Properties

Label 8008.2
Level 8008
Weight 2
Dimension 1009720
Nonzero newspaces 180
Sturm bound 7741440

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Defining parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 180 \)
Sturm bound: \(7741440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8008))\).

Total New Old
Modular forms 1952640 1017640 935000
Cusp forms 1918081 1009720 908361
Eisenstein series 34559 7920 26639

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8008))\)

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
8008.2.a \(\chi_{8008}(1, \cdot)\) 8008.2.a.a 1 1
8008.2.a.b 1
8008.2.a.c 1
8008.2.a.d 1
8008.2.a.e 1
8008.2.a.f 2
8008.2.a.g 2
8008.2.a.h 2
8008.2.a.i 3
8008.2.a.j 5
8008.2.a.k 6
8008.2.a.l 8
8008.2.a.m 9
8008.2.a.n 9
8008.2.a.o 9
8008.2.a.p 9
8008.2.a.q 9
8008.2.a.r 9
8008.2.a.s 10
8008.2.a.t 10
8008.2.a.u 10
8008.2.a.v 11
8008.2.a.w 11
8008.2.a.x 12
8008.2.a.y 14
8008.2.a.z 15
8008.2.b \(\chi_{8008}(3431, \cdot)\) None 0 1
8008.2.d \(\chi_{8008}(4731, \cdot)\) n/a 1120 1
8008.2.g \(\chi_{8008}(4005, \cdot)\) n/a 720 1
8008.2.i \(\chi_{8008}(3849, \cdot)\) n/a 288 1
8008.2.j \(\chi_{8008}(6579, \cdot)\) n/a 960 1
8008.2.l \(\chi_{8008}(5279, \cdot)\) None 0 1
8008.2.o \(\chi_{8008}(2001, \cdot)\) n/a 336 1
8008.2.q \(\chi_{8008}(2157, \cdot)\) n/a 840 1
8008.2.r \(\chi_{8008}(1275, \cdot)\) n/a 864 1
8008.2.t \(\chi_{8008}(2575, \cdot)\) None 0 1
8008.2.w \(\chi_{8008}(6161, \cdot)\) n/a 212 1
8008.2.y \(\chi_{8008}(6005, \cdot)\) n/a 1336 1
8008.2.z \(\chi_{8008}(727, \cdot)\) None 0 1
8008.2.bb \(\chi_{8008}(7435, \cdot)\) n/a 1008 1
8008.2.be \(\chi_{8008}(7853, \cdot)\) n/a 1152 1
8008.2.bg \(\chi_{8008}(529, \cdot)\) n/a 560 2
8008.2.bh \(\chi_{8008}(1145, \cdot)\) n/a 480 2
8008.2.bi \(\chi_{8008}(1849, \cdot)\) n/a 416 2
8008.2.bj \(\chi_{8008}(2993, \cdot)\) n/a 560 2
8008.2.bm \(\chi_{8008}(307, \cdot)\) n/a 2672 2
8008.2.bn \(\chi_{8008}(463, \cdot)\) None 0 2
8008.2.bo \(\chi_{8008}(5741, \cdot)\) n/a 2016 2
8008.2.bp \(\chi_{8008}(265, \cdot)\) n/a 560 2
8008.2.bu \(\chi_{8008}(4467, \cdot)\) n/a 1680 2
8008.2.bv \(\chi_{8008}(4311, \cdot)\) None 0 2
8008.2.bw \(\chi_{8008}(3037, \cdot)\) n/a 2240 2
8008.2.bx \(\chi_{8008}(1737, \cdot)\) n/a 504 2
8008.2.ca \(\chi_{8008}(729, \cdot)\) n/a 864 4
8008.2.cb \(\chi_{8008}(4905, \cdot)\) n/a 672 2
8008.2.cd \(\chi_{8008}(485, \cdot)\) n/a 2240 2
8008.2.cg \(\chi_{8008}(243, \cdot)\) n/a 2240 2
8008.2.ci \(\chi_{8008}(263, \cdot)\) None 0 2
8008.2.cj \(\chi_{8008}(1101, \cdot)\) n/a 2240 2
8008.2.cl \(\chi_{8008}(4553, \cdot)\) n/a 672 2
8008.2.co \(\chi_{8008}(1759, \cdot)\) None 0 2
8008.2.cq \(\chi_{8008}(1739, \cdot)\) n/a 2240 2
8008.2.cr \(\chi_{8008}(4157, \cdot)\) n/a 2672 2
8008.2.ct \(\chi_{8008}(4313, \cdot)\) n/a 424 2
8008.2.cw \(\chi_{8008}(1959, \cdot)\) None 0 2
8008.2.cy \(\chi_{8008}(659, \cdot)\) n/a 2016 2
8008.2.cz \(\chi_{8008}(1187, \cdot)\) n/a 2672 2
8008.2.db \(\chi_{8008}(199, \cdot)\) None 0 2
8008.2.df \(\chi_{8008}(3981, \cdot)\) n/a 2672 2
8008.2.dh \(\chi_{8008}(2133, \cdot)\) n/a 2304 2
8008.2.dk \(\chi_{8008}(571, \cdot)\) n/a 2672 2
8008.2.dm \(\chi_{8008}(3015, \cdot)\) None 0 2
8008.2.dn \(\chi_{8008}(285, \cdot)\) n/a 2672 2
8008.2.dp \(\chi_{8008}(3873, \cdot)\) n/a 560 2
8008.2.ds \(\chi_{8008}(1431, \cdot)\) None 0 2
8008.2.du \(\chi_{8008}(2419, \cdot)\) n/a 2304 2
8008.2.dv \(\chi_{8008}(815, \cdot)\) None 0 2
8008.2.dx \(\chi_{8008}(835, \cdot)\) n/a 2672 2
8008.2.ea \(\chi_{8008}(5477, \cdot)\) n/a 2672 2
8008.2.ec \(\chi_{8008}(2025, \cdot)\) n/a 560 2
8008.2.ee \(\chi_{8008}(1693, \cdot)\) n/a 2672 2
8008.2.eh \(\chi_{8008}(43, \cdot)\) n/a 2016 2
8008.2.ej \(\chi_{8008}(1343, \cdot)\) None 0 2
8008.2.ek \(\chi_{8008}(3233, \cdot)\) n/a 672 2
8008.2.em \(\chi_{8008}(3389, \cdot)\) n/a 1680 2
8008.2.ep \(\chi_{8008}(2883, \cdot)\) n/a 2240 2
8008.2.er \(\chi_{8008}(1583, \cdot)\) None 0 2
8008.2.es \(\chi_{8008}(3301, \cdot)\) n/a 2240 2
8008.2.eu \(\chi_{8008}(857, \cdot)\) n/a 672 2
8008.2.ex \(\chi_{8008}(2991, \cdot)\) None 0 2
8008.2.ez \(\chi_{8008}(859, \cdot)\) n/a 1920 2
8008.2.fa \(\chi_{8008}(4839, \cdot)\) None 0 2
8008.2.fc \(\chi_{8008}(2707, \cdot)\) n/a 2240 2
8008.2.ff \(\chi_{8008}(3917, \cdot)\) n/a 2240 2
8008.2.fh \(\chi_{8008}(1473, \cdot)\) n/a 672 2
8008.2.fi \(\chi_{8008}(4203, \cdot)\) n/a 2240 2
8008.2.fk \(\chi_{8008}(5191, \cdot)\) None 0 2
8008.2.fn \(\chi_{8008}(2089, \cdot)\) n/a 672 2
8008.2.fp \(\chi_{8008}(3565, \cdot)\) n/a 2240 2
8008.2.fq \(\chi_{8008}(2705, \cdot)\) n/a 576 2
8008.2.fs \(\chi_{8008}(1717, \cdot)\) n/a 1920 2
8008.2.fv \(\chi_{8008}(3587, \cdot)\) n/a 2240 2
8008.2.fx \(\chi_{8008}(1143, \cdot)\) None 0 2
8008.2.fy \(\chi_{8008}(309, \cdot)\) n/a 1680 2
8008.2.ga \(\chi_{8008}(153, \cdot)\) n/a 672 2
8008.2.gd \(\chi_{8008}(4663, \cdot)\) None 0 2
8008.2.gf \(\chi_{8008}(419, \cdot)\) n/a 2240 2
8008.2.gg \(\chi_{8008}(549, \cdot)\) n/a 2672 2
8008.2.gk \(\chi_{8008}(3631, \cdot)\) None 0 2
8008.2.gm \(\chi_{8008}(5763, \cdot)\) n/a 2672 2
8008.2.gn \(\chi_{8008}(4489, \cdot)\) n/a 560 2
8008.2.gp \(\chi_{8008}(901, \cdot)\) n/a 2672 2
8008.2.gs \(\chi_{8008}(4267, \cdot)\) n/a 2672 2
8008.2.gu \(\chi_{8008}(3279, \cdot)\) None 0 2
8008.2.gx \(\chi_{8008}(2757, \cdot)\) n/a 4608 4
8008.2.gy \(\chi_{8008}(2339, \cdot)\) n/a 4032 4
8008.2.ha \(\chi_{8008}(1455, \cdot)\) None 0 4
8008.2.hd \(\chi_{8008}(909, \cdot)\) n/a 5344 4
8008.2.hf \(\chi_{8008}(1065, \cdot)\) n/a 1008 4
8008.2.hg \(\chi_{8008}(3303, \cdot)\) None 0 4
8008.2.hi \(\chi_{8008}(547, \cdot)\) n/a 3456 4
8008.2.hl \(\chi_{8008}(2885, \cdot)\) n/a 4032 4
8008.2.hn \(\chi_{8008}(545, \cdot)\) n/a 1344 4
8008.2.ho \(\chi_{8008}(183, \cdot)\) None 0 4
8008.2.hq \(\chi_{8008}(27, \cdot)\) n/a 4608 4
8008.2.ht \(\chi_{8008}(937, \cdot)\) n/a 1152 4
8008.2.hv \(\chi_{8008}(1093, \cdot)\) n/a 3456 4
8008.2.hw \(\chi_{8008}(1819, \cdot)\) n/a 5344 4
8008.2.hy \(\chi_{8008}(519, \cdot)\) None 0 4
8008.2.ic \(\chi_{8008}(353, \cdot)\) n/a 1120 4
8008.2.id \(\chi_{8008}(1341, \cdot)\) n/a 5344 4
8008.2.ie \(\chi_{8008}(375, \cdot)\) None 0 4
8008.2.if \(\chi_{8008}(747, \cdot)\) n/a 5344 4
8008.2.ik \(\chi_{8008}(1055, \cdot)\) None 0 4
8008.2.il \(\chi_{8008}(683, \cdot)\) n/a 4480 4
8008.2.iq \(\chi_{8008}(1189, \cdot)\) n/a 4480 4
8008.2.ir \(\chi_{8008}(505, \cdot)\) n/a 1008 4
8008.2.is \(\chi_{8008}(681, \cdot)\) n/a 1344 4
8008.2.it \(\chi_{8008}(1893, \cdot)\) n/a 4480 4
8008.2.iu \(\chi_{8008}(2619, \cdot)\) n/a 3360 4
8008.2.iv \(\chi_{8008}(2463, \cdot)\) None 0 4
8008.2.iw \(\chi_{8008}(3167, \cdot)\) None 0 4
8008.2.ix \(\chi_{8008}(2179, \cdot)\) n/a 4480 4
8008.2.jc \(\chi_{8008}(1033, \cdot)\) n/a 1344 4
8008.2.jd \(\chi_{8008}(45, \cdot)\) n/a 4480 4
8008.2.ji \(\chi_{8008}(639, \cdot)\) None 0 4
8008.2.jj \(\chi_{8008}(1363, \cdot)\) n/a 5344 4
8008.2.jo \(\chi_{8008}(197, \cdot)\) n/a 4032 4
8008.2.jp \(\chi_{8008}(1497, \cdot)\) n/a 1120 4
8008.2.jq \(\chi_{8008}(1321, \cdot)\) n/a 1120 4
8008.2.jr \(\chi_{8008}(109, \cdot)\) n/a 5344 4
8008.2.js \(\chi_{8008}(2771, \cdot)\) n/a 5344 4
8008.2.jt \(\chi_{8008}(2927, \cdot)\) None 0 4
8008.2.ju \(\chi_{8008}(1607, \cdot)\) None 0 4
8008.2.jv \(\chi_{8008}(395, \cdot)\) n/a 5344 4
8008.2.ka \(\chi_{8008}(89, \cdot)\) n/a 1120 4
8008.2.kb \(\chi_{8008}(1957, \cdot)\) n/a 5344 4
8008.2.kg \(\chi_{8008}(1649, \cdot)\) n/a 1344 4
8008.2.kh \(\chi_{8008}(397, \cdot)\) n/a 4480 4
8008.2.ki \(\chi_{8008}(1671, \cdot)\) None 0 4
8008.2.kj \(\chi_{8008}(67, \cdot)\) n/a 4480 4
8008.2.km \(\chi_{8008}(9, \cdot)\) n/a 2688 8
8008.2.kn \(\chi_{8008}(113, \cdot)\) n/a 2016 8
8008.2.ko \(\chi_{8008}(625, \cdot)\) n/a 2304 8
8008.2.kp \(\chi_{8008}(289, \cdot)\) n/a 2688 8
8008.2.kq \(\chi_{8008}(57, \cdot)\) n/a 2016 8
8008.2.kr \(\chi_{8008}(125, \cdot)\) n/a 10688 8
8008.2.kw \(\chi_{8008}(447, \cdot)\) None 0 8
8008.2.kx \(\chi_{8008}(603, \cdot)\) n/a 8064 8
8008.2.ky \(\chi_{8008}(489, \cdot)\) n/a 2688 8
8008.2.kz \(\chi_{8008}(645, \cdot)\) n/a 8064 8
8008.2.le \(\chi_{8008}(1191, \cdot)\) None 0 8
8008.2.lf \(\chi_{8008}(83, \cdot)\) n/a 10688 8
8008.2.lh \(\chi_{8008}(367, \cdot)\) None 0 8
8008.2.lj \(\chi_{8008}(1283, \cdot)\) n/a 10688 8
8008.2.lk \(\chi_{8008}(101, \cdot)\) n/a 10688 8
8008.2.lm \(\chi_{8008}(361, \cdot)\) n/a 2688 8
8008.2.lp \(\chi_{8008}(667, \cdot)\) n/a 10688 8
8008.2.lr \(\chi_{8008}(647, \cdot)\) None 0 8
8008.2.lt \(\chi_{8008}(61, \cdot)\) n/a 10688 8
8008.2.lw \(\chi_{8008}(867, \cdot)\) n/a 10688 8
8008.2.ly \(\chi_{8008}(1751, \cdot)\) None 0 8
8008.2.lz \(\chi_{8008}(1161, \cdot)\) n/a 2688 8
8008.2.mb \(\chi_{8008}(1037, \cdot)\) n/a 8064 8
8008.2.me \(\chi_{8008}(415, \cdot)\) None 0 8
8008.2.mg \(\chi_{8008}(467, \cdot)\) n/a 10688 8
8008.2.mh \(\chi_{8008}(53, \cdot)\) n/a 9216 8
8008.2.mj \(\chi_{8008}(1041, \cdot)\) n/a 2304 8
8008.2.mm \(\chi_{8008}(653, \cdot)\) n/a 10688 8
8008.2.mo \(\chi_{8008}(633, \cdot)\) n/a 2688 8
8008.2.mp \(\chi_{8008}(95, \cdot)\) None 0 8
8008.2.mr \(\chi_{8008}(75, \cdot)\) n/a 10688 8
8008.2.mu \(\chi_{8008}(17, \cdot)\) n/a 2688 8
8008.2.mw \(\chi_{8008}(933, \cdot)\) n/a 10688 8
8008.2.mx \(\chi_{8008}(1907, \cdot)\) n/a 10688 8
8008.2.mz \(\chi_{8008}(711, \cdot)\) None 0 8
8008.2.nc \(\chi_{8008}(339, \cdot)\) n/a 9216 8
8008.2.ne \(\chi_{8008}(79, \cdot)\) None 0 8
8008.2.nf \(\chi_{8008}(129, \cdot)\) n/a 2688 8
8008.2.nh \(\chi_{8008}(389, \cdot)\) n/a 10688 8
8008.2.nk \(\chi_{8008}(127, \cdot)\) None 0 8
8008.2.nm \(\chi_{8008}(251, \cdot)\) n/a 10688 8
8008.2.nn \(\chi_{8008}(477, \cdot)\) n/a 8064 8
8008.2.np \(\chi_{8008}(321, \cdot)\) n/a 2688 8
8008.2.ns \(\chi_{8008}(335, \cdot)\) None 0 8
8008.2.nu \(\chi_{8008}(491, \cdot)\) n/a 8064 8
8008.2.nv \(\chi_{8008}(237, \cdot)\) n/a 10688 8
8008.2.nz \(\chi_{8008}(641, \cdot)\) n/a 2688 8
8008.2.ob \(\chi_{8008}(381, \cdot)\) n/a 10688 8
8008.2.oc \(\chi_{8008}(107, \cdot)\) n/a 10688 8
8008.2.oe \(\chi_{8008}(159, \cdot)\) None 0 8
8008.2.oh \(\chi_{8008}(963, \cdot)\) n/a 9216 8
8008.2.oj \(\chi_{8008}(1951, \cdot)\) None 0 8
8008.2.ok \(\chi_{8008}(25, \cdot)\) n/a 2688 8
8008.2.om \(\chi_{8008}(1949, \cdot)\) n/a 10688 8
8008.2.op \(\chi_{8008}(103, \cdot)\) None 0 8
8008.2.or \(\chi_{8008}(51, \cdot)\) n/a 10688 8
8008.2.os \(\chi_{8008}(677, \cdot)\) n/a 9216 8
8008.2.ow \(\chi_{8008}(997, \cdot)\) n/a 10688 8
8008.2.oy \(\chi_{8008}(927, \cdot)\) None 0 8
8008.2.pa \(\chi_{8008}(387, \cdot)\) n/a 10688 8
8008.2.pd \(\chi_{8008}(211, \cdot)\) n/a 8064 8
8008.2.pf \(\chi_{8008}(1511, \cdot)\) None 0 8
8008.2.pg \(\chi_{8008}(225, \cdot)\) n/a 2016 8
8008.2.pi \(\chi_{8008}(1245, \cdot)\) n/a 10688 8
8008.2.pl \(\chi_{8008}(355, \cdot)\) n/a 10688 8
8008.2.pn \(\chi_{8008}(303, \cdot)\) None 0 8
8008.2.po \(\chi_{8008}(425, \cdot)\) n/a 2688 8
8008.2.pq \(\chi_{8008}(445, \cdot)\) n/a 10688 8
8008.2.pt \(\chi_{8008}(919, \cdot)\) None 0 8
8008.2.pv \(\chi_{8008}(3, \cdot)\) n/a 10688 8
8008.2.pw \(\chi_{8008}(1213, \cdot)\) n/a 10688 8
8008.2.py \(\chi_{8008}(1921, \cdot)\) n/a 2688 8
8008.2.qa \(\chi_{8008}(163, \cdot)\) n/a 21376 16
8008.2.qb \(\chi_{8008}(215, \cdot)\) None 0 16
8008.2.qg \(\chi_{8008}(565, \cdot)\) n/a 21376 16
8008.2.qh \(\chi_{8008}(193, \cdot)\) n/a 5376 16
8008.2.qi \(\chi_{8008}(501, \cdot)\) n/a 21376 16
8008.2.qj \(\chi_{8008}(817, \cdot)\) n/a 5376 16
8008.2.qm \(\chi_{8008}(915, \cdot)\) n/a 21376 16
8008.2.qn \(\chi_{8008}(135, \cdot)\) None 0 16
8008.2.qo \(\chi_{8008}(15, \cdot)\) None 0 16
8008.2.qp \(\chi_{8008}(475, \cdot)\) n/a 21376 16
8008.2.qy \(\chi_{8008}(541, \cdot)\) n/a 21376 16
8008.2.qz \(\chi_{8008}(577, \cdot)\) n/a 5376 16
8008.2.ra \(\chi_{8008}(97, \cdot)\) n/a 5376 16
8008.2.rb \(\chi_{8008}(85, \cdot)\) n/a 16128 16
8008.2.re \(\chi_{8008}(227, \cdot)\) n/a 21376 16
8008.2.rf \(\chi_{8008}(487, \cdot)\) None 0 16
8008.2.rg \(\chi_{8008}(509, \cdot)\) n/a 21376 16
8008.2.rh \(\chi_{8008}(305, \cdot)\) n/a 5376 16
8008.2.rk \(\chi_{8008}(291, \cdot)\) n/a 21376 16
8008.2.rl \(\chi_{8008}(255, \cdot)\) None 0 16
8008.2.rm \(\chi_{8008}(167, \cdot)\) None 0 16
8008.2.rn \(\chi_{8008}(267, \cdot)\) n/a 16128 16
8008.2.rw \(\chi_{8008}(5, \cdot)\) n/a 21376 16
8008.2.rx \(\chi_{8008}(1201, \cdot)\) n/a 5376 16
8008.2.ry \(\chi_{8008}(1289, \cdot)\) n/a 4032 16
8008.2.rz \(\chi_{8008}(405, \cdot)\) n/a 21376 16
8008.2.sc \(\chi_{8008}(851, \cdot)\) n/a 21376 16
8008.2.sd \(\chi_{8008}(271, \cdot)\) None 0 16
8008.2.se \(\chi_{8008}(19, \cdot)\) n/a 21376 16
8008.2.sf \(\chi_{8008}(1103, \cdot)\) None 0 16
8008.2.sk \(\chi_{8008}(149, \cdot)\) n/a 21376 16
8008.2.sl \(\chi_{8008}(201, \cdot)\) n/a 5376 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8008))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2002))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4004))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 3 T + 5 T^{2} - 9 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 5 T^{2} - 5 T^{3} + 15 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 - T + 5 T^{2} + 11 T^{4} + 14 T^{5} + 33 T^{6} + 135 T^{8} - 81 T^{9} + 243 T^{10} \))(\( 1 + T + 5 T^{2} + 4 T^{3} + 8 T^{4} - 14 T^{5} + 8 T^{6} - 42 T^{7} + 72 T^{8} + 108 T^{9} + 405 T^{10} + 243 T^{11} + 729 T^{12} \))(\( 1 + 5 T + 21 T^{2} + 62 T^{3} + 168 T^{4} + 387 T^{5} + 844 T^{6} + 1634 T^{7} + 2991 T^{8} + 4902 T^{9} + 7596 T^{10} + 10449 T^{11} + 13608 T^{12} + 15066 T^{13} + 15309 T^{14} + 10935 T^{15} + 6561 T^{16} \))(\( 1 + 5 T + 20 T^{2} + 61 T^{3} + 161 T^{4} + 365 T^{5} + 776 T^{6} + 1479 T^{7} + 2739 T^{8} + 4800 T^{9} + 8217 T^{10} + 13311 T^{11} + 20952 T^{12} + 29565 T^{13} + 39123 T^{14} + 44469 T^{15} + 43740 T^{16} + 32805 T^{17} + 19683 T^{18} \))(\( 1 + 3 T + 12 T^{2} + 27 T^{3} + 73 T^{4} + 147 T^{5} + 330 T^{6} + 591 T^{7} + 1227 T^{8} + 1988 T^{9} + 3681 T^{10} + 5319 T^{11} + 8910 T^{12} + 11907 T^{13} + 17739 T^{14} + 19683 T^{15} + 26244 T^{16} + 19683 T^{17} + 19683 T^{18} \))(\( 1 + 2 T + 15 T^{2} + 28 T^{3} + 119 T^{4} + 199 T^{5} + 637 T^{6} + 947 T^{7} + 2505 T^{8} + 3297 T^{9} + 7515 T^{10} + 8523 T^{11} + 17199 T^{12} + 16119 T^{13} + 28917 T^{14} + 20412 T^{15} + 32805 T^{16} + 13122 T^{17} + 19683 T^{18} \))(\( 1 - T + 12 T^{2} - 9 T^{3} + 75 T^{4} - 41 T^{5} + 346 T^{6} - 161 T^{7} + 1289 T^{8} - 554 T^{9} + 3867 T^{10} - 1449 T^{11} + 9342 T^{12} - 3321 T^{13} + 18225 T^{14} - 6561 T^{15} + 26244 T^{16} - 6561 T^{17} + 19683 T^{18} \))(\( 1 - 3 T + 12 T^{2} - 27 T^{3} + 73 T^{4} - 147 T^{5} + 340 T^{6} - 621 T^{7} + 1245 T^{8} - 2078 T^{9} + 3735 T^{10} - 5589 T^{11} + 9180 T^{12} - 11907 T^{13} + 17739 T^{14} - 19683 T^{15} + 26244 T^{16} - 19683 T^{17} + 19683 T^{18} \))(\( 1 - 5 T + 22 T^{2} - 65 T^{3} + 171 T^{4} - 367 T^{5} + 722 T^{6} - 1261 T^{7} + 2181 T^{8} - 3668 T^{9} + 6543 T^{10} - 11349 T^{11} + 19494 T^{12} - 29727 T^{13} + 41553 T^{14} - 47385 T^{15} + 48114 T^{16} - 32805 T^{17} + 19683 T^{18} \))(\( 1 + 3 T + 15 T^{2} + 38 T^{3} + 111 T^{4} + 242 T^{5} + 521 T^{6} + 1026 T^{7} + 1815 T^{8} + 3421 T^{9} + 5570 T^{10} + 10263 T^{11} + 16335 T^{12} + 27702 T^{13} + 42201 T^{14} + 58806 T^{15} + 80919 T^{16} + 83106 T^{17} + 98415 T^{18} + 59049 T^{19} + 59049 T^{20} \))(\( 1 - T + 13 T^{2} - 14 T^{3} + 93 T^{4} - 100 T^{5} + 477 T^{6} - 488 T^{7} + 1951 T^{8} - 1821 T^{9} + 6490 T^{10} - 5463 T^{11} + 17559 T^{12} - 13176 T^{13} + 38637 T^{14} - 24300 T^{15} + 67797 T^{16} - 30618 T^{17} + 85293 T^{18} - 19683 T^{19} + 59049 T^{20} \))(\( 1 - 2 T + 14 T^{2} - 28 T^{3} + 114 T^{4} - 215 T^{5} + 652 T^{6} - 1120 T^{7} + 2814 T^{8} - 4354 T^{9} + 9530 T^{10} - 13062 T^{11} + 25326 T^{12} - 30240 T^{13} + 52812 T^{14} - 52245 T^{15} + 83106 T^{16} - 61236 T^{17} + 91854 T^{18} - 39366 T^{19} + 59049 T^{20} \))(\( 1 + 2 T + 14 T^{2} + 27 T^{3} + 102 T^{4} + 196 T^{5} + 523 T^{6} + 988 T^{7} + 2158 T^{8} + 3889 T^{9} + 7545 T^{10} + 12668 T^{11} + 22635 T^{12} + 35001 T^{13} + 58266 T^{14} + 80028 T^{15} + 127089 T^{16} + 142884 T^{17} + 223074 T^{18} + 177147 T^{19} + 275562 T^{20} + 118098 T^{21} + 177147 T^{22} \))(\( 1 - 3 T + 14 T^{2} - 35 T^{3} + 110 T^{4} - 256 T^{5} + 644 T^{6} - 1346 T^{7} + 2900 T^{8} - 5551 T^{9} + 10617 T^{10} - 18530 T^{11} + 31851 T^{12} - 49959 T^{13} + 78300 T^{14} - 109026 T^{15} + 156492 T^{16} - 186624 T^{17} + 240570 T^{18} - 229635 T^{19} + 275562 T^{20} - 177147 T^{21} + 177147 T^{22} \))(\( 1 - 4 T + 19 T^{2} - 53 T^{3} + 164 T^{4} - 383 T^{5} + 971 T^{6} - 1996 T^{7} + 4421 T^{8} - 8223 T^{9} + 16591 T^{10} - 28629 T^{11} + 53546 T^{12} - 85887 T^{13} + 149319 T^{14} - 222021 T^{15} + 358101 T^{16} - 485028 T^{17} + 707859 T^{18} - 837621 T^{19} + 1076004 T^{20} - 1043199 T^{21} + 1121931 T^{22} - 708588 T^{23} + 531441 T^{24} \))(\( 1 + 3 T + 15 T^{2} + 39 T^{3} + 120 T^{4} + 282 T^{5} + 674 T^{6} + 1428 T^{7} + 2918 T^{8} + 5592 T^{9} + 10453 T^{10} + 18549 T^{11} + 33283 T^{12} + 56463 T^{13} + 100624 T^{14} + 169389 T^{15} + 299547 T^{16} + 500823 T^{17} + 846693 T^{18} + 1358856 T^{19} + 2127222 T^{20} + 3123036 T^{21} + 4422114 T^{22} + 5550606 T^{23} + 7085880 T^{24} + 6908733 T^{25} + 7971615 T^{26} + 4782969 T^{27} + 4782969 T^{28} \))(\( 1 + T + 10 T^{2} + 10 T^{3} + 57 T^{4} + 59 T^{5} + 220 T^{6} + 250 T^{7} + 728 T^{8} + 960 T^{9} + 2519 T^{10} + 3371 T^{11} + 9426 T^{12} + 11368 T^{13} + 33071 T^{14} + 34778 T^{15} + 99213 T^{16} + 102312 T^{17} + 254502 T^{18} + 273051 T^{19} + 612117 T^{20} + 699840 T^{21} + 1592136 T^{22} + 1640250 T^{23} + 4330260 T^{24} + 3483891 T^{25} + 10097379 T^{26} + 5314410 T^{27} + 15943230 T^{28} + 4782969 T^{29} + 14348907 T^{30} \))
