Properties

Label 80.10
Level 80
Weight 10
Dimension 878
Nonzero newspaces 7
Newform subspaces 22
Sturm bound 3840
Trace bound 3

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 22 \)
Sturm bound: \(3840\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(80))\).

Total New Old
Modular forms 1784 904 880
Cusp forms 1672 878 794
Eisenstein series 112 26 86

Trace form

\( 878q - 4q^{2} + 158q^{3} - 344q^{4} + 352q^{5} + 4368q^{6} - 2758q^{7} + 1424q^{8} - 11628q^{9} + O(q^{10}) \) \( 878q - 4q^{2} + 158q^{3} - 344q^{4} + 352q^{5} + 4368q^{6} - 2758q^{7} + 1424q^{8} - 11628q^{9} - 4692q^{10} - 109744q^{11} - 434320q^{12} + 258470q^{13} + 267072q^{14} - 586422q^{15} + 1634496q^{16} + 63774q^{17} - 4359812q^{18} - 9404q^{19} + 3277980q^{20} + 1863124q^{21} + 68592q^{22} + 53934q^{23} - 3727720q^{24} + 4399438q^{25} + 12695520q^{26} - 2152252q^{27} - 5161912q^{28} - 4307876q^{29} - 28678652q^{30} + 1005852q^{31} + 54633616q^{32} + 17285584q^{33} - 53682096q^{34} - 14276726q^{35} - 118931880q^{36} + 6023202q^{37} + 117230112q^{38} - 55844140q^{39} + 167248960q^{40} + 4940236q^{41} - 340456648q^{42} + 173446230q^{43} - 25460920q^{44} - 95141798q^{45} + 24967448q^{46} - 298361894q^{47} + 429751400q^{48} + 331049448q^{49} - 126115488q^{50} + 253264412q^{51} - 362935120q^{52} + 467993418q^{53} - 130000456q^{54} - 36232116q^{55} - 53022528q^{56} - 176735592q^{57} + 356543560q^{58} - 176837116q^{59} - 231131272q^{60} + 110282384q^{61} + 273577880q^{62} + 511442458q^{63} + 764733664q^{64} + 447916894q^{65} + 573711560q^{66} + 535990418q^{67} - 969283648q^{68} - 1007670132q^{69} - 1401948640q^{70} - 1090988692q^{71} + 977392504q^{72} + 713861754q^{73} + 2188462584q^{74} - 1303824246q^{75} + 875120008q^{76} + 25935928q^{77} - 1448704456q^{78} + 750500312q^{79} - 2174562432q^{80} + 1375360318q^{81} + 1080832776q^{82} + 928974710q^{83} + 3673592496q^{84} - 2162681882q^{85} + 3074251816q^{86} - 4838564236q^{87} - 2311113872q^{88} - 1605217032q^{89} - 10365321320q^{90} + 2129646988q^{91} - 144567840q^{92} + 3624143176q^{93} + 4867285360q^{94} + 1612367188q^{95} + 18717655632q^{96} - 787562518q^{97} + 2236117908q^{98} - 11854403736q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.10.a \(\chi_{80}(1, \cdot)\) 80.10.a.a 1 1
80.10.a.b 1
80.10.a.c 1
80.10.a.d 1
80.10.a.e 1
80.10.a.f 2
80.10.a.g 2
80.10.a.h 2
80.10.a.i 2
80.10.a.j 2
80.10.a.k 3
80.10.c \(\chi_{80}(49, \cdot)\) 80.10.c.a 4 1
80.10.c.b 4
80.10.c.c 4
80.10.c.d 14
80.10.d \(\chi_{80}(41, \cdot)\) None 0 1
80.10.f \(\chi_{80}(9, \cdot)\) None 0 1
80.10.j \(\chi_{80}(43, \cdot)\) 80.10.j.a 212 2
80.10.l \(\chi_{80}(21, \cdot)\) 80.10.l.a 144 2
80.10.n \(\chi_{80}(47, \cdot)\) 80.10.n.a 2 2
80.10.n.b 16
80.10.n.c 36
80.10.o \(\chi_{80}(7, \cdot)\) None 0 2
80.10.q \(\chi_{80}(29, \cdot)\) 80.10.q.a 212 2
80.10.s \(\chi_{80}(3, \cdot)\) 80.10.s.a 212 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 174 T + 19683 T^{2} \))(\( 1 + 46 T + 19683 T^{2} \))(\( 1 - 48 T + 19683 T^{2} \))(\( 1 - 114 T + 19683 T^{2} \))(\( 1 - 204 T + 19683 T^{2} \))(\( 1 + 260 T + 52230 T^{2} + 5117580 T^{3} + 387420489 T^{4} \))(\( 1 + 108 T + 15786 T^{2} + 2125764 T^{3} + 387420489 T^{4} \))(\( 1 - 92 T + 17286 T^{2} - 1810836 T^{3} + 387420489 T^{4} \))(\( 1 - 116 T + 7530 T^{2} - 2283228 T^{3} + 387420489 T^{4} \))(\( 1 - 260 T + 36042 T^{2} - 5117580 T^{3} + 387420489 T^{4} \))(\( 1 + 84 T + 9513 T^{2} + 2615544 T^{3} + 187244379 T^{4} + 32543321076 T^{5} + 7625597484987 T^{6} \))(\( 1 - 3380 T^{2} + 40679478 T^{4} - 1309481252820 T^{6} + 150094635296999121 T^{8} \))(\( 1 - 34844 T^{2} + 897243462 T^{4} - 13499279518716 T^{6} + 150094635296999121 T^{8} \))(\( 1 - 45180 T^{2} + 1049244678 T^{4} - 17503657693020 T^{6} + 150094635296999121 T^{8} \))(\( 1 - 93742 T^{2} + 4759475539 T^{4} - 176347473539148 T^{6} + 5386668367500943641 T^{8} - \)\(14\!\cdots\!22\)\( T^{10} + \)\(33\!\cdots\!39\)\( T^{12} - \)\(70\!\cdots\!88\)\( T^{14} + \)\(13\!\cdots\!71\)\( T^{16} - \)\(21\!\cdots\!62\)\( T^{18} + \)\(31\!\cdots\!29\)\( T^{20} - \)\(39\!\cdots\!68\)\( T^{22} + \)\(41\!\cdots\!11\)\( T^{24} - \)\(31\!\cdots\!62\)\( T^{26} + \)\(13\!\cdots\!29\)\( T^{28} \))(\( 1 + 387420489 T^{4} \))(\( 1 - 1136193188 T^{4} + 814764797677189188 T^{8} - \)\(45\!\cdots\!36\)\( T^{12} + \)\(19\!\cdots\!70\)\( T^{16} - \)\(67\!\cdots\!56\)\( T^{20} + \)\(18\!\cdots\!08\)\( T^{24} - \)\(38\!\cdots\!68\)\( T^{28} + \)\(50\!\cdots\!81\)\( T^{32} \))
$5$ (\( 1 + 625 T \))(\( 1 + 625 T \))(\( 1 - 625 T \))(\( 1 + 625 T \))(\( 1 - 625 T \))(\( ( 1 - 625 T )^{2} \))(\( ( 1 + 625 T )^{2} \))(\( ( 1 - 625 T )^{2} \))(\( ( 1 + 625 T )^{2} \))(\( ( 1 + 625 T )^{2} \))(\( ( 1 - 625 T )^{3} \))(\( 1 + 2580 T + 3528750 T^{2} + 5039062500 T^{3} + 3814697265625 T^{4} \))(\( 1 - 660 T + 318750 T^{2} - 1289062500 T^{3} + 3814697265625 T^{4} \))(\( 1 - 1140 T + 1318750 T^{2} - 2226562500 T^{3} + 3814697265625 T^{4} \))(\( 1 - 1138 T - 298345 T^{2} + 2116016700 T^{3} - 6164172423375 T^{4} + 3490502269781250 T^{5} + 8054678883193359375 T^{6} - \)\(17\!\cdots\!00\)\( T^{7} + \)\(15\!\cdots\!75\)\( T^{8} + \)\(13\!\cdots\!50\)\( T^{9} - \)\(45\!\cdots\!75\)\( T^{10} + \)\(30\!\cdots\!00\)\( T^{11} - \)\(84\!\cdots\!25\)\( T^{12} - \)\(63\!\cdots\!50\)\( T^{13} + \)\(10\!\cdots\!25\)\( T^{14} \))(\( 1 + 1436 T + 1953125 T^{2} \))(\( ( 1 - 150 T - 1677000 T^{2} + 1428168750 T^{3} + 4828636718750 T^{4} + 2789392089843750 T^{5} - 6397247314453125000 T^{6} - \)\(11\!\cdots\!50\)\( T^{7} + \)\(14\!\cdots\!25\)\( T^{8} )^{2} \))
$7$ (\( 1 + 4658 T + 40353607 T^{2} \))(\( 1 - 10318 T + 40353607 T^{2} \))(\( 1 - 532 T + 40353607 T^{2} \))(\( 1 + 4242 T + 40353607 T^{2} \))(\( 1 + 5432 T + 40353607 T^{2} \))(\( 1 + 1700 T + 35221550 T^{2} + 68601131900 T^{3} + 1628413597910449 T^{4} \))(\( 1 - 908 T + 76435506 T^{2} - 36641075156 T^{3} + 1628413597910449 T^{4} \))(\( 1 - 6908 T + 59513006 T^{2} - 278762717156 T^{3} + 1628413597910449 T^{4} \))(\( 1 + 11284 T + 69419378 T^{2} + 455350101388 T^{3} + 1628413597910449 T^{4} \))(\( 1 - 380 T - 15543150 T^{2} - 15334370660 T^{3} + 1628413597910449 T^{4} \))(\( 1 - 5520 T + 62218149 T^{2} - 328164567136 T^{3} + 2510726733013443 T^{4} - 8988843060465678480 T^{5} + \)\(65\!\cdots\!43\)\( T^{6} \))(\( 1 - 26720900 T^{2} + 1462069499709798 T^{4} - \)\(43\!\cdots\!00\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 153156620 T^{2} + 9120528185156598 T^{4} - \)\(24\!\cdots\!80\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 57246700 T^{2} + 3508143545353398 T^{4} - \)\(93\!\cdots\!00\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 259361446 T^{2} + 35746542547041547 T^{4} - \)\(34\!\cdots\!24\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} - \)\(16\!\cdots\!90\)\( T^{10} + \)\(84\!\cdots\!55\)\( T^{12} - \)\(36\!\cdots\!80\)\( T^{14} + \)\(13\!\cdots\!95\)\( T^{16} - \)\(43\!\cdots\!90\)\( T^{18} + \)\(11\!\cdots\!49\)\( T^{20} - \)\(24\!\cdots\!24\)\( T^{22} + \)\(40\!\cdots\!03\)\( T^{24} - \)\(48\!\cdots\!46\)\( T^{26} + \)\(30\!\cdots\!49\)\( T^{28} \))(\( 1 + 1628413597910449 T^{4} \))(\( 1 - 701053336331908 T^{4} + \)\(26\!\cdots\!28\)\( T^{8} - \)\(24\!\cdots\!56\)\( T^{12} - \)\(49\!\cdots\!30\)\( T^{16} - \)\(65\!\cdots\!56\)\( T^{20} + \)\(18\!\cdots\!28\)\( T^{24} - \)\(13\!\cdots\!08\)\( T^{28} + \)\(49\!\cdots\!01\)\( T^{32} \))
