Properties

 Label 6039.2 Level 6039 Weight 2 Dimension 1.03719e+06 Nonzero newspaces 210 Sturm bound 5.3568e+06

Defining parameters

 Level: $$N$$ = $$6039 = 3^{2} \cdot 11 \cdot 61$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$210$$ Sturm bound: $$5356800$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6039))$$.

Total New Old
Modular forms 1348800 1046750 302050
Cusp forms 1329601 1037190 292411
Eisenstein series 19199 9560 9639

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6039))$$

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
6039.2.a $$\chi_{6039}(1, \cdot)$$ 6039.2.a.a 5 1
6039.2.a.b 6
6039.2.a.c 11
6039.2.a.d 11
6039.2.a.e 12
6039.2.a.f 12
6039.2.a.g 13
6039.2.a.h 13
6039.2.a.i 13
6039.2.a.j 14
6039.2.a.k 19
6039.2.a.l 21
6039.2.a.m 25
6039.2.a.n 25
6039.2.a.o 25
6039.2.a.p 25
6039.2.b $$\chi_{6039}(6038, \cdot)$$ n/a 248 1
6039.2.e $$\chi_{6039}(1585, \cdot)$$ n/a 256 1
6039.2.f $$\chi_{6039}(4454, \cdot)$$ n/a 240 1
6039.2.i $$\chi_{6039}(2575, \cdot)$$ n/a 520 2
6039.2.j $$\chi_{6039}(2014, \cdot)$$ n/a 1200 2
6039.2.k $$\chi_{6039}(3829, \cdot)$$ n/a 1240 2
6039.2.l $$\chi_{6039}(562, \cdot)$$ n/a 1240 2
6039.2.m $$\chi_{6039}(4564, \cdot)$$ n/a 616 2
6039.2.p $$\chi_{6039}(782, \cdot)$$ n/a 408 2
6039.2.q $$\chi_{6039}(874, \cdot)$$ n/a 1232 4
6039.2.r $$\chi_{6039}(3070, \cdot)$$ n/a 1032 4
6039.2.s $$\chi_{6039}(1648, \cdot)$$ n/a 1200 4
6039.2.t $$\chi_{6039}(1351, \cdot)$$ n/a 1232 4
6039.2.u $$\chi_{6039}(1522, \cdot)$$ n/a 1232 4
6039.2.v $$\chi_{6039}(973, \cdot)$$ n/a 1232 4
6039.2.w $$\chi_{6039}(3037, \cdot)$$ n/a 1240 2
6039.2.z $$\chi_{6039}(4223, \cdot)$$ n/a 1480 2
6039.2.ba $$\chi_{6039}(230, \cdot)$$ n/a 1480 2
6039.2.bf $$\chi_{6039}(428, \cdot)$$ n/a 1440 2
6039.2.bh $$\chi_{6039}(989, \cdot)$$ n/a 496 2
6039.2.bj $$\chi_{6039}(1451, \cdot)$$ n/a 1480 2
6039.2.bl $$\chi_{6039}(3598, \cdot)$$ n/a 1240 2
6039.2.bn $$\chi_{6039}(1783, \cdot)$$ n/a 516 2
6039.2.bq $$\chi_{6039}(197, \cdot)$$ n/a 496 2
6039.2.bs $$\chi_{6039}(2012, \cdot)$$ n/a 1480 2
6039.2.bu $$\chi_{6039}(1024, \cdot)$$ n/a 1240 2
6039.2.bx $$\chi_{6039}(2243, \cdot)$$ n/a 1480 2
6039.2.by $$\chi_{6039}(163, \cdot)$$ n/a 1232 4
6039.2.cb $$\chi_{6039}(1322, \cdot)$$ n/a 992 4
6039.2.cd $$\chi_{6039}(314, \cdot)$$ n/a 992 4
6039.2.cj $$\chi_{6039}(2510, \cdot)$$ n/a 992 4
6039.2.cl $$\chi_{6039}(62, \cdot)$$ n/a 960 4
6039.2.cm $$\chi_{6039}(1484, \cdot)$$ n/a 992 4
6039.2.co $$\chi_{6039}(3572, \cdot)$$ n/a 992 4
6039.2.cs $$\chi_{6039}(332, \cdot)$$ n/a 992 4
6039.2.ct $$\chi_{6039}(1369, \cdot)$$ n/a 1232 4
6039.2.cv $$\chi_{6039}(487, \cdot)$$ n/a 1232 4
6039.2.cy $$\chi_{6039}(64, \cdot)$$ n/a 1232 4
6039.2.da $$\chi_{6039}(1882, \cdot)$$ n/a 1024 4
6039.2.db $$\chi_{6039}(296, \cdot)$$ n/a 992 4
6039.2.dd $$\chi_{6039}(1223, \cdot)$$ n/a 992 4
6039.2.dg $$\chi_{6039}(1097, \cdot)$$ n/a 992 4
6039.2.di $$\chi_{6039}(3968, \cdot)$$ n/a 992 4
6039.2.dj $$\chi_{6039}(2809, \cdot)$$ n/a 1232 4
6039.2.dn $$\chi_{6039}(3779, \cdot)$$ n/a 992 4
6039.2.do $$\chi_{6039}(947, \cdot)$$ n/a 2480 4
6039.2.dr $$\chi_{6039}(1363, \cdot)$$ n/a 2960 4
6039.2.ds $$\chi_{6039}(1066, \cdot)$$ n/a 2960 4
6039.2.du $$\chi_{6039}(2795, \cdot)$$ n/a 2480 4
6039.2.dv $$\chi_{6039}(2663, \cdot)$$ n/a 832 4
6039.2.ea $$\chi_{6039}(406, \cdot)$$ n/a 1232 4
6039.2.eb $$\chi_{6039}(538, \cdot)$$ n/a 2960 4
6039.2.ed $$\chi_{6039}(650, \cdot)$$ n/a 2480 4
6039.2.ee $$\chi_{6039}(850, \cdot)$$ n/a 5920 8
6039.2.ef $$\chi_{6039}(400, \cdot)$$ n/a 5920 8
6039.2.eg $$\chi_{6039}(757, \cdot)$$ n/a 2464 8
6039.2.eh $$\chi_{6039}(25, \cdot)$$ n/a 5920 8
6039.2.ei $$\chi_{6039}(169, \cdot)$$ n/a 5920 8
6039.2.ej $$\chi_{6039}(1123, \cdot)$$ n/a 4960 8
6039.2.ek $$\chi_{6039}(1093, \cdot)$$ n/a 5920 8
6039.2.el $$\chi_{6039}(1582, \cdot)$$ n/a 5920 8
6039.2.em $$\chi_{6039}(1534, \cdot)$$ n/a 5920 8
6039.2.en $$\chi_{6039}(1765, \cdot)$$ n/a 2464 8
6039.2.eo $$\chi_{6039}(565, \cdot)$$ n/a 5920 8
6039.2.ep $$\chi_{6039}(196, \cdot)$$ n/a 5920 8
6039.2.eq $$\chi_{6039}(16, \cdot)$$ n/a 5920 8
6039.2.er $$\chi_{6039}(727, \cdot)$$ n/a 4960 8
6039.2.es $$\chi_{6039}(58, \cdot)$$ n/a 5920 8
6039.2.et $$\chi_{6039}(361, \cdot)$$ n/a 2464 8
6039.2.eu $$\chi_{6039}(379, \cdot)$$ n/a 2464 8
6039.2.ev $$\chi_{6039}(34, \cdot)$$ n/a 4960 8
6039.2.ew $$\chi_{6039}(70, \cdot)$$ n/a 5920 8
6039.2.ex $$\chi_{6039}(199, \cdot)$$ n/a 2080 8
6039.2.ey $$\chi_{6039}(2269, \cdot)$$ n/a 2464 8
6039.2.ez $$\chi_{6039}(367, \cdot)$$ n/a 5760 8
6039.2.fa $$\chi_{6039}(103, \cdot)$$ n/a 5920 8
6039.2.fb $$\chi_{6039}(1642, \cdot)$$ n/a 5920 8
6039.2.fc $$\chi_{6039}(647, \cdot)$$ n/a 1984 8
6039.2.ff $$\chi_{6039}(28, \cdot)$$ n/a 2464 8
6039.2.fh $$\chi_{6039}(541, \cdot)$$ n/a 2464 8
6039.2.fj $$\chi_{6039}(1070, \cdot)$$ n/a 1984 8
6039.2.fk $$\chi_{6039}(1061, \cdot)$$ n/a 1984 8
6039.2.fl $$\chi_{6039}(377, \cdot)$$ n/a 1984 8
6039.2.fp $$\chi_{6039}(89, \cdot)$$ n/a 1632 8
6039.2.fq $$\chi_{6039}(1000, \cdot)$$ n/a 2464 8
6039.2.fu $$\chi_{6039}(172, \cdot)$$ n/a 2464 8
6039.2.fv $$\chi_{6039}(2224, \cdot)$$ n/a 2464 8
6039.2.fw $$\chi_{6039}(145, \cdot)$$ n/a 2464 8
6039.2.fy $$\chi_{6039}(53, \cdot)$$ n/a 1984 8
6039.2.ga $$\chi_{6039}(167, \cdot)$$ n/a 5920 8
6039.2.gd $$\chi_{6039}(97, \cdot)$$ n/a 5920 8
6039.2.gf $$\chi_{6039}(1052, \cdot)$$ n/a 1984 8
6039.2.gh $$\chi_{6039}(95, \cdot)$$ n/a 5920 8
6039.2.gm $$\chi_{6039}(83, \cdot)$$ n/a 5920 8
6039.2.go $$\chi_{6039}(1262, \cdot)$$ n/a 5920 8
6039.2.gr $$\chi_{6039}(266, \cdot)$$ n/a 5920 8
6039.2.gt $$\chi_{6039}(164, \cdot)$$ n/a 5920 8
6039.2.gu $$\chi_{6039}(596, \cdot)$$ n/a 5920 8
6039.2.ha $$\chi_{6039}(1337, \cdot)$$ n/a 5920 8
6039.2.hd $$\chi_{6039}(248, \cdot)$$ n/a 5920 8
6039.2.hf $$\chi_{6039}(289, \cdot)$$ n/a 2464 8
6039.2.hh $$\chi_{6039}(796, \cdot)$$ n/a 5920 8
6039.2.hj $$\chi_{6039}(4, \cdot)$$ n/a 5920 8
6039.2.hl $$\chi_{6039}(463, \cdot)$$ n/a 4960 8
6039.2.hm $$\chi_{6039}(1417, \cdot)$$ n/a 5920 8
6039.2.ho $$\chi_{6039}(49, \cdot)$$ n/a 5920 8
6039.2.hq $$\chi_{6039}(149, \cdot)$$ n/a 5920 8
6039.2.hs $$\chi_{6039}(431, \cdot)$$ n/a 1984 8
6039.2.hu $$\chi_{6039}(1295, \cdot)$$ n/a 1984 8
6039.2.hx $$\chi_{6039}(1064, \cdot)$$ n/a 5920 8
6039.2.hz $$\chi_{6039}(857, \cdot)$$ n/a 5920 8
6039.2.ib $$\chi_{6039}(107, \cdot)$$ n/a 1984 8
6039.2.id $$\chi_{6039}(890, \cdot)$$ n/a 1984 8
6039.2.ie $$\chi_{6039}(182, \cdot)$$ n/a 5920 8
6039.2.ih $$\chi_{6039}(1219, \cdot)$$ n/a 5920 8
6039.2.ii $$\chi_{6039}(100, \cdot)$$ n/a 2064 8
6039.2.ik $$\chi_{6039}(280, \cdot)$$ n/a 2464 8
6039.2.im $$\chi_{6039}(430, \cdot)$$ n/a 4960 8
6039.2.io $$\chi_{6039}(346, \cdot)$$ n/a 5920 8
6039.2.ir $$\chi_{6039}(136, \cdot)$$ n/a 2464 8
6039.2.it $$\chi_{6039}(829, \cdot)$$ n/a 2464 8
6039.2.iv $$\chi_{6039}(895, \cdot)$$ n/a 5920 8
6039.2.ix $$\chi_{6039}(842, \cdot)$$ n/a 5920 8
6039.2.iz $$\chi_{6039}(563, \cdot)$$ n/a 5920 8
6039.2.ja $$\chi_{6039}(2540, \cdot)$$ n/a 5920 8
6039.2.jc $$\chi_{6039}(893, \cdot)$$ n/a 5920 8
6039.2.je $$\chi_{6039}(41, \cdot)$$ n/a 5920 8
6039.2.jg $$\chi_{6039}(161, \cdot)$$ n/a 1984 8
6039.2.ji $$\chi_{6039}(202, \cdot)$$ n/a 5920 8
6039.2.jl $$\chi_{6039}(545, \cdot)$$ n/a 5920 8
6039.2.js $$\chi_{6039}(794, \cdot)$$ n/a 5760 8
6039.2.jv $$\chi_{6039}(503, \cdot)$$ n/a 1984 8
6039.2.jx $$\chi_{6039}(1781, \cdot)$$ n/a 1984 8
6039.2.jz $$\chi_{6039}(1559, \cdot)$$ n/a 5920 8
6039.2.kb $$\chi_{6039}(131, \cdot)$$ n/a 5920 8
6039.2.kc $$\chi_{6039}(413, \cdot)$$ n/a 1984 8
6039.2.ke $$\chi_{6039}(260, \cdot)$$ n/a 1984 8
6039.2.kg $$\chi_{6039}(497, \cdot)$$ n/a 5920 8
6039.2.kq $$\chi_{6039}(1154, \cdot)$$ n/a 5920 8
6039.2.ks $$\chi_{6039}(1733, \cdot)$$ n/a 5920 8
6039.2.kv $$\chi_{6039}(74, \cdot)$$ n/a 5920 8
6039.2.kx $$\chi_{6039}(1184, \cdot)$$ n/a 5920 8
6039.2.ky $$\chi_{6039}(134, \cdot)$$ n/a 1984 8
6039.2.la $$\chi_{6039}(569, \cdot)$$ n/a 5920 8
6039.2.le $$\chi_{6039}(229, \cdot)$$ n/a 5920 8
6039.2.lf $$\chi_{6039}(380, \cdot)$$ n/a 5920 8
6039.2.li $$\chi_{6039}(1073, \cdot)$$ n/a 5920 8
6039.2.lk $$\chi_{6039}(65, \cdot)$$ n/a 5920 8
6039.2.ll $$\chi_{6039}(524, \cdot)$$ n/a 5920 8
6039.2.lo $$\chi_{6039}(1285, \cdot)$$ n/a 5920 8
6039.2.lp $$\chi_{6039}(232, \cdot)$$ n/a 4960 8
6039.2.lr $$\chi_{6039}(1483, \cdot)$$ n/a 5920 8
6039.2.lu $$\chi_{6039}(841, \cdot)$$ n/a 5920 8
6039.2.lv $$\chi_{6039}(1910, \cdot)$$ n/a 5920 8
6039.2.lx $$\chi_{6039}(553, \cdot)$$ n/a 5920 8
6039.2.lz $$\chi_{6039}(1040, \cdot)$$ n/a 5920 8
6039.2.mb $$\chi_{6039}(656, \cdot)$$ n/a 1984 8
6039.2.me $$\chi_{6039}(1666, \cdot)$$ n/a 2464 8
6039.2.mg $$\chi_{6039}(247, \cdot)$$ n/a 5920 8
6039.2.mi $$\chi_{6039}(293, \cdot)$$ n/a 5920 8
6039.2.mj $$\chi_{6039}(239, \cdot)$$ n/a 5920 8
6039.2.mm $$\chi_{6039}(349, \cdot)$$ n/a 11840 16
6039.2.mp $$\chi_{6039}(311, \cdot)$$ n/a 11840 16
6039.2.mr $$\chi_{6039}(79, \cdot)$$ n/a 11840 16
6039.2.mu $$\chi_{6039}(26, \cdot)$$ n/a 3968 16
6039.2.mv $$\chi_{6039}(38, \cdot)$$ n/a 11840 16
6039.2.mx $$\chi_{6039}(212, \cdot)$$ n/a 11840 16
6039.2.my $$\chi_{6039}(434, \cdot)$$ n/a 11840 16
6039.2.mz $$\chi_{6039}(383, \cdot)$$ n/a 11840 16
6039.2.nd $$\chi_{6039}(518, \cdot)$$ n/a 9920 16
6039.2.ng $$\chi_{6039}(226, \cdot)$$ n/a 4928 16
6039.2.nh $$\chi_{6039}(211, \cdot)$$ n/a 11840 16
6039.2.ni $$\chi_{6039}(904, \cdot)$$ n/a 11840 16
6039.2.nj $$\chi_{6039}(1432, \cdot)$$ n/a 4928 16
6039.2.nk $$\chi_{6039}(811, \cdot)$$ n/a 4928 16
6039.2.nl $$\chi_{6039}(358, \cdot)$$ n/a 11840 16
6039.2.ns $$\chi_{6039}(175, \cdot)$$ n/a 11840 16
6039.2.nt $$\chi_{6039}(10, \cdot)$$ n/a 4928 16
6039.2.nu $$\chi_{6039}(287, \cdot)$$ n/a 3328 16
6039.2.nv $$\chi_{6039}(23, \cdot)$$ n/a 9920 16
6039.2.oc $$\chi_{6039}(236, \cdot)$$ n/a 11840 16
6039.2.od $$\chi_{6039}(872, \cdot)$$ n/a 3968 16
6039.2.oe $$\chi_{6039}(467, \cdot)$$ n/a 3968 16
6039.2.of $$\chi_{6039}(416, \cdot)$$ n/a 11840 16
6039.2.og $$\chi_{6039}(389, \cdot)$$ n/a 11840 16
6039.2.oh $$\chi_{6039}(71, \cdot)$$ n/a 3968 16
6039.2.ok $$\chi_{6039}(43, \cdot)$$ n/a 11840 16
6039.2.oo $$\chi_{6039}(7, \cdot)$$ n/a 11840 16
6039.2.op $$\chi_{6039}(139, \cdot)$$ n/a 11840 16
6039.2.oq $$\chi_{6039}(337, \cdot)$$ n/a 11840 16
6039.2.os $$\chi_{6039}(85, \cdot)$$ n/a 11840 16
6039.2.ot $$\chi_{6039}(1063, \cdot)$$ n/a 4928 16
6039.2.ow $$\chi_{6039}(542, \cdot)$$ n/a 11840 16
6039.2.oz $$\chi_{6039}(59, \cdot)$$ n/a 11840 16
6039.2.pb $$\chi_{6039}(871, \cdot)$$ n/a 11840 16
6039.2.pc $$\chi_{6039}(238, \cdot)$$ n/a 11840 16
6039.2.pd $$\chi_{6039}(40, \cdot)$$ n/a 11840 16
6039.2.ph $$\chi_{6039}(340, \cdot)$$ n/a 11840 16
6039.2.pi $$\chi_{6039}(254, \cdot)$$ n/a 9920 16
6039.2.pm $$\chi_{6039}(284, \cdot)$$ n/a 11840 16
6039.2.pn $$\chi_{6039}(185, \cdot)$$ n/a 11840 16
6039.2.po $$\chi_{6039}(92, \cdot)$$ n/a 11840 16
6039.2.pq $$\chi_{6039}(376, \cdot)$$ n/a 11840 16
6039.2.ps $$\chi_{6039}(356, \cdot)$$ n/a 11840 16
6039.2.pu $$\chi_{6039}(94, \cdot)$$ n/a 11840 16
6039.2.pv $$\chi_{6039}(523, \cdot)$$ n/a 4928 16
6039.2.qa $$\chi_{6039}(152, \cdot)$$ n/a 3968 16
6039.2.qb $$\chi_{6039}(191, \cdot)$$ n/a 11840 16
6039.2.qd $$\chi_{6039}(250, \cdot)$$ n/a 11840 16

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6039))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6039)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(61))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(183))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(549))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(671))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2013))$$$$^{\oplus 2}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - 2 T + 7 T^{2} - 12 T^{3} + 24 T^{4} - 33 T^{5} + 48 T^{6} - 48 T^{7} + 56 T^{8} - 32 T^{9} + 32 T^{10}$$)($$1 + 5 T^{2} - 2 T^{3} + 16 T^{4} - 7 T^{5} + 38 T^{6} - 14 T^{7} + 64 T^{8} - 16 T^{9} + 80 T^{10} + 64 T^{12}$$)($$1 - 2 T + 8 T^{2} - 13 T^{3} + 34 T^{4} - 53 T^{5} + 113 T^{6} - 169 T^{7} + 306 T^{8} - 437 T^{9} + 706 T^{10} - 957 T^{11} + 1412 T^{12} - 1748 T^{13} + 2448 T^{14} - 2704 T^{15} + 3616 T^{16} - 3392 T^{17} + 4352 T^{18} - 3328 T^{19} + 4096 T^{20} - 2048 T^{21} + 2048 T^{22}$$)($$1 - 4 T + 16 T^{2} - 43 T^{3} + 110 T^{4} - 237 T^{5} + 483 T^{6} - 889 T^{7} + 1554 T^{8} - 2513 T^{9} + 3886 T^{10} - 5609 T^{11} + 7772 T^{12} - 10052 T^{13} + 12432 T^{14} - 14224 T^{15} + 15456 T^{16} - 15168 T^{17} + 14080 T^{18} - 11008 T^{19} + 8192 T^{20} - 4096 T^{21} + 2048 T^{22}$$)($$1 + T + 8 T^{2} + 9 T^{3} + 37 T^{4} + 45 T^{5} + 130 T^{6} + 166 T^{7} + 377 T^{8} + 491 T^{9} + 931 T^{10} + 1189 T^{11} + 1989 T^{12} + 2378 T^{13} + 3724 T^{14} + 3928 T^{15} + 6032 T^{16} + 5312 T^{17} + 8320 T^{18} + 5760 T^{19} + 9472 T^{20} + 4608 T^{21} + 8192 T^{22} + 2048 T^{23} + 4096 T^{24}$$)($$1 - 7 T + 30 T^{2} - 97 T^{3} + 261 T^{4} - 611 T^{5} + 1286 T^{6} - 2482 T^{7} + 4459 T^{8} - 7521 T^{9} + 12001 T^{10} - 18203 T^{11} + 26347 T^{12} - 36406 T^{13} + 48004 T^{14} - 60168 T^{15} + 71344 T^{16} - 79424 T^{17} + 82304 T^{18} - 78208 T^{19} + 66816 T^{20} - 49664 T^{21} + 30720 T^{22} - 14336 T^{23} + 4096 T^{24}$$)($$1 + 4 T + 15 T^{2} + 41 T^{3} + 102 T^{4} + 222 T^{5} + 457 T^{6} + 862 T^{7} + 1569 T^{8} + 2668 T^{9} + 4388 T^{10} + 6818 T^{11} + 10284 T^{12} + 14739 T^{13} + 20568 T^{14} + 27272 T^{15} + 35104 T^{16} + 42688 T^{17} + 50208 T^{18} + 55168 T^{19} + 58496 T^{20} + 56832 T^{21} + 52224 T^{22} + 41984 T^{23} + 30720 T^{24} + 16384 T^{25} + 8192 T^{26}$$)($$1 + 4 T + 15 T^{2} + 39 T^{3} + 98 T^{4} + 206 T^{5} + 423 T^{6} + 776 T^{7} + 1407 T^{8} + 2352 T^{9} + 3888 T^{10} + 6000 T^{11} + 9138 T^{12} + 13027 T^{13} + 18276 T^{14} + 24000 T^{15} + 31104 T^{16} + 37632 T^{17} + 45024 T^{18} + 49664 T^{19} + 54144 T^{20} + 52736 T^{21} + 50176 T^{22} + 39936 T^{23} + 30720 T^{24} + 16384 T^{25} + 8192 T^{26}$$)($$1 + 2 T + 7 T^{2} + 13 T^{3} + 30 T^{4} + 48 T^{5} + 87 T^{6} + 130 T^{7} + 219 T^{8} + 320 T^{9} + 528 T^{10} + 762 T^{11} + 1208 T^{12} + 1655 T^{13} + 2416 T^{14} + 3048 T^{15} + 4224 T^{16} + 5120 T^{17} + 7008 T^{18} + 8320 T^{19} + 11136 T^{20} + 12288 T^{21} + 15360 T^{22} + 13312 T^{23} + 14336 T^{24} + 8192 T^{25} + 8192 T^{26}$$)($$1 - T + 7 T^{2} - 6 T^{3} + 27 T^{4} - 20 T^{5} + 81 T^{6} - 55 T^{7} + 207 T^{8} - 139 T^{9} + 514 T^{10} - 356 T^{11} + 1230 T^{12} - 851 T^{13} + 2615 T^{14} - 1702 T^{15} + 4920 T^{16} - 2848 T^{17} + 8224 T^{18} - 4448 T^{19} + 13248 T^{20} - 7040 T^{21} + 20736 T^{22} - 10240 T^{23} + 27648 T^{24} - 12288 T^{25} + 28672 T^{26} - 8192 T^{27} + 16384 T^{28}$$)($$1 + 5 T + 20 T^{2} + 58 T^{3} + 150 T^{4} + 333 T^{5} + 687 T^{6} + 1281 T^{7} + 2245 T^{8} + 3601 T^{9} + 5389 T^{10} + 7263 T^{11} + 8807 T^{12} + 8713 T^{13} + 5731 T^{14} - 2894 T^{15} - 18702 T^{16} - 44917 T^{17} - 79669 T^{18} - 122313 T^{19} - 159338 T^{20} - 179668 T^{21} - 149616 T^{22} - 46304 T^{23} + 183392 T^{24} + 557632 T^{25} + 1127296 T^{26} + 1859328 T^{27} + 2759168 T^{28} + 3687424 T^{29} + 4597760 T^{30} + 5246976 T^{31} + 5627904 T^{32} + 5455872 T^{33} + 4915200 T^{34} + 3801088 T^{35} + 2621440 T^{36} + 1310720 T^{37} + 524288 T^{38}$$)
$3$ 1
