Properties

Label 7524.2
Level 7524
Weight 2
Dimension 699556
Nonzero newspaces 128
Sturm bound 6220800

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Defining parameters

Level: \( N \) = \( 7524\( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 128 \)
Sturm bound: \(6220800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7524))\).

Total New Old
Modular forms 1569600 705060 864540
Cusp forms 1540801 699556 841245
Eisenstein series 28799 5504 23295

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7524))\)

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
7524.2.a \(\chi_{7524}(1, \cdot)\) 7524.2.a.a 1 1
7524.2.a.b 1
7524.2.a.c 1
7524.2.a.d 1
7524.2.a.e 1
7524.2.a.f 1
7524.2.a.g 1
7524.2.a.h 2
7524.2.a.i 3
7524.2.a.j 3
7524.2.a.k 3
7524.2.a.l 3
7524.2.a.m 3
7524.2.a.n 4
7524.2.a.o 4
7524.2.a.p 4
7524.2.a.q 6
7524.2.a.r 6
7524.2.a.s 7
7524.2.a.t 7
7524.2.a.u 7
7524.2.a.v 7
7524.2.c \(\chi_{7524}(989, \cdot)\) 7524.2.c.a 72 1
7524.2.d \(\chi_{7524}(5435, \cdot)\) n/a 360 1
7524.2.f \(\chi_{7524}(4445, \cdot)\) 7524.2.f.a 64 1
7524.2.i \(\chi_{7524}(7523, \cdot)\) n/a 480 1
7524.2.k \(\chi_{7524}(6535, \cdot)\) n/a 500 1
7524.2.l \(\chi_{7524}(2089, \cdot)\) 7524.2.l.a 4 1
7524.2.l.b 8
7524.2.l.c 8
7524.2.l.d 16
7524.2.l.e 24
7524.2.l.f 40
7524.2.n \(\chi_{7524}(3079, \cdot)\) n/a 540 1
7524.2.q \(\chi_{7524}(2509, \cdot)\) n/a 360 2
7524.2.r \(\chi_{7524}(1717, \cdot)\) n/a 400 2
7524.2.s \(\chi_{7524}(1189, \cdot)\) n/a 164 2
7524.2.t \(\chi_{7524}(3697, \cdot)\) n/a 400 2
7524.2.u \(\chi_{7524}(685, \cdot)\) n/a 360 4
7524.2.v \(\chi_{7524}(3299, \cdot)\) n/a 2864 2
7524.2.y \(\chi_{7524}(221, \cdot)\) n/a 400 2
7524.2.ba \(\chi_{7524}(4115, \cdot)\) n/a 2400 2
7524.2.bb \(\chi_{7524}(2705, \cdot)\) n/a 480 2
7524.2.be \(\chi_{7524}(901, \cdot)\) n/a 200 2
7524.2.bf \(\chi_{7524}(5347, \cdot)\) n/a 1000 2
7524.2.bi \(\chi_{7524}(1759, \cdot)\) n/a 2864 2
7524.2.bk \(\chi_{7524}(571, \cdot)\) n/a 2592 2
7524.2.bn \(\chi_{7524}(2311, \cdot)\) n/a 2400 2
7524.2.bp \(\chi_{7524}(4597, \cdot)\) n/a 480 2
7524.2.bs \(\chi_{7524}(1519, \cdot)\) n/a 2400 2
7524.2.bu \(\chi_{7524}(5389, \cdot)\) n/a 480 2
7524.2.bx \(\chi_{7524}(2287, \cdot)\) n/a 1192 2
7524.2.bz \(\chi_{7524}(4643, \cdot)\) n/a 800 2
7524.2.ca \(\chi_{7524}(197, \cdot)\) n/a 160 2
7524.2.cd \(\chi_{7524}(2729, \cdot)\) n/a 400 2
7524.2.cf \(\chi_{7524}(2507, \cdot)\) n/a 2864 2
7524.2.cg \(\chi_{7524}(1937, \cdot)\) n/a 400 2
7524.2.ci \(\chi_{7524}(1319, \cdot)\) n/a 2864 2
7524.2.ck \(\chi_{7524}(4685, \cdot)\) n/a 480 2
7524.2.cm \(\chi_{7524}(419, \cdot)\) n/a 2160 2
7524.2.cp \(\chi_{7524}(3497, \cdot)\) n/a 432 2
7524.2.cr \(\chi_{7524}(1607, \cdot)\) n/a 2400 2
7524.2.cs \(\chi_{7524}(791, \cdot)\) n/a 960 2
7524.2.cv \(\chi_{7524}(3257, \cdot)\) n/a 128 2
7524.2.cy \(\chi_{7524}(6775, \cdot)\) n/a 2864 2
7524.2.da \(\chi_{7524}(373, \cdot)\) n/a 480 2
7524.2.db \(\chi_{7524}(331, \cdot)\) n/a 2400 2
7524.2.dd \(\chi_{7524}(397, \cdot)\) n/a 504 6
7524.2.de \(\chi_{7524}(2113, \cdot)\) n/a 1200 6
7524.2.df \(\chi_{7524}(529, \cdot)\) n/a 1200 6
7524.2.di \(\chi_{7524}(343, \cdot)\) n/a 2160 4
7524.2.dk \(\chi_{7524}(721, \cdot)\) n/a 400 4
7524.2.dl \(\chi_{7524}(379, \cdot)\) n/a 2384 4
7524.2.dn \(\chi_{7524}(2735, \cdot)\) n/a 1920 4
7524.2.dq \(\chi_{7524}(1709, \cdot)\) n/a 320 4
7524.2.ds \(\chi_{7524}(647, \cdot)\) n/a 1728 4
7524.2.dt \(\chi_{7524}(305, \cdot)\) n/a 288 4
7524.2.dv \(\chi_{7524}(961, \cdot)\) n/a 1920 8
7524.2.dw \(\chi_{7524}(577, \cdot)\) n/a 800 8
7524.2.dx \(\chi_{7524}(49, \cdot)\) n/a 1920 8
7524.2.dy \(\chi_{7524}(229, \cdot)\) n/a 1728 8
7524.2.ea \(\chi_{7524}(67, \cdot)\) n/a 7200 6
7524.2.eb \(\chi_{7524}(329, \cdot)\) n/a 1440 6
7524.2.ed \(\chi_{7524}(2617, \cdot)\) n/a 1440 6
7524.2.eg \(\chi_{7524}(23, \cdot)\) n/a 7200 6
7524.2.ei \(\chi_{7524}(1409, \cdot)\) n/a 1200 6
7524.2.ej \(\chi_{7524}(967, \cdot)\) n/a 8592 6
7524.2.em \(\chi_{7524}(395, \cdot)\) n/a 2880 6
7524.2.eo \(\chi_{7524}(89, \cdot)\) n/a 408 6
7524.2.er \(\chi_{7524}(1099, \cdot)\) n/a 3576 6
7524.2.es \(\chi_{7524}(527, \cdot)\) n/a 8592 6
7524.2.ew \(\chi_{7524}(241, \cdot)\) n/a 1440 6
7524.2.ex \(\chi_{7524}(815, \cdot)\) n/a 7200 6
7524.2.fa \(\chi_{7524}(991, \cdot)\) n/a 3000 6
7524.2.fb \(\chi_{7524}(593, \cdot)\) n/a 480 6
7524.2.fd \(\chi_{7524}(109, \cdot)\) n/a 600 6
7524.2.fg \(\chi_{7524}(1871, \cdot)\) n/a 2400 6
7524.2.fh \(\chi_{7524}(1915, \cdot)\) n/a 7200 6
7524.2.fk \(\chi_{7524}(1517, \cdot)\) n/a 1440 6
7524.2.fm \(\chi_{7524}(2903, \cdot)\) n/a 8592 6
7524.2.fo \(\chi_{7524}(1541, \cdot)\) n/a 1200 6
7524.2.fr \(\chi_{7524}(43, \cdot)\) n/a 8592 6
7524.2.ft \(\chi_{7524}(31, \cdot)\) n/a 11456 8
7524.2.fu \(\chi_{7524}(673, \cdot)\) n/a 1920 8
7524.2.fw \(\chi_{7524}(1987, \cdot)\) n/a 11456 8
7524.2.fz \(\chi_{7524}(449, \cdot)\) n/a 640 8
7524.2.gc \(\chi_{7524}(107, \cdot)\) n/a 3840 8
7524.2.gd \(\chi_{7524}(2291, \cdot)\) n/a 11456 8
7524.2.gf \(\chi_{7524}(761, \cdot)\) n/a 1728 8
7524.2.gi \(\chi_{7524}(191, \cdot)\) n/a 10368 8
7524.2.gk \(\chi_{7524}(425, \cdot)\) n/a 1920 8
7524.2.gm \(\chi_{7524}(635, \cdot)\) n/a 11456 8
7524.2.go \(\chi_{7524}(113, \cdot)\) n/a 1920 8
7524.2.gp \(\chi_{7524}(227, \cdot)\) n/a 11456 8
7524.2.gr \(\chi_{7524}(977, \cdot)\) n/a 1920 8
7524.2.gu \(\chi_{7524}(809, \cdot)\) n/a 640 8
7524.2.gv \(\chi_{7524}(467, \cdot)\) n/a 3840 8
7524.2.gx \(\chi_{7524}(919, \cdot)\) n/a 4768 8
7524.2.ha \(\chi_{7524}(601, \cdot)\) n/a 1920 8
7524.2.hc \(\chi_{7524}(1291, \cdot)\) n/a 11456 8
7524.2.hf \(\chi_{7524}(1861, \cdot)\) n/a 1920 8
7524.2.hh \(\chi_{7524}(103, \cdot)\) n/a 11456 8
7524.2.hk \(\chi_{7524}(799, \cdot)\) n/a 10368 8
7524.2.hm \(\chi_{7524}(7, \cdot)\) n/a 11456 8
7524.2.hp \(\chi_{7524}(487, \cdot)\) n/a 4768 8
7524.2.hq \(\chi_{7524}(145, \cdot)\) n/a 800 8
7524.2.ht \(\chi_{7524}(1337, \cdot)\) n/a 1920 8
7524.2.hu \(\chi_{7524}(311, \cdot)\) n/a 11456 8
7524.2.hw \(\chi_{7524}(905, \cdot)\) n/a 1920 8
7524.2.hz \(\chi_{7524}(563, \cdot)\) n/a 11456 8
7524.2.ia \(\chi_{7524}(169, \cdot)\) n/a 5760 24
7524.2.ib \(\chi_{7524}(25, \cdot)\) n/a 5760 24
7524.2.ic \(\chi_{7524}(289, \cdot)\) n/a 2400 24
7524.2.ie \(\chi_{7524}(139, \cdot)\) n/a 34368 24
7524.2.if \(\chi_{7524}(257, \cdot)\) n/a 5760 24
7524.2.ij \(\chi_{7524}(167, \cdot)\) n/a 34368 24
7524.2.il \(\chi_{7524}(101, \cdot)\) n/a 5760 24
7524.2.im \(\chi_{7524}(295, \cdot)\) n/a 34368 24
7524.2.ip \(\chi_{7524}(251, \cdot)\) n/a 11520 24
7524.2.iq \(\chi_{7524}(325, \cdot)\) n/a 2400 24
7524.2.is \(\chi_{7524}(17, \cdot)\) n/a 1920 24
7524.2.iv \(\chi_{7524}(91, \cdot)\) n/a 14304 24
7524.2.iw \(\chi_{7524}(47, \cdot)\) n/a 34368 24
7524.2.iz \(\chi_{7524}(193, \cdot)\) n/a 5760 24
7524.2.jb \(\chi_{7524}(371, \cdot)\) n/a 34368 24
7524.2.je \(\chi_{7524}(271, \cdot)\) n/a 14304 24
7524.2.jf \(\chi_{7524}(53, \cdot)\) n/a 1920 24
7524.2.jj \(\chi_{7524}(431, \cdot)\) n/a 11520 24
7524.2.jk \(\chi_{7524}(283, \cdot)\) n/a 34368 24
7524.2.jn \(\chi_{7524}(185, \cdot)\) n/a 5760 24
7524.2.jp \(\chi_{7524}(119, \cdot)\) n/a 34368 24
7524.2.jq \(\chi_{7524}(13, \cdot)\) n/a 5760 24
7524.2.js \(\chi_{7524}(365, \cdot)\) n/a 5760 24
