Properties

Label 1620.2
Level 1620
Weight 2
Dimension 29232
Nonzero newspaces 24
Sturm bound 279936
Trace bound 16

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1620\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(279936\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1620))\).

Total New Old
Modular forms 72144 29904 42240
Cusp forms 67825 29232 38593
Eisenstein series 4319 672 3647

Trace form

\( 29232q - 24q^{2} - 40q^{4} - 69q^{5} - 108q^{6} + 6q^{7} - 30q^{8} - 72q^{9} + O(q^{10}) \) \( 29232q - 24q^{2} - 40q^{4} - 69q^{5} - 108q^{6} + 6q^{7} - 30q^{8} - 72q^{9} - 91q^{10} + 6q^{11} - 36q^{12} - 86q^{13} - 54q^{14} - 144q^{16} - 84q^{17} - 36q^{18} - 36q^{19} - 57q^{20} - 270q^{21} - 56q^{22} - 114q^{23} - 36q^{24} - 147q^{25} - 42q^{26} - 54q^{27} - 50q^{28} - 174q^{29} - 54q^{30} - 54q^{31} + 36q^{32} - 126q^{33} + 24q^{34} - 84q^{35} - 108q^{36} - 188q^{37} + 24q^{38} - 7q^{40} - 174q^{41} + 54q^{42} + 6q^{43} + 270q^{44} - 54q^{45} + 2q^{46} + 138q^{47} + 162q^{48} - 42q^{49} + 159q^{50} + 126q^{51} + 102q^{52} + 192q^{53} + 216q^{54} + 66q^{55} + 390q^{56} + 36q^{57} + 118q^{58} + 234q^{59} + 63q^{60} - 126q^{61} + 366q^{62} + 108q^{63} + 122q^{64} + 75q^{65} + 36q^{66} + 18q^{67} + 228q^{68} + 108q^{69} + 41q^{70} + 120q^{71} - 36q^{72} - 62q^{73} + 114q^{74} + 44q^{76} + 234q^{77} - 90q^{78} - 42q^{79} + 132q^{80} - 72q^{81} - 12q^{82} + 174q^{83} + 18q^{84} - 20q^{85} + 96q^{86} + 288q^{87} - 56q^{88} + 282q^{89} - 117q^{90} + 126q^{91} - 210q^{92} + 324q^{93} - 86q^{94} + 252q^{95} - 342q^{96} + 70q^{97} - 486q^{98} + 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1620))\)

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
1620.2.a \(\chi_{1620}(1, \cdot)\) 1620.2.a.a 1 1
1620.2.a.b 1
1620.2.a.c 1
1620.2.a.d 1
1620.2.a.e 1
1620.2.a.f 1
1620.2.a.g 2
1620.2.a.h 2
1620.2.a.i 3
1620.2.a.j 3
1620.2.d \(\chi_{1620}(649, \cdot)\) 1620.2.d.a 2 1
1620.2.d.b 2
1620.2.d.c 6
1620.2.d.d 6
1620.2.d.e 8
1620.2.e \(\chi_{1620}(971, \cdot)\) 1620.2.e.a 48 1
1620.2.e.b 48
1620.2.h \(\chi_{1620}(1619, \cdot)\) n/a 136 1
1620.2.i \(\chi_{1620}(541, \cdot)\) 1620.2.i.a 2 2
1620.2.i.b 2
1620.2.i.c 2
1620.2.i.d 2
1620.2.i.e 2
1620.2.i.f 2
1620.2.i.g 2
1620.2.i.h 2
1620.2.i.i 2
1620.2.i.j 2
1620.2.i.k 2
1620.2.i.l 2
1620.2.i.m 4
1620.2.i.n 4
1620.2.j \(\chi_{1620}(1133, \cdot)\) 1620.2.j.a 24 2
1620.2.j.b 24
1620.2.k \(\chi_{1620}(163, \cdot)\) n/a 272 2
1620.2.n \(\chi_{1620}(539, \cdot)\) n/a 280 2
1620.2.q \(\chi_{1620}(431, \cdot)\) n/a 192 2
1620.2.r \(\chi_{1620}(109, \cdot)\) 1620.2.r.a 4 2
1620.2.r.b 4
1620.2.r.c 4
1620.2.r.d 4
1620.2.r.e 4
1620.2.r.f 4
1620.2.r.g 8
1620.2.r.h 16
1620.2.u \(\chi_{1620}(181, \cdot)\) 1620.2.u.a 30 6
1620.2.u.b 42
1620.2.x \(\chi_{1620}(53, \cdot)\) 1620.2.x.a 8 4
1620.2.x.b 8
1620.2.x.c 16
1620.2.x.d 16
1620.2.x.e 24
1620.2.x.f 24
1620.2.y \(\chi_{1620}(703, \cdot)\) n/a 560 4
1620.2.bb \(\chi_{1620}(179, \cdot)\) n/a 624 6
1620.2.bd \(\chi_{1620}(289, \cdot)\) n/a 108 6
1620.2.be \(\chi_{1620}(71, \cdot)\) n/a 432 6
1620.2.bg \(\chi_{1620}(61, \cdot)\) n/a 648 18
1620.2.bi \(\chi_{1620}(127, \cdot)\) n/a 1248 12
1620.2.bk \(\chi_{1620}(17, \cdot)\) n/a 216 12
1620.2.bm \(\chi_{1620}(59, \cdot)\) n/a 5760 18
1620.2.bo \(\chi_{1620}(11, \cdot)\) n/a 3888 18
1620.2.br \(\chi_{1620}(49, \cdot)\) n/a 972 18
1620.2.bs \(\chi_{1620}(77, \cdot)\) n/a 1944 36
1620.2.bv \(\chi_{1620}(7, \cdot)\) n/a 11520 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1620))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1620)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + T - T^{2} + 6 T^{3} - 5 T^{4} + 25 T^{5} + 125 T^{6} \))(\( 1 - T - T^{2} - 6 T^{3} - 5 T^{4} - 25 T^{5} + 125 T^{6} \))(\( 1 - 3 T^{2} + 20 T^{4} - 75 T^{6} + 625 T^{8} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 - 25 T^{4} + 625 T^{8} \))(\( 1 + 3 T^{2} - 11 T^{4} - 90 T^{6} - 450 T^{8} - 2250 T^{10} - 6875 T^{12} + 46875 T^{14} + 390625 T^{16} \))(\( 1 - 8 T^{2} + 39 T^{4} - 200 T^{6} + 625 T^{8} \))(\( ( 1 + 5 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 + 4 T^{2} - 9 T^{4} + 100 T^{6} + 625 T^{8} )^{2} \))(\( 1 - 4 T^{2} + 16 T^{4} + 200 T^{6} - 1025 T^{8} + 5000 T^{10} + 10000 T^{12} - 62500 T^{14} + 390625 T^{16} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 2 T + 12 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 12 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 - 3 T + 6 T^{2} + T^{3} + 42 T^{4} - 147 T^{5} + 343 T^{6} \))(\( 1 - 3 T + 6 T^{2} + T^{3} + 42 T^{4} - 147 T^{5} + 343 T^{6} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 21 T^{2} + 252 T^{4} - 2035 T^{6} + 12348 T^{8} - 50421 T^{10} + 117649 T^{12} \))(\( 1 - 21 T^{2} + 252 T^{4} - 2035 T^{6} + 12348 T^{8} - 50421 T^{10} + 117649 T^{12} \))(\( ( 1 - 2 T^{2} - 30 T^{4} - 98 T^{6} + 2401 T^{8} )^{2} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))(\( 1 - 2 T - 8 T^{2} + 4 T^{3} + 67 T^{4} + 28 T^{5} - 392 T^{6} - 686 T^{7} + 2401 T^{8} \))(\( 1 - 2 T - 8 T^{2} + 4 T^{3} + 67 T^{4} + 28 T^{5} - 392 T^{6} - 686 T^{7} + 2401 T^{8} \))(\( 1 + 10 T^{2} + 51 T^{4} + 490 T^{6} + 2401 T^{8} \))(\( 1 + 10 T^{2} + 51 T^{4} + 490 T^{6} + 2401 T^{8} \))(\( ( 1 - 13 T^{2} + 49 T^{4} )( 1 + 11 T^{2} + 49 T^{4} ) \))(\( ( 1 - 13 T^{2} + 49 T^{4} )( 1 + 11 T^{2} + 49 T^{4} ) \))(\( 1 + 10 T^{2} + 51 T^{4} + 490 T^{6} + 2401 T^{8} \))(\( 1 + 10 T^{2} + 51 T^{4} + 490 T^{6} + 2401 T^{8} \))(\( ( 1 + 2 T^{2} + 49 T^{4} )^{2}( 1 + 11 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 34 T^{4} - 256 T^{6} - 1697 T^{8} - 12544 T^{10} + 81634 T^{12} + 235298 T^{14} + 5764801 T^{16} )^{2} \))(\( ( 1 + 4 T + 8 T^{2} - 24 T^{3} - 97 T^{4} - 168 T^{5} + 392 T^{6} + 1372 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 - 2 T + 2 T^{2} + 24 T^{3} - 73 T^{4} + 168 T^{5} + 98 T^{6} - 686 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 + 2 T + 2 T^{2} + 16 T^{3} + 98 T^{4} + 274 T^{5} + 480 T^{6} + 1542 T^{7} + 6619 T^{8} + 10794 T^{9} + 23520 T^{10} + 93982 T^{11} + 235298 T^{12} + 268912 T^{13} + 235298 T^{14} + 1647086 T^{15} + 5764801 T^{16} )^{2} \))(\( ( 1 - 4 T + 8 T^{2} + 16 T^{3} - 103 T^{4} + 208 T^{5} + 120 T^{6} - 1956 T^{7} + 6448 T^{8} - 13692 T^{9} + 5880 T^{10} + 71344 T^{11} - 247303 T^{12} + 268912 T^{13} + 941192 T^{14} - 3294172 T^{15} + 5764801 T^{16} )^{2} \))
