Properties

Label 147.4.e
Level 147
Weight 4
Character orbit e
Rep. character \(\chi_{147}(67,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 40
Newform subspaces 14
Sturm bound 74
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(74\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(147, [\chi])\).

Total New Old
Modular forms 128 40 88
Cusp forms 96 40 56
Eisenstein series 32 0 32

Trace form

\( 40q - 4q^{2} - 6q^{3} - 60q^{4} + 8q^{5} + 24q^{6} - 156q^{8} - 180q^{9} + O(q^{10}) \) \( 40q - 4q^{2} - 6q^{3} - 60q^{4} + 8q^{5} + 24q^{6} - 156q^{8} - 180q^{9} - 46q^{10} + 40q^{11} - 72q^{12} + 4q^{13} + 84q^{15} - 164q^{16} + 132q^{17} - 36q^{18} - 218q^{19} - 872q^{20} - 180q^{22} + 208q^{23} - 54q^{24} - 686q^{25} + 466q^{26} + 108q^{27} + 920q^{29} + 216q^{30} - 348q^{31} + 1050q^{32} - 150q^{33} + 552q^{34} + 1080q^{36} + 550q^{37} - 350q^{38} + 42q^{39} - 42q^{40} - 1208q^{41} - 2076q^{43} - 1112q^{44} + 72q^{45} - 1076q^{46} - 240q^{47} + 1872q^{48} - 920q^{50} + 48q^{51} + 260q^{52} + 2884q^{53} - 108q^{54} + 1972q^{55} - 1140q^{57} + 418q^{58} + 1128q^{59} - 1938q^{60} - 188q^{61} - 3636q^{62} + 2664q^{64} - 336q^{65} + 156q^{66} - 2290q^{67} + 2028q^{68} + 1800q^{69} + 376q^{71} + 702q^{72} + 1350q^{73} + 1534q^{74} - 738q^{75} + 4712q^{76} - 108q^{78} + 248q^{79} + 388q^{80} - 1620q^{81} - 956q^{82} - 1992q^{83} + 2264q^{85} + 4670q^{86} - 1050q^{87} + 6198q^{88} + 2672q^{89} + 828q^{90} - 10360q^{92} - 3006q^{93} - 3204q^{94} - 928q^{95} - 1914q^{96} - 1044q^{97} - 720q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
147.4.e.a \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(-3\) \(-18\) \(0\) \(q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.b \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(-3\) \(-4\) \(0\) \(q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.c \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(3\) \(4\) \(0\) \(q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.d \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(3\) \(18\) \(0\) \(q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.e \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(12\) \(0\) \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
147.4.e.f \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-12\) \(0\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
147.4.e.g \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(3\) \(-3\) \(-18\) \(0\) \(q+3\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.h \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(-3\) \(0\) \(q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.i \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(18\) \(0\) \(q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.j \(4\) \(8.673\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-6\) \(20\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.k \(4\) \(8.673\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(6\) \(-20\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}-3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.l \(4\) \(8.673\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(3\) \(-6\) \(-6\) \(0\) \(q+(1+\beta _{1}+\beta _{3})q^{2}+3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.m \(4\) \(8.673\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(3\) \(6\) \(6\) \(0\) \(q+(1+\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.n \(6\) \(8.673\) 6.0.9924270768.1 None \(-1\) \(-9\) \(11\) \(0\) \(q-\beta _{1}q^{2}+(-3+3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T + 8 T^{2} + 32 T^{3} + 64 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 32 T^{3} + 64 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 32 T^{3} + 64 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 32 T^{3} + 64 T^{4} \))(\( 1 - T - 7 T^{2} - 8 T^{3} + 64 T^{4} \))(\( 1 - T - 7 T^{2} - 8 T^{3} + 64 T^{4} \))(\( 1 - 3 T + T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 - 3 T + T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 - 3 T + T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 + 2 T - 11 T^{2} - 2 T^{3} + 129 T^{4} - 16 T^{5} - 704 T^{6} + 1024 T^{7} + 4096 T^{8} \))(\( 1 + 2 T - 11 T^{2} - 2 T^{3} + 129 T^{4} - 16 T^{5} - 704 T^{6} + 1024 T^{7} + 4096 T^{8} \))(\( 1 - 3 T + 5 T^{2} + 36 T^{3} - 120 T^{4} + 288 T^{5} + 320 T^{6} - 1536 T^{7} + 4096 T^{8} \))(\( 1 - 3 T + 5 T^{2} + 36 T^{3} - 120 T^{4} + 288 T^{5} + 320 T^{6} - 1536 T^{7} + 4096 T^{8} \))(\( 1 + T + T^{2} - 20 T^{3} - 10 T^{4} + 64 T^{5} + 1060 T^{6} + 512 T^{7} - 640 T^{8} - 10240 T^{9} + 4096 T^{10} + 32768 T^{11} + 262144 T^{12} \))
