Properties

Label 4004.2
Level 4004
Weight 2
Dimension 260824
Nonzero newspaces 120
Sturm bound 1935360

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Defining parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(1935360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4004))\).

Total New Old
Modular forms 491040 264792 226248
Cusp forms 476641 260824 215817
Eisenstein series 14399 3968 10431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4004))\)

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
4004.2.a \(\chi_{4004}(1, \cdot)\) 4004.2.a.a 1 1
4004.2.a.b 1
4004.2.a.c 1
4004.2.a.d 4
4004.2.a.e 4
4004.2.a.f 5
4004.2.a.g 6
4004.2.a.h 9
4004.2.a.i 9
4004.2.a.j 10
4004.2.a.k 10
4004.2.b \(\chi_{4004}(3431, \cdot)\) n/a 504 1
4004.2.e \(\chi_{4004}(3849, \cdot)\) 4004.2.e.a 48 1
4004.2.e.b 48
4004.2.f \(\chi_{4004}(1275, \cdot)\) n/a 432 1
4004.2.i \(\chi_{4004}(2001, \cdot)\) n/a 112 1
4004.2.j \(\chi_{4004}(2575, \cdot)\) n/a 480 1
4004.2.m \(\chi_{4004}(2157, \cdot)\) 4004.2.m.a 2 1
4004.2.m.b 30
4004.2.m.c 36
4004.2.n \(\chi_{4004}(727, \cdot)\) n/a 560 1
4004.2.q \(\chi_{4004}(529, \cdot)\) n/a 188 2
4004.2.r \(\chi_{4004}(1145, \cdot)\) n/a 160 2
4004.2.s \(\chi_{4004}(1849, \cdot)\) n/a 144 2
4004.2.t \(\chi_{4004}(1101, \cdot)\) n/a 188 2
4004.2.v \(\chi_{4004}(463, \cdot)\) n/a 840 2
4004.2.w \(\chi_{4004}(265, \cdot)\) n/a 192 2
4004.2.z \(\chi_{4004}(307, \cdot)\) n/a 1328 2
4004.2.ba \(\chi_{4004}(1737, \cdot)\) n/a 168 2
4004.2.bc \(\chi_{4004}(729, \cdot)\) n/a 288 4
4004.2.bd \(\chi_{4004}(901, \cdot)\) n/a 224 2
4004.2.bg \(\chi_{4004}(263, \cdot)\) n/a 1328 2
4004.2.bh \(\chi_{4004}(549, \cdot)\) n/a 224 2
4004.2.bk \(\chi_{4004}(1759, \cdot)\) n/a 1328 2
4004.2.bl \(\chi_{4004}(309, \cdot)\) n/a 136 2
4004.2.bo \(\chi_{4004}(419, \cdot)\) n/a 1120 2
4004.2.bp \(\chi_{4004}(199, \cdot)\) n/a 1120 2
4004.2.bu \(\chi_{4004}(3015, \cdot)\) n/a 1120 2
4004.2.bv \(\chi_{4004}(3301, \cdot)\) n/a 184 2
4004.2.by \(\chi_{4004}(859, \cdot)\) n/a 960 2
4004.2.bz \(\chi_{4004}(815, \cdot)\) n/a 1120 2
4004.2.cc \(\chi_{4004}(2025, \cdot)\) n/a 188 2
4004.2.cf \(\chi_{4004}(1343, \cdot)\) n/a 1120 2
4004.2.cg \(\chi_{4004}(1693, \cdot)\) n/a 224 2
4004.2.cj \(\chi_{4004}(43, \cdot)\) n/a 1008 2
4004.2.ck \(\chi_{4004}(285, \cdot)\) n/a 224 2
4004.2.cn \(\chi_{4004}(2419, \cdot)\) n/a 1152 2
4004.2.co \(\chi_{4004}(835, \cdot)\) n/a 1328 2
4004.2.cr \(\chi_{4004}(1473, \cdot)\) n/a 224 2
4004.2.cs \(\chi_{4004}(1187, \cdot)\) n/a 1328 2
4004.2.cv \(\chi_{4004}(2089, \cdot)\) n/a 224 2
4004.2.cw \(\chi_{4004}(2133, \cdot)\) n/a 192 2
4004.2.cz \(\chi_{4004}(571, \cdot)\) n/a 1328 2
4004.2.da \(\chi_{4004}(153, \cdot)\) n/a 224 2
4004.2.dd \(\chi_{4004}(659, \cdot)\) n/a 1008 2
4004.2.dg \(\chi_{4004}(1739, \cdot)\) n/a 1120 2
4004.2.dh \(\chi_{4004}(485, \cdot)\) n/a 188 2
4004.2.dk \(\chi_{4004}(243, \cdot)\) n/a 1120 2
4004.2.dm \(\chi_{4004}(1455, \cdot)\) n/a 2656 4
4004.2.dp \(\chi_{4004}(1065, \cdot)\) n/a 336 4
4004.2.dq \(\chi_{4004}(27, \cdot)\) n/a 2304 4
4004.2.dt \(\chi_{4004}(545, \cdot)\) n/a 448 4
4004.2.du \(\chi_{4004}(183, \cdot)\) n/a 1728 4
4004.2.dx \(\chi_{4004}(937, \cdot)\) n/a 384 4
4004.2.dy \(\chi_{4004}(519, \cdot)\) n/a 2016 4
4004.2.eb \(\chi_{4004}(353, \cdot)\) n/a 376 4
4004.2.ec \(\chi_{4004}(67, \cdot)\) n/a 2240 4
4004.2.ef \(\chi_{4004}(1055, \cdot)\) n/a 2656 4
4004.2.ei \(\chi_{4004}(197, \cdot)\) n/a 336 4
4004.2.ej \(\chi_{4004}(109, \cdot)\) n/a 448 4
4004.2.ek \(\chi_{4004}(2463, \cdot)\) n/a 2656 4
4004.2.el \(\chi_{4004}(395, \cdot)\) n/a 2656 4
4004.2.eo \(\chi_{4004}(1033, \cdot)\) n/a 448 4
4004.2.er \(\chi_{4004}(639, \cdot)\) n/a 2240 4
4004.2.eu \(\chi_{4004}(1189, \cdot)\) n/a 368 4
4004.2.ev \(\chi_{4004}(1321, \cdot)\) n/a 368 4
4004.2.ew \(\chi_{4004}(2619, \cdot)\) n/a 1680 4
4004.2.ex \(\chi_{4004}(1607, \cdot)\) n/a 2240 4
4004.2.fa \(\chi_{4004}(45, \cdot)\) n/a 376 4
4004.2.fd \(\chi_{4004}(1341, \cdot)\) n/a 448 4
4004.2.fe \(\chi_{4004}(747, \cdot)\) n/a 2656 4
4004.2.fg \(\chi_{4004}(9, \cdot)\) n/a 896 8
4004.2.fh \(\chi_{4004}(113, \cdot)\) n/a 672 8
4004.2.fi \(\chi_{4004}(53, \cdot)\) n/a 768 8
4004.2.fj \(\chi_{4004}(289, \cdot)\) n/a 896 8
4004.2.fk \(\chi_{4004}(57, \cdot)\) n/a 672 8
4004.2.fn \(\chi_{4004}(83, \cdot)\) n/a 5312 8
4004.2.fo \(\chi_{4004}(125, \cdot)\) n/a 896 8
4004.2.fr \(\chi_{4004}(603, \cdot)\) n/a 4032 8
4004.2.ft \(\chi_{4004}(3, \cdot)\) n/a 5312 8
4004.2.fu \(\chi_{4004}(361, \cdot)\) n/a 896 8
4004.2.fx \(\chi_{4004}(355, \cdot)\) n/a 5312 8
4004.2.ga \(\chi_{4004}(211, \cdot)\) n/a 4032 8
4004.2.gb \(\chi_{4004}(1161, \cdot)\) n/a 896 8
4004.2.ge \(\chi_{4004}(51, \cdot)\) n/a 5312 8
4004.2.gf \(\chi_{4004}(677, \cdot)\) n/a 768 8
4004.2.gi \(\chi_{4004}(633, \cdot)\) n/a 896 8
4004.2.gj \(\chi_{4004}(95, \cdot)\) n/a 5312 8
4004.2.gm \(\chi_{4004}(17, \cdot)\) n/a 896 8
4004.2.gn \(\chi_{4004}(107, \cdot)\) n/a 5312 8
4004.2.gq \(\chi_{4004}(79, \cdot)\) n/a 4608 8
4004.2.gr \(\chi_{4004}(129, \cdot)\) n/a 896 8
4004.2.gu \(\chi_{4004}(127, \cdot)\) n/a 4032 8
4004.2.gv \(\chi_{4004}(237, \cdot)\) n/a 896 8
4004.2.gy \(\chi_{4004}(251, \cdot)\) n/a 5312 8
4004.2.hb \(\chi_{4004}(641, \cdot)\) n/a 896 8
4004.2.hc \(\chi_{4004}(159, \cdot)\) n/a 5312 8
4004.2.hf \(\chi_{4004}(339, \cdot)\) n/a 4608 8
4004.2.hg \(\chi_{4004}(25, \cdot)\) n/a 896 8
4004.2.hj \(\chi_{4004}(103, \cdot)\) n/a 5312 8
4004.2.hm \(\chi_{4004}(75, \cdot)\) n/a 5312 8
4004.2.hp \(\chi_{4004}(867, \cdot)\) n/a 5312 8
4004.2.hq \(\chi_{4004}(225, \cdot)\) n/a 672 8
4004.2.ht \(\chi_{4004}(303, \cdot)\) n/a 5312 8
4004.2.hu \(\chi_{4004}(61, \cdot)\) n/a 896 8
4004.2.hx \(\chi_{4004}(919, \cdot)\) n/a 5312 8
4004.2.hy \(\chi_{4004}(101, \cdot)\) n/a 896 8
4004.2.ia \(\chi_{4004}(19, \cdot)\) n/a 10624 16
4004.2.id \(\chi_{4004}(149, \cdot)\) n/a 1792 16
4004.2.ie \(\chi_{4004}(509, \cdot)\) n/a 1792 16
4004.2.ig \(\chi_{4004}(135, \cdot)\) n/a 10624 16
4004.2.ih \(\chi_{4004}(15, \cdot)\) n/a 8064 16
4004.2.im \(\chi_{4004}(5, \cdot)\) n/a 1792 16
4004.2.in \(\chi_{4004}(97, \cdot)\) n/a 1792 16
4004.2.ip \(\chi_{4004}(487, \cdot)\) n/a 10624 16
4004.2.iq \(\chi_{4004}(305, \cdot)\) n/a 1792 16
4004.2.is \(\chi_{4004}(255, \cdot)\) n/a 10624 16
4004.2.it \(\chi_{4004}(167, \cdot)\) n/a 10624 16
4004.2.iy \(\chi_{4004}(541, \cdot)\) n/a 1792 16
