Properties

Label 2450.2
Level 2450
Weight 2
Dimension 52006
Nonzero newspaces 24
Sturm bound 705600
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(705600\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2450))\).

Total New Old
Modular forms 179760 52006 127754
Cusp forms 173041 52006 121035
Eisenstein series 6719 0 6719

Trace form

\( 52006q - q^{2} - 8q^{3} - 5q^{4} - 5q^{5} - 16q^{6} - 8q^{7} - q^{8} - 41q^{9} + O(q^{10}) \) \( 52006q - q^{2} - 8q^{3} - 5q^{4} - 5q^{5} - 16q^{6} - 8q^{7} - q^{8} - 41q^{9} - 5q^{10} - 36q^{11} - 8q^{12} - 34q^{13} - 6q^{14} - 20q^{15} - 5q^{16} - 46q^{17} - 12q^{18} - 24q^{19} - 26q^{21} + 4q^{22} - 32q^{23} + 4q^{24} + 83q^{25} + 66q^{26} + 220q^{27} + 40q^{28} + 154q^{29} + 164q^{30} + 144q^{31} + 4q^{32} + 376q^{33} + 175q^{34} + 72q^{35} + 151q^{36} + 231q^{37} + 178q^{38} + 434q^{39} - 5q^{40} + 158q^{41} + 198q^{42} + 168q^{43} + 102q^{44} + 159q^{45} + 150q^{46} + 100q^{47} + 6q^{48} + 118q^{49} - 25q^{50} + 36q^{51} - 20q^{52} - 45q^{53} + 14q^{54} + 28q^{55} + 36q^{56} + 124q^{57} - 18q^{58} + 168q^{59} + 244q^{61} - 2q^{62} + 156q^{63} - 5q^{64} + 179q^{65} - 84q^{66} + 268q^{67} - 6q^{68} + 236q^{69} + 56q^{71} - 37q^{72} + 238q^{73} - 10q^{74} + 252q^{75} - 24q^{76} + 60q^{77} - 52q^{78} + 208q^{79} - 5q^{80} + 111q^{81} - 34q^{82} + 196q^{83} - 26q^{84} + 111q^{85} + 40q^{86} + 308q^{87} + 60q^{88} + 411q^{89} + 187q^{90} + 182q^{91} + 140q^{92} + 584q^{93} + 216q^{94} + 324q^{95} + 80q^{96} + 406q^{97} + 240q^{98} + 528q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2450))\)

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
2450.2.a \(\chi_{2450}(1, \cdot)\) 2450.2.a.a 1 1
2450.2.a.b 1
2450.2.a.c 1
2450.2.a.d 1
2450.2.a.e 1
2450.2.a.f 1
2450.2.a.g 1
2450.2.a.h 1
2450.2.a.i 1
2450.2.a.j 1
2450.2.a.k 1
2450.2.a.l 1
2450.2.a.m 1
2450.2.a.n 1
2450.2.a.o 1
2450.2.a.p 1
2450.2.a.q 1
2450.2.a.r 1
2450.2.a.s 1
2450.2.a.t 1
2450.2.a.u 1
2450.2.a.v 1
2450.2.a.w 1
2450.2.a.x 1
2450.2.a.y 1
2450.2.a.z 1
2450.2.a.ba 1
2450.2.a.bb 1
2450.2.a.bc 1
2450.2.a.bd 1
2450.2.a.be 1
2450.2.a.bf 1
2450.2.a.bg 1
2450.2.a.bh 1
2450.2.a.bi 2
2450.2.a.bj 2
2450.2.a.bk 2
2450.2.a.bl 2
2450.2.a.bm 2
2450.2.a.bn 2
2450.2.a.bo 2
2450.2.a.bp 2
2450.2.a.bq 2
2450.2.a.br 2
2450.2.a.bs 2
2450.2.a.bt 4
2450.2.a.bu 4
2450.2.c \(\chi_{2450}(99, \cdot)\) 2450.2.c.a 2 1
2450.2.c.b 2
2450.2.c.c 2
2450.2.c.d 2
2450.2.c.e 2
2450.2.c.f 2
2450.2.c.g 2
2450.2.c.h 2
2450.2.c.i 2
2450.2.c.j 2
2450.2.c.k 2
2450.2.c.l 2
2450.2.c.m 2
2450.2.c.n 2
2450.2.c.o 2
2450.2.c.p 2
2450.2.c.q 2
2450.2.c.r 2
2450.2.c.s 2
2450.2.c.t 4
2450.2.c.u 4
2450.2.c.v 4
2450.2.c.w 4
2450.2.c.x 8
2450.2.e \(\chi_{2450}(851, \cdot)\) n/a 128 2
2450.2.g \(\chi_{2450}(293, \cdot)\) n/a 120 2
2450.2.h \(\chi_{2450}(491, \cdot)\) n/a 412 4
2450.2.j \(\chi_{2450}(949, \cdot)\) n/a 120 2
2450.2.l \(\chi_{2450}(351, \cdot)\) n/a 540 6
2450.2.n \(\chi_{2450}(589, \cdot)\) n/a 408 4
2450.2.p \(\chi_{2450}(607, \cdot)\) n/a 240 4
2450.2.t \(\chi_{2450}(449, \cdot)\) n/a 504 6
2450.2.u \(\chi_{2450}(361, \cdot)\) n/a 800 8
2450.2.v \(\chi_{2450}(97, \cdot)\) n/a 800 8
2450.2.x \(\chi_{2450}(51, \cdot)\) n/a 1056 12
2450.2.z \(\chi_{2450}(307, \cdot)\) n/a 1008 12
2450.2.bb \(\chi_{2450}(79, \cdot)\) n/a 800 8
2450.2.bd \(\chi_{2450}(71, \cdot)\) n/a 3360 24
2450.2.be \(\chi_{2450}(149, \cdot)\) n/a 1008 12
2450.2.bi \(\chi_{2450}(117, \cdot)\) n/a 1600 16
2450.2.bj \(\chi_{2450}(29, \cdot)\) n/a 3360 24
2450.2.bm \(\chi_{2450}(143, \cdot)\) n/a 2016 24
2450.2.bo \(\chi_{2450}(11, \cdot)\) n/a 6720 48
2450.2.bp \(\chi_{2450}(13, \cdot)\) n/a 6720 48
2450.2.bt \(\chi_{2450}(9, \cdot)\) n/a 6720 48
2450.2.bv \(\chi_{2450}(3, \cdot)\) n/a 13440 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( ( 1 + 3 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 - T^{2} + 9 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} \))(\( ( 1 + 3 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 - T^{2} + 9 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} \))(\( 1 + 7 T^{4} + 81 T^{8} \))(\( 1 + 7 T^{4} + 81 T^{8} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( ( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} )( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} ) \))(\( ( 1 + T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} )( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} ) \))(\( ( 1 + 7 T^{4} + 81 T^{8} )^{2} \))
