Properties

Label 1617.2
Level 1617
Weight 2
Dimension 65706
Nonzero newspaces 32
Sturm bound 376320
Trace bound 4

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1617\( 1617 = 3 \cdot 7^{2} \cdot 11 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(376320\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1617))\).

Total New Old
Modular forms 96480 67454 29026
Cusp forms 91681 65706 25975
Eisenstein series 4799 1748 3051

Trace form

\( 65706q - 6q^{2} - 123q^{3} - 232q^{4} + 12q^{5} - 90q^{6} - 272q^{7} + 62q^{8} - 89q^{9} + O(q^{10}) \) \( 65706q - 6q^{2} - 123q^{3} - 232q^{4} + 12q^{5} - 90q^{6} - 272q^{7} + 62q^{8} - 89q^{9} - 136q^{10} + 34q^{11} - 222q^{12} - 188q^{13} + 48q^{14} - 189q^{15} - 108q^{16} + 42q^{17} - 104q^{18} - 180q^{19} + 110q^{20} - 130q^{21} - 400q^{22} + 68q^{23} - 46q^{24} - 104q^{25} + 134q^{26} - 114q^{27} - 144q^{28} + 104q^{29} - 48q^{30} - 118q^{31} + 158q^{32} - 120q^{33} - 364q^{34} + 84q^{35} - 214q^{36} - 214q^{37} - 22q^{38} - 158q^{39} - 464q^{40} - 96q^{41} - 282q^{42} - 420q^{43} - 58q^{44} - 295q^{45} - 456q^{46} + 22q^{47} - 362q^{48} - 516q^{49} - 52q^{50} - 214q^{51} - 540q^{52} - 14q^{53} - 104q^{54} - 326q^{55} - 300q^{56} - 150q^{57} - 316q^{58} + 78q^{59} - 592q^{60} - 368q^{61} - 12q^{62} - 198q^{63} - 780q^{64} - 108q^{65} - 583q^{66} - 598q^{67} - 344q^{68} - 355q^{69} - 420q^{70} - 324q^{71} - 796q^{72} - 468q^{73} - 210q^{74} - 546q^{75} - 1076q^{76} - 108q^{77} - 1010q^{78} - 304q^{79} - 894q^{80} - 785q^{81} - 692q^{82} - 398q^{83} - 868q^{84} - 816q^{85} - 928q^{86} - 648q^{87} - 1086q^{88} - 436q^{89} - 1314q^{90} - 584q^{91} - 562q^{92} - 749q^{93} - 736q^{94} - 426q^{95} - 1020q^{96} - 306q^{97} - 876q^{98} - 551q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)

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
1617.2.a \(\chi_{1617}(1, \cdot)\) 1617.2.a.a 1 1
1617.2.a.b 1
1617.2.a.c 1
1617.2.a.d 1
1617.2.a.e 1
1617.2.a.f 1
1617.2.a.g 1
1617.2.a.h 1
1617.2.a.i 1
1617.2.a.j 1
1617.2.a.k 2
1617.2.a.l 2
1617.2.a.m 2
1617.2.a.n 2
1617.2.a.o 2
1617.2.a.p 2
1617.2.a.q 3
1617.2.a.r 3
1617.2.a.s 3
1617.2.a.t 3
1617.2.a.u 4
1617.2.a.v 4
1617.2.a.w 4
1617.2.a.x 4
1617.2.a.y 4
1617.2.a.z 4
1617.2.a.ba 5
1617.2.a.bb 5
1617.2.c \(\chi_{1617}(538, \cdot)\) 1617.2.c.a 32 1
1617.2.c.b 48
1617.2.e \(\chi_{1617}(881, \cdot)\) n/a 132 1
1617.2.g \(\chi_{1617}(197, \cdot)\) n/a 154 1
1617.2.i \(\chi_{1617}(67, \cdot)\) n/a 132 2
1617.2.j \(\chi_{1617}(148, \cdot)\) n/a 328 4
1617.2.l \(\chi_{1617}(263, \cdot)\) n/a 304 2
1617.2.n \(\chi_{1617}(815, \cdot)\) n/a 268 2
1617.2.p \(\chi_{1617}(472, \cdot)\) n/a 160 2
1617.2.r \(\chi_{1617}(232, \cdot)\) n/a 552 6
1617.2.t \(\chi_{1617}(50, \cdot)\) n/a 616 4
1617.2.v \(\chi_{1617}(146, \cdot)\) n/a 608 4
1617.2.x \(\chi_{1617}(244, \cdot)\) n/a 320 4
1617.2.ba \(\chi_{1617}(428, \cdot)\) n/a 1320 6
1617.2.bc \(\chi_{1617}(188, \cdot)\) n/a 1128 6
1617.2.be \(\chi_{1617}(76, \cdot)\) n/a 672 6
1617.2.bg \(\chi_{1617}(214, \cdot)\) n/a 640 8
1617.2.bh \(\chi_{1617}(100, \cdot)\) n/a 1128 12
1617.2.bj \(\chi_{1617}(19, \cdot)\) n/a 640 8
1617.2.bl \(\chi_{1617}(80, \cdot)\) n/a 1216 8
1617.2.bn \(\chi_{1617}(116, \cdot)\) n/a 1216 8
1617.2.bp \(\chi_{1617}(64, \cdot)\) n/a 2688 24
1617.2.br \(\chi_{1617}(10, \cdot)\) n/a 1344 12
1617.2.bt \(\chi_{1617}(89, \cdot)\) n/a 2232 12
1617.2.bv \(\chi_{1617}(32, \cdot)\) n/a 2640 12
1617.2.by \(\chi_{1617}(13, \cdot)\) n/a 2688 24
1617.2.ca \(\chi_{1617}(20, \cdot)\) n/a 5280 24
1617.2.cc \(\chi_{1617}(8, \cdot)\) n/a 5280 24
1617.2.ce \(\chi_{1617}(4, \cdot)\) n/a 5376 48
1617.2.cg \(\chi_{1617}(2, \cdot)\) n/a 10560 48
1617.2.ci \(\chi_{1617}(5, \cdot)\) n/a 10560 48
1617.2.ck \(\chi_{1617}(40, \cdot)\) n/a 5376 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1617))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1617)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4} \))(\( 1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4} \))(\( 1 + T - T^{2} + 2 T^{3} + 4 T^{4} \))(\( 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 + 2 T^{2} - T^{3} + 4 T^{4} + 8 T^{6} \))(\( 1 + 2 T^{2} - T^{3} + 4 T^{4} + 8 T^{6} \))(\( 1 - T^{3} + 8 T^{6} \))(\( 1 - 2 T + 2 T^{2} - T^{3} + 4 T^{4} - 8 T^{5} + 8 T^{6} \))(\( 1 + 2 T + 5 T^{2} + 6 T^{3} + 11 T^{4} + 12 T^{5} + 20 T^{6} + 16 T^{7} + 16 T^{8} \))(\( 1 + 2 T + 5 T^{2} + 6 T^{3} + 11 T^{4} + 12 T^{5} + 20 T^{6} + 16 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 5 T^{2} - 6 T^{3} + 11 T^{4} - 12 T^{5} + 20 T^{6} - 16 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 4 T^{2} - 8 T^{3} + 11 T^{4} - 16 T^{5} + 16 T^{6} - 16 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 5 T^{2} - 6 T^{3} + 11 T^{4} - 12 T^{5} + 20 T^{6} - 16 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 4 T^{2} - 8 T^{3} + 11 T^{4} - 16 T^{5} + 16 T^{6} - 16 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 2 T^{2} - 2 T^{3} + 3 T^{4} - 2 T^{5} + 6 T^{6} - 8 T^{7} + 16 T^{8} - 32 T^{9} + 32 T^{10} \))(\( 1 - 2 T + 2 T^{2} - 2 T^{3} + 3 T^{4} - 2 T^{5} + 6 T^{6} - 8 T^{7} + 16 T^{8} - 32 T^{9} + 32 T^{10} \))
