Properties

Label 387.2
Level 387
Weight 2
Dimension 4200
Nonzero newspaces 20
Newform subspaces 48
Sturm bound 22176
Trace bound 5

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Defining parameters

Level: \( N \) = \( 387\( 387 = 3^{2} \cdot 43 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 48 \)
Sturm bound: \(22176\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(387))\).

Total New Old
Modular forms 5880 4568 1312
Cusp forms 5209 4200 1009
Eisenstein series 671 368 303

Trace form

\( 4200q - 63q^{2} - 84q^{3} - 63q^{4} - 63q^{5} - 84q^{6} - 63q^{7} - 63q^{8} - 84q^{9} + O(q^{10}) \) \( 4200q - 63q^{2} - 84q^{3} - 63q^{4} - 63q^{5} - 84q^{6} - 63q^{7} - 63q^{8} - 84q^{9} - 189q^{10} - 63q^{11} - 84q^{12} - 63q^{13} - 63q^{14} - 84q^{15} - 63q^{16} - 63q^{17} - 84q^{18} - 189q^{19} - 63q^{20} - 84q^{21} - 63q^{22} - 63q^{23} - 84q^{24} - 63q^{25} - 63q^{26} - 84q^{27} - 189q^{28} - 63q^{29} - 84q^{30} - 70q^{31} - 105q^{32} - 84q^{33} - 126q^{34} - 105q^{35} - 84q^{36} - 231q^{37} - 147q^{38} - 84q^{39} - 231q^{40} - 84q^{41} - 84q^{42} - 168q^{43} - 210q^{44} - 84q^{45} - 273q^{46} - 84q^{47} - 84q^{48} - 112q^{49} - 147q^{50} - 84q^{51} - 175q^{52} - 105q^{53} - 84q^{54} - 231q^{55} - 105q^{56} - 84q^{57} - 63q^{58} - 63q^{59} - 84q^{60} - 63q^{61} - 63q^{62} - 84q^{63} - 189q^{64} - 63q^{65} - 84q^{66} - 63q^{67} - 63q^{68} - 84q^{69} - 147q^{70} - 105q^{71} - 84q^{72} - 231q^{73} - 210q^{74} - 84q^{75} - 210q^{76} - 189q^{77} - 84q^{78} - 147q^{79} - 231q^{80} - 84q^{81} - 399q^{82} - 147q^{83} - 168q^{85} - 231q^{86} - 168q^{87} - 273q^{88} - 147q^{89} - 84q^{90} - 273q^{91} - 273q^{92} - 84q^{93} - 231q^{94} - 147q^{95} - 84q^{96} - 189q^{97} - 210q^{98} - 84q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)

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
387.2.a \(\chi_{387}(1, \cdot)\) 387.2.a.a 1 1
387.2.a.b 1
387.2.a.c 1
387.2.a.d 1
387.2.a.e 1
387.2.a.f 2
387.2.a.g 2
387.2.a.h 2
387.2.a.i 3
387.2.a.j 4
387.2.d \(\chi_{387}(386, \cdot)\) 387.2.d.a 4 1
387.2.d.b 12
387.2.e \(\chi_{387}(49, \cdot)\) 387.2.e.a 84 2
387.2.f \(\chi_{387}(130, \cdot)\) 387.2.f.a 2 2
387.2.f.b 4
387.2.f.c 38
387.2.f.d 40
387.2.g \(\chi_{387}(178, \cdot)\) 387.2.g.a 84 2
387.2.h \(\chi_{387}(208, \cdot)\) 387.2.h.a 2 2
387.2.h.b 2
387.2.h.c 2
387.2.h.d 4
387.2.h.e 6
387.2.h.f 6
387.2.h.g 12
387.2.k \(\chi_{387}(308, \cdot)\) 387.2.k.a 84 2
387.2.l \(\chi_{387}(128, \cdot)\) 387.2.l.a 84 2
387.2.m \(\chi_{387}(50, \cdot)\) 387.2.m.a 84 2
387.2.t \(\chi_{387}(80, \cdot)\) 387.2.t.a 28 2
387.2.u \(\chi_{387}(64, \cdot)\) 387.2.u.a 6 6
387.2.u.b 6
387.2.u.c 6
387.2.u.d 12
387.2.u.e 30
387.2.u.f 48
387.2.v \(\chi_{387}(8, \cdot)\) 387.2.v.a 96 6
387.2.y \(\chi_{387}(10, \cdot)\) 387.2.y.a 12 12
387.2.y.b 36
387.2.y.c 36
387.2.y.d 48
387.2.y.e 72
387.2.z \(\chi_{387}(13, \cdot)\) 387.2.z.a 504 12
387.2.ba \(\chi_{387}(4, \cdot)\) 387.2.ba.a 504 12
387.2.bb \(\chi_{387}(25, \cdot)\) 387.2.bb.a 504 12
387.2.bc \(\chi_{387}(26, \cdot)\) 387.2.bc.a 168 12
387.2.bj \(\chi_{387}(20, \cdot)\) 387.2.bj.a 504 12
387.2.bk \(\chi_{387}(2, \cdot)\) 387.2.bk.a 504 12
387.2.bl \(\chi_{387}(5, \cdot)\) 387.2.bl.a 504 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(387)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T + T^{2} + 2 T^{4} - 8 T^{5} + 8 T^{6} \))(\( ( 1 - T^{2} + 4 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} )^{4} \))(\( ( 1 - T^{2} + 5 T^{4} - 9 T^{6} + 20 T^{8} - 16 T^{10} + 64 T^{12} )^{2} \))(\( 1 + T - T^{2} + 2 T^{3} + 4 T^{4} \))(\( 1 + T - 2 T^{2} - T^{3} + 3 T^{4} - 2 T^{5} - 8 T^{6} + 8 T^{7} + 16 T^{8} \))(\( ( 1 + T + 2 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( ( 1 - 2 T + 2 T^{2} )^{2} \))(\( ( 1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4} )^{2} \))(\( ( 1 + T + 4 T^{2} + 3 T^{3} + 8 T^{4} + 4 T^{5} + 8 T^{6} )^{2} \))(\( ( 1 - T + 2 T^{2} - T^{3} + 4 T^{4} - 4 T^{5} + 8 T^{6} )^{2} \))(\( ( 1 + T^{2} + 4 T^{4} + 5 T^{6} + 16 T^{8} + 16 T^{10} + 64 T^{12} )^{2} \))(\( 1 + 3 T + 7 T^{2} + 15 T^{3} + 31 T^{4} + 49 T^{5} + 71 T^{6} + 98 T^{7} + 124 T^{8} + 120 T^{9} + 112 T^{10} + 96 T^{11} + 64 T^{12} \))(\( 1 - 5 T + 9 T^{2} - 7 T^{3} + 3 T^{4} - T^{5} - T^{6} - 2 T^{7} + 12 T^{8} - 56 T^{9} + 144 T^{10} - 160 T^{11} + 64 T^{12} \))(\( 1 - 5 T + 9 T^{2} - 7 T^{3} + 3 T^{4} - T^{5} - T^{6} - 2 T^{7} + 12 T^{8} - 56 T^{9} + 144 T^{10} - 160 T^{11} + 64 T^{12} \))(\( 1 + 3 T + 5 T^{2} + 9 T^{3} + 14 T^{4} + 24 T^{5} + 43 T^{6} + 78 T^{7} + 150 T^{8} + 223 T^{9} + 309 T^{10} + 427 T^{11} + 559 T^{12} + 854 T^{13} + 1236 T^{14} + 1784 T^{15} + 2400 T^{16} + 2496 T^{17} + 2752 T^{18} + 3072 T^{19} + 3584 T^{20} + 4608 T^{21} + 5120 T^{22} + 6144 T^{23} + 4096 T^{24} \))(\( ( 1 - 2 T^{2} + 4 T^{4} - 8 T^{6} + 16 T^{8} - 32 T^{10} + 64 T^{12} )^{2} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( ( 1 - 3 T + 3 T^{2} )^{2} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 9 T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( 1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4} \))(\( 1 - 4 T + 14 T^{2} - 38 T^{3} + 70 T^{4} - 100 T^{5} + 125 T^{6} \))(\( 1 + 11 T^{2} + 64 T^{4} + 275 T^{6} + 625 T^{8} \))(\( ( 1 + 5 T^{2} )^{4} \))(\( ( 1 + 6 T^{2} + 44 T^{4} + 178 T^{6} + 1100 T^{8} + 3750 T^{10} + 15625 T^{12} )^{2} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 4 T + 7 T^{2} - 4 T^{3} - 24 T^{4} - 20 T^{5} + 175 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - 2 T^{2} - 8 T^{3} - 9 T^{4} - 40 T^{5} - 50 T^{6} + 250 T^{7} + 625 T^{8} \))(\( 1 + T + 2 T^{2} + 37 T^{3} + 25 T^{4} + 54 T^{5} + 581 T^{6} + 270 T^{7} + 625 T^{8} + 4625 T^{9} + 1250 T^{10} + 3125 T^{11} + 15625 T^{12} \))(\( 1 - 3 T - 4 T^{2} + 7 T^{3} + 35 T^{4} + 16 T^{5} - 291 T^{6} + 80 T^{7} + 875 T^{8} + 875 T^{9} - 2500 T^{10} - 9375 T^{11} + 15625 T^{12} \))(\( 1 - 17 T^{2} + 140 T^{4} - 791 T^{6} + 3669 T^{8} - 13754 T^{10} + 54241 T^{12} - 343850 T^{14} + 2293125 T^{16} - 12359375 T^{18} + 54687500 T^{20} - 166015625 T^{22} + 244140625 T^{24} \))(\( 1 + 2 T - T^{2} - 12 T^{3} - 19 T^{4} + 22 T^{5} + 139 T^{6} + 110 T^{7} - 475 T^{8} - 1500 T^{9} - 625 T^{10} + 6250 T^{11} + 15625 T^{12} \))(\( 1 + 10 T + 60 T^{2} + 263 T^{3} + 923 T^{4} + 2665 T^{5} + 6481 T^{6} + 13325 T^{7} + 23075 T^{8} + 32875 T^{9} + 37500 T^{10} + 31250 T^{11} + 15625 T^{12} \))(\( 1 - 3 T + 4 T^{2} - 18 T^{3} + 76 T^{4} - 145 T^{5} + 251 T^{6} - 725 T^{7} + 1900 T^{8} - 2250 T^{9} + 2500 T^{10} - 9375 T^{11} + 15625 T^{12} \))(\( ( 1 - 5 T + 6 T^{2} + 2 T^{3} + 9 T^{4} - 13 T^{5} - 64 T^{6} - 65 T^{7} + 225 T^{8} + 250 T^{9} + 3750 T^{10} - 15625 T^{11} + 15625 T^{12} )^{2} \))(\( 1 + 5 T^{2} - 125 T^{6} - 625 T^{8} + 15625 T^{12} - 390625 T^{16} - 1953125 T^{18} + 48828125 T^{22} + 244140625 T^{24} \))
