Properties

Label 175.4
Level 175
Weight 4
Dimension 3077
Nonzero newspaces 12
Newform subspaces 46
Sturm bound 9600
Trace bound 2

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Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 46 \)
Sturm bound: \(9600\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(175))\).

Total New Old
Modular forms 3768 3281 487
Cusp forms 3432 3077 355
Eisenstein series 336 204 132

Trace form

\( 3077q - 35q^{2} - 17q^{3} + 13q^{4} - 38q^{5} - 26q^{6} + 7q^{7} - 85q^{8} - 153q^{9} + O(q^{10}) \) \( 3077q - 35q^{2} - 17q^{3} + 13q^{4} - 38q^{5} - 26q^{6} + 7q^{7} - 85q^{8} - 153q^{9} + 12q^{10} + 101q^{11} + 90q^{12} - 168q^{13} - 53q^{14} - 96q^{15} + 289q^{16} + 803q^{17} + 1231q^{18} + 465q^{19} - 388q^{20} - 489q^{21} - 2016q^{22} - 1001q^{23} - 1202q^{24} - 746q^{25} + 1488q^{26} + 118q^{27} + 307q^{28} - 598q^{29} - 476q^{30} - 927q^{31} - 1105q^{32} - 1629q^{33} - 510q^{34} - 432q^{35} - 4227q^{36} - 363q^{37} + 1264q^{38} + 2922q^{39} + 3784q^{40} + 2250q^{41} + 4124q^{42} + 2860q^{43} + 3760q^{44} - 1702q^{45} + 1758q^{46} - 2785q^{47} - 7710q^{48} - 1659q^{49} - 9096q^{50} - 5457q^{51} - 7528q^{52} - 3803q^{53} - 802q^{54} + 1516q^{55} + 10121q^{56} + 11126q^{57} + 16094q^{58} + 13435q^{59} + 25412q^{60} + 5901q^{61} + 20020q^{62} + 3049q^{63} + 2817q^{64} + 334q^{65} - 14194q^{66} - 13219q^{67} - 24822q^{68} - 22346q^{69} - 16658q^{70} - 11460q^{71} - 40821q^{72} - 19821q^{73} - 32180q^{74} - 15512q^{75} - 14758q^{76} - 6723q^{77} - 10168q^{78} + 2639q^{79} - 6512q^{80} + 15264q^{81} + 33310q^{82} + 26402q^{83} + 45328q^{84} + 27402q^{85} + 40856q^{86} + 42638q^{87} + 61424q^{88} + 32013q^{89} + 29040q^{90} + 8202q^{91} + 23324q^{92} - 5549q^{93} - 14094q^{94} - 15012q^{95} - 21166q^{96} - 32894q^{97} - 25153q^{98} - 40980q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.4.a \(\chi_{175}(1, \cdot)\) 175.4.a.a 1 1
175.4.a.b 1
175.4.a.c 2
175.4.a.d 2
175.4.a.e 2
175.4.a.f 3
175.4.a.g 4
175.4.a.h 4
175.4.a.i 5
175.4.a.j 5
175.4.b \(\chi_{175}(99, \cdot)\) 175.4.b.a 2 1
175.4.b.b 2
175.4.b.c 4
175.4.b.d 4
175.4.b.e 6
175.4.b.f 8
175.4.e \(\chi_{175}(51, \cdot)\) 175.4.e.a 2 2
175.4.e.b 2
175.4.e.c 4
175.4.e.d 10
175.4.e.e 16
175.4.e.f 16
175.4.e.g 20
175.4.f \(\chi_{175}(118, \cdot)\) 175.4.f.a 4 2
175.4.f.b 4
175.4.f.c 4
175.4.f.d 4
175.4.f.e 4
175.4.f.f 8
175.4.f.g 16
175.4.f.h 24
175.4.h \(\chi_{175}(36, \cdot)\) 175.4.h.a 88 4
175.4.h.b 88
175.4.k \(\chi_{175}(74, \cdot)\) 175.4.k.a 4 2
175.4.k.b 4
175.4.k.c 8
175.4.k.d 20
175.4.k.e 32
175.4.n \(\chi_{175}(29, \cdot)\) 175.4.n.a 184 4
175.4.o \(\chi_{175}(68, \cdot)\) 175.4.o.a 32 4
175.4.o.b 40
175.4.o.c 64
175.4.q \(\chi_{175}(11, \cdot)\) 175.4.q.a 464 8
175.4.s \(\chi_{175}(13, \cdot)\) 175.4.s.a 464 8
175.4.t \(\chi_{175}(4, \cdot)\) 175.4.t.a 464 8
175.4.x \(\chi_{175}(3, \cdot)\) 175.4.x.a 928 16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 8 T^{2} \))(\( 1 - T + 8 T^{2} \))(\( 1 + 8 T + 30 T^{2} + 64 T^{3} + 64 T^{4} \))(\( 1 + T + 6 T^{2} + 8 T^{3} + 64 T^{4} \))(\( 1 - T + 6 T^{2} - 8 T^{3} + 64 T^{4} \))(\( 1 - 3 T + 10 T^{2} - 18 T^{3} + 80 T^{4} - 192 T^{5} + 512 T^{6} \))(\( 1 + 4 T + 6 T^{2} + T^{3} + 22 T^{4} + 8 T^{5} + 384 T^{6} + 2048 T^{7} + 4096 T^{8} \))(\( 1 - 4 T + 6 T^{2} - T^{3} + 22 T^{4} - 8 T^{5} + 384 T^{6} - 2048 T^{7} + 4096 T^{8} \))(\( 1 + 4 T + 19 T^{2} + 58 T^{3} + 190 T^{4} + 576 T^{5} + 1520 T^{6} + 3712 T^{7} + 9728 T^{8} + 16384 T^{9} + 32768 T^{10} \))(\( 1 - 4 T + 19 T^{2} - 58 T^{3} + 190 T^{4} - 576 T^{5} + 1520 T^{6} - 3712 T^{7} + 9728 T^{8} - 16384 T^{9} + 32768 T^{10} \))(\( 1 - 15 T^{2} + 64 T^{4} \))(\( 1 - 15 T^{2} + 64 T^{4} \))(\( 1 + 4 T^{2} + 4 T^{4} + 256 T^{6} + 4096 T^{8} \))(\( 1 - 11 T^{2} + 148 T^{4} - 704 T^{6} + 4096 T^{8} \))(\( 1 - 11 T^{2} + 152 T^{4} - 1148 T^{6} + 9728 T^{8} - 45056 T^{10} + 262144 T^{12} \))(\( 1 + 4 T^{2} + 72 T^{4} - 967 T^{6} - 3116 T^{8} - 61888 T^{10} + 294912 T^{12} + 1048576 T^{14} + 16777216 T^{16} \))(\( 1 - 2 T - 4 T^{2} - 16 T^{3} + 64 T^{4} \))(\( 1 - 3 T + T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 42 T^{3} + 177 T^{4} + 336 T^{5} + 832 T^{6} + 3072 T^{7} + 4096 T^{8} \))(\( 1 - T - 2 T^{2} + 19 T^{3} - 42 T^{4} + 63 T^{5} + 657 T^{6} - 1560 T^{7} + 688 T^{8} + 12224 T^{9} - 47936 T^{10} + 97792 T^{11} + 44032 T^{12} - 798720 T^{13} + 2691072 T^{14} + 2064384 T^{15} - 11010048 T^{16} + 39845888 T^{17} - 33554432 T^{18} - 134217728 T^{19} + 1073741824 T^{20} \))(\( 1 + T - 18 T^{2} - 41 T^{3} + 133 T^{4} + 615 T^{5} - 443 T^{6} - 5196 T^{7} - 2836 T^{8} + 24118 T^{9} + 41437 T^{10} - 48746 T^{11} - 119020 T^{12} - 246928 T^{13} - 506480 T^{14} + 1978496 T^{15} + 8495424 T^{16} + 15827968 T^{17} - 32414720 T^{18} - 126427136 T^{19} - 487505920 T^{20} - 1597308928 T^{21} + 10862460928 T^{22} + 50579111936 T^{23} - 47580184576 T^{24} - 697395314688 T^{25} - 475667628032 T^{26} + 5282809774080 T^{27} + 9139690405888 T^{28} - 22539988369408 T^{29} - 79164837199872 T^{30} + 35184372088832 T^{31} + 281474976710656 T^{32} \))(\( 1 - T - 18 T^{2} + 41 T^{3} + 133 T^{4} - 615 T^{5} - 443 T^{6} + 5196 T^{7} - 2836 T^{8} - 24118 T^{9} + 41437 T^{10} + 48746 T^{11} - 119020 T^{12} + 246928 T^{13} - 506480 T^{14} - 1978496 T^{15} + 8495424 T^{16} - 15827968 T^{17} - 32414720 T^{18} + 126427136 T^{19} - 487505920 T^{20} + 1597308928 T^{21} + 10862460928 T^{22} - 50579111936 T^{23} - 47580184576 T^{24} + 697395314688 T^{25} - 475667628032 T^{26} - 5282809774080 T^{27} + 9139690405888 T^{28} + 22539988369408 T^{29} - 79164837199872 T^{30} - 35184372088832 T^{31} + 281474976710656 T^{32} \))(\( 1 - 25 T^{2} + 258 T^{4} - 33 T^{6} - 25502 T^{8} + 235267 T^{10} + 345717 T^{12} - 20966068 T^{14} + 119154704 T^{16} + 842590720 T^{18} - 14784910336 T^{20} + 53925806080 T^{22} + 488057667584 T^{24} - 5496128929792 T^{26} + 5800168783872 T^{28} + 252616017707008 T^{30} - 1752484095721472 T^{32} - 145135534866432 T^{34} + 72620543991349248 T^{36} - 450359962737049600 T^{38} + 1152921504606846976 T^{40} \))(\( ( 1 + 6 T + 18 T^{2} + 48 T^{3} + 64 T^{4} )^{2} \))(\( 1 - 47 T^{4} + 4096 T^{8} \))(\( ( 1 - 4 T + 8 T^{2} )^{2}( 1 + 4 T + 8 T^{2} )^{2} \))(\( ( 1 - 4 T + 8 T^{2} - 32 T^{3} + 64 T^{4} )^{2} \))(\( ( 1 - 6 T + 18 T^{2} - 48 T^{3} + 64 T^{4} )^{2} \))(\( 1 + 47 T^{4} - 1887 T^{8} + 192512 T^{12} + 16777216 T^{16} \))(\( ( 1 + 2 T + 2 T^{2} + 36 T^{3} + 69 T^{4} - 30 T^{5} + 450 T^{6} + 1060 T^{7} - 2140 T^{8} + 8480 T^{9} + 28800 T^{10} - 15360 T^{11} + 282624 T^{12} + 1179648 T^{13} + 524288 T^{14} + 4194304 T^{15} + 16777216 T^{16} )^{2} \))(\( 1 + 12 T^{2} + 80 T^{4} + 768 T^{6} + 4096 T^{8} \))(\( 1 + 7 T^{2} - 15 T^{4} + 448 T^{6} + 4096 T^{8} \))(\( 1 + 10 T^{2} + 19 T^{4} - 470 T^{6} - 3935 T^{8} - 30080 T^{10} + 77824 T^{12} + 2621440 T^{14} + 16777216 T^{16} \))(\( 1 + 5 T^{2} - 42 T^{4} - 1247 T^{6} - 5002 T^{8} + 74053 T^{10} + 581297 T^{12} - 849312 T^{14} - 38700416 T^{16} - 348160 T^{18} + 2175545344 T^{20} - 22282240 T^{22} - 158516903936 T^{24} - 222642044928 T^{26} + 9752545329152 T^{28} + 79513803292672 T^{30} - 343734822633472 T^{32} - 5484363999346688 T^{34} - 11821949021847552 T^{36} + 90071992547409920 T^{38} + 1152921504606846976 T^{40} \))
$3$ (\( 1 - 8 T + 27 T^{2} \))(\( 1 - 2 T + 27 T^{2} \))(\( 1 + 2 T + 23 T^{2} + 54 T^{3} + 729 T^{4} \))(\( 1 - 5 T + 50 T^{2} - 135 T^{3} + 729 T^{4} \))(\( 1 + 5 T + 50 T^{2} + 135 T^{3} + 729 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 40 T^{3} + 54 T^{4} + 1458 T^{5} + 19683 T^{6} \))(\( 1 - 3 T + 28 T^{2} - 195 T^{3} + 1150 T^{4} - 5265 T^{5} + 20412 T^{6} - 59049 T^{7} + 531441 T^{8} \))(\( 1 + 3 T + 28 T^{2} + 195 T^{3} + 1150 T^{4} + 5265 T^{5} + 20412 T^{6} + 59049 T^{7} + 531441 T^{8} \))(\( 1 + 10 T + 106 T^{2} + 748 T^{3} + 5191 T^{4} + 27220 T^{5} + 140157 T^{6} + 545292 T^{7} + 2086398 T^{8} + 5314410 T^{9} + 14348907 T^{10} \))(\( 1 - 10 T + 106 T^{2} - 748 T^{3} + 5191 T^{4} - 27220 T^{5} + 140157 T^{6} - 545292 T^{7} + 2086398 T^{8} - 5314410 T^{9} + 14348907 T^{10} \))(\( 1 + 10 T^{2} + 729 T^{4} \))(\( 1 - 50 T^{2} + 729 T^{4} \))(\( 1 - 42 T^{2} + 1771 T^{4} - 30618 T^{6} + 531441 T^{8} \))(\( 1 - 75 T^{2} + 2608 T^{4} - 54675 T^{6} + 531441 T^{8} \))(\( 1 - 48 T^{4} - 32150 T^{6} - 34992 T^{8} + 387420489 T^{12} \))(\( 1 - 47 T^{2} + 1914 T^{4} - 35609 T^{6} + 1120810 T^{8} - 25958961 T^{10} + 1017178074 T^{12} - 18208762983 T^{14} + 282429536481 T^{16} \))(\( 1 - 7 T + 22 T^{2} - 189 T^{3} + 729 T^{4} \))(\( 1 + 2 T - 23 T^{2} + 54 T^{3} + 729 T^{4} \))(\( 1 + 2 T - 33 T^{2} - 34 T^{3} + 532 T^{4} - 918 T^{5} - 24057 T^{6} + 39366 T^{7} + 531441 T^{8} \))(\( 1 + 8 T + 5 T^{2} - 332 T^{3} - 2600 T^{4} - 7952 T^{5} + 33919 T^{6} + 391568 T^{7} + 1475571 T^{8} - 3518628 T^{9} - 49970576 T^{10} - 95002956 T^{11} + 1075691259 T^{12} + 7707232944 T^{13} + 18025947279 T^{14} - 114102508464 T^{15} - 1007293271400 T^{16} - 3472837263396 T^{17} + 1412147682405 T^{18} + 61004779879896 T^{19} + 205891132094649 T^{20} \))(\( 1 - 6 T - 69 T^{2} + 514 T^{3} + 2419 T^{4} - 26582 T^{5} - 29586 T^{6} + 938022 T^{7} - 1159244 T^{8} - 27164430 T^{9} + 91695880 T^{10} + 692985440 T^{11} - 4031260012 T^{12} - 14195761608 T^{13} + 140868806033 T^{14} + 154368510422 T^{15} - 4199229772643 T^{16} + 4167949781394 T^{17} + 102693359598057 T^{18} - 279415175730264 T^{19} - 2142376852037292 T^{20} + 9943583630914080 T^{21} + 35524862668885320 T^{22} - 284149532358169290 T^{23} - 327404745588380364 T^{24} + 7152978204062475714 T^{25} - 6091495034152285314 T^{26} - \)\(14\!\cdots\!86\)\( T^{27} + \)\(36\!\cdots\!99\)\( T^{28} + \)\(20\!\cdots\!38\)\( T^{29} - \)\(75\!\cdots\!21\)\( T^{30} - \)\(17\!\cdots\!58\)\( T^{31} + \)\(79\!\cdots\!61\)\( T^{32} \))(\( 1 + 6 T - 69 T^{2} - 514 T^{3} + 2419 T^{4} + 26582 T^{5} - 29586 T^{6} - 938022 T^{7} - 1159244 T^{8} + 27164430 T^{9} + 91695880 T^{10} - 692985440 T^{11} - 4031260012 T^{12} + 14195761608 T^{13} + 140868806033 T^{14} - 154368510422 T^{15} - 4199229772643 T^{16} - 4167949781394 T^{17} + 102693359598057 T^{18} + 279415175730264 T^{19} - 2142376852037292 T^{20} - 9943583630914080 T^{21} + 35524862668885320 T^{22} + 284149532358169290 T^{23} - 327404745588380364 T^{24} - 7152978204062475714 T^{25} - 6091495034152285314 T^{26} + \)\(14\!\cdots\!86\)\( T^{27} + \)\(36\!\cdots\!99\)\( T^{28} - \)\(20\!\cdots\!38\)\( T^{29} - \)\(75\!\cdots\!21\)\( T^{30} + \)\(17\!\cdots\!58\)\( T^{31} + \)\(79\!\cdots\!61\)\( T^{32} \))(\( 1 - 94 T^{2} + 3897 T^{4} - 63714 T^{6} - 1432644 T^{8} + 117895374 T^{10} - 3905926665 T^{12} + 76543542222 T^{14} + 35136880767 T^{16} - 71543747590012 T^{18} + 2847783100372168 T^{20} - 52155391993118748 T^{22} + 18673179051695247 T^{24} + 29654536557439386558 T^{26} - \)\(11\!\cdots\!65\)\( T^{28} + \)\(24\!\cdots\!26\)\( T^{30} - \)\(21\!\cdots\!24\)\( T^{32} - \)\(69\!\cdots\!26\)\( T^{34} + \)\(31\!\cdots\!17\)\( T^{36} - \)\(54\!\cdots\!86\)\( T^{38} + \)\(42\!\cdots\!01\)\( T^{40} \))(\( 1 - 1457 T^{4} + 531441 T^{8} \))(\( ( 1 + 729 T^{4} )^{2} \))(\( 1 - 782 T^{4} + 531441 T^{8} \))(\( ( 1 - 14 T + 98 T^{2} - 378 T^{3} + 729 T^{4} )( 1 + 14 T + 98 T^{2} + 378 T^{3} + 729 T^{4} ) \))(\( 1 - 1457 T^{4} + 531441 T^{8} \))(\( ( 1 + 729 T^{4} )^{4} \))(\( 1 - 578 T^{4} + 569733 T^{8} - 419608166 T^{12} + 7995847720 T^{16} - 222996983347206 T^{20} + 160909427107929573 T^{24} - 86754699201665491938 T^{28} + \)\(79\!\cdots\!61\)\( T^{32} \))(\( 1 + 5 T^{2} - 704 T^{4} + 3645 T^{6} + 531441 T^{8} \))(\( 1 + 50 T^{2} + 1771 T^{4} + 36450 T^{6} + 531441 T^{8} \))(\( 1 + 70 T^{2} + 2289 T^{4} + 80710 T^{6} + 2713780 T^{8} + 58837590 T^{10} + 1216468449 T^{12} + 27119434230 T^{14} + 282429536481 T^{16} \))(\( 1 + 54 T^{2} + 137 T^{4} - 58846 T^{6} - 1494884 T^{8} + 8499346 T^{10} + 540381895 T^{12} - 11072139622 T^{14} - 452635720033 T^{16} + 11084429886492 T^{18} + 757150666499848 T^{20} + 8080549387252668 T^{22} - 240549179690057553 T^{24} - 4289573746631515158 T^{26} + \)\(15\!\cdots\!95\)\( T^{28} + \)\(17\!\cdots\!54\)\( T^{30} - \)\(22\!\cdots\!64\)\( T^{32} - \)\(64\!\cdots\!14\)\( T^{34} + \)\(10\!\cdots\!57\)\( T^{36} + \)\(31\!\cdots\!26\)\( T^{38} + \)\(42\!\cdots\!01\)\( T^{40} \))
$5$ 1