4004.2.iz \(\chi_{4004}(85, \cdot)\) n/a 1344 16
4004.2.jb \(\chi_{4004}(227, \cdot)\) n/a 10624 16
4004.2.jc \(\chi_{4004}(163, \cdot)\) n/a 10624 16
4004.2.jf \(\chi_{4004}(201, \cdot)\) n/a 1792 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2002))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + 3 T + 10 T^{2} + 21 T^{3} + 45 T^{4} + 63 T^{5} + 90 T^{6} + 81 T^{7} + 81 T^{8} \))(\( 1 - T + 8 T^{2} - 5 T^{3} + 31 T^{4} - 15 T^{5} + 72 T^{6} - 27 T^{7} + 81 T^{8} \))(\( 1 - 3 T + 11 T^{2} - 22 T^{3} + 51 T^{4} - 84 T^{5} + 153 T^{6} - 198 T^{7} + 297 T^{8} - 243 T^{9} + 243 T^{10} \))(\( 1 + 2 T + 9 T^{2} + 16 T^{3} + 42 T^{4} + 67 T^{5} + 134 T^{6} + 201 T^{7} + 378 T^{8} + 432 T^{9} + 729 T^{10} + 486 T^{11} + 729 T^{12} \))(\( 1 - 3 T + 8 T^{2} - 21 T^{3} + 41 T^{4} - 85 T^{5} + 168 T^{6} - 327 T^{7} + 639 T^{8} - 1094 T^{9} + 1917 T^{10} - 2943 T^{11} + 4536 T^{12} - 6885 T^{13} + 9963 T^{14} - 15309 T^{15} + 17496 T^{16} - 19683 T^{17} + 19683 T^{18} \))(\( 1 - 4 T + 15 T^{2} - 36 T^{3} + 87 T^{4} - 161 T^{5} + 299 T^{6} - 473 T^{7} + 815 T^{8} - 1323 T^{9} + 2445 T^{10} - 4257 T^{11} + 8073 T^{12} - 13041 T^{13} + 21141 T^{14} - 26244 T^{15} + 32805 T^{16} - 26244 T^{17} + 19683 T^{18} \))(\( 1 + 2 T + 12 T^{2} + 22 T^{3} + 66 T^{4} + 95 T^{5} + 204 T^{6} + 166 T^{7} + 312 T^{8} - 64 T^{9} + 304 T^{10} - 192 T^{11} + 2808 T^{12} + 4482 T^{13} + 16524 T^{14} + 23085 T^{15} + 48114 T^{16} + 48114 T^{17} + 78732 T^{18} + 39366 T^{19} + 59049 T^{20} \))(\( 1 - T + 7 T^{2} - 4 T^{3} + 23 T^{4} - 6 T^{5} + 93 T^{6} - 36 T^{7} + 363 T^{8} - 129 T^{9} + 1086 T^{10} - 387 T^{11} + 3267 T^{12} - 972 T^{13} + 7533 T^{14} - 1458 T^{15} + 16767 T^{16} - 8748 T^{17} + 45927 T^{18} - 19683 T^{19} + 59049 T^{20} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))
$5$ (\( 1 + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + T + 12 T^{2} + 21 T^{3} + 69 T^{4} + 105 T^{5} + 300 T^{6} + 125 T^{7} + 625 T^{8} \))(\( 1 - T + 16 T^{2} - 11 T^{3} + 111 T^{4} - 55 T^{5} + 400 T^{6} - 125 T^{7} + 625 T^{8} \))(\( 1 + 12 T^{2} - 12 T^{3} + 74 T^{4} - 107 T^{5} + 370 T^{6} - 300 T^{7} + 1500 T^{8} + 3125 T^{10} \))(\( 1 + 3 T + 21 T^{2} + 50 T^{3} + 212 T^{4} + 421 T^{5} + 1319 T^{6} + 2105 T^{7} + 5300 T^{8} + 6250 T^{9} + 13125 T^{10} + 9375 T^{11} + 15625 T^{12} \))(\( 1 + 21 T^{2} + 4 T^{3} + 231 T^{4} + 125 T^{5} + 1723 T^{6} + 1475 T^{7} + 10031 T^{8} + 9583 T^{9} + 50155 T^{10} + 36875 T^{11} + 215375 T^{12} + 78125 T^{13} + 721875 T^{14} + 62500 T^{15} + 1640625 T^{16} + 1953125 T^{18} \))(\( 1 - 4 T + 13 T^{2} - 24 T^{3} + 49 T^{4} - 63 T^{5} + 131 T^{6} - 541 T^{7} + 1767 T^{8} - 4913 T^{9} + 8835 T^{10} - 13525 T^{11} + 16375 T^{12} - 39375 T^{13} + 153125 T^{14} - 375000 T^{15} + 1015625 T^{16} - 1562500 T^{17} + 1953125 T^{18} \))(\( 1 + 2 T + 16 T^{2} + 6 T^{3} + 96 T^{4} - 81 T^{5} + 562 T^{6} - 814 T^{7} + 2628 T^{8} - 7328 T^{9} + 9650 T^{10} - 36640 T^{11} + 65700 T^{12} - 101750 T^{13} + 351250 T^{14} - 253125 T^{15} + 1500000 T^{16} + 468750 T^{17} + 6250000 T^{18} + 3906250 T^{19} + 9765625 T^{20} \))(\( 1 - 4 T + 22 T^{2} - 66 T^{3} + 244 T^{4} - 639 T^{5} + 2066 T^{6} - 4878 T^{7} + 13658 T^{8} - 28914 T^{9} + 73054 T^{10} - 144570 T^{11} + 341450 T^{12} - 609750 T^{13} + 1291250 T^{14} - 1996875 T^{15} + 3812500 T^{16} - 5156250 T^{17} + 8593750 T^{18} - 7812500 T^{19} + 9765625 T^{20} \))(\( 1 - 9 T^{2} + 25 T^{4} \))
$7$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{10} \))(\( 1 + T^{2} \))
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))(\( 1 + T^{2} \))
$13$ (\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))(\( 1 - 4 T + 13 T^{2} \))
$17$ (\( 1 - 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 7 T + 78 T^{2} + 339 T^{3} + 2037 T^{4} + 5763 T^{5} + 22542 T^{6} + 34391 T^{7} + 83521 T^{8} \))(\( 1 - T + 44 T^{2} + 23 T^{3} + 859 T^{4} + 391 T^{5} + 12716 T^{6} - 4913 T^{7} + 83521 T^{8} \))(\( 1 + 9 T + 83 T^{2} + 500 T^{3} + 2859 T^{4} + 11932 T^{5} + 48603 T^{6} + 144500 T^{7} + 407779 T^{8} + 751689 T^{9} + 1419857 T^{10} \))(\( 1 + T + 70 T^{2} + 49 T^{3} + 2404 T^{4} + 1316 T^{5} + 50846 T^{6} + 22372 T^{7} + 694756 T^{8} + 240737 T^{9} + 5846470 T^{10} + 1419857 T^{11} + 24137569 T^{12} \))(\( 1 - 5 T + 58 T^{2} - 269 T^{3} + 1851 T^{4} - 6863 T^{5} + 35928 T^{6} - 115557 T^{7} + 557691 T^{8} - 1709086 T^{9} + 9480747 T^{10} - 33395973 T^{11} + 176514264 T^{12} - 573204623 T^{13} + 2628155307 T^{14} - 6493006061 T^{15} + 23799643034 T^{16} - 34878787205 T^{17} + 118587876497 T^{18} \))(\( 1 + 5 T + 112 T^{2} + 435 T^{3} + 5849 T^{4} + 18779 T^{5} + 193018 T^{6} + 525275 T^{7} + 4474639 T^{8} + 10441272 T^{9} + 76068863 T^{10} + 151804475 T^{11} + 948297434 T^{12} + 1568440859 T^{13} + 8304743593 T^{14} + 10499842515 T^{15} + 45957931376 T^{16} + 34878787205 T^{17} + 118587876497 T^{18} \))(\( 1 - 9 T + 69 T^{2} - 436 T^{3} + 2695 T^{4} - 12760 T^{5} + 58397 T^{6} - 236522 T^{7} + 993569 T^{8} - 3610763 T^{9} + 14884862 T^{10} - 61382971 T^{11} + 287141441 T^{12} - 1162032586 T^{13} + 4877375837 T^{14} - 18117375320 T^{15} + 65050748455 T^{16} - 178907661428 T^{17} + 481327263429 T^{18} - 1067290888473 T^{19} + 2015993900449 T^{20} \))(\( 1 - 3 T + 67 T^{2} - 106 T^{3} + 1907 T^{4} - 606 T^{5} + 39625 T^{6} - 208 T^{7} + 923147 T^{8} - 619153 T^{9} + 18874930 T^{10} - 10525601 T^{11} + 266789483 T^{12} - 1021904 T^{13} + 3309519625 T^{14} - 860433342 T^{15} + 46030344083 T^{16} - 43495899338 T^{17} + 467375748547 T^{18} - 355763629491 T^{19} + 2015993900449 T^{20} \))(\( ( 1 + 4 T + 17 T^{2} )^{2} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 9 T + 98 T^{2} + 525 T^{3} + 3003 T^{4} + 9975 T^{5} + 35378 T^{6} + 61731 T^{7} + 130321 T^{8} \))(\( 1 + 3 T + 60 T^{2} + 153 T^{3} + 1589 T^{4} + 2907 T^{5} + 21660 T^{6} + 20577 T^{7} + 130321 T^{8} \))(\( 1 + 4 T + 74 T^{2} + 228 T^{3} + 2452 T^{4} + 5875 T^{5} + 46588 T^{6} + 82308 T^{7} + 507566 T^{8} + 521284 T^{9} + 2476099 T^{10} \))(\( 1 + 12 T + 131 T^{2} + 1004 T^{3} + 6562 T^{4} + 35859 T^{5} + 168496 T^{6} + 681321 T^{7} + 2368882 T^{8} + 6886436 T^{9} + 17072051 T^{10} + 29713188 T^{11} + 47045881 T^{12} \))(\( 1 - 10 T + 129 T^{2} - 858 T^{3} + 6799 T^{4} - 36687 T^{5} + 230863 T^{6} - 1094153 T^{7} + 5856445 T^{8} - 24273225 T^{9} + 111272455 T^{10} - 394989233 T^{11} + 1583489317 T^{12} - 4781086527 T^{13} + 16834997101 T^{14} - 