$7$ (\( 1 + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} - 14 T^{3} + 49 T^{4} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( 1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 46 T^{3} + 126 T^{4} - 196 T^{5} + 343 T^{6} \))(\( ( 1 + T - 2 T^{2} + 7 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 7 T^{2} )^{4} \))(\( ( 1 - 12 T^{2} + 132 T^{4} - 934 T^{6} + 6468 T^{8} - 28812 T^{10} + 117649 T^{12} )^{2} \))(\( 1 - 3 T + 2 T^{2} - 21 T^{3} + 49 T^{4} \))(\( 1 - 7 T + 24 T^{2} - 77 T^{3} + 233 T^{4} - 539 T^{5} + 1176 T^{6} - 2401 T^{7} + 2401 T^{8} \))(\( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} \))(\( 1 - 4 T + 3 T^{2} + 4 T^{3} + 8 T^{4} + 28 T^{5} + 147 T^{6} - 1372 T^{7} + 2401 T^{8} \))(\( 1 - 5 T - 2 T^{2} + 7 T^{3} + 185 T^{4} - 272 T^{5} - 601 T^{6} - 1904 T^{7} + 9065 T^{8} + 2401 T^{9} - 4802 T^{10} - 84035 T^{11} + 117649 T^{12} \))(\( 1 + 3 T - 10 T^{2} - 25 T^{3} + 105 T^{4} + 128 T^{5} - 601 T^{6} + 896 T^{7} + 5145 T^{8} - 8575 T^{9} - 24010 T^{10} + 50421 T^{11} + 117649 T^{12} \))(\( ( 1 - T - 10 T^{2} + 35 T^{3} + 21 T^{4} - 148 T^{5} + 319 T^{6} - 1036 T^{7} + 1029 T^{8} + 12005 T^{9} - 24010 T^{10} - 16807 T^{11} + 117649 T^{12} )^{2} \))(\( ( 1 + 8 T + 40 T^{2} + 125 T^{3} + 280 T^{4} + 392 T^{5} + 343 T^{6} )^{2} \))(\( ( 1 + 14 T^{2} + 7 T^{3} + 98 T^{4} + 343 T^{6} )^{2} \))(\( ( 1 + 14 T^{2} + 7 T^{3} + 98 T^{4} + 343 T^{6} )^{2} \))(\( ( 1 - 7 T + 44 T^{2} - 168 T^{3} + 601 T^{4} - 1652 T^{5} + 4745 T^{6} - 11564 T^{7} + 29449 T^{8} - 57624 T^{9} + 105644 T^{10} - 117649 T^{11} + 117649 T^{12} )^{2} \))(\( ( 1 - 4 T + 9 T^{2} - 8 T^{3} - 31 T^{4} + 180 T^{5} - 503 T^{6} + 1260 T^{7} - 1519 T^{8} - 2744 T^{9} + 21609 T^{10} - 67228 T^{11} + 117649 T^{12} )( 1 + 5 T + 18 T^{2} + 55 T^{3} + 149 T^{4} + 360 T^{5} + 757 T^{6} + 2520 T^{7} + 7301 T^{8} + 18865 T^{9} + 43218 T^{10} + 84035 T^{11} + 117649 T^{12} ) \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 6 T + 29 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 5 T^{2} + 121 T^{4} \))(\( 1 - 2 T + 15 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 + T + 14 T^{2} + 47 T^{3} + 154 T^{4} + 121 T^{5} + 1331 T^{6} \))(\( 1 + 35 T^{2} + 532 T^{4} + 4235 T^{6} + 14641 T^{8} \))(\( 1 + 199 T^{4} + 14641 T^{8} \))(\( ( 1 - 40 T^{2} + 856 T^{4} - 11572 T^{6} + 103576 T^{8} - 585640 T^{10} + 1771561 T^{12} )^{2} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 14 T^{2} + 3 T^{3} + 309 T^{4} + 33 T^{5} - 1694 T^{6} + 3993 T^{7} + 14641 T^{8} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 5 T + 27 T^{2} - 55 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 10 T + 50 T^{2} + 179 T^{3} + 550 T^{4} + 1210 T^{5} + 1331 T^{6} )^{2} \))(\( ( 1 + 4 T + 34 T^{2} + 83 T^{3} + 374 T^{4} + 484 T^{5} + 1331 T^{6} )^{2} \))(\( ( 1 + 24 T^{2} + 406 T^{4} + 5615 T^{6} + 49126 T^{8} + 351384 T^{10} + 1771561 T^{12} )^{2} \))(\( 1 + 14 T + 80 T^{2} + 231 T^{3} + 149 T^{4} - 2135 T^{5} - 11369 T^{6} - 23485 T^{7} + 18029 T^{8} + 307461 T^{9} + 1171280 T^{10} + 2254714 T^{11} + 1771561 T^{12} \))(\( 1 + T + 18 T^{2} + 14 T^{3} + 306 T^{4} + 257 T^{5} + 4115 T^{6} + 2827 T^{7} + 37026 T^{8} + 18634 T^{9} + 263538 T^{10} + 161051 T^{11} + 1771561 T^{12} \))(\( 1 - 10 T + 26 T^{2} + 81 T^{3} - 529 T^{4} + 199 T^{5} + 3535 T^{6} + 2189 T^{7} - 64009 T^{8} + 107811 T^{9} + 380666 T^{10} - 1610510 T^{11} + 1771561 T^{12} \))(\( 1 - 9 T + 31 T^{2} - 40 T^{3} - 56 T^{4} + 811 T^{5} - 4927 T^{6} + 15544 T^{7} - 25460 T^{8} + 21398 T^{9} + 173681 T^{10} - 1932224 T^{11} + 8912161 T^{12} - 21254464 T^{13} + 21015401 T^{14} + 28480738 T^{15} - 372759860 T^{16} + 2503376744 T^{17} - 8728481047 T^{18} + 15804095681 T^{19} - 12004097336 T^{20} - 94317907640 T^{21} + 804060162631 T^{22} - 2567805035499 T^{23} + 3138428376721 T^{24} \))(\( ( 1 - 11 T^{2} + 121 T^{4} - 1331 T^{6} + 14641 T^{8} - 161051 T^{10} + 1771561 T^{12} )^{2} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( ( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2} \))(\( 1 - 2 T + 19 T^{2} - 26 T^{3} + 169 T^{4} \))(\( ( 1 - 3 T + 13 T^{2} )^{3} \))(\( ( 1 - 5 T + 16 T^{2} - 65 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 - 17 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 6 T + 44 T^{2} + 152 T^{3} + 572 T^{4} + 1014 T^{5} + 2197 T^{6} )^{4} \))(\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + 5 T + 4 T^{2} - 25 T^{3} - 53 T^{4} - 325 T^{5} + 676 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} ) \))(\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 25 T^{3} + 467 T^{4} + 325 T^{5} - 1014 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( 1 + 3 T - 12 T^{2} - 39 T^{3} + 15 T^{4} - 60 T^{5} - 259 T^{6} - 780 T^{7} + 2535 T^{8} - 85683 T^{9} - 342732 T^{10} + 1113879 T^{11} + 4826809 T^{12} \))(\( 1 - T - 12 T^{2} + 69 T^{3} - 41 T^{4} - 364 T^{5} + 3709 T^{6} - 4732 T^{7} - 6929 T^{8} + 151593 T^{9} - 342732 T^{10} - 371293 T^{11} + 4826809 T^{12} \))(\( ( 1 + 3 T - 28 T^{2} - 43 T^{3} + 657 T^{4} + 470 T^{5} - 8995 T^{6} + 6110 T^{7} + 111033 T^{8} - 94471 T^{9} - 799708 T^{10} + 1113879 T^{11} + 4826809 T^{12} )^{2} \))(\( 1 + 9 T + 12 T^{2} - 142 T^{3} - 524 T^{4} + 1141 T^{5} + 11103 T^{6} + 14833 T^{7} - 88556 T^{8} - 311974 T^{9} + 342732 T^{10} + 3341637 T^{11} + 4826809 T^{12} \))(\( 1 - 5 T - 16 T^{2} + 208 T^{3} - 538 T^{4} - 1841 T^{5} + 15135 T^{6} - 23933 T^{7} - 90922 T^{8} + 456976 T^{9} - 456976 T^{10} - 1856465 T^{11} + 4826809 T^{12} \))(\( 1 - 5 T + 40 T^{2} - 212 T^{3} + 953 T^{4} - 4319 T^{5} + 14876 T^{6} - 56147 T^{7} + 161057 T^{8} - 465764 T^{9} + 1142440 T^{10} - 1856465 T^{11} + 4826809 T^{12} \))(\( 1 - 9 T + 14 T^{2} - 11 T^{3} + 654 T^{4} - 2081 T^{5} + 1027 T^{6} - 25505 T^{7} + 49163 T^{8} + 144826 T^{9} + 1407638 T^{10} - 2489080 T^{11} - 20298693 T^{12} - 32358040 T^{13} + 237890822 T^{14} + 318182722 T^{15} + 1404144443 T^{16} - 9469827965 T^{17} + 4957132843 T^{18} - 130579663877 T^{19} + 533487891534 T^{20} - 116649493103 T^{21} + 1930018885886 T^{22} - 16129443546333 T^{23} + 23298085122481 T^{24} \))(\( ( 1 + 2 T - 9 T^{2} - 44 T^{3} + 29 T^{4} + 630 T^{5} + 883 T^{6} + 8190 T^{7} + 4901 T^{8} - 96668 T^{9} - 257049 T^{10} + 742586 T^{11} + 4826809 T^{12} )( 1 + 5 T + 12 T^{2} - 5 T^{3} - 181 T^{4} - 840 T^{5} - 1847 T^{6} - 10920 T^{7} - 30589 T^{8} - 10985 T^{9} + 342732 T^{10} + 1856465 T^{11} + 4826809 T^{12} ) \))
$17$ (\( 1 - 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 4 T + 30 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 31 T^{2} + 289 T^{4} \))(\( 1 + 10 T + 51 T^{2} + 170 T^{3} + 289 T^{4} \))(\( 1 + T + 43 T^{2} + 30 T^{3} + 731 T^{4} + 289 T^{5} + 4913 T^{6} \))(\( 1 + 32 T^{2} + 574 T^{4} + 9248 T^{6} + 83521 T^{8} \))(\( 1 - 497 T^{4} + 83521 T^{8} \))(\( ( 1 - 36 T^{2} + 743 T^{4} - 12232 T^{6} + 214727 T^{8} - 3006756 T^{10} + 24137569 T^{12} )^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 18 T^{2} - 68 T^{3} + 289 T^{4} )^{2} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - T - 2 T^{2} + 31 T^{3} - 297 T^{4} + 527 T^{5} - 578 T^{6} - 4913 T^{7} + 83521 T^{8} \))(\( 1 - 4 T - 24 T^{2} + 110 T^{3} + 380 T^{4} - 1116 T^{5} - 3773 T^{6} - 18972 T^{7} + 109820 T^{8} + 540430 T^{9} - 2004504 T^{10} - 5679428 T^{11} + 24137569 T^{12} \))(\( 1 + 10 T + 20 T^{2} + 78 T^{3} + 1430 T^{4} + 4570 T^{5} + 2447 T^{6} + 77690 T^{7} + 413270 T^{8} + 383214 T^{9} + 1670420 T^{10} + 14198570 T^{11} + 24137569 T^{12} \))(\( 1 - 60 T^{2} + 1682 T^{4} - 34706 T^{6} + 713202 T^{8} - 15573686 T^{10} + 299443271 T^{12} - 4500795254 T^{14} + 59567344242 T^{16} - 837718469714 T^{18} + 11733224015762 T^{20} - 120959634026940 T^{22} + 582622237229761 T^{24} \))(\( 1 + 8 T + 19 T^{2} + 30 T^{3} - 55 T^{4} - 2588 T^{5} - 16885 T^{6} - 43996 T^{7} - 15895 T^{8} + 147390 T^{9} + 1586899 T^{10} + 11358856 T^{11} + 24137569 T^{12} \))(\( 1 - 4 T - T^{2} + 72 T^{3} + 93 T^{4} + 42 T^{5} - 293 T^{6} + 714 T^{7} + 26877 T^{8} + 353736 T^{9} - 83521 T^{10} - 5679428 T^{11} + 24137569 T^{12} \))(\( 1 - 4 T - T^{2} + 72 T^{3} + 93 T^{4} + 42 T^{5} - 293 T^{6} + 714 T^{7} + 26877 T^{8} + 353736 T^{9} - 83521 T^{10} - 5679428 T^{11} + 24137569 T^{12} \))(\( 1 + 4 T + 67 T^{3} + 391 T^{4} + 1541 T^{5} + 7131 T^{6} - 21699 T^{7} - 118425 T^{8} + 181255 T^{9} - 1038014 T^{10} - 14680516 T^{11} - 62265527 T^{12} - 249568772 T^{13} - 299986046 T^{14} + 890505815 T^{15} - 9890974425 T^{16} - 30809477043 T^{17} + 172125004539 T^{18} + 632331895093 T^{19} + 2727521159431 T^{20} + 7945387725299 T^{21} + 137087585230532 T^{23} + 582622237229761 T^{24} \))(\( 1 + 17 T^{2} - 4913 T^{6} - 83521 T^{8} + 24137569 T^{12} - 6975757441 T^{16} - 118587876497 T^{18} + 34271896307633 T^{22} + 582622237229761 T^{24} \))