$11$ (\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 19 T^{2} + 121 T^{4} \))(\( 1 + 19 T^{2} + 121 T^{4} \))(\( 1 + 9 T^{2} - 36 T^{3} + 99 T^{4} + 1331 T^{6} \))(\( 1 + 9 T^{2} + 36 T^{3} + 99 T^{4} + 1331 T^{6} \))(\( ( 1 - T + 11 T^{2} )^{2} \))(\( ( 1 + T + 11 T^{2} )^{2} \))(\( ( 1 + T + 11 T^{2} - 24 T^{3} + 121 T^{4} + 121 T^{5} + 1331 T^{6} )^{2} \))(\( ( 1 - T + 11 T^{2} + 24 T^{3} + 121 T^{4} - 121 T^{5} + 1331 T^{6} )^{2} \))(\( ( 1 + 21 T^{2} + 320 T^{4} + 2541 T^{6} + 14641 T^{8} )^{2} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 - 19 T^{2} + 240 T^{4} - 2299 T^{6} + 14641 T^{8} \))(\( 1 - 19 T^{2} + 240 T^{4} - 2299 T^{6} + 14641 T^{8} \))(\( ( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 12 T^{2} + 23 T^{4} - 1452 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 - 21 T^{2} + 121 T^{4} )^{4}( 1 + 21 T^{2} + 320 T^{4} + 2541 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} )^{2}( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} - 117 T^{4} + 242 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 + 34 T^{2} + 646 T^{4} + 9112 T^{6} + 105583 T^{8} + 1102552 T^{10} + 9458086 T^{12} + 60233074 T^{14} + 214358881 T^{16} )^{2} \))(\( ( 1 + 4 T^{2} - 80 T^{4} - 584 T^{6} - 7361 T^{8} - 70664 T^{10} - 1171280 T^{12} + 7086244 T^{14} + 214358881 T^{16} )^{2} \))
$13$ (\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 18 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 27 T^{2} - 80 T^{3} + 351 T^{4} - 1014 T^{5} + 2197 T^{6} \))(\( 1 - 6 T + 27 T^{2} - 80 T^{3} + 351 T^{4} - 1014 T^{5} + 2197 T^{6} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 39 T^{2} + 867 T^{4} - 13430 T^{6} + 146523 T^{8} - 1113879 T^{10} + 4826809 T^{12} \))(\( 1 - 39 T^{2} + 867 T^{4} - 13430 T^{6} + 146523 T^{8} - 1113879 T^{10} + 4826809 T^{12} \))(\( ( 1 - T^{2} + 48 T^{4} - 169 T^{6} + 28561 T^{8} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T - 2 T^{2} - 32 T^{3} - 53 T^{4} - 416 T^{5} - 338 T^{6} + 8788 T^{7} + 28561 T^{8} \))(\( 1 + 4 T - 2 T^{2} - 32 T^{3} - 53 T^{4} - 416 T^{5} - 338 T^{6} + 8788 T^{7} + 28561 T^{8} \))(\( ( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} )( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} ) \))(\( ( 1 + 13 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 13 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 13 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 13 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} )( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} ) \))(\( ( 1 + 17 T^{2} + 120 T^{4} + 2873 T^{6} + 28561 T^{8} )^{2} \))(\( ( 1 + T^{2} - 47 T^{4} - 290 T^{6} - 26426 T^{8} - 49010 T^{10} - 1342367 T^{12} + 4826809 T^{14} + 815730721 T^{16} )^{2} \))(\( ( 1 + 6 T + 18 T^{2} - 48 T^{3} - 313 T^{4} - 624 T^{5} + 3042 T^{6} + 13182 T^{7} + 28561 T^{8} )^{2} \))(\( ( 1 - 6 T + 18 T^{2} + 48 T^{3} - 313 T^{4} + 624 T^{5} + 3042 T^{6} - 13182 T^{7} + 28561 T^{8} )^{2} \))(\( ( 1 + 6 T + 18 T^{2} + 24 T^{3} + 10 T^{4} + 558 T^{5} + 3456 T^{6} + 14382 T^{7} + 55779 T^{8} + 186966 T^{9} + 584064 T^{10} + 1225926 T^{11} + 285610 T^{12} + 8911032 T^{13} + 86882562 T^{14} + 376491102 T^{15} + 815730721 T^{16} )^{2} \))(\( ( 1 - 337 T^{4} + 28561 T^{8} )^{2}( 1 + 146 T^{4} + 28561 T^{8} )^{2} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 40 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 40 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 27 T^{2} + 36 T^{3} + 459 T^{4} + 4913 T^{6} \))(\( 1 + 27 T^{2} - 36 T^{3} + 459 T^{4} + 4913 T^{6} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 66 T^{2} + 1995 T^{4} - 39444 T^{6} + 576555 T^{8} - 5512386 T^{10} + 24137569 T^{12} \))(\( 1 - 66 T^{2} + 1995 T^{4} - 39444 T^{6} + 576555 T^{8} - 5512386 T^{10} + 24137569 T^{12} \))(\( ( 1 + 15 T^{2} + 602 T^{4} + 4335 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 40 T^{2} - 102 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 + 6 T + 40 T^{2} + 102 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 33 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 - 18 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 - 33 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 289 T^{4} )^{4} \))(\( ( 1 + 15 T^{2} + 602 T^{4} + 4335 T^{6} + 83521 T^{8} )^{4} \))(\( ( 1 - 16 T^{2} + 289 T^{4} )^{2}( 1 + 16 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 2 T^{4} + 83521 T^{8} )^{2} \))(\( ( 1 - 466 T^{4} + 209235 T^{8} - 38920786 T^{12} + 6975757441 T^{16} )^{2} \))(\( ( 1 + 116 T^{4} + 84006 T^{8} + 9688436 T^{12} + 6975757441 T^{16} )^{2} \))
