Properties

Label 210.4
Level 210
Weight 4
Dimension 760
Nonzero newspaces 12
Newform subspaces 43
Sturm bound 9216
Trace bound 4

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Defining parameters

Level: \( N \) = \( 210\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 43 \)
Sturm bound: \(9216\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(210))\).

Total New Old
Modular forms 3648 760 2888
Cusp forms 3264 760 2504
Eisenstein series 384 0 384

Trace form

\( 760q - 4q^{3} - 56q^{5} - 64q^{6} - 232q^{7} + 84q^{9} + O(q^{10}) \) \( 760q - 4q^{3} - 56q^{5} - 64q^{6} - 232q^{7} + 84q^{9} + 152q^{10} + 104q^{11} + 112q^{12} + 280q^{13} + 64q^{14} + 224q^{15} + 256q^{16} + 120q^{17} + 368q^{18} + 736q^{19} + 32q^{20} + 736q^{21} - 672q^{22} - 312q^{23} - 2908q^{25} - 1488q^{26} - 424q^{27} - 352q^{28} + 624q^{29} + 168q^{30} + 672q^{31} + 284q^{33} + 2080q^{34} + 3796q^{35} - 1120q^{36} + 4072q^{37} + 1680q^{38} + 3240q^{39} + 480q^{40} + 752q^{41} + 152q^{42} + 1456q^{43} - 32q^{44} - 782q^{45} - 2560q^{46} - 4848q^{47} - 128q^{48} - 8832q^{49} - 1856q^{50} - 6644q^{51} - 2144q^{52} - 2808q^{53} - 576q^{54} - 8804q^{55} + 512q^{56} - 2800q^{57} - 336q^{58} - 2272q^{59} - 808q^{60} + 13808q^{61} + 4416q^{62} + 8476q^{63} + 1536q^{64} + 5712q^{65} + 3680q^{66} + 11440q^{67} + 480q^{68} + 4080q^{69} + 1872q^{70} + 2256q^{71} - 1472q^{72} - 1760q^{73} + 848q^{74} - 314q^{75} + 544q^{76} + 3816q^{77} + 1488q^{78} - 3920q^{79} - 896q^{80} + 7732q^{81} - 6624q^{82} - 2592q^{83} - 2112q^{84} - 12776q^{85} - 5264q^{86} - 4504q^{87} - 1344q^{88} - 8624q^{89} - 1672q^{90} - 5120q^{91} - 4800q^{92} - 1156q^{93} - 8704q^{94} - 2184q^{95} + 256q^{96} + 7096q^{97} + 384q^{98} - 9240q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(210))\)

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
210.4.a \(\chi_{210}(1, \cdot)\) 210.4.a.a 1 1
210.4.a.b 1
210.4.a.c 1
210.4.a.d 1
210.4.a.e 1
210.4.a.f 1
210.4.a.g 1
210.4.a.h 1
210.4.a.i 1
210.4.a.j 1
210.4.a.k 2
210.4.b \(\chi_{210}(41, \cdot)\) 210.4.b.a 16 1
210.4.b.b 16
210.4.d \(\chi_{210}(209, \cdot)\) 210.4.d.a 24 1
210.4.d.b 24
210.4.g \(\chi_{210}(169, \cdot)\) 210.4.g.a 4 1
210.4.g.b 4
210.4.g.c 6
210.4.g.d 6
210.4.i \(\chi_{210}(121, \cdot)\) 210.4.i.a 2 2
210.4.i.b 2
210.4.i.c 2
210.4.i.d 2
210.4.i.e 2
210.4.i.f 2
210.4.i.g 2
210.4.i.h 4
210.4.i.i 4
210.4.i.j 4
210.4.i.k 6
210.4.j \(\chi_{210}(113, \cdot)\) 210.4.j.a 36 2
210.4.j.b 36
210.4.m \(\chi_{210}(13, \cdot)\) 210.4.m.a 24 2
210.4.m.b 24
210.4.n \(\chi_{210}(79, \cdot)\) 210.4.n.a 20 2
210.4.n.b 28
210.4.r \(\chi_{210}(101, \cdot)\) 210.4.r.a 32 2
210.4.r.b 32
210.4.t \(\chi_{210}(59, \cdot)\) 210.4.t.a 48 2
210.4.t.b 48
210.4.u \(\chi_{210}(73, \cdot)\) 210.4.u.a 48 4
210.4.u.b 48
210.4.x \(\chi_{210}(23, \cdot)\) 210.4.x.a 192 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(210))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(210)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 - 2 T \))(\( 1 - 2 T \))(\( 1 - 2 T \))(\( 1 - 2 T \))(\( ( 1 - 2 T )^{2} \))(\( ( 1 + 4 T^{2} )^{8} \))(\( ( 1 + 4 T^{2} )^{8} \))(\( ( 1 + 4 T^{2} )^{2} \))(\( ( 1 + 4 T^{2} )^{2} \))(\( ( 1 + 4 T^{2} )^{3} \))(\( ( 1 + 4 T^{2} )^{3} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))(\( ( 1 + 2 T + 4 T^{2} )^{2} \))(\( ( 1 + 2 T + 4 T^{2} )^{2} \))(\( ( 1 - 2 T + 4 T^{2} )^{2} \))(\( ( 1 - 2 T + 4 T^{2} )^{3} \))(\( ( 1 - 4 T^{2} + 16 T^{4} )^{5} \))
$3$ (\( 1 + 3 T \))(\( 1 + 3 T \))(\( 1 + 3 T \))(\( 1 - 3 T \))(\( 1 - 3 T \))(\( 1 - 3 T \))(\( 1 + 3 T \))(\( 1 + 3 T \))(\( 1 + 3 T \))(\( 1 - 3 T \))(\( ( 1 - 3 T )^{2} \))(\( 1 + 4 T - 7 T^{2} - 42 T^{3} - 462 T^{4} + 3906 T^{5} + 13167 T^{6} - 147528 T^{7} - 689958 T^{8} - 3983256 T^{9} + 9598743 T^{10} + 76881798 T^{11} - 245525742 T^{12} - 602654094 T^{13} - 2711943423 T^{14} + 41841412812 T^{15} + 282429536481 T^{16} \))(\( 1 - 4 T - 7 T^{2} + 42 T^{3} - 462 T^{4} - 3906 T^{5} + 13167 T^{6} + 147528 T^{7} - 689958 T^{8} + 3983256 T^{9} + 9598743 T^{10} - 76881798 T^{11} - 245525742 T^{12} + 602654094 T^{13} - 2711943423 T^{14} - 41841412812 T^{15} + 282429536481 T^{16} \))(\( ( 1 + 9 T^{2} )^{2} \))(\( ( 1 + 9 T^{2} )^{2} \))(\( ( 1 + 9 T^{2} )^{3} \))(\( ( 1 + 9 T^{2} )^{3} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 - 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{3} \))(\( ( 1 - 9 T^{2} + 81 T^{4} )^{5} \))
$5$ (\( 1 + 5 T \))(\( 1 - 5 T \))(\( 1 - 5 T \))(\( 1 + 5 T \))(\( 1 + 5 T \))(\( 1 - 5 T \))(\( 1 + 5 T \))(\( 1 + 5 T \))(\( 1 - 5 T \))(\( 1 + 5 T \))(\( ( 1 - 5 T )^{2} \))(\( ( 1 - 5 T )^{16} \))(\( ( 1 + 5 T )^{16} \))(\( 1 + 4 T - 130 T^{2} + 500 T^{3} + 15625 T^{4} \))(\( 1 - 16 T + 230 T^{2} - 2000 T^{3} + 15625 T^{4} \))(\( 1 + 2 T + 11 T^{2} + 1260 T^{3} + 1375 T^{4} + 31250 T^{5} + 1953125 T^{6} \))(\( 1 - 14 T + 203 T^{2} - 1140 T^{3} + 25375 T^{4} - 218750 T^{5} + 1953125 T^{6} \))(\( 1 + 5 T + 25 T^{2} \))(\( 1 - 5 T + 25 T^{2} \))(\( 1 - 5 T + 25 T^{2} \))(\( 1 - 5 T + 25 T^{2} \))(\( 1 + 5 T + 25 T^{2} \))(\( 1 + 5 T + 25 T^{2} \))(\( 1 - 5 T + 25 T^{2} \))(\( ( 1 + 5 T + 25 T^{2} )^{2} \))(\( ( 1 - 5 T + 25 T^{2} )^{2} \))(\( ( 1 - 5 T + 25 T^{2} )^{2} \))(\( ( 1 + 5 T + 25 T^{2} )^{3} \))(\( 1 - 10 T + 71 T^{2} + 2110 T^{3} - 28909 T^{4} + 112700 T^{5} + 3287750 T^{6} - 50202500 T^{7} + 320078125 T^{8} + 5414531250 T^{9} - 70473046875 T^{10} + 676816406250 T^{11} + 5001220703125 T^{12} - 98051757812500 T^{13} + 802673339843750 T^{14} + 3439331054687500 T^{15} - 110279083251953125 T^{16} + 1006126403808593750 T^{17} + 4231929779052734375 T^{18} - 74505805969238281250 T^{19} + \)\(93\!\cdots\!25\)\( T^{20} \))
$7$ (\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 + 7 T \))(\( ( 1 - 7 T )^{2} \))(\( 1 + 10 T + 564 T^{2} - 2678 T^{3} + 109108 T^{4} - 2382030 T^{5} + 73938060 T^{6} + 141172626 T^{7} + 41375314134 T^{8} + 48422210718 T^{9} + 8698738820940 T^{10} - 96123502482210 T^{11} + 1510195163926708 T^{12} - 12713969723627354 T^{13} + 918425269221493236 T^{14} + 5585458640832840070 T^{15} + \)\(19\!\cdots\!01\)\( T^{16} \))(\( 1 + 10 T + 564 T^{2} - 2678 T^{3} + 109108 T^{4} - 2382030 T^{5} + 73938060 T^{6} + 141172626 T^{7} + 41375314134 T^{8} + 48422210718 T^{9} + 8698738820940 T^{10} - 96123502482210 T^{11} + 1510195163926708 T^{12} - 12713969723627354 T^{13} + 918425269221493236 T^{14} + 5585458640832840070 T^{15} + \)\(19\!\cdots\!01\)\( T^{16} \))(\( ( 1 + 49 T^{2} )^{2} \))(\( ( 1 + 49 T^{2} )^{2} \))(\( ( 1 + 49 T^{2} )^{3} \))(\( ( 1 + 49 T^{2} )^{3} \))(\( 1 - 35 T + 343 T^{2} \))(\( 1 + 20 T + 343 T^{2} \))(\( 1 + 7 T + 343 T^{2} \))(\( 1 + 28 T + 343 T^{2} \))(\( 1 - 7 T + 343 T^{2} \))(\( 1 - 20 T + 343 T^{2} \))(\( 1 + 35 T + 343 T^{2} \))(\( 1 + 6 T - 455 T^{2} + 2058 T^{3} + 117649 T^{4} \))(\( 1 - 24 T + 535 T^{2} - 8232 T^{3} + 117649 T^{4} \))(\( 1 + 20 T + 651 T^{2} + 6860 T^{3} + 117649 T^{4} \))(\( 1 + 22 T + 44 T^{2} - 3248 T^{3} + 15092 T^{4} + 2588278 T^{5} + 40353607 T^{6} \))(\( 1 + 598 T^{2} + 210219 T^{4} + 56736708 T^{6} + 14005678869 T^{8} + 1905392144334 T^{10} + 1647754113258981 T^{12} + 785309070267274308 T^{14} + \)\(34\!\cdots\!31\)\( T^{16} + \)\(11\!\cdots\!98\)\( T^{18} + \)\(22\!\cdots\!49\)\( T^{20} \))
$11$ (\( 1 - 12 T + 1331 T^{2} \))(\( 1 + 44 T + 1331 T^{2} \))(\( 1 - 12 T + 1331 T^{2} \))(\( 1 - 28 T + 1331 T^{2} \))(\( 1 + 1331 T^{2} \))(\( 1 - 28 T + 1331 T^{2} \))(\( 1 + 4 T + 1331 T^{2} \))(\( 1 - 24 T + 1331 T^{2} \))(\( 1 - 16 T + 1331 T^{2} \))(\( 1 - 56 T + 1331 T^{2} \))(\( 1 - 32 T + 1222 T^{2} - 42592 T^{3} + 1771561 T^{4} \))(\( 1 - 10034 T^{2} + 51687381 T^{4} - 179409136098 T^{6} + 469883068836582 T^{8} - 991634344369444734 T^{10} + \)\(17\!\cdots\!27\)\( T^{12} - \)\(27\!\cdots\!98\)\( T^{14} + \)\(38\!\cdots\!66\)\( T^{16} - \)\(48\!\cdots\!78\)\( T^{18} + \)\(55\!\cdots\!67\)\( T^{20} - \)\(55\!\cdots\!54\)\( T^{22} + \)\(46\!\cdots\!62\)\( T^{24} - \)\(31\!\cdots\!98\)\( T^{26} + \)\(15\!\cdots\!41\)\( T^{28} - \)\(54\!\cdots\!14\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))(\( 1 - 10034 T^{2} + 51687381 T^{4} - 179409136098 T^{6} + 469883068836582 T^{8} - 991634344369444734 T^{10} + \)\(17\!\cdots\!27\)\( T^{12} - \)\(27\!\cdots\!98\)\( T^{14} + \)\(38\!\cdots\!66\)\( T^{16} - \)\(48\!\cdots\!78\)\( T^{18} + \)\(55\!\cdots\!67\)\( T^{20} - \)\(55\!\cdots\!54\)\( T^{22} + \)\(46\!\cdots\!62\)\( T^{24} - \)\(31\!\cdots\!98\)\( T^{26} + \)\(15\!\cdots\!41\)\( T^{28} - \)\(54\!\cdots\!14\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 12 T + 2314 T^{2} - 15972 T^{3} + 1771561 T^{4} )^{2} \))(\( ( 1 + 12 T + 1354 T^{2} + 15972 T^{3} + 1771561 T^{4} )^{2} \))(\( ( 1 - 38 T + 3765 T^{2} - 96236 T^{3} + 5011215 T^{4} - 67319318 T^{5} + 2357947691 T^{6} )^{2} \))(\( ( 1 + 38 T + 1029 T^{2} - 244 T^{3} + 1369599 T^{4} + 67319318 T^{5} + 2357947691 T^{6} )^{2} \))(\( 1 - 4 T - 1315 T^{2} - 5324 T^{3} + 1771561 T^{4} \))(\( 1 - 19 T - 970 T^{2} - 25289 T^{3} + 1771561 T^{4} \))(\( 1 - 6 T - 1295 T^{2} - 7986 T^{3} + 1771561 T^{4} \))(\( 1 - 15 T - 1106 T^{2} - 19965 T^{3} + 1771561 T^{4} \))(\( 1 - 32 T - 307 T^{2} - 42592 T^{3} + 1771561 T^{4} \))(\( 1 + 33 T - 242 T^{2} + 43923 T^{3} + 1771561 T^{4} \))(\( 1 - 2 T - 1327 T^{2} - 2662 T^{3} + 1771561 T^{4} \))(\( 1 - 20 T - 1212 T^{2} + 21000 T^{3} + 294583 T^{4} + 27951000 T^{5} - 2147131932 T^{6} - 47158953820 T^{7} + 3138428376721 T^{8} \))(\( 1 + 50 T - 492 T^{2} + 16500 T^{3} + 3853003 T^{4} + 21961500 T^{5} - 871608012 T^{6} + 117897384550 T^{7} + 3138428376721 T^{8} \))(\( 1 - 18 T - 1204 T^{2} + 20412 T^{3} + 131979 T^{4} + 27168372 T^{5} - 2132959444 T^{6} - 42443058438 T^{7} + 3138428376721 T^{8} \))(\( 1 + 61 T + 2794 T^{2} + 107515 T^{3} + 1180016 T^{4} - 66086561 T^{5} - 2370415742 T^{6} - 87961212691 T^{7} + 2090470324976 T^{8} + 253514745997865 T^{9} + 8768768884558474 T^{10} + 254812138334354711 T^{11} + 5559917313492231481 T^{12} \))(\( ( 1 - 79 T - 72 T^{2} + 152649 T^{3} - 2086463 T^{4} - 108093636 T^{5} - 1570678364 T^{6} + 183175284504 T^{7} + 3091174127605 T^{8} - 211331548126503 T^{9} + 2713169633759986 T^{10} - 281282290556375493 T^{11} + 5476203528674041405 T^{12} + \)\(43\!\cdots\!64\)\( T^{13} - \)\(49\!\cdots\!44\)\( T^{14} - \)\(45\!\cdots\!36\)\( T^{15} - \)\(11\!\cdots\!03\)\( T^{16} + \)\(11\!\cdots\!39\)\( T^{17} - \)\(70\!\cdots\!52\)\( T^{18} - \)\(10\!\cdots\!09\)\( T^{19} + \)\(17\!\cdots\!01\)\( T^{20} )^{2} \))
