# Properties

 Label 8001.2 Level 8001 Weight 2 Dimension 1.75614e+06 Nonzero newspaces 184 Sturm bound 9.28973e+06

## Defining parameters

 Level: $$N$$ = $$8001 = 3^{2} \cdot 7 \cdot 127$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$184$$ Sturm bound: $$9289728$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8001))$$.

Total New Old
Modular forms 2334528 1767392 567136
Cusp forms 2310337 1756140 554197
Eisenstein series 24191 11252 12939

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8001))$$

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
8001.2.a $$\chi_{8001}(1, \cdot)$$ 8001.2.a.a 1 1
8001.2.a.b 1
8001.2.a.c 1
8001.2.a.d 1
8001.2.a.e 1
8001.2.a.f 1
8001.2.a.g 1
8001.2.a.h 2
8001.2.a.i 2
8001.2.a.j 2
8001.2.a.k 2
8001.2.a.l 7
8001.2.a.m 11
8001.2.a.n 12
8001.2.a.o 13
8001.2.a.p 14
8001.2.a.q 15
8001.2.a.r 16
8001.2.a.s 16
8001.2.a.t 16
8001.2.a.u 18
8001.2.a.v 19
8001.2.a.w 20
8001.2.a.x 22
8001.2.a.y 28
8001.2.a.z 32
8001.2.a.ba 40
8001.2.d $$\chi_{8001}(7748, \cdot)$$ n/a 336 1
8001.2.e $$\chi_{8001}(1142, \cdot)$$ n/a 256 1
8001.2.h $$\chi_{8001}(7111, \cdot)$$ n/a 426 1
8001.2.i $$\chi_{8001}(361, \cdot)$$ n/a 848 2
8001.2.j $$\chi_{8001}(4573, \cdot)$$ n/a 840 2
8001.2.k $$\chi_{8001}(3448, \cdot)$$ n/a 848 2
8001.2.l $$\chi_{8001}(400, \cdot)$$ n/a 1536 2
8001.2.m $$\chi_{8001}(2668, \cdot)$$ n/a 1512 2
8001.2.n $$\chi_{8001}(3067, \cdot)$$ n/a 1536 2
8001.2.o $$\chi_{8001}(4552, \cdot)$$ n/a 2040 2
8001.2.p $$\chi_{8001}(3028, \cdot)$$ n/a 2040 2
8001.2.q $$\chi_{8001}(382, \cdot)$$ n/a 2016 2
8001.2.r $$\chi_{8001}(3049, \cdot)$$ n/a 2016 2
8001.2.s $$\chi_{8001}(781, \cdot)$$ n/a 2040 2
8001.2.t $$\chi_{8001}(4972, \cdot)$$ n/a 2040 2
8001.2.u $$\chi_{8001}(2647, \cdot)$$ n/a 640 2
8001.2.x $$\chi_{8001}(5315, \cdot)$$ n/a 2040 2
8001.2.y $$\chi_{8001}(6242, \cdot)$$ n/a 2040 2
8001.2.z $$\chi_{8001}(2432, \cdot)$$ n/a 2040 2
8001.2.ba $$\chi_{8001}(1523, \cdot)$$ n/a 2040 2
8001.2.bb $$\chi_{8001}(509, \cdot)$$ n/a 2016 2
8001.2.bc $$\chi_{8001}(401, \cdot)$$ n/a 2040 2
8001.2.bj $$\chi_{8001}(3410, \cdot)$$ n/a 512 2
8001.2.bk $$\chi_{8001}(2393, \cdot)$$ n/a 688 2
8001.2.br $$\chi_{8001}(1396, \cdot)$$ n/a 848 2
8001.2.bs $$\chi_{8001}(4807, \cdot)$$ n/a 848 2
8001.2.bt $$\chi_{8001}(3664, \cdot)$$ n/a 848 2
8001.2.bu $$\chi_{8001}(1777, \cdot)$$ n/a 2040 2
8001.2.bv $$\chi_{8001}(1798, \cdot)$$ n/a 2040 2
8001.2.bw $$\chi_{8001}(6712, \cdot)$$ n/a 2040 2
8001.2.cj $$\chi_{8001}(1417, \cdot)$$ n/a 2040 2
8001.2.ck $$\chi_{8001}(5227, \cdot)$$ n/a 2040 2
8001.2.cl $$\chi_{8001}(4063, \cdot)$$ n/a 2040 2
8001.2.cs $$\chi_{8001}(146, \cdot)$$ n/a 2040 2
8001.2.ct $$\chi_{8001}(3830, \cdot)$$ n/a 1536 2
8001.2.cu $$\chi_{8001}(3809, \cdot)$$ n/a 1536 2
8001.2.cv $$\chi_{8001}(743, \cdot)$$ n/a 1536 2
8001.2.cw $$\chi_{8001}(2813, \cdot)$$ n/a 2040 2
8001.2.cx $$\chi_{8001}(2414, \cdot)$$ n/a 2016 2
8001.2.cy $$\chi_{8001}(1124, \cdot)$$ n/a 680 2
8001.2.cz $$\chi_{8001}(5822, \cdot)$$ n/a 680 2
8001.2.da $$\chi_{8001}(2033, \cdot)$$ n/a 672 2
8001.2.db $$\chi_{8001}(4211, \cdot)$$ n/a 680 2
8001.2.dc $$\chi_{8001}(908, \cdot)$$ n/a 680 2
8001.2.dd $$\chi_{8001}(5714, \cdot)$$ n/a 680 2
8001.2.dq $$\chi_{8001}(380, \cdot)$$ n/a 2040 2
8001.2.dr $$\chi_{8001}(5843, \cdot)$$ n/a 2016 2
8001.2.ds $$\chi_{8001}(2012, \cdot)$$ n/a 2040 2
8001.2.dt $$\chi_{8001}(5735, \cdot)$$ n/a 2040 2
8001.2.du $$\chi_{8001}(488, \cdot)$$ n/a 2040 2
8001.2.dv $$\chi_{8001}(1544, \cdot)$$ n/a 2040 2
8001.2.dy $$\chi_{8001}(997, \cdot)$$ n/a 2040 2
8001.2.dz $$\chi_{8001}(5206, \cdot)$$ n/a 2040 2
8001.2.ea $$\chi_{8001}(4084, \cdot)$$ n/a 2040 2
8001.2.eh $$\chi_{8001}(1378, \cdot)$$ n/a 852 2
8001.2.ei $$\chi_{8001}(64, \cdot)$$ n/a 1920 6
8001.2.ej $$\chi_{8001}(3481, \cdot)$$ n/a 6120 6
8001.2.ek $$\chi_{8001}(22, \cdot)$$ n/a 4608 6
8001.2.el $$\chi_{8001}(37, \cdot)$$ n/a 2550 6
8001.2.em $$\chi_{8001}(1465, \cdot)$$ n/a 6120 6
8001.2.en $$\chi_{8001}(799, \cdot)$$ n/a 4608 6
8001.2.eo $$\chi_{8001}(226, \cdot)$$ n/a 2550 6
8001.2.ep $$\chi_{8001}(1576, \cdot)$$ n/a 1920 6
8001.2.eq $$\chi_{8001}(403, \cdot)$$ n/a 6120 6
8001.2.er $$\chi_{8001}(2704, \cdot)$$ n/a 6120 6
8001.2.es $$\chi_{8001}(1000, \cdot)$$ n/a 2556 6
8001.2.ev $$\chi_{8001}(1079, \cdot)$$ n/a 1536 6
8001.2.ew $$\chi_{8001}(3842, \cdot)$$ n/a 2064 6
8001.2.fb $$\chi_{8001}(1583, \cdot)$$ n/a 1536 6
8001.2.fc $$\chi_{8001}(1472, \cdot)$$ n/a 6120 6
8001.2.fd $$\chi_{8001}(164, \cdot)$$ n/a 6120 6
8001.2.fe $$\chi_{8001}(1322, \cdot)$$ n/a 2040 6
8001.2.fj $$\chi_{8001}(68, \cdot)$$ n/a 6120 6
8001.2.fk $$\chi_{8001}(3488, \cdot)$$ n/a 6120 6
8001.2.fp $$\chi_{8001}(790, \cdot)$$ n/a 6120 6
8001.2.fq $$\chi_{8001}(598, \cdot)$$ n/a 6120 6
8001.2.fr $$\chi_{8001}(313, \cdot)$$ n/a 6120 6
8001.2.fs $$\chi_{8001}(2980, \cdot)$$ n/a 2550 6
8001.2.gb $$\chi_{8001}(964, \cdot)$$ n/a 2550 6
8001.2.gc $$\chi_{8001}(202, \cdot)$$ n/a 6120 6
8001.2.gh $$\chi_{8001}(530, \cdot)$$ n/a 2052 6
8001.2.gi $$\chi_{8001}(941, \cdot)$$ n/a 6120 6
8001.2.gj $$\chi_{8001}(536, \cdot)$$ n/a 6120 6
8001.2.gk $$\chi_{8001}(359, \cdot)$$ n/a 2052 6
8001.2.gl $$\chi_{8001}(155, \cdot)$$ n/a 4608 6
8001.2.gm $$\chi_{8001}(725, \cdot)$$ n/a 6120 6
8001.2.gn $$\chi_{8001}(992, \cdot)$$ n/a 6120 6
8001.2.go $$\chi_{8001}(545, \cdot)$$ n/a 6120 6
8001.2.gx $$\chi_{8001}(1502, \cdot)$$ n/a 2052 6
8001.2.gy $$\chi_{8001}(344, \cdot)$$ n/a 4608 6
8001.2.gz $$\chi_{8001}(230, \cdot)$$ n/a 6120 6
8001.2.ha $$\chi_{8001}(1592, \cdot)$$ n/a 2052 6
8001.2.hd $$\chi_{8001}(1375, \cdot)$$ n/a 6120 6
8001.2.he $$\chi_{8001}(1756, \cdot)$$ n/a 2544 6
8001.2.hj $$\chi_{8001}(1741, \cdot)$$ n/a 6120 6
8001.2.hk $$\chi_{8001}(442, \cdot)$$ n/a 3840 12
8001.2.hl $$\chi_{8001}(214, \cdot)$$ n/a 12240 12
8001.2.hm $$\chi_{8001}(25, \cdot)$$ n/a 12240 12
8001.2.hn $$\chi_{8001}(1159, \cdot)$$ n/a 12240 12
8001.2.ho $$\chi_{8001}(4, \cdot)$$ n/a 12240 12
8001.2.hp $$\chi_{8001}(457, \cdot)$$ n/a 12240 12
8001.2.hq $$\chi_{8001}(2209, \cdot)$$ n/a 12240 12
8001.2.hr $$\chi_{8001}(673, \cdot)$$ n/a 9216 12
8001.2.hs $$\chi_{8001}(778, \cdot)$$ n/a 9216 12
8001.2.ht $$\chi_{8001}(1219, \cdot)$$ n/a 9216 12
8001.2.hu $$\chi_{8001}(856, \cdot)$$ n/a 5088 12
8001.2.hv $$\chi_{8001}(667, \cdot)$$ n/a 5088 12
8001.2.hw $$\chi_{8001}(100, \cdot)$$ n/a 5088 12
8001.2.hx $$\chi_{8001}(181, \cdot)$$ n/a 5112 12
8001.2.ie $$\chi_{8001}(229, \cdot)$$ n/a 12240 12
8001.2.if $$\chi_{8001}(619, \cdot)$$ n/a 12240 12
8001.2.ig $$\chi_{8001}(40, \cdot)$$ n/a 12240 12
8001.2.ij $$\chi_{8001}(1451, \cdot)$$ n/a 12240 12
8001.2.ik $$\chi_{8001}(47, \cdot)$$ n/a 12240 12
8001.2.il $$\chi_{8001}(662, \cdot)$$ n/a 12240 12
8001.2.im $$\chi_{8001}(122, \cdot)$$ n/a 12240 12
8001.2.in $$\chi_{8001}(1937, \cdot)$$ n/a 12240 12
8001.2.io $$\chi_{8001}(95, \cdot)$$ n/a 12240 12
8001.2.jb $$\chi_{8001}(746, \cdot)$$ n/a 4080 12
8001.2.jc $$\chi_{8001}(152, \cdot)$$ n/a 4080 12
8001.2.jd $$\chi_{8001}(737, \cdot)$$ n/a 4080 12
8001.2.je $$\chi_{8001}(143, \cdot)$$ n/a 4080 12
8001.2.jf $$\chi_{8001}(341, \cdot)$$ n/a 4080 12
8001.2.jg $$\chi_{8001}(305, \cdot)$$ n/a 4080 12
8001.2.jh $$\chi_{8001}(524, \cdot)$$ n/a 12240 12
8001.2.ji $$\chi_{8001}(419, \cdot)$$ n/a 12240 12
8001.2.jj $$\chi_{8001}(1499, \cdot)$$ n/a 9216 12
8001.2.jk $$\chi_{8001}(365, \cdot)$$ n/a 9216 12
8001.2.jl $$\chi_{8001}(281, \cdot)$$ n/a 9216 12
8001.2.jm $$\chi_{8001}(965, \cdot)$$ n/a 12240 12
8001.2.jt $$\chi_{8001}(250, \cdot)$$ n/a 12240 12
8001.2.ju $$\chi_{8001}(535, \cdot)$$ n/a 12240 12
8001.2.jv $$\chi_{8001}(943, \cdot)$$ n/a 12240 12
8001.2.ki $$\chi_{8001}(391, \cdot)$$ n/a 12240 12
8001.2.kj $$\chi_{8001}(160, \cdot)$$ n/a 12240 12
8001.2.kk $$\chi_{8001}(349, \cdot)$$ n/a 12240 12
8001.2.kl $$\chi_{8001}(334, \cdot)$$ n/a 5088 12
8001.2.km $$\chi_{8001}(10, \cdot)$$ n/a 5088 12
8001.2.kn $$\chi_{8001}(1333, \cdot)$$ n/a 5088 12
8001.2.ku $$\chi_{8001}(188, \cdot)$$ n/a 4128 12
8001.2.kv $$\chi_{8001}(386, \cdot)$$ n/a 3072 12
8001.2.lc $$\chi_{8001}(842, \cdot)$$ n/a 12240 12
8001.2.ld $$\chi_{8001}(131, \cdot)$$ n/a 12240 12
8001.2.le $$\chi_{8001}(1460, \cdot)$$ n/a 12240 12
8001.2.lf $$\chi_{8001}(38, \cdot)$$ n/a 12240 12
8001.2.lg $$\chi_{8001}(983, \cdot)$$ n/a 12240 12
8001.2.lh $$\chi_{8001}(137, \cdot)$$ n/a 12240 12
8001.2.lk $$\chi_{8001}(970, \cdot)$$ n/a 36720 36
8001.2.ll $$\chi_{8001}(88, \cdot)$$ n/a 36720 36
8001.2.lm $$\chi_{8001}(316, \cdot)$$ n/a 11520 36
8001.2.ln $$\chi_{8001}(289, \cdot)$$ n/a 15300 36
8001.2.lo $$\chi_{8001}(169, \cdot)$$ n/a 27648 36
8001.2.lp $$\chi_{8001}(646, \cdot)$$ n/a 36720 36
8001.2.lq $$\chi_{8001}(163, \cdot)$$ n/a 15300 36
8001.2.lr $$\chi_{8001}(148, \cdot)$$ n/a 27648 36
8001.2.ls $$\chi_{8001}(79, \cdot)$$ n/a 36720 36
8001.2.lt $$\chi_{8001}(166, \cdot)$$ n/a 36720 36
8001.2.ly $$\chi_{8001}(55, \cdot)$$ n/a 15264 36
8001.2.lz $$\chi_{8001}(355, \cdot)$$ n/a 36720 36
8001.2.mc $$\chi_{8001}(29, \cdot)$$ n/a 27648 36
8001.2.md $$\chi_{8001}(53, \cdot)$$ n/a 12312 36
8001.2.me $$\chi_{8001}(17, \cdot)$$ n/a 12312 36
8001.2.mf $$\chi_{8001}(104, \cdot)$$ n/a 36720 36
8001.2.mo $$\chi_{8001}(65, \cdot)$$ n/a 36720 36
8001.2.mp $$\chi_{8001}(92, \cdot)$$ n/a 27648 36
8001.2.mq $$\chi_{8001}(41, \cdot)$$ n/a 36720 36
8001.2.mr $$\chi_{8001}(866, \cdot)$$ n/a 36720 36
8001.2.ms $$\chi_{8001}(248, \cdot)$$ n/a 36720 36
8001.2.mt $$\chi_{8001}(206, \cdot)$$ n/a 12312 36
8001.2.mu $$\chi_{8001}(170, \cdot)$$ n/a 12312 36
8001.2.mv $$\chi_{8001}(473, \cdot)$$ n/a 36720 36
8001.2.na $$\chi_{8001}(139, \cdot)$$ n/a 36720 36
8001.2.nb $$\chi_{8001}(649, \cdot)$$ n/a 15300 36
8001.2.nk $$\chi_{8001}(388, \cdot)$$ n/a 15300 36
8001.2.nl $$\chi_{8001}(346, \cdot)$$ n/a 36720 36
8001.2.nm $$\chi_{8001}(220, \cdot)$$ n/a 36720 36
8001.2.nn $$\chi_{8001}(97, \cdot)$$ n/a 36720 36
8001.2.ns $$\chi_{8001}(416, \cdot)$$ n/a 36720 36
8001.2.nt $$\chi_{8001}(86, \cdot)$$ n/a 36720 36
8001.2.ny $$\chi_{8001}(23, \cdot)$$ n/a 36720 36
8001.2.nz $$\chi_{8001}(134, \cdot)$$ n/a 9216 36
8001.2.oa $$\chi_{8001}(62, \cdot)$$ n/a 12240 36
8001.2.ob $$\chi_{8001}(290, \cdot)$$ n/a 36720 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8001))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8001)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(127))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(381))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(889))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1143))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2667))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2}$$)($$1 + 2 T + 2 T^{2}$$)($$1 + 2 T^{2}$$)($$1 - T + 2 T^{2}$$)($$1 - T + 2 T^{2}$$)($$1 - 2 T + 2 T^{2}$$)($$1 - 2 T + 2 T^{2}$$)($$1 + T + 2 T^{3} + 4 T^{4}$$)($$( 1 + 2 T^{2} )^{2}$$)($$1 + 2 T^{2} + 4 T^{4}$$)($$1 - 2 T^{2} + 4 T^{4}$$)($$1 - 2 T + 7 T^{2} - 13 T^{3} + 28 T^{4} - 41 T^{5} + 73 T^{6} - 94 T^{7} + 146 T^{8} - 164 T^{9} + 224 T^{10} - 208 T^{11} + 224 T^{12} - 128 T^{13} + 128 T^{14}$$)($$1 - 2 T + 7 T^{2} - 15 T^{3} + 38 T^{4} - 72 T^{5} + 145 T^{6} - 249 T^{7} + 435 T^{8} - 690 T^{9} + 1061 T^{10} - 1511 T^{11} + 2122 T^{12} - 2760 T^{13} + 3480 T^{14} - 3984 T^{15} + 4640 T^{16} - 4608 T^{17} + 4864 T^{18} - 3840 T^{19} + 3584 T^{20} - 2048 T^{21} + 2048 T^{22}$$)($$1 - 7 T + 32 T^{2} - 110 T^{3} + 317 T^{4} - 795 T^{5} + 1791 T^{6} - 3678 T^{7} + 6974 T^{8} - 12301 T^{9} + 20304 T^{10} - 31466 T^{11} + 45871 T^{12} - 62932 T^{13} + 81216 T^{14} - 98408 T^{15} + 111584 T^{16} - 117696 T^{17} + 114624 T^{18} - 101760 T^{19} + 81152 T^{20} - 56320 T^{21} + 32768 T^{22} - 14336 T^{23} + 4096 T^{24}$$)($$1 + 4 T + 16 T^{2} + 43 T^{3} + 111 T^{4} + 238 T^{5} + 491 T^{6} + 905 T^{7} + 1619 T^{8} + 2672 T^{9} + 4312 T^{10} + 6552 T^{11} + 9792 T^{12} + 13944 T^{13} + 19584 T^{14} + 26208 T^{15} + 34496 T^{16} + 42752 T^{17} + 51808 T^{18} + 57920 T^{19} + 62848 T^{20} + 60928 T^{21} + 56832 T^{22} + 44032 T^{23} + 32768 T^{24} + 16384 T^{25} + 8192 T^{26}$$)($$1 - 5 T + 19 T^{2} - 54 T^{3} + 136 T^{4} - 302 T^{5} + 627 T^{6} - 1213 T^{7} + 2245 T^{8} - 3945 T^{9} + 6666 T^{10} - 10741 T^{11} + 16698 T^{12} - 24876 T^{13} + 35892 T^{14} - 49752 T^{15} + 66792 T^{16} - 85928 T^{17} + 106656 T^{18} - 126240 T^{19} + 143680 T^{20} - 155264 T^{21} + 160512 T^{22} - 154624 T^{23} + 139264 T^{24} - 110592 T^{25} + 77824 T^{26} - 40960 T^{27} + 16384 T^{28}$$)($$1 + 8 T^{2} + 34 T^{4} + 105 T^{6} - 7 T^{7} + 278 T^{8} - 48 T^{9} + 671 T^{10} - 201 T^{11} + 1484 T^{12} - 631 T^{13} + 3081 T^{14} - 1473 T^{15} + 6162 T^{16} - 2524 T^{17} + 11872 T^{18} - 3216 T^{19} + 21472 T^{20} - 3072 T^{21} + 35584 T^{22} - 1792 T^{23} + 53760 T^{24} + 69632 T^{26} + 65536 T^{28} + 32768 T^{30}$$)($$1 + 5 T + 19 T^{2} + 52 T^{3} + 125 T^{4} + 264 T^{5} + 529 T^{6} + 1006 T^{7} + 1858 T^{8} + 3287 T^{9} + 5617 T^{10} + 9208 T^{11} + 14687 T^{12} + 22750 T^{13} + 34532 T^{14} + 50960 T^{15} + 73260 T^{16} + 101920 T^{17} + 138128 T^{18} + 182000 T^{19} + 234992 T^{20} + 294656 T^{21} + 359488 T^{22} + 420736 T^{23} + 475648 T^{24} + 515072 T^{25} + 541696 T^{26} + 540672 T^{27} + 512000 T^{28} + 425984 T^{29} + 311296 T^{30} + 163840 T^{31} + 65536 T^{32}$$)($$1 + 4 T + 14 T^{2} + 37 T^{3} + 88 T^{4} + 190 T^{5} + 381 T^{6} + 712 T^{7} + 1274 T^{8} + 2174 T^{9} + 3615 T^{10} + 5835 T^{11} + 9161 T^{12} + 14072 T^{13} + 21098 T^{14} + 30924 T^{15} + 44348 T^{16} + 61848 T^{17} + 84392 T^{18} + 112576 T^{19} + 146576 T^{20} + 186720 T^{21} + 231360 T^{22} + 278272 T^{23} + 326144 T^{24} + 364544 T^{25} + 390144 T^{26} + 389120 T^{27} + 360448 T^{28} + 303104 T^{29} + 229376 T^{30} + 131072 T^{31} + 65536 T^{32}$$)($$1 - 2 T + 12 T^{2} - 22 T^{3} + 75 T^{4} - 127 T^{5} + 327 T^{6} - 517 T^{7} + 1117 T^{8} - 1665 T^{9} + 3198 T^{10} - 4555 T^{11} + 8050 T^{12} - 11054 T^{13} + 18325 T^{14} - 24255 T^{15} + 38213 T^{16} - 48510 T^{17} + 73300 T^{18} - 88432 T^{19} + 128800 T^{20} - 145760 T^{21} + 204672 T^{22} - 213120 T^{23} + 285952 T^{24} - 264704 T^{25} + 334848 T^{26} - 260096 T^{27} + 307200 T^{28} - 180224 T^{29} + 196608 T^{30} - 65536 T^{31} + 65536 T^{32}$$)($$1 - 6 T + 25 T^{2} - 81 T^{3} + 225 T^{4} - 556 T^{5} + 1256 T^{6} - 2640 T^{7} + 5231 T^{8} - 9842 T^{9} + 17724 T^{10} - 30680 T^{11} + 51321 T^{12} - 83210 T^{13} + 131171 T^{14} - 201431 T^{15} + 301850 T^{16} - 441694 T^{17} + 631856 T^{18} - 883388 T^{19} + 1207400 T^{20} - 1611448 T^{21} + 2098736 T^{22} - 2662720 T^{23} + 3284544 T^{24} - 3927040 T^{25} + 4537344 T^{26} - 5039104 T^{27} + 5356544 T^{28} - 5406720 T^{29} + 5144576 T^{30} - 4554752 T^{31} + 3686400 T^{32} - 2654208 T^{33} + 1638400 T^{34} - 786432 T^{35} + 262144 T^{36}$$)($$1 + 4 T + 16 T^{2} + 43 T^{3} + 114 T^{4} + 251 T^{5} + 541 T^{6} + 1040 T^{7} + 1959 T^{8} + 3404 T^{9} + 5807 T^{10} + 9344 T^{11} + 14813 T^{12} + 22536 T^{13} + 33898 T^{14} + 49667 T^{15} + 72273 T^{16} + 103641 T^{17} + 148038 T^{18} + 209658 T^{19} + 296076 T^{20} + 414564 T^{21} + 578184 T^{22} + 794672 T^{23} + 1084736 T^{24} + 1442304 T^{25} + 1896064 T^{26} + 2392064 T^{27} + 2973184 T^{28} + 3485696 T^{29} + 4012032 T^{30} + 4259840 T^{31} + 4431872 T^{32} + 4112384 T^{33} + 3735552 T^{34} + 2818048 T^{35} + 2097152 T^{36} + 1048576 T^{37} + 524288 T^{38}$$)($$1 + 8 T + 40 T^{2} + 152 T^{3} + 486 T^{4} + 1365 T^{5} + 3477 T^{6} + 8181 T^{7} + 18026 T^{8} + 37522 T^{9} + 74311 T^{10} + 140720 T^{11} + 255933 T^{12} + 448587 T^{13} + 760073 T^{14} + 1247786 T^{15} + 1988749 T^{16} + 3081632 T^{17} + 4648149 T^{18} + 6829961 T^{19} + 9782715 T^{20} + 13659922 T^{21} + 18592596 T^{22} + 24653056 T^{23} + 31819984 T^{24} + 39929152 T^{25} + 48644672 T^{26} + 57419136 T^{27} + 65518848 T^{28} + 72048640 T^{29} + 76094464 T^{30} + 76845056 T^{31} + 73834496 T^{32} + 67018752 T^{33} + 56967168 T^{34} + 44728320 T^{35} + 31850496 T^{36} + 19922944 T^{37} + 10485760 T^{38} + 4194304 T^{39} + 1048576 T^{40}$$)
$3$ 1
$5$ ($$1 + 3 T + 5 T^{2}$$)($$1 + T + 5 T^{2}$$)($$1 + 3 T + 5 T^{2}$$)($$1 + 4 T + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 - T + 5 T^{2}$$)($$1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 + 8 T^{2} + 25 T^{4}$$)($$1 + 4 T^{2} + 25 T^{4}$$)($$1 - 8 T + 48 T^{2} - 198 T^{3} + 701 T^{4} - 2022 T^{5} + 5344 T^{6} - 12315 T^{7} + 26720 T^{8} - 50550 T^{9} + 87625 T^{10} - 123750 T^{11} + 150000 T^{12} - 125000 T^{13} + 78125 T^{14}$$)($$1 + T + 23 T^{2} + 18 T^{3} + 254 T^{4} + 42 T^{5} + 1659 T^{6} - 1512 T^{7} + 6662 T^{8} - 20507 T^{9} + 19405 T^{10} - 134932 T^{11} + 97025 T^{12} - 512675 T^{13} + 832750 T^{14} - 945000 T^{15} + 5184375 T^{16} + 656250 T^{17} + 19843750 T^{18} + 7031250 T^{19} + 44921875 T^{20} + 9765625 T^{21} + 48828125 T^{22}$$)($$1 - 7 T + 53 T^{2} - 246 T^{3} + 1136 T^{4} - 4123 T^{5} + 14704 T^{6} - 44997 T^{7} + 135045 T^{8} - 361862 T^{9} + 950265 T^{10} - 2268970 T^{11} + 5306511 T^{12} - 11344850 T^{13} + 23756625 T^{14} - 45232750 T^{15} + 84403125 T^{16} - 140615625 T^{17} + 229750000 T^{18} - 322109375 T^{19} + 443750000 T^{20} - 480468750 T^{21} + 517578125 T^{22} - 341796875 T^{23} + 244140625 T^{24}$$)($$1 + 12 T + 104 T^{2} + 670 T^{3} + 3638 T^{4} + 16960 T^{5} + 70302 T^{6} + 262027 T^{7} + 890580 T^{8} + 2778820 T^{9} + 8011459 T^{10} + 21421987 T^{11} + 53271576 T^{12} + 123398136 T^{13} + 266357880 T^{14} + 535549675 T^{15} + 1001432375 T^{16} + 1736762500 T^{17} + 2783062500 T^{18} + 4094171875 T^{19} + 5492343750 T^{20} + 6625000000 T^{21} + 7105468750 T^{22} + 6542968750 T^{23} + 5078125000 T^{24} + 2929687500 T^{25} + 1220703125 T^{26}$$)($$1 - 4 T + 41 T^{2} - 150 T^{3} + 870 T^{4} - 2908 T^{5} + 12492 T^{6} - 38021 T^{7} + 133996 T^{8} - 370873 T^{9} + 1127299 T^{10} - 2836015 T^{11} + 7634651 T^{12} - 17439737 T^{13} + 42178904 T^{14} - 87198685 T^{15} + 190866275 T^{16} - 354501875 T^{17} + 704561875 T^{18} - 1158978125 T^{19} + 2093687500 T^{20} - 2970390625 T^{21} + 4879687500 T^{22} - 5679687500 T^{23} + 8496093750 T^{24} - 7324218750 T^{25} + 10009765625 T^{26} - 4882812500 T^{27} + 6103515625 T^{28}$$)($$1 + 7 T + 62 T^{2} + 323 T^{3} + 1738 T^{4} + 7382 T^{5} + 30572 T^{6} + 110791 T^{7} + 384068 T^{8} + 1219524 T^{9} + 3681308 T^{10} + 10409846 T^{11} + 27934651 T^{12} + 71019999 T^{13} + 171277768 T^{14} + 393239734 T^{15} + 856388840 T^{16} + 1775499975 T^{17} + 3491831375 T^{18} + 6506153750 T^{19} + 11504087500 T^{20} + 19055062500 T^{21} + 30005312500 T^{22} + 43277734375 T^{23} + 59710937500 T^{24} + 72089843750 T^{25} + 84863281250 T^{26} + 78857421875 T^{27} + 75683593750 T^{28} + 42724609375 T^{29} + 30517578125 T^{30}$$)($$1 - T + 24 T^{2} - 19 T^{3} + 329 T^{4} - 170 T^{5} + 3169 T^{6} - 250 T^{7} + 23164 T^{8} + 13164 T^{9} + 133265 T^{10} + 205344 T^{11} + 624119 T^{12} + 1857497 T^{13} + 2603502 T^{14} + 12171723 T^{15} + 11656934 T^{16} + 60858615 T^{17} + 65087550 T^{18} + 232187125 T^{19} + 390074375 T^{20} + 641700000 T^{21} + 2082265625 T^{22} + 1028437500 T^{23} + 9048437500 T^{24} - 488281250 T^{25} + 30947265625 T^{26} - 8300781250 T^{27} + 80322265625 T^{28} - 23193359375 T^{29} + 146484375000 T^{30} - 30517578125 T^{31} + 152587890625 T^{32}$$)($$1 + 5 T + 44 T^{2} + 165 T^{3} + 915 T^{4} + 2942 T^{5} + 12907 T^{6} + 37018 T^{7} + 138404 T^{8} + 361252 T^{9} + 1199295 T^{10} + 2886522 T^{11} + 8700809 T^{12} + 19438343 T^{13} + 53957730 T^{14} + 112352057 T^{15} + 289570702 T^{16} + 561760285 T^{17} + 1348943250 T^{18} + 2429792875 T^{19} + 5438005625 T^{20} + 9020381250 T^{21} + 18738984375 T^{22} + 28222812500 T^{23} + 54064062500 T^{24} + 72300781250 T^{25} + 126044921875 T^{26} + 143652343750 T^{27} + 223388671875 T^{28} + 201416015625 T^{29} + 268554687500 T^{30} + 152587890625 T^{31} + 152587890625 T^{32}$$)($$1 - 9 T + 73 T^{2} - 402 T^{3} + 1978 T^{4} - 8015 T^{5} + 29678 T^{6} - 96727 T^{7} + 295846 T^{8} - 831141 T^{9} + 2261906 T^{10} - 5860568 T^{11} + 15073267 T^{12} - 37453319 T^{13} + 92144207 T^{14} - 216794219 T^{15} + 497747736 T^{16} - 1083971095 T^{17} + 2303605175 T^{18} - 4681664875 T^{19} + 9420791875 T^{20} - 18314275000 T^{21} + 35342281250 T^{22} - 64932890625 T^{23} + 115564843750 T^{24} - 188919921875 T^{25} + 289824218750 T^{26} - 391357421875 T^{27} + 482910156250 T^{28} - 490722656250 T^{29} + 445556640625 T^{30} - 274658203125 T^{31} + 152587890625 T^{32}$$)($$1 - 10 T + 81 T^{2} - 476 T^{3} + 2454 T^{4} - 10782 T^{5} + 43074 T^{6} - 154195 T^{7} + 511259 T^{8} - 1553151 T^{9} + 4417176 T^{10} - 11648601 T^{11} + 29006707 T^{12} - 67663733 T^{13} + 151179610 T^{14} - 322803966 T^{15} + 682949075 T^{16} - 1441859622 T^{17} + 3174135542 T^{18} - 7209298110 T^{19} + 17073726875 T^{20} - 40350495750 T^{21} + 94487256250 T^{22} - 211449165625 T^{23} + 453229796875 T^{24} - 910046953125 T^{25} + 1725459375000 T^{26} - 3033498046875 T^{27} + 4992763671875 T^{28} - 7529052734375 T^{29} + 10516113281250 T^{30} - 13161621093750 T^{31} + 14978027343750 T^{32} - 14526367187500 T^{33} + 12359619140625 T^{34} - 7629394531250 T^{35} + 3814697265625 T^{36}$$)($$1 + 5 T + 41 T^{2} + 168 T^{3} + 832 T^{4} + 2996 T^{5} + 11691 T^{6} + 37986 T^{7} + 128552 T^{8} + 382033 T^{9} + 1168939 T^{10} + 3222334 T^{11} + 9102821 T^{12} + 23575655 T^{13} + 62285480 T^{14} + 152712478 T^{15} + 380888120 T^{16} + 886961463 T^{17} + 2101604027 T^{18} + 4656991668 T^{19} + 10508020135 T^{20} + 22174036575 T^{21} + 47611015000 T^{22} + 95445298750 T^{23} + 194642125000 T^{24} + 368369609375 T^{25} + 711157890625 T^{26} + 1258724218750 T^{27} + 2283083984375 T^{28} + 3730791015625 T^{29} + 6276953125000 T^{30} + 9273925781250 T^{31} + 14271240234375 T^{32} + 18286132812500 T^{33} + 25390625000000 T^{34} + 25634765625000 T^{35} + 31280517578125 T^{36} + 19073486328125 T^{37} + 19073486328125 T^{38}$$)($$1 + 3 T + 41 T^{2} + 102 T^{3} + 852 T^{4} + 1789 T^{5} + 11896 T^{6} + 21175 T^{7} + 126095 T^{8} + 190114 T^{9} + 1091285 T^{10} + 1389004 T^{11} + 8094983 T^{12} + 8669778 T^{13} + 53198371 T^{14} + 48017284 T^{15} + 316996324 T^{16} + 245397320 T^{17} + 1744322639 T^{18} + 1214931511 T^{19} + 8987882722 T^{20} + 6074657555 T^{21} + 43608065975 T^{22} + 30674665000 T^{23} + 198122702500 T^{24} + 150054012500 T^{25} + 831224546875 T^{26} + 677326406250 T^{27} + 3162102734375 T^{28} + 2712898437500 T^{29} + 10657080078125 T^{30} + 9282910156250 T^{31} + 30784912109375 T^{32} + 25848388671875 T^{33} + 72607421875000 T^{34} + 54595947265625 T^{35} + 130004882812500 T^{36} + 77819824218750 T^{37} + 156402587890625 T^{38} + 57220458984375 T^{39} + 95367431640625 T^{40}$$)
$7$ ($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 + T$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{7}$$)($$( 1 + T )^{11}$$)($$( 1 - T )^{12}$$)($$( 1 - T )^{13}$$)($$( 1 + T )^{14}$$)($$( 1 + T )^{15}$$)($$( 1 + T )^{16}$$)($$( 1 + T )^{16}$$)($$( 1 + T )^{16}$$)($$( 1 - T )^{18}$$)($$( 1 - T )^{19}$$)($$( 1 - T )^{20}$$)
