#######################################################################
# Ancillary file for arXiv:2308.08199 [hep-th],
# "An Eight Loop Amplitude via Antipodal Duality",
# by Lance Dixon and Yu-Ting (Andy) Liu.
#######################################################################
# This file provides conversions from the f-alphabet used in this paper,
# to more conventional MZV representations, through weight16.
#
# Our conventions follow the program "HyperlogProcedures" by Oliver Schnetz,
# at   https://www.math.fau.de/person/oliver-schnetz/
#
# See also                 F. Brown, arXiv:1102.1310, 
#          E. Panzer and O. Schnetz, arXiv:1603.04289,
#                        O. Schnetz, arXiv:1711.05118.
#
# Below, f[i,j,...] = f_{i,j,...} in the paper.
# "zi" = zeta[i], the Riemann zeta value.
# Zeta53 = zeta[5,3], the multiple zeta value, with index ordering such that
#   zeta[5,3] = 0.037707672984847544011304782293659914822601319415278
# Also, Zeta113 = zeta[11,3] and Zeta115 = zeta[11,5]
# (in a real abuse of notation).
#
# The conversion table:
#
ftoMZV16 := [
  f[3] = z3,
  f[5] = z5,
  f[3,3] = 1/2*z3^2,
  f[7] = z7,
#
  f[3,5] = z3*z5+1/5*Zeta53,
  f[5,3] = -1/5*Zeta53,
#
  f[9] = z9,
  f[3,3,3] = 1/6*z3^3,
#
  f[3,7] = z3*z7+3/14*z5^2+1/14*Zeta73,
  f[7,3] = -1/14*(Zeta73+3*z5^2),
  f[5,5] = 1/2*z5^2,
# 
  f[11] = z11,
  f[3,3,5] = 1/2*z3^2*z5-1/5*Zeta533+1/5*z3*Zeta53+1/2*z5*z6-9*z2*z9-3/5*z4*z7,
  f[3,5,3] = -1/5*z3*Zeta53+18*z2*z9+6/5*z4*z7-z5*z6+2/5*Zeta533,
  f[5,3,3] = 1/2*z5*z6-9*z2*z9-3/5*z4*z7-1/5*Zeta533,
#
  f[3,3,3,3] = 1/24*z3^4,
  f[3,9] = 3671/2073*z3*z9-4/691*z3^4-480/691*z2*z3*z7-168/691*z2*z5^2
    +108/691*z6*z3^2+24/691*z4*z3*z5-72/691*z4*Zeta53-144/691*z2*Zeta73
    -54/691*z5*z7+223/691*Zeta93+48/691*Zeta6411,
  f[9,3] = 4/691*z3^4+480/691*z2*z3*z7+168/691*z2*z5^2-108/691*z6*z3^2
    -24/691*z4*z3*z5+72/691*z4*Zeta53+144/691*z2*Zeta73-1598/2073*z3*z9
    +54/691*z5*z7-223/691*Zeta93-48/691*Zeta6411,
  f[5,7] = 3941/2073*z5*z7-5330/6219*Zeta93+12/691*z3^4+1440/691*z2*z3*z7
    +504/691*z2*z5^2-324/691*z6*z3^2-72/691*z4*z3*z5+216/691*z4*Zeta53
    +432/691*z2*Zeta73-1598/691*z3*z9-144/691*Zeta6411,
  f[7,5] = -1868/2073*z5*z7+5330/6219*Zeta93-12/691*z3^4-1440/691*z2*z3*z7
    -504/691*z2*z5^2+324/691*z6*z3^2+72/691*z4*z3*z5-216/691*z4*Zeta53
    -432/691*z2*Zeta73+1598/691*z3*z9+144/691*Zeta6411,