$7$ (\( 1 + 7 T \))(\( 1 - 7 T \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 + 7 T )^{3} \))(\( ( 1 + 7 T )^{4} \))(\( ( 1 - 7 T )^{4} \))(\( ( 1 + 7 T )^{5} \))(\( ( 1 - 7 T )^{5} \))(\( 1 + 49 T^{2} \))(\( 1 + 49 T^{2} \))(\( ( 1 + 49 T^{2} )^{2} \))(\( ( 1 + 49 T^{2} )^{2} \))(\( ( 1 + 49 T^{2} )^{3} \))(\( ( 1 + 49 T^{2} )^{4} \))(\( 1 + 28 T + 343 T^{2} \))(\( 1 - 28 T + 343 T^{2} \))(\( 1 + 22 T + 357 T^{2} + 7546 T^{3} + 117649 T^{4} \))(\( 1 - 62 T + 1423 T^{2} - 21774 T^{3} + 645505 T^{4} - 16781324 T^{5} + 221408215 T^{6} - 2561689326 T^{7} + 57423182761 T^{8} - 858159806462 T^{9} + 4747561509943 T^{10} \))(\( 1 - 16 T + 685 T^{2} - 12830 T^{3} + 162567 T^{4} - 2779728 T^{5} - 4771375 T^{6} + 582590988 T^{7} - 13523658911 T^{8} + 199828708884 T^{9} - 561347497375 T^{10} - 112172051278896 T^{11} + 2250136536404967 T^{12} - 60911214172568690 T^{13} + 1115463314568657565 T^{14} - 8936733825332544112 T^{15} + \)\(19\!\cdots\!01\)\( T^{16} \))(\( 1 + 16 T + 685 T^{2} + 12830 T^{3} + 162567 T^{4} + 2779728 T^{5} - 4771375 T^{6} - 582590988 T^{7} - 13523658911 T^{8} - 199828708884 T^{9} - 561347497375 T^{10} + 112172051278896 T^{11} + 2250136536404967 T^{12} + 60911214172568690 T^{13} + 1115463314568657565 T^{14} + 8936733825332544112 T^{15} + \)\(19\!\cdots\!01\)\( T^{16} \))(\( 1 - 163 T^{2} - 85392 T^{4} - 47561997 T^{6} + 18120709551 T^{8} + 2661841566720 T^{10} + 2131883357965599 T^{12} - 658319260330100397 T^{14} - \)\(13\!\cdots\!08\)\( T^{16} - \)\(31\!\cdots\!63\)\( T^{18} + \)\(22\!\cdots\!49\)\( T^{20} \))(\( 1 + 48 T + 1152 T^{2} + 16464 T^{3} + 117649 T^{4} \))(\( 1 + 117649 T^{4} \))(\( 1 + 117649 T^{4} \))(\( 1 - 42 T + 882 T^{2} - 14406 T^{3} + 117649 T^{4} \))(\( 1 - 48 T + 1152 T^{2} - 16464 T^{3} + 117649 T^{4} \))(\( ( 1 + 117649 T^{4} )^{2} \))(\( 1 + 32 T + 512 T^{2} + 11776 T^{3} + 157796 T^{4} + 2653504 T^{5} + 73457664 T^{6} + 1223791072 T^{7} + 21739628806 T^{8} + 419760337696 T^{9} + 8642220711936 T^{10} + 107078457588928 T^{11} + 2184099755168996 T^{12} + 55907284341088768 T^{13} + 833747762130149888 T^{14} + 17873467650665088224 T^{15} + \)\(19\!\cdots\!01\)\( T^{16} \))(\( 1 + 98 T^{2} + 117649 T^{4} \))(\( 1 + 98 T^{2} + 117649 T^{4} \))(\( 1 - 230 T^{2} + 30723 T^{4} - 27059270 T^{6} + 13841287201 T^{8} \))(\( 1 + 998 T^{2} + 615963 T^{4} + 275067592 T^{6} + 113208276461 T^{8} + 40819377158070 T^{10} + 13318840517360189 T^{12} + 3807289540559489992 T^{14} + \)\(10\!\cdots\!87\)\( T^{16} + \)\(19\!\cdots\!98\)\( T^{18} + \)\(22\!\cdots\!49\)\( T^{20} \))
$11$ (\( 1 - 12 T + 1331 T^{2} \))(\( 1 + 8 T + 1331 T^{2} \))(\( 1 + 14 T + 663 T^{2} + 18634 T^{3} + 1771561 T^{4} \))(\( 1 + 56 T + 2421 T^{2} + 74536 T^{3} + 1771561 T^{4} \))(\( 1 + 56 T + 2421 T^{2} + 74536 T^{3} + 1771561 T^{4} \))(\( 1 + 74 T + 5570 T^{2} + 204680 T^{3} + 7413670 T^{4} + 131095514 T^{5} + 2357947691 T^{6} \))(\( 1 - 100 T + 4738 T^{2} - 106848 T^{3} + 2242403 T^{4} - 142214688 T^{5} + 8393656018 T^{6} - 235794769100 T^{7} + 3138428376721 T^{8} \))(\( 1 - 100 T + 4738 T^{2} - 106848 T^{3} + 2242403 T^{4} - 142214688 T^{5} + 8393656018 T^{6} - 235794769100 T^{7} + 3138428376721 T^{8} \))(\( 1 - 42 T + 4384 T^{2} - 71864 T^{3} + 6091387 T^{4} - 31351772 T^{5} + 8107636097 T^{6} - 127311459704 T^{7} + 10337242677344 T^{8} - 131813991822282 T^{9} + 4177248169415651 T^{10} \))(\( 1 - 42 T + 4384 T^{2} - 71864 T^{3} + 6091387 T^{4} - 31351772 T^{5} + 8107636097 T^{6} - 127311459704 T^{7} + 10337242677344 T^{8} - 131813991822282 T^{9} + 4177248169415651 T^{10} \))(\( ( 1 - 12 T + 1331 T^{2} )^{2} \))(\( ( 1 + 8 T + 1331 T^{2} )^{2} \))(\( ( 1 + 14 T + 663 T^{2} + 18634 T^{3} + 1771561 T^{4} )^{2} \))(\( ( 1 + 56 T + 2421 T^{2} + 74536 T^{3} + 1771561 T^{4} )^{2} \))(\( ( 1 + 74 T + 5570 T^{2} + 204680 T^{3} + 7413670 T^{4} + 131095514 T^{5} + 2357947691 T^{6} )^{2} \))(\( ( 1 - 100 T + 4738 T^{2} - 106848 T^{3} + 2242403 T^{4} - 142214688 T^{5} + 8393656018 T^{6} - 235794769100 T^{7} + 3138428376721 T^{8} )^{2} \))(\( 1 - 5 T - 1306 T^{2} - 6655 T^{3} + 1771561 T^{4} \))(\( 1 - 45 T + 694 T^{2} - 59895 T^{3} + 1771561 T^{4} \))(\( 1 + 28 T - 1874 T^{2} - 112 T^{3} + 4249899 T^{4} - 149072 T^{5} - 3319905314 T^{6} + 66022535348 T^{7} + 3138428376721 T^{8} \))(\( 1 + 47 T - 2290 T^{2} - 69067 T^{3} + 5592863 T^{4} + 81640994 T^{5} - 4895628428 T^{6} + 11964087958 T^{7} + 250747435653 T^{8} - 11800753851543 T^{9} + 6322646842057914 T^{10} - 15706803376403733 T^{11} + 444214377852864333 T^{12} + 28210693575487004978 T^{13} - \)\(15\!\cdots\!88\)\( T^{14} + \)\(34\!\cdots\!94\)\( T^{15} + \)\(31\!\cdots\!03\)\( T^{16} - \)\(51\!\cdots\!37\)\( T^{17} - \)\(22\!\cdots\!90\)\( T^{18} + \)\(61\!\cdots\!37\)\( T^{19} + \)\(17\!\cdots\!01\)\( T^{20} \))(\( 1 - 5814 T^{2} + 7688 T^{3} + 16903561 T^{4} - 44212556 T^{5} - 33446100132 T^{6} + 135306544050 T^{7} + 49297025908393 T^{8} - 290510305713892 T^{9} - 48147700566776172 T^{10} + 462486453397566408 T^{11} + 12577040984874145907 T^{12} - \)\(50\!\cdots\!88\)\( T^{13} + \)\(49\!\cdots\!88\)\( T^{14} + \)\(25\!\cdots\!44\)\( T^{15} - \)\(10\!\cdots\!07\)\( T^{16} + \)\(34\!\cdots\!64\)\( T^{17} + \)\(88\!\cdots\!68\)\( T^{18} - \)\(11\!\cdots\!08\)\( T^{19} + \)\(39\!\cdots\!47\)\( T^{20} + \)\(19\!\cdots\!08\)\( T^{21} - \)\(26\!\cdots\!32\)\( T^{22} - \)\(21\!\cdots\!12\)\( T^{23} + \)\(48\!\cdots\!13\)\( T^{24} + \)\(17\!\cdots\!50\)\( T^{25} - \)\(58\!\cdots\!32\)\( T^{26} - \)\(10\!\cdots\!36\)\( T^{27} + \)\(52\!\cdots\!21\)\( T^{28} + \)\(31\!\cdots\!08\)\( T^{29} - \)\(31\!\cdots\!94\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))(\( 1 - 5814 T^{2} + 7688 T^{3} + 16903561 T^{4} - 44212556 T^{5} - 33446100132 T^{6} + 135306544050 T^{7} + 49297025908393 T^{8} - 290510305713892 T^{9} - 48147700566776172 T^{10} + 462486453397566408 T^{11} + 12577040984874145907 T^{12} - \)\(50\!\cdots\!88\)\( T^{13} + \)\(49\!\cdots\!88\)\( T^{14} + \)\(25\!\cdots\!44\)\( T^{15} - \)\(10\!\cdots\!07\)\( T^{16} + \)\(34\!\cdots\!64\)\( T^{17} + \)\(88\!\cdots\!68\)\( T^{18} - \)\(11\!\cdots\!08\)\( T^{19} + \)\(39\!\cdots\!47\)\( T^{20} + \)\(19\!\cdots\!08\)\( T^{21} - \)\(26\!\cdots\!32\)\( T^{22} - \)\(21\!\cdots\!12\)\( T^{23} + \)\(48\!\cdots\!13\)\( T^{24} + \)\(17\!\cdots\!50\)\( T^{25} - \)\(58\!\cdots\!32\)\( T^{26} - \)\(10\!\cdots\!36\)\( T^{27} + \)\(52\!\cdots\!21\)\( T^{28} + \)\(31\!\cdots\!08\)\( T^{29} - \)\(31\!\cdots\!94\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 18 T - 2320 T^{2} - 14512 T^{3} + 3066033 T^{4} + 114865384 T^{5} + 843320902 T^{6} - 324387374202 T^{7} - 4324951728847 T^{8} + 184633610607512 T^{9} + 10564962314685174 T^{10} + 245747335718598472 T^{11} - 7661915809707920167 T^{12} - \)\(76\!\cdots\!82\)\( T^{13} + \)\(26\!\cdots\!42\)\( T^{14} + \)\(47\!\cdots\!84\)\( T^{15} + \)\(17\!\cdots\!73\)\( T^{16} - \)\(10\!\cdots\!32\)\( T^{17} - \)\(22\!\cdots\!20\)\( T^{18} - \)\(23\!\cdots\!78\)\( T^{19} + \)\(17\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 - 9 T + 1331 T^{2} )^{4} \))(\( ( 1 + 68 T + 1331 T^{2} )^{4} \))(\( ( 1 - 72 T + 1331 T^{2} )^{4} \))(\( ( 1 - 24 T + 1331 T^{2} )^{4} \))(\( ( 1 - 9 T + 1331 T^{2} )^{4} \))(\( ( 1 - 68 T + 3293 T^{2} - 90508 T^{3} + 1771561 T^{4} )^{4} \))(\( ( 1 + 38 T + 5001 T^{2} + 128438 T^{3} + 9570204 T^{4} + 170950978 T^{5} + 8859576561 T^{6} + 89602012258 T^{7} + 3138428376721 T^{8} )^{4} \))(\( ( 1 - 5 T - 1306 T^{2} - 6655 T^{3} + 1771561 T^{4} )^{2} \))(\( ( 1 - 45 T + 694 T^{2} - 59895 T^{3} + 1771561 T^{4} )^{2} \))(\( ( 1 + 28 T - 1874 T^{2} - 112 T^{3} + 4249899 T^{4} - 149072 T^{5} - 3319905314 T^{6} + 66022535348 T^{7} + 3138428376721 T^{8} )^{2} \))(\( ( 1 + 47 T - 2290 T^{2} - 69067 T^{3} + 5592863 T^{4} + 81640994 T^{5} - 4895628428 T^{6} + 11964087958 T^{7} + 250747435653 T^{8} - 11800753851543 T^{9} + 6322646842057914 T^{10} - 15706803376403733 T^{11} + 444214377852864333 T^{12} + 28210693575487004978 T^{13} - \)\(15\!\cdots\!88\)\( T^{14} + \)\(34\!\cdots\!94\)\( T^{15} + \)\(31\!\cdots\!03\)\( T^{16} - \)\(51\!\cdots\!37\)\( T^{17} - \)\(22\!\cdots\!90\)\( T^{18} + \)\(61\!\cdots\!37\)\( T^{19} + \)\(17\!\cdots\!01\)\( T^{20} )^{2} \))
$13$ (\( 1 - 78 T + 2197 T^{2} \))(\( 1 + 28 T + 2197 T^{2} \))(\( 1 + 50 T + 4987 T^{2} + 109850 T^{3} + 4826809 T^{4} \))(\( 1 + 52 T + 4414 T^{2} + 114244 T^{3} + 4826809 T^{4} \))(\( 1 - 52 T + 4414 T^{2} - 114244 T^{3} + 4826809 T^{4} \))(\( 1 + 44 T + 3100 T^{2} + 238206 T^{3} + 6810700 T^{4} + 212379596 T^{5} + 10604499373 T^{6} \))(\( 1 + 44 T + 4820 T^{2} + 154316 T^{3} + 10485014 T^{4} + 339032252 T^{5} + 23265219380 T^{6} + 466597972412 T^{7} + 23298085122481 T^{8} \))(\( 1 - 44 T + 4820 T^{2} - 154316 T^{3} + 10485014 T^{4} - 339032252 T^{5} + 23265219380 T^{6} - 466597972412 T^{7} + 23298085122481 T^{8} \))(\( 1 + 34 T + 3152 T^{2} + 188164 T^{3} + 9277969 T^{4} + 549902524 T^{5} + 20383697893 T^{6} + 908231688676 T^{7} + 33425382023696 T^{8} + 792134894164354 T^{9} + 51185893014090757 T^{10} \))(\( 1 - 34 T + 3152 T^{2} - 188164 T^{3} + 9277969 T^{4} - 549902524 T^{5} + 20383697893 T^{6} - 908231688676 T^{7} + 33425382023696 T^{8} - 792134894164354 T^{9} + 51185893014090757 T^{10} \))(\( ( 1 - 52 T + 2197 T^{2} )( 1 + 52 T + 2197 T^{2} ) \))(\( 1 - 3610 T^{2} + 4826809 T^{4} \))(\( 1 - 7474 T^{2} + 23538787 T^{4} - 36075570466 T^{6} + 23298085122481 T^{8} \))(\( 1 - 6124 T^{2} + 17255638 T^{4} - 29559378316 T^{6} + 23298085122481 T^{8} \))(\( 1 - 4264 T^{2} + 2269272 T^{4} + 11996164138 T^{6} + 10953342513048 T^{8} - 99343034962258984 T^{10} + \)\(11\!\cdots\!29\)\( T^{12} \))(\( 1 - 7704 T^{2} + 30622620 T^{4} - 93957707688 T^{6} + 235111580076838 T^{8} - 453515909087807592 T^{10} + \)\(71\!\cdots\!20\)\( T^{12} - \)\(86\!\cdots\!16\)\( T^{14} + \)\(54\!\cdots\!61\)\( T^{16} \))(\( ( 1 - 14 T + 2197 T^{2} )^{2} \))(\( ( 1 + 59 T + 2197 T^{2} )^{2} \))(\( ( 1 - 36 T + 4518 T^{2} - 79092 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 + T + 3333 T^{2} + 85816 T^{3} + 12357966 T^{4} + 60104190 T^{5} + 27150451302 T^{6} + 414217441144 T^{7} + 35344796410209 T^{8} + 23298085122481 T^{9} + 51185893014090757 T^{10} )^{2} \))(\( ( 1 + 138 T + 15006 T^{2} + 973960 T^{3} + 60849525 T^{4} + 3061603664 T^{5} + 188727298827 T^{6} + 9870415468524 T^{7} + 534416101471438 T^{8} + 21685302784347228 T^{9} + 910950624523853043 T^{10} + 32466774135262502672 T^{11} + \)\(14\!\cdots\!25\)\( T^{12} + \)\(49\!\cdots\!20\)\( T^{13} + \)\(16\!\cdots\!74\)\( T^{14} + \)\(34\!\cdots\!94\)\( T^{15} + \)\(54\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 138 T + 15006 T^{2} - 973960 T^{3} + 60849525 T^{4} - 3061603664 T^{5} + 188727298827 T^{6} - 9870415468524 T^{7} + 534416101471438 T^{8} - 21685302784347228 T^{9} + 910950624523853043 T^{10} - 32466774135262502672 T^{11} + \)\(14\!\cdots\!25\)\( T^{12} - \)\(49\!\cdots\!20\)\( T^{13} + \)\(16\!\cdots\!74\)\( T^{14} - \)\(34\!\cdots\!94\)\( T^{15} + \)\(54\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 18525 T^{2} + 160006609 T^{4} + 849909002004 T^{6} + 3078968672040518 T^{8} + 7957049203639338622 T^{10} + \)\(14\!\cdots\!62\)\( T^{12} + \)\(19\!\cdots\!24\)\( T^{14} + \)\(17\!\cdots\!61\)\( T^{16} + \)\(10\!\cdots\!25\)\( T^{18} + \)\(26\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 - 4541497 T^{4} + 23298085122481 T^{8} \))(\( ( 1 + 4826809 T^{4} )^{2} \))(\( 1 - 1958542 T^{4} + 23298085122481 T^{8} \))(\( 1 - 9038962 T^{4} + 23298085122481 T^{8} \))(\( 1 - 4541497 T^{4} + 23298085122481 T^{8} \))(\( ( 1 + 4826809 T^{4} )^{4} \))(\( 1 - 10320258 T^{4} + 44629878227173 T^{8} - 7691523192689518726 T^{12} - \)\(43\!\cdots\!80\)\( T^{16} - \)\(17\!\cdots\!06\)\( T^{20} + \)\(24\!\cdots\!53\)\( T^{24} - \)\(13\!\cdots\!78\)\( T^{28} + \)\(29\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 4198 T^{2} + 4826809 T^{4} )^{2} \))(\( ( 1 - 913 T^{2} + 4826809 T^{4} )^{2} \))(\( ( 1 - 7740 T^{2} + 24371318 T^{4} - 37359501660 T^{6} + 23298085122481 T^{8} )^{2} \))(\( ( 1 - 6665 T^{2} + 35653189 T^{4} - 129194509724 T^{6} + 393249587636338 T^{8} - 934276829363950102 T^{10} + \)\(18\!\cdots\!42\)\( T^{12} - \)\(30\!\cdots\!44\)\( T^{14} + \)\(40\!\cdots\!81\)\( T^{16} - \)\(36\!\cdots\!65\)\( T^{18} + \)\(26\!\cdots\!49\)\( T^{20} )^{2} \))
