Properties

Label 4410.2
Level 4410
Weight 2
Dimension 117929
Nonzero newspaces 60
Sturm bound 2032128

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4410\( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(2032128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4410))\).

Total New Old
Modular forms 515712 117929 397783
Cusp forms 500353 117929 382424
Eisenstein series 15359 0 15359

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4410))\)

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
4410.2.a \(\chi_{4410}(1, \cdot)\) 4410.2.a.a 1 1
4410.2.a.b 1
4410.2.a.c 1
4410.2.a.d 1
4410.2.a.e 1
4410.2.a.f 1
4410.2.a.g 1
4410.2.a.h 1
4410.2.a.i 1
4410.2.a.j 1
4410.2.a.k 1
4410.2.a.l 1
4410.2.a.m 1
4410.2.a.n 1
4410.2.a.o 1
4410.2.a.p 1
4410.2.a.q 1
4410.2.a.r 1
4410.2.a.s 1
4410.2.a.t 1
4410.2.a.u 1
4410.2.a.v 1
4410.2.a.w 1
4410.2.a.x 1
4410.2.a.y 1
4410.2.a.z 1
4410.2.a.ba 1
4410.2.a.bb 1
4410.2.a.bc 1
4410.2.a.bd 1
4410.2.a.be 1
4410.2.a.bf 1
4410.2.a.bg 1
4410.2.a.bh 1
4410.2.a.bi 1
4410.2.a.bj 1
4410.2.a.bk 1
4410.2.a.bl 1
4410.2.a.bm 1
4410.2.a.bn 2
4410.2.a.bo 2
4410.2.a.bp 2
4410.2.a.bq 2
4410.2.a.br 2
4410.2.a.bs 2
4410.2.a.bt 2
4410.2.a.bu 2
4410.2.a.bv 2
4410.2.a.bw 2
4410.2.a.bx 2
4410.2.a.by 2
4410.2.a.bz 2
4410.2.a.ca 2
4410.2.b \(\chi_{4410}(881, \cdot)\) 4410.2.b.a 8 1
4410.2.b.b 8
4410.2.b.c 8
4410.2.b.d 8
4410.2.b.e 8
4410.2.b.f 8
4410.2.d \(\chi_{4410}(4409, \cdot)\) 4410.2.d.a 16 1
4410.2.d.b 16
4410.2.d.c 24
4410.2.d.d 24
4410.2.g \(\chi_{4410}(3529, \cdot)\) n/a 102 1
4410.2.i \(\chi_{4410}(3301, \cdot)\) n/a 320 2
4410.2.j \(\chi_{4410}(1471, \cdot)\) n/a 328 2
4410.2.k \(\chi_{4410}(361, \cdot)\) n/a 136 2
4410.2.l \(\chi_{4410}(961, \cdot)\) n/a 320 2
4410.2.m \(\chi_{4410}(197, \cdot)\) n/a 164 2
4410.2.p \(\chi_{4410}(1567, \cdot)\) n/a 200 2
4410.2.r \(\chi_{4410}(2579, \cdot)\) n/a 480 2
4410.2.t \(\chi_{4410}(3461, \cdot)\) n/a 320 2
4410.2.u \(\chi_{4410}(1549, \cdot)\) n/a 200 2
4410.2.z \(\chi_{4410}(589, \cdot)\) n/a 492 2
4410.2.ba \(\chi_{4410}(2419, \cdot)\) n/a 480 2
4410.2.be \(\chi_{4410}(521, \cdot)\) n/a 112 2
4410.2.bf \(\chi_{4410}(1469, \cdot)\) n/a 480 2
4410.2.bi \(\chi_{4410}(509, \cdot)\) n/a 480 2
4410.2.bk \(\chi_{4410}(1391, \cdot)\) n/a 320 2
4410.2.bl \(\chi_{4410}(2351, \cdot)\) n/a 320 2
4410.2.bo \(\chi_{4410}(1979, \cdot)\) n/a 160 2
4410.2.bq \(\chi_{4410}(79, \cdot)\) n/a 480 2
4410.2.bs \(\chi_{4410}(631, \cdot)\) n/a 576 6
4410.2.bu \(\chi_{4410}(1733, \cdot)\) n/a 960 4
4410.2.bw \(\chi_{4410}(1207, \cdot)\) n/a 400 4
4410.2.bx \(\chi_{4410}(607, \cdot)\) n/a 960 4
4410.2.ca \(\chi_{4410}(97, \cdot)\) n/a 960 4
4410.2.cb \(\chi_{4410}(1373, \cdot)\) n/a 984 4
4410.2.ce \(\chi_{4410}(263, \cdot)\) n/a 960 4
4410.2.cf \(\chi_{4410}(557, \cdot)\) n/a 320 4
4410.2.ch \(\chi_{4410}(313, \cdot)\) n/a 960 4
4410.2.cl \(\chi_{4410}(379, \cdot)\) n/a 840 6
4410.2.cm \(\chi_{4410}(629, \cdot)\) n/a 672 6
4410.2.co \(\chi_{4410}(251, \cdot)\) n/a 480 6
4410.2.cq \(\chi_{4410}(331, \cdot)\) n/a 2688 12
4410.2.cr \(\chi_{4410}(541, \cdot)\) n/a 1104 12
4410.2.cs \(\chi_{4410}(211, \cdot)\) n/a 2688 12
4410.2.ct \(\chi_{4410}(121, \cdot)\) n/a 2688 12
4410.2.cv \(\chi_{4410}(307, \cdot)\) n/a 1680 12
4410.2.cw \(\chi_{4410}(323, \cdot)\) n/a 1344 12
4410.2.cy \(\chi_{4410}(319, \cdot)\) n/a 4032 12
4410.2.dc \(\chi_{4410}(89, \cdot)\) n/a 1344 12
4410.2.dd \(\chi_{4410}(41, \cdot)\) n/a 2688 12
4410.2.dg \(\chi_{4410}(101, \cdot)\) n/a 2688 12
4410.2.di \(\chi_{4410}(479, \cdot)\) n/a 4032 12
4410.2.dj \(\chi_{4410}(209, \cdot)\) n/a 4032 12
4410.2.dm \(\chi_{4410}(341, \cdot)\) n/a 864 12
4410.2.do \(\chi_{4410}(499, \cdot)\) n/a 4032 12
4410.2.dr \(\chi_{4410}(169, \cdot)\) n/a 4032 12
4410.2.du \(\chi_{4410}(109, \cdot)\) n/a 1680 12
4410.2.dx \(\chi_{4410}(311, \cdot)\) n/a 2688 12
4410.2.dz \(\chi_{4410}(59, \cdot)\) n/a 4032 12
4410.2.ea \(\chi_{4410}(157, \cdot)\) n/a 8064 24
4410.2.ec \(\chi_{4410}(113, \cdot)\) n/a 8064 24
4410.2.ef \(\chi_{4410}(53, \cdot)\) n/a 2688 24
4410.2.eg \(\chi_{4410}(23, \cdot)\) n/a 8064 24
4410.2.ej \(\chi_{4410}(103, \cdot)\) n/a 8064 24
4410.2.ek \(\chi_{4410}(73, \cdot)\) n/a 3360 24
4410.2.en \(\chi_{4410}(13, \cdot)\) n/a 8064 24
4410.2.ep \(\chi_{4410}(317, \cdot)\) n/a 8064 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4410))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4410)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2205))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{16} \))
$3$ 1
$5$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{8} \))(\( ( 1 + T )^{8} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{8} \))(\( 1 - 6 T^{2} + 17 T^{4} + 42 T^{6} - 876 T^{8} + 1050 T^{10} + 10625 T^{12} - 93750 T^{14} + 390625 T^{16} \))(\( 1 - 6 T^{2} + 17 T^{4} + 42 T^{6} - 876 T^{8} + 1050 T^{10} + 10625 T^{12} - 93750 T^{14} + 390625 T^{16} \))
$7$ 1