$19$ (\( 1 - 4 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 7 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( 1 + 4 T + 34 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 150 T^{3} + 722 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( ( 1 + T + 22 T^{2} + 19 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 40 T^{2} + 1324 T^{4} - 28366 T^{6} + 477964 T^{8} - 5212840 T^{10} + 47045881 T^{12} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} - 76 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( ( 1 + T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 2 T - 30 T^{2} - 8 T^{3} + 719 T^{4} - 152 T^{5} - 10830 T^{6} + 13718 T^{7} + 130321 T^{8} \))(\( 1 + 5 T - 10 T^{2} - 11 T^{3} + 95 T^{4} - 1590 T^{5} - 9933 T^{6} - 30210 T^{7} + 34295 T^{8} - 75449 T^{9} - 1303210 T^{10} + 12380495 T^{11} + 47045881 T^{12} \))(\( 1 - 3 T - 46 T^{2} + 49 T^{3} + 1659 T^{4} - 698 T^{5} - 35557 T^{6} - 13262 T^{7} + 598899 T^{8} + 336091 T^{9} - 5994766 T^{10} - 7428297 T^{11} + 47045881 T^{12} \))(\( ( 1 - 9 T + 38 T^{2} - 97 T^{3} - 273 T^{4} + 5222 T^{5} - 29629 T^{6} + 99218 T^{7} - 98553 T^{8} - 665323 T^{9} + 4952198 T^{10} - 22284891 T^{11} + 47045881 T^{12} )^{2} \))(\( 1 + 4 T - 24 T^{2} - 207 T^{3} - 659 T^{4} + 2459 T^{5} + 28923 T^{6} + 46721 T^{7} - 237899 T^{8} - 1419813 T^{9} - 3127704 T^{10} + 9904396 T^{11} + 47045881 T^{12} \))(\( 1 + T + 10 T^{2} + 26 T^{3} + 11 T^{4} - 931 T^{5} + 6084 T^{6} - 17689 T^{7} + 3971 T^{8} + 178334 T^{9} + 1303210 T^{10} + 2476099 T^{11} + 47045881 T^{12} \))(\( 1 - 2 T + 13 T^{2} + 40 T^{3} + 23 T^{4} + 1756 T^{5} - 1723 T^{6} + 33364 T^{7} + 8303 T^{8} + 274360 T^{9} + 1694173 T^{10} - 4952198 T^{11} + 47045881 T^{12} \))(\( 1 - T + 4 T^{2} - 47 T^{3} - 332 T^{4} + 525 T^{5} - 5061 T^{6} - 4969 T^{7} + 39183 T^{8} - 26048 T^{9} + 2190826 T^{10} - 1117158 T^{11} + 6498785 T^{12} - 21226002 T^{13} + 790888186 T^{14} - 178663232 T^{15} + 5106367743 T^{16} - 12303735931 T^{17} - 238099203741 T^{18} + 469282662975 T^{19} - 5638542929612 T^{20} - 15166321795613 T^{21} + 24524265031204 T^{22} - 116490258898219 T^{23} + 2213314919066161 T^{24} \))(\( ( 1 - 7 T + 30 T^{2} - 77 T^{3} - 31 T^{4} + 1680 T^{5} - 11171 T^{6} + 31920 T^{7} - 11191 T^{8} - 528143 T^{9} + 3909630 T^{10} - 17332693 T^{11} + 47045881 T^{12} )( 1 - T - 18 T^{2} + 37 T^{3} + 305 T^{4} - 1008 T^{5} - 4787 T^{6} - 19152 T^{7} + 110105 T^{8} + 253783 T^{9} - 2345778 T^{10} - 2476099 T^{11} + 47045881 T^{12} ) \))
$23$ (\( 1 - 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( 1 + 43 T^{2} + 529 T^{4} \))(\( 1 + 2 T + 15 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 + 11 T + 37 T^{2} + 54 T^{3} + 851 T^{4} + 5819 T^{5} + 12167 T^{6} \))(\( 1 + 56 T^{2} + 1582 T^{4} + 29624 T^{6} + 279841 T^{8} \))(\( 1 - 1049 T^{4} + 279841 T^{8} \))(\( ( 1 - 92 T^{2} + 4147 T^{4} - 116792 T^{6} + 2193763 T^{8} - 25745372 T^{10} + 148035889 T^{12} )^{2} \))(\( 1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 3 T - 28 T^{2} + 27 T^{3} + 633 T^{4} + 621 T^{5} - 14812 T^{6} - 36501 T^{7} + 279841 T^{8} \))(\( 1 + 7 T + 26 T^{2} + 161 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 11 T + 46 T^{2} - 319 T^{3} + 2313 T^{4} - 7337 T^{5} + 24334 T^{6} - 133837 T^{7} + 279841 T^{8} \))(\( 1 - 2 T - 36 T^{2} - 38 T^{3} + 638 T^{4} + 1782 T^{5} - 14141 T^{6} + 40986 T^{7} + 337502 T^{8} - 462346 T^{9} - 10074276 T^{10} - 12872686 T^{11} + 148035889 T^{12} \))(\( 1 + 4 T - 50 T^{2} - 86 T^{3} + 2138 T^{4} + 1522 T^{5} - 53693 T^{6} + 35006 T^{7} + 1131002 T^{8} - 1046362 T^{9} - 13992050 T^{10} + 25745372 T^{11} + 148035889 T^{12} \))(\( 1 - 110 T^{2} + 6548 T^{4} - 284066 T^{6} + 9921726 T^{8} - 291432254 T^{10} + 7279436191 T^{12} - 154167662366 T^{14} + 2776505725566 T^{16} - 42051962844674 T^{18} + 512780331619988 T^{20} - 4556916233501390 T^{22} + 21914624432020321 T^{24} \))(\( 1 + T - 8 T^{2} + 60 T^{3} - 169 T^{4} - 1465 T^{5} - 1792 T^{6} - 33695 T^{7} - 89401 T^{8} + 730020 T^{9} - 2238728 T^{10} + 6436343 T^{11} + 148035889 T^{12} \))(\( 1 - 6 T + 41 T^{2} - 150 T^{3} + 1105 T^{4} - 5854 T^{5} + 42735 T^{6} - 134642 T^{7} + 584545 T^{8} - 1825050 T^{9} + 11473481 T^{10} - 38618058 T^{11} + 148035889 T^{12} \))(\( 1 + T - 8 T^{2} - 255 T^{3} - 57 T^{4} + 1090 T^{5} + 35133 T^{6} + 25070 T^{7} - 30153 T^{8} - 3102585 T^{9} - 2238728 T^{10} + 6436343 T^{11} + 148035889 T^{12} \))(\( 1 + 2 T - 36 T^{2} - 57 T^{3} + 644 T^{4} + 3353 T^{5} + 4228 T^{6} - 178904 T^{7} - 647167 T^{8} + 4759053 T^{9} + 17963391 T^{10} - 50202467 T^{11} - 381286661 T^{12} - 1154656741 T^{13} + 9502633839 T^{14} + 57903397851 T^{15} - 181103860447 T^{16} - 1151487508072 T^{17} + 625895738692 T^{18} + 11416379723791 T^{19} + 50432274520964 T^{20} - 102665701703391 T^{21} - 1491354403691364 T^{22} + 1905619515827854 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 23 T^{2} - 12167 T^{6} - 279841 T^{8} + 148035889 T^{12} - 78310985281 T^{16} - 1801152661463 T^{18} + 952809757913927 T^{22} + 21914624432020321 T^{24} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 49 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 + 10 T^{2} + 841 T^{4} \))(\( 1 + 40 T^{2} + 841 T^{4} \))(\( 1 + 2 T + 82 T^{2} + 108 T^{3} + 2378 T^{4} + 1682 T^{5} + 24389 T^{6} \))(\( 1 + 35 T^{2} + 672 T^{4} + 29435 T^{6} + 707281 T^{8} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 + 86 T^{2} + 3844 T^{4} + 126866 T^{6} + 3232804 T^{8} + 60826166 T^{10} + 594823321 T^{12} )^{2} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 - 3 T - 40 T^{2} + 27 T^{3} + 1299 T^{4} + 783 T^{5} - 33640 T^{6} - 73167 T^{7} + 707281 T^{8} \))(\( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( ( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} )^{2} \))(\( 1 + 4 T - 60 T^{2} - 158 T^{3} + 2648 T^{4} + 3288 T^{5} - 78821 T^{6} + 95352 T^{7} + 2226968 T^{8} - 3853462 T^{9} - 42436860 T^{10} + 82044596 T^{11} + 594823321 T^{12} \))(\( 1 + 6 T + 30 T^{2} + 366 T^{3} + 852 T^{4} + 1968 T^{5} + 44683 T^{6} + 57072 T^{7} + 716532 T^{8} + 8926374 T^{9} + 21218430 T^{10} + 123066894 T^{11} + 594823321 T^{12} \))(\( 1 + 6 T^{2} - 528 T^{4} - 62770 T^{6} - 354690 T^{8} + 17207226 T^{10} + 1990753719 T^{12} + 14471277066 T^{14} - 250865497890 T^{16} - 37337059859170 T^{18} - 264130106043408 T^{20} + 2524243399801206 T^{22} + 353814783205469041 T^{24} \))(\( 1 + 9 T + 24 T^{2} + 242 T^{3} + 1881 T^{4} + 5333 T^{5} + 16380 T^{6} + 154657 T^{7} + 1581921 T^{8} + 5902138 T^{9} + 16974744 T^{10} + 184600341 T^{11} + 594823321 T^{12} \))(\( 1 - 8 T + 35 T^{2} + 36 T^{3} - 589 T^{4} - 3346 T^{5} + 28603 T^{6} - 97034 T^{7} - 495349 T^{8} + 878004 T^{9} + 24754835 T^{10} - 164089192 T^{11} + 594823321 T^{12} \))(\( 1 + 6 T + 7 T^{2} - 132 T^{3} - 995 T^{4} - 2142 T^{5} + 16003 T^{6} - 62118 T^{7} - 836795 T^{8} - 3219348 T^{9} + 4950967 T^{10} + 123066894 T^{11} + 594823321 T^{12} \))(\( 1 - 12 T + 23 T^{2} + 93 T^{3} + 955 T^{4} - 11707 T^{5} + 42165 T^{6} - 173101 T^{7} + 2220044 T^{8} - 15924018 T^{9} + 62926845 T^{10} - 210804153 T^{11} + 905123491 T^{12} - 6113320437 T^{13} + 52921476645 T^{14} - 388370875002 T^{15} + 1570194940364 T^{16} - 3550500403049 T^{17} + 25080725329965 T^{18} - 201944301949463 T^{19} + 477735324377755 T^{20} + 1349164575755817 T^{21} + 9676266365904623 T^{22} - 146406117188469948 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 29 T^{2} - 24389 T^{6} - 707281 T^{8} + 594823321 T^{12} - 500246412961 T^{16} - 14507145975869 T^{18} + 12200509765705829 T^{22} + 353814783205469041 T^{24} \))