#
  f[13] = z13,
  f[3,3,7] = 1/2*z3^2*z7+3/14*z3*z5^2+1/14*z3*Zeta73-11/4*z11*z2+1/7*z4*z9
    +2/7*z6*z7+3/35*Zeta553-1/14*Zeta733,
  f[3,7,3] = -3/14*z3*z5^2-1/14*z3*Zeta73+11/2*z11*z2-2/7*z4*z9-4/7*z6*z7
    -6/35*Zeta553+1/7*Zeta733,
  f[7,3,3] = -11/4*z11*z2+1/7*z4*z9+2/7*z6*z7+3/35*Zeta553-1/14*Zeta733,
  f[3,5,5] = 1/2*z3*z5^2+1/5*z5*Zeta53+11/2*z11*z2+z4*z9+1/25*Zeta553,
  f[5,3,5] = -1/5*z5*Zeta53-11*z11*z2-2*z4*z9-2/25*Zeta553,
  f[5,5,3] = 11/2*z11*z2+z4*z9+1/25*Zeta553,
#
  f[3,11] = z3*z11-23/33*z5*z9-235/396*z7^2-23/198*Zeta113+1/27*Zeta95,
  f[11,3] = 23/33*z5*z9+235/396*z7^2+23/198*Zeta113-1/27*Zeta95,
  f[5,9] = 8/3*z5*z9+55/36*z7^2-2/27*Zeta95+5/18*Zeta113,
  f[9,5] = -55/36*z7^2+2/27*Zeta95-5/3*z5*z9-5/18*Zeta113,
  f[7,7] = 1/2*z7^2,
  f[3,3,3,5] = 1/6*z3^3*z5+1/10*z3^2*Zeta53-9*z2*z3*z9-3/5*z4*z3*z7
    +1/2*z6*z3*z5-1/5*z3*Zeta533+4*z2*z5*z7+1/10*Zeta53*z6+2/3*z2*Zeta93
    -12775/198*z5*z9-647287/11880*z7^2-12841/1188*Zeta113+232/81*Zeta95
    +1/5*Zeta5333,
  f[3,3,5,3] = -1/10*z3^2*Zeta53+18*z2*z3*z9+6/5*z4*z3*z7-z6*z3*z5
    +2/5*z3*Zeta533-12*z2*z5*z7-3/10*Zeta53*z6-2*z2*Zeta93+12775/66*z5*z9
    +647287/3960*z7^2+12841/396*Zeta113-232/27*Zeta95-3/5*Zeta5333,
  f[3,5,3,3] = -9*z2*z3*z9-3/5*z4*z3*z7+1/2*z6*z3*z5-1/5*z3*Zeta533
    +12*z2*z5*z7+3/10*Zeta53*z6+2*z2*Zeta93-12775/66*z5*z9-647287/3960*z7^2
    -12841/396*Zeta113+232/27*Zeta95+3/5*Zeta5333,
  f[5,3,3,3] = -4*z2*z5*z7-1/10*Zeta53*z6-2/3*z2*Zeta93+12775/198*z5*z9
    +647287/11880*z7^2+12841/1188*Zeta113-232/81*Zeta95-1/5*Zeta5333,
#
  f[15] = z15, f[5,5,5] = 1/6*z5^3, f[3,3,3,3,3] = 1/120*z3^5,
  f[3,3,9] = 7934/266035*z5*Zeta73+120/691*z7*Zeta53-600/7601*z4*z3*Zeta53
    -1296/7601*z3*z2*Zeta73-9827/48370*z5^3-204/38005*z3^5+590/7601*z3*z5*z7
    -4032/7601*z7*z3^2*z2-1464/7601*z5^2*z3*z2+540/7601*z5*z3^2*z4
    -504/7601*z2*z5*Zeta53-48/7601*Zeta64311-4645943/152020*z13*z2
    +187199/106414*z4*z11-86067/24185*z6*z9+14803/15202*z3^2*z9
    +38992/114015*z8*z7+321242/266035*z10*z5-362993/1432443*z12*z3
    +1116/7601*z6*z3^3-655/22803*Zeta933-17203/532070*Zeta735
    +480/7601*Zeta6411*z3+672/38005*z2*Zeta553-96/7601*Zeta733*z2
    -480/7601*z4*Zeta533+6895/22803*z3*Zeta93,
  f[3,9,3] = -15868/266035*z5*Zeta73-240/691*z7*Zeta53+408/7601*z4*z3*Zeta53
    +1008/7601*z3*z2*Zeta73+9827/24185*z5^3+188/38005*z3^5-1774/7601*z3*z5*z7