$11$ (\( 1 + 28992 T + 2357947691 T^{2} \))(\( 1 - 5568 T + 2357947691 T^{2} \))(\( 1 - 33180 T + 2357947691 T^{2} \))(\( 1 - 46208 T + 2357947691 T^{2} \))(\( 1 + 73932 T + 2357947691 T^{2} \))(\( 1 + 23984 T + 1217213446 T^{2} + 56553017420944 T^{3} + 5559917313492231481 T^{4} \))(\( 1 + 25120 T + 4397886806 T^{2} + 59231645997920 T^{3} + 5559917313492231481 T^{4} \))(\( 1 - 8080 T + 4065472006 T^{2} - 19052217343280 T^{3} + 5559917313492231481 T^{4} \))(\( 1 - 101408 T + 6891283798 T^{2} - 239114759448928 T^{3} + 5559917313492231481 T^{4} \))(\( 1 + 102720 T + 7335543382 T^{2} + 242208386819520 T^{3} + 5559917313492231481 T^{4} \))(\( 1 + 5556 T + 2594856177 T^{2} + 72877014191416 T^{3} + 6118535131034237307 T^{4} + \)\(30\!\cdots\!36\)\( T^{5} + \)\(13\!\cdots\!71\)\( T^{6} \))(\( ( 1 - 51816 T + 3027030246 T^{2} - 122179417556856 T^{3} + 5559917313492231481 T^{4} )^{2} \))(\( ( 1 - 17400 T + 2292818982 T^{2} - 41028289823400 T^{3} + 5559917313492231481 T^{4} )^{2} \))(\( ( 1 + 54984 T + 5180465446 T^{2} + 129649395841944 T^{3} + 5559917313492231481 T^{4} )^{2} \))(\( ( 1 - 29692 T + 7596945533 T^{2} - 151295324016312 T^{3} + 31880247193689460701 T^{4} - \)\(45\!\cdots\!24\)\( T^{5} + \)\(93\!\cdots\!13\)\( T^{6} - \)\(93\!\cdots\!92\)\( T^{7} + \)\(22\!\cdots\!83\)\( T^{8} - \)\(25\!\cdots\!44\)\( T^{9} + \)\(41\!\cdots\!71\)\( T^{10} - \)\(46\!\cdots\!32\)\( T^{11} + \)\(55\!\cdots\!83\)\( T^{12} - \)\(51\!\cdots\!72\)\( T^{13} + \)\(40\!\cdots\!31\)\( T^{14} )^{2} \))(\( ( 1 - 2357947691 T^{2} )^{2} \))(\( ( 1 - 8548727028 T^{2} + 38998875797591474468 T^{4} - \)\(11\!\cdots\!76\)\( T^{6} + \)\(29\!\cdots\!70\)\( T^{8} - \)\(65\!\cdots\!56\)\( T^{10} + \)\(12\!\cdots\!48\)\( T^{12} - \)\(14\!\cdots\!48\)\( T^{14} + \)\(95\!\cdots\!21\)\( T^{16} )^{2} \))
$13$ (\( 1 + 164446 T + 10604499373 T^{2} \))(\( 1 - 45986 T + 10604499373 T^{2} \))(\( 1 + 99682 T + 10604499373 T^{2} \))(\( 1 + 115934 T + 10604499373 T^{2} \))(\( 1 + 114514 T + 10604499373 T^{2} \))(\( 1 - 115020 T + 22672043710 T^{2} - 1219729517882460 T^{3} + \)\(11\!\cdots\!29\)\( T^{4} \))(\( 1 - 146948 T + 18650572638 T^{2} - 1558309973863604 T^{3} + \)\(11\!\cdots\!29\)\( T^{4} \))(\( 1 - 111948 T + 22805544638 T^{2} - 1187152495808604 T^{3} + \)\(11\!\cdots\!29\)\( T^{4} \))(\( 1 + 21372 T + 21196469342 T^{2} + 226639360599756 T^{3} + \)\(11\!\cdots\!29\)\( T^{4} \))(\( 1 - 179140 T + 22798610142 T^{2} - 1899690017679220 T^{3} + \)\(11\!\cdots\!29\)\( T^{4} \))(\( 1 + 83094 T + 20077033299 T^{2} + 754871996338436 T^{3} + \)\(21\!\cdots\!27\)\( T^{4} + \)\(93\!\cdots\!26\)\( T^{5} + \)\(11\!\cdots\!17\)\( T^{6} \))(\( 1 - 22383928660 T^{2} + \)\(29\!\cdots\!58\)\( T^{4} - \)\(25\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!41\)\( T^{8} \))(\( 1 - 14000436724 T^{2} + 83025702170976147702 T^{4} - \)\(15\!\cdots\!96\)\( T^{6} + \)\(12\!\cdots\!41\)\( T^{8} \))(\( 1 - 35613791860 T^{2} + \)\(53\!\cdots\!58\)\( T^{4} - \)\(40\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!41\)\( T^{8} \))(\( 1 - 61833347974 T^{2} + \)\(22\!\cdots\!47\)\( T^{4} - \)\(57\!\cdots\!76\)\( T^{6} + \)\(11\!\cdots\!41\)\( T^{8} - \)\(18\!\cdots\!10\)\( T^{10} + \)\(25\!\cdots\!55\)\( T^{12} - \)\(29\!\cdots\!20\)\( T^{14} + \)\(28\!\cdots\!95\)\( T^{16} - \)\(23\!\cdots\!10\)\( T^{18} + \)\(16\!\cdots\!49\)\( T^{20} - \)\(91\!\cdots\!56\)\( T^{22} + \)\(40\!\cdots\!03\)\( T^{24} - \)\(12\!\cdots\!54\)\( T^{26} + \)\(22\!\cdots\!09\)\( T^{28} \))(\( ( 1 - 172316 T + 10604499373 T^{2} )( 1 + 112806 T + 10604499373 T^{2} ) \))(\( ( 1 + 22820 T + 260376200 T^{2} - 459643085995140 T^{3} - \)\(38\!\cdots\!84\)\( T^{4} - \)\(74\!\cdots\!60\)\( T^{5} + \)\(34\!\cdots\!00\)\( T^{6} + \)\(97\!\cdots\!20\)\( T^{7} + \)\(60\!\cdots\!46\)\( T^{8} + \)\(10\!\cdots\!60\)\( T^{9} + \)\(38\!\cdots\!00\)\( T^{10} - \)\(88\!\cdots\!20\)\( T^{11} - \)\(48\!\cdots\!44\)\( T^{12} - \)\(61\!\cdots\!20\)\( T^{13} + \)\(37\!\cdots\!00\)\( T^{14} + \)\(34\!\cdots\!40\)\( T^{15} + \)\(15\!\cdots\!81\)\( T^{16} )^{2} \))
$17$ (\( 1 + 594822 T + 118587876497 T^{2} \))(\( 1 + 381318 T + 118587876497 T^{2} \))(\( 1 + 443454 T + 118587876497 T^{2} \))(\( 1 - 494842 T + 118587876497 T^{2} \))(\( 1 - 41682 T + 118587876497 T^{2} \))(\( 1 - 412820 T + 113016614470 T^{2} - 48955447175491540 T^{3} + \)\(14\!\cdots\!09\)\( T^{4} \))(\( 1 - 169268 T + 244287370694 T^{2} - 20073132678894196 T^{3} + \)\(14\!\cdots\!09\)\( T^{4} \))(\( 1 + 327532 T + 241881460294 T^{2} + 38841324364815404 T^{3} + \)\(14\!\cdots\!09\)\( T^{4} \))(\( 1 + 296780 T + 144639901894 T^{2} + 35194509986779660 T^{3} + \)\(14\!\cdots\!09\)\( T^{4} \))(\( 1 - 316020 T + 259693705798 T^{2} - 37476140730581940 T^{3} + \)\(14\!\cdots\!09\)\( T^{4} \))(\( 1 - 367062 T + 268505189631 T^{2} - 69711192496917428 T^{3} + \)\(31\!\cdots\!07\)\( T^{4} - \)\(51\!\cdots\!58\)\( T^{5} + \)\(16\!\cdots\!73\)\( T^{6} \))(\( 1 - 468221105220 T^{2} + \)\(82\!\cdots\!18\)\( T^{4} - \)\(65\!\cdots\!80\)\( T^{6} + \)\(19\!\cdots\!81\)\( T^{8} \))(\( 1 - 181978394436 T^{2} + \)\(34\!\cdots\!42\)\( T^{4} - \)\(25\!\cdots\!24\)\( T^{6} + \)\(19\!\cdots\!81\)\( T^{8} \))(\( 1 - 285780369220 T^{2} + \)\(48\!\cdots\!18\)\( T^{4} - \)\(40\!\cdots\!80\)\( T^{6} + \)\(19\!\cdots\!81\)\( T^{8} \))(\( 1 - 488846414830 T^{2} + \)\(17\!\cdots\!23\)\( T^{4} - \)\(43\!\cdots\!60\)\( T^{6} + \)\(89\!\cdots\!81\)\( T^{8} - \)\(15\!\cdots\!14\)\( T^{10} + \)\(23\!\cdots\!15\)\( T^{12} - \)\(29\!\cdots\!72\)\( T^{14} + \)\(32\!\cdots\!35\)\( T^{16} - \)\(30\!\cdots\!34\)\( T^{18} + \)\(25\!\cdots\!49\)\( T^{20} - \)\(16\!\cdots\!60\)\( T^{22} + \)\(93\!\cdots\!27\)\( T^{24} - \)\(37\!\cdots\!30\)\( T^{26} + \)\(10\!\cdots\!69\)\( T^{28} \))(\( ( 1 - 407992 T + 118587876497 T^{2} )( 1 + 554882 T + 118587876497 T^{2} ) \))(\( ( 1 - 348780 T + 60823744200 T^{2} - 32159831018370660 T^{3} + \)\(29\!\cdots\!36\)\( T^{4} - \)\(80\!\cdots\!60\)\( T^{5} + \)\(15\!\cdots\!00\)\( T^{6} - \)\(78\!\cdots\!20\)\( T^{7} + \)\(38\!\cdots\!86\)\( T^{8} - \)\(92\!\cdots\!40\)\( T^{9} + \)\(21\!\cdots\!00\)\( T^{10} - \)\(13\!\cdots\!80\)\( T^{11} + \)\(59\!\cdots\!16\)\( T^{12} - \)\(75\!\cdots\!20\)\( T^{13} + \)\(16\!\cdots\!00\)\( T^{14} - \)\(11\!\cdots\!40\)\( T^{15} + \)\(39\!\cdots\!61\)\( T^{16} )^{2} \))