40365365898 T^{15} + 115309454331 T^{16} - 169835630410 T^{17} + 322687697779 T^{18} \))(\( 1 - 17 T + 232 T^{2} - 2147 T^{3} + 17621 T^{4} - 118587 T^{5} + 739064 T^{6} - 4008751 T^{7} + 20396271 T^{8} - 91757468 T^{9} + 387529149 T^{10} - 1447159111 T^{11} + 5069239976 T^{12} - 15454376427 T^{13} + 43631340479 T^{14} - 101007506507 T^{15} + 207378243448 T^{16} - 288720571697 T^{17} + 322687697779 T^{18} \))(\( 1 - 3 T + 33 T^{2} - 56 T^{3} + 545 T^{4} + 40 T^{5} + 13755 T^{6} - 6782 T^{7} + 226825 T^{8} + 626813 T^{9} + 2545914 T^{10} + 11909447 T^{11} + 81883825 T^{12} - 46517738 T^{13} + 1792565355 T^{14} + 99043960 T^{15} + 25640005145 T^{16} - 50056817384 T^{17} + 560457580353 T^{18} - 968063093337 T^{19} + 6131066257801 T^{20} \))(\( 1 - 6 T + 106 T^{2} - 536 T^{3} + 5848 T^{4} - 26069 T^{5} + 217866 T^{6} - 857970 T^{7} + 6003504 T^{8} - 21091948 T^{9} + 128702906 T^{10} - 400747012 T^{11} + 2167264944 T^{12} - 5884816230 T^{13} + 28392514986 T^{14} - 64549424831 T^{15} + 275124312088 T^{16} - 479115252104 T^{17} + 1800257682346 T^{18} - 1936126186674 T^{19} + 6131066257801 T^{20} \))(\( 1 - 13 T^{2} + 361 T^{4} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 3 T + 36 T^{2} + 45 T^{3} + 463 T^{4} + 1035 T^{5} + 19044 T^{6} - 36501 T^{7} + 279841 T^{8} \))(\( 1 + T + 88 T^{2} + 65 T^{3} + 2991 T^{4} + 1495 T^{5} + 46552 T^{6} + 12167 T^{7} + 279841 T^{8} \))(\( 1 + 4 T + 86 T^{2} + 268 T^{3} + 3474 T^{4} + 8683 T^{5} + 79902 T^{6} + 141772 T^{7} + 1046362 T^{8} + 1119364 T^{9} + 6436343 T^{10} \))(\( 1 - 5 T + 101 T^{2} - 382 T^{3} + 4460 T^{4} - 13183 T^{5} + 122637 T^{6} - 303209 T^{7} + 2359340 T^{8} - 4647794 T^{9} + 28263941 T^{10} - 32181715 T^{11} + 148035889 T^{12} \))(\( 1 - 8 T + 146 T^{2} - 896 T^{3} + 9956 T^{4} - 51621 T^{5} + 438850 T^{6} - 1963688 T^{7} + 13741055 T^{8} - 53051974 T^{9} + 316044265 T^{10} - 1038790952 T^{11} + 5339487950 T^{12} - 14445672261 T^{13} + 64080230908 T^{14} - 132640156544 T^{15} + 497104515262 T^{16} - 626487882248 T^{17} + 1801152661463 T^{18} \))(\( 1 + 8 T + 142 T^{2} + 900 T^{3} + 8348 T^{4} + 43931 T^{5} + 277858 T^{6} + 1305284 T^{7} + 6658435 T^{8} + 30989946 T^{9} + 153144005 T^{10} + 690495236 T^{11} + 3380698286 T^{12} + 12293694971 T^{13} + 53730591364 T^{14} + 133232300100 T^{15} + 483485213474 T^{16} + 626487882248 T^{17} + 1801152661463 T^{18} \))(\( 1 + 4 T + 45 T^{2} + 388 T^{3} + 1822 T^{4} + 9827 T^{5} + 54710 T^{6} + 168189 T^{7} + 709681 T^{8} + 2498658 T^{9} + 8288154 T^{10} + 57469134 T^{11} + 375421249 T^{12} + 2046355563 T^{13} + 15310101110 T^{14} + 63249942661 T^{15} + 269721389758 T^{16} + 1321072273436 T^{17} + 3523994337645 T^{18} + 7204610645852 T^{19} + 41426511213649 T^{20} \))(\( 1 - 4 T + 89 T^{2} - 568 T^{3} + 4642 T^{4} - 34097 T^{5} + 200694 T^{6} - 1267095 T^{7} + 7066605 T^{8} - 35247826 T^{9} + 188451394 T^{10} - 810699998 T^{11} + 3738234045 T^{12} - 15416744865 T^{13} + 56162409654 T^{14} - 219459987271 T^{15} + 687182596738 T^{16} - 1933940853896 T^{17} + 6969677690009 T^{18} - 7204610645852 T^{19} + 41426511213649 T^{20} \))(\( ( 1 + 9 T + 23 T^{2} )^{2} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 3 T + 84 T^{2} + 237 T^{3} + 3391 T^{4} + 6873 T^{5} + 70644 T^{6} + 73167 T^{7} + 707281 T^{8} \))(\( 1 - 3 T + 80 T^{2} - 153 T^{3} + 3039 T^{4} - 4437 T^{5} + 67280 T^{6} - 73167 T^{7} + 707281 T^{8} \))(\( 1 + 8 T + 116 T^{2} + 722 T^{3} + 6196 T^{4} + 29231 T^{5} + 179684 T^{6} + 607202 T^{7} + 2829124 T^{8} + 5658248 T^{9} + 20511149 T^{10} \))(\( 1 + 14 T + 215 T^{2} + 1916 T^{3} + 16936 T^{4} + 107937 T^{5} + 669980 T^{6} + 3130173 T^{7} + 14243176 T^{8} + 46729324 T^{9} + 152065415 T^{10} + 287156086 T^{11} + 594823321 T^{12} \))(\( 1 - 14 T + 214 T^{2} - 1810 T^{3} + 15904 T^{4} - 98781 T^{5} + 676330 T^{6} - 3606286 T^{7} + 22533647 T^{8} - 111646538 T^{9} + 653475763 T^{10} - 3032886526 T^{11} + 16495012370 T^{12} - 69865924461 T^{13} + 326209313696 T^{14} - 1076630211010 T^{15} + 3691473530126 T^{16} - 7003449781454 T^{17} + 14507145975869 T^{18} \))(\( 1 + 3 T + 133 T^{2} + 432 T^{3} + 8825 T^{4} + 31164 T^{5} + 408405 T^{6} + 1502576 T^{7} + 14859460 T^{8} + 51506786 T^{9} + 430924340 T^{10} + 1263666416 T^{11} + 9960589545 T^{12} + 22041705084 T^{13} + 181010889925 T^{14} + 256963674672 T^{15} + 2294233549097 T^{16} + 1500739238883 T^{17} + 14507145975869 T^{18} \))(\( 1 - 13 T + 180 T^{2} - 1277 T^{3} + 9282 T^{4} - 39834 T^{5} + 239498 T^{6} - 1116042 T^{7} + 10642989 T^{8} - 64784774 T^{9} + 453617540 T^{10} - 1878758446 T^{11} + 8950753749 T^{12} - 27219148338 T^{13} + 169392384938 T^{14} - 817041109266 T^{15} + 5521150065522 T^{16} - 22028092046593 T^{17} + 90044354332980 T^{18} - 188592897686297 T^{19} + 420707233300201 T^{20} \))(\( 1 - 10 T + 189 T^{2} - 1474 T^{3} + 16002 T^{4} - 102647 T^{5} + 843184 T^{6} - 4679811 T^{7} + 32667181 T^{8} - 163727734 T^{9} + 1030736646 T^{10} - 4748104286 T^{11} + 27473099221 T^{12} - 114135910479 T^{13} + 596368022704 T^{14} - 2105407911403 T^{15} + 9518362782642 T^{16} - 25426317679466 T^{17} + 94546572049629 T^{18} - 145071459758690 T^{19} + 420707233300201 T^{20} \))(\( ( 1 - 5 T + 29 T^{2} )^{2} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 102 T^{2} + 32 T^{3} + 4407 T^{4} + 992 T^{5} + 98022 T^{6} + 923521 T^{8} \))(\( 1 - 6 T + 120 T^{2} - 504 T^{3} + 5489 T^{4} - 15624 T^{5} + 115320 T^{6} - 178746 T^{7} + 923521 T^{8} \))(\( 1 - 7 T + 81 T^{2} - 606 T^{3} + 4417 T^{4} - 22245 T^{5} + 136927 T^{6} - 582366 T^{7} + 2413071 T^{8} - 6464647 T^{9} + 28629151 T^{10} \))(\( 1 + 4 T + 91 T^{2} + 484 T^{3} + 3958 T^{4} + 28516 T^{5} + 130351 T^{6} + 883996 T^{7} + 3803638 T^{8} + 14418844 T^{9} + 84040411 T^{10} + 114516604 T^{11} + 887503681 T^{12} \))(\( 1 - 11 T + 93 T^{2} - 474 T^{3} + 4027 T^{4} - 25667 T^{5} + 195325 T^{6} - 1011266 T^{7} + 7205150 T^{8} - 36845532 T^{9} + 223359650 T^{10} - 971826626 T^{11} + 5818927075 T^{12} - 23704013507 T^{13} + 115289591077 T^{14} - 420676744794 T^{15} + 2558673112323 T^{16} - 9381801411851 T^{17} + 26439622160671 T^{18} \))(\( 1 - 9 T + 189 T^{2} - 1422 T^{3} + 17963 T^{4} - 115249 T^{5} + 1088445 T^{6} - 6024758 T^{7} + 46368142 T^{8} - 220727252 T^{9} + 1437412402 T^{10} - 5789792438 T^{11} + 32425864995 T^{12} - 106434871729 T^{13} + 514265439413 T^{14} - 1262030234382 T^{15} + 5199884066979 T^{16} - 7676019336969 T^{17} + 