(********************************************************************) (* *) (* Ancillary file to *) (* "Lifting Heptagon Symbols to Functions" *) (* by L. J. Dixon and Y.-T. Liu *) (* arXiv:2007.12966 *) (* *) (* In the HO basis, the odd parts of the 3 loop amplitudes, and *) (* all of the 4 loop amplitudes' {6,1,1} odd coproducts span a *) (* space with a dimension of only 406 *) (* --- out of 412 possible weight 6 parity odd functions. *) (* Each such function consists of a symbol-level function, *) (* HO[6, i], with i = 1,2,...,406, *) (* plus a specific linear combination of the 6 beyond-the-symbol *) (* functions, HO(6,i), i = 407,408,...,412. *) (* These 406 linear combinations are given below. *) (* It is still possible that the 5 loop amplitudes will require *) (* all 412 functions, not just these 406. *) (* *) (********************************************************************) { HO[6, 1], HO[6, 2], HO[6, 3], HO[6, 4] - (436781*HO[6, 410])/1260 - (436781*HO[6, 412])/1260, HO[6, 5] - (183769*HO[6, 410])/504 + (878161*HO[6, 412])/2520, HO[6, 6] - (2922617*HO[6, 410])/2240 - (2922617*HO[6, 412])/2240, HO[6, 7], HO[6, 8] + (881633*HO[6, 410])/2520 + (299501*HO[6, 412])/420, HO[6, 9] - (7*HO[6, 410])/40, HO[6, 10] - (122775299*HO[6, 410])/20160 + (18339619*HO[6, 412])/6720, HO[6, 11] - (149083*HO[6, 410])/63 + (26385733*HO[6, 412])/20160, HO[6, 12] - (25209691*HO[6, 410])/20160 - (183769*HO[6, 412])/504, HO[6, 13] + (6746351*HO[6, 410])/2880 - (13547603*HO[6, 412])/6720, HO[6, 14] + (946433*HO[6, 410])/1680 + (436781*HO[6, 412])/1260, HO[6, 15] + (423*HO[6, 410])/16 + (878161*HO[6, 412])/2520, HO[6, 16] + (3955529*HO[6, 410])/4032 - (48030361*HO[6, 412])/20160, HO[6, 17] + (234607*HO[6, 410])/336 + (6082091*HO[6, 412])/6720, HO[6, 18] + (59371*HO[6, 410])/315 + (183769*HO[6, 412])/504, HO[6, 19] + (21197641*HO[6, 410])/20160, HO[6, 20] + (4045679*HO[6, 410])/2880, HO[6, 21] + (399183*HO[6, 410])/560 - (3786197*HO[6, 412])/20160, HO[6, 22] + (299501*HO[6, 410])/420 + (881633*HO[6, 412])/2520, HO[6, 23] + (13559867*HO[6, 410])/6720 - (12815147*HO[6, 412])/20160, HO[6, 24] + (7*HO[6, 412])/40, HO[6, 25] - (2523337*HO[6, 410])/5040 - (37031777*HO[6, 412])/20160, HO[6, 26] - (441037*HO[6, 410])/1260 - (943207*HO[6, 412])/1344, HO[6, 27] + (7159163*HO[6, 410])/5040 - (41957407*HO[6, 412])/20160, HO[6, 28] - (13547603*HO[6, 410])/6720 + (6746351*HO[6, 412])/2880, HO[6, 29] + (1453*HO[6, 410])/90 + (954433*HO[6, 412])/2520, HO[6, 30] + (878161*HO[6, 410])/2520 + (423*HO[6, 412])/16, HO[6, 31] - (439301*HO[6, 410])/1260 - (2511569*HO[6, 412])/2016, HO[6, 32] - (39873697*HO[6, 410])/20160 + (4901131*HO[6, 412])/2880, HO[6, 33] + (101881667*HO[6, 410])/20160 + (307663*HO[6, 412])/1120, HO[6, 34] + (2417429*HO[6, 410])/960 - (3564863*HO[6, 412])/4032, HO[6, 35] + (299501*HO[6, 410])/420 + (881633*HO[6, 412])/2520, HO[6, 36] + (298661*HO[6, 410])/420 - (8288513*HO[6, 412])/20160, HO[6, 37] + (3786197*HO[6, 410])/20160 - (399183*HO[6, 412])/560, HO[6, 38] + (7*HO[6, 410])/40 - (809035*HO[6, 412])/576, HO[6, 39] + (12815147*HO[6, 410])/20160 - (13559867*HO[6, 412])/6720, HO[6, 40] + (441037*HO[6, 410])/1260 + (452689*HO[6, 412])/840, HO[6, 41] + (2500609*HO[6, 410])/3360 - (299501*HO[6, 412])/420, HO[6, 42] - (1115663*HO[6, 410])/1680 - (878161*HO[6, 412])/2520, HO[6, 43] - (22692521*HO[6, 410])/20160 - (2533417*HO[6, 412])/5040, HO[6, 44] + (48235573*HO[6, 410])/20160 - (53404321*HO[6, 412])/10080, HO[6, 45] + (886673*HO[6, 410])/2520 - (4039919*HO[6, 412])/2880, HO[6, 46] + (95687*HO[6, 410])/336 - (1452263*HO[6, 412])/2520, HO[6, 47] + (5110383*HO[6, 410])/2240 - (4756007*HO[6, 412])/2880, HO[6, 48] + (436781*HO[6, 407])/1260 + (436781*HO[6, 409])/1260, HO[6, 49] + (183769*HO[6, 407])/504 - (878161*HO[6, 409])/2520, HO[6, 50] + (597469*HO[6, 407])/840 - (13547603*HO[6, 409])/6720, HO[6, 51] + (13547603*HO[6, 407])/6720 - (597469*HO[6, 409])/840, HO[6, 52] + (423*HO[6, 407])/16 + (878161*HO[6, 409])/2520, HO[6, 53] + (25327*HO[6, 407])/2240, HO[6, 54] + (591329*HO[6, 407])/720, HO[6, 55] + (6746351*HO[6, 407])/2880 - (13547603*HO[6, 409])/6720, HO[6, 