Properties

Label 4018.2
Level 4018
Weight 2
Dimension 157800
Nonzero newspaces 32
Sturm bound 1975680

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Defining parameters

Level: \( N \) = \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1975680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4018))\).

Total New Old
Modular forms 498720 157800 340920
Cusp forms 489121 157800 331321
Eisenstein series 9599 0 9599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4018))\)

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
4018.2.a \(\chi_{4018}(1, \cdot)\) 4018.2.a.a 1 1
4018.2.a.b 1
4018.2.a.c 1
4018.2.a.d 1
4018.2.a.e 1
4018.2.a.f 1
4018.2.a.g 1
4018.2.a.h 1
4018.2.a.i 1
4018.2.a.j 1
4018.2.a.k 1
4018.2.a.l 1
4018.2.a.m 1
4018.2.a.n 1
4018.2.a.o 1
4018.2.a.p 1
4018.2.a.q 1
4018.2.a.r 1
4018.2.a.s 1
4018.2.a.t 2
4018.2.a.u 2
4018.2.a.v 2
4018.2.a.w 2
4018.2.a.x 2
4018.2.a.y 2
4018.2.a.z 2
4018.2.a.ba 2
4018.2.a.bb 2
4018.2.a.bc 2
4018.2.a.bd 3
4018.2.a.be 3
4018.2.a.bf 3
4018.2.a.bg 3
4018.2.a.bh 3
4018.2.a.bi 4
4018.2.a.bj 4
4018.2.a.bk 4
4018.2.a.bl 4
4018.2.a.bm 4
4018.2.a.bn 6
4018.2.a.bo 6
4018.2.a.bp 6
4018.2.a.bq 6
4018.2.a.br 10
4018.2.a.bs 10
4018.2.a.bt 10
4018.2.a.bu 10
4018.2.c \(\chi_{4018}(491, \cdot)\) n/a 144 1
4018.2.e \(\chi_{4018}(165, \cdot)\) n/a 264 2
4018.2.f \(\chi_{4018}(2059, \cdot)\) n/a 286 2
4018.2.h \(\chi_{4018}(1863, \cdot)\) n/a 576 4
4018.2.j \(\chi_{4018}(655, \cdot)\) n/a 280 2
4018.2.l \(\chi_{4018}(575, \cdot)\) n/a 1104 6
4018.2.n \(\chi_{4018}(489, \cdot)\) n/a 560 4
4018.2.o \(\chi_{4018}(687, \cdot)\) n/a 576 4
4018.2.s \(\chi_{4018}(1157, \cdot)\) n/a 560 4
4018.2.u \(\chi_{4018}(1065, \cdot)\) n/a 1176 6
4018.2.w \(\chi_{4018}(961, \cdot)\) n/a 1120 8
4018.2.y \(\chi_{4018}(197, \cdot)\) n/a 1144 8
4018.2.z \(\chi_{4018}(247, \cdot)\) n/a 2256 12
4018.2.ba \(\chi_{4018}(325, \cdot)\) n/a 1120 8
4018.2.bd \(\chi_{4018}(155, \cdot)\) n/a 2352 12
4018.2.bg \(\chi_{4018}(373, \cdot)\) n/a 1120 8
4018.2.bh \(\chi_{4018}(57, \cdot)\) n/a 4704 24
4018.2.bi \(\chi_{4018}(97, \cdot)\) n/a 2240 16
4018.2.bl \(\chi_{4018}(81, \cdot)\) n/a 2352 12
4018.2.bo \(\chi_{4018}(27, \cdot)\) n/a 4704 24
4018.2.bp \(\chi_{4018}(361, \cdot)\) n/a 2240 16
4018.2.bt \(\chi_{4018}(113, \cdot)\) n/a 4704 24
4018.2.bu \(\chi_{4018}(9, \cdot)\) n/a 4704 24
4018.2.bw \(\chi_{4018}(37, \cdot)\) n/a 9408 48
4018.2.by \(\chi_{4018}(19, \cdot)\) n/a 4480 32
4018.2.bz \(\chi_{4018}(43, \cdot)\) n/a 9408 48
4018.2.cb \(\chi_{4018}(3, \cdot)\) n/a 9408 48
4018.2.cd \(\chi_{4018}(23, \cdot)\) n/a 9408 48
4018.2.cg \(\chi_{4018}(13, \cdot)\) n/a 18816 96
4018.2.cj \(\chi_{4018}(39, \cdot)\) n/a 18816 96
4018.2.cl \(\chi_{4018}(17, \cdot)\) n/a 37632 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2009))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))(\( ( 1 - T )^{10} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( ( 1 + T + 3 T^{2} )^{2} \))(\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( 1 + 2 T + 5 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 2 T + 5 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 - 2 T + 5 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 5 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + T^{2} + 4 T^{3} + 3 T^{4} + 27 T^{6} \))(\( 1 + T^{2} - 4 T^{3} + 3 T^{4} + 27 T^{6} \))(\( ( 1 + T + 3 T^{2} )^{3} \))(\( 1 + T + T^{2} + 2 T^{3} + 3 T^{4} + 9 T^{5} + 27 T^{6} \))(\( ( 1 - T + 3 T^{2} )^{3} \))(\( ( 1 + T + 3 T^{2} )^{4} \))(\( 1 - T + 2 T^{2} - 5 T^{3} + 2 T^{4} - 15 T^{5} + 18 T^{6} - 27 T^{7} + 81 T^{8} \))(\( ( 1 - T + 3 T^{2} )^{4} \))(\( 1 + 3 T + 6 T^{2} + 11 T^{3} + 22 T^{4} + 33 T^{5} + 54 T^{6} + 81 T^{7} + 81 T^{8} \))(\( 1 - 3 T + 6 T^{2} - 11 T^{3} + 22 T^{4} - 33 T^{5} + 54 T^{6} - 81 T^{7} + 81 T^{8} \))(\( 1 + T + 7 T^{2} + 10 T^{3} + 33 T^{4} + 41 T^{5} + 122 T^{6} + 123 T^{7} + 297 T^{8} + 270 T^{9} + 567 T^{10} + 243 T^{11} + 729 T^{12} \))(\( 1 - T + 7 T^{2} - 10 T^{3} + 33 T^{4} - 41 T^{5} + 122 T^{6} - 123 T^{7} + 297 T^{8} - 270 T^{9} + 567 T^{10} - 243 T^{11} + 729 T^{12} \))(\( 1 + 4 T + 8 T^{2} + 16 T^{3} + 35 T^{4} + 68 T^{5} + 124 T^{6} + 204 T^{7} + 315 T^{8} + 432 T^{9} + 648 T^{10} + 972 T^{11} + 729 T^{12} \))(\( 1 - 4 T + 8 T^{2} - 16 T^{3} + 35 T^{4} - 68 T^{5} + 124 T^{6} - 204 T^{7} + 315 T^{8} - 432 T^{9} + 648 T^{10} - 972 T^{11} + 729 T^{12} \))(\( 1 + 4 T + 18 T^{2} + 52 T^{3} + 158 T^{4} + 384 T^{5} + 952 T^{6} + 2004 T^{7} + 4229 T^{8} + 7788 T^{9} + 14376 T^{10} + 23364 T^{11} + 38061 T^{12} + 54108 T^{13} + 77112 T^{14} + 93312 T^{15} + 115182 T^{16} + 113724 T^{17} + 118098 T^{18} + 78732 T^{19} + 59049 T^{20} \))(\( 1 - 4 T + 18 T^{2} - 52 T^{3} + 158 T^{4} - 384 T^{5} + 952 T^{6} - 2004 T^{7} + 4229 T^{8} - 7788 T^{9} + 14376 T^{10} - 23364 T^{11} + 38061 T^{12} - 54108 T^{13} + 77112 T^{14} - 93312 T^{15} + 115182 T^{16} - 113724 T^{17} + 118098 T^{18} - 78732 T^{19} + 59049 T^{20} \))(\( 1 + T + 7 T^{2} + 8 T^{3} + 34 T^{4} + 34 T^{5} + 123 T^{6} + 81 T^{7} + 329 T^{8} + 186 T^{9} + 936 T^{10} + 558 T^{11} + 2961 T^{12} + 2187 T^{13} + 9963 T^{14} + 8262 T^{15} + 24786 T^{16} + 17496 T^{17} + 45927 T^{18} + 19683 T^{19} + 59049 T^{20} \))(\( 1 - T + 7 T^{2} - 8 T^{3} + 34 T^{4} - 34 T^{5} + 123 T^{6} - 81 T^{7} + 329 T^{8} - 186 T^{9} + 936 T^{10} - 558 T^{11} + 2961 T^{12} - 2187 T^{13} + 9963 T^{14} - 8262 T^{15} + 24786 T^{16} - 17496 T^{17} + 45927 T^{18} - 19683 T^{19} + 59049 T^{20} \))
$5$ (\( 1 + T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 5 T^{2} + 25 T^{4} \))(\( 1 - T + 2 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 + T + 2 T^{2} + 5 T^{3} + 25 T^{4} \))(\( 1 + 5 T^{2} + 25 T^{4} \))(\( 1 + 2 T + 8 T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T + 3 T^{2} + 10 T^{3} + 25 T^{4} \))(\( ( 1 - T + 5 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( ( 1 + T + 5 T^{2} )^{2} \))(\( 1 - 2 T + 3 T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T + 11 T^{2} + 14 T^{3} + 55 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 11 T^{2} - 14 T^{3} + 55 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 - 4 T + 14 T^{2} - 39 T^{3} + 70 T^{4} - 100 T^{5} + 125 T^{6} \))(\( 1 + T + 9 T^{2} + 12 T^{3} + 45 T^{4} + 25 T^{5} + 125 T^{6} \))(\( 1 + 4 T + 14 T^{2} + 39 T^{3} + 70 T^{4} + 100 T^{5} + 125 T^{6} \))(\( 1 + 3 T + 5 T^{2} - 5 T^{3} - 27 T^{4} - 25 T^{5} + 125 T^{6} + 375 T^{7} + 625 T^{8} \))(\( 1 + 3 T + 8 T^{2} + 5 T^{3} + 2 T^{4} + 25 T^{5} + 200 T^{6} + 375 T^{7} + 625 T^{8} \))(\( 1 - 3 T + 5 T^{2} + 5 T^{3} - 27 T^{4} + 25 T^{5} + 125 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 + 3 T + 16 T^{2} + 37 T^{3} + 116 T^{4} + 185 T^{5} + 400 T^{6} + 375 T^{7} + 625 T^{8} \))(\( 1 - 3 T + 16 T^{2} - 37 T^{3} + 116 T^{4} - 185 T^{5} + 400 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 + 15 T^{2} - T^{3} + 131 T^{4} - 3 T^{5} + 798 T^{6} - 15 T^{7} + 3275 T^{8} - 125 T^{9} + 9375 T^{10} + 15625 T^{12} \))(\( 1 + 15 T^{2} + T^{3} + 131 T^{4} + 3 T^{5} + 798 T^{6} + 15 T^{7} + 3275 T^{8} + 125 T^{9} + 9375 T^{10} + 15625 T^{12} \))(\( 1 + 12 T + 80 T^{2} + 368 T^{3} + 1307 T^{4} + 3772 T^{5} + 9162 T^{6} + 18860 T^{7} + 32675 T^{8} + 46000 T^{9} + 50000 T^{10} + 37500 T^{11} + 15625 T^{12} \))(\( 1 - 12 T + 80 T^{2} - 368 T^{3} + 1307 T^{4} - 3772 T^{5} + 9162 T^{6} - 18860 T^{7} + 32675 T^{8} - 46000 T^{9} + 50000 T^{10} - 37500 T^{11} + 15625 T^{12} \))(\( 1 + 4 T + 30 T^{2} + 104 T^{3} + 426 T^{4} + 1280 T^{5} + 3870 T^{6} + 10220 T^{7} + 25849 T^{8} + 61816 T^{9} + 140242 T^{10} + 309080 T^{11} + 646225 T^{12} + 1277500 T^{13} + 2418750 T^{14} + 4000000 T^{15} + 6656250 T^{16} + 8125000 T^{17} + 11718750 T^{18} + 7812500 T^{19} + 9765625 T^{20} \))(\( 1 - 4 T + 30 T^{2} - 104 T^{3} + 426 T^{4} - 1280 T^{5} + 3870 T^{6} - 10220 T^{7} + 25849 T^{8} - 61816 T^{9} + 140242 T^{10} - 309080 T^{11} + 646225 T^{12} - 1277500 T^{13} + 2418750 T^{14} - 4000000 T^{15} + 6656250 T^{16} - 8125000 T^{17} + 11718750 T^{18} - 7812500 T^{19} + 9765625 T^{20} \))(\( 1 - 2 T + 15 T^{2} - 19 T^{3} + 98 T^{4} - 123 T^{5} + 553 T^{6} - 962 T^{7} + 2643 T^{8} - 5170 T^{9} + 10864 T^{10} - 25850 T^{11} + 66075 T^{12} - 120250 T^{13} + 345625 T^{14} - 384375 T^{15} + 1531250 T^{16} - 1484375 T^{17} + 5859375 T^{18} - 3906250 T^{19} + 9765625 T^{20} \))(\( 1 + 2 T + 15 T^{2} + 19 T^{3} + 98 T^{4} + 123 T^{5} + 553 T^{6} + 962 T^{7} + 2643 T^{8} + 5170 T^{9} + 10864 T^{10} + 25850 T^{11} + 66075 T^{12} + 120250 T^{13} + 345625 T^{14} + 384375 T^{15} + 1531250 T^{16} + 1484375 T^{17} + 5859375 T^{18} + 3906250 T^{19} + 9765625 T^{20} \))
$7$ 1
$11$ (\( 1 + 5 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T^{2} + 121 T^{4} \))(\( 1 + 3 T + 16 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 16 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 2 T^{2} + 121 T^{4} \))(\( 1 + 2 T + 20 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T^{2} + 121 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 27 T^{2} - 46 T^{3} + 297 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( 1 - 2 T + 27 T^{2} - 46 T^{3} + 297 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( 1 + 5 T + 37 T^{2} + 107 T^{3} + 407 T^{4} + 605 T^{5} + 1331 T^{6} \))(\( 1 - 6 T + 35 T^{2} - 112 T^{3} + 385 T^{4} - 726 T^{5} + 1331 T^{6} \))(\( 1 + 5 T + 37 T^{2} + 107 T^{3} + 407 T^{4} + 605 T^{5} + 1331 T^{6} \))(\( 1 + 11 T^{2} - 49 T^{3} + 15 T^{4} - 539 T^{5} + 1331 T^{6} + 14641 T^{8} \))(\( 1 - 4 T + 36 T^{2} - 104 T^{3} + 534 T^{4} - 1144 T^{5} + 4356 T^{6} - 5324 T^{7} + 14641 T^{8} \))(\( 1 + 11 T^{2} - 49 T^{3} + 15 T^{4} - 539 T^{5} + 1331 T^{6} + 14641 T^{8} \))(\( 1 + 24 T^{2} - 10 T^{3} + 294 T^{4} - 110 T^{5} + 2904 T^{6} + 14641 T^{8} \))(\( 1 + 24 T^{2} - 10 T^{3} + 294 T^{4} - 110 T^{5} + 2904 T^{6} + 14641 T^{8} \))(\( 1 - T + 28 T^{2} - 48 T^{3} + 463 T^{4} - 1027 T^{5} + 5388 T^{6} - 11297 T^{7} + 56023 T^{8} - 63888 T^{9} + 409948 T^{10} - 161051 T^{11} + 1771561 T^{12} \))(\( 1 - T + 28 T^{2} - 48 T^{3} + 463 T^{4} - 1027 T^{5} + 5388 T^{6} - 11297 T^{7} + 56023 T^{8} - 63888 T^{9} + 409948 T^{10} - 161051 T^{11} + 1771561 T^{12} \))(\( 1 + 16 T^{2} + 8 T^{3} + 113 T^{4} - 36 T^{5} + 878 T^{6} - 396 T^{7} + 13673 T^{8} + 10648 T^{9} + 234256 T^{10} + 1771561 T^{12} \))(\( 1 + 16 T^{2} + 8 T^{3} + 113 T^{4} - 36 T^{5} + 878 T^{6} - 396 T^{7} + 13673 T^{8} + 10648 T^{9} + 234256 T^{10} + 1771561 T^{12} \))(\( 1 - 4 T + 56 T^{2} - 212 T^{3} + 1703 T^{4} - 5724 T^{5} + 35078 T^{6} - 105956 T^{7} + 541704 T^{8} - 1474696 T^{9} + 6642204 T^{10} - 16221656 T^{11} + 65546184 T^{12} - 141027436 T^{13} + 513576998 T^{14} - 921855924 T^{15} + 3016968383 T^{16} - 4131280252 T^{17} + 12004097336 T^{18} - 9431790764 T^{19} + 25937424601 T^{20} \))(\( 1 - 4 T + 56 T^{2} - 212 T^{3} + 1703 T^{4} - 5724 T^{5} + 35078 T^{6} - 105956 T^{7} + 541704 T^{8} - 1474696 T^{9} + 6642204 T^{10} - 16221656 T^{11} + 65546184 T^{12} - 141027436 T^{13} + 513576998 T^{14} - 921855924 T^{15} + 3016968383 T^{16} - 4131280252 T^{17} + 12004097336 T^{18} - 9431790764 T^{19} + 25937424601 T^{20} \))(\( 1 - 11 T + 104 T^{2} - 674 T^{3} + 4072 T^{4} - 20390 T^{5} + 97692 T^{6} - 410335 T^{7} + 1657881 T^{8} - 5996712 T^{9} + 20946088 T^{10} - 65963832 T^{11} + 200603601 T^{12} - 546155885 T^{13} + 1430308572 T^{14} - 3283829890 T^{15} + 7213796392 T^{16} - 13134353254 T^{17} + 22293323624 T^{18} - 25937424601 T^{19} + 25937424601 T^{20} \))(\( 1 - 11 T + 104 T^{2} - 674 T^{3} + 4072 T^{4} - 20390 T^{5} + 97692 T^{6} - 410335 T^{7} + 1657881 T^{8} - 5996712 T^{9} + 20946088 T^{10} - 65963832 T^{11} + 200603601 T^{12} - 546155885 T^{13} + 1430308572 T^{14} - 3283829890 T^{15} + 7213796392 T^{16} - 13134353254 T^{17} + 22293323624 T^{18} - 25937424601 T^{19} + 25937424601 T^{20} \))
