Properties

Label 90.6
Level 90
Weight 6
Dimension 259
Nonzero newspaces 6
Newform subspaces 20
Sturm bound 2592
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 20 \)
Sturm bound: \(2592\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(90))\).

Total New Old
Modular forms 1144 259 885
Cusp forms 1016 259 757
Eisenstein series 128 0 128

Trace form

\( 259q + 12q^{2} - 18q^{3} + 80q^{4} + 127q^{5} + 168q^{6} + 44q^{7} - 192q^{8} - 1406q^{9} + O(q^{10}) \) \( 259q + 12q^{2} - 18q^{3} + 80q^{4} + 127q^{5} + 168q^{6} + 44q^{7} - 192q^{8} - 1406q^{9} + 1300q^{10} + 2966q^{11} + 640q^{12} - 2150q^{13} - 1648q^{14} - 7008q^{15} + 2304q^{16} - 3402q^{17} - 592q^{18} + 11248q^{19} + 5936q^{20} + 22500q^{21} + 6136q^{22} + 18828q^{23} - 1152q^{24} - 1911q^{25} - 31944q^{26} - 46392q^{27} - 4864q^{28} - 8106q^{29} + 7488q^{30} + 1224q^{31} + 3072q^{32} + 66562q^{33} + 31344q^{34} + 33488q^{35} - 9440q^{36} + 48694q^{37} - 20280q^{38} + 1408q^{39} - 7872q^{40} - 59128q^{41} + 7744q^{42} - 11990q^{43} - 13952q^{44} + 143396q^{45} - 94240q^{46} - 72084q^{47} - 3584q^{48} + 30909q^{49} - 58916q^{50} - 21402q^{51} + 58144q^{52} + 36030q^{53} + 75576q^{54} + 104868q^{55} + 30976q^{56} - 80902q^{57} - 57112q^{58} - 317638q^{59} - 96512q^{60} - 122126q^{61} - 156960q^{62} + 29960q^{63} - 102400q^{64} + 307002q^{65} + 42432q^{66} + 216542q^{67} + 131904q^{68} + 172280q^{69} + 151440q^{70} + 290376q^{71} + 119424q^{72} - 128274q^{73} - 319144q^{74} - 323706q^{75} - 263904q^{76} - 984324q^{77} - 585520q^{78} - 323456q^{79} - 50432q^{80} - 423694q^{81} - 123464q^{82} + 241164q^{83} + 199488q^{84} + 498130q^{85} + 935464q^{86} + 806668q^{87} + 98176q^{88} + 620590q^{89} + 441280q^{90} + 227072q^{91} + 301248q^{92} + 882152q^{93} + 387504q^{94} + 640044q^{95} + 16384q^{96} + 52708q^{97} - 1247148q^{98} - 2187572q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.6.a \(\chi_{90}(1, \cdot)\) 90.6.a.a 1 1
90.6.a.b 1
90.6.a.c 1
90.6.a.d 1
90.6.a.e 1
90.6.a.f 1
90.6.a.g 1
90.6.c \(\chi_{90}(19, \cdot)\) 90.6.c.a 2 1
90.6.c.b 2
90.6.c.c 4
90.6.c.d 4
90.6.e \(\chi_{90}(31, \cdot)\) 90.6.e.a 8 2
90.6.e.b 10
90.6.e.c 10
90.6.e.d 12
90.6.f \(\chi_{90}(17, \cdot)\) 90.6.f.a 4 2
90.6.f.b 4
90.6.f.c 12
90.6.i \(\chi_{90}(49, \cdot)\) 90.6.i.a 60 2
90.6.l \(\chi_{90}(23, \cdot)\) 90.6.l.a 120 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(90)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( 1 + 16 T^{2} \))(\( 1 + 16 T^{2} \))(\( ( 1 + 16 T^{2} )^{2} \))(\( ( 1 + 16 T^{2} )^{2} \))(\( ( 1 + 4 T + 16 T^{2} )^{4} \))(\( ( 1 + 4 T + 16 T^{2} )^{5} \))(\( ( 1 - 4 T + 16 T^{2} )^{5} \))(\( ( 1 - 4 T + 16 T^{2} )^{6} \))(\( 1 + 256 T^{4} \))(\( 1 + 256 T^{4} \))(\( ( 1 + 256 T^{4} )^{3} \))
$3$ (\( 1 - 24 T + 144 T^{2} + 6642 T^{3} - 161109 T^{4} + 1614006 T^{5} + 8503056 T^{6} - 344373768 T^{7} + 3486784401 T^{8} \))(\( 1 + 39 T + 885 T^{2} + 17172 T^{3} + 363609 T^{4} + 6571935 T^{5} + 88356987 T^{6} + 1013989428 T^{7} + 12698782695 T^{8} + 135984591639 T^{9} + 847288609443 T^{10} \))(\( 1 - 9 T + 435 T^{2} - 2322 T^{3} + 33129 T^{4} - 142155 T^{5} + 8050347 T^{6} - 137111778 T^{7} + 6241774545 T^{8} - 31381059609 T^{9} + 847288609443 T^{10} \))(\( 1 + 16 T + 79 T^{2} + 2010 T^{3} + 104688 T^{4} + 1501092 T^{5} + 10253385 T^{6} + 364765356 T^{7} + 6181721712 T^{8} + 28841303070 T^{9} + 275455967679 T^{10} + 13556617751088 T^{11} + 205891132094649 T^{12} \))
$5$ (\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 110 T + 3125 T^{2} \))(\( 1 - 110 T + 3125 T^{2} \))(\( 1 + 6 T + 5010 T^{2} + 18750 T^{3} + 9765625 T^{4} \))(\( 1 - 1350 T^{2} + 9765625 T^{4} \))(\( ( 1 + 25 T + 625 T^{2} )^{4} \))(\( ( 1 - 25 T + 625 T^{2} )^{5} \))(\( ( 1 + 25 T + 625 T^{2} )^{5} \))(\( ( 1 - 25 T + 625 T^{2} )^{6} \))(\( 1 - 2200 T^{2} + 9765625 T^{4} \))(\( 1 + 5000 T^{2} + 9765625 T^{4} \))(\( 1 - 5352 T^{2} + 1274475 T^{4} + 45260750000 T^{6} + 12446044921875 T^{8} - 510406494140625000 T^{10} + \)\(93\!\cdots\!25\)\( T^{12} \))
$7$ (\( 1 - 32 T + 16807 T^{2} \))(\( 1 + 118 T + 16807 T^{2} \))(\( 1 - 98 T + 16807 T^{2} \))(\( 1 + 172 T + 16807 T^{2} \))(\( 1 - 98 T + 16807 T^{2} \))(\( 1 + 22 T + 16807 T^{2} \))(\( 1 - 164 T + 16807 T^{2} \))(\( 1 - 8650 T^{2} + 282475249 T^{4} \))(\( 1 - 33598 T^{2} + 282475249 T^{4} \))(\( 1 + 1720 T^{2} + 159889998 T^{4} + 485857428280 T^{6} + 79792266297612001 T^{8} \))(\( ( 1 - 33310 T^{2} + 282475249 T^{4} )^{2} \))(\( 1 - 172 T - 45396 T^{2} + 4483036 T^{3} + 2175130973 T^{4} - 126045374202 T^{5} - 53625693538328 T^{6} + 477599996839466 T^{7} + 1155074616048760236 T^{8} + 8027023146880905062 T^{9} - \)\(15\!\cdots\!72\)\( T^{10} - \)\(59\!\cdots\!86\)\( T^{11} + \)\(17\!\cdots\!73\)\( T^{12} + \)\(60\!\cdots\!52\)\( T^{13} - \)\(10\!\cdots\!04\)\( T^{14} - \)\(65\!\cdots\!96\)\( T^{15} + \)\(63\!\cdots\!01\)\( T^{16} \))(\( 1 + 109 T - 45284 T^{2} - 6332271 T^{3} + 893253900 T^{4} + 135029011215 T^{5} - 16072152357720 T^{6} - 1016358090080655 T^{7} + 440886843277697463 T^{8} + 710062828789658758 T^{9} - \)\(95\!\cdots\!76\)\( T^{10} + \)\(11\!\cdots\!06\)\( T^{11} + \)\(12\!\cdots\!87\)\( T^{12} - \)\(48\!\cdots\!65\)\( T^{13} - \)\(12\!\cdots\!20\)\( T^{14} + \)\(18\!\cdots\!05\)\( T^{15} + \)\(20\!\cdots\!00\)\( T^{16} - \)\(23\!\cdots\!53\)\( T^{17} - \)\(28\!\cdots\!84\)\( T^{18} + \)\(11\!\cdots\!63\)\( T^{19} + \)\(17\!\cdots\!49\)\( T^{20} \))(\( 1 + 16 T - 26339 T^{2} - 4492644 T^{3} + 306137190 T^{4} + 138997375950 T^{5} + 7223822420325 T^{6} - 2848865108541960 T^{7} - 344303877707569947 T^{8} + 18850999602565435642 T^{9} + \)\(87\!\cdots\!24\)\( T^{10} + \)\(31\!\cdots\!94\)\( T^{11} - \)\(97\!\cdots\!03\)\( T^{12} - \)\(13\!\cdots\!80\)\( T^{13} + \)\(57\!\cdots\!25\)\( T^{14} + \)\(18\!\cdots\!50\)\( T^{15} + \)\(69\!\cdots\!10\)\( T^{16} - \)\(17\!\cdots\!92\)\( T^{17} - \)\(16\!\cdots\!39\)\( T^{18} + \)\(17\!\cdots\!12\)\( T^{19} + \)\(17\!\cdots\!49\)\( T^{20} \))(\( 1 - 69 T - 15123 T^{2} + 9219538 T^{3} - 564600675 T^{4} - 110074553673 T^{5} + 40905159128884 T^{6} - 2213351391830553 T^{7} - 377816222838627693 T^{8} + \)\(12\!\cdots\!26\)\( T^{9} - \)\(59\!\cdots\!89\)\( T^{10} - \)\(85\!\cdots\!97\)\( T^{11} + \)\(28\!\cdots\!02\)\( T^{12} - \)\(14\!\cdots\!79\)\( T^{13} - \)\(16\!\cdots\!61\)\( T^{14} + \)\(57\!\cdots\!18\)\( T^{15} - \)\(30\!\cdots\!93\)\( T^{16} - \)\(29\!\cdots\!71\)\( T^{17} + \)\(92\!\cdots\!16\)\( T^{18} - \)\(41\!\cdots\!39\)\( T^{19} - \)\(35\!\cdots\!75\)\( T^{20} + \)\(98\!\cdots\!66\)\( T^{21} - \)\(27\!\cdots\!27\)\( T^{22} - \)\(20\!\cdots\!67\)\( T^{23} + \)\(50\!\cdots\!01\)\( T^{24} \))(\( ( 1 + 104 T + 5408 T^{2} + 1747928 T^{3} + 282475249 T^{4} )^{2} \))(\( ( 1 + 44 T + 968 T^{2} + 739508 T^{3} + 282475249 T^{4} )^{2} \))(\( ( 1 - 72 T + 2592 T^{2} + 1653800 T^{3} - 278157165 T^{4} - 13719293232 T^{5} + 3076299704384 T^{6} - 230580161350224 T^{7} - 78572514444509085 T^{8} + 7851517225143733400 T^{9} + \)\(20\!\cdots\!92\)\( T^{10} - \)\(96\!\cdots\!04\)\( T^{11} + \)\(22\!\cdots\!49\)\( T^{12} )^{2} \))
$11$ (\( 1 + 12 T + 161051 T^{2} \))(\( 1 + 192 T + 161051 T^{2} \))(\( 1 + 354 T + 161051 T^{2} \))(\( 1 + 132 T + 161051 T^{2} \))(\( 1 - 354 T + 161051 T^{2} \))(\( 1 - 768 T + 161051 T^{2} \))(\( 1 + 720 T + 161051 T^{2} \))(\( ( 1 - 148 T + 161051 T^{2} )^{2} \))(\( ( 1 - 500 T + 161051 T^{2} )^{2} \))(\( ( 1 + 174 T + 298446 T^{2} + 28022874 T^{3} + 25937424601 T^{4} )^{2} \))(\( ( 1 - 94074 T^{2} + 25937424601 T^{4} )^{2} \))(\( 1 - 462 T - 303056 T^{2} + 221323836 T^{3} + 45997960606 T^{4} - 49996168402446 T^{5} + 3416857639497808 T^{6} + 3802463213931170034 T^{7} - \)\(12\!\cdots\!53\)\( T^{8} + \)\(61\!\cdots\!34\)\( T^{9} + \)\(88\!\cdots\!08\)\( T^{10} - \)\(20\!\cdots\!46\)\( T^{11} + \)\(30\!\cdots\!06\)\( T^{12} + \)\(23\!\cdots\!36\)\( T^{13} - \)\(52\!\cdots\!56\)\( T^{14} - \)\(12\!\cdots\!62\)\( T^{15} + \)\(45\!\cdots\!01\)\( T^{16} \))(\( 1 + 264 T - 242143 T^{2} - 10127664 T^{3} + 19457306511 T^{4} - 10329110462988 T^{5} + 200813313659502 T^{6} + 855135722680122204 T^{7} - \)\(11\!\cdots\!19\)\( T^{8} + \)\(34\!\cdots\!68\)\( T^{9} + \)\(67\!\cdots\!39\)\( T^{10} + \)\(55\!\cdots\!68\)\( T^{11} - \)\(30\!\cdots\!19\)\( T^{12} + \)\(35\!\cdots\!04\)\( T^{13} + \)\(13\!\cdots\!02\)\( T^{14} - \)\(11\!\cdots\!88\)\( T^{15} + \)\(33\!\cdots\!11\)\( T^{16} - \)\(28\!\cdots\!64\)\( T^{17} - \)\(10\!\cdots\!43\)\( T^{18} + \)\(19\!\cdots\!64\)\( T^{19} + \)\(11\!