$31$ (\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 5 T + 31 T^{2} )^{2} \))(\( ( 1 + 3 T + 31 T^{2} )^{2} \))(\( 1 + 5 T + 77 T^{2} + 246 T^{3} + 2387 T^{4} + 4805 T^{5} + 29791 T^{6} \))(\( ( 1 + 31 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 2 T + 77 T^{2} + 108 T^{3} + 2387 T^{4} + 1922 T^{5} + 29791 T^{6} )^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( ( 1 - 4 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( ( 1 - 31 T^{2} + 961 T^{4} )^{2} \))(\( 1 + T - 76 T^{2} + 11 T^{3} + 3509 T^{4} - 1272 T^{5} - 124089 T^{6} - 39432 T^{7} + 3372149 T^{8} + 327701 T^{9} - 70187596 T^{10} + 28629151 T^{11} + 887503681 T^{12} \))(\( 1 - 3 T - 48 T^{2} + 211 T^{3} + 909 T^{4} - 3168 T^{5} - 13305 T^{6} - 98208 T^{7} + 873549 T^{8} + 6285901 T^{9} - 44329008 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( ( 1 - T - 68 T^{2} - 35 T^{3} + 2605 T^{4} + 2144 T^{5} - 88681 T^{6} + 66464 T^{7} + 2503405 T^{8} - 1042685 T^{9} - 62799428 T^{10} - 28629151 T^{11} + 887503681 T^{12} )^{2} \))(\( 1 + 18 T + 125 T^{2} + 572 T^{3} + 3467 T^{4} + 20608 T^{5} + 104889 T^{6} + 638848 T^{7} + 3331787 T^{8} + 17040452 T^{9} + 115440125 T^{10} + 515324718 T^{11} + 887503681 T^{12} \))(\( 1 + 11 T + 48 T^{2} + 334 T^{3} + 3383 T^{4} + 18543 T^{5} + 83056 T^{6} + 574833 T^{7} + 3251063 T^{8} + 9950194 T^{9} + 44329008 T^{10} + 314920661 T^{11} + 887503681 T^{12} \))(\( 1 + 6 T - 23 T^{2} - 478 T^{3} - 1763 T^{4} + 9154 T^{5} + 96655 T^{6} + 283774 T^{7} - 1694243 T^{8} - 14240098 T^{9} - 21240983 T^{10} + 171774906 T^{11} + 887503681 T^{12} \))(\( 1 + 13 T + 36 T^{2} + 185 T^{3} + 2700 T^{4} + 673 T^{5} - 53345 T^{6} - 56043 T^{7} - 532481 T^{8} - 606329 T^{9} + 9508655 T^{10} + 250694263 T^{11} + 3041746803 T^{12} + 7771522153 T^{13} + 9137817455 T^{14} - 18063147239 T^{15} - 491757385601 T^{16} - 1604463509493 T^{17} - 47343883862945 T^{18} + 18515989296703 T^{19} + 2302805801090700 T^{20} + 4891330099724135 T^{21} + 29506618331308836 T^{22} + 330310199653262803 T^{23} + 787662783788549761 T^{24} \))(\( ( 1 - 11 T + 31 T^{2} )^{6}( 1 - 4 T - 15 T^{2} + 184 T^{3} - 271 T^{4} - 4620 T^{5} + 26881 T^{6} - 143220 T^{7} - 260431 T^{8} + 5481544 T^{9} - 13852815 T^{10} - 114516604 T^{11} + 887503681 T^{12} ) \))
$37$ (\( 1 - 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 + 8 T + 82 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 1369 T^{4} \))(\( 1 + 71 T^{2} + 64 T^{3} + 2627 T^{4} + 50653 T^{6} \))(\( ( 1 - 6 T + 37 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 102 T^{2} + 5771 T^{4} - 242300 T^{6} + 7900499 T^{8} - 191164422 T^{10} + 2565726409 T^{12} )^{2} \))(\( ( 1 + 12 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 70 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 9 T + 44 T^{2} - 333 T^{3} + 1369 T^{4} \))(\( ( 1 + T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 56 T^{2} + 27 T^{3} + 2523 T^{4} + 999 T^{5} - 76664 T^{6} - 151959 T^{7} + 1874161 T^{8} \))(\( 1 + 9 T - 8 T^{2} - 193 T^{3} + 155 T^{4} - 2720 T^{5} - 55651 T^{6} - 100640 T^{7} + 212195 T^{8} - 9776029 T^{9} - 14993288 T^{10} + 624095613 T^{11} + 2565726409 T^{12} \))(\( 1 + 9 T - 16 T^{2} - 65 T^{3} + 1599 T^{4} - 6788 T^{5} - 137755 T^{6} - 251156 T^{7} + 2189031 T^{8} - 3292445 T^{9} - 29986576 T^{10} + 624095613 T^{11} + 2565726409 T^{12} \))(\( ( 1 - 15 T + 78 T^{2} - 39 T^{3} - 75 T^{4} - 16566 T^{5} + 166637 T^{6} - 612942 T^{7} - 102675 T^{8} - 1975467 T^{9} + 146184558 T^{10} - 1040159355 T^{11} + 2565726409 T^{12} )^{2} \))(\( ( 1 + 2 T + 26 T^{2} + 399 T^{3} + 962 T^{4} + 2738 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 13 T + 130 T^{2} - 865 T^{3} + 4810 T^{4} - 17797 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 7 T + 97 T^{2} + 427 T^{3} + 3589 T^{4} + 9583 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - T + 64 T^{2} - 304 T^{3} + 3526 T^{4} - 21119 T^{5} + 116817 T^{6} - 781403 T^{7} + 4827094 T^{8} - 15398512 T^{9} + 119946304 T^{10} - 69343957 T^{11} + 2565726409 T^{12} )^{2} \))(\( ( 1 - 10 T + 63 T^{2} - 260 T^{3} + 269 T^{4} + 6930 T^{5} - 79253 T^{6} + 256410 T^{7} + 368261 T^{8} - 13169780 T^{9} + 118072143 T^{10} - 693439570 T^{11} + 2565726409 T^{12} )( 1 - T - 36 T^{2} + 73 T^{3} + 1259 T^{4} - 3960 T^{5} - 42623 T^{6} - 146520 T^{7} + 1723571 T^{8} + 3697669 T^{9} - 67469796 T^{10} - 69343957 T^{11} + 2565726409 T^{12} ) \))
$41$ (\( 1 + 2 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 50 T^{2} + 1681 T^{4} \))(\( 1 + 55 T^{2} + 1681 T^{4} \))(\( 1 - 2 T + 75 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 15 T + 155 T^{2} - 1198 T^{3} + 6355 T^{4} - 25215 T^{5} + 68921 T^{6} \))(\( 1 + 20 T^{2} - 698 T^{4} + 33620 T^{6} + 2825761 T^{8} \))(\( 1 - 1841 T^{4} + 2825761 T^{8} \))(\( ( 1 - 212 T^{2} + 19783 T^{4} - 1047272 T^{6} + 33255223 T^{8} - 599061332 T^{10} + 4750104241 T^{12} )^{2} \))(\( 1 + 2 T - 37 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 + 9 T - 20 T^{2} + 171 T^{3} + 5199 T^{4} + 7011 T^{5} - 33620 T^{6} + 620289 T^{7} + 2825761 T^{8} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 87 T^{2} + 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 6 T + 2 T^{2} - 67 T^{3} + 82 T^{4} + 10086 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 - 10 T + 100 T^{2} - 575 T^{3} + 4100 T^{4} - 16810 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 134 T^{2} + 9422 T^{4} + 448063 T^{6} + 15838382 T^{8} + 378651974 T^{10} + 4750104241 T^{12} )^{2} \))(\( 1 + 23 T + 208 T^{2} + 1146 T^{3} + 6840 T^{4} + 44849 T^{5} + 273267 T^{6} + 1838809 T^{7} + 11498040 T^{8} + 78983466 T^{9} + 587758288 T^{10} + 2664692623 T^{11} + 4750104241 T^{12} \))(\( 1 + 12 T - 2 T^{2} - 747 T^{3} - 3359 T^{4} + 15043 T^{5} + 215825 T^{6} + 616763 T^{7} - 5646479 T^{8} - 51483987 T^{9} - 5651522 T^{10} + 1390274412 T^{11} + 4750104241 T^{12} \))(\( 1 + 2 T + 19 T^{2} - 30 T^{3} - 307 T^{4} + 4018 T^{5} + 60803 T^{6} + 164738 T^{7} - 516067 T^{8} - 2067630 T^{9} + 53689459 T^{10} + 231712402 T^{11} + 4750104241 T^{12} \))(\( 1 - 19 T + 139 T^{2} + 224 T^{3} - 11683 T^{4} + 84252 T^{5} - 5914 T^{6} - 3937444 T^{7} + 28367166 T^{8} - 51931227 T^{9} - 400937075 T^{10} + 3254706154 T^{11} - 15903259707 T^{12} + 133442952314 T^{13} - 673975223075 T^{14} - 3579152096067 T^{15} + 80158831363326 T^{16} - 456177303490244 T^{17} - 28092116481274 T^{18} + 16408437083022012 T^{19} - 93287881451820643 T^{20} + 73333553304247264 T^{21} + 1865749644111183739 T^{22} - 10456251602608720379 T^{23} + 22563490300366186081 T^{24} \))(\( ( 1 - 41 T^{2} + 1681 T^{4} - 68921 T^{6} + 2825761 T^{8} - 115856201 T^{10} + 4750104241 T^{12} )^{2} \))
$43$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( ( 1 + 14 T + 177 T^{2} + 1220 T^{3} + 7611 T^{4} + 25886 T^{5} + 79507 T^{6} )^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( ( 1 + 13 T + 43 T^{2} )^{2} \))(\( 1 - 18 T + 216 T^{2} - 1645 T^{3} + 9288 T^{4} - 33282 T^{5} + 79507 T^{6} \))(\( 1 - 2 T - 4 T^{2} - 221 T^{3} - 172 T^{4} - 3698 T^{5} + 79507 T^{6} \))(\( ( 1 - 20 T + 182 T^{2} - 1205 T^{3} + 7826 T^{4} - 36980 T^{5} + 79507 T^{6} )^{2} \))(\( 1 + 29 T + 393 T^{2} + 3221 T^{3} + 16899 T^{4} + 53621 T^{5} + 79507 T^{6} \))(\( 1 - 13 T - 27 T^{2} + 911 T^{3} - 1161 T^{4} - 24037 T^{5} + 79507 T^{6} \))(\( 1 + 13 T + 141 T^{2} + 895 T^{3} + 6063 T^{4} + 24037 T^{5} + 79507 T^{6} \))(\( 1 - 28 T + 316 T^{2} - 1953 T^{3} + 12559 T^{4} - 139139 T^{5} + 1197673 T^{6} - 5982977 T^{7} + 23221591 T^{8} - 155277171 T^{9} + 1080341116 T^{10} - 4116236404 T^{11} + 6321363049 T^{12} \))(\( 1 + 8 T + 21 T^{2} - 176 T^{3} - 2311 T^{4} - 10920 T^{5} + 12013 T^{6} - 469560 T^{7} - 4273039 T^{8} - 13993232 T^{9} + 71794821 T^{10} + 1176067544 T^{11} + 6321363049 T^{12} \))