    +2784/7601*z7*z3^2*z2+1080/7601*z5^2*z3*z2-816/7601*z5*z3^2*z4
    +1008/7601*z2*z5*Zeta53+96/7601*Zeta64311+4645943/76010*z13*z2
    -187199/53207*z4*z11+172134/24185*z6*z9-4028/22803*z3^2*z9
    -77984/114015*z8*z7-642484/266035*z10*z5+725986/1432443*z12*z3
    -1044/7601*z6*z3^3+1310/22803*Zeta933+17203/266035*Zeta735
    -432/7601*Zeta6411*z3-1344/38005*z2*Zeta553+192/7601*Zeta733*z2
    +960/7601*z4*Zeta533-6431/22803*z3*Zeta93,
  f[9,3,3] = 7934/266035*z5*Zeta73+120/691*z7*Zeta53+192/7601*z4*z3*Zeta53
    +288/7601*z3*z2*Zeta73-9827/48370*z5^3+16/38005*z3^5+1184/7601*z3*z5*z7
    +1248/7601*z7*z3^2*z2+384/7601*z5^2*z3*z2+276/7601*z5*z3^2*z4
    -504/7601*z2*z5*Zeta53-48/7601*Zeta64311-4645943/152020*z13*z2
    +187199/106414*z4*z11-86067/24185*z6*z9-6775/22803*z3^2*z9
    +38992/114015*z8*z7+321242/266035*z10*z5-362993/1432443*z12*z3
    -72/7601*z6*z3^3-655/22803*Zeta933-17203/532070*Zeta735
    -48/7601*Zeta6411*z3+672/38005*z2*Zeta553-96/7601*Zeta733*z2
    -480/7601*z4*Zeta533-464/22803*z3*Zeta93,
  f[3,5,7] = 35008/798105*z5*Zeta73-1109/3455*z7*Zeta53
    +1800/7601*z4*z3*Zeta53+3888/7601*z3*z2*Zeta73+107791/145110*z5^3
    +612/38005*z3^5+32695/22803*z3*z5*z7+12096/7601*z7*z3^2*z2
    +4392/7601*z5^2*z3*z2-1620/7601*z5*z3^2*z4+1512/7601*z2*z5*Zeta53
    +144/7601*Zeta64311-6417649/152020*z13*z2-8495287/319242*z4*z11
    +4933001/435330*z6*z9-10803/7601*z3^2*z9+57847/114015*z8*z7
    -857312/266035*z10*z5+362993/477481*z12*z3-3348/7601*z6*z3^3
    -1706/68409*Zeta933-58001/1596210*Zeta735-1440/7601*Zeta6411*z3
    -2016/38005*z2*Zeta553+288/7601*Zeta733*z2+1440/7601*z4*Zeta533
    -54454/68409*z3*Zeta93,
  f[3,7,5] = 33401/798105*z5*Zeta73+360/691*z7*Zeta53-1800/7601*z4*z3*Zeta53
    -3888/7601*z3*z2*Zeta73-42494/72555*z5^3-612/38005*z3^5
    -9892/22803*z3*z5*z7-12096/7601*z7*z3^2*z2-4392/7601*z5^2*z3*z2
    +1620/7601*z5*z3^2*z4-1512/7601*z2*z5*Zeta53-144/7601*Zeta64311
    +2665353/76010*z13*z2+4122227/159621*z4*z11-2413639/217665*z6*z9
    +10803/7601*z3^2*z9-35044/114015*z8*z7+1737427/532070*z10*z5
    -362993/477481*z12*z3+3348/7601*z6*z3^3+1706/68409*Zeta933
    +17599/798105*Zeta735+1440/7601*Zeta6411*z3+2016/38005*z2*Zeta553
    -288/7601*Zeta733*z2-1440/7601*z4*Zeta533+54454/68409*z3*Zeta93,
  f[5,3,7] = -1/5*z7*Zeta53+2/35*z5^3-1/70*z5*Zeta73-3/70*z10*z5
    +143/20*z13*z2+11/14*z4*z11-17/70*z6*z9-1/5*z8*z7+1/70*Zeta735,