$19$ (\( 1 - 5 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 + 2 T + 27 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 27 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 45 T^{2} - 224 T^{3} + 855 T^{4} - 2166 T^{5} + 6859 T^{6} \))(\( 1 - 6 T + 45 T^{2} - 224 T^{3} + 855 T^{4} - 2166 T^{5} + 6859 T^{6} \))(\( ( 1 - 3 T + 19 T^{2} )^{2} \))(\( ( 1 - 3 T + 19 T^{2} )^{2} \))(\( ( 1 + 15 T^{2} + 72 T^{3} + 285 T^{4} + 6859 T^{6} )^{2} \))(\( ( 1 + 15 T^{2} + 72 T^{3} + 285 T^{4} + 6859 T^{6} )^{2} \))(\( ( 1 + 3 T + 8 T^{2} + 57 T^{3} + 361 T^{4} )^{4} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 2 T + 27 T^{2} + 38 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 2 T + 27 T^{2} + 38 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 3 T + 19 T^{2} )^{4} \))(\( ( 1 - 3 T + 19 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 - 3 T + 19 T^{2} )^{4} \))(\( ( 1 - 3 T + 19 T^{2} )^{4} \))(\( ( 1 + 3 T + 19 T^{2} )^{8} \))(\( ( 1 + 3 T + 8 T^{2} + 57 T^{3} + 361 T^{4} )^{8} \))(\( ( 1 - 22 T^{2} + 361 T^{4} )^{4} \))(\( ( 1 - 34 T^{2} + 361 T^{4} )^{4} \))(\( ( 1 - 26 T^{2} + 555 T^{4} - 9386 T^{6} + 130321 T^{8} )^{4} \))(\( ( 1 - 26 T^{2} + 795 T^{4} - 9386 T^{6} + 130321 T^{8} )^{4} \))
$23$ (\( 1 - 6 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 34 T^{2} + 529 T^{4} \))(\( 1 + 34 T^{2} + 529 T^{4} \))(\( 1 + 3 T + 54 T^{2} + 147 T^{3} + 1242 T^{4} + 1587 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 54 T^{2} - 147 T^{3} + 1242 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 45 T^{2} + 2220 T^{4} - 50283 T^{6} + 1174380 T^{8} - 12592845 T^{10} + 148035889 T^{12} \))(\( 1 - 45 T^{2} + 2220 T^{4} - 50283 T^{6} + 1174380 T^{8} - 12592845 T^{10} + 148035889 T^{12} \))(\( ( 1 - 24 T^{2} + 686 T^{4} - 12696 T^{6} + 279841 T^{8} )^{2} \))(\( 1 + 3 T - 14 T^{2} + 69 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 34 T^{2} + 627 T^{4} - 17986 T^{6} + 279841 T^{8} \))(\( 1 - 34 T^{2} + 627 T^{4} - 17986 T^{6} + 279841 T^{8} \))(\( 1 - 3 T^{2} - 520 T^{4} - 1587 T^{6} + 279841 T^{8} \))(\( 1 + 30 T^{2} + 371 T^{4} + 15870 T^{6} + 279841 T^{8} \))(\( 1 + 30 T^{2} + 371 T^{4} + 15870 T^{6} + 279841 T^{8} \))(\( 1 + 30 T^{2} + 371 T^{4} + 15870 T^{6} + 279841 T^{8} \))(\( 1 + 30 T^{2} + 371 T^{4} + 15870 T^{6} + 279841 T^{8} \))(\( 1 - 3 T^{2} - 520 T^{4} - 1587 T^{6} + 279841 T^{8} \))(\( ( 1 + 36 T^{2} + 767 T^{4} + 19044 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 + 24 T^{2} - 110 T^{4} - 8928 T^{6} - 113949 T^{8} - 4722912 T^{10} - 30782510 T^{12} + 3552861336 T^{14} + 78310985281 T^{16} )^{2} \))(\( 1 + 734 T^{4} + 258915 T^{8} + 205403294 T^{12} + 78310985281 T^{16} \))(\( 1 - 238 T^{4} - 223197 T^{8} - 66602158 T^{12} + 78310985281 T^{16} \))(\( ( 1 - 463 T^{4} - 65472 T^{8} - 129566383 T^{12} + 78310985281 T^{16} )^{2} \))(\( 1 - 656 T^{4} - 42530 T^{8} + 56951296 T^{12} + 24865612099 T^{16} + 15937307623936 T^{20} - 3330566204000930 T^{24} - 14375993627405330576 T^{28} + \)\(61\!\cdots\!61\)\( T^{32} \))
$29$ (\( 1 - 9 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 12 T + 91 T^{2} + 348 T^{3} + 841 T^{4} \))(\( 1 - 12 T + 91 T^{2} - 348 T^{3} + 841 T^{4} \))(\( 1 + 3 T + 18 T^{2} - 105 T^{3} + 522 T^{4} + 2523 T^{5} + 24389 T^{6} \))(\( 1 - 3 T + 18 T^{2} + 105 T^{3} + 522 T^{4} - 2523 T^{5} + 24389 T^{6} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{6} \))(\( ( 1 + 3 T + 29 T^{2} )^{6} \))(\( ( 1 + 31 T^{2} + 841 T^{4} )^{4} \))(\( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 + 3 T - 20 T^{2} + 87 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} \))(\( 1 + 12 T + 53 T^{2} + 396 T^{3} + 3264 T^{4} + 11484 T^{5} + 44573 T^{6} + 292668 T^{7} + 707281 T^{8} \))(\( 1 - 12 T + 53 T^{2} - 396 T^{3} + 3264 T^{4} - 11484 T^{5} + 44573 T^{6} - 292668 T^{7} + 707281 T^{8} \))(\( ( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 3 T - 20 T^{2} + 87 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 32 T^{2} + 183 T^{4} + 26912 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 - 31 T^{2} + 120 T^{4} - 26071 T^{6} + 707281 T^{8} )^{4} \))(\( ( 1 + 40 T^{2} + 759 T^{4} + 33640 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 - 38 T^{2} + 603 T^{4} - 31958 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 - 34 T^{2} - 290 T^{4} + 8024 T^{6} + 411439 T^{8} + 6748184 T^{10} - 205111490 T^{12} - 20223992914 T^{14} + 500246412961 T^{16} )^{2} \))(\( ( 1 - 76 T^{2} + 2800 T^{4} - 98344 T^{6} + 3291679 T^{8} - 82707304 T^{10} + 1980386800 T^{12} - 45206572396 T^{14} + 500246412961 T^{16} )^{2} \))
$31$ (\( 1 - 5 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 2 T + 15 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 + 2 T + 15 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 81 T^{2} - 368 T^{3} + 2511 T^{4} - 5766 T^{5} + 29791 T^{6} \))(\( 1 - 6 T + 81 T^{2} - 368 T^{3} + 2511 T^{4} - 5766 T^{5} + 29791 T^{6} \))(\( ( 1 - T + 31 T^{2} )^{2} \))(\( ( 1 - T + 31 T^{2} )^{2} \))(\( ( 1 + 3 T + 15 T^{2} - 172 T^{3} + 465 T^{4} + 2883 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 + 3 T + 15 T^{2} - 172 T^{3} + 465 T^{4} + 2883 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 + T + 30 T^{2} + 31 T^{3} + 961 T^{4} )^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 - 2 T - 11 T^{2} + 94 T^{3} - 860 T^{4} + 2914 T^{5} - 10571 T^{6} - 59582 T^{7} + 923521 T^{8} \))(\( 1 - 2 T - 11 T^{2} + 94 T^{3} - 860 T^{4} + 2914 T^{5} - 10571 T^{6} - 59582 T^{7} + 923521 T^{8} \))(\( ( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 7 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} \))(\( ( 1 - 7 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} \))(\( ( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} )^{4} \))(\( ( 1 - T - 29 T^{2} + 32 T^{3} - 92 T^{4} + 992 T^{5} - 27869 T^{6} - 29791 T^{7} + 923521 T^{8} )^{4} \))(\( ( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} )^{4} \))(\( ( 