$5$ 1
$7$ 1
$11$ (\( 1 + 5 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 121 T^{4} \))(\( ( 1 - 5 T + 11 T^{2} )^{2} \))(\( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 121 T^{4} \))(\( ( 1 - 5 T + 11 T^{2} )^{2} \))(\( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} \))(\( ( 1 - 4 T + 15 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 15 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 + 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 5 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 5 T + 11 T^{2} )^{4} \))(\( ( 1 + 2 T + 11 T^{2} )^{4} \))(\( ( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 15 T^{2} - 44 T^{3} + 121 T^{4} )^{4} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 2 T^{2} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 2 T^{2} + 169 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T^{2} + 166 T^{4} + 676 T^{6} + 28561 T^{8} \))(\( 1 + 4 T^{2} + 166 T^{4} + 676 T^{6} + 28561 T^{8} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( 1 - T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - T^{2} + 169 T^{4} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 28 T^{2} + 406 T^{4} - 4732 T^{6} + 28561 T^{8} \))(\( ( 1 + 2 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( 1 - 28 T^{2} + 406 T^{4} - 4732 T^{6} + 28561 T^{8} \))(\( ( 1 - 4 T^{2} + 166 T^{4} - 676 T^{6} + 28561 T^{8} )^{2} \))
$17$ (\( 1 + T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( 1 + 27 T^{2} + 289 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( 1 + 27 T^{2} + 289 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 + 8 T^{2} + 55 T^{4} + 2312 T^{6} + 83521 T^{8} \))(\( 1 + 8 T^{2} + 55 T^{4} + 2312 T^{6} + 83521 T^{8} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( 1 + 15 T^{2} + 289 T^{4} \))(\( 1 + 15 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 - 33 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 32 T^{2} + 706 T^{4} - 9248 T^{6} + 83521 T^{8} \))(\( ( 1 - 27 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 32 T^{2} + 289 T^{4} )^{2} \))(\( 1 - 32 T^{2} + 706 T^{4} - 9248 T^{6} + 83521 T^{8} \))(\( ( 1 - 8 T^{2} + 55 T^{4} - 2312 T^{6} + 83521 T^{8} )^{2} \))
$19$ (\( 1 - 3 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T^{2} + 361 T^{4} \))(\( 1 - 12 T^{2} + 361 T^{4} \))(\( 1 + 20 T^{2} + 361 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 - 25 T^{2} + 361 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 6 T^{2} + 361 T^{4} \))(\( 1 + 20 T^{2} + 361 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 - 25 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 40 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 64 T^{2} + 1735 T^{4} + 23104 T^{6} + 130321 T^{8} \))(\( 1 + 64 T^{2} + 1735 T^{4} + 23104 T^{6} + 130321 T^{8} \))(\( ( 1 + 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 6 T + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 - 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 + 3 T + 19 T^{2} )^{2} \))(\( ( 1 - 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 40 T^{2} + 76 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 25 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 12 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 64 T^{2} + 1735 T^{4} + 23104 T^{6} + 130321 T^{8} )^{2} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( 1 + 4 T + 26 T^{2} + 92 T^{3} + 529 T^{4} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( 1 - 4 T + 26 T^{2} - 92 T^{3} + 529 T^{4} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( ( 1 - 4 T + 6 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 4 T + 6 T^{2} + 92 T^{3} + 529 T^{4} )^{2} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 44 T^{2} + 1030 