7524.2.jv \(\chi_{7524}(223, \cdot)\) n/a 34368 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7524))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7524)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(836))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1254))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1881))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2508))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3762))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( ( 1 - T + 5 T^{2} )^{2} \))(\( 1 + T + 9 T^{2} + 13 T^{3} + 45 T^{4} + 25 T^{5} + 125 T^{6} \))(\( 1 + T + 9 T^{2} + 7 T^{3} + 45 T^{4} + 25 T^{5} + 125 T^{6} \))(\( 1 + T + 5 T^{2} - 5 T^{3} + 25 T^{4} + 25 T^{5} + 125 T^{6} \))(\( 1 - 3 T + 11 T^{2} - 31 T^{3} + 55 T^{4} - 75 T^{5} + 125 T^{6} \))(\( 1 - 3 T + 15 T^{2} - 29 T^{3} + 75 T^{4} - 75 T^{5} + 125 T^{6} \))(\( 1 + T + 6 T^{2} + 6 T^{3} + 54 T^{4} + 30 T^{5} + 150 T^{6} + 125 T^{7} + 625 T^{8} \))(\( 1 - 3 T + 16 T^{2} - 40 T^{3} + 114 T^{4} - 200 T^{5} + 400 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 - 3 T + 8 T^{2} - 2 T^{3} - 2 T^{4} - 10 T^{5} + 200 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 + 5 T + 21 T^{2} + 48 T^{3} + 96 T^{4} + 86 T^{5} + 178 T^{6} + 430 T^{7} + 2400 T^{8} + 6000 T^{9} + 13125 T^{10} + 15625 T^{11} + 15625 T^{12} \))(\( 1 + 2 T^{2} + 6 T^{3} + 43 T^{4} + 42 T^{5} + 37 T^{6} + 210 T^{7} + 1075 T^{8} + 750 T^{9} + 1250 T^{10} + 15625 T^{12} \))(\( 1 + 4 T + 16 T^{2} + 48 T^{3} + 142 T^{4} + 280 T^{5} + 696 T^{6} + 1490 T^{7} + 3480 T^{8} + 7000 T^{9} + 17750 T^{10} + 30000 T^{11} + 50000 T^{12} + 62500 T^{13} + 78125 T^{14} \))(\( 1 + 2 T + 16 T^{2} + 46 T^{3} + 158 T^{4} + 458 T^{5} + 1104 T^{6} + 2828 T^{7} + 5520 T^{8} + 11450 T^{9} + 19750 T^{10} + 28750 T^{11} + 50000 T^{12} + 31250 T^{13} + 78125 T^{14} \))(\( 1 - 2 T + 16 T^{2} - 46 T^{3} + 158 T^{4} - 458 T^{5} + 1104 T^{6} - 2828 T^{7} + 5520 T^{8} - 11450 T^{9} + 19750 T^{10} - 28750 T^{11} + 50000 T^{12} - 31250 T^{13} + 78125 T^{14} \))(\( 1 - 4 T + 16 T^{2} - 48 T^{3} + 142 T^{4} - 280 T^{5} + 696 T^{6} - 1490 T^{7} + 3480 T^{8} - 7000 T^{9} + 17750 T^{10} - 30000 T^{11} + 50000 T^{12} - 62500 T^{13} + 78125 T^{14} \))(\( ( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 + 5 T^{2} )^{8} \))(\( ( 1 + 9 T^{2} + 56 T^{4} + 225 T^{6} + 625 T^{8} )^{2} \))(\( ( 1 + T + 14 T^{2} + 14 T^{3} + 93 T^{4} + 70 T^{5} + 350 T^{6} + 125 T^{7} + 625 T^{8} )^{4} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 12 T^{2} + 49 T^{4} \))(\( 1 + 5 T + 25 T^{2} + 67 T^{3} + 175 T^{4} + 245 T^{5} + 343 T^{6} \))(\( 1 + T + 7 T^{2} - T^{3} + 49 T^{4} + 49 T^{5} + 343 T^{6} \))(\( 1 + T + 5 T^{2} - 11 T^{3} + 35 T^{4} + 49 T^{5} + 343 T^{6} \))(\( 1 + 3 T + 17 T^{2} + 43 T^{3} + 119 T^{4} + 147 T^{5} + 343 T^{6} \))(\( 1 + 3 T + 15 T^{2} + 43 T^{3} + 105 T^{4} + 147 T^{5} + 343 T^{6} \))(\( 1 - 5 T + 24 T^{2} - 62 T^{3} + 200 T^{4} - 434 T^{5} + 1176 T^{6} - 1715 T^{7} + 2401 T^{8} \))(\( 1 - 3 T + 18 T^{2} - 40 T^{3} + 160 T^{4} - 280 T^{5} + 882 T^{6} - 1029 T^{7} + 2401 T^{8} \))(\( 1 - 3 T + 8 T^{2} - 8 T^{3} + 28 T^{4} - 56 T^{5} + 392 T^{6} - 1029 T^{7} + 2401 T^{8} \))(\( 1 + 2 T + 17 T^{2} + 12 T^{3} + 116 T^{4} - 82 T^{5} + 548 T^{6} - 574 T^{7} + 5684 T^{8} + 4116 T^{9} + 40817 T^{10} + 33614 T^{11} + 117649 T^{12} \))(\( 1 - 2 T - T^{2} + 8 T^{3} + 78 T^{4} - 102 T^{5} + 138 T^{6} - 714 T^{7} + 3822 T^{8} + 2744 T^{9} - 2401 T^{10} - 33614 T^{11} + 117649 T^{12} \))(\( 1 + 2 T + 16 T^{2} + 22 T^{3} + 122 T^{4} + 210 T^{5} + 812 T^{6} + 1676 T^{7} + 5684 T^{8} + 10290 T^{9} + 41846 T^{10} + 52822 T^{11} + 268912 T^{12} + 235298 T^{13} + 823543 T^{14} \))(\( 1 - 6 T + 48 T^{2} - 206 T^{3} + 970 T^{4} - 3198 T^{5} + 11020 T^{6} - 28676 T^{7} + 77140 T^{8} - 156702 T^{9} + 332710 T^{10} - 494606 T^{11} + 806736 T^{12} - 705894 T^{13} + 823543 T^{14} \))(\( 1 - 6 T + 48 T^{2} - 206 T^{3} + 970 T^{4} - 3198 T^{5} + 11020 T^{6} - 28676 T^{7} + 77140 T^{8} - 156702 T^{9} + 332710 T^{10} - 494606 T^{11} + 806736 T^{12} - 705894 T^{13} + 823543 T^{14} \))(\( 1 + 2 T + 16 T^{2} + 22 T^{3} + 122 T^{4} + 210 T^{5} + 812 T^{6} + 1676 T^{7} + 5684 T^{8} + 10290 T^{9} + 41846 T^{10} + 52822 T^{11} + 268912 T^{12} + 235298 T^{13} + 823543 T^{14} \))(\( ( 1 - 3 T + 2 T^{2} - 21 T^{3} + 49 T^{4} )( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} ) \))(\( ( 1 - 7 T^{2} )^{8} \))(\( ( 1 - 3 T + 2 T^{2} - 21 T^{3} + 49 T^{4} )^{2}( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 27 T^{2} + 401 T^{4} - 4271 T^{6} + 34558 T^{8} - 209279 T^{10} + 962801 T^{12} - 3176523 T^{14} + 5764801 T^{16} )^{2} \))
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{7} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( ( 1 + 11 T^{2} )^{4} \))(\( 1 - 3 T^{2} - 112 T^{4} - 363 T^{6} + 14641 T^{8} \))(\( ( 1 - 8 T^{2} - 16 T^{3} + 158 T^{4} - 176 T^{5} - 968 T^{6} + 14641 T^{8} )^{2} \))
$13$ (\( 1 - T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 24 T^{2} + 169 T^{4} \))(\( 1 - T + 27 T^{2} - 35 T^{3} + 351 T^{4} - 169 T^{5} + 2197 T^{6} \))(\( 1 + 3 T + 27 T^{2} + 77 T^{3} + 351 T^{4} + 507 T^{5} + 2197 T^{6} \))(\( 1 + 7 T + 49 T^{2} + 177 T^{3} + 637 T^{4} + 1183 T^{5} + 2197 T^{6} \))(\( 1 + 5 T + 31 T^{2} + 89 T^{3} + 403 T^{4} + 845 T^{5} + 2197 T^{6} \))(\( 1 - 3 T + 15 T^{2} - 79 T^{3} + 195 T^{4} - 507 T^{5} + 2197 T^{6} \))(\( 1 + 33 T^{2} + 37 T^{3} + 507 T^{4} + 481 T^{5} + 5577 T^{6} + 28561 T^{8} \))(\( 1 - 4 T + 25 T^{2} - 39 T^{3} + 285 T^{4} - 507 T^{5} + 4225 T^{6} - 8788 T^{7} + 28561 T^{8} \))(\( 1 + 6 T + 39 T^{2} + 163 T^{3} + 715 T^{4} + 2119 T^{5} + 6591 T^{6} + 13182 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 55 T^{2} - 274 T^{3} + 1148 T^{4} - 4180 T^{5} + 15612 T^{6} - 54340 T^{7} + 194012 T^{8} - 601978 T^{9} + 1570855 T^{10} - 2970344 T^{11} + 4826809 T^{12} \))(\( 1 - 2 T + 29 T^{2} + 26 T^{3} + 462 T^{4} + 300 T^{5} + 9066 T^{6} + 3900 T^{7} + 78078 T^{8} + 57122 T^{9} + 828269 T^{10} - 742586 T^{11} + 4826809 T^{12} \))(\( 1 + 3 T + 24 T^{2} + 71 T^{3} + 400 T^{4} + 1473 T^{5} + 6162 T^{6} + 19909 T^{7} + 80106 T^{8} + 248937 T^{9} + 878800 T^{10} + 2027831 T^{11} + 8911032 T^{12} + 14480427 T^{13} + 62748517 T^{14} \))(\( 1 + 50 T^{2} - 80 T^{3} + 1164 T^{4} - 3412 T^{5} + 18324 T^{6} - 62742 T^{7} + 238212 T^{8} - 576628 T^{9} + 2557308 T^{10} - 2284880 T^{11} + 18564650 T^{12} + 62748517 T^{14} \))(\( 1 + 50 T^{2} - 80 T^{3} + 1164 T^{4} - 3412 T^{5} + 18324 T^{6} - 62742 T^{7} + 238212 T^{8} - 576628 T^{9} + 2557308 T^{10} - 2284880 T^{11} + 18564650 T^{12} + 62748517 T^{14} \))(\( 1 + 3 T + 24 T^{2} + 71 T^{3} + 400 T^{4} + 1473 T^{5} + 6162 T^{6} + 19909 T^{7} + 80106 T^{8} + 248937 T^{9} + 878800 T^{10} + 2027831 T^{11} + 8911032 T^{12} + 14480427 T^{13} + 62748517 T^{14} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 - 7 T^{2} - 120 T^{4} - 1183 T^{6} + 28561 T^{8} )^{2} \))(\( ( 1 + 13 T^{2} )^{8} \))(\( ( 1 + 35 T^{2} + 835 T^{4} + 14799 T^{6} + 205786 T^{8} + 2501031 T^{10} + 23848435 T^{12} + 168938315 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( 1 - 3 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 4 T + 44 T^{2} + 135 T^{3} + 748 T^{4} + 1156 T^{5} + 4913 T^{6} \))(\( 1 - 6 T + 48 T^{2} - 195 T^{3} + 816 T^{4} - 1734 T^{5} + 4913 T^{6} \))(\( 1 + 2 T + 46 T^{2} + 67 T^{3} + 782 T^{4} + 578 T^{5} + 4913 T^{6} \))(\( 1 - 16 T + 120 T^{2} - 585 T^{3} + 2040 T^{4} - 4624 T^{5} + 4913 T^{6} \))(\( 1 - 6 T + 60 T^{2} - 207 T^{3} + 1020 T^{4} - 1734 T^{5} + 4913 T^{6} \))(\( 1 + 5 T + 39 T^{2} + 99 T^{3} + 589 T^{4} + 1683 T^{5} + 11271 T^{6} + 24565 T^{7} + 83521 T^{8} \))(\( 1 + 3 T + 33 T^{2} - 17 T^{3} + 351 T^{4} - 289 T^{5} + 9537 T^{6} + 14739 T^{7} + 83521 