Properties

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

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