$3$ (\( 1 + 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 - 3 T + 9 T^{2} \))(\( 1 - 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 - 3 T + 9 T^{2} \))(\( 1 + 3 T + 9 T^{2} \))(\( 1 - 3 T + 9 T^{2} \))(\( 1 - 3 T + 9 T^{2} \))(\( ( 1 + 3 T + 9 T^{2} )^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{2} \))(\( ( 1 + 3 T + 9 T^{2} )^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{2} \))(\( ( 1 + 3 T + 9 T^{2} )^{3} \))
$5$ (\( 1 + 18 T + 199 T^{2} + 2250 T^{3} + 15625 T^{4} \))(\( 1 + 4 T - 109 T^{2} + 500 T^{3} + 15625 T^{4} \))(\( 1 - 4 T - 109 T^{2} - 500 T^{3} + 15625 T^{4} \))(\( 1 - 18 T + 199 T^{2} - 2250 T^{3} + 15625 T^{4} \))(\( 1 - 12 T + 19 T^{2} - 1500 T^{3} + 15625 T^{4} \))(\( 1 + 12 T + 19 T^{2} + 1500 T^{3} + 15625 T^{4} \))(\( 1 + 18 T + 199 T^{2} + 2250 T^{3} + 15625 T^{4} \))(\( 1 + 3 T - 116 T^{2} + 375 T^{3} + 15625 T^{4} \))(\( 1 - 18 T + 199 T^{2} - 2250 T^{3} + 15625 T^{4} \))(\( 1 - 20 T + 148 T^{2} - 40 T^{3} - 2121 T^{4} - 5000 T^{5} + 2312500 T^{6} - 39062500 T^{7} + 244140625 T^{8} \))(\( 1 + 20 T + 148 T^{2} + 40 T^{3} - 2121 T^{4} + 5000 T^{5} + 2312500 T^{6} + 39062500 T^{7} + 244140625 T^{8} \))(\( 1 + 6 T - 166 T^{2} - 288 T^{3} + 20679 T^{4} - 36000 T^{5} - 2593750 T^{6} + 11718750 T^{7} + 244140625 T^{8} \))(\( 1 - 6 T - 166 T^{2} + 288 T^{3} + 20679 T^{4} + 36000 T^{5} - 2593750 T^{6} - 11718750 T^{7} + 244140625 T^{8} \))(\( 1 - 11 T - 62 T^{2} + 1015 T^{3} - 6040 T^{4} + 54313 T^{5} + 121696 T^{6} + 6789125 T^{7} - 94375000 T^{8} + 1982421875 T^{9} - 15136718750 T^{10} - 335693359375 T^{11} + 3814697265625 T^{12} \))
$7$ 1
$11$ (\( 1 - 50 T + 1169 T^{2} - 66550 T^{3} + 1771561 T^{4} \))(\( 1 + 62 T + 2513 T^{2} + 82522 T^{3} + 1771561 T^{4} \))(\( 1 + 62 T + 2513 T^{2} + 82522 T^{3} + 1771561 T^{4} \))(\( 1 - 50 T + 1169 T^{2} - 66550 T^{3} + 1771561 T^{4} \))(\( 1 + 20 T - 931 T^{2} + 26620 T^{3} + 1771561 T^{4} \))(\( 1 + 20 T - 931 T^{2} + 26620 T^{3} + 1771561 T^{4} \))(\( 1 - 36 T - 35 T^{2} - 47916 T^{3} + 1771561 T^{4} \))(\( 1 - 15 T - 1106 T^{2} - 19965 T^{3} + 1771561 T^{4} \))(\( 1 - 36 T - 35 T^{2} - 47916 T^{3} + 1771561 T^{4} \))(\( 1 - 20 T - 1210 T^{2} + 21040 T^{3} + 288139 T^{4} + 28004240 T^{5} - 2143588810 T^{6} - 47158953820 T^{7} + 3138428376721 T^{8} \))(\( 1 - 20 T - 1210 T^{2} + 21040 T^{3} + 288139 T^{4} + 28004240 T^{5} - 2143588810 T^{6} - 47158953820 T^{7} + 3138428376721 T^{8} \))(\( 1 - 6 T - 1210 T^{2} + 8496 T^{3} - 266961 T^{4} + 11308176 T^{5} - 2143588810 T^{6} - 14147686146 T^{7} + 3138428376721 T^{8} \))(\( 1 - 6 T - 1210 T^{2} + 8496 T^{3} - 266961 T^{4} + 11308176 T^{5} - 2143588810 T^{6} - 14147686146 T^{7} + 3138428376721 T^{8} \))(\( 1 + 35 T - 1400 T^{2} - 113593 T^{3} - 198940 T^{4} + 87110135 T^{5} + 3928586038 T^{6} + 115943589685 T^{7} - 352434345340 T^{8} - 267846352063763 T^{9} - 4393799727409400 T^{10} + 146203685929547785 T^{11} + 5559917313492231481 T^{12} \))
$13$ (\( ( 1 + 36 T + 2197 T^{2} )^{2} \))(\( ( 1 - 62 T + 2197 T^{2} )^{2} \))(\( ( 1 + 62 T + 2197 T^{2} )^{2} \))(\( ( 1 - 36 T + 2197 T^{2} )^{2} \))(\( ( 1 - 84 T + 2197 T^{2} )^{2} \))(\( ( 1 + 84 T + 2197 T^{2} )^{2} \))(\( ( 1 - 34 T + 2197 T^{2} )^{2} \))(\( ( 1 - 64 T + 2197 T^{2} )^{2} \))(\( ( 1 + 34 T + 2197 T^{2} )^{2} \))(\( ( 1 + 104 T + 5848 T^{2} + 228488 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 - 104 T + 5848 T^{2} - 228488 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 - 16 T + 2406 T^{2} - 35152 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 + 16 T + 2406 T^{2} + 35152 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 + 62 T + 7016 T^{2} + 253976 T^{3} + 15414152 T^{4} + 299262158 T^{5} + 10604499373 T^{6} )^{2} \))