26439622160671 T^{18} \))(\( 1 + 17 T + 280 T^{2} + 3041 T^{3} + 30402 T^{4} + 252539 T^{5} + 1965786 T^{6} + 13700501 T^{7} + 91046269 T^{8} + 553126762 T^{9} + 3217992092 T^{10} + 17146929622 T^{11} + 87495464509 T^{12} + 408151625291 T^{13} + 1815444652506 T^{14} + 7229977164389 T^{15} + 26981886909762 T^{16} + 83665859511551 T^{17} + 238809490483480 T^{18} + 449473576731407 T^{19} + 819628286980801 T^{20} \))(\( 1 + T + 132 T^{2} + 97 T^{3} + 9474 T^{4} + 7035 T^{5} + 492894 T^{6} + 437061 T^{7} + 20131597 T^{8} + 18540970 T^{9} + 678680924 T^{10} + 574770070 T^{11} + 19346464717 T^{12} + 13020484251 T^{13} + 455197959774 T^{14} + 201406077285 T^{15} + 8408209873794 T^{16} + 2668723568767 T^{17} + 112581616942212 T^{18} + 26439622160671 T^{19} + 819628286980801 T^{20} \))(\( 1 - 13 T^{2} + 961 T^{4} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 18 T + 220 T^{2} + 1809 T^{3} + 12489 T^{4} + 66933 T^{5} + 301180 T^{6} + 911754 T^{7} + 1874161 T^{8} \))(\( 1 - 4 T + 94 T^{2} - 373 T^{3} + 4249 T^{4} - 13801 T^{5} + 128686 T^{6} - 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 10 T + 191 T^{2} + 1303 T^{3} + 13987 T^{4} + 69244 T^{5} + 517519 T^{6} + 1783807 T^{7} + 9674723 T^{8} + 18741610 T^{9} + 69343957 T^{10} \))(\( 1 + 3 T + 138 T^{2} + 314 T^{3} + 9027 T^{4} + 17766 T^{5} + 393998 T^{6} + 657342 T^{7} + 12357963 T^{8} + 15905042 T^{9} + 258634218 T^{10} + 208031871 T^{11} + 2565726409 T^{12} \))(\( 1 + 145 T^{2} - 175 T^{3} + 9615 T^{4} - 26440 T^{5} + 384903 T^{6} - 1904977 T^{7} + 12041144 T^{8} - 86185728 T^{9} + 445522328 T^{10} - 2607913513 T^{11} + 19496491659 T^{12} - 49552816840 T^{13} + 666742146555 T^{14} - 449002121575 T^{15} + 13765122184285 T^{16} + 129961739795077 T^{18} \))(\( 1 - 7 T + 147 T^{2} - 663 T^{3} + 8476 T^{4} - 29797 T^{5} + 380684 T^{6} - 1550701 T^{7} + 18320960 T^{8} - 73203984 T^{9} + 677875520 T^{10} - 2122909669 T^{11} + 19282786652 T^{12} - 55844375317 T^{13} + 587759379532 T^{14} - 1701076609167 T^{15} + 13954985938551 T^{16} - 24587356177447 T^{17} + 129961739795077 T^{18} \))(\( 1 - 11 T + 238 T^{2} - 2392 T^{3} + 28861 T^{4} - 253174 T^{5} + 2292794 T^{6} - 17316624 T^{7} + 130729698 T^{8} - 852163815 T^{9} + 5565969504 T^{10} - 31530061155 T^{11} + 178968956562 T^{12} - 877138955472 T^{13} + 4297065095834 T^{14} - 17556086969518 T^{15} + 74049429890149 T^{16} - 227077050102136 T^{17} + 835970110033198 T^{18} - 1429579137745847 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 20 T + 356 T^{2} - 4035 T^{3} + 39174 T^{4} - 276725 T^{5} + 1549834 T^{6} - 4392123 T^{7} - 11642247 T^{8} + 313449567 T^{9} - 2332182844 T^{10} + 11597633979 T^{11} - 15938236143 T^{12} - 222474206319 T^{13} + 2904638439274 T^{14} - 19189206500825 T^{15} + 100509766346166 T^{16} - 383050124231655 T^{17} + 1250442685595876 T^{18} - 2599234795901540 T^{19} + 4808584372417849 T^{20} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 14 T + 172 T^{2} + 1451 T^{3} + 11121 T^{4} + 59491 T^{5} + 289132 T^{6} + 964894 T^{7} + 2825761 T^{8} \))(\( 1 + 6 T + 100 T^{2} + 249 T^{3} + 4179 T^{4} + 10209 T^{5} + 168100 T^{6} + 413526 T^{7} + 2825761 T^{8} \))(\( 1 + 18 T + 325 T^{2} + 3309 T^{3} + 32009 T^{4} + 210964 T^{5} + 1312369 T^{6} + 5562429 T^{7} + 22399325 T^{8} + 50863698 T^{9} + 115856201 T^{10} \))(\( 1 - 6 T + 166 T^{2} - 579 T^{3} + 11948 T^{4} - 28229 T^{5} + 572510 T^{6} - 1157389 T^{7} + 20084588 T^{8} - 39905259 T^{9} + 469076326 T^{10} - 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 14 T + 283 T^{2} - 3147 T^{3} + 38143 T^{4} - 345712 T^{5} + 3189999 T^{6} - 24091885 T^{7} + 183199126 T^{8} - 1168958292 T^{9} + 7511164166 T^{10} - 40498458685 T^{11} + 219857921079 T^{12} - 976899486832 T^{13} + 4419103074743 T^{14} - 14948578046427 T^{15} + 55115459508323 T^{16} - 111788953207694 T^{17} + 327381934393961 T^{18} \))(\( 1 - 14 T + 215 T^{2} - 1941 T^{3} + 17113 T^{4} - 117718 T^{5} + 752369 T^{6} - 4616331 T^{7} + 25703150 T^{8} - 172452312 T^{9} + 1053829150 T^{10} - 7760052411 T^{11} + 51854023849 T^{12} - 332642933398 T^{13} + 1982647167713 T^{14} - 9219952331781 T^{15} + 41872168884415 T^{16} - 111788953207694 T^{17} + 327381934393961 T^{18} \))(\( 1 - 8 T + 196 T^{2} - 1079 T^{3} + 19480 T^{4} - 90187 T^{5} + 1377642 T^{6} - 5219677 T^{7} + 73916439 T^{8} - 246950713 T^{9} + 3327447044 T^{10} - 10124979233 T^{11} + 124253533959 T^{12} - 359745358517 T^{13} + 3892887035562 T^{14} - 10448723199587 T^{15} + 92532030614680 T^{16} - 210139861517599 T^{17} + 1565045344907716 T^{18} - 2619055475151688 T^{19} + 13422659310152401 T^{20} \))(\( 1 + 64 T^{2} - 281 T^{3} + 4670 T^{4} - 11107 T^{5} + 306890 T^{6} - 633177 T^{7} + 15457121 T^{8} - 40876763 T^{9} + 624010988 T^{10} - 1675947283 T^{11} + 25983420401 T^{12} - 43639192017 T^{13} + 867197793290 T^{14} - 1286814824507 T^{15} + 22182986805470 T^{16} - 54725950960561 T^{17} + 511035214663744 T^{18} + 13422659310152401 T^{20} \))(\( 1 - 46 T^{2} + 1681 T^{4} \))
$43$ (\( 1 - 2 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + T + 109 T^{2} - 68 T^{3} + 5677 T^{4} - 2924 T^{5} + 201541 T^{6} + 79507 T^{7} + 3418801 T^{8} \))(\( 1 + 3 T + 141 T^{2} + 384 T^{3} + 8429 T^{4} + 16512 T^{5} + 260709 T^{6} + 238521 T^{7} + 3418801 T^{8} \))(\( 1 + 22 T + 353 T^{2} + 3670 T^{3} + 32572 T^{4} + 225121 T^{5} + 1400596 T^{6} + 6785830 T^{7} + 28065971 T^{8} + 75213622 T^{9} + 147008443 T^{10} \))(\( 1 + 14 T + 290 T^{2} + 2934 T^{3} + 33137 T^{4} + 249245 T^{5} + 1936322 T^{6} + 10717535 T^{7} + 61270313 T^{8} + 233273538 T^{9} + 991452290 T^{10} + 2058118202 T^{11} + 6321363049 T^{12} \))(\( 1 - 8 T + 176 T^{2} - 946 T^{3} + 13274 T^{4} - 55927 T^{5} + 667442 T^{6} - 2392933 T^{7} + 27280255 T^{8} - 92929925 T^{9} + 1173050965 T^{10} - 4424533117 T^{11} + 53066311094 T^{12} - 191203283527 T^{13} + 1951390072382 T^{14} - 5980009444354 T^{15} + 47840075554832 T^{16} - 93505602220808 T^{17} + 502592611936843 T^{18} \))(\( 1 - 21 T + 395 T^{2} - 4694 T^{3} + 49931 T^{4} - 403182 T^{5} + 3019603 T^{6} - 18398443 T^{7} + 117340899 T^{8} - 694152558 T^{9} + 5045658657 T^{10} - 34018721107 T^{11} + 240079575721 T^{12} - 1378399024782 T^{13} + 7340278567433 T^{14} - 29672478152006 T^{15} + 107368351387265 T^{16} - 245452205829621 T^{17} + 502592611936843 T^{18} \))(\( 1 - 21 T + 360 T^{2} - 4077 T^{3} + 40248 T^{4} - 299870 T^{5} + 1910548 T^{6} - 