$5$ ($$1 - 2 T + 22 T^{2} - 34 T^{3} + 205 T^{4} - 241 T^{5} + 1025 T^{6} - 850 T^{7} + 2750 T^{8} - 1250 T^{9} + 3125 T^{10}$$)($$1 - T + 21 T^{2} - 22 T^{3} + 201 T^{4} - 206 T^{5} + 1209 T^{6} - 1030 T^{7} + 5025 T^{8} - 2750 T^{9} + 13125 T^{10} - 3125 T^{11} + 15625 T^{12}$$)($$1 - T + 22 T^{2} - 10 T^{3} + 250 T^{4} - 92 T^{5} + 2061 T^{6} - 941 T^{7} + 13377 T^{8} - 8028 T^{9} + 75394 T^{10} - 50051 T^{11} + 376970 T^{12} - 200700 T^{13} + 1672125 T^{14} - 588125 T^{15} + 6440625 T^{16} - 1437500 T^{17} + 19531250 T^{18} - 3906250 T^{19} + 42968750 T^{20} - 9765625 T^{21} + 48828125 T^{22}$$)($$1 - 13 T + 110 T^{2} - 692 T^{3} + 3574 T^{4} - 15712 T^{5} + 60545 T^{6} - 207607 T^{7} + 641391 T^{8} - 1797574 T^{9} + 4595382 T^{10} - 10739601 T^{11} + 22976910 T^{12} - 44939350 T^{13} + 80173875 T^{14} - 129754375 T^{15} + 189203125 T^{16} - 245500000 T^{17} + 279218750 T^{18} - 270312500 T^{19} + 214843750 T^{20} - 126953125 T^{21} + 48828125 T^{22}$$)($$1 - 3 T + 33 T^{2} - 91 T^{3} + 564 T^{4} - 1426 T^{5} + 6531 T^{6} - 15207 T^{7} + 56736 T^{8} - 121503 T^{9} + 388835 T^{10} - 760775 T^{11} + 2154302 T^{12} - 3803875 T^{13} + 9720875 T^{14} - 15187875 T^{15} + 35460000 T^{16} - 47521875 T^{17} + 102046875 T^{18} - 111406250 T^{19} + 220312500 T^{20} - 177734375 T^{21} + 322265625 T^{22} - 146484375 T^{23} + 244140625 T^{24}$$)($$1 - 7 T + 49 T^{2} - 225 T^{3} + 972 T^{4} - 3480 T^{5} + 11659 T^{6} - 35101 T^{7} + 99430 T^{8} - 262799 T^{9} + 659489 T^{10} - 1575031 T^{11} + 3598106 T^{12} - 7875155 T^{13} + 16487225 T^{14} - 32849875 T^{15} + 62143750 T^{16} - 109690625 T^{17} + 182171875 T^{18} - 271875000 T^{19} + 379687500 T^{20} - 439453125 T^{21} + 478515625 T^{22} - 341796875 T^{23} + 244140625 T^{24}$$)($$1 + 7 T + 52 T^{2} + 250 T^{3} + 1179 T^{4} + 4487 T^{5} + 16623 T^{6} + 53521 T^{7} + 167951 T^{8} + 473540 T^{9} + 1304029 T^{10} + 3279296 T^{11} + 8063973 T^{12} + 18231446 T^{13} + 40319865 T^{14} + 81982400 T^{15} + 163003625 T^{16} + 295962500 T^{17} + 524846875 T^{18} + 836265625 T^{19} + 1298671875 T^{20} + 1752734375 T^{21} + 2302734375 T^{22} + 2441406250 T^{23} + 2539062500 T^{24} + 1708984375 T^{25} + 1220703125 T^{26}$$)($$1 + 7 T + 56 T^{2} + 258 T^{3} + 1255 T^{4} + 4503 T^{5} + 16859 T^{6} + 50885 T^{7} + 160423 T^{8} + 425008 T^{9} + 1180717 T^{10} + 2815444 T^{11} + 7070565 T^{12} + 15390246 T^{13} + 35352825 T^{14} + 70386100 T^{15} + 147589625 T^{16} + 265630000 T^{17} + 501321875 T^{18} + 795078125 T^{19} + 1317109375 T^{20} + 1758984375 T^{21} + 2451171875 T^{22} + 2519531250 T^{23} + 2734375000 T^{24} + 1708984375 T^{25} + 1220703125 T^{26}$$)($$1 + 3 T + 28 T^{2} + 76 T^{3} + 391 T^{4} + 1035 T^{5} + 3891 T^{6} + 10101 T^{7} + 31341 T^{8} + 77614 T^{9} + 214033 T^{10} + 494844 T^{11} + 1255819 T^{12} + 2680782 T^{13} + 6279095 T^{14} + 12371100 T^{15} + 26754125 T^{16} + 48508750 T^{17} + 97940625 T^{18} + 157828125 T^{19} + 303984375 T^{20} + 404296875 T^{21} + 763671875 T^{22} + 742187500 T^{23} + 1367187500 T^{24} + 732421875 T^{25} + 1220703125 T^{26}$$)($$1 + T + 23 T^{2} + 35 T^{3} + 331 T^{4} + 561 T^{5} + 3552 T^{6} + 6250 T^{7} + 30710 T^{8} + 53589 T^{9} + 222534 T^{10} + 374432 T^{11} + 1380392 T^{12} + 2199712 T^{13} + 7403730 T^{14} + 10998560 T^{15} + 34509800 T^{16} + 46804000 T^{17} + 139083750 T^{18} + 167465625 T^{19} + 479843750 T^{20} + 488281250 T^{21} + 1387500000 T^{22} + 1095703125 T^{23} + 3232421875 T^{24} + 1708984375 T^{25} + 5615234375 T^{26} + 1220703125 T^{27} + 6103515625 T^{28}$$)($$1 + 25 T^{2} - 20 T^{3} + 364 T^{4} - 535 T^{5} + 4067 T^{6} - 7933 T^{7} + 38993 T^{8} - 85681 T^{9} + 330223 T^{10} - 753981 T^{11} + 2490057 T^{12} - 5697247 T^{13} + 16785768 T^{14} - 37904374 T^{15} + 101886947 T^{16} - 224216574 T^{17} + 560432351 T^{18} - 1185201854 T^{19} + 2802161755 T^{20} - 5605414350 T^{21} + 12735868375 T^{22} - 23690233750 T^{23} + 52455525000 T^{24} - 89019484375 T^{25} + 194535703125 T^{26} - 294523828125 T^{27} + 644966796875 T^{28} - 836728515625 T^{29} + 1903955078125 T^{30} - 1936767578125 T^{31} + 4964599609375 T^{32} - 3265380859375 T^{33} + 11108398437500 T^{34} - 3051757812500 T^{35} + 19073486328125 T^{36} + 19073486328125 T^{38}$$)
$7$ ($$1 + T + 21 T^{2} + 27 T^{3} + 233 T^{4} + 257 T^{5} + 1631 T^{6} + 1323 T^{7} + 7203 T^{8} + 2401 T^{9} + 16807 T^{10}$$)($$1 + 5 T + 46 T^{2} + 164 T^{3} + 834 T^{4} + 2222 T^{5} + 7858 T^{6} + 15554 T^{7} + 40866 T^{8} + 56252 T^{9} + 110446 T^{10} + 84035 T^{11} + 117649 T^{12}$$)($$1 + 11 T + 108 T^{2} + 729 T^{3} + 4381 T^{4} + 21873 T^{5} + 98878 T^{6} + 393345 T^{7} + 1434035 T^{8} + 4707756 T^{9} + 14259573 T^{10} + 39234779 T^{11} + 99817011 T^{12} + 230680044 T^{13} + 491874005 T^{14} + 944421345 T^{15} + 1661842546 T^{16} + 2573336577 T^{17} + 3607941883 T^{18} + 4202539929 T^{19} + 4358189556 T^{20} + 3107227739 T^{21} + 1977326743 T^{22}$$)($$1 + 5 T + 52 T^{2} + 213 T^{3} + 1237 T^{4} + 4185 T^{5} + 18144 T^{6} + 51991 T^{7} + 189551 T^{8} + 479150 T^{9} + 1566501 T^{10} + 3629137 T^{11} + 10965507 T^{12} + 23478350 T^{13} + 65015993 T^{14} + 124830391 T^{15} + 304946208 T^{16} + 492361065 T^{17} + 1018722691 T^{18} + 1227902613 T^{19} + 2098387564 T^{20} + 1412376245 T^{21} + 1977326743 T^{22}$$)($$1 + 9 T + 75 T^{2} + 426 T^{3} + 2257 T^{4} + 10006 T^{5} + 42027 T^{6} + 157220 T^{7} + 560377 T^{8} + 1823035 T^{9} + 5668638 T^{10} + 16269029 T^{11} + 44727158 T^{12} + 113883203 T^{13} + 277763262 T^{14} + 625301005 T^{15} + 1345465177 T^{16} + 2642396540 T^{17} + 4944434523 T^{18} + 8240371258 T^{19} + 13011155857 T^{20} + 17190636582 T^{21} + 21185643675 T^{22} + 17795940687 T^{23} + 13841287201 T^{24}$$)($$1 + 15 T + 139 T^{2} + 948 T^{3} + 5305 T^{4} + 25518 T^{5} + 109397 T^{6} + 426094 T^{7} + 1529603 T^{8} + 5096399 T^{9} + 15850126 T^{10} + 46134877 T^{11} + 126000578 T^{12} + 322944139 T^{13} + 776656174 T^{14} + 1748064857 T^{15} + 3672576803 T^{16} + 7161361858 T^{17} + 12870447653 T^{18} + 21015170274 T^{19} + 30582269305 T^{20} + 38255219436 T^{21} + 39264059611 T^{22} + 29659901145 T^{23} + 13841287201 T^{24}$$)($$1 - 5 T + 54 T^{2} - 211 T^{3} + 1344 T^{4} - 4456 T^{5} + 21864 T^{6} - 64578 T^{7} + 269196 T^{8} - 723175 T^{9} + 2673431 T^{10} - 6578374 T^{11} + 22087536 T^{12} - 50044702 T^{13} + 154612752 T^{14} - 322340326 T^{15} + 916986833 T^{16} - 1736343175 T^{17} + 4524377172 T^{18} - 7597537122 T^{19} + 18005944152 T^{20} - 25687953256 T^{21} + 54235247808 T^{22} - 59602277539 T^{23} + 106775644122 T^{24} - 69206436005 T^{25} + 96889010407 T^{26}$$)($$1 - 7 T + 70 T^{2} - 369 T^{3} + 2288 T^{4} - 9950 T^{5} + 47642 T^{6} - 178052 T^{7} + 711086 T^{8} - 2332387 T^{9} + 8053671 T^{10} - 23432188 T^{11} + 71259100 T^{12} - 184614114 T^{13} + 498813700 T^{14} - 1148177212 T^{15} + 2762409153 T^{16} - 5600061187 T^{17} + 11951222402 T^{18} - 20947639748 T^{19} + 39235235606 T^{20} - 57359769950 T^{21} + 92329052816 T^{22} - 104233366881 T^{23} + 138412872010 T^{24} - 96889010407 T^{25} + 96889010407 T^{26}$$)($$1 - 11 T + 102 T^{2} - 671 T^{3} + 3836 T^{4} - 18778 T^{5} + 82582 T^{6} - 330300 T^{7} + 1216388 T^{8} - 4178141 T^{9} + 13438677 T^{10} - 40755778 T^{11} + 116913072 T^{12} - 317503782 T^{13} + 818391504 T^{14} - 1997033122 T^{15} + 4609466211 T^{16} - 10031716541 T^{17} + 20443833116 T^{18} - 38859464700 T^{19} + 68009828026 T^{20} - 108251433178 T^{21} + 154796436452 T^{22} - 189540892079 T^{23} + 201687327786 T^{24} - 152254159211 T^{25} + 96889010407 T^{26}$$)($$1 - 9 T + 77 T^{2} - 432 T^{3} + 2270 T^{4} - 9803 T^{5} + 40388 T^{6} - 149410 T^{7} + 533718 T^{8} - 1782087 T^{9} + 5737179 T^{10} - 17535815 T^{11} + 51464307 T^{12} - 144627270 T^{13} + 390279048 T^{14} - 1012390890 T^{15} + 2521751043 T^{16} - 6014784545 T^{17} + 13774966779 T^{18} - 29951536209 T^{19} + 62791388982 T^{20} - 123045559630 T^{21} + 232828782788 T^{22} - 395586409421 T^{23} + 641218815230 T^{24} - 854205152976 T^{25} + 1065779114477 T^{26} - 872001093663 T^{27} + 678223072849 T^{28}$$)($$1 - 9 T + 86 T^{2} - 532 T^{3} + 3193 T^{4} - 15715 T^{5} + 74445 T^{6} - 312953 T^{7} + 1270779 T^{8} - 4747891 T^{9} + 17215303 T^{10} - 58598584 T^{11} + 194409144 T^{12} - 613151707 T^{13} + 1892262155 T^{14} - 5598730940 T^{15} + 16264737590 T^{16} - 45556518226 T^{17} + 125587504358 T^{18} - 334782347206 T^{19} + 879112530506 T^{20} - 2232269393074 T^{21} + 5578804993370 T^{22} - 13442552986940 T^{23} + 31803250039085 T^{24} - 72136685176843 T^{25} + 160104289677192 T^{26} - 337809175641784 T^{27} + 694699571647921 T^{28} - 1341161692449859 T^{29} + 2512745301142797 T^{30} - 4331672353414553 T^{31} + 7212902379749115 T^{32} - 10658275589822035 T^{33} + 15158963901247999 T^{34} - 17679919063027732 T^{35} + 20006224202899802 T^{36} - 14655722381194041 T^{37} + 11398895185373143 T^{38}$$)
$11$ ($$( 1 + T )^{5}$$)($$( 1 - T )^{6}$$)($$( 1 + T )^{11}$$)($$( 1 - T )^{11}$$)($$( 1 - T )^{12}$$)($$( 1 + T )^{12}$$)($$( 1 - T )^{13}$$)($$( 1 + T )^{13}$$)($$( 1 + T )^{13}$$)($$( 1 - T )^{14}$$)($$( 1 + T )^{19}$$)
$13$ ($$1 + 10 T + 99 T^{2} + 561 T^{3} + 3014 T^{4} + 11183 T^{5} + 39182 T^{6} + 94809 T^{7} + 217503 T^{8} + 285610 T^{9} + 371293 T^{10}$$)($$1 + 4 T + 66 T^{2} + 197 T^{3} + 1875 T^{4} + 4358 T^{5} + 30838 T^{6} + 56654 T^{7} + 316875 T^{8} + 432809 T^{9} + 1885026 T^{10} + 1485172 T^{11} + 4826809 T^{12}$$)($$1 + 13 T + 150 T^{2} + 1197 T^{3} + 8477 T^{4} + 50644 T^{5} + 275926 T^{6} + 1352043 T^{7} + 6176229 T^{8} + 26038009 T^{9} + 103599080 T^{10} + 383806651 T^{11} + 1346788040 T^{12} + 4400423521 T^{13} + 13569175113 T^{14} + 38615700123 T^{15} + 102449392318 T^{16} + 244448914996 T^{17} + 531919178609 T^{18} + 976429673037 T^{19} + 1590674905950 T^{20} + 1792160394037 T^{21} + 1792160394037 T^{22}$$)($$1 + 3 T + 78 T^{2} + 149 T^{3} + 2849 T^{4} + 2712 T^{5} + 65044 T^{6} - 1789 T^{7} + 1072181 T^{8} - 998985 T^{9} + 14705402 T^{10} - 19849203 T^{11} + 191170226 T^{12} - 168828465 T^{13} + 2355581657 T^{14} - 51095629 T^{15} + 24150381892 T^{16} + 13090306008 T^{17} + 178770524933 T^{18} + 121543877429 T^{19} + 827150951094 T^{20} + 413575475547 T^{21} + 1792160394037 T^{22}$$)($$1 + T + 97 T^{2} + 92 T^{3} + 4545 T^{4} + 3929 T^{5} + 138095 T^{6} + 103737 T^{7} + 3081009 T^{8} + 1945842 T^{9} + 54034051 T^{10} + 29087982 T^{11} + 773051714 T^{12} + 378143766 T^{13} + 9131754619 T^{14} + 4275014874 T^{15} + 87996698049 T^{16} + 38516821941 T^{17} + 666558188855 T^{18} + 246538923293 T^{19} + 3707496126945 T^{20} + 975613942316 T^{21} + 13372273709353 T^{22} + 1792160394037 T^{23} + 23298085122481 T^{24}$$)($$1 + 11 T + 97 T^{2} + 662 T^{3} + 4145 T^{4} + 22669 T^{5} + 115669 T^{6} + 537401 T^{7} + 2387791 T^{8} + 9912352 T^{9} + 39737149 T^{10} + 150753874 T^{11} + 556680330 T^{12} + 1959800362 T^{13} + 6715578181 T^{14} + 21777437344 T^{15} + 68197698751 T^{16} + 199533229493 T^{17} + 558312170221 T^{18} + 1422446131873 T^{19} + 3381203838545 T^{20} + 7020178584926 T^{21} + 13372273709353 T^{22} + 19713764334407 T^{23} + 23298085122481 T^{24}$$)($$1 + 9 T + 126 T^{2} + 897 T^{3} + 7314 T^{4} + 43127 T^{5} + 266094 T^{6} + 1341054 T^{7} + 6894558 T^{8} + 30470425 T^{9} + 136685974 T^{10} + 540624532 T^{11} + 2168911565 T^{12} + 7765534072 T^{13} + 28195850345 T^{14} + 91365545908 T^{15} + 300299084878 T^{16} + 870265808425 T^{17} + 2559901123494 T^{18} + 6473011516686 T^{19} + 16697003882598 T^{20} + 35180018804567 T^{21} + 77561308414122 T^{22} + 123659067188553 T^{23} + 225812209648662 T^{24} + 209682766102329 T^{25} + 302875106592253 T^{26}$$)($$1 - 9 T + 142 T^{2} - 963 T^{3} + 8890 T^{4} - 49469 T^{5} + 343406 T^{6} - 1641094 T^{7} + 9394370 T^{8} - 39521641 T^{9} + 194950678 T^{10} - 730889714 T^{11} + 3178238861 T^{12} - 10658263028 T^{13} + 41317105193 T^{14} - 123520361666 T^{15} + 428306639566 T^{16} - 1128777588601 T^{17} + 3488063820410 T^{18} - 7921247289046 T^{19} + 21548217228902 T^{20} - 40353383037149 T^{21} + 94273999425970 T^{22} - 132757727650587 T^{23} + 254486775953254 T^{24} - 209682766102329 T^{25} + 302875106592253 T^{26}$$)($$1 - 13 T + 166 T^{2} - 1371 T^{3} + 10842 T^{4} - 68851 T^{5} + 422468 T^{6} - 2243530 T^{7} + 11585898 T^{8} - 53508605 T^{9} + 240926658 T^{10} - 985066146 T^{11} + 3931490743 T^{12} - 14343563288 T^{13} + 51109379659 T^{14} - 166476178674 T^{15} + 529315867626 T^{16} - 1528259267405 T^{17} + 4301762826114 T^{18} - 10829090795770 T^{19} + 26509240479956 T^{20} - 56163875871571 T^{21} + 114973982202066 T^{22} - 189003992324979 T^{23} + 297498625410142 T^{24} - 302875106592253 T^{25} + 302875106592253 T^{26}$$)($$1 - T + 81 T^{2} - 98 T^{3} + 3422 T^{4} - 4866 T^{5} + 100104 T^{6} - 160773 T^{7} + 2269434 T^{8} - 3949833 T^{9} + 42329042 T^{10} - 76600455 T^{11} + 673466313 T^{12} - 1208879886 T^{13} + 9341312614 T^{14} - 15715438518 T^{15} + 113815806897 T^{16} - 168291199635 T^{17} + 1208959768562 T^{18} - 1466545344069 T^{19} + 10954124456106 T^{20} - 10088267323641 T^{21} + 81657908094984 T^{22} - 51601493949018 T^{23} + 471751759107278 T^{24} - 175631718615626 T^{25} + 1887144894920961 T^{26} - 302875106592253 T^{27} + 3937376385699289 T^{28}$$)($$1 - 8 T + 125 T^{2} - 879 T^{3} + 8055 T^{4} - 49937 T^{5} + 352375 T^{6} - 1957698 T^{7} + 11695722 T^{8} - 59256283 T^{9} + 313383086 T^{10} - 1465953928 T^{11} + 7038581274 T^{12} - 30646578609 T^{13} + 135623829486 T^{14} - 552635331582 T^{15} + 2275267941252 T^{16} - 8702950115787 T^{17} + 33531541709632 T^{18} - 120515386387602 T^{19} + 435910042225216 T^{20} - 1470798569568003 T^{21} + 4998763666930644 T^{22} - 15783817705313502 T^{23} + 50356178521345398 T^{24} - 147925181449128681 T^{25} + 441660536727470658 T^{26} - 1195823654640222088 T^{27} + 3323270738995805078 T^{28} - 8168981806957537267 T^{29} + 20960609748067209714 T^{30} - 45610614648110808738 T^{31} +$$$$10\!\cdots\!75$$$$T^{32} -$$$$19\!\cdots\!93$$$$T^{33} +$$$$41\!\cdots\!35$$$$T^{34} -$$$$58\!\cdots\!39$$$$T^{35} +$$$$10\!\cdots\!25$$$$T^{36} -$$$$89\!\cdots\!32$$$$T^{37} +$$$$14\!\cdots\!77$$$$T^{38}$$)
$17$ ($$1 - 3 T + 84 T^{2} - 199 T^{3} + 2839 T^{4} - 5033 T^{5} + 48263 T^{6} - 57511 T^{7} + 412692 T^{8} - 250563 T^{9} + 1419857 T^{10}$$)($$1 - 5 T + 63 T^{2} - 282 T^{3} + 2011 T^{4} - 7720 T^{5} + 40860 T^{6} - 131240 T^{7} + 581179 T^{8} - 1385466 T^{9} + 5261823 T^{10} - 7099285 T^{11} + 24137569 T^{12}$$)($$1 - 13 T + 156 T^{2} - 1360 T^{3} + 10974 T^{4} - 74673 T^{5} + 474033 T^{6} - 2699445 T^{7} + 14398643 T^{8} - 70304093 T^{9} + 323291325 T^{10} - 1374162515 T^{11} + 5495952525 T^{12} - 20317882877 T^{13} + 70740533059 T^{14} - 225460345845 T^{15} + 673059073281 T^{16} - 1802424689937 T^{17} + 4503056597502 T^{18} - 9487030119760 T^{19} + 18499708733532 T^{20} - 26207920705837 T^{21} + 34271896307633 T^{22}$$)($$1 - 7 T + 132 T^{2} - 776 T^{3} + 8030 T^{4} - 40947 T^{5} + 305355 T^{6} - 1379147 T^{7} + 8298275 T^{8} - 33705949 T^{9} + 174595051 T^{10} - 641474955 T^{11} + 2968115867 T^{12} - 9741019261 T^{13} + 40769425075 T^{14} - 115187736587 T^{15} + 433560434235 T^{16} - 988361037843 T^{17} + 3295019544190 T^{18} - 5413187774216 T^{19} + 15653599697604 T^{20} - 14111957303143 T^{21} + 34271896307633 T^{22}$$)($$1 + 9 T + 173 T^{2} + 1255 T^{3} + 13720 T^{4} + 83733 T^{5} + 672737 T^{6} + 3543080 T^{7} + 23011888 T^{8} + 106083784 T^{9} + 583441380 T^{10} + 2367329066 T^{11} + 11297633016 T^{12} + 40244594122 T^{13} + 168614558820 T^{14} + 521189630792 T^{15} + 1921975897648 T^{16} + 5030666939560 T^{17} + 16238235756353 T^{18} + 34358888106309 T^{19} + 95707392090520 T^{20} + 148827785003735 T^{21} + 348766944777677 T^{22} + 308447066768697 T^{23} + 582622237229761 T^{24}$$)($$1 - 33 T + 597 T^{2} - 7431 T^{3} + 70404 T^{4} - 532853 T^{5} + 3320531 T^{6} - 17322548 T^{7} + 76479658 T^{8} - 288030690 T^{9} + 946301382 T^{10} - 2935275070 T^{11} + 10476783848 T^{12} - 49899676190 T^{13} + 273481099398 T^{14} - 1415094779970 T^{15} + 6387657515818 T^{16} - 24595541035636 T^{17} + 80149546129139 T^{18} - 218650192924069 T^{19} + 491121226876164 T^{20} - 881226510249207 T^{21} + 1203548358568053 T^{22} - 1130972578151889 T^{23} + 582622237229761 T^{24}$$)($$1 + 7 T + 172 T^{2} + 1134 T^{3} + 14517 T^{4} + 87622 T^{5} + 787227 T^{6} + 4278285 T^{7} + 30327181 T^{8} + 147154624 T^{9} + 871359928 T^{10} + 3756415546 T^{11} + 19150454978 T^{12} + 72946960856 T^{13} + 325557734626 T^{14} + 1085604092794 T^{15} + 4280991326264 T^{16} + 12290501351104 T^{17} + 43060260233117 T^{18} + 103267399389165 T^{19} + 323029682529771 T^{20} + 611229818495302 T^{21} + 1721540203106949 T^{22} + 2286137083109166 T^{23} + 5894766164912876 T^{24} + 4078355660608327 T^{25} + 9904578032905937 T^{26}$$)($$1 + 19 T + 286 T^{2} + 3030 T^{3} + 27921 T^{4} + 216056 T^{5} + 1519141 T^{6} + 9542471 T^{7} + 55860051 T^{8} + 300909000 T^{9} + 1531481120 T^{10} + 7271209038 T^{11} + 32798268168 T^{12} + 138656460496 T^{13} + 557570558856 T^{14} + 2101379411982 T^{15} + 7524166742560 T^{16} + 25132220589000 T^{17} + 79313284432707 T^{18} + 230332052192999 T^{19} + 623362302039893 T^{20} + 1507154249672696 T^{21} + 3311092099672737 T^{22} + 6108461518360470 T^{23} + 9801762343983038 T^{24} + 11069822507365459 T^{25} + 9904578032905937 T^{26}$$)($$1 + 17 T + 272 T^{2} + 2926 T^{3} + 28825 T^{4} + 235090 T^{5} + 1768253 T^{6} + 11778123 T^{7} + 72933433 T^{8} + 411775206 T^{9} + 2173525244 T^{10} + 10605747960 T^{11} + 48539734912 T^{12} + 206539615464 T^{13} + 825175493504 T^{14} + 3065061160440 T^{15} + 10678529523772 T^{16} + 34391876980326 T^{17} + 103555045379081 T^{18} + 284295256602987 T^{19} + 725582589548269 T^{20} + 1639930816804690 T^{21} + 3418295540026025 T^{22} + 5898798152713774 T^{23} + 9321955795676176 T^{24} + 9904578032905937 T^{25} + 9904578032905937 T^{26}$$)($$1 - 9 T + 161 T^{2} - 1229 T^{3} + 12271 T^{4} - 79788 T^{5} + 588756 T^{6} - 3306669 T^{7} + 20089312 T^{8} - 99501923 T^{9} + 526646471 T^{10} - 2355773010 T^{11} + 11265239146 T^{12} - 46479022192 T^{13} + 205561578844 T^{14} - 790143377264 T^{15} + 3255654113194 T^{16} - 11573912798130 T^{17} + 43986039904391 T^{18} - 141278501885011 T^{19} + 484907154562528 T^{20} - 1356854169510237 T^{21} + 4107019047933396 T^{22} - 9461889489942636 T^{23} + 24738261152409679 T^{24} - 42120160562080957 T^{25} + 93802180193991521 T^{26} - 89141202296153433 T^{27} + 168377826559400929 T^{28}$$)($$1 + 9 T + 155 T^{2} + 1150 T^{3} + 12186 T^{4} + 80063 T^{5} + 660999 T^{6} + 3950590 T^{7} + 27673665 T^{8} + 152720701 T^{9} + 947579608 T^{10} + 4871861803 T^{11} + 27433956192 T^{12} + 132108866795 T^{13} + 685419029810 T^{14} + 3101461999645 T^{15} + 14969290650336 T^{16} + 63739222793853 T^{17} + 287928271918558 T^{18} + 1153564810721111 T^{19} + 4894780622615486 T^{20} + 18420635387423517 T^{21} + 73544124965100768 T^{22} + 259037207672350045 T^{23} + 973197007408937170 T^{24} + 3188786887776121355 T^{25} + 11257213178965413216 T^{26} + 33984926223800926123 T^{27} +$$$$11\!\cdots\!76$$$$T^{28} +$$$$30\!\cdots\!49$$$$T^{29} +$$$$94\!\cdots\!45$$$$T^{30} +$$$$23\!\cdots\!90$$$$T^{31} +$$$$65\!\cdots\!63$$$$T^{32} +$$$$13\!\cdots\!27$$$$T^{33} +$$$$34\!\cdots\!98$$$$T^{34} +$$$$55\!\cdots\!50$$$$T^{35} +$$$$12\!\cdots\!35$$$$T^{36} +$$$$12\!\cdots\!81$$$$T^{37} +$$$$23\!\cdots\!53$$$$T^{38}$$)