1 - 7 T + 31 T^{2} )^{4}( 1 + 11 T + 31 T^{2} )^{4} \))(\( ( 1 + 8 T + 7 T^{2} - 40 T^{3} + 304 T^{4} - 1240 T^{5} + 6727 T^{6} + 238328 T^{7} + 923521 T^{8} )^{4} \))(\( ( 1 - 4 T - 44 T^{2} + 8 T^{3} + 2143 T^{4} + 248 T^{5} - 42284 T^{6} - 119164 T^{7} + 923521 T^{8} )^{4} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 2 T + 48 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T + 48 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 12 T + 75 T^{2} - 452 T^{3} + 2775 T^{4} - 16428 T^{5} + 50653 T^{6} \))(\( 1 - 12 T + 75 T^{2} - 452 T^{3} + 2775 T^{4} - 16428 T^{5} + 50653 T^{6} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 162 T^{2} + 12051 T^{4} - 549268 T^{6} + 16497819 T^{8} - 303614082 T^{10} + 2565726409 T^{12} \))(\( 1 - 162 T^{2} + 12051 T^{4} - 549268 T^{6} + 16497819 T^{8} - 303614082 T^{10} + 2565726409 T^{12} \))(\( ( 1 - 59 T^{2} + 3318 T^{4} - 80771 T^{6} + 1874161 T^{8} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 7 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 7 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 48 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 2 T + 48 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 73 T^{2} + 1369 T^{4} )^{4} \))(\( ( 1 - 59 T^{2} + 3318 T^{4} - 80771 T^{6} + 1874161 T^{8} )^{4} \))(\( ( 1 + 6 T + 18 T^{2} + 222 T^{3} + 1369 T^{4} )^{4} \))(\( ( 1 + 6 T + 18 T^{2} + 222 T^{3} + 1369 T^{4} )^{4} \))(\( ( 1 - 6 T + 18 T^{2} - 222 T^{3} + 1369 T^{4} )^{8} \))(\( ( 1 - 529 T^{4} + 1874161 T^{8} )^{4} \))
$41$ (\( 1 - 9 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 12 T + 91 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 91 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 - 3 T + 42 T^{2} - 327 T^{3} + 1722 T^{4} - 5043 T^{5} + 68921 T^{6} \))(\( 1 + 3 T + 42 T^{2} + 327 T^{3} + 1722 T^{4} + 5043 T^{5} + 68921 T^{6} \))(\( ( 1 - T + 41 T^{2} )^{2} \))(\( ( 1 + T + 41 T^{2} )^{2} \))(\( ( 1 + 7 T + 104 T^{2} + 477 T^{3} + 4264 T^{4} + 11767 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 - 7 T + 104 T^{2} - 477 T^{3} + 4264 T^{4} - 11767 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 129 T^{2} + 7232 T^{4} + 216849 T^{6} + 2825761 T^{8} )^{2} \))(\( 1 + 12 T + 103 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 + 3 T - 32 T^{2} + 123 T^{3} + 1681 T^{4} \))(\( 1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 103 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 53 T^{2} + 108 T^{3} + 696 T^{4} + 4428 T^{5} + 89093 T^{6} + 827052 T^{7} + 2825761 T^{8} \))(\( 1 - 12 T + 53 T^{2} - 108 T^{3} + 696 T^{4} - 4428 T^{5} + 89093 T^{6} - 827052 T^{7} + 2825761 T^{8} \))(\( ( 1 + 10 T + 59 T^{2} + 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - T - 40 T^{2} - 41 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 10 T + 59 T^{2} - 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 10 T + 59 T^{2} + 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + T - 40 T^{2} + 41 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 10 T + 59 T^{2} - 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 72 T^{2} + 3503 T^{4} - 121032 T^{6} + 2825761 T^{8} )^{2} \))(\( ( 1 - 129 T^{2} + 9409 T^{4} - 499230 T^{6} + 21502542 T^{8} - 839205630 T^{10} + 26587585249 T^{12} - 612763447089 T^{14} + 7984925229121 T^{16} )^{2} \))(\( ( 1 + 80 T^{2} + 4719 T^{4} + 134480 T^{6} + 2825761 T^{8} )^{2} \))(\( ( 1 + 2 T^{2} - 1677 T^{4} + 3362 T^{6} + 2825761 T^{8} )^{2} \))(\( ( 1 + 82 T^{2} + 2206 T^{4} + 94792 T^{6} + 6283519 T^{8} + 159345352 T^{10} + 6233628766 T^{12} + 389508547762 T^{14} + 7984925229121 T^{16} )^{2} \))(\( ( 1 + 4 T^{2} - 3200 T^{4} - 584 T^{6} + 7489999 T^{8} - 981704 T^{10} - 9042435200 T^{12} + 19000416964 T^{14} + 7984925229121 T^{16} )^{2} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 10 T + 108 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 108 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 117 T^{2} - 440 T^{3} + 5031 T^{4} - 11094 T^{5} + 79507 T^{6} \))(\( 1 - 6 T + 117 T^{2} - 440 T^{3} + 5031 T^{4} - 11094 T^{5} + 79507 T^{6} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 27 T^{2} + 2091 T^{4} - 147790 T^{6} + 3866259 T^{8} - 92307627 T^{10} + 6321363049 T^{12} \))(\( 1 - 27 T^{2} + 2091 T^{4} - 147790 T^{6} + 3866259 T^{8} - 92307627 T^{10} + 6321363049 T^{12} \))(\( ( 1 - 146 T^{2} + 8898 T^{4} - 269954 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 + 2 T - 39 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 2 T - 39 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 + 10 T - 8 T^{2} + 220 T^{3} + 5515 T^{4} + 9460 T^{5} - 14792 T^{6} + 795070 T^{7} + 3418801 T^{8} \))(\( 1 + 10 T - 8 T^{2} + 220 T^{3} + 5515 T^{4} + 9460 T^{5} - 14792 T^{6} + 795070 T^{7} + 3418801 T^{8} \))(\( 1 + 82 T^{2} + 4875 T^{4} + 151618 T^{6} + 3418801 T^{8} \))(\( 1 - 14 T^{2} - 1653 T^{4} - 25886 T^{6} + 3418801 T^{8} \))(\( 1 + 70 T^{2} + 3051 T^{4} + 129430 T^{6} + 3418801 T^{8} \))(\( 1 + 70 T^{2} + 3051 T^{4} + 129430 T^{6} + 3418801 T^{8} \))(\( 1 - 14 T^{2} - 1653 T^{4} - 25886 T^{6} + 3418801 T^{8} \))(\( 1 + 82 T^{2} + 4875 T^{4} + 151618 T^{6} + 3418801 T^{8} \))(\( ( 1 - 14 T^{2} - 1653 T^{4} - 25886 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 + 146 T^{2} + 12418 T^{4} + 759200 T^{6} + 36342319 T^{8} + 1403760800 T^{10} + 42454670818 T^{12} + 922919005154 T^{14} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - 1849 T^{4} + 3418801 T^{8} )^{2} \))(\( ( 1 - 6 T + 18 T^{2} + 408 T^{3} - 3073 T^{4} + 17544 T^{5} + 33282 T^{6} - 477042 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 