# Properties

 Label 64.6 Level 64 Weight 6 Dimension 349 Nonzero newspaces 4 Newform subspaces 12 Sturm bound 1536 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$64\( 64 = 2^{6}$$ \) Weight: $$k$$ = $$6$$ Nonzero newspaces: $$4$$ Newform subspaces: $$12$$ Sturm bound: $$1536$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(64))$$.

Total New Old
Modular forms 676 371 305
Cusp forms 604 349 255
Eisenstein series 72 22 50

## Trace form

 $$349q - 8q^{2} - 6q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 253q^{9} + O(q^{10})$$ $$349q - 8q^{2} - 6q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 253q^{9} - 8q^{10} + 598q^{11} - 8q^{12} - 240q^{13} - 8q^{14} - 1804q^{15} - 8q^{16} - 822q^{17} - 8q^{18} + 2354q^{19} - 8q^{20} + 5212q^{21} + 13584q^{22} - 8q^{23} - 22048q^{24} - 15599q^{25} - 25968q^{26} - 4224q^{27} + 4352q^{28} + 8136q^{29} + 64872q^{30} + 11536q^{31} + 37152q^{32} + 22196q^{33} + 12752q^{34} - 8644q^{35} - 62328q^{36} - 23456q^{37} - 69648q^{38} - 8q^{39} - 62368q^{40} + 13302q^{41} + 46352q^{42} + 15374q^{43} + 65504q^{44} - 23532q^{45} - 8q^{46} - 44184q^{47} - 8q^{48} - 12471q^{49} - 137072q^{50} + 44500q^{51} + 73480q^{52} + 38848q^{53} + 233272q^{54} - 220104q^{55} + 150912q^{56} + 35344q^{57} + 25984q^{58} + 87646q^{59} - 197864q^{60} - 50160q^{61} - 175384q^{62} + 329660q^{63} - 374888q^{64} + 13736q^{65} - 254632q^{66} + 197522q^{67} - 7160q^{68} + 143500q^{69} + 286936q^{70} - 287688q^{71} + 414064q^{72} - 85002q^{73} + 377712q^{74} - 541230q^{75} + 268472q^{76} - 53284q^{77} + 332656q^{78} + 408216q^{79} - 299872q^{80} - 205643q^{81} - 503128q^{82} - 227846q^{83} - 985048q^{84} - 248992q^{85} - 721872q^{86} - 8q^{87} - 223288q^{88} + 115174q^{89} + 284392q^{90} + 231156q^{91} + 921264q^{92} + 361312q^{93} + 821272q^{94} + 250380q^{95} + 1214336q^{96} + 515266q^{97} + 957296q^{98} + 298706q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(64))$$

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
64.6.a $$\chi_{64}(1, \cdot)$$ 64.6.a.a 1 1
64.6.a.b 1
64.6.a.c 1
64.6.a.d 1
64.6.a.e 1
64.6.a.f 1
64.6.a.g 1
64.6.a.h 2
64.6.b $$\chi_{64}(33, \cdot)$$ 64.6.b.a 2 1
64.6.b.b 8
64.6.e $$\chi_{64}(17, \cdot)$$ 64.6.e.a 18 2
64.6.g $$\chi_{64}(9, \cdot)$$ None 0 4
64.6.i $$\chi_{64}(5, \cdot)$$ 64.6.i.a 312 8

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(64))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(64)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 5}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 + 20 T + 243 T^{2}$$)($$1 + 12 T + 243 T^{2}$$)($$1 + 8 T + 243 T^{2}$$)($$1 + 243 T^{2}$$)($$1 - 8 T + 243 T^{2}$$)($$1 - 12 T + 243 T^{2}$$)($$1 - 20 T + 243 T^{2}$$)($$1 - 282 T^{2} + 59049 T^{4}$$)($$1 - 482 T^{2} + 59049 T^{4}$$)($$( 1 - 164 T^{2} + 99990 T^{4} - 9684036 T^{6} + 3486784401 T^{8} )^{2}$$)($$1 - 2 T + 2 T^{2} + 1242 T^{3} - 68095 T^{4} + 1694480 T^{5} - 2481488 T^{6} + 216052656 T^{7} + 2316653620 T^{8} - 75354919544 T^{9} + 1681068240440 T^{10} - 18830919106920 T^{11} + 275841168192612 T^{12} + 818526941437680 T^{13} - 9703676745696816 T^{14} + 1168069411502412624 T^{15} - 5089895017200009810 T^{16} +$$$$12\!\cdots\!96$$$$T^{17} -$$$$25\!\cdots\!80$$$$T^{18} +$$$$31\!\cdots\!28$$$$T^{19} -$$$$30\!\cdots\!90$$$$T^{20} +$$$$16\!\cdots\!68$$$$T^{21} -$$$$33\!\cdots\!16$$$$T^{22} +$$$$69\!\cdots\!40$$$$T^{23} +$$$$56\!\cdots\!88$$$$T^{24} -$$$$94\!\cdots\!40$$$$T^{25} +$$$$20\!\cdots\!40$$$$T^{26} -$$$$22\!\cdots\!92$$$$T^{27} +$$$$16\!\cdots\!80$$$$T^{28} +$$$$37\!\cdots\!92$$$$T^{29} -$$$$10\!\cdots\!88$$$$T^{30} +$$$$17\!\cdots\!40$$$$T^{31} -$$$$17\!\cdots\!55$$$$T^{32} +$$$$75\!\cdots\!94$$$$T^{33} +$$$$29\!\cdots\!02$$$$T^{34} -$$$$71\!\cdots\!86$$$$T^{35} +$$$$87\!\cdots\!49$$$$T^{36}$$)
