# Properties

 Label 108.6 Level 108 Weight 6 Dimension 731 Nonzero newspaces 6 Newform subspaces 11 Sturm bound 3888 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$108\( 108 = 2^{2} \cdot 3^{3}$$ \) Weight: $$k$$ = $$6$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$3888$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(108))$$.

Total New Old
Modular forms 1695 763 932
Cusp forms 1545 731 814
Eisenstein series 150 32 118

## Trace form

 $$731q - 3q^{2} + 3q^{4} - 72q^{5} - 6q^{6} - 2q^{7} - 9q^{8} + 318q^{9} + O(q^{10})$$ $$731q - 3q^{2} + 3q^{4} - 72q^{5} - 6q^{6} - 2q^{7} - 9q^{8} + 318q^{9} - 405q^{10} - 1434q^{11} + 1173q^{12} + 568q^{13} + 3027q^{14} + 531q^{15} - 2685q^{16} - 5766q^{17} - 5697q^{18} - 209q^{19} + 2475q^{20} + 12882q^{21} + 4803q^{22} + 7707q^{23} + 8988q^{24} - 6736q^{25} - 17415q^{27} - 7206q^{28} + 33375q^{29} - 18135q^{30} + 2896q^{31} + 14457q^{32} + 12342q^{33} + 1431q^{34} - 45375q^{35} + 35664q^{36} - 40325q^{37} + 29745q^{38} - 10545q^{39} + 13419q^{40} + 174162q^{41} - 25506q^{42} + 57448q^{43} - 158049q^{44} - 35781q^{45} - 27651q^{46} - 31932q^{47} + 14469q^{48} - 93090q^{49} + 66756q^{50} + 42831q^{51} - 3465q^{52} - 120990q^{53} + 231414q^{54} - 75942q^{55} + 172449q^{56} + 72048q^{57} + 10743q^{58} + 95925q^{59} - 326058q^{60} + 92380q^{61} - 461448q^{62} - 98115q^{63} + 14637q^{64} - 95976q^{65} - 24771q^{66} + 16903q^{67} + 357870q^{68} + 345801q^{69} + 227715q^{70} - 161556q^{71} + 110388q^{72} - 292772q^{73} + 40803q^{74} - 75273q^{75} + 111135q^{76} + 183600q^{77} + 178248q^{78} + 62164q^{79} - 7926q^{81} + 63030q^{82} + 152226q^{83} - 307308q^{84} - 125652q^{85} - 558483q^{86} - 201483q^{87} - 198645q^{88} - 222162q^{89} - 840048q^{90} - 421192q^{91} - 600627q^{92} - 526815q^{93} - 156753q^{94} + 251274q^{95} + 992022q^{96} + 190771q^{97} + 1307970q^{98} + 13635q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(108))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
108.6.a $$\chi_{108}(1, \cdot)$$ 108.6.a.a 1 1
108.6.a.b 2
108.6.a.c 2
108.6.a.d 2
108.6.b $$\chi_{108}(107, \cdot)$$ 108.6.b.a 4 1
108.6.b.b 16
108.6.b.c 20
108.6.e $$\chi_{108}(37, \cdot)$$ 108.6.e.a 10 2
108.6.h $$\chi_{108}(35, \cdot)$$ 108.6.h.a 56 2
108.6.i $$\chi_{108}(13, \cdot)$$ 108.6.i.a 90 6
108.6.l $$\chi_{108}(11, \cdot)$$ 108.6.l.a 528 6

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(108))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(108)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 9}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 52 T^{2} + 1024 T^{4}$$)($$1 - 47 T^{2} + 1060 T^{4} - 30080 T^{6} + 762880 T^{8} - 30801920 T^{10} + 1111490560 T^{12} - 50465865728 T^{14} + 1099511627776 T^{16}$$)($$1 - 10 T^{2} + 1092 T^{4} - 9504 T^{6} - 1286400 T^{8} - 761856 T^{10} - 1317273600 T^{12} - 9965666304 T^{14} + 1172526071808 T^{16} - 10995116277760 T^{18} + 1125899906842624 T^{20}$$)
$3$ 1
$5$ ($$1 + 3125 T^{2}$$)($$1 + 2929 T^{2} + 9765625 T^{4}$$)($$1 + 2929 T^{2} + 9765625 T^{4}$$)($$1 - 1526 T^{2} + 9765625 T^{4}$$)($$( 1 + 2131 T^{2} + 9765625 T^{4} )^{2}$$)($$( 1 - 14972 T^{2} + 119342578 T^{4} - 617133972224 T^{6} + 2271820128564475 T^{8} - 6026698947500000000 T^{10} +$$$$11\!\cdots\!50$$$$T^{12} -$$$$13\!\cdots\!00$$$$T^{14} +$$$$90\!\cdots\!25$$$$T^{16} )^{2}$$)($$( 1 - 11818 T^{2} + 71630853 T^{4} - 313823973048 T^{6} + 1185932779192818 T^{8} - 3986228637264265212 T^{10} +$$$$11\!\cdots\!50$$$$T^{12} -$$$$29\!\cdots\!00$$$$T^{14} +$$$$66\!\cdots\!25$$$$T^{16} -$$$$10\!\cdots\!50$$$$T^{18} +$$$$88\!\cdots\!25$$$$T^{20} )^{2}$$)($$1 - 21 T - 5203 T^{2} + 519930 T^{3} + 14035794 T^{4} - 2854822770 T^{5} + 76722872007 T^{6} + 9761967315441 T^{7} - 599011867854189 T^{8} - 11924309583255600 T^{9} + 2533145723872694124 T^{10} - 37263467447673750000 T^{11} -$$$$58\!\cdots\!25$$$$T^{12} +$$$$29\!\cdots\!25$$$$T^{13} +$$$$73\!\cdots\!75$$$$T^{14} -$$$$85\!\cdots\!50$$$$T^{15} +$$$$13\!\cdots\!50$$$$T^{16} +$$$$15\!\cdots\!50$$$$T^{17} -$$$$47\!\cdots\!75$$$$T^{18} -$$$$59\!\cdots\!25$$$$T^{19} +$$$$88\!\cdots\!25$$$$T^{20}$$)
