Properties

Label 252.2
Level 252
Weight 2
Dimension 718
Nonzero newspaces 20
Newform subspaces 40
Sturm bound 6912
Trace bound 11

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Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 40 \)
Sturm bound: \(6912\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(252))\).

Total New Old
Modular forms 1968 810 1158
Cusp forms 1489 718 771
Eisenstein series 479 92 387

Trace form

\( 718q - 3q^{2} + q^{4} - 3q^{5} - 6q^{6} - q^{7} - 15q^{8} + O(q^{10}) \) \( 718q - 3q^{2} + q^{4} - 3q^{5} - 6q^{6} - q^{7} - 15q^{8} - 10q^{10} + 9q^{11} - 24q^{12} + 10q^{13} - 9q^{14} - 6q^{15} - 11q^{16} - 9q^{17} - 48q^{18} + 29q^{19} - 54q^{20} - 3q^{21} - 36q^{22} + 27q^{23} - 18q^{24} + 36q^{25} - 42q^{26} + 18q^{27} - 39q^{28} - 6q^{29} - 6q^{30} + 5q^{31} - 3q^{32} - 78q^{33} - 52q^{34} - 51q^{35} - 18q^{36} - 69q^{37} - 54q^{38} - 30q^{39} - 118q^{40} - 162q^{41} - 60q^{42} - 74q^{43} - 120q^{44} - 102q^{45} - 156q^{46} - 81q^{47} - 114q^{48} - 71q^{49} - 171q^{50} - 72q^{51} - 142q^{52} - 87q^{53} - 108q^{54} - 54q^{55} - 99q^{56} - 108q^{57} - 76q^{58} - 45q^{59} - 30q^{60} + 7q^{61} - 81q^{63} - 59q^{64} - 114q^{65} + 54q^{66} + 63q^{67} + 84q^{68} - 42q^{69} + 102q^{70} - 24q^{71} + 96q^{72} - 29q^{73} + 210q^{74} - 72q^{75} + 144q^{76} - 126q^{77} + 84q^{78} - 3q^{79} + 198q^{80} - 132q^{81} + 80q^{82} - 66q^{83} + 66q^{84} - 158q^{85} + 126q^{86} + 198q^{88} - 201q^{89} + 90q^{90} - 10q^{91} + 102q^{92} - 144q^{93} + 144q^{94} + 3q^{95} + 48q^{96} - 158q^{97} + 111q^{98} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)

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
252.2.a \(\chi_{252}(1, \cdot)\) 252.2.a.a 1 1
252.2.a.b 1
252.2.b \(\chi_{252}(55, \cdot)\) 252.2.b.a 2 1
252.2.b.b 4
252.2.b.c 4
252.2.b.d 4
252.2.b.e 4
252.2.e \(\chi_{252}(71, \cdot)\) 252.2.e.a 12 1
252.2.f \(\chi_{252}(125, \cdot)\) 252.2.f.a 4 1
252.2.i \(\chi_{252}(25, \cdot)\) 252.2.i.a 2 2
252.2.i.b 14
252.2.j \(\chi_{252}(85, \cdot)\) 252.2.j.a 6 2
252.2.j.b 6
252.2.k \(\chi_{252}(37, \cdot)\) 252.2.k.a 2 2
252.2.k.b 2
252.2.k.c 2
252.2.l \(\chi_{252}(193, \cdot)\) 252.2.l.a 2 2
252.2.l.b 14
252.2.n \(\chi_{252}(31, \cdot)\) 252.2.n.a 4 2
252.2.n.b 84
252.2.o \(\chi_{252}(95, \cdot)\) 252.2.o.a 88 2
252.2.t \(\chi_{252}(17, \cdot)\) 252.2.t.a 4 2
252.2.w \(\chi_{252}(5, \cdot)\) 252.2.w.a 16 2
252.2.x \(\chi_{252}(41, \cdot)\) 252.2.x.a 16 2
252.2.ba \(\chi_{252}(155, \cdot)\) 252.2.ba.a 72 2
252.2.bb \(\chi_{252}(11, \cdot)\) 252.2.bb.a 88 2
252.2.be \(\chi_{252}(107, \cdot)\) 252.2.be.a 32 2
252.2.bf \(\chi_{252}(19, \cdot)\) 252.2.bf.a 4 2
252.2.bf.b 4
252.2.bf.c 4
252.2.bf.d 4
252.2.bf.e 4
252.2.bf.f 8
252.2.bf.g 8
252.2.bi \(\chi_{252}(139, \cdot)\) 252.2.bi.a 4 2
252.2.bi.b 4
252.2.bi.c 80
252.2.bj \(\chi_{252}(103, \cdot)\) 252.2.bj.a 4 2
252.2.bj.b 84
252.2.bm \(\chi_{252}(173, \cdot)\) 252.2.bm.a 16 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T + 2 T^{2} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( 1 - 3 T^{2} + 4 T^{4} \))(\( 1 - T - 2 T^{3} + 4 T^{4} \))(\( 1 - T - 2 T^{3} + 4 T^{4} \))(\( 1 - 4 T^{2} + 13 T^{4} - 28 T^{6} + 52 T^{8} - 64 T^{10} + 64 T^{12} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( 1 + T - T^{2} + 2 T^{3} + 4 T^{4} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 4 T^{4} \))(\( 1 - T - T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( 1 + T + T^{2} + 2 T^{3} + 4 T^{5} + 4 T^{6} + 8 T^{7} + 16 T^{8} \))(\( 1 + T + T^{2} + 2 T^{3} + 6 T^{4} + 4 T^{5} + 4 T^{6} + 8 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( ( 1 + 2 T + 2 T^{2} )^{2} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 - 3 T + 7 T^{2} - 15 T^{3} + 34 T^{4} - 78 T^{5} + 144 T^{6} - 252 T^{7} + 432 T^{8} - 702 T^{9} + 918 T^{10} - 1215 T^{11} + 1701 T^{12} - 2187 T^{13} + 2187 T^{14} \))(\( 1 + 2 T - 2 T^{2} - 9 T^{3} - 6 T^{4} + 18 T^{5} + 27 T^{6} \))(\( 1 - 2 T + 4 T^{2} - 3 T^{3} + 12 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 + 3 T^{2} \))(\( 1 - 5 T^{2} - 3 T^{3} + 7 T^{4} + 30 T^{5} - 117 T^{7} + 270 T^{9} + 189 T^{10} - 243 T^{11} - 1215 T^{12} + 2187 T^{14} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( 1 - 3 T^{2} - 3 T^{3} - 9 T^{5} + 36 T^{6} + 18 T^{7} - 72 T^{8} + 54 T^{9} + 324 T^{10} - 243 T^{11} - 729 T^{13} - 2187 T^{14} + 6561 T^{16} \))(\( 1 + 9 T^{4} - 45 T^{6} - 18 T^{8} - 405 T^{10} + 729 T^{12} + 6561 T^{16} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 + 3 T^{3} - 27 T^{5} + 27 T^{6} + 9 T^{7} - 72 T^{8} + 27 T^{9} + 243 T^{10} - 729 T^{11} + 729 T^{13} + 6561 T^{16} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 + 4 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 5 T^{2} )^{4} \))(\( 1 - 6 T^{2} + 42 T^{4} - 150 T^{6} + 625 T^{8} \))(\( 1 - 6 T^{2} + 42 T^{4} - 150 T^{6} + 625 T^{8} \))(\( ( 1 - 12 T^{2} + 95 T^{4} - 568 T^{6} + 2375 T^{8} - 7500 T^{10} + 15625 T^{12} )^{2} \))(\( ( 1 - 2 T^{2} + 25 T^{4} )^{2} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - 11 T^{2} - 66 T^{3} - 25 T^{4} + 533 T^{5} + 1540 T^{6} - 603 T^{7} - 11032 T^{8} - 21691 T^{9} + 19925 T^{10} + 156945 T^{11} + 233805 T^{12} - 385788 T^{13} - 1886454 T^{14} - 1928940 T^{15} + 5845125 T^{16} + 19618125 T^{17} + 12453125 T^{18} - 67784375 T^{19} - 172375000 T^{20} - 47109375 T^{21} + 601562500 T^{22} + 1041015625 T^{23} - 244140625 T^{24} - 3222656250 T^{25} - 2685546875 T^{26} + 2441406250 T^{27} + 6103515625 T^{28} \))(\( 1 + T - 10 T^{2} - 7 T^{3} + 57 T^{4} + 14 T^{5} - 299 T^{6} + 70 T^{7} + 1425 T^{8} - 875 T^{9} - 6250 T^{10} + 3125 T^{11} + 15625 T^{12} \))(\( 1 - 3 T + 15 T^{3} - 27 T^{4} + 6 T^{5} + 61 T^{6} + 30 T^{7} - 675 T^{8} + 1875 T^{9} - 9375 T^{11} + 15625 T^{12} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} \))(\( ( 1 - 2 T + 5 T^{2} )^{2} \))(\( ( 1 - 2 T + 15 T^{2} - 48 T^{3} + 154 T^{4} - 429 T^{5} + 1202 T^{6} - 2471 T^{7} + 6010 T^{8} - 10725 T^{9} + 19250 T^{10} - 30000 T^{11} + 46875 T^{12} - 31250 T^{13} + 78125 T^{14} )^{2} \))(\( ( 1 + 2 T^{2} + 25 T^{4} )^{2} \))(\( 1 - 4 T^{2} - 9 T^{4} - 100 T^{6} + 625 T^{8} \))(\( 1 - 16 T^{2} - 24 T^{3} + 105 T^{4} + 357 T^{5} - 80 T^{6} - 2232 T^{7} - 2857 T^{8} + 6027 T^{9} + 16041 T^{10} + 777 T^{11} - 31496 T^{12} - 32724 T^{13} + 43664 T^{14} + 15327 T^{15} - 229716 T^{16} + 76635 T^{17} + 1091600 T^{18} - 4090500 T^{19} - 19685000 T^{20} + 2428125 T^{21} + 250640625 T^{22} + 470859375 T^{23} - 1116015625 T^{24} - 4359375000 T^{25} - 781250000 T^{26} + 17431640625 T^{27} + 25634765625 T^{28} - 29296875000 T^{29} - 97656250000 T^{30} + 152587890625 T^{32} \))(\( 1 - 16 T^{2} + 159 T^{4} - 998 T^{6} + 4298 T^{8} - 12066 T^{10} + 21316 T^{12} - 64633 T^{14} + 271566 T^{16} - 1615825 T^{18} + 13322500 T^{20} - 188531250 T^{22} + 1678906250 T^{24} - 9746093750 T^{26} + 38818359375 T^{28} - 97656250000 T^{30} + 152587890625 T^{32} \))(\( ( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} )^{2} \))(\( 1 + 2 T^{2} - 21 T^{4} + 50 T^{6} + 625 T^{8} \))(\( 1 + 2 T^{2} - 21 T^{4} + 50 T^{6} + 625 T^{8} \))(\( ( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} )^{2} \))(\( 1 + 9 T^{2} + 45 T^{4} - 96 T^{5} + 66 T^{6} - 864 T^{7} - 394 T^{8} - 4320 T^{9} + 1650 T^{10} - 12000 T^{11} + 28125 T^{12} + 140625 T^{14} + 390625 T^{16} \))(\( 1 + 9 T^{2} + 45 T^{4} - 96 T^{5} + 66 T^{6} - 864 T^{7} - 394 T^{8} - 4320 T^{9} + 1650 T^{10} - 12000 T^{11} + 28125 T^{12} + 140625 T^{14} + 390625 T^{16} \))(\( ( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 + 16 T^{2} + 12 T^{3} + 151 T^{4} + 165 T^{5} + 1096 T^{6} + 1236 T^{7} + 6142 T^{8} + 6180 T^{9} + 27400 T^{10} + 20625 T^{11} + 94375 T^{12} + 37500 T^{13} + 250000 T^{14} + 390625 T^{16} )^{2} \))
$7$ (\( 1 + T \))(\( 1 - T \))(\( 1 + 7 T^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( 1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 - 2 T - 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( ( 1 + T^{2} )^{6} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 - 6 T + 20 T^{2} - 77 T^{3} + 309 T^{4} - 961 T^{5} + 2706 T^{6} - 7572 T^{7} + 18942 T^{8} - 47089 T^{9} + 105987 T^{10} - 184877 T^{11} + 336140 T^{12} - 705894 T^{13} + 823543 T^{14} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 3 T + 11 T^{2} - 5 T^{3} - 15 T^{4} - 88 T^{5} + 312 T^{6} + 753 T^{7} + 2184 T^{8} - 4312 T^{9} - 5145 T^{10} - 12005 T^{11} + 184877 T^{12} + 352947 T^{13} + 823543 T^{14} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( 1 + T + 3 T^{2} - 7 T^{3} - 82 T^{4} - 141 T^{5} - 20 T^{6} + 1111 T^{7} + 5328 T^{8} + 7777 T^{9} - 980 T^{10} - 48363 T^{11} - 196882 T^{12} - 117649 T^{13} + 352947 T^{14} + 823543 T^{15} + 5764801 T^{16} \))(\( 1 + T + 3 T^{2} + 20 T^{3} + 53 T^{4} + 21 T^{5} - 74 T^{6} + 355 T^{7} - 1314 T^{8} + 2485 T^{9} - 3626 T^{10} + 7203 T^{11} + 127253 T^{12} + 336140 T^{13} + 352947 T^{14} + 823543 T^{15} + 5764801 T^{16} \))(\( 1 - 7 T^{2} + 49 T^{4} \))(\( ( 1 + T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( 1 - 7 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T + 16 T^{3} + 65 T^{4} + 112 T^{5} + 686 T^{7} + 2401 T^{8} \))(\( 1 - 2 T - 16 T^{3} + 65 T^{4} - 112 T^{5} - 686 T^{7} + 2401 T^{8} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 + T - 6 T^{2} - 16 T^{3} - 10 T^{4} + 39 T^{5} + 385 T^{6} - 239 T^{7} - 2880 T^{8} - 1673 T^{9} + 18865 T^{10} + 13377 T^{11} - 24010 T^{12} - 268912 T^{13} - 705894 T^{14} + 823543 T^{15} + 5764801 T^{16} \))
$11$ (\( 1 + 2 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( ( 1 - 4 T + 11 T^{2} )( 1 + 4 T + 11 T^{2} ) \))(\( ( 1 - 20 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 6 T^{2} + 121 T^{4} )^{2} \))(\( 1 - 34 T^{2} + 514 T^{4} - 4114 T^{6} + 14641 T^{8} \))(\( 1 - 34 T^{2} + 514 T^{4} - 4114 T^{6} + 14641 T^{8} \))(\( ( 1 + 38 T^{2} + 715 T^{4} + 9068 T^{6} + 86515 T^{8} + 556358 T^{10} + 1771561 T^{12} )^{2} \))(\( ( 1 - 4 T^{2} + 121 T^{4} )^{2} \))(\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T - 32 T^{2} + 42 T^{3} + 722 T^{4} - 614 T^{5} - 9113 T^{6} - 2733 T^{7} + 72959 T^{8} + 126076 T^{9} + 256457 T^{10} - 2291538 T^{11} - 13152543 T^{12} + 8654619 T^{13} + 213521742 T^{14} + 95200809 T^{15} - 1591457703 T^{16} - 3050037078 T^{17} + 3754786937 T^{18} + 20304665876 T^{19} + 129251318999 T^{20} - 53258438343 T^{21} - 1953452482553 T^{22} - 1447779882274 T^{23} + 18726820561922 T^{24} + 11983090165662 T^{25} - 100429708055072 T^{26} - 69045424287862 T^{27} + 379749833583241 T^{28} \))(\( 1 + 2 T - 4 T^{2} + 46 T^{3} + 6 T^{4} - 230 T^{5} + 1699 T^{6} - 2530 T^{7} + 726 T^{8} + 61226 T^{9} - 58564 T^{10} + 322102 T^{11} + 1771561 T^{12} \))(\( 1 - 6 T + 30 T^{3} + 162 T^{4} - 402 T^{5} - 821 T^{6} - 4422 T^{7} + 19602 T^{8} + 39930 T^{9} - 966306 T^{11} + 1771561 T^{12} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 36 T^{2} + 57 T^{3} + 460 T^{4} + 402 T^{5} + 2501 T^{6} + 455 T^{7} + 27511 T^{8} + 48642 T^{9} + 612260 T^{10} + 834537 T^{11} + 5797836 T^{12} + 3543122 T^{13} + 19487171 T^{14} )^{2} \))(\( ( 1 - 18 T^{2} + 121 T^{4} )^{2} \))(\( 1 + 4 T^{2} - 105 T^{4} + 484 T^{6} + 14641 T^{8} \))(\( 1 + 6 T + 61 T^{2} + 294 T^{3} + 1701 T^{4} + 6204 T^{5} + 24845 T^{6} + 59553 T^{7} + 143666 T^{8} - 78393 T^{9} - 1097631 T^{10} - 8096325 T^{11} - 21925205 T^{12} - 68059401 T^{13} - 34454504 T^{14} + 43343730 T^{15} + 1352446632 T^{16} + 476781030 T^{17} - 4168994984 T^{18} - 90587062731 T^{19} - 321006926405 T^{20} - 1303921237575 T^{21} - 1944520271991 T^{22} - 1527657796203 T^{23} + 30796082997746 T^{24} + 140422858842123 T^{25} + 644415314211845 T^{26} + 1770073604470644 T^{27} + 5338466668802421 T^{28} + 10149677370315714 T^{29} + 23164739848577701 T^{30} + 25063489016493906 T^{31} + 45949729863572161 T^{32} \))(\( ( 1 - 3 T + 26 T^{2} - 69 T^{3} + 265 T^{4} - 756 T^{5} + 2585 T^{6} - 8259 T^{7} + 34846 T^{8} - 90849 T^{9} + 312785 T^{10} - 1006236 T^{11} + 3879865 T^{12} - 11112519 T^{13} + 46060586 T^{14} - 58461513 T^{15} + 214358881 T^{16} )^{2} \))(\( 1 + 15 T^{2} + 104 T^{4} + 1815 T^{6} + 14641 T^{8} \))(\( 1 - 10 T^{2} - 21 T^{4} - 1210 T^{6} + 14641 T^{8} \))(\( 1 - 10 T^{2} - 21 T^{4} - 1210 T^{6} + 14641 T^{8} \))(\( 1 + 15 T^{2} + 104 T^{4} + 1815 T^{6} + 14641 T^{8} \))(\( 1 + 21 T^{2} + 320 T^{4} + 2541 T^{6} + 14641 T^{8} \))(\( ( 1 - 8 T + 34 T^{2} - 112 T^{3} + 339 T^{4} - 1232 T^{5} + 4114 T^{6} - 10648 T^{7} + 14641 T^{8} )( 1 + 2 T + 25 T^{2} + 58 T^{3} + 372 T^{4} + 638 T^{5} + 3025 T^{6} + 2662 T^{7} + 14641 T^{8} ) \))(\( ( 1 - 2 T + 25 T^{2} - 58 T^{3} + 372 T^{4} - 638 T^{5} + 3025 T^{6} - 2662 T^{7} + 14641 T^{8} )( 1 + 8 T + 34 T^{2} + 112 T^{3} + 339 T^{4} + 1232 T^{5} + 4114 T^{6} + 10648 T^{7} + 14641 T^{8} ) \))(\( 1 + 21 T^{2} + 320 T^{4} + 2541 T^{6} + 14641 T^{8} \))(\( 1 + 21 T^{2} + 320 T^{4} + 2541 T^{6} + 14641 T^{8} \))(\( 1 + 18 T^{2} + 203 T^{4} + 2178 T^{6} + 14641 T^{8} \))(\( 1 - 86 T^{2} + 3801 T^{4} - 115279 T^{6} + 2684372 T^{8} - 50825121 T^{10} + 808796131 T^{12} - 