8211053 T^{7} + 21721750 T^{8} + 88768841 T^{9} - 948396026 T^{10} + 3817060163 T^{11} + 40163515750 T^{12} - 652836190871 T^{13} + 6531783412948 T^{14} - 44083421802410 T^{15} + 254422219996152 T^{16} - 1108204477483239 T^{17} + 4207752099936360 T^{18} - 10554444850673703 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 193 T^{2} - 408 T^{3} + 22210 T^{4} - 56277 T^{5} + 1831614 T^{6} - 5104952 T^{7} + 112508301 T^{8} - 302767828 T^{9} + 5498399520 T^{10} - 13019016604 T^{11} + 208027848549 T^{12} - 405879418664 T^{13} + 6261923774814 T^{14} - 8273194146711 T^{15} + 140397473318290 T^{16} - 110901993331656 T^{17} + 2255822653576993 T^{18} + 21611482313284249 T^{20} \))(\( ( 1 + 11 T + 43 T^{2} )^{2} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 3 T + 116 T^{2} + 423 T^{3} + 7215 T^{4} + 19881 T^{5} + 256244 T^{6} + 311469 T^{7} + 4879681 T^{8} \))(\( 1 + 7 T + 142 T^{2} + 785 T^{3} + 9741 T^{4} + 36895 T^{5} + 313678 T^{6} + 726761 T^{7} + 4879681 T^{8} \))(\( 1 - 12 T + 208 T^{2} - 1566 T^{3} + 16364 T^{4} - 92857 T^{5} + 769108 T^{6} - 3459294 T^{7} + 21595184 T^{8} - 58556172 T^{9} + 229345007 T^{10} \))(\( 1 - 2 T + 159 T^{2} - 180 T^{3} + 14256 T^{4} - 13271 T^{5} + 818896 T^{6} - 623737 T^{7} + 31491504 T^{8} - 18688140 T^{9} + 775869279 T^{10} - 458690014 T^{11} + 10779215329 T^{12} \))(\( 1 - 10 T + 182 T^{2} - 1176 T^{3} + 16608 T^{4} - 94125 T^{5} + 1162654 T^{6} - 5625600 T^{7} + 62630179 T^{8} - 270886898 T^{9} + 2943618413 T^{10} - 12426950400 T^{11} + 120710226242 T^{12} - 459299974125 T^{13} + 3808961876256 T^{14} - 12676357226904 T^{15} + 92205407924266 T^{16} - 238112866617610 T^{17} + 1119130473102767 T^{18} \))(\( 1 - T + 97 T^{2} + 200 T^{3} + 5791 T^{4} + 21672 T^{5} + 416053 T^{6} + 1080856 T^{7} + 22279878 T^{8} + 55018994 T^{9} + 1047154266 T^{10} + 2387610904 T^{11} + 43195870619 T^{12} + 105752446632 T^{13} + 1328136935537 T^{14} + 2155843065800 T^{15} + 49142442684911 T^{16} - 23811286661761 T^{17} + 1119130473102767 T^{18} \))(\( 1 - T + 90 T^{2} - 205 T^{3} + 4576 T^{4} - 27410 T^{5} + 313322 T^{6} - 1926546 T^{7} + 20277487 T^{8} - 66073692 T^{9} + 1051044312 T^{10} - 3105463524 T^{11} + 44792968783 T^{12} - 200019785358 T^{13} + 1528911410282 T^{14} - 6286346641870 T^{15} + 49325689345504 T^{16} - 103857739694915 T^{17} + 2143015799558490 T^{18} - 1119130473102767 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 4 T + 329 T^{2} - 1432 T^{3} + 53170 T^{4} - 232337 T^{5} + 5543238 T^{6} - 22864431 T^{7} + 409961757 T^{8} - 1522478962 T^{9} + 22334479810 T^{10} - 71556511214 T^{11} + 905605521213 T^{12} - 2373853819713 T^{13} + 27049233147078 T^{14} - 53285330891359 T^{15} + 573130879042930 T^{16} - 725484308503016 T^{17} + 7833913311719369 T^{18} - 4476521892411068 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 93 T^{2} + 2209 T^{4} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 4 T + 159 T^{2} - 426 T^{3} + 11119 T^{4} - 22578 T^{5} + 446631 T^{6} - 595508 T^{7} + 7890481 T^{8} \))(\( 1 + 20 T + 247 T^{2} + 1870 T^{3} + 13959 T^{4} + 99110 T^{5} + 693823 T^{6} + 2977540 T^{7} + 7890481 T^{8} \))(\( 1 - 7 T + 204 T^{2} - 891 T^{3} + 17116 T^{4} - 54613 T^{5} + 907148 T^{6} - 2502819 T^{7} + 30370908 T^{8} - 55233367 T^{9} + 418195493 T^{10} \))(\( 1 + 3 T + 211 T^{2} + 738 T^{3} + 21098 T^{4} + 77572 T^{5} + 1348262 T^{6} + 4111316 T^{7} + 59264282 T^{8} + 109871226 T^{9} + 1664891491 T^{10} + 1254586479 T^{11} + 22164361129 T^{12} \))(\( 1 - 21 T + 277 T^{2} - 2968 T^{3} + 30947 T^{4} - 288185 T^{5} + 2342249 T^{6} - 18000300 T^{7} + 137833141 T^{8} - 1040546905 T^{9} + 7305156473 T^{10} - 50562842700 T^{11} + 348707004373 T^{12} - 2273918266985 T^{13} + 12941895921871 T^{14} - 65783823830872 T^{15} + 325394985734849 T^{16} - 1307453498638581 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 8 T + 287 T^{2} + 2286 T^{3} + 41111 T^{4} + 313016 T^{5} + 3907455 T^{6} + 27566774 T^{7} + 272219877 T^{8} + 1718117526 T^{9} + 14427653481 T^{10} + 77435068166 T^{11} + 581730178035 T^{12} + 2469846800696 T^{13} + 17192434912723 T^{14} + 50667729540894 T^{15} + 337142097133219 T^{16} + 498077523290888 T^{17} + 3299763591802133 T^{18} \))(\( 1 - 22 T + 564 T^{2} - 8556 T^{3} + 132190 T^{4} - 1557388 T^{5} + 18086130 T^{6} - 174153460 T^{7} + 1635733868 T^{8} - 13168910514 T^{9} + 103076722766 T^{10} - 697952257242 T^{11} + 4594776435212 T^{12} - 25927444664420 T^{13} + 142708265128530 T^{14} - 651292642452284 T^{15} + 2929906897642510 T^{16} - 10050828512445372 T^{17} + 35114465392007604 T^{18} - 72594799019646926 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 5 T + 376 T^{2} + 1913 T^{3} + 69148 T^{4} + 338693 T^{5} + 8156430 T^{6} + 36950489 T^{7} + 680034810 T^{8} + 2756338605 T^{9} + 41751994840 T^{10} + 146085946065 T^{11} + 1910217781290 T^{12} + 5501077950853 T^{13} + 64358155942830 T^{14} + 141639886110649 T^{15} + 1532621243348092 T^{16} + 2247222410508181 T^{17} + 23409643594671736 T^{18} + 16498817959010665 T^{19} + 174887470365513049 T^{20} \))(\( ( 1 + T + 53 T^{2} )^{2} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 7 T + 217 T^{2} + 1240 T^{3} + 18645 T^{4} + 73160 T^{5} + 755377 T^{6} + 1437653 T^{7} + 12117361 T^{8} \))(\( 1 + 11 T + 127 T^{2} + 1078 T^{3} + 10335 T^{4} + 63602 T^{5} + 442087 T^{6} + 2259169 T^{7} + 12117361 T^{8} \))(\( 1 + T + 188 T^{2} + 301 T^{3} + 17716 T^{4} + 28988 T^{5} + 1045244 T^{6} + 1047781 T^{7} + 38611252 T^{8} + 12117361 T^{9} + 714924299 T^{10} \))(\( 1 - 2 T + 230 T^{2} - 504 T^{3} + 25733 T^{4} - 60007 T^{5} + 1847032 T^{6} - 3540413 T^{7} + 89576573 T^{8} - 103511016 T^{9} + 2786993030 T^{10} - 1429848598 T^{11} + 42180533641 T^{12} \))(\( 1 - 23 T + 518 T^{2} - 8163 T^{3} + 115526 T^{4} - 1388946 T^{5} + 15076132 T^{6} - 146537445 T^{7} + 1293518891 T^{8} - 10417971342 T^{9} + 76317614569 T^{10} - 510096846045 T^{11} + 3096320914028 T^{12} - 16830360091506 T^{13} + 82592344566274 T^{14} - 344319696111483 T^{15} + 1289121469136242 T^{16} - 3377100064899383 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 4 T + 267 T^{2} + 620 T^{3} + 35132 T^{4} + 34249 T^{5} + 3125936 T^{6} - 33172 T^{7} + 218144930 T^{8} - 76875498 T^{9} + 12870550870 T^{10} - 115471732 T^{11} + 642001609744 T^{12} + 415007496889 T^{13} + 25116720472468 T^{14} + 26151930857420 T^{15} + 664469946446673 T^{16} + 587321750417284 