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 19 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 19 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 19 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 19 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 64 T^{2} + 1952 T^{4} - 37312 T^{6} + 489570 T^{8} - 4514752 T^{10} + 28579232 T^{12} - 113379904 T^{14} + 214358881 T^{16} \))(\( 1 - 32 T^{2} + 670 T^{4} - 9920 T^{6} + 121411 T^{8} - 1200320 T^{10} + 9809470 T^{12} - 56689952 T^{14} + 214358881 T^{16} \))(\( 1 - 32 T^{2} + 544 T^{4} - 8352 T^{6} + 109154 T^{8} - 1010592 T^{10} + 7964704 T^{12} - 56689952 T^{14} + 214358881 T^{16} \))(\( 1 - 64 T^{2} + 1952 T^{4} - 37312 T^{6} + 489570 T^{8} - 4514752 T^{10} + 28579232 T^{12} - 113379904 T^{14} + 214358881 T^{16} \))(\( 1 - 32 T^{2} + 670 T^{4} - 9920 T^{6} + 121411 T^{8} - 1200320 T^{10} + 9809470 T^{12} - 56689952 T^{14} + 214358881 T^{16} \))(\( 1 - 32 T^{2} + 544 T^{4} - 8352 T^{6} + 109154 T^{8} - 1010592 T^{10} + 7964704 T^{12} - 56689952 T^{14} + 214358881 T^{16} \))(\( ( 1 - 38 T^{2} + 514 T^{4} - 1376 T^{6} - 21281 T^{8} - 166496 T^{10} + 7525474 T^{12} - 67319318 T^{14} + 214358881 T^{16} )^{2} \))(\( ( 1 - 38 T^{2} + 514 T^{4} - 1376 T^{6} - 21281 T^{8} - 166496 T^{10} + 7525474 T^{12} - 67319318 T^{14} + 214358881 T^{16} )^{2} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 7 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 4 T + 23 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 8 T + 34 T^{2} + 104 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 23 T^{2} + 52 T^{3} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 8 T + 34 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 8 T + 34 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 23 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))(\( 1 + 8 T + 34 T^{2} + 104 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))(\( 1 - 4 T + 23 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 16 T^{2} + 308 T^{4} - 5424 T^{6} + 50118 T^{8} - 916656 T^{10} + 8796788 T^{12} - 77228944 T^{14} + 815730721 T^{16} \))(\( 1 - 80 T^{2} + 3006 T^{4} - 69568 T^{6} + 1087139 T^{8} - 11756992 T^{10} + 85854366 T^{12} - 386144720 T^{14} + 815730721 T^{16} \))(\( 1 - 80 T^{2} + 2996 T^{4} - 69104 T^{6} + 1078470 T^{8} - 11678576 T^{10} + 85568756 T^{12} - 386144720 T^{14} + 815730721 T^{16} \))(\( 1 - 16 T^{2} + 308 T^{4} - 5424 T^{6} + 50118 T^{8} - 916656 T^{10} + 8796788 T^{12} - 77228944 T^{14} + 815730721 T^{16} \))(\( 1 - 80 T^{2} + 3006 T^{4} - 69568 T^{6} + 1087139 T^{8} - 11756992 T^{10} + 85854366 T^{12} - 386144720 T^{14} + 815730721 T^{16} \))(\( 1 - 80 T^{2} + 2996 T^{4} - 69104 T^{6} + 1078470 T^{8} - 11678576 T^{10} + 85568756 T^{12} - 386144720 T^{14} + 815730721 T^{16} \))(\( ( 1 + 32 T^{2} + 473 T^{4} + 8616 T^{6} + 148784 T^{8} + 1456104 T^{10} + 13509353 T^{12} + 154457888 T^{14} + 815730721 T^{16} )^{2} \))(\( ( 1 + 32 T^{2} + 473 T^{4} + 8616 T^{6} + 148784 T^{8} + 1456104 T^{10} + 13509353 T^{12} + 154457888 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 4 T + 10 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 36 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 10 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 4 T + 36 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 36 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 10 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 36 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 10 T^{2} - 68 T^{3} + 289 T^{4} \))(\( ( 1 + 28 T^{2} - 72 T^{3} + 468 T^{4} - 1224 T^{5} + 8092 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 28 T^{2} + 96 T^{3} + 342 T^{4} + 1632 T^{5} + 8092 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 60 T^{2} + 8 T^{3} + 1460 T^{4} + 136 T^{5} + 17340 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 28 T^{2} + 72 T^{3} + 468 T^{4} + 1224 T^{5} + 8092 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 28 T^{2} - 96 T^{3} + 342 T^{4} - 1632 T^{5} + 8092 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 60 T^{2} - 8 T^{3} + 1460 T^{4} - 136 T^{5} + 17340 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 - 52 T^{2} + 1784 T^{4} - 42108 T^{6} + 805934 T^{8} - 12169212 T^{10} + 149001464 T^{12} - 1255153588 T^{14} + 6975757441 T^{16} )^{2} \))(\( ( 1 - 52 T^{2} + 1784 T^{4} - 42108 T^{6} + 805934 T^{8} - 12169212 T^{10} + 149001464 T^{12} - 1255153588 T^{14} + 6975757441 T^{16} )^{2} \))