11028714095 T^{14} + 130183029216 T^{16} - 1334474405495 T^{18} + 11841584153971 T^{20} - 90039802183881 T^{22} + 575418978107732 T^{24} - 2990040370578679 T^{26} + 11929166259916521 T^{28} - 32658485688158726 T^{30} + 45949729863572161 T^{32} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( 1 - 12 T^{2} + 102 T^{4} - 2028 T^{6} + 28561 T^{8} \))(\( 1 - 12 T^{2} + 102 T^{4} - 2028 T^{6} + 28561 T^{8} \))(\( ( 1 + 11 T^{2} - 16 T^{3} + 143 T^{4} + 2197 T^{6} )^{4} \))(\( ( 1 - 2 T^{2} + 169 T^{4} )^{2} \))(\( 1 + 3 T - 4 T^{2} + 39 T^{3} + 169 T^{4} \))(\( 1 - 2 T - 25 T^{2} - 20 T^{3} + 172 T^{4} + 1281 T^{5} + 1882 T^{6} - 1142 T^{7} - 27931 T^{8} - 309997 T^{9} + 9092 T^{10} + 1859069 T^{11} + 4530175 T^{12} + 5185603 T^{13} - 73974588 T^{14} + 67412839 T^{15} + 765599575 T^{16} + 4084374593 T^{17} + 259676612 T^{18} - 115099716121 T^{19} - 134817602179 T^{20} - 71658806414 T^{21} + 1535205216922 T^{22} + 13584363696813 T^{23} + 23711660598028 T^{24} - 35843207880740 T^{25} - 582452128062025 T^{26} - 605750213184506 T^{27} + 3937376385699289 T^{28} \))(\( 1 + 3 T + 3 T^{2} - 84 T^{3} - 195 T^{4} + 345 T^{5} + 5006 T^{6} + 4485 T^{7} - 32955 T^{8} - 184548 T^{9} + 85683 T^{10} + 1113879 T^{11} + 4826809 T^{12} \))(\( ( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} )^{3} \))(\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( 1 + 3 T - 4 T^{2} + 39 T^{3} + 169 T^{4} \))(\( 1 - 2 T - 25 T^{2} - 20 T^{3} + 172 T^{4} + 1281 T^{5} + 1882 T^{6} - 1142 T^{7} - 27931 T^{8} - 309997 T^{9} + 9092 T^{10} + 1859069 T^{11} + 4530175 T^{12} + 5185603 T^{13} - 73974588 T^{14} + 67412839 T^{15} + 765599575 T^{16} + 4084374593 T^{17} + 259676612 T^{18} - 115099716121 T^{19} - 134817602179 T^{20} - 71658806414 T^{21} + 1535205216922 T^{22} + 13584363696813 T^{23} + 23711660598028 T^{24} - 35843207880740 T^{25} - 582452128062025 T^{26} - 605750213184506 T^{27} + 3937376385699289 T^{28} \))(\( ( 1 - 7 T + 13 T^{2} )^{2}( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 7 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2} \))(\( 1 + 3 T + 53 T^{2} + 150 T^{3} + 1317 T^{4} + 4452 T^{5} + 23056 T^{6} + 90522 T^{7} + 327950 T^{8} + 1218621 T^{9} + 4082037 T^{10} + 12551466 T^{11} + 42977824 T^{12} + 136810599 T^{13} + 317458436 T^{14} + 1828010007 T^{15} + 2359677564 T^{16} + 23764130091 T^{17} + 53650475684 T^{18} + 300572886003 T^{19} + 1227489631264 T^{20} + 4660271465538 T^{21} + 19703212929933 T^{22} + 76466660535057 T^{23} + 267518889951950 T^{24} + 959940492242706 T^{25} + 3178465388070544 T^{26} + 7978698074252724 T^{27} + 30683578106307477 T^{28} + 45431265988837950 T^{29} + 208680948442062317 T^{30} + 153557679042272271 T^{31} + 665416609183179841 T^{32} \))(\( 1 + 56 T^{2} + 1590 T^{4} + 26848 T^{6} + 274865 T^{8} + 1615656 T^{10} + 12863830 T^{12} + 363405056 T^{14} + 6601006116 T^{16} + 61415454464 T^{18} + 367403848630 T^{20} + 7798462921704 T^{22} + 224215824627665 T^{24} + 3701224789161952 T^{26} + 37043955344744790 T^{28} + 220493077599160184 T^{30} + 665416609183179841 T^{32} \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2}( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2}( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( 1 - 66 T^{2} + 2241 T^{4} - 49362 T^{6} + 759092 T^{8} - 8342178 T^{10} + 64005201 T^{12} - 318569394 T^{14} + 815730721 T^{16} \))(\( 1 - 66 T^{2} + 2241 T^{4} - 49362 T^{6} + 759092 T^{8} - 8342178 T^{10} + 64005201 T^{12} - 318569394 T^{14} + 815730721 T^{16} \))(\( ( 1 - 5 T + 13 T^{2} )^{2}( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2}( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2} \))(\( 1 - 3 T + 53 T^{2} - 150 T^{3} + 1317 T^{4} - 4452 T^{5} + 23056 T^{6} - 90522 T^{7} + 327950 T^{8} - 1218621 T^{9} + 4082037 T^{10} - 12551466 T^{11} + 42977824 T^{12} - 136810599 T^{13} + 317458436 T^{14} - 1828010007 T^{15} + 2359677564 T^{16} - 23764130091 T^{17} + 53650475684 T^{18} - 300572886003 T^{19} + 1227489631264 T^{20} - 4660271465538 T^{21} + 19703212929933 T^{22} - 76466660535057 T^{23} + 267518889951950 T^{24} - 959940492242706 T^{25} + 3178465388070544 T^{26} - 7978698074252724 T^{27} + 30683578106307477 T^{28} - 45431265988837950 T^{29} + 208680948442062317 T^{30} - 153557679042272271 T^{31} + 665416609183179841 T^{32} \))
$17$ (\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 20 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 17 T^{2} )^{4} \))(\( 1 - 22 T^{2} + 682 T^{4} - 6358 T^{6} + 83521 T^{8} \))(\( 1 - 22 T^{2} + 682 T^{4} - 6358 T^{6} + 83521 T^{8} \))(\( ( 1 - 68 T^{2} + 2167 T^{4} - 44168 T^{6} + 626263 T^{8} - 5679428 T^{10} + 24137569 T^{12} )^{2} \))(\( ( 1 + 22 T^{2} + 289 T^{4} )^{2} \))(\( 1 + 7 T + 32 T^{2} + 119 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 65 T^{2} + 210 T^{3} + 2087 T^{4} - 9143 T^{5} - 37340 T^{6} + 240381 T^{7} + 293834 T^{8} - 4176065 T^{9} + 3382763 T^{10} + 47662233 T^{11} - 157347285 T^{12} - 273515658 T^{13} + 3170983122 T^{14} - 4649766186 T^{15} - 45473365365 T^{16} + 234164550729 T^{17} + 282531748523 T^{18} - 5929415122705 T^{19} + 7092438449546 T^{20} + 98637620554413 T^{21} - 260474782846940 T^{22} - 1084248954812071 T^{23} + 4207379270237063 T^{24} + 7197098224602930 T^{25} - 37870445419934465 T^{26} - 19809156065811874 T^{27} + 168377826559400929 T^{28} \))(\( ( 1 - 2 T + 32 T^{2} - 21 T^{3} + 544 T^{4} - 578 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 18 T^{2} + 9 T^{3} + 306 T^{4} + 4913 T^{6} )^{2} \))(\( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 + 7 T + 32 T^{2} + 119 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 65 T^{2} + 210 T^{3} + 2087 T^{4} - 9143 T^{5} - 37340 T^{6} + 240381 T^{7} + 293834 T^{8} - 4176065 T^{9} + 3382763 T^{10} + 47662233 T^{11} - 157347285 T^{12} - 273515658 T^{13} + 3170983122 T^{14} - 4649766186 T^{15} - 45473365365 T^{16} + 234164550729 T^{17} + 282531748523 T^{18} - 5929415122705 T^{19} + 7092438449546 T^{20} + 98637620554413 T^{21} - 260474782846940 T^{22} - 1084248954812071 T^{23} + 4207379270237063 T^{24} + 7197098224602930 T^{25} - 37870445419934465 T^{26} - 19809156065811874 T^{27} + 168377826559400929 T^{28} \))(\( ( 1 + 9 T + 44 T^{2} + 153 T^{3} + 289 T^{4} )^{2} \))(\( 1 - 10 T^{2} - 189 T^{4} - 2890 T^{6} + 83521 T^{8} \))(\( 1 - 9 T - 31 T^{2} + 498 T^{3} + 6 T^{4} - 11613 T^{5} + 1180 T^{6} + 197118 T^{7} + 356723 T^{8} - 3738756 T^{9} - 13114257 T^{10} + 60977685 T^{11} + 321880693 T^{12} - 548795961 T^{13} - 7936687522 T^{14} + 1772823582 T^{15} + 160937528238 T^{16} + 30138000894 T^{17} - 2293702693858 T^{18} - 2696234556393 T^{19} + 26883797360053 T^{20} + 86579592891045 T^{21} - 316546283221233 T^{22} - 1534156175710788 T^{23} + 2488413121625843 T^{24} + 23375805039335646 T^{25} + 2378872802529820 T^{26} - 397999531820542029 T^{27} + 3495733423378566 T^{28} + 4932479860387156626 T^{29} - 5219712623341428799 T^{30} - 25761807463588342137 T^{31} + 48661191875666868481 T^{32} \))(\( ( 1 + 58 T^{2} + 1603 T^{4} + 30013 T^{6} + 497674 T^{8} + 8673757 T^{10} + 133884163 T^{12} + 1399979002 T^{14} + 6975757441 T^{16} )^{2} \))(\( ( 1 - 12 T + 65 T^{2} - 204 T^{3} + 289 T^{4} )^{2} \))(\( 1 + 26 T^{2} + 387 T^{4} + 7514 T^{6} + 83521 T^{8} \))(\( 1 + 26 T^{2} + 387 T^{4} + 7514 T^{6} + 83521 T^{8} \))(\( ( 1 + 12 T + 65 T^{2} + 204 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 3 T + 20 T^{2} - 51 T^{3} + 289 T^{4} )^{2} \))(\( 1 + 40 T^{2} + 786 T^{4} - 1104 T^{5} + 10208 T^{6} - 39072 T^{7} + 129731 T^{8} - 664224 T^{9} + 2950112 T^{10} - 5423952 T^{11} + 65647506 T^{12} + 965502760 T^{14} + 6975757441 T^{16} \))(\( 1 + 40 T^{2} + 786 T^{4} - 1104 T^{5} + 10208 T^{6} - 39072 T^{7} + 129731 T^{8} - 664224 T^{9} + 2950112 T^{10} - 5423952 T^{11} + 65647506 T^{12} + 965502760 T^{14} + 6975757441 T^{16} \))(\( ( 1 - 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 + 9 T + 44 T^{2} + 153 T^{3} + 289 T^{4} )^{2} \))(\( 1 + 9 T - 31 T^{2} - 498 T^{3} + 6 T^{4} + 11613 T^{5} + 1180 T^{6} - 197118 T^{7} + 356723 T^{8} + 3738756 T^{9} - 13114257 T^{10} - 60977685 T^{11} + 321880693 T^{12} + 548795961 T^{13} - 7936687522 T^{14} - 1772823582 T^{15} + 160937528238 T^{16} - 30138000894 T^{17} - 2293702693858 T^{18} + 2696234556393 T^{19} + 26883797360053 T^{20} - 86579592891045 T^{21} - 316546283221233 T^{22} + 1534156175710788 T^{23} + 2488413121625843 T^{24} - 23375805039335646 T^{25} + 2378872802529820 T^{26} + 397999531820542029 T^{27} + 3495733423378566 T^{28} - 4932479860387156626 T^{29} - 5219712623341428799 T^{30} + 25761807463588342137 T^{31} + 48661191875666868481 T^{32} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 10 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 + 6 T + 30 T^{2} + 114 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 6 T + 30 T^{2} - 114 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 1639 T^{4} - 35804 T^{6} + 591679 T^{8} - 6516050 T^{10} + 47045881 T^{12} )^{2} \))(\( ( 1 - 14 T^{2} + 361 T^{4} )^{2} \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( 1 - 7 T - 54 T^{2} + 381 T^{3} + 1875 T^{4} - 9873 T^{5} - 65652 T^{6} + 221430 T^{7} + 1870425 T^{8} - 4319703 T^{9} - 46476858 T^{10} + 61637031 T^{11} + 1073881146 T^{12} - 457871775 T^{13} - 21789737442 T^{14} - 8699563725 T^{15} + 387671093706 T^{16} + 422768395629 T^{17} - 6056910611418 T^{18} - 10696012278597 T^{19} + 87995791969425 T^{20} + 197930019166770 T^{21} - 1115004880767732 T^{22} - 3185895640172067 T^{23} + 11495749233376875 T^{24} + 44382788640221439 T^{25} - 119519005629572694 T^{26} - 294370884235799413 T^{27} + 799006685782884121 T^{28} \))(\( ( 1 - 3 T + 33 T^{2} - 35 T^{3} + 627 T^{4} - 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 3 T + 21 T^{2} - 65 T^{3} + 399 T^{4} - 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( 1 - 7 T - 54 T^{2} + 381 T^{3} + 1875 T^{4} - 9873 T^{5} - 65652 T^{6} + 221430 T^{7} + 1870425 T^{8} - 4319703 T^{9} - 46476858 T^{10} + 61637031 T^{11} + 1073881146 T^{12} - 457871775 T^{13} - 21789737442 T^{14} - 8699563725 T^{15} + 387671093706 T^{16} + 422768395629 T^{17} - 6056910611418 T^{18} - 10696012278597 T^{19} + 87995791969425 T^{20} + 197930019166770 T^{21} - 1115004880767732 T^{22} - 3185895640172067 T^{23} + 11495749233376875 T^{24} + 44382788640221439 T^{25} - 119519005629572694 T^{26} - 294370884235799413 T^{27} + 799006685782884121 T^{28} \))(\( 1 - 35 T^{2} + 864 T^{4} - 12635 T^{6} + 130321 T^{8} \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 - T + 19 T^{2} )^{2} \))(\( 1 + 59 T^{2} + 1482 T^{4} + 279 T^{5} + 21358 T^{6} - 23166 T^{7} + 284075 T^{8} - 1924515 T^{9} + 8259087 T^{10} - 60795468 T^{11} + 210571285 T^{12} - 1125692802 T^{13} + 3051652292 T^{14} - 14070928500 T^{15} + 40349090466 T^{16} - 267347641500 T^{17} + 1101646477412 T^{18} - 7721126928918 T^{19} + 27441860432485 T^{20} - 150535597519332 T^{21} + 388556024170647 T^{22} - 1720269569781585 T^{23} + 4824605670872075 T^{24} - 7475383206748314 T^{25} + 130947313134113758 T^{26} + 32500782232603101 T^{27} + 3280132710056050602 T^{28} + 47141394461190163139 T^{30} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 77 T^{2} + 3034 T^{4} - 84368 T^{6} + 1811980 T^{8} - 30456848 T^{10} + 395393914 T^{12} - 3622532837 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 - 19 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 19 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 37 T^{2} + 361 T^{4} )( 1 + 26 T^{2} + 361 T^{4} ) \))(\( 1 - 6 T - 33 T^{2} + 150 T^{3} + 1165 T^{4} - 1968 T^{5} - 34182 T^{6} + 11868 T^{7} + 759066 T^{8} + 225492 T^{9} - 12339702 T^{10} - 13498512 T^{11} + 151823965 T^{12} + 371414850 T^{13} - 1552514073 T^{14} - 5363230434 T^{15} + 16983563041 T^{16} \))(\( 1 + 6 T - 33 T^{2} - 150 T^{3} + 1165 T^{4} + 1968 T^{5} - 34182 T^{6} - 11868 T^{7} + 759066 T^{8} - 225492 T^{9} - 12339702 T^{10} + 13498512 T^{11} + 151823965 T^{12} - 371414850 T^{13} - 1552514073 T^{14} + 5363230434 T^{15} + 16983563041 T^{16} \))(\( ( 1 - 10 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 361 T^{4} )^{2} \))(\( 1 - 35 T^{2} + 864 T^{4} - 12635 T^{6} + 130321 T^{8} \))(\( 1 + 59 T^{2} + 1482 T^{4} + 279 T^{5} + 21358 T^{6} - 23166 T^{7} + 284075 T^{8} - 1924515 T^{9} + 8259087 T^{10} - 60795468 T^{11} + 210571285 T^{12} - 1125692802 T^{13} + 3051652292 T^{14} - 14070928500 T^{15} + 40349090466 T^{16} - 267347641500 T^{17} + 1101646477412 T^{18} - 7721126928918 T^{19} + 27441860432485 T^{20} - 150535597519332 T^{21} + 388556024170647 T^{22} - 1720269569781585 T^{23} + 4824605670872075 T^{24} - 7475383206748314 T^{25} + 130947313134113758 T^{26} + 32500782232603101 T^{27} + 3280132710056050602 T^{28} + 47141394461190163139 T^{30} + \)\(28\!\cdots\!81\)\( T^{32} \))