$19$ ($$1 + 13 T + 144 T^{2} + 1024 T^{3} + 6356 T^{4} + 29521 T^{5} + 120764 T^{6} + 369664 T^{7} + 987696 T^{8} + 1694173 T^{9} + 2476099 T^{10}$$)($$1 + 3 T + 105 T^{2} + 245 T^{3} + 4688 T^{4} + 8533 T^{5} + 116050 T^{6} + 162127 T^{7} + 1692368 T^{8} + 1680455 T^{9} + 13683705 T^{10} + 7428297 T^{11} + 47045881 T^{12}$$)($$1 + 12 T + 192 T^{2} + 1600 T^{3} + 14502 T^{4} + 94088 T^{5} + 619600 T^{6} + 3372332 T^{7} + 17991486 T^{8} + 87117584 T^{9} + 405441617 T^{10} + 1808732257 T^{11} + 7703390723 T^{12} + 31449447824 T^{13} + 123403602474 T^{14} + 439485678572 T^{15} + 1534190940400 T^{16} + 4426452851528 T^{17} + 12962927958978 T^{18} + 27173700865600 T^{19} + 61956037973568 T^{20} + 73572795093612 T^{21} + 116490258898219 T^{22}$$)($$1 + 8 T + 134 T^{2} + 712 T^{3} + 6920 T^{4} + 25198 T^{5} + 201182 T^{6} + 516168 T^{7} + 4479068 T^{8} + 9368738 T^{9} + 94516729 T^{10} + 183055555 T^{11} + 1795817851 T^{12} + 3382114418 T^{13} + 30721927412 T^{14} + 67267529928 T^{15} + 498146549018 T^{16} + 1185462109438 T^{17} + 6185592433880 T^{18} + 12092296885192 T^{19} + 43240151502386 T^{20} + 49048530062408 T^{21} + 116490258898219 T^{22}$$)($$1 + 20 T + 289 T^{2} + 3124 T^{3} + 28884 T^{4} + 228638 T^{5} + 1628560 T^{6} + 10438498 T^{7} + 61730866 T^{8} + 336497366 T^{9} + 1718654485 T^{10} + 8195882293 T^{11} + 36888603196 T^{12} + 155721763567 T^{13} + 620434269085 T^{14} + 2308035433394 T^{15} + 8044828187986 T^{16} + 25846754459302 T^{17} + 76617039961360 T^{18} + 204373046661482 T^{19} + 490553234876244 T^{20} + 1008076367861596 T^{21} + 1771878148504489 T^{22} + 2329805177964380 T^{23} + 2213314919066161 T^{24}$$)($$1 + 24 T + 371 T^{2} + 4280 T^{3} + 41156 T^{4} + 341152 T^{5} + 2518088 T^{6} + 16766116 T^{7} + 102173034 T^{8} + 573298456 T^{9} + 2983989899 T^{10} + 14439165481 T^{11} + 65182491500 T^{12} + 274344144139 T^{13} + 1077220353539 T^{14} + 3932254109704 T^{15} + 13315291963914 T^{16} + 41514563061484 T^{17} + 118465668395528 T^{18} + 304946131503328 T^{19} + 698975520515396 T^{20} + 1381103346494120 T^{21} + 2274625581644171 T^{22} + 2795766213557256 T^{23} + 2213314919066161 T^{24}$$)($$1 - 2 T + 158 T^{2} - 284 T^{3} + 12041 T^{4} - 19844 T^{5} + 594592 T^{6} - 900328 T^{7} + 21505328 T^{8} - 29700114 T^{9} + 608699913 T^{10} - 762713263 T^{11} + 13995831467 T^{12} - 15936313000 T^{13} + 265920797873 T^{14} - 275339487943 T^{15} + 4175072703267 T^{16} - 3870548556594 T^{17} + 53249321155472 T^{18} - 42356723948968 T^{19} + 531488985035488 T^{20} - 337021824985604 T^{21} + 3885482568956939 T^{22} - 1741222817215484 T^{23} + 18405460905918602 T^{24} - 4426629838132322 T^{25} + 42052983462257059 T^{26}$$)($$1 - 14 T + 248 T^{2} - 2424 T^{3} + 25701 T^{4} - 198294 T^{5} + 1592044 T^{6} - 10285272 T^{7} + 68058462 T^{8} - 379790666 T^{9} + 2155393863 T^{10} - 10559591841 T^{11} + 52449577423 T^{12} - 227152092088 T^{13} + 996541971037 T^{14} - 3812012654601 T^{15} + 14783846506317 T^{16} - 49494699383786 T^{17} + 168519489699738 T^{18} - 483879682564632 T^{19} + 1423083138844516 T^{20} - 3367738649652054 T^{21} + 8293396520618079 T^{22} - 14861704608909624 T^{23} + 28889584206758312 T^{24} - 30986408866926254 T^{25} + 42052983462257059 T^{26}$$)($$1 - 14 T + 204 T^{2} - 1808 T^{3} + 15631 T^{4} - 105346 T^{5} + 685720 T^{6} - 3820068 T^{7} + 20509216 T^{8} - 99372182 T^{9} + 468152039 T^{10} - 2085072809 T^{11} + 9228604441 T^{12} - 40078657088 T^{13} + 175343484379 T^{14} - 752711284049 T^{15} + 3211054835501 T^{16} - 12950282130422 T^{17} + 50782849228384 T^{18} - 179718464539908 T^{19} + 612945728867080 T^{20} - 1789150432117186 T^{21} + 5043931403983549 T^{22} - 11084967794104208 T^{23} + 23764012815236676 T^{24} - 30986408866926254 T^{25} + 42052983462257059 T^{26}$$)($$1 - 22 T + 405 T^{2} - 5162 T^{3} + 58169 T^{4} - 545208 T^{5} + 4656573 T^{6} - 35148668 T^{7} + 245940070 T^{8} - 1563436698 T^{9} + 9305286079 T^{10} - 51028457017 T^{11} + 263455290000 T^{12} - 1261886979845 T^{13} + 5704736463782 T^{14} - 23975852617055 T^{15} + 95107359690000 T^{16} - 350004186679603 T^{17} + 1212674187101359 T^{18} - 3871224044481102 T^{19} + 11570467266351670 T^{20} - 31418400988693652 T^{21} + 79085201100518493 T^{22} - 175931914330693032 T^{23} + 356637993150026369 T^{24} - 601322716432606478 T^{25} + 896392542221795205 T^{26} - 925165636169655298 T^{27} + 799006685782884121 T^{28}$$)($$1 - 17 T + 288 T^{2} - 3268 T^{3} + 35007 T^{4} - 308746 T^{5} + 2573440 T^{6} - 18867802 T^{7} + 131543937 T^{8} - 831239199 T^{9} + 5027031863 T^{10} - 28015530644 T^{11} + 150536367591 T^{12} - 754277236101 T^{13} + 3683036143953 T^{14} - 16981481460006 T^{15} + 77564728648267 T^{16} - 339994280939897 T^{17} + 1506214010137031 T^{18} - 6497393486738832 T^{19} + 28618066192603589 T^{20} - 122737935419302817 T^{21} + 532016473798463353 T^{22} - 2213043645349441926 T^{23} + 9119562113005879347 T^{24} - 35485637090616549981 T^{25} +$$$$13\!\cdots\!49$$$$T^{26} -$$$$47\!\cdots\!04$$$$T^{27} +$$$$16\!\cdots\!77$$$$T^{28} -$$$$50\!\cdots\!99$$$$T^{29} +$$$$15\!\cdots\!03$$$$T^{30} -$$$$41\!\cdots\!22$$$$T^{31} +$$$$10\!\cdots\!60$$$$T^{32} -$$$$24\!\cdots\!66$$$$T^{33} +$$$$53\!\cdots\!93$$$$T^{34} -$$$$94\!\cdots\!08$$$$T^{35} +$$$$15\!\cdots\!32$$$$T^{36} -$$$$17\!\cdots\!97$$$$T^{37} +$$$$19\!\cdots\!79$$$$T^{38}$$)
$23$ ($$1 + 80 T^{2} - 101 T^{3} + 2826 T^{4} - 4587 T^{5} + 64998 T^{6} - 53429 T^{7} + 973360 T^{8} + 6436343 T^{10}$$)($$1 - 3 T + 95 T^{2} - 271 T^{3} + 4115 T^{4} - 11062 T^{5} + 113245 T^{6} - 254426 T^{7} + 2176835 T^{8} - 3297257 T^{9} + 26584895 T^{10} - 19309029 T^{11} + 148035889 T^{12}$$)($$1 - 3 T + 145 T^{2} - 198 T^{3} + 9728 T^{4} - 454 T^{5} + 429546 T^{6} + 396773 T^{7} + 14564661 T^{8} + 21122959 T^{9} + 403088352 T^{10} + 613049799 T^{11} + 9271032096 T^{12} + 11174045311 T^{13} + 177208230387 T^{14} + 111033353093 T^{15} + 2764705390278 T^{16} - 67208293606 T^{17} + 33122141948416 T^{18} - 15505575085638 T^{19} + 261167135912135 T^{20} - 124279533640947 T^{21} + 952809757913927 T^{22}$$)($$1 - 15 T + 225 T^{2} - 2156 T^{3} + 19470 T^{4} - 138000 T^{5} + 926178 T^{6} - 5233421 T^{7} + 28727483 T^{8} - 139631979 T^{9} + 695111660 T^{10} - 3230420623 T^{11} + 15987568180 T^{12} - 73865316891 T^{13} + 349527285661 T^{14} - 1464525766061 T^{15} + 5961199287054 T^{16} - 20428952682000 T^{17} + 66291951453090 T^{18} - 168838484265836 T^{19} + 405259348829175 T^{20} - 621397668204735 T^{21} + 952809757913927 T^{22}$$)($$1 - 9 T + 174 T^{2} - 1201 T^{3} + 13433 T^{4} - 78562 T^{5} + 668726 T^{6} - 3550447 T^{7} + 25346027 T^{8} - 125061048 T^{9} + 777228859 T^{10} - 3541789790 T^{11} + 19634776696 T^{12} - 81461165170 T^{13} + 411154066411 T^{14} - 1521617771016 T^{15} + 7092857541707 T^{16} - 22851894695321 T^{17} + 98995447907414 T^{18} - 267489896767214 T^{19} + 1051951465279673 T^{20} - 2163184346417063 T^{21} + 7208212951174926 T^{22} - 8575287821225343 T^{23} + 21914624432020321 T^{24}$$)($$1 - 9 T + 122 T^{2} - 871 T^{3} + 8659 T^{4} - 52566 T^{5} + 409672 T^{6} - 2213499 T^{7} + 15173441 T^{8} - 73639616 T^{9} + 449170145 T^{10} - 2008306342 T^{11} + 11293340992 T^{12} - 46191045866 T^{13} + 237611006705 T^{14} - 895973207872 T^{15} + 4246150902881 T^{16} - 14246838794157 T^{17} + 60646158718408 T^{18} - 178978054447002 T^{19} + 678094821548179 T^{20} - 1568803968134273 T^{21} + 5054034368065178 T^{22} - 8575287821225343 T^{23} + 21914624432020321 T^{24}$$)($$1 + 23 T + 405 T^{2} + 5212 T^{3} + 57841 T^{4} + 550153 T^{5} + 4713705 T^{6} + 36379173 T^{7} + 258356891 T^{8} + 1689249269 T^{9} + 10279724648 T^{10} + 58203767172 T^{11} + 308458660933 T^{12} + 1527720335132 T^{13} + 7094549201459 T^{14} + 30789792833988 T^{15} + 125073409792216 T^{16} + 472721204686229 T^{17} + 1662873566889613 T^{18} + 5385423216139797 T^{19} + 16049342733651135 T^{20} + 43083023485297993 T^{21} + 104180471091681383 T^{22} + 215914976445538588 T^{23} + 385887951955140435 T^{24} + 504036361936467383 T^{25} + 504036361936467383 T^{26}$$)($$1 + 5 T + 215 T^{2} + 1100 T^{3} + 22269 T^{4} + 114329 T^{5} + 1478099 T^{6} + 7463909 T^{7} + 70504439 T^{8} + 342737121 T^{9} + 2566070728 T^{10} + 11715614720 T^{11} + 73674321281 T^{12} + 306620883056 T^{13} + 1694509389463 T^{14} + 6197560186880 T^{15} + 31221382547576 T^{16} + 95911898677761 T^{17} + 453790752426577 T^{18} + 1104926404230101 T^{19} + 5032669088385253 T^{20} + 8953216636191449 T^{21} + 40109868618119547 T^{22} + 45569162335013900 T^{23} + 204854097951494305 T^{24} + 109573122160101605 T^{25} + 504036361936467383 T^{26}$$)($$1 + 7 T + 173 T^{2} + 922 T^{3} + 13503 T^{4} + 58167 T^{5} + 665521 T^{6} + 2367741 T^{7} + 23755639 T^{8} + 69941305 T^{9} + 671953888 T^{10} + 1681077876 T^{11} + 16541939243 T^{12} + 38191222924 T^{13} + 380464602589 T^{14} + 889290196404 T^{15} + 8175662955296 T^{16} + 19572444732505 T^{17} + 152899440788177 T^{18} + 350510643856749 T^{19} + 2265982836312887 T^{20} + 4555115080839927 T^{21} + 24320964387734889 T^{22} + 38195243338984378 T^{23} + 164836088119109371 T^{24} + 153402371024142247 T^{25} + 504036361936467383 T^{26}$$)($$1 + T + 162 T^{2} + 129 T^{3} + 13736 T^{4} + 8073 T^{5} + 796428 T^{6} + 295782 T^{7} + 35119436 T^{8} + 6199464 T^{9} + 1245290749 T^{10} + 41635747 T^{11} + 36690460719 T^{12} - 1399840196 T^{13} + 914656857314 T^{14} - 32196324508 T^{15} + 19409253720351 T^{16} + 506582133749 T^{17} + 348483408490909 T^{18} + 39901876720152 T^{19} + 5198936929438604 T^{20} + 1007086080364554 T^{21} + 62369061385376268 T^{22} + 14540705435990799 T^{23} + 569034558030682664 T^{24} + 122912458770896583 T^{25} + 3550169157987292002 T^{26} + 504036361936467383 T^{27} + 11592836324538749809 T^{28}$$)($$1 - 10 T + 230 T^{2} - 2089 T^{3} + 27593 T^{4} - 227939 T^{5} + 2262592 T^{6} - 17086886 T^{7} + 141160625 T^{8} - 979720939 T^{9} + 7085381547 T^{10} - 45421660648 T^{11} + 295739078543 T^{12} - 1758638785657 T^{13} + 10479904969397 T^{14} - 58000348761914 T^{15} + 319464719445611 T^{16} - 1648981055585327 T^{17} + 8443403994806727 T^{18} - 40675585999222302 T^{19} + 194198291880554721 T^{20} - 872310978404637983 T^{21} + 3886927241494749037 T^{22} - 16230875597882775674 T^{23} + 67452262990443595171 T^{24} -$$$$26\!\cdots\!73$$$$T^{25} +$$$$10\!\cdots\!21$$$$T^{26} -$$$$35\!\cdots\!88$$$$T^{27} +$$$$12\!\cdots\!61$$$$T^{28} -$$$$40\!\cdots\!11$$$$T^{29} +$$$$13\!\cdots\!75$$$$T^{30} -$$$$37\!\cdots\!06$$$$T^{31} +$$$$11\!\cdots\!36$$$$T^{32} -$$$$26\!\cdots\!51$$$$T^{33} +$$$$73\!\cdots\!51$$$$T^{34} -$$$$12\!\cdots\!29$$$$T^{35} +$$$$32\!\cdots\!90$$$$T^{36} -$$$$32\!\cdots\!90$$$$T^{37} +$$$$74\!\cdots\!87$$$$T^{38}$$)
$29$ ($$1 - 7 T + 78 T^{2} - 6 T^{3} - 100 T^{4} + 14311 T^{5} - 2900 T^{6} - 5046 T^{7} + 1902342 T^{8} - 4950967 T^{9} + 20511149 T^{10}$$)($$1 - T + 165 T^{2} - 133 T^{3} + 11578 T^{4} - 7373 T^{5} + 442770 T^{6} - 213817 T^{7} + 9737098 T^{8} - 3243737 T^{9} + 116701365 T^{10} - 20511149 T^{11} + 594823321 T^{12}$$)($$1 + 2 T + 89 T^{2} + 122 T^{3} + 4647 T^{4} + 7017 T^{5} + 218100 T^{6} + 326437 T^{7} + 8599199 T^{8} + 11638759 T^{9} + 284538994 T^{10} + 368929043 T^{11} + 8251630826 T^{12} + 9788196319 T^{13} + 209725864411 T^{14} + 230882687797 T^{15} + 4473481596900 T^{16} + 4173875243457 T^{17} + 80160175207923 T^{18} + 61030062381242 T^{19} + 1291135991852341 T^{20} + 841414466600402 T^{21} + 12200509765705829 T^{22}$$)($$1 - 8 T + 181 T^{2} - 1016 T^{3} + 13989 T^{4} - 54615 T^{5} + 647036 T^{6} - 1622755 T^{7} + 21855327 T^{8} - 31449701 T^{9} + 644765272 T^{10} - 649073461 T^{11} + 18698192888 T^{12} - 26449198541 T^{13} + 533029570203 T^{14} - 1147743779155 T^{15} + 13271451804364 T^{16} - 32486275676415 T^{17} + 241308519686601 T^{18} - 508250355568376 T^{19} + 2625793421632289 T^{20} - 3365657866401608 T^{21} + 12200509765705829 T^{22}$$)($$1 + 18 T + 326 T^{2} + 3622 T^{3} + 39184 T^{4} + 323391 T^{5} + 2622529 T^{6} + 17431968 T^{7} + 116436705 T^{8} + 661332434 T^{9} + 3927443207 T^{10} + 20477068722 T^{11} + 116636944574 T^{12} + 593834992938 T^{13} + 3302979737087 T^{14} + 16129236732826 T^{15} + 82353469149105 T^{16} + 357549693011232 T^{17} + 1559941409198809 T^{18} + 5578454749443819 T^{19} + 19601655445463824 T^{20} + 52544882724597518 T^{21} + 137150558055865526 T^{22} + 219609175782704922 T^{23} + 353814783205469041 T^{24}$$)($$1 - 16 T + 250 T^{2} - 2714 T^{3} + 27246 T^{4} - 229891 T^{5} + 1814447 T^{6} - 12769588 T^{7} + 85498737 T^{8} - 527376390 T^{9} + 3151032337 T^{10} - 17723986898 T^{11} + 97961804350 T^{12} - 513995620042 T^{13} + 2650018195417 T^{14} - 12862182775710 T^{15} + 60471632204097 T^{16} - 261918922136612 T^{17} + 1079275390318487 T^{18} - 3965591314552319 T^{19} + 13629713767535406 T^{20} - 39372394178508466 T^{21} + 105176808325050250 T^{22} - 195208156251293264 T^{23} + 353814783205469041 T^{24}$$)($$1 + 16 T + 339 T^{2} + 3906 T^{3} + 49572 T^{4} + 460161 T^{5} + 4444691 T^{6} + 35015453 T^{7} + 280272252 T^{8} + 1924075768 T^{9} + 13277547428 T^{10} + 80523088202 T^{11} + 488644075869 T^{12} + 2632299221416 T^{13} + 14170678200201 T^{14} + 67719917177882 T^{15} + 323826104221492 T^{16} + 1360862233266808 T^{17} + 5748705921337548 T^{18} + 20828008039779413 T^{19} + 76670369981725519 T^{20} + 230193889634546721 T^{21} + 719148240315778068 T^{22} + 1643282453270585106 T^{23} + 4135972810574276031 T^{24} + 5661036531287504656 T^{25} + 10260628712958602189 T^{26}$$)($$1 + 10 T + 271 T^{2} + 2320 T^{3} + 34320 T^{4} + 250863 T^{5} + 2687247 T^{6} + 16896957 T^{7} + 146990240 T^{8} + 807948642 T^{9} + 6107409596 T^{10} + 30083037390 T^{11} + 206972882469 T^{12} + 938460561856 T^{13} + 6002213591601 T^{14} + 25299834444990 T^{15} + 148953612636844 T^{16} + 571446723462402 T^{17} + 3014938714185760 T^{18} + 10050704077534197 T^{19} + 46354678361731323 T^{20} + 125493315894635343 T^{21} + 497885249891824080 T^{22} + 976040781256466320 T^{23} + 3306338146506279659 T^{24} + 3538147832054690410 T^{25} + 10260628712958602189 T^{26}$$)($$1 - 6 T + 247 T^{2} - 1340 T^{3} + 30322 T^{4} - 150945 T^{5} + 2453163 T^{6} - 11230145 T^{7} + 145432146 T^{8} - 610197940 T^{9} + 6649767014 T^{10} - 25405586634 T^{11} + 240773801099 T^{12} - 829277813728 T^{13} + 6982440231871 T^{14} - 21366098359194 T^{15} + 162181167704446 T^{16} - 431581409201140 T^{17} + 2982980415995754 T^{18} - 6679952144211545 T^{19} + 42316758315815367 T^{20} - 75509694804398145 T^{21} + 439885680280299818 T^{22} - 563747692622269340 T^{23} + 3013525912129339763 T^{24} - 2122888699232814246 T^{25} + 10260628712958602189 T^{26}$$)($$1 - 6 T + 164 T^{2} - 548 T^{3} + 11705 T^{4} - 21353 T^{5} + 580119 T^{6} - 778214 T^{7} + 25224091 T^{8} - 43384579 T^{9} + 965373316 T^{10} - 1935780164 T^{11} + 30569274113 T^{12} - 61567478972 T^{13} + 883259702894 T^{14} - 1785456890188 T^{15} + 25708759529033 T^{16} - 47211742419796 T^{17} + 682790204313796 T^{18} - 889867564171271 T^{19} + 15003877577826211 T^{20} - 13424095241932126 T^{21} + 290202448840522359 T^{22} - 309771088022730757 T^{23} + 4924378165778852705 T^{24} - 6685879351606794292 T^{25} + 58025624445696922724 T^{26} - 61563772277751613134 T^{27} +$$$$29\!\cdots\!81$$$$T^{28}$$)($$1 + 27 T + 543 T^{2} + 7731 T^{3} + 94409 T^{4} + 972228 T^{5} + 9099203 T^{6} + 76790998 T^{7} + 609906611 T^{8} + 4538969769 T^{9} + 32519557765 T^{10} + 223195611792 T^{11} + 1489413751209 T^{12} + 9601114071190 T^{13} + 60213588863043 T^{14} + 365598701408931 T^{15} + 2159271329728813 T^{16} + 12384125184864807 T^{17} + 69251480492257511 T^{18} + 377365268591971366 T^{19} + 2008292934275467819 T^{20} + 10415049280471302687 T^{21} + 52662468460756020257 T^{22} +$$$$25\!\cdots\!11$$$$T^{23} +$$$$12\!\cdots\!07$$$$T^{24} +$$$$57\!\cdots\!90$$$$T^{25} +$$$$25\!\cdots\!81$$$$T^{26} +$$$$11\!\cdots\!12$$$$T^{27} +$$$$47\!\cdots\!85$$$$T^{28} +$$$$19\!\cdots\!69$$$$T^{29} +$$$$74\!\cdots\!19$$$$T^{30} +$$$$27\!\cdots\!18$$$$T^{31} +$$$$93\!\cdots\!67$$$$T^{32} +$$$$28\!\cdots\!68$$$$T^{33} +$$$$81\!\cdots\!41$$$$T^{34} +$$$$19\!\cdots\!51$$$$T^{35} +$$$$39\!\cdots\!87$$$$T^{36} +$$$$56\!\cdots\!47$$$$T^{37} +$$$$61\!\cdots\!69$$$$T^{38}$$)