$5$ ($$1 - 74 T + 3125 T^{2}$$)($$1 + 54 T + 3125 T^{2}$$)($$1 + 14 T + 3125 T^{2}$$)($$1 - 82 T + 3125 T^{2}$$)($$1 + 14 T + 3125 T^{2}$$)($$1 + 54 T + 3125 T^{2}$$)($$1 - 74 T + 3125 T^{2}$$)($$( 1 + 46 T + 3125 T^{2} )^{2}$$)($$( 1 - 3125 T^{2} )^{2}$$)($$( 1 - 788 T^{2} - 2662314 T^{4} - 7695312500 T^{6} + 95367431640625 T^{8} )^{2}$$)($$1 + 2 T + 2 T^{2} + 113130 T^{3} - 6970831 T^{4} - 777846032 T^{5} + 4857448048 T^{6} - 2837940430160 T^{7} + 18448919077076 T^{8} + 6174607723271992 T^{9} + 27638790927349432 T^{10} + 10853707976731014040 T^{11} +$$$$24\!\cdots\!24$$$$T^{12} -$$$$26\!\cdots\!12$$$$T^{13} +$$$$49\!\cdots\!28$$$$T^{14} +$$$$86\!\cdots\!80$$$$T^{15} -$$$$56\!\cdots\!34$$$$T^{16} -$$$$90\!\cdots\!88$$$$T^{17} +$$$$77\!\cdots\!92$$$$T^{18} -$$$$28\!\cdots\!00$$$$T^{19} -$$$$55\!\cdots\!50$$$$T^{20} +$$$$26\!\cdots\!00$$$$T^{21} +$$$$47\!\cdots\!00$$$$T^{22} -$$$$78\!\cdots\!00$$$$T^{23} +$$$$22\!\cdots\!00$$$$T^{24} +$$$$31\!\cdots\!00$$$$T^{25} +$$$$25\!\cdots\!00$$$$T^{26} +$$$$17\!\cdots\!00$$$$T^{27} +$$$$16\!\cdots\!00$$$$T^{28} -$$$$78\!\cdots\!00$$$$T^{29} +$$$$42\!\cdots\!00$$$$T^{30} -$$$$21\!\cdots\!00$$$$T^{31} -$$$$59\!\cdots\!75$$$$T^{32} +$$$$29\!\cdots\!50$$$$T^{33} +$$$$16\!\cdots\!50$$$$T^{34} +$$$$51\!\cdots\!50$$$$T^{35} +$$$$80\!\cdots\!25$$$$T^{36}$$)
$7$ ($$1 + 24 T + 16807 T^{2}$$)($$1 - 88 T + 16807 T^{2}$$)($$1 - 208 T + 16807 T^{2}$$)($$1 + 16807 T^{2}$$)($$1 + 208 T + 16807 T^{2}$$)($$1 + 88 T + 16807 T^{2}$$)($$1 - 24 T + 16807 T^{2}$$)($$1 + 5966 T^{2} + 282475249 T^{4}$$)($$( 1 + 16807 T^{2} )^{2}$$)($$( 1 + 26524 T^{2} + 612102054 T^{4} + 7492373504476 T^{6} + 79792266297612001 T^{8} )^{2}$$)($$1 - 144058 T^{2} + 10408827913 T^{4} - 492522532520944 T^{6} + 16882861815154133876 T^{8} -$$$$44\!\cdots\!52$$$$T^{10} +$$$$90\!\cdots\!56$$$$T^{12} -$$$$15\!\cdots\!64$$$$T^{14} +$$$$22\!\cdots\!98$$$$T^{16} -$$$$34\!\cdots\!24$$$$T^{18} +$$$$62\!\cdots\!02$$$$T^{20} -$$$$11\!\cdots\!64$$$$T^{22} +$$$$20\!\cdots\!44$$$$T^{24} -$$$$28\!\cdots\!52$$$$T^{26} +$$$$30\!\cdots\!24$$$$T^{28} -$$$$25\!\cdots\!44$$$$T^{30} +$$$$14\!\cdots\!37$$$$T^{32} -$$$$58\!\cdots\!58$$$$T^{34} +$$$$11\!\cdots\!49$$$$T^{36}$$)
$11$ ($$1 + 124 T + 161051 T^{2}$$)($$1 - 540 T + 161051 T^{2}$$)($$1 + 536 T + 161051 T^{2}$$)($$1 + 161051 T^{2}$$)($$1 - 536 T + 161051 T^{2}$$)($$1 + 540 T + 161051 T^{2}$$)($$1 - 124 T + 161051 T^{2}$$)($$1 + 315190 T^{2} + 25937424601 T^{4}$$)($$1 - 97426 T^{2} + 25937424601 T^{4}$$)($$( 1 - 457220 T^{2} + 102880261302 T^{4} - 11859109276069220 T^{6} +$$$$67\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 606 T + 183618 T^{2} - 79034538 T^{3} + 37127673265 T^{4} + 7247852140784 T^{5} - 8086278408451152 T^{6} + 5838566410456886736 T^{7} -$$$$27\!\cdots\!64$$$$T^{8} +$$$$87\!\cdots\!28$$$$T^{9} -$$$$15\!\cdots\!76$$$$T^{10} +$$$$25\!\cdots\!04$$$$T^{11} +$$$$50\!\cdots\!64$$$$T^{12} -$$$$23\!\cdots\!16$$$$T^{13} +$$$$97\!\cdots\!04$$$$T^{14} -$$$$24\!\cdots\!64$$$$T^{15} -$$$$29\!\cdots\!50$$$$T^{16} +$$$$39\!\cdots\!24$$$$T^{17} -$$$$65\!\cdots\!16$$$$T^{18} +$$$$64\!\cdots\!24$$$$T^{19} -$$$$77\!\cdots\!50$$$$T^{20} -$$$$10\!\cdots\!64$$$$T^{21} +$$$$65\!\cdots\!04$$$$T^{22} -$$$$25\!\cdots\!16$$$$T^{23} +$$$$87\!\cdots\!64$$$$T^{24} +$$$$72\!\cdots\!04$$$$T^{25} -$$$$70\!\cdots\!76$$$$T^{26} +$$$$63\!\cdots\!28$$$$T^{27} -$$$$32\!\cdots\!64$$$$T^{28} +$$$$11\!\cdots\!36$$$$T^{29} -$$$$24\!\cdots\!52$$$$T^{30} +$$$$35\!\cdots\!84$$$$T^{31} +$$$$29\!\cdots\!65$$$$T^{32} -$$$$10\!\cdots\!38$$$$T^{33} +$$$$37\!\cdots\!18$$$$T^{34} -$$$$19\!\cdots\!06$$$$T^{35} +$$$$53\!\cdots\!01$$$$T^{36}$$)
$13$ ($$1 + 478 T + 371293 T^{2}$$)($$1 - 418 T + 371293 T^{2}$$)($$1 + 694 T + 371293 T^{2}$$)($$1 - 1194 T + 371293 T^{2}$$)($$1 + 694 T + 371293 T^{2}$$)($$1 - 418 T + 371293 T^{2}$$)($$1 + 478 T + 371293 T^{2}$$)($$( 1 - 42 T + 371293 T^{2} )^{2}$$)($$( 1 - 371293 T^{2} )^{2}$$)($$( 1 - 233908 T^{2} + 52296802614 T^{4} - 32246204111415892 T^{6} +$$$$19\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 + 2 T + 2 T^{2} + 153133114 T^{3} - 141881992575 T^{4} - 61264536987664 T^{5} + 11602629991678320 T^{6} - 36328073410169002704 T^{7} -$$$$23\!\cdots\!16$$$$T^{8} +$$$$19\!\cdots\!52$$$$T^{9} -$$$$20\!