$7$ ($$1 + 25 T + 16807 T^{2}$$)($$1 + 32 T + 3981 T^{2} + 537824 T^{3} + 282475249 T^{4}$$)($$1 + 32 T + 3981 T^{2} + 537824 T^{3} + 282475249 T^{4}$$)($$( 1 - 29 T + 16807 T^{2} )^{2}$$)($$( 1 - 8471 T^{2} + 282475249 T^{4} )^{2}$$)($$( 1 - 54884 T^{2} + 1251149938 T^{4} - 15826547698400 T^{6} + 189674874534565723 T^{8} -$$$$44\!\cdots\!00$$$$T^{10} +$$$$99\!\cdots\!38$$$$T^{12} -$$$$12\!\cdots\!16$$$$T^{14} +$$$$63\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 72919 T^{2} + 2924383791 T^{4} - 81340986295962 T^{6} + 1774418094261308301 T^{8} -$$$$32\!\cdots\!57$$$$T^{10} +$$$$50\!\cdots\!49$$$$T^{12} -$$$$64\!\cdots\!62$$$$T^{14} +$$$$65\!\cdots\!59$$$$T^{16} -$$$$46\!\cdots\!19$$$$T^{18} +$$$$17\!\cdots\!49$$$$T^{20} )^{2}$$)($$1 - 29 T - 39569 T^{2} + 3762444 T^{3} + 440397336 T^{4} - 77352503496 T^{5} - 2769093584103 T^{6} - 560172784984473 T^{7} + 238615372451780007 T^{8} + 16031898530170676332 T^{9} -$$$$69\!\cdots\!60$$$$T^{10} +$$$$26\!\cdots\!24$$$$T^{11} +$$$$67\!\cdots\!43$$$$T^{12} -$$$$26\!\cdots\!39$$$$T^{13} -$$$$22\!\cdots\!03$$$$T^{14} -$$$$10\!\cdots\!72$$$$T^{15} +$$$$99\!\cdots\!64$$$$T^{16} +$$$$14\!\cdots\!92$$$$T^{17} -$$$$25\!\cdots\!69$$$$T^{18} -$$$$31\!\cdots\!03$$$$T^{19} +$$$$17\!\cdots\!49$$$$T^{20}$$)
$11$ ($$1 + 161051 T^{2}$$)($$1 + 486 T + 168607 T^{2} + 78270786 T^{3} + 25937424601 T^{4}$$)($$1 - 486 T + 168607 T^{2} - 78270786 T^{3} + 25937424601 T^{4}$$)($$1 + 314326 T^{2} + 25937424601 T^{4}$$)($$( 1 - 14573 T^{2} + 25937424601 T^{4} )^{2}$$)($$( 1 + 741148 T^{2} + 299964078250 T^{4} + 79656648391789648 T^{6} +$$$$15\!\cdots\!99$$$$T^{8} +$$$$20\!\cdots\!48$$$$T^{10} +$$$$20\!\cdots\!50$$$$T^{12} +$$$$12\!\cdots\!48$$$$T^{14} +$$$$45\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 822230 T^{2} + 360495679845 T^{4} + 108431998645925448 T^{6} +$$$$24\!\cdots\!70$$$$T^{8} +$$$$44\!\cdots\!92$$$$T^{10} +$$$$64\!\cdots\!70$$$$T^{12} +$$$$72\!\cdots\!48$$$$T^{14} +$$$$62\!\cdots\!45$$$$T^{16} +$$$$37\!\cdots\!30$$$$T^{18} +$$$$11\!\cdots\!01$$$$T^{20} )^{2}$$)($$1 + 177 T - 396232 T^{2} + 71434269 T^{3} + 104816625882 T^{4} - 33726096455301 T^{5} - 6913987980717606 T^{6} + 8552599160812456257 T^{7} -$$$$10\!\cdots\!51$$$$T^{8} -$$$$50\!\cdots\!82$$$$T^{9} +$$$$47\!\cdots\!16$$$$T^{10} -$$$$81\!\cdots\!82$$$$T^{11} -$$$$27\!\cdots\!51$$$$T^{12} +$$$$35\!\cdots\!07$$$$T^{13} -$$$$46\!\cdots\!06$$$$T^{14} -$$$$36\!\cdots\!51$$$$T^{15} +$$$$18\!\cdots\!82$$$$T^{16} +$$$$20\!\cdots\!19$$$$T^{17} -$$$$17\!\cdots\!32$$$$T^{18} +$$$$12\!\cdots\!27$$$$T^{19} +$$$$11\!\cdots\!01$$$$T^{20}$$)
$13$ ($$1 + 427 T + 371293 T^{2}$$)($$1 - 208 T + 275178 T^{2} - 77228944 T^{3} + 137858491849 T^{4}$$)($$1 - 208 T + 275178 T^{2} - 77228944 T^{3} + 137858491849 T^{4}$$)($$( 1 - 329 T + 371293 T^{2} )^{2}$$)($$( 1 + 166 T + 371293 T^{2} )^{4}$$)($$( 1 - 224 T + 554236 T^{2} + 77263648 T^{3} + 200668790230 T^{4} + 28687451656864 T^{5} + 76406139088422364 T^{6} - 11465640035156329568 T^{7} +$$$$19\!\cdots\!01$$$$T^{8} )^{4}$$)($$( 1 + 29 T + 791115 T^{2} + 39777006 T^{3} + 380980388709 T^{4} + 35518566649227 T^{5} + 141455351464930737 T^{6} + 5483598057428624094 T^{7} +$$$$40\!\cdots\!55$$$$T^{8} +$$$$55\!\cdots\!29$$$$T^{9} +$$$$70\!\cdots\!93$$$$T^{10} )^{4}$$)($$1 + 181 T - 1012331 T^{2} + 14482182 T^{3} + 446454243174 T^{4} - 84043375137762 T^{5} - 192479505557683773 T^{6} - 802846347498861897 T^{7} +$$$$98\!\cdots\!51$$$$T^{8} +$$$$77\!\cdots\!72$$$$T^{9} -$$$$41\!\cdots\!24$$$$T^{10} +$$$$28\!\cdots\!96$$$$T^{11} +$$$$13\!\cdots\!99$$$$T^{12} -$$$$41\!\cdots\!29$$$$T^{13} -$$$$36\!\cdots\!73$$$$T^{14} -$$$$59\!\cdots\!66$$$$T^{15} +$$$$11\!\cdots\!26$$$$T^{16} +$$$$14\!\cdots\!74$$$$T^{17} -$$$$36\!\cdots\!31$$$$T^{18} +$$$$24\!\cdots\!33$$$$T^{19} +$$$$49\!\cdots\!49$$$$T^{20}$$)
