S^6)*HPL[{1}, -S^2]^4)/(540*S^3) + ((Pi^2*(15 - 1246*S^6))/(6480*S^3) + (810 - 357*S^2 - 6423*S^4 - 21619*S^6 - 16813*S^8)/(12960*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((5 - 142*S^6)*HPL[{2}, -S^2]^2)/(720*S^3) + HPL[{1}, -S^2]^2*((-427*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(2160*S^3) + (260 - 3856*S^2 - 60801*S^4 - 102784*S^6 - 48799*S^8)/(38880*S^3*(1 + S^2)) - (461*(1 + S^6)*HPL[{2}, -S^2])/(1080*S^3)) + ((12 - 6*S^4 + S^6 + 13*S^8)*HPL[{3}, -S^2])/(432*S^3*(1 + S^2)) + ((-1 - 2*S^6)*HPL[{4}, -S^2])/(24*S^3) + ((302 + 1249*S^2 + 511*S^4 + 582*S^6 - 365*S^8)*HPL[{2, 1}, -S^2])/(1080*S^3*(1 + S^2)) + (9*S^3*HPL[{3, 1}, -S^2])/10 + ((15 - 511*S^6)*HPL[{2, 1, 1}, -S^2])/(270*S^3) + ((-24 - 12*S^2 - 377*S^4 - 353*S^6)*Zeta[3])/(216*S*(1 + S^2)) + HPL[{1}, -S^2]*((15400 + 29623*S^2 - 170598*S^4 - 343355*S^6 - 166634*S^8)/(116640*S^3*(1 + S^2)) + (Pi^2*(2659 - 12788*S^2 - 7836*S^4 - 34559*S^6 - 19112*S^8))/(38880*S^3*(1 + S^2)) + ((-202 - 2071*S^2 - 972*S^4 - 3598*S^6 - 1729*S^8)*HPL[{2}, -S^2])/(2160*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{3}, -S^2])/(36*S^3) + (461*(1 + S^6)*HPL[{2, 1}, -S^2])/(540*S^3) - ((1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + ((258010 + 303953*S^2 - 37396*S^4 - 76859*S^6)/(1944*S*(1 + S^2)) + (Pi^2*(7694 + 8449*S^2 - 91*S^4 - 1080*S^6))/(324*S*(1 + S^2)))*Zeta[5] + HPL[{0}, S^2]^4*((-1255440 - 1459869*S^2 - 7642466*S^4 - 7508021*S^6)/(839808*S*(1 + S^2)) + (Pi^2*(-34002 - 88173*S^2 - 496415*S^4 - 453908*S^6))/(139968*S*(1 + S^2)) + (Pi^4*(-6624 - 3312*S^2 - 16417*S^4 - 9793*S^6))/(25920*S*(1 + S^2)) + ((-457 - 2704*S^2 - 1146*S^4 - 4153*S^6 - 1906*S^8)*HPL[{1}, -S^2]^4)/(1296*S^3*(1 + S^2)) - (31*(1 + S^6)*HPL[{1}, -S^2]^5)/(90*S^3) + ((-1 - 465*S^2 - 232*S^4 - 1257*S^6 - 793*S^8)*HPL[{2}, -S^2]^2)/(432*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-391*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(648*S^3) + (-631 - 1826*S^2 - 6864*S^4 - 10306*S^6 - 4817*S^8)/(1296*S^3*(1 + S^2)) - (245*(1 + S^6)*HPL[{2}, -S^2])/(162*S^3)) + ((Pi^2*(-5 + 11*S^6))/(216*S^3) + (-335 - 230*S^2 - 177*S^4 - 905*S^6 - 407*S^8)/(1296*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-35 - 71*S^2 - 179*S^6 - 143*S^8)*HPL[{4}, -S^2])/(216*S^3*(1 + S^2)) + ((5 + 4*S^6)*HPL[{5}, -S^2])/(18*S^3) + ((Pi^2*(985 - 122*S^6))/(648*S^3) + (5374 + 7141*S^2 + 32559*S^4 + 27419*S^6 - 3319*S^8)/(3888*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-100 + 864*S^2 + 464*S^4 + 2761*S^6 + 1797*S^8)*HPL[{3, 1}, -S^2])/(216*S^3*(1 + S^2)) - HPL[{3, 2}, -S^2]/(6*S^3) + ((-7 - 8*S^6)*HPL[{4, 1}, -S^2])/(36*S^3) + ((45 - 445*S^2 - 245*S^4 - 1444*S^6 - 954*S^8)*HPL[{2, 1, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((-473 - 4*S^6)*HPL[{2, 2, 1}, -S^2])/(54*S^3) + ((-161 + S^6)*HPL[{3, 1, 1}, -S^2])/(6*S^3) + ((505 - 32*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3) + ((-281*Pi^2*S^3)/324 + (342 - 480*S^2 - 6001*S^4 - 5629*S^6)/(1296*S*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((-16537 - 39919*S^2 - 183429*S^4 - 302071*S^6 - 145912*S^8)/(23328*S^3*(1 + S^2)) + (Pi^2*(-517 - 5254*S^2 - 2436*S^4 - 9133*S^6 - 4396*S^8))/(2592*S^3*(1 + S^2)) + ((-382 - 2343*S^2 - 982*S^4 - 3666*S^6 - 1705*S^8)*HPL[{2}, -S^2])/(432*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{3}, -S^2])/(9*S^3) + (245*(1 + S^6)*HPL[{2, 1}, -S^2])/(54*S^3) - (19*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(54*S^3)) + HPL[{2}, -S^2]*((-5235 - 19584*S^2 - 44916*S^4 - 179371*S^6 - 146212*S^8)/(23328*S^3*(1 + S^2)) + (Pi^2*(45 - 925*S^2 - 485*S^4 - 3259*S^6 - 2289*S^8))/(1296*S^3*(1 + S^2)) + HPL[{3}, -S^2]/(12*S^3) + ((473 + 4*S^6)*HPL[{2, 1}, -S^2])/(108*S^3) - (5*(1 + 2*S^6)*Zeta[3])/(36*S^3)) + HPL[{1}, -S^2]*((-23*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(90*S^3) + (-157850 - 334523*S^2 - 1188771*S^4 - 1987877*S^6 - 987443*S^8)/(139968*S^3*(1 + S^2)) + (Pi^2*(-1979 - 4529*S^2 - 22431*S^4 - 37679*S^6 - 18608*S^8))/(7776*S^3*(1 + S^2)) + ((-485*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(648*S^3) + (-2477 - 6947*S^2 - 27111*S^4 - 42965*S^6 - 20378*S^8)/(3888*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (29*(1 + S^6)*HPL[{2}, -S^2]^2)/(27*S^3) + ((4 - 15*S^6 - 11*S^8)*HPL[{3}, -S^2])/(24*S^3*(1 + S^2)) - (2*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + ((382 + 2343*S^2 + 982*S^4 + 3666*S^6 + 1705*S^8)*HPL[{2, 1}, -S^2])/(216*S^3*(1 + S^2)) + (122*(1 + S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (245*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + ((29 - 30*S^2 - 42*S^4 - 119*S^6 - 60*S^8)*Zeta[3])/(72*S^3*(1 + S^2))) - (125*S^3*Zeta[5])/27) + Log[T]^4*((-16465 - 27256*S^2)/(2916*S) + (Pi^2*(-13638 - 14094*S^2 - 25949*S^4))/(1458*S) + (Pi^4*(-7422 - 3711*S^2 - 14132*S^4 - 6710*S^6))/(1620*S*(1 + S^2)) - (283*S^3*HPL[{0}, S^2]^5)/810 - (35*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)) - (112*(1 + S^6)*HPL[{1}, -S^2]^5)/(9*S^3) + HPL[{0}, S^2]^4*((-186 - 93*S^2 - 535*S^4 - 349*S^6)/(108*S*(1 + S^2)) - (31*(1 + S^6)*HPL[{1}, -S^2])/(18*S^3)) + ((-698 - 1874*S^2 - 588*S^4 - 2211*S^6 - 1035*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + HPL[{0}, S^2]^3*((-613*Pi^2*S^3)/243 + (-12762 - 29655*S^2 - 64159*S^4 - 47914*S^6)/(2916*S*(1 + S^2)) + ((-745 - 3337*S^2 - 1314*S^4 - 4606*S^6 - 2014*S^8)*HPL[{1}, -S^2])/(162*S^3*(1 + S^2)) - (215*(1 + S^6)*HPL[{1}, -S^2]^2)/(27*S^3) + ((6 - 205*S^6)*HPL[{2}, -S^2])/(27*S^3)) + HPL[{1}, -S^2]^3*((-460*Pi^2*(1 + S^6))/(27*S^3) - (5*(928 + 1317*S^2 + 1710*S^4 + 1321*S^6))/(81*S^3) - (100*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((2*Pi^2*(7 + 585*S^6))/(81*S^3) + (346 + 27243*S^2 + 6777*S^4 + 12147*S^6)/(243*S^3))*HPL[{3}, -S^2] + (2*(552 + 1830*S^2 + 639*S^4 + 1976*S^6 + 698*S^8)*HPL[{4}, -S^2])/(81*S^3*(1 + S^2)) + (4*(-15 + 113*S^6)*HPL[{5}, -S^2])/(27*S^3) + ((17192 - 17163*S^2 + 32787*S^4 - 12763*S^6)/(243*S^3) - (274*Pi^2*(-11 + 4*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] + (2*(-5759 - 5903*S^2 - 72*S^4 + 5783*S^6 + 5927*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) - (4*(-83 + 1027*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) - (40*(-1 + 37*S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (20*(-311 - 221*S^2 + 45*S^4 + 541*S^6 + 451*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(227 + 162*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(333 + 58*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (160*(-25 + 17*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((1124*Pi^2*S^3)/81 + (22752 + 4887*S^2 + 12763*S^4)/(243*S))*Zeta[3] + HPL[{0}, S^2]^2*((-15126 - 12573*S^2 - 51898*S^4)/(972*S) + (Pi^2*(-2736 - 1368*S^2 - 7085*S^4 - 4349*S^6))/(324*S*(1 + S^2)) - (5*(233 + 881*S^2 + 324*S^4 + 1112*S^6 + 464*S^8)*HPL[{1}, -S^2]^2)/(54*S^3*(1 + S^2)) - (20*(1 + S^6)*HPL[{1}, -S^2]^3)/S^3 + ((529 - 3773*S^2 - 2151*S^4 - 11171*S^6 - 6869*S^8)*HPL[{2}, -S^2])/(162*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-5728 - 9285*S^2 - 19854*S^4 - 16081*S^6)/(324*S^3) - (76*Pi^2*(1 + S^6))/(9*S^3) - (239*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-31 + 60*S^6)*HPL[{3}, -S^2])/(27*S^3) - (2*(-757 + 38*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (104*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^2*((-5*(1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(972*S^3) - (5*Pi^2*(716 + 2372*S^2 + 828*S^4 + 2729*S^6 + 1073*S^8))/(162*S^3*(1 + S^2)) - (5*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (800*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (100*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (200*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((13796 - 2976*S^2 - 1347*S^4 - 25949*S^6)/(243*S^3) + (Pi^2*(2597 - 229*S^2 - 1413*S^4 - 9643*S^6 - 6817*S^8))/(243*S^3*(1 + S^2)) + (4*(-24 + 181*S^6)*HPL[{3}, -S^2])/(9*S^3) + (4*(227 + 162*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(7 + 472*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]*((-1237*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) - ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(2916*S^3) - (2*Pi^2*(2456 + 3630*S^2 + 5688*S^4 + 4487*S^6))/(243*S^3) + ((1975 + 1743*S^2 - 6087*S^4 - 5855*S^6)/(81*S^3) - (314*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2] - (392*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + (2*(562 + 1362*S^2 + 400*S^4 + 1113*S^6 + 313*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (284*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (10*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (32*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (200*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (50*(50 + 122*S^2 + 36*S^4 + 101*S^6 + 29*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]*((-10279*Pi^4*S^3)/2430 + (-216747 - 77397*S^2 - 396484*S^4)/(2916*S) + (Pi^2*(-53532 - 94725*S^2 - 147904*S^4 - 107359*S^6))/(2916*S*(1 + S^2)) - (70*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^3)/(27*S^3*(1 + S^2)) - (280*(1 + S^6)*HPL[{1}, -S^2]^4)/(9*S^3) + ((4466 - 38115*S^2 - 21123*S^4 - 59095*S^6)/(486*S^3) + (Pi^2*(31 - 600*S^6))/(27*S^3))*HPL[{2}, -S^2] + ((-17 - 1142*S^6)*HPL[{2}, -S^2]^2)/(27*S^3) + HPL[{1}, -S^2]^2*((-635*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (5*(1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(54*S^3) - (250*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + ((-319 + 41*S^2 + 234*S^4 + 651*S^6 + 291*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) - (4*(-1 + 13*S^6)*HPL[{4}, -S^2])/(9*S^3) - (10*(-478 - 928*S^2 - 225*S^4 - 412*S^6 + 38*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-29 + 391*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (40*(-5 + 79*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(738 + 369*S^2 + 1576*S^4 + 838*S^6)*Zeta[3])/(81*S*(1 + S^2)) + HPL[{1}, -S^2]*((-5*(1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(972*S^3) + (Pi^2*(-3160 - 10792*S^2 - 3834*S^4 - 12691*S^6 - 5059*S^8))/(162*S^3*(1 + S^2)) - (5*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{3}, -S^2])/S^3 + (500*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (164*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3))) + (2000*S^3*Zeta[5])/27) + HPL[{1}, -S^2]^4*(-((1 + S^2)*(422663 + 99650*S^2 + 875723*S^4))/(11664*S^3) + (Pi^2*(-35631 - 49802*S^2 - 90717*S^4 - 76258*S^6))/(3888*S^3) + (Pi^4*(-33926 - 122951*S^2 - 44454*S^4 - 151082*S^6 - 62057*S^8))/(19440*S^3*(1 + S^2)) + ((-1163 - 3515*S^2 - 1176*S^4 - 3737*S^6 - 1385*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((205*Pi^2*(1 + S^6))/(27*S^3) + (10561 + 13896*S^2 + 7515*S^4 + 4252*S^6)/(162*S^3))*HPL[{3}, -S^2] + ((228 + 511*S^2 + 140*S^4 + 369*S^6 + 86*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (62*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((314*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(81*S^3))*HPL[{2, 1}, -S^2] + (2*(-523 - 571*S^2 - 24*S^4 + 398*S^6 + 446*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (220*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) - (2264*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (10*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (1568*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (3104*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (200*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((55*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (4096 + 5235*S^2 + 2898*S^4 + 1867*S^6)/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(324*S^3) + (Pi^2*(-521 - 4277*S^2 - 1860*S^4 - 7253*S^6 - 3497*S^8))/(324*S^3*(1 + S^2)) + (110*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (784*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (328*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (268*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{4}, -S^2]*((441402 + 2403648*S^2 + 1196007*S^4 - 2403691*S^6 - 1497484*S^8)/(34992*S^3*(1 + S^2)) + (Pi^2*(13935 + 83718*S^2 + 66945*S^4 - 40391*S^6 - 34961*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(2075 + 5588*S^2 + 2022*S^4 + 1661*S^6 - 1852*S^8))/(4860*S^3*(1 + S^2)) + (2*(-145 + 12*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-18508 - 4473*S^2 - 11403*S^4 - 5024*S^6)/(162*S^3) + (13*Pi^2*(-29 + 4*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (2*(-472 + 599*S^2 + 603*S^4 + 1845*S^6 + 774*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-43 + 68*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (8*(-44 + 57*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (2*(-829 + 1217*S^2 + 1041*S^4 + 3699*S^6 + 1653*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(395 + 56*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (4*(1211 + 72*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (32*(-100 + 11*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((Pi^2*(-35 + 32*S^6))/(27*S^3) + (-144 + 1854*S^2 + 1404*S^4 + 53*S^6 + 323*S^8)/(162*S^3*(1 + S^2)))*Zeta[3] + (2*(-39 + 32*S^6)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]^2*((-236556 - 128079*S^2 - 124836*S^4 - 506035*S^6)/(5832*S^3) + (Pi^2*(-82249 - 106353*S^2 - 99864*S^4 - 294007*S^6))/(11664*S^3) + (Pi^4*(-7690 - 37384*S^2 - 14847*S^4 - 66957*S^6 - 37263*S^8))/(9720*S^3*(1 + S^2)) + ((7*Pi^2*(5 + 81*S^6))/(54*S^3) + (375 + 26655*S^2 + 7809*S^4 + 14143*S^6)/(324*S^3))*HPL[{3}, -S^2] + ((197 + 863*S^2 + 333*S^4 + 1119*S^6 + 453*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + ((-23 + 86*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((8656 - 8223*S^2 + 14619*S^4 - 6014*S^6)/(162*S^3) - (2*Pi^2*(-353 + 123*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((-5383 - 5743*S^2 - 180*S^4 + 5004*S^6 + 5364*S^8)*HPL[{3, 1}, -S^2])/(54*S^3*(1 + S^2)) - (5*(-19 + 204*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + ((73 - 3284*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + ((4385 + 3269*S^2 - 558*S^4 - 6919*S^6 - 5803*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(325 + 242*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (2*(1871 + 363*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (112*(-25 + 17*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((Pi^2*(-29 + 247*S^6))/(27*S^3) + (-2938 + 21543*S^2 + 4407*S^4 + 11447*S^6)/(324*S^3))*Zeta[3] + (2*(-26 + 187*S^6)*Zeta[5])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((5128337 - 1454691*S^2 - 1380333*S^4 - 13692565*S^6)/(17496*S^3) + (Pi^2*(173211 + 54234*S^2 - 217749*S^4 - 730234*S^6 - 627574*S^8))/(2916*S^3*(1 + S^2)) + (Pi^4*(41807 - 37771*S^2 - 39789*S^4 - 249427*S^6 - 169849*S^8))/(4860*S^3*(1 + S^2)) - (448*(-25 + 17*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (32*(-326 + 57*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (32*(227 + 162*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((8*Pi^2*(2 + 259*S^6))/(27*S^3) + (2*(-1046 + 21265*S^2 + 27621*S^4 + 17818*S^6 + 11860*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] + (8*(-14 + 417*S^6)*Zeta[5])/(9*S^3)) + HPL[{3, 1}, -S^2]*((-6864445 - 960018*S^2 + 777513*S^4 + 13754448*S^6)/(34992*S^3) + (Pi^4*(-50565 + 17577*S^2 + 33540*S^4 + 225634*S^6 + 157492*S^8))/(9720*S^3*(1 + S^2)) + (Pi^2*(-217561 - 154207*S^2 + 137004*S^4 + 688914*S^6 + 611376*S^8))/(5832*S^3*(1 + S^2)) + (8*(-4 + 509*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (4*(-265 + 3274*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(5161 + 12211*S^2 + 3516*S^4 + 12511*S^6 + 5461*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-571 + 605*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(3087 + 1210*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (32*(278 + 305*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-2*Pi^2*(1 + 175*S^6))/(9*S^3) + (800 - 22066*S^2 - 28317*S^4 - 18501*S^6 - 12294*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (4*(-5 + 431*S^6)*Zeta[5])/(9*S^3)) + Zeta[3]*((1457092 + 240735*S^2 - 571445*S^4)/(11664*S) + (Pi^4*(190890 + 208989*S^2 - 8197*S^4 - 34990*S^6))/(58320*S*(1 + S^2)) + (Pi^2*(917574 + 1117893*S^2 + 242534*S^4 + 22775*S^6))/(34992*S*(1 + S^2)) + (4*(-264 - 132*S^2 + 251*S^4 + 515*S^6)*Zeta[5])/(27*S*(1 + S^2))) + HPL[{3}, -S^2]*((442764 + 6579405*S^2 - 1013511*S^4 - 511124*S^6)/(34992*S^3) + (Pi^6*(-725 + 7439*S^6))/(22680*S^3) + (Pi^2*(12704 + 530522*S^2 + 521322*S^4 + 12535*S^6 + 18751*S^8))/(17496*S^3*(1 + S^2)) + (Pi^4*(-4231 + 101480*S^2 + 119667*S^4 + 34562*S^6 + 25412*S^8))/(29160*S^3*(1 + S^2)) + ((-2*Pi^2*(-5 + 29*S^6))/(27*S^3) + (-14 - 1075*S^2 - 1045*S^4 + 390*S^6 + 644*S^8)/(54*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((390 + 339*S^2 - 264*S^4 + 865*S^6 + 916*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (2*(145 + 44*S^6)*HPL[{6}, -S^2])/(9*S^3) - (2*(79 + 1089*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-2*Pi^2*(-79 + 566*S^6))/(27*S^3) + (5063 - 19492*S^2 - 28644*S^4 - 16856*S^6 - 12659*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((421 + 1792*S^2 + 690*S^4 + 2341*S^6 + 970*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-93 - 54*S^2 + 27*S^4 + 62*S^6 + 23*S^8)*HPL[{4, 1}, -S^2])/(3*S^3*(1 + S^2)) - (2*(7 + 58*S^6)*HPL[{4, 2}, -S^2])/(9*S^3) - (4*(51 + 10*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((2*Pi^2*(-137 + 1131*S^6))/(27*S^3) + (-9353 + 49080*S^2 + 9057*S^4 + 24622*S^6)/(81*S^3))*HPL[{2, 1, 1}, -S^2] + (2*(9543 + 16815*S^2 + 3636*S^4 + 7720*S^6 + 448*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(9675 + 16499*S^2 + 3406*S^4 + 6962*S^6 + 138*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(9 + S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) + (4*(-49 + 359*S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (20*(-268 + 6921*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (8*(-1591 - 2580*S^2 - 493*S^4 - 932*S^6 + 57*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(-169 + 1081*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (32*(-24 + 181*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(325 + 811*S^2 + 198*S^4 + 744*S^6 + 258*S^8))/(162*S^3*(1 + S^2)) + (4865 + 19817*S^2 + 16206*S^4 + 14404*S^6 + 9262*S^8)/(972*S^3*(1 + S^2)))*Zeta[3] + (2*(-3 + 11*S^6)*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*((-348935 - 65745*S^2 - 145215*S^4 - 9433*S^6)/(972*S^3) + (Pi^2*(-10031 - 16271*S^2 - 3102*S^4 - 6208*S^6 + 32*S^8))/(162*S^3*(1 + S^2)) + (4*(-63 + 11*S^6)*Zeta[3])/(9*S^3)) + ((207 + 531*S^2 + 108*S^4 + 56*S^6 - 268*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((Pi^6*(59902 - 15063*S^6))/(34020*S^3) + (3283424 - 3594147*S^2 + 14922183*S^4 + 1714335*S^6)/(34992*S^3) + (Pi^4*(339494 + 284498*S^2 + 821895*S^4 + 765369*S^6 - 125400*S^8))/(58320*S^3*(1 + S^2)) + (Pi^2*(425979 + 135192*S^2 + 1538367*S^4 + 1872995*S^6 + 32177*S^8))/(17496*S^3*(1 + S^2)) + ((-2653 - 10878*S^2 - 12765*S^4 - 4198*S^6)/(27*S^3) - (2*Pi^2*(425 + 213*S^6))/(9*S^3))*HPL[{3, 1}, -S^2] + ((18231 + 31371*S^2 + 6570*S^4 + 13370*S^6 + 230*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-29458 - 49228*S^2 - 9867*S^4 - 19461*S^6 + 309*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(137 + 20*S^6)*HPL[{4, 2}, -S^2])/(3*S^3) + (4*(927 + 17*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-8*Pi^2*(703 + 256*S^6))/(27*S^3) - (2*(4321 + 9831*S^2 + 13653*S^4 + 3089*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(-4385 - 3269*S^2 + 558*S^4 + 6919*S^6 + 5803*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-1203 + 1891*S^2 + 1544*S^4 + 8783*S^6 + 5689*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (52*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 + (4*(1183 + 851*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (16*(775 + 748*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (16*(698 + 1874*S^2 + 588*S^4 + 2211*S^6 + 1035*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (32*(278 + 305*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (32*(227 + 162*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-157893 - 205446*S^2 - 113997*S^4 - 75130*S^6 - 4798*S^8)/(486*S^3*(1 + S^2)) + (Pi^2*(-4748 - 7988*S^2 - 1629*S^4 - 3254*S^6 - 14*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] - (4*(-9 + 20*S^6)*Zeta[3]^2)/(9*S^3) + (2*(-3956 - 6389*S^2 - 1221*S^4 - 2389*S^6 + 44*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((-17153*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(22680*S^3) - ((1 + S^2)*(3757531 + 762416*S^2 + 9134503*S^4))/(52488*S^3) + (Pi^2*(-1796785 - 2369925*S^2 - 5012091*S^4 - 4431175*S^6))/(104976*S^3) + (Pi^4*(-178487 - 451049*S^2 - 798153*S^4 - 953759*S^6 - 426764*S^8))/(58320*S^3*(1 + S^2)) + ((-6683 - 9489*S^2 - 11754*S^4 - 9020*S^6)/(162*S^3) - (319*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2]^2 - (62*(1 + S^6)*HPL[{2}, -S^2]^3)/(27*S^3) - (74*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((401*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + (24043 + 58261*S^2 + 45549*S^4 + 13783*S^6 + 1804*S^8)/(486*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(-613 - 983*S^2 - 182*S^4 - 191*S^6 + 179*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) - (70*(1 + S^6)*HPL[{6}, -S^2])/(9*S^3) + (1568*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((152*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (2*(1 + S^2)*(-3878 - 529*S^2 + 4768*S^4))/(81*S^3))*HPL[{3, 1}, -S^2] - (4*(1344 + 3323*S^2 + 988*S^4 + 2798*S^6 + 819*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (4*(4714 + 11503*S^2 + 3390*S^4 + 9502*S^6 + 2713*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) - (26*(1 + S^6)*HPL[{4, 2}, -S^2])/S^3 - (1168*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-1256*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (4*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(81*S^3))*HPL[{2, 1, 1}, -S^2] - (8*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(601 + 2153*S^2 + 776*S^4 + 2624*S^6 + 1072*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (352*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (40*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (128*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (800*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((48677 + 60294*S^2 + 30519*S^4 + 19766*S^6)/(486*S^3) + (Pi^2*(1407 + 3386*S^2 + 988*S^4 + 2750*S^6 + 771*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(81*S^3) + (Pi^2*(521 + 4277*S^2 + 1860*S^4 + 7253*S^6 + 3497*S^8))/(81*S^3*(1 + S^2)) - (1312*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((61939 + 78816*S^2 + 34365*S^4 + 17704*S^6)/(486*S^3) + (Pi^2*(5390 + 12791*S^2 + 3732*S^4 + 10073*S^6 + 2672*S^8))/(243*S^3*(1 + S^2)) - (440*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((-4421*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) - ((1 + S^2)*(-233717 - 5557*S^2 + 945778*S^4))/(8748*S^3) + (Pi^2*(-2149 - 14560*S^2 - 104004*S^4 - 175732*S^6 - 82843*S^8))/(2916*S^3*(1 + S^2)) + (10*(806 + 1994*S^2 + 594*S^4 + 1679*S^6 + 491*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (226*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (1568*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(1351 + 3307*S^2 + 960*S^4 + 2773*S^6 + 817*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + (2*(1220 + 2829*S^2 + 806*S^4 + 2178*S^6 + 569*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + Log[T]^3*((35159*Pi^6*S^3)/34020 + (5*(518 + 1017*S^2))/(486*S) + (Pi^2*(223890 + 199713*S^2 + 676271*S^4))/(17496*S) + (Pi^4*(228726 + 495648*S^2 + 706255*S^4 + 438280*S^6))/(43740*S*(1 + S^2)) + (11*S^3*HPL[{0}, S^2]^6)/81 + (28*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^5)/(27*S^3*(1 + S^2)) + (224*(1 + S^6)*HPL[{1}, -S^2]^6)/(27*S^3) + HPL[{0}, S^2]^5*((13*(126 + 63*S^2 + 403*S^4 + 277*S^6))/(2430*S*(1 + S^2)) + (91*(1 + S^6)*HPL[{1}, -S^2])/(135*S^3)) + ((2*Pi^2*(254 + 701*S^6))/(81*S^3) + (9045 + 9147*S^2 + 9855*S^4 + 14951*S^6)/(162*S^3))*HPL[{2}, -S^2]^2 + (4*(-257 + 331*S^6)*HPL[{2}, -S^2]^3)/(81*S^3) + HPL[{1}, -S^2]^4*((460*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (5*(1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(81*S^3) + (100*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + HPL[{0}, S^2]^4*((613*Pi^2*S^3)/486 + (3843 + 12033*S^2 + 32342*S^4 + 24557*S^6)/(2916*S*(1 + S^2)) + ((457 + 2704*S^2 + 1146*S^4 + 4153*S^6 + 1906*S^8)*HPL[{1}, -S^2])/(324*S^3*(1 + S^2)) + (31*(1 + S^6)*HPL[{1}, -S^2]^2)/(9*S^3) + ((-5 + 174*S^6)*HPL[{2}, -S^2])/(54*S^3)) + (4*(-13 + 107*S^6)*HPL[{3}, -S^2]^2)/(27*S^3) + ((-2*Pi^2*(93 + 313*S^6))/(81*S^3) + (-6117 - 28113*S^2 - 24921*S^4 - 6058*S^6 - 2809*S^8)/(243*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(-426 - 1542*S^2 - 558*S^4 - 709*S^6 + 407*S^8)*HPL[{5}, -S^2])/(81*S^3*(1 + S^2)) + (4*(54 + 115*S^6)*HPL[{6}, -S^2])/(27*S^3) - (40*(33 + 46*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + HPL[{0}, S^2]^3*((Pi^2*(2382 + 1191*S^2 + 6959*S^4 + 4577*S^6))/(486*S*(1 + S^2)) + (17948 + 39283*S^2 + 125828*S^4 + 105573*S^6)/(2916*S*(1 + S^2)) + ((745 + 3337*S^2 + 1314*S^4 + 4606*S^6 + 2014*S^8)*HPL[{1}, -S^2]^2)/(81*S^3*(1 + S^2)) + (860*(1 + S^6)*HPL[{1}, -S^2]^3)/(81*S^3) + ((-338 + 3187*S^2 + 1758*S^4 + 9570*S^6 + 6045*S^8)*HPL[{2}, -S^2])/(243*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((397*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + (4907 + 13775*S^2 + 35340*S^4 + 47579*S^6 + 21755*S^8)/(729*S^3*(1 + S^2)) + (392*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) - (2*(-11 + 4*S^6)*HPL[{3}, -S^2])/(27*S^3) + (4*(-202 + 9*S^6)*HPL[{2, 1}, -S^2])/(27*S^3)) + ((-8*Pi^2*(-354 + 671*S^6))/(81*S^3) - (2*(-35539 - 1449*S^2 - 1971*S^4 + 43635*S^6))/(243*S^3))*HPL[{3, 1}, -S^2] + (20*(-202 + 986*S^2 + 594*S^4 + 2177*S^6 + 989*S^8)*HPL[{3, 2}, -S^2])/(81*S^3*(1 + S^2)) + (8*(-729 + 9459*S^2 + 5094*S^4 + 18142*S^6 + 7954*S^8)*HPL[{4, 1}, -S^2])/(81*S^3*(1 + S^2)) + (148*(-1 + 11*S^6)*HPL[{4, 2}, -S^2])/(27*S^3) + (400*(1 + 17*S^6)*HPL[{5, 1}, -S^2])/(27*S^3) + ((40*Pi^2*(-113 + 298*S^6))/(81*S^3) + (4*(-29042 + 6705*S^2 + 3735*S^4 + 47893*S^6))/(243*S^3))*HPL[{2, 1, 1}, -S^2] + (16*(465 + 1641*S^2 + 588*S^4 + 1526*S^6 + 350*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(8201 + 22169*S^2 + 6984*S^4 + 14917*S^6 + 949*S^8)*HPL[{3, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) - (16*(-61 + 59*S^6)*HPL[{3, 1, 2}, -S^2])/(27*S^3) + (16*(-151 + 201*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (32*(-271 + 272*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (80*(-76 - 106*S^2 - 15*S^4 + 31*S^6 + 61*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (640*(-11 + 10*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (2240*(-5 + 7*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-2*(24762 + 5175*S^2 + 8287*S^4))/(243*S) - (2*Pi^2*(2970 + 1485*S^2 + 5876*S^4 + 2906*S^6))/(243*S*(1 + S^2)))*Zeta[3] - (16*S^3*Zeta[3]^2)/9 + HPL[{1}, -S^2]^3*((5*(1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(729*S^3) + (10*Pi^2*(716 + 2372*S^2 + 828*S^4 + 2729*S^6 + 1073*S^8))/(243*S^3*(1 + S^2)) + (20*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2}, -S^2])/(81*S^3*(1 + S^2)) - (3200*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) - (400*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (800*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((2*(-14341 + 18753*S^2 - 41367*S^4 + 8287*S^6))/(243*S^3) + (2*Pi^2*(-6757 - 12373*S^2 - 2754*S^4 - 2473*S^6 + 3143*S^8))/(243*S^3*(1 + S^2)) + (80*(97 + 4*S^6)*Zeta[3])/(27*S^3)) + HPL[{3}, -S^2]*((-3152 - 111471*S^2 - 20034*S^4 - 35271*S^6)/(486*S^3) + (Pi^2*(-42 - 7461*S^2 - 3768*S^4 - 12859*S^6 - 5440*S^8))/(243*S^3*(1 + S^2)) - (16*(-189 + 16*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (8*(19 + 53*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]^2*((1237*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) + ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(1458*S^3) + (4*Pi^2*(2456 + 3630*S^2 + 5688*S^4 + 4487*S^6))/(243*S^3) + ((628*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(81*S^3))*HPL[{2}, -S^2] + (784*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) - (4*(562 + 1362*S^2 + 400*S^4 + 1113*S^6 + 313*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (568*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (20*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (64*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (400*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (100*(50 + 122*S^2 + 36*S^4 + 101*S^6 + 29*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^4*(-4256 + 17677*S^6))/(2430*S^3) + (-307463 + 72027*S^2 + 40689*S^4 + 676271*S^6)/(2916*S^3) + (Pi^2*(-31189 - 6763*S^2 + 45135*S^4 + 117866*S^6 + 96509*S^8))/(1458*S^3*(1 + S^2)) - (4*(-743 + 2230*S^2 + 1491*S^4 + 5599*S^6 + 2626*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) - (4*(-61 + 383*S^6)*HPL[{4}, -S^2])/(27*S^3) - (8*(465 + 1641*S^2 + 588*S^4 + 1526*S^6 + 350*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(310 + 283*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (80*(33 + 46*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (4*(-83 + 2833*S^2 + 1404*S^4 + 5263*S^6 + 2347*S^8)*Zeta[3])/(81*S^3*(1 + S^2))) + HPL[{0}, S^2]^2*((16369*Pi^4*S^3)/4860 + (154140 + 99153*S^2 + 676271*S^4)/(5832*S) + (Pi^2*(27216 + 62631*S^2 + 131612*S^4 + 97007*S^6))/(2916*S*(1 + S^2)) + (10*(233 + 881*S^2 + 324*S^4 + 1112*S^6 + 464*S^8)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)) + (20*(1 + S^6)*HPL[{1}, -S^2]^4)/S^3 + ((Pi^2*(-55 + 1277*S^6))/(81*S^3) + (-2147 + 15574*S^2 + 34695*S^4 + 66238*S^6 + 48616*S^8)/(486*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((13 + 712*S^6)*HPL[{2}, -S^2]^2)/(27*S^3) + HPL[{1}, -S^2]^2*((152*Pi^2*(1 + S^6))/(9*S^3) + (5728 + 9285*S^2 + 19854*S^4 + 16081*S^6)/(162*S^3) + (478*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((127 - 92*S^2 - 168*S^4 - 308*S^6 - 89*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (2*(-9 + 41*S^6)*HPL[{4}, -S^2])/(27*S^3) + (2*(-3337 - 7603*S^2 - 2079*S^4 - 3868*S^6 + 398*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) - (8*(-24 + 371*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (40*(-8 + 151*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) - (2*(270 + 135*S^2 + 431*S^4 + 161*S^6)*Zeta[3])/(81*S*(1 + S^2)) + HPL[{1}, -S^2]*((7277 + 11139*S^2 + 30204*S^4 + 26126*S^6)/(243*S^3) + (Pi^2*(1622 + 7109*S^2 + 2766*S^4 + 9713*S^6 + 4226*S^8))/(162*S^3*(1 + S^2)) + ((312 + 1264*S^2 + 470*S^4 + 1671*S^6 + 719*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (20*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (956*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3))) - (8*(402 + 201*S^2 + 853*S^4 + 451*S^6)*Zeta[5])/(27*S*(1 + S^2)) + HPL[{0}, S^2]*((420200 + 118145*S^2 + 875723*S^4)/(2916*S) + (Pi^4*(40488 + 20244*S^2 + 104059*S^4 + 63571*S^6))/(4860*S*(1 + S^2)) + (Pi^2*(94088 + 150748*S^2 + 285423*S^4 + 229843*S^6))/(2916*S*(1 + S^2)) + (70*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^4)/(27*S^3*(1 + S^2)) + (224*(1 + S^6)*HPL[{1}, -S^2]^5)/(9*S^3) + ((-31 + 6989*S^2 + 3456*S^4 + 15473*S^6 + 8453*S^8)*HPL[{2}, -S^2]^2)/(81*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((2540*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + (10*(1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(81*S^3) + (1000*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-2*Pi^2*(-83 + 97*S^6))/(81*S^3) + (2040 - 3579*S^2 + 1362*S^4 + 1397*S^6)/(243*S^3))*HPL[{3}, -S^2] + (2*(-237 + 150*S^2 + 207*S^4 + 1181*S^6 + 794*S^8)*HPL[{4}, -S^2])/(81*S^3*(1 + S^2)) + (8*(5 + 3*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((4*Pi^2*(-602 + 29*S^6))/(27*S^3) + (2*(-41768 - 14247*S^2 - 50175*S^4 + 1561*S^6))/(243*S^3))*HPL[{2, 1}, -S^2] - (8*(-526 + 2840*S^2 + 1683*S^4 + 7738*S^6 + 4372*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) + (4*(53 + 157*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) + (16*(-1 + 40*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (40*(-61 + 389*S^2 + 225*S^4 + 1046*S^6 + 596*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(1159 + 34*S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) + (16*(3527 + 17*S^6)*HPL[{3, 1, 1}, -S^2])/(27*S^3) + (640*(-20 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-20*Pi^2*S^3)/3 - (4*(2853 + 783*S^2 + 2129*S^4))/(243*S))*Zeta[3] + HPL[{1}, -S^2]^2*((5*(1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(486*S^3) + (Pi^2*(3160 + 10792*S^2 + 3834*S^4 + 12691*S^6 + 5059*S^8))/(81*S^3*(1 + S^2)) + (10*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{3}, -S^2])/S^3 - (1000*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (328*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((-6507 + 72198*S^2 + 35907*S^4 + 123562*S^6)/(486*S^3) + (Pi^2*(-1253 + 9022*S^2 + 5133*S^4 + 25260*S^6 + 14985*S^8))/(243*S^3*(1 + S^2)) - (4*(7 + 25*S^6)*HPL[{3}, -S^2])/(9*S^3) - (8*(1159 + 34*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (8*(-1 + 122*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]*((3374*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(1458*S^3) + (Pi^2*(51574 + 128575*S^2 + 206895*S^4 + 231553*S^6 + 102955*S^8))/(1458*S^3*(1 + S^2)) + ((1142*Pi^2*(1 + S^6))/(27*S^3) + (2*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(81*S^3))*HPL[{2}, -S^2] + (784*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) - (4*(13 + 25*S^2 + 6*S^4 + 12*S^6)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) + (28*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (20*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2992*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (2000*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(319 + 811*S^2 + 246*S^4 + 706*S^6 + 214*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) - (832*S^3*Zeta[5])/27) + HPL[{1}, -S^2]*(((1 + S^2)*(422663 + 99650*S^2 + 875723*S^4))/(2916*S^3) + (Pi^2*(35631 + 49802*S^2 + 90717*S^4 + 76258*S^6))/(972*S^3) + (Pi^4*(33926 + 122951*S^2 + 44454*S^4 + 151082*S^6 + 62057*S^8))/(4860*S^3*(1 + S^2)) + (2*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((-820*Pi^2*(1 + S^6))/(27*S^3) - (2*(10561 + 13896*S^2 + 7515*S^4 + 4252*S^6))/(81*S^3))*HPL[{3}, -S^2] - (4*(228 + 511*S^2 + 140*S^4 + 369*S^6 + 86*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (248*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-1256*Pi^2*(1 + S^6))/(27*S^3) - (4*(-1975 - 1743*S^2 + 6087*S^4 + 5855*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] - (8*(-523 - 571*S^2 - 24*S^4 + 398*S^6 + 446*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (880*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (9056*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (40*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (6272*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (12416*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (800*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-220*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (4*(4096 + 5235*S^2 + 2898*S^4 + 1867*S^6))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(81*S^3) + (Pi^2*(521 + 4277*S^2 + 1860*S^4 + 7253*S^6 + 3497*S^8))/(81*S^3*(1 + S^2)) - (440*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (3136*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (1312*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (1072*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + HPL[{0}, S^2]^3*((-35159*Pi^6*S^3)/272160 + (998498 - 549895*S^2 - 17576919*S^4)/(419904*S) + (Pi^2*(11538 - 277389*S^2 - 5025185*S^4 - 4751810*S^6))/(419904*S*(1 + S^2)) + (Pi^4*(2754 - 143676*S^2 - 571624*S^4 - 430027*S^6))/(174960*S*(1 + S^2)) + ((-745 - 3337*S^2 - 1314*S^4 - 4606*S^6 - 2014*S^8)*HPL[{1}, -S^2]^5)/(810*S^3*(1 + S^2)) - (43*(1 + S^6)*HPL[{1}, -S^2]^6)/(81*S^3) + ((Pi^2*(24 - 995*S^6))/(648*S^3) + (156 - 11757*S^2 - 25734*S^4 - 52904*S^6 - 39407*S^8)/(3888*S^3*(1 + S^2)))*HPL[{2}, -S^2]^2 + ((1 - 45*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{1}, -S^2]^4*((-397*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(324*S^3) + (-4907 - 13775*S^2 - 35340*S^4 - 47579*S^6 - 21755*S^8)/(2916*S^3*(1 + S^2)) - (98*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((1 + 23*S^6)*HPL[{3}, -S^2]^2)/(54*S^3) + ((Pi^2*(-21 - 79*S^6))/(162*S^3) + (1964 + 1643*S^2 - 2946*S^4 - 7954*S^6 - 5653*S^8)/(1944*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((488 + 341*S^2 - 204*S^4 - 31*S^6 + 116*S^8)*HPL[{5}, -S^2])/(324*S^3*(1 + S^2)) + ((-20 - 17*S^6)*HPL[{6}, -S^2])/(9*S^3) + ((-9 + 569*S^6)*HPL[{2, 1}, -S^2]^2)/(27*S^3) + ((Pi^2*(-18 + 1091*S^6))/(162*S^3) + (-533 + 5521*S^2 + 13863*S^4 + 29324*S^6 + 21407*S^8)/(486*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((40 - 317*S^2 - 246*S^4 + 219*S^6 + 576*S^8)*HPL[{3, 2}, -S^2])/(324*S^3*(1 + S^2)) + ((102 - 141*S^2 - 198*S^4 + 551*S^6 + 794*S^8)*HPL[{4, 1}, -S^2])/(162*S^3*(1 + S^2)) + (2*S^3*HPL[{4, 2}, -S^2])/27 + (2*(12 + 47*S^6)*HPL[{5, 1}, -S^2])/(27*S^3) + ((1190 - 11892*S^2 - 15582*S^4 - 44241*S^6)/(486*S^3) + (Pi^2*(33 - 1126*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] + ((-2112 - 5499*S^2 - 1734*S^4 - 3136*S^6 + 251*S^8)*HPL[{2, 2, 1}, -S^2])/(81*S^3*(1 + S^2)) + (4*(-538 - 1394*S^2 - 434*S^4 - 801*S^6 + 55*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*S^3*HPL[{3, 1, 2}, -S^2])/27 - (2*(-12 + 541*S^6)*HPL[{3, 2, 1}, -S^2])/(27*S^3) - (2*(-39 + 1688*S^6)*HPL[{4, 1, 1}, -S^2])/(27*S^3) - (2*(-2281 - 5812*S^2 - 1770*S^4 - 3137*S^6 + 394*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) + (4*(-18 + 605*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3) - (8*(-6 + 205*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((23772 + 26178*S^2 - 38891*S^4 - 37085*S^6)/(5832*S*(1 + S^2)) - (5*Pi^2*(22 + 11*S^2 + 408*S^4 + 386*S^6))/(324*S*(1 + S^2)))*Zeta[3] + (2*S^3*Zeta[3]^2)/9 + HPL[{3}, -S^2]*((6520 + 7423*S^2 - 28794*S^4 - 66090*S^6 - 37689*S^8)/(11664*S^3*(1 + S^2)) + (Pi^2*(20 - 77*S^2 - 32*S^4 - 63*S^6 + 34*S^8))/(648*S^3*(1 + S^2)) - (2*(5 + 17*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (2*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^3*((-43685 - 120527*S^2 - 405513*S^4 - 610577*S^6 - 288386*S^8)/(17496*S^3*(1 + S^2)) + (Pi^2*(-2831 - 17234*S^2 - 7368*S^4 - 26747*S^6 - 12344*S^8))/(2916*S^3*(1 + S^2)) + ((-1943 - 8999*S^2 - 3528*S^4 - 12707*S^6 - 5651*S^8)*HPL[{2}, -S^2])/(486*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) + (392*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(81*S^3)) + HPL[{2, 1}, -S^2]*((48076 + 24264*S^2 + 252063*S^4 + 9356*S^6)/(5832*S^3) + (Pi^2*(3187 + 9559*S^2 + 3303*S^4 + 4883*S^6 - 1489*S^8))/(972*S^3*(1 + S^2)) + (4*(1 + 5*S^6)*Zeta[3])/(27*S^3)) + HPL[{2}, -S^2]*((Pi^4*(26 - 1283*S^6))/(1620*S^3) + (51030 - 56235*S^2 - 337569*S^4 - 1174453*S^6 - 955813*S^8)/(34992*S^3*(1 + S^2)) + (Pi^2*(3620 - 11773*S^2 - 46743*S^4 - 124680*S^6 - 94680*S^8))/(11664*S^3*(1 + S^2)) + ((-11 + 79*S^2 + 63*S^4 - 60*S^6 - 150*S^8)*HPL[{3}, -S^2])/(162*S^3*(1 + S^2)) + ((-1 - 24*S^6)*HPL[{4}, -S^2])/(27*S^3) + ((2112 + 5499*S^2 + 1734*S^4 + 3136*S^6 - 251*S^8)*HPL[{2, 1}, -S^2])/(162*S^3*(1 + S^2)) + (2*(-1 + 287*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (2*(-9 + 569*S^6)*HPL[{2, 1, 1}, -S^2])/(27*S^3) + ((-10 - 8*S^2 + 19*S^4 - 78*S^6 - 80*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) + HPL[{1}, -S^2]^2*((-1001*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1215*S^3) + (-173348 - 484253*S^2 - 2394693*S^4 - 3975587*S^6 - 1922903*S^8)/(69984*S^3*(1 + S^2)) + (Pi^2*(-9554 - 31406*S^2 - 131481*S^4 - 197942*S^6 - 92309*S^8))/(11664*S^3*(1 + S^2)) + ((-4538 - 8031*S^2 - 24501*S^4 - 21332*S^6)/(972*S^3) - (1049*Pi^2*(1 + S^6))/(324*S^3))*HPL[{2}, -S^2] - (140*(1 + S^6)*HPL[{2}, -S^2]^2)/(27*S^3) + ((101 - 28*S^2 - 42*S^4 - 406*S^6 - 277*S^8)*HPL[{3}, -S^2])/(162*S^3*(1 + S^2)) - (23*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) + ((1943 + 8999*S^2 + 3528*S^4 + 12707*S^6 + 5651*S^8)*HPL[{2, 1}, -S^2])/(162*S^3*(1 + S^2)) + (584*(1 + S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (392*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((71 + 79*S^2 + S^4 - 47*S^6 - 55*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) - (4*(2 + S^2 + 74*S^4 + 72*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((13933 - 224552*S^2 - 7273662*S^4 - 13631312*S^6 - 6689447*S^8)/(209952*S^3*(1 + S^2)) + (Pi^2*(-4295 - 20427*S^2 - 248903*S^4 - 432429*S^6 - 207218*S^8))/(23328*S^3*(1 + S^2)) + (Pi^4*(-2 - 10739*S^2 - 5458*S^4 - 22137*S^6 - 11400*S^8))/(6480*S^3*(1 + S^2)) + ((-1048 - 4417*S^2 - 1698*S^4 - 5929*S^6 - 2560*S^8)*HPL[{2}, -S^2]^2)/(324*S^3*(1 + S^2)) + (-(Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(6*S^3) + (50 + 111*S^2 - 607*S^4 - 1887*S^6 - 1039*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((23 - 262*S^2 - 156*S^4 - 595*S^6 - 310*S^8)*HPL[{4}, -S^2])/(162*S^3*(1 + S^2)) - (5*(1 + S^6)*HPL[{5}, -S^2])/(27*S^3) + ((1049*Pi^2*(1 + S^6))/(162*S^3) + (4538 + 8031*S^2 + 24501*S^4 + 21332*S^6)/(486*S^3))*HPL[{2, 1}, -S^2] + ((947 + 4445*S^2 + 1740*S^4 + 6335*S^6 + 2837*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) - (26*(1 + S^6)*HPL[{3, 2}, -S^2])/(27*S^3) - (32*(1 + S^6)*HPL[{4, 1}, -S^2])/(27*S^3) + ((-1943 - 8999*S^2 - 3528*S^4 - 12707*S^6 - 5651*S^8)*HPL[{2, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) - (1120*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) - (1136*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (784*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((-55*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (3494 + 8054*S^2 + 1317*S^4 - 5770*S^6 - 2959*S^8)/(972*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-13882 - 24901*S^2 - 109054*S^4 - 100195*S^6)/(3888*S^3) + (Pi^2*(-2549 - 15212*S^2 - 6444*S^4 - 23501*S^6 - 10838*S^8))/(1944*S^3*(1 + S^2)) + (13*(1 + S^6)*HPL[{3}, -S^2])/(27*S^3) + (560*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (5*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) - (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + ((7716 + 8259*S^2 + 974*S^4 + 971*S^6)*Zeta[7])/(54*S*(1 + S^2)) + HPL[{0}, S^2]^2*((-14851413 - 1904961*S^2 - 60108952*S^4)/(419904*S) + (Pi^2*(-5113902 - 6736731*S^2 - 30191468*S^4 - 28708607*S^6))/(839808*S*(1 + S^2)) + (Pi^4*(-430282 - 933887*S^2 - 3779403*S^4 - 3323750*S^6))/(466560*S*(1 + S^2)) + (Pi^6*(-872634 - 436317*S^2 - 2223701*S^4 - 1351067*S^6))/(1632960*S*(1 + S^2)) + ((-233 - 881*S^2 - 324*S^4 - 1112*S^6 - 464*S^8)*HPL[{1}, -S^2]^6)/(162*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^7)/(7*S^3) + ((357 - 3735*S^2 - 2046*S^4 - 10159*S^6 - 6067*S^8)*HPL[{2}, -S^2]^3)/(648*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((-5728 - 9285*S^2 - 19854*S^4 - 16081*S^6)/(1620*S^3) - (76*Pi^2*(1 + S^6))/(45*S^3) - (239*(1 + S^6)*HPL[{2}, -S^2])/(45*S^3)) + ((-26 + 34*S^2 + 21*S^4 + 298*S^6 + 238*S^8)*HPL[{3}, -S^2]^2)/(108*S^3*(1 + S^2)) + ((Pi^2*(43 + 69*S^6))/(108*S^3) + (-1525 + 1829*S^2 + 291*S^4 - 11877*S^6 - 7842*S^8)/(648*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-355 - 877*S^2 + 9*S^4 - 2196*S^6 - 1674*S^8)*HPL[{6}, -S^2])/(108*S^3*(1 + S^2)) + (5*(21 + 2*S^6)*HPL[{7}, -S^2])/(18*S^3) + ((147 + 4575*S^2 + 2214*S^4 + 10762*S^6 + 6334*S^8)*HPL[{2, 1}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((Pi^2*(-57 - 89*S^6))/(108*S^3) + (-393 - 5283*S^2 - 7269*S^4 + 3905*S^6 + 5528*S^8)/(648*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((Pi^2*(-8 - 175*S^6))/(54*S^3) + (329 - 7915*S^2 - 8757*S^4 + 11873*S^6 + 10766*S^8)/(324*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((85 + 145*S^2 + 39*S^4 + 191*S^6 + 131*S^8)*HPL[{4, 2}, -S^2])/(108*S^3*(1 + S^2)) + (2*(3 + 11*S^6)*HPL[{4, 3}, -S^2])/(9*S^3) + ((-53 + 42*S^2 + 22*S^4 + 549*S^6 + 454*S^8)*HPL[{5, 1}, -S^2])/(18*S^3*(1 + S^2)) + ((29 + 149*S^6)*HPL[{5, 2}, -S^2])/(18*S^3) + ((32 + 153*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((-2*Pi^2*(599 + 15*S^6))/(27*S^3) + (-15901 - 7950*S^2 - 36552*S^4 + 2180*S^6)/(162*S^3))*HPL[{2, 2, 1}, -S^2] + ((Pi^2*(-3655 - 9*S^6))/(27*S^3) + (-48346 - 69184*S^2 - 131973*S^4 - 108089*S^6 + 3802*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1, 1}, -S^2] + ((-95 - 3*S^2 - 3*S^4 - 22*S^6)*HPL[{3, 1, 2}, -S^2])/(54*S^3) + ((619 - 7568*S^2 - 4098*S^4 - 20343*S^6 - 12156*S^8)*HPL[{3, 2, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((-33 + 185*S^6)*HPL[{3, 2, 2}, -S^2])/(18*S^3) + (8*(-1 + 36*S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) + ((1282 - 11138*S^2 - 6201*S^4 - 31298*S^6 - 18878*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-6 + 287*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) + ((6 + 863*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) + (2*(1 + 885*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((-4*Pi^2*(-631 + 35*S^6))/(27*S^3) + (5382 + 7098*S^2 + 14415*S^4 + 12614*S^6 - 301*S^8)/(27*S^3*(1 + S^2)))*HPL[{2, 1, 1, 1}, -S^2] - (32*(-89 + 2*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + (2*(-644 + 3601*S^2 + 2118*S^4 + 10958*S^6 + 6713*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-4293 + 7*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) + (2*(-4293 + 7*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) + (2*(-8565 + 103*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) + (4*(-12803 + 137*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3) - (4*(-529 + 3773*S^2 + 2151*S^4 + 11171*S^6 + 6869*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(725 + 26*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3) + (8*(725 + 26*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3) + (16*(1797 + 95*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3) - (16*(-757 + 38*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-23*Pi^4*S^3)/20 + (19758 + 34287*S^2 - 32992*S^4 - 57241*S^6)/(5832*S*(1 + S^2)) + (Pi^2*(208 + 83*S^2 - 1009*S^4 - 962*S^6))/(108*S*(1 + S^2)))*Zeta[3] + ((-78 - 39*S^2 - 38*S^4 + 40*S^6)*Zeta[3]^2)/(18*S*(1 + S^2)) + HPL[{4}, -S^2]*((-1833 + 392*S^2 - 3029*S^4 - 26859*S^6 - 19877*S^8)/(1296*S^3*(1 + S^2)) + (Pi^2*(1 - 359*S^2 - 63*S^4 - 1895*S^6 - 1535*S^8))/(648*S^3*(1 + S^2)) + ((23 + 8*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (8*Zeta[3])/(3*S^3)) + HPL[{1}, -S^2]^4*((-7277 - 11139*S^2 - 30204*S^4 - 26126*S^6)/(972*S^3) + (Pi^2*(-1622 - 7109*S^2 - 2766*S^4 - 9713*S^6 - 4226*S^8))/(648*S^3*(1 + S^2)) + ((-312 - 1264*S^2 - 470*S^4 - 1671*S^6 - 719*S^8)*HPL[{2}, -S^2])/(36*S^3*(1 + S^2)) + (5*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (239*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (5*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*((-5907 - 88749*S^2 - 65853*S^4 - 294607*S^6)/(7776*S^3) + (Pi^2*(-153 - 7365*S^2 - 3606*S^4 - 18304*S^6 - 11092*S^8))/(1296*S^3*(1 + S^2)) + ((-1 + 5*S^6)*HPL[{3}, -S^2])/(4*S^3) - (4*(-89 + 