\cdots\!01\)\( T^{20} \))(\( 1 + 501 T - 543544 T^{2} - 202598235 T^{3} + 226553056161 T^{4} + 54666802768230 T^{5} - 65419717497300510 T^{6} - 7878441590002987596 T^{7} + \)\(15\!\cdots\!61\)\( T^{8} + \)\(59\!\cdots\!45\)\( T^{9} - \)\(27\!\cdots\!94\)\( T^{10} + \)\(95\!\cdots\!95\)\( T^{11} + \)\(39\!\cdots\!61\)\( T^{12} - \)\(32\!\cdots\!96\)\( T^{13} - \)\(44\!\cdots\!10\)\( T^{14} + \)\(59\!\cdots\!30\)\( T^{15} + \)\(39\!\cdots\!61\)\( T^{16} - \)\(56\!\cdots\!85\)\( T^{17} - \)\(24\!\cdots\!44\)\( T^{18} + \)\(36\!\cdots\!51\)\( T^{19} + \)\(11\!\cdots\!01\)\( T^{20} \))(\( 1 - 225 T - 246117 T^{2} - 36238464 T^{3} + 35914478430 T^{4} + 23978532106782 T^{5} - 2155553447828647 T^{6} - 4783681608653568591 T^{7} - \)\(83\!\cdots\!16\)\( T^{8} + \)\(64\!\cdots\!25\)\( T^{9} + \)\(33\!\cdots\!23\)\( T^{10} - \)\(41\!\cdots\!94\)\( T^{11} - \)\(68\!\cdots\!08\)\( T^{12} - \)\(66\!\cdots\!94\)\( T^{13} + \)\(87\!\cdots\!23\)\( T^{14} + \)\(26\!\cdots\!75\)\( T^{15} - \)\(56\!\cdots\!16\)\( T^{16} - \)\(51\!\cdots\!41\)\( T^{17} - \)\(37\!\cdots\!47\)\( T^{18} + \)\(67\!\cdots\!82\)\( T^{19} + \)\(16\!\cdots\!30\)\( T^{20} - \)\(26\!\cdots\!64\)\( T^{21} - \)\(28\!\cdots\!17\)\( T^{22} - \)\(42\!\cdots\!75\)\( T^{23} + \)\(30\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 306614 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 - 292334 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 - 92322 T^{2} + 23752309431 T^{4} + 209720571966532 T^{6} + \)\(61\!\cdots\!31\)\( T^{8} - \)\(62\!\cdots\!22\)\( T^{10} + \)\(17\!\cdots\!01\)\( T^{12} )^{2} \))
$13$ (\( 1 + 154 T + 371293 T^{2} \))(\( 1 - 1106 T + 371293 T^{2} \))(\( 1 - 404 T + 371293 T^{2} \))(\( 1 + 946 T + 371293 T^{2} \))(\( 1 - 404 T + 371293 T^{2} \))(\( 1 + 46 T + 371293 T^{2} \))(\( 1 - 698 T + 371293 T^{2} \))(\( 1 - 274730 T^{2} + 137858491849 T^{4} \))(\( 1 - 659642 T^{2} + 137858491849 T^{4} \))(\( 1 - 717040 T^{2} + 288425185998 T^{4} - 98850052995406960 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 463990 T^{2} + 137858491849 T^{4} )^{2} \))(\( 1 - 136 T - 482988 T^{2} + 699817912 T^{3} + 113442358490 T^{4} - 311812348096140 T^{5} + 223303725133607680 T^{6} + 93684720316858324880 T^{7} - \)\(99\!\cdots\!09\)\( T^{8} + \)\(34\!\cdots\!40\)\( T^{9} + \)\(30\!\cdots\!20\)\( T^{10} - \)\(15\!\cdots\!80\)\( T^{11} + \)\(21\!\cdots\!90\)\( T^{12} + \)\(49\!\cdots\!16\)\( T^{13} - \)\(12\!\cdots\!12\)\( T^{14} - \)\(13\!\cdots\!52\)\( T^{15} + \)\(36\!\cdots\!01\)\( T^{16} \))(\( 1 - 338 T - 859745 T^{2} - 1909554 T^{3} + 430793958603 T^{4} + 127716979353456 T^{5} - 88897082134649754 T^{6} - \)\(10\!\cdots\!12\)\( T^{7} + \)\(78\!\cdots\!61\)\( T^{8} + \)\(18\!\cdots\!18\)\( T^{9} + \)\(54\!\cdots\!81\)\( T^{10} + \)\(68\!\cdots\!74\)\( T^{11} + \)\(10\!\cdots\!89\)\( T^{12} - \)\(54\!\cdots\!84\)\( T^{13} - \)\(16\!\cdots\!54\)\( T^{14} + \)\(90\!\cdots\!08\)\( T^{15} + \)\(11\!\cdots\!47\)\( T^{16} - \)\(18\!\cdots\!78\)\( T^{17} - \)\(31\!\cdots\!45\)\( T^{18} - \)\(45\!\cdots\!34\)\( T^{19} + \)\(49\!\cdots\!49\)\( T^{20} \))(\( 1 + 700 T - 934121 T^{2} - 916032444 T^{3} + 406291160559 T^{4} + 540441366675132 T^{5} - 92310879990466686 T^{6} - \)\(16\!\cdots\!08\)\( T^{7} + \)\(25\!\cdots\!41\)\( T^{8} + \)\(22\!\cdots\!84\)\( T^{9} - \)\(98\!\cdots\!67\)\( T^{10} + \)\(85\!\cdots\!12\)\( T^{11} + \)\(35\!\cdots\!09\)\( T^{12} - \)\(85\!\cdots\!56\)\( T^{13} - \)\(17\!\cdots\!86\)\( T^{14} + \)\(38\!\cdots\!76\)\( T^{15} + \)\(10\!\cdots\!91\)\( T^{16} - \)\(89\!\cdots\!08\)\( T^{17} - \)\(33\!\cdots\!21\)\( T^{18} + \)\(93\!\cdots\!00\)\( T^{19} + \)\(49\!\cdots\!49\)\( T^{20} \))(\( 1 + 498 T - 913566 T^{2} + 338874328 T^{3} + 864329125137 T^{4} - 448782098947440 T^{5} - 193520749525139474 T^{6} + \)\(42\!\cdots\!50\)\( T^{7} - \)\(37\!\cdots\!10\)\( T^{8} - \)\(14\!\cdots\!34\)\( T^{9} + \)\(10\!\cdots\!74\)\( T^{10} + \)\(30\!\cdots\!64\)\( T^{11} - \)\(45\!\cdots\!15\)\( T^{12} + \)\(11\!\cdots\!52\)\( T^{13} + \)\(14\!\cdots\!26\)\( T^{14} - \)\(75\!\cdots\!38\)\( T^{15} - \)\(71\!\cdots\!10\)\( T^{16} + \)\(29\!\cdots\!50\)\( T^{17} - \)\(50\!\cdots\!26\)\( T^{18} - \)\(43\!\cdots\!80\)\( T^{19} + \)\(31\!\cdots\!37\)\( T^{20} + \)\(45\!\cdots\!04\)\( T^{21} - \)\(45\!\cdots\!34\)\( T^{22} + \)\(92\!\cdots\!86\)\( T^{23} + \)\(68\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 366 T + 66978 T^{2} - 135893238 T^{3} + 137858491849 T^{4} )^{2} \))(\( ( 1 + 1674 T + 1401138 T^{2} + 621544482 T^{3} + 137858491849 T^{4} )^{2} \))(\( ( 1 + 138 T + 9522 T^{2} + 71250978 T^{3} + 207133277751 T^{4} - 9625164888756 T^{5} - 762244892415108 T^{6} - 3573756347040881508 T^{7} + \)\(28\!\cdots\!99\)\( T^{8} + \)\(36\!\cdots\!46\)\( T^{9} + \)\(18\!\cdots\!22\)\( T^{10} + \)\(97\!\cdots\!34\)\( T^{11} + \)\(26\!\cdots\!49\)\( T^{12} )^{2} \))
$17$ (\( 1 - 918 T + 1419857 T^{2} \))(\( 1 + 762 T + 1419857 T^{2} \))(\( 1 + 654 T + 1419857 T^{2} \))(\( 1 - 222 T + 1419857 T^{2} \))(\( 1 - 654 T + 1419857 T^{2} \))(\( 1 + 378 T + 1419857 T^{2} \))(\( 1 - 2226 T + 1419857 T^{2} \))(\( 1 + 1354590 T^{2} + 2015993900449 T^{4} \))(\( 1 - 541458 T^{2} + 2015993900449 T^{4} \))(\( 1 - 3971280 T^{2} + 7330589629598 T^{4} - 8006076256975104720 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 1480158 T^{2} + 2015993900449 T^{4} )^{2} \))(\( ( 1 + 1872 T + 3794636 T^{2} + 2645799444 T^{3} + 4180559355678 T^{4} + 3756656861159508 T^{5} + 7649963030424191564 T^{6} + \)\(53\!\cdots\!96\)\( T^{7} + \)\(40\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 492 T + 3904033 T^{2} + 3239257908 T^{3} + 7962665263390 T^{4} + 6808878717770016 T^{5} + 11305846012881135230 T^{6} + \)\(65\!\cdots\!92\)\( T^{7} + \)\(11\!\cdots\!69\)\( T^{8} + \)\(19\!\cdots\!92\)\( T^{9} + \)\(57\!\cdots\!57\)\( T^{10} )^{2} \))(\( ( 1 - 819 T + 1975117 T^{2} + 369884160 T^{3} + 3253099748158 T^{4} - 680822236871442 T^{5} + 4618936449120373406 T^{6} + \)\(74\!\cdots\!40\)\( T^{7} + \)\(56\!\cdots\!81\)\( T^{8} - \)\(33\!\cdots\!19\)\( T^{9} + \)\(57\!\cdots\!57\)\( T^{10} )^{2} \))(\( ( 1 + 1269 T + 6614490 T^{2} + 6028419897 T^{3} + 18956669986995 T^{4} + 13244017420009890 T^{5} + 32956696132039955140 T^{6} + \)\(18\!\cdots\!30\)\( T^{7} + \)\(38\!\cdots\!55\)\( T^{8} + \)\(17\!\cdots\!21\)\( T^{9} + \)\(26\!\cdots\!90\)\( T^{10} + \)\(73\!\cdots\!33\)\( T^{11} + \)\(81\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 + 2695281514306 T^{4} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 + 3574123893826 T^{4} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 - 3104114865402 T^{4} + \)\(11\!\cdots\!71\)\( T^{8} - \)\(23\!\cdots\!08\)\( T^{12} + \)\(47\!\cdots\!71\)\( T^{16} - \)\(51\!\cdots\!02\)\( T^{20} + \)\(67\!\cdots\!01\)\( T^{24} \))
$19$ (\( 1 + 1060 T + 2476099 T^{2} \))(\( 1 + 2740 T + 2476099 T^{2} \))(\( 1 - 1796 T + 2476099 T^{2} \))(\( 1 - 500 T + 2476099 T^{2} \))(\( 1 - 1796 T + 2476099 T^{2} \))(\( 1 - 1100 T + 2476099 T^{2} \))(\( 1 - 356 T + 2476099 T^{2} \))(\( ( 1 + 2220 T + 2476099 T^{2} )^{2} \))(\( ( 1 - 1344 T + 2476099 T^{2} )^{2} \))(\( ( 1 - 120 T + 459398 T^{2} - 297131880 T^{3} + 6131066257801 T^{4} )^{2} \))(\( ( 1 - 2244 T + 2476099 T^{2} )^{4} \))(\( ( 1 + 466 T + 2210488 T^{2} - 3506353154 T^{3} - 2846142426506 T^{4} - 8682077538266246 T^{5} + 13552648390074016888 T^{6} + \)\(70\!\cdots\!34\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 250 T + 6795111 T^{2} - 1728324828 T^{3} + 21209524020690 T^{4} - 5394895814500836 T^{5} + 52516881218106488310 T^{6} - \)\(10\!\cdots\!28\)\( T^{7} + \)\(10\!\cdots\!89\)\( T^{8} - \)\(93\!\cdots\!50\)\( T^{9} + \)\(93\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 - 259 T + 4448397 T^{2} - 3281576220 T^{3} + 10296478633956 T^{4} - 12717409476018282 T^{5} + 25495100449059817644 T^{6} - \)\(20\!\cdots\!20\)\( T^{7} + \)\(67\!\cdots\!03\)\( T^{8} - \)\(97\!\cdots\!59\)\( T^{9} + \)\(93\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 - 975 T + 8270652 T^{2} - 4390145941 T^{3} + 32179762169955 T^{4} - 7961562935739306 T^{5} + 87653732374730312448 T^{6} - \)\(19\!\cdots\!94\)\( T^{7} + \)\(19\!\cdots\!55\)\( T^{8} - \)\(66\!\cdots\!59\)\( T^{9} + \)\(31\!\cdots\!52\)\( T^{10} - \)\(90\!\cdots\!25\)\( T^{11} + \)\(23\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 - 508534 T^{2} + 6131066257801 T^{4} )^{2} \))(\( ( 1 - 3928054 T^{2} + 6131066257801 T^{4} )^{2} \))(\( ( 1 - 11705682 T^{2} + 61048847304711 T^{4} - \)\(18\!\cdots\!48\)\( T^{6} + \)\(37\!\cdots\!11\)\( T^{8} - \)\(44\!\cdots\!82\)\( T^{10} + \)\(23\!\cdots\!01\)\( T^{12} )^{2} \))