$19$ (\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 34 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 11 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 - 4 T + 34 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 34 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 11 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 46 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 34 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 40 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 8 T + 46 T^{2} - 152 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 112 T^{2} + 5956 T^{4} - 197328 T^{6} + 4474022 T^{8} - 71235408 T^{10} + 776191876 T^{12} - 5269138672 T^{14} + 16983563041 T^{16} \))(\( 1 - 116 T^{2} + 6330 T^{4} - 213136 T^{6} + 4859555 T^{8} - 76942096 T^{10} + 824931930 T^{12} - 5457322196 T^{14} + 16983563041 T^{16} \))(\( 1 - 48 T^{2} + 1092 T^{4} - 20496 T^{6} + 392870 T^{8} - 7399056 T^{10} + 142310532 T^{12} - 2258202288 T^{14} + 16983563041 T^{16} \))(\( 1 - 112 T^{2} + 5956 T^{4} - 197328 T^{6} + 4474022 T^{8} - 71235408 T^{10} + 776191876 T^{12} - 5269138672 T^{14} + 16983563041 T^{16} \))(\( 1 - 116 T^{2} + 6330 T^{4} - 213136 T^{6} + 4859555 T^{8} - 76942096 T^{10} + 824931930 T^{12} - 5457322196 T^{14} + 16983563041 T^{16} \))(\( 1 - 48 T^{2} + 1092 T^{4} - 20496 T^{6} + 392870 T^{8} - 7399056 T^{10} + 142310532 T^{12} - 2258202288 T^{14} + 16983563041 T^{16} \))(\( ( 1 - 42 T^{2} + 1613 T^{4} - 45630 T^{6} + 903912 T^{8} - 16472430 T^{10} + 210207773 T^{12} - 1975927002 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 - 42 T^{2} + 1613 T^{4} - 45630 T^{6} + 903912 T^{8} - 16472430 T^{10} + 210207773 T^{12} - 1975927002 T^{14} + 16983563041 T^{16} )^{2} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( 1 + 12 T + 74 T^{2} + 276 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 12 T + 74 T^{2} + 276 T^{3} + 529 T^{4} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( 1 + 48 T^{2} + 980 T^{4} - 4592 T^{6} - 398298 T^{8} - 2429168 T^{10} + 274244180 T^{12} + 7105722672 T^{14} + 78310985281 T^{16} \))(\( ( 1 - 78 T^{2} + 2531 T^{4} - 41262 T^{6} + 279841 T^{8} )^{2} \))(\( 1 - 144 T^{2} + 9428 T^{4} - 376368 T^{6} + 10282534 T^{8} - 199098672 T^{10} + 2638340948 T^{12} - 21317168016 T^{14} + 78310985281 T^{16} \))(\( 1 + 48 T^{2} + 980 T^{4} - 4592 T^{6} - 398298 T^{8} - 2429168 T^{10} + 274244180 T^{12} + 7105722672 T^{14} + 78310985281 T^{16} \))(\( ( 1 - 78 T^{2} + 2531 T^{4} - 41262 T^{6} + 279841 T^{8} )^{2} \))(\( 1 - 144 T^{2} + 9428 T^{4} - 376368 T^{6} + 10282534 T^{8} - 199098672 T^{10} + 2638340948 T^{12} - 21317168016 T^{14} + 78310985281 T^{16} \))(\( ( 1 + 4 T + 39 T^{2} + 12 T^{3} + 442 T^{4} + 276 T^{5} + 20631 T^{6} + 48668 T^{7} + 279841 T^{8} )^{4} \))(\( ( 1 - 4 T + 39 T^{2} - 12 T^{3} + 442 T^{4} - 276 T^{5} + 20631 T^{6} - 48668 T^{7} + 279841 T^{8} )^{4} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 8 T + 56 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 - 8 T + 72 T^{2} - 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 + 8 T + 56 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 72 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 - 144 T^{2} + 8384 T^{4} - 272784 T^{6} + 7329058 T^{8} - 229411344 T^{10} + 5929843904 T^{12} - 85654558224 T^{14} + 500246412961 T^{16} \))(\( ( 1 - 36 T^{2} + 470 T^{4} - 30276 T^{6} + 707281 T^{8} )^{2} \))(\( 1 - 112 T^{2} + 7488 T^{4} - 339056 T^{6} + 11412770 T^{8} - 285146096 T^{10} + 5296120128 T^{12} - 66620211952 T^{14} + 500246412961 T^{16} \))(\( 1 - 144 T^{2} + 8384 T^{4} - 272784 T^{6} + 7329058 T^{8} - 229411344 T^{10} + 5929843904 T^{12} - 85654558224 T^{14} + 500246412961 T^{16} \))(\( ( 1 - 36 T^{2} + 470 T^{4} - 30276 T^{6} + 707281 T^{8} )^{2} \))(\( 1 - 112 T^{2} + 7488 T^{4} - 339056 T^{6} + 11412770 T^{8} - 285146096 T^{10} + 5296120128 T^{12} - 66620211952 T^{14} + 500246412961 T^{16} \))(\( ( 1 - 110 T^{2} + 5617 T^{4} - 185030 T^{6} + 5268820 T^{8} - 155610230 T^{10} + 3972797377 T^{12} - 65430565310 T^{14} + 500246412961 T^{16} )^{2} \))(\( ( 1 - 110 T^{2} + 5617 T^{4} - 185030 T^{6} + 5268820 T^{8} - 155610230 T^{10} + 3972797377 T^{12} - 65430565310 T^{14} + 500246412961 T^{16} )^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 16 T^{2} + 124 T^{3} + 961 T^{4} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( 1 + 12 T + 96 T^{2} + 372 T^{3} + 961 T^{4} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( 1 - 4 T + 16 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 - 12 T + 96 T^{2} - 372 T^{3} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( 1 - 12 T + 96 T^{2} - 372 T^{3} + 961 T^{4} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( 1 + 12 T + 80 T^{2} + 372 T^{3} + 961 T^{4} \))(\( 1 + 12 T + 96 T^{2} + 372 T^{3} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( 1 - 12 T + 80 T^{2} - 372 T^{3} + 961 T^{4} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( 1 - 112 T^{2} + 5984 T^{4} - 201840 T^{6} + 5984898 T^{8} - 193968240 T^{10} + 5526349664 T^{12} - 99400412272 T^{14} + 852891037441 T^{16} \))(\( ( 1 - 100 T^{2} + 4294 T^{4} - 96100 T^{6} + 923521 T^{8} )^{2} \))(\( 1 - 176 T^{2} + 14816 T^{4} - 791216 T^{6} + 29218434 T^{8} - 760358576 T^{10} + 13682887136 T^{12} - 156200647856 T^{14} + 852891037441 T^{16} \))(\( 1 - 112 T^{2} + 5984 T^{4} - 201840 T^{6} + 5984898 T^{8} - 