$13$ (\( 1 - 6 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 4 T + 10 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 5 T + 24 T^{2} - 65 T^{3} + 169 T^{4} \))(\( 1 + 5 T + 24 T^{2} + 65 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 10 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 28 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 12 T^{2} + 52 T^{3} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 4 T + 12 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 28 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 2 T + 23 T^{2} - 56 T^{3} + 299 T^{4} - 338 T^{5} + 2197 T^{6} \))(\( 1 + 2 T + 23 T^{2} + 56 T^{3} + 299 T^{4} + 338 T^{5} + 2197 T^{6} \))(\( 1 - T + 14 T^{2} + 23 T^{3} + 182 T^{4} - 169 T^{5} + 2197 T^{6} \))(\( ( 1 + 13 T^{2} )^{3} \))(\( 1 + T + 14 T^{2} - 23 T^{3} + 182 T^{4} + 169 T^{5} + 2197 T^{6} \))(\( 1 - T + 25 T^{2} - 14 T^{3} + 434 T^{4} - 182 T^{5} + 4225 T^{6} - 2197 T^{7} + 28561 T^{8} \))(\( 1 - 6 T + 44 T^{2} - 170 T^{3} + 774 T^{4} - 2210 T^{5} + 7436 T^{6} - 13182 T^{7} + 28561 T^{8} \))(\( 1 + T + 25 T^{2} + 14 T^{3} + 434 T^{4} + 182 T^{5} + 4225 T^{6} + 2197 T^{7} + 28561 T^{8} \))(\( 1 + 10 T + 72 T^{2} + 354 T^{3} + 1478 T^{4} + 4602 T^{5} + 12168 T^{6} + 21970 T^{7} + 28561 T^{8} \))(\( 1 - 10 T + 72 T^{2} - 354 T^{3} + 1478 T^{4} - 4602 T^{5} + 12168 T^{6} - 21970 T^{7} + 28561 T^{8} \))(\( 1 + 4 T + 53 T^{2} + 130 T^{3} + 1064 T^{4} + 1632 T^{5} + 14139 T^{6} + 21216 T^{7} + 179816 T^{8} + 285610 T^{9} + 1513733 T^{10} + 1485172 T^{11} + 4826809 T^{12} \))(\( 1 - 4 T + 53 T^{2} - 130 T^{3} + 1064 T^{4} - 1632 T^{5} + 14139 T^{6} - 21216 T^{7} + 179816 T^{8} - 285610 T^{9} + 1513733 T^{10} - 1485172 T^{11} + 4826809 T^{12} \))(\( 1 + 8 T + 72 T^{2} + 404 T^{3} + 2275 T^{4} + 9484 T^{5} + 38732 T^{6} + 123292 T^{7} + 384475 T^{8} + 887588 T^{9} + 2056392 T^{10} + 2970344 T^{11} + 4826809 T^{12} \))(\( 1 - 8 T + 72 T^{2} - 404 T^{3} + 2275 T^{4} - 9484 T^{5} + 38732 T^{6} - 123292 T^{7} + 384475 T^{8} - 887588 T^{9} + 2056392 T^{10} - 2970344 T^{11} + 4826809 T^{12} \))(\( 1 + 4 T + 84 T^{2} + 376 T^{3} + 3589 T^{4} + 16004 T^{5} + 102524 T^{6} + 415772 T^{7} + 2114898 T^{8} + 7444340 T^{9} + 32048656 T^{10} + 96776420 T^{11} + 357417762 T^{12} + 913451084 T^{13} + 2928187964 T^{14} + 5942173172 T^{15} + 17323417501 T^{16} + 23593442392 T^{17} + 68521380564 T^{18} + 42417997492 T^{19} + 137858491849 T^{20} \))(\( 1 - 4 T + 84 T^{2} - 376 T^{3} + 3589 T^{4} - 16004 T^{5} + 102524 T^{6} - 415772 T^{7} + 2114898 T^{8} - 7444340 T^{9} + 32048656 T^{10} - 96776420 T^{11} + 357417762 T^{12} - 913451084 T^{13} + 2928187964 T^{14} - 5942173172 T^{15} + 17323417501 T^{16} - 23593442392 T^{17} + 68521380564 T^{18} - 42417997492 T^{19} + 137858491849 T^{20} \))(\( 1 + 4 T + 31 T^{2} + 162 T^{3} + 1170 T^{4} + 4680 T^{5} + 23727 T^{6} + 95988 T^{7} + 468201 T^{8} + 1570950 T^{9} + 6225084 T^{10} + 20422350 T^{11} + 79125969 T^{12} + 210885636 T^{13} + 677666847 T^{14} + 1737651240 T^{15} + 5647366530 T^{16} + 10165259754 T^{17} + 25287652351 T^{18} + 42417997492 T^{19} + 137858491849 T^{20} \))(\( 1 - 4 T + 31 T^{2} - 162 T^{3} + 1170 T^{4} - 4680 T^{5} + 23727 T^{6} - 95988 T^{7} + 468201 T^{8} - 1570950 T^{9} + 6225084 T^{10} - 20422350 T^{11} + 79125969 T^{12} - 210885636 T^{13} + 677666847 T^{14} - 1737651240 T^{15} + 5647366530 T^{16} - 10165259754 T^{17} + 25287652351 T^{18} - 42417997492 T^{19} + 137858491849 T^{20} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( 1 + 2 T + 2 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( 1 + 2 T + 27 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 + 10 T + 51 T^{2} + 170 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 6 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 10 T + 51 T^{2} - 170 T^{3} + 289 T^{4} \))(\( 1 - 2 T + 27 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 12 T + 91 T^{2} + 436 T^{3} + 1547 T^{4} + 3468 T^{5} + 4913 T^{6} \))(\( 1 - 12 T + 91 T^{2} - 436 T^{3} + 1547 T^{4} - 3468 T^{5} + 4913 T^{6} \))(\( 1 + 5 T + 39 T^{2} + 107 T^{3} + 663 T^{4} + 1445 T^{5} + 4913 T^{6} \))(\( 1 - 7 T + 59 T^{2} - 230 T^{3} + 1003 T^{4} - 2023 T^{5} + 4913 T^{6} \))(\( 1 - 5 T + 39 T^{2} - 107 T^{3} + 663 T^{4} - 1445 T^{5} + 4913 T^{6} \))(\( 1 - 3 T + 26 T^{2} - 62 T^{3} + 354 T^{4} - 1054 T^{5} + 7514 T^{6} - 14739 T^{7} + 83521 T^{8} \))(\( 1 - T + 10 T^{2} - 23 T^{3} - 86 T^{4} - 391 T^{5} + 2890 T^{6} - 4913 T^{7} + 83521 T^{8} \))(\( 1 + 3 T + 26 T^{2} + 62 T^{3} + 354 T^{4} + 1054 T^{5} + 7514 T^{6} + 14739 T^{7} + 83521 T^{8} \))(\( 1 - T + 36 T^{2} - 115 T^{3} + 618 T^{4} - 1955 T^{5} + 10404 T^{6} - 4913 T^{7} + 83521 T^{8} \))(\( 1 + T + 36 T^{2} + 115 T^{3} + 618 T^{4} + 1955 T^{5} + 10404 T^{6} + 4913 T^{7} + 83521 T^{8} \))(\( 1 - T + 86 T^{2} - 90 T^{3} + 3291 T^{4} - 3133 T^{5} + 71976 T^{6} - 53261 T^{7} + 951099 T^{8} - 442170 T^{9} + 7182806 T^{10} - 1419857 T^{11} + 24137569 T^{12} \))(\( 1 + T + 86 T^{2} + 90 T^{3} + 3291 T^{4} + 3133 T^{5} + 71976 T^{6} + 53261 T^{7} + 951099 T^{8} + 442170 T^{9} + 7182806 T^{10} + 1419857 T^{11} + 24137569 T^{12} \))(\( 1 + 16 T + 156 T^{2} + 1092 T^{3} + 6311 T^{4} + 31084 T^{5} + 136444 T^{6} + 528428 T^{7} + 1823879 T^{8} + 5364996 T^{9} + 13029276 T^{10} + 22717712 T^{11} + 24137569 T^{12} \))(\( 1 - 16 T + 156 T^{2} - 1092 T^{3} + 6311 T^{4} - 31084 T^{5} + 136444 T^{6} - 528428 T^{7} + 1823879 T^{8} - 5364996 T^{9} + 13029276 T^{10} - 22717712 T^{11} + 24137569 T^{12} \))(\( 1 + 20 T + 270 T^{2} + 2732 T^{3} + 23170 T^{4} + 168248 T^{5} + 1082200 T^{6} + 6215012 T^{7} + 32344925 T^{8} + 152774628 T^{9} + 659622840 T^{10} + 2597168676 T^{11} + 9347683325 T^{12} + 30534353956 T^{13} + 90386426200 T^{14} + 238888100536 T^{15} + 559267473730 T^{16} + 1121045254636 T^{17} + 1883454509070 T^{18} + 2371757529940 T^{19} + 2015993900449 T^{20} \))(\( 1 - 20 T + 270 T^{2} - 2732 T^{3} + 23170 T^{4} - 168248 T^{5} + 1082200 T^{6} - 6215012 T^{7} + 32344925 T^{8} - 152774628 T^{9} + 659622840 T^{10} - 2597168676 T^{11} + 9347683325 T^{12} - 30534353956 T^{13} + 90386426200 T^{14} - 238888100536 T^{15} + 559267473730 T^{16} - 1121045254636 T^{17} + 1883454509070 T^{18} - 2371757529940 T^{19} + 2015993900449 T^{20} \))(\( 1 + 5 T + 118 T^{2} + 490 T^{3} + 6751 T^{4} + 24171 T^{5} + 248640 T^{6} + 778673 T^{7} + 6536080 T^{8} + 17936741 T^{9} + 127993012 T^{10} + 304924597 T^{11} + 1888927120 T^{12} + 3825620449 T^{13} + 20766661440 T^{14} + 34319363547 T^{15} + 162952728319 T^{16} + 201065949770 T^{17} + 823139378038 T^{18} + 592939382485 T^{19} + 2015993900449 T^{20} \))(\( 1 - 5 T + 118 T^{2} - 490 T^{3} + 6751 T^{4} - 24171 T^{5} + 248640 T^{6} - 778673 T^{7} + 6536080 T^{8} - 17936741 T^{9} + 127993012 T^{10} - 304924597 T^{11} + 1888927120 T^{12} - 3825620449 T^{13} + 20766661440 T^{14} - 34319363547 T^{15} + 162952728319 T^{16} - 201065949770 T^{17} + 823139378038 T^{18} - 592939382485 T^{19} + 2015993900449 T^{20} \))
$19$ (\( 1 - T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( 1 - 5 T + 36 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 + 5 T + 36 T^{2} + 95 T^{3} + 361 T^{4} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 - 8 T + 52 T^{2} - 152 T^{3} + 361 T^{4} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 45 T^{2} + 116 T^{3} + 855 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 - 4 T + 45 T^{2} - 116 T^{3} + 855 T^{4} - 1444 T^{5} + 6859 T^{6} \))(\( 1 - 3 T + 33 T^{2} - 141 T^{3} + 627 T^{4} - 1083 T^{5} + 6859 T^{6} \))(\( 1 + 4 T + 29 T^{2} + 120 T^{3} + 551 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 + 3 T + 33 T^{2} + 141 T^{3} + 627 T^{4} + 1083 T^{5} + 6859 T^{6} \))(\( 1 + 2 T + 13 T^{2} + 63 T^{3} + 453 T^{4} + 1197 T^{5} + 4693 T^{6} + 13718 T^{7} + 130321 T^{8} \))(\( 1 + 2 T + 56 T^{2} + 106 T^{3} + 1438 T^{4} + 2014 T^{5} + 20216 T^{6} + 13718 T^{7} + 130321 T^{8} \))(\( 1 - 2 T + 13 T^{2} - 63 T^{3} + 453 T^{4} - 1197 T^{5} + 4693 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( 1 + 14 T + 132 T^{2} + 858 T^{3} + 4310 T^{4} + 16302 T^{5} + 47652 T^{6} + 96026 T^{7} + 130321 T^{8} \))(\( 1 - 14 T + 132 T^{2} - 858 T^{3} + 4310 T^{4} - 16302 T^{5} + 47652 T^{6} - 96026 T^{7} + 130321 T^{8} \))(\( 1 - 3 T + 58 T^{2} - 272 T^{3} + 2021 T^{4} - 8421 T^{5} + 49416 T^{6} - 159999 T^{7} + 729581 T^{8} - 1865648 T^{9} + 7558618 T^{10} - 7428297 T^{11} + 47045881 T^{12} \))(\( 1 + 3 T + 58 T^{2} + 272 T^{3} + 2021 T^{4} + 8421 T^{5} + 49416 T^{6} + 159999 T^{7} + 729581 T^{8} + 1865648 T^{9} + 7558618 T^{10} + 7428297 T^{11} + 47045881 T^{12} \))(\( 1 + 12 T + 128 T^{2} + 952 T^{3} + 6203 T^{4} + 32708 T^{5} + 157212 T^{6} + 621452 T^{7} + 2239283 T^{8} + 6529768 T^{9} + 16681088 T^{10} + 29713188 T^{11} + 47045881 T^{12} \))(\( 1 - 12 T + 128 T^{2} - 952 T^{3} + 6203 T^{4} - 32708 T^{5} + 157212 T^{6} - 621452 T^{7} + 2239283 T^{8} - 6529768 T^{9} + 16681088 T^{10} - 29713188 T^{11} + 47045881 T^{12} \))(\( 1 + 56 T^{2} - 220 T^{3} + 1745 T^{4} - 11364 T^{5} + 65212 T^{6} - 305044 T^{7} + 1873190 T^{8} - 7472140 T^{9} + 38409720 T^{10} - 141970660 T^{11} + 676221590 T^{12} - 2092296796 T^{13} + 8498493052 T^{14} - 28138389036 T^{15} + 82095062345 T^{16} - 196651782580 T^{17} + 951079530296 T^{18} + 6131066257801 T^{20} \))(\( 1 + 56 T^{2} + 220 T^{3} + 1745 T^{4} + 11364 T^{5} + 65212 T^{6} + 305044 T^{7} + 1873190 T^{8} + 7472140 T^{9} + 38409720 T^{10} + 141970660 T^{11} + 676221590 T^{12} + 2092296796 T^{13} + 8498493052 T^{14} + 28138389036 T^{15} + 82095062345 T^{16} + 196651782580 T^{17} + 951079530296 T^{18} + 6131066257801 T^{20} \))(\( 1 - T + 120 T^{2} - 160 T^{3} + 7208 T^{4} - 10476 T^{5} + 284244 T^{6} - 412117 T^{7} + 8125861 T^{8} - 11020860 T^{9} + 176144404 T^{10} - 209396340 T^{11} + 2933435821 T^{12} - 2826710503 T^{13} + 37042962324 T^{14} - 25939613124 