$23$ (\( 1 + 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( ( 1 - 8 T + 23 T^{2} )( 1 + 8 T + 23 T^{2} ) \))(\( ( 1 + 4 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 18 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 82 T^{2} + 2722 T^{4} - 43378 T^{6} + 279841 T^{8} \))(\( 1 - 82 T^{2} + 2722 T^{4} - 43378 T^{6} + 279841 T^{8} \))(\( ( 1 - 2 T^{2} + 979 T^{4} + 3772 T^{6} + 517891 T^{8} - 559682 T^{10} + 148035889 T^{12} )^{2} \))(\( ( 1 - 28 T^{2} + 529 T^{4} )^{2} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 11 T - 8 T^{2} + 333 T^{3} + 401 T^{4} - 3407 T^{5} - 42005 T^{6} + 36987 T^{7} + 1121822 T^{8} + 103015 T^{9} - 29774440 T^{10} + 52947609 T^{11} + 527481093 T^{12} - 1421356596 T^{13} - 4817982924 T^{14} - 32691201708 T^{15} + 279037498197 T^{16} + 644213558703 T^{17} - 8332109064040 T^{18} + 663039874145 T^{19} + 166069917069758 T^{20} + 125934278808189 T^{21} - 3289452936728405 T^{22} - 6136527117604441 T^{23} + 16612030996673249 T^{24} + 317285649385337691 T^{25} - 175316995456162568 T^{26} - 5544399981301141213 T^{27} + 11592836324538749809 T^{28} \))(\( 1 + 14 T + 74 T^{2} + 358 T^{3} + 2628 T^{4} + 11188 T^{5} + 33943 T^{6} + 257324 T^{7} + 1390212 T^{8} + 4355786 T^{9} + 20708234 T^{10} + 90108802 T^{11} + 148035889 T^{12} \))(\( 1 - 6 T - 18 T^{2} + 30 T^{3} + 612 T^{4} + 2172 T^{5} - 30449 T^{6} + 49956 T^{7} + 323748 T^{8} + 365010 T^{9} - 5037138 T^{10} - 38618058 T^{11} + 148035889 T^{12} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 11 T + 129 T^{2} + 876 T^{3} + 6604 T^{4} + 35691 T^{5} + 217568 T^{6} + 992939 T^{7} + 5004064 T^{8} + 18880539 T^{9} + 80350868 T^{10} + 245140716 T^{11} + 830288247 T^{12} + 1628394779 T^{13} + 3404825447 T^{14} )^{2} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 23 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 21 T + 283 T^{2} - 2856 T^{3} + 23904 T^{4} - 177009 T^{5} + 1214978 T^{6} - 7994925 T^{7} + 50784536 T^{8} - 310700127 T^{9} + 1817756595 T^{10} - 10184685783 T^{11} + 55106115085 T^{12} - 290568927984 T^{13} + 1499561670325 T^{14} - 7546165977213 T^{15} + 36821082385998 T^{16} - 173561817475899 T^{17} + 793268123601925 T^{18} - 3535352146781328 T^{19} + 15420950351501485 T^{20} - 65552131046611569 T^{21} + 269093213526437955 T^{22} - 1057879698795731769 T^{23} + 3976987051198414616 T^{24} - 14400080441947075275 T^{25} + 50332299741336834722 T^{26} - \)\(16\!\cdots\!43\)\( T^{27} + \)\(52\!\cdots\!84\)\( T^{28} - \)\(14\!\cdots\!48\)\( T^{29} + \)\(32\!\cdots\!47\)\( T^{30} - \)\(55\!\cdots\!47\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 3 T + 56 T^{2} - 159 T^{3} + 1321 T^{4} - 3510 T^{5} + 30863 T^{6} - 67173 T^{7} + 842170 T^{8} - 1544979 T^{9} + 16326527 T^{10} - 42706170 T^{11} + 369669961 T^{12} - 1023378537 T^{13} + 8290009784 T^{14} - 10214476341 T^{15} + 78310985281 T^{16} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} )( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} ) \))(\( 1 + 38 T^{2} + 915 T^{4} + 20102 T^{6} + 279841 T^{8} \))(\( 1 + 38 T^{2} + 915 T^{4} + 20102 T^{6} + 279841 T^{8} \))(\( ( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} )( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} ) \))(\( 1 + 45 T^{2} + 1496 T^{4} + 23805 T^{6} + 279841 T^{8} \))(\( 1 + 52 T^{2} + 1242 T^{4} + 2784 T^{5} + 24080 T^{6} + 140352 T^{7} + 497843 T^{8} + 3228096 T^{9} + 12738320 T^{10} + 33872928 T^{11} + 347562522 T^{12} + 7697866228 T^{14} + 78310985281 T^{16} \))(\( 1 + 52 T^{2} + 1242 T^{4} - 2784 T^{5} + 24080 T^{6} - 140352 T^{7} + 497843 T^{8} - 3228096 T^{9} + 12738320 T^{10} - 33872928 T^{11} + 347562522 T^{12} + 7697866228 T^{14} + 78310985281 T^{16} \))(\( 1 + 21 T^{2} - 88 T^{4} + 11109 T^{6} + 279841 T^{8} \))(\( 1 + 21 T^{2} - 88 T^{4} + 11109 T^{6} + 279841 T^{8} \))(\( 1 + 30 T^{2} + 371 T^{4} + 15870 T^{6} + 279841 T^{8} \))(\( 1 - 125 T^{2} + 7680 T^{4} - 295747 T^{6} + 8228447 T^{8} - 202400565 T^{10} + 5673034564 T^{12} - 171801092192 T^{14} + 4463691201090 T^{16} - 90882777769568 T^{18} + 1587547665424324 T^{20} - 29962547573877285 T^{22} + 644377791902488607 T^{24} - 12251766411903050803 T^{26} + \)\(16\!\cdots\!80\)\( T^{28} - \)\(14\!\cdots\!25\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))
$29$ (\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 - 54 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{4} \))(\( ( 1 - 2 T + 29 T^{2} )^{4} \))(\( ( 1 - 56 T^{2} + 841 T^{4} )^{6} \))(\( ( 1 - 40 T^{2} + 841 T^{4} )^{2} \))(\( 1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 - T - 89 T^{2} + 606 T^{3} + 3413 T^{4} - 45595 T^{5} + 49603 T^{6} + 1643802 T^{7} - 7893892 T^{8} - 19552444 T^{9} + 271585946 T^{10} - 420585531 T^{11} - 3441402105 T^{12} + 10956432363 T^{13} + 10513309734 T^{14} + 317736538527 T^{15} - 2894219170305 T^{16} - 10257660515559 T^{17} + 192087579472826 T^{18} - 401043092198156 T^{19} - 4695471055055332 T^{20} + 28355381176486818 T^{21} + 24813722822104483 T^{22} - 661453320769747055 T^{23} + 1435873787253586013 T^{24} + 7393508918017732374 T^{25} - 31489515705286744649 T^{26} - 10260628712958602189 T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( 1 + T - 46 T^{2} + 149 T^{3} + 897 T^{4} - 4282 T^{5} - 13523 T^{6} - 124178 T^{7} + 754377 T^{8} + 3633961 T^{9} - 32534926 T^{10} + 20511149 T^{11} + 594823321 T^{12} \))(\( 1 - 15 T + 90 T^{2} - 411 T^{3} + 2205 T^{4} - 4110 T^{5} - 17723 T^{6} - 119190 T^{7} + 1854405 T^{8} - 10023879 T^{9} + 63655290 T^{10} - 307667235 T^{11} + 594823321 T^{12} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 - T - 89 T^{2} + 606 T^{3} + 3413 T^{4} - 45595 T^{5} + 49603 T^{6} + 1643802 T^{7} - 7893892 T^{8} - 19552444 T^{9} + 271585946 T^{10} - 420585531 T^{11} - 3441402105 T^{12} + 10956432363 T^{13} + 10513309734 T^{14} + 317736538527 T^{15} - 2894219170305 T^{16} - 10257660515559 T^{17} + 192087579472826 T^{18} - 401043092198156 T^{19} - 4695471055055332 T^{20} + 28355381176486818 T^{21} + 24813722822104483 T^{22} - 661453320769747055 T^{23} + 1435873787253586013 T^{24} + 7393508918017732374 T^{25} - 31489515705286744649 T^{26} - 10260628712958602189 T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( ( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 14 T^{2} + 841 T^{4} )^{2} \))(\( 1 - 6 T + 106 T^{2} - 564 T^{3} + 5445 T^{4} - 23700 T^{5} + 153455 T^{6} - 499140 T^{7} + 2268674 T^{8} - 3839766 T^{9} + 25367247 T^{10} - 108756381 T^{11} + 2283543946 T^{12} - 15452150286 T^{13} + 152754700246 T^{14} - 806878620189 T^{15} + 5726182499856 T^{16} - 23399479985481 T^{17} + 128466702906886 T^{18} - 376862493325254 T^{19} + 1615107245670826 T^{20} - 2230718335391769 T^{21} + 15089030105167287 T^{22} - 66235488555503694 T^{23} + 1134896030677883714 T^{24} - 7241096842395252660 T^{25} + 64559628486082344455 T^{26} - \)\(28\!\cdots\!00\)\( T^{27} + \)\(19\!\cdots\!45\)\( T^{28} - \)\(57\!\cdots\!96\)\( T^{29} + \)\(31\!\cdots\!86\)\( T^{30} - \)\(51\!\cdots\!94\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 6 T + 53 T^{2} + 246 T^{3} + 580 T^{4} + 540 T^{5} - 22066 T^{6} - 299625 T^{7} - 1268282 T^{8} - 8689125 T^{9} - 18557506 T^{10} + 13170060 T^{11} + 410222980 T^{12} + 5045742654 T^{13} + 31525636013 T^{14} + 103499257854 T^{15} + 500246412961 T^{16} )^{2} \))(\( ( 1 - 5 T + 29 T^{2} )^{4} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 + 5 T + 29 T^{2} )^{4} \))(\( ( 1 + 4 T + 29 T^{2} )^{4} \))(\( ( 1 - 8 T + 71 T^{2} - 344 T^{3} + 1924 T^{4} - 9976 T^{5} + 59711 T^{6} - 195112 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} - 344 T^{3} + 1924 T^{4} - 9976 T^{5} + 59711 T^{6} - 195112 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} )^{2} \))(\( 1 - 6 T + 106 T^{2} - 564 T^{3} + 5445 T^{4} - 23700 T^{5} + 153455 T^{6} - 499140 T^{7} + 2268674 T^{8} - 3839766 T^{9} + 25367247 T^{10} - 108756381 T^{11} + 2283543946 T^{12} - 15452150286 T^{13} + 152754700246 T^{14} - 806878620189 T^{15} + 5726182499856 T^{16} - 23399479985481 T^{17} + 128466702906886 T^{18} - 376862493325254 T^{19} + 1615107245670826 T^{20} - 2230718335391769 T^{21} + 15089030105167287 T^{22} - 66235488555503694 T^{23} + 1134896030677883714 T^{24} - 7241096842395252660 T^{25} + 64559628486082344455 T^{26} - \)\(28\!\cdots\!00\)\( T^{27} + \)\(19\!\cdots\!45\)\( T^{28} - \)\(57\!\cdots\!96\)\( T^{29} + \)\(31\!\cdots\!86\)\( T^{30} - \)\(51\!\cdots\!94\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 31 T^{2} )^{4} \))(\( ( 1 + 31 T^{2} )^{4} \))(\( ( 1 + 31 T^{2} )^{4} \))(\( ( 1 - 58 T^{2} + 3727 T^{4} - 113644 T^{6} + 3581647 T^{8} - 53564218 T^{10} + 887503681 T^{12} )^{2} \))(\( ( 1 - 31 T^{2} )^{4} \))(\( ( 1 + 3 T + 31 T^{2} )^{2} \))(\( ( 1 - T + 86 T^{2} - 194 T^{3} + 4879 T^{4} - 9670 T^{5} + 191454 T^{6} - 403758 T^{7} + 5935074 T^{8} - 9292870 T^{9} + 145350289 T^{10} - 179163074 T^{11} + 2462106986 T^{12} - 887503681 T^{13} + 27512614111 T^{14} )^{2} \))(\( 1 - 3 T - 48 T^{2} + 147 T^{3} + 1005 T^{4} - 1344 T^{5} - 24505 T^{6} - 41664 T^{7} + 965805 T^{8} + 4379277 T^{9} - 44329008 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( 1 - 3 T - 6 T^{2} + 221 T^{3} - 639 T^{4} - 2088 T^{5} + 61647 T^{6} - 64728 T^{7} - 614079 T^{8} + 6583811 T^{9} - 5541126 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 3 T - 22 T^{2} + 93 T^{3} + 961 T^{4} \))(\( ( 1 + 4 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 - 3 T - 22 T^{2} - 93 T^{3} + 961 T^{4} \))(\( 1 + T - 85 T^{2} - 302 T^{3} + 2323 T^{4} + 16596 T^{5} - 8720 T^{6} - 121502 T^{7} + 336059 T^{8} - 5031700 T^{9} - 52734649 T^{10} - 249456712 T^{11} - 356372186 T^{12} + 8588183707 T^{13} + 82956488229 T^{14} + 266233694917 T^{15} - 342473670746 T^{16} - 7431564907192 T^{17} - 48701555779129 T^{18} - 144053299086700 T^{19} + 298253599533179 T^{20} - 3342837639714722 T^{21} - 7437209846485520 T^{22} + 438791969378495916 T^{23} + 1903996510656400723 T^{24} - 7673360022714258962 T^{25} - 66951336622026729685 T^{26} + 24417546297445042591 T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 - 35 T^{2} + 264 T^{4} - 33635 T^{6} + 923521 T^{8} \))(\( ( 1 - 4 T + 31 T^{2} )^{2}( 1 + 7 T + 31 T^{2} )^{2} \))(\( 1 - 220 T^{2} + 25434 T^{4} - 2035931 T^{6} + 125854031 T^{8} - 6377263569 T^{10} + 274749236767 T^{12} - 10292358079372 T^{14} + 339402697885782 T^{16} - 9890956114276492 T^{18} + 253736689888296607 T^{20} - 5659844892194697489 T^{22} + \)\(10\!\cdots\!71\)\( T^{24} - \)\(16\!\cdots\!31\)\( T^{26} + \)\(20\!\cdots\!74\)\( T^{28} - \)\(16\!\cdots\!20\)\( T^{30} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 + 176 T^{2} + 16407 T^{4} + 1045570 T^{6} + 50906954 T^{8} + 2036295270 T^{10} + 71233973380 T^{12} + 2306080860179 T^{14} + 72156636517806 T^{16} + 2216143706632019 T^{18} + 65786070329870980 T^{20} + 1807219547727888870 T^{22} + 43418084810021264714 T^{24} + \)\(85\!\cdots\!70\)\( T^{26} + \)\(12\!\cdots\!27\)\( T^{28} + \)\(13\!\cdots\!96\)\( T^{30} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 41 T^{2} + 720 T^{4} - 39401 T^{6} + 923521 T^{8} \))(\( ( 1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} )^{2} \))(\( 1 - 41 T^{2} + 720 T^{4} - 39401 T^{6} + 923521 T^{8} \))(\( ( 1 - 46 T^{2} + 961 T^{4} )( 1 - 13 T^{2} + 961 T^{4} ) \))(\( 1 + 6 T - 4 T^{2} - 336 T^{3} - 2729 T^{4} - 10764 T^{5} + 2216 T^{6} + 444234 T^{7} + 3877768 T^{8} + 13771254 T^{9} + 2129576 T^{10} - 320670324 T^{11} - 2520288809 T^{12} - 9619394736 T^{13} - 3550014724 T^{14} + 165075684666 T^{15} + 852891037441 T^{16} \))(\( 1 - 6 T - 4 T^{2} + 336 T^{3} - 2729 T^{4} + 10764 T^{5} + 2216 T^{6} - 444234 T^{7} + 3877768 T^{8} - 13771254 T^{9} + 2129576 T^{10} + 320670324 T^{11} - 2520288809 T^{12} + 9619394736 T^{13} - 3550014724 T^{14} - 165075684666 T^{15} + 852891037441 T^{16} \))(\( ( 1 - 46 T^{2} + 961 T^{4} )( 1 + 59 T^{2} + 961 T^{4} ) \))(\( ( 1 - 46 T^{2} + 961 T^{4} )( 1 + 59 T^{2} + 961 T^{4} ) \))(\( ( 1 + 35 T^{2} + 961 T^{4} )^{2} \))(\( 1 - 6 T + 128 T^{2} - 696 T^{3} + 7467 T^{4} - 41745 T^{5} + 298711 T^{6} - 1778985 T^{7} + 10180130 T^{8} - 58737741 T^{9} + 320070333 T^{10} - 1687070526 T^{11} + 8941505953 T^{12} - 50372743224 T^{13} + 219778671713 T^{14} - 1637243989362 T^{15} + 5894911299924 T^{16} - 50754563670222 T^{17} + 211207303516193 T^{18} - 1500654393386184 T^{19} + 8257668519220513 T^{20} - 48299396836503426 T^{21} + 284063598716395773 T^{22} - 1616028801884863251 T^{23} + 8682541636984247330 T^{24} - 47035691229501298935 T^{25} + \)\(24\!\cdots\!11\)\( T^{26} - \)\(10\!\cdots\!95\)\( T^{27} + \)\(58\!\cdots\!87\)\( T^{28} - \)\(16\!\cdots\!36\)\( T^{29} + \)\(96\!\cdots\!88\)\( T^{30} - \)\(14\!\cdots\!06\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{4} \))(\( ( 1 + 6 T + 37 T^{2} )^{4} \))(\( ( 1 + 6 T + 66 T^{2} + 222 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 6 T + 66 T^{2} + 222 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 2 T + 47 T^{2} - 276 T^{3} + 1739 T^{4} - 2738 T^{5} + 50653 T^{6} )^{4} \))(\( ( 1 + 8 T + 37 T^{2} )^{4} \))(\( ( 1 + T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 - 10 T - 84 T^{2} + 1296 T^{3} + 1134 T^{4} - 66630 T^{5} + 77382 T^{6} + 1851174 T^{7} - 1251993 T^{8} - 21837810 T^{9} - 268575252 T^{10} - 774884982 T^{11} + 27666538119 T^{12} + 26159905206 T^{13} - 1381876923558 T^{14} + 967916492622 T^{15} + 37875490684911 T^{16} - 39250248993246 T^{17} - 503353262863572 T^{18} - 1514320157614170 T^{19} - 3212271503983137 T^{20} + 175735422719804142 T^{21} + 271802685103314822 T^{22} - 8659350722545980510 T^{23} + 5452934678321840766 T^{24} + \)\(23\!