$17$ (\( 1 - 94 T + 4913 T^{2} \))(\( 1 + 54 T + 4913 T^{2} \))(\( 1 - 50 T + 6579 T^{2} - 245650 T^{3} + 24137569 T^{4} \))(\( 1 - 103 T + 12222 T^{2} - 506039 T^{3} + 24137569 T^{4} \))(\( 1 + 103 T + 12222 T^{2} + 506039 T^{3} + 24137569 T^{4} \))(\( 1 - 52 T + 2992 T^{2} - 454246 T^{3} + 14699696 T^{4} - 1255153588 T^{5} + 118587876497 T^{6} \))(\( 1 - 53 T + 15496 T^{2} - 576511 T^{3} + 103902926 T^{4} - 2832398543 T^{5} + 374035769224 T^{6} - 6285157454341 T^{7} + 582622237229761 T^{8} \))(\( 1 + 53 T + 15496 T^{2} + 576511 T^{3} + 103902926 T^{4} + 2832398543 T^{5} + 374035769224 T^{6} + 6285157454341 T^{7} + 582622237229761 T^{8} \))(\( 1 + 238 T + 42226 T^{2} + 4957176 T^{3} + 487734053 T^{4} + 36859744740 T^{5} + 2396237402389 T^{6} + 119654177745144 T^{7} + 5007491672962322 T^{8} + 138664092460683118 T^{9} + 2862423051509815793 T^{10} \))(\( 1 - 238 T + 42226 T^{2} - 4957176 T^{3} + 487734053 T^{4} - 36859744740 T^{5} + 2396237402389 T^{6} - 119654177745144 T^{7} + 5007491672962322 T^{8} - 138664092460683118 T^{9} + 2862423051509815793 T^{10} \))(\( ( 1 - 104 T + 4913 T^{2} )( 1 + 104 T + 4913 T^{2} ) \))(\( 1 - 6910 T^{2} + 24137569 T^{4} \))(\( 1 - 10658 T^{2} + 66993379 T^{4} - 257258210402 T^{6} + 582622237229761 T^{8} \))(\( 1 - 13835 T^{2} + 93408388 T^{4} - 333943267115 T^{6} + 582622237229761 T^{8} \))(\( 1 - 3280 T^{2} - 8890128 T^{4} + 11736667810 T^{6} - 214586078018832 T^{8} - 1911000938113616080 T^{10} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 - 28183 T^{2} + 386821702 T^{4} - 3335631842361 T^{6} + 19621134542604114 T^{8} - 80514043753585760409 T^{10} + \)\(22\!\cdots\!22\)\( T^{12} - \)\(39\!\cdots\!47\)\( T^{14} + \)\(33\!\cdots\!21\)\( T^{16} \))(\( 1 + 21 T - 4472 T^{2} + 103173 T^{3} + 24137569 T^{4} \))(\( 1 + 54 T - 1997 T^{2} + 265302 T^{3} + 24137569 T^{4} \))(\( 1 + 76 T + 338 T^{2} - 333488 T^{3} - 22943213 T^{4} - 1638426544 T^{5} + 8158498322 T^{6} + 9012678613772 T^{7} + 582622237229761 T^{8} \))(\( 1 + 2 T - 14261 T^{2} - 138958 T^{3} + 98300987 T^{4} + 1490182020 T^{5} - 460609812434 T^{6} - 8569542609964 T^{7} + 1925726567282549 T^{8} + 18628621470376406 T^{9} - 8447181344461544071 T^{10} + 91522417283959282678 T^{11} + \)\(46\!\cdots\!81\)\( T^{12} - \)\(10\!\cdots\!08\)\( T^{13} - \)\(26\!\cdots\!74\)\( T^{14} + \)\(42\!\cdots\!60\)\( T^{15} + \)\(13\!\cdots\!83\)\( T^{16} - \)\(96\!\cdots\!86\)\( T^{17} - \)\(48\!\cdots\!81\)\( T^{18} + \)\(33\!\cdots\!46\)\( T^{19} + \)\(81\!\cdots\!49\)\( T^{20} \))(\( 1 - 138 T - 8811 T^{2} + 1741618 T^{3} + 59726664 T^{4} - 12983863906 T^{5} - 279117565829 T^{6} + 55368603342554 T^{7} + 1472665936250391 T^{8} - 168061643591407460 T^{9} + 1278926604479627300 T^{10} + 5945173892973942320 T^{11} - \)\(69\!\cdots\!87\)\( T^{12} + \)\(20\!\cdots\!46\)\( T^{13} + \)\(65\!\cdots\!57\)\( T^{14} - \)\(80\!\cdots\!46\)\( T^{15} - \)\(35\!\cdots\!48\)\( T^{16} - \)\(39\!\cdots\!98\)\( T^{17} + \)\(15\!\cdots\!33\)\( T^{18} + \)\(24\!\cdots\!62\)\( T^{19} - \)\(40\!\cdots\!07\)\( T^{20} + \)\(17\!\cdots\!60\)\( T^{21} + \)\(17\!\cdots\!00\)\( T^{22} - \)\(11\!\cdots\!20\)\( T^{23} + \)\(49\!\cdots\!11\)\( T^{24} + \)\(92\!\cdots\!42\)\( T^{25} - \)\(22\!\cdots\!21\)\( T^{26} - \)\(52\!\cdots\!22\)\( T^{27} + \)\(11\!\cdots\!84\)\( T^{28} + \)\(16\!\cdots\!54\)\( T^{29} - \)\(42\!\cdots\!79\)\( T^{30} - \)\(32\!\cdots\!66\)\( T^{31} + \)\(11\!\cdots\!41\)\( T^{32} \))(\( 1 + 138 T - 8811 T^{2} - 1741618 T^{3} + 59726664 T^{4} + 12983863906 T^{5} - 279117565829 T^{6} - 55368603342554 T^{7} + 1472665936250391 T^{8} + 168061643591407460 T^{9} + 1278926604479627300 T^{10} - 5945173892973942320 T^{11} - \)\(69\!\cdots\!87\)\( T^{12} - \)\(20\!\cdots\!46\)\( T^{13} + \)\(65\!\cdots\!57\)\( T^{14} + \)\(80\!\cdots\!46\)\( T^{15} - \)\(35\!\cdots\!48\)\( T^{16} + \)\(39\!\cdots\!98\)\( T^{17} + \)\(15\!\cdots\!33\)\( T^{18} - \)\(24\!\cdots\!62\)\( T^{19} - \)\(40\!\cdots\!07\)\( T^{20} - \)\(17\!\cdots\!60\)\( T^{21} + \)\(17\!\cdots\!00\)\( T^{22} + \)\(11\!\cdots\!20\)\( T^{23} + \)\(49\!\cdots\!11\)\( T^{24} - \)\(92\!\cdots\!42\)\( T^{25} - \)\(22\!\cdots\!21\)\( T^{26} + \)\(52\!\cdots\!22\)\( T^{27} + \)\(11\!\cdots\!84\)\( T^{28} - \)\(16\!\cdots\!54\)\( T^{29} - \)\(42\!\cdots\!79\)\( T^{30} + \)\(32\!\cdots\!66\)\( T^{31} + \)\(11\!\cdots\!41\)\( T^{32} \))(\( 1 - 24871 T^{2} + 310754372 T^{4} - 2565664433651 T^{6} + 15392238159232011 T^{8} - 69187097376257387954 T^{10} + \)\(20\!\cdots\!20\)\( T^{12} + \)\(13\!\cdots\!18\)\( T^{14} - \)\(74\!\cdots\!43\)\( T^{16} + \)\(65\!\cdots\!47\)\( T^{18} - \)\(38\!\cdots\!52\)\( T^{20} + \)\(15\!\cdots\!43\)\( T^{22} - \)\(43\!\cdots\!23\)\( T^{24} + \)\(19\!\cdots\!62\)\( T^{26} + \)\(68\!\cdots\!20\)\( T^{28} - \)\(56\!\cdots\!46\)\( T^{30} + \)\(30\!\cdots\!91\)\( T^{32} - \)\(12\!\cdots\!39\)\( T^{34} + \)\(35\!\cdots\!52\)\( T^{36} - \)\(69\!\cdots\!59\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( 1 - 19427497 T^{4} + 582622237229761 T^{8} \))(\( ( 1 + 24137569 T^{4} )^{2} \))(\( 1 - 47706622 T^{4} + 582622237229761 T^{8} \))(\( 1 + 501118 T^{4} + 582622237229761 T^{8} \))(\( 1 - 19427497 T^{4} + 582622237229761 T^{8} \))(\( ( 1 + 24137569 T^{4} )^{4} \))(\( 1 + 56587042 T^{4} + 2629953035023393 T^{8} + \)\(89\!\cdots\!54\)\( T^{12} + \)\(23\!\cdots\!20\)\( T^{16} + \)\(51\!\cdots\!94\)\( T^{20} + \)\(89\!\cdots\!53\)\( T^{24} + \)\(11\!\cdots\!02\)\( T^{28} + \)\(11\!\cdots\!41\)\( T^{32} \))(\( 1 + 9385 T^{2} + 63940656 T^{4} + 226531085065 T^{6} + 582622237229761 T^{8} \))(\( 1 + 6910 T^{2} + 23610531 T^{4} + 166790601790 T^{6} + 582622237229761 T^{8} \))(\( 1 + 5100 T^{2} + 4917994 T^{4} - 138633973200 T^{6} - 765567689815725 T^{8} - 3346287093859150800 T^{10} + \)\(28\!\cdots\!34\)\( T^{12} + \)\(71\!\cdots\!00\)\( T^{14} + \)\(33\!\cdots\!21\)\( T^{16} \))(\( 1 + 28526 T^{2} + 400533927 T^{4} + 3750230429926 T^{6} + 27100473846691991 T^{8} + \)\(16\!\cdots\!84\)\( T^{10} + \)\(95\!\cdots\!50\)\( T^{12} + \)\(53\!\cdots\!72\)\( T^{14} + \)\(30\!\cdots\!97\)\( T^{16} + \)\(17\!\cdots\!58\)\( T^{18} + \)\(88\!\cdots\!13\)\( T^{20} + \)\(41\!\cdots\!02\)\( T^{22} + \)\(17\!\cdots\!17\)\( T^{24} + \)\(75\!\cdots\!48\)\( T^{26} + \)\(32\!\cdots\!50\)\( T^{28} + \)\(13\!\cdots\!16\)\( T^{30} + \)\(53\!\cdots\!71\)\( T^{32} + \)\(17\!\cdots\!14\)\( T^{34} + \)\(46\!\cdots\!07\)\( T^{36} + \)\(79\!\cdots\!54\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))
$19$ (\( 1 - 40 T + 6859 T^{2} \))(\( 1 + 110 T + 6859 T^{2} \))(\( 1 - 36 T + 10170 T^{2} - 246924 T^{3} + 47045881 T^{4} \))(\( 1 + 57 T + 14028 T^{2} + 390963 T^{3} + 47045881 T^{4} \))(\( 1 + 57 T + 14028 T^{2} + 390963 T^{3} + 47045881 T^{4} \))(\( 1 - 168 T + 26197 T^{2} - 2333344 T^{3} + 179685223 T^{4} - 7903708008 T^{5} + 322687697779 T^{6} \))(\( 1 + 29 T + 6638 T^{2} + 258553 T^{3} + 53805642 T^{4} + 1773415027 T^{5} + 312290558078 T^{6} + 9357943235591 T^{7} + 2213314919066161 T^{8} \))(\( 1 + 29 T + 6638 T^{2} + 258553 T^{3} + 53805642 T^{4} + 1773415027 T^{5} + 312290558078 T^{6} + 9357943235591 T^{7} + 2213314919066161 T^{8} \))(\( 1 + 36 T + 16945 T^{2} + 428680 T^{3} + 139308340 T^{4} + 2473195688 T^{5} + 955515904060 T^{6} + 20167628267080 T^{7} + 5467943038865155 T^{8} + 79679337086381796 T^{9} + 15181127029874798299 T^{10} \))(\( 1 + 36 T + 16945 T^{2} + 428680 T^{3} + 139308340 T^{4} + 2473195688 T^{5} + 955515904060 T^{6} + 20167628267080 T^{7} + 5467943038865155 T^{8} + 79679337086381796 T^{9} + 15181127029874798299 T^{10} \))(\( ( 1 + 40 T + 6859 T^{2} )^{2} \))(\( ( 1 - 110 T + 6859 T^{2} )^{2} \))(\( ( 1 + 36 T + 10170 T^{2} + 246924 T^{3} + 47045881 T^{4} )^{2} \))(\( ( 1 - 57 T + 14028 T^{2} - 390963 T^{3} + 47045881 T^{4} )^{2} \))(\( ( 1 + 168 T + 26197 T^{2} + 2333344 T^{3} + 179685223 T^{4} + 7903708008 T^{5} + 322687697779 T^{6} )^{2} \))(\( ( 1 - 29 T + 6638 T^{2} - 258553 T^{3} + 53805642 T^{4} - 1773415027 T^{5} + 312290558078 T^{6} - 9357943235591 T^{7} + 2213314919066161 T^{8} )^{2} \))(\( 1 + 49 T - 4458 T^{2} + 336091 T^{3} + 47045881 T^{4} \))(\( 1 - 121 T + 7782 T^{2} - 829939 T^{3} + 47045881 T^{4} \))(\( 1 + 160 T + 6834 T^{2} + 807680 T^{3} + 129526475 T^{4} + 5539877120 T^{5} + 321511550754 T^{6} + 51630031644640 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 21 T - 20094 T^{2} + 939517 T^{3} + 167437943 T^{4} - 9799934370 T^{5} - 1287146857848 T^{6} + 7008445096094 T^{7} + 14499989680340221 T^{8} + 155708744157753493 T^{9} - \)\(12\!\cdots\!86\)\( T^{10} + \)\(10\!\cdots\!87\)\( T^{11} + \)\(68\!\cdots\!01\)\( T^{12} + \)\(22\!\cdots\!26\)\( T^{13} - \)\(28\!\cdots\!28\)\( T^{14} - \)\(14\!\cdots\!30\)\( T^{15} + \)\(17\!\cdots\!63\)\( T^{16} + \)\(67\!\cdots\!23\)\( T^{17} - \)\(98\!\cdots\!74\)\( T^{18} - \)\(70\!\cdots\!19\)\( T^{19} + \)\(23\!\cdots\!01\)\( T^{20} \))(\( 1 - 42 T - 18052 T^{2} - 512428 T^{3} + 151661579 T^{4} + 13704191886 T^{5} - 115292977838 T^{6} - 37904485522162 T^{7} - 6147861322333405 T^{8} - 682834619106920882 T^{9} - 12334597439812380934 T^{10} + \)\(40\!\cdots\!56\)\( T^{11} + \)\(41\!\cdots\!09\)\( T^{12} + \)\(26\!\cdots\!86\)\( T^{13} + \)\(14\!\cdots\!80\)\( T^{14} - \)\(19\!\cdots\!08\)\( T^{15} - \)\(35\!\cdots\!75\)\( T^{16} - \)\(13\!\cdots\!72\)\( T^{17} + \)\(70\!\cdots\!80\)\( T^{18} + \)\(86\!\cdots\!94\)\( T^{19} + \)\(90\!\cdots\!49\)\( T^{20} + \)\(61\!\cdots\!44\)\( T^{21} - \)\(12\!\cdots\!94\)\( T^{22} - \)\(48\!\cdots\!58\)\( T^{23} - \)\(30\!\cdots\!05\)\( T^{24} - \)\(12\!\cdots\!18\)\( T^{25} - \)\(26\!\cdots\!38\)\( T^{26} + \)\(21\!\cdots\!74\)\( T^{27} + \)\(16\!\cdots\!99\)\( T^{28} - \)\(38\!\cdots\!12\)\( T^{29} - \)\(92\!\cdots\!72\)\( T^{30} - \)\(14\!\cdots\!58\)\( T^{31} + \)\(23\!\cdots\!41\)\( T^{32} \))(\( 1 - 42 T - 18052 T^{2} - 512428 T^{3} + 151661579 T^{4} + 13704191886 T^{5} - 115292977838 T^{6} - 37904485522162 T^{7} - 6147861322333405 T^{8} - 682834619106920882 T^{9} - 12334597439812380934 T^{10} + \)\(40\!\cdots\!56\)\( T^{11} + \)\(41\!\cdots\!09\)\( T^{12} + \)\(26\!\cdots\!86\)\( T^{13} + \)\(14\!\cdots\!80\)\( T^{14} - \)\(19\!\cdots\!08\)\( T^{15} - \)\(35\!\cdots\!75\)\( T^{16} - \)\(13\!\cdots\!72\)\( T^{17} + \)\(70\!\cdots\!80\)\( T^{18} + \)\(86\!\cdots\!94\)\( T^{19} + \)\(90\!\cdots\!49\)\( T^{20} + \)\(61\!\cdots\!44\)\( T^{21} - \)\(12\!\cdots\!94\)\( T^{22} - \)\(48\!\cdots\!58\)\( T^{23} - \)\(30\!\cdots\!05\)\( T^{24} - \)\(12\!\cdots\!18\)\( T^{25} - \)\(26\!\cdots\!38\)\( T^{26} + \)\(21\!\cdots\!74\)\( T^{27} + \)\(16\!\cdots\!99\)\( T^{28} - \)\(38\!\cdots\!12\)\( T^{29} - \)\(92\!\cdots\!72\)\( T^{30} - \)\(14\!\cdots\!58\)\( T^{31} + \)\(23\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 96 T - 21064 T^{2} + 1349852 T^{3} + 327425553 T^{4} - 10949009820 T^{5} - 3811487661418 T^{6} + 64847940490544 T^{7} + 34272562484687481 T^{8} - 175161053358359992 T^{9} - \)\(25\!\cdots\!46\)\( T^{10} - \)\(12\!\cdots\!28\)\( T^{11} + \)\(16\!\cdots\!61\)\( T^{12} + \)\(20\!\cdots\!76\)\( T^{13} - \)\(84\!\cdots\!98\)\( T^{14} - \)\(16\!\cdots\!80\)\( T^{15} + \)\(34\!\cdots\!73\)\( T^{16} + \)\(96\!\cdots\!88\)\( T^{17} - \)\(10\!\cdots\!44\)\( T^{18} - \)\(32\!\cdots\!44\)\( T^{19} + \)\(23\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 - 2122 T^{2} + 47045881 T^{4} )^{2} \))(\( ( 1 + 6859 T^{2} )^{4} \))(\( ( 1 + 6859 T^{2} )^{4} \))(\( ( 1 + 7238 T^{2} + 47045881 T^{4} )^{2} \))(\( ( 1 - 2122 T^{2} + 47045881 T^{4} )^{2} \))(\( ( 1 + 6859 T^{2} )^{8} \))(\( ( 1 + 34112 T^{2} + 604486178 T^{4} + 6969705935024 T^{6} + 56454362274260770 T^{8} + \)\(32\!\cdots\!44\)\( T^{10} + \)\(13\!\cdots\!58\)\( T^{12} + \)\(35\!\cdots\!92\)\( T^{14} + \)\(48\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 49 T - 4458 T^{2} - 336091 T^{3} + 47045881 T^{4} )^{2} \))(\( ( 1 + 121 T + 7782 T^{2} + 829939 T^{3} + 47045881 T^{4} )^{2} \))(\( ( 1 - 160 T + 6834 T^{2} - 807680 T^{3} + 129526475 T^{4} - 5539877120 T^{5} + 321511550754 T^{6} - 51630031644640 T^{7} + 2213314919066161 T^{8} )^{2} \))(\( ( 1 + 21 T - 20094 T^{2} - 939517 T^{3} + 167437943 T^{4} + 9799934370 T^{5} - 1287146857848 T^{6} - 7008445096094 T^{7} + 14499989680340221 T^{8} - 155708744157753493 T^{9} - \)\(12\!\cdots\!86\)\( T^{10} - \)\(10\!\cdots\!87\)\( T^{11} + \)\(68\!\cdots\!01\)\( T^{12} - \)\(22\!\cdots\!26\)\( T^{13} - \)\(28\!\cdots\!28\)\( T^{14} + \)\(14\!\cdots\!30\)\( T^{15} + \)\(17\!\cdots\!63\)\( T^{16} - \)\(67\!\cdots\!23\)\( T^{17} - \)\(98\!\cdots\!74\)\( T^{18} + \)\(70\!\cdots\!19\)\( T^{19} + \)\(23\!\cdots\!01\)\( T^{20} )^{2} \))