$17$ ($$1 + 1419857 T^{2}$$)($$1 + 1944 T + 2456098 T^{2} + 2760202008 T^{3} + 2015993900449 T^{4}$$)($$1 - 1944 T + 2456098 T^{2} - 2760202008 T^{3} + 2015993900449 T^{4}$$)($$1 - 2020286 T^{2} + 2015993900449 T^{4}$$)($$( 1 - 2151950 T^{2} + 2015993900449 T^{4} )^{2}$$)($$( 1 - 4946936 T^{2} + 15515554849948 T^{4} - 34385249721915417800 T^{6} +$$$$55\!\cdots\!90$$$$T^{8} -$$$$69\!\cdots\!00$$$$T^{10} +$$$$63\!\cdots\!48$$$$T^{12} -$$$$40\!\cdots\!64$$$$T^{14} +$$$$16\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 6202690 T^{2} + 18689060069517 T^{4} - 34705007722821565080 T^{6} +$$$$46\!\cdots\!02$$$$T^{8} -$$$$60\!\cdots\!16$$$$T^{10} +$$$$94\!\cdots\!98$$$$T^{12} -$$$$14\!\cdots\!80$$$$T^{14} +$$$$15\!\cdots\!33$$$$T^{16} -$$$$10\!\cdots\!90$$$$T^{18} +$$$$33\!\cdots\!49$$$$T^{20} )^{2}$$)($$( 1 + 1140 T + 4980550 T^{2} + 3443850354 T^{3} + 10068870522169 T^{4} + 5069379208548852 T^{5} + 14296356292995309833 T^{6} +$$$$69\!\cdots\!46$$$$T^{7} +$$$$14\!\cdots\!50$$$$T^{8} +$$$$46\!\cdots\!40$$$$T^{9} +$$$$57\!\cdots\!57$$$$T^{10} )^{2}$$)
$19$ ($$1 + 1711 T + 2476099 T^{2}$$)($$1 + 632 T + 4932498 T^{2} + 1564894568 T^{3} + 6131066257801 T^{4}$$)($$1 + 632 T + 4932498 T^{2} + 1564894568 T^{3} + 6131066257801 T^{4}$$)($$( 1 - 1799 T + 2476099 T^{2} )^{2}$$)($$( 1 - 4501190 T^{2} + 6131066257801 T^{4} )^{2}$$)($$( 1 - 9713816 T^{2} + 55349997016060 T^{4} -$$$$21\!\cdots\!72$$$$T^{6} +$$$$61\!\cdots\!02$$$$T^{8} -$$$$13\!\cdots\!72$$$$T^{10} +$$$$20\!\cdots\!60$$$$T^{12} -$$$$22\!\cdots\!16$$$$T^{14} +$$$$14\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 13782439 T^{2} + 98755621335207 T^{4} -$$$$47\!\cdots\!14$$$$T^{6} +$$$$17\!\cdots\!01$$$$T^{8} -$$$$48\!\cdots\!01$$$$T^{10} +$$$$10\!\cdots\!01$$$$T^{12} -$$$$17\!\cdots\!14$$$$T^{14} +$$$$22\!\cdots\!07$$$$T^{16} -$$$$19\!\cdots\!39$$$$T^{18} +$$$$86\!\cdots\!01$$$$T^{20} )^{2}$$)($$( 1 + 416 T + 5046258 T^{2} + 6215761044 T^{3} + 20272296121125 T^{4} + 15898268281316088 T^{5} + 50196212153221491375 T^{6} +$$$$38\!\cdots\!44$$$$T^{7} +$$$$76\!\cdots\!42$$$$T^{8} +$$$$15\!\cdots\!16$$$$T^{9} +$$$$93\!\cdots\!99$$$$T^{10} )^{2}$$)
$23$ ($$1 + 6436343 T^{2}$$)($$1 + 6804 T + 24393154 T^{2} + 43792877772 T^{3} + 41426511213649 T^{4}$$)($$1 - 6804 T + 24393154 T^{2} - 43792877772 T^{3} + 41426511213649 T^{4}$$)($$1 - 198770 T^{2} + 41426511213649 T^{4}$$)($$( 1 - 2019266 T^{2} + 41426511213649 T^{4} )^{2}$$)($$( 1 + 29994040 T^{2} + 487786705761244 T^{4} +$$$$51\!\cdots\!44$$$$T^{6} +$$$$39\!\cdots\!14$$$$T^{8} +$$$$21\!\cdots\!56$$$$T^{10} +$$$$83\!\cdots\!44$$$$T^{12} +$$$$21\!\cdots\!60$$$$T^{14} +$$$$29\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 42721646 T^{2} + 918206452664445 T^{4} +$$$$12\!\cdots\!28$$$$T^{6} +$$$$12\!\cdots\!34$$$$T^{8} +$$$$95\!\cdots\!68$$$$T^{10} +$$$$53\!\cdots\!66$$$$T^{12} +$$$$22\!\cdots\!28$$$$T^{14} +$$$$65\!\cdots\!05$$$$T^{16} +$$$$12\!\cdots\!46$$$$T^{18} +$$$$12\!\cdots\!49$$$$T^{20} )^{2}$$)($$1 + 399 T - 16077241 T^{2} + 38108825820 T^{3} + 155650662506976 T^{4} - 562944417983120520 T^{5} - 48522958516353490863 T^{6} +$$$$48\!\cdots\!51$$$$T^{7} -$$$$71\!\cdots\!41$$$$T^{8} -$$$$11\!\cdots\!52$$$$T^{9} +$$$$81\!\cdots\!80$$$$T^{10} -$$$$74\!\cdots\!36$$$$T^{11} -$$$$29\!\cdots\!09$$$$T^{12} +$$$$12\!\cdots\!57$$$$T^{13} -$$$$83\!\cdots\!63$$$$T^{14} -$$$$62\!\cdots\!60$$$$T^{15} +$$$$11\!\cdots\!24$$$$T^{16} +$$$$17\!\cdots\!40$$$$T^{17} -$$$$47\!\cdots\!41$$$$T^{18} +$$$$75\!\cdots\!57$$$$T^{19} +$$$$12\!\cdots\!49$$$$T^{20}$$)
$29$ ($$1 + 20511149 T^{2}$$)($$1 + 11664 T + 70238998 T^{2} + 239242041936 T^{3} + 420707233300201 T^{4}$$)($$1 - 11664 T + 70238998 T^{2} - 239242041936 T^{3} + 420707233300201 T^{4}$$)($$1 + 39031642 T^{2} + 420707233300201 T^{4}$$)($$( 1 - 29365574 T^{2} + 420707233300201 T^{4} )^{2}$$)($$( 1 - 26575640 T^{2} + 859790443267708 T^{4} -$$$$25\!\cdots\!88$$$$T^{6} +$$$$44\!\cdots\!26$$$$T^{8} -$$$$10\!\cdots\!88$$$$T^{10} +$$$$15\!\cdots\!08$$$$T^{12} -$$$$19\!\cdots\!40$$$$T^{14} +$$$$31\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 142578466 T^{2} + 9766751584325109 T^{4} -$$$$42\!\cdots\!00$$$$T^{6} +$$$$13\!\cdots\!22$$$$T^{8} -$$$$31\!\cdots\!16$$$$T^{10} +$$$$56\!\cdots\!22$$$$T^{12} -$$$$75\!\cdots\!00$$$$T^{14} +$$$$72\!\cdots\!09$$$$T^{16} -$$$$44\!