56] + (29203*HO[6, 407])/720 + (299501*HO[6, 409])/420, HO[6, 57] - (5498509*HO[6, 407])/10080 - (597469*HO[6, 409])/840, HO[6, 58] + (881633*HO[6, 407])/2520 + (299501*HO[6, 409])/420, HO[6, 59] - (149675*HO[6, 407])/48 + (12046477*HO[6, 409])/20160, HO[6, 60] - (7*HO[6, 409])/40, HO[6, 61] - (299501*HO[6, 407])/420 + (2501197*HO[6, 409])/3360, HO[6, 62] - (4045679*HO[6, 407])/2880, HO[6, 63] - (809035*HO[6, 407])/576, HO[6, 64] - (398161*HO[6, 407])/560 + (3626527*HO[6, 409])/6720, HO[6, 65] - (13559867*HO[6, 407])/6720 + (12815147*HO[6, 409])/20160, HO[6, 66] - (8261*HO[6, 409])/240 - (886673*HO[6, 410])/2520 - (73*HO[6, 412])/40, HO[6, 67] - (597469*HO[6, 407])/840 - (1533247*HO[6, 409])/960, HO[6, 68] - (597469*HO[6, 407])/840 - (5498509*HO[6, 409])/10080, HO[6, 69] - (225815*HO[6, 409])/336, HO[6, 70] - (436781*HO[6, 411])/1260, HO[6, 71] - (195371*HO[6, 409])/504, HO[6, 72] - (183769*HO[6, 407])/504 - (678667*HO[6, 409])/630, HO[6, 73] + (156151*HO[6, 409])/720, HO[6, 74] - (3626527*HO[6, 407])/6720 + (398161*HO[6, 409])/560, HO[6, 75] - (13547603*HO[6, 407])/6720 + (6746351*HO[6, 409])/2880, HO[6, 76] + (18339619*HO[6, 407])/6720 - (1196471*HO[6, 409])/840, HO[6, 77] + (2501197*HO[6, 407])/3360 - (299501*HO[6, 409])/420, HO[6, 78] + (183769*HO[6, 407])/504 - (878161*HO[6, 409])/2520, HO[6, 79] + (7815151*HO[6, 409])/6720, HO[6, 80] - (1790783*HO[6, 407])/2520 + (61*HO[6, 409])/45, HO[6, 81] - (12046477*HO[6, 407])/20160 + (149675*HO[6, 409])/48, HO[6, 82] + (141347*HO[6, 407])/1008 - (241147*HO[6, 409])/144 + (117349*HO[6, 410])/168 + (878161*HO[6, 412])/2520, HO[6, 83] + (13559867*HO[6, 407])/6720 - (8213249*HO[6, 409])/2016, HO[6, 84] + (1115663*HO[6, 407])/1680 + (878161*HO[6, 409])/2520, HO[6, 85] + (23983081*HO[6, 407])/20160 - (48030361*HO[6, 409])/20160, HO[6, 86] + (4045679*HO[6, 409])/2880, HO[6, 87] - (631753*HO[6, 407])/840 + (878161*HO[6, 409])/2520, HO[6, 88] - (38282509*HO[6, 407])/20160 + (18916001*HO[6, 409])/20160, HO[6, 89] + (48771*HO[6, 409])/280, HO[6, 90] - (2922617*HO[6, 411])/2240, HO[6, 91] + (2678639*HO[6, 411])/2520, HO[6, 92] - (13364489*HO[6, 407])/5040 + (18339619*HO[6, 409])/6720, HO[6, 93] - (299501*HO[6, 407])/420 + (42692273*HO[6, 409])/20160, HO[6, 94] - (7*HO[6, 411])/40, HO[6, 95] - (109415119*HO[6, 407])/20160 + (38264153*HO[6, 409])/20160, HO[6, 96] + (21201169*HO[6, 411])/20160, HO[6, 97] + (48771*HO[6, 411])/280, HO[6, 98] - (954433*HO[6, 411])/2520, HO[6, 99] - (423*HO[6, 411])/16, HO[6, 100] + (591329*HO[6, 411])/720, HO[6, 101] - (13*HO[6, 411])/48, HO[6, 102] - (6746351*HO[6, 411])/2880, HO[6, 103] - (1446633*HO[6, 411])/560, HO[6, 104], HO[6, 105] - (40067729*HO[6, 411])/20160, HO[6, 106] + (399183*HO[6, 411])/560, HO[6, 107] + (809035*HO[6, 411])/576, HO[6, 108] + (299501*HO[6, 411])/420, HO[6, 109] + (13559867*HO[6, 411])/6720, HO[6, 110] + (183769*HO[6, 411])/504, HO[6, 111], HO[6, 112] + (183769*HO[6, 411])/504, HO[6, 113] + (183769*HO[6, 411])/504, HO[6, 114], HO[6, 115] - (299501*HO[6, 411])/420, HO[6, 116] + (183769*HO[6, 411])/504, HO[6, 117] + (299501*HO[6, 411])/420, HO[6, 118], HO[6, 119] + (26344643*HO[6, 411])/10080, HO[6, 120] + (3786197*HO[6, 411])/20160, HO[6, 121], HO[6, 122] - (13547603*HO[6, 411])/6720, HO[6, 123] + (8019757*HO[6, 411])/2240, HO[6, 124] - (299501*HO[6, 411])/420, HO[6, 125] - (62369617*HO[6, 411])/20160, HO[6, 126] - (22692521*HO[6, 411])/20160, HO[6, 127] - (12815147*HO[6, 411])/20160, HO[6, 128] + (15073*HO[6, 411])/480, HO[6, 129] + (7516891*HO[6, 411])/2880, HO[6, 130] - (2244197*HO[6, 411])/4032, HO[6, 131], HO[6, 132] + (436781*HO[6, 408])/1260 + (436781*HO[6, 410])/1260, HO[6, 133] + (183769*HO[6, 408])/504 - (878161*HO[6, 410])/2520, HO[6, 134] + (597469*HO[6, 408])/840 - (13547603*HO[6, 410])/6720, HO[6, 135] + (13547603*HO[6, 408])/6720 - (597469*HO[6, 410])/840, HO[6, 136] - (6746351*HO[6, 408])/2880 + (13547603*HO[6, 410])/6720, HO[6, 137] - (3153607*HO[6, 408])/2520 - (183769*HO[6, 410])/504, HO[6, 138] + (423*HO[6, 408])/16 + (878161*HO[6, 410])/2520, HO[6, 139] - (7122817*HO[6, 408])/20160 + (878161*HO[6, 410])/2520, HO[6, 140] - (8759521*HO[6, 