$23$ (\( 1 + 32 T + 12167 T^{2} \))(\( 1 + 48 T + 12167 T^{2} \))(\( 1 + 244 T + 29970 T^{2} + 2968748 T^{3} + 148035889 T^{4} \))(\( 1 - 31 T + 24318 T^{2} - 377177 T^{3} + 148035889 T^{4} \))(\( 1 + 31 T + 24318 T^{2} + 377177 T^{3} + 148035889 T^{4} \))(\( 1 - 124 T + 38233 T^{2} - 2923048 T^{3} + 465180911 T^{4} - 18356450236 T^{5} + 1801152661463 T^{6} \))(\( 1 + 295 T + 54367 T^{2} + 7704248 T^{3} + 887991584 T^{4} + 93737585416 T^{5} + 8048267177263 T^{6} + 531340035131585 T^{7} + 21914624432020321 T^{8} \))(\( 1 - 295 T + 54367 T^{2} - 7704248 T^{3} + 887991584 T^{4} - 93737585416 T^{5} + 8048267177263 T^{6} - 531340035131585 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 152 T + 34259 T^{2} + 2438912 T^{3} + 421222474 T^{4} + 23076423760 T^{5} + 5125013841158 T^{6} + 361046506112768 T^{7} + 61705689029060917 T^{8} + 3331022913667088792 T^{9} + \)\(26\!\cdots\!07\)\( T^{10} \))(\( 1 - 152 T + 34259 T^{2} - 2438912 T^{3} + 421222474 T^{4} - 23076423760 T^{5} + 5125013841158 T^{6} - 361046506112768 T^{7} + 61705689029060917 T^{8} - 3331022913667088792 T^{9} + \)\(26\!\cdots\!07\)\( T^{10} \))(\( 1 - 23310 T^{2} + 148035889 T^{4} \))(\( 1 - 22030 T^{2} + 148035889 T^{4} \))(\( 1 - 404 T^{2} - 254476346 T^{4} - 59806499156 T^{6} + 21914624432020321 T^{8} \))(\( 1 - 47675 T^{2} + 864051928 T^{4} - 7057611008075 T^{6} + 21914624432020321 T^{8} \))(\( 1 - 61090 T^{2} + 1667208207 T^{4} - 26076219594620 T^{6} + 246806649071341023 T^{8} - \)\(13\!\cdots\!90\)\( T^{10} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 - 21709 T^{2} + 186247537 T^{4} + 2009201391762 T^{6} - 50367245288344746 T^{8} + \)\(29\!\cdots\!18\)\( T^{10} + \)\(40\!\cdots\!77\)\( T^{12} - \)\(70\!\cdots\!21\)\( T^{14} + \)\(48\!\cdots\!41\)\( T^{16} \))(\( 1 + 159 T + 13114 T^{2} + 1934553 T^{3} + 148035889 T^{4} \))(\( 1 - 69 T - 7406 T^{2} - 839523 T^{3} + 148035889 T^{4} \))(\( 1 + 22 T + 3407 T^{2} - 599654 T^{3} - 145380788 T^{4} - 7295990218 T^{5} + 504358273823 T^{6} + 39625358552186 T^{7} + 21914624432020321 T^{8} \))(\( 1 - 201 T - 8588 T^{2} + 2602055 T^{3} + 123259362 T^{4} + 4272835029 T^{5} - 7259002378338 T^{6} + 285773779105835 T^{7} + 81100284674964733 T^{8} - 4436119997844018170 T^{9} - \)\(41\!\cdots\!12\)\( T^{10} - \)\(53\!\cdots\!90\)\( T^{11} + \)\(12\!\cdots\!37\)\( T^{12} + \)\(51\!\cdots\!05\)\( T^{13} - \)\(15\!\cdots\!98\)\( T^{14} + \)\(11\!\cdots\!03\)\( T^{15} + \)\(39\!\cdots\!78\)\( T^{16} + \)\(10\!\cdots\!65\)\( T^{17} - \)\(41\!\cdots\!08\)\( T^{18} - \)\(11\!\cdots\!47\)\( T^{19} + \)\(71\!\cdots\!49\)\( T^{20} \))(\( 1 - 124 T - 42692 T^{2} + 1884328 T^{3} + 1263105255 T^{4} + 31189442778 T^{5} - 23727031011278 T^{6} - 1564012482605818 T^{7} + 286014490125502622 T^{8} + 26803038826508878986 T^{9} - \)\(24\!\cdots\!50\)\( T^{10} - \)\(26\!\cdots\!68\)\( T^{11} + \)\(25\!\cdots\!72\)\( T^{12} + \)\(15\!\cdots\!00\)\( T^{13} - \)\(37\!\cdots\!71\)\( T^{14} - \)\(40\!\cdots\!62\)\( T^{15} + \)\(51\!\cdots\!50\)\( T^{16} - \)\(49\!\cdots\!54\)\( T^{17} - \)\(55\!\cdots\!19\)\( T^{18} + \)\(28\!\cdots\!00\)\( T^{19} + \)\(54\!\cdots\!12\)\( T^{20} - \)\(70\!\cdots\!76\)\( T^{21} - \)\(80\!\cdots\!50\)\( T^{22} + \)\(10\!\cdots\!78\)\( T^{23} + \)\(13\!\cdots\!02\)\( T^{24} - \)\(91\!\cdots\!46\)\( T^{25} - \)\(16\!\cdots\!22\)\( T^{26} + \)\(26\!\cdots\!74\)\( T^{27} + \)\(13\!\cdots\!55\)\( T^{28} + \)\(24\!\cdots\!36\)\( T^{29} - \)\(66\!\cdots\!68\)\( T^{30} - \)\(23\!\cdots\!32\)\( T^{31} + \)\(23\!\cdots\!81\)\( T^{32} \))(\( 1 + 124 T - 42692 T^{2} - 1884328 T^{3} + 1263105255 T^{4} - 31189442778 T^{5} - 23727031011278 T^{6} + 1564012482605818 T^{7} + 286014490125502622 T^{8} - 26803038826508878986 T^{9} - \)\(24\!\cdots\!50\)\( T^{10} + \)\(26\!\cdots\!68\)\( T^{11} + \)\(25\!\cdots\!72\)\( T^{12} - \)\(15\!\cdots\!00\)\( T^{13} - \)\(37\!\cdots\!71\)\( T^{14} + \)\(40\!\cdots\!62\)\( T^{15} + \)\(51\!\cdots\!50\)\( T^{16} + \)\(49\!\cdots\!54\)\( T^{17} - \)\(55\!\cdots\!19\)\( T^{18} - \)\(28\!\cdots\!00\)\( T^{19} + \)\(54\!\cdots\!12\)\( T^{20} + \)\(70\!\cdots\!76\)\( T^{21} - \)\(80\!\cdots\!50\)\( T^{22} - \)\(10\!\cdots\!78\)\( T^{23} + \)\(13\!\cdots\!02\)\( T^{24} + \)\(91\!\cdots\!46\)\( T^{25} - \)\(16\!\cdots\!22\)\( T^{26} - \)\(26\!\cdots\!74\)\( T^{27} + \)\(13\!\cdots\!55\)\( T^{28} - \)\(24\!\cdots\!36\)\( T^{29} - \)\(66\!\cdots\!68\)\( T^{30} + \)\(23\!\cdots\!32\)\( T^{31} + \)\(23\!\cdots\!81\)\( T^{32} \))(\( 1 - 86997 T^{2} + 3851234318 T^{4} - 120213119227875 T^{6} + 3024885906662880458 T^{8} - \)\(65\!\cdots\!75\)\( T^{10} + \)\(12\!\cdots\!72\)\( T^{12} - \)\(20\!\cdots\!59\)\( T^{14} + \)\(31\!\cdots\!69\)\( T^{16} - \)\(44\!\cdots\!70\)\( T^{18} + \)\(56\!\cdots\!84\)\( T^{20} - \)\(65\!\cdots\!30\)\( T^{22} + \)\(69\!\cdots\!49\)\( T^{24} - \)\(67\!\cdots\!71\)\( T^{26} + \)\(59\!\cdots\!52\)\( T^{28} - \)\(46\!\cdots\!75\)\( T^{30} + \)\(31\!\cdots\!38\)\( T^{32} - \)\(18\!\cdots\!75\)\( T^{34} + \)\(88\!\cdots\!58\)\( T^{36} - \)\(29\!\cdots\!73\)\( T^{38} + \)\(50\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 168 T + 14112 T^{2} - 2044056 T^{3} + 148035889 T^{4} )^{2} \))(\( 1 + 220762978 T^{4} + 21914624432020321 T^{8} \))(\( ( 1 + 148035889 T^{4} )^{2} \))(\( ( 1 - 118 T + 6962 T^{2} - 1435706 T^{3} + 148035889 T^{4} )^{2} \))(\( ( 1 + 168 T + 14112 T^{2} + 2044056 T^{3} + 148035889 T^{4} )^{2} \))(\( 1 - 220762978 T^{4} + 26821668023408163 T^{8} - \)\(48\!\cdots\!38\)\( T^{12} + \)\(48\!\cdots\!41\)\( T^{16} \))(\( ( 1 - 36 T + 648 T^{2} + 285388 T^{3} + 164757104 T^{4} - 18803211700 T^{5} + 610876173080 T^{6} - 124249589297060 T^{7} + 7200722074542750 T^{8} - 1511744752977329020 T^{9} + 90431597350815668120 T^{10} - \)\(33\!\cdots\!00\)\( T^{11} + \)\(36\!\cdots\!84\)\( T^{12} + \)\(76\!\cdots\!16\)\( T^{13} + \)\(21\!\cdots\!12\)\( T^{14} - \)\(14\!\cdots\!28\)\( T^{15} + \)\(48\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 - 947 T^{2} - 147139080 T^{4} - 140189986883 T^{6} + 21914624432020321 T^{8} \))(\( 1 + 19573 T^{2} + 235066440 T^{4} + 2897506455397 T^{6} + 21914624432020321 T^{8} \))(\( 1 - 6330 T^{2} - 252769151 T^{4} + 20469491910 T^{6} + 57907864448706180 T^{8} + 3030219432275157990 T^{10} - \)\(55\!\cdots\!71\)\( T^{12} - \)\(20\!\cdots\!70\)\( T^{14} + \)\(48\!\cdots\!41\)\( T^{16} \))(\( 1 + 57577 T^{2} + 1366298578 T^{4} + 21688118099755 T^{6} + 394718820218686478 T^{8} + \)\(73\!\cdots\!75\)\( T^{10} + \)\(10\!\cdots\!12\)\( T^{12} + \)\(13\!\cdots\!59\)\( T^{14} + \)\(19\!\cdots\!69\)\( T^{16} + \)\(25\!\cdots\!90\)\( T^{18} + \)\(29\!\cdots\!44\)\( T^{20} + \)\(37\!\cdots\!10\)\( T^{22} + \)\(43\!\cdots\!49\)\( T^{24} + \)\(44\!\cdots\!71\)\( T^{26} + \)\(49\!\cdots\!92\)\( T^{28} + \)\(51\!\cdots\!75\)\( T^{30} + \)\(41\!\cdots\!58\)\( T^{32} + \)\(33\!\cdots\!95\)\( T^{34} + \)\(31\!\cdots\!18\)\( T^{36} + \)\(19\!\cdots\!93\)\( T^{38} + \)\(50\!\cdots\!01\)\( T^{40} \))
$29$ (\( 1 + 50 T + 24389 T^{2} \))(\( 1 + 110 T + 24389 T^{2} \))(\( 1 + 26 T + 47795 T^{2} + 634114 T^{3} + 594823321 T^{4} \))(\( 1 + 413 T + 83948 T^{2} + 10072657 T^{3} + 594823321 T^{4} \))(\( 1 + 413 T + 83948 T^{2} + 10072657 T^{3} + 594823321 T^{4} \))(\( 1 - 332 T + 80572 T^{2} - 13628846 T^{3} + 1965070508 T^{4} - 197481342572 T^{5} + 14507145975869 T^{6} \))(\( 1 - 129 T + 83933 T^{2} - 9167698 T^{3} + 2922882282 T^{4} - 223590986522 T^{5} + 49925305801493 T^{6} - 1871421830887101 T^{7} + 353814783205469041 T^{8} \))(\( 1 - 129 T + 83933 T^{2} - 9167698 T^{3} + 2922882282 T^{4} - 223590986522 T^{5} + 49925305801493 T^{6} - 1871421830887101 T^{7} + 353814783205469041 T^{8} \))(\( 1 + 44 T + 5930 T^{2} - 1541470 T^{3} + 551498365 T^{4} - 1453032508 T^{5} + 13450493623985 T^{6} - 916902304621870 T^{7} + 86027375636903170 T^{8} + 15567850461040637804 T^{9} + \)\(86\!\cdots\!49\)\( T^{10} \))(\( 1 + 44 T + 5930 T^{2} - 1541470 T^{3} + 551498365 T^{4} - 1453032508 T^{5} + 13450493623985 T^{6} - 916902304621870 T^{7} + 86027375636903170 T^{8} + 15567850461040637804 T^{9} + \)\(86\!\cdots\!49\)\( T^{10} \))(\( ( 1 - 50 T + 24389 T^{2} )^{2} \))(\( ( 1 - 110 T + 24389 T^{2} )^{2} \))(\( ( 1 - 26 T + 47795 T^{2} - 634114 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 413 T + 83948 T^{2} - 10072657 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 + 332 T + 80572 T^{2} + 13628846 T^{3} + 1965070508 T^{4} + 197481342572 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 + 129 T + 83933 T^{2} + 9167698 T^{3} + 2922882282 T^{4} + 223590986522 T^{5} + 49925305801493 T^{6} + 1871421830887101 T^{7} + 353814783205469041 T^{8} )^{2} \))(\( ( 1 - 58 T + 24389 T^{2} )^{2} \))(\( ( 1 + 162 T + 24389 T^{2} )^{2} \))(\( ( 1 + 250 T + 57203 T^{2} + 6097250 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 190 T + 63587 T^{2} - 10646688 T^{3} + 1713461669 T^{4} - 306482100734 T^{5} + 41789616645241 T^{6} - 6332898313810848 T^{7} + 922465891167582103 T^{8} - 67224808809039117790 T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 288 T + 152114 T^{2} - 31811758 T^{3} + 10075953665 T^{4} - 1703801073128 T^{5} + 411664346969823 T^{6} - 58555016290643690 T^{7} + 11755136863588236914 T^{8} - \)\(14\!\cdots\!10\)\( T^{9} + \)\(24\!\cdots\!83\)\( T^{10} - \)\(24\!\cdots\!32\)\( T^{11} + \)\(35\!\cdots\!65\)\( T^{12} - \)\(27\!\cdots\!42\)\( T^{13} + \)\(32\!\cdots\!54\)\( T^{14} - \)\(14\!\cdots\!52\)\( T^{15} + \)\(12\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 288 T + 152114 T^{2} - 31811758 T^{3} + 10075953665 T^{4} - 1703801073128 T^{5} + 411664346969823 T^{6} - 58555016290643690 T^{7} + 11755136863588236914 T^{8} - \)\(14\!\cdots\!10\)\( T^{9} + \)\(24\!\cdots\!83\)\( T^{10} - \)\(24\!\cdots\!32\)\( T^{11} + \)\(35\!\cdots\!65\)\( T^{12} - \)\(27\!\cdots\!42\)\( T^{13} + \)\(32\!\cdots\!54\)\( T^{14} - \)\(14\!\cdots\!52\)\( T^{15} + \)\(12\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 65 T + 90182 T^{2} + 6713567 T^{3} + 3728949859 T^{4} + 248936343596 T^{5} + 90945358111151 T^{6} + 3993386218696007 T^{7} + 1308283438395818158 T^{8} + 22997960908355487665 T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{4} \))(\( ( 1 - 25369 T^{2} + 594823321 T^{4} )^{2} \))(\( ( 1 - 21222 T^{2} + 594823321 T^{4} )^{2} \))(\( ( 1 - 45862 T^{2} + 594823321 T^{4} )^{2} \))(\( ( 1 - 46074 T^{2} + 594823321 T^{4} )^{2} \))(\( ( 1 - 25369 T^{2} + 594823321 T^{4} )^{2} \))(\( ( 1 + 21222 T^{2} - 144450037 T^{4} + 12623340518262 T^{6} + 353814783205469041 T^{8} )^{2} \))(\( ( 1 - 112382 T^{2} + 6958299041 T^{4} - 280305393329582 T^{6} + 8070801965751649684 T^{8} - \)\(16\!\cdots\!22\)\( T^{10} + \)\(24\!\cdots\!81\)\( T^{12} - \)\(23\!\cdots\!02\)\( T^{14} + \)\(12\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 58 T + 24389 T^{2} )^{4} \))(\( ( 1 - 162 T + 24389 T^{2} )^{4} \))(\( ( 1 - 250 T + 57203 T^{2} - 6097250 T^{3} + 594823321 T^{4} )^{4} \))(\( ( 1 + 190 T + 63587 T^{2} + 10646688 T^{3} + 1713461669 T^{4} + 306482100734 T^{5} + 41789616645241 T^{6} + 6332898313810848 T^{7} + 922465891167582103 T^{8} + 67224808809039117790 T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{4} \))