\cdots\!48\)\( T^{25} - \)\(55\!\cdots\!04\)\( T^{26} - \)\(24\!\cdots\!70\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( ( 1 + 3 T + 81 T^{2} + 199 T^{3} + 2997 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 3 T + 33 T^{2} + 115 T^{3} + 1221 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( ( 1 + T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( ( 1 + T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 - 10 T - 84 T^{2} + 1296 T^{3} + 1134 T^{4} - 66630 T^{5} + 77382 T^{6} + 1851174 T^{7} - 1251993 T^{8} - 21837810 T^{9} - 268575252 T^{10} - 774884982 T^{11} + 27666538119 T^{12} + 26159905206 T^{13} - 1381876923558 T^{14} + 967916492622 T^{15} + 37875490684911 T^{16} - 39250248993246 T^{17} - 503353262863572 T^{18} - 1514320157614170 T^{19} - 3212271503983137 T^{20} + 175735422719804142 T^{21} + 271802685103314822 T^{22} - 8659350722545980510 T^{23} + 5452934678321840766 T^{24} + \)\(23\!\cdots\!48\)\( T^{25} - \)\(55\!\cdots\!04\)\( T^{26} - \)\(24\!\cdots\!70\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( ( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - T - 188 T^{2} + 55 T^{3} + 18431 T^{4} + 6958 T^{5} - 1220598 T^{6} - 1466820 T^{7} + 61023285 T^{8} + 128763363 T^{9} - 2426865150 T^{10} - 7087005807 T^{11} + 80710069782 T^{12} + 247085609469 T^{13} - 2444398029834 T^{14} - 3801878390997 T^{15} + 81128049964254 T^{16} - 140669500466889 T^{17} - 3346380902842746 T^{18} + 12515627376433257 T^{19} + 151263665092702902 T^{20} - 491441025939358299 T^{21} - 6226672006436746350 T^{22} + 12223747755547878279 T^{23} + \)\(21\!\cdots\!85\)\( T^{24} - \)\(19\!\cdots\!40\)\( T^{25} - \)\(58\!\cdots\!02\)\( T^{26} + \)\(12\!\cdots\!54\)\( T^{27} + \)\(12\!\cdots\!11\)\( T^{28} + \)\(13\!\cdots\!35\)\( T^{29} - \)\(16\!\cdots\!32\)\( T^{30} - \)\(33\!\cdots\!93\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( ( 1 - T + 82 T^{2} - 88 T^{3} + 3940 T^{4} - 3256 T^{5} + 112258 T^{6} - 50653 T^{7} + 1874161 T^{8} )^{4} \))(\( ( 1 - 37 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 5 T - 12 T^{2} + 185 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 5 T - 12 T^{2} + 185 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 37 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 6 T - 69 T^{2} - 18 T^{3} + 4753 T^{4} + 9780 T^{5} - 152586 T^{6} - 146184 T^{7} + 2893194 T^{8} - 5408808 T^{9} - 208890234 T^{10} + 495386340 T^{11} + 8907887233 T^{12} - 1248191226 T^{13} - 177035122221 T^{14} - 569591262798 T^{15} + 3512479453921 T^{16} \))(\( 1 - 6 T - 69 T^{2} - 18 T^{3} + 4753 T^{4} + 9780 T^{5} - 152586 T^{6} - 146184 T^{7} + 2893194 T^{8} - 5408808 T^{9} - 208890234 T^{10} + 495386340 T^{11} + 8907887233 T^{12} - 1248191226 T^{13} - 177035122221 T^{14} - 569591262798 T^{15} + 3512479453921 T^{16} \))(\( ( 1 + 37 T^{2} )^{4} \))(\( ( 1 + 37 T^{2} )^{4} \))(\( ( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - T - 188 T^{2} + 55 T^{3} + 18431 T^{4} + 6958 T^{5} - 1220598 T^{6} - 1466820 T^{7} + 61023285 T^{8} + 128763363 T^{9} - 2426865150 T^{10} - 7087005807 T^{11} + 80710069782 T^{12} + 247085609469 T^{13} - 2444398029834 T^{14} - 3801878390997 T^{15} + 81128049964254 T^{16} - 140669500466889 T^{17} - 3346380902842746 T^{18} + 12515627376433257 T^{19} + 151263665092702902 T^{20} - 491441025939358299 T^{21} - 6226672006436746350 T^{22} + 12223747755547878279 T^{23} + \)\(21\!\cdots\!85\)\( T^{24} - \)\(19\!\cdots\!40\)\( T^{25} - \)\(58\!\cdots\!02\)\( T^{26} + \)\(12\!\cdots\!54\)\( T^{27} + \)\(12\!\cdots\!11\)\( T^{28} + \)\(13\!\cdots\!35\)\( T^{29} - \)\(16\!\cdots\!32\)\( T^{30} - \)\(33\!\cdots\!93\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( ( 1 - 41 T^{2} )^{2} \))(\( ( 1 - 68 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 41 T^{2} )^{4} \))(\( 1 - 102 T^{2} + 5130 T^{4} - 171462 T^{6} + 2825761 T^{8} \))(\( 1 - 102 T^{2} + 5130 T^{4} - 171462 T^{6} + 2825761 T^{8} \))(\( ( 1 - 132 T^{2} + 10823 T^{4} - 527752 T^{6} + 18193463 T^{8} - 373000452 T^{10} + 4750104241 T^{12} )^{2} \))(\( ( 1 + 70 T^{2} + 1681 T^{4} )^{2} \))(\( 1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 + 33 T + 463 T^{2} + 3882 T^{3} + 26359 T^{4} + 177381 T^{5} + 987377 T^{6} + 3338436 T^{7} - 1489480 T^{8} - 146370792 T^{9} - 1532374696 T^{10} - 10553354379 T^{11} - 66691501599 T^{12} - 460808734581 T^{13} - 3110830401306 T^{14} - 18893158117821 T^{15} - 112108414187919 T^{16} - 727347737155059 T^{17} - 4330124653343656 T^{18} - 16957963898481192 T^{19} - 7075185264884680 T^{20} + 650174679078190116 T^{21} + 7884131517953805617 T^{22} + 58071334904735196141 T^{23} + \)\(35\!\cdots\!59\)\( T^{24} + \)\(21\!\cdots\!62\)\( T^{25} + \)\(10\!\cdots\!03\)\( T^{26} + \)\(30\!\cdots\!93\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 - 90 T^{2} + 18 T^{3} + 4410 T^{4} - 810 T^{5} - 194177 T^{6} - 33210 T^{7} + 7413210 T^{8} + 1240578 T^{9} - 254318490 T^{10} + 4750104241 T^{12} \))(\( 1 - 6 T - 90 T^{2} + 210 T^{3} + 7812 T^{4} - 8952 T^{5} - 340301 T^{6} - 367032 T^{7} + 13131972 T^{8} + 14473410 T^{9} - 254318490 T^{10} - 695137206 T^{11} + 4750104241 T^{12} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( 1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 + 33 T + 463 T^{2} + 3882 T^{3} + 26359 T^{4} + 177381 T^{5} + 987377 T^{6} + 3338436 T^{7} - 1489480 T^{8} - 146370792 T^{9} - 1532374696 T^{10} - 10553354379 T^{11} - 66691501599 T^{12} - 460808734581 T^{13} - 3110830401306 T^{14} - 18893158117821 T^{15} - 112108414187919 T^{16} - 727347737155059 T^{17} - 4330124653343656 T^{18} - 16957963898481192 T^{19} - 7075185264884680 T^{20} + 650174679078190116 T^{21} + 7884131517953805617 T^{22} + 58071334904735196141 T^{23} + \)\(35\!\cdots\!59\)\( T^{24} + \)\(21\!\cdots\!62\)\( T^{25} + \)\(10\!\cdots\!03\)\( T^{26} + \)\(30\!\cdots\!93\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( ( 1 - 3 T + 44 T^{2} - 123 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 68 T^{2} + 1681 T^{4} )^{2} \))(\( 1 + 6 T - 142 T^{2} - 1146 T^{3} + 7575 T^{4} + 89148 T^{5} - 186515 T^{6} - 3858942 T^{7} + 5165546 T^{8} + 137269398 T^{9} - 383379603 T^{10} - 6275799867 T^{11} + 14048576428 T^{12} + 262470296220 T^{13} + 63020850350 T^{14} - 4818424458177 T^{15} - 18114488698896 T^{16} - 197555402785257 T^{17} + 105938049438350 T^{18} + 18089715285778620 T^{19} + 39697919375761708 T^{20} - 727090330826925267 T^{21} - 1821093078123196323 T^{22} + 26733801933571993638 T^{23} + 41246498577585065066 T^{24} - \)\(12\!\cdots\!62\)\( T^{25} - \)\(25\!\cdots\!15\)\( T^{26} + \)\(49\!\cdots\!68\)\( T^{27} + \)\(17\!\cdots\!75\)\( T^{28} - \)\(10\!\cdots\!66\)\( T^{29} - \)\(53\!\cdots\!62\)\( T^{30} + \)\(93\!\cdots\!06\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 151 T^{2} + 9564 T^{4} - 353897 T^{6} + 12352577 T^{8} - 588962616 T^{10} + 30503470855 T^{12} - 1573469011633 T^{14} + 72313421958936 T^{16} - 2645001408555073 T^{18} + 86195518306695655 T^{20} - 2797633820052054456 T^{22} + 98634403731959794817 T^{24} - \)\(47\!\cdots\!97\)\( T^{26} + \)\(21\!\cdots\!84\)\( T^{28} - \)\(57\!\cdots\!11\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 70 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 1681 T^{4} )^{2} \))(\( 1 - 120 T^{2} + 9948 T^{4} - 607176 T^{6} + 27583238 T^{8} - 1020662856 T^{10} + 28110670428 T^{12} - 570012508920 T^{14} + 7984925229121 T^{16} \))(\( 1 - 120 T^{2} + 9948 T^{4} - 607176 T^{6} + 27583238 T^{8} - 1020662856 T^{10} + 28110670428 T^{12} - 570012508920 T^{14} + 7984925229121 T^{16} \))(\( ( 1 - 15 T + 116 T^{2} - 615 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 15 T + 116 T^{2} + 615 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 3 T + 44 T^{2} + 123 T^{3} + 1681 T^{4} )^{2} \))(\( 1 - 6 T - 142 T^{2} + 1146 T^{3} + 7575 T^{4} - 89148 T^{5} - 186515 T^{6} + 3858942 T^{7} + 5165546 T^{8} - 137269398 T^{9} - 383379603 T^{10} + 6275799867 T^{11} + 14048576428 T^{12} - 262470296220 T^{13} + 63020850350 T^{14} + 4818424458177 T^{15} - 18114488698896 T^{16} + 197555402785257 T^{17} + 105938049438350 T^{18} - 18089715285778620 T^{19} + 39697919375761708 T^{20} + 727090330826925267 T^{21} - 1821093078123196323 T^{22} - 26733801933571993638 T^{23} + 41246498577585065066 T^{24} + \)\(12\!\cdots\!62\)\( T^{25} - \)\(25\!\cdots\!15\)\( T^{26} - \)\(49\!\cdots\!68\)\( T^{27} + \)\(17\!\cdots\!75\)\( T^{28} + \)\(10\!\cdots\!66\)\( T^{29} - \)\(53\!\cdots\!62\)\( T^{30} - \)\(93\!\cdots\!06\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( ( 1 - 12 T + 43 T^{2} )( 1 + 12 T + 43 T^{2} ) \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 12 T + 43 T^{2} )^{2}( 1 + 12 T + 43 T^{2} )^{2} \))(\( 1 - 24 T^{2} + 3774 T^{4} - 44376 T^{6} + 3418801 T^{8} \))(\( 1 - 24 T^{2} + 3774 T^{4} - 44376 T^{6} + 3418801 T^{8} \))(\( ( 1 - 98 T^{2} + 4567 T^{4} - 172988 T^{6} + 8444383 T^{8} - 335042498 T^{10} + 6321363049 T^{12} )^{2} \))(\( ( 1 + 2 T + 43 T^{2} )^{4} \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 7 T - 222 T^{2} + 1221 T^{3} + 30003 T^{4} - 121065 T^{5} - 2964828 T^{6} + 8400318 T^{7} + 232132089 T^{8} - 430114695 T^{9} - 14993117802 T^{10} + 15328887375 T^{11} + 817956723570 T^{12} - 259275458991 T^{13} - 38016795252930 T^{14} - 11148844736613 T^{15} + 1512401981880930 T^{16} + 1218753848524125 T^{17} - 51258486134595402 T^{18} - 63230491623369885 T^{19} + 1467391209891779361 T^{20} + 2283362771617132026 T^{21} - 34653503452639217628 T^{22} - 60846374564133897795 T^{23} + \)\(64\!\cdots\!47\)\( T^{24} + \)\(11\!\cdots\!47\)\( T^{25} - \)\(88\!\cdots\!22\)\( T^{26} - \)\(12\!\cdots\!01\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 + 3 T - 24 T^{2} - 979 T^{3} - 1947 T^{4} + 14820 T^{5} + 386067 T^{6} + 637260 T^{7} - 3600003 T^{8} - 77837353 T^{9} - 82051224 T^{10} + 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 + 3 T - 12 T^{2} + 473 T^{3} + 153 T^{4} - 4176 T^{5} + 165435 T^{6} - 179568 T^{7} + 282897 T^{8} + 37606811 T^{9} - 41025612 T^{10} + 441025329 T^{11} + 6321363049 T^{12} \))(\( ( 1 - 11 T + 43 T^{2} )^{2} \))(\( ( 1 + 13 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 7 T - 222 T^{2} + 1221 T^{3} + 30003 T^{4} - 121065 T^{5} - 2964828 T^{6} + 8400318 T^{7} + 232132089 T^{8} - 430114695 T^{9} - 14993117802 T^{10} + 15328887375 T^{11} + 817956723570 T^{12} - 259275458991 T^{13} - 38016795252930 T^{14} - 11148844736613 T^{15} + 1512401981880930 T^{16} + 1218753848524125 T^{17} - 51258486134595402 T^{18} - 63230491623369885 T^{19} + 1467391209891779361 T^{20} + 2283362771617132026 T^{21} - 34653503452639217628 T^{22} - 60846374564133897795 T^{23} + \)\(64\!\cdots\!47\)\( T^{24} + \)\(11\!\cdots\!47\)\( T^{25} - \)\(88\!\cdots\!22\)\( T^{26} - \)\(12\!\cdots\!01\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 - 35 T^{2} - 624 T^{4} - 64715 T^{6} + 3418801 T^{8} \))(\( ( 1 + 11 T + 43 T^{2} )^{4} \))(\( 1 + 2 T - 137 T^{2} - 620 T^{3} + 8660 T^{4} + 62377 T^{5} - 131688 T^{6} - 3324402 T^{7} - 16902063 T^{8} + 47132751 T^{9} + 1398120027 T^{10} + 5063156292 T^{11} - 36164979717 T^{12} - 388120390392 T^{13} - 815732360646 T^{14} + 8046953157708 T^{15} + 93229603031718 T^{16} + 346018985781444 T^{17} - 1508289134834454 T^{18} - 30858287878896744 T^{19} - 123640868821459317 T^{20} + 744326723152573356 T^{21} + 8838024276744682323 T^{22} + 12811558914472065357 T^{23} - \)\(19\!\cdots\!63\)\( T^{24} - \)\(16\!\cdots\!86\)\( T^{25} - \)\(28\!\cdots\!12\)\( T^{26} + \)\(57\!\cdots\!39\)\( T^{27} + \)\(34\!\cdots\!60\)\( T^{28} - \)\(10\!\cdots\!60\)\( T^{29} - \)\(10\!\cdots\!13\)\( T^{30} + \)\(63\!\cdots\!14\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( ( 1 - 2 T - 93 T^{2} - 64 T^{3} + 3956 T^{4} + 12192 T^{5} - 158990 T^{6} - 321485 T^{7} + 7972668 T^{8} - 13823855 T^{9} - 293972510 T^{10} + 969349344 T^{11} + 13524776756 T^{12} - 9408540352 T^{13} - 587886763557 T^{14} - 543637222214 T^{15} + 11688200277601 T^{16} )^{2} \))(\( ( 1 + 26 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 59 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 59 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 210 T^{2} + 23793 T^{4} - 1729746 T^{6} + 88400276 T^{8} - 3198300354 T^{10} + 81343532193 T^{12} - 1327486240290 T^{14} + 11688200277601 T^{16} \))(\( 1 - 210 T^{2} + 23793 T^{4} - 1729746 T^{6} + 88400276 T^{8} - 3198300354 T^{10} + 81343532193 T^{12} - 1327486240290 T^{14} + 11688200277601 T^{16} \))(\( 1 + 85 T^{2} + 5376 T^{4} + 157165 T^{6} + 3418801 T^{8} \))(\( 1 + 85 T^{2} + 5376 T^{4} + 157165 T^{6} + 3418801 T^{8} \))(\( 1 - 35 T^{2} - 624 T^{4} - 64715 T^{6} + 3418801 T^{8} \))(\( 1 + 2 T - 137 T^{2} - 620 T^{3} + 8660 T^{4} + 62377 T^{5} - 131688 T^{6} - 3324402 T^{7} - 16902063 T^{8} + 47132751 T^{9} + 1398120027 T^{10} + 5063156292 T^{11} - 36164979717 T^{12} - 388120390392 T^{13} - 815732360646 T^{14} + 8046953157708 T^{15} + 93229603031718 T^{16} + 346018985781444 T^{17} - 1508289134834454 T^{18} - 30858287878896744 T^{19} - 123640868821459317 T^{20} + 744326723152573356 T^{21} + 8838024276744682323 T^{22} + 12811558914472065357 T^{23} - \)\(19\!\cdots\!63\)\( T^{24} - \)\(16\!\cdots\!86\)\( T^{25} - \)\(28\!\cdots\!12\)\( T^{26} + \)\(57\!\cdots\!39\)\( T^{27} + \)\(34\!\cdots\!60\)\( T^{28} - \)\(10\!\cdots\!60\)\( T^{29} - \)\(10\!\cdots\!13\)\( T^{30} + \)\(63\!\cdots\!14\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))