$13$ (\( 1 - 2 T + 2197 T^{2} \))(\( 1 - 54 T + 2197 T^{2} \))(\( 1 + 58 T + 2197 T^{2} \))(\( 1 + 86 T + 2197 T^{2} \))(\( 1 - 26 T + 2197 T^{2} \))(\( 1 - 54 T + 2197 T^{2} \))(\( 1 + 42 T + 2197 T^{2} \))(\( 1 - 14 T + 2197 T^{2} \))(\( 1 - 58 T + 2197 T^{2} \))(\( 1 - 54 T + 2197 T^{2} \))(\( 1 + 12 T - 2354 T^{2} + 26364 T^{3} + 4826809 T^{4} \))(\( 1 - 11950 T^{2} + 70124061 T^{4} - 289417975130 T^{6} + 1023857768500718 T^{8} - 3315080851850053710 T^{10} + \)\(95\!\cdots\!83\)\( T^{12} - \)\(23\!\cdots\!70\)\( T^{14} + \)\(54\!\cdots\!94\)\( T^{16} - \)\(11\!\cdots\!30\)\( T^{18} + \)\(22\!\cdots\!23\)\( T^{20} - \)\(37\!\cdots\!90\)\( T^{22} + \)\(55\!\cdots\!98\)\( T^{24} - \)\(75\!\cdots\!70\)\( T^{26} + \)\(88\!\cdots\!01\)\( T^{28} - \)\(72\!\cdots\!50\)\( T^{30} + \)\(29\!\cdots\!21\)\( T^{32} \))(\( 1 - 11950 T^{2} + 70124061 T^{4} - 289417975130 T^{6} + 1023857768500718 T^{8} - 3315080851850053710 T^{10} + \)\(95\!\cdots\!83\)\( T^{12} - \)\(23\!\cdots\!70\)\( T^{14} + \)\(54\!\cdots\!94\)\( T^{16} - \)\(11\!\cdots\!30\)\( T^{18} + \)\(22\!\cdots\!23\)\( T^{20} - \)\(37\!\cdots\!90\)\( T^{22} + \)\(55\!\cdots\!98\)\( T^{24} - \)\(75\!\cdots\!70\)\( T^{26} + \)\(88\!\cdots\!01\)\( T^{28} - \)\(72\!\cdots\!50\)\( T^{30} + \)\(29\!\cdots\!21\)\( T^{32} \))(\( 1 - 716 T^{2} - 5578218 T^{4} - 3455995244 T^{6} + 23298085122481 T^{8} \))(\( 1 - 428 T^{2} + 8323158 T^{4} - 2065874252 T^{6} + 23298085122481 T^{8} \))(\( 1 - 12066 T^{2} + 62845911 T^{4} - 180859775548 T^{6} + 303345208827999 T^{8} - 281114695087855746 T^{10} + \)\(11\!\cdots\!29\)\( T^{12} \))(\( 1 - 1858 T^{2} + 4549847 T^{4} - 23193640444 T^{6} + 21961242448223 T^{8} - 43287842157569698 T^{10} + \)\(11\!\cdots\!29\)\( T^{12} \))(\( ( 1 + 77 T + 2197 T^{2} )^{2} \))(\( ( 1 - 33 T + 2197 T^{2} )^{2} \))(\( ( 1 + 19 T + 2197 T^{2} )^{2} \))(\( ( 1 - 77 T + 2197 T^{2} )^{2} \))(\( ( 1 - 15 T + 2197 T^{2} )^{2} \))(\( ( 1 + 37 T + 2197 T^{2} )^{2} \))(\( ( 1 + 47 T + 2197 T^{2} )^{2} \))(\( ( 1 - 42 T + 4789 T^{2} - 92274 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 + 100 T + 6599 T^{2} + 219700 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 - 64 T + 4203 T^{2} - 140608 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 - 37 T + 112 T^{2} + 29125 T^{3} + 246064 T^{4} - 178591933 T^{5} + 10604499373 T^{6} )^{2} \))(\( ( 1 - 13973 T^{2} + 91334055 T^{4} - 376337122338 T^{6} + 1129523189228145 T^{8} - 2718491774422565883 T^{10} + \)\(54\!\cdots\!05\)\( T^{12} - \)\(87\!\cdots\!78\)\( T^{14} + \)\(10\!\cdots\!95\)\( T^{16} - \)\(75\!\cdots\!53\)\( T^{18} + \)\(26\!\cdots\!49\)\( T^{20} )^{2} \))
$17$ (\( 1 + 18 T + 4913 T^{2} \))(\( 1 - 98 T + 4913 T^{2} \))(\( 1 - 42 T + 4913 T^{2} \))(\( 1 + 66 T + 4913 T^{2} \))(\( 1 - 18 T + 4913 T^{2} \))(\( 1 + 46 T + 4913 T^{2} \))(\( 1 + 86 T + 4913 T^{2} \))(\( 1 - 54 T + 4913 T^{2} \))(\( 1 - 34 T + 4913 T^{2} \))(\( 1 - 94 T + 4913 T^{2} \))(\( 1 - 4 T + 8134 T^{2} - 19652 T^{3} + 24137569 T^{4} \))(\( ( 1 + 72 T + 19633 T^{2} + 1185258 T^{3} + 182285950 T^{4} + 9543478194 T^{5} + 1169867027615 T^{6} + 53849652782460 T^{7} + 6162611136840098 T^{8} + 264563344120225980 T^{9} + 28237746099881967935 T^{10} + \)\(11\!\cdots\!18\)\( T^{11} + \)\(10\!\cdots\!50\)\( T^{12} + \)\(33\!\cdots\!94\)\( T^{13} + \)\(27\!\cdots\!97\)\( T^{14} + \)\(49\!\cdots\!24\)\( T^{15} + \)\(33\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 72 T + 19633 T^{2} - 1185258 T^{3} + 182285950 T^{4} - 9543478194 T^{5} + 1169867027615 T^{6} - 53849652782460 T^{7} + 6162611136840098 T^{8} - 264563344120225980 T^{9} + 28237746099881967935 T^{10} - \)\(11\!\cdots\!18\)\( T^{11} + \)\(10\!\cdots\!50\)\( T^{12} - \)\(33\!\cdots\!94\)\( T^{13} + \)\(27\!\cdots\!97\)\( T^{14} - \)\(49\!\cdots\!24\)\( T^{15} + \)\(33\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 9540 T^{2} + 48909638 T^{4} - 230272408260 T^{6} + 582622237229761 T^{8} \))(\( 1 - 3732 T^{2} + 20295398 T^{4} - 90081407508 T^{6} + 582622237229761 T^{8} \))(\( 1 - 15654 T^{2} + 139325871 T^{4} - 817403685972 T^{6} + 3362987824747599 T^{8} - 9120368501594678694 T^{10} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 - 14982 T^{2} + 129721647 T^{4} - 756260384916 T^{6} + 3131165205256143 T^{8} - 8728846358176279302 T^{10} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 - 26 T - 4237 T^{2} - 127738 T^{3} + 24137569 T^{4} \))(\( 1 + 64 T - 817 T^{2} + 314432 T^{3} + 24137569 T^{4} \))(\( 1 + 12 T - 4769 T^{2} + 58956 T^{3} + 24137569 T^{4} \))(\( 1 - 96 T + 4303 T^{2} - 471648 T^{3} + 24137569 T^{4} \))(\( 1 - 70 T - 13 T^{2} - 343910 T^{3} + 24137569 T^{4} \))(\( 1 + 60 T - 1313 T^{2} + 294780 T^{3} + 24137569 T^{4} \))(\( 1 - 4913 T^{2} + 24137569 T^{4} \))(\( 1 + 76 T + 72 T^{2} - 313272 T^{3} - 19979441 T^{4} - 1539105336 T^{5} + 1737904968 T^{6} + 9012678613772 T^{7} + 582622237229761 T^{8} \))(\( 1 + 34 T - 1584 T^{2} - 240924 T^{3} - 22309397 T^{4} - 1183659612 T^{5} - 38233909296 T^{6} + 4031987800898 T^{7} + 582622237229761 T^{8} \))(\( 1 + 102 T - 808 T^{2} + 141372 T^{3} + 50456523 T^{4} + 694560636 T^{5} - 19503155752 T^{6} + 12095963402694 T^{7} + 582622237229761 T^{8} \))(\( 1 - 148 T + 6799 T^{2} + 12716 T^{3} - 12420784 T^{4} + 1414102388 T^{5} - 148824913823 T^{6} + 6947485032244 T^{7} - 299807530834096 T^{8} + 1507963437535852 T^{9} + 3961248590925145039 T^{10} - \)\(42\!\cdots\!64\)\( T^{11} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 + 32658 T^{2} + 566087827 T^{4} + 6665894788410 T^{6} + 58610887815796791 T^{8} + \)\(39\!\cdots\!60\)\( T^{10} + \)\(20\!\cdots\!54\)\( T^{12} + \)\(79\!\cdots\!16\)\( T^{14} + \)\(16\!\cdots\!05\)\( T^{16} - \)\(24\!\cdots\!10\)\( T^{18} - \)\(33\!\cdots\!35\)\( T^{20} - \)\(59\!\cdots\!90\)\( T^{22} + \)\(97\!\cdots\!05\)\( T^{24} + \)\(11\!\cdots\!44\)\( T^{26} + \)\(70\!\cdots\!34\)\( T^{28} + \)\(32\!\cdots\!40\)\( T^{30} + \)\(11\!\cdots\!71\)\( T^{32} + \)\(31\!\cdots\!90\)\( T^{34} + \)\(65\!\cdots\!07\)\( T^{36} + \)\(90\!\cdots\!82\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))
$19$ (\( 1 - 56 T + 6859 T^{2} \))(\( 1 + 60 T + 6859 T^{2} \))(\( 1 + 4 T + 6859 T^{2} \))(\( 1 + 48 T + 6859 T^{2} \))(\( 1 - 92 T + 6859 T^{2} \))(\( 1 - 12 T + 6859 T^{2} \))(\( 1 + 96 T + 6859 T^{2} \))(\( 1 - 44 T + 6859 T^{2} \))(\( 1 - 64 T + 6859 T^{2} \))(\( 1 - 36 T + 6859 T^{2} \))(\( 1 - 64 T - 522 T^{2} - 438976 T^{3} + 47045881 T^{4} \))(\( 1 - 54976 T^{2} + 1457658264 T^{4} - 24777858354368 T^{6} + 304232180604401948 T^{8} - \)\(29\!\cdots\!00\)\( T^{10} + \)\(22\!\cdots\!00\)\( T^{12} - \)\(16\!\cdots\!32\)\( T^{14} + \)\(10\!\cdots\!26\)\( T^{16} - \)\(75\!\cdots\!92\)\( T^{18} + \)\(50\!\cdots\!00\)\( T^{20} - \)\(30\!\cdots\!00\)\( T^{22} + \)\(14\!\cdots\!08\)\( T^{24} - \)\(57\!\cdots\!68\)\( T^{26} + \)\(15\!\cdots\!84\)\( T^{28} - \)\(28\!\cdots\!36\)\( T^{30} + \)\(23\!\cdots\!41\)\( T^{32} \))(\( 1 - 54976 T^{2} + 1457658264 T^{4} - 24777858354368 T^{6} + 304232180604401948 T^{8} - \)\(29\!\cdots\!00\)\( T^{10} + \)\(22\!\cdots\!00\)\( T^{12} - \)\(16\!\cdots\!32\)\( T^{14} + \)\(10\!\cdots\!26\)\( T^{16} - \)\(75\!\cdots\!92\)\( T^{18} + \)\(50\!\cdots\!00\)\( T^{20} - \)\(30\!\cdots\!00\)\( T^{22} + \)\(14\!\cdots\!08\)\( T^{24} - \)\(57\!\cdots\!68\)\( T^{26} + \)\(15\!\cdots\!84\)\( T^{28} - \)\(28\!\cdots\!36\)\( T^{30} + \)\(23\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 4 T + 13626 T^{2} - 27436 T^{3} + 47045881 T^{4} )^{2} \))(\( ( 1 - 28 T + 5514 T^{2} - 192052 T^{3} + 47045881 T^{4} )^{2} \))(\( ( 1 + 54 T + 12597 T^{2} + 638572 T^{3} + 86402823 T^{4} + 2540477574 T^{5} + 322687697779 T^{6} )^{2} \))(\( ( 1 - 70 T + 6469 T^{2} - 893708 T^{3} + 44370871 T^{4} - 3293211670 T^{5} + 322687697779 T^{6} )^{2} \))(\( 1 - 121 T + 7782 T^{2} - 829939 T^{3} + 47045881 T^{4} \))(\( 1 - 141 T + 13022 T^{2} - 967119 T^{3} + 47045881 T^{4} \))(\( 1 + 119 T + 7302 T^{2} + 816221 T^{3} + 47045881 T^{4} \))(\( 1 - 37 T - 5490 T^{2} - 253783 T^{3} + 47045881 T^{4} \))(\( 1 + 15 T - 6634 T^{2} + 102885 T^{3} + 47045881 T^{4} \))(\( 1 + 119 T + 7302 T^{2} + 816221 T^{3} + 47045881 T^{4} \))(\( 1 + 39 T - 5338 T^{2} + 267501 T^{3} + 47045881 T^{4} \))(\( 1 + 90 T - 7459 T^{2} + 165690 T^{3} + 139478700 T^{4} + 1136467710 T^{5} - 350915226379 T^{6} + 29041892800110 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 46 T - 7411 T^{2} + 192786 T^{3} + 29204204 T^{4} + 1322319174 T^{5} - 348657024091 T^{6} - 14843634097834 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 62 T - 8675 T^{2} + 74338 T^{3} + 83313484 T^{4} + 509884342 T^{5} - 408123017675 T^{6} - 20006637262298 T^{7} + 2213314919066161 T^{8} \))(\( 1 + T - 3351 T^{2} - 1751970 T^{3} - 12633125 T^{4} + 2942982817 T^{5} + 1338550115062 T^{6} + 20185919141803 T^{7} - 594336495408125 T^{8} - 565339165877874630 T^{9} - 7416818293790705511 T^{10} + 15181127029874798299 T^{11} + \)\(10\!\cdots\!41\)\( T^{12} \))(\( ( 1 + 31 T - 18428 T^{2} + 358335 T^{3} + 204799062 T^{4} - 8954945175 T^{5} - 905578119114 T^{6} + 97711362873411 T^{7} - 34880026939047 T^{8} - 267034200873349118 T^{9} + 33339863594994669964 T^{10} - \)\(18\!\cdots\!62\)\( T^{11} - \)\(16\!\cdots\!07\)\( T^{12} + \)\(31\!\cdots\!69\)\( T^{13} - \)\(20\!\cdots\!54\)\( T^{14} - \)\(13\!\cdots\!25\)\( T^{15} + \)\(21\!\cdots\!42\)\( T^{16} + \)\(25\!\cdots\!65\)\( T^{17} - \)\(90\!\cdots\!88\)\( T^{18} + \)\(10\!\cdots\!09\)\( T^{19} + \)\(23\!\cdots\!01\)\( T^{20} )^{2} \))