$23$ (\( 1 - 4224 T + 6436343 T^{2} \))(\( 1 + 1566 T + 6436343 T^{2} \))(\( 1 - 1080 T + 6436343 T^{2} \))(\( 1 + 3564 T + 6436343 T^{2} \))(\( 1 + 1080 T + 6436343 T^{2} \))(\( 1 - 1986 T + 6436343 T^{2} \))(\( 1 - 1800 T + 6436343 T^{2} \))(\( 1 - 11320170 T^{2} + 41426511213649 T^{4} \))(\( 1 + 3937314 T^{2} + 41426511213649 T^{4} \))(\( 1 - 7282620 T^{2} + 10950776597798 T^{4} - \)\(30\!\cdots\!80\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 12622686 T^{2} + 41426511213649 T^{4} )^{2} \))(\( 1 - 876 T - 22945100 T^{2} + 11314251660 T^{3} + 324819095054305 T^{4} - 92271394417398786 T^{5} - \)\(31\!\cdots\!80\)\( T^{6} + \)\(21\!\cdots\!38\)\( T^{7} + \)\(23\!\cdots\!16\)\( T^{8} + \)\(14\!\cdots\!34\)\( T^{9} - \)\(13\!\cdots\!20\)\( T^{10} - \)\(24\!\cdots\!02\)\( T^{11} + \)\(55\!\cdots\!05\)\( T^{12} + \)\(12\!\cdots\!80\)\( T^{13} - \)\(16\!\cdots\!00\)\( T^{14} - \)\(40\!\cdots\!32\)\( T^{15} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( 1 + 1995 T - 8843428 T^{2} - 52369990785 T^{3} - 56544416568624 T^{4} + 208462575158730225 T^{5} + \)\(96\!\cdots\!64\)\( T^{6} + \)\(18\!\cdots\!35\)\( T^{7} + \)\(79\!\cdots\!11\)\( T^{8} - \)\(11\!\cdots\!10\)\( T^{9} - \)\(46\!\cdots\!44\)\( T^{10} - \)\(71\!\cdots\!30\)\( T^{11} + \)\(33\!\cdots\!39\)\( T^{12} + \)\(49\!\cdots\!45\)\( T^{13} + \)\(16\!\cdots\!64\)\( T^{14} + \)\(23\!\cdots\!75\)\( T^{15} - \)\(40\!\cdots\!76\)\( T^{16} - \)\(23\!\cdots\!95\)\( T^{17} - \)\(26\!\cdots\!28\)\( T^{18} + \)\(37\!\cdots\!85\)\( T^{19} + \)\(12\!\cdots\!49\)\( T^{20} \))(\( 1 + 810 T - 6194863 T^{2} + 1220802570 T^{3} - 14856700757934 T^{4} + 30122683412187240 T^{5} + \)\(27\!\cdots\!69\)\( T^{6} - \)\(10\!\cdots\!10\)\( T^{7} - \)\(96\!\cdots\!59\)\( T^{8} + \)\(43\!\cdots\!90\)\( T^{9} + \)\(21\!\cdots\!36\)\( T^{10} + \)\(28\!\cdots\!70\)\( T^{11} - \)\(40\!\cdots\!91\)\( T^{12} - \)\(26\!\cdots\!70\)\( T^{13} + \)\(47\!\cdots\!69\)\( T^{14} + \)\(33\!\cdots\!20\)\( T^{15} - \)\(10\!\cdots\!66\)\( T^{16} + \)\(55\!\cdots\!90\)\( T^{17} - \)\(18\!\cdots\!63\)\( T^{18} + \)\(15\!\cdots\!30\)\( T^{19} + \)\(12\!\cdots\!49\)\( T^{20} \))(\( 1 - 2061 T - 18746553 T^{2} - 21079270044 T^{3} + 322107222978921 T^{4} + 599334834670754661 T^{5} - \)\(17\!\cdots\!40\)\( T^{6} - \)\(10\!\cdots\!47\)\( T^{7} + \)\(75\!\cdots\!71\)\( T^{8} + \)\(69\!\cdots\!72\)\( T^{9} + \)\(16\!\cdots\!57\)\( T^{10} - \)\(25\!\cdots\!53\)\( T^{11} - \)\(13\!\cdots\!50\)\( T^{12} - \)\(16\!\cdots\!79\)\( T^{13} + \)\(68\!\cdots\!93\)\( T^{14} + \)\(18\!\cdots\!04\)\( T^{15} + \)\(13\!\cdots\!71\)\( T^{16} - \)\(11\!\cdots\!21\)\( T^{17} - \)\(12\!\cdots\!60\)\( T^{18} + \)\(27\!\cdots\!27\)\( T^{19} + \)\(94\!\cdots\!21\)\( T^{20} - \)\(39\!\cdots\!92\)\( T^{21} - \)\(22\!\cdots\!97\)\( T^{22} - \)\(16\!\cdots\!27\)\( T^{23} + \)\(50\!\cdots\!01\)\( T^{24} \))(\( 1 - 43180786439198 T^{4} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 81675775727198 T^{4} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 54021755287194 T^{4} + \)\(80\!\cdots\!15\)\( T^{8} - \)\(23\!\cdots\!80\)\( T^{12} + \)\(13\!\cdots\!15\)\( T^{16} - \)\(15\!\cdots\!94\)\( T^{20} + \)\(50\!\cdots\!01\)\( T^{24} \))
$29$ (\( 1 - 7890 T + 20511149 T^{2} \))(\( 1 + 5910 T + 20511149 T^{2} \))(\( 1 - 5754 T + 20511149 T^{2} \))(\( 1 + 2190 T + 20511149 T^{2} \))(\( 1 + 5754 T + 20511149 T^{2} \))(\( 1 - 5610 T + 20511149 T^{2} \))(\( 1 + 714 T + 20511149 T^{2} \))(\( ( 1 + 270 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 2646 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 2430 T + 19735498 T^{2} + 49842092070 T^{3} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 40800682 T^{2} + 420707233300201 T^{4} )^{2} \))(\( 1 - 2352 T - 3047102 T^{2} + 41638754352 T^{3} - 486818037718643 T^{4} + 1395113101298994600 T^{5} + \)\(24\!\cdots\!10\)\( T^{6} - \)\(32\!\cdots\!24\)\( T^{7} + \)\(10\!\cdots\!04\)\( T^{8} - \)\(67\!\cdots\!76\)\( T^{9} + \)\(10\!\cdots\!10\)\( T^{10} + \)\(12\!\cdots\!00\)\( T^{11} - \)\(86\!\cdots\!43\)\( T^{12} + \)\(15\!\cdots\!48\)\( T^{13} - \)\(22\!\cdots\!02\)\( T^{14} - \)\(35\!\cdots\!48\)\( T^{15} + \)\(31\!\cdots\!01\)\( T^{16} \))(\( 1 + 771 T - 47387698 T^{2} + 39384396333 T^{3} + 1217810625785070 T^{4} - 2435140763127788355 T^{5} - \)\(70\!\cdots\!08\)\( T^{6} + \)\(82\!\cdots\!97\)\( T^{7} - \)\(30\!\cdots\!91\)\( T^{8} - \)\(68\!\cdots\!74\)\( T^{9} + \)\(12\!\cdots\!04\)\( T^{10} - \)\(14\!\cdots\!26\)\( T^{11} - \)\(12\!\cdots\!91\)\( T^{12} + \)\(71\!\cdots\!53\)\( T^{13} - \)\(12\!\cdots\!08\)\( T^{14} - \)\(88\!\cdots\!95\)\( T^{15} + \)\(90\!\cdots\!70\)\( T^{16} + \)\(60\!\cdots\!17\)\( T^{17} - \)\(14\!\cdots\!98\)\( T^{18} + \)\(49\!\cdots\!79\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} \))(\( 1 + 1614 T - 63758527 T^{2} - 11772044190 T^{3} + 2175748192265748 T^{4} - 1777321347190125894 T^{5} - \)\(52\!\cdots\!65\)\( T^{6} + \)\(68\!\cdots\!66\)\( T^{7} + \)\(10\!\cdots\!27\)\( T^{8} - \)\(71\!\cdots\!00\)\( T^{9} - \)\(21\!\cdots\!24\)\( T^{10} - \)\(14\!\cdots\!00\)\( T^{11} + \)\(45\!\cdots\!27\)\( T^{12} + \)\(58\!\cdots\!34\)\( T^{13} - \)\(92\!\cdots\!65\)\( T^{14} - \)\(64\!\cdots\!06\)\( T^{15} + \)\(16\!\cdots\!48\)\( T^{16} - \)\(17\!\cdots\!10\)\( T^{17} - \)\(19\!\cdots\!27\)\( T^{18} + \)\(10\!\cdots\!86\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} \))(\( 1 - 3195 T - 63657129 T^{2} + 266123296332 T^{3} + 1815328277785353 T^{4} - 9220282428748151385 T^{5} - \)\(34\!\cdots\!56\)\( T^{6} + \)\(18\!\cdots\!21\)\( T^{7} + \)\(61\!\cdots\!55\)\( T^{8} - \)\(25\!\cdots\!56\)\( T^{9} - \)\(10\!\cdots\!43\)\( T^{10} + \)\(18\!\cdots\!55\)\( T^{11} + \)\(19\!\cdots\!26\)\( T^{12} + \)\(38\!\cdots\!95\)\( T^{13} - \)\(45\!\cdots\!43\)\( T^{14} - \)\(21\!\cdots\!44\)\( T^{15} + \)\(10\!\cdots\!55\)\( T^{16} + \)\(66\!\cdots\!29\)\( T^{17} - \)\(25\!\cdots\!56\)\( T^{18} - \)\(14\!\cdots\!65\)\( T^{19} + \)\(56\!\cdots\!53\)\( T^{20} + \)\(17\!\cdots\!68\)\( T^{21} - \)\(83\!\cdots\!29\)\( T^{22} - \)\(86\!\cdots\!55\)\( T^{23} + \)\(55\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 7962904 T^{2} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 33409496 T^{2} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 23780088 T^{2} + 922477841694651 T^{4} + \)\(20\!\cdots\!12\)\( T^{6} + \)\(38\!\cdots\!51\)\( T^{8} + \)\(42\!\cdots\!88\)\( T^{10} + \)\(74\!\cdots\!01\)\( T^{12} )^{2} \))
$31$ (\( 1 - 5192 T + 28629151 T^{2} \))(\( 1 + 6868 T + 28629151 T^{2} \))(\( 1 - 10196 T + 28629151 T^{2} \))(\( 1 - 2312 T + 28629151 T^{2} \))(\( 1 - 10196 T + 28629151 T^{2} \))(\( 1 + 3988 T + 28629151 T^{2} \))(\( 1 - 848 T + 28629151 T^{2} \))(\( ( 1 + 2048 T + 28629151 T^{2} )^{2} \))(\( ( 1 + 5612 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 11684 T + 90263166 T^{2} - 334503000284 T^{3} + 819628286980801 T^{4} )^{2} \))(\( ( 1 - 3856 T + 28629151 T^{2} )^{4} \))(\( 1 - 11458 T + 2347620 T^{2} + 294478499788 T^{3} + 928456183073870 T^{4} - 12508826345102438754 T^{5} - \)\(94\!\cdots\!36\)\( T^{6} + \)\(14\!\cdots\!30\)\( T^{7} + \)\(14\!\cdots\!27\)\( T^{8} + \)\(42\!\cdots\!30\)\( T^{9} - \)\(77\!\cdots\!36\)\( T^{10} - \)\(29\!\cdots\!54\)\( T^{11} + \)\(62\!\cdots\!70\)\( T^{12} + \)\(56\!\cdots\!88\)\( T^{13} + \)\(12\!\cdots\!20\)\( T^{14} - \)\(18\!\cdots\!58\)\( T^{15} + \)\(45\!\cdots\!01\)\( T^{16} \))(\( 1 + 1978 T - 21400463 T^{2} - 319010673066 T^{3} - 1092922494246609 T^{4} - 220050919658841072 T^{5} + \)\(76\!\cdots\!18\)\( T^{6} + \)\(45\!\cdots\!72\)\( T^{7} + \)\(78\!\cdots\!73\)\( T^{8} - \)\(11\!\cdots\!58\)\( T^{9} - \)\(73\!\cdots\!57\)\( T^{10} - \)\(32\!\cdots\!58\)\( T^{11} + \)\(64\!\cdots\!73\)\( T^{12} + \)\(10\!\cdots\!72\)\( T^{13} + \)\(51\!\cdots\!18\)\( T^{14} - \)\(42\!\cdots\!72\)\( T^{15} - \)\(60\!\cdots\!09\)\( T^{16} - \)\(50\!\cdots\!66\)\( T^{17} - \)\(96\!\cdots\!63\)\( T^{18} + \)\(25\!\cdots\!78\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} \))(\( 1 - 1436 T - 125650523 T^{2} + 71524107156 T^{3} + 9253897212766431 T^{4} - 1519865806440593868 T^{5} - \)\(47\!\cdots\!58\)\( T^{6} + \)\(95\!\cdots\!24\)\( T^{7} + \)\(18\!\cdots\!21\)\( T^{8} + \)\(19\!\cdots\!28\)\( T^{9} - \)\(59\!\cdots\!61\)\( T^{10} + \)\(57\!\cdots\!28\)\( T^{11} + \)\(15\!\cdots\!21\)\( T^{12} + \)\(22\!\cdots\!24\)\( T^{13} - \)\(31\!\cdots\!58\)\( T^{14} - \)\(29\!\cdots\!68\)\( T^{15} + \)\(50\!\cdots\!31\)\( T^{16} + \)\(11\!\cdots\!56\)\( T^{17} - \)\(56\!\cdots\!23\)\( T^{18} - \)\(18\!\cdots\!36\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} \))(\( 1 + 12000 T - 12074070 T^{2} - 906849964520 T^{3} - 3426912857104563 T^{4} + 21506496427327731852 T^{5} + \)\(19\!\cdots\!66\)\( T^{6} + \)\(36\!\cdots\!52\)\( T^{7} - \)\(20\!\cdots\!74\)\( T^{8} - \)\(29\!\cdots\!64\)\( T^{9} - \)\(14\!\cdots\!10\)\( T^{10} + \)\(45\!\cdots\!04\)\( T^{11} + \)\(72\!\cdots\!73\)\( T^{12} + \)\(12\!\cdots\!04\)\( T^{13} - \)\(11\!\cdots\!10\)\( T^{14} - \)\(68\!\cdots\!64\)\( T^{15} - \)\(14\!\cdots\!74\)\( T^{16} + \)\(69\!\cdots\!52\)\( T^{17} + \)\(10\!\cdots\!66\)\( T^{18} + \)\(33\!\cdots\!52\)\( T^{19} - \)\(15\!\cdots\!63\)\( T^{20} - \)\(11\!\cdots\!20\)\( T^{21} - \)\(44\!\cdots\!70\)\( T^{22} + \)\(12\!\cdots\!00\)\( T^{23} + \)\(30\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 6784 T + 28629151 T^{2} )^{4} \))(\( ( 1 + 4136 T + 28629151 T^{2} )^{4} \))(\( ( 1 + 14628 T + 134742381 T^{2} + 812936587832 T^{3} + 3857559971748531 T^{4} + 11989522581955157028 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} )^{4} \))