6 T + 18 T^{2} - 336 T^{3} - 3710 T^{4} - 18882 T^{5} + 9936 T^{6} + 932922 T^{7} + 6888219 T^{8} + 40115646 T^{9} + 18371664 T^{10} - 1501251174 T^{11} - 12683751710 T^{12} - 49394836848 T^{13} + 113784534882 T^{14} + 1630911666642 T^{15} + 11688200277601 T^{16} )^{2} \))(\( ( 1 + 12 T + 72 T^{2} - 312 T^{3} - 6638 T^{4} - 46764 T^{5} - 34560 T^{6} + 1713132 T^{7} + 17741763 T^{8} + 73664676 T^{9} - 63901440 T^{10} - 3718065348 T^{11} - 22694001038 T^{12} - 45866634216 T^{13} + 455138139528 T^{14} + 3261823333284 T^{15} + 11688200277601 T^{16} )^{2} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 100 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 100 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 15 T + 180 T^{2} - 1437 T^{3} + 8460 T^{4} - 33135 T^{5} + 103823 T^{6} \))(\( 1 + 15 T + 180 T^{2} + 1437 T^{3} + 8460 T^{4} + 33135 T^{5} + 103823 T^{6} \))(\( 1 + 6 T^{2} + 2209 T^{4} \))(\( 1 + 6 T^{2} + 2209 T^{4} \))(\( 1 - 177 T^{2} + 14352 T^{4} - 773787 T^{6} + 31703568 T^{8} - 863703537 T^{10} + 10779215329 T^{12} \))(\( 1 - 177 T^{2} + 14352 T^{4} - 773787 T^{6} + 31703568 T^{8} - 863703537 T^{10} + 10779215329 T^{12} \))(\( ( 1 - 18 T^{2} + 1274 T^{4} - 39762 T^{6} + 4879681 T^{8} )^{2} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 6 T - 64 T^{2} + 36 T^{3} + 6099 T^{4} + 1692 T^{5} - 141376 T^{6} + 622938 T^{7} + 4879681 T^{8} \))(\( 1 - 6 T - 64 T^{2} - 36 T^{3} + 6099 T^{4} - 1692 T^{5} - 141376 T^{6} - 622938 T^{7} + 4879681 T^{8} \))(\( 1 + 30 T^{2} - 1309 T^{4} + 66270 T^{6} + 4879681 T^{8} \))(\( 1 - 6 T^{2} - 2173 T^{4} - 13254 T^{6} + 4879681 T^{8} \))(\( 1 + 78 T^{2} + 3875 T^{4} + 172302 T^{6} + 4879681 T^{8} \))(\( 1 + 78 T^{2} + 3875 T^{4} + 172302 T^{6} + 4879681 T^{8} \))(\( 1 - 6 T^{2} - 2173 T^{4} - 13254 T^{6} + 4879681 T^{8} \))(\( 1 + 30 T^{2} - 1309 T^{4} + 66270 T^{6} + 4879681 T^{8} \))(\( ( 1 + 54 T^{2} + 707 T^{4} + 119286 T^{6} + 4879681 T^{8} )^{2} \))(\( ( 1 + 18 T^{2} - 950 T^{4} - 56592 T^{6} - 3972321 T^{8} - 125011728 T^{10} - 4635696950 T^{12} + 194025875922 T^{14} + 23811286661761 T^{16} )^{2} \))(\( 1 + 1918 T^{4} - 1200957 T^{8} + 9359228158 T^{12} + 23811286661761 T^{16} \))(\( ( 1 - 14 T + 98 T^{2} - 56 T^{3} - 1817 T^{4} - 2632 T^{5} + 216482 T^{6} - 1453522 T^{7} + 4879681 T^{8} )( 1 + 14 T + 98 T^{2} + 56 T^{3} - 1817 T^{4} + 2632 T^{5} + 216482 T^{6} + 1453522 T^{7} + 4879681 T^{8} ) \))(\( 1 - 4804 T^{4} + 7984906 T^{8} - 25625246992 T^{12} + 91387449393043 T^{16} - 125043030867169552 T^{20} + \)\(19\!\cdots\!66\)\( T^{24} - \)\(55\!\cdots\!64\)\( T^{28} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 2209 T^{4} + 4879681 T^{8} )^{4} \))
$53$ (\( 1 - 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 18 T + 184 T^{2} + 954 T^{3} + 2809 T^{4} \))(\( 1 - 18 T + 184 T^{2} - 954 T^{3} + 2809 T^{4} \))(\( 1 + 6 T + 99 T^{2} + 708 T^{3} + 5247 T^{4} + 16854 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 99 T^{2} - 708 T^{3} + 5247 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 54 T^{2} + 6183 T^{4} - 318004 T^{6} + 17368047 T^{8} - 426085974 T^{10} + 22164361129 T^{12} \))(\( 1 - 54 T^{2} + 6183 T^{4} - 318004 T^{6} + 17368047 T^{8} - 426085974 T^{10} + 22164361129 T^{12} \))(\( ( 1 - 134 T^{2} + 8946 T^{4} - 376406 T^{6} + 7890481 T^{8} )^{2} \))(\( ( 1 + 3 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 9 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 3 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 9 T + 53 T^{2} )^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 18 T + 184 T^{2} - 954 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 18 T + 184 T^{2} + 954 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 - 25 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 38 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 38 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 25 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 16 T^{2} + 2809 T^{4} )^{4} \))(\( ( 1 - 134 T^{2} + 8946 T^{4} - 376406 T^{6} + 7890481 T^{8} )^{4} \))(\( ( 1 - 5582 T^{4} + 7890481 T^{8} )^{2} \))(\( ( 1 + 3598 T^{4} + 7890481 T^{8} )^{2} \))(\( ( 1 - 5026 T^{4} + 21116355 T^{8} - 39657557506 T^{12} + 62259690411361 T^{16} )^{2} \))(\( ( 1 + 176 T^{4} - 7733694 T^{8} + 1388724656 T^{12} + 62259690411361 T^{16} )^{2} \))
$59$ (\( 1 + 9 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 12 T + 151 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 151 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 117 T^{2} - 780 T^{3} + 6903 T^{4} - 20886 T^{5} + 205379 T^{6} \))(\( 1 + 6 T + 117 T^{2} + 780 T^{3} + 6903 T^{4} + 20886 T^{5} + 205379 T^{6} \))(\( ( 1 - 13 T + 59 T^{2} )^{2} \))(\( ( 1 + 13 T + 59 T^{2} )^{2} \))(\( ( 1 - 17 T + 257 T^{2} - 2094 T^{3} + 15163 T^{4} - 59177 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 + 17 T + 257 T^{2} + 2094 T^{3} + 15163 T^{4} + 59177 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 + 177 T^{2} + 13988 T^{4} + 616137 T^{6} + 12117361 T^{8} )^{2} \))(\( 1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 9 T + 22 T^{2} + 531 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 9 T + 22 T^{2} - 531 T^{3} + 3481 T^{4} \))(\( 1 + 12 T - 7 T^{2} + 396 T^{3} + 10824 T^{4} + 23364 T^{5} - 24367 T^{6} + 2464548 T^{7} + 12117361 T^{8} \))(\( 1 - 12 T - 7 T^{2} - 396 T^{3} + 10824 T^{4} - 23364 T^{5} - 24367 T^{6} - 2464548 T^{7} + 12117361 T^{8} \))(\( ( 1 + 10 T + 41 T^{2} + 590 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 13 T + 110 T^{2} - 767 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 13 T + 110 