Properties

Label 225.2
Level 225
Weight 2
Dimension 1221
Nonzero newspaces 12
Newform subspaces 34
Sturm bound 7200
Trace bound 2

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Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 34 \)
Sturm bound: \(7200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(225))\).

Total New Old
Modular forms 2024 1406 618
Cusp forms 1577 1221 356
Eisenstein series 447 185 262

Trace form

\( 1221q - 16q^{2} - 24q^{3} - 8q^{4} - 21q^{5} - 40q^{6} - 6q^{7} - 24q^{8} - 32q^{9} + O(q^{10}) \) \( 1221q - 16q^{2} - 24q^{3} - 8q^{4} - 21q^{5} - 40q^{6} - 6q^{7} - 24q^{8} - 32q^{9} - 75q^{10} - 46q^{11} - 56q^{12} - 26q^{13} - 54q^{14} - 44q^{15} - 56q^{16} - 44q^{17} - 72q^{18} - 70q^{19} - 90q^{20} - 72q^{21} - 86q^{22} - 74q^{23} - 112q^{24} - 63q^{25} - 132q^{26} - 72q^{27} - 166q^{28} - 94q^{29} - 72q^{30} - 58q^{31} - 91q^{32} - 56q^{33} - 83q^{34} - 32q^{35} - 8q^{36} - 99q^{37} - 28q^{38} + 24q^{39} - 57q^{40} + 26q^{41} + 32q^{42} - 6q^{43} + 36q^{44} - 12q^{45} - 142q^{46} + 10q^{47} + 80q^{48} - 91q^{49} - 89q^{50} - 80q^{51} - 144q^{52} - 79q^{53} - 32q^{54} - 142q^{55} - 66q^{56} - 72q^{57} - 152q^{58} - 128q^{59} + 20q^{60} - 66q^{61} - 68q^{62} - 60q^{63} + 22q^{64} + 53q^{65} - 128q^{66} + 42q^{67} + 190q^{68} - 20q^{69} + 150q^{70} - 62q^{71} + 192q^{72} + 34q^{73} + 304q^{74} + 128q^{75} + 52q^{76} + 234q^{77} + 240q^{78} + 114q^{79} + 425q^{80} + 88q^{81} + 170q^{82} + 284q^{83} + 344q^{84} + 21q^{85} + 266q^{86} + 148q^{87} + 90q^{88} + 177q^{89} + 184q^{90} - 86q^{91} + 182q^{92} + 100q^{93} - 182q^{94} - 70q^{95} + 136q^{96} - 174q^{97} + 56q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.2.a \(\chi_{225}(1, \cdot)\) 225.2.a.a 1 1
225.2.a.b 1
225.2.a.c 1
225.2.a.d 1
225.2.a.e 1
225.2.a.f 2
225.2.b \(\chi_{225}(199, \cdot)\) 225.2.b.a 2 1
225.2.b.b 2
225.2.b.c 2
225.2.e \(\chi_{225}(76, \cdot)\) 225.2.e.a 2 2
225.2.e.b 6
225.2.e.c 8
225.2.e.d 8
225.2.e.e 8
225.2.f \(\chi_{225}(107, \cdot)\) 225.2.f.a 4 2
225.2.f.b 8
225.2.h \(\chi_{225}(46, \cdot)\) 225.2.h.a 4 4
225.2.h.b 4
225.2.h.c 8
225.2.h.d 12
225.2.h.e 16
225.2.k \(\chi_{225}(49, \cdot)\) 225.2.k.a 4 2
225.2.k.b 12
225.2.k.c 16
225.2.m \(\chi_{225}(19, \cdot)\) 225.2.m.a 8 4
225.2.m.b 16
225.2.m.c 24
225.2.p \(\chi_{225}(32, \cdot)\) 225.2.p.a 16 4
225.2.p.b 16
225.2.p.c 32
225.2.q \(\chi_{225}(16, \cdot)\) 225.2.q.a 224 8
225.2.s \(\chi_{225}(8, \cdot)\) 225.2.s.a 80 8
225.2.u \(\chi_{225}(4, \cdot)\) 225.2.u.a 224 8
225.2.w \(\chi_{225}(2, \cdot)\) 225.2.w.a 448 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 - T^{2} + 4 T^{4} \))(\( ( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} ) \))(\( 1 - 3 T^{2} + 4 T^{4} \))(\( ( 1 - 2 T^{2} )^{2} \))(\( 1 - T - T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 - T + T^{3} - 2 T^{4} - T^{5} + 11 T^{6} - 2 T^{7} - 8 T^{8} + 8 T^{9} - 32 T^{11} + 64 T^{12} \))(\( 1 + 2 T - 6 T^{3} - 9 T^{4} - 2 T^{5} + 9 T^{6} + 13 T^{7} + 7 T^{8} + 26 T^{9} + 36 T^{10} - 16 T^{11} - 144 T^{12} - 192 T^{13} + 256 T^{15} + 256 T^{16} \))(\( 1 - 4 T^{2} + 7 T^{4} - 4 T^{6} + T^{8} - 16 T^{10} + 112 T^{12} - 256 T^{14} + 256 T^{16} \))(\( 1 - 2 T + 6 T^{3} - 9 T^{4} + 2 T^{5} + 9 T^{6} - 13 T^{7} + 7 T^{8} - 26 T^{9} + 36 T^{10} + 16 T^{11} - 144 T^{12} + 192 T^{13} - 256 T^{15} + 256 T^{16} \))(\( 1 + T^{4} + 16 T^{8} \))(\( ( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} )^{2}( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} )^{2} \))(\( 1 - T - T^{2} + 3 T^{3} - T^{4} + 6 T^{5} - 4 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 2 T^{2} - 5 T^{3} + 11 T^{4} - 10 T^{5} + 8 T^{6} - 16 T^{7} + 16 T^{8} \))(\( ( 1 - 3 T + 2 T^{2} + T^{4} + 8 T^{6} - 24 T^{7} + 16 T^{8} )( 1 + 2 T + 2 T^{2} + 5 T^{3} + 11 T^{4} + 10 T^{5} + 8 T^{6} + 16 T^{7} + 16 T^{8} ) \))(\( 1 + 2 T^{2} + 3 T^{3} - 2 T^{4} + 2 T^{5} - 5 T^{6} - 10 T^{7} - 18 T^{8} - T^{9} - 2 T^{10} - 22 T^{11} + 121 T^{12} - 44 T^{13} - 8 T^{14} - 8 T^{15} - 288 T^{16} - 320 T^{17} - 320 T^{18} + 256 T^{19} - 512 T^{20} + 1536 T^{21} + 2048 T^{22} + 4096 T^{24} \))(\( 1 - 3 T^{2} + 15 T^{6} - 15 T^{8} - 99 T^{10} + 242 T^{12} + 105 T^{14} - 915 T^{16} + 420 T^{18} + 3872 T^{20} - 6336 T^{22} - 3840 T^{24} + 15360 T^{26} - 49152 T^{30} + 65536 T^{32} \))(\( 1 + 3 T^{2} + 5 T^{4} + 12 T^{6} + 16 T^{8} \))(\( 1 + T^{2} - 2 T^{4} - 19 T^{6} - 14 T^{8} + 25 T^{10} + 197 T^{12} + 100 T^{14} - 224 T^{16} - 1216 T^{18} - 512 T^{20} + 1024 T^{22} + 4096 T^{24} \))(\( 1 + 4 T^{2} + 6 T^{4} + 10 T^{6} + 19 T^{8} + 42 T^{10} + 95 T^{12} + 11 T^{14} - 267 T^{16} + 44 T^{18} + 1520 T^{20} + 2688 T^{22} + 4864 T^{24} + 10240 T^{26} + 24576 T^{28} + 65536 T^{30} + 65536 T^{32} \))(\( 1 - 5 T + 15 T^{2} - 30 T^{3} + 41 T^{4} - 30 T^{5} - 20 T^{6} + 110 T^{7} - 199 T^{8} + 220 T^{9} - 80 T^{10} - 240 T^{11} + 656 T^{12} - 960 T^{13} + 960 T^{14} - 640 T^{15} + 256 T^{16} \))(\( 1 + 3 T^{2} - 10 T^{3} + 6 T^{4} - 30 T^{5} + 61 T^{6} - 80 T^{7} + 165 T^{8} - 310 T^{9} + 503 T^{10} - 690 T^{11} + 1290 T^{12} - 2060 T^{13} + 2585 T^{14} - 4150 T^{15} + 6461 T^{16} - 8300 T^{17} + 10340 T^{18} - 16480 T^{19} + 20640 T^{20} - 22080 T^{21} + 32192 T^{22} - 39680 T^{23} + 42240 T^{24} - 40960 T^{25} + 62464 T^{26} - 61440 T^{27} + 24576 T^{28} - 81920 T^{29} + 49152 T^{30} + 65536 T^{32} \))(\( 1 + 2 T^{4} - 5 T^{8} - 46 T^{12} - 239 T^{16} - 736 T^{20} - 1280 T^{24} + 8192 T^{28} + 65536 T^{32} \))(\( 1 - 6 T + 18 T^{2} - 36 T^{3} + 58 T^{4} - 78 T^{5} + 72 T^{6} - 149 T^{8} + 354 T^{9} - 576 T^{10} + 732 T^{11} - 530 T^{12} - 480 T^{13} + 2592 T^{14} - 5496 T^{15} + 8641 T^{16} - 10992 T^{17} + 10368 T^{18} - 3840 T^{19} - 8480 T^{20} + 23424 T^{21} - 36864 T^{22} + 45312 T^{23} - 38144 T^{24} + 73728 T^{26} - 159744 T^{27} + 237568 T^{28} - 294912 T^{29} + 294912 T^{30} - 196608 T^{31} + 65536 T^{32} \))
$3$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + T + 4 T^{2} + 3 T^{3} + 12 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 - T - 2 T^{2} + 3 T^{3} - 3 T^{4} + 9 T^{5} - 18 T^{6} - 27 T^{7} + 81 T^{8} \))(\( 1 - 9 T^{4} + 81 T^{8} \))(\( 1 + T - 2 T^{2} - 3 T^{3} - 3 T^{4} - 9 T^{5} - 18 T^{6} + 27 T^{7} + 81 T^{8} \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 - 7 T^{2} + 34 T^{4} - 123 T^{6} + 306 T^{8} - 567 T^{10} + 729 T^{12} \))(\( 1 + 5 T^{2} + 4 T^{4} + 15 T^{6} + 135 T^{8} + 135 T^{10} + 324 T^{12} + 3645 T^{14} + 6561 T^{16} \))(\( \))(\( \))(\( 1 - 6 T^{4} - 45 T^{8} - 486 T^{12} + 6561 T^{16} \))(\( 1 - 6 T + 18 T^{2} - 30 T^{3} + 30 T^{4} - 36 T^{5} + 126 T^{6} - 396 T^{7} + 819 T^{8} - 1188 T^{9} + 1134 T^{10} - 972 T^{11} + 2430 T^{12} - 7290 T^{13} + 13122 T^{14} - 13122 T^{15} + 6561 T^{16} \))
$5$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( 1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4} \))(\( 1 - 5 T + 15 T^{2} - 25 T^{3} + 25 T^{4} \))(\( 1 - 5 T + 20 T^{2} - 65 T^{3} + 155 T^{4} - 325 T^{5} + 500 T^{6} - 625 T^{7} + 625 T^{8} \))(\( 1 - 6 T + 16 T^{2} - 21 T^{3} - 4 T^{4} + 100 T^{5} - 285 T^{6} + 500 T^{7} - 100 T^{8} - 2625 T^{9} + 10000 T^{10} - 18750 T^{11} + 15625 T^{12} \))(\( 1 - 5 T^{2} + 50 T^{4} - 375 T^{6} + 1375 T^{8} - 9375 T^{10} + 31250 T^{12} - 78125 T^{14} + 390625 T^{16} \))(\( \))(\( \))(\( \))(\( 1 + 5 T^{2} + 20 T^{3} + 5 T^{4} + 100 T^{5} + 125 T^{6} + 625 T^{8} \))(\( 1 + 5 T^{2} - 10 T^{3} + 10 T^{4} + 50 T^{5} + 25 T^{6} + 450 T^{7} - 725 T^{8} + 2250 T^{9} + 625 T^{10} + 6250 T^{11} + 6250 T^{12} - 31250 T^{13} + 78125 T^{14} + 390625 T^{16} \))(\( \))(\( \))
$7$ (\( 1 + 3 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( 1 - 5 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} \))(\( 1 - 5 T + T^{2} + 14 T^{3} + 73 T^{4} - 173 T^{5} - 82 T^{6} - 1211 T^{7} + 3577 T^{8} + 4802 T^{9} + 2401 T^{10} - 84035 T^{11} + 117649 T^{12} \))(\( 1 - T - 15 T^{2} - 22 T^{3} + 142 T^{4} + 303 T^{5} - 274 T^{6} - 1448 T^{7} - 633 T^{8} - 10136 T^{9} - 13426 T^{10} + 103929 T^{11} + 340942 T^{12} - 369754 T^{13} - 1764735 T^{14} - 823543 T^{15} + 5764801 T^{16} \))(\( 1 - 16 T^{2} + 121 T^{4} - 592 T^{6} + 3280 T^{8} - 29008 T^{10} + 290521 T^{12} - 1882384 T^{14} + 5764801 T^{16} \))(\( 1 + T - 15 T^{2} + 22 T^{3} + 142 T^{4} - 303 T^{5} - 274 T^{6} + 1448 T^{7} - 633 T^{8} + 10136 T^{9} - 13426 T^{10} - 103929 T^{11} + 340942 T^{12} + 369754 T^{13} - 1764735 T^{14} + 823543 T^{15} + 5764801 T^{16} \))(\( ( 1 - 4 T + 8 T^{2} - 28 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 + 23 T^{4} + 2401 T^{8} )^{2} \))(\( ( 1 - 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + T + 13 T^{2} + 7 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 2 T + 12 T^{2} - 15 T^{3} + 61 T^{4} - 105 T^{5} + 588 T^{6} - 686 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 + 6 T + 46 T^{2} + 185 T^{3} + 822 T^{4} + 2435 T^{5} + 7706 T^{6} + 17045 T^{7} + 40278 T^{8} + 63455 T^{9} + 110446 T^{10} + 100842 T^{11} + 117649 T^{12} )^{2} \))(\( ( 1 + 18 T^{2} + 5 T^{3} + 159 T^{4} + 35 T^{5} + 882 T^{6} + 2401 T^{8} )^{4} \))(\( 1 + 5 T^{2} - 24 T^{4} + 245 T^{6} + 2401 T^{8} \))(\( 1 + 23 T^{2} + 287 T^{4} + 1944 T^{6} + 5053 T^{8} - 51983 T^{10} - 624746 T^{12} - 2547167 T^{14} + 12132253 T^{16} + 228709656 T^{18} + 1654497887 T^{20} + 6496930727 T^{22} + 13841287201 T^{24} \))(\( 1 + 31 T^{2} + 465 T^{4} + 4686 T^{6} + 37554 T^{8} + 261471 T^{10} + 1619330 T^{12} + 9344750 T^{14} + 58806225 T^{16} + 457892750 T^{18} + 3888011330 T^{20} + 30761801679 T^{22} + 216491336754 T^{24} + 1323679016814 T^{26} + 6436198548465 T^{28} + 21024915258319 T^{30} + 33232930569601 T^{32} \))(\( 1 - 35 T^{2} + 611 T^{4} - 7045 T^{6} + 57976 T^{8} - 345205 T^{10} + 1467011 T^{12} - 4117715 T^{14} + 5764801 T^{16} \))(\( 1 - 56 T^{2} + 1628 T^{4} - 32234 T^{6} + 485518 T^{8} - 5899406 T^{10} + 59922825 T^{12} - 520141390 T^{14} + 3906488461 T^{16} - 25486928110 T^{18} + 143874702825 T^{20} - 694059216494 T^{22} + 2798914651918 T^{24} - 9105307176266 T^{26} + 22533615563228 T^{28} - 37980492079544 T^{30} + 33232930569601 T^{32} \))(\( 1 + 38 T^{4} + 1681 T^{8} - 191482 T^{12} - 9175676 T^{16} - 459748282 T^{20} + 9690630481 T^{24} + 525968913638 T^{28} + 33232930569601 T^{32} \))(\( 1 - 2 T + 2 T^{2} + 16 T^{3} - 66 T^{4} + 104 T^{5} + 52 T^{6} - 1072 T^{7} - 235 T^{8} - 2614 T^{9} - 2614 T^{10} - 626 T^{11} + 8430 T^{12} + 20146 T^{13} + 75264 T^{14} + 1168356 T^{15} + 4373152 T^{16} + 8178492 T^{17} + 3687936 T^{18} + 6910078 T^{19} + 20240430 T^{20} - 10521182 T^{21} - 307534486 T^{22} - 2152741402 T^{23} - 1354728235 T^{24} - 43259066704 T^{25} + 14688712948 T^{26} + 205641981272 T^{27} - 913524955266 T^{28} + 1550224166512 T^{29} + 1356446145698 T^{30} - 9495123019886 T^{31} + 33232930569601 T^{32} \))
$11$ (\( 1 + 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T - 21 T^{2} + 14 T^{3} + 286 T^{4} + 58 T^{5} - 3673 T^{6} + 638 T^{7} + 34606 T^{8} + 18634 T^{9} - 307461 T^{10} - 322102 T^{11} + 1771561 T^{12} \))(\( 1 - T - 18 T^{2} + 129 T^{3} + 120 T^{4} - 1886 T^{5} + 6087 T^{6} + 14944 T^{7} - 88007 T^{8} + 164384 T^{9} + 736527 T^{10} - 2510266 T^{11} + 1756920 T^{12} + 20775579 T^{13} - 31888098 T^{14} - 19487171 T^{15} + 214358881 T^{16} \))(\( ( 1 + 6 T + 8 T^{2} + 36 T^{3} + 267 T^{4} + 396 T^{5} + 968 T^{6} + 7986 T^{7} + 14641 T^{8} )^{2} \))(\( 1 - T - 18 T^{2} + 129 T^{3} + 120 T^{4} - 1886 T^{5} + 6087 T^{6} + 14944 T^{7} - 88007 T^{8} + 164384 T^{9} + 736527 T^{10} - 2510266 T^{11} + 1756920 T^{12} + 20775579 T^{13} - 31888098 T^{14} - 19487171 T^{15} + 214358881 T^{16} \))(\( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T^{2} + 121 T^{4} )^{4} \))(\( 1 - 6 T + 5 T^{2} + 6 T^{3} + 49 T^{4} + 66 T^{5} + 605 T^{6} - 7986 T^{7} + 14641 T^{8} \))(\( 1 - 2 T + 13 T^{2} - 34 T^{3} + 225 T^{4} - 374 T^{5} + 1573 T^{6} - 2662 T^{7} + 14641 T^{8} \))(\( 1 + 16 T + 105 T^{2} + 340 T^{3} + 390 T^{4} - 1332 T^{5} - 9707 T^{6} - 42730 T^{7} - 156045 T^{8} - 470030 T^{9} - 1174547 T^{10} - 1772892 T^{11} + 5709990 T^{12} + 54757340 T^{13} + 186013905 T^{14} + 311794736 T^{15} + 214358881 T^{16} \))(\( 1 - 4 T - 22 T^{2} + 120 T^{3} + 58 T^{4} - 900 T^{5} + 1437 T^{6} - 4466 T^{7} - 10704 T^{8} + 67762 T^{9} + 285698 T^{10} - 117068 T^{11} - 5557163 T^{12} - 1287748 T^{13} + 34569458 T^{14} + 90191222 T^{15} - 156717264 T^{16} - 719253766 T^{17} + 2545733157 T^{18} - 17538453900 T^{19} + 12432815098 T^{20} + 282953722920 T^{21} - 570623341222 T^{22} - 1141246682444 T^{23} + 3138428376721 T^{24} \))(\( 1 - 14 T^{2} + 255 T^{4} - 3590 T^{6} + 31630 T^{8} - 26672 T^{10} - 1618917 T^{12} + 54477410 T^{14} - 819034805 T^{16} + 6591766610 T^{18} - 23702563797 T^{20} - 47251074992 T^{22} + 6780171406030 T^{24} - 93115354317590 T^{26} + 800299236063855 T^{28} - 5316497670165374 T^{30} + 45949729863572161 T^{32} \))(\( ( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 2 T - 21 T^{2} + 14 T^{3} + 286 T^{4} + 58 T^{5} - 3673 T^{6} + 638 T^{7} + 34606 T^{8} + 18634 T^{9} - 307461 T^{10} - 322102 T^{11} + 1771561 T^{12} )^{2} \))(\( ( 1 - T - 18 T^{2} + 129 T^{3} + 120 T^{4} - 1886 T^{5} + 6087 T^{6} + 14944 T^{7} - 88007 T^{8} + 164384 T^{9} + 736527 T^{10} - 2510266 T^{11} + 1756920 T^{12} + 20775579 T^{13} - 31888098 T^{14} - 19487171 T^{15} + 214358881 T^{16} )^{2} \))(\( ( 1 - 2 T - 7 T^{2} + 36 T^{3} + 5 T^{4} + 396 T^{5} - 847 T^{6} - 2662 T^{7} + 14641 T^{8} )^{2} \))(\( 1 - 6 T + 4 T^{2} + 68 T^{3} - 237 T^{4} + 38 T^{5} + 2400 T^{6} - 9328 T^{7} - 1188 T^{8} + 114992 T^{9} - 345452 T^{10} + 52314 T^{11} + 3321817 T^{12} - 16648114 T^{13} + 30762856 T^{14} + 86386670 T^{15} - 607501509 T^{16} + 950253370 T^{17} + 3722305576 T^{18} - 22158639734 T^{19} + 48634722697 T^{20} + 8425222014 T^{21} - 611989290572 T^{22} + 2240868767632 T^{23} - 254658350628 T^{24} - 21994936061648 T^{25} + 62249819042400 T^{26} + 10841843483218 T^{27} - 743807525282877 T^{28} + 2347544425787308 T^{29} + 1518999334332964 T^{30} - 25063489016493906 T^{31} + 45949729863572161 T^{32} \))(\( ( 1 + 4 T^{2} - 105 T^{4} + 484 T^{6} + 14641 T^{8} )^{4} \))(\( ( 1 + 34 T^{2} + 652 T^{4} - 414 T^{5} + 9016 T^{6} - 9072 T^{7} + 100687 T^{8} - 99792 T^{9} + 1090936 T^{10} - 551034 T^{11} + 9545932 T^{12} + 60233074 T^{14} + 214358881 T^{16} )^{2} \))