$3$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))
$5$ (\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} + 25 T^{4} \))(\( 1 + 5 T^{2} + 25 T^{4} \))(\( ( 1 - 2 T + 5 T^{2} )^{2} \))(\( ( 1 + 2 T + 5 T^{2} )^{2} \))(\( ( 1 + 3 T + 5 T^{2} )^{2} \))(\( ( 1 + T + 5 T^{2} )^{2} \))(\( 1 + 4 T + 14 T^{2} + 32 T^{3} + 70 T^{4} + 100 T^{5} + 125 T^{6} \))(\( 1 - 4 T + 14 T^{2} - 32 T^{3} + 70 T^{4} - 100 T^{5} + 125 T^{6} \))(\( 1 - 2 T^{3} + 125 T^{6} \))(\( 1 + 4 T + 8 T^{2} + 14 T^{3} + 40 T^{4} + 100 T^{5} + 125 T^{6} \))(\( 1 - 8 T + 36 T^{2} - 116 T^{3} + 293 T^{4} - 580 T^{5} + 900 T^{6} - 1000 T^{7} + 625 T^{8} \))(\( 1 + 8 T + 36 T^{2} + 116 T^{3} + 293 T^{4} + 580 T^{5} + 900 T^{6} + 1000 T^{7} + 625 T^{8} \))(\( 1 + 12 T^{2} - 4 T^{3} + 77 T^{4} - 20 T^{5} + 300 T^{6} + 625 T^{8} \))(\( 1 + 4 T + 16 T^{2} + 40 T^{3} + 98 T^{4} + 200 T^{5} + 400 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 + 12 T^{2} + 4 T^{3} + 77 T^{4} + 20 T^{5} + 300 T^{6} + 625 T^{8} \))(\( 1 - 4 T + 16 T^{2} - 40 T^{3} + 98 T^{4} - 200 T^{5} + 400 T^{6} - 500 T^{7} + 625 T^{8} \))(\( 1 + 4 T + 17 T^{2} + 52 T^{3} + 150 T^{4} + 352 T^{5} + 750 T^{6} + 1300 T^{7} + 2125 T^{8} + 2500 T^{9} + 3125 T^{10} \))(\( 1 - 4 T + 17 T^{2} - 52 T^{3} + 150 T^{4} - 352 T^{5} + 750 T^{6} - 1300 T^{7} + 2125 T^{8} - 2500 T^{9} + 3125 T^{10} \))
$7$ 1
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))
$13$ (\( 1 + 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 7 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 - 2 T + 7 T^{2} - 26 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( 1 - 2 T + 7 T^{2} - 26 T^{3} + 169 T^{4} \))(\( 1 + 2 T + 28 T^{2} + 56 T^{3} + 364 T^{4} + 338 T^{5} + 2197 T^{6} \))(\( 1 - 2 T + 28 T^{2} - 56 T^{3} + 364 T^{4} - 338 T^{5} + 2197 T^{6} \))(\( 1 + 24 T^{2} - 2 T^{3} + 312 T^{4} + 2197 T^{6} \))(\( 1 - 4 T + 12 T^{2} - 10 T^{3} + 156 T^{4} - 676 T^{5} + 2197 T^{6} \))(\( 1 - 8 T + 50 T^{2} - 240 T^{3} + 915 T^{4} - 3120 T^{5} + 8450 T^{6} - 17576 T^{7} + 28561 T^{8} \))(\( 1 + 8 T + 50 T^{2} + 240 T^{3} + 915 T^{4} + 3120 T^{5} + 8450 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 + 8 T + 58 T^{2} + 288 T^{3} + 1163 T^{4} + 3744 T^{5} + 9802 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 - 2 T + 44 T^{2} - 62 T^{3} + 802 T^{4} - 806 T^{5} + 7436 T^{6} - 4394 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 58 T^{2} - 288 T^{3} + 1163 T^{4} - 3744 T^{5} + 9802 T^{6} - 17576 T^{7} + 28561 T^{8} \))(\( 1 + 2 T + 44 T^{2} + 62 T^{3} + 802 T^{4} + 806 T^{5} + 7436 T^{6} + 4394 T^{7} + 28561 T^{8} \))(\( 1 - 5 T + 27 T^{2} - 180 T^{3} + 732 T^{4} - 2514 T^{5} + 9516 T^{6} - 30420 T^{7} + 59319 T^{8} - 142805 T^{9} + 371293 T^{10} \))(\( 1 + 5 T + 27 T^{2} + 180 T^{3} + 732 T^{4} + 2514 T^{5} + 9516 T^{6} + 30420 T^{7} + 59319 T^{8} + 142805 T^{9} + 371293 T^{10} \))
$17$ (\( 1 - 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( 1 - 6 T + 41 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 41 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 22 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 38 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 31 T^{2} + 120 T^{3} + 527 T^{4} + 1156 T^{5} + 4913 T^{6} \))(\( 1 - 4 T + 31 T^{2} - 120 T^{3} + 527 T^{4} - 1156 T^{5} + 4913 T^{6} \))(\( 1 + 27 T^{2} - 8 T^{3} + 459 T^{4} + 4913 T^{6} \))(\( 1 + 8 T + 11 T^{2} - 56 T^{3} + 187 T^{4} + 2312 T^{5} + 4913 T^{6} \))(\( 1 + 46 T^{2} + 48 T^{3} + 958 T^{4} + 816 T^{5} + 13294 T^{6} + 83521 T^{8} \))(\( 1 + 46 T^{2} - 48 T^{3} + 958 T^{4} - 816 T^{5} + 13294 T^{6} + 83521 T^{8} \))(\( 1 + 8 T + 62 T^{2} + 360 T^{3} + 1502 T^{4} + 6120 T^{5} + 17918 T^{6} + 39304 T^{7} + 83521 T^{8} \))(\( 1 + 2 T + 28 T^{2} - 22 T^{3} + 389 T^{4} - 374 T^{5} + 8092 T^{6} + 9826 T^{7} + 83521 T^{8} \))(\( 1 - 8 T + 62 T^{2} - 360 T^{3} + 1502 T^{4} - 6120 T^{5} + 17918 T^{6} - 39304 T^{7} + 83521 T^{8} \))(\( 1 - 2 T + 28 T^{2} + 22 T^{3} + 389 T^{4} + 374 T^{5} + 8092 T^{6} - 9826 T^{7} + 83521 T^{8} \))(\( 1 - 2 T + 77 T^{2} - 122 T^{3} + 2493 T^{4} - 3002 T^{5} + 42381 T^{6} - 35258 T^{7} + 378301 T^{8} - 167042 T^{9} + 1419857 T^{10} \))(\( 1 + 2 T + 77 T^{2} + 122 T^{3} + 2493 T^{4} + 3002 T^{5} + 42381 T^{6} + 35258 T^{7} + 378301 T^{8} + 167042 T^{9} + 1419857 T^{10} \))