$37$ (\( 1 - 16382 T + 69343957 T^{2} \))(\( 1 + 5518 T + 69343957 T^{2} \))(\( 1 - 5552 T + 69343957 T^{2} \))(\( 1 + 11242 T + 69343957 T^{2} \))(\( 1 - 5552 T + 69343957 T^{2} \))(\( 1 + 142 T + 69343957 T^{2} \))(\( 1 + 11302 T + 69343957 T^{2} \))(\( 1 - 119573530 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 85572970 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 100197680 T^{2} + 8640930841305198 T^{4} - \)\(48\!\cdots\!20\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 89804410 T^{2} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 + 13372 T + 263740816 T^{2} + 2274729462592 T^{3} + 26570216989261894 T^{4} + \)\(15\!\cdots\!44\)\( T^{5} + \)\(12\!\cdots\!84\)\( T^{6} + \)\(44\!\cdots\!96\)\( T^{7} + \)\(23\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 1640 T + 269252409 T^{2} + 458769755124 T^{3} + 33431182180071882 T^{4} + 46062611379522285960 T^{5} + \)\(23\!\cdots\!74\)\( T^{6} + \)\(22\!\cdots\!76\)\( T^{7} + \)\(89\!\cdots\!37\)\( T^{8} + \)\(37\!\cdots\!40\)\( T^{9} + \)\(16\!\cdots\!57\)\( T^{10} )^{2} \))(\( ( 1 + 12344 T + 315634101 T^{2} + 2758124333820 T^{3} + 41335090557952374 T^{4} + \)\(27\!\cdots\!56\)\( T^{5} + \)\(28\!\cdots\!18\)\( T^{6} + \)\(13\!\cdots\!80\)\( T^{7} + \)\(10\!\cdots\!93\)\( T^{8} + \)\(28\!\cdots\!44\)\( T^{9} + \)\(16\!\cdots\!57\)\( T^{10} )^{2} \))(\( ( 1 - 17040 T + 196739742 T^{2} - 1566434671276 T^{3} + 19165052595313431 T^{4} - \)\(18\!\cdots\!20\)\( T^{5} + \)\(18\!\cdots\!92\)\( T^{6} - \)\(13\!\cdots\!40\)\( T^{7} + \)\(92\!\cdots\!19\)\( T^{8} - \)\(52\!\cdots\!68\)\( T^{9} + \)\(45\!\cdots\!42\)\( T^{10} - \)\(27\!\cdots\!80\)\( T^{11} + \)\(11\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 7446 T + 27721458 T^{2} - 516335103822 T^{3} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 + 5334 T + 14225778 T^{2} + 369880666638 T^{3} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 - 12882 T + 82972962 T^{2} - 847667990010 T^{3} + 1418198677343175 T^{4} + 36911476364572499268 T^{5} - \)\(23\!\cdots\!76\)\( T^{6} + \)\(25\!\cdots\!76\)\( T^{7} + \)\(68\!\cdots\!75\)\( T^{8} - \)\(28\!\cdots\!30\)\( T^{9} + \)\(19\!\cdots\!62\)\( T^{10} - \)\(20\!\cdots\!74\)\( T^{11} + \)\(11\!\cdots\!49\)\( T^{12} )^{2} \))
$41$ (\( 1 + 3642 T + 115856201 T^{2} \))(\( 1 - 378 T + 115856201 T^{2} \))(\( 1 - 12960 T + 115856201 T^{2} \))(\( 1 + 1242 T + 115856201 T^{2} \))(\( 1 + 12960 T + 115856201 T^{2} \))(\( 1 + 1542 T + 115856201 T^{2} \))(\( 1 + 9354 T + 115856201 T^{2} \))(\( ( 1 - 2398 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 18986 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 24984 T + 351666366 T^{2} + 2894551325784 T^{3} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 + 139752402 T^{2} + 13422659310152401 T^{4} )^{2} \))(\( 1 + 4296 T - 192014234 T^{2} + 1741256315592 T^{3} + 26890179274320277 T^{4} - \)\(30\!\cdots\!84\)\( T^{5} + \)\(19\!\cdots\!82\)\( T^{6} + \)\(31\!\cdots\!52\)\( T^{7} - \)\(36\!\cdots\!64\)\( T^{8} + \)\(36\!\cdots\!52\)\( T^{9} + \)\(26\!\cdots\!82\)\( T^{10} - \)\(46\!\cdots\!84\)\( T^{11} + \)\(48\!\cdots\!77\)\( T^{12} + \)\(36\!\cdots\!92\)\( T^{13} - \)\(46\!\cdots\!34\)\( T^{14} + \)\(12\!\cdots\!96\)\( T^{15} + \)\(32\!\cdots\!01\)\( T^{16} \))(\( 1 + 29193 T + 115787906 T^{2} - 3956073117021 T^{3} - 17456442139370838 T^{4} + \)\(54\!\cdots\!59\)\( T^{5} + \)\(37\!\cdots\!80\)\( T^{6} + \)\(12\!\cdots\!15\)\( T^{7} + \)\(63\!\cdots\!05\)\( T^{8} + \)\(13\!\cdots\!70\)\( T^{9} - \)\(74\!\cdots\!40\)\( T^{10} + \)\(16\!\cdots\!70\)\( T^{11} + \)\(84\!\cdots\!05\)\( T^{12} + \)\(19\!\cdots\!15\)\( T^{13} + \)\(67\!\cdots\!80\)\( T^{14} + \)\(11\!\cdots\!59\)\( T^{15} - \)\(42\!\cdots\!38\)\( T^{16} - \)\(11\!\cdots\!21\)\( T^{17} + \)\(37\!\cdots\!06\)\( T^{18} + \)\(10\!\cdots\!93\)\( T^{19} + \)\(43\!\cdots\!01\)\( T^{20} \))(\( 1 + 21093 T - 261139114 T^{2} - 4866644388861 T^{3} + 112517416140745182 T^{4} + \)\(12\!\cdots\!99\)\( T^{5} - \)\(22\!\cdots\!80\)\( T^{6} - \)\(11\!\cdots\!65\)\( T^{7} + \)\(44\!\cdots\!45\)\( T^{8} + \)\(85\!\cdots\!10\)\( T^{9} - \)\(54\!\cdots\!20\)\( T^{10} + \)\(98\!\cdots\!10\)\( T^{11} + \)\(60\!\cdots\!45\)\( T^{12} - \)\(17\!\cdots\!65\)\( T^{13} - \)\(41\!\cdots\!80\)\( T^{14} + \)\(25\!\cdots\!99\)\( T^{15} + \)\(27\!\cdots\!82\)\( T^{16} - \)\(13\!\cdots\!61\)\( T^{17} - \)\(84\!\cdots\!14\)\( T^{18} + \)\(79\!\cdots\!93\)\( T^{19} + \)\(43\!\cdots\!01\)\( T^{20} \))(\( 1 - 1530 T - 251739345 T^{2} + 1890121356882 T^{3} + 19028993435088735 T^{4} - \)\(26\!\cdots\!60\)\( T^{5} + \)\(25\!\cdots\!88\)\( T^{6} - \)\(16\!\cdots\!80\)\( T^{7} - \)\(35\!\cdots\!95\)\( T^{8} + \)\(88\!\cdots\!94\)\( T^{9} - \)\(27\!\cdots\!75\)\( T^{10} - \)\(58\!\cdots\!50\)\( T^{11} + \)\(96\!\cdots\!70\)\( T^{12} - \)\(67\!\cdots\!50\)\( T^{13} - \)\(37\!\cdots\!75\)\( T^{14} + \)\(13\!\cdots\!94\)\( T^{15} - \)\(64\!\cdots\!95\)\( T^{16} - \)\(33\!\cdots\!80\)\( T^{17} + \)\(62\!\cdots\!88\)\( T^{18} - \)\(74\!\cdots\!60\)\( T^{19} + \)\(61\!\cdots\!35\)\( T^{20} + \)\(71\!\cdots\!82\)\( T^{21} - \)\(10\!\cdots\!45\)\( T^{22} - \)\(77\!\cdots\!30\)\( T^{23} + \)\(58\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 82655024 T^{2} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 - 123873104 T^{2} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 - 675414192 T^{2} + 192260052740082291 T^{4} - \)\(29\!\cdots\!28\)\( T^{6} + \)\(25\!\cdots\!91\)\( T^{8} - \)\(12\!\cdots\!92\)\( T^{10} + \)\(24\!\cdots\!01\)\( T^{12} )^{2} \))
$43$ (\( 1 - 15116 T + 147008443 T^{2} \))(\( 1 + 2434 T + 147008443 T^{2} \))(\( 1 + 8968 T + 147008443 T^{2} \))(\( 1 - 20624 T + 147008443 T^{2} \))(\( 1 + 8968 T + 147008443 T^{2} \))(\( 1 + 5026 T + 147008443 T^{2} \))(\( 1 + 5956 T + 147008443 T^{2} \))(\( 1 - 288754450 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 288237670 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 100144460 T^{2} - 11465052277897002 T^{4} - \)\(21\!\cdots\!40\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 265922422 T^{2} + 21611482313284249 T^{4} )^{2} \))(\( 1 - 23770 T - 164635740 T^{2} + 3500677134460 T^{3} + 114383162822941622 T^{4} - \)\(10\!\cdots\!70\)\( T^{5} - \)\(20\!\cdots\!00\)\( T^{6} + \)\(10\!\cdots\!70\)\( T^{7} + \)\(46\!\cdots\!83\)\( T^{8} + \)\(16\!\cdots\!10\)\( T^{9} - \)\(44\!\cdots\!00\)\( T^{10} - \)\(33\!\cdots\!90\)\( T^{11} + \)\(53\!\cdots\!22\)\( T^{12} + \)\(24\!\cdots\!80\)\( T^{13} - \)\(16\!\cdots\!60\)\( T^{14} - \)\(35\!\cdots\!90\)\( T^{15} + \)\(21\!\cdots\!01\)\( T^{16} \))(\( 1 + 7402 T - 243037859 T^{2} + 1837282206 T^{3} + 34323815609555151 T^{4} - \)\(33\!\cdots\!76\)\( T^{5} + \)\(89\!\cdots\!82\)\( T^{6} + \)\(11\!\cdots\!12\)\( T^{7} - \)\(50\!\cdots\!19\)\( T^{8} - \)\(69\!\cdots\!54\)\( T^{9} + \)\(12\!\cdots\!43\)\( T^{10} - \)\(10\!\cdots\!22\)\( T^{11} - \)\(10\!\cdots\!31\)\( T^{12} + \)\(36\!\cdots\!84\)\( T^{13} + \)\(41\!\cdots\!82\)\( T^{14} - \)\(23\!\cdots\!68\)\( T^{15} + \)\(34\!\cdots\!99\)\( T^{16} + \)\(27\!\cdots\!42\)\( T^{17} - \)\(53\!\cdots\!59\)\( T^{18} + \)\(23\!\cdots\!86\)\( T^{19} + \)\(47\!\cdots\!49\)\( T^{20} \))(\( 1 + 5929 T - 339625112 T^{2} + 2808287371497 T^{3} + 78853119760641261 T^{4} - \)\(10\!\cdots\!82\)\( T^{5} - \)\(37\!