\cdots\!72$$$$T^{10} +$$$$28\!\cdots\!00$$$$T^{11} +$$$$71\!\cdots\!32$$$$T^{12} +$$$$62\!\cdots\!96$$$$T^{13} -$$$$72\!\cdots\!72$$$$T^{14} +$$$$12\!\cdots\!24$$$$T^{15} -$$$$47\!\cdots\!78$$$$T^{16} -$$$$61\!\cdots\!20$$$$T^{17} +$$$$11\!\cdots\!68$$$$T^{18} -$$$$22\!\cdots\!60$$$$T^{19} -$$$$66\!\cdots\!22$$$$T^{20} +$$$$62\!\cdots\!68$$$$T^{21} -$$$$13\!\cdots\!72$$$$T^{22} +$$$$44\!\cdots\!28$$$$T^{23} +$$$$18\!\cdots\!68$$$$T^{24} +$$$$28\!\cdots\!00$$$$T^{25} -$$$$72\!\cdots\!72$$$$T^{26} +$$$$25\!\cdots\!36$$$$T^{27} -$$$$11\!\cdots\!84$$$$T^{28} -$$$$67\!\cdots\!28$$$$T^{29} +$$$$79\!\cdots\!20$$$$T^{30} -$$$$15\!\cdots\!52$$$$T^{31} -$$$$13\!\cdots\!75$$$$T^{32} +$$$$53\!\cdots\!98$$$$T^{33} +$$$$26\!\cdots\!02$$$$T^{34} +$$$$96\!\cdots\!86$$$$T^{35} +$$$$17\!\cdots\!49$$$$T^{36}$$)
$17$ ($$1 + 1198 T + 1419857 T^{2}$$)($$1 - 594 T + 1419857 T^{2}$$)($$1 + 1278 T + 1419857 T^{2}$$)($$1 - 2242 T + 1419857 T^{2}$$)($$1 + 1278 T + 1419857 T^{2}$$)($$1 - 594 T + 1419857 T^{2}$$)($$1 + 1198 T + 1419857 T^{2}$$)($$( 1 - 962 T + 1419857 T^{2} )^{2}$$)($$( 1 - 1914 T + 1419857 T^{2} )^{2}$$)($$( 1 + 1260 T + 1225222 T^{2} + 1789019820 T^{3} + 2015993900449 T^{4} )^{4}$$)($$( 1 + 2 T + 6455241 T^{2} - 1592311056 T^{3} + 20528805234836 T^{4} - 8775071708574920 T^{5} + 45691426381806375332 T^{6} -$$$$22\!\cdots\!56$$$$T^{7} +$$$$80\!\cdots\!02$$$$T^{8} -$$$$37\!\cdots\!28$$$$T^{9} +$$$$11\!\cdots\!14$$$$T^{10} -$$$$45\!\cdots\!44$$$$T^{11} +$$$$13\!\cdots\!76$$$$T^{12} -$$$$35\!\cdots\!20$$$$T^{13} +$$$$11\!\cdots\!52$$$$T^{14} -$$$$13\!\cdots\!44$$$$T^{15} +$$$$75\!\cdots\!13$$$$T^{16} +$$$$33\!\cdots\!02$$$$T^{17} +$$$$23\!\cdots\!57$$$$T^{18} )^{2}$$)
$19$ ($$1 + 3044 T + 2476099 T^{2}$$)($$1 - 836 T + 2476099 T^{2}$$)($$1 - 1112 T + 2476099 T^{2}$$)($$1 + 2476099 T^{2}$$)($$1 + 1112 T + 2476099 T^{2}$$)($$1 + 836 T + 2476099 T^{2}$$)($$1 - 3044 T + 2476099 T^{2}$$)($$1 + 632198 T^{2} + 6131066257801 T^{4}$$)($$1 + 3353726 T^{2} + 6131066257801 T^{4}$$)($$( 1 - 7777508 T^{2} + 27043670703318 T^{4} - 47684416868577339908 T^{6} +$$$$37\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 2362 T + 2789522 T^{2} - 6676713326 T^{3} + 18957362429153 T^{4} - 27681948489238576 T^{5} + 34792033192278772784 T^{6} -$$$$80\!\cdots\!40$$$$T^{7} +$$$$10\!\cdots\!32$$$$T^{8} -$$$$57\!\cdots\!00$$$$T^{9} +$$$$11\!\cdots\!72$$$$T^{10} -$$$$22\!\cdots\!12$$$$T^{11} +$$$$12\!\cdots\!40$$$$T^{12} -$$$$11\!\cdots\!36$$$$T^{13} +$$$$58\!\cdots\!60$$$$T^{14} -$$$$88\!\cdots\!08$$$$T^{15} +$$$$18\!\cdots\!50$$$$T^{16} -$$$$39\!\cdots\!36$$$$T^{17} +$$$$64\!\cdots\!12$$$$T^{18} -$$$$99\!\cdots\!64$$$$T^{19} +$$$$11\!\cdots\!50$$$$T^{20} -$$$$13\!\cdots\!92$$$$T^{21} +$$$$21\!\cdots\!60$$$$T^{22} -$$$$10\!\cdots\!64$$$$T^{23} +$$$$29\!\cdots\!40$$$$T^{24} -$$$$13\!\cdots\!88$$$$T^{25} +$$$$16\!\cdots\!72$$$$T^{26} -$$$$20\!\cdots\!00$$$$T^{27} +$$$$87\!\cdots\!32$$$$T^{28} -$$$$17\!\cdots\!60$$$$T^{29} +$$$$18\!\cdots\!84$$$$T^{30} -$$$$36\!\cdots\!24$$$$T^{31} +$$$$61\!\cdots\!53$$$$T^{32} -$$$$53\!\cdots\!74$$$$T^{33} +$$$$55\!\cdots\!22$$$$T^{34} -$$$$11\!\cdots\!38$$$$T^{35} +$$$$12\!\cdots\!01$$$$T^{36}$$)
$23$ ($$1 - 184 T + 6436343 T^{2}$$)($$1 - 4104 T + 6436343 T^{2}$$)($$1 + 3216 T + 6436343 T^{2}$$)($$1 + 6436343 T^{2}$$)($$1 - 3216 T + 6436343 T^{2}$$)($$1 + 4104 T + 6436343 T^{2}$$)($$1 + 184 T + 6436343 T^{2}$$)($$1 + 2891758 T^{2} + 41426511213649 T^{4}$$)($$( 1 + 6436343 T^{2} )^{2}$$)($$( 1 + 11284700 T^{2} + 69827892672486 T^{4} +$$$$46\!\cdots\!00$$$$T^{6} +$$$$17\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 65704890 T^{2} + 2176003725806697 T^{4} -$$$$48\!\cdots\!28$$$$T^{6} +$$$$80\!\cdots\!92$$$$T^{8} -$$$$10\!\cdots\!92$$$$T^{10} +$$$$11\!\cdots\!28$$$$T^{12} -$$$$11\!\cdots\!20$$$$T^{14} +$$$$88\!\cdots\!26$$$$T^{16} -$$$$61\!\cdots\!80$$$$T^{18} +$$$$36\!\cdots\!74$$$$T^{20} -$$$$18\!\cdots\!20$$$$T^{22} +$$$$84\!\cdots\!72$$$$T^{24} -$$$$31\!\cdots\!92$$$$T^{26} +$$$$98\!\cdots\!08$$$$T^{28} -$$$$24\!\cdots\!28$$$$T^{30} +$$$$45\!\cdots\!53$$$$T^{32} -$$$$56\!\cdots\!90$$$$T^{34} +$$$$35\!\cdots\!49$$$$T^{36}$$)