193968240 T^{10} + 5526349664 T^{12} - 99400412272 T^{14} + 852891037441 T^{16} \))(\( ( 1 - 100 T^{2} + 4294 T^{4} - 96100 T^{6} + 923521 T^{8} )^{2} \))(\( 1 - 176 T^{2} + 14816 T^{4} - 791216 T^{6} + 29218434 T^{8} - 760358576 T^{10} + 13682887136 T^{12} - 156200647856 T^{14} + 852891037441 T^{16} \))(\( ( 1 - 6 T^{2} + 1673 T^{4} - 1134 T^{6} + 1898388 T^{8} - 1089774 T^{10} + 1545050633 T^{12} - 5325022086 T^{14} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 6 T^{2} + 1673 T^{4} - 1134 T^{6} + 1898388 T^{8} - 1089774 T^{10} + 1545050633 T^{12} - 5325022086 T^{14} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 - 8 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 72 T^{2} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 72 T^{2} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 8 T + 132 T^{2} + 784 T^{3} + 7188 T^{4} + 29008 T^{5} + 180708 T^{6} + 405224 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 24 T + 360 T^{2} + 3480 T^{3} + 25055 T^{4} + 128760 T^{5} + 492840 T^{6} + 1215672 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 8 T + 52 T^{2} - 432 T^{3} + 3764 T^{4} - 15984 T^{5} + 71188 T^{6} - 405224 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 8 T + 132 T^{2} + 784 T^{3} + 7188 T^{4} + 29008 T^{5} + 180708 T^{6} + 405224 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 24 T + 360 T^{2} + 3480 T^{3} + 25055 T^{4} + 128760 T^{5} + 492840 T^{6} + 1215672 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 8 T + 52 T^{2} - 432 T^{3} + 3764 T^{4} - 15984 T^{5} + 71188 T^{6} - 405224 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 184 T^{2} + 15497 T^{4} - 826872 T^{6} + 33651488 T^{8} - 1131987768 T^{10} + 29043873017 T^{12} - 472093659256 T^{14} + 3512479453921 T^{16} )^{2} \))(\( ( 1 - 184 T^{2} + 15497 T^{4} - 826872 T^{6} + 33651488 T^{8} - 1131987768 T^{10} + 29043873017 T^{12} - 472093659256 T^{14} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 11 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 12 T + 110 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 91 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 91 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 110 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 + 4 T + 54 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 91 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 4 T + 14 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 + 4 T + 54 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 14 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 91 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( ( 1 + 24 T + 372 T^{2} + 3720 T^{3} + 28158 T^{4} + 152520 T^{5} + 625332 T^{6} + 1654104 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 - 16 T + 232 T^{2} - 2000 T^{3} + 15591 T^{4} - 82000 T^{5} + 389992 T^{6} - 1102736 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 - 8 T + 116 T^{2} - 664 T^{3} + 6526 T^{4} - 27224 T^{5} + 194996 T^{6} - 551368 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 - 24 T + 372 T^{2} - 3720 T^{3} + 28158 T^{4} - 152520 T^{5} + 625332 T^{6} - 1654104 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 + 16 T + 232 T^{2} + 2000 T^{3} + 15591 T^{4} + 82000 T^{5} + 389992 T^{6} + 1102736 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 + 8 T + 116 T^{2} + 664 T^{3} + 6526 T^{4} + 27224 T^{5} + 194996 T^{6} + 551368 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 + 84 T^{2} + 9077 T^{4} + 448128 T^{6} + 24944604 T^{8} + 753303168 T^{10} + 25649432597 T^{12} + 399008756244 T^{14} + 7984925229121 T^{16} )^{2} \))(\( ( 1 + 84 T^{2} + 9077 T^{4} + 448128 T^{6} + 24944604 T^{8} + 753303168 T^{10} + 25649432597 T^{12} + 399008756244 T^{14} + 7984925229121 T^{16} )^{2} \))
$43$ (\( 1 + 2 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - 12 T + 120 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 120 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 + 12 T + 114 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 + 12 T + 114 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( ( 1 + 8 T + 76 T^{2} + 256 T^{3} + 1492 T^{4} + 11008 T^{5} + 140524 T^{6} + 636056 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 8 T + 180 T^{2} + 1000 T^{3} + 11750 T^{4} + 43000 T^{5} + 332820 T^{6} + 636056 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 8 T + 124 T^{2} + 720 T^{3} + 7508 T^{4} + 30960 T^{5} + 229276 T^{6} + 636056 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 8 T + 76 T^{2} + 256 T^{3} + 1492 T^{4} + 11008 T^{5} + 140524 T^{6} + 636056 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 8 T + 180 T^{2} + 1000 T^{3} + 11750 T^{4} + 43000 T^{5} + 332820 T^{6} + 636056 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 8 T + 124 T^{2} + 720 T^{3} + 7508 T^{4} + 30960 T^{5} + 229276 T^{6} + 636056 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 - 196 T^{2} + 20648 T^{4} - 1438284 T^{6} + 72218798 T^{8} - 2659387116 T^{10} + 70591403048 T^{12} - 1238987157604 T^{14} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - 196 T^{2} + 20648 T^{4} - 1438284 T^{6} + 72218798 T^{8} - 2659387116 T^{10} + 70591403048 T^{12} - 1238987157604 T^{14} + 11688200277601 T^{16} )^{2} \))