$5$ (\( 1 + T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 - 5 T + 13 T^{2} - 25 T^{3} + 25 T^{4} \))(\( 1 - 6 T + 23 T^{2} - 59 T^{3} + 115 T^{4} - 150 T^{5} + 125 T^{6} \))(\( 1 + T + 7 T^{2} + 4 T^{3} + 19 T^{4} + 95 T^{6} + 100 T^{7} + 875 T^{8} + 625 T^{9} + 3125 T^{10} \))(\( 1 - T + 11 T^{2} - 16 T^{3} + 80 T^{4} - 88 T^{5} + 502 T^{6} - 440 T^{7} + 2000 T^{8} - 2000 T^{9} + 6875 T^{10} - 3125 T^{11} + 15625 T^{12} \))(\( 1 + 7 T + 37 T^{2} + 138 T^{3} + 470 T^{4} + 1387 T^{5} + 3910 T^{6} + 9826 T^{7} + 23297 T^{8} + 49130 T^{9} + 97750 T^{10} + 173375 T^{11} + 293750 T^{12} + 431250 T^{13} + 578125 T^{14} + 546875 T^{15} + 390625 T^{16} \))(\( 1 + 5 T + 28 T^{2} + 85 T^{3} + 303 T^{4} + 743 T^{5} + 2182 T^{6} + 4649 T^{7} + 12119 T^{8} + 23998 T^{9} + 60595 T^{10} + 116225 T^{11} + 272750 T^{12} + 464375 T^{13} + 946875 T^{14} + 1328125 T^{15} + 2187500 T^{16} + 1953125 T^{17} + 1953125 T^{18} \))(\( 1 - T + 14 T^{2} - 13 T^{3} + 135 T^{4} - 137 T^{5} + 998 T^{6} - 1043 T^{7} + 5921 T^{8} - 5886 T^{9} + 29605 T^{10} - 26075 T^{11} + 124750 T^{12} - 85625 T^{13} + 421875 T^{14} - 203125 T^{15} + 1093750 T^{16} - 390625 T^{17} + 1953125 T^{18} \))(\( 1 + 4 T + 31 T^{2} + 104 T^{3} + 489 T^{4} + 1379 T^{5} + 4881 T^{6} + 11791 T^{7} + 33957 T^{8} + 69937 T^{9} + 169785 T^{10} + 294775 T^{11} + 610125 T^{12} + 861875 T^{13} + 1528125 T^{14} + 1625000 T^{15} + 2421875 T^{16} + 1562500 T^{17} + 1953125 T^{18} \))(\( 1 + 4 T + 31 T^{2} + 110 T^{3} + 483 T^{4} + 1473 T^{5} + 4837 T^{6} + 12551 T^{7} + 33717 T^{8} + 74369 T^{9} + 168585 T^{10} + 313775 T^{11} + 604625 T^{12} + 920625 T^{13} + 1509375 T^{14} + 1718750 T^{15} + 2421875 T^{16} + 1562500 T^{17} + 1953125 T^{18} \))(\( 1 - 8 T + 49 T^{2} - 202 T^{3} + 721 T^{4} - 2151 T^{5} + 6083 T^{6} - 15811 T^{7} + 39727 T^{8} - 91337 T^{9} + 198635 T^{10} - 395275 T^{11} + 760375 T^{12} - 1344375 T^{13} + 2253125 T^{14} - 3156250 T^{15} + 3828125 T^{16} - 3125000 T^{17} + 1953125 T^{18} \))(\( 1 - 3 T + 28 T^{2} - 71 T^{3} + 363 T^{4} - 787 T^{5} + 3016 T^{6} - 5699 T^{7} + 18739 T^{8} - 31646 T^{9} + 93695 T^{10} - 142475 T^{11} + 377000 T^{12} - 491875 T^{13} + 1134375 T^{14} - 1109375 T^{15} + 2187500 T^{16} - 1171875 T^{17} + 1953125 T^{18} \))(\( 1 + 4 T + 32 T^{2} + 98 T^{3} + 452 T^{4} + 1161 T^{5} + 3978 T^{6} + 9108 T^{7} + 25908 T^{8} + 54954 T^{9} + 139448 T^{10} + 274770 T^{11} + 647700 T^{12} + 1138500 T^{13} + 2486250 T^{14} + 3628125 T^{15} + 7062500 T^{16} + 7656250 T^{17} + 12500000 T^{18} + 7812500 T^{19} + 9765625 T^{20} \))(\( 1 - 3 T + 23 T^{2} - 78 T^{3} + 335 T^{4} - 1022 T^{5} + 3385 T^{6} - 9156 T^{7} + 25295 T^{8} - 60239 T^{9} + 144342 T^{10} - 301195 T^{11} + 632375 T^{12} - 1144500 T^{13} + 2115625 T^{14} - 3193750 T^{15} + 5234375 T^{16} - 6093750 T^{17} + 8984375 T^{18} - 5859375 T^{19} + 9765625 T^{20} \))(\( 1 + 4 T + 30 T^{2} + 102 T^{3} + 432 T^{4} + 1249 T^{5} + 4028 T^{6} + 10212 T^{7} + 27828 T^{8} + 63842 T^{9} + 153622 T^{10} + 319210 T^{11} + 695700 T^{12} + 1276500 T^{13} + 2517500 T^{14} + 3903125 T^{15} + 6750000 T^{16} + 7968750 T^{17} + 11718750 T^{18} + 7812500 T^{19} + 9765625 T^{20} \))(\( 1 - 2 T + 24 T^{2} - 41 T^{3} + 252 T^{4} - 288 T^{5} + 1337 T^{6} - 22 T^{7} + 2086 T^{8} + 13787 T^{9} - 16063 T^{10} + 105706 T^{11} - 80315 T^{12} + 344675 T^{13} + 260750 T^{14} - 13750 T^{15} + 4178125 T^{16} - 4500000 T^{17} + 19687500 T^{18} - 16015625 T^{19} + 46875000 T^{20} - 19531250 T^{21} + 48828125 T^{22} \))(\( 1 + 2 T + 23 T^{2} + 50 T^{3} + 298 T^{4} + 659 T^{5} + 2740 T^{6} + 6083 T^{7} + 19590 T^{8} + 42828 T^{9} + 115828 T^{10} + 238548 T^{11} + 579140 T^{12} + 1070700 T^{13} + 2448750 T^{14} + 3801875 T^{15} + 8562500 T^{16} + 10296875 T^{17} + 23281250 T^{18} + 19531250 T^{19} + 44921875 T^{20} + 19531250 T^{21} + 48828125 T^{22} \))(\( 1 - 6 T + 41 T^{2} - 173 T^{3} + 738 T^{4} - 2495 T^{5} + 8461 T^{6} - 24696 T^{7} + 72431 T^{8} - 188937 T^{9} + 493833 T^{10} - 1162965 T^{11} + 2734438 T^{12} - 5814825 T^{13} + 12345825 T^{14} - 23617125 T^{15} + 45269375 T^{16} - 77175000 T^{17} + 132203125 T^{18} - 194921875 T^{19} + 288281250 T^{20} - 337890625 T^{21} + 400390625 T^{22} - 292968750 T^{23} + 244140625 T^{24} \))(\( 1 + 6 T + 42 T^{2} + 189 T^{3} + 824 T^{4} + 2966 T^{5} + 10278 T^{6} + 31586 T^{7} + 94870 T^{8} + 261850 T^{9} + 710789 T^{10} + 1806536 T^{11} + 4513040 T^{12} + 10601849 T^{13} + 24455060 T^{14} + 53009245 T^{15} + 112826000 T^{16} + 225817000 T^{17} + 444243125 T^{18} + 818281250 T^{19} + 1482343750 T^{20} + 2467656250 T^{21} + 4014843750 T^{22} + 5792968750 T^{23} + 8046875000 T^{24} + 9228515625 T^{25} + 10253906250 T^{26} + 7324218750 T^{27} + 6103515625 T^{28} \))(\( 1 - 4 T + 29 T^{2} - 93 T^{3} + 418 T^{4} - 1139 T^{5} + 4074 T^{6} - 9998 T^{7} + 31084 T^{8} - 70952 T^{9} + 201211 T^{10} - 437948 T^{11} + 1167979 T^{12} - 2466049 T^{13} + 6281244 T^{14} - 12839570 T^{15} + 31406220 T^{16} - 61651225 T^{17} + 145997375 T^{18} - 273717500 T^{19} + 628784375 T^{20} - 1108625000 T^{21} + 2428437500 T^{22} - 3905468750 T^{23} + 7957031250 T^{24} - 11123046875 T^{25} + 20410156250 T^{26} - 22705078125 T^{27} + 35400390625 T^{28} - 24414062500 T^{29} + 30517578125 T^{30} \))
$7$ (\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{10} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{11} \))(\( ( 1 + T )^{11} \))(\( ( 1 - T )^{12} \))(\( ( 1 - T )^{14} \))(\( ( 1 + T )^{15} \))
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{11} \))(\( ( 1 - T )^{11} \))(\( ( 1 - T )^{12} \))(\( ( 1 + T )^{14} \))(\( ( 1 + T )^{15} \))
$13$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{11} \))(\( ( 1 - T )^{11} \))(\( ( 1 - T )^{12} \))(\( ( 1 + T )^{14} \))(\( ( 1 - T )^{15} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 5 T + 29 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 + 9 T + 43 T^{2} + 153 T^{3} + 289 T^{4} \))(\( 1 + 5 T + 37 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 + 13 T + 88 T^{2} + 414 T^{3} + 1496 T^{4} + 3757 T^{5} + 4913 T^{6} \))(\( 1 - 19 T + 211 T^{2} - 1636 T^{3} + 9643 T^{4} - 44660 T^{5} + 163931 T^{6} - 472804 T^{7} + 1036643 T^{8} - 1586899 T^{9} + 1419857 T^{10} \))(\( 1 + 31 T^{2} - 20 T^{3} + 732 T^{4} - 820 T^{5} + 15004 T^{6} - 13940 T^{7} + 211548 T^{8} - 98260 T^{9} + 2589151 T^{10} + 24137569 T^{12} \))(\( 1 - 3 T + 93 T^{2} - 252 T^{3} + 4302 T^{4} - 10279 T^{5} + 126478 T^{6} - 261210 T^{7} + 2561201 T^{8} - 4440570 T^{9} + 36552142 T^{10} - 50500727 T^{11} + 359307342 T^{12} - 357803964 T^{13} + 2244793917 T^{14} - 1231016019 T^{15} + 6975757441 T^{16} \))(\( 1 - 13 T + 138 T^{2} - 939 T^{3} + 5755 T^{4} - 27985 T^{5} + 133828 T^{6} - 565357 T^{7} + 2490751 T^{8} - 10032198 T^{9} + 42342767 T^{10} - 163388173 T^{11} + 657496964 T^{12} - 2337335185 T^{13} + 8171277035 T^{14} - 22665177291 T^{15} + 56626736874 T^{16} - 90684846733 T^{17} + 118587876497 T^{18} \))(\( 1 - 7 T + 94 T^{2} - 469 T^{3} + 3935 T^{4} - 16357 T^{5} + 111908 T^{6} - 418759 T^{7} + 2477121 T^{8} - 8244238 T^{9} + 42111057 T^{10} - 121021351 T^{11} + 549804004 T^{12} - 1366152997 T^{13} + 5587137295 T^{14} - 11320519861 T^{15} + 38571835262 T^{16} - 48830302087 T^{17} + 118587876497 T^{18} \))(\( 1 + 9 T + 120 T^{2} + 789 T^{3} + 6265 T^{4} + 32807 T^{5} + 198452 T^{6} + 873261 T^{7} + 4434291 T^{8} + 16989184 T^{9} + 75382947 T^{10} + 252372429 T^{11} + 974994676 T^{12} + 2740073447 T^{13} + 8895404105 T^{14} + 19044541941 T^{15} + 49240640760 T^{16} + 62781816969 T^{17} + 118587876497 T^{18} \))(\( 1 + 11 T + 128 T^{2} + 877 T^{3} + 6361 T^{4} + 33933 T^{5} + 193412 T^{6} + 867961 T^{7} + 4213319 T^{8} + 16606726 T^{9} + 71626423 T^{10} + 250840729 T^{11} + 950233156 T^{12} + 2834118093 T^{13} + 9031710377 T^{14} + 21168648013 T^{15} + 52523350144 T^{16} + 76733331851 T^{17} + 118587876497 T^{18} \))(\( 1 - T + 104 T^{2} - 99 T^{3} + 5393 T^{4} - 4769 T^{5} + 179386 T^{6} - 143669 T^{7} + 4194185 T^{8} - 2933622 T^{9} + 71301145 T^{10} - 41520341 T^{11} + 881323418 T^{12} - 398311649 T^{13} + 7657288801 T^{14} - 2389619331 T^{15} + 42675221992 T^{16} - 6975757441 T^{17} + 118587876497 T^{18} \))(\( 1 + 7 T + 82 T^{2} + 259 T^{3} + 2045 T^{4} + 1873 T^{5} + 36924 T^{6} + 24031 T^{7} + 942421 T^{8} + 1108142 T^{9} + 16021157 T^{10} + 6944959 T^{11} + 181407612 T^{12} + 156434833 T^{13} + 2903607565 T^{14} + 6251630371 T^{15} + 33647771186 T^{16} + 48830302087 T^{17} + 118587876497 T^{18} \))(\( 1 + 11 T + 165 T^{2} + 1334 T^{3} + 11945 T^{4} + 76914 T^{5} + 515157 T^{6} + 2741930 T^{7} + 14828041 T^{8} + 66343271 T^{9} + 299048318 T^{10} + 1127835607 T^{11} + 4285303849 T^{12} + 13471102090 T^{13} + 43026427797 T^{14} + 109206881298 T^{15} + 288323261705 T^{16} + 547391789782 T^{17} + 1150999977765 T^{18} + 1304466641467 T^{19} + 2015993900449 T^{20} \))(\( 1 - 7 T + 109 T^{2} - 652 T^{3} + 6053 T^{4} - 31510 T^{5} + 218775 T^{6} - 1000716 T^{7} + 5689753 T^{8} - 22870289 T^{9} + 110945974 T^{10} - 388794913 T^{11} + 1644338617 T^{12} - 4916517708 T^{13} + 18272306775 T^{14} - 44739694070 T^{15} + 146104705157 T^{16} - 267540814796 T^{17} + 760357561069 T^{18} - 830115135479 T^{19} + 2015993900449 T^{20} \))(\( 1 + 3 T + 95 T^{2} + 256 T^{3} + 4627 T^{4} + 11410 T^{5} + 152327 T^{6} + 339784 T^{7} + 3740319 T^{8} + 7485571 T^{9} + 71600122 T^{10} + 127254707 T^{11} + 1080952191 T^{12} + 1669358792 T^{13} + 12722503367 T^{14} + 16200568370 T^{15} + 111684531763 T^{16} + 105046700288 T^{17} + 662696956895 T^{18} + 355763629491 T^{19} + 2015993900449 T^{20} \))(\( 1 + 4 T + 112 T^{2} + 399 T^{3} + 6538 T^{4} + 21364 T^{5} + 254625 T^{6} + 759042 T^{7} + 7270384 T^{8} + 19632831 T^{9} + 158781009 T^{10} + 382181206 T^{11} + 2699277153 T^{12} + 5673888159 T^{13} + 35719396592 T^{14} + 63395946882 T^{15} + 361531088625 T^{16} + 515675024116 T^{17} + 2682794244074 T^{18} + 2783327218959 T^{19} + 13281842167664 T^{20} + 8063975601796 T^{21} + 34271896307633 T^{22} \))(\( 1 - 9 T + 134 T^{2} - 851 T^{3} + 7210 T^{4} - 35742 T^{5} + 228876 T^{6} - 978070 T^{7} + 5442480 T^{8} - 21635441 T^{9} + 109691371 T^{10} - 404886510 T^{11} + 1864753307 T^{12} - 6252642449 T^{13} + 26738904240 T^{14} - 81689384470 T^{15} + 324971190732 T^{16} - 862724991198 T^{17} + 2958541832330 T^{18} - 5936369582291 T^{19} + 15890775450598 T^{20} - 18143945104041 T^{21} + 34271896307633 T^{22} \))(\( 1 - 16 T + 211 T^{2} - 1961 T^{3} + 16114 T^{4} - 110471 T^{5} + 697371 T^{6} - 3909704 T^{7} + 20731413 T^{8} - 100930925 T^{9} + 473280721 T^{10} - 2072962831 T^{11} + 8820341514 T^{12} - 35240368127 T^{13} + 136778128369 T^{14} - 495873634525 T^{15} + 1731508345173 T^{16} - 5551220592328 T^{17} + 16832840631099 T^{18} - 45330523544983 T^{19} + 112407355404274 T^{20} - 232550825810617 T^{21} + 425374712994739 T^{22} - 548350340922128 T^{23} + 582622237229761 T^{24} \))(\( 1 + 6 T + 125 T^{2} + 515 T^{3} + 6753 T^{4} + 18337 T^{5} + 220618 T^{6} + 322913 T^{7} + 5225037 T^{8} + 1329144 T^{9} + 102567474 T^{10} - 85892375 T^{11} + 1827876641 T^{12} - 2813704060 T^{13} + 31314357998 T^{14} - 47832969020 T^{15} + 528256349249 T^{16} - 421989238375 T^{17} + 8566537995954 T^{18} + 1887194412408 T^{19} + 126119691115053 T^{20} + 132503691914449 T^{21} + 1538977655118538 T^{22} + 2174545891325489 T^{23} + 13614006809732097 T^{24} + 17650026598430995 T^{25} + 72827779653720125 T^{26} + 59427468197435622 T^{27} + 168377826559400929 T^{28} \))(\( 1 - 8 T + 120 T^{2} - 745 T^{3} + 6822 T^{4} - 35300 T^{5} + 254707 T^{6} - 1139054 T^{7} + 7157815 T^{8} - 28432407 T^{9} + 164539483 T^{10} - 595647129 T^{11} + 3295262805 T^{12} - 11160918365 T^{13} + 60157749367 T^{14} - 195072983200 T^{15} + 1022681739239 T^{16} - 3225505407485 T^{17} + 16189626160965 T^{18} - 49749043861209 T^{19} + 233622536713931 T^{20} - 686289185798583 T^{21} + 2937128308679495 T^{22} - 7945764416200814 T^{23} + 30205162258921379 T^{24} - 71164584685849700 T^{25} + 233802876610672326 T^{26} - 434053566736171945 T^{27} + 1188549363948712440 T^{28} - 1347022612475207432 T^{29} + 2862423051509815793 T^{30} \))
$19$ (\( 1 + 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 3 T + 9 T^{2} - 57 T^{3} + 361 T^{4} \))(\( 1 - 3 T + 39 T^{2} - 57 T^{3} + 361 T^{4} \))(\( 1 - T + 9 T^{2} - 19 T^{3} + 361 T^{4} \))(\( 1 - T + 42 T^{2} - 10 T^{3} + 798 T^{4} - 361 T^{5} + 6859 T^{6} \))(\( 1 + 5 T + 65 T^{2} + 260 T^{3} + 2113 T^{4} + 6722 T^{5} + 40147 T^{6} + 93860 T^{7} + 445835 T^{8} + 651605 T^{9} + 2476099 T^{10} \))(\( 1 - 2 T + 35 T^{2} - 6 T^{3} + 874 T^{4} - 808 T^{5} + 22748 T^{6} - 15352 T^{7} + 315514 T^{8} - 41154 T^{9} + 4561235 T^{10} - 4952198 T^{11} + 47045881 T^{12} \))(\( 1 + 19 T + 227 T^{2} + 1954 T^{3} + 14128 T^{4} + 87909 T^{5} + 494602 T^{6} + 2495046 T^{7} + 11479137 T^{8} + 47405874 T^{9} + 178551322 T^{10} + 602967831 T^{11} + 1841175088 T^{12} + 4838297446 T^{13} + 10679414987 T^{14} + 16983563041 T^{15} + 16983563041 T^{16} \))(\( 1 + 5 T + 120 T^{2} + 501 T^{3} + 6879 T^{4} + 25133 T^{5} + 252736 T^{6} + 812339 T^{7} + 6555771 T^{8} + 18285248 T^{9} + 124559649 T^{10} + 293254379 T^{11} + 1733516224 T^{12} + 3275357693 T^{13} + 17033085021 T^{14} + 23569986381 T^{15} + 107264608680 T^{16} + 84917815205 T^{17} + 322687697779 T^{18} \))(\( 1 + 17 T + 250 T^{2} + 2543 T^{3} + 22649 T^{4} + 166717 T^{5} + 1096064 T^{6} + 6273913 T^{7} + 32423845 T^{8} + 148492824 T^{9} + 616053055 T^{10} + 2264882593 T^{11} + 7517902976 T^{12} + 21726726157 T^{13} + 56081166251 T^{14} + 119637675383 T^{15} + 223467934750 T^{16} + 288720571697 T^{17} + 322687697779 T^{18} \))(\( 1 - 9 T + 132 T^{2} - 829 T^{3} + 6787 T^{4} - 31451 T^{5} + 187802 T^{6} - 681719 T^{7} + 3614441 T^{8} - 12226396 T^{9} + 68674379 T^{10} - 246100559 T^{11} + 1288133918 T^{12} - 4098725771 T^{13} + 16805283913 T^{14} - 39001035349 T^{15} + 117991069548 T^{16} - 152852067369 T^{17} + 322687697779 T^{18} \))(\( 1 - 10 T + 143 T^{2} - 1144 T^{3} + 9691 T^{4} - 62585 T^{5} + 400065 T^{6} - 2121153 T^{7} + 11016921 T^{8} - 48502067 T^{9} + 209321499 T^{10} - 765736233 T^{11} + 2744045835 T^{12} - 8156139785 T^{13} + 23995875409 T^{14} - 53820487864 T^{15} + 127823658677 T^{16} - 169835630410 T^{17} + 322687697779 T^{18} \))(\( 1 - 16 T + 191 T^{2} - 1592 T^{3} + 11391 T^{4} - 66729 T^{5} + 355199 T^{6} - 1670749 T^{7} + 7632049 T^{8} - 32985135 T^{9} + 145008931 T^{10} - 603140389 T^{11} + 2436309941 T^{12} - 8696190009 T^{13} + 28205243709 T^{14} - 74897042552 T^{15} + 170729502149 T^{16} - 271737008656 T^{17} + 322687697779 T^{18} \))(\( 1 - 13 T + 178 T^{2} - 1405 T^{3} + 10931 T^{4} - 60977 T^{5} + 343000 T^{6} - 1500671 T^{7} + 7197879 T^{8} - 28886252 T^{9} + 136759701 T^{10} - 541742231 T^{11} + 2352637000 T^{12} - 7946583617 T^{13} + 27066238169 T^{14} - 66099462805 T^{15} + 159109169542 T^{16} - 220786319533 T^{17} + 322687697779 T^{18} \))(\( 1 - 2 T + 106 T^{2} - 364 T^{3} + 5898 T^{4} - 23557 T^{5} + 232308 T^{6} - 889420 T^{7} + 6771210 T^{8} - 23334494 T^{9} + 147824662 T^{10} - 443355386 T^{11} + 2444406810 T^{12} - 6100531780 T^{13} + 30274610868 T^{14} - 58329464143 T^{15} + 277476606138 T^{16} - 325369312996 T^{17} + 1800257682346 T^{18} - 645375395558 T^{19} + 6131066257801 T^{20} \))(\( 1 - 17 T + 235 T^{2} - 2374 T^{3} + 20639 T^{4} - 154644 T^{5} + 1031117 T^{6} - 6191480 T^{7} + 33704953 T^{8} - 167726555 T^{9} + 763211182 T^{10} - 3186804545 T^{11} + 12167488033 T^{12} - 42467361320 T^{13} + 134376198557 T^{14} - 382913853756 T^{15} + 970979937959 T^{16} - 2122051508386 T^{17} + 3991137314635 T^{18} - 5485690862243 T^{19} + 6131066257801 T^{20} \))(\( 1 - 13 T + 189 T^{2} - 1706 T^{3} + 14745 T^{4} - 102986 T^{5} + 667771 T^{6} - 3833770 T^{7} + 20319745 T^{8} - 99300871 T^{9} + 447982818 T^{10} - 1886716549 T^{11} + 7335427945 T^{12} - 26295828430 T^{13} + 87024584491 T^{14} - 255003531614 T^{15} + 693691515345 T^{16} - 1524945186734 T^{17} + 3209893414749 T^{18} - 4194940071127 T^{19} + 6131066257801 T^{20} \))(\( 1 + 16 T + 216 T^{2} + 2141 T^{3} + 18674 T^{4} + 140308 T^{5} + 955767 T^{6} + 5889704 T^{7} + 33407142 T^{8} + 174970235 T^{9} + 849975391 T^{10} + 3842050048 T^{11} + 16149532429 T^{12} + 63164254835 T^{13} + 229139586978 T^{14} + 767552114984 T^{15} + 2366573712933 T^{16} + 6600913471348 T^{17} + 16692160854086 T^{18} + 36361808470781 T^{19} + 69700542720264 T^{20} + 98097060124816 T^{21} + 116490258898219 T^{22} \))(\( 1 - 20 T + 317 T^{2} - 3546 T^{3} + 34648 T^{4} - 282731 T^{5} + 2085336 T^{6} - 13545407 T^{7} + 80854454 T^{8} - 434652258 T^{9} + 2164177438 T^{10} - 9790215924 T^{11} + 41119371322 T^{12} - 156909465138 T^{13} + 554580699986 T^{14} - 1765250985647 T^{15} + 5163498384264 T^{16} - 13301328981011 T^{17} + 30970868012872 T^{18} - 60223714543386 T^{19} + 102292000195943 T^{20} - 122621325156020 T^{21} + 116490258898219 T^{22} \))(\( 1 + 2 T + 119 T^{2} + 227 T^{3} + 7232 T^{4} + 13089 T^{5} + 301553 T^{6} + 512004 T^{7} + 9617251 T^{8} + 15173117 T^{9} + 245871887 T^{10} + 356948497 T^{11} + 5146385410 T^{12} + 6782021443 T^{13} + 88759751207 T^{14} + 104072409503 T^{15} + 1253329767571 T^{16} + 1267772592396 T^{17} + 14186826553193 T^{18} + 11699887191771 T^{19} + 122825127912512 T^{20} + 73250107395833 T^{21} + 729596884678319 T^{22} + 232980517796438 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 13 T + 177 T^{2} + 1445 T^{3} + 12090 T^{4} + 77374 T^{5} + 508114 T^{6} + 2775804 T^{7} + 15625190 T^{8} + 76300460 T^{9} + 389531889 T^{10} + 1764326347 T^{11} + 8473468513 T^{12} + 36406412321 T^{13} + 167526243796 T^{14} + 691721834099 T^{15} + 3058922133193 T^{16} + 12101514414073 T^{17} + 50764185306369 T^{18} + 188927492705540 T^{19} + 735100829342390 T^{20} + 2481212748603156 T^{21} + 8629586151014674 T^{22} + 24967637927952346 T^{23} + 74124591056814090 T^{24} + 168328424107926455 T^{25} + 391756740674710497 T^{26} + 546688785009341767 T^{27} + 799006685782884121 T^{28} \))(\( 1 + 17 T + 218 T^{2} + 2358 T^{3} + 22059 T^{4} + 183391 T^{5} + 1402092 T^{6} + 9858112 T^{7} + 64663374 T^{8} + 397927430 T^{9} + 2306295963 T^{10} + 12634290121 T^{11} + 65691592760 T^{12} + 324047945166 T^{13} + 1521234848033 T^{14} + 6796937301946 T^{15} + 28903462112627 T^{16} + 116981308204926 T^{17} + 450578634740840 T^{18} + 1646513322858841 T^{19} + 5710617127688337 T^{20} + 18720846518415830 T^{21} + 57800762566987386 T^{22} + 167425866617238592 T^{23} + 452437839554353668 T^{24} + 1124382372084383191 T^{25} + 2569658621035812921 T^{26} + 5218996579158007638 T^{27} + 9167550394772038862 T^{28} + 13583113658309030057 T^{29} + 15181127029874798299 T^{30} \))
$23$ (\( 1 - T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 4 T + 30 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( 1 + 13 T + 75 T^{2} + 330 T^{3} + 1725 T^{4} + 6877 T^{5} + 12167 T^{6} \))(\( 1 - 5 T + 79 T^{2} - 466 T^{3} + 2923 T^{4} - 16082 T^{5} + 67229 T^{6} - 246514 T^{7} + 961193 T^{8} - 1399205 T^{9} + 6436343 T^{10} \))(\( 1 - 11 T + 112 T^{2} - 685 T^{3} + 3951 T^{4} - 18154 T^{5} + 89568 T^{6} - 417542 T^{7} + 2090079 T^{8} - 8334395 T^{9} + 31342192 T^{10} - 70799773 T^{11} + 148035889 T^{12} \))(\( 1 - T + 88 T^{2} - 43 T^{3} + 3913 T^{4} - 1631 T^{5} + 125444 T^{6} - 59829 T^{7} + 3200004 T^{8} - 1376067 T^{9} + 66359876 T^{10} - 19844377 T^{11} + 1095017833 T^{12} - 276762749 T^{13} + 13027158232 T^{14} - 3404825447 T^{15} + 78310985281 T^{16} \))(\( 1 + 7 T + 135 T^{2} + 882 T^{3} + 8317 T^{4} + 49936 T^{5} + 316783 T^{6} + 1756846 T^{7} + 8844136 T^{8} + 45525138 T^{9} + 203415128 T^{10} + 929371534 T^{11} + 3854298761 T^{12} + 13974140176 T^{13} + 53531064731 T^{14} + 130567654098 T^{15} + 459651435345 T^{16} + 548176896967 T^{17} + 1801152661463 T^{18} \))(\( 1 - 11 T + 133 T^{2} - 918 T^{3} + 6479 T^{4} - 32786 T^{5} + 171365 T^{6} - 682762 T^{7} + 3177562 T^{8} - 12706630 T^{9} + 73083926 T^{10} - 361181098 T^{11} + 2084997955 T^{12} - 9174867026 T^{13} + 41701066297 T^{14} - 135896946102 T^{15} + 452841784451 T^{16} - 861420838091 T^{17} + 1801152661463 T^{18} \))(\( 1 + 10 T + 170 T^{2} + 1374 T^{3} + 13456 T^{4} + 88531 T^{5} + 646064 T^{6} + 3546760 T^{7} + 20956189 T^{8} + 97321142 T^{9} + 481992347 T^{10} + 1876236040 T^{11} + 7860660688 T^{12} + 24774603571 T^{13} + 86607431408 T^{14} + 203401311486 T^{15} + 578820325990 T^{16} + 783109852810 T^{17} + 1801152661463 T^{18} \))(\( 1 + 14 T + 246 T^{2} + 2286 T^{3} + 23368 T^{4} + 164703 T^{5} + 1237044 T^{6} + 7013716 T^{7} + 41988877 T^{8} + 196159902 T^{9} + 965744171 T^{10} + 3710255764 T^{11} + 15051114348 T^{12} + 46090652223 T^{13} + 150404463224 T^{14} + 338410042254 T^{15} + 837587059962 T^{16} + 1096353793934 T^{17} + 1801152661463 T^{18} \))(\( 1 - 6 T + 118 T^{2} - 562 T^{3} + 6844 T^{4} - 26025 T^{5} + 256264 T^{6} - 819608 T^{7} + 7248129 T^{8} - 20428834 T^{9} + 166706967 T^{10} - 433572632 T^{11} + 3117964088 T^{12} - 7282862025 T^{13} + 44050331492 T^{14} - 83196169618 T^{15} + 401769402746 T^{16} - 469865911686 T^{17} + 1801152661463 T^{18} \))(\( 1 - 9 T + 169 T^{2} - 1328 T^{3} + 13931 T^{4} - 90824 T^{5} + 701323 T^{6} - 3805908 T^{7} + 23406036 T^{8} - 106261174 T^{9} + 538338828 T^{10} - 2013325332 T^{11} + 8532996941 T^{12} - 25416278984 T^{13} + 89664694333 T^{14} - 196591660592 T^{15} + 575415500543 T^{16} - 704798867529 T^{17} + 1801152661463 T^{18} \))(\( 1 + 8 T + 173 T^{2} + 1108 T^{3} + 14006 T^{4} + 75877 T^{5} + 715666 T^{6} + 3348305 T^{7} + 25743697 T^{8} + 104738964 T^{9} + 684091730 T^{10} + 2408996172 T^{11} + 13618415713 T^{12} + 40738826935 T^{13} + 200272689106 T^{14} + 488370397811 T^{15} + 2073390661334 T^{16} + 3772546595276 T^{17} + 13547800453613 T^{18} + 14409221291704 T^{19} + 41426511213649 T^{20} \))(\( 1 - 15 T + 214 T^{2} - 2069 T^{3} + 18798 T^{4} - 140562 T^{5} + 994940 T^{6} - 6146374 T^{7} + 36233261 T^{8} - 191190354 T^{9} + 965821028 T^{10} - 4397378142 T^{11} + 19167395069 T^{12} - 74782932458 T^{13} + 278425004540 T^{14} - 904705244766 T^{15} + 2782778641422 T^{16} - 7044583849843 T^{17} + 16758550850134 T^{18} - 27017289921945 T^{19} + 41426511213649 T^{20} \))(\( 1 + 105 T^{2} - 56 T^{3} + 6074 T^{4} - 5543 T^{5} + 250282 T^{6} - 280479 T^{7} + 7945845 T^{8} - 9305572 T^{9} + 202470282 T^{10} - 214028156 T^{11} + 4203352005 T^{12} - 3412587993 T^{13} + 70039165162 T^{14} - 35676649249 T^{15} + 899169989786 T^{16} - 190670225032 T^{17} + 8222653454505 T^{18} + 41426511213649 T^{20} \))(\( 1 + 3 T + 145 T^{2} + 160 T^{3} + 9212 T^{4} - 7673 T^{5} + 352856 T^{6} - 1099400 T^{7} + 9550075 T^{8} - 54376154 T^{9} + 216513103 T^{10} - 1575350576 T^{11} + 4979801369 T^{12} - 28764985466 T^{13} + 116195762525 T^{14} - 307657195400 T^{15} + 2271102245608 T^{16} - 1135879376297 T^{17} + 31365252017764 T^{18} + 12529757644960 T^{19} + 261167135912135 T^{20} + 124279533640947 T^{21} + 952809757913927 T^{22} \))(\( 1 - 12 T + 192 T^{2} - 1500 T^{3} + 14405 T^{4} - 84603 T^{5} + 622928 T^{6} - 2921524 T^{7} + 18550871 T^{8} - 73654597 T^{9} + 448012645 T^{10} - 1670444328 T^{11} + 10304290835 T^{12} - 38963281813 T^{13} + 225708447457 T^{14} - 817562197684 T^{15} + 4009378272304 T^{16} - 12524280317067 T^{17} + 49046510564035 T^{18} - 117466477921500 T^{19} + 345821311000896 T^{20} - 497118134563788 T^{21} + 952809757913927 T^{22} \))(\( 1 - 9 T + 184 T^{2} - 1075 T^{3} + 13311 T^{4} - 52305 T^{5} + 559200 T^{6} - 1464883 T^{7} + 17622859 T^{8} - 32751842 T^{9} + 495005608 T^{10} - 773379158 T^{11} + 12357715050 T^{12} - 17787720634 T^{13} + 261857966632 T^{14} - 398491661614 T^{15} + 4931598485419 T^{16} - 9428489442869 T^{17} + 82781669128800 T^{18} - 178089395005335 T^{19} + 1042397525075391 T^{20} - 1936239111072725 T^{21} + 7622478063311416 T^{22} - 8575287821225343 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 9 T + 177 T^{2} + 1168 T^{3} + 14180 T^{4} + 77547 T^{5} + 744449 T^{6} + 3525981 T^{7} + 29157698 T^{8} + 122624518 T^{9} + 923220827 T^{10} + 3543101159 T^{11} + 25075850057 T^{12} + 89764496346 T^{13} + 606199986790 T^{14} + 2064583415958 T^{15} + 13265124680153 T^{16} + 43108911801553 T^{17} + 258355039448507 T^{18} + 789253458057674 T^{19} + 4316385744623522 T^{20} + 12005349834438507 T^{21} + 58298534681455169 T^{22} + 139673985438471261 T^{23} + 587427929009542820 T^{24} + 1112881797243466736 T^{25} + 3878888524467596817 T^{26} + 4536327257428206447 T^{27} + 11592836324538749809 T^{28} \))(\( 1 - 7 T + 196 T^{2} - 1293 T^{3} + 19463 T^{4} - 117533 T^{5} + 1283813 T^{6} - 7048114 T^{7} + 62795109 T^{8} - 314313823 T^{9} + 2424826937 T^{10} - 11136954051 T^{11} + 77022976854 T^{12} - 326683289245 T^{13} + 2067593471497 T^{14} - 8126177374012 T^{15} + 47554649844431 T^{16} - 172815460010605 T^{17} + 937138559382618 T^{18} - 3116576358585891 T^{19} + 15607017882171391 T^{20} - 46529726212793647 T^{21} + 213806385070338723 T^{22} - 551944751712810034 T^{23} + 2312343201770798419 T^{24} - 4868982142473807917 T^{25} + 18544536318278761201 T^{26} - 28335609390602275053 T^{27} + 98791126939547607068 T^{28} - 81149854271771248663 T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))