$47$ (\( 1 + 12 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{4} \))(\( ( 1 + 47 T^{2} )^{4} \))(\( ( 1 + 4 T + 30 T^{2} + 188 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 - 4 T + 30 T^{2} - 188 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 10 T^{2} + 4591 T^{4} + 70732 T^{6} + 10141519 T^{8} + 48796810 T^{10} + 10779215329 T^{12} )^{2} \))(\( ( 1 + 46 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 3 T + 47 T^{2} )^{2} \))(\( ( 1 - 3 T + 224 T^{2} - 711 T^{3} + 24846 T^{4} - 72810 T^{5} + 1742359 T^{6} - 4337544 T^{7} + 81890873 T^{8} - 160837290 T^{9} + 2579586258 T^{10} - 3469453191 T^{11} + 51373281568 T^{12} - 32337645987 T^{13} + 506623120463 T^{14} )^{2} \))(\( 1 + 21 T + 180 T^{2} + 1119 T^{3} + 10053 T^{4} + 100416 T^{5} + 788551 T^{6} + 4719552 T^{7} + 22207077 T^{8} + 116177937 T^{9} + 878342580 T^{10} + 4816245147 T^{11} + 10779215329 T^{12} \))(\( 1 - 15 T + 48 T^{2} + 3 T^{3} + 3075 T^{4} - 18798 T^{5} + 4399 T^{6} - 883506 T^{7} + 6792675 T^{8} + 311469 T^{9} + 234224688 T^{10} - 3440175105 T^{11} + 10779215329 T^{12} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 9 T + 34 T^{2} + 423 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 215 T^{2} - 750 T^{3} + 23197 T^{4} + 82998 T^{5} - 1793695 T^{6} - 5388753 T^{7} + 119401781 T^{8} + 227010657 T^{9} - 7448336422 T^{10} - 6436178352 T^{11} + 428559183834 T^{12} + 95001497937 T^{13} - 21681767924409 T^{14} + 4465070403039 T^{15} + 946687237089306 T^{16} - 668223345039696 T^{17} - 36345505720041382 T^{18} + 52063760718739599 T^{19} + 1287057508065100949 T^{20} - 2730066860264352639 T^{21} - 42710185828767396895 T^{22} + 92885591006583455466 T^{23} + \)\(12\!\cdots\!53\)\( T^{24} - \)\(18\!\cdots\!50\)\( T^{25} - \)\(24\!\cdots\!15\)\( T^{26} + \)\(16\!\cdots\!81\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 - 91 T^{2} + 6072 T^{4} - 201019 T^{6} + 4879681 T^{8} \))(\( 1 - 88 T^{2} + 5535 T^{4} - 194392 T^{6} + 4879681 T^{8} \))(\( ( 1 + 18 T + 262 T^{2} + 2454 T^{3} + 20893 T^{4} + 154293 T^{5} + 1267261 T^{6} + 9657933 T^{7} + 72865294 T^{8} + 453922851 T^{9} + 2799379549 T^{10} + 16019162139 T^{11} + 101951175133 T^{12} + 562812647178 T^{13} + 2824154416198 T^{14} + 9119216168334 T^{15} + 23811286661761 T^{16} )^{2} \))(\( 1 - 154 T^{2} + 7683 T^{4} - 245888 T^{6} + 25028264 T^{8} - 1538143278 T^{10} + 38475997042 T^{12} - 2602469435029 T^{14} + 205422570296046 T^{16} - 5748854981979061 T^{18} + 187750591721903602 T^{20} - 16579977600415908462 T^{22} + \)\(59\!\cdots\!04\)\( T^{24} - \)\(12\!\cdots\!12\)\( T^{26} + \)\(89\!\cdots\!03\)\( T^{28} - \)\(39\!\cdots\!26\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 10 T^{2} - 2109 T^{4} - 22090 T^{6} + 4879681 T^{8} \))(\( 1 - 70 T^{2} + 2691 T^{4} - 154630 T^{6} + 4879681 T^{8} \))(\( 1 - 70 T^{2} + 2691 T^{4} - 154630 T^{6} + 4879681 T^{8} \))(\( 1 - 10 T^{2} - 2109 T^{4} - 22090 T^{6} + 4879681 T^{8} \))(\( 1 - 19 T^{2} - 1848 T^{4} - 41971 T^{6} + 4879681 T^{8} \))(\( 1 - 4 T - 144 T^{2} + 456 T^{3} + 12722 T^{4} - 27948 T^{5} - 805600 T^{6} + 556940 T^{7} + 41968563 T^{8} + 26176180 T^{9} - 1779570400 T^{10} - 2901645204 T^{11} + 62079301682 T^{12} + 104581323192 T^{13} - 1552207007376 T^{14} - 2026492481852 T^{15} + 23811286661761 T^{16} \))(\( 1 + 4 T - 144 T^{2} - 456 T^{3} + 12722 T^{4} + 27948 T^{5} - 805600 T^{6} - 556940 T^{7} + 41968563 T^{8} - 26176180 T^{9} - 1779570400 T^{10} + 2901645204 T^{11} + 62079301682 T^{12} - 104581323192 T^{13} - 1552207007376 T^{14} + 2026492481852 T^{15} + 23811286661761 T^{16} \))(\( 1 - 67 T^{2} + 2280 T^{4} - 148003 T^{6} + 4879681 T^{8} \))(\( 1 - 67 T^{2} + 2280 T^{4} - 148003 T^{6} + 4879681 T^{8} \))(\( ( 1 + 91 T^{2} + 2209 T^{4} )^{2} \))(\( 1 + 18 T + 62 T^{2} - 192 T^{3} + 3579 T^{4} + 45093 T^{5} + 305398 T^{6} + 2890521 T^{7} + 680339 T^{8} - 61965303 T^{9} + 840301383 T^{10} + 4943829948 T^{11} + 3397740844 T^{12} + 111292595154 T^{13} - 711051013816 T^{14} - 459408198168 T^{15} + 101830826927016 T^{16} - 21592185313896 T^{17} - 1570711689519544 T^{18} + 11554731106673742 T^{19} + 16579891439390764 T^{20} + 1133842714030869636 T^{21} + 9057789548613500007 T^{22} - 31393055166295295289 T^{23} + 16199746956175816979 T^{24} + \)\(32\!\cdots\!07\)\( T^{25} + \)\(16\!\cdots\!02\)\( T^{26} + \)\(11\!\cdots\!79\)\( T^{27} + \)\(41\!\cdots\!39\)\( T^{28} - \)\(10\!\cdots\!84\)\( T^{29} + \)\(15\!\cdots\!78\)\( T^{30} + \)\(21\!\cdots\!74\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 53 T^{2} )^{4} \))(\( ( 1 - 6 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 8 T + 54 T^{2} + 424 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 8 T + 54 T^{2} + 424 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 - 184 T^{2} + 16171 T^{4} - 975856 T^{6} + 45424339 T^{8} - 1451848504 T^{10} + 22164361129 T^{12} )^{2} \))(\( ( 1 + 56 T^{2} + 2809 T^{4} )^{2} \))(\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 15 T - 44 T^{2} - 1563 T^{3} + 1621 T^{4} + 132831 T^{5} + 280796 T^{6} - 6875916 T^{7} - 32544895 T^{8} + 334617081 T^{9} + 3332374934 T^{10} - 9404405181 T^{11} - 219667861866 T^{12} + 268474558113 T^{13} + 14089335458730 T^{14} + 14229151579989 T^{15} - 617047023981594 T^{16} - 1400099630131737 T^{17} + 26294041101603254 T^{18} + 139935355155015933 T^{19} - 721336805685386455 T^{20} - 8077215121783465692 T^{21} + 17482272028748523356 T^{22} + \)\(43\!\cdots\!23\)\( T^{23} + \)\(28\!\cdots\!29\)\( T^{24} - \)\(14\!\cdots\!11\)\( T^{25} - \)\(21\!\cdots\!04\)\( T^{26} + \)\(39\!\cdots\!95\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( ( 1 - 6 T + 162 T^{2} - 627 T^{3} + 8586 T^{4} - 16854 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 18 T + 198 T^{2} + 1521 T^{3} + 10494 T^{4} + 50562 T^{5} + 148877 T^{6} )^{2} \))(\( 1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 - 3 T - 44 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 15 T - 44 T^{2} - 1563 T^{3} + 1621 T^{4} + 132831 T^{5} + 280796 T^{6} - 6875916 T^{7} - 32544895 T^{8} + 334617081 T^{9} + 3332374934 T^{10} - 9404405181 T^{11} - 219667861866 T^{12} + 268474558113 T^{13} + 14089335458730 T^{14} + 14229151579989 T^{15} - 617047023981594 T^{16} - 1400099630131737 T^{17} + 26294041101603254 T^{18} + 139935355155015933 T^{19} - 721336805685386455 T^{20} - 8077215121783465692 T^{21} + 17482272028748523356 T^{22} + \)\(43\!\cdots\!23\)\( T^{23} + \)\(28\!\cdots\!29\)\( T^{24} - \)\(14\!\cdots\!11\)\( T^{25} - \)\(21\!\cdots\!04\)\( T^{26} + \)\(39\!\cdots\!95\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( ( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} )^{2} \))(\( 1 + 34 T^{2} - 1653 T^{4} + 95506 T^{6} + 7890481 T^{8} \))(\( 1 + 271 T^{2} + 39798 T^{4} + 8019 T^{5} + 3882470 T^{6} + 3112830 T^{7} + 272618249 T^{8} + 573793713 T^{9} + 13751201223 T^{10} + 69938411256 T^{11} + 461723008303 T^{12} + 6218775316710 T^{13} + 7202514917530 T^{14} + 423085276358208 T^{15} - 24546838659498 T^{16} + 22423519646985024 T^{17} + 20231864403341770 T^{18} + 925832612825834670 T^{19} + 3643216624277663743 T^{20} + 29247928374839669208 T^{21} + \)\(30\!\cdots\!67\)\( T^{22} + \)\(67\!\cdots\!81\)\( T^{23} + \)\(16\!\cdots\!89\)\( T^{24} + \)\(10\!\cdots\!90\)\( T^{25} + \)\(67\!\cdots\!30\)\( T^{26} + \)\(74\!\cdots\!43\)\( T^{27} + \)\(19\!\cdots\!18\)\( T^{28} + \)\(37\!\cdots\!99\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 10 T^{2} + 3133 T^{4} + 54785 T^{6} + 5778574 T^{8} + 153891065 T^{10} + 24720876973 T^{12} - 221643611290 T^{14} + 62259690411361 T^{16} )^{2} \))(\( ( 1 + 7 T - 4 T^{2} + 371 T^{3} + 2809 T^{4} )^{2} \))(\( 1 - 82 T^{2} + 3915 T^{4} - 230338 T^{6} + 7890481 T^{8} \))(\( 1 - 82 T^{2} + 3915 T^{4} - 230338 T^{6} + 7890481 T^{8} \))(\( ( 1 - 7 T - 4 T^{2} - 371 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} )^{2} \))(\( 1 - 4 T - 135 T^{2} + 900 T^{3} + 9413 T^{4} - 70368 T^{5} - 312982 T^{6} + 1938608 T^{7} + 10598262 T^{8} + 102746224 T^{9} - 879166438 T^{10} - 10476176736 T^{11} + 74273097653 T^{12} + 376375943700 T^{13} - 2992188752415 T^{14} - 4698844559348 T^{15} + 62259690411361 T^{16} \))(\( 1 - 4 T - 135 T^{2} + 900 T^{3} + 9413 T^{4} - 70368 T^{5} - 312982 T^{6} + 1938608 T^{7} + 10598262 T^{8} + 102746224 T^{9} - 879166438 T^{10} - 10476176736 T^{11} + 74273097653 T^{12} + 376375943700 T^{13} - 2992188752415 T^{14} - 4698844559348 T^{15} + 62259690411361 T^{16} \))(\( ( 1 - 4 T + 53 T^{2} )^{4} \))(\( ( 1 - 4 T + 53 T^{2} )^{4} \))(\( ( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} )^{2} \))(\( 1 + 271 T^{2} + 39798 T^{4} - 8019 T^{5} + 3882470 T^{6} - 3112830 T^{7} + 272618249 T^{8} - 573793713 T^{9} + 13751201223 T^{10} - 69938411256 T^{11} + 461723008303 T^{12} - 6218775316710 T^{13} + 7202514917530 T^{14} - 423085276358208 T^{15} - 24546838659498 T^{16} - 22423519646985024 T^{17} + 20231864403341770 T^{18} - 925832612825834670 T^{19} + 3643216624277663743 T^{20} - 29247928374839669208 T^{21} + \)\(30\!\cdots\!67\)\( T^{22} - \)\(67\!\cdots\!81\)\( T^{23} + \)\(16\!\cdots\!89\)\( T^{24} - \)\(10\!\cdots\!90\)\( T^{25} + \)\(67\!\cdots\!30\)\( T^{26} - \)\(74\!\cdots\!43\)\( T^{27} + \)\(19\!\cdots\!18\)\( T^{28} + \)\(37\!\cdots\!99\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( 1 - 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{4} \))(\( ( 1 + 59 T^{2} )^{4} \))(\( ( 1 - 4 T + 59 T^{2} )^{4} \))(\( ( 1 + 4 T + 59 T^{2} )^{4} \))(\( ( 1 + 146 T^{2} + 7799 T^{4} + 306396 T^{6} + 27148319 T^{8} + 1769134706 T^{10} + 42180533641 T^{12} )^{2} \))(\( ( 1 - 74 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 7 T + 59 T^{2} )^{2} \))(\( ( 1 - 14 T + 237 T^{2} - 2625 T^{3} + 28687 T^{4} - 249069 T^{5} + 2197811 T^{6} - 16839260 T^{7} + 129670849 T^{8} - 867009189 T^{9} + 5891707373 T^{10} - 31808072625 T^{11} + 169437058863 T^{12} - 590527470974 T^{13} + 2488651484819 T^{14} )^{2} \))(\( 1 + 31 T + 476 T^{2} + 5741 T^{3} + 62553 T^{4} + 587576 T^{5} + 4781851 T^{6} + 34666984 T^{7} + 217746993 T^{8} + 1179080839 T^{9} + 5767863836 T^{10} + 22162653269 T^{11} + 42180533641 T^{12} \))(\( 1 - 3 T - 114 T^{2} + 501 T^{3} + 6567 T^{4} - 20406 T^{5} - 323957 T^{6} - 1203954 T^{7} + 22859727 T^{8} + 102894879 T^{9} - 1381379154 T^{10} - 2144772897 T^{11} + 42180533641 T^{12} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 9 T + 22 T^{2} - 531 T^{3} + 3481 T^{4} \))(\( 1 - 7 T - 10 T^{2} - 413 T^{3} + 3481 T^{4} \))(\( 1 + 14 T - 41 T^{2} - 1932 T^{3} - 9268 T^{4} + 67958 T^{5} + 1000462 T^{6} + 4853283 T^{7} - 9914932 T^{8} - 321187219 T^{9} - 1782148489 T^{10} - 6021692682 T^{11} - 34607406657 T^{12} + 638777810472 T^{13} + 11047710270819 T^{14} + 37687890817848 T^{15} - 120468382573017 T^{16} - 1236729221336478 T^{17} - 21594936596817529 T^{18} - 229624547391334481 T^{19} - 418217122774227412 T^{20} + 12078129944196810777 T^{21} + \)\(14\!\cdots\!02\)\( T^{22} + \)\(58\!\cdots\!62\)\( T^{23} - \)\(47\!\cdots\!68\)\( T^{24} - \)\(58\!\cdots\!88\)\( T^{25} - \)\(72\!\cdots\!21\)\( T^{26} + \)\(14\!\cdots\!06\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 - 115 T^{2} + 9744 T^{4} - 400315 T^{6} + 12117361 T^{8} \))(\( 1 - 94 T^{2} + 5355 T^{4} - 327214 T^{6} + 12117361 T^{8} \))(\( ( 1 + 15 T + 304 T^{2} + 2994 T^{3} + 35017 T^{4} + 245181 T^{5} + 2158909 T^{6} + 12195126 T^{7} + 111191710 T^{8} + 719512434 T^{9} + 7515162229 T^{10} + 50355028599 T^{11} + 424313630137 T^{12} + 2140483351206 T^{13} + 12822882226864 T^{14} + 37329772272285 T^{15} + 146830437604321 T^{16} )^{2} \))(\( 1 - 376 T^{2} + 75453 T^{4} - 10695122 T^{6} + 1193881406 T^{8} - 111003832932 T^{10} + 8882998756942 T^{12} - 624280670070511 T^{14} + 38988958528434078 T^{16} - 2173121012515448791 T^{18} + \)\(10\!\cdots\!62\)\( T^{20} - \)\(46\!\cdots\!12\)\( T^{22} + \)\(17\!\cdots\!26\)\( T^{24} - \)\(54\!\cdots\!22\)\( T^{26} + \)\(13\!\cdots\!93\)\( T^{28} - \)\(23\!