$19$ (\( 1 - 295780 T + 322687697779 T^{2} \))(\( 1 + 610460 T + 322687697779 T^{2} \))(\( 1 - 357244 T + 322687697779 T^{2} \))(\( 1 - 1008740 T + 322687697779 T^{2} \))(\( 1 + 1057460 T + 322687697779 T^{2} \))(\( 1 - 296520 T + 659218232758 T^{2} - 95683356145429080 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} \))(\( 1 - 25480 T + 371498689782 T^{2} - 8222082539408920 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} \))(\( 1 - 1156680 T + 686155308982 T^{2} - 373246406267013720 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} \))(\( 1 + 275832 T + 612347527414 T^{2} + 89007593053777128 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} \))(\( 1 + 137272 T + 111610161654 T^{2} + 44295985649518888 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} \))(\( 1 + 1489116 T + 1342580105481 T^{2} + 830560424045529832 T^{3} + \)\(43\!\cdots\!99\)\( T^{4} + \)\(15\!\cdots\!56\)\( T^{5} + \)\(33\!\cdots\!39\)\( T^{6} \))(\( ( 1 + 158760 T + 642783370358 T^{2} + 51229898899394040 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} )^{2} \))(\( ( 1 - 113832 T + 402567657014 T^{2} - 36732186013579128 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} )^{2} \))(\( ( 1 - 318440 T + 505756418358 T^{2} - 102756670480744760 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} )^{2} \))(\( ( 1 + 544252 T + 742560136309 T^{2} + 572575037587188728 T^{3} + \)\(48\!\cdots\!01\)\( T^{4} + \)\(29\!\cdots\!84\)\( T^{5} + \)\(20\!\cdots\!13\)\( T^{6} + \)\(11\!\cdots\!76\)\( T^{7} + \)\(67\!\cdots\!27\)\( T^{8} + \)\(30\!\cdots\!44\)\( T^{9} + \)\(16\!\cdots\!39\)\( T^{10} + \)\(62\!\cdots\!68\)\( T^{11} + \)\(25\!\cdots\!91\)\( T^{12} + \)\(61\!\cdots\!92\)\( T^{13} + \)\(36\!\cdots\!59\)\( T^{14} )^{2} \))(\( ( 1 + 322687697779 T^{2} )^{2} \))(\( ( 1 + 37278684232 T^{2} + \)\(87\!\cdots\!48\)\( T^{4} - \)\(92\!\cdots\!16\)\( T^{6} + \)\(17\!\cdots\!70\)\( T^{8} - \)\(96\!\cdots\!56\)\( T^{10} + \)\(94\!\cdots\!88\)\( T^{12} + \)\(42\!\cdots\!72\)\( T^{14} + \)\(11\!\cdots\!61\)\( T^{16} )^{2} \))
$23$ (\( 1 + 2544534 T + 1801152661463 T^{2} \))(\( 1 - 1447914 T + 1801152661463 T^{2} \))(\( 1 - 142956 T + 1801152661463 T^{2} \))(\( 1 - 532554 T + 1801152661463 T^{2} \))(\( 1 + 1599336 T + 1801152661463 T^{2} \))(\( 1 - 1049220 T + 3497852029390 T^{2} - 1889805395460208860 T^{3} + \)\(32\!\cdots\!69\)\( T^{4} \))(\( 1 + 1782748 T + 3965893132658 T^{2} + 3211001304917840324 T^{3} + \)\(32\!\cdots\!69\)\( T^{4} \))(\( 1 - 1057252 T + 1690239470158 T^{2} - 1904272253637079676 T^{3} + \)\(32\!\cdots\!69\)\( T^{4} \))(\( 1 - 585284 T + 3430385383090 T^{2} - 1054185834311710492 T^{3} + \)\(32\!\cdots\!69\)\( T^{4} \))(\( 1 - 665460 T + 2886450615250 T^{2} - 1198595050097167980 T^{3} + \)\(32\!\cdots\!69\)\( T^{4} \))(\( 1 - 499920 T - 191246545323 T^{2} + 4150866877865471776 T^{3} - \)\(34\!\cdots\!49\)\( T^{4} - \)\(16\!\cdots\!80\)\( T^{5} + \)\(58\!\cdots\!47\)\( T^{6} \))(\( 1 - 1626654345540 T^{2} + \)\(46\!\cdots\!38\)\( T^{4} - \)\(52\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 + 820282526580 T^{2} + \)\(11\!\cdots\!38\)\( T^{4} + \)\(26\!\cdots\!20\)\( T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 5779790962540 T^{2} + \)\(14\!\cdots\!38\)\( T^{4} - \)\(18\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 13986110408070 T^{2} + \)\(10\!\cdots\!23\)\( T^{4} - \)\(49\!\cdots\!60\)\( T^{6} + \)\(18\!\cdots\!61\)\( T^{8} - \)\(53\!\cdots\!62\)\( T^{10} + \)\(12\!\cdots\!95\)\( T^{12} - \)\(25\!\cdots\!96\)\( T^{14} + \)\(41\!\cdots\!55\)\( T^{16} - \)\(56\!\cdots\!82\)\( T^{18} + \)\(62\!\cdots\!49\)\( T^{20} - \)\(55\!\cdots\!60\)\( T^{22} + \)\(36\!\cdots\!27\)\( T^{24} - \)\(16\!\cdots\!70\)\( T^{26} + \)\(37\!\cdots\!89\)\( T^{28} \))(\( 1 + \)\(32\!\cdots\!69\)\( T^{4} \))(\( 1 - \)\(87\!\cdots\!48\)\( T^{4} + \)\(59\!\cdots\!08\)\( T^{8} - \)\(25\!\cdots\!96\)\( T^{12} + \)\(95\!\cdots\!70\)\( T^{16} - \)\(26\!\cdots\!56\)\( T^{20} + \)\(65\!\cdots\!68\)\( T^{24} - \)\(10\!\cdots\!88\)\( T^{28} + \)\(12\!\cdots\!41\)\( T^{32} \))
$29$ (\( 1 + 3722970 T + 14507145975869 T^{2} \))(\( 1 - 5385510 T + 14507145975869 T^{2} \))(\( 1 - 1527966 T + 14507145975869 T^{2} \))(\( 1 - 4196390 T + 14507145975869 T^{2} \))(\( 1 - 2184510 T + 14507145975869 T^{2} \))(\( 1 + 3666980 T + 20832571957438 T^{2} + 53197414150592105620 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 - 7323340 T + 29495257443614 T^{2} - \)\(10\!\cdots\!60\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 + 4212260 T + 32604383130814 T^{2} + 61107870708313953940 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 + 9928756 T + 50878662529822 T^{2} + \)\(14\!\cdots\!64\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 + 6893748 T + 40195999658014 T^{2} + \)\(10\!\cdots\!12\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 - 5234682 T + 42736985914563 T^{2} - \)\(14\!\cdots\!08\)\( T^{3} + \)\(61\!\cdots\!47\)\( T^{4} - \)\(11\!\cdots\!02\)\( T^{5} + \)\(30\!\cdots\!09\)\( T^{6} \))(\( ( 1 - 3334140 T + 25948591194238 T^{2} - 48368855683983867660 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 - 3132828 T + 12854589500734 T^{2} - 45448393113289727532 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 + 1765860 T + 26950935551038 T^{2} + 25617588792948032340 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 + 6202286 T + 52806733369727 T^{2} + \)\(14\!\cdots\!64\)\( T^{3} + \)\(73\!\cdots\!81\)\( T^{4} + \)\(33\!\cdots\!82\)\( T^{5} + \)\(49\!\cdots\!47\)\( T^{6} - \)\(10\!\cdots\!36\)\( T^{7} + \)\(71\!\cdots\!43\)\( T^{8} + \)\(71\!\cdots\!02\)\( T^{9} + \)\(22\!\cdots\!29\)\( T^{10} + \)\(65\!\cdots\!44\)\( T^{11} + \)\(33\!\cdots\!23\)\( T^{12} + \)\(57\!\cdots\!66\)\( T^{13} + \)\(13\!\cdots\!89\)\( T^{14} )^{2} \))(\( ( 1 - 7314710 T + 14507145975869 T^{2} )( 1 + 7314710 T + 14507145975869 T^{2} ) \))(\( ( 1 - 65546926289448 T^{2} + \)\(17\!\cdots\!08\)\( T^{4} - \)\(23\!\cdots\!96\)\( T^{6} + \)\(28\!\cdots\!70\)\( T^{8} - \)\(50\!\cdots\!56\)\( T^{10} + \)\(75\!\cdots\!68\)\( T^{12} - \)\(61\!\cdots\!88\)\( T^{14} + \)\(19\!\cdots\!41\)\( T^{16} )^{2} \))