$31$ ($$1 + 13 T + 163 T^{2} + 1437 T^{3} + 10393 T^{4} + 64421 T^{5} + 322183 T^{6} + 1380957 T^{7} + 4855933 T^{8} + 12005773 T^{9} + 28629151 T^{10}$$)($$1 + 10 T + 211 T^{2} + 1529 T^{3} + 17373 T^{4} + 94023 T^{5} + 731173 T^{6} + 2914713 T^{7} + 16695453 T^{8} + 45550439 T^{9} + 194862931 T^{10} + 286291510 T^{11} + 887503681 T^{12}$$)($$1 - T + 222 T^{2} - 230 T^{3} + 24244 T^{4} - 24897 T^{5} + 1733170 T^{6} - 1711674 T^{7} + 90227039 T^{8} - 83314829 T^{9} + 3588768283 T^{10} - 2991531987 T^{11} + 111251816773 T^{12} - 80065550669 T^{13} + 2687953718849 T^{14} - 1580766884154 T^{15} + 49619185638670 T^{16} - 22096179145857 T^{17} + 667015816507084 T^{18} - 196164938611430 T^{19} + 5869596119668962 T^{20} - 819628286980801 T^{21} + 25408476896404831 T^{22}$$)($$1 + 17 T + 310 T^{2} + 3218 T^{3} + 33228 T^{4} + 243289 T^{5} + 1753078 T^{6} + 9348476 T^{7} + 49878537 T^{8} + 190694315 T^{9} + 875576853 T^{10} + 3377656593 T^{11} + 27142882443 T^{12} + 183257236715 T^{13} + 1485931495767 T^{14} + 8633513903996 T^{15} + 50189134776778 T^{16} + 215919883046809 T^{17} + 914189141680308 T^{18} + 2744603358485138 T^{19} + 8196282869808010 T^{20} + 13933680878673617 T^{21} + 25408476896404831 T^{22}$$)($$1 + 21 T + 333 T^{2} + 3979 T^{3} + 42452 T^{4} + 397509 T^{5} + 3424048 T^{6} + 26877869 T^{7} + 197677279 T^{8} + 1352657357 T^{9} + 8742645356 T^{10} + 52938971212 T^{11} + 303940288824 T^{12} + 1641108107572 T^{13} + 8401682187116 T^{14} + 40297015322387 T^{15} + 182559118379359 T^{16} + 769490570159219 T^{17} + 3038855203920688 T^{18} + 10936511722649499 T^{19} + 36206930321445332 T^{20} + 105203256577309909 T^{21} + 272936219564606733 T^{22} + 533578014824501451 T^{23} + 787662783788549761 T^{24}$$)($$1 - T + 129 T^{2} - 543 T^{3} + 9764 T^{4} - 58349 T^{5} + 613100 T^{6} - 3780663 T^{7} + 31015429 T^{8} - 186699029 T^{9} + 1266384968 T^{10} - 7274116808 T^{11} + 42944835044 T^{12} - 225497621048 T^{13} + 1216995954248 T^{14} - 5561950772939 T^{15} + 28643400005509 T^{16} - 108237171907113 T^{17} + 544128506821100 T^{18} - 1605333520762739 T^{19} + 8327628089573924 T^{20} - 14356714833244353 T^{21} + 105732049020523329 T^{22} - 25408476896404831 T^{23} + 787662783788549761 T^{24}$$)($$1 - 9 T + 244 T^{2} - 1906 T^{3} + 27879 T^{4} - 201154 T^{5} + 2080402 T^{6} - 14398334 T^{7} + 116789053 T^{8} - 780130930 T^{9} + 5250384513 T^{10} - 33363036399 T^{11} + 194535543362 T^{12} - 1148596132950 T^{13} + 6030601844222 T^{14} - 32061877979439 T^{15} + 156414205026783 T^{16} - 720467296604530 T^{17} + 3343571433484003 T^{18} - 12778574425267454 T^{19} + 57237297421752622 T^{20} - 171562443745406914 T^{21} + 737110226217346809 T^{22} - 1562211514985406706 T^{23} + 6199668362722778764 T^{24} - 7088965054096947849 T^{25} + 24417546297445042591 T^{26}$$)($$1 + T + 288 T^{2} + 128 T^{3} + 40625 T^{4} + 2854 T^{5} + 3714170 T^{6} - 635768 T^{7} + 245031489 T^{8} - 75359216 T^{9} + 12295404095 T^{10} - 4425200321 T^{11} + 482112034156 T^{12} - 167128670114 T^{13} + 14945473058836 T^{14} - 4252617508481 T^{15} + 366292383394145 T^{16} - 69595818519536 T^{17} + 7015043498335839 T^{18} - 564246440262008 T^{19} + 102186525952652870 T^{20} + 2434151020856614 T^{21} + 1074109650277259375 T^{22} + 104912420733542528 T^{23} + 7317641346164591328 T^{24} + 787662783788549761 T^{25} + 24417546297445042591 T^{26}$$)($$1 - 27 T + 600 T^{2} - 9126 T^{3} + 121595 T^{4} - 1335774 T^{5} + 13339118 T^{6} - 117336124 T^{7} + 960676419 T^{8} - 7155706592 T^{9} + 50280686263 T^{10} - 326325952633 T^{11} + 2008518015006 T^{12} - 11477446488818 T^{13} + 62264058465186 T^{14} - 313599240480313 T^{15} + 1497911924461033 T^{16} - 6608445307550432 T^{17} + 27503350261690269 T^{18} - 104136241964272444 T^{19} + 366994006115094098 T^{20} - 1139269672646714334 T^{21} + 3214925856626790245 T^{22} - 7479927746986789926 T^{23} + 15245086137842898600 T^{24} - 21266895162290843547 T^{25} + 24417546297445042591 T^{26}$$)($$1 - 9 T + 239 T^{2} - 1595 T^{3} + 24505 T^{4} - 122870 T^{5} + 1461485 T^{6} - 5328640 T^{7} + 58869289 T^{8} - 145579448 T^{9} + 1870221962 T^{10} - 3013751093 T^{11} + 56112840139 T^{12} - 69208980055 T^{13} + 1726770502432 T^{14} - 2145478381705 T^{15} + 53924439373579 T^{16} - 89782658811563 T^{17} + 1727189256568202 T^{18} - 4167815999288648 T^{19} + 52246710685352809 T^{20} - 146604816056439040 T^{21} + 1246487457854459885 T^{22} - 3248636374881645770 T^{23} + 20084991172464528505 T^{24} - 40526520649765705445 T^{25} +$$$$18\!\cdots\!79$$$$T^{26} -$$$$21\!\cdots\!19$$$$T^{27} +$$$$75\!\cdots\!21$$$$T^{28}$$)($$1 - 7 T + 313 T^{2} - 1745 T^{3} + 48034 T^{4} - 228546 T^{5} + 4976968 T^{6} - 21203546 T^{7} + 393833617 T^{8} - 1547203197 T^{9} + 25251760587 T^{10} - 93132965616 T^{11} + 1358073204047 T^{12} - 4750647003895 T^{13} + 62639119135757 T^{14} - 208507084444934 T^{15} + 2512919669470499 T^{16} - 7940015937146499 T^{17} + 88435740818992781 T^{18} - 263486053627797950 T^{19} + 2741507965388776211 T^{20} - 7630355315597785539 T^{21} + 74862389873195635709 T^{22} -$$$$19\!\cdots\!14$$$$T^{23} +$$$$17\!\cdots\!07$$$$T^{24} -$$$$42\!\cdots\!95$$$$T^{25} +$$$$37\!\cdots\!17$$$$T^{26} -$$$$79\!\cdots\!56$$$$T^{27} +$$$$66\!\cdots\!77$$$$T^{28} -$$$$12\!\cdots\!97$$$$T^{29} +$$$$10\!\cdots\!27$$$$T^{30} -$$$$16\!\cdots\!06$$$$T^{31} +$$$$12\!\cdots\!88$$$$T^{32} -$$$$17\!\cdots\!66$$$$T^{33} +$$$$11\!\cdots\!34$$$$T^{34} -$$$$12\!\cdots\!45$$$$T^{35} +$$$$70\!\cdots\!43$$$$T^{36} -$$$$48\!\cdots\!87$$$$T^{37} +$$$$21\!\cdots\!71$$$$T^{38}$$)
$37$ ($$1 + 6 T + 153 T^{2} + 749 T^{3} + 10446 T^{4} + 39095 T^{5} + 386502 T^{6} + 1025381 T^{7} + 7749909 T^{8} + 11244966 T^{9} + 69343957 T^{10}$$)($$1 + 19 T + 254 T^{2} + 2282 T^{3} + 17160 T^{4} + 108036 T^{5} + 672701 T^{6} + 3997332 T^{7} + 23492040 T^{8} + 115590146 T^{9} + 476036894 T^{10} + 1317535183 T^{11} + 2565726409 T^{12}$$)($$1 + 14 T + 291 T^{2} + 3245 T^{3} + 40744 T^{4} + 377581 T^{5} + 3641975 T^{6} + 28907272 T^{7} + 232333899 T^{8} + 1607659582 T^{9} + 11160234151 T^{10} + 67840750825 T^{11} + 412928663587 T^{12} + 2200885967758 T^{13} + 11768408986047 T^{14} + 54176881798792 T^{15} + 252548957795075 T^{16} + 968769543236629 T^{17} + 3867904401906952 T^{18} + 11397995827973645 T^{19} + 37818866280367407 T^{20} + 67320181213849886 T^{21} + 177917621779460413 T^{22}$$)($$1 + 10 T + 207 T^{2} + 1333 T^{3} + 16830 T^{4} + 69415 T^{5} + 800297 T^{6} + 1988856 T^{7} + 31872061 T^{8} + 57245062 T^{9} + 1311962749 T^{10} + 2206143033 T^{11} + 48542621713 T^{12} + 78368489878 T^{13} + 1614415505833 T^{14} + 3727436349816 T^{15} + 55495760755229 T^{16} + 178099898680735 T^{17} + 1597703492148390 T^{18} + 4682135112076693 T^{19} + 26902080137580939 T^{20} + 48085843724178490 T^{21} + 177917621779460413 T^{22}$$)($$1 + 18 T + 464 T^{2} + 6109 T^{3} + 91979 T^{4} + 966128 T^{5} + 10819707 T^{6} + 94823629 T^{7} + 861280056 T^{8} + 6451176732 T^{9} + 49458121400 T^{10} + 320260046983 T^{11} + 2112270198676 T^{12} + 11849621738371 T^{13} + 67708168196600 T^{14} + 326771455005996 T^{15} + 1614177491033016 T^{16} + 6575445651959953 T^{17} + 27760407987542163 T^{18} + 91716344590751024 T^{19} + 323074347692199659 T^{20} + 793936268408125393 T^{21} + 2231183148801881936 T^{22} + 3202517192030287434 T^{23} + 6582952005840035281 T^{24}$$)($$1 + 6 T + 212 T^{2} + 777 T^{3} + 20725 T^{4} + 41254 T^{5} + 1358539 T^{6} + 1119107 T^{7} + 72741900 T^{8} + 23069488 T^{9} + 3440579340 T^{10} + 894799187 T^{11} + 139567844104 T^{12} + 33107569919 T^{13} + 4710153116460 T^{14} + 1168538775664 T^{15} + 136330032045900 T^{16} + 77603307686399 T^{17} + 3485639389956451 T^{18} + 3916319659244782 T^{19} + 72796136682512725 T^{20} + 100980271820774829 T^{21} + 1019419886952583988 T^{22} + 1067505730676762478 T^{23} + 6582952005840035281 T^{24}$$)($$1 - 14 T + 415 T^{2} - 4761 T^{3} + 79829 T^{4} - 777369 T^{5} + 9566800 T^{6} - 80759411 T^{7} + 803041239 T^{8} - 5948863461 T^{9} + 50052301916 T^{10} - 327293775093 T^{11} + 2387786137488 T^{12} - 13787787297494 T^{13} + 88348087087056 T^{14} - 448065178102317 T^{15} + 2535299248951148 T^{16} - 11149127892931221 T^{17} + 55686057146442723 T^{18} - 207206553577985099 T^{19} + 908194282155984400 T^{20} - 2730492640615113849 T^{21} + 10374715726101201833 T^{22} - 22893670197081379089 T^{23} + 73835813038476071395 T^{24} - 92161328081760493934 T^{25} +$$$$24\!\cdots\!97$$$$T^{26}$$)($$1 + 8 T + 275 T^{2} + 1701 T^{3} + 34615 T^{4} + 165433 T^{5} + 2730912 T^{6} + 9899925 T^{7} + 157492443 T^{8} + 426504573 T^{9} + 7393508744 T^{10} + 15442255673 T^{11} + 303399072842 T^{12} + 552624316190 T^{13} + 11225765695154 T^{14} + 21140448016337 T^{15} + 374503398409832 T^{16} + 799338237038253 T^{17} + 10921149195216951 T^{18} + 25400499019619325 T^{19} + 259250602445035296 T^{20} + 581080013500512793 T^{21} + 4498625623006590355 T^{22} + 8179402017482761149 T^{23} + 48927345989351613575 T^{24} + 52663616046720282248 T^{25} +$$$$24\!\cdots\!97$$$$T^{26}$$)($$1 - 10 T + 287 T^{2} - 2385 T^{3} + 39619 T^{4} - 285347 T^{5} + 3602946 T^{6} - 23124531 T^{7} + 245436067 T^{8} - 1428276167 T^{9} + 13329360568 T^{10} - 70866824157 T^{11} + 594175785360 T^{12} - 2885985951366 T^{13} + 21984504058320 T^{14} - 97016682270933 T^{15} + 675172100850904 T^{16} - 2676819489420887 T^{17} + 17019508076297119 T^{18} - 59331219882439179 T^{19} + 342034426988833818 T^{20} - 1002275474737995587 T^{21} + 5148954168941155663 T^{22} - 11468473728216569865 T^{23} + 51062357450705138531 T^{24} - 65829520058400352810 T^{25} +$$$$24\!\cdots\!97$$$$T^{26}$$)($$1 - 18 T + 432 T^{2} - 5905 T^{3} + 85438 T^{4} - 946870 T^{5} + 10472125 T^{6} - 98228108 T^{7} + 903726227 T^{8} - 7378741926 T^{9} + 58846420685 T^{10} - 425956868704 T^{11} + 3011460506632 T^{12} - 19535248148689 T^{13} + 123848656581976 T^{14} - 722804181501493 T^{15} + 4122689433579208 T^{16} - 21575993270463712 T^{17} + 110287666637420285 T^{18} - 511671162830641182 T^{19} + 2318714247119828843 T^{20} - 9324978679663054364 T^{21} + 36783123901392452125 T^{22} -$$$$12\!\cdots\!90$$$$T^{23} +$$$$41\!\cdots\!62$$$$T^{24} -$$$$10\!\cdots\!65$$$$T^{25} +$$$$28\!\cdots\!92$$$$T^{26} -$$$$43\!\cdots\!46$$$$T^{27} +$$$$90\!\cdots\!89$$$$T^{28}$$)($$1 - 20 T + 529 T^{2} - 7579 T^{3} + 121179 T^{4} - 1399089 T^{5} + 17203375 T^{6} - 170179590 T^{7} + 1761811754 T^{8} - 15480072247 T^{9} + 141219691014 T^{10} - 1126765129536 T^{11} + 9296912563794 T^{12} - 68317644444629 T^{13} + 518158068049246 T^{14} - 3539692761737466 T^{15} + 24938736417249380 T^{16} - 159309392255327519 T^{17} + 1049317852548917248 T^{18} - 6285947908952657866 T^{19} + 38824760544309938176 T^{20} -$$$$21\!\cdots\!11$$$$T^{21} +$$$$12\!\cdots\!40$$$$T^{22} -$$$$66\!\cdots\!26$$$$T^{23} +$$$$35\!\cdots\!22$$$$T^{24} -$$$$17\!\cdots\!61$$$$T^{25} +$$$$88\!\cdots\!02$$$$T^{26} -$$$$39\!\cdots\!56$$$$T^{27} +$$$$18\!\cdots\!78$$$$T^{28} -$$$$74\!\cdots\!03$$$$T^{29} +$$$$31\!\cdots\!02$$$$T^{30} -$$$$11\!\cdots\!90$$$$T^{31} +$$$$41\!\cdots\!75$$$$T^{32} -$$$$12\!\cdots\!21$$$$T^{33} +$$$$40\!\cdots\!47$$$$T^{34} -$$$$93\!\cdots\!39$$$$T^{35} +$$$$24\!\cdots\!93$$$$T^{36} -$$$$33\!\cdots\!80$$$$T^{37} +$$$$62\!\cdots\!73$$$$T^{38}$$)
$41$ ($$1 - 9 T + 206 T^{2} - 1354 T^{3} + 16734 T^{4} - 80727 T^{5} + 686094 T^{6} - 2276074 T^{7} + 14197726 T^{8} - 25431849 T^{9} + 115856201 T^{10}$$)($$1 - 7 T + 157 T^{2} - 1231 T^{3} + 11116 T^{4} - 93909 T^{5} + 522244 T^{6} - 3850269 T^{7} + 18685996 T^{8} - 84841751 T^{9} + 443644477 T^{10} - 810993407 T^{11} + 4750104241 T^{12}$$)($$1 + 3 T + 200 T^{2} + 948 T^{3} + 21068 T^{4} + 116950 T^{5} + 1665137 T^{6} + 8954847 T^{7} + 104162277 T^{8} + 528618594 T^{9} + 5171339938 T^{10} + 24698308195 T^{11} + 212024937458 T^{12} + 888607856514 T^{13} + 7178968293117 T^{14} + 25304257413567 T^{15} + 192916446964537 T^{16} + 555524690984950 T^{17} + 4103083042124908 T^{18} + 7569709117206708 T^{19} + 65476386878792200 T^{20} + 40267977930457203 T^{21} + 550329031716248441 T^{22}$$)($$1 - 25 T + 444 T^{2} - 5294 T^{3} + 53796 T^{4} - 461206 T^{5} + 3822131 T^{6} - 29662347 T^{7} + 223780129 T^{8} - 1555934808 T^{9} + 10388757942 T^{10} - 66515240905 T^{11} + 425939075622 T^{12} - 2615526412248 T^{13} + 15423150270809 T^{14} - 83818703321067 T^{15} + 442817577384331 T^{16} - 2190776576574646 T^{17} + 10477000917702276 T^{18} - 42272194162966574 T^{19} + 145357578870918684 T^{20} - 335566482753810025 T^{21} + 550329031716248441 T^{22}$$)($$1 + 15 T + 269 T^{2} + 2159 T^{3} + 19144 T^{4} + 68668 T^{5} + 273637 T^{6} - 1540565 T^{7} - 5806536 T^{8} - 2472043 T^{9} + 917142791 T^{10} + 9886660827 T^{11} + 77102984112 T^{12} + 405353093907 T^{13} + 1541717031671 T^{14} - 170375675603 T^{15} - 16407882973896 T^{16} - 178484008293565 T^{17} + 1299804274194517 T^{18} + 13373386478860508 T^{19} + 152863408586292424 T^{20} + 706817596356561799 T^{21} + 3610695354430995869 T^{22} + 8254935475743726615 T^{23} + 22563490300366186081 T^{24}$$)($$1 - 21 T + 409 T^{2} - 5323 T^{3} + 65528 T^{4} - 669694 T^{5} + 6574879 T^{6} - 57551319 T^{7} + 484655090 T^{8} - 3742091431 T^{9} + 27770380575 T^{10} - 191467662475 T^{11} + 1269193856456 T^{12} - 7850174161475 T^{13} + 46682009746575 T^{14} - 257908683515951 T^{15} + 1369519451773490 T^{16} - 6667677181879119 T^{17} + 31231360621961839 T^{18} - 130425768692462414 T^{19} + 523236180413840888 T^{20} - 1742654036779054403 T^{21} + 5489867657852332009 T^{22} - 11556909666041217261 T^{23} + 22563490300366186081 T^{24}$$)($$1 + 19 T + 570 T^{2} + 8078 T^{3} + 140623 T^{4} + 1604457 T^{5} + 20664839 T^{6} + 197699421 T^{7} + 2057334849 T^{8} + 16890207028 T^{9} + 148144053509 T^{10} + 1056883015886 T^{11} + 7987872705573 T^{12} + 49754457667820 T^{13} + 327502780928493 T^{14} + 1776620349704366 T^{15} + 10210236311893789 T^{16} + 47727688301648308 T^{17} + 238354999790048649 T^{18} + 939092858135344461 T^{19} + 4024565714312770159 T^{20} + 12811469178339792297 T^{21} + 46037429760281977703 T^{22} +$$$$10\!\cdots\!78$$$$T^{23} +$$$$31\!\cdots\!70$$$$T^{24} +$$$$42\!\cdots\!39$$$$T^{25} +$$$$92\!\cdots\!21$$$$T^{26}$$)($$1 + 21 T + 540 T^{2} + 7636 T^{3} + 116825 T^{4} + 1280643 T^{5} + 14810923 T^{6} + 135199551 T^{7} + 1296033361 T^{8} + 10264106178 T^{9} + 85277910821 T^{10} + 598271745082 T^{11} + 4396906526603 T^{12} + 27518809751956 T^{13} + 180273167590723 T^{14} + 1005694803482842 T^{15} + 5877438891694141 T^{16} + 29003910937651458 T^{17} + 150153501574721561 T^{18} + 642211960586395791 T^{19} + 2884490554372402163 T^{20} + 10225838600197204803 T^{21} + 38246394485574493825 T^{22} +$$$$10\!\cdots\!36$$$$T^{23} +$$$$29\!\cdots\!40$$$$T^{24} +$$$$47\!\cdots\!01$$$$T^{25} +$$$$92\!\cdots\!21$$$$T^{26}$$)($$1 + 3 T + 326 T^{2} + 824 T^{3} + 52843 T^{4} + 112289 T^{5} + 5665641 T^{6} + 10220209 T^{7} + 450062925 T^{8} + 702745206 T^{9} + 28028911215 T^{10} + 38691561568 T^{11} + 1408022472661 T^{12} + 1746777455844 T^{13} + 57728921379101 T^{14} + 65040514995808 T^{15} + 1931780589849015 T^{16} + 1985789996051766 T^{17} + 52142580701447925 T^{18} + 48547058114806369 T^{19} + 1103407799025422721 T^{20} + 896619269052767969 T^{21} + 17299843559180081123 T^{22} + 11060271271565578424 T^{23} +$$$$17\!\cdots\!66$$$$T^{24} + 67690470901098558243 T^{25} +$$$$92\!\cdots\!21$$$$T^{26}$$)($$1 - 25 T + 555 T^{2} - 8481 T^{3} + 115073 T^{4} - 1302241 T^{5} + 13419824 T^{6} - 122695156 T^{7} + 1044133400 T^{8} - 8136457371 T^{9} + 60228332496 T^{10} - 418792302802 T^{11} + 2832480690002 T^{12} - 18464723912586 T^{13} + 119639509456198 T^{14} - 757053680416026 T^{15} + 4761400039893362 T^{16} - 28863584301416642 T^{17} + 170190873062229456 T^{18} - 942659040602507571 T^{19} + 4959742491509749400 T^{20} - 23895406015496020436 T^{21} +$$$$10\!\cdots\!04$$$$T^{22} -$$$$42\!\cdots\!01$$$$T^{23} +$$$$15\!\cdots\!73$$$$T^{24} -$$$$46\!\cdots\!21$$$$T^{25} +$$$$12\!\cdots\!55$$$$T^{26} -$$$$23\!\cdots\!25$$$$T^{27} +$$$$37\!\cdots\!61$$$$T^{28}$$)($$1 + 19 T + 506 T^{2} + 6636 T^{3} + 107341 T^{4} + 1105926 T^{5} + 13788708 T^{6} + 118113822 T^{7} + 1248252525 T^{8} + 9179930965 T^{9} + 87252857649 T^{10} + 564463578812 T^{11} + 5060173753283 T^{12} + 29512057711503 T^{13} + 258914623693343 T^{14} + 1396951401567362 T^{15} + 12193461557429751 T^{16} + 62175477043936019 T^{17} + 536335147097237381 T^{18} + 2622017764078053616 T^{19} + 21989741030986732621 T^{20} +$$$$10\!\cdots\!39$$$$T^{21} +$$$$84\!\cdots\!71$$$$T^{22} +$$$$39\!\cdots\!82$$$$T^{23} +$$$$29\!\cdots\!43$$$$T^{24} +$$$$14\!\cdots\!23$$$$T^{25} +$$$$98\!\cdots\!23$$$$T^{26} +$$$$45\!\cdots\!52$$$$T^{27} +$$$$28\!\cdots\!89$$$$T^{28} +$$$$12\!\cdots\!65$$$$T^{29} +$$$$68\!\cdots\!25$$$$T^{30} +$$$$26\!\cdots\!82$$$$T^{31} +$$$$12\!\cdots\!68$$$$T^{32} +$$$$41\!\cdots\!86$$$$T^{33} +$$$$16\!\cdots\!41$$$$T^{34} +$$$$42\!\cdots\!76$$$$T^{35} +$$$$13\!\cdots\!86$$$$T^{36} +$$$$20\!\cdots\!99$$$$T^{37} +$$$$43\!\cdots\!61$$$$T^{38}$$)