$11$ ($$1 + 2 T + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 6 T + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 - 2 T + 6 T^{2} - 22 T^{3} + 121 T^{4}$$)($$1 - 2 T + 6 T^{2} - 22 T^{3} + 121 T^{4}$$)($$1 + 14 T^{2} + 121 T^{4}$$)($$( 1 + 11 T^{2} )^{2}$$)($$1 - 3 T + 31 T^{2} - 93 T^{3} + 656 T^{4} - 1715 T^{5} + 9199 T^{6} - 22080 T^{7} + 101189 T^{8} - 207515 T^{9} + 873136 T^{10} - 1361613 T^{11} + 4992581 T^{12} - 5314683 T^{13} + 19487171 T^{14}$$)($$1 - 7 T + 102 T^{2} - 550 T^{3} + 4620 T^{4} - 20475 T^{5} + 127969 T^{6} - 483479 T^{7} + 2471330 T^{8} - 8122440 T^{9} + 35508279 T^{10} - 102345862 T^{11} + 390591069 T^{12} - 982815240 T^{13} + 3289340230 T^{14} - 7078616039 T^{15} + 20609535419 T^{16} - 36272711475 T^{17} + 90030730020 T^{18} - 117897384550 T^{19} + 240510664482 T^{20} - 181561972207 T^{21} + 285311670611 T^{22}$$)($$1 - 22 T + 310 T^{2} - 3233 T^{3} + 27525 T^{4} - 198779 T^{5} + 1252854 T^{6} - 7006099 T^{7} + 35184038 T^{8} - 159974396 T^{9} + 662234726 T^{10} - 2505459725 T^{11} + 8680044717 T^{12} - 27560056975 T^{13} + 80130401846 T^{14} - 212925921076 T^{15} + 515129500358 T^{16} - 1128339250049 T^{17} + 2219507285094 T^{18} - 3873640364209 T^{19} + 5900228199525 T^{20} - 7623244885003 T^{21} + 8040601626310 T^{22} - 6276856753442 T^{23} + 3138428376721 T^{24}$$)($$1 + 3 T + 83 T^{2} + 231 T^{3} + 3487 T^{4} + 8594 T^{5} + 96020 T^{6} + 206021 T^{7} + 1938774 T^{8} + 3603777 T^{9} + 30713596 T^{10} + 50136844 T^{11} + 400155761 T^{12} + 591166452 T^{13} + 4401713371 T^{14} + 6066558124 T^{15} + 40879796276 T^{16} + 52762899057 T^{17} + 312241491474 T^{18} + 364978768781 T^{19} + 1871158159420 T^{20} + 1842200223314 T^{21} + 8222163598517 T^{22} + 5991545082831 T^{23} + 23680868660713 T^{24} + 9415285130163 T^{25} + 34522712143931 T^{26}$$)($$1 - 3 T + 82 T^{2} - 256 T^{3} + 3350 T^{4} - 10553 T^{5} + 92717 T^{6} - 284301 T^{7} + 1964384 T^{8} - 5713164 T^{9} + 33629114 T^{10} - 91772019 T^{11} + 477433889 T^{12} - 1214718248 T^{13} + 5707030766 T^{14} - 13361900728 T^{15} + 57769500569 T^{16} - 122148557289 T^{17} + 492363858074 T^{18} - 920110775364 T^{19} + 3480026083424 T^{20} - 5540222202471 T^{21} + 19874712369677 T^{22} - 24883421983123 T^{23} + 86890372413350 T^{24} - 73039787676416 T^{25} + 257351126891122 T^{26} - 103568136431793 T^{27} + 379749833583241 T^{28}$$)($$1 + 14 T + 167 T^{2} + 1413 T^{3} + 10646 T^{4} + 68458 T^{5} + 403828 T^{6} + 2160209 T^{7} + 10789709 T^{8} + 50218601 T^{9} + 220459489 T^{10} + 914244521 T^{11} + 3596539995 T^{12} + 13459900091 T^{13} + 47930979387 T^{14} + 162887274074 T^{15} + 527240773257 T^{16} + 1628647911011 T^{17} + 4786994733345 T^{18} + 13385454031961 T^{19} + 35505221162939 T^{20} + 88965315006161 T^{21} + 210260904323239 T^{22} + 463059983966129 T^{23} + 952205300161148 T^{24} + 1775624213335258 T^{25} + 3037428045324706 T^{26} + 4434599296306773 T^{27} + 5765292928036477 T^{28} + 5316497670165374 T^{29} + 4177248169415651 T^{30}$$)($$1 + 11 T + 127 T^{2} + 927 T^{3} + 6546 T^{4} + 37443 T^{5} + 205797 T^{6} + 996578 T^{7} + 4658508 T^{8} + 19883514 T^{9} + 82587628 T^{10} + 319384657 T^{11} + 1213890104 T^{12} + 4356733405 T^{13} + 15506991000 T^{14} + 52671594431 T^{15} + 178444424018 T^{16} + 579387538741 T^{17} + 1876345911000 T^{18} + 5798812162055 T^{19} + 17772565012664 T^{20} + 51437218394507 T^{21} + 146309020847308 T^{22} + 387473437398894 T^{23} + 998592562009548 T^{24} + 2349878794001398 T^{25} + 5337844170611997 T^{26} + 10682924882687673 T^{27} + 20544152154015666 T^{28} + 32002554157424037 T^{29} + 48228228865071607 T^{30} + 45949729863572161 T^{31} + 45949729863572161 T^{32}$$)($$1 + T + 92 T^{2} + 96 T^{3} + 4181 T^{4} + 4100 T^{5} + 126197 T^{6} + 107277 T^{7} + 2867972 T^{8} + 2007877 T^{9} + 52697233 T^{10} + 30067300 T^{11} + 817852019 T^{12} + 392443888 T^{13} + 10985297878 T^{14} + 4676327073 T^{15} + 129047873478 T^{16} + 51439597803 T^{17} + 1329221043238 T^{18} + 522342814928 T^{19} + 11974171410179 T^{20} + 4842368732300 T^{21} + 93356362790713 T^{22} + 39127842445967 T^{23} + 614775268659332 T^{24} + 252953554447407 T^{25} + 3273225172372397 T^{26} + 1169777849505100 T^{27} + 13121769043070501 T^{28} + 3314180365817376 T^{29} + 34936984689658172 T^{30} + 4177248169415651 T^{31} + 45949729863572161 T^{32}$$)($$1 - 22 T + 303 T^{2} - 3067 T^{3} + 25368 T^{4} - 177770 T^{5} + 1090130 T^{6} - 5934857 T^{7} + 29109808 T^{8} - 129561057 T^{9} + 528043225 T^{10} - 1982539376 T^{11} + 6932748788 T^{12} - 22873704378 T^{13} + 72928938613 T^{14} - 231216828675 T^{15} + 752600334649 T^{16} - 2543385115425 T^{17} + 8824401572173 T^{18} - 30444900527118 T^{19} + 101502375005108 T^{20} - 319289949044176 T^{21} + 935460783724225 T^{22} - 2524778472699747 T^{23} + 6239945869004848 T^{24} - 13994082359565187 T^{25} + 28275164680288130 T^{26} - 50719855684517470 T^{27} + 79615651060658328 T^{28} - 105881158145436377 T^{29} + 115064199575722023 T^{30} - 91899459727144322 T^{31} + 45949729863572161 T^{32}$$)($$1 - 9 T + 123 T^{2} - 853 T^{3} + 7075 T^{4} - 40936 T^{5} + 262862 T^{6} - 1328997 T^{7} + 7225154 T^{8} - 32841991 T^{9} + 157994657 T^{10} - 657379783 T^{11} + 2869404622 T^{12} - 11054117909 T^{13} + 44448793774 T^{14} - 159662650340 T^{15} + 596925478628 T^{16} - 2006578164628 T^{17} + 7011320772848 T^{18} - 22072359810908 T^{19} + 72227982913988 T^{20} - 212510987602540 T^{21} + 650774789645134 T^{22} - 1780276743362359 T^{23} + 5083325321554942 T^{24} - 12810472243263893 T^{25} + 33867557878498817 T^{26} - 77439696846292781 T^{27} + 187401887105613554 T^{28} - 379178354307007167 T^{29} + 824973559961635502 T^{30} - 1413221744323959416 T^{31} + 2686730072601430075 T^{32} - 3563192688511550303 T^{33} + 5651816773219375803 T^{34} - 4549023256493643939 T^{35} + 5559917313492231481 T^{36}$$)($$1 - 9 T + 114 T^{2} - 846 T^{3} + 6834 T^{4} - 43631 T^{5} + 279049 T^{6} - 1570491 T^{7} + 8622246 T^{8} - 43583626 T^{9} + 213037611 T^{10} - 979860254 T^{11} + 4350940113 T^{12} - 18383133454 T^{13} + 75002259850 T^{14} - 292955898389 T^{15} + 1105867682544 T^{16} - 4009634203784 T^{17} + 14057469809074 T^{18} - 47407746375208 T^{19} + 154632167899814 T^{20} - 485165738657864 T^{21} + 1471909885466064 T^{22} - 4289167308313349 T^{23} + 12079188951102350 T^{24} - 32566842284901694 T^{25} + 84787513992790323 T^{26} - 210041747583815774 T^{27} + 502331542953606201 T^{28} - 1130447013213183226 T^{29} + 2460027410679012306 T^{30} - 4928873519784940011 T^{31} + 9633528301051801619 T^{32} - 16568864989070388071 T^{33} + 28547313989786558934 T^{34} - 38873471464582048206 T^{35} + 57620961248919489894 T^{36} - 50039255821430083329 T^{37} + 61159090448414546291 T^{38}$$)($$1 + 26 T + 451 T^{2} + 5745 T^{3} + 60390 T^{4} + 539974 T^{5} + 4256816 T^{6} + 30041049 T^{7} + 193010981 T^{8} + 1139446445 T^{9} + 6242249652 T^{10} + 31935452615 T^{11} + 153602642308 T^{12} + 697892207262 T^{13} + 3010361369953 T^{14} + 12374514757616 T^{15} + 48663255845401 T^{16} + 183604003037714 T^{17} + 666451122560284 T^{18} + 2331322386267096 T^{19} + 7870077151801638 T^{20} + 25644546248938056 T^{21} + 80640585829794364 T^{22} + 244376928043197334 T^{23} + 712478728832516041 T^{24} + 1992927976228814416 T^{25} + 5333038798915306633 T^{26} + 13599944782482035802 T^{27} + 32926090523786137348 T^{28} + 75302126754579161965 T^{29} +$$$$16\!\cdots\!52$$$$T^{30} +$$$$32\!\cdots\!95$$$$T^{31} +$$$$60\!\cdots\!01$$$$T^{32} +$$$$10\!\cdots\!19$$$$T^{33} +$$$$16\!\cdots\!56$$$$T^{34} +$$$$22\!\cdots\!74$$$$T^{35} +$$$$27\!\cdots\!90$$$$T^{36} +$$$$29\!\cdots\!95$$$$T^{37} +$$$$25\!\cdots\!31$$$$T^{38} +$$$$15\!\cdots\!66$$$$T^{39} +$$$$67\!\cdots\!01$$$$T^{40}$$)
$13$ ($$1 - 5 T + 13 T^{2}$$)($$1 + T + 13 T^{2}$$)($$1 + T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 + T + 13 T^{2}$$)($$1 + 3 T + 24 T^{2} + 39 T^{3} + 169 T^{4}$$)($$1 + 3 T + 24 T^{2} + 39 T^{3} + 169 T^{4}$$)($$( 1 + 2 T + 13 T^{2} )^{2}$$)($$1 - 4 T + 6 T^{2} - 52 T^{3} + 169 T^{4}$$)($$1 + 23 T + 289 T^{2} + 2532 T^{3} + 17108 T^{4} + 93828 T^{5} + 430561 T^{6} + 1679255 T^{7} + 5597293 T^{8} + 15856932 T^{9} + 37586276 T^{10} + 72316452 T^{11} + 107303677 T^{12} + 111016607 T^{13} + 62748517 T^{14}$$)($$1 + 24 T + 346 T^{2} + 3680 T^{3} + 31746 T^{4} + 231850 T^{5} + 1475347 T^{6} + 8317190 T^{7} + 42047204 T^{8} + 192032718 T^{9} + 796510865 T^{10} + 3007998246 T^{11} + 10354641245 T^{12} + 32453529342 T^{13} + 92377707188 T^{14} + 237547263590 T^{15} + 547786013671 T^{16} + 1119095666650 T^{17} + 1992014420682 T^{18} + 3001889053280 T^{19} + 3669156783058 T^{20} + 3308603804376 T^{21} + 1792160394037 T^{22}$$)($$1 + 78 T^{2} + 6 T^{3} + 3142 T^{4} + 126 T^{5} + 85177 T^{6} - 5639 T^{7} + 1751144 T^{8} - 334994 T^{9} + 29187591 T^{10} - 7762560 T^{11} + 410472133 T^{12} - 100913280 T^{13} + 4932702879 T^{14} - 735981818 T^{15} + 50014423784 T^{16} - 2093721227 T^{17} + 411133110193 T^{18} + 7906313142 T^{19} + 2563025925382 T^{20} + 63626996238 T^{21} + 10752962364222 T^{22} + 23298085122481 T^{24}$$)($$1 - 21 T + 303 T^{2} - 3206 T^{3} + 28249 T^{4} - 211775 T^{5} + 1406812 T^{6} - 8366101 T^{7} + 45400042 T^{8} - 225933653 T^{9} + 1041869982 T^{10} - 4459348525 T^{11} + 17818659263 T^{12} - 66419150254 T^{13} + 231642570419 T^{14} - 753629900725 T^{15} + 2288988350454 T^{16} - 6452891063333 T^{17} + 16856717794306 T^{18} - 40381571601709 T^{19} + 88275366697804 T^{20} - 172751373439775 T^{21} + 299566502787877 T^{22} - 441974324867894 T^{23} + 543024599393211 T^{24} - 489259787572101 T^{25} + 302875106592253 T^{26}$$)($$1 + 13 T + 182 T^{2} + 1585 T^{3} + 13608 T^{4} + 92167 T^{5} + 606905 T^{6} + 3422512 T^{7} + 18744862 T^{8} + 91352922 T^{9} + 433195838 T^{10} + 1864962208 T^{11} + 7828834193 T^{12} + 30141395677 T^{13} + 113300440326 T^{14} + 391838143801 T^{15} + 1323072978617 T^{16} + 4097321970976 T^{17} + 12372506329118 T^{18} + 33918700468146 T^{19} + 90477868605358 T^{20} + 214757552414704 T^{21} + 495071053228505 T^{22} + 977384893711291 T^{23} + 1875978357081192 T^{24} + 2840574224548645 T^{25} + 4240251492291542 T^{26} + 3937376385699289 T^{27} + 3937376385699289 T^{28}$$)($$1 - 6 T + 133 T^{2} - 774 T^{3} + 8561 T^{4} - 47366 T^{5} + 355898 T^{6} - 1836543 T^{7} + 10757093 T^{8} - 50957299 T^{9} + 252119588 T^{10} - 1085754117 T^{11} + 4763675761 T^{12} - 18617446491 T^{13} + 74253115613 T^{14} - 264522490424 T^{15} + 965290502969 T^{16} - 3146348456979 T^{17} + 10465795646917 T^{18} - 31010223335637 T^{19} + 93610238187284 T^{20} - 245961149428891 T^{21} + 674991632981081 T^{22} - 1498124545537503 T^{23} + 3774120117851954 T^{24} - 6529805324919734 T^{25} + 15342685133350757 T^{26} - 18032717884800294 T^{27} + 40282389176769649 T^{28} - 23624258314195734 T^{29} + 51185893014090757 T^{30}$$)($$1 - 18 T + 219 T^{2} - 1948 T^{3} + 14614 T^{4} - 94646 T^{5} + 555983 T^{6} - 2985822 T^{7} + 14990448 T^{8} - 70533970 T^{9} + 315528362 T^{10} - 1344918094 T^{11} + 5522268604 T^{12} - 21859541176 T^{13} + 84090414036 T^{14} - 314220696382 T^{15} + 1147549597242 T^{16} - 4084869052966 T^{17} + 14211279972084 T^{18} - 48025411963672 T^{19} + 157721513598844 T^{20} - 499358673875542 T^{21} + 1522995137456858 T^{22} - 4425902015622490 T^{23} + 12228168955153008 T^{24} - 31663147526889606 T^{25} + 76646977873682567 T^{26} - 169620812654025902 T^{27} + 340478215979937334 T^{28} - 590000707641708844 T^{29} + 862285428468144291 T^{30} - 921346074253633626 T^{31} + 665416609183179841 T^{32}$$)($$1 - 20 T + 290 T^{2} - 3026 T^{3} + 26451 T^{4} - 193872 T^{5} + 1250917 T^{6} - 7096516 T^{7} + 36195640 T^{8} - 165179444 T^{9} + 682331085 T^{10} - 2528068092 T^{11} + 8470190389 T^{12} - 25438784618 T^{13} + 70775694820 T^{14} - 192799829316 T^{15} + 616167289950 T^{16} - 2506397781108 T^{17} + 11961092424580 T^{18} - 55889009805746 T^{19} + 241917107700229 T^{20} - 938653986082956 T^{21} + 3293481822057765 T^{22} - 10364765149884548 T^{23} + 29525895514256440 T^{24} - 75254999472484468 T^{25} + 172449531048275533 T^{26} - 347449719912741264 T^{27} + 616257649574744931 T^{28} - 916500072548157578 T^{29} + 1141839151852793810 T^{30} - 1023717860281815140 T^{31} + 665416609183179841 T^{32}$$)($$1 + 4 T + 107 T^{2} + 380 T^{3} + 5789 T^{4} + 19050 T^{5} + 212144 T^{6} + 652425 T^{7} + 5882030 T^{8} + 16921131 T^{9} + 131205020 T^{10} + 352876433 T^{11} + 2446352235 T^{12} + 6149085091 T^{13} + 39093257012 T^{14} + 91927991319 T^{15} + 543536230395 T^{16} + 1195063887147 T^{17} + 6606760435028 T^{18} + 13509539944927 T^{19} + 69870266183835 T^{20} + 131020549437869 T^{21} + 633301571381180 T^{22} + 1061775876212727 T^{23} + 4798152572843630 T^{24} + 6918640503429525 T^{25} + 29245851894814256 T^{26} + 34140655506404850 T^{27} + 134872614774042509 T^{28} + 115092540505056140 T^{29} + 421299273269823923 T^{30} + 204743572056363028 T^{31} + 665416609183179841 T^{32}$$)($$1 + 25 T + 385 T^{2} + 4370 T^{3} + 40821 T^{4} + 328011 T^{5} + 2348286 T^{6} + 15262673 T^{7} + 91519666 T^{8} + 511265569 T^{9} + 2684450093 T^{10} + 13324020516 T^{11} + 62851127050 T^{12} + 282769818174 T^{13} + 1217464085422 T^{14} + 5026930729070 T^{15} + 19945274556838 T^{16} + 76121573741284 T^{17} + 279708125871724 T^{18} + 989580458636692 T^{19} + 3370751400105622 T^{20} + 11044166811766790 T^{21} + 34771991743737742 T^{22} + 104990454099278982 T^{23} + 303370385705083450 T^{24} + 836062527856574772 T^{25} + 2189788409851407053 T^{26} + 5421715405896988237 T^{27} + 12616763129284202434 T^{28} + 27353158057737880901 T^{29} + 54710567119930417566 T^{30} + 99346366588431498783 T^{31} +$$$$16\!\cdots\!69$$$$T^{32} +$$$$22\!\cdots\!90$$$$T^{33} +$$$$25\!\cdots\!85$$$$T^{34} +$$$$21\!\cdots\!25$$$$T^{35} +$$$$11\!\cdots\!29$$$$T^{36}$$)($$1 - 24 T + 402 T^{2} - 5026 T^{3} + 52972 T^{4} - 482098 T^{5} + 3925963 T^{6} - 28966932 T^{7} + 196682920 T^{8} - 1238002338 T^{9} + 7283995209 T^{10} - 40243236364 T^{11} + 209809038801 T^{12} - 1035189853758 T^{13} + 4848463373224 T^{14} - 21594807026076 T^{15} + 91636684117992 T^{16} - 370834674951958 T^{17} + 1432622313733372 T^{18} - 5285005449943492 T^{19} + 18624090078533836 T^{20} - 62671060066880902 T^{21} + 201325795007228424 T^{22} - 616769283471756636 T^{23} + 1800200511234458632 T^{24} - 4996663702827798222 T^{25} + 13165206037958208117 T^{26} - 32827644214579138444 T^{27} + 77243122626775503957 T^{28} -$$$$17\!\cdots\!62$$$$T^{29} +$$$$35\!\cdots\!40$$$$T^{30} -$$$$67\!\cdots\!92$$$$T^{31} +$$$$11\!\cdots\!39$$$$T^{32} -$$$$18\!\cdots\!22$$$$T^{33} +$$$$27\!\cdots\!04$$$$T^{34} -$$$$33\!\cdots\!66$$$$T^{35} +$$$$34\!\cdots\!66$$$$T^{36} -$$$$26\!\cdots\!96$$$$T^{37} +$$$$14\!\cdots\!77$$$$T^{38}$$)($$1 + 4 T + 147 T^{2} + 612 T^{3} + 10965 T^{4} + 46930 T^{5} + 551382 T^{6} + 2393971 T^{7} + 20938477 T^{8} + 90968199 T^{9} + 637211719 T^{10} + 2733708791 T^{11} + 16093496584 T^{12} + 67342306759 T^{13} + 344740815492 T^{14} + 1391161764554 T^{15} + 6350216567005 T^{16} + 24452183743506 T^{17} + 101441444392152 T^{18} + 368871001513274 T^{19} + 1411805054266120 T^{20} + 4795323019672562 T^{21} + 17143604102273688 T^{22} + 53721447684482682 T^{23} + 181368535370229805 T^{24} + 516528625046548322 T^{25} + 1663998070884125028 T^{26} + 4225629880486326403 T^{27} + 13127959571877357064 T^{28} + 28989613160124088043 T^{29} + 87845046569848778431 T^{30} +$$$$16\!\cdots\!63$$$$T^{31} +$$$$48\!\cdots\!37$$$$T^{32} +$$$$72\!\cdots\!63$$$$T^{33} +$$$$21\!\cdots\!98$$$$T^{34} +$$$$24\!\cdots\!10$$$$T^{35} +$$$$72\!\cdots\!65$$$$T^{36} +$$$$52\!\cdots\!96$$$$T^{37} +$$$$16\!\cdots\!63$$$$T^{38} +$$$$58\!\cdots\!08$$$$T^{39} +$$$$19\!\cdots\!01$$$$T^{40}$$)
$17$ ($$1 + 6 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$( 1 + 4 T + 17 T^{2} )^{2}$$)($$1 + 9 T + 50 T^{2} + 153 T^{3} + 289 T^{4}$$)($$1 - 6 T + 35 T^{2} - 102 T^{3} + 289 T^{4}$$)($$1 - 6 T + 37 T^{2} - 102 T^{3} + 289 T^{4}$$)($$1 + 3 T + 50 T^{2} + 146 T^{3} + 1373 T^{4} + 4645 T^{5} + 30241 T^{6} + 99122 T^{7} + 514097 T^{8} + 1342405 T^{9} + 6745549 T^{10} + 12194066 T^{11} + 70992850 T^{12} + 72412707 T^{13} + 410338673 T^{14}$$)($$1 - 15 T + 185 T^{2} - 1553 T^{3} + 11942 T^{4} - 75526 T^{5} + 456245 T^{6} - 2418698 T^{7} + 12494286 T^{8} - 58193991 T^{9} + 266122262 T^{10} - 1106913944 T^{11} + 4524078454 T^{12} - 16818063399 T^{13} + 61384427118 T^{14} - 202012075658 T^{15} + 647802656965 T^{16} - 1823014036294 T^{17} + 4900264432966 T^{18} - 10833351305873 T^{19} + 21938757151945 T^{20} - 30239908506735 T^{21} + 34271896307633 T^{22}$$)($$1 - 6 T + 150 T^{2} - 861 T^{3} + 11039 T^{4} - 58946 T^{5} + 524291 T^{6} - 2547955 T^{7} + 17782322 T^{8} - 77457818 T^{9} + 451150636 T^{10} - 1742252808 T^{11} + 8746331963 T^{12} - 29618297736 T^{13} + 130382533804 T^{14} - 380550259834 T^{15} + 1485197315762 T^{16} - 3617731742435 T^{17} + 12655110188579 T^{18} - 24187823418658 T^{19} + 77005386391199 T^{20} - 102104161663917 T^{21} + 302399085067350 T^{22} - 205631377845798 T^{23} + 582622237229761 T^{24}$$)($$1 + 17 T + 258 T^{2} + 2538 T^{3} + 22321 T^{4} + 152819 T^{5} + 941699 T^{6} + 4671056 T^{7} + 20527283 T^{8} + 67321211 T^{9} + 167904403 T^{10} + 10092848 T^{11} - 1775763501 T^{12} - 11811409138 T^{13} - 30187979517 T^{14} + 2916833072 T^{15} + 824914331939 T^{16} + 5622734863931 T^{17} + 29145806458531 T^{18} + 112747936502864 T^{19} + 386415518025427 T^{20} + 1066028276376179 T^{21} + 2646999991289537 T^{22} + 5116592519339562 T^{23} + 8842149247369314 T^{24} + 9904578032905937 T^{25} + 9904578032905937 T^{26}$$)($$1 - 5 T + 130 T^{2} - 468 T^{3} + 7643 T^{4} - 20469 T^{5} + 287362 T^{6} - 594229 T^{7} + 8149596 T^{8} - 13821766 T^{9} + 190977908 T^{10} - 284790841 T^{11} + 3876597272 T^{12} - 5340393118 T^{13} + 69746292016 T^{14} - 90786683006 T^{15} + 1120336611608 T^{16} - 1399177401833 T^{17} + 15950665854068 T^{18} - 19624931207462 T^{19} + 196711435772124 T^{20} - 243835139318117 T^{21} + 2004567609760642 T^{22} - 2427375244017093 T^{23} + 15408241381131707 T^{24} - 16039247471972244 T^{25} + 75740890839868930 T^{26} - 49522890164529685 T^{27} + 168377826559400929 T^{28}$$)($$1 + 10 T + 207 T^{2} + 1775 T^{3} + 20208 T^{4} + 150815 T^{5} + 1244627 T^{6} + 8171636 T^{7} + 54477014 T^{8} + 317264820 T^{9} + 1805939268 T^{10} + 9392982639 T^{11} + 47074285810 T^{12} + 219869149681 T^{13} + 985970961441 T^{14} + 4149634681808 T^{15} + 16761506344497 T^{16} + 63542184257809 T^{17} + 231275966184530 T^{18} + 784511302991919 T^{19} + 2564175511244676 T^{20} + 7658001484022580 T^{21} + 22354025633762422 T^{22} + 57003350632143476 T^{23} + 147597672960831619 T^{24} + 304042120096215935 T^{25} + 692566480584647664 T^{26} + 1034154471082825775 T^{27} + 2050247652811528959 T^{28} + 1683778265594009290 T^{29} + 2862423051509815793 T^{30}$$)($$1 - 5 T + 158 T^{2} - 540 T^{3} + 11588 T^{4} - 27066 T^{5} + 558089 T^{6} - 870456 T^{7} + 20459225 T^{8} - 20581469 T^{9} + 610166673 T^{10} - 380514409 T^{11} + 15256129494 T^{12} - 5823688053 T^{13} + 325009231345 T^{14} - 84738254968 T^{15} + 5951336176930 T^{16} - 1440550334456 T^{17} + 93927667858705 T^{18} - 28611779404389 T^{19} + 1274207191468374 T^{20} - 540276047219513 T^{21} + 14727940171037937 T^{22} - 8445372677850637 T^{23} + 142718591030843225 T^{24} - 103225528624072632 T^{25} + 1125104019907681961 T^{26} - 927603145462394778 T^{27} + 6751426485018470468 T^{28} - 5348472137769205980 T^{29} + 26603696596385346782 T^{30} - 14312115257549078965 T^{31} + 48661191875666868481 T^{32}$$)($$1 + 3 T + 119 T^{2} + 197 T^{3} + 7224 T^{4} + 5540 T^{5} + 310835 T^{6} + 34062 T^{7} + 10484647 T^{8} - 4461310 T^{9} + 291065858 T^{10} - 241198952 T^{11} + 6894239766 T^{12} - 7415074569 T^{13} + 141937841380 T^{14} - 165486582283 T^{15} + 2567277444404 T^{16} - 2813271898811 T^{17} + 41020036158820 T^{18} - 36430261357497 T^{19} + 575813799496086 T^{20} - 342468020389864 T^{21} + 7025622231019202 T^{22} - 1830648025241630 T^{23} + 73138354326508327 T^{24} + 4039340249240814 T^{25} + 626641464046064915 T^{26} + 189866305544286820 T^{27} + 4208863041747793464 T^{28} + 1951201872482469589 T^{29} + 20036961360568710551 T^{30} + 8587269154529447379 T^{31} + 48661191875666868481 T^{32}$$)($$1 - 18 T + 273 T^{2} - 2781 T^{3} + 25658 T^{4} - 193733 T^{5} + 1383023 T^{6} - 8697320 T^{7} + 53036891 T^{8} - 294777276 T^{9} + 1607117632 T^{10} - 8112035114 T^{11} + 40363531935 T^{12} - 187473496595 T^{13} + 860633799060 T^{14} - 3703086251987 T^{15} + 15762439781607 T^{16} - 62952466283779 T^{17} + 248723167928340 T^{18} - 921057288771235 T^{19} + 3371202550743135 T^{20} - 11517929840858698 T^{21} + 38791912733516608 T^{22} - 120958516264394748 T^{23} + 369972487040755931 T^{24} - 1031396710014888040 T^{25} + 2788165932180677327 T^{26} - 6639597287366663989 T^{27} + 14948921362841207738 T^{28} - 27544631509511410797 T^{29} + 45967146650716453617 T^{30} - 51523614927176684274 T^{31} + 48661191875666868481 T^{32}$$)($$1 - 17 T + 271 T^{2} - 2811 T^{3} + 27324 T^{4} - 215198 T^{5} + 1613920 T^{6} - 10643807 T^{7} + 67598476 T^{8} - 393720197 T^{9} + 2219851055 T^{10} - 11763913489 T^{11} + 60437526881 T^{12} - 296473981529 T^{13} + 1409837991942 T^{14} - 6467854453086 T^{15} + 28753111843606 T^{16} - 124072891149114 T^{17} + 518698939431416 T^{18} - 2109239149534938 T^{19} + 8309649322802134 T^{20} - 31776568928011518 T^{21} + 117751078924987782 T^{22} - 420950657991821353 T^{23} + 1458814975279492289 T^{24} - 4827188650363060097 T^{25} + 15485142514827950255 T^{26} - 46690442096210509909 T^{27} +$$$$13\!\cdots\!24$$$$T^{28} -$$$$36\!\cdots\!31$$$$T^{29} +$$$$94\!\cdots\!20$$$$T^{30} -$$$$21\!\cdots\!26$$$$T^{31} +$$$$46\!\cdots\!96$$$$T^{32} -$$$$80\!\cdots\!23$$$$T^{33} +$$$$13\!\cdots\!51$$$$T^{34} -$$$$14\!\cdots\!09$$$$T^{35} +$$$$14\!\cdots\!09$$$$T^{36}$$)($$1 + 17 T + 284 T^{2} + 3184 T^{3} + 32551 T^{4} + 278609 T^{5} + 2179544 T^{6} + 15312493 T^{7} + 99697602 T^{8} + 601566144 T^{9} + 3415708339 T^{10} + 18303102870 T^{11} + 93623696982 T^{12} + 457896515162 T^{13} + 2163836903127 T^{14} + 9881182119343 T^{15} + 43988887312946 T^{16} + 190801647107236 T^{17} + 811083332879856 T^{18} + 3375158517221308 T^{19} + 13788416658957552 T^{20} + 55141676013991204 T^{21} + 216117403368503698 T^{22} + 825286211789646703 T^{23} + 3072338973763192839 T^{24} + 11052508729582321178 T^{25} + 38417423580947984886 T^{26} +$$$$12\!\cdots\!70$$$$T^{27} +$$$$40\!\cdots\!83$$$$T^{28} +$$$$12\!\cdots\!56$$$$T^{29} +$$$$34\!\cdots\!66$$$$T^{30} +$$$$89\!\cdots\!73$$$$T^{31} +$$$$21\!\cdots\!28$$$$T^{32} +$$$$46\!\cdots\!61$$$$T^{33} +$$$$93\!\cdots\!43$$$$T^{34} +$$$$15\!\cdots\!04$$$$T^{35} +$$$$23\!\cdots\!68$$$$T^{36} +$$$$23\!\cdots\!53$$$$T^{37} +$$$$23\!\cdots\!53$$$$T^{38}$$)($$1 + 4 T + 183 T^{2} + 657 T^{3} + 16646 T^{4} + 53973 T^{5} + 1003885 T^{6} + 2955994 T^{7} + 45271848 T^{8} + 121833860 T^{9} + 1633898241 T^{10} + 4051003521 T^{11} + 49301704657 T^{12} + 113655742290 T^{13} + 1280577022539 T^{14} + 2768680397715 T^{15} + 29171755167306 T^{16} + 59503142298315 T^{17} + 589114026053452 T^{18} + 1136153545521719 T^{19} + 10601403457616084 T^{20} + 19314610273869223 T^{21} + 170253953529447628 T^{22} + 292338938111621595 T^{23} + 2436454163328564426 T^{24} + 3931130243458426755 T^{25} + 30910016241349667691 T^{26} + 46637346470108581170 T^{27} +$$$$34\!\cdots\!37$$$$T^{28} +$$$$48\!\cdots\!37$$$$T^{29} +$$$$32\!\cdots\!09$$$$T^{30} +$$$$41\!\cdots\!80$$$$T^{31} +$$$$26\!\cdots\!28$$$$T^{32} +$$$$29\!\cdots\!78$$$$T^{33} +$$$$16\!\cdots\!65$$$$T^{34} +$$$$15\!\cdots\!89$$$$T^{35} +$$$$81\!\cdots\!26$$$$T^{36} +$$$$54\!\cdots\!89$$$$T^{37} +$$$$25\!\cdots\!47$$$$T^{38} +$$$$95\!\cdots\!12$$$$T^{39} +$$$$40\!\cdots\!01$$$$T^{40}$$)
$19$ ($$1 + 8 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$1 + 6 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$1 + 8 T + 36 T^{2} + 152 T^{3} + 361 T^{4}$$)($$1 - 4 T + 36 T^{2} - 76 T^{3} + 361 T^{4}$$)($$1 + 9 T + 127 T^{2} + 828 T^{3} + 6701 T^{4} + 34195 T^{5} + 201852 T^{6} + 825304 T^{7} + 3835188 T^{8} + 12344395 T^{9} + 45962159 T^{10} + 107905788 T^{11} + 314464573 T^{12} + 423412929 T^{13} + 893871739 T^{14}$$)($$1 + 19 T + 234 T^{2} + 2045 T^{3} + 14527 T^{4} + 83422 T^{5} + 399009 T^{6} + 1485464 T^{7} + 3888135 T^{8} + 1769859 T^{9} - 45008345 T^{10} - 294336390 T^{11} - 855158555 T^{12} + 638919099 T^{13} + 26668717965 T^{14} + 193587153944 T^{15} + 987985785891 T^{16} + 3924661484782 T^{17} + 12985274752453 T^{18} + 34731386418845 T^{19} + 75508921280286 T^{20} + 116490258898219 T^{21} + 116490258898219 T^{22}$$)($$1 + 7 T + 113 T^{2} + 557 T^{3} + 5849 T^{4} + 24530 T^{5} + 212023 T^{6} + 802042 T^{7} + 6029495 T^{8} + 21080957 T^{9} + 143612483 T^{10} + 471134705 T^{11} + 2944902893 T^{12} + 8951559395 T^{13} + 51844106363 T^{14} + 144594284063 T^{15} + 785769817895 T^{16} + 1985935394158 T^{17} + 9974808827263 T^{18} + 21926673757670 T^{19} + 99336860226809 T^{20} + 179737047662903 T^{21} + 692810487131513 T^{22} + 815431812287533 T^{23} + 2213314919066161 T^{24}$$)($$1 - 5 T + 173 T^{2} - 864 T^{3} + 14502 T^{4} - 70542 T^{5} + 782707 T^{6} - 3630922 T^{7} + 30483684 T^{8} - 132517839 T^{9} + 909405816 T^{10} - 3646806238 T^{11} + 21484456413 T^{12} - 78131794348 T^{13} + 408204671847 T^{14} - 1316497051918 T^{15} + 6237614491944 T^{16} - 17269857296319 T^{17} + 75480619468716 T^{18} - 170819924332282 T^{19} + 699639667217473 T^{20} - 1198054504038222 T^{21} + 4679616993191058 T^{22} - 5297241246740064 T^{23} + 20152814789391887 T^{24} - 11066574595330805 T^{25} + 42052983462257059 T^{26}$$)($$1 - 21 T + 374 T^{2} - 4569 T^{3} + 49627 T^{4} - 447130 T^{5} + 3686027 T^{6} - 26871562 T^{7} + 182306081 T^{8} - 1126820515 T^{9} + 6549395980 T^{10} - 35231461213 T^{11} + 179334900367 T^{12} - 851666403346 T^{13} + 3838575491950 T^{14} - 16181661663574 T^{15} + 64739899032487 T^{16} - 241652592459967 T^{17} + 853523833509580 T^{18} - 2790119150370985 T^{19} + 8576750192302361 T^{20} - 24019729854586318 T^{21} + 62601871925328107 T^{22} - 144283350307924270 T^{23} + 304266425175890227 T^{24} - 532243992905962611 T^{25} + 827779779730744214 T^{26} - 883112652707398239 T^{27} + 799006685782884121 T^{28}$$)($$1 - 13 T + 242 T^{2} - 2450 T^{3} + 27197 T^{4} - 226930 T^{5} + 1919820 T^{6} - 13675328 T^{7} + 96099554 T^{8} - 597938602 T^{9} + 3632296392 T^{10} - 20032584862 T^{11} + 107415475528 T^{12} - 529641457367 T^{13} + 2534855671164 T^{14} - 11217526412978 T^{15} + 48162257752116 T^{16} - 191200566109487 T^{17} + 736762746646552 T^{18} - 2610666491800702 T^{19} + 8993925463934808 T^{20} - 28130548314998362 T^{21} + 85900675451104406 T^{22} - 232255795194352448 T^{23} + 619502295950079780 T^{24} - 1391322865882780930 T^{25} + 3168185571254862143 T^{26} - 5422621551712094450 T^{27} + 10176821997866208278 T^{28} - 10387086915177493573 T^{29} + 15181127029874798299 T^{30}$$)($$1 + 11 T + 181 T^{2} + 1462 T^{3} + 14335 T^{4} + 95375 T^{5} + 719296 T^{6} + 4211650 T^{7} + 26971845 T^{8} + 143986816 T^{9} + 822044549 T^{10} + 4072545605 T^{11} + 21330650499 T^{12} + 99112960004 T^{13} + 484717258250 T^{14} + 2123022393713 T^{15} + 9768224694024 T^{16} + 40337425480547 T^{17} + 174982930228250 T^{18} + 679815792667436 T^{19} + 2779831703680179 T^{20} + 10084026099994895 T^{21} + 38673810028952669 T^{22} + 128705745610993024 T^{23} + 458078029889580645 T^{24} + 1359047642350925350 T^{25} + 4410051434971228096 T^{26} + 11110258442417637125 T^{27} + 31727869364813417935 T^{28} + 61481461821819820258 T^{29} +$$$$14\!\cdots\!01$$$$T^{30} +$$$$16\!\cdots\!89$$$$T^{31} +$$$$28\!\cdots\!81$$$$T^{32}$$)($$1 - 13 T + 224 T^{2} - 2227 T^{3} + 23556 T^{4} - 193353 T^{5} + 1589551 T^{6} - 11232515 T^{7} + 77919882 T^{8} - 486334465 T^{9} + 2959429581 T^{10} - 16577586969 T^{11} + 90351387300 T^{12} - 458691179259 T^{13} + 2264953054380 T^{14} - 10477514679859 T^{15} + 47144548718330 T^{16} - 199072778917321 T^{17} + 817648052631180 T^{18} - 3146162798537481 T^{19} + 11774683144323300 T^{20} - 41047746516353931 T^{21} + 139228971895605861 T^{22} - 434720633965184635 T^{23} + 1323357228094281162 T^{24} - 3624594405618084185 T^{25} + 9745642501153837351 T^{26} - 22523741028747338307 T^{27} + 52136846233522488516 T^{28} - 93651994170446470393 T^{29} +$$$$17\!\cdots\!04$$$$T^{30} -$$$$19\!\cdots\!87$$$$T^{31} +$$$$28\!\cdots\!81$$$$T^{32}$$)($$1 + 15 T + 248 T^{2} + 2524 T^{3} + 25137 T^{4} + 195368 T^{5} + 1456692 T^{6} + 9129794 T^{7} + 54772327 T^{8} + 283776189 T^{9} + 1411840969 T^{10} + 6094322619 T^{11} + 25604146193 T^{12} + 93020585977 T^{13} + 350079022597 T^{14} + 1197314079224 T^{15} + 5166511617041 T^{16} + 22748967505256 T^{17} + 126378527157517 T^{18} + 638028199216243 T^{19} + 3336757936017953 T^{20} + 15090146142583281 T^{21} + 66421302218498689 T^{22} + 253659515548222671 T^{23} + 930229268506766407 T^{24} + 2946072207056527526 T^{25} + 8931075169208654292 T^{26} + 22758468900427249592 T^{27} + 55636097120566089057 T^{28} +$$$$10\!\cdots\!16$$$$T^{29} +$$$$19\!\cdots\!08$$$$T^{30} +$$$$22\!\cdots\!85$$$$T^{31} +$$$$28\!\cdots\!81$$$$T^{32}$$)($$1 + 5 T + 147 T^{2} + 706 T^{3} + 11220 T^{4} + 54388 T^{5} + 598059 T^{6} + 2947928 T^{7} + 24930876 T^{8} + 123855871 T^{9} + 863216513 T^{10} + 4247612067 T^{11} + 25659749354 T^{12} + 122670371696 T^{13} + 666353734551 T^{14} + 3046885890738 T^{15} + 15241373221617 T^{16} + 65964543118195 T^{17} + 307973464968892 T^{18} + 1253326319245705 T^{19} + 5502135733003737 T^{20} + 20898590324571942 T^{21} + 86839885040420871 T^{22} + 303743984686093904 T^{23} + 1207185514598110874 T^{24} + 3796820384926674513 T^{25} + 14660492066567696033 T^{26} + 39966765869402810509 T^{27} +$$$$15\!\cdots\!76$$$$T^{28} +$$$$34\!\cdots\!32$$$$T^{29} +$$$$13\!\cdots\!99$$$$T^{30} +$$$$22\!\cdots\!92$$$$T^{31} +$$$$89\!\cdots\!20$$$$T^{32} +$$$$10\!\cdots\!94$$$$T^{33} +$$$$42\!\cdots\!07$$$$T^{34} +$$$$27\!\cdots\!95$$$$T^{35} +$$$$10\!\cdots\!41$$$$T^{36}$$)($$1 - 23 T + 416 T^{2} - 5333 T^{3} + 59693 T^{4} - 564360 T^{5} + 4868647 T^{6} - 37688990 T^{7} + 272710055 T^{8} - 1823898623 T^{9} + 11572107859 T^{10} - 69036155352 T^{11} + 394624910977 T^{12} - 2144671314045 T^{13} + 11249450770817 T^{14} - 56533025766972 T^{15} + 275667627613884 T^{16} - 1294507948679753 T^{17} + 5918690016197407 T^{18} - 26130047561244090 T^{19} + 112455110307750733 T^{20} - 467317369473390833 T^{21} + 1890804257803630356 T^{22} - 7367440450977558012 T^{23} + 27854753804169202883 T^{24} -$$$$10\!\cdots\!45$$$$T^{25} +$$$$35\!\cdots\!03$$$$T^{26} -$$$$11\!\cdots\!32$$$$T^{27} +$$$$37\!\cdots\!61$$$$T^{28} -$$$$11\!\cdots\!23$$$$T^{29} +$$$$31\!\cdots\!45$$$$T^{30} -$$$$83\!\cdots\!90$$$$T^{31} +$$$$20\!\cdots\!73$$$$T^{32} -$$$$45\!\cdots\!60$$$$T^{33} +$$$$90\!\cdots\!07$$$$T^{34} -$$$$15\!\cdots\!73$$$$T^{35} +$$$$22\!\cdots\!24$$$$T^{36} -$$$$23\!\cdots\!43$$$$T^{37} +$$$$19\!\cdots\!79$$$$T^{38}$$)($$1 - T + 168 T^{2} - 22 T^{3} + 14607 T^{4} + 7772 T^{5} + 881922 T^{6} + 903038 T^{7} + 41475084 T^{8} + 56620098 T^{9} + 1610059343 T^{10} + 2542393063 T^{11} + 53307795046 T^{12} + 90285835997 T^{13} + 1535187711513 T^{14} + 2663902287560 T^{15} + 38939941596646 T^{16} + 67089130901567 T^{17} + 877089383861008 T^{18} + 1463016008143316 T^{19} + 17627732755396580 T^{20} + 27797304154723004 T^{21} + 316629267573823888 T^{22} + 460164348853848053 T^{23} + 5074692128816503366 T^{24} + 6596085790325028440 T^{25} + 72224258388502927953 T^{26} + 80703957229707188783 T^{27} +$$$$90\!\cdots\!86$$$$T^{28} +$$$$82\!\cdots\!77$$$$T^{29} +$$$$98\!\cdots\!43$$$$T^{30} +$$$$65\!\cdots\!62$$$$T^{31} +$$$$91\!\cdots\!24$$$$T^{32} +$$$$37\!\cdots\!42$$$$T^{33} +$$$$70\!\cdots\!62$$$$T^{34} +$$$$11\!\cdots\!28$$$$T^{35} +$$$$42\!\cdots\!67$$$$T^{36} -$$$$12\!\cdots\!58$$$$T^{37} +$$$$17\!\cdots\!88$$$$T^{38} -$$$$19\!\cdots\!79$$$$T^{39} +$$$$37\!\cdots\!01$$$$T^{40}$$)