$19$ (\( 1 - 7 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 37 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 37 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 29 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 29 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 21 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 7 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 56 T^{2} + 144 T^{3} + 1064 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 - 4 T + 56 T^{2} - 144 T^{3} + 1064 T^{4} - 1444 T^{5} + 6859 T^{6} \))(\( 1 + 12 T + 84 T^{2} + 420 T^{3} + 1596 T^{4} + 4332 T^{5} + 6859 T^{6} \))(\( 1 - 8 T + 72 T^{2} - 308 T^{3} + 1368 T^{4} - 2888 T^{5} + 6859 T^{6} \))(\( 1 - 8 T + 58 T^{2} - 192 T^{3} + 971 T^{4} - 3648 T^{5} + 20938 T^{6} - 54872 T^{7} + 130321 T^{8} \))(\( 1 + 8 T + 58 T^{2} + 192 T^{3} + 971 T^{4} + 3648 T^{5} + 20938 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 + 8 T + 82 T^{2} + 432 T^{3} + 2387 T^{4} + 8208 T^{5} + 29602 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 + 36 T^{2} + 122 T^{3} + 557 T^{4} + 2318 T^{5} + 12996 T^{6} + 130321 T^{8} \))(\( 1 - 8 T + 82 T^{2} - 432 T^{3} + 2387 T^{4} - 8208 T^{5} + 29602 T^{6} - 54872 T^{7} + 130321 T^{8} \))(\( 1 + 36 T^{2} - 122 T^{3} + 557 T^{4} - 2318 T^{5} + 12996 T^{6} + 130321 T^{8} \))(\( 1 + 3 T + 53 T^{2} + 120 T^{3} + 1459 T^{4} + 2997 T^{5} + 27721 T^{6} + 43320 T^{7} + 363527 T^{8} + 390963 T^{9} + 2476099 T^{10} \))(\( 1 - 3 T + 53 T^{2} - 120 T^{3} + 1459 T^{4} - 2997 T^{5} + 27721 T^{6} - 43320 T^{7} + 363527 T^{8} - 390963 T^{9} + 2476099 T^{10} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 4 T + 30 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 92 T^{3} + 529 T^{4} \))(\( ( 1 + 7 T + 23 T^{2} )^{2} \))(\( ( 1 + 7 T + 23 T^{2} )^{2} \))(\( 1 + 2 T + 26 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} \))(\( ( 1 + 23 T^{2} )^{3} \))(\( ( 1 + 23 T^{2} )^{3} \))(\( 1 + 6 T + 57 T^{2} + 244 T^{3} + 1311 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 - 10 T + 81 T^{2} - 396 T^{3} + 1863 T^{4} - 5290 T^{5} + 12167 T^{6} \))(\( 1 + 38 T^{2} + 200 T^{3} + 494 T^{4} + 4600 T^{5} + 20102 T^{6} + 279841 T^{8} \))(\( 1 + 38 T^{2} + 200 T^{3} + 494 T^{4} + 4600 T^{5} + 20102 T^{6} + 279841 T^{8} \))(\( 1 - 8 T + 102 T^{2} - 512 T^{3} + 3566 T^{4} - 11776 T^{5} + 53958 T^{6} - 97336 T^{7} + 279841 T^{8} \))(\( 1 - 4 T + 50 T^{2} - 200 T^{3} + 1707 T^{4} - 4600 T^{5} + 26450 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 - 8 T + 102 T^{2} - 512 T^{3} + 3566 T^{4} - 11776 T^{5} + 53958 T^{6} - 97336 T^{7} + 279841 T^{8} \))(\( 1 - 4 T + 50 T^{2} - 200 T^{3} + 1707 T^{4} - 4600 T^{5} + 26450 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 - 16 T + 185 T^{2} - 1516 T^{3} + 9945 T^{4} - 52612 T^{5} + 228735 T^{6} - 801964 T^{7} + 2250895 T^{8} - 4477456 T^{9} + 6436343 T^{10} \))(\( 1 - 16 T + 185 T^{2} - 1516 T^{3} + 9945 T^{4} - 52612 T^{5} + 228735 T^{6} - 801964 T^{7} + 2250895 T^{8} - 4477456 T^{9} + 6436343 T^{10} \))
$29$ (\( 1 + 2 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 16 T + 117 T^{2} + 464 T^{3} + 841 T^{4} \))(\( 1 + 16 T + 117 T^{2} + 464 T^{3} + 841 T^{4} \))(\( 1 + 2 T + 41 T^{2} + 58 T^{3} + 841 T^{4} \))(\( 1 + 2 T + 41 T^{2} + 58 T^{3} + 841 T^{4} \))(\( 1 - 2 T - 25 T^{2} - 58 T^{3} + 841 T^{4} \))(\( ( 1 - 5 T + 29 T^{2} )^{2} \))(\( 1 - 6 T + 38 T^{2} - 266 T^{3} + 1102 T^{4} - 5046 T^{5} + 24389 T^{6} \))(\( 1 - 6 T + 38 T^{2} - 266 T^{3} + 1102 T^{4} - 5046 T^{5} + 24389 T^{6} \))(\( 1 - 12 T + 120 T^{2} - 702 T^{3} + 3480 T^{4} - 10092 T^{5} + 24389 T^{6} \))(\( 1 + 4 T + 60 T^{2} + 138 T^{3} + 1740 T^{4} + 3364 T^{5} + 24389 T^{6} \))(\( 1 + 16 T + 180 T^{2} + 1372 T^{3} + 8501 T^{4} + 39788 T^{5} + 151380 T^{6} + 390224 T^{7} + 707281 T^{8} \))(\( 1 + 16 T + 180 T^{2} + 1372 T^{3} + 8501 T^{4} + 39788 T^{5} + 151380 T^{6} + 390224 T^{7} + 707281 T^{8} \))(\( 1 - 16 T + 196 T^{2} - 1532 T^{3} + 9733 T^{4} - 44428 T^{5} + 164836 T^{6} - 390224 T^{7} + 707281 T^{8} \))(\( 1 - 8 T + 128 T^{2} - 682 T^{3} + 5745 T^{4} - 19778 T^{5} + 107648 T^{6} - 195112 T^{7} + 707281 T^{8} \))(\( 1 - 16 T + 196 T^{2} - 1532 T^{3} + 9733 T^{4} - 44428 T^{5} + 164836 T^{6} - 390224 T^{7} + 707281 T^{8} \))(\( 1 - 8 T + 128 T^{2} - 682 T^{3} + 5745 T^{4} - 19778 T^{5} + 107648 T^{6} - 195112 T^{7} + 707281 T^{8} \))(\( 1 + 49 T^{2} + 24 T^{3} + 1765 T^{4} + 102 T^{5} + 51185 T^{6} + 20184 T^{7} + 1195061 T^{8} + 20511149 T^{10} \))(\( 1 + 49 T^{2} + 24 T^{3} + 1765 T^{4} + 102 T^{5} + 51185 T^{6} + 20184 T^{7} + 1195061 T^{8} + 20511149 T^{10} \))