$31$ (\( 1 + 2335772 T + 26439622160671 T^{2} \))(\( 1 + 3053852 T + 26439622160671 T^{2} \))(\( 1 + 7323416 T + 26439622160671 T^{2} \))(\( 1 - 3365028 T + 26439622160671 T^{2} \))(\( 1 - 9619648 T + 26439622160671 T^{2} \))(\( 1 + 1613144 T + 29382323902526 T^{2} + 42650917850753459624 T^{3} + \)\(69\!\cdots\!41\)\( T^{4} \))(\( 1 + 10677272 T + 73017326150862 T^{2} + \)\(28\!\cdots\!12\)\( T^{3} + \)\(69\!\cdots\!41\)\( T^{4} \))(\( 1 - 11361128 T + 71055092544062 T^{2} - \)\(30\!\cdots\!88\)\( T^{3} + \)\(69\!\cdots\!41\)\( T^{4} \))(\( 1 + 5131480 T + 36749057608142 T^{2} + \)\(13\!\cdots\!80\)\( T^{3} + \)\(69\!\cdots\!41\)\( T^{4} \))(\( 1 + 291832 T + 38964935800398 T^{2} + 7715927814392939272 T^{3} + \)\(69\!\cdots\!41\)\( T^{4} \))(\( 1 + 12708912 T + 128130963574173 T^{2} + \)\(72\!\cdots\!04\)\( T^{3} + \)\(33\!\cdots\!83\)\( T^{4} + \)\(88\!\cdots\!92\)\( T^{5} + \)\(18\!\cdots\!11\)\( T^{6} \))(\( ( 1 + 9623744 T + 71729043019326 T^{2} + \)\(25\!\cdots\!24\)\( T^{3} + \)\(69\!\cdots\!41\)\( T^{4} )^{2} \))(\( ( 1 + 187232 T + 40099942836798 T^{2} + 4950343336386752672 T^{3} + \)\(69\!\cdots\!41\)\( T^{4} )^{2} \))(\( ( 1 - 5293856 T + 59464921598526 T^{2} - \)\(13\!\cdots\!76\)\( T^{3} + \)\(69\!\cdots\!41\)\( T^{4} )^{2} \))(\( ( 1 - 3332736 T + 65032381480921 T^{2} - \)\(51\!\cdots\!36\)\( T^{3} + \)\(31\!\cdots\!81\)\( T^{4} - \)\(22\!\cdots\!40\)\( T^{5} + \)\(14\!\cdots\!25\)\( T^{6} - \)\(61\!\cdots\!20\)\( T^{7} + \)\(38\!\cdots\!75\)\( T^{8} - \)\(15\!\cdots\!40\)\( T^{9} + \)\(58\!\cdots\!91\)\( T^{10} - \)\(25\!\cdots\!16\)\( T^{11} + \)\(84\!\cdots\!71\)\( T^{12} - \)\(11\!\cdots\!56\)\( T^{13} + \)\(90\!\cdots\!91\)\( T^{14} )^{2} \))(\( ( 1 - 26439622160671 T^{2} )^{2} \))(\( ( 1 - 157811224054868 T^{2} + \)\(11\!\cdots\!48\)\( T^{4} - \)\(53\!\cdots\!16\)\( T^{6} + \)\(16\!\cdots\!70\)\( T^{8} - \)\(37\!\cdots\!56\)\( T^{10} + \)\(56\!\cdots\!88\)\( T^{12} - \)\(53\!\cdots\!28\)\( T^{14} + \)\(23\!\cdots\!61\)\( T^{16} )^{2} \))
$37$ (\( 1 - 10840418 T + 129961739795077 T^{2} \))(\( 1 - 12889442 T + 129961739795077 T^{2} \))(\( 1 + 2666842 T + 129961739795077 T^{2} \))(\( 1 + 14931358 T + 129961739795077 T^{2} \))(\( 1 - 4799942 T + 129961739795077 T^{2} \))(\( 1 + 21121940 T + 328931801286510 T^{2} + \)\(27\!\cdots\!80\)\( T^{3} + \)\(16\!\cdots\!29\)\( T^{4} \))(\( 1 + 5750460 T + 104099098360718 T^{2} + \)\(74\!\cdots\!20\)\( T^{3} + \)\(16\!\cdots\!29\)\( T^{4} \))(\( 1 + 7251860 T + 207906306187118 T^{2} + \)\(94\!\cdots\!20\)\( T^{3} + \)\(16\!\cdots\!29\)\( T^{4} \))(\( 1 + 11007932 T + 240473943386510 T^{2} + \)\(14\!\cdots\!64\)\( T^{3} + \)\(16\!\cdots\!29\)\( T^{4} \))(\( 1 - 11261380 T + 218879982937230 T^{2} - \)\(14\!\cdots\!60\)\( T^{3} + \)\(16\!\cdots\!29\)\( T^{4} \))(\( 1 - 21724434 T + 286542561812475 T^{2} - \)\(28\!\cdots\!32\)\( T^{3} + \)\(37\!\cdots\!75\)\( T^{4} - \)\(36\!\cdots\!86\)\( T^{5} + \)\(21\!\cdots\!33\)\( T^{6} \))(\( 1 + 73233430078540 T^{2} + \)\(20\!\cdots\!58\)\( T^{4} + \)\(12\!\cdots\!60\)\( T^{6} + \)\(28\!\cdots\!41\)\( T^{8} \))(\( 1 - 462603258659540 T^{2} + \)\(87\!\cdots\!58\)\( T^{4} - \)\(78\!\cdots\!60\)\( T^{6} + \)\(28\!\cdots\!41\)\( T^{8} \))(\( 1 - 231603274936660 T^{2} + \)\(44\!\cdots\!58\)\( T^{4} - \)\(39\!\cdots\!40\)\( T^{6} + \)\(28\!\cdots\!41\)\( T^{8} \))(\( 1 - 1025915145171286 T^{2} + \)\(51\!\cdots\!87\)\( T^{4} - \)\(16\!\cdots\!84\)\( T^{6} + \)\(41\!\cdots\!01\)\( T^{8} - \)\(81\!\cdots\!38\)\( T^{10} + \)\(13\!\cdots\!23\)\( T^{12} - \)\(19\!\cdots\!96\)\( T^{14} + \)\(22\!\cdots\!67\)\( T^{16} - \)\(23\!\cdots\!58\)\( T^{18} + \)\(19\!\cdots\!89\)\( T^{20} - \)\(13\!\cdots\!04\)\( T^{22} + \)\(70\!\cdots\!63\)\( T^{24} - \)\(23\!\cdots\!06\)\( T^{26} + \)\(39\!\cdots\!09\)\( T^{28} \))(\( ( 1 - 1923372 T + 129961739795077 T^{2} )( 1 + 22718882 T + 129961739795077 T^{2} ) \))(\( ( 1 - 28334920 T + 401433845703200 T^{2} - \)\(35\!\cdots\!40\)\( T^{3} + \)\(15\!\cdots\!16\)\( T^{4} + \)\(54\!\cdots\!60\)\( T^{5} - \)\(14\!\cdots\!00\)\( T^{6} + \)\(25\!\cdots\!20\)\( T^{7} - \)\(34\!\cdots\!54\)\( T^{8} + \)\(33\!\cdots\!40\)\( T^{9} - \)\(23\!\cdots\!00\)\( T^{10} + \)\(12\!\cdots\!80\)\( T^{11} + \)\(42\!\cdots\!56\)\( T^{12} - \)\(13\!\cdots\!80\)\( T^{13} + \)\(19\!\cdots\!00\)\( T^{14} - \)\(17\!\cdots\!60\)\( T^{15} + \)\(81\!\cdots\!81\)\( T^{16} )^{2} \))
$41$ (\( 1 - 21593862 T + 327381934393961 T^{2} \))(\( 1 + 33786618 T + 327381934393961 T^{2} \))(\( 1 + 7939014 T + 327381934393961 T^{2} \))(\( 1 - 11056262 T + 327381934393961 T^{2} \))(\( 1 - 9531882 T + 327381934393961 T^{2} \))(\( 1 + 26957276 T + 811945448362966 T^{2} + \)\(88\!\cdots\!36\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))(\( 1 + 7795764 T + 505248245475190 T^{2} + \)\(25\!\cdots\!04\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))(\( 1 - 13030436 T - 112698304084010 T^{2} - \)\(42\!\cdots\!96\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))(\( 1 + 41835956 T + 1084325213081206 T^{2} + \)\(13\!\cdots\!16\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))(\( 1 - 29773452 T + 771012402449398 T^{2} - \)\(97\!\cdots\!72\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))(\( 1 - 27440478 T + 1215792148252263 T^{2} - \)\(18\!\cdots\!72\)\( T^{3} + \)\(39\!\cdots\!43\)\( T^{4} - \)\(29\!\cdots\!38\)\( T^{5} + \)\(35\!\cdots\!81\)\( T^{6} \))(\( ( 1 - 11387124 T + 602060396517366 T^{2} - \)\(37\!\cdots\!64\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} )^{2} \))(\( ( 1 + 8824068 T + 671552976228678 T^{2} + \)\(28\!\cdots\!48\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} )^{2} \))(\( ( 1 + 8394276 T + 221313076168966 T^{2} + \)\(27\!\cdots\!36\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} )^{2} \))(\( ( 1 - 5794478 T + 825450149265203 T^{2} + \)\(46\!\cdots\!92\)\( T^{3} + \)\(31\!\cdots\!81\)\( T^{4} + \)\(62\!\cdots\!38\)\( T^{5} + \)\(91\!\cdots\!31\)\( T^{6} + \)\(27\!\cdots\!44\)\( T^{7} + \)\(29\!\cdots\!91\)\( T^{8} + \)\(67\!\cdots\!98\)\( T^{9} + \)\(11\!\cdots\!61\)\( T^{10} + \)\(52\!\cdots\!72\)\( T^{11} + \)\(31\!\cdots\!03\)\( T^{12} - \)\(71\!\cdots\!58\)\( T^{13} + \)\(40\!\cdots\!21\)\( T^{14} )^{2} \))(\( ( 1 + 7561912 T + 327381934393961 T^{2} )^{2} \))(\( ( 1 + 4650498 T + 372490914476608 T^{2} - \)\(90\!\cdots\!54\)\( T^{3} - \)\(21\!\cdots\!30\)\( T^{4} - \)\(29\!\cdots\!94\)\( T^{5} + \)\(39\!\cdots\!68\)\( T^{6} + \)\(16\!\cdots\!38\)\( T^{7} + \)\(11\!\cdots\!41\)\( T^{8} )^{4} \))