$23$ ($$1 + 5 T + 23 T^{2}$$)($$1 + 9 T + 23 T^{2}$$)($$1 + 3 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 8 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 9 T + 23 T^{2}$$)($$1 - 5 T + 48 T^{2} - 115 T^{3} + 529 T^{4}$$)($$1 + 3 T + 10 T^{2} + 69 T^{3} + 529 T^{4}$$)($$1 + 38 T^{2} + 529 T^{4}$$)($$( 1 + 6 T + 23 T^{2} )^{2}$$)($$1 + 12 T + 150 T^{2} + 1067 T^{3} + 8328 T^{4} + 46995 T^{5} + 292164 T^{6} + 1356265 T^{7} + 6719772 T^{8} + 24860355 T^{9} + 101326776 T^{10} + 298590347 T^{11} + 965451450 T^{12} + 1776430668 T^{13} + 3404825447 T^{14}$$)($$1 - 11 T + 183 T^{2} - 1415 T^{3} + 13556 T^{4} - 84717 T^{5} + 612371 T^{6} - 3414518 T^{7} + 20798264 T^{8} - 108054544 T^{9} + 578865979 T^{10} - 2768846230 T^{11} + 13313917517 T^{12} - 57160853776 T^{13} + 253052478088 T^{14} - 955522131638 T^{15} + 3941429799253 T^{16} - 12541156408413 T^{17} + 46155813759532 T^{18} - 110810044172615 T^{19} + 329610937047729 T^{20} - 455691623350139 T^{21} + 952809757913927 T^{22}$$)($$1 - 29 T + 542 T^{2} - 7573 T^{3} + 87342 T^{4} - 861461 T^{5} + 7482463 T^{6} - 58099514 T^{7} + 408414306 T^{8} - 2617981756 T^{9} + 15395107951 T^{10} - 83316425431 T^{11} + 415948195901 T^{12} - 1916277784913 T^{13} + 8144012106079 T^{14} - 31852984025252 T^{15} + 114291067805346 T^{16} - 373948400237302 T^{17} + 1107673062114607 T^{18} - 2933124334398067 T^{19} + 6839838076413102 T^{20} - 13640129105259299 T^{21} + 22453169077797758 T^{22} - 27631482979503883 T^{23} + 21914624432020321 T^{24}$$)($$1 + 4 T + 184 T^{2} + 613 T^{3} + 16621 T^{4} + 45907 T^{5} + 981152 T^{6} + 2240102 T^{7} + 42577347 T^{8} + 80788590 T^{9} + 1448692280 T^{10} + 2339155653 T^{11} + 40151933279 T^{12} + 57649846102 T^{13} + 923494465417 T^{14} + 1237413340437 T^{15} + 17626238970760 T^{16} + 22607959814190 T^{17} + 274042409322021 T^{18} + 331615491020678 T^{19} + 3340651296974944 T^{20} + 3595022401294867 T^{21} + 29936958386176523 T^{22} + 25394451373966837 T^{23} + 175316995456162568 T^{24} + 87658497728081284 T^{25} + 504036361936467383 T^{26}$$)($$1 - 10 T + 197 T^{2} - 1651 T^{3} + 18643 T^{4} - 131352 T^{5} + 1107307 T^{6} - 6674025 T^{7} + 46362563 T^{8} - 244354670 T^{9} + 1483666023 T^{10} - 7040607329 T^{11} + 39336210461 T^{12} - 174731022341 T^{13} + 936647851466 T^{14} - 4018813513843 T^{15} + 20808855333869 T^{16} - 85663069371943 T^{17} + 415190583542343 T^{18} - 1572750469771810 T^{19} + 6863323230023507 T^{20} - 22723890153914175 T^{21} + 86714302178548267 T^{22} - 236585004388487976 T^{23} + 772314448556058307 T^{24} - 1573088910315893477 T^{25} + 4317181013108003237 T^{26} - 5040363619364673830 T^{27} + 11592836324538749809 T^{28}$$)($$1 + 15 T + 319 T^{2} + 3514 T^{3} + 43459 T^{4} + 379903 T^{5} + 3477374 T^{6} + 25218919 T^{7} + 186966261 T^{8} + 1160793560 T^{9} + 7337809832 T^{10} + 40158240336 T^{11} + 225676584167 T^{12} + 1125042894714 T^{13} + 5842956250911 T^{14} + 27348850752266 T^{15} + 134387993770953 T^{16} + 595147691303706 T^{17} + 2745806999559889 T^{18} + 11237922133866576 T^{19} + 47228660947524376 T^{20} + 171839106600074840 T^{21} + 636587483183243667 T^{22} + 1974918394611731239 T^{23} + 6263281435002238162 T^{24} + 15738055889598896047 T^{25} + 41408159269181353493 T^{26} + 77007990254119407994 T^{27} +$$$$16\!\cdots\!77$$$$T^{28} +$$$$17\!\cdots\!35$$$$T^{29} +$$$$26\!\cdots\!07$$$$T^{30}$$)($$1 + 13 T + 208 T^{2} + 2018 T^{3} + 20375 T^{4} + 160550 T^{5} + 1275907 T^{6} + 8665917 T^{7} + 58792152 T^{8} + 357162729 T^{9} + 2165764215 T^{10} + 12076345886 T^{11} + 67338196417 T^{12} + 351022119450 T^{13} + 1831885262566 T^{14} + 9017382569929 T^{15} + 44472265582174 T^{16} + 207399799108367 T^{17} + 969067303897414 T^{18} + 4270886127348150 T^{19} + 18843988223529697 T^{20} + 77727504308934898 T^{21} + 320610830931912135 T^{22} + 1216076748419164863 T^{23} + 4604071349910314712 T^{24} + 15608639468567456571 T^{25} + 52856375643073254643 T^{26} +$$$$15\!\cdots\!50$$$$T^{27} +$$$$44\!\cdots\!75$$$$T^{28} +$$$$10\!\cdots\!94$$$$T^{29} +$$$$24\!\cdots\!72$$$$T^{30} +$$$$34\!\cdots\!91$$$$T^{31} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 + 5 T + 182 T^{2} + 756 T^{3} + 15727 T^{4} + 54038 T^{5} + 854995 T^{6} + 2305237 T^{7} + 32132604 T^{8} + 57324585 T^{9} + 857073607 T^{10} + 371762126 T^{11} + 15989916385 T^{12} - 32570990844 T^{13} + 206622863040 T^{14} - 1527911913935 T^{15} + 2891712727590 T^{16} - 35141974020505 T^{17} + 109303494548160 T^{18} - 396291245598948 T^{19} + 4474634191094785 T^{20} + 2392788557345218 T^{21} + 126877653350681623 T^{22} + 195180205746714495 T^{23} + 2516335878884201724 T^{24} + 4152083757852981731 T^{25} + 35419459955113826755 T^{26} + 51487933698152787226 T^{27} +$$$$34\!\cdots\!67$$$$T^{28} +$$$$38\!\cdots\!48$$$$T^{29} +$$$$21\!\cdots\!38$$$$T^{30} +$$$$13\!\cdots\!35$$$$T^{31} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 - 5 T + 180 T^{2} - 911 T^{3} + 16850 T^{4} - 85251 T^{5} + 1077221 T^{6} - 5402068 T^{7} + 52468559 T^{8} - 258760441 T^{9} + 2064324615 T^{10} - 9931668180 T^{11} + 68039962889 T^{12} - 316125223782 T^{13} + 1923834329544 T^{14} - 8513441106040 T^{15} + 47326552683658 T^{16} - 195809145438920 T^{17} + 1017708360328776 T^{18} - 3846295597755594 T^{19} + 19040371254820649 T^{20} - 63923622968665740 T^{21} + 305594129566107735 T^{22} - 881034134193742127 T^{23} + 4108864551564280079 T^{24} - 9729949155604105484 T^{25} + 44625507836078189429 T^{26} - 81227984671920190677 T^{27} +$$$$36\!\cdots\!50$$$$T^{28} -$$$$45\!\cdots\!13$$$$T^{29} +$$$$20\!\cdots\!20$$$$T^{30} -$$$$13\!\cdots\!35$$$$T^{31} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 - 14 T + 241 T^{2} - 2165 T^{3} + 22937 T^{4} - 159770 T^{5} + 1348211 T^{6} - 7982781 T^{7} + 59782924 T^{8} - 318639178 T^{9} + 2236451198 T^{10} - 11093814756 T^{11} + 74232434192 T^{12} - 346225007891 T^{13} + 2204529109109 T^{14} - 9680284070456 T^{15} + 58671559445850 T^{16} - 244022213085305 T^{17} + 1413668128204946 T^{18} - 5612510900962015 T^{19} + 31037254946854650 T^{20} - 117780016285238152 T^{21} + 616917630422171669 T^{22} - 2228422905964182613 T^{23} + 10989064388246716688 T^{24} - 37772502785532895932 T^{25} +$$$$17\!\cdots\!38$$$$T^{26} -$$$$57\!\cdots\!14$$$$T^{27} +$$$$24\!\cdots\!76$$$$T^{28} -$$$$76\!\cdots\!87$$$$T^{29} +$$$$29\!\cdots\!31$$$$T^{30} -$$$$80\!\cdots\!10$$$$T^{31} +$$$$26\!\cdots\!33$$$$T^{32} -$$$$57\!\cdots\!55$$$$T^{33} +$$$$14\!\cdots\!01$$$$T^{34} -$$$$19\!\cdots\!42$$$$T^{35} +$$$$32\!\cdots\!69$$$$T^{36}$$)($$1 - 17 T + 391 T^{2} - 4769 T^{3} + 65448 T^{4} - 640527 T^{5} + 6681855 T^{6} - 55642304 T^{7} + 483186514 T^{8} - 3544873790 T^{9} + 26828147273 T^{10} - 177193952328 T^{11} + 1199885605017 T^{12} - 7232532287266 T^{13} + 44528435308294 T^{14} - 247034068307600 T^{15} + 1396581507639034 T^{16} - 7165658273752720 T^{17} + 37417693376472169 T^{18} - 177916417007843598 T^{19} + 860606947658859887 T^{20} - 3790633226815188880 T^{21} + 16992207203444126678 T^{22} - 69130260709267091600 T^{23} +$$$$28\!\cdots\!42$$$$T^{24} -$$$$10\!\cdots\!74$$$$T^{25} +$$$$40\!\cdots\!99$$$$T^{26} -$$$$13\!\cdots\!68$$$$T^{27} +$$$$48\!\cdots\!99$$$$T^{28} -$$$$14\!\cdots\!10$$$$T^{29} +$$$$46\!\cdots\!78$$$$T^{30} -$$$$12\!\cdots\!84$$$$T^{31} +$$$$33\!\cdots\!65$$$$T^{32} -$$$$74\!\cdots\!43$$$$T^{33} +$$$$17\!\cdots\!36$$$$T^{34} -$$$$29\!\cdots\!09$$$$T^{35} +$$$$55\!\cdots\!73$$$$T^{36} -$$$$55\!\cdots\!73$$$$T^{37} +$$$$74\!\cdots\!87$$$$T^{38}$$)($$1 + 31 T + 692 T^{2} + 11153 T^{3} + 151248 T^{4} + 1734815 T^{5} + 17720485 T^{6} + 161884250 T^{7} + 1358181700 T^{8} + 10498603348 T^{9} + 76056972053 T^{10} + 517541354301 T^{11} + 3348917400973 T^{12} + 20629077972721 T^{13} + 122097347658439 T^{14} + 694208163015300 T^{15} + 3818664081897215 T^{16} + 20293567559402971 T^{17} + 104766417002832779 T^{18} + 524141981778219074 T^{19} + 2552226400117829118 T^{20} + 12055265580899038702 T^{21} + 55421434594498540091 T^{22} +$$$$24\!\cdots\!57$$$$T^{23} +$$$$10\!\cdots\!15$$$$T^{24} +$$$$44\!\cdots\!00$$$$T^{25} +$$$$18\!\cdots\!71$$$$T^{26} +$$$$70\!\cdots\!87$$$$T^{27} +$$$$26\!\cdots\!13$$$$T^{28} +$$$$93\!\cdots\!63$$$$T^{29} +$$$$31\!\cdots\!97$$$$T^{30} +$$$$10\!\cdots\!96$$$$T^{31} +$$$$29\!\cdots\!00$$$$T^{32} +$$$$81\!\cdots\!50$$$$T^{33} +$$$$20\!\cdots\!65$$$$T^{34} +$$$$46\!\cdots\!05$$$$T^{35} +$$$$92\!\cdots\!28$$$$T^{36} +$$$$15\!\cdots\!59$$$$T^{37} +$$$$22\!\cdots\!48$$$$T^{38} +$$$$23\!\cdots\!97$$$$T^{39} +$$$$17\!\cdots\!01$$$$T^{40}$$)
$29$ ($$1 - 3 T + 29 T^{2}$$)($$1 + 5 T + 29 T^{2}$$)($$1 + 3 T + 29 T^{2}$$)($$1 - 10 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 - 9 T + 29 T^{2}$$)($$1 - 5 T + 29 T^{2}$$)($$1 + 9 T + 74 T^{2} + 261 T^{3} + 841 T^{4}$$)($$1 + 41 T^{2} + 841 T^{4}$$)($$1 - 6 T + 65 T^{2} - 174 T^{3} + 841 T^{4}$$)($$1 - 6 T + 43 T^{2} - 174 T^{3} + 841 T^{4}$$)($$1 - 9 T + 107 T^{2} - 652 T^{3} + 4764 T^{4} - 22810 T^{5} + 134487 T^{6} - 612145 T^{7} + 3900123 T^{8} - 19183210 T^{9} + 116189196 T^{10} - 461147212 T^{11} + 2194692943 T^{12} - 5353409889 T^{13} + 17249876309 T^{14}$$)($$1 - 10 T + 181 T^{2} - 1710 T^{3} + 17914 T^{4} - 147510 T^{5} + 1186021 T^{6} - 8528670 T^{7} + 57349064 T^{8} - 364258800 T^{9} + 2122703783 T^{10} - 11977573672 T^{11} + 61558409707 T^{12} - 306341650800 T^{13} + 1398686321896 T^{14} - 6032166246270 T^{15} + 24326653448129 T^{16} - 87742388080710 T^{17} + 309014284199426 T^{18} - 855421366163310 T^{19} + 2625793421632289 T^{20} - 4207072333002010 T^{21} + 12200509765705829 T^{22}$$)($$1 - 22 T + 444 T^{2} - 5948 T^{3} + 73244 T^{4} - 735689 T^{5} + 6885195 T^{6} - 56276420 T^{7} + 432301143 T^{8} - 2987132731 T^{9} + 19491587322 T^{10} - 115935681738 T^{11} + 652645944087 T^{12} - 3362134770402 T^{13} + 16392424937802 T^{14} - 72853180176359 T^{15} + 305758384722183 T^{16} - 1154294035806580 T^{17} + 4095474555632595 T^{18} - 12690544251891901 T^{19} + 36640048270915484 T^{20} - 86288504264468812 T^{21} + 186794011585289244 T^{22} - 268411214845528238 T^{23} + 353814783205469041 T^{24}$$)($$1 + 21 T + 421 T^{2} + 5324 T^{3} + 64636 T^{4} + 613764 T^{5} + 5683567 T^{6} + 44367699 T^{7} + 342010383 T^{8} + 2302116496 T^{9} + 15447960508 T^{10} + 92186196428 T^{11} + 551990408672 T^{12} + 2963927041432 T^{13} + 16007721851488 T^{14} + 77528591195948 T^{15} + 376760308829612 T^{16} + 1628243257407376 T^{17} + 7015025925260067 T^{18} + 26390942064308379 T^{19} + 98040827743914203 T^{20} + 307033239404595204 T^{21} + 937683887296268684 T^{22} + 2239845310090270124 T^{23} + 5136414611362154009 T^{24} + 7430110447314849861 T^{25} + 10260628712958602189 T^{26}$$)($$1 - 15 T + 325 T^{2} - 3542 T^{3} + 45090 T^{4} - 389302 T^{5} + 3709822 T^{6} - 26645384 T^{7} + 208750551 T^{8} - 1291861725 T^{9} + 8811883923 T^{10} - 48651787808 T^{11} + 303330222126 T^{12} - 1554455012568 T^{13} + 9203796607924 T^{14} - 45079195364472 T^{15} + 255100716807966 T^{16} - 1186568452849312 T^{17} + 6232478072943363 T^{18} - 26497568328872025 T^{19} + 124169696006399871 T^{20} - 459629578205807656 T^{21} + 1855825148223802942 T^{22} - 5647660942697753438 T^{23} + 18969689149506063090 T^{24} - 43214205590130046318 T^{25} +$$$$11\!\cdots\!25$$$$T^{26} -$$$$15\!\cdots\!35$$$$T^{27} +$$$$29\!\cdots\!81$$$$T^{28}$$)($$1 + 16 T + 379 T^{2} + 4614 T^{3} + 64307 T^{4} + 640183 T^{5} + 6718538 T^{6} + 56998817 T^{7} + 493332872 T^{8} + 3661907872 T^{9} + 27353673352 T^{10} + 180793063122 T^{11} + 1196007936757 T^{12} + 7118154232879 T^{13} + 42323896693918 T^{14} + 228075963529810 T^{15} + 1227393004123622 T^{16} + 5986367709851239 T^{17} + 29169437569566473 T^{18} + 127871498477991282 T^{19} + 561055269820201448 T^{20} + 2178188201619082912 T^{21} + 8509931021163729448 T^{22} + 28513453747270467137 T^{23} + 97466811510422959522 T^{24} +$$$$26\!\cdots\!83$$$$T^{25} +$$$$78\!\cdots\!03$$$$T^{26} +$$$$16\!\cdots\!74$$$$T^{27} +$$$$38\!\cdots\!31$$$$T^{28} +$$$$47\!\cdots\!96$$$$T^{29} +$$$$86\!\cdots\!49$$$$T^{30}$$)($$1 + 24 T + 472 T^{2} + 6622 T^{3} + 82320 T^{4} + 873128 T^{5} + 8519727 T^{6} + 75217422 T^{7} + 623444003 T^{8} + 4802217916 T^{9} + 35136436698 T^{10} + 242281577588 T^{11} + 1597747487582 T^{12} + 10006074679634 T^{13} + 60158248780719 T^{14} + 344816413108922 T^{15} + 1900626864033788 T^{16} + 9999675980158738 T^{17} + 50593087224584679 T^{18} + 244038155361593626 T^{19} + 1130056440764484542 T^{20} + 4969473537862528612 T^{21} + 20899971964810634058 T^{22} + 82837665059863752044 T^{23} +$$$$31\!\cdots\!83$$$$T^{24} +$$$$10\!\cdots\!18$$$$T^{25} +$$$$35\!\cdots\!27$$$$T^{26} +$$$$10\!\cdots\!12$$$$T^{27} +$$$$29\!\cdots\!20$$$$T^{28} +$$$$67\!\cdots\!58$$$$T^{29} +$$$$14\!\cdots\!32$$$$T^{30} +$$$$20\!\cdots\!76$$$$T^{31} +$$$$25\!\cdots\!21$$$$T^{32}$$)($$1 + 22 T + 522 T^{2} + 7766 T^{3} + 112692 T^{4} + 1304358 T^{5} + 14474109 T^{6} + 139071516 T^{7} + 1278513361 T^{8} + 10568056376 T^{9} + 83695188240 T^{10} + 607919137474 T^{11} + 4238256585198 T^{12} + 27397319711554 T^{13} + 170225839422745 T^{14} + 986146653004046 T^{15} + 5495004250987864 T^{16} + 28598252937117334 T^{17} + 143159930954528545 T^{18} + 668193230445090506 T^{19} + 2997638355835426638 T^{20} + 12469120008680697626 T^{21} + 49783849820636945040 T^{22} +$$$$18\!\cdots\!84$$$$T^{23} +$$$$63\!\cdots\!21$$$$T^{24} +$$$$20\!\cdots\!04$$$$T^{25} +$$$$60\!\cdots\!09$$$$T^{26} +$$$$15\!\cdots\!82$$$$T^{27} +$$$$39\!\cdots\!72$$$$T^{28} +$$$$79\!\cdots\!74$$$$T^{29} +$$$$15\!\cdots\!82$$$$T^{30} +$$$$18\!\cdots\!78$$$$T^{31} +$$$$25\!\cdots\!21$$$$T^{32}$$)($$1 - 12 T + 296 T^{2} - 2842 T^{3} + 41236 T^{4} - 340889 T^{5} + 3735779 T^{6} - 27481870 T^{7} + 249794460 T^{8} - 1665448573 T^{9} + 13186445822 T^{10} - 80594686502 T^{11} + 572307864911 T^{12} - 3229196488825 T^{13} + 20940762186163 T^{14} - 109497405605747 T^{15} + 655215411792280 T^{16} - 3175424762566663 T^{17} + 17611180998563083 T^{18} - 78756873165952925 T^{19} + 404782479002116991 T^{20} - 1653089623450810798 T^{21} + 7843605496028614862 T^{22} - 28728781883250557057 T^{23} +$$$$12\!\cdots\!60$$$$T^{24} -$$$$39\!\cdots\!30$$$$T^{25} +$$$$15\!\cdots\!79$$$$T^{26} -$$$$41\!\cdots\!81$$$$T^{27} +$$$$14\!\cdots\!76$$$$T^{28} -$$$$29\!\cdots\!38$$$$T^{29} +$$$$88\!\cdots\!76$$$$T^{30} -$$$$10\!\cdots\!88$$$$T^{31} +$$$$25\!\cdots\!21$$$$T^{32}$$)($$1 - 17 T + 417 T^{2} - 5334 T^{3} + 78106 T^{4} - 813038 T^{5} + 9035294 T^{6} - 80040114 T^{7} + 737367708 T^{8} - 5722271524 T^{9} + 45743439048 T^{10} - 317607890130 T^{11} + 2268138488862 T^{12} - 14333282840010 T^{13} + 93413372409634 T^{14} - 545192523955726 T^{15} + 3295455203397803 T^{16} - 17965463101032459 T^{17} + 101749592417859630 T^{18} - 520998429929941311 T^{19} + 2771477826057552323 T^{20} - 13296700466756201414 T^{21} + 66069503451258345154 T^{22} -$$$$29\!\cdots\!90$$$$T^{23} +$$$$13\!\cdots\!02$$$$T^{24} -$$$$54\!\cdots\!70$$$$T^{25} +$$$$22\!\cdots\!28$$$$T^{26} -$$$$83\!\cdots\!56$$$$T^{27} +$$$$31\!\cdots\!08$$$$T^{28} -$$$$97\!\cdots\!06$$$$T^{29} +$$$$31\!\cdots\!54$$$$T^{30} -$$$$83\!\cdots\!82$$$$T^{31} +$$$$23\!\cdots\!86$$$$T^{32} -$$$$46\!\cdots\!66$$$$T^{33} +$$$$10\!\cdots\!57$$$$T^{34} -$$$$12\!\cdots\!53$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 + 2 T + 250 T^{2} + 416 T^{3} + 31743 T^{4} + 40300 T^{5} + 2734376 T^{6} + 2380316 T^{7} + 180736146 T^{8} + 93979076 T^{9} + 9822415154 T^{10} + 2467083804 T^{11} + 457248535436 T^{12} + 31843829608 T^{13} + 18656669806136 T^{14} - 735202286540 T^{15} + 675508971482301 T^{16} - 63722501247098 T^{17} + 21852698540725853 T^{18} - 2340535489419288 T^{19} + 633728257681049737 T^{20} - 53590623548809418 T^{21} + 16474988305481839089 T^{22} - 519994608426297740 T^{23} +$$$$38\!\cdots\!64$$$$T^{24} + 18941452480788688168 T^{25} +$$$$78\!\cdots\!24$$$$T^{26} +$$$$12\!\cdots\!44$$$$T^{27} +$$$$14\!\cdots\!26$$$$T^{28} +$$$$39\!\cdots\!76$$$$T^{29} +$$$$22\!\cdots\!34$$$$T^{30} +$$$$84\!\cdots\!56$$$$T^{31} +$$$$28\!\cdots\!64$$$$T^{32} +$$$$11\!\cdots\!00$$$$T^{33} +$$$$27\!\cdots\!07$$$$T^{34} +$$$$10\!\cdots\!36$$$$T^{35} +$$$$18\!\cdots\!50$$$$T^{36} +$$$$42\!\cdots\!22$$$$T^{37} +$$$$61\!\cdots\!69$$$$T^{38}$$)($$1 + 16 T + 356 T^{2} + 4090 T^{3} + 54774 T^{4} + 503499 T^{5} + 5185947 T^{6} + 40664010 T^{7} + 355565661 T^{8} + 2486474985 T^{9} + 19496647316 T^{10} + 125387959304 T^{11} + 909855586995 T^{12} + 5484428987080 T^{13} + 37452135569274 T^{14} + 213835811773071 T^{15} + 1385703445491510 T^{16} + 7532573989645114 T^{17} + 46469947093723675 T^{18} + 240781898786988183 T^{19} + 1414696368543280646 T^{20} + 6982675064822657307 T^{21} + 39081225505821610675 T^{22} +$$$$18\!\cdots\!46$$$$T^{23} +$$$$98\!\cdots\!10$$$$T^{24} +$$$$43\!\cdots\!79$$$$T^{25} +$$$$22\!\cdots\!54$$$$T^{26} +$$$$94\!\cdots\!20$$$$T^{27} +$$$$45\!\cdots\!95$$$$T^{28} +$$$$18\!\cdots\!76$$$$T^{29} +$$$$82\!\cdots\!16$$$$T^{30} +$$$$30\!\cdots\!65$$$$T^{31} +$$$$12\!\cdots\!01$$$$T^{32} +$$$$41\!\cdots\!90$$$$T^{33} +$$$$15\!\cdots\!07$$$$T^{34} +$$$$43\!\cdots\!51$$$$T^{35} +$$$$13\!\cdots\!54$$$$T^{36} +$$$$29\!\cdots\!10$$$$T^{37} +$$$$74\!\cdots\!16$$$$T^{38} +$$$$97\!\cdots\!04$$$$T^{39} +$$$$17\!\cdots\!01$$$$T^{40}$$)
$31$ ($$1 + T + 31 T^{2}$$)($$1 + 3 T + 31 T^{2}$$)($$1 - 5 T + 31 T^{2}$$)($$1 - 6 T + 31 T^{2}$$)($$1 + 2 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 3 T + 31 T^{2}$$)($$1 - 9 T + 78 T^{2} - 279 T^{3} + 961 T^{4}$$)($$1 + 3 T + 26 T^{2} + 93 T^{3} + 961 T^{4}$$)($$( 1 - 4 T + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$1 + 33 T + 645 T^{2} + 8883 T^{3} + 95284 T^{4} + 826887 T^{5} + 5965621 T^{6} + 36144101 T^{7} + 184934251 T^{8} + 794638407 T^{9} + 2838605644 T^{10} + 8203637043 T^{11} + 18465802395 T^{12} + 29287621473 T^{13} + 27512614111 T^{14}$$)($$1 + 20 T + 316 T^{2} + 3441 T^{3} + 34953 T^{4} + 299945 T^{5} + 2479883 T^{6} + 18060107 T^{7} + 127136571 T^{8} + 809510497 T^{9} + 5025593175 T^{10} + 28399375380 T^{11} + 155793388425 T^{12} + 777939587617 T^{13} + 3787525586661 T^{14} + 16678888076747 T^{15} + 70996944869333 T^{16} + 266202291597545 T^{17} + 961648401021783 T^{18} + 2934798059834481 T^{19} + 8354920602772036 T^{20} + 16392565739616020 T^{21} + 25408476896404831 T^{22}$$)($$1 + 16 T + 287 T^{2} + 2874 T^{3} + 31158 T^{4} + 237487 T^{5} + 2009279 T^{6} + 12848798 T^{7} + 94191169 T^{8} + 534755984 T^{9} + 3587688040 T^{10} + 18769932379 T^{11} + 118295445101 T^{12} + 581867903749 T^{13} + 3447768206440 T^{14} + 15930915519344 T^{15} + 86987522586049 T^{16} + 367850178110498 T^{17} + 1783242508655999 T^{18} + 6533888187379057 T^{19} + 26574378944586678 T^{20} + 75987474089768454 T^{21} + 235233318363489887 T^{22} + 406535630342477296 T^{23} + 787662783788549761 T^{24}$$)($$1 + 7 T + 217 T^{2} + 1437 T^{3} + 23361 T^{4} + 141394 T^{5} + 1651220 T^{6} + 9026082 T^{7} + 86549696 T^{8} + 428736095 T^{9} + 3637767504 T^{10} + 16521213633 T^{11} + 129439998267 T^{12} + 546785963664 T^{13} + 4012639946277 T^{14} + 15876886301313 T^{15} + 108372731711664 T^{16} + 395946787190495 T^{17} + 2477844315788096 T^{18} + 8010681000007842 T^{19} + 45429378672365420 T^{20} + 120593675347932754 T^{21} + 617656013295435231 T^{22} + 1177805848391411037 T^{23} + 5513639486519848327 T^{24} + 5513639486519848327 T^{25} + 24417546297445042591 T^{26}$$)($$1 - 33 T + 772 T^{2} - 13150 T^{3} + 188546 T^{4} - 2298977 T^{5} + 24968647 T^{6} - 242769108 T^{7} + 2159103944 T^{8} - 17604871449 T^{9} + 133190121022 T^{10} - 935380216908 T^{11} + 6142523519475 T^{12} - 37677429544483 T^{13} + 216850565998226 T^{14} - 1168000315878973 T^{15} + 5902965102215475 T^{16} - 27865912041906228 T^{17} + 123003873756358462 T^{18} - 504012523049009799 T^{19} + 1916212697961617864 T^{20} - 6679212786475682988 T^{21} + 21295535243328112327 T^{22} - 60784083236072933567 T^{23} +$$$$15\!\cdots\!46$$$$T^{24} -$$$$33\!\cdots\!50$$$$T^{25} +$$$$60\!\cdots\!92$$$$T^{26} -$$$$80\!\cdots\!03$$$$T^{27} +$$$$75\!\cdots\!21$$$$T^{28}$$)($$1 - 22 T + 474 T^{2} - 7120 T^{3} + 96914 T^{4} - 1130351 T^{5} + 12021443 T^{6} - 115999913 T^{7} + 1034977627 T^{8} - 8563103055 T^{9} + 66223444534 T^{10} - 479776903952 T^{11} + 3271499383577 T^{12} - 21006345812376 T^{13} + 127423644360050 T^{14} - 729507315777320 T^{15} + 3950132975161550 T^{16} - 20187098325693336 T^{17} + 97461238136142407 T^{18} - 443084046114654992 T^{19} + 1895920993304010634 T^{20} - 7599785482094845455 T^{21} + 28474940065169494597 T^{22} - 98935286141635742633 T^{23} +$$$$31\!\cdots\!53$$$$T^{24} -$$$$92\!\cdots\!51$$$$T^{25} +$$$$24\!\cdots\!34$$$$T^{26} -$$$$56\!\cdots\!20$$$$T^{27} +$$$$11\!\cdots\!34$$$$T^{28} -$$$$16\!\cdots\!62$$$$T^{29} +$$$$23\!\cdots\!51$$$$T^{30}$$)($$1 + 42 T + 1103 T^{2} + 21297 T^{3} + 334685 T^{4} + 4460298 T^{5} + 52049742 T^{6} + 541781390 T^{7} + 5109757813 T^{8} + 44140935934 T^{9} + 352708311097 T^{10} + 2626670113330 T^{11} + 18362034468729 T^{12} + 121180561220341 T^{13} + 758925862323514 T^{14} + 4526798708422582 T^{15} + 25783901132438856 T^{16} + 140330759961100042 T^{17} + 729327753692896954 T^{18} + 3610090099315178731 T^{19} + 16957724434595074809 T^{20} + 75199335301711682830 T^{21} +$$$$31\!\cdots\!57$$$$T^{22} +$$$$12\!\cdots\!74$$$$T^{23} +$$$$43\!\cdots\!33$$$$T^{24} +$$$$14\!\cdots\!90$$$$T^{25} +$$$$42\!\cdots\!42$$$$T^{26} +$$$$11\!\cdots\!38$$$$T^{27} +$$$$26\!\cdots\!85$$$$T^{28} +$$$$52\!\cdots\!27$$$$T^{29} +$$$$83\!\cdots\!63$$$$T^{30} +$$$$98\!\cdots\!42$$$$T^{31} +$$$$72\!\cdots\!81$$$$T^{32}$$)($$1 - 26 T + 544 T^{2} - 8205 T^{3} + 108390 T^{4} - 1223221 T^{5} + 12591467 T^{6} - 117150234 T^{7} + 1016820642 T^{8} - 8192223962 T^{9} + 62402913981 T^{10} - 447676790195 T^{11} + 3061424282902 T^{12} - 19881426212383 T^{13} + 123673849035384 T^{14} - 733836777735502 T^{15} + 4180499851186114 T^{16} - 22748940109800562 T^{17} + 118850568923004024 T^{18} - 592287568293101953 T^{19} + 2827289615169937942 T^{20} - 12816606425687974445 T^{21} + 55382815863263864061 T^{22} -$$$$22\!\cdots\!82$$$$T^{23} +$$$$86\!\cdots\!22$$$$T^{24} -$$$$30\!\cdots\!14$$$$T^{25} +$$$$10\!\cdots\!67$$$$T^{26} -$$$$31\!\cdots\!51$$$$T^{27} +$$$$85\!\cdots\!90$$$$T^{28} -$$$$20\!\cdots\!55$$$$T^{29} +$$$$41\!\cdots\!24$$$$T^{30} -$$$$61\!\cdots\!26$$$$T^{31} +$$$$72\!\cdots\!81$$$$T^{32}$$)($$1 + 32 T + 744 T^{2} + 13016 T^{3} + 192404 T^{4} + 2460971 T^{5} + 28126531 T^{6} + 290885953 T^{7} + 2761525270 T^{8} + 24235747979 T^{9} + 198158955757 T^{10} + 1515764606612 T^{11} + 10895848982445 T^{12} + 73780338113067 T^{13} + 471827014000243 T^{14} + 2852663099422432 T^{15} + 16325698746086223 T^{16} + 88432556082095392 T^{17} + 453425760454233523 T^{18} + 2197990052726378997 T^{19} + 10062545348116588845 T^{20} + 43395053803150546412 T^{21} +$$$$17\!\cdots\!17$$$$T^{22} +$$$$66\!\cdots\!69$$$$T^{23} +$$$$23\!\cdots\!70$$$$T^{24} +$$$$76\!\cdots\!63$$$$T^{25} +$$$$23\!\cdots\!31$$$$T^{26} +$$$$62\!\cdots\!01$$$$T^{27} +$$$$15\!\cdots\!44$$$$T^{28} +$$$$31\!\cdots\!56$$$$T^{29} +$$$$56\!\cdots\!24$$$$T^{30} +$$$$75\!\cdots\!32$$$$T^{31} +$$$$72\!\cdots\!81$$$$T^{32}$$)($$1 - 5 T + 345 T^{2} - 1457 T^{3} + 56911 T^{4} - 201348 T^{5} + 6039940 T^{6} - 17777850 T^{7} + 469396428 T^{8} - 1148134577 T^{9} + 28833727003 T^{10} - 59197956874 T^{11} + 1470588580318 T^{12} - 2592870701857 T^{13} + 64165914583760 T^{14} - 100158175269391 T^{15} + 2432313210501904 T^{16} - 3462335844380129 T^{17} + 80591864885992316 T^{18} - 107332411175783999 T^{19} + 2337452995292329744 T^{20} - 2983812199450427281 T^{21} + 59258569602308618960 T^{22} - 74231686846940033407 T^{23} +$$$$13\!\cdots\!58$$$$T^{24} -$$$$16\!\cdots\!14$$$$T^{25} +$$$$24\!\cdots\!23$$$$T^{26} -$$$$30\!\cdots\!67$$$$T^{27} +$$$$38\!\cdots\!28$$$$T^{28} -$$$$45\!\cdots\!50$$$$T^{29} +$$$$47\!\cdots\!40$$$$T^{30} -$$$$49\!\cdots\!68$$$$T^{31} +$$$$43\!\cdots\!31$$$$T^{32} -$$$$34\!\cdots\!07$$$$T^{33} +$$$$25\!\cdots\!45$$$$T^{34} -$$$$11\!\cdots\!55$$$$T^{35} +$$$$69\!\cdots\!41$$$$T^{36}$$)($$1 - 16 T + 444 T^{2} - 5891 T^{3} + 94707 T^{4} - 1068715 T^{5} + 12949771 T^{6} - 127334359 T^{7} + 1280574803 T^{8} - 11191113269 T^{9} + 97892201385 T^{10} - 771667588986 T^{11} + 6026996383307 T^{12} - 43307805557421 T^{13} + 306799204066761 T^{14} - 2023856746847967 T^{15} + 13129737685672700 T^{16} - 79857016141786523 T^{17} + 477117795202829813 T^{18} - 2680713867518439722 T^{19} + 14790651651287724203 T^{20} - 76742592512256848603 T^{21} +$$$$39\!\cdots\!00$$$$T^{22} -$$$$18\!\cdots\!07$$$$T^{23} +$$$$87\!\cdots\!11$$$$T^{24} -$$$$38\!\cdots\!01$$$$T^{25} +$$$$16\!\cdots\!77$$$$T^{26} -$$$$65\!\cdots\!26$$$$T^{27} +$$$$25\!\cdots\!35$$$$T^{28} -$$$$91\!\cdots\!69$$$$T^{29} +$$$$32\!\cdots\!93$$$$T^{30} -$$$$10\!\cdots\!99$$$$T^{31} +$$$$31\!\cdots\!61$$$$T^{32} -$$$$80\!\cdots\!15$$$$T^{33} +$$$$22\!\cdots\!57$$$$T^{34} -$$$$42\!\cdots\!71$$$$T^{35} +$$$$10\!\cdots\!84$$$$T^{36} -$$$$11\!\cdots\!56$$$$T^{37} +$$$$21\!\cdots\!71$$$$T^{38}$$)($$1 - 6 T + 318 T^{2} - 1518 T^{3} + 50004 T^{4} - 189505 T^{5} + 5236681 T^{6} - 15524147 T^{7} + 413848915 T^{8} - 934471947 T^{9} + 26425681433 T^{10} - 43790363774 T^{11} + 1421493925351 T^{12} - 1653825118500 T^{13} + 66176781521440 T^{14} - 51939856393273 T^{15} + 2713695257514807 T^{16} - 1433424696071581 T^{17} + 99105886692289330 T^{18} - 39032877693138405 T^{19} + 3242764231950792144 T^{20} - 1210019208487290555 T^{21} + 95240757111290046130 T^{22} - 42703155120668469571 T^{23} +$$$$25\!\cdots\!47$$$$T^{24} -$$$$14\!\cdots\!23$$$$T^{25} +$$$$58\!\cdots\!40$$$$T^{26} -$$$$45\!\cdots\!00$$$$T^{27} +$$$$12\!\cdots\!91$$$$T^{28} -$$$$11\!\cdots\!54$$$$T^{29} +$$$$21\!\cdots\!33$$$$T^{30} -$$$$23\!\cdots\!57$$$$T^{31} +$$$$32\!\cdots\!15$$$$T^{32} -$$$$37\!\cdots\!77$$$$T^{33} +$$$$39\!\cdots\!01$$$$T^{34} -$$$$44\!\cdots\!55$$$$T^{35} +$$$$36\!\cdots\!24$$$$T^{36} -$$$$34\!\cdots\!98$$$$T^{37} +$$$$22\!\cdots\!38$$$$T^{38} -$$$$13\!\cdots\!26$$$$T^{39} +$$$$67\!\cdots\!01$$$$T^{40}$$)