T^{8} \))(\( 1 + 3 T + 43 T^{2} + 107 T^{3} + 867 T^{4} + 1819 T^{5} + 12427 T^{6} + 14739 T^{7} + 83521 T^{8} \))(\( 1 - 2 T + 30 T^{2} - 122 T^{3} + 607 T^{4} - 2084 T^{5} + 12868 T^{6} - 35428 T^{7} + 175423 T^{8} - 599386 T^{9} + 2505630 T^{10} - 2839714 T^{11} + 24137569 T^{12} \))(\( 1 + 12 T + 84 T^{2} + 540 T^{3} + 3015 T^{4} + 14232 T^{5} + 61192 T^{6} + 241944 T^{7} + 871335 T^{8} + 2653020 T^{9} + 7015764 T^{10} + 17038284 T^{11} + 24137569 T^{12} \))(\( 1 + 3 T + 75 T^{2} + 132 T^{3} + 2360 T^{4} + 1514 T^{5} + 46221 T^{6} + 4675 T^{7} + 785757 T^{8} + 437546 T^{9} + 11594680 T^{10} + 11024772 T^{11} + 106489275 T^{12} + 72412707 T^{13} + 410338673 T^{14} \))(\( 1 + 8 T + 87 T^{2} + 486 T^{3} + 3214 T^{4} + 14514 T^{5} + 73961 T^{6} + 286532 T^{7} + 1257337 T^{8} + 4194546 T^{9} + 15790382 T^{10} + 40591206 T^{11} + 123527559 T^{12} + 193100552 T^{13} + 410338673 T^{14} \))(\( 1 - 8 T + 87 T^{2} - 486 T^{3} + 3214 T^{4} - 14514 T^{5} + 73961 T^{6} - 286532 T^{7} + 1257337 T^{8} - 4194546 T^{9} + 15790382 T^{10} - 40591206 T^{11} + 123527559 T^{12} - 193100552 T^{13} + 410338673 T^{14} \))(\( 1 - 3 T + 75 T^{2} - 132 T^{3} + 2360 T^{4} - 1514 T^{5} + 46221 T^{6} - 4675 T^{7} + 785757 T^{8} - 437546 T^{9} + 11594680 T^{10} - 11024772 T^{11} + 106489275 T^{12} - 72412707 T^{13} + 410338673 T^{14} \))(\( ( 1 - 7 T + 32 T^{2} - 119 T^{3} + 289 T^{4} )( 1 + 7 T + 32 T^{2} + 119 T^{3} + 289 T^{4} ) \))(\( ( 1 + 23 T^{2} + 240 T^{4} + 6647 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 - 15 T^{2} - 64 T^{4} - 4335 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 - 68 T^{2} + 2562 T^{4} - 67908 T^{6} + 1329770 T^{8} - 19625412 T^{10} + 213980802 T^{12} - 1641354692 T^{14} + 6975757441 T^{16} )^{2} \))
$19$ (\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( 1 - 72 T^{2} + 2596 T^{4} - 62296 T^{6} + 1241878 T^{8} - 22488856 T^{10} + 338313316 T^{12} - 3387303432 T^{14} + 16983563041 T^{16} \))
$23$ (\( 1 - 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 2 T + 15 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 36 T^{2} - 95 T^{3} + 828 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( ( 1 - 3 T + 23 T^{2} )^{3} \))(\( ( 1 + T + 23 T^{2} )^{3} \))(\( 1 + T + 4 T^{2} - 123 T^{3} + 92 T^{4} + 529 T^{5} + 12167 T^{6} \))(\( 1 - 9 T + 84 T^{2} - 397 T^{3} + 1932 T^{4} - 4761 T^{5} + 12167 T^{6} \))(\( 1 + 3 T + 61 T^{2} + 140 T^{3} + 1930 T^{4} + 3220 T^{5} + 32269 T^{6} + 36501 T^{7} + 279841 T^{8} \))(\( 1 + T + 77 T^{2} + 60 T^{3} + 2530 T^{4} + 1380 T^{5} + 40733 T^{6} + 12167 T^{7} + 279841 T^{8} \))(\( 1 + 7 T + 37 T^{2} + 100 T^{3} + 250 T^{4} + 2300 T^{5} + 19573 T^{6} + 85169 T^{7} + 279841 T^{8} \))(\( 1 + 5 T + 50 T^{2} + 243 T^{3} + 1967 T^{4} + 8550 T^{5} + 54684 T^{6} + 196650 T^{7} + 1040543 T^{8} + 2956581 T^{9} + 13992050 T^{10} + 32181715 T^{11} + 148035889 T^{12} \))(\( 1 - 2 T + 63 T^{2} - 110 T^{3} + 2079 T^{4} - 3404 T^{5} + 51730 T^{6} - 78292 T^{7} + 1099791 T^{8} - 1338370 T^{9} + 17629983 T^{10} - 12872686 T^{11} + 148035889 T^{12} \))(\( 1 + 2 T + 114 T^{2} + 220 T^{3} + 6243 T^{4} + 10872 T^{5} + 213425 T^{6} + 316432 T^{7} + 4908775 T^{8} + 5751288 T^{9} + 75958581 T^{10} + 61565020 T^{11} + 733743102 T^{12} + 296071778 T^{13} + 3404825447 T^{14} \))(\( 1 + 10 T + 114 T^{2} + 828 T^{3} + 6547 T^{4} + 37560 T^{5} + 226529 T^{6} + 1064656 T^{7} + 5210167 T^{8} + 19869240 T^{9} + 79657349 T^{10} + 231708348 T^{11} + 733743102 T^{12} + 1480358890 T^{13} + 3404825447 T^{14} \))(\( 1 - 10 T + 114 T^{2} - 828 T^{3} + 6547 T^{4} - 37560 T^{5} + 226529 T^{6} - 1064656 T^{7} + 5210167 T^{8} - 19869240 T^{9} + 79657349 T^{10} - 231708348 T^{11} + 733743102 T^{12} - 1480358890 T^{13} + 3404825447 T^{14} \))(\( 1 - 2 T + 114 T^{2} - 220 T^{3} + 6243 T^{4} - 10872 T^{5} + 213425 T^{6} - 316432 T^{7} + 4908775 T^{8} - 5751288 T^{9} + 75958581 T^{10} - 61565020 T^{11} + 733743102 T^{12} - 296071778 T^{13} + 3404825447 T^{14} \))(\( ( 1 - 4 T + 23 T^{2} )^{4} \))(\( ( 1 + 23 T^{2} )^{8} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{4} \))(\( ( 1 + 6 T + 31 T^{2} - 50 T^{3} - 208 T^{4} - 1150 T^{5} + 16399 T^{6} + 73002 T^{7} + 279841 T^{8} )^{4} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 56 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 + 48 T^{2} - 11 T^{3} + 1392 T^{4} + 24389 T^{6} \))(\( 1 + 6 T + 48 T^{2} + 115 T^{3} + 1392 T^{4} + 5046 T^{5} + 24389 T^{6} \))(\( 1 + 8 T + 92 T^{2} + 459 T^{3} + 2668 T^{4} + 6728 T^{5} + 24389 T^{6} \))(\( 1 - 10 T + 48 T^{2} - 231 T^{3} + 1392 T^{4} - 8410 T^{5} + 24389 T^{6} \))(\( 1 + 84 T^{2} - T^{3} + 2436 T^{4} + 24389 T^{6} \))(\( 1 + 14 T + 145 T^{2} + 947 T^{3} + 5772 T^{4} + 27463 T^{5} + 121945 T^{6} + 341446 T^{7} + 707281 T^{8} \))(\( 1 - 10 T + 121 T^{2} - 763 T^{3} + 5164 T^{4} - 22127 T^{5} + 101761 T^{6} - 243890 T^{7} + 707281 T^{8} \))(\( 1 - 16 T + 157 T^{2} - 1063 T^{3} + 6272 T^{4} - 30827 T^{5} + 132037 T^{6} - 390224 T^{7} + 707281 T^{8} \))(\( 1 + 10 T + 83 T^{2} + 422 T^{3} + 2572 T^{4} + 8554 T^{5} + 46924 T^{6} + 248066 T^{7} + 2163052 T^{8} + 10292158 T^{9} + 58704323 T^{10} + 205111490 T^{11} + 594823321 T^{12} \))(\( 1 + 4 T + 105 T^{2} + 406 T^{3} + 5874 T^{4} + 19558 T^{5} + 210178 T^{6} + 567182 T^{7} + 4940034 T^{8} + 9901934 T^{9} + 74264505 T^{10} + 82044596 T^{11} + 594823321 T^{12} \))(\( 1 + 18 T + 259 T^{2} + 2502 T^{3} + 20952 T^{4} + 141994 T^{5} + 893433 T^{6} + 4903522 T^{7} + 25909557 T^{8} + 119416954 T^{9} + 510998328 T^{10} + 1769617062 T^{11} + 5312387591 T^{12} + 10706819778 T^{13} + 17249876309 T^{14} \))(\( 1 + 8 T + 115 T^{2} + 1018 T^{3} + 8132 T^{4} + 58178 T^{5} + 362901 T^{6} + 2098112 T^{7} + 10524129 T^{8} + 48927698 T^{9} + 198331348 T^{10} + 720012058 T^{11} + 2358782135 T^{12} + 4758586568 T^{13} + 17249876309 T^{14} \))(\( 1 - 8 T + 115 T^{2} - 1018 T^{3} + 8132 T^{4} - 58178 T^{5} + 362901 T^{6} - 2098112 T^{7} + 10524129 T^{8} - 48927698 T^{9} + 198331348 T^{10} - 720012058 T^{11} + 2358782135 T^{12} - 4758586568 T^{13} + 17249876309 T^{14} \))(\( 1 - 18 T + 259 T^{2} - 2502 T^{3} + 20952 T^{4} - 141994 T^{5} + 893433 T^{6} - 4903522 T^{7} + 25909557 T^{8} - 119416954 T^{9} + 510998328 T^{10} - 1769617062 T^{11} + 5312387591 T^{12} - 10706819778 T^{13} + 17249876309 T^{14} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 + 29 T^{2} )^{8} \))(\( ( 1 + 29 T^{2} )^{8} \))(\( ( 1 + 9 T^{2} + 2487 T^{4} + 14677 T^{6} + 2851658 T^{8} + 12343357 T^{10} + 1759007847 T^{12} + 5353409889 T^{14} + 500246412961 T^{16} )^{2} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 2 T + 45 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 + 54 T^{2} + 11 T^{3} + 1674 T^{4} + 29791 T^{6} \))(\( 1 + 8 T + 100 T^{2} + 487 T^{3} + 3100 T^{4} + 7688 T^{5} + 29791 T^{6} \))(\( 1 - 12 T + 124 T^{2} - 739 T^{3} + 3844 T^{4} - 11532 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 78 T^{2} - 137 T^{3} + 2418 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 + 6 T + 48 T^{2} + 103 T^{3} + 1488 T^{4} + 5766 T^{5} + 29791 T^{6} \))(\( 1 - 8 T + 97 T^{2} - 599 T^{3} + 4444 T^{4} - 18569 T^{5} + 93217 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( 1 - 6 T + 35 T^{2} - 205 T^{3} + 2116 T^{4} - 6355 T^{5} + 33635 T^{6} - 178746 T^{7} + 923521 T^{8} \))(\( 1 - 6 T + 109 T^{2} - 449 T^{3} + 4764 T^{4} - 13919 T^{5} + 104749 T^{6} - 178746 T^{7} + 923521 T^{8} \))(\( 1 - 3 T + 107 T^{2} - 78 T^{3} + 4418 T^{4} + 6464 T^{5} + 127702 T^{6} + 200384 T^{7} + 4245698 T^{8} - 