T^{4} - 23276 T^{6} + 279841 T^{8} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 1030 T^{4} - 23276 T^{6} + 279841 T^{8} \))(\( ( 1 + 4 T^{2} + 358 T^{4} + 2116 T^{6} + 279841 T^{8} )^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 + 4 T + 54 T^{2} + 116 T^{3} + 841 T^{4} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 + 4 T + 54 T^{2} + 116 T^{3} + 841 T^{4} \))(\( ( 1 - 8 T + 30 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 8 T + 30 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{4} \))(\( ( 1 + 2 T + 29 T^{2} )^{4} \))(\( ( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 8 T + 30 T^{2} + 232 T^{3} + 841 T^{4} )^{4} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( 1 - 10 T^{2} + 961 T^{4} \))(\( 1 - 10 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( 1 - 10 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 5 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 7 T + 31 T^{2} )^{2} \))(\( ( 1 - 7 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 5 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 54 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 54 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{4} \))
$37$ (\( 1 + 8 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( 1 - 4 T + 46 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( 1 - 4 T + 46 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 4 T + 34 T^{2} + 148 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 4 T + 34 T^{2} - 148 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 76 T^{2} + 3670 T^{4} - 104044 T^{6} + 1874161 T^{8} \))(\( ( 1 - 58 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 1369 T^{4} )^{2} \))(\( 1 - 76 T^{2} + 3670 T^{4} - 104044 T^{6} + 1874161 T^{8} \))(\( ( 1 - 52 T^{2} + 2710 T^{4} - 71188 T^{6} + 1874161 T^{8} )^{2} \))
$41$ (\( 1 + 11 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 80 T^{2} + 1681 T^{4} \))(\( 1 - 16 T^{2} + 1681 T^{4} \))(\( 1 + 10 T^{2} + 1681 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 75 T^{2} + 1681 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 80 T^{2} + 1681 T^{4} \))(\( 1 + 10 T^{2} + 1681 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 75 T^{2} + 1681 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 + 104 T^{2} + 5527 T^{4} + 174824 T^{6} + 2825761 T^{8} \))(\( 1 + 104 T^{2} + 5527 T^{4} + 174824 T^{6} + 2825761 T^{8} \))(\( ( 1 - 7 T + 41 T^{2} )^{2} \))(\( ( 1 + 4 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 + 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 9 T + 41 T^{2} )^{2} \))(\( ( 1 - 9 T + 41 T^{2} )^{2} \))(\( ( 1 + 7 T + 41 T^{2} )^{2} \))(\( ( 1 - 7 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 9 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 + 3 T + 41 T^{2} )^{2} \))(\( ( 1 + 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 + 11 T + 41 T^{2} )^{2} \))(\( ( 1 + 7 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 75 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 16 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 8 T + 48 T^{2} + 328 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 104 T^{2} + 5527 T^{4} + 174824 T^{6} + 2825761 T^{8} )^{2} \))
$43$ (\( 1 - 8 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( 1 - 8 T + 78 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( 1 - 12 T + 114 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( 1 + 8 T + 78 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( 1 - 12 T + 114 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( ( 1 + 42 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 42 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 61 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 37 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 37 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 61 T^{2} + 1849 T^{4} \))(\( 1 - 84 T^{2} + 4310 T^{4} - 155316 T^{6} + 3418801 T^{8} \))(\( ( 1 - 22 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 84 T^{2} + 4310 T^{4} - 155316 T^{6} + 3418801 T^{8} \))(\( ( 1 - 42 