$43$ ($$1 - 2 T + 149 T^{2} - 97 T^{3} + 10204 T^{4} - 1983 T^{5} + 438772 T^{6} - 179353 T^{7} + 11846543 T^{8} - 6837602 T^{9} + 147008443 T^{10}$$)($$1 + 2 T + 184 T^{2} + 585 T^{3} + 15115 T^{4} + 56676 T^{5} + 778470 T^{6} + 2437068 T^{7} + 27947635 T^{8} + 46511595 T^{9} + 629059384 T^{10} + 294016886 T^{11} + 6321363049 T^{12}$$)($$1 + 21 T + 411 T^{2} + 5608 T^{3} + 71396 T^{4} + 760537 T^{5} + 7616040 T^{6} + 68041789 T^{7} + 573679600 T^{8} + 4423116819 T^{9} + 32274274640 T^{10} + 217535136353 T^{11} + 1387793809520 T^{12} + 8178342998331 T^{13} + 45611543957200 T^{14} + 232621336274989 T^{15} + 1119622182225720 T^{16} + 4807630489197313 T^{17} + 19406761558595372 T^{18} + 65547427156786408 T^{19} + 206565563506042473 T^{20} + 453841128578969229 T^{21} + 929293739471222707 T^{22}$$)($$1 + 7 T + 257 T^{2} + 1702 T^{3} + 32058 T^{4} + 202021 T^{5} + 2679008 T^{6} + 15738739 T^{7} + 171349212 T^{8} + 915571567 T^{9} + 8888066250 T^{10} + 43079314303 T^{11} + 382186848750 T^{12} + 1692891827383 T^{13} + 13623461798484 T^{14} + 53807616631939 T^{15} + 393836794864544 T^{16} + 1277048084522029 T^{17} + 8713961034868206 T^{18} + 19893316872476902 T^{19} + 129166301267768651 T^{20} + 151280376192989743 T^{21} + 929293739471222707 T^{22}$$)($$1 + 33 T + 786 T^{2} + 13455 T^{3} + 191905 T^{4} + 2292699 T^{5} + 24054598 T^{6} + 223131068 T^{7} + 1878427460 T^{8} + 14501256530 T^{9} + 105025004902 T^{10} + 723201077622 T^{11} + 4817021641096 T^{12} + 31097646337746 T^{13} + 194191234063798 T^{14} + 1152951402930710 T^{15} + 6421969678675460 T^{16} + 32802150891607124 T^{17} + 152057846955749302 T^{18} + 623198257866407793 T^{19} + 2243024074273019905 T^{20} + 6762383593610222565 T^{21} + 16986625098241419714 T^{22} + 30666693402550349331 T^{23} + 39959630797262576401 T^{24}$$)($$1 + 39 T + 916 T^{2} + 15723 T^{3} + 221865 T^{4} + 2696997 T^{5} + 29240744 T^{6} + 287210810 T^{7} + 2589998088 T^{8} + 21591484480 T^{9} + 167516124308 T^{10} + 1213165093292 T^{11} + 8223006197160 T^{12} + 52166099011556 T^{13} + 309737313845492 T^{14} + 1716674156551360 T^{15} + 8854688053252488 T^{16} + 42222413990868830 T^{17} + 184841358646868456 T^{18} + 733093978699745679 T^{19} + 2593202554589945865 T^{20} + 7902263637482982489 T^{21} + 19796117798968372084 T^{22} + 36242455839377685573 T^{23} + 39959630797262576401 T^{24}$$)($$1 - 7 T + 411 T^{2} - 3130 T^{3} + 81725 T^{4} - 651656 T^{5} + 10451069 T^{6} - 84087081 T^{7} + 960506150 T^{8} - 7525014680 T^{9} + 66998871224 T^{10} - 493515264974 T^{11} + 3647340651788 T^{12} - 24361840908780 T^{13} + 156835648026884 T^{14} - 912509724936926 T^{15} + 5326879254406568 T^{16} - 25726527712998680 T^{17} + 141202513603424450 T^{18} - 531544966731669969 T^{19} + 2840795060163423383 T^{20} - 7616685840100357256 T^{21} + 41074381210538494175 T^{22} - 67643939640579699370 T^{23} +$$$$38\!\cdots\!77$$$$T^{24} -$$$$27\!\cdots\!07$$$$T^{25} +$$$$17\!\cdots\!43$$$$T^{26}$$)($$1 - 11 T + 343 T^{2} - 2734 T^{3} + 54061 T^{4} - 355546 T^{5} + 5728635 T^{6} - 33015751 T^{7} + 460695872 T^{8} - 2369020056 T^{9} + 29408375578 T^{10} - 136593716802 T^{11} + 1532816968042 T^{12} - 6469732775516 T^{13} + 65911129625806 T^{14} - 252561782366898 T^{15} + 2338171717080046 T^{16} - 8099208136472856 T^{17} + 67726182839247296 T^{18} - 208704548406384799 T^{19} + 1557149609238948945 T^{20} - 4155692855899925146 T^{21} + 27170659193917669423 T^{22} - 59085792644519136766 T^{23} +$$$$31\!\cdots\!01$$$$T^{24} -$$$$43\!\cdots\!11$$$$T^{25} +$$$$17\!\cdots\!43$$$$T^{26}$$)($$1 - 29 T + 757 T^{2} - 13060 T^{3} + 205803 T^{4} - 2620114 T^{5} + 31060811 T^{6} - 318713121 T^{7} + 3089837128 T^{8} - 26804861612 T^{9} + 222110611870 T^{10} - 1677111262894 T^{11} + 12183450031082 T^{12} - 81345159312664 T^{13} + 523888351336526 T^{14} - 3100978725091006 T^{15} + 17659348417948090 T^{16} - 91640487683967212 T^{17} + 454232145310871704 T^{18} - 2014701346320865929 T^{19} + 8442906505877027777 T^{20} - 30624417182146266514 T^{21} +$$$$10\!\cdots\!29$$$$T^{22} -$$$$28\!\cdots\!40$$$$T^{23} +$$$$70\!\cdots\!99$$$$T^{24} -$$$$11\!\cdots\!29$$$$T^{25} +$$$$17\!\cdots\!43$$$$T^{26}$$)($$1 - 25 T + 532 T^{2} - 8239 T^{3} + 114958 T^{4} - 1374000 T^{5} + 15215678 T^{6} - 152200843 T^{7} + 1433865593 T^{8} - 12506182861 T^{9} + 103731364030 T^{10} - 807115680118 T^{11} + 6006992048132 T^{12} - 42217165145506 T^{13} + 284592836335592 T^{14} - 1815338101256758 T^{15} + 11106928296996068 T^{16} - 64171346379141826 T^{17} + 354636891077128030 T^{18} - 1838514470268895423 T^{19} + 9063984976822673057 T^{20} - 41371021753574563201 T^{21} +$$$$17\!\cdots\!78$$$$T^{22} -$$$$69\!\cdots\!00$$$$T^{23} +$$$$24\!\cdots\!42$$$$T^{24} -$$$$76\!\cdots\!73$$$$T^{25} +$$$$21\!\cdots\!32$$$$T^{26} -$$$$42\!\cdots\!75$$$$T^{27} +$$$$73\!\cdots\!49$$$$T^{28}$$)($$1 - 20 T + 572 T^{2} - 8077 T^{3} + 135512 T^{4} - 1497988 T^{5} + 18790148 T^{6} - 171851865 T^{7} + 1774200657 T^{8} - 13927589453 T^{9} + 125276923181 T^{10} - 868765034041 T^{11} + 7102666891208 T^{12} - 44614823605178 T^{13} + 343538447765116 T^{14} - 2004023717345733 T^{15} + 15033040387500544 T^{16} - 84102416638225978 T^{17} + 634888635999058653 T^{18} - 3543965150345565646 T^{19} + 27300211347959522079 T^{20} -$$$$15\!\cdots\!22$$$$T^{21} +$$$$11\!\cdots\!08$$$$T^{22} -$$$$68\!\cdots\!33$$$$T^{23} +$$$$50\!\cdots\!88$$$$T^{24} -$$$$28\!\cdots\!22$$$$T^{25} +$$$$19\!\cdots\!56$$$$T^{26} -$$$$10\!\cdots\!41$$$$T^{27} +$$$$62\!\cdots\!83$$$$T^{28} -$$$$30\!\cdots\!97$$$$T^{29} +$$$$16\!\cdots\!99$$$$T^{30} -$$$$68\!\cdots\!65$$$$T^{31} +$$$$32\!\cdots\!64$$$$T^{32} -$$$$11\!\cdots\!12$$$$T^{33} +$$$$43\!\cdots\!84$$$$T^{34} -$$$$11\!\cdots\!77$$$$T^{35} +$$$$33\!\cdots\!96$$$$T^{36} -$$$$50\!\cdots\!80$$$$T^{37} +$$$$10\!\cdots\!07$$$$T^{38}$$)
$47$ ($$1 - 3 T + 213 T^{2} - 457 T^{3} + 18859 T^{4} - 29687 T^{5} + 886373 T^{6} - 1009513 T^{7} + 22114299 T^{8} - 14639043 T^{9} + 229345007 T^{10}$$)($$1 + 5 T + 172 T^{2} + 706 T^{3} + 15414 T^{4} + 52066 T^{5} + 869866 T^{6} + 2447102 T^{7} + 34049526 T^{8} + 73299038 T^{9} + 839305132 T^{10} + 1146725035 T^{11} + 10779215329 T^{12}$$)($$1 - 16 T + 408 T^{2} - 4882 T^{3} + 75334 T^{4} - 741371 T^{5} + 8694921 T^{6} - 73191812 T^{7} + 709299677 T^{8} - 5211390271 T^{9} + 43378149237 T^{10} - 280028273333 T^{11} + 2038773014139 T^{12} - 11511961108639 T^{13} + 73641620365171 T^{14} - 357152694371972 T^{15} + 1994136717609447 T^{16} - 7991397647676059 T^{17} + 38165946156959642 T^{18} - 116246701482717202 T^{19} + 456605233025928936 T^{20} - 841586115773280784 T^{21} + 2472159215084012303 T^{22}$$)($$1 - 30 T + 660 T^{2} - 10476 T^{3} + 142954 T^{4} - 1679519 T^{5} + 17880827 T^{6} - 172567758 T^{7} + 1534962263 T^{8} - 12605212479 T^{9} + 96157731545 T^{10} - 682902362183 T^{11} + 4519413382615 T^{12} - 27844914366111 T^{13} + 159364387031449 T^{14} - 842075609925198 T^{15} + 4100878393480789 T^{16} - 18103896950146751 T^{17} + 72423801562667702 T^{18} - 249447039068608236 T^{19} + 738626112247826220 T^{20} - 1577973967074901470 T^{21} + 2472159215084012303 T^{22}$$)($$1 - 20 T + 519 T^{2} - 7274 T^{3} + 112850 T^{4} - 1252185 T^{5} + 14697139 T^{6} - 136760569 T^{7} + 1325195640 T^{8} - 10691882163 T^{9} + 89448478852 T^{10} - 638258250214 T^{11} + 4720464981838 T^{12} - 29998137760058 T^{13} + 197591689784068 T^{14} - 1110063281809149 T^{15} + 6466531985790840 T^{16} - 31365353654628983 T^{17} + 158423626001243731 T^{18} - 634385872096961655 T^{19} + 2687103699779728850 T^{20} - 8140555061349527158 T^{21} + 27298949630395795431 T^{22} - 49443184301680246060 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 - 18 T + 379 T^{2} - 4654 T^{3} + 57946 T^{4} - 554755 T^{5} + 5371745 T^{6} - 44514567 T^{7} + 383459216 T^{8} - 2951440873 T^{9} + 23624359086 T^{10} - 168738502880 T^{11} + 1228757363190 T^{12} - 7930709635360 T^{13} + 52186209220974 T^{14} - 306427445757479 T^{15} + 1871158650590096 T^{16} - 10209193680216969 T^{17} + 57903196047479105 T^{18} - 281051709192451565 T^{19} + 1379768816902402906 T^{20} - 5208433221820277618 T^{21} + 19935071117379588571 T^{22} - 44498865871512221454 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 26 T + 650 T^{2} + 11372 T^{3} + 180271 T^{4} + 2414607 T^{5} + 29737747 T^{6} + 326628724 T^{7} + 3338580611 T^{8} + 31177483834 T^{9} + 272772989422 T^{10} + 2206112519221 T^{11} + 16781305763628 T^{12} + 118546280860676 T^{13} + 788721370890516 T^{14} + 4873302554959189 T^{15} + 28320110080760306 T^{16} + 152136175492576954 T^{17} + 765686793599859277 T^{18} + 3520801348632510196 T^{19} + 15065830180679216861 T^{20} + 57494899452494742927 T^{21} +$$$$20\!\cdots\!57$$$$T^{22} +$$$$59\!\cdots\!28$$$$T^{23} +$$$$16\!\cdots\!50$$$$T^{24} +$$$$30\!\cdots\!66$$$$T^{25} +$$$$54\!\cdots\!27$$$$T^{26}$$)($$1 + 22 T + 642 T^{2} + 10096 T^{3} + 174563 T^{4} + 2175831 T^{5} + 28224583 T^{6} + 293657148 T^{7} + 3111592527 T^{8} + 27806395138 T^{9} + 250636904182 T^{10} + 1953859409661 T^{11} + 15297994055552 T^{12} + 104712788542460 T^{13} + 719005720610944 T^{14} + 4316075435941149 T^{15} + 26021875302887786 T^{16} + 135686338033390978 T^{17} + 713628209885962689 T^{18} + 3165393631192021692 T^{19} + 14299226313226941929 T^{20} + 51809335668546098391 T^{21} +$$$$19\!\cdots\!21$$$$T^{22} +$$$$53\!\cdots\!04$$$$T^{23} +$$$$15\!\cdots\!26$$$$T^{24} +$$$$25\!\cdots\!02$$$$T^{25} +$$$$54\!\cdots\!27$$$$T^{26}$$)($$1 + 8 T + 382 T^{2} + 2706 T^{3} + 71179 T^{4} + 457541 T^{5} + 8750573 T^{6} + 51750872 T^{7} + 798880953 T^{8} + 4357243002 T^{9} + 57183188436 T^{10} + 286237174457 T^{11} + 3296350058422 T^{12} + 15005322289016 T^{13} + 154928452745834 T^{14} + 632297918375513 T^{15} + 5936930172990828 T^{16} + 21261955889242362 T^{17} + 183219357757951671 T^{18} + 557833792751516888 T^{19} + 4433242599099275299 T^{20} + 10894639910508789701 T^{21} + 79658587944981852293 T^{22} +$$$$14\!\cdots\!94$$$$T^{23} +$$$$94\!\cdots\!46$$$$T^{24} +$$$$92\!\cdots\!28$$$$T^{25} +$$$$54\!\cdots\!27$$$$T^{26}$$)($$1 + 36 T + 781 T^{2} + 11882 T^{3} + 146937 T^{4} + 1545655 T^{5} + 14728490 T^{6} + 128324787 T^{7} + 1055895172 T^{8} + 8241399586 T^{9} + 63121300759 T^{10} + 471780048623 T^{11} + 3479881314414 T^{12} + 24801469326359 T^{13} + 173052355308364 T^{14} + 1165669058338873 T^{15} + 7687057823540526 T^{16} + 48981619988185729 T^{17} + 308011812008977879 T^{18} + 1890123845740967102 T^{19} + 11381721423839491588 T^{20} + 65012304022689816381 T^{21} +$$$$35\!\cdots\!90$$$$T^{22} +$$$$17\!\cdots\!85$$$$T^{23} +$$$$77\!\cdots\!13$$$$T^{24} +$$$$29\!\cdots\!46$$$$T^{25} +$$$$90\!\cdots\!21$$$$T^{26} +$$$$19\!\cdots\!72$$$$T^{27} +$$$$25\!\cdots\!69$$$$T^{28}$$)($$1 - 19 T + 486 T^{2} - 6712 T^{3} + 102965 T^{4} - 1146923 T^{5} + 13578502 T^{6} - 130762400 T^{7} + 1326239937 T^{8} - 11621437031 T^{9} + 106840792116 T^{10} - 879080625727 T^{11} + 7526347922476 T^{12} - 58855151532759 T^{13} + 474007528803564 T^{14} - 3531745422259027 T^{15} + 26901966093952584 T^{16} - 191280615501341947 T^{17} + 1385568946871706288 T^{18} - 9415498032408347691 T^{19} + 65121740502970195536 T^{20} -$$$$42\!\cdots\!23$$$$T^{21} +$$$$27\!\cdots\!32$$$$T^{22} -$$$$17\!\cdots\!87$$$$T^{23} +$$$$10\!\cdots\!48$$$$T^{24} -$$$$63\!\cdots\!11$$$$T^{25} +$$$$38\!\cdots\!88$$$$T^{26} -$$$$20\!\cdots\!47$$$$T^{27} +$$$$11\!\cdots\!72$$$$T^{28} -$$$$61\!\cdots\!19$$$$T^{29} +$$$$32\!\cdots\!11$$$$T^{30} -$$$$15\!\cdots\!00$$$$T^{31} +$$$$74\!\cdots\!54$$$$T^{32} -$$$$29\!\cdots\!87$$$$T^{33} +$$$$12\!\cdots\!95$$$$T^{34} -$$$$38\!\cdots\!52$$$$T^{35} +$$$$12\!\cdots\!82$$$$T^{36} -$$$$23\!\cdots\!91$$$$T^{37} +$$$$58\!\cdots\!83$$$$T^{38}$$)
$53$ ($$1 + 3 T + 135 T^{2} + 607 T^{3} + 10497 T^{4} + 45141 T^{5} + 556341 T^{6} + 1705063 T^{7} + 20098395 T^{8} + 23671443 T^{9} + 418195493 T^{10}$$)($$1 - 9 T + 236 T^{2} - 1806 T^{3} + 26894 T^{4} - 167050 T^{5} + 1820956 T^{6} - 8853650 T^{7} + 75545246 T^{8} - 268871862 T^{9} + 1862153516 T^{10} - 3763759437 T^{11} + 22164361129 T^{12}$$)($$1 + 171 T^{2} + 447 T^{3} + 19622 T^{4} + 55268 T^{5} + 1874340 T^{6} + 4981360 T^{7} + 138786662 T^{8} + 376151679 T^{9} + 8696488649 T^{10} + 21797865799 T^{11} + 460913898397 T^{12} + 1056610066311 T^{13} + 20662141878574 T^{14} + 39305326434160 T^{15} + 783840540349620 T^{16} + 1224979910877572 T^{17} + 23050181985881614 T^{18} + 27830081613878367 T^{19} + 564259574198164743 T^{20} + 9269035929372191597 T^{22}$$)($$1 - 18 T + 461 T^{2} - 6111 T^{3} + 90600 T^{4} - 966884 T^{5} + 10734996 T^{6} - 97512162 T^{7} + 901339176 T^{8} - 7233346119 T^{9} + 58832102057 T^{10} - 425427147299 T^{11} + 3118101409021 T^{12} - 20318469248271 T^{13} + 134188672505352 T^{14} - 769417861529922 T^{15} + 4489326944573028 T^{16} - 21430366145852036 T^{17} + 106428829269232200 T^{18} - 380468968103827071 T^{19} + 1521191015820783313 T^{20} - 3147974466579234882 T^{21} + 9269035929372191597 T^{22}$$)($$1 + 386 T^{2} + 427 T^{3} + 73251 T^{4} + 150893 T^{5} + 9138826 T^{6} + 25421902 T^{7} + 843858452 T^{8} + 2689153945 T^{9} + 61213957311 T^{10} + 197523968540 T^{11} + 3591646359094 T^{12} + 10468770332620 T^{13} + 171950006086599 T^{14} + 400353171869765 T^{15} + 6658449082195412 T^{16} + 10631324839887686 T^{17} + 202556239759094554 T^{18} + 177255688023424441 T^{19} + 4560584582322604611 T^{20} + 1408999053699510791 T^{21} + 67506563561088036914 T^{22} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 - 14 T + 404 T^{2} - 4409 T^{3} + 75815 T^{4} - 695281 T^{5} + 9143452 T^{6} - 73386372 T^{7} + 812507082 T^{8} - 5855303311 T^{9} + 57239299361 T^{10} - 375557294264 T^{11} + 3321887781522 T^{12} - 19904536595992 T^{13} + 160785191905049 T^{14} - 871719991031747 T^{15} + 6411071692886442 T^{16} - 30689850018021396 T^{17} + 202658772093677308 T^{18} - 816754336017009197 T^{19} + 4720218428537334215 T^{20} - 14548657676255604397 T^{21} + 70654538027667271796 T^{22} -$$$$12\!\cdots\!58$$$$T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 + 18 T + 397 T^{2} + 5159 T^{3} + 69779 T^{4} + 685382 T^{5} + 6697901 T^{6} + 48698795 T^{7} + 339648838 T^{8} + 1360288879 T^{9} + 2739046927 T^{10} - 66090461863 T^{11} - 752023040015 T^{12} - 7444225952930 T^{13} - 39857221120795 T^{14} - 185648107373167 T^{15} + 407781089350979 T^{16} + 10733333554260799 T^{17} + 142039613254287134 T^{18} + 1079377678927139555 T^{19} + 7868098918225382137 T^{20} + 42671671133519424902 T^{21} +$$$$23\!\cdots\!07$$$$T^{22} +$$$$90\!\cdots\!91$$$$T^{23} +$$$$36\!\cdots\!09$$$$T^{24} +$$$$88\!\cdots\!38$$$$T^{25} +$$$$26\!\cdots\!73$$$$T^{26}$$)($$1 + 16 T + 703 T^{2} + 9307 T^{3} + 224125 T^{4} + 2520330 T^{5} + 43323009 T^{6} + 420329087 T^{7} + 5696644844 T^{8} + 48096154711 T^{9} + 539874071107 T^{10} + 3978515326043 T^{11} + 38008878473513 T^{12} + 243974894241370 T^{13} + 2014470559096189 T^{14} + 11175649550854787 T^{15} + 80374832084196839 T^{16} + 379501794920205991 T^{17} + 2382311198982488092 T^{18} + 9316325677290859223 T^{19} + 50892021283558609533 T^{20} +$$$$15\!\cdots\!30$$$$T^{21} +$$$$73\!\cdots\!25$$$$T^{22} +$$$$16\!\cdots\!43$$$$T^{23} +$$$$65\!\cdots\!91$$$$T^{24} +$$$$78\!\cdots\!56$$$$T^{25} +$$$$26\!\cdots\!73$$$$T^{26}$$)($$1 - 24 T + 475 T^{2} - 5611 T^{3} + 61605 T^{4} - 485724 T^{5} + 4243647 T^{6} - 28236809 T^{7} + 240196766 T^{8} - 1331226943 T^{9} + 10272475875 T^{10} - 37967197175 T^{11} + 334747029319 T^{12} - 1010333089226 T^{13} + 17741592553907 T^{14} - 106649856864575 T^{15} + 1529335390842375 T^{16} - 10504020900429583 T^{17} + 100449204974375638 T^{18} - 625850831806597361 T^{19} + 4985059404435865539 T^{20} - 30241025865367910364 T^{21} +$$$$20\!\cdots\!65$$$$T^{22} -$$$$98\!\cdots\!39$$$$T^{23} +$$$$44\!\cdots\!75$$$$T^{24} -$$$$11\!\cdots\!84$$$$T^{25} +$$$$26\!\cdots\!73$$$$T^{26}$$)($$1 + 402 T^{2} - 227 T^{3} + 83634 T^{4} - 79457 T^{5} + 11882258 T^{6} - 14130355 T^{7} + 1278036905 T^{8} - 1675943848 T^{9} + 109466085477 T^{10} - 146445928242 T^{11} + 7669739305332 T^{12} - 9873375239069 T^{13} + 445518985784738 T^{14} - 523288887670657 T^{15} + 21544297708677588 T^{16} - 21802430458884234 T^{17} + 863740067600644437 T^{18} - 700872163754677064 T^{19} + 28326871498609465745 T^{20} - 16599085428351452135 T^{21} +$$$$73\!\cdots\!38$$$$T^{22} -$$$$26\!\cdots\!81$$$$T^{23} +$$$$14\!\cdots\!66$$$$T^{24} -$$$$21\!\cdots\!19$$$$T^{25} +$$$$19\!\cdots\!82$$$$T^{26} +$$$$13\!\cdots\!69$$$$T^{28}$$)($$1 + 3 T + 553 T^{2} + 1479 T^{3} + 152698 T^{4} + 391018 T^{5} + 28234280 T^{6} + 72193850 T^{7} + 3938669069 T^{8} + 10194471857 T^{9} + 441688867147 T^{10} + 1151757712728 T^{11} + 41342815285789 T^{12} + 107148447751419 T^{13} + 3305250065811811 T^{14} + 8375541396988102 T^{15} + 228888609419105435 T^{16} + 557600895340413919 T^{17} + 13840952306811604433 T^{18} + 31860554916814458306 T^{19} +$$$$73\!\cdots\!49$$$$T^{20} +$$$$15\!\cdots\!71$$$$T^{21} +$$$$34\!\cdots\!95$$$$T^{22} +$$$$66\!\cdots\!62$$$$T^{23} +$$$$13\!\cdots\!23$$$$T^{24} +$$$$23\!\cdots\!51$$$$T^{25} +$$$$48\!\cdots\!93$$$$T^{26} +$$$$71\!\cdots\!08$$$$T^{27} +$$$$14\!\cdots\!51$$$$T^{28} +$$$$17\!\cdots\!93$$$$T^{29} +$$$$36\!\cdots\!93$$$$T^{30} +$$$$35\!\cdots\!50$$$$T^{31} +$$$$73\!\cdots\!40$$$$T^{32} +$$$$53\!\cdots\!42$$$$T^{33} +$$$$11\!\cdots\!86$$$$T^{34} +$$$$57\!\cdots\!59$$$$T^{35} +$$$$11\!\cdots\!89$$$$T^{36} +$$$$32\!\cdots\!67$$$$T^{37} +$$$$57\!\cdots\!17$$$$T^{38}$$)