2323698 T^{9} + 98816747 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 20 T + 274 T^{2} + 2576 T^{3} + 20343 T^{4} + 132078 T^{5} + 786627 T^{6} + 4094418 T^{7} + 19549623 T^{8} + 76741616 T^{9} + 253044754 T^{10} + 572583020 T^{11} + 887503681 T^{12} \))(\( 1 + 4 T + 51 T^{2} + 506 T^{3} + 4084 T^{4} + 19858 T^{5} + 163169 T^{6} + 931748 T^{7} + 5058239 T^{8} + 19083538 T^{9} + 121666444 T^{10} + 467301626 T^{11} + 1460086701 T^{12} + 3550014724 T^{13} + 27512614111 T^{14} \))(\( 1 + 155 T^{2} + 22 T^{3} + 11352 T^{4} + 2678 T^{5} + 518889 T^{6} + 123972 T^{7} + 16085559 T^{8} + 2573558 T^{9} + 338187432 T^{10} + 20317462 T^{11} + 4437518405 T^{12} + 27512614111 T^{14} \))(\( 1 + 155 T^{2} + 22 T^{3} + 11352 T^{4} + 2678 T^{5} + 518889 T^{6} + 123972 T^{7} + 16085559 T^{8} + 2573558 T^{9} + 338187432 T^{10} + 20317462 T^{11} + 4437518405 T^{12} + 27512614111 T^{14} \))(\( 1 + 4 T + 51 T^{2} + 506 T^{3} + 4084 T^{4} + 19858 T^{5} + 163169 T^{6} + 931748 T^{7} + 5058239 T^{8} + 19083538 T^{9} + 121666444 T^{10} + 467301626 T^{11} + 1460086701 T^{12} + 3550014724 T^{13} + 27512614111 T^{14} \))(\( ( 1 - 31 T^{2} )^{4} \))(\( ( 1 - 31 T^{2} )^{8} \))(\( ( 1 - 31 T^{2} )^{8} \))(\( ( 1 - 103 T^{2} + 4002 T^{4} - 49206 T^{6} - 337155 T^{8} - 47286966 T^{10} + 3695931042 T^{12} - 91412879143 T^{14} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 - 8 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 14 T + 121 T^{2} + 518 T^{3} + 1369 T^{4} \))(\( 1 - 3 T + 78 T^{2} - 195 T^{3} + 2886 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 + T + 86 T^{2} + 73 T^{3} + 3182 T^{4} + 1369 T^{5} + 50653 T^{6} \))(\( 1 - 17 T + 166 T^{2} - 1113 T^{3} + 6142 T^{4} - 23273 T^{5} + 50653 T^{6} \))(\( ( 1 + 3 T + 37 T^{2} )^{3} \))(\( 1 - 3 T + 102 T^{2} - 203 T^{3} + 3774 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 + 13 T + 177 T^{2} + 1374 T^{3} + 10378 T^{4} + 50838 T^{5} + 242313 T^{6} + 658489 T^{7} + 1874161 T^{8} \))(\( 1 - 3 T + 85 T^{2} - 122 T^{3} + 3606 T^{4} - 4514 T^{5} + 116365 T^{6} - 151959 T^{7} + 1874161 T^{8} \))(\( 1 + T + 57 T^{2} + 202 T^{3} + 2494 T^{4} + 7474 T^{5} + 78033 T^{6} + 50653 T^{7} + 1874161 T^{8} \))(\( 1 - 7 T + 112 T^{2} - 967 T^{3} + 8191 T^{4} - 54478 T^{5} + 394928 T^{6} - 2015686 T^{7} + 11213479 T^{8} - 48981451 T^{9} + 209906032 T^{10} - 485407699 T^{11} + 2565726409 T^{12} \))(\( 1 - 22 T + 289 T^{2} - 2614 T^{3} + 20331 T^{4} - 140172 T^{5} + 906342 T^{6} - 5186364 T^{7} + 27833139 T^{8} - 132406942 T^{9} + 541632529 T^{10} - 1525567054 T^{11} + 2565726409 T^{12} \))(\( 1 + 10 T + 224 T^{2} + 1960 T^{3} + 23409 T^{4} + 165840 T^{5} + 1419021 T^{6} + 7919628 T^{7} + 52503777 T^{8} + 227034960 T^{9} + 1185736077 T^{10} + 3673355560 T^{11} + 15533046368 T^{12} + 25657264090 T^{13} + 94931877133 T^{14} \))(\( 1 + 4 T + 136 T^{2} + 790 T^{3} + 10825 T^{4} + 59284 T^{5} + 591605 T^{6} + 2707322 T^{7} + 21889385 T^{8} + 81159796 T^{9} + 548318725 T^{10} + 1480587190 T^{11} + 9430778152 T^{12} + 10262905636 T^{13} + 94931877133 T^{14} \))(\( 1 + 4 T + 136 T^{2} + 790 T^{3} + 10825 T^{4} + 59284 T^{5} + 591605 T^{6} + 2707322 T^{7} + 21889385 T^{8} + 81159796 T^{9} + 548318725 T^{10} + 1480587190 T^{11} + 9430778152 T^{12} + 10262905636 T^{13} + 94931877133 T^{14} \))(\( 1 + 10 T + 224 T^{2} + 1960 T^{3} + 23409 T^{4} + 165840 T^{5} + 1419021 T^{6} + 7919628 T^{7} + 52503777 T^{8} + 227034960 T^{9} + 1185736077 T^{10} + 3673355560 T^{11} + 15533046368 T^{12} + 25657264090 T^{13} + 94931877133 T^{14} \))(\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} )^{8} \))(\( ( 1 - 37 T^{2} )^{8} \))(\( ( 1 - 210 T^{2} + 21323 T^{4} - 1365278 T^{6} + 60199048 T^{8} - 1869065582 T^{10} + 39962735003 T^{12} - 538802545890 T^{14} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( 1 + 5 T + 91 T^{2} + 443 T^{3} + 3731 T^{4} + 8405 T^{5} + 68921 T^{6} \))(\( 1 + 7 T + 85 T^{2} + 613 T^{3} + 3485 T^{4} + 11767 T^{5} + 68921 T^{6} \))(\( 1 + 7 T + 39 T^{2} + 149 T^{3} + 1599 T^{4} + 11767 T^{5} + 68921 T^{6} \))(\( 1 - 15 T + 149 T^{2} - 1201 T^{3} + 6109 T^{4} - 25215 T^{5} + 68921 T^{6} \))(\( 1 - 9 T + 87 T^{2} - 567 T^{3} + 3567 T^{4} - 15129 T^{5} + 68921 T^{6} \))(\( 1 - T + 96 T^{2} + 30 T^{3} + 4932 T^{4} + 1230 T^{5} + 161376 T^{6} - 68921 T^{7} + 2825761 T^{8} \))(\( 1 + 5 T + 44 T^{2} + 298 T^{3} + 3024 T^{4} + 12218 T^{5} + 73964 T^{6} + 344605 T^{7} + 2825761 T^{8} \))(\( 1 - 5 T + 114 T^{2} - 346 T^{3} + 5680 T^{4} - 14186 T^{5} + 191634 T^{6} - 344605 T^{7} + 2825761 T^{8} \))(\( 1 + 6 T + 203 T^{2} + 766 T^{3} + 16684 T^{4} + 41824 T^{5} + 822548 T^{6} + 1714784 T^{7} + 28045804 T^{8} + 52793486 T^{9} + 573629483 T^{10} + 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 2 T + 87 T^{2} + 34 T^{3} + 3864 T^{4} - 1352 T^{5} + 187108 T^{6} - 55432 T^{7} + 6495384 T^{8} + 2343314 T^{9} + 245841207 T^{10} - 231712402 T^{11} + 4750104241 T^{12} \))(\( 1 + 6 T + 170 T^{2} + 842 T^{3} + 14028 T^{4} + 65082 T^{5} + 797634 T^{6} + 3334024 T^{7} + 32702994 T^{8} + 109402842 T^{9} + 966823788 T^{10} + 2379290762 T^{11} + 19695554170 T^{12} + 28500625446 T^{13} + 194754273881 T^{14} \))(\( 1 + 10 T + 230 T^{2} + 2046 T^{3} + 23928 T^{4} + 187794 T^{5} + 1496158 T^{6} + 9899668 T^{7} + 61342478 T^{8} + 315681714 T^{9} + 1649141688 T^{10} + 5781507006 T^{11} + 26646926230 T^{12} + 47501042410 T^{13} + 194754273881 T^{14} \))(\( 1 - 10 T + 230 T^{2} - 2046 T^{3} + 23928 T^{4} - 187794 T^{5} + 1496158 T^{6} - 9899668 T^{7} + 61342478 T^{8} - 315681714 T^{9} + 1649141688 T^{10} - 5781507006 T^{11} + 26646926230 T^{12} - 47501042410 T^{13} + 194754273881 T^{14} \))(\( 1 - 6 T + 170 T^{2} - 842 T^{3} + 14028 T^{4} - 65082 T^{5} + 797634 T^{6} - 3334024 T^{7} + 32702994 T^{8} - 109402842 T^{9} + 966823788 T^{10} - 2379290762 T^{11} + 19695554170 T^{12} - 28500625446 T^{13} + 194754273881 T^{14} \))(\( ( 1 + 41 T^{2} )^{4} \))(\( ( 1 + 41 T^{2} )^{8} \))(\( ( 1 + 41 T^{2} )^{8} \))(\( ( 1 + 87 T^{2} + 5553 T^{4} + 235189 T^{6} + 10743668 T^{8} + 395352709 T^{10} + 15691450833 T^{12} + 413259068967 T^{14} + 7984925229121 T^{16} )^{2} \))
$43$ (\( 1 + 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( ( 1 + 6 T + 43 T^{2} )^{2} \))(\( 1 + 20 T + 242 T^{2} + 1847 T^{3} + 10406 T^{4} + 36980 T^{5} + 79507 T^{6} \))(\( 1 + 2 T + 78 T^{2} + 283 T^{3} + 3354 T^{4} + 3698 T^{5} + 79507 T^{6} \))(\( 1 - 4 T + 24 T^{2} - 11 T^{3} + 1032 T^{4} - 7396 T^{5} + 79507 T^{6} \))(\( 1 + 16 T + 128 T^{2} + 759 T^{3} + 5504 T^{4} + 29584 T^{5} + 79507 T^{6} \))(\( 1 + 6 T + 84 T^{2} + 247 T^{3} + 3612 T^{4} + 11094 T^{5} + 79507 T^{6} \))(\( 1 - 18 T + 227 T^{2} - 2073 T^{3} + 15536 T^{4} - 89139 T^{5} + 419723 T^{6} - 1431126 T^{7} + 3418801 T^{8} \))(\( 1 - 12 T + 213 T^{2} - 1583 T^{3} + 14600 T^{4} - 68069 T^{5} + 393837 T^{6} - 954084 T^{7} + 3418801 T^{8} \))(\( 1 - 6 T + 45 T^{2} - 301 T^{3} + 3908 T^{4} - 12943 T^{5} + 83205 T^{6} - 477042 T^{7} + 3418801 T^{8} \))(\( 1 - 16 T + 209 T^{2} - 1924 T^{3} + 18072 T^{4} - 134610 T^{5} + 980204 T^{6} - 5788230 T^{7} + 33415128 T^{8} - 152971468 T^{9} + 714529409 T^{10} - 2352135088 T^{11} + 6321363049 T^{12} \))(\( 1 - 10 T + 233 T^{2} - 1680 T^{3} + 22528 T^{4} - 126170 T^{5} + 1239688 T^{6} - 5425310 T^{7} + 41654272 T^{8} - 133571760 T^{9} + 796580633 T^{10} - 1470084430 T^{11} + 6321363049 T^{12} \))(\( 1 + 12 T + 285 T^{2} + 2514 T^{3} + 33872 T^{4} + 234458 T^{5} + 2298613 T^{6} + 12777196 T^{7} + 98840359 T^{8} + 433512842 T^{9} + 2693061104 