  f[5,7,3] = -47213/1596210*z5*Zeta73+360/691*z7*Zeta53
    +576/7601*z4*z3*Zeta53+864/7601*z3*z2*Zeta73-116083/145110*z5^3
    +48/38005*z3^5+3552/7601*z3*z5*z7+3744/7601*z7*z3^2*z2
    +1152/7601*z5^2*z3*z2+828/7601*z5*z3^2*z4-1512/7601*z2*z5*Zeta53
    -144/7601*Zeta64311+2665353/76010*z13*z2+4122227/159621*z4*z11
    -2413639/217665*z6*z9-6775/7601*z3^2*z9-35044/114015*z8*z7
    +1737427/532070*z10*z5-362993/477481*z12*z3-216/7601*z6*z3^3
    +1706/68409*Zeta933+17599/798105*Zeta735-144/7601*Zeta6411*z3
    +2016/38005*z2*Zeta553-288/7601*Zeta733*z2-1440/7601*z4*Zeta533
    -464/7601*z3*Zeta93,
  f[7,3,5] = -11/70*z5^3-3/35*z5*Zeta73-3/70*z10*z5+143/20*z13*z2
    +11/14*z4*z11-17/70*z6*z9-1/5*z8*z7+1/70*Zeta735,
  f[7,5,3] = 35008/798105*z5*Zeta73-360/691*z7*Zeta53-576/7601*z4*z3*Zeta53
    -864/7601*z3*z2*Zeta73+107791/145110*z5^3-48/38005*z3^5
    -3552/7601*z3*z5*z7-3744/7601*z7*z3^2*z2-1152/7601*z5^2*z3*z2
    -828/7601*z5*z3^2*z4+1512/7601*z2*z5*Zeta53+144/7601*Zeta64311
    -6417649/152020*z13*z2-8495287/319242*z4*z11+4933001/435330*z6*z9
    +6775/7601*z3^2*z9+57847/114015*z8*z7-857312/266035*z10*z5
    +362993/477481*z12*z3+216/7601*z6*z3^3-1706/68409*Zeta933
    -58001/1596210*Zeta735+144/7601*Zeta6411*z3-2016/38005*z2*Zeta553
    +288/7601*Zeta733*z2+1440/7601*z4*Zeta533+464/7601*z3*Zeta93,
#
  f[3,13] = 3600/25319*z4*z3*z9-14400/39787*z8*z3*z5-152640/278509*z6*z3*z7
    +1023888/278509*z4*z5*z7+5630472/278509*z7^2*z2+27360/278509*Zeta7333
    -156096/1392545*Zeta5533-1440/39787*Zeta8611-18360/278509*z10*z3^2
    +51120/278509*z6*z5^2-1760771/278509*z3*z13-575722347/18103085*z5*z11
    -779769603/28447705*z7*z9-175335439/36206170*Zeta133
    +3505167/6127198*Zeta115+197280/39787*z3*z11*z2+8958960/278509*z5*z9*z2
    +130320/25319*z2*Zeta113-334560/278509*z2*Zeta95+13024/25319*z4*Zeta93
    +576/39787*z5*Zeta533+11160/278509*z6*Zeta73-1296/39787*z8*Zeta53
    +480/39787*z3^3*z7+5760/278509*z3^2*z5^2-1440/278509*z3^2*Zeta73
    +8640/278509*z3*Zeta553-7200/278509*z3*Zeta733,
  f[13,3] = -3600/25319*z4*z3*z9+14400/39787*z8*z3*z5+152640/278509*z6*z3*z7
    -1023888/278509*z4*z5*z7-5630472/278509*z7^2*z2-27360/278509*Zeta7333
    +156096/1392545*Zeta5533+1440/39787*Zeta8611+18360/278509*z10*z3^2
    -51120/278509*z6*z5^2+2039280/278509*z3*z13+575722347/18103085*z5*z11
    +779769603/28447705*z7*z9+175335439/36206170*Zeta133