$37$ ($$1 + 11 T + 37 T^{2}$$)($$1 - T + 37 T^{2}$$)($$1 + 7 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 + T + 37 T^{2}$$)($$1 - T + 37 T^{2}$$)($$1 + 5 T + 76 T^{2} + 185 T^{3} + 1369 T^{4}$$)($$1 + 12 T + 93 T^{2} + 444 T^{3} + 1369 T^{4}$$)($$1 - 6 T + 11 T^{2} - 222 T^{3} + 1369 T^{4}$$)($$( 1 + 7 T + 37 T^{2} )^{2}$$)($$1 + 33 T + 653 T^{2} + 9315 T^{3} + 105122 T^{4} + 971473 T^{5} + 7548399 T^{6} + 49726081 T^{7} + 279290763 T^{8} + 1329946537 T^{9} + 5324744666 T^{10} + 17457809715 T^{11} + 45281603921 T^{12} + 84668971497 T^{13} + 94931877133 T^{14}$$)($$1 + 22 T + 454 T^{2} + 6487 T^{3} + 83295 T^{4} + 901639 T^{5} + 8870009 T^{6} + 77946725 T^{7} + 629881853 T^{8} + 4654816069 T^{9} + 31844505529 T^{10} + 201114366430 T^{11} + 1178246704573 T^{12} + 6372443198461 T^{13} + 31905405500009 T^{14} + 146084712072725 T^{15} + 615081522685613 T^{16} + 2313358993684351 T^{17} + 7907350705793235 T^{18} + 22785454217585527 T^{19} + 59002629866964958 T^{20} + 105788856193192678 T^{21} + 177917621779460413 T^{22}$$)($$1 + 4 T + 181 T^{2} + 510 T^{3} + 15686 T^{4} + 21336 T^{5} + 848235 T^{6} - 767510 T^{7} + 30486755 T^{8} - 151748820 T^{9} + 782416647 T^{10} - 9627135267 T^{11} + 21532144847 T^{12} - 356204004879 T^{13} + 1071128389743 T^{14} - 7686532979460 T^{15} + 57137087237555 T^{16} - 53222180437070 T^{17} + 2176338940538115 T^{18} + 2025466530509688 T^{19} + 55096752714204806 T^{20} + 66280487295489270 T^{21} + 870353771407630669 T^{22} + 711670487117841652 T^{23} + 6582952005840035281 T^{24}$$)($$1 - 7 T + 349 T^{2} - 2305 T^{3} + 57994 T^{4} - 369015 T^{5} + 6147489 T^{6} - 37952961 T^{7} + 468210685 T^{8} - 2784936853 T^{9} + 27265286966 T^{10} - 153098638011 T^{11} + 1255909686356 T^{12} - 6449571361272 T^{13} + 46468658395172 T^{14} - 209592035437059 T^{15} + 1381068580688798 T^{16} - 5219420037355333 T^{17} + 32467581607580545 T^{18} - 97376914337447049 T^{19} + 583592670424469037 T^{20} - 1296157605688657815 T^{21} + 7537001137675695538 T^{22} - 11083786978423141945 T^{23} + 62093250001031684137 T^{24} - 46080664040880246967 T^{25} +$$$$24\!\cdots\!97$$$$T^{26}$$)($$1 + 29 T + 693 T^{2} + 11721 T^{3} + 173826 T^{4} + 2176097 T^{5} + 24709960 T^{6} + 250869276 T^{7} + 2356076231 T^{8} + 20315367197 T^{9} + 163971869231 T^{10} + 1232026880055 T^{11} + 8724657176274 T^{12} + 57914924180169 T^{13} + 363474458224772 T^{14} + 2142852194666253 T^{15} + 11944055674319106 T^{16} + 62405857555425915 T^{17} + 307309682409840191 T^{18} + 1408747949347978529 T^{19} + 6045047007493884479 T^{20} + 23815491285676665708 T^{21} + 86793226807209753160 T^{22} +$$$$28\!\cdots\!69$$$$T^{23} +$$$$83\!\cdots\!74$$$$T^{24} +$$$$20\!\cdots\!73$$$$T^{25} +$$$$45\!\cdots\!33$$$$T^{26} +$$$$70\!\cdots\!13$$$$T^{27} +$$$$90\!\cdots\!89$$$$T^{28}$$)($$1 + 14 T + 288 T^{2} + 2748 T^{3} + 35324 T^{4} + 271284 T^{5} + 2852101 T^{6} + 19453960 T^{7} + 185158539 T^{8} + 1173233154 T^{9} + 10308679891 T^{10} + 60801417791 T^{11} + 494016436494 T^{12} + 2714240787458 T^{13} + 20617596357650 T^{14} + 106455120276378 T^{15} + 762851065233050 T^{16} + 3715795638030002 T^{17} + 25023414557730582 T^{18} + 113951645968598351 T^{19} + 714844655088268687 T^{20} + 3010195287132163986 T^{21} + 17577447674473788687 T^{22} + 68331634797400977160 T^{23} +$$$$37\!\cdots\!77$$$$T^{24} +$$$$13\!\cdots\!16$$$$T^{25} +$$$$62\!\cdots\!12$$$$T^{26} +$$$$18\!\cdots\!88$$$$T^{27} +$$$$70\!\cdots\!36$$$$T^{28} +$$$$12\!\cdots\!46$$$$T^{29} +$$$$33\!\cdots\!93$$$$T^{30}$$)($$1 - 40 T + 1093 T^{2} - 21915 T^{3} + 365384 T^{4} - 5189918 T^{5} + 65263975 T^{6} - 735690707 T^{7} + 7568509040 T^{8} - 71598368286 T^{9} + 629373118507 T^{10} - 5166707785384 T^{11} + 39884876555089 T^{12} - 290489859017229 T^{13} + 2005230244594602 T^{14} - 13140503504719049 T^{15} + 81949219635694490 T^{16} - 486198629674604813 T^{17} + 2745160204850010138 T^{18} - 14714182828799700537 T^{19} + 74750680129362155329 T^{20} -$$$$35\!\cdots\!88$$$$T^{21} +$$$$16\!\cdots\!63$$$$T^{22} -$$$$67\!\cdots\!38$$$$T^{23} +$$$$26\!\cdots\!40$$$$T^{24} -$$$$95\!\cdots\!39$$$$T^{25} +$$$$31\!\cdots\!75$$$$T^{26} -$$$$92\!\cdots\!34$$$$T^{27} +$$$$24\!\cdots\!04$$$$T^{28} -$$$$53\!\cdots\!55$$$$T^{29} +$$$$98\!\cdots\!77$$$$T^{30} -$$$$13\!\cdots\!20$$$$T^{31} +$$$$12\!\cdots\!41$$$$T^{32}$$)($$1 - 30 T + 806 T^{2} - 14673 T^{3} + 242625 T^{4} - 3312475 T^{5} + 41848747 T^{6} - 466357225 T^{7} + 4870920594 T^{8} - 46271902891 T^{9} + 415447002148 T^{10} - 3448551643407 T^{11} + 27200630462421 T^{12} - 200172652127761 T^{13} + 1404240604044519 T^{14} - 9234259977455106 T^{15} + 57972877864016510 T^{16} - 341667619165838922 T^{17} + 1922405386936946511 T^{18} - 10139345348227477933 T^{19} + 50978360788081403781 T^{20} -$$$$23\!\cdots\!99$$$$T^{21} +$$$$10\!\cdots\!32$$$$T^{22} -$$$$43\!\cdots\!03$$$$T^{23} +$$$$17\!\cdots\!74$$$$T^{24} -$$$$60\!\cdots\!25$$$$T^{25} +$$$$20\!\cdots\!03$$$$T^{26} -$$$$58\!\cdots\!75$$$$T^{27} +$$$$15\!\cdots\!25$$$$T^{28} -$$$$35\!\cdots\!81$$$$T^{29} +$$$$72\!\cdots\!34$$$$T^{30} -$$$$10\!\cdots\!90$$$$T^{31} +$$$$12\!\cdots\!41$$$$T^{32}$$)($$1 + 2 T + 264 T^{2} + 460 T^{3} + 36898 T^{4} + 50046 T^{5} + 3563953 T^{6} + 3368000 T^{7} + 264976726 T^{8} + 146604940 T^{9} + 16104532122 T^{10} + 3592350051 T^{11} + 830343504612 T^{12} - 7778681402 T^{13} + 37173486688105 T^{14} - 4566087322258 T^{15} + 1463655345234495 T^{16} - 168945230923546 T^{17} + 50890503276015745 T^{18} - 394013549055506 T^{19} + 1556197412947130532 T^{20} + 249107767465491807 T^{21} + 41319823370004209898 T^{22} + 13917482151170837020 T^{23} +$$$$93\!\cdots\!46$$$$T^{24} +$$$$43\!\cdots\!00$$$$T^{25} +$$$$17\!\cdots\!97$$$$T^{26} +$$$$89\!\cdots\!98$$$$T^{27} +$$$$24\!\cdots\!38$$$$T^{28} +$$$$11\!\cdots\!20$$$$T^{29} +$$$$23\!\cdots\!96$$$$T^{30} +$$$$66\!\cdots\!86$$$$T^{31} +$$$$12\!\cdots\!41$$$$T^{32}$$)($$1 + 15 T + 366 T^{2} + 4166 T^{3} + 63112 T^{4} + 600801 T^{5} + 7118236 T^{6} + 59182921 T^{7} + 595812423 T^{8} + 4428544822 T^{9} + 39581642519 T^{10} + 267508054476 T^{11} + 2185412894544 T^{12} + 13627736681152 T^{13} + 104028964880528 T^{14} + 607397885300872 T^{15} + 4406318113508128 T^{16} + 24433425678421227 T^{17} + 170043359575354066 T^{18} + 904036750101585399 T^{19} + 6032249497392627232 T^{20} + 30766525084145069416 T^{21} +$$$$19\!\cdots\!08$$$$T^{22} +$$$$94\!\cdots\!64$$$$T^{23} +$$$$56\!\cdots\!96$$$$T^{24} +$$$$25\!\cdots\!08$$$$T^{25} +$$$$13\!\cdots\!99$$$$T^{26} +$$$$57\!\cdots\!94$$$$T^{27} +$$$$28\!\cdots\!27$$$$T^{28} +$$$$10\!\cdots\!73$$$$T^{29} +$$$$46\!\cdots\!16$$$$T^{30} +$$$$14\!\cdots\!97$$$$T^{31} +$$$$56\!\cdots\!68$$$$T^{32} +$$$$13\!\cdots\!38$$$$T^{33} +$$$$45\!\cdots\!06$$$$T^{34} +$$$$68\!\cdots\!55$$$$T^{35} +$$$$16\!\cdots\!29$$$$T^{36}$$)($$1 - 56 T + 1919 T^{2} - 48113 T^{3} + 978205 T^{4} - 16860046 T^{5} + 254586879 T^{6} - 3434890242 T^{7} + 42066352834 T^{8} - 472720007895 T^{9} + 4918349057024 T^{10} - 47690421274916 T^{11} + 433348998146773 T^{12} - 3705349253519629 T^{13} + 29916574318889081 T^{14} - 228662300563992558 T^{15} + 1658031228676445269 T^{16} - 11421713005692758978 T^{17} + 74832242387766162423 T^{18} -$$$$46\!\cdots\!78$$$$T^{19} +$$$$27\!\cdots\!51$$$$T^{20} -$$$$15\!\cdots\!82$$$$T^{21} +$$$$83\!\cdots\!57$$$$T^{22} -$$$$42\!\cdots\!38$$$$T^{23} +$$$$20\!\cdots\!17$$$$T^{24} -$$$$95\!\cdots\!61$$$$T^{25} +$$$$41\!\cdots\!09$$$$T^{26} -$$$$16\!\cdots\!36$$$$T^{27} +$$$$63\!\cdots\!48$$$$T^{28} -$$$$22\!\cdots\!55$$$$T^{29} +$$$$74\!\cdots\!42$$$$T^{30} -$$$$22\!\cdots\!02$$$$T^{31} +$$$$62\!\cdots\!63$$$$T^{32} -$$$$15\!\cdots\!94$$$$T^{33} +$$$$32\!\cdots\!65$$$$T^{34} -$$$$59\!\cdots\!33$$$$T^{35} +$$$$87\!\cdots\!23$$$$T^{36} -$$$$94\!\cdots\!24$$$$T^{37} +$$$$62\!\cdots\!73$$$$T^{38}$$)($$1 - 2 T + 436 T^{2} - 636 T^{3} + 94484 T^{4} - 96806 T^{5} + 13573717 T^{6} - 9079400 T^{7} + 1452889835 T^{8} - 545246494 T^{9} + 123414777016 T^{10} - 16711275309 T^{11} + 8652333784042 T^{12} + 463394612292 T^{13} + 514000404908958 T^{14} + 98194267690708 T^{15} + 26349138021430845 T^{16} + 7256885305064918 T^{17} + 1179935948825639157 T^{18} + 361679909566421909 T^{19} + 46488733595387500290 T^{20} + 13382156653957610633 T^{21} +$$$$16\!\cdots\!33$$$$T^{22} +$$$$36\!\cdots\!54$$$$T^{23} +$$$$49\!\cdots\!45$$$$T^{24} +$$$$68\!\cdots\!56$$$$T^{25} +$$$$13\!\cdots\!22$$$$T^{26} +$$$$43\!\cdots\!36$$$$T^{27} +$$$$30\!\cdots\!82$$$$T^{28} -$$$$21\!\cdots\!93$$$$T^{29} +$$$$59\!\cdots\!84$$$$T^{30} -$$$$97\!\cdots\!22$$$$T^{31} +$$$$95\!\cdots\!35$$$$T^{32} -$$$$22\!\cdots\!00$$$$T^{33} +$$$$12\!\cdots\!13$$$$T^{34} -$$$$32\!\cdots\!58$$$$T^{35} +$$$$11\!\cdots\!44$$$$T^{36} -$$$$29\!\cdots\!12$$$$T^{37} +$$$$73\!\cdots\!44$$$$T^{38} -$$$$12\!\cdots\!46$$$$T^{39} +$$$$23\!\cdots\!01$$$$T^{40}$$)
$41$ ($$1 + 6 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 - 3 T + 41 T^{2}$$)($$1 - 10 T + 41 T^{2}$$)($$1 + 6 T + 74 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 - T - 24 T^{2} - 41 T^{3} + 1681 T^{4}$$)($$1 - 6 T + 59 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 + 6 T + 85 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 - 3 T + 170 T^{2} - 50 T^{3} + 11626 T^{4} + 29278 T^{5} + 496448 T^{6} + 2150172 T^{7} + 20354368 T^{8} + 49216318 T^{9} + 801275546 T^{10} - 141288050 T^{11} + 19695554170 T^{12} - 14250312723 T^{13} + 194754273881 T^{14}$$)($$1 + 9 T + 199 T^{2} + 1511 T^{3} + 21975 T^{4} + 155965 T^{5} + 1759117 T^{6} + 11369627 T^{7} + 108763053 T^{8} + 644974505 T^{9} + 5441506152 T^{10} + 29350169344 T^{11} + 223101752232 T^{12} + 1084202142905 T^{13} + 7496058375813 T^{14} + 32127848561147 T^{15} + 203804612734517 T^{16} + 740850007947565 T^{17} + 4279725168534975 T^{18} + 12065222021201831 T^{19} + 65149004944398239 T^{20} + 120803933791371609 T^{21} + 550329031716248441 T^{22}$$)($$1 - 21 T + 397 T^{2} - 4961 T^{3} + 60353 T^{4} - 595870 T^{5} + 5804080 T^{6} - 48840010 T^{7} + 407453481 T^{8} - 3030450751 T^{9} + 22467228151 T^{10} - 150878853149 T^{11} + 1012729360251 T^{12} - 6186032979109 T^{13} + 37767410521831 T^{14} - 208861696209671 T^{15} + 1151366155924041 T^{16} - 5658418015402010 T^{17} + 27569985023103280 T^{18} - 116048229177471470 T^{19} + 481914192353139713 T^{20} - 1624141776528440521 T^{21} + 5328795746130503197 T^{22} - 11556909666041217261 T^{23} + 22563490300366186081 T^{24}$$)($$1 + 21 T + 616 T^{2} + 9402 T^{3} + 160488 T^{4} + 1938936 T^{5} + 24485336 T^{6} + 245110356 T^{7} + 2497863778 T^{8} + 21278259882 T^{9} + 182459787904 T^{10} + 1342887611296 T^{11} + 9902669942613 T^{12} + 63386892075414 T^{13} + 406009467647133 T^{14} + 2257394074588576 T^{15} + 12575311042131584 T^{16} + 60127276922420202 T^{17} + 289393007934587378 T^{18} + 1164299741548619796 T^{19} + 4768623833412309016 T^{20} + 15482258984050955256 T^{21} + 52540871887018012968 T^{22} +$$$$12\!\cdots\!02$$$$T^{23} +$$$$33\!\cdots\!56$$$$T^{24} +$$$$47\!\cdots\!01$$$$T^{25} +$$$$92\!\cdots\!21$$$$T^{26}$$)($$1 - T + 206 T^{2} - 42 T^{3} + 22600 T^{4} + 5720 T^{5} + 1802471 T^{6} + 973585 T^{7} + 116330717 T^{8} + 88412265 T^{9} + 6386509096 T^{10} + 5890073146 T^{11} + 308288137130 T^{12} + 303314192679 T^{13} + 13329630557542 T^{14} + 12435881899839 T^{15} + 518232358515530 T^{16} + 405949731295466 T^{17} + 18046748329622056 T^{18} + 10243109144705265 T^{19} + 552583032180270797 T^{20} + 189609839736433385 T^{21} + 14392596162658957991 T^{22} + 1872624664733456920 T^{23} +$$$$30\!\cdots\!00$$$$T^{24} - 23113819332082434522 T^{25} +$$$$46\!\cdots\!86$$$$T^{26} -$$$$92\!\cdots\!21$$$$T^{27} +$$$$37\!\cdots\!61$$$$T^{28}$$)($$1 + 19 T + 532 T^{2} + 7338 T^{3} + 121645 T^{4} + 1345432 T^{5} + 16855523 T^{6} + 157724050 T^{7} + 1637222589 T^{8} + 13397789210 T^{9} + 120864639297 T^{10} + 884486368766 T^{11} + 7136153432277 T^{12} + 47424413455885 T^{13} + 348181555651272 T^{14} + 2119997251802376 T^{15} + 14275443781702152 T^{16} + 79720439019342685 T^{17} + 491830830705963117 T^{18} + 2499347085890580926 T^{19} + 14002917944185730697 T^{20} + 63640895346445039610 T^{21} +$$$$31\!\cdots\!09$$$$T^{22} +$$$$12\!\cdots\!50$$$$T^{23} +$$$$55\!\cdots\!03$$$$T^{24} +$$$$18\!\cdots\!32$$$$T^{25} +$$$$66\!\cdots\!45$$$$T^{26} +$$$$16\!\cdots\!78$$$$T^{27} +$$$$49\!\cdots\!72$$$$T^{28} +$$$$72\!\cdots\!59$$$$T^{29} +$$$$15\!\cdots\!01$$$$T^{30}$$)($$1 + 9 T + 262 T^{2} + 2416 T^{3} + 37769 T^{4} + 315207 T^{5} + 3782416 T^{6} + 28401838 T^{7} + 290262313 T^{8} + 2011916927 T^{9} + 18444064407 T^{10} + 119441768717 T^{11} + 1012122769428 T^{12} + 6182374690503 T^{13} + 49052876571800 T^{14} + 283552719845861 T^{15} + 2125239007937044 T^{16} + 11625661513680301 T^{17} + 82457885517195800 T^{18} + 426095446044157263 T^{19} + 2860017049061634708 T^{20} + 13838069564272264117 T^{21} + 87611228560967850087 T^{22} +$$$$39\!\cdots\!87$$$$T^{23} +$$$$23\!\cdots\!73$$$$T^{24} +$$$$92\!\cdots\!18$$$$T^{25} +$$$$50\!\cdots\!16$$$$T^{26} +$$$$17\!\cdots\!87$$$$T^{27} +$$$$85\!\cdots\!89$$$$T^{28} +$$$$22\!\cdots\!36$$$$T^{29} +$$$$99\!\cdots\!82$$$$T^{30} +$$$$13\!\cdots\!09$$$$T^{31} +$$$$63\!\cdots\!41$$$$T^{32}$$)($$1 + T + 381 T^{2} + 753 T^{3} + 71193 T^{4} + 206003 T^{5} + 8769091 T^{6} + 32248993 T^{7} + 807996980 T^{8} + 3423817656 T^{9} + 59693127474 T^{10} + 269410101834 T^{11} + 3672268203653 T^{12} + 16586234784178 T^{13} + 191391546657934 T^{14} + 826335588463734 T^{15} + 8497746395094842 T^{16} + 33879759127013094 T^{17} + 321729189931987054 T^{18} + 1143139887560331938 T^{19} + 10376952271422704933 T^{20} + 31212830909510372634 T^{21} +$$$$28\!\cdots\!34$$$$T^{22} +$$$$66\!\cdots\!36$$$$T^{23} +$$$$64\!\cdots\!80$$$$T^{24} +$$$$10\!\cdots\!73$$$$T^{25} +$$$$11\!\cdots\!91$$$$T^{26} +$$$$11\!\cdots\!23$$$$T^{27} +$$$$16\!\cdots\!33$$$$T^{28} +$$$$69\!\cdots\!13$$$$T^{29} +$$$$14\!\cdots\!41$$$$T^{30} +$$$$15\!\cdots\!01$$$$T^{31} +$$$$63\!\cdots\!41$$$$T^{32}$$)($$1 - 45 T + 1354 T^{2} - 29742 T^{3} + 539561 T^{4} - 8306060 T^{5} + 112851209 T^{6} - 1371437510 T^{7} + 15189795372 T^{8} - 154507375963 T^{9} + 1458900626256 T^{10} - 12844913969889 T^{11} + 106153970573282 T^{12} - 825425574095967 T^{13} + 6063417597356300 T^{14} - 42109583127809282 T^{15} + 277097438585419287 T^{16} - 1726492908240180562 T^{17} + 10192604981155940300 T^{18} - 56889155992268141607 T^{19} +$$$$29\!\cdots\!02$$$$T^{20} -$$$$14\!\cdots\!89$$$$T^{21} +$$$$69\!\cdots\!96$$$$T^{22} -$$$$30\!\cdots\!03$$$$T^{23} +$$$$12\!\cdots\!12$$$$T^{24} -$$$$44\!\cdots\!10$$$$T^{25} +$$$$15\!\cdots\!09$$$$T^{26} -$$$$45\!\cdots\!60$$$$T^{27} +$$$$12\!\cdots\!41$$$$T^{28} -$$$$27\!\cdots\!82$$$$T^{29} +$$$$51\!\cdots\!94$$$$T^{30} -$$$$69\!\cdots\!45$$$$T^{31} +$$$$63\!\cdots\!41$$$$T^{32}$$)($$1 - 17 T + 587 T^{2} - 7983 T^{3} + 157437 T^{4} - 1804251 T^{5} + 26303394 T^{6} - 262317360 T^{7} + 3118583347 T^{8} - 27662680979 T^{9} + 282270497714 T^{10} - 2263125901586 T^{11} + 20458023064018 T^{12} - 150120482591273 T^{13} + 1228554873931248 T^{14} - 8330642142077100 T^{15} + 62666398844152637 T^{16} - 395131743262021859 T^{17} + 2758290334846420354 T^{18} - 16200401473742896219 T^{19} +$$$$10\!\cdots\!97$$$$T^{20} -$$$$57\!\cdots\!00$$$$T^{21} +$$$$34\!\cdots\!28$$$$T^{22} -$$$$17\!\cdots\!73$$$$T^{23} +$$$$97\!\cdots\!38$$$$T^{24} -$$$$44\!\cdots\!66$$$$T^{25} +$$$$22\!\cdots\!94$$$$T^{26} -$$$$90\!\cdots\!19$$$$T^{27} +$$$$41\!\cdots\!47$$$$T^{28} -$$$$14\!\cdots\!60$$$$T^{29} +$$$$59\!\cdots\!14$$$$T^{30} -$$$$16\!\cdots\!71$$$$T^{31} +$$$$59\!\cdots\!57$$$$T^{32} -$$$$12\!\cdots\!83$$$$T^{33} +$$$$37\!\cdots\!67$$$$T^{34} -$$$$44\!\cdots\!77$$$$T^{35} +$$$$10\!\cdots\!21$$$$T^{36}$$)($$1 - 7 T + 372 T^{2} - 2494 T^{3} + 72192 T^{4} - 464718 T^{5} + 9659139 T^{6} - 59703885 T^{7} + 994893253 T^{8} - 5895564041 T^{9} + 83515099021 T^{10} - 473396571593 T^{11} + 5907087984900 T^{12} - 31939933276623 T^{13} + 359380353673970 T^{14} - 1847303925885007 T^{15} + 19050148050782657 T^{16} - 92701601847103523 T^{17} + 886536429602488599 T^{18} - 4062791660052265530 T^{19} + 36347993613702032559 T^{20} -$$$$15\!\cdots\!63$$$$T^{21} +$$$$13\!\cdots\!97$$$$T^{22} -$$$$52\!\cdots\!27$$$$T^{23} +$$$$41\!\cdots\!70$$$$T^{24} -$$$$15\!\cdots\!43$$$$T^{25} +$$$$11\!\cdots\!00$$$$T^{26} -$$$$37\!\cdots\!53$$$$T^{27} +$$$$27\!\cdots\!81$$$$T^{28} -$$$$79\!\cdots\!41$$$$T^{29} +$$$$54\!\cdots\!73$$$$T^{30} -$$$$13\!\cdots\!85$$$$T^{31} +$$$$89\!\cdots\!19$$$$T^{32} -$$$$17\!\cdots\!98$$$$T^{33} +$$$$11\!\cdots\!92$$$$T^{34} -$$$$15\!\cdots\!54$$$$T^{35} +$$$$97\!\cdots\!32$$$$T^{36} -$$$$75\!\cdots\!47$$$$T^{37} +$$$$43\!\cdots\!61$$$$T^{38}$$)($$1 + 25 T + 696 T^{2} + 12098 T^{3} + 210607 T^{4} + 2933554 T^{5} + 39929227 T^{6} + 474261550 T^{7} + 5464594445 T^{8} + 57229450190 T^{9} + 580264984256 T^{10} + 5467190547761 T^{11} + 49861714090633 T^{12} + 428109710343371 T^{13} + 3559450256532479 T^{14} + 28082973862518910 T^{15} + 214665825107524323 T^{16} + 1564541885634587045 T^{17} + 11052155258273894274 T^{18} + 74631837884937612416 T^{19} +$$$$48\!\cdots\!02$$$$T^{20} +$$$$30\!\cdots\!56$$$$T^{21} +$$$$18\!\cdots\!94$$$$T^{22} +$$$$10\!\cdots\!45$$$$T^{23} +$$$$60\!\cdots\!03$$$$T^{24} +$$$$32\!\cdots\!10$$$$T^{25} +$$$$16\!\cdots\!39$$$$T^{26} +$$$$83\!\cdots\!51$$$$T^{27} +$$$$39\!\cdots\!93$$$$T^{28} +$$$$17\!\cdots\!21$$$$T^{29} +$$$$77\!\cdots\!56$$$$T^{30} +$$$$31\!\cdots\!90$$$$T^{31} +$$$$12\!\cdots\!45$$$$T^{32} +$$$$43\!\cdots\!50$$$$T^{33} +$$$$15\!\cdots\!47$$$$T^{34} +$$$$45\!\cdots\!54$$$$T^{35} +$$$$13\!\cdots\!87$$$$T^{36} +$$$$31\!\cdots\!38$$$$T^{37} +$$$$74\!\cdots\!16$$$$T^{38} +$$$$10\!\cdots\!25$$$$T^{39} +$$$$18\!\cdots\!01$$$$T^{40}$$)
$43$ ($$1 + 8 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 + 6 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 - 6 T + 78 T^{2} - 258 T^{3} + 1849 T^{4}$$)($$1 - 8 T + 34 T^{2} - 344 T^{3} + 1849 T^{4}$$)($$( 1 + 10 T + 43 T^{2} )^{2}$$)($$( 1 - 2 T + 43 T^{2} )^{2}$$)($$1 + 9 T + 217 T^{2} + 1559 T^{3} + 22058 T^{4} + 131173 T^{5} + 1390533 T^{6} + 6894030 T^{7} + 59792919 T^{8} + 242538877 T^{9} + 1753765406 T^{10} + 5329910759 T^{11} + 31900832131 T^{12} + 56892267441 T^{13} + 271818611107 T^{14}$$)($$1 + 17 T + 261 T^{2} + 2371 T^{3} + 23234 T^{4} + 176729 T^{5} + 1611187 T^{6} + 11859504 T^{7} + 98425636 T^{8} + 660659206 T^{9} + 4960731363 T^{10} + 30775020746 T^{11} + 213311448609 T^{12} + 1221558871894 T^{13} + 7825527041452 T^{14} + 40545284134704 T^{15} + 236858092251841 T^{16} + 1117168170286721 T^{17} + 6315433610460038 T^{18} + 27712722858191971 T^{19} + 131176671715516023 T^{20} + 367395199325832233 T^{21} + 929293739471222707 T^{22}$$)($$1 - 11 T + 433 T^{2} - 3791 T^{3} + 84876 T^{4} - 619672 T^{5} + 10284562 T^{6} - 64446156 T^{7} + 874248113 T^{8} - 4782575521 T^{9} + 55476814996 T^{10} - 267170950199 T^{11} + 2707748351749 T^{12} - 11488350858557 T^{13} + 102576630927604 T^{14} - 380248231948147 T^{15} + 2988880322972513 T^{16} - 9474129050895108 T^{17} + 65012450201949538 T^{18} - 168438382381896904 T^{19} + 992047686761662476 T^{20} - 1905328591852571813 T^{21} + 9357771841652079817 T^{22} - 10222231134183449777 T^{23} + 39959630797262576401 T^{24}$$)($$1 + 9 T + 363 T^{2} + 2829 T^{3} + 62991 T^{4} + 434130 T^{5} + 7053472 T^{6} + 43885133 T^{7} + 580184802 T^{8} + 3304680495 T^{9} + 37503098992 T^{10} + 196157482974 T^{11} + 1966417783053 T^{12} + 9376737802572 T^{13} + 84555964671279 T^{14} + 362695186018926 T^{15} + 2981758891556944 T^{16} + 11298044980986495 T^{17} + 85292064394283286 T^{18} + 277413858146650517 T^{19} + 1917264962522113504 T^{20} + 5074198386514922130 T^{21} + 31658811218513677413 T^{22} + 61138883464281140421 T^{23} +$$$$33\!\cdots\!41$$$$T^{24} +$$$$35\!\cdots\!09$$$$T^{25} +$$$$17\!\cdots\!43$$$$T^{26}$$)($$1 + 25 T + 530 T^{2} + 7932 T^{3} + 110412 T^{4} + 1292969 T^{5} + 14382905 T^{6} + 142501427 T^{7} + 1353730590 T^{8} + 11754987450 T^{9} + 98445954790 T^{10} + 763920391599 T^{11} + 5734234384189 T^{12} + 40147595965818 T^{13} + 272318392470142 T^{14} + 1726346626530174 T^{15} + 10602599376365461 T^{16} + 60737018574861693 T^{17} + 336567128682006790 T^{18} + 1728082402509040350 T^{19} + 8557422529926968910 T^{20} + 38734539967905549689 T^{21} +$$$$16\!\cdots\!05$$$$T^{22} +$$$$64\!\cdots\!67$$$$T^{23} +$$$$23\!\cdots\!88$$$$T^{24} +$$$$73\!\cdots\!24$$$$T^{25} +$$$$21\!\cdots\!30$$$$T^{26} +$$$$42\!\cdots\!75$$$$T^{27} +$$$$73\!\cdots\!49$$$$T^{28}$$)($$1 + T + 330 T^{2} + 38 T^{3} + 53720 T^{4} - 28248 T^{5} + 5826528 T^{6} - 5492086 T^{7} + 478656266 T^{8} - 552517270 T^{9} + 31981624259 T^{10} - 38704211440 T^{11} + 1811181410982 T^{12} - 2134620863615 T^{13} + 88930689853300 T^{14} - 98993796885108 T^{15} + 3824019663691900 T^{16} - 3946913976824135 T^{17} + 144001600442945874 T^{18} - 132321996775283440 T^{19} + 4701568786926618737 T^{20} - 3492662254512356230 T^{21} +$$$$13\!\cdots\!62$$$$T^{22} - 64192601109808565686 T^{23} +$$$$29\!\cdots\!04$$$$T^{24} -$$$$61\!\cdots\!52$$$$T^{25} +$$$$49\!\cdots\!40$$$$T^{26} +$$$$15\!\cdots\!38$$$$T^{27} +$$$$56\!\cdots\!90$$$$T^{28} +$$$$73\!\cdots\!49$$$$T^{29} +$$$$31\!\cdots\!07$$$$T^{30}$$)($$1 - 7 T + 372 T^{2} - 3138 T^{3} + 73315 T^{4} - 666780 T^{5} + 10087481 T^{6} - 91367841 T^{7} + 1064678040 T^{8} - 9159628901 T^{9} + 89637382245 T^{10} - 716798756168 T^{11} + 6144361260517 T^{12} - 45322086179990 T^{13} + 347525991033990 T^{14} - 2355177051473659 T^{15} + 16357027715502558 T^{16} - 101272613213367337 T^{17} + 642575557421847510 T^{18} - 3603423105912464930 T^{19} + 21006348421816780117 T^{20} -$$$$10\!\cdots\!24$$$$T^{21} +$$$$56\!\cdots\!05$$$$T^{22} -$$$$24\!\cdots\!07$$$$T^{23} +$$$$12\!\cdots\!40$$$$T^{24} -$$$$45\!\cdots\!63$$$$T^{25} +$$$$21\!\cdots\!69$$$$T^{26} -$$$$61\!\cdots\!60$$$$T^{27} +$$$$29\!\cdots\!15$$$$T^{28} -$$$$53\!\cdots\!34$$$$T^{29} +$$$$27\!\cdots\!28$$$$T^{30} -$$$$22\!\cdots\!49$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 - 31 T + 852 T^{2} - 15670 T^{3} + 264821 T^{4} - 3665962 T^{5} + 47706251 T^{6} - 544725555 T^{7} + 5919219884 T^{8} - 58255247771 T^{9} + 549520016843 T^{10} - 4775114475230 T^{11} + 39944199949147 T^{12} - 310729232709570 T^{13} + 2332751593885182 T^{14} - 16365338610668583 T^{15} + 110929007559371878 T^{16} - 703709560258749069 T^{17} + 4313257697093701518 T^{18} - 24705149105039781990 T^{19} +$$$$13\!\cdots\!47$$$$T^{20} -$$$$70\!\cdots\!90$$$$T^{21} +$$$$34\!\cdots\!07$$$$T^{22} -$$$$15\!\cdots\!97$$$$T^{23} +$$$$69\!\cdots\!84$$$$T^{24} -$$$$27\!\cdots\!65$$$$T^{25} +$$$$10\!\cdots\!99$$$$T^{26} -$$$$34\!\cdots\!34$$$$T^{27} +$$$$10\!\cdots\!21$$$$T^{28} -$$$$26\!\cdots\!10$$$$T^{29} +$$$$62\!\cdots\!48$$$$T^{30} -$$$$98\!\cdots\!17$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 + 3 T + 319 T^{2} + 1413 T^{3} + 52260 T^{4} + 283684 T^{5} + 5926636 T^{6} + 35363672 T^{7} + 524737548 T^{8} + 3196631298 T^{9} + 38404648775 T^{10} + 228421070856 T^{11} + 2385008618577 T^{12} + 13544694897079 T^{13} + 127279992634462 T^{14} + 681564642539867 T^{15} + 5876893897353148 T^{16} + 29307279629214281 T^{17} + 235340706381120238 T^{18} + 1076898057182060053 T^{19} + 8153869850199666177 T^{20} + 33579825974933237208 T^{21} +$$$$24\!\cdots\!75$$$$T^{22} +$$$$86\!\cdots\!86$$$$T^{23} +$$$$61\!\cdots\!48$$$$T^{24} +$$$$17\!\cdots\!96$$$$T^{25} +$$$$12\!\cdots\!64$$$$T^{26} +$$$$26\!\cdots\!88$$$$T^{27} +$$$$20\!\cdots\!60$$$$T^{28} +$$$$24\!\cdots\!59$$$$T^{29} +$$$$23\!\cdots\!31$$$$T^{30} +$$$$95\!\cdots\!21$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 - T + 388 T^{2} - 878 T^{3} + 73702 T^{4} - 275013 T^{5} + 9240295 T^{6} - 48874735 T^{7} + 876579751 T^{8} - 5864621513 T^{9} + 68610867706 T^{10} - 521103359185 T^{11} + 4672717098109 T^{12} - 36435312822151 T^{13} + 282210282216185 T^{14} - 2100029747349757 T^{15} + 15017594037839229 T^{16} - 103445385887703081 T^{17} + 694702110628981988 T^{18} - 4448151593171232483 T^{19} + 27767531375964734421 T^{20} -$$$$16\!\cdots\!99$$$$T^{21} +$$$$96\!\cdots\!85$$$$T^{22} -$$$$53\!\cdots\!93$$$$T^{23} +$$$$29\!\cdots\!41$$$$T^{24} -$$$$14\!\cdots\!95$$$$T^{25} +$$$$80\!\cdots\!06$$$$T^{26} -$$$$29\!\cdots\!59$$$$T^{27} +$$$$18\!\cdots\!99$$$$T^{28} -$$$$45\!\cdots\!45$$$$T^{29} +$$$$36\!\cdots\!95$$$$T^{30} -$$$$47\!\cdots\!59$$$$T^{31} +$$$$54\!\cdots\!98$$$$T^{32} -$$$$27\!\cdots\!46$$$$T^{33} +$$$$53\!\cdots\!88$$$$T^{34} -$$$$58\!\cdots\!43$$$$T^{35} +$$$$25\!\cdots\!49$$$$T^{36}$$)($$1 - 19 T + 541 T^{2} - 8177 T^{3} + 138902 T^{4} - 1756335 T^{5} + 22810067 T^{6} - 249749424 T^{7} + 2714308406 T^{8} - 26376020952 T^{9} + 251013493425 T^{10} - 2205434613904 T^{11} + 18891895734477 T^{12} - 152330616533600 T^{13} + 1197167503618210 T^{14} - 8968364455463072 T^{15} + 65582001060951154 T^{16} - 460827672059565390 T^{17} + 3166245237871279593 T^{18} - 20989222701232991902 T^{19} +$$$$13\!\cdots\!99$$$$T^{20} -$$$$85\!\cdots\!10$$$$T^{21} +$$$$52\!\cdots\!78$$$$T^{22} -$$$$30\!\cdots\!72$$$$T^{23} +$$$$17\!\cdots\!30$$$$T^{24} -$$$$96\!\cdots\!00$$$$T^{25} +$$$$51\!\cdots\!39$$$$T^{26} -$$$$25\!\cdots\!04$$$$T^{27} +$$$$12\!\cdots\!75$$$$T^{28} -$$$$57\!\cdots\!48$$$$T^{29} +$$$$25\!\cdots\!42$$$$T^{30} -$$$$99\!\cdots\!24$$$$T^{31} +$$$$39\!\cdots\!81$$$$T^{32} -$$$$12\!\cdots\!15$$$$T^{33} +$$$$44\!\cdots\!14$$$$T^{34} -$$$$11\!\cdots\!77$$$$T^{35} +$$$$31\!\cdots\!63$$$$T^{36} -$$$$47\!\cdots\!31$$$$T^{37} +$$$$10\!\cdots\!07$$$$T^{38}$$)($$1 - 13 T + 471 T^{2} - 6283 T^{3} + 120422 T^{4} - 1515822 T^{5} + 21422518 T^{6} - 245586530 T^{7} + 2891592693 T^{8} - 30027599711 T^{9} + 310306876222 T^{10} - 2936062274715 T^{11} + 27307558269017 T^{12} - 237138824626569 T^{13} + 2013092147719312 T^{14} - 16135263794711645 T^{15} + 126104976690593190 T^{16} - 936396434766212447 T^{17} + 6773410299108949813 T^{18} - 46695524115296682981 T^{19} +$$$$31\!\cdots\!58$$$$T^{20} -$$$$20\!\cdots\!83$$$$T^{21} +$$$$12\!\cdots\!37$$$$T^{22} -$$$$74\!\cdots\!29$$$$T^{23} +$$$$43\!\cdots\!90$$$$T^{24} -$$$$23\!\cdots\!35$$$$T^{25} +$$$$12\!\cdots\!88$$$$T^{26} -$$$$64\!\cdots\!83$$$$T^{27} +$$$$31\!\cdots\!17$$$$T^{28} -$$$$14\!\cdots\!45$$$$T^{29} +$$$$67\!\cdots\!78$$$$T^{30} -$$$$27\!\cdots\!77$$$$T^{31} +$$$$11\!\cdots\!93$$$$T^{32} -$$$$42\!\cdots\!90$$$$T^{33} +$$$$15\!\cdots\!82$$$$T^{34} -$$$$48\!\cdots\!54$$$$T^{35} +$$$$16\!\cdots\!22$$$$T^{36} -$$$$36\!\cdots\!69$$$$T^{37} +$$$$11\!\cdots\!79$$$$T^{38} -$$$$14\!\cdots\!91$$$$T^{39} +$$$$46\!\cdots\!01$$$$T^{40}$$)