\cdots\!14\)\( T^{6} + \)\(19\!\cdots\!24\)\( T^{7} - \)\(80\!\cdots\!19\)\( T^{8} - \)\(95\!\cdots\!83\)\( T^{9} + \)\(26\!\cdots\!14\)\( T^{10} - \)\(14\!\cdots\!69\)\( T^{11} - \)\(17\!\cdots\!31\)\( T^{12} + \)\(62\!\cdots\!68\)\( T^{13} - \)\(17\!\cdots\!14\)\( T^{14} - \)\(74\!\cdots\!26\)\( T^{15} + \)\(79\!\cdots\!89\)\( T^{16} + \)\(41\!\cdots\!79\)\( T^{17} - \)\(74\!\cdots\!12\)\( T^{18} + \)\(19\!\cdots\!47\)\( T^{19} + \)\(47\!\cdots\!49\)\( T^{20} \))(\( 1 + 13377 T - 236492571 T^{2} - 8146134029402 T^{3} - 25767119893097694 T^{4} + \)\(16\!\cdots\!88\)\( T^{5} + \)\(18\!\cdots\!59\)\( T^{6} - \)\(14\!\cdots\!05\)\( T^{7} - \)\(37\!\cdots\!68\)\( T^{8} + \)\(86\!\cdots\!59\)\( T^{9} + \)\(44\!\cdots\!69\)\( T^{10} + \)\(52\!\cdots\!32\)\( T^{11} - \)\(51\!\cdots\!44\)\( T^{12} + \)\(77\!\cdots\!76\)\( T^{13} + \)\(95\!\cdots\!81\)\( T^{14} + \)\(27\!\cdots\!13\)\( T^{15} - \)\(17\!\cdots\!68\)\( T^{16} - \)\(97\!\cdots\!15\)\( T^{17} + \)\(19\!\cdots\!91\)\( T^{18} + \)\(24\!\cdots\!16\)\( T^{19} - \)\(56\!\cdots\!94\)\( T^{20} - \)\(26\!\cdots\!86\)\( T^{21} - \)\(11\!\cdots\!79\)\( T^{22} + \)\(92\!\cdots\!39\)\( T^{23} + \)\(10\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 6360 T + 20224800 T^{2} - 934973697480 T^{3} + 21611482313284249 T^{4} )^{2} \))(\( ( 1 + 21120 T + 223027200 T^{2} + 3104818316160 T^{3} + 21611482313284249 T^{4} )^{2} \))(\( ( 1 - 8040 T + 32320800 T^{2} - 1027788105720 T^{3} + 39748209890076747 T^{4} - \)\(20\!\cdots\!20\)\( T^{5} + \)\(90\!\cdots\!00\)\( T^{6} - \)\(30\!\cdots\!60\)\( T^{7} + \)\(85\!\cdots\!03\)\( T^{8} - \)\(32\!\cdots\!40\)\( T^{9} + \)\(15\!\cdots\!00\)\( T^{10} - \)\(55\!\cdots\!20\)\( T^{11} + \)\(10\!\cdots\!49\)\( T^{12} )^{2} \))
$47$ (\( 1 + 23592 T + 229345007 T^{2} \))(\( 1 + 13122 T + 229345007 T^{2} \))(\( 1 - 5400 T + 229345007 T^{2} \))(\( 1 + 6588 T + 229345007 T^{2} \))(\( 1 + 5400 T + 229345007 T^{2} \))(\( 1 + 24738 T + 229345007 T^{2} \))(\( 1 - 11160 T + 229345007 T^{2} \))(\( 1 - 344584890 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 379480014 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 826473900 T^{2} + 275763720563232998 T^{4} - \)\(43\!\cdots\!00\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 62680014 T^{2} + 52599132235830049 T^{4} )^{2} \))(\( 1 - 10566 T - 344370320 T^{2} + 3238452649044 T^{3} + 38576738551699429 T^{4} - 81182241280271459646 T^{5} - \)\(33\!\cdots\!04\)\( T^{6} - \)\(49\!\cdots\!12\)\( T^{7} + \)\(13\!\cdots\!80\)\( T^{8} - \)\(11\!\cdots\!84\)\( T^{9} - \)\(17\!\cdots\!96\)\( T^{10} - \)\(97\!\cdots\!78\)\( T^{11} + \)\(10\!\cdots\!29\)\( T^{12} + \)\(20\!\cdots\!08\)\( T^{13} - \)\(50\!\cdots\!80\)\( T^{14} - \)\(35\!\cdots\!38\)\( T^{15} + \)\(76\!\cdots\!01\)\( T^{16} \))(\( 1 + 26937 T + 167592494 T^{2} + 13417233173703 T^{3} + 374995873080471714 T^{4} + \)\(21\!\cdots\!15\)\( T^{5} + \)\(86\!\cdots\!20\)\( T^{6} + \)\(26\!\cdots\!69\)\( T^{7} + \)\(16\!\cdots\!81\)\( T^{8} + \)\(33\!\cdots\!04\)\( T^{9} + \)\(11\!\cdots\!04\)\( T^{10} + \)\(76\!\cdots\!28\)\( T^{11} + \)\(84\!\cdots\!69\)\( T^{12} + \)\(31\!\cdots\!67\)\( T^{13} + \)\(23\!\cdots\!20\)\( T^{14} + \)\(13\!\cdots\!05\)\( T^{15} + \)\(54\!\cdots\!86\)\( T^{16} + \)\(44\!\cdots\!29\)\( T^{17} + \)\(12\!\cdots\!94\)\( T^{18} + \)\(47\!\cdots\!59\)\( T^{19} + \)\(40\!\cdots\!49\)\( T^{20} \))(\( 1 + 34206 T + 83424233 T^{2} - 4839948665766 T^{3} + 62351496072338298 T^{4} + \)\(13\!\cdots\!68\)\( T^{5} - \)\(10\!\cdots\!87\)\( T^{6} - \)\(10\!\cdots\!86\)\( T^{7} - \)\(49\!\cdots\!91\)\( T^{8} - \)\(46\!\cdots\!06\)\( T^{9} - \)\(84\!\cdots\!72\)\( T^{10} - \)\(10\!\cdots\!42\)\( T^{11} - \)\(25\!\cdots\!59\)\( T^{12} - \)\(13\!\cdots\!98\)\( T^{13} - \)\(29\!\cdots\!87\)\( T^{14} + \)\(84\!\cdots\!76\)\( T^{15} + \)\(90\!\cdots\!02\)\( T^{16} - \)\(16\!\cdots\!38\)\( T^{17} + \)\(63\!\cdots\!33\)\( T^{18} + \)\(60\!\cdots\!42\)\( T^{19} + \)\(40\!\cdots\!49\)\( T^{20} \))(\( 1 - 5805 T - 1071018381 T^{2} + 4619967383484 T^{3} + 630735710194832781 T^{4} - \)\(19\!\cdots\!67\)\( T^{5} - \)\(27\!\cdots\!16\)\( T^{6} + \)\(52\!\cdots\!85\)\( T^{7} + \)\(94\!\cdots\!55\)\( T^{8} - \)\(97\!\cdots\!88\)\( T^{9} - \)\(27\!\cdots\!51\)\( T^{10} + \)\(85\!\cdots\!59\)\( T^{11} + \)\(68\!\cdots\!26\)\( T^{12} + \)\(19\!\cdots\!13\)\( T^{13} - \)\(14\!\cdots\!99\)\( T^{14} - \)\(11\!\cdots\!84\)\( T^{15} + \)\(26\!\cdots\!55\)\( T^{16} + \)\(33\!\cdots\!95\)\( T^{17} - \)\(39\!\cdots\!84\)\( T^{18} - \)\(64\!\cdots\!81\)\( T^{19} + \)\(48\!\cdots\!81\)\( T^{20} + \)\(81\!\cdots\!88\)\( T^{21} - \)\(43\!\cdots\!69\)\( T^{22} - \)\(53\!\cdots\!15\)\( T^{23} + \)\(21\!\cdots\!01\)\( T^{24} \))(\( 1 + 9133371392128898 T^{4} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 104206670445208702 T^{4} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 44718551206350906 T^{4} - \)\(15\!\cdots\!85\)\( T^{8} + \)\(28\!\cdots\!80\)\( T^{12} - \)\(42\!\cdots\!85\)\( T^{16} - \)\(34\!\cdots\!06\)\( T^{20} + \)\(21\!\cdots\!01\)\( T^{24} \))
$53$ (\( 1 - 16074 T + 418195493 T^{2} \))(\( 1 - 9174 T + 418195493 T^{2} \))(\( 1 + 8214 T + 418195493 T^{2} \))(\( 1 - 21066 T + 418195493 T^{2} \))(\( 1 - 8214 T + 418195493 T^{2} \))(\( 1 - 14166 T + 418195493 T^{2} \))(\( 1 + 14106 T + 418195493 T^{2} \))(\( 1 - 827605690 T^{2} + 174887470365513049 T^{4} \))(\( 1 + 747967430 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 809517920 T^{2} + 441417135624894798 T^{4} - \)\(14\!\cdots\!80\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 835077670 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 + 34560 T + 895160108 T^{2} + 24050392743600 T^{3} + 663857841798351030 T^{4} + \)\(10\!\cdots\!00\)\( T^{5} + \)\(15\!\cdots\!92\)\( T^{6} + \)\(25\!\cdots\!20\)\( T^{7} + \)\(30\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 31974 T + 604146361 T^{2} - 5051882553672 T^{3} + 210449741600065834 T^{4} - \)\(55\!\cdots\!00\)\( T^{5} + \)\(88\!\cdots\!62\)\( T^{6} - \)\(88\!\cdots\!28\)\( T^{7} + \)\(44\!\cdots\!77\)\( T^{8} - \)\(97\!\cdots\!74\)\( T^{9} + \)\(12\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 - 31974 T + 2339085361 T^{2} - 53321103054552 T^{3} + 2059350674820910354 T^{4} - \)\(33\!\cdots\!60\)\( T^{5} + \)\(86\!\cdots\!22\)\( T^{6} - \)\(93\!\cdots\!48\)\( T^{7} + \)\(17\!\cdots\!77\)\( T^{8} - \)\(97\!\cdots\!74\)\( T^{9} + \)\(12\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 + 34560 T + 1441267482 T^{2} + 27238570939440 T^{3} + 704648529275605431 T^{4} + \)\(95\!\cdots\!20\)\( T^{5} + \)\(26\!\cdots\!24\)\( T^{6} + \)\(40\!\cdots\!60\)\( T^{7} + \)\(12\!\cdots\!19\)\( T^{8} + \)\(19\!\cdots\!80\)\( T^{9} + \)\(44\!\cdots\!82\)\( T^{10} + \)\(44\!\cdots\!80\)\( T^{11} + \)\(53\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 - 306323542400025998 T^{4} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 - 126160742020349198 T^{4} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 + 138029827723659606 T^{4} + \)\(13\!\cdots\!15\)\( T^{8} + \)\(26\!\cdots\!20\)\( T^{12} + \)\(41\!\cdots\!15\)\( T^{16} + \)\(12\!\cdots\!06\)\( T^{20} + \)\(28\!\cdots\!01\)\( T^{24} \))
$59$ (\( 1 - 14340 T + 714924299 T^{2} \))(\( 1 - 34980 T + 714924299 T^{2} \))(\( 1 + 3954 T + 714924299 T^{2} \))(\( 1 + 7980 T + 714924299 T^{2} \))(\( 1 - 3954 T + 714924299 T^{2} \))(\( 1 + 28380 T + 714924299 T^{2} \))(\( 1 + 7920 T + 714924299 T^{2} \))(\( ( 1 + 39740 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 28300 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 23730 T + 501951198 T^{2} + 16965153615270 T^{3} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 33744102 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( 1 - 1824 T - 1187721932 T^{2} - 347976643296 T^{3} + 722501062807894762 T^{4} + \)\(79\!\cdots\!64\)\( T^{5} + \)\(39\!\cdots\!72\)\( T^{6} - \)\(85\!\cdots\!36\)\( T^{7} - \)\(50\!\cdots\!13\)\( T^{8} - \)\(61\!\cdots\!64\)\( T^{9} + \)\(19\!\cdots\!72\)\( T^{10} + \)\(29\!\cdots\!36\)\( T^{11} + \)\(18\!\cdots\!62\)\( T^{12} - \)\(64\!\cdots\!04\)\( T^{13} - \)\(15\!\cdots\!32\)\( T^{14} - \)\(17\!\cdots\!76\)\( T^{15} + \)\(68\!\cdots\!01\)\( T^{16} \))(\( 1 + 78522 T + 2087265221 T^{2} + 59705711508438 T^{3} + 2917620928750405407 T^{4} + \)\(67\!\cdots\!12\)\( T^{5} + \)\(11\!\cdots\!54\)\( T^{6} + \)\(29\!\cdots\!96\)\( T^{7} - \)\(17\!\cdots\!87\)\( T^{8} - \)\(81\!\cdots\!22\)\( T^{9} + \)\(90\!\cdots\!75\)\( T^{10} - \)\(58\!\cdots\!78\)\( T^{11} - \)\(88\!