T^{15} + 339106710248 T^{16} - 143019478240 T^{17} + 2038027564920 T^{18} - 322687697779 T^{19} + 6131066257801 T^{20} \))(\( 1 + T + 120 T^{2} + 160 T^{3} + 7208 T^{4} + 10476 T^{5} + 284244 T^{6} + 412117 T^{7} + 8125861 T^{8} + 11020860 T^{9} + 176144404 T^{10} + 209396340 T^{11} + 2933435821 T^{12} + 2826710503 T^{13} + 37042962324 T^{14} + 25939613124 T^{15} + 339106710248 T^{16} + 143019478240 T^{17} + 2038027564920 T^{18} + 322687697779 T^{19} + 6131066257801 T^{20} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 8 T + 42 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 22 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 22 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 184 T^{3} + 529 T^{4} \))(\( ( 1 + 2 T + 23 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 529 T^{4} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 529 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 76 T^{3} + 759 T^{4} + 4232 T^{5} + 12167 T^{6} \))(\( 1 + 8 T + 33 T^{2} + 76 T^{3} + 759 T^{4} + 4232 T^{5} + 12167 T^{6} \))(\( 1 + 9 T + 57 T^{2} + 335 T^{3} + 1311 T^{4} + 4761 T^{5} + 12167 T^{6} \))(\( 1 - 4 T + 49 T^{2} - 120 T^{3} + 1127 T^{4} - 2116 T^{5} + 12167 T^{6} \))(\( 1 + 9 T + 57 T^{2} + 335 T^{3} + 1311 T^{4} + 4761 T^{5} + 12167 T^{6} \))(\( 1 + 9 T + 86 T^{2} + 440 T^{3} + 2670 T^{4} + 10120 T^{5} + 45494 T^{6} + 109503 T^{7} + 279841 T^{8} \))(\( 1 - 6 T + 84 T^{2} - 350 T^{3} + 2774 T^{4} - 8050 T^{5} + 44436 T^{6} - 73002 T^{7} + 279841 T^{8} \))(\( 1 + 9 T + 86 T^{2} + 440 T^{3} + 2670 T^{4} + 10120 T^{5} + 45494 T^{6} + 109503 T^{7} + 279841 T^{8} \))(\( 1 + 4 T + 52 T^{2} + 208 T^{3} + 1366 T^{4} + 4784 T^{5} + 27508 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 + 4 T + 52 T^{2} + 208 T^{3} + 1366 T^{4} + 4784 T^{5} + 27508 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 - 21 T + 286 T^{2} - 2780 T^{3} + 21501 T^{4} - 135231 T^{5} + 710192 T^{6} - 3110313 T^{7} + 11374029 T^{8} - 33824260 T^{9} + 80034526 T^{10} - 135163203 T^{11} + 148035889 T^{12} \))(\( 1 - 21 T + 286 T^{2} - 2780 T^{3} + 21501 T^{4} - 135231 T^{5} + 710192 T^{6} - 3110313 T^{7} + 11374029 T^{8} - 33824260 T^{9} + 80034526 T^{10} - 135163203 T^{11} + 148035889 T^{12} \))(\( 1 - 12 T + 134 T^{2} - 992 T^{3} + 7183 T^{4} - 40036 T^{5} + 214808 T^{6} - 920828 T^{7} + 3799807 T^{8} - 12069664 T^{9} + 37498694 T^{10} - 77236116 T^{11} + 148035889 T^{12} \))(\( 1 - 12 T + 134 T^{2} - 992 T^{3} + 7183 T^{4} - 40036 T^{5} + 214808 T^{6} - 920828 T^{7} + 3799807 T^{8} - 12069664 T^{9} + 37498694 T^{10} - 77236116 T^{11} + 148035889 T^{12} \))(\( 1 - 4 T + 154 T^{2} - 704 T^{3} + 11405 T^{4} - 54132 T^{5} + 550428 T^{6} - 2477604 T^{7} + 19320594 T^{8} - 77660236 T^{9} + 510605492 T^{10} - 1786185428 T^{11} + 10220594226 T^{12} - 30145007868 T^{13} + 154032321948 T^{14} - 348412119276 T^{15} + 1688349314045 T^{16} - 2396997114688 T^{17} + 12059891733274 T^{18} - 7204610645852 T^{19} + 41426511213649 T^{20} \))(\( 1 - 4 T + 154 T^{2} - 704 T^{3} + 11405 T^{4} - 54132 T^{5} + 550428 T^{6} - 2477604 T^{7} + 19320594 T^{8} - 77660236 T^{9} + 510605492 T^{10} - 1786185428 T^{11} + 10220594226 T^{12} - 30145007868 T^{13} + 154032321948 T^{14} - 348412119276 T^{15} + 1688349314045 T^{16} - 2396997114688 T^{17} + 12059891733274 T^{18} - 7204610645852 T^{19} + 41426511213649 T^{20} \))(\( 1 - 9 T + 168 T^{2} - 1090 T^{3} + 12175 T^{4} - 62579 T^{5} + 541580 T^{6} - 2324207 T^{7} + 17335456 T^{8} - 65014125 T^{9} + 439664024 T^{10} - 1495324875 T^{11} + 9170456224 T^{12} - 28278626569 T^{13} + 151556288780 T^{14} - 402779908597 T^{15} + 1802336948575 T^{16} - 3711259737230 T^{17} + 13156245527208 T^{18} - 16210373953167 T^{19} + 41426511213649 T^{20} \))(\( 1 - 9 T + 168 T^{2} - 1090 T^{3} + 12175 T^{4} - 62579 T^{5} + 541580 T^{6} - 2324207 T^{7} + 17335456 T^{8} - 65014125 T^{9} + 439664024 T^{10} - 1495324875 T^{11} + 9170456224 T^{12} - 28278626569 T^{13} + 151556288780 T^{14} - 402779908597 T^{15} + 1802336948575 T^{16} - 3711259737230 T^{17} + 13156245527208 T^{18} - 16210373953167 T^{19} + 41426511213649 T^{20} \))
$29$ (\( 1 + 8 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 8 T + 69 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 3 T - 14 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 3 T - 14 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 69 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 2 T - 16 T^{2} - 58 T^{3} + 841 T^{4} \))(\( ( 1 + 5 T + 29 T^{2} )^{2} \))(\( 1 - 2 T + 51 T^{2} - 58 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 2 T + 51 T^{2} - 58 T^{3} + 841 T^{4} \))(\( ( 1 + 5 T + 29 T^{2} )^{2} \))(\( 1 + 13 T^{2} - 66 T^{3} + 377 T^{4} + 24389 T^{6} \))(\( 1 + 13 T^{2} - 66 T^{3} + 377 T^{4} + 24389 T^{6} \))(\( 1 + 12 T + 108 T^{2} + 599 T^{3} + 3132 T^{4} + 10092 T^{5} + 24389 T^{6} \))(\( 1 - 5 T + 89 T^{2} - 280 T^{3} + 2581 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 + 12 T + 108 T^{2} + 599 T^{3} + 3132 T^{4} + 10092 T^{5} + 24389 T^{6} \))(\( 1 + 18 T + 215 T^{2} + 1689 T^{3} + 10572 T^{4} + 48981 T^{5} + 180815 T^{6} + 439002 T^{7} + 707281 T^{8} \))(\( 1 - 17 T + 178 T^{2} - 1231 T^{3} + 7294 T^{4} - 35699 T^{5} + 149698 T^{6} - 414613 T^{7} + 707281 T^{8} \))(\( 1 + 18 T + 215 T^{2} + 1689 T^{3} + 10572 T^{4} + 48981 T^{5} + 180815 T^{6} + 439002 T^{7} + 707281 T^{8} \))(\( 1 + 3 T + 94 T^{2} + 259 T^{3} + 3776 T^{4} + 7511 T^{5} + 79054 T^{6} + 73167 T^{7} + 707281 T^{8} \))(\( 1 + 3 T + 94 T^{2} + 259 T^{3} + 3776 T^{4} + 7511 T^{5} + 79054 T^{6} + 73167 T^{7} + 707281 T^{8} \))(\( 1 - 5 T + 158 T^{2} - 624 T^{3} + 10767 T^{4} - 33725 T^{5} + 407883 T^{6} - 978025 T^{7} + 9055047 T^{8} - 15218736 T^{9} + 111750398 T^{10} - 102555745 T^{11} + 594823321 T^{12} \))(\( 1 - 5 T + 158 T^{2} - 624 T^{3} + 10767 T^{4} - 33725 T^{5} + 407883 T^{6} - 978025 T^{7} + 9055047 T^{8} - 15218736 T^{9} + 111750398 T^{10} - 102555745 T^{11} + 594823321 T^{12} \))(\( 1 + 96 T^{2} + 48 T^{3} + 4853 T^{4} + 3300 T^{5} + 165406 T^{6} + 95700 T^{7} + 4081373 T^{8} + 1170672 T^{9} + 67898976 T^{10} + 594823321 T^{12} \))(\( 1 + 96 T^{2} + 48 T^{3} + 4853 T^{4} + 3300 T^{5} + 165406 T^{6} + 95700 T^{7} + 4081373 T^{8} + 1170672 T^{9} + 67898976 T^{10} + 594823321 T^{12} \))(\( 1 + 4 T + 154 T^{2} + 676 T^{3} + 12796 T^{4} + 54880 T^{5} + 736946 T^{6} + 2928168 T^{7} + 31527057 T^{8} + 113549636 T^{9} + 1036422246 T^{10} + 3292939444 T^{11} + 26514254937 T^{12} + 71415089352 T^{13} + 521227903826 T^{14} + 1125651857120 T^{15} + 7611359215516 T^{16} + 11660916384884 T^{17} + 77037947595994 T^{18} + 58028583903476 T^{19} + 420707233300201 T^{20} \))(\( 1 + 4 T + 154 T^{2} + 676 T^{3} + 12796 T^{4} + 54880 T^{5} + 736946 T^{6} + 2928168 T^{7} + 31527057 T^{8} + 113549636 T^{9} + 1036422246 T^{10} + 3292939444 T^{11} + 26514254937 T^{12} + 71415089352 T^{13} + 521227903826 T^{14} + 1125651857120 T^{15} + 7611359215516 T^{16} + 11660916384884 T^{17} + 77037947595994 T^{18} + 58028583903476 T^{19} + 420707233300201 T^{20} \))(\( 1 - 23 T + 408 T^{2} - 5128 T^{3} + 55655 T^{4} - 506987 T^{5} + 4175621 T^{6} - 30484005 T^{7} + 205212340 T^{8} - 1249333725 T^{9} + 7057521630 T^{10} - 36230678025 T^{11} + 172583577940 T^{12} - 743474397945 T^{13} + 2953337396501 T^{14} - 10398885898063 T^{15} + 33104891930255 T^{16} - 88457365712552 T^{17} + 204100536488088 T^{18} - 333664357444987 T^{19} + 420707233300201 T^{20} \))(\( 1 - 23 T + 408 T^{2} - 5128 T^{3} + 55655 T^{4} - 506987 T^{5} + 4175621 T^{6} - 30484005 T^{7} + 205212340 T^{8} - 1249333725 T^{9} + 7057521630 T^{10} - 36230678025 T^{11} + 172583577940 T^{12} - 743474397945 T^{13} + 2953337396501 T^{14} - 10398885898063 T^{15} + 33104891930255 T^{16} - 88457365712552 T^{17} + 204100536488088 T^{18} - 333664357444987 T^{19} + 420707233300201 T^{20} \))
$31$ (\( 1 - 6 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 8 T + 73 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 38 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 38 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 73 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 - 14 T + 109 T^{2} - 434 T^{3} + 961 T^{4} \))(\( 1 + 14 T + 109 T^{2} + 434 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 70 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 14 T + 109 T^{2} - 434 T^{3} + 961 T^{4} \))(\( 1 + 14 T + 109 T^{2} + 434 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 97 T^{2} + 612 T^{3} + 3007 T^{4} + 9610 T^{5} + 29791 T^{6} \))(\( 1 - 10 T + 97 T^{2} - 612 T^{3} + 3007 T^{4} - 9610 T^{5} + 29791 T^{6} \))(\( 1 + 11 T + 116 T^{2} + 671 T^{3} + 3596 T^{4} + 10571 T^{5} + 29791 T^{6} \))(\( 1 + 7 T + 101 T^{2} + 426 T^{3} + 3131 T^{4} + 6727 T^{5} + 29791 T^{6} \))(\( 1 - 11 T + 116 T^{2} - 671 T^{3} + 3596 T^{4} - 10571 T^{5} + 29791 T^{6} \))(\( 1 - 19 T + 205 T^{2} - 1484 T^{3} + 8978 T^{4} - 46004 T^{5} + 197005 T^{6} - 566029 T^{7} + 923521 T^{8} \))(\( 1 + 5 T + 68 T^{2} + 289 T^{3} + 2326 T^{4} + 8959 T^{5} + 65348 T^{6} + 148955 T^{7} + 923521 T^{8} \))(\( 1 + 19 T + 205 T^{2} + 1484 T^{3} + 8978 T^{4} + 46004 T^{5} + 197005 T^{6} + 566029 T^{7} + 923521 T^{8} \))(\( 1 + 3 T + 102 T^{2} + 251 T^{3} + 4394 T^{4} + 7781 T^{5} + 98022 T^{6} + 89373 T^{7} + 923521 T^{8} \))(\( 1 - 3 T + 102 T^{2} - 251 T^{3} + 4394 T^{4} - 7781 T^{5} + 98022 T^{6} - 89373 T^{7} + 923521 T^{8} \))(\( 1 + 3 T + 133 T^{2} + 238 T^{3} + 7871 T^{4} + 8247 T^{5} + 291654 T^{6} + 255657 T^{7} + 7564031 T^{8} + 7090258 T^{9} + 122828293 T^{10} + 85887453 T^{11} + 887503681 T^{12} \))(\( 1 - 3 T + 133 T^{2} - 238 T^{3} + 7871 T^{4} - 8247 T^{5} + 291654 T^{6} - 255657 T^{7} + 7564031 T^{8} - 7090258 T^{9} + 122828293 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( 1 - 4 T + 96 T^{2} - 492 T^{3} + 5139 T^{4} - 23896 T^{5} + 194656 T^{6} - 740776 T^{7} + 4938579 T^{8} - 14657172 T^{9} + 88658016 T^{10} - 114516604 T^{11} + 887503681 T^{12} \))(\( 1 + 4 T + 96 T^{2} + 492 T^{3} + 5139 T^{4} + 23896 T^{5} + 194656 T^{6} + 740776 T^{7} + 4938579 T^{8} + 14657172 T^{9} + 88658016 T^{10} + 114516604 T^{11} + 887503681 T^{12} \))(\( 1 - 4 T + 198 T^{2} - 508 T^{3} + 17854 T^{4} - 24492 T^{5} + 1008216 T^{6} - 396612 T^{7} + 41612613 T^{8} + 8285408 T^{9} + 1397476804 T^{10} + 256847648 T^{11} + 39989721093 T^{12} - 11815468092 T^{13} + 931108648536 T^{14} - 701185166292 T^{15} + 15845490720574 T^{16} - 13976407968388 T^{17} + 168872425413318 T^{18} - 105758488642684 T^{19} + 819628286980801 T^{20} \))(\( 1 + 4 T + 198 T^{2} + 508 T^{3} + 17854 T^{4} + 24492 T^{5} + 1008216 T^{6} + 396612 T^{7} + 41612613 T^{8} - 8285408 T^{9} + 1397476804 T^{10} - 256847648 T^{11} + 39989721093 T^{12} + 11815468092 T^{13} + 931108648536 T^{14} + 701185166292 T^{15} + 15845490720574 T^{16} + 13976407968388 T^{17} + 168872425413318 