T^{10} + 8594865714 T^{11} + 41897406255 T^{12} + 75856356588 T^{13} + 271818611107 T^{14} \))(\( 1 - 4 T + 133 T^{2} - 130 T^{3} + 8368 T^{4} + 3626 T^{5} + 450501 T^{6} + 200748 T^{7} + 19371543 T^{8} + 6704474 T^{9} + 665314576 T^{10} - 444444130 T^{11} + 19552122919 T^{12} - 25285452196 T^{13} + 271818611107 T^{14} \))(\( 1 - 4 T + 133 T^{2} - 130 T^{3} + 8368 T^{4} + 3626 T^{5} + 450501 T^{6} + 200748 T^{7} + 19371543 T^{8} + 6704474 T^{9} + 665314576 T^{10} - 444444130 T^{11} + 19552122919 T^{12} - 25285452196 T^{13} + 271818611107 T^{14} \))(\( 1 + 12 T + 285 T^{2} + 2514 T^{3} + 33872 T^{4} + 234458 T^{5} + 2298613 T^{6} + 12777196 T^{7} + 98840359 T^{8} + 433512842 T^{9} + 2693061104 T^{10} + 8594865714 T^{11} + 41897406255 T^{12} + 75856356588 T^{13} + 271818611107 T^{14} \))(\( ( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} )( 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} ) \))(\( ( 1 - 43 T^{2} )^{8} \))(\( ( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} )^{2}( 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 91 T^{2} + 3663 T^{4} - 229353 T^{6} + 13812624 T^{8} - 424073697 T^{10} + 12523068063 T^{12} - 575244037459 T^{14} + 11688200277601 T^{16} )^{2} \))
$47$ (\( 1 - 2 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 4 T + 26 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 - 16 T + 214 T^{2} - 1603 T^{3} + 10058 T^{4} - 35344 T^{5} + 103823 T^{6} \))(\( 1 - 8 T + 108 T^{2} - 473 T^{3} + 5076 T^{4} - 17672 T^{5} + 103823 T^{6} \))(\( 1 + 12 T + 132 T^{2} + 1043 T^{3} + 6204 T^{4} + 26508 T^{5} + 103823 T^{6} \))(\( 1 + 2 T + 70 T^{2} + 285 T^{3} + 3290 T^{4} + 4418 T^{5} + 103823 T^{6} \))(\( 1 - 6 T + 132 T^{2} - 513 T^{3} + 6204 T^{4} - 13254 T^{5} + 103823 T^{6} \))(\( 1 + 14 T + 153 T^{2} + 1257 T^{3} + 9462 T^{4} + 59079 T^{5} + 337977 T^{6} + 1453522 T^{7} + 4879681 T^{8} \))(\( 1 - 4 T + 59 T^{2} - 335 T^{3} + 1974 T^{4} - 15745 T^{5} + 130331 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( 1 + 16 T + 233 T^{2} + 2075 T^{3} + 17250 T^{4} + 97525 T^{5} + 514697 T^{6} + 1661168 T^{7} + 4879681 T^{8} \))(\( 1 + 158 T^{2} - 176 T^{3} + 13039 T^{4} - 13104 T^{5} + 746020 T^{6} - 615888 T^{7} + 28803151 T^{8} - 18272848 T^{9} + 770989598 T^{10} + 10779215329 T^{12} \))(\( 1 + 16 T + 186 T^{2} + 1264 T^{3} + 11055 T^{4} + 88096 T^{5} + 753964 T^{6} + 4140512 T^{7} + 24420495 T^{8} + 131232272 T^{9} + 907620666 T^{10} + 3669520112 T^{11} + 10779215329 T^{12} \))(\( 1 - 22 T + 365 T^{2} - 4366 T^{3} + 47884 T^{4} - 434326 T^{5} + 3592387 T^{6} - 25483614 T^{7} + 168842189 T^{8} - 959426134 T^{9} + 4971460532 T^{10} - 21304687246 T^{11} + 83710927555 T^{12} - 237142737238 T^{13} + 506623120463 T^{14} \))(\( 1 + 12 T + 257 T^{2} + 2286 T^{3} + 29328 T^{4} + 214362 T^{5} + 2088847 T^{6} + 12592020 T^{7} + 98175809 T^{8} + 473525658 T^{9} + 3044920944 T^{10} + 11154950766 T^{11} + 58941666799 T^{12} + 129350583948 T^{13} + 506623120463 T^{14} \))(\( 1 - 12 T + 257 T^{2} - 2286 T^{3} + 29328 T^{4} - 214362 T^{5} + 2088847 T^{6} - 12592020 T^{7} + 98175809 T^{8} - 473525658 T^{9} + 3044920944 T^{10} - 11154950766 T^{11} + 58941666799 T^{12} - 129350583948 T^{13} + 506623120463 T^{14} \))(\( 1 + 22 T + 365 T^{2} + 4366 T^{3} + 47884 T^{4} + 434326 T^{5} + 3592387 T^{6} + 25483614 T^{7} + 168842189 T^{8} + 959426134 T^{9} + 4971460532 T^{10} + 21304687246 T^{11} + 83710927555 T^{12} + 237142737238 T^{13} + 506623120463 T^{14} \))(\( ( 1 - 13 T + 122 T^{2} - 611 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 47 T^{2} )^{8} \))(\( ( 1 - 75 T^{2} + 3416 T^{4} - 165675 T^{6} + 4879681 T^{8} )^{2} \))(\( ( 1 + 130 T^{2} - 160 T^{3} + 7730 T^{4} - 7520 T^{5} + 287170 T^{6} + 4879681 T^{8} )^{4} \))
$53$ (\( 1 + 9 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 8 T + 114 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 + 2 T + 96 T^{2} + 65 T^{3} + 5088 T^{4} + 5618 T^{5} + 148877 T^{6} \))(\( 1 - 2 T + 154 T^{2} - 209 T^{3} + 8162 T^{4} - 5618 T^{5} + 148877 T^{6} \))(\( 1 + 6 T + 58 T^{2} - 39 T^{3} + 3074 T^{4} + 16854 T^{5} + 148877 T^{6} \))(\( 1 + 12 T^{2} + 637 T^{3} + 636 T^{4} + 148877 T^{6} \))(\( 1 - 12 T + 186 T^{2} - 1289 T^{3} + 9858 T^{4} - 33708 T^{5} + 148877 T^{6} \))(\( 1 + T + 127 T^{2} + 333 T^{3} + 7805 T^{4} + 17649 T^{5} + 356743 T^{6} + 148877 T^{7} + 7890481 T^{8} \))(\( 1 - 3 T + 143 T^{2} - 217 T^{3} + 9565 T^{4} - 11501 T^{5} + 401687 T^{6} - 446631 T^{7} + 7890481 T^{8} \))(\( 1 - 19 T + 265 T^{2} - 2541 T^{3} + 20475 T^{4} - 134673 T^{5} + 744385 T^{6} - 2828663 T^{7} + 7890481 T^{8} \))(\( 1 + 20 T + 370 T^{2} + 4436 T^{3} + 49815 T^{4} + 434728 T^{5} + 3532444 T^{6} + 23040584 T^{7} + 139930335 T^{8} + 660418372 T^{9} + 2919477970 T^{10} + 8363909860 T^{11} + 22164361129 T^{12} \))(\( 1 + 12 T + 222 T^{2} + 1884 T^{3} + 22695 T^{4} + 150600 T^{5} + 1425124 T^{6} + 7981800 T^{7} + 63750255 T^{8} + 280484268 T^{9} + 1751686782 T^{10} + 5018345916 T^{11} + 22164361129 T^{12} \))(\( 1 + 13 T + 131 T^{2} + 584 T^{3} + 3656 T^{4} + 15150 T^{5} + 357099 T^{6} + 2594831 T^{7} + 18926247 T^{8} + 42556350 T^{9} + 544294312 T^{10} + 4608040904 T^{11} + 54783609583 T^{12} + 288136694677 T^{13} + 1174711139837 T^{14} \))(\( 1 + 8 T + 327 T^{2} + 1974 T^{3} + 45790 T^{4} + 215610 T^{5} + 3731207 T^{6} + 14147156 T^{7} + 197753971 T^{8} + 605648490 T^{9} + 6817077830 T^{10} + 15575809494 T^{11} + 136749926211 T^{12} + 177314889032 T^{13} + 1174711139837 T^{14} \))(\( 1 - 8 T + 327 T^{2} - 1974 T^{3} + 45790 T^{4} - 215610 T^{5} + 3731207 T^{6} - 14147156 T^{7} + 197753971 T^{8} - 605648490 T^{9} + 6817077830 T^{10} - 15575809494 T^{11} + 136749926211 T^{12} - 177314889032 T^{13} + 1174711139837 T^{14} \))(\( 1 - 13 T + 131 T^{2} - 584 T^{3} + 3656 T^{4} - 15150 T^{5} + 357099 T^{6} - 2594831 T^{7} + 18926247 T^{8} - 42556350 T^{9} + 544294312 T^{10} - 4608040904 T^{11} + 54783609583 T^{12} - 288136694677 T^{13} + 1174711139837 T^{14} \))(\( ( 1 - 53 T^{2} )^{4} \))(\( ( 1 - 103 T^{2} + 7800 T^{4} - 289327 T^{6} + 7890481 T^{8} )^{2} \))(\( ( 1 - 53 T^{2} )^{8} \))(\( ( 1 - 200 T^{2} + 24072 T^{4} - 1954968 T^{6} + 119756942 T^{8} - 5491505112 T^{10} + 189939658632 T^{12} - 4432872225800 T^{14} + 62259690411361 T^{16} )^{2} \))
$59$ (\( 1 - 3 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 6 T + 109 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 171 T^{2} + 981 T^{3} + 10089 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 51 T^{2} + 51 T^{3} + 3009 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 + 3 T + 163 T^{2} + 337 T^{3} + 9617 T^{4} + 10443 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 33 T^{2} + 429 T^{3} + 1947 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 - 15 T + 213 T^{2} - 1681 T^{3} + 12567 T^{4} - 52215 T^{5} + 205379 T^{6} \))(\( 1 + 18 T + 255 T^{2} + 2769 T^{3} + 22375 T^{4} + 163371 T^{5} + 887655 T^{6} + 3696822 T^{7} + 12117361 T^{8} \))(\( 1 + 8 T + 55 T^{2} - 109 T^{3} - 877 T^{4} - 6431 T^{5} + 191455 T^{6} + 1643032 T^{7} + 12117361 T^{8} \))(\( 1 + 4 T + 187 T^{2} + 457 T^{3} + 14957 T^{4} + 26963 T^{5} + 650947 T^{6} + 821516 T^{7} + 12117361 T^{8} \))(\( 1 + 15 T + 248 T^{2} + 3029 T^{3} + 31879 T^{4} + 292034 T^{5} + 2417840 T^{6} + 17230006 T^{7} + 110970799 T^{8} + 622092991 T^{9} + 3005105528 T^{10} + 10723864485 T^{11} + 42180533641 T^{12} \))(\( 1 - 14 T + 273 T^{2} - 2918 T^{3} + 33999 T^{4} - 296864 T^{5} + 2553550 T^{6} - 17514976 T^{7} + 118350519 T^{8} - 599295922 T^{9} + 