$17$ (\( 1 + 126 T + 10963 T^{2} + 619038 T^{3} + 24137569 T^{4} \))(\( 1 - 84 T + 2143 T^{2} - 412692 T^{3} + 24137569 T^{4} \))(\( 1 + 84 T + 2143 T^{2} + 412692 T^{3} + 24137569 T^{4} \))(\( 1 - 126 T + 10963 T^{2} - 619038 T^{3} + 24137569 T^{4} \))(\( 1 + 96 T + 4303 T^{2} + 471648 T^{3} + 24137569 T^{4} \))(\( 1 - 96 T + 4303 T^{2} - 471648 T^{3} + 24137569 T^{4} \))(\( 1 - 42 T - 3149 T^{2} - 206346 T^{3} + 24137569 T^{4} \))(\( 1 - 84 T + 2143 T^{2} - 412692 T^{3} + 24137569 T^{4} \))(\( 1 + 42 T - 3149 T^{2} + 206346 T^{3} + 24137569 T^{4} \))(\( 1 - 116 T + 4316 T^{2} + 79576 T^{3} - 6707297 T^{4} + 390956888 T^{5} + 104177747804 T^{6} - 13756193673652 T^{7} + 582622237229761 T^{8} \))(\( 1 + 116 T + 4316 T^{2} - 79576 T^{3} - 6707297 T^{4} - 390956888 T^{5} + 104177747804 T^{6} + 13756193673652 T^{7} + 582622237229761 T^{8} \))(\( 1 - 6 T - 9742 T^{2} + 288 T^{3} + 71294847 T^{4} + 1414944 T^{5} - 235148197198 T^{6} - 711527258982 T^{7} + 582622237229761 T^{8} \))(\( 1 + 6 T - 9742 T^{2} - 288 T^{3} + 71294847 T^{4} - 1414944 T^{5} - 235148197198 T^{6} + 711527258982 T^{7} + 582622237229761 T^{8} \))(\( 1 - 48 T - 10035 T^{2} + 125232 T^{3} + 74409318 T^{4} + 234420432 T^{5} - 437742983351 T^{6} + 1151707582416 T^{7} + 1796060047467942 T^{8} + 14850996949472304 T^{9} - 5846614150600651635 T^{10} - \)\(13\!\cdots\!64\)\( T^{11} + \)\(14\!\cdots\!09\)\( T^{12} \))
$19$ (\( 1 - 72 T - 1675 T^{2} - 493848 T^{3} + 47045881 T^{4} \))(\( 1 - 100 T + 3141 T^{2} - 685900 T^{3} + 47045881 T^{4} \))(\( 1 + 100 T + 3141 T^{2} + 685900 T^{3} + 47045881 T^{4} \))(\( 1 + 72 T - 1675 T^{2} + 493848 T^{3} + 47045881 T^{4} \))(\( 1 - 12 T - 6715 T^{2} - 82308 T^{3} + 47045881 T^{4} \))(\( 1 + 12 T - 6715 T^{2} + 82308 T^{3} + 47045881 T^{4} \))(\( 1 + 124 T + 8517 T^{2} + 850516 T^{3} + 47045881 T^{4} \))(\( 1 + 16 T - 6603 T^{2} + 109744 T^{3} + 47045881 T^{4} \))(\( 1 - 124 T + 8517 T^{2} - 850516 T^{3} + 47045881 T^{4} \))(\( 1 - 192 T + 14898 T^{2} - 1583616 T^{3} + 182609099 T^{4} - 10862022144 T^{5} + 700889535138 T^{6} - 61956037973568 T^{7} + 2213314919066161 T^{8} \))(\( 1 + 192 T + 14898 T^{2} + 1583616 T^{3} + 182609099 T^{4} + 10862022144 T^{5} + 700889535138 T^{6} + 61956037973568 T^{7} + 2213314919066161 T^{8} \))(\( 1 + 64 T - 2438 T^{2} - 459776 T^{3} - 32447189 T^{4} - 3153603584 T^{5} - 114697857878 T^{6} + 20652012657856 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 64 T - 2438 T^{2} + 459776 T^{3} - 32447189 T^{4} + 3153603584 T^{5} - 114697857878 T^{6} - 20652012657856 T^{7} + 2213314919066161 T^{8} \))(\( 1 + 202 T + 7946 T^{2} + 627636 T^{3} + 247297462 T^{4} + 17185599794 T^{5} + 349471935958 T^{6} + 117876028987046 T^{7} + 11634326968854022 T^{8} + 202530415883220444 T^{9} + 17587000346899715306 T^{10} + \)\(30\!\cdots\!98\)\( T^{11} + \)\(10\!\cdots\!41\)\( T^{12} \))
$23$ (\( 1 + 14 T - 11971 T^{2} + 170338 T^{3} + 148035889 T^{4} \))(\( 1 - 42 T - 10403 T^{2} - 511014 T^{3} + 148035889 T^{4} \))(\( 1 - 42 T - 10403 T^{2} - 511014 T^{3} + 148035889 T^{4} \))(\( 1 + 14 T - 11971 T^{2} + 170338 T^{3} + 148035889 T^{4} \))(\( 1 - 176 T + 18809 T^{2} - 2141392 T^{3} + 148035889 T^{4} \))(\( 1 - 176 T + 18809 T^{2} - 2141392 T^{3} + 148035889 T^{4} \))(\( 1 - 12167 T^{2} + 148035889 T^{4} \))(\( 1 - 84 T - 5111 T^{2} - 1022028 T^{3} + 148035889 T^{4} \))(\( 1 - 12167 T^{2} + 148035889 T^{4} \))(\( 1 + 28 T - 22178 T^{2} - 38416 T^{3} + 369678627 T^{4} - 467407472 T^{5} - 3283139946242 T^{6} + 50432274520964 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 28 T - 22178 T^{2} - 38416 T^{3} + 369678627 T^{4} - 467407472 T^{5} - 3283139946242 T^{6} + 50432274520964 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 6 T - 7834 T^{2} - 98784 T^{3} - 86537001 T^{4} - 1201904928 T^{5} - 1159713154426 T^{6} + 10806915968778 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 6 T - 7834 T^{2} - 98784 T^{3} - 86537001 T^{4} - 1201904928 T^{5} - 1159713154426 T^{6} + 10806915968778 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 216 T + 10827 T^{2} + 387864 T^{3} + 53856198 T^{4} - 24653558952 T^{5} - 5413409425505 T^{6} - 299959851768984 T^{7} + 7972650149090022 T^{8} + 698602275885685032 T^{9} + \)\(23\!\cdots\!67\)\( T^{10} + \)\(57\!\cdots\!12\)\( T^{11} + \)\(32\!\cdots\!69\)\( T^{12} \))