$31$ (\( 1 + 7 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 8 T + 58 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 58 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( 1 - 2 T + 42 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 66 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 65 T^{2} + 288 T^{3} + 2015 T^{4} + 7688 T^{5} + 29791 T^{6} \))(\( 1 - 8 T + 65 T^{2} - 288 T^{3} + 2015 T^{4} - 7688 T^{5} + 29791 T^{6} \))(\( 1 - 6 T + 57 T^{2} - 404 T^{3} + 1767 T^{4} - 5766 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 17 T^{2} + 132 T^{3} + 527 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 - 16 T + 190 T^{2} - 1464 T^{3} + 9470 T^{4} - 45384 T^{5} + 182590 T^{6} - 476656 T^{7} + 923521 T^{8} \))(\( 1 + 16 T + 190 T^{2} + 1464 T^{3} + 9470 T^{4} + 45384 T^{5} + 182590 T^{6} + 476656 T^{7} + 923521 T^{8} \))(\( 1 + 8 T + 110 T^{2} + 704 T^{3} + 4926 T^{4} + 21824 T^{5} + 105710 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 - 12 T + 116 T^{2} - 616 T^{3} + 3874 T^{4} - 19096 T^{5} + 111476 T^{6} - 357492 T^{7} + 923521 T^{8} \))(\( 1 - 8 T + 110 T^{2} - 704 T^{3} + 4926 T^{4} - 21824 T^{5} + 105710 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( 1 + 12 T + 116 T^{2} + 616 T^{3} + 3874 T^{4} + 19096 T^{5} + 111476 T^{6} + 357492 T^{7} + 923521 T^{8} \))(\( 1 - 5 T + 147 T^{2} - 588 T^{3} + 8922 T^{4} - 26826 T^{5} + 276582 T^{6} - 565068 T^{7} + 4379277 T^{8} - 4617605 T^{9} + 28629151 T^{10} \))(\( 1 + 5 T + 147 T^{2} + 588 T^{3} + 8922 T^{4} + 26826 T^{5} + 276582 T^{6} + 565068 T^{7} + 4379277 T^{8} + 4617605 T^{9} + 28629151 T^{10} \))
$37$ (\( 1 - 7 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 10 T + 79 T^{2} + 370 T^{3} + 1369 T^{4} \))(\( 1 + 10 T + 79 T^{2} + 370 T^{3} + 1369 T^{4} \))(\( 1 + 2 T + 3 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T + 3 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( ( 1 - T + 37 T^{2} )^{2} \))(\( ( 1 + 7 T + 37 T^{2} )^{2} \))(\( 1 + 8 T + 120 T^{2} + 590 T^{3} + 4440 T^{4} + 10952 T^{5} + 50653 T^{6} \))(\( 1 + 8 T + 120 T^{2} + 590 T^{3} + 4440 T^{4} + 10952 T^{5} + 50653 T^{6} \))(\( 1 + 36 T^{2} - 246 T^{3} + 1332 T^{4} + 50653 T^{6} \))(\( 1 + 68 T^{2} + 106 T^{3} + 2516 T^{4} + 50653 T^{6} \))(\( 1 + 4 T + 66 T^{2} - 112 T^{3} + 1227 T^{4} - 4144 T^{5} + 90354 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 66 T^{2} - 112 T^{3} + 1227 T^{4} - 4144 T^{5} + 90354 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 98 T^{2} + 208 T^{3} + 4395 T^{4} + 7696 T^{5} + 134162 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 138 T^{2} + 444 T^{3} + 7475 T^{4} + 16428 T^{5} + 188922 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 98 T^{2} + 208 T^{3} + 4395 T^{4} + 7696 T^{5} + 134162 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 138 T^{2} + 444 T^{3} + 7475 T^{4} + 16428 T^{5} + 188922 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 - 15 T + 215 T^{2} - 1914 T^{3} + 16201 T^{4} - 100365 T^{5} + 599437 T^{6} - 2620266 T^{7} + 10890395 T^{8} - 28112415 T^{9} + 69343957 T^{10} \))(\( 1 - 15 T + 215 T^{2} - 1914 T^{3} + 16201 T^{4} - 100365 T^{5} + 599437 T^{6} - 2620266 T^{7} + 10890395 T^{8} - 28112415 T^{9} + 69343957 T^{10} \))
$41$ (\( 1 - 4 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( 1 - 8 T + 90 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 90 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 2 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 + 4 T + 66 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 95 T^{2} - 448 T^{3} + 3895 T^{4} - 13448 T^{5} + 68921 T^{6} \))(\( 1 + 8 T + 95 T^{2} + 448 T^{3} + 3895 T^{4} + 13448 T^{5} + 68921 T^{6} \))(\( 1 + 6 T + 51 T^{2} + 460 T^{3} + 2091 T^{4} + 10086 T^{5} + 68921 T^{6} \))(\( 1 + 14 T + 163 T^{2} + 1116 T^{3} + 6683 T^{4} + 23534 T^{5} + 68921 T^{6} \))(\( 1 - 4 T + 60 T^{2} - 436 T^{3} + 3410 T^{4} - 17876 T^{5} + 100860 T^{6} - 275684 T^{7} + 2825761 T^{8} \))(\( 1 + 4 T + 60 T^{2} + 436 T^{3} + 3410 T^{4} + 17876 T^{5} + 100860 T^{6} + 275684 T^{7} + 2825761 T^{8} \))(\( 1 + 12 T + 188 T^{2} + 1468 T^{3} + 12050 T^{4} + 60188 T^{5} + 316028 T^{6} + 827052 T^{7} + 2825761 T^{8} \))(\( 1 + 2 T + 120 T^{2} + 310 T^{3} + 6538 T^{4} + 12710 T^{5} + 201720 T^{6} + 137842 T^{7} + 2825761 T^{8} \))(\( 1 - 12 T + 188 T^{2} - 1468 T^{3} + 12050 T^{4} - 60188 T^{5} + 316028 T^{6} - 827052 T^{7} + 2825761 T^{8} \))(\( 1 - 2 T + 120 T^{2} - 310 T^{3} + 6538 T^{4} - 12710 T^{5} + 201720 T^{6} - 137842 T^{7} + 2825761 T^{8} \))(\( 1 + 22 T + 329 T^{2} + 3256 T^{3} + 27018 T^{4} + 181492 T^{5} + 1107738 T^{6} + 5473336 T^{7} + 22675009 T^{8} + 62166742 T^{9} + 115856201 T^{10} \))(\( 1 - 22 T + 329 T^{2} - 3256 T^{3} + 27018 T^{4} - 181492 T^{5} + 1107738 T^{6} - 5473336 T^{7} + 22675009 T^{8} - 62166742 T^{9} + 115856201 T^{10} \))
$43$ (\( 1 + 9 T + 43 T^{2} \))(\( 1 + 9 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 8 T + 82 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 - 8 T + 82 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 + 14 T + 117 T^{2} + 602 T^{3} + 1849 T^{4} \))(\( 1 + 14 T + 117 T^{2} + 602 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 74 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 2 T + 42 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 101 T^{2} + 480 T^{3} + 4343 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 101 T^{2} + 480 T^{3} + 4343 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 - 6 T + 117 T^{2} - 468 T^{3} + 5031 T^{4} - 11094 T^{5} + 79507 T^{6} \))(\( 1 + 14 T + 85 T^{2} + 356 