$31$ (\( 1 + 248 T + 29791 T^{2} \))(\( 1 - 12 T + 29791 T^{2} \))(\( 1 + 120 T - 1618 T^{2} + 3574920 T^{3} + 887503681 T^{4} \))(\( 1 + 162 T + 21494 T^{2} + 4826142 T^{3} + 887503681 T^{4} \))(\( 1 + 162 T + 21494 T^{2} + 4826142 T^{3} + 887503681 T^{4} \))(\( 1 - 320 T + 113341 T^{2} - 19016064 T^{3} + 3376541731 T^{4} - 284001177920 T^{5} + 26439622160671 T^{6} \))(\( 1 - 114 T + 80728 T^{2} - 5927082 T^{3} + 3079701134 T^{4} - 176573699862 T^{5} + 71646397159768 T^{6} - 3014116926316494 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 114 T + 80728 T^{2} - 5927082 T^{3} + 3079701134 T^{4} - 176573699862 T^{5} + 71646397159768 T^{6} - 3014116926316494 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 60 T + 93703 T^{2} - 4540464 T^{3} + 4639455974 T^{4} - 198463065128 T^{5} + 138214032921434 T^{6} - 4029678513447984 T^{7} + 2477471915321354713 T^{8} - 47259767027312985660 T^{9} + \)\(23\!\cdots\!51\)\( T^{10} \))(\( 1 - 60 T + 93703 T^{2} - 4540464 T^{3} + 4639455974 T^{4} - 198463065128 T^{5} + 138214032921434 T^{6} - 4029678513447984 T^{7} + 2477471915321354713 T^{8} - 47259767027312985660 T^{9} + \)\(23\!\cdots\!51\)\( T^{10} \))(\( ( 1 + 248 T + 29791 T^{2} )^{2} \))(\( ( 1 - 12 T + 29791 T^{2} )^{2} \))(\( ( 1 + 120 T - 1618 T^{2} + 3574920 T^{3} + 887503681 T^{4} )^{2} \))(\( ( 1 + 162 T + 21494 T^{2} + 4826142 T^{3} + 887503681 T^{4} )^{2} \))(\( ( 1 - 320 T + 113341 T^{2} - 19016064 T^{3} + 3376541731 T^{4} - 284001177920 T^{5} + 26439622160671 T^{6} )^{2} \))(\( ( 1 - 114 T + 80728 T^{2} - 5927082 T^{3} + 3079701134 T^{4} - 176573699862 T^{5} + 71646397159768 T^{6} - 3014116926316494 T^{7} + 787662783788549761 T^{8} )^{2} \))(\( 1 + 147 T - 8182 T^{2} + 4379277 T^{3} + 887503681 T^{4} \))(\( 1 - 88 T - 22047 T^{2} - 2621608 T^{3} + 887503681 T^{4} \))(\( 1 - 132 T - 26514 T^{2} + 2065008 T^{3} + 523965779 T^{4} + 61518653328 T^{5} - 23531272598034 T^{6} - 3490030125208572 T^{7} + 787662783788549761 T^{8} \))(\( 1 + 388 T - 22159 T^{2} - 20563236 T^{3} + 2008090307 T^{4} + 1081135761624 T^{5} - 53801367425630 T^{6} - 25898096736714840 T^{7} + 2959646551177751045 T^{8} + \)\(44\!\cdots\!60\)\( T^{9} - \)\(63\!\cdots\!45\)\( T^{10} + \)\(13\!\cdots\!60\)\( T^{11} + \)\(26\!\cdots\!45\)\( T^{12} - \)\(68\!\cdots\!40\)\( T^{13} - \)\(42\!\cdots\!30\)\( T^{14} + \)\(25\!\cdots\!24\)\( T^{15} + \)\(14\!\cdots\!87\)\( T^{16} - \)\(42\!\cdots\!16\)\( T^{17} - \)\(13\!\cdots\!39\)\( T^{18} + \)\(71\!\cdots\!68\)\( T^{19} + \)\(55\!\cdots\!01\)\( T^{20} \))(\( 1 + 18 T - 110984 T^{2} - 10329900 T^{3} + 6620415625 T^{4} + 1000886934300 T^{5} - 208705232127310 T^{6} - 54446646628747230 T^{7} + 1823782176995369490 T^{8} + \)\(17\!\cdots\!10\)\( T^{9} + \)\(16\!\cdots\!80\)\( T^{10} - \)\(33\!\cdots\!90\)\( T^{11} - \)\(93\!\cdots\!50\)\( T^{12} + \)\(26\!\cdots\!50\)\( T^{13} + \)\(30\!\cdots\!75\)\( T^{14} + \)\(85\!\cdots\!98\)\( T^{15} - \)\(88\!\cdots\!86\)\( T^{16} + \)\(25\!\cdots\!18\)\( T^{17} + \)\(27\!\cdots\!75\)\( T^{18} + \)\(70\!\cdots\!50\)\( T^{19} - \)\(73\!\cdots\!50\)\( T^{20} - \)\(79\!\cdots\!90\)\( T^{21} + \)\(11\!\cdots\!80\)\( T^{22} + \)\(37\!\cdots\!10\)\( T^{23} + \)\(11\!\cdots\!90\)\( T^{24} - \)\(10\!\cdots\!30\)\( T^{25} - \)\(11\!\cdots\!10\)\( T^{26} + \)\(16\!\cdots\!00\)\( T^{27} + \)\(32\!\cdots\!25\)\( T^{28} - \)\(15\!\cdots\!00\)\( T^{29} - \)\(48\!\cdots\!24\)\( T^{30} + \)\(23\!\cdots\!18\)\( T^{31} + \)\(38\!\cdots\!41\)\( T^{32} \))(\( 1 + 18 T - 110984 T^{2} - 10329900 T^{3} + 6620415625 T^{4} + 1000886934300 T^{5} - 208705232127310 T^{6} - 54446646628747230 T^{7} + 1823782176995369490 T^{8} + \)\(17\!\cdots\!10\)\( T^{9} + \)\(16\!\cdots\!80\)\( T^{10} - \)\(33\!\cdots\!90\)\( T^{11} - \)\(93\!\cdots\!50\)\( T^{12} + \)\(26\!\cdots\!50\)\( T^{13} + \)\(30\!\cdots\!75\)\( T^{14} + \)\(85\!\cdots\!98\)\( T^{15} - \)\(88\!\cdots\!86\)\( T^{16} + \)\(25\!\cdots\!18\)\( T^{17} + \)\(27\!\cdots\!75\)\( T^{18} + \)\(70\!\cdots\!50\)\( T^{19} - \)\(73\!\cdots\!50\)\( T^{20} - \)\(79\!\cdots\!90\)\( T^{21} + \)\(11\!\cdots\!80\)\( T^{22} + \)\(37\!\cdots\!10\)\( T^{23} + \)\(11\!\cdots\!90\)\( T^{24} - \)\(10\!\cdots\!30\)\( T^{25} - \)\(11\!\cdots\!10\)\( T^{26} + \)\(16\!\cdots\!00\)\( T^{27} + \)\(32\!\cdots\!25\)\( T^{28} - \)\(15\!\cdots\!00\)\( T^{29} - \)\(48\!\cdots\!24\)\( T^{30} + \)\(23\!\cdots\!18\)\( T^{31} + \)\(38\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 417 T + 56846 T^{2} - 11580411 T^{3} + 3514034027 T^{4} - 410962717846 T^{5} + 101522259384800 T^{6} - 32401580870656750 T^{7} + 3387898207635269725 T^{8} - \)\(49\!\cdots\!35\)\( T^{9} + \)\(14\!\cdots\!70\)\( T^{10} - \)\(14\!\cdots\!85\)\( T^{11} + \)\(30\!\cdots\!25\)\( T^{12} - \)\(85\!\cdots\!50\)\( T^{13} + \)\(79\!\cdots\!00\)\( T^{14} - \)\(96\!\cdots\!46\)\( T^{15} + \)\(24\!\cdots\!07\)\( T^{16} - \)\(24\!\cdots\!41\)\( T^{17} + \)\(35\!\cdots\!66\)\( T^{18} - \)\(77\!\cdots\!87\)\( T^{19} + \)\(55\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 - 43742 T^{2} + 887503681 T^{4} )^{2} \))(\( ( 1 - 29791 T^{2} )^{4} \))(\( ( 1 - 29791 T^{2} )^{4} \))(\( ( 1 - 56202 T^{2} + 887503681 T^{4} )^{2} \))(\( ( 1 - 43742 T^{2} + 887503681 T^{4} )^{2} \))(\( ( 1 - 29791 T^{2} )^{8} \))(\( ( 1 - 131748 T^{2} + 6374620088 T^{4} - 129464520417676 T^{6} + 1790519884005949870 T^{8} - \)\(11\!\cdots\!56\)\( T^{10} + \)\(50\!\cdots\!68\)\( T^{12} - \)\(92\!\cdots\!68\)\( T^{14} + \)\(62\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 147 T - 8182 T^{2} + 4379277 T^{3} + 887503681 T^{4} )^{2} \))(\( ( 1 - 88 T - 22047 T^{2} - 2621608 T^{3} + 887503681 T^{4} )^{2} \))(\( ( 1 - 132 T - 26514 T^{2} + 2065008 T^{3} + 523965779 T^{4} + 61518653328 T^{5} - 23531272598034 T^{6} - 3490030125208572 T^{7} + 787662783788549761 T^{8} )^{2} \))(\( ( 1 + 388 T - 22159 T^{2} - 20563236 T^{3} + 2008090307 T^{4} + 1081135761624 T^{5} - 53801367425630 T^{6} - 25898096736714840 T^{7} + 2959646551177751045 T^{8} + \)\(44\!\cdots\!60\)\( T^{9} - \)\(63\!\cdots\!45\)\( T^{10} + \)\(13\!\cdots\!60\)\( T^{11} + \)\(26\!\cdots\!45\)\( T^{12} - \)\(68\!\cdots\!40\)\( T^{13} - \)\(42\!\cdots\!30\)\( T^{14} + \)\(25\!\cdots\!24\)\( T^{15} + \)\(14\!\cdots\!87\)\( T^{16} - \)\(42\!\cdots\!16\)\( T^{17} - \)\(13\!\cdots\!39\)\( T^{18} + \)\(71\!\cdots\!68\)\( T^{19} + \)\(55\!\cdots\!01\)\( T^{20} )^{2} \))
$37$ (\( 1 - 434 T + 50653 T^{2} \))(\( 1 - 246 T + 50653 T^{2} \))(\( 1 + 564 T + 173630 T^{2} + 28568292 T^{3} + 2565726409 T^{4} \))(\( 1 + 75 T + 69410 T^{2} + 3798975 T^{3} + 2565726409 T^{4} \))(\( 1 - 75 T + 69410 T^{2} - 3798975 T^{3} + 2565726409 T^{4} \))(\( 1 - 54 T + 139843 T^{2} - 5496260 T^{3} + 7083467479 T^{4} - 138549226086 T^{5} + 129961739795077 T^{6} \))(\( 1 + 403 T + 202319 T^{2} + 46625606 T^{3} + 14127493020 T^{4} + 2361726820718 T^{5} + 519095201342471 T^{6} + 52374581137416031 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 403 T + 202319 T^{2} - 46625606 T^{3} + 14127493020 T^{4} - 2361726820718 T^{5} + 519095201342471 T^{6} - 52374581137416031 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 312 T + 219609 T^{2} + 44149856 T^{3} + 18744782946 T^{4} + 2828243620176 T^{5} + 949479490563738 T^{6} + 113276451492747104 T^{7} + 28540767714657064893 T^{8} + \)\(20\!\cdots\!72\)\( T^{9} + \)\(33\!\cdots\!93\)\( T^{10} \))(\( 1 - 312 T + 219609 T^{2} - 44149856 T^{3} + 18744782946 T^{4} - 2828243620176 T^{5} + 949479490563738 T^{6} - 113276451492747104 T^{7} + 28540767714657064893 T^{8} - \)\(20\!\cdots\!72\)\( T^{9} + \)\(33\!\cdots\!93\)\( T^{10} \))(\( 1 + 87050 T^{2} + 2565726409 T^{4} \))(\( 1 - 40790 T^{2} + 2565726409 T^{4} \))(\( 1 - 29164 T^{2} + 3053796342 T^{4} - 74826844992076 T^{6} + 6582952005840035281 T^{8} \))(\( 1 - 133195 T^{2} + 9379354668 T^{4} - 341741929046755 T^{6} + 6582952005840035281 T^{8} \))(\( 1 - 276770 T^{2} + 33129403527 T^{4} - 2195897974516860 T^{6} + 85000985543641644543 T^{8} - \)\(18\!\cdots\!70\)\( T^{10} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( 1 - 242229 T^{2} + 31607725365 T^{4} - 2677211970945758 T^{6} + \)\(16\!\cdots\!58\)\( T^{8} - \)\(68\!\cdots\!22\)\( T^{10} + \)\(20\!\cdots\!65\)\( T^{12} - \)\(40\!\cdots\!41\)\( T^{14} + \)\(43\!\cdots\!61\)\( T^{16} \))(\( 1 - 219 T - 2692 T^{2} - 11093007 T^{3} + 2565726409 T^{4} \))(\( 1 + 259 T + 16428 T^{2} + 13119127 T^{3} + 2565726409 T^{4} \))(\( 1 + 416 T + 65478 T^{2} + 2609152 T^{3} + 241494107 T^{4} + 132161376256 T^{5} + 167998633808502 T^{6} + 54064083754752032 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 145 T - 115656 T^{2} - 19216271 T^{3} + 5000432907 T^{4} + 642783651926 T^{5} - 165614030132196 T^{6} + 34861351624072058 T^{7} + 17483682674137096733 T^{8} - \)\(17\!\cdots\!33\)\( T^{9} - \)\(12\!\cdots\!64\)\( T^{10} - \)\(89\!\cdots\!49\)\( T^{11} + \)\(44\!\cdots\!97\)\( T^{12} + \)\(45\!\cdots\!66\)\( T^{13} - \)\(10\!\cdots\!76\)\( T^{14} + \)\(21\!\cdots\!18\)\( T^{15} + \)\(84\!\cdots\!03\)\( T^{16} - \)\(16\!\cdots\!27\)\( T^{17} - \)\(50\!\cdots\!16\)\( T^{18} + \)\(31\!\cdots\!85\)\( T^{19} + \)\(11\!\cdots\!49\)\( T^{20} \))(\( 1 - 220 T - 185206 T^{2} + 30687580 T^{3} + 18834137027 T^{4} - 1625457137040 T^{5} - 1291922944920804 T^{6} - 25157116118690320 T^{7} + 70857435741614456881 T^{8} + \)\(79\!\cdots\!00\)\( T^{9} - \)\(34\!\cdots\!50\)\( T^{10} - \)\(42\!\cdots\!00\)\( T^{11} + \)\(15\!\cdots\!83\)\( T^{12} + \)\(94\!\cdots\!80\)\( T^{13} - \)\(60\!\cdots\!48\)\( T^{14} - \)\(40\!\cdots\!00\)\( T^{15} + \)\(25\!\cdots\!41\)\( T^{16} - \)\(20\!\cdots\!00\)\( T^{17} - \)\(15\!\cdots\!32\)\( T^{18} + \)\(12\!\cdots\!60\)\( T^{19} + \)\(99\!\cdots\!23\)\( T^{20} - \)\(14\!\cdots\!00\)\( T^{21} - \)\(58\!\cdots\!50\)\( T^{22} + \)\(68\!\cdots\!00\)\( T^{23} + \)\(30\!\cdots\!41\)\( T^{24} - \)\(55\!\cdots\!60\)\( T^{25} - \)\(14\!\cdots\!96\)\( T^{26} - \)\(91\!\cdots\!80\)\( T^{27} + \)\(53\!\cdots\!07\)\( T^{28} + \)\(44\!\cdots\!40\)\( T^{29} - \)\(13\!\cdots\!14\)\( T^{30} - \)\(81\!\cdots\!40\)\( T^{31} + \)\(18\!\cdots\!21\)\( T^{32} \))(\( 1 + 220 T - 185206 T^{2} - 30687580 T^{3} + 18834137027 T^{4} + 1625457137040 T^{5} - 1291922944920804 T^{6} + 25157116118690320 T^{7} + 70857435741614456881 T^{8} - \)\(79\!\cdots\!00\)\( T^{9} - \)\(34\!\cdots\!50\)\( T^{10} + \)\(42\!\cdots\!00\)\( T^{11} + \)\(15\!\cdots\!83\)\( T^{12} - \)\(94\!\cdots\!80\)\( T^{13} - \)\(60\!\cdots\!48\)\( T^{14} + \)\(40\!\cdots\!00\)\( T^{15} + \)\(25\!\cdots\!41\)\( T^{16} + \)\(20\!\cdots\!00\)\( T^{17} - \)\(15\!\cdots\!32\)\( T^{18} - \)\(12\!\cdots\!60\)\( T^{19} + \)\(99\!\cdots\!23\)\( T^{20} + \)\(14\!\cdots\!00\)\( T^{21} - \)\(58\!\cdots\!50\)\( T^{22} - \)\(68\!\cdots\!00\)\( T^{23} + \)\(30\!\cdots\!41\)\( T^{24} + \)\(55\!\cdots\!60\)\( T^{25} - \)\(14\!\cdots\!96\)\( T^{26} + \)\(91\!\cdots\!80\)\( T^{27} + \)\(53\!\cdots\!07\)\( T^{28} - \)\(44\!\cdots\!40\)\( T^{29} - \)\(13\!\cdots\!14\)\( T^{30} + \)\(81\!\cdots\!40\)\( T^{31} + \)\(18\!\cdots\!21\)\( T^{32} \))(\( 1 - 341982 T^{2} + 60045301980 T^{4} - 7262673706709132 T^{6} + \)\(68\!\cdots\!29\)\( T^{8} - \)\(53\!\cdots\!88\)\( T^{10} + \)\(36\!\cdots\!98\)\( T^{12} - \)\(21\!\cdots\!74\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} - \)\(65\!\cdots\!56\)\( T^{18} + \)\(33\!\cdots\!82\)\( T^{20} - \)\(16\!\cdots\!04\)\( T^{22} + \)\(81\!\cdots\!21\)\( T^{24} - \)\(37\!\cdots\!46\)\( T^{26} + \)\(15\!\cdots\!78\)\( T^{28} - \)\(59\!\cdots\!12\)\( T^{30} + \)\(19\!\cdots\!89\)\( T^{32} - \)\(53\!\cdots\!08\)\( T^{34} + \)\(11\!\cdots\!80\)\( T^{36} - \)\(16\!\cdots\!98\)\( T^{38} + \)\(12\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 24 T + 288 T^{2} - 1215672 T^{3} + 2565726409 T^{4} )^{2} \))(\( 1 + 5108772818 T^{4} + 6582952005840035281 T^{8} \))(\( ( 1 + 2565726409 T^{4} )^{2} \))(\( ( 1 + 186 T + 17298 T^{2} + 9421458 T^{3} + 2565726409 T^{4} )^{2} \))(\( ( 1 + 24 T + 288 T^{2} + 1215672 T^{3} + 2565726409 T^{4} )^{2} \))(\( 1 - 5108772818 T^{4} + 19516607700095625843 T^{8} - \)\(33\!\cdots\!58\)\( T^{12} + \)\(43\!\cdots\!61\)\( T^{16} \))(\( ( 1 - 128 T + 8192 T^{2} - 12209344 T^{3} + 2617912324 T^{4} + 578850045760 T^{5} - 21004703160320 T^{6} + 19309031650910720 T^{7} - 10318342014772450650 T^{8} + \)\(97\!\cdots\!60\)\( T^{9} - \)\(53\!\cdots\!80\)\( T^{10} + \)\(75\!\cdots\!20\)\( T^{11} + \)\(17\!\cdots\!44\)\( T^{12} - \)\(40\!\cdots\!92\)\( T^{13} + \)\(13\!\cdots\!68\)\( T^{14} - \)\(10\!\cdots\!36\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 + 53345 T^{2} + 279962616 T^{4} + 136868675288105 T^{6} + 6582952005840035281 T^{8} \))(\( 1 + 34225 T^{2} - 1394375784 T^{4} + 87811986348025 T^{6} + 6582952005840035281 T^{8} \))(\( 1 + 42100 T^{2} + 2599542234 T^{4} - 250856430689200 T^{6} - 10446323417893894525 T^{8} - \)\(64\!\cdots\!00\)\( T^{10} + \)\(17\!\cdots\!54\)\( T^{12} + \)\(71\!\cdots\!00\)\( T^{14} + \)\(43\!\cdots\!61\)\( T^{16} \))(\( 1 + 252337 T^{2} + 28949894740 T^{4} + 2043560527052357 T^{6} + \)\(11\!\cdots\!39\)\( T^{8} + \)\(68\!\cdots\!38\)\( T^{10} + \)\(50\!\cdots\!48\)\( T^{12} + \)\(35\!\cdots\!94\)\( T^{14} + \)\(19\!\cdots\!81\)\( T^{16} + \)\(90\!\cdots\!31\)\( T^{18} + \)\(42\!\cdots\!12\)\( T^{20} + \)\(23\!\cdots\!79\)\( T^{22} + \)\(12\!\cdots\!61\)\( T^{24} + \)\(59\!\cdots\!26\)\( T^{26} + \)\(21\!\cdots\!28\)\( T^{28} + \)\(76\!