$13$ (\( 1 - T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - T^{2} + 169 T^{4} \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 4 T - 19 T^{2} + 60 T^{3} + 370 T^{4} - 536 T^{5} - 4235 T^{6} - 6968 T^{7} + 62530 T^{8} + 131820 T^{9} - 542659 T^{10} - 1485172 T^{11} + 4826809 T^{12} \))(\( 1 + 2 T - 18 T^{2} - 102 T^{3} - 3 T^{4} + 1191 T^{5} + 3365 T^{6} - 5033 T^{7} - 45777 T^{8} - 65429 T^{9} + 568685 T^{10} + 2616627 T^{11} - 85683 T^{12} - 37871886 T^{13} - 86882562 T^{14} + 125497034 T^{15} + 815730721 T^{16} \))(\( ( 1 - 20 T^{2} + 231 T^{4} - 3380 T^{6} + 28561 T^{8} )^{2} \))(\( 1 - 2 T - 18 T^{2} + 102 T^{3} - 3 T^{4} - 1191 T^{5} + 3365 T^{6} + 5033 T^{7} - 45777 T^{8} + 65429 T^{9} + 568685 T^{10} - 2616627 T^{11} - 85683 T^{12} + 37871886 T^{13} - 86882562 T^{14} - 125497034 T^{15} + 815730721 T^{16} \))(\( ( 1 - 4 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 337 T^{4} + 28561 T^{8} )^{2} \))(\( 1 + 2 T + 11 T^{2} + 16 T^{3} + 49 T^{4} + 208 T^{5} + 1859 T^{6} + 4394 T^{7} + 28561 T^{8} \))(\( 1 - 9 T + 23 T^{2} - 15 T^{3} + 16 T^{4} - 195 T^{5} + 3887 T^{6} - 19773 T^{7} + 28561 T^{8} \))(\( 1 + 8 T + 17 T^{2} + 14 T^{3} + 276 T^{4} + 578 T^{5} - 4815 T^{6} - 18048 T^{7} - 25061 T^{8} - 234624 T^{9} - 813735 T^{10} + 1269866 T^{11} + 7882836 T^{12} + 5198102 T^{13} + 82055753 T^{14} + 501988136 T^{15} + 815730721 T^{16} \))(\( 1 + 2 T - 20 T^{2} + 8 T^{3} + 236 T^{4} - 1188 T^{5} - 3563 T^{6} + 9192 T^{7} - 20810 T^{8} - 140028 T^{9} + 822700 T^{10} + 1862120 T^{11} - 6309151 T^{12} + 24207560 T^{13} + 139036300 T^{14} - 307641516 T^{15} - 594354410 T^{16} + 3412925256 T^{17} - 17197920467 T^{18} - 74545238196 T^{19} + 192512450156 T^{20} + 84835994984 T^{21} - 2757169836980 T^{22} + 3584320788074 T^{23} + 23298085122481 T^{24} \))(\( ( 1 - 31 T^{2} - 70 T^{3} + 232 T^{4} + 1950 T^{5} + 6617 T^{6} - 14700 T^{7} - 162685 T^{8} - 191100 T^{9} + 1118273 T^{10} + 4284150 T^{11} + 6626152 T^{12} - 25990510 T^{13} - 149631079 T^{14} + 815730721 T^{16} )^{2} \))(\( ( 1 - T^{2} + 169 T^{4} )( 1 + 23 T^{2} + 169 T^{4} ) \))(\( 1 + 54 T^{2} + 1581 T^{4} + 30418 T^{6} + 431466 T^{8} + 4991934 T^{10} + 59312613 T^{12} + 843636846 T^{14} + 12323100426 T^{16} + 146821876162 T^{18} + 1289670269901 T^{20} + 7444358559846 T^{22} + 23298085122481 T^{24} \))(\( 1 + 40 T^{2} + 726 T^{4} + 8330 T^{6} + 50411 T^{8} - 581655 T^{10} - 20871557 T^{12} - 333628385 T^{14} - 4436735157 T^{16} - 56383197065 T^{18} - 596112539477 T^{20} - 2807537588895 T^{22} + 41121801376331 T^{24} + 1148361237102170 T^{26} + 16914409798921206 T^{28} + 157495055427971560 T^{30} + 665416609183179841 T^{32} \))(\( 1 + 5 T + 30 T^{2} + 60 T^{3} + 346 T^{4} + 655 T^{5} + 6335 T^{6} + 13320 T^{7} + 88856 T^{8} + 173160 T^{9} + 1070615 T^{10} + 1439035 T^{11} + 9882106 T^{12} + 22277580 T^{13} + 144804270 T^{14} + 313742585 T^{15} + 815730721 T^{16} \))(\( 1 + 22 T^{2} + 80 T^{3} + 81 T^{4} + 1760 T^{5} + 1994 T^{6} + 7400 T^{7} + 54580 T^{8} + 208560 T^{9} + 320132 T^{10} + 4629240 T^{11} + 13798055 T^{12} + 28576760 T^{13} + 253427140 T^{14} + 524829280 T^{15} + 2023398311 T^{16} + 6822780640 T^{17} + 42829186660 T^{18} + 62783141720 T^{19} + 394086248855 T^{20} + 1718804407320 T^{21} + 1545216018788 T^{22} + 13086830705520 T^{23} + 44522582752180 T^{24} + 78473295360200 T^{25} + 274889832746906 T^{26} + 3154202293505120 T^{27} + 1887144894920961 T^{28} + 24230008527380240 T^{29} + 86622280485384358 T^{30} + 665416609183179841 T^{32} \))(\( 1 + 116 T^{4} + 8266 T^{8} - 6024112 T^{12} - 1173111437 T^{16} - 172054662832 T^{20} + 6742830139786 T^{24} + 2702577874207796 T^{28} + 665416609183179841 T^{32} \))(\( 1 - 2 T + 2 T^{2} - 56 T^{3} + 144 T^{4} - 658 T^{5} + 2596 T^{6} - 4150 T^{7} + 35702 T^{8} + 23108 T^{9} - 42562 T^{10} - 1025978 T^{11} - 7929096 T^{12} + 10433170 T^{13} - 40700658 T^{14} + 417980868 T^{15} - 885935405 T^{16} + 5433751284 T^{17} - 6878411202 T^{18} + 22921674490 T^{19} - 226462910856 T^{20} - 380938449554 T^{21} - 205438644658 T^{22} + 1449992730836 T^{23} + 29123218201142 T^{24} - 44008672397950 T^{25} + 357880644840004 T^{26} - 1179241539276346 T^{27} + 3354924257637264 T^{28} - 16961005969166168 T^{29} + 7874752771398578 T^{30} - 102371786028181514 T^{31} + 665416609183179841 T^{32} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 14 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 + 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} - 56 T^{3} + 731 T^{4} - 578 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 11 T + 88 T^{2} - 451 T^{3} + 2111 T^{4} - 7667 T^{5} + 25432 T^{6} - 54043 T^{7} + 83521 T^{8} )^{2} \))(\( ( 1 + 40 T^{2} + 786 T^{4} + 11560 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 + 11 T + 88 T^{2} + 451 T^{3} + 2111 T^{4} + 7667 T^{5} + 25432 T^{6} + 54043 T^{7} + 83521 T^{8} )^{2} \))(\( 1 - 254 T^{4} + 83521 T^{8} \))(\( ( 1 + 206 T^{4} + 83521 T^{8} )^{2} \))(\( 1 - 8 T + 17 T^{2} - 60 T^{3} + 461 T^{4} - 1020 T^{5} + 4913 T^{6} - 39304 T^{7} + 83521 T^{8} \))(\( 1 + 8 T + 7 T^{2} - 110 T^{3} - 579 T^{4} - 1870 T^{5} + 2023 T^{6} + 39304 T^{7} + 83521 T^{8} \))(\( 1 - T - 27 T^{2} + 38 T^{3} + 591 T^{4} - 456 T^{5} - 11720 T^{6} + 3109 T^{7} + 167979 T^{8} + 52853 T^{9} - 3387080 T^{10} - 2240328 T^{11} + 49360911 T^{12} + 53954566 T^{13} - 651714363 T^{14} - 410338673 T^{15} + 6975757441 T^{16} \))(\( 1 - T - 22 T^{2} - 27 T^{3} - 141 T^{4} + 1839 T^{5} + 11791 T^{6} + 5192 T^{7} - 114598 T^{8} - 1351839 T^{9} - 1459527 T^{10} + 15628812 T^{11} + 54801289 T^{12} + 265689804 T^{13} - 421803303 T^{14} - 6641585007 T^{15} - 9571339558 T^{16} + 7371897544 T^{17} + 284606076079 T^{18} + 754612819647 T^{19} - 983581799181 T^{20} - 3201872665419 T^{21} - 44351865809878 T^{22} - 34271896307633 T^{23} + 582622237229761 T^{24} \))(\( 1 - 53 T^{2} + 1125 T^{4} - 4010 T^{6} - 312365 T^{8} + 7565836 T^{10} - 61832928 T^{12} - 561210595 T^{14} + 22136734435 T^{16} - 162189861955 T^{18} - 5164347979488 T^{20} + 182620888492684 T^{22} - 2178982473057965 T^{24} - 8084135540800490 T^{26} + 655450016883481125 T^{28} - 8924024807648249237 T^{30} + 48661191875666868481 T^{32} \))(\( ( 1 - 18 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 3087 T^{4} - 67244 T^{6} + 892143 T^{8} - 6848722 T^{10} + 24137569 T^{12} )^{2} \))(\( ( 1 - 55 T^{2} + 2044 T^{4} - 50325 T^{6} + 994815 T^{8} - 14543925 T^{10} + 170716924 T^{12} - 1327566295 T^{14} + 6975757441 T^{16} )^{2} \))(\( 1 - 10 T + 90 T^{2} - 720 T^{3} + 4451 T^{4} - 26310 T^{5} + 136780 T^{6} - 638720 T^{7} + 2802941 T^{8} - 10858240 T^{9} + 39529420 T^{10} - 129261030 T^{11} + 371751971 T^{12} - 1022297040 T^{13} + 2172381210 T^{14} - 4103386730 T^{15} + 6975757441 T^{16} \))(\( 1 + 10 T + 55 T^{2} + 550 T^{3} + 4137 T^{4} + 21370 T^{5} + 140590 T^{6} + 875240 T^{7} + 4267373 T^{8} + 23180400 T^{9} + 125011430 T^{10} + 567252720 T^{11} + 2721539524 T^{12} + 13138878600 T^{13} + 55061701425 T^{14} + 238439860100 T^{15} + 1051104835255 T^{16} + 4053477621700 T^{17} + 15912831711825 T^{18} + 64551310561800 T^{19} + 227305702584004 T^{20} + 805417745261040 T^{21} + 3017472017413670 T^{22} + 9511814575609200 T^{23} + 29768158958272493 T^{24} + 103792853025234280 T^{25} + 283428582464124910 T^{26} + 732390424094117210 T^{27} + 2410308195419521257 T^{28} + 5447517918098265350 T^{29} + 9260780460767051095 T^{30} + 28624230515098157930 T^{31} + 48661191875666868481 T^{32} \))(\( ( 1 + 460 T^{4} + 144678 T^{8} + 38419660 T^{12} + 6975757441 T^{16} )^{2} \))(\( 1 + 964 T^{4} + 237772 T^{8} - 70157828 T^{12} - 47638889354 T^{16} - 5859651952388 T^{20} + 1658639798261452 T^{24} + 561647836689489604 T^{28} + 48661191875666868481 T^{32} \))
$19$ (\( 1 + 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 53 T^{2} - 148 T^{3} + 1007 T^{4} - 1444 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 2 T + 49 T^{2} - 34 T^{3} + 1115 T^{4} - 646 T^{5} + 17689 T^{6} - 13718 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - 2 T + 36 T^{2} - 38 T^{3} + 361 T^{4} )^{4} \))(\( ( 1 - 2 T + 49 T^{2} - 34 T^{3} + 1115 T^{4} - 646 T^{5} + 17689 T^{6} - 13718 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 13 T^{2} + 361 T^{4} )^{4} \))(\( 1 + 4 T - 3 T^{2} + 62 T^{3} + 605 T^{4} + 1178 T^{5} - 1083 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 + 5 T + 21 T^{2} + 145 T^{3} + 956 T^{4} + 2755 T^{5} + 7581 T^{6} + 34295 T^{7} + 130321 T^{8} \))(\( 1 + 5 T - 33 T^{2} - 265 T^{3} - 47 T^{4} + 6980 T^{5} + 26814 T^{6} - 68150 T^{7} - 765695 T^{8} - 1294850 T^{9} + 9679854 T^{10} + 47875820 T^{11} - 6125087 T^{12} - 656166235 T^{13} - 1552514073 T^{14} + 4469358695 T^{15} + 16983563041 T^{16} \))(\( 1 - 7 T + 16 T^{2} - 122 T^{3} + 1071 T^{4} - 728 T^{5} - 5797 T^{6} - 36918 T^{7} + 65678 T^{8} + 636002 T^{9} + 4923209 T^{10} - 25899375 T^{11} + 44345259 T^{12} - 492088125 T^{13} + 1777278449 T^{14} + 4362337718 T^{15} + 8559222638 T^{16} - 91412622882 T^{17} - 272724972157 T^{18} - 650738625992 T^{19} + 18189396016911 T^{20} - 39367899129038 T^{21} + 98097060124816 T^{22} - 815431812287533 T^{23} + 2213314919066161 T^{24} \))(\( ( 1 - 7 T + 15 T^{2} - 45 T^{3} + 495 T^{4} - 1926 T^{5} + 4452 T^{6} - 54240 T^{7} + 359505 T^{8} - 1030560 T^{9} + 1607172 T^{10} - 13210434 T^{11} + 64508895 T^{12} - 111424455 T^{13} + 705688215 T^{14} - 6257102173 T^{15} + 16983563041 T^{16} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{4} \))(\( ( 1 + 4 T + 53 T^{2} + 148 T^{3} + 1007 T^{4} + 1444 T^{5} + 6859 T^{6} )^{4} \))(\( ( 1 + 2 T + 49 T^{2} + 34 T^{3} + 1115 T^{4} + 646 T^{5} + 17689 T^{6} + 13718 T^{7} + 130321 T^{8} )^{4} \))(\( 1 + 5 T - 8 T^{2} + 40 T^{3} + 878 T^{4} + 1705 T^{5} - 1861 T^{6} + 31550 T^{7} + 293380 T^{8} + 599450 T^{9} - 671821 T^{10} + 11694595 T^{11} + 114421838 T^{12} + 99043960 T^{13} - 376367048 T^{14} + 4469358695 T^{15} + 16983563041 T^{16} \))(\( 1 + 2 T - 53 T^{2} - 216 T^{3} + 1273 T^{4} + 10232 T^{5} - 10629 T^{6} - 233030 T^{7} - 154021 T^{8} + 2536598 T^{9} + 3525662 T^{10} + 321666 T^{11} + 122263380 T^{12} - 353312856 T^{13} - 6187122082 T^{14} + 3769508888 T^{15} + 148112464363 T^{16} + 71620668872 T^{17} - 2233551071602 T^{18} - 2423372879304 T^{19} + 15933485944980 T^{20} + 796476860934 T^{21} + 165867874898222 T^{22} + 2267393265403922 T^{23} - 2615825363137861 T^{24} - 75195914213440370 T^{25} - 65167103254166829 T^{26} + 1191928329046576808 T^{27} + 2817549891971222953 T^{28} - 9083444427847524744 T^{29} - 42347354346492858413 T^{30} + 30362254059749596598 T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 56 T^{2} + 1410 T^{4} - 20216 T^{6} + 130321 T^{8} )^{4} \))(\( ( 1 - 92 T^{2} + 4132 T^{4} - 123032 T^{6} + 2693650 T^{8} - 44414552 T^{10} + 538486372 T^{12} - 4328221052 T^{14} + 16983563041 T^{16} )^{2} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 34 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 - 3 T - 27 T^{2} - 66 T^{3} + 405 T^{4} + 2625 T^{5} - 9794 T^{6} + 60375 T^{7} + 214245 T^{8} - 803022 T^{9} - 7555707 T^{10} - 19309029 T^{11} + 148035889 T^{12} \))(\( 1 + 15 T + 76 T^{2} + 183 T^{3} + 1258 T^{4} + 9882 T^{5} + 28951 T^{6} + 29994 T^{7} + 75241 T^{8} + 689862 T^{9} + 15315079 T^{10} + 120234294 T^{11} + 352039978 T^{12} + 1177850769 T^{13} + 11250727564 T^{14} + 51072381705 T^{15} + 78310985281 T^{16} \))(\( 1 - 88 T^{2} + 4753 T^{4} - 170104 T^{6} + 4569664 T^{8} - 89985016 T^{10} + 1330084273 T^{12} - 13027158232 T^{14} + 78310985281 T^{16} \))(\( 1 - 15 T + 76 T^{2} - 183 T^{3} + 1258 T^{4} - 9882 T^{5} + 28951 T^{6} - 29994 T^{7} + 75241 T^{8} - 689862 T^{9} + 15315079 T^{10} - 120234294 T^{11} + 352039978 T^{12} - 1177850769 T^{13} + 11250727564 T^{14} - 51072381705 T^{15} + 78310985281 T^{16} \))(\( 1 - 158 T^{4} + 279841 T^{8} \))(\( ( 1 + 542 T^{4} + 279841 T^{8} )^{2} \))(\( 1 + 10 T + 37 T^{2} + 200 T^{3} + 1389 T^{4} + 4600 T^{5} + 19573 T^{6} + 121670 T^{7} + 279841 T^{8} \))(\( 1 - 11 T + 28 T^{2} + 245 T^{3} - 2259 T^{4} + 5635 T^{5} + 14812 T^{6} - 133837 T^{7} + 279841 T^{8} \))(\( 1 + 7 T + 12 T^{2} + 31 T^{3} + 1026 T^{4} + 672 T^{5} - 34550 T^{6} - 127672 T^{7} - 3411 T^{8} - 2936456 T^{9} - 18276950 T^{10} + 8176224 T^{11} + 287116866 T^{12} + 199526633 T^{13} + 1776430668 T^{14} + 23833778129 T^{15} + 78310985281 T^{16} \))(\( 1 + 19 T + 87 T^{2} - 664 T^{3} - 8155 T^{4} - 10802 T^{5} + 276289 T^{6} + 1712486 T^{7} - 1232028 T^{8} - 57899808 T^{9} - 214047367 T^{10} + 649484443 T^{11} + 7850412157 T^{12} + 14938142189 T^{13} - 113231057143 T^{14} - 704466963936 T^{15} - 344771947548 T^{16} + 11022147278698 T^{17} + 40900687735921 T^{18} - 36778924478494 T^{19} - 638626084966555 T^{20} - 1195965367211432 T^{21} + 3604106475587463 T^{22} + 18103385400364613 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 17 T^{2} + 180 T^{4} + 12295 T^{6} - 136670 T^{8} - 4324196 T^{10} + 92201472 T^{12} + 1128216050 T^{14} - 139454538005 T^{16} + 596826290450 T^{18} + 25801752125952 T^{20} - 640136199070244 T^{22} - 10702762358354270 T^{24} + 509338955371814455 T^{26} + 3944632397763657780 T^{28} - \)\(19\!