T^{3} + 3655 T^{4} + 25886 T^{5} + 79507 T^{6} \))(\( 1 - 16 T + 158 T^{2} - 1432 T^{3} + 11262 T^{4} - 61576 T^{5} + 292142 T^{6} - 1272112 T^{7} + 3418801 T^{8} \))(\( 1 - 16 T + 158 T^{2} - 1432 T^{3} + 11262 T^{4} - 61576 T^{5} + 292142 T^{6} - 1272112 T^{7} + 3418801 T^{8} \))(\( 1 + 142 T^{2} - 40 T^{3} + 8510 T^{4} - 1720 T^{5} + 262558 T^{6} + 3418801 T^{8} \))(\( 1 - 18 T + 232 T^{2} - 2014 T^{3} + 14869 T^{4} - 86602 T^{5} + 428968 T^{6} - 1431126 T^{7} + 3418801 T^{8} \))(\( 1 + 142 T^{2} - 40 T^{3} + 8510 T^{4} - 1720 T^{5} + 262558 T^{6} + 3418801 T^{8} \))(\( 1 - 18 T + 232 T^{2} - 2014 T^{3} + 14869 T^{4} - 86602 T^{5} + 428968 T^{6} - 1431126 T^{7} + 3418801 T^{8} \))(\( 1 - 3 T + 107 T^{2} - 114 T^{3} + 5299 T^{4} - 1683 T^{5} + 227857 T^{6} - 210786 T^{7} + 8507249 T^{8} - 10256403 T^{9} + 147008443 T^{10} \))(\( 1 - 3 T + 107 T^{2} - 114 T^{3} + 5299 T^{4} - 1683 T^{5} + 227857 T^{6} - 210786 T^{7} + 8507249 T^{8} - 10256403 T^{9} + 147008443 T^{10} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 14 T + 123 T^{2} - 658 T^{3} + 2209 T^{4} \))(\( 1 + 14 T + 123 T^{2} + 658 T^{3} + 2209 T^{4} \))(\( 1 + 14 T + 135 T^{2} + 658 T^{3} + 2209 T^{4} \))(\( 1 - 14 T + 135 T^{2} - 658 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 109 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 93 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 10 T + 142 T^{2} + 816 T^{3} + 6674 T^{4} + 22090 T^{5} + 103823 T^{6} \))(\( 1 - 10 T + 142 T^{2} - 816 T^{3} + 6674 T^{4} - 22090 T^{5} + 103823 T^{6} \))(\( 1 - 24 T + 312 T^{2} - 2584 T^{3} + 14664 T^{4} - 53016 T^{5} + 103823 T^{6} \))(\( 1 + 80 T^{2} - 32 T^{3} + 3760 T^{4} + 103823 T^{6} \))(\( 1 - 36 T + 660 T^{2} - 7756 T^{3} + 63197 T^{4} - 364532 T^{5} + 1457940 T^{6} - 3737628 T^{7} + 4879681 T^{8} \))(\( 1 + 36 T + 660 T^{2} + 7756 T^{3} + 63197 T^{4} + 364532 T^{5} + 1457940 T^{6} + 3737628 T^{7} + 4879681 T^{8} \))(\( 1 + 20 T + 300 T^{2} + 3060 T^{3} + 23957 T^{4} + 143820 T^{5} + 662700 T^{6} + 2076460 T^{7} + 4879681 T^{8} \))(\( 1 + 12 T + 226 T^{2} + 1732 T^{3} + 16835 T^{4} + 81404 T^{5} + 499234 T^{6} + 1245876 T^{7} + 4879681 T^{8} \))(\( 1 - 20 T + 300 T^{2} - 3060 T^{3} + 23957 T^{4} - 143820 T^{5} + 662700 T^{6} - 2076460 T^{7} + 4879681 T^{8} \))(\( 1 - 12 T + 226 T^{2} - 1732 T^{3} + 16835 T^{4} - 81404 T^{5} + 499234 T^{6} - 1245876 T^{7} + 4879681 T^{8} \))(\( 1 + 2 T + 41 T^{2} - 136 T^{3} + 3873 T^{4} + 6374 T^{5} + 182031 T^{6} - 300424 T^{7} + 4256743 T^{8} + 9759362 T^{9} + 229345007 T^{10} \))(\( 1 - 2 T + 41 T^{2} + 136 T^{3} + 3873 T^{4} - 6374 T^{5} + 182031 T^{6} + 300424 T^{7} + 4256743 T^{8} - 9759362 T^{9} + 229345007 T^{10} \))
$53$ (\( 1 + 2 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 8 T + 42 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 + 8 T + 42 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 + 20 T + 198 T^{2} + 1060 T^{3} + 2809 T^{4} \))(\( 1 + 20 T + 198 T^{2} + 1060 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 110 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 2 T - 18 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 167 T^{2} - 1028 T^{3} + 8851 T^{4} - 28090 T^{5} + 148877 T^{6} \))(\( 1 - 10 T + 167 T^{2} - 1028 T^{3} + 8851 T^{4} - 28090 T^{5} + 148877 T^{6} \))(\( 1 + 111 T^{2} - 120 T^{3} + 5883 T^{4} + 148877 T^{6} \))(\( 1 + 143 T^{2} + 8 T^{3} + 7579 T^{4} + 148877 T^{6} \))(\( 1 + 16 T + 270 T^{2} + 2376 T^{3} + 22070 T^{4} + 125928 T^{5} + 758430 T^{6} + 2382032 T^{7} + 7890481 T^{8} \))(\( 1 + 16 T + 270 T^{2} + 2376 T^{3} + 22070 T^{4} + 125928 T^{5} + 758430 T^{6} + 2382032 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T + 142 T^{2} - 784 T^{3} + 9910 T^{4} - 41552 T^{5} + 398878 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 12 T + 88 T^{2} + 944 T^{3} + 9962 T^{4} + 50032 T^{5} + 247192 T^{6} + 1786524 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T + 142 T^{2} - 784 T^{3} + 9910 T^{4} - 41552 T^{5} + 398878 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 12 T + 88 T^{2} + 944 T^{3} + 9962 T^{4} + 50032 T^{5} + 247192 T^{6} + 1786524 T^{7} + 7890481 T^{8} \))(\( 1 - 6 T + 169 T^{2} - 684 T^{3} + 13870 T^{4} - 45300 T^{5} + 735110 T^{6} - 1921356 T^{7} + 25160213 T^{8} - 47342886 T^{9} + 418195493 T^{10} \))(\( 1 - 6 T + 169 T^{2} - 684 T^{3} + 13870 T^{4} - 45300 T^{5} + 735110 T^{6} - 1921356 T^{7} + 25160213 T^{8} - 47342886 T^{9} + 418195493 T^{10} \))