\cdots\!66$$$$T^{18} +$$$$13\!\cdots\!01$$$$T^{20} )^{2}$$)($$1 - 6033 T + 3652157 T^{2} - 31641196734 T^{3} + 283528398607854 T^{4} - 668469168127712358 T^{5} +$$$$64\!\cdots\!39$$$$T^{6} -$$$$82\!\cdots\!55$$$$T^{7} -$$$$90\!\cdots\!17$$$$T^{8} -$$$$14\!\cdots\!60$$$$T^{9} +$$$$58\!\cdots\!16$$$$T^{10} -$$$$29\!\cdots\!40$$$$T^{11} -$$$$38\!\cdots\!17$$$$T^{12} -$$$$71\!\cdots\!95$$$$T^{13} +$$$$11\!\cdots\!39$$$$T^{14} -$$$$24\!\cdots\!42$$$$T^{15} +$$$$21\!\cdots\!54$$$$T^{16} -$$$$48\!\cdots\!66$$$$T^{17} +$$$$11\!\cdots\!57$$$$T^{18} -$$$$38\!\cdots\!17$$$$T^{19} +$$$$13\!\cdots\!01$$$$T^{20}$$)
$31$ ($$1 + 10324 T + 28629151 T^{2}$$)($$1 - 3328 T + 38238117 T^{2} - 95277814528 T^{3} + 819628286980801 T^{4}$$)($$1 - 3328 T + 38238117 T^{2} - 95277814528 T^{3} + 819628286980801 T^{4}$$)($$( 1 - 5228 T + 28629151 T^{2} )^{2}$$)($$( 1 - 17147735 T^{2} + 819628286980801 T^{4} )^{2}$$)($$( 1 - 160216820 T^{2} + 12412163878108546 T^{4} -$$$$60\!\cdots\!08$$$$T^{6} +$$$$20\!\cdots\!87$$$$T^{8} -$$$$49\!\cdots\!08$$$$T^{10} +$$$$83\!\cdots\!46$$$$T^{12} -$$$$88\!\cdots\!20$$$$T^{14} +$$$$45\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 53059450 T^{2} + 1830387109253997 T^{4} -$$$$54\!\cdots\!08$$$$T^{6} +$$$$17\!\cdots\!98$$$$T^{8} -$$$$63\!\cdots\!76$$$$T^{10} +$$$$14\!\cdots\!98$$$$T^{12} -$$$$36\!\cdots\!08$$$$T^{14} +$$$$10\!\cdots\!97$$$$T^{16} -$$$$23\!\cdots\!50$$$$T^{18} +$$$$36\!\cdots\!01$$$$T^{20} )^{2}$$)($$1 - 2759 T - 54902477 T^{2} - 189444651072 T^{3} + 2052158291804100 T^{4} + 13274031992302596720 T^{5} -$$$$32\!\cdots\!47$$$$T^{6} -$$$$42\!\cdots\!39$$$$T^{7} -$$$$13\!\cdots\!49$$$$T^{8} +$$$$36\!\cdots\!48$$$$T^{9} +$$$$63\!\cdots\!24$$$$T^{10} +$$$$10\!\cdots\!48$$$$T^{11} -$$$$11\!\cdots\!49$$$$T^{12} -$$$$99\!\cdots\!89$$$$T^{13} -$$$$21\!\cdots\!47$$$$T^{14} +$$$$25\!\cdots\!20$$$$T^{15} +$$$$11\!\cdots\!00$$$$T^{16} -$$$$29\!\cdots\!72$$$$T^{17} -$$$$24\!\cdots\!77$$$$T^{18} -$$$$35\!\cdots\!09$$$$T^{19} +$$$$36\!\cdots\!01$$$$T^{20}$$)
$37$ ($$1 + 6661 T + 69343957 T^{2}$$)($$1 + 9956 T + 151512798 T^{2} + 690388435892 T^{3} + 4808584372417849 T^{4}$$)($$1 + 9956 T + 151512798 T^{2} + 690388435892 T^{3} + 4808584372417849 T^{4}$$)($$( 1 - 8783 T + 69343957 T^{2} )^{2}$$)($$( 1 - 15332 T + 69343957 T^{2} )^{4}$$)($$( 1 + 17752 T + 254119924 T^{2} + 2137611581224 T^{3} + 19827261455867542 T^{4} +$$$$14\!\cdots\!68$$$$T^{5} +$$$$12\!\cdots\!76$$$$T^{6} +$$$$59\!\cdots\!36$$$$T^{7} +$$$$23\!\cdots\!01$$$$T^{8} )^{4}$$)($$( 1 + 1613 T + 123026979 T^{2} + 343711884654 T^{3} + 5803261980890325 T^{4} + 31670451235762477275 T^{5} +$$$$40\!\cdots\!25$$$$T^{6} +$$$$16\!\cdots\!46$$$$T^{7} +$$$$41\!\cdots\!47$$$$T^{8} +$$$$37\!\cdots\!13$$$$T^{9} +$$$$16\!\cdots\!57$$$$T^{10} )^{4}$$)($$( 1 + 7586 T + 201201093 T^{2} + 803146672896 T^{3} + 19241810738464926 T^{4} + 60351714230064941916 T^{5} +$$$$13\!\cdots\!82$$$$T^{6} +$$$$38\!\cdots\!04$$$$T^{7} +$$$$67\!\cdots\!49$$$$T^{8} +$$$$17\!\cdots\!86$$$$T^{9} +$$$$16\!\cdots\!57$$$$T^{10} )^{2}$$)
$41$ ($$1 + 115856201 T^{2}$$)($$1 + 13608 T + 266834974 T^{2} + 1576571183208 T^{3} + 13422659310152401 T^{4}$$)($$1 - 13608 T + 266834974 T^{2} - 1576571183208 T^{3} + 13422659310152401 T^{4}$$)($$1 - 9156974 T^{2} + 13422659310152401 T^{4}$$)($$( 1 - 129650498 T^{2} + 13422659310152401 T^{4} )^{2}$$)($$( 1 - 667999304 T^{2} + 215857510496501980 T^{4} -$$$$43\!\cdots\!84$$$$T^{6} +$$$$60\!\cdots\!14$$$$T^{8} -$$$$58\!\cdots\!84$$$$T^{10} +$$$$38\!\cdots\!80$$$$T^{12} -$$$$16\!\cdots\!04$$$$T^{14} +$$$$32\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 204662074 T^{2} + 6421654936070589 T^{4} +$$$$14\!\cdots\!28$$$$T^{6} -$$$$52\!\cdots\!06$$$$T^{8} -$$$$96\!\cdots\!76$$$$T^{10} -$$$$70\!\cdots\!06$$$$T^{12} +$$$$26\!\cdots\!28$$$$T^{14} +$$$$15\!\cdots\!89$$$$T^{16} -$$$$66\!\cdots\!74$$$$T^{18} +$$$$43\!\cdots\!01$$$$T^{20} )^{2}$$)($$1 - 18435 T - 117679042 T^{2} + 4344492069675 T^{3} - 505249106564622 T^{4} -$$$$52\!\cdots\!97$$$$T^{5} +$$$$16\!\cdots\!40$$$$T^{6} +$$$$39\!\cdots\!43$$$$T^{7} -$$$$31\!\cdots\!03$$$$T^{8} -$$$$10\!\cdots\!42$$$$T^{9} +$$$$29\!\cdots\!40$$$$T^{10} -$$$$11\!\cdots\!42$$$$T^{11} -$$$$41\!\cdots\!03$$$$T^{12} +$$$$62\!\cdots\!43$$$$T^{13} +$$$$30\!\cdots\!40$$$$T^{14} -$$$$10\!\cdots\!97$$$$T^{15} -$$$$12\!\cdots\!22$$$$T^{16} +$$$$12\!\cdots\!75$$$$T^{17} -$$$$38\!\cdots\!42$$$$T^{18} -$$$$69\!\cdots\!35$$$$T^{19} +$$$$43\!\cdots\!01$$$$T^{20}$$)