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 24 T + 640 T^{2} + 10496 T^{3} + 168853 T^{4} + 2126939 T^{5} + 25741320 T^{6} + 263425889 T^{7} + 2583730626 T^{8} + 22080281658 T^{9} + 180948061616 T^{10} + 1302736617822 T^{11} + 8993966309106 T^{12} + 54102145656931 T^{13} + 311916867056520 T^{14} + 1520600373590761 T^{15} + 7122309646883773 T^{16} + 26120885984660224 T^{17} + 93971480066765440 T^{18} + 207911899647718536 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 11 T + 435 T^{2} - 3622 T^{3} + 84214 T^{4} - 562789 T^{5} + 10153794 T^{6} - 56970701 T^{7} + 881350905 T^{8} - 4292587607 T^{9} + 58788179638 T^{10} - 253262668813 T^{11} + 3067982500305 T^{12} - 11700585600679 T^{13} + 123037187417634 T^{14} - 402351531309911 T^{15} + 3552191460043174 T^{16} - 9013895678014418 T^{17} + 63871240357879635 T^{18} - 95292954005204329 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 14 T + 200 T^{2} + 1725 T^{3} + 16819 T^{4} + 105225 T^{5} + 744200 T^{6} + 3177734 T^{7} + 13845841 T^{8} \))(\( 1 + 18 T + 318 T^{2} + 3291 T^{3} + 31325 T^{4} + 200751 T^{5} + 1183278 T^{6} + 4085658 T^{7} + 13845841 T^{8} \))(\( 1 + 26 T + 455 T^{2} + 5547 T^{3} + 55807 T^{4} + 464404 T^{5} + 3404227 T^{6} + 20640387 T^{7} + 103276355 T^{8} + 359991866 T^{9} + 844596301 T^{10} \))(\( 1 + 26 T + 526 T^{2} + 7131 T^{3} + 82356 T^{4} + 773629 T^{5} + 6526846 T^{6} + 47191369 T^{7} + 306446676 T^{8} + 1618601511 T^{9} + 7282912366 T^{10} + 21959503826 T^{11} + 51520374361 T^{12} \))(\( 1 - 34 T + 860 T^{2} - 15381 T^{3} + 233681 T^{4} - 2948067 T^{5} + 33192584 T^{6} - 328091222 T^{7} + 2968578671 T^{8} - 24128224246 T^{9} + 181083298931 T^{10} - 1220827437062 T^{11} + 7534085908904 T^{12} - 40818466939347 T^{13} + 197366108213981 T^{14} - 792434878046541 T^{15} + 2702758838978060 T^{16} - 6518048641907554 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 30 T + 716 T^{2} - 11943 T^{3} + 175473 T^{4} - 2139867 T^{5} + 23818644 T^{6} - 232195520 T^{7} + 2101070175 T^{8} - 16987691396 T^{9} + 128165280675 T^{10} - 863999529920 T^{11} + 5406379633764 T^{12} - 29628258243147 T^{13} + 148203846725373 T^{14} - 615307830993423 T^{15} + 2250203870591036 T^{16} - 5751219389918430 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 16 T + 379 T^{2} - 5007 T^{3} + 75323 T^{4} - 829200 T^{5} + 9762023 T^{6} - 92713521 T^{7} + 910053001 T^{8} - 7527931174 T^{9} + 63764442150 T^{10} - 459203801614 T^{11} + 3386307216721 T^{12} - 21044207710101 T^{13} + 135163418296343 T^{14} - 700339252789200 T^{15} + 3880669157993603 T^{16} - 15735713379957147 T^{17} + 72657071625969499 T^{18} - 187106337485346256 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 12 T + 435 T^{2} - 4649 T^{3} + 90899 T^{4} - 874306 T^{5} + 12155071 T^{6} - 104460383 T^{7} + 1153654937 T^{8} - 8748667246 T^{9} + 81208239906 T^{10} - 533668702006 T^{11} + 4292750020577 T^{12} - 23710522193723 T^{13} + 168297180409711 T^{14} - 738435613542106 T^{15} + 4683150509040539 T^{16} - 14610611444661629 T^{17} + 83392681153817235 T^{18} - 140329753114009692 T^{19} + 713342911662882601 T^{20} \))(\( ( 1 + 6 T + 61 T^{2} )^{2} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))(\( 1 + 15 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 218 T^{2} + 96 T^{3} + 20235 T^{4} + 6432 T^{5} + 978602 T^{6} + 20151121 T^{8} \))(\( 1 + 16 T + 294 T^{2} + 3032 T^{3} + 30479 T^{4} + 203144 T^{5} + 1319766 T^{6} + 4812208 T^{7} + 20151121 T^{8} \))(\( 1 + 8 T + 219 T^{2} + 1662 T^{3} + 25753 T^{4} + 146030 T^{5} + 1725451 T^{6} + 7460718 T^{7} + 65867097 T^{8} + 161208968 T^{9} + 1350125107 T^{10} \))(\( 1 - 9 T + 254 T^{2} - 1897 T^{3} + 32416 T^{4} - 199521 T^{5} + 2614228 T^{6} - 13367907 T^{7} + 145515424 T^{8} - 570547411 T^{9} + 5118384734 T^{10} - 12151125963 T^{11} + 90458382169 T^{12} \))(\( 1 - 10 T + 350 T^{2} - 3424 T^{3} + 56851 T^{4} - 534274 T^{5} + 5808712 T^{6} - 52969882 T^{7} + 447475317 T^{8} - 3957619294 T^{9} + 29980846239 T^{10} - 237781800298 T^{11} + 1747045647256 T^{12} - 10766220021154 T^{13} + 76755962458057 T^{14} - 309729500546656 T^{15} + 2121249061863050 T^{16} - 4060676775566410 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 15 T + 274 T^{2} - 3475 T^{3} + 50073 T^{4} - 537804 T^{5} + 5945176 T^{6} - 55267900 T^{7} + 531241911 T^{8} - 4317339305 T^{9} + 35593208037 T^{10} - 248097603100 T^{11} + 1788088969288 T^{12} - 10837353478284 T^{13} + 67604814482811 T^{14} - 314342878037275 T^{15} + 1660634979858502 T^{16} - 6091015163349615 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 19 T + 501 T^{2} - 7052 T^{3} + 116259 T^{4} - 1338197 T^{5} + 16999939 T^{6} - 166830980 T^{7} + 1763105291 T^{8} - 14994874833 T^{9} + 135971961918 T^{10} - 1004656613811 T^{11} + 7914579651299 T^{12} - 50176586037740 T^{13} + 342567827781619 T^{14} - 1806733367812079 T^{15} + 10516601052585771 T^{16} - 42740138240737796 T^{17} + 203439906455877141 T^{18} - 516924153529603993 T^{19} + 1822837804551761449 T^{20} \))(\( 1 + 2 T + 337 T^{2} + 1558 T^{3} + 54861 T^{4} + 380974 T^{5} + 6238057 T^{6} + 50098140 T^{7} + 576557197 T^{8} + 4423963664 T^{9} + 43368686470 T^{10} + 296405565488 T^{11} + 2588165257333 T^{12} + 15067666880820 T^{13} + 125703841411897 T^{14} + 514362562514218 T^{15} + 4962637304173509 T^{16} + 9442588681093234 T^{17} + 136844807336588017 T^{18} + 54413068792589894 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 34 T^{2} + 4489 T^{4} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 - T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 196 T^{2} - 256 T^{3} + 17830 T^{4} - 18176 T^{5} + 988036 T^{6} + 25411681 T^{8} \))(\( ( 1 + 8 T + 138 T^{2} + 568 T^{3} + 5041 T^{4} )^{2} \))(\( 1 - 18 T + 331 T^{2} - 4296 T^{3} + 46658 T^{4} - 432044 T^{5} + 3312718 T^{6} - 21656136 T^{7} + 118468541 T^{8} - 457410258 T^{9} + 1804229351 T^{10} \))(\( 1 - 3 T + 212 T^{2} - 801 T^{3} + 25047 T^{4} - 107526 T^{5} + 2087912 T^{6} - 7634346 T^{7} + 126261927 T^{8} - 286686711 T^{9} + 5387276372 T^{10} - 5412688053 T^{11} + 128100283921 T^{12} \))(\( 1 - 4 T + 386 T^{2} - 1012 T^{3} + 74320 T^{4} - 132554 T^{5} + 9430158 T^{6} - 11810548 T^{7} + 876200831 T^{8} - 881477364 T^{9} + 62210259001 T^{10} - 59536972468 T^{11} + 3375157279938 T^{12} - 3368419963274 T^{13} + 134090325366320 T^{14} - 129637487328052 T^{15} + 3510716381138926 T^{16} - 2583014124983044 T^{17} + 45848500718449031 T^{18} \))(\( 