$23$ (\( 1 + 156 T + 12167 T^{2} \))(\( 1 + 144 T + 12167 T^{2} \))(\( 1 - 24 T + 12167 T^{2} \))(\( 1 - 140 T + 12167 T^{2} \))(\( 1 + 12167 T^{2} \))(\( 1 + 12167 T^{2} \))(\( 1 + 96 T + 12167 T^{2} \))(\( 1 - 156 T + 12167 T^{2} \))(\( 1 + 16 T + 12167 T^{2} \))(\( 1 + 84 T + 12167 T^{2} \))(\( 1 - 32 T + 22894 T^{2} - 389344 T^{3} + 148035889 T^{4} \))(\( 1 - 59504 T^{2} + 1980011352 T^{4} - 46969162810064 T^{6} + 876298741037185372 T^{8} - \)\(13\!\cdots\!04\)\( T^{10} + \)\(18\!\cdots\!08\)\( T^{12} - \)\(22\!\cdots\!80\)\( T^{14} + \)\(27\!\cdots\!94\)\( T^{16} - \)\(33\!\cdots\!20\)\( T^{18} + \)\(40\!\cdots\!68\)\( T^{20} - \)\(44\!\cdots\!76\)\( T^{22} + \)\(42\!\cdots\!52\)\( T^{24} - \)\(33\!\cdots\!36\)\( T^{26} + \)\(20\!\cdots\!72\)\( T^{28} - \)\(92\!\cdots\!16\)\( T^{30} + \)\(23\!\cdots\!81\)\( T^{32} \))(\( 1 - 59504 T^{2} + 1980011352 T^{4} - 46969162810064 T^{6} + 876298741037185372 T^{8} - \)\(13\!\cdots\!04\)\( T^{10} + \)\(18\!\cdots\!08\)\( T^{12} - \)\(22\!\cdots\!80\)\( T^{14} + \)\(27\!\cdots\!94\)\( T^{16} - \)\(33\!\cdots\!20\)\( T^{18} + \)\(40\!\cdots\!68\)\( T^{20} - \)\(44\!\cdots\!76\)\( T^{22} + \)\(42\!\cdots\!52\)\( T^{24} - \)\(33\!\cdots\!36\)\( T^{26} + \)\(20\!\cdots\!72\)\( T^{28} - \)\(92\!\cdots\!16\)\( T^{30} + \)\(23\!\cdots\!81\)\( T^{32} \))(\( 1 - 14172 T^{2} + 279829670 T^{4} - 2097964618908 T^{6} + 21914624432020321 T^{8} \))(\( 1 - 10236 T^{2} - 41151898 T^{4} - 1515295359804 T^{6} + 21914624432020321 T^{8} \))(\( 1 - 39802 T^{2} + 775805919 T^{4} - 10456103945516 T^{6} + 114847118910626991 T^{8} - \)\(87\!\cdots\!42\)\( T^{10} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 - 6810 T^{2} + 57452895 T^{4} - 2061747101676 T^{6} + 8505090386948655 T^{8} - \)\(14\!\cdots\!10\)\( T^{10} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 - 166 T + 15389 T^{2} - 2019722 T^{3} + 148035889 T^{4} \))(\( 1 - 51 T - 9566 T^{2} - 620517 T^{3} + 148035889 T^{4} \))(\( 1 - 12 T - 12023 T^{2} - 146004 T^{3} + 148035889 T^{4} \))(\( 1 - 99 T - 2366 T^{2} - 1204533 T^{3} + 148035889 T^{4} \))(\( 1 - 42 T - 10403 T^{2} - 511014 T^{3} + 148035889 T^{4} \))(\( 1 + 75 T - 6542 T^{2} + 912525 T^{3} + 148035889 T^{4} \))(\( 1 + 80 T - 5767 T^{2} + 973360 T^{3} + 148035889 T^{4} \))(\( 1 + 44 T - 17316 T^{2} - 223608 T^{3} + 199048303 T^{4} - 2720638536 T^{5} - 2563389453924 T^{6} + 79250717104372 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 126 T + 11468 T^{2} - 2510676 T^{3} - 321768717 T^{4} - 30547394892 T^{5} + 1697675575052 T^{6} + 226945235344338 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 42 T - 16396 T^{2} - 259308 T^{3} + 160287123 T^{4} - 3155000436 T^{5} - 2427196436044 T^{6} + 75648411781446 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 3 T - 7890 T^{2} + 2253801 T^{3} - 30367776 T^{4} - 8940330879 T^{5} + 4085163719062 T^{6} - 108777005804793 T^{7} - 4495520717112864 T^{8} + 4059439669557970863 T^{9} - \)\(17\!\cdots\!90\)\( T^{10} + \)\(79\!\cdots\!21\)\( T^{11} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 + 84817 T^{2} + 3785763380 T^{4} + 115580111077173 T^{6} + 2679863593077523067 T^{8} + \)\(49\!\cdots\!70\)\( T^{10} + \)\(76\!\cdots\!24\)\( T^{12} + \)\(99\!\cdots\!54\)\( T^{14} + \)\(11\!\cdots\!21\)\( T^{16} + \)\(12\!\cdots\!87\)\( T^{18} + \)\(14\!\cdots\!52\)\( T^{20} + \)\(18\!\cdots\!43\)\( T^{22} + \)\(24\!\cdots\!41\)\( T^{24} + \)\(32\!\cdots\!26\)\( T^{26} + \)\(36\!\cdots\!84\)\( T^{28} + \)\(35\!\cdots\!30\)\( T^{30} + \)\(28\!\cdots\!87\)\( T^{32} + \)\(18\!\cdots\!17\)\( T^{34} + \)\(87\!\cdots\!80\)\( T^{36} + \)\(28\!\cdots\!53\)\( T^{38} + \)\(50\!\cdots\!01\)\( T^{40} \))
$29$ (\( 1 + 186 T + 24389 T^{2} \))(\( 1 + 210 T + 24389 T^{2} \))(\( 1 - 294 T + 24389 T^{2} \))(\( 1 + 34 T + 24389 T^{2} \))(\( 1 + 6 T + 24389 T^{2} \))(\( 1 - 6 T + 24389 T^{2} \))(\( 1 + 78 T + 24389 T^{2} \))(\( 1 - 174 T + 24389 T^{2} \))(\( 1 - 62 T + 24389 T^{2} \))(\( 1 + 258 T + 24389 T^{2} \))(\( 1 + 84 T + 35278 T^{2} + 2048676 T^{3} + 594823321 T^{4} \))(\( 1 - 165662 T^{2} + 14279529309 T^{4} - 833335828031834 T^{6} + 36714534788487929998 T^{8} - \)\(13\!\cdots\!46\)\( T^{10} + \)\(39\!\cdots\!47\)\( T^{12} - \)\(10\!\cdots\!82\)\( T^{14} + \)\(26\!\cdots\!58\)\( T^{16} - \)\(62\!\cdots\!22\)\( T^{18} + \)\(13\!\cdots\!27\)\( T^{20} - \)\(27\!\cdots\!06\)\( T^{22} + \)\(45\!\cdots\!38\)\( T^{24} - \)\(62\!\cdots\!34\)\( T^{26} + \)\(63\!\cdots\!89\)\( T^{28} - \)\(43\!\cdots\!42\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 165662 T^{2} + 14279529309 T^{4} - 833335828031834 T^{6} + 36714534788487929998 T^{8} - \)\(13\!\cdots\!46\)\( T^{10} + \)\(39\!\cdots\!47\)\( T^{12} - \)\(10\!\cdots\!82\)\( T^{14} + \)\(26\!\cdots\!58\)\( T^{16} - \)\(62\!\cdots\!22\)\( T^{18} + \)\(13\!\cdots\!27\)\( T^{20} - \)\(27\!\cdots\!06\)\( T^{22} + \)\(45\!\cdots\!38\)\( T^{24} - \)\(62\!\cdots\!34\)\( T^{26} + \)\(63\!\cdots\!89\)\( T^{28} - \)\(43\!\cdots\!42\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 20 T + 48782 T^{2} + 487780 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 224 T + 57206 T^{2} - 5463136 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 + 146 T + 65467 T^{2} + 7150988 T^{3} + 1596674663 T^{4} + 86844204866 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 - 182 T + 31387 T^{2} - 2082020 T^{3} + 765497543 T^{4} - 108257844422 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 - 6 T + 24389 T^{2} )^{2} \))(\( ( 1 - 216 T + 24389 T^{2} )^{2} \))(\( ( 1 + 252 T + 24389 T^{2} )^{2} \))(\( ( 1 - 240 T + 24389 T^{2} )^{2} \))(\( ( 1 - 90 T + 24389 T^{2} )^{2} \))(\( ( 1 + 144 T + 24389 T^{2} )^{2} \))(\( ( 1 - 56 T + 24389 T^{2} )^{2} \))(\( ( 1 + 160 T + 54028 T^{2} + 3902240 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 + 150 T + 51748 T^{2} + 3658350 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 222 T + 54484 T^{2} - 5414358 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 + 180 T + 63249 T^{2} + 7428312 T^{3} + 1542579861 T^{4} + 107068197780 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 - 246 T + 78695 T^{2} - 12569070 T^{3} + 3055996238 T^{4} - 411184153104 T^{5} + 74532692248582 T^{6} - 7476375959281470 T^{7} + 1141639852571010955 T^{8} - 87038436668545384086 T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{4} \))
$31$ (\( 1 + 52 T + 29791 T^{2} \))(\( 1 + 208 T + 29791 T^{2} \))(\( 1 - 128 T + 29791 T^{2} \))(\( 1 + 284 T + 29791 T^{2} \))(\( 1 + 4 T + 29791 T^{2} \))(\( 1 - 296 T + 29791 T^{2} \))(\( 1 - 80 T + 29791 T^{2} \))(\( 1 + 88 T + 29791 T^{2} \))(\( 1 - 60 T + 29791 T^{2} \))(\( 1 + 40 T + 29791 T^{2} \))(\( 1 + 72 T + 54094 T^{2} + 2144952 T^{3} + 887503681 T^{4} \))(\( 1 - 284716 T^{2} + 40589680656 T^{4} - 3861606805305572 T^{6} + \)\(27\!\cdots\!80\)\( T^{8} - \)\(15\!\cdots\!80\)\( T^{10} + \)\(71\!\cdots\!60\)\( T^{12} - \)\(27\!\cdots\!56\)\( T^{14} + \)\(89\!\cdots\!74\)\( T^{16} - \)\(24\!\cdots\!36\)\( T^{18} + \)\(56\!\cdots\!60\)\( T^{20} - \)\(10\!\cdots\!80\)\( T^{22} + \)\(17\!\cdots\!80\)\( T^{24} - \)\(21\!\cdots\!72\)\( T^{26} + \)\(19\!\cdots\!36\)\( T^{28} - \)\(12\!\cdots\!76\)\( T^{30} + \)\(38\!\cdots\!41\)\( T^{32} \))(\( 1 - 284716 T^{2} + 40589680656 T^{4} - 3861606805305572 T^{6} + \)\(27\!\cdots\!80\)\( T^{8} - \)\(15\!\cdots\!80\)\( T^{10} + \)\(71\!\cdots\!60\)\( T^{12} - \)\(27\!\cdots\!56\)\( T^{14} + \)\(89\!\cdots\!74\)\( T^{16} - \)\(24\!\cdots\!36\)\( T^{18} + \)\(56\!\cdots\!60\)\( T^{20} - \)\(10\!\cdots\!80\)\( T^{22} + \)\(17\!\cdots\!80\)\( T^{24} - \)\(21\!\cdots\!72\)\( T^{26} + \)\(19\!\cdots\!36\)\( T^{28} - \)\(12\!\cdots\!76\)\( T^{30} + \)\(38\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 292 T + 80514 T^{2} + 8698972 T^{3} + 887503681 T^{4} )^{2} \))(\( ( 1 - 8 T + 35322 T^{2} - 238328 T^{3} + 887503681 T^{4} )^{2} \))(\( ( 1 - 170 T - 12719 T^{2} + 7098716 T^{3} - 378911729 T^{4} - 150875625770 T^{5} + 26439622160671 T^{6} )^{2} \))(\( ( 1 - 6 T + 57393 T^{2} - 286492 T^{3} + 1709794863 T^{4} - 5325022086 T^{5} + 26439622160671 T^{6} )^{2} \))(\( 1 + 235 T + 25434 T^{2} + 7000885 T^{3} + 887503681 T^{4} \))(\( 1 + 290 T + 54309 T^{2} + 8639390 T^{3} + 887503681 T^{4} \))(\( 1 + 251 T + 33210 T^{2} + 7477541 T^{3} + 887503681 T^{4} \))(\( 1 - 166 T - 2235 T^{2} - 4945306 T^{3} + 887503681 T^{4} \))(\( 1 - 85 T - 22566 T^{2} - 2532235 T^{3} + 887503681 T^{4} \))(\( 1 - 46 T - 27675 T^{2} - 1370386 T^{3} + 887503681 T^{4} \))(\( ( 1 - 289 T + 29791 T^{2} )( 1 + 308 T + 29791 T^{2} ) \))(\( 1 + 62 T - 53755 T^{2} - 122946 T^{3} + 2315624516 T^{4} - 3662684286 T^{5} - 47707760372155 T^{6} + 1639256573961602 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 74 T - 12995 T^{2} + 3042214 T^{3} - 709461356 T^{4} + 90630597274 T^{5} - 11533110334595 T^{6} - 1956532039889654 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 50 T + 20053 T^{2} + 3856750 T^{3} - 653873372 T^{4} + 114896439250 T^{5} + 17797111315093 T^{6} - 1321981108033550 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 312 T - 11514 T^{2} + 3597692 T^{3} + 2747498958 T^{4} - 297705000852 T^{5} - 33824708390010 T^{6} - 8868929680381932 T^{7} + 2438415438768664398 T^{8} + 95121617130468771332 T^{9} - \)\(90\!\cdots\!54\)\( T^{10} - \)\(73\!\cdots\!12\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} \))(\( ( 1 - 266 T - 68857 T^{2} + 15325750 T^{3} + 4779968136 T^{4} - 633952659910 T^{5} - 219860652920179 T^{6} + 15883241830235502 T^{7} + 7848166237367881915 T^{8} - \)\(12\!\cdots\!00\)\( T^{9} - \)\(26\!\cdots\!60\)\( T^{10} - \)\(37\!\cdots\!00\)\( T^{11} + \)\(69\!\cdots\!15\)\( T^{12} + \)\(41\!\cdots\!42\)\( T^{13} - \)\(17\!\cdots\!19\)\( T^{14} - \)\(14\!\cdots\!10\)\( T^{15} + \)\(33\!\cdots\!76\)\( T^{16} + \)\(31\!\cdots\!50\)\( T^{17} - \)\(42\!\cdots\!97\)\( T^{18} - \)\(49\!\cdots\!26\)\( T^{19} + \)\(55\!\cdots\!01\)\( T^{20} )^{2} \))