2*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + ((-7 + 17*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((Pi^2*(-944 + 6193*S^2 + 3510*S^4 + 19241*S^6 + 12104*S^8))/(324*S^3*(1 + S^2)) + (-13974 + 63906*S^2 + 163743*S^4 + 408131*S^6 + 318380*S^8)/(1944*S^3*(1 + S^2)) - (4*(-3 + 23*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((7659 - 75606*S^2 - 165873*S^4 - 402682*S^6 - 316186*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(799 - 6443*S^2 - 3621*S^4 - 19835*S^6 - 12593*S^8))/(162*S^3*(1 + S^2)) + (4*(-3 + 46*S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((Pi^4*(-613 + 1137*S^6))/(6480*S^3) + (-49225 + 36917*S^2 - 117903*S^4 - 596767*S^6 - 353842*S^8)/(23328*S^3*(1 + S^2)) + (Pi^2*(-2653 + 989*S^2 + 471*S^4 - 10403*S^6 - 5180*S^8))/(3888*S^3*(1 + S^2)) + ((-3 - 10*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-485 - 791*S^2 - 144*S^4 - 616*S^6 - 310*S^8)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((-11 - 51*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (2*(7 + 45*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((76 + 133*S^2 - 12*S^4 + 23*S^6 - 34*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((Pi^4*(14373 - 1424*S^6))/(3240*S^3) + (Pi^2*(21520 + 28435*S^2 + 75804*S^4 + 65261*S^6 - 4222*S^8))/(1944*S^3*(1 + S^2)) + (397003 + 510058*S^2 + 2012988*S^4 + 2124872*S^6 + 201611*S^8)/(11664*S^3*(1 + S^2)) - (2*(719 + 29*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (4*(725 + 26*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-68 - 100*S^2 - 17*S^4 - 22*S^6 + 10*S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((-3299*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1944*S^3) + (-480187 - 678537*S^2 - 2258397*S^4 - 2052271*S^6)/(34992*S^3) + (Pi^2*(-7621 - 20491*S^2 - 49731*S^4 - 66853*S^6 - 30532*S^8))/(1944*S^3*(1 + S^2)) + ((-1207*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (-13999 - 36868*S^2 - 77940*S^4 - 104080*S^6 - 47713*S^8)/(972*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (41*(1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + ((332 + 533*S^2 + 132*S^4 + 56*S^6 - 145*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) - (25*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) + ((312 + 1264*S^2 + 470*S^4 + 1671*S^6 + 719*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (472*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (956*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((157 + 336*S^2 + 88*S^4 + 225*S^6 + 46*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((-250*Pi^2*S^3)/27 + (1626 + 255*S^2 - 13517*S^4 - 12902*S^6)/(324*S*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^2*((-497937 - 640787*S^2 - 2466905*S^4 - 2316279*S^6)/(23328*S^3) + (Pi^2*(-60199 - 150415*S^2 - 431487*S^4 - 640051*S^6 - 302668*S^8))/(11664*S^3*(1 + S^2)) + (Pi^4*(-14161 - 80453*S^2 - 33614*S^4 - 122030*S^6 - 55738*S^8))/(12960*S^3*(1 + S^2)) + ((-842 - 3056*S^2 - 1107*S^4 - 3758*S^6 - 1544*S^8)*HPL[{2}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(18*S^3) + (1525 + 3880*S^2 + 1380*S^4 - 4670*S^6 - 2939*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((323 + 41*S^2 - 114*S^4 - 904*S^6 - 622*S^8)*HPL[{4}, -S^2])/(108*S^3*(1 + S^2)) - (11*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((1207*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (13999 + 36868*S^2 + 77940*S^4 + 104080*S^6 + 47713*S^8)/(324*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((1352 + 5579*S^2 + 2082*S^4 + 7460*S^6 + 3233*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (52*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (131*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + ((-312 - 1264*S^2 - 470*S^4 - 1671*S^6 - 719*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (164*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 - (1456*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (956*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((7*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (856 + 2179*S^2 + 1629*S^4 + 325*S^6 - 17*S^8)/(108*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((-70438 - 179701*S^2 - 468537*S^4 - 695275*S^6 - 328225*S^8)/(3888*S^3*(1 + S^2)) + (Pi^2*(-1318 - 6135*S^2 - 2392*S^4 - 8679*S^6 - 3862*S^8))/(216*S^3*(1 + S^2)) + (26*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (82*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (47*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - ((1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*((-549007 - 3065590*S^2 - 5607960*S^4 - 17063878*S^6 - 13692565*S^8)/(139968*S^3*(1 + S^2)) + (Pi^2*(-937 - 38258*S^2 - 85235*S^4 - 253808*S^6 - 202870*S^8))/(7776*S^3*(1 + S^2)) + (Pi^4*(7435 - 75863*S^2 - 41649*S^4 - 253999*S^6 - 170701*S^8))/(38880*S^3*(1 + S^2)) + ((5*Pi^2*(5 + 9*S^6))/(108*S^3) + (-105 + 2247*S^2 + 3597*S^4 - 2245*S^6 - 3058*S^8)/(648*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-29 - 167*S^2 - 51*S^4 - 705*S^6 - 567*S^8)*HPL[{4}, -S^2])/(108*S^3*(1 + S^2)) + ((15 + 7*S^6)*HPL[{5}, -S^2])/(18*S^3) + ((15901 + 7950*S^2 + 36552*S^4 - 2180*S^6)/(324*S^3) + (Pi^2*(599 + 15*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((128 + 4526*S^2 + 2190*S^4 + 10775*S^6 + 6377*S^8)*HPL[{3, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((5 - 31*S^6)*HPL[{3, 2}, -S^2])/(6*S^3) + ((4 - 143*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + ((-147 - 4575*S^2 - 2214*S^4 - 10762*S^6 - 6334*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(-89 + 2*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (2*(-2143 + 3*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (4*(725 + 26*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((Pi^2*(-9 + 8*S^6))/(27*S^3) + (-208 + 2393*S^2 + 2610*S^4 + 79*S^6 + 124*S^8)/(324*S^3*(1 + S^2)))*Zeta[3] - (5*(6 + S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((-20777*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(38880*S^3) - ((1 + S^2)*(1967575 + 343724*S^2 + 8210359*S^4))/(69984*S^3) + (Pi^2*(-795887 - 1827770*S^2 - 5314476*S^4 - 8286422*S^6 - 4027157*S^8))/(139968*S^3*(1 + S^2)) + (Pi^4*(-237683 - 596117*S^2 - 1832049*S^4 - 2752283*S^6 - 1312364*S^8))/(233280*S^3*(1 + S^2)) + ((-601*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(108*S^3) - ((1 + S^2)*(2771 + 1712*S^2 + 7118*S^4))/(216*S^3))*HPL[{2}, -S^2]^2 - (341*(1 + S^6)*HPL[{2}, -S^2]^3)/(54*S^3) + (11*(1 + S^6)*HPL[{3}, -S^2]^2)/(18*S^3) + ((-73*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(108*S^3) + (291 + 1117*S^2 - 955*S^4 - 4817*S^6 - 2820*S^8)/(216*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((117 + 82*S^2 - 4*S^4 - 200*S^6 - 165*S^8)*HPL[{5}, -S^2])/(18*S^3*(1 + S^2)) - (13*(1 + S^6)*HPL[{6}, -S^2])/(2*S^3) + (82*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/S^3 + ((598*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (6788 + 17882*S^2 + 38559*S^4 + 52514*S^6 + 24293*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-428 - 1073*S^2 - 354*S^4 - 875*S^6 - 230*S^8)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)) + ((-1601 - 3263*S^2 - 966*S^4 - 1724*S^6 - 62*S^8)*HPL[{4, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((1 + S^6)*HPL[{4, 2}, -S^2])/(2*S^3) + (56*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-1207*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-13999 - 36868*S^2 - 77940*S^4 - 104080*S^6 - 47713*S^8)/(162*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (4*(842 + 3056*S^2 + 1107*S^4 + 3758*S^6 + 1544*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(4720 + 17803*S^2 + 6510*S^4 + 22492*S^6 + 9409*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (1364*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (4142*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (2*(312 + 1264*S^2 + 470*S^4 + 1671*S^6 + 719*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (944*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (1912*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((5141 + 9174*S^2 + 2631*S^4 - 1888*S^6)/(972*S^3) + (Pi^2*(122 + 123*S^2 - 19*S^4 - 66*S^6 - 67*S^8))/(54*S^3*(1 + S^2)))*Zeta[3] - (13*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*((Pi^2*(1318 + 6135*S^2 + 2392*S^4 + 8679*S^6 + 3862*S^8))/(108*S^3*(1 + S^2)) + (70438 + 179701*S^2 + 468537*S^4 + 695275*S^6 + 328225*S^8)/(1944*S^3*(1 + S^2)) - (94*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((2985 + 7331*S^2 - 2777*S^4 - 18631*S^6 - 10212*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(440 + 533*S^2 + 132*S^4 - 349*S^6 - 442*S^8))/(324*S^3*(1 + S^2)) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{2, 1}, -S^2])/(9*S^3) + (14*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((-13883*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(6480*S^3) + (-193954 - 462385*S^2 - 1453503*S^4 - 2334547*S^6 - 1126147*S^8)/(11664*S^3*(1 + S^2)) + (Pi^2*(-18953 - 50762*S^2 - 132162*S^4 - 190010*S^6 - 88469*S^8))/(3888*S^3*(1 + S^2)) + ((71 + 179*S^2 + 60*S^4 + 146*S^6 + 38*S^8)*HPL[{3}, -S^2])/(18*S^3*(1 + S^2)) - (25*(1 + S^6)*HPL[{4}, -S^2])/(18*S^3) + (2*(842 + 3056*S^2 + 1107*S^4 + 3758*S^6 + 1544*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (734*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (164*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + ((62 + 125*S^2 + 32*S^4 + 69*S^6 + 6*S^8)*Zeta[3])/(6*S^3*(1 + S^2))) + ((451 + 397*S^2 - 90*S^4 - 332*S^6 - 278*S^8)*Zeta[5])/(54*S^3*(1 + S^2))) - 62*S^3*Zeta[7]) + Log[T]^2*((-131811 - 322213*S^2)/(34992*S) + (Pi^2*(-3195762 - 2195187*S^2 - 13692565*S^4))/(209952*S) + (Pi^4*(-1789146 - 3683007*S^2 - 7674307*S^4 - 5761006*S^6))/(349920*S*(1 + S^2)) + (Pi^6*(-926262 - 463131*S^2 - 2034011*S^4 - 1107749*S^6))/(408240*S*(1 + S^2)) - (7*S^3*HPL[{0}, S^2]^7)/216 - (14*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)) - (32*(1 + S^6)*HPL[{1}, -S^2]^7)/(9*S^3) + HPL[{0}, S^2]^6*((-82 - 41*S^2 - 268*S^4 - 186*S^6)/(432*S*(1 + S^2)) - (41*(1 + S^6)*HPL[{1}, -S^2])/(216*S^3)) + ((4385 + 3269*S^2 - 558*S^4 - 6919*S^6 - 5803*S^8)*HPL[{2}, -S^2]^3)/(162*S^3*(1 + S^2)) + HPL[{0}, S^2]^5*((-1301*Pi^2*S^3)/3240 + (-1012 - 7163*S^2 - 24944*S^4 - 19243*S^6)/(6480*S*(1 + S^2)) + ((-596 - 7223*S^2 - 3426*S^4 - 12929*S^6 - 6302*S^8)*HPL[{1}, -S^2])/(3240*S^3*(1 + S^2)) - (91*(1 + S^6)*HPL[{1}, -S^2]^2)/(90*S^3) + ((15 - 511*S^6)*HPL[{2}, -S^2])/(540*S^3)) + HPL[{1}, -S^2]^5*((-92*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - ((1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(27*S^3) - (20*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + ((66 - 158*S^2 - 115*S^4 - 379*S^6 - 155*S^8)*HPL[{3}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((Pi^2*(-47 + 247*S^6))/(27*S^3) + (2153 + 20891*S^2 + 12339*S^4 - 19699*S^6 - 13516*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((801 + 171*S^2 - 315*S^4 - 4552*S^6 - 3922*S^8)*HPL[{6}, -S^2])/(27*S^3*(1 + S^2)) - (2*(135 + 266*S^6)*HPL[{7}, -S^2])/(9*S^3) + (4*(698 + 1874*S^2 + 588*S^4 + 2211*S^6 + 1035*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((Pi^2*(145 - 2143*S^6))/(27*S^3) + (13049 - 82207*S^2 - 115515*S^4 - 67207*S^6 - 46732*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-2*Pi^2*(-103 + 3481*S^6))/(27*S^3) + (10133 - 149329*S^2 - 195039*S^4 - 108762*S^6 - 72861*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((469 - 1637*S^2 - 1053*S^4 - 4163*S^6 - 2057*S^8)*HPL[{4, 2}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-25 + 44*S^6)*HPL[{4, 3}, -S^2])/(9*S^3) - (2*(1124 + 6380*S^2 + 2628*S^4 + 8411*S^6 + 3155*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-53 + 59*S^6)*HPL[{5, 2}, -S^2])/(3*S^3) - (4*(84 + 25*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((-8*Pi^2*(703 + 256*S^6))/(27*S^3) - (2*(4321 + 9831*S^2 + 13653*S^4 + 3089*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((-8*Pi^2*(2102 + 183*S^6))/(27*S^3) - (2*(38197 + 33993*S^2 + 109323*S^4 + 3507*S^6))/(81*S^3))*HPL[{3, 1, 1}, -S^2] + (4*(-472 + 311*S^6)*HPL[{3, 1, 2}, -S^2])/(27*S^3) - (4*(-3913 - 2797*S^2 + 558*S^4 + 6608*S^6 + 5492*S^8)*HPL[{3, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-49 + 4001*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) + (16*(-64 + 1571*S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) - (4*(-14259 - 13467*S^2 + 396*S^4 + 16805*S^6 + 16013*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-289 + 6215*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) + (4*(-829 + 19235*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) + (32*(-210 + 4939*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((-1096*Pi^2*(-11 + 4*S^6))/(27*S^3) - (4*(-17192 + 17163*S^2 - 32787*S^4 + 12763*S^6))/(81*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (448*(-25 + 17*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + (8*(-5759 - 5903*S^2 - 72*S^4 + 5783*S^6 + 5927*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (16*(-2017 + 401*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) + (16*(-2017 + 401*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) + (16*(-4117 + 1829*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) + (32*(-695 + 291*S^6)*HPL[{4, 1, 1, 1}, -S^2])/S^3 - (80*(-311 - 221*S^2 + 45*S^4 + 541*S^6 + 451*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(227 + 162*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (32*(227 + 162*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (320*(115 + 118*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) - (640*(-25 + 17*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((23*Pi^4*S^3)/5 + (878058 + 171261*S^2 + 137257*S^4)/(2916*S) + (Pi^2*(25470 + 30573*S^2 + 17491*S^4 + 12334*S^6))/(486*S*(1 + S^2)))*Zeta[3] + (2*(-60 - 30*S^2 + 7*S^4 + 67*S^6)*Zeta[3]^2)/(9*S*(1 + S^2)) + HPL[{0}, S^2]^4*((-30834 - 85131*S^2 - 381295*S^4 - 330886*S^6)/(23328*S*(1 + S^2)) + (Pi^2*(-782 - 391*S^2 - 2410*S^4 - 1628*S^6))/(432*S*(1 + S^2)) + ((-457 - 2704*S^2 - 1146*S^4 - 4153*S^6 - 1906*S^8)*HPL[{1}, -S^2]^2)/(216*S^3*(1 + S^2)) - (31*(1 + S^6)*HPL[{1}, -S^2]^3)/(9*S^3) + ((45 - 445*S^2 - 245*S^4 - 1444*S^6 - 954*S^8)*HPL[{2}, -S^2])/(108*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((-391*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(216*S^3) + (-631 - 1826*S^2 - 6864*S^4 - 10306*S^6 - 4817*S^8)/(432*S^3*(1 + S^2)) - (245*(1 + S^6)*HPL[{2}, -S^2])/(54*S^3)) + ((-10 + 7*S^6)*HPL[{3}, -S^2])/(36*S^3) + ((505 - 32*S^6)*HPL[{2, 1}, -S^2])/(54*S^3) - (26*S^3*Zeta[3])/27) + HPL[{1}, -S^2]^4*((-5*(1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(972*S^3) - (5*Pi^2*(716 + 2372*S^2 + 828*S^4 + 2729*S^6 + 1073*S^8))/(162*S^3*(1 + S^2)) - (5*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) + (800*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (100*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (200*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((33369 + 132891*S^2 + 10086*S^4 - 10291*S^6)/(972*S^3) + (Pi^2*(1315 + 3727*S^2 + 1215*S^4 + 3131*S^6 + 719*S^8))/(162*S^3*(1 + S^2)) + (16*(-100 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(-11 + 32*S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((-158591 - 123957*S^2 - 133875*S^4 - 293407*S^6)/(1944*S^3) + (Pi^2*(-4335 - 15819*S^2 - 5742*S^4 - 24028*S^6 - 12544*S^8))/(324*S^3*(1 + S^2)) + ((79 + 1089*S^6)*HPL[{3}, -S^2])/(9*S^3) - (56*(-25 + 17*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(-11 + 115*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((-4*(-13796 + 2976*S^2 + 1347*S^4 + 25949*S^6))/(81*S^3) - (4*Pi^2*(-2597 + 229*S^2 + 1413*S^4 + 9643*S^6 + 6817*S^8))/(81*S^3*(1 + S^2)) + (16*(7 + 472*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((-203587 - 14526*S^2 - 12213*S^4 + 292996*S^6)/(486*S^3) + (Pi^2*(-6403 - 2302*S^2 + 2046*S^4 + 16741*S^6 + 12640*S^8))/(81*S^3*(1 + S^2)) - (8*(9 + 479*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((454955 - 694629*S^2 + 1758375*S^4 - 137257*S^6)/(2916*S^3) + (Pi^4*(17519 - 4414*S^6))/(810*S^3) + (Pi^2*(33338 + 21323*S^2 + 58869*S^4 + 57866*S^6 - 13666*S^8))/(486*S^3*(1 + S^2)) - (16*(278 + 305*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (16*(227 + 162*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (16*(1034 + 1772*S^2 + 369*S^4 + 764*S^6 + 26*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((-1237*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(1458*S^3) - (4*Pi^2*(2456 + 3630*S^2 + 5688*S^4 + 4487*S^6))/(243*S^3) + ((-628*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (2*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(81*S^3))*HPL[{2}, -S^2] - (784*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + (4*(562 + 1362*S^2 + 400*S^4 + 1113*S^6 + 313*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (568*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + (20*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (64*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (400*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (100*(50 + 122*S^2 + 36*S^4 + 101*S^6 + 29*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^4*(-377 + 8665*S^6))/(1620*S^3) + (100041 + 1985130*S^2 + 218061*S^4 + 428846*S^6)/(5832*S^3) + (Pi^2*(49 + 57547*S^2 + 69573*S^4 + 32875*S^6 + 21556*S^8))/(972*S^3*(1 + S^2)) - (4*(-13 + 48*S^6)*HPL[{4}, -S^2])/(9*S^3) + (4*(-1591 - 2580*S^2 - 493*S^4 - 932*S^6 + 57*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(-169 + 1081*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (16*(-24 + 181*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(249 + 678*S^2 + 210*S^4 + 721*S^6 + 292*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^3*((-16369*Pi^4*S^3)/9720 + (-241302 - 473352*S^2 - 2303813*S^4 - 2087315*S^6)/(34992*S*(1 + S^2)) + (Pi^2*(-15798 - 51144*S^2 - 138991*S^4 - 105643*S^6))/(5832*S*(1 + S^2)) + ((-745 - 3337*S^2 - 1314*S^4 - 4606*S^6 - 2014*S^8)*HPL[{1}, -S^2]^3)/(81*S^3*(1 + S^2)) - (215*(1 + S^6)*HPL[{1}, -S^2]^4)/(27*S^3) + ((1190 - 11892*S^2 - 15582*S^4 - 44241*S^6)/(972*S^3) + (Pi^2*(33 - 1126*S^6))/(162*S^3))*HPL[{2}, -S^2] + ((9 - 569*S^6)*HPL[{2}, -S^2]^2)/(54*S^3) + HPL[{1}, -S^2]^2*((-397*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (-4907 - 13775*S^2 - 35340*S^4 - 47579*S^6 - 21755*S^8)/(486*S^3*(1 + S^2)) - (196*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((-40 - 77*S^2 - 2*S^4 - 68*S^6 - 31*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) + ((3 - 68*S^6)*HPL[{4}, -S^2])/(27*S^3) + ((2281 + 5812*S^2 + 1770*S^4 + 3137*S^6 - 394*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) + (2*(-18 + 605*S^6)*HPL[{3, 1}, -S^2])/(27*S^3) - (4*(-6 + 205*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (5*(-2 - S^2 + 31*S^4 + 33*S^6)*Zeta[3])/(27*S*(1 + S^2)) + HPL[{1}, -S^2]*((-43685 - 120527*S^2 - 405513*S^4 - 610577*S^6 - 288386*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(-2831 - 17234*S^2 - 7368*S^4 - 26747*S^6 - 12344*S^8))/(972*S^3*(1 + S^2)) + ((-1943 - 8999*S^2 - 3528*S^4 - 12707*S^6 - 5651*S^8)*HPL[{2}, -S^2])/(162*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (392*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3))) + HPL[{0}, S^2]^2*((-2603022 - 1213971*S^2 - 13692565*S^4)/(69984*S) + (Pi^2*(-121590 - 251325*S^2 - 768121*S^4 - 642274*S^6))/(11664*S*(1 + S^2)) + (Pi^4*(-98970 - 49485*S^2 - 278147*S^4 - 179177*S^6))/(19440*S*(1 + S^2)) - (5*(233 + 881*S^2 + 324*S^4 + 1112*S^6 + 464*S^8)*HPL[{1}, -S^2]^4)/(54*S^3*(1 + S^2)) - (12*(1 + S^6)*HPL[{1}, -S^2]^5)/S^3 + ((-147 - 4575*S^2 - 2214*S^4 - 10762*S^6 - 6334*S^8)*HPL[{2}, -S^2]^2)/(108*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((-5728 - 9285*S^2 - 19854*S^4 - 16081*S^6)/(162*S^3) - (152*Pi^2*(1 + S^6))/(9*S^3) - (478*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((Pi^2*(-61 + 81*S^6))/(54*S^3) + (-643 + 2369*S^2 + 1533*S^4 - 4973*S^6 - 2738*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((211 + 67*S^2 - 63*S^4 - 821*S^6 - 677*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) + ((-17 + 21*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-2*Pi^2*(-631 + 35*S^6))/(27*S^3) + (5382 + 7098*S^2 + 14415*S^4 + 12614*S^6 - 301*S^8)/(54*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] + ((-644 + 3601*S^2 + 2118*S^4 + 10958*S^6 + 6713*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-21 - 89*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (2*(-13 + 151*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (2*(-529 + 3773*S^2 + 2151*S^4 + 11171*S^6 + 6869*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(725 + 26*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (8*(1103 + 9*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (8*(-757 + 38*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((906 + 978*S^2 - 53*S^4 - 143*S^6)*Zeta[3])/(54*S*(1 + S^2)) + HPL[{1}, -S^2]^2*((-7277 - 11139*S^2 - 30204*S^4 - 26126*S^6)/(162*S^3) + (Pi^2*(-1622 - 7109*S^2 - 2766*S^4 - 9713*S^6 - 4226*S^8))/(108*S^3*(1 + S^2)) + ((-312 - 1264*S^2 - 470*S^4 - 1671*S^6 - 719*S^8)*HPL[{2}, -S^2])/(6*S^3*(1 + S^2)) + (10*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (478*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2}, -S^2]*((7659 - 75606*S^2 - 165873*S^4 - 402682*S^6 - 316186*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(799 - 6443*S^2 - 3621*S^4 - 19835*S^6 - 12593*S^8))/(324*S^3*(1 + S^2)) + ((7 + 45*S^6)*HPL[{3}, -S^2])/(9*S^3) + (2*(725 + 26*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(-3 + 46*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]*((-3299*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(648*S^3) + (-480187 - 678537*S^2 - 2258397*S^4 - 2052271*S^6)/(11664*S^3) + (Pi^2*(-7621 - 20491*S^2 - 49731*S^4 - 66853*S^6 - 30532*S^8))/(648*S^3*(1 + S^2)) + ((-1207*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (-13999 - 36868*S^2 - 77940*S^4 - 104080*S^6 - 47713*S^8)/(324*S^3*(1 + S^2)))*HPL[{2}, -S^2] - (41*(1 + S^6)*HPL[{2}, -S^2]^2)/S^3 + ((332 + 533*S^2 + 132*S^4 + 56*S^6 - 145*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (25*(1 + S^2)*(1 - S^2 + S^4)*HPL[{4}, -S^2])/(9*S^3) + ((312 + 1264*S^2 + 470*S^4 + 1671*S^6 + 719*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (472*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (956*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((157 + 336*S^2 + 88*S^4 + 225*S^6 + 46*S^8)*Zeta[3])/(9*S^3*(1 + S^2)))) + ((1000*Pi^2*S^3)/27 + (2*(10728 + 12546*S^2 + 6622*S^4 + 4831*S^6))/(81*S*(1 + S^2)))*Zeta[5] + HPL[{1}, -S^2]^2*(-((1 + S^2)*(422663 + 99650*S^2 + 875723*S^4))/(1944*S^3) + (Pi^2*(-35631 - 49802*S^2 - 90717*S^4 - 76258*S^6))/(648*S^3) + (Pi^4*(-33926 - 122951*S^2 - 44454*S^4 - 151082*S^6 - 62057*S^8))/(3240*S^3*(1 + S^2)) + ((-1163 - 3515*S^2 - 1176*S^4 - 3737*S^6 - 1385*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((410*Pi^2*(1 + S^6))/(9*S^3) + (10561 + 13896*S^2 + 7515*S^4 + 4252*S^6)/(27*S^3))*HPL[{3}, -S^2] + (2*(228 + 511*S^2 + 140*S^4 + 369*S^6 + 86*S^8)*HPL[{4}, -S^2])/(3*S^3*(1 + S^2)) + (124*(1 + S^6)*HPL[{5}, -S^2])/(3*S^3) + ((628*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (2*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(27*S^3))*HPL[{2, 1}, -S^2] + (4*(-523 - 571*S^2 - 24*S^4 + 398*S^6 + 446*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (440*(1 + S^6)*HPL[{3, 2}, -S^2])/S^3 - (4528*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (20*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (3136*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (6208*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (400*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((110*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (2*(4096 + 5235*S^2 + 2898*S^4 + 1867*S^6))/(27*S^3))*Zeta[3] + HPL[{2}, -S^2]*(-((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(54*S^3) + (Pi^2*(-521 - 4277*S^2 - 1860*S^4 - 7253*S^6 - 3497*S^8))/(54*S^3*(1 + S^2)) + (220*(1 + S^6)*HPL[{3}, -S^2])/S^3 + (1568*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (656*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + (536*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((5128337 - 1454691*S^2 - 1380333*S^4 - 13692565*S^6)/(34992*S^3) + (Pi^2*(173211 + 54234*S^2 - 217749*S^4 - 730234*S^6 - 627574*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(41807 - 37771*S^2 - 39789*S^4 - 249427*S^6 - 169849*S^8))/(9720*S^3*(1 + S^2)) + ((Pi^2*(-137 + 1131*S^6))/(27*S^3) + (-9353 + 49080*S^2 + 9057*S^4 + 24622*S^6)/(162*S^3))*HPL[{3}, -S^2] + ((-829 + 1217*S^2 + 1041*S^4 + 3699*S^6 + 1653*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (10*(-5 + 39*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((4*Pi^2*(703 + 256*S^6))/(27*S^3) + (4321 + 9831*S^2 + 13653*S^4 + 3089*S^6)/(27*S^3))*HPL[{2, 1}, -S^2] + (2*(5161 + 12211*S^2 + 3516*S^4 + 12511*S^6 + 5461*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(41 + 2061*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (4*(-163 + 3311*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (8*(698 + 1874*S^2 + 588*S^4 + 2211*S^6 + 1035*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (224*(-25 + 17*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (16*(-326 + 57*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (16*(227 + 162*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((4*Pi^2*(2 + 259*S^6))/(27*S^3) + (-1046 + 21265*S^2 + 27621*S^4 + 17818*S^6 + 11860*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] + (4*(-14 + 417*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((-17153*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(7560*S^3) - ((1 + S^2)*(3757531 + 762416*S^2 + 9134503*S^4))/(17496*S^3) + (Pi^2*(-1796785 - 2369925*S^2 - 5012091*S^4 - 4431175*S^6))/(34992*S^3) + (Pi^4*(-178487 - 451049*S^2 - 798153*S^4 - 953759*S^6 - 426764*S^8))/(19440*S^3*(1 + S^2)) + ((-6683 - 9489*S^2 - 11754*S^4 - 9020*S^6)/(54*S^3) - (319*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2}, -S^2]^2 - (62*(1 + S^6)*HPL[{2}, -S^2]^3)/(9*S^3) - (74*(1 + S^6)*HPL[{3}, -S^2]^2)/(3*S^3) + ((401*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (24043 + 58261*S^2 + 45549*S^4 + 13783*S^6 + 1804*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] - (2*(-613 - 983*S^2 - 182*S^4 - 191*S^6 + 179*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (70*(1 + S^6)*HPL[{6}, -S^2])/(3*S^3) + (1568*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((152*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (2*(1 + S^2)*(-3878 - 529*S^2 + 4768*S^4))/(27*S^3))*HPL[{3, 1}, -S^2] - (4*(1344 + 3323*S^2 + 988*S^4 + 2798*S^6 + 819*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(4714 + 11503*S^2 + 3390*S^4 + 9502*S^6 + 2713*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (78*(1 + S^6)*HPL[{4, 2}, -S^2])/S^3 - (1168*(1 + S^6)*HPL[{5, 1}, -S^2])/(3*S^3) + ((-1256*Pi^2*(1 + S^6))/(9*S^3) - (4*(-1975 - 1743*S^2 + 6087*S^4 + 5855*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (8*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8*(601 + 2153*S^2 + 776*S^4 + 2624*S^6 + 1072*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) - (352*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (40*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (128*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (800*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((48677 + 60294*S^2 + 30519*S^4 + 19766*S^6)/(162*S^3) + (Pi^2*(1407 + 3386*S^2 + 988*S^4 + 2750*S^6 + 771*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] - (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(27*S^3) + (Pi^2*(521 + 4277*S^2 + 1860*S^4 + 7253*S^6 + 3497*S^8))/(27*S^3*(1 + S^2)) - (1312*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((61939 + 78816*S^2 + 34365*S^4 + 17704*S^6)/(162*S^3) + (Pi^2*(5390 + 12791*S^2 + 3732*S^4 + 10073*S^6 + 2672*S^8))/(81*S^3*(1 + S^2)) - (440*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2}, -S^2]*((-4421*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) - ((1 + S^2)*(-233717 - 5557*S^2 + 945778*S^4))/(2916*S^3) + (Pi^2*(-2149 - 14560*S^2 - 104004*S^4 - 175732*S^6 - 82843*S^8))/(972*S^3*(1 + S^2)) + (10*(806 + 1994*S^2 + 594*S^4 + 1679*S^6 + 491*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (226*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1568*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(1351 + 3307*S^2 + 960*S^4 + 2773*S^6 + 817*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + (2*(1220 + 2829*S^2 + 806*S^4 + 2178*S^6 + 569*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{0}, S^2]*((-147719*Pi^6*S^3)/68040 + (-3750279 - 868422*S^2 - 9134503*S^4)/(17496*S) + (Pi^2*(-1541784 - 2238216*S^2 - 5147099*S^4 - 4466219*S^6))/(34992*S*(1 + S^2)) + (Pi^4*(-460182 - 956283*S^2 - 1853137*S^4 - 1371670*S^6))/(58320*S*(1 + S^2)) - (14*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^5)/(9*S^3*(1 + S^2)) - (112*(1 + S^6)*HPL[{1}, -S^2]^6)/(9*S^3) + ((403 - 19368*S^2 - 10818*S^4 - 27995*S^6)/(162*S^3) + (Pi^2*(-8 - 1711*S^6))/(54*S^3))*HPL[{2}, -S^2]^2 - (4*(-19 + 275*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{1}, -S^2]^4*((-635*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (5*(1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(54*S^3) - (250*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + (2*(-8 + 19*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((Pi^2*(9 - 146*S^6))/(27*S^3) + (662 - 109*S^2 - 3594*S^4 - 8949*S^6 - 6450*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-5 - 115*S^2 - 46*S^4 - 271*S^6 - 161*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) - (8*(5 + 29*S^6)*HPL[{6}, -S^2])/(9*S^3) + (4*(17 + 1142*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((14*Pi^2*(-15 + 254*S^6))/(27*S^3) + (-4866 + 38163*S^2 + 20874*S^4 + 58189*S^6)/(81*S^3))*HPL[{3, 1}, -S^2] + ((-361 - 1795*S^2 - 816*S^4 - 1906*S^6 - 472*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) - (2*(9 + 1782*S^2 + 1035*S^4 + 2435*S^6 + 662*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(1 + 2*S^2)*(1 - 2*S^2 + 4*S^4)*HPL[{4, 2}, -S^2])/(9*S^3) + (136*S^3*HPL[{5, 1}, -S^2])/3 + ((-4*Pi^2*(-31 + 600*S^6))/(9*S^3) - (2*(-4466 + 38115*S^2 + 21123*S^4 + 59095*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] + (4*(-7009 - 14101*S^2 - 3600*S^4 - 6949*S^6 + 143*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-10673 - 21131*S^2 - 5283*S^4 - 10098*S^6 + 360*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(11 + 7*S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (4*(-141 + 2207*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (16*(-39 + 563*S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (40*(-478 - 928*S^2 - 225*S^4 - 412*S^6 + 38*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (16*(-29 + 391*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (160*(-5 + 79*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(768 + 384*S^2 + 1111*S^4 + 343*S^6))/(81*S*(1 + S^2)) + (36834 + 46875*S^2 + 27785*S^4 + 18392*S^6)/(486*S*(1 + S^2)))*Zeta[3] - (20*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((-5*(1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(486*S^3) + (Pi^2*(-3160 - 10792*S^2 - 3834*S^4 - 12691*S^6 - 5059*S^8))/(81*S^3*(1 + S^2)) - (10*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{3}, -S^2])/S^3 + (1000*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (328*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((77359 + 22788*S^2 + 113253*S^4 + 3192*S^6)/(162*S^3) + (Pi^2*(9451 + 19732*S^2 + 5145*S^4 + 9317*S^6 - 964*S^8))/(81*S^3*(1 + S^2)) - (8*(124 + S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((-10459 + 470*S^2 - 12972*S^4 - 50918*S^6 - 28313*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-439 - 190*S^2 + 228*S^4 + 447*S^6 + 198*S^8))/(162*S^3*(1 + S^2)) - (4*(31 + 13*S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (4*(5 + 3*S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((-1687*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(135*S^3) - ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(972*S^3) + (Pi^2*(-51574 - 128575*S^2 - 206895*S^4 - 231553*S^6 - 102955*S^8))/(972*S^3*(1 + S^2)) + ((-6217 - 8727*S^2 - 11883*S^4 - 9589*S^6)/(27*S^3) - (571*Pi^2*(1 + S^6))/(9*S^3))*HPL[{2}, -S^2] - (392*(1 + S^6)*HPL[{2}, -S^2]^2)/(3*S^3) + (2*(13 + 25*S^2 + 6*S^4 + 12*S^6)*HPL[{3}, -S^2])/(S^3*(1 + S^2)) - (14*(1 + S^6)*HPL[{4}, -S^2])/S^3 + (10*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (1496*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (1000*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(319 + 811*S^2 + 246*S^4 + 706*S^6 + 214*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((42989 - 614466*S^2 - 308682*S^4 - 1177723*S^6)/(2916*S^3) + (Pi^2*(5656 - 50007*S^2 - 36705*S^4 - 103336*S^6))/(972*S^3) + (Pi^4*(415 - 9577*S^6))/(810*S^3) + ((39 + 279*S^2 + 138*S^4 + 302*S^6 + 62*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (2*(-19 + 44*S^6)*HPL[{4}, -S^2])/(9*S^3) - (2*(-7009 - 14101*S^2 - 3600*S^4 - 6949*S^6 + 143*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (68*(1 + 67*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (8*(17 + 1142*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(-23 + 718*S^2 + 375*S^4 + 1411*S^6 + 670*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + (4*(92 + 46*S^2 + 143*S^4 + 51*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(422663 + 99650*S^2 + 875723*S^4))/(1944*S^3) + (Pi^4*(-81677 - 325418*S^2 - 123090*S^4 - 422852*S^6 - 179111*S^8))/(9720*S^3*(1 + S^2)) + (Pi^2*(-69260 - 167108*S^2 - 293517*S^4 - 359348*S^6 - 165299*S^8))/(1458*S^3*(1 + S^2)) + ((-1163 - 3515*S^2 - 1176*S^4 - 3737*S^6 - 1385*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((10*Pi^2*(1 + S^6))/(9*S^3) - (2*(-505 - 1038*S^2 + 150*S^4 + 899*S^6))/(81*S^3))*HPL[{3}, -S^2] + ((-35 - 293*S^2 - 138*S^4 - 488*S^6 - 230*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (116*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((1142*Pi^2*(1 + S^6))/(9*S^3) + (2*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + (4*(1046 + 3290*S^2 + 1122*S^4 + 3629*S^6 + 1385*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (152*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) - (124*(1 + S^6)*HPL[{4, 1}, -S^2])/S^3 - (20*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (3136*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (3088*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 + (2000*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((256*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(6097 + 2105*S^2 + 3352*S^4))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-35426 - 47493*S^2 - 74580*S^4 - 63377*S^6)/(162*S^3) + (Pi^2*(-8198 - 28754*S^2 - 10278*S^4 - 34577*S^6 - 14021*S^8))/(162*S^3*(1 + S^2)) + (76*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (1568*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (164*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + (368*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + 248*S^3*Zeta[7]) + HPL[{1}, -S^2]^2*(-((1 + S^2)*(44150029 + 8482853*S^2 + 134931142*S^4))/(419904*S^3) + (Pi^2*(-882963 - 1103863*S^2 - 2696512*S^4 - 2471724*S^6))/(34992*S^3) + (Pi^4*(-2898599 - 6970289*S^2 - 13596651*S^4 - 17849939*S^6 - 8286098*S^8))/(699840*S^3*(1 + S^2)) + (Pi^6*(-195079 - 811628*S^2 - 306836*S^4 - 1084304*S^6 - 467755*S^8))/(272160*S^3*(1 + S^2)) + ((541 - 575*S^2 - 558*S^4 - 2816*S^6 - 1700*S^8)*HPL[{2}, -S^2]^3)/(162*S^3*(1 + S^2)) + ((-821 - 2159*S^2 - 678*S^4 - 1952*S^6 - 614*S^8)*HPL[{3}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((82*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (10535 + 25682*S^2 + 9378*S^4 - 15934*S^6 - 10381*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] - (5*(-835 - 586*S^2 + 120*S^4 + 1286*S^6 + 1037*S^8)*HPL[{6}, -S^2])/(54*S^3*(1 + S^2)) - (164*(1 + S^6)*HPL[{7}, -S^2])/(3*S^3) + (2*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-1042*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-25681 - 58873*S^2 - 53037*S^4 - 32611*S^6 - 12658*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-3527*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-177811 - 410875*S^2 - 363807*S^4 - 208825*S^6 - 77434*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-2581 - 6769*S^2 - 2058*S^4 - 6202*S^6 - 2014*S^8)*HPL[{4, 2}, -S^2])/(54*S^3*(1 + S^2)) + (12*(1 + S^6)*HPL[{4, 3}, -S^2])/S^3 - (2*(1462 + 3206*S^2 + 860*S^4 + 2219*S^6 + 475*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) + (76*(1 + S^6)*HPL[{5, 2}, -S^2])/(3*S^3) + (30*(1 + S^6)*HPL[{6, 1}, -S^2])/S^3 + ((-1276*Pi^2*(1 + S^6))/(9*S^3) - (2*(6683 + 9489*S^2 + 11754*S^4 + 9020*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((-3008*Pi^2*(1 + S^6))/(9*S^3) - (2*(9488 + 14571*S^2 + 27747*S^4 + 22808*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + (4*(1 + S^2)*(2 - 5*S^2 + 2*S^4)*HPL[{3, 1, 2}, -S^2])/(27*S^3) - (4*(-181 + 192*S^2 + 188*S^4 + 939*S^6 + 566*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1382*(1 + S^6)*HPL[{3, 2, 2}, -S^2])/(3*S^3) + (4240*(1 + S^6)*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (4*(-1225 - 958*S^2 + 138*S^4 + 1709*S^6 + 1442*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4162*(1 + S^6)*HPL[{4, 1, 2}, -S^2])/(3*S^3) + (12970*(1 + S^6)*HPL[{4, 2, 1}, -S^2])/(3*S^3) + (26672*(1 + S^6)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((1256*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (4*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (496*(1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) + (8*(-523 - 571*S^2 - 24*S^4 + 398*S^6 + 446*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1376*(1 + S^6)*HPL[{3, 1, 1, 2}, -S^2])/S^3 - (1376*(1 + S^6)*HPL[{3, 1, 2, 1}, -S^2])/S^3 - (1872*(1 + S^6)*HPL[{3, 2, 1, 1}, -S^2])/S^3 - (17984*(1 + S^6)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) - (40*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (6272*(1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (6272*(1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (37760*(1 + S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + (800*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((109*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (836411 + 1012851*S^2 + 495297*S^4 + 326633*S^6)/(5832*S^3) + (Pi^2*(3016 + 6947*S^2 + 5965*S^4 + 3285*S^6 + 1239*S^8))/(108*S^3*(1 + S^2)))*Zeta[3] + ((-166 - 559*S^2 - 246*S^4 - 568*S^6 - 175*S^8)*Zeta[3]^2)/(27*S^3*(1 + S^2)) + HPL[{3, 1}, -S^2]*((-25115 - 28926*S^2 + 35115*S^4 + 38710*S^6)/(162*S^3) + (Pi^2*(-217 + 3866*S^2 + 2010*S^4 + 8654*S^6 + 4571*S^8))/(81*S^3*(1 + S^2)) - (680*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((47285 + 68707*S^2 + 10183*S^4 - 10375*S^6)/(648*S^3) + (Pi^2*(4427 + 9239*S^2 + 2406*S^4 + 5738*S^6 + 926*S^8))/(324*S^3*(1 + S^2)) - (226*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (62*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(18412 + 6533*S^2 + 28207*S^4))/(324*S^3) + (Pi^2*(-5173 - 16657*S^2 - 5742*S^4 - 18727*S^6 - 7243*S^8))/(324*S^3*(1 + S^2)) + (202*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (62*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (146*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*(-((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(27*S^3) + (Pi^2*(-521 - 4277*S^2 - 1860*S^4 - 7253*S^6 - 3497*S^8))/(27*S^3*(1 + S^2)) + (1312*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((419*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(162*S^3) + (1087487 + 1344375*S^2 + 428949*S^4 + 164285*S^6)/(5832*S^3) + (Pi^2*(33208 + 77251*S^2 + 65613*S^4 + 30631*S^6 + 9817*S^8))/(972*S^3*(1 + S^2)) - (34*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (10*(806 + 1994*S^2 + 594*S^4 + 1679*S^6 + 491*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (220*(1 + S^6)*HPL[{3, 1}, -S^2])/S^3 + (440*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 + (2*(97 + 234*S^2 + 58*S^4 + 207*S^6 + 70*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((4421*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + ((1 + S^2)*(-233717 - 5557*S^2 + 945778*S^4))/(2916*S^3) + (Pi^2*(2149 + 14560*S^2 + 104004*S^4 + 175732*S^6 + 82843*S^8))/(972*S^3*(1 + S^2)) - (1568*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(1351 + 3307*S^2 + 960*S^4 + 2773*S^6 + 817*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((401*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (23749 + 54439*S^2 + 43335*S^4 + 18997*S^6 + 6460*S^8)/(162*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*(-((1 + S^2)*(-205501 - 13863*S^2 + 1164362*S^4))/(5832*S^3) + (Pi^2*(9068 - 23389*S^2 - 656097*S^4 - 1221307*S^6 - 589891*S^8))/(11664*S^3*(1 + S^2)) + (Pi^4*(-10285 - 63080*S^2 - 26012*S^4 - 99284*S^6 - 46489*S^8))/(6480*S^3*(1 + S^2)) + ((521*Pi^2*(1 + S^6))/(27*S^3) + (25628 + 33141*S^2 + 19902*S^4 + 12605*S^6)/(162*S^3))*HPL[{3}, -S^2] + ((835 + 2191*S^2 + 678*S^4 + 1990*S^6 + 634*S^8)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)) + (22*(1 + S^6)*HPL[{5}, -S^2])/S^3 + ((638*Pi^2*(1 + S^6))/(9*S^3) + (6683 + 9489*S^2 + 11754*S^4 + 9020*S^6)/(27*S^3))*HPL[{2, 1}, -S^2] + (2*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (730*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) - (2198*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (248*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (688*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 + (3136*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((539*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (25849 + 59176*S^2 + 51876*S^4 + 32428*S^6 + 12583*S^8)/(162*S^3*(1 + S^2)))*Zeta[3] + (90*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/S^3) + (84*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3) + HPL[{2}, -S^2]*((5386374 - 6163581*S^2 - 8337909*S^4 - 30054476*S^6)/(104976*S^3) + (Pi^2*(2289665 + 304028*S^2 - 4221492*S^4 - 16068388*S^6 - 13692565*S^8))/(209952*S^3*(1 + S^2)) + (Pi^4*(590000 - 100498*S^2 - 1466721*S^4 - 4803631*S^6 - 3966496*S^8))/(349920*S^3*(1 + S^2)) + (Pi^6*(37239 - 61923*S^2 - 49581*S^4 - 329267*S^6 - 230105*S^8))/(136080*S^3*(1 + S^2)) + ((-168 - 855*S^2 - 348*S^4 - 1166*S^6 - 479*S^8)*HPL[{3}, -S^2]^2)/(54*S^3*(1 + S^2)) + ((Pi^2*(-5 + 101*S^6))/(27*S^3) + (-1017 + 5538*S^2 + 7323*S^4 - 4105*S^6 - 5953*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] - (2*(113 + 96*S^2 - 52*S^4 + 347*S^6 + 364*S^8)*HPL[{6}, -S^2])/(9*S^3*(1 + S^2)) - (2*(85 + 208*S^6)*HPL[{7}, -S^2])/(9*S^3) + ((-4385 - 3269*S^2 + 558*S^4 + 6919*S^6 + 5803*S^8)*HPL[{2, 1}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((855 - 24864*S^2 - 6414*S^4 - 13201*S^6)/(81*S^3) + (Pi^2*(-13 - 1077*S^6))/(27*S^3))*HPL[{3, 2}, -S^2] + ((16258 - 155457*S^2 - 35451*S^4 - 79834*S^6)/(162*S^3) + (Pi^2*(167 - 3454*S^6))/(27*S^3))*HPL[{4, 1}, -S^2] - (4*(17 + 131*S^2 + 57*S^4 + 206*S^6 + 92*S^8)*HPL[{4, 2}, -S^2])/(9*S^3*(1 + S^2)) + (2*(-49 + 16*S^6)*HPL[{4, 3}, -S^2])/(9*S^3) + ((945 - 4518*S^2 - 2880*S^4 - 8942*S^6 - 3479*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-71 + S^6)*HPL[{5, 2}, -S^2])/(9*S^3) - (4*(119 + 69*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((8*Pi^2*(-353 + 123*S^6))/(27*S^3) + (2*(-8656 + 8223*S^2 - 14619*S^4 + 6014*S^6))/(81*S^3))*HPL[{2, 2, 1}, -S^2] + ((42583 - 258*S^2 + 96771*S^4 - 11462*S^6)/(81*S^3) - (2*Pi^2*(-4099 + 345*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] + ((95 + 251*S^2 + 78*S^4 + 230*S^6 + 74*S^8)*HPL[{3, 1, 2}, -S^2])/(3*S^3*(1 + S^2)) + ((-7465 - 19885*S^2 - 6210*S^4 - 23378*S^6 - 10958*S^8)*HPL[{3, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-129 + 1984*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) + (160*(-1 + 26*S^6)*HPL[{3, 3, 1}, -S^2])/(3*S^3) - (2*(13309 + 31999*S^2 + 9327*S^4 + 34473*S^6 + 15783*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-191 + 6172*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) + (2*(-707 + 19108*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) + (188*(-17 + 417*S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((8*Pi^2*(703 + 256*S^6))/(27*S^3) + (2*(4321 + 9831*S^2 + 13653*S^4 + 3089*S^6))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (16*(325 + 242*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) + (4*(-47459 - 27017*S^2 + 10212*S^4 + 95539*S^6 + 75097*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(3859 + 843*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) + (4*(3859 + 843*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) + (4*(7759 + 3747*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) + (8*(11863 + 5401*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3) - (16*(698 + 1874*S^2 + 588*S^4 + 2211*S^6 + 1035*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (448*(-25 + 17*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3) - (448*(-25 + 17*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3) + (32*(-1822 + 1733*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3) + (32*(227 + 162*S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^4*(-71 + 1721*S^6))/(810*S^3) + (Pi^2*(-1254 + 23658*S^2 + 30231*S^4 + 17897*S^6 + 11984*S^8))/(972*S^3*(1 + S^2)) + (-28976 + 374866*S^2 + 474621*S^4 + 251877*S^6 + 169434*S^8)/(2916*S^3*(1 + S^2)))*Zeta[3] + ((101 + 89*S^2 - 15*S^4 - 299*S^6 - 287*S^8)*Zeta[3]^2)/(27*S^3*(1 + S^2)) + HPL[{4}, -S^2]*((-19085 + 47322*S^2 + 22536*S^4 + 3633*S^6)/(972*S^3) + (Pi^2*(-143 + 175*S^2 + 165*S^4 + 499*S^6 + 181*S^8))/(54*S^3*(1 + S^2)) - (2*(395 + 56*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(-1 + 32*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((-158591 - 123957*S^2 - 133875*S^4 - 293407*S^6)/(486*S^3) + (Pi^2*(-4335 - 15819*S^2 - 5742*S^4 - 24028*S^6 - 12544*S^8))/(81*S^3*(1 + S^2)) + (32*(-11 + 115*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((190311 + 105345*S^2 + 143667*S^4 + 278849*S^6)/(972*S^3) + (Pi^2*(1763 + 5579*S^2 + 1902*S^4 + 7762*S^6 + 3946*S^8))/(54*S^3*(1 + S^2)) - (4*(-17 + 157*S^6)*Zeta[3])/(3*S^3)) + HPL[{2, 1}, -S^2]*((Pi^4*(8172 + 1853*S^6))/(810*S^3) + (Pi^2*(28864 + 37443*S^2 + 77511*S^4 + 7087*S^6))/(972*S^3) + (151273 + 487836*S^2 + 929547*S^4 + 117836*S^6)/(2916*S^3) + (4*(-571 + 605*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (224*(-25 + 17*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(-4041 - 6669*S^2 - 1314*S^4 - 2504*S^6 + 124*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^4*(-87 + 1010*S^6))/(405*S^3) + (Pi^2*(-4729 + 20987*S^2 + 30867*S^4 + 15717*S^6 + 10782*S^8))/(972*S^3*(1 + S^2)) + (-123793 + 758498*S^2 + 1013838*S^4 + 426906*S^6 + 272031*S^8)/(5832*S^3*(1 + S^2)) - (4*(-12 + 17*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-9543 - 16815*S^2 - 3636*S^4 - 7720*S^6 - 448*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (20*(7 + 108*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (4*(79 + 1089*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-155 + 169*S^2 + 162*S^4 + 842*S^6 + 518*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((4*Pi^2*(-11 + 103*S^6))/(27*S^3) + (-1306 + 18776*S^2 + 22605*S^4 + 9293*S^6 + 5852*S^8)/(162*S^3*(1 + S^2)))*Zeta[5] + (2*(-35 + 116*S^6)*Zeta[7])/(3*S^3)) + HPL[{1}, -S^2]*((-55259*Pi^8*(1 + S^2)*(1 - S^2 + S^4))/(255150*S^3) - (Pi^2*(1 + S^2)*(2862553 + 553070*S^2 + 8672431*S^4))/(104976*S^3) - ((1 + S^2)*(36840015 + 8677697*S^2 + 179968230*S^4))/(419904*S^3) + (Pi^4*(-4365026 - 9919382*S^2 - 20372259*S^4 - 28575752*S^6 - 13658705*S^8))/(1049760*S^3*(1 + S^2)) + (Pi^6*(-818602 - 2014552*S^2 - 4124319*S^4 - 5490730*S^6 - 2536468*S^8))/(1224720*S^3*(1 + S^2)) + ((885 + 761*S^2 - 2533*S^4 - 2409*S^6)/(162*S^3) - (217*Pi^2*(1 + S^6))/(81*S^3))*HPL[{2}, -S^2]^3 - (16*(1 + S^6)*HPL[{2}, -S^2]^4)/(3*S^3) + ((-50*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-4327 - 11308*S^2 - 12198*S^4 - 7996*S^6 - 2995*S^8)/(324*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 - (8*(1 + S^6)*HPL[{4}, -S^2]^2)/(3*S^3) + ((-37*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (3188 + 11636*S^2 - 3354*S^4 - 28324*S^6 - 16387*S^8)/(81*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((5420 + 2249*S^2 - 1914*S^4 - 10882*S^6 - 7711*S^8)*HPL[{7}, -S^2])/(27*S^3*(1 + S^2)) - (560*(1 + S^6)*HPL[{8}, -S^2])/(3*S^3) + ((638*Pi^2*(1 + S^6))/(9*S^3) + (6683 + 9489*S^2 + 11754*S^4 + 9020*S^6)/(27*S^3))*HPL[{2, 1}, -S^2]^2 - (932*(1 + S^6)*HPL[{3, 1}, -S^2]^2)/(3*S^3) + ((-19*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (-3796 - 9271*S^2 - 9546*S^4 - 7219*S^6 - 2932*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((788 + 1355*S^2 + 162*S^4 + 644*S^6 + 77*S^8)*HPL[{4, 3}, -S^2])/(27*S^3*(1 + S^2)) + ((-820*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (2*(12563 + 30995*S^2 + 23508*S^4 + 5795*S^6 + 287*S^8))/(81*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((628 + 1009*S^2 + 78*S^4 + 397*S^6 + 16*S^8)*HPL[{5, 2}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{5, 3}, -S^2])/(3*S^3) + (5*(-529 - 268*S^2 + 36*S^4 + 1190*S^6 + 929*S^8)*HPL[{6, 1}, -S^2])/(27*S^3*(1 + S^2)) + (20*(1 + S^6)*HPL[{6, 2}, -S^2])/(3*S^3) + (128*(1 + S^6)*HPL[{7, 1}, -S^2])/S^3 - (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + (2*(53 + 104*S^2 - 6*S^4 + 104*S^6 + 53*S^8)*HPL[{3, 1, 2}, -S^2])/(81*S^3*(1 + S^2)) + ((-1736*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (2*(-5363 - 9980*S^2 + 10638*S^4 + 29548*S^6 + 14401*S^8))/(81*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((17107 + 41983*S^2 + 12438*S^4 + 34918*S^6 + 10042*S^8)*HPL[{3, 2, 2}, -S^2])/(27*S^3*(1 + S^2)) + (8*(6539 + 16076*S^2 + 4764*S^4 + 13412*S^6 + 3875*S^8)*HPL[{3, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (224*(1 + S^6)*HPL[{3, 3, 2}, -S^2])/(3*S^3) + ((-4406*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (55903 + 117517*S^2 - 18243*S^4 - 164129*S^6 - 84920*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((51457 + 126349*S^2 + 37410*S^4 + 105226*S^6 + 30334*S^8)*HPL[{4, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + (128*(1 + S^6)*HPL[{4, 1, 3}, -S^2])/S^3 + ((159637 + 393001*S^2 + 116538*S^4 + 328570*S^6 + 95206*S^8)*HPL[{4, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (136*(1 + S^6)*HPL[{4, 2, 2}, -S^2])/(3*S^3) + (1312*(1 + S^6)*HPL[{4, 3, 1}, -S^2])/(3*S^3) + (4*(27658 + 67646*S^2 + 19964*S^4 + 56027*S^6 + 16039*S^8)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (800*(1 + S^6)*HPL[{5, 1, 2}, -S^2])/(3*S^3) + (5360*(1 + S^6)*HPL[{5, 2, 1}, -S^2])/(3*S^3) + (13540*(1 + S^6)*HPL[{6, 1, 1}, -S^2])/(3*S^3) + (8*(-541 + 575*S^2 + 558*S^4 + 2816*S^6 + 1700*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((304*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) + (4*(1 + S^2)*(-3878 - 529*S^2 + 4768*S^4))/(27*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (8*(803 + 3898*S^2 + 1546*S^4 + 5614*S^6 + 2519*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) - (8*(803 + 3898*S^2 + 1546*S^4 + 5614*S^6 + 2519*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (52*(1 + S^6)*HPL[{3, 1, 2, 2}, -S^2])/S^3 - (8*(262 + 4473*S^2 + 2104*S^4 + 8430*S^6 + 4219*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (52*(1 + S^6)*HPL[{3, 2, 1, 2}, -S^2])/S^3 + (308*(1 + S^6)*HPL[{3, 2, 2, 1}, -S^2])/(3*S^3) + (464*(1 + S^6)*HPL[{3, 3, 1, 1}, -S^2])/S^3 - (8*(1468 + 14953*S^2 + 6738*S^4 + 26398*S^6 + 12913*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (156*(1 + S^6)*HPL[{4, 1, 1, 2}, -S^2])/S^3 + (308*(1 + S^6)*HPL[{4, 1, 2, 1}, -S^2])/S^3 + (1236*(1 + S^6)*HPL[{4, 2, 1, 1}, -S^2])/S^3 + (6016*(1 + S^6)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((-2512*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (8*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(27*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] + (16*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (16*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (992*(1 + S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(3*S^3) + (992*(1 + S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/S^3 + (16*(7501 + 21661*S^2 + 7080*S^4 + 22024*S^6 + 7864*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1984*(1 + S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/S^3 - (9920*(1 + S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) - (3968*(1 + S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/S^3 - (24800*(1 + S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) - (72128*(1 + S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3) + (80*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (256*(1 + S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (1600*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-23*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (-2081 - 4253*S^2 - 4713*S^4 - 3155*S^6 - 1802*S^8)/(162*S^3*(1 + S^2)))*Zeta[3]^2 + HPL[{2, 1, 1, 1}, -S^2]*((2*(1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(27*S^3) + (2*Pi^2*(521 + 4277*S^2 + 1860*S^4 + 7253*S^6 + 3497*S^8))/(27*S^3*(1 + S^2)) - (2624*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*((-344507 - 436837*S^2 - 207169*S^4 - 115703*S^6)/(324*S^3) + (Pi^2*(-29885 - 72281*S^2 - 21306*S^4 - 58736*S^6 - 16340*S^8))/(162*S^3*(1 + S^2)) - (772*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3, 2}, -S^2]*(-((1 + S^2)*(74480 + 17995*S^2 + 31694*S^4))/(243*S^3) + (Pi^2*(-8492 - 21011*S^2 - 6282*S^4 - 17663*S^6 - 5144*S^8))/(162*S^3*(1 + S^2)) - (24*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{5}, -S^2]*((71171 + 103554*S^2 - 71649*S^4 - 97876*S^6)/(972*S^3) + (Pi^2*(730 + 1065*S^2 + 178*S^4 - 9*S^6 - 344*S^8))/(54*S^3*(1 + S^2)) - (44*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (4*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 2, 1}, -S^2]*((-2*(1 + S^2)*(18412 + 6533*S^2 + 28207*S^4))/(81*S^3) - (2*Pi^2*(5173 + 16657*S^2 + 5742*S^4 + 18727*S^6 + 7243*S^8))/(81*S^3*(1 + S^2)) + (1168*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3, 1, 1}, -S^2]*((-48533 - 70854*S^2 - 174075*S^4 - 151538*S^6)/(81*S^3) - (2*Pi^2*(10129 + 37180*S^2 + 13494*S^4 + 46108*S^6 + 19057*S^8))/(81*S^3*(1 + S^2)) + (1232*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{4}, -S^2]*((278*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (Pi^2*(6229 + 9174*S^2 + 1497*S^4 - 1664*S^6))/(486*S^3) + (207232 + 516931*S^2 + 290673*S^4 - 156071*S^6 - 125381*S^8)/(2916*S^3*(1 + S^2)) + ((-835 - 2191*S^2 - 678*S^4 - 1990*S^6 - 634*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (76*(1 + S^6)*HPL[{3, 1}, -S^2])/S^3 + (452*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((367 + 721*S^2 + 150*S^4 + 424*S^6 + 70*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((-4421*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) - ((1 + S^2)*(-233717 - 5557*S^2 + 945778*S^4))/(1458*S^3) + (Pi^2*(-2149 - 14560*S^2 - 104004*S^4 - 175732*S^6 - 82843*S^8))/(486*S^3*(1 + S^2)) + (4*(1351 + 3307*S^2 + 960*S^4 + 2773*S^6 + 817*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]^2*((-4949*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (-101320 - 130581*S^2 - 207528*S^4 - 175675*S^6)/(1944*S^3) + (Pi^2*(-4727 - 6986*S^2 - 10292*S^4 - 8069*S^6))/(324*S^3) + ((2459 + 6095*S^2 + 1818*S^4 + 5141*S^6 + 1505*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (74*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + ((-541 + 575*S^2 + 558*S^4 + 2816*S^6 + 1700*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (20*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (124*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((1805 + 4433*S^2 + 1314*S^4 + 3695*S^6 + 1067*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((2854*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (-479567 - 560889*S^2 + 816219*S^4 + 889765*S^6)/(2916*S^3) + (Pi^2*(-4846 - 6973*S^2 + 38055*S^4 + 79535*S^6 + 38597*S^8))/(486*S^3*(1 + S^2)) + (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(2096 + 5135*S^2 + 1488*S^4 + 4316*S^6 + 1277*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((137813 + 174480*S^2 + 63195*S^4 + 28148*S^6)/(972*S^3) + (Pi^2*(4111 + 8884*S^2 + 2328*S^4 + 6202*S^6 + 1429*S^8))/(162*S^3*(1 + S^2)))*Zeta[5] + HPL[{2, 1}, -S^2]*(((1 + S^2)*(-205501 - 13863*S^2 + 1164362*S^4))/(2916*S^3) + (Pi^4*(10285 + 63080*S^2 + 26012*S^4 + 99284*S^6 + 46489*S^8))/(3240*S^3*(1 + S^2)) + (Pi^2*(-9068 + 23389*S^2 + 656097*S^4 + 1221307*S^6 + 589891*S^8))/(5832*S^3*(1 + S^2)) - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1460*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (4396*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (8*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (496*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (1376*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 + (6272*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-1078*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-25849 - 59176*S^2 - 51876*S^4 - 32428*S^6 - 12583*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (180*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/S^3) + Zeta[3]*((Pi^2*(156313 + 199230*S^2 + 96819*S^4 + 55522*S^6))/(5832*S^3) + (385026 + 463076*S^2 + 229607*S^4 + 155445*S^6)/(2916*S^3) + (Pi^4*(10889 + 23808*S^2 + 6218*S^4 + 16938*S^6 + 4019*S^8))/(3240*S^3*(1 + S^2)) - (352*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{3}, -S^2]*(-((1 + S^2)*(-279097 - 56808*S^2 + 10760*S^4))/(1458*S^3) + (Pi^2*(32462 + 74043*S^2 + 55202*S^4 + 16719*S^6 + 3746*S^8))/(972*S^3*(1 + S^2)) + (Pi^4*(20077 + 45484*S^2 + 13104*S^4 + 32704*S^6 + 7297*S^8))/(4860*S^3*(1 + S^2)) + ((-631 - 1198*S^2 - 216*S^4 - 694*S^6 - 127*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (4*(1 + S^2)*(1 - S^2 + S^4)*HPL[{5}, -S^2])/S^3 + ((-25628 - 33141*S^2 - 19902*S^4 - 12605*S^6)/(81*S^3) - (1042*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (2*(4097 + 10031*S^2 + 2958*S^4 + 8330*S^6 + 2396*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (152*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 2}, -S^2])/(3*S^3) + (68*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (20*(806 + 1994*S^2 + 594*S^4 + 1679*S^6 + 491*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (1616*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (4552*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (880*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((86*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (1613 + 3845*S^2 + 3033*S^4 + 2549*S^6 + 992*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] + (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(3*S^3)) + HPL[{2}, -S^2]*((-787*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(1080*S^3) - ((1 + S^2)*(-343123 - 48191*S^2 + 4468700*S^4))/(17496*S^3) + (Pi^2*(39763 + 10606*S^2 - 2154450*S^4 - 4220546*S^6 - 2071925*S^8))/(34992*S^3*(1 + S^2)) + (Pi^4*(-17579 - 57937*S^2 - 241207*S^4 - 387595*S^6 - 182120*S^8))/(19440*S^3*(1 + S^2)) - (38*(1 + S^6)*HPL[{3}, -S^2]^2)/(3*S^3) + ((157*Pi^2*(1 + S^6))/(27*S^3) + (6893 + 10665*S^2 + 7893*S^4 + 4985*S^6)/(162*S^3))*HPL[{4}, -S^2] + ((1109 + 2237*S^2 + 474*S^4 + 1436*S^6 + 308*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) - (8*(1 + S^2)*(1 - S^2 + S^4)*HPL[{6}, -S^2])/(3*S^3) + (124*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((1910*Pi^2*(1 + S^6))/(27*S^3) + (20318 + 28575*S^2 + 35100*S^4 + 27059*S^6)/(81*S^3))*HPL[{3, 1}, -S^2] + ((-8981 - 22121*S^2 - 6570*S^4 - 18494*S^6 - 5354*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((-9001 - 22189*S^2 - 6594*S^4 - 18574*S^6 - 5386*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) - (152*(1 + S^6)*HPL[{4, 2}, -S^2])/(3*S^3) - (596*(1 + S^6)*HPL[{5, 1}, -S^2])/(3*S^3) + ((-1276*Pi^2*(1 + S^6))/(9*S^3) - (2*(6683 + 9489*S^2 + 11754*S^4 + 9020*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(-541 + 575*S^2 + 558*S^4 + 2816*S^6 + 1700*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(2407 + 11695*S^2 + 4644*S^4 + 16843*S^6 + 7555*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (52*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/S^3 - (460*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 - (4156*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) + (8*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (9088*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (6272*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(1537 + 3682*S^2 + 1056*S^4 + 2980*S^6 + 835*S^8))/(54*S^3*(1 + S^2)) + (149944 + 336013*S^2 + 280977*S^4 + 169243*S^6 + 66559*S^8)/(972*S^3*(1 + S^2)))*Zeta[3] - (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*(((1 + S^2)*(18412 + 6533*S^2 + 28207*S^4))/(81*S^3) + (Pi^2*(5173 + 16657*S^2 + 5742*S^4 + 18727*S^6 + 7243*S^8))/(81*S^3*(1 + S^2)) - (584*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*(((1 + S^2)*(49537 + 11818*S^2 + 21013*S^4))/(324*S^3) + (Pi^2*(4243 + 10507*S^2 + 3150*S^4 + 8833*S^6 + 2569*S^8))/(162*S^3*(1 + S^2)) - (808*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (12*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + ((3817 + 8626*S^2 + 2328*S^4 + 6430*S^6 + 1621*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + ((1496 + 3038*S^2 + 816*S^4 + 1769*S^6 + 227*S^8)*Zeta[7])/(9*S^3*(1 + S^2))) + Log[T]*((135211*Pi^8*S^3)/408240 + (351067 + 1210816*S^2)/(209952*S) + (Pi^2*(3285240 + 1378053*S^2 + 16160465*S^4))/(209952*S) + (Pi^6*(922770 + 2246229*S^2 + 4160731*S^4 + 2820010*S^6))/(816480*S*(1 + S^2)) + (Pi^4*(8402466 + 14757999*S^2 + 44501596*S^4 + 37947775*S^6))/(2099520*S*(1 + S^2)) + (S^3*HPL[{0}, S^2]^8)/144 + (4*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{1}, -S^2]^8)/(9*S^3) + HPL[{0}, S^2]^7*((42 + 21*S^2 + 164*S^4 + 122*S^6)/(1296*S*(1 + S^2)) + (7*(1 + S^6)*HPL[{1}, -S^2])/(216*S^3)) + ((136*Pi^2*(-2 + 5*S^6))/(81*S^3) + (-13966 + 3657*S^2 + 579*S^4 + 20468*S^6)/(486*S^3))*HPL[{2}, -S^2]^3 + ((251 + 334*S^6)*HPL[{2}, -S^2]^4)/(54*S^3) + HPL[{0}, S^2]^6*((8*Pi^2*S^3)/81 + (72 + 1548*S^2 + 6407*S^4 + 5039*S^6)/(7776*S*(1 + S^2)) + ((2 + 85*S^2 + 43*S^4 + 166*S^6 + 83*S^8)*HPL[{1}, -S^2])/(216*S^3*(1 + S^2)) + (41*(1 + S^6)*HPL[{1}, -S^2]^2)/(216*S^3) + (19*S^3*HPL[{2}, -S^2])/108) + HPL[{1}, -S^2]^6*((92*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(81*S^3) + (20*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((Pi^2*(-14 + 99*S^6))/(27*S^3) + (-1111 + 3770*S^2 + 6378*S^4 + 2900*S^6 + 1511*S^8)/(162*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + (8*(10 + 3*S^6)*HPL[{4}, -S^2]^2)/(9*S^3) + ((4*Pi^2*(31 + 61*S^6))/(27*S^3) + (-1760 - 20204*S^2 + 2397*S^4 + 69681*S^6 + 48570*S^8)/(162*S^3*(1 + S^2)))*HPL[{6}, -S^2] + ((-4165 - 1213*S^2 + 1476*S^4 + 14610*S^6 + 11658*S^8)*HPL[{7}, -S^2])/(27*S^3*(1 + S^2)) + (2*(735 + 1556*S^6)*HPL[{8}, -S^2])/(9*S^3) + ((-9045 - 9147*S^2 - 9855*S^4 - 14951*S^6)/(27*S^3) - (4*Pi^2*(254 + 701*S^6))/(27*S^3))*HPL[{2, 1}, -S^2]^2 + (8*(381 + 344*S^6)*HPL[{3, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(-39 + 406*S^6))/(27*S^3) + (-852 + 4955*S^2 + 7348*S^4 + 4521*S^6 + 2836*S^8)/(54*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + (4*(75 + 21*S^2 - 27*S^4 - 32*S^6 + 22*S^8)*HPL[{4, 3}, -S^2])/(9*S^3*(1 + S^2)) + ((2*Pi^2*(43 + 787*S^6))/(27*S^3) + (6695 + 56393*S^2 + 53109*S^4 + 7747*S^6 + 3472*S^8)/(81*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((2353 + 985*S^2 - 684*S^4 - 961*S^6 + 407*S^8)*HPL[{5, 2}, -S^2])/(27*S^3*(1 + S^2)) - (4*(1 + 2*S^2)*(1 - 2*S^2 + 4*S^4)*HPL[{5, 3}, -S^2])/(9*S^3) - (2*(-3719 - 2909*S^2 + 405*S^4 + 3368*S^6 + 2558*S^8)*HPL[{6, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(-18 + 43*S^6)*HPL[{6, 2}, -S^2])/(9*S^3) - (4*(203 + 562*S^6)*HPL[{7, 1}, -S^2])/(9*S^3) + (80*(33 + 46*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(3*S^3) + ((-2*Pi^2*(-129 + 119*S^6))/(27*S^3) + (1815 + 779*S^2 - 245*S^4 - 189*S^6 - 908*S^8)/(27*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((2*Pi^2*(-959 + 2601*S^6))/(27*S^3) + (-50419 - 38899*S^2 + 16209*S^4 + 83621*S^6 + 79148*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((1517 - 23359*S^2 - 12438*S^4 - 45128*S^6 - 20252*S^8)*HPL[{3, 2, 2}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-1007 + 8533*S^2 + 4770*S^4 + 17416*S^6 + 7876*S^8)*HPL[{3, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(32 + 335*S^6)*HPL[{3, 3, 2}, -S^2])/(9*S^3) + ((4*Pi^2*(-1725 + 3767*S^6))/(27*S^3) + (2*(-89913 - 89967*S^2 + 495*S^4 + 120224*S^6 + 119999*S^8))/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] - (2*(-4425 + 33033*S^2 + 18729*S^4 + 68351*S^6 + 30893*S^8)*HPL[{4, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) - (8*(33 + 283*S^6)*HPL[{4, 1, 3}, -S^2])/(9*S^3) - (2*(-13137 + 103593*S^2 + 58365*S^4 + 212699*S^6 + 95969*S^8)*HPL[{4, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-13 + 474*S^6)*HPL[{4, 2, 2}, -S^2])/(9*S^3) - (8*(89 + 969*S^6)*HPL[{4, 3, 1}, -S^2])/(9*S^3) - (4*(-12642 + 107382*S^2 + 60012*S^4 + 217231*S^6 + 97207*S^8)*HPL[{5, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(111 + 1171*S^6)*HPL[{5, 1, 2}, -S^2])/(9*S^3) - (4*(711 + 7951*S^6)*HPL[{5, 2, 1}, -S^2])/(9*S^3) - (8*(846 + 10055*S^6)*HPL[{6, 1, 1}, -S^2])/(9*S^3) + (8*(-367 - 491*S^2 - 62*S^4 + 143*S^6 + 267*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)) + ((-16*Pi^2*(-354 + 671*S^6))/(27*S^3) - (4*(-35539 - 1449*S^2 - 1971*S^4 + 43635*S^6))/(81*S^3))*HPL[{3, 1, 1, 1}, -S^2] - (8*(-8899 - 18187*S^2 - 4644*S^4 - 7024*S^6 + 2264*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-8899 - 18187*S^2 - 4644*S^4 - 7024*S^6 + 2264*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(131 + 121*S^6)*HPL[{3, 1, 2, 2}, -S^2])/(9*S^3) - (8*(-18808 - 31444*S^2 - 6318*S^4 - 3163*S^6 + 9473*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(131 + 121*S^6)*HPL[{3, 2, 1, 2}, -S^2])/(9*S^3) - (4*(-2187 + 2527*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(9*S^3) - (32*(-257 + 331*S^6)*HPL[{3, 3, 1, 1}, -S^2])/(3*S^3) - (16*(-28998 - 49230*S^2 - 10116*S^4 - 6559*S^6 + 13673*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (296*(-1 + 11*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(9*S^3) - (8*(-3047 + 3565*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(9*S^3) - (8*(-9215 + 11509*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(9*S^3) - (32*(-4651 + 5533*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(9*S^3) + ((80*Pi^2*(-113 + 298*S^6))/(27*S^3) + (8*(-29042 + 6705*S^2 + 3735*S^4 + 47893*S^6))/(81*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (32*(465 + 1641*S^2 + 588*S^4 + 1526*S^6 + 350*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (32*(465 + 1641*S^2 + 588*S^4 + 1526*S^6 + 350*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (64*(-257 + 331*S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(9*S^3) - (64*(-257 + 331*S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(3*S^3) - (16*(14119 + 56599*S^2 + 21240*S^4 + 58331*S^6 + 15851*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(-3023 + 3913*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(9*S^3) + (32*(-1693 + 2187*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(3*S^3) + (32*(-6107 + 7885*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(9*S^3) + (32*(-4263 + 5497*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(3*S^3) + (64*(-6439 + 8216*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3) + (160*(-76 - 106*S^2 - 15*S^4 + 31*S^6 + 61*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (1280*(-11 + 10*S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + (4480*(-5 + 7*S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((2*Pi^2*S^3)/3 - (2*(-118 - 260*S^2 + 5*S^4 + 48*S^6))/(27*S*(1 + S^2)))*Zeta[3]^2 + HPL[{0}, S^2]^5*((Pi^2*(7686 + 3843*S^2 + 27698*S^4 + 20012*S^6))/(19440*S*(1 + S^2)) + (-3040 + 16201*S^2 + 150337*S^4 + 133796*S^6)/(38880*S*(1 + S^2)) + ((596 + 7223*S^2 + 3426*S^4 + 12929*S^6 + 6302*S^8)*HPL[{1}, -S^2]^2)/(3240*S^3*(1 + S^2)) + (91*(1 + S^6)*HPL[{1}, -S^2]^3)/(135*S^3) + ((-100 + 822*S^2 + 461*S^4 + 3016*S^6 + 2094*S^8)*HPL[{2}, -S^2])/(1080*S^3*(1 + S^2)) + HPL[{1}, -S^2]*((427*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(1080*S^3) + (-260 + 3856*S^2 + 60801*S^4 + 102784*S^6 + 48799*S^8)/(19440*S^3*(1 + S^2)) + (461*(1 + S^6)*HPL[{2}, -S^2])/(540*S^3)) + ((1 - 2*S^6)*HPL[{3}, -S^2])/(36*S^3) + ((-238 + 25*S^6)*HPL[{2, 1}, -S^2])/(135*S^3) + (S^3*Zeta[3])/2) + HPL[{1}, -S^2]^5*(((1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(486*S^3) + (Pi^2*(716 + 2372*S^2 + 828*S^4 + 2729*S^6 + 1073*S^8))/(81*S^3*(1 + S^2)) + (2*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2}, -S^2])/(27*S^3*(1 + S^2)) - (320*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (40*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (80*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{5}, -S^2]*((-17151 - 127356*S^2 + 55695*S^4 + 134764*S^6)/(972*S^3) + (Pi^2*(-697 - 1696*S^2 - 522*S^4 - 124*S^6 + 875*S^8))/(162*S^3*(1 + S^2)) + (4*(223 + 3*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (8*(-8 + 3*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1, 1}, -S^2]*((4*(-14341 + 18753*S^2 - 41367*S^4 + 8287*S^6))/(81*S^3) + (4*Pi^2*(-6757 - 12373*S^2 - 2754*S^4 - 2473*S^6 + 3143*S^8))/(81*S^3*(1 + S^2)) + (160*(97 + 4*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 2, 1}, -S^2]*((62353 + 175383*S^2 + 283005*S^4 + 45077*S^6)/(243*S^3) + (2*Pi^2*(6011 + 17495*S^2 + 5742*S^4 + 13426*S^6 + 1942*S^8))/(81*S^3*(1 + S^2)) + (32*(-241 + 11*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 1, 1}, -S^2]*((59201 + 63912*S^2 + 262971*S^4 + 9806*S^6)/(81*S^3) + (2*Pi^2*(17991 + 45024*S^2 + 13458*S^4 + 27419*S^6 + 386*S^8))/(81*S^3*(1 + S^2)) + (16*(-1465 + 13*S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 2}, -S^2]*((-70959 + 588165*S^2 + 114963*S^4 + 221063*S^6)/(972*S^3) + (Pi^2*(-2039 + 10522*S^2 + 6366*S^4 + 22313*S^6 + 9752*S^8))/(162*S^3*(1 + S^2)) + (4*(-5 + 41*S^6)*Zeta[3])/(3*S^3)) + HPL[{4, 1}, -S^2]*((-46653 + 980385*S^2 + 175776*S^4 + 329101*S^6)/(486*S^3) + (Pi^2*(-1523 + 19741*S^2 + 10785*S^4 + 36981*S^6 + 15717*S^8))/(81*S^3*(1 + S^2)) + (8*(15 + 194*S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((Pi^4*(1726 + 8045*S^6))/(1620*S^3) + (Pi^2*(27860 + 46389*S^2 + 45993*S^4 + 89741*S^6))/(1944*S^3) + (456647 + 295650*S^2 + 315621*S^4 + 936214*S^6)/(5832*S^3) + ((-293 - 7565*S^2 - 3636*S^4 - 12844*S^6 - 