\cdots\!62\)\( T^{30} + \)\(32\!\cdots\!99\)\( T^{32} + \)\(14\!\cdots\!33\)\( T^{34} + \)\(54\!\cdots\!40\)\( T^{36} + \)\(12\!\cdots\!93\)\( T^{38} + \)\(12\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 - 402 T + 68921 T^{2} \))(\( 1 - 182 T + 68921 T^{2} \))(\( 1 + 328 T + 133986 T^{2} + 22606088 T^{3} + 4750104241 T^{4} \))(\( 1 + 505 T + 163458 T^{2} + 34805105 T^{3} + 4750104241 T^{4} \))(\( 1 + 505 T + 163458 T^{2} + 34805105 T^{3} + 4750104241 T^{4} \))(\( 1 - 362 T + 248299 T^{2} - 51434996 T^{3} + 17113015379 T^{4} - 1719537735242 T^{5} + 327381934393961 T^{6} \))(\( 1 - 671 T + 399120 T^{2} - 139154877 T^{3} + 44432315734 T^{4} - 9590693277717 T^{5} + 1895861604667920 T^{6} - 219673277978347831 T^{7} + 22563490300366186081 T^{8} \))(\( 1 - 671 T + 399120 T^{2} - 139154877 T^{3} + 44432315734 T^{4} - 9590693277717 T^{5} + 1895861604667920 T^{6} - 219673277978347831 T^{7} + 22563490300366186081 T^{8} \))(\( 1 + 426 T + 295309 T^{2} + 96639912 T^{3} + 38701723370 T^{4} + 9383799279644 T^{5} + 2667361476383770 T^{6} + 459049655841066792 T^{7} + 96678831663946228949 T^{8} + \)\(96\!\cdots\!06\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} \))(\( 1 + 426 T + 295309 T^{2} + 96639912 T^{3} + 38701723370 T^{4} + 9383799279644 T^{5} + 2667361476383770 T^{6} + 459049655841066792 T^{7} + 96678831663946228949 T^{8} + \)\(96\!\cdots\!06\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} \))(\( ( 1 - 402 T + 68921 T^{2} )^{2} \))(\( ( 1 - 182 T + 68921 T^{2} )^{2} \))(\( ( 1 + 328 T + 133986 T^{2} + 22606088 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 505 T + 163458 T^{2} + 34805105 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 362 T + 248299 T^{2} - 51434996 T^{3} + 17113015379 T^{4} - 1719537735242 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 - 671 T + 399120 T^{2} - 139154877 T^{3} + 44432315734 T^{4} - 9590693277717 T^{5} + 1895861604667920 T^{6} - 219673277978347831 T^{7} + 22563490300366186081 T^{8} )^{2} \))(\( ( 1 - 350 T + 68921 T^{2} )^{2} \))(\( ( 1 - 195 T + 68921 T^{2} )^{2} \))(\( ( 1 + 106 T + 138851 T^{2} + 7305626 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 281 T + 269231 T^{2} + 52376686 T^{3} + 31133332221 T^{4} + 4627148668935 T^{5} + 2145740390003541 T^{6} + 248794718298125326 T^{7} + 88141365578820513991 T^{8} + \)\(63\!\cdots\!61\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 - 168 T + 255674 T^{2} - 46771914 T^{3} + 36731732203 T^{4} - 6357178842532 T^{5} + 3845709559776789 T^{6} - 597312242537958612 T^{7} + \)\(30\!\cdots\!83\)\( T^{8} - \)\(41\!\cdots\!52\)\( T^{9} + \)\(18\!\cdots\!49\)\( T^{10} - \)\(20\!\cdots\!52\)\( T^{11} + \)\(82\!\cdots\!43\)\( T^{12} - \)\(72\!\cdots\!14\)\( T^{13} + \)\(27\!\cdots\!54\)\( T^{14} - \)\(12\!\cdots\!88\)\( T^{15} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 168 T + 255674 T^{2} - 46771914 T^{3} + 36731732203 T^{4} - 6357178842532 T^{5} + 3845709559776789 T^{6} - 597312242537958612 T^{7} + \)\(30\!\cdots\!83\)\( T^{8} - \)\(41\!\cdots\!52\)\( T^{9} + \)\(18\!\cdots\!49\)\( T^{10} - \)\(20\!\cdots\!52\)\( T^{11} + \)\(82\!\cdots\!43\)\( T^{12} - \)\(72\!\cdots\!14\)\( T^{13} + \)\(27\!\cdots\!54\)\( T^{14} - \)\(12\!\cdots\!88\)\( T^{15} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 306 T + 238411 T^{2} + 72369516 T^{3} + 26948434661 T^{4} + 7098521786510 T^{5} + 1857313065270781 T^{6} + 343762744870717356 T^{7} + 78051454360798635971 T^{8} + \)\(69\!\cdots\!86\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{4} \))(\( ( 1 + 4718 T^{2} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 68921 T^{2} )^{4} \))(\( ( 1 - 68921 T^{2} )^{4} \))(\( ( 1 - 137122 T^{2} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 4718 T^{2} + 4750104241 T^{4} )^{2} \))(\( ( 1 - 68921 T^{2} )^{8} \))(\( ( 1 - 150948 T^{2} + 22824779528 T^{4} - 2154287110206316 T^{6} + \)\(17\!\cdots\!70\)\( T^{8} - \)\(10\!\cdots\!56\)\( T^{10} + \)\(51\!\cdots\!68\)\( T^{12} - \)\(16\!\cdots\!08\)\( T^{14} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 350 T + 68921 T^{2} )^{4} \))(\( ( 1 - 195 T + 68921 T^{2} )^{4} \))(\( ( 1 + 106 T + 138851 T^{2} + 7305626 T^{3} + 4750104241 T^{4} )^{4} \))(\( ( 1 + 281 T + 269231 T^{2} + 52376686 T^{3} + 31133332221 T^{4} + 4627148668935 T^{5} + 2145740390003541 T^{6} + 248794718298125326 T^{7} + 88141365578820513991 T^{8} + \)\(63\!\cdots\!61\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{4} \))
$43$ (\( 1 - 68 T + 79507 T^{2} \))(\( 1 + 128 T + 79507 T^{2} \))(\( 1 - 260 T + 166666 T^{2} - 20671820 T^{3} + 6321363049 T^{4} \))(\( 1 - 73 T + 99574 T^{2} - 5804011 T^{3} + 6321363049 T^{4} \))(\( 1 + 73 T + 99574 T^{2} + 5804011 T^{3} + 6321363049 T^{4} \))(\( 1 - 16 T + 149005 T^{2} - 1019664 T^{3} + 11846940535 T^{4} - 101141808784 T^{5} + 502592611936843 T^{6} \))(\( 1 - 411 T + 213439 T^{2} - 60368868 T^{3} + 23440158536 T^{4} - 4799747588076 T^{5} + 1349225407815511 T^{6} - 206565563506042473 T^{7} + 39959630797262576401 T^{8} \))(\( 1 + 411 T + 213439 T^{2} + 60368868 T^{3} + 23440158536 T^{4} + 4799747588076 T^{5} + 1349225407815511 T^{6} + 206565563506042473 T^{7} + 39959630797262576401 T^{8} \))(\( 1 + 304 T + 332071 T^{2} + 86435200 T^{3} + 48749244834 T^{4} + 9950645484448 T^{5} + 3875906209016838 T^{6} + 546388279412924800 T^{7} + \)\(16\!\cdots\!53\)\( T^{8} + \)\(12\!\cdots\!04\)\( T^{9} + \)\(31\!\cdots\!07\)\( T^{10} \))(\( 1 - 304 T + 332071 T^{2} - 86435200 T^{3} + 48749244834 T^{4} - 9950645484448 T^{5} + 3875906209016838 T^{6} - 546388279412924800 T^{7} + \)\(16\!\cdots\!53\)\( T^{8} - \)\(12\!\cdots\!04\)\( T^{9} + \)\(31\!\cdots\!07\)\( T^{10} \))(\( 1 - 154390 T^{2} + 6321363049 T^{4} \))(\( 1 - 142630 T^{2} + 6321363049 T^{4} \))(\( 1 - 265732 T^{2} + 29670935254 T^{4} - 1679788445736868 T^{6} + 39959630797262576401 T^{8} \))(\( 1 - 193819 T^{2} + 21710321968 T^{4} - 1225200264794131 T^{6} + 39959630797262576401 T^{8} \))(\( 1 - 297754 T^{2} + 45863741847 T^{4} - 4531415720155052 T^{6} + \)\(28\!\cdots\!03\)\( T^{8} - \)\(11\!\cdots\!54\)\( T^{10} + \)\(25\!\cdots\!49\)\( T^{12} \))(\( 1 - 257957 T^{2} + 42813314297 T^{4} - 5114746070161734 T^{6} + \)\(45\!\cdots\!14\)\( T^{8} - \)\(32\!\cdots\!66\)\( T^{10} + \)\(17\!\cdots\!97\)\( T^{12} - \)\(65\!\cdots\!93\)\( T^{14} + \)\(15\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 124 T + 79507 T^{2} )^{2} \))(\( ( 1 - 286 T + 79507 T^{2} )^{2} \))(\( ( 1 - 666 T + 269853 T^{2} - 52951662 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 + 568 T + 328987 T^{2} + 103968566 T^{3} + 38129237297 T^{4} + 9424317397102 T^{5} + 3031541269772579 T^{6} + 657223051369917734 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} + \)\(22\!\cdots\!68\)\( T^{9} + \)\(31\!\cdots\!07\)\( T^{10} )^{2} \))(\( ( 1 + 60 T + 390019 T^{2} - 25075490 T^{3} + 63997636304 T^{4} - 12914717467960 T^{5} + 6370401328936198 T^{6} - 2083625256775008960 T^{7} + \)\(51\!\cdots\!40\)\( T^{8} - \)\(16\!\cdots\!20\)\( T^{9} + \)\(40\!\cdots\!02\)\( T^{10} - \)\(64\!\cdots\!80\)\( T^{11} + \)\(25\!\cdots\!04\)\( T^{12} - \)\(79\!\cdots\!30\)\( T^{13} + \)\(98\!\cdots\!31\)\( T^{14} + \)\(12\!\cdots\!80\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 60 T + 390019 T^{2} + 25075490 T^{3} + 63997636304 T^{4} + 12914717467960 T^{5} + 6370401328936198 T^{6} + 2083625256775008960 T^{7} + \)\(51\!\cdots\!40\)\( T^{8} + \)\(16\!\cdots\!20\)\( T^{9} + \)\(40\!\cdots\!02\)\( T^{10} + \)\(64\!\cdots\!80\)\( T^{11} + \)\(25\!\cdots\!04\)\( T^{12} + \)\(79\!\cdots\!30\)\( T^{13} + \)\(98\!\cdots\!31\)\( T^{14} - \)\(12\!\cdots\!80\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 498625 T^{2} + 123288342332 T^{4} + 20092366583326983 T^{6} + \)\(23\!\cdots\!19\)\( T^{8} + \)\(21\!\cdots\!84\)\( T^{10} + \)\(15\!\cdots\!31\)\( T^{12} + \)\(80\!\cdots\!83\)\( T^{14} + \)\(31\!\cdots\!68\)\( T^{16} + \)\(79\!\cdots\!25\)\( T^{18} + \)\(10\!\cdots\!49\)\( T^{20} )^{2} \))(\( ( 1 + 552 T + 152352 T^{2} + 43887864 T^{3} + 6321363049 T^{4} )^{2} \))(\( 1 + 3388378898 T^{4} + 39959630797262576401 T^{8} \))(\( ( 1 + 6321363049 T^{4} )^{2} \))(\( ( 1 + 442 T + 97682 T^{2} + 35142094 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 552 T + 152352 T^{2} - 43887864 T^{3} + 6321363049 T^{4} )^{2} \))(\( 1 - 3388378898 T^{4} - 28478519240850881997 T^{8} - \)\(13\!\cdots\!98\)\( T^{12} + \)\(15\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 156 T + 12168 T^{2} - 7825772 T^{3} + 5356042944 T^{4} - 572935296700 T^{5} + 54826929440600 T^{6} - 21251541125198220 T^{7} - 3798023677929840290 T^{8} - \)\(16\!\cdots\!40\)\( T^{9} + \)\(34\!\cdots\!00\)\( T^{10} - \)\(28\!\cdots\!00\)\( T^{11} + \)\(21\!\cdots\!44\)\( T^{12} - \)\(24\!\cdots\!04\)\( T^{13} + \)\(30\!\cdots\!32\)\( T^{14} - \)\(31\!\cdots\!08\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 143638 T^{2} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 77218 T^{2} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 96150 T^{2} + 14931753923 T^{4} - 607799057161350 T^{6} + 39959630797262576401 T^{8} )^{2} \))(\( ( 1 - 335350 T^{2} + 66382629787 T^{4} - 9635642041597208 T^{6} + \)\(10\!\cdots\!49\)\( T^{8} - \)\(95\!\cdots\!34\)\( T^{10} + \)\(67\!\cdots\!01\)\( T^{12} - \)\(38\!\cdots\!08\)\( T^{14} + \)\(16\!\cdots\!63\)\( T^{16} - \)\(53\!\cdots\!50\)\( T^{18} + \)\(10\!\cdots\!49\)\( T^{20} )^{2} \))
$47$ (\( 1 + 536 T + 103823 T^{2} \))(\( 1 + 324 T + 103823 T^{2} \))(\( 1 - 350 T + 203423 T^{2} - 36338050 T^{3} + 10779215329 T^{4} \))(\( 1 + 224 T + 100634 T^{2} + 23256352 T^{3} + 10779215329 T^{4} \))(\( 1 - 224 T + 100634 T^{2} - 23256352 T^{3} + 10779215329 T^{4} \))(\( 1 - 730 T + 427526 T^{2} - 156550492 T^{3} + 44387031898 T^{4} - 7868827190170 T^{5} + 1119130473102767 T^{6} \))(\( 1 - 8 T + 160820 T^{2} + 20939512 T^{3} + 12301264614 T^{4} + 2174002954376 T^{5} + 1733513409209780 T^{6} - 8953043784822136 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 8 T + 160820 T^{2} - 20939512 T^{3} + 12301264614 T^{4} - 2174002954376 T^{5} + 1733513409209780 T^{6} + 8953043784822136 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 370 T + 463844 T^{2} + 142508488 T^{3} + 91924962535 T^{4} + 21582260378444 T^{5} + 9543925385271305 T^{6} + 1536129678362212552 T^{7} + \)\(51\!\cdots\!48\)\( T^{8} + \)\(42\!\cdots\!70\)\( T^{9} + \)\(12\!\cdots\!43\)\( T^{10} \))(\( 1 - 370 T + 463844 T^{2} - 142508488 T^{3} + 91924962535 T^{4} - 21582260378444 T^{5} + 9543925385271305 T^{6} - 1536129678362212552 T^{7} + \)\(51\!\cdots\!48\)\( T^{8} - \)\(42\!\cdots\!70\)\( T^{9} + \)\(12\!\cdots\!43\)\( T^{10} \))(\( 1 + 79650 T^{2} + 10779215329 T^{4} \))(\( 1 - 102670 T^{2} + 10779215329 T^{4} \))(\( 1 - 284346 T^{2} + 37502712587 T^{4} - 3065026761939834 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 151092 T^{2} + 21266786918 T^{4} - 1628653202489268 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 322152 T^{2} + 42988826152 T^{4} - 4194937101563966 T^{6} + \)\(46\!\cdots\!08\)\( T^{8} - \)\(37\!\cdots\!32\)\( T^{10} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 - 321576 T^{2} + 50800633820 T^{4} - 7019926453338392 T^{6} + \)\(85\!\cdots\!78\)\( T^{8} - \)\(75\!\cdots\!68\)\( T^{10} + \)\(59\!\cdots\!20\)\( T^{12} - \)\(40\!\cdots\!64\)\( T^{14} + \)\(13\!\cdots\!81\)\( T^{16} \))(\( 1 - 525 T + 171802 T^{2} - 54507075 T^{3} + 10779215329 T^{4} \))(\( 1 - 45 T - 101798 T^{2} - 4672035 T^{3} + 10779215329 T^{4} \))(\( 1 + 196 T - 170642 T^{2} + 276752 T^{3} + 28937567667 T^{4} + 28733222896 T^{5} - 1839386862171218 T^{6} + 219349572728142332 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 473 T - 199186 T^{2} - 58080717 T^{3} + 49165993755 T^{4} + 5867004935190 T^{5} - 5795165507082528 T^{6} - 101648572991175666 T^{7} + \)\(44\!\cdots\!01\)\( T^{8} - \)\(23\!\cdots\!89\)\( T^{9} - \)\(43\!\cdots\!94\)\( T^{10} - \)\(24\!\cdots\!47\)\( T^{11} + \)\(48\!\cdots\!29\)\( T^{12} - \)\(11\!\cdots\!22\)\( T^{13} - \)\(67\!\cdots\!48\)\( T^{14} + \)\(70\!\cdots\!70\)\( T^{15} + \)\(61\!\cdots\!95\)\( T^{16} - \)\(75\!\cdots\!99\)\( T^{17} - \)\(26\!\cdots\!66\)\( T^{18} + \)\(66\!\cdots\!99\)\( T^{19} + \)\(14\!\cdots\!49\)\( T^{20} \))(\( 1 - 1098 T + 113511 T^{2} + 261463230 T^{3} - 49854020808 T^{4} - 44879169218864 T^{5} + 7131800794134569 T^{6} + 6709692485206028374 T^{7} - \)\(29\!