    -3505167/6127198*Zeta115-197280/39787*z3*z11*z2-8958960/278509*z5*z9*z2
    -130320/25319*z2*Zeta113+334560/278509*z2*Zeta95-13024/25319*z4*Zeta93
    -576/39787*z5*Zeta533-11160/278509*z6*Zeta73+1296/39787*z8*Zeta53
    -480/39787*z3^3*z7-5760/278509*z3^2*z5^2+1440/278509*z3^2*Zeta73
    -8640/278509*z3*Zeta553+7200/278509*z3*Zeta733,
  f[5,11] = -1800/3617*z4*z3*z9+50400/39787*z8*z3*z5+76320/39787*z6*z3*z7
    -511944/39787*z4*z5*z7-2815236/39787*z7^2*z2-13680/39787*Zeta7333
    +78048/198935*Zeta5533+5040/39787*Zeta8611+9180/39787*z10*z3^2
    -25560/39787*z6*z5^2+1019640/39787*z3*z13+22227332/198935*z5*z11
    +207527796/2188285*z7*z9+3352707/198935*Zeta133-866345/437657*Zeta115
    -690480/39787*z3*z11*z2-4479480/39787*z5*z9*z2-65160/3617*z2*Zeta113
    +167280/39787*z2*Zeta95-6512/3617*z4*Zeta93-2016/39787*z5*Zeta533
    -5580/39787*z6*Zeta73+4536/39787*z8*Zeta53-1680/39787*z3^3*z7
    -2880/39787*z3^2*z5^2+720/39787*z3^2*Zeta73-4320/39787*z3*Zeta553
    +3600/39787*z3*Zeta733,
  f[11,5] = 1800/3617*z4*z3*z9-50400/39787*z8*z3*z5-76320/39787*z6*z3*z7
    +511944/39787*z4*z5*z7+2815236/39787*z7^2*z2+13680/39787*Zeta7333
    -78048/198935*Zeta5533-5040/39787*Zeta8611-9180/39787*z10*z3^2
    +25560/39787*z6*z5^2-1019640/39787*z3*z13-22028397/198935*z5*z11
    -207527796/2188285*z7*z9-3352707/198935*Zeta133+866345/437657*Zeta115
    +690480/39787*z3*z11*z2+4479480/39787*z5*z9*z2+65160/3617*z2*Zeta113
    -167280/39787*z2*Zeta95+6512/3617*z4*Zeta93+2016/39787*z5*Zeta533
    +5580/39787*z6*Zeta73-4536/39787*z8*Zeta53+1680/39787*z3^3*z7
    +2880/39787*z3^2*z5^2-720/39787*z3^2*Zeta73+4320/39787*z3*Zeta553
    -3600/39787*z3*Zeta733,
  f[7,9] = 19800/25319*z4*z3*z9-7200/3617*z8*z3*z5-76320/25319*z6*z3*z7
    +511944/25319*z4*z5*z7+2815236/25319*z7^2*z2+13680/25319*Zeta7333
    -78048/126595*Zeta5533-720/3617*Zeta8611-9180/25319*z10*z3^2
    +25560/25319*z6*z5^2-1019640/25319*z3*z13-21865632/126595*z5*z11
    -28905343/198935*z7*z9-6651159/253190*Zeta133+1714605/557018*Zeta115
    +98640/3617*z3*z11*z2+4479480/25319*z5*z9*z2+716760/25319*z2*Zeta113
    -167280/25319*z2*Zeta95+71632/25319*z4*Zeta93+288/3617*z5*Zeta533
    +5580/25319*z6*Zeta73-648/3617*z8*Zeta53+240/3617*z3^3*z7
    +2880/25319*z3^2*z5^2-720/25319*z3^2*Zeta73+4320/25319*z3*Zeta553
    -3600/25319*z3*Zeta733,
  f[9,7] = -19800/25319*z4*z3*z9+7200/3617*z8*z3*z5+76320/25319*z6*z3*z7