\cdots\!53\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 37 T^{2} + 840 T^{4} + 19573 T^{6} + 279841 T^{8} \))(\( 1 + 63 T^{2} + 1143 T^{4} + 30064 T^{6} + 1830141 T^{8} + 38353041 T^{10} + 434719014 T^{12} + 20288758689 T^{14} + 512148487581 T^{16} + 4450550966896 T^{18} + 89509456176183 T^{20} + 2609870206459887 T^{22} + 21914624432020321 T^{24} \))(\( 1 + 73 T^{2} + 2802 T^{4} + 80831 T^{6} + 1616966 T^{8} + 14420082 T^{10} - 392881007 T^{12} - 25025527652 T^{14} - 736058803599 T^{16} - 13238504127908 T^{18} - 109944213879887 T^{20} + 2134689658322898 T^{22} + 126626200625877446 T^{24} + 3348546327910462319 T^{26} + 61404777658520939442 T^{28} + \)\(84\!\cdots\!57\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 5 T + 45 T^{2} - 100 T^{3} - 104 T^{4} - 7645 T^{5} + 18890 T^{6} - 8420 T^{7} + 1238691 T^{8} - 193660 T^{9} + 9992810 T^{10} - 93016715 T^{11} - 29103464 T^{12} - 643634300 T^{13} + 6661615005 T^{14} + 17024127235 T^{15} + 78310985281 T^{16} \))(\( 1 - 20 T + 181 T^{2} - 1150 T^{3} + 7948 T^{4} - 59890 T^{5} + 379519 T^{6} - 2059710 T^{7} + 11607418 T^{8} - 70214570 T^{9} + 395238326 T^{10} - 1984546720 T^{11} + 9942722840 T^{12} - 53914737500 T^{13} + 283746609760 T^{14} - 1328416871210 T^{15} + 6099237415331 T^{16} - 30553588037830 T^{17} + 150101956563040 T^{18} - 655980611162500 T^{19} + 2782381502268440 T^{20} - 12773223389444960 T^{21} + 58509456956281814 T^{22} - 239068354686162790 T^{23} + 908988340148414458 T^{24} - 3709852148341955730 T^{25} + 15722148109292854831 T^{26} - 57063776401465088030 T^{27} + \)\(17\!\cdots\!08\)\( T^{28} - \)\(57\!\cdots\!50\)\( T^{29} + \)\(20\!\cdots\!29\)\( T^{30} - \)\(53\!\cdots\!40\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 58 T^{4} + 491185 T^{8} + 60755174 T^{12} + 158716957636 T^{16} + 17001788647334 T^{20} + 38465181305247985 T^{24} - 1271048217057178618 T^{28} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 18 T + 162 T^{2} + 972 T^{3} + 4138 T^{4} + 11184 T^{5} + 3348 T^{6} - 119100 T^{7} - 338219 T^{8} + 2163498 T^{9} + 26656146 T^{10} + 182453766 T^{11} + 892508410 T^{12} + 1883089950 T^{13} - 11227491072 T^{14} - 141260851668 T^{15} - 837597200144 T^{16} - 3248999588364 T^{17} - 5939342777088 T^{18} + 22911555421650 T^{19} + 249760445962810 T^{20} + 1174335019617738 T^{21} + 3946066270423794 T^{22} + 7366333044933606 T^{23} - 26486263130754539 T^{24} - 214517281980243300 T^{25} + 138695959543296852 T^{26} + 10656224332509359568 T^{27} + 90682715899700088298 T^{28} + \)\(48\!\cdots\!76\)\( T^{29} + \)\(18\!\cdots\!58\)\( T^{30} + \)\(47\!\cdots\!26\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))
$29$ (\( 1 + 10 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 - 7 T - 9 T^{2} + 304 T^{3} - 803 T^{4} - 2929 T^{5} + 36038 T^{6} - 84941 T^{7} - 675323 T^{8} + 7414256 T^{9} - 6365529 T^{10} - 143578043 T^{11} + 594823321 T^{12} \))(\( 1 + T - 75 T^{2} + 186 T^{3} + 3234 T^{4} - 10969 T^{5} - 64920 T^{6} + 187910 T^{7} + 1140565 T^{8} + 5449390 T^{9} - 54597720 T^{10} - 267522941 T^{11} + 2287346754 T^{12} + 3815073714 T^{13} - 44611749075 T^{14} + 17249876309 T^{15} + 500246412961 T^{16} \))(\( ( 1 + 6 T - 19 T^{2} - 18 T^{3} + 1140 T^{4} - 522 T^{5} - 15979 T^{6} + 146334 T^{7} + 707281 T^{8} )^{2} \))(\( 1 + T - 75 T^{2} + 186 T^{3} + 3234 T^{4} - 10969 T^{5} - 64920 T^{6} + 187910 T^{7} + 1140565 T^{8} + 5449390 T^{9} - 54597720 T^{10} - 267522941 T^{11} + 2287346754 T^{12} + 3815073714 T^{13} - 44611749075 T^{14} + 17249876309 T^{15} + 500246412961 T^{16} \))(\( ( 1 + 40 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 40 T^{2} + 841 T^{4} )^{4} \))(\( 1 - 8 T + 5 T^{2} + 232 T^{3} - 1711 T^{4} + 6728 T^{5} + 4205 T^{6} - 195112 T^{7} + 707281 T^{8} \))(\( 1 + 5 T - 19 T^{2} - 145 T^{3} - 4 T^{4} - 4205 T^{5} - 15979 T^{6} + 121945 T^{7} + 707281 T^{8} \))(\( 1 + 5 T + 12 T^{2} - 110 T^{3} - 322 T^{4} - 4795 T^{5} - 5456 T^{6} - 22500 T^{7} + 487955 T^{8} - 652500 T^{9} - 4588496 T^{10} - 116945255 T^{11} - 227744482 T^{12} - 2256226390 T^{13} + 7137879852 T^{14} + 86249381545 T^{15} + 500246412961 T^{16} \))(\( 1 - T - 75 T^{2} + 3 T^{3} + 2691 T^{4} - 6800 T^{5} - 35703 T^{6} + 577442 T^{7} - 700036 T^{8} - 20501600 T^{9} + 54541649 T^{10} + 290598314 T^{11} - 2133422469 T^{12} + 8427351106 T^{13} + 45869526809 T^{14} - 500013522400 T^{15} - 495122162116 T^{16} + 11843998900858 T^{17} - 21236977029663 T^{18} - 117299158901200 T^{19} + 1346163097278051 T^{20} + 43521437927607 T^{21} - 31553042497515075 T^{22} - 12200509765705829 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 39 T^{2} + 1290 T^{4} + 19350 T^{6} - 930210 T^{8} - 20945943 T^{10} - 6111982 T^{12} + 30999707520 T^{14} + 1820594900175 T^{16} + 26070754024320 T^{18} - 4322888740942 T^{20} - 12459135376736703 T^{22} - 465334215800451810 T^{24} + 8140684964358889350 T^{26} + \)\(45\!\cdots\!90\)\( T^{28} + \)\(11\!\cdots\!59\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( ( 1 + T - 28 T^{2} + 29 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 7 T - 9 T^{2} - 304 T^{3} - 803 T^{4} + 2929 T^{5} + 36038 T^{6} + 84941 T^{7} - 675323 T^{8} - 7414256 T^{9} - 6365529 T^{10} + 143578043 T^{11} + 594823321 T^{12} )^{2} \))(\( ( 1 - T - 75 T^{2} - 186 T^{3} + 3234 T^{4} + 10969 T^{5} - 64920 T^{6} - 187910 T^{7} + 1140565 T^{8} - 5449390 T^{9} - 54597720 T^{10} + 267522941 T^{11} + 2287346754 T^{12} - 3815073714 T^{13} - 44611749075 T^{14} - 17249876309 T^{15} + 500246412961 T^{16} )^{2} \))(\( 1 - 5 T - 28 T^{2} - 140 T^{3} + 1268 T^{4} + 5045 T^{5} + 48219 T^{6} - 207000 T^{7} - 1738520 T^{8} - 6003000 T^{9} + 40552179 T^{10} + 123042505 T^{11} + 896832308 T^{12} - 2871560860 T^{13} - 16655052988 T^{14} - 86249381545 T^{15} + 500246412961 T^{16} \))(\( 1 + 16 T + 101 T^{2} + 378 T^{3} + 2782 T^{4} + 28638 T^{5} + 156384 T^{6} + 372476 T^{7} + 1621718 T^{8} + 24643166 T^{9} + 158941381 T^{10} + 390275636 T^{11} + 1282706252 T^{12} + 24547929228 T^{13} + 196193283170 T^{14} + 670123125368 T^{15} + 1692236078907 T^{16} + 19433570635672 T^{17} + 164998551145970 T^{18} + 598699445941692 T^{19} + 907233760620812 T^{20} + 8005001721065764 T^{21} + 94542040090746301 T^{22} + 425091565362154294 T^{23} + 811258612334286998 T^{24} + 5403563704507781644 T^{25} + 65791879972418633184 T^{26} + \)\(34\!\cdots\!02\)\( T^{27} + \)\(98\!\cdots\!62\)\( T^{28} + \)\(38\!\cdots\!42\)\( T^{29} + \)\(30\!\cdots\!81\)\( T^{30} + \)\(13\!\cdots\!84\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 31 T^{2} + 120 T^{4} - 26071 T^{6} + 707281 T^{8} )^{4} \))(\( 1 - 148 T^{2} + 10806 T^{4} - 562376 T^{6} + 24743345 T^{8} - 973959144 T^{10} + 34914297094 T^{12} - 1155748123996 T^{14} + 35134519733316 T^{16} - 971984172280636 T^{18} + 24694218962941414 T^{20} - 579333612552397224 T^{22} + 12377769580906494545 T^{24} - \)\(23\!\cdots\!76\)\( T^{26} + \)\(38\!\cdots\!46\)\( T^{28} - \)\(44\!\cdots\!88\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 + 3 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 3 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 7 T + 31 T^{2} )^{2} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 31 T^{2} + 208 T^{3} - 158 T^{4} - 7756 T^{5} - 34897 T^{6} - 240436 T^{7} - 151838 T^{8} + 6196528 T^{9} + 28629151 T^{10} + 229033208 T^{11} + 887503681 T^{12} \))(\( 1 - 4 T - 66 T^{2} + 362 T^{3} + 1939 T^{4} - 11745 T^{5} - 45361 T^{6} + 144883 T^{7} + 1472277 T^{8} + 4491373 T^{9} - 43591921 T^{10} - 349895295 T^{11} + 1790707219 T^{12} + 10363752662 T^{13} - 58575242946 T^{14} - 110050456444 T^{15} + 852891037441 T^{16} \))(\( ( 1 - 2 T - 56 T^{2} + 4 T^{3} + 2515 T^{4} + 124 T^{5} - 53816 T^{6} - 59582 T^{7} + 923521 T^{8} )^{2} \))(\( 1 - 4 T - 66 T^{2} + 362 T^{3} + 1939 T^{4} - 11745 T^{5} - 45361 T^{6} + 144883 T^{7} + 1472277 T^{8} + 4491373 T^{9} - 43591921 T^{10} - 349895295 T^{11} + 1790707219 T^{12} + 10363752662 T^{13} - 58575242946 T^{14} - 110050456444 T^{15} + 852891037441 T^{16} \))(\( ( 1 + 4 T + 31 T^{2} )^{4} \))(\( ( 1 - T + 31 T^{2} )^{8} \))(\( 1 + 9 T^{2} - 110 T^{3} + 741 T^{4} - 3410 T^{5} + 8649 T^{6} + 923521 T^{8} \))(\( 1 - 3 T - 22 T^{2} + 159 T^{3} + 205 T^{4} + 4929 T^{5} - 21142 T^{6} - 89373 T^{7} + 923521 T^{8} \))(\( 1 + 19 T + 110 T^{2} - 455 T^{3} - 10080 T^{4} - 55148 T^{5} - 24492 T^{6} + 1584870 T^{7} + 12593785 T^{8} + 49130970 T^{9} - 23536812 T^{10} - 1642914068 T^{11} - 9309091680 T^{12} - 13026263705 T^{13} + 97625404910 T^{14} + 522739668109 T^{15} + 852891037441 T^{16} \))(\( 1 - 13 T - 49 T^{2} + 1410 T^{3} - 4283 T^{4} - 42518 T^{5} + 442503 T^{6} - 1354402 T^{7} - 10366302 T^{8} + 126161252 T^{9} - 343254057 T^{10} - 2277200953 T^{11} + 23831716157 T^{12} - 70593229543 T^{13} - 329867148777 T^{14} + 3758469858332 T^{15} - 9573497589342 T^{16} - 38775379372702 T^{17} + 392723041353543 T^{18} - 1169781326771498 T^{19} - 3652932313359803 T^{20} + 37279867246546110 T^{21} - 40161786062059249 T^{22} - 330310199653262803 T^{23} + 787662783788549761 T^{24} \))(\( ( 1 - 9 T + 20 T^{2} + 35 T^{3} + 430 T^{4} - 19992 T^{5} + 129878 T^{6} - 181500 T^{7} - 383755 T^{8} - 5626500 T^{9} + 124812758 T^{10} - 595581672 T^{11} + 397114030 T^{12} + 1002020285 T^{13} + 17750073620 T^{14} - 247613526999 T^{15} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 31 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} + 208 T^{3} - 158 T^{4} - 7756 T^{5} - 34897 T^{6} - 240436 T^{7} - 151838 T^{8} + 6196528 T^{9} + 28629151 T^{10} + 229033208 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 - 4 T - 66 T^{2} + 362 T^{3} + 1939 T^{4} - 11745 T^{5} - 45361 T^{6} + 144883 T^{7} + 1472277 T^{8} + 4491373 T^{9} - 43591921 T^{10} - 349895295 T^{11} + 1790707219 T^{12} + 10363752662 T^{13} - 58575242946 T^{14} - 110050456444 T^{15} + 852891037441 T^{16} )^{2} \))(\( 1 + 9 T + 55 T^{2} + 390 T^{3} + 2980 T^{4} + 20297 T^{5} + 114748 T^{6} + 589990 T^{7} + 3582095 T^{8} + 18289690 T^{9} + 110272828 T^{10} + 604667927 T^{11} + 2752092580 T^{12} + 11165368890 T^{13} + 48812702455 T^{14} + 247613526999 T^{15} + 852891037441 T^{16} \))(\( 1 - 6 T - 27 T^{2} + 222 T^{3} + 1398 T^{4} - 1096 T^{5} - 82911 T^{6} + 83080 T^{7} + 2495194 T^{8} + 3301786 T^{9} - 44430232 T^{10} - 311988762 T^{11} + 1830869280 T^{12} + 7523309618 T^{13} - 27963150078 T^{14} + 31095224934 T^{15} - 66108612217 T^{16} + 963951972954 T^{17} - 26872587224958 T^{18} + 224126916829838 T^{19} + 1690846228334880 T^{20} - 8931973377601062 T^{21} - 39431994447683992 T^{22} + 90840764095102246 T^{23} + 2128128599276558554 T^{24} + 2196603809108546680 T^{25} - 67956200901865191711 T^{26} - 27847690678459694776 T^{27} + \)\(11\!\cdots\!78\)\( T^{28} + \)\(54\!\cdots\!02\)\( T^{29} - \)\(20\!\cdots\!67\)\( T^{30} - \)\(14\!