$47$ (\( 1 + 10 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 11 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 11 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 5 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 5 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 48 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 2 T - 17 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 108 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 2 T - 17 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 48 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 108 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 752 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 108 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 2 T - 17 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 80 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 108 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 752 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 80 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 2 T - 17 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( ( 1 - 24 T + 380 T^{2} - 3968 T^{3} + 31844 T^{4} - 186496 T^{5} + 839420 T^{6} - 2491752 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 - 8 T + 142 T^{2} - 688 T^{3} + 8355 T^{4} - 32336 T^{5} + 313678 T^{6} - 830584 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 + 8 T + 156 T^{2} + 880 T^{3} + 10404 T^{4} + 41360 T^{5} + 344604 T^{6} + 830584 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 + 24 T + 380 T^{2} + 3968 T^{3} + 31844 T^{4} + 186496 T^{5} + 839420 T^{6} + 2491752 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 + 8 T + 142 T^{2} + 688 T^{3} + 8355 T^{4} + 32336 T^{5} + 313678 T^{6} + 830584 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 - 8 T + 156 T^{2} - 880 T^{3} + 10404 T^{4} - 41360 T^{5} + 344604 T^{6} - 830584 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 - 270 T^{2} + 34853 T^{4} - 2827818 T^{6} + 158149800 T^{8} - 6246649962 T^{10} + 170071521893 T^{12} - 2910388138830 T^{14} + 23811286661761 T^{16} )^{2} \))(\( ( 1 - 270 T^{2} + 34853 T^{4} - 2827818 T^{6} + 158149800 T^{8} - 6246649962 T^{10} + 170071521893 T^{12} - 2910388138830 T^{14} + 23811286661761 T^{16} )^{2} \))
$53$ (\( 1 - 14 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 11 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 11 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T - 18 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 103 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 103 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 4 T - 18 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 103 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 110 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 110 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 103 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 120 T^{2} + 14060 T^{4} - 973896 T^{6} + 61968070 T^{8} - 2735673864 T^{10} + 110940162860 T^{12} - 2659723335480 T^{14} + 62259690411361 T^{16} \))(\( 1 - 148 T^{2} + 10938 T^{4} - 528080 T^{6} + 25559075 T^{8} - 1483376720 T^{10} + 86306081178 T^{12} - 3280325447092 T^{14} + 62259690411361 T^{16} \))(\( 1 - 248 T^{2} + 34028 T^{4} - 3010504 T^{6} + 189188806 T^{8} - 8456505736 T^{10} + 268497287468 T^{12} - 5496761559992 T^{14} + 62259690411361 T^{16} \))(\( 1 - 120 T^{2} + 14060 T^{4} - 973896 T^{6} + 61968070 T^{8} - 2735673864 T^{10} + 110940162860 T^{12} - 2659723335480 T^{14} + 62259690411361 T^{16} \))(\( 1 - 148 T^{2} + 10938 T^{4} - 528080 T^{6} + 25559075 T^{8} - 1483376720 T^{10} + 86306081178 T^{12} - 3280325447092 T^{14} + 62259690411361 T^{16} \))(\( 1 - 248 T^{2} + 34028 T^{4} - 3010504 T^{6} + 189188806 T^{8} - 8456505736 T^{10} + 268497287468 T^{12} - 5496761559992 T^{14} + 62259690411361 T^{16} \))(\( ( 1 - 8 T + 168 T^{2} - 1044 T^{3} + 13021 T^{4} - 55332 T^{5} + 471912 T^{6} - 1191016 T^{7} + 7890481 T^{8} )^{4} \))(\( ( 1 + 8 T + 168 T^{2} + 1044 T^{3} + 13021 T^{4} + 55332 T^{5} + 471912 T^{6} + 1191016 T^{7} + 7890481 T^{8} )^{4} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 12 T + 82 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 4 T + 114 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 82 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 + 4 T + 114 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 20 T + 216 T^{2} + 1180 T^{3} + 3481 T^{4} \))(\( 1 - 4 T + 114 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 146 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 4 T + 114 