$37$ (\( 1 + 178 T + 50653 T^{2} \))(\( 1 + 226 T + 50653 T^{2} \))(\( 1 + 58 T + 50653 T^{2} \))(\( 1 + 346 T + 50653 T^{2} \))(\( 1 - 410 T + 50653 T^{2} \))(\( 1 - 134 T + 50653 T^{2} \))(\( 1 - 50 T + 50653 T^{2} \))(\( 1 + 34 T + 50653 T^{2} \))(\( 1 - 150 T + 50653 T^{2} \))(\( 1 + 178 T + 50653 T^{2} \))(\( 1 - 60 T + 100510 T^{2} - 3039180 T^{3} + 2565726409 T^{4} \))(\( ( 1 - 350 T + 301140 T^{2} - 67833530 T^{3} + 33506294356 T^{4} - 4512328259190 T^{5} + 1931723348659980 T^{6} - 134484666443341890 T^{7} + 88868523477214550646 T^{8} - \)\(68\!\cdots\!70\)\( T^{9} + \)\(49\!\cdots\!20\)\( T^{10} - \)\(58\!\cdots\!30\)\( T^{11} + \)\(22\!\cdots\!36\)\( T^{12} - \)\(22\!\cdots\!90\)\( T^{13} + \)\(50\!\cdots\!60\)\( T^{14} - \)\(29\!\cdots\!50\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 350 T + 301140 T^{2} - 67833530 T^{3} + 33506294356 T^{4} - 4512328259190 T^{5} + 1931723348659980 T^{6} - 134484666443341890 T^{7} + 88868523477214550646 T^{8} - \)\(68\!\cdots\!70\)\( T^{9} + \)\(49\!\cdots\!20\)\( T^{10} - \)\(58\!\cdots\!30\)\( T^{11} + \)\(22\!\cdots\!36\)\( T^{12} - \)\(22\!\cdots\!90\)\( T^{13} + \)\(50\!\cdots\!60\)\( T^{14} - \)\(29\!\cdots\!50\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 122420 T^{2} + 7280062518 T^{4} - 314096226989780 T^{6} + 6582952005840035281 T^{8} \))(\( 1 - 155204 T^{2} + 10693572822 T^{4} - 398211001582436 T^{6} + 6582952005840035281 T^{8} \))(\( 1 - 89790 T^{2} + 9716587527 T^{4} - 473963917953220 T^{6} + 24930105223383900543 T^{8} - \)\(59\!\cdots\!90\)\( T^{10} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( 1 - 120318 T^{2} + 4479772935 T^{4} - 96237632387140 T^{6} + 11493871725652940415 T^{8} - \)\(79\!\cdots\!58\)\( T^{10} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( 1 - 419 T + 124908 T^{2} - 21223607 T^{3} + 2565726409 T^{4} \))(\( 1 - 109 T - 38772 T^{2} - 5521177 T^{3} + 2565726409 T^{4} \))(\( 1 + 359 T + 78228 T^{2} + 18184427 T^{3} + 2565726409 T^{4} \))(\( 1 + 335 T + 61572 T^{2} + 16968755 T^{3} + 2565726409 T^{4} \))(\( 1 + 113 T - 37884 T^{2} + 5723789 T^{3} + 2565726409 T^{4} \))(\( 1 - 199 T - 11052 T^{2} - 10079947 T^{3} + 2565726409 T^{4} \))(\( 1 + 131 T - 33492 T^{2} + 6635543 T^{3} + 2565726409 T^{4} \))(\( 1 - 358 T + 39023 T^{2} + 4355070 T^{3} - 1111499620 T^{4} + 220597360710 T^{5} + 100122341658407 T^{6} - 46526302846637566 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 176 T - 54179 T^{2} + 2842576 T^{3} + 3116620288 T^{4} + 143985002128 T^{5} - 139008491113211 T^{6} - 22873266203933552 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 572 T + 150697 T^{2} - 43003532 T^{3} + 12009083608 T^{4} - 2178257906396 T^{5} + 386647272657073 T^{6} - 74338115162784044 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 195 T - 105891 T^{2} - 8652334 T^{3} + 9842232393 T^{4} + 299310179967 T^{5} - 549738515611110 T^{6} + 15160958545868451 T^{7} + 25252475574235366737 T^{8} - \)\(11\!\cdots\!18\)\( T^{9} - \)\(69\!\cdots\!71\)\( T^{10} + \)\(65\!\cdots\!35\)\( T^{11} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( 1 + 242417 T^{2} + 35634665494 T^{4} + 4032882415267071 T^{6} + \)\(37\!\cdots\!86\)\( T^{8} + \)\(30\!\cdots\!47\)\( T^{10} + \)\(21\!\cdots\!40\)\( T^{12} + \)\(13\!\cdots\!27\)\( T^{14} + \)\(82\!\cdots\!09\)\( T^{16} + \)\(45\!\cdots\!66\)\( T^{18} + \)\(23\!\cdots\!32\)\( T^{20} + \)\(11\!\cdots\!94\)\( T^{22} + \)\(54\!\cdots\!29\)\( T^{24} + \)\(23\!\cdots\!83\)\( T^{26} + \)\(93\!\cdots\!40\)\( T^{28} + \)\(33\!\cdots\!03\)\( T^{30} + \)\(10\!\cdots\!26\)\( T^{32} + \)\(29\!\cdots\!99\)\( T^{34} + \)\(66\!\cdots\!74\)\( T^{36} + \)\(11\!\cdots\!13\)\( T^{38} + \)\(12\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 + 138 T + 68921 T^{2} \))(\( 1 + 502 T + 68921 T^{2} \))(\( 1 - 282 T + 68921 T^{2} \))(\( 1 + 274 T + 68921 T^{2} \))(\( 1 - 174 T + 68921 T^{2} \))(\( 1 - 146 T + 68921 T^{2} \))(\( 1 + 26 T + 68921 T^{2} \))(\( 1 + 138 T + 68921 T^{2} \))(\( 1 - 474 T + 68921 T^{2} \))(\( 1 + 146 T + 68921 T^{2} \))(\( 1 + 92 T + 31414 T^{2} + 6340732 T^{3} + 4750104241 T^{4} \))(\( ( 1 + 384 T + 281428 T^{2} + 105708592 T^{3} + 51353310484 T^{4} + 16077858061552 T^{5} + 5868595243880940 T^{6} + 1585105235409552352 T^{7} + \)\(48\!\cdots\!34\)\( T^{8} + \)\(10\!\cdots\!92\)\( T^{9} + \)\(27\!\cdots\!40\)\( T^{10} + \)\(52\!\cdots\!72\)\( T^{11} + \)\(11\!\cdots\!04\)\( T^{12} + \)\(16\!\cdots\!92\)\( T^{13} + \)\(30\!\cdots\!88\)\( T^{14} + \)\(28\!\cdots\!44\)\( T^{15} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 384 T + 281428 T^{2} - 105708592 T^{3} + 51353310484 T^{4} - 16077858061552 T^{5} + 5868595243880940 T^{6} - 1585105235409552352 T^{7} + \)\(48\!\cdots\!34\)\( T^{8} - \)\(10\!\cdots\!92\)\( T^{9} + \)\(27\!\cdots\!40\)\( T^{10} - \)\(52\!\cdots\!72\)\( T^{11} + \)\(11\!\cdots\!04\)\( T^{12} - \)\(16\!\cdots\!92\)\( T^{13} + \)\(30\!\cdots\!88\)\( T^{14} - \)\(28\!\cdots\!44\)\( T^{15} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 132 T + 136054 T^{2} + 9097572 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 144 T + 118750 T^{2} + 9924624 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 246 T + 124959 T^{2} - 14318868 T^{3} + 8612299239 T^{4} - 1168525643286 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 - 142 T + 65151 T^{2} - 33815908 T^{3} + 4490272071 T^{4} - 674514802222 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 + 128 T + 68921 T^{2} )^{2} \))(\( ( 1 - 457 T + 68921 T^{2} )^{2} \))(\( ( 1 - 54 T + 68921 T^{2} )^{2} \))(\( ( 1 - 21 T + 68921 T^{2} )^{2} \))(\( ( 1 - 164 T + 68921 T^{2} )^{2} \))(\( ( 1 + 135 T + 68921 T^{2} )^{2} \))(\( ( 1 + 310 T + 68921 T^{2} )^{2} \))(\( ( 1 - 36 T + 104632 T^{2} - 2481156 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 10 T + 52612 T^{2} - 689210 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 54 T + 137356 T^{2} - 3721734 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 53 T + 78633 T^{2} + 11653648 T^{3} + 5419464993 T^{4} - 251755524773 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 - 279 T + 206191 T^{2} - 41213196 T^{3} + 21551274604 T^{4} - 3465456471252 T^{5} + 1485335396982284 T^{6} - 195766977104764236 T^{7} + 67503208434625212551 T^{8} - \)\(62\!\cdots\!99\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{4} \))
$43$ (\( 1 + 412 T + 79507 T^{2} \))(\( 1 - 484 T + 79507 T^{2} \))(\( 1 - 428 T + 79507 T^{2} \))(\( 1 + 4 T + 79507 T^{2} \))(\( 1 - 248 T + 79507 T^{2} \))(\( 1 - 556 T + 79507 T^{2} \))(\( 1 + 32 T + 79507 T^{2} \))(\( 1 - 164 T + 79507 T^{2} \))(\( 1 + 292 T + 79507 T^{2} \))(\( 1 - 148 T + 79507 T^{2} \))(\( 1 + 184 T + 165782 T^{2} + 14629288 T^{3} + 6321363049 T^{4} \))(\( ( 1 - 176 T + 372924 T^{2} - 56978704 T^{3} + 68435561252 T^{4} - 10077032231568 T^{5} + 8462340518628068 T^{6} - 1198041702823287088 T^{7} + \)\(77\!\cdots\!22\)\( T^{8} - \)\(95\!\cdots\!16\)\( T^{9} + \)\(53\!\cdots\!32\)\( T^{10} - \)\(50\!\cdots\!24\)\( T^{11} + \)\(27\!\cdots\!52\)\( T^{12} - \)\(18\!\cdots\!28\)\( T^{13} + \)\(94\!\cdots\!76\)\( T^{14} - \)\(35\!\cdots\!68\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 176 T + 372924 T^{2} - 56978704 T^{3} + 68435561252 T^{4} - 10077032231568 T^{5} + 8462340518628068 T^{6} - 1198041702823287088 T^{7} + \)\(77\!\cdots\!22\)\( T^{8} - \)\(95\!\cdots\!16\)\( T^{9} + \)\(53\!\cdots\!32\)\( T^{10} - \)\(50\!\cdots\!24\)\( T^{11} + \)\(27\!\cdots\!52\)\( T^{12} - \)\(18\!\cdots\!28\)\( T^{13} + \)\(94\!\cdots\!76\)\( T^{14} - \)\(35\!\cdots\!68\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 82316 T^{2} + 14216284662 T^{4} - 520349320741484 T^{6} + 39959630797262576401 T^{8} \))(\( 1 - 149660 T^{2} + 18213997398 T^{4} - 946055193913340 T^{6} + 39959630797262576401 T^{8} \))(\( 1 - 366786 T^{2} + 62778101991 T^{4} - 6350466408051388 T^{6} + \)\(39\!\cdots\!59\)\( T^{8} - \)\(14\!\cdots\!86\)\( T^{10} + \)\(25\!\cdots\!49\)\( T^{12} \))(\( 1 - 439170 T^{2} + 82872950247 T^{4} - 8630827857145660 T^{6} + \)\(52\!\cdots\!03\)\( T^{8} - \)\(17\!\cdots\!70\)\( T^{10} + \)\(25\!\cdots\!49\)\( T^{12} \))(\( ( 1 + 291 T + 79507 T^{2} )^{2} \))(\( ( 1 - 184 T + 79507 T^{2} )^{2} \))(\( ( 1 + 37 T + 79507 T^{2} )^{2} \))(\( ( 1 + 40 T + 79507 T^{2} )^{2} \))(\( ( 1 - 169 T + 79507 T^{2} )^{2} \))(\( ( 1 - 260 T + 79507 T^{2} )^{2} \))(\( ( 1 + 265 T + 79507 T^{2} )^{2} \))(\( ( 1 + 134 T + 129969 T^{2} + 10653938 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 132 T + 148915 T^{2} - 10494924 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 + 248 T + 171015 T^{2} + 19717736 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 + 574 T + 271520 T^{2} + 86016712 T^{3} + 21587740640 T^{4} + 3628462390126 T^{5} + 502592611936843 T^{6} )^{2} \))(\( ( 1 - 370442 T^{2} + 71009084619 T^{4} - 9685108128083400 T^{6} + \)\(10\!\cdots\!29\)\( T^{8} - \)\(92\!\cdots\!66\)\( T^{10} + \)\(66\!\cdots\!21\)\( T^{12} - \)\(38\!\cdots\!00\)\( T^{14} + \)\(17\!\cdots\!31\)\( T^{16} - \)\(59\!\cdots\!42\)\( T^{18} + \)\(10\!\cdots\!49\)\( T^{20} )^{2} \))