$29$ (\( ( 1 - 158 T + 24389 T^{2} )^{2} \))(\( ( 1 + 10 T + 24389 T^{2} )^{2} \))(\( ( 1 + 10 T + 24389 T^{2} )^{2} \))(\( ( 1 - 158 T + 24389 T^{2} )^{2} \))(\( ( 1 - 58 T + 24389 T^{2} )^{2} \))(\( ( 1 - 58 T + 24389 T^{2} )^{2} \))(\( ( 1 - 102 T + 24389 T^{2} )^{2} \))(\( ( 1 + 297 T + 24389 T^{2} )^{2} \))(\( ( 1 - 102 T + 24389 T^{2} )^{2} \))(\( ( 1 - 296 T + 62994 T^{2} - 7219144 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 296 T + 62994 T^{2} - 7219144 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 + 252 T + 56446 T^{2} + 6146028 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 + 252 T + 56446 T^{2} + 6146028 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 53 T + 52695 T^{2} - 3410210 T^{3} + 1285178355 T^{4} - 31525636013 T^{5} + 14507145975869 T^{6} )^{2} \))
$31$ (\( 1 - 36 T - 28495 T^{2} - 1072476 T^{3} + 887503681 T^{4} \))(\( 1 + 48 T - 27487 T^{2} + 1429968 T^{3} + 887503681 T^{4} \))(\( 1 - 48 T - 27487 T^{2} - 1429968 T^{3} + 887503681 T^{4} \))(\( 1 + 36 T - 28495 T^{2} + 1072476 T^{3} + 887503681 T^{4} \))(\( 1 + 264 T + 39905 T^{2} + 7864824 T^{3} + 887503681 T^{4} \))(\( 1 - 264 T + 39905 T^{2} - 7864824 T^{3} + 887503681 T^{4} \))(\( 1 + 160 T - 4191 T^{2} + 4766560 T^{3} + 887503681 T^{4} \))(\( 1 + 253 T + 34218 T^{2} + 7537123 T^{3} + 887503681 T^{4} \))(\( 1 - 160 T - 4191 T^{2} - 4766560 T^{3} + 887503681 T^{4} \))(\( 1 + 104 T - 46470 T^{2} - 238784 T^{3} + 2071962659 T^{4} - 7113614144 T^{5} - 41242296056070 T^{6} + 2749720704709784 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 104 T - 46470 T^{2} + 238784 T^{3} + 2071962659 T^{4} + 7113614144 T^{5} - 41242296056070 T^{6} - 2749720704709784 T^{7} + 787662783788549761 T^{8} \))(\( 1 + 40 T + 15490 T^{2} - 2938880 T^{3} - 742237181 T^{4} - 87552174080 T^{5} + 13747432018690 T^{6} + 1057584886426840 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 40 T + 15490 T^{2} + 2938880 T^{3} - 742237181 T^{4} + 87552174080 T^{5} + 13747432018690 T^{6} - 1057584886426840 T^{7} + 787662783788549761 T^{8} \))(\( 1 + 95 T - 70347 T^{2} - 3756594 T^{3} + 3398738767 T^{4} + 83374434539 T^{5} - 110906046363338 T^{6} + 2483807779351349 T^{7} + 3016393166469901327 T^{8} - 99322925971043714574 T^{9} - \)\(55\!\cdots\!67\)\( T^{10} + \)\(22\!\cdots\!45\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} \))
$37$ (\( 1 - 162 T - 24409 T^{2} - 8205786 T^{3} + 2565726409 T^{4} \))(\( 1 - 246 T + 9863 T^{2} - 12460638 T^{3} + 2565726409 T^{4} \))(\( 1 - 246 T + 9863 T^{2} - 12460638 T^{3} + 2565726409 T^{4} \))(\( 1 - 162 T - 24409 T^{2} - 8205786 T^{3} + 2565726409 T^{4} \))(\( 1 + 258 T + 15911 T^{2} + 13068474 T^{3} + 2565726409 T^{4} \))(\( 1 + 258 T + 15911 T^{2} + 13068474 T^{3} + 2565726409 T^{4} \))(\( 1 + 398 T + 107751 T^{2} + 20159894 T^{3} + 2565726409 T^{4} \))(\( 1 - 316 T + 49203 T^{2} - 16006348 T^{3} + 2565726409 T^{4} \))(\( 1 + 398 T + 107751 T^{2} + 20159894 T^{3} + 2565726409 T^{4} \))(\( 1 - 248 T - 50570 T^{2} - 2670464 T^{3} + 6879492955 T^{4} - 135267012992 T^{5} - 129748784503130 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 248 T - 50570 T^{2} - 2670464 T^{3} + 6879492955 T^{4} - 135267012992 T^{5} - 129748784503130 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 248 T - 36710 T^{2} + 766816 T^{3} + 3964901275 T^{4} + 38841530848 T^{5} - 94187816474390 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 248 T - 36710 T^{2} + 766816 T^{3} + 3964901275 T^{4} + 38841530848 T^{5} - 94187816474390 T^{6} - 32230511469179096 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 262 T - 97404 T^{2} - 9678072 T^{3} + 12194182072 T^{4} + 680381910454 T^{5} - 605701122868778 T^{6} + 34463384910226462 T^{7} + 31286934978284739448 T^{8} - \)\(12\!\cdots\!44\)\( T^{9} - \)\(64\!\cdots\!24\)\( T^{10} + \)\(87\!\cdots\!66\)\( T^{11} + \)\(16\!\cdots\!29\)\( T^{12} \))
$41$ (\( ( 1 + 270 T + 68921 T^{2} )^{2} \))(\( ( 1 - 248 T + 68921 T^{2} )^{2} \))(\( ( 1 + 248 T + 68921 T^{2} )^{2} \))(\( ( 1 - 270 T + 68921 T^{2} )^{2} \))(\( ( 1 + 68921 T^{2} )^{2} \))(\( ( 1 + 68921 T^{2} )^{2} \))(\( ( 1 - 318 T + 68921 T^{2} )^{2} \))(\( ( 1 + 360 T + 68921 T^{2} )^{2} \))(\( ( 1 + 318 T + 68921 T^{2} )^{2} \))(\( ( 1 + 20 T + 42020 T^{2} + 1378420 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 20 T + 42020 T^{2} - 1378420 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 450 T + 175642 T^{2} + 31014450 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 450 T + 175642 T^{2} - 31014450 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 244 T + 187983 T^{2} + 33933832 T^{3} + 12955976343 T^{4} + 1159025434804 T^{5} + 327381934393961 T^{6} )^{2} \))