$29$ ($$1 - 3282 T + 20511149 T^{2}$$)($$1 - 594 T + 20511149 T^{2}$$)($$1 + 2918 T + 20511149 T^{2}$$)($$1 + 2950 T + 20511149 T^{2}$$)($$1 + 2918 T + 20511149 T^{2}$$)($$1 - 594 T + 20511149 T^{2}$$)($$1 - 3282 T + 20511149 T^{2}$$)($$( 1 - 2554 T + 20511149 T^{2} )^{2}$$)($$( 1 - 20511149 T^{2} )^{2}$$)($$( 1 - 46615796 T^{2} + 1180167087778806 T^{4} -$$$$19\!\cdots\!96$$$$T^{6} +$$$$17\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 4070 T + 8282450 T^{2} - 236838145262 T^{3} + 574654149127841 T^{4} + 2895398974324775728 T^{5} +$$$$11\!\cdots\!12$$$$T^{6} +$$$$73\!\cdots\!44$$$$T^{7} -$$$$73\!\cdots\!36$$$$T^{8} -$$$$40\!\cdots\!64$$$$T^{9} +$$$$35\!\cdots\!52$$$$T^{10} +$$$$33\!\cdots\!76$$$$T^{11} +$$$$20\!\cdots\!80$$$$T^{12} -$$$$10\!\cdots\!76$$$$T^{13} -$$$$30\!\cdots\!16$$$$T^{14} -$$$$12\!\cdots\!80$$$$T^{15} +$$$$55\!\cdots\!90$$$$T^{16} +$$$$24\!\cdots\!64$$$$T^{17} -$$$$24\!\cdots\!88$$$$T^{18} +$$$$51\!\cdots\!36$$$$T^{19} +$$$$23\!\cdots\!90$$$$T^{20} -$$$$11\!\cdots\!20$$$$T^{21} -$$$$53\!\cdots\!16$$$$T^{22} -$$$$36\!\cdots\!24$$$$T^{23} +$$$$15\!\cdots\!80$$$$T^{24} +$$$$51\!\cdots\!24$$$$T^{25} +$$$$11\!\cdots\!52$$$$T^{26} -$$$$25\!\cdots\!36$$$$T^{27} -$$$$96\!\cdots\!36$$$$T^{28} +$$$$19\!\cdots\!56$$$$T^{29} +$$$$63\!\cdots\!12$$$$T^{30} +$$$$32\!\cdots\!72$$$$T^{31} +$$$$13\!\cdots\!41$$$$T^{32} -$$$$11\!\cdots\!38$$$$T^{33} +$$$$81\!\cdots\!50$$$$T^{34} -$$$$81\!\cdots\!30$$$$T^{35} +$$$$41\!\cdots\!01$$$$T^{36}$$)
$31$ ($$1 + 5728 T + 28629151 T^{2}$$)($$1 + 4256 T + 28629151 T^{2}$$)($$1 - 2624 T + 28629151 T^{2}$$)($$1 + 28629151 T^{2}$$)($$1 + 2624 T + 28629151 T^{2}$$)($$1 - 4256 T + 28629151 T^{2}$$)($$1 - 5728 T + 28629151 T^{2}$$)($$1 + 53276990 T^{2} + 819628286980801 T^{4}$$)($$( 1 + 28629151 T^{2} )^{2}$$)($$( 1 + 84570748 T^{2} + 3405599639474310 T^{4} +$$$$69\!\cdots\!48$$$$T^{6} +$$$$67\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 - 5768 T + 125978903 T^{2} - 474315485120 T^{3} + 6741247446930084 T^{4} - 13397153796297127648 T^{5} +$$$$19\!\cdots\!68$$$$T^{6} +$$$$47\!\cdots\!68$$$$T^{7} +$$$$41\!\cdots\!66$$$$T^{8} +$$$$94\!\cdots\!20$$$$T^{9} +$$$$11\!\cdots\!66$$$$T^{10} +$$$$38\!\cdots\!68$$$$T^{11} +$$$$46\!\cdots\!68$$$$T^{12} -$$$$90\!\cdots\!48$$$$T^{13} +$$$$12\!\cdots\!84$$$$T^{14} -$$$$26\!\cdots\!20$$$$T^{15} +$$$$19\!\cdots\!53$$$$T^{16} -$$$$26\!\cdots\!68$$$$T^{17} +$$$$12\!\cdots\!51$$$$T^{18} )^{2}$$)
$37$ ($$1 + 10326 T + 69343957 T^{2}$$)($$1 - 298 T + 69343957 T^{2}$$)($$1 - 9458 T + 69343957 T^{2}$$)($$1 - 12242 T + 69343957 T^{2}$$)($$1 - 9458 T + 69343957 T^{2}$$)($$1 - 298 T + 69343957 T^{2}$$)($$1 + 10326 T + 69343957 T^{2}$$)($$( 1 + 11950 T + 69343957 T^{2} )^{2}$$)($$( 1 - 69343957 T^{2} )^{2}$$)($$( 1 - 207752596 T^{2} + 19864489018719702 T^{4} -$$$$99\!\cdots\!04$$$$T^{6} +$$$$23\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 + 10650 T + 56711250 T^{2} + 917226642594 T^{3} - 532232178061711 T^{4} -$$$$12\!\cdots\!04$$$$T^{5} -$$$$89\!\cdots\!32$$$$T^{6} -$$$$15\!\cdots\!28$$$$T^{7} -$$$$15\!\cdots\!88$$$$T^{8} -$$$$22\!\cdots\!08$$$$T^{9} +$$$$23\!\cdots\!24$$$$T^{10} +$$$$55\!\cdots\!64$$$$T^{11} +$$$$14\!\cdots\!68$$$$T^{12} +$$$$86\!\cdots\!44$$$$T^{13} +$$$$37\!\cdots\!88$$$$T^{14} +$$$$35\!\cdots\!24$$$$T^{15} -$$$$38\!\cdots\!10$$$$T^{16} -$$$$59\!\cdots\!16$$$$T^{17} -$$$$31\!\cdots\!24$$$$T^{18} -$$$$40\!\cdots\!12$$$$T^{19} -$$$$18\!\cdots\!90$$$$T^{20} +$$$$11\!\cdots\!32$$$$T^{21} +$$$$86\!\cdots\!88$$$$T^{22} +$$$$13\!\cdots\!08$$$$T^{23} +$$$$16\!\cdots\!32$$$$T^{24} +$$$$42\!\cdots\!52$$$$T^{25} +$$$$12\!\cdots\!24$$$$T^{26} -$$$$82\!\cdots\!56$$$$T^{27} -$$$$40\!\cdots\!12$$$$T^{28} -$$$$27\!\cdots\!04$$$$T^{29} -$$$$11\!\cdots\!32$$$$T^{30} -$$$$10\!\cdots\!28$$$$T^{31} -$$$$31\!\cdots\!39$$$$T^{32} +$$$$37\!\cdots\!42$$$$T^{33} +$$$$16\!\cdots\!50$$$$T^{34} +$$$$21\!\cdots\!50$$$$T^{35} +$$$$13\!\cdots\!49$$$$T^{36}$$)