$47$ (\( 1 + 456 T + 103823 T^{2} \))(\( 1 + 232 T + 103823 T^{2} \))(\( 1 - 384 T + 103823 T^{2} \))(\( 1 + 448 T + 103823 T^{2} \))(\( 1 - 420 T + 103823 T^{2} \))(\( 1 + 448 T + 103823 T^{2} \))(\( 1 + 20 T + 103823 T^{2} \))(\( 1 + 216 T + 103823 T^{2} \))(\( 1 - 240 T + 103823 T^{2} \))(\( 1 + 200 T + 103823 T^{2} \))(\( 1 + 208 T + 176062 T^{2} + 21595184 T^{3} + 10779215329 T^{4} \))(\( ( 1 - 858 T + 955969 T^{2} - 587185450 T^{3} + 373443109558 T^{4} - 175648411265938 T^{5} + 80317465979296719 T^{6} - 29785292967980964418 T^{7} + \)\(10\!\cdots\!02\)\( T^{8} - \)\(30\!\cdots\!14\)\( T^{9} + \)\(86\!\cdots\!51\)\( T^{10} - \)\(19\!\cdots\!46\)\( T^{11} + \)\(43\!\cdots\!78\)\( T^{12} - \)\(70\!\cdots\!50\)\( T^{13} + \)\(11\!\cdots\!41\)\( T^{14} - \)\(11\!\cdots\!26\)\( T^{15} + \)\(13\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 858 T + 955969 T^{2} + 587185450 T^{3} + 373443109558 T^{4} + 175648411265938 T^{5} + 80317465979296719 T^{6} + 29785292967980964418 T^{7} + \)\(10\!\cdots\!02\)\( T^{8} + \)\(30\!\cdots\!14\)\( T^{9} + \)\(86\!\cdots\!51\)\( T^{10} + \)\(19\!\cdots\!46\)\( T^{11} + \)\(43\!\cdots\!78\)\( T^{12} + \)\(70\!\cdots\!50\)\( T^{13} + \)\(11\!\cdots\!41\)\( T^{14} + \)\(11\!\cdots\!26\)\( T^{15} + \)\(13\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 198492 T^{2} + 22457318918 T^{4} - 2139588009083868 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 169524 T^{2} + 28738348838 T^{4} + 1827335699433396 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 229722 T^{2} + 35022837807 T^{4} - 4467393070748076 T^{6} + \)\(37\!\cdots\!03\)\( T^{8} - \)\(26\!\cdots\!02\)\( T^{10} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 - 195738 T^{2} + 29564447535 T^{4} - 2803156118922540 T^{6} + \)\(31\!\cdots\!15\)\( T^{8} - \)\(22\!\cdots\!58\)\( T^{10} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 - 442 T + 91541 T^{2} - 45889766 T^{3} + 10779215329 T^{4} \))(\( 1 + 313 T - 5854 T^{2} + 32496599 T^{3} + 10779215329 T^{4} \))(\( 1 - 246 T - 43307 T^{2} - 25540458 T^{3} + 10779215329 T^{4} \))(\( 1 - 639 T + 304498 T^{2} - 66342897 T^{3} + 10779215329 T^{4} \))(\( 1 + 326 T + 2453 T^{2} + 33846298 T^{3} + 10779215329 T^{4} \))(\( 1 + 183 T - 70334 T^{2} + 18999609 T^{3} + 10779215329 T^{4} \))(\( 1 + 218 T - 56299 T^{2} + 22633414 T^{3} + 10779215329 T^{4} \))(\( 1 + 684 T + 202862 T^{2} + 39226032 T^{3} + 10868391219 T^{4} + 4072564320336 T^{5} + 2186693180071598 T^{6} + 765485243602292628 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 316 T - 128034 T^{2} + 6397104 T^{3} + 30787287283 T^{4} + 664166528592 T^{5} - 1380106055433186 T^{6} + 353645229500474372 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 444 T - 57634 T^{2} + 20923056 T^{3} + 33661286643 T^{4} + 2172294443088 T^{5} - 621249296271586 T^{6} + 496893930057628548 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 421 T - 49052 T^{2} + 21374219 T^{3} + 3160631804 T^{4} + 2046438500231 T^{5} - 1587449599620686 T^{6} + 212467384409483113 T^{7} + 34069130791001723516 T^{8} + \)\(23\!\cdots\!73\)\( T^{9} - \)\(56\!\cdots\!32\)\( T^{10} - \)\(50\!\cdots\!03\)\( T^{11} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 + 568497 T^{2} + 156615859096 T^{4} + 28122133375457937 T^{6} + \)\(38\!\cdots\!91\)\( T^{8} + \)\(43\!\cdots\!62\)\( T^{10} + \)\(48\!\cdots\!40\)\( T^{12} + \)\(58\!\cdots\!70\)\( T^{14} + \)\(74\!\cdots\!45\)\( T^{16} + \)\(90\!\cdots\!75\)\( T^{18} + \)\(10\!\cdots\!00\)\( T^{20} + \)\(97\!\cdots\!75\)\( T^{22} + \)\(86\!\cdots\!45\)\( T^{24} + \)\(72\!\cdots\!30\)\( T^{26} + \)\(65\!\cdots\!40\)\( T^{28} + \)\(63\!\cdots\!38\)\( T^{30} + \)\(59\!\cdots\!11\)\( T^{32} + \)\(47\!\cdots\!33\)\( T^{34} + \)\(28\!\cdots\!56\)\( T^{36} + \)\(11\!\cdots\!93\)\( T^{38} + \)\(21\!\cdots\!01\)\( T^{40} \))
$53$ (\( 1 + 198 T + 148877 T^{2} \))(\( 1 + 530 T + 148877 T^{2} \))(\( 1 + 138 T + 148877 T^{2} \))(\( 1 + 94 T + 148877 T^{2} \))(\( 1 - 102 T + 148877 T^{2} \))(\( 1 - 46 T + 148877 T^{2} \))(\( 1 + 382 T + 148877 T^{2} \))(\( 1 - 318 T + 148877 T^{2} \))(\( 1 + 662 T + 148877 T^{2} \))(\( 1 + 130 T + 148877 T^{2} \))(\( 1 + 300 T + 304990 T^{2} + 44663100 T^{3} + 22164361129 T^{4} \))(\( 1 - 834320 T^{2} + 360937926168 T^{4} - 108015576851126320 T^{6} + \)\(24\!\cdots\!56\)\( T^{8} - \)\(45\!\cdots\!20\)\( T^{10} + \)\(69\!\cdots\!88\)\( T^{12} - \)\(98\!\cdots\!00\)\( T^{14} + \)\(14\!\cdots\!54\)\( T^{16} - \)\(21\!\cdots\!00\)\( T^{18} + \)\(34\!\cdots\!08\)\( T^{20} - \)\(49\!\cdots\!80\)\( T^{22} + \)\(59\!\cdots\!36\)\( T^{24} - \)\(57\!\cdots\!80\)\( T^{26} + \)\(42\!\cdots\!28\)\( T^{28} - \)\(21\!\cdots\!80\)\( T^{30} + \)\(58\!\cdots\!61\)\( T^{32} \))(\( 1 - 834320 T^{2} + 360937926168 T^{4} - 108015576851126320 T^{6} + \)\(24\!\cdots\!56\)\( T^{8} - \)\(45\!\cdots\!20\)\( T^{10} + \)\(69\!\cdots\!88\)\( T^{12} - \)\(98\!\cdots\!00\)\( T^{14} + \)\(14\!\cdots\!54\)\( T^{16} - \)\(21\!\cdots\!00\)\( T^{18} + \)\(34\!\cdots\!08\)\( T^{20} - \)\(49\!\cdots\!80\)\( T^{22} + \)\(59\!\cdots\!36\)\( T^{24} - \)\(57\!\cdots\!80\)\( T^{26} + \)\(42\!\cdots\!28\)\( T^{28} - \)\(21\!\cdots\!80\)\( T^{30} + \)\(58\!\cdots\!61\)\( T^{32} \))(\( 1 - 110828 T^{2} + 21717634998 T^{4} - 2456431815204812 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 263564 T^{2} + 41315828598 T^{4} - 5841727676603756 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 598514 T^{2} + 178638061927 T^{4} - 33258243946651612 T^{6} + \)\(39\!\cdots\!83\)\( T^{8} - \)\(29\!\cdots\!74\)\( T^{10} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 - 65490 T^{2} + 6210301287 T^{4} - 5420683421947420 T^{6} + \)\(13\!\cdots\!23\)\( T^{8} - \)\(32\!\cdots\!90\)\( T^{10} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 + 276 T - 72701 T^{2} + 41090052 T^{3} + 22164361129 T^{4} \))(\( 1 - 319 T - 47116 T^{2} - 47491763 T^{3} + 22164361129 T^{4} \))(\( 1 + 552 T + 155827 T^{2} + 82180104 T^{3} + 22164361129 T^{4} \))(\( 1 + 153 T - 125468 T^{2} + 22778181 T^{3} + 22164361129 T^{4} \))(\( 1 - 44 T - 146941 T^{2} - 6550588 T^{3} + 22164361129 T^{4} \))(\( 1 + 411 T + 20044 T^{2} + 61188447 T^{3} + 22164361129 T^{4} \))(\( 1 + 296 T - 61261 T^{2} + 44067592 T^{3} + 22164361129 T^{4} \))(\( 1 + 16 T - 182562 T^{2} - 1838976 T^{3} + 11219947483 T^{4} - 273781229952 T^{5} - 4046370096432498 T^{6} + 52796217468834128 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 236 T - 226482 T^{2} - 3675936 T^{3} + 49168209163 T^{4} - 547262323872 T^{5} - 5019828837218178 T^{6} + 778744207665303388 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 12 T - 141586 T^{2} + 1872288 T^{3} - 2098406517 T^{4} + 278740620576 T^{5} - 3138163234810594 T^{6} - 39597163101625596 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 725 T + 99682 T^{2} + 67769521 T^{3} - 18495272812 T^{4} - 4320566871989 T^{5} + 3391796417753872 T^{6} - 643233034201106353 T^{7} - \)\(40\!\cdots\!48\)\( T^{8} + \)\(22\!\cdots\!93\)\( T^{9} + \)\(48\!\cdots\!62\)\( T^{10} - \)\(53\!\cdots\!25\)\( T^{11} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 + 382009 T^{2} + 69892799684 T^{4} - 4161698541922739 T^{6} - \)\(33\!\cdots\!69\)\( T^{8} - \)\(52\!\cdots\!90\)\( T^{10} + \)\(40\!\cdots\!60\)\( T^{12} + \)\(21\!\cdots\!14\)\( T^{14} + \)\(23\!\cdots\!49\)\( T^{16} - \)\(25\!\cdots\!61\)\( T^{18} - \)\(83\!\cdots\!88\)\( T^{20} - \)\(56\!\cdots\!69\)\( T^{22} + \)\(11\!\cdots\!09\)\( T^{24} + \)\(23\!\cdots\!46\)\( T^{26} + \)\(98\!\cdots\!60\)\( T^{28} - \)\(27\!\cdots\!10\)\( T^{30} - \)\(40\!\cdots\!49\)\( T^{32} - \)\(10\!\cdots\!51\)\( T^{34} + \)\(40\!\cdots\!24\)\( T^{36} + \)\(49\!\cdots\!21\)\( T^{38} + \)\(28\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 - 348 T + 205379 T^{2} \))(\( 1 + 764 T + 205379 T^{2} \))(\( 1 - 468 T + 205379 T^{2} \))(\( 1 - 308 T + 205379 T^{2} \))(\( 1 + 588 T + 205379 T^{2} \))(\( 1 - 748 T + 205379 T^{2} \))(\( 1 - 356 T + 205379 T^{2} \))(\( 1 + 204 T + 205379 T^{2} \))(\( 1 + 324 T + 205379 T^{2} \))(\( 1 - 188 T + 205379 T^{2} \))(\( 1 + 568 T + 464278 T^{2} + 116655272 T^{3} + 42180533641 T^{4} \))(\( ( 1 + 300 T + 1113832 T^{2} + 198585900 T^{3} + 562798324300 T^{4} + 52144634984940 T^{5} + 179162366140286936 T^{6} + 7713639777795763980 T^{7} + \)\(41\!\cdots\!22\)\( T^{8} + \)\(15\!\cdots\!20\)\( T^{9} + \)\(75\!\cdots\!76\)\( T^{10} + \)\(45\!\cdots\!60\)\( T^{11} + \)\(10\!\cdots\!00\)\( T^{12} + \)\(72\!\cdots\!00\)\( T^{13} + \)\(83\!\cdots\!72\)\( T^{14} + \)\(46\!\cdots\!00\)\( T^{15} + \)\(31\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 300 T + 1113832 T^{2} - 198585900 T^{3} + 562798324300 T^{4} - 52144634984940 T^{5} + 179162366140286936 T^{6} - 7713639777795763980 T^{7} + \)\(41\!\cdots\!22\)\( T^{8} - \)\(15\!\cdots\!20\)\( T^{9} + \)\(75\!\cdots\!76\)\( T^{10} - \)\(45\!\cdots\!60\)\( T^{11} + \)\(10\!\cdots\!00\)\( T^{12} - \)\(72\!\cdots\!00\)\( T^{13} + \)\(83\!\cdots\!72\)\( T^{14} - \)\(46\!\cdots\!00\)\( T^{15} + \)\(31\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 224 T + 30086 T^{2} + 46004896 T^{3} + 42180533641 T^{4} )^{2} \))(\( ( 1 + 256 T + 292742 T^{2} + 52577024 T^{3} + 42180533641 T^{4} )^{2} \))(\( ( 1 + 568 T + 634889 T^{2} + 215755344 T^{3} + 130392867931 T^{4} + 23958543108088 T^{5} + 8662995818654939 T^{6} )^{2} \))(\( ( 1 - 696 T + 503817 T^{2} - 219950416 T^{3} + 103473431643 T^{4} - 29357651414136 T^{5} + 8662995818654939 T^{6} )^{2} \))(\( 1 - 706 T + 293057 T^{2} - 144997574 T^{3} + 42180533641 T^{4} \))(\( 1 + 44 T - 203443 T^{2} + 9036676 T^{3} + 42180533641 T^{4} \))(\( 1 + 408 T - 38915 T^{2} + 83794632 T^{3} + 42180533641 T^{4} \))(\( 1 - 684 T + 262477 T^{2} - 140479236 T^{3} + 42180533641 T^{4} \))(\( 1 - 782 T + 406145 T^{2} - 160606378 T^{3} + 42180533641 T^{4} \))(\( 1 + 492 T + 36685 T^{2} + 101046468 T^{3} + 42180533641 T^{4} \))(\( 1 + 92 T - 196915 T^{2} + 18894868 T^{3} + 42180533641 T^{4} \))(\( 1 + 552 T - 171880 T^{2} + 36335952 T^{3} + 122371972599 T^{4} + 7462641485808 T^{5} - 7249990122215080 T^{6} + 4781973691897526328 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 58 T + 300060 T^{2} + 41032332 T^{3} + 45157087819 T^{4} + 8427179313828 T^{5} + 12656690924318460 T^{6} - 502453757481986462 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 258 T - 87460 T^{2} - 66237372 T^{3} - 32127988821 T^{4} - 13603765223988 T^{5} - 3689109472241860 T^{6} + 2235052921212974262 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 664 T - 232235 T^{2} - 60404072 T^{3} + 146413836920 T^{4} + 15176796611920 T^{5} - 29975241547520693 T^{6} + 3116995311359517680 T^{7} + \)\(61\!