$43$ ($$1 + 3352 T + 147008443 T^{2}$$)($$1 - 4960 T + 213010962 T^{2} - 729161877280 T^{3} + 21611482313284249 T^{4}$$)($$1 - 4960 T + 213010962 T^{2} - 729161877280 T^{3} + 21611482313284249 T^{4}$$)($$( 1 - 19976 T + 147008443 T^{2} )^{2}$$)($$( 1 - 284996378 T^{2} + 21611482313284249 T^{4} )^{2}$$)($$( 1 - 271892936 T^{2} + 81822516500494204 T^{4} -$$$$14\!\cdots\!72$$$$T^{6} +$$$$26\!\cdots\!02$$$$T^{8} -$$$$30\!\cdots\!28$$$$T^{10} +$$$$38\!\cdots\!04$$$$T^{12} -$$$$27\!\cdots\!64$$$$T^{14} +$$$$21\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 1038109906 T^{2} + 527969585590823397 T^{4} -$$$$17\!\cdots\!40$$$$T^{6} +$$$$39\!\cdots\!02$$$$T^{8} -$$$$67\!\cdots\!12$$$$T^{10} +$$$$85\!\cdots\!98$$$$T^{12} -$$$$80\!\cdots\!40$$$$T^{14} +$$$$53\!\cdots\!53$$$$T^{16} -$$$$22\!\cdots\!06$$$$T^{18} +$$$$47\!\cdots\!49$$$$T^{20} )^{2}$$)($$1 - 1469 T - 271863536 T^{2} + 4016430594327 T^{3} + 12129147672135834 T^{4} -$$$$75\!\cdots\!27$$$$T^{5} +$$$$55\!\cdots\!62$$$$T^{6} -$$$$12\!\cdots\!57$$$$T^{7} -$$$$29\!\cdots\!39$$$$T^{8} +$$$$61\!\cdots\!62$$$$T^{9} -$$$$11\!\cdots\!84$$$$T^{10} +$$$$90\!\cdots\!66$$$$T^{11} -$$$$64\!\cdots\!11$$$$T^{12} -$$$$38\!\cdots\!99$$$$T^{13} +$$$$26\!\cdots\!62$$$$T^{14} -$$$$52\!\cdots\!61$$$$T^{15} +$$$$12\!\cdots\!66$$$$T^{16} +$$$$59\!\cdots\!89$$$$T^{17} -$$$$59\!\cdots\!36$$$$T^{18} -$$$$47\!\cdots\!67$$$$T^{19} +$$$$47\!\cdots\!49$$$$T^{20}$$)
$47$ ($$1 + 229345007 T^{2}$$)($$1 + 18468 T + 312496354 T^{2} + 4235543589276 T^{3} + 52599132235830049 T^{4}$$)($$1 - 18468 T + 312496354 T^{2} - 4235543589276 T^{3} + 52599132235830049 T^{4}$$)($$1 + 341046910 T^{2} + 52599132235830049 T^{4}$$)($$( 1 + 408701842 T^{2} + 52599132235830049 T^{4} )^{2}$$)($$( 1 + 1268760328 T^{2} + 775645167851419804 T^{4} +$$$$30\!\cdots\!92$$$$T^{6} +$$$$81\!\cdots\!58$$$$T^{8} +$$$$15\!\cdots\!08$$$$T^{10} +$$$$21\!\cdots\!04$$$$T^{12} +$$$$18\!\cdots\!72$$$$T^{14} +$$$$76\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 920931614 T^{2} + 499070896097327373 T^{4} +$$$$18\!\cdots\!24$$$$T^{6} +$$$$53\!\cdots\!58$$$$T^{8} +$$$$12\!\cdots\!24$$$$T^{10} +$$$$27\!\cdots\!42$$$$T^{12} +$$$$50\!\cdots\!24$$$$T^{14} +$$$$72\!\cdots\!77$$$$T^{16} +$$$$70\!\cdots\!14$$$$T^{18} +$$$$40\!\cdots\!49$$$$T^{20} )^{2}$$)($$1 - 25155 T - 401246233 T^{2} + 14349179861244 T^{3} + 97557609874842960 T^{4} -$$$$41\!\cdots\!12$$$$T^{5} -$$$$25\!\cdots\!27$$$$T^{6} +$$$$55\!\cdots\!85$$$$T^{7} +$$$$12\!\cdots\!11$$$$T^{8} -$$$$42\!\cdots\!56$$$$T^{9} -$$$$37\!\cdots\!60$$$$T^{10} -$$$$96\!\cdots\!92$$$$T^{11} +$$$$67\!\cdots\!39$$$$T^{12} +$$$$67\!\cdots\!55$$$$T^{13} -$$$$71\!\cdots\!27$$$$T^{14} -$$$$26\!\cdots\!84$$$$T^{15} +$$$$14\!\cdots\!40$$$$T^{16} +$$$$47\!\cdots\!92$$$$T^{17} -$$$$30\!\cdots\!33$$$$T^{18} -$$$$44\!\cdots\!85$$$$T^{19} +$$$$40\!\cdots\!49$$$$T^{20}$$)
$53$ ($$1 + 418195493 T^{2}$$)($$1 - 11664 T + 484234009 T^{2} - 4877832230352 T^{3} + 174887470365513049 T^{4}$$)($$1 + 11664 T + 484234009 T^{2} + 4877832230352 T^{3} + 174887470365513049 T^{4}$$)($$1 - 31068470 T^{2} + 174887470365513049 T^{4}$$)($$( 1 - 537758237 T^{2} + 174887470365513049 T^{4} )^{2}$$)($$( 1 - 1665548972 T^{2} + 1494189343182800962 T^{4} -$$$$95\!\cdots\!20$$$$T^{6} +$$$$46\!\cdots\!75$$$$T^{8} -$$$$16\!\cdots\!80$$$$T^{10} +$$$$45\!\cdots\!62$$$$T^{12} -$$$$89\!\cdots\!28$$$$T^{14} +$$$$93\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 1301597650 T^{2} + 1197727639041193893 T^{4} -$$$$82\!\cdots\!04$$$$T^{6} +$$$$45\!\cdots\!18$$$$T^{8} -$$$$21\!\cdots\!32$$$$T^{10} +$$$$79\!\cdots\!82$$$$T^{12} -$$$$25\!\cdots\!04$$$$T^{14} +$$$$64\!\cdots\!57$$$$T^{16} -$$$$12\!\cdots\!50$$$$T^{18} +$$$$16\!\cdots\!49$$$$T^{20} )^{2}$$)($$( 1 + 58422 T + 3354568213 T^{2} + 110313236959296 T^{3} + 3390725554692289246 T^{4} +$$$$71\!\cdots\!28$$$$T^{5} +$$$$14\!\cdots\!78$$$$T^{6} +$$$$19\!\cdots\!04$$$$T^{7} +$$$$24\!\cdots\!41$$$$T^{8} +$$$$17\!\cdots\!22$$$$T^{9} +$$$$12\!\cdots\!93$$$$T^{10} )^{2}$$)