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( 1 - 2 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 66 T^{2} + 2209 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 752 T^{3} + 2209 T^{4} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( 1 - 8 T + 86 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 66 T^{2} + 2209 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 752 T^{3} + 2209 T^{4} \))(\( 1 + 140 T^{2} + 9142 T^{4} + 309260 T^{6} + 4879681 T^{8} \))(\( 1 + 140 T^{2} + 9142 T^{4} + 309260 T^{6} + 4879681 T^{8} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 13 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 13 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \))(\( ( 1 - 66 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \))(\( ( 1 - 140 T^{2} + 9142 T^{4} - 309260 T^{6} + 4879681 T^{8} )^{2} \))
$53$ (\( 1 + 4 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( 1 + 12 T + 118 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( ( 1 + 4 T + 53 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( 1 - 12 T + 118 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( ( 1 + 8 T + 53 T^{2} )^{4} \))(\( ( 1 - 8 T + 53 T^{2} )^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 25 T^{2} + 2809 T^{4} \))(\( 1 - 97 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 + 38 T^{2} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 97 T^{2} + 2809 T^{4} \))(\( 1 - 25 T^{2} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 60 T^{2} + 5366 T^{4} - 168540 T^{6} + 7890481 T^{8} \))(\( ( 1 - 14 T + 53 T^{2} )^{2}( 1 + 14 T + 53 T^{2} )^{2} \))(\( ( 1 - 102 T^{2} + 2809 T^{4} )^{2} \))(\( 1 - 60 T^{2} + 5366 T^{4} - 168540 T^{6} + 7890481 T^{8} \))(\( ( 1 - 42 T^{2} + 2809 T^{4} )^{4} \))
$59$ (\( 1 + 4 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 2 T + 59 T^{2} \))(\( 1 - 2 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))(\( 1 + 116 T^{2} + 3481 T^{4} \))(\( 1 + 100 T^{2} + 3481 T^{4} \))(\( 1 - 8 T + 128 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 90 T^{2} + 3481 T^{4} \))(\( 1 - 20 T + 216 T^{2} - 1180 T^{3} + 3481 T^{4} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))(\( 1 + 100 T^{2} + 3481 T^{4} \))(\( 1 - 8 T + 128 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 90 T^{2} + 3481 T^{4} \))(\( 1 + 20 T + 216 T^{2} + 1180 T^{3} + 3481 T^{4} \))(\( 1 + 176 T^{2} + 14002 T^{4} + 612656 T^{6} + 12117361 T^{8} \))(\( 1 + 176 T^{2} + 14002 T^{4} + 612656 T^{6} + 12117361 T^{8} \))(\( ( 1 - 10 T + 59 T^{2} )^{2} \))(\( ( 1 + 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 10 T + 59 T^{2} )^{2} \))(\( ( 1 + 20 T + 216 T^{2} + 1180 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 90 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 116 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 20 T + 216 T^{2} - 1180 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 176 T^{2} + 14002 T^{4} + 612656 T^{6} + 12117361 T^{8} )^{2} \))
$61$ (\( 1 - 2 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 9 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 9 T + 61 T^{2} \))(\( 1 + 9 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 9 T + 61 T^{2} \))(\( 1 + 72 T^{2} + 3721 T^{4} \))(\( 1 + 114 T^{2} + 3721 T^{4} \))(\( 1 + 104 T^{2} + 3721 T^{4} \))(\( 1 + 12 T + 152 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 94 T^{2} + 3721 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 72 T^{2} + 3721 T^{4} \))(\( 1 + 104 T^{2} + 3721 T^{4} \))(\( 1 + 12 T + 152 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 94 T^{2} + 3721 T^{4} \))(\( 1 - 4 T - 2 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 196 T^{2} + 16870 T^{4} + 729316 T^{6} + 13845841 T^{8} \))(\( 1 + 196 T^{2} + 16870 T^{4} + 729316 T^{6} + 13845841 T^{8} \))(\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 - 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 - 5 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 14 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2} \))(\( ( 1 + 5 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 - 4 T + 61 T^{2} )^{2} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T - 2 T^{2} + 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 94 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 + 114 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 4 T - 2 T^{2} - 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 196 T^{2} + 16870 T^{4} + 729316 T^{6} + 13845841 T^{8} )^{2} \))