1 + T + 308 T^{2} + 263 T^{3} + 52152 T^{4} + 15517 T^{5} + 6102418 T^{6} - 606011 T^{7} + 542916157 T^{8} - 122916004 T^{9} + 38547047147 T^{10} - 3054901451 T^{11} + 2184122528798 T^{12} + 394313054077 T^{13} + 94094169113352 T^{14} + 33690374671223 T^{15} + 2801297008784428 T^{16} + 645753531245761 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 25 T + 571 T^{2} + 9230 T^{3} + 142268 T^{4} + 1835238 T^{5} + 22435602 T^{6} + 242676200 T^{7} + 2497305027 T^{8} + 23174712103 T^{9} + 204886130086 T^{10} + 1645404559313 T^{11} + 12588914641107 T^{12} + 86856481418200 T^{13} + 570126361066962 T^{14} + 3311190265670538 T^{15} + 18224571192872828 T^{16} + 83947959061948930 T^{17} + 368725266341329531 T^{18} + 1146212517961225775 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 28 T + 561 T^{2} - 7544 T^{3} + 85222 T^{4} - 740510 T^{5} + 5713998 T^{6} - 35344402 T^{7} + 227321625 T^{8} - 1316810464 T^{9} + 11061781762 T^{10} - 93493542944 T^{11} + 1145928311625 T^{12} - 12650150264222 T^{13} + 145202294410638 T^{14} - 1336049876709010 T^{15} + 10916962396315462 T^{16} - 68613586474901704 T^{17} + 362267731028871921 T^{18} - 1283758020116572868 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 126 T^{2} + 5041 T^{4} \))
$73$ (\( 1 - 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 6 T + 126 T^{2} + 877 T^{3} + 8853 T^{4} + 64021 T^{5} + 671454 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 - 4 T + 178 T^{2} - 1135 T^{3} + 15751 T^{4} - 82855 T^{5} + 948562 T^{6} - 1556068 T^{7} + 28398241 T^{8} \))(\( 1 + 25 T + 449 T^{2} + 6145 T^{3} + 69028 T^{4} + 629569 T^{5} + 5039044 T^{6} + 32746705 T^{7} + 174668633 T^{8} + 709956025 T^{9} + 2073071593 T^{10} \))(\( 1 + 7 T + 278 T^{2} + 1322 T^{3} + 36673 T^{4} + 136952 T^{5} + 3198634 T^{6} + 9997496 T^{7} + 195430417 T^{8} + 514280474 T^{9} + 7894710998 T^{10} + 14511501151 T^{11} + 151334226289 T^{12} \))(\( 1 - 9 T + 193 T^{2} - 663 T^{3} + 12610 T^{4} + 34115 T^{5} + 857410 T^{6} - 120365 T^{7} + 134510578 T^{8} - 427210620 T^{9} + 9819272194 T^{10} - 641425085 T^{11} + 333547065970 T^{12} + 968805991715 T^{13} + 26141432787730 T^{14} - 100334592029607 T^{15} + 2132147914185721 T^{16} - 7258140827046729 T^{17} + 58871586708267913 T^{18} \))(\( 1 - 18 T + 507 T^{2} - 6843 T^{3} + 113603 T^{4} - 1227540 T^{5} + 15477139 T^{6} - 140656093 T^{7} + 1485962414 T^{8} - 11757700036 T^{9} + 108475256222 T^{10} - 749556319597 T^{11} + 6020870182363 T^{12} - 34859976757140 T^{13} + 235507152179579 T^{14} - 1035580110495627 T^{15} + 5601031049182179 T^{16} - 14516281654093458 T^{17} + 58871586708267913 T^{18} \))(\( 1 - 22 T + 432 T^{2} - 5767 T^{3} + 76062 T^{4} - 850931 T^{5} + 9365994 T^{6} - 91345865 T^{7} + 882474529 T^{8} - 7774430663 T^{9} + 69193245708 T^{10} - 567533438399 T^{11} + 4702706765041 T^{12} - 35535094364705 T^{13} + 265977754816554 T^{14} - 1764040883703083 T^{15} + 11510783919993918 T^{16} - 63710347259632399 T^{17} + 348390759698242992 T^{18} - 1295174907581894086 T^{19} + 4297625829703557649 T^{20} \))(\( 1 - 11 T + 510 T^{2} - 3876 T^{3} + 107427 T^{4} - 503382 T^{5} + 12454094 T^{6} - 21917736 T^{7} + 945186916 T^{8} + 866262141 T^{9} + 64033920600 T^{10} + 63237136293 T^{11} + 5036901075364 T^{12} - 8526371905512 T^{13} + 353674362848654 T^{14} - 1043546924627526 T^{15} + 16257381927548403 T^{16} - 42819716660019972 T^{17} + 411294646865981310 T^{18} - 647587453790947043 T^{19} + 4297625829703557649 T^{20} \))(\( 1 - 137 T^{2} + 5329 T^{4} \))
$79$ (\( 1 + 10 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 7 T + 167 T^{2} - 1026 T^{3} + 16003 T^{4} - 81054 T^{5} + 1042247 T^{6} - 3451273 T^{7} + 38950081 T^{8} \))(\( 1 - 9 T + 247 T^{2} - 1242 T^{3} + 24375 T^{4} - 98118 T^{5} + 1541527 T^{6} - 4437351 T^{7} + 38950081 T^{8} \))(\( 1 + 6 T + 173 T^{2} + 796 T^{3} + 19216 T^{4} + 63383 T^{5} + 1518064 T^{6} + 4967836 T^{7} + 85295747 T^{8} + 233700486 T^{9} + 3077056399 T^{10} \))(\( 1 + 334 T^{2} + 378 T^{3} + 53773 T^{4} + 68977 T^{5} + 5331516 T^{6} + 5449183 T^{7} + 335597293 T^{8} + 186368742 T^{9} + 13009327054 T^{10} + 243087455521 T^{12} \))(\( 1 + 34 T + 954 T^{2} + 18742 T^{3} + 323460 T^{4} + 4647733 T^{5} + 60285514 T^{6} + 685620581 T^{7} + 7129338937 T^{8} + 66150889905 T^{9} + 563217776023 T^{10} + 4278958046021 T^{11} + 29723109537046 T^{12} + 181029576816373 T^{13} + 995304662820540 T^{14} + 4555945091374582 T^{15} + 18320529172795686 T^{16} + 51581699536823074 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 13 T + 347 T^{2} - 3078 T^{3} + 56981 T^{4} - 453136 T^{5} + 7041845 T^{6} - 49917247 T^{7} + 659623475 T^{8} - 4209775716 T^{9} + 52110254525 T^{10} - 311533538527 T^{11} + 3471904216955 T^{12} - 17649683904016 T^{13} + 175333750671419 T^{14} - 748223188093638 T^{15} + 6663756418197173 T^{16} - 19722414528785293 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 41 T + 1172 T^{2} - 24261 T^{3} + 420666 T^{4} - 6157896 T^{5} + 80129312 T^{6} - 931290075 T^{7} + 9950641968 T^{8} - 97876201325 T^{9} + 901731524938 T^{10} - 7732219904675 T^{11} + 62101956522288 T^{12} - 459162327287925 T^{13} + 3121043192874272 T^{14} - 18948193291176504 T^{15} + 102258627564196986 T^{16} - 465906035913203499 T^{17} + 1778051525210489492 T^{18} - 4913915435287351079 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + 10 T + 419 T^{2} + 5562 T^{3} + 100146 T^{4} + 1304087 T^{5} + 17192560 T^{6} + 193333974 T^{7} + 2112022323 T^{8} + 20791995852 T^{9} + 191448301804 T^{10} + 1642567672308 T^{11} + 13181131317843 T^{12} + 95321189206986 T^{13} + 669651604597360 T^{14} + 4012749248202713 T^{15} + 24344236320606066 T^{16} + 106812141781016358 T^{17} + 635668591350849059 T^{18} + 1198515959826183190 T^{19} + 9468276082626847201 T^{20} \))(\( ( 1 - 11 T + 79 T^{2} )^{2} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 8 T + 166 T^{2} - 1127 T^{3} + 17547 T^{4} - 93541 T^{5} + 1143574 T^{6} - 4574296 T^{7} + 47458321 T^{8} \))(\( 1 + 14 T + 358 T^{2} + 3385 T^{3} + 45681 T^{4} + 280955 T^{5} + 2466262 T^{6} + 8005018 T^{7} + 47458321 T^{8} \))(\( 1 - 11 T + 285 T^{2} - 2745 T^{3} + 41044 T^{4} - 300215 T^{5} + 3406652 T^{6} - 18910305 T^{7} + 162959295 T^{8} - 522041531 T^{9} + 3939040643 T^{10} \))(\( 1 + 15 T + 328 T^{2} + 3830 T^{3} + 52011 T^{4} + 495484 T^{5} + 5109378 T^{6} + 41125172 T^{7} + 358303779 T^{8} + 2189944210 T^{9} + 