$29$ (\( 1 + 5 T + 29 T^{2} \))(\( 1 - 7 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 - 8 T + 54 T^{2} - 232 T^{3} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( 1 - 8 T + 59 T^{2} - 256 T^{3} + 1711 T^{4} - 6728 T^{5} + 24389 T^{6} \))(\( 1 + 17 T + 173 T^{2} + 1010 T^{3} + 4519 T^{4} + 18428 T^{5} + 131051 T^{6} + 849410 T^{7} + 4219297 T^{8} + 12023777 T^{9} + 20511149 T^{10} \))(\( 1 - 14 T + 198 T^{2} - 1774 T^{3} + 14615 T^{4} - 95404 T^{5} + 563924 T^{6} - 2766716 T^{7} + 12291215 T^{8} - 43266086 T^{9} + 140041638 T^{10} - 287156086 T^{11} + 594823321 T^{12} \))(\( 1 + 21 T + 274 T^{2} + 2507 T^{3} + 18563 T^{4} + 119277 T^{5} + 715198 T^{6} + 4125387 T^{7} + 22760696 T^{8} + 119636223 T^{9} + 601481518 T^{10} + 2909046753 T^{11} + 13129257203 T^{12} + 51421450543 T^{13} + 162981589954 T^{14} + 362247402489 T^{15} + 500246412961 T^{16} \))(\( 1 + 19 T + 329 T^{2} + 3782 T^{3} + 39477 T^{4} + 335122 T^{5} + 2622217 T^{6} + 17766634 T^{7} + 111992816 T^{8} + 624363670 T^{9} + 3247791664 T^{10} + 14941739194 T^{11} + 63953250413 T^{12} + 237025423282 T^{13} + 809718629073 T^{14} + 2249621800022 T^{15} + 5675209305661 T^{16} + 9504681846259 T^{17} + 14507145975869 T^{18} \))(\( 1 - 9 T + 151 T^{2} - 1528 T^{3} + 13853 T^{4} - 114984 T^{5} + 851637 T^{6} - 5649704 T^{7} + 34782342 T^{8} - 196302174 T^{9} + 1008687918 T^{10} - 4751401064 T^{11} + 20770574793 T^{12} - 81325998504 T^{13} + 284140947097 T^{14} - 908890034488 T^{15} + 2604731322659 T^{16} - 4502217716649 T^{17} + 14507145975869 T^{18} \))(\( 1 + 13 T + 181 T^{2} + 1642 T^{3} + 14303 T^{4} + 102576 T^{5} + 703913 T^{6} + 4238350 T^{7} + 25372950 T^{8} + 135705638 T^{9} + 735815550 T^{10} + 3564452350 T^{11} + 17167734157 T^{12} + 72550055856 T^{13} + 293370964147 T^{14} + 976699893082 T^{15} + 3122227611929 T^{16} + 6503203368493 T^{17} + 14507145975869 T^{18} \))(\( 1 + 10 T + 210 T^{2} + 1588 T^{3} + 19184 T^{4} + 116385 T^{5} + 1055760 T^{6} + 5377410 T^{7} + 40660657 T^{8} + 179445442 T^{9} + 1179159053 T^{10} + 4522401810 T^{11} + 25748930640 T^{12} + 82316899185 T^{13} + 393485882416 T^{14} + 944579433748 T^{15} + 3622474024890 T^{16} + 5002464129610 T^{17} + 14507145975869 T^{18} \))(\( 1 + 2 T + 184 T^{2} + 322 T^{3} + 16170 T^{4} + 24471 T^{5} + 901824 T^{6} + 1175640 T^{7} + 35510257 T^{8} + 39904238 T^{9} + 1029797453 T^{10} + 988713240 T^{11} + 21994585536 T^{12} + 17307873351 T^{13} + 331665279330 T^{14} + 191533109362 T^{15} + 3173977240856 T^{16} + 1000492825922 T^{17} + 14507145975869 T^{18} \))(\( 1 - T + 173 T^{2} - 346 T^{3} + 14427 T^{4} - 37748 T^{5} + 780989 T^{6} - 2179586 T^{7} + 30433390 T^{8} - 78376534 T^{9} + 882568310 T^{10} - 1833031826 T^{11} + 19047540721 T^{12} - 26698443188 T^{13} + 295914346623 T^{14} - 205808869066 T^{15} + 2984228601457 T^{16} - 500246412961 T^{17} + 14507145975869 T^{18} \))(\( 1 + 8 T + 161 T^{2} + 968 T^{3} + 12066 T^{4} + 58869 T^{5} + 584656 T^{6} + 2397855 T^{7} + 21304721 T^{8} + 77493084 T^{9} + 656370238 T^{10} + 2247299436 T^{11} + 17917270361 T^{12} + 58481285595 T^{13} + 413516080336 T^{14} + 1207470830481 T^{15} + 7177138191186 T^{16} + 16697880267112 T^{17} + 80539672486721 T^{18} + 116057167806952 T^{19} + 420707233300201 T^{20} \))(\( 1 + T + 182 T^{2} + 435 T^{3} + 15352 T^{4} + 58230 T^{5} + 820164 T^{6} + 4104326 T^{7} + 32224627 T^{8} + 180134460 T^{9} + 1021924084 T^{10} + 5223899340 T^{11} + 27100911307 T^{12} + 100100406814 T^{13} + 580086414084 T^{14} + 1194364206270 T^{15} + 9131727623992 T^{16} + 7503696194415 T^{17} + 91044847158902 T^{18} + 14507145975869 T^{19} + 420707233300201 T^{20} \))(\( 1 + 3 T + 166 T^{2} + 737 T^{3} + 14060 T^{4} + 73454 T^{5} + 825636 T^{6} + 4263066 T^{7} + 36555311 T^{8} + 168616816 T^{9} + 1223436068 T^{10} + 4889887664 T^{11} + 30743016551 T^{12} + 103971916674 T^{13} + 583956655716 T^{14} + 1506625938646 T^{15} + 8363215893260 T^{16} + 12713158839733 T^{17} + 83040904551526 T^{18} + 43521437927607 T^{19} + 420707233300201 T^{20} \))(\( 1 - T + 137 T^{2} - 90 T^{3} + 9528 T^{4} + 4979 T^{5} + 424978 T^{6} + 977800 T^{7} + 13642225 T^{8} + 62749830 T^{9} + 374654387 T^{10} + 2314314212 T^{11} + 10864977223 T^{12} + 52772607030 T^{13} + 332720225525 T^{14} + 691579361800 T^{15} + 8716787079722 T^{16} + 2961625315259 T^{17} + 164356821472152 T^{18} - 45022177166490 T^{19} + 1987478998694053 T^{20} - 420707233300201 T^{21} + 12200509765705829 T^{22} \))(\( 1 - 8 T + 156 T^{2} - 642 T^{3} + 9613 T^{4} - 22149 T^{5} + 463232 T^{6} - 864816 T^{7} + 20159887 T^{8} - 29244127 T^{9} + 676855499 T^{10} - 744028548 T^{11} + 19628809471 T^{12} - 24594310807 T^{13} + 491679484043 T^{14} - 611667925296 T^{15} + 9501420573568 T^{16} - 13174741736829 T^{17} + 165823060958417 T^{18} - 321158197120962 T^{19} + 2263114772235564 T^{20} - 3365657866401608 T^{21} + 12200509765705829 T^{22} \))(\( 1 - 15 T + 342 T^{2} - 3705 T^{3} + 49229 T^{4} - 425353 T^{5} + 4212598 T^{6} - 30586247 T^{7} + 247361139 T^{8} - 1552956678 T^{9} + 10709846884 T^{10} - 58911009530 T^{11} + 353795172606 T^{12} - 1708419276370 T^{13} + 9006981229444 T^{14} - 37875060419742 T^{15} + 174953833753059 T^{16} - 627359069567803 T^{17} + 2505751532397958 T^{18} - 7337286637662077 T^{19} + 24626630663657069 T^{20} - 53748975840594645 T^{21} + 143881873788668742 T^{22} - 183007646485587435 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 2 T + 131 T^{2} - 424 T^{3} + 9782 T^{4} - 39951 T^{5} + 553934 T^{6} - 2444591 T^{7} + 26176336 T^{8} - 114401364 T^{9} + 1060231021 T^{10} - 4429263778 T^{11} + 37271285121 T^{12} - 147239416334 T^{13} + 1151457791716 T^{14} - 4269943073686 T^{15} + 31345150786761 T^{16} - 108025314281642 T^{17} + 749881256763901 T^{18} - 2346503422807236 T^{19} + 15570295111131856 T^{20} - 42168892376094619 T^{21} + 277103496517138574 T^{22} - 579574988881942419 T^{23} + 4115358156142566182 T^{24} - 5173016140659271496 T^{25} + 46349736599916444371 T^{26} - 20521257425917204378 T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( 1 - 14 T + 258 T^{2} - 2600 T^{3} + 30427 T^{4} - 253281 T^{5} + 2349006 T^{6} - 17062918 T^{7} + 135918664 T^{8} - 888915969 T^{9} + 6332093199 T^{10} - 37985691424 T^{11} + 247438247672 T^{12} - 1375717671976 T^{13} + 8290822947461 T^{14} - 42894510399012 T^{15} + 240433865476369 T^{16} - 1156978562131816 T^{17} + 6034771422472408 T^{18} - 26866557816058144 T^{19} + 129878507086575651 T^{20} - 528747948770513049 T^{21} + 2344580142084531176 T^{22} - 8535663524147680198 T^{23} + 34077372940192136214 T^{24} - \)\(10\!\cdots\!81\)\( T^{25} + \)\(37\!\cdots\!83\)\( T^{26} - \)\(91\!\cdots\!00\)\( T^{27} + \)\(26\!\cdots\!62\)\( T^{28} - \)\(41\!\cdots\!34\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))
$31$ (\( 1 + 7 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( 1 + 10 T + 82 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 + 4 T + 14 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 + 17 T + 183 T^{2} + 1202 T^{3} + 5673 T^{4} + 16337 T^{5} + 29791 T^{6} \))(\( 1 - 4 T + 77 T^{2} - 512 T^{3} + 2801 T^{4} - 24388 T^{5} + 86831 T^{6} - 492032 T^{7} + 2293907 T^{8} - 3694084 T^{9} + 28629151 T^{10} \))(\( 1 - 21 T + 282 T^{2} - 2687 T^{3} + 20679 T^{4} - 134058 T^{5} + 786940 T^{6} - 4155798 T^{7} + 19872519 T^{8} - 80048417 T^{9} + 260432922 T^{10} - 601212171 T^{11} + 887503681 T^{12} \))(\( 1 - 2 T + 92 T^{2} - 92 T^{3} + 4979 T^{4} - 2492 T^{5} + 206564 T^{6} - 93938 T^{7} + 7282920 T^{8} - 2912078 T^{9} + 198508004 T^{10} - 74239172 T^{11} + 4598211059 T^{12} - 2633881892 T^{13} + 81650338652 T^{14} - 55025228222 T^{15} + 852891037441 T^{16} \))(\( 1 - 2 T + 159 T^{2} - 486 T^{3} + 12303 T^{4} - 49676 T^{5} + 627273 T^{6} - 2949818 T^{7} + 24094632 T^{8} - 112648484 T^{9} + 746933592 T^{10} - 2834775098 T^{11} + 18687089943 T^{12} - 45876829196 T^{13} + 352224444753 T^{14} - 431326788966 T^{15} + 4374505643649 T^{16} - 1705782074882 T^{17} + 26439622160671 T^{18} \))(\( 1 + 8 T + 185 T^{2} + 1552 T^{3} + 17539 T^{4} + 137544 T^{5} + 1085741 T^{6} + 7483048 T^{7} + 47024194 T^{8} + 277210160 T^{9} + 1457750014 T^{10} + 7191209128 T^{11} + 32345310131 T^{12} + 127024772424 T^{13} + 502126679389 T^{14} + 1377405712912 T^{15} + 5089833610535 T^{16} + 6823128299528 T^{17} + 26439622160671 T^{18} \))(\( 1 - 7 T + 217 T^{2} - 1002 T^{3} + 19047 T^{4} - 52631 T^{5} + 939105 T^{6} - 1211942 T^{7} + 32752862 T^{8} - 20744960 T^{9} + 1015338722 T^{10} - 1164676262 T^{11} + 27976877055 T^{12} - 48605833751 T^{13} + 545299439097 T^{14} - 889278688362 T^{15} + 5970237262087 T^{16} - 5970237262087 T^{17} + 26439622160671 T^{18} \))(\( 1 - 5 T + 105 T^{2} - 658 T^{3} + 7331 T^{4} - 47729 T^{5} + 378881 T^{6} - 2212118 T^{7} + 15351802 T^{8} - 78722536 T^{9} + 475905862 T^{10} - 2125845398 T^{11} + 11287243871 T^{12} - 44078733809 T^{13} + 209880305981 T^{14} - 583977422098 T^{15} + 2888824481655 T^{16} - 4264455187205 T^{17} + 26439622160671 T^{18} \))(\( 1 - 3 T + 163 T^{2} - 250 T^{3} + 12705 T^{4} - 6555 T^{5} + 654589 T^{6} + 95762 T^{7} + 25271694 T^{8} + 9268056 T^{9} + 783422514 T^{10} + 92027282 T^{11} + 19500860899 T^{12} - 6053680155 T^{13} + 363733363455 T^{14} - 221875920250 T^{15} + 4484556100093 T^{16} - 2558673112323 T^{17} + 26439622160671 T^{18} \))(\( 1 - 10 T + 229 T^{2} - 1956 T^{3} + 24783 T^{4} - 180686 T^{5} + 1644385 T^{6} - 10194632 T^{7} + 73319162 T^{8} - 382975896 T^{9} + 2272894022 T^{10} - 9797041352 T^{11} + 48987873535 T^{12} - 166867315406 T^{13} + 709516249233 T^{14} - 1735957200036 T^{15} + 6300388631419 T^{16} - 8528910374410 T^{17} + 26439622160671 T^{18} \))(\( 1 + 23 T + 444 T^{2} + 5927 T^{3} + 69838 T^{4} + 680889 T^{5} + 6017694 T^{6} + 46520575 T^{7} + 330538885 T^{8} + 2099194338 T^{9} + 12325983924 T^{10} + 65075024478 T^{11} + 317647868485 T^{12} + 1385894449825 T^{13} + 5557466780574 T^{14} + 19493273995239 T^{15} + 61981482073678 T^{16} + 163067263835897 T^{17} + 378683620623804 T^{18} + 608111309695433 T^{19} + 819628286980801 T^{20} \))(\( 1 + 6 T + 170 T^{2} + 864 T^{3} + 14504 T^{4} + 67206 T^{5} + 864018 T^{6} + 3656354 T^{7} + 38766747 T^{8} + 146828014 T^{9} + 1350192256 T^{10} + 4551668434 T^{11} + 37254843867 T^{12} + 108926442014 T^{13} + 797938767378 T^{14} + 1924050722106 T^{15} + 12872353389224 T^{16} + 23770898591904 T^{17} + 144991476364970 T^{18} + 158637732964026 T^{19} + 819628286980801 T^{20} \))(\( 1 + T + 118 T^{2} + 473 T^{3} + 7514 T^{4} + 40895 T^{5} + 418680 T^{6} + 1990441 T^{7} + 18318393 T^{8} + 79682742 T^{9} + 618259844 T^{10} + 2470165002 T^{11} + 17603975673 T^{12} + 59297227831 T^{13} + 386659772280 T^{14} + 1170789130145 T^{15} + 6668702659034 T^{16} + 13013466474503 T^{17} + 100641142418038 T^{18} + 26439622160671 T^{19} + 819628286980801 T^{20} \))(\( 1 - 14 T + 163 T^{2} - 1460 T^{3} + 12282 T^{4} - 94416 T^{5} + 709108 T^{6} - 4968372 T^{7} + 32760639 T^{8} - 204496002 T^{9} + 1211833827 T^{10} - 6877502064 T^{11} + 37566848637 T^{12} - 196520657922 T^{13} + 975972196449 T^{14} - 4588395877812 T^{15} + 20301160007308 T^{16} - 83794547545296 T^{17} + 337909926511302 T^{18} - 1245220914663860 T^{19} + 4309658412189373 T^{20} - 11474796017731214 T^{21} + 25408476896404831 T^{22} \))(\( 1 - 7 T + 249 T^{2} - 1248 T^{3} + 26392 T^{4} - 87502 T^{5} + 1595246 T^{6} - 2689786 T^{7} + 63810197 T^{8} - 10013439 T^{9} + 2018346295 T^{10} + 1239762012 T^{11} + 62568735145 T^{12} - 9622914879 T^{13} + 1900969578827 T^{14} - 2484073856506 T^{15} + 45670538616146 T^{16} - 77658347094862 T^{17} + 726112911617512 T^{18} - 1064408014726368 T^{19} + 6583465918007079 T^{20} - 5737398008865607 T^{21} + 25408476896404831 T^{22} \))(\( 1 - 10 T + 228 T^{2} - 1888 T^{3} + 24885 T^{4} - 176800 T^{5} + 1769128 T^{6} - 11161470 T^{7} + 93758891 T^{8} - 536477444 T^{9} + 3953158516 T^{10} - 20580707600 T^{11} + 135615848510 T^{12} - 638001935600 T^{13} + 3798985333876 T^{14} - 15982199534204 T^{15} + 86588304775211 T^{16} - 319543410011970 T^{17} + 1570107612160168 T^{18} - 4864230174824800 T^{19} + 21224193466719285 T^{20} - 49918006639346848 T^{21} + 186875249431622628 T^{22} - 254084768964048310 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 2 T + 193 T^{2} + 142 T^{3} + 19282 T^{4} - 4218 T^{5} + 1361141 T^{6} - 1144066 T^{7} + 76099680 T^{8} - 91588918 T^{9} + 3518325899 T^{10} - 4867518722 T^{11} + 137460954317 T^{12} - 194278895624 T^{13} + 4596872833022 T^{14} - 6022645764344 T^{15} + 132099977098637 T^{16} - 145008250247102 T^{17} + 3249247852570379 T^{18} - 2622112963348618 T^{19} + 67538746122922080 T^{20} - 31476246375515326 T^{21} + 1160904959593480181 T^{22} - 111522326273710278 T^{23} + 15804072629563804882 T^{24} + 3608003719289486002 T^{25} + \)\(15\!\cdots\!73\)\( T^{26} + 48835092594890085182 T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 + 4 T + 200 T^{2} + 1074 T^{3} + 20745 T^{4} + 124892 T^{5} + 1533011 T^{6} + 9113990 T^{7} + 89376771 T^{8} + 499876668 T^{9} + 4281189627 T^{10} + 22591424214 T^{11} + 174211127490 T^{12} + 871049967716 T^{13} + 6165340566297 T^{14} + 28999128746980 T^{15} + 191125557555207 T^{16} + 837079018975076 T^{17} + 5189923699054590 T^{18} + 20863654681537494 T^{19} + 122566824291016677 T^{20} + 443642382896014908 T^{21} + 2458988611010215581 T^{22} + 7773240386326899590 T^{23} + 40532231608152410381 T^{24} + \)\(10\!\cdots\!92\)\( T^{25} + \)\(52\!\cdots\!95\)\( T^{26} + \)\(84\!\cdots\!14\)\( T^{27} + \)\(48\!\cdots\!00\)\( T^{28} + \)\(30\!\cdots\!84\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 9 T + 37 T^{2} \))(\( 1 - 10 T + 94 T^{2} - 370 T^{3} + 1369 T^{4} \))(\( 1 - 10 T + 54 T^{2} - 370 T^{3} + 1369 T^{4} \))(\( 1 - 10 T + 86 T^{2} - 370 T^{3} + 1369 T^{4} \))(\( 1 - 7 T + 121 T^{2} - 514 T^{3} + 4477 T^{4} - 9583 T^{5} + 50653 T^{6} \))(\( 1 - 10 T + 125 T^{2} - 585 T^{3} + 4387 T^{4} - 14264 T^{5} + 162319 T^{6} - 800865 T^{7} + 6331625 T^{8} - 18741610 T^{9} + 69343957 T^{10} \))(\( 1 + 5 T + 128 T^{2} + 245 T^{3} + 6815 T^{4} + 1946 T^{5} + 269040 T^{6} + 72002 T^{7} + 9329735 T^{8} + 12409985 T^{9} + 239892608 T^{10} + 346719785 T^{11} + 2565726409 T^{12} \))(\( 1 + 12 T + 204 T^{2} + 1347 T^{3} + 13057 T^{4} + 43327 T^{5} + 342344 T^{6} - 172162 T^{7} + 6121444 T^{8} - 6369994 T^{9} + 468668936 T^{10} + 2194642531 T^{11} + 24470920177 T^{12} + 93406310079 T^{13} + 523408187436 T^{14} + 1139182525596 T^{15} + 3512479453921 T^{16} \))(\( 1 - 4 T + 107 T^{2} - 1097 T^{3} + 9183 T^{4} - 79748 T^{5} + 716531 T^{6} - 4515735 T^{7} + 31612618 T^{8} - 216156032 T^{9} + 1169666866 T^{10} - 6182041215 T^{11} + 36294444743 T^{12} - 149460591428 T^{13} + 636785557131 T^{14} - 2814601870673 T^{15} + 10157710853231 T^{16} - 14049917815684 T^{17} + 129961739795077 T^{18} \))(\( 1 - 2 T + 183 T^{2} - 305 T^{3} + 15447 T^{4} - 26690 T^{5} + 831383 T^{6} - 1647047 T^{7} + 34407826 T^{8} - 72172888 T^{9} + 1273089562 T^{10} - 2254807343 T^{11} + 42112043099 T^{12} - 50021357090 T^{13} + 1071156103779 T^{14} - 782546554745 T^{15} + 17372533515339 T^{16} - 7024958907842 T^{17} + 129961739795077 T^{18} \))(\( 1 + 15 T + 271 T^{2} + 2951 T^{3} + 33082 T^{4} + 286083 T^{5} + 2477078 T^{6} + 17875819 T^{7} + 127898212 T^{8} + 782239268 T^{9} + 4732233844 T^{10} + 24471996211 T^{11} + 125471431934 T^{12} + 536165601363 T^{13} + 2294036785474 T^{14} + 7571458632959 T^{15} + 25726538703043 T^{16} + 52687191808815 T^{17} + 129961739795077 T^{18} \))(\( 1 + 16 T + 265 T^{2} + 2821 T^{3} + 30825 T^{4} + 265958 T^{5} + 2261395 T^{6} + 16306323 T^{7} + 115417966 T^{8} + 711331820 T^{9} + 4270464742 T^{10} + 22323356187 T^{11} + 114546440935 T^{12} + 498448111238 T^{13} + 2137527474525 T^{14} + 7237914199789 T^{15} + 25156947440245 T^{16} + 56199671262736 T^{17} + 129961739795077 T^{18} \))(\( 1 + 4 T + 199 T^{2} + 905 T^{3} + 19593 T^{4} + 94140 T^{5} + 1296903 T^{6} + 5973127 T^{7} + 63514660 T^{8} + 260942712 T^{9} + 2350042420 T^{10} + 8177210863 T^{11} + 65692027659 T^{12} + 176433516540 T^{13} + 1358656149501 T^{14} + 2321982400145 T^{15} + 18891443549467 T^{16} + 14049917815684 T^{17} + 129961739795077 T^{18} \))(\( 1 - 14 T + 337 T^{2} - 3471 T^{3} + 47889 T^{4} - 392212 T^{5} + 3960123 T^{6} - 26698793 T^{7} + 214442638 T^{8} - 1201000340 T^{9} + 7934377606 T^{10} - 36550647617 T^{11} + 200592110319 T^{12} - 735068434132 T^{13} + 3320812756773 T^{14} - 8905636365639 T^{15} + 31992042593821 T^{16} - 49174712354894 T^{17} + 129961739795077 T^{18} \))(\( 1 - 10 T + 220 T^{2} - 1553 T^{3} + 21750 T^{4} - 122189 T^{5} + 1420560 T^{6} - 6947203 T^{7} + 72917701 T^{8} - 321967157 T^{9} + 3020323856 T^{10} - 11912784809 T^{11} + 99824332669 T^{12} - 351896673559 T^{13} + 2662358150160 T^{14} - 8473068761873 T^{15} + 55804549395750 T^{16} - 147429205187549 T^{17} + 772745479862620 T^{18} - 1299617397950770 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 12 T + 316 T^{2} + 2769 T^{3} + 42506 T^{4} + 296565 T^{5} + 3444344 T^{6} + 20109567 T^{7} + 194618729 T^{8} + 980068335 T^{9} + 8230616688 T^{10} + 36262528395 T^{11} + 266433040001 T^{12} + 1018609897251 T^{13} + 6455255195384 T^{14} + 20564990607705 T^{15} + 109058766740954 T^{16} + 262866367781277 T^{17} + 1109943507439036 T^{18} + 1559540877540924 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 5 T + 192 T^{2} + 546 T^{3} + 18077 T^{4} + 28360 T^{5} + 1158424 T^{6} + 685440 T^{7} + 56455010 T^{8} + 3760805 T^{9} + 2277323592 T^{10} + 139149785 T^{11} + 77286908690 T^{12} + 34719592320 T^{13} + 2171073082264 T^{14} + 1966594620520 T^{15} + 46380636295493 T^{16} + 51832804914618 T^{17} + 674396055152832 T^{18} + 649808698975385 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 8 T + 197 T^{2} + 1579 T^{3} + 21296 T^{4} + 165610 T^{5} + 1619742 T^{6} + 12033248 T^{7} + 93804021 T^{8} + 652027294 T^{9} + 4308623407 T^{10} + 27269000138 T^{11} + 159419066059 T^{12} + 892625365486 T^{13} + 4751455075713 T^{14} + 22552244104928 T^{15} + 112319319599094 T^{16} + 424909950594490 T^{17} + 2021669255424368 T^{18} + 5546205057741259 T^{19} + 25602462739630169 T^{20} + 38468674979342792 T^{21} + 177917621779460413 T^{22} \))(\( 1 + 10 T + 319 T^{2} + 2837 T^{3} + 47082 T^{4} + 374492 T^{5} + 4295164 T^{6} + 30718176 T^{7} + 273936311 T^{8} + 1762949114 T^{9} + 13082515083 T^{10} + 75043044598 T^{11} + 484053058071 T^{12} + 2413477337066 T^{13} + 13875695961083 T^{14} + 57570807450336 T^{15} + 297843667723948 T^{16} + 960844014359228 T^{17} + 4469582639175906 T^{18} + 9964904210773877 T^{19} + 41457794994629563 T^{20} + 48085843724178490 T^{21} + 177917621779460413 T^{22} \))(\( 1 - 18 T + 400 T^{2} - 4703 T^{3} + 61741 T^{4} - 545409 T^{5} + 5344224 T^{6} - 37731872 T^{7} + 304942131 T^{8} - 1806250110 T^{9} + 13101978320 T^{10} - 70072610276 T^{11} + 494967445438 T^{12} - 2592686580212 T^{13} + 17936608320080 T^{14} - 91491986821830 T^{15} + 571510649177091 T^{16} - 2616477309497504 T^{17} + 13711816652411616 T^{18} - 51776700175232397 T^{19} + 216863993964536461 T^{20} - 611210062256247131 T^{21} + 1923433748967139600 T^{22} - 3202517192030287434 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + T + 240 T^{2} + 884 T^{3} + 29557 T^{4} + 168552 T^{5} + 2647062 T^{6} + 17648308 T^{7} + 190289403 T^{8} + 1293660034 T^{9} + 11221241000 T^{10} + 72896296341 T^{11} + 548585617487 T^{12} + 3292627621292 T^{13} + 22284414206436 T^{14} + 121827221987804 T^{15} + 751013710339703 T^{16} + 3692416098560673 T^{17} + 21030412253801000 T^{18} + 89707505770314538 T^{19} + 488230546629943827 T^{20} + 1675387006661340964 T^{21} + 9297750888255030102 T^{22} + 21905311165939818504 T^{23} + \)\(14\!