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 20 T + 216 T^{2} - 1180 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 146 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( ( 1 + 8 T + 176 T^{2} + 888 T^{3} + 12914 T^{4} + 52392 T^{5} + 612656 T^{6} + 1643032 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 24 T + 352 T^{2} - 3528 T^{3} + 29874 T^{4} - 208152 T^{5} + 1225312 T^{6} - 4929096 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 + 24 T + 432 T^{2} + 4904 T^{3} + 44786 T^{4} + 289336 T^{5} + 1503792 T^{6} + 4929096 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 8 T + 176 T^{2} - 888 T^{3} + 12914 T^{4} - 52392 T^{5} + 612656 T^{6} - 1643032 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 + 24 T + 352 T^{2} + 3528 T^{3} + 29874 T^{4} + 208152 T^{5} + 1225312 T^{6} + 4929096 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 24 T + 432 T^{2} - 4904 T^{3} + 44786 T^{4} - 289336 T^{5} + 1503792 T^{6} - 4929096 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 + 426 T^{2} + 81485 T^{4} + 9169758 T^{6} + 665481384 T^{8} + 31919927598 T^{10} + 987383161085 T^{12} + 17968907331066 T^{14} + 146830437604321 T^{16} )^{2} \))(\( ( 1 + 426 T^{2} + 81485 T^{4} + 9169758 T^{6} + 665481384 T^{8} + 31919927598 T^{10} + 987383161085 T^{12} + 17968907331066 T^{14} + 146830437604321 T^{16} )^{2} \))
$61$ (\( 1 - 8 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 12 T + 126 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 130 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 130 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 126 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 130 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 126 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 2 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 126 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 130 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 - 304 T^{2} + 47620 T^{4} - 4871952 T^{6} + 350453414 T^{8} - 18128533392 T^{10} + 659338948420 T^{12} - 15662193805744 T^{14} + 191707312997281 T^{16} \))(\( 1 - 248 T^{2} + 33756 T^{4} - 3125128 T^{6} + 217206374 T^{8} - 11628601288 T^{10} + 467380208796 T^{12} - 12777052841528 T^{14} + 191707312997281 T^{16} \))(\( 1 - 432 T^{2} + 84740 T^{4} - 9833616 T^{6} + 737501350 T^{8} - 36590885136 T^{10} + 1173296566340 T^{12} - 22256801723952 T^{14} + 191707312997281 T^{16} \))(\( 1 - 304 T^{2} + 47620 T^{4} - 4871952 T^{6} + 350453414 T^{8} - 18128533392 T^{10} + 659338948420 T^{12} - 15662193805744 T^{14} + 191707312997281 T^{16} \))(\( 1 - 248 T^{2} + 33756 T^{4} - 3125128 T^{6} + 217206374 T^{8} - 11628601288 T^{10} + 467380208796 T^{12} - 12777052841528 T^{14} + 191707312997281 T^{16} \))(\( 1 - 432 T^{2} + 84740 T^{4} - 9833616 T^{6} + 737501350 T^{8} - 36590885136 T^{10} + 1173296566340 T^{12} - 22256801723952 T^{14} + 191707312997281 T^{16} \))(\( ( 1 - 68 T^{2} + 13144 T^{4} - 707276 T^{6} + 70076494 T^{8} - 2631773996 T^{10} + 181989734104 T^{12} - 3503385456548 T^{14} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 68 T^{2} + 13144 T^{4} - 707276 T^{6} + 70076494 T^{8} - 2631773996 T^{10} + 181989734104 T^{12} - 3503385456548 T^{14} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 - 6 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 40 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( 1 + 4 T + 40 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 88 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 88 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( ( 1 + 164 T^{2} - 200 T^{3} + 14052 T^{4} - 13400 T^{5} + 736196 T^{6} + 20151121 T^{8} )^{2} \))(\( ( 1 - 24 T + 244 T^{2} - 1080 T^{3} + 2694 T^{4} - 72360 T^{5} + 1095316 T^{6} - 7218312 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 + 16 T + 276 T^{2} + 2936 T^{3} + 27492 T^{4} + 196712 T^{5} + 1238964 T^{6} + 4812208 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 + 164 T^{2} - 200 T^{3} + 14052 T^{4} - 13400 T^{5} + 736196 T^{6} + 20151121 T^{8} )^{2} \))(\( ( 1 - 24 T + 244 T^{2} - 1080 T^{3} + 2694 T^{4} - 72360 T^{5} + 1095316 T^{6} - 7218312 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 + 16 T + 276 T^{2} + 2936 T^{3} + 27492 T^{4} + 196712 T^{5} + 1238964 T^{6} + 4812208 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 - 352 T^{2} + 61868 T^{4} - 7006944 T^{6} + 554935238 T^{8} - 31454171616 T^{10} + 1246709554028 T^{12} - 31841350523488 T^{14} + 406067677556641 T^{16} )^{2} \))(\( ( 1 - 352 T^{2} + 61868 T^{4} - 7006944 T^{6} + 554935238 T^{8} - 31454171616 T^{10} + 1246709554028 T^{12} - 31841350523488 T^{14} + 406067677556641 T^{16} )^{2} \))