411])/10080, HO[6, 141] - (47668097*HO[6, 411])/20160, HO[6, 142] + (149675*HO[6, 408])/48 - (12046477*HO[6, 410])/20160, HO[6, 143] + (881633*HO[6, 408])/2520 + (299501*HO[6, 410])/420, HO[6, 144] + (2678639*HO[6, 408])/2520, HO[6, 145] + (33583549*HO[6, 408])/10080 - (5320591*HO[6, 410])/5040, HO[6, 146] + (1080871*HO[6, 408])/672 + (597469*HO[6, 410])/840, HO[6, 147] + (82737*HO[6, 408])/560 - (9526261*HO[6, 410])/4032, HO[6, 148] - (3934401*HO[6, 408])/2240 - (73*HO[6, 410])/40, HO[6, 149] - (299501*HO[6, 408])/420 - (881633*HO[6, 410])/2520, HO[6, 150] - (399183*HO[6, 408])/560 + (3786197*HO[6, 410])/20160, HO[6, 151] - (13559867*HO[6, 408])/6720 + (12815147*HO[6, 410])/20160, HO[6, 152] - (809035*HO[6, 408])/576, HO[6, 153] - (6469*HO[6, 408])/360 - (306851*HO[6, 410])/420, HO[6, 154] + (4045679*HO[6, 410])/2880, HO[6, 155] + (21201169*HO[6, 410])/20160, HO[6, 156] + (436781*HO[6, 408])/1260 - (1640101*HO[6, 410])/5040, HO[6, 157] - (183769*HO[6, 408])/504 - (474527*HO[6, 410])/2520, HO[6, 158] - (436781*HO[6, 407])/1260 - (436781*HO[6, 412])/1260, HO[6, 159] - (183769*HO[6, 407])/504 + (878161*HO[6, 412])/2520, HO[6, 160] + (299501*HO[6, 407])/420 - (299501*HO[6, 412])/420, HO[6, 161], HO[6, 162] - (13547603*HO[6, 408])/6720 + (6746351*HO[6, 410])/2880, HO[6, 163] - (13547603*HO[6, 408])/6720 + (292069*HO[6, 410])/192, HO[6, 164] + (183769*HO[6, 408])/504 - (25571059*HO[6, 410])/20160, HO[6, 165] + (12815147*HO[6, 408])/20160 - (13559867*HO[6, 410])/6720, HO[6, 166] - (436781*HO[6, 408])/1260 + (16456957*HO[6, 410])/20160, HO[6, 167] + (1375867*HO[6, 408])/6720 - (503*HO[6, 410])/240, HO[6, 168] + (44188817*HO[6, 408])/20160 - (5314537*HO[6, 410])/1120, HO[6, 169], HO[6, 170] + (102574*HO[6, 408])/315 + (881633*HO[6, 410])/2520, HO[6, 171] - (379865*HO[6, 408])/336 - (11030123*HO[6, 410])/10080, HO[6, 172] - (12046477*HO[6, 408])/20160 + (149675*HO[6, 410])/48, HO[6, 173] - (37031777*HO[6, 408])/20160 - (2524219*HO[6, 410])/5040, HO[6, 174] - (488207*HO[6, 410])/1260, HO[6, 175], HO[6, 176] + (299501*HO[6, 408])/420 - (452689*HO[6, 410])/840, HO[6, 177] - (2922617*HO[6, 408])/2240 + (2836523*HO[6, 410])/720, HO[6, 178] + (5017181*HO[6, 408])/5040 - (11030123*HO[6, 410])/10080, HO[6, 179] + (47668097*HO[6, 408])/20160 - (12523999*HO[6, 410])/3360, HO[6, 180] + (13547603*HO[6, 407])/6720 - (597469*HO[6, 412])/840, HO[6, 181] + (597469*HO[6, 407])/840 - (13547603*HO[6, 412])/6720, HO[6, 182] - (19598431*HO[6, 408])/20160 - (5222383*HO[6, 410])/20160, HO[6, 183] - (379865*HO[6, 408])/336, HO[6, 184] - (841303*HO[6, 408])/4032 - (5950303*HO[6, 410])/6720, HO[6, 185] + (954433*HO[6, 407])/2520 + (1453*HO[6, 412])/90, HO[6, 186] + (1533247*HO[6, 407])/960 + (597469*HO[6, 412])/840, HO[6, 187] + (5498509*HO[6, 407])/10080 + (597469*HO[6, 412])/840, HO[6, 188] - (6746351*HO[6, 407])/2880 + (13547603*HO[6, 412])/6720, HO[6, 189] - (423*HO[6, 407])/16 - (878161*HO[6, 412])/2520, HO[6, 190] + (48771*HO[6, 407])/280, HO[6, 191] + (2678639*HO[6, 412])/2520, HO[6, 192] - (591329*HO[6, 412])/720, HO[6, 193] + (2236133*HO[6, 407])/4032 + (398161*HO[6, 412])/560, HO[6, 194] + (591329*HO[6, 407])/720, HO[6, 195] + (597469*HO[6, 407])/840 + (5498509*HO[6, 412])/10080, HO[6, 196] - (183769*HO[6, 407])/504 - (474527*HO[6, 412])/2520, HO[6, 197] - (878161*HO[6, 407])/2520 - (423*HO[6, 412])/16, HO[6, 198] - (399183*HO[6, 407])/560 + (3786197*HO[6, 412])/20160, HO[6, 199] - (3786197*HO[6, 407])/20160 + (399183*HO[6, 412])/560, HO[6, 200] + (809035*HO[6, 412])/576, HO[6, 201] + (47668097*HO[6, 407])/20160 - (1942217*HO[6, 412])/6720, HO[6, 202] - (597469*HO[6, 407])/840 - (7781*HO[6, 412])/240, HO[6, 203] - (488207*HO[6, 412])/1260, HO[6, 204] + (7815151*HO[6, 412])/6720, HO[6, 205] - (1999651*HO[6, 407])/1680 + (1756387*HO[6, 412])/1344, HO[6, 206] - (1606811*HO[6, 407])/480 + (22872673*HO[6, 412])/6720, HO[6, 207] + (1583723*HO[6, 407])/5040 - (183769*HO[6, 412])/504, HO[6, 208] - (488207*HO[6, 407])/1260, HO[6, 209] + (313531*HO[6, 407])/1120 - (567733*HO[6, 412])/420, HO[6, 210] - (21403007*HO[6, 407])/20160 + (26344643*HO[6, 412])/10080, HO[6, 211], HO[6, 212] + (12416171*HO[6, 