$59$ ($$1 + 714924299 T^{2}$$)($$1 + 1944 T + 961283686 T^{2} + 1389812837256 T^{3} + 511116753300641401 T^{4}$$)($$1 - 1944 T + 961283686 T^{2} - 1389812837256 T^{3} + 511116753300641401 T^{4}$$)($$1 + 1396994998 T^{2} + 511116753300641401 T^{4}$$)($$( 1 + 621590410 T^{2} + 511116753300641401 T^{4} )^{2}$$)($$( 1 + 4822767208 T^{2} + 10641078380871180220 T^{4} +$$$$14\!\cdots\!92$$$$T^{6} +$$$$12\!\cdots\!22$$$$T^{8} +$$$$71\!\cdots\!92$$$$T^{10} +$$$$27\!\cdots\!20$$$$T^{12} +$$$$64\!\cdots\!08$$$$T^{14} +$$$$68\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 1806503990 T^{2} + 2218805640623321733 T^{4} +$$$$21\!\cdots\!92$$$$T^{6} +$$$$17\!\cdots\!70$$$$T^{8} +$$$$12\!\cdots\!12$$$$T^{10} +$$$$87\!\cdots\!70$$$$T^{12} +$$$$55\!\cdots\!92$$$$T^{14} +$$$$29\!\cdots\!33$$$$T^{16} +$$$$12\!\cdots\!90$$$$T^{18} +$$$$34\!\cdots\!01$$$$T^{20} )^{2}$$)($$1 - 90537 T + 2831117840 T^{2} - 13805150996349 T^{3} - 966660594685472478 T^{4} +$$$$10\!\cdots\!09$$$$T^{5} +$$$$69\!\cdots\!78$$$$T^{6} -$$$$39\!\cdots\!93$$$$T^{7} +$$$$84\!\cdots\!01$$$$T^{8} +$$$$17\!\cdots\!74$$$$T^{9} -$$$$12\!\cdots\!20$$$$T^{10} +$$$$12\!\cdots\!26$$$$T^{11} +$$$$42\!\cdots\!01$$$$T^{12} -$$$$14\!\cdots\!07$$$$T^{13} +$$$$18\!\cdots\!78$$$$T^{14} +$$$$19\!\cdots\!91$$$$T^{15} -$$$$12\!\cdots\!78$$$$T^{16} -$$$$13\!\cdots\!51$$$$T^{17} +$$$$19\!\cdots\!40$$$$T^{18} -$$$$44\!\cdots\!63$$$$T^{19} +$$$$34\!\cdots\!01$$$$T^{20}$$)
$61$ ($$1 - 56927 T + 844596301 T^{2}$$)($$1 - 8176 T - 15702054 T^{2} - 6905419356976 T^{3} + 713342911662882601 T^{4}$$)($$1 - 8176 T - 15702054 T^{2} - 6905419356976 T^{3} + 713342911662882601 T^{4}$$)($$( 1 + 1069 T + 844596301 T^{2} )^{2}$$)($$( 1 + 53188 T + 844596301 T^{2} )^{4}$$)($$( 1 - 19472 T + 1261489684 T^{2} - 43949943879536 T^{3} + 833752337244254902 T^{4} -$$$$37\!\cdots\!36$$$$T^{5} +$$$$89\!\cdots\!84$$$$T^{6} -$$$$11\!\cdots\!72$$$$T^{7} +$$$$50\!\cdots\!01$$$$T^{8} )^{4}$$)($$( 1 - 21151 T + 2606330283 T^{2} - 19051394797770 T^{3} + 2604033901923348357 T^{4} -$$$$93\!\cdots\!13$$$$T^{5} +$$$$21\!\cdots\!57$$$$T^{6} -$$$$13\!\cdots\!70$$$$T^{7} +$$$$15\!\cdots\!83$$$$T^{8} -$$$$10\!\cdots\!51$$$$T^{9} +$$$$42\!\cdots\!01$$$$T^{10} )^{4}$$)($$1 - 1403 T - 3536905883 T^{2} - 452840008146 T^{3} + 7065863261737144698 T^{4} +$$$$54\!\cdots\!90$$$$T^{5} -$$$$10\!\cdots\!33$$$$T^{6} -$$$$70\!\cdots\!89$$$$T^{7} +$$$$11\!\cdots\!67$$$$T^{8} +$$$$32\!\cdots\!04$$$$T^{9} -$$$$10\!\cdots\!12$$$$T^{10} +$$$$27\!\cdots\!04$$$$T^{11} +$$$$80\!\cdots\!67$$$$T^{12} -$$$$42\!\cdots\!89$$$$T^{13} -$$$$51\!\cdots\!33$$$$T^{14} +$$$$23\!\cdots\!90$$$$T^{15} +$$$$25\!\cdots\!98$$$$T^{16} -$$$$13\!\cdots\!46$$$$T^{17} -$$$$91\!\cdots\!83$$$$T^{18} -$$$$30\!\cdots\!03$$$$T^{19} +$$$$18\!\cdots\!01$$$$T^{20}$$)
$67$ ($$1 + 37939 T + 1350125107 T^{2}$$)($$1 - 90064 T + 4055628738 T^{2} - 121597667636848 T^{3} + 1822837804551761449 T^{4}$$)($$1 - 90064 T + 4055628738 T^{2} - 121597667636848 T^{3} + 1822837804551761449 T^{4}$$)($$( 1 + 62077 T + 1350125107 T^{2} )^{2}$$)($$( 1 - 1014398666 T^{2} + 1822837804551761449 T^{4} )^{2}$$)($$( 1 - 1447449416 T^{2} + 2915553445416739516 T^{4} -$$$$52\!\cdots\!68$$$$T^{6} +$$$$74\!\cdots\!58$$$$T^{8} -$$$$95\!\cdots\!32$$$$T^{10} +$$$$96\!\cdots\!16$$$$T^{12} -$$$$87\!\cdots\!84$$$$T^{14} +$$$$11\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 10598201455 T^{2} + 53515912648993384359 T^{4} -$$$$16\!\cdots\!10$$$$T^{6} +$$$$36\!\cdots\!89$$$$T^{8} -$$$$58\!\cdots\!01$$$$T^{10} +$$$$67\!\cdots\!61$$$$T^{12} -$$$$56\!\cdots\!10$$$$T^{14} +$$$$32\!\cdots\!91$$$$T^{16} -$$$$11\!\cdots\!55$$$$T^{18} +$$$$20\!\cdots\!49$$$$T^{20} )^{2}$$)($$1 - 13907 T - 3876685544 T^{2} - 77425491657903 T^{3} + 10014688417385231130 T^{4} +$$$$30\!\cdots\!39$$$$T^{5} -$$$$79\!\cdots\!54$$$$T^{6} -$$$$69\!\cdots\!51$$$$T^{7} -$$$$33\!\cdots\!67$$$$T^{8} +$$$$37\!\cdots\!46$$$$T^{9} +$$$$22\!\cdots\!76$$$$T^{10} +$$$$51\!\cdots\!22$$$$T^{11} -$$$$60\!\cdots\!83$$$$T^{12} -$$$$16\!\cdots\!93$$$$T^{13} -$$$$26\!\cdots\!54$$$$T^{14} +$$$$13\!\cdots\!73$$$$T^{15} +$$$$60\!\cdots\!70$$$$T^{16} -$$$$63\!\cdots\!29$$$$T^{17} -$$$$42\!\cdots\!44$$$$T^{18} -$$$$20\!\cdots\!49$$$$T^{19} +$$$$20\!\cdots\!49$$$$T^{20}$$)