$47$ (\( 1 + 4 T + 47 T^{2} \))(\( 1 + T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 2 T - 3 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( 1 - 14 T^{2} + 2209 T^{4} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( 1 - 2 T + 8 T^{2} + 476 T^{3} + 376 T^{4} - 4418 T^{5} + 103823 T^{6} \))(\( 1 + 107 T^{2} + 5964 T^{4} + 236363 T^{6} + 4879681 T^{8} \))(\( 1 + 1666 T^{4} + 4879681 T^{8} \))(\( ( 1 - 120 T^{2} + 4056 T^{4} - 57292 T^{6} + 8959704 T^{8} - 585561720 T^{10} + 10779215329 T^{12} )^{2} \))(\( 1 + 10 T + 53 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 + 8 T - 26 T^{2} - 32 T^{3} + 2883 T^{4} - 1504 T^{5} - 57434 T^{6} + 830584 T^{7} + 4879681 T^{8} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 9 T + 103 T^{2} + 423 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 4 T + 74 T^{2} + 347 T^{3} + 3478 T^{4} + 8836 T^{5} + 103823 T^{6} )^{2} \))(\( ( 1 + 8 T + 60 T^{2} + 691 T^{3} + 2820 T^{4} + 17672 T^{5} + 103823 T^{6} )^{2} \))(\( ( 1 + 134 T^{2} + 6814 T^{4} + 254611 T^{6} + 15052126 T^{8} + 653877254 T^{10} + 10779215329 T^{12} )^{2} \))(\( 1 + T - 46 T^{2} - 93 T^{3} + 2069 T^{4} + 6440 T^{5} - 90803 T^{6} + 302680 T^{7} + 4570421 T^{8} - 9655539 T^{9} - 224465326 T^{10} + 229345007 T^{11} + 10779215329 T^{12} \))(\( 1 - 20 T + 157 T^{2} - 786 T^{3} + 2139 T^{4} + 27706 T^{5} - 369921 T^{6} + 1302182 T^{7} + 4725051 T^{8} - 81604878 T^{9} + 766109917 T^{10} - 4586900140 T^{11} + 10779215329 T^{12} \))(\( 1 + 17 T + 158 T^{2} + 816 T^{3} + 3471 T^{4} + 14523 T^{5} + 108772 T^{6} + 682581 T^{7} + 7667439 T^{8} + 84719568 T^{9} + 770989598 T^{10} + 3898865119 T^{11} + 10779215329 T^{12} \))(\( 1 + 9 T - 14 T^{2} - 12 T^{3} + 2064 T^{4} + 7332 T^{5} - 83746 T^{6} - 119385 T^{7} + 15092852 T^{8} + 42083157 T^{9} - 261959781 T^{10} + 1321995669 T^{11} + 19827763015 T^{12} + 62133796443 T^{13} - 578669156229 T^{14} + 4369199609211 T^{15} + 73648303140212 T^{16} - 27380353660695 T^{17} - 902716166942434 T^{18} + 3714560719234716 T^{19} + 49146495669874704 T^{20} - 13429565677233204 T^{21} - 736387851301620686 T^{22} + 22249432935756110727 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 47 T^{2} + 2209 T^{4} - 103823 T^{6} + 4879681 T^{8} - 229345007 T^{10} + 10779215329 T^{12} )^{2} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 - 5 T + 53 T^{2} \))(\( 1 - 22 T^{2} + 2809 T^{4} \))(\( 1 - 41 T^{2} + 2809 T^{4} \))(\( 1 + 22 T + 219 T^{2} + 1166 T^{3} + 2809 T^{4} \))(\( 1 - 5 T + 143 T^{2} - 466 T^{3} + 7579 T^{4} - 14045 T^{5} + 148877 T^{6} \))(\( 1 + 68 T^{2} + 2614 T^{4} + 191012 T^{6} + 7890481 T^{8} \))(\( 1 - 1649 T^{4} + 7890481 T^{8} \))(\( ( 1 - 172 T^{2} + 12847 T^{4} - 691192 T^{6} + 36087223 T^{8} - 1357162732 T^{10} + 22164361129 T^{12} )^{2} \))(\( ( 1 - T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 95 T^{2} - 318 T^{3} + 2809 T^{4} )^{2} \))(\( 1 + 5 T - 28 T^{2} + 265 T^{3} + 2809 T^{4} \))(\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 5 T - 86 T^{2} + 25 T^{3} + 8187 T^{4} + 1325 T^{5} - 241574 T^{6} + 744385 T^{7} + 7890481 T^{8} \))(\( 1 + 5 T - 112 T^{2} - 349 T^{3} + 8923 T^{4} + 12264 T^{5} - 499939 T^{6} + 649992 T^{7} + 25064707 T^{8} - 51958073 T^{9} - 883733872 T^{10} + 2090977465 T^{11} + 22164361129 T^{12} \))(\( 1 + 3 T - 46 T^{2} - 621 T^{3} - 1069 T^{4} + 12552 T^{5} + 266597 T^{6} + 665256 T^{7} - 3002821 T^{8} - 92452617 T^{9} - 362962126 T^{10} + 1254586479 T^{11} + 22164361129 T^{12} \))(\( 1 - 263 T^{2} + 37922 T^{4} - 3954107 T^{6} + 327905385 T^{8} - 22523014574 T^{10} + 1301027375017 T^{12} - 63267147938366 T^{14} + 2587331210140185 T^{16} - 87640255490706803 T^{18} + 2361011979779631842 T^{20} - 45995404706129931887 T^{22} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 10 T + 47 T^{2} - 528 T^{3} + 8081 T^{4} - 52826 T^{5} + 297535 T^{6} - 2799778 T^{7} + 22699529 T^{8} - 78607056 T^{9} + 370852607 T^{10} - 4181954930 T^{11} + 22164361129 T^{12} \))(\( 1 + 17 T + 145 T^{2} + 423 T^{3} - 3462 T^{4} - 51376 T^{5} - 414771 T^{6} - 2722928 T^{7} - 9724758 T^{8} + 62974971 T^{9} + 1144119745 T^{10} + 7109323381 T^{11} + 22164361129 T^{12} \))(\( 1 - 2 T + 56 T^{2} - 531 T^{3} + 6599 T^{4} - 27685 T^{5} + 387913 T^{6} - 1467305 T^{7} + 18536591 T^{8} - 79053687 T^{9} + 441866936 T^{10} - 836390986 T^{11} + 22164361129 T^{12} \))(\( 1 - 6 T + 82 T^{2} - 589 T^{3} + 5607 T^{4} - 46193 T^{5} + 168595 T^{6} - 2627309 T^{7} + 14239569 T^{8} - 123535407 T^{9} + 916404376 T^{10} - 5626848248 T^{11} + 72652183961 T^{12} - 298222957144 T^{13} + 2574179892184 T^{14} - 18391580787939 T^{15} + 112357048642689 T^{16} - 1098728782518337 T^{17} + 3736800464543755 T^{18} - 54263431682490541 T^{19} + 349090084136501127 T^{20} - 1943560755571456337 T^{21} + 14340772569972070018 T^{22} - 55614215576233149582 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 53 T^{2} - 148877 T^{6} - 7890481 T^{8} + 22164361129 T^{12} - 62259690411361 T^{16} - 3299763591802133 T^{18} + 9269035929372191597 T^{22} + \)\(49\!\cdots\!41\)\( T^{24} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 4 T - 6 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 10 T^{2} + 3481 T^{4} \))(\( 1 - 4 T + 114 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 165 T^{2} + 864 T^{3} + 9735 T^{4} + 27848 T^{5} + 205379 T^{6} \))(\( 1 + 200 T^{2} + 16702 T^{4} + 696200 T^{6} + 12117361 T^{8} \))(\( 1 - 4046 T^{4} + 12117361 T^{8} \))(\( ( 1 - 68 T^{2} + 8075 T^{4} - 302664 T^{6} + 28109075 T^{8} - 823980548 T^{10} + 42180533641 T^{12} )^{2} \))(\( 1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 + 5 T + 52 T^{2} - 725 T^{3} - 4227 T^{4} - 42775 T^{5} + 181012 T^{6} + 1026895 T^{7} + 12117361 T^{8} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - T + 87 T^{2} - 59 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 7 T + 93 T^{2} - 525 T^{3} + 5487 T^{4} - 24367 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 + 13 T + 155 T^{2} + 1351 T^{3} + 9145 T^{4} + 45253 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 + 189 T^{2} + 19729 T^{4} + 1361231 T^{6} + 68676649 T^{8} + 2290181229 T^{10} + 42180533641 T^{12} )^{2} \))(\( 1 + 22 T + 152 T^{2} - 201 T^{3} - 5011 T^{4} + 58697 T^{5} + 1026535 T^{6} + 3463123 T^{7} - 17443291 T^{8} - 41281179 T^{9} + 1841838872 T^{10} + 15728334578 T^{11} + 42180533641 T^{12} \))(\( 1 - 5 T + 78 T^{2} + 80 T^{3} + 3048 T^{4} + 37391 T^{5} - 23773 T^{6} + 2206069 T^{7} + 10610088 T^{8} + 16430320 T^{9} + 945154158 T^{10} - 3574621495 T^{11} + 42180533641 T^{12} \))(\( 1 + 12 T - 20 T^{2} - 1053 T^{3} - 3791 T^{4} + 30145 T^{5} + 385979 T^{6} + 1778555 T^{7} - 13196471 T^{8} - 216264087 T^{9} - 242347220 T^{10} + 8579091588 T^{11} + 42180533641 T^{12} \))(\( 1 - 53 T + 1303 T^{2} - 18772 T^{3} + 160421 T^{4} - 633059 T^{5} - 633045 T^{6} - 18441685 T^{7} + 928499384 T^{8} - 12194999818 T^{9} + 76925172279 T^{10} - 138282850223 T^{11} - 878582350829 T^{12} - 8158688163157 T^{13} + 267776524703199 T^{14} - 2504596867621022 T^{15} + 11250962224205624 T^{16} - 13184408721003815 T^{17} - 26702175918766845 T^{18} - 1575463220328031321 T^{19} + 23554685630922779141 T^{20} - \)\(16\!\cdots\!08\)\( T^{21} + \)\(66\!\cdots\!03\)\( T^{22} - \)\(15\!\cdots\!27\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 59 T^{2} + 3481 T^{4} - 205379 T^{6} + 12117361 T^{8} - 714924299 T^{10} + 42180533641 T^{12} )^{2} \))