407])/3360 - (41005073*HO[6, 412])/20160, HO[6, 213] + (111985*HO[6, 407])/126, HO[6, 214] - (7*HO[6, 412])/40, HO[6, 215], HO[6, 216] - (21160849*HO[6, 407])/20160 - (597469*HO[6, 412])/840, HO[6, 217] + (13*HO[6, 407])/48 - (11217457*HO[6, 412])/20160, HO[6, 218] + (3564269*HO[6, 407])/5040 + (928405*HO[6, 412])/4032, HO[6, 219] + (886673*HO[6, 407])/2520 - (8014499*HO[6, 412])/6720, HO[6, 220] - (330191*HO[6, 407])/252 + (6399973*HO[6, 412])/5040, HO[6, 221] - (809035*HO[6, 407])/576, HO[6, 222] + (436781*HO[6, 408])/1260, HO[6, 223] + (436781*HO[6, 409])/1260 + (436781*HO[6, 411])/1260, HO[6, 224] + (1691317*HO[6, 407])/20160 + (436781*HO[6, 412])/1260, HO[6, 225] + (183769*HO[6, 408])/504, HO[6, 226] + (13547603*HO[6, 408])/6720, HO[6, 227] + (306851*HO[6, 408])/420, HO[6, 228] - (19520269*HO[6, 407])/20160 + (2489561*HO[6, 412])/2016, HO[6, 229] - (1533247*HO[6, 408])/960, HO[6, 230] + (5498509*HO[6, 408])/10080, HO[6, 231] - (474527*HO[6, 408])/2520, HO[6, 232] - (591329*HO[6, 408])/720, HO[6, 233] + (183769*HO[6, 409])/504 - (878161*HO[6, 411])/2520, HO[6, 234] - (878161*HO[6, 409])/2520 + (183769*HO[6, 411])/504, HO[6, 235] - (1640101*HO[6, 408])/5040, HO[6, 236] + (2947379*HO[6, 408])/1344, HO[6, 237] + (12459067*HO[6, 408])/3360, HO[6, 238] + (9526261*HO[6, 409])/4032 - (183769*HO[6, 411])/504, HO[6, 239] + (1271*HO[6, 409])/90 + (183769*HO[6, 411])/504, HO[6, 240] - (1533247*HO[6, 409])/960 - (597469*HO[6, 411])/840, HO[6, 241] - (6746351*HO[6, 409])/2880 + (13547603*HO[6, 411])/6720, HO[6, 242] - (82737*HO[6, 409])/560 + (878161*HO[6, 411])/2520, HO[6, 243] - (21201169*HO[6, 409])/20160, HO[6, 244] - (399183*HO[6, 409])/560 + (3786197*HO[6, 411])/20160, HO[6, 245] + (299501*HO[6, 409])/420 - (2501197*HO[6, 411])/3360, HO[6, 246] - (809035*HO[6, 408])/576, HO[6, 247] - (13559867*HO[6, 408])/6720, HO[6, 248] + (4045679*HO[6, 408])/2880, HO[6, 249] - (809035*HO[6, 409])/576, HO[6, 250] - (988249*HO[6, 409])/3360 + (12046477*HO[6, 411])/20160, HO[6, 251] + (21403007*HO[6, 409])/20160 - (26344643*HO[6, 411])/10080, HO[6, 252] + 2*HO[6, 407] - (1640101*HO[6, 409])/5040 + (436781*HO[6, 411])/1260 - (597469*HO[6, 412])/840, HO[6, 253] - (48771*HO[6, 409])/280, HO[6, 254] + (2392487*HO[6, 408])/1680, HO[6, 255] - (13559867*HO[6, 409])/6720 + (12815147*HO[6, 411])/20160, HO[6, 256] + (73*HO[6, 408])/40, HO[6, 257] - (299501*HO[6, 408])/420, HO[6, 258] - (8213249*HO[6, 409])/2016 + (13559867*HO[6, 411])/6720, HO[6, 259] + (183769*HO[6, 408])/504, HO[6, 260] + (436781*HO[6, 411])/1260, HO[6, 261] + (13547603*HO[6, 408])/6720, HO[6, 262] + (7*HO[6, 411])/40, HO[6, 263] + (73*HO[6, 409])/40 + (886673*HO[6, 411])/2520, HO[6, 264] - (399183*HO[6, 408])/560, HO[6, 265] + (878161*HO[6, 408])/2520, HO[6, 266] + (3626527*HO[6, 408])/6720, HO[6, 267] - (2501197*HO[6, 408])/3360, HO[6, 268], HO[6, 269], HO[6, 270], HO[6, 271] - (436781*HO[6, 407])/1260 + (121532*HO[6, 408])/315 - (436781*HO[6, 412])/1260, HO[6, 272] + (12815147*HO[6, 408])/20160, HO[6, 273] - (6061661*HO[6, 408])/10080, HO[6, 274] - (878161*HO[6, 408])/2520, HO[6, 275] - (2995591*HO[6, 408])/1680, HO[6, 276] + (47668097*HO[6, 408])/20160, HO[6, 277] + (271403*HO[6, 408])/1260, HO[6, 278] + (900239*HO[6, 408])/1260, HO[6, 279] + (4732523*HO[6, 408])/3360, HO[6, 280] - (488207*HO[6, 408])/1260, HO[6, 281] - (113609*HO[6, 408])/840, HO[6, 282] - (41621219*HO[6, 408])/20160, HO[6, 283], HO[6, 284] - (436781*HO[6, 407])/1260 - (3190907*HO[6, 408])/2240 + (1533247*HO[6, 410])/960 - (436781*HO[6, 411])/1260 + (183769*HO[6, 412])/504, HO[6, 285] - (3564269*HO[6, 408])/5040, HO[6, 286] + (8261*HO[6, 411])/240, HO[6, 287] - (293299*HO[6, 409])/420 + (10917*HO[6, 411])/280, HO[6, 288] + (597469*HO[6, 409])/840 + (1533247*HO[6, 411])/960, HO[6, 289] + (597469*HO[6, 409])/840 + (5498509*HO[6, 411])/10080, HO[6, 290] + (13547603*HO[6, 409])/6720 - (6746351*HO[6, 411])/2880, HO[6, 291] - (436781*HO[6, 409])/1260 + (1640101*HO[6, 411])/5040, HO[6, 292] + (3786197*HO[6, 409])/20160 - (399183*HO[6, 411])/560, HO[6, 293] + (436781*HO[6, 409])/1260 + (1352861*HO[6, 411])/1008, HO[6, 294] - (19520269*HO[6, 