$67$ (\( 1 + 9 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( ( 1 - 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 5 T + 67 T^{2} )^{2} \))(\( 1 - 8 T + 118 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 5 T + 67 T^{2} )^{2} \))(\( 1 - 8 T + 118 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( ( 1 - 10 T + 115 T^{2} - 670 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 10 T + 115 T^{2} + 670 T^{3} + 4489 T^{4} )^{2} \))(\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 109 T^{2} + 4489 T^{4} \))(\( 1 - 85 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 109 T^{2} + 4489 T^{4} \))(\( 1 + 35 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 - 172 T^{2} + 14326 T^{4} - 772108 T^{6} + 20151121 T^{8} \))(\( ( 1 - 109 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 10 T^{2} + 4489 T^{4} )^{2} \))(\( 1 - 172 T^{2} + 14326 T^{4} - 772108 T^{6} + 20151121 T^{8} \))(\( ( 1 - 130 T^{2} + 8803 T^{4} - 583570 T^{6} + 20151121 T^{8} )^{2} \))
$71$ (\( 1 + 10 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 + 12 T + 154 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 + 12 T + 154 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} \))(\( ( 1 + 2 T + 71 T^{2} )^{4} \))(\( ( 1 + 2 T + 71 T^{2} )^{4} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + T + 71 T^{2} )^{2} \))(\( ( 1 + T + 71 T^{2} )^{2} \))(\( ( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{4} \))(\( ( 1 + 12 T + 71 T^{2} )^{4} \))(\( ( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 2 T + 71 T^{2} )^{8} \))
$73$ (\( 1 + 7 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 5 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 128 T^{2} + 5329 T^{4} \))(\( 1 + 144 T^{2} + 5329 T^{4} \))(\( 1 + 74 T^{2} + 5329 T^{4} \))(\( 1 - 4 T + 126 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 139 T^{2} + 5329 T^{4} \))(\( 1 - 16 T + 208 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( 1 + 128 T^{2} + 5329 T^{4} \))(\( 1 + 74 T^{2} + 5329 T^{4} \))(\( 1 + 4 T + 126 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 139 T^{2} + 5329 T^{4} \))(\( 1 + 16 T + 208 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 + 232 T^{2} + 23575 T^{4} + 1236328 T^{6} + 28398241 T^{8} \))(\( 1 + 232 T^{2} + 23575 T^{4} + 1236328 T^{6} + 28398241 T^{8} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( ( 1 - 6 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( 1 - 121 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( ( 1 - 6 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( 1 - 25 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 97 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 160 T^{2} + 16546 T^{4} - 852640 T^{6} + 28398241 T^{8} \))(\( ( 1 - 139 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 144 T^{2} + 5329 T^{4} )^{2} \))(\( 1 - 160 T^{2} + 16546 T^{4} - 852640 T^{6} + 28398241 T^{8} \))(\( ( 1 - 232 T^{2} + 23575 T^{4} - 1236328 T^{6} + 28398241 T^{8} )^{2} \))
$79$ (\( 1 + 2 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( 1 - 4 T + 138 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( 1 - 4 T + 138 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 16 T + 178 T^{2} - 1264 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 16 T + 178 T^{2} - 1264 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 5 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 2 T + 79 T^{2} )^{2} \))(\( ( 1 + 14 T + 79 T^{2} )^{2} \))(\( ( 1 - 11 T + 79 T^{2} )^{2} \))(\( ( 1 - 11 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 2 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 5 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 2 T + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 166 T^{2} - 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{4} \))(\( ( 1 - 4 T + 79 T^{2} )^{4} \))(\( ( 1 - 8 T + 166 T^{2} - 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 16 T + 178 T^{2} + 1264 T^{3} + 6241 T^{4} )^{4} \))