T^{18} + 105758488642684 T^{19} + 819628286980801 T^{20} \))(\( 1 - 5 T + 157 T^{2} - 710 T^{3} + 11877 T^{4} - 47207 T^{5} + 617020 T^{6} - 2225635 T^{7} + 25547802 T^{8} - 86657629 T^{9} + 872978638 T^{10} - 2686386499 T^{11} + 24551437722 T^{12} - 66303892285 T^{13} + 569830927420 T^{14} - 1351496331257 T^{15} + 10540881219237 T^{16} - 19533956018810 T^{17} + 133903892878237 T^{18} - 132198110803355 T^{19} + 819628286980801 T^{20} \))(\( 1 + 5 T + 157 T^{2} + 710 T^{3} + 11877 T^{4} + 47207 T^{5} + 617020 T^{6} + 2225635 T^{7} + 25547802 T^{8} + 86657629 T^{9} + 872978638 T^{10} + 2686386499 T^{11} + 24551437722 T^{12} + 66303892285 T^{13} + 569830927420 T^{14} + 1351496331257 T^{15} + 10540881219237 T^{16} + 19533956018810 T^{17} + 133903892878237 T^{18} + 132198110803355 T^{19} + 819628286980801 T^{20} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 8 T + 70 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( 1 + 8 T + 70 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 30 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 16 T + 136 T^{2} - 592 T^{3} + 1369 T^{4} \))(\( 1 + 72 T^{2} + 1369 T^{4} \))(\( 1 + 2 T^{2} + 1369 T^{4} \))(\( 1 + 72 T^{2} + 1369 T^{4} \))(\( 1 - 16 T + 136 T^{2} - 592 T^{3} + 1369 T^{4} \))(\( 1 - 18 T + 187 T^{2} - 1324 T^{3} + 6919 T^{4} - 24642 T^{5} + 50653 T^{6} \))(\( 1 - 18 T + 187 T^{2} - 1324 T^{3} + 6919 T^{4} - 24642 T^{5} + 50653 T^{6} \))(\( 1 + 18 T + 210 T^{2} + 1493 T^{3} + 7770 T^{4} + 24642 T^{5} + 50653 T^{6} \))(\( ( 1 - 2 T + 37 T^{2} )^{3} \))(\( 1 + 18 T + 210 T^{2} + 1493 T^{3} + 7770 T^{4} + 24642 T^{5} + 50653 T^{6} \))(\( 1 - 2 T + 55 T^{2} + 61 T^{3} + 2110 T^{4} + 2257 T^{5} + 75295 T^{6} - 101306 T^{7} + 1874161 T^{8} \))(\( 1 + 6 T + 120 T^{2} + 546 T^{3} + 6174 T^{4} + 20202 T^{5} + 164280 T^{6} + 303918 T^{7} + 1874161 T^{8} \))(\( 1 - 2 T + 55 T^{2} + 61 T^{3} + 2110 T^{4} + 2257 T^{5} + 75295 T^{6} - 101306 T^{7} + 1874161 T^{8} \))(\( 1 + 14 T + 184 T^{2} + 1434 T^{3} + 10654 T^{4} + 53058 T^{5} + 251896 T^{6} + 709142 T^{7} + 1874161 T^{8} \))(\( 1 + 14 T + 184 T^{2} + 1434 T^{3} + 10654 T^{4} + 53058 T^{5} + 251896 T^{6} + 709142 T^{7} + 1874161 T^{8} \))(\( 1 + 2 T + 81 T^{2} + 293 T^{3} + 4297 T^{4} + 15765 T^{5} + 170250 T^{6} + 583305 T^{7} + 5882593 T^{8} + 14841329 T^{9} + 151807041 T^{10} + 138687914 T^{11} + 2565726409 T^{12} \))(\( 1 + 2 T + 81 T^{2} + 293 T^{3} + 4297 T^{4} + 15765 T^{5} + 170250 T^{6} + 583305 T^{7} + 5882593 T^{8} + 14841329 T^{9} + 151807041 T^{10} + 138687914 T^{11} + 2565726409 T^{12} \))(\( 1 + 24 T + 398 T^{2} + 4600 T^{3} + 43895 T^{4} + 339152 T^{5} + 2260068 T^{6} + 12548624 T^{7} + 60092255 T^{8} + 233003800 T^{9} + 745916078 T^{10} + 1664254968 T^{11} + 2565726409 T^{12} \))(\( 1 + 24 T + 398 T^{2} + 4600 T^{3} + 43895 T^{4} + 339152 T^{5} + 2260068 T^{6} + 12548624 T^{7} + 60092255 T^{8} + 233003800 T^{9} + 745916078 T^{10} + 1664254968 T^{11} + 2565726409 T^{12} \))(\( 1 + 16 T + 358 T^{2} + 4432 T^{3} + 57353 T^{4} + 569536 T^{5} + 5474048 T^{6} + 44713024 T^{7} + 346781998 T^{8} + 2366254304 T^{9} + 15280917108 T^{10} + 87551409248 T^{11} + 474744555262 T^{12} + 2264848804672 T^{13} + 10259247273728 T^{14} + 39493879893952 T^{15} + 147152106735377 T^{16} + 420738079453456 T^{17} + 1257467644503718 T^{18} + 2079387836721232 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 16 T + 358 T^{2} + 4432 T^{3} + 57353 T^{4} + 569536 T^{5} + 5474048 T^{6} + 44713024 T^{7} + 346781998 T^{8} + 2366254304 T^{9} + 15280917108 T^{10} + 87551409248 T^{11} + 474744555262 T^{12} + 2264848804672 T^{13} + 10259247273728 T^{14} + 39493879893952 T^{15} + 147152106735377 T^{16} + 420738079453456 T^{17} + 1257467644503718 T^{18} + 2079387836721232 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 16 T + 297 T^{2} - 2617 T^{3} + 27363 T^{4} - 156623 T^{5} + 1351272 T^{6} - 6377993 T^{7} + 61637924 T^{8} - 295553271 T^{9} + 2657103486 T^{10} - 10935471027 T^{11} + 84382317956 T^{12} - 323064479429 T^{13} + 2532501282792 T^{14} - 10860858577211 T^{15} + 70205971729467 T^{16} - 248436722457061 T^{17} + 1043206397814537 T^{18} - 2079387836721232 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 16 T + 297 T^{2} - 2617 T^{3} + 27363 T^{4} - 156623 T^{5} + 1351272 T^{6} - 6377993 T^{7} + 61637924 T^{8} - 295553271 T^{9} + 2657103486 T^{10} - 10935471027 T^{11} + 84382317956 T^{12} - 323064479429 T^{13} + 2532501282792 T^{14} - 10860858577211 T^{15} + 70205971729467 T^{16} - 248436722457061 T^{17} + 1043206397814537 T^{18} - 2079387836721232 T^{19} + 4808584372417849 T^{20} \))
$41$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))
$43$ (\( 1 - 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( ( 1 - 9 T + 43 T^{2} )^{2} \))(\( 1 + 7 T + 90 T^{2} + 301 T^{3} + 1849 T^{4} \))(\( 1 + 7 T + 90 T^{2} + 301 T^{3} + 1849 T^{4} \))(\( ( 1 - 9 T + 43 T^{2} )^{2} \))(\( 1 - 4 T - 18 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 77 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 2 T + 37 T^{2} - 86 T^{3} + 1849 T^{4} \))(\( 1 - 8 T + 70 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 - 2 T + 37 T^{2} - 86 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 77 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 145 T^{2} + 936 T^{3} + 6235 T^{4} + 22188 T^{5} + 79507 T^{6} \))(\( 1 + 12 T + 145 T^{2} + 936 T^{3} + 6235 T^{4} + 22188 T^{5} + 79507 T^{6} \))(\( 1 + 13 T + 104 T^{2} + 577 T^{3} + 4472 T^{4} + 24037 T^{5} + 79507 T^{6} \))(\( 1 + 9 T + 81 T^{2} + 542 T^{3} + 3483 T^{4} + 16641 T^{5} + 79507 T^{6} \))(\( 1 + 13 T + 104 T^{2} + 577 T^{3} + 4472 T^{4} + 24037 T^{5} + 79507 T^{6} \))(\( 1 - 5 T + 127 T^{2} - 696 T^{3} + 7236 T^{4} - 29928 T^{5} + 234823 T^{6} - 397535 T^{7} + 3418801 T^{8} \))(\( 1 + 13 T + 220 T^{2} + 1709 T^{3} + 15190 T^{4} + 73487 T^{5} + 406780 T^{6} + 1033591 T^{7} + 3418801 T^{8} \))(\( 1 - 5 T + 127 T^{2} - 696 T^{3} + 7236 T^{4} - 29928 T^{5} + 234823 T^{6} - 397535 T^{7} + 3418801 T^{8} \))(\( 1 - T + 112 T^{2} + 127 T^{3} + 5646 T^{4} + 5461 T^{5} + 207088 T^{6} - 79507 T^{7} + 3418801 T^{8} \))(\( 1 - T + 112 T^{2} + 127 T^{3} + 5646 T^{4} + 5461 T^{5} + 207088 T^{6} - 79507 T^{7} + 3418801 T^{8} \))(\( 1 - 12 T + 207 T^{2} - 1548 T^{3} + 15734 T^{4} - 87500 T^{5} + 747019 T^{6} - 3762500 T^{7} + 29092166 T^{8} - 123076836 T^{9} + 707691807 T^{10} - 1764101316 T^{11} + 6321363049 T^{12} \))(\( 1 - 12 T + 207 T^{2} - 1548 T^{3} + 15734 T^{4} - 87500 T^{5} + 747019 T^{6} - 3762500 T^{7} + 29092166 T^{8} - 123076836 T^{9} + 707691807 T^{10} - 1764101316 T^{11} + 6321363049 T^{12} \))(\( 1 - 4 T + 150 T^{2} - 708 T^{3} + 11959 T^{4} - 55888 T^{5} + 614084 T^{6} - 2403184 T^{7} + 22112191 T^{8} - 56290956 T^{9} + 512820150 T^{10} - 588033772 T^{11} + 6321363049 T^{12} \))(\( 1 - 4 T + 150 T^{2} - 708 T^{3} + 11959 T^{4} - 55888 T^{5} + 614084 T^{6} - 2403184 T^{7} + 22112191 T^{8} - 56290956 T^{9} + 512820150 T^{10} - 588033772 T^{11} + 6321363049 T^{12} \))(\( 1 + 8 T + 156 T^{2} + 1708 T^{3} + 17262 T^{4} + 158080 T^{5} + 1448222 T^{6} + 10630400 T^{7} + 85213937 T^{8} + 589574964 T^{9} + 3956312860 T^{10} + 25351723452 T^{11} + 157560569513 T^{12} + 845191212800 T^{13} + 4951182821822 T^{14} + 23239094669440 T^{15} + 109119368951838 T^{16} + 464266187770756 T^{17} + 1823359243305756 T^{18} + 4020740895494744 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 8 T + 156 T^{2} + 1708 T^{3} + 17262 T^{4} + 158080 T^{5} + 1448222 T^{6} + 10630400 T^{7} + 85213937 T^{8} + 589574964 T^{9} + 3956312860 T^{10} + 25351723452 T^{11} + 157560569513 T^{12} + 845191212800 T^{13} + 4951182821822 T^{14} + 23239094669440 T^{15} + 109119368951838 T^{16} + 464266187770756 T^{17} + 1823359243305756 T^{18} + 4020740895494744 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 20 T + 387 T^{2} - 4356 T^{3} + 50352 T^{4} - 426716 T^{5} + 3988561 T^{6} - 29462196 T^{7} + 243795075 T^{8} - 1609225832 T^{9} + 11807019104 T^{10} - 69196710776 T^{11} + 450777093675 T^{12} - 2342450817372 T^{13} + 13636096335361 T^{14} - 62730854763188 T^{15} + 318293272243248 T^{16} - 1184041869982092 T^{17} + 4523333507431587 T^{18} - 10051852238736860 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 20 T + 387 T^{2} - 4356 T^{3} + 50352 T^{4} - 426716 T^{5} + 3988561 T^{6} - 29462196 T^{7} + 243795075 T^{8} - 1609225832 T^{9} + 11807019104 T^{10} - 69196710776 T^{11} + 450777093675 T^{12} - 2342450817372 T^{13} + 13636096335361 T^{14} - 62730854763188 T^{15} + 318293272243248 T^{16} - 1184041869982092 T^{17} + 4523333507431587 T^{18} - 10051852238736860 T^{19} + 21611482313284249 T^{20} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 8 T + 30 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( 1 + 8 T + 30 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 98 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 112 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 + 20 T + 192 T^{2} + 940 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 48 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 20 T + 192 T^{2} - 940 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 112 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 22 T + 285 T^{2} + 2320 T^{3} + 13395 T^{4} + 48598 T^{5} + 103823 T^{6} \))(\( 1 - 22 T + 285 T^{2} - 2320 T^{3} + 13395 T^{4} - 48598 T^{5} + 103823 T^{6} \))(\( 1 - 2 T + 34 T^{2} - 167 T^{3} + 1598 T^{4} - 4418 T^{5} + 103823 T^{6} \))(\( ( 1 + 2 T + 47 T^{2} )^{3} \))(\( 1 + 2 T + 34 T^{2} + 167 T^{3} + 1598 T^{4} + 4418 T^{5} + 103823 T^{6} \))(\( 1 + 155 T^{2} + 37 T^{3} + 10176 T^{4} + 1739 T^{5} + 342395 T^{6} + 4879681 T^{8} \))(\( 1 + 6 T + 108 T^{2} + 190 T^{3} + 4550 T^{4} + 8930 T^{5} + 238572 T^{6} + 622938 T^{7} + 4879681 T^{8} \))(\( 1 + 155 T^{2} - 37 T^{3} + 10176 T^{4} - 1739 T^{5} + 342395 T^{6} + 4879681 T^{8} \))(\( 1 - 2 T + 96 T^{2} - 662 T^{3} + 4158 T^{4} - 31114 T^{5} + 212064 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 + 2 T + 96 T^{2} + 662 T^{3} + 4158 T^{4} + 31114 T^{5} + 212064 T^{6} + 207646 T^{7} + 4879681 T^{8} \))(\( 1 - 18 T + 367 T^{2} - 4187 T^{3} + 48285 T^{4} - 390765 T^{5} + 3124970 T^{6} - 18365955 T^{7} + 106661565 T^{8} - 434706901 T^{9} + 1790842927 T^{10} - 4128210126 T^{11} + 10779215329 T^{12} \))(\( 1 + 18 T + 367 T^{2} + 4187 T^{3} + 48285 T^{4} + 390765 T^{5} + 3124970 T^{6} + 18365955 T^{7} + 106661565 T^{8} + 434706901 T^{9} + 1790842927 T^{10} + 4128210126 T^{11} + 10779215329 T^{12} \))(\( 1 - 16 T + 256 T^{2} - 2652 T^{3} + 27239 T^{4} - 215852 T^{5} + 1650068 T^{6} - 10145044 T^{7} + 60170951 T^{8} - 275338596 T^{9} + 1249198336 T^{10} - 3669520112 T^{11} + 10779215329 T^{12} \))(\( 1 + 16 T + 256 T^{2} + 2652 T^{3} + 27239 T^{4} + 215852 T^{5} + 1650068 T^{6} + 10145044 T^{7} + 60170951 T^{8} + 275338596 T^{9} + 1249198336 T^{10} + 3669520112 