$71$ ($$1 + 1804229351 T^{2}$$)($$1 - 44712 T + 2046094414 T^{2} - 80670702741912 T^{3} + 3255243551009881201 T^{4}$$)($$1 + 44712 T + 2046094414 T^{2} + 80670702741912 T^{3} + 3255243551009881201 T^{4}$$)($$1 + 1457026126 T^{2} + 3255243551009881201 T^{4}$$)($$( 1 + 2889010114 T^{2} + 3255243551009881201 T^{4} )^{2}$$)($$( 1 + 9830208232 T^{2} + 46886702724166517020 T^{4} +$$$$14\!\cdots\!88$$$$T^{6} +$$$$30\!\cdots\!22$$$$T^{8} +$$$$46\!\cdots\!88$$$$T^{10} +$$$$49\!\cdots\!20$$$$T^{12} +$$$$33\!\cdots\!32$$$$T^{14} +$$$$11\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 6724308230 T^{2} + 20388189580420161501 T^{4} +$$$$45\!\cdots\!64$$$$T^{6} +$$$$10\!\cdots\!26$$$$T^{8} +$$$$22\!\cdots\!68$$$$T^{10} +$$$$34\!\cdots\!26$$$$T^{12} +$$$$48\!\cdots\!64$$$$T^{14} +$$$$70\!\cdots\!01$$$$T^{16} +$$$$75\!\cdots\!30$$$$T^{18} +$$$$36\!\cdots\!01$$$$T^{20} )^{2}$$)($$( 1 + 114684 T + 7758380659 T^{2} + 426246123888336 T^{3} + 19260501229393543450 T^{4} +$$$$77\!\cdots\!40$$$$T^{5} +$$$$34\!\cdots\!50$$$$T^{6} +$$$$13\!\cdots\!36$$$$T^{7} +$$$$45\!\cdots\!09$$$$T^{8} +$$$$12\!\cdots\!84$$$$T^{9} +$$$$19\!\cdots\!51$$$$T^{10} )^{2}$$)
$73$ ($$1 - 79577 T + 2073071593 T^{2}$$)($$1 + 121214 T + 6975764499 T^{2} + 251285300073902 T^{3} + 4297625829703557649 T^{4}$$)($$1 + 121214 T + 6975764499 T^{2} + 251285300073902 T^{3} + 4297625829703557649 T^{4}$$)($$( 1 + 48079 T + 2073071593 T^{2} )^{2}$$)($$( 1 + 30739 T + 2073071593 T^{2} )^{4}$$)($$( 1 + 9508 T + 3097043794 T^{2} - 21796113866240 T^{3} + 7953703459188333211 T^{4} -$$$$45\!\cdots\!20$$$$T^{5} +$$$$13\!\cdots\!06$$$$T^{6} +$$$$84\!\cdots\!56$$$$T^{7} +$$$$18\!\cdots\!01$$$$T^{8} )^{4}$$)($$( 1 - 21355 T + 2385405975 T^{2} - 91039324043106 T^{3} + 7775807385428270205 T^{4} -$$$$26\!\cdots\!29$$$$T^{5} +$$$$16\!\cdots\!65$$$$T^{6} -$$$$39\!\cdots\!94$$$$T^{7} +$$$$21\!\cdots\!75$$$$T^{8} -$$$$39\!\cdots\!55$$$$T^{9} +$$$$38\!\cdots\!93$$$$T^{10} )^{4}$$)($$( 1 - 7600 T + 3606834246 T^{2} - 31056473559714 T^{3} + 12288417972789256281 T^{4} -$$$$80\!\cdots\!84$$$$T^{5} +$$$$25\!\cdots\!33$$$$T^{6} -$$$$13\!\cdots\!86$$$$T^{7} +$$$$32\!\cdots\!22$$$$T^{8} -$$$$14\!\cdots\!00$$$$T^{9} +$$$$38\!\cdots\!93$$$$T^{10} )^{2}$$)
$79$ ($$1 - 90857 T + 3077056399 T^{2}$$)($$1 - 28768 T + 4017714654 T^{2} - 88520758486432 T^{3} + 9468276082626847201 T^{4}$$)($$1 - 28768 T + 4017714654 T^{2} - 88520758486432 T^{3} + 9468276082626847201 T^{4}$$)($$( 1 - 49979 T + 3077056399 T^{2} )^{2}$$)($$( 1 - 1226373986 T^{2} + 9468276082626847201 T^{4} )^{2}$$)($$( 1 + 99394360 T^{2} + 19778301042529431580 T^{4} -$$$$22\!\cdots\!96$$$$T^{6} +$$$$20\!\cdots\!66$$$$T^{8} -$$$$21\!\cdots\!96$$$$T^{10} +$$$$17\!\cdots\!80$$$$T^{12} +$$$$84\!\cdots\!60$$$$T^{14} +$$$$80\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 13863408967 T^{2} + 96370465581362357535 T^{4} -$$$$46\!\cdots\!74$$$$T^{6} +$$$$17\!\cdots\!65$$$$T^{8} -$$$$59\!\cdots\!89$$$$T^{10} +$$$$16\!\cdots\!65$$$$T^{12} -$$$$41\!\cdots\!74$$$$T^{14} +$$$$81\!\cdots\!35$$$$T^{16} -$$$$11\!\cdots\!67$$$$T^{18} +$$$$76\!\cdots\!01$$$$T^{20} )^{2}$$)($$1 - 29993 T - 5352351629 T^{2} - 358913063028768 T^{3} + 26234825811851125236 T^{4} +$$$$21\!\cdots\!52$$$$T^{5} +$$$$27\!\cdots\!85$$$$T^{6} -$$$$84\!\cdots\!45$$$$T^{7} -$$$$35\!\cdots\!45$$$$T^{8} +$$$$81\!\cdots\!80$$$$T^{9} +$$$$16\!\cdots\!00$$$$T^{10} +$$$$25\!\cdots\!20$$$$T^{11} -$$$$33\!\cdots\!45$$$$T^{12} -$$$$24\!\cdots\!55$$$$T^{13} +$$$$24\!\cdots\!85$$$$T^{14} +$$$$60\!\cdots\!48$$$$T^{15} +$$$$22\!\cdots\!36$$$$T^{16} -$$$$93\!\cdots\!32$$$$T^{17} -$$$$43\!\cdots\!29$$$$T^{18} -$$$$74\!\cdots\!07$$$$T^{19} +$$$$76\!\cdots\!01$$$$T^{20}$$)