$59$ (\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 6 T + 47 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 47 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 95 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 95 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 + 97 T^{2} + 3481 T^{4} \))(\( 1 - 7 T^{2} + 3481 T^{4} \))(\( 1 + 6 T + 86 T^{2} + 904 T^{3} + 5074 T^{4} + 20886 T^{5} + 205379 T^{6} \))(\( 1 - 6 T + 86 T^{2} - 904 T^{3} + 5074 T^{4} - 20886 T^{5} + 205379 T^{6} \))(\( 1 - 24 T + 264 T^{2} - 2116 T^{3} + 15576 T^{4} - 83544 T^{5} + 205379 T^{6} \))(\( 1 + 120 T^{2} + 52 T^{3} + 7080 T^{4} + 205379 T^{6} \))(\( 1 + 148 T^{2} + 180 T^{3} + 10701 T^{4} + 10620 T^{5} + 515188 T^{6} + 12117361 T^{8} \))(\( 1 + 148 T^{2} - 180 T^{3} + 10701 T^{4} - 10620 T^{5} + 515188 T^{6} + 12117361 T^{8} \))(\( 1 + 8 T + 188 T^{2} + 1268 T^{3} + 15733 T^{4} + 74812 T^{5} + 654428 T^{6} + 1643032 T^{7} + 12117361 T^{8} \))(\( 1 + 12 T + 218 T^{2} + 1912 T^{3} + 19011 T^{4} + 112808 T^{5} + 758858 T^{6} + 2464548 T^{7} + 12117361 T^{8} \))(\( 1 - 8 T + 188 T^{2} - 1268 T^{3} + 15733 T^{4} - 74812 T^{5} + 654428 T^{6} - 1643032 T^{7} + 12117361 T^{8} \))(\( 1 - 12 T + 218 T^{2} - 1912 T^{3} + 19011 T^{4} - 112808 T^{5} + 758858 T^{6} - 2464548 T^{7} + 12117361 T^{8} \))(\( 1 - 16 T + 365 T^{2} - 3820 T^{3} + 47025 T^{4} - 339172 T^{5} + 2774475 T^{6} - 13297420 T^{7} + 74963335 T^{8} - 193877776 T^{9} + 714924299 T^{10} \))(\( 1 + 16 T + 365 T^{2} + 3820 T^{3} + 47025 T^{4} + 339172 T^{5} + 2774475 T^{6} + 13297420 T^{7} + 74963335 T^{8} + 193877776 T^{9} + 714924299 T^{10} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 4 T + 46 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( ( 1 - 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( 1 + 16 T + 219 T^{2} + 1936 T^{3} + 13359 T^{4} + 59536 T^{5} + 226981 T^{6} \))(\( 1 - 16 T + 219 T^{2} - 1936 T^{3} + 13359 T^{4} - 59536 T^{5} + 226981 T^{6} \))(\( ( 1 + 6 T + 61 T^{2} )^{3} \))(\( ( 1 - 2 T + 61 T^{2} )^{3} \))(\( 1 + 8 T + 156 T^{2} + 1048 T^{3} + 13782 T^{4} + 63928 T^{5} + 580476 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T + 156 T^{2} - 1048 T^{3} + 13782 T^{4} - 63928 T^{5} + 580476 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 24 T + 188 T^{2} + 56 T^{3} - 8298 T^{4} + 3416 T^{5} + 699548 T^{6} - 5447544 T^{7} + 13845841 T^{8} \))(\( 1 + 2 T + 220 T^{2} + 334 T^{3} + 19418 T^{4} + 20374 T^{5} + 818620 T^{6} + 453962 T^{7} + 13845841 T^{8} \))(\( 1 + 24 T + 188 T^{2} - 56 T^{3} - 8298 T^{4} - 3416 T^{5} + 699548 T^{6} + 5447544 T^{7} + 13845841 T^{8} \))(\( 1 - 2 T + 220 T^{2} - 334 T^{3} + 19418 T^{4} - 20374 T^{5} + 818620 T^{6} - 453962 T^{7} + 13845841 T^{8} \))(\( 1 - 12 T + 125 T^{2} - 1200 T^{3} + 13666 T^{4} - 105696 T^{5} + 833626 T^{6} - 4465200 T^{7} + 28372625 T^{8} - 166150092 T^{9} + 844596301 T^{10} \))(\( 1 + 12 T + 125 T^{2} + 1200 T^{3} + 13666 T^{4} + 105696 T^{5} + 833626 T^{6} + 4465200 T^{7} + 28372625 T^{8} + 166150092 T^{9} + 844596301 T^{10} \))
$67$ (\( 1 - 7 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 125 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 125 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 162 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 162 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 129 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 24 T + 273 T^{2} + 1608 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 64 T^{2} - 428 T^{3} + 4288 T^{4} - 35912 T^{5} + 300763 T^{6} \))(\( 1 - 8 T + 64 T^{2} - 428 T^{3} + 4288 T^{4} - 35912 T^{5} + 300763 T^{6} \))(\( 1 - 12 T + 228 T^{2} - 1604 T^{3} + 15276 T^{4} - 53868 T^{5} + 300763 T^{6} \))(\( 1 + 4 T + 116 T^{2} + 300 T^{3} + 7772 T^{4} + 17956 T^{5} + 300763 T^{6} \))(\( 1 - 20 T + 194 T^{2} - 1256 T^{3} + 7947 T^{4} - 84152 T^{5} + 870866 T^{6} - 6015260 T^{7} + 20151121 T^{8} \))(\( 1 - 20 T + 194 T^{2} - 1256 T^{3} + 7947 T^{4} - 84152 T^{5} + 870866 T^{6} - 6015260 T^{7} + 20151121 T^{8} \))(\( 1 + 28 T + 434 T^{2} + 4952 T^{3} + 45307 T^{4} + 331784 T^{5} + 1948226 T^{6} + 8421364 T^{7} + 20151121 T^{8} \))(\( 1 - 28 T + 460 T^{2} - 5496 T^{3} + 51202 T^{4} - 368232 T^{5} + 2064940 T^{6} - 8421364 T^{7} + 20151121 T^{8} \))(\( 1 + 28 T + 434 T^{2} + 4952 T^{3} + 45307 T^{4} + 331784 T^{5} + 1948226 T^{6} + 8421364 T^{7} + 20151121 T^{8} \))(\( 1 - 28 T + 460 T^{2} - 5496 T^{3} + 51202 T^{4} - 368232 T^{5} + 2064940 T^{6} - 8421364 T^{7} + 20151121 T^{8} \))(\( 1 - 7 T + 243 T^{2} - 1452 T^{3} + 27462 T^{4} - 134766 T^{5} + 1839954 T^{6} - 6518028 T^{7} + 73085409 T^{8} - 141057847 T^{9} + 1350125107 T^{10} \))(\( 1 - 7 T + 243 T^{2} - 1452 T^{3} + 27462 T^{4} - 134766 T^{5} + 1839954 T^{6} - 6518028 T^{7} + 73085409 T^{8} - 141057847 T^{9} + 1350125107 T^{10} \))