T^{2} + 767 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} - 590 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 78 T^{2} + 2603 T^{4} - 271518 T^{6} + 12117361 T^{8} )^{2} \))(\( ( 1 - 177 T^{2} + 17341 T^{4} - 1243602 T^{6} + 74490534 T^{8} - 4328978562 T^{10} + 210127157101 T^{12} - 7465954454457 T^{14} + 146830437604321 T^{16} )^{2} \))(\( ( 1 - 110 T^{2} + 8619 T^{4} - 382910 T^{6} + 12117361 T^{8} )^{2} \))(\( ( 1 - 38 T^{2} - 2037 T^{4} - 132278 T^{6} + 12117361 T^{8} )^{2} \))(\( ( 1 + 14 T^{2} - 5114 T^{4} - 23128 T^{6} + 15396463 T^{8} - 80508568 T^{10} - 61968184154 T^{12} + 590527470974 T^{14} + 146830437604321 T^{16} )^{2} \))(\( ( 1 - 76 T^{2} + 2770 T^{4} + 300656 T^{6} - 23187581 T^{8} + 1046583536 T^{10} + 33565089970 T^{12} - 3205720556716 T^{14} + 146830437604321 T^{16} )^{2} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( 1 - 21 T + 246 T^{2} - 2153 T^{3} + 15006 T^{4} - 78141 T^{5} + 226981 T^{6} \))(\( 1 - 21 T + 246 T^{2} - 2153 T^{3} + 15006 T^{4} - 78141 T^{5} + 226981 T^{6} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 3 T + 144 T^{2} + 397 T^{3} + 8784 T^{4} + 11163 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 + 3 T + 144 T^{2} + 397 T^{3} + 8784 T^{4} + 11163 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 - 7 T + 102 T^{2} - 427 T^{3} + 3721 T^{4} )^{4} \))(\( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} \))(\( 1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4} \))(\( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( ( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 5 T - 36 T^{2} + 305 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 5 T - 36 T^{2} + 305 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{4}( 1 + 13 T + 61 T^{2} )^{4} \))(\( ( 1 + 7 T - 53 T^{2} - 140 T^{3} + 3694 T^{4} - 8540 T^{5} - 197213 T^{6} + 1588867 T^{7} + 13845841 T^{8} )^{4} \))(\( ( 1 - 61 T^{2} + 3721 T^{4} )^{4} \))(\( ( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} )^{4} \))(\( ( 1 - 6 T - 11 T^{2} + 450 T^{3} - 3708 T^{4} + 27450 T^{5} - 40931 T^{6} - 1361886 T^{7} + 13845841 T^{8} )^{4} \))(\( ( 1 + 6 T + T^{2} - 522 T^{3} - 4692 T^{4} - 31842 T^{5} + 3721 T^{6} + 1361886 T^{7} + 13845841 T^{8} )^{4} \))
$67$ (\( 1 - 2 T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 8 T + 42 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 42 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 180 T^{2} - 1055 T^{3} + 12060 T^{4} - 40401 T^{5} + 300763 T^{6} \))(\( 1 - 9 T + 180 T^{2} - 1055 T^{3} + 12060 T^{4} - 40401 T^{5} + 300763 T^{6} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 297 T^{2} + 41736 T^{4} - 3513043 T^{6} + 187352904 T^{8} - 5984882937 T^{10} + 90458382169 T^{12} \))(\( 1 - 297 T^{2} + 41736 T^{4} - 3513043 T^{6} + 187352904 T^{8} - 5984882937 T^{10} + 90458382169 T^{12} \))(\( ( 1 - 8 T^{2} - 3906 T^{4} - 35912 T^{6} + 20151121 T^{8} )^{2} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 22 T^{2} + 736 T^{3} - 7013 T^{4} + 49312 T^{5} + 98758 T^{6} - 2406104 T^{7} + 20151121 T^{8} \))(\( 1 - 8 T + 22 T^{2} + 736 T^{3} - 7013 T^{4} + 49312 T^{5} + 98758 T^{6} - 2406104 T^{7} + 20151121 T^{8} \))(\( 1 + 70 T^{2} + 411 T^{4} + 314230 T^{6} + 20151121 T^{8} \))(\( 1 + 70 T^{2} + 411 T^{4} + 314230 T^{6} + 20151121 T^{8} \))(\( 1 + 118 T^{2} + 9435 T^{4} + 529702 T^{6} + 20151121 T^{8} \))(\( 1 + 118 T^{2} + 9435 T^{4} + 529702 T^{6} + 20151121 T^{8} \))(\( 1 + 70 T^{2} + 411 T^{4} + 314230 T^{6} + 20151121 T^{8} \))(\( 1 + 70 T^{2} + 411 T^{4} + 314230 T^{6} + 20151121 T^{8} \))(\( ( 1 - 109 T^{2} + 4489 T^{4} )^{2}( 1 + 122 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 8 T^{2} + 3970 T^{4} - 103072 T^{6} - 5181581 T^{8} - 462690208 T^{10} + 79999950370 T^{12} + 723667057352 T^{14} + 406067677556641 T^{16} )^{2} \))(\( ( 1 + 16 T + 128 T^{2} - 96 T^{3} - 5257 T^{4} - 6432 T^{5} + 574592 T^{6} + 4812208 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 - 2 T + 2 T^{2} + 264 T^{3} - 4753 T^{4} + 17688 T^{5} + 8978 T^{6} - 601526 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 - 14 T + 98 T^{2} + 504 T^{3} - 8017 T^{4} + 33768 T^{5} + 439922 T^{6} - 4210682 T^{7} + 20151121 T^{8} )^{4} \))(\( ( 1 + 20 T + 200 T^{2} + 400 T^{3} - 11671 T^{4} - 146240 T^{5} - 510600 T^{6} + 3939060 T^{7} + 69399520 T^{8} + 263917020 T^{9} - 2292083400 T^{10} - 43983581120 T^{11} - 235183733191 T^{12} + 540050042800 T^{13} + 18091676433800 T^{14} + 121214232106460 T^{15} + 406067677556641 T^{16} )^{2} \))
$71$ (\( 1 + 3 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 15 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 12 T + 151 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 151 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 - 24 T + 321 T^{2} - 3084 T^{3} + 22791 T^{4} - 120984 T^{5} + 357911 T^{6} \))(\( 1 + 24 T + 321 T^{2} + 3084 T^{3} + 22791 T^{4} + 120984 T^{5} + 357911 T^{6} \))(\( ( 1 - 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 171 T^{2} - 72 T^{3} + 12141 T^{4} + 357911 T^{6} )^{2} \))(\( ( 1 + 171 T^{2} + 72 T^{3} + 12141 T^{4} + 357911 T^{6} )^{2} \))(\( ( 1 + 53 T^{2} + 3528 T^{4} + 267173 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 15 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 15 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 3 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 151 T^{2} - 852 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 12 T + 151 T^{2} + 852 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{4} \))(\( ( 1 + 9 T + 71 T^{2} )^{4} \))(\( ( 1 + 71 T^{2} )^{4} \))(\( ( 1 + 71 