$61$ (\( 1 - 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 8 T + 130 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( 1 - 8 T + 120 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 191 T^{2} + 1440 T^{3} + 11651 T^{4} + 59536 T^{5} + 226981 T^{6} \))(\( ( 1 + 2 T + 61 T^{2} )^{4} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 182 T^{2} + 19675 T^{4} - 1472732 T^{6} + 73210675 T^{8} - 2519943062 T^{10} + 51520374361 T^{12} )^{2} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 - 5 T - 42 T^{2} + 275 T^{3} - 757 T^{4} + 16775 T^{5} - 156282 T^{6} - 1134905 T^{7} + 13845841 T^{8} \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + T + 61 T^{2} ) \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 - T - 110 T^{2} + 11 T^{3} + 8539 T^{4} + 671 T^{5} - 409310 T^{6} - 226981 T^{7} + 13845841 T^{8} \))(\( 1 - T - 124 T^{2} + 145 T^{3} + 7865 T^{4} - 5346 T^{5} - 484659 T^{6} - 326106 T^{7} + 29265665 T^{8} + 32912245 T^{9} - 1716884284 T^{10} - 844596301 T^{11} + 51520374361 T^{12} \))(\( 1 + 11 T - 92 T^{2} - 339 T^{3} + 17625 T^{4} + 40718 T^{5} - 965507 T^{6} + 2483798 T^{7} + 65582625 T^{8} - 76946559 T^{9} - 1273817372 T^{10} + 9290559311 T^{11} + 51520374361 T^{12} \))(\( ( 1 - 11 T - 22 T^{2} + 69 T^{3} + 2695 T^{4} + 33572 T^{5} - 569627 T^{6} + 2047892 T^{7} + 10028095 T^{8} + 15661689 T^{9} - 304608502 T^{10} - 9290559311 T^{11} + 51520374361 T^{12} )^{2} \))(\( 1 - 19 T + 90 T^{2} + 436 T^{3} - 5311 T^{4} + 40503 T^{5} - 386744 T^{6} + 2470683 T^{7} - 19762231 T^{8} + 98963716 T^{9} + 1246125690 T^{10} - 16047329719 T^{11} + 51520374361 T^{12} \))(\( 1 - 3 T - 66 T^{2} + 752 T^{3} - 71 T^{4} - 31589 T^{5} + 214416 T^{6} - 1926929 T^{7} - 264191 T^{8} + 170689712 T^{9} - 913825506 T^{10} - 2533788903 T^{11} + 51520374361 T^{12} \))(\( 1 - 12 T + 27 T^{2} - 404 T^{3} + 3229 T^{4} + 16766 T^{5} - 226185 T^{6} + 1022726 T^{7} + 12015109 T^{8} - 91700324 T^{9} + 373837707 T^{10} - 10135155612 T^{11} + 51520374361 T^{12} \))(\( 1 + 15 T + 105 T^{2} - 94 T^{3} - 7240 T^{4} - 77647 T^{5} - 629057 T^{6} - 6832110 T^{7} - 43927502 T^{8} - 54083270 T^{9} + 2664690109 T^{10} + 31203423256 T^{11} + 269060632069 T^{12} + 1903408818616 T^{13} + 9915311895589 T^{14} - 12275874707870 T^{15} - 608213208219182 T^{16} - 5770374834025110 T^{17} - 32409252134407577 T^{18} - 244024552988522587 T^{19} - 1387960946100314440 T^{20} - 1099249732726409254 T^{21} + 74901005724602673105 T^{22} + \)\(65\!\cdots\!15\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 13 T + 108 T^{2} - 611 T^{3} + 1355 T^{4} + 19656 T^{5} - 338183 T^{6} + 1199016 T^{7} + 5041955 T^{8} - 138685391 T^{9} + 1495350828 T^{10} - 10979751913 T^{11} + 51520374361 T^{12} )( 1 - T - 60 T^{2} + 121 T^{3} + 3539 T^{4} - 10920 T^{5} - 204959 T^{6} - 666120 T^{7} + 13168619 T^{8} + 27464701 T^{9} - 830750460 T^{10} - 844596301 T^{11} + 51520374361 T^{12} ) \))
$67$ (\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 15 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + 12 T + 98 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( ( 1 + T + 67 T^{2} )^{2} \))(\( 1 - 2 T + 63 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 + 11 T + 121 T^{2} + 1142 T^{3} + 8107 T^{4} + 49379 T^{5} + 300763 T^{6} \))(\( ( 1 - 4 T + 67 T^{2} )^{4} \))(\( ( 1 + 91 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 4 T + 47 T^{2} - 852 T^{3} + 3149 T^{4} - 17956 T^{5} + 300763 T^{6} )^{4} \))(\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 6 T - 62 T^{2} + 216 T^{3} + 2703 T^{4} + 14472 T^{5} - 278318 T^{6} - 1804578 T^{7} + 20151121 T^{8} \))(\( 1 - 3 T - 58 T^{2} - 201 T^{3} + 4489 T^{4} \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( 1 + 9 T + 14 T^{2} + 603 T^{3} + 4489 T^{4} \))(\( 1 - T - 122 T^{2} + 11 T^{3} + 10573 T^{4} + 737 T^{5} - 547658 T^{6} - 300763 T^{7} + 20151121 T^{8} \))(\( 1 + 13 T - 72 T^{2} - 325 T^{3} + 19457 T^{4} + 55224 T^{5} - 1059101 T^{6} + 3700008 T^{7} + 87342473 T^{8} - 97747975 T^{9} - 1450880712 T^{10} + 17551626391 T^{11} + 90458382169 T^{12} \))(\( 1 - 15 T + 132 T^{2} - 669 T^{3} - 3027 T^{4} + 85836 T^{5} - 856213 T^{6} + 5751012 T^{7} - 13588203 T^{8} - 201210447 T^{9} + 2659947972 T^{10} - 20251876605 T^{11} + 90458382169 T^{12} \))(\( ( 1 - T - 66 T^{2} - 165 T^{3} + 49 T^{4} + 7772 T^{5} + 298675 T^{6} + 520724 T^{7} + 219961 T^{8} - 49625895 T^{9} - 1329973986 T^{10} - 1350125107 T^{11} + 90458382169 T^{12} )^{2} \))(\( 1 + 4 T - 30 T^{2} - 745 T^{3} + 2831 T^{4} + 213 T^{5} + 116347 T^{6} + 14271 T^{7} + 12708359 T^{8} - 224068435 T^{9} - 604533630 T^{10} + 5400500428 T^{11} + 90458382169 T^{12} \))(\( 1 - 2 T + 21 T^{2} + 890 T^{3} + 3617 T^{4} + 6342 T^{5} + 684895 T^{6} + 424914 T^{7} + 16236713 T^{8} + 267679070 T^{9} + 423173541 T^{10} - 2700250214 T^{11} + 90458382169 T^{12} \))(\( 1 + 18 T + 117 T^{2} + 704 T^{3} + 12085 T^{4} + 129244 T^{5} + 998865 T^{6} + 8659348 T^{7} + 54249565 T^{8} + 211737152 T^{9} + 2357681157 T^{10} + 24302251926 T^{11} + 90458382169 T^{12} \))(\( 1 - 39 T + 607 T^{2} - 5298 T^{3} + 42409 T^{4} - 410176 T^{5} + 2817352 T^{6} - 10700926 T^{7} + 74266750 T^{8} - 1179098659 T^{9} + 13524630855 T^{10} - 130583010882 T^{11} + 1143820688565 T^{12} - 8749061729094 T^{13} + 60712067908095 T^{14} - 354629249976817 T^{15} + 1496558265526750 T^{16} - 14447588860749082 T^{17} + 254853103920596488 T^{18} - 2485958443424966848 T^{19} + 17220924137499588169 T^{20} - \)\(14\!\cdots\!06\)\( T^{21} + \)\(11\!\cdots\!43\)\( T^{22} - \)\(47\!\cdots\!37\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 16 T + 189 T^{2} - 1952 T^{3} + 18569 T^{4} - 166320 T^{5} + 1416997 T^{6} - 11143440 T^{7} + 83356241 T^{8} - 587089376 T^{9} + 3808561869 T^{10} - 21602001712 T^{11} + 90458382169 T^{12} )( 1 + 11 T + 54 T^{2} - 143 T^{3} - 5191 T^{4} - 47520 T^{5} - 174923 T^{6} - 3183840 T^{7} - 23302399 T^{8} - 43009109 T^{9} + 1088160534 T^{10} + 14851376177 T^{11} + 90458382169 T^{12} ) \))
$71$ (\( 1 + 8 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 12 T + 170 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( 1 + 130 T^{2} + 5041 T^{4} \))(\( 1 - 12 T + 170 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 + 22 T + 297 T^{2} + 2700 T^{3} + 21087 T^{4} + 110902 T^{5} + 357911 T^{6} \))(\( 1 + 40 T^{2} + 8142 T^{4} + 201640 T^{6} + 25411681 T^{8} \))(\( ( 1 + 71 T^{2} )^{4} \))(\( ( 1 + 218 T^{2} + 29087 T^{4} + 2431212 T^{6} + 146627567 T^{8} + 5539746458 T^{10} + 128100283921 T^{12} )^{2} \))(\( ( 1 + 7 T + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 101 T^{2} + 639 T^{3} + 5041 T^{4} )^{2} \))(\( 1 + T - 70 T^{2} + 71 T^{3} + 5041 T^{4} \))(\( 1 - 71 T^{2} + 5041 T^{4} \))(\( 1 - 2 T - 67 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 - 3 T + 16 T^{2} + 447 T^{3} - 5631 T^{4} + 31737 T^{5} + 80656 T^{6} - 1073733 T^{7} + 25411681 T^{8} \))(\( 1 + 8 T - 161 T^{2} - 456 T^{3} + 25626 T^{4} + 38528 T^{5} - 1928793 T^{6} + 2735488 T^{7} + 129180666 T^{8} - 163207416 T^{9} - 4091280641 T^{10} + 14433834808 T^{11} + 128100283921 T^{12} \))(\( 1 + 8 T - 129 T^{2} - 744 T^{3} + 14394 T^{4} + 41872 T^{5} - 942745 T^{6} + 2972912 T^{7} + 72560154 T^{8} - 266285784 T^{9} - 3278106849 T^{10} + 14433834808 T^{11} + 128100283921 T^{12} \))(\( 1 - 250 T^{2} + 28437 T^{4} - 2570382 T^{6} + 245405386 T^{8} - 21755663842 T^{10} + 1655809017469 T^{12} - 109670301427522 T^{14} + 6236163384713866 T^{16} - 329266663985427822 T^{18} + 18363293168035705557 T^{20} - \)\(81\!