\cdots\!93\)\( T^{24} + \)\(15\!\cdots\!92\)\( T^{25} + \)\(15\!\cdots\!40\)\( T^{26} + \)\(24\!\cdots\!97\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 - 3 T + 131 T^{2} + 83 T^{3} + 11701 T^{4} + 24020 T^{5} + 837795 T^{6} + 3030996 T^{7} + 50616661 T^{8} + 216229926 T^{9} + 2787134275 T^{10} + 12194090517 T^{11} + 133398808365 T^{12} + 567199674001 T^{13} + 5674087233247 T^{14} + 22419138935784 T^{15} + 209941227630139 T^{16} + 776496353707369 T^{17} + 6757049840112345 T^{18} + 22853688877431237 T^{19} + 193270919318826175 T^{20} + 554786831554315734 T^{21} + 4805134642934712913 T^{22} + 10646311174916735316 T^{23} + \)\(10\!\cdots\!15\)\( T^{24} + \)\(11\!\cdots\!80\)\( T^{25} + \)\(20\!\cdots\!13\)\( T^{26} + \)\(54\!\cdots\!23\)\( T^{27} + \)\(31\!\cdots\!07\)\( T^{28} - \)\(27\!\cdots\!67\)\( T^{29} + \)\(33\!\cdots\!93\)\( T^{30} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 10 T + 62 T^{2} + 410 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 86 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 + 2 T + 70 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 + 10 T - T^{2} - 364 T^{3} - 41 T^{4} + 16810 T^{5} + 68921 T^{6} \))(\( 1 - 10 T + 93 T^{2} - 615 T^{3} + 4027 T^{4} - 29860 T^{5} + 165107 T^{6} - 1033815 T^{7} + 6409653 T^{8} - 28257610 T^{9} + 115856201 T^{10} \))(\( 1 + 162 T^{2} - 112 T^{3} + 12639 T^{4} - 12464 T^{5} + 627932 T^{6} - 511024 T^{7} + 21246159 T^{8} - 7719152 T^{9} + 457773282 T^{10} + 4750104241 T^{12} \))(\( 1 + 6 T + 160 T^{2} + 933 T^{3} + 14271 T^{4} + 75809 T^{5} + 908892 T^{6} + 4330220 T^{7} + 43151784 T^{8} + 177539020 T^{9} + 1527847452 T^{10} + 5224832089 T^{11} + 40326435231 T^{12} + 108093835533 T^{13} + 760016678560 T^{14} + 1168525643286 T^{15} + 7984925229121 T^{16} \))(\( 1 - 10 T + 305 T^{2} - 2593 T^{3} + 42979 T^{4} - 313468 T^{5} + 3711175 T^{6} - 23176807 T^{7} + 216910916 T^{8} - 1147525828 T^{9} + 8893347556 T^{10} - 38960212567 T^{11} + 255777892175 T^{12} - 885785649148 T^{13} + 4979383662779 T^{14} - 12317020296913 T^{15} + 59400053533705 T^{16} - 79849252291210 T^{17} + 327381934393961 T^{18} \))(\( 1 - 18 T + 405 T^{2} - 5187 T^{3} + 68489 T^{4} - 678734 T^{5} + 6603241 T^{6} - 52672845 T^{7} + 406456472 T^{8} - 2650507104 T^{9} + 16664715352 T^{10} - 88543052445 T^{11} + 455101972961 T^{12} - 1917940066574 T^{13} + 7934875350289 T^{14} - 24638790698067 T^{15} + 78875480921805 T^{16} - 143728654124178 T^{17} + 327381934393961 T^{18} \))(\( 1 + 18 T + 345 T^{2} + 4085 T^{3} + 49063 T^{4} + 455052 T^{5} + 4188125 T^{6} + 32041759 T^{7} + 242001654 T^{8} + 1561168108 T^{9} + 9922067814 T^{10} + 53862196879 T^{11} + 288649763125 T^{12} + 1285868194572 T^{13} + 5684252789663 T^{14} + 19404175824485 T^{15} + 67190224488945 T^{16} + 143728654124178 T^{17} + 327381934393961 T^{18} \))(\( 1 - 2 T + 169 T^{2} - 579 T^{3} + 15219 T^{4} - 66790 T^{5} + 963781 T^{6} - 4783605 T^{7} + 47526626 T^{8} - 235382632 T^{9} + 1948591666 T^{10} - 8041240005 T^{11} + 66424750301 T^{12} - 188732577190 T^{13} + 1763215523019 T^{14} - 2750310355539 T^{15} + 32913472285889 T^{16} - 15969850458242 T^{17} + 327381934393961 T^{18} \))(\( 1 - 20 T + 493 T^{2} - 6609 T^{3} + 93979 T^{4} - 947284 T^{5} + 9733005 T^{6} - 77446719 T^{7} + 619706166 T^{8} - 3963833944 T^{9} + 25407952806 T^{10} - 130187934639 T^{11} + 670808437605 T^{12} - 2676798183124 T^{13} + 10888049913779 T^{14} - 31393438928769 T^{15} + 96013857023333 T^{16} - 159698504582420 T^{17} + 327381934393961 T^{18} \))(\( 1 + 2 T + 221 T^{2} + 223 T^{3} + 24657 T^{4} + 12100 T^{5} + 1839835 T^{6} + 407801 T^{7} + 99897770 T^{8} + 12312092 T^{9} + 4095808570 T^{10} + 685513481 T^{11} + 126803268035 T^{12} + 34191708100 T^{13} + 2856666348057 T^{14} + 1059273245743 T^{15} + 43040694527701 T^{16} + 15969850458242 T^{17} + 327381934393961 T^{18} \))(\( 1 + 18 T + 238 T^{2} + 2393 T^{3} + 20962 T^{4} + 161885 T^{5} + 1160836 T^{6} + 8080847 T^{7} + 56310233 T^{8} + 374883769 T^{9} + 2462477380 T^{10} + 15370234529 T^{11} + 94657501673 T^{12} + 556940056087 T^{13} + 3280245096196 T^{14} + 18755381098885 T^{15} + 99571685099842 T^{16} + 466046977397233 T^{17} + 1900412204530798 T^{18} + 5892874819091298 T^{19} + 13422659310152401 T^{20} \))(\( 1 - 4 T + 178 T^{2} - 871 T^{3} + 17106 T^{4} - 96357 T^{5} + 1184836 T^{6} - 7246923 T^{7} + 64574417 T^{8} - 396259501 T^{9} + 2896480188 T^{10} - 16246639541 T^{11} + 108549594977 T^{12} - 499465180083 T^{13} + 3348063360196 T^{14} - 11163555959757 T^{15} + 81255283146546 T^{16} - 169630972550351 T^{17} + 1421316690783538 T^{18} - 1309527737575844 T^{19} + 13422659310152401 T^{20} \))(\( 1 - 4 T + 278 T^{2} - 797 T^{3} + 35548 T^{4} - 67687 T^{5} + 2842396 T^{6} - 3261309 T^{7} + 164091039 T^{8} - 114961499 T^{9} + 7459923348 T^{10} - 4713421459 T^{11} + 275837036559 T^{12} - 224772677589 T^{13} + 8031931763356 T^{14} - 7841958677087 T^{15} + 168856705559068 T^{16} - 155219156283157 T^{17} + 2219809213695638 T^{18} - 1309527737575844 T^{19} + 13422659310152401 T^{20} \))(\( 1 - 4 T + 275 T^{2} - 1143 T^{3} + 38766 T^{4} - 158458 T^{5} + 3644434 T^{6} - 14144600 T^{7} + 250935913 T^{8} - 899641506 T^{9} + 13215630467 T^{10} - 42526117282 T^{11} + 541840849147 T^{12} - 1512297371586 T^{13} + 17294754059873 T^{14} - 39969259040600 T^{15} + 422230278035234 T^{16} - 752692017820378 T^{17} + 7549844181270846 T^{18} - 9126769536885303 T^{19} + 90030031958339275 T^{20} - 53690637240609604 T^{21} + 550329031716248441 T^{22} \))(\( 1 + 2 T + 235 T^{2} + 329 T^{3} + 26186 T^{4} + 12410 T^{5} + 1884556 T^{6} - 1260320 T^{7} + 101198111 T^{8} - 172222516 T^{9} + 4539153071 T^{10} - 9570361186 T^{11} + 186105275911 T^{12} - 289506049396 T^{13} + 6974675008231 T^{14} - 3561363103520 T^{15} + 218337498731756 T^{16} + 58948793630810 T^{17} + 5099835415847866 T^{18} + 2627040400380809 T^{19} + 76934754582580835 T^{20} + 26845318620304802 T^{21} + 550329031716248441 T^{22} \))(\( 1 - 24 T + 592 T^{2} - 9145 T^{3} + 135923 T^{4} - 1587575 T^{5} + 17745648 T^{6} - 168497974 T^{7} + 1537561483 T^{8} - 12356100946 T^{9} + 95927124352 T^{10} - 667506056728 T^{11} + 4502339860738 T^{12} - 27367748325848 T^{13} + 161253496035712 T^{14} - 851594833299266 T^{15} + 4344781273763563 T^{16} - 19521535143836774 T^{17} + 84293677824093168 T^{18} - 309187016356628575 T^{19} + 1085334991917813683 T^{20} - 2993907790032773345 T^{21} + 7946214311610221392 T^{22} - 13207896761189962584 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 16 T + 302 T^{2} + 3549 T^{3} + 42886 T^{4} + 415443 T^{5} + 3972034 T^{6} + 33427935 T^{7} + 273739496 T^{8} + 2061101889 T^{9} + 15157144858 T^{10} + 105047722746 T^{11} + 719033079201 T^{12} + 4706763404598 T^{13} + 30747567688428 T^{14} + 192977299588518 T^{15} + 1208694606136881 T^{16} + 7239994099377066 T^{17} + 42830468811086938 T^{18} + 238791434733463689 T^{19} + 1300291140878802536 T^{20} + 6510233208266265735 T^{21} + 31716394497526402114 T^{22} + \)\(13\!\cdots\!23\)\( T^{23} + \)\(57\!\cdots\!86\)\( T^{24} + \)\(19\!\cdots\!09\)\( T^{25} + \)\(68\!\cdots\!62\)\( T^{26} + \)\(14\!\cdots\!36\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 + 291 T^{2} + 307 T^{3} + 39842 T^{4} + 85756 T^{5} + 3535218 T^{6} + 11415230 T^{7} + 238801324 T^{8} + 1003089484 T^{9} + 13512049536 T^{10} + 67792818653 T^{11} + 670668767475 T^{12} + 3751815794808 T^{13} + 29952562762201 T^{14} + 170438037304868 T^{15} + 1228055073250241 T^{16} + 6306802351072248 T^{17} + 46223162123144475 T^{18} + 191566303029719933 T^{19} + 1565454726964772736 T^{20} + 4764779612050901644 T^{21} + 46507578457441418444 T^{22} + 91149758023218912830 T^{23} + \)\(11\!\cdots\!98\)\( T^{24} + \)\(11\!\cdots\!56\)\( T^{25} + \)\(21\!\cdots\!22\)\( T^{26} + \)\(69\!\cdots\!67\)\( T^{27} + \)\(26\!\cdots\!11\)\( T^{28} + \)\(15\!\cdots\!01\)\( T^{30} \))
$43$ (\( 1 - T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 3 T + 57 T^{2} + 129 T^{3} + 1849 T^{4} \))(\( 1 + 3 T + 87 T^{2} + 129 T^{3} + 1849 T^{4} \))(\( 1 + T + 57 T^{2} + 43 T^{3} + 1849 T^{4} \))(\( 1 - 9 T + 120 T^{2} - 720 T^{3} + 5160 T^{4} - 16641 T^{5} + 79507 T^{6} \))(\( 1 + 25 T + 344 T^{2} + 3373 T^{3} + 27232 T^{4} + 190396 T^{5} + 1170976 T^{6} + 6236677 T^{7} + 27350408 T^{8} + 85470025 T^{9} + 147008443 T^{10} \))(\( 1 - 12 T + 259 T^{2} - 2254 T^{3} + 27430 T^{4} - 181840 T^{5} + 1563900 T^{6} - 7819120 T^{7} + 50718070 T^{8} - 179208778 T^{9} + 885469459 T^{10} - 1764101316 T^{11} + 6321363049 T^{12} \))(\( 1 + 19 T + 258 T^{2} + 2289 T^{3} + 18927 T^{4} + 137407 T^{5} + 1154882 T^{6} + 8749350 T^{7} + 64231879 T^{8} + 376222050 T^{9} + 2135376818 T^{10} + 10924818349 T^{11} + 64707646527 T^{12} + 336502326027 T^{13} + 1630911666642 T^{14} + 5164553611033 T^{15} + 11688200277601 T^{16} \))(\( 1 + 17 T + 233 T^{2} + 2784 T^{3} + 27999 T^{4} + 258892 T^{5} + 2171739 T^{6} + 16696805 T^{7} + 121449257 T^{8} + 821565760 T^{9} + 5222318051 T^{10} + 30872392445 T^{11} + 172668452673 T^{12} + 885100228492 T^{13} + 4116089395557 T^{14} + 17598674728416 T^{15} + 63333736387931 T^{16} + 198699404719217 T^{17} + 502592611936843 T^{18} \))(\( 1 - 7 T + 191 T^{2} - 706 T^{3} + 15597 T^{4} - 17440 T^{5} + 811461 T^{6} + 888253 T^{7} + 35770279 T^{8} + 73478904 T^{9} + 1538121997 T^{10} + 1642379797 T^{11} + 64516829727 T^{12} - 59623889440 T^{13} + 2292890685471 T^{14} - 4462882312594 T^{15} + 51917354721437 T^{16} - 81817401943207 T^{17} + 502592611936843 T^{18} \))(\( 1 - 7 T + 61 T^{2} - 420 T^{3} + 5141 T^{4} - 19212 T^{5} + 161003 T^{6} - 985085 T^{7} + 7221957 T^{8} - 15032210 T^{9} + 310544151 T^{10} - 1821422165 T^{11} + 12800865521 T^{12} - 65682004812 T^{13} + 755770405463 T^{14} - 2654972480580 T^{15} + 16580935277527 T^{16} - 81817401943207 T^{17} + 502592611936843 T^{18} \))(\( 1 - 4 T + 294 T^{2} - 1178 T^{3} + 41242 T^{4} - 156793 T^{5} + 3623594 T^{6} - 12457441 T^{7} + 219052649 T^{8} - 651472055 T^{9} + 9419263907 T^{10} - 23033808409 T^{11} + 288101088158 T^{12} - 536044065193 T^{13} + 6062922206206 T^{14} - 7446565671722 T^{15} + 79914671665458 T^{16} - 46752801110404 T^{17} + 502592611936843 T^{18} \))(\( 1 - 20 T + 298 T^{2} - 3208 T^{3} + 31722 T^{4} - 267061 T^{5} + 2171148 T^{6} - 15926071 T^{7} + 114361811 T^{8} - 753220727 T^{9} + 4917557873 T^{10} - 29447305279 T^{11} + 172621464036 T^{12} - 913028413861 T^{13} + 4663401828846 T^{14} - 20278932661192 T^{15} + 81001946109886 T^{16} - 233764005552020 T^{17} + 502592611936843 T^{18} \))(\( 1 - 5 T + 123 T^{2} - 1154 T^{3} + 10921 T^{4} - 107984 T^{5} + 828763 T^{6} - 6379915 T^{7} + 50015045 T^{8} - 295475136 T^{9} + 2150646935 T^{10} - 11796462835 T^{11} + 65892459841 T^{12} - 369175807184 T^{13} + 1605479206003 T^{14} - 7294852958546 T^{15} + 33433689166161 T^{16} - 58441001388005 T^{17} + 502592611936843 T^{18} \))(\( 1 - 12 T + 363 T^{2} - 3490 T^{3} + 59662 T^{4} - 477863 T^{5} + 5989474 T^{6} - 40894050 T^{7} + 413451091 T^{8} - 2430753754 T^{9} + 20706867338 T^{10} - 104522411422 T^{11} + 764471067259 T^{12} - 3251363233350 T^{13} + 20476819700674 T^{14} - 70249895597309 T^{15} + 377145162229438 T^{16} - 948646952763430 T^{17} + 4242816700769163 T^{18} - 6031111343242116 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 17 T + 460 T^{2} - 5855 T^{3} + 90846 T^{4} - 921856 T^{5} + 10441040 T^{6} - 87166185 T^{7} + 783676608 T^{8} - 5457455619 T^{9} + 40379761954 T^{10} - 234670591617 T^{11} + 1449018048192 T^{12} - 6930321870795 T^{13} + 35695837993040 T^{14} - 135520615230208 T^{15} + 574270547549454 T^{16} - 1591497968031485 T^{17} + 5376572127696460 T^{18} - 8544074402926331 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 19 T + 438 T^{2} - 5579 T^{3} + 78112 T^{4} - 777998 T^{5} + 8241420 T^{6} - 67747847 T^{7} + 585058732 T^{8} - 4067915183 T^{9} + 29578624826 T^{10} - 174920352869 T^{11} + 1081773595468 T^{12} - 5386428071429 T^{13} + 28175774937420 T^{14} - 114372274637114 T^{15} + 493774310483488 T^{16} - 1516476031365953 T^{17} + 5119431721589238 T^{18} - 9549259626800017 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 30 T + 731 T^{2} + 12239 T^{3} + 179360 T^{4} + 2166645 T^{5} + 23769869 T^{6} + 228499151 T^{7} + 2033334848 T^{8} + 16268540337 T^{9} + 121507108082 T^{10} + 823769045648 T^{11} + 5224805647526 T^{12} + 30080531083113 T^{13} + 161664353759936 T^{14} + 781193125937951 T^{15} + 3494371432003967 T^{16} + 13696149643300605 T^{17} + 48753386088151520 T^{18} + 143051883197558639 T^{19} + 367395199325832233 T^{20} + 648344469398527470 T^{21} + 929293739471222707 T^{22} \))(\( 1 - 24 T + 570 T^{2} - 8624 T^{3} + 124347 T^{4} - 1424297 T^{5} + 15555778 T^{6} - 145133755 T^{7} + 1294429263 T^{8} - 10163934916 T^{9} + 76425625783 T^{10} - 511951909880 T^{11} + 3286301908669 T^{12} - 18793115659684 T^{13} + 102916187413341 T^{14} - 496183426727755 T^{15} + 2286830703433654 T^{16} - 9003498426601553 T^{17} + 33799828835322129 T^{18} - 100799039194031024 T^{19} + 286477788804000510 T^{20} - 518675575518821976 T^{21} + 929293739471222707 T^{22} \))(\( 1 + 316 T^{2} + 33 T^{3} + 49829 T^{4} + 12802 T^{5} + 5191007 T^{6} + 2081294 T^{7} + 398575433 T^{8} + 197860778 T^{9} + 23828620162 T^{10} + 12384779685 T^{11} + 1140340377072 T^{12} + 532545526455 T^{13} + 44059118679538 T^{14} + 15731316876446 T^{15} + 1362650088915833 T^{16} + 305967790365242 T^{17} + 32814239836900343 T^{18} + 3479821859391814 T^{19} + 582411331632580229 T^{20} + 16585556193915819 T^{21} + 6829228410997822684 T^{22} + 39959630797262576401 T^{24} \))(\( 1 + 15 T + 336 T^{2} + 3374 T^{3} + 45297 T^{4} + 338699 T^{5} + 3582506 T^{6} + 20769669 T^{7} + 197655186 T^{8} + 856749570 T^{9} + 8209699801 T^{10} + 22145523430 T^{11} + 275650539450 T^{12} + 294459638821 T^{13} + 9893392599182 T^{14} + 12661764469303 T^{15} + 509677847443050 T^{16} + 1760724131349010 T^{17} + 28067329889358601 T^{18} + 125949420326619510 T^{19} + 1249450189223622114 T^{20} + 5645582580732113583 T^{21} + 41873047623707248106 T^{22} + \)\(17\!\cdots\!57\)\( T^{23} + \)\(97\!\cdots\!53\)\( T^{24} + \)\(31\!\cdots\!18\)\( T^{25} + \)\(13\!\cdots\!36\)\( T^{26} + \)\(25\!\cdots\!45\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 + 13 T + 363 T^{2} + 3507 T^{3} + 64199 T^{4} + 539267 T^{5} + 7851519 T^{6} + 58584272 T^{7} + 724633166 T^{8} + 4902529455 T^{9} + 53628994839 T^{10} + 331833674252 T^{11} + 3264883402003 T^{12} + 18550128996653 T^{13} + 166502977137532 T^{14} + 870403433097786 T^{15} + 7159628016913876 T^{16} + 34299188514811397 T^{17} + 259581084643052521 T^{18} + 1134473297366411852 T^{19} + 7883915030936425677 T^{20} + 30990668543471108295 T^{21} + \)\(19\!\cdots\!62\)\( T^{22} + \)\(68\!\cdots\!72\)\( T^{23} + \)\(39\!\cdots\!17\)\( T^{24} + \)\(11\!\cdots\!83\)\( T^{25} + \)\(59\!\cdots\!93\)\( T^{26} + \)\(14\!\cdots\!07\)\( T^{27} + \)\(62\!\cdots\!09\)\( T^{28} + \)\(96\!\cdots\!37\)\( T^{29} + \)\(31\!\cdots\!07\)\( T^{30} \))