3308039553 T^{10} - 10008940186 T^{11} + 42180533641 T^{12} \))(\( 1 + 23 T + 464 T^{2} + 6581 T^{3} + 83440 T^{4} + 863177 T^{5} + 8146894 T^{6} + 65432379 T^{7} + 480666746 T^{8} + 3004719137 T^{9} + 17136823760 T^{10} + 79744352741 T^{11} + 331724874736 T^{12} + 970152273743 T^{13} + 2488651484819 T^{14} \))(\( 1 + 10 T + 146 T^{2} + 1830 T^{3} + 21948 T^{4} + 166110 T^{5} + 1682932 T^{6} + 13502860 T^{7} + 99292988 T^{8} + 578228910 T^{9} + 4507658292 T^{10} + 22174770630 T^{11} + 104378947654 T^{12} + 421805336410 T^{13} + 2488651484819 T^{14} \))(\( 1 - 10 T + 146 T^{2} - 1830 T^{3} + 21948 T^{4} - 166110 T^{5} + 1682932 T^{6} - 13502860 T^{7} + 99292988 T^{8} - 578228910 T^{9} + 4507658292 T^{10} - 22174770630 T^{11} + 104378947654 T^{12} - 421805336410 T^{13} + 2488651484819 T^{14} \))(\( 1 - 23 T + 464 T^{2} - 6581 T^{3} + 83440 T^{4} - 863177 T^{5} + 8146894 T^{6} - 65432379 T^{7} + 480666746 T^{8} - 3004719137 T^{9} + 17136823760 T^{10} - 79744352741 T^{11} + 331724874736 T^{12} - 970152273743 T^{13} + 2488651484819 T^{14} \))(\( ( 1 - 59 T^{2} )^{4} \))(\( ( 1 - 91 T^{2} + 4800 T^{4} - 316771 T^{6} + 12117361 T^{8} )^{2} \))(\( ( 1 - 59 T^{2} )^{8} \))(\( ( 1 - 170 T^{2} + 16291 T^{4} - 1174630 T^{6} + 72800408 T^{8} - 4088887030 T^{10} + 197403928051 T^{12} - 7170690718970 T^{14} + 146830437604321 T^{16} )^{2} \))
$61$ (\( 1 - 10 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 4 T + 124 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + T + 25 T^{2} - 565 T^{3} + 1525 T^{4} + 3721 T^{5} + 226981 T^{6} \))(\( 1 + 7 T + 119 T^{2} + 631 T^{3} + 7259 T^{4} + 26047 T^{5} + 226981 T^{6} \))(\( 1 + 7 T + 163 T^{2} + 713 T^{3} + 9943 T^{4} + 26047 T^{5} + 226981 T^{6} \))(\( 1 - 11 T + 207 T^{2} - 1313 T^{3} + 12627 T^{4} - 40931 T^{5} + 226981 T^{6} \))(\( 1 + 3 T + 57 T^{2} + 167 T^{3} + 3477 T^{4} + 11163 T^{5} + 226981 T^{6} \))(\( 1 + 3 T + 72 T^{2} + 728 T^{3} + 4284 T^{4} + 44408 T^{5} + 267912 T^{6} + 680943 T^{7} + 13845841 T^{8} \))(\( 1 - 3 T + 204 T^{2} - 406 T^{3} + 17392 T^{4} - 24766 T^{5} + 759084 T^{6} - 680943 T^{7} + 13845841 T^{8} \))(\( 1 - 5 T + 158 T^{2} - 824 T^{3} + 12496 T^{4} - 50264 T^{5} + 587918 T^{6} - 1134905 T^{7} + 13845841 T^{8} \))(\( 1 - 24 T + 426 T^{2} - 5624 T^{3} + 63015 T^{4} - 601104 T^{5} + 4996652 T^{6} - 36667344 T^{7} + 234478815 T^{8} - 1276541144 T^{9} + 5898328266 T^{10} - 20270311224 T^{11} + 51520374361 T^{12} \))(\( 1 - 12 T + 152 T^{2} - 1172 T^{3} + 14159 T^{4} - 116176 T^{5} + 1159904 T^{6} - 7086736 T^{7} + 52685639 T^{8} - 266021732 T^{9} + 2104567832 T^{10} - 10135155612 T^{11} + 51520374361 T^{12} \))(\( 1 + 4 T + 234 T^{2} + 748 T^{3} + 18734 T^{4} + 48912 T^{5} + 664012 T^{6} + 2216538 T^{7} + 40504732 T^{8} + 182001552 T^{9} + 4252262054 T^{10} + 10356689068 T^{11} + 197635534434 T^{12} + 206081497444 T^{13} + 3142742836021 T^{14} \))(\( 1 + 16 T + 394 T^{2} + 4612 T^{3} + 64990 T^{4} + 601888 T^{5} + 6179612 T^{6} + 46318466 T^{7} + 376956332 T^{8} + 2239625248 T^{9} + 14751495190 T^{10} + 63857018692 T^{11} + 332770942594 T^{12} + 824325989776 T^{13} + 3142742836021 T^{14} \))(\( 1 + 16 T + 394 T^{2} + 4612 T^{3} + 64990 T^{4} + 601888 T^{5} + 6179612 T^{6} + 46318466 T^{7} + 376956332 T^{8} + 2239625248 T^{9} + 14751495190 T^{10} + 63857018692 T^{11} + 332770942594 T^{12} + 824325989776 T^{13} + 3142742836021 T^{14} \))(\( 1 + 4 T + 234 T^{2} + 748 T^{3} + 18734 T^{4} + 48912 T^{5} + 664012 T^{6} + 2216538 T^{7} + 40504732 T^{8} + 182001552 T^{9} + 4252262054 T^{10} + 10356689068 T^{11} + 197635534434 T^{12} + 206081497444 T^{13} + 3142742836021 T^{14} \))(\( ( 1 - 15 T + 164 T^{2} - 915 T^{3} + 3721 T^{4} )( 1 + 15 T + 164 T^{2} + 915 T^{3} + 3721 T^{4} ) \))(\( ( 1 - 61 T^{2} )^{8} \))(\( ( 1 - 15 T + 164 T^{2} - 915 T^{3} + 3721 T^{4} )^{2}( 1 + 15 T + 164 T^{2} + 915 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 284 T^{2} + 34578 T^{4} - 2519772 T^{6} + 151403786 T^{8} - 9376071612 T^{10} + 478761490098 T^{12} - 14631786318524 T^{14} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 - 4 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 6 T - 19 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 17 T + 241 T^{2} + 2299 T^{3} + 16147 T^{4} + 76313 T^{5} + 300763 T^{6} \))(\( 1 + 15 T + 261 T^{2} + 2047 T^{3} + 17487 T^{4} + 67335 T^{5} + 300763 T^{6} \))(\( 1 - 11 T + 193 T^{2} - 1447 T^{3} + 12931 T^{4} - 49379 T^{5} + 300763 T^{6} \))(\( 1 + 13 T + 227 T^{2} + 1743 T^{3} + 15209 T^{4} + 58357 T^{5} + 300763 T^{6} \))(\( 1 + 3 T + 183 T^{2} + 399 T^{3} + 12261 T^{4} + 13467 T^{5} + 300763 T^{6} \))(\( 1 + 17 T + 314 T^{2} + 3084 T^{3} + 31864 T^{4} + 206628 T^{5} + 1409546 T^{6} + 5112971 T^{7} + 20151121 T^{8} \))(\( 1 - 21 T + 232 T^{2} - 1386 T^{3} + 8340 T^{4} - 92862 T^{5} + 1041448 T^{6} - 6316023 T^{7} + 20151121 T^{8} \))(\( 1 + T + 240 T^{2} + 192 T^{3} + 23184 T^{4} + 12864 T^{5} + 1077360 T^{6} + 300763 T^{7} + 20151121 T^{8} \))(\( 1 - 25 T + 479 T^{2} - 5946 T^{3} + 65282 T^{4} - 570676 T^{5} + 4992830 T^{6} - 38235292 T^{7} + 293050898 T^{8} - 1788336798 T^{9} + 9652386959 T^{10} - 33753127675 T^{11} + 90458382169 T^{12} \))(\( 1 + 12 T + 218 T^{2} + 1720 T^{3} + 23423 T^{4} + 187358 T^{5} + 2036891 T^{6} + 12552986 T^{7} + 105145847 T^{8} + 517312360 T^{9} + 4392944378 T^{10} + 16201501284 T^{11} + 90458382169 T^{12} \))(\( 1 + 14 T + 432 T^{2} + 4238 T^{3} + 74860 T^{4} + 560618 T^{5} + 7464700 T^{6} + 45513772 T^{7} + 500134900 T^{8} + 2516614202 T^{9} + 22515118180 T^{10} + 85400450798 T^{11} + 583254046224 T^{12} + 1266417350366 T^{13} + 6060711605323 T^{14} \))(\( 1 - 2 T + 112 T^{2} + 754 T^{3} + 6748 T^{4} + 80878 T^{5} + 775832 T^{6} + 4708100 T^{7} + 51980744 T^{8} + 363061342 T^{9} + 2029548724 T^{10} + 15193945234 T^{11} + 151214011984 T^{12} - 180916764338 T^{13} + 6060711605323 T^{14} \))(\( 1 - 2 T + 112 T^{2} + 754 T^{3} + 6748 T^{4} + 80878 T^{5} + 775832 T^{6} + 4708100 T^{7} + 51980744 T^{8} + 363061342 T^{9} + 2029548724 T^{10} + 15193945234 T^{11} + 151214011984 T^{12} - 180916764338 T^{13} + 6060711605323 T^{14} \))(\( 1 + 14 T + 432 T^{2} + 4238 T^{3} + 74860 T^{4} + 560618 T^{5} + 7464700 T^{6} + 45513772 T^{7} + 500134900 T^{8} + 2516614202 T^{9} + 22515118180 T^{10} + 85400450798 T^{11} + 583254046224 T^{12} + 1266417350366 T^{13} + 6060711605323 T^{14} \))(\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 - 67 T^{2} )^{8} \))(\( ( 1 - 67 T^{2} )^{8} \))(\( ( 1 - 271 T^{2} + 44118 T^{4} - 4721574 T^{6} + 371643813 T^{8} - 21195145686 T^{10} + 889027156278 T^{12} - 24514221567799 T^{14} + 406067677556641 T^{16} )^{2} \))