$59$ ($$1 - 14 T + 322 T^{2} - 2995 T^{3} + 38600 T^{4} - 256597 T^{5} + 2277400 T^{6} - 10425595 T^{7} + 66132038 T^{8} - 169643054 T^{9} + 714924299 T^{10}$$)($$1 - 5 T + 295 T^{2} - 1301 T^{3} + 39467 T^{4} - 144034 T^{5} + 3009281 T^{6} - 8498006 T^{7} + 137384627 T^{8} - 267198079 T^{9} + 3574621495 T^{10} - 3574621495 T^{11} + 42180533641 T^{12}$$)($$1 + 3 T + 504 T^{2} + 1533 T^{3} + 119624 T^{4} + 367229 T^{5} + 17792142 T^{6} + 53981851 T^{7} + 1858021409 T^{8} + 5363837721 T^{9} + 144074909069 T^{10} + 375090942553 T^{11} + 8500419635071 T^{12} + 18671519106801 T^{13} + 381598578959011 T^{14} + 654117576015211 T^{15} + 12720034647058458 T^{16} + 15489915188450789 T^{17} + 297702445219988056 T^{18} + 225091060847424093 T^{19} + 4366149892602089256 T^{20} + 1533350259901924203 T^{21} + 30155888444737842659 T^{22}$$)($$1 - 43 T + 1238 T^{2} - 25369 T^{3} + 424358 T^{4} - 5889111 T^{5} + 71249636 T^{6} - 758289209 T^{7} + 7328225443 T^{8} - 64866807821 T^{9} + 539935788257 T^{10} - 4240654651317 T^{11} + 31856211507163 T^{12} - 225801358024901 T^{13} + 1505063613257897 T^{14} - 9188464087857449 T^{15} + 50938096071305164 T^{16} - 248405844651083151 T^{17} + 1056079166794821202 T^{18} - 3724941371584019449 T^{19} + 10724788823494814482 T^{20} - 21978020391927580243 T^{21} + 30155888444737842659 T^{22}$$)($$1 - 21 T + 593 T^{2} - 8480 T^{3} + 141522 T^{4} - 1578402 T^{5} + 20114270 T^{6} - 189845050 T^{7} + 2055625629 T^{8} - 17259654548 T^{9} + 166172308270 T^{10} - 1260432657194 T^{11} + 10892836503218 T^{12} - 74365526774446 T^{13} + 578445805087870 T^{14} - 3544770591413692 T^{15} + 24908757827445069 T^{16} - 135724839289869950 T^{17} + 848430642399157070 T^{18} - 3928092480941279238 T^{19} + 20779737190638716562 T^{20} - 73462204542193882720 T^{21} +$$$$30\!\cdots\!93$$$$T^{22} -$$$$63\!\cdots\!39$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 - 23 T + 515 T^{2} - 7688 T^{3} + 104142 T^{4} - 1187224 T^{5} + 12217738 T^{6} - 114370298 T^{7} + 980246121 T^{8} - 7957083742 T^{9} + 61521602112 T^{10} - 468570698606 T^{11} + 3582366333314 T^{12} - 27645671217754 T^{13} + 214156696951872 T^{14} - 1634217901848218 T^{15} + 11877996117006681 T^{16} - 81766105124071102 T^{17} + 515350708725924058 T^{18} - 2954586770412752456 T^{19} + 15291215432989197582 T^{20} - 66601111853819171032 T^{21} +$$$$26\!\cdots\!15$$$$T^{22} -$$$$69\!\cdots\!57$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 + 31 T + 758 T^{2} + 11717 T^{3} + 161239 T^{4} + 1691848 T^{5} + 17364310 T^{6} + 146609274 T^{7} + 1343833743 T^{8} + 10554092416 T^{9} + 97314500021 T^{10} + 763530615380 T^{11} + 6882032222794 T^{12} + 50283233012916 T^{13} + 406039901144846 T^{14} + 2657850072137780 T^{15} + 19986354699812959 T^{16} + 127887747832034176 T^{17} + 960739396686821157 T^{18} + 6184057414039586634 T^{19} + 43213715864357409890 T^{20} +$$$$24\!\cdots\!08$$$$T^{21} +$$$$13\!\cdots\!21$$$$T^{22} +$$$$59\!\cdots\!17$$$$T^{23} +$$$$22\!\cdots\!22$$$$T^{24} +$$$$55\!\cdots\!11$$$$T^{25} +$$$$10\!\cdots\!79$$$$T^{26}$$)($$1 + 19 T + 588 T^{2} + 8387 T^{3} + 150323 T^{4} + 1725136 T^{5} + 23246896 T^{6} + 226730256 T^{7} + 2557136489 T^{8} + 22130373950 T^{9} + 220805866149 T^{10} + 1736747698856 T^{11} + 15678767927188 T^{12} + 112576920082032 T^{13} + 925047307704092 T^{14} + 6045618739717736 T^{15} + 45348887983815471 T^{16} + 268161730217145950 T^{17} + 1828159011845646211 T^{18} + 9563603190640542096 T^{19} + 57853422247832871824 T^{20} +$$$$25\!\cdots\!56$$$$T^{21} +$$$$13\!\cdots\!97$$$$T^{22} +$$$$42\!\cdots\!87$$$$T^{23} +$$$$17\!\cdots\!92$$$$T^{24} +$$$$33\!\cdots\!39$$$$T^{25} +$$$$10\!\cdots\!79$$$$T^{26}$$)($$1 + 13 T + 548 T^{2} + 5579 T^{3} + 133861 T^{4} + 1099286 T^{5} + 19937846 T^{6} + 134753940 T^{7} + 2096039823 T^{8} + 11909036154 T^{9} + 171318435787 T^{10} + 845692358222 T^{11} + 11668320878576 T^{12} + 52471781246340 T^{13} + 688430931835984 T^{14} + 2943855098970782 T^{15} + 35185209023498273 T^{16} + 144306090240069594 T^{17} + 1498509801134359077 T^{18} + 5683993099427295540 T^{19} + 49618350051992559874 T^{20} +$$$$16\!\cdots\!06$$$$T^{21} +$$$$11\!\cdots\!79$$$$T^{22} +$$$$28\!\cdots\!79$$$$T^{23} +$$$$16\!\cdots\!32$$$$T^{24} +$$$$23\!\cdots\!53$$$$T^{25} +$$$$10\!\cdots\!79$$$$T^{26}$$)($$1 + 17 T + 389 T^{2} + 4740 T^{3} + 64287 T^{4} + 608577 T^{5} + 6371355 T^{6} + 49592532 T^{7} + 442577701 T^{8} + 2858040770 T^{9} + 22812298546 T^{10} + 115897267986 T^{11} + 906553113883 T^{12} + 3650539556082 T^{13} + 39630010779372 T^{14} + 215381833808838 T^{15} + 3155711389426723 T^{16} + 23802865001696694 T^{17} + 276424856721657106 T^{18} + 2043282794005670230 T^{19} + 18668163605786939341 T^{20} +$$$$12\!\cdots\!08$$$$T^{21} +$$$$93\!\cdots\!55$$$$T^{22} +$$$$52\!\cdots\!03$$$$T^{23} +$$$$32\!\cdots\!87$$$$T^{24} +$$$$14\!\cdots\!60$$$$T^{25} +$$$$69\!\cdots\!09$$$$T^{26} +$$$$17\!\cdots\!43$$$$T^{27} +$$$$61\!\cdots\!61$$$$T^{28}$$)($$1 - 28 T + 710 T^{2} - 12043 T^{3} + 193793 T^{4} - 2523471 T^{5} + 31692672 T^{6} - 342644362 T^{7} + 3627986625 T^{8} - 33994128649 T^{9} + 317195915191 T^{10} - 2654252058056 T^{11} + 22606553903935 T^{12} - 173800732721867 T^{13} + 1400519610931769 T^{14} - 10218195396510582 T^{15} + 80843054411446731 T^{16} - 579240599508755665 T^{17} + 4631677843792297891 T^{18} - 33493722583958564698 T^{19} +$$$$27\!\cdots\!69$$$$T^{20} -$$$$20\!\cdots\!65$$$$T^{21} +$$$$16\!\cdots\!49$$$$T^{22} -$$$$12\!\cdots\!02$$$$T^{23} +$$$$10\!\cdots\!31$$$$T^{24} -$$$$73\!\cdots\!47$$$$T^{25} +$$$$56\!\cdots\!65$$$$T^{26} -$$$$38\!\cdots\!76$$$$T^{27} +$$$$27\!\cdots\!49$$$$T^{28} -$$$$17\!\cdots\!49$$$$T^{29} +$$$$10\!\cdots\!75$$$$T^{30} -$$$$60\!\cdots\!22$$$$T^{31} +$$$$33\!\cdots\!88$$$$T^{32} -$$$$15\!\cdots\!31$$$$T^{33} +$$$$70\!\cdots\!07$$$$T^{34} -$$$$25\!\cdots\!63$$$$T^{35} +$$$$90\!\cdots\!90$$$$T^{36} -$$$$21\!\cdots\!88$$$$T^{37} +$$$$44\!\cdots\!39$$$$T^{38}$$)
$61$ ($$( 1 - T )^{5}$$)($$( 1 + T )^{6}$$)($$( 1 - T )^{11}$$)($$( 1 - T )^{11}$$)($$( 1 + T )^{12}$$)($$( 1 + T )^{12}$$)($$( 1 + T )^{13}$$)($$( 1 - T )^{13}$$)($$( 1 + T )^{13}$$)($$( 1 - T )^{14}$$)($$( 1 + T )^{19}$$)
$67$ ($$1 + 5 T + 249 T^{2} + 870 T^{3} + 27449 T^{4} + 72939 T^{5} + 1839083 T^{6} + 3905430 T^{7} + 74889987 T^{8} + 100755605 T^{9} + 1350125107 T^{10}$$)($$1 + 14 T + 345 T^{2} + 2734 T^{3} + 39586 T^{4} + 203614 T^{5} + 2781137 T^{6} + 13642138 T^{7} + 177701554 T^{8} + 822286042 T^{9} + 6952136745 T^{10} + 18901751498 T^{11} + 90458382169 T^{12}$$)($$1 + 24 T + 746 T^{2} + 11525 T^{3} + 205735 T^{4} + 2338279 T^{5} + 30851917 T^{6} + 278464946 T^{7} + 3068071825 T^{8} + 23594529666 T^{9} + 236961820908 T^{10} + 1668482725813 T^{11} + 15876442000836 T^{12} + 105915843670674 T^{13} + 922762486302475 T^{14} + 5611380821104466 T^{15} + 41653947740780119 T^{16} + 211516935399747151 T^{17} + 1246900502121127405 T^{18} + 4679929983840287525 T^{19} + 20296074659636030462 T^{20} + 43748107309242274776 T^{21} +$$$$12\!\cdots\!83$$$$T^{22}$$)($$1 + 30 T + 832 T^{2} + 16439 T^{3} + 285861 T^{4} + 4265651 T^{5} + 57057821 T^{6} + 686646642 T^{7} + 7541342515 T^{8} + 75698105858 T^{9} + 700958561188 T^{10} + 5963213140161 T^{11} + 46964223599596 T^{12} + 339808797196562 T^{13} + 2268156798838945 T^{14} + 13836699567185682 T^{15} + 77035196682811847 T^{16} + 385863888357577019 T^{17} + 1732521080209238103 T^{18} + 6675346551353621399 T^{19} + 22635836617717395904 T^{20} + 54685134136552843470 T^{21} +$$$$12\!\cdots\!83$$$$T^{22}$$)($$1 + 34 T + 1015 T^{2} + 20841 T^{3} + 385611 T^{4} + 5926892 T^{5} + 83782486 T^{6} + 1045433763 T^{7} + 12148991386 T^{8} + 127955606772 T^{9} + 1264315584635 T^{10} + 11458792405175 T^{11} + 97761523076214 T^{12} + 767739091146725 T^{13} + 5675512659426515 T^{14} + 38484312159567036 T^{15} + 244815795447243706 T^{16} + 1411466371131787641 T^{17} + 7578828137656892134 T^{18} + 35921183127896046116 T^{19} +$$$$15\!\cdots\!51$$$$T^{20} +$$$$56\!\cdots\!27$$$$T^{21} +$$$$18\!\cdots\!35$$$$T^{22} +$$$$41\!\cdots\!22$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 449 T^{2} + 173 T^{3} + 90315 T^{4} + 119182 T^{5} + 10802408 T^{6} + 33210707 T^{7} + 873198976 T^{8} + 5211503508 T^{9} + 54633204281 T^{10} + 521654265811 T^{11} + 3370799768398 T^{12} + 34950835809337 T^{13} + 245248454017409 T^{14} + 1567427429576604 T^{15} + 17595938222452096 T^{16} + 44838609341920649 T^{17} + 977168351209462952 T^{18} + 722327730545605786 T^{19} + 36674002298528031915 T^{20} + 4706730450559025831 T^{21} +$$$$81\!\cdots\!01$$$$T^{22} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 - 14 T + 462 T^{2} - 5387 T^{3} + 105068 T^{4} - 1066907 T^{5} + 15781773 T^{6} - 145190299 T^{7} + 1792731622 T^{8} - 15258806275 T^{9} + 165152548835 T^{10} - 1313267597677 T^{11} + 12847016504773 T^{12} - 95311824122652 T^{13} + 860750105819791 T^{14} - 5895258245972053 T^{15} + 49671776045261105 T^{16} - 307482051563084275 T^{17} + 2420411972975033554 T^{18} - 13133679554173378531 T^{19} + 95648774773673177679 T^{20} -$$$$43\!\cdots\!87$$$$T^{21} +$$$$28\!\cdots\!96$$$$T^{22} -$$$$98\!\cdots\!63$$$$T^{23} +$$$$56\!\cdots\!46$$$$T^{24} -$$$$11\!\cdots\!54$$$$T^{25} +$$$$54\!\cdots\!87$$$$T^{26}$$)($$1 - 12 T + 476 T^{2} - 5497 T^{3} + 116752 T^{4} - 1262381 T^{5} + 19411279 T^{6} - 192068545 T^{7} + 2419350272 T^{8} - 21779688147 T^{9} + 238485194313 T^{10} - 1959319395389 T^{11} + 19212910079827 T^{12} - 144341874973268 T^{13} + 1287264975348409 T^{14} - 8795384765901221 T^{15} + 71727522497160819 T^{16} - 438885131192462787 T^{17} + 3266425544854479104 T^{18} - 17374209846253774105 T^{19} +$$$$11\!\cdots\!17$$$$T^{20} -$$$$51\!\cdots\!21$$$$T^{21} +$$$$31\!\cdots\!44$$$$T^{22} -$$$$10\!\cdots\!53$$$$T^{23} +$$$$58\!\cdots\!08$$$$T^{24} -$$$$98\!\cdots\!32$$$$T^{25} +$$$$54\!\cdots\!87$$$$T^{26}$$)($$1 - 44 T + 1188 T^{2} - 24193 T^{3} + 411170 T^{4} - 6078465 T^{5} + 80297323 T^{6} - 965078585 T^{7} + 10701564022 T^{8} - 110643777683 T^{9} + 1075723589435 T^{10} - 9903635405709 T^{11} + 86805253524531 T^{12} - 726645176472648 T^{13} + 5815951986143577 T^{14} - 44457419336227701 T^{15} + 323537853929238905 T^{16} - 2229596151987232643 T^{17} + 14448450270270100354 T^{18} - 87299447465047750865 T^{19} +$$$$48\!\cdots\!29$$$$T^{20} -$$$$24\!\cdots\!65$$$$T^{21} +$$$$11\!\cdots\!90$$$$T^{22} -$$$$44\!\cdots\!57$$$$T^{23} +$$$$14\!\cdots\!04$$$$T^{24} -$$$$36\!\cdots\!84$$$$T^{25} +$$$$54\!\cdots\!87$$$$T^{26}$$)($$1 - 22 T + 681 T^{2} - 10157 T^{3} + 186696 T^{4} - 2114640 T^{5} + 29260327 T^{6} - 261335976 T^{7} + 2995953959 T^{8} - 21040316696 T^{9} + 216281497981 T^{10} - 1160965161854 T^{11} + 12304472925340 T^{12} - 52683459033475 T^{13} + 722943372345054 T^{14} - 3529791755242825 T^{15} + 55234778961851260 T^{16} - 349175364974694602 T^{17} + 4358314635876386701 T^{18} - 28407059830500886472 T^{19} +$$$$27\!\cdots\!71$$$$T^{20} -$$$$15\!\cdots\!48$$$$T^{21} +$$$$11\!\cdots\!07$$$$T^{22} -$$$$57\!\cdots\!80$$$$T^{23} +$$$$34\!\cdots\!04$$$$T^{24} -$$$$12\!\cdots\!31$$$$T^{25} +$$$$55\!\cdots\!41$$$$T^{26} -$$$$12\!\cdots\!14$$$$T^{27} +$$$$36\!\cdots\!29$$$$T^{28}$$)($$1 - 3 T + 617 T^{2} - 1296 T^{3} + 195240 T^{4} - 274406 T^{5} + 42305846 T^{6} - 35902906 T^{7} + 7029083151 T^{8} - 2751947733 T^{9} + 949648979305 T^{10} - 21362463620 T^{11} + 108075690044113 T^{12} + 27914267730953 T^{13} + 10597462643039983 T^{14} + 4749868698195514 T^{15} + 908526944174305233 T^{16} + 495817426944109421 T^{17} + 68710270553343799099 T^{18} + 38074969022944131304 T^{19} +$$$$46\!\cdots\!33$$$$T^{20} +$$$$22\!\cdots\!69$$$$T^{21} +$$$$27\!\cdots\!79$$$$T^{22} +$$$$95\!\cdots\!94$$$$T^{23} +$$$$14\!\cdots\!81$$$$T^{24} +$$$$25\!\cdots\!57$$$$T^{25} +$$$$65\!\cdots\!99$$$$T^{26} -$$$$86\!\cdots\!20$$$$T^{27} +$$$$25\!\cdots\!35$$$$T^{28} -$$$$50\!\cdots\!17$$$$T^{29} +$$$$85\!\cdots\!33$$$$T^{30} -$$$$29\!\cdots\!66$$$$T^{31} +$$$$23\!\cdots\!02$$$$T^{32} -$$$$10\!\cdots\!74$$$$T^{33} +$$$$48\!\cdots\!20$$$$T^{34} -$$$$21\!\cdots\!76$$$$T^{35} +$$$$68\!\cdots\!59$$$$T^{36} -$$$$22\!\cdots\!27$$$$T^{37} +$$$$49\!\cdots\!03$$$$T^{38}$$)
$71$ ($$1 + 3 T + 282 T^{2} + 1111 T^{3} + 34521 T^{4} + 127665 T^{5} + 2450991 T^{6} + 5600551 T^{7} + 100930902 T^{8} + 76235043 T^{9} + 1804229351 T^{10}$$)($$1 - 14 T + 370 T^{2} - 4244 T^{3} + 60622 T^{4} - 557781 T^{5} + 5582929 T^{6} - 39602451 T^{7} + 305595502 T^{8} - 1518974284 T^{9} + 9402321970 T^{10} - 25259210914 T^{11} + 128100283921 T^{12}$$)($$1 + 7 T + 423 T^{2} + 2938 T^{3} + 94891 T^{4} + 634016 T^{5} + 14512884 T^{6} + 91820873 T^{7} + 1664655219 T^{8} + 9737118634 T^{9} + 148962046506 T^{10} + 787502321349 T^{11} + 10576305301926 T^{12} + 49084815033994 T^{13} + 595798414087509 T^{14} + 2333322733817513 T^{15} + 26184571280458284 T^{16} + 81217629610456736 T^{17} + 863045046949880381 T^{18} + 1897223874800045818 T^{19} + 19393915803903940113 T^{20} + 22786704857069168407 T^{21} +$$$$23\!\cdots\!71$$$$T^{22}$$)($$1 - 7 T + 139 T^{2} - 694 T^{3} + 20409 T^{4} - 107338 T^{5} + 2127578 T^{6} - 10625821 T^{7} + 204961981 T^{8} - 972345748 T^{9} + 16031632136 T^{10} - 69696118649 T^{11} + 1138245881656 T^{12} - 4901594915668 T^{13} + 73358147581691 T^{14} - 270019973615101 T^{15} + 3838638674141878 T^{16} - 13750028275512298 T^{17} + 185622307312601919 T^{18} - 448152950684558134 T^{19} + 6372941599864415309 T^{20} - 22786704857069168407 T^{21} +$$$$23\!\cdots\!71$$$$T^{22}$$)($$1 - 5 T + 436 T^{2} - 2661 T^{3} + 101370 T^{4} - 701404 T^{5} + 16097289 T^{6} - 120113549 T^{7} + 1936214187 T^{8} - 14781599809 T^{9} + 185383670159 T^{10} - 1368839453739 T^{11} + 14506152869548 T^{12} - 97187601215469 T^{13} + 934519081271519 T^{14} - 5290497169238999 T^{15} + 49202457267718347 T^{16} - 216712390558576699 T^{17} + 2062067291258390169 T^{18} - 6379353659576080964 T^{19} + 65460035462382792570 T^{20} -$$$$12\!\cdots\!91$$$$T^{21} +$$$$14\!\cdots\!36$$$$T^{22} -$$$$11\!\cdots\!55$$$$T^{23} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$1 - 19 T + 608 T^{2} - 9307 T^{3} + 179552 T^{4} - 2303574 T^{5} + 33989917 T^{6} - 377566421 T^{7} + 4624247615 T^{8} - 45164214709 T^{9} + 476984599751 T^{10} - 4124585113695 T^{11} + 38252651163656 T^{12} - 292845543072345 T^{13} + 2404479367344791 T^{14} - 16164769250712899 T^{15} + 117509905257390815 T^{16} - 681216418720222771 T^{17} + 4354118018151224557 T^{18} - 20951282323745389434 T^{19} +$$$$11\!\cdots\!72$$$$T^{20} -$$$$42\!\cdots\!17$$$$T^{21} +$$$$19\!\cdots\!08$$$$T^{22} -$$$$43\!\cdots\!49$$$$T^{23} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$1 + 37 T + 901 T^{2} + 14746 T^{3} + 206290 T^{4} + 2506621 T^{5} + 30453105 T^{6} + 345876887 T^{7} + 3803389784 T^{8} + 37856060224 T^{9} + 366954231344 T^{10} + 3367335479732 T^{11} + 30842666414903 T^{12} + 263798235920490 T^{13} + 2189829315458113 T^{14} + 16974738153329012 T^{15} + 131336955894562384 T^{16} + 961986126329076544 T^{17} + 6862187481586350184 T^{18} + 44306927426411633927 T^{19} +$$$$27\!\cdots\!55$$$$T^{20} +$$$$16\!\cdots\!81$$$$T^{21} +$$$$94\!\cdots\!90$$$$T^{22} +$$$$48\!