\cdots\!36\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 71 T^{2} + 1560 T^{4} + 247151 T^{6} + 12117361 T^{8} \))(\( 1 - 94 T^{2} + 5355 T^{4} - 327214 T^{6} + 12117361 T^{8} \))(\( 1 - 94 T^{2} + 5355 T^{4} - 327214 T^{6} + 12117361 T^{8} \))(\( 1 + 71 T^{2} + 1560 T^{4} + 247151 T^{6} + 12117361 T^{8} \))(\( 1 - 91 T^{2} + 4800 T^{4} - 316771 T^{6} + 12117361 T^{8} \))(\( 1 + 14 T - 13 T^{2} - 1110 T^{3} - 3463 T^{4} + 11848 T^{5} - 87914 T^{6} + 1416852 T^{7} + 32978194 T^{8} + 83594268 T^{9} - 306028634 T^{10} + 2433330392 T^{11} - 41962421143 T^{12} - 793565971890 T^{13} - 548346937333 T^{14} + 34841120787466 T^{15} + 146830437604321 T^{16} \))(\( 1 - 14 T - 13 T^{2} + 1110 T^{3} - 3463 T^{4} - 11848 T^{5} - 87914 T^{6} - 1416852 T^{7} + 32978194 T^{8} - 83594268 T^{9} - 306028634 T^{10} - 2433330392 T^{11} - 41962421143 T^{12} + 793565971890 T^{13} - 548346937333 T^{14} - 34841120787466 T^{15} + 146830437604321 T^{16} \))(\( 1 - 43 T^{2} - 1632 T^{4} - 149683 T^{6} + 12117361 T^{8} \))(\( 1 - 43 T^{2} - 1632 T^{4} - 149683 T^{6} + 12117361 T^{8} \))(\( ( 1 + 115 T^{2} + 3481 T^{4} )^{2} \))(\( 1 + 15 T - 79 T^{2} - 1428 T^{3} + 12489 T^{4} + 104847 T^{5} - 1041029 T^{6} + 349611 T^{7} + 90472109 T^{8} - 405874929 T^{9} - 2700289995 T^{10} + 51789934650 T^{11} - 105592258130 T^{12} - 2611128991413 T^{13} + 30211727298980 T^{14} + 82730812140738 T^{15} - 2120569425031284 T^{16} + 4881117916303542 T^{17} + 105167022727749380 T^{18} - 536271061127410527 T^{19} - 1279499510566394930 T^{20} + 37025882724907060350 T^{21} - \)\(11\!\cdots\!95\)\( T^{22} - \)\(10\!\cdots\!51\)\( T^{23} + \)\(13\!\cdots\!89\)\( T^{24} + \)\(30\!\cdots\!29\)\( T^{25} - \)\(53\!\cdots\!29\)\( T^{26} + \)\(31\!\cdots\!73\)\( T^{27} + \)\(22\!\cdots\!09\)\( T^{28} - \)\(14\!\cdots\!12\)\( T^{29} - \)\(48\!\cdots\!19\)\( T^{30} + \)\(54\!\cdots\!85\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 - 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( ( 1 - 61 T^{2} )^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( 1 - 132 T^{2} + 10710 T^{4} - 491172 T^{6} + 13845841 T^{8} \))(\( 1 - 132 T^{2} + 10710 T^{4} - 491172 T^{6} + 13845841 T^{8} \))(\( ( 1 - 14 T + 187 T^{2} - 1700 T^{3} + 11407 T^{4} - 52094 T^{5} + 226981 T^{6} )^{4} \))(\( ( 1 - 26 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 3 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 377 T^{2} - 2981 T^{3} + 62533 T^{4} - 402217 T^{5} + 6040473 T^{6} - 31437684 T^{7} + 368468853 T^{8} - 1496649457 T^{9} + 14193802873 T^{10} - 41274452021 T^{11} + 318412805477 T^{12} - 515203743610 T^{13} + 3142742836021 T^{14} )^{2} \))(\( 1 + 6 T + 48 T^{2} + 642 T^{3} + 3018 T^{4} + 35394 T^{5} + 438671 T^{6} + 2159034 T^{7} + 11229978 T^{8} + 145721802 T^{9} + 664600368 T^{10} + 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 - 6 T - 102 T^{2} + 698 T^{3} + 6048 T^{4} - 26604 T^{5} - 259509 T^{6} - 1622844 T^{7} + 22504608 T^{8} + 158432738 T^{9} - 1412275782 T^{10} - 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 + 3 T - 52 T^{2} + 183 T^{3} + 3721 T^{4} \))(\( 1 + 10 T - 277 T^{2} - 2192 T^{3} + 49786 T^{4} + 275394 T^{5} - 6629804 T^{6} - 25018331 T^{7} + 694393718 T^{8} + 1681932119 T^{9} - 61000901305 T^{10} - 82163567860 T^{11} + 4597121803909 T^{12} + 1969709923870 T^{13} - 300133324238415 T^{14} + 120152305356070 T^{15} + 17105890232345389 T^{16} - 18649568796430660 T^{17} - 844608780325722505 T^{18} + 1420553646240491819 T^{19} + 35775424305286664198 T^{20} - 78626180519452100951 T^{21} - \)\(12\!\cdots\!24\)\( T^{22} + \)\(32\!\cdots\!54\)\( T^{23} + \)\(35\!\cdots\!86\)\( T^{24} - \)\(95\!\cdots\!12\)\( T^{25} - \)\(73\!\cdots\!17\)\( T^{26} + \)\(16\!\cdots\!10\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( ( 1 - 9 T + 88 T^{2} - 549 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 6 T + 73 T^{2} + 366 T^{3} + 3721 T^{4} )^{2} \))(\( 1 - 745 T^{2} + 270666 T^{4} - 63553928 T^{6} + 10780728317 T^{8} - 1399459132305 T^{10} + 143698232661445 T^{12} - 11899376361024010 T^{14} + 802850906302349022 T^{16} - 44277579439370341210 T^{18} + \)\(19\!\cdots\!45\)\( T^{20} - \)\(72\!\cdots\!05\)\( T^{22} + \)\(20\!\cdots\!77\)\( T^{24} - \)\(45\!\cdots\!28\)\( T^{26} + \)\(71\!\cdots\!86\)\( T^{28} - \)\(73\!\cdots\!45\)\( T^{30} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 + 137 T^{2} + 306 T^{4} - 368483 T^{6} + 33183791 T^{8} + 2225199582 T^{10} - 143899132121 T^{12} + 1205057298539 T^{14} + 1133086682080440 T^{16} + 4484018207863619 T^{18} - 1992404503385358761 T^{20} + \)\(11\!\cdots\!02\)\( T^{22} + \)\(63\!\cdots\!71\)\( T^{24} - \)\(26\!\cdots\!83\)\( T^{26} + \)\(81\!\cdots\!26\)\( T^{28} + \)\(13\!\cdots\!17\)\( T^{30} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 18 T + 169 T^{2} + 1098 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 13 T + 61 T^{2} )^{2}( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 13 T + 61 T^{2} )^{2}( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 + 18 T + 169 T^{2} + 1098 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 9 T + 88 T^{2} + 549 T^{3} + 3721 T^{4} )^{2} \))(\( 1 - 12 T + 180 T^{2} - 1584 T^{3} + 12426 T^{4} - 46860 T^{5} + 10032 T^{6} + 3576756 T^{7} - 33274477 T^{8} + 218182116 T^{9} + 37329072 T^{10} - 10636329660 T^{11} + 172048420266 T^{12} - 1337840540784 T^{13} + 9273667384980 T^{14} - 37712914032252 T^{15} + 191707312997281 T^{16} \))(\( 1 - 12 T + 180 T^{2} - 1584 T^{3} + 12426 T^{4} - 46860 T^{5} + 10032 T^{6} + 3576756 T^{7} - 33274477 T^{8} + 218182116 T^{9} + 37329072 T^{10} - 10636329660 T^{11} + 172048420266 T^{12} - 1337840540784 T^{13} + 9273667384980 T^{14} - 37712914032252 T^{15} + 191707312997281 T^{16} \))(\( ( 1 + 9 T + 88 T^{2} + 549 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 9 T + 88 T^{2} - 549 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 95 T^{2} + 3721 T^{4} )^{2} \))(\( 1 - 3 T + 377 T^{2} - 1122 T^{3} + 74481 T^{4} - 239253 T^{5} + 10537021 T^{6} - 36111681 T^{7} + 1196449751 T^{8} - 4163017557 T^{9} + 114788648541 T^{10} - 392960339076 T^{11} + 9549397216930 T^{12} - 31727661059931 T^{13} + 697503406538990 T^{14} - 2222103948983802 T^{15} + 45117478421428590 T^{16} - 135548340888011922 T^{17} + 2595410175731581790 T^{18} - 7201576235044198311 T^{19} + \)\(13\!\cdots\!30\)\( T^{20} - \)\(33\!\cdots\!76\)\( T^{21} + \)\(59\!\cdots\!01\)\( T^{22} - \)\(13\!\cdots\!97\)\( T^{23} + \)\(22\!\cdots\!31\)\( T^{24} - \)\(42\!\cdots\!21\)\( T^{25} + \)\(75\!\cdots\!21\)\( T^{26} - \)\(10\!\cdots\!33\)\( T^{27} + \)\(19\!\cdots\!01\)\( T^{28} - \)\(18\!\cdots\!82\)\( T^{29} + \)\(37\!\cdots\!57\)\( T^{30} - \)\(18\!\cdots\!03\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))
$67$ (\( 1 + 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( ( 1 - 4 T + 67 T^{2} )( 1 + 4 T + 67 T^{2} ) \))(\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 - 4 T + 67 T^{2} )^{2}( 1 + 4 T + 67 T^{2} )^{2} \))(\( 1 - 144 T^{2} + 10830 T^{4} - 646416 T^{6} + 20151121 T^{8} \))(\( 1 - 144 T^{2} + 10830 T^{4} - 646416 T^{6} + 20151121 T^{8} \))(\( ( 1 - 186 T^{2} + 13175 T^{4} - 680684 T^{6} + 59142575 T^{8} - 3748108506 T^{10} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{4} \))(\( ( 1 - 13 T + 67 T^{2} )^{2} \))(\( ( 1 + 6 T + 344 T^{2} + 1114 T^{3} + 48744 T^{4} + 55499 T^{5} + 4192269 T^{6} + 1055346 T^{7} + 280882023 T^{8} + 249135011 T^{9} + 14660391672 T^{10} + 22448348794 T^{11} + 464443036808 T^{12} + 542750293014 T^{13} + 6060711605323 T^{14} )^{2} \))(\( 1 + 6 T - 150 T^{2} - 506 T^{3} + 17268 T^{4} + 28236 T^{5} - 1220289 T^{6} + 1891812 T^{7} + 77516052 T^{8} - 152186078 T^{9} - 3022668150 T^{10} + 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 - 6 T - 138 T^{2} + 446 T^{3} + 14148 T^{4} - 16668 T^{5} - 1033545 T^{6} - 1116756 T^{7} + 63510372 T^{8} + 134140298 T^{9} - 2780854698 T^{10} - 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 + 13 T + 102 T^{2} + 871 T^{3} + 4489 T^{4} \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 + 13 T + 102 T^{2} + 871 T^{3} + 4489 T^{4} \))(\( 1 - 6 T - 308 T^{2} + 164 T^{3} + 62908 T^{4} + 146213 T^{5} - 7475396 T^{6} - 42326464 T^{7} + 603793243 T^{8} + 5085070936 T^{9} - 25351846493 T^{10} - 374911832519 T^{11} + 131329441787 T^{12} + 10392590626498 T^{13} + 54642703536353 T^{14} + 696303571975366 T^{15} + 589537864181843 T^{16} - 112759607483911997 T^{17} - 510868126253868653 T^{18} + 6865481941569590152 T^{19} + 54618159926353884067 T^{20} - \)\(25\!\cdots\!72\)\( T^{21} - \)\(30\!\cdots\!36\)\( T^{22} + \)\(39\!\cdots\!11\)\( T^{23} + \)\(11\!\cdots\!92\)\( T^{24} + \)\(20\!\cdots\!12\)\( T^{25} - \)\(25\!\cdots\!88\)\( T^{26} - \)\(32\!\cdots\!22\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 53 T^{2} - 1680 T^{4} + 237917 T^{6} + 20151121 T^{8} \))(\( ( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 7 T + 315 T^{2} - 1580 T^{3} + 47600 T^{4} - 182439 T^{5} + 4735936 T^{6} - 14472934 T^{7} + 354986784 T^{8} - 969686578 T^{9} + 21259616704 T^{10} - 54870900957 T^{11} + 959193359600 T^{12} - 2133197669060 T^{13} + 28494390383235 T^{14} - 42424981237261 T^{15} + 406067677556641 T^{16} )^{2} \))(\( ( 1 - 7 T - 108 T^{2} - 293 T^{3} + 11753 T^{4} + 50778 T^{5} - 198827 T^{6} - 2620663 T^{7} - 10701486 T^{8} - 175584421 T^{9} - 892534403 T^{10} + 15272143614 T^{11} + 236836125113 T^{12} - 395586656351 T^{13} - 9769505274252 T^{14} - 42424981237261 T^{15} + 406067677556641 T^{16} )^{2} \))(\( ( 1 + 67 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 67 T^{2} + 4489 T^{4} )^{2} \))(\( 1 + 125 T^{2} + 11136 T^{4} + 561125 T^{6} + 20151121 T^{8} \))(\( 1 + 42 T + 1023 T^{2} + 18270 T^{3} + 261141 T^{4} + 3133152 T^{5} + 32837970 T^{6} + 307895844 T^{7} + 2631022010 T^{8} + 20629021548 T^{9} + 147409647330 T^{10} + 942336194976 T^{11} + 5262283889061 T^{12} + 24666785704890 T^{13} + 92538924958887 T^{14} + 254549887423566 T^{15} + 406067677556641 T^{16} \))(\( 1 - 42 T + 1023 T^{2} - 18270 T^{3} + 261141 T^{4} - 3133152 T^{5} + 32837970 T^{6} - 307895844 T^{7} + 2631022010 T^{8} - 20629021548 T^{9} + 147409647330 T^{10} - 942336194976 T^{11} + 5262283889061 T^{12} - 24666785704890 T^{13} + 92538924958887 T^{14} - 254549887423566 T^{15} + 406067677556641 T^{16} \))(\( 1 - 91 T^{2} + 3792 T^{4} - 408499 T^{6} + 20151121 T^{8} \))(\( 1 - 91 T^{2} + 3792 T^{4} - 408499 T^{6} + 20151121 T^{8} \))(\( ( 1 - 53 T^{2} + 4489 T^{4} )^{2} \))(\( 1 + 7 T - 266 T^{2} - 955 T^{3} + 40565 T^{4} + 13739 T^{5} - 4302801 T^{6} + 7895916 T^{7} + 333320832 T^{8} - 1176952818 T^{9} - 19419549429 T^{10} + 109762768995 T^{11} + 793012008891 T^{12} - 6957819527658 T^{13} - 12193565486865 T^{14} + 198908265810519 T^{15} - 461225363558112 T^{16} + 13326853809304773 T^{17} - 54736915470536985 T^{18} - 2092654674597003054 T^{19} + 15980080945615616811 T^{20} + \)\(14\!\cdots\!65\)\( T^{21} - \)\(17\!\cdots\!01\)\( T^{22} - \)\(71\!\cdots\!14\)\( T^{23} + \)\(13\!\cdots\!12\)\( T^{24} + \)\(21\!\cdots\!52\)\( T^{25} - \)\(78\!\cdots\!49\)\( T^{26} + \)\(16\!\cdots\!37\)\( T^{27} + \)\(33\!\cdots\!65\)\( T^{28} - \)\(52\!\cdots\!85\)\( T^{29} - \)\(97\!\cdots\!14\)\( T^{30} + \)\(17\!\cdots\!01\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))
$71$ (\( 1 + 14 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( ( 1 - 16 T + 71 T^{2} )( 1 + 16 T + 71 T^{2} ) \))(\( ( 1 + 100 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 114 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 114 T^{2} + 8418 T^{4} - 574674 T^{6} + 25411681 T^{8} \))(\( 1 - 114 T^{2} + 8418 T^{4} - 574674 T^{6} + 25411681 T^{8} \))(\( ( 1 + 158 T^{2} + 5683 T^{4} - 107140 T^{6} + 28648003 T^{8} + 4015045598 T^{10} + 128100283921 T^{12} )^{2} \))(\( ( 1 - 124 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - T + 381 T^{2} - 417 T^{3} + 66850 T^{4} - 68550 T^{5} + 7142942 T^{6} - 6246700 T^{7} + 507148882 T^{8} - 345560550 T^{9} + 23926350350 T^{10} - 10596670977 T^{11} + 687411382731 T^{12} - 128100283921 T^{13} + 9095120158391 T^{14} )^{2} \))(\( ( 1 - 17 T + 119 T^{2} - 507 T^{3} + 8449 T^{4} - 85697 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 15 T + 231 T^{2} + 1833 T^{3} + 16401 T^{4} + 75615 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - T + 381 T^{2} - 417 T^{3} + 66850 T^{4} - 68550 T^{5} + 7142942 T^{6} - 6246700 T^{7} + 507148882 T^{8} - 345560550 T^{9} + 23926350350 T^{10} - 10596670977 T^{11} + 687411382731 T^{12} - 128100283921 T^{13} + 9095120158391 T^{14} )^{2} \))(\( ( 1 - 138 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 20 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 389 T^{2} + 95718 T^{4} - 16982206 T^{6} + 2417461733 T^{8} - 285171142929 T^{10} + 28739565041956 T^{12} - 2501948752776044 T^{14} + 190114711967546784 T^{16} - 12612323662744037804 T^{18} + \)\(73\!\cdots\!36\)\( T^{20} - \)\(36\!\cdots\!09\)\( T^{22} + \)\(15\!\cdots\!13\)\( T^{24} - \)\(55\!\cdots\!06\)\( T^{26} + \)\(15\!\cdots\!38\)\( T^{28} - \)\(32\!