$43$ (\( ( 1 + 324 T + 79507 T^{2} )^{2} \))(\( ( 1 - 68 T + 79507 T^{2} )^{2} \))(\( ( 1 - 68 T + 79507 T^{2} )^{2} \))(\( ( 1 + 324 T + 79507 T^{2} )^{2} \))(\( ( 1 - 156 T + 79507 T^{2} )^{2} \))(\( ( 1 - 156 T + 79507 T^{2} )^{2} \))(\( ( 1 + 268 T + 79507 T^{2} )^{2} \))(\( ( 1 - 26 T + 79507 T^{2} )^{2} \))(\( ( 1 + 268 T + 79507 T^{2} )^{2} \))(\( ( 1 + 720 T + 268614 T^{2} + 57245040 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 + 720 T + 268614 T^{2} + 57245040 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 376 T + 161526 T^{2} - 29894632 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 376 T + 161526 T^{2} - 29894632 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 360 T + 166158 T^{2} - 38975294 T^{3} + 13210724106 T^{4} - 2275690697640 T^{5} + 502592611936843 T^{6} )^{2} \))
$47$ (\( 1 - 72 T - 98639 T^{2} - 7475256 T^{3} + 10779215329 T^{4} \))(\( 1 - 324 T + 1153 T^{2} - 33638652 T^{3} + 10779215329 T^{4} \))(\( 1 + 324 T + 1153 T^{2} + 33638652 T^{3} + 10779215329 T^{4} \))(\( 1 + 72 T - 98639 T^{2} + 7475256 T^{3} + 10779215329 T^{4} \))(\( 1 + 408 T + 62641 T^{2} + 42359784 T^{3} + 10779215329 T^{4} \))(\( 1 - 408 T + 62641 T^{2} - 42359784 T^{3} + 10779215329 T^{4} \))(\( 1 - 240 T - 46223 T^{2} - 24917520 T^{3} + 10779215329 T^{4} \))(\( 1 + 30 T - 102923 T^{2} + 3114690 T^{3} + 10779215329 T^{4} \))(\( 1 + 240 T - 46223 T^{2} + 24917520 T^{3} + 10779215329 T^{4} \))(\( 1 + 96 T - 75734 T^{2} - 11778816 T^{3} - 4519545597 T^{4} - 1222912013568 T^{5} - 816353093726486 T^{6} + 107436525417865632 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 96 T - 75734 T^{2} + 11778816 T^{3} - 4519545597 T^{4} + 1222912013568 T^{5} - 816353093726486 T^{6} - 107436525417865632 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 12 T - 141646 T^{2} + 790272 T^{3} + 9310238259 T^{4} + 82048409856 T^{5} - 1526832734491534 T^{6} - 13429565677233204 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 12 T - 141646 T^{2} - 790272 T^{3} + 9310238259 T^{4} - 82048409856 T^{5} - 1526832734491534 T^{6} + 13429565677233204 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 210 T - 20853 T^{2} - 83809446 T^{3} - 12756928590 T^{4} + 2596137940074 T^{5} + 3698984470026571 T^{6} + 269538829352302902 T^{7} - \)\(13\!\cdots\!10\)\( T^{8} - \)\(93\!\cdots\!82\)\( T^{9} - \)\(24\!\cdots\!73\)\( T^{10} + \)\(25\!\cdots\!30\)\( T^{11} + \)\(12\!\cdots\!89\)\( T^{12} \))
$53$ (\( 1 - 22 T - 148393 T^{2} - 3275294 T^{3} + 22164361129 T^{4} \))(\( 1 + 258 T - 82313 T^{2} + 38410266 T^{3} + 22164361129 T^{4} \))(\( 1 + 258 T - 82313 T^{2} + 38410266 T^{3} + 22164361129 T^{4} \))(\( 1 - 22 T - 148393 T^{2} - 3275294 T^{3} + 22164361129 T^{4} \))(\( 1 - 722 T + 372407 T^{2} - 107489194 T^{3} + 22164361129 T^{4} \))(\( 1 - 722 T + 372407 T^{2} - 107489194 T^{3} + 22164361129 T^{4} \))(\( 1 - 498 T + 99127 T^{2} - 74140746 T^{3} + 22164361129 T^{4} \))(\( 1 + 363 T - 17108 T^{2} + 54042351 T^{3} + 22164361129 T^{4} \))(\( 1 - 498 T + 99127 T^{2} - 74140746 T^{3} + 22164361129 T^{4} \))(\( 1 + 268 T + 15314 T^{2} - 64653392 T^{3} - 29663922677 T^{4} - 9625403040784 T^{5} + 339425026329506 T^{6} + 884336642602971644 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 268 T + 15314 T^{2} - 64653392 T^{3} - 29663922677 T^{4} - 9625403040784 T^{5} + 339425026329506 T^{6} + 884336642602971644 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 1104 T + 616586 T^{2} - 336141504 T^{3} + 159062942139 T^{4} - 50043738691008 T^{5} + 13666234771085594 T^{6} - 3642939005349554832 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 1104 T + 616586 T^{2} - 336141504 T^{3} + 159062942139 T^{4} - 50043738691008 T^{5} + 13666234771085594 T^{6} - 3642939005349554832 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 393 T - 211446 T^{2} - 23899125 T^{3} + 46453564620 T^{4} - 3425920762143 T^{5} - 9724787230272680 T^{6} - 510040805305563411 T^{7} + \)\(10\!\cdots\!80\)\( T^{8} - \)\(78\!\cdots\!25\)\( T^{9} - \)\(10\!\cdots\!86\)\( T^{10} + \)\(28\!\cdots\!01\)\( T^{11} + \)\(10\!\cdots\!89\)\( T^{12} \))