$71$ (\( 1 + 2 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 16 T + 198 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 - 16 T + 178 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 74 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 - 16 T + 178 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 198 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 74 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 - 352 T^{2} + 54788 T^{4} - 5305888 T^{6} + 402214086 T^{8} - 26746981408 T^{10} + 1392255178628 T^{12} - 45091299940192 T^{14} + 645753531245761 T^{16} \))(\( 1 - 280 T^{2} + 41532 T^{4} - 4371368 T^{6} + 352979654 T^{8} - 22036066088 T^{10} + 1055397935292 T^{12} - 35868079497880 T^{14} + 645753531245761 T^{16} \))(\( 1 - 416 T^{2} + 80900 T^{4} - 9781984 T^{6} + 820517062 T^{8} - 49310981344 T^{10} + 2055804992900 T^{12} - 53289718111136 T^{14} + 645753531245761 T^{16} \))(\( 1 - 352 T^{2} + 54788 T^{4} - 5305888 T^{6} + 402214086 T^{8} - 26746981408 T^{10} + 1392255178628 T^{12} - 45091299940192 T^{14} + 645753531245761 T^{16} \))(\( 1 - 280 T^{2} + 41532 T^{4} - 4371368 T^{6} + 352979654 T^{8} - 22036066088 T^{10} + 1055397935292 T^{12} - 35868079497880 T^{14} + 645753531245761 T^{16} \))(\( 1 - 416 T^{2} + 80900 T^{4} - 9781984 T^{6} + 820517062 T^{8} - 49310981344 T^{10} + 2055804992900 T^{12} - 53289718111136 T^{14} + 645753531245761 T^{16} \))(\( ( 1 + 52 T^{2} + 10456 T^{4} + 567388 T^{6} + 78505582 T^{8} + 2860202908 T^{10} + 265704536536 T^{12} + 6661214763892 T^{14} + 645753531245761 T^{16} )^{2} \))(\( ( 1 + 52 T^{2} + 10456 T^{4} + 567388 T^{6} + 78505582 T^{8} + 2860202908 T^{10} + 265704536536 T^{12} + 6661214763892 T^{14} + 645753531245761 T^{16} )^{2} \))
$73$ (\( 1 - 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 4 T + 118 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( 1 + 20 T + 238 T^{2} + 1460 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( 1 + 4 T + 118 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1460 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 208 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1460 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( 1 + 20 T + 238 T^{2} + 1460 T^{3} + 5329 T^{4} \))(\( 1 - 16 T + 208 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( 1 - 184 T^{2} + 31436 T^{4} - 3096008 T^{6} + 278954470 T^{8} - 16498626632 T^{10} + 892727104076 T^{12} - 27845497637176 T^{14} + 806460091894081 T^{16} \))(\( ( 1 - 156 T^{2} + 12134 T^{4} - 831324 T^{6} + 28398241 T^{8} )^{2} \))(\( 1 - 248 T^{2} + 27212 T^{4} - 1705864 T^{6} + 97521382 T^{8} - 9090549256 T^{10} + 772772934092 T^{12} - 37530888119672 T^{14} + 806460091894081 T^{16} \))(\( 1 - 184 T^{2} + 31436 T^{4} - 3096008 T^{6} + 278954470 T^{8} - 16498626632 T^{10} + 892727104076 T^{12} - 27845497637176 T^{14} + 806460091894081 T^{16} \))(\( ( 1 - 156 T^{2} + 12134 T^{4} - 831324 T^{6} + 28398241 T^{8} )^{2} \))(\( 1 - 248 T^{2} + 27212 T^{4} - 1705864 T^{6} + 97521382 T^{8} - 9090549256 T^{10} + 772772934092 T^{12} - 37530888119672 T^{14} + 806460091894081 T^{16} \))(\( ( 1 + 312 T^{2} + 51644 T^{4} + 5812104 T^{6} + 484685382 T^{8} + 30972702216 T^{10} + 1466598758204 T^{12} + 47216278602168 T^{14} + 806460091894081 T^{16} )^{2} \))(\( ( 1 + 312 T^{2} + 51644 T^{4} + 5812104 T^{6} + 484685382 T^{8} + 30972702216 T^{10} + 1466598758204 T^{12} + 47216278602168 T^{14} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( ( 1 + 126 T^{2} + 6241 T^{4} )^{4} \))(\( ( 1 - 24 T + 324 T^{2} - 3096 T^{3} + 25622 T^{4} - 244584 T^{5} + 2022084 T^{6} - 11832936 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 + 188 T^{2} + 19270 T^{4} + 1173308 T^{6} + 38950081 T^{8} )^{2} \))(\( ( 1 + 126 T^{2} + 6241 T^{4} )^{4} \))(\( ( 1 - 24 T + 324 T^{2} - 3096 T^{3} + 25622 T^{4} - 244584 T^{5} + 2022084 T^{6} - 11832936 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 + 188 T^{2} + 19270 T^{4} + 1173308 T^{6} + 38950081 T^{8} )^{2} \))(\( ( 1 + 2 T + 59 T^{2} + 870 T^{3} + 6116 T^{4} + 68730 T^{5} + 368219 T^{6} + 986078 T^{7} + 38950081 T^{8} )^{4} \))(\( ( 1 + 2 T + 59 T^{2} + 870 T^{3} + 6116 T^{4} + 68730 T^{5} + 368219 T^{6} + 986078 T^{7} + 38950081 T^{8} )^{4} \))
$83$ (\( 1 - 8 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 16 T + 222 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1660 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 158 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 + 20 T + 238 T^{2} + 1660 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 222 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 158 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 152 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 158 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1660 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 222 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 158 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 152 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 222 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 20 T + 238 T^{2} + 1660 T^{3} + 6889 T^{4} \))(\( ( 1 + 8 T + 324 T^{2} + 1896 T^{3} + 40022 