\cdots\!06\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 4 T - 44 T^{2} + 8 T^{3} + 2143 T^{4} + 248 T^{5} - 42284 T^{6} - 119164 T^{7} + 923521 T^{8} )^{4} \))(\( ( 1 + 2 T - 78 T^{2} + 76 T^{3} + 3500 T^{4} - 7572 T^{5} - 100340 T^{6} + 131474 T^{7} + 2627523 T^{8} + 4075694 T^{9} - 96426740 T^{10} - 225577452 T^{11} + 3232323500 T^{12} + 2175815476 T^{13} - 69225287118 T^{14} + 55025228222 T^{15} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( ( 1 + 37 T^{2} )^{2} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 99 T^{2} + 440 T^{3} + 3663 T^{4} + 8214 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + T + 49 T^{2} - 392 T^{3} + 241 T^{4} - 14504 T^{5} + 67081 T^{6} + 50653 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 56 T^{2} + 1369 T^{4} )^{4} \))(\( ( 1 - T + 49 T^{2} + 392 T^{3} + 241 T^{4} + 14504 T^{5} + 67081 T^{6} - 50653 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 2 T + 2 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 1106 T^{4} + 1874161 T^{8} )^{2} \))(\( 1 + 15 T + 63 T^{2} + 65 T^{3} + 144 T^{4} + 2405 T^{5} + 86247 T^{6} + 759795 T^{7} + 1874161 T^{8} \))(\( 1 + 7 T - 18 T^{2} - 145 T^{3} + 371 T^{4} - 5365 T^{5} - 24642 T^{6} + 354571 T^{7} + 1874161 T^{8} \))(\( 1 + T + 3 T^{2} + 42 T^{3} + 2811 T^{4} + 3486 T^{5} - 59280 T^{6} + 126501 T^{7} + 3465939 T^{8} + 4680537 T^{9} - 81154320 T^{10} + 176576358 T^{11} + 5268266571 T^{12} + 2912446194 T^{13} + 7697179227 T^{14} + 94931877133 T^{15} + 3512479453921 T^{16} \))(\( 1 - 8 T - 67 T^{2} + 1147 T^{3} - 3085 T^{4} - 39031 T^{5} + 455721 T^{6} - 1535453 T^{7} - 11486553 T^{8} + 153908236 T^{9} - 464906763 T^{10} - 3103077939 T^{11} + 36758415492 T^{12} - 114813883743 T^{13} - 636457358547 T^{14} + 7795913878108 T^{15} - 21527649657033 T^{16} - 106474386807521 T^{17} + 1169255404835889 T^{18} - 3705286096378123 T^{19} - 10835999115346285 T^{20} + 149066115544953319 T^{21} - 322175152951995883 T^{22} - 1423340974235683304 T^{23} + 6582952005840035281 T^{24} \))(\( ( 1 - 5 T + 81 T^{2} - 230 T^{3} + 5257 T^{4} - 7670 T^{5} + 184608 T^{6} - 6325 T^{7} + 7711315 T^{8} - 234025 T^{9} + 252728352 T^{10} - 388508510 T^{11} + 9852464377 T^{12} - 15949110110 T^{13} + 207823839129 T^{14} - 474659385665 T^{15} + 3512479453921 T^{16} )^{2} \))(\( ( 1 - 58 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 162 T^{2} + 11847 T^{4} - 534412 T^{6} + 16218543 T^{8} - 303614082 T^{10} + 2565726409 T^{12} )^{2} \))(\( ( 1 - 97 T^{2} + 3667 T^{4} - 33124 T^{6} - 1092101 T^{8} - 45346756 T^{10} + 6872548387 T^{12} - 248875461673 T^{14} + 3512479453921 T^{16} )^{2} \))(\( 1 - 30 T + 480 T^{2} - 5675 T^{3} + 56171 T^{4} - 489630 T^{5} + 3826535 T^{6} - 26904445 T^{7} + 171416106 T^{8} - 995464465 T^{9} + 5238526415 T^{10} - 24801228390 T^{11} + 105273497531 T^{12} - 393526955975 T^{13} + 1231548676320 T^{14} - 2847956313990 T^{15} + 3512479453921 T^{16} \))(\( 1 + 10 T + 159 T^{2} + 1490 T^{3} + 15403 T^{4} + 128130 T^{5} + 1158066 T^{6} + 8990890 T^{7} + 72816793 T^{8} + 529727610 T^{9} + 3982453044 T^{10} + 27036193580 T^{11} + 190987118220 T^{12} + 1239202673080 T^{13} + 8238752278565 T^{14} + 50853391327250 T^{15} + 322012573505931 T^{16} + 1881575479108250 T^{17} + 11278851869355485 T^{18} + 62769332999521240 T^{19} + 357940608470313420 T^{20} + 1874796645055196060 T^{21} + 10217884947593238996 T^{22} + 50288036386477742130 T^{23} + \)\(25\!\cdots\!53\)\( T^{24} + \)\(11\!\cdots\!30\)\( T^{25} + \)\(55\!\cdots\!34\)\( T^{26} + \)\(22\!\cdots\!90\)\( T^{27} + \)\(10\!\cdots\!43\)\( T^{28} + \)\(36\!\cdots\!30\)\( T^{29} + \)\(14\!\cdots\!51\)\( T^{30} + \)\(33\!\cdots\!30\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 4244 T^{4} + 7905606 T^{8} - 7953939284 T^{12} + 3512479453921 T^{16} )^{2} \))(\( ( 1 + 2 T + 2 T^{2} - 50 T^{3} + 680 T^{4} + 6430 T^{5} + 12750 T^{6} + 67506 T^{7} - 1916078 T^{8} + 2497722 T^{9} + 17454750 T^{10} + 325698790 T^{11} + 1274429480 T^{12} - 3467197850 T^{13} + 5131452818 T^{14} + 189863754266 T^{15} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 - 8 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( 1 + 5 T - 16 T^{2} + 205 T^{3} + 1681 T^{4} \))(\( 1 - 13 T + 27 T^{2} + 292 T^{3} + 445 T^{4} - 22279 T^{5} + 169790 T^{6} - 913439 T^{7} + 748045 T^{8} + 20124932 T^{9} + 76295547 T^{10} - 1506130613 T^{11} + 4750104241 T^{12} \))(\( 1 - 5 T - 114 T^{2} + 213 T^{3} + 9222 T^{4} - 3430 T^{5} - 507867 T^{6} + 107426 T^{7} + 20984173 T^{8} + 4404466 T^{9} - 853724427 T^{10} - 236399030 T^{11} + 26059167942 T^{12} + 24677370813 T^{13} - 541511883474 T^{14} - 973771369405 T^{15} + 7984925229121 T^{16} \))(\( ( 1 + 12 T + 29 T^{2} + 396 T^{3} + 5640 T^{4} + 16236 T^{5} + 48749 T^{6} + 827052 T^{7} + 2825761 T^{8} )^{2} \))(\( 1 - 5 T - 114 T^{2} + 213 T^{3} + 9222 T^{4} - 3430 T^{5} - 507867 T^{6} + 107426 T^{7} + 20984173 T^{8} + 4404466 T^{9} - 853724427 T^{10} - 236399030 T^{11} + 26059167942 T^{12} + 24677370813 T^{13} - 541511883474 T^{14} - 973771369405 T^{15} + 7984925229121 T^{16} \))(\( ( 1 - 80 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 1681 T^{4} )^{4} \))(\( 1 - 31 T^{2} - 180 T^{3} + 1501 T^{4} - 7380 T^{5} - 52111 T^{6} + 2825761 T^{8} \))(\( 1 + 8 T - 17 T^{2} - 254 T^{3} - 435 T^{4} - 10414 T^{5} - 28577 T^{6} + 551368 T^{7} + 2825761 T^{8} \))(\( ( 1 - 7 T + 28 T^{2} - 389 T^{3} + 3975 T^{4} - 15949 T^{5} + 47068 T^{6} - 482447 T^{7} + 2825761 T^{8} )^{2} \))(\( 1 + 8 T + 56 T^{2} + 840 T^{3} + 5172 T^{4} + 38968 T^{5} + 387993 T^{6} + 1909992 T^{7} + 12984488 T^{8} + 115425908 T^{9} + 544467188 T^{10} + 3312068648 T^{11} + 28013676237 T^{12} + 135794814568 T^{13} + 915249343028 T^{14} + 7955269005268 T^{15} + 36691059795368 T^{16} + 221284417060392 T^{17} + 1843007194778313 T^{18} + 7589184544594808 T^{19} + 41298033285013812 T^{20} + 275000824890927240 T^{21} + 751668921368534456 T^{22} + 4402632253729987528 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 104 T^{2} + 1575 T^{4} + 194440 T^{6} - 5957900 T^{8} - 330995792 T^{10} + 19929404133 T^{12} + 140417241800 T^{14} - 34203961093745 T^{16} + 236041383465800 T^{18} + 56315732952270213 T^{20} - 1572264515332353872 T^{22} - 47573386022580005900 T^{24} + \)\(26\!\cdots\!40\)\( T^{26} + \)\(35\!\cdots\!75\)\( T^{28} - \)\(39\!\cdots\!44\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 5 T - 16 T^{2} + 205 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 13 T + 27 T^{2} + 292 T^{3} + 445 T^{4} - 22279 T^{5} + 169790 T^{6} - 913439 T^{7} + 748045 T^{8} + 20124932 T^{9} + 76295547 T^{10} - 1506130613 T^{11} + 4750104241 T^{12} )^{2} \))(\( ( 1 - 5 T - 114 T^{2} + 213 T^{3} + 9222 T^{4} - 3430 T^{5} - 507867 T^{6} + 107426 T^{7} + 20984173 T^{8} + 4404466 T^{9} - 853724427 T^{10} - 236399030 T^{11} + 26059167942 T^{12} + 24677370813 T^{13} - 541511883474 T^{14} - 973771369405 T^{15} + 7984925229121 T^{16} )^{2} \))(\( 1 - 4 T - 30 T^{2} + 240 T^{3} + 195 T^{4} - 18372 T^{5} + 77388 T^{6} + 230240 T^{7} - 1438395 T^{8} + 9439840 T^{9} + 130089228 T^{10} - 1266216612 T^{11} + 551023395 T^{12} + 27805488240 T^{13} - 142503127230 T^{14} - 779017095524 T^{15} + 7984925229121 T^{16} \))(\( 1 - 14 T - 82 T^{2} + 2028 T^{3} - 747 T^{4} - 120014 T^{5} + 311054 T^{6} + 3602970 T^{7} - 14348876 T^{8} - 63645696 T^{9} + 522280968 T^{10} + 1039813212 T^{11} - 35365817705 T^{12} - 21504097848 T^{13} + 2388690604652 T^{14} + 220861336106 T^{15} - 115364883721937 T^{16} + 9055314780346 T^{17} + 4015388906420012 T^{18} - 1482083927782008 T^{19} - 99935348403898505 T^{20} + 120468808491927612 T^{21} + 2480889041090385288 T^{22} - 12395271310130866176 T^{23} - \)\(11\!\cdots\!96\)\( T^{24} + \)\(11\!\cdots\!70\)\( T^{25} + \)\(41\!\cdots\!54\)\( T^{26} - \)\(66\!\cdots\!74\)\( T^{27} - \)\(16\!\cdots\!07\)\( T^{28} + \)\(18\!\cdots\!88\)\( T^{29} - \)\(31\!\cdots\!02\)\( T^{30} - \)\(21\!\cdots\!14\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 18 T + 199 T^{2} + 1638 T^{3} + 11028 T^{4} + 67158 T^{5} + 334519 T^{6} + 1240578 T^{7} + 2825761 T^{8} )^{4} \))(\( ( 1 + 12 T + 190 T^{2} + 1704 T^{3} + 16861 T^{4} + 130290 T^{5} + 1067482 T^{6} + 7225794 T^{7} + 51027208 T^{8} + 296257554 T^{9} + 1794437242 T^{10} + 8979717090 T^{11} + 47645156221 T^{12} + 197418966504 T^{13} + 902519805790 T^{14} + 2337051286572 T^{15} + 7984925229121 T^{16} )^{2} \))
$43$ (\( 1 - T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( ( 1 + 43 T^{2} )^{2} \))(\( 1 - 85 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 61 T^{2} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 10 T - 25 T^{2} + 462 T^{3} + 1690 T^{4} - 17990 T^{5} + 34975 T^{6} - 773570 T^{7} + 3124810 T^{8} + 36732234 T^{9} - 85470025 T^{10} - 1470084430 T^{11} + 6321363049 T^{12} \))(\( 1 - 10 T - 24 T^{2} + 168 T^{3} + 2043 T^{4} + 8292 T^{5} - 128884 T^{6} - 10646 T^{7} + 2342736 T^{8} - 457778 T^{9} - 238306516 T^{10} + 659272044 T^{11} + 6984610443 T^{12} + 24697418424 T^{13} - 151712713176 T^{14} - 2718186111070 T^{15} + 11688200277601 T^{16} \))(\( 1 - 88 T^{2} + 3838 T^{4} - 18304 T^{6} - 2480621 T^{8} - 33844096 T^{10} + 13121358238 T^{12} - 556279948312 T^{14} + 11688200277601 T^{16} \))(\( 1 + 10 T - 24 T^{2} - 168 T^{3} + 2043 T^{4} - 8292 T^{5} - 128884 T^{6} + 10646 T^{7} + 2342736 T^{8} + 457778 T^{9} - 238306516 T^{10} - 659272044 T^{11} + 6984610443 T^{12} - 24697418424 T^{13} - 151712713176 T^{14} + 2718186111070 T^{15} + 11688200277601 T^{16} \))(\( ( 1 - 16 T + 128 T^{2} - 688 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 3191 T^{4} + 3418801 T^{8} )^{2} \))(\( ( 1 - 2 T + 42 T^{2} - 86 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 3 T + 77 T^{2} + 129 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 16 T + 233 T^{2} - 2040 T^{3} + 16241 T^{4} - 87720 T^{5} + 430817 T^{6} - 1272112 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 2 T + 167 T^{2} + 256 T^{3} + 13452 T^{4} + 15956 T^{5} + 692036 T^{6} + 686108 T^{7} + 24872748 T^{8} + 20353792 T^{9} + 570939767 T^{10} + 294016886 T^{11} + 6321363049 T^{12} )^{2} \))(\( ( 1 + 20 T + 287 T^{2} + 2730 T^{3} + 20939 T^{4} + 117390 T^{5} + 530663 T^{6} + 1590140 T^{7} + 3418801 T^{8} )^{4} \))(\( ( 1 - 61 T^{2} + 1849 T^{4} )( 1 + 83 T^{2} + 1849 T^{4} ) \))(\( 1 + 150 T^{2} + 13245 T^{4} + 587794 T^{6} + 8508330 T^{8} - 916818210 T^{10} - 62473985643 T^{12} - 1695196870290 T^{14} + 29088287112330 T^{16} + 3715659272023906 T^{18} + 154810212676825245 T^{20} + 3241722346992637350 T^{22} + 39959630797262576401 T^{24} \))(\( 1 + 148 T^{2} + 8022 T^{4} + 218216 T^{6} + 12046721 T^{8} + 1190020152 T^{10} + 65107245958 T^{12} + 1936378110508 T^{14} + 52508765640996 T^{16} + 3580363126329292 T^{18} + 222588717588456358 T^{20} + 7522549416418163448 T^{22} + \)\(14\!\cdots\!21\)\( T^{24} + \)\(47\!\cdots\!84\)\( T^{26} + \)\(32\!\cdots\!22\)\( T^{28} + \)\(10\!\cdots\!52\)\( T^{30} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 215 T^{2} + 22911 T^{4} - 1578205 T^{6} + 78597176 T^{8} - 2918101045 T^{10} + 78328149711 T^{12} - 1359093055535 T^{14} + 11688200277601 T^{16} \))(\( 1 - 300 T^{2} + 44842 T^{4} - 4521820 T^{6} + 352848163 T^{8} - 23099919100 T^{10} + 1325953845604 T^{12} - 67791756187600 T^{14} + 3089570546914805 T^{16} - 125346957190872400 T^{18} + 4533172333304800804 T^{20} - \)\(14\!\cdots\!00\)\( T^{22} + \)\(41\!\cdots\!63\)\( T^{24} - \)\(97\!\cdots\!80\)\( T^{26} + \)\(17\!\cdots\!42\)\( T^{28} - \)\(22\!\cdots\!00\)\( T^{30} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 2284 T^{4} + 1070026 T^{8} + 6146180048 T^{12} - 12328368670157 T^{16} + 21012566494282448 T^{20} + 12506678190240287626 T^{24} - \)\(91\!\cdots\!84\)\( T^{28} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 2 T + 2 T^{2} + 112 T^{3} - 3840 T^{4} + 7982 T^{5} - 2012 T^{6} - 464698 T^{7} + 6098798 T^{8} - 19506388 T^{9} - 1100914 T^{10} + 890327938 T^{11} - 7456003800 T^{12} + 38444523010 T^{13} - 1944910962 T^{14} - 1611174599916 T^{15} + 14665036034491 T^{16} - 69280507796388 T^{17} - 3596140368738 T^{18} + 3056608690956070 T^{19} - 25490593247443800 T^{20} + 130885723924780534 T^{21} - 6959277079726786 T^{22} - 5302199293874251516 T^{23} + 71283972476632423598 T^{24} - \)\(23\!\cdots\!14\)\( T^{25} - 43482302414327908988 T^{26} + \)\(74\!\cdots\!74\)\( T^{27} - \)\(15\!\cdots\!40\)\( T^{28} + \)\(19\!\cdots\!16\)\( T^{29} + \)\(14\!\cdots\!98\)\( T^{30} - \)\(63\!\cdots\!14\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))