$41$ ($$1 + 8886 T + 115856201 T^{2}$$)($$1 - 17226 T + 115856201 T^{2}$$)($$1 - 170 T + 115856201 T^{2}$$)($$1 + 20950 T + 115856201 T^{2}$$)($$1 - 170 T + 115856201 T^{2}$$)($$1 - 17226 T + 115856201 T^{2}$$)($$1 + 8886 T + 115856201 T^{2}$$)($$( 1 + 5078 T + 115856201 T^{2} )^{2}$$)($$( 1 + 13926 T + 115856201 T^{2} )^{2}$$)($$( 1 - 13812 T + 278511286 T^{2} - 1600205848212 T^{3} + 13422659310152401 T^{4} )^{4}$$)($$1 - 1023541794 T^{2} + 517343071862859497 T^{4} -$$$$17\!\cdots\!60$$$$T^{6} +$$$$44\!\cdots\!84$$$$T^{8} -$$$$90\!\cdots\!12$$$$T^{10} +$$$$15\!\cdots\!68$$$$T^{12} -$$$$24\!\cdots\!32$$$$T^{14} +$$$$33\!\cdots\!66$$$$T^{16} -$$$$41\!\cdots\!36$$$$T^{18} +$$$$45\!\cdots\!66$$$$T^{20} -$$$$44\!\cdots\!32$$$$T^{22} +$$$$38\!\cdots\!68$$$$T^{24} -$$$$29\!\cdots\!12$$$$T^{26} +$$$$19\!\cdots\!84$$$$T^{28} -$$$$10\!\cdots\!60$$$$T^{30} +$$$$40\!\cdots\!97$$$$T^{32} -$$$$10\!\cdots\!94$$$$T^{34} +$$$$14\!\cdots\!01$$$$T^{36}$$)
$43$ ($$1 - 9188 T + 147008443 T^{2}$$)($$1 + 12100 T + 147008443 T^{2}$$)($$1 + 19928 T + 147008443 T^{2}$$)($$1 + 147008443 T^{2}$$)($$1 - 19928 T + 147008443 T^{2}$$)($$1 - 12100 T + 147008443 T^{2}$$)($$1 + 9188 T + 147008443 T^{2}$$)($$1 + 136416374 T^{2} + 21611482313284249 T^{4}$$)($$1 + 214485614 T^{2} + 21611482313284249 T^{4}$$)($$( 1 - 404372228 T^{2} + 75777916135242294 T^{4} -$$$$87\!\cdots\!72$$$$T^{6} +$$$$46\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 15382 T + 118302962 T^{2} - 3612143928786 T^{3} + 172512293409905 T^{4} +$$$$70\!\cdots\!60$$$$T^{5} -$$$$44\!\cdots\!32$$$$T^{6} +$$$$13\!\cdots\!32$$$$T^{7} -$$$$19\!\cdots\!68$$$$T^{8} -$$$$31\!\cdots\!20$$$$T^{9} +$$$$30\!\cdots\!64$$$$T^{10} -$$$$10\!\cdots\!12$$$$T^{11} +$$$$47\!\cdots\!52$$$$T^{12} -$$$$27\!\cdots\!88$$$$T^{13} +$$$$11\!\cdots\!40$$$$T^{14} -$$$$24\!\cdots\!52$$$$T^{15} -$$$$32\!\cdots\!70$$$$T^{16} +$$$$60\!\cdots\!56$$$$T^{17} -$$$$33\!\cdots\!28$$$$T^{18} +$$$$88\!\cdots\!08$$$$T^{19} -$$$$69\!\cdots\!30$$$$T^{20} -$$$$78\!\cdots\!64$$$$T^{21} +$$$$55\!\cdots\!40$$$$T^{22} -$$$$19\!\cdots\!84$$$$T^{23} +$$$$47\!\cdots\!48$$$$T^{24} -$$$$15\!\cdots\!84$$$$T^{25} +$$$$67\!\cdots\!64$$$$T^{26} -$$$$10\!\cdots\!60$$$$T^{27} -$$$$91\!\cdots\!32$$$$T^{28} +$$$$96\!\cdots\!24$$$$T^{29} -$$$$44\!\cdots\!32$$$$T^{30} +$$$$10\!\cdots\!80$$$$T^{31} +$$$$37\!\cdots\!45$$$$T^{32} -$$$$11\!\cdots\!02$$$$T^{33} +$$$$56\!\cdots\!62$$$$T^{34} -$$$$10\!\cdots\!26$$$$T^{35} +$$$$10\!\cdots\!49$$$$T^{36}$$)
$47$ ($$1 - 23664 T + 229345007 T^{2}$$)($$1 - 1296 T + 229345007 T^{2}$$)($$1 + 32 T + 229345007 T^{2}$$)($$1 + 229345007 T^{2}$$)($$1 - 32 T + 229345007 T^{2}$$)($$1 + 1296 T + 229345007 T^{2}$$)($$1 + 23664 T + 229345007 T^{2}$$)($$1 + 307289566 T^{2} + 52599132235830049 T^{4}$$)($$( 1 + 229345007 T^{2} )^{2}$$)($$( 1 + 193552316 T^{2} + 109332805721221830 T^{4} +$$$$10\!\cdots\!84$$$$T^{6} +$$$$27\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 + 22088 T + 1356331495 T^{2} + 27020989683136 T^{3} + 853008998941628452 T^{4} +$$$$14\!\cdots\!20$$$$T^{5} +$$$$33\!\cdots\!56$$$$T^{6} +$$$$49\!\cdots\!76$$$$T^{7} +$$$$97\!\cdots\!78$$$$T^{8} +$$$$12\!\cdots\!16$$$$T^{9} +$$$$22\!\cdots\!46$$$$T^{10} +$$$$26\!\cdots\!24$$$$T^{11} +$$$$40\!\cdots\!08$$$$T^{12} +$$$$40\!\cdots\!20$$$$T^{13} +$$$$54\!\cdots\!64$$$$T^{14} +$$$$39\!\cdots\!64$$$$T^{15} +$$$$45\!\cdots\!85$$$$T^{16} +$$$$16\!\cdots\!88$$$$T^{17} +$$$$17\!\cdots\!07$$$$T^{18} )^{2}$$)