$47$ ($$1 - 2 T + 47 T^{2}$$)($$1 + 12 T + 47 T^{2}$$)($$1 + 6 T + 47 T^{2}$$)($$1 - 6 T + 47 T^{2}$$)($$1 + 2 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 12 T + 47 T^{2}$$)($$( 1 - 10 T + 47 T^{2} )^{2}$$)($$1 - 18 T + 158 T^{2} - 846 T^{3} + 2209 T^{4}$$)($$1 - 12 T + 122 T^{2} - 564 T^{3} + 2209 T^{4}$$)($$( 1 - 12 T + 47 T^{2} )^{2}$$)($$1 + 11 T + 145 T^{2} + 1339 T^{3} + 14705 T^{4} + 119758 T^{5} + 953008 T^{6} + 6346454 T^{7} + 44791376 T^{8} + 264545422 T^{9} + 1526717215 T^{10} + 6533892859 T^{11} + 33255026015 T^{12} + 118571368619 T^{13} + 506623120463 T^{14}$$)($$1 - 7 T + 348 T^{2} - 2664 T^{3} + 61373 T^{4} - 467056 T^{5} + 7133325 T^{6} - 50680040 T^{7} + 596259485 T^{8} - 3809875568 T^{9} + 37124292907 T^{10} - 208420861194 T^{11} + 1744841766629 T^{12} - 8416015129712 T^{13} + 61905448511155 T^{14} - 247302428267240 T^{15} + 1635992472058275 T^{16} - 5034497194701424 T^{17} + 31092980772175699 T^{18} - 63433267666931304 T^{19} + 389457404639762916 T^{20} - 368193925650810343 T^{21} + 2472159215084012303 T^{22}$$)($$1 - 31 T + 851 T^{2} - 15591 T^{3} + 257616 T^{4} - 3460144 T^{5} + 42762377 T^{6} - 458816246 T^{7} + 4589623268 T^{8} - 41052380290 T^{9} + 345041231405 T^{10} - 2628912170117 T^{11} + 18890968445127 T^{12} - 123558871995499 T^{13} + 762196080173645 T^{14} - 4262181278848670 T^{15} + 22395897458017508 T^{16} - 105227215150583722 T^{17} + 460944869662877033 T^{18} - 1752988950531326672 T^{19} + 6134168424656221776 T^{20} - 17448363206145240297 T^{21} + 44761861532691371699 T^{22} - 76636935667604381393 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 23 T + 607 T^{2} + 9855 T^{3} + 158534 T^{4} + 2026095 T^{5} + 24946377 T^{6} + 265384987 T^{7} + 2704629542 T^{8} + 24695815357 T^{9} + 215886050220 T^{10} + 1720118801318 T^{11} + 13126247577063 T^{12} + 91942347287866 T^{13} + 616933636121961 T^{14} + 3799742432111462 T^{15} + 22413937391991060 T^{16} + 120507700977061117 T^{17} + 620293281242396794 T^{18} + 2860641919956865723 T^{19} + 12638411359986412551 T^{20} + 48243928848960653295 T^{21} +$$$$17\!\cdots\!78$$$$T^{22} +$$$$51\!\cdots\!95$$$$T^{23} +$$$$15\!\cdots\!21$$$$T^{24} +$$$$26\!\cdots\!43$$$$T^{25} +$$$$54\!\cdots\!27$$$$T^{26}$$)($$1 - 9 T + 350 T^{2} - 3582 T^{3} + 68307 T^{4} - 684242 T^{5} + 9374099 T^{6} - 86334288 T^{7} + 965719113 T^{8} - 8092193530 T^{9} + 77594134130 T^{10} - 590988285775 T^{11} + 4991471177695 T^{12} - 34417211240088 T^{13} + 260228788002610 T^{14} - 1617608928284136 T^{15} + 11026159831528255 T^{16} - 61358176794017825 T^{17} + 378634622025612530 T^{18} - 1855904181783204710 T^{19} + 10409694266357883177 T^{20} - 43738946389511335344 T^{21} +$$$$22\!\cdots\!39$$$$T^{22} -$$$$76\!\cdots\!14$$$$T^{23} +$$$$35\!\cdots\!43$$$$T^{24} -$$$$88\!\cdots\!46$$$$T^{25} +$$$$40\!\cdots\!50$$$$T^{26} -$$$$49\!\cdots\!43$$$$T^{27} +$$$$25\!\cdots\!69$$$$T^{28}$$)($$1 + 49 T + 1434 T^{2} + 30746 T^{3} + 537586 T^{4} + 8047024 T^{5} + 106717719 T^{6} + 1278768232 T^{7} + 14052035680 T^{8} + 142912564543 T^{9} + 1355206857946 T^{10} + 12040876058313 T^{11} + 100648277341743 T^{12} + 793498139366530 T^{13} + 5912196812097671 T^{14} + 41665525117345972 T^{15} + 277873250168590537 T^{16} + 1752837389860664770 T^{17} + 10449606098451783489 T^{18} + 58755634125104838153 T^{19} +$$$$31\!\cdots\!22$$$$T^{20} +$$$$15\!\cdots\!47$$$$T^{21} +$$$$71\!\cdots\!40$$$$T^{22} +$$$$30\!\cdots\!52$$$$T^{23} +$$$$11\!\cdots\!73$$$$T^{24} +$$$$42\!\cdots\!76$$$$T^{25} +$$$$13\!\cdots\!58$$$$T^{26} +$$$$35\!\cdots\!86$$$$T^{27} +$$$$78\!\cdots\!18$$$$T^{28} +$$$$12\!\cdots\!81$$$$T^{29} +$$$$12\!\cdots\!43$$$$T^{30}$$)($$1 + 31 T + 941 T^{2} + 18281 T^{3} + 336231 T^{4} + 4931218 T^{5} + 68745838 T^{6} + 824945998 T^{7} + 9479210063 T^{8} + 97272427247 T^{9} + 962214491659 T^{10} + 8677297342675 T^{11} + 75838894223815 T^{12} + 611669521060006 T^{13} + 4799477730874298 T^{14} + 34983489091252572 T^{15} + 248573892822537796 T^{16} + 1644223987288870884 T^{17} + 10602046307501324282 T^{18} + 63505364685013002938 T^{19} +$$$$37\!\cdots\!15$$$$T^{20} +$$$$19\!\cdots\!25$$$$T^{21} +$$$$10\!\cdots\!11$$$$T^{22} +$$$$49\!\cdots\!61$$$$T^{23} +$$$$22\!\cdots\!43$$$$T^{24} +$$$$92\!\cdots\!66$$$$T^{25} +$$$$36\!\cdots\!62$$$$T^{26} +$$$$12\!\cdots\!54$$$$T^{27} +$$$$39\!\cdots\!71$$$$T^{28} +$$$$99\!\cdots\!87$$$$T^{29} +$$$$24\!\cdots\!29$$$$T^{30} +$$$$37\!\cdots\!33$$$$T^{31} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$1 - T + 360 T^{2} - 1350 T^{3} + 63404 T^{4} - 418163 T^{5} + 7649067 T^{6} - 68548326 T^{7} + 747449622 T^{8} - 7437562764 T^{9} + 63784570875 T^{10} - 597692191691 T^{11} + 4745753222012 T^{12} - 38339036949818 T^{13} + 298426805613138 T^{14} - 2072618878066403 T^{15} + 15494086707737218 T^{16} - 97413087269120941 T^{17} + 659224813599421842 T^{18} - 3980473833240954214 T^{19} + 23157761828140738172 T^{20} -$$$$13\!\cdots\!37$$$$T^{21} +$$$$68\!\cdots\!75$$$$T^{22} -$$$$37\!\cdots\!32$$$$T^{23} +$$$$17\!\cdots\!42$$$$T^{24} -$$$$76\!\cdots\!42$$$$T^{25} +$$$$40\!\cdots\!83$$$$T^{26} -$$$$10\!\cdots\!89$$$$T^{27} +$$$$73\!\cdots\!64$$$$T^{28} -$$$$73\!\cdots\!50$$$$T^{29} +$$$$92\!\cdots\!40$$$$T^{30} -$$$$12\!\cdots\!43$$$$T^{31} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$1 - 49 T + 1540 T^{2} - 35932 T^{3} + 690686 T^{4} - 11356182 T^{5} + 164930169 T^{6} - 2151451498 T^{7} + 25587688149 T^{8} - 280001642018 T^{9} + 2842901625207 T^{10} - 26927822341974 T^{11} + 239153197112559 T^{12} - 1997966659820780 T^{13} + 15747902890384486 T^{14} - 117290786155418928 T^{15} + 826596227322674813 T^{16} - 5512666949304689616 T^{17} + 34787117484859329574 T^{18} -$$$$20\!\cdots\!40$$$$T^{19} +$$$$11\!\cdots\!79$$$$T^{20} -$$$$61\!\cdots\!18$$$$T^{21} +$$$$30\!\cdots\!03$$$$T^{22} -$$$$14\!\cdots\!34$$$$T^{23} +$$$$60\!\cdots\!89$$$$T^{24} -$$$$24\!\cdots\!66$$$$T^{25} +$$$$86\!\cdots\!81$$$$T^{26} -$$$$28\!\cdots\!46$$$$T^{27} +$$$$80\!\cdots\!26$$$$T^{28} -$$$$19\!\cdots\!64$$$$T^{29} +$$$$39\!\cdots\!60$$$$T^{30} -$$$$59\!\cdots\!07$$$$T^{31} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$1 - 31 T + 753 T^{2} - 13091 T^{3} + 197274 T^{4} - 2525137 T^{5} + 29473827 T^{6} - 311740727 T^{7} + 3111974218 T^{8} - 29220169105 T^{9} + 264679717261 T^{10} - 2297383543981 T^{11} + 19369688968200 T^{12} - 157133862498639 T^{13} + 1237282175874877 T^{14} - 9385007085387867 T^{15} + 69206387033259215 T^{16} - 493641831656169754 T^{17} + 3436277445562061196 T^{18} - 23201166087839978438 T^{19} +$$$$15\!\cdots\!35$$$$T^{20} -$$$$97\!\cdots\!41$$$$T^{21} +$$$$60\!\cdots\!37$$$$T^{22} -$$$$36\!\cdots\!73$$$$T^{23} +$$$$20\!\cdots\!00$$$$T^{24} -$$$$11\!\cdots\!03$$$$T^{25} +$$$$63\!\cdots\!21$$$$T^{26} -$$$$32\!\cdots\!35$$$$T^{27} +$$$$16\!\cdots\!82$$$$T^{28} -$$$$77\!\cdots\!81$$$$T^{29} +$$$$34\!\cdots\!07$$$$T^{30} -$$$$13\!\cdots\!99$$$$T^{31} +$$$$50\!\cdots\!06$$$$T^{32} -$$$$15\!\cdots\!13$$$$T^{33} +$$$$42\!\cdots\!13$$$$T^{34} -$$$$82\!\cdots\!97$$$$T^{35} +$$$$12\!\cdots\!89$$$$T^{36}$$)($$1 + 25 T + 904 T^{2} + 16894 T^{3} + 361649 T^{4} + 5490414 T^{5} + 88619801 T^{6} + 1143888312 T^{7} + 15210985459 T^{8} + 171652595794 T^{9} + 1965291833203 T^{10} + 19743875550578 T^{11} + 199637602810875 T^{12} + 1807202412082554 T^{13} + 16393786057089957 T^{14} + 134786478179220970 T^{15} + 1107872880178406762 T^{16} + 8312551665909679693 T^{17} + 62279110124776561297 T^{18} +$$$$42\!\cdots\!32$$$$T^{19} +$$$$29\!\cdots\!59$$$$T^{20} +$$$$18\!\cdots\!37$$$$T^{21} +$$$$11\!\cdots\!26$$$$T^{22} +$$$$65\!\cdots\!70$$$$T^{23} +$$$$37\!\cdots\!99$$$$T^{24} +$$$$19\!\cdots\!66$$$$T^{25} +$$$$10\!\cdots\!25$$$$T^{26} +$$$$47\!\cdots\!58$$$$T^{27} +$$$$21\!\cdots\!01$$$$T^{28} +$$$$90\!\cdots\!06$$$$T^{29} +$$$$37\!\cdots\!77$$$$T^{30} +$$$$13\!\cdots\!92$$$$T^{31} +$$$$48\!\cdots\!27$$$$T^{32} +$$$$14\!\cdots\!66$$$$T^{33} +$$$$43\!\cdots\!07$$$$T^{34} +$$$$95\!\cdots\!74$$$$T^{35} +$$$$24\!\cdots\!48$$$$T^{36} +$$$$31\!\cdots\!25$$$$T^{37} +$$$$58\!\cdots\!83$$$$T^{38}$$)($$1 + 19 T + 774 T^{2} + 11872 T^{3} + 273276 T^{4} + 3551724 T^{5} + 60026983 T^{6} + 681902290 T^{7} + 9358794360 T^{8} + 94919407161 T^{9} + 1115094426107 T^{10} + 10251596671240 T^{11} + 106457690519673 T^{12} + 897170926294968 T^{13} + 8415041365773569 T^{14} + 65562559430606980 T^{15} + 563889426336727830 T^{16} + 4086881137017435528 T^{17} + 32568007441163889159 T^{18} +$$$$22\!\cdots\!48$$$$T^{19} +$$$$16\!\cdots\!12$$$$T^{20} +$$$$10\!\cdots\!56$$$$T^{21} +$$$$71\!\cdots\!31$$$$T^{22} +$$$$42\!\cdots\!44$$$$T^{23} +$$$$27\!\cdots\!30$$$$T^{24} +$$$$15\!\cdots\!60$$$$T^{25} +$$$$90\!\cdots\!01$$$$T^{26} +$$$$45\!\cdots\!84$$$$T^{27} +$$$$25\!\cdots\!53$$$$T^{28} +$$$$11\!\cdots\!80$$$$T^{29} +$$$$58\!\cdots\!43$$$$T^{30} +$$$$23\!\cdots\!83$$$$T^{31} +$$$$10\!\cdots\!60$$$$T^{32} +$$$$37\!\cdots\!30$$$$T^{33} +$$$$15\!\cdots\!27$$$$T^{34} +$$$$42\!\cdots\!32$$$$T^{35} +$$$$15\!\cdots\!96$$$$T^{36} +$$$$31\!\cdots\!64$$$$T^{37} +$$$$96\!\cdots\!86$$$$T^{38} +$$$$11\!\cdots\!77$$$$T^{39} +$$$$27\!\cdots\!01$$$$T^{40}$$)
$53$ ($$1 + 3 T + 53 T^{2}$$)($$1 + 3 T + 53 T^{2}$$)($$1 + 9 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 2 T + 53 T^{2}$$)($$1 + 11 T + 53 T^{2}$$)($$1 - 3 T + 53 T^{2}$$)($$1 - 5 T + 74 T^{2} - 265 T^{3} + 2809 T^{4}$$)($$( 1 - 11 T + 53 T^{2} )^{2}$$)($$1 - 18 T + 185 T^{2} - 954 T^{3} + 2809 T^{4}$$)($$1 - 6 T + 91 T^{2} - 318 T^{3} + 2809 T^{4}$$)($$1 + T + 216 T^{2} - 139 T^{3} + 22869 T^{4} - 30467 T^{5} + 1664224 T^{6} - 2175415 T^{7} + 88203872 T^{8} - 85581803 T^{9} + 3404668113 T^{10} - 1096776859 T^{11} + 90330226488 T^{12} + 22164361129 T^{13} + 1174711139837 T^{14}$$)($$1 - 28 T + 760 T^{2} - 13988 T^{3} + 232097 T^{4} - 3194819 T^{5} + 39947629 T^{6} - 438470374 T^{7} + 4419138620 T^{8} - 39984022809 T^{9} + 334085184597 T^{10} - 2528924844716 T^{11} + 17706514783641 T^{12} - 112315120070481 T^{13} + 657908100329740 T^{14} - 3459742155109894 T^{15} + 16705918403836097 T^{16} - 70811122057790651 T^{17} + 272646931422748189 T^{18} - 870888549474117668 T^{19} + 2507820329769621080 T^{20} - 4896849170234365372 T^{21} + 9269035929372191597 T^{22}$$)($$1 - 38 T + 1114 T^{2} - 23200 T^{3} + 413253 T^{4} - 6166493 T^{5} + 82074452 T^{6} - 965485995 T^{7} + 10351010793 T^{8} - 100472784479 T^{9} + 899169946060 T^{10} - 7368541365910 T^{11} + 55963916662751 T^{12} - 390532692393230 T^{13} + 2525768378482540 T^{14} - 14958086734880083 T^{15} + 81674453992961433 T^{16} - 403761891663620535 T^{17} + 1819127793592776308 T^{18} - 7243848020826881641 T^{19} + 25729003841566167333 T^{20} - 76554515329809485600 T^{21} +$$$$19\!\cdots\!86$$$$T^{22} -$$$$35\!\cdots\!86$$$$T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 + 31 T + 936 T^{2} + 18071 T^{3} + 328569 T^{4} + 4749105 T^{5} + 64916194 T^{6} + 760070261 T^{7} + 8473173808 T^{8} + 83734170303 T^{9} + 791809806079 T^{10} + 6750789985461 T^{11} + 55228222405121 T^{12} + 410273915363592 T^{13} + 2927095787471413 T^{14} + 18962969069159949 T^{15} + 117882268499623283 T^{16} + 660702879826585743 T^{17} + 3543443097911247344 T^{18} + 16846471748217284669 T^{19} + 76257776247619820378 T^{20} +$$$$29\!\cdots\!05$$$$T^{21} +$$$$10\!\cdots\!77$$$$T^{22} +$$$$31\!\cdots\!79$$$$T^{23} +$$$$86\!\cdots\!92$$$$T^{24} +$$$$15\!\cdots\!71$$$$T^{25} +$$$$26\!\cdots\!73$$$$T^{26}$$)($$1 - 35 T + 934 T^{2} - 17975 T^{3} + 299033 T^{4} - 4227887 T^{5} + 54144485 T^{6} - 622708390 T^{7} + 6648233679 T^{8} - 65496431709 T^{9} + 608126212712 T^{10} - 5291692221571 T^{11} + 43805743758863 T^{12} - 342748023160961 T^{13} + 2563077085008698 T^{14} - 18165645227530933 T^{15} + 123050334218646167 T^{16} - 787811262870825767 T^{17} + 4798408327005994472 T^{18} - 27390312548286087537 T^{19} +$$$$14\!\cdots\!91$$$$T^{20} -$$$$73\!\cdots\!30$$$$T^{21} +$$$$33\!\cdots\!85$$$$T^{22} -$$$$13\!\cdots\!71$$$$T^{23} +$$$$52\!\cdots\!17$$$$T^{24} -$$$$16\!\cdots\!75$$$$T^{25} +$$$$45\!\cdots\!94$$$$T^{26} -$$$$91\!\cdots\!55$$$$T^{27} +$$$$13\!\cdots\!69$$$$T^{28}$$)($$1 - 28 T + 893 T^{2} - 17122 T^{3} + 331666 T^{4} - 4977591 T^{5} + 73393432 T^{6} - 916167356 T^{7} + 11140949120 T^{8} - 119513436347 T^{9} + 1245525940040 T^{10} - 11699341693109 T^{11} + 106674030249872 T^{12} - 886636387615880 T^{13} + 7152223363507572 T^{14} - 52854190040185918 T^{15} + 379067838265901316 T^{16} - 2490561612813006920 T^{17} + 15881309601510193744 T^{18} - 92313433341984395429 T^{19} +$$$$52\!\cdots\!20$$$$T^{20} -$$$$26\!\cdots\!63$$$$T^{21} +$$$$13\!\cdots\!40$$$$T^{22} -$$$$57\!\cdots\!16$$$$T^{23} +$$$$24\!\cdots\!56$$$$T^{24} -$$$$87\!\cdots\!59$$$$T^{25} +$$$$30\!\cdots\!02$$$$T^{26} -$$$$84\!\cdots\!02$$$$T^{27} +$$$$23\!\cdots\!89$$$$T^{28} -$$$$38\!\cdots\!32$$$$T^{29} +$$$$73\!\cdots\!57$$$$T^{30}$$)($$1 + 66 T + 2621 T^{2} + 76058 T^{3} + 1781762 T^{4} + 35276871 T^{5} + 609041687 T^{6} + 9347868667 T^{7} + 129408562699 T^{8} + 1632151424402 T^{9} + 18901860842316 T^{10} + 202148349366060 T^{11} + 2005406612147776 T^{12} + 18514212309862079 T^{13} + 159456108398381176 T^{14} + 1283208801034658221 T^{15} + 9658332823518811780 T^{16} + 68010066454836885713 T^{17} +$$$$44\!\cdots\!84$$$$T^{18} +$$$$27\!\cdots\!83$$$$T^{19} +$$$$15\!\cdots\!56$$$$T^{20} +$$$$84\!\cdots\!80$$$$T^{21} +$$$$41\!\cdots\!64$$$$T^{22} +$$$$19\!\cdots\!74$$$$T^{23} +$$$$80\!\cdots\!39$$$$T^{24} +$$$$30\!\cdots\!11$$$$T^{25} +$$$$10\!\cdots\!63$$$$T^{26} +$$$$32\!\cdots\!87$$$$T^{27} +$$$$87\!\cdots\!42$$$$T^{28} +$$$$19\!\cdots\!34$$$$T^{29} +$$$$36\!\cdots\!49$$$$T^{30} +$$$$48\!\cdots\!62$$$$T^{31} +$$$$38\!\cdots\!21$$$$T^{32}$$)($$1 + 24 T + 623 T^{2} + 9286 T^{3} + 145196 T^{4} + 1667275 T^{5} + 20422321 T^{6} + 202557693 T^{7} + 2163294243 T^{8} + 19651949700 T^{9} + 190486009842 T^{10} + 1611744454580 T^{11} + 14312697141274 T^{12} + 112880703254671 T^{13} + 924871830380006 T^{14} + 6823886144051675 T^{15} + 52193981804810860 T^{16} + 361665965634738775 T^{17} + 2597964971537436854 T^{18} + 16805340458445654467 T^{19} +$$$$11\!\cdots\!94$$$$T^{20} +$$$$67\!\cdots\!40$$$$T^{21} +$$$$42\!\cdots\!18$$$$T^{22} +$$$$23\!\cdots\!00$$$$T^{23} +$$$$13\!\cdots\!23$$$$T^{24} +$$$$66\!\cdots\!69$$$$T^{25} +$$$$35\!\cdots\!29$$$$T^{26} +$$$$15\!\cdots\!75$$$$T^{27} +$$$$71\!\cdots\!36$$$$T^{28} +$$$$24\!\cdots\!78$$$$T^{29} +$$$$85\!\cdots\!87$$$$T^{30} +$$$$17\!\cdots\!68$$$$T^{31} +$$$$38\!\cdots\!21$$$$T^{32}$$)($$1 + 16 T + 448 T^{2} + 5762 T^{3} + 91393 T^{4} + 983901 T^{5} + 11466518 T^{6} + 104957901 T^{7} + 986290946 T^{8} + 7672516319 T^{9} + 60304654022 T^{10} + 392902225816 T^{11} + 2604421123952 T^{12} + 13876036558043 T^{13} + 79983593725448 T^{14} + 378455027503734 T^{15} + 2705248289657184 T^{16} + 20058116457697902 T^{17} + 224673914774783432 T^{18} + 2065822694651767711 T^{19} + 20550135394541900912 T^{20} +$$$$16\!\cdots\!88$$$$T^{21} +$$$$13\!\cdots\!38$$$$T^{22} +$$$$90\!\cdots\!03$$$$T^{23} +$$$$61\!\cdots\!06$$$$T^{24} +$$$$34\!\cdots\!33$$$$T^{25} +$$$$20\!\cdots\!82$$$$T^{26} +$$$$91\!\cdots\!97$$$$T^{27} +$$$$44\!\cdots\!13$$$$T^{28} +$$$$15\!\cdots\!26$$$$T^{29} +$$$$61\!\cdots\!12$$$$T^{30} +$$$$11\!\cdots\!12$$$$T^{31} +$$$$38\!\cdots\!21$$$$T^{32}$$)($$1 - 35 T + 1002 T^{2} - 20303 T^{3} + 359179 T^{4} - 5356293 T^{5} + 72450797 T^{6} - 876498168 T^{7} + 9860866190 T^{8} - 102370151648 T^{9} + 1007118215698 T^{10} - 9336961305420 T^{11} + 83269959064210 T^{12} - 710236502930910 T^{13} + 5888264586633139 T^{14} - 47091839467003009 T^{15} + 367936393518839916 T^{16} - 2782388009045035942 T^{17} + 20583240410282150440 T^{18} -$$$$14\!\cdots\!26$$$$T^{19} +$$$$10\!\cdots\!44$$$$T^{20} -$$$$70\!\cdots\!93$$$$T^{21} +$$$$46\!\cdots\!59$$$$T^{22} -$$$$29\!\cdots\!30$$$$T^{23} +$$$$18\!\cdots\!90$$$$T^{24} -$$$$10\!\cdots\!40$$$$T^{25} +$$$$62\!\cdots\!78$$$$T^{26} -$$$$33\!\cdots\!84$$$$T^{27} +$$$$17\!\cdots\!10$$$$T^{28} -$$$$81\!\cdots\!96$$$$T^{29} +$$$$35\!\cdots\!77$$$$T^{30} -$$$$13\!\cdots\!89$$$$T^{31} +$$$$49\!\cdots\!51$$$$T^{32} -$$$$14\!\cdots\!71$$$$T^{33} +$$$$38\!\cdots\!42$$$$T^{34} -$$$$71\!\cdots\!55$$$$T^{35} +$$$$10\!\cdots\!89$$$$T^{36}$$)($$1 + 18 T + 729 T^{2} + 10786 T^{3} + 248005 T^{4} + 3156553 T^{5} + 53632959 T^{6} + 604817569 T^{7} + 8403382051 T^{8} + 85661456697 T^{9} + 1025414824379 T^{10} + 9578389113218 T^{11} + 101873882940499 T^{12} + 879848025198707 T^{13} + 8477677851613975 T^{14} + 68061668751127647 T^{15} + 601679391573782590 T^{16} + 4501409880480265273 T^{17} + 36809960564576726564 T^{18} +$$$$25\!\cdots\!92$$$$T^{19} +$$$$19\!\cdots\!92$$$$T^{20} +$$$$12\!\cdots\!57$$$$T^{21} +$$$$89\!\cdots\!30$$$$T^{22} +$$$$53\!\cdots\!07$$$$T^{23} +$$$$35\!\cdots\!75$$$$T^{24} +$$$$19\!\cdots\!03$$$$T^{25} +$$$$11\!\cdots\!63$$$$T^{26} +$$$$59\!\cdots\!98$$$$T^{27} +$$$$33\!\cdots\!07$$$$T^{28} +$$$$14\!\cdots\!53$$$$T^{29} +$$$$77\!\cdots\!47$$$$T^{30} +$$$$29\!\cdots\!29$$$$T^{31} +$$$$13\!\cdots\!07$$$$T^{32} +$$$$43\!\cdots\!57$$$$T^{33} +$$$$18\!\cdots\!85$$$$T^{34} +$$$$41\!\cdots\!06$$$$T^{35} +$$$$14\!\cdots\!77$$$$T^{36} +$$$$19\!\cdots\!02$$$$T^{37} +$$$$57\!\cdots\!17$$$$T^{38}$$)($$1 + 24 T + 752 T^{2} + 12714 T^{3} + 241627 T^{4} + 3275489 T^{5} + 47980334 T^{6} + 556894589 T^{7} + 6886482945 T^{8} + 71132417785 T^{9} + 778084195202 T^{10} + 7330484721748 T^{11} + 72925359990441 T^{12} + 637044558919314 T^{13} + 5866379765742918 T^{14} + 48032253020185635 T^{15} + 413966785474461514 T^{16} + 3196625429282140999 T^{17} + 25947703842724984442 T^{18} +$$$$18\!\cdots\!27$$$$T^{19} +$$$$14\!\cdots\!16$$$$T^{20} +$$$$10\!\cdots\!31$$$$T^{21} +$$$$72\!\cdots\!78$$$$T^{22} +$$$$47\!\cdots\!23$$$$T^{23} +$$$$32\!\cdots\!34$$$$T^{24} +$$$$20\!\cdots\!55$$$$T^{25} +$$$$13\!\cdots\!22$$$$T^{26} +$$$$74\!\cdots\!18$$$$T^{27} +$$$$45\!\cdots\!01$$$$T^{28} +$$$$24\!\cdots\!84$$$$T^{29} +$$$$13\!\cdots\!98$$$$T^{30} +$$$$65\!\cdots\!45$$$$T^{31} +$$$$33\!\cdots\!45$$$$T^{32} +$$$$14\!\cdots\!97$$$$T^{33} +$$$$66\!\cdots\!46$$$$T^{34} +$$$$23\!\cdots\!73$$$$T^{35} +$$$$93\!\cdots\!67$$$$T^{36} +$$$$26\!\cdots\!82$$$$T^{37} +$$$$81\!\cdots\!28$$$$T^{38} +$$$$13\!\cdots\!08$$$$T^{39} +$$$$30\!\cdots\!01$$$$T^{40}$$)
$59$ ($$1 - 3 T + 59 T^{2}$$)($$1 + 3 T + 59 T^{2}$$)($$1 - 3 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 + 4 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 - 3 T + 59 T^{2}$$)($$1 - 5 T + 86 T^{2} - 295 T^{3} + 3481 T^{4}$$)($$1 - 13 T + 156 T^{2} - 767 T^{3} + 3481 T^{4}$$)($$1 + 68 T^{2} + 3481 T^{4}$$)($$1 + 112 T^{2} + 3481 T^{4}$$)($$1 - 30 T + 570 T^{2} - 7389 T^{3} + 75460 T^{4} - 617301 T^{5} + 4593588 T^{6} - 33613111 T^{7} + 271021692 T^{8} - 2148824781 T^{9} + 15497899340 T^{10} - 89535180429 T^{11} + 407506850430 T^{12} - 1265416009230 T^{13} + 2488651484819 T^{14}$$)($$1 + 35 T + 929 T^{2} + 17931 T^{3} + 295556 T^{4} + 4135295 T^{5} + 51799617 T^{6} + 579088080 T^{7} + 5930670234 T^{8} + 55413165022 T^{9} + 479604963105 T^{10} + 3821238360890 T^{11} + 28296692823195 T^{12} + 192893227441582 T^{13} + 1218035121988686 T^{14} + 7017019316156880 T^{15} + 37032804872193483 T^{16} + 174428949862959095 T^{17} + 735535878247164364 T^{18} + 2632816576683079851 T^{19} + 8047923115530438331 T^{20} + 17889086365522449035 T^{21} + 30155888444737842659 T^{22}$$)($$1 - 15 T + 557 T^{2} - 7228 T^{3} + 148191 T^{4} - 1667699 T^{5} + 24849493 T^{6} - 244376286 T^{7} + 2931747227 T^{8} - 25366461556 T^{9} + 257317271117 T^{10} - 1963795581714 T^{11} + 17280433060643 T^{12} - 115863939321126 T^{13} + 895721420758277 T^{14} - 5209738507909724 T^{15} + 35525039510307947 T^{16} - 174710544960773514 T^{17} + 1048164875448294013 T^{18} - 4150321592581161481 T^{19} + 21758949379021933311 T^{20} - 62616133777237899092 T^{21} +$$$$28\!\cdots\!57$$$$T^{22} -$$$$45\!\cdots\!85$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 + 28 T + 748 T^{2} + 12353 T^{3} + 200007 T^{4} + 2482731 T^{5} + 31037042 T^{6} + 320236588 T^{7} + 3396643521 T^{8} + 30749512300 T^{9} + 290422351830 T^{10} + 2376472711159 T^{11} + 20434393717531 T^{12} + 152974888166578 T^{13} + 1205629229334329 T^{14} + 8272501507544479 T^{15} + 59646652196493570 T^{16} + 372602941113040300 T^{17} + 2428342988203816779 T^{18} + 13507750173213056908 T^{19} + 77240380657689665398 T^{20} +$$$$36\!\cdots\!51$$$$T^{21} +$$$$17\!\cdots\!73$$$$T^{22} +$$$$63\!\cdots\!53$$$$T^{23} +$$$$22\!\cdots\!32$$$$T^{24} +$$$$49\!\cdots\!68$$$$T^{25} +$$$$10\!\cdots\!79$$$$T^{26}$$)($$1 + 10 T + 389 T^{2} + 3033 T^{3} + 74371 T^{4} + 531008 T^{5} + 10011285 T^{6} + 70337571 T^{7} + 1054894651 T^{8} + 7383068244 T^{9} + 90904277275 T^{10} + 631193665181 T^{11} + 6652047058913 T^{12} + 44814617366759 T^{13} + 421301398427094 T^{14} + 2644062424638781 T^{15} + 23155775812076153 T^{16} + 129633923761208599 T^{17} + 1101519944185271275 T^{18} + 5278334888810860956 T^{19} + 44496019314216454291 T^{20} +$$$$17\!\cdots\!49$$$$T^{21} +$$$$14\!\cdots\!85$$$$T^{22} +$$$$46\!\cdots\!12$$$$T^{23} +$$$$38\!\cdots\!71$$$$T^{24} +$$$$91\!\cdots\!47$$$$T^{25} +$$$$69\!\cdots\!09$$$$T^{26} +$$$$10\!\cdots\!90$$$$T^{27} +$$$$61\!\cdots\!61$$$$T^{28}$$)($$1 + 43 T + 1156 T^{2} + 22561 T^{3} + 359863 T^{4} + 4876122 T^{5} + 58319530 T^{6} + 625342312 T^{7} + 6122995252 T^{8} + 55250448075 T^{9} + 465868338618 T^{10} + 3708053643183 T^{11} + 28343891411622 T^{12} + 211583215348728 T^{13} + 1579066430020326 T^{14} + 11974711862120544 T^{15} + 93164919371199234 T^{16} + 736521172628922168 T^{17} + 5821240074227514738 T^{18} + 44931824601813600063 T^{19} +$$$$33\!\cdots\!82$$$$T^{20} +$$$$23\!\cdots\!75$$$$T^{21} +$$$$15\!\cdots\!88$$$$T^{22} +$$$$91\!\cdots\!52$$$$T^{23} +$$$$50\!\cdots\!70$$$$T^{24} +$$$$24\!\cdots\!22$$$$T^{25} +$$$$10\!\cdots\!17$$$$T^{26} +$$$$40\!\cdots\!41$$$$T^{27} +$$$$12\!\cdots\!24$$$$T^{28} +$$$$26\!\cdots\!23$$$$T^{29} +$$$$36\!\cdots\!99$$$$T^{30}$$)($$1 - 7 T + 442 T^{2} - 3508 T^{3} + 105593 T^{4} - 856382 T^{5} + 17639389 T^{6} - 139554059 T^{7} + 2261197320 T^{8} - 17115674831 T^{9} + 234152631353 T^{10} - 1678592886254 T^{11} + 20227940459783 T^{12} - 136519444242156 T^{13} + 1488182686904536 T^{14} - 9408447183719123 T^{15} + 94379018439678286 T^{16} - 555098383839428257 T^{17} + 5180363933114689816 T^{18} - 28038226939009757124 T^{19} +$$$$24\!\cdots\!63$$$$T^{20} -$$$$12\!\cdots\!46$$$$T^{21} +$$$$98\!\cdots\!73$$$$T^{22} -$$$$42\!\cdots\!89$$$$T^{23} +$$$$33\!\cdots\!20$$$$T^{24} -$$$$12\!\cdots\!01$$$$T^{25} +$$$$90\!\cdots\!89$$$$T^{26} -$$$$25\!\cdots\!38$$$$T^{27} +$$$$18\!\cdots\!33$$$$T^{28} -$$$$36\!\cdots\!32$$$$T^{29} +$$$$27\!\cdots\!62$$$$T^{30} -$$$$25\!\cdots\!93$$$$T^{31} +$$$$21\!