\cdots\!46$$$$T^{23} +$$$$20\!\cdots\!71$$$$T^{24} +$$$$60\!\cdots\!17$$$$T^{25} +$$$$11\!\cdots\!11$$$$T^{26}$$)($$1 + 5 T + 667 T^{2} + 2790 T^{3} + 210426 T^{4} + 721315 T^{5} + 41963243 T^{6} + 115239987 T^{7} + 5974373412 T^{8} + 12982883096 T^{9} + 650776182024 T^{10} + 1141711263752 T^{11} + 56611739724711 T^{12} + 85847839551638 T^{13} + 4019433520454481 T^{14} + 5755366480573832 T^{15} + 232919954084391864 T^{16} + 329916883695844376 T^{17} + 10779139863764415612 T^{18} + 14762275053752349027 T^{19} +$$$$38\!\cdots\!13$$$$T^{20} +$$$$46\!\cdots\!15$$$$T^{21} +$$$$96\!\cdots\!06$$$$T^{22} +$$$$90\!\cdots\!90$$$$T^{23} +$$$$15\!\cdots\!57$$$$T^{24} +$$$$82\!\cdots\!05$$$$T^{25} +$$$$11\!\cdots\!11$$$$T^{26}$$)($$1 + 3 T + 485 T^{2} + 1762 T^{3} + 117464 T^{4} + 493261 T^{5} + 19221703 T^{6} + 87958469 T^{7} + 2395386368 T^{8} + 11333779128 T^{9} + 240956043280 T^{10} + 1127862193268 T^{11} + 20201203996895 T^{12} + 89372246452338 T^{13} + 1434285483779545 T^{14} + 5685553316263988 T^{15} + 86240818406388080 T^{16} + 288010379725194168 T^{17} + 4321826392130887168 T^{18} + 11267504852156476949 T^{19} +$$$$17\!\cdots\!73$$$$T^{20} +$$$$31\!\cdots\!21$$$$T^{21} +$$$$53\!\cdots\!84$$$$T^{22} +$$$$57\!\cdots\!62$$$$T^{23} +$$$$11\!\cdots\!35$$$$T^{24} +$$$$49\!\cdots\!23$$$$T^{25} +$$$$11\!\cdots\!11$$$$T^{26}$$)($$1 - 13 T + 466 T^{2} - 4633 T^{3} + 99121 T^{4} - 892267 T^{5} + 14927077 T^{6} - 133506138 T^{7} + 1828465207 T^{8} - 15985056605 T^{9} + 184637787060 T^{10} - 1563978150040 T^{11} + 16068717568391 T^{12} - 130982142754738 T^{13} + 1226932266157194 T^{14} - 9299732135586398 T^{15} + 81002405262259031 T^{16} - 559764983658966440 T^{17} + 4691956545314647860 T^{18} - 28840708304137413355 T^{19} +$$$$23\!\cdots\!47$$$$T^{20} -$$$$12\!\cdots\!58$$$$T^{21} +$$$$96\!\cdots\!97$$$$T^{22} -$$$$40\!\cdots\!77$$$$T^{23} +$$$$32\!\cdots\!21$$$$T^{24} -$$$$10\!\cdots\!43$$$$T^{25} +$$$$76\!\cdots\!06$$$$T^{26} -$$$$15\!\cdots\!43$$$$T^{27} +$$$$82\!\cdots\!81$$$$T^{28}$$)($$1 - 19 T + 878 T^{2} - 14241 T^{3} + 374920 T^{4} - 5352616 T^{5} + 104752181 T^{6} - 1343370758 T^{7} + 21623226530 T^{8} - 252588529195 T^{9} + 3518873427046 T^{10} - 37800903314792 T^{11} + 469312958702142 T^{12} - 4665621917976129 T^{13} + 52560369889705106 T^{14} - 485419890861740250 T^{15} + 5019201466897587468 T^{16} - 43139697670195372617 T^{17} +$$$$41\!\cdots\!54$$$$T^{18} -$$$$32\!\cdots\!34$$$$T^{19} +$$$$29\!\cdots\!34$$$$T^{20} -$$$$21\!\cdots\!97$$$$T^{21} +$$$$17\!\cdots\!48$$$$T^{22} -$$$$12\!\cdots\!50$$$$T^{23} +$$$$94\!\cdots\!06$$$$T^{24} -$$$$59\!\cdots\!09$$$$T^{25} +$$$$42\!\cdots\!22$$$$T^{26} -$$$$24\!\cdots\!12$$$$T^{27} +$$$$16\!\cdots\!26$$$$T^{28} -$$$$82\!\cdots\!95$$$$T^{29} +$$$$49\!\cdots\!30$$$$T^{30} -$$$$22\!\cdots\!78$$$$T^{31} +$$$$12\!\cdots\!91$$$$T^{32} -$$$$44\!\cdots\!96$$$$T^{33} +$$$$22\!\cdots\!20$$$$T^{34} -$$$$59\!\cdots\!61$$$$T^{35} +$$$$25\!\cdots\!98$$$$T^{36} -$$$$39\!\cdots\!59$$$$T^{37} +$$$$14\!\cdots\!31$$$$T^{38}$$)
$73$ ($$1 + 4 T + 247 T^{2} + 1069 T^{3} + 28266 T^{4} + 113873 T^{5} + 2063418 T^{6} + 5696701 T^{7} + 96087199 T^{8} + 113592964 T^{9} + 2073071593 T^{10}$$)($$1 + 14 T + 238 T^{2} + 1833 T^{3} + 26783 T^{4} + 214906 T^{5} + 2618754 T^{6} + 15688138 T^{7} + 142726607 T^{8} + 713068161 T^{9} + 6758781358 T^{10} + 29023002302 T^{11} + 151334226289 T^{12}$$)($$1 + 42 T + 1222 T^{2} + 25622 T^{3} + 447305 T^{4} + 6597184 T^{5} + 86476323 T^{6} + 1015901577 T^{7} + 10992487226 T^{8} + 109895882058 T^{9} + 1031664342334 T^{10} + 9069041561577 T^{11} + 75311496990382 T^{12} + 585635155487082 T^{13} + 4276264403196842 T^{14} + 28849817815926057 T^{15} + 179271608678392539 T^{16} + 998379736326170176 T^{17} + 4941556594584683585 T^{18} + 20663120474510143382 T^{19} + 71941078957503389686 T^{20} +$$$$18\!\cdots\!58$$$$T^{21} +$$$$31\!\cdots\!77$$$$T^{22}$$)($$1 - 6 T + 314 T^{2} - 1146 T^{3} + 45031 T^{4} - 57542 T^{5} + 4317965 T^{6} + 5955239 T^{7} + 332665660 T^{8} + 1327226302 T^{9} + 23359265340 T^{10} + 125872665635 T^{11} + 1705226369820 T^{12} + 7072788963358 T^{13} + 129412597056220 T^{14} + 169118312334599 T^{15} + 8951450581068245 T^{16} - 8708074049121638 T^{17} + 497475402713457007 T^{18} - 924203265310616826 T^{19} + 18485678226396124682 T^{20} - 25785754978221345894 T^{21} +$$$$31\!\cdots\!77$$$$T^{22}$$)($$1 + 2 T + 595 T^{2} + 598 T^{3} + 171665 T^{4} + 44530 T^{5} + 32125678 T^{6} - 7547733 T^{7} + 4371288811 T^{8} - 2179159199 T^{9} + 456343710966 T^{10} - 262228646139 T^{11} + 37446061911870 T^{12} - 19142691168147 T^{13} + 2431855635737814 T^{14} - 847729974117383 T^{15} + 124136913135381451 T^{16} - 15646990873848669 T^{17} + 4861714624139548942 T^{18} + 491940656055389410 T^{19} +$$$$13\!\cdots\!65$$$$T^{20} + 35205208851544211974 T^{21} +$$$$25\!\cdots\!55$$$$T^{22} +$$$$62\!\cdots\!54$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 + 42 T + 1043 T^{2} + 17998 T^{3} + 245747 T^{4} + 2754720 T^{5} + 26880038 T^{6} + 230692403 T^{7} + 1799301587 T^{8} + 12486762683 T^{9} + 80041477558 T^{10} + 485176939647 T^{11} + 3589099987174 T^{12} + 35417916594231 T^{13} + 426541033906582 T^{14} + 4857562958652611 T^{15} + 51097000099308467 T^{16} + 478241867380207979 T^{17} + 4067869753348918982 T^{18} + 30432489648526887840 T^{19} +$$$$19\!\cdots\!07$$$$T^{20} +$$$$10\!\cdots\!74$$$$T^{21} +$$$$44\!\cdots\!07$$$$T^{22} +$$$$13\!\cdots\!34$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 + 16 T + 630 T^{2} + 8528 T^{3} + 185642 T^{4} + 2185728 T^{5} + 34781245 T^{6} + 364567989 T^{7} + 4741032295 T^{8} + 45021431638 T^{9} + 506918130739 T^{10} + 4405175370490 T^{11} + 44355380310892 T^{12} + 353337388110734 T^{13} + 3237942762695116 T^{14} + 23475179549341210 T^{15} + 197199770465693563 T^{16} + 1278529465820948758 T^{17} + 9828499372260095935 T^{18} + 55171614545051662821 T^{19} +$$$$38\!\cdots\!65$$$$T^{20} +$$$$17\!\cdots\!68$$$$T^{21} +$$$$10\!\cdots\!46$$$$T^{22} +$$$$36\!\cdots\!72$$$$T^{23} +$$$$19\!\cdots\!10$$$$T^{24} +$$$$36\!\cdots\!36$$$$T^{25} +$$$$16\!\cdots\!33$$$$T^{26}$$)($$1 - 18 T + 722 T^{2} - 11164 T^{3} + 249956 T^{4} - 3378036 T^{5} + 55268985 T^{6} - 658789573 T^{7} + 8728233621 T^{8} - 92269947656 T^{9} + 1040846671509 T^{10} - 9788272584286 T^{11} + 96495170021146 T^{12} - 807214488838654 T^{13} + 7044147411543658 T^{14} - 52161704601660094 T^{15} + 404907049610416653 T^{16} - 2620304210592473096 T^{17} + 18094253176762628253 T^{18} - 99697410317215684597 T^{19} +$$$$61\!\cdots\!45$$$$T^{20} -$$$$27\!\cdots\!16$$$$T^{21} +$$$$14\!\cdots\!28$$$$T^{22} -$$$$47\!\cdots\!36$$$$T^{23} +$$$$22\!\cdots\!94$$$$T^{24} -$$$$41\!\cdots\!78$$$$T^{25} +$$$$16\!\cdots\!33$$$$T^{26}$$)($$1 - 48 T + 1522 T^{2} - 34880 T^{3} + 653072 T^{4} - 10263838 T^{5} + 140801067 T^{6} - 1710105013 T^{7} + 18793932243 T^{8} - 189235230100 T^{9} + 1781965804351 T^{10} - 15946799449806 T^{11} + 138757519977572 T^{12} - 1188994646402494 T^{13} + 10129298958362756 T^{14} - 84980494268016174 T^{15} + 693214991311212967 T^{16} - 5373947670070254100 T^{17} + 38961167053730073099 T^{18} -$$$$25\!\cdots\!57$$$$T^{19} +$$$$15\!\cdots\!99$$$$T^{20} -$$$$82\!\cdots\!78$$$$T^{21} +$$$$38\!\cdots\!36$$$$T^{22} -$$$$14\!\cdots\!20$$$$T^{23} +$$$$47\!\cdots\!94$$$$T^{24} -$$$$10\!\cdots\!08$$$$T^{25} +$$$$16\!\cdots\!33$$$$T^{26}$$)($$1 - 20 T + 815 T^{2} - 13122 T^{3} + 300368 T^{4} - 3986354 T^{5} + 66684005 T^{6} - 744919067 T^{7} + 10089838918 T^{8} - 96900011919 T^{9} + 1130454581090 T^{10} - 9593322829902 T^{11} + 101395062590991 T^{12} - 788574260711128 T^{13} + 7838904257943112 T^{14} - 57565921031912344 T^{15} + 540334288547391039 T^{16} - 3731965667319986334 T^{17} + 32102921633347862690 T^{18} -$$$$20\!\cdots\!67$$$$T^{19} +$$$$15\!\cdots\!02$$$$T^{20} -$$$$82\!\cdots\!99$$$$T^{21} +$$$$53\!\cdots\!05$$$$T^{22} -$$$$23\!\cdots\!02$$$$T^{23} +$$$$12\!\cdots\!32$$$$T^{24} -$$$$41\!\cdots\!94$$$$T^{25} +$$$$18\!\cdots\!15$$$$T^{26} -$$$$33\!\cdots\!60$$$$T^{27} +$$$$12\!\cdots\!09$$$$T^{28}$$)($$1 - 20 T + 983 T^{2} - 15447 T^{3} + 442119 T^{4} - 5776019 T^{5} + 124649027 T^{6} - 1395944110 T^{7} + 25117566350 T^{8} - 245527957621 T^{9} + 3892497812088 T^{10} - 33616760931648 T^{11} + 487253061211176 T^{12} - 3757469846070647 T^{13} + 51174778307022026 T^{14} - 357004941641166770 T^{15} + 4656335452940103068 T^{16} - 29922965328739857229 T^{17} +$$$$37\!\cdots\!70$$$$T^{18} -$$$$22\!\cdots\!34$$$$T^{19} +$$$$27\!\cdots\!10$$$$T^{20} -$$$$15\!\cdots\!41$$$$T^{21} +$$$$18\!\cdots\!56$$$$T^{22} -$$$$10\!\cdots\!70$$$$T^{23} +$$$$10\!\cdots\!18$$$$T^{24} -$$$$56\!\cdots\!83$$$$T^{25} +$$$$53\!\cdots\!72$$$$T^{26} -$$$$27\!\cdots\!88$$$$T^{27} +$$$$22\!\cdots\!44$$$$T^{28} -$$$$10\!\cdots\!29$$$$T^{29} +$$$$78\!\cdots\!50$$$$T^{30} -$$$$31\!\cdots\!10$$$$T^{31} +$$$$20\!\cdots\!91$$$$T^{32} -$$$$70\!\cdots\!71$$$$T^{33} +$$$$39\!\cdots\!83$$$$T^{34} -$$$$10\!\cdots\!67$$$$T^{35} +$$$$46\!\cdots\!99$$$$T^{36} -$$$$69\!\cdots\!80$$$$T^{37} +$$$$25\!\cdots\!37$$$$T^{38}$$)
$79$ ($$1 + 27 T + 654 T^{2} + 9608 T^{3} + 125752 T^{4} + 1182335 T^{5} + 9934408 T^{6} + 59963528 T^{7} + 322447506 T^{8} + 1051652187 T^{9} + 3077056399 T^{10}$$)($$1 - 5 T + 311 T^{2} - 1249 T^{3} + 49564 T^{4} - 164781 T^{5} + 4854524 T^{6} - 13017699 T^{7} + 309328924 T^{8} - 615805711 T^{9} + 12113475191 T^{10} - 15385281995 T^{11} + 243087455521 T^{12}$$)($$1 + 11 T + 690 T^{2} + 6490 T^{3} + 218178 T^{4} + 1770975 T^{5} + 42469286 T^{6} + 300331876 T^{7} + 5775405374 T^{8} + 35916525340 T^{9} + 588476371774 T^{10} + 3234511194975 T^{11} + 46489633370146 T^{12} + 224155034646940 T^{13} + 2847500090191586 T^{14} + 11697950897081956 T^{15} + 130680388247261114 T^{16} + 430501806541302975 T^{17} + 4189870454782198302 T^{18} + 9846036176293580890 T^{19} + 82697601228006640110 T^{20} +$$$$10\!\cdots\!11$$$$T^{21} +$$$$74\!\cdots\!79$$$$T^{22}$$)($$1 - 17 T + 510 T^{2} - 7990 T^{3} + 139448 T^{4} - 1901341 T^{5} + 25726134 T^{6} - 302390608 T^{7} + 3455558864 T^{8} - 35459924532 T^{9} + 352399281068 T^{10} - 3185312378827 T^{11} + 27839543204372 T^{12} - 221305389004212 T^{13} + 1703725286747696 T^{14} - 11778138675239248 T^{15} + 79160765246231466 T^{16} - 462192145767753661 T^{17} + 2677946700301900232 T^{18} - 12121699391153422390 T^{19} + 61124313951135342690 T^{20} -$$$$16\!\cdots\!17$$$$T^{21} +$$$$74\!\cdots\!79$$$$T^{22}$$)($$1 + 31 T + 691 T^{2} + 10467 T^{3} + 141414 T^{4} + 1662705 T^{5} + 19748172 T^{6} + 218165545 T^{7} + 2387782966 T^{8} + 24007153734 T^{9} + 238793154852 T^{10} + 2218538296175 T^{11} + 20439922610232 T^{12} + 175264525397825 T^{13} + 1490308079431332 T^{14} + 11836463069857626 T^{15} + 93004339936120246 T^{16} + 671307686283572455 T^{17} + 4800532882671057612 T^{18} + 31930435490831500095 T^{19} +$$$$21\!\cdots\!54$$$$T^{20} +$$$$12\!\cdots\!73$$$$T^{21} +$$$$65\!\cdots\!91$$$$T^{22} +$$$$23\!\cdots\!49$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 + 11 T + 375 T^{2} + 1971 T^{3} + 61812 T^{4} + 141297 T^{5} + 8030226 T^{6} + 5418989 T^{7} + 921051700 T^{8} + 1159310 T^{9} + 93618602276 T^{10} + 97393057 T^{11} + 8156189470360 T^{12} + 7694051503 T^{13} + 584273696804516 T^{14} + 571585043090 T^{15} + 35875038320187700 T^{16} + 16674534778560611 T^{17} + 1952047205598577746 T^{18} + 2713454728017308223 T^{19} + 93775529757944348532 T^{20} +$$$$23\!\cdots\!49$$$$T^{21} +$$$$35\!\cdots\!75$$$$T^{22} +$$$$82\!\cdots\!69$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 + 17 T + 622 T^{2} + 8010 T^{3} + 182593 T^{4} + 1960260 T^{5} + 35114164 T^{6} + 328234756 T^{7} + 5053274170 T^{8} + 42318143615 T^{9} + 581709871210 T^{10} + 4424991480327 T^{11} + 55189321376644 T^{12} + 383304844703314 T^{13} + 4359956388754876 T^{14} + 27616371828720807 T^{15} + 286805653191507190 T^{16} + 1648295121573882815 T^{17} + 15549209620699913830 T^{18} + 79789751649596287876 T^{19} +$$$$67\!\cdots\!76$$$$T^{20} +$$$$29\!\cdots\!60$$$$T^{21} +$$$$21\!\cdots\!67$$$$T^{22} +$$$$75\!\cdots\!10$$$$T^{23} +$$$$46\!\cdots\!38$$$$T^{24} +$$$$10\!\cdots\!97$$$$T^{25} +$$$$46\!\cdots\!39$$$$T^{26}$$)($$1 + T + 592 T^{2} + 1682 T^{3} + 175369 T^{4} + 744808 T^{5} + 34871614 T^{6} + 181072780 T^{7} + 5201860224 T^{8} + 29584351201 T^{9} + 613761565080 T^{10} + 3530100791245 T^{11} + 58889113102736 T^{12} + 318873705758666 T^{13} + 4652239935116144 T^{14} + 22031359038160045 T^{15} + 302608388285478120 T^{16} + 1152312875611397281 T^{17} + 16006417288962773376 T^{18} + 44016521354313818380 T^{19} +$$$$66\!\cdots\!26$$$$T^{20} +$$$$11\!\cdots\!88$$$$T^{21} +$$$$21\!\cdots\!11$$$$T^{22} +$$$$15\!\cdots\!82$$$$T^{23} +$$$$44\!\cdots\!68$$$$T^{24} +$$$$59\!\cdots\!41$$$$T^{25} +$$$$46\!\cdots\!39$$$$T^{26}$$)($$1 + 17 T + 542 T^{2} + 7530 T^{3} + 155435 T^{4} + 1879772 T^{5} + 30500780 T^{6} + 329653304 T^{7} + 4538991666 T^{8} + 44343627643 T^{9} + 536172795588 T^{10} + 4759796653037 T^{11} + 51529110799964 T^{12} + 415643920998238 T^{13} + 4070799753197156 T^{14} + 29705890911603917 T^{15} + 264354098963911932 T^{16} + 1727187888528689083 T^{17} + 13966733350872970734 T^{18} + 80134582873450691384 T^{19} +$$$$58\!\cdots\!20$$$$T^{20} +$$$$28\!\cdots\!92$$$$T^{21} +$$$$18\!\cdots\!65$$$$T^{22} +$$$$71\!\cdots\!30$$$$T^{23} +$$$$40\!\cdots\!18$$$$T^{24} +$$$$10\!\cdots\!97$$$$T^{25} +$$$$46\!\cdots\!39$$$$T^{26}$$)($$1 - 31 T + 1023 T^{2} - 21323 T^{3} + 433671 T^{4} - 7070910 T^{5} + 110900735 T^{6} - 1512216248 T^{7} + 19835673362 T^{8} - 234800713163 T^{9} + 2683673218946 T^{10} - 28224264814010 T^{11} + 287742543203814 T^{12} - 2726029592624301 T^{13} + 25095925876714032 T^{14} - 215356337817319779 T^{15} + 1795801212135003174 T^{16} - 13915663299634676390 T^{17} +$$$$10\!\cdots\!26$$$$T^{18} -$$$$72\!\cdots\!37$$$$T^{19} +$$$$48\!\cdots\!02$$$$T^{20} -$$$$29\!\cdots\!32$$$$T^{21} +$$$$16\!\cdots\!35$$$$T^{22} -$$$$84\!\cdots\!90$$$$T^{23} +$$$$41\!\cdots\!71$$$$T^{24} -$$$$15\!\cdots\!17$$$$T^{25} +$$$$60\!\cdots\!43$$$$T^{26} -$$$$14\!\cdots\!09$$$$T^{27} +$$$$36\!\cdots\!81$$$$T^{28}$$)($$1 - 69 T + 2783 T^{2} - 80271 T^{3} + 1833295 T^{4} - 34810424 T^{5} + 569306503 T^{6} - 8213895354 T^{7} + 106756573323 T^{8} - 1272070190155 T^{9} + 14143909234770 T^{10} - 149273308631457 T^{11} + 1522063396688776 T^{12} - 15229257243053839 T^{13} + 151241951360093818 T^{14} - 1495740235635165111 T^{15} + 14669808097880173198 T^{16} -$$$$14\!\cdots\!01$$$$T^{17} +$$$$13\!\cdots\!22$$$$T^{18} -$$$$11\!\cdots\!37$$$$T^{19} +$$$$10\!\cdots\!38$$$$T^{20} -$$$$88\!\cdots\!41$$$$T^{21} +$$$$72\!\cdots\!22$$$$T^{22} -$$$$58\!\cdots\!91$$$$T^{23} +$$$$46\!\cdots\!82$$$$T^{24} -$$$$37\!\cdots\!19$$$$T^{25} +$$$$29\!\cdots\!84$$$$T^{26} -$$$$22\!\cdots\!77$$$$T^{27} +$$$$16\!\cdots\!30$$$$T^{28} -$$$$12\!\cdots\!55$$$$T^{29} +$$$$79\!\cdots\!17$$$$T^{30} -$$$$48\!\cdots\!14$$$$T^{31} +$$$$26\!\cdots\!17$$$$T^{32} -$$$$12\!\cdots\!44$$$$T^{33} +$$$$53\!\cdots\!05$$$$T^{34} -$$$$18\!\cdots\!91$$$$T^{35} +$$$$50\!\cdots\!97$$$$T^{36} -$$$$99\!\cdots\!09$$$$T^{37} +$$$$11\!\cdots\!19$$$$T^{38}$$)