$53$ ($$1 + 11686 T + 418195493 T^{2}$$)($$1 + 19494 T + 418195493 T^{2}$$)($$1 - 22178 T + 418195493 T^{2}$$)($$1 + 7294 T + 418195493 T^{2}$$)($$1 - 22178 T + 418195493 T^{2}$$)($$1 + 19494 T + 418195493 T^{2}$$)($$1 + 11686 T + 418195493 T^{2}$$)($$( 1 - 19714 T + 418195493 T^{2} )^{2}$$)($$( 1 - 418195493 T^{2} )^{2}$$)($$( 1 - 636002516 T^{2} + 183817193534771862 T^{4} -$$$$11\!\cdots\!84$$$$T^{6} +$$$$30\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 24726 T + 305687538 T^{2} - 10125112960046 T^{3} + 254917191364521361 T^{4} -$$$$21\!\cdots\!64$$$$T^{5} +$$$$27\!\cdots\!04$$$$T^{6} -$$$$63\!\cdots\!44$$$$T^{7} -$$$$55\!\cdots\!48$$$$T^{8} +$$$$13\!\cdots\!00$$$$T^{9} -$$$$14\!\cdots\!48$$$$T^{10} +$$$$52\!\cdots\!88$$$$T^{11} -$$$$14\!\cdots\!40$$$$T^{12} +$$$$86\!\cdots\!12$$$$T^{13} -$$$$39\!\cdots\!52$$$$T^{14} -$$$$92\!\cdots\!88$$$$T^{15} +$$$$25\!\cdots\!74$$$$T^{16} -$$$$44\!\cdots\!92$$$$T^{17} +$$$$49\!\cdots\!16$$$$T^{18} -$$$$18\!\cdots\!56$$$$T^{19} +$$$$44\!\cdots\!26$$$$T^{20} -$$$$67\!\cdots\!16$$$$T^{21} -$$$$11\!\cdots\!52$$$$T^{22} +$$$$11\!\cdots\!16$$$$T^{23} -$$$$79\!\cdots\!60$$$$T^{24} +$$$$11\!\cdots\!16$$$$T^{25} -$$$$13\!\cdots\!48$$$$T^{26} +$$$$52\!\cdots\!00$$$$T^{27} -$$$$91\!\cdots\!52$$$$T^{28} -$$$$43\!\cdots\!08$$$$T^{29} +$$$$78\!\cdots\!04$$$$T^{30} -$$$$26\!\cdots\!52$$$$T^{31} +$$$$12\!\cdots\!89$$$$T^{32} -$$$$21\!\cdots\!22$$$$T^{33} +$$$$26\!\cdots\!38$$$$T^{34} -$$$$90\!\cdots\!18$$$$T^{35} +$$$$15\!\cdots\!49$$$$T^{36}$$)
$59$ ($$1 + 16876 T + 714924299 T^{2}$$)($$1 + 7668 T + 714924299 T^{2}$$)($$1 - 41480 T + 714924299 T^{2}$$)($$1 + 714924299 T^{2}$$)($$1 + 41480 T + 714924299 T^{2}$$)($$1 - 7668 T + 714924299 T^{2}$$)($$1 - 16876 T + 714924299 T^{2}$$)($$1 + 1350713110 T^{2} + 511116753300641401 T^{4}$$)($$1 + 921043598 T^{2} + 511116753300641401 T^{4}$$)($$( 1 - 710599364 T^{2} + 399210125791716726 T^{4} -$$$$36\!\cdots\!64$$$$T^{6} +$$$$26\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 29734 T + 442055378 T^{2} + 11048743474590 T^{3} + 1067338799101245777 T^{4} -$$$$43\!\cdots\!64$$$$T^{5} +$$$$88\!\cdots\!20$$$$T^{6} +$$$$20\!\cdots\!96$$$$T^{7} +$$$$35\!\cdots\!12$$$$T^{8} -$$$$35\!\cdots\!00$$$$T^{9} +$$$$11\!\cdots\!12$$$$T^{10} +$$$$12\!\cdots\!28$$$$T^{11} -$$$$11\!\cdots\!04$$$$T^{12} -$$$$17\!\cdots\!76$$$$T^{13} +$$$$94\!\cdots\!60$$$$T^{14} +$$$$13\!\cdots\!24$$$$T^{15} -$$$$15\!\cdots\!82$$$$T^{16} -$$$$51\!\cdots\!12$$$$T^{17} +$$$$57\!\cdots\!32$$$$T^{18} -$$$$36\!\cdots\!88$$$$T^{19} -$$$$79\!\cdots\!82$$$$T^{20} +$$$$49\!\cdots\!76$$$$T^{21} +$$$$24\!\cdots\!60$$$$T^{22} -$$$$32\!\cdots\!24$$$$T^{23} -$$$$15\!\cdots\!04$$$$T^{24} +$$$$12\!\cdots\!72$$$$T^{25} +$$$$76\!\cdots\!12$$$$T^{26} -$$$$17\!\cdots\!00$$$$T^{27} +$$$$12\!\cdots\!12$$$$T^{28} +$$$$51\!\cdots\!04$$$$T^{29} +$$$$15\!\cdots\!20$$$$T^{30} -$$$$55\!\cdots\!36$$$$T^{31} +$$$$97\!\cdots\!77$$$$T^{32} +$$$$71\!\cdots\!10$$$$T^{33} +$$$$20\!\cdots\!78$$$$T^{34} -$$$$99\!\cdots\!66$$$$T^{35} +$$$$23\!\cdots\!01$$$$T^{36}$$)
$61$ ($$1 - 18482 T + 844596301 T^{2}$$)($$1 - 34738 T + 844596301 T^{2}$$)($$1 + 15462 T + 844596301 T^{2}$$)($$1 + 18950 T + 844596301 T^{2}$$)($$1 + 15462 T + 844596301 T^{2}$$)($$1 - 34738 T + 844596301 T^{2}$$)($$1 - 18482 T + 844596301 T^{2}$$)($$( 1 + 29318 T + 844596301 T^{2} )^{2}$$)($$( 1 - 844596301 T^{2} )^{2}$$)($$( 1 - 592981876 T^{2} + 819511289079885174 T^{4} -$$$$42\!\cdots\!76$$$$T^{6} +$$$$50\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 + 48082 T + 1155939362 T^{2} + 42137800674218 T^{3} + 3237087838918633697 T^{4} +$$$$11\!\cdots\!96$$$$T^{5} +$$$$27\!\cdots\!20$$$$T^{6} +$$$$10\!\cdots\!24$$$$T^{7} +$$$$41\!\cdots\!04$$$$T^{8} +$$$$10\!\cdots\!44$$$$T^{9} +$$$$22\!\cdots\!60$$$$T^{10} +$$$$77\!\cdots\!28$$$$T^{11} +$$$$17\!\cdots\!60$$$$T^{12} +$$$$16\!\cdots\!16$$$$T^{13} +$$$$25\!\cdots\!08$$$$T^{14} -$$$$46\!\cdots\!56$$$$T^{15} -$$$$79\!\cdots\!18$$$$T^{16} -$$$$25\!\cdots\!40$$$$T^{17} -$$$$51\!\cdots\!12$$$$T^{18} -$$$$21\!\cdots\!40$$$$T^{19} -$$$$56\!\cdots\!18$$$$T^{20} -$$$$27\!\cdots\!56$$$$T^{21} +$$$$12\!\cdots\!08$$$$T^{22} +$$$$70\!\cdots\!16$$$$T^{23} +$$$$64\!\cdots\!60$$$$T^{24} +$$$$23\!\cdots\!28$$$$T^{25} +$$$$58\!\cdots\!60$$$$T^{26} +$$$$22\!\cdots\!44$$$$T^{27} +$$$$76\!\cdots\!04$$$$T^{28} +$$$$15\!\cdots\!24$$$$T^{29} +$$$$36\!\cdots\!20$$$$T^{30} +$$$$13\!\cdots\!96$$$$T^{31} +$$$$30\!\cdots\!97$$$$T^{32} +$$$$33\!\cdots\!18$$$$T^{33} +$$$$77\!\cdots\!62$$$$T^{34} +$$$$27\!\cdots\!82$$$$T^{35} +$$$$47\!\cdots\!01$$$$T^{36}$$)