409])/20160 + (2489561*HO[6, 411])/2016, HO[6, 295] - (1115663*HO[6, 409])/1680 - (878161*HO[6, 411])/2520, HO[6, 296] - (77243*HO[6, 409])/210 - (119879*HO[6, 411])/315, HO[6, 297] - (11217457*HO[6, 409])/20160 + (13*HO[6, 411])/48, HO[6, 298] - (5425681*HO[6, 409])/4032 + (18351883*HO[6, 411])/6720, HO[6, 299] + (194363*HO[6, 409])/504 - (886673*HO[6, 411])/2520, HO[6, 300] - (7815151*HO[6, 409])/6720, HO[6, 301] - (19397237*HO[6, 409])/20160 + (14765939*HO[6, 411])/5040, HO[6, 302] - (597469*HO[6, 409])/420 + (4235113*HO[6, 411])/2880, HO[6, 303] + (2244197*HO[6, 409])/4032 - (13*HO[6, 411])/48, HO[6, 304] - (8896207*HO[6, 409])/5040 + (3317221*HO[6, 411])/2016, HO[6, 305] - 2*HO[6, 407] + (55340353*HO[6, 409])/20160 - (12789149*HO[6, 411])/20160 + (597469*HO[6, 412])/840, HO[6, 306] + (886673*HO[6, 407])/2520 - (62406409*HO[6, 409])/20160 + (27165197*HO[6, 411])/20160 + (73*HO[6, 412])/40, HO[6, 307] - (183769*HO[6, 409])/504 + (24520009*HO[6, 411])/20160, HO[6, 308] + 2*HO[6, 407] - (707617*HO[6, 409])/5040 + (743669*HO[6, 411])/560 - (597469*HO[6, 412])/840, HO[6, 309] + (13559867*HO[6, 409])/6720 - (41064481*HO[6, 411])/10080, HO[6, 310] - (18339619*HO[6, 407])/6720 + (183769*HO[6, 408])/504 + (299501*HO[6, 409])/420 - (821399*HO[6, 410])/4032 - (8426647*HO[6, 412])/10080, HO[6, 311] + (299501*HO[6, 407])/420 - (1640101*HO[6, 410])/5040 - (37721*HO[6, 412])/720, HO[6, 312] + (299501*HO[6, 407])/420 + (25068227*HO[6, 409])/20160 - (6746351*HO[6, 410])/2880 + (2922617*HO[6, 412])/2240, HO[6, 313] - (8733679*HO[6, 407])/6720 - (7*HO[6, 408])/40 + (41460493*HO[6, 409])/20160 + (910333*HO[6, 410])/2520 + (1278155*HO[6, 411])/1008 - (6769159*HO[6, 412])/10080, HO[6, 314] + (117349*HO[6, 407])/168 + (1745759*HO[6, 408])/5040 + (183769*HO[6, 411])/504, HO[6, 315] + (12531773*HO[6, 407])/20160 - (12531773*HO[6, 409])/20160 - (22851601*HO[6, 410])/20160 + (2401937*HO[6, 411])/4032 + (4756007*HO[6, 412])/2880, HO[6, 316] - (878161*HO[6, 407])/2520 - (73*HO[6, 408])/40 + (13547603*HO[6, 409])/6720 - (719585*HO[6, 410])/504 - (881633*HO[6, 412])/2520, HO[6, 317] - (436781*HO[6, 407])/1260 + (30569293*HO[6, 408])/10080 + (183769*HO[6, 409])/504 - (306851*HO[6, 410])/420 - (2148619*HO[6, 411])/1008 - (436781*HO[6, 412])/1260, HO[6, 318] + (73*HO[6, 407])/40 + (1422709*HO[6, 408])/960 + (10625809*HO[6, 410])/3360 + (117349*HO[6, 411])/168 - (954433*HO[6, 412])/2520, HO[6, 319] + (183769*HO[6, 410])/504 - (183769*HO[6, 412])/504, HO[6, 320] + (922261*HO[6, 407])/2520 + (24701203*HO[6, 408])/2880 - (436781*HO[6, 409])/1260 - (373585*HO[6, 410])/2016 + (299501*HO[6, 411])/420 + (23050007*HO[6, 412])/20160, HO[6, 321] - (597469*HO[6, 409])/840 - (2011171*HO[6, 410])/5040 - (436781*HO[6, 411])/1260 + (183769*HO[6, 412])/504, HO[6, 322] + (5278775*HO[6, 407])/4032 - (597469*HO[6, 409])/840 + (2918529*HO[6, 410])/2240 - (878161*HO[6, 411])/2520 + 2*HO[6, 412], HO[6, 323] + (6469*HO[6, 407])/360 + (14723899*HO[6, 408])/10080 + (954433*HO[6, 409])/2520 - (436781*HO[6, 410])/1260 - (1287667*HO[6, 411])/672, HO[6, 324] + (18105947*HO[6, 407])/6720 - (842573*HO[6, 408])/2520 + (1341619*HO[6, 409])/1260 - (66977*HO[6, 410])/63 + (1287667*HO[6, 411])/672 + (395249*HO[6, 412])/280, HO[6, 325] + (183769*HO[6, 407])/504 - (436781*HO[6, 408])/1260 - (47649701*HO[6, 409])/10080 + (962603*HO[6, 410])/576 + (183769*HO[6, 411])/504 + (3855653*HO[6, 412])/4032, HO[6, 326] + (183769*HO[6, 407])/504 - (8769671*HO[6, 408])/6720 - (878161*HO[6, 409])/1260 - (299501*HO[6, 410])/420 - (454213*HO[6, 411])/720 - (293299*HO[6, 412])/420, HO[6, 327] - (1420957*HO[6, 407])/960 - (19520269*HO[6, 408])/20160 + (367099*HO[6, 410])/1344 - (597469*HO[6, 411])/840 + (4807759*HO[6, 412])/2880, HO[6, 328] + (183769*HO[6, 407])/504 + (1018373*HO[6, 408])/840 + (3577879*HO[6, 409])/1120 + (156151*HO[6, 410])/720 - (299501*HO[6, 411])/420 + (183769*HO[6, 412])/504, HO[6, 329] - (436781*HO[6, 407])/1260 + (886673*HO[6, 408])/2520 + (38681339*HO[6, 409])/20160 - (4756007*HO[6, 410])/2880 + (3626527*HO[6, 411])/6720 - (40317337*HO[6, 412])/20160, HO[6, 330] - (13765471*HO[6, 407])/6720 + (878161*HO[6, 