$43$ (\( 1 + 10832294 T + 502592611936843 T^{2} \))(\( 1 - 36886234 T + 502592611936843 T^{2} \))(\( 1 - 21174520 T + 502592611936843 T^{2} \))(\( 1 - 6396794 T + 502592611936843 T^{2} \))(\( 1 - 13464484 T + 502592611936843 T^{2} \))(\( 1 + 52889700 T + 1703843788760950 T^{2} + \)\(26\!\cdots\!00\)\( T^{3} + \)\(25\!\cdots\!49\)\( T^{4} \))(\( 1 + 16770524 T + 1074543668703834 T^{2} + \)\(84\!\cdots\!32\)\( T^{3} + \)\(25\!\cdots\!49\)\( T^{4} \))(\( 1 - 47934076 T + 1577772318092534 T^{2} - \)\(24\!\cdots\!68\)\( T^{3} + \)\(25\!\cdots\!49\)\( T^{4} \))(\( 1 - 23394052 T + 925906061281562 T^{2} - \)\(11\!\cdots\!36\)\( T^{3} + \)\(25\!\cdots\!49\)\( T^{4} \))(\( 1 - 11708180 T + 838769843899386 T^{2} - \)\(58\!\cdots\!40\)\( T^{3} + \)\(25\!\cdots\!49\)\( T^{4} \))(\( 1 - 23218260 T + 251755624778721 T^{2} - \)\(25\!\cdots\!68\)\( T^{3} + \)\(12\!\cdots\!03\)\( T^{4} - \)\(58\!\cdots\!40\)\( T^{5} + \)\(12\!\cdots\!07\)\( T^{6} \))(\( 1 - 1938214042750100 T^{2} + \)\(14\!\cdots\!98\)\( T^{4} - \)\(48\!\cdots\!00\)\( T^{6} + \)\(63\!\cdots\!01\)\( T^{8} \))(\( 1 - 358707990293372 T^{2} + \)\(21\!\cdots\!94\)\( T^{4} - \)\(90\!\cdots\!28\)\( T^{6} + \)\(63\!\cdots\!01\)\( T^{8} \))(\( 1 - 614109141147100 T^{2} + \)\(57\!\cdots\!98\)\( T^{4} - \)\(15\!\cdots\!00\)\( T^{6} + \)\(63\!\cdots\!01\)\( T^{8} \))(\( 1 - 4167742879568894 T^{2} + \)\(88\!\cdots\!27\)\( T^{4} - \)\(12\!\cdots\!36\)\( T^{6} + \)\(13\!\cdots\!01\)\( T^{8} - \)\(11\!\cdots\!10\)\( T^{10} + \)\(76\!\cdots\!55\)\( T^{12} - \)\(42\!\cdots\!20\)\( T^{14} + \)\(19\!\cdots\!95\)\( T^{16} - \)\(72\!\cdots\!10\)\( T^{18} + \)\(21\!\cdots\!49\)\( T^{20} - \)\(51\!\cdots\!36\)\( T^{22} + \)\(91\!\cdots\!23\)\( T^{24} - \)\(10\!\cdots\!94\)\( T^{26} + \)\(65\!\cdots\!49\)\( T^{28} \))(\( 1 + \)\(25\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(22\!\cdots\!92\)\( T^{4} - \)\(14\!\cdots\!72\)\( T^{8} - \)\(15\!\cdots\!56\)\( T^{12} + \)\(11\!\cdots\!70\)\( T^{16} - \)\(97\!\cdots\!56\)\( T^{20} - \)\(60\!\cdots\!72\)\( T^{24} + \)\(58\!\cdots\!92\)\( T^{28} + \)\(16\!\cdots\!01\)\( T^{32} \))
$47$ (\( 1 + 5172138 T + 1119130473102767 T^{2} \))(\( 1 - 44163798 T + 1119130473102767 T^{2} \))(\( 1 + 16059636 T + 1119130473102767 T^{2} \))(\( 1 - 35559158 T + 1119130473102767 T^{2} \))(\( 1 + 11441952 T + 1119130473102767 T^{2} \))(\( 1 + 58412180 T + 2814913257457630 T^{2} + \)\(65\!\cdots\!60\)\( T^{3} + \)\(12\!\cdots\!89\)\( T^{4} \))(\( 1 + 15393892 T + 1097719682118050 T^{2} + \)\(17\!\cdots\!64\)\( T^{3} + \)\(12\!\cdots\!89\)\( T^{4} \))(\( 1 + 30914292 T + 2034610190905950 T^{2} + \)\(34\!\cdots\!64\)\( T^{3} + \)\(12\!\cdots\!89\)\( T^{4} \))(\( 1 + 11711748 T - 733120788879390 T^{2} + \)\(13\!\cdots\!16\)\( T^{3} + \)\(12\!\cdots\!89\)\( T^{4} \))(\( 1 + 62493300 T + 3177958884734338 T^{2} + \)\(69\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!89\)\( T^{4} \))(\( 1 - 28701528 T + 2689800471894429 T^{2} - \)\(45\!\cdots\!28\)\( T^{3} + \)\(30\!\cdots\!43\)\( T^{4} - \)\(35\!\cdots\!92\)\( T^{5} + \)\(14\!\cdots\!63\)\( T^{6} \))(\( 1 - 3434853059674980 T^{2} + \)\(54\!\cdots\!78\)\( T^{4} - \)\(43\!\cdots\!20\)\( T^{6} + \)\(15\!\cdots\!21\)\( T^{8} \))(\( 1 - 1037666802860076 T^{2} + \)\(16\!\cdots\!22\)\( T^{4} - \)\(12\!\cdots\!64\)\( T^{6} + \)\(15\!\cdots\!21\)\( T^{8} \))(\( 1 - 1368976020813580 T^{2} + \)\(29\!\cdots\!78\)\( T^{4} - \)\(17\!\cdots\!20\)\( T^{6} + \)\(15\!\cdots\!21\)\( T^{8} \))(\( 1 - 10781677744658806 T^{2} + \)\(55\!\cdots\!67\)\( T^{4} - \)\(18\!\cdots\!24\)\( T^{6} + \)\(43\!\cdots\!81\)\( T^{8} - \)\(80\!\cdots\!38\)\( T^{10} + \)\(12\!\cdots\!83\)\( T^{12} - \)\(14\!\cdots\!36\)\( T^{14} + \)\(15\!\cdots\!87\)\( T^{16} - \)\(12\!\cdots\!98\)\( T^{18} + \)\(85\!\cdots\!89\)\( T^{20} - \)\(44\!\cdots\!84\)\( T^{22} + \)\(17\!\cdots\!83\)\( T^{24} - \)\(41\!\cdots\!66\)\( T^{26} + \)\(48\!\cdots\!29\)\( T^{28} \))(\( 1 + \)\(12\!\cdots\!89\)\( T^{4} \))(\( 1 - \)\(98\!\cdots\!88\)\( T^{4} - \)\(31\!\cdots\!12\)\( T^{8} + \)\(10\!\cdots\!64\)\( T^{12} + \)\(61\!\cdots\!70\)\( T^{16} + \)\(16\!\cdots\!44\)\( T^{20} - \)\(76\!\cdots\!92\)\( T^{24} - \)\(38\!\cdots\!68\)\( T^{28} + \)\(60\!\cdots\!81\)\( T^{32} \))
$53$ (\( 1 - 98179674 T + 3299763591802133 T^{2} \))(\( 1 - 29746266 T + 3299763591802133 T^{2} \))(\( 1 + 87822234 T + 3299763591802133 T^{2} \))(\( 1 - 39738586 T + 3299763591802133 T^{2} \))(\( 1 - 53615766 T + 3299763591802133 T^{2} \))(\( 1 + 39035140 T + 5675030678030830 T^{2} + \)\(12\!\cdots\!20\)\( T^{3} + \)\(10\!\cdots\!89\)\( T^{4} \))(\( 1 + 58529292 T + 3439533688251982 T^{2} + \)\(19\!\cdots\!36\)\( T^{3} + \)\(10\!\cdots\!89\)\( T^{4} \))(\( 1 - 100922108 T + 9120851179993582 T^{2} - \)\(33\!\cdots\!64\)\( T^{3} + \)\(10\!\cdots\!89\)\( T^{4} \))(\( 1 + 46384268 T + 6816046668377422 T^{2} + \)\(15\!\cdots\!44\)\( T^{3} + \)\(10\!\cdots\!89\)\( T^{4} \))(\( 1 - 9417780 T + 5708185761526990 T^{2} - \)\(31\!\cdots\!40\)\( T^{3} + \)\(10\!\cdots\!89\)\( T^{4} \))(\( 1 + 45629982 T + 7541283402476907 T^{2} + \)\(30\!\cdots\!96\)\( T^{3} + \)\(24\!\cdots\!31\)\( T^{4} + \)\(49\!\cdots\!98\)\( T^{5} + \)\(35\!\cdots\!37\)\( T^{6} \))(\( 1 - 3945786642536180 T^{2} + \)\(65\!\cdots\!78\)\( T^{4} - \)\(42\!\cdots\!20\)\( T^{6} + \)\(11\!\cdots\!21\)\( T^{8} \))(\( 1 - 5310844341928340 T^{2} + \)\(28\!\cdots\!78\)\( T^{4} - \)\(57\!\cdots\!60\)\( T^{6} + \)\(11\!\cdots\!21\)\( T^{8} \))(\( 1 - 7684297973864980 T^{2} + \)\(36\!\cdots\!78\)\( T^{4} - \)\(83\!\cdots\!20\)\( T^{6} + \)\(11\!\cdots\!21\)\( T^{8} \))(\( 1 - 26261729912123190 T^{2} + \)\(32\!\cdots\!23\)\( T^{4} - \)\(25\!\cdots\!60\)\( T^{6} + \)\(14\!\cdots\!41\)\( T^{8} - \)\(71\!\cdots\!50\)\( T^{10} + \)\(29\!\cdots\!15\)\( T^{12} - \)\(10\!\cdots\!00\)\( T^{14} + \)\(32\!\cdots\!35\)\( T^{16} - \)\(84\!\cdots\!50\)\( T^{18} + \)\(19\!\cdots\!29\)\( T^{20} - \)\(35\!\cdots\!60\)\( T^{22} + \)\(49\!\cdots\!27\)\( T^{24} - \)\(43\!\cdots\!90\)\( T^{26} + \)\(18\!\cdots\!29\)\( T^{28} \))(\( ( 1 + 68323684 T + 3299763591802133 T^{2} )( 1 + 92363026 T + 3299763591802133 T^{2} ) \))(\( ( 1 - 189005520 T + 17861543295235200 T^{2} - \)\(12\!\cdots\!60\)\( T^{3} + \)\(96\!\cdots\!56\)\( T^{4} - \)\(73\!\cdots\!40\)\( T^{5} + \)\(50\!\cdots\!00\)\( T^{6} - \)\(31\!\cdots\!20\)\( T^{7} + \)\(18\!\cdots\!26\)\( T^{8} - \)\(10\!\cdots\!60\)\( T^{9} + \)\(55\!\cdots\!00\)\( T^{10} - \)\(26\!\cdots\!80\)\( T^{11} + \)\(11\!\cdots\!76\)\( T^{12} - \)\(50\!\cdots\!80\)\( T^{13} + \)\(23\!\cdots\!00\)\( T^{14} - \)\(80\!\cdots\!40\)\( T^{15} + \)\(14\!\cdots\!41\)\( T^{16} )^{2} \))