$59$ (\( 1 + 468 T + 13645 T^{2} + 96117372 T^{3} + 42180533641 T^{4} \))(\( 1 - 120 T - 190979 T^{2} - 24645480 T^{3} + 42180533641 T^{4} \))(\( 1 + 120 T - 190979 T^{2} + 24645480 T^{3} + 42180533641 T^{4} \))(\( 1 - 468 T + 13645 T^{2} - 96117372 T^{3} + 42180533641 T^{4} \))(\( 1 - 492 T + 36685 T^{2} - 101046468 T^{3} + 42180533641 T^{4} \))(\( 1 + 492 T + 36685 T^{2} + 101046468 T^{3} + 42180533641 T^{4} \))(\( 1 + 132 T - 187955 T^{2} + 27110028 T^{3} + 42180533641 T^{4} \))(\( 1 + 15 T - 205154 T^{2} + 3080685 T^{3} + 42180533641 T^{4} \))(\( 1 - 132 T - 187955 T^{2} - 27110028 T^{3} + 42180533641 T^{4} \))(\( 1 + 616 T - 24014 T^{2} - 4489408 T^{3} + 42675213435 T^{4} - 922030125632 T^{5} - 1012923334854974 T^{6} + 5336405424291442424 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 616 T - 24014 T^{2} + 4489408 T^{3} + 42675213435 T^{4} + 922030125632 T^{5} - 1012923334854974 T^{6} - 5336405424291442424 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 804 T + 265802 T^{2} - 24235776 T^{3} - 30073788309 T^{4} - 4977519439104 T^{5} + 11211670202845082 T^{6} + 6965048638198570956 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 804 T + 265802 T^{2} + 24235776 T^{3} - 30073788309 T^{4} + 4977519439104 T^{5} + 11211670202845082 T^{6} - 6965048638198570956 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 1143 T + 557208 T^{2} - 118327563 T^{3} - 14314666608 T^{4} + 27063102119841 T^{5} - 16891447327378130 T^{6} + 5558192850270824739 T^{7} - \)\(60\!\cdots\!28\)\( T^{8} - \)\(10\!\cdots\!57\)\( T^{9} + \)\(99\!\cdots\!48\)\( T^{10} - \)\(41\!\cdots\!57\)\( T^{11} + \)\(75\!\cdots\!21\)\( T^{12} \))
$61$ (\( 1 + 792 T + 400283 T^{2} + 179768952 T^{3} + 51520374361 T^{4} \))(\( 1 - 622 T + 159903 T^{2} - 141182182 T^{3} + 51520374361 T^{4} \))(\( 1 + 622 T + 159903 T^{2} + 141182182 T^{3} + 51520374361 T^{4} \))(\( 1 - 792 T + 400283 T^{2} - 179768952 T^{3} + 51520374361 T^{4} \))(\( 1 + 492 T + 15083 T^{2} + 111674652 T^{3} + 51520374361 T^{4} \))(\( 1 - 492 T + 15083 T^{2} - 111674652 T^{3} + 51520374361 T^{4} \))(\( 1 - 398 T - 68577 T^{2} - 90338438 T^{3} + 51520374361 T^{4} \))(\( 1 + 118 T - 213057 T^{2} + 26783758 T^{3} + 51520374361 T^{4} \))(\( 1 + 398 T - 68577 T^{2} + 90338438 T^{3} + 51520374361 T^{4} \))(\( 1 - 16 T - 453752 T^{2} - 736 T^{3} + 154544782567 T^{4} - 167058016 T^{5} - 23377472907052472 T^{6} - 187106337485346256 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 16 T - 453752 T^{2} + 736 T^{3} + 154544782567 T^{4} + 167058016 T^{5} - 23377472907052472 T^{6} + 187106337485346256 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 428 T - 242702 T^{2} + 12016528 T^{3} + 88279223131 T^{4} + 2727523541968 T^{5} - 12504097898163422 T^{6} - 5005094527733012348 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 428 T - 242702 T^{2} - 12016528 T^{3} + 88279223131 T^{4} - 2727523541968 T^{5} - 12504097898163422 T^{6} + 5005094527733012348 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 70 T - 335143 T^{2} + 129510330 T^{3} + 42145697866 T^{4} - 25171752927730 T^{5} - 316289217432887 T^{6} - 5713509651289083130 T^{7} + \)\(21\!\cdots\!26\)\( T^{8} + \)\(15\!\cdots\!30\)\( T^{9} - \)\(88\!\cdots\!03\)\( T^{10} + \)\(42\!\cdots\!70\)\( T^{11} + \)\(13\!\cdots\!81\)\( T^{12} \))
$67$ (\( 1 + 232 T - 246939 T^{2} + 69777016 T^{3} + 90458382169 T^{4} \))(\( 1 + 904 T + 516453 T^{2} + 271889752 T^{3} + 90458382169 T^{4} \))(\( 1 + 904 T + 516453 T^{2} + 271889752 T^{3} + 90458382169 T^{4} \))(\( 1 + 232 T - 246939 T^{2} + 69777016 T^{3} + 90458382169 T^{4} \))(\( 1 + 412 T - 131019 T^{2} + 123914356 T^{3} + 90458382169 T^{4} \))(\( 1 + 412 T - 131019 T^{2} + 123914356 T^{3} + 90458382169 T^{4} \))(\( 1 + 92 T - 292299 T^{2} + 27670196 T^{3} + 90458382169 T^{4} \))(\( 1 - 370 T - 163863 T^{2} - 111282310 T^{3} + 90458382169 T^{4} \))(\( 1 + 92 T - 292299 T^{2} + 27670196 T^{3} + 90458382169 T^{4} \))(\( 1 - 144 T - 36822 T^{2} + 78331392 T^{3} - 93382080373 T^{4} + 23559184452096 T^{5} - 3330858548226918 T^{6} - 3917740953066472368 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 144 T - 36822 T^{2} + 