$67$ ($$1 - 15532 T + 1350125107 T^{2}$$)($$1 - 21812 T + 1350125107 T^{2}$$)($$1 + 20744 T + 1350125107 T^{2}$$)($$1 + 1350125107 T^{2}$$)($$1 - 20744 T + 1350125107 T^{2}$$)($$1 + 21812 T + 1350125107 T^{2}$$)($$1 + 15532 T + 1350125107 T^{2}$$)($$1 + 2415413606 T^{2} + 1822837804551761449 T^{4}$$)($$1 + 1813708382 T^{2} + 1822837804551761449 T^{4}$$)($$( 1 - 2595461924 T^{2} + 4235124730923029142 T^{4} -$$$$47\!\cdots\!76$$$$T^{6} +$$$$33\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 75210 T + 2828272050 T^{2} - 170812394979710 T^{3} + 12219123993490668673 T^{4} -$$$$43\!\cdots\!80$$$$T^{5} +$$$$13\!\cdots\!00$$$$T^{6} -$$$$65\!\cdots\!12$$$$T^{7} +$$$$31\!\cdots\!44$$$$T^{8} -$$$$90\!\cdots\!60$$$$T^{9} +$$$$26\!\cdots\!20$$$$T^{10} -$$$$13\!\cdots\!56$$$$T^{11} +$$$$68\!\cdots\!32$$$$T^{12} -$$$$17\!\cdots\!60$$$$T^{13} +$$$$48\!\cdots\!72$$$$T^{14} -$$$$23\!\cdots\!60$$$$T^{15} +$$$$96\!\cdots\!06$$$$T^{16} -$$$$20\!\cdots\!36$$$$T^{17} +$$$$51\!\cdots\!96$$$$T^{18} -$$$$27\!\cdots\!52$$$$T^{19} +$$$$17\!\cdots\!94$$$$T^{20} -$$$$57\!\cdots\!80$$$$T^{21} +$$$$15\!\cdots\!72$$$$T^{22} -$$$$80\!\cdots\!20$$$$T^{23} +$$$$41\!\cdots\!68$$$$T^{24} -$$$$11\!\cdots\!08$$$$T^{25} +$$$$29\!\cdots\!20$$$$T^{26} -$$$$13\!\cdots\!20$$$$T^{27} +$$$$64\!\cdots\!56$$$$T^{28} -$$$$17\!\cdots\!16$$$$T^{29} +$$$$47\!\cdots\!00$$$$T^{30} -$$$$21\!\cdots\!60$$$$T^{31} +$$$$81\!\cdots\!77$$$$T^{32} -$$$$15\!\cdots\!30$$$$T^{33} +$$$$34\!\cdots\!50$$$$T^{34} -$$$$12\!\cdots\!70$$$$T^{35} +$$$$22\!\cdots\!49$$$$T^{36}$$)
$71$ ($$1 + 31960 T + 1804229351 T^{2}$$)($$1 - 46872 T + 1804229351 T^{2}$$)($$1 + 28592 T + 1804229351 T^{2}$$)($$1 + 1804229351 T^{2}$$)($$1 - 28592 T + 1804229351 T^{2}$$)($$1 + 46872 T + 1804229351 T^{2}$$)($$1 - 31960 T + 1804229351 T^{2}$$)($$1 - 2948789810 T^{2} + 3255243551009881201 T^{4}$$)($$( 1 + 1804229351 T^{2} )^{2}$$)($$( 1 + 6856248476 T^{2} + 18258947260812228774 T^{4} +$$$$22\!\cdots\!76$$$$T^{6} +$$$$10\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 - 22544733018 T^{2} +$$$$24\!\cdots\!73$$$$T^{4} -$$$$17\!\cdots\!92$$$$T^{6} +$$$$91\!\cdots\!04$$$$T^{8} -$$$$36\!\cdots\!20$$$$T^{10} +$$$$11\!\cdots\!44$$$$T^{12} -$$$$32\!\cdots\!12$$$$T^{14} +$$$$73\!\cdots\!82$$$$T^{16} -$$$$14\!\cdots\!24$$$$T^{18} +$$$$23\!\cdots\!82$$$$T^{20} -$$$$34\!\cdots\!12$$$$T^{22} +$$$$41\!\cdots\!44$$$$T^{24} -$$$$41\!\cdots\!20$$$$T^{26} +$$$$33\!\cdots\!04$$$$T^{28} -$$$$21\!\cdots\!92$$$$T^{30} +$$$$96\!\cdots\!73$$$$T^{32} -$$$$28\!\cdots\!18$$$$T^{34} +$$$$41\!\cdots\!01$$$$T^{36}$$)
$73$ ($$1 + 4886 T + 2073071593 T^{2}$$)($$1 - 67562 T + 2073071593 T^{2}$$)($$1 + 53670 T + 2073071593 T^{2}$$)($$1 + 88806 T + 2073071593 T^{2}$$)($$1 + 53670 T + 2073071593 T^{2}$$)($$1 - 67562 T + 2073071593 T^{2}$$)($$1 + 4886 T + 2073071593 T^{2}$$)($$( 1 - 37914 T + 2073071593 T^{2} )^{2}$$)($$( 1 - 50402 T + 2073071593 T^{2} )^{2}$$)($$( 1 + 47708 T + 3883557654 T^{2} + 98902099558844 T^{3} + 4297625829703557649 T^{4} )^{4}$$)($$1 - 20520707858 T^{2} +$$$$20\!\cdots\!01$$$$T^{4} -$$$$14\!\cdots\!56$$$$T^{6} +$$$$71\!\cdots\!32$$$$T^{8} -$$$$28\!\cdots\!92$$$$T^{10} +$$$$97\!\cdots\!12$$$$T^{12} -$$$$27\!\cdots\!16$$$$T^{14} +$$$$69\!\cdots\!66$$$$T^{16} -$$$$15\!\cdots\!56$$$$T^{18} +$$$$30\!\cdots\!34$$$$T^{20} -$$$$51\!\cdots\!16$$$$T^{22} +$$$$77\!\cdots\!88$$$$T^{24} -$$$$98\!\cdots\!92$$$$T^{26} +$$$$10\!\cdots\!68$$$$T^{28} -$$$$88\!\cdots\!56$$$$T^{30} +$$$$56\!\cdots\!49$$$$T^{32} -$$$$23\!\cdots\!58$$$$T^{34} +$$$$50\!\cdots\!49$$$$T^{36}$$)