T^{11} + 10779215329 T^{12} \))(\( 1 + 24 T + 416 T^{2} + 4844 T^{3} + 48025 T^{4} + 393252 T^{5} + 3157396 T^{6} + 24584516 T^{7} + 202236454 T^{8} + 1564612916 T^{9} + 11446650088 T^{10} + 73536807052 T^{11} + 446740326886 T^{12} + 2552438204668 T^{13} + 15407085270676 T^{14} + 90190382692764 T^{15} + 517671816175225 T^{16} + 2454082395522772 T^{17} + 9905495251292576 T^{18} + 26859131354466408 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 24 T + 416 T^{2} - 4844 T^{3} + 48025 T^{4} - 393252 T^{5} + 3157396 T^{6} - 24584516 T^{7} + 202236454 T^{8} - 1564612916 T^{9} + 11446650088 T^{10} - 73536807052 T^{11} + 446740326886 T^{12} - 2552438204668 T^{13} + 15407085270676 T^{14} - 90190382692764 T^{15} + 517671816175225 T^{16} - 2454082395522772 T^{17} + 9905495251292576 T^{18} - 26859131354466408 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 16 T + 241 T^{2} - 2509 T^{3} + 25991 T^{4} - 214893 T^{5} + 1859544 T^{6} - 13689933 T^{7} + 107568832 T^{8} - 741660077 T^{9} + 5459961710 T^{10} - 34858023619 T^{11} + 237619549888 T^{12} - 1421329913859 T^{13} + 9073981525464 T^{14} - 49284636589251 T^{15} + 280162585616039 T^{16} - 1271117409241667 T^{17} + 5738520085484401 T^{18} - 17906087569644272 T^{19} + 52599132235830049 T^{20} \))(\( 1 + 16 T + 241 T^{2} + 2509 T^{3} + 25991 T^{4} + 214893 T^{5} + 1859544 T^{6} + 13689933 T^{7} + 107568832 T^{8} + 741660077 T^{9} + 5459961710 T^{10} + 34858023619 T^{11} + 237619549888 T^{12} + 1421329913859 T^{13} + 9073981525464 T^{14} + 49284636589251 T^{15} + 280162585616039 T^{16} + 1271117409241667 T^{17} + 5738520085484401 T^{18} + 17906087569644272 T^{19} + 52599132235830049 T^{20} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 13 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 61 T^{2} + 2809 T^{4} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( 1 + 61 T^{2} + 2809 T^{4} \))(\( 1 + 2 T + 32 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 - 2 T + 35 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 - 6 T + 83 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( 1 - 6 T + 83 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 2 T + 35 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 173 T^{2} + 1002 T^{3} + 9169 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( 1 + 10 T + 173 T^{2} + 1002 T^{3} + 9169 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( 1 + 8 T + 124 T^{2} + 875 T^{3} + 6572 T^{4} + 22472 T^{5} + 148877 T^{6} \))(\( 1 + 7 T + 113 T^{2} + 632 T^{3} + 5989 T^{4} + 19663 T^{5} + 148877 T^{6} \))(\( 1 + 8 T + 124 T^{2} + 875 T^{3} + 6572 T^{4} + 22472 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 215 T^{2} - 929 T^{3} + 17154 T^{4} - 49237 T^{5} + 603935 T^{6} - 893262 T^{7} + 7890481 T^{8} \))(\( 1 - 29 T + 362 T^{2} - 2619 T^{3} + 16622 T^{4} - 138807 T^{5} + 1016858 T^{6} - 4317433 T^{7} + 7890481 T^{8} \))(\( 1 - 6 T + 215 T^{2} - 929 T^{3} + 17154 T^{4} - 49237 T^{5} + 603935 T^{6} - 893262 T^{7} + 7890481 T^{8} \))(\( 1 - 11 T + 112 T^{2} - 723 T^{3} + 6700 T^{4} - 38319 T^{5} + 314608 T^{6} - 1637647 T^{7} + 7890481 T^{8} \))(\( 1 - 11 T + 112 T^{2} - 723 T^{3} + 6700 T^{4} - 38319 T^{5} + 314608 T^{6} - 1637647 T^{7} + 7890481 T^{8} \))(\( 1 - 14 T + 243 T^{2} - 2555 T^{3} + 28319 T^{4} - 233939 T^{5} + 1903710 T^{6} - 12398767 T^{7} + 79548071 T^{8} - 380380735 T^{9} + 1917386883 T^{10} - 5854736902 T^{11} + 22164361129 T^{12} \))(\( 1 - 14 T + 243 T^{2} - 2555 T^{3} + 28319 T^{4} - 233939 T^{5} + 1903710 T^{6} - 12398767 T^{7} + 79548071 T^{8} - 380380735 T^{9} + 1917386883 T^{10} - 5854736902 T^{11} + 22164361129 T^{12} \))(\( 1 + 16 T + 234 T^{2} + 1596 T^{3} + 10025 T^{4} + 6328 T^{5} + 37970 T^{6} + 335384 T^{7} + 28160225 T^{8} + 237607692 T^{9} + 1846372554 T^{10} + 6691127888 T^{11} + 22164361129 T^{12} \))(\( 1 + 16 T + 234 T^{2} + 1596 T^{3} + 10025 T^{4} + 6328 T^{5} + 37970 T^{6} + 335384 T^{7} + 28160225 T^{8} + 237607692 T^{9} + 1846372554 T^{10} + 6691127888 T^{11} + 22164361129 T^{12} \))(\( 1 + 4 T + 268 T^{2} + 1160 T^{3} + 36052 T^{4} + 190492 T^{5} + 3281812 T^{6} + 20651104 T^{7} + 228036701 T^{8} + 1544728772 T^{9} + 13081613782 T^{10} + 81870624916 T^{11} + 640555093109 T^{12} + 3074474410208 T^{13} + 25895075231572 T^{14} + 79662895852556 T^{15} + 799069547422708 T^{16} + 1362664922210920 T^{17} + 16685597030244748 T^{18} + 13199054367208532 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 4 T + 268 T^{2} + 1160 T^{3} + 36052 T^{4} + 190492 T^{5} + 3281812 T^{6} + 20651104 T^{7} + 228036701 T^{8} + 1544728772 T^{9} + 13081613782 T^{10} + 81870624916 T^{11} + 640555093109 T^{12} + 3074474410208 T^{13} + 25895075231572 T^{14} + 79662895852556 T^{15} + 799069547422708 T^{16} + 1362664922210920 T^{17} + 16685597030244748 T^{18} + 13199054367208532 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 26 T + 601 T^{2} - 9515 T^{3} + 137765 T^{4} - 1642903 T^{5} + 18256856 T^{6} - 177050001 T^{7} + 1613772770 T^{8} - 13131416435 T^{9} + 100857559838 T^{10} - 695965071055 T^{11} + 4533087710930 T^{12} - 26358672998877 T^{13} + 144055375387736 T^{14} - 687054630036179 T^{15} + 3053473210936685 T^{16} - 11177376495549055 T^{17} + 37418073937227961 T^{18} - 85793853386855458 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 26 T + 601 T^{2} - 9515 T^{3} + 137765 T^{4} - 1642903 T^{5} + 18256856 T^{6} - 177050001 T^{7} + 1613772770 T^{8} - 13131416435 T^{9} + 100857559838 T^{10} - 695965071055 T^{11} + 4533087710930 T^{12} - 26358672998877 T^{13} + 144055375387736 T^{14} - 687054630036179 T^{15} + 3053473210936685 T^{16} - 11177376495549055 T^{17} + 37418073937227961 T^{18} - 85793853386855458 T^{19} + 174887470365513049 T^{20} \))
$59$ (\( 1 - 2 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 + T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 16 T + 162 T^{2} + 944 T^{3} + 3481 T^{4} \))(\( 1 + 5 T + 116 T^{2} + 295 T^{3} + 3481 T^{4} \))(\( 1 - 5 T + 116 T^{2} - 295 T^{3} + 3481 T^{4} \))(\( 1 - 16 T + 162 T^{2} - 944 T^{3} + 3481 T^{4} \))(\( 1 + 2 T - 28 T^{2} + 118 T^{3} + 3481 T^{4} \))(\( 1 + 4 T + 50 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T + 114 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 126 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 4 T + 114 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T + 50 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 177 T^{2} + 1362 T^{3} + 10443 T^{4} + 41772 T^{5} + 205379 T^{6} \))(\( 1 - 12 T + 177 T^{2} - 1362 T^{3} + 10443 T^{4} - 41772 T^{5} + 205379 T^{6} \))(\( 1 - 7 T + 143 T^{2} - 609 T^{3} + 8437 T^{4} - 24367 T^{5} + 205379 T^{6} \))(\( 1 - 2 T + 127 T^{2} - 336 T^{3} + 7493 T^{4} - 6962 T^{5} + 205379 T^{6} \))(\( 1 + 7 T + 143 T^{2} + 609 T^{3} + 8437 T^{4} + 24367 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 68 T^{2} - 322 T^{3} + 7560 T^{4} - 18998 T^{5} + 236708 T^{6} - 616137 T^{7} + 12117361 T^{8} \))(\( 1 + 16 T + 264 T^{2} + 2444 T^{3} + 23526 T^{4} + 144196 T^{5} + 918984 T^{6} + 3286064 T^{7} + 12117361 T^{8} \))(\( 1 + 3 T + 68 T^{2} + 322 T^{3} + 7560 T^{4} + 18998 T^{5} + 236708 T^{6} + 616137 T^{7} + 12117361 T^{8} \))(\( 1 - 2 T + 154 T^{2} - 560 T^{3} + 11126 T^{4} - 33040 T^{5} + 536074 T^{6} - 410758 T^{7} + 12117361 T^{8} \))(\( 1 + 2 T + 154 T^{2} + 560 T^{3} + 11126 T^{4} + 33040 T^{5} + 536074 T^{6} + 410758 T^{7} + 12117361 T^{8} \))(\( 1 + 16 T + 238 T^{2} + 2547 T^{3} + 26935 T^{4} + 227428 T^{5} + 1910883 T^{6} + 13418252 T^{7} + 93760735 T^{8} + 523100313 T^{9} + 2883931918 T^{10} + 11438788784 T^{11} + 42180533641 T^{12} \))(\( 1 - 16 T + 238 T^{2} - 2547 T^{3} + 26935 T^{4} - 227428 T^{5} + 1910883 T^{6} - 13418252 T^{7} + 93760735 T^{8} - 523100313 T^{9} + 2883931918 T^{10} - 11438788784 T^{11} + 42180533641 T^{12} \))(\( 1 + 16 T + 120 T^{2} + 1140 T^{3} + 13555 T^{4} + 89804 T^{5} + 500490 T^{6} + 5298436 T^{7} + 47184955 T^{8} + 234132060 T^{9} + 1454083320 T^{10} + 11438788784 T^{11} + 42180533641 T^{12} \))(\( 1 - 16 T + 120 T^{2} - 1140 T^{3} + 13555 T^{4} - 89804 T^{5} + 500490 T^{6} - 5298436 T^{7} + 47184955 T^{8} - 234132060 T^{9} + 1454083320 T^{10} - 11438788784 T^{11} + 42180533641 T^{12} \))(\( 1 + 392 T^{2} + 124 T^{3} + 72653 T^{4} + 53436 T^{5} + 8565058 T^{6} + 9694268 T^{7} + 730980722 T^{8} + 964042332 T^{9} + 48398429980 T^{10} + 56878497588 T^{11} + 2544543893282 T^{12} + 1990999067572 T^{13} + 103785899771938 T^{14} + 38202694841364 T^{15} + 3064542310619573 T^{16} + 308592784117556 T^{17} + 57557531540893832 T^{18} + 511116753300641401 T^{20} \))(\( 1 + 392 T^{2} - 124 T^{3} + 72653 T^{4} - 53436 T^{5} + 8565058 T^{6} - 9694268 T^{7} + 730980722 T^{8} - 964042332 T^{9} + 48398429980 T^{10} - 56878497588 T^{11} + 2544543893282 T^{12} - 1990999067572 T^{13} + 103785899771938 T^{14} - 38202694841364 T^{15} + 3064542310619573 T^{16} - 308592784117556 T^{17} + 57557531540893832 T^{18} + 511116753300641401 T^{20} \))(\( 1 - 10 T + 464 T^{2} - 3933 T^{3} + 100547 T^{4} - 739002 T^{5} + 13587671 T^{6} - 87375608 T^{7} + 1277936808 T^{8} - 7168651661 T^{9} + 87686002282 T^{10} - 422950447999 T^{11} + 4448498028648 T^{12} - 17945114995432 T^{13} + 164646714656231 T^{14} - 528330486809598 T^{15} + 4241126116001627 T^{16} - 9787866289793127 T^{17} + 68129323048404944 T^{18} - 86629958186549390 T^{19} + 511116753300641401 T^{20} \))(\( 1 + 10 T + 464 T^{2} + 3933 T^{3} + 100547 T^{4} + 739002 T^{5} + 13587671 T^{6} + 87375608 T^{7} + 1277936808 T^{8} + 7168651661 T^{9} + 87686002282 T^{10} + 422950447999 T^{11} + 4448498028648 T^{12} + 17945114995432 T^{13} + 164646714656231 T^{14} + 528330486809598 T^{15} + 4241126116001627 T^{16} + 9787866289793127 T^{17} + 68129323048404944 T^{18} + 86629958186549390 T^{19} + 511116753300641401 T^{20} \))