408])/2520 + (10003717*HO[6, 409])/20160 - (183769*HO[6, 410])/504 + (21537163*HO[6, 411])/10080 - (6469*HO[6, 412])/360, HO[6, 331] - (2590477*HO[6, 407])/5040 - (3046607*HO[6, 408])/2520 - (84683*HO[6, 409])/1260 + (15788473*HO[6, 410])/10080 + (293299*HO[6, 412])/420, HO[6, 332] + (2683679*HO[6, 408])/2520 + (5226377*HO[6, 410])/4032 - (7598957*HO[6, 412])/6720, HO[6, 333] - (53107301*HO[6, 407])/20160 + (299501*HO[6, 408])/420 - (183769*HO[6, 410])/504 + (2922617*HO[6, 411])/2240 - (662197*HO[6, 412])/2520, HO[6, 334] - (2992103*HO[6, 407])/6720 + (371891*HO[6, 408])/420 - (1524109*HO[6, 409])/20160 + (4721371*HO[6, 410])/2880 - (12046477*HO[6, 411])/20160 - (132188093*HO[6, 412])/20160, HO[6, 335] + (120289*HO[6, 407])/168 + (3454747*HO[6, 408])/2880 + (1751*HO[6, 409])/120 + (29203*HO[6, 410])/720 - (15299789*HO[6, 412])/5040, HO[6, 336] - (301187*HO[6, 407])/448 - (949793*HO[6, 408])/1680 - (25941289*HO[6, 409])/20160 + (25946509*HO[6, 410])/6720 + (601787*HO[6, 411])/672 - (98629231*HO[6, 412])/20160, HO[6, 337] + (4790381*HO[6, 407])/1440 + (65053981*HO[6, 408])/20160 - (930529*HO[6, 409])/420 - (24725927*HO[6, 410])/20160 - (11257535*HO[6, 411])/4032 + (4761073*HO[6, 412])/2880, HO[6, 338] + (173495*HO[6, 407])/576 + (599149*HO[6, 408])/840 - (597469*HO[6, 410])/840 - (361114*HO[6, 411])/315 - (58741*HO[6, 412])/315, HO[6, 339] + (5737847*HO[6, 407])/2240 + (367811*HO[6, 408])/1008 - (979441*HO[6, 409])/672 - (299501*HO[6, 410])/210 - (7*HO[6, 411])/40 + (641923*HO[6, 412])/160, HO[6, 340] - (2439787*HO[6, 407])/960 + (4303543*HO[6, 408])/2880 - (1671041*HO[6, 409])/5040 + (3106271*HO[6, 410])/2880 - (582853*HO[6, 411])/1680 + (31926331*HO[6, 412])/20160, HO[6, 341] + (34620917*HO[6, 407])/3360 + (599149*HO[6, 408])/840 - (36486959*HO[6, 409])/4032 + (436781*HO[6, 410])/1260 - (436781*HO[6, 411])/1260 - (12746561*HO[6, 412])/2880, HO[6, 342] + (886673*HO[6, 408])/2520 - (597469*HO[6, 409])/840 - (7359439*HO[6, 411])/5040 + (597469*HO[6, 412])/840, HO[6, 343] - (1229041*HO[6, 407])/2016 + (4557793*HO[6, 408])/4032 + (23058757*HO[6, 409])/10080 + (11405603*HO[6, 410])/10080 + (4750247*HO[6, 411])/2880 + (8186281*HO[6, 412])/2240, HO[6, 344] + (1434383*HO[6, 407])/2520 + (3946471*HO[6, 409])/2520 - (878161*HO[6, 410])/2520 + (47668097*HO[6, 411])/20160 - (66977*HO[6, 412])/63, HO[6, 345] + (2590027*HO[6, 407])/3360 - (76907*HO[6, 410])/720 + (545291*HO[6, 412])/5040, HO[6, 346] + (14751803*HO[6, 408])/2240 - (554489*HO[6, 409])/5040 - (432727*HO[6, 410])/1120 - (299501*HO[6, 412])/420, HO[6, 347] - (66977*HO[6, 407])/63 + (183769*HO[6, 410])/504, HO[6, 348] + (2041229*HO[6, 407])/5040 + (1724647*HO[6, 408])/2520 - (886673*HO[6, 409])/2520 - (12451883*HO[6, 410])/4032 + (299501*HO[6, 411])/420 + (38379577*HO[6, 412])/20160, HO[6, 349] + (12408829*HO[6, 407])/4032 + (366847*HO[6, 408])/280 - (881633*HO[6, 409])/2520 - (2876633*HO[6, 410])/3360 - (25249859*HO[6, 411])/20160 + (1307321*HO[6, 412])/6720, HO[6, 350] + 2*HO[6, 407] - (76948547*HO[6, 408])/20160 - (183769*HO[6, 409])/504 - (27912319*HO[6, 410])/20160 - (62360153*HO[6, 411])/20160 - (19356917*HO[6, 412])/20160, HO[6, 351] - (73*HO[6, 407])/40 + (103471*HO[6, 408])/1440 + (5438389*HO[6, 409])/20160 + (423*HO[6, 410])/16 - (12531773*HO[6, 411])/20160 + (333821*HO[6, 412])/315, HO[6, 352] - (21500113*HO[6, 407])/10080 + (306851*HO[6, 408])/420 + (2683679*HO[6, 409])/2520 + (5117347*HO[6, 410])/20160 + (2922617*HO[6, 411])/2240 - (475037*HO[6, 412])/252, HO[6, 353] + (4757359*HO[6, 407])/2880 - (105317833*HO[6, 408])/10080 - (183769*HO[6, 409])/504 + (66830587*HO[6, 410])/20160 - (599149*HO[6, 411])/840 - (52156351*HO[6, 412])/20160, HO[6, 354] - (34491571*HO[6, 407])/10080 - (553381*HO[6, 408])/240 + (105923*HO[6, 409])/504 - (117349*HO[6, 410])/168 - (2615113*HO[6, 411])/2520 - (22069*HO[6, 412])/63, HO[6, 355] + (25681769*HO[6, 407])/20160 + (12789149*HO[6, 408])/20160 + (44176579*HO[6, 409])/10080 - (6615247*HO[6, 410])/6720 + (299501*HO[6, 411])/420 - (15066439*HO[6, 412])/10080, HO[6, 356] - (11031887*HO[6, 407])/10080 - (910333*HO[6, 409])/2520 + (230861*HO[6, 411])/630 + (37373717*HO[6, 