$47$ (\( 1 + 2 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 14 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 7 T + 2 T^{2} - 329 T^{3} + 2209 T^{4} \))(\( 1 - 13 T + 39 T^{2} + 16 T^{3} - 299 T^{4} + 19253 T^{5} - 232366 T^{6} + 904891 T^{7} - 660491 T^{8} + 1661168 T^{9} + 190307559 T^{10} - 2981485091 T^{11} + 10779215329 T^{12} \))(\( 1 + 20 T + 105 T^{2} + 120 T^{3} + 6294 T^{4} + 71140 T^{5} + 174165 T^{6} + 1240450 T^{7} + 19222555 T^{8} + 58301150 T^{9} + 384730485 T^{10} + 7385968220 T^{11} + 30712712214 T^{12} + 27521400840 T^{13} + 1131817609545 T^{14} + 10132462409260 T^{15} + 23811286661761 T^{16} \))(\( 1 - 160 T^{2} + 14809 T^{4} - 1019680 T^{6} + 55015600 T^{8} - 2252473120 T^{10} + 72263195929 T^{12} - 1724674452640 T^{14} + 23811286661761 T^{16} \))(\( 1 - 20 T + 105 T^{2} - 120 T^{3} + 6294 T^{4} - 71140 T^{5} + 174165 T^{6} - 1240450 T^{7} + 19222555 T^{8} - 58301150 T^{9} + 384730485 T^{10} - 7385968220 T^{11} + 30712712214 T^{12} - 27521400840 T^{13} + 1131817609545 T^{14} - 10132462409260 T^{15} + 23811286661761 T^{16} \))(\( 1 - 3518 T^{4} + 4879681 T^{8} \))(\( ( 1 - 2818 T^{4} + 4879681 T^{8} )^{2} \))(\( 1 - 2 T - 23 T^{2} - 250 T^{3} + 2601 T^{4} - 11750 T^{5} - 50807 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 - 2 T - 43 T^{2} - 50 T^{3} + 2351 T^{4} - 2350 T^{5} - 94987 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 - T - 62 T^{2} + 78 T^{3} + 3466 T^{4} - 4691 T^{5} - 155900 T^{6} + 95604 T^{7} + 3265179 T^{8} + 4493388 T^{9} - 344383100 T^{10} - 487033693 T^{11} + 16912974346 T^{12} + 17888910546 T^{13} - 668311350398 T^{14} - 506623120463 T^{15} + 23811286661761 T^{16} \))(\( 1 - 13 T + 37 T^{2} - 325 T^{3} + 7867 T^{4} - 56088 T^{5} + 222715 T^{6} - 1098334 T^{7} + 12592498 T^{8} - 108988468 T^{9} + 281826965 T^{10} - 1078581014 T^{11} + 21055334183 T^{12} - 50693307658 T^{13} + 622555765685 T^{14} - 11315509713164 T^{15} + 61447373233138 T^{16} - 251897418918338 T^{17} + 2400692941998235 T^{18} - 28415477580528744 T^{19} + 187323392168073787 T^{20} - 363717403758399275 T^{21} + 1946167892725711813 T^{22} - 32138069796092159939 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 - 213 T^{2} + 20670 T^{4} - 1200990 T^{6} + 43061190 T^{8} - 552221379 T^{10} - 52474967158 T^{12} + 5507563494060 T^{14} - 317764676162385 T^{16} + 12166207758378540 T^{18} - 256061100216516598 T^{20} - 5952513153518318691 T^{22} + \)\(10\!\cdots\!90\)\( T^{24} - \)\(63\!\cdots\!10\)\( T^{26} + \)\(24\!\cdots\!70\)\( T^{28} - \)\(54\!\cdots\!97\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 45 T^{2} - 184 T^{4} + 99405 T^{6} + 4879681 T^{8} \))(\( 1 + 91 T^{2} + 1339 T^{4} - 12268 T^{6} + 3554941 T^{8} - 111607535 T^{10} - 21624150754 T^{12} - 246541044815 T^{14} + 17346978053821 T^{16} - 132239413656172 T^{18} + 31883312840097979 T^{20} + 4786521033460534459 T^{22} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 190 T^{2} + 18813 T^{4} + 1189930 T^{6} + 47942596 T^{8} + 692067060 T^{10} - 71396434957 T^{12} - 7544792481460 T^{14} - 431982830702721 T^{16} - 16666446591545140 T^{18} - 348391827127408717 T^{20} + 7459939861847962740 T^{22} + \)\(11\!\cdots\!56\)\( T^{24} + \)\(62\!\cdots\!70\)\( T^{26} + \)\(21\!\cdots\!33\)\( T^{28} + \)\(48\!\cdots\!10\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 110 T^{2} + 90 T^{3} + 4101 T^{4} + 9900 T^{5} - 3830 T^{6} + 910260 T^{7} - 5610889 T^{8} + 42782220 T^{9} - 8460470 T^{10} + 1027847700 T^{11} + 20011571781 T^{12} + 20641050630 T^{13} + 1185713686190 T^{14} + 23811286661761 T^{16} \))(\( 1 + 40 T + 865 T^{2} + 12910 T^{3} + 142622 T^{4} + 1167030 T^{5} + 6143280 T^{6} - 637840 T^{7} - 479197322 T^{8} - 6905707270 T^{9} - 64790306935 T^{10} - 444387466120 T^{11} - 1988154991916 T^{12} - 288127717900 T^{13} + 103937589685250 T^{14} + 1288860429553200 T^{15} + 10336092465289955 T^{16} + 60576440189000400 T^{17} + 229598135614717250 T^{18} - 29914284055531700 T^{19} - 9701562139107658796 T^{20} - \)\(10\!\cdots\!40\)\( T^{21} - \)\(69\!\cdots\!15\)\( T^{22} - \)\(34\!\cdots\!10\)\( T^{23} - \)\(11\!\cdots\!42\)\( T^{24} - \)\(71\!\cdots\!80\)\( T^{25} + \)\(32\!\cdots\!20\)\( T^{26} + \)\(28\!\cdots\!90\)\( T^{27} + \)\(16\!\cdots\!02\)\( T^{28} + \)\(70\!\cdots\!70\)\( T^{29} + \)\(22\!\cdots\!85\)\( T^{30} + \)\(48\!\cdots\!20\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 5722 T^{4} + 16357201 T^{8} - 37906653562 T^{12} + 84859867638724 T^{16} - 184972377160073722 T^{20} + \)\(38\!\cdots\!61\)\( T^{24} - \)\(66\!\cdots\!02\)\( T^{28} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 12 T + 72 T^{2} - 288 T^{3} - 134 T^{4} + 24762 T^{5} - 246024 T^{6} + 2286006 T^{7} - 18983651 T^{8} + 98916168 T^{9} - 204929766 T^{10} - 1977304884 T^{11} + 21327903874 T^{12} - 124668663210 T^{13} + 894258211950 T^{14} - 7685415723390 T^{15} + 46309407650224 T^{16} - 361214538999330 T^{17} + 1975416390197550 T^{18} - 12943474620451830 T^{19} + 104073367303784194 T^{20} - 453485002462114188 T^{21} - 2208982075035583014 T^{22} + 50113217696402345784 T^{23} - \)\(45\!\cdots\!11\)\( T^{24} + \)\(25\!\cdots\!02\)\( T^{25} - \)\(12\!\cdots\!76\)\( T^{26} + \)\(61\!\cdots\!86\)\( T^{27} - \)\(15\!\cdots\!94\)\( T^{28} - \)\(15\!\cdots\!76\)\( T^{29} + \)\(18\!\cdots\!68\)\( T^{30} - \)\(14\!\cdots\!16\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 - 4 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 86 T^{2} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( ( 1 - 53 T^{2} )^{2} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 2 T + 139 T^{2} - 188 T^{3} + 7367 T^{4} - 5618 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 - 20 T + 298 T^{2} - 3001 T^{3} + 25499 T^{4} - 159053 T^{5} + 837082 T^{6} - 2977540 T^{7} + 7890481 T^{8} )^{2} \))(\( ( 1 + 196 T^{2} + 15174 T^{4} + 550564 T^{6} + 7890481 T^{8} )^{2} \))(\( ( 1 + 20 T + 298 T^{2} + 3001 T^{3} + 25499 T^{4} + 159053 T^{5} + 837082 T^{6} + 2977540 T^{7} + 7890481 T^{8} )^{2} \))(\( ( 1 - 56 T^{2} + 2809 T^{4} )( 1 + 56 T^{2} + 2809 T^{4} ) \))(\( ( 1 - 5518 T^{4} + 7890481 T^{8} )^{2} \))(\( 1 - 5 T - 43 T^{2} + 265 T^{3} + 1244 T^{4} + 14045 T^{5} - 120787 T^{6} - 744385 T^{7} + 7890481 T^{8} \))(\( 1 + 9 T + 8 T^{2} + 315 T^{3} + 5131 T^{4} + 16695 T^{5} + 22472 T^{6} + 1339893 T^{7} + 7890481 T^{8} \))(\( 1 - 3 T - 63 T^{2} + 6 T^{3} + 4741 T^{4} + 3522 T^{5} - 240240 T^{6} + 209553 T^{7} + 7555219 T^{8} + 11106309 T^{9} - 674834160 T^{10} + 524344794 T^{11} + 37408770421 T^{12} + 2509172958 T^{13} - 1396354751127 T^{14} - 3524133419511 T^{15} + 62259690411361 T^{16} \))(\( 1 + 44 T + 817 T^{2} + 7511 T^{3} + 18675 T^{4} - 371047 T^{5} - 5505981 T^{6} - 45196759 T^{7} - 286840983 T^{8} - 1119924348 T^{9} + 5970507613 T^{10} + 163921234483 T^{11} + 1596195784652 T^{12} + 8687825427599 T^{13} + 16771155884917 T^{14} - 166730977157196 T^{15} - 2263313326382823 T^{16} - 18901080912007187 T^{17} - 122036551253412549 T^{18} - 435873044303099339 T^{19} + 1162699718432166675 T^{20} + 24784524338025820963 T^{21} + \)\(14\!\cdots\!33\)\( T^{22} + \)\(40\!\cdots\!68\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 43 T^{2} - 3135 T^{4} + 82870 T^{6} + 4231795 T^{8} - 1030728416 T^{10} + 14362866672 T^{12} + 1344642401885 T^{14} - 126528175677005 T^{16} + 3777100506894965 T^{18} + 113329926580949232 T^{20} - 22845436838146141664 T^{22} + \)\(26\!\cdots\!95\)\( T^{24} + \)\(14\!\cdots\!30\)\( T^{26} - \)\(15\!\cdots\!35\)\( T^{28} + \)\(59\!\cdots\!67\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 102 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 274 T^{2} + 33303 T^{4} - 2287964 T^{6} + 93548127 T^{8} - 2161991794 T^{10} + 22164361129 T^{12} )^{2} \))(\( ( 1 - 196 T^{2} + 19762 T^{4} - 1503447 T^{6} + 91143129 T^{8} - 4223182623 T^{10} + 155931685522 T^{12} - 4344214781284 T^{14} + 62259690411361 T^{16} )^{2} \))(\( 1 - 10 T + 100 T^{2} - 1625 T^{3} + 11531 T^{4} - 95310 T^{5} + 857875 T^{6} - 5635035 T^{7} + 42472426 T^{8} - 298656855 T^{9} + 2409770875 T^{10} - 14189466870 T^{11} + 90985136411 T^{12} - 679567676125 T^{13} + 2216436112900 T^{14} - 11747111398370 T^{15} + 62259690411361 T^{16} \))(\( 1 + 10 T + 31 T^{2} - 750 T^{3} - 4567 T^{4} + 7470 T^{5} + 369374 T^{6} + 601780 T^{7} - 13186187 T^{8} - 114344200 T^{9} + 595715966 T^{10} + 8185408800 T^{11} + 16758234740 T^{12} - 506558110520 T^{13} - 2917035559495 T^{14} + 4163213158300 T^{15} + 189869197228511 T^{16} + 220650297389900 T^{17} - 8193952886621455 T^{18} - 75414851819886040 T^{19} + 132230532809509940 T^{20} + 3423101068522538400 T^{21} + 13203663800735085614 T^{22} - \)\(13\!\cdots\!00\)\( T^{23} - \)\(82\!\cdots\!07\)\( T^{24} + \)\(19\!\cdots\!40\)\( T^{25} + \)\(64\!\cdots\!26\)\( T^{26} + \)\(69\!\cdots\!90\)\( T^{27} - \)\(22\!\cdots\!47\)\( T^{28} - \)\(19\!\cdots\!50\)\( T^{29} + \)\(42\!\cdots\!39\)\( T^{30} + \)\(73\!\cdots\!70\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 1244 T^{4} + 14286246 T^{8} - 9815758364 T^{12} + 62259690411361 T^{16} )^{2} \))(\( 1 - 6680 T^{4} + 12266524 T^{8} + 25145244376 T^{12} - 161780081477882 T^{16} + 198408072989184856 T^{20} + \)\(76\!\cdots\!64\)\( T^{24} - \)\(32\!\cdots\!80\)\( T^{28} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( 1 - 10 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 10 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( 1 - 14 T + 137 T^{2} - 826 T^{3} + 3481 T^{4} \))(\( 1 - 2 T - 153 T^{2} + 110 T^{3} + 14962 T^{4} - 3194 T^{5} - 1012513 T^{6} - 188446 T^{7} + 52082722 T^{8} + 22591690 T^{9} - 1853956233 T^{10} - 1429848598 T^{11} + 42180533641 T^{12} \))(\( 1 + 17 T + 51 T^{2} - 144 T^{3} + 2220 T^{4} - 17291 T^{5} - 531846 T^{6} - 1855556 T^{7} + 4239943 T^{8} - 109477804 T^{9} - 1851355926 T^{10} - 3551208289 T^{11} + 26900541420 T^{12} - 102949099056 T^{13} + 2151207215691 T^{14} + 42307075241923 T^{15} + 146830437604321 T^{16} \))(\( ( 1 + 12 T + 2 T^{2} + 288 T^{3} + 8187 T^{4} + 16992 T^{5} + 6962 T^{6} + 2464548 T^{7} + 12117361 T^{8} )^{2} \))(\( 1 + 17 T + 51 T^{2} - 144 T^{3} + 2220 T^{4} - 17291 T^{5} - 531846 T^{6} - 1855556 T^{7} + 4239943 T^{8} - 109477804 T^{9} - 1851355926 T^{10} - 3551208289 T^{11} + 26900541420 T^{12} - 102949099056 T^{13} + 2151207215691 T^{14} + 42307075241923 T^{15} + 146830437604321 T^{16} \))(\( ( 1 + 46 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 44 T^{2} + 3481 T^{4} )^{4} \))(\( 1 + 4 T - 43 T^{2} - 408 T^{3} + 905 T^{4} - 24072 T^{5} - 149683 T^{6} + 821516 T^{7} + 12117361 T^{8} \))(\( 1 + 31 T^{2} - 210 T^{3} + 2851 T^{4} - 12390 T^{5} + 107911 T^{6} + 12117361 T^{8} \))(\( 1 + 30 T + 377 T^{2} + 2475 T^{3} + 8643 T^{4} + 1155 T^{5} - 582521 T^{6} - 10821600 T^{7} - 108687625 T^{8} - 638474400 T^{9} - 2027755601 T^{10} + 237212745 T^{11} + 104730351123 T^{12} + 1769437640025 T^{13} + 15902061182657 T^{14} + 74659544544570 T^{15} + 146830437604321 T^{16} \))(\( 1 - 22 T + 36 T^{2} + 2583 T^{3} - 16419 T^{4} - 137618 T^{5} + 1667358 T^{6} + 2698622 T^{7} - 107608927 T^{8} + 155893882 T^{9} + 5010588449 T^{10} - 10213783795 T^{11} - 198548784261 T^{12} - 602613243905 T^{13} + 17441858390969 T^{14} + 32017329591278 T^{15} - 1303936215281647 T^{16} + 1929310441615978 T^{17} + 70330050210590478 T^{18} - 342483240037821142 T^{19} - 2410808955025346499 T^{20} + 22376518199585707437 T^{21} + 18400203118823090436 T^{22} - \)\(66\!\cdots\!98\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 224 T^{2} + 24195 T^{4} + 2068305 T^{6} + 171667695 T^{8} + 11805210387 T^{10} + 664199677293 T^{12} + 39649746993960 T^{14} + 2482020647300265 T^{16} + 138020769285974760 T^{18} + 8048347265842783773 T^{20} + \)\(49\!\cdots\!67\)\( T^{22} + \)\(25\!\cdots\!95\)\( T^{24} + \)\(10\!\cdots\!05\)\( T^{26} + \)\(43\!\cdots\!95\)\( T^{28} + \)\(13\!\cdots\!64\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 14 T + 137 T^{2} + 826 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 2 T - 153 T^{2} - 110 T^{3} + 14962 T^{4} + 3194 T^{5} - 1012513 T^{6} + 188446 T^{7} + 52082722 T^{8} - 22591690 T^{9} - 1853956233 T^{10} + 1429848598 T^{11} + 42180533641 T^{12} )^{2} \))(\( ( 1 - 17 T + 51 T^{2} + 144 T^{3} + 2220 T^{4} + 17291 T^{5} - 531846 T^{6} + 1855556 T^{7} + 4239943 T^{8} + 109477804 T^{9} - 1851355926 T^{10} + 3551208289 T^{11} + 26900541420 T^{12} + 102949099056 T^{13} + 2151207215691 T^{14} - 42307075241923 T^{15} + 146830437604321 T^{16} )^{2} \))(\( 1 - 118 T^{2} - 900 T^{3} + 3393 T^{4} + 96300 T^{5} + 615034 T^{6} - 2943900 T^{7} - 65890945 T^{8} - 173690100 T^{9} + 2140933354 T^{10} + 19777997700 T^{11} + 41114205873 T^{12} - 643431869100 T^{13} - 4977302969638 T^{14} + 146830437604321 T^{16} \))(\( 1 + 12 T - 48 T^{2} - 796 T^{3} + 7633 T^{4} + 76112 T^{5} - 428429 T^{6} - 2657110 T^{7} + 51753489 T^{8} + 263375518 T^{9} - 2799769853 T^{10} - 8680064174 T^{11} + 262778488535 T^{12} + 989243918004 T^{13} - 11934572611572 T^{14} - 2210541870272 T^{15} + 962870787479413 T^{16} - 130421970346048 T^{17} - 41544247260882132 T^{18} + 203169926635743516 T^{19} + 3184181808612956135 T^{20} - 6205588794871964026 T^{21} - \)\(11\!