$47$ (\( 1 - 7 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( ( 1 + 4 T + 47 T^{2} )^{2} \))(\( 1 + 14 T + 138 T^{2} + 658 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 46 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 2 T + 81 T^{2} - 36 T^{3} + 3807 T^{4} + 4418 T^{5} + 103823 T^{6} \))(\( 1 - 3 T + 137 T^{2} - 818 T^{3} + 8733 T^{4} - 62242 T^{5} + 410451 T^{6} - 1806962 T^{7} + 14223751 T^{8} - 14639043 T^{9} + 229345007 T^{10} \))(\( 1 - 2 T + 158 T^{2} - 222 T^{3} + 11087 T^{4} - 11004 T^{5} + 550756 T^{6} - 517188 T^{7} + 24491183 T^{8} - 23048706 T^{9} + 770989598 T^{10} - 458690014 T^{11} + 10779215329 T^{12} \))(\( 1 + 7 T + 262 T^{2} + 1287 T^{3} + 31427 T^{4} + 121039 T^{5} + 2455918 T^{6} + 8002831 T^{7} + 136663328 T^{8} + 376133057 T^{9} + 5425122862 T^{10} + 12566632097 T^{11} + 153353734787 T^{12} + 295167024009 T^{13} + 2824154416198 T^{14} + 3546361843241 T^{15} + 23811286661761 T^{16} \))(\( 1 + 5 T + 171 T^{2} + 1432 T^{3} + 18895 T^{4} + 166252 T^{5} + 1568597 T^{6} + 12737544 T^{7} + 95627888 T^{8} + 707398878 T^{9} + 4494510736 T^{10} + 28137234696 T^{11} + 162856446331 T^{12} + 811256725612 T^{13} + 4333473907265 T^{14} + 15435836351128 T^{15} + 86632553599173 T^{16} + 119056433308805 T^{17} + 1119130473102767 T^{18} \))(\( 1 - 15 T + 257 T^{2} - 2386 T^{3} + 24847 T^{4} - 170378 T^{5} + 1469333 T^{6} - 8622622 T^{7} + 71632534 T^{8} - 404371246 T^{9} + 3366729098 T^{10} - 19047371998 T^{11} + 152550560059 T^{12} - 831390289418 T^{13} + 5698535388929 T^{14} - 25719207774994 T^{15} + 130202141958991 T^{16} - 357169299926415 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 11 T + 245 T^{2} + 2038 T^{3} + 29393 T^{4} + 221144 T^{5} + 2501209 T^{6} + 16628618 T^{7} + 154121744 T^{8} + 896462330 T^{9} + 7243721968 T^{10} + 36732617162 T^{11} + 259683022007 T^{12} + 1079112175064 T^{13} + 6741137790751 T^{14} + 21968040840502 T^{15} + 124122664513435 T^{16} + 261924153279371 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 222 T^{2} - 498 T^{3} + 22064 T^{4} - 114863 T^{5} + 1342868 T^{6} - 11892176 T^{7} + 63370253 T^{8} - 713495866 T^{9} + 2978401891 T^{10} - 26269816784 T^{11} + 139420584364 T^{12} - 560494798703 T^{13} + 5060268234448 T^{14} - 5368049233842 T^{15} + 112470332742786 T^{16} + 1119130473102767 T^{18} \))(\( 1 + 6 T + 334 T^{2} + 1714 T^{3} + 52372 T^{4} + 230217 T^{5} + 5070928 T^{6} + 19104728 T^{7} + 335510073 T^{8} + 1076038498 T^{9} + 15768973431 T^{10} + 42202344152 T^{11} + 526478957744 T^{12} + 1123385520777 T^{13} + 12011256706604 T^{14} + 18475575073906 T^{15} + 169212122234642 T^{16} + 142867719970566 T^{17} + 1119130473102767 T^{18} \))(\( 1 - 13 T + 299 T^{2} - 3256 T^{3} + 43497 T^{4} - 405584 T^{5} + 4045121 T^{6} - 32451124 T^{7} + 262651918 T^{8} - 1807952110 T^{9} + 12344640146 T^{10} - 71684532916 T^{11} + 419976597583 T^{12} - 1979120538704 T^{13} + 9975819769479 T^{14} - 35097125111224 T^{15} + 151480313018437 T^{16} - 309546726602893 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 36 T + 813 T^{2} + 13040 T^{3} + 170094 T^{4} + 1865695 T^{5} + 18186994 T^{6} + 159801787 T^{7} + 1302432025 T^{8} + 9841123220 T^{9} + 69881745858 T^{10} + 462532791340 T^{11} + 2877072343225 T^{12} + 16591100931701 T^{13} + 88746729068914 T^{14} + 427887832834865 T^{15} + 1833479852170926 T^{16} + 6606365490837520 T^{17} + 19358576056011693 T^{18} + 40288697031699612 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 21 T + 424 T^{2} - 6033 T^{3} + 78380 T^{4} - 862634 T^{5} + 8757000 T^{6} - 79302854 T^{7} + 669562711 T^{8} - 5128198592 T^{9} + 36836951704 T^{10} - 241025333824 T^{11} + 1479064028599 T^{12} - 8233460210842 T^{13} + 42731366517000 T^{14} - 197840800768438 T^{15} + 844874897487020 T^{16} - 3056457285753279 T^{17} + 10095985544586664 T^{18} - 23501739935158107 T^{19} + 52599132235830049 T^{20} \))(\( 1 - T + 262 T^{2} + 153 T^{3} + 30894 T^{4} + 83172 T^{5} + 2165372 T^{6} + 12067076 T^{7} + 107046149 T^{8} + 936776498 T^{9} + 4811878804 T^{10} + 44028495406 T^{11} + 236464943141 T^{12} + 1252840031548 T^{13} + 10566324606332 T^{14} + 19075082922204 T^{15} + 333013078374126 T^{16} + 77513337430839 T^{17} + 6238557105381382 T^{18} - 1119130473102767 T^{19} + 52599132235830049 T^{20} \))(\( 1 + 3 T + 409 T^{2} + 880 T^{3} + 78284 T^{4} + 117367 T^{5} + 9359720 T^{6} + 9619768 T^{7} + 783709483 T^{8} + 571072870 T^{9} + 48580055095 T^{10} + 28339767472 T^{11} + 2283262589465 T^{12} + 1261499969830 T^{13} + 81367069653509 T^{14} + 46941399134008 T^{15} + 2146605048918040 T^{16} + 1265124165518743 T^{17} + 39660484362325492 T^{18} + 20953932262349680 T^{19} + 457724363499031703 T^{20} + 157797396707490147 T^{21} + 2472159215084012303 T^{22} \))(\( 1 - 2 T + 212 T^{2} - 828 T^{3} + 21145 T^{4} - 135423 T^{5} + 1494800 T^{6} - 12228020 T^{7} + 94899263 T^{8} - 744129267 T^{9} + 5452191061 T^{10} - 36881557944 T^{11} + 256252979867 T^{12} - 1643781550803 T^{13} + 9852726182449 T^{14} - 59668836861620 T^{15} + 342824916463600 T^{16} - 1459753677499167 T^{17} + 10712545882190135 T^{18} - 19715745355938108 T^{19} + 237255660297786604 T^{20} - 105198264471660098 T^{21} + 2472159215084012303 T^{22} \))(\( 1 - 5 T + 346 T^{2} - 1713 T^{3} + 56181 T^{4} - 253035 T^{5} + 5702186 T^{6} - 21506087 T^{7} + 410639379 T^{8} - 1219863618 T^{9} + 23208237052 T^{10} - 55748468730 T^{11} + 1140261929070 T^{12} - 2620178030310 T^{13} + 51266995647868 T^{14} - 126649900411614 T^{15} + 2003789175558099 T^{16} - 4932313673557609 T^{17} + 61465090740009194 T^{18} - 128193381286355205 T^{19} + 1337741895944394741 T^{20} - 1917070500425039871 T^{21} + 18199299753597196954 T^{22} - 12360796075420061515 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 8 T + 289 T^{2} + 2362 T^{3} + 44718 T^{4} + 364149 T^{5} + 4864454 T^{6} + 38963871 T^{7} + 413624720 T^{8} + 3229358318 T^{9} + 28933451071 T^{10} + 217464293092 T^{11} + 1712063558113 T^{12} + 12171411708098 T^{13} + 86785002166068 T^{14} + 572056350280606 T^{15} + 3781948399871617 T^{16} + 22577795301690716 T^{17} + 141186011455588351 T^{18} + 740637206047218226 T^{19} + 4458549922277332880 T^{20} + 19739997911337792273 T^{21} + \)\(11\!\cdots\!94\)\( T^{22} + \)\(40\!\cdots\!83\)\( T^{23} + \)\(23\!\cdots\!82\)\( T^{24} + \)\(58\!\cdots\!86\)\( T^{25} + \)\(33\!\cdots\!49\)\( T^{26} + \)\(43\!\cdots\!16\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 - 6 T + 236 T^{2} - 1058 T^{3} + 26117 T^{4} - 62755 T^{5} + 1664840 T^{6} + 1129038 T^{7} + 69936714 T^{8} + 373370701 T^{9} + 3146709967 T^{10} + 20978621562 T^{11} + 245145540998 T^{12} + 383221503932 T^{13} + 17590302582323 T^{14} - 2302400683852 T^{15} + 826744221369181 T^{16} + 846536302185788 T^{17} + 25451745503035354 T^{18} + 102368981042281722 T^{19} + 721682219408584769 T^{20} + 4024643183618675629 T^{21} + 35431556281608378582 T^{22} + 26883847470021315918 T^{23} + \)\(18\!\cdots\!80\)\( T^{24} - \)\(33\!\cdots\!95\)\( T^{25} + \)\(64\!\cdots\!51\)\( T^{26} - \)\(12\!\cdots\!78\)\( T^{27} + \)\(12\!\cdots\!72\)\( T^{28} - \)\(15\!\cdots\!14\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))
$53$ (\( 1 + 13 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 13 T + 147 T^{2} - 689 T^{3} + 2809 T^{4} \))(\( 1 - 3 T + 107 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 - 13 T + 119 T^{2} - 689 T^{3} + 2809 T^{4} \))(\( 1 + 11 T + 98 T^{2} + 712 T^{3} + 5194 T^{4} + 30899 T^{5} + 148877 T^{6} \))(\( 1 - 22 T + 412 T^{2} - 4808 T^{3} + 49834 T^{4} - 382030 T^{5} + 2641202 T^{6} - 13505672 T^{7} + 61337324 T^{8} - 173590582 T^{9} + 418195493 T^{10} \))(\( 1 - 2 T + 87 T^{2} - 598 T^{3} + 7102 T^{4} - 44548 T^{5} + 450724 T^{6} - 2361044 T^{7} + 19949518 T^{8} - 89028446 T^{9} + 686471847 T^{10} - 836390986 T^{11} + 22164361129 T^{12} \))(\( 1 + 26 T + 466 T^{2} + 6604 T^{3} + 78009 T^{4} + 791550 T^{5} + 7255826 T^{6} + 59916664 T^{7} + 453887083 T^{8} + 3175583192 T^{9} + 20381615234 T^{10} + 117843589350 T^{11} + 615528532329 T^{12} + 2761763035772 T^{13} + 10328592286114 T^{14} + 30542489635762 T^{15} + 62259690411361 T^{16} \))(\( 1 + 24 T + 635 T^{2} + 9974 T^{3} + 153135 T^{4} + 1794104 T^{5} + 20023523 T^{6} + 185341542 T^{7} + 1623719005 T^{8} + 12157983174 T^{9} + 86057107265 T^{10} + 520624391478 T^{11} + 2981042033671 T^{12} + 14156343524024 T^{13} + 64040366820555 T^{14} + 221067337900646 T^{15} + 745941573796495 T^{16} + 1494232569872664 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 4 T + 433 T^{2} + 1608 T^{3} + 85377 T^{4} + 287138 T^{5} + 10060393 T^{6} + 29749398 T^{7} + 780717777 T^{8} + 1955958154 T^{9} + 41378042181 T^{10} + 83566058982 T^{11} + 1497761128661 T^{12} + 2265656933378 T^{13} + 35704276605861 T^{14} + 35640292695432 T^{15} + 508649923549421 T^{16} + 249038761645444 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 16 T + 523 T^{2} + 6354 T^{3} + 115185 T^{4} + 1116480 T^{5} + 14427267 T^{6} + 114190326 T^{7} + 1150196321 T^{8} + 7471217514 T^{9} + 60960405013 T^{10} + 320760625734 T^{11} + 2147888229159 T^{12} + 8809564226880 T^{13} + 48169847861205 T^{14} + 140832350613666 T^{15} + 614373926134751 T^{16} + 996155046581776 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 23 T + 373 T^{2} + 3836 T^{3} + 30233 T^{4} + 153061 T^{5} + 385401 T^{6} - 2970078 T^{7} - 44656139 T^{8} - 401911747 T^{9} - 2366775367 T^{10} - 8342949102 T^{11} + 57377344677 T^{12} + 1207724912341 T^{13} + 12643304339869 T^{14} + 85022489290844 T^{15} + 438167255159201 T^{16} + 1431972879461303 T^{17} + 3299763591802133 T^{18} \))(\( 1 - 15 T + 483 T^{2} - 5670 T^{3} + 101563 T^{4} - 967615 T^{5} + 12405351 T^{6} - 97502542 T^{7} + 978301257 T^{8} - 6350774257 T^{9} + 51849966621 T^{10} - 273884640478 T^{11} + 1846871440827 T^{12} - 7634947772815 T^{13} + 42473188855559 T^{14} - 125671927601430 T^{15} + 567385480541271 T^{16} - 933895356170415 T^{17} + 3299763591802133 T^{18} \))(\( 1 - 22 T + 491 T^{2} - 7108 T^{3} + 99627 T^{4} - 1104726 T^{5} + 11770375 T^{6} - 105785560 T^{7} + 911903901 T^{8} - 6777044994 T^{9} + 48330906753 T^{10} - 297151638040 T^{11} + 1752338118875 T^{12} - 8716819513206 T^{13} + 41663562381111 T^{14} - 157544278904932 T^{15} + 576783169659967 T^{16} - 1369713189049942 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 21 T + 458 T^{2} + 5917 T^{3} + 75896 T^{4} + 742237 T^{5} + 7436742 T^{6} + 63387885 T^{7} + 560781624 T^{8} + 4336221081 T^{9} + 33872463384 T^{10} + 229819717293 T^{11} + 1575235581816 T^{12} + 9436998155145 T^{13} + 58679471452902 T^{14} + 310400168137841 T^{15} + 1682186352246584 T^{16} + 6950765814415529 T^{17} + 28514938208403338 T^{18} + 69295035427844793 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 20 T + 434 T^{2} - 5914 T^{3} + 81878 T^{4} - 888676 T^{5} + 9608886 T^{6} - 87548938 T^{7} + 791216730 T^{8} - 6213763184 T^{9} + 48324004990 T^{10} - 329329448752 T^{11} + 2222527794570 T^{12} - 13034023242626 T^{13} + 75818732414166 T^{14} - 371640297937268 T^{15} + 1814773560520262 T^{16} - 6947241680996018 T^{17} + 27020705638530674 T^{18} - 65995271836042660 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 6 T + 262 T^{2} + 1050 T^{3} + 25644 T^{4} + 61244 T^{5} + 1085656 T^{6} + 1138714 T^{7} + 6402542 T^{8} - 13499098 T^{9} - 1084113186 T^{10} - 715452194 T^{11} + 17984740478 T^{12} + 169528324178 T^{13} + 8566348040536 T^{14} + 25611964773292 T^{15} + 568382876792076 T^{16} + 1233446696828850 T^{17} + 16312038887776582 T^{18} + 19798581550812798 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 5 T + 276 T^{2} + 1510 T^{3} + 42137 T^{4} + 233300 T^{5} + 4536915 T^{6} + 24053034 T^{7} + 374104317 T^{8} + 1846750136 T^{9} + 24522279021 T^{10} + 110391555996 T^{11} + 1299680788113 T^{12} + 5187521132024 T^{13} + 55695528402009 T^{14} + 189790007769354 T^{15} + 1897317405124095 T^{16} + 5170945451395700 T^{17} + 49498803299311669 T^{18} + 94012132521155110 T^{19} + 910734751337388708 T^{20} + 874437351827565245 T^{21} + 9269035929372191597 T^{22} \))(\( 1 - 3 T + 387 T^{2} - 1280 T^{3} + 73310 T^{4} - 252172 T^{5} + 8990200 T^{6} - 30805260 T^{7} + 797190694 T^{8} - 2608887812 T^{9} + 53993953024 T^{10} - 160882747794 T^{11} + 2861679510272 T^{12} - 7328365863908 T^{13} + 118683358950638 T^{14} - 243068318730060 T^{15} + 3759661121168600 T^{16} - 5589231274622188 T^{17} + 86118073661450470 T^{18} - 79692403726542080 T^{19} + 1277008510027425471 T^{20} - 524662411096539147 T^{21} + 9269035929372191597 T^{22} \))(\( 1 - 15 T + 305 T^{2} - 3267 T^{3} + 47109 T^{4} - 438960 T^{5} + 5140772 T^{6} - 42574892 T^{7} + 436563076 T^{8} - 3306878376 T^{9} + 30416687250 T^{10} - 210524517754 T^{11} + 1759227109198 T^{12} - 11157799440962 T^{13} + 85440474485250 T^{14} - 492318131983752 T^{15} + 3444692656479556 T^{16} - 17804627949361756 T^{17} + 113941927089851588 T^{18} - 515651201942849520 T^{19} + 2932991755588805349 T^{20} - 10780327654417568511 T^{21} + 53340678461481479945 T^{22} - \)\(13\!\cdots\!55\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 6 T + 324 T^{2} + 1847 T^{3} + 55604 T^{4} + 290811 T^{5} + 6694500 T^{6} + 32263054 T^{7} + 630763809 T^{8} + 2821235856 T^{9} + 49138133942 T^{10} + 204330165508 T^{11} + 3252236231832 T^{12} + 12595312667282 T^{13} + 185334448559896 T^{14} + 667551571365946 T^{15} + 9135531575216088 T^{16} + 30420062050334516 T^{17} + 387723512244806102 T^{18} + 1179828119669197008 T^{19} + 13980476849779580361 T^{20} + 37899768938962682198 T^{21} + \)\(41\!\cdots\!00\)\( T^{22} + \)\(95\!\cdots\!63\)\( T^{23} + \)\(97\!\cdots\!96\)\( T^{24} + \)\(17\!\cdots\!59\)\( T^{25} + \)\(15\!\cdots\!84\)\( T^{26} + \)\(15\!\cdots\!38\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( 1 - 38 T + 1021 T^{2} - 21113 T^{3} + 369550 T^{4} - 5649486 T^{5} + 77513658 T^{6} - 968453681 T^{7} + 11152049289 T^{8} - 119296415474 T^{9} + 1192853598075 T^{10} - 11199728578696 T^{11} + 99062741459886 T^{12} - 827519814443622 T^{13} + 6538341060258048 T^{14} - 48913174229725172 T^{15} + 346532076193676544 T^{16} - 2324503158772134198 T^{17} + 14748163760323448022 T^{18} - 88371245555357792776 T^{19} + \)\(49\!\cdots\!75\)\( T^{20} - \)\(26\!\cdots\!46\)\( T^{21} + \)\(13\!\cdots\!93\)\( T^{22} - \)\(60\!\cdots\!41\)\( T^{23} + \)\(25\!\cdots\!14\)\( T^{24} - \)\(98\!\cdots\!14\)\( T^{25} + \)\(34\!\cdots\!50\)\( T^{26} - \)\(10\!\cdots\!33\)\( T^{27} + \)\(26\!\cdots\!33\)\( T^{28} - \)\(52\!\cdots\!22\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 11 T + 59 T^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( 1 + 2 T + 114 T^{2} + 118 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 82 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 9 T + 147 T^{2} - 866 T^{3} + 8673 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 - 21 T + 186 T^{2} - 1247 T^{3} + 15310 T^{4} - 157544 T^{5} + 903290 T^{6} - 4340807 T^{7} + 38200494 T^{8} - 254464581 T^{9} + 714924299 T^{10} \))(\( 1 - 3 T + 62 T^{2} - 553 T^{3} + 6167 T^{4} - 20370 T^{5} + 412516 T^{6} - 1201830 T^{7} + 21467327 T^{8} - 113574587 T^{9} + 751276382 T^{10} - 2144772897 T^{11} + 42180533641 T^{12} \))(\( 1 + 17 T + 437 T^{2} + 5468 T^{3} + 81413 T^{4} + 802050 T^{5} + 8853287 T^{6} + 71237211 T^{7} + 633150684 T^{8} + 4202995449 T^{9} + 30818292047 T^{10} + 164724226950 T^{11} + 986510711093 T^{12} + 3909206066932 T^{13} + 18432893201117 T^{14} + 42307075241923 T^{15} + 146830437604321 T^{16} \))(\( 1 + 19 T + 272 T^{2} + 3015 T^{3} + 30368 T^{4} + 277598 T^{5} + 2498362 T^{6} + 21379857 T^{7} + 181132049 T^{8} + 1446807518 T^{9} + 10686790891 T^{10} + 74423282217 T^{11} + 513111089198 T^{12} + 3363755178878 T^{13} + 21710821112032 T^{14} + 127174308927615 T^{15} + 676913203870768 T^{16} + 2789778314482099 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 23 T + 624 T^{2} + 9259 T^{3} + 146388 T^{4} + 1629728 T^{5} + 19041742 T^{6} + 170883333 T^{7} + 1611774001 T^{8} + 12064362626 T^{9} + 95094666059 T^{10} + 594844882173 T^{11} + 3910773930218 T^{12} + 19748002507808 T^{13} + 104656338282012 T^{14} + 390549560982019 T^{15} + 1552918526527056 T^{16} + 3377100064899383 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 2 T + 299 T^{2} + 550 T^{3} + 47196 T^{4} + 80167 T^{5} + 5054384 T^{6} + 7804728 T^{7} + 395148434 T^{8} + 539990030 T^{9} + 23313757606 T^{10} + 27168258168 T^{11} + 1038064331536 T^{12} + 971412479287 T^{13} + 33741567215604 T^{14} + 23199293502550 T^{15} + 744106793960881 T^{16} + 293660875208642 T^{17} + 8662995818654939 T^{18} \))(\( 1 - 9 T + 230 T^{2} - 1145 T^{3} + 18312 T^{4} - 37652 T^{5} + 1061744 T^{6} - 2277979 T^{7} + 88624297 T^{8} - 259246958 T^{9} + 5228833523 T^{10} - 7929644899 T^{11} + 218059920976 T^{12} - 456242876372 T^{13} + 13091693763288 T^{14} - 48296711018945 T^{15} + 572389841508370 T^{16} - 1321473938438889 T^{17} + 8662995818654939 T^{18} \))(\( 1 - 21 T + 516 T^{2} - 6703 T^{3} + 98416 T^{4} - 978496 T^{5} + 11218572 T^{6} - 94334561 T^{7} + 911554971 T^{8} - 6565904646 T^{9} + 53781743289 T^{10} - 328378606841 T^{11} + 2304059098788 T^{12} - 11856789269056 T^{13} + 70359989810384 T^{14} - 282736116995623 T^{15} + 1284144166166604 T^{16} - 3083439189690741 T^{17} + 8662995818654939 T^{18} \))(\( 1 - 43 T + 1232 T^{2} - 25283 T^{3} + 422904 T^{4} - 5872392 T^{5} + 70486296 T^{6} - 735093349 T^{7} + 6779740091 T^{8} - 55202302762 T^{9} + 400004665369 T^{10} - 2558859947869 T^{11} + 14476404986184 T^{12} - 71157893797512 T^{13} + 302344345744296 T^{14} - 1066450432045403 T^{15} + 3066018629297008 T^{16} - 6313708816985803 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 13 T + 425 T^{2} + 4830 T^{3} + 83498 T^{4} + 837647 T^{5} + 10216944 T^{6} + 91417039 T^{7} + 889363057 T^{8} + 7127736941 T^{9} + 59241940758 T^{10} + 420536479519 T^{11} + 3095872801417 T^{12} + 18775140052781 T^{13} + 123802398764784 T^{14} + 598854194284453 T^{15} + 3521990197956218 T^{16} + 12020186671675770 T^{17} + 62402935981836425 T^{18} + 112618945642514207 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 9 T + 463 T^{2} - 4082 T^{3} + 101612 T^{4} - 859171 T^{5} + 13933940 T^{6} - 109769087 T^{7} + 1323840183 T^{8} - 9362791153 T^{9} + 91152075346 T^{10} - 552404678027 T^{11} + 4608287677023 T^{12} - 22544265318973 T^{13} + 168842581132340 T^{14} - 614242224896129 T^{15} + 4286048384329292 T^{16} - 10158675361031158 T^{17} + 67982492610800623 T^{18} - 77966962367894451 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 4 T + 376 T^{2} - 542 T^{3} + 62849 T^{4} + 67055 T^{5} + 6391122 T^{6} + 22760843 T^{7} + 468791946 T^{8} + 2519238602 T^{9} + 28958736180 T^{10} + 148635077518 T^{11} + 1631864764026 T^{12} + 4674599174497 T^{13} + 77443532469042 T^{14} + 47939248869445 T^{15} + 2651004358803209 T^{16} - 1348849104771898 T^{17} + 55208244539224696 T^{18} - 34651983274619756 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 11 T + 512 T^{2} - 4749 T^{3} + 122537 T^{4} - 977559 T^{5} + 18325788 T^{6} - 127351140 T^{7} + 1921247727 T^{8} - 11702824390 T^{9} + 149293481449 T^{10} - 796492462910 T^{11} + 8808315405491 T^{12} - 40737531701590 T^{13} + 394583936923533 T^{14} - 1543159737141540 T^{15} + 13101551139522612 T^{16} - 41233960285562319 T^{17} + 304951886995265803 T^{18} - 697297748182920429 T^{19} + 4435453859151328768 T^{20} - 5622284286307055411 T^{21} + 30155888444737842659 T^{22} \))(\( 1 - T + 224 T^{2} + 133 T^{3} + 36141 T^{4} + 15757 T^{5} + 4070190 T^{6} + 3199184 T^{7} + 364899481 T^{8} + 236484468 T^{9} + 26261474493 T^{10} + 18909200678 T^{11} + 1549426995087 T^{12} + 823202433108 T^{13} + 74942690508299 T^{14} + 38765667433424 T^{15} + 2909877732546810 T^{16} + 664638668581237 T^{17} + 89942353312843479 T^{18} + 19528448201374693 T^{19} + 1940511063378706336 T^{20} - 511116753300641401 T^{21} + 30155888444737842659 T^{22} \))(\( 1 - 15 T + 497 T^{2} - 5972 T^{3} + 111147 T^{4} - 1115036 T^{5} + 15379017 T^{6} - 133502249 T^{7} + 1531622995 T^{8} - 11852322966 T^{9} + 120085400126 T^{10} - 843967286368 T^{11} + 7756624922434 T^{12} - 49794069895712 T^{13} + 418017277838606 T^{14} - 2434218238434114 T^{15} + 18559228746316195 T^{16} - 95444001781248451 T^{17} + 648695143934010897 T^{18} - 2774935997026638484 T^{19} + 16319762648407466187 T^{20} - 51735411029007295708 T^{21} + \)\(25\!\cdots\!97\)\( T^{22} - \)\(45\!\cdots\!85\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 36 T + 800 T^{2} + 11228 T^{3} + 113301 T^{4} + 706097 T^{5} + 2128468 T^{6} - 9773013 T^{7} - 10607461 T^{8} + 2033390616 T^{9} + 37219938784 T^{10} + 303590472216 T^{11} + 1463457167503 T^{12} - 1034423862650 T^{13} - 40220641379624 T^{14} - 61031007896350 T^{15} + 5094294400077943 T^{16} + 62351107593249864 T^{17} + 451007434643629024 T^{18} + 1453720360736978184 T^{19} - 447428365556095501 T^{20} - 24321623313605389647 T^{21} + \)\(31\!\cdots\!28\)\( T^{22} + \)\(61\!\cdots\!83\)\( T^{23} + \)\(57\!\cdots\!01\)\( T^{24} + \)\(33\!\cdots\!52\)\( T^{25} + \)\(14\!\cdots\!00\)\( T^{26} + \)\(37\!\cdots\!44\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 + 18 T + 613 T^{2} + 9172 T^{3} + 182387 T^{4} + 2349109 T^{5} + 35158441 T^{6} + 399343126 T^{7} + 4941206641 T^{8} + 50269339101 T^{9} + 538425977927 T^{10} + 4952774206676 T^{11} + 47089092137177 T^{12} + 393546606396132 T^{13} + 3368429758889681 T^{14} + 25602427657100356 T^{15} + 198737355774491179 T^{16} + 1369935736864935492 T^{17} + 9671110654041275083 T^{18} + 60014553013781702036 T^{19} + \)\(38\!\cdots\!73\)\( T^{20} + \)\(21\!\cdots\!41\)\( T^{21} + \)\(12\!\cdots\!79\)\( T^{22} + \)\(58\!\cdots\!46\)\( T^{23} + \)\(30\!\cdots\!99\)\( T^{24} + \)\(12\!\cdots\!09\)\( T^{25} + \)\(55\!\cdots\!33\)\( T^{26} + \)\(16\!\cdots\!32\)\( T^{27} + \)\(64\!\cdots\!27\)\( T^{28} + \)\(11\!\cdots\!98\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))