\cdots\!20\)\( T^{8} - \)\(52\!\cdots\!08\)\( T^{9} - \)\(41\!\cdots\!35\)\( T^{10} + \)\(24\!\cdots\!36\)\( T^{11} + \)\(75\!\cdots\!21\)\( T^{12} \))(\( ( 1 + 934 T - 493 T^{2} - 218695798 T^{3} - 52451385265 T^{4} - 17994609914090 T^{5} - 25968147230175238 T^{6} - 5024150872521968242 T^{7} + \)\(61\!\cdots\!79\)\( T^{8} + \)\(20\!\cdots\!24\)\( T^{9} - \)\(69\!\cdots\!61\)\( T^{10} + \)\(42\!\cdots\!96\)\( T^{11} + \)\(25\!\cdots\!39\)\( T^{12} - \)\(43\!\cdots\!38\)\( T^{13} - \)\(46\!\cdots\!78\)\( T^{14} - \)\(65\!\cdots\!10\)\( T^{15} - \)\(39\!\cdots\!65\)\( T^{16} - \)\(33\!\cdots\!82\)\( T^{17} - \)\(15\!\cdots\!73\)\( T^{18} + \)\(60\!\cdots\!46\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} )^{2} \))
$61$ (\( 1 - 110 T + 226981 T^{2} \))(\( 1 - 814 T + 226981 T^{2} \))(\( 1 + 250 T + 226981 T^{2} \))(\( 1 - 510 T + 226981 T^{2} \))(\( 1 - 650 T + 226981 T^{2} \))(\( 1 + 50 T + 226981 T^{2} \))(\( 1 + 134 T + 226981 T^{2} \))(\( 1 + 442 T + 226981 T^{2} \))(\( 1 + 514 T + 226981 T^{2} \))(\( 1 - 94 T + 226981 T^{2} \))(\( 1 + 516 T + 478126 T^{2} + 117122196 T^{3} + 51520374361 T^{4} \))(\( 1 - 1352500 T^{2} + 1110370200096 T^{4} - 654126813416254556 T^{6} + \)\(30\!\cdots\!80\)\( T^{8} - \)\(11\!\cdots\!04\)\( T^{10} + \)\(38\!\cdots\!48\)\( T^{12} - \)\(10\!\cdots\!96\)\( T^{14} + \)\(26\!\cdots\!42\)\( T^{16} - \)\(55\!\cdots\!56\)\( T^{18} + \)\(10\!\cdots\!08\)\( T^{20} - \)\(16\!\cdots\!24\)\( T^{22} + \)\(21\!\cdots\!80\)\( T^{24} - \)\(23\!\cdots\!56\)\( T^{26} + \)\(20\!\cdots\!56\)\( T^{28} - \)\(13\!\cdots\!00\)\( T^{30} + \)\(49\!\cdots\!81\)\( T^{32} \))(\( 1 - 1352500 T^{2} + 1110370200096 T^{4} - 654126813416254556 T^{6} + \)\(30\!\cdots\!80\)\( T^{8} - \)\(11\!\cdots\!04\)\( T^{10} + \)\(38\!\cdots\!48\)\( T^{12} - \)\(10\!\cdots\!96\)\( T^{14} + \)\(26\!\cdots\!42\)\( T^{16} - \)\(55\!\cdots\!56\)\( T^{18} + \)\(10\!\cdots\!08\)\( T^{20} - \)\(16\!\cdots\!24\)\( T^{22} + \)\(21\!\cdots\!80\)\( T^{24} - \)\(23\!\cdots\!56\)\( T^{26} + \)\(20\!\cdots\!56\)\( T^{28} - \)\(13\!\cdots\!00\)\( T^{30} + \)\(49\!\cdots\!81\)\( T^{32} \))(\( ( 1 + 12 T + 292622 T^{2} + 2723772 T^{3} + 51520374361 T^{4} )^{2} \))(\( ( 1 + 456 T + 213542 T^{2} + 103503336 T^{3} + 51520374361 T^{4} )^{2} \))(\( ( 1 - 418 T + 349083 T^{2} - 45463532 T^{3} + 79235208423 T^{4} - 21535516482898 T^{5} + 11694146092834141 T^{6} )^{2} \))(\( ( 1 - 962 T + 934299 T^{2} - 448181164 T^{3} + 212068121319 T^{4} - 49562600135282 T^{5} + 11694146092834141 T^{6} )^{2} \))(\( 1 + 442 T - 31617 T^{2} + 100325602 T^{3} + 51520374361 T^{4} \))(\( 1 - 368 T - 91557 T^{2} - 83529008 T^{3} + 51520374361 T^{4} \))(\( 1 + 386 T - 77985 T^{2} + 87614666 T^{3} + 51520374361 T^{4} \))(\( 1 + 488 T + 11163 T^{2} + 110766728 T^{3} + 51520374361 T^{4} \))(\( 1 + 658 T + 205983 T^{2} + 149353498 T^{3} + 51520374361 T^{4} \))(\( 1 - 460 T - 15381 T^{2} - 104411260 T^{3} + 51520374361 T^{4} \))(\( 1 - 870 T + 529919 T^{2} - 197473470 T^{3} + 51520374361 T^{4} \))(\( 1 + 1312 T + 851950 T^{2} + 545046784 T^{3} + 313613170411 T^{4} + 123715264079104 T^{5} + 43892782936853950 T^{6} + 15342719673798392992 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 792 T + 21206 T^{2} - 120460032 T^{3} + 173408915019 T^{4} - 27342138523392 T^{5} + 1092541058699366 T^{6} - 9261763705524639672 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 64 T - 442250 T^{2} - 487424 T^{3} + 146774663179 T^{4} - 110635986944 T^{5} - 22784885561152250 T^{6} + 748425349941385024 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 556 T + 133049 T^{2} + 34983612 T^{3} - 45904631330 T^{4} + 4099613157844 T^{5} + 4838377569939061 T^{6} + 930534294180588964 T^{7} - \)\(23\!\cdots\!30\)\( T^{8} + \)\(40\!\cdots\!92\)\( T^{9} + \)\(35\!\cdots\!29\)\( T^{10} - \)\(33\!\cdots\!56\)\( T^{11} + \)\(13\!\cdots\!81\)\( T^{12} \))(\( ( 1 - 458 T - 599329 T^{2} + 261049590 T^{3} + 186342899591 T^{4} - 56414115488952 T^{5} - 59794178984884502 T^{6} + 5418549476778598536 T^{7} + \)\(20\!\cdots\!21\)\( T^{8} - \)\(17\!\cdots\!02\)\( T^{9} - \)\(52\!\cdots\!31\)\( T^{10} - \)\(40\!\cdots\!62\)\( T^{11} + \)\(10\!\cdots\!81\)\( T^{12} + \)\(63\!\cdots\!76\)\( T^{13} - \)\(15\!\cdots\!42\)\( T^{14} - \)\(33\!\cdots\!52\)\( T^{15} + \)\(25\!\cdots\!71\)\( T^{16} + \)\(81\!\cdots\!90\)\( T^{17} - \)\(42\!\cdots\!89\)\( T^{18} - \)\(73\!\cdots\!18\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} )^{2} \))
$67$ (\( 1 + 196 T + 300763 T^{2} \))(\( 1 - 60 T + 300763 T^{2} \))(\( 1 + 556 T + 300763 T^{2} \))(\( 1 + 156 T + 300763 T^{2} \))(\( 1 - 152 T + 300763 T^{2} \))(\( 1 + 156 T + 300763 T^{2} \))(\( 1 - 888 T + 300763 T^{2} \))(\( 1 + 316 T + 300763 T^{2} \))(\( 1 + 372 T + 300763 T^{2} \))(\( 1 + 444 T + 300763 T^{2} \))(\( 1 - 392 T + 597542 T^{2} - 117899096 T^{3} + 90458382169 T^{4} \))(\( ( 1 - 256 T + 1043388 T^{2} - 240989056 T^{3} + 613102614628 T^{4} - 136189720815936 T^{5} + 257909199963511460 T^{6} - 53731823759552116928 T^{7} + \)\(86\!\cdots\!70\)\( T^{8} - \)\(16\!\cdots\!64\)\( T^{9} + \)\(23\!\cdots\!40\)\( T^{10} - \)\(37\!\cdots\!92\)\( T^{11} + \)\(50\!\cdots\!08\)\( T^{12} - \)\(59\!\cdots\!08\)\( T^{13} + \)\(77\!\cdots\!92\)\( T^{14} - \)\(56\!\cdots\!52\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 256 T + 1043388 T^{2} - 240989056 T^{3} + 613102614628 T^{4} - 136189720815936 T^{5} + 257909199963511460 T^{6} - 53731823759552116928 T^{7} + \)\(86\!\cdots\!70\)\( T^{8} - \)\(16\!\cdots\!64\)\( T^{9} + \)\(23\!\cdots\!40\)\( T^{10} - \)\(37\!\cdots\!92\)\( T^{11} + \)\(50\!\cdots\!08\)\( T^{12} - \)\(59\!\cdots\!08\)\( T^{13} + \)\(77\!\cdots\!92\)\( T^{14} - \)\(56\!\cdots\!52\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 487820 T^{2} + 116820910038 T^{4} - 44127407989681580 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 21700 T^{2} - 83331153162 T^{4} + 1962946893067300 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 885346 T^{2} + 313839676727 T^{4} - 82817585551333948 T^{6} + \)\(28\!\cdots\!63\)\( T^{8} - \)\(72\!\cdots\!06\)\( T^{10} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 - 973026 T^{2} + 498922982199 T^{4} - 175505144106486076 T^{6} + \)\(45\!\cdots\!31\)\( T^{8} - \)\(79\!\cdots\!86\)\( T^{10} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 + 531 T - 18802 T^{2} + 159705153 T^{3} + 90458382169 T^{4} \))(\( 1 + 216 T - 254107 T^{2} + 64964808 T^{3} + 90458382169 T^{4} \))(\( 1 - 811 T + 356958 T^{2} - 243918793 T^{3} + 90458382169 T^{4} \))(\( 1 + 608 T + 68901 T^{2} + 182863904 T^{3} + 90458382169 T^{4} \))(\( 1 + 1071 T + 846278 T^{2} + 322117173 T^{3} + 90458382169 T^{4} \))(\( 1 + 980 T + 659637 T^{2} + 294747740 T^{3} + 90458382169 T^{4} \))(\( 1 - 255 T - 235738 T^{2} - 76694565 T^{3} + 90458382169 T^{4} \))(\( 1 + 194 T - 495973 T^{2} - 13175898 T^{3} + 182960666444 T^{4} - 3962822610174 T^{5} - 44864915179505437 T^{6} + 5278067672881219718 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 868 T + 13397 T^{2} - 120218868 T^{3} + 230579516048 T^{4} - 36157387396284 T^{5} + 1211870945918093 T^{6} - 23615271855984013996 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 632 T - 117143 T^{2} + 53694088 T^{3} + 56251122808 T^{4} + 16149194989144 T^{5} - 10596566262423167 T^{6} - 17194529738458406504 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 182 T - 627156 T^{2} + 18613584 T^{3} + 224752491256 T^{4} + 10004201974042 T^{5} - 74891535629673278 T^{6} + 3008893798318794046 T^{7} + \)\(20\!\cdots\!64\)\( T^{8} + \)\(50\!\cdots\!48\)\( T^{9} - \)\(51\!\cdots\!16\)\( T^{10} - \)\(44\!\cdots\!26\)\( T^{11} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 + 1936326 T^{2} + 1854314251241 T^{4} + 1236120267448418698 T^{6} + \)\(67\!\cdots\!64\)\( T^{8} + \)\(32\!\cdots\!06\)\( T^{10} + \)\(14\!\cdots\!95\)\( T^{12} + \)\(55\!\cdots\!46\)\( T^{14} + \)\(20\!\cdots\!31\)\( T^{16} + \)\(68\!\cdots\!48\)\( T^{18} + \)\(21\!\cdots\!20\)\( T^{20} + \)\(61\!\cdots\!12\)\( T^{22} + \)\(16\!\cdots\!91\)\( T^{24} + \)\(41\!\cdots\!14\)\( T^{26} + \)\(94\!\cdots\!95\)\( T^{28} + \)\(19\!\cdots\!94\)\( T^{30} + \)\(36\!\cdots\!84\)\( T^{32} + \)\(61\!\cdots\!22\)\( T^{34} + \)\(83\!\cdots\!81\)\( T^{36} + \)\(78\!\cdots\!54\)\( T^{38} + \)\(36\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 + 936 T + 357911 T^{2} \))(\( 1 - 848 T + 357911 T^{2} \))(\( 1 - 624 T + 357911 T^{2} \))(\( 1 - 336 T + 357911 T^{2} \))(\( 1 + 168 T + 357911 T^{2} \))(\( 1 + 1024 T + 357911 T^{2} \))(\( 1 - 868 T + 357911 T^{2} \))(\( 1 + 252 T + 357911 T^{2} \))(\( 1 + 412 T + 357911 T^{2} \))(\( 1 - 532 T + 357911 T^{2} \))(\( 1 + 1448 T + 1212862 T^{2} + 518255128 T^{3} + 128100283921 T^{4} \))(\( 1 - 2765804 T^{2} + 3883548071760 T^{4} - 3732203414532225892 T^{6} + \)\(27\!\cdots\!36\)\( T^{8} - \)\(16\!\cdots\!04\)\( T^{10} + \)\(86\!\cdots\!32\)\( T^{12} - \)\(37\!\cdots\!56\)\( T^{14} + \)\(14\!\cdots\!54\)\( T^{16} - \)\(48\!\cdots\!76\)\( T^{18} + \)\(14\!