\cdots\!73\)\( T^{22} + \)\(65\!\cdots\!42\)\( T^{23} + \)\(75\!\cdots\!69\)\( T^{24} - \)\(23\!\cdots\!90\)\( T^{25} - \)\(21\!\cdots\!29\)\( T^{26} + \)\(22\!\cdots\!08\)\( T^{27} + \)\(13\!\cdots\!73\)\( T^{28} - \)\(83\!\cdots\!84\)\( T^{29} - \)\(29\!\cdots\!28\)\( T^{30} + \)\(43\!\cdots\!88\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 46 T^{2} - 1365 T^{4} - 160126 T^{6} + 12117361 T^{8} )^{4} \))(\( 1 - 328 T^{2} + 54732 T^{4} - 6528848 T^{6} + 640897706 T^{8} - 55004293416 T^{10} + 4215408852016 T^{12} - 289798546717912 T^{14} + 17966936709291123 T^{16} - 1008788741125051672 T^{18} + 51079630822473449776 T^{20} - \)\(23\!\cdots\!56\)\( T^{22} + \)\(94\!\cdots\!26\)\( T^{24} - \)\(33\!\cdots\!48\)\( T^{26} + \)\(97\!\cdots\!92\)\( T^{28} - \)\(20\!\cdots\!08\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 - 7 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 7 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 13 T + 61 T^{2} )^{2} \))(\( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} \))(\( 1 + T - 145 T^{2} - 240 T^{3} + 12217 T^{4} + 14087 T^{5} - 812786 T^{6} + 859307 T^{7} + 45459457 T^{8} - 54475440 T^{9} - 2007646945 T^{10} + 844596301 T^{11} + 51520374361 T^{12} \))(\( 1 - 13 T - 72 T^{2} + 1443 T^{3} + 6378 T^{4} - 120042 T^{5} - 78037 T^{6} + 2420938 T^{7} + 9620433 T^{8} + 147677218 T^{9} - 290375677 T^{10} - 27247253202 T^{11} + 88308773898 T^{12} + 1218752462343 T^{13} - 3709466953992 T^{14} - 40855656868273 T^{15} + 191707312997281 T^{16} \))(\( ( 1 + 4 T - 35 T^{2} - 284 T^{3} - 2096 T^{4} - 17324 T^{5} - 130235 T^{6} + 907924 T^{7} + 13845841 T^{8} )^{2} \))(\( 1 - 13 T - 72 T^{2} + 1443 T^{3} + 6378 T^{4} - 120042 T^{5} - 78037 T^{6} + 2420938 T^{7} + 9620433 T^{8} + 147677218 T^{9} - 290375677 T^{10} - 27247253202 T^{11} + 88308773898 T^{12} + 1218752462343 T^{13} - 3709466953992 T^{14} - 40855656868273 T^{15} + 191707312997281 T^{16} \))(\( ( 1 - 8 T + 61 T^{2} )^{4} \))(\( ( 1 + 7 T + 61 T^{2} )^{8} \))(\( 1 - 2 T - 57 T^{2} - 64 T^{3} + 3905 T^{4} - 3904 T^{5} - 212097 T^{6} - 453962 T^{7} + 13845841 T^{8} \))(\( 1 - 13 T + 78 T^{2} - 941 T^{3} + 11075 T^{4} - 57401 T^{5} + 290238 T^{6} - 2950753 T^{7} + 13845841 T^{8} \))(\( 1 + 14 T + 35 T^{2} + 110 T^{3} + 8070 T^{4} + 33812 T^{5} - 419217 T^{6} - 1871430 T^{7} + 12043555 T^{8} - 114157230 T^{9} - 1559906457 T^{10} + 7674681572 T^{11} + 111735936870 T^{12} + 92905593110 T^{13} + 1803213102635 T^{14} + 43998399704294 T^{15} + 191707312997281 T^{16} \))(\( 1 + 8 T - 130 T^{2} - 1358 T^{3} + 564 T^{4} + 21392 T^{5} + 487611 T^{6} + 8007850 T^{7} - 7109096 T^{8} - 542757032 T^{9} - 551554860 T^{10} + 10321250720 T^{11} + 3604709585 T^{12} + 629596293920 T^{13} - 2052335634060 T^{14} - 123195533880392 T^{15} - 98431412869736 T^{16} + 6763400488962850 T^{17} + 25121901262541571 T^{18} + 67229554748161232 T^{19} + 108122924530466484 T^{20} - 15880650394068763478 T^{21} - 92734578516174738130 T^{22} + \)\(34\!\cdots\!88\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 16 T + 15 T^{2} + 960 T^{3} - 3000 T^{4} - 9768 T^{5} - 217407 T^{6} + 637260 T^{7} + 14903655 T^{8} + 38872860 T^{9} - 808971447 T^{10} - 2217150408 T^{11} - 41537523000 T^{12} + 810812448960 T^{13} + 772805615415 T^{14} - 50283885376336 T^{15} + 191707312997281 T^{16} )^{2} \))(\( ( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + T - 145 T^{2} - 240 T^{3} + 12217 T^{4} + 14087 T^{5} - 812786 T^{6} + 859307 T^{7} + 45459457 T^{8} - 54475440 T^{9} - 2007646945 T^{10} + 844596301 T^{11} + 51520374361 T^{12} )^{2} \))(\( ( 1 - 13 T - 72 T^{2} + 1443 T^{3} + 6378 T^{4} - 120042 T^{5} - 78037 T^{6} + 2420938 T^{7} + 9620433 T^{8} + 147677218 T^{9} - 290375677 T^{10} - 27247253202 T^{11} + 88308773898 T^{12} + 1218752462343 T^{13} - 3709466953992 T^{14} - 40855656868273 T^{15} + 191707312997281 T^{16} )^{2} \))(\( 1 + 9 T - 165 T^{2} - 1800 T^{3} + 7560 T^{4} + 154437 T^{5} + 526138 T^{6} - 4559670 T^{7} - 69838275 T^{8} - 278139870 T^{9} + 1957759498 T^{10} + 35054264697 T^{11} + 104674557960 T^{12} - 1520273341800 T^{13} - 8500861769565 T^{14} + 28284685524189 T^{15} + 191707312997281 T^{16} \))(\( 1 - 66 T^{2} + 280 T^{3} + 2565 T^{4} + 73000 T^{5} - 42550 T^{6} - 4179060 T^{7} + 27062520 T^{8} + 116843800 T^{9} + 1866464452 T^{10} + 5426819300 T^{11} - 75968338617 T^{12} + 773051497020 T^{13} + 3102841052040 T^{14} + 12380110098160 T^{15} + 378207085764575 T^{16} + 755186715987760 T^{17} + 11545671554640840 T^{18} + 175468001845096620 T^{19} - 1051845537525141897 T^{20} + 4583471506975409300 T^{21} + 96160947298538715172 T^{22} + \)\(36\!\cdots\!00\)\( T^{23} + \)\(51\!\cdots\!20\)\( T^{24} - \)\(48\!\cdots\!60\)\( T^{25} - \)\(30\!\cdots\!50\)\( T^{26} + \)\(31\!\cdots\!00\)\( T^{27} + \)\(68\!\cdots\!65\)\( T^{28} + \)\(45\!\cdots\!80\)\( T^{29} - \)\(65\!\cdots\!06\)\( T^{30} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 10 T - 41 T^{2} + 190 T^{3} + 10060 T^{4} + 11590 T^{5} - 152561 T^{6} + 2269810 T^{7} + 13845841 T^{8} )^{4} \))(\( ( 1 - 4 T - 126 T^{2} + 1444 T^{3} + 6365 T^{4} - 126018 T^{5} + 435286 T^{6} + 4572842 T^{7} - 47796264 T^{8} + 278943362 T^{9} + 1619699206 T^{10} - 28603691658 T^{11} + 88128777965 T^{12} + 1219597058644 T^{13} - 6491567169486 T^{14} - 12570971344084 T^{15} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 + 3 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( 1 - 125 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 109 T^{2} + 4489 T^{4} \))(\( 1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4} \))(\( 1 - 11 T - 41 T^{2} + 152 T^{3} + 4753 T^{4} + 32755 T^{5} - 764902 T^{6} + 2194585 T^{7} + 21336217 T^{8} + 45715976 T^{9} - 826195961 T^{10} - 14851376177 T^{11} + 90458382169 T^{12} \))(\( 1 + 17 T - 15 T^{2} - 1066 T^{3} + 7426 T^{4} + 68373 T^{5} - 833566 T^{6} + 1085128 T^{7} + 111947307 T^{8} + 72703576 T^{9} - 3741877774 T^{10} + 20564068599 T^{11} + 149642224546 T^{12} - 1439233364062 T^{13} - 1356875732535 T^{14} + 103032097290491 T^{15} + 406067677556641 T^{16} \))(\( 1 - 184 T^{2} + 16657 T^{4} - 1512664 T^{6} + 123674896 T^{8} - 6790348696 T^{10} + 335657222497 T^{12} - 16644342319096 T^{14} + 406067677556641 T^{16} \))(\( 1 - 17 T - 15 T^{2} + 1066 T^{3} + 7426 T^{4} - 68373 T^{5} - 833566 T^{6} - 1085128 T^{7} + 111947307 T^{8} - 72703576 T^{9} - 3741877774 T^{10} - 20564068599 T^{11} + 149642224546 T^{12} + 1439233364062 T^{13} - 1356875732535 T^{14} - 103032097290491 T^{15} + 406067677556641 T^{16} \))(\( ( 1 + 8 T + 32 T^{2} + 536 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 2471 T^{4} + 20151121 T^{8} )^{2} \))(\( 1 - 2 T - 43 T^{2} - 370 T^{3} + 5041 T^{4} - 24790 T^{5} - 193027 T^{6} - 601526 T^{7} + 20151121 T^{8} \))(\( 1 + 2 T - 3 T^{2} - 410 T^{3} + 1601 T^{4} - 27470 T^{5} - 13467 T^{6} + 601526 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T - 97 T^{2} + 122 T^{3} + 9681 T^{4} - 8074 T^{5} - 723795 T^{6} + 600576 T^{7} + 39163204 T^{8} + 40238592 T^{9} - 3249115755 T^{10} - 2428360462 T^{11} + 195083002401 T^{12} + 164715263054 T^{13} - 8774463070393 T^{14} - 24242846421292 T^{15} + 406067677556641 T^{16} \))(\( 1 + 6 T - 172 T^{2} - 858 T^{3} + 11749 T^{4} + 57666 T^{5} - 232014 T^{6} - 4755072 T^{7} - 22912618 T^{8} + 467752054 T^{9} + 2928188158 T^{10} - 17377714672 T^{11} - 223143036976 T^{12} - 1164306883024 T^{13} + 13144636641262 T^{14} + 140682511017202 T^{15} - 461714937744778 T^{16} - 6419942092792704 T^{17} - 20987611080558366 T^{18} + 349496995432556118 T^{19} + 4770889143612975109 T^{20} - 23343206512021064526 T^{21} - \)\(31\!\cdots\!28\)\( T^{22} + \)\(73\!\cdots\!98\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 20 T + 261 T^{2} + 3240 T^{3} + 34947 T^{4} + 325680 T^{5} + 3089343 T^{6} + 27153900 T^{7} + 224184240 T^{8} + 1819311300 T^{9} + 13868060727 T^{10} + 97952493840 T^{11} + 704221225587 T^{12} + 4374405346680 T^{13} + 23609637746109 T^{14} + 121214232106460 T^{15} + 406067677556641 T^{16} )^{2} \))(\( 1 + 125 T^{2} + 11136 T^{4} + 561125 T^{6} + 20151121 T^{8} \))(\( 1 + 203 T^{2} + 14531 T^{4} + 1222044 T^{6} + 166308757 T^{8} + 11407412521 T^{10} + 552166785598 T^{12} + 51207874806769 T^{14} + 3351307885666597 T^{16} + 110544123179333436 T^{18} + 5900569422575550371 T^{20} + \)\(37\!\cdots\!47\)\( T^{22} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 + 319 T^{2} + 51321 T^{4} + 5350950 T^{6} + 412923954 T^{8} + 28055592807 T^{10} + 2076453240410 T^{12} + 167751222063326 T^{14} + 12304355330991753 T^{16} + 753035235842270414 T^{18} + 41842860498343999610 T^{20} + \)\(25\!\cdots\!83\)\( T^{22} + \)\(16\!\cdots\!14\)\( T^{24} + \)\(97\!\cdots\!50\)\( T^{26} + \)\(41\!\cdots\!81\)\( T^{28} + \)\(11\!\cdots\!51\)\( T^{30} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 20 T + 250 T^{2} - 2600 T^{3} + 26091 T^{4} - 241820 T^{5} + 2034700 T^{6} - 15361680 T^{7} + 117317461 T^{8} - 1029232560 T^{9} + 9133768300 T^{10} - 72730508660 T^{11} + 525762898011 T^{12} - 3510325278200 T^{13} + 22614595542250 T^{14} - 121214232106460 T^{15} + 406067677556641 T^{16} \))(\( 1 + 40 T + 1030 T^{2} + 19080 T^{3} + 285687 T^{4} + 3555880 T^{5} + 38106080 T^{6} + 351599640 T^{7} + 2795567883 T^{8} + 18168145600 T^{9} + 82372777780 T^{10} - 40068357040 T^{11} - 6615976940891 T^{12} - 103670166025040 T^{13} - 1174625422928650 T^{14} - 11401205121382320 T^{15} - 98095935267474960 T^{16} - 763880743132615440 T^{17} - 5272893523526709850 T^{18} - 31180150144189105520 T^{19} - \)\(13\!\cdots\!11\)\( T^{20} - 54097294835944203280 T^{21} + \)\(74\!\cdots\!20\)\( T^{22} + \)\(11\!\cdots\!00\)\( T^{23} + \)\(11\!\cdots\!03\)\( T^{24} + \)\(95\!\cdots\!80\)\( T^{25} + \)\(69\!\cdots\!20\)\( T^{26} + \)\(43\!\cdots\!40\)\( T^{27} + \)\(23\!\cdots\!07\)\( T^{28} + \)\(10\!\cdots\!60\)\( T^{29} + \)\(37\!\cdots\!70\)\( T^{30} + \)\(98\!\cdots\!20\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 5914 T^{4} + 8186161 T^{8} + 79915923398 T^{12} - 393198002490332 T^{16} + 1610395442219829158 T^{20} + \)\(33\!\cdots\!01\)\( T^{24} - \)\(48\!\cdots\!54\)\( T^{28} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 + 4 T + 8 T^{2} - 1436 T^{3} - 5070 T^{4} - 45274 T^{5} + 890512 T^{6} + 2479154 T^{7} + 72952373 T^{8} - 410747644 T^{9} - 246911326 T^{10} - 51154442144 T^{11} + 220045950810 T^{12} - 1378484916350 T^{13} + 21635958751422 T^{14} - 133914238479582 T^{15} + 1373516219103616 T^{16} - 8972253978131994 T^{17} + 97123818835133358 T^{18} - 414597258896175050 T^{19} + 4434172580332358010 T^{20} - 69064896673193309408 T^{21} - 22335199089162546094 T^{22} - \)\(24\!\cdots\!12\)\( T^{23} + \)\(29\!\cdots\!93\)\( T^{24} + \)\(67\!\cdots\!38\)\( T^{25} + \)\(16\!\cdots\!88\)\( T^{26} - \)\(55\!\cdots\!42\)\( T^{27} - \)\(41\!\cdots\!70\)\( T^{28} - \)\(78\!\cdots\!32\)\( T^{29} + \)\(29\!\cdots\!32\)\( T^{30} + \)\(98\!\cdots\!72\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))