$59$ (\( 1 + 16162860 T + 8662995818654939 T^{2} \))(\( 1 - 65575380 T + 8662995818654939 T^{2} \))(\( 1 + 120625212 T + 8662995818654939 T^{2} \))(\( 1 - 85185620 T + 8662995818654939 T^{2} \))(\( 1 + 81862620 T + 8662995818654939 T^{2} \))(\( 1 - 54995560 T + 15674484224932678 T^{2} - \)\(47\!\cdots\!40\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} \))(\( 1 + 59618264 T + 11433756193805126 T^{2} + \)\(51\!\cdots\!96\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} \))(\( 1 - 47362536 T + 6051611540480326 T^{2} - \)\(41\!\cdots\!04\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} \))(\( 1 + 178239576 T + 18856238015031622 T^{2} + \)\(15\!\cdots\!64\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} \))(\( 1 - 92930856 T + 16656477955483462 T^{2} - \)\(80\!\cdots\!84\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} \))(\( 1 - 268721868 T + 46457702853914817 T^{2} - \)\(50\!\cdots\!40\)\( T^{3} + \)\(40\!\cdots\!63\)\( T^{4} - \)\(20\!\cdots\!28\)\( T^{5} + \)\(65\!\cdots\!19\)\( T^{6} \))(\( ( 1 + 127330680 T + 20590638486439878 T^{2} + \)\(11\!\cdots\!20\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} )^{2} \))(\( ( 1 + 219497736 T + 28852098295168902 T^{2} + \)\(19\!\cdots\!04\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} )^{2} \))(\( ( 1 - 230414520 T + 28555631923987078 T^{2} - \)\(19\!\cdots\!80\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} )^{2} \))(\( ( 1 - 43367052 T + 19626240684596429 T^{2} - \)\(14\!\cdots\!08\)\( T^{3} + \)\(35\!\cdots\!21\)\( T^{4} - \)\(18\!\cdots\!68\)\( T^{5} + \)\(39\!\cdots\!41\)\( T^{6} - \)\(22\!\cdots\!92\)\( T^{7} + \)\(34\!\cdots\!99\)\( T^{8} - \)\(13\!\cdots\!28\)\( T^{9} + \)\(23\!\cdots\!99\)\( T^{10} - \)\(80\!\cdots\!28\)\( T^{11} + \)\(95\!\cdots\!71\)\( T^{12} - \)\(18\!\cdots\!72\)\( T^{13} + \)\(36\!\cdots\!79\)\( T^{14} )^{2} \))(\( ( 1 + 8662995818654939 T^{2} )^{2} \))(\( ( 1 + 25255897035301512 T^{2} + \)\(26\!\cdots\!88\)\( T^{4} + \)\(71\!\cdots\!64\)\( T^{6} - \)\(32\!\cdots\!30\)\( T^{8} + \)\(53\!\cdots\!44\)\( T^{10} + \)\(14\!\cdots\!08\)\( T^{12} + \)\(10\!\cdots\!32\)\( T^{14} + \)\(31\!\cdots\!81\)\( T^{16} )^{2} \))
$61$ (\( 1 + 43928158 T + 11694146092834141 T^{2} \))(\( 1 - 40183202 T + 11694146092834141 T^{2} \))(\( 1 - 93576542 T + 11694146092834141 T^{2} \))(\( 1 - 45748642 T + 11694146092834141 T^{2} \))(\( 1 + 104691298 T + 11694146092834141 T^{2} \))(\( 1 + 274579716 T + 41753623519328446 T^{2} + \)\(32\!\cdots\!56\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} \))(\( 1 + 188163772 T + 22324076261167422 T^{2} + \)\(22\!\cdots\!52\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} \))(\( 1 - 203634428 T + 30920737906297022 T^{2} - \)\(23\!\cdots\!48\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} \))(\( 1 - 31825220 T + 17079149243685182 T^{2} - \)\(37\!\cdots\!20\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} \))(\( 1 - 195673924 T + 22434263296171326 T^{2} - \)\(22\!\cdots\!84\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} \))(\( 1 - 155970138 T + 27601780143557283 T^{2} - \)\(34\!\cdots\!16\)\( T^{3} + \)\(32\!\cdots\!03\)\( T^{4} - \)\(21\!\cdots\!78\)\( T^{5} + \)\(15\!\cdots\!21\)\( T^{6} \))(\( ( 1 + 143290916 T + 28088617153288446 T^{2} + \)\(16\!\cdots\!56\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} )^{2} \))(\( ( 1 + 51522236 T - 2665246277981394 T^{2} + \)\(60\!\cdots\!76\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} )^{2} \))(\( ( 1 - 180245284 T + 30154717014478446 T^{2} - \)\(21\!\cdots\!44\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} )^{2} \))(\( ( 1 + 98036614 T + 22387014560482111 T^{2} + \)\(12\!\cdots\!44\)\( T^{3} + \)\(28\!\cdots\!21\)\( T^{4} + \)\(25\!\cdots\!10\)\( T^{5} + \)\(49\!\cdots\!75\)\( T^{6} + \)\(39\!\cdots\!80\)\( T^{7} + \)\(57\!\cdots\!75\)\( T^{8} + \)\(34\!\cdots\!10\)\( T^{9} + \)\(46\!\cdots\!41\)\( T^{10} + \)\(23\!\cdots\!84\)\( T^{11} + \)\(48\!\cdots\!11\)\( T^{12} + \)\(25\!\cdots\!74\)\( T^{13} + \)\(29\!\cdots\!81\)\( T^{14} )^{2} \))(\( ( 1 + 216178092 T + 11694146092834141 T^{2} )^{2} \))(\( ( 1 - 218440382 T + 51172298068805048 T^{2} - \)\(68\!\cdots\!34\)\( T^{3} + \)\(92\!\cdots\!70\)\( T^{4} - \)\(80\!\cdots\!94\)\( T^{5} + \)\(69\!\cdots\!88\)\( T^{6} - \)\(34\!\cdots\!22\)\( T^{7} + \)\(18\!\cdots\!61\)\( T^{8} )^{4} \))
$67$ (\( 1 - 81557422 T + 27206534396294947 T^{2} \))(\( 1 - 115706158 T + 27206534396294947 T^{2} \))(\( 1 + 193621688 T + 27206534396294947 T^{2} \))(\( 1 - 45286158 T + 27206534396294947 T^{2} \))(\( 1 + 140571092 T + 27206534396294947 T^{2} \))(\( 1 - 318580 T + 48520062064444070 T^{2} - \)\(86\!\cdots\!60\)\( T^{3} + \)\(74\!\cdots\!09\)\( T^{4} \))(\( 1 - 105998252 T + 21995694557368746 T^{2} - \)\(28\!\cdots\!44\)\( T^{3} + \)\(74\!\cdots\!09\)\( T^{4} \))(\( 1 - 58872852 T + 54767076047787046 T^{2} - \)\(16\!\cdots\!44\)\( T^{3} + \)\(74\!\cdots\!09\)\( T^{4} \))(\( 1 + 89480628 T + 42050726086531690 T^{2} + \)\(24\!\cdots\!16\)\( T^{3} + \)\(74\!\cdots\!09\)\( T^{4} \))(\( 1 - 219767420 T + 65652945987990090 T^{2} - \)\(59\!\cdots\!40\)\( T^{3} + \)\(74\!\cdots\!09\)\( T^{4} \))(\( 1 - 526916604 T + 169230786613422441 T^{2} - \)\(33\!\cdots\!48\)\( T^{3} + \)\(46\!\cdots\!27\)\( T^{4} - \)\(39\!\cdots\!36\)\( T^{5} + \)\(20\!\cdots\!23\)\( T^{6} \))(\( 1 - 105856746688500020 T^{2} + \)\(42\!\cdots\!18\)\( T^{4} - \)\(78\!\cdots\!80\)\( T^{6} + \)\(54\!\cdots\!81\)\( T^{8} \))(\( 1 - 83417417389239260 T^{2} + \)\(31\!\cdots\!18\)\( T^{4} - \)\(61\!\cdots\!40\)\( T^{6} + \)\(54\!\cdots\!81\)\( T^{8} \))(\( 1 + 41160407446058180 T^{2} + \)\(18\!\cdots\!18\)\( T^{4} + \)\(30\!\cdots\!20\)\( T^{6} + \)\(54\!\cdots\!81\)\( T^{8} \))(\( 1 - 177004327823371630 T^{2} + \)\(17\!\cdots\!03\)\( T^{4} - \)\(12\!\cdots\!40\)\( T^{6} + \)\(67\!\cdots\!81\)\( T^{8} - \)\(29\!\cdots\!38\)\( T^{10} + \)\(10\!\cdots\!95\)\( T^{12} - \)\(30\!\cdots\!44\)\( T^{14} + \)\(76\!\cdots\!55\)\( T^{16} - \)\(15\!\cdots\!78\)\( T^{18} + \)\(27\!\cdots\!49\)\( T^{20} - \)\(37\!\cdots\!40\)\( T^{22} + \)\(39\!\cdots\!47\)\( T^{24} - \)\(29\!\cdots\!30\)\( T^{26} + \)\(12\!\cdots\!69\)\( T^{28} \))(\( 1 + \)\(74\!\cdots\!09\)\( T^{4} \))(\( 1 - \)\(66\!\cdots\!28\)\( T^{4} + \)\(49\!\cdots\!68\)\( T^{8} + \)\(25\!\cdots\!24\)\( T^{12} - \)\(73\!\cdots\!30\)\( T^{16} + \)\(13\!\cdots\!44\)\( T^{20} + \)\(14\!\cdots\!48\)\( T^{24} - \)\(10\!\cdots\!48\)\( T^{28} + \)\(90\!\cdots\!21\)\( T^{32} \))