\cdots\!09\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 361 T^{2} + 64216 T^{4} - 7488268 T^{6} + 623512600 T^{8} - 37748358988 T^{10} + 1631836507096 T^{12} - 46244202495481 T^{14} + 645753531245761 T^{16} )^{2} \))(\( ( 1 - 16 T + 71 T^{2} )^{2}( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 16 T + 71 T^{2} )^{2}( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 54 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 288 T^{2} + 41724 T^{4} - 4336608 T^{6} + 350671046 T^{8} - 21860840928 T^{10} + 1060276978044 T^{12} - 36892881769248 T^{14} + 645753531245761 T^{16} \))(\( 1 - 288 T^{2} + 41724 T^{4} - 4336608 T^{6} + 350671046 T^{8} - 21860840928 T^{10} + 1060276978044 T^{12} - 36892881769248 T^{14} + 645753531245761 T^{16} \))(\( ( 1 - 126 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 126 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 138 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 389 T^{2} + 95718 T^{4} - 16982206 T^{6} + 2417461733 T^{8} - 285171142929 T^{10} + 28739565041956 T^{12} - 2501948752776044 T^{14} + 190114711967546784 T^{16} - 12612323662744037804 T^{18} + \)\(73\!\cdots\!36\)\( T^{20} - \)\(36\!\cdots\!09\)\( T^{22} + \)\(15\!\cdots\!13\)\( T^{24} - \)\(55\!\cdots\!06\)\( T^{26} + \)\(15\!\cdots\!38\)\( T^{28} - \)\(32\!\cdots\!09\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( 1 - 236 T^{2} + 24310 T^{4} - 1257644 T^{6} + 28398241 T^{8} \))(\( 1 - 236 T^{2} + 24310 T^{4} - 1257644 T^{6} + 28398241 T^{8} \))(\( ( 1 + 47 T^{2} - 352 T^{3} + 3431 T^{4} + 389017 T^{6} )^{4} \))(\( ( 1 - 122 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 21 T - 107 T^{2} + 4532 T^{3} + 8593 T^{4} - 574123 T^{5} - 1508435 T^{6} + 52395764 T^{7} + 342478696 T^{8} - 4227610868 T^{9} - 46283154524 T^{10} + 253115011813 T^{11} + 4673586532751 T^{12} - 7744045394141 T^{13} - 369527474872486 T^{14} - 565315313772293 T^{15} + 24905542633030079 T^{16} + 98466042550457821 T^{17} - 1314360176412792284 T^{18} - 8764139996708872724 T^{19} + 51828748479625639144 T^{20} + \)\(57\!\cdots\!08\)\( T^{21} - \)\(12\!\cdots\!35\)\( T^{22} - \)\(33\!\cdots\!99\)\( T^{23} + \)\(36\!\cdots\!57\)\( T^{24} + \)\(14\!\cdots\!64\)\( T^{25} - \)\(24\!\cdots\!47\)\( T^{26} - \)\(35\!\cdots\!93\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( ( 1 + 3 T + 195 T^{2} + 359 T^{3} + 14235 T^{4} + 15987 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 - 9 T + 207 T^{2} - 1235 T^{3} + 15111 T^{4} - 47961 T^{5} + 389017 T^{6} )^{2} \))(\( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} \))(\( ( 1 + 7 T + 73 T^{2} )( 1 + 10 T + 73 T^{2} ) \))(\( 1 - T - 72 T^{2} - 73 T^{3} + 5329 T^{4} \))(\( ( 1 - 10 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 21 T - 107 T^{2} + 4532 T^{3} + 8593 T^{4} - 574123 T^{5} - 1508435 T^{6} + 52395764 T^{7} + 342478696 T^{8} - 4227610868 T^{9} - 46283154524 T^{10} + 253115011813 T^{11} + 4673586532751 T^{12} - 7744045394141 T^{13} - 369527474872486 T^{14} - 565315313772293 T^{15} + 24905542633030079 T^{16} + 98466042550457821 T^{17} - 1314360176412792284 T^{18} - 8764139996708872724 T^{19} + 51828748479625639144 T^{20} + \)\(57\!\cdots\!08\)\( T^{21} - \)\(12\!\cdots\!35\)\( T^{22} - \)\(33\!\cdots\!99\)\( T^{23} + \)\(36\!\cdots\!57\)\( T^{24} + \)\(14\!\cdots\!64\)\( T^{25} - \)\(24\!\cdots\!47\)\( T^{26} - \)\(35\!\cdots\!93\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( ( 1 + 21 T + 220 T^{2} + 1533 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 17 T + 73 T^{2} )^{2}( 1 - 10 T + 73 T^{2} )^{2} \))(\( 1 + 278 T^{2} + 39699 T^{4} - 160362 T^{5} + 4049527 T^{6} - 43185312 T^{7} + 316493258 T^{8} - 5978310966 T^{9} + 30516141699 T^{10} - 573490190745 T^{11} + 3892519182646 T^{12} - 40210747978752 T^{13} + 436575836052170 T^{14} - 2488085380264887 T^{15} + 37348173312201540 T^{16} - 181630232759336751 T^{17} + 2326512630322013930 T^{18} - 15642664546450166784 T^{19} + \)\(11\!\cdots\!86\)\( T^{20} - \)\(11\!\cdots\!85\)\( T^{21} + \)\(46\!\cdots\!11\)\( T^{22} - \)\(66\!\cdots\!02\)\( T^{23} + \)\(25\!\cdots\!98\)\( T^{24} - \)\(25\!\cdots\!56\)\( T^{25} + \)\(17\!\cdots\!23\)\( T^{26} - \)\(50\!\cdots\!74\)\( T^{27} + \)\(90\!\cdots\!79\)\( T^{28} + \)\(33\!\cdots\!02\)\( T^{30} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 341 T^{2} + 62398 T^{4} - 7562288 T^{6} + 647645452 T^{8} - 40299432752 T^{10} + 1771993441918 T^{12} - 51604971164549 T^{14} + 806460091894081 T^{16} )^{2} \))(\( ( 1 + 12 T + 121 T^{2} + 876 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2}( 1 + 7 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2}( 1 + 7 T + 73 T^{2} )^{2} \))(\( ( 1 + 12 T + 121 T^{2} + 876 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 15 T + 148 T^{2} - 1095 T^{3} + 5329 T^{4} )^{2} \))(\( 1 + 18 T + 347 T^{2} + 4302 T^{3} + 50601 T^{4} + 463140 T^{5} + 4384558 T^{6} + 34967736 T^{7} + 313616978 T^{8} + 2552644728 T^{9} + 23365309582 T^{10} + 180169333380 T^{11} + 1436979392841 T^{12} + 8918353993086 T^{13} + 52512976522283 T^{14} + 198853173343746 T^{15} + 806460091894081 T^{16} \))(\( 1 + 18 T + 347 T^{2} + 4302 T^{3} + 50601 T^{4} + 463140 T^{5} + 4384558 T^{6} + 34967736 T^{7} + 313616978 T^{8} + 2552644728 T^{9} + 23365309582 T^{10} + 180169333380 T^{11} + 1436979392841 T^{12} + 8918353993086 T^{13} + 52512976522283 T^{14} + 198853173343746 T^{15} + 806460091894081 T^{16} \))(\( ( 1 - 38 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 21 T + 220 T^{2} + 1533 T^{3} + 5329 T^{4} )^{2} \))(\( 1 + 278 T^{2} + 39699 T^{4} - 160362 T^{5} + 4049527 T^{6} - 43185312 T^{7} + 316493258 T^{8} - 5978310966 T^{9} + 30516141699 T^{10} - 573490190745 T^{11} + 3892519182646 T^{12} - 40210747978752 T^{13} + 436575836052170 T^{14} - 2488085380264887 T^{15} + 37348173312201540 T^{16} - 181630232759336751 T^{17} + 2326512630322013930 T^{18} - 15642664546450166784 T^{19} + \)\(11\!\cdots\!86\)\( T^{20} - \)\(11\!\cdots\!85\)\( T^{21} + \)\(46\!\cdots\!11\)\( T^{22} - \)\(66\!\cdots\!02\)\( T^{23} + \)\(25\!\cdots\!98\)\( T^{24} - \)\(25\!\cdots\!56\)\( T^{25} + \)\(17\!\cdots\!23\)\( T^{26} - \)\(50\!\cdots\!74\)\( T^{27} + \)\(90\!\cdots\!79\)\( T^{28} + \)\(33\!\cdots\!02\)\( T^{30} + \)\(65\!\cdots\!61\)\( T^{32} \))
$79$ (\( 1 - 12 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( ( 1 - 8 T + 79 T^{2} )( 1 + 8 T + 79 T^{2} ) \))(\( ( 1 - 79 T^{2} )^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2}( 1 + 8 T + 79 T^{2} )^{2} \))(\( 1 - 288 T^{2} + 33150 T^{4} - 1797408 T^{6} + 38950081 T^{8} \))(\( 1 - 288 T^{2} + 33150 T^{4} - 1797408 T^{6} + 38950081 T^{8} \))(\( ( 1 - 162 T^{2} + 19359 T^{4} - 2006332 T^{6} + 120819519 T^{8} - 6309913122 T^{10} + 243087455521 T^{12} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{4} \))(\( ( 1 + 9 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 326 T^{2} - 3770 T^{3} + 58966 T^{4} - 604927 T^{5} + 7130289 T^{6} - 58615338 T^{7} + 563292831 T^{8} - 3775349407 T^{9} + 29072537674 T^{10} - 146841805370 T^{11} + 1003120386074 T^{12} - 2430874555210 T^{13} + 19203908986159 T^{14} )^{2} \))(\( 1 - 9 T - 114 T^{2} + 351 T^{3} + 13143 T^{4} + 15786 T^{5} - 1414609 T^{6} + 1247094 T^{7} + 82025463 T^{8} + 173056689 T^{9} - 4440309234 T^{10} - 27693507591 T^{11} + 243087455521 T^{12} \))(\( 1 + 3 T + 6 T^{2} + 1787 T^{3} + 2439 T^{4} + 14634 T^{5} + 1719519 T^{6} + 1156086 T^{7} + 15221799 T^{8} + 881060693 T^{9} + 233700486 T^{10} + 9231169197 T^{11} + 243087455521 T^{12} \))(\( 1 - 3 T - 70 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( ( 1 + 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( 1 - 9 T + 2 T^{2} - 711 T^{3} + 6241 T^{4} \))(\( 1 + 10 T - 226 T^{2} - 4280 T^{3} + 9610 T^{4} + 654627 T^{5} + 3201292 T^{6} - 42192356 T^{7} - 519045919 T^{8} - 901423894 T^{9} + 24953123963 T^{10} + 320449224329 T^{11} + 1694205545953 T^{12} - 14615843505140 T^{13} - 287108375549019 T^{14} - 1154651636906060 T^{15} + 10573536812292673 T^{16} + 157993965113945831 T^{17} + 971926199561891003 T^{18} - 2773732161244197706 T^{19} - \)\(12\!\cdots\!99\)\( T^{20} - \)\(81\!\cdots\!04\)\( T^{21} + \)\(48\!\cdots\!12\)\( T^{22} + \)\(78\!\cdots\!13\)\( T^{23} + \)\(90\!\cdots\!10\)\( T^{24} - \)\(32\!\cdots\!20\)\( T^{25} - \)\(13\!\cdots\!66\)\( T^{26} + \)\(46\!\cdots\!90\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 + 149 T^{2} + 15960 T^{4} + 929909 T^{6} + 38950081 T^{8} \))(\( ( 1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - T + 489 T^{2} - 92 T^{3} + 108962 T^{4} + 44511 T^{5} + 14856838 T^{6} + 9973310 T^{7} + 1391605452 T^{8} + 787891490 T^{9} + 92721525958 T^{10} + 21945658929 T^{11} + 4244078725922 T^{12} - 283089188708 T^{13} + 118869765749769 T^{14} - 19203908986159 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 - 10 T - 123 T^{2} + 844 T^{3} + 11042 T^{4} + 2166 T^{5} - 1268066 T^{6} - 531391 T^{7} + 106354368 T^{8} - 41979889 T^{9} - 7913999906 T^{10} + 1067922474 T^{11} + 430086794402 T^{12} + 2597035600756 T^{13} - 29899757029083 T^{14} - 192039089861590 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( 1 + 95 T^{2} + 2784 T^{4} + 592895 T^{6} + 38950081 T^{8} \))(\( ( 1 - 3 T + 82 T^{2} - 237 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 3 T + 82 T^{2} + 237 T^{3} + 6241 T^{4} )^{2} \))(\( 1 + 95 T^{2} + 2784 T^{4} + 592895 T^{6} + 38950081 T^{8} \))(\( 1 + 77 T^{2} - 312 T^{4} + 480557 T^{6} + 38950081 T^{8} \))(\( 1 - 6 T + 132 T^{2} - 720 T^{3} + 9999 T^{4} - 52644 T^{5} - 314880 T^{6} - 1496442 T^{7} - 48671848 T^{8} - 118218918 T^{9} - 1965166080 T^{10} - 25955545116 T^{11} + 389461859919 T^{12} - 2215480607280 T^{13} + 32087544128772 T^{14} - 115223453916954 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 6 T + 132 T^{2} + 720 T^{3} + 9999 T^{4} + 52644 T^{5} - 314880 T^{6} + 1496442 T^{7} - 48671848 T^{8} + 118218918 T^{9} - 1965166080 T^{10} + 25955545116 T^{11} + 389461859919 T^{12} + 2215480607280 T^{13} + 32087544128772 T^{14} + 115223453916954 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 149 T^{2} + 15960 T^{4} + 929909 T^{6} + 38950081 T^{8} \))(\( 1 + 149 T^{2} + 15960 T^{4} + 929909 T^{6} + 38950081 T^{8} \))(\( ( 1 - 149 T^{2} + 6241 T^{4} )^{2} \))(\( 1 + T - 488 T^{2} + 305 T^{3} + 130067 T^{4} - 217447 T^{5} - 23515767 T^{6} + 58439790 T^{7} + 3200266602 T^{8} - 9493225932 T^{9} - 346875510927 T^{10} + 1047490944351 T^{11} + 31673904979161 T^{12} - 75618180243888 T^{13} - 2595852946891617 T^{14} + 2451851231878899 T^{15} + 205361771983476300 T^{16} + 193696247318433021 T^{17} - 16200718241550581697 T^{18} - 37282711969266295632 T^{19} + \)\(12\!\cdots\!41\)\( T^{20} + \)\(32\!\cdots\!49\)\( T^{21} - \)\(84\!\cdots\!67\)\( T^{22} - \)\(18\!\cdots\!88\)\( T^{23} + \)\(48\!\cdots\!22\)\( T^{24} + \)\(70\!\cdots\!10\)\( T^{25} - \)\(22\!\cdots\!67\)\( T^{26} - \)\(16\!\cdots\!13\)\( T^{27} + \)\(76\!\cdots\!47\)\( T^{28} + \)\(14\!\cdots\!95\)\( T^{29} - \)\(17\!\cdots\!28\)\( T^{30} + \)\(29\!\cdots\!99\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))
$83$ (\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 4 T + 102 T^{2} + 332 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 4 T + 102 T^{2} - 332 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 370 T^{2} + 65191 T^{4} + 6834652 T^{6} + 449100799 T^{8} + 17559578770 T^{10} + 326940373369 T^{12} )^{2} \))(\( ( 1 + 118 T^{2} + 6889 T^{4} )^{2} \))(\( 1 + T - 82 T^{2} + 83 T^{3} + 6889 T^{4} \))(\( 1 + 25 T + 157 T^{2} - 750 T^{3} - 6622 T^{4} + 69964 T^{5} + 1466905 T^{6} + 20424981 T^{7} + 74872112 T^{8} - 997051343 T^{9} + 7203133487 T^{10} + 269189728764 T^{11} + 1307717205141 T^{12} - 2467734607815 T^{13} - 39825488981322 T^{14} - 204821972448645 T^{15} + 9008863826216349 T^{16} + 153919187440781268 T^{17} + 341848621231895327 T^{18} - 3927425763234733549 T^{19} + 24478716252205585328 T^{20} + \)\(55\!\cdots\!87\)\( T^{21} + \)\(33\!\cdots\!05\)\( T^{22} + \)\(13\!\cdots\!92\)\( T^{23} - \)\(10\!\cdots\!78\)\( T^{24} - \)\(96\!\cdots\!50\)\( T^{25} + \)\(16\!\cdots\!77\)\( T^{26} + \)\(22\!\cdots\!75\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 + 20 T + 38 T^{2} + 346 T^{3} + 32058 T^{4} + 183754 T^{5} - 606869 T^{6} + 15251582 T^{7} + 220847562 T^{8} + 197838302 T^{9} + 1803416198 T^{10} + 78780812860 T^{11} + 326940373369 T^{12} \))(\( 1 - 18 T + 198 T^{3} + 23814 T^{4} - 132750 T^{5} - 711245 T^{6} - 11018250 T^{7} + 164054646 T^{8} + 113213826 T^{9} - 70902731574 T^{11} + 326940373369 T^{12} \))(\( ( 1 + 2 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( 1 + T - 82 T^{2} + 83 T^{3} + 6889 T^{4} \))(\( 1 + 25 T + 157 T^{2} - 750 T^{3} - 6622 T^{4} + 69964 T^{5} + 1466905 T^{6} + 20424981 T^{7} + 74872112 T^{8} - 997051343 T^{9} + 7203133487 T^{10} + 269189728764 T^{11} + 1307717205141 T^{12} - 2467734607815 T^{13} - 39825488981322 T^{14} - 204821972448645 T^{15} + 9008863826216349 T^{16} + 153919187440781268 T^{17} + 341848621231895327 T^{18} - 3927425763234733549 T^{19} + 24478716252205585328 T^{20} + \)\(55\!\cdots\!87\)\( T^{21} + \)\(33\!\cdots\!05\)\( T^{22} + \)\(13\!\cdots\!92\)\( T^{23} - \)\(10\!\cdots\!78\)\( T^{24} - \)\(96\!\cdots\!50\)\( T^{25} + \)\(16\!\cdots\!77\)\( T^{26} + \)\(22\!