$83$ ($$1 - 3 T + 272 T^{2} - 278 T^{3} + 34402 T^{4} - 8271 T^{5} + 2855366 T^{6} - 1915142 T^{7} + 155526064 T^{8} - 142374963 T^{9} + 3939040643 T^{10}$$)($$1 + 17 T + 327 T^{2} + 4281 T^{3} + 55034 T^{4} + 551657 T^{5} + 5713940 T^{6} + 45787531 T^{7} + 379129226 T^{8} + 2447820147 T^{9} + 15518870967 T^{10} + 66963690931 T^{11} + 326940373369 T^{12}$$)($$1 - 34 T + 1164 T^{2} - 24674 T^{3} + 499533 T^{4} - 7832010 T^{5} + 117485561 T^{6} - 1476053272 T^{7} + 17943932359 T^{8} - 189853527918 T^{9} + 1966784410629 T^{10} - 18060985019151 T^{11} + 163243106082207 T^{12} - 1307900953827102 T^{13} + 10260107251755533 T^{14} - 70051009995676312 T^{15} + 462780399744655723 T^{16} - 2560600273629741690 T^{17} + 13555352959001344191 T^{18} - 55573058535798697634 T^{19} +$$$$21\!\cdots\!92$$$$T^{20} -$$$$52\!\cdots\!66$$$$T^{21} +$$$$12\!\cdots\!67$$$$T^{22}$$)($$1 - 34 T + 960 T^{2} - 18266 T^{3} + 322939 T^{4} - 4691920 T^{5} + 65456303 T^{6} - 795285212 T^{7} + 9366195719 T^{8} - 98485660756 T^{9} + 1008682396977 T^{10} - 9309164570275 T^{11} + 83720638949091 T^{12} - 678467716948084 T^{13} + 5355468951579853 T^{14} - 37742900877649052 T^{15} + 257835037857522829 T^{16} - 1533978076617478480 T^{17} + 8763289170539153753 T^{18} - 41140369912251722906 T^{19} +$$$$17\!\cdots\!80$$$$T^{20} -$$$$52\!\cdots\!66$$$$T^{21} +$$$$12\!\cdots\!67$$$$T^{22}$$)($$1 - 32 T + 955 T^{2} - 18166 T^{3} + 328925 T^{4} - 4631812 T^{5} + 63373588 T^{6} - 721281496 T^{7} + 8187904876 T^{8} - 80106634838 T^{9} + 810259467204 T^{10} - 7268466154033 T^{11} + 69811468720106 T^{12} - 603282690784739 T^{13} + 5581877469568356 T^{14} - 45803932414115506 T^{15} + 388584217922673196 T^{16} - 2841157127787841928 T^{17} + 20719384522453177972 T^{18} -$$$$12\!\cdots\!24$$$$T^{19} +$$$$74\!\cdots\!25$$$$T^{20} -$$$$33\!\cdots\!98$$$$T^{21} +$$$$14\!\cdots\!95$$$$T^{22} -$$$$41\!\cdots\!44$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 - 56 T + 1951 T^{2} - 49386 T^{3} + 1022271 T^{4} - 17968694 T^{5} + 278807356 T^{6} - 3878361170 T^{7} + 49264947230 T^{8} - 575419961940 T^{9} + 6239757087976 T^{10} - 62947612589627 T^{11} + 593568643259770 T^{12} - 5224651844939041 T^{13} + 42985686579066664 T^{14} - 329017653777786780 T^{15} + 2338031679689400830 T^{16} - 15277022276863032310 T^{17} + 91153381068663702364 T^{18} -$$$$48\!\cdots\!38$$$$T^{19} +$$$$23\!\cdots\!11$$$$T^{20} -$$$$92\!\cdots\!58$$$$T^{21} +$$$$30\!\cdots\!99$$$$T^{22} -$$$$72\!\cdots\!52$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 + 30 T + 974 T^{2} + 18458 T^{3} + 366294 T^{4} + 5398142 T^{5} + 83760451 T^{6} + 1050757230 T^{7} + 13881448384 T^{8} + 153604165536 T^{9} + 1782849294068 T^{10} + 17626677690403 T^{11} + 182574569560402 T^{12} + 1624662755159746 T^{13} + 15153689273513366 T^{14} + 121430182609186267 T^{15} + 1019410049307259516 T^{16} + 7289795794944625056 T^{17} + 54679589368282670912 T^{18} +$$$$34\!\cdots\!70$$$$T^{19} +$$$$22\!\cdots\!77$$$$T^{20} +$$$$12\!\cdots\!22$$$$T^{21} +$$$$68\!\cdots\!82$$$$T^{22} +$$$$28\!\cdots\!42$$$$T^{23} +$$$$12\!\cdots\!58$$$$T^{24} +$$$$32\!\cdots\!30$$$$T^{25} +$$$$88\!\cdots\!63$$$$T^{26}$$)($$1 + 48 T + 1946 T^{2} + 54074 T^{3} + 1322286 T^{4} + 26651308 T^{5} + 485319219 T^{6} + 7734534804 T^{7} + 113100793526 T^{8} + 1486614970798 T^{9} + 18090592348036 T^{10} + 200478795669543 T^{11} + 2066582253204772 T^{12} + 19506872219703810 T^{13} + 171526327015996076 T^{14} + 1381098423367481727 T^{15} + 10343965526906460332 T^{16} + 70552250487537110158 T^{17} +$$$$44\!\cdots\!18$$$$T^{18} +$$$$25\!\cdots\!76$$$$T^{19} +$$$$13\!\cdots\!13$$$$T^{20} +$$$$60\!\cdots\!28$$$$T^{21} +$$$$24\!\cdots\!58$$$$T^{22} +$$$$83\!\cdots\!26$$$$T^{23} +$$$$25\!\cdots\!82$$$$T^{24} +$$$$51\!\cdots\!28$$$$T^{25} +$$$$88\!\cdots\!63$$$$T^{26}$$)($$1 + 50 T + 1798 T^{2} + 46774 T^{3} + 1033384 T^{4} + 19372996 T^{5} + 325384261 T^{6} + 4885010702 T^{7} + 67314181298 T^{8} + 848528007260 T^{9} + 9938314273754 T^{10} + 107686123909759 T^{11} + 1090671424852278 T^{12} + 10268166394136662 T^{13} + 90525728262739074 T^{14} + 741849707614329751 T^{15} + 5682598903646978398 T^{16} + 40269714546035410460 T^{17} +$$$$26\!\cdots\!14$$$$T^{18} +$$$$15\!\cdots\!38$$$$T^{19} +$$$$88\!\cdots\!47$$$$T^{20} +$$$$43\!\cdots\!36$$$$T^{21} +$$$$19\!\cdots\!52$$$$T^{22} +$$$$72\!\cdots\!26$$$$T^{23} +$$$$23\!\cdots\!66$$$$T^{24} +$$$$53\!\cdots\!50$$$$T^{25} +$$$$88\!\cdots\!63$$$$T^{26}$$)($$1 + 32 T + 1197 T^{2} + 27366 T^{3} + 616486 T^{4} + 11110672 T^{5} + 190171157 T^{6} + 2848502518 T^{7} + 40231880855 T^{8} + 516914651030 T^{9} + 6266878895874 T^{10} + 70420077805961 T^{11} + 748268506372730 T^{12} + 7434734385528863 T^{13} + 69953545105194072 T^{14} + 617082953998895629 T^{15} + 5154821740401736970 T^{16} + 40265285028437022307 T^{17} +$$$$29\!\cdots\!54$$$$T^{18} +$$$$20\!\cdots\!90$$$$T^{19} +$$$$13\!\cdots\!95$$$$T^{20} +$$$$77\!\cdots\!86$$$$T^{21} +$$$$42\!\cdots\!37$$$$T^{22} +$$$$20\!\cdots\!16$$$$T^{23} +$$$$95\!\cdots\!14$$$$T^{24} +$$$$35\!\cdots\!22$$$$T^{25} +$$$$12\!\cdots\!17$$$$T^{26} +$$$$28\!\cdots\!16$$$$T^{27} +$$$$73\!\cdots\!29$$$$T^{28}$$)($$1 + T + 546 T^{2} - 622 T^{3} + 151951 T^{4} - 457032 T^{5} + 29392894 T^{6} - 133790922 T^{7} + 4497136511 T^{8} - 25906914375 T^{9} + 583122186185 T^{10} - 3883388716012 T^{11} + 66936907499529 T^{12} - 486267239143469 T^{13} + 6998628514481439 T^{14} - 53000991615274038 T^{15} + 676682691789200105 T^{16} - 5139164953933873773 T^{17} + 60700141269974555373 T^{18} -$$$$44\!\cdots\!16$$$$T^{19} +$$$$50\!\cdots\!59$$$$T^{20} -$$$$35\!\cdots\!97$$$$T^{21} +$$$$38\!\cdots\!35$$$$T^{22} -$$$$25\!\cdots\!98$$$$T^{23} +$$$$27\!\cdots\!77$$$$T^{24} -$$$$15\!\cdots\!61$$$$T^{25} +$$$$18\!\cdots\!83$$$$T^{26} -$$$$87\!\cdots\!92$$$$T^{27} +$$$$10\!\cdots\!55$$$$T^{28} -$$$$40\!\cdots\!75$$$$T^{29} +$$$$57\!\cdots\!37$$$$T^{30} -$$$$14\!\cdots\!42$$$$T^{31} +$$$$26\!\cdots\!22$$$$T^{32} -$$$$33\!\cdots\!28$$$$T^{33} +$$$$92\!\cdots\!57$$$$T^{34} -$$$$31\!\cdots\!82$$$$T^{35} +$$$$22\!\cdots\!58$$$$T^{36} +$$$$34\!\cdots\!09$$$$T^{37} +$$$$29\!\cdots\!47$$$$T^{38}$$)
$89$ ($$1 - 12 T + 370 T^{2} - 3531 T^{3} + 58932 T^{4} - 442409 T^{5} + 5244948 T^{6} - 27969051 T^{7} + 260838530 T^{8} - 752906892 T^{9} + 5584059449 T^{10}$$)($$1 - 25 T + 649 T^{2} - 10981 T^{3} + 159015 T^{4} - 1943100 T^{5} + 19432603 T^{6} - 172935900 T^{7} + 1259557815 T^{8} - 7741264589 T^{9} + 40719714409 T^{10} - 139601486225 T^{11} + 496981290961 T^{12}$$)($$1 + 29 T + 1006 T^{2} + 20891 T^{3} + 434731 T^{4} + 7113247 T^{5} + 111586710 T^{6} + 1505638719 T^{7} + 19231282025 T^{8} + 219069317588 T^{9} + 2354328494051 T^{10} + 22873997682689 T^{11} + 209535235970539 T^{12} + 1735248064614548 T^{13} + 13557457657882225 T^{14} + 94467147366429279 T^{15} + 623106822358322790 T^{16} + 3535150676984460367 T^{17} + 19228732450468217699 T^{18} + 82239276739922174171 T^{19} +$$$$35\!\cdots\!54$$$$T^{20} +$$$$90\!\cdots\!29$$$$T^{21} +$$$$27\!\cdots\!89$$$$T^{22}$$)($$1 - 41 T + 1100 T^{2} - 20271 T^{3} + 316687 T^{4} - 4289405 T^{5} + 56485928 T^{6} - 695401739 T^{7} + 8201672365 T^{8} - 87701882052 T^{9} + 891074197783 T^{10} - 8478025448085 T^{11} + 79305603602687 T^{12} - 694686607733892 T^{13} + 5781924765481685 T^{14} - 43631063500157099 T^{15} + 315420779983933672 T^{16} - 2131754034354568205 T^{17} + 14007488754060392423 T^{18} - 79798591680386883951 T^{19} +$$$$38\!\cdots\!00$$$$T^{20} -$$$$12\!\cdots\!41$$$$T^{21} +$$$$27\!\cdots\!89$$$$T^{22}$$)($$1 + 27 T + 847 T^{2} + 15572 T^{3} + 288379 T^{4} + 4134838 T^{5} + 58695353 T^{6} + 717071370 T^{7} + 8761760559 T^{8} + 96250677487 T^{9} + 1060385422624 T^{10} + 10571701084571 T^{11} + 104982457822002 T^{12} + 940881396526819 T^{13} + 8399312932604704 T^{14} + 67853743857332903 T^{15} + 549732492577072719 T^{16} + 4004169159255875130 T^{17} + 29170492307351604233 T^{18} +$$$$18\!\cdots\!02$$$$T^{19} +$$$$11\!\cdots\!99$$$$T^{20} +$$$$54\!\cdots\!48$$$$T^{21} +$$$$26\!\cdots\!47$$$$T^{22} +$$$$74\!\cdots\!03$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 - 55 T + 2149 T^{2} - 60868 T^{3} + 1441797 T^{4} - 28799664 T^{5} + 507606343 T^{6} - 7923948344 T^{7} + 111878225657 T^{8} - 1429878368183 T^{9} + 16734332409804 T^{10} - 179077113801815 T^{11} + 1764114163881438 T^{12} - 15937863128361535 T^{13} + 132552647018057484 T^{14} - 1008019923339601327 T^{15} + 7019490596823877337 T^{16} - 44247798623701102456 T^{17} +$$$$25\!\cdots\!23$$$$T^{18} -$$$$12\!\cdots\!56$$$$T^{19} +$$$$56\!\cdots\!57$$$$T^{20} -$$$$21\!\cdots\!12$$$$T^{21} +$$$$67\!\cdots\!49$$$$T^{22} -$$$$15\!\cdots\!95$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 + 35 T + 1184 T^{2} + 25669 T^{3} + 516942 T^{4} + 8370310 T^{5} + 127074742 T^{6} + 1696233422 T^{7} + 21565020894 T^{8} + 253402493441 T^{9} + 2858507560085 T^{10} + 30474939017346 T^{11} + 310586541225446 T^{12} + 3003263361737920 T^{13} + 27642202169064694 T^{14} + 241391991956397666 T^{15} + 2015159216125562365 T^{16} + 15899040313476141281 T^{17} +$$$$12\!\cdots\!06$$$$T^{18} +$$$$84\!\cdots\!42$$$$T^{19} +$$$$56\!\cdots\!18$$$$T^{20} +$$$$32\!\cdots\!10$$$$T^{21} +$$$$18\!\cdots\!78$$$$T^{22} +$$$$80\!\cdots\!69$$$$T^{23} +$$$$32\!\cdots\!76$$$$T^{24} +$$$$86\!\cdots\!35$$$$T^{25} +$$$$21\!\cdots\!69$$$$T^{26}$$)($$1 + 15 T + 786 T^{2} + 11565 T^{3} + 310984 T^{4} + 4296636 T^{5} + 81310600 T^{6} + 1023800184 T^{7} + 15480612414 T^{8} + 175057827139 T^{9} + 2244424047975 T^{10} + 22673108801304 T^{11} + 253614549212220 T^{12} + 2281130993837004 T^{13} + 22571694879887580 T^{14} + 179593694815128984 T^{15} + 1582249376676887775 T^{16} + 10983520379291478499 T^{17} + 86444660026703399886 T^{18} +$$$$50\!\cdots\!24$$$$T^{19} +$$$$35\!\cdots\!00$$$$T^{20} +$$$$16\!\cdots\!16$$$$T^{21} +$$$$10\!\cdots\!56$$$$T^{22} +$$$$36\!\cdots\!65$$$$T^{23} +$$$$21\!\cdots\!54$$$$T^{24} +$$$$37\!\cdots\!15$$$$T^{25} +$$$$21\!\cdots\!69$$$$T^{26}$$)($$1 - 15 T + 758 T^{2} - 8993 T^{3} + 264074 T^{4} - 2598648 T^{5} + 58536502 T^{6} - 495288546 T^{7} + 9541671058 T^{8} - 71450887279 T^{9} + 1235582283815 T^{10} - 8354202545906 T^{11} + 131850752462226 T^{12} - 812884574460588 T^{13} + 11734716969138114 T^{14} - 66173638366121426 T^{15} + 871047207038776735 T^{16} - 4482988789322852239 T^{17} + 53281258430674727042 T^{18} -$$$$24\!\cdots\!06$$$$T^{19} +$$$$25\!\cdots\!58$$$$T^{20} -$$$$10\!\cdots\!88$$$$T^{21} +$$$$92\!\cdots\!66$$$$T^{22} -$$$$28\!\cdots\!93$$$$T^{23} +$$$$21\!\cdots\!62$$$$T^{24} -$$$$37\!\cdots\!15$$$$T^{25} +$$$$21\!\cdots\!69$$$$T^{26}$$)($$1 - 21 T + 607 T^{2} - 8920 T^{3} + 171262 T^{4} - 2101735 T^{5} + 32830164 T^{6} - 352108686 T^{7} + 4829265654 T^{8} - 46726972789 T^{9} + 586211633725 T^{10} - 5219427228739 T^{11} + 61415310081737 T^{12} - 512935261401252 T^{13} + 5745185914786624 T^{14} - 45651238264711428 T^{15} + 486470671157438777 T^{16} - 3679534394016904091 T^{17} + 36780231600177677725 T^{18} -$$$$26\!\cdots\!61$$$$T^{19} +$$$$24\!\cdots\!94$$$$T^{20} -$$$$15\!\cdots\!94$$$$T^{21} +$$$$12\!\cdots\!84$$$$T^{22} -$$$$73\!\cdots\!15$$$$T^{23} +$$$$53\!\cdots\!62$$$$T^{24} -$$$$24\!\cdots\!80$$$$T^{25} +$$$$14\!\cdots\!47$$$$T^{26} -$$$$46\!\cdots\!49$$$$T^{27} +$$$$19\!\cdots\!41$$$$T^{28}$$)($$1 + 712 T^{2} - 987 T^{3} + 245239 T^{4} - 620559 T^{5} + 55410092 T^{6} - 193333154 T^{7} + 9368692181 T^{8} - 41204661989 T^{9} + 1279635571133 T^{10} - 6988180468952 T^{11} + 149026463314535 T^{12} - 1016065923599399 T^{13} + 15504500517386055 T^{14} - 129196593580182910 T^{15} + 1501138729702439567 T^{16} - 14299173695878752965 T^{17} +$$$$13\!\cdots\!37$$$$T^{18} -$$$$13\!\cdots\!42$$$$T^{19} +$$$$12\!\cdots\!93$$$$T^{20} -$$$$11\!\cdots\!65$$$$T^{21} +$$$$10\!\cdots\!23$$$$T^{22} -$$$$81\!\cdots\!10$$$$T^{23} +$$$$86\!\cdots\!95$$$$T^{24} -$$$$50\!\cdots\!39$$$$T^{25} +$$$$65\!\cdots\!15$$$$T^{26} -$$$$27\!\cdots\!12$$$$T^{27} +$$$$44\!\cdots\!97$$$$T^{28} -$$$$12\!\cdots\!89$$$$T^{29} +$$$$25\!\cdots\!09$$$$T^{30} -$$$$47\!\cdots\!34$$$$T^{31} +$$$$12\!\cdots\!48$$$$T^{32} -$$$$12\!\cdots\!19$$$$T^{33} +$$$$42\!\cdots\!11$$$$T^{34} -$$$$15\!\cdots\!07$$$$T^{35} +$$$$98\!\cdots\!48$$$$T^{36} +$$$$10\!\cdots\!09$$$$T^{38}$$)
$97$ ($$1 + 5 T + 258 T^{2} + 578 T^{3} + 37892 T^{4} + 80189 T^{5} + 3675524 T^{6} + 5438402 T^{7} + 235469634 T^{8} + 442646405 T^{9} + 8587340257 T^{10}$$)($$1 + 24 T + 678 T^{2} + 10373 T^{3} + 170592 T^{4} + 1896695 T^{5} + 22185859 T^{6} + 183979415 T^{7} + 1605100128 T^{8} + 9467157029 T^{9} + 60022852518 T^{10} + 206096166168 T^{11} + 832972004929 T^{12}$$)($$1 + 45 T + 1376 T^{2} + 29931 T^{3} + 545438 T^{4} + 8375059 T^{5} + 116449942 T^{6} + 1465766429 T^{7} + 17473897571 T^{8} + 194927586130 T^{9} + 2087374168964 T^{10} + 20998963042063 T^{11} + 202475294389508 T^{12} + 1834073657897170 T^{13} + 15947954517817283 T^{14} + 129763248073307549 T^{15} + 999995274861915094 T^{16} + 6976189686628665811 T^{17} + 44070454689172998494 T^{18} +$$$$23\!\cdots\!91$$$$T^{19} +$$$$10\!\cdots\!92$$$$T^{20} +$$$$33\!\cdots\!05$$$$T^{21} +$$$$71\!\cdots\!53$$$$T^{22}$$)($$1 + 41 T + 1360 T^{2} + 30915 T^{3} + 623782 T^{4} + 10465719 T^{5} + 162260178 T^{6} + 2228939233 T^{7} + 28726923179 T^{8} + 336165881822 T^{9} + 3712591176360 T^{10} + 37598782574515 T^{11} + 360121344106920 T^{12} + 3162984782063198 T^{13} + 26218287158547467 T^{14} + 197326387690181473 T^{15} + 1393383358647385746 T^{16} + 8717650938453528951 T^{17} + 50400515488326283366 T^{18} +$$$$24\!\cdots\!15$$$$T^{19} +$$$$10\!\cdots\!20$$$$T^{20} +$$$$30\!\cdots\!09$$$$T^{21} +$$$$71\!\cdots\!53$$$$T^{22}$$)($$1 + 19 T + 651 T^{2} + 9836 T^{3} + 198464 T^{4} + 2643990 T^{5} + 39962302 T^{6} + 493734300 T^{7} + 6109191987 T^{8} + 71319348041 T^{9} + 759458844371 T^{10} + 8351792047457 T^{11} + 79662888691254 T^{12} + 810123828603329 T^{13} + 7145748266686739 T^{14} + 65091243334623593 T^{15} + 540842374100071347 T^{16} + 4239864430651715100 T^{17} + 33287478818518186558 T^{18} +$$$$21\!\cdots\!70$$$$T^{19} +$$$$15\!\cdots\!04$$$$T^{20} +$$$$74\!\cdots\!12$$$$T^{21} +$$$$48\!\cdots\!99$$$$T^{22} +$$$$13\!\cdots\!07$$$$T^{23} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$1 + 7 T + 483 T^{2} + 3384 T^{3} + 135472 T^{4} + 1005978 T^{5} + 27299194 T^{6} + 202779564 T^{7} + 4278918623 T^{8} + 31268940433 T^{9} + 548132714887 T^{10} + 3783249792977 T^{11} + 58040314464774 T^{12} + 366975229918769 T^{13} + 5157380714371783 T^{14} + 28538317671807409 T^{15} + 378809589151700063 T^{16} + 1741337113234107948 T^{17} + 22739464359125727226 T^{18} + 81281296622723159514 T^{19} +$$$$10\!\cdots\!92$$$$T^{20} +$$$$25\!\cdots\!28$$$$T^{21} +$$$$35\!\cdots\!67$$$$T^{22} +$$$$50\!\cdots\!71$$$$T^{23} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$1 + T + 606 T^{2} - 479 T^{3} + 180587 T^{4} - 591622 T^{5} + 35070746 T^{6} - 224773222 T^{7} + 5007271033 T^{8} - 50444281573 T^{9} + 575603368072 T^{10} - 7793122388836 T^{11} + 58515039743159 T^{12} - 878038609738246 T^{13} + 5675958855086423 T^{14} - 73325488556557924 T^{15} + 525337652748376456 T^{16} - 4465795978219239013 T^{17} + 42999140119390875481 T^{18} -$$$$18\!\cdots\!38$$$$T^{19} +$$$$28\!\cdots\!98$$$$T^{20} -$$$$46\!\cdots\!42$$$$T^{21} +$$$$13\!\cdots\!79$$$$T^{22} -$$$$35\!\cdots\!71$$$$T^{23} +$$$$43\!\cdots\!18$$$$T^{24} +$$$$69\!\cdots\!41$$$$T^{25} +$$$$67\!\cdots\!77$$$$T^{26}$$)($$1 + 17 T + 938 T^{2} + 14141 T^{3} + 424719 T^{4} + 5744714 T^{5} + 123323034 T^{6} + 1505382982 T^{7} + 25668744301 T^{8} + 283066250203 T^{9} + 4047350409404 T^{10} + 40194221467436 T^{11} + 497446404474603 T^{12} + 4416178399171106 T^{13} + 48252301234036491 T^{14} + 378187429787105324 T^{15} + 3693907440201976892 T^{16} + 25059651605837694043 T^{17} +$$$$22\!\cdots\!57$$$$T^{18} +$$$$12\!\cdots\!78$$$$T^{19} +$$$$99\!\cdots\!42$$$$T^{20} +$$$$45\!\cdots\!54$$$$T^{21} +$$$$32\!\cdots\!23$$$$T^{22} +$$$$10\!\cdots\!09$$$$T^{23} +$$$$67\!\cdots\!14$$$$T^{24} +$$$$11\!\cdots\!97$$$$T^{25} +$$$$67\!\cdots\!77$$$$T^{26}$$)($$1 - 27 T + 846 T^{2} - 16071 T^{3} + 316643 T^{4} - 4868078 T^{5} + 75911390 T^{6} - 1006444954 T^{7} + 13447787513 T^{8} - 158930900501 T^{9} + 1889630845088 T^{10} - 20281662413284 T^{11} + 218857804683067 T^{12} - 2150177092562598 T^{13} + 21229207054257499 T^{14} - 190830161646589156 T^{15} + 1724615052279000224 T^{16} - 14070038350036069781 T^{17} +$$$$11\!\cdots\!41$$$$T^{18} -$$$$83\!\cdots\!66$$$$T^{19} +$$$$61\!\cdots\!70$$$$T^{20} -$$$$38\!\cdots\!58$$$$T^{21} +$$$$24\!\cdots\!31$$$$T^{22} -$$$$11\!\cdots\!79$$$$T^{23} +$$$$60\!\cdots\!38$$$$T^{24} -$$$$18\!\cdots\!07$$$$T^{25} +$$$$67\!\cdots\!77$$$$T^{26}$$)($$1 - 37 T + 1265 T^{2} - 30962 T^{3} + 679791 T^{4} - 12841719 T^{5} + 221642161 T^{6} - 3474922608 T^{7} + 50579995695 T^{8} - 684170650429 T^{9} + 8690333561707 T^{10} - 103729058988553 T^{11} + 1171015994366347 T^{12} - 12490999256601712 T^{13} + 126454166386797242 T^{14} - 1211626927890366064 T^{15} + 11018089490992958923 T^{16} - 94670711454259632169 T^{17} +$$$$76\!\cdots\!67$$$$T^{18} -$$$$58\!\cdots\!53$$$$T^{19} +$$$$42\!\cdots\!55$$$$T^{20} -$$$$28\!\cdots\!04$$$$T^{21} +$$$$17\!\cdots\!21$$$$T^{22} -$$$$97\!\cdots\!23$$$$T^{23} +$$$$50\!\cdots\!59$$$$T^{24} -$$$$22\!\cdots\!86$$$$T^{25} +$$$$87\!\cdots\!65$$$$T^{26} -$$$$24\!\cdots\!49$$$$T^{27} +$$$$65\!\cdots\!69$$$$T^{28}$$)($$1 - 21 T + 847 T^{2} - 11527 T^{3} + 298607 T^{4} - 2986298 T^{5} + 68446913 T^{6} - 534920010 T^{7} + 12571255465 T^{8} - 79993220799 T^{9} + 2032794671226 T^{10} - 10864472031073 T^{11} + 294914282878728 T^{12} - 1337284301131743 T^{13} + 38226363126660730 T^{14} - 149144666063131807 T^{15} + 4466890173200617866 T^{16} - 15529883283856504905 T^{17} +$$$$47\!\cdots\!92$$$$T^{18} -$$$$15\!\cdots\!23$$$$T^{19} +$$$$46\!\cdots\!24$$$$T^{20} -$$$$14\!\cdots\!45$$$$T^{21} +$$$$40\!\cdots\!18$$$$T^{22} -$$$$13\!\cdots\!67$$$$T^{23} +$$$$32\!\cdots\!10$$$$T^{24} -$$$$11\!\cdots\!47$$$$T^{25} +$$$$23\!\cdots\!64$$$$T^{26} -$$$$85\!\cdots\!53$$$$T^{27} +$$$$15\!\cdots\!42$$$$T^{28} -$$$$58\!\cdots\!51$$$$T^{29} +$$$$89\!\cdots\!45$$$$T^{30} -$$$$37\!\cdots\!10$$$$T^{31} +$$$$46\!\cdots\!01$$$$T^{32} -$$$$19\!\cdots\!62$$$$T^{33} +$$$$18\!\cdots\!51$$$$T^{34} -$$$$70\!\cdots\!67$$$$T^{35} +$$$$50\!\cdots\!39$$$$T^{36} -$$$$12\!\cdots\!69$$$$T^{37} +$$$$56\!\cdots\!33$$$$T^{38}$$)