78331392 T^{3} - 93382080373 T^{4} + 23559184452096 T^{5} - 3330858548226918 T^{6} - 3917740953066472368 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 148 T - 418886 T^{2} - 23788928 T^{3} + 97249529179 T^{4} - 7154829352064 T^{5} - 37891749873243734 T^{6} + 4026567090651652156 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 148 T - 418886 T^{2} - 23788928 T^{3} + 97249529179 T^{4} - 7154829352064 T^{5} - 37891749873243734 T^{6} + 4026567090651652156 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 628 T - 202942 T^{2} + 436381932 T^{3} - 77667044702 T^{4} - 73528811914784 T^{5} + 76060129771959310 T^{6} - 22114746057926180192 T^{7} - \)\(70\!\cdots\!38\)\( T^{8} + \)\(11\!\cdots\!04\)\( T^{9} - \)\(16\!\cdots\!62\)\( T^{10} - \)\(15\!\cdots\!04\)\( T^{11} + \)\(74\!\cdots\!09\)\( T^{12} \))
$71$ (\( ( 1 + 734 T + 357911 T^{2} )^{2} \))(\( ( 1 + 678 T + 357911 T^{2} )^{2} \))(\( ( 1 + 678 T + 357911 T^{2} )^{2} \))(\( ( 1 + 734 T + 357911 T^{2} )^{2} \))(\( ( 1 - 296 T + 357911 T^{2} )^{2} \))(\( ( 1 - 296 T + 357911 T^{2} )^{2} \))(\( ( 1 + 720 T + 357911 T^{2} )^{2} \))(\( ( 1 + 342 T + 357911 T^{2} )^{2} \))(\( ( 1 + 720 T + 357911 T^{2} )^{2} \))(\( ( 1 - 988 T + 852210 T^{2} - 353616068 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 988 T + 852210 T^{2} - 353616068 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 954 T + 930526 T^{2} - 341447094 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 954 T + 930526 T^{2} - 341447094 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 318 T + 742929 T^{2} - 256167372 T^{3} + 265902461319 T^{4} - 40735890286878 T^{5} + 45848500718449031 T^{6} )^{2} \))
$73$ (\( 1 + 180 T - 356617 T^{2} + 70023060 T^{3} + 151334226289 T^{4} \))(\( 1 + 642 T + 23147 T^{2} + 249748914 T^{3} + 151334226289 T^{4} \))(\( 1 - 642 T + 23147 T^{2} - 249748914 T^{3} + 151334226289 T^{4} \))(\( 1 - 180 T - 356617 T^{2} - 70023060 T^{3} + 151334226289 T^{4} \))(\( 1 - 240 T - 331417 T^{2} - 93364080 T^{3} + 151334226289 T^{4} \))(\( 1 + 240 T - 331417 T^{2} + 93364080 T^{3} + 151334226289 T^{4} \))(\( 1 + 502 T - 137013 T^{2} + 195286534 T^{3} + 151334226289 T^{4} \))(\( 1 - 362 T - 257973 T^{2} - 140824154 T^{3} + 151334226289 T^{4} \))(\( 1 - 502 T - 137013 T^{2} - 195286534 T^{3} + 151334226289 T^{4} \))(\( 1 - 104 T - 448320 T^{2} + 33165392 T^{3} + 55264032335 T^{4} + 12901901299664 T^{5} - 67846160329884480 T^{6} - 6122645017659862952 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 104 T - 448320 T^{2} - 33165392 T^{3} + 55264032335 T^{4} - 12901901299664 T^{5} - 67846160329884480 T^{6} + 6122645017659862952 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 1072 T + 85906 T^{2} + 305781568 T^{3} + 532173766867 T^{4} + 118954228238656 T^{5} + 13000518043582834 T^{6} + 63110340951263202736 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 1072 T + 85906 T^{2} - 305781568 T^{3} + 532173766867 T^{4} - 118954228238656 T^{5} + 13000518043582834 T^{6} - 63110340951263202736 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 988 T - 186552 T^{2} + 102237300 T^{3} + 281568890272 T^{4} + 16988127696596 T^{5} - 164639785652996186 T^{6} + 6608670472146686132 T^{7} + \)\(42\!\cdots\!08\)\( T^{8} + \)\(60\!\cdots\!00\)\( T^{9} - \)\(42\!\cdots\!92\)\( T^{10} - \)\(88\!\cdots\!16\)\( T^{11} + \)\(34\!\cdots\!69\)\( T^{12} \))
$79$ (\( 1 + 236 T - 437343 T^{2} + 116357204 T^{3} + 243087455521 T^{4} \))(\( 1 + 740 T + 54561 T^{2} + 364848860 T^{3} + 243087455521 T^{4} \))(\( 1 + 740 T + 54561 T^{2} + 364848860 T^{3} + 243087455521 T^{4} \))(\( 1 + 236 T - 437343 T^{2} + 116357204 T^{3} + 243087455521 T^{4} \))(\( 1 + 776 T + 109137 T^{2} + 382598264 T^{3} + 243087455521 T^{4} \))(\( 1 + 776 T + 109137 T^{2} + 382598264 T^{3} + 243087455521 T^{4} \))(\( 1 - 1024 T + 555537 T^{2} - 504871936 T^{3} + 243087455521 T^{4} \))(\( 1 + 467 T - 274950 T^{2} + 230249213 T^{3} + 243087455521 T^{4} \))(\( 1 - 1024 T + 555537 T^{2} - 504871936 T^{3} + 243087455521 T^{4} \))(\( 1 - 944 T - 206334 T^{2} - 105154048 T^{3} + 521988143075 T^{4} - 51845046671872 T^{5} - 50157207047470014 T^{6} - \)\(11\!\cdots\!36\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 944 T - 206334 T^{2} - 105154048 T^{3} + 521988143075 T^{4} - 51845046671872 T^{5} - 50157207047470014 T^{6} - \)\(11\!