$61$ (\( 1 - 13 T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 9 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 - 3 T + 61 T^{2} \))(\( 1 - 9 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 + 16 T + 141 T^{2} + 976 T^{3} + 3721 T^{4} \))(\( 1 + 11 T + 144 T^{2} + 671 T^{3} + 3721 T^{4} \))(\( 1 - 11 T + 144 T^{2} - 671 T^{3} + 3721 T^{4} \))(\( 1 - 16 T + 141 T^{2} - 976 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 144 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 + 6 T + 59 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 99 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( ( 1 + 6 T + 61 T^{2} )^{2} \))(\( 1 + 6 T + 99 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 59 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 24 T + 271 T^{2} - 2202 T^{3} + 16531 T^{4} - 89304 T^{5} + 226981 T^{6} \))(\( 1 + 24 T + 271 T^{2} + 2202 T^{3} + 16531 T^{4} + 89304 T^{5} + 226981 T^{6} \))(\( 1 - 10 T + 64 T^{2} - 269 T^{3} + 3904 T^{4} - 37210 T^{5} + 226981 T^{6} \))(\( 1 - 13 T + 209 T^{2} - 1596 T^{3} + 12749 T^{4} - 48373 T^{5} + 226981 T^{6} \))(\( 1 + 10 T + 64 T^{2} + 269 T^{3} + 3904 T^{4} + 37210 T^{5} + 226981 T^{6} \))(\( 1 - T + 73 T^{2} - 671 T^{3} + 1181 T^{4} - 40931 T^{5} + 271633 T^{6} - 226981 T^{7} + 13845841 T^{8} \))(\( 1 + 21 T + 276 T^{2} + 2979 T^{3} + 26922 T^{4} + 181719 T^{5} + 1026996 T^{6} + 4766601 T^{7} + 13845841 T^{8} \))(\( 1 + T + 73 T^{2} + 671 T^{3} + 1181 T^{4} + 40931 T^{5} + 271633 T^{6} + 226981 T^{7} + 13845841 T^{8} \))(\( 1 + 15 T + 262 T^{2} + 2421 T^{3} + 24360 T^{4} + 147681 T^{5} + 974902 T^{6} + 3404715 T^{7} + 13845841 T^{8} \))(\( 1 - 15 T + 262 T^{2} - 2421 T^{3} + 24360 T^{4} - 147681 T^{5} + 974902 T^{6} - 3404715 T^{7} + 13845841 T^{8} \))(\( 1 - 20 T + 453 T^{2} - 5909 T^{3} + 76465 T^{4} - 709515 T^{5} + 6412098 T^{6} - 43280415 T^{7} + 284526265 T^{8} - 1341230729 T^{9} + 6272165973 T^{10} - 16891926020 T^{11} + 51520374361 T^{12} \))(\( 1 + 20 T + 453 T^{2} + 5909 T^{3} + 76465 T^{4} + 709515 T^{5} + 6412098 T^{6} + 43280415 T^{7} + 284526265 T^{8} + 1341230729 T^{9} + 6272165973 T^{10} + 16891926020 T^{11} + 51520374361 T^{12} \))(\( 1 + 32 T + 726 T^{2} + 11300 T^{3} + 143695 T^{4} + 1456668 T^{5} + 12552758 T^{6} + 88856748 T^{7} + 534689095 T^{8} + 2564885300 T^{9} + 10052080566 T^{10} + 27027081632 T^{11} + 51520374361 T^{12} \))(\( 1 - 32 T + 726 T^{2} - 11300 T^{3} + 143695 T^{4} - 1456668 T^{5} + 12552758 T^{6} - 88856748 T^{7} + 534689095 T^{8} - 2564885300 T^{9} + 10052080566 T^{10} - 27027081632 T^{11} + 51520374361 T^{12} \))(\( 1 + 380 T^{2} + 36 T^{3} + 72834 T^{4} + 9300 T^{5} + 9196908 T^{6} + 1146808 T^{7} + 844205981 T^{8} + 93522728 T^{9} + 58775394162 T^{10} + 5704886408 T^{11} + 3141290455301 T^{12} + 260303626648 T^{13} + 127338925859628 T^{14} + 7854745599300 T^{15} + 3752434946209074 T^{16} + 113138742096756 T^{17} + 72848778938966780 T^{18} + 713342911662882601 T^{20} \))(\( 1 + 380 T^{2} - 36 T^{3} + 72834 T^{4} - 9300 T^{5} + 9196908 T^{6} - 1146808 T^{7} + 844205981 T^{8} - 93522728 T^{9} + 58775394162 T^{10} - 5704886408 T^{11} + 3141290455301 T^{12} - 260303626648 T^{13} + 127338925859628 T^{14} - 7854745599300 T^{15} + 3752434946209074 T^{16} - 113138742096756 T^{17} + 72848778938966780 T^{18} + 713342911662882601 T^{20} \))(\( 1 + 325 T^{2} + 341 T^{3} + 55126 T^{4} + 87657 T^{5} + 6440407 T^{6} + 11319704 T^{7} + 568806163 T^{8} + 962936366 T^{9} + 39149474996 T^{10} + 58739118326 T^{11} + 2116527732523 T^{12} + 2569357733624 T^{13} + 89172851297287 T^{14} + 74034777956757 T^{15} + 2840112157024486 T^{16} + 1071675307083161 T^{17} + 62304876724116325 T^{18} + 713342911662882601 T^{20} \))(\( 1 + 325 T^{2} - 341 T^{3} + 55126 T^{4} - 87657 T^{5} + 6440407 T^{6} - 11319704 T^{7} + 568806163 T^{8} - 962936366 T^{9} + 39149474996 T^{10} - 58739118326 T^{11} + 2116527732523 T^{12} - 2569357733624 T^{13} + 89172851297287 T^{14} - 74034777956757 T^{15} + 2840112157024486 T^{16} - 1071675307083161 T^{17} + 62304876724116325 T^{18} + 713342911662882601 T^{20} \))
$67$ (\( 1 - 16 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 14 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 4 T - 42 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( 1 - 4 T - 42 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 10 T + 132 T^{2} + 670 T^{3} + 4489 T^{4} \))(\( 1 + 20 T + 226 T^{2} + 1340 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 162 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 132 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 162 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 20 T + 226 T^{2} + 1340 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 91 T^{2} - 294 T^{3} + 6097 T^{4} - 17956 T^{5} + 300763 T^{6} \))(\( 1 - 4 T + 91 T^{2} - 294 T^{3} + 6097 T^{4} - 17956 T^{5} + 300763 T^{6} \))(\( 1 + 23 T + 365 T^{2} + 3425 T^{3} + 24455 T^{4} + 103247 T^{5} + 300763 T^{6} \))(\( 1 - 22 T + 267 T^{2} - 2368 T^{3} + 17889 T^{4} - 98758 T^{5} + 300763 T^{6} \))(\( 1 + 23 T + 365 T^{2} + 3425 T^{3} + 24455 T^{4} + 103247 T^{5} + 300763 T^{6} \))(\( 1 - 11 T + 268 T^{2} - 2026 T^{3} + 26702 T^{4} - 135742 T^{5} + 1203052 T^{6} - 3308393 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T + 172 T^{2} - 384 T^{3} + 14822 T^{4} - 25728 T^{5} + 772108 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 - 11 T + 268 T^{2} - 2026 T^{3} + 26702 T^{4} - 135742 T^{5} + 1203052 T^{6} - 3308393 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T + 192 T^{2} - 618 T^{3} + 17954 T^{4} - 41406 T^{5} + 861888 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T + 192 T^{2} - 618 T^{3} + 17954 T^{4} - 41406 T^{5} + 861888 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 + 13 T + 176 T^{2} + 1888 T^{3} + 17413 T^{4} + 153731 T^{5} + 1305512 T^{6} + 10299977 T^{7} + 78166957 T^{8} + 567840544 T^{9} + 3546597296 T^{10} + 17551626391 T^{11} + 90458382169 T^{12} \))(\( 1 + 13 T + 176 T^{2} + 1888 T^{3} + 17413 T^{4} + 153731 T^{5} + 1305512 T^{6} + 10299977 T^{7} + 78166957 T^{8} + 567840544 T^{9} + 3546597296 T^{10} + 17551626391 T^{11} + 90458382169 T^{12} \))(\( 1 + 20 T + 362 T^{2} + 4304 T^{3} + 50513 T^{4} + 485936 T^{5} + 4399546 T^{6} + 32557712 T^{7} + 226752857 T^{8} + 1294483952 T^{9} + 7294705802 T^{10} + 27002502140 T^{11} + 90458382169 T^{12} \))(\( 1 + 20 T + 362 T^{2} + 4304 T^{3} + 50513 T^{4} + 485936 T^{5} + 4399546 T^{6} + 32557712 T^{7} + 226752857 T^{8} + 1294483952 T^{9} + 7294705802 T^{10} + 27002502140 T^{11} + 90458382169 T^{12} \))(\( 1 - 8 T + 470 T^{2} - 2780 T^{3} + 100899 T^{4} - 430000 T^{5} + 13375686 T^{6} - 39953160 T^{7} + 1265966028 T^{8} - 2789089532 T^{9} + 94002716856 T^{10} - 186868998644 T^{11} + 5682921499692 T^{12} - 12016432261080 T^{13} + 269535067044006 T^{14} - 580553796010000 T^{15} + 9127160302469931 T^{16} - 16848778262797940 T^{17} + 190851808451621270 T^{18} - 217652275170359576 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 8 T + 470 T^{2} - 2780 T^{3} + 100899 T^{4} - 430000 T^{5} + 13375686 T^{6} - 39953160 T^{7} + 1265966028 T^{8} - 2789089532 T^{9} + 94002716856 T^{10} - 186868998644 T^{11} + 5682921499692 T^{12} - 12016432261080 T^{13} + 269535067044006 T^{14} - 580553796010000 T^{15} + 9127160302469931 T^{16} - 16848778262797940 T^{17} + 190851808451621270 T^{18} - 217652275170359576 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 7 T + 602 T^{2} - 3866 T^{3} + 167009 T^{4} - 969997 T^{5} + 28116436 T^{6} - 145123217 T^{7} + 3181082822 T^{8} - 14267922051 T^{9} + 252734277332 T^{10} - 955950777417 T^{11} + 14279880787958 T^{12} - 43647694114571 T^{13} + 566577703924756 T^{14} - 1309617303414679 T^{15} + 15107363947662521 T^{16} - 23430711066178718 T^{17} + 244452741889097882 T^{18} - 190445740774064629 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 7 T + 602 T^{2} - 3866 T^{3} + 167009 T^{4} - 969997 T^{5} + 28116436 T^{6} - 145123217 T^{7} + 3181082822 T^{8} - 14267922051 T^{9} + 252734277332 T^{10} - 955950777417 T^{11} + 14279880787958 T^{12} - 43647694114571 T^{13} + 566577703924756 T^{14} - 1309617303414679 T^{15} + 15107363947662521 T^{16} - 23430711066178718 T^{17} + 244452741889097882 T^{18} - 190445740774064629 T^{19} + 1822837804551761449 T^{20} \))
$71$ (\( 1 + 3 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 137 T^{2} + 5041 T^{4} \))(\( 1 + 12 T + 145 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( 1 + 12 T + 145 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( 1 + 137 T^{2} + 5041 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 + 2 T + 45 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 + 6 T + 133 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 144 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 + 6 T + 133 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 2 T + 45 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 117 T^{2} + 712 T^{3} + 8307 T^{4} + 20164 T^{5} + 357911 T^{6} \))(\( 1 + 4 T + 117 T^{2} + 712 T^{3} + 8307 T^{4} + 20164 T^{5} + 357911 T^{6} \))(\( 1 + 180 T^{2} + 9 T^{3} + 12780 T^{4} + 357911 T^{6} \))(\( 1 - 7 T + 109 T^{2} - 666 T^{3} + 7739 T^{4} - 35287 T^{5} + 357911 T^{6} \))(\( 1 + 180 T^{2} + 9 T^{3} + 12780 T^{4} + 357911 T^{6} \))(\( 1 + 9 T + 107 T^{2} + 199 T^{3} + 1653 T^{4} + 14129 T^{5} + 539387 T^{6} + 3221199 T^{7} + 25411681 T^{8} \))(\( 1 - 17 T + 84 T^{2} + 1019 T^{3} - 16170 T^{4} + 72349 T^{5} + 423444 T^{6} - 6084487 T^{7} + 25411681 T^{8} \))(\( 1 + 9 T + 107 T^{2} + 199 T^{3} + 1653 T^{4} + 14129 T^{5} + 539387 T^{6} + 3221199 T^{7} + 25411681 T^{8} \))(\( 1 - 15 T + 340 T^{2} - 3251 T^{3} + 38214 T^{4} - 230821 T^{5} + 1713940 T^{6} - 5368665 T^{7} + 25411681 T^{8} \))(\( 1 - 15 T + 340 T^{2} - 3251 T^{3} + 38214 T^{4} - 230821 T^{5} + 1713940 T^{6} - 5368665 T^{7} + 25411681 T^{8} \))(\( 1 - 11 T + 136 T^{2} + 162 T^{3} + 2821 T^{4} + 3931 T^{5} + 799059 T^{6} + 279101 T^{7} + 14220661 T^{8} + 57981582 T^{9} + 3455988616 T^{10} - 19846522861 T^{11} + 128100283921 T^{12} \))(\( 1 - 11 T + 136 T^{2} + 162 T^{3} + 2821 T^{4} + 3931 T^{5} + 799059 T^{6} + 279101 T^{7} + 14220661 T^{8} + 57981582 T^{9} + 3455988616 T^{10} - 19846522861 T^{11} + 128100283921 T^{12} \))(\( 1 - 12 T + 334 T^{2} - 2596 T^{3} + 45983 T^{4} - 276920 T^{5} + 3969444 T^{6} - 19661320 T^{7} + 231800303 T^{8} - 929136956 T^{9} + 8487501454 T^{10} - 21650752212 T^{11} + 128100283921 T^{12} \))(\( 1 - 12 T + 334 T^{2} - 2596 T^{3} + 45983 T^{4} - 276920 T^{5} + 3969444 T^{6} - 19661320 T^{7} + 231800303 T^{8} - 929136956 T^{9} + 8487501454 T^{10} - 21650752212 T^{11} + 128100283921 T^{12} \))(\( 1 - 4 T + 484 T^{2} - 2076 T^{3} + 115006 T^{4} - 485372 T^{5} + 17684686 T^{6} - 69611060 T^{7} + 1941910673 T^{8} - 6877557968 T^{9} + 158787895516 T^{10} - 488306615728 T^{11} + 9789171702593 T^{12} - 24914564095660 T^{13} + 449397599217166 T^{14} - 875722408553572 T^{15} + 14732301252618526 T^{16} - 18881469448819716 T^{17} + 312544709122948324 T^{18} - 183394002873796124 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 4 T + 484 T^{2} - 2076 T^{3} + 115006 T^{4} - 485372 T^{5} + 17684686 T^{6} - 69611060 T^{7} + 1941910673 T^{8} - 6877557968 T^{9} + 158787895516 T^{10} - 488306615728 T^{11} + 9789171702593 T^{12} - 24914564095660 T^{13} + 449397599217166 T^{14} - 875722408553572 T^{15} + 14732301252618526 T^{16} - 18881469448819716 T^{17} + 312544709122948324 T^{18} - 183394002873796124 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 5 T + 312 T^{2} - 1090 T^{3} + 56870 T^{4} - 195450 T^{5} + 7498233 T^{6} - 22581087 T^{7} + 744547841 T^{8} - 2080097600 T^{9} + 59734234259 T^{10} - 147686929600 T^{11} + 3753265666481 T^{12} - 8082019429257 T^{13} + 190542705059673 T^{14} - 352636626652950 T^{15} + 7285063146587270 T^{16} - 9913680972646190 T^{17} + 201475101748677432 T^{18} - 229242503592245155 