\cdots\!41$$$$T^{32}$$)($$1 - 17 T + 846 T^{2} - 11802 T^{3} + 329143 T^{4} - 3917144 T^{5} + 79697417 T^{6} - 829139959 T^{7} + 13603939474 T^{8} - 125686534583 T^{9} + 1749118455509 T^{10} - 14494136574176 T^{11} + 176087374935777 T^{12} - 1316023362978522 T^{13} + 14200806947115068 T^{14} - 95904511241320065 T^{15} + 928657148255566346 T^{16} - 5658366163237883835 T^{17} + 49433008982907551708 T^{18} -$$$$27\!\cdots\!38$$$$T^{19} +$$$$21\!\cdots\!97$$$$T^{20} -$$$$10\!\cdots\!24$$$$T^{21} +$$$$73\!\cdots\!69$$$$T^{22} -$$$$31\!\cdots\!77$$$$T^{23} +$$$$19\!\cdots\!54$$$$T^{24} -$$$$71\!\cdots\!01$$$$T^{25} +$$$$40\!\cdots\!17$$$$T^{26} -$$$$11\!\cdots\!96$$$$T^{27} +$$$$58\!\cdots\!83$$$$T^{28} -$$$$12\!\cdots\!58$$$$T^{29} +$$$$52\!\cdots\!06$$$$T^{30} -$$$$62\!\cdots\!83$$$$T^{31} +$$$$21\!\cdots\!41$$$$T^{32}$$)($$1 - 35 T + 1021 T^{2} - 21516 T^{3} + 399391 T^{4} - 6359827 T^{5} + 92325471 T^{6} - 1214213044 T^{7} + 14857011894 T^{8} - 168822031893 T^{9} + 1807192395472 T^{10} - 18205365400176 T^{11} + 174114971113366 T^{12} - 1578868728093535 T^{13} + 13654772717571364 T^{14} - 112408551214928210 T^{15} + 884444434014014104 T^{16} - 6632104521680764390 T^{17} + 47532263829865918084 T^{18} -$$$$32\!\cdots\!65$$$$T^{19} +$$$$21\!\cdots\!26$$$$T^{20} -$$$$13\!\cdots\!24$$$$T^{21} +$$$$76\!\cdots\!52$$$$T^{22} -$$$$42\!\cdots\!67$$$$T^{23} +$$$$21\!\cdots\!74$$$$T^{24} -$$$$10\!\cdots\!16$$$$T^{25} +$$$$47\!\cdots\!71$$$$T^{26} -$$$$19\!\cdots\!93$$$$T^{27} +$$$$71\!\cdots\!71$$$$T^{28} -$$$$22\!\cdots\!64$$$$T^{29} +$$$$63\!\cdots\!81$$$$T^{30} -$$$$12\!\cdots\!65$$$$T^{31} +$$$$21\!\cdots\!41$$$$T^{32}$$)($$1 - 46 T + 1709 T^{2} - 44939 T^{3} + 1028319 T^{4} - 19836014 T^{5} + 345643777 T^{6} - 5379928797 T^{7} + 77278229780 T^{8} - 1019115860932 T^{9} + 12568554567858 T^{10} - 144505310405158 T^{11} + 1567113639682192 T^{12} - 15990154268072311 T^{13} + 154748085150649455 T^{14} - 1416913606523974460 T^{15} + 12346169576116035044 T^{16} -$$$$10\!\cdots\!35$$$$T^{17} +$$$$80\!\cdots\!90$$$$T^{18} -$$$$60\!\cdots\!65$$$$T^{19} +$$$$42\!\cdots\!64$$$$T^{20} -$$$$29\!\cdots\!40$$$$T^{21} +$$$$18\!\cdots\!55$$$$T^{22} -$$$$11\!\cdots\!89$$$$T^{23} +$$$$66\!\cdots\!72$$$$T^{24} -$$$$35\!\cdots\!02$$$$T^{25} +$$$$18\!\cdots\!18$$$$T^{26} -$$$$88\!\cdots\!48$$$$T^{27} +$$$$39\!\cdots\!80$$$$T^{28} -$$$$16\!\cdots\!23$$$$T^{29} +$$$$61\!\cdots\!37$$$$T^{30} -$$$$20\!\cdots\!06$$$$T^{31} +$$$$63\!\cdots\!59$$$$T^{32} -$$$$16\!\cdots\!61$$$$T^{33} +$$$$36\!\cdots\!69$$$$T^{34} -$$$$58\!\cdots\!74$$$$T^{35} +$$$$75\!\cdots\!21$$$$T^{36}$$)($$1 + 11 T + 625 T^{2} + 6723 T^{3} + 195828 T^{4} + 2071013 T^{5} + 41248883 T^{6} + 425750946 T^{7} + 6571435112 T^{8} + 65378594338 T^{9} + 841495712425 T^{10} + 7973031579512 T^{11} + 89681549643081 T^{12} + 802152520437678 T^{13} + 8123426402651024 T^{14} + 68246189918775774 T^{15} + 633654102053130070 T^{16} + 4987112049848041672 T^{17} + 42904033250390068767 T^{18} +$$$$31\!\cdots\!46$$$$T^{19} +$$$$25\!\cdots\!53$$$$T^{20} +$$$$17\!\cdots\!32$$$$T^{21} +$$$$13\!\cdots\!30$$$$T^{22} +$$$$82\!\cdots\!14$$$$T^{23} +$$$$58\!\cdots\!76$$$$T^{24} +$$$$33\!\cdots\!98$$$$T^{25} +$$$$22\!\cdots\!39$$$$T^{26} +$$$$11\!\cdots\!52$$$$T^{27} +$$$$72\!\cdots\!75$$$$T^{28} +$$$$33\!\cdots\!38$$$$T^{29} +$$$$19\!\cdots\!08$$$$T^{30} +$$$$75\!\cdots\!26$$$$T^{31} +$$$$43\!\cdots\!57$$$$T^{32} +$$$$12\!\cdots\!93$$$$T^{33} +$$$$71\!\cdots\!72$$$$T^{34} +$$$$14\!\cdots\!43$$$$T^{35} +$$$$79\!\cdots\!75$$$$T^{36} +$$$$82\!\cdots\!31$$$$T^{37} +$$$$44\!\cdots\!39$$$$T^{38}$$)($$1 + 23 T + 835 T^{2} + 14786 T^{3} + 314559 T^{4} + 4632805 T^{5} + 74385661 T^{6} + 955001616 T^{7} + 12748655041 T^{8} + 147128015000 T^{9} + 1716324613351 T^{10} + 18163752339784 T^{11} + 190575665724983 T^{12} + 1872219326295796 T^{13} + 17979789322374275 T^{14} + 165115335732762556 T^{15} + 1467551308043410298 T^{16} + 12644429046237961845 T^{17} +$$$$10\!\cdots\!46$$$$T^{18} +$$$$84\!\cdots\!39$$$$T^{19} +$$$$65\!\cdots\!12$$$$T^{20} +$$$$50\!\cdots\!01$$$$T^{21} +$$$$36\!\cdots\!26$$$$T^{22} +$$$$25\!\cdots\!55$$$$T^{23} +$$$$17\!\cdots\!78$$$$T^{24} +$$$$11\!\cdots\!44$$$$T^{25} +$$$$75\!\cdots\!75$$$$T^{26} +$$$$46\!\cdots\!24$$$$T^{27} +$$$$27\!\cdots\!43$$$$T^{28} +$$$$15\!\cdots\!76$$$$T^{29} +$$$$87\!\cdots\!51$$$$T^{30} +$$$$44\!\cdots\!00$$$$T^{31} +$$$$22\!\cdots\!21$$$$T^{32} +$$$$10\!\cdots\!64$$$$T^{33} +$$$$46\!\cdots\!21$$$$T^{34} +$$$$16\!\cdots\!95$$$$T^{35} +$$$$67\!\cdots\!19$$$$T^{36} +$$$$18\!\cdots\!34$$$$T^{37} +$$$$62\!\cdots\!35$$$$T^{38} +$$$$10\!\cdots\!97$$$$T^{39} +$$$$26\!\cdots\!01$$$$T^{40}$$)
$61$ ($$1 + T + 61 T^{2}$$)($$1 + 3 T + 61 T^{2}$$)($$1 + 7 T + 61 T^{2}$$)($$1 + 6 T + 61 T^{2}$$)($$1 - 10 T + 61 T^{2}$$)($$1 + 10 T + 61 T^{2}$$)($$1 + 3 T + 61 T^{2}$$)($$1 + 13 T + 160 T^{2} + 793 T^{3} + 3721 T^{4}$$)($$1 + 15 T + 174 T^{2} + 915 T^{3} + 3721 T^{4}$$)($$1 + 16 T + 168 T^{2} + 976 T^{3} + 3721 T^{4}$$)($$1 - 4 T + 120 T^{2} - 244 T^{3} + 3721 T^{4}$$)($$1 + 19 T + 427 T^{2} + 5649 T^{3} + 75542 T^{4} + 765723 T^{5} + 7510227 T^{6} + 59966461 T^{7} + 458123847 T^{8} + 2849255283 T^{9} + 17146598702 T^{10} + 78215155809 T^{11} + 360642620527 T^{12} + 978887112859 T^{13} + 3142742836021 T^{14}$$)($$1 + 6 T + 578 T^{2} + 2995 T^{3} + 155515 T^{4} + 699413 T^{5} + 25807191 T^{6} + 100980199 T^{7} + 2944011895 T^{8} + 10017465515 T^{9} + 242968967593 T^{10} + 715340296626 T^{11} + 14821107023173 T^{12} + 37274989181315 T^{13} + 668234763938995 T^{14} + 1398155779502359 T^{15} + 21796658057800491 T^{16} + 36034019592950093 T^{17} + 488743652143805815 T^{18} + 574163402426856595 T^{19} + 6759216441658133498 T^{20} + 4280057469977295606 T^{21} + 43513917611435838661 T^{22}$$)($$1 + 3 T + 432 T^{2} + 1230 T^{3} + 90161 T^{4} + 273851 T^{5} + 12309892 T^{6} + 42041210 T^{7} + 1247608113 T^{8} + 4675036486 T^{9} + 100502461314 T^{10} + 383065843548 T^{11} + 6694800790131 T^{12} + 23367016456428 T^{13} + 373969658549394 T^{14} + 1061144456628766 T^{15} + 17274183562908033 T^{16} + 35507850455564210 T^{17} + 634210244183479012 T^{18} + 860643268387186871 T^{19} + 17284523047147852241 T^{20} + 14383799694185993430 T^{21} +$$$$30\!\cdots\!32$$$$T^{22} +$$$$13\!\cdots\!83$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 - 29 T + 1023 T^{2} - 20439 T^{3} + 425921 T^{4} - 6588276 T^{5} + 102071192 T^{6} - 1292237308 T^{7} + 16152643052 T^{8} - 172446855471 T^{9} + 1807344944080 T^{10} - 16534828328737 T^{11} + 148161174495311 T^{12} - 1169622992942008 T^{13} + 9037831644213971 T^{14} - 61526096211230377 T^{15} + 410232962752222480 T^{16} - 2387671741801446111 T^{17} + 13642462573092550652 T^{18} - 66576549871410860188 T^{19} +$$$$32\!\cdots\!32$$$$T^{20} -$$$$12\!\cdots\!56$$$$T^{21} +$$$$49\!\cdots\!61$$$$T^{22} -$$$$14\!\cdots\!39$$$$T^{23} +$$$$44\!\cdots\!03$$$$T^{24} -$$$$76\!\cdots\!09$$$$T^{25} +$$$$16\!\cdots\!81$$$$T^{26}$$)($$1 - T + 410 T^{2} - 890 T^{3} + 87588 T^{4} - 279433 T^{5} + 12931865 T^{6} - 50711894 T^{7} + 1484437808 T^{8} - 6339757701 T^{9} + 139727676318 T^{10} - 597738020304 T^{11} + 11017030143027 T^{12} - 44768426473041 T^{13} + 731807583059774 T^{14} - 2730874014855501 T^{15} + 40994369162203467 T^{16} - 135675173586622224 T^{17} + 1934647189598493438 T^{18} - 5354535903500864001 T^{19} + 76478791583782240688 T^{20} -$$$$15\!\cdots\!74$$$$T^{21} +$$$$24\!\cdots\!65$$$$T^{22} -$$$$32\!\cdots\!53$$$$T^{23} +$$$$62\!\cdots\!88$$$$T^{24} -$$$$38\!\cdots\!90$$$$T^{25} +$$$$10\!\cdots\!10$$$$T^{26} -$$$$16\!\cdots\!81$$$$T^{27} +$$$$98\!\cdots\!41$$$$T^{28}$$)($$1 - 27 T + 721 T^{2} - 11873 T^{3} + 185956 T^{4} - 2263878 T^{5} + 26233158 T^{6} - 256288316 T^{7} + 2354109666 T^{8} - 18705554295 T^{9} + 133271191906 T^{10} - 807430101147 T^{11} + 3693776056040 T^{12} - 11284956262802 T^{13} - 39808083940908 T^{14} + 467116003789060 T^{15} - 2428293120395388 T^{16} - 41991322253886242 T^{17} + 838416982976015240 T^{18} - 11179548799095279627 T^{19} +$$$$11\!\cdots\!06$$$$T^{20} -$$$$96\!\cdots\!95$$$$T^{21} +$$$$73\!\cdots\!86$$$$T^{22} -$$$$49\!\cdots\!96$$$$T^{23} +$$$$30\!\cdots\!78$$$$T^{24} -$$$$16\!\cdots\!78$$$$T^{25} +$$$$80\!\cdots\!16$$$$T^{26} -$$$$31\!\cdots\!33$$$$T^{27} +$$$$11\!\cdots\!01$$$$T^{28} -$$$$26\!\cdots\!07$$$$T^{29} +$$$$60\!\cdots\!01$$$$T^{30}$$)($$1 - 6 T + 323 T^{2} - 1803 T^{3} + 51999 T^{4} - 310708 T^{5} + 5859564 T^{6} - 41551842 T^{7} + 551504573 T^{8} - 4527561984 T^{9} + 47537189043 T^{10} - 403868693098 T^{11} + 3813583117651 T^{12} - 30173927981267 T^{13} + 277792860692578 T^{14} - 1985788550129320 T^{15} + 18004760530932760 T^{16} - 121133101557888520 T^{17} + 1033667234637082738 T^{18} - 6848908347115964927 T^{19} + 52802265487280039491 T^{20} -$$$$34\!\cdots\!98$$$$T^{21} +$$$$24\!\cdots\!23$$$$T^{22} -$$$$14\!\cdots\!64$$$$T^{23} +$$$$10\!\cdots\!13$$$$T^{24} -$$$$48\!\cdots\!22$$$$T^{25} +$$$$41\!\cdots\!64$$$$T^{26} -$$$$13\!\cdots\!88$$$$T^{27} +$$$$13\!\cdots\!79$$$$T^{28} -$$$$29\!\cdots\!43$$$$T^{29} +$$$$31\!\cdots\!43$$$$T^{30} -$$$$36\!\cdots\!06$$$$T^{31} +$$$$36\!\cdots\!61$$$$T^{32}$$)($$1 - 32 T + 1206 T^{2} - 25791 T^{3} + 574786 T^{4} - 9432859 T^{5} + 157027093 T^{6} - 2115073800 T^{7} + 28728344596 T^{8} - 330500301176 T^{9} + 3837456872265 T^{10} - 38710131992009 T^{11} + 395349964688070 T^{12} - 3560087269732381 T^{13} + 32564374072402884 T^{14} - 264721387143865088 T^{15} + 2190402127678037446 T^{16} - 16148004615775770368 T^{17} +$$$$12\!\cdots\!64$$$$T^{18} -$$$$80\!\cdots\!61$$$$T^{19} +$$$$54\!\cdots\!70$$$$T^{20} -$$$$32\!\cdots\!09$$$$T^{21} +$$$$19\!\cdots\!65$$$$T^{22} -$$$$10\!\cdots\!96$$$$T^{23} +$$$$55\!\cdots\!76$$$$T^{24} -$$$$24\!\cdots\!00$$$$T^{25} +$$$$11\!\cdots\!93$$$$T^{26} -$$$$41\!\cdots\!99$$$$T^{27} +$$$$15\!\cdots\!06$$$$T^{28} -$$$$41\!\cdots\!71$$$$T^{29} +$$$$11\!\cdots\!46$$$$T^{30} -$$$$19\!\cdots\!32$$$$T^{31} +$$$$36\!\cdots\!61$$$$T^{32}$$)($$1 + 11 T + 419 T^{2} + 4705 T^{3} + 92988 T^{4} + 974800 T^{5} + 13961938 T^{6} + 134959200 T^{7} + 1572046887 T^{8} + 14256371308 T^{9} + 143581697680 T^{10} + 1243450323409 T^{11} + 11282707752897 T^{12} + 94414288868823 T^{13} + 792313173380726 T^{14} + 6401161235238468 T^{15} + 50597238264220389 T^{16} + 390470835349546548 T^{17} + 2948197318149681446 T^{18} + 21430249701734313363 T^{19} +$$$$15\!\cdots\!77$$$$T^{20} +$$$$10\!\cdots\!09$$$$T^{21} +$$$$73\!\cdots\!80$$$$T^{22} +$$$$44\!\cdots\!68$$$$T^{23} +$$$$30\!\cdots\!47$$$$T^{24} +$$$$15\!\cdots\!00$$$$T^{25} +$$$$99\!\cdots\!38$$$$T^{26} +$$$$42\!\cdots\!00$$$$T^{27} +$$$$24\!\cdots\!48$$$$T^{28} +$$$$76\!\cdots\!05$$$$T^{29} +$$$$41\!\cdots\!79$$$$T^{30} +$$$$66\!\cdots\!11$$$$T^{31} +$$$$36\!\cdots\!61$$$$T^{32}$$)($$1 + 5 T + 313 T^{2} + 823 T^{3} + 52165 T^{4} + 17522 T^{5} + 6076918 T^{6} - 11076242 T^{7} + 573805076 T^{8} - 2160722153 T^{9} + 47466893999 T^{10} - 243623260628 T^{11} + 3639796890962 T^{12} - 20608000137639 T^{13} + 266055733023234 T^{14} - 1442983180432481 T^{15} + 18359172200402956 T^{16} - 91434935405685095 T^{17} + 1172250317548098592 T^{18} - 5577531059746790795 T^{19} + 68314479757699399276 T^{20} -$$$$32\!\cdots\!61$$$$T^{21} +$$$$36\!\cdots\!94$$$$T^{22} -$$$$17\!\cdots\!39$$$$T^{23} +$$$$18\!\cdots\!82$$$$T^{24} -$$$$76\!\cdots\!88$$$$T^{25} +$$$$90\!\cdots\!19$$$$T^{26} -$$$$25\!\cdots\!73$$$$T^{27} +$$$$40\!\cdots\!76$$$$T^{28} -$$$$48\!\cdots\!62$$$$T^{29} +$$$$16\!\cdots\!78$$$$T^{30} +$$$$28\!\cdots\!82$$$$T^{31} +$$$$51\!\cdots\!65$$$$T^{32} +$$$$49\!\cdots\!23$$$$T^{33} +$$$$11\!\cdots\!93$$$$T^{34} +$$$$11\!\cdots\!05$$$$T^{35} +$$$$13\!\cdots\!81$$$$T^{36}$$)($$1 - 26 T + 838 T^{2} - 15329 T^{3} + 298583 T^{4} - 4294165 T^{5} + 63615119 T^{6} - 761644687 T^{7} + 9351456495 T^{8} - 96581854497 T^{9} + 1031428248461 T^{10} - 9443877771964 T^{11} + 90986491118717 T^{12} - 758071858895611 T^{13} + 6812650245376485 T^{14} - 53082743698333913 T^{15} + 458408958260406348 T^{16} - 3427992803436643349 T^{17} + 29015749356968724265 T^{18} -$$$$21\!\cdots\!10$$$$T^{19} +$$$$17\!\cdots\!65$$$$T^{20} -$$$$12\!\cdots\!29$$$$T^{21} +$$$$10\!\cdots\!88$$$$T^{22} -$$$$73\!\cdots\!33$$$$T^{23} +$$$$57\!\cdots\!85$$$$T^{24} -$$$$39\!\cdots\!71$$$$T^{25} +$$$$28\!\cdots\!57$$$$T^{26} -$$$$18\!\cdots\!84$$$$T^{27} +$$$$12\!\cdots\!01$$$$T^{28} -$$$$68\!\cdots\!97$$$$T^{29} +$$$$40\!\cdots\!95$$$$T^{30} -$$$$20\!\cdots\!27$$$$T^{31} +$$$$10\!\cdots\!39$$$$T^{32} -$$$$42\!\cdots\!65$$$$T^{33} +$$$$17\!\cdots\!83$$$$T^{34} -$$$$56\!\cdots\!69$$$$T^{35} +$$$$18\!\cdots\!98$$$$T^{36} -$$$$35\!\cdots\!06$$$$T^{37} +$$$$83\!\cdots\!41$$$$T^{38}$$)($$1 + 27 T + 875 T^{2} + 17033 T^{3} + 331994 T^{4} + 5116610 T^{5} + 76175542 T^{6} + 982572262 T^{7} + 12203408370 T^{8} + 136820170557 T^{9} + 1484538070309 T^{10} + 14880081183760 T^{11} + 145384403908907 T^{12} + 1332681712720025 T^{13} + 12007469649060554 T^{14} + 102707680608618470 T^{15} + 871687045460596794 T^{16} + 7092973046188373144 T^{17} + 57801758671098466844 T^{18} +$$$$45\!\cdots\!44$$$$T^{19} +$$$$36\!\cdots\!60$$$$T^{20} +$$$$27\!\cdots\!84$$$$T^{21} +$$$$21\!\cdots\!24$$$$T^{22} +$$$$16\!\cdots\!64$$$$T^{23} +$$$$12\!\cdots\!54$$$$T^{24} +$$$$86\!\cdots\!70$$$$T^{25} +$$$$61\!\cdots\!94$$$$T^{26} +$$$$41\!\cdots\!25$$$$T^{27} +$$$$27\!\cdots\!67$$$$T^{28} +$$$$17\!\cdots\!60$$$$T^{29} +$$$$10\!\cdots\!09$$$$T^{30} +$$$$59\!\cdots\!77$$$$T^{31} +$$$$32\!\cdots\!70$$$$T^{32} +$$$$15\!\cdots\!22$$$$T^{33} +$$$$75\!\cdots\!22$$$$T^{34} +$$$$30\!\cdots\!10$$$$T^{35} +$$$$12\!\cdots\!34$$$$T^{36} +$$$$38\!\cdots\!93$$$$T^{37} +$$$$11\!\cdots\!75$$$$T^{38} +$$$$22\!\cdots\!07$$$$T^{39} +$$$$50\!\cdots\!01$$$$T^{40}$$)
$67$ ($$1 - 2 T + 67 T^{2}$$)($$1 - 12 T + 67 T^{2}$$)($$1 + 10 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 - 12 T + 67 T^{2}$$)($$1 - 6 T + 126 T^{2} - 402 T^{3} + 4489 T^{4}$$)($$( 1 + 2 T + 67 T^{2} )^{2}$$)($$1 + 116 T^{2} + 4489 T^{4}$$)($$1 - 4 T - 12 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 + 30 T + 675 T^{2} + 11360 T^{3} + 157485 T^{4} + 1838995 T^{5} + 18608402 T^{6} + 162480644 T^{7} + 1246762934 T^{8} + 8255248555 T^{9} + 47365661055 T^{10} + 228916734560 T^{11} + 911334447225 T^{12} + 2713751465070 T^{13} + 6060711605323 T^{14}$$)($$1 + 22 T + 283 T^{2} + 2634 T^{3} + 21175 T^{4} + 155113 T^{5} + 1264826 T^{6} + 10435972 T^{7} + 93771899 T^{8} + 1070765649 T^{9} + 11695961050 T^{10} + 106234297972 T^{11} + 783629390350 T^{12} + 4806666998361 T^{13} + 28203117658937 T^{14} + 210296534524612 T^{15} + 1707673338586382 T^{16} + 14031271033380097 T^{17} + 128335568242714525 T^{18} + 1069582262684192394 T^{19} + 7699449234151470001 T^{20} + 40102431700138751878 T^{21} +$$$$12\!\cdots\!83$$$$T^{22}$$)($$1 + T + 435 T^{2} + 1226 T^{3} + 93877 T^{4} + 376053 T^{5} + 13893378 T^{6} + 61837204 T^{7} + 1579932599 T^{8} + 6958693447 T^{9} + 143413068674 T^{10} + 595120533863 T^{11} + 10600062861109 T^{12} + 39873075768821 T^{13} + 643781265277586 T^{14} + 2092917517200061 T^{15} + 31837412974293479 T^{16} + 83487961667080828 T^{17} + 1256772496742376882 T^{18} + 2279148781316530119 T^{19} + 38120415365984787157 T^{20} + 33355211169857605022 T^{21} +$$$$79\!\cdots\!15$$$$T^{22} +$$$$12\!\cdots\!83$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 18 T + 515 T^{2} + 7308 T^{3} + 124920 T^{4} + 1475761 T^{5} + 19125783 T^{6} + 196479200 T^{7} + 2123208520 T^{8} + 19682935334 T^{9} + 187612591758 T^{10} + 1616331925468 T^{11} + 14149667857895 T^{12} + 115112160627838 T^{13} + 948027746478965 T^{14} + 7255714013425852 T^{15} + 56426925934911354 T^{16} + 396633211550609414 T^{17} + 2866597130248311640 T^{18} + 17773190561859384800 T^{19} +$$$$11\!\cdots\!09$$$$T^{20} +$$$$59\!\cdots\!01$$$$T^{21} +$$$$33\!\cdots\!40$$$$T^{22} +$$$$13\!\cdots\!92$$$$T^{23} +$$$$62\!\cdots\!45$$$$T^{24} +$$$$14\!\cdots\!98$$$$T^{25} +$$$$54\!\cdots\!87$$$$T^{26}$$)($$1 + 38 T + 1174 T^{2} + 23934 T^{3} + 422665 T^{4} + 5839509 T^{5} + 71970295 T^{6} + 723216019 T^{7} + 6601917413 T^{8} + 48533153402 T^{9} + 331369870442 T^{10} + 1636952749842 T^{11} + 8113580369697 T^{12} + 14028985989802 T^{13} + 123870851464306 T^{14} + 939942061316734 T^{15} + 36421862279569833 T^{16} + 492334819900729446 T^{17} + 6677474355031065482 T^{18} + 65525828929922664014 T^{19} +$$$$59\!\cdots\!97$$$$T^{20} +$$$$43\!\cdots\!37$$$$T^{21} +$$$$29\!\cdots\!95$$$$T^{22} +$$$$15\!\cdots\!23$$$$T^{23} +$$$$77\!\cdots\!85$$$$T^{24} +$$$$29\!\cdots\!22$$$$T^{25} +$$$$96\!\cdots\!14$$$$T^{26} +$$$$20\!\cdots\!06$$$$T^{27} +$$$$36\!\cdots\!29$$$$T^{28}$$)($$1 - 3 T + 576 T^{2} - 2705 T^{3} + 166067 T^{4} - 1024378 T^{5} + 32254475 T^{6} - 231648370 T^{7} + 4766074801 T^{8} - 36195460120 T^{9} + 566959421282 T^{10} - 4232810253731 T^{11} + 55503986966566 T^{12} - 388903213413955 T^{13} + 4495264645998566 T^{14} - 28860521166489764 T^{15} + 301182731281903922 T^{16} - 1745786525015243995 T^{17} + 16693545632025289858 T^{18} - 85295871592974082451 T^{19} +$$$$76\!\cdots\!74$$$$T^{20} -$$$$32\!\cdots\!80$$$$T^{21} +$$$$28\!\cdots\!23$$$$T^{22} -$$$$94\!\cdots\!70$$$$T^{23} +$$$$87\!\cdots\!25$$$$T^{24} -$$$$18\!\cdots\!22$$$$T^{25} +$$$$20\!\cdots\!61$$$$T^{26} -$$$$22\!\cdots\!05$$$$T^{27} +$$$$31\!\cdots\!12$$$$T^{28} -$$$$11\!\cdots\!87$$$$T^{29} +$$$$24\!\cdots\!43$$$$T^{30}$$)($$1 - 16 T + 766 T^{2} - 9522 T^{3} + 266198 T^{4} - 2737347 T^{5} + 58496417 T^{6} - 519287669 T^{7} + 9388084842 T^{8} - 74027457819 T^{9} + 1185159368461 T^{10} - 8444953971409 T^{11} + 122332956376634 T^{12} - 795520428449380 T^{13} + 10542611262284876 T^{14} - 62937864816399986 T^{15} + 767216039759836106 T^{16} - 4216836942698799062 T^{17} + 47325781956396808364 T^{18} -$$$$23\!\cdots\!40$$$$T^{19} +$$$$24\!\cdots\!14$$$$T^{20} -$$$$11\!\cdots\!63$$$$T^{21} +$$$$10\!\cdots\!09$$$$T^{22} -$$$$44\!\cdots\!37$$$$T^{23} +$$$$38\!\cdots\!22$$$$T^{24} -$$$$14\!\cdots\!43$$$$T^{25} +$$$$10\!\cdots\!33$$$$T^{26} -$$$$33\!\cdots\!01$$$$T^{27} +$$$$21\!\cdots\!78$$$$T^{28} -$$$$52\!\cdots\!14$$$$T^{29} +$$$$28\!\cdots\!14$$$$T^{30} -$$$$39\!\cdots\!88$$$$T^{31} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 - 16 T + 628 T^{2} - 8280 T^{3} + 190794 T^{4} - 2210435 T^{5} + 38583413 T^{6} - 404285065 T^{7} + 5872118516 T^{8} - 56444576871 T^{9} + 715144787325 T^{10} - 6351231831685 T^{11} + 72089223934430 T^{12} - 593244848334966 T^{13} + 6130469576154946 T^{14} - 46757932432905050 T^{15} + 444257383187169606 T^{16} - 3132781473004638350 T^{17} + 27519677927359552594 T^{18} -$$$$17\!\cdots\!58$$$$T^{19} +$$$$14\!\cdots\!30$$$$T^{20} -$$$$85\!\cdots\!95$$$$T^{21} +$$$$64\!\cdots\!25$$$$T^{22} -$$$$34\!\cdots\!33$$$$T^{23} +$$$$23\!\cdots\!56$$$$T^{24} -$$$$10\!\cdots\!55$$$$T^{25} +$$$$70\!\cdots\!37$$$$T^{26} -$$$$26\!\cdots\!05$$$$T^{27} +$$$$15\!\cdots\!34$$$$T^{28} -$$$$45\!\cdots\!60$$$$T^{29} +$$$$23\!\cdots\!12$$$$T^{30} -$$$$39\!\cdots\!88$$$$T^{31} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 - 17 T + 771 T^{2} - 11012 T^{3} + 278161 T^{4} - 3391789 T^{5} + 62501406 T^{6} - 658812412 T^{7} + 9849603202 T^{8} - 90727821928 T^{9} + 1168800833925 T^{10} - 9528902740863 T^{11} + 110551691797174 T^{12} - 813252069755460 T^{13} + 8808924372578782 T^{14} - 60086690319593739 T^{15} + 620944719838574180 T^{16} - 4025808251412780513 T^{17} + 39543261508506152398 T^{18} -$$$$24\!\cdots\!80$$$$T^{19} +$$$$22\!\cdots\!54$$$$T^{20} -$$$$12\!\cdots\!41$$$$T^{21} +$$$$10\!\cdots\!25$$$$T^{22} -$$$$54\!\cdots\!44$$$$T^{23} +$$$$39\!\cdots\!82$$$$T^{24} -$$$$17\!\cdots\!64$$$$T^{25} +$$$$11\!\cdots\!94$$$$T^{26} -$$$$41\!\cdots\!87$$$$T^{27} +$$$$22\!\cdots\!21$$$$T^{28} -$$$$60\!\cdots\!44$$$$T^{29} +$$$$28\!\cdots\!59$$$$T^{30} -$$$$41\!\cdots\!31$$$$T^{31} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 - 6 T + 660 T^{2} - 2744 T^{3} + 206847 T^{4} - 546815 T^{5} + 41865837 T^{6} - 58775543 T^{7} + 6267210834 T^{8} - 2850792910 T^{9} + 751996954474 T^{10} + 126073507818 T^{11} + 76266450675238 T^{12} + 35752074266697 T^{13} + 6762717540256435 T^{14} + 3616840565032217 T^{15} + 533791607456110448 T^{16} + 269073439163604974 T^{17} + 37755976465866968420 T^{18} + 18027920423961533258 T^{19} +$$$$23\!\cdots\!72$$$$T^{20} +$$$$10\!\cdots\!71$$$$T^{21} +$$$$13\!\cdots\!35$$$$T^{22} +$$$$48\!\cdots\!79$$$$T^{23} +$$$$68\!\cdots\!22$$$$T^{24} +$$$$76\!\cdots\!14$$$$T^{25} +$$$$30\!\cdots\!34$$$$T^{26} -$$$$77\!\cdots\!70$$$$T^{27} +$$$$11\!\cdots\!66$$$$T^{28} -$$$$71\!\cdots\!69$$$$T^{29} +$$$$34\!\cdots\!57$$$$T^{30} -$$$$29\!\cdots\!05$$$$T^{31} +$$$$75\!\cdots\!63$$$$T^{32} -$$$$67\!\cdots\!92$$$$T^{33} +$$$$10\!\cdots\!60$$$$T^{34} -$$$$66\!\cdots\!62$$$$T^{35} +$$$$74\!\cdots\!09$$$$T^{36}$$)($$1 - 24 T + 1065 T^{2} - 20598 T^{3} + 528809 T^{4} - 8644973 T^{5} + 165769208 T^{6} - 2361709360 T^{7} + 37198542309 T^{8} - 471412532131 T^{9} + 6396164360286 T^{10} - 73119929927616 T^{11} + 878356408508454 T^{12} - 9144679664174609 T^{13} + 98919019711057509 T^{14} - 943722960976640048 T^{15} + 9291719328933613139 T^{16} - 81516068920894131031 T^{17} +$$$$73\!\cdots\!96$$$$T^{18} -$$$$59\!\cdots\!16$$$$T^{19} +$$$$49\!\cdots\!32$$$$T^{20} -$$$$36\!\cdots\!59$$$$T^{21} +$$$$27\!\cdots\!57$$$$T^{22} -$$$$19\!\cdots\!08$$$$T^{23} +$$$$13\!\cdots\!63$$$$T^{24} -$$$$82\!\cdots\!21$$$$T^{25} +$$$$53\!\cdots\!42$$$$T^{26} -$$$$29\!\cdots\!56$$$$T^{27} +$$$$17\!\cdots\!42$$$$T^{28} -$$$$85\!\cdots\!19$$$$T^{29} +$$$$45\!\cdots\!47$$$$T^{30} -$$$$19\!\cdots\!60$$$$T^{31} +$$$$90\!\cdots\!96$$$$T^{32} -$$$$31\!\cdots\!17$$$$T^{33} +$$$$13\!\cdots\!87$$$$T^{34} -$$$$33\!\cdots\!38$$$$T^{35} +$$$$11\!\cdots\!55$$$$T^{36} -$$$$17\!\cdots\!16$$$$T^{37} +$$$$49\!\cdots\!03$$$$T^{38}$$)($$1 - 9 T + 591 T^{2} - 4752 T^{3} + 170755 T^{4} - 1206847 T^{5} + 32101040 T^{6} - 197318136 T^{7} + 4462893877 T^{8} - 23737930247 T^{9} + 500089616732 T^{10} - 2319275613331 T^{11} + 48393933613827 T^{12} - 200872169616621 T^{13} + 4252058182022998 T^{14} - 16383764790112677 T^{15} + 347117079633002046 T^{16} - 1274967067532347537 T^{17} + 26328418982796754431 T^{18} - 92887292534777448481 T^{19} +$$$$18\!\cdots\!00$$$$T^{20} -$$$$62\!\cdots\!27$$$$T^{21} +$$$$11\!\cdots\!59$$$$T^{22} -$$$$38\!\cdots\!31$$$$T^{23} +$$$$69\!\cdots\!66$$$$T^{24} -$$$$22\!\cdots\!39$$$$T^{25} +$$$$38\!\cdots\!62$$$$T^{26} -$$$$12\!\cdots\!83$$$$T^{27} +$$$$19\!\cdots\!07$$$$T^{28} -$$$$63\!\cdots\!57$$$$T^{29} +$$$$91\!\cdots\!68$$$$T^{30} -$$$$28\!\cdots\!01$$$$T^{31} +$$$$36\!\cdots\!97$$$$T^{32} -$$$$10\!\cdots\!32$$$$T^{33} +$$$$11\!\cdots\!60$$$$T^{34} -$$$$29\!\cdots\!21$$$$T^{35} +$$$$28\!\cdots\!55$$$$T^{36} -$$$$52\!\cdots\!04$$$$T^{37} +$$$$43\!\cdots\!19$$$$T^{38} -$$$$44\!\cdots\!27$$$$T^{39} +$$$$33\!\cdots\!01$$$$T^{40}$$)