$83$ (\( 1 - 11 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 122 T^{2} + 6889 T^{4} \))(\( 1 + 68 T^{2} + 6889 T^{4} \))(\( 1 - 76 T^{2} + 6889 T^{4} \))(\( 1 + 160 T^{2} + 6889 T^{4} \))(\( 1 + 159 T^{2} + 6889 T^{4} \))(\( 1 + 4 T + 152 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 122 T^{2} + 6889 T^{4} \))(\( 1 - 76 T^{2} + 6889 T^{4} \))(\( 1 + 160 T^{2} + 6889 T^{4} \))(\( 1 + 159 T^{2} + 6889 T^{4} \))(\( 1 - 4 T + 152 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 + 96 T^{2} + 13607 T^{4} + 661344 T^{6} + 47458321 T^{8} \))(\( 1 + 96 T^{2} + 13607 T^{4} + 661344 T^{6} + 47458321 T^{8} \))(\( 1 - 117 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 157 T^{2} + 6889 T^{4} \))(\( 1 - 85 T^{2} + 6889 T^{4} \))(\( 1 + 30 T^{2} + 6889 T^{4} \))(\( 1 + 30 T^{2} + 6889 T^{4} \))(\( 1 - 102 T^{2} + 6889 T^{4} \))(\( 1 - 157 T^{2} + 6889 T^{4} \))(\( 1 - 85 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 45 T^{2} + 6889 T^{4} \))(\( 1 - 117 T^{2} + 6889 T^{4} \))(\( 1 - 288 T^{2} + 34226 T^{4} - 1984032 T^{6} + 47458321 T^{8} \))(\( ( 1 - 159 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 68 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 288 T^{2} + 34226 T^{4} - 1984032 T^{6} + 47458321 T^{8} \))(\( ( 1 - 96 T^{2} + 13607 T^{4} - 661344 T^{6} + 47458321 T^{8} )^{2} \))
$89$ (\( 1 - 11 T + 89 T^{2} \))(\( 1 - T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 11 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 160 T^{2} + 7921 T^{4} \))(\( 1 + 128 T^{2} + 7921 T^{4} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 + 3 T^{2} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 + 160 T^{2} + 7921 T^{4} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 + 3 T^{2} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 + 248 T^{2} + 30327 T^{4} + 1964408 T^{6} + 62742241 T^{8} \))(\( 1 + 248 T^{2} + 30327 T^{4} + 1964408 T^{6} + 62742241 T^{8} \))(\( ( 1 - T + 89 T^{2} )^{2} \))(\( ( 1 - 8 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 3 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 7 T + 89 T^{2} )^{2} \))(\( ( 1 - 7 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 15 T + 89 T^{2} )^{2} \))(\( ( 1 - 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 8 T + 89 T^{2} )^{2} \))(\( ( 1 + 3 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 11 T + 89 T^{2} )^{2} \))(\( ( 1 + T + 89 T^{2} )^{2} \))(\( ( 1 + 16 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 3 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 128 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 16 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 248 T^{2} + 30327 T^{4} + 1964408 T^{6} + 62742241 T^{8} )^{2} \))
$97$ (\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 176 T^{2} + 9409 T^{4} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 12 T + 134 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( 1 + 176 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 - 12 T + 134 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} \))(\( ( 1 + 176 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 + 176 T^{2} + 9409 T^{4} )^{2} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( ( 1 - 97 T^{2} )^{2} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 145 T^{2} + 9409 T^{4} \))(\( 1 - 145 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( ( 1 - 97 T^{2} )^{2} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 64 T^{2} + 9474 T^{4} - 602176 T^{6} + 88529281 T^{8} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 96 T^{2} + 9409 T^{4} )^{2} \))(\( 1 - 64 T^{2} + 9474 T^{4} - 602176 T^{6} + 88529281 T^{8} \))(\( ( 1 - 176 T^{2} + 9409 T^{4} )^{4} \))
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