\cdots\!12\)\( T^{20} - \)\(35\!\cdots\!44\)\( T^{22} + \)\(74\!\cdots\!16\)\( T^{24} - \)\(12\!\cdots\!92\)\( T^{26} + \)\(17\!\cdots\!60\)\( T^{28} - \)\(15\!\cdots\!64\)\( T^{30} + \)\(72\!\cdots\!61\)\( T^{32} \))(\( 1 - 2765804 T^{2} + 3883548071760 T^{4} - 3732203414532225892 T^{6} + \)\(27\!\cdots\!36\)\( T^{8} - \)\(16\!\cdots\!04\)\( T^{10} + \)\(86\!\cdots\!32\)\( T^{12} - \)\(37\!\cdots\!56\)\( T^{14} + \)\(14\!\cdots\!54\)\( T^{16} - \)\(48\!\cdots\!76\)\( T^{18} + \)\(14\!\cdots\!12\)\( T^{20} - \)\(35\!\cdots\!44\)\( T^{22} + \)\(74\!\cdots\!16\)\( T^{24} - \)\(12\!\cdots\!92\)\( T^{26} + \)\(17\!\cdots\!60\)\( T^{28} - \)\(15\!\cdots\!64\)\( T^{30} + \)\(72\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 156 T + 491410 T^{2} + 55834116 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 + 984 T + 580810 T^{2} + 352184424 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 830 T + 1103889 T^{2} - 560563820 T^{3} + 395094015879 T^{4} - 106323235654430 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 - 138 T + 397569 T^{2} - 279828804 T^{3} + 142294318359 T^{4} - 17677839181098 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 - 1036 T + 357911 T^{2} )^{2} \))(\( ( 1 + 314 T + 357911 T^{2} )^{2} \))(\( ( 1 + 54 T + 357911 T^{2} )^{2} \))(\( ( 1 - 198 T + 357911 T^{2} )^{2} \))(\( ( 1 - 344 T + 357911 T^{2} )^{2} \))(\( ( 1 + 306 T + 357911 T^{2} )^{2} \))(\( ( 1 + 426 T + 357911 T^{2} )^{2} \))(\( ( 1 - 380 T - 111452 T^{2} - 136006180 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 + 386 T + 568696 T^{2} + 138153646 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 + 78 T + 443968 T^{2} + 27917058 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 + 34 T + 984147 T^{2} + 13328824 T^{3} + 352237036917 T^{4} + 4355409653314 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 + 1552 T + 2408917 T^{2} + 2217558230 T^{3} + 1929541049398 T^{4} + 1189160101174152 T^{5} + 690603966531087578 T^{6} + \)\(28\!\cdots\!30\)\( T^{7} + \)\(11\!\cdots\!27\)\( T^{8} + \)\(25\!\cdots\!32\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{4} \))
$73$ (\( 1 - 542 T + 389017 T^{2} \))(\( 1 + 958 T + 389017 T^{2} \))(\( 1 + 958 T + 389017 T^{2} \))(\( 1 + 1170 T + 389017 T^{2} \))(\( 1 + 610 T + 389017 T^{2} \))(\( 1 + 310 T + 389017 T^{2} \))(\( 1 + 70 T + 389017 T^{2} \))(\( 1 - 98 T + 389017 T^{2} \))(\( 1 + 770 T + 389017 T^{2} \))(\( 1 - 770 T + 389017 T^{2} \))(\( 1 + 756 T + 751318 T^{2} + 294096852 T^{3} + 151334226289 T^{4} \))(\( 1 - 1835236 T^{2} + 2090939017824 T^{4} - 1804912151311918732 T^{6} + \)\(12\!\cdots\!32\)\( T^{8} - \)\(77\!\cdots\!56\)\( T^{10} + \)\(41\!\cdots\!20\)\( T^{12} - \)\(19\!\cdots\!80\)\( T^{14} + \)\(78\!\cdots\!46\)\( T^{16} - \)\(28\!\cdots\!20\)\( T^{18} + \)\(94\!\cdots\!20\)\( T^{20} - \)\(27\!\cdots\!64\)\( T^{22} + \)\(67\!\cdots\!12\)\( T^{24} - \)\(14\!\cdots\!68\)\( T^{26} + \)\(25\!\cdots\!64\)\( T^{28} - \)\(33\!\cdots\!44\)\( T^{30} + \)\(27\!\cdots\!81\)\( T^{32} \))(\( 1 - 1835236 T^{2} + 2090939017824 T^{4} - 1804912151311918732 T^{6} + \)\(12\!\cdots\!32\)\( T^{8} - \)\(77\!\cdots\!56\)\( T^{10} + \)\(41\!\cdots\!20\)\( T^{12} - \)\(19\!\cdots\!80\)\( T^{14} + \)\(78\!\cdots\!46\)\( T^{16} - \)\(28\!\cdots\!20\)\( T^{18} + \)\(94\!\cdots\!20\)\( T^{20} - \)\(27\!\cdots\!64\)\( T^{22} + \)\(67\!\cdots\!12\)\( T^{24} - \)\(14\!\cdots\!68\)\( T^{26} + \)\(25\!\cdots\!64\)\( T^{28} - \)\(33\!\cdots\!44\)\( T^{30} + \)\(27\!\cdots\!81\)\( T^{32} \))(\( 1 - 1463324 T^{2} + 835923760038 T^{4} - 221451005350124636 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 1476764 T^{2} + 846383359398 T^{4} - 223484937351448796 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 713370 T^{2} + 395161775967 T^{4} - 142355949083594860 T^{6} + \)\(59\!\cdots\!63\)\( T^{8} - \)\(16\!\cdots\!70\)\( T^{10} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( 1 - 2205402 T^{2} + 2074092672735 T^{4} - 1063933110613812460 T^{6} + \)\(31\!\cdots\!15\)\( T^{8} - \)\(50\!\cdots\!42\)\( T^{10} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( 1 + 427 T - 206688 T^{2} + 166110259 T^{3} + 151334226289 T^{4} \))(\( 1 + 602 T - 26613 T^{2} + 234188234 T^{3} + 151334226289 T^{4} \))(\( 1 + 173 T - 359088 T^{2} + 67299941 T^{3} + 151334226289 T^{4} \))(\( 1 + 338 T - 274773 T^{2} + 131487746 T^{3} + 151334226289 T^{4} \))(\( 1 + 431 T - 203256 T^{2} + 167666327 T^{3} + 151334226289 T^{4} \))(\( 1 - 934 T + 483339 T^{2} - 363341878 T^{3} + 151334226289 T^{4} \))(\( 1 + 1161 T + 958904 T^{2} + 451648737 T^{3} + 151334226289 T^{4} \))(\( 1 + 198 T - 743065 T^{2} + 838530 T^{3} + 445359539604 T^{4} + 326202425010 T^{5} - 112451166857435785 T^{6} + 11656574168237046774 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 1220 T + 404641 T^{2} - 372984500 T^{3} + 444186440992 T^{4} - 145097311236500 T^{5} + 61236032659807249 T^{6} - 71823335784086853860 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 464 T - 586187 T^{2} - 10880336 T^{3} + 407286968968 T^{4} - 4232635669712 T^{5} - 88710156105670043 T^{6} - 27316416232636311632 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 732 T - 687678 T^{2} + 184096076 T^{3} + 625824034830 T^{4} - 74473981428312 T^{5} - 254249340170492478 T^{6} - 28971644833297649304 T^{7} + \)\(94\!\cdots\!70\)\( T^{8} + \)\(10\!\cdots\!88\)\( T^{9} - \)\(15\!\cdots\!38\)\( T^{10} - \)\(65\!\cdots\!24\)\( T^{11} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( 1 + 2661650 T^{2} + 3602544283705 T^{4} + 3393522114663874950 T^{6} + \)\(25\!\cdots\!40\)\( T^{8} + \)\(16\!\cdots\!50\)\( T^{10} + \)\(90\!\cdots\!55\)\( T^{12} + \)\(45\!\cdots\!50\)\( T^{14} + \)\(21\!\cdots\!95\)\( T^{16} + \)\(90\!\cdots\!00\)\( T^{18} + \)\(36\!\cdots\!76\)\( T^{20} + \)\(13\!\cdots\!00\)\( T^{22} + \)\(48\!\cdots\!95\)\( T^{24} + \)\(15\!\cdots\!50\)\( T^{26} + \)\(47\!\cdots\!55\)\( T^{28} + \)\(12\!\cdots\!50\)\( T^{30} + \)\(30\!\cdots\!40\)\( T^{32} + \)\(61\!\cdots\!50\)\( T^{34} + \)\(99\!\cdots\!05\)\( T^{36} + \)\(11\!\cdots\!50\)\( T^{38} + \)\(63\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 - 992 T + 493039 T^{2} \))(\( 1 + 152 T + 493039 T^{2} \))(\( 1 - 632 T + 493039 T^{2} \))(\( 1 - 16 T + 493039 T^{2} \))(\( 1 + 1048 T + 493039 T^{2} \))(\( 1 - 856 T + 493039 T^{2} \))(\( 1 - 400 T + 493039 T^{2} \))(\( 1 + 1000 T + 493039 T^{2} \))(\( 1 + 560 T + 493039 T^{2} \))(\( 1 + 536 T + 493039 T^{2} \))(\( 1 - 416 T + 1022558 T^{2} - 205104224 T^{3} + 243087455521 T^{4} \))(\( ( 1 + 1658 T + 3436425 T^{2} + 4440372482 T^{3} + 5366340107206 T^{4} + 5404156074057258 T^{5} + 4990582086520209255 T^{6} + \)\(39\!\cdots\!90\)\( T^{7} + \)\(30\!\cdots\!06\)\( T^{8} + \)\(19\!\cdots\!10\)\( T^{9} + \)\(12\!\cdots\!55\)\( T^{10} + \)\(64\!\cdots\!02\)\( T^{11} + \)\(31\!\cdots\!46\)\( T^{12} + \)\(12\!\cdots\!18\)\( T^{13} + \)\(49\!\cdots\!25\)\( T^{14} + \)\(11\!\cdots\!82\)\( T^{15} + \)\(34\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 1658 T + 3436425 T^{2} + 4440372482 T^{3} + 5366340107206 T^{4} + 5404156074057258 T^{5} + 4990582086520209255 T^{6} + \)\(39\!\cdots\!90\)\( T^{7} + \)\(30\!\cdots\!06\)\( T^{8} + \)\(19\!\cdots\!10\)\( T^{9} + \)\(12\!\cdots\!55\)\( T^{10} + \)\(64\!\cdots\!02\)\( T^{11} + \)\(31\!\cdots\!46\)\( T^{12} + \)\(12\!\cdots\!18\)\( T^{13} + \)\(49\!\cdots\!25\)\( T^{14} + \)\(11\!\cdots\!82\)\( T^{15} + \)\(34\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 376 T + 1015278 T^{2} + 185382664 T^{3} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 224 T + 716046 T^{2} - 110440736 T^{3} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 556 T + 1042205 T^{2} - 585208168 T^{3} + 513847710995 T^{4} - 135156625269676 T^{5} + 119851595982618319 T^{6} )^{2} \))(\( ( 1 + 412 T - 220643 T^{2} - 164825464 T^{3} - 108785604077 T^{4} + 100152031674652 T^{5} + 119851595982618319 T^{6} )^{2} \))(\( 1 + 1317 T + 1241450 T^{2} + 649332363 T^{3} + 243087455521 T^{4} \))(\( 1 + 112 T - 480495 T^{2} + 55220368 T^{3} + 243087455521 T^{4} \))(\( 1 + 1061 T + 632682 T^{2} + 523114379 T^{3} + 243087455521 T^{4} \))(\( 1 - 736 T + 48657 T^{2} - 362876704 T^{3} + 243087455521 T^{4} \))(\( 1 + 397 T - 335430 T^{2} + 195736483 T^{3} + 243087455521 T^{4} \))(\( 1 - 604 T - 128223 T^{2} - 297795556 T^{3} + 243087455521 T^{4} \))(\( 1 - 299 T - 403638 T^{2} - 147418661 T^{3} + 243087455521 T^{4} \))(\( 1 + 126 T + 293405 T^{2} - 159214482 T^{3} - 173892596844 T^{4} - 78498948990798 T^{5} + 71323074887139005 T^{6} + 15101301093809908194 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 + 54 T - 412771 T^{2} - 30801114 T^{3} - 71729475276 T^{4} - 15186150445446 T^{5} - 100339452102858691 T^{6} + 6471986183061389226 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 1946 T + 1856269 T^{2} - 1838131274 T^{3} + 1617213105364 T^{4} - 906270405201686 T^{5} + 451235707972511149 T^{6} - \)\(23\!\cdots\!74\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 + 3002 T + 4766846 T^{2} + 5383909980 T^{3} + 4880896431466 T^{4} + 3785502469133938 T^{5} + 2706361537019657182 T^{6} + \)\(18\!\cdots\!82\)\( T^{7} + \)\(11\!\cdots\!86\)\( T^{8} + \)\(64\!\cdots\!20\)\( T^{9} + \)\(28\!\cdots\!86\)\( T^{10} + \)\(87\!\cdots\!98\)\( T^{11} + \)\(14\!\cdots\!61\)\( T^{12} \))(\( ( 1 - 210 T - 1898629 T^{2} + 117776758 T^{3} + 2042025827280 T^{4} + 34991647794278 T^{5} - 1568482659669333655 T^{6} - 61976947269881898930 T^{7} + \)\(95\!\cdots\!15\)\( T^{8} + \)\(20\!\cdots\!40\)\( T^{9} - \)\(50\!\cdots\!20\)\( T^{10} + \)\(10\!\cdots\!60\)\( T^{11} + \)\(23\!\cdots\!15\)\( T^{12} - \)\(74\!\cdots\!70\)\( T^{13} - \)\(92\!\cdots\!55\)\( T^{14} + \)\(10\!\cdots\!22\)\( T^{15} + \)\(29\!\cdots\!80\)\( T^{16} + \)\(83\!\cdots\!82\)\( T^{17} - \)\(66\!\cdots\!49\)\( T^{18} - \)\(36\!\cdots\!90\)\( T^{19} + \)\(84\!\cdots\!01\)\( T^{20} )^{2} \))