$71$ ($$1 + 10 T + 71 T^{2}$$)($$1 + 6 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 8 T + 71 T^{2}$$)($$1 - 6 T + 71 T^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$1 - 18 T + 206 T^{2} - 1278 T^{3} + 5041 T^{4}$$)($$1 + 12 T + 176 T^{2} + 852 T^{3} + 5041 T^{4}$$)($$1 + 12 T + 172 T^{2} + 852 T^{3} + 5041 T^{4}$$)($$1 + 8 T + 246 T^{2} + 1787 T^{3} + 34468 T^{4} + 225343 T^{5} + 3268094 T^{6} + 18726838 T^{7} + 232034674 T^{8} + 1135954063 T^{9} + 12336476348 T^{10} + 45410673947 T^{11} + 443840420346 T^{12} + 1024802271368 T^{13} + 9095120158391 T^{14}$$)($$1 - 22 T + 619 T^{2} - 9193 T^{3} + 157535 T^{4} - 1875828 T^{5} + 25189813 T^{6} - 258501834 T^{7} + 2939448413 T^{8} - 26553256573 T^{9} + 263699709796 T^{10} - 2119146874428 T^{11} + 18722679395516 T^{12} - 133854966384493 T^{13} + 1052060920945243 T^{14} - 6568966143522954 T^{15} + 45448199960801363 T^{16} - 240294099386961588 T^{17} + 1432799754152126185 T^{18} - 5936412212742280873 T^{19} + 28380221944719950189 T^{20} - 71615358122217386422 T^{21} +$$$$23\!\cdots\!71$$$$T^{22}$$)($$1 - 57 T + 1863 T^{2} - 43083 T^{3} + 789480 T^{4} - 12133524 T^{5} + 163477864 T^{6} - 1985571923 T^{7} + 22205022013 T^{8} - 231246886523 T^{9} + 2259759437514 T^{10} - 20781791620062 T^{11} + 180293488087779 T^{12} - 1475507205024402 T^{13} + 11391447324508074 T^{14} - 82765804402333453 T^{15} + 564266935992333853 T^{16} - 3582427141998111973 T^{17} + 20941560793198624744 T^{18} -$$$$11\!\cdots\!84$$$$T^{19} +$$$$50\!\cdots\!80$$$$T^{20} -$$$$19\!\cdots\!73$$$$T^{21} +$$$$60\!\cdots\!63$$$$T^{22} -$$$$13\!\cdots\!47$$$$T^{23} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$1 + 10 T + 556 T^{2} + 4573 T^{3} + 149491 T^{4} + 1052465 T^{5} + 26282634 T^{6} + 161622081 T^{7} + 3414944265 T^{8} + 18615640006 T^{9} + 350734762938 T^{10} + 1720351297082 T^{11} + 29653858976227 T^{12} + 132764914433646 T^{13} + 2105423987312117 T^{14} + 8672290888590362 T^{15} + 125531829737902518 T^{16} + 473054705443310086 T^{17} + 6161342674942122015 T^{18} + 20703834464002859601 T^{19} +$$$$23\!\cdots\!94$$$$T^{20} +$$$$67\!\cdots\!65$$$$T^{21} +$$$$68\!\cdots\!21$$$$T^{22} +$$$$14\!\cdots\!73$$$$T^{23} +$$$$12\!\cdots\!76$$$$T^{24} +$$$$16\!\cdots\!10$$$$T^{25} +$$$$11\!\cdots\!11$$$$T^{26}$$)($$1 - 10 T + 621 T^{2} - 5411 T^{3} + 182283 T^{4} - 1425360 T^{5} + 34456003 T^{6} - 247816664 T^{7} + 4799991247 T^{8} - 32264035049 T^{9} + 530496962459 T^{10} - 3348973491864 T^{11} + 48460938627045 T^{12} - 285739722695784 T^{13} + 3734602641050538 T^{14} - 20287520311400664 T^{15} + 244291591618933845 T^{16} - 1198634451446536104 T^{17} + 13480819581477083579 T^{18} - 58211719017098523199 T^{19} +$$$$61\!\cdots\!87$$$$T^{20} -$$$$22\!\cdots\!24$$$$T^{21} +$$$$22\!\cdots\!83$$$$T^{22} -$$$$65\!\cdots\!60$$$$T^{23} +$$$$59\!\cdots\!83$$$$T^{24} -$$$$12\!\cdots\!81$$$$T^{25} +$$$$10\!\cdots\!61$$$$T^{26} -$$$$11\!\cdots\!10$$$$T^{27} +$$$$82\!\cdots\!81$$$$T^{28}$$)($$1 + 55 T + 2072 T^{2} + 56220 T^{3} + 1261178 T^{4} + 23751782 T^{5} + 393120384 T^{6} + 5760964589 T^{7} + 76536328702 T^{8} + 926256666977 T^{9} + 10380978809587 T^{10} + 108218029385410 T^{11} + 1064396494086232 T^{12} + 9918377198060630 T^{13} + 88623617446446226 T^{14} + 759902916103906834 T^{15} + 6292276838697682046 T^{16} + 49998539455423635830 T^{17} +$$$$38\!\cdots\!52$$$$T^{18} +$$$$27\!\cdots\!10$$$$T^{19} +$$$$18\!\cdots\!37$$$$T^{20} +$$$$11\!\cdots\!17$$$$T^{21} +$$$$69\!\cdots\!82$$$$T^{22} +$$$$37\!\cdots\!29$$$$T^{23} +$$$$18\!\cdots\!04$$$$T^{24} +$$$$77\!\cdots\!82$$$$T^{25} +$$$$29\!\cdots\!38$$$$T^{26} +$$$$92\!\cdots\!20$$$$T^{27} +$$$$24\!\cdots\!92$$$$T^{28} +$$$$45\!\cdots\!55$$$$T^{29} +$$$$58\!\cdots\!51$$$$T^{30}$$)($$1 + 46 T + 1696 T^{2} + 44053 T^{3} + 1001168 T^{4} + 19136619 T^{5} + 332551066 T^{6} + 5155299858 T^{7} + 74144424281 T^{8} + 977582113019 T^{9} + 12099134092469 T^{10} + 139298259299498 T^{11} + 1516078883966442 T^{12} + 15474989005321276 T^{13} + 149928022065044389 T^{14} + 1368030361292835759 T^{15} + 11870282787987010192 T^{16} + 97130155651791338889 T^{17} +$$$$75\!\cdots\!49$$$$T^{18} +$$$$55\!\cdots\!36$$$$T^{19} +$$$$38\!\cdots\!02$$$$T^{20} +$$$$25\!\cdots\!98$$$$T^{21} +$$$$15\!\cdots\!49$$$$T^{22} +$$$$88\!\cdots\!29$$$$T^{23} +$$$$47\!\cdots\!41$$$$T^{24} +$$$$23\!\cdots\!98$$$$T^{25} +$$$$10\!\cdots\!66$$$$T^{26} +$$$$44\!\cdots\!49$$$$T^{27} +$$$$16\!\cdots\!88$$$$T^{28} +$$$$51\!\cdots\!83$$$$T^{29} +$$$$14\!\cdots\!76$$$$T^{30} +$$$$27\!\cdots\!46$$$$T^{31} +$$$$41\!\cdots\!21$$$$T^{32}$$)($$1 - 10 T + 733 T^{2} - 8415 T^{3} + 271870 T^{4} - 3298766 T^{5} + 67832304 T^{6} - 816827387 T^{7} + 12630578324 T^{8} - 144866921557 T^{9} + 1840550492694 T^{10} - 19647637055160 T^{11} + 215273356920058 T^{12} - 2113451975430609 T^{13} + 20509996777358637 T^{14} - 183899987372631804 T^{15} + 1604770401332365030 T^{16} - 13056899103456858084 T^{17} +$$$$10\!\cdots\!17$$$$T^{18} -$$$$75\!\cdots\!99$$$$T^{19} +$$$$54\!\cdots\!98$$$$T^{20} -$$$$35\!\cdots\!60$$$$T^{21} +$$$$23\!\cdots\!74$$$$T^{22} -$$$$13\!\cdots\!87$$$$T^{23} +$$$$81\!\cdots\!64$$$$T^{24} -$$$$37\!\cdots\!97$$$$T^{25} +$$$$22\!\cdots\!04$$$$T^{26} -$$$$76\!\cdots\!86$$$$T^{27} +$$$$44\!\cdots\!70$$$$T^{28} -$$$$98\!\cdots\!65$$$$T^{29} +$$$$60\!\cdots\!73$$$$T^{30} -$$$$58\!\cdots\!10$$$$T^{31} +$$$$41\!\cdots\!21$$$$T^{32}$$)($$1 - 81 T + 3660 T^{2} - 117320 T^{3} + 2956912 T^{4} - 61849848 T^{5} + 1111681964 T^{6} - 17583755239 T^{7} + 249175830053 T^{8} - 3208020444766 T^{9} + 37964594128726 T^{10} - 417199533670751 T^{11} + 4297142430881890 T^{12} - 41845239261162310 T^{13} + 388313109620644892 T^{14} - 3456595818162838275 T^{15} + 29647910999176336857 T^{16} -$$$$24\!\cdots\!25$$$$T^{17} +$$$$19\!\cdots\!72$$$$T^{18} -$$$$14\!\cdots\!10$$$$T^{19} +$$$$10\!\cdots\!90$$$$T^{20} -$$$$75\!\cdots\!01$$$$T^{21} +$$$$48\!\cdots\!46$$$$T^{22} -$$$$29\!\cdots\!06$$$$T^{23} +$$$$16\!\cdots\!33$$$$T^{24} -$$$$80\!\cdots\!09$$$$T^{25} +$$$$36\!\cdots\!64$$$$T^{26} -$$$$14\!\cdots\!08$$$$T^{27} +$$$$48\!\cdots\!92$$$$T^{28} -$$$$13\!\cdots\!20$$$$T^{29} +$$$$30\!\cdots\!60$$$$T^{30} -$$$$47\!\cdots\!31$$$$T^{31} +$$$$41\!\cdots\!21$$$$T^{32}$$)($$1 - 22 T + 816 T^{2} - 13317 T^{3} + 296343 T^{4} - 3949811 T^{5} + 67461988 T^{6} - 771642797 T^{7} + 11118168119 T^{8} - 112487037082 T^{9} + 1438298463717 T^{10} - 13144317642374 T^{11} + 154065969757915 T^{12} - 1293495497977143 T^{13} + 14217749002563904 T^{14} - 111372864315380429 T^{15} + 1165348206806512150 T^{16} - 8636949642215036499 T^{17} + 86585290392974234382 T^{18} -$$$$61\!\cdots\!29$$$$T^{19} +$$$$58\!\cdots\!50$$$$T^{20} -$$$$39\!\cdots\!19$$$$T^{21} +$$$$36\!\cdots\!24$$$$T^{22} -$$$$23\!\cdots\!93$$$$T^{23} +$$$$19\!\cdots\!15$$$$T^{24} -$$$$11\!\cdots\!34$$$$T^{25} +$$$$92\!\cdots\!37$$$$T^{26} -$$$$51\!\cdots\!42$$$$T^{27} +$$$$36\!\cdots\!19$$$$T^{28} -$$$$17\!\cdots\!87$$$$T^{29} +$$$$11\!\cdots\!08$$$$T^{30} -$$$$46\!\cdots\!21$$$$T^{31} +$$$$24\!\cdots\!83$$$$T^{32} -$$$$78\!\cdots\!67$$$$T^{33} +$$$$34\!\cdots\!36$$$$T^{34} -$$$$65\!\cdots\!02$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 - 32 T + 1227 T^{2} - 28835 T^{3} + 680427 T^{4} - 12842100 T^{5} + 234406211 T^{6} - 3740306330 T^{7} + 57238298625 T^{8} - 796894059719 T^{9} + 10634242395334 T^{10} - 131843183828886 T^{11} + 1569149036104108 T^{12} - 17561592195883763 T^{13} + 189022343080292513 T^{14} - 1927041274911330686 T^{15} + 18922276766488552162 T^{16} -$$$$17\!\cdots\!86$$$$T^{17} +$$$$15\!\cdots\!38$$$$T^{18} -$$$$13\!\cdots\!34$$$$T^{19} +$$$$11\!\cdots\!98$$$$T^{20} -$$$$89\!\cdots\!26$$$$T^{21} +$$$$67\!\cdots\!82$$$$T^{22} -$$$$48\!\cdots\!66$$$$T^{23} +$$$$34\!\cdots\!63$$$$T^{24} -$$$$22\!\cdots\!23$$$$T^{25} +$$$$14\!\cdots\!28$$$$T^{26} -$$$$85\!\cdots\!46$$$$T^{27} +$$$$48\!\cdots\!54$$$$T^{28} -$$$$25\!\cdots\!19$$$$T^{29} +$$$$13\!\cdots\!75$$$$T^{30} -$$$$61\!\cdots\!30$$$$T^{31} +$$$$27\!\cdots\!21$$$$T^{32} -$$$$10\!\cdots\!00$$$$T^{33} +$$$$39\!\cdots\!77$$$$T^{34} -$$$$12\!\cdots\!35$$$$T^{35} +$$$$36\!\cdots\!57$$$$T^{36} -$$$$67\!\cdots\!52$$$$T^{37} +$$$$14\!\cdots\!31$$$$T^{38}$$)($$1 + 63 T + 2596 T^{2} + 78560 T^{3} + 1968706 T^{4} + 42263598 T^{5} + 807471444 T^{6} + 13947310273 T^{7} + 221613295558 T^{8} + 3266810090497 T^{9} + 45096447088326 T^{10} + 585913588994251 T^{11} + 7204919382169096 T^{12} + 84116808873980238 T^{13} + 935676611913596316 T^{14} + 9935597569031351192 T^{15} +$$$$10\!\cdots\!58$$$$T^{16} +$$$$98\!\cdots\!37$$$$T^{17} +$$$$91\!\cdots\!02$$$$T^{18} +$$$$82\!\cdots\!29$$$$T^{19} +$$$$70\!\cdots\!14$$$$T^{20} +$$$$58\!\cdots\!59$$$$T^{21} +$$$$46\!\cdots\!82$$$$T^{22} +$$$$35\!\cdots\!07$$$$T^{23} +$$$$25\!\cdots\!98$$$$T^{24} +$$$$17\!\cdots\!92$$$$T^{25} +$$$$11\!\cdots\!36$$$$T^{26} +$$$$76\!\cdots\!58$$$$T^{27} +$$$$46\!\cdots\!56$$$$T^{28} +$$$$26\!\cdots\!81$$$$T^{29} +$$$$14\!\cdots\!26$$$$T^{30} +$$$$75\!\cdots\!87$$$$T^{31} +$$$$36\!\cdots\!78$$$$T^{32} +$$$$16\!\cdots\!03$$$$T^{33} +$$$$66\!\cdots\!64$$$$T^{34} +$$$$24\!\cdots\!98$$$$T^{35} +$$$$82\!\cdots\!26$$$$T^{36} +$$$$23\!\cdots\!60$$$$T^{37} +$$$$54\!\cdots\!56$$$$T^{38} +$$$$94\!\cdots\!53$$$$T^{39} +$$$$10\!\cdots\!01$$$$T^{40}$$)
$73$ ($$1 - 11 T + 73 T^{2}$$)($$1 + 7 T + 73 T^{2}$$)($$1 + 7 T + 73 T^{2}$$)($$1 - 14 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 + 4 T + 73 T^{2}$$)($$1 + 7 T + 73 T^{2}$$)($$1 + 13 T + 184 T^{2} + 949 T^{3} + 5329 T^{4}$$)($$1 + 13 T + 184 T^{2} + 949 T^{3} + 5329 T^{4}$$)($$1 - 4 T - 12 T^{2} - 292 T^{3} + 5329 T^{4}$$)($$1 + 8 T + 108 T^{2} + 584 T^{3} + 5329 T^{4}$$)($$1 + 20 T + 510 T^{2} + 6961 T^{3} + 102634 T^{4} + 1069123 T^{5} + 11655826 T^{6} + 97527765 T^{7} + 850875298 T^{8} + 5697356467 T^{9} + 39926370778 T^{10} + 197680155601 T^{11} + 1057266512430 T^{12} + 3026684525780 T^{13} + 11047398519097 T^{14}$$)($$1 + 29 T + 576 T^{2} + 8358 T^{3} + 105962 T^{4} + 1144815 T^{5} + 11352193 T^{6} + 99293139 T^{7} + 816363138 T^{8} + 6266682434 T^{9} + 49949153545 T^{10} + 406427719068 T^{11} + 3646288208785 T^{12} + 33395150690786 T^{13} + 317579138855346 T^{14} + 2819750490968499 T^{15} + 23533908826553449 T^{16} + 173249692269041535 T^{17} + 1170604441880556314 T^{18} + 6740393448050728998 T^{19} + 33910033943962317888 T^{20} +$$$$12\!\cdots\!21$$$$T^{21} +$$$$31\!\cdots\!77$$$$T^{22}$$)($$1 + 7 T + 587 T^{2} + 3074 T^{3} + 157312 T^{4} + 583506 T^{5} + 26023030 T^{6} + 60949389 T^{7} + 3052742503 T^{8} + 3650320080 T^{9} + 280386426518 T^{10} + 138384443368 T^{11} + 21843447058245 T^{12} + 10102064365864 T^{13} + 1494179266914422 T^{14} + 1420036566561360 T^{15} + 86692517311137223 T^{16} + 126352446946606677 T^{17} + 3938175110745435670 T^{18} + 6446223320284214082 T^{19} +$$$$12\!\cdots\!72$$$$T^{20} +$$$$18\!\cdots\!62$$$$T^{21} +$$$$25\!\cdots\!63$$$$T^{22} +$$$$21\!\cdots\!39$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 - 24 T + 870 T^{2} - 15387 T^{3} + 325681 T^{4} - 4669441 T^{5} + 74019844 T^{6} - 905055656 T^{7} + 11773114747 T^{8} - 126039249920 T^{9} + 1404528656478 T^{10} - 13325817517321 T^{11} + 130094309435051 T^{12} - 1097731775448310 T^{13} + 9496884588758723 T^{14} - 71013281549803609 T^{15} + 546385524357102126 T^{16} - 3579292994687390720 T^{17} + 24406509743135081971 T^{18} -$$$$13\!\cdots\!84$$$$T^{19} +$$$$81\!\cdots\!68$$$$T^{20} -$$$$37\!\cdots\!21$$$$T^{21} +$$$$19\!\cdots\!53$$$$T^{22} -$$$$66\!\cdots\!63$$$$T^{23} +$$$$27\!\cdots\!90$$$$T^{24} -$$$$54\!\cdots\!04$$$$T^{25} +$$$$16\!\cdots\!33$$$$T^{26}$$)($$1 - 8 T + 547 T^{2} - 3939 T^{3} + 156457 T^{4} - 1057340 T^{5} + 30751475 T^{6} - 195813211 T^{7} + 4575405639 T^{8} - 27362929950 T^{9} + 541643272461 T^{10} - 3022765696423 T^{11} + 52384471961759 T^{12} - 270009836377377 T^{13} + 4193767875322650 T^{14} - 19710718055548521 T^{15} + 279156851084213711 T^{16} - 1175907242925386191 T^{17} + 15381716187376141101 T^{18} - 56725312780593910350 T^{19} +$$$$69\!\cdots\!71$$$$T^{20} -$$$$21\!\cdots\!67$$$$T^{21} +$$$$24\!\cdots\!75$$$$T^{22} -$$$$62\!\cdots\!20$$$$T^{23} +$$$$67\!\cdots\!93$$$$T^{24} -$$$$12\!\cdots\!03$$$$T^{25} +$$$$12\!\cdots\!87$$$$T^{26} -$$$$13\!\cdots\!64$$$$T^{27} +$$$$12\!\cdots\!09$$$$T^{28}$$)($$1 + 3 T + 598 T^{2} - 153 T^{3} + 164770 T^{4} - 611311 T^{5} + 29401478 T^{6} - 206330032 T^{7} + 4115534744 T^{8} - 37479019847 T^{9} + 503329722743 T^{10} - 4641410795609 T^{11} + 54066551464868 T^{12} - 441674923905531 T^{13} + 4868516952319638 T^{14} - 34879506586221136 T^{15} + 355401737519333574 T^{16} - 2353685669492574699 T^{17} + 21032807651208554756 T^{18} -$$$$13\!\cdots\!69$$$$T^{19} +$$$$10\!\cdots\!99$$$$T^{20} -$$$$56\!\cdots\!83$$$$T^{21} +$$$$45\!\cdots\!68$$$$T^{22} -$$$$16\!\cdots\!92$$$$T^{23} +$$$$17\!\cdots\!14$$$$T^{24} -$$$$26\!\cdots\!39$$$$T^{25} +$$$$51\!\cdots\!90$$$$T^{26} -$$$$35\!\cdots\!13$$$$T^{27} +$$$$99\!\cdots\!34$$$$T^{28} +$$$$36\!\cdots\!27$$$$T^{29} +$$$$89\!\cdots\!57$$$$T^{30}$$)($$1 - 39 T + 1449 T^{2} - 35633 T^{3} + 819016 T^{4} - 15354005 T^{5} + 270847213 T^{6} - 4181000932 T^{7} + 61166945860 T^{8} - 808996878016 T^{9} + 10194855445346 T^{10} - 118177368250479 T^{11} + 1310024305648818 T^{12} - 13487234128627491 T^{13} + 133088301010306108 T^{14} - 1225754844226755877 T^{15} + 10832013228567582618 T^{16} - 89480103628553179021 T^{17} +$$$$70\!\cdots\!32$$$$T^{18} -$$$$52\!\cdots\!47$$$$T^{19} +$$$$37\!\cdots\!38$$$$T^{20} -$$$$24\!\cdots\!47$$$$T^{21} +$$$$15\!\cdots\!94$$$$T^{22} -$$$$89\!\cdots\!52$$$$T^{23} +$$$$49\!\cdots\!60$$$$T^{24} -$$$$24\!\cdots\!16$$$$T^{25} +$$$$11\!\cdots\!37$$$$T^{26} -$$$$48\!\cdots\!85$$$$T^{27} +$$$$18\!\cdots\!36$$$$T^{28} -$$$$59\!\cdots\!89$$$$T^{29} +$$$$17\!\cdots\!41$$$$T^{30} -$$$$34\!\cdots\!23$$$$T^{31} +$$$$65\!\cdots\!61$$$$T^{32}$$)($$1 - 23 T + 844 T^{2} - 14258 T^{3} + 313221 T^{4} - 4311528 T^{5} + 72723743 T^{6} - 863577203 T^{7} + 12288571822 T^{8} - 130212669665 T^{9} + 1636466187575 T^{10} - 15774708137328 T^{11} + 179347554825123 T^{12} - 1589309353137782 T^{13} + 16565296817973582 T^{14} - 135691770432833349 T^{15} + 1306081775474694290 T^{16} - 9905499241596834477 T^{17} + 88276466742981218478 T^{18} -$$$$61\!\cdots\!94$$$$T^{19} +$$$$50\!\cdots\!43$$$$T^{20} -$$$$32\!\cdots\!04$$$$T^{21} +$$$$24\!\cdots\!75$$$$T^{22} -$$$$14\!\cdots\!05$$$$T^{23} +$$$$99\!\cdots\!82$$$$T^{24} -$$$$50\!\cdots\!39$$$$T^{25} +$$$$31\!\cdots\!07$$$$T^{26} -$$$$13\!\cdots\!56$$$$T^{27} +$$$$71\!\cdots\!41$$$$T^{28} -$$$$23\!\cdots\!14$$$$T^{29} +$$$$10\!\cdots\!96$$$$T^{30} -$$$$20\!\cdots\!11$$$$T^{31} +$$$$65\!\cdots\!61$$$$T^{32}$$)($$1 + 15 T + 582 T^{2} + 7407 T^{3} + 162930 T^{4} + 1750115 T^{5} + 28761720 T^{6} + 257676340 T^{7} + 3508004421 T^{8} + 25338350866 T^{9} + 305254006734 T^{10} + 1605840841813 T^{11} + 19003953434058 T^{12} + 49834092699619 T^{13} + 876101742410588 T^{14} - 909694021596467 T^{15} + 44804948940816447 T^{16} - 66407663576542091 T^{17} + 4668746185306023452 T^{18} + 19386309239727684523 T^{19} +$$$$53\!\cdots\!78$$$$T^{20} +$$$$33\!\cdots\!09$$$$T^{21} +$$$$46\!\cdots\!26$$$$T^{22} +$$$$27\!\cdots\!02$$$$T^{23} +$$$$28\!\cdots\!01$$$$T^{24} +$$$$15\!\cdots\!20$$$$T^{25} +$$$$12\!\cdots\!80$$$$T^{26} +$$$$54\!\cdots\!55$$$$T^{27} +$$$$37\!\cdots\!30$$$$T^{28} +$$$$12\!\cdots\!31$$$$T^{29} +$$$$71\!\cdots\!38$$$$T^{30} +$$$$13\!\cdots\!55$$$$T^{31} +$$$$65\!\cdots\!61$$$$T^{32}$$)($$1 + 16 T + 774 T^{2} + 11991 T^{3} + 310425 T^{4} + 4494649 T^{5} + 84044592 T^{6} + 1122180182 T^{7} + 17029645739 T^{8} + 209114736738 T^{9} + 2728250649635 T^{10} + 30858797839849 T^{11} + 357339169674251 T^{12} + 3732467329882239 T^{13} + 39092259481718292 T^{14} + 377781559757387694 T^{15} + 3620052404771985744 T^{16} + 32383355156256234226 T^{17} +$$$$28\!\cdots\!94$$$$T^{18} +$$$$23\!\cdots\!98$$$$T^{19} +$$$$19\!\cdots\!76$$$$T^{20} +$$$$14\!\cdots\!98$$$$T^{21} +$$$$11\!\cdots\!72$$$$T^{22} +$$$$77\!\cdots\!27$$$$T^{23} +$$$$54\!\cdots\!39$$$$T^{24} +$$$$34\!\cdots\!53$$$$T^{25} +$$$$22\!\cdots\!35$$$$T^{26} +$$$$12\!\cdots\!94$$$$T^{27} +$$$$73\!\cdots\!11$$$$T^{28} +$$$$35\!\cdots\!14$$$$T^{29} +$$$$19\!\cdots\!32$$$$T^{30} +$$$$75\!\cdots\!17$$$$T^{31} +$$$$37\!\cdots\!25$$$$T^{32} +$$$$10\!\cdots\!87$$$$T^{33} +$$$$50\!\cdots\!14$$$$T^{34} +$$$$75\!\cdots\!48$$$$T^{35} +$$$$34\!\cdots\!69$$$$T^{36}$$)($$1 - 51 T + 2082 T^{2} - 60320 T^{3} + 1520884 T^{4} - 32377455 T^{5} + 624053883 T^{6} - 10764805837 T^{7} + 171927543584 T^{8} - 2527267835368 T^{9} + 34877971935503 T^{10} - 450100748228450 T^{11} + 5502830968614309 T^{12} - 63523695181462276 T^{13} + 698837312980657430 T^{14} - 7303189643834057099 T^{15} + 73007994854064934486 T^{16} -$$$$69\!\cdots\!98$$$$T^{17} +$$$$63\!\cdots\!58$$$$T^{18} -$$$$55\!\cdots\!84$$$$T^{19} +$$$$46\!\cdots\!34$$$$T^{20} -$$$$37\!\cdots\!42$$$$T^{21} +$$$$28\!\cdots\!62$$$$T^{22} -$$$$20\!\cdots\!59$$$$T^{23} +$$$$14\!\cdots\!90$$$$T^{24} -$$$$96\!\cdots\!64$$$$T^{25} +$$$$60\!\cdots\!73$$$$T^{26} -$$$$36\!\cdots\!50$$$$T^{27} +$$$$20\!\cdots\!39$$$$T^{28} -$$$$10\!\cdots\!32$$$$T^{29} +$$$$53\!\cdots\!68$$$$T^{30} -$$$$24\!\cdots\!77$$$$T^{31} +$$$$10\!\cdots\!39$$$$T^{32} -$$$$39\!\cdots\!95$$$$T^{33} +$$$$13\!\cdots\!88$$$$T^{34} -$$$$39\!\cdots\!20$$$$T^{35} +$$$$98\!\cdots\!46$$$$T^{36} -$$$$17\!\cdots\!19$$$$T^{37} +$$$$25\!\cdots\!37$$$$T^{38}$$)($$1 + 21 T + 916 T^{2} + 15097 T^{3} + 380738 T^{4} + 5228211 T^{5} + 98720492 T^{6} + 1169044476 T^{7} + 18261023340 T^{8} + 190285062363 T^{9} + 2593445804090 T^{10} + 24049645680336 T^{11} + 296353479113844 T^{12} + 2462421964424588 T^{13} + 28282525841124194 T^{14} + 212323680749559685 T^{15} + 2347288002490873928 T^{16} + 16218471867962234439 T^{17} +$$$$17\!\cdots\!16$$$$T^{18} +$$$$11\!\cdots\!68$$$$T^{19} +$$$$13\!\cdots\!66$$$$T^{20} +$$$$85\!\cdots\!64$$$$T^{21} +$$$$95\!\cdots\!64$$$$T^{22} +$$$$63\!\cdots\!63$$$$T^{23} +$$$$66\!\cdots\!48$$$$T^{24} +$$$$44\!\cdots\!05$$$$T^{25} +$$$$42\!\cdots\!66$$$$T^{26} +$$$$27\!\cdots\!36$$$$T^{27} +$$$$23\!\cdots\!64$$$$T^{28} +$$$$14\!\cdots\!68$$$$T^{29} +$$$$11\!\cdots\!10$$$$T^{30} +$$$$59\!\cdots\!51$$$$T^{31} +$$$$41\!\cdots\!40$$$$T^{32} +$$$$19\!\cdots\!08$$$$T^{33} +$$$$12\!\cdots\!28$$$$T^{34} +$$$$46\!\cdots\!27$$$$T^{35} +$$$$24\!\cdots\!18$$$$T^{36} +$$$$71\!\cdots\!41$$$$T^{37} +$$$$31\!\cdots\!04$$$$T^{38} +$$$$53\!\cdots\!77$$$$T^{39} +$$$$18\!\cdots\!01$$$$T^{40}$$)
$79$ ($$1 + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 + 4 T + 79 T^{2}$$)($$1 + 12 T + 79 T^{2}$$)($$1 + 12 T + 79 T^{2}$$)($$1 + 13 T + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 + 4 T + 94 T^{2} + 316 T^{3} + 6241 T^{4}$$)($$1 + 13 T + 162 T^{2} + 1027 T^{3} + 6241 T^{4}$$)($$( 1 + 11 T + 79 T^{2} )^{2}$$)($$1 + 2 T + 135 T^{2} + 158 T^{3} + 6241 T^{4}$$)($$1 - 8 T + 273 T^{2} - 2858 T^{3} + 45901 T^{4} - 424499 T^{5} + 5436714 T^{6} - 39832374 T^{7} + 429500406 T^{8} - 2649298259 T^{9} + 22630983139 T^{10} - 111319331498 T^{11} + 840036396927 T^{12} - 1944699644168 T^{13} + 19203908986159 T^{14}$$)($$1 + 20 T + 558 T^{2} + 8066 T^{3} + 147283 T^{4} + 1803439 T^{5} + 25866209 T^{6} + 275681257 T^{7} + 3338940595 T^{8} + 31609800198 T^{9} + 333856936437 T^{10} + 2814728702072 T^{11} + 26374697978523 T^{12} + 197276763035718 T^{13} + 1646227932018205 T^{14} + 10737807290331817 T^{15} + 79591783921321391 T^{16} + 438393397697336719 T^{17} + 2828409327208455997 T^{18} + 12236999660706321026 T^{19} + 66877190558301022002 T^{20} +$$$$18\!\cdots\!20$$$$T^{21} +$$$$74\!\cdots\!79$$$$T^{22}$$)($$1 + 18 T + 559 T^{2} + 8811 T^{3} + 152764 T^{4} + 2049448 T^{5} + 27037636 T^{6} + 311089904 T^{7} + 3508827540 T^{8} + 35662362397 T^{9} + 361263751482 T^{10} + 3338367560519 T^{11} + 30997455703321 T^{12} + 263731037281001 T^{13} + 2254647072999162 T^{14} + 17582935493854483 T^{15} + 136669116898030740 T^{16} + 957241179767495696 T^{17} + 6572510138542988356 T^{18} + 39357412863865590232 T^{19} +$$$$23\!\cdots\!04$$$$T^{20} +$$$$10\!\cdots\!09$$$$T^{21} +$$$$52\!\cdots\!59$$$$T^{22} +$$$$13\!\cdots\!22$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 + 28 T + 1025 T^{2} + 19014 T^{3} + 398721 T^{4} + 5420565 T^{5} + 81531672 T^{6} + 832892678 T^{7} + 9725170712 T^{8} + 72303138705 T^{9} + 699331712541 T^{10} + 3412737965740 T^{11} + 35417479052632 T^{12} + 139160460017484 T^{13} + 2797980845157928 T^{14} + 21298897644183340 T^{15} + 344797808219502099 T^{16} + 2816213109113985105 T^{17} + 29924898770726986088 T^{18} +$$$$20\!\cdots\!38$$$$T^{19} +$$$$15\!\cdots\!48$$$$T^{20} +$$$$82\!\cdots\!65$$$$T^{21} +$$$$47\!\cdots\!99$$$$T^{22} +$$$$18\!\cdots\!14$$$$T^{23} +$$$$76\!\cdots\!75$$$$T^{24} +$$$$16\!\cdots\!48$$$$T^{25} +$$$$46\!\cdots\!39$$$$T^{26}$$)($$1 - 26 T + 995 T^{2} - 18888 T^{3} + 423915 T^{4} - 6445491 T^{5} + 108617293 T^{6} - 1396649186 T^{7} + 19434091386 T^{8} - 218844443965 T^{9} + 2638999284435 T^{10} - 26567340357667 T^{11} + 284690572139722 T^{12} - 2585314414532307 T^{13} + 24906831120291546 T^{14} - 204239838748052253 T^{15} + 1776753860724005002 T^{16} - 13098734922603780013 T^{17} +$$$$10\!\cdots\!35$$$$T^{18} -$$$$67\!\cdots\!35$$$$T^{19} +$$$$47\!\cdots\!06$$$$T^{20} -$$$$26\!\cdots\!74$$$$T^{21} +$$$$16\!\cdots\!73$$$$T^{22} -$$$$77\!\cdots\!29$$$$T^{23} +$$$$40\!\cdots\!15$$$$T^{24} -$$$$14\!\cdots\!52$$$$T^{25} +$$$$58\!\cdots\!95$$$$T^{26} -$$$$12\!\cdots\!14$$$$T^{27} +$$$$36\!\cdots\!81$$$$T^{28}$$)($$1 - 18 T + 460 T^{2} - 6687 T^{3} + 116374 T^{4} - 1391891 T^{5} + 19636756 T^{6} - 205932437 T^{7} + 2497929957 T^{8} - 23266932306 T^{9} + 257455206682 T^{10} - 2178022362864 T^{11} + 22652395170843 T^{12} - 180936380619929 T^{13} + 1844016490716529 T^{14} - 14307814705947112 T^{15} + 145677302766605791 T^{16} - 1129223951448976889 T^{17} + 11168514262637261877 T^{18} - 84834147453364191984 T^{19} +$$$$79\!\cdots\!18$$$$T^{20} -$$$$56\!\cdots\!26$$$$T^{21} +$$$$47\!\cdots\!63$$$$T^{22} -$$$$31\!\cdots\!57$$$$T^{23} +$$$$23\!\cdots\!64$$$$T^{24} -$$$$13\!\cdots\!91$$$$T^{25} +$$$$87\!\cdots\!46$$$$T^{26} -$$$$39\!\cdots\!67$$$$T^{27} +$$$$21\!\cdots\!40$$$$T^{28} -$$$$66\!\cdots\!58$$$$T^{29} +$$$$29\!\cdots\!99$$$$T^{30}$$)($$1 - 4 T + 523 T^{2} - 2502 T^{3} + 139646 T^{4} - 789723 T^{5} + 25317681 T^{6} - 164597190 T^{7} + 3543641120 T^{8} - 25365204188 T^{9} + 414143422875 T^{10} - 3092572364282 T^{11} + 42450546057593 T^{12} - 314223074160542 T^{13} + 3907176098450002 T^{14} - 27774453730301147 T^{15} + 324801875822633630 T^{16} - 2194181844693790613 T^{17} + 24384686030426462482 T^{18} -$$$$15\!\cdots\!38$$$$T^{19} +$$$$16\!\cdots\!33$$$$T^{20} -$$$$95\!\cdots\!18$$$$T^{21} +$$$$10\!\cdots\!75$$$$T^{22} -$$$$48\!\cdots\!92$$$$T^{23} +$$$$53\!\cdots\!20$$$$T^{24} -$$$$19\!\cdots\!10$$$$T^{25} +$$$$23\!\cdots\!81$$$$T^{26} -$$$$59\!\cdots\!17$$$$T^{27} +$$$$82\!\cdots\!86$$$$T^{28} -$$$$11\!\cdots\!78$$$$T^{29} +$$$$19\!\cdots\!63$$$$T^{30} -$$$$11\!\cdots\!96$$$$T^{31} +$$$$23\!\cdots\!21$$$$T^{32}$$)($$1 - 48 T + 1790 T^{2} - 48298 T^{3} + 1116249 T^{4} - 21951489 T^{5} + 387171727 T^{6} - 6133408839 T^{7} + 89467750466 T^{8} - 1204253173348 T^{9} + 15175235165324 T^{10} - 179254222560342 T^{11} + 2002963195844289 T^{12} - 21170098555741523 T^{13} + 212885951986436599 T^{14} - 2034025008309474401 T^{15} + 18535129089765807910 T^{16} -$$$$16\!\cdots\!79$$$$T^{17} +$$$$13\!\cdots\!59$$$$T^{18} -$$$$10\!\cdots\!97$$$$T^{19} +$$$$78\!\cdots\!09$$$$T^{20} -$$$$55\!\cdots\!58$$$$T^{21} +$$$$36\!\cdots\!04$$$$T^{22} -$$$$23\!\cdots\!32$$$$T^{23} +$$$$13\!\cdots\!26$$$$T^{24} -$$$$73\!\cdots\!41$$$$T^{25} +$$$$36\!\cdots\!27$$$$T^{26} -$$$$16\!\cdots\!31$$$$T^{27} +$$$$65\!\cdots\!09$$$$T^{28} -$$$$22\!\cdots\!22$$$$T^{29} +$$$$66\!\cdots\!90$$$$T^{30} -$$$$13\!\cdots\!52$$$$T^{31} +$$$$23\!\cdots\!21$$$$T^{32}$$)($$1 + 34 T + 972 T^{2} + 20901 T^{3} + 402056 T^{4} + 6757725 T^{5} + 104967360 T^{6} + 1495027893 T^{7} + 20022350636 T^{8} + 251334088386 T^{9} + 2996721539937 T^{10} + 33875654453595 T^{11} + 365933241542311 T^{12} + 3771156649534113 T^{13} + 37263605828858117 T^{14} + 352390219640645688 T^{15} + 3200138285073873965 T^{16} + 27838827351611009352 T^{17} +$$$$23\!\cdots\!97$$$$T^{18} +$$$$18\!\cdots\!07$$$$T^{19} +$$$$14\!\cdots\!91$$$$T^{20} +$$$$10\!\cdots\!05$$$$T^{21} +$$$$72\!\cdots\!77$$$$T^{22} +$$$$48\!\cdots\!74$$$$T^{23} +$$$$30\!\cdots\!96$$$$T^{24} +$$$$17\!\cdots\!67$$$$T^{25} +$$$$99\!\cdots\!60$$$$T^{26} +$$$$50\!\cdots\!75$$$$T^{27} +$$$$23\!\cdots\!96$$$$T^{28} +$$$$97\!\cdots\!39$$$$T^{29} +$$$$35\!\cdots\!32$$$$T^{30} +$$$$99\!\cdots\!66$$$$T^{31} +$$$$23\!\cdots\!21$$$$T^{32}$$)($$1 - 46 T + 1652 T^{2} - 41934 T^{3} + 913375 T^{4} - 16648169 T^{5} + 272067184 T^{6} - 3944716283 T^{7} + 52754177710 T^{8} - 647408799368 T^{9} + 7513495891584 T^{10} - 82278295480761 T^{11} + 872957218286027 T^{12} - 8937344998796532 T^{13} + 90009306584051938 T^{14} - 881338931700124702 T^{15} + 8477537143157484023 T^{16} - 78804698976013235469 T^{17} +$$$$71\!\cdots\!12$$$$T^{18} -$$$$62\!\cdots\!51$$$$T^{19} +$$$$52\!\cdots\!43$$$$T^{20} -$$$$43\!\cdots\!78$$$$T^{21} +$$$$35\!\cdots\!78$$$$T^{22} -$$$$27\!\cdots\!68$$$$T^{23} +$$$$21\!\cdots\!67$$$$T^{24} -$$$$15\!\cdots\!99$$$$T^{25} +$$$$11\!\cdots\!24$$$$T^{26} -$$$$77\!\cdots\!92$$$$T^{27} +$$$$49\!\cdots\!10$$$$T^{28} -$$$$29\!\cdots\!57$$$$T^{29} +$$$$16\!\cdots\!44$$$$T^{30} -$$$$77\!\cdots\!91$$$$T^{31} +$$$$33\!\cdots\!75$$$$T^{32} -$$$$12\!\cdots\!66$$$$T^{33} +$$$$38\!\cdots\!92$$$$T^{34} -$$$$83\!\cdots\!14$$$$T^{35} +$$$$14\!\cdots\!61$$$$T^{36}$$)($$1 - 30 T + 1323 T^{2} - 30260 T^{3} + 793055 T^{4} - 14916571 T^{5} + 296531429 T^{6} - 4783765086 T^{7} + 78863642538 T^{8} - 1120203367049 T^{9} + 16007575831074 T^{10} - 203725377221417 T^{11} + 2588519002910803 T^{12} - 29871844374454987 T^{13} + 342857430889264467 T^{14} - 3616829807433295478 T^{15} + 37877700456738271513 T^{16} -$$$$36\!\cdots\!51$$$$T^{17} +$$$$35\!\cdots\!65$$$$T^{18} -$$$$31\!\cdots\!06$$$$T^{19} +$$$$27\!\cdots\!35$$$$T^{20} -$$$$22\!\cdots\!91$$$$T^{21} +$$$$18\!\cdots\!07$$$$T^{22} -$$$$14\!\cdots\!18$$$$T^{23} +$$$$10\!\cdots\!33$$$$T^{24} -$$$$72\!\cdots\!27$$$$T^{25} +$$$$49\!\cdots\!77$$$$T^{26} -$$$$30\!\cdots\!37$$$$T^{27} +$$$$19\!\cdots\!06$$$$T^{28} -$$$$10\!\cdots\!49$$$$T^{29} +$$$$58\!\cdots\!02$$$$T^{30} -$$$$28\!\cdots\!26$$$$T^{31} +$$$$13\!\cdots\!31$$$$T^{32} -$$$$55\!\cdots\!51$$$$T^{33} +$$$$23\!\cdots\!45$$$$T^{34} -$$$$69\!\cdots\!60$$$$T^{35} +$$$$24\!\cdots\!57$$$$T^{36} -$$$$43\!\cdots\!30$$$$T^{37} +$$$$11\!\cdots\!19$$$$T^{38}$$)($$1 - 18 T + 1184 T^{2} - 19119 T^{3} + 677618 T^{4} - 9886627 T^{5} + 249669964 T^{6} - 3315237533 T^{7} + 66604748933 T^{8} - 810231025074 T^{9} + 13722285935097 T^{10} - 153803296119898 T^{11} + 2274301424731523 T^{12} - 23596328615581358 T^{13} + 311767076012223811 T^{14} - 3004511485146333437 T^{15} + 36040317878578482083 T^{16} -$$$$32\!\cdots\!52$$$$T^{17} +$$$$35\!\cdots\!28$$$$T^{18} -$$$$29\!\cdots\!26$$$$T^{19} +$$$$30\!\cdots\!92$$$$T^{20} -$$$$23\!\cdots\!54$$$$T^{21} +$$$$22\!\cdots\!48$$$$T^{22} -$$$$15\!\cdots\!28$$$$T^{23} +$$$$14\!\cdots\!23$$$$T^{24} -$$$$92\!\cdots\!63$$$$T^{25} +$$$$75\!\cdots\!31$$$$T^{26} -$$$$45\!\cdots\!22$$$$T^{27} +$$$$34\!\cdots\!03$$$$T^{28} -$$$$18\!\cdots\!62$$$$T^{29} +$$$$12\!\cdots\!97$$$$T^{30} -$$$$60\!\cdots\!46$$$$T^{31} +$$$$39\!\cdots\!53$$$$T^{32} -$$$$15\!\cdots\!87$$$$T^{33} +$$$$92\!\cdots\!84$$$$T^{34} -$$$$28\!\cdots\!73$$$$T^{35} +$$$$15\!\cdots\!78$$$$T^{36} -$$$$34\!\cdots\!21$$$$T^{37} +$$$$17\!\cdots\!24$$$$T^{38} -$$$$20\!\cdots\!42$$$$T^{39} +$$$$89\!\cdots\!01$$$$T^{40}$$)