$71$ (\( 1 - 8 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 122 T^{2} + 5041 T^{4} \))(\( 1 + 122 T^{2} + 5041 T^{4} \))(\( 1 + 14 T + 183 T^{2} + 994 T^{3} + 5041 T^{4} \))(\( 1 + 14 T + 183 T^{2} + 994 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 62 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 - 15 T^{2} - 416 T^{3} - 1065 T^{4} + 357911 T^{6} \))(\( 1 - 15 T^{2} - 416 T^{3} - 1065 T^{4} + 357911 T^{6} \))(\( 1 - 12 T + 165 T^{2} - 1320 T^{3} + 11715 T^{4} - 60492 T^{5} + 357911 T^{6} \))(\( 1 + 12 T + 197 T^{2} + 1448 T^{3} + 13987 T^{4} + 60492 T^{5} + 357911 T^{6} \))(\( 1 + 20 T + 372 T^{2} + 3948 T^{3} + 40754 T^{4} + 280308 T^{5} + 1875252 T^{6} + 7158220 T^{7} + 25411681 T^{8} \))(\( 1 + 20 T + 372 T^{2} + 3948 T^{3} + 40754 T^{4} + 280308 T^{5} + 1875252 T^{6} + 7158220 T^{7} + 25411681 T^{8} \))(\( 1 - 12 T + 228 T^{2} - 1844 T^{3} + 22706 T^{4} - 130924 T^{5} + 1149348 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))(\( 1 - 12 T + 286 T^{2} - 2260 T^{3} + 29831 T^{4} - 160460 T^{5} + 1441726 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))(\( 1 - 12 T + 228 T^{2} - 1844 T^{3} + 22706 T^{4} - 130924 T^{5} + 1149348 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))(\( 1 - 12 T + 286 T^{2} - 2260 T^{3} + 29831 T^{4} - 160460 T^{5} + 1441726 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))(\( 1 - 24 T + 421 T^{2} - 5436 T^{3} + 57793 T^{4} - 524712 T^{5} + 4103303 T^{6} - 27402876 T^{7} + 150680531 T^{8} - 609880344 T^{9} + 1804229351 T^{10} \))(\( 1 - 24 T + 421 T^{2} - 5436 T^{3} + 57793 T^{4} - 524712 T^{5} + 4103303 T^{6} - 27402876 T^{7} + 150680531 T^{8} - 609880344 T^{9} + 1804229351 T^{10} \))
$73$ (\( 1 + 5 T + 73 T^{2} \))(\( 1 - 5 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( ( 1 + T + 73 T^{2} )^{2} \))(\( ( 1 - T + 73 T^{2} )^{2} \))(\( 1 + 12 T + 150 T^{2} + 876 T^{3} + 5329 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 876 T^{3} + 5329 T^{4} \))(\( ( 1 + 7 T + 73 T^{2} )^{2} \))(\( 1 + 18 T + 207 T^{2} + 1314 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 68 T^{2} + 504 T^{3} + 4964 T^{4} + 10658 T^{5} + 389017 T^{6} \))(\( 1 - 2 T + 68 T^{2} - 504 T^{3} + 4964 T^{4} - 10658 T^{5} + 389017 T^{6} \))(\( 1 + 24 T + 396 T^{2} + 3898 T^{3} + 28908 T^{4} + 127896 T^{5} + 389017 T^{6} \))(\( 1 - 20 T + 320 T^{2} - 3054 T^{3} + 23360 T^{4} - 106580 T^{5} + 389017 T^{6} \))(\( 1 - 4 T + 98 T^{2} - 96 T^{3} + 4875 T^{4} - 7008 T^{5} + 522242 T^{6} - 1556068 T^{7} + 28398241 T^{8} \))(\( 1 + 4 T + 98 T^{2} + 96 T^{3} + 4875 T^{4} + 7008 T^{5} + 522242 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 + 20 T + 410 T^{2} + 4528 T^{3} + 48979 T^{4} + 330544 T^{5} + 2184890 T^{6} + 7780340 T^{7} + 28398241 T^{8} \))(\( 1 + 6 T + 20 T^{2} + 602 T^{3} + 9418 T^{4} + 43946 T^{5} + 106580 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 - 20 T + 410 T^{2} - 4528 T^{3} + 48979 T^{4} - 330544 T^{5} + 2184890 T^{6} - 7780340 T^{7} + 28398241 T^{8} \))(\( 1 - 6 T + 20 T^{2} - 602 T^{3} + 9418 T^{4} - 43946 T^{5} + 106580 T^{6} - 2334102 T^{7} + 28398241 T^{8} \))(\( 1 - 17 T + 267 T^{2} - 2244 T^{3} + 20712 T^{4} - 143394 T^{5} + 1511976 T^{6} - 11958276 T^{7} + 103867539 T^{8} - 482770097 T^{9} + 2073071593 T^{10} \))(\( 1 + 17 T + 267 T^{2} + 2244 T^{3} + 20712 T^{4} + 143394 T^{5} + 1511976 T^{6} + 11958276 T^{7} + 103867539 T^{8} + 482770097 T^{9} + 2073071593 T^{10} \))
$79$ (\( 1 + 11 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 4 T + 142 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( 1 - 4 T + 142 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( 1 - 4 T + 34 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( 1 - 4 T + 34 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 78 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 + 20 T + 238 T^{2} + 1580 T^{3} + 6241 T^{4} \))(\( 1 + 12 T + 221 T^{2} + 1768 T^{3} + 17459 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 + 12 T + 221 T^{2} + 1768 T^{3} + 17459 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 189 T^{2} - 1640 T^{3} + 14931 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 221 T^{2} - 1640 T^{3} + 17459 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 16 T + 356 T^{2} - 3472 T^{3} + 42678 T^{4} - 274288 T^{5} + 2221796 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 356 T^{2} - 3472 T^{3} + 42678 T^{4} - 274288 T^{5} + 2221796 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 164 T^{2} - 640 T^{3} + 13494 T^{4} - 50560 T^{5} + 1023524 T^{6} + 38950081 T^{8} \))(\( 1 - 2 T + 168 T^{2} - 906 T^{3} + 14450 T^{4} - 71574 T^{5} + 1048488 T^{6} - 986078 T^{7} + 38950081 T^{8} \))(\( 1 + 164 T^{2} - 640 T^{3} + 13494 T^{4} - 50560 T^{5} + 1023524 T^{6} + 38950081 T^{8} \))(\( 1 - 2 T + 168 T^{2} - 906 T^{3} + 14450 T^{4} - 71574 T^{5} + 1048488 T^{6} - 986078 T^{7} + 38950081 T^{8} \))(\( 1 - 7 T + 141 T^{2} + 24 T^{3} + 11736 T^{4} - 3702 T^{5} + 927144 T^{6} + 149784 T^{7} + 69518499 T^{8} - 272650567 T^{9} + 3077056399 T^{10} \))(\( 1 - 7 T + 141 T^{2} + 24 T^{3} + 11736 T^{4} - 3702 T^{5} + 927144 T^{6} + 149784 T^{7} + 69518499 T^{8} - 272650567 T^{9} + 3077056399 T^{10} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 16 T + 210 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 210 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 + 158 T^{2} + 6889 T^{4} \))(\( 1 + 158 T^{2} + 6889 T^{4} \))(\( 1 - 14 T + 194 T^{2} - 1162 T^{3} + 6889 