$79$ ($$1 - 44560 T + 3077056399 T^{2}$$)($$1 - 76912 T + 3077056399 T^{2}$$)($$1 - 69152 T + 3077056399 T^{2}$$)($$1 + 3077056399 T^{2}$$)($$1 + 69152 T + 3077056399 T^{2}$$)($$1 + 76912 T + 3077056399 T^{2}$$)($$1 + 44560 T + 3077056399 T^{2}$$)($$1 - 1729880290 T^{2} + 9468276082626847201 T^{4}$$)($$( 1 + 3077056399 T^{2} )^{2}$$)($$( 1 + 1040777788 T^{2} + 2897024027638170438 T^{4} +$$$$98\!\cdots\!88$$$$T^{6} +$$$$89\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 - 26432 T + 16735348231 T^{2} - 147423503361536 T^{3} +$$$$12\!\cdots\!52$$$$T^{4} +$$$$13\!\cdots\!88$$$$T^{5} +$$$$53\!\cdots\!44$$$$T^{6} +$$$$16\!\cdots\!52$$$$T^{7} +$$$$17\!\cdots\!94$$$$T^{8} +$$$$75\!\cdots\!96$$$$T^{9} +$$$$53\!\cdots\!06$$$$T^{10} +$$$$15\!\cdots\!52$$$$T^{11} +$$$$15\!\cdots\!56$$$$T^{12} +$$$$11\!\cdots\!88$$$$T^{13} +$$$$33\!\cdots\!48$$$$T^{14} -$$$$12\!\cdots\!36$$$$T^{15} +$$$$43\!\cdots\!69$$$$T^{16} -$$$$21\!\cdots\!32$$$$T^{17} +$$$$24\!\cdots\!99$$$$T^{18} )^{2}$$)
$83$ ($$1 + 67364 T + 3939040643 T^{2}$$)($$1 - 67716 T + 3939040643 T^{2}$$)($$1 + 37800 T + 3939040643 T^{2}$$)($$1 + 3939040643 T^{2}$$)($$1 - 37800 T + 3939040643 T^{2}$$)($$1 + 67716 T + 3939040643 T^{2}$$)($$1 - 67364 T + 3939040643 T^{2}$$)($$1 + 6331666438 T^{2} + 15516041187205853449 T^{4}$$)($$1 + 96051518 T^{2} + 15516041187205853449 T^{4}$$)($$( 1 - 9252333668 T^{2} + 44623630841831701206 T^{4} -$$$$14\!\cdots\!32$$$$T^{6} +$$$$24\!\cdots\!01$$$$T^{8} )^{2}$$)($$1 + 227838 T + 25955077122 T^{2} + 1270371885318330 T^{3} - 42899065933744508063 T^{4} -$$$$92\!\cdots\!00$$$$T^{5} -$$$$19\!\cdots\!64$$$$T^{6} +$$$$59\!\cdots\!12$$$$T^{7} +$$$$62\!\cdots\!00$$$$T^{8} +$$$$15\!\cdots\!60$$$$T^{9} -$$$$15\!\cdots\!92$$$$T^{10} -$$$$12\!\cdots\!00$$$$T^{11} +$$$$17\!\cdots\!16$$$$T^{12} +$$$$69\!\cdots\!96$$$$T^{13} +$$$$30\!\cdots\!72$$$$T^{14} -$$$$79\!\cdots\!68$$$$T^{15} -$$$$93\!\cdots\!34$$$$T^{16} +$$$$21\!\cdots\!76$$$$T^{17} +$$$$49\!\cdots\!56$$$$T^{18} +$$$$82\!\cdots\!68$$$$T^{19} -$$$$14\!\cdots\!66$$$$T^{20} -$$$$48\!\cdots\!76$$$$T^{21} +$$$$72\!\cdots\!72$$$$T^{22} +$$$$65\!\cdots\!28$$$$T^{23} +$$$$66\!\cdots\!84$$$$T^{24} -$$$$18\!\cdots\!00$$$$T^{25} -$$$$91\!\cdots\!92$$$$T^{26} +$$$$35\!\cdots\!80$$$$T^{27} +$$$$55\!\cdots\!00$$$$T^{28} +$$$$20\!\cdots\!84$$$$T^{29} -$$$$26\!\cdots\!64$$$$T^{30} -$$$$50\!\cdots\!00$$$$T^{31} -$$$$92\!\cdots\!87$$$$T^{32} +$$$$10\!\cdots\!10$$$$T^{33} +$$$$87\!\cdots\!22$$$$T^{34} +$$$$30\!\cdots\!34$$$$T^{35} +$$$$52\!\cdots\!49$$$$T^{36}$$)
$89$ ($$1 - 71994 T + 5584059449 T^{2}$$)($$1 - 29754 T + 5584059449 T^{2}$$)($$1 + 126806 T + 5584059449 T^{2}$$)($$1 - 51050 T + 5584059449 T^{2}$$)($$1 + 126806 T + 5584059449 T^{2}$$)($$1 - 29754 T + 5584059449 T^{2}$$)($$1 - 71994 T + 5584059449 T^{2}$$)($$( 1 - 13930 T + 5584059449 T^{2} )^{2}$$)($$( 1 - 7218 T + 5584059449 T^{2} )^{2}$$)($$( 1 - 17988 T + 11168331766 T^{2} - 100446061368612 T^{3} + 31181719929966183601 T^{4} )^{4}$$)($$1 - 48706783410 T^{2} +$$$$12\!\cdots\!33$$$$T^{4} -$$$$20\!\cdots\!28$$$$T^{6} +$$$$26\!\cdots\!60$$$$T^{8} -$$$$26\!\cdots\!24$$$$T^{10} +$$$$22\!\cdots\!84$$$$T^{12} -$$$$16\!\cdots\!64$$$$T^{14} +$$$$10\!\cdots\!38$$$$T^{16} -$$$$60\!\cdots\!40$$$$T^{18} +$$$$32\!\cdots\!38$$$$T^{20} -$$$$15\!\cdots\!64$$$$T^{22} +$$$$67\!\cdots\!84$$$$T^{24} -$$$$24\!\cdots\!24$$$$T^{26} +$$$$76\!\cdots\!60$$$$T^{28} -$$$$18\!\cdots\!28$$$$T^{30} +$$$$34\!\cdots\!33$$$$T^{32} -$$$$43\!\cdots\!10$$$$T^{34} +$$$$27\!\cdots\!01$$$$T^{36}$$)
$97$ ($$1 - 48866 T + 8587340257 T^{2}$$)($$1 + 122398 T + 8587340257 T^{2}$$)($$1 - 62290 T + 8587340257 T^{2}$$)($$1 + 92142 T + 8587340257 T^{2}$$)($$1 - 62290 T + 8587340257 T^{2}$$)($$1 + 122398 T + 8587340257 T^{2}$$)($$1 - 48866 T + 8587340257 T^{2}$$)($$( 1 - 163602 T + 8587340257 T^{2} )^{2}$$)($$( 1 - 85450 T + 8587340257 T^{2} )^{2}$$)($$( 1 - 32948 T + 15595369062 T^{2} - 282935686787636 T^{3} + 73742412689492826049 T^{4} )^{4}$$)($$( 1 + 2 T + 45080913113 T^{2} + 68457506698736 T^{3} +$$$$92\!\cdots\!28$$$$T^{4} +$$$$19\!\cdots\!44$$$$T^{5} +$$$$11\!\cdots\!24$$$$T^{6} +$$$$24\!\cdots\!52$$$$T^{7} +$$$$11\!\cdots\!78$$$$T^{8} +$$$$23\!\cdots\!24$$$$T^{9} +$$$$98\!\cdots\!46$$$$T^{10} +$$$$18\!\cdots\!48$$$$T^{11} +$$$$75\!\cdots\!32$$$$T^{12} +$$$$10\!\cdots\!44$$$$T^{13} +$$$$43\!\cdots\!96$$$$T^{14} +$$$$27\!\cdots\!64$$$$T^{15} +$$$$15\!\cdots\!09$$$$T^{16} +$$$$59\!\cdots\!02$$$$T^{17} +$$$$25\!\cdots\!57$$$$T^{18} )^{2}$$)