$71$ (\( 1 + 3 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 5 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 - 6 T + 133 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 - 18 T + 210 T^{2} - 1753 T^{3} + 14910 T^{4} - 90738 T^{5} + 357911 T^{6} \))(\( 1 + 12 T + 246 T^{2} + 1721 T^{3} + 17466 T^{4} + 60492 T^{5} + 357911 T^{6} \))(\( 1 + 8 T + 134 T^{2} + 1091 T^{3} + 9514 T^{4} + 40328 T^{5} + 357911 T^{6} \))(\( 1 + 12 T + 128 T^{2} + 1327 T^{3} + 9088 T^{4} + 60492 T^{5} + 357911 T^{6} \))(\( 1 - 6 T - 12 T^{2} + 117 T^{3} - 852 T^{4} - 30246 T^{5} + 357911 T^{6} \))(\( 1 - 5 T + 231 T^{2} - 807 T^{3} + 22521 T^{4} - 57297 T^{5} + 1164471 T^{6} - 1789555 T^{7} + 25411681 T^{8} \))(\( 1 + 9 T + 249 T^{2} + 1741 T^{3} + 25317 T^{4} + 123611 T^{5} + 1255209 T^{6} + 3221199 T^{7} + 25411681 T^{8} \))(\( 1 + 19 T + 391 T^{2} + 4201 T^{3} + 45287 T^{4} + 298271 T^{5} + 1971031 T^{6} + 6800309 T^{7} + 25411681 T^{8} \))(\( 1 - 9 T + 269 T^{2} - 1862 T^{3} + 35908 T^{4} - 199430 T^{5} + 3020546 T^{6} - 14159530 T^{7} + 181012228 T^{8} - 666430282 T^{9} + 6835742189 T^{10} - 16238064159 T^{11} + 128100283921 T^{12} \))(\( 1 - 30 T + 678 T^{2} - 10974 T^{3} + 145239 T^{4} - 1578396 T^{5} + 14506351 T^{6} - 112066116 T^{7} + 732149799 T^{8} - 3927715314 T^{9} + 17229119718 T^{10} - 54126880530 T^{11} + 128100283921 T^{12} \))(\( 1 - 5 T + 317 T^{2} - 1460 T^{3} + 52474 T^{4} - 214412 T^{5} + 5493301 T^{6} - 19027587 T^{7} + 390024371 T^{8} - 1080850892 T^{9} + 18781021814 T^{10} - 37101054260 T^{11} + 571940704267 T^{12} - 640501419605 T^{13} + 9095120158391 T^{14} \))(\( 1 + 8 T + 189 T^{2} + 1146 T^{3} + 13756 T^{4} + 96270 T^{5} + 804257 T^{6} + 7631048 T^{7} + 57102247 T^{8} + 485297070 T^{9} + 4923423716 T^{10} + 29121786426 T^{11} + 340999347339 T^{12} + 1024802271368 T^{13} + 9095120158391 T^{14} \))(\( 1 - 8 T + 189 T^{2} - 1146 T^{3} + 13756 T^{4} - 96270 T^{5} + 804257 T^{6} - 7631048 T^{7} + 57102247 T^{8} - 485297070 T^{9} + 4923423716 T^{10} - 29121786426 T^{11} + 340999347339 T^{12} - 1024802271368 T^{13} + 9095120158391 T^{14} \))(\( 1 + 5 T + 317 T^{2} + 1460 T^{3} + 52474 T^{4} + 214412 T^{5} + 5493301 T^{6} + 19027587 T^{7} + 390024371 T^{8} + 1080850892 T^{9} + 18781021814 T^{10} + 37101054260 T^{11} + 571940704267 T^{12} + 640501419605 T^{13} + 9095120158391 T^{14} \))(\( ( 1 - 71 T^{2} )^{4} \))(\( ( 1 - 67 T^{2} - 552 T^{4} - 337747 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 - 71 T^{2} )^{8} \))(\( ( 1 - 297 T^{2} + 43322 T^{4} - 4385978 T^{6} + 347841481 T^{8} - 22109715098 T^{10} + 1100884844282 T^{12} - 38045784324537 T^{14} + 645753531245761 T^{16} )^{2} \))
$73$ (\( 1 - 4 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 16 T + 138 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 1115 T^{3} + 5110 T^{4} - 21316 T^{5} + 389017 T^{6} \))(\( 1 + 18 T + 312 T^{2} + 2741 T^{3} + 22776 T^{4} + 95922 T^{5} + 389017 T^{6} \))(\( 1 + 14 T + 278 T^{2} + 2119 T^{3} + 20294 T^{4} + 74606 T^{5} + 389017 T^{6} \))(\( 1 + 18 T + 194 T^{2} + 1745 T^{3} + 14162 T^{4} + 95922 T^{5} + 389017 T^{6} \))(\( 1 - 12 T + 264 T^{2} - 1803 T^{3} + 19272 T^{4} - 63948 T^{5} + 389017 T^{6} \))(\( 1 - 12 T + 189 T^{2} - 1789 T^{3} + 19692 T^{4} - 130597 T^{5} + 1007181 T^{6} - 4668204 T^{7} + 28398241 T^{8} \))(\( 1 - 12 T + 75 T^{2} + 443 T^{3} - 6476 T^{4} + 32339 T^{5} + 399675 T^{6} - 4668204 T^{7} + 28398241 T^{8} \))(\( 1 - 18 T + 309 T^{2} - 3167 T^{3} + 33172 T^{4} - 231191 T^{5} + 1646661 T^{6} - 7002306 T^{7} + 28398241 T^{8} \))(\( 1 + 26 T + 458 T^{2} + 6474 T^{3} + 75263 T^{4} + 760652 T^{5} + 6945740 T^{6} + 55527596 T^{7} + 401076527 T^{8} + 2518496058 T^{9} + 13006394378 T^{10} + 53899861418 T^{11} + 151334226289 T^{12} \))(\( 1 - 24 T + 386 T^{2} - 3464 T^{3} + 15071 T^{4} + 58784 T^{5} - 1353316 T^{6} + 4291232 T^{7} + 80313359 T^{8} - 1347554888 T^{9} + 10961721026 T^{10} - 49753718232 T^{11} + 151334226289 T^{12} \))(\( 1 + 357 T^{2} + 654 T^{3} + 57062 T^{4} + 182450 T^{5} + 5712649 T^{6} + 19674160 T^{7} + 417023377 T^{8} + 972276050 T^{9} + 22198088054 T^{10} + 18572449614 T^{11} + 740086558701 T^{12} + 11047398519097 T^{14} \))(\( 1 - 2 T + 157 T^{2} - 866 T^{3} + 14842 T^{4} - 124682 T^{5} + 1358129 T^{6} - 11185354 T^{7} + 99143417 T^{8} - 664430378 T^{9} + 5773790314 T^{10} - 24592876706 T^{11} + 325472240101 T^{12} - 302668452578 T^{13} + 11047398519097 T^{14} \))(\( 1 - 2 T + 157 T^{2} - 866 T^{3} + 14842 T^{4} - 124682 T^{5} + 1358129 T^{6} - 11185354 T^{7} + 99143417 T^{8} - 664430378 T^{9} + 5773790314 T^{10} - 24592876706 T^{11} + 325472240101 T^{12} - 302668452578 T^{13} + 11047398519097 T^{14} \))(\( 1 + 357 T^{2} + 654 T^{3} + 57062 T^{4} + 182450 T^{5} + 5712649 T^{6} + 19674160 T^{7} + 417023377 T^{8} + 972276050 T^{9} + 22198088054 T^{10} + 18572449614 T^{11} + 740086558701 T^{12} + 11047398519097 T^{14} \))(\( ( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} )( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} ) \))(\( ( 1 - 73 T^{2} )^{8} \))(\( ( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} )^{2}( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 84 T^{2} + 15956 T^{4} - 1023404 T^{6} + 121082902 T^{8} - 5453719916 T^{10} + 453122333396 T^{12} - 12712075008276 T^{14} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 - 15 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 15 T + 79 T^{2} \))(\( 1 - 4 T - 316 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 104 T^{2} + 137 T^{3} + 8216 T^{4} + 49928 T^{5} + 493039 T^{6} \))(\( 1 - 4 T + 124 T^{2} - 935 T^{3} + 9796 T^{4} - 24964 T^{5} + 493039 T^{6} \))(\( 1 - 4 T + 146 T^{2} - 143 T^{3} + 11534 T^{4} - 24964 T^{5} + 493039 T^{6} \))(\( 1 + 10 T + 226 T^{2} + 1357 T^{3} + 17854 T^{4} + 62410 T^{5} + 493039 T^{6} \))(\( 1 - 6 T + 210 T^{2} - 859 T^{3} + 16590 T^{4} - 37446 T^{5} + 493039 T^{6} \))(\( 1 + 11 T + 249 T^{2} + 1731 T^{3} + 25399 T^{4} + 136749 T^{5} + 1554009 T^{6} + 5423429 T^{7} + 38950081 T^{8} \))(\( 1 - 29 T + 609 T^{2} - 8121 T^{3} + 85649 T^{4} - 641559 T^{5} + 3800769 T^{6} - 14298131 T^{7} + 38950081 T^{8} \))(\( 1 - 27 T + 561 T^{2} - 7241 T^{3} + 76907 T^{4} - 572039 T^{5} + 3501201 T^{6} - 13312053 T^{7} + 38950081 T^{8} \))(\( 1 + 16 T + 454 T^{2} + 5264 T^{3} + 82511 T^{4} + 740480 T^{5} + 8351892 T^{6} + 58497920 T^{7} + 514951151 T^{8} + 2595357296 T^{9} + 17683336774 T^{10} + 49232902384 T^{11} + 243087455521 T^{12} \))(\( 1 + 104 T^{2} - 1184 T^{3} + 8831 T^{4} - 48736 T^{5} + 1512080 T^{6} - 3850144 T^{7} + 55114271 T^{8} - 583758176 T^{9} + 4050808424 T^{10} + 243087455521 T^{12} \))(\( 1 - 13 T + 363 T^{2} - 3926 T^{3} + 64496 T^{4} - 585768 T^{5} + 7455475 T^{6} - 56303069 T^{7} + 588982525 T^{8} - 3655778088 T^{9} + 31799043344 T^{10} - 152918018006 T^{11} + 1116971472837 T^{12} - 3160136921773 T^{13} + 19203908986159 T^{14} \))(\( 1 + 8 T + 499 T^{2} + 3530 T^{3} + 110758 T^{4} + 667490 T^{5} + 14126271 T^{6} + 69288240 T^{7} + 1115975409 T^{8} + 4165805090 T^{9} + 54608013562 T^{10} + 137493785930 T^{11} + 1535451143101 T^{12} + 1944699644168 T^{13} + 19203908986159 T^{14} \))(\( 1 + 8 T + 499 T^{2} + 3530 T^{3} + 110758 T^{4} + 667490 T^{5} + 14126271 T^{6} + 69288240 T^{7} + 1115975409 T^{8} + 4165805090 T^{9} + 54608013562 T^{10} + 137493785930 T^{11} + 1535451143101 T^{12} + 1944699644168 T^{13} + 19203908986159 T^{14} \))(\( 1 - 13 T + 363 T^{2} - 3926 T^{3} + 64496 T^{4} - 585768 T^{5} + 7455475 T^{6} - 56303069 T^{7} + 588982525 T^{8} - 3655778088 T^{9} + 31799043344 T^{10} - 152918018006 T^{11} + 1116971472837 T^{12} - 3160136921773 T^{13} + 19203908986159 T^{14} \))(\( ( 1 + 79 T^{2} )^{4} \))(\( ( 1 - 139 T^{2} + 13080 T^{4} - 867499 T^{6} + 38950081 T^{8} )^{2} \))(\( ( 1 + 79 T^{2} )^{8} \))(\( ( 1 + 404 T^{2} + 79470 T^{4} + 10151916 T^{6} + 932638722 T^{8} + 63358107756 T^{10} + 3095362937070 T^{12} + 98207332030484 T^{14} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( 1 + 9 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 76 T^{2} + 6889 T^{4} \))(\( 1 - 23 T + 419 T^{2} - 4215 T^{3} + 34777 T^{4} - 158447 T^{5} + 571787 T^{6} \))(\( 1 - 9 T + 201 T^{2} - 1377 T^{3} + 16683 T^{4} - 62001 T^{5} + 571787 T^{6} \))(\( 1 + 7 T + 229 T^{2} + 1021 T^{3} + 19007 T^{4} + 48223 T^{5} + 571787 T^{6} \))(\( 1 - 27 T + 471 T^{2} - 5015 T^{3} + 39093 T^{4} - 186003 T^{5} + 571787 