$61$ (\( 1 - 6 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 15 T + 167 T^{2} - 915 T^{3} + 3721 T^{4} \))(\( 1 + 19 T + 201 T^{2} + 1159 T^{3} + 3721 T^{4} \))(\( 1 + T - 37 T^{2} + 61 T^{3} + 3721 T^{4} \))(\( 1 - 9 T + 206 T^{2} - 1114 T^{3} + 12566 T^{4} - 33489 T^{5} + 226981 T^{6} \))(\( 1 - 26 T + 547 T^{2} - 7381 T^{3} + 83563 T^{4} - 708520 T^{5} + 5097343 T^{6} - 27464701 T^{7} + 124158607 T^{8} - 359991866 T^{9} + 844596301 T^{10} \))(\( 1 + 18 T + 273 T^{2} + 3482 T^{3} + 34994 T^{4} + 313654 T^{5} + 2699140 T^{6} + 19132894 T^{7} + 130212674 T^{8} + 790347842 T^{9} + 3779914593 T^{10} + 15202733418 T^{11} + 51520374361 T^{12} \))(\( 1 + 117 T^{2} + 253 T^{3} + 13510 T^{4} + 29064 T^{5} + 1010996 T^{6} + 2355402 T^{7} + 73020483 T^{8} + 143679522 T^{9} + 3761916116 T^{10} + 6596975784 T^{11} + 187057311910 T^{12} + 213682864153 T^{13} + 6027883800237 T^{14} + 191707312997281 T^{16} \))(\( 1 + 184 T^{2} - 107 T^{3} + 23133 T^{4} - 35349 T^{5} + 2105984 T^{6} - 2837584 T^{7} + 160711743 T^{8} - 220063166 T^{9} + 9803416323 T^{10} - 10558650064 T^{11} + 478018354304 T^{12} - 489436633509 T^{13} + 19538046231033 T^{14} - 5512680056627 T^{15} + 578264681827864 T^{16} + 11694146092834141 T^{18} \))(\( 1 - 12 T + 272 T^{2} - 3187 T^{3} + 44467 T^{4} - 447587 T^{5} + 4792264 T^{6} - 43060656 T^{7} + 382986649 T^{8} - 3016756990 T^{9} + 23362185589 T^{10} - 160228700976 T^{11} + 1087752874984 T^{12} - 6197218435667 T^{13} + 37556663716567 T^{14} - 164195433088507 T^{15} + 854826051397712 T^{16} - 2300487755967372 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 2 T + 348 T^{2} - 965 T^{3} + 60423 T^{4} - 194607 T^{5} + 6835280 T^{6} - 22728918 T^{7} + 556994785 T^{8} - 1705134628 T^{9} + 33976681885 T^{10} - 84574303878 T^{11} + 1551478689680 T^{12} - 2694497579487 T^{13} + 51033042295323 T^{14} - 49717161258365 T^{15} + 1093674506935308 T^{16} - 383414625994562 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 14 T + 378 T^{2} + 3195 T^{3} + 52101 T^{4} + 260475 T^{5} + 3732090 T^{6} + 7203456 T^{7} + 183524293 T^{8} - 2793938 T^{9} + 11194981873 T^{10} + 26804059776 T^{11} + 847113520290 T^{12} + 3606495434475 T^{13} + 44004311878401 T^{14} + 164607596083395 T^{15} + 1187956792015938 T^{16} + 2683902381961934 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 378 T^{2} - 213 T^{3} + 66867 T^{4} - 75511 T^{5} + 7446012 T^{6} - 11236176 T^{7} + 594640367 T^{8} - 905637462 T^{9} + 36273062387 T^{10} - 41809810896 T^{11} + 1690103249772 T^{12} - 1045513299751 T^{13} + 56475620858967 T^{14} - 10973839738893 T^{15} + 1187956792015938 T^{16} + 11694146092834141 T^{18} \))(\( 1 + 10 T + 236 T^{2} + 1473 T^{3} + 27947 T^{4} + 138579 T^{5} + 2411530 T^{6} + 9032442 T^{7} + 164334623 T^{8} + 540869862 T^{9} + 10024412003 T^{10} + 33609716682 T^{11} + 547371490930 T^{12} + 1918742799939 T^{13} + 23603932824047 T^{14} + 75889511433753 T^{15} + 741687309300956 T^{16} + 1917073129972810 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 2 T + 269 T^{2} + 985 T^{3} + 39081 T^{4} + 178586 T^{5} + 4174189 T^{6} + 19263885 T^{7} + 354834971 T^{8} + 1492227926 T^{9} + 24194541034 T^{10} + 91025903486 T^{11} + 1320340927091 T^{12} + 4372535881185 T^{13} + 57795157197949 T^{14} + 150833075010386 T^{15} + 2013467750402241 T^{16} + 3095601693480685 T^{17} + 51569267196268589 T^{18} + 23388292185668282 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 6 T + 427 T^{2} - 2153 T^{3} + 87513 T^{4} - 374620 T^{5} + 11442591 T^{6} - 41917997 T^{7} + 1066358197 T^{8} - 3380343492 T^{9} + 74537737950 T^{10} - 206200953012 T^{11} + 3967918851037 T^{12} - 9514588877057 T^{13} + 158432295614031 T^{14} - 316402666280620 T^{15} + 4508702521454193 T^{16} - 6766325325953213 T^{17} + 81859022649838987 T^{18} - 70164876557004846 T^{19} + 713342911662882601 T^{20} \))(\( 1 + 18 T + 579 T^{2} + 7993 T^{3} + 146405 T^{4} + 1650448 T^{5} + 22082673 T^{6} + 209469501 T^{7} + 2240011157 T^{8} + 18081424190 T^{9} + 161060962142 T^{10} + 1102966875590 T^{11} + 8335081515197 T^{12} + 47545596806481 T^{13} + 305753179212993 T^{14} + 1393962275792848 T^{15} + 7542840408322205 T^{16} + 25119943488315853 T^{17} + 110998534225425699 T^{18} + 210494629671014538 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 15 T + 533 T^{2} - 6666 T^{3} + 134981 T^{4} - 1436831 T^{5} + 21448049 T^{6} - 197344763 T^{7} + 2379699357 T^{8} - 19060272832 T^{9} + 193787624380 T^{10} - 1349725783396 T^{11} + 11821045087180 T^{12} - 70923275207872 T^{13} + 540146539751217 T^{14} - 2732404210680683 T^{15} + 18114942849066749 T^{16} - 74026071013489991 T^{17} + 424210570748950601 T^{18} - 1277920948439875146 T^{19} + 6232979867480597153 T^{20} - 10700143674943239015 T^{21} + 43513917611435838661 T^{22} \))(\( 1 + 22 T + 618 T^{2} + 9937 T^{3} + 169986 T^{4} + 2182629 T^{5} + 28409784 T^{6} + 304289221 T^{7} + 3247908158 T^{8} + 29662032931 T^{9} + 268209689585 T^{10} + 2107055396584 T^{11} + 16360791064685 T^{12} + 110372424536251 T^{13} + 737213441610998 T^{14} + 4213140171979861 T^{15} + 23994798478608984 T^{16} + 112449863171175069 T^{17} + 534222283723865706 T^{18} + 1904995569253981297 T^{19} + 7226982285371499138 T^{20} + 15693544056583417222 T^{21} + 43513917611435838661 T^{22} \))(\( 1 - 17 T + 634 T^{2} - 7615 T^{3} + 159274 T^{4} - 1374135 T^{5} + 21117796 T^{6} - 121640684 T^{7} + 1623272092 T^{8} - 4428396481 T^{9} + 78245904489 T^{10} + 60399524268 T^{11} + 3609628488004 T^{12} + 3684370980348 T^{13} + 291153010603569 T^{14} - 1005161861653861 T^{15} + 22475567285569372 T^{16} - 102737271757509884 T^{17} + 1087996755599228356 T^{18} - 4318552926975716835 T^{19} + 30533990570328933994 T^{20} - 89050922496931983715 T^{21} + \)\(45\!\cdots\!34\)\( T^{22} - \)\(73\!\cdots\!37\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 + 19 T + 812 T^{2} + 12653 T^{3} + 302669 T^{4} + 4002670 T^{5} + 69528906 T^{6} + 796657719 T^{7} + 11074581272 T^{8} + 111311100780 T^{9} + 1299083256663 T^{10} + 11529535430834 T^{11} + 116004513520730 T^{12} + 910789974264773 T^{13} + 8020722386537382 T^{14} + 55558188430151153 T^{15} + 431652794810636330 T^{16} + 2616985481626132154 T^{17} + 17986900217518088583 T^{18} + 94012943979026214780 T^{19} + \)\(57\!\cdots\!92\)\( T^{20} + \)\(25\!\cdots\!99\)\( T^{21} + \)\(13\!\cdots\!86\)\( T^{22} + \)\(46\!\cdots\!70\)\( T^{23} + \)\(21\!\cdots\!69\)\( T^{24} + \)\(55\!\cdots\!33\)\( T^{25} + \)\(21\!\cdots\!52\)\( T^{26} + \)\(30\!\cdots\!39\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( 1 - 23 T + 717 T^{2} - 12428 T^{3} + 230125 T^{4} - 3217367 T^{5} + 45271509 T^{6} - 534731291 T^{7} + 6265033030 T^{8} - 64694387541 T^{9} + 662152887891 T^{10} - 6133913826684 T^{11} + 56506417301801 T^{12} - 478249962563133 T^{13} + 4039132908736010 T^{14} - 31557821001339482 T^{15} + 246387107432896610 T^{16} - 1779568110697417893 T^{17} + 12825883105580092781 T^{18} - 84929195551968221244 T^{19} + \)\(55\!\cdots\!91\)\( T^{20} - \)\(33\!\cdots\!01\)\( T^{21} + \)\(19\!\cdots\!30\)\( T^{22} - \)\(10\!\cdots\!71\)\( T^{23} + \)\(52\!\cdots\!69\)\( T^{24} - \)\(22\!\cdots\!67\)\( T^{25} + \)\(10\!\cdots\!25\)\( T^{26} - \)\(32\!\cdots\!88\)\( T^{27} + \)\(11\!\cdots\!77\)\( T^{28} - \)\(22\!\cdots\!43\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))
$67$ (\( 1 + 14 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 - 21 T + 243 T^{2} - 1407 T^{3} + 4489 T^{4} \))(\( 1 - 15 T + 159 T^{2} - 1005 T^{3} + 4489 T^{4} \))(\( 1 - 15 T + 187 T^{2} - 1005 T^{3} + 4489 T^{4} \))(\( 1 + 10 T + 219 T^{2} + 1303 T^{3} + 14673 T^{4} + 44890 T^{5} + 300763 T^{6} \))(\( 1 - 28 T + 545 T^{2} - 7368 T^{3} + 82657 T^{4} - 735404 T^{5} + 5538019 T^{6} - 33074952 T^{7} + 163915835 T^{8} - 564231388 T^{9} + 1350125107 T^{10} \))(\( 1 + 25 T + 501 T^{2} + 6006 T^{3} + 65326 T^{4} + 531374 T^{5} + 4704996 T^{6} + 35602058 T^{7} + 293248414 T^{8} + 1806382578 T^{9} + 10095711621 T^{10} + 33753127675 T^{11} + 90458382169 T^{12} \))(\( 1 + 24 T + 571 T^{2} + 9254 T^{3} + 134590 T^{4} + 1627284 T^{5} + 17856782 T^{6} + 169814174 T^{7} + 1487571735 T^{8} + 11377549658 T^{9} + 80159094398 T^{10} + 489426817692 T^{11} + 2712139375390 T^{12} + 12494057740178 T^{13} + 51651736218499 T^{14} + 145457078527752 T^{15} + 406067677556641 T^{16} \))(\( 1 - 2 T + 232 T^{2} + 218 T^{3} + 32861 T^{4} + 80466 T^{5} + 3212210 T^{6} + 13028828 T^{7} + 253369485 T^{8} + 1062328520 T^{9} + 16975755495 T^{10} + 58486408892 T^{11} + 966113916230 T^{12} + 1621480102386 T^{13} + 44366461141127 T^{14} + 19719927312842 T^{15} + 1406085092434936 T^{16} - 812135355113282 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 16 T + 408 T^{2} + 5156 T^{3} + 80279 T^{4} + 839402 T^{5} + 10079582 T^{6} + 90178442 T^{7} + 905262375 T^{8} + 7006843812 T^{9} + 60652579125 T^{10} + 404811026138 T^{11} + 3031565321066 T^{12} + 16914891269642 T^{13} + 108386693464853 T^{14} + 466403418463364 T^{15} + 2472770334971784 T^{16} + 6497082840906256 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 13 T + 470 T^{2} - 5233 T^{3} + 104399 T^{4} - 1005462 T^{5} + 14400790 T^{6} - 119892164 T^{7} + 1360153193 T^{8} - 9662409341 T^{9} + 91130263931 T^{10} - 538195924196 T^{11} + 4331224802770 T^{12} - 20261186422902 T^{13} + 140951711045693 T^{14} - 473368713890377 T^{15} + 2848534454501810 T^{16} - 5278879808236333 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 8 T + 384 T^{2} - 2940 T^{3} + 74527 T^{4} - 530450 T^{5} + 9470316 T^{6} - 61039356 T^{7} + 859218535 T^{8} - 4862583934 T^{9} + 57567641845 T^{10} - 274005669084 T^{11} + 2848320651108 T^{12} - 10689162134450 T^{13} + 100620773849389 T^{14} - 265947643576860 T^{15} + 2327313256444032 T^{16} - 3248541420453128 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 18 T + 600 T^{2} - 7680 T^{3} + 144869 T^{4} - 1427420 T^{5} + 19816942 T^{6} - 158969984 T^{7} + 1813609293 T^{8} - 12380944006 T^{9} + 121511822631 T^{10} - 713616258176 T^{11} + 5960202926746 T^{12} - 28764113137820 T^{13} + 195591274125983 T^{14} - 694720375057920 T^{15} + 3636426963193800 T^{16} - 7309218196019538 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 26 T + 566 T^{2} - 7610 T^{3} + 97755 T^{4} - 966248 T^{5} + 10180100 T^{6} - 89786202 T^{7} + 864941829 T^{8} - 6868878016 T^{9} + 57951102543 T^{10} - 403050260778 T^{11} + 3061797416300 T^{12} - 19470980364008 T^{13} + 131981479834785 T^{14} - 688388288306090 T^{15} + 3430362768612818 T^{16} - 10557759616472666 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 4 T + 361 T^{2} + 974 T^{3} + 53789 T^{4} + 52384 T^{5} + 4197223 T^{6} - 8053586 T^{7} + 184733463 T^{8} - 1469351166 T^{9} + 7578251062 T^{10} - 98446528122 T^{11} + 829268515407 T^{12} - 2422220686118 T^{13} + 84578748536983 T^{14} + 70724953605088 T^{15} + 4865665918488341 T^{16} + 5903133103584602 T^{17} + 146590431597947401 T^{18} + 108826137585179788 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 26 T + 603 T^{2} - 9778 T^{3} + 136523 T^{4} - 1581548 T^{5} + 16389951 T^{6} - 148561414 T^{7} + 1272883541 T^{8} - 10235423362 T^{9} + 83938763714 T^{10} - 685773365254 T^{11} + 5713974215549 T^{12} - 44681776558882 T^{13} + 330275885785071 T^{14} - 2135287662725636 T^{15} + 12349649708858387 T^{16} - 59261638076848294 T^{17} + 244858809566654523 T^{18} - 707369894303668622 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - T + 323 T^{2} - 496 T^{3} + 56629 T^{4} - 104683 T^{5} + 6895709 T^{6} - 14257376 T^{7} + 643359771 T^{8} - 1339953987 T^{9} + 47989270290 T^{10} - 89776917129 T^{11} + 2888042012019 T^{12} - 4288091177888 T^{13} + 138956266439789 T^{14} - 141335146576081 T^{15} + 5122567723848301 T^{16} - 3006112956240208 T^{17} + 131159859850795043 T^{18} - 27206534396294947 T^{19} + 1822837804551761449 T^{20} \))(\( 1 + 41 T + 1283 T^{2} + 28647 T^{3} + 544892 T^{4} + 8698625 T^{5} + 123454265 T^{6} + 1547239523 T^{7} + 17591283388 T^{8} + 180388257753 T^{9} + 1694120695490 T^{10} + 14469404196866 T^{11} + 113506086597830 T^{12} + 809762889053217 T^{13} + 5290807165625044 T^{14} + 31178610843955283 T^{15} + 166678702742731355 T^{16} + 786863544594817625 T^{17} + 3302433268047660116 T^{18} + 11632620758965094727 T^{19} + 34905983630446417001 T^{20} + 74736349986622219409 T^{21} + \)\(12\!\cdots\!83\)\( T^{22} \))(\( 1 - 14 T + 424 T^{2} - 5390 T^{3} + 93554 T^{4} - 1043318 T^{5} + 13734392 T^{6} - 134567702 T^{7} + 1484214336 T^{8} - 12925275678 T^{9} + 124679534891 T^{10} - 971445857060 T^{11} + 8353528837697 T^{12} - 58021562518542 T^{13} + 446396756338368 T^{14} - 2711690045693942 T^{15} + 18543147468579944 T^{16} - 94376858367796742 T^{17} + 567003813524387942 T^{18} - 2188704782030294990 T^{19} + 11535570584029057528 T^{20} - 25519729263724660286 T^{21} + \)\(12\!\cdots\!83\)\( T^{22} \))(\( 1 + 7 T + 196 T^{2} + 214 T^{3} + 25987 T^{4} + 21650 T^{5} + 3125071 T^{6} - 3878446 T^{7} + 267172845 T^{8} - 574587254 T^{9} + 22841656932 T^{10} - 57214232749 T^{11} + 1533020496008 T^{12} - 3833353594183 T^{13} + 102536197967748 T^{14} - 172814586274802 T^{15} + 5383832327509245 T^{16} - 5236387320743722 T^{17} + 282688866823258999 T^{18} + 131214406255242950 T^{19} + 10552480736664429667 T^{20} + 5822198360807118658 T^{21} + \)\(35\!\cdots\!04\)\( T^{22} + \)\(85\!\cdots\!81\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 + 34 T + 851 T^{2} + 16345 T^{3} + 277159 T^{4} + 4101262 T^{5} + 55898615 T^{6} + 697339932 T^{7} + 8160527492 T^{8} + 89090190714 T^{9} + 922212957831 T^{10} + 8996734465478 T^{11} + 83598220748658 T^{12} + 735840864521105 T^{13} + 6185093252722946 T^{14} + 49301337922914035 T^{15} + 375272412940725762 T^{16} + 2705884848040559714 T^{17} + 18583624901020378551 T^{18} + \)\(12\!\cdots\!98\)\( T^{19} + \)\(73\!\cdots\!48\)\( T^{20} + \)\(42\!\cdots\!36\)\( T^{21} + \)\(22\!\cdots\!15\)\( T^{22} + \)\(11\!\cdots\!14\)\( T^{23} + \)\(50\!\cdots\!91\)\( T^{24} + \)\(19\!\cdots\!35\)\( T^{25} + \)\(69\!\cdots\!11\)\( T^{26} + \)\(18\!\cdots\!58\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 8 T + 630 T^{2} + 3815 T^{3} + 190604 T^{4} + 899685 T^{5} + 37901868 T^{6} + 143517584 T^{7} + 5618996293 T^{8} + 17543460986 T^{9} + 659719808995 T^{10} + 1745912523478 T^{11} + 63341238307215 T^{12} + 146486436710149 T^{13} + 5060986569228680 T^{14} + 10559295793687294 T^{15} + 339086100138321560 T^{16} + 657577614391858861 T^{17} + 19050700856992905045 T^{18} + 35182094516020518838 T^{19} + \)\(89\!\cdots\!65\)\( T^{20} + \)\(15\!\cdots\!34\)\( T^{21} + \)\(34\!\cdots\!39\)\( T^{22} + \)\(58\!\cdots\!44\)\( T^{23} + \)\(10\!\cdots\!96\)\( T^{24} + \)\(16\!\cdots\!65\)\( T^{25} + \)\(23\!\cdots\!32\)\( T^{26} + \)\(31\!\cdots\!15\)\( T^{27} + \)\(34\!\cdots\!10\)\( T^{28} + \)\(29\!\cdots\!32\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))
$71$ (\( 1 + 6 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 - T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - T + 71 T^{2} \))(\( 1 - 15 T + 167 T^{2} - 1065 T^{3} + 5041 T^{4} \))(\( 1 + 5 T + 47 T^{2} + 355 T^{3} + 5041 T^{4} \))(\( 1 + 7 T - 5 T^{2} + 497 T^{3} + 5041 T^{4} \))(\( 1 + 22 T + 355 T^{2} + 3351 T^{3} + 25205 T^{4} + 110902 T^{5} + 357911 T^{6} \))(\( 1 - 28 T + 563 T^{2} - 7840 T^{3} + 91306 T^{4} - 835592 T^{5} + 6482726 T^{6} - 39521440 T^{7} + 201503893 T^{8} - 711527068 T^{9} + 1804229351 T^{10} \))(\( 1 + 11 T + 373 T^{2} + 2602 T^{3} + 53240 T^{4} + 259420 T^{5} + 4499622 T^{6} + 18418820 T^{7} + 268382840 T^{8} + 931284422 T^{9} + 9478557013 T^{10} + 19846522861 T^{11} + 128100283921 T^{12} \))(\( 1 - 2 T + 171 T^{2} - 44 T^{3} + 6659 T^{4} + 7580 T^{5} - 470127 T^{6} - 2077898 T^{7} - 62333328 T^{8} - 147530758 T^{9} - 2369910207 T^{10} + 2712965380 T^{11} + 169216383779 T^{12} - 79386091444 T^{13} + 21905148550491 T^{14} - 18190240316782 T^{15} + 645753531245761 T^{16} \))(\( 1 + 2 T + 442 T^{2} + 1474 T^{3} + 92256 T^{4} + 390440 T^{5} + 12280054 T^{6} + 55691390 T^{7} + 1168753487 T^{8} + 4925309932 T^{9} + 82981497577 T^{10} + 280740296990 T^{11} + 4395166407194 T^{12} + 9921736729640 T^{13} + 166450983005856 T^{14} + 188819818499554 T^{15} + 4020043110008822 T^{16} + 1291507062491522 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 6 T + 370 T^{2} + 2194 T^{3} + 70740 T^{4} + 395820 T^{5} + 9084418 T^{6} + 46344734 T^{7} + 852168895 T^{8} + 3855170876 T^{9} + 60503991545 T^{10} + 233623804094 T^{11} + 3251413130798 T^{12} + 10058451573420 T^{13} + 127631184289740 T^{14} + 281052022922674 T^{15} + 3365194458604670 T^{16} + 3874521187474566 T^{17} + 45848500718449031 T^{18} \))(\( 1 + T + 296 T^{2} + 311 T^{3} + 45796 T^{4} - 2563 T^{5} + 4864354 T^{6} - 5552387 T^{7} + 399025173 T^{8} - 607006804 T^{9} + 28330787283 T^{10} - 27989582867 T^{11} + 1741005804494 T^{12} - 65130138403 T^{13} + 82626487358396 T^{14} + 39839188299431 T^{15} + 2692155566883736 T^{16} + 645753531245761 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 20 T + 454 T^{2} + 7144 T^{3} + 102488 T^{4} + 1271930 T^{5} + 14515646 T^{6} + 149060480 T^{7} + 1421630731 T^{8} + 12439035124 T^{9} + 100935781901 T^{10} + 751413879680 T^{11} + 5195309375506 T^{12} + 32321879414330 T^{13} + 184911857725288 T^{14} + 915148428331624 T^{15} + 4129184551909514 T^{16} + 12915070624915220 T^{17} + 45848500718449031 T^{18} \))(\( 1 - 12 T + 490 T^{2} - 5372 T^{3} + 116032 T^{4} - 1122366 T^{5} + 17151790 T^{6} - 143431996 T^{7} + 1728699351 T^{8} - 12288005660 T^{9} + 122737653921 T^{10} - 723040691836 T^{11} + 6138814310690 T^{12} - 28521206757246 T^{13} + 209348340055232 T^{14} - 688154725223612 T^{15} + 4456608877611590 T^{16} - 7749042374949132 T^{17} + 45848500718449031 T^{18} \))(\( 1 - 18 T + 458 T^{2} - 6234 T^{3} + 102872 T^{4} - 1164860 T^{5} + 14660798 T^{6} - 139687702 T^{7} + 1450238575 T^{8} - 11784537732 T^{9} + 102966938825 T^{10} - 704165705782 T^{11} + 5247260872978 T^{12} - 29601050729660 T^{13} + 185604681796072 T^{14} - 798577169963514 T^{15} + 4165565032543078 T^{16} - 11623563562423698 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 24 T + 693 T^{2} + 11236 T^{3} + 198090 T^{4} + 2528474 T^{5} + 33949518 T^{6} + 359734038 T^{7} + 3953042517 T^{8} + 35526391064 T^{9} + 329357805242 T^{10} + 2522373765544 T^{11} + 19927287328197 T^{12} + 128752769274618 T^{13} + 862714321519758 T^{14} + 4561947004040374 T^{15} + 25375385241910890 T^{16} + 102192770099681276 T^{17} + 447507197153312373 T^{18} + 1100364017242776744 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 18 T + 345 T^{2} - 3992 T^{3} + 56862 T^{4} - 614218 T^{5} + 7298310 T^{6} - 68516546 T^{7} + 699959265 T^{8} - 6059573774 T^{9} + 55909618242 T^{10} - 430229737954 T^{11} + 3528494654865 T^{12} - 24522825495406 T^{13} + 185462325559110 T^{14} - 1108190143512518 T^{15} + 7284038344315902 T^{16} - 36307719672296872 T^{17} + 222784968279787545 T^{18} - 825273012932082558 T^{19} + 3255243551009881201 T^{20} \))(\( 1 + 21 T + 595 T^{2} + 9050 T^{3} + 153296 T^{4} + 1846290 T^{5} + 23670438 T^{6} + 238641380 T^{7} + 2537102703 T^{8} + 22180291527 T^{9} + 204716901198 T^{10} + 1574800698417 T^{11} + 12789534725823 T^{12} + 85412374957180 T^{13} + 601505619586278 T^{14} + 3331130608457790 T^{15} + 19637261123953616 T^{16} + 82310837433438550 T^{17} + 384223351091227795 T^{18} + 962818515087429651 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - T + 235 T^{2} - 1295 T^{3} + 34735 T^{4} - 241618 T^{5} + 4237546 T^{6} - 31825546 T^{7} + 390365867 T^{8} - 3226920813 T^{9} + 32243910302 T^{10} - 247104099150 T^{11} + 2289317631442 T^{12} - 16266907818333 T^{13} + 139716237823837 T^{14} - 808740622602826 T^{15} + 7645504869412646 T^{16} - 30951334400424178 T^{17} + 315918998701711385 T^{18} - 836250822963260495 T^{19} + 10774397668835522285 T^{20} - 3255243551009881201 T^{21} + \)\(23\!\cdots\!71\)\( T^{22} \))(\( 1 - 6 T + 608 T^{2} - 4098 T^{3} + 175185 T^{4} - 1254282 T^{5} + 31750168 T^{6} - 228972208 T^{7} + 4038464595 T^{8} - 27776745808 T^{9} + 379629912533 T^{10} - 2347019342620 T^{11} + 26953723789843 T^{12} - 140022575618128 T^{13} + 1445410901661045 T^{14} - 5818568707561648 T^{15} + 57284585004780968 T^{16} - 160673880316999722 T^{17} + 1593328624947727335 T^{18} - 2646297971045128578 T^{19} + 27875888436817010848 T^{20} - 19531461306059287206 T^{21} + \)\(23\!\cdots\!71\)\( T^{22} \))(\( 1 - 9 T + 686 T^{2} - 6258 T^{3} + 225184 T^{4} - 2018187 T^{5} + 46683075 T^{6} - 399383232 T^{7} + 6795071369 T^{8} - 53961123035 T^{9} + 730500570239 T^{10} - 5230986878517 T^{11} + 59414532368812 T^{12} - 371400068374707 T^{13} + 3682453374574799 T^{14} - 19313279506579885 T^{15} + 172674186001261289 T^{16} - 720578949471642432 T^{17} + 5980115161805337075 T^{18} - 18355653267102657117 T^{19} + \)\(14\!\cdots\!24\)\( T^{20} - \)\(28\!\cdots\!98\)\( T^{21} + \)\(22\!\cdots\!86\)\( T^{22} - \)\(20\!\cdots\!39\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 10 T + 375 T^{2} + 2499 T^{3} + 70626 T^{4} + 396726 T^{5} + 10411386 T^{6} + 54557665 T^{7} + 1262447246 T^{8} + 6019054996 T^{9} + 127018525469 T^{10} + 560078700775 T^{11} + 11099678873503 T^{12} + 46082983434959 T^{13} + 847015029744292 T^{14} + 3271891823882089 T^{15} + 55953481201328623 T^{16} + 200458327873081025 T^{17} + 3227754250308603389 T^{18} + 10859755689066387596 T^{19} + \)\(16\!\cdots\!66\)\( T^{20} + \)\(49\!\cdots\!15\)\( T^{21} + \)\(67\!\cdots\!46\)\( T^{22} + \)\(18\!\cdots\!06\)\( T^{23} + \)\(22\!\cdots\!26\)\( T^{24} + \)\(57\!\cdots\!29\)\( T^{25} + \)\(61\!\cdots\!75\)\( T^{26} + \)\(11\!\cdots\!10\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))(\( 1 + 12 T + 666 T^{2} + 7403 T^{3} + 224165 T^{4} + 2315187 T^{5} + 50263636 T^{6} + 482943115 T^{7} + 8356948634 T^{8} + 74582593467 T^{9} + 1087297712591 T^{10} + 8981419039945 T^{11} + 114060419793308 T^{12} + 867341168198422 T^{13} + 9807461166607391 T^{14} + 68130690928213890 T^{15} + 696329742829124761 T^{16} + 4372266828888245302 T^{17} + 40823478908642659588 T^{18} + \)\(22\!\cdots\!45\)\( T^{19} + \)\(19\!\cdots\!41\)\( T^{20} + \)\(95\!\cdots\!07\)\( T^{21} + \)\(76\!\cdots\!94\)\( T^{22} + \)\(31\!\cdots\!15\)\( T^{23} + \)\(23\!\cdots\!16\)\( T^{24} + \)\(75\!\cdots\!87\)\( T^{25} + \)\(51\!\cdots\!15\)\( T^{26} + \)\(12\!\cdots\!23\)\( T^{27} + \)\(77\!\cdots\!26\)\( T^{28} + \)\(99\!\cdots\!72\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))