T^{2} )^{4} \))(\( ( 1 - 9 T + 71 T^{2} )^{4} \))(\( ( 1 - 6 T + 71 T^{2} )^{4} \))(\( ( 1 + 52 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 + 53 T^{2} + 3528 T^{4} + 267173 T^{6} + 25411681 T^{8} )^{4} \))(\( ( 1 - 110 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 - 122 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 + 62 T^{2} + 10014 T^{4} + 312542 T^{6} + 25411681 T^{8} )^{4} \))(\( ( 1 - 124 T^{2} + 13776 T^{4} - 625084 T^{6} + 25411681 T^{8} )^{4} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 10 T + 144 T^{2} - 730 T^{3} + 5329 T^{4} \))(\( 1 - 10 T + 144 T^{2} - 730 T^{3} + 5329 T^{4} \))(\( ( 1 - 8 T + 73 T^{2} )^{3} \))(\( ( 1 - 8 T + 73 T^{2} )^{3} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 54 T^{2} - 2049 T^{4} + 466316 T^{6} - 10919121 T^{8} - 1533505014 T^{10} + 151334226289 T^{12} \))(\( 1 - 54 T^{2} - 2049 T^{4} + 466316 T^{6} - 10919121 T^{8} - 1533505014 T^{10} + 151334226289 T^{12} \))(\( ( 1 - 227 T^{2} + 22734 T^{4} - 1209683 T^{6} + 28398241 T^{8} )^{2} \))(\( ( 1 + 16 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 11 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 16 T + 73 T^{2} )^{2} \))(\( ( 1 - 11 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 144 T^{2} - 730 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 10 T + 144 T^{2} - 730 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 142 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 50 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 50 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 142 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 23 T^{2} + 5329 T^{4} )^{4} \))(\( ( 1 - 227 T^{2} + 22734 T^{4} - 1209683 T^{6} + 28398241 T^{8} )^{4} \))(\( ( 1 - 14 T + 98 T^{2} - 1022 T^{3} + 5329 T^{4} )^{4} \))(\( ( 1 - 2 T + 2 T^{2} - 146 T^{3} + 5329 T^{4} )^{4} \))(\( ( 1 + 14 T + 98 T^{2} + 1218 T^{3} + 14942 T^{4} + 88914 T^{5} + 522242 T^{6} + 5446238 T^{7} + 28398241 T^{8} )^{4} \))(\( ( 1 + 20 T + 200 T^{2} + 2400 T^{3} + 26591 T^{4} + 175200 T^{5} + 1065800 T^{6} + 7780340 T^{7} + 28398241 T^{8} )^{4} \))
$79$ (\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 66 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 66 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 2 T + 79 T^{2} )^{3} \))(\( ( 1 - 2 T + 79 T^{2} )^{3} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 3 T + 93 T^{2} - 366 T^{3} + 7347 T^{4} - 18723 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 3 T + 93 T^{2} - 366 T^{3} + 7347 T^{4} - 18723 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 + 6 T + 79 T^{2} )^{8} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 - 8 T - 2 T^{2} + 736 T^{3} - 6941 T^{4} + 58144 T^{5} - 12482 T^{6} - 3944312 T^{7} + 38950081 T^{8} \))(\( 1 - 8 T - 2 T^{2} + 736 T^{3} - 6941 T^{4} + 58144 T^{5} - 12482 T^{6} - 3944312 T^{7} + 38950081 T^{8} \))(\( ( 1 - 15 T + 146 T^{2} - 1185 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 79 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 12 T + 65 T^{2} + 948 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 12 T + 65 T^{2} + 948 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 79 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 15 T + 146 T^{2} - 1185 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 3 T - 70 T^{2} + 237 T^{3} + 6241 T^{4} )^{4} \))(\( ( 1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4} )^{8} \))(\( ( 1 + 79 T^{2} + 6241 T^{4} )^{4} \))(\( ( 1 + 122 T^{2} + 8643 T^{4} + 761402 T^{6} + 38950081 T^{8} )^{2} \))(\( ( 1 + 130 T^{2} + 3217 T^{4} + 156130 T^{6} + 42801508 T^{8} + 974407330 T^{10} + 125302410577 T^{12} + 31601369217730 T^{14} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 - 2 T^{2} - 7079 T^{4} + 10798 T^{6} + 11193844 T^{8} + 67390318 T^{10} - 275727623399 T^{12} - 486174911042 T^{14} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( 1 + 6 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 6 T + 28 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 - 6 T + 28 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 21 T + 378 T^{2} + 3729 T^{3} + 31374 T^{4} + 144669 T^{5} + 571787 T^{6} \))(\( 1 - 21 T + 378 T^{2} - 3729 T^{3} + 31374 T^{4} - 144669 T^{5} + 571787 T^{6} \))(\( 1 - 66 T^{2} + 6889 T^{4} \))(\( 1 - 66 T^{2} + 6889 T^{4} \))(\( 1 - 93 T^{2} + 18516 T^{4} - 1028715 T^{6} + 127556724 T^{8} - 4413623853 T^{10} + 326940373369 T^{12} \))(\( 1 - 93 T^{2} + 18516 T^{4} - 1028715 T^{6} + 127556724 T^{8} - 4413623853 T^{10} + 326940373369 T^{12} \))(\( ( 1 - 210 T^{2} + 23642 T^{4} - 1446690 T^{6} + 47458321 T^{8} )^{2} \))(\( 1 - 15 T + 142 T^{2} - 1245 T^{3} + 6889 T^{4} \))(\( 1 - 6 T - 47 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 + 6 T - 47 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 + 6 T - 47 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 + 6 T - 47 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 + 15 T + 142 T^{2} + 1245 T^{3} + 6889 T^{4} \))(\( 1 - 6 T - 47 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 - 6 T - 47 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 6 T + 8 T^{2} - 828 T^{3} - 9093 T^{4} - 68724 T^{5} + 55112 T^{6} + 3430722 T^{7} + 47458321 T^{8} \))(\( 1 - 6 T + 8 T^{2} + 828 T^{3} - 9093 T^{4} + 68724 T^{5} + 55112 T^{6} - 3430722 T^{7} + 47458321 T^{8} \))(\( 1 - 3 T^{2} - 6880 T^{4} - 20667 T^{6} + 47458321 T^{8} \))(\( 1 + 66 T^{2} - 2533 T^{4} + 454674 T^{6} + 47458321 T^{8} \))(\( 1 + 150 T^{2} + 15611 T^{4} + 1033350 T^{6} + 47458321 T^{8} \))(\( 1 + 150 T^{2} + 15611 T^{4} + 1033350 T^{6} + 47458321 T^{8} \))(\( 