\cdots\!11\)\( T^{8} - \)\(95\!\cdots\!46\)\( T^{9} - \)\(50\!\cdots\!20\)\( T^{10} + \)\(99\!\cdots\!32\)\( T^{11} + \)\(21\!\cdots\!95\)\( T^{12} - \)\(85\!\cdots\!14\)\( T^{13} - \)\(34\!\cdots\!47\)\( T^{14} + \)\(32\!\cdots\!78\)\( T^{15} + \)\(41\!\cdots\!76\)\( T^{16} + \)\(34\!\cdots\!94\)\( T^{17} - \)\(36\!\cdots\!63\)\( T^{18} - \)\(95\!\cdots\!38\)\( T^{19} + \)\(24\!\cdots\!95\)\( T^{20} + \)\(12\!\cdots\!76\)\( T^{21} - \)\(63\!\cdots\!80\)\( T^{22} - \)\(12\!\cdots\!62\)\( T^{23} - \)\(39\!\cdots\!91\)\( T^{24} + \)\(94\!\cdots\!62\)\( T^{25} + \)\(10\!\cdots\!81\)\( T^{26} - \)\(67\!\cdots\!28\)\( T^{27} - \)\(78\!\cdots\!68\)\( T^{28} + \)\(42\!\cdots\!90\)\( T^{29} + \)\(19\!\cdots\!99\)\( T^{30} - \)\(19\!\cdots\!86\)\( T^{31} + \)\(18\!\cdots\!61\)\( T^{32} \))(\( 1 + 1098 T + 113511 T^{2} - 261463230 T^{3} - 49854020808 T^{4} + 44879169218864 T^{5} + 7131800794134569 T^{6} - 6709692485206028374 T^{7} - \)\(29\!\cdots\!11\)\( T^{8} + \)\(95\!\cdots\!46\)\( T^{9} - \)\(50\!\cdots\!20\)\( T^{10} - \)\(99\!\cdots\!32\)\( T^{11} + \)\(21\!\cdots\!95\)\( T^{12} + \)\(85\!\cdots\!14\)\( T^{13} - \)\(34\!\cdots\!47\)\( T^{14} - \)\(32\!\cdots\!78\)\( T^{15} + \)\(41\!\cdots\!76\)\( T^{16} - \)\(34\!\cdots\!94\)\( T^{17} - \)\(36\!\cdots\!63\)\( T^{18} + \)\(95\!\cdots\!38\)\( T^{19} + \)\(24\!\cdots\!95\)\( T^{20} - \)\(12\!\cdots\!76\)\( T^{21} - \)\(63\!\cdots\!80\)\( T^{22} + \)\(12\!\cdots\!62\)\( T^{23} - \)\(39\!\cdots\!91\)\( T^{24} - \)\(94\!\cdots\!62\)\( T^{25} + \)\(10\!\cdots\!81\)\( T^{26} + \)\(67\!\cdots\!28\)\( T^{27} - \)\(78\!\cdots\!68\)\( T^{28} - \)\(42\!\cdots\!90\)\( T^{29} + \)\(19\!\cdots\!99\)\( T^{30} + \)\(19\!\cdots\!86\)\( T^{31} + \)\(18\!\cdots\!61\)\( T^{32} \))(\( 1 - 586566 T^{2} + 176578551908 T^{4} - 36486163260401340 T^{6} + \)\(57\!\cdots\!69\)\( T^{8} - \)\(67\!\cdots\!20\)\( T^{10} + \)\(56\!\cdots\!06\)\( T^{12} - \)\(16\!\cdots\!82\)\( T^{14} - \)\(40\!\cdots\!95\)\( T^{16} + \)\(95\!\cdots\!20\)\( T^{18} - \)\(12\!\cdots\!18\)\( T^{20} + \)\(10\!\cdots\!80\)\( T^{22} - \)\(47\!\cdots\!95\)\( T^{24} - \)\(20\!\cdots\!98\)\( T^{26} + \)\(75\!\cdots\!86\)\( T^{28} - \)\(98\!\cdots\!80\)\( T^{30} + \)\(89\!\cdots\!49\)\( T^{32} - \)\(61\!\cdots\!60\)\( T^{34} + \)\(32\!\cdots\!88\)\( T^{36} - \)\(11\!\cdots\!54\)\( T^{38} + \)\(21\!\cdots\!01\)\( T^{40} \))(\( 1 + 6514906943 T^{4} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( ( 1 + 10779215329 T^{4} )^{2} \))(\( 1 + 9293086658 T^{4} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 19389520078 T^{4} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 6514906943 T^{4} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( ( 1 + 10779215329 T^{4} )^{4} \))(\( 1 + 7709822402 T^{4} + \)\(18\!\cdots\!53\)\( T^{8} + \)\(15\!\cdots\!34\)\( T^{12} + \)\(37\!\cdots\!20\)\( T^{16} + \)\(17\!\cdots\!94\)\( T^{20} + \)\(24\!\cdots\!93\)\( T^{24} + \)\(12\!\cdots\!42\)\( T^{28} + \)\(18\!\cdots\!61\)\( T^{32} \))(\( 1 - 67979 T^{2} - 6158070888 T^{4} - 732760278850091 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 205621 T^{2} + 31500780312 T^{4} + 2216433035164309 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 379700 T^{2} + 86885340714 T^{4} + 13566042583051600 T^{6} + \)\(16\!\cdots\!55\)\( T^{8} + \)\(14\!\cdots\!00\)\( T^{10} + \)\(10\!\cdots\!74\)\( T^{12} + \)\(47\!\cdots\!00\)\( T^{14} + \)\(13\!\cdots\!81\)\( T^{16} \))(\( 1 + 622101 T^{2} + 192951408388 T^{4} + 40100242634255745 T^{6} + \)\(63\!\cdots\!39\)\( T^{8} + \)\(85\!\cdots\!90\)\( T^{10} + \)\(10\!\cdots\!36\)\( T^{12} + \)\(12\!\cdots\!02\)\( T^{14} + \)\(15\!\cdots\!45\)\( T^{16} + \)\(17\!\cdots\!95\)\( T^{18} + \)\(18\!\cdots\!92\)\( T^{20} + \)\(18\!\cdots\!55\)\( T^{22} + \)\(17\!\cdots\!45\)\( T^{24} + \)\(15\!\cdots\!78\)\( T^{26} + \)\(14\!\cdots\!16\)\( T^{28} + \)\(12\!\cdots\!10\)\( T^{30} + \)\(10\!\cdots\!19\)\( T^{32} + \)\(67\!\cdots\!05\)\( T^{34} + \)\(35\!\cdots\!68\)\( T^{36} + \)\(12\!\cdots\!69\)\( T^{38} + \)\(21\!\cdots\!01\)\( T^{40} \))
$53$ (\( 1 + 22 T + 148877 T^{2} \))(\( 1 - 162 T + 148877 T^{2} \))(\( 1 - 56 T + 265770 T^{2} - 8337112 T^{3} + 22164361129 T^{4} \))(\( 1 - 262 T + 239106 T^{2} - 39005774 T^{3} + 22164361129 T^{4} \))(\( 1 + 262 T + 239106 T^{2} + 39005774 T^{3} + 22164361129 T^{4} \))(\( 1 + 110 T + 105959 T^{2} - 57565396 T^{3} + 15774858043 T^{4} + 2438079724190 T^{5} + 3299763591802133 T^{6} \))(\( 1 + 90 T + 133752 T^{2} - 19514962 T^{3} + 19633648894 T^{4} - 2905328997674 T^{5} + 2964527629726008 T^{6} + 296978723262191970 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 90 T + 133752 T^{2} + 19514962 T^{3} + 19633648894 T^{4} + 2905328997674 T^{5} + 2964527629726008 T^{6} - 296978723262191970 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 976 T + 962689 T^{2} + 581217760 T^{3} + 317107543306 T^{4} + 129795824400416 T^{5} + 47210019724767362 T^{6} + 12882320327228451040 T^{7} + \)\(31\!\cdots\!37\)\( T^{8} + \)\(47\!\cdots\!16\)\( T^{9} + \)\(73\!\cdots\!57\)\( T^{10} \))(\( 1 - 976 T + 962689 T^{2} - 581217760 T^{3} + 317107543306 T^{4} - 129795824400416 T^{5} + 47210019724767362 T^{6} - 12882320327228451040 T^{7} + \)\(31\!\cdots\!37\)\( T^{8} - \)\(47\!\cdots\!16\)\( T^{9} + \)\(73\!\cdots\!57\)\( T^{10} \))(\( 1 - 297270 T^{2} + 22164361129 T^{4} \))(\( 1 - 271510 T^{2} + 22164361129 T^{4} \))(\( 1 - 528404 T^{2} + 114028658614 T^{4} - 11711737078008116 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 409568 T^{2} + 81061375918 T^{4} - 9077813058882272 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 199818 T^{2} + 55441412887 T^{4} - 6092351194402124 T^{6} + \)\(12\!\cdots\!23\)\( T^{8} - \)\(98\!\cdots\!38\)\( T^{10} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 - 259404 T^{2} + 60669588452 T^{4} - 11323260350912468 T^{6} + \)\(19\!\cdots\!74\)\( T^{8} - \)\(25\!\cdots\!72\)\( T^{10} + \)\(29\!\cdots\!32\)\( T^{12} - \)\(28\!\cdots\!56\)\( T^{14} + \)\(24\!\cdots\!81\)\( T^{16} \))(\( 1 - 303 T - 57068 T^{2} - 45109731 T^{3} + 22164361129 T^{4} \))(\( 1 - 597 T + 207532 T^{2} - 88879569 T^{3} + 22164361129 T^{4} \))(\( 1 + 952 T + 422302 T^{2} + 177308096 T^{3} + 77165754267 T^{4} + 26397097408192 T^{5} + 9360054033498958 T^{6} + 3141374939395630616 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 351 T - 584980 T^{2} + 134936885 T^{3} + 229763822323 T^{4} - 33792782771134 T^{5} - 61716154410935792 T^{6} + 4669968185983210370 T^{7} + \)\(12\!\cdots\!13\)\( T^{8} - \)\(30\!\cdots\!53\)\( T^{9} - \)\(21\!\cdots\!12\)\( T^{10} - \)\(44\!\cdots\!81\)\( T^{11} + \)\(28\!\cdots\!77\)\( T^{12} + \)\(15\!\cdots\!10\)\( T^{13} - \)\(30\!\cdots\!72\)\( T^{14} - \)\(24\!\cdots\!38\)\( T^{15} + \)\(25\!\cdots\!47\)\( T^{16} + \)\(21\!\cdots\!05\)\( T^{17} - \)\(14\!\cdots\!80\)\( T^{18} - \)\(12\!\cdots\!87\)\( T^{19} + \)\(53\!\cdots\!49\)\( T^{20} \))(\( 1 + 734 T - 382430 T^{2} - 387452692 T^{3} + 81146131455 T^{4} + 122549867586436 T^{5} - 7937649254975140 T^{6} - 30296526399555473538 T^{7} - \)\(23\!\cdots\!79\)\( T^{8} + \)\(57\!\cdots\!80\)\( T^{9} + \)\(12\!\cdots\!90\)\( T^{10} - \)\(90\!\cdots\!40\)\( T^{11} - \)\(33\!\cdots\!77\)\( T^{12} + \)\(10\!\cdots\!22\)\( T^{13} + \)\(68\!\cdots\!40\)\( T^{14} - \)\(57\!\cdots\!36\)\( T^{15} - \)\(11\!\cdots\!35\)\( T^{16} - \)\(85\!\cdots\!72\)\( T^{17} + \)\(15\!\cdots\!60\)\( T^{18} + \)\(34\!\cdots\!26\)\( T^{19} - \)\(16\!\cdots\!57\)\( T^{20} - \)\(66\!\cdots\!80\)\( T^{21} + \)\(13\!\cdots\!10\)\( T^{22} + \)\(93\!\cdots\!40\)\( T^{23} - \)\(57\!\cdots\!99\)\( T^{24} - \)\(10\!\cdots\!06\)\( T^{25} - \)\(42\!\cdots\!60\)\( T^{26} + \)\(97\!\cdots\!28\)\( T^{27} + \)\(96\!\cdots\!55\)\( T^{28} - \)\(68\!\cdots\!64\)\( T^{29} - \)\(10\!\cdots\!70\)\( T^{30} + \)\(28\!\cdots\!62\)\( T^{31} + \)\(58\!\cdots\!61\)\( T^{32} \))(\( 1 - 734 T - 382430 T^{2} + 387452692 T^{3} + 81146131455 T^{4} - 122549867586436 T^{5} - 7937649254975140 T^{6} + 30296526399555473538 T^{7} - \)\(23\!\cdots\!79\)\( T^{8} - \)\(57\!\cdots\!80\)\( T^{9} + \)\(12\!\cdots\!90\)\( T^{10} + \)\(90\!\cdots\!40\)\( T^{11} - \)\(33\!\cdots\!77\)\( T^{12} - \)\(10\!\cdots\!22\)\( T^{13} + \)\(68\!\cdots\!40\)\( T^{14} + \)\(57\!\cdots\!36\)\( T^{15} - \)\(11\!\cdots\!35\)\( T^{16} + \)\(85\!\cdots\!72\)\( T^{17} + \)\(15\!\cdots\!60\)\( T^{18} - \)\(34\!\cdots\!26\)\( T^{19} - \)\(16\!\cdots\!57\)\( T^{20} + \)\(66\!\cdots\!80\)\( T^{21} + \)\(13\!\cdots\!10\)\( T^{22} - \)\(93\!\cdots\!40\)\( T^{23} - \)\(57\!\cdots\!99\)\( T^{24} + \)\(10\!\cdots\!06\)\( T^{25} - \)\(42\!\cdots\!60\)\( T^{26} - \)\(97\!\cdots\!28\)\( T^{27} + \)\(96\!\cdots\!55\)\( T^{28} + \)\(68\!\cdots\!64\)\( T^{29} - \)\(10\!\cdots\!70\)\( T^{30} - \)\(28\!\cdots\!62\)\( T^{31} + \)\(58\!\cdots\!61\)\( T^{32} \))(\( 1 - 296626 T^{2} + 51825139476 T^{4} + 234602868312748 T^{6} - \)\(10\!\cdots\!55\)\( T^{8} + \)\(17\!\cdots\!32\)\( T^{10} + \)\(16\!\cdots\!94\)\( T^{12} - \)\(69\!\cdots\!02\)\( T^{14} + \)\(80\!\cdots\!09\)\( T^{16} + \)\(61\!\cdots\!84\)\( T^{18} - \)\(20\!\cdots\!90\)\( T^{20} + \)\(13\!\cdots\!36\)\( T^{22} + \)\(39\!\cdots\!69\)\( T^{24} - \)\(76\!\cdots\!78\)\( T^{26} + \)\(40\!\cdots\!14\)\( T^{28} + \)\(96\!\cdots\!68\)\( T^{30} - \)\(12\!\cdots\!55\)\( T^{32} + \)\(61\!\cdots\!32\)\( T^{34} + \)\(30\!\cdots\!36\)\( T^{36} - \)\(38\!\cdots\!94\)\( T^{38} + \)\(28\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 864 T + 373248 T^{2} - 128629728 T^{3} + 22164361129 T^{4} )^{2} \))(\( 1 - 41794002542 T^{4} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( ( 1 + 22164361129 T^{4} )^{2} \))(\( ( 1 - 174 T + 15138 T^{2} - 25904598 T^{3} + 22164361129 T^{4} )^{2} \))(\( ( 1 + 864 T + 373248 T^{2} + 128629728 T^{3} + 22164361129 T^{4} )^{2} \))(\( ( 1 - 41794002542 T^{4} + \)\(49\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 + 884 T + 390728 T^{2} + 186770028 T^{3} + 56931497936 T^{4} - 1204571535772 T^{5} - 5868049883599464 T^{6} - 4928363332779316004 T^{7} - \)\(28\!\cdots\!94\)\( T^{8} - \)\(73\!\cdots\!08\)\( T^{9} - \)\(13\!\cdots\!56\)\( T^{10} - \)\(39\!\cdots\!76\)\( T^{11} + \)\(27\!\cdots\!76\)\( T^{12} + \)\(13\!\cdots\!96\)\( T^{13} + \)\(42\!\cdots\!92\)\( T^{14} + \)\(14\!\cdots\!52\)\( T^{15} + \)\(24\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 + 205945 T^{2} + 20248981896 T^{4} + 4564639352711905 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 58655 T^{2} - 18723952104 T^{4} - 1300050602021495 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 61700 T^{2} - 4924127046 T^{4} - 2196378411580400 T^{6} - \)\(49\!\cdots\!25\)\( T^{8} - \)\(48\!\cdots\!00\)\( T^{10} - \)\(24\!\cdots\!86\)\( T^{12} + \)\(67\!\cdots\!00\)\( T^{14} + \)\(24\!\cdots\!81\)\( T^{16} \))(\( 1 + 1293161 T^{2} + 896454938316 T^{4} + 434177286825727957 T^{6} + \)\(16\!\cdots\!95\)\( T^{8} + \)\(50\!\cdots\!98\)\( T^{10} + \)\(13\!\cdots\!44\)\( T^{12} + \)\(29\!\cdots\!22\)\( T^{14} + \)\(59\!\cdots\!69\)\( T^{16} + \)\(10\!\cdots\!91\)\( T^{18} + \)\(16\!\cdots\!60\)\( T^{20} + \)\(23\!\cdots\!39\)\( T^{22} + \)\(29\!\cdots\!29\)\( T^{24} + \)\(32\!\cdots\!58\)\( T^{26} + \)\(31\!\cdots\!64\)\( T^{28} + \)\(26\!\cdots\!02\)\( T^{30} + \)\(19\!\cdots\!95\)\( T^{32} + \)\(11\!\cdots\!13\)\( T^{34} + \)\(52\!\cdots\!76\)\( T^{36} + \)\(16\!\cdots\!09\)\( T^{38} + \)\(28\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 + 560 T + 205379 T^{2} \))(\( 1 - 810 T + 205379 T^{2} \))(\( ( 1 + 616 T + 205379 T^{2} )^{2} \))(\( 1 - 190 T - 32242 T^{2} - 39022010 T^{3} + 42180533641 T^{4} \))(\( 1 - 190 T - 32242 T^{2} - 39022010 T^{3} + 42180533641 T^{4} \))(\( 1 + 180 T + 3577 T^{2} - 128522760 T^{3} + 734640683 T^{4} + 7592496055380 T^{5} + 8662995818654939 T^{6} \))(\( 1 - 1018 T + 1189512 T^{2} - 683319466 T^{3} + 407279566174 T^{4} - 140339468607614 T^{5} + 50174250932373192 T^{6} - 8818929743390727902 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 1018 T + 1189512 T^{2} - 683319466 T^{3} + 407279566174 T^{4} - 140339468607614 T^{5} + 50174250932373192 T^{6} - 8818929743390727902 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 432 T + 700701 T^{2} + 268108032 T^{3} + 242314293152 T^{4} + 78692992197632 T^{5} + 49766267213264608 T^{6} + 11308939863198304512 T^{7} + \)\(60\!