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 5 T + 312 T^{2} - 1090 T^{3} + 56870 T^{4} - 195450 T^{5} + 7498233 T^{6} - 22581087 T^{7} + 744547841 T^{8} - 2080097600 T^{9} + 59734234259 T^{10} - 147686929600 T^{11} + 3753265666481 T^{12} - 8082019429257 T^{13} + 190542705059673 T^{14} - 352636626652950 T^{15} + 7285063146587270 T^{16} - 9913680972646190 T^{17} + 201475101748677432 T^{18} - 229242503592245155 T^{19} + 3255243551009881201 T^{20} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 7 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( 1 + 9 T + 92 T^{2} + 657 T^{3} + 5329 T^{4} \))(\( 1 - 9 T + 92 T^{2} - 657 T^{3} + 5329 T^{4} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( 1 - 4 T + 102 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( ( 1 + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( 1 - 16 T + 178 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( ( 1 - 4 T + 73 T^{2} )^{2} \))(\( ( 1 + 73 T^{2} )^{2} \))(\( 1 + 12 T + 235 T^{2} + 1720 T^{3} + 17155 T^{4} + 63948 T^{5} + 389017 T^{6} \))(\( 1 - 12 T + 235 T^{2} - 1720 T^{3} + 17155 T^{4} - 63948 T^{5} + 389017 T^{6} \))(\( 1 + 8 T + 176 T^{2} + 911 T^{3} + 12848 T^{4} + 42632 T^{5} + 389017 T^{6} \))(\( 1 - 28 T + 447 T^{2} - 4600 T^{3} + 32631 T^{4} - 149212 T^{5} + 389017 T^{6} \))(\( 1 - 8 T + 176 T^{2} - 911 T^{3} + 12848 T^{4} - 42632 T^{5} + 389017 T^{6} \))(\( 1 - 22 T + 409 T^{2} - 4787 T^{3} + 48782 T^{4} - 349451 T^{5} + 2179561 T^{6} - 8558374 T^{7} + 28398241 T^{8} \))(\( 1 + 12 T + 116 T^{2} + 276 T^{3} + 3382 T^{4} + 20148 T^{5} + 618164 T^{6} + 4668204 T^{7} + 28398241 T^{8} \))(\( 1 + 22 T + 409 T^{2} + 4787 T^{3} + 48782 T^{4} + 349451 T^{5} + 2179561 T^{6} + 8558374 T^{7} + 28398241 T^{8} \))(\( 1 + 4 T + 228 T^{2} + 652 T^{3} + 23142 T^{4} + 47596 T^{5} + 1215012 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 - 4 T + 228 T^{2} - 652 T^{3} + 23142 T^{4} - 47596 T^{5} + 1215012 T^{6} - 1556068 T^{7} + 28398241 T^{8} \))(\( 1 + T + 254 T^{2} - 330 T^{3} + 30443 T^{4} - 87177 T^{5} + 2509711 T^{6} - 6363921 T^{7} + 162230747 T^{8} - 128375610 T^{9} + 7213153214 T^{10} + 2073071593 T^{11} + 151334226289 T^{12} \))(\( 1 - T + 254 T^{2} + 330 T^{3} + 30443 T^{4} + 87177 T^{5} + 2509711 T^{6} + 6363921 T^{7} + 162230747 T^{8} + 128375610 T^{9} + 7213153214 T^{10} - 2073071593 T^{11} + 151334226289 T^{12} \))(\( 1 + 16 T + 512 T^{2} + 5856 T^{3} + 101027 T^{4} + 855728 T^{5} + 10072096 T^{6} + 62468144 T^{7} + 538372883 T^{8} + 2278083552 T^{9} + 14539899392 T^{10} + 33169145488 T^{11} + 151334226289 T^{12} \))(\( 1 - 16 T + 512 T^{2} - 5856 T^{3} + 101027 T^{4} - 855728 T^{5} + 10072096 T^{6} - 62468144 T^{7} + 538372883 T^{8} - 2278083552 T^{9} + 14539899392 T^{10} - 33169145488 T^{11} + 151334226289 T^{12} \))(\( 1 - 24 T + 540 T^{2} - 7768 T^{3} + 107529 T^{4} - 1154336 T^{5} + 12519760 T^{6} - 113733984 T^{7} + 1100583206 T^{8} - 9222885584 T^{9} + 84373616616 T^{10} - 673270647632 T^{11} + 5865007904774 T^{12} - 44244453253728 T^{13} + 355539161742160 T^{14} - 2393021170377248 T^{15} + 16272818018629881 T^{16} - 85816191696345496 T^{17} + 435488449622803740 T^{18} - 1412918080998429912 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 24 T + 540 T^{2} + 7768 T^{3} + 107529 T^{4} + 1154336 T^{5} + 12519760 T^{6} + 113733984 T^{7} + 1100583206 T^{8} + 9222885584 T^{9} + 84373616616 T^{10} + 673270647632 T^{11} + 5865007904774 T^{12} + 44244453253728 T^{13} + 355539161742160 T^{14} + 2393021170377248 T^{15} + 16272818018629881 T^{16} + 85816191696345496 T^{17} + 435488449622803740 T^{18} + 1412918080998429912 T^{19} + 4297625829703557649 T^{20} \))(\( 1 - 13 T + 250 T^{2} - 2110 T^{3} + 24489 T^{4} - 122685 T^{5} + 1653191 T^{6} - 9421251 T^{7} + 193642338 T^{8} - 1495731037 T^{9} + 19158703894 T^{10} - 109188365701 T^{11} + 1031920019202 T^{12} - 3665026800267 T^{13} + 46947716437031 T^{14} - 254334788387205 T^{15} + 3706023867591321 T^{16} - 23310010875294670 T^{17} + 201615022973520250 T^{18} - 765330627207482869 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 13 T + 250 T^{2} + 2110 T^{3} + 24489 T^{4} + 122685 T^{5} + 1653191 T^{6} + 9421251 T^{7} + 193642338 T^{8} + 1495731037 T^{9} + 19158703894 T^{10} + 109188365701 T^{11} + 1031920019202 T^{12} + 3665026800267 T^{13} + 46947716437031 T^{14} + 254334788387205 T^{15} + 3706023867591321 T^{16} + 23310010875294670 T^{17} + 201615022973520250 T^{18} + 765330627207482869 T^{19} + 4297625829703557649 T^{20} \))
$79$ (\( 1 + 11 T + 79 T^{2} \))(\( 1 - 7 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 15 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 3 T + 79 T^{2} \))(\( 1 - 15 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 - 7 T + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 - 8 T + 129 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 15 T + 206 T^{2} + 1185 T^{3} + 6241 T^{4} \))(\( 1 + 15 T + 206 T^{2} + 1185 T^{3} + 6241 T^{4} \))(\( 1 - 8 T + 129 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( 1 + 10 T + 165 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 - 2 T + 141 T^{2} - 158 T^{3} + 6241 T^{4} \))(\( 1 + 12 T + 176 T^{2} + 948 T^{3} + 6241 T^{4} \))(\( 1 - 2 T + 141 T^{2} - 158 T^{3} + 6241 T^{4} \))(\( 1 + 10 T + 165 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 - 8 T + 173 T^{2} - 880 T^{3} + 13667 T^{4} - 49928 T^{5} + 493039 T^{6} \))(\( 1 - 8 T + 173 T^{2} - 880 T^{3} + 13667 T^{4} - 49928 T^{5} + 493039 T^{6} \))(\( 1 - T + 45 T^{2} - 167 T^{3} + 3555 T^{4} - 6241 T^{5} + 493039 T^{6} \))(\( 1 - 19 T + 333 T^{2} - 3130 T^{3} + 26307 T^{4} - 118579 T^{5} + 493039 T^{6} \))(\( 1 - T + 45 T^{2} - 167 T^{3} + 3555 T^{4} - 6241 T^{5} + 493039 T^{6} \))(\( 1 + 28 T + 541 T^{2} + 7283 T^{3} + 73511 T^{4} + 575357 T^{5} + 3376381 T^{6} + 13805092 T^{7} + 38950081 T^{8} \))(\( 1 + 27 T + 548 T^{2} + 7039 T^{3} + 74358 T^{4} + 556081 T^{5} + 3420068 T^{6} + 13312053 T^{7} + 38950081 T^{8} \))(\( 1 + 28 T + 541 T^{2} + 7283 T^{3} + 73511 T^{4} + 575357 T^{5} + 3376381 T^{6} + 13805092 T^{7} + 38950081 T^{8} \))(\( 1 - 15 T + 292 T^{2} - 3043 T^{3} + 34422 T^{4} - 240397 T^{5} + 1822372 T^{6} - 7395585 T^{7} + 38950081 T^{8} \))(\( 1 - 15 T + 292 T^{2} - 3043 T^{3} + 34422 T^{4} - 240397 T^{5} + 1822372 T^{6} - 7395585 T^{7} + 38950081 T^{8} \))(\( 1 - 19 T + 440 T^{2} - 4604 T^{3} + 60189 T^{4} - 431041 T^{5} + 4937144 T^{6} - 34052239 T^{7} + 375639549 T^{8} - 2269951556 T^{9} + 17138035640 T^{10} - 58464071581 T^{11} + 243087455521 T^{12} \))(\( 1 - 19 T + 440 T^{2} - 4604 T^{3} + 60189 T^{4} - 431041 T^{5} + 4937144 T^{6} - 34052239 T^{7} + 375639549 T^{8} - 2269951556 T^{9} + 17138035640 T^{10} - 58464071581 T^{11} + 243087455521 T^{12} \))(\( 1 + 386 T^{2} - 288 T^{3} + 65775 T^{4} - 67872 T^{5} + 6560348 T^{6} - 5361888 T^{7} + 410501775 T^{8} - 141995232 T^{9} + 15034731266 T^{10} + 243087455521 T^{12} \))(\( 1 + 386 T^{2} - 288 T^{3} + 65775 T^{4} - 67872 T^{5} + 6560348 T^{6} - 5361888 T^{7} + 410501775 T^{8} - 141995232 T^{9} + 15034731266 T^{10} + 243087455521 T^{12} \))(\( 1 - 24 T + 552 T^{2} - 8800 T^{3} + 125510 T^{4} - 1488232 T^{5} + 16674002 T^{6} - 163960520 T^{7} + 1599848841 T^{8} - 14392945192 T^{9} + 131572455532 T^{10} - 1137042670168 T^{11} + 9984656616681 T^{12} - 80838930820280 T^{13} + 649453728494162 T^{14} - 4579373798796568 T^{15} + 30509906542440710 T^{16} - 168994399078199200 T^{17} + 837444063068421672 T^{18} - 2876438303582839656 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 24 T + 552 T^{2} - 8800 T^{3} + 125510 T^{4} - 1488232 T^{5} + 16674002 T^{6} - 163960520 T^{7} + 1599848841 T^{8} - 14392945192 T^{9} + 131572455532 T^{10} - 1137042670168 T^{11} + 9984656616681 T^{12} - 80838930820280 T^{13} + 649453728494162 T^{14} - 4579373798796568 T^{15} + 30509906542440710 T^{16} - 168994399078199200 T^{17} + 837444063068421672 T^{18} - 2876438303582839656 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + T + 364 T^{2} - 252 T^{3} + 70672 T^{4} - 126376 T^{5} + 9900124 T^{6} - 21591815 T^{7} + 1095541909 T^{8} - 2270815516 T^{9} + 97073937704 T^{10} - 179394425764 T^{11} + 6837277054069 T^{12} - 10645606875785 T^{13} + 385610631710044 T^{14} - 388866079480024 T^{15} + 17179476656580112 T^{16} - 4839385064512068 T^{17} + 552227606805988204 T^{18} + 119851595982618319 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + T + 364 T^{2} - 252 T^{3} + 70672 T^{4} - 126376 T^{5} + 9900124 T^{6} - 21591815 T^{7} + 1095541909 T^{8} - 2270815516 T^{9} + 97073937704 T^{10} - 179394425764 T^{11} + 6837277054069 T^{12} - 10645606875785 T^{13} + 385610631710044 T^{14} - 388866079480024 T^{15} + 17179476656580112 T^{16} - 4839385064512068 T^{17} + 552227606805988204 T^{18} + 119851595982618319 T^{19} + 9468276082626847201 T^{20} \))
$83$ (\( 1 + 14 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 12 T + 122 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( 1 + 5 T + 164 T^{2} + 415 T^{3} + 6889 T^{4} \))(\( 1 - 5 T + 164 T^{2} - 415 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 122 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 + 6 T + 172 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 + 20 T + 248 T^{2} + 1660 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 152 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 + 24 T + 278 T^{2} + 1992 T^{3} + 6889 T^{4} \))(\( 1 + 12 T + 152 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( 1 - 20 T + 248 T^{2} - 1660 T^{3} + 6889 T^{4} \))(\( 1 - 24 T + 397 T^{2} - 4138 T^{3} + 32951 T^{4} - 165336 T^{5} + 571787 T^{6} \))(\( 1 + 24 T + 397 T^{2} + 4138 T^{3} + 32951 T^{4} + 165336 T^{5} + 571787 T^{6} \))(\( 1 - 4 T + 204 T^{2} - 487 T^{3} + 16932 T^{4} - 27556 T^{5} + 571787 T^{6} \))(\( 1 - 14 T + 295 T^{2} - 2304 T^{3} + 24485 T^{4} - 96446 T^{5} + 571787 T^{6} \))(\( 1 + 4 T + 204 T^{2} + 487 T^{3} + 16932 T^{4} + 27556 T^{5} + 571787 T^{6} \))(\( 1 - 12 T + 125 T^{2} - 957 T^{3} + 3390 T^{4} - 79431 T^{5} + 861125 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))(\( 1 - 18 T + 412 T^{2} - 4590 T^{3} + 54630 T^{4} - 380970 T^{5} + 2838268 T^{6} - 10292166 T^{7} + 47458321 T^{8} \))(\( 1 + 12 T + 125 T^{2} + 957 T^{3} + 3390 T^{4} + 79431 T^{5} + 861125 T^{6} + 6861444 T^{7} + 47458321 T^{8} \))(\( 1 + 12 T + 286 T^{2} + 2126 T^{3} + 31506 T^{4} + 176458 T^{5} + 1970254 T^{6} + 6861444 T^{7} + 47458321 T^{8} \))(\( 1 - 12 T + 286 T^{2} - 2126 T^{3} + 31506 T^{4} - 176458 T^{5} + 1970254 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))(\( 1 + 15 T + 500 T^{2} + 5412 T^{3} + 100709 T^{4} + 829239 T^{5} + 10974575 T^{6} + 68826837 T^{7} + 693784301 T^{8} + 3094511244 T^{9} + 23729160500 T^{10} + 59085609645 T^{11} + 326940373369 T^{12} \))(\( 1 - 15 T + 500 T^{2} - 5412 T^{3} + 100709 T^{4} - 829239 T^{5} + 10974575 