1 + 66 T^{2} - 2533 T^{4} + 454674 T^{6} + 47458321 T^{8} \))(\( 1 - 3 T^{2} - 6880 T^{4} - 20667 T^{6} + 47458321 T^{8} \))(\( ( 1 - 84 T^{2} + 167 T^{4} - 578676 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 + 210 T^{2} + 20458 T^{4} + 2071440 T^{6} + 207680943 T^{8} + 14270150160 T^{10} + 970902331018 T^{12} + 68657478407490 T^{14} + 2252292232139041 T^{16} )^{2} \))(\( 1 + 13294 T^{4} + 129272115 T^{8} + 630910919374 T^{12} + 2252292232139041 T^{16} \))(\( ( 1 - 22 T + 242 T^{2} - 1672 T^{3} + 11503 T^{4} - 138776 T^{5} + 1667138 T^{6} - 12579314 T^{7} + 47458321 T^{8} )( 1 + 22 T + 242 T^{2} + 1672 T^{3} + 11503 T^{4} + 138776 T^{5} + 1667138 T^{6} + 12579314 T^{7} + 47458321 T^{8} ) \))(\( ( 1 - 12791 T^{4} + 116151360 T^{8} - 607039383911 T^{12} + 2252292232139041 T^{16} )^{2} \))(\( 1 + 2384 T^{4} - 29979650 T^{8} - 141260429824 T^{12} - 1250162381809181 T^{16} - 6703982823185365504 T^{20} - \)\(67\!\cdots\!50\)\( T^{24} + \)\(25\!\cdots\!24\)\( T^{28} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 - 9 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 151 T^{2} + 7921 T^{4} \))(\( 1 + 151 T^{2} + 7921 T^{4} \))(\( ( 1 + 3 T + 89 T^{2} )^{3} \))(\( ( 1 - 3 T + 89 T^{2} )^{3} \))(\( ( 1 + 13 T + 89 T^{2} )^{2} \))(\( ( 1 - 13 T + 89 T^{2} )^{2} \))(\( ( 1 - 28 T + 512 T^{2} - 5646 T^{3} + 45568 T^{4} - 221788 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 + 28 T + 512 T^{2} + 5646 T^{3} + 45568 T^{4} + 221788 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 + 246 T^{2} + 28907 T^{4} + 1948566 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 + 12 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 12 T + 89 T^{2} )^{2} \))(\( ( 1 + 9 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 12 T + 89 T^{2} )^{2} \))(\( ( 1 - 12 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 9 T + 89 T^{2} )^{2} \))(\( ( 1 + 151 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 151 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{4} \))(\( ( 1 - 13 T + 89 T^{2} )^{4} \))(\( ( 1 - 10 T + 89 T^{2} )^{4} \))(\( ( 1 + 10 T + 89 T^{2} )^{4} \))(\( ( 1 + 13 T + 89 T^{2} )^{4} \))(\( ( 1 + 2 T + 89 T^{2} )^{4} \))(\( ( 1 + 18 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 + 246 T^{2} + 28907 T^{4} + 1948566 T^{6} + 62742241 T^{8} )^{4} \))(\( ( 1 + 176 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 + 158 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 - 14 T^{2} + 6630 T^{4} - 110894 T^{6} + 62742241 T^{8} )^{4} \))(\( ( 1 + 196 T^{2} + 20046 T^{4} + 1552516 T^{6} + 62742241 T^{8} )^{4} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 2 T + 192 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 + 2 T + 192 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 327 T^{2} - 3068 T^{3} + 31719 T^{4} - 169362 T^{5} + 912673 T^{6} \))(\( 1 - 18 T + 327 T^{2} - 3068 T^{3} + 31719 T^{4} - 169362 T^{5} + 912673 T^{6} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 243 T^{2} + 18171 T^{4} - 722050 T^{6} + 170970939 T^{8} - 21512615283 T^{10} + 832972004929 T^{12} \))(\( 1 - 243 T^{2} + 18171 T^{4} - 722050 T^{6} + 170970939 T^{8} - 21512615283 T^{10} + 832972004929 T^{12} \))(\( ( 1 - 182 T^{2} + 16650 T^{4} - 1712438 T^{6} + 88529281 T^{8} )^{2} \))(\( 1 - 16 T + 159 T^{2} - 1552 T^{3} + 9409 T^{4} \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 - 13 T + 72 T^{2} - 1261 T^{3} + 9409 T^{4} \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - 16 T + 159 T^{2} - 1552 T^{3} + 9409 T^{4} \))(\( 1 - 13 T + 72 T^{2} - 1261 T^{3} + 9409 T^{4} \))(\( 1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - 2 T - 188 T^{2} + 4 T^{3} + 27067 T^{4} + 388 T^{5} - 1768892 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 - 2 T - 188 T^{2} + 4 T^{3} + 27067 T^{4} + 388 T^{5} - 1768892 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( ( 1 - 18 T + 227 T^{2} - 1746 T^{3} + 9409 T^{4} )( 1 + 18 T + 227 T^{2} + 1746 T^{3} + 9409 T^{4} ) \))(\( 1 + 94 T^{2} - 573 T^{4} + 884446 T^{6} + 88529281 T^{8} \))(\( ( 1 - 18 T + 227 T^{2} - 1746 T^{3} + 9409 T^{4} )( 1 + 18 T + 227 T^{2} + 1746 T^{3} + 9409 T^{4} ) \))(\( ( 1 - 18 T + 227 T^{2} - 1746 T^{3} + 9409 T^{4} )( 1 + 18 T + 227 T^{2} + 1746 T^{3} + 9409 T^{4} ) \))(\( 1 + 94 T^{2} - 573 T^{4} + 884446 T^{6} + 88529281 T^{8} \))(\( ( 1 - 18 T + 227 T^{2} - 1746 T^{3} + 9409 T^{4} )( 1 + 18 T + 227 T^{2} + 1746 T^{3} + 9409 T^{4} ) \))(\( ( 1 + 193 T^{2} + 27840 T^{4} + 1815937 T^{6} + 88529281 T^{8} )^{2} \))(\( ( 1 + 182 T^{2} + 16474 T^{4} - 394576 T^{6} - 122970497 T^{8} - 3712565584 T^{10} + 1458431375194 T^{12} + 151600904897078 T^{14} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 + 6 T + 18 T^{2} - 1056 T^{3} - 12577 T^{4} - 102432 T^{5} + 169362 T^{6} + 5476038 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 + 18 T + 162 T^{2} - 576 T^{3} - 14593 T^{4} - 55872 T^{5} + 1524258 T^{6} + 16428114 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 + 12 T + 72 T^{2} - 888 T^{3} - 15410 T^{4} - 93924 T^{5} + 376704 T^{6} + 15677316 T^{7} + 152755539 T^{8} + 1520699652 T^{9} + 3544407936 T^{10} - 85721898852 T^{11} - 1364236220210 T^{12} - 7625558148216 T^{13} + 59973984354888 T^{14} + 969579413737356 T^{15} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 - 24 T + 288 T^{2} + 1056 T^{3} - 63023 T^{4} + 883008 T^{5} - 2484000 T^{6} - 64943496 T^{7} + 1178064288 T^{8} - 6299519112 T^{9} - 23371956000 T^{10} + 805897560384 T^{11} - 5579380876463 T^{12} + 9068231311392 T^{13} + 239895937419552 T^{14} - 1939158827474712 T^{15} + 7837433594376961 T^{16} )^{2} \))
show more
show less