5572*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) + ((-49 - 388*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-367 - 491*S^2 - 62*S^4 + 143*S^6 + 267*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (2*(-631 + 545*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (8*(-257 + 331*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((431 - 2197*S^2 - 1314*S^4 - 4886*S^6 - 2258*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{4}, -S^2]*((Pi^4*(-121 - 240*S^6))/(324*S^3) + (Pi^2*(-7004 - 23286*S^2 - 804*S^4 + 4059*S^6))/(972*S^3) + (-184828 - 950647*S^2 - 728190*S^4 + 299786*S^6 + 238829*S^8)/(5832*S^3*(1 + S^2)) + (2*(3334 + 5356*S^2 + 993*S^4 + 2271*S^6 + 249*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-79 + 382*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (8*(-61 + 383*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(97 - 86*S^2 - 87*S^4 - 163*S^6 + 20*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^4*((1237*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) + ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(2916*S^3) + (2*Pi^2*(2456 + 3630*S^2 + 5688*S^4 + 4487*S^6))/(243*S^3) + ((314*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(81*S^3))*HPL[{2}, -S^2] + (392*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) - (2*(562 + 1362*S^2 + 400*S^4 + 1113*S^6 + 313*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) - (284*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) - (10*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (200*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (50*(50 + 122*S^2 + 36*S^4 + 101*S^6 + 29*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((Pi^4*(-4256 + 17677*S^6))/(405*S^3) + (-307463 + 72027*S^2 + 40689*S^4 + 676271*S^6)/(486*S^3) + (Pi^2*(-31189 - 6763*S^2 + 45135*S^4 + 117866*S^6 + 96509*S^8))/(243*S^3*(1 + S^2)) - (8*(-83 + 2833*S^2 + 1404*S^4 + 5263*S^6 + 2347*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((387213 + 37440*S^2 + 2865*S^4 - 657568*S^6)/(972*S^3) + (Pi^4*(1061 - 3275*S^6))/(162*S^3) + (Pi^2*(38507 + 22706*S^2 - 30729*S^4 - 107347*S^6 - 91663*S^8))/(486*S^3*(1 + S^2)) - (32*(310 + 283*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (4*(-98 + 2923*S^2 + 1452*S^4 + 5407*S^6 + 2386*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^4*((10279*Pi^4*S^3)/19440 + (Pi^2*(8766 + 47286*S^2 + 160789*S^4 + 124699*S^6))/(23328*S*(1 + S^2)) + (222204 + 356073*S^2 + 2301940*S^4 + 2179735*S^6)/(139968*S*(1 + S^2)) + ((457 + 2704*S^2 + 1146*S^4 + 4153*S^6 + 1906*S^8)*HPL[{1}, -S^2]^3)/(324*S^3*(1 + S^2)) + (31*(1 + S^6)*HPL[{1}, -S^2]^4)/(18*S^3) + ((Pi^2*(-5 + 364*S^6))/(216*S^3) + (-420 + 6753*S^2 + 21663*S^4 + 58511*S^6 + 44075*S^8)/(3888*S^3*(1 + S^2)))*HPL[{2}, -S^2] + ((-9 + 460*S^6)*HPL[{2}, -S^2]^2)/(216*S^3) + HPL[{1}, -S^2]^2*((391*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(216*S^3) + (631 + 1826*S^2 + 6864*S^4 + 10306*S^6 + 4817*S^8)/(432*S^3*(1 + S^2)) + (245*(1 + S^6)*HPL[{2}, -S^2])/(54*S^3)) + ((30 + 66*S^2 + 23*S^6 - 13*S^8)*HPL[{3}, -S^2])/(216*S^3*(1 + S^2)) + ((5 + 24*S^6)*HPL[{4}, -S^2])/(36*S^3) + ((-472 - 1453*S^2 - 492*S^4 - 778*S^6 + 203*S^8)*HPL[{2, 1}, -S^2])/(108*S^3*(1 + S^2)) - (5*(-3 + 101*S^6)*HPL[{3, 1}, -S^2])/(54*S^3) + ((-5 + 174*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((76 + 38*S^2 + 543*S^4 + 467*S^6)*Zeta[3])/(108*S*(1 + S^2)) + HPL[{1}, -S^2]*((Pi^2*(517 + 5254*S^2 + 2436*S^4 + 9133*S^6 + 4396*S^8))/(1296*S^3*(1 + S^2)) + (16537 + 39919*S^2 + 183429*S^4 + 302071*S^6 + 145912*S^8)/(11664*S^3*(1 + S^2)) + ((382 + 2343*S^2 + 982*S^4 + 3666*S^6 + 1705*S^8)*HPL[{2}, -S^2])/(216*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (245*(1 + S^6)*HPL[{2, 1}, -S^2])/(27*S^3) + (19*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3))) + ((-46766 - 8447*S^2 - 3156*S^4)/(162*S) + (Pi^2*(-802 - 401*S^2 - 1399*S^4 - 597*S^6))/(27*S*(1 + S^2)))*Zeta[5] + Zeta[3]*((Pi^2*(-163332 - 35820*S^2 - 40933*S^4))/(2916*S) + (-4966014 - 902559*S^2 + 279779*S^4)/(17496*S) + (Pi^4*(-9810 - 4905*S^2 - 15479*S^4 - 5669*S^6))/(2430*S*(1 + S^2)) - (184*S^3*Zeta[5])/9) + HPL[{0}, S^2]^3*((Pi^4*(96096 + 48048*S^2 + 316249*S^4 + 220153*S^6))/(58320*S*(1 + S^2)) + (Pi^2*(14908 + 55484*S^2 + 276165*S^4 + 239369*S^6))/(11664*S*(1 + S^2)) + (740784 + 1660452*S^2 + 15216463*S^4 + 14390107*S^6)/(209952*S*(1 + S^2)) + ((745 + 3337*S^2 + 1314*S^4 + 4606*S^6 + 2014*S^8)*HPL[{1}, -S^2]^4)/(162*S^3*(1 + S^2)) + (86*(1 + S^6)*HPL[{1}, -S^2]^5)/(27*S^3) + ((-16 + 3335*S^2 + 1662*S^4 + 8722*S^6 + 5371*S^8)*HPL[{2}, -S^2]^2)/(324*S^3*(1 + S^2)) + HPL[{1}, -S^2]^3*((397*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + (4907 + 13775*S^2 + 35340*S^4 + 47579*S^6 + 21755*S^8)/(729*S^3*(1 + S^2)) + (392*(1 + S^6)*HPL[{2}, -S^2])/(27*S^3)) + ((Pi^2*(8 - 7*S^6))/(27*S^3) + (610 + 49*S^2 + 1650*S^4 + 5578*S^6 + 2827*S^8)/(972*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-82 + 191*S^2 + 132*S^4 + 999*S^6 + 726*S^8)*HPL[{4}, -S^2])/(162*S^3*(1 + S^2)) - (2*(2 + 5*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((Pi^2*(-1082 + 77*S^6))/(81*S^3) + (-10266 - 4170*S^2 - 33420*S^4 + 1577*S^6)/(486*S^3))*HPL[{2, 1}, -S^2] - (2*(-169 + 1580*S^2 + 870*S^4 + 4665*S^6 + 2916*S^8)*HPL[{3, 1}, -S^2])/(81*S^3*(1 + S^2)) - (2*(-16 + 7*S^6)*HPL[{3, 2}, -S^2])/(27*S^3) - (2*(1 + 2*S^6)*HPL[{4, 1}, -S^2])/(27*S^3) + (2*(-338 + 3187*S^2 + 1758*S^4 + 9570*S^6 + 6045*S^8)*HPL[{2, 1, 1}, -S^2])/(81*S^3*(1 + S^2)) - (4*(-569 + 9*S^6)*HPL[{2, 2, 1}, -S^2])/(27*S^3) - (4*(-580 + 13*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) + (8*(-202 + 9*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((5*Pi^2*S^3)/3 + (-2448 - 1305*S^2 + 6323*S^4 + 5396*S^6)/(486*S*(1 + S^2)))*Zeta[3] + HPL[{1}, -S^2]^2*((Pi^2*(2831 + 17234*S^2 + 7368*S^4 + 26747*S^6 + 12344*S^8))/(972*S^3*(1 + S^2)) + (43685 + 120527*S^2 + 405513*S^4 + 610577*S^6 + 288386*S^8)/(5832*S^3*(1 + S^2)) + ((1943 + 8999*S^2 + 3528*S^4 + 12707*S^6 + 5651*S^8)*HPL[{2}, -S^2])/(162*S^3*(1 + S^2)) + (8*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (392*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(27*S^3)) + HPL[{2}, -S^2]*((-6430 + 50439*S^2 + 75099*S^4 + 291229*S^6)/(5832*S^3) + (Pi^2*(-638 + 5653*S^2 + 3141*S^4 + 18618*S^6 + 12327*S^8))/(972*S^3*(1 + S^2)) + (8*(-2 + S^6)*HPL[{3}, -S^2])/(27*S^3) + (2*(-569 + 9*S^6)*HPL[{2, 1}, -S^2])/(27*S^3) - (2*(-3 + 5*S^6)*Zeta[3])/(27*S^3)) + HPL[{1}, -S^2]*((2002*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1215*S^3) + (Pi^2*(9554 + 31406*S^2 + 131481*S^4 + 197942*S^6 + 92309*S^8))/(5832*S^3*(1 + S^2)) + (173348 + 484253*S^2 + 2394693*S^4 + 3975587*S^6 + 1922903*S^8)/(34992*S^3*(1 + S^2)) + ((1049*Pi^2*(1 + S^6))/(162*S^3) + (4538 + 8031*S^2 + 24501*S^4 + 21332*S^6)/(486*S^3))*HPL[{2}, -S^2] + (280*(1 + S^6)*HPL[{2}, -S^2]^2)/(27*S^3) + ((-101 + 28*S^2 + 42*S^4 + 406*S^6 + 277*S^8)*HPL[{3}, -S^2])/(81*S^3*(1 + S^2)) + (46*(1 + S^6)*HPL[{4}, -S^2])/(27*S^3) + ((-1943 - 8999*S^2 - 3528*S^4 - 12707*S^6 - 5651*S^8)*HPL[{2, 1}, -S^2])/(81*S^3*(1 + S^2)) - (1168*(1 + S^6)*HPL[{3, 1}, -S^2])/(27*S^3) + (784*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + (2*(-71 - 79*S^2 - S^4 + 47*S^6 + 55*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + (208*S^3*Zeta[5])/27) + HPL[{1}, -S^2]^3*(((1 + S^2)*(422663 + 99650*S^2 + 875723*S^4))/(2916*S^3) + (Pi^2*(35631 + 49802*S^2 + 90717*S^4 + 76258*S^6))/(972*S^3) + (Pi^4*(33926 + 122951*S^2 + 44454*S^4 + 151082*S^6 + 62057*S^8))/(4860*S^3*(1 + S^2)) + (2*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((-820*Pi^2*(1 + S^6))/(27*S^3) - (2*(10561 + 13896*S^2 + 7515*S^4 + 4252*S^6))/(81*S^3))*HPL[{3}, -S^2] - (4*(228 + 511*S^2 + 140*S^4 + 369*S^6 + 86*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (248*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-1256*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - (4*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(81*S^3))*HPL[{2, 1}, -S^2] - (8*(-523 - 571*S^2 - 24*S^4 + 398*S^6 + 446*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (880*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (9056*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (40*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (6272*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (12416*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (800*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-220*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (4*(4096 + 5235*S^2 + 2898*S^4 + 1867*S^6))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*(((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(81*S^3) + (Pi^2*(521 + 4277*S^2 + 1860*S^4 + 7253*S^6 + 3497*S^8))/(81*S^3*(1 + S^2)) - (440*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (3136*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (1312*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) - (1072*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{3}, -S^2]*((-854867 - 12089526*S^2 + 8247*S^4 - 1093128*S^6)/(34992*S^3) + (Pi^2*(-7485 - 357105*S^2 - 386994*S^4 - 101800*S^6 - 68314*S^8))/(5832*S^3*(1 + S^2)) + (Pi^4*(1017 - 49977*S^2 - 26568*S^4 - 88622*S^6 - 37628*S^8))/(9720*S^3*(1 + S^2)) - (2*(235 - 71*S^2 - 153*S^4 - 301*S^6 + 5*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (4*(39 + 10*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-2*Pi^2*(-1179 + 89*S^6))/(27*S^3) + (20203 + 5734*S^2 + 10249*S^4 + 196*S^6)/(27*S^3))*HPL[{2, 1}, -S^2] + (2*(-1745 + 4195*S^2 + 2970*S^4 + 11214*S^6 + 5274*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(11 + 225*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (8*(-45 + 46*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) - (8*(-743 + 2230*S^2 + 1491*S^4 + 5599*S^6 + 2626*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(1133 + 123*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (40*(685 + 31*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (32*(-189 + 16*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-10*Pi^2*(5 + 11*S^6))/(27*S^3) + (-1088 - 4229*S^2 - 3699*S^4 - 2451*S^6 - 1137*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (4*(13 + 3*S^6)*Zeta[5])/(9*S^3)) + HPL[{2, 1}, -S^2]*((-2662325 + 4087059*S^2 - 12425655*S^4 - 279779*S^6)/(17496*S^3) + (Pi^4*(-72662 - 151469*S^2 - 38247*S^4 - 48425*S^6 + 30382*S^8))/(4860*S^3*(1 + S^2)) + (Pi^2*(-164143 - 77623*S^2 - 438348*S^4 - 491073*S^6 + 37683*S^8))/(2916*S^3*(1 + S^2)) + (4*(1817 + 8879*S^2 + 3540*S^4 + 9911*S^6 + 2849*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (4*(2149 + 129*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (16*(-1730 + 7*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (16*(465 + 1641*S^2 + 588*S^4 + 1526*S^6 + 350*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(-257 + 331*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (32*(-68 + 315*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (160*(33 + 46*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((4*Pi^2*(535 + 21*S^6))/(27*S^3) + (2*(8965 + 12637*S^2 + 8085*S^4 + 4870*S^6 + 241*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] - (8*(-419 + 12*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]^2*((17153*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(7560*S^3) + ((1 + S^2)*(3757531 + 762416*S^2 + 9134503*S^4))/(17496*S^3) + (Pi^2*(1796785 + 2369925*S^2 + 5012091*S^4 + 4431175*S^6))/(34992*S^3) + (Pi^4*(178487 + 451049*S^2 + 798153*S^4 + 953759*S^6 + 426764*S^8))/(19440*S^3*(1 + S^2)) + ((319*Pi^2*(1 + S^6))/(9*S^3) + (6683 + 9489*S^2 + 11754*S^4 + 9020*S^6)/(54*S^3))*HPL[{2}, -S^2]^2 + (62*(1 + S^6)*HPL[{2}, -S^2]^3)/(9*S^3) + (74*(1 + S^6)*HPL[{3}, -S^2]^2)/(3*S^3) + ((-401*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-24043 - 58261*S^2 - 45549*S^4 - 13783*S^6 - 1804*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(-613 - 983*S^2 - 182*S^4 - 191*S^6 + 179*S^8)*HPL[{5}, -S^2])/(9*S^3*(1 + S^2)) + (70*(1 + S^6)*HPL[{6}, -S^2])/(3*S^3) - (1568*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-152*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(3*S^3) - (2*(1 + S^2)*(-3878 - 529*S^2 + 4768*S^4))/(27*S^3))*HPL[{3, 1}, -S^2] + (4*(1344 + 3323*S^2 + 988*S^4 + 2798*S^6 + 819*S^8)*HPL[{3, 2}, -S^2])/(9*S^3*(1 + S^2)) + (4*(4714 + 11503*S^2 + 3390*S^4 + 9502*S^6 + 2713*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + (78*(1 + S^6)*HPL[{4, 2}, -S^2])/S^3 + (1168*(1 + S^6)*HPL[{5, 1}, -S^2])/(3*S^3) + ((1256*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (4*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (8*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(601 + 2153*S^2 + 776*S^4 + 2624*S^6 + 1072*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (496*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/(3*S^3) + (352*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/(3*S^3) - (40*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (128*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (800*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-48677 - 60294*S^2 - 30519*S^4 - 19766*S^6)/(162*S^3) + (Pi^2*(-1407 - 3386*S^2 - 988*S^4 - 2750*S^6 - 771*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*((-61939 - 78816*S^2 - 34365*S^4 - 17704*S^6)/(162*S^3) + (Pi^2*(-5390 - 12791*S^2 - 3732*S^4 - 10073*S^6 - 2672*S^8))/(81*S^3*(1 + S^2)) + (440*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/S^3) + HPL[{2, 1}, -S^2]*(-((1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(27*S^3) + (Pi^2*(-521 - 4277*S^2 - 1860*S^4 - 7253*S^6 - 3497*S^8))/(27*S^3*(1 + S^2)) + (1312*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((4421*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(540*S^3) + ((1 + S^2)*(-233717 - 5557*S^2 + 945778*S^4))/(2916*S^3) + (Pi^2*(2149 + 14560*S^2 + 104004*S^4 + 175732*S^6 + 82843*S^8))/(972*S^3*(1 + S^2)) - (10*(806 + 1994*S^2 + 594*S^4 + 1679*S^6 + 491*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) - (226*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1568*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(1351 + 3307*S^2 + 960*S^4 + 2773*S^6 + 817*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) - (2*(1220 + 2829*S^2 + 806*S^4 + 2178*S^6 + 569*S^8)*Zeta[5])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^6*(-10321 + 64644*S^6))/(34020*S^3) + (-4655916 + 2028891*S^2 + 2759853*S^4 + 16160465*S^6)/(34992*S^3) + (Pi^4*(-234020 + 63124*S^2 + 625347*S^4 + 1560201*S^6 + 1218120*S^8))/(58320*S^3*(1 + S^2)) + (Pi^2*(-465742 - 145798*S^2 + 616083*S^4 + 2347551*S^6 + 2039748*S^8))/(17496*S^3*(1 + S^2)) + (2*(1 + 112*S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((4722 - 16857*S^2 - 4383*S^4 - 4946*S^6)/(162*S^3) + (Pi^2*(21 - 122*S^6))/(9*S^3))*HPL[{4}, -S^2] + ((871 - 314*S^2 - 588*S^4 - 906*S^6 + 279*S^8)*HPL[{5}, -S^2])/(27*S^3*(1 + S^2)) + (4*(6 + 11*S^6)*HPL[{6}, -S^2])/(3*S^3) - (8*(-257 + 331*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((-32677 - 24516*S^2 - 31905*S^4 - 41524*S^6)/(81*S^3) - (2*Pi^2*(635 + 1271*S^6))/(27*S^3))*HPL[{3, 1}, -S^2] + ((-269 + 12871*S^2 + 6570*S^4 + 23618*S^6 + 10478*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-2455 + 17339*S^2 + 9915*S^4 + 36261*S^6 + 16467*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(5 + 44*S^6)*HPL[{4, 2}, -S^2])/S^3 + (4*(-33 + 877*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((8*Pi^2*(254 + 701*S^6))/(27*S^3) + (2*(9045 + 9147*S^2 + 9855*S^4 + 14951*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(-367 - 491*S^2 - 62*S^4 + 143*S^6 + 267*S^8)*HPL[{2, 2, 1}, -S^2])/(3*S^3*(1 + S^2)) + (4*(-8423 - 17717*S^2 - 4656*S^4 - 7337*S^6 + 1957*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (52*(1 + S^2)*(1 - S^2 + S^4)*HPL[{3, 1, 2}, -S^2])/S^3 + (4*(887 + 1219*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (8*(1567 + 1621*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (16*(465 + 1641*S^2 + 588*S^4 + 1526*S^6 + 350*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (32*(-2774 + 4255*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (160*(33 + 46*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((7949 - 130567*S^2 - 166980*S^4 - 94113*S^6 - 61761*S^8)/(486*S^3*(1 + S^2)) + (Pi^2*(137 - 3058*S^2 - 1539*S^4 - 5686*S^6 - 2491*S^8))/(81*S^3*(1 + S^2)))*Zeta[3] + (4*(-8 + 21*S^6)*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*((-62353 - 175383*S^2 - 283005*S^4 - 45077*S^6)/(486*S^3) + (Pi^2*(-6011 - 17495*S^2 - 5742*S^4 - 13426*S^6 - 1942*S^8))/(81*S^3*(1 + S^2)) - (16*(-241 + 11*S^6)*Zeta[3])/(9*S^3)) + HPL[{3}, -S^2]*((51713 - 302385*S^2 - 51771*S^4 - 116645*S^6)/(972*S^3) + (Pi^2*(1545 - 4743*S^2 - 3198*S^4 - 11458*S^6 - 5170*S^8))/(162*S^3*(1 + S^2)) + (4*(1133 + 123*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(-9 + 65*S^6)*Zeta[3])/(9*S^3)) - (2*(-139 + 2237*S^2 + 1107*S^4 + 4041*S^6 + 1665*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{0}, S^2]^2*((147719*Pi^6*S^3)/136080 + (3005520 + 828873*S^2 + 16160465*S^4)/(69984*S) + (Pi^2*(171156 + 278988*S^2 + 1157053*S^4 + 1052137*S^6))/(17496*S*(1 + S^2)) + (Pi^4*(237258 + 713655*S^2 + 1888579*S^4 + 1429030*S^6))/(116640*S*(1 + S^2)) + ((233 + 881*S^2 + 324*S^4 + 1112*S^6 + 464*S^8)*HPL[{1}, -S^2]^5)/(27*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{1}, -S^2]^6)/S^3 + ((Pi^2*(1 + 293*S^6))/(27*S^3) + (725 + 18948*S^2 + 16428*S^4 + 44888*S^6)/(648*S^3))*HPL[{2}, -S^2]^2 + ((-15 + 349*S^6)*HPL[{2}, -S^2]^3)/(27*S^3) + HPL[{1}, -S^2]^4*((76*Pi^2*(1 + S^6))/(9*S^3) + (5728 + 9285*S^2 + 19854*S^4 + 16081*S^6)/(324*S^3) + (239*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) - ((1 + 2*S^2)*(1 - 2*S^2 + 4*S^4)*HPL[{3}, -S^2]^2)/(9*S^3) + ((Pi^2*(6 + 113*S^6))/(54*S^3) + (-887 - 2177*S^2 + 831*S^4 + 9313*S^6 + 6868*S^8)/(324*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-271 - 154*S^2 + 36*S^4 + 585*S^6 + 468*S^8)*HPL[{5}, -S^2])/(54*S^3*(1 + S^2)) + ((70 + 129*S^6)*HPL[{6}, -S^2])/(9*S^3) - (2*(13 + 712*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(63 - 1247*S^6))/(27*S^3) + (2968 - 14282*S^2 - 34149*S^4 - 65683*S^6 - 48028*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1}, -S^2] + ((-19 + 662*S^2 + 426*S^4 + 543*S^6 - 138*S^8)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)) + ((-65 + 823*S^2 + 597*S^4 + 697*S^6 - 191*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-2 - S^6)*HPL[{4, 2}, -S^2])/(9*S^3) - (14*(1 + 9*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((2*Pi^2*(-55 + 1277*S^6))/(27*S^3) + (-2147 + 15574*S^2 + 34695*S^4 + 66238*S^6 + 48616*S^8)/(81*S^3*(1 + S^2)))*HPL[{2, 1, 1}, -S^2] - (2*(-3221 - 7649*S^2 - 2214*S^4 - 4270*S^6 + 158*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-9790 - 22855*S^2 - 6474*S^4 - 12502*S^6 + 563*S^8)*HPL[{3, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-7 + S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) + (2*(-53 + 1395*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) + (4*(-99 + 2135*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) + (4*(-3337 - 7603*S^2 - 2079*S^4 - 3868*S^6 + 398*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(-24 + 371*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) + (80*(-8 + 151*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((-14760 - 4770*S^2 + 8789*S^4)/(972*S) + (Pi^2*(-42 - 21*S^2 + 1198*S^4 + 1240*S^6))/(162*S*(1 + S^2)))*Zeta[3] + (10*S^3*Zeta[3]^2)/3 + HPL[{1}, -S^2]^3*((7277 + 11139*S^2 + 30204*S^4 + 26126*S^6)/(243*S^3) + (Pi^2*(1622 + 7109*S^2 + 2766*S^4 + 9713*S^6 + 4226*S^8))/(162*S^3*(1 + S^2)) + ((312 + 1264*S^2 + 470*S^4 + 1671*S^6 + 719*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (20*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (956*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (20*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((Pi^2*(217 + 106*S^2 - 168*S^4 - 239*S^6 - 128*S^8))/(324*S^3*(1 + S^2)) + (1971 - 13236*S^2 + 7521*S^4 + 64115*S^6 + 37499*S^8)/(1944*S^3*(1 + S^2)) + (2*(45 + 7*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (4*(3 + S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((-78097 - 104095*S^2 - 302664*S^4 - 292593*S^6 - 12039*S^8)/(972*S^3*(1 + S^2)) + (Pi^2*(-4753 - 11962*S^2 - 3555*S^4 - 6202*S^6 + 1007*S^8))/(162*S^3*(1 + S^2)) + (4*(50 + S^6)*Zeta[3])/(9*S^3)) + HPL[{1}, -S^2]^2*((3299*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(648*S^3) + (480187 + 678537*S^2 + 2258397*S^4 + 2052271*S^6)/(11664*S^3) + (Pi^2*(7621 + 20491*S^2 + 49731*S^4 + 66853*S^6 + 30532*S^8))/(648*S^3*(1 + S^2)) + ((1207*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (13999 + 36868*S^2 + 77940*S^4 + 104080*S^6 + 47713*S^8)/(324*S^3*(1 + S^2)))*HPL[{2}, -S^2] + (41*(1 + S^6)*HPL[{2}, -S^2]^2)/S^3 + ((-332 - 533*S^2 - 132*S^4 - 56*S^6 + 145*S^8)*HPL[{3}, -S^2])/(27*S^3*(1 + S^2)) + (25*(1 + S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-312 - 1264*S^2 - 470*S^4 - 1671*S^6 - 719*S^8)*HPL[{2, 1}, -S^2])/(3*S^3*(1 + S^2)) - (472*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (956*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((-157 - 336*S^2 - 88*S^4 - 225*S^6 - 46*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2}, -S^2]*((Pi^4*(-490 + 15307*S^6))/(3240*S^3) + (Pi^2*(-2567 + 22327*S^2 + 56358*S^4 + 124749*S^6 + 92691*S^8))/(1944*S^3*(1 + S^2)) + (-9095 + 414712*S^2 + 894018*S^4 + 2544222*S^6 + 2050683*S^8)/(11664*S^3*(1 + S^2)) + ((59 - 283*S^2 - 216*S^4 - 260*S^6 + 82*S^8)*HPL[{3}, -S^2])/(54*S^3*(1 + S^2)) + ((2 + 17*S^6)*HPL[{4}, -S^2])/(9*S^3) + ((-3221 - 7649*S^2 - 2214*S^4 - 4270*S^6 + 158*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (10*(1 + 47*S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (4*(13 + 712*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((6 - 25*S^2 - 15*S^4 - 47*S^6 - 16*S^8)*Zeta[3])/(3*S^3*(1 + S^2))) + ((2 + S^2 + 307*S^4 + 305*S^6)*Zeta[5])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*((497937 + 640787*S^2 + 2466905*S^4 + 2316279*S^6)/(11664*S^3) + (Pi^4*(14161 + 80453*S^2 + 33614*S^4 + 122030*S^6 + 55738*S^8))/(6480*S^3*(1 + S^2)) + (Pi^2*(60199 + 150415*S^2 + 431487*S^4 + 640051*S^6 + 302668*S^8))/(5832*S^3*(1 + S^2)) + ((842 + 3056*S^2 + 1107*S^4 + 3758*S^6 + 1544*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + (-(Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) + (-1525 - 3880*S^2 - 1380*S^4 + 4670*S^6 + 2939*S^8)/(162*S^3*(1 + S^2)))*HPL[{3}, -S^2] + ((-323 - 41*S^2 + 114*S^4 + 904*S^6 + 622*S^8)*HPL[{4}, -S^2])/(54*S^3*(1 + S^2)) + (22*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-1207*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-13999 - 36868*S^2 - 77940*S^4 - 104080*S^6 - 47713*S^8)/(162*S^3*(1 + S^2)))*HPL[{2, 1}, -S^2] - (2*(1352 + 5579*S^2 + 2082*S^4 + 7460*S^6 + 3233*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (104*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (262*(1 + S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (2*(312 + 1264*S^2 + 470*S^4 + 1671*S^6 + 719*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (328*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 + (2912*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (1912*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-7*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-856 - 2179*S^2 - 1629*S^4 - 325*S^6 + 17*S^8)/(54*S^3*(1 + S^2)))*Zeta[3] + HPL[{2}, -S^2]*((Pi^2*(1318 + 6135*S^2 + 2392*S^4 + 8679*S^6 + 3862*S^8))/(108*S^3*(1 + S^2)) + (70438 + 179701*S^2 + 468537*S^4 + 695275*S^6 + 328225*S^8)/(1944*S^3*(1 + S^2)) - (52*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) - (164*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (94*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (2*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3))) + HPL[{0}, S^2]*((44172342 + 9331269*S^2 + 134931142*S^4)/(209952*S) + (Pi^6*(145500 + 72750*S^2 + 418907*S^4 + 273407*S^6))/(68040*S*(1 + S^2)) + (Pi^4*(181315 + 339407*S^2 + 906548*S^4 + 755233*S^6))/(29160*S*(1 + S^2)) + (Pi^2*(8304384 + 11350662*S^2 + 33106087*S^4 + 30153121*S^6))/(209952*S*(1 + S^2)) + (14*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^6)/(27*S^3*(1 + S^2)) + (32*(1 + S^6)*HPL[{1}, -S^2]^7)/(9*S^3) + ((-775 + 5597*S^2 + 3186*S^4 + 14309*S^6 + 7937*S^8)*HPL[{2}, -S^2]^3)/(162*S^3*(1 + S^2)) + HPL[{1}, -S^2]^5*((254*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(27*S^3) + (100*(1 + S^6)*HPL[{2}, -S^2])/(3*S^3)) + ((81 + 51*S^2 - 15*S^4 - 236*S^6 - 206*S^8)*HPL[{3}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((-2*Pi^2*(-3 + 2*S^6))/(9*S^3) + (1804 + 2119*S^2 + 3834*S^4 + 9831*S^6 + 6528*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((205 + 667*S^2 + 186*S^4 + 1331*S^6 + 869*S^8)*HPL[{6}, -S^2])/(27*S^3*(1 + S^2)) - (2*(25 + 32*S^6)*HPL[{7}, -S^2])/(3*S^3) - (2*(-31 + 6989*S^2 + 3456*S^4 + 15473*S^6 + 8453*S^8)*HPL[{2, 1}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((Pi^2*(85 + 143*S^6))/(27*S^3) + (1676 + 11237*S^2 + 13389*S^4 + 2267*S^6 - 1777*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((14*Pi^2*(-1 + 34*S^6))/(27*S^3) + (-1110 + 11781*S^2 + 14820*S^4 - 1957*S^6 - 4210*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((-61 - 46*S^2 + 3*S^4 - 175*S^6 - 190*S^8)*HPL[{4, 2}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-14 + 11*S^6)*HPL[{4, 3}, -S^2])/(9*S^3) - (2*(-101 + 289*S^2 + 204*S^4 + 1561*S^6 + 1171*S^8)*HPL[{5, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-80 + 59*S^6)*HPL[{5, 2}, -S^2])/(9*S^3) + (8*(-86 + 57*S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((4*Pi^2*(1728 + 25*S^6))/(27*S^3) - (4*(-20452 - 9099*S^2 - 24444*S^4 + 935*S^6))/(81*S^3))*HPL[{2, 2, 1}, -S^2] + ((-4*Pi^2*(-5267 + 22*S^6))/(27*S^3) - (2*(-124752 - 51015*S^2 - 148026*S^4 + 4213*S^6))/(81*S^3))*HPL[{3, 1, 1}, -S^2] + (2*(119 + 6*S^2 + 6*S^4 + 92*S^6)*HPL[{3, 1, 2}, -S^2])/(27*S^3) + (2*(-477 + 3773*S^2 + 2128*S^4 + 9572*S^6 + 5322*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2*(-45 + 421*S^6)*HPL[{3, 2, 2}, -S^2])/(9*S^3) - (32*(1 + 73*S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) + (4*(-2562 + 16941*S^2 + 9765*S^4 + 44108*S^6 + 24605*S^8)*HPL[{4, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (20*(3 + 116*S^6)*HPL[{4, 1, 2}, -S^2])/(9*S^3) - (4*(87 + 1696*S^6)*HPL[{4, 2, 1}, -S^2])/(9*S^3) - (16*(13 + 276*S^6)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((8*Pi^2*(-602 + 29*S^6))/(9*S^3) + (4*(-41768 - 14247*S^2 - 50175*S^4 + 1561*S^6))/(81*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (32*(-569 + 19*S^6)*HPL[{2, 2, 2, 1}, -S^2])/(9*S^3) - (16*(-526 + 2840*S^2 + 1683*S^4 + 7738*S^6 + 4372*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-6881 + 71*S^6)*HPL[{3, 1, 1, 2}, -S^2])/(9*S^3) - (8*(-6881 + 71*S^6)*HPL[{3, 1, 2, 1}, -S^2])/(9*S^3) - (8*(-13709 + 299*S^6)*HPL[{3, 2, 1, 1}, -S^2])/(9*S^3) - (32*(-3413 + 74*S^6)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (80*(-61 + 389*S^2 + 225*S^4 + 1046*S^6 + 596*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (32*(1159 + 34*S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(9*S^3) - (32*(1159 + 34*S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/(3*S^3) - (160*(383 + 17*S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + (1280*(-20 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + ((-81888 - 104148*S^2 - 38371*S^4 - 18703*S^6)/(972*S*(1 + S^2)) + (Pi^2*(-8154 - 8577*S^2 + 499*S^4 + 1138*S^6))/(486*S*(1 + S^2)))*Zeta[3] + (4*(24 + 12*S^2 + 41*S^4 + 17*S^6)*Zeta[3]^2)/(9*S*(1 + S^2)) + HPL[{1}, -S^2]^4*((5*(1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(972*S^3) + (Pi^2*(3160 + 10792*S^2 + 3834*S^4 + 12691*S^6 + 5059*S^8))/(162*S^3*(1 + S^2)) + (5*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{3}, -S^2])/S^3 - (500*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (164*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{4}, -S^2]*((Pi^2*(-319 + 341*S^2 + 339*S^4 + 2180*S^6 + 1520*S^8))/(162*S^3*(1 + S^2)) + (-981 + 7518*S^2 + 33036*S^4 + 76111*S^6 + 54166*S^8)/(972*S^3*(1 + S^2)) + (28*(-4 + 5*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (4*(16 + 7*S^6)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*((-2417 + 71640*S^2 + 31965*S^4 + 116790*S^6)/(648*S^3) + (Pi^2*(-47 + 10324*S^2 + 5118*S^4 + 24195*S^6 + 13824*S^8))/(324*S^3*(1 + S^2)) + ((7 - 107*S^6)*HPL[{3}, -S^2])/(9*S^3) + (4*(-569 + 19*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) - (2*(-2 + 39*S^6)*Zeta[3])/(3*S^3)) + HPL[{3, 1}, -S^2]*((17830 - 200165*S^2 - 327765*S^4 - 478633*S^6 - 370159*S^8)/(486*S^3*(1 + S^2)) - (2*Pi^2*(-695 + 4420*S^2 + 2553*S^4 + 12403*S^6 + 7288*S^8))/(81*S^3*(1 + S^2)) + (8*(-7 + 118*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1, 1}, -S^2]*((-6507 + 72198*S^2 + 35907*S^4 + 123562*S^6)/(81*S^3) + (2*Pi^2*(-1253 + 9022*S^2 + 5133*S^4 + 25260*S^6 + 14985*S^8))/(81*S^3*(1 + S^2)) - (16*(-1 + 122*S^6)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((-645683 - 159111*S^2 - 1126836*S^4 - 94688*S^6)/(1458*S^3) + (8*Pi^4*(-1171 + 78*S^6))/(405*S^3) + (Pi^2*(-52034 - 18417*S^2 - 83595*S^4 + 3138*S^6))/(486*S^3) + (8*(1159 + 37*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (16*(1159 + 34*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (4*(-971 - 1706*S^2 - 363*S^4 - 716*S^6 + 19*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{3}, -S^2]*((Pi^4*(985 - 869*S^6))/(1620*S^3) + (Pi^2*(2650 - 1490*S^2 - 567*S^4 + 8337*S^6 + 4224*S^8))/(972*S^3*(1 + S^2)) + (26516 + 22892*S^2 + 121803*S^4 + 272675*S^6 + 155024*S^8)/(2916*S^3*(1 + S^2)) - (8*(-7 + 5*S^6)*HPL[{4}, -S^2])/(9*S^3) + (2*(241 + 457*S^2 + 90*S^4 + 368*S^6 + 152*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(19 + 79*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (8*(7 + 25*S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(-133 - 151*S^2 + 26*S^6 + 44*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^3*((3374*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(1458*S^3) + (Pi^2*(51574 + 128575*S^2 + 206895*S^4 + 231553*S^6 + 102955*S^8))/(1458*S^3*(1 + S^2)) + ((1142*Pi^2*(1 + S^6))/(27*S^3) + (2*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(81*S^3))*HPL[{2}, -S^2] + (784*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) - (4*(13 + 25*S^2 + 6*S^4 + 12*S^6)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) + (28*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (20*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2992*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (2000*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (4*(319 + 811*S^2 + 246*S^4 + 706*S^6 + 214*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((-6330 - 6387*S^2 + 473*S^4 + 476*S^6)*Zeta[5])/(81*S*(1 + S^2)) + HPL[{1}, -S^2]^2*(((1 + S^2)*(422663 + 99650*S^2 + 875723*S^4))/(1944*S^3) + (Pi^2*(69260 + 167108*S^2 + 293517*S^4 + 359348*S^6 + 165299*S^8))/(1458*S^3*(1 + S^2)) + (Pi^4*(81677 + 325418*S^2 + 123090*S^4 + 422852*S^6 + 179111*S^8))/(9720*S^3*(1 + S^2)) + ((1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-10*Pi^2*(1 + S^6))/(9*S^3) + (2*(-505 - 1038*S^2 + 150*S^4 + 899*S^6))/(81*S^3))*HPL[{3}, -S^2] + ((35 + 293*S^2 + 138*S^4 + 488*S^6 + 230*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) + (116*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-1142*Pi^2*(1 + S^6))/(9*S^3) - (2*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (4*(1046 + 3290*S^2 + 1122*S^4 + 3629*S^6 + 1385*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (152*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (124*(1 + S^6)*HPL[{4, 1}, -S^2])/S^3 + (20*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (3136*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) + (3088*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 - (2000*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/S^3 + ((-256*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) - ((1 + S^2)*(6097 + 2105*S^2 + 3352*S^4))/(81*S^3))*Zeta[3] + HPL[{2}, -S^2]*((35426 + 47493*S^2 + 74580*S^4 + 63377*S^6)/(162*S^3) + (Pi^2*(8198 + 28754*S^2 + 10278*S^4 + 34577*S^6 + 14021*S^8))/(162*S^3*(1 + S^2)) - (76*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (1568*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (164*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) - (368*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*((Pi^2*(-25951 + 267033*S^2 + 182820*S^4 + 661915*S^6))/(5832*S^3) + (-508025 + 7011603*S^2 + 4135617*S^4 + 15557905*S^6)/(34992*S^3) + (Pi^4*(-13245 + 94161*S^2 + 53658*S^4 + 286118*S^6 + 178712*S^8))/(9720*S^3*(1 + S^2)) + ((Pi^2*(-37 - 67*S^6))/(27*S^3) + (-546 - 4653*S^2 - 1926*S^4 + 1283*S^6)/(162*S^3))*HPL[{3}, -S^2] + ((-143 - 95*S^2 + 15*S^4 + 586*S^6 + 538*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (4*(-17 + 12*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-2*Pi^2*(1728 + 25*S^6))/(27*S^3) + (2*(-20452 - 9099*S^2 - 24444*S^4 + 935*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] - (2*(-52 + 6968*S^2 + 3456*S^4 + 15413*S^6 + 8393*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-5 + 71*S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (4*(7 + 286*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(-31 + 6989*S^2 + 3456*S^4 + 15473*S^6 + 8453*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (16*(-569 + 19*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (8*(-1145 + 13*S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) - (16*(1159 + 34*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((19 - 5481*S^2 - 1557*S^4 - 3240*S^6)/(81*S^3) - (2*Pi^2*(-4 + 127*S^6))/(27*S^3))*Zeta[3] - (16*(-3 + 20*S^6)*Zeta[5])/(9*S^3)) + HPL[{1}, -S^2]*((2425*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(1134*S^3) + ((1 + S^2)*(3757531 + 762416*S^2 + 9134503*S^4))/(17496*S^3) + (Pi^4*(406640 + 1063703*S^2 + 2202228*S^4 + 2777429*S^6 + 1261532*S^8))/(58320*S^3*(1 + S^2)) + (Pi^2*(1489946 + 3492239*S^2 + 6839775*S^4 + 9108185*S^6 + 4301807*S^8))/(34992*S^3*(1 + S^2)) + ((868*Pi^2*(1 + S^6))/(27*S^3) + (6683 + 9489*S^2 + 11754*S^4 + 9020*S^6)/(54*S^3))*HPL[{2}, -S^2]^2 + (118*(1 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) - (10*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((109*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2086 + 3925*S^2 + 8511*S^4 + 12835*S^6 + 6811*S^8)/(162*S^3*(1 + S^2)))*HPL[{4}, -S^2] + (2*(118 + 62*S^2 + 241*S^4 + 123*S^6)*HPL[{5}, -S^2])/(9*S*(1 + S^2)) + (164*(1 + S^6)*HPL[{6}, -S^2])/(9*S^3) - (1568*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((-3412*Pi^2*(1 + S^6))/(27*S^3) - (2*(19039 + 26391*S^2 + 35562*S^4 + 28858*S^6))/(81*S^3))*HPL[{3, 1}, -S^2] + (4*(422 + 1103*S^2 + 336*S^4 + 1004*S^6 + 323*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + (2*(805 + 1915*S^2 + 546*S^4 + 1522*S^6 + 412*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{4, 2}, -S^2])/(3*S^3) - (256*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((2284*Pi^2*(1 + S^6))/(9*S^3) + (4*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] + (8*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (8*(1124 + 3440*S^2 + 1158*S^4 + 3701*S^6 + 1385*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (944*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 + (2888*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/S^3 - (40*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (5984*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) + (4000*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((-13242 - 30455*S^2 - 27355*S^4 - 15665*S^6 - 5955*S^8)/(162*S^3*(1 + S^2)) + (Pi^2*(-461 - 969*S^2 - 248*S^4 - 612*S^6 - 104*S^8))/(27*S^3*(1 + S^2)))*Zeta[3] + (32*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{3}, -S^2]*((Pi^2*(-452 - 647*S^2 - 120*S^4 + 82*S^6 + 277*S^8))/(81*S^3*(1 + S^2)) + (-20 - 1329*S^2 + 4987*S^4 + 13881*S^6 + 8017*S^8)/(162*S^3*(1 + S^2)) + (152*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2, 1}, -S^2]*((-35426 - 47493*S^2 - 74580*S^4 - 63377*S^6)/(81*S^3) + (Pi^2*(-8198 - 28754*S^2 - 10278*S^4 - 34577*S^6 - 14021*S^8))/(81*S^3*(1 + S^2)) + (328*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]*((8953*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(23189 + 34212*S^2 + 60150*S^4 + 50099*S^6))/(486*S^3) + (66966 + 85953*S^2 + 159502*S^4 + 141379*S^6)/(324*S^3) - (2*(140 + 368*S^2 + 114*S^4 + 335*S^6 + 107*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{4}, -S^2])/S^3 - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (1568*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(316 + 808*S^2 + 246*S^4 + 709*S^6 + 217*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) - (2*(1127 + 2234*S^2 + 558*S^4 + 1172*S^6 + 65*S^8)*Zeta[5])/(27*S^3*(1 + S^2)))) - (4*(378 + 189*S^2 + 799*S^4 + 421*S^6)*Zeta[7])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(((1 + S^2)*(44150029 + 8482853*S^2 + 134931142*S^4))/(209952*S^3) + (Pi^2*(882963 + 1103863*S^2 + 2696512*S^4 + 2471724*S^6))/(17496*S^3) + (Pi^6*(195079 + 811628*S^2 + 306836*S^4 + 1084304*S^6 + 467755*S^8))/(136080*S^3*(1 + S^2)) + (Pi^4*(2898599 + 6970289*S^2 + 13596651*S^4 + 17849939*S^6 + 8286098*S^8))/(349920*S^3*(1 + S^2)) + ((-541 + 575*S^2 + 558*S^4 + 2816*S^6 + 1700*S^8)*HPL[{2}, -S^2]^3)/(81*S^3*(1 + S^2)) + ((821 + 2159*S^2 + 678*S^4 + 1952*S^6 + 614*S^8)*HPL[{3}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((-164*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-10535 - 25682*S^2 - 9378*S^4 + 15934*S^6 + 10381*S^8)/(81*S^3*(1 + S^2)))*HPL[{5}, -S^2] + (5*(-835 - 586*S^2 + 120*S^4 + 1286*S^6 + 1037*S^8)*HPL[{6}, -S^2])/(27*S^3*(1 + S^2)) + (328*(1 + S^6)*HPL[{7}, -S^2])/(3*S^3) - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((2084*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2*(25681 + 58873*S^2 + 53037*S^4 + 32611*S^6 + 12658*S^8))/(81*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((7054*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (177811 + 410875*S^2 + 363807*S^4 + 208825*S^6 + 77434*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((2581 + 6769*S^2 + 2058*S^4 + 6202*S^6 + 2014*S^8)*HPL[{4, 2}, -S^2])/(27*S^3*(1 + S^2)) - (24*(1 + S^6)*HPL[{4, 3}, -S^2])/S^3 + (4*(1462 + 3206*S^2 + 860*S^4 + 2219*S^6 + 475*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) - (152*(1 + S^6)*HPL[{5, 2}, -S^2])/(3*S^3) - (60*(1 + S^6)*HPL[{6, 1}, -S^2])/S^3 + ((2552*Pi^2*(1 + S^6))/(9*S^3) + (4*(6683 + 9489*S^2 + 11754*S^4 + 9020*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((6016*Pi^2*(1 + S^6))/(9*S^3) + (4*(9488 + 14571*S^2 + 27747*S^4 + 22808*S^6))/(27*S^3))*HPL[{3, 1, 1}, -S^2] - (8*(1 + S^2)*(2 - 5*S^2 + 2*S^4)*HPL[{3, 1, 2}, -S^2])/(27*S^3) + (8*(-181 + 192*S^2 + 188*S^4 + 939*S^6 + 566*S^8)*HPL[{3, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (2764*(1 + S^6)*HPL[{3, 2, 2}, -S^2])/(3*S^3) - (8480*(1 + S^6)*HPL[{3, 3, 1}, -S^2])/(3*S^3) + (8*(-1225 - 958*S^2 + 138*S^4 + 1709*S^6 + 1442*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8324*(1 + S^6)*HPL[{4, 1, 2}, -S^2])/(3*S^3) - (25940*(1 + S^6)*HPL[{4, 2, 1}, -S^2])/(3*S^3) - (53344*(1 + S^6)*HPL[{5, 1, 1}, -S^2])/(3*S^3) + ((-2512*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(9*S^3) - (8*(1 + S^2)*(-1975 + 232*S^2 + 5855*S^4))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] - (992*(1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/(3*S^3) - (16*(-523 - 571*S^2 - 24*S^4 + 398*S^6 + 446*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2752*(1 + S^6)*HPL[{3, 1, 1, 2}, -S^2])/S^3 + (2752*(1 + S^6)*HPL[{3, 1, 2, 1}, -S^2])/S^3 + (3744*(1 + S^6)*HPL[{3, 2, 1, 1}, -S^2])/S^3 + (35968*(1 + S^6)*HPL[{4, 1, 1, 1}, -S^2])/(3*S^3) + (80*(-83 + 97*S^2 + 90*S^4 + 448*S^6 + 268*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (12544*(1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) - (12544*(1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 - (75520*(1 + S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) - (1600*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((-109*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-836411 - 1012851*S^2 - 495297*S^4 - 326633*S^6)/(2916*S^3) + (Pi^2*(-3016 - 6947*S^2 - 5965*S^4 - 3285*S^6 - 1239*S^8))/(54*S^3*(1 + S^2)))*Zeta[3] + (2*(166 + 559*S^2 + 246*S^4 + 568*S^6 + 175*S^8)*Zeta[3]^2)/(27*S^3*(1 + S^2)) + HPL[{2, 1, 1}, -S^2]*((2*(1 + S^2)*(-4417 + 150*S^2 + 14537*S^4))/(27*S^3) + (2*Pi^2*(521 + 4277*S^2 + 1860*S^4 + 7253*S^6 + 3497*S^8))/(27*S^3*(1 + S^2)) - (2624*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2}, -S^2]^2*(((1 + S^2)*(18412 + 6533*S^2 + 28207*S^4))/(162*S^3) + (Pi^2*(5173 + 16657*S^2 + 5742*S^4 + 18727*S^6 + 7243*S^8))/(162*S^3*(1 + S^2)) - (404*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) - (124*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (292*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{4}, -S^2]*((-47285 - 68707*S^2 - 10183*S^4 + 10375*S^6)/(324*S^3) + (Pi^2*(-4427 - 9239*S^2 - 2406*S^4 - 5738*S^6 - 926*S^8))/(162*S^3*(1 + S^2)) + (452*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) - (124*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{3, 1}, -S^2]*((25115 + 28926*S^2 - 35115*S^4 - 38710*S^6)/(81*S^3) - (2*Pi^2*(-217 + 3866*S^2 + 2010*S^4 + 8654*S^6 + 4571*S^8))/(81*S^3*(1 + S^2)) + (1360*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((-419*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + (-1087487 - 1344375*S^2 - 428949*S^4 - 164285*S^6)/(2916*S^3) + (Pi^2*(-33208 - 77251*S^2 - 65613*S^4 - 30631*S^6 - 9817*S^8))/(486*S^3*(1 + S^2)) + (68*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + (20*(806 + 1994*S^2 + 594*S^4 + 1679*S^6 + 491*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (440*(1 + S^6)*HPL[{3, 1}, -S^2])/S^3 - (880*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/S^3 - (4*(97 + 234*S^2 + 58*S^4 + 207*S^6 + 70*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((-4421*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(270*S^3) - ((1 + S^2)*(-233717 - 5557*S^2 + 945778*S^4))/(1458*S^3) + (Pi^2*(-2149 - 14560*S^2 - 104004*S^4 - 175732*S^6 - 82843*S^8))/(486*S^3*(1 + S^2)) + (3136*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) + (6272*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (4*(1351 + 3307*S^2 + 960*S^4 + 2773*S^6 + 817*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((-802*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-23749 - 54439*S^2 - 43335*S^4 - 18997*S^6 - 6460*S^8)/(81*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*(((1 + S^2)*(-205501 - 13863*S^2 + 1164362*S^4))/(2916*S^3) + (Pi^4*(10285 + 63080*S^2 + 26012*S^4 + 99284*S^6 + 46489*S^8))/(3240*S^3*(1 + S^2)) + (Pi^2*(-9068 + 23389*S^2 + 656097*S^4 + 1221307*S^6 + 589891*S^8))/(5832*S^3*(1 + S^2)) + ((-25628 - 33141*S^2 - 19902*S^4 - 12605*S^6)/(81*S^3) - (1042*Pi^2*(1 + S^6))/(27*S^3))*HPL[{3}, -S^2] + ((-835 - 2191*S^2 - 678*S^4 - 1990*S^6 - 634*S^8)*HPL[{4}, -S^2])/(9*S^3*(1 + S^2)) - (44*(1 + S^6)*HPL[{5}, -S^2])/S^3 + ((-1276*Pi^2*(1 + S^6))/(9*S^3) - (2*(6683 + 9489*S^2 + 11754*S^4 + 9020*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) + (1460*(1 + S^6)*HPL[{3, 2}, -S^2])/(3*S^3) + (4396*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) + (8*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (496*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(3*S^3) - (1376*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/S^3 - (6272*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((-1078*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-25849 - 59176*S^2 - 51876*S^4 - 32428*S^6 - 12583*S^8)/(81*S^3*(1 + S^2)))*Zeta[3] - (180*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/S^3) - (168*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3)) + HPL[{0}, S^2]*((-135211*Pi^8*S^3)/816480 + (-36959227 - 9271471*S^2 - 179968230*S^4)/(419904*S) + (Pi^2*(-6502060 - 2286739*S^2 - 35845925*S^4))/(419904*S) + (Pi^4*(-9961794 - 16521363*S^2 - 66203276*S^4 - 59799227*S^6))/(4199040*S*(1 + S^2)) + (Pi^6*(-1813422 - 6144819*S^2 - 16393441*S^4 - 12159946*S^6))/(4898880*S*(1 + S^2)) - (2*(23 + 71*S^2 + 24*S^4 + 77*S^6 + 29*S^8)*HPL[{1}, -S^2]^7)/(27*S^3*(1 + S^2)) - (4*(1 + S^6)*HPL[{1}, -S^2]^8)/(9*S^3) + ((2230 - 18675*S^2 - 9351*S^4 - 26174*S^6)/(972*S^3) - (2*Pi^2*(-11 + 205*S^6))/(81*S^3))*HPL[{2}, -S^2]^3 + ((-5 - 182*S^6)*HPL[{2}, -S^2]^4)/(36*S^3) + HPL[{1}, -S^2]^6*((-127*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) - ((1 + S^2)*(928 + 389*S^2 + 1321*S^4))/(162*S^3) - (50*(1 + S^6)*HPL[{2}, -S^2])/(9*S^3)) + ((7*Pi^2*(-1 + 6*S^6))/(54*S^3) + (-16 + 5*S^2 + 36*S^4 + 614*S^6 + 635*S^8)/(108*S^3*(1 + S^2)))*HPL[{3}, -S^2]^2 + ((13 - 36*S^6)*HPL[{4}, -S^2]^2)/(9*S^3) + ((-804 - 2571*S^2 - 4085*S^4 - 2228*S^6)/(108*S*(1 + S^2)) + (Pi^2*(-70 - 109*S^6))/(27*S^3))*HPL[{6}, -S^2] + ((655 + 599*S^2 - 178*S^4 + 84*S^6 + 140*S^8)*HPL[{7}, -S^2])/(18*S^3*(1 + S^2)) + ((-105 - 52*S^6)*HPL[{8}, -S^2])/(3*S^3) + ((Pi^2*(8 + 1711*S^6))/(27*S^3) + (-403 + 19368*S^2 + 10818*S^4 + 27995*S^6)/(81*S^3))*HPL[{2, 1}, -S^2]^2 - (8*(4 + 283*S^6)*HPL[{3, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(1 + 12*S^6))/(54*S^3) + (36 - 465*S^2 - 696*S^4 + 197*S^6 + 824*S^8)/(324*S^3*(1 + S^2)))*HPL[{4, 2}, -S^2] + ((128 + 200*S^2 - 27*S^4 + 46*S^6 - 26*S^8)*HPL[{4, 3}, -S^2])/(27*S^3*(1 + S^2)) + ((4*Pi^2*(6 + 49*S^6))/(27*S^3) + (116 + 743*S^2 + 4332*S^4 + 12037*S^6 + 9196*S^8)/(162*S^3*(1 + S^2)))*HPL[{5, 1}, -S^2] + ((747 + 1119*S^2 - 192*S^4 + 431*S^6 + 59*S^8)*HPL[{5, 2}, -S^2])/(54*S^3*(1 + S^2)) + (14*S^3*HPL[{5, 3}, -S^2])/9 + ((457 + 1159*S^2 + 36*S^4 + 1197*S^6 + 495*S^8)*HPL[{6, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-1 + 14*S^6)*HPL[{6, 2}, -S^2])/(9*S^3) + (2*(63 + 146*S^6)*HPL[{7, 1}, -S^2])/(9*S^3) - (8*(17 + 1142*S^6)*HPL[{2, 1, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(-11 - 9*S^6))/(27*S^3) + (-372 - 423*S^2 - 255*S^4 - 565*S^6 - 577*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 1, 2}, -S^2] + ((-11*Pi^2*(-15 + 299*S^6))/(27*S^3) + (8548 - 66203*S^2 - 112359*S^4 - 142665*S^6 - 105273*S^8)/(162*S^3*(1 + S^2)))*HPL[{3, 2, 1}, -S^2] + ((-691 + 1673*S^2 + 1326*S^4 + 5354*S^6 + 2990*S^8)*HPL[{3, 2, 2}, -S^2])/(54*S^3*(1 + S^2)) + (4*(-99 + 825*S^2 + 516*S^4 + 1894*S^6 + 970*S^8)*HPL[{3, 3, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-19 + 2*S^6)*HPL[{3, 3, 2}, -S^2])/(9*S^3) + ((-2*Pi^2*(-273 + 5066*S^6))/(27*S^3) + (14042 - 98779*S^2 - 171750*S^4 - 222099*S^6 - 163494*S^8)/(81*S^3*(1 + S^2)))*HPL[{4, 1, 1}, -S^2] + ((-123 + 1110*S^2 + 693*S^4 + 2507*S^6 + 1274*S^8)*HPL[{4, 1, 2}, -S^2])/(9*S^3*(1 + S^2)) - (4*(-19 + 4*S^6)*HPL[{4, 1, 3}, -S^2])/(9*S^3) + ((-239 + 3514*S^2 + 2097*S^4 + 7403*S^6 + 3650*S^8)*HPL[{4, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) + ((-29 + 12*S^6)*HPL[{4, 2, 2}, -S^2])/(9*S^3) + (164*HPL[{4, 3, 1}, -S^2])/(9*S^3) + (2*(-179 + 