$73$ (\( 1 + 3 T + 73 T^{2} \))(\( 1 + T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 102 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 126 T^{2} + 5329 T^{4} \))(\( 1 + 10 T + 158 T^{2} + 730 T^{3} + 5329 T^{4} \))(\( 1 + 18 T + 263 T^{2} + 2524 T^{3} + 19199 T^{4} + 95922 T^{5} + 389017 T^{6} \))(\( 1 + 4 T + 193 T^{2} + 29 T^{3} + 15799 T^{4} - 36904 T^{5} + 1153327 T^{6} + 154541 T^{7} + 75080281 T^{8} + 113592964 T^{9} + 2073071593 T^{10} \))(\( 1 - 14 T + 190 T^{2} - 1302 T^{3} + 18847 T^{4} - 163404 T^{5} + 1950180 T^{6} - 11928492 T^{7} + 100435663 T^{8} - 506500134 T^{9} + 5395665790 T^{10} - 29023002302 T^{11} + 151334226289 T^{12} \))(\( 1 - 2 T + 206 T^{2} + 31 T^{3} + 24051 T^{4} + 39147 T^{5} + 2118898 T^{6} + 5259840 T^{7} + 163712008 T^{8} + 383968320 T^{9} + 11291607442 T^{10} + 15228848499 T^{11} + 683006094291 T^{12} + 64265219383 T^{13} + 31174850615534 T^{14} - 22094797038194 T^{15} + 806460091894081 T^{16} \))(\( 1 - 34 T + 917 T^{2} - 17149 T^{3} + 282119 T^{4} - 3831704 T^{5} + 47461111 T^{6} - 512294339 T^{7} + 5117529820 T^{8} - 45367142732 T^{9} + 373579676860 T^{10} - 2730016532531 T^{11} + 18463179017887 T^{12} - 108813653632664 T^{13} + 584852884745567 T^{14} - 2595230646630061 T^{15} + 10130464442011949 T^{16} - 27419643124398754 T^{17} + 58871586708267913 T^{18} \))(\( 1 - 4 T + 491 T^{2} - 2057 T^{3} + 116707 T^{4} - 475090 T^{5} + 17415531 T^{6} - 65174039 T^{7} + 1787196518 T^{8} - 5823984148 T^{9} + 130465345814 T^{10} - 347312453831 T^{11} + 6774937623027 T^{12} - 13491720316690 T^{13} + 241941966404251 T^{14} - 311294503476473 T^{15} + 5424272672876627 T^{16} - 3225840367576324 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 6 T + 501 T^{2} + 2659 T^{3} + 118749 T^{4} + 565694 T^{5} + 17579767 T^{6} + 74368717 T^{7} + 1793609410 T^{8} + 6556393616 T^{9} + 130933486930 T^{10} + 396310892893 T^{11} + 6838828219039 T^{12} + 16064714544254 T^{13} + 246175178597157 T^{14} + 402397707702451 T^{15} + 5534746658067597 T^{16} + 4838760551364486 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 23 T + 525 T^{2} + 7059 T^{3} + 89094 T^{4} + 760469 T^{5} + 5999086 T^{6} + 26398007 T^{7} + 112110246 T^{8} - 65659504 T^{9} + 8184047958 T^{10} + 140674979303 T^{11} + 2333746438462 T^{12} + 21595981935029 T^{13} + 184698240506742 T^{14} + 1068268303374051 T^{15} + 5799884222525925 T^{16} + 18548582113563863 T^{17} + 58871586708267913 T^{18} \))(\( 1 - 29 T + 851 T^{2} - 15071 T^{3} + 261502 T^{4} - 3427767 T^{5} + 44099470 T^{6} - 461359703 T^{7} + 4753437500 T^{8} - 40895914752 T^{9} + 347000937500 T^{10} - 2458585857287 T^{11} + 17155443520990 T^{12} - 97342553357847 T^{13} + 542112367712686 T^{14} - 2280758124401519 T^{15} + 9401336139751547 T^{16} - 23387342664928349 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 8 T + 397 T^{2} + 2345 T^{3} + 79739 T^{4} + 390610 T^{5} + 10694461 T^{6} + 44434099 T^{7} + 1040954774 T^{8} + 3746189660 T^{9} + 75989698502 T^{10} + 236789313571 T^{11} + 4160327134837 T^{12} + 11092636917010 T^{13} + 165304655754227 T^{14} + 354878760647705 T^{15} + 4385817212081509 T^{16} + 6451680735152648 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 23 T + 676 T^{2} + 11028 T^{3} + 188109 T^{4} + 2401330 T^{5} + 30299132 T^{6} + 321664326 T^{7} + 3320214618 T^{8} + 30614873121 T^{9} + 273932980024 T^{10} + 2234885737833 T^{11} + 17693423699322 T^{12} + 125132891107542 T^{13} + 860442052626812 T^{14} + 4978129008418690 T^{15} + 28467329972997501 T^{16} + 121830710868601716 T^{17} + 545167022120398756 T^{18} + 1354046494290161999 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 4 T + 358 T^{2} + 1303 T^{3} + 64652 T^{4} + 261627 T^{5} + 8170680 T^{6} + 36966125 T^{7} + 801232191 T^{8} + 3681786581 T^{9} + 64037832188 T^{10} + 268770420413 T^{11} + 4269766345839 T^{12} + 14380451049125 T^{13} + 232032939773880 T^{14} + 542371501661811 T^{15} + 9784060398036428 T^{16} + 14394760270383391 T^{17} + 288712712898080998 T^{18} + 235486346833071652 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 10 T + 430 T^{2} + 3123 T^{3} + 84218 T^{4} + 459825 T^{5} + 10645064 T^{6} + 45251323 T^{7} + 1024123009 T^{8} + 3639285855 T^{9} + 81388231564 T^{10} + 265667867415 T^{11} + 5457551514961 T^{12} + 17603533919491 T^{13} + 302301092932424 T^{14} + 953250145251225 T^{15} + 12745065869607002 T^{16} + 34501025575139931 T^{17} + 346777839514454830 T^{18} + 588715867082679130 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 8 T + 353 T^{2} + 1571 T^{3} + 58426 T^{4} + 131772 T^{5} + 7058980 T^{6} + 8016780 T^{7} + 725969247 T^{8} + 545803068 T^{9} + 63509283505 T^{10} + 40525991010 T^{11} + 4636177695865 T^{12} + 2908584549372 T^{13} + 282414378560199 T^{14} + 227662450483980 T^{15} + 14633770913555140 T^{16} + 19941613666554108 T^{17} + 645455305876761322 T^{18} + 1266948804365601251 T^{19} + 20781670108018573289 T^{20} + 34381006637628461192 T^{21} + \)\(31\!\cdots\!77\)\( T^{22} \))(\( 1 - 3 T + 417 T^{2} - 1931 T^{3} + 76749 T^{4} - 469436 T^{5} + 8556635 T^{6} - 60136020 T^{7} + 704611696 T^{8} - 4924805341 T^{9} + 51542750918 T^{10} - 346096909546 T^{11} + 3762620817014 T^{12} - 26244287662189 T^{13} + 274105928142832 T^{14} - 1707757188740820 T^{15} + 17738516950169555 T^{16} - 71041733852203004 T^{17} + 847876788942175653 T^{18} - 1557274437447470411 T^{19} + 24549451657347719721 T^{20} - 12892877489110672947 T^{21} + \)\(31\!\cdots\!77\)\( T^{22} \))(\( 1 - 32 T + 966 T^{2} - 18843 T^{3} + 346883 T^{4} - 5083441 T^{5} + 71412650 T^{6} - 859595654 T^{7} + 10051470483 T^{8} - 104216970266 T^{9} + 1058215085296 T^{10} - 9676402331468 T^{11} + 86933039646418 T^{12} - 706377370197164 T^{13} + 5639228189542384 T^{14} - 40542173121968522 T^{15} + 285444081180620403 T^{16} - 1782003331773656822 T^{17} + 10807178134997155850 T^{18} - 56158798575316972777 T^{19} + \)\(27\!\cdots\!23\)\( T^{20} - \)\(11\!\cdots\!59\)\( T^{21} + \)\(41\!\cdots\!34\)\( T^{22} - \)\(10\!\cdots\!64\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 9 T + 242 T^{2} - 2372 T^{3} + 33335 T^{4} - 316118 T^{5} + 3805894 T^{6} - 30207174 T^{7} + 363893261 T^{8} - 2773971382 T^{9} + 31161508470 T^{10} - 249046406381 T^{11} + 2625574822235 T^{12} - 19680414958604 T^{13} + 206018157714596 T^{14} - 1436670291978092 T^{15} + 13991688227690315 T^{16} - 96883285871117477 T^{17} + 884932027454601270 T^{18} - 5750641271819151526 T^{19} + 55069505105216138429 T^{20} - \)\(33\!\cdots\!78\)\( T^{21} + \)\(30\!\cdots\!14\)\( T^{22} - \)\(18\!\cdots\!34\)\( T^{23} + \)\(14\!\cdots\!15\)\( T^{24} - \)\(74\!\cdots\!44\)\( T^{25} + \)\(55\!\cdots\!82\)\( T^{26} - \)\(15\!\cdots\!97\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( 1 - 11 T + 523 T^{2} - 5907 T^{3} + 156789 T^{4} - 1674732 T^{5} + 32828087 T^{6} - 328344092 T^{7} + 5250631221 T^{8} - 48850469370 T^{9} + 671356634095 T^{10} - 5788508806085 T^{11} + 70371828996961 T^{12} - 560333701040543 T^{13} + 6136479844376291 T^{14} - 44873933628961880 T^{15} + 447963028639469243 T^{16} - 2986018292845053647 T^{17} + 27375837800910777337 T^{18} - \)\(16\!\cdots\!85\)\( T^{19} + \)\(13\!\cdots\!35\)\( T^{20} - \)\(73\!\cdots\!30\)\( T^{21} + \)\(58\!\cdots\!37\)\( T^{22} - \)\(26\!\cdots\!52\)\( T^{23} + \)\(19\!\cdots\!31\)\( T^{24} - \)\(71\!\cdots\!68\)\( T^{25} + \)\(49\!\cdots\!53\)\( T^{26} - \)\(13\!\cdots\!47\)\( T^{27} + \)\(87\!\cdots\!59\)\( T^{28} - \)\(13\!\cdots\!99\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))
$79$ (\( 1 + 11 T + 79 T^{2} \))(\( 1 + 7 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 7 T + 169 T^{2} - 553 T^{3} + 6241 T^{4} \))(\( 1 + T - 53 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 7 T + 141 T^{2} + 553 T^{3} + 6241 T^{4} \))(\( 1 + 3 T + 158 T^{2} + 286 T^{3} + 12482 T^{4} + 18723 T^{5} + 493039 T^{6} \))(\( 1 + 11 T + 182 T^{2} + 1077 T^{3} + 22036 T^{4} + 150844 T^{5} + 1740844 T^{6} + 6721557 T^{7} + 89733098 T^{8} + 428450891 T^{9} + 3077056399 T^{10} \))(\( 1 - 24 T + 541 T^{2} - 7436 T^{3} + 100976 T^{4} - 1022182 T^{5} + 10348020 T^{6} - 80752378 T^{7} + 630191216 T^{8} - 3666238004 T^{9} + 21071993821 T^{10} - 73849353576 T^{11} + 243087455521 T^{12} \))(\( 1 - 7 T + 510 T^{2} - 2915 T^{3} + 119649 T^{4} - 564031 T^{5} + 17024124 T^{6} - 66706738 T^{7} + 1621590849 T^{8} - 5269832302 T^{9} + 106247557884 T^{10} - 278089280209 T^{11} + 4660338241569 T^{12} - 8969619403085 T^{13} + 123974602315710 T^{14} - 134427362903113 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 5 T + 523 T^{2} - 2086 T^{3} + 130785 T^{4} - 432318 T^{5} + 20668229 T^{6} - 57814181 T^{7} + 2269679833 T^{8} - 5404767844 T^{9} + 179304706807 T^{10} - 360818303621 T^{11} + 10190242957931 T^{12} - 16838821117758 T^{13} + 402432821143215 T^{14} - 507080432216806 T^{15} + 10043644399761157 T^{16} - 7585544049532805 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 21 T + 693 T^{2} - 11140 T^{3} + 211527 T^{4} - 2728732 T^{5} + 37906651 T^{6} - 401639805 T^{7} + 4422828729 T^{8} - 38747122180 T^{9} + 349403469591 T^{10} - 2506634023005 T^{11} + 18689457302389 T^{12} - 106284332427292 T^{13} + 650880508911273 T^{14} - 2707994254503940 T^{15} + 13308308927408187 T^{16} - 31859285008037781 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 21 T + 659 T^{2} + 10018 T^{3} + 185523 T^{4} + 2225394 T^{5} + 30786185 T^{6} + 305138079 T^{7} + 3429732173 T^{8} + 28677730516 T^{9} + 270948841667 T^{10} + 1904366751039 T^{11} + 15178789866215 T^{12} + 86679276556914 T^{13} + 570864734311677 T^{14} + 2435250129409378 T^{15} + 12655376021878781 T^{16} + 31859285008037781 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 2 T + 374 T^{2} - 658 T^{3} + 78602 T^{4} - 106303 T^{5} + 11131368 T^{6} - 13006721 T^{7} + 1164179101 T^{8} - 1141949343 T^{9} + 91970148979 T^{10} - 81174945761 T^{11} + 5488198547352 T^{12} - 4140510460543 T^{13} + 241862787074198 T^{14} - 159951545732818 T^{15} + 7182261960823466 T^{16} - 3034217619813122 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 6 T + 476 T^{2} + 2926 T^{3} + 114650 T^{4} + 668789 T^{5} + 17846114 T^{6} + 94140885 T^{7} + 1949108027 T^{8} + 8950152563 T^{9} + 153979534133 T^{10} + 587533263285 T^{11} + 8798830200446 T^{12} + 26049385721909 T^{13} + 352784516145350 T^{14} + 711273894854446 T^{15} + 9141060677411684 T^{16} + 9102652859439366 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 9 T + 557 T^{2} + 4916 T^{3} + 144985 T^{4} + 1224674 T^{5} + 23345681 T^{6} + 181746505 T^{7} + 2580593467 T^{8} + 17576249308 T^{9} + 203866883893 T^{10} + 1134279937705 T^{11} + 11510331214559 T^{12} + 47701151498594 T^{13} + 446127022009015 T^{14} + 1195017931341236 T^{15} + 10696577305290563 T^{16} + 13653979289159049 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 14 T + 397 T^{2} - 5082 T^{3} + 94296 T^{4} - 1053191 T^{5} + 14985812 T^{6} - 148481456 T^{7} + 1777691157 T^{8} - 15481851080 T^{9} + 159375689706 T^{10} - 1223066235320 T^{11} + 11094570510837 T^{12} - 73207148584784 T^{13} + 583698591250772 T^{14} - 3240728105919209 T^{15} + 22922174705808216 T^{16} - 97594265467660038 T^{17} + 602292197532904717 T^{18} - 1677922343756656466 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 19 T + 440 T^{2} - 5243 T^{3} + 76166 T^{4} - 666018 T^{5} + 7679296 T^{6} - 49777213 T^{7} + 529124724 T^{8} - 2658749639 T^{9} + 35085071098 T^{10} - 210041221481 T^{11} + 3302267402484 T^{12} - 24542107320307 T^{13} + 299109201222976 T^{14} - 2049374948749182 T^{15} + 18514999137212486 T^{16} - 100686094814431637 T^{17} + 667527876358886840 T^{18} - 2277180323669748061 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 3 T + 254 T^{2} + 531 T^{3} + 31102 T^{4} + 158392 T^{5} + 3948602 T^{6} + 17160001 T^{7} + 400678518 T^{8} + 2118028899 T^{9} + 31049075910 T^{10} + 167324283021 T^{11} + 2500634630838 T^{12} + 8460549733039 T^{13} + 153798367736762 T^{14} + 487381117150408 T^{15} + 7560506041614142 T^{16} + 10197275671650429 T^{17} + 385345637716266494 T^{18} - 359554787947854957 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + 26 T + 713 T^{2} + 13585 T^{3} + 236394 T^{4} + 3511029 T^{5} + 48072505 T^{6} + 590102751 T^{7} + 6773619566 T^{8} + 71211867659 T^{9} + 704931052524 T^{10} + 6449584232316 T^{11} + 55689553149396 T^{12} + 444433266059819 T^{13} + 3339658617201074 T^{14} + 22984549949772831 T^{15} + 147921809126209495 T^{16} + 853487105870441109 T^{17} + 4539688860874070646 T^{18} + 20609923182580631185 T^{19} + 85454187935606861447 T^{20} + \)\(24\!\cdots\!26\)\( T^{21} + \)\(74\!\cdots\!79\)\( T^{22} \))(\( 1 - 8 T + 522 T^{2} - 2838 T^{3} + 124107 T^{4} - 440869 T^{5} + 19198670 T^{6} - 46106323 T^{7} + 2302081539 T^{8} - 4421151020 T^{9} + 225768765741 T^{10} - 385980877516 T^{11} + 17835732493539 T^{12} - 27592403515820 T^{13} + 1135015979907021 T^{14} - 1795845015462163 T^{15} + 59075390375789330 T^{16} - 107169723428087749 T^{17} + 2383339532545235013 T^{18} - 4305554802514820118 T^{19} + 62562533102926762518 T^{20} - 75746208661014777608 T^{21} + \)\(74\!\cdots\!79\)\( T^{22} \))(\( 1 - 20 T + 620 T^{2} - 9591 T^{3} + 189613 T^{4} - 2467030 T^{5} + 37841553 T^{6} - 428231206 T^{7} + 5517662987 T^{8} - 55242217774 T^{9} + 618585528106 T^{10} - 5525133807751 T^{11} + 54799478126000 T^{12} - 436485570812329 T^{13} + 3860592280909546 T^{14} - 27236567809075186 T^{15} + 214913420274351947 T^{16} - 1317691572673787194 T^{17} + 9198806831733064113 T^{18} - 47376619586123837770 T^{19} + \)\(28\!\cdots\!93\)\( T^{20} - \)\(11\!\cdots\!29\)\( T^{21} + \)\(58\!\cdots\!20\)\( T^{22} - \)\(14\!\cdots\!80\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 + T + 386 T^{2} + 1416 T^{3} + 79967 T^{4} + 545493 T^{5} + 12150136 T^{6} + 114987281 T^{7} + 1553099390 T^{8} + 16723447350 T^{9} + 176946990837 T^{10} + 1874608151808 T^{11} + 17773299148510 T^{12} + 172980225033289 T^{13} + 1527398914876074 T^{14} + 13665437777629831 T^{15} + 110923159985850910 T^{16} + 924254928559264512 T^{17} + 6892099625807407797 T^{18} + 51458990681657092650 T^{19} + \)\(37\!\cdots\!90\)\( T^{20} + \)\(22\!\cdots\!79\)\( T^{21} + \)\(18\!\cdots\!96\)\( T^{22} + \)\(65\!\cdots\!67\)\( T^{23} + \)\(75\!\cdots\!67\)\( T^{24} + \)\(10\!\cdots\!64\)\( T^{25} + \)\(22\!\cdots\!26\)\( T^{26} + \)\(46\!\cdots\!39\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 + T + 397 T^{2} + 731 T^{3} + 95267 T^{4} + 214961 T^{5} + 16910497 T^{6} + 44201348 T^{7} + 2420946702 T^{8} + 6861710085 T^{9} + 290920557003 T^{10} + 855470648298 T^{11} + 30075876564869 T^{12} + 87970264860981 T^{13} + 2709937932210182 T^{14} + 7587735924000854 T^{15} + 214085096644604378 T^{16} + 549022422997382421 T^{17} + 14828580105666446891 T^{18} + 33320651044329612138 T^{19} + \)\(89\!\cdots\!97\)\( T^{20} + \)\(16\!\cdots\!85\)\( T^{21} + \)\(46\!\cdots\!18\)\( T^{22} + \)\(67\!\cdots\!28\)\( T^{23} + \)\(20\!\cdots\!43\)\( T^{24} + \)\(20\!\cdots\!61\)\( T^{25} + \)\(71\!\cdots\!93\)\( T^{26} + \)\(43\!\cdots\!71\)\( T^{27} + \)\(18\!\cdots\!83\)\( T^{28} + \)\(36\!\cdots\!81\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))
$83$ (\( 1 + 13 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 19 T + 245 T^{2} - 1577 T^{3} + 6889 T^{4} \))(\( 1 - 3 T + 167 T^{2} - 249 T^{3} + 6889 T^{4} \))(\( 1 - 25 T + 293 T^{2} - 2075 T^{3} + 6889 T^{4} \))(\( 1 + T + 168 T^{2} - 108 T^{3} + 13944 T^{4} + 6889 T^{5} + 571787 T^{6} \))(\( 1 + 193 T^{2} - 195 T^{3} + 20681 T^{4} - 45478 T^{5} + 1716523 T^{6} - 1343355 T^{7} + 110354891 T^{8} + 3939040643 T^{10} \))(\( 1 - 24 T + 479 T^{2} - 5766 T^{3} + 65522 T^{4} - 554148 T^{5} + 5427132 T^{6} - 45994284 T^{7} + 451381058 T^{8} - 3296923842 T^{9} + 22732535759 T^{10} - 94536975432 T^{11} + 326940373369 T^{12} \))(\( 1 + 6 T + 387 T^{2} + 1621 T^{3} + 68918 T^{4} + 161888 T^{5} + 7853966 T^{6} + 8489740 T^{7} + 701863969 T^{8} + 704648420 T^{9} + 54105971774 T^{10} + 92565453856 T^{11} + 3270732566678 T^{12} + 6385184882303 T^{13} + 126525924493803 T^{14} + 162816305937762 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 24 T + 668 T^{2} + 9323 T^{3} + 141569 T^{4} + 1289391 T^{5} + 13743858 T^{6} + 84075958 T^{7} + 829150087 T^{8} + 4609755868 T^{9} + 68819457221 T^{10} + 579199274662 T^{11} + 7858559334246 T^{12} + 61192331972511 T^{13} + 557646044788867 T^{14} + 3048065100919187 T^{15} + 18126882061070836 T^{16} + 54055013571336984 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 16 T + 360 T^{2} + 4569 T^{3} + 66641 T^{4} + 736949 T^{5} + 9003496 T^{6} + 87090600 T^{7} + 930887019 T^{8} + 8038020744 T^{9} + 77263622577 T^{10} + 599967143400 T^{11} + 5148081967352 T^{12} + 34974362202629 T^{13} + 262501607490163 T^{14} + 1493790565922961 T^{15} + 9768978356265720 T^{16} + 36036675714224656 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 30 T + 922 T^{2} + 17901 T^{3} + 329919 T^{4} + 4793475 T^{5} + 65588342 T^{6} + 756834308 T^{7} + 8230181793 T^{8} + 77212382454 T^{9} + 683105088819 T^{10} + 5213831547812 T^{11} + 37502561307154 T^{12} + 227490275255475 T^{13} + 1299564349897917 T^{14} + 5852559623678469 T^{15} + 25019439012436094 T^{16} + 67568766964171230 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 9 T + 610 T^{2} + 4938 T^{3} + 174722 T^{4} + 1258235 T^{5} + 30717460 T^{6} + 193361618 T^{7} + 3645460843 T^{8} + 19557099679 T^{9} + 302573249969 T^{10} + 1332068186402 T^{11} + 17563844301020 T^{12} + 59713720523435 T^{13} + 688237059226246 T^{14} + 1614431563696122 T^{15} + 16552991103672470 T^{16} + 20270630089251369 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 25 T + 696 T^{2} - 11912 T^{3} + 201264 T^{4} - 2673409 T^{5} + 34479974 T^{6} - 377766240 T^{7} + 4011262661 T^{8} - 37124280585 T^{9} + 332934800863 T^{10} - 2602431627360 T^{11} + 19715200893538 T^{12} - 126875502486289 T^{13} + 792787075972752 T^{14} - 3894513727571528 T^{15} + 18886691488780392 T^{16} - 56307305803476025 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 4 T + 480 T^{2} - 2095 T^{3} + 113607 T^{4} - 509061 T^{5} + 17525726 T^{6} - 75538206 T^{7} + 1947321779 T^{8} - 7539999324 T^{9} + 161627707657 T^{10} - 520382701134 T^{11} + 10020982292362 T^{12} - 24159180346581 T^{13} + 447502590329301 T^{14} - 684940082208055 T^{15} + 13025304475020960 T^{16} - 9009168928556164 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 9 T + 465 T^{2} + 4111 T^{3} + 110304 T^{4} + 956241 T^{5} + 17536156 T^{6} + 145998105 T^{7} + 2079412063 T^{8} + 16132314327 T^{9} + 193464771898 T^{10} + 1338982089141 T^{11} + 14325069702007 T^{12} + 83479818463635 T^{13} + 832236520554076 T^{14} + 3766672163502963 T^{15} + 36062830944094176 T^{16} + 111556305618356597 T^{17} + 1047315887944654065 T^{18} + 1682462297407863627 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 40 T + 1105 T^{2} - 22199 T^{3} + 377813 T^{4} - 5474612 T^{5} + 71183247 T^{6} - 832331919 T^{7} + 9011327949 T^{8} - 90263536224 T^{9} + 850825410842 T^{10} - 7491873506592 T^{11} + 62079038240661 T^{12} - 475916570969253 T^{13} + 3378237385948287 T^{14} - 21564719172655516 T^{15} + 123522323283661997 T^{16} - 602393195918729773 T^{17} + 2488782916513640305 T^{18} - 7477610210701616120 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 6 T + 539 T^{2} - 4201 T^{3} + 143119 T^{4} - 1270904 T^{5} + 24914087 T^{6} - 227115441 T^{7} + 3148075691 T^{8} - 27015619936 T^{9} + 299677355034 T^{10} - 2242296454688 T^{11} + 21687093435299 T^{12} - 129861656663067 T^{13} + 1182380738267927 T^{14} - 5006142509351272 T^{15} + 46791379296197911 T^{16} - 113998550207423027 T^{17} + 1213985513122943099 T^{18} - 1121641531605242418 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 31 T + 611 T^{2} + 10730 T^{3} + 164653 T^{4} + 2177051 T^{5} + 26401659 T^{6} + 300406681 T^{7} + 3183266353 T^{8} + 31741364834 T^{9} + 306185009862 T^{10} + 2852573314610 T^{11} + 25413355818546 T^{12} + 218666262341426 T^{13} + 1820150318182811 T^{14} + 14256796697442601 T^{15} + 103997207843626737 T^{16} + 711765866783354819 T^{17} + 4468032203595054431 T^{18} + 24167095650851909930 T^{19} + \)\(11\!