    -511944/25319*z4*z5*z7-2815236/25319*z7^2*z2-13680/25319*Zeta7333
    +78048/126595*Zeta5533+720/3617*Zeta8611+9180/25319*z10*z3^2
    -25560/25319*z6*z5^2+1019640/25319*z3*z13+21865632/126595*z5*z11
    +29104278/198935*z7*z9+6651159/253190*Zeta133-1714605/557018*Zeta115
    -98640/3617*z3*z11*z2-4479480/25319*z5*z9*z2-716760/25319*z2*Zeta113
    +167280/25319*z2*Zeta95-71632/25319*z4*Zeta93-288/3617*z5*Zeta533
    -5580/25319*z6*Zeta73+648/3617*z8*Zeta53-240/3617*z3^3*z7
    -2880/25319*z3^2*z5^2+720/25319*z3^2*Zeta73-4320/25319*z3*Zeta553
    +3600/25319*z3*Zeta733,
  f[3,3,3,7] = -72076/177233*z4*z3*z9+389580/278509*z8*z3*z5
    +4686566/1949563*z6*z3*z7-121791643/9747815*z4*z5*z7
    -4746518101/77982520*z7^2*z2-1201895/3899126*Zeta7333
    +16937601/48739075*Zeta5533+38958/278509*Zeta8611+993429/3899126*z10*z3^2
    -4696509/7798252*z6*z5^2+55171021/1949563*z3*z13
    +539049410681/5068863800*z5*z11+1146118067441/11948036100*z7*z9
    +20218682509/1267215950*Zeta133-390507127/214451930*Zeta115
    -24412583/1114036*z3*z11*z2-383655627/3899126*z5*z9*z2
    -11039197/708932*z2*Zeta113+41217529/11697378*z2*Zeta95
    -4525732/2658495*z4*Zeta93-77916/1392545*z5*Zeta533
    -929189/7798252*z6*Zeta73+175311/1392545*z8*Zeta53+200593/1671054*z3^3*z7
    +212199/7798252*z3^2*z5^2+434341/7798252*z3^2*Zeta73
    -333213/9747815*z3*Zeta553+111071/3899126*z3*Zeta733,
  f[3,3,7,3] = 241547/177233*z4*z3*z9-1168740/278509*z8*z3*z5
    -13502680/1949563*z6*z3*z7+365374929/9747815*z4*z5*z7
    +14239554303/77982520*z7^2*z2+3605685/3899126*Zeta7333
    -50812803/48739075*Zeta5533-116874/278509*Zeta8611
    -2980287/3899126*z10*z3^2+14089527/7798252*z6*z5^2
    -165513063/1949563*z3*z13-1617148232043/5068863800*z5*z11
    -1146118067441/3982678700*z7*z9-60656047527/1267215950*Zeta133
    +1171521381/214451930*Zeta115+35087075/557018*z3*z11*z2
    +1150966881/3899126*z5*z9*z2+33117591/708932*z2*Zeta113
    -41217529/3899126*z2*Zeta95+4525732/886165*z4*Zeta93
    +233748/1392545*z5*Zeta533+2787567/7798252*z6*Zeta73
    -525933/1392545*z8*Zeta53+38958/278509*z3^3*z7
    +1034457/7798252*z3^2*z5^2-746005/7798252*z3^2*Zeta73
    +1835166/9747815*z3*Zeta553-305861/1949563*z3*Zeta733,
  f[3,7,3,3] = -266866/177233*z4*z3*z9+1168740/278509*z8*z3*z5
    +12945662/1949563*z6*z3*z7-365374929/9747815*z4*z5*z7
    -14239554303/77982520*z7^2*z2-3605685/3899126*Zeta7333