$83$ ($$1 + 17 T + 83 T^{2}$$)($$1 - 9 T + 83 T^{2}$$)($$1 + 9 T + 83 T^{2}$$)($$1 + 83 T^{2}$$)($$1 + 8 T + 83 T^{2}$$)($$1 - 6 T + 83 T^{2}$$)($$1 + 9 T + 83 T^{2}$$)($$1 + 3 T + 130 T^{2} + 249 T^{3} + 6889 T^{4}$$)($$1 + 15 T + 116 T^{2} + 1245 T^{3} + 6889 T^{4}$$)($$1 + 12 T + 170 T^{2} + 996 T^{3} + 6889 T^{4}$$)($$( 1 + 6 T + 83 T^{2} )^{2}$$)($$1 - 34 T + 962 T^{2} - 18636 T^{3} + 304656 T^{4} - 4073018 T^{5} + 46715214 T^{6} - 458242049 T^{7} + 3877362762 T^{8} - 28059021002 T^{9} + 174198340272 T^{10} - 884433270156 T^{11} + 3789357098566 T^{12} - 11115972694546 T^{13} + 27136050989627 T^{14}$$)($$1 + 17 T + 727 T^{2} + 10718 T^{3} + 256585 T^{4} + 3261797 T^{5} + 56903318 T^{6} + 626753150 T^{7} + 8759367643 T^{8} + 83774195962 T^{9} + 980570063180 T^{10} + 8118034148760 T^{11} + 81387315243940 T^{12} + 577120435982218 T^{13} + 5008492546488041 T^{14} + 29744652180461150 T^{15} + 224144482323553474 T^{16} + 1066413129033884093 T^{17} + 6962703643173443795 T^{18} + 24140068144066241438 T^{19} +$$$$13\!\cdots\!81$$$$T^{20} +$$$$26\!\cdots\!33$$$$T^{21} +$$$$12\!\cdots\!67$$$$T^{22}$$)($$1 - 21 T + 663 T^{2} - 10210 T^{3} + 205019 T^{4} - 2643048 T^{5} + 41783428 T^{6} - 470349966 T^{7} + 6284996835 T^{8} - 62840031715 T^{9} + 733381689758 T^{10} - 6562524873910 T^{11} + 68041602774789 T^{12} - 544689564534530 T^{13} + 5052266460742862 T^{14} - 35931113214224705 T^{15} + 298275397279414035 T^{16} - 1852727632507668138 T^{17} + 13660689550956728932 T^{18} - 71721885296031663096 T^{19} +$$$$46\!\cdots\!79$$$$T^{20} -$$$$19\!\cdots\!30$$$$T^{21} +$$$$10\!\cdots\!87$$$$T^{22} -$$$$27\!\cdots\!07$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 + 26 T + 912 T^{2} + 16870 T^{3} + 351403 T^{4} + 5167744 T^{5} + 81355420 T^{6} + 1007182561 T^{7} + 13151871421 T^{8} + 142231819988 T^{9} + 1621508875722 T^{10} + 15730315041009 T^{11} + 161523128267333 T^{12} + 1428718611245444 T^{13} + 13406419646188639 T^{14} + 108366140317511001 T^{15} + 927157695522455214 T^{16} + 6750083369404720148 T^{17} + 51805756058829163703 T^{18} +$$$$32\!\cdots\!09$$$$T^{19} +$$$$22\!\cdots\!40$$$$T^{20} +$$$$11\!\cdots\!04$$$$T^{21} +$$$$65\!\cdots\!09$$$$T^{22} +$$$$26\!\cdots\!30$$$$T^{23} +$$$$11\!\cdots\!04$$$$T^{24} +$$$$27\!\cdots\!86$$$$T^{25} +$$$$88\!\cdots\!63$$$$T^{26}$$)($$1 - 30 T + 969 T^{2} - 18676 T^{3} + 365335 T^{4} - 5350552 T^{5} + 79155481 T^{6} - 943348279 T^{7} + 11483465659 T^{8} - 115946714119 T^{9} + 1228033468687 T^{10} - 10957644918809 T^{11} + 107585686563309 T^{12} - 906460220784007 T^{13} + 8857114926688414 T^{14} - 75236198325072581 T^{15} + 741157794734635701 T^{16} - 6265438915191041683 T^{17} + 58280406555691094527 T^{18} -$$$$45\!\cdots\!17$$$$T^{19} +$$$$37\!\cdots\!71$$$$T^{20} -$$$$25\!\cdots\!33$$$$T^{21} +$$$$17\!\cdots\!21$$$$T^{22} -$$$$10\!\cdots\!56$$$$T^{23} +$$$$56\!\cdots\!15$$$$T^{24} -$$$$24\!\cdots\!92$$$$T^{25} +$$$$10\!\cdots\!09$$$$T^{26} -$$$$26\!\cdots\!90$$$$T^{27} +$$$$73\!\cdots\!29$$$$T^{28}$$)($$1 + 17 T + 548 T^{2} + 7235 T^{3} + 159717 T^{4} + 1868913 T^{5} + 32854279 T^{6} + 344359561 T^{7} + 5233963035 T^{8} + 50310979703 T^{9} + 683634439156 T^{10} + 6066266298761 T^{11} + 75529628557040 T^{12} + 624497670828251 T^{13} + 7199668162970602 T^{14} + 55521239292649406 T^{15} + 597572457526559966 T^{16} + 4302164454335821139 T^{17} + 43186859723744230480 T^{18} +$$$$28\!\cdots\!81$$$$T^{19} +$$$$26\!\cdots\!08$$$$T^{20} +$$$$16\!\cdots\!07$$$$T^{21} +$$$$14\!\cdots\!45$$$$T^{22} +$$$$77\!\cdots\!01$$$$T^{23} +$$$$61\!\cdots\!37$$$$T^{24} +$$$$28\!\cdots\!37$$$$T^{25} +$$$$20\!\cdots\!39$$$$T^{26} +$$$$77\!\cdots\!35$$$$T^{27} +$$$$48\!\cdots\!24$$$$T^{28} +$$$$12\!\cdots\!93$$$$T^{29} +$$$$61\!\cdots\!07$$$$T^{30}$$)($$1 + 15 T + 838 T^{2} + 11765 T^{3} + 347274 T^{4} + 4483083 T^{5} + 94328215 T^{6} + 1114931415 T^{7} + 18851537694 T^{8} + 204626105391 T^{9} + 2955643532351 T^{10} + 29598435804255 T^{11} + 378062838968094 T^{12} + 3501719008421705 T^{13} + 40369874910747532 T^{14} + 345564045988135983 T^{15} + 3640146863496575154 T^{16} + 28681815817015286589 T^{17} +$$$$27\!\cdots\!48$$$$T^{18} +$$$$20\!\cdots\!35$$$$T^{19} +$$$$17\!\cdots\!74$$$$T^{20} +$$$$11\!\cdots\!65$$$$T^{21} +$$$$96\!\cdots\!19$$$$T^{22} +$$$$55\!\cdots\!57$$$$T^{23} +$$$$42\!\cdots\!54$$$$T^{24} +$$$$20\!\cdots\!45$$$$T^{25} +$$$$14\!\cdots\!35$$$$T^{26} +$$$$57\!\cdots\!61$$$$T^{27} +$$$$37\!\cdots\!14$$$$T^{28} +$$$$10\!\cdots\!95$$$$T^{29} +$$$$61\!\cdots\!02$$$$T^{30} +$$$$91\!\cdots\!05$$$$T^{31} +$$$$50\!\cdots\!81$$$$T^{32}$$)($$1 + 9 T + 922 T^{2} + 8751 T^{3} + 425274 T^{4} + 4060279 T^{5} + 129458581 T^{6} + 1203835783 T^{7} + 28912374714 T^{8} + 256282046515 T^{9} + 4995921340093 T^{10} + 41580737482759 T^{11} + 688346845936766 T^{12} + 5315373706784247 T^{13} + 76961879728256332 T^{14} + 545261754693266101 T^{15} + 7047910466107914458 T^{16} + 45256725639541086383 T^{17} +$$$$53\!\cdots\!48$$$$T^{18} +$$$$30\!\cdots\!89$$$$T^{19} +$$$$32\!\cdots\!86$$$$T^{20} +$$$$16\!\cdots\!37$$$$T^{21} +$$$$16\!\cdots\!17$$$$T^{22} +$$$$69\!\cdots\!05$$$$T^{23} +$$$$65\!\cdots\!74$$$$T^{24} +$$$$22\!\cdots\!49$$$$T^{25} +$$$$20\!\cdots\!69$$$$T^{26} +$$$$52\!\cdots\!93$$$$T^{27} +$$$$45\!\cdots\!14$$$$T^{28} +$$$$77\!\cdots\!13$$$$T^{29} +$$$$67\!\cdots\!38$$$$T^{30} +$$$$55\!\cdots\!63$$$$T^{31} +$$$$50\!\cdots\!81$$$$T^{32}$$)($$1 - 39 T + 1431 T^{2} - 34708 T^{3} + 773041 T^{4} - 13965708 T^{5} + 234032966 T^{6} - 3403017682 T^{7} + 46448294726 T^{8} - 568019341368 T^{9} + 6603756562163 T^{10} - 70248493932706 T^{11} + 722668603920858 T^{12} - 6946547612092480 T^{13} + 66186053085590476 T^{14} - 603454190232013975 T^{15} + 5584537825414777508 T^{16} - 50086697789257159925 T^{17} +$$$$45\!\cdots\!64$$$$T^{18} -$$$$39\!\cdots\!60$$$$T^{19} +$$$$34\!\cdots\!18$$$$T^{20} -$$$$27\!\cdots\!58$$$$T^{21} +$$$$21\!\cdots\!47$$$$T^{22} -$$$$15\!\cdots\!36$$$$T^{23} +$$$$10\!\cdots\!66$$$$T^{24} -$$$$63\!\cdots\!46$$$$T^{25} +$$$$36\!\cdots\!34$$$$T^{26} -$$$$17\!\cdots\!36$$$$T^{27} +$$$$82\!\cdots\!01$$$$T^{28} -$$$$30\!\cdots\!04$$$$T^{29} +$$$$10\!\cdots\!99$$$$T^{30} -$$$$23\!\cdots\!73$$$$T^{31} +$$$$50\!\cdots\!81$$$$T^{32}$$)($$1 - 46 T + 1803 T^{2} - 49450 T^{3} + 1213637 T^{4} - 25057794 T^{5} + 476001267 T^{6} - 8084141739 T^{7} + 128449477860 T^{8} - 1877750632737 T^{9} + 25963046510186 T^{10} - 335627644220575 T^{11} + 4134348251646044 T^{12} - 48084643546611681 T^{13} + 535631470942771309 T^{14} - 5667781749956354908 T^{15} + 57627441353791009762 T^{16} -$$$$55\!\cdots\!66$$$$T^{17} +$$$$52\!\cdots\!58$$$$T^{18} -$$$$46\!\cdots\!78$$$$T^{19} +$$$$39\!\cdots\!18$$$$T^{20} -$$$$32\!\cdots\!96$$$$T^{21} +$$$$25\!\cdots\!89$$$$T^{22} -$$$$18\!\cdots\!83$$$$T^{23} +$$$$13\!\cdots\!36$$$$T^{24} -$$$$91\!\cdots\!25$$$$T^{25} +$$$$58\!\cdots\!26$$$$T^{26} -$$$$35\!\cdots\!11$$$$T^{27} +$$$$19\!\cdots\!40$$$$T^{28} -$$$$10\!\cdots\!13$$$$T^{29} +$$$$50\!\cdots\!87$$$$T^{30} -$$$$22\!\cdots\!22$$$$T^{31} +$$$$89\!\cdots\!73$$$$T^{32} -$$$$30\!\cdots\!50$$$$T^{33} +$$$$91\!\cdots\!43$$$$T^{34} -$$$$19\!\cdots\!58$$$$T^{35} +$$$$34\!\cdots\!09$$$$T^{36}$$)($$1 + T + 913 T^{2} + 180 T^{3} + 412053 T^{4} - 180103 T^{5} + 122830140 T^{6} - 112698348 T^{7} + 27225502887 T^{8} - 34293478900 T^{9} + 4787033795008 T^{10} - 7085502677768 T^{11} + 695564964961644 T^{12} - 1111539579594292 T^{13} + 85892305345946283 T^{14} - 140345510451137812 T^{15} + 9192190781252108163 T^{16} - 14778538914349895882 T^{17} +$$$$86\!\cdots\!08$$$$T^{18} -$$$$13\!\cdots\!36$$$$T^{19} +$$$$71\!\cdots\!64$$$$T^{20} -$$$$10\!\cdots\!98$$$$T^{21} +$$$$52\!\cdots\!81$$$$T^{22} -$$$$66\!\cdots\!52$$$$T^{23} +$$$$33\!\cdots\!69$$$$T^{24} -$$$$36\!\cdots\!48$$$$T^{25} +$$$$18\!\cdots\!88$$$$T^{26} -$$$$15\!\cdots\!88$$$$T^{27} +$$$$89\!\cdots\!24$$$$T^{28} -$$$$53\!\cdots\!00$$$$T^{29} +$$$$35\!\cdots\!29$$$$T^{30} -$$$$12\!\cdots\!28$$$$T^{31} +$$$$10\!\cdots\!20$$$$T^{32} -$$$$13\!\cdots\!87$$$$T^{33} +$$$$25\!\cdots\!71$$$$T^{34} +$$$$91\!\cdots\!80$$$$T^{35} +$$$$38\!\cdots\!99$$$$T^{36} +$$$$34\!\cdots\!09$$$$T^{37} +$$$$29\!\cdots\!47$$$$T^{38}$$)($$1 - T + 887 T^{2} - 696 T^{3} + 387443 T^{4} - 295714 T^{5} + 111591936 T^{6} - 99249840 T^{7} + 23963641195 T^{8} - 26427369351 T^{9} + 4117436531106 T^{10} - 5497886185864 T^{11} + 593163051161905 T^{12} - 904000829396146 T^{13} + 73957076079070724 T^{14} - 120559785802295129 T^{15} + 8138620605331576032 T^{16} - 13425709742136785765 T^{17} +$$$$79\!\cdots\!35$$$$T^{18} -$$$$12\!\cdots\!00$$$$T^{19} +$$$$70\!\cdots\!44$$$$T^{20} -$$$$10\!\cdots\!00$$$$T^{21} +$$$$54\!\cdots\!15$$$$T^{22} -$$$$76\!\cdots\!55$$$$T^{23} +$$$$38\!\cdots\!72$$$$T^{24} -$$$$47\!\cdots\!47$$$$T^{25} +$$$$24\!\cdots\!56$$$$T^{26} -$$$$24\!\cdots\!42$$$$T^{27} +$$$$13\!\cdots\!05$$$$T^{28} -$$$$10\!\cdots\!92$$$$T^{29} +$$$$63\!\cdots\!94$$$$T^{30} -$$$$34\!\cdots\!17$$$$T^{31} +$$$$25\!\cdots\!95$$$$T^{32} -$$$$88\!\cdots\!20$$$$T^{33} +$$$$82\!\cdots\!44$$$$T^{34} -$$$$18\!\cdots\!98$$$$T^{35} +$$$$19\!\cdots\!83$$$$T^{36} -$$$$29\!\cdots\!08$$$$T^{37} +$$$$30\!\cdots\!83$$$$T^{38} -$$$$29\!\cdots\!47$$$$T^{39} +$$$$24\!\cdots\!01$$$$T^{40}$$)
$89$ ($$1 - T + 89 T^{2}$$)($$1 + T + 89 T^{2}$$)($$1 - 9 T + 89 T^{2}$$)($$1 - 8 T + 89 T^{2}$$)($$1 - 12 T + 89 T^{2}$$)($$1 + 12 T + 89 T^{2}$$)($$1 - T + 89 T^{2}$$)($$1 + 23 T + 272 T^{2} + 2047 T^{3} + 7921 T^{4}$$)($$1 - 5 T + 78 T^{2} - 445 T^{3} + 7921 T^{4}$$)($$1 + 24 T + 314 T^{2} + 2136 T^{3} + 7921 T^{4}$$)($$1 + 82 T^{2} + 7921 T^{4}$$)($$1 - 12 T + 151 T^{2} - 2659 T^{3} + 35240 T^{4} - 317069 T^{5} + 3805221 T^{6} - 40673821 T^{7} + 338664669 T^{8} - 2511503549 T^{9} + 24843107560 T^{10} - 166831618819 T^{11} + 843192976799 T^{12} - 5963775491532 T^{13} + 44231334895529 T^{14}$$)($$1 - T + 464 T^{2} + 24 T^{3} + 111297 T^{4} + 87447 T^{5} + 18619837 T^{6} + 19886272 T^{7} + 2448903052 T^{8} + 2538261642 T^{9} + 263858245381 T^{10} + 245368640400 T^{11} + 23483383838909 T^{12} + 20105570466282 T^{13} + 1726400735665388 T^{14} + 1247709270415552 T^{15} + 103974276738689813 T^{16} + 43459522950666567 T^{17} + 4922814879867691113 T^{18} + 94478131336849944 T^{19} +$$$$16\!\cdots\!76$$$$T^{20} - 31181719929966183601 T^{21} +$$$$27\!\cdots\!89$$$$T^{22}$$)($$1 + 6 T + 248 T^{2} + 1937 T^{3} + 46222 T^{4} + 282188 T^{5} + 5446195 T^{6} + 28943943 T^{7} + 518826385 T^{8} + 1848017586 T^{9} + 40371147531 T^{10} + 102610466949 T^{11} + 3352784006073 T^{12} + 9132331558461 T^{13} + 319779859593051 T^{14} + 1302795109584834 T^{15} + 32552330084828785 T^{16} + 161624698400467407 T^{17} + 2706657021925343395 T^{18} + 12481551931499537452 T^{19} +$$$$18\!\cdots\!82$$$$T^{20} +$$$$67\!\cdots\!33$$$$T^{21} +$$$$77\!\cdots\!48$$$$T^{22} +$$$$16\!\cdots\!34$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 + 44 T + 1789 T^{2} + 48025 T^{3} + 1179457 T^{4} + 23460109 T^{5} + 431592848 T^{6} + 6880773166 T^{7} + 102377806578 T^{8} + 1360607322250 T^{9} + 16975488400752 T^{10} + 191986074688377 T^{11} + 2045012097441543 T^{12} + 19868978401857274 T^{13} + 182006076672297327 T^{14} + 1520721697606634217 T^{15} + 11967193082389736688 T^{16} + 85367552518974162250 T^{17} +$$$$57\!\cdots\!22$$$$T^{18} +$$$$34\!\cdots\!26$$$$T^{19} +$$$$19\!\cdots\!92$$$$T^{20} +$$$$92\!\cdots\!29$$$$T^{21} +$$$$41\!\cdots\!13$$$$T^{22} +$$$$14\!\cdots\!25$$$$T^{23} +$$$$49\!\cdots\!21$$$$T^{24} +$$$$10\!\cdots\!24$$$$T^{25} +$$$$21\!\cdots\!69$$$$T^{26}$$)($$1 + 4 T + 780 T^{2} + 1881 T^{3} + 289356 T^{4} + 274990 T^{5} + 69261693 T^{6} - 17925425 T^{7} + 12271686510 T^{8} - 13239275906 T^{9} + 1735603354082 T^{10} - 2547188943427 T^{11} + 202853568948719 T^{12} - 309799827574717 T^{13} + 19768290680155150 T^{14} - 27572184654149813 T^{15} + 1606803119642803199 T^{16} - 1795689242258788763 T^{17} +$$$$10\!\cdots\!62$$$$T^{18} - 73928903720817335794 T^{19} +$$$$60\!\cdots\!10$$$$T^{20} -$$$$79\!\cdots\!25$$$$T^{21} +$$$$27\!\cdots\!33$$$$T^{22} +$$$$96\!\cdots\!10$$$$T^{23} +$$$$90\!\cdots\!56$$$$T^{24} +$$$$52\!\cdots\!09$$$$T^{25} +$$$$19\!\cdots\!80$$$$T^{26} +$$$$87\!\cdots\!76$$$$T^{27} +$$$$19\!\cdots\!41$$$$T^{28}$$)($$1 + 36 T + 1309 T^{2} + 32167 T^{3} + 741397 T^{4} + 14246239 T^{5} + 256274512 T^{6} + 4104163126 T^{7} + 61882765454 T^{8} + 854773274590 T^{9} + 11174770511625 T^{10} + 135771629168046 T^{11} + 1567154404772610 T^{12} + 16936566839775001 T^{13} + 174266534670496584 T^{14} + 1684298621219882344 T^{15} + 15509721585674195976 T^{16} +$$$$13\!\cdots\!21$$$$T^{17} +$$$$11\!\cdots\!90$$$$T^{18} +$$$$85\!\cdots\!86$$$$T^{19} +$$$$62\!\cdots\!25$$$$T^{20} +$$$$42\!\cdots\!90$$$$T^{21} +$$$$27\!\cdots\!66$$$$T^{22} +$$$$16\!\cdots\!06$$$$T^{23} +$$$$89\!\cdots\!08$$$$T^{24} +$$$$44\!\cdots\!39$$$$T^{25} +$$$$20\!\cdots\!33$$$$T^{26} +$$$$79\!\cdots\!07$$$$T^{27} +$$$$28\!\cdots\!21$$$$T^{28} +$$$$70\!\cdots\!76$$$$T^{29} +$$$$17\!\cdots\!49$$$$T^{30}$$)($$1 - T + 543 T^{2} + 671 T^{3} + 152533 T^{4} + 517635 T^{5} + 30165176 T^{6} + 157224139 T^{7} + 4823063548 T^{8} + 30855005869 T^{9} + 665165199182 T^{10} + 4562642804149 T^{11} + 80959528623427 T^{12} + 549124327434249 T^{13} + 8716291116419723 T^{14} + 56211725364021865 T^{15} + 827104459422306710 T^{16} + 5002843557397945985 T^{17} + 69041741933160625883 T^{18} +$$$$38\!\cdots\!81$$$$T^{19} +$$$$50\!\cdots\!07$$$$T^{20} +$$$$25\!\cdots\!01$$$$T^{21} +$$$$33\!\cdots\!02$$$$T^{22} +$$$$13\!\cdots\!01$$$$T^{23} +$$$$18\!\cdots\!88$$$$T^{24} +$$$$55\!\cdots\!51$$$$T^{25} +$$$$94\!\cdots\!76$$$$T^{26} +$$$$14\!\cdots\!15$$$$T^{27} +$$$$37\!\cdots\!93$$$$T^{28} +$$$$14\!\cdots\!99$$$$T^{29} +$$$$10\!\cdots\!63$$$$T^{30} -$$$$17\!\cdots\!49$$$$T^{31} +$$$$15\!\cdots\!61$$$$T^{32}$$)($$1 + 17 T + 1127 T^{2} + 15983 T^{3} + 586311 T^{4} + 7166681 T^{5} + 191074546 T^{6} + 2062455143 T^{7} + 44443133398 T^{8} + 431204254609 T^{9} + 7927842129958 T^{10} + 69953463871825 T^{11} + 1131788728858665 T^{12} + 9138323523354515 T^{13} + 132584056451488545 T^{14} + 980924964406358011 T^{15} + 12914003614443073682 T^{16} + 87302321832165862979 T^{17} +$$$$10\!\cdots\!45$$$$T^{18} +$$$$64\!\cdots\!35$$$$T^{19} +$$$$71\!\cdots\!65$$$$T^{20} +$$$$39\!\cdots\!25$$$$T^{21} +$$$$39\!\cdots\!38$$$$T^{22} +$$$$19\!\cdots\!61$$$$T^{23} +$$$$17\!\cdots\!38$$$$T^{24} +$$$$72\!\cdots\!87$$$$T^{25} +$$$$59\!\cdots\!46$$$$T^{26} +$$$$19\!\cdots\!09$$$$T^{27} +$$$$14\!\cdots\!31$$$$T^{28} +$$$$35\!\cdots\!27$$$$T^{29} +$$$$22\!\cdots\!07$$$$T^{30} +$$$$29\!\cdots\!33$$$$T^{31} +$$$$15\!\cdots\!61$$$$T^{32}$$)($$1 - 32 T + 1088 T^{2} - 23137 T^{3} + 486714 T^{4} - 8120366 T^{5} + 133448243 T^{6} - 1889856135 T^{7} + 26464403740 T^{8} - 331997649864 T^{9} + 4133229432635 T^{10} - 47071798951924 T^{11} + 533593796463199 T^{12} - 5601161866848319 T^{13} + 58673100952596054 T^{14} - 572968389460590927 T^{15} + 5592319039158292684 T^{16} - 50994186661992592503 T^{17} +$$$$46\!\cdots\!34$$$$T^{18} -$$$$39\!\cdots\!11$$$$T^{19} +$$$$33\!\cdots\!59$$$$T^{20} -$$$$26\!\cdots\!76$$$$T^{21} +$$$$20\!\cdots\!35$$$$T^{22} -$$$$14\!\cdots\!56$$$$T^{23} +$$$$10\!\cdots\!40$$$$T^{24} -$$$$66\!\cdots\!15$$$$T^{25} +$$$$41\!\cdots\!43$$$$T^{26} -$$$$22\!\cdots\!74$$$$T^{27} +$$$$12\!\cdots\!94$$$$T^{28} -$$$$50\!\cdots\!53$$$$T^{29} +$$$$21\!\cdots\!08$$$$T^{30} -$$$$55\!\cdots\!68$$$$T^{31} +$$$$15\!\cdots\!61$$$$T^{32}$$)($$1 - 42 T + 1798 T^{2} - 48793 T^{3} + 1279302 T^{4} - 26760790 T^{5} + 539059369 T^{6} - 9388573567 T^{7} + 157864657375 T^{8} - 2384001838238 T^{9} + 34852410451996 T^{10} - 467195821431568 T^{11} + 6075757390898767 T^{12} - 73334134581530775 T^{13} + 860024600762049203 T^{14} - 9427780194222755892 T^{15} +$$$$10\!\cdots\!59$$$$T^{16} -$$$$10\!\cdots\!07$$$$T^{17} +$$$$97\!\cdots\!68$$$$T^{18} -$$$$89\!\cdots\!23$$$$T^{19} +$$$$79\!\cdots\!39$$$$T^{20} -$$$$66\!\cdots\!48$$$$T^{21} +$$$$53\!\cdots\!23$$$$T^{22} -$$$$40\!\cdots\!75$$$$T^{23} +$$$$30\!\cdots\!87$$$$T^{24} -$$$$20\!\cdots\!72$$$$T^{25} +$$$$13\!\cdots\!76$$$$T^{26} -$$$$83\!\cdots\!42$$$$T^{27} +$$$$49\!\cdots\!75$$$$T^{28} -$$$$26\!\cdots\!63$$$$T^{29} +$$$$13\!\cdots\!49$$$$T^{30} -$$$$58\!\cdots\!10$$$$T^{31} +$$$$25\!\cdots\!82$$$$T^{32} -$$$$84\!\cdots\!57$$$$T^{33} +$$$$27\!\cdots\!78$$$$T^{34} -$$$$57\!\cdots\!18$$$$T^{35} +$$$$12\!\cdots\!81$$$$T^{36}$$)($$1 + 5 T + 900 T^{2} + 5208 T^{3} + 408753 T^{4} + 2600183 T^{5} + 124544985 T^{6} + 845207354 T^{7} + 28548725824 T^{8} + 202656062858 T^{9} + 5238694079121 T^{10} + 38292815208174 T^{11} + 800260312469475 T^{12} + 5932265418022598 T^{13} + 104523943291455492 T^{14} + 772530166737831198 T^{15} + 11892279508870100778 T^{16} + 85898464458081369316 T^{17} +$$$$11\!\cdots\!55$$$$T^{18} +$$$$82\!\cdots\!80$$$$T^{19} +$$$$10\!\cdots\!95$$$$T^{20} +$$$$68\!\cdots\!36$$$$T^{21} +$$$$83\!\cdots\!82$$$$T^{22} +$$$$48\!\cdots\!18$$$$T^{23} +$$$$58\!\cdots\!08$$$$T^{24} +$$$$29\!\cdots\!78$$$$T^{25} +$$$$35\!\cdots\!75$$$$T^{26} +$$$$15\!\cdots\!94$$$$T^{27} +$$$$18\!\cdots\!89$$$$T^{28} +$$$$63\!\cdots\!58$$$$T^{29} +$$$$79\!\cdots\!36$$$$T^{30} +$$$$20\!\cdots\!34$$$$T^{31} +$$$$27\!\cdots\!65$$$$T^{32} +$$$$50\!\cdots\!03$$$$T^{33} +$$$$71\!\cdots\!97$$$$T^{34} +$$$$80\!\cdots\!88$$$$T^{35} +$$$$12\!\cdots\!00$$$$T^{36} +$$$$61\!\cdots\!05$$$$T^{37} +$$$$10\!\cdots\!09$$$$T^{38}$$)($$1 - 16 T + 1054 T^{2} - 12313 T^{3} + 495452 T^{4} - 4181350 T^{5} + 143352715 T^{6} - 815178841 T^{7} + 29862289153 T^{8} - 95871706672 T^{9} + 4986555809317 T^{10} - 5188938821125 T^{11} + 718166918489319 T^{12} + 484338156975993 T^{13} + 92377826244411923 T^{14} + 171552993935159192 T^{15} + 10685149175823232350 T^{16} + 27269038279907589269 T^{17} +$$$$11\!\cdots\!99$$$$T^{18} +$$$$31\!\cdots\!79$$$$T^{19} +$$$$10\!\cdots\!30$$$$T^{20} +$$$$27\!\cdots\!31$$$$T^{21} +$$$$87\!\cdots\!79$$$$T^{22} +$$$$19\!\cdots\!61$$$$T^{23} +$$$$67\!\cdots\!50$$$$T^{24} +$$$$95\!\cdots\!08$$$$T^{25} +$$$$45\!\cdots\!03$$$$T^{26} +$$$$21\!\cdots\!97$$$$T^{27} +$$$$28\!\cdots\!39$$$$T^{28} -$$$$18\!\cdots\!25$$$$T^{29} +$$$$15\!\cdots\!17$$$$T^{30} -$$$$26\!\cdots\!08$$$$T^{31} +$$$$73\!\cdots\!13$$$$T^{32} -$$$$17\!\cdots\!29$$$$T^{33} +$$$$28\!\cdots\!15$$$$T^{34} -$$$$72\!\cdots\!50$$$$T^{35} +$$$$76\!\cdots\!72$$$$T^{36} -$$$$16\!\cdots\!77$$$$T^{37} +$$$$12\!\cdots\!74$$$$T^{38} -$$$$17\!\cdots\!44$$$$T^{39} +$$$$97\!\cdots\!01$$$$T^{40}$$)
$97$ ($$1 + 6 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 - 8 T + 97 T^{2}$$)($$1 + 4 T + 97 T^{2}$$)($$1 + 16 T + 97 T^{2}$$)($$1 + 7 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 + 26 T + 346 T^{2} + 2522 T^{3} + 9409 T^{4}$$)($$1 - 3 T + 90 T^{2} - 291 T^{3} + 9409 T^{4}$$)($$1 - 14 T + 225 T^{2} - 1358 T^{3} + 9409 T^{4}$$)($$1 - 10 T + 165 T^{2} - 970 T^{3} + 9409 T^{4}$$)($$1 - 7 T + 326 T^{2} - 2842 T^{3} + 55405 T^{4} - 456619 T^{5} + 7188211 T^{6} - 47880078 T^{7} + 697256467 T^{8} - 4296328171 T^{9} + 50566647565 T^{10} - 251600216602 T^{11} + 2799472923782 T^{12} - 5830804034503 T^{13} + 80798284478113 T^{14}$$)($$1 + 45 T + 1820 T^{2} + 48766 T^{3} + 1176007 T^{4} + 22870361 T^{5} + 405854399 T^{6} + 6187284940 T^{7} + 86893093162 T^{8} + 1076504810282 T^{9} + 12349988741891 T^{10} + 126294350302956 T^{11} + 1197948907963427 T^{12} + 10128833759943338 T^{13} + 79304980015442026 T^{14} + 547755887080328140 T^{15} + 3485209819013240543 T^{16} + 19050370455620009369 T^{17} + 95019348134252234791 T^{18} +$$$$38\!\cdots\!26$$$$T^{19} +$$$$13\!\cdots\!40$$$$T^{20} +$$$$33\!\cdots\!05$$$$T^{21} +$$$$71\!\cdots\!53$$$$T^{22}$$)($$1 - 4 T + 389 T^{2} - 889 T^{3} + 83868 T^{4} - 183451 T^{5} + 14101452 T^{6} - 37965828 T^{7} + 1915592806 T^{8} - 5833378176 T^{9} + 221723974008 T^{10} - 732128943698 T^{11} + 22870071327251 T^{12} - 71016507538706 T^{13} + 2086200871441272 T^{14} - 5323966760024448 T^{15} + 169586053803952486 T^{16} - 326025483174737796 T^{17} + 11746114744850056908 T^{18} - 14822526085794307963 T^{19} +$$$$65\!\cdots\!48$$$$T^{20} -$$$$67\!\cdots\!13$$$$T^{21} +$$$$28\!\cdots\!61$$$$T^{22} -$$$$28\!\cdots\!12$$$$T^{23} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$1 - 17 T + 998 T^{2} - 14430 T^{3} + 471225 T^{4} - 5972993 T^{5} + 141228807 T^{6} - 1591368836 T^{7} + 30095354665 T^{8} - 303043084483 T^{9} + 4820083155707 T^{10} - 43368648096954 T^{11} + 597070384172585 T^{12} - 4777592162764534 T^{13} + 57915827264740745 T^{14} - 408055609944240186 T^{15} + 4399159753968574811 T^{16} - 26828186381302246723 T^{17} +$$$$25\!\cdots\!05$$$$T^{18} -$$$$13\!\cdots\!44$$$$T^{19} +$$$$11\!\cdots\!91$$$$T^{20} -$$$$46\!\cdots\!73$$$$T^{21} +$$$$35\!\cdots\!25$$$$T^{22} -$$$$10\!\cdots\!70$$$$T^{23} +$$$$71\!\cdots\!94$$$$T^{24} -$$$$11\!\cdots\!97$$$$T^{25} +$$$$67\!\cdots\!77$$$$T^{26}$$)($$1 - 15 T + 688 T^{2} - 9074 T^{3} + 232439 T^{4} - 2674739 T^{5} + 50852864 T^{6} - 510202963 T^{7} + 8088855856 T^{8} - 71493024766 T^{9} + 1014684615820 T^{10} - 8074806425495 T^{11} + 108805877810262 T^{12} - 810761204923202 T^{13} + 10784014670664272 T^{14} - 78643836877550594 T^{15} + 1023754504316755158 T^{16} - 7369657804775798135 T^{17} + 89829299480305825420 T^{18} -$$$$61\!\cdots\!62$$$$T^{19} +$$$$67\!\cdots\!24$$$$T^{20} -$$$$41\!\cdots\!19$$$$T^{21} +$$$$39\!\cdots\!04$$$$T^{22} -$$$$20\!\cdots\!63$$$$T^{23} +$$$$17\!\cdots\!11$$$$T^{24} -$$$$64\!\cdots\!22$$$$T^{25} +$$$$47\!\cdots\!08$$$$T^{26} -$$$$10\!\cdots\!55$$$$T^{27} +$$$$65\!\cdots\!69$$$$T^{28}$$)($$1 + 2 T + 916 T^{2} + 635 T^{3} + 412628 T^{4} - 81694 T^{5} + 123034822 T^{6} - 92508076 T^{7} + 27263497789 T^{8} - 29074002036 T^{9} + 4750843331690 T^{10} - 5774001717499 T^{11} + 671586651094183 T^{12} - 833726764140702 T^{13} + 78347351598109205 T^{14} - 91916345086808106 T^{15} + 7599693105016592885 T^{16} - 7844535123799865118 T^{17} +$$$$61\!\cdots\!59$$$$T^{18} -$$$$51\!\cdots\!19$$$$T^{19} +$$$$40\!\cdots\!30$$$$T^{20} -$$$$24\!\cdots\!44$$$$T^{21} +$$$$22\!\cdots\!57$$$$T^{22} -$$$$72\!\cdots\!36$$$$T^{23} +$$$$93\!\cdots\!74$$$$T^{24} -$$$$60\!\cdots\!06$$$$T^{25} +$$$$29\!\cdots\!84$$$$T^{26} +$$$$44\!\cdots\!35$$$$T^{27} +$$$$61\!\cdots\!32$$$$T^{28} +$$$$13\!\cdots\!38$$$$T^{29} +$$$$63\!\cdots\!93$$$$T^{30}$$)($$1 - 41 T + 1499 T^{2} - 38587 T^{3} + 902626 T^{4} - 17930470 T^{5} + 329984509 T^{6} - 5477364638 T^{7} + 85335761433 T^{8} - 1232122907558 T^{9} + 16844252420378 T^{10} - 216472222887038 T^{11} + 2649198951432652 T^{12} - 30719144250882281 T^{13} + 340398004753863806 T^{14} - 3588518828385646187 T^{15} + 36211946895519678800 T^{16} -$$$$34\!\cdots\!39$$$$T^{17} +$$$$32\!\cdots\!54$$$$T^{18} -$$$$28\!\cdots\!13$$$$T^{19} +$$$$23\!\cdots\!12$$$$T^{20} -$$$$18\!\cdots\!66$$$$T^{21} +$$$$14\!\cdots\!62$$$$T^{22} -$$$$99\!\cdots\!54$$$$T^{23} +$$$$66\!\cdots\!13$$$$T^{24} -$$$$41\!\cdots\!46$$$$T^{25} +$$$$24\!\cdots\!41$$$$T^{26} -$$$$12\!\cdots\!10$$$$T^{27} +$$$$62\!\cdots\!66$$$$T^{28} -$$$$25\!\cdots\!99$$$$T^{29} +$$$$97\!\cdots\!31$$$$T^{30} -$$$$25\!\cdots\!13$$$$T^{31} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 - 17 T + 913 T^{2} - 13489 T^{3} + 407538 T^{4} - 5428802 T^{5} + 120440919 T^{6} - 1477034756 T^{7} + 26668402651 T^{8} - 304251849558 T^{9} + 4714542700790 T^{10} - 50215256728296 T^{11} + 689165255502424 T^{12} - 6848160468346513 T^{13} + 84938546496995736 T^{14} - 784702342845576967 T^{15} + 8914605800421217636 T^{16} - 76116127256020965799 T^{17} +$$$$79\!\cdots\!24$$$$T^{18} -$$$$62\!\cdots\!49$$$$T^{19} +$$$$61\!\cdots\!44$$$$T^{20} -$$$$43\!\cdots\!72$$$$T^{21} +$$$$39\!\cdots\!10$$$$T^{22} -$$$$24\!\cdots\!54$$$$T^{23} +$$$$20\!\cdots\!11$$$$T^{24} -$$$$11\!\cdots\!52$$$$T^{25} +$$$$88\!\cdots\!31$$$$T^{26} -$$$$38\!\cdots\!06$$$$T^{27} +$$$$28\!\cdots\!58$$$$T^{28} -$$$$90\!\cdots\!53$$$$T^{29} +$$$$59\!\cdots\!97$$$$T^{30} -$$$$10\!\cdots\!81$$$$T^{31} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 + 4 T + 855 T^{2} + 4309 T^{3} + 352124 T^{4} + 1945811 T^{5} + 93690966 T^{6} + 504108188 T^{7} + 18128480187 T^{8} + 84709603850 T^{9} + 2718723343687 T^{10} + 9828561478241 T^{11} + 332212996296665 T^{12} + 837257682488933 T^{13} + 35171789290194436 T^{14} + 62777578584495400 T^{15} + 3469534574436373438 T^{16} + 6089425122696053800 T^{17} +$$$$33\!\cdots\!24$$$$T^{18} +$$$$76\!\cdots\!09$$$$T^{19} +$$$$29\!\cdots\!65$$$$T^{20} +$$$$84\!\cdots\!37$$$$T^{21} +$$$$22\!\cdots\!23$$$$T^{22} +$$$$68\!\cdots\!50$$$$T^{23} +$$$$14\!\cdots\!07$$$$T^{24} +$$$$38\!\cdots\!96$$$$T^{25} +$$$$69\!\cdots\!34$$$$T^{26} +$$$$13\!\cdots\!83$$$$T^{27} +$$$$24\!\cdots\!84$$$$T^{28} +$$$$29\!\cdots\!93$$$$T^{29} +$$$$55\!\cdots\!95$$$$T^{30} +$$$$25\!\cdots\!72$$$$T^{31} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 + 35 T + 1444 T^{2} + 34718 T^{3} + 871617 T^{4} + 16689897 T^{5} + 324272940 T^{6} + 5304501825 T^{7} + 87089442417 T^{8} + 1261878995611 T^{9} + 18253738121908 T^{10} + 239093914197707 T^{11} + 3119110855161003 T^{12} + 37405451259827487 T^{13} + 446307927225846884 T^{14} + 4938726924768483995 T^{15} + 54347074761442941730 T^{16} +$$$$55\!\cdots\!57$$$$T^{17} +$$$$56\!\cdots\!04$$$$T^{18} +$$$$54\!\cdots\!29$$$$T^{19} +$$$$51\!\cdots\!70$$$$T^{20} +$$$$45\!\cdots\!35$$$$T^{21} +$$$$39\!\cdots\!04$$$$T^{22} +$$$$32\!\cdots\!59$$$$T^{23} +$$$$25\!\cdots\!87$$$$T^{24} +$$$$19\!\cdots\!91$$$$T^{25} +$$$$14\!\cdots\!88$$$$T^{26} +$$$$95\!\cdots\!87$$$$T^{27} +$$$$64\!\cdots\!33$$$$T^{28} +$$$$37\!\cdots\!25$$$$T^{29} +$$$$22\!\cdots\!40$$$$T^{30} +$$$$11\!\cdots\!69$$$$T^{31} +$$$$56\!\cdots\!73$$$$T^{32} +$$$$21\!\cdots\!74$$$$T^{33} +$$$$88\!\cdots\!24$$$$T^{34} +$$$$20\!\cdots\!95$$$$T^{35} +$$$$57\!\cdots\!89$$$$T^{36}$$)($$1 - 5 T + 1119 T^{2} - 7425 T^{3} + 626161 T^{4} - 4997793 T^{5} + 234060233 T^{6} - 2106203122 T^{7} + 65583827219 T^{8} - 634772102388 T^{9} + 14616979308761 T^{10} - 146747567731490 T^{11} + 2681647163351003 T^{12} - 27114376204648986 T^{13} + 413553226986122049 T^{14} - 4106187033289173770 T^{15} + 54307299971976751138 T^{16} -$$$$51\!\cdots\!28$$$$T^{17} +$$$$61\!\cdots\!00$$$$T^{18} -$$$$54\!\cdots\!70$$$$T^{19} +$$$$59\!\cdots\!00$$$$T^{20} -$$$$48\!\cdots\!52$$$$T^{21} +$$$$49\!\cdots\!74$$$$T^{22} -$$$$36\!\cdots\!70$$$$T^{23} +$$$$35\!\cdots\!93$$$$T^{24} -$$$$22\!\cdots\!94$$$$T^{25} +$$$$21\!\cdots\!39$$$$T^{26} -$$$$11\!\cdots\!90$$$$T^{27} +$$$$11\!\cdots\!37$$$$T^{28} -$$$$46\!\cdots\!12$$$$T^{29} +$$$$46\!\cdots\!07$$$$T^{30} -$$$$14\!\cdots\!02$$$$T^{31} +$$$$15\!\cdots\!41$$$$T^{32} -$$$$32\!\cdots\!17$$$$T^{33} +$$$$39\!\cdots\!73$$$$T^{34} -$$$$45\!\cdots\!25$$$$T^{35} +$$$$66\!\cdots\!03$$$$T^{36} -$$$$28\!\cdots\!45$$$$T^{37} +$$$$56\!\cdots\!33$$$$T^{38}$$)($$1 + 32 T + 1491 T^{2} + 35175 T^{3} + 973478 T^{4} + 18675375 T^{5} + 393370752 T^{6} + 6490900374 T^{7} + 114399025400 T^{8} + 1681555576436 T^{9} + 26020622897892 T^{10} + 348211972917488 T^{11} + 4860356046062111 T^{12} + 59995895481335366 T^{13} + 767559931026210100 T^{14} + 8808788952687065688 T^{15} +$$$$10\!\cdots\!79$$$$T^{16} +$$$$11\!\cdots\!30$$$$T^{17} +$$$$12\!\cdots\!97$$$$T^{18} +$$$$12\!\cdots\!32$$$$T^{19} +$$$$12\!\cdots\!86$$$$T^{20} +$$$$12\!\cdots\!04$$$$T^{21} +$$$$11\!\cdots\!73$$$$T^{22} +$$$$10\!\cdots\!90$$$$T^{23} +$$$$92\!\cdots\!99$$$$T^{24} +$$$$75\!\cdots\!16$$$$T^{25} +$$$$63\!\cdots\!00$$$$T^{26} +$$$$48\!\cdots\!58$$$$T^{27} +$$$$38\!\cdots\!71$$$$T^{28} +$$$$26\!\cdots\!96$$$$T^{29} +$$$$19\!\cdots\!08$$$$T^{30} +$$$$12\!\cdots\!08$$$$T^{31} +$$$$79\!\cdots\!00$$$$T^{32} +$$$$43\!\cdots\!98$$$$T^{33} +$$$$25\!\cdots\!88$$$$T^{34} +$$$$11\!\cdots\!75$$$$T^{35} +$$$$59\!\cdots\!38$$$$T^{36} +$$$$20\!\cdots\!75$$$$T^{37} +$$$$86\!\cdots\!99$$$$T^{38} +$$$$17\!\cdots\!56$$$$T^{39} +$$$$54\!\cdots\!01$$$$T^{40}$$)