\cdots\!87\)\( T^{12} + \)\(10\!\cdots\!04\)\( T^{13} + \)\(29\!\cdots\!54\)\( T^{14} + \)\(12\!\cdots\!88\)\( T^{15} + \)\(38\!\cdots\!07\)\( T^{16} + \)\(56\!\cdots\!62\)\( T^{17} + \)\(14\!\cdots\!21\)\( T^{18} + \)\(38\!\cdots\!78\)\( T^{19} + \)\(34\!\cdots\!01\)\( T^{20} \))(\( 1 + 52233 T + 740448170 T^{2} + 14998252248423 T^{3} - 9077740305330261 T^{4} - \)\(40\!\cdots\!02\)\( T^{5} - \)\(11\!\cdots\!20\)\( T^{6} - \)\(11\!\cdots\!62\)\( T^{7} + \)\(12\!\cdots\!89\)\( T^{8} + \)\(21\!\cdots\!55\)\( T^{9} + \)\(85\!\cdots\!58\)\( T^{10} + \)\(15\!\cdots\!45\)\( T^{11} + \)\(63\!\cdots\!89\)\( T^{12} - \)\(42\!\cdots\!38\)\( T^{13} - \)\(30\!\cdots\!20\)\( T^{14} - \)\(76\!\cdots\!98\)\( T^{15} - \)\(12\!\cdots\!61\)\( T^{16} + \)\(14\!\cdots\!77\)\( T^{17} + \)\(50\!\cdots\!70\)\( T^{18} + \)\(25\!\cdots\!67\)\( T^{19} + \)\(34\!\cdots\!01\)\( T^{20} \))(\( 1 - 24021 T - 1347829167 T^{2} - 17804310200658 T^{3} + 2113670627153449914 T^{4} + \)\(50\!\cdots\!04\)\( T^{5} - \)\(83\!\cdots\!13\)\( T^{6} - \)\(84\!\cdots\!67\)\( T^{7} - \)\(34\!\cdots\!84\)\( T^{8} + \)\(54\!\cdots\!33\)\( T^{9} + \)\(17\!\cdots\!33\)\( T^{10} - \)\(22\!\cdots\!92\)\( T^{11} - \)\(14\!\cdots\!44\)\( T^{12} - \)\(16\!\cdots\!08\)\( T^{13} + \)\(88\!\cdots\!33\)\( T^{14} + \)\(19\!\cdots\!67\)\( T^{15} - \)\(89\!\cdots\!84\)\( T^{16} - \)\(15\!\cdots\!33\)\( T^{17} - \)\(11\!\cdots\!13\)\( T^{18} + \)\(47\!\cdots\!96\)\( T^{19} + \)\(14\!\cdots\!14\)\( T^{20} - \)\(86\!\cdots\!42\)\( T^{21} - \)\(47\!\cdots\!67\)\( T^{22} - \)\(59\!\cdots\!79\)\( T^{23} + \)\(17\!\cdots\!01\)\( T^{24} \))(\( ( 1 + 144806390 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 824189390 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 2197871970 T^{2} + 2372494875416951703 T^{4} + \)\(18\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!03\)\( T^{8} + \)\(57\!\cdots\!70\)\( T^{10} + \)\(13\!\cdots\!01\)\( T^{12} )^{2} \))
$61$ (\( 1 + 47938 T + 844596301 T^{2} \))(\( 1 + 9838 T + 844596301 T^{2} \))(\( 1 - 962 T + 844596301 T^{2} \))(\( 1 - 16622 T + 844596301 T^{2} \))(\( 1 - 962 T + 844596301 T^{2} \))(\( 1 - 5522 T + 844596301 T^{2} \))(\( 1 + 13450 T + 844596301 T^{2} \))(\( ( 1 + 42298 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 18290 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 57124 T + 2217210846 T^{2} - 48246719098324 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 + 38158 T + 844596301 T^{2} )^{4} \))(\( 1 - 57520 T + 1418366670 T^{2} + 7035843244312 T^{3} - 1738648172331337435 T^{4} + \)\(69\!\cdots\!64\)\( T^{5} - \)\(51\!\cdots\!74\)\( T^{6} - \)\(42\!\cdots\!00\)\( T^{7} + \)\(20\!\cdots\!88\)\( T^{8} - \)\(35\!\cdots\!00\)\( T^{9} - \)\(36\!\cdots\!74\)\( T^{10} + \)\(42\!\cdots\!64\)\( T^{11} - \)\(88\!\cdots\!35\)\( T^{12} + \)\(30\!\cdots\!12\)\( T^{13} + \)\(51\!\cdots\!70\)\( T^{14} - \)\(17\!\cdots\!20\)\( T^{15} + \)\(25\!\cdots\!01\)\( T^{16} \))(\( 1 - 34913 T - 1912941482 T^{2} + 44830555547529 T^{3} + 2753728722918045570 T^{4} - \)\(22\!\cdots\!15\)\( T^{5} - \)\(33\!\cdots\!52\)\( T^{6} + \)\(15\!\cdots\!61\)\( T^{7} + \)\(28\!\cdots\!09\)\( T^{8} - \)\(74\!\cdots\!38\)\( T^{9} - \)\(22\!\cdots\!44\)\( T^{10} - \)\(63\!\cdots\!38\)\( T^{11} + \)\(20\!\cdots\!09\)\( T^{12} + \)\(93\!\cdots\!61\)\( T^{13} - \)\(16\!\cdots\!52\)\( T^{14} - \)\(95\!\cdots\!15\)\( T^{15} + \)\(99\!\cdots\!70\)\( T^{16} + \)\(13\!\cdots\!29\)\( T^{17} - \)\(49\!\cdots\!82\)\( T^{18} - \)\(76\!\cdots\!13\)\( T^{19} + \)\(18\!\cdots\!01\)\( T^{20} \))(\( 1 - 50210 T + 314443669 T^{2} + 102926813701602 T^{3} - 4299685567452044304 T^{4} + \)\(40\!\cdots\!22\)\( T^{5} + \)\(41\!\cdots\!71\)\( T^{6} - \)\(17\!\cdots\!82\)\( T^{7} + \)\(24\!\cdots\!07\)\( T^{8} + \)\(10\!\cdots\!24\)\( T^{9} - \)\(50\!\cdots\!76\)\( T^{10} + \)\(84\!\cdots\!24\)\( T^{11} + \)\(17\!\cdots\!07\)\( T^{12} - \)\(10\!\cdots\!82\)\( T^{13} + \)\(21\!\cdots\!71\)\( T^{14} + \)\(17\!\cdots\!22\)\( T^{15} - \)\(15\!\cdots\!04\)\( T^{16} + \)\(31\!\cdots\!02\)\( T^{17} + \)\(81\!\cdots\!69\)\( T^{18} - \)\(10\!\cdots\!10\)\( T^{19} + \)\(18\!\cdots\!01\)\( T^{20} \))(\( 1 + 20181 T - 3100873557 T^{2} - 97738185604112 T^{3} + 4904422504254660309 T^{4} + \)\(20\!\cdots\!11\)\( T^{5} - \)\(40\!\cdots\!60\)\( T^{6} - \)\(26\!\cdots\!07\)\( T^{7} + \)\(95\!\cdots\!43\)\( T^{8} + \)\(20\!\cdots\!68\)\( T^{9} + \)\(20\!\cdots\!33\)\( T^{10} - \)\(73\!\cdots\!57\)\( T^{11} - \)\(28\!\cdots\!70\)\( T^{12} - \)\(62\!\cdots\!57\)\( T^{13} + \)\(14\!\cdots\!33\)\( T^{14} + \)\(12\!\cdots\!68\)\( T^{15} + \)\(48\!\cdots\!43\)\( T^{16} - \)\(11\!\cdots\!07\)\( T^{17} - \)\(14\!\cdots\!60\)\( T^{18} + \)\(62\!\cdots\!11\)\( T^{19} + \)\(12\!\cdots\!09\)\( T^{20} - \)\(21\!\cdots\!12\)\( T^{21} - \)\(57\!\cdots\!57\)\( T^{22} + \)\(31\!\cdots\!81\)\( T^{23} + \)\(13\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 13740 T + 844596301 T^{2} )^{4} \))(\( ( 1 + 11040 T + 844596301 T^{2} )^{4} \))(\( ( 1 + 36300 T + 1780029303 T^{2} + 33645024252600 T^{3} + 1503406164985408203 T^{4} + \)\(25\!\cdots\!00\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{4} \))
$67$ (\( 1 - 33092 T + 1350125107 T^{2} \))(\( 1 - 33722 T + 1350125107 T^{2} \))(\( 1 + 17956 T + 1350125107 T^{2} \))(\( 1 - 1808 T + 1350125107 T^{2} \))(\( 1 + 17956 T + 1350125107 T^{2} \))(\( 1 + 24742 T + 1350125107 T^{2} \))(\( 1 + 65476 T + 1350125107 T^{2} \))(\( 1 - 1669968610 T^{2} + 1822837804551761449 T^{4} \))(\( 1 + 1649943722 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 4204562300 T^{2} + 7726214820152619798 T^{4} - \)\(76\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 1387552678 T^{2} + 1822837804551761449 T^{4} )^{2} \))(\( 1 + 15410 T - 2762611140 T^{2} - 79938025554716 T^{3} + 2671599603823634633 T^{4} + \)\(10\!\cdots\!86\)\( T^{5} - \)\(24\!\cdots\!56\)\( T^{6} - \)\(50\!\cdots\!04\)\( T^{7} + \)\(47\!\cdots\!20\)\( T^{8} - \)\(68\!\cdots\!28\)\( T^{9} - \)\(44\!\cdots\!44\)\( T^{10} + \)\(26\!\cdots\!98\)\( T^{11} + \)\(88\!\cdots\!33\)\( T^{12} - \)\(35\!\cdots\!12\)\( T^{13} - \)\(16\!\cdots\!60\)\( T^{14} + \)\(12\!\cdots\!30\)\( T^{15} + \)\(11\!\cdots\!01\)\( T^{16} \))(\( 1 - 26177 T - 3708980858 T^{2} + 65223510793185 T^{3} + 7531665187158904494 T^{4} - \)\(65\!\cdots\!47\)\( T^{5} - \)\(12\!\cdots\!68\)\( T^{6} + \)\(82\!\cdots\!39\)\( T^{7} + \)\(15\!\cdots\!09\)\( T^{8} - \)\(69\!\cdots\!28\)\( T^{9} - \)\(19\!\cdots\!56\)\( T^{10} - \)\(93\!\cdots\!96\)\( T^{11} + \)\(29\!\cdots\!41\)\( T^{12} + \)\(20\!\cdots\!77\)\( T^{13} - \)\(40\!\cdots\!68\)\( T^{14} - \)\(29\!\cdots\!29\)\( T^{15} + \)\(45\!\cdots\!06\)\( T^{16} + \)\(53\!\cdots\!55\)\( T^{17} - \)\(40\!\cdots\!58\)\( T^{18} - \)\(39\!\cdots\!39\)\( T^{19} + \)\(20\!\cdots\!49\)\( T^{20} \))(\( 1 - 27185 T - 1384104872 T^{2} + 168654927678591 T^{3} - 4275027751655371668 T^{4} - \)\(66\!\cdots\!03\)\( T^{5} + \)\(12\!\cdots\!28\)\( T^{6} - \)\(48\!\cdots\!25\)\( T^{7} + \)\(68\!\cdots\!19\)\( T^{8} + \)\(56\!\cdots\!66\)\( T^{9} - \)\(33\!\cdots\!88\)\( T^{10} + \)\(76\!\cdots\!62\)\( T^{11} + \)\(12\!\cdots\!31\)\( T^{12} - \)\(11\!\cdots\!75\)\( T^{13} + \)\(41\!\cdots\!28\)\( T^{14} - \)\(29\!\cdots\!21\)\( T^{15} - \)\(25\!\cdots\!32\)\( T^{16} + \)\(13\!\cdots\!13\)\( T^{17} - \)\(15\!\cdots\!72\)\( T^{18} - \)\(40\!\cdots\!95\)\( T^{19} + \)\(20\!\cdots\!49\)\( T^{20} \))(\( 1 + 56514 T - 3046119267 T^{2} - 80758311069338 T^{3} + 12130996363340465625 T^{4} + \)\(70\!\cdots\!26\)\( T^{5} - \)\(21\!\cdots\!98\)\( T^{6} + \)\(33\!\cdots\!00\)\( T^{7} + \)\(26\!\cdots\!29\)\( T^{8} - \)\(60\!\cdots\!66\)\( T^{9} - \)\(95\!\cdots\!15\)\( T^{10} + \)\(57\!\cdots\!00\)\( T^{11} + \)\(49\!\cdots\!14\)\( T^{12} + \)\(77\!\cdots\!00\)\( T^{13} - \)\(17\!\cdots\!35\)\( T^{14} - \)\(14\!\cdots\!38\)\( T^{15} + \)\(88\!\cdots\!29\)\( T^{16} + \)\(14\!\cdots\!00\)\( T^{17} - \)\(12\!\cdots\!02\)\( T^{18} + \)\(57\!\cdots\!18\)\( T^{19} + \)\(13\!\cdots\!25\)\( T^{20} - \)\(12\!\cdots\!66\)\( T^{21} - \)\(61\!\cdots\!83\)\( T^{22} + \)\(15\!\cdots\!02\)\( T^{23} + \)\(36\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 68128 T + 2320712192 T^{2} - 91981323289696 T^{3} + 1822837804551761449 T^{4} )^{2} \))(\( ( 1 - 55888 T + 1561734272 T^{2} - 75455791980016 T^{3} + 1822837804551761449 T^{4} )^{2} \))(\( ( 1 - 16776 T + 140717088 T^{2} - 71734444130584 T^{3} - 1822301007087929349 T^{4} + \)\(12\!\cdots\!32\)\( T^{5} + \)\(71\!\cdots\!08\)\( T^{6} + \)\(17\!\cdots\!24\)\( T^{7} - \)\(33\!\cdots\!01\)\( T^{8} - \)\(17\!\cdots\!12\)\( T^{9} + \)\(46\!\cdots\!88\)\( T^{10} - \)\(75\!\cdots\!32\)\( T^{11} + \)\(60\!\cdots\!49\)\( T^{12} )^{2} \))