T^{4} + 157368 T^{5} + 2232036 T^{6} + 4574296 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 + 8 T + 148 T^{2} + 1192 T^{3} + 18438 T^{4} + 98936 T^{5} + 1019572 T^{6} + 4574296 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 8 T + 68 T^{2} - 360 T^{3} + 7766 T^{4} - 29880 T^{5} + 468452 T^{6} - 4574296 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 8 T + 324 T^{2} - 1896 T^{3} + 40022 T^{4} - 157368 T^{5} + 2232036 T^{6} - 4574296 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 8 T + 148 T^{2} - 1192 T^{3} + 18438 T^{4} - 98936 T^{5} + 1019572 T^{6} - 4574296 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 + 8 T + 68 T^{2} + 360 T^{3} + 7766 T^{4} + 29880 T^{5} + 468452 T^{6} + 4574296 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 250 T^{2} + 32249 T^{4} - 3769146 T^{6} + 372693188 T^{8} - 25965646794 T^{10} + 1530483393929 T^{12} - 81735093342250 T^{14} + 2252292232139041 T^{16} )^{2} \))(\( ( 1 - 250 T^{2} + 32249 T^{4} - 3769146 T^{6} + 372693188 T^{8} - 25965646794 T^{10} + 1530483393929 T^{12} - 81735093342250 T^{14} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( 1 + 2 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 4 T + 110 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 82 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 142 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 82 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 - 4 T + 110 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 142 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 - 12 T + 142 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 82 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 + 4 T + 174 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 142 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 - 4 T + 174 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 82 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( ( 1 - 24 T + 428 T^{2} - 5032 T^{3} + 54470 T^{4} - 447848 T^{5} + 3390188 T^{6} - 16919256 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 - 16 T + 304 T^{2} - 3344 T^{3} + 36834 T^{4} - 297616 T^{5} + 2407984 T^{6} - 11279504 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 40 T + 876 T^{2} + 12824 T^{3} + 139590 T^{4} + 1141336 T^{5} + 6938796 T^{6} + 28198760 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 24 T + 428 T^{2} + 5032 T^{3} + 54470 T^{4} + 447848 T^{5} + 3390188 T^{6} + 16919256 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 16 T + 304 T^{2} + 3344 T^{3} + 36834 T^{4} + 297616 T^{5} + 2407984 T^{6} + 11279504 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 - 40 T + 876 T^{2} - 12824 T^{3} + 139590 T^{4} - 1141336 T^{5} + 6938796 T^{6} - 28198760 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 492 T^{2} + 112712 T^{4} + 16213956 T^{6} + 1669259214 T^{8} + 128430745476 T^{10} + 7071803467592 T^{12} + 244514795152812 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 + 492 T^{2} + 112712 T^{4} + 16213956 T^{6} + 1669259214 T^{8} + 128430745476 T^{10} + 7071803467592 T^{12} + 244514795152812 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 12 T + 222 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( ( 1 - 4 T + 97 T^{2} )^{2} \))(\( 1 + 12 T + 158 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( 1 + 12 T + 222 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 158 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 158 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( 1 - 4 T + 126 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 158 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( 1 + 4 T + 126 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( ( 1 - 4 T + 97 T^{2} )^{2} \))(\( 1 - 504 T^{2} + 122652 T^{4} - 19352520 T^{6} + 2189485382 T^{8} - 182087860680 T^{10} + 10858293373212 T^{12} - 419817890484216 T^{14} + 7837433594376961 T^{16} \))(\( 1 + 24 T^{2} + 19036 T^{4} - 653400 T^{6} + 157960902 T^{8} - 6147840600 T^{10} + 1685243393116 T^{12} + 19991328118296 T^{14} + 7837433594376961 T^{16} \))(\( ( 1 - 316 T^{2} + 43270 T^{4} - 2973244 T^{6} + 88529281 T^{8} )^{2} \))(\( 1 - 504 T^{2} + 122652 T^{4} - 19352520 T^{6} + 2189485382 T^{8} - 182087860680 T^{10} + 10858293373212 T^{12} - 419817890484216 T^{14} + 7837433594376961 T^{16} \))(\( 1 + 24 T^{2} + 19036 T^{4} - 653400 T^{6} + 157960902 T^{8} - 6147840600 T^{10} + 1685243393116 T^{12} + 19991328118296 T^{14} + 7837433594376961 T^{16} \))(\( ( 1 - 316 T^{2} + 43270 T^{4} - 2973244 T^{6} + 88529281 T^{8} )^{2} \))(\( ( 1 + 438 T^{2} + 104849 T^{4} + 16454334 T^{6} + 1868658564 T^{8} + 154818828606 T^{10} + 9282206583569 T^{12} + 364841738158902 T^{14} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 + 438 T^{2} + 104849 T^{4} + 16454334 T^{6} + 1868658564 T^{8} + 154818828606 T^{10} + 9282206583569 T^{12} + 364841738158902 T^{14} + 7837433594376961 T^{16} )^{2} \))
show more
show less