$71$ (\( 1 - 8 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 121 T^{2} + 712 T^{3} + 8591 T^{4} + 50410 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 8 T + 244 T^{2} + 1441 T^{3} + 24947 T^{4} + 102311 T^{5} + 1230004 T^{6} + 2863288 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 - 18 T + 196 T^{2} - 1278 T^{3} + 5041 T^{4} )^{4} \))(\( ( 1 + 8 T + 244 T^{2} + 1441 T^{3} + 24947 T^{4} + 102311 T^{5} + 1230004 T^{6} + 2863288 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 - 110 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 5041 T^{4} )^{4} \))(\( 1 + 8 T - 47 T^{2} - 434 T^{3} + 1365 T^{4} - 30814 T^{5} - 236927 T^{6} + 2863288 T^{7} + 25411681 T^{8} \))(\( 1 + 8 T - 37 T^{2} - 694 T^{3} - 2425 T^{4} - 49274 T^{5} - 186517 T^{6} + 2863288 T^{7} + 25411681 T^{8} \))(\( 1 + 21 T + 305 T^{2} + 2480 T^{3} + 13165 T^{4} - 10682 T^{5} - 810942 T^{6} - 9320005 T^{7} - 80224815 T^{8} - 661720355 T^{9} - 4087958622 T^{10} - 3823205302 T^{11} + 334544780365 T^{12} + 4474488790480 T^{13} + 39070586595905 T^{14} + 190997523326211 T^{15} + 645753531245761 T^{16} \))(\( 1 - 21 T + 46 T^{2} + 1289 T^{3} + 2891 T^{4} - 230821 T^{5} + 1592921 T^{6} + 6954484 T^{7} - 90555524 T^{8} - 1177173511 T^{9} + 16628404231 T^{10} - 5732671986 T^{11} - 764574531549 T^{12} - 407019711006 T^{13} + 83823785728471 T^{14} - 421323348495521 T^{15} - 2301168088675844 T^{16} + 12547484153859884 T^{17} + 204053632363723241 T^{18} - 2099344730079969011 T^{19} + 1866873458831495051 T^{20} + 59098717426080800959 T^{21} + \)\(14\!\cdots\!46\)\( T^{22} - \)\(48\!\cdots\!91\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 141 T^{2} + 4485 T^{4} + 192330 T^{6} + 69422535 T^{8} + 3292611048 T^{10} - 213402155272 T^{12} - 5365589194005 T^{14} + 1200886789327035 T^{16} - 27047935126979205 T^{18} - 5422907494484532232 T^{20} + \)\(42\!\cdots\!08\)\( T^{22} + \)\(44\!\cdots\!35\)\( T^{24} + \)\(62\!\cdots\!30\)\( T^{26} + \)\(73\!\cdots\!85\)\( T^{28} + \)\(11\!\cdots\!21\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 2 T + 71 T^{2} )^{4} \))(\( ( 1 + 10 T + 121 T^{2} + 712 T^{3} + 8591 T^{4} + 50410 T^{5} + 357911 T^{6} )^{4} \))(\( ( 1 + 8 T + 244 T^{2} + 1441 T^{3} + 24947 T^{4} + 102311 T^{5} + 1230004 T^{6} + 2863288 T^{7} + 25411681 T^{8} )^{4} \))(\( 1 + 6 T + 910 T^{3} + 4875 T^{4} - 34402 T^{5} + 474398 T^{6} + 3835500 T^{7} - 25760305 T^{8} + 272320500 T^{9} + 2391440318 T^{10} - 12312854222 T^{11} + 123881944875 T^{12} + 1641848709410 T^{13} + 54570720950346 T^{15} + 645753531245761 T^{16} \))(\( 1 - 8 T - 249 T^{2} + 2580 T^{3} + 22325 T^{4} - 321084 T^{5} - 587178 T^{6} + 14941106 T^{7} - 19432655 T^{8} + 485658130 T^{9} - 1289469490 T^{10} - 87893386040 T^{11} + 259786638060 T^{12} + 3694736827880 T^{13} + 7661490804445 T^{14} - 51486950465450 T^{15} - 2151535697455665 T^{16} - 3655573483046950 T^{17} + 38621575145207245 T^{18} + 1322386952803358680 T^{19} + 6601615174443178860 T^{20} - \)\(15\!\cdots\!40\)\( T^{21} - \)\(16\!\cdots\!90\)\( T^{22} + \)\(44\!\cdots\!30\)\( T^{23} - \)\(12\!\cdots\!55\)\( T^{24} + \)\(68\!\cdots\!86\)\( T^{25} - \)\(19\!\cdots\!78\)\( T^{26} - \)\(74\!\cdots\!64\)\( T^{27} + \)\(36\!\cdots\!25\)\( T^{28} + \)\(30\!\cdots\!80\)\( T^{29} - \)\(20\!\cdots\!69\)\( T^{30} - \)\(46\!\cdots\!08\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 32 T^{2} + 2562 T^{4} - 161312 T^{6} + 25411681 T^{8} )^{4} \))(\( ( 1 - 452 T^{2} + 95704 T^{4} - 12356144 T^{6} + 1062541066 T^{8} - 62287321904 T^{10} + 2431999518424 T^{12} - 57901328332292 T^{14} + 645753531245761 T^{16} )^{2} \))
$73$ (\( 1 + 14 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( ( 1 + 73 T^{2} )^{2} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( ( 1 - 8 T + 155 T^{2} - 1040 T^{3} + 11315 T^{4} - 42632 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 - 2 T + 196 T^{2} - 679 T^{3} + 18071 T^{4} - 49567 T^{5} + 1044484 T^{6} - 778034 T^{7} + 28398241 T^{8} )^{2} \))(\( ( 1 + 74 T^{2} + 5329 T^{4} )^{4} \))(\( ( 1 + 2 T + 196 T^{2} + 679 T^{3} + 18071 T^{4} + 49567 T^{5} + 1044484 T^{6} + 778034 T^{7} + 28398241 T^{8} )^{2} \))(\( ( 1 + 2 T + 2 T^{2} + 146 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 7298 T^{4} + 28398241 T^{8} )^{2} \))(\( 1 + 10 T + 27 T^{2} + 740 T^{3} + 11429 T^{4} + 54020 T^{5} + 143883 T^{6} + 3890170 T^{7} + 28398241 T^{8} \))(\( 1 - 9 T + 8 T^{2} + 585 T^{3} - 5849 T^{4} + 42705 T^{5} + 42632 T^{6} - 3501153 T^{7} + 28398241 T^{8} \))(\( 1 - 2 T - 163 T^{2} - 986 T^{3} + 8481 T^{4} + 176518 T^{5} + 938895 T^{6} - 6925578 T^{7} - 156207836 T^{8} - 505567194 T^{9} + 5003371455 T^{10} + 68668502806 T^{11} + 240845481921 T^{12} - 2044048590698 T^{13} - 24667478885107 T^{14} - 22094797038194 T^{15} + 806460091894081 T^{16} \))(\( 1 + 16 T - 28 T^{2} - 506 T^{3} + 12385 T^{4} - 2328 T^{5} - 561526 T^{6} + 14932744 T^{7} + 69930462 T^{8} - 421338712 T^{9} + 9017966158 T^{10} + 43966609042 T^{11} - 621466327768 T^{12} + 3209562460066 T^{13} + 48056741655982 T^{14} - 163907921726104 T^{15} + 1985902113117342 T^{16} + 30956647391941192 T^{17} - 84978102751157014 T^{18} - 25718343752457816 T^{19} + 9988008238108193185 T^{20} - 29789022874383563978 T^{21} - \)\(12\!\cdots\!72\)\( T^{22} + \)\(50\!\cdots\!32\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 30 T + 569 T^{2} - 8290 T^{3} + 100537 T^{4} - 1081770 T^{5} + 10670867 T^{6} - 98572950 T^{7} + 862584500 T^{8} - 7195825350 T^{9} + 56865050243 T^{10} - 420826920090 T^{11} + 2855073955417 T^{12} - 17185763505970 T^{13} + 86109174758441 T^{14} - 331421955572910 T^{15} + 806460091894081 T^{16} )^{2} \))(\( ( 1 - 130 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 246 T^{2} + 30015 T^{4} - 2521972 T^{6} + 159949935 T^{8} - 6985967286 T^{10} + 151334226289 T^{12} )^{2} \))(\( ( 1 - 388 T^{2} + 71842 T^{4} - 8513491 T^{6} + 722371129 T^{8} - 45368393539 T^{10} + 2040186429922 T^{12} - 58717679800132 T^{14} + 806460091894081 T^{16} )^{2} \))(\( 1 - 15 T + 195 T^{2} - 1340 T^{3} + 15786 T^{4} - 132465 T^{5} + 1900340 T^{6} - 14658400 T^{7} + 154250461 T^{8} - 1070063200 T^{9} + 10126911860 T^{10} - 51531136905 T^{11} + 448294632426 T^{12} - 2777915934620 T^{13} + 29510174126355 T^{14} - 165710977786455 T^{15} + 806460091894081 T^{16} \))(\( 1 + 20 T + 426 T^{2} + 5180 T^{3} + 61943 T^{4} + 512020 T^{5} + 4294444 T^{6} + 28526480 T^{7} + 237139103 T^{8} + 1934704520 T^{9} + 18247662296 T^{10} + 153434416460 T^{11} + 1126098548485 T^{12} + 8592560378500 T^{13} + 56602836572850 T^{14} + 546633756136020 T^{15} + 3853646456873416 T^{16} + 39904264197929460 T^{17} + 301636516096717650 T^{18} + 3342652060762934500 T^{19} + 31979217969627214885 T^{20} + \)\(31\!\cdots\!80\)\( T^{21} + \)\(27\!\cdots\!44\)\( T^{22} + \)\(21\!\cdots\!40\)\( T^{23} + \)\(19\!\cdots\!43\)\( T^{24} + \)\(16\!\cdots\!40\)\( T^{25} + \)\(18\!\cdots\!56\)\( T^{26} + \)\(16\!\cdots\!40\)\( T^{27} + \)\(14\!\cdots\!03\)\( T^{28} + \)\(86\!\cdots\!40\)\( T^{29} + \)\(51\!\cdots\!34\)\( T^{30} + \)\(17\!\cdots\!40\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 5329 T^{4} )^{8} \))(\( ( 1 - 4 T + 8 T^{2} + 292 T^{3} - 844 T^{4} - 28196 T^{5} + 162168 T^{6} + 417348 T^{7} - 41227034 T^{8} + 30466404 T^{9} + 864193272 T^{10} - 10968723332 T^{11} - 23968115404 T^{12} + 605336905156 T^{13} + 1210673810312 T^{14} - 44189594076388 T^{15} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( 1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( 1 + 2 T - 149 T^{2} - 374 T^{3} + 10642 T^{4} + 16154 T^{5} - 772597 T^{6} + 1276166 T^{7} + 66416722 T^{8} - 184396586 T^{9} - 5803562069 T^{10} + 6154112798 T^{11} + 243087455521 T^{12} \))(\( 1 - 7 T - 234 T^{2} + 1199 T^{3} + 36520 T^{4} - 121434 T^{5} - 3999001 T^{6} + 3702556 T^{7} + 362101113 T^{8} + 292501924 T^{9} - 24957765241 T^{10} - 59871697926 T^{11} + 1422456958120 T^{12} + 3689390622401 T^{13} - 56882464591914 T^{14} - 134427362903113 T^{15} + 1517108809906561 T^{16} \))(\( ( 1 + 8 T - 98 T^{2} + 32 T^{3} + 14947 T^{4} + 2528 T^{5} - 611618 T^{6} + 3944312 T^{7} + 38950081 T^{8} )^{2} \))(\( 1 - 7 T - 234 T^{2} + 1199 T^{3} + 36520 T^{4} - 121434 T^{5} - 3999001 T^{6} + 3702556 T^{7} + 362101113 T^{8} + 292501924 T^{9} - 24957765241 T^{10} - 59871697926 T^{11} + 1422456958120 T^{12} + 3689390622401 T^{13} - 56882464591914 T^{14} - 134427362903113 T^{15} + 1517108809906561 T^{16} \))(\( ( 1 - 14 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 154 T^{2} + 6241 T^{4} )^{4} \))(\( 1 - 79 T^{2} + 6241 T^{4} - 493039 T^{6} + 38950081 T^{8} \))(\( 1 - 15 T + 21 T^{2} + 145 T^{3} + 2916 T^{4} + 11455 T^{5} + 131061 T^{6} - 7395585 T^{7} + 38950081 T^{8} \))(\( 1 + 30 T + 447 T^{2} + 5690 T^{3} + 63618 T^{4} + 615980 T^{5} + 6355819 T^{6} + 63162750 T^{7} + 565067755 T^{8} + 4989857250 T^{9} + 39666666379 T^{10} + 303702163220 T^{11} + 2477926253058 T^{12} + 17508450910310 T^{13} + 108660092617887 T^{14} + 576117269584770 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 10 T - 272 T^{2} + 2840 T^{3} + 26866 T^{4} - 289420 T^{5} - 489675 T^{6} + 1858730 T^{7} - 91007200 T^{8} + 1966674780 T^{9} + 3705819298 T^{10} - 105092388950 T^{11} + 146277106069 T^{12} - 8302298727050 T^{13} + 23128018238818 T^{14} + 969647366856420 T^{15} - 3544737811583200 T^{16} + 5719417040513270 T^{17} - 119033849782245675 T^{18} - 5557995338774137780 T^{19} + 40758645286949667826 T^{20} + \)\(34\!\cdots\!60\)\( T^{21} - \)\(25\!\cdots\!72\)\( T^{22} - \)\(74\!\cdots\!90\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 18 T + 195 T^{2} - 2670 T^{3} + 31590 T^{4} - 298764 T^{5} + 3295307 T^{6} - 34117590 T^{7} + 300163995 T^{8} - 2695289610 T^{9} + 20566010987 T^{10} - 147302303796 T^{11} + 1230433058790 T^{12} - 8215740585330 T^{13} + 47402053826595 T^{14} - 345670361750862 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 + 6 T - 43 T^{2} + 474 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 2 T - 149 T^{2} + 374 T^{3} + 10642 T^{4} - 16154 T^{5} - 772597 T^{6} - 1276166 T^{7} + 66416722 T^{8} + 184396586 T^{9} - 5803562069 T^{10} - 6154112798 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 + 7 T - 234 T^{2} - 1199 T^{3} + 36520 T^{4} + 121434 T^{5} - 3999001 T^{6} - 3702556 T^{7} + 362101113 T^{8} - 292501924 T^{9} - 24957765241 T^{10} + 59871697926 T^{11} + 1422456958120 T^{12} - 3689390622401 T^{13} - 56882464591914 T^{14} + 134427362903113 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( 1 - 15 T - 58 T^{2} + 2180 T^{3} - 7802 T^{4} - 148865 T^{5} + 1559169 T^{6} + 5584500 T^{7} - 169067020 T^{8} + 441175500 T^{9} + 9730773729 T^{10} - 73396250735 T^{11} - 303888531962 T^{12} + 6707982949820 T^{13} - 14099072420218 T^{14} - 288058634792385 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 20 T - 26 T^{2} - 3900 T^{3} - 29155 T^{4} + 347300 T^{5} + 6752970 T^{6} + 1986700 T^{7} - 796980480 T^{8} - 5624999100 T^{9} + 44951710692 T^{10} + 864380570440 T^{11} + 1361154199023 T^{12} - 70535599976700 T^{13} - 564113457968440 T^{14} + 2384852381457900 T^{15} + 60762066594476935 T^{16} + 188403338135174100 T^{17} - 3520632091181034040 T^{18} - 34776801676912191300 T^{19} + 53017066305435970863 T^{20} + \)\(26\!\cdots\!60\)\( T^{21} + \)\(10\!\cdots\!32\)\( T^{22} - \)\(10\!\cdots\!00\)\( T^{23} - \)\(12\!\cdots\!80\)\( T^{24} + \)\(23\!\cdots\!00\)\( T^{25} + \)\(63\!\cdots\!70\)\( T^{26} + \)\(25\!\cdots\!00\)\( T^{27} - \)\(17\!\cdots\!55\)\( T^{28} - \)\(18\!\cdots\!00\)\( T^{29} - \)\(95\!\cdots\!06\)\( T^{30} + \)\(58\!\cdots\!80\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 116 T^{2} - 854 T^{4} + 212048 T^{6} + 81847123 T^{8} + 1323391568 T^{10} - 33263369174 T^{12} + 28198144840436 T^{14} + 1517108809906561 T^{16} )^{2} \))(\( 1 + 260 T^{2} + 23724 T^{4} + 1706392 T^{6} + 225017642 T^{8} + 14869625148 T^{10} - 181450880816 T^{12} - 19987311435172 T^{14} + 2160188956785123 T^{16} - 124740810666908452 T^{18} - 7067526505304546096 T^{20} + \)\(36\!\cdots\!08\)\( T^{22} + \)\(34\!\cdots\!62\)\( T^{24} + \)\(16\!\cdots\!92\)\( T^{26} + \)\(14\!\cdots\!84\)\( T^{28} + \)\(95\!\cdots\!60\)\( T^{30} + \)\(23\!\cdots\!21\)\( T^{32} \))
$83$ (\( 1 + 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 154 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 + 15 T - 51 T^{2} - 678 T^{3} + 17133 T^{4} + 80979 T^{5} - 925778 T^{6} + 6721257 T^{7} + 118029237 T^{8} - 387671586 T^{9} - 2420374371 T^{10} + 59085609645 T^{11} + 326940373369 T^{12} \))(\( 1 + 30 T + 280 T^{2} + 1770 T^{3} + 42079 T^{4} + 523485 T^{5} + 2681215 T^{6} + 35481675 T^{7} + 533008645 T^{8} + 2944979025 T^{9} + 18470890135 T^{10} + 299321917695 T^{11} + 1996998689359 T^{12} + 6972101938110 T^{13} + 91543304543320 T^{14} + 814081529688810 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 160 T^{2} + 5929 T^{4} - 942880 T^{6} + 163131520 T^{8} - 6495500320 T^{10} + 281380385209 T^{12} - 52310459739040 T^{14} + 2252292232139041 T^{16} \))(\( 1 - 30 T + 280 T^{2} - 1770 T^{3} + 42079 T^{4} - 523485 T^{5} + 2681215 T^{6} - 35481675 T^{7} + 533008645 T^{8} - 2944979025 T^{9} + 18470890135 T^{10} - 299321917695 T^{11} + 1996998689359 T^{12} - 6972101938110 T^{13} + 91543304543320 T^{14} - 814081529688810 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 8722 T^{4} + 47458321 T^{8} \))(\( ( 1 + 11822 T^{4} + 47458321 T^{8} )^{2} \))(\( 1 - 18 T + 41 T^{2} + 1416 T^{3} - 18731 T^{4} + 117528 T^{5} + 282449 T^{6} - 10292166 T^{7} + 47458321 T^{8} \))(\( 1 + 9 T - 52 T^{2} - 675 T^{3} + 121 T^{4} - 56025 T^{5} - 358228 T^{6} + 5146083 T^{7} + 47458321 T^{8} \))(\( 1 + 2 T - 123 T^{2} + 626 T^{3} + 1416 T^{4} - 170328 T^{5} + 1146775 T^{6} + 9202888 T^{7} - 131919081 T^{8} + 763839704 T^{9} + 7900132975 T^{10} - 97391336136 T^{11} + 67200982536 T^{12} + 2465839442518 T^{13} - 40213665924387 T^{14} + 54272101979254 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 10 T - 32 T^{2} + 586 T^{3} + 7028 T^{4} - 84104 T^{5} - 240235 T^{6} + 5165580 T^{7} + 16282512 T^{8} - 55940648 T^{9} - 5964955348 T^{10} + 18358343086 T^{11} + 292581600901 T^{12} + 1523742476138 T^{13} - 41092577392372 T^{14} - 31986135297976 T^{15} + 772740681182352 T^{16} + 20347429564667940 T^{17} - 78542520596301715 T^{18} - 2282250432431589208 T^{19} + 15829109807473180148 T^{20} + \)\(10\!\cdots\!58\)\( T^{21} - \)\(49\!\cdots\!68\)\( T^{22} - \)\(12\!