$71$ (\( 1 + 51912 T + 1804229351 T^{2} \))(\( 1 + 70212 T + 1804229351 T^{2} \))(\( 1 - 56148 T + 1804229351 T^{2} \))(\( 1 - 24528 T + 1804229351 T^{2} \))(\( 1 + 56148 T + 1804229351 T^{2} \))(\( 1 + 42372 T + 1804229351 T^{2} \))(\( 1 + 34560 T + 1804229351 T^{2} \))(\( ( 1 - 4248 T + 1804229351 T^{2} )^{2} \))(\( ( 1 - 28800 T + 1804229351 T^{2} )^{2} \))(\( ( 1 - 11076 T + 940164046 T^{2} - 19983644291676 T^{3} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 3331783438 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 11478 T + 2278374080 T^{2} + 120923485355106 T^{3} + 3899926197050715726 T^{4} + \)\(21\!\cdots\!06\)\( T^{5} + \)\(74\!\cdots\!80\)\( T^{6} + \)\(67\!\cdots\!78\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 81456 T + 5489372479 T^{2} - 158736667499436 T^{3} + 3633747220898407702 T^{4} + \)\(16\!\cdots\!28\)\( T^{5} + \)\(65\!\cdots\!02\)\( T^{6} - \)\(51\!\cdots\!36\)\( T^{7} + \)\(32\!\cdots\!29\)\( T^{8} - \)\(86\!\cdots\!56\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 - 129468 T + 10847432083 T^{2} - 612079132097796 T^{3} + 31103438841842580370 T^{4} - \)\(13\!\cdots\!44\)\( T^{5} + \)\(56\!\cdots\!70\)\( T^{6} - \)\(19\!\cdots\!96\)\( T^{7} + \)\(63\!\cdots\!33\)\( T^{8} - \)\(13\!\cdots\!68\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 + 59490 T + 9820969734 T^{2} + 448612867252962 T^{3} + 41306104706320741335 T^{4} + \)\(14\!\cdots\!84\)\( T^{5} + \)\(97\!\cdots\!92\)\( T^{6} + \)\(26\!\cdots\!84\)\( T^{7} + \)\(13\!\cdots\!35\)\( T^{8} + \)\(26\!\cdots\!62\)\( T^{9} + \)\(10\!\cdots\!34\)\( T^{10} + \)\(11\!\cdots\!90\)\( T^{11} + \)\(34\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 - 1301352110 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 - 1808938670 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 - 9374370570 T^{2} + 38765983187289347103 T^{4} - \)\(90\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!03\)\( T^{8} - \)\(99\!\cdots\!70\)\( T^{10} + \)\(34\!\cdots\!01\)\( T^{12} )^{2} \))
$73$ (\( 1 - 12026 T + 2073071593 T^{2} \))(\( 1 - 21986 T + 2073071593 T^{2} \))(\( 1 + 85690 T + 2073071593 T^{2} \))(\( 1 - 20474 T + 2073071593 T^{2} \))(\( 1 + 85690 T + 2073071593 T^{2} \))(\( 1 + 52126 T + 2073071593 T^{2} \))(\( 1 - 86258 T + 2073071593 T^{2} \))(\( 1 - 3239892370 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 3197010322 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 3772142420 T^{2} + 9801194247527769798 T^{4} - \)\(16\!\cdots\!80\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 669338414 T^{2} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 - 3668 T + 5892681412 T^{2} + 2198141843236 T^{3} + 16330035279071841958 T^{4} + \)\(45\!\cdots\!48\)\( T^{5} + \)\(25\!\cdots\!88\)\( T^{6} - \)\(32\!\cdots\!76\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 90352 T + 12916081917 T^{2} - 776138728696896 T^{3} + 58922123979905053050 T^{4} - \)\(24\!\cdots\!76\)\( T^{5} + \)\(12\!\cdots\!50\)\( T^{6} - \)\(33\!\cdots\!04\)\( T^{7} + \)\(11\!\cdots\!69\)\( T^{8} - \)\(16\!\cdots\!52\)\( T^{9} + \)\(38\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 + 34931 T + 7088014209 T^{2} + 183604966475724 T^{3} + 23462736012088276326 T^{4} + \)\(45\!\cdots\!98\)\( T^{5} + \)\(48\!\cdots\!18\)\( T^{6} + \)\(78\!\cdots\!76\)\( T^{7} + \)\(63\!\cdots\!13\)\( T^{8} + \)\(64\!\cdots\!31\)\( T^{9} + \)\(38\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 - 51753 T + 931091646 T^{2} - 5069690931685 T^{3} + 4742157800710078623 T^{4} - \)\(18\!\cdots\!62\)\( T^{5} + \)\(48\!\cdots\!68\)\( T^{6} - \)\(37\!\cdots\!66\)\( T^{7} + \)\(20\!\cdots\!27\)\( T^{8} - \)\(45\!\cdots\!45\)\( T^{9} + \)\(17\!\cdots\!46\)\( T^{10} - \)\(19\!\cdots\!29\)\( T^{11} + \)\(79\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 + 59782 T + 1786943762 T^{2} + 123932365972726 T^{3} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 - 5678 T + 16119842 T^{2} - 11770900505054 T^{3} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 + 79494 T + 3159648018 T^{2} - 50403657969290 T^{3} - 1967048070000525585 T^{4} + \)\(27\!\cdots\!24\)\( T^{5} + \)\(29\!\cdots\!36\)\( T^{6} + \)\(57\!\cdots\!32\)\( T^{7} - \)\(84\!\cdots\!65\)\( T^{8} - \)\(44\!\cdots\!30\)\( T^{9} + \)\(58\!\cdots\!18\)\( T^{10} + \)\(30\!\cdots\!42\)\( T^{11} + \)\(79\!\cdots\!49\)\( T^{12} )^{2} \))
$79$ (\( 1 - 25160 T + 3077056399 T^{2} \))(\( 1 - 4520 T + 3077056399 T^{2} \))(\( 1 + 26044 T + 3077056399 T^{2} \))(\( 1 + 46240 T + 3077056399 T^{2} \))(\( 1 + 26044 T + 3077056399 T^{2} \))(\( 1 + 39640 T + 3077056399 T^{2} \))(\( 1 + 108832 T + 3077056399 T^{2} \))(\( ( 1 + 35280 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 60228 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 14220 T + 4980519998 T^{2} + 43755741993780 T^{3} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 - 20664 T + 3077056399 T^{2} )^{4} \))(\( 1 - 60556 T - 8628563004 T^{2} + 278368565833096 T^{3} + 64100205595980453866 T^{4} - \)\(10\!\cdots\!40\)\( T^{5} - \)\(29\!\cdots\!28\)\( T^{6} + \)\(11\!\cdots\!08\)\( T^{7} + \)\(10\!\cdots\!27\)\( T^{8} + \)\(36\!\cdots\!92\)\( T^{9} - \)\(27\!\cdots\!28\)\( T^{10} - \)\(31\!\cdots\!60\)\( T^{11} + \)\(57\!\cdots\!66\)\( T^{12} + \)\(76\!\cdots\!04\)\( T^{13} - \)\(73\!\cdots\!04\)\( T^{14} - \)\(15\!\cdots\!44\)\( T^{15} + \)\(80\!\cdots\!01\)\( T^{16} \))(\( 1 + 42274 T - 7769077223 T^{2} - 342098771794170 T^{3} + 28935868839563979183 T^{4} + \)\(12\!\cdots\!40\)\( T^{5} - \)\(88\!\cdots\!06\)\( T^{6} - \)\(41\!\cdots\!56\)\( T^{7} + \)\(21\!\cdots\!05\)\( T^{8} + \)\(68\!\cdots\!10\)\( T^{9} - \)\(46\!\cdots\!89\)\( T^{10} + \)\(21\!\cdots\!90\)\( T^{11} + \)\(20\!\cdots\!05\)\( T^{12} - \)\(12\!\cdots\!44\)\( T^{13} - \)\(79\!\cdots\!06\)\( T^{14} + \)\(34\!\cdots\!60\)\( T^{15} + \)\(24\!\cdots\!83\)\( T^{16} - \)\(89\!\cdots\!30\)\( T^{17} - \)\(62\!\cdots\!23\)\( T^{18} + \)\(10\!\cdots\!26\)\( T^{19} + \)\(76\!\cdots\!01\)\( T^{20} \))(\( 1 - 48782 T - 5566576991 T^{2} + 670722299040774 T^{3} - 4343482442408674713 T^{4} - \)\(22\!\cdots\!64\)\( T^{5} + \)\(10\!\cdots\!06\)\( T^{6} - \)\(45\!\cdots\!32\)\( T^{7} - \)\(11\!\cdots\!11\)\( T^{8} + \)\(71\!\cdots\!38\)\( T^{9} - \)\(52\!\cdots\!01\)\( T^{10} + \)\(22\!\cdots\!62\)\( T^{11} - \)\(11\!\cdots\!11\)\( T^{12} - \)\(13\!\cdots\!68\)\( T^{13} + \)\(93\!\cdots\!06\)\( T^{14} - \)\(60\!\cdots\!36\)\( T^{15} - \)\(36\!\cdots\!13\)\( T^{16} + \)\(17\!\cdots\!26\)\( T^{17} - \)\(44\!\cdots\!91\)\( T^{18} - \)\(12\!\cdots\!18\)\( T^{19} + \)\(76\!\cdots\!01\)\( T^{20} \))(\( 1 + 54048 T - 12987444774 T^{2} - 627804357498368 T^{3} + 99516898601932741557 T^{4} + \)\(38\!\cdots\!44\)\( T^{5} - \)\(57\!\cdots\!14\)\( T^{6} - \)\(14\!\cdots\!08\)\( T^{7} + \)\(27\!\cdots\!14\)\( T^{8} + \)\(38\!\cdots\!92\)\( T^{9} - \)\(11\!\cdots\!50\)\( T^{10} - \)\(44\!\cdots\!40\)\( T^{11} + \)\(38\!\cdots\!05\)\( T^{12} - \)\(13\!\cdots\!60\)\( T^{13} - \)\(10\!\cdots\!50\)\( T^{14} + \)\(11\!\cdots\!08\)\( T^{15} + \)\(24\!\cdots\!14\)\( T^{16} - \)\(41\!\cdots\!92\)\( T^{17} - \)\(48\!\cdots\!14\)\( T^{18} + \)\(10\!\cdots\!56\)\( T^{19} + \)\(79\!\cdots\!57\)\( T^{20} - \)\(15\!\cdots\!32\)\( T^{21} - \)\(98\!\cdots\!74\)\( T^{22} + \)\(12\!\cdots\!52\)\( T^{23} + \)\(72\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 2634301214 T^{2} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 + 3585208546 T^{2} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 - 12913071402 T^{2} + 82695789000125977071 T^{4} - \)\(31\!\cdots\!08\)\( T^{6} + \)\(78\!\cdots\!71\)\( T^{8} - \)\(11\!\cdots\!02\)\( T^{10} + \)\(84\!\cdots\!01\)\( T^{12} )^{2} \))