3491*S^2 + 2060*S^4 + 7073*S^6 + 3403*S^8)*HPL[{5, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (4*(24 + S^6)*HPL[{5, 1, 2}, -S^2])/(9*S^3) + (4*(174 + S^6)*HPL[{5, 2, 1}, -S^2])/(9*S^3) - (8*(-215 + 58*S^6)*HPL[{6, 1, 1}, -S^2])/(9*S^3) - (4*(-6913 - 13285*S^2 - 3186*S^4 - 6103*S^6 + 269*S^8)*HPL[{2, 2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((28*Pi^2*(-15 + 254*S^6))/(27*S^3) + (2*(-4866 + 38163*S^2 + 20874*S^4 + 58189*S^6))/(81*S^3))*HPL[{3, 1, 1, 1}, -S^2] + (2*(-41839 - 81505*S^2 - 19932*S^4 - 38524*S^6 + 1142*S^8)*HPL[{3, 1, 1, 2}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-41839 - 81505*S^2 - 19932*S^4 - 38524*S^6 + 1142*S^8)*HPL[{3, 1, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (10*(3 + S^6)*HPL[{3, 1, 2, 2}, -S^2])/(9*S^3) + (2*(-83317 - 161215*S^2 - 39048*S^4 - 75142*S^6 + 2756*S^8)*HPL[{3, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (10*(3 + S^6)*HPL[{3, 2, 1, 2}, -S^2])/(9*S^3) + (2*(-303 + 4411*S^6)*HPL[{3, 2, 2, 1}, -S^2])/(9*S^3) + (64*(-3 + 46*S^6)*HPL[{3, 3, 1, 1}, -S^2])/S^3 + (4*(-124443 - 240912*S^2 - 58383*S^4 - 112289*S^6 + 4180*S^8)*HPL[{4, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (4*(1 + 8*S^6)*HPL[{4, 1, 1, 2}, -S^2])/(9*S^3) + (4*(-431 + 6632*S^6)*HPL[{4, 1, 2, 1}, -S^2])/(9*S^3) + (140*(-37 + 568*S^6)*HPL[{4, 2, 1, 1}, -S^2])/(9*S^3) + (16*(-216 + 3329*S^6)*HPL[{5, 1, 1, 1}, -S^2])/(3*S^3) + ((-8*Pi^2*(-31 + 600*S^6))/(9*S^3) - (4*(-4466 + 38115*S^2 + 21123*S^4 + 59095*S^6))/(81*S^3))*HPL[{2, 1, 1, 1, 1}, -S^2] - (8*(-7009 - 14101*S^2 - 3600*S^4 - 6949*S^6 + 143*S^8)*HPL[{2, 1, 2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-7009 - 14101*S^2 - 3600*S^4 - 6949*S^6 + 143*S^8)*HPL[{2, 2, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (64*(-19 + 275*S^6)*HPL[{2, 2, 1, 2, 1}, -S^2])/(9*S^3) + (64*(-19 + 275*S^6)*HPL[{2, 2, 2, 1, 1}, -S^2])/(3*S^3) - (16*(-17363 - 35273*S^2 - 9117*S^4 - 17698*S^6 + 212*S^8)*HPL[{3, 1, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (8*(-901 + 13207*S^6)*HPL[{3, 1, 1, 1, 2}, -S^2])/(9*S^3) - (8*(-1509 + 22007*S^6)*HPL[{3, 1, 1, 2, 1}, -S^2])/(9*S^3) - (8*(-1813 + 26407*S^6)*HPL[{3, 1, 2, 1, 1}, -S^2])/(9*S^3) - (8*(-3789 + 55007*S^6)*HPL[{3, 2, 1, 1, 1}, -S^2])/(9*S^3) - (32*(-951 + 13763*S^6)*HPL[{4, 1, 1, 1, 1}, -S^2])/(3*S^3) - (80*(-478 - 928*S^2 - 225*S^4 - 412*S^6 + 38*S^8)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (32*(-29 + 391*S^6)*HPL[{3, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) - (320*(-5 + 79*S^6)*HPL[{2, 1, 1, 1, 1, 1, 1}, -S^2])/(3*S^3) + (-(Pi^2*S^3)/3 + (166 - 193*S^2 - 923*S^4 - 546*S^6)/(54*S*(1 + S^2)))*Zeta[3]^2 + HPL[{1}, -S^2]^5*(-((1 + S^2)*(15557 + 5413*S^2 + 24854*S^4))/(972*S^3) + (Pi^2*(-3160 - 10792*S^2 - 3834*S^4 - 12691*S^6 - 5059*S^8))/(810*S^3*(1 + S^2)) + ((-139 - 439*S^2 - 150*S^4 - 486*S^6 - 186*S^8)*HPL[{2}, -S^2])/(9*S^3*(1 + S^2)) + (4*(1 + S^6)*HPL[{3}, -S^2])/(5*S^3) + (100*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (164*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(45*S^3)) + HPL[{2, 2, 1}, -S^2]*((-76065 - 28140*S^2 - 106995*S^4 + 3962*S^6)/(162*S^3) + (Pi^2*(-9121 - 19600*S^2 - 5334*S^4 - 10085*S^6 + 394*S^8))/(81*S^3*(1 + S^2)) + (8*(42 + S^6)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1, 1}, -S^2]*((77359 + 22788*S^2 + 113253*S^4 + 3192*S^6)/(81*S^3) - (2*Pi^2*(-9451 - 19732*S^2 - 5145*S^4 - 9317*S^6 + 964*S^8))/(81*S^3*(1 + S^2)) - (16*(124 + S^6)*Zeta[3])/(9*S^3)) + HPL[{3, 2}, -S^2]*((-12109 - 42723*S^2 - 19197*S^4 + 29465*S^6)/(1944*S^3) + (Pi^2*(-321 - 2112*S^2 - 1062*S^4 - 1687*S^6 + 104*S^8))/(324*S^3*(1 + S^2)) - (2*(1 + 3*S^6)*Zeta[3])/S^3) + HPL[{4, 1}, -S^2]*((Pi^2*(31 - 641*S^2 - 411*S^4 - 628*S^6 + 44*S^8))/(54*S^3*(1 + S^2)) + (2535 - 50436*S^2 - 35796*S^4 + 79541*S^6 + 64958*S^8)/(972*S^3*(1 + S^2)) - (4*(2 + 3*S^6)*Zeta[3])/S^3) + HPL[{3, 1, 1}, -S^2]*((2*Pi^2*(-13901 - 29495*S^2 - 7887*S^4 - 14904*S^6 + 690*S^8))/(81*S^3*(1 + S^2)) + (-695044 - 937375*S^2 - 1229187*S^4 - 978215*S^6 + 7345*S^8)/(486*S^3*(1 + S^2)) + (8*(383 + 12*S^6)*Zeta[3])/(9*S^3)) + HPL[{5}, -S^2]*((-4149 - 13839*S^2 - 64983*S^4 - 108521*S^6 - 65540*S^8)/(1944*S^3*(1 + S^2)) + (Pi^2*(473 - 4*S^2 - 342*S^4 - 844*S^6 - 367*S^8))/(324*S^3*(1 + S^2)) - (116*S^3*HPL[{2, 1}, -S^2])/9 - (2*(-17 + 37*S^6)*Zeta[3])/(9*S^3)) + HPL[{4}, -S^2]*((Pi^4*(-387 - 2552*S^6))/(3240*S^3) + (12288 - 6463*S^2 - 107570*S^4 - 243772*S^6 - 157545*S^8)/(3888*S^3*(1 + S^2)) + (Pi^2*(2626 + 1534*S^2 - 6540*S^4 - 16903*S^6 - 12103*S^8))/(1944*S^3*(1 + S^2)) + ((212 + 290*S^2 + 75*S^4 - 436*S^6 - 514*S^8)*HPL[{2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-17 + 40*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (4*(-19 + 44*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((-49 - 124*S^2 + 21*S^4 - 388*S^6 - 313*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^4*((-1687*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) - ((1 + S^2)*(219433 + 62465*S^2 + 396484*S^4))/(5832*S^3) + (Pi^2*(-51574 - 128575*S^2 - 206895*S^4 - 231553*S^6 - 102955*S^8))/(5832*S^3*(1 + S^2)) + ((-6217 - 8727*S^2 - 11883*S^4 - 9589*S^6)/(162*S^3) - (571*Pi^2*(1 + S^6))/(54*S^3))*HPL[{2}, -S^2] - (196*(1 + S^6)*HPL[{2}, -S^2]^2)/(9*S^3) + ((13 + 25*S^2 + 6*S^4 + 12*S^6)*HPL[{3}, -S^2])/(3*S^3*(1 + S^2)) - (7*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) + (5*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (748*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (500*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((319 + 811*S^2 + 246*S^4 + 706*S^6 + 214*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2}, -S^2]^2*((28976 - 595629*S^2 - 212328*S^4 - 1094713*S^6)/(11664*S^3) + (Pi^4*(90 - 8743*S^6))/(3240*S^3) + (Pi^2*(962 - 49687*S^2 - 86106*S^4 - 130530*S^6 - 95397*S^8))/(3888*S^3*(1 + S^2)) + ((-143 + 451*S^2 + 324*S^4 + 1370*S^6 + 776*S^8)*HPL[{3}, -S^2])/(108*S^3*(1 + S^2)) + ((13 + 4*S^6)*HPL[{4}, -S^2])/(18*S^3) + ((6913 + 13285*S^2 + 3186*S^4 + 6103*S^6 - 269*S^8)*HPL[{2, 1}, -S^2])/(54*S^3*(1 + S^2)) + ((-73 + 1103*S^6)*HPL[{3, 1}, -S^2])/(9*S^3) - (8*(-19 + 275*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) + ((19 + 748*S^2 + 378*S^4 + 1235*S^6 + 506*S^8)*Zeta[3])/(54*S^3*(1 + S^2))) + HPL[{3, 1}, -S^2]*((Pi^4*(-789 + 18731*S^6))/(1620*S^3) + (Pi^2*(-5932 + 44339*S^2 + 86763*S^4 + 137711*S^6 + 101003*S^8))/(972*S^3*(1 + S^2)) + (-6220 + 204714*S^2 + 322085*S^4 + 507659*S^6 + 399100*S^8)/(972*S^3*(1 + S^2)) + (136*(1 + 67*S^6)*HPL[{2, 1, 1}, -S^2])/(9*S^3) - (2*(-84 + 663*S^2 + 378*S^4 + 1345*S^6 + 598*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + HPL[{2, 1, 1}, -S^2]*((42989 - 614466*S^2 - 308682*S^4 - 1177723*S^6)/(1458*S^3) + (Pi^2*(5656 - 50007*S^2 - 36705*S^4 - 103336*S^6))/(486*S^3) + (Pi^4*(415 - 9577*S^6))/(405*S^3) + (4*(-23 + 718*S^2 + 375*S^4 + 1411*S^6 + 670*S^8)*Zeta[3])/(27*S^3*(1 + S^2))) + ((14292 + 15894*S^2 - 4871*S^4 - 4934*S^6)/(243*S*(1 + S^2)) + (Pi^2*(68 + 34*S^2 - 745*S^4 - 813*S^6))/(27*S*(1 + S^2)))*Zeta[5] + Zeta[3]*((1911372 + 2436726*S^2 + 276847*S^4 - 61883*S^6)/(34992*S*(1 + S^2)) + (Pi^4*(190 + 95*S^2 - 2221*S^4 - 2411*S^6))/(648*S*(1 + S^2)) + (Pi^2*(6734 + 8117*S^2 - 1234*S^4 - 2077*S^6))/(648*S*(1 + S^2)) + (92*S^3*Zeta[5])/9) + HPL[{1}, -S^2]^3*(-((1 + S^2)*(422663 + 99650*S^2 + 875723*S^4))/(5832*S^3) + (Pi^4*(-81677 - 325418*S^2 - 123090*S^4 - 422852*S^6 - 179111*S^8))/(29160*S^3*(1 + S^2)) + (Pi^2*(-69260 - 167108*S^2 - 293517*S^4 - 359348*S^6 - 165299*S^8))/(4374*S^3*(1 + S^2)) + ((-1163 - 3515*S^2 - 1176*S^4 - 3737*S^6 - 1385*S^8)*HPL[{2}, -S^2]^2)/(27*S^3*(1 + S^2)) + ((10*Pi^2*(1 + S^6))/(27*S^3) - (2*(-505 - 1038*S^2 + 150*S^4 + 899*S^6))/(243*S^3))*HPL[{3}, -S^2] + ((-35 - 293*S^2 - 138*S^4 - 488*S^6 - 230*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) - (116*(1 + S^6)*HPL[{5}, -S^2])/(27*S^3) + ((1142*Pi^2*(1 + S^6))/(27*S^3) + (2*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(81*S^3))*HPL[{2, 1}, -S^2] + (4*(1046 + 3290*S^2 + 1122*S^4 + 3629*S^6 + 1385*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (152*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (124*(1 + S^6)*HPL[{4, 1}, -S^2])/(3*S^3) - (20*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (3136*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (3088*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (2000*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((256*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(81*S^3) + ((1 + S^2)*(6097 + 2105*S^2 + 3352*S^4))/(243*S^3))*Zeta[3] + HPL[{2}, -S^2]*((-35426 - 47493*S^2 - 74580*S^4 - 63377*S^6)/(486*S^3) + (Pi^2*(-8198 - 28754*S^2 - 10278*S^4 - 34577*S^6 - 14021*S^8))/(486*S^3*(1 + S^2)) + (76*(1 + S^6)*HPL[{3}, -S^2])/(9*S^3) + (1568*(1 + S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (164*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + (368*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(27*S^3)) + HPL[{2, 1}, -S^2]*((Pi^2*(280153 + 92628*S^2 + 591822*S^4 + 18932*S^6))/(5832*S^3) + (7282637 + 1469853*S^2 + 15180939*S^4 + 2145119*S^6)/(34992*S^3) + (Pi^4*(83678 + 191597*S^2 + 54684*S^4 + 89748*S^6 - 18171*S^8))/(9720*S^3*(1 + S^2)) + (2*(-7030 - 14122*S^2 - 3600*S^4 - 7009*S^6 + 83*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-205 + 23*S^6)*HPL[{3, 2}, -S^2])/(9*S^3) + (4*(290 + 11*S^6)*HPL[{4, 1}, -S^2])/(9*S^3) + (4*(-7009 - 14101*S^2 - 3600*S^4 - 6949*S^6 + 143*S^8)*HPL[{2, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) - (32*(-19 + 275*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) - (8*(-15 + 371*S^6)*HPL[{3, 1, 1}, -S^2])/S^3 + (16*(17 + 1142*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(9*S^3) + ((2*Pi^2*(-122 + 9*S^6))/(27*S^3) + (-5411 - 2385*S^2 - 4041*S^4 + 116*S^6)/(81*S^3))*Zeta[3] + (8*(-37 + 9*S^6)*Zeta[5])/(9*S^3)) + HPL[{3}, -S^2]*((-46557 - 314823*S^2 - 3096069*S^4 - 5610887*S^6 - 3156332*S^8)/(69984*S^3*(1 + S^2)) + (Pi^2*(-3939 + 7893*S^2 - 41766*S^4 - 117008*S^6 - 66002*S^8))/(11664*S^3*(1 + S^2)) + (Pi^4*(-2149 - 3751*S^2 + 180*S^4 - 1450*S^6 + 152*S^8))/(19440*S^3*(1 + S^2)) + (2*(-31 - 58*S^2 - 7*S^6 + 20*S^8)*HPL[{4}, -S^2])/(27*S^3*(1 + S^2)) + (2*(-13 + 34*S^6)*HPL[{5}, -S^2])/(9*S^3) + ((-3766 - 1557*S^2 - 2790*S^4 - 3669*S^6)/(162*S^3) + (Pi^2*(-103 - 73*S^6))/(27*S^3))*HPL[{2, 1}, -S^2] + ((-85 - 751*S^2 - 378*S^4 - 1078*S^6 - 412*S^8)*HPL[{3, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-9 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - 8*S^3*HPL[{4, 1}, -S^2] + (2*(39 + 279*S^2 + 138*S^4 + 302*S^6 + 62*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(-103 + 11*S^6)*HPL[{2, 2, 1}, -S^2])/(9*S^3) + (4*(293 + 5*S^6)*HPL[{3, 1, 1}, -S^2])/(9*S^3) - (8*(31 + 13*S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((Pi^2*(23 + 3*S^6))/(27*S^3) + (409 + 790*S^2 + 357*S^4 - 931*S^6 - 1123*S^8)/(162*S^3*(1 + S^2)))*Zeta[3] - (2*(-17 + 29*S^6)*Zeta[5])/(9*S^3)) + HPL[{2}, -S^2]*((1076004 - 6446187*S^2 - 5445525*S^4 - 18008753*S^6)/(69984*S^3) + (Pi^6*(1807 - 70075*S^6))/(68040*S^3) + (Pi^2*(94019 - 627712*S^2 - 1260717*S^4 - 2660858*S^6 - 2133536*S^8))/(34992*S^3*(1 + S^2)) + (Pi^4*(64420 - 363812*S^2 - 870153*S^4 - 1719871*S^6 - 1286104*S^8))/(116640*S^3*(1 + S^2)) + ((-4 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((Pi^2*(17 - 92*S^6))/(54*S^3) + (250 + 589*S^2 + 480*S^4 - 4131*S^6 - 4596*S^8)/(324*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((163 + 340*S^2 + 48*S^4 - 86*S^6 - 263*S^8)*HPL[{5}, -S^2])/(54*S^3*(1 + S^2)) - (2*(-10 + 31*S^6)*HPL[{6}, -S^2])/(9*S^3) + (8*(-19 + 275*S^6)*HPL[{2, 1}, -S^2]^2)/(9*S^3) + ((Pi^2*(5 + 571*S^6))/(9*S^3) + (-694 + 38907*S^2 + 21492*S^4 + 56017*S^6)/(162*S^3))*HPL[{3, 1}, -S^2] + ((283 - 899*S^2 - 654*S^4 - 2710*S^6 - 1528*S^8)*HPL[{3, 2}, -S^2])/(54*S^3*(1 + S^2)) + ((217 - 1643*S^2 - 1047*S^4 - 3674*S^6 - 1814*S^8)*HPL[{4, 1}, -S^2])/(27*S^3*(1 + S^2)) + ((-5 - 8*S^6)*HPL[{4, 2}, -S^2])/(9*S^3) + (8*(-7 + 9*S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-2*Pi^2*(8 + 1711*S^6))/(27*S^3) - (2*(-403 + 19368*S^2 + 10818*S^4 + 27995*S^6))/(81*S^3))*HPL[{2, 1, 1}, -S^2] + (2*(-6913 - 13285*S^2 - 3186*S^4 - 6103*S^6 + 269*S^8)*HPL[{2, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) - (2*(-6952 - 13564*S^2 - 3324*S^4 - 6405*S^6 + 207*S^8)*HPL[{3, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{3, 1, 2}, -S^2])/(9*S^3) - (118*(1 + 37*S^6)*HPL[{3, 2, 1}, -S^2])/(9*S^3) - (4*(71 + 3320*S^6)*HPL[{4, 1, 1}, -S^2])/(9*S^3) - (4*(-7009 - 14101*S^2 - 3600*S^4 - 6949*S^6 + 143*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(27*S^3*(1 + S^2)) + (8*(-895 + 14339*S^6)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3) - (16*(17 + 1142*S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/(9*S^3) + ((747 + 33354*S^2 + 9126*S^4 + 15902*S^6)/(972*S^3) + (Pi^2*(-53 + 694*S^2 + 432*S^4 + 1177*S^6 + 430*S^8))/(162*S^3*(1 + S^2)))*Zeta[3] - (4*(-1 + 12*S^6)*Zeta[3]^2)/(9*S^3) + HPL[{2, 1}, -S^2]*((76065 + 28140*S^2 + 106995*S^4 - 3962*S^6)/(324*S^3) + (Pi^2*(9121 + 19600*S^2 + 5334*S^4 + 10085*S^6 - 394*S^8))/(162*S^3*(1 + S^2)) - (4*(42 + S^6)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((5853 + 18951*S^2 + 8781*S^4 - 17155*S^6)/(1944*S^3) + (Pi^2*(95 + 995*S^2 + 540*S^4 + 786*S^6 - 114*S^8))/(324*S^3*(1 + S^2)) + (2*(-103 + 11*S^6)*HPL[{2, 1}, -S^2])/(9*S^3) + (2*(7 + 13*S^6)*Zeta[3])/(9*S^3)) + ((45 + 471*S^2 + 294*S^4 + 344*S^6 - 82*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + HPL[{1}, -S^2]^2*((-2425*Pi^6*(1 + S^2)*(1 - S^2 + S^4))/(2268*S^3) - ((1 + S^2)*(3757531 + 762416*S^2 + 9134503*S^4))/(34992*S^3) + (Pi^2*(-1489946 - 3492239*S^2 - 6839775*S^4 - 9108185*S^6 - 4301807*S^8))/(69984*S^3*(1 + S^2)) + (Pi^4*(-406640 - 1063703*S^2 - 2202228*S^4 - 2777429*S^6 - 1261532*S^8))/(116640*S^3*(1 + S^2)) + ((-6683 - 9489*S^2 - 11754*S^4 - 9020*S^6)/(108*S^3) - (434*Pi^2*(1 + S^6))/(27*S^3))*HPL[{2}, -S^2]^2 - (59*(1 + S^6)*HPL[{2}, -S^2]^3)/(3*S^3) + (5*(1 + S^6)*HPL[{3}, -S^2]^2)/(9*S^3) + ((-109*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(54*S^3) + (-2086 - 3925*S^2 - 8511*S^4 - 12835*S^6 - 6811*S^8)/(324*S^3*(1 + S^2)))*HPL[{4}, -S^2] + ((-118 - 62*S^2 - 241*S^4 - 123*S^6)*HPL[{5}, -S^2])/(9*S*(1 + S^2)) - (82*(1 + S^6)*HPL[{6}, -S^2])/(9*S^3) + (784*(1 + S^6)*HPL[{2, 1}, -S^2]^2)/(3*S^3) + ((1706*Pi^2*(1 + S^6))/(27*S^3) + (19039 + 26391*S^2 + 35562*S^4 + 28858*S^6)/(81*S^3))*HPL[{3, 1}, -S^2] - (2*(422 + 1103*S^2 + 336*S^4 + 1004*S^6 + 323*S^8)*HPL[{3, 2}, -S^2])/(27*S^3*(1 + S^2)) + ((-805 - 1915*S^2 - 546*S^4 - 1522*S^6 - 412*S^8)*HPL[{4, 1}, -S^2])/(9*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{4, 2}, -S^2])/(3*S^3) + (128*(1 + S^6)*HPL[{5, 1}, -S^2])/(9*S^3) + ((-1142*Pi^2*(1 + S^6))/(9*S^3) - (2*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(27*S^3))*HPL[{2, 1, 1}, -S^2] - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (4*(1124 + 3440*S^2 + 1158*S^4 + 3701*S^6 + 1385*S^8)*HPL[{3, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) - (472*(1 + S^6)*HPL[{3, 2, 1}, -S^2])/S^3 - (1444*(1 + S^6)*HPL[{4, 1, 1}, -S^2])/S^3 + (20*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (2992*(1 + S^6)*HPL[{3, 1, 1, 1}, -S^2])/(3*S^3) - (2000*(1 + S^6)*HPL[{2, 1, 1, 1, 1}, -S^2])/S^3 + ((Pi^2*(461 + 969*S^2 + 248*S^4 + 612*S^6 + 104*S^8))/(54*S^3*(1 + S^2)) + (13242 + 30455*S^2 + 27355*S^4 + 15665*S^6 + 5955*S^8)/(324*S^3*(1 + S^2)))*Zeta[3] - (16*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3]^2)/(3*S^3) + HPL[{2, 1}, -S^2]*((35426 + 47493*S^2 + 74580*S^4 + 63377*S^6)/(162*S^3) + (Pi^2*(8198 + 28754*S^2 + 10278*S^4 + 34577*S^6 + 14021*S^8))/(162*S^3*(1 + S^2)) - (164*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((20 + 1329*S^2 - 4987*S^4 - 13881*S^6 - 8017*S^8)/(324*S^3*(1 + S^2)) + (Pi^2*(452 + 647*S^2 + 120*S^4 - 82*S^6 - 277*S^8))/(162*S^3*(1 + S^2)) - (76*(1 + S^6)*HPL[{2, 1}, -S^2])/(3*S^3) + (8*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]*((-8953*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(1620*S^3) + (-66966 - 85953*S^2 - 159502*S^4 - 141379*S^6)/(648*S^3) + (Pi^2*(-23189 - 34212*S^2 - 60150*S^4 - 50099*S^6))/(972*S^3) + ((140 + 368*S^2 + 114*S^4 + 335*S^6 + 107*S^8)*HPL[{3}, -S^2])/(9*S^3*(1 + S^2)) + ((-1 - S^6)*HPL[{4}, -S^2])/S^3 + (2*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) + (784*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (1568*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + ((316 + 808*S^2 + 246*S^4 + 709*S^6 + 217*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((1127 + 2234*S^2 + 558*S^4 + 1172*S^6 + 65*S^8)*Zeta[5])/(27*S^3*(1 + S^2))) + ((90 + 45*S^2 - 1639*S^4 - 1729*S^6)*Zeta[7])/(9*S*(1 + S^2)) + HPL[{1}, -S^2]*(-((1 + S^2)*(44150029 + 8482853*S^2 + 134931142*S^4))/(419904*S^3) + (Pi^2*(-1895017 - 4364668*S^2 - 10376418*S^4 - 15145588*S^6 - 7285477*S^8))/(104976*S^3*(1 + S^2)) + (Pi^4*(-628621 - 1595621*S^2 - 4144709*S^4 - 5883011*S^6 - 2759518*S^8))/(233280*S^3*(1 + S^2)) + (Pi^6*(-323921 - 2075360*S^2 - 883878*S^4 - 3303086*S^6 - 1551647*S^8))/(816480*S^3*(1 + S^2)) + ((-341 - 1049*S^2 - 354*S^4 - 1134*S^6 - 426*S^8)*HPL[{2}, -S^2]^3)/(18*S^3*(1 + S^2)) + ((11 + 33*S^2 + 14*S^4 + 30*S^6 + 8*S^8)*HPL[{3}, -S^2]^2)/(18*S^3*(1 + S^2)) + ((-34*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-1316 - 2654*S^2 - 5367*S^4 - 8198*S^6 - 4385*S^8)/(162*S^3*(1 + S^2)))*HPL[{5}, -S^2] + ((-79 - 402*S^2 - 154*S^4 - 606*S^6 - 283*S^8)*HPL[{6}, -S^2])/(18*S^3*(1 + S^2)) + (22*(1 + S^6)*HPL[{7}, -S^2])/(9*S^3) + (2*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1}, -S^2]^2)/(9*S^3*(1 + S^2)) + ((-140*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-2209 - 5365*S^2 - 5457*S^4 - 3655*S^6 - 1246*S^8)/(81*S^3*(1 + S^2)))*HPL[{3, 2}, -S^2] + ((-311*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (-10850 - 27641*S^2 - 24267*S^4 - 8471*S^6 - 347*S^8)/(162*S^3*(1 + S^2)))*HPL[{4, 1}, -S^2] + ((5 - 7*S^2 + 30*S^4 - 88*S^6 - 76*S^8)*HPL[{4, 2}, -S^2])/(54*S^3*(1 + S^2)) + (38*(1 + S^6)*HPL[{4, 3}, -S^2])/(9*S^3) + (2*(13 + 149*S^2 + 80*S^4 + 251*S^6 + 115*S^8)*HPL[{5, 1}, -S^2])/(9*S^3*(1 + S^2)) + (104*(1 + S^6)*HPL[{5, 2}, -S^2])/(9*S^3) + (304*(1 + S^6)*HPL[{6, 1}, -S^2])/(9*S^3) + ((-3472*Pi^2*(1 + S^6))/(27*S^3) - (2*(6683 + 9489*S^2 + 11754*S^4 + 9020*S^6))/(27*S^3))*HPL[{2, 2, 1}, -S^2] + ((-3452*Pi^2*(1 + S^6))/(9*S^3) - (2*(59137 + 83325*S^2 + 106086*S^4 + 82978*S^6))/(81*S^3))*HPL[{3, 1, 1}, -S^2] + (4*(1 + S^2)*(2 - 5*S^2 + 2*S^4)*HPL[{3, 1, 2}, -S^2])/(27*S^3) - (4*(3067 + 9442*S^2 + 3192*S^4 + 10207*S^6 + 3832*S^8)*HPL[{3, 2, 1}, -S^2])/(27*S^3*(1 + S^2)) + (42*(1 + S^6)*HPL[{3, 2, 2}, -S^2])/S^3 + (1184*(1 + S^6)*HPL[{3, 3, 1}, -S^2])/(9*S^3) - (2*(6173 + 19175*S^2 + 6510*S^4 + 20900*S^6 + 7898*S^8)*HPL[{4, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) + (394*(1 + S^6)*HPL[{4, 1, 2}, -S^2])/(3*S^3) + (1202*(1 + S^6)*HPL[{4, 2, 1}, -S^2])/(3*S^3) + (7040*(1 + S^6)*HPL[{5, 1, 1}, -S^2])/(9*S^3) + ((2284*Pi^2*(1 + S^6))/(9*S^3) + (4*(6217 + 8727*S^2 + 11883*S^4 + 9589*S^6))/(27*S^3))*HPL[{2, 1, 1, 1}, -S^2] + (944*(1 + S^6)*HPL[{2, 2, 2, 1}, -S^2])/S^3 + (8*(1046 + 3290*S^2 + 1122*S^4 + 3629*S^6 + 1385*S^8)*HPL[{3, 1, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (8800*(1 + S^6)*HPL[{3, 1, 1, 2}, -S^2])/(3*S^3) - (8800*(1 + S^6)*HPL[{3, 1, 2, 1}, -S^2])/(3*S^3) - (17296*(1 + S^6)*HPL[{3, 2, 1, 1}, -S^2])/(3*S^3) - (17240*(1 + S^6)*HPL[{4, 1, 1, 1}, -S^2])/S^3 - (40*(139 + 439*S^2 + 150*S^4 + 486*S^6 + 186*S^8)*HPL[{2, 1, 1, 1, 1}, -S^2])/(3*S^3*(1 + S^2)) + (6272*(1 + S^6)*HPL[{2, 1, 2, 1, 1}, -S^2])/(3*S^3) + (6272*(1 + S^6)*HPL[{2, 2, 1, 1, 1}, -S^2])/S^3 + (31648*(1 + S^6)*HPL[{3, 1, 1, 1, 1}, -S^2])/(3*S^3) + (4000*(1 + S^6)*HPL[{2, 1, 1, 1, 1, 1}, -S^2])/S^3 + ((95*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(324*S^3) + (Pi^2*(3197 + 7451*S^2 + 4992*S^4 + 1013*S^6 + 131*S^8))/(324*S^3*(1 + S^2)) + (287908 + 652981*S^2 + 545277*S^4 + 259915*S^6 + 95263*S^8)/(5832*S^3*(1 + S^2)))*Zeta[3] + ((71 - 214*S^2 - 138*S^4 - 682*S^6 - 397*S^8)*Zeta[3]^2)/(27*S^3*(1 + S^2)) + HPL[{3, 1}, -S^2]*((Pi^2*(4085 + 14315*S^2 + 5106*S^4 + 17222*S^6 + 6992*S^8))/(81*S^3*(1 + S^2)) + (36804 + 85385*S^2 + 124357*S^4 + 139775*S^6 + 64431*S^8)/(162*S^3*(1 + S^2)) - (496*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{4}, -S^2]*((-6371 - 10498*S^2 - 26812*S^4 - 43510*S^6 - 22553*S^8)/(648*S^3*(1 + S^2)) + (Pi^2*(-59 - 1403*S^2 - 726*S^4 - 2654*S^6 - 1310*S^8))/(324*S^3*(1 + S^2)) + (2*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 - (38*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(9*S^3)) + HPL[{2}, -S^2]^2*(-((1 + S^2)*(18412 + 6533*S^2 + 28207*S^4))/(324*S^3) + (Pi^2*(-4537 - 14962*S^2 - 5226*S^4 - 17140*S^6 - 6715*S^8))/(324*S^3*(1 + S^2)) + (16*(1 + S^6)*HPL[{3}, -S^2])/(3*S^3) + (118*(1 + S^6)*HPL[{2, 1}, -S^2])/S^3 + (40*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{2, 1, 1}, -S^2]*((-35426 - 47493*S^2 - 74580*S^4 - 63377*S^6)/(81*S^3) + (Pi^2*(-8198 - 28754*S^2 - 10278*S^4 - 34577*S^6 - 14021*S^8))/(81*S^3*(1 + S^2)) + (328*(1 + S^2)*(1 - S^2 + S^4)*Zeta[3])/(3*S^3)) + HPL[{3}, -S^2]*((-47*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(405*S^3) + (-36832 - 70381*S^2 - 280101*S^4 - 488611*S^6 - 257611*S^8)/(5832*S^3*(1 + S^2)) + (Pi^2*(1160 + 3419*S^2 - 45*S^4 - 7759*S^6 - 4915*S^8))/(972*S^3*(1 + S^2)) - (8*(1 + S^6)*HPL[{4}, -S^2])/(3*S^3) - (2*(140 + 368*S^2 + 114*S^4 + 335*S^6 + 107*S^8)*HPL[{2, 1}, -S^2])/(9*S^3*(1 + S^2)) - (212*(1 + S^6)*HPL[{3, 1}, -S^2])/(9*S^3) + (152*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) + (2*(5 + 11*S^2 + 14*S^6 + 8*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + HPL[{2, 1}, -S^2]*((8953*Pi^4*(1 + S^2)*(1 - S^2 + S^4))/(810*S^3) + (Pi^2*(23189 + 34212*S^2 + 60150*S^4 + 50099*S^6))/(486*S^3) + (66966 + 85953*S^2 + 159502*S^4 + 141379*S^6)/(324*S^3) - (1568*(1 + S^6)*HPL[{3, 1}, -S^2])/(3*S^3) - (3136*(1 + S^6)*HPL[{2, 1, 1}, -S^2])/(3*S^3) - (2*(316 + 808*S^2 + 246*S^4 + 709*S^6 + 217*S^8)*Zeta[3])/(9*S^3*(1 + S^2))) + ((68*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + (2882 + 6429*S^2 + 3884*S^4 - 153*S^6 - 454*S^8)/(54*S^3*(1 + S^2)))*Zeta[5] + HPL[{2}, -S^2]*((-564551 - 706788*S^2 - 1609713*S^4 - 1475252*S^6)/(5832*S^3) + (Pi^2*(-84734 - 119887*S^2 - 258214*S^4 - 226949*S^6))/(3888*S^3) + (Pi^4*(-70433 - 285758*S^2 - 108342*S^4 - 375866*S^6 - 160541*S^8))/(19440*S^3*(1 + S^2)) + ((70*Pi^2*(1 + S^6))/(27*S^3) + (2156 + 3105*S^2 + 2358*S^4 + 1193*S^6)/(162*S^3))*HPL[{3}, -S^2] + ((-23 - 65*S^2 - 30*S^4 - 50*S^6 - 8*S^8)*HPL[{4}, -S^2])/(18*S^3*(1 + S^2)) + (34*(1 + S^6)*HPL[{5}, -S^2])/(9*S^3) + ((1736*Pi^2*(1 + S^6))/(27*S^3) + (6683 + 9489*S^2 + 11754*S^4 + 9020*S^6)/(27*S^3))*HPL[{2, 1}, -S^2] + (2*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{3, 1}, -S^2])/(9*S^3*(1 + S^2)) - (190*(1 + S^6)*HPL[{3, 2}, -S^2])/(9*S^3) - (66*(1 + S^6)*HPL[{4, 1}, -S^2])/S^3 - (4*(1163 + 3515*S^2 + 1176*S^4 + 3737*S^6 + 1385*S^8)*HPL[{2, 1, 1}, -S^2])/(9*S^3*(1 + S^2)) - (472*(1 + S^6)*HPL[{2, 2, 1}, -S^2])/S^3 + (4400*(1 + S^6)*HPL[{3, 1, 1}, -S^2])/(3*S^3) + (3136*(1 + S^6)*HPL[{2, 1, 1, 1}, -S^2])/(3*S^3) + ((118*Pi^2*(1 + S^2)*(1 - S^2 + S^4))/(27*S^3) + ((1 + S^2)*(2696 + 1237*S^2 + 1562*S^4))/(81*S^3))*Zeta[3] + (124*(1 + S^2)*(1 - S^2 + S^4)*Zeta[5])/(9*S^3)) + (10*(1 + S^2)*(1 - S^2 + S^4)*Zeta[7])/S^3));
Et5vwuT=T*Et5vwuT1F1*(F-1/F)+T^2*(Et5vwuT2F2*(F^2-1/F^2))+T^3*(Et5vwuT3F1*(F-1/F)+Et5vwuT3F3*(F^3-1/F^3));