\cdots\!33\)\( T^{20} + \)\(48\!\cdots\!19\)\( T^{21} + \)\(12\!\cdots\!67\)\( T^{22} \))(\( 1 - 29 T + 1022 T^{2} - 21484 T^{3} + 447233 T^{4} - 7344360 T^{5} + 114115596 T^{6} - 1525731728 T^{7} + 19142277847 T^{8} - 213330073578 T^{9} + 2232579781879 T^{10} - 20979351912130 T^{11} + 185304121895957 T^{12} - 1469630876878842 T^{13} + 10945305623302589 T^{14} - 72408666107308688 T^{15} + 449505970644168228 T^{16} - 2401167800556348840 T^{17} + 12136137492243852091 T^{18} - 48388246315275156844 T^{19} + \)\(19\!\cdots\!66\)\( T^{20} - \)\(44\!\cdots\!21\)\( T^{21} + \)\(12\!\cdots\!67\)\( T^{22} \))(\( 1 + 5 T + 604 T^{2} + 3475 T^{3} + 187228 T^{4} + 1128595 T^{5} + 38970972 T^{6} + 231152698 T^{7} + 5990217416 T^{8} + 33606481203 T^{9} + 709744711247 T^{10} + 3655009061046 T^{11} + 66184054895520 T^{12} + 303365752066818 T^{13} + 4889431315780583 T^{14} + 19215749067619761 T^{15} + 284285660988318536 T^{16} + 910519872161104814 T^{17} + 12741184136232844668 T^{18} + 30625611466638084065 T^{19} + \)\(42\!\cdots\!48\)\( T^{20} + \)\(64\!\cdots\!25\)\( T^{21} + \)\(93\!\cdots\!96\)\( T^{22} + \)\(64\!\cdots\!35\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 56 T + 2167 T^{2} + 60980 T^{3} + 1422861 T^{4} + 28092496 T^{5} + 489520736 T^{6} + 7613933487 T^{7} + 107924339781 T^{8} + 1403626861998 T^{9} + 16955727287038 T^{10} + 190939488480515 T^{11} + 2019339529338617 T^{12} + 20075959659636872 T^{13} + 188396842699524894 T^{14} + 1666304651749860376 T^{15} + 13911230017613732513 T^{16} + \)\(10\!\cdots\!05\)\( T^{17} + \)\(80\!\cdots\!98\)\( T^{18} + \)\(55\!\cdots\!14\)\( T^{19} + \)\(35\!\cdots\!89\)\( T^{20} + \)\(20\!\cdots\!49\)\( T^{21} + \)\(11\!\cdots\!76\)\( T^{22} + \)\(52\!\cdots\!88\)\( T^{23} + \)\(22\!\cdots\!89\)\( T^{24} + \)\(78\!\cdots\!60\)\( T^{25} + \)\(23\!\cdots\!87\)\( T^{26} + \)\(49\!\cdots\!28\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 + 16 T + 604 T^{2} + 7504 T^{3} + 173628 T^{4} + 1922444 T^{5} + 34769177 T^{6} + 367060091 T^{7} + 5505944843 T^{8} + 55997468167 T^{9} + 716822102117 T^{10} + 7022940829917 T^{11} + 79108079275955 T^{12} + 742929365829845 T^{13} + 7555999277359853 T^{14} + 66867985832462624 T^{15} + 627147940020867799 T^{16} + 5118040401201802205 T^{17} + 45232971324960481585 T^{18} + \)\(33\!\cdots\!57\)\( T^{19} + \)\(28\!\cdots\!31\)\( T^{20} + \)\(18\!\cdots\!23\)\( T^{21} + \)\(14\!\cdots\!61\)\( T^{22} + \)\(82\!\cdots\!31\)\( T^{23} + \)\(64\!\cdots\!31\)\( T^{24} + \)\(29\!\cdots\!56\)\( T^{25} + \)\(22\!\cdots\!76\)\( T^{26} + \)\(80\!\cdots\!44\)\( T^{27} + \)\(53\!\cdots\!52\)\( T^{28} + \)\(11\!\cdots\!64\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))
$89$ (\( 1 - 9 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 13 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 9 T + 187 T^{2} + 801 T^{3} + 7921 T^{4} \))(\( 1 + 35 T + 483 T^{2} + 3115 T^{3} + 7921 T^{4} \))(\( 1 - 7 T + 187 T^{2} - 623 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 295 T^{2} - 2607 T^{3} + 26255 T^{4} - 126736 T^{5} + 704969 T^{6} \))(\( 1 + 37 T + 945 T^{2} + 16086 T^{3} + 218857 T^{4} + 2276992 T^{5} + 19478273 T^{6} + 127417206 T^{7} + 666195705 T^{8} + 2321462917 T^{9} + 5584059449 T^{10} \))(\( 1 - 55 T + 1703 T^{2} - 36314 T^{3} + 589608 T^{4} - 7583834 T^{5} + 79229360 T^{6} - 674961226 T^{7} + 4670284968 T^{8} - 25600244266 T^{9} + 106850036423 T^{10} - 307123269695 T^{11} + 496981290961 T^{12} \))(\( 1 - 13 T + 367 T^{2} - 5350 T^{3} + 85200 T^{4} - 1030769 T^{5} + 13079114 T^{6} - 132929866 T^{7} + 1373226193 T^{8} - 11830758074 T^{9} + 103599661994 T^{10} - 726660191161 T^{11} + 5345638933200 T^{12} - 29874718052150 T^{13} + 182392133782687 T^{14} - 575007353641877 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 11 T + 440 T^{2} + 4713 T^{3} + 92131 T^{4} + 904647 T^{5} + 12523078 T^{6} + 110132047 T^{7} + 1302015983 T^{8} + 10536868290 T^{9} + 115879422487 T^{10} + 872355944287 T^{11} + 8828381774582 T^{12} + 56759580093927 T^{13} + 514464981095819 T^{14} + 2342272824299193 T^{15} + 19461787354032760 T^{16} + 43302476862722891 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 5 T + 204 T^{2} - 679 T^{3} + 36443 T^{4} - 121843 T^{5} + 4398946 T^{6} - 10639421 T^{7} + 472479025 T^{8} - 1329308246 T^{9} + 42050633225 T^{10} - 84274853741 T^{11} + 3101120562674 T^{12} - 7644702870163 T^{13} + 203499878499907 T^{14} - 337450296562519 T^{15} + 9023192318687916 T^{16} - 19682944028510405 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 36 T + 837 T^{2} + 14566 T^{3} + 229521 T^{4} + 3176651 T^{5} + 40106351 T^{6} + 456095235 T^{7} + 4883465149 T^{8} + 47791352761 T^{9} + 434628398261 T^{10} + 3612730356435 T^{11} + 28273734158119 T^{12} + 199310202614891 T^{13} + 1281658908793929 T^{14} + 7239029484137926 T^{15} + 37021627307557773 T^{16} + 141717197005274916 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 6 T + 677 T^{2} + 4094 T^{3} + 212857 T^{4} + 1228167 T^{5} + 40743411 T^{6} + 213245353 T^{7} + 5224210325 T^{8} + 23520533541 T^{9} + 464954718925 T^{10} + 1689116441113 T^{11} + 28722841709259 T^{12} + 77057949902247 T^{13} + 1188606142135793 T^{14} + 2034641405194334 T^{15} + 29944613724273133 T^{16} + 23619532834212486 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 32 T + 1109 T^{2} - 23480 T^{3} + 472337 T^{4} - 7444883 T^{5} + 108350271 T^{6} - 1337555909 T^{7} + 15130693509 T^{8} - 149232925195 T^{9} + 1346631722301 T^{10} - 10594780355189 T^{11} + 76383582196599 T^{12} - 467108643402803 T^{13} + 2637557887962313 T^{14} - 11669120711764280 T^{15} + 49052550399141661 T^{16} - 125970841782466592 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 7 T + 618 T^{2} - 3859 T^{3} + 179101 T^{4} - 1003609 T^{5} + 32276296 T^{6} - 160578387 T^{7} + 4008678339 T^{8} - 17246000590 T^{9} + 356772372171 T^{10} - 1271941403427 T^{11} + 22753788114824 T^{12} - 62968677747769 T^{13} + 1000110631375349 T^{14} - 1917850801818499 T^{15} + 27334964965436922 T^{16} - 27556121639914567 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 18 T + 498 T^{2} + 6870 T^{3} + 114090 T^{4} + 1249991 T^{5} + 16070698 T^{6} + 144657182 T^{7} + 1627247754 T^{8} + 13217567006 T^{9} + 145173992544 T^{10} + 1176363463534 T^{11} + 12889429459434 T^{12} + 101978828937358 T^{13} + 1008311606954218 T^{14} + 6980024054714959 T^{15} + 56700595485740490 T^{16} + 303869270732284230 T^{17} + 1960421225239636338 T^{18} + 6306415266734733762 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 19 T + 639 T^{2} + 10004 T^{3} + 203345 T^{4} + 2686574 T^{5} + 41140911 T^{6} + 466507158 T^{7} + 5835782923 T^{8} + 57092647305 T^{9} + 604183241618 T^{10} + 5081245610145 T^{11} + 46225236533083 T^{12} + 328873084668102 T^{13} + 2581272952921551 T^{14} + 15001988930137726 T^{15} + 101058660610464545 T^{16} + 442490274294872116 T^{17} + 2515480246843629759 T^{18} + 6656771670442218971 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 22 T + 656 T^{2} + 12304 T^{3} + 222916 T^{4} + 3358293 T^{5} + 47532416 T^{6} + 590926676 T^{7} + 6925796868 T^{8} + 72929260954 T^{9} + 722999129492 T^{10} + 6490704224906 T^{11} + 54859236991428 T^{12} + 416584987853044 T^{13} + 2982290299984256 T^{14} + 18752907759160557 T^{15} + 110785081455862276 T^{16} + 544222344554588816 T^{17} + 2582402256540565136 T^{18} + 7707840881564674598 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 2 T + 596 T^{2} - 1695 T^{3} + 172400 T^{4} - 654480 T^{5} + 32360761 T^{6} - 150913266 T^{7} + 4465378150 T^{8} - 23067477511 T^{9} + 486095075877 T^{10} - 2447511368550 T^{11} + 43262461753053 T^{12} - 182717489364631 T^{13} + 3147953169027350 T^{14} - 9468636505469106 T^{15} + 180704413238880689 T^{16} - 325264315308155280 T^{17} + 7625482135989199600 T^{18} - 6672518025665027295 T^{19} + \)\(20\!\cdots\!64\)\( T^{20} - 62363439859932367202 T^{21} + \)\(27\!\cdots\!89\)\( T^{22} \))(\( 1 - 20 T + 591 T^{2} - 8534 T^{3} + 147340 T^{4} - 1724615 T^{5} + 23172868 T^{6} - 245128371 T^{7} + 2937871924 T^{8} - 29454684006 T^{9} + 321616971802 T^{10} - 2943714830264 T^{11} + 28623910490378 T^{12} - 233310552011526 T^{13} + 2071108632390356 T^{14} - 15379903329219411 T^{15} + 129398672515829732 T^{16} - 857101389110705015 T^{17} + 6517044883507242860 T^{18} - 33594848867861559254 T^{19} + \)\(20\!\cdots\!19\)\( T^{20} - \)\(62\!\cdots\!20\)\( T^{21} + \)\(27\!\cdots\!89\)\( T^{22} \))(\( 1 - 16 T + 831 T^{2} - 11421 T^{3} + 320830 T^{4} - 3837719 T^{5} + 77030181 T^{6} - 811422304 T^{7} + 13007984019 T^{8} - 121856521649 T^{9} + 1655812465625 T^{10} - 13871191724275 T^{11} + 165297472930578 T^{12} - 1234536063460475 T^{13} + 13115690540215625 T^{14} - 85905070210373881 T^{15} + 816150068244246579 T^{16} - 4531030383780550496 T^{17} + 38282558796339493941 T^{18} - \)\(16\!\cdots\!51\)\( T^{19} + \)\(12\!\cdots\!30\)\( T^{20} - \)\(40\!\cdots\!89\)\( T^{21} + \)\(25\!\cdots\!31\)\( T^{22} - \)\(44\!\cdots\!24\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 14 T + 658 T^{2} + 7597 T^{3} + 203770 T^{4} + 2023268 T^{5} + 40236108 T^{6} + 361835378 T^{7} + 5901285772 T^{8} + 50770589224 T^{9} + 713243319919 T^{10} + 6074505002968 T^{11} + 75488770285506 T^{12} + 630554511356379 T^{13} + 7119284468506396 T^{14} + 56119351510717731 T^{15} + 597946549431493026 T^{16} + 4282337717437347992 T^{17} + 44750484269997998479 T^{18} + \)\(28\!\cdots\!76\)\( T^{19} + \)\(29\!\cdots\!92\)\( T^{20} + \)\(16\!\cdots\!62\)\( T^{21} + \)\(15\!\cdots\!48\)\( T^{22} + \)\(70\!\cdots\!12\)\( T^{23} + \)\(63\!\cdots\!70\)\( T^{24} + \)\(21\!\cdots\!33\)\( T^{25} + \)\(16\!\cdots\!18\)\( T^{26} + \)\(30\!\cdots\!66\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( 1 - 28 T + 1311 T^{2} - 28655 T^{3} + 767942 T^{4} - 13835479 T^{5} + 273267078 T^{6} - 4196252010 T^{7} + 67115772982 T^{8} - 898097191562 T^{9} + 12197399026975 T^{10} - 144360876609698 T^{11} + 1711020324535483 T^{12} - 18076483853316727 T^{13} + 190021712832571156 T^{14} - 1798857198578466754 T^{15} + 16911932442098832884 T^{16} - \)\(14\!\cdots\!67\)\( T^{17} + \)\(12\!\cdots\!27\)\( T^{18} - \)\(90\!\cdots\!18\)\( T^{19} + \)\(68\!\cdots\!75\)\( T^{20} - \)\(44\!\cdots\!82\)\( T^{21} + \)\(29\!\cdots\!78\)\( T^{22} - \)\(16\!\cdots\!10\)\( T^{23} + \)\(95\!\cdots\!02\)\( T^{24} - \)\(43\!\cdots\!79\)\( T^{25} + \)\(21\!\cdots\!38\)\( T^{26} - \)\(70\!\cdots\!55\)\( T^{27} + \)\(28\!\cdots\!59\)\( T^{28} - \)\(54\!\cdots\!48\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))
$97$ (\( 1 - 17 T + 97 T^{2} \))(\( 1 + 9 T + 97 T^{2} \))(\( 1 + 11 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 12 T + 150 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( 1 - T + 35 T^{2} - 630 T^{3} + 3395 T^{4} - 9409 T^{5} + 912673 T^{6} \))(\( 1 - 18 T + 469 T^{2} - 6621 T^{3} + 89573 T^{4} - 946052 T^{5} + 8688581 T^{6} - 62296989 T^{7} + 428043637 T^{8} - 1593527058 T^{9} + 8587340257 T^{10} \))(\( 1 - 37 T + 866 T^{2} - 14993 T^{3} + 216399 T^{4} - 2619306 T^{5} + 27731228 T^{6} - 254072682 T^{7} + 2036098191 T^{8} - 13683706289 T^{9} + 76666357346 T^{10} - 317731589509 T^{11} + 832972004929 T^{12} \))(\( 1 - 18 T + 752 T^{2} - 10531 T^{3} + 246943 T^{4} - 2791331 T^{5} + 46835252 T^{6} - 431230216 T^{7} + 5633846776 T^{8} - 41829330952 T^{9} + 440672886068 T^{10} - 2547572437763 T^{11} + 21861686237983 T^{12} - 90433280246467 T^{13} + 626394947706608 T^{14} - 1454369120606034 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 187 T^{2} - 1603 T^{3} + 28071 T^{4} - 201640 T^{5} + 5440447 T^{6} - 25034565 T^{7} + 521044510 T^{8} - 4053338400 T^{9} + 50541317470 T^{10} - 235550222085 T^{11} + 4965349084831 T^{12} - 17851044220840 T^{13} + 241055228354247 T^{14} - 1335254123901187 T^{15} + 15109279197407131 T^{16} + 760231058654565217 T^{18} \))(\( 1 - 18 T + 675 T^{2} - 9315 T^{3} + 194149 T^{4} - 2183092 T^{5} + 33162181 T^{6} - 320173045 T^{7} + 4028505266 T^{8} - 34845875524 T^{9} + 390765010802 T^{10} - 3012508180405 T^{11} + 30266227219813 T^{12} - 193267565116852 T^{13} + 1667223523556293 T^{14} - 7759134225913635 T^{15} + 54538842022726275 T^{16} - 141073804698785298 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 5 T + 353 T^{2} + 1825 T^{3} + 63896 T^{4} + 373303 T^{5} + 8320220 T^{6} + 54846839 T^{7} + 882994154 T^{8} + 6081964552 T^{9} + 85650432938 T^{10} + 516053908151 T^{11} + 7593640148060 T^{12} + 33048246185143 T^{13} + 548696693061272 T^{14} + 1520173908995425 T^{15} + 28521794420773889 T^{16} + 39187167971884805 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 3 T + 491 T^{2} + 525 T^{3} + 120154 T^{4} - 3579 T^{5} + 19862938 T^{6} - 11754741 T^{7} + 2459126496 T^{8} - 1757418096 T^{9} + 238535270112 T^{10} - 110600358069 T^{11} + 18128367213274 T^{12} - 316846296699 T^{13} + 1031803281239578 T^{14} + 437310302587725 T^{15} + 39671957678753483 T^{16} + 23512300783130883 T^{17} + 760231058654565217 T^{18} \))(\( 1 - 17 T + 571 T^{2} - 6955 T^{3} + 149788 T^{4} - 1492511 T^{5} + 25365804 T^{6} - 214611237 T^{7} + 3149062076 T^{8} - 23486266064 T^{9} + 305459021372 T^{10} - 2019277128933 T^{11} + 23150684434092 T^{12} - 132130925714591 T^{13} + 1286280522415516 T^{14} - 5793320294281195 T^{15} + 46135820437002523 T^{16} - 133236371104408337 T^{17} + 760231058654565217 T^{18} \))(\( 1 - 2 T + 505 T^{2} - 51 T^{3} + 128739 T^{4} + 115864 T^{5} + 22391131 T^{6} + 27065123 T^{7} + 2878949816 T^{8} + 3334138196 T^{9} + 279258132152 T^{10} + 254655742307 T^{11} + 20435780703163 T^{12} + 10257356613784 T^{13} + 1105525597345923 T^{14} - 42481572251379 T^{15} + 40803133661447065 T^{16} - 15674867188753922 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 9 T + 686 T^{2} + 5198 T^{3} + 225881 T^{4} + 1477486 T^{5} + 47611206 T^{6} + 272379076 T^{7} + 7147461446 T^{8} + 35836368167 T^{9} + 798742143352 T^{10} + 3476127712199 T^{11} + 67250464745414 T^{12} + 248593028430148 T^{13} + 4214985834722886 T^{14} + 12687675006953902 T^{15} + 188152549445367449 T^{16} + 419989482717231374 T^{17} + 5376479445742595246 T^{18} + 6842079527891086953 T^{19} + 73742412689492826049 T^{20} \))(\( 1 + 22 T + 608 T^{2} + 9933 T^{3} + 172256 T^{4} + 2343065 T^{5} + 32087298 T^{6} + 374806683 T^{7} + 4407454543 T^{8} + 45463808297 T^{9} + 477107673948 T^{10} + 4409989404809 T^{11} + 41469739795087 T^{12} + 342075939793659 T^{13} + 2840665421172738 T^{14} + 20120696399267705 T^{15} + 143484425681049824 T^{16} + 802569359721096429 T^{17} + 4765159625381192288 T^{18} + 16725083290400434774 T^{19} + 73742412689492826049 T^{20} \))(\( 1 + 9 T + 736 T^{2} + 5626 T^{3} + 257179 T^{4} + 1707422 T^{5} + 56621714 T^{6} + 329089196 T^{7} + 8722674276 T^{8} + 44244616163 T^{9} + 983033276348 T^{10} + 4291727767811 T^{11} + 82071642262884 T^{12} + 300350823780908 T^{13} + 5012679629407634 T^{14} + 14662213676287454 T^{15} + 214222907255635291 T^{16} + 454571148473863738 T^{17} + 5768351125461443296 T^{18} + 6842079527891086953 T^{19} + 73742412689492826049 T^{20} \))(\( 1 + 6 T + 157 T^{2} - 903 T^{3} + 8316 T^{4} - 139260 T^{5} + 1894990 T^{6} + 1885736 T^{7} + 293559165 T^{8} + 300116246 T^{9} + 9525182171 T^{10} - 132594826882 T^{11} + 923942670587 T^{12} + 2823793758614 T^{13} + 267923523798045 T^{14} + 166942852235816 T^{15} + 16272923913612430 T^{16} - 115999681406412540 T^{17} + 671918533719987708 T^{18} - 7077202535722395783 T^{19} + \)\(11\!\cdots\!69\)\( T^{20} + \)\(44\!\cdots\!94\)\( T^{21} + \)\(71\!\cdots\!53\)\( T^{22} \))(\( 1 + 25 T + 835 T^{2} + 16799 T^{3} + 339933 T^{4} + 5591948 T^{5} + 86844721 T^{6} + 1201983042 T^{7} + 15427260042 T^{8} + 183131036395 T^{9} + 2004145990212 T^{10} + 20569760330974 T^{11} + 194402161050564 T^{12} + 1723079921440555 T^{13} + 14080043704312266 T^{14} + 106410694482452802 T^{15} + 745765168751233297 T^{16} + 4657936137018711692 T^{17} + 27466003237498386429 T^{18} + \)\(13\!\cdots\!39\)\( T^{19} + \)\(63\!\cdots\!95\)\( T^{20} + \)\(18\!\cdots\!25\)\( T^{21} + \)\(71\!\cdots\!53\)\( T^{22} \))(\( 1 - 10 T + 744 T^{2} - 6827 T^{3} + 259085 T^{4} - 2139471 T^{5} + 55799064 T^{6} - 412053170 T^{7} + 8444186291 T^{8} - 56300324940 T^{9} + 996377177536 T^{10} - 6172818417374 T^{11} + 101485807573758 T^{12} - 598763386485278 T^{13} + 9374912863436224 T^{14} - 51383786463964620 T^{15} + 747557740972286771 T^{16} - 3538440774765464690 T^{17} + 46479058213241586456 T^{18} - \)\(17\!\cdots\!23\)\( T^{19} + \)\(20\!\cdots\!85\)\( T^{20} - \)\(51\!\cdots\!59\)\( T^{21} + \)\(54\!\cdots\!56\)\( T^{22} - \)\(71\!\cdots\!30\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 + 14 T + 1083 T^{2} + 13769 T^{3} + 558390 T^{4} + 6519662 T^{5} + 182759573 T^{6} + 1968215482 T^{7} + 42581168816 T^{8} + 422441805565 T^{9} + 7488822917177 T^{10} + 68026332894612 T^{11} + 1026781284240793 T^{12} + 8450645219888272 T^{13} + 111584666631063150 T^{14} + 819712586329162384 T^{15} + 9660985103421621337 T^{16} + 62085797321924217876 T^{17} + \)\(66\!\cdots\!37\)\( T^{18} + \)\(36\!\cdots\!05\)\( T^{19} + \)\(35\!\cdots\!64\)\( T^{20} + \)\(15\!\cdots\!66\)\( T^{21} + \)\(14\!\cdots\!53\)\( T^{22} + \)\(49\!\cdots\!54\)\( T^{23} + \)\(41\!\cdots\!10\)\( T^{24} + \)\(98\!\cdots\!57\)\( T^{25} + \)\(75\!\cdots\!03\)\( T^{26} + \)\(94\!\cdots\!78\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 - 30 T + 1116 T^{2} - 24937 T^{3} + 563543 T^{4} - 10136247 T^{5} + 175815277 T^{6} - 2669157828 T^{7} + 38675518343 T^{8} - 512301049383 T^{9} + 6483047554095 T^{10} - 76873805033215 T^{11} + 874810798838950 T^{12} - 9475428309895364 T^{13} + 98939872576286179 T^{14} - 991531554936053416 T^{15} + 9597167639899759363 T^{16} - 89154304967805479876 T^{17} + \)\(79\!\cdots\!50\)\( T^{18} - \)\(68\!\cdots\!15\)\( T^{19} + \)\(55\!\cdots\!15\)\( T^{20} - \)\(42\!\cdots\!07\)\( T^{21} + \)\(31\!\cdots\!59\)\( T^{22} - \)\(20\!\cdots\!08\)\( T^{23} + \)\(13\!\cdots\!09\)\( T^{24} - \)\(74\!\cdots\!03\)\( T^{25} + \)\(40\!\cdots\!79\)\( T^{26} - \)\(17\!\cdots\!17\)\( T^{27} + \)\(75\!\cdots\!32\)\( T^{28} - \)\(19\!\cdots\!70\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))
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