$83$ ($$1 + 3939040643 T^{2}$$)($$1 - 15066 T - 2258995409 T^{2} - 59345586327438 T^{3} + 15516041187205853449 T^{4}$$)($$1 + 15066 T - 2258995409 T^{2} + 59345586327438 T^{3} + 15516041187205853449 T^{4}$$)($$1 + 4552161670 T^{2} + 15516041187205853449 T^{4}$$)($$( 1 + 7748073619 T^{2} + 15516041187205853449 T^{4} )^{2}$$)($$( 1 + 20559730876 T^{2} +$$$$21\!\cdots\!14$$$$T^{4} +$$$$14\!\cdots\!68$$$$T^{6} +$$$$70\!\cdots\!39$$$$T^{8} +$$$$23\!\cdots\!32$$$$T^{10} +$$$$52\!\cdots\!14$$$$T^{12} +$$$$76\!\cdots\!24$$$$T^{14} +$$$$57\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 15102812222 T^{2} +$$$$16\!\cdots\!49$$$$T^{4} +$$$$11\!\cdots\!68$$$$T^{6} +$$$$64\!\cdots\!90$$$$T^{8} +$$$$28\!\cdots\!80$$$$T^{10} +$$$$10\!\cdots\!10$$$$T^{12} +$$$$27\!\cdots\!68$$$$T^{14} +$$$$60\!\cdots\!01$$$$T^{16} +$$$$87\!\cdots\!22$$$$T^{18} +$$$$89\!\cdots\!49$$$$T^{20} )^{2}$$)($$1 - 228951 T + 21403431983 T^{2} - 1202282302650156 T^{3} + 62567029919071222368 T^{4} -$$$$36\!\cdots\!68$$$$T^{5} +$$$$11\!\cdots\!01$$$$T^{6} +$$$$11\!\cdots\!41$$$$T^{7} -$$$$18\!\cdots\!73$$$$T^{8} +$$$$14\!\cdots\!84$$$$T^{9} -$$$$88\!\cdots\!72$$$$T^{10} +$$$$55\!\cdots\!12$$$$T^{11} -$$$$28\!\cdots\!77$$$$T^{12} +$$$$67\!\cdots\!87$$$$T^{13} +$$$$28\!\cdots\!01$$$$T^{14} -$$$$34\!\cdots\!24$$$$T^{15} +$$$$23\!\cdots\!32$$$$T^{16} -$$$$17\!\cdots\!92$$$$T^{17} +$$$$12\!\cdots\!83$$$$T^{18} -$$$$52\!\cdots\!93$$$$T^{19} +$$$$89\!\cdots\!49$$$$T^{20}$$)
$89$ ($$1 + 5584059449 T^{2}$$)($$1 - 178848 T + 18739138030 T^{2} - 998697864334752 T^{3} + 31181719929966183601 T^{4}$$)($$1 + 178848 T + 18739138030 T^{2} + 998697864334752 T^{3} + 31181719929966183601 T^{4}$$)($$1 + 3438704914 T^{2} + 31181719929966183601 T^{4}$$)($$( 1 - 6450847934 T^{2} + 31181719929966183601 T^{4} )^{2}$$)($$( 1 - 30119375768 T^{2} +$$$$43\!\cdots\!12$$$$T^{4} -$$$$41\!\cdots\!60$$$$T^{6} +$$$$27\!\cdots\!18$$$$T^{8} -$$$$12\!\cdots\!60$$$$T^{10} +$$$$42\!\cdots\!12$$$$T^{12} -$$$$91\!\cdots\!68$$$$T^{14} +$$$$94\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 46714027858 T^{2} +$$$$10\!\cdots\!53$$$$T^{4} -$$$$13\!\cdots\!72$$$$T^{6} +$$$$12\!\cdots\!82$$$$T^{8} -$$$$83\!\cdots\!68$$$$T^{10} +$$$$39\!\cdots\!82$$$$T^{12} -$$$$13\!\cdots\!72$$$$T^{14} +$$$$31\!\cdots\!53$$$$T^{16} -$$$$44\!\cdots\!58$$$$T^{18} +$$$$29\!\cdots\!01$$$$T^{20} )^{2}$$)($$( 1 + 299166 T + 52616244181 T^{2} + 6660261403977288 T^{3} +$$$$67\!\cdots\!10$$$$T^{4} +$$$$55\!\cdots\!64$$$$T^{5} +$$$$37\!\cdots\!90$$$$T^{6} +$$$$20\!\cdots\!88$$$$T^{7} +$$$$91\!\cdots\!69$$$$T^{8} +$$$$29\!\cdots\!66$$$$T^{9} +$$$$54\!\cdots\!49$$$$T^{10} )^{2}$$)
$97$ ($$1 - 177725 T + 8587340257 T^{2}$$)($$1 - 88942 T + 13779025491 T^{2} - 763775217138094 T^{3} + 73742412689492826049 T^{4}$$)($$1 - 88942 T + 13779025491 T^{2} - 763775217138094 T^{3} + 73742412689492826049 T^{4}$$)($$( 1 - 12917 T + 8587340257 T^{2} )^{2}$$)($$( 1 + 13717 T + 8587340257 T^{2} )^{4}$$)($$( 1 + 244 T + 6580710202 T^{2} + 1109461517844208 T^{3} - 18256445891874654653 T^{4} +$$$$95\!\cdots\!56$$$$T^{5} +$$$$48\!\cdots\!98$$$$T^{6} +$$$$15\!\cdots\!92$$$$T^{7} +$$$$54\!\cdots\!01$$$$T^{8} )^{4}$$)($$( 1 + 54977 T + 25395595455 T^{2} + 1194992001523350 T^{3} +$$$$29\!\cdots\!17$$$$T^{4} +$$$$12\!\cdots\!15$$$$T^{5} +$$$$24\!\cdots\!69$$$$T^{6} +$$$$88\!\cdots\!50$$$$T^{7} +$$$$16\!\cdots\!15$$$$T^{8} +$$$$29\!\cdots\!77$$$$T^{9} +$$$$46\!\cdots\!57$$$$T^{10} )^{4}$$)($$1 - 40541 T - 17893496138 T^{2} + 2263333692661293 T^{3} + 99710157551726941410 T^{4} -$$$$30\!\cdots\!95$$$$T^{5} +$$$$10\!\cdots\!20$$$$T^{6} +$$$$21\!\cdots\!29$$$$T^{7} -$$$$20\!\cdots\!15$$$$T^{8} -$$$$65\!\cdots\!06$$$$T^{9} +$$$$19\!\cdots\!00$$$$T^{10} -$$$$56\!\cdots\!42$$$$T^{11} -$$$$15\!\cdots\!35$$$$T^{12} +$$$$13\!\cdots\!97$$$$T^{13} +$$$$56\!\cdots\!20$$$$T^{14} -$$$$14\!\cdots\!15$$$$T^{15} +$$$$39\!\cdots\!90$$$$T^{16} +$$$$77\!\cdots\!49$$$$T^{17} -$$$$52\!\cdots\!38$$$$T^{18} -$$$$10\!\cdots\!37$$$$T^{19} +$$$$21\!\cdots\!49$$$$T^{20}$$)