\cdots\!36\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 572 T - 574478 T^{2} + 48285952 T^{3} + 408592434547 T^{4} + 23806857488128 T^{5} - 139648395272793038 T^{6} - 68555112902057678468 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 572 T - 574478 T^{2} + 48285952 T^{3} + 408592434547 T^{4} + 23806857488128 T^{5} - 139648395272793038 T^{6} - 68555112902057678468 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 + 861 T - 479895 T^{2} - 258646666 T^{3} + 325257480351 T^{4} - 27564282842211 T^{5} - 246706047980056146 T^{6} - 13590266448240869229 T^{7} + \)\(79\!\cdots\!71\)\( T^{8} - \)\(30\!\cdots\!54\)\( T^{9} - \)\(28\!\cdots\!95\)\( T^{10} + \)\(25\!\cdots\!39\)\( T^{11} + \)\(14\!\cdots\!61\)\( T^{12} \))
$83$ (\( ( 1 - 36 T + 571787 T^{2} )^{2} \))(\( ( 1 + 468 T + 571787 T^{2} )^{2} \))(\( ( 1 - 468 T + 571787 T^{2} )^{2} \))(\( ( 1 + 36 T + 571787 T^{2} )^{2} \))(\( ( 1 + 924 T + 571787 T^{2} )^{2} \))(\( ( 1 - 924 T + 571787 T^{2} )^{2} \))(\( ( 1 - 204 T + 571787 T^{2} )^{2} \))(\( ( 1 + 477 T + 571787 T^{2} )^{2} \))(\( ( 1 + 204 T + 571787 T^{2} )^{2} \))(\( ( 1 + 1016 T + 1388838 T^{2} + 580935592 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 1016 T + 1388838 T^{2} - 580935592 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 1944 T + 1957030 T^{2} - 1111553928 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 1944 T + 1957030 T^{2} + 1111553928 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 519 T + 1583745 T^{2} + 545598870 T^{3} + 905564802315 T^{4} + 169682053778511 T^{5} + 186940255267540403 T^{6} )^{2} \))
$89$ (\( 1 + 234 T - 650213 T^{2} + 164962746 T^{3} + 496981290961 T^{4} \))(\( 1 - 200 T - 664969 T^{2} - 140993800 T^{3} + 496981290961 T^{4} \))(\( 1 + 200 T - 664969 T^{2} + 140993800 T^{3} + 496981290961 T^{4} \))(\( 1 - 234 T - 650213 T^{2} - 164962746 T^{3} + 496981290961 T^{4} \))(\( 1 + 744 T - 151433 T^{2} + 524496936 T^{3} + 496981290961 T^{4} \))(\( 1 - 744 T - 151433 T^{2} - 524496936 T^{3} + 496981290961 T^{4} \))(\( 1 - 354 T - 579653 T^{2} - 249559026 T^{3} + 496981290961 T^{4} \))(\( 1 - 906 T + 115867 T^{2} - 638701914 T^{3} + 496981290961 T^{4} \))(\( 1 + 354 T - 579653 T^{2} + 249559026 T^{3} + 496981290961 T^{4} \))(\( 1 + 388 T - 1067188 T^{2} - 74575928 T^{3} + 879761079727 T^{4} - 52573717386232 T^{5} - 530372469938087668 T^{6} + \)\(13\!\cdots\!92\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 388 T - 1067188 T^{2} + 74575928 T^{3} + 879761079727 T^{4} + 52573717386232 T^{5} - 530372469938087668 T^{6} - \)\(13\!\cdots\!92\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 366 T - 1022134 T^{2} - 92908368 T^{3} + 745127969775 T^{4} - 65497519280592 T^{5} - 507981474855130774 T^{6} + \)\(12\!\cdots\!94\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 366 T - 1022134 T^{2} + 92908368 T^{3} + 745127969775 T^{4} + 65497519280592 T^{5} - 507981474855130774 T^{6} - \)\(12\!\cdots\!94\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 1766 T + 725929 T^{2} + 728159446 T^{3} - 335534377858 T^{4} - 846551335831238 T^{5} + 1249625385561159997 T^{6} - \)\(59\!\cdots\!22\)\( T^{7} - \)\(16\!\cdots\!38\)\( T^{8} + \)\(25\!\cdots\!14\)\( T^{9} + \)\(17\!\cdots\!09\)\( T^{10} - \)\(30\!\cdots\!34\)\( T^{11} + \)\(12\!\cdots\!81\)\( T^{12} \))
$97$ (\( ( 1 - 468 T + 912673 T^{2} )^{2} \))(\( ( 1 - 1266 T + 912673 T^{2} )^{2} \))(\( ( 1 + 1266 T + 912673 T^{2} )^{2} \))(\( ( 1 + 468 T + 912673 T^{2} )^{2} \))(\( ( 1 - 168 T + 912673 T^{2} )^{2} \))(\( ( 1 + 168 T + 912673 T^{2} )^{2} \))(\( ( 1 - 286 T + 912673 T^{2} )^{2} \))(\( ( 1 + 503 T + 912673 T^{2} )^{2} \))(\( ( 1 + 286 T + 912673 T^{2} )^{2} \))(\( ( 1 + 488 T + 1167280 T^{2} + 445384424 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 488 T + 1167280 T^{2} - 445384424 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 808 T + 903054 T^{2} - 737439784 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 + 808 T + 903054 T^{2} + 737439784 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 + 19 T + 2168419 T^{2} - 10094878 T^{3} + 1979057473987 T^{4} + 15826468093651 T^{5} + 760231058654565217 T^{6} )^{2} \))
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