\cdots\!50\)\( T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 28 T + 293 T^{2} + 1470 T^{3} + 953 T^{4} - 112168 T^{5} - 1557515 T^{6} - 7963928 T^{7} + 4804073 T^{8} + 526129170 T^{9} + 7445622533 T^{10} + 50518421828 T^{11} + 128100283921 T^{12} \))(\( 1 + 2 T - 81 T^{2} - 1046 T^{3} - 2361 T^{4} + 53584 T^{5} + 675521 T^{6} + 3804464 T^{7} - 11901801 T^{8} - 374374906 T^{9} - 2058346161 T^{10} + 3608458702 T^{11} + 128100283921 T^{12} \))(\( 1 + 26 T + 101 T^{2} - 3378 T^{3} - 35947 T^{4} + 149374 T^{5} + 4056325 T^{6} + 10605554 T^{7} - 181208827 T^{8} - 1209023358 T^{9} + 2566579781 T^{10} + 46909963126 T^{11} + 128100283921 T^{12} \))(\( 1 - 30 T^{2} + 1267 T^{3} + 6268 T^{4} - 26243 T^{5} + 771410 T^{6} + 9765840 T^{7} + 12480543 T^{8} + 124457403 T^{9} + 7797845889 T^{10} + 41706137193 T^{11} - 40911265213 T^{12} + 2961135740703 T^{13} + 39308941126449 T^{14} + 44544673565133 T^{15} + 317151577422783 T^{16} + 17619815165169840 T^{17} + 98817840019498610 T^{18} - 238683238316655013 T^{19} + 4047583133848429948 T^{20} + 58090050410274922277 T^{21} - 97657306530296436030 T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 71 T^{2} - 357911 T^{6} - 25411681 T^{8} + 128100283921 T^{12} - 645753531245761 T^{16} - 45848500718449031 T^{18} + \)\(23\!\cdots\!71\)\( T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))
$73$ (\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 4 T + 118 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( 1 + 24 T + 272 T^{2} + 1752 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 271 T^{2} + 2320 T^{3} + 19783 T^{4} + 85264 T^{5} + 389017 T^{6} \))(\( ( 1 - 6 T + 73 T^{2} )^{4} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 - 262 T^{2} + 36239 T^{4} - 3269748 T^{6} + 193117631 T^{8} - 7440339142 T^{10} + 151334226289 T^{12} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 8 T + 157 T^{2} + 584 T^{3} + 5329 T^{4} )^{2} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 10 T + 73 T^{2} ) \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 10 T + 73 T^{2} ) \))(\( 1 - 3 T - 128 T^{2} + 27 T^{3} + 12783 T^{4} + 1971 T^{5} - 682112 T^{6} - 1167051 T^{7} + 28398241 T^{8} \))(\( 1 - 7 T - 30 T^{2} + 1897 T^{3} - 8101 T^{4} - 53340 T^{5} + 1561945 T^{6} - 3893820 T^{7} - 43170229 T^{8} + 737965249 T^{9} - 851947230 T^{10} - 14511501151 T^{11} + 151334226289 T^{12} \))(\( 1 + T - 130 T^{2} - 35 T^{3} + 7515 T^{4} - 2924 T^{5} - 473159 T^{6} - 213452 T^{7} + 40047435 T^{8} - 13615595 T^{9} - 3691771330 T^{10} + 2073071593 T^{11} + 151334226289 T^{12} \))(\( ( 1 - T - 194 T^{2} + 7 T^{3} + 23689 T^{4} + 3446 T^{5} - 1992919 T^{6} + 251558 T^{7} + 126238681 T^{8} + 2723119 T^{9} - 5509258754 T^{10} - 2073071593 T^{11} + 151334226289 T^{12} )^{2} \))(\( 1 - 21 T + 277 T^{2} - 3395 T^{3} + 42226 T^{4} - 408520 T^{5} + 3543793 T^{6} - 29821960 T^{7} + 225022354 T^{8} - 1320712715 T^{9} + 7866312757 T^{10} - 43534503453 T^{11} + 151334226289 T^{12} \))(\( 1 + 11 T + 146 T^{2} + 1727 T^{3} + 15871 T^{4} + 144704 T^{5} + 1559321 T^{6} + 10563392 T^{7} + 84576559 T^{8} + 671832359 T^{9} + 4146143186 T^{10} + 22803787523 T^{11} + 151334226289 T^{12} \))(\( 1 + 9 T - 6 T^{2} + 430 T^{3} - 1187 T^{4} - 23719 T^{5} + 416688 T^{6} - 1731487 T^{7} - 6325523 T^{8} + 167277310 T^{9} - 170389446 T^{10} + 18657644337 T^{11} + 151334226289 T^{12} \))(\( 1 - 30 T + 299 T^{2} - 900 T^{3} + 6036 T^{4} - 248142 T^{5} + 3708047 T^{6} - 34928706 T^{7} + 262505641 T^{8} - 1561574680 T^{9} + 12839130010 T^{10} - 219611035700 T^{11} + 2587880427833 T^{12} - 16031605606100 T^{13} + 68419723823290 T^{14} - 607479097289560 T^{15} + 7454698456977481 T^{16} - 72409708188848658 T^{17} + 561154423788247583 T^{18} - 2741323563325767774 T^{19} + 4867793114672672916 T^{20} - 52984428037441121700 T^{21} + \)\(12\!\cdots\!51\)\( T^{22} - \)\(94\!\cdots\!10\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 10 T + 27 T^{2} + 460 T^{3} - 6571 T^{4} + 32130 T^{5} + 158383 T^{6} + 2345490 T^{7} - 35016859 T^{8} + 178947820 T^{9} + 766752507 T^{10} - 20730715930 T^{11} + 151334226289 T^{12} )( 1 + 17 T + 216 T^{2} + 2431 T^{3} + 25559 T^{4} + 257040 T^{5} + 2503873 T^{6} + 18763920 T^{7} + 136203911 T^{8} + 945700327 T^{9} + 6134020056 T^{10} + 35242217081 T^{11} + 151334226289 T^{12} ) \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 102 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( 1 - 4 T + 154 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( 1 - 24 T + 389 T^{2} - 4048 T^{3} + 30731 T^{4} - 149784 T^{5} + 493039 T^{6} \))(\( ( 1 + 14 T + 142 T^{2} + 1106 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 16 T + 211 T^{2} + 2356 T^{3} + 16669 T^{4} + 99856 T^{5} + 493039 T^{6} )^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( 1 - 4 T - 101 T^{2} + 164 T^{3} + 6184 T^{4} + 12956 T^{5} - 630341 T^{6} - 1972156 T^{7} + 38950081 T^{8} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( 1 - 5 T - 138 T^{2} - 25 T^{3} + 18353 T^{4} - 1975 T^{5} - 861258 T^{6} - 2465195 T^{7} + 38950081 T^{8} \))(\( 1 + 12 T + 34 T^{2} + 550 T^{3} - 1210 T^{4} - 91318 T^{5} - 720301 T^{6} - 7214122 T^{7} - 7551610 T^{8} + 271171450 T^{9} + 1324302754 T^{10} + 36924676788 T^{11} + 243087455521 T^{12} \))(\( 1 + 4 T + 38 T^{2} + 1998 T^{3} + 6394 T^{4} + 61814 T^{5} + 1935835 T^{6} + 4883306 T^{7} + 39904954 T^{8} + 985091922 T^{9} + 1480103078 T^{10} + 12308225596 T^{11} + 243087455521 T^{12} \))(\( ( 1 + 8 T - 20 T^{2} - 378 T^{3} - 3780 T^{4} - 12148 T^{5} + 304855 T^{6} - 959692 T^{7} - 23590980 T^{8} - 186368742 T^{9} - 779001620 T^{10} + 24616451192 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 - 3 T + 212 T^{2} - 391 T^{3} + 16748 T^{4} - 18723 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 + 14 T + 300 T^{2} + 2303 T^{3} + 23700 T^{4} + 87374 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 + 10 T + 254 T^{2} + 1581 T^{3} + 20066 T^{4} + 62410 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 + 17 T + 366 T^{2} + 3071 T^{3} + 35336 T^{4} + 144497 T^{5} + 1991527 T^{6} + 11415263 T^{7} + 220531976 T^{8} + 1514122769 T^{9} + 14255729646 T^{10} + 52309958783 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 - 13 T + 90 T^{2} - 143 T^{3} - 5251 T^{4} + 79560 T^{5} - 619451 T^{6} + 6285240 T^{7} - 32771491 T^{8} - 70504577 T^{9} + 3505507290 T^{10} - 40001733187 T^{11} + 243087455521 T^{12} )( 1 + 17 T + 210 T^{2} + 2227 T^{3} + 21269 T^{4} + 185640 T^{5} + 1475629 T^{6} + 14665560 T^{7} + 132739829 T^{8} + 1097997853 T^{9} + 8179517010 T^{10} + 52309958783 T^{11} + 243087455521 T^{12} ) \))