$83$ (\( 1 + 276 T + 571787 T^{2} \))(\( 1 - 308 T + 571787 T^{2} \))(\( 1 - 84 T + 571787 T^{2} \))(\( 1 - 772 T + 571787 T^{2} \))(\( 1 + 684 T + 571787 T^{2} \))(\( 1 + 628 T + 571787 T^{2} \))(\( 1 + 1052 T + 571787 T^{2} \))(\( 1 - 516 T + 571787 T^{2} \))(\( 1 + 852 T + 571787 T^{2} \))(\( 1 + 1076 T + 571787 T^{2} \))(\( 1 + 1752 T + 1666726 T^{2} + 1001770824 T^{3} + 326940373369 T^{4} \))(\( ( 1 + 1194 T + 3547564 T^{2} + 3600220642 T^{3} + 5895339127780 T^{4} + 5112664392679330 T^{5} + 6016092667783107636 T^{6} + \)\(44\!\cdots\!06\)\( T^{7} + \)\(41\!\cdots\!78\)\( T^{8} + \)\(25\!\cdots\!22\)\( T^{9} + \)\(19\!\cdots\!84\)\( T^{10} + \)\(95\!\cdots\!90\)\( T^{11} + \)\(63\!\cdots\!80\)\( T^{12} + \)\(22\!\cdots\!94\)\( T^{13} + \)\(12\!\cdots\!76\)\( T^{14} + \)\(23\!\cdots\!02\)\( T^{15} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 1194 T + 3547564 T^{2} - 3600220642 T^{3} + 5895339127780 T^{4} - 5112664392679330 T^{5} + 6016092667783107636 T^{6} - \)\(44\!\cdots\!06\)\( T^{7} + \)\(41\!\cdots\!78\)\( T^{8} - \)\(25\!\cdots\!22\)\( T^{9} + \)\(19\!\cdots\!84\)\( T^{10} - \)\(95\!\cdots\!90\)\( T^{11} + \)\(63\!\cdots\!80\)\( T^{12} - \)\(22\!\cdots\!94\)\( T^{13} + \)\(12\!\cdots\!76\)\( T^{14} - \)\(23\!\cdots\!02\)\( T^{15} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 125228 T^{2} + 394047302358 T^{4} - 40942089076253132 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 989036 T^{2} + 799488357462 T^{4} - 323355799115382284 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 2875778 T^{2} + 3676743405847 T^{4} - 2697385183347767164 T^{6} + \)\(12\!\cdots\!43\)\( T^{8} - \)\(30\!\cdots\!58\)\( T^{10} + \)\(34\!\cdots\!09\)\( T^{12} \))(\( 1 + 1186942 T^{2} + 1222620326167 T^{4} + 734180698603019396 T^{6} + \)\(39\!\cdots\!23\)\( T^{8} + \)\(12\!\cdots\!62\)\( T^{10} + \)\(34\!\cdots\!09\)\( T^{12} \))(\( ( 1 + 1188 T + 571787 T^{2} )^{2} \))(\( ( 1 - 712 T + 571787 T^{2} )^{2} \))(\( ( 1 - 1206 T + 571787 T^{2} )^{2} \))(\( ( 1 + 571787 T^{2} )^{2} \))(\( ( 1 - 680 T + 571787 T^{2} )^{2} \))(\( ( 1 - 108 T + 571787 T^{2} )^{2} \))(\( ( 1 + 1022 T + 571787 T^{2} )^{2} \))(\( ( 1 - 864 T + 336184 T^{2} - 494023968 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 182 T + 54160 T^{2} + 104065234 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 234 T + 181888 T^{2} + 133798158 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 80 T + 1565859 T^{2} - 105254696 T^{3} + 895337820033 T^{4} - 26155229869520 T^{5} + 186940255267540403 T^{6} )^{2} \))(\( ( 1 - 3608566 T^{2} + 6580342203809 T^{4} - 7907457450088030316 T^{6} + \)\(68\!\cdots\!58\)\( T^{8} - \)\(45\!\cdots\!56\)\( T^{10} + \)\(22\!\cdots\!02\)\( T^{12} - \)\(84\!\cdots\!76\)\( T^{14} + \)\(22\!\cdots\!81\)\( T^{16} - \)\(41\!\cdots\!86\)\( T^{18} + \)\(37\!\cdots\!49\)\( T^{20} )^{2} \))
$89$ (\( 1 - 630 T + 704969 T^{2} \))(\( 1 + 1094 T + 704969 T^{2} \))(\( 1 - 810 T + 704969 T^{2} \))(\( 1 - 1630 T + 704969 T^{2} \))(\( 1 + 834 T + 704969 T^{2} \))(\( 1 + 590 T + 704969 T^{2} \))(\( 1 + 634 T + 704969 T^{2} \))(\( 1 + 522 T + 704969 T^{2} \))(\( 1 - 1466 T + 704969 T^{2} \))(\( 1 + 1090 T + 704969 T^{2} \))(\( 1 + 956 T + 1529878 T^{2} + 673950364 T^{3} + 496981290961 T^{4} \))(\( ( 1 - 4020 T + 10535776 T^{2} - 20097193100 T^{3} + 31469824221436 T^{4} - 41440376118201860 T^{5} + 47585136580912111776 T^{6} - \)\(47\!\cdots\!80\)\( T^{7} + \)\(42\!\cdots\!22\)\( T^{8} - \)\(33\!\cdots\!20\)\( T^{9} + \)\(23\!\cdots\!36\)\( T^{10} - \)\(14\!\cdots\!40\)\( T^{11} + \)\(77\!\cdots\!56\)\( T^{12} - \)\(34\!\cdots\!00\)\( T^{13} + \)\(12\!\cdots\!56\)\( T^{14} - \)\(34\!\cdots\!80\)\( T^{15} + \)\(61\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 4020 T + 10535776 T^{2} + 20097193100 T^{3} + 31469824221436 T^{4} + 41440376118201860 T^{5} + 47585136580912111776 T^{6} + \)\(47\!\cdots\!80\)\( T^{7} + \)\(42\!\cdots\!22\)\( T^{8} + \)\(33\!\cdots\!20\)\( T^{9} + \)\(23\!\cdots\!36\)\( T^{10} + \)\(14\!\cdots\!40\)\( T^{11} + \)\(77\!\cdots\!56\)\( T^{12} + \)\(34\!\cdots\!00\)\( T^{13} + \)\(12\!\cdots\!56\)\( T^{14} + \)\(34\!\cdots\!80\)\( T^{15} + \)\(61\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 548 T + 237398 T^{2} + 386323012 T^{3} + 496981290961 T^{4} )^{2} \))(\( ( 1 + 40 T + 1391438 T^{2} + 28198760 T^{3} + 496981290961 T^{4} )^{2} \))(\( ( 1 + 970 T - 146209 T^{2} - 916907700 T^{3} - 103072812521 T^{4} + 482071852232170 T^{5} + 350356403707485209 T^{6} )^{2} \))(\( ( 1 + 1298 T + 1798175 T^{2} + 1697578620 T^{3} + 1267657631575 T^{4} + 645081715667378 T^{5} + 350356403707485209 T^{6} )^{2} \))(\( 1 - 38 T - 703525 T^{2} - 26788822 T^{3} + 496981290961 T^{4} \))(\( 1 - 1018 T + 331355 T^{2} - 717658442 T^{3} + 496981290961 T^{4} \))(\( 1 + 672 T - 253385 T^{2} + 473739168 T^{3} + 496981290961 T^{4} \))(\( 1 - 1290 T + 959131 T^{2} - 909410010 T^{3} + 496981290961 T^{4} \))(\( 1 + 1534 T + 1648187 T^{2} + 1081422446 T^{3} + 496981290961 T^{4} \))(\( 1 - 546 T - 406853 T^{2} - 384913074 T^{3} + 496981290961 T^{4} \))(\( 1 - 236 T - 649273 T^{2} - 166372684 T^{3} + 496981290961 T^{4} \))(\( 1 - 184 T - 250692 T^{2} + 207071760 T^{3} - 439881157121 T^{4} + 145979171575440 T^{5} - 124589233793595012 T^{6} - 64465578282177278456 T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 418 T - 1122840 T^{2} + 46972332 T^{3} + 1063516039579 T^{4} + 33114037917708 T^{5} - 558030472742649240 T^{6} - \)\(14\!\cdots\!62\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 1674 T + 708104 T^{2} + 1145407716 T^{3} + 1913057365179 T^{4} + 807476932140804 T^{5} + 351914440054647944 T^{6} + \)\(58\!\cdots\!66\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 686 T - 629105 T^{2} + 1142668090 T^{3} - 216605425636 T^{4} - 320380174707266 T^{5} + 513998559124648237 T^{6} - \)\(22\!\cdots\!54\)\( T^{7} - \)\(10\!\cdots\!96\)\( T^{8} + \)\(40\!\cdots\!10\)\( T^{9} - \)\(15\!\cdots\!05\)\( T^{10} - \)\(11\!\cdots\!14\)\( T^{11} + \)\(12\!\cdots\!81\)\( T^{12} \))(\( ( 1 - 38 T - 1441195 T^{2} + 1465259138 T^{3} + 747195546647 T^{4} - 1721448700906430 T^{5} + 507462621666847214 T^{6} + \)\(68\!\cdots\!34\)\( T^{7} - \)\(65\!\cdots\!49\)\( T^{8} - \)\(91\!\cdots\!08\)\( T^{9} + \)\(32\!\cdots\!77\)\( T^{10} - \)\(64\!\cdots\!52\)\( T^{11} - \)\(32\!\cdots\!89\)\( T^{12} + \)\(23\!\cdots\!06\)\( T^{13} + \)\(12\!\cdots\!94\)\( T^{14} - \)\(29\!\cdots\!70\)\( T^{15} + \)\(91\!\cdots\!07\)\( T^{16} + \)\(12\!\cdots\!82\)\( T^{17} - \)\(87\!\cdots\!95\)\( T^{18} - \)\(16\!\cdots\!02\)\( T^{19} + \)\(30\!\cdots\!01\)\( T^{20} )^{2} \))
$97$ (\( 1 - 110 T + 912673 T^{2} \))(\( 1 - 554 T + 912673 T^{2} \))(\( 1 + 790 T + 912673 T^{2} \))(\( 1 - 110 T + 912673 T^{2} \))(\( 1 - 110 T + 912673 T^{2} \))(\( 1 + 1390 T + 912673 T^{2} \))(\( 1 - 1202 T + 912673 T^{2} \))(\( 1 + 310 T + 912673 T^{2} \))(\( 1 + 178 T + 912673 T^{2} \))(\( 1 - 1274 T + 912673 T^{2} \))(\( 1 - 684 T + 795814 T^{2} - 624268332 T^{3} + 832972004929 T^{4} \))(\( 1 - 3233374 T^{2} + 6280804884237 T^{4} - 9000408539875374394 T^{6} + \)\(10\!\cdots\!42\)\( T^{8} - \)\(12\!\cdots\!14\)\( T^{10} + \)\(13\!\cdots\!03\)\( T^{12} - \)\(14\!\cdots\!50\)\( T^{14} + \)\(13\!\cdots\!54\)\( T^{16} - \)\(11\!\cdots\!50\)\( T^{18} + \)\(92\!\cdots\!23\)\( T^{20} - \)\(70\!\cdots\!46\)\( T^{22} + \)\(52\!\cdots\!02\)\( T^{24} - \)\(36\!\cdots\!06\)\( T^{26} + \)\(20\!\cdots\!77\)\( T^{28} - \)\(89\!\cdots\!66\)\( T^{30} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( 1 - 3233374 T^{2} + 6280804884237 T^{4} - 9000408539875374394 T^{6} + \)\(10\!\cdots\!42\)\( T^{8} - \)\(12\!\cdots\!14\)\( T^{10} + \)\(13\!\cdots\!03\)\( T^{12} - \)\(14\!\cdots\!50\)\( T^{14} + \)\(13\!\cdots\!54\)\( T^{16} - \)\(11\!\cdots\!50\)\( T^{18} + \)\(92\!\cdots\!23\)\( T^{20} - \)\(70\!\cdots\!46\)\( T^{22} + \)\(52\!\cdots\!02\)\( T^{24} - \)\(36\!\cdots\!06\)\( T^{26} + \)\(20\!\cdots\!77\)\( T^{28} - \)\(89\!\cdots\!66\)\( T^{30} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( 1 - 2031292 T^{2} + 2294372967174 T^{4} - 1692009369836238268 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 - 158236 T^{2} - 84748847802 T^{4} - 131806158171945244 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 + 874198 T^{2} + 2442139048847 T^{4} + 1399641920325930484 T^{6} + \)\(20\!\cdots\!63\)\( T^{8} + \)\(60\!\cdots\!18\)\( T^{10} + \)\(57\!\cdots\!89\)\( T^{12} \))(\( 1 - 3586730 T^{2} + 6514584896015 T^{4} - 7325710695468303884 T^{6} + \)\(54\!\cdots\!35\)\( T^{8} - \)\(24\!\cdots\!30\)\( T^{10} + \)\(57\!\cdots\!89\)\( T^{12} \))(\( ( 1 + 866 T + 912673 T^{2} )^{2} \))(\( ( 1 - 584 T + 912673 T^{2} )^{2} \))(\( ( 1 - 818 T + 912673 T^{2} )^{2} \))(\( ( 1 + 1456 T + 912673 T^{2} )^{2} \))(\( ( 1 + 1234 T + 912673 T^{2} )^{2} \))(\( ( 1 - 1808 T + 912673 T^{2} )^{2} \))(\( ( 1 + 862 T + 912673 T^{2} )^{2} \))(\( ( 1 - 568 T + 1864602 T^{2} - 518398264 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 + 392 T + 1821282 T^{2} + 357767816 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 832 T + 1782402 T^{2} - 759343936 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 + 1080 T + 2795931 T^{2} + 1947979312 T^{3} + 2551770733563 T^{4} + 899609765323320 T^{5} + 760231058654565217 T^{6} )^{2} \))(\( ( 1 - 2102214 T^{2} + 4229943906469 T^{4} - 5222274044863846424 T^{6} + \)\(67\!\cdots\!98\)\( T^{8} - \)\(61\!\cdots\!44\)\( T^{10} + \)\(56\!\cdots\!42\)\( T^{12} - \)\(36\!\cdots\!84\)\( T^{14} + \)\(24\!\cdots\!41\)\( T^{16} - \)\(10\!\cdots\!34\)\( T^{18} + \)\(40\!\cdots\!49\)\( T^{20} )^{2} \))
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