\cdots\!75\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 - 139 T^{2} + 12432 T^{4} - 957571 T^{6} + 47458321 T^{8} \))(\( ( 1 + 16 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 334 T^{2} - 1272 T^{3} + 54816 T^{4} + 395796 T^{5} - 5397056 T^{6} - 60133572 T^{7} + 310945691 T^{8} + 6455120304 T^{9} - 3389068248 T^{10} - 563598757704 T^{11} - 2368219763012 T^{12} + 39202056035964 T^{13} + 437295746267318 T^{14} - 1352773893773628 T^{15} - 45259898774669136 T^{16} - 112280233183211124 T^{17} + 3012530396035553702 T^{18} + 22415226014635747668 T^{19} - \)\(11\!\cdots\!52\)\( T^{20} - \)\(22\!\cdots\!72\)\( T^{21} - \)\(11\!\cdots\!12\)\( T^{22} + \)\(17\!\cdots\!08\)\( T^{23} + \)\(70\!\cdots\!31\)\( T^{24} - \)\(11\!\cdots\!16\)\( T^{25} - \)\(83\!\cdots\!44\)\( T^{26} + \)\(50\!\cdots\!32\)\( T^{27} + \)\(58\!\cdots\!76\)\( T^{28} - \)\(11\!\cdots\!36\)\( T^{29} - \)\(24\!\cdots\!86\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 397 T^{2} + 87990 T^{4} - 12501089 T^{6} + 1185510017 T^{8} - 57837981066 T^{10} - 2507933243939 T^{12} + 849901181197043 T^{14} - 92913215010718536 T^{16} + 5854969237266429227 T^{18} - \)\(11\!\cdots\!19\)\( T^{20} - \)\(18\!\cdots\!54\)\( T^{22} + \)\(26\!\cdots\!97\)\( T^{24} - \)\(19\!\cdots\!61\)\( T^{26} + \)\(94\!\cdots\!90\)\( T^{28} - \)\(29\!\cdots\!13\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( ( 1 + 145 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 145 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 2 T + 229 T^{2} - 802 T^{3} + 24432 T^{4} - 66566 T^{5} + 1577581 T^{6} - 1143574 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 + 2 T + 229 T^{2} + 802 T^{3} + 24432 T^{4} + 66566 T^{5} + 1577581 T^{6} + 1143574 T^{7} + 47458321 T^{8} )^{2} \))(\( 1 - 163 T^{2} + 19680 T^{4} - 1122907 T^{6} + 47458321 T^{8} \))(\( 1 - 163 T^{2} + 19680 T^{4} - 1122907 T^{6} + 47458321 T^{8} \))(\( 1 - 139 T^{2} + 12432 T^{4} - 957571 T^{6} + 47458321 T^{8} \))(\( 1 - 334 T^{2} + 1272 T^{3} + 54816 T^{4} - 395796 T^{5} - 5397056 T^{6} + 60133572 T^{7} + 310945691 T^{8} - 6455120304 T^{9} - 3389068248 T^{10} + 563598757704 T^{11} - 2368219763012 T^{12} - 39202056035964 T^{13} + 437295746267318 T^{14} + 1352773893773628 T^{15} - 45259898774669136 T^{16} + 112280233183211124 T^{17} + 3012530396035553702 T^{18} - 22415226014635747668 T^{19} - \)\(11\!\cdots\!52\)\( T^{20} + \)\(22\!\cdots\!72\)\( T^{21} - \)\(11\!\cdots\!12\)\( T^{22} - \)\(17\!\cdots\!08\)\( T^{23} + \)\(70\!\cdots\!31\)\( T^{24} + \)\(11\!\cdots\!16\)\( T^{25} - \)\(83\!\cdots\!44\)\( T^{26} - \)\(50\!\cdots\!32\)\( T^{27} + \)\(58\!\cdots\!76\)\( T^{28} + \)\(11\!\cdots\!36\)\( T^{29} - \)\(24\!\cdots\!86\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 + 172 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 89 T^{2} )^{4} \))(\( 1 - 294 T^{2} + 36618 T^{4} - 2328774 T^{6} + 62742241 T^{8} \))(\( 1 - 294 T^{2} + 36618 T^{4} - 2328774 T^{6} + 62742241 T^{8} \))(\( ( 1 - 308 T^{2} + 49895 T^{4} - 5241384 T^{6} + 395218295 T^{8} - 19324610228 T^{10} + 496981290961 T^{12} )^{2} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \))(\( 1 + 15 T + 136 T^{2} + 1335 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 395 T^{2} - 1770 T^{3} + 83413 T^{4} + 244017 T^{5} - 12791578 T^{6} - 19742595 T^{7} + 1607888462 T^{8} + 933579267 T^{9} - 173735706451 T^{10} - 11863751967 T^{11} + 16888438123377 T^{12} - 583089996186 T^{13} - 1538438146646466 T^{14} - 51895009660554 T^{15} + 133773318375269217 T^{16} - 8363577360424023 T^{17} - 10900567564453896691 T^{18} + 5213162127281843883 T^{19} + \)\(79\!\cdots\!82\)\( T^{20} - \)\(87\!\cdots\!55\)\( T^{21} - \)\(50\!\cdots\!18\)\( T^{22} + \)\(85\!\cdots\!53\)\( T^{23} + \)\(26\!\cdots\!13\)\( T^{24} - \)\(49\!\cdots\!30\)\( T^{25} - \)\(97\!\cdots\!95\)\( T^{26} + \)\(13\!\cdots\!14\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( ( 1 - 12 T + 216 T^{2} - 1425 T^{3} + 19224 T^{4} - 95052 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 6 T + 72 T^{2} + 21 T^{3} + 6408 T^{4} - 47526 T^{5} + 704969 T^{6} )^{2} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 15 T + 136 T^{2} - 1335 T^{3} + 7921 T^{4} \))(\( 1 + 15 T + 136 T^{2} + 1335 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 395 T^{2} - 1770 T^{3} + 83413 T^{4} + 244017 T^{5} - 12791578 T^{6} - 19742595 T^{7} + 1607888462 T^{8} + 933579267 T^{9} - 173735706451 T^{10} - 11863751967 T^{11} + 16888438123377 T^{12} - 583089996186 T^{13} - 1538438146646466 T^{14} - 51895009660554 T^{15} + 133773318375269217 T^{16} - 8363577360424023 T^{17} - 10900567564453896691 T^{18} + 5213162127281843883 T^{19} + \)\(79\!\cdots\!82\)\( T^{20} - \)\(87\!\cdots\!55\)\( T^{21} - \)\(50\!\cdots\!18\)\( T^{22} + \)\(85\!\cdots\!53\)\( T^{23} + \)\(26\!\cdots\!13\)\( T^{24} - \)\(49\!\cdots\!30\)\( T^{25} - \)\(97\!\cdots\!95\)\( T^{26} + \)\(13\!\cdots\!14\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( ( 1 - 15 T + 164 T^{2} - 1335 T^{3} + 7921 T^{4} )^{2} \))(\( 1 + 38 T^{2} - 6477 T^{4} + 300998 T^{6} + 62742241 T^{8} \))(\( 1 - 21 T - 253 T^{2} + 6084 T^{3} + 64134 T^{4} - 1086543 T^{5} - 14444834 T^{6} + 154075794 T^{7} + 2457441293 T^{8} - 16916386392 T^{9} - 343956627405 T^{10} + 1437006555873 T^{11} + 41653185355711 T^{12} - 92739461592729 T^{13} - 4399434577615834 T^{14} + 3097874885577318 T^{15} + 411982470004053510 T^{16} + 275710864816381302 T^{17} - 34847921289295021114 T^{18} - 65378445499564570401 T^{19} + \)\(26\!\cdots\!51\)\( T^{20} + \)\(80\!\cdots\!77\)\( T^{21} - \)\(17\!\cdots\!05\)\( T^{22} - \)\(74\!\cdots\!68\)\( T^{23} + \)\(96\!\cdots\!33\)\( T^{24} + \)\(53\!\cdots\!46\)\( T^{25} - \)\(45\!\cdots\!34\)\( T^{26} - \)\(30\!\cdots\!27\)\( T^{27} + \)\(15\!\cdots\!14\)\( T^{28} + \)\(13\!\cdots\!96\)\( T^{29} - \)\(49\!\cdots\!73\)\( T^{30} - \)\(36\!\cdots\!29\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 64 T^{2} + 9487 T^{4} + 662335 T^{6} + 143358802 T^{8} + 5246355535 T^{10} + 595235640367 T^{12} + 31806802621504 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 + 18 T + 197 T^{2} + 1602 T^{3} + 7921 T^{4} )^{2} \))(\( 1 + 50 T^{2} - 5421 T^{4} + 396050 T^{6} + 62742241 T^{8} \))(\( 1 + 50 T^{2} - 5421 T^{4} + 396050 T^{6} + 62742241 T^{8} \))(\( ( 1 - 18 T + 197 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 27 T + 332 T^{2} + 2403 T^{3} + 7921 T^{4} )^{2} \))(\( 1 + 264 T^{2} + 38610 T^{4} - 50400 T^{5} + 4052064 T^{6} - 8952768 T^{7} + 353995811 T^{8} - 796796352 T^{9} + 32096398944 T^{10} - 35530437600 T^{11} + 2422477925010 T^{12} + 131203060813704 T^{14} + 3936588805702081 T^{16} \))(\( 1 + 264 T^{2} + 38610 T^{4} - 50400 T^{5} + 4052064 T^{6} - 8952768 T^{7} + 353995811 T^{8} - 796796352 T^{9} + 32096398944 T^{10} - 35530437600 T^{11} + 2422477925010 T^{12} + 131203060813704 T^{14} + 3936588805702081 T^{16} \))(\( ( 1 + 122 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 122 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 15 T + 164 T^{2} - 1335 T^{3} + 7921 T^{4} )^{2} \))(\( 1 + 21 T - 253 T^{2} - 6084 T^{3} + 64134 T^{4} + 1086543 T^{5} - 14444834 T^{6} - 154075794 T^{7} + 2457441293 T^{8} + 16916386392 T^{9} - 343956627405 T^{10} - 1437006555873 T^{11} + 41653185355711 T^{12} + 92739461592729 T^{13} - 4399434577615834 T^{14} - 3097874885577318 T^{15} + 411982470004053510 T^{16} - 275710864816381302 T^{17} - 34847921289295021114 T^{18} + 65378445499564570401 T^{19} + \)\(26\!\cdots\!51\)\( T^{20} - \)\(80\!\cdots\!77\)\( T^{21} - \)\(17\!\cdots\!05\)\( T^{22} + \)\(74\!\cdots\!68\)\( T^{23} + \)\(96\!\cdots\!33\)\( T^{24} - \)\(53\!\cdots\!46\)\( T^{25} - \)\(45\!\cdots\!34\)\( T^{26} + \)\(30\!\cdots\!27\)\( T^{27} + \)\(15\!\cdots\!14\)\( T^{28} - \)\(13\!\cdots\!96\)\( T^{29} - \)\(49\!\cdots\!73\)\( T^{30} + \)\(36\!\cdots\!29\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( ( 1 - 97 T^{2} )^{2} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( 1 - 204 T^{2} + 28950 T^{4} - 1919436 T^{6} + 88529281 T^{8} \))(\( 1 - 204 T^{2} + 28950 T^{4} - 1919436 T^{6} + 88529281 T^{8} \))(\( ( 1 + 135 T^{2} + 128 T^{3} + 13095 T^{4} + 912673 T^{6} )^{4} \))(\( ( 1 - 170 T^{2} + 9409 T^{4} )^{2} \))(\( 1 - 17 T + 192 T^{2} - 1649 T^{3} + 9409 T^{4} \))(\( 1 + 18 T - 332 T^{2} - 7282 T^{3} + 70792 T^{4} + 1694642 T^{5} - 11251793 T^{6} - 262778647 T^{7} + 1667779429 T^{8} + 30411590872 T^{9} - 218639545013 T^{10} - 2436064838528 T^{11} + 25890765026051 T^{12} + 94489464293929 T^{13} - 2645836565169718 T^{14} + 9165478036511113 T^{15} + 243606208130113859 T^{16} - 2223330604373865344 T^{17} - 19356001718168025653 T^{18} + \)\(26\!\cdots\!04\)\( T^{19} + \)\(13\!\cdots\!41\)\( T^{20} - \)\(21\!\cdots\!11\)\( T^{21} - \)\(88\!\cdots\!73\)\( T^{22} + \)\(12\!\cdots\!14\)\( T^{23} + \)\(52\!\cdots\!08\)\( T^{24} - \)\(52\!\cdots\!46\)\( T^{25} - \)\(23\!\cdots\!12\)\( T^{26} + \)\(12\!\cdots\!86\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 - 9 T - 66 T^{2} + 2023 T^{3} - 7707 T^{4} - 73950 T^{5} + 1766073 T^{6} - 7173150 T^{7} - 72515163 T^{8} + 1846337479 T^{9} - 5842932546 T^{10} - 77286062313 T^{11} + 832972004929 T^{12} \))(\( 1 - 15 T - 84 T^{2} + 1139 T^{3} + 22203 T^{4} - 134028 T^{5} - 1218567 T^{6} - 13000716 T^{7} + 208908027 T^{8} + 1039534547 T^{9} - 7436459604 T^{10} - 128810103855 T^{11} + 832972004929 T^{12} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( 1 - 17 T + 192 T^{2} - 1649 T^{3} + 9409 T^{4} \))(\( 1 + 18 T - 332 T^{2} - 7282 T^{3} + 70792 T^{4} + 1694642 T^{5} - 11251793 T^{6} - 262778647 T^{7} + 1667779429 T^{8} + 30411590872 T^{9} - 218639545013 T^{10} - 2436064838528 T^{11} + 25890765026051 T^{12} + 94489464293929 T^{13} - 2645836565169718 T^{14} + 9165478036511113 T^{15} + 243606208130113859 T^{16} - 2223330604373865344 T^{17} - 19356001718168025653 T^{18} + \)\(26\!\cdots\!04\)\( T^{19} + \)\(13\!\cdots\!41\)\( T^{20} - \)\(21\!\cdots\!11\)\( T^{21} - \)\(88\!\cdots\!73\)\( T^{22} + \)\(12\!\cdots\!14\)\( T^{23} + \)\(52\!\cdots\!08\)\( T^{24} - \)\(52\!\cdots\!46\)\( T^{25} - \)\(23\!\cdots\!12\)\( T^{26} + \)\(12\!\cdots\!86\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( ( 1 - 3 T + 100 T^{2} - 291 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 182 T^{2} + 9409 T^{4} )^{2} \))(\( 1 + 3 T + 392 T^{2} + 1167 T^{3} + 75243 T^{4} + 248802 T^{5} + 9281977 T^{6} + 31870980 T^{7} + 787182476 T^{8} + 2086019346 T^{9} + 40966656945 T^{10} - 99548858823 T^{11} - 1131878124686 T^{12} - 48785193558327 T^{13} - 618766130152816 T^{14} - 7413615555033420 T^{15} - 81803373889459032 T^{16} - 719120708838241740 T^{17} - 5821970518607845744 T^{18} - 44524928960458978071 T^{19} - \)\(10\!\cdots\!66\)\( T^{20} - \)\(85\!\cdots\!11\)\( T^{21} + \)\(34\!\cdots\!05\)\( T^{22} + \)\(16\!\cdots\!98\)\( T^{23} + \)\(61\!\cdots\!36\)\( T^{24} + \)\(24\!\cdots\!60\)\( T^{25} + \)\(68\!\cdots\!73\)\( T^{26} + \)\(17\!\cdots\!06\)\( T^{27} + \)\(52\!\cdots\!63\)\( T^{28} + \)\(78\!\cdots\!59\)\( T^{29} + \)\(25\!\cdots\!48\)\( T^{30} + \)\(18\!\cdots\!79\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 404 T^{2} + 81609 T^{4} + 10963666 T^{6} + 1046175986 T^{8} + 57359540784 T^{10} - 1663618077194 T^{12} - 785812116013063 T^{14} - 99406691908304130 T^{16} - 7393706199566909767 T^{18} - \)\(14\!\cdots\!14\)\( T^{20} + \)\(47\!\cdots\!36\)\( T^{22} + \)\(81\!\cdots\!46\)\( T^{24} + \)\(80\!\cdots\!34\)\( T^{26} + \)\(56\!\cdots\!69\)\( T^{28} + \)\(26\!\cdots\!76\)\( T^{30} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 119 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 119 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 + 106 T^{2} + 9409 T^{4} )^{2} \))(\( 1 - 594 T^{2} + 165777 T^{4} - 28537554 T^{6} + 3324136868 T^{8} - 268509845586 T^{10} + 14676118616337 T^{12} - 494785370927826 T^{14} + 7837433594376961 T^{16} \))(\( 1 - 594 T^{2} + 165777 T^{4} - 28537554 T^{6} + 3324136868 T^{8} - 268509845586 T^{10} + 14676118616337 T^{12} - 494785370927826 T^{14} + 7837433594376961 T^{16} \))(\( ( 1 - 5 T + 97 T^{2} )^{2}( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2}( 1 + 5 T + 97 T^{2} )^{2} \))(\( ( 1 + 3 T + 100 T^{2} + 291 T^{3} + 9409 T^{4} )^{2} \))(\( 1 - 3 T + 392 T^{2} - 1167 T^{3} + 75243 T^{4} - 248802 T^{5} + 9281977 T^{6} - 31870980 T^{7} + 787182476 T^{8} - 2086019346 T^{9} + 40966656945 T^{10} + 99548858823 T^{11} - 1131878124686 T^{12} + 48785193558327 T^{13} - 618766130152816 T^{14} + 7413615555033420 T^{15} - 81803373889459032 T^{16} + 719120708838241740 T^{17} - 5821970518607845744 T^{18} + 44524928960458978071 T^{19} - \)\(10\!\cdots\!66\)\( T^{20} + \)\(85\!\cdots\!11\)\( T^{21} + \)\(34\!\cdots\!05\)\( T^{22} - \)\(16\!\cdots\!98\)\( T^{23} + \)\(61\!\cdots\!36\)\( T^{24} - \)\(24\!\cdots\!60\)\( T^{25} + \)\(68\!\cdots\!73\)\( T^{26} - \)\(17\!\cdots\!06\)\( T^{27} + \)\(52\!\cdots\!63\)\( T^{28} - \)\(78\!\cdots\!59\)\( T^{29} + \)\(25\!\cdots\!48\)\( T^{30} - \)\(18\!\cdots\!79\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))
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