$83$ (\( 1 + 83 T^{2} \))(\( 1 - 15 T + 83 T^{2} \))(\( 1 + 15 T + 83 T^{2} \))(\( 1 + 15 T + 83 T^{2} \))(\( 1 + 15 T + 83 T^{2} \))(\( 1 - 14 T + 213 T^{2} - 1162 T^{3} + 6889 T^{4} \))(\( 1 + 163 T^{2} + 6889 T^{4} \))(\( 1 + 18 T + 215 T^{2} + 1494 T^{3} + 6889 T^{4} \))(\( 1 - 7 T + 170 T^{2} - 677 T^{3} + 14110 T^{4} - 48223 T^{5} + 571787 T^{6} \))(\( 1 + 211 T^{2} + 21252 T^{4} + 1453579 T^{6} + 47458321 T^{8} \))(\( 1 + 1351 T^{4} + 47458321 T^{8} \))(\( ( 1 - 32 T^{2} + 14608 T^{4} - 338084 T^{6} + 100634512 T^{8} - 1518666272 T^{10} + 326940373369 T^{12} )^{2} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 + 8 T - 98 T^{2} - 32 T^{3} + 14043 T^{4} - 2656 T^{5} - 675122 T^{6} + 4574296 T^{7} + 47458321 T^{8} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( 1 - 3 T + 52 T^{2} + 627 T^{3} - 5787 T^{4} + 52041 T^{5} + 358228 T^{6} - 1715361 T^{7} + 47458321 T^{8} \))(\( 1 + T - 232 T^{2} - 41 T^{3} + 34813 T^{4} + 132 T^{5} - 3350533 T^{6} + 10956 T^{7} + 239826757 T^{8} - 23443267 T^{9} - 11010330472 T^{10} + 3939040643 T^{11} + 326940373369 T^{12} \))(\( 1 + 5 T - 130 T^{2} - 939 T^{3} + 6875 T^{4} + 38630 T^{5} - 288277 T^{6} + 3206290 T^{7} + 47361875 T^{8} - 536907993 T^{9} - 6169581730 T^{10} + 19695203215 T^{11} + 326940373369 T^{12} \))(\( 1 - 149 T^{2} + 5744 T^{4} + 618033 T^{6} - 71263811 T^{8} + 1451115734 T^{10} + 90909479425 T^{12} + 9996736291526 T^{14} - 3382060818121331 T^{16} + 202059939774363177 T^{18} + 12937166581406651504 T^{20} - \)\(23\!\cdots\!01\)\( T^{22} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 39 T + 640 T^{2} - 6519 T^{3} + 67141 T^{4} - 848516 T^{5} + 9110429 T^{6} - 70426828 T^{7} + 462534349 T^{8} - 3727479453 T^{9} + 30373325440 T^{10} - 153622585077 T^{11} + 326940373369 T^{12} \))(\( 1 + 18 T + 73 T^{2} - 922 T^{3} - 8739 T^{4} + 72034 T^{5} + 1632945 T^{6} + 5978822 T^{7} - 60202971 T^{8} - 527187614 T^{9} + 3464457433 T^{10} + 70902731574 T^{11} + 326940373369 T^{12} \))(\( 1 + 20 T + 72 T^{2} - 1865 T^{3} - 18531 T^{4} + 47725 T^{5} + 1743083 T^{6} + 3961175 T^{7} - 127660059 T^{8} - 1066382755 T^{9} + 3416999112 T^{10} + 78780812860 T^{11} + 326940373369 T^{12} \))(\( 1 + 9 T + 282 T^{2} + 3659 T^{3} + 59452 T^{4} + 741286 T^{5} + 9593990 T^{6} + 112313549 T^{7} + 1262380485 T^{8} + 13236741386 T^{9} + 138879306764 T^{10} + 1301167953743 T^{11} + 12611315727233 T^{12} + 107996940160669 T^{13} + 956739544297196 T^{14} + 7568596646876782 T^{15} + 59910458281265685 T^{16} + 442407634270572007 T^{17} + 3136662672698452310 T^{18} + 20115574693896640322 T^{19} + \)\(13\!\cdots\!32\)\( T^{20} + \)\(68\!\cdots\!77\)\( T^{21} + \)\(43\!\cdots\!18\)\( T^{22} + \)\(11\!\cdots\!03\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 83 T^{2} - 571787 T^{6} - 47458321 T^{8} + 326940373369 T^{12} - 2252292232139041 T^{16} - 186940255267540403 T^{18} + \)\(12\!\cdots\!67\)\( T^{22} + \)\(10\!\cdots\!61\)\( T^{24} \))
$89$ (\( 1 + 14 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 + 106 T^{2} + 7921 T^{4} \))(\( 1 - 122 T^{2} + 7921 T^{4} \))(\( 1 - 12 T + 196 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 38 T + 723 T^{2} - 8508 T^{3} + 64347 T^{4} - 300998 T^{5} + 704969 T^{6} \))(\( ( 1 - 2 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 89 T^{2} )^{4} \))(\( ( 1 + 310 T^{2} + 40291 T^{4} + 3669868 T^{6} + 319145011 T^{8} + 19450094710 T^{10} + 496981290961 T^{12} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 3 T + 89 T^{2} )^{4} \))(\( 1 + T - 88 T^{2} + 89 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 8 T - 25 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 - 3 T - 160 T^{2} + 27 T^{3} + 19839 T^{4} + 2403 T^{5} - 1267360 T^{6} - 2114907 T^{7} + 62742241 T^{8} \))(\( 1 - 10 T - 191 T^{2} + 666 T^{3} + 40902 T^{4} - 81538 T^{5} - 3721827 T^{6} - 7256882 T^{7} + 323984742 T^{8} + 469509354 T^{9} - 11983768031 T^{10} - 55840594490 T^{11} + 496981290961 T^{12} \))(\( 1 - 10 T - 95 T^{2} + 602 T^{3} + 7910 T^{4} + 19070 T^{5} - 1138211 T^{6} + 1697230 T^{7} + 62655110 T^{8} + 424391338 T^{9} - 5960512895 T^{10} - 55840594490 T^{11} + 496981290961 T^{12} \))(\( 1 + 58 T^{2} - 15291 T^{4} - 226770 T^{6} + 162288730 T^{8} - 1294376702 T^{10} - 1545468619427 T^{12} - 10252757856542 T^{14} + 10182358609243930 T^{16} - 112700447351225970 T^{18} - 60194379427990520571 T^{20} + \)\(18\!\cdots\!58\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 11 T - 143 T^{2} - 3063 T^{3} - 12244 T^{4} + 185572 T^{5} + 3036725 T^{6} + 16515908 T^{7} - 96984724 T^{8} - 2159320047 T^{9} - 8972140463 T^{10} + 61424653939 T^{11} + 496981290961 T^{12} \))(\( 1 - 11 T - 10 T^{2} + 2069 T^{3} - 11243 T^{4} - 102286 T^{5} + 2490921 T^{6} - 9103454 T^{7} - 89055803 T^{8} + 1458580861 T^{9} - 627422410 T^{10} - 61424653939 T^{11} + 496981290961 T^{12} \))(\( 1 + 11 T + 81 T^{2} - 431 T^{3} + 2694 T^{4} + 97288 T^{5} + 1979249 T^{6} + 8658632 T^{7} + 21339174 T^{8} - 303841639 T^{9} + 5082121521 T^{10} + 61424653939 T^{11} + 496981290961 T^{12} \))(\( 1 + 15 T + 45 T^{2} - 669 T^{3} - 9958 T^{4} + 2386 T^{5} + 1055356 T^{6} + 10481535 T^{7} - 61117399 T^{8} - 1680656946 T^{9} - 7549117333 T^{10} + 55601208553 T^{11} + 1192127543653 T^{12} + 4948507561217 T^{13} - 59796558394693 T^{14} - 1184811046564674 T^{15} - 3834642577351159 T^{16} + 58529514556774215 T^{17} + 524492187303437116 T^{18} + 105535965060732194 T^{19} - 39200551327181322598 T^{20} - \)\(23\!\cdots\!21\)\( T^{21} + \)\(14\!\cdots\!45\)\( T^{22} + \)\(41\!\cdots\!35\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 89 T^{2} - 704969 T^{6} - 62742241 T^{8} + 496981290961 T^{12} - 3936588805702081 T^{16} - 350356403707485209 T^{18} + \)\(27\!\cdots\!89\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))
$97$ (\( 1 + 14 T + 97 T^{2} \))(\( 1 + 11 T + 97 T^{2} \))(\( 1 - 11 T + 97 T^{2} \))(\( 1 + 11 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 2 T + 187 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( ( 1 + 13 T + 97 T^{2} )^{2} \))(\( 1 + 2 T + 187 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - T + 214 T^{2} + 83 T^{3} + 20758 T^{4} - 9409 T^{5} + 912673 T^{6} \))(\( ( 1 - 19 T + 268 T^{2} - 1843 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + T + 97 T^{2} )^{4} \))(\( ( 1 - 14 T + 316 T^{2} - 2570 T^{3} + 30652 T^{4} - 131726 T^{5} + 912673 T^{6} )^{4} \))(\( ( 1 - 19 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( 1 + 25 T + 276 T^{2} + 3875 T^{3} + 51767 T^{4} + 375875 T^{5} + 2596884 T^{6} + 22816825 T^{7} + 88529281 T^{8} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 238 T^{2} + 1358 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 16 T + 136 T^{2} - 1045 T^{3} + 13192 T^{4} - 150544 T^{5} + 912673 T^{6} )^{2} \))(\( ( 1 + 160 T^{2} - 469 T^{3} + 15520 T^{4} + 912673 T^{6} )^{2} \))(\( ( 1 + 4 T + 276 T^{2} + 783 T^{3} + 26772 T^{4} + 37636 T^{5} + 912673 T^{6} )^{4} \))(\( 1 + 19 T + 145 T^{2} + 793 T^{3} + 5720 T^{4} - 26012 T^{5} - 1115155 T^{6} - 2523164 T^{7} + 53819480 T^{8} + 723749689 T^{9} + 12836745745 T^{10} + 163159464883 T^{11} + 832972004929 T^{12} \))(\( 1 - 28 T + 379 T^{2} - 3752 T^{3} + 38627 T^{4} - 507626 T^{5} + 6017103 T^{6} - 49239722 T^{7} + 363441443 T^{8} - 3424349096 T^{9} + 33552597499 T^{10} - 240445527196 T^{11} + 832972004929 T^{12} \))(\( 1 - 28 T + 449 T^{2} - 5950 T^{3} + 80095 T^{4} - 914662 T^{5} + 9384215 T^{6} - 88722214 T^{7} + 753613855 T^{8} - 5430404350 T^{9} + 39749647169 T^{10} - 240445527196 T^{11} + 832972004929 T^{12} \))(\( 1 + 2 T - 210 T^{2} - 94 T^{3} + 15760 T^{4} - 228758 T^{5} - 171320 T^{6} + 47974700 T^{7} - 136016753 T^{8} - 4087595515 T^{9} + 36928825634 T^{10} + 142574423991 T^{11} - 5090122960211 T^{12} + 13829719127127 T^{13} + 347463320390306 T^{14} - 3730638061461595 T^{15} - 12041465347044593 T^{16} + 411975072627497900 T^{17} - 142704763884436280 T^{18} - 18483253960644173654 T^{19} + \)\(12\!\cdots\!60\)\( T^{20} - 71461719513529130398 T^{21} - \)\(15\!\cdots\!90\)\( T^{22} + \)\(14\!\cdots\!06\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 14 T + 99 T^{2} + 28 T^{3} - 9211 T^{4} - 131670 T^{5} - 949913 T^{6} - 12771990 T^{7} - 86666299 T^{8} + 25554844 T^{9} + 8764398819 T^{10} + 120222763598 T^{11} + 832972004929 T^{12} )^{2} \))
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