    +50812803/48739075*Zeta5533+116874/278509*Zeta8611
    +2980287/3899126*z10*z3^2-14089527/7798252*z6*z5^2
    +165513063/1949563*z3*z13+1617148232043/5068863800*z5*z11
    +1146118067441/3982678700*z7*z9+60656047527/1267215950*Zeta133
    -1171521381/214451930*Zeta115-67110551/1114036*z3*z11*z2
    -1150966881/3899126*z5*z9*z2-33117591/708932*z2*Zeta113
    +41217529/3899126*z2*Zeta95-4525732/886165*z4*Zeta93
    -233748/1392545*z5*Zeta533-2787567/7798252*z6*Zeta73
    +525933/1392545*z8*Zeta53-38958/278509*z3^3*z7-467496/1949563*z3^2*z5^2
    +116874/1949563*z3^2*Zeta73-2670693/9747815*z3*Zeta553
    +890231/3899126*z3*Zeta733,
  f[7,3,3,3] = 97395/177233*z4*z3*z9-389580/278509*z8*z3*z5
    -4129548/1949563*z6*z3*z7+121791643/9747815*z4*z5*z7
    +4746518101/77982520*z7^2*z2+1201895/3899126*Zeta7333
    -16937601/48739075*Zeta5533-38958/278509*Zeta8611
    -993429/3899126*z10*z3^2+4696509/7798252*z6*z5^2
    -55171021/1949563*z3*z13-539049410681/5068863800*z5*z11
    -1146118067441/11948036100*z7*z9-20218682509/1267215950*Zeta133
    +390507127/214451930*Zeta115+5337246/278509*z3*z11*z2
    +383655627/3899126*z5*z9*z2+11039197/708932*z2*Zeta113
    -41217529/11697378*z2*Zeta95+4525732/2658495*z4*Zeta93
    +77916/1392545*z5*Zeta533+929189/7798252*z6*Zeta73
    -175311/1392545*z8*Zeta53+12986/278509*z3^3*z7+155832/1949563*z3^2*z5^2
    -38958/1949563*z3^2*Zeta73+233748/1949563*z3*Zeta553
    -194790/1949563*z3*Zeta733,
  f[3,3,5,5] = -123379/25319*z4*z3*z9+54072/3617*z8*z3*z5
    +2865816/126595*z6*z3*z7-95611106/632975*z4*z5*z7
    -2072086101/2531900*z7^2*z2-513684/126595*Zeta7333
    +14526917/3164875*Zeta5533+27036/18085*Zeta8611+344709/126595*z10*z3^2
    -3712517/506380*z6*z5^2+38287482/126595*z3*z13
    +216136837851/164573500*z5*z11+73743346881/64653875*z7*z9
    +32911411431/164573500*Zeta133-655341663/27850900*Zeta115
    -7208929/36170*z3*z11*z2-165545979/126595*z5*z9*z2
    -52942511/253190*z2*Zeta113+6154769/126595*z2*Zeta95
    -40093534/1898925*z4*Zeta93-72157/90425*z5*Zeta533
    -209529/126595*z6*Zeta73+121662/90425*z8*Zeta53-9012/18085*z3^3*z7
    -305981/506380*z3^2*z5^2+27036/126595*z3^2*Zeta73
    -785761/632975*z3*Zeta553+27036/25319*z3*Zeta733+1/5*z5*z3*Zeta53,
  f[3,5,3,5] = 246758/25319*z4*z3*z9-108144/3617*z8*z3*z5
    -5731632/126595*z6*z3*z7+191222212/632975*z4*z5*z7