$71$ (\( 1 + 161307732 T + 45848500718449031 T^{2} \))(\( 1 - 231681708 T + 45848500718449031 T^{2} \))(\( 1 + 417763488 T + 45848500718449031 T^{2} \))(\( 1 - 189967468 T + 45848500718449031 T^{2} \))(\( 1 + 97098792 T + 45848500718449031 T^{2} \))(\( 1 - 7130936 T + 51935375688707086 T^{2} - \)\(32\!\cdots\!16\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 - 168665592 T + 68474091725761822 T^{2} - \)\(77\!\cdots\!52\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 - 349900792 T + 118671349360183822 T^{2} - \)\(16\!\cdots\!52\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 + 112319176 T + 82264334516632606 T^{2} + \)\(51\!\cdots\!56\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 + 311207016 T + 76405636625293726 T^{2} + \)\(14\!\cdots\!96\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))(\( 1 - 239894424 T + 117827037562982037 T^{2} - \)\(16\!\cdots\!88\)\( T^{3} + \)\(54\!\cdots\!47\)\( T^{4} - \)\(50\!\cdots\!64\)\( T^{5} + \)\(96\!\cdots\!91\)\( T^{6} \))(\( ( 1 + 401435664 T + 127868030128292686 T^{2} + \)\(18\!\cdots\!84\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 - 252040944 T + 101042798798695246 T^{2} - \)\(11\!\cdots\!64\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 - 23805936 T + 85782754020107086 T^{2} - \)\(10\!\cdots\!16\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 + 225576440 T + 245415872052380657 T^{2} + \)\(51\!\cdots\!60\)\( T^{3} + \)\(29\!\cdots\!61\)\( T^{4} + \)\(52\!\cdots\!48\)\( T^{5} + \)\(20\!\cdots\!25\)\( T^{6} + \)\(30\!\cdots\!36\)\( T^{7} + \)\(95\!\cdots\!75\)\( T^{8} + \)\(10\!\cdots\!28\)\( T^{9} + \)\(28\!\cdots\!51\)\( T^{10} + \)\(22\!\cdots\!60\)\( T^{11} + \)\(49\!\cdots\!07\)\( T^{12} + \)\(20\!\cdots\!40\)\( T^{13} + \)\(42\!\cdots\!11\)\( T^{14} )^{2} \))(\( ( 1 - 45848500718449031 T^{2} )^{2} \))(\( ( 1 - 184367065216517748 T^{2} + \)\(12\!\cdots\!08\)\( T^{4} - \)\(37\!\cdots\!96\)\( T^{6} + \)\(75\!\cdots\!70\)\( T^{8} - \)\(79\!\cdots\!56\)\( T^{10} + \)\(56\!\cdots\!68\)\( T^{12} - \)\(17\!\cdots\!88\)\( T^{14} + \)\(19\!\cdots\!41\)\( T^{16} )^{2} \))
$73$ (\( 1 + 247147966 T + 58871586708267913 T^{2} \))(\( 1 - 358691906 T + 58871586708267913 T^{2} \))(\( 1 + 450372742 T + 58871586708267913 T^{2} \))(\( 1 - 412170946 T + 58871586708267913 T^{2} \))(\( 1 - 171848906 T + 58871586708267913 T^{2} \))(\( 1 - 120858180 T + 42707263689423190 T^{2} - \)\(71\!\cdots\!40\)\( T^{3} + \)\(34\!\cdots\!69\)\( T^{4} \))(\( 1 + 390212412 T + 130694746296409238 T^{2} + \)\(22\!\cdots\!56\)\( T^{3} + \)\(34\!\cdots\!69\)\( T^{4} \))(\( 1 - 71160388 T - 50883178339169962 T^{2} - \)\(41\!\cdots\!44\)\( T^{3} + \)\(34\!\cdots\!69\)\( T^{4} \))(\( 1 + 93294524 T + 109959841455461270 T^{2} + \)\(54\!\cdots\!12\)\( T^{3} + \)\(34\!\cdots\!69\)\( T^{4} \))(\( 1 + 99224060 T + 35402447061205782 T^{2} + \)\(58\!\cdots\!80\)\( T^{3} + \)\(34\!\cdots\!69\)\( T^{4} \))(\( 1 - 198362430 T + 177547240540777287 T^{2} - \)\(22\!\cdots\!56\)\( T^{3} + \)\(10\!\cdots\!31\)\( T^{4} - \)\(68\!\cdots\!70\)\( T^{5} + \)\(20\!\cdots\!97\)\( T^{6} \))(\( 1 - 30314907095525540 T^{2} + \)\(69\!\cdots\!38\)\( T^{4} - \)\(10\!\cdots\!60\)\( T^{6} + \)\(12\!\cdots\!61\)\( T^{8} \))(\( 1 - 79546297979572004 T^{2} + \)\(52\!\cdots\!42\)\( T^{4} - \)\(27\!\cdots\!76\)\( T^{6} + \)\(12\!\cdots\!61\)\( T^{8} \))(\( 1 - 229489314868712740 T^{2} + \)\(20\!\cdots\!38\)\( T^{4} - \)\(79\!\cdots\!60\)\( T^{6} + \)\(12\!\cdots\!61\)\( T^{8} \))(\( 1 - 503564451255364030 T^{2} + \)\(12\!\cdots\!23\)\( T^{4} - \)\(20\!\cdots\!00\)\( T^{6} + \)\(23\!\cdots\!61\)\( T^{8} - \)\(22\!\cdots\!62\)\( T^{10} + \)\(16\!\cdots\!15\)\( T^{12} - \)\(10\!\cdots\!96\)\( T^{14} + \)\(58\!\cdots\!35\)\( T^{16} - \)\(26\!\cdots\!82\)\( T^{18} + \)\(98\!\cdots\!49\)\( T^{20} - \)\(28\!\cdots\!00\)\( T^{22} + \)\(62\!\cdots\!27\)\( T^{24} - \)\(87\!\cdots\!30\)\( T^{26} + \)\(60\!\cdots\!89\)\( T^{28} \))(\( ( 1 - 42331194 T + 58871586708267913 T^{2} )( 1 + 483419504 T + 58871586708267913 T^{2} ) \))(\( ( 1 - 560456720 T + 157055867496579200 T^{2} - \)\(36\!\cdots\!60\)\( T^{3} + \)\(62\!\cdots\!76\)\( T^{4} - \)\(11\!\cdots\!40\)\( T^{5} + \)\(34\!\cdots\!00\)\( T^{6} - \)\(97\!\cdots\!20\)\( T^{7} + \)\(26\!\cdots\!66\)\( T^{8} - \)\(57\!\cdots\!60\)\( T^{9} + \)\(11\!\cdots\!00\)\( T^{10} - \)\(24\!\cdots\!80\)\( T^{11} + \)\(75\!\cdots\!36\)\( T^{12} - \)\(25\!\cdots\!80\)\( T^{13} + \)\(65\!\cdots\!00\)\( T^{14} - \)\(13\!\cdots\!40\)\( T^{15} + \)\(14\!\cdots\!21\)\( T^{16} )^{2} \))
$79$ (\( 1 - 583345720 T + 119851595982618319 T^{2} \))(\( 1 - 486017080 T + 119851595982618319 T^{2} \))(\( 1 - 91425472 T + 119851595982618319 T^{2} \))(\( 1 + 95040840 T + 119851595982618319 T^{2} \))(\( 1 - 117380080 T + 119851595982618319 T^{2} \))(\( 1 + 6877520 T - 115982362290712162 T^{2} + \)\(82\!\cdots\!80\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} \))(\( 1 + 466946256 T + 276599246367485918 T^{2} + \)\(55\!\cdots\!64\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} \))(\( 1 - 452087344 T + 272781342616725918 T^{2} - \)\(54\!\cdots\!36\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} \))(\( 1 - 191601328 T - 39905777688415266 T^{2} - \)\(22\!\cdots\!32\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} \))(\( 1 + 542261776 T + 313115996157615582 T^{2} + \)\(64\!\cdots\!44\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} \))(\( 1 - 413839728 T + 365148310414214253 T^{2} - \)\(92\!\cdots\!64\)\( T^{3} + \)\(43\!\cdots\!07\)\( T^{4} - \)\(59\!\cdots\!08\)\( T^{5} + \)\(17\!\cdots\!59\)\( T^{6} \))(\( ( 1 - 516584160 T + 303933580876193438 T^{2} - \)\(61\!\cdots\!40\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 + 897477504 T + 421888354983619742 T^{2} + \)\(10\!\cdots\!76\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 - 364021760 T + 220545463862625438 T^{2} - \)\(43\!\cdots\!40\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} )^{2} \))(\( ( 1 - 135399280 T + 706461139065345193 T^{2} - \)\(91\!\cdots\!80\)\( T^{3} + \)\(22\!\cdots\!61\)\( T^{4} - \)\(26\!\cdots\!36\)\( T^{5} + \)\(42\!\cdots\!25\)\( T^{6} - \)\(41\!\cdots\!48\)\( T^{7} + \)\(51\!\cdots\!75\)\( T^{8} - \)\(37\!\cdots\!96\)\( T^{9} + \)\(38\!\cdots\!99\)\( T^{10} - \)\(18\!\cdots\!80\)\( T^{11} + \)\(17\!\cdots\!07\)\( T^{12} - \)\(40\!\cdots\!80\)\( T^{13} + \)\(35\!\cdots\!39\)\( T^{14} )^{2} \))(\( ( 1 + 119851595982618319 T^{2} )^{2} \))(\( ( 1 - 11636561178925448 T^{2} + \)\(17\!\cdots\!08\)\( T^{4} + \)\(34\!\cdots\!04\)\( T^{6} - \)\(53\!\cdots\!30\)\( T^{8} + \)\(49\!\cdots\!44\)\( T^{10} + \)\(35\!\cdots\!68\)\( T^{12} - \)\(34\!\cdots\!88\)\( T^{14} + \)\(42\!\cdots\!41\)\( T^{16} )^{2} \))