\cdots\!70\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 152 T^{2} + 24675 T^{4} - 2817320 T^{6} + 356430460 T^{8} - 31958826416 T^{10} + 3318429986817 T^{12} - 268566824475880 T^{14} + 24918932909158855 T^{16} - 1850156853814337320 T^{18} + \)\(15\!\cdots\!57\)\( T^{20} - \)\(10\!\cdots\!04\)\( T^{22} + \)\(80\!\cdots\!60\)\( T^{24} - \)\(43\!\cdots\!80\)\( T^{26} + \)\(26\!\cdots\!75\)\( T^{28} - \)\(11\!\cdots\!08\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 85 T^{2} + 336 T^{4} + 585565 T^{6} + 47458321 T^{8} \))(\( 1 + 327 T^{2} + 57207 T^{4} + 6488176 T^{6} + 532197333 T^{8} + 34415866233 T^{10} + 2415401371734 T^{12} + 237090902479137 T^{14} + 25257191864857893 T^{16} + 2121246683923784944 T^{18} + \)\(12\!\cdots\!87\)\( T^{20} + \)\(50\!\cdots\!23\)\( T^{22} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 340 T^{2} + 56358 T^{4} + 5615330 T^{6} + 356102531 T^{8} + 15268102785 T^{10} + 850761191503 T^{12} + 106079060220415 T^{14} + 11086543633870179 T^{16} + 730778645858438935 T^{18} + 40375697720691846463 T^{20} + \)\(49\!\cdots\!65\)\( T^{22} + \)\(80\!\cdots\!71\)\( T^{24} + \)\(87\!\cdots\!70\)\( T^{26} + \)\(60\!\cdots\!38\)\( T^{28} + \)\(25\!\cdots\!60\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 45 T + 1115 T^{2} - 19890 T^{3} + 284376 T^{4} - 3450645 T^{5} + 37197280 T^{6} - 367888080 T^{7} + 3431240591 T^{8} - 30534710640 T^{9} + 256252061920 T^{10} - 1973033952615 T^{11} + 13496007492696 T^{12} - 78347518389270 T^{13} + 364538516306435 T^{14} - 1221122294533215 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 10 T + 202 T^{2} - 1560 T^{3} - 11179 T^{4} - 496950 T^{5} + 1018034 T^{6} - 15276030 T^{7} + 550764400 T^{8} - 1724892540 T^{9} + 40801859152 T^{10} - 455708099560 T^{11} + 3046921596515 T^{12} - 45917600363320 T^{13} + 368604392570920 T^{14} - 3224407333551250 T^{15} + 38409379558310191 T^{16} - 267625808684753750 T^{17} + 2539315660421067880 T^{18} - 26255086958941652840 T^{19} + \)\(14\!\cdots\!15\)\( T^{20} - \)\(17\!\cdots\!80\)\( T^{21} + \)\(13\!\cdots\!88\)\( T^{22} - \)\(46\!\cdots\!80\)\( T^{23} + \)\(12\!\cdots\!00\)\( T^{24} - \)\(28\!\cdots\!90\)\( T^{25} + \)\(15\!\cdots\!66\)\( T^{26} - \)\(63\!\cdots\!50\)\( T^{27} - \)\(11\!\cdots\!19\)\( T^{28} - \)\(13\!\cdots\!80\)\( T^{29} + \)\(14\!\cdots\!58\)\( T^{30} + \)\(61\!\cdots\!70\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 922 T^{4} - 40638479 T^{8} + 49260688838 T^{12} - 571334931683036 T^{16} + 2337829583554920998 T^{20} - \)\(91\!\cdots\!39\)\( T^{24} - \)\(98\!\cdots\!42\)\( T^{28} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 66 T + 2178 T^{2} - 47916 T^{3} + 791830 T^{4} - 10596156 T^{5} + 122712084 T^{6} - 1311937572 T^{7} + 13564902253 T^{8} - 136924099746 T^{9} + 1327585690602 T^{10} - 12258029803398 T^{11} + 109901521003222 T^{12} - 994600086849090 T^{13} + 9293464416138048 T^{14} - 88105947208965780 T^{15} + 817933709355268336 T^{16} - 7312793618344159740 T^{17} + 64022676362775012672 T^{18} - \)\(56\!\cdots\!30\)\( T^{19} + \)\(52\!\cdots\!62\)\( T^{20} - \)\(48\!\cdots\!14\)\( T^{21} + \)\(43\!\cdots\!38\)\( T^{22} - \)\(37\!\cdots\!42\)\( T^{23} + \)\(30\!\cdots\!73\)\( T^{24} - \)\(24\!\cdots\!16\)\( T^{25} + \)\(19\!\cdots\!16\)\( T^{26} - \)\(13\!\cdots\!52\)\( T^{27} + \)\(84\!\cdots\!30\)\( T^{28} - \)\(42\!\cdots\!08\)\( T^{29} + \)\(16\!\cdots\!62\)\( T^{30} - \)\(40\!\cdots\!62\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 3 T + 89 T^{2} )^{6} \))(\( ( 1 + 9 T + 257 T^{2} + 1998 T^{3} + 31929 T^{4} + 177822 T^{5} + 2035697 T^{6} + 6344721 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 - 6 T + 79 T^{2} - 534 T^{3} + 7921 T^{4} )^{4} \))(\( ( 1 + 9 T + 257 T^{2} + 1998 T^{3} + 31929 T^{4} + 177822 T^{5} + 2035697 T^{6} + 6344721 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 16 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 106 T^{2} + 7921 T^{4} )^{4} \))(\( 1 - 9 T - 43 T^{2} + 993 T^{3} - 4460 T^{4} + 88377 T^{5} - 340603 T^{6} - 6344721 T^{7} + 62742241 T^{8} \))(\( 1 - 20 T + 151 T^{2} - 1600 T^{3} + 21441 T^{4} - 142400 T^{5} + 1196071 T^{6} - 14099380 T^{7} + 62742241 T^{8} \))(\( 1 + 77 T^{2} - 700 T^{3} + 12658 T^{4} - 121100 T^{5} + 1037049 T^{6} - 10883950 T^{7} + 150329955 T^{8} - 968671550 T^{9} + 8214465129 T^{10} - 85371745900 T^{11} + 794191286578 T^{12} - 3908841614300 T^{13} + 38267559403997 T^{14} + 3936588805702081 T^{16} \))(\( 1 + 57 T + 1416 T^{2} + 19412 T^{3} + 146681 T^{4} + 436608 T^{5} + 1888 T^{6} + 50698623 T^{7} + 1130538888 T^{8} + 10860338043 T^{9} + 55652919649 T^{10} + 136415194025 T^{11} + 148330818154 T^{12} + 12140952268225 T^{13} + 440826776539729 T^{14} + 7656201649835667 T^{15} + 70932543370768008 T^{16} + 283104124814438727 T^{17} + 938300677334368 T^{18} + 19311754666067125632 T^{19} + \)\(57\!\cdots\!61\)\( T^{20} + \)\(68\!\cdots\!08\)\( T^{21} + \)\(44\!\cdots\!16\)\( T^{22} + \)\(15\!\cdots\!73\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 94 T^{2} - 1665 T^{4} + 1016470 T^{6} + 167043310 T^{8} + 4324962352 T^{10} + 640161517323 T^{12} + 105517486987430 T^{14} + 7276045289401435 T^{16} + 835804014427433030 T^{18} + 40165168198805340843 T^{20} + \)\(21\!\cdots\!72\)\( T^{22} + \)\(65\!\cdots\!10\)\( T^{24} + \)\(31\!\cdots\!70\)\( T^{26} - \)\(41\!\cdots\!65\)\( T^{28} + \)\(18\!\cdots\!54\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 15 T + 89 T^{2} )^{4} \))(\( ( 1 - 3 T + 89 T^{2} )^{12} \))(\( ( 1 - 9 T + 257 T^{2} - 1998 T^{3} + 31929 T^{4} - 177822 T^{5} + 2035697 T^{6} - 6344721 T^{7} + 62742241 T^{8} )^{4} \))(\( 1 - 25 T + 342 T^{2} - 5000 T^{3} + 78868 T^{4} - 928525 T^{5} + 9098049 T^{6} - 101226750 T^{7} + 1076434080 T^{8} - 9009180750 T^{9} + 72065646129 T^{10} - 654581340725 T^{11} + 4948355063188 T^{12} - 27920297245000 T^{13} + 169967601508662 T^{14} - 1105783372388225 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 18 T - 288 T^{2} - 7264 T^{3} + 14783 T^{4} + 1100918 T^{5} + 4764016 T^{6} - 40139780 T^{7} - 746571076 T^{8} - 9051008048 T^{9} + 13821315872 T^{10} + 1302515170094 T^{11} + 4134501893785 T^{12} - 64272919989494 T^{13} - 170401937947852 T^{14} + 989839747535702 T^{15} - 10684112304900357 T^{16} + 88095737530677478 T^{17} - 1349753750484935692 T^{18} - 45310416132073595686 T^{19} + \)\(25\!\cdots\!85\)\( T^{20} + \)\(72\!\cdots\!06\)\( T^{21} + \)\(68\!\cdots\!92\)\( T^{22} - \)\(40\!\cdots\!92\)\( T^{23} - \)\(29\!\cdots\!56\)\( T^{24} - \)\(14\!\cdots\!20\)\( T^{25} + \)\(14\!\cdots\!16\)\( T^{26} + \)\(30\!\cdots\!02\)\( T^{27} + \)\(36\!\cdots\!43\)\( T^{28} - \)\(15\!\cdots\!16\)\( T^{29} - \)\(56\!\cdots\!08\)\( T^{30} + \)\(31\!\cdots\!82\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 158 T^{2} + 14307 T^{4} + 1251518 T^{6} + 62742241 T^{8} )^{4} \))(\( ( 1 + 412 T^{2} + 69850 T^{4} + 6725680 T^{6} + 546021283 T^{8} + 53274111280 T^{10} + 4382545533850 T^{12} + 204756291875932 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( 1 - 17 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 95 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 - 2 T - 93 T^{2} - 194 T^{3} + 9409 T^{4} \))(\( 1 + 18 T + 69 T^{2} + 214 T^{3} + 906 T^{4} - 163158 T^{5} - 2743251 T^{6} - 15826326 T^{7} + 8524554 T^{8} + 195312022 T^{9} + 6108520389 T^{10} + 154572124626 T^{11} + 832972004929 T^{12} \))(\( 1 - 19 T - 108 T^{2} + 1825 T^{3} + 46754 T^{4} - 332118 T^{5} - 5651993 T^{6} + 4946342 T^{7} + 777287673 T^{8} + 479795174 T^{9} - 53179602137 T^{10} - 303115131414 T^{11} + 4139098003874 T^{12} + 15671895969025 T^{13} - 89960976532332 T^{14} - 1535167405084147 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 52 T^{2} - 12902 T^{4} + 167024 T^{6} + 129576019 T^{8} + 1571528816 T^{10} - 1142204783462 T^{12} - 43314544256308 T^{14} + 7837433594376961 T^{16} \))(\( 1 + 19 T - 108 T^{2} - 1825 T^{3} + 46754 T^{4} + 332118 T^{5} - 5651993 T^{6} - 4946342 T^{7} + 777287673 T^{8} - 479795174 T^{9} - 53179602137 T^{10} + 303115131414 T^{11} + 4139098003874 T^{12} - 15671895969025 T^{13} - 89960976532332 T^{14} + 1535167405084147 T^{15} + 7837433594376961 T^{16} \))(\( ( 1 - 22 T + 242 T^{2} - 2134 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 16609 T^{4} + 88529281 T^{8} )^{2} \))(\( 1 - 2 T - 33 T^{2} - 820 T^{3} + 10061 T^{4} - 79540 T^{5} - 310497 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 - 8 T - 63 T^{2} + 20 T^{3} + 9821 T^{4} + 1940 T^{5} - 592767 T^{6} - 7301384 T^{7} + 88529281 T^{8} \))(\( 1 + 6 T - 187 T^{2} - 1878 T^{3} + 3816 T^{4} + 286836 T^{5} + 2735335 T^{6} - 15219804 T^{7} - 421030321 T^{8} - 1476320988 T^{9} + 25736767015 T^{10} + 261787472628 T^{11} + 337827736296 T^{12} - 16127025002646 T^{13} - 155765764921723 T^{14} + 484789706868678 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 4 T - 152 T^{2} - 258 T^{3} + 15244 T^{4} + 16576 T^{5} - 519489 T^{6} - 1347552 T^{7} - 32374768 T^{8} + 207718764 T^{9} + 20086873388 T^{10} - 47224426932 T^{11} - 2473927275691 T^{12} - 4580769412404 T^{13} + 188997391707692 T^{14} + 189579307496172 T^{15} - 2866114933581808 T^{16} - 11571887538000864 T^{17} - 432719793868561281 T^{18} + 1339312363509201088 T^{19} + \)\(11\!\cdots\!84\)\( T^{20} - \)\(19\!\cdots\!86\)\( T^{21} - \)\(11\!\cdots\!48\)\( T^{22} - \)\(28\!\cdots\!12\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 20 T + 291 T^{2} - 4700 T^{3} + 64912 T^{4} - 730280 T^{5} + 8764653 T^{6} - 95559100 T^{7} + 946211815 T^{8} - 9269232700 T^{9} + 82466620077 T^{10} - 666506838440 T^{11} + 5746612688272 T^{12} - 40360499207900 T^{13} + 242394853434339 T^{14} - 1615965689562260 T^{15} + 7837433594376961 T^{16} )^{2} \))(\( 1 + 190 T^{2} + 26691 T^{4} + 1787710 T^{6} + 88529281 T^{8} \))(\( 1 + 186 T^{2} - 1131 T^{4} - 466418 T^{6} + 278880666 T^{8} + 18455439810 T^{10} - 762781062579 T^{12} + 173647233172290 T^{14} + 24689104845781146 T^{16} - 388513136594974322 T^{18} - 8864137395240342891 T^{20} + \)\(13\!\cdots\!14\)\( T^{22} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 + 577 T^{2} + 174522 T^{4} + 37353959 T^{6} + 6361534046 T^{8} + 912884200698 T^{10} + 114408541714153 T^{12} + 12837001127592472 T^{14} + 1305837592754805081 T^{16} + \)\(12\!\cdots\!48\)\( T^{18} + \)\(10\!\cdots\!93\)\( T^{20} + \)\(76\!\cdots\!42\)\( T^{22} + \)\(49\!\cdots\!06\)\( T^{24} + \)\(27\!\cdots\!91\)\( T^{26} + \)\(12\!\cdots\!02\)\( T^{28} + \)\(37\!\cdots\!13\)\( T^{30} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 60 T + 1830 T^{2} + 35660 T^{3} + 467711 T^{4} + 3770460 T^{5} + 6583460 T^{6} - 292271720 T^{7} - 4451764059 T^{8} - 28350356840 T^{9} + 61943775140 T^{10} + 3441197039580 T^{11} + 41406118545791 T^{12} + 306224553564620 T^{13} + 1524338769020070 T^{14} + 4847897068686780 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 40 T + 1170 T^{2} - 28840 T^{3} + 597037 T^{4} - 11124280 T^{5} + 188742510 T^{6} - 2956583740 T^{7} + 43370532748 T^{8} - 598437364480 T^{9} + 7830452653220 T^{10} - 97502185336460 T^{11} + 1158651974029219 T^{12} - 13184566116562660 T^{13} + 143770204308646900 T^{14} - 1504531362263433880 T^{15} + 15122407401217954415 T^{16} - \)\(14\!\cdots\!60\)\( T^{17} + \)\(13\!\cdots\!00\)\( T^{18} - \)\(12\!\cdots\!80\)\( T^{19} + \)\(10\!\cdots\!39\)\( T^{20} - \)\(83\!\cdots\!20\)\( T^{21} + \)\(65\!\cdots\!80\)\( T^{22} - \)\(48\!\cdots\!40\)\( T^{23} + \)\(33\!\cdots\!28\)\( T^{24} - \)\(22\!\cdots\!80\)\( T^{25} + \)\(13\!\cdots\!90\)\( T^{26} - \)\(79\!\cdots\!40\)\( T^{27} + \)\(41\!\cdots\!17\)\( T^{28} - \)\(19\!\cdots\!80\)\( T^{29} + \)\(76\!\cdots\!30\)\( T^{30} - \)\(25\!\cdots\!20\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 21116 T^{4} + 182916106 T^{8} + 1814092199408 T^{12} + 21841526617008403 T^{16} + \)\(16\!\cdots\!48\)\( T^{20} + \)\(14\!\cdots\!66\)\( T^{24} + \)\(14\!\cdots\!56\)\( T^{28} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 28 T + 392 T^{2} - 872 T^{3} - 117924 T^{4} - 2250436 T^{5} - 16405808 T^{6} + 121301108 T^{7} + 5089087514 T^{8} + 63345173552 T^{9} + 270560580248 T^{10} - 4797083097932 T^{11} - 105427115995440 T^{12} - 964302703147436 T^{13} - 1291090828127400 T^{14} + 85355358908186064 T^{15} + 1288991316725561923 T^{16} + 8279469814094048208 T^{17} - 12147873601850706600 T^{18} - \)\(88\!\cdots\!28\)\( T^{19} - \)\(93\!\cdots\!40\)\( T^{20} - \)\(41\!\cdots\!24\)\( T^{21} + \)\(22\!\cdots\!92\)\( T^{22} + \)\(51\!\cdots\!76\)\( T^{23} + \)\(39\!\cdots\!54\)\( T^{24} + \)\(92\!\cdots\!36\)\( T^{25} - \)\(12\!\cdots\!92\)\( T^{26} - \)\(16\!\cdots\!08\)\( T^{27} - \)\(81\!\cdots\!84\)\( T^{28} - \)\(58\!\cdots\!44\)\( T^{29} + \)\(25\!\cdots\!48\)\( T^{30} + \)\(17\!\cdots\!04\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))
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