15566329288 T^{10} + 59085609645 T^{11} + 326940373369 T^{12} \))(\( 1 - 15 T + 486 T^{2} - 7454 T^{3} + 124002 T^{4} - 1678655 T^{5} + 21032850 T^{6} - 233678476 T^{7} + 2484495939 T^{8} - 22761826039 T^{9} + 206213162937 T^{10} - 1609811021164 T^{11} + 12026310202950 T^{12} - 79666147838255 T^{13} + 488448917813286 T^{14} - 2437013543092526 T^{15} + 13188120780958722 T^{16} - 33784383482085615 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 2 T + 364 T^{2} - 1367 T^{3} + 69441 T^{4} - 357405 T^{5} + 9123390 T^{6} - 55363134 T^{7} + 925368647 T^{8} - 5606818522 T^{9} + 76805597701 T^{10} - 381396630126 T^{11} + 5216635797930 T^{12} - 16961841217005 T^{13} + 273530921290563 T^{14} - 446927490395423 T^{15} + 9877522560224228 T^{16} - 4504584464278082 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 8 T + 403 T^{2} - 3715 T^{3} + 86075 T^{4} - 911994 T^{5} + 12759747 T^{6} - 145050787 T^{7} + 1448607213 T^{8} - 16410880286 T^{9} + 132994013602 T^{10} - 1362103063738 T^{11} + 9979455090357 T^{12} - 82938154346369 T^{13} + 605556169004787 T^{14} - 3592381432172142 T^{15} + 28141392637736675 T^{16} - 100810429426464305 T^{17} + 907673769552033523 T^{18} - 1495522042140323224 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 7 T + 419 T^{2} - 2713 T^{3} + 92752 T^{4} - 546245 T^{5} + 13858840 T^{6} - 74597083 T^{7} + 1575729275 T^{8} - 7744325731 T^{9} + 144155004454 T^{10} - 642779035673 T^{11} + 10855198975475 T^{12} - 42653642297321 T^{13} + 657717277407640 T^{14} - 2151681256035535 T^{15} + 30324373510721488 T^{16} - 73620106334858051 T^{17} + 943710445266258179 T^{18} - 1308581786872782821 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 85 T^{2} + 6889 T^{4} \))
$89$ (\( 1 + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 9 T + 196 T^{2} - 2057 T^{3} + 21133 T^{4} - 183073 T^{5} + 1552516 T^{6} - 6344721 T^{7} + 62742241 T^{8} \))(\( 1 + 23 T + 410 T^{2} + 4313 T^{3} + 46459 T^{4} + 383857 T^{5} + 3247610 T^{6} + 16214287 T^{7} + 62742241 T^{8} \))(\( 1 + 14 T + 220 T^{2} + 2384 T^{3} + 33436 T^{4} + 304315 T^{5} + 2975804 T^{6} + 18883664 T^{7} + 155093180 T^{8} + 878391374 T^{9} + 5584059449 T^{10} \))(\( 1 + T + 217 T^{2} - 684 T^{3} + 11028 T^{4} - 204809 T^{5} - 70125 T^{6} - 18228001 T^{7} + 87352788 T^{8} - 482198796 T^{9} + 13615066297 T^{10} + 5584059449 T^{11} + 496981290961 T^{12} \))(\( 1 + 263 T^{2} - 80 T^{3} + 42883 T^{4} - 86953 T^{5} + 5161687 T^{6} - 14370001 T^{7} + 526563995 T^{8} - 1611468791 T^{9} + 46864195555 T^{10} - 113824777921 T^{11} + 3638829322703 T^{12} - 5455626081673 T^{13} + 239461221351467 T^{14} - 39758503276880 T^{15} + 11632841077524127 T^{16} + 350356403707485209 T^{18} \))(\( 1 + 459 T^{2} - 602 T^{3} + 107035 T^{4} - 232167 T^{5} + 16743355 T^{6} - 43127025 T^{7} + 1933853371 T^{8} - 4847269619 T^{9} + 172112950019 T^{10} - 341609165025 T^{11} + 11803546230995 T^{12} - 14566677866247 T^{13} + 597689803123715 T^{14} - 299182737158522 T^{15} + 20302182717047811 T^{16} + 350356403707485209 T^{18} \))(\( 1 - 36 T + 978 T^{2} - 18914 T^{3} + 316604 T^{4} - 4465163 T^{5} + 57229676 T^{6} - 660203752 T^{7} + 7155669276 T^{8} - 72396285400 T^{9} + 701911581402 T^{10} - 6443269400600 T^{11} + 56680056335196 T^{12} - 465423178843688 T^{13} + 3590718123943916 T^{14} - 24933735641475187 T^{15} + 157346264643416444 T^{16} - 836591468214035506 T^{17} + 3849983851976635218 T^{18} - 12612830533469467524 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 30 T + 720 T^{2} - 10616 T^{3} + 133146 T^{4} - 1151417 T^{5} + 8467506 T^{6} - 27649542 T^{7} - 60454374 T^{8} + 4001725886 T^{9} - 38334028578 T^{10} + 356153603854 T^{11} - 478859096454 T^{12} - 19492069974198 T^{13} + 531270302120946 T^{14} - 6429580978589233 T^{15} + 66171070966293306 T^{16} - 469559851250935864 T^{17} + 2834343940105498320 T^{18} - 10510692111224556270 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 47 T^{2} + 7921 T^{4} \))
$97$ (\( 1 + 4 T + 97 T^{2} \))(\( 1 + 3 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 16 T + 438 T^{2} + 4611 T^{3} + 66127 T^{4} + 447267 T^{5} + 4121142 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 - 14 T + 204 T^{2} - 2593 T^{3} + 32969 T^{4} - 251521 T^{5} + 1919436 T^{6} - 12777422 T^{7} + 88529281 T^{8} \))(\( 1 + 33 T + 877 T^{2} + 14745 T^{3} + 211376 T^{4} + 2239577 T^{5} + 20503472 T^{6} + 138735705 T^{7} + 800414221 T^{8} + 2921466273 T^{9} + 8587340257 T^{10} \))(\( 1 + 16 T + 593 T^{2} + 7277 T^{3} + 145318 T^{4} + 1366256 T^{5} + 18857263 T^{6} + 132526832 T^{7} + 1367297062 T^{8} + 6641521421 T^{9} + 52497863633 T^{10} + 137397444112 T^{11} + 832972004929 T^{12} \))(\( 1 - 15 T + 783 T^{2} - 9737 T^{3} + 277122 T^{4} - 2896117 T^{5} + 58631534 T^{6} - 517666299 T^{7} + 8231099808 T^{8} - 61045311040 T^{9} + 798416681376 T^{10} - 4870722207291 T^{11} + 53511418030382 T^{12} - 256391155701877 T^{13} + 2379740906700354 T^{14} - 8110648411993673 T^{15} + 63265056746362479 T^{16} - 117561503915654415 T^{17} + 760231058654565217 T^{18} \))(\( 1 - 29 T + 869 T^{2} - 15245 T^{3} + 269006 T^{4} - 3475931 T^{5} + 46249846 T^{6} - 489985103 T^{7} + 5557828502 T^{8} - 52338872712 T^{9} + 539109364694 T^{10} - 4610269834127 T^{11} + 42210985698358 T^{12} - 307721672235611 T^{13} + 2310046053174542 T^{14} - 12698658215142605 T^{15} + 70213709211480197 T^{16} - 227285574236931869 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 5 T + 270 T^{2} + 560 T^{3} + 42375 T^{4} - 42794 T^{5} + 4025428 T^{6} - 28038084 T^{7} + 301112696 T^{8} - 4782252055 T^{9} + 21196253372 T^{10} - 463878449335 T^{11} + 2833169356664 T^{12} - 25589602238532 T^{13} + 356368246557268 T^{14} - 367486638958058 T^{15} + 35297188708866375 T^{16} + 45247039307743280 T^{17} + 2116107070481779470 T^{18} + 3801155293272826085 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 55 T + 1700 T^{2} - 38512 T^{3} + 715495 T^{4} - 11557266 T^{5} + 167029752 T^{6} - 2190126020 T^{7} + 26278509800 T^{8} - 290387953875 T^{9} + 2970183426280 T^{10} - 28167631525875 T^{11} + 247254498708200 T^{12} - 1998868885051460 T^{13} + 14787023850168312 T^{14} - 99246175582657362 T^{15} + 595987304666674855 T^{16} - 3111703531821087856 T^{17} + 13323637110440833700 T^{18} - 41812708226001086935 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 145 T^{2} + 9409 T^{4} \))
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