$83$ (\( 1 - 14571786 T + 186940255267540403 T^{2} \))(\( 1 + 251168886 T + 186940255267540403 T^{2} \))(\( 1 - 652637376 T + 186940255267540403 T^{2} \))(\( 1 + 261706326 T + 186940255267540403 T^{2} \))(\( 1 + 323637636 T + 186940255267540403 T^{2} \))(\( 1 + 1402348740 T + 857904310704391270 T^{2} + \)\(26\!\cdots\!20\)\( T^{3} + \)\(34\!\cdots\!09\)\( T^{4} \))(\( 1 + 329535164 T + 370572645121965674 T^{2} + \)\(61\!\cdots\!92\)\( T^{3} + \)\(34\!\cdots\!09\)\( T^{4} \))(\( 1 - 244865436 T + 172811505943449574 T^{2} - \)\(45\!\cdots\!08\)\( T^{3} + \)\(34\!\cdots\!09\)\( T^{4} \))(\( 1 - 17270436 T + 372491529649343530 T^{2} - \)\(32\!\cdots\!08\)\( T^{3} + \)\(34\!\cdots\!09\)\( T^{4} \))(\( 1 - 1256915700 T + 768086791626261130 T^{2} - \)\(23\!\cdots\!00\)\( T^{3} + \)\(34\!\cdots\!09\)\( T^{4} \))(\( 1 + 371949828 T + 338245334081122329 T^{2} + \)\(14\!\cdots\!04\)\( T^{3} + \)\(63\!\cdots\!87\)\( T^{4} + \)\(12\!\cdots\!52\)\( T^{5} + \)\(65\!\cdots\!27\)\( T^{6} \))(\( 1 - 597414961848210420 T^{2} + \)\(15\!\cdots\!18\)\( T^{4} - \)\(20\!\cdots\!80\)\( T^{6} + \)\(12\!\cdots\!81\)\( T^{8} \))(\( 1 - 186261173343564060 T^{2} + \)\(18\!\cdots\!18\)\( T^{4} - \)\(65\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!81\)\( T^{8} \))(\( 1 - 434569632367965820 T^{2} + \)\(10\!\cdots\!18\)\( T^{4} - \)\(15\!\cdots\!80\)\( T^{6} + \)\(12\!\cdots\!81\)\( T^{8} \))(\( 1 - 1418592974331058830 T^{2} + \)\(10\!\cdots\!03\)\( T^{4} - \)\(51\!\cdots\!00\)\( T^{6} + \)\(19\!\cdots\!81\)\( T^{8} - \)\(57\!\cdots\!62\)\( T^{10} + \)\(13\!\cdots\!15\)\( T^{12} - \)\(28\!\cdots\!56\)\( T^{14} + \)\(48\!\cdots\!35\)\( T^{16} - \)\(69\!\cdots\!22\)\( T^{18} + \)\(81\!\cdots\!49\)\( T^{20} - \)\(76\!\cdots\!00\)\( T^{22} + \)\(54\!\cdots\!47\)\( T^{24} - \)\(25\!\cdots\!30\)\( T^{26} + \)\(63\!\cdots\!69\)\( T^{28} \))(\( 1 + \)\(34\!\cdots\!09\)\( T^{4} \))(\( 1 - \)\(15\!\cdots\!28\)\( T^{4} + \)\(13\!\cdots\!68\)\( T^{8} - \)\(78\!\cdots\!76\)\( T^{12} + \)\(32\!\cdots\!70\)\( T^{16} - \)\(95\!\cdots\!56\)\( T^{20} + \)\(20\!\cdots\!48\)\( T^{24} - \)\(28\!\cdots\!48\)\( T^{28} + \)\(22\!\cdots\!21\)\( T^{32} \))
$89$ (\( 1 - 470133690 T + 350356403707485209 T^{2} \))(\( 1 + 526039110 T + 350356403707485209 T^{2} \))(\( 1 + 170059206 T + 350356403707485209 T^{2} \))(\( 1 + 19938630 T + 350356403707485209 T^{2} \))(\( 1 + 894379110 T + 350356403707485209 T^{2} \))(\( 1 - 830088660 T + 692293619421117718 T^{2} - \)\(29\!\cdots\!40\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))(\( 1 + 108334860 T - 479764388871867818 T^{2} + \)\(37\!\cdots\!40\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))(\( 1 + 256073260 T + 592174274852066582 T^{2} + \)\(89\!\cdots\!40\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))(\( 1 + 615067148 T + 322694158807723094 T^{2} + \)\(21\!\cdots\!32\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))(\( 1 + 462291852 T + 159603168035249494 T^{2} + \)\(16\!\cdots\!68\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))(\( 1 - 754926606 T + 926540806511526711 T^{2} - \)\(52\!\cdots\!12\)\( T^{3} + \)\(32\!\cdots\!99\)\( T^{4} - \)\(92\!\cdots\!86\)\( T^{5} + \)\(43\!\cdots\!29\)\( T^{6} \))(\( ( 1 + 138178380 T + 45471108987586518 T^{2} + \)\(48\!\cdots\!20\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} )^{2} \))(\( ( 1 - 1190659092 T + 825013495390166934 T^{2} - \)\(41\!\cdots\!28\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} )^{2} \))(\( ( 1 + 791350380 T + 832192702699668118 T^{2} + \)\(27\!\cdots\!20\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} )^{2} \))(\( ( 1 + 565221738 T + 1470744865980476579 T^{2} + \)\(55\!\cdots\!72\)\( T^{3} + \)\(10\!\cdots\!41\)\( T^{4} + \)\(31\!\cdots\!66\)\( T^{5} + \)\(51\!\cdots\!03\)\( T^{6} + \)\(12\!\cdots\!44\)\( T^{7} + \)\(17\!\cdots\!27\)\( T^{8} + \)\(38\!\cdots\!46\)\( T^{9} + \)\(45\!\cdots\!89\)\( T^{10} + \)\(83\!\cdots\!92\)\( T^{11} + \)\(77\!\cdots\!71\)\( T^{12} + \)\(10\!\cdots\!58\)\( T^{13} + \)\(64\!\cdots\!69\)\( T^{14} )^{2} \))(\( ( 1 - 1125568310 T + 350356403707485209 T^{2} )( 1 + 1125568310 T + 350356403707485209 T^{2} ) \))(\( ( 1 - 2338374212589272328 T^{2} + \)\(25\!\cdots\!68\)\( T^{4} - \)\(16\!\cdots\!76\)\( T^{6} + \)\(70\!\cdots\!70\)\( T^{8} - \)\(20\!\cdots\!56\)\( T^{10} + \)\(38\!\cdots\!48\)\( T^{12} - \)\(43\!\cdots\!48\)\( T^{14} + \)\(22\!\cdots\!21\)\( T^{16} )^{2} \))
$97$ (\( 1 + 117838462 T + 760231058654565217 T^{2} \))(\( 1 + 1075981438 T + 760231058654565217 T^{2} \))(\( 1 + 10947022 T + 760231058654565217 T^{2} \))(\( 1 + 19503358 T + 760231058654565217 T^{2} \))(\( 1 - 232678562 T + 760231058654565217 T^{2} \))(\( 1 - 638394580 T + 1615411126351062630 T^{2} - \)\(48\!\cdots\!60\)\( T^{3} + \)\(57\!\cdots\!89\)\( T^{4} \))(\( 1 - 2043058628 T + 2509217520410601030 T^{2} - \)\(15\!\cdots\!76\)\( T^{3} + \)\(57\!\cdots\!89\)\( T^{4} \))(\( 1 + 184950572 T - 615454564650127770 T^{2} + \)\(14\!\cdots\!24\)\( T^{3} + \)\(57\!\cdots\!89\)\( T^{4} \))(\( 1 + 996545468 T + 943405561624881990 T^{2} + \)\(75\!\cdots\!56\)\( T^{3} + \)\(57\!\cdots\!89\)\( T^{4} \))(\( 1 - 1671716740 T + 2048690578856969670 T^{2} - \)\(12\!\cdots\!80\)\( T^{3} + \)\(57\!\cdots\!89\)\( T^{4} \))(\( 1 + 903451002 T + 2439888940908067119 T^{2} + \)\(13\!\cdots\!72\)\( T^{3} + \)\(18\!\cdots\!23\)\( T^{4} + \)\(52\!\cdots\!78\)\( T^{5} + \)\(43\!\cdots\!13\)\( T^{6} \))(\( 1 - 228500609440802180 T^{2} - \)\(20\!\cdots\!22\)\( T^{4} - \)\(13\!\cdots\!20\)\( T^{6} + \)\(33\!\cdots\!21\)\( T^{8} \))(\( 1 - 899946211039106180 T^{2} + \)\(23\!\cdots\!78\)\( T^{4} - \)\(52\!\cdots\!20\)\( T^{6} + \)\(33\!\cdots\!21\)\( T^{8} \))(\( 1 - 2561123777205326980 T^{2} + \)\(27\!\cdots\!78\)\( T^{4} - \)\(14\!\cdots\!20\)\( T^{6} + \)\(33\!\cdots\!21\)\( T^{8} \))(\( 1 - 2780080466788768846 T^{2} + \)\(63\!\cdots\!87\)\( T^{4} - \)\(10\!\cdots\!84\)\( T^{6} + \)\(13\!\cdots\!81\)\( T^{8} - \)\(14\!\cdots\!38\)\( T^{10} + \)\(14\!\cdots\!03\)\( T^{12} - \)\(11\!\cdots\!96\)\( T^{14} + \)\(81\!\cdots\!67\)\( T^{16} - \)\(49\!\cdots\!98\)\( T^{18} + \)\(25\!\cdots\!89\)\( T^{20} - \)\(11\!\cdots\!44\)\( T^{22} + \)\(40\!\cdots\!63\)\( T^{24} - \)\(10\!\cdots\!06\)\( T^{26} + \)\(21\!\cdots\!29\)\( T^{28} \))(\( ( 1 - 1016663992 T + 760231058654565217 T^{2} )( 1 + 1416798702 T + 760231058654565217 T^{2} ) \))(\( ( 1 - 598067120 T + 178842140012547200 T^{2} - \)\(85\!\cdots\!40\)\( T^{3} + \)\(56\!\cdots\!56\)\( T^{4} + \)\(60\!\cdots\!60\)\( T^{5} - \)\(10\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!20\)\( T^{7} - \)\(75\!\cdots\!74\)\( T^{8} + \)\(25\!\cdots\!40\)\( T^{9} - \)\(58\!\cdots\!00\)\( T^{10} + \)\(26\!\cdots\!80\)\( T^{11} + \)\(18\!\cdots\!76\)\( T^{12} - \)\(21\!\cdots\!80\)\( T^{13} + \)\(34\!\cdots\!00\)\( T^{14} - \)\(87\!\cdots\!60\)\( T^{15} + \)\(11\!\cdots\!41\)\( T^{16} )^{2} \))
show more
show less