412])/6720, HO[6, 357] - (88981*HO[6, 407])/280 - (2533417*HO[6, 408])/5040 + (436781*HO[6, 409])/1260 + (1293889*HO[6, 410])/2240 - (2922617*HO[6, 411])/2240 + (18348677*HO[6, 412])/6720, HO[6, 358] + (91392401*HO[6, 407])/20160 + (113236531*HO[6, 409])/20160 + (299501*HO[6, 410])/420 + (299501*HO[6, 411])/420 - (9095417*HO[6, 412])/5040, HO[6, 359] - (878161*HO[6, 407])/2520 - (878161*HO[6, 408])/2520 + (183769*HO[6, 409])/504 - (3686237*HO[6, 410])/5040 - (5401763*HO[6, 411])/2240 + (60069593*HO[6, 412])/20160, HO[6, 360] + (902759*HO[6, 407])/1260 - (73*HO[6, 408])/40 + (13559867*HO[6, 409])/6720 - (63883669*HO[6, 410])/20160 - (597469*HO[6, 411])/840 - (5577869*HO[6, 412])/3360, HO[6, 361] + (6105157*HO[6, 407])/1440 + (11334271*HO[6, 408])/5040 - (922261*HO[6, 409])/2520 - (229601*HO[6, 410])/630 - (4756007*HO[6, 411])/2880 - (40962973*HO[6, 412])/20160, HO[6, 362] - (29998231*HO[6, 407])/10080 - (4264223*HO[6, 408])/2880 + (508647*HO[6, 409])/224 - (118660447*HO[6, 410])/20160 + (51950699*HO[6, 411])/10080 + (13349489*HO[6, 412])/6720, HO[6, 363] - (183769*HO[6, 408])/504 + (878161*HO[6, 410])/2520 - (21201169*HO[6, 412])/20160, HO[6, 364] + (46848593*HO[6, 407])/6720 + (441037*HO[6, 408])/1260 - (47956777*HO[6, 409])/20160 - (41951947*HO[6, 410])/20160 - (183769*HO[6, 411])/504 - (18509153*HO[6, 412])/20160, HO[6, 365] + (18339619*HO[6, 407])/6720 - (299501*HO[6, 408])/420 - (117100843*HO[6, 410])/20160 - (299501*HO[6, 411])/420 - (13511219*HO[6, 412])/6720, HO[6, 366] - (3167099*HO[6, 407])/2520 - (436781*HO[6, 408])/1260 + (463657*HO[6, 409])/336 + (679927*HO[6, 410])/630 - (183769*HO[6, 411])/504 - (18637189*HO[6, 412])/20160, HO[6, 367] - 2*HO[6, 407] - (299501*HO[6, 410])/420 + (1196471*HO[6, 412])/840, HO[6, 368] - (10923791*HO[6, 407])/2520 - (968479*HO[6, 409])/576 + (654569*HO[6, 410])/10080 - (6535219*HO[6, 412])/10080, HO[6, 369] + (158161463*HO[6, 407])/20160 - (29092513*HO[6, 408])/20160 - (25421509*HO[6, 409])/10080 + (2607977*HO[6, 410])/1120 + (8193953*HO[6, 411])/4032 - (34513393*HO[6, 412])/6720, HO[6, 370] - (82774667*HO[6, 407])/10080 + (130180247*HO[6, 409])/20160 + (878161*HO[6, 410])/2520 + (37148561*HO[6, 411])/10080 + (2922617*HO[6, 412])/2240, HO[6, 371] - (20761*HO[6, 407])/84 - (117349*HO[6, 410])/168 + (23807*HO[6, 411])/720 - (394689*HO[6, 412])/280, HO[6, 372] - (62264729*HO[6, 407])/20160 + (29653937*HO[6, 408])/20160 - (2449501*HO[6, 409])/5040 - (84094951*HO[6, 410])/20160 + (7029691*HO[6, 411])/2240 - (24414203*HO[6, 412])/20160, HO[6, 373] - (48030361*HO[6, 407])/20160 + (597469*HO[6, 408])/840 + (4222987*HO[6, 409])/10080 + (4807759*HO[6, 410])/2880 - (293299*HO[6, 411])/420 + (4891907*HO[6, 412])/2880, HO[6, 374] + (212465*HO[6, 407])/112 - (3614263*HO[6, 408])/6720 - (2707339*HO[6, 409])/2520 - (4687069*HO[6, 410])/5040 - (463067*HO[6, 411])/720 - (2129573*HO[6, 412])/1120, HO[6, 375] + (1246459*HO[6, 407])/576 + (120107*HO[6, 408])/168 + (886673*HO[6, 409])/2520 - (4929499*HO[6, 410])/2880 + (299501*HO[6, 411])/420 - (42680873*HO[6, 412])/20160, HO[6, 376] - (117349*HO[6, 407])/168 + (44615591*HO[6, 408])/10080 - (878161*HO[6, 409])/2520 + (2842067*HO[6, 410])/4032 - (4202203*HO[6, 411])/2520 - (51103261*HO[6, 412])/10080, HO[6, 377] - (4394063*HO[6, 407])/3360 - (878161*HO[6, 408])/2520 - (878161*HO[6, 410])/2520 - (12639517*HO[6, 411])/3360 + (230861*HO[6, 412])/630, HO[6, 378] - (2501197*HO[6, 407])/3360 - (7166597*HO[6, 408])/10080 - (2594051*HO[6, 410])/960 + (19418201*HO[6, 411])/20160, HO[6, 379] - (62112241*HO[6, 407])/20160 - (11443697*HO[6, 408])/10080 + (26871029*HO[6, 409])/20160 - (683633*HO[6, 410])/1008 + (18690803*HO[6, 411])/4032 + (794327*HO[6, 412])/1680, HO[6, 380] - (897437*HO[6, 407])/3360 + (44155453*HO[6, 408])/10080 - (13106197*HO[6, 409])/2240 + (91129679*HO[6, 410])/20160 + (117349*HO[6, 411])/168 - (2679679*HO[6, 412])/504, HO[6, 381] + (597469*HO[6, 407])/840 - (8611193*HO[6, 408])/5040 - (54656593*HO[6, 409])/20160 - (949793*HO[6, 410])/1680 + (3715871*HO[6, 411])/2016 + (54976757*HO[6, 412])/20160, HO[6, 382] + (67384097*HO[6, 407])/20160 + (16421353*HO[6, 408])/6720 + (2150891*HO[6, 410])/576 - (299501*HO[6, 411])/210 - (22251281*HO[6, 412])/10080, HO[6, 383] - (29323051*HO[6, 407])/20160 + (5501879*HO[6, 408])/1440 - (6840731*HO[6, 409])/4032 - (144038581*HO[6, 410])/20160 + (395249*HO[6, 411])/280 + (26345653*HO[6, 412])/20160, HO[6, 384] - (3681359*HO[6, 407])/1440 + (36774343*HO[6, 408])/20160 + (992683*HO[6, 409])/336 - (8312681*HO[6, 410])/4032 - (11496847*HO[6, 411])/10080 + (5356173*HO[6, 412])/2240, HO[6, 385] + (436781*HO[6, 407])/1260 + (3594593*HO[6, 408])/4032 + (2698561*HO[6, 410])/3360 + (47668097*HO[6, 411])/20160 - (454337*HO[6, 412])/315, HO[6, 386] - (6114571*HO[6, 407])/2016 - (62082169*HO[6, 408])/20160 + (158906*HO[6, 409])/315 - (62900597*HO[6, 410])/6720 - (680149*HO[6, 411])/2520 + (117376991*HO[6, 412])/20160, HO[6, 387] - (87877*HO[6, 408])/168 - (21151*HO[6, 410])/140 + (230861*HO[6, 411])/630, HO[6, 388] - (14831797*HO[6, 407])/20160 + (1369361*HO[6, 408])/288 + (1048353*HO[6, 409])/448 + (3851249*HO[6, 410])/6720 - (436781*HO[6, 411])/1260 - (18339619*HO[6, 412])/6720, HO[6, 389] + (3580019*HO[6, 407])/2520 + (5802281*HO[6, 408])/2016 + (13855097*HO[6, 409])/10080 + (40927513*HO[6, 410])/20160 - (20305687*HO[6, 411])/2016 + (41857253*HO[6, 412])/20160, HO[6, 390] - (299501*HO[6, 410])/420 - (183769*HO[6, 411])/504 + (299501*HO[6, 412])/420, HO[6, 391] - (298661*HO[6, 407])/420 + (597469*HO[6, 408])/840 - (17820787*HO[6, 409])/20160 - (436781*HO[6, 410])/1260 + (9051911*HO[6, 411])/6720 + (2922617*HO[6, 412])/2240, HO[6, 392] - (3632449*HO[6, 407])/4032 - (1133467*HO[6, 408])/1260 - (20698387*HO[6, 409])/20160 + (538127*HO[6, 410])/2520 + (399183*HO[6, 411])/560 + (399183*HO[6, 412])/560, HO[6, 393] - (340979*HO[6, 407])/5040 - (465561*HO[6, 408])/160 - (92969*HO[6, 409])/144 + (1594105*HO[6, 410])/4032 + (183769*HO[6, 411])/504 + (18351883*HO[6, 412])/6720, HO[6, 394] + (5018063*HO[6, 407])/5040 + (73*HO[6, 409])/40 + (399183*HO[6, 410])/560 - (42416207*HO[6, 412])/20160, HO[6, 395] - (587831*HO[6, 407])/576 - (183769*HO[6, 408])/504 + (17868077*HO[6, 409])/20160 + (184669*HO[6, 410])/140 - (5427971*HO[6, 411])/5040 - (76045189*HO[6, 412])/20160, HO[6, 396] + (9152779*HO[6, 407])/6720 + (1795823*HO[6, 408])/2520 + (40132511*HO[6, 409])/10080 - (2162527*HO[6, 410])/5040 - (398161*HO[6, 411])/560 + (2852813*HO[6, 412])/1260, HO[6, 397] - (36140119*HO[6, 407])/10080 - (10259021*HO[6, 408])/20160 + (298921*HO[6, 409])/80 + (4688241*HO[6, 410])/2240 + (19640483*HO[6, 411])/10080 - (24949079*HO[6, 412])/10080, HO[6, 398] - (13388569*HO[6, 407])/4032 + (24234997*HO[6, 408])/20160 + (29252627*HO[6, 409])/20160 - (36427303*HO[6, 410])/6720 + (44399*HO[6, 411])/112 + (1705181*HO[6, 412])/720, HO[6, 399] - (886673*HO[6, 407])/2520 + (2491757*HO[6, 408])/5040 - (32207333*HO[6, 409])/20160 - (154889*HO[6, 410])/180 + (12095427*HO[6, 411])/2240 + (14707267*HO[6, 412])/10080, HO[6, 400] + (441037*HO[6, 407])/1260 + (230861*HO[6, 408])/630 + (5433067*HO[6, 409])/5040 - (4252033*HO[6, 410])/3360 - (474219*HO[6, 411])/448 - (8131289*HO[6, 412])/20160, HO[6, 401] - (5228891*HO[6, 407])/5040 - (1312501*HO[6, 408])/2520 + (133805447*HO[6, 409])/20160 - (471853*HO[6, 410])/336 - (3314507*HO[6, 411])/720 + (41953879*HO[6, 412])/20160, HO[6, 402] - (299501*HO[6, 407])/420 - (183769*HO[6, 408])/504 + (26207257*HO[6, 409])/6720 + (2764721*HO[6, 410])/960 - (3565753*HO[6, 411])/2520 - (5989621*HO[6, 412])/4032, HO[6, 403] - (1873*HO[6, 407])/360 - (1255073*HO[6, 408])/2520 + (17868077*HO[6, 409])/20160 - (223697*HO[6, 410])/1680 - (2367973*HO[6, 411])/1680 - (230861*HO[6, 412])/630, HO[6, 404] - (436781*HO[6, 407])/1260 + (829791*HO[6, 408])/112 + (46091*HO[6, 409])/126 - (36323839*HO[6, 410])/20160 + (9096461*HO[6, 411])/2880 + (299501*HO[6, 412])/420, HO[6, 405] + (52660031*HO[6, 407])/20160 - (1312501*HO[6, 408])/2520 - (40289869*HO[6, 409])/10080 - (6773503*HO[6, 410])/5040 - (11610283*HO[6, 411])/20160 + (18326179*HO[6, 412])/6720, HO[6, 406] - (31649321*HO[6, 407])/20160 + (2458969*HO[6, 408])/2520 + (1020853*HO[6, 409])/420 - (649687*HO[6, 410])/448 - (14629177*HO[6, 411])/5040 + (7157399*HO[6, 412])/5040 }