$83$ (\( 1 + 35796 T + 3939040643 T^{2} \))(\( 1 - 109074 T + 3939040643 T^{2} \))(\( 1 - 93468 T + 3939040643 T^{2} \))(\( 1 - 51576 T + 3939040643 T^{2} \))(\( 1 + 93468 T + 3939040643 T^{2} \))(\( 1 - 59826 T + 3939040643 T^{2} \))(\( 1 + 10668 T + 3939040643 T^{2} \))(\( 1 - 7103795010 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 7871990262 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 2811580140 T^{2} + 17974811933757230198 T^{4} - \)\(43\!\cdots\!60\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 1524711738 T^{2} + 15516041187205853449 T^{4} )^{2} \))(\( 1 - 167904 T + 5556934612 T^{2} + 271703243009196 T^{3} + 23887443275134833373 T^{4} - \)\(48\!\cdots\!30\)\( T^{5} + \)\(18\!\cdots\!20\)\( T^{6} - \)\(46\!\cdots\!62\)\( T^{7} + \)\(41\!\cdots\!52\)\( T^{8} - \)\(18\!\cdots\!66\)\( T^{9} + \)\(28\!\cdots\!80\)\( T^{10} - \)\(29\!\cdots\!10\)\( T^{11} + \)\(57\!\cdots\!73\)\( T^{12} + \)\(25\!\cdots\!28\)\( T^{13} + \)\(20\!\cdots\!88\)\( T^{14} - \)\(24\!\cdots\!28\)\( T^{15} + \)\(57\!\cdots\!01\)\( T^{16} \))(\( 1 + 37245 T - 10498145776 T^{2} - 1111031143604451 T^{3} + 48764588096891771484 T^{4} + \)\(94\!\cdots\!43\)\( T^{5} + \)\(16\!\cdots\!24\)\( T^{6} - \)\(46\!\cdots\!67\)\( T^{7} - \)\(25\!\cdots\!29\)\( T^{8} + \)\(76\!\cdots\!06\)\( T^{9} + \)\(14\!\cdots\!68\)\( T^{10} + \)\(30\!\cdots\!58\)\( T^{11} - \)\(40\!\cdots\!21\)\( T^{12} - \)\(28\!\cdots\!69\)\( T^{13} + \)\(39\!\cdots\!24\)\( T^{14} + \)\(89\!\cdots\!49\)\( T^{15} + \)\(18\!\cdots\!16\)\( T^{16} - \)\(16\!\cdots\!57\)\( T^{17} - \)\(60\!\cdots\!76\)\( T^{18} + \)\(85\!\cdots\!35\)\( T^{19} + \)\(89\!\cdots\!49\)\( T^{20} \))(\( 1 + 71172 T - 10143727495 T^{2} - 470937354085152 T^{3} + 77822119348806820542 T^{4} + \)\(17\!\cdots\!62\)\( T^{5} - \)\(39\!\cdots\!03\)\( T^{6} - \)\(42\!\cdots\!00\)\( T^{7} + \)\(14\!\cdots\!65\)\( T^{8} + \)\(21\!\cdots\!14\)\( T^{9} - \)\(56\!\cdots\!52\)\( T^{10} + \)\(82\!\cdots\!02\)\( T^{11} + \)\(22\!\cdots\!85\)\( T^{12} - \)\(26\!\cdots\!00\)\( T^{13} - \)\(95\!\cdots\!03\)\( T^{14} + \)\(16\!\cdots\!66\)\( T^{15} + \)\(29\!\cdots\!58\)\( T^{16} - \)\(69\!\cdots\!64\)\( T^{17} - \)\(58\!\cdots\!95\)\( T^{18} + \)\(16\!\cdots\!96\)\( T^{19} + \)\(89\!\cdots\!49\)\( T^{20} \))(\( 1 - 54405 T - 11164391391 T^{2} + 117086680358190 T^{3} + 82065291112366675833 T^{4} + \)\(17\!\cdots\!43\)\( T^{5} - \)\(37\!\cdots\!68\)\( T^{6} - \)\(13\!\cdots\!77\)\( T^{7} + \)\(11\!\cdots\!87\)\( T^{8} + \)\(41\!\cdots\!58\)\( T^{9} - \)\(34\!\cdots\!73\)\( T^{10} - \)\(61\!\cdots\!49\)\( T^{11} + \)\(13\!\cdots\!74\)\( T^{12} - \)\(24\!\cdots\!07\)\( T^{13} - \)\(53\!\cdots\!77\)\( T^{14} + \)\(25\!\cdots\!06\)\( T^{15} + \)\(27\!\cdots\!87\)\( T^{16} - \)\(12\!\cdots\!11\)\( T^{17} - \)\(14\!\cdots\!32\)\( T^{18} + \)\(26\!\cdots\!01\)\( T^{19} + \)\(47\!\cdots\!33\)\( T^{20} + \)\(26\!\cdots\!70\)\( T^{21} - \)\(10\!\cdots\!59\)\( T^{22} - \)\(19\!\cdots\!35\)\( T^{23} + \)\(13\!\cdots\!01\)\( T^{24} \))(\( 1 - 6332652458657888494 T^{4} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 + 27652369579660332626 T^{4} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 + 22486620193935462198 T^{4} + \)\(77\!\cdots\!71\)\( T^{8} + \)\(10\!\cdots\!92\)\( T^{12} + \)\(18\!\cdots\!71\)\( T^{16} + \)\(13\!\cdots\!98\)\( T^{20} + \)\(13\!\cdots\!01\)\( T^{24} \))
$89$ (\( 1 - 75510 T + 5584059449 T^{2} \))(\( 1 + 38490 T + 5584059449 T^{2} \))(\( 1 + 73428 T + 5584059449 T^{2} \))(\( 1 - 110310 T + 5584059449 T^{2} \))(\( 1 - 73428 T + 5584059449 T^{2} \))(\( 1 + 57690 T + 5584059449 T^{2} \))(\( 1 + 10818 T + 5584059449 T^{2} \))(\( ( 1 + 85210 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 22678 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 60420 T + 10831762998 T^{2} + 337388871908580 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 7604090994 T^{2} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 147072 T + 25215325934 T^{2} + 2372989576350888 T^{3} + \)\(21\!\cdots\!15\)\( T^{4} + \)\(13\!\cdots\!12\)\( T^{5} + \)\(78\!\cdots\!34\)\( T^{6} + \)\(25\!\cdots\!28\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 48777 T + 19526630215 T^{2} - 1005681751538070 T^{3} + \)\(18\!\cdots\!49\)\( T^{4} - \)\(79\!\cdots\!71\)\( T^{5} + \)\(10\!\cdots\!01\)\( T^{6} - \)\(31\!\cdots\!70\)\( T^{7} + \)\(33\!\cdots\!35\)\( T^{8} - \)\(47\!\cdots\!77\)\( T^{9} + \)\(54\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 86454 T + 13109831671 T^{2} - 1357305077402748 T^{3} + \)\(11\!\cdots\!93\)\( T^{4} - \)\(96\!\cdots\!66\)\( T^{5} + \)\(63\!\cdots\!57\)\( T^{6} - \)\(42\!\cdots\!48\)\( T^{7} + \)\(22\!\cdots\!79\)\( T^{8} - \)\(84\!\cdots\!54\)\( T^{9} + \)\(54\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 + 100017 T + 25595297454 T^{2} + 2278544136621183 T^{3} + \)\(31\!\cdots\!76\)\( T^{4} + \)\(22\!\cdots\!29\)\( T^{5} + \)\(22\!\cdots\!28\)\( T^{6} + \)\(12\!\cdots\!21\)\( T^{7} + \)\(99\!\cdots\!76\)\( T^{8} + \)\(39\!\cdots\!67\)\( T^{9} + \)\(24\!\cdots\!54\)\( T^{10} + \)\(54\!\cdots\!33\)\( T^{11} + \)\(30\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 10877569280 T^{2} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 - 2039231440 T^{2} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 5060350560 T^{2} + 16753820650674742803 T^{4} - \)\(12\!\cdots\!80\)\( T^{6} + \)\(52\!\cdots\!03\)\( T^{8} + \)\(49\!\cdots\!60\)\( T^{10} + \)\(30\!\cdots\!01\)\( T^{12} )^{2} \))
$97$ (\( 1 + 44158 T + 8587340257 T^{2} \))(\( 1 + 1918 T + 8587340257 T^{2} \))(\( 1 - 128978 T + 8587340257 T^{2} \))(\( 1 + 78382 T + 8587340257 T^{2} \))(\( 1 - 128978 T + 8587340257 T^{2} \))(\( 1 + 144382 T + 8587340257 T^{2} \))(\( 1 - 4418 T + 8587340257 T^{2} \))(\( 1 - 7720618690 T^{2} + 73742412689492826049 T^{4} \))(\( 1 - 15808047490 T^{2} + 73742412689492826049 T^{4} \))(\( 1 - 19675914500 T^{2} + \)\(24\!\cdots\!98\)\( T^{4} - \)\(14\!\cdots\!00\)\( T^{6} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 17140767490 T^{2} + 73742412689492826049 T^{4} )^{2} \))(\( 1 - 81556 T - 14710237764 T^{2} + 2303239215653608 T^{3} + 71979872186618570474 T^{4} - \)\(24\!\cdots\!04\)\( T^{5} + \)\(11\!\cdots\!48\)\( T^{6} + \)\(11\!\cdots\!84\)\( T^{7} - \)\(17\!\cdots\!13\)\( T^{8} + \)\(10\!\cdots\!88\)\( T^{9} + \)\(83\!\cdots\!52\)\( T^{10} - \)\(15\!\cdots\!72\)\( T^{11} + \)\(39\!\cdots\!74\)\( T^{12} + \)\(10\!\cdots\!56\)\( T^{13} - \)\(58\!\cdots\!36\)\( T^{14} - \)\(28\!\cdots\!08\)\( T^{15} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( 1 + 160582 T - 10109446385 T^{2} - 1467151204627410 T^{3} + \)\(19\!\cdots\!23\)\( T^{4} + \)\(51\!\cdots\!16\)\( T^{5} - \)\(29\!\cdots\!94\)\( T^{6} - \)\(54\!\cdots\!84\)\( T^{7} + \)\(22\!\cdots\!17\)\( T^{8} + \)\(22\!\cdots\!14\)\( T^{9} - \)\(16\!\cdots\!39\)\( T^{10} + \)\(19\!\cdots\!98\)\( T^{11} + \)\(16\!\cdots\!33\)\( T^{12} - \)\(34\!\cdots\!12\)\( T^{13} - \)\(16\!\cdots\!94\)\( T^{14} + \)\(24\!\cdots\!12\)\( T^{15} + \)\(78\!\cdots\!27\)\( T^{16} - \)\(50\!\cdots\!30\)\( T^{17} - \)\(29\!\cdots\!85\)\( T^{18} + \)\(40\!\cdots\!74\)\( T^{19} + \)\(21\!\cdots\!49\)\( T^{20} \))(\( 1 - 179825 T - 1348471616 T^{2} + 3245021810789943 T^{3} - \)\(23\!\cdots\!37\)\( T^{4} - \)\(17\!\cdots\!50\)\( T^{5} + \)\(32\!\cdots\!20\)\( T^{6} - \)\(77\!\cdots\!86\)\( T^{7} - \)\(13\!\cdots\!59\)\( T^{8} + \)\(86\!\cdots\!29\)\( T^{9} - \)\(14\!\cdots\!92\)\( T^{10} + \)\(74\!\cdots\!53\)\( T^{11} - \)\(10\!\cdots\!91\)\( T^{12} - \)\(48\!\cdots\!98\)\( T^{13} + \)\(17\!\cdots\!20\)\( T^{14} - \)\(80\!\cdots\!50\)\( T^{15} - \)\(95\!\cdots\!13\)\( T^{16} + \)\(11\!\cdots\!99\)\( T^{17} - \)\(39\!\cdots\!16\)\( T^{18} - \)\(45\!\cdots\!25\)\( T^{19} + \)\(21\!\cdots\!49\)\( T^{20} \))(\( 1 - 96063 T - 12846441423 T^{2} - 944789536939130 T^{3} + \)\(29\!\cdots\!08\)\( T^{4} + \)\(23\!\cdots\!24\)\( T^{5} - \)\(10\!\cdots\!25\)\( T^{6} - \)\(49\!\cdots\!11\)\( T^{7} - \)\(87\!\cdots\!72\)\( T^{8} + \)\(36\!\cdots\!35\)\( T^{9} + \)\(42\!\cdots\!89\)\( T^{10} - \)\(18\!\cdots\!16\)\( T^{11} - \)\(41\!\cdots\!50\)\( T^{12} - \)\(15\!\cdots\!12\)\( T^{13} + \)\(31\!\cdots\!61\)\( T^{14} + \)\(22\!\cdots\!55\)\( T^{15} - \)\(47\!\cdots\!72\)\( T^{16} - \)\(22\!\cdots\!27\)\( T^{17} - \)\(43\!\cdots\!25\)\( T^{18} + \)\(81\!\cdots\!32\)\( T^{19} + \)\(87\!\cdots\!08\)\( T^{20} - \)\(23\!\cdots\!10\)\( T^{21} - \)\(28\!\cdots\!27\)\( T^{22} - \)\(17\!\cdots\!59\)\( T^{23} + \)\(16\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 192186 T + 18467729298 T^{2} - 1650366574631802 T^{3} + 73742412689492826049 T^{4} )^{2} \))(\( ( 1 - 46086 T + 1061959698 T^{2} - 395756163084102 T^{3} + 73742412689492826049 T^{4} )^{2} \))(\( ( 1 + 315558 T + 49788425682 T^{2} + 5316509668950630 T^{3} + \)\(47\!\cdots\!15\)\( T^{4} + \)\(43\!\cdots\!68\)\( T^{5} + \)\(40\!\cdots\!64\)\( T^{6} + \)\(36\!\cdots\!76\)\( T^{7} + \)\(34\!\cdots\!35\)\( T^{8} + \)\(33\!\cdots\!90\)\( T^{9} + \)\(27\!\cdots\!82\)\( T^{10} + \)\(14\!\cdots\!06\)\( T^{11} + \)\(40\!\cdots\!49\)\( T^{12} )^{2} \))
show more
show less