T^{4} \))(\( 1 + 18 T + 242 T^{2} + 1494 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 205 T^{2} - 696 T^{3} + 17015 T^{4} - 27556 T^{5} + 571787 T^{6} \))(\( 1 + 4 T + 205 T^{2} + 696 T^{3} + 17015 T^{4} + 27556 T^{5} + 571787 T^{6} \))(\( 1 - 18 T + 309 T^{2} - 3036 T^{3} + 25647 T^{4} - 124002 T^{5} + 571787 T^{6} \))(\( 1 + 6 T + 117 T^{2} + 500 T^{3} + 9711 T^{4} + 41334 T^{5} + 571787 T^{6} \))(\( 1 - 24 T + 414 T^{2} - 4872 T^{3} + 49254 T^{4} - 404376 T^{5} + 2852046 T^{6} - 13722888 T^{7} + 47458321 T^{8} \))(\( 1 + 24 T + 414 T^{2} + 4872 T^{3} + 49254 T^{4} + 404376 T^{5} + 2852046 T^{6} + 13722888 T^{7} + 47458321 T^{8} \))(\( 1 + 32 T + 590 T^{2} + 7568 T^{3} + 77062 T^{4} + 628144 T^{5} + 4064510 T^{6} + 18297184 T^{7} + 47458321 T^{8} \))(\( 1 - 12 T + 236 T^{2} - 2044 T^{3} + 27990 T^{4} - 169652 T^{5} + 1625804 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))(\( 1 - 32 T + 590 T^{2} - 7568 T^{3} + 77062 T^{4} - 628144 T^{5} + 4064510 T^{6} - 18297184 T^{7} + 47458321 T^{8} \))(\( 1 + 12 T + 236 T^{2} + 2044 T^{3} + 27990 T^{4} + 169652 T^{5} + 1625804 T^{6} + 6861444 T^{7} + 47458321 T^{8} \))(\( 1 + 12 T + 295 T^{2} + 3168 T^{3} + 40450 T^{4} + 363240 T^{5} + 3357350 T^{6} + 21824352 T^{7} + 168677165 T^{8} + 569499852 T^{9} + 3939040643 T^{10} \))(\( 1 - 12 T + 295 T^{2} - 3168 T^{3} + 40450 T^{4} - 363240 T^{5} + 3357350 T^{6} - 21824352 T^{7} + 168677165 T^{8} - 569499852 T^{9} + 3939040643 T^{10} \))
$89$ (\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 2 T^{2} + 7921 T^{4} \))(\( 1 - 2 T^{2} + 7921 T^{4} \))(\( 1 - 22 T^{2} + 7921 T^{4} \))(\( 1 - 22 T^{2} + 7921 T^{4} \))(\( 1 + 94 T^{2} + 7921 T^{4} \))(\( 1 + 158 T^{2} + 7921 T^{4} \))(\( 1 + 16 T + 327 T^{2} + 2880 T^{3} + 29103 T^{4} + 126736 T^{5} + 704969 T^{6} \))(\( 1 - 16 T + 327 T^{2} - 2880 T^{3} + 29103 T^{4} - 126736 T^{5} + 704969 T^{6} \))(\( 1 + 18 T + 183 T^{2} + 1308 T^{3} + 16287 T^{4} + 142578 T^{5} + 704969 T^{6} \))(\( 1 + 26 T + 407 T^{2} + 4300 T^{3} + 36223 T^{4} + 205946 T^{5} + 704969 T^{6} \))(\( 1 + 4 T + 200 T^{2} + 380 T^{3} + 20926 T^{4} + 33820 T^{5} + 1584200 T^{6} + 2819876 T^{7} + 62742241 T^{8} \))(\( 1 - 4 T + 200 T^{2} - 380 T^{3} + 20926 T^{4} - 33820 T^{5} + 1584200 T^{6} - 2819876 T^{7} + 62742241 T^{8} \))(\( 1 + 4 T + 232 T^{2} + 956 T^{3} + 28542 T^{4} + 85084 T^{5} + 1837672 T^{6} + 2819876 T^{7} + 62742241 T^{8} \))(\( 1 + 8 T + 124 T^{2} + 920 T^{3} + 18278 T^{4} + 81880 T^{5} + 982204 T^{6} + 5639752 T^{7} + 62742241 T^{8} \))(\( 1 - 4 T + 232 T^{2} - 956 T^{3} + 28542 T^{4} - 85084 T^{5} + 1837672 T^{6} - 2819876 T^{7} + 62742241 T^{8} \))(\( 1 - 8 T + 124 T^{2} - 920 T^{3} + 18278 T^{4} - 81880 T^{5} + 982204 T^{6} - 5639752 T^{7} + 62742241 T^{8} \))(\( 1 + 6 T + 277 T^{2} + 1320 T^{3} + 40258 T^{4} + 157668 T^{5} + 3582962 T^{6} + 10455720 T^{7} + 195276413 T^{8} + 376453446 T^{9} + 5584059449 T^{10} \))(\( 1 - 6 T + 277 T^{2} - 1320 T^{3} + 40258 T^{4} - 157668 T^{5} + 3582962 T^{6} - 10455720 T^{7} + 195276413 T^{8} - 376453446 T^{9} + 5584059449 T^{10} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 4 T + 118 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 + 4 T + 118 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( 1 - 6 T + 131 T^{2} - 582 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 131 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 - 14 T + 222 T^{2} - 1358 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 158 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 111 T^{2} - 16 T^{3} + 10767 T^{4} + 75272 T^{5} + 912673 T^{6} \))(\( 1 - 8 T + 111 T^{2} + 16 T^{3} + 10767 T^{4} - 75272 T^{5} + 912673 T^{6} \))(\( 1 + 24 T + 435 T^{2} + 4664 T^{3} + 42195 T^{4} + 225816 T^{5} + 912673 T^{6} \))(\( 1 - 4 T + 171 T^{2} - 544 T^{3} + 16587 T^{4} - 37636 T^{5} + 912673 T^{6} \))(\( 1 - 16 T + 382 T^{2} - 4376 T^{3} + 54838 T^{4} - 424472 T^{5} + 3594238 T^{6} - 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 382 T^{2} + 4376 T^{3} + 54838 T^{4} + 424472 T^{5} + 3594238 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 8 T + 254 T^{2} + 1824 T^{3} + 34806 T^{4} + 176928 T^{5} + 2389886 T^{6} + 7301384 T^{7} + 88529281 T^{8} \))(\( 1 - 44 T + 1070 T^{2} - 17084 T^{3} + 197263 T^{4} - 1657148 T^{5} + 10067630 T^{6} - 40157612 T^{7} + 88529281 T^{8} \))(\( 1 - 8 T + 254 T^{2} - 1824 T^{3} + 34806 T^{4} - 176928 T^{5} + 2389886 T^{6} - 7301384 T^{7} + 88529281 T^{8} \))(\( 1 + 44 T + 1070 T^{2} + 17084 T^{3} + 197263 T^{4} + 1657148 T^{5} + 10067630 T^{6} + 40157612 T^{7} + 88529281 T^{8} \))(\( 1 + 14 T + 159 T^{2} + 2856 T^{3} + 33045 T^{4} + 251706 T^{5} + 3205365 T^{6} + 26872104 T^{7} + 145115007 T^{8} + 1239409934 T^{9} + 8587340257 T^{10} \))(\( 1 - 14 T + 159 T^{2} - 2856 T^{3} + 33045 T^{4} - 251706 T^{5} + 3205365 T^{6} - 26872104 T^{7} + 145115007 T^{8} - 1239409934 T^{9} + 8587340257 T^{10} \))
show more
show less