T^{6} \))(\( 1 - 9 T + 129 T^{2} - 397 T^{3} + 10707 T^{4} - 62001 T^{5} + 571787 T^{6} \))(\( 1 + 6 T + 279 T^{2} + 1293 T^{3} + 33085 T^{4} + 107319 T^{5} + 1922031 T^{6} + 3430722 T^{7} + 47458321 T^{8} \))(\( 1 + 12 T + 207 T^{2} + 1891 T^{3} + 24435 T^{4} + 156953 T^{5} + 1426023 T^{6} + 6861444 T^{7} + 47458321 T^{8} \))(\( 1 + 161 T^{2} + 59 T^{3} + 13255 T^{4} + 4897 T^{5} + 1109129 T^{6} + 47458321 T^{8} \))(\( 1 - 2 T + 421 T^{2} - 744 T^{3} + 79316 T^{4} - 117434 T^{5} + 8501524 T^{6} - 9747022 T^{7} + 546407924 T^{8} - 425409528 T^{9} + 19979953141 T^{10} - 7878081286 T^{11} + 326940373369 T^{12} \))(\( 1 - 14 T + 363 T^{2} - 4364 T^{3} + 66390 T^{4} - 642158 T^{5} + 6985258 T^{6} - 53299114 T^{7} + 457360710 T^{8} - 2495278468 T^{9} + 17227370523 T^{10} - 55146569002 T^{11} + 326940373369 T^{12} \))(\( 1 + T + 370 T^{2} + 453 T^{3} + 70050 T^{4} + 86423 T^{5} + 8517744 T^{6} + 9005211 T^{7} + 706972752 T^{8} + 595368047 T^{9} + 40053679350 T^{10} + 21498619413 T^{11} + 1457445037910 T^{12} + 326940373369 T^{13} + 27136050989627 T^{14} \))(\( 1 + 6 T + 248 T^{2} + 2674 T^{3} + 36330 T^{4} + 426182 T^{5} + 4406386 T^{6} + 41154240 T^{7} + 365730038 T^{8} + 2935967798 T^{9} + 20773021710 T^{10} + 126903550354 T^{11} + 976882079464 T^{12} + 1961642240214 T^{13} + 27136050989627 T^{14} \))(\( 1 - 6 T + 248 T^{2} - 2674 T^{3} + 36330 T^{4} - 426182 T^{5} + 4406386 T^{6} - 41154240 T^{7} + 365730038 T^{8} - 2935967798 T^{9} + 20773021710 T^{10} - 126903550354 T^{11} + 976882079464 T^{12} - 1961642240214 T^{13} + 27136050989627 T^{14} \))(\( 1 - T + 370 T^{2} - 453 T^{3} + 70050 T^{4} - 86423 T^{5} + 8517744 T^{6} - 9005211 T^{7} + 706972752 T^{8} - 595368047 T^{9} + 40053679350 T^{10} - 21498619413 T^{11} + 1457445037910 T^{12} - 326940373369 T^{13} + 27136050989627 T^{14} \))(\( ( 1 - 16 T + 83 T^{2} )^{2}( 1 + 16 T + 83 T^{2} )^{2} \))(\( ( 1 - 109 T^{2} + 4992 T^{4} - 750901 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 + 90 T^{2} + 6889 T^{4} )^{4} \))(\( ( 1 - 279 T^{2} + 48153 T^{4} - 5919251 T^{6} + 567786878 T^{8} - 40777720139 T^{10} + 2285260531113 T^{12} - 91216364169951 T^{14} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( 1 - T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 + 2 T + 177 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 + 2 T + 56 T^{2} + 75 T^{3} + 4984 T^{4} + 15842 T^{5} + 704969 T^{6} \))(\( 1 - 4 T + 134 T^{2} - 87 T^{3} + 11926 T^{4} - 31684 T^{5} + 704969 T^{6} \))(\( 1 + 4 T + 26 T^{2} - 1097 T^{3} + 2314 T^{4} + 31684 T^{5} + 704969 T^{6} \))(\( 1 - 2 T + 210 T^{2} - 285 T^{3} + 18690 T^{4} - 15842 T^{5} + 704969 T^{6} \))(\( 1 - 24 T + 384 T^{2} - 4059 T^{3} + 34176 T^{4} - 190104 T^{5} + 704969 T^{6} \))(\( 1 - T + 303 T^{2} - 93 T^{3} + 38029 T^{4} - 8277 T^{5} + 2400063 T^{6} - 704969 T^{7} + 62742241 T^{8} \))(\( 1 + 7 T + 205 T^{2} + 1419 T^{3} + 21193 T^{4} + 126291 T^{5} + 1623805 T^{6} + 4934783 T^{7} + 62742241 T^{8} \))(\( 1 + 9 T + 41 T^{2} + 185 T^{3} + 6835 T^{4} + 16465 T^{5} + 324761 T^{6} + 6344721 T^{7} + 62742241 T^{8} \))(\( 1 + 7 T + 308 T^{2} + 1931 T^{3} + 43111 T^{4} + 259078 T^{5} + 4205512 T^{6} + 23057942 T^{7} + 341482231 T^{8} + 1361295139 T^{9} + 19324610228 T^{10} + 39088416143 T^{11} + 496981290961 T^{12} \))(\( 1 - 14 T + 361 T^{2} - 4970 T^{3} + 71459 T^{4} - 741128 T^{5} + 8430454 T^{6} - 65960392 T^{7} + 566026739 T^{8} - 3503695930 T^{9} + 22649949001 T^{10} - 78176832286 T^{11} + 496981290961 T^{12} \))(\( 1 + 11 T + 541 T^{2} + 5090 T^{3} + 131896 T^{4} + 1039032 T^{5} + 18729117 T^{6} + 119811073 T^{7} + 1666891413 T^{8} + 8230172472 T^{9} + 92982591224 T^{10} + 319358006690 T^{11} + 3020976161909 T^{12} + 5466794200571 T^{13} + 44231334895529 T^{14} \))(\( 1 + 24 T + 665 T^{2} + 8954 T^{3} + 136470 T^{4} + 1223878 T^{5} + 14428489 T^{6} + 109305060 T^{7} + 1284135521 T^{8} + 9694337638 T^{9} + 96207119430 T^{10} + 561794025914 T^{11} + 3713399533585 T^{12} + 11927550983064 T^{13} + 44231334895529 T^{14} \))(\( 1 - 24 T + 665 T^{2} - 8954 T^{3} + 136470 T^{4} - 1223878 T^{5} + 14428489 T^{6} - 109305060 T^{7} + 1284135521 T^{8} - 9694337638 T^{9} + 96207119430 T^{10} - 561794025914 T^{11} + 3713399533585 T^{12} - 11927550983064 T^{13} + 44231334895529 T^{14} \))(\( 1 - 11 T + 541 T^{2} - 5090 T^{3} + 131896 T^{4} - 1039032 T^{5} + 18729117 T^{6} - 119811073 T^{7} + 1666891413 T^{8} - 8230172472 T^{9} + 92982591224 T^{10} - 319358006690 T^{11} + 3020976161909 T^{12} - 5466794200571 T^{13} + 44231334895529 T^{14} \))(\( ( 1 - 89 T^{2} )^{4} \))(\( ( 1 - 31 T^{2} - 6960 T^{4} - 245551 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 89 T^{2} )^{8} \))(\( ( 1 - 378 T^{2} + 61403 T^{4} - 6095438 T^{6} + 519716488 T^{8} - 48281964398 T^{10} + 3852561824123 T^{12} - 187858927983258 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( 1 + 8 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 6 T + 201 T^{2} - 582 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 264 T^{2} + 1105 T^{3} + 25608 T^{4} + 56454 T^{5} + 912673 T^{6} \))(\( 1 + 14 T + 194 T^{2} + 2009 T^{3} + 18818 T^{4} + 131726 T^{5} + 912673 T^{6} \))(\( 1 + 6 T + 286 T^{2} + 1139 T^{3} + 27742 T^{4} + 56454 T^{5} + 912673 T^{6} \))(\( 1 - 4 T - 28 T^{2} + 1353 T^{3} - 2716 T^{4} - 37636 T^{5} + 912673 T^{6} \))(\( 1 + 12 T + 138 T^{2} + 1461 T^{3} + 13386 T^{4} + 112908 T^{5} + 912673 T^{6} \))(\( 1 + 165 T^{2} - 163 T^{3} + 13770 T^{4} - 15811 T^{5} + 1552485 T^{6} + 88529281 T^{8} \))(\( 1 - 42 T + 1003 T^{2} - 15865 T^{3} + 182710 T^{4} - 1538905 T^{5} + 9437227 T^{6} - 38332266 T^{7} + 88529281 T^{8} \))(\( 1 - 18 T + 241 T^{2} - 2861 T^{3} + 28582 T^{4} - 277517 T^{5} + 2267569 T^{6} - 16428114 T^{7} + 88529281 T^{8} \))(\( 1 - 37 T + 916 T^{2} - 16581 T^{3} + 246255 T^{4} - 3080646 T^{5} + 32767192 T^{6} - 298822662 T^{7} + 2317013295 T^{8} - 15133031013 T^{9} + 81092821396 T^{10} - 317731589509 T^{11} + 832972004929 T^{12} \))(\( 1 + 46 T + 1373 T^{2} + 28598 T^{3} + 470895 T^{4} + 6187836 T^{5} + 67342614 T^{6} + 600220092 T^{7} + 4430651055 T^{8} + 26100622454 T^{9} + 121550702813 T^{10} + 395017651822 T^{11} + 832972004929 T^{12} \))(\( 1 + 4 T + 329 T^{2} + 2166 T^{3} + 46520 T^{4} + 471462 T^{5} + 4258677 T^{6} + 58421052 T^{7} + 413091669 T^{8} + 4435985958 T^{9} + 42457547960 T^{10} + 191754422646 T^{11} + 2825234944553 T^{12} + 3331888019716 T^{13} + 80798284478113 T^{14} \))(\( 1 - 2 T + 433 T^{2} - 1366 T^{3} + 88712 T^{4} - 349822 T^{5} + 11831541 T^{6} - 45812838 T^{7} + 1147659477 T^{8} - 3291475198 T^{9} + 80965047176 T^{10} - 120930997846 T^{11} + 3718318331281 T^{12} - 1665944009858 T^{13} + 80798284478113 T^{14} \))(\( 1 - 2 T + 433 T^{2} - 1366 T^{3} + 88712 T^{4} - 349822 T^{5} + 11831541 T^{6} - 45812838 T^{7} + 1147659477 T^{8} - 3291475198 T^{9} + 80965047176 T^{10} - 120930997846 T^{11} + 3718318331281 T^{12} - 1665944009858 T^{13} + 80798284478113 T^{14} \))(\( 1 + 4 T + 329 T^{2} + 2166 T^{3} + 46520 T^{4} + 471462 T^{5} + 4258677 T^{6} + 58421052 T^{7} + 413091669 T^{8} + 4435985958 T^{9} + 42457547960 T^{10} + 191754422646 T^{11} + 2825234944553 T^{12} + 3331888019716 T^{13} + 80798284478113 T^{14} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 97 T^{2} )^{8} \))(\( ( 1 - 97 T^{2} )^{8} \))(\( ( 1 - 358 T^{2} + 74235 T^{4} - 10905078 T^{6} + 1222175376 T^{8} - 102605878902 T^{10} + 6571971175035 T^{12} - 298203977764582 T^{14} + 7837433594376961 T^{16} )^{2} \))
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