T^{6} - 68826837 T^{7} + 693784301 T^{8} - 3094511244 T^{9} + 23729160500 T^{10} - 59085609645 T^{11} + 326940373369 T^{12} \))(\( 1 + 32 T + 632 T^{2} + 9580 T^{3} + 121787 T^{4} + 1345308 T^{5} + 13167754 T^{6} + 111660564 T^{7} + 838990643 T^{8} + 5477719460 T^{9} + 29993658872 T^{10} + 126049300576 T^{11} + 326940373369 T^{12} \))(\( 1 - 32 T + 632 T^{2} - 9580 T^{3} + 121787 T^{4} - 1345308 T^{5} + 13167754 T^{6} - 111660564 T^{7} + 838990643 T^{8} - 5477719460 T^{9} + 29993658872 T^{10} - 126049300576 T^{11} + 326940373369 T^{12} \))(\( 1 + 48 T + 1548 T^{2} + 36724 T^{3} + 724417 T^{4} + 12098348 T^{5} + 177754882 T^{6} + 2311132348 T^{7} + 27054069462 T^{8} + 285199949076 T^{9} + 2731301924780 T^{10} + 23671595773308 T^{11} + 186375484523718 T^{12} + 1321475431865876 T^{13} + 8435948249273122 T^{14} + 47655884485157764 T^{15} + 236841164454850873 T^{16} + 996544336543061948 T^{17} + 3486548375351235468 T^{18} + 8973132252841939344 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 48 T + 1548 T^{2} - 36724 T^{3} + 724417 T^{4} - 12098348 T^{5} + 177754882 T^{6} - 2311132348 T^{7} + 27054069462 T^{8} - 285199949076 T^{9} + 2731301924780 T^{10} - 23671595773308 T^{11} + 186375484523718 T^{12} - 1321475431865876 T^{13} + 8435948249273122 T^{14} - 47655884485157764 T^{15} + 236841164454850873 T^{16} - 996544336543061948 T^{17} + 3486548375351235468 T^{18} - 8973132252841939344 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 21 T + 584 T^{2} + 7822 T^{3} + 137615 T^{4} + 1481099 T^{5} + 21400343 T^{6} + 200504223 T^{7} + 2508803676 T^{8} + 20728996337 T^{9} + 231117196858 T^{10} + 1720506695971 T^{11} + 17283148523964 T^{12} + 114645708156501 T^{13} + 1015624347604103 T^{14} + 5834109157306657 T^{15} + 44991899481174935 T^{16} + 212258190840862394 T^{17} + 1315338663569199944 T^{18} + 3925745360618348463 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 21 T + 584 T^{2} - 7822 T^{3} + 137615 T^{4} - 1481099 T^{5} + 21400343 T^{6} - 200504223 T^{7} + 2508803676 T^{8} - 20728996337 T^{9} + 231117196858 T^{10} - 1720506695971 T^{11} + 17283148523964 T^{12} - 114645708156501 T^{13} + 1015624347604103 T^{14} - 5834109157306657 T^{15} + 44991899481174935 T^{16} - 212258190840862394 T^{17} + 1315338663569199944 T^{18} - 3925745360618348463 T^{19} + 15516041187205853449 T^{20} \))
$89$ (\( 1 - 14 T + 89 T^{2} \))(\( 1 + 5 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 + 13 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 5 T + 89 T^{2} \))(\( 1 - T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - T + 89 T^{2} \))(\( ( 1 - 3 T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 3 T + 89 T^{2} )^{2} \))(\( 1 + 12 T + 166 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 2 T + 171 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 + 10 T + 195 T^{2} + 890 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 182 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 10 T + 195 T^{2} - 890 T^{3} + 7921 T^{4} \))(\( 1 - 2 T + 171 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 6 T + 103 T^{2} + 676 T^{3} + 9167 T^{4} + 47526 T^{5} + 704969 T^{6} \))(\( 1 - 6 T + 103 T^{2} - 676 T^{3} + 9167 T^{4} - 47526 T^{5} + 704969 T^{6} \))(\( 1 + 10 T + 216 T^{2} + 1657 T^{3} + 19224 T^{4} + 79210 T^{5} + 704969 T^{6} \))(\( 1 + 23 T + 419 T^{2} + 4330 T^{3} + 37291 T^{4} + 182183 T^{5} + 704969 T^{6} \))(\( 1 - 10 T + 216 T^{2} - 1657 T^{3} + 19224 T^{4} - 79210 T^{5} + 704969 T^{6} \))(\( 1 + 6 T + 305 T^{2} + 1435 T^{3} + 39018 T^{4} + 127715 T^{5} + 2415905 T^{6} + 4229814 T^{7} + 62742241 T^{8} \))(\( 1 + 37 T + 814 T^{2} + 11891 T^{3} + 130434 T^{4} + 1058299 T^{5} + 6447694 T^{6} + 26083853 T^{7} + 62742241 T^{8} \))(\( 1 - 6 T + 305 T^{2} - 1435 T^{3} + 39018 T^{4} - 127715 T^{5} + 2415905 T^{6} - 4229814 T^{7} + 62742241 T^{8} \))(\( 1 + 35 T + 790 T^{2} + 11589 T^{3} + 128770 T^{4} + 1031421 T^{5} + 6257590 T^{6} + 24673915 T^{7} + 62742241 T^{8} \))(\( 1 - 35 T + 790 T^{2} - 11589 T^{3} + 128770 T^{4} - 1031421 T^{5} + 6257590 T^{6} - 24673915 T^{7} + 62742241 T^{8} \))(\( 1 - 14 T + 431 T^{2} - 3891 T^{3} + 73571 T^{4} - 493163 T^{5} + 7716806 T^{6} - 43891507 T^{7} + 582755891 T^{8} - 2743034379 T^{9} + 27041905871 T^{10} - 78176832286 T^{11} + 496981290961 T^{12} \))(\( 1 + 14 T + 431 T^{2} + 3891 T^{3} + 73571 T^{4} + 493163 T^{5} + 7716806 T^{6} + 43891507 T^{7} + 582755891 T^{8} + 2743034379 T^{9} + 27041905871 T^{10} + 78176832286 T^{11} + 496981290961 T^{12} \))(\( 1 + 8 T + 406 T^{2} + 3056 T^{3} + 76583 T^{4} + 508264 T^{5} + 8599604 T^{6} + 45235496 T^{7} + 606613943 T^{8} + 2154385264 T^{9} + 25473349846 T^{10} + 44672475592 T^{11} + 496981290961 T^{12} \))(\( 1 - 8 T + 406 T^{2} - 3056 T^{3} + 76583 T^{4} - 508264 T^{5} + 8599604 T^{6} - 45235496 T^{7} + 606613943 T^{8} - 2154385264 T^{9} + 25473349846 T^{10} - 44672475592 T^{11} + 496981290961 T^{12} \))(\( 1 + 20 T + 464 T^{2} + 6416 T^{3} + 107990 T^{4} + 1259284 T^{5} + 17047382 T^{6} + 177374772 T^{7} + 2141128769 T^{8} + 19963266644 T^{9} + 211631427220 T^{10} + 1776730731316 T^{11} + 16959880979249 T^{12} + 125043715642068 T^{13} + 1069590949863062 T^{14} + 7031916719174516 T^{15} + 53669009610878390 T^{16} + 283788244689714064 T^{17} + 1826577205845765584 T^{18} + 7007128074149704180 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 20 T + 464 T^{2} - 6416 T^{3} + 107990 T^{4} - 1259284 T^{5} + 17047382 T^{6} - 177374772 T^{7} + 2141128769 T^{8} - 19963266644 T^{9} + 211631427220 T^{10} - 1776730731316 T^{11} + 16959880979249 T^{12} - 125043715642068 T^{13} + 1069590949863062 T^{14} - 7031916719174516 T^{15} + 53669009610878390 T^{16} - 283788244689714064 T^{17} + 1826577205845765584 T^{18} - 7007128074149704180 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 6 T + 363 T^{2} + 2853 T^{3} + 66271 T^{4} + 646201 T^{5} + 9034652 T^{6} + 90887475 T^{7} + 1070787904 T^{8} + 9430571081 T^{9} + 106341932306 T^{10} + 839320826209 T^{11} + 8481710987584 T^{12} + 64072852363275 T^{13} + 566854313135132 T^{14} + 3608424800003249 T^{15} + 32935447133276431 T^{16} + 126191998456944237 T^{17} + 1428981736469855403 T^{18} + 2102138422244911254 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 6 T + 363 T^{2} - 2853 T^{3} + 66271 T^{4} - 646201 T^{5} + 9034652 T^{6} - 90887475 T^{7} + 1070787904 T^{8} - 9430571081 T^{9} + 106341932306 T^{10} - 839320826209 T^{11} + 8481710987584 T^{12} - 64072852363275 T^{13} + 566854313135132 T^{14} - 3608424800003249 T^{15} + 32935447133276431 T^{16} - 126191998456944237 T^{17} + 1428981736469855403 T^{18} - 2102138422244911254 T^{19} + 31181719929966183601 T^{20} \))
$97$ (\( 1 + 8 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 4 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( ( 1 + T + 97 T^{2} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 - T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( 1 + 6 T + 195 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 30 T + 411 T^{2} + 2910 T^{3} + 9409 T^{4} \))(\( 1 - 4 T + 166 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 - 30 T + 411 T^{2} - 2910 T^{3} + 9409 T^{4} \))(\( 1 - 6 T + 195 T^{2} - 582 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 271 T^{2} - 3196 T^{3} + 26287 T^{4} - 169362 T^{5} + 912673 T^{6} \))(\( 1 + 18 T + 271 T^{2} + 3196 T^{3} + 26287 T^{4} + 169362 T^{5} + 912673 T^{6} \))(\( 1 + 3 T + 213 T^{2} + 529 T^{3} + 20661 T^{4} + 28227 T^{5} + 912673 T^{6} \))(\( 1 - 25 T + 475 T^{2} - 5254 T^{3} + 46075 T^{4} - 235225 T^{5} + 912673 T^{6} \))(\( 1 - 3 T + 213 T^{2} - 529 T^{3} + 20661 T^{4} - 28227 T^{5} + 912673 T^{6} \))(\( 1 + 11 T + 298 T^{2} + 2922 T^{3} + 39354 T^{4} + 283434 T^{5} + 2803882 T^{6} + 10039403 T^{7} + 88529281 T^{8} \))(\( 1 - 3 T + 290 T^{2} - 621 T^{3} + 37786 T^{4} - 60237 T^{5} + 2728610 T^{6} - 2738019 T^{7} + 88529281 T^{8} \))(\( 1 - 11 T + 298 T^{2} - 2922 T^{3} + 39354 T^{4} - 283434 T^{5} + 2803882 T^{6} - 10039403 T^{7} + 88529281 T^{8} \))(\( 1 - 5 T + 202 T^{2} - 555 T^{3} + 24202 T^{4} - 53835 T^{5} + 1900618 T^{6} - 4563365 T^{7} + 88529281 T^{8} \))(\( 1 + 5 T + 202 T^{2} + 555 T^{3} + 24202 T^{4} + 53835 T^{5} + 1900618 T^{6} + 4563365 T^{7} + 88529281 T^{8} \))(\( 1 + T + 368 T^{2} - 414 T^{3} + 58751 T^{4} - 162591 T^{5} + 6301840 T^{6} - 15771327 T^{7} + 552788159 T^{8} - 377846622 T^{9} + 32578775408 T^{10} + 8587340257 T^{11} + 832972004929 T^{12} \))(\( 1 - T + 368 T^{2} + 414 T^{3} + 58751 T^{4} + 162591 T^{5} + 6301840 T^{6} + 15771327 T^{7} + 552788159 T^{8} + 377846622 T^{9} + 32578775408 T^{10} - 8587340257 T^{11} + 832972004929 T^{12} \))(\( 1 + 8 T + 142 T^{2} + 584 T^{3} + 14639 T^{4} + 14000 T^{5} + 886340 T^{6} + 1358000 T^{7} + 137738351 T^{8} + 533001032 T^{9} + 12571157902 T^{10} + 68698722056 T^{11} + 832972004929 T^{12} \))(\( 1 - 8 T + 142 T^{2} - 584 T^{3} + 14639 T^{4} - 14000 T^{5} + 886340 T^{6} - 1358000 T^{7} + 137738351 T^{8} - 533001032 T^{9} + 12571157902 T^{10} - 68698722056 T^{11} + 832972004929 T^{12} \))(\( 1 + 4 T + 456 T^{2} + 1808 T^{3} + 105758 T^{4} + 345612 T^{5} + 17311342 T^{6} + 44385844 T^{7} + 2229385937 T^{8} + 5003762220 T^{9} + 236215189236 T^{10} + 485364935340 T^{11} + 20976292281233 T^{12} + 40509761401012 T^{13} + 1532560660405102 T^{14} + 2967887840902284 T^{15} + 88093453297281182 T^{16} + 146083298336428304 T^{17} + 3573869719035894216 T^{18} + 3040924234618260868 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 4 T + 456 T^{2} - 1808 T^{3} + 105758 T^{4} - 345612 T^{5} + 17311342 T^{6} - 44385844 T^{7} + 2229385937 T^{8} - 5003762220 T^{9} + 236215189236 T^{10} - 485364935340 T^{11} + 20976292281233 T^{12} - 40509761401012 T^{13} + 1532560660405102 T^{14} - 2967887840902284 T^{15} + 88093453297281182 T^{16} - 146083298336428304 T^{17} + 3573869719035894216 T^{18} - 3040924234618260868 T^{19} + 73742412689492826049 T^{20} \))(\( 1 + 29 T + 668 T^{2} + 11220 T^{3} + 178105 T^{4} + 2387957 T^{5} + 30935208 T^{6} + 361493303 T^{7} + 4156434566 T^{8} + 43540141251 T^{9} + 447164066424 T^{10} + 4223393701347 T^{11} + 39107892831494 T^{12} + 329925177328919 T^{13} + 2738671721825448 T^{14} + 20506199278084949 T^{15} + 148356478937879545 T^{16} + 906556751844427860 T^{17} + 5235405641043809948 T^{18} + 22046700700982391293 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 29 T + 668 T^{2} - 11220 T^{3} + 178105 T^{4} - 2387957 T^{5} + 30935208 T^{6} - 361493303 T^{7} + 4156434566 T^{8} - 43540141251 T^{9} + 447164066424 T^{10} - 4223393701347 T^{11} + 39107892831494 T^{12} - 329925177328919 T^{13} + 2738671721825448 T^{14} - 20506199278084949 T^{15} + 148356478937879545 T^{16} - 906556751844427860 T^{17} + 5235405641043809948 T^{18} - 22046700700982391293 T^{19} + 73742412689492826049 T^{20} \))
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