    +2072086101/1265950*z7^2*z2+1027368/126595*Zeta7333
    -29053834/3164875*Zeta5533-54072/18085*Zeta8611-689418/126595*z10*z3^2
    +3712517/253190*z6*z5^2-76574964/126595*z3*z13
    -216136837851/82286750*z5*z11-147486693762/64653875*z7*z9
    -32911411431/82286750*Zeta133+655341663/13925450*Zeta115
    +7208929/18085*z3*z11*z2+331091958/126595*z5*z9*z2
    +52942511/126595*z2*Zeta113-12309538/126595*z2*Zeta95
    +80187068/1898925*z4*Zeta93+144314/90425*z5*Zeta533
    +419058/126595*z6*Zeta73-243324/90425*z8*Zeta53+1/50*Zeta53^2
    +18024/18085*z3^3*z7+216288/126595*z3^2*z5^2-54072/126595*z3^2*Zeta73
    +1571522/632975*z3*Zeta553-54072/25319*z3*Zeta733-1/5*z5*z3*Zeta53,
  f[3,5,5,3] = 11/2*z3*z11*z2+z4*z3*z9-1/50*Zeta53^2+1/25*z3*Zeta553,
  f[5,3,3,5] = -9*z5*z9*z2-3/5*z4*z5*z7+1/2*z6*z5^2-1/50*Zeta53^2
    -1/5*z5*Zeta533,
  f[5,3,5,3] = -297396/25319*z4*z3*z9+108144/3617*z8*z3*z5
    +5731632/126595*z6*z3*z7-190462642/632975*z4*z5*z7
    -2072086101/1265950*z7^2*z2-1027368/126595*Zeta7333
    +29053834/3164875*Zeta5533+54072/18085*Zeta8611+689418/126595*z10*z3^2
    -3965707/253190*z6*z5^2+76574964/126595*z3*z13
    +216136837851/82286750*z5*z11+147486693762/64653875*z7*z9
    +32911411431/82286750*Zeta133-655341663/13925450*Zeta115
    -7407864/18085*z3*z11*z2-328813248/126595*z5*z9*z2
    -52942511/126595*z2*Zeta113+12309538/126595*z2*Zeta95
    -80187068/1898925*z4*Zeta93-108144/90425*z5*Zeta533
    -419058/126595*z6*Zeta73+243324/90425*z8*Zeta53+1/50*Zeta53^2
    -18024/18085*z3^3*z7-216288/126595*z3^2*z5^2+54072/126595*z3^2*Zeta73
    -324432/126595*z3*Zeta553+54072/25319*z3*Zeta733,
  f[5,5,3,3] = 148698/25319*z4*z3*z9-54072/3617*z8*z3*z5
    -2865816/126595*z6*z3*z7+95231321/632975*z4*z5*z7
    +2072086101/2531900*z7^2*z2+513684/126595*Zeta7333
    -14526917/3164875*Zeta5533-27036/18085*Zeta8611-344709/126595*z10*z3^2
    +3965707/506380*z6*z5^2-38287482/126595*z3*z13
    -216136837851/164573500*z5*z11-73743346881/64653875*z7*z9
    -32911411431/164573500*Zeta133+655341663/27850900*Zeta115
    +3703932/18085*z3*z11*z2+164406624/126595*z5*z9*z2
    +52942511/253190*z2*Zeta113-6154769/126595*z2*Zeta95
    +40093534/1898925*z4*Zeta93+54072/90425*z5*Zeta533
    +209529/126595*z6*Zeta73-121662/90425*z8*Zeta53+9012/18085*z3^3*z7
    +108144/126595*z3^2*z5^2-27036/126595*z3^2*Zeta73
    +162216/126595*z3*Zeta553-27036/25319*z3*Zeta733
 ] :
#