\cdots\!39\)\( T^{8} + \)\(76\!\cdots\!92\)\( T^{9} + \)\(36\!\cdots\!99\)\( T^{10} \))(\( 1 + 432 T + 700701 T^{2} + 268108032 T^{3} + 242314293152 T^{4} + 78692992197632 T^{5} + 49766267213264608 T^{6} + 11308939863198304512 T^{7} + \)\(60\!\cdots\!39\)\( T^{8} + \)\(76\!\cdots\!92\)\( T^{9} + \)\(36\!\cdots\!99\)\( T^{10} \))(\( ( 1 - 560 T + 205379 T^{2} )^{2} \))(\( ( 1 + 810 T + 205379 T^{2} )^{2} \))(\( ( 1 - 616 T + 205379 T^{2} )^{4} \))(\( ( 1 + 190 T - 32242 T^{2} + 39022010 T^{3} + 42180533641 T^{4} )^{2} \))(\( ( 1 - 180 T + 3577 T^{2} + 128522760 T^{3} + 734640683 T^{4} - 7592496055380 T^{5} + 8662995818654939 T^{6} )^{2} \))(\( ( 1 + 1018 T + 1189512 T^{2} + 683319466 T^{3} + 407279566174 T^{4} + 140339468607614 T^{5} + 50174250932373192 T^{6} + 8818929743390727902 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} )^{2} \))(\( 1 - 105 T - 194354 T^{2} - 21564795 T^{3} + 42180533641 T^{4} \))(\( 1 - 360 T - 75779 T^{2} - 73936440 T^{3} + 42180533641 T^{4} \))(\( 1 + 840 T + 259954 T^{2} + 29305920 T^{3} + 11504401275 T^{4} + 6018820543680 T^{5} + 10964998442112514 T^{6} + 7276916487670148760 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 708 T - 594963 T^{2} - 347355028 T^{3} + 339076027067 T^{4} + 128485265745528 T^{5} - 124220569667051830 T^{6} - 22490966070804129944 T^{7} + \)\(39\!\cdots\!17\)\( T^{8} + \)\(24\!\cdots\!56\)\( T^{9} - \)\(88\!\cdots\!49\)\( T^{10} + \)\(49\!\cdots\!24\)\( T^{11} + \)\(16\!\cdots\!97\)\( T^{12} - \)\(19\!\cdots\!16\)\( T^{13} - \)\(22\!\cdots\!30\)\( T^{14} + \)\(46\!\cdots\!72\)\( T^{15} + \)\(25\!\cdots\!07\)\( T^{16} - \)\(53\!\cdots\!52\)\( T^{17} - \)\(18\!\cdots\!43\)\( T^{18} + \)\(46\!\cdots\!52\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} \))(\( 1 + 558 T - 535213 T^{2} + 51793382 T^{3} + 346552924987 T^{4} - 92921108052302 T^{5} - 65082660728694202 T^{6} + 63554581311093718850 T^{7} + \)\(20\!\cdots\!28\)\( T^{8} - \)\(14\!\cdots\!38\)\( T^{9} + \)\(55\!\cdots\!72\)\( T^{10} + \)\(12\!\cdots\!08\)\( T^{11} - \)\(13\!\cdots\!72\)\( T^{12} + \)\(19\!\cdots\!60\)\( T^{13} + \)\(11\!\cdots\!73\)\( T^{14} - \)\(38\!\cdots\!78\)\( T^{15} - \)\(10\!\cdots\!63\)\( T^{16} - \)\(78\!\cdots\!62\)\( T^{17} + \)\(48\!\cdots\!93\)\( T^{18} + \)\(17\!\cdots\!40\)\( T^{19} - \)\(24\!\cdots\!32\)\( T^{20} + \)\(47\!\cdots\!92\)\( T^{21} + \)\(41\!\cdots\!12\)\( T^{22} - \)\(21\!\cdots\!42\)\( T^{23} + \)\(65\!\cdots\!08\)\( T^{24} + \)\(41\!\cdots\!50\)\( T^{25} - \)\(86\!\cdots\!02\)\( T^{26} - \)\(25\!\cdots\!58\)\( T^{27} + \)\(19\!\cdots\!67\)\( T^{28} + \)\(59\!\cdots\!98\)\( T^{29} - \)\(12\!\cdots\!53\)\( T^{30} + \)\(27\!\cdots\!42\)\( T^{31} + \)\(10\!\cdots\!21\)\( T^{32} \))(\( 1 + 558 T - 535213 T^{2} + 51793382 T^{3} + 346552924987 T^{4} - 92921108052302 T^{5} - 65082660728694202 T^{6} + 63554581311093718850 T^{7} + \)\(20\!\cdots\!28\)\( T^{8} - \)\(14\!\cdots\!38\)\( T^{9} + \)\(55\!\cdots\!72\)\( T^{10} + \)\(12\!\cdots\!08\)\( T^{11} - \)\(13\!\cdots\!72\)\( T^{12} + \)\(19\!\cdots\!60\)\( T^{13} + \)\(11\!\cdots\!73\)\( T^{14} - \)\(38\!\cdots\!78\)\( T^{15} - \)\(10\!\cdots\!63\)\( T^{16} - \)\(78\!\cdots\!62\)\( T^{17} + \)\(48\!\cdots\!93\)\( T^{18} + \)\(17\!\cdots\!40\)\( T^{19} - \)\(24\!\cdots\!32\)\( T^{20} + \)\(47\!\cdots\!92\)\( T^{21} + \)\(41\!\cdots\!12\)\( T^{22} - \)\(21\!\cdots\!42\)\( T^{23} + \)\(65\!\cdots\!08\)\( T^{24} + \)\(41\!\cdots\!50\)\( T^{25} - \)\(86\!\cdots\!02\)\( T^{26} - \)\(25\!\cdots\!58\)\( T^{27} + \)\(19\!\cdots\!67\)\( T^{28} + \)\(59\!\cdots\!98\)\( T^{29} - \)\(12\!\cdots\!53\)\( T^{30} + \)\(27\!\cdots\!42\)\( T^{31} + \)\(10\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 1257 T + 28812 T^{2} + 249631107 T^{3} + 284096537737 T^{4} - 190598573007302 T^{5} - 67351197370118230 T^{6} + 17879205302394815916 T^{7} + \)\(35\!\cdots\!17\)\( T^{8} - \)\(50\!\cdots\!09\)\( T^{9} - \)\(62\!\cdots\!14\)\( T^{10} - \)\(10\!\cdots\!11\)\( T^{11} + \)\(15\!\cdots\!97\)\( T^{12} + \)\(15\!\cdots\!24\)\( T^{13} - \)\(11\!\cdots\!30\)\( T^{14} - \)\(69\!\cdots\!98\)\( T^{15} + \)\(21\!\cdots\!77\)\( T^{16} + \)\(38\!\cdots\!13\)\( T^{17} + \)\(91\!\cdots\!32\)\( T^{18} - \)\(81\!\cdots\!83\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 + 347398 T^{2} + 42180533641 T^{4} )^{2} \))(\( ( 1 + 205379 T^{2} )^{4} \))(\( ( 1 + 205379 T^{2} )^{4} \))(\( ( 1 + 234038 T^{2} + 42180533641 T^{4} )^{2} \))(\( ( 1 + 347398 T^{2} + 42180533641 T^{4} )^{2} \))(\( ( 1 + 205379 T^{2} )^{8} \))(\( ( 1 + 564992 T^{2} + 242975513538 T^{4} + 70586293205624784 T^{6} + \)\(16\!\cdots\!70\)\( T^{8} + \)\(29\!\cdots\!44\)\( T^{10} + \)\(43\!\cdots\!78\)\( T^{12} + \)\(42\!\cdots\!32\)\( T^{14} + \)\(31\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 105 T - 194354 T^{2} + 21564795 T^{3} + 42180533641 T^{4} )^{2} \))(\( ( 1 + 360 T - 75779 T^{2} + 73936440 T^{3} + 42180533641 T^{4} )^{2} \))(\( ( 1 - 840 T + 259954 T^{2} - 29305920 T^{3} + 11504401275 T^{4} - 6018820543680 T^{5} + 10964998442112514 T^{6} - 7276916487670148760 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} )^{2} \))(\( ( 1 - 708 T - 594963 T^{2} + 347355028 T^{3} + 339076027067 T^{4} - 128485265745528 T^{5} - 124220569667051830 T^{6} + 22490966070804129944 T^{7} + \)\(39\!\cdots\!17\)\( T^{8} - \)\(24\!\cdots\!56\)\( T^{9} - \)\(88\!\cdots\!49\)\( T^{10} - \)\(49\!\cdots\!24\)\( T^{11} + \)\(16\!\cdots\!97\)\( T^{12} + \)\(19\!\cdots\!16\)\( T^{13} - \)\(22\!\cdots\!30\)\( T^{14} - \)\(46\!\cdots\!72\)\( T^{15} + \)\(25\!\cdots\!07\)\( T^{16} + \)\(53\!\cdots\!52\)\( T^{17} - \)\(18\!\cdots\!43\)\( T^{18} - \)\(46\!\cdots\!52\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} )^{2} \))
$61$ (\( 1 + 278 T + 226981 T^{2} \))(\( 1 + 488 T + 226981 T^{2} \))(\( 1 - 336 T + 458858 T^{2} - 76265616 T^{3} + 51520374361 T^{4} \))(\( 1 - 990 T + 669098 T^{2} - 224711190 T^{3} + 51520374361 T^{4} \))(\( 1 - 990 T + 669098 T^{2} - 224711190 T^{3} + 51520374361 T^{4} \))(\( 1 - 1222 T + 1103759 T^{2} - 593135356 T^{3} + 250532321579 T^{4} - 62957897469142 T^{5} + 11694146092834141 T^{6} \))(\( 1 - 50 T + 722188 T^{2} - 51306118 T^{3} + 225994176278 T^{4} - 11645513969758 T^{5} + 37207396119021868 T^{6} - 584707304641707050 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 50 T + 722188 T^{2} - 51306118 T^{3} + 225994176278 T^{4} - 11645513969758 T^{5} + 37207396119021868 T^{6} - 584707304641707050 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 442 T + 798959 T^{2} + 288407548 T^{3} + 306199000900 T^{4} + 84731818304260 T^{5} + 69501355423282900 T^{6} + 14858864841498076828 T^{7} + \)\(93\!\cdots\!19\)\( T^{8} + \)\(11\!\cdots\!82\)\( T^{9} + \)\(60\!\cdots\!01\)\( T^{10} \))(\( 1 + 442 T + 798959 T^{2} + 288407548 T^{3} + 306199000900 T^{4} + 84731818304260 T^{5} + 69501355423282900 T^{6} + 14858864841498076828 T^{7} + \)\(93\!\cdots\!19\)\( T^{8} + \)\(11\!\cdots\!82\)\( T^{9} + \)\(60\!\cdots\!01\)\( T^{10} \))(\( ( 1 + 278 T + 226981 T^{2} )^{2} \))(\( ( 1 + 488 T + 226981 T^{2} )^{2} \))(\( ( 1 - 336 T + 458858 T^{2} - 76265616 T^{3} + 51520374361 T^{4} )^{2} \))(\( ( 1 - 990 T + 669098 T^{2} - 224711190 T^{3} + 51520374361 T^{4} )^{2} \))(\( ( 1 - 1222 T + 1103759 T^{2} - 593135356 T^{3} + 250532321579 T^{4} - 62957897469142 T^{5} + 11694146092834141 T^{6} )^{2} \))(\( ( 1 - 50 T + 722188 T^{2} - 51306118 T^{3} + 225994176278 T^{4} - 11645513969758 T^{5} + 37207396119021868 T^{6} - 584707304641707050 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} )^{2} \))(\( 1 - 413 T - 56412 T^{2} - 93743153 T^{3} + 51520374361 T^{4} \))(\( 1 + 392 T - 73317 T^{2} + 88976552 T^{3} + 51520374361 T^{4} \))(\( 1 + 98 T + 203041 T^{2} - 63445102 T^{3} - 16282426916 T^{4} - 14400832697062 T^{5} + 10460748330631801 T^{6} + 1146026317097745818 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 1944 T + 1201957 T^{2} + 465031984 T^{3} + 642573181668 T^{4} + 544248825687640 T^{5} + 179953145332374091 T^{6} + 96783385662450749352 T^{7} + \)\(99\!\cdots\!11\)\( T^{8} + \)\(41\!\cdots\!76\)\( T^{9} + \)\(10\!\cdots\!72\)\( T^{10} + \)\(94\!\cdots\!56\)\( T^{11} + \)\(51\!\cdots\!71\)\( T^{12} + \)\(11\!\cdots\!32\)\( T^{13} + \)\(47\!\cdots\!11\)\( T^{14} + \)\(32\!\cdots\!40\)\( T^{15} + \)\(87\!\cdots\!08\)\( T^{16} + \)\(14\!\cdots\!24\)\( T^{17} + \)\(84\!\cdots\!37\)\( T^{18} + \)\(31\!\cdots\!24\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} \))(\( 1 - 1496 T + 349707 T^{2} + 193316720 T^{3} + 223176165577 T^{4} - 191297494889548 T^{5} - 31123897081438784 T^{6} - 16956756955360354126 T^{7} + \)\(44\!\cdots\!28\)\( T^{8} + \)\(90\!\cdots\!22\)\( T^{9} - \)\(24\!\cdots\!64\)\( T^{10} - \)\(64\!\cdots\!46\)\( T^{11} + \)\(11\!\cdots\!08\)\( T^{12} + \)\(56\!\cdots\!68\)\( T^{13} + \)\(67\!\cdots\!75\)\( T^{14} - \)\(23\!\cdots\!28\)\( T^{15} - \)\(82\!\cdots\!43\)\( T^{16} - \)\(53\!\cdots\!68\)\( T^{17} + \)\(34\!\cdots\!75\)\( T^{18} + \)\(66\!\cdots\!88\)\( T^{19} + \)\(29\!\cdots\!68\)\( T^{20} - \)\(39\!\cdots\!46\)\( T^{21} - \)\(33\!\cdots\!84\)\( T^{22} + \)\(28\!\cdots\!42\)\( T^{23} + \)\(31\!\cdots\!48\)\( T^{24} - \)\(27\!\cdots\!46\)\( T^{25} - \)\(11\!\cdots\!84\)\( T^{26} - \)\(15\!\cdots\!88\)\( T^{27} + \)\(41\!\cdots\!97\)\( T^{28} + \)\(82\!\cdots\!20\)\( T^{29} + \)\(33\!\cdots\!47\)\( T^{30} - \)\(32\!\cdots\!96\)\( T^{31} + \)\(49\!\cdots\!81\)\( T^{32} \))(\( 1 - 1496 T + 349707 T^{2} + 193316720 T^{3} + 223176165577 T^{4} - 191297494889548 T^{5} - 31123897081438784 T^{6} - 16956756955360354126 T^{7} + \)\(44\!\cdots\!28\)\( T^{8} + \)\(90\!\cdots\!22\)\( T^{9} - \)\(24\!\cdots\!64\)\( T^{10} - \)\(64\!\cdots\!46\)\( T^{11} + \)\(11\!\cdots\!08\)\( T^{12} + \)\(56\!\cdots\!68\)\( T^{13} + \)\(67\!\cdots\!75\)\( T^{14} - \)\(23\!\cdots\!28\)\( T^{15} - \)\(82\!\cdots\!43\)\( T^{16} - \)\(53\!\cdots\!68\)\( T^{17} + \)\(34\!\cdots\!75\)\( T^{18} + \)\(66\!\cdots\!88\)\( T^{19} + \)\(29\!\cdots\!68\)\( T^{20} - \)\(39\!\cdots\!46\)\( T^{21} - \)\(33\!\cdots\!84\)\( T^{22} + \)\(28\!\cdots\!42\)\( T^{23} + \)\(31\!\cdots\!48\)\( T^{24} - \)\(27\!\cdots\!46\)\( T^{25} - \)\(11\!\cdots\!84\)\( T^{26} - \)\(15\!\cdots\!88\)\( T^{27} + \)\(41\!\cdots\!97\)\( T^{28} + \)\(82\!\cdots\!20\)\( T^{29} + \)\(33\!\cdots\!47\)\( T^{30} - \)\(32\!\cdots\!96\)\( T^{31} + \)\(49\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 256 T - 751153 T^{2} + 204835764 T^{3} + 291945445208 T^{4} - 69908506373860 T^{5} - 90828760031755899 T^{6} + 11422899003515573152 T^{7} + \)\(26\!\cdots\!11\)\( T^{8} - \)\(72\!\cdots\!04\)\( T^{9} - \)\(65\!\cdots\!08\)\( T^{10} - \)\(16\!\cdots\!24\)\( T^{11} + \)\(13\!\cdots\!71\)\( T^{12} + \)\(13\!\cdots\!32\)\( T^{13} - \)\(24\!\cdots\!79\)\( T^{14} - \)\(42\!\cdots\!60\)\( T^{15} + \)\(39\!\cdots\!48\)\( T^{16} + \)\(63\!\cdots\!04\)\( T^{17} - \)\(52\!\cdots\!73\)\( T^{18} - \)\(40\!\cdots\!76\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 - 311402 T^{2} + 51520374361 T^{4} )^{2} \))(\( ( 1 - 226981 T^{2} )^{4} \))(\( ( 1 - 226981 T^{2} )^{4} \))(\( ( 1 - 338442 T^{2} + 51520374361 T^{4} )^{2} \))(\( ( 1 - 311402 T^{2} + 51520374361 T^{4} )^{2} \))(\( ( 1 - 226981 T^{2} )^{8} \))(\( ( 1 - 1255428 T^{2} + 726056294438 T^{4} - 264100181504479396 T^{6} + \)\(69\!\cdots\!70\)\( T^{8} - \)\(13\!\cdots\!56\)\( T^{10} + \)\(19\!\cdots\!98\)\( T^{12} - \)\(17\!\cdots\!68\)\( T^{14} + \)\(70\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 413 T - 56412 T^{2} - 93743153 T^{3} + 51520374361 T^{4} )^{2} \))(\( ( 1 + 392 T - 73317 T^{2} + 88976552 T^{3} + 51520374361 T^{4} )^{2} \))(\( ( 1 + 98 T + 203041 T^{2} - 63445102 T^{3} - 16282426916 T^{4} - 14400832697062 T^{5} + 10460748330631801 T^{6} + 1146026317097745818 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} )^{2} \))(\( ( 1 + 1944 T + 1201957 T^{2} + 465031984 T^{3} + 642573181668 T^{4} + 544248825687640 T^{5} + 179953145332374091 T^{6} + 96783385662450749352 T^{7} + \)\(99\!\cdots\!11\)\( T^{8} + \)\(41\!\cdots\!76\)\( T^{9} + \)\(10\!\cdots\!72\)\( T^{10} + \)\(94\!\cdots\!56\)\( T^{11} + \)\(51\!\cdots\!71\)\( T^{12} + \)\(11\!\cdots\!32\)\( T^{13} + \)\(47\!\cdots\!11\)\( T^{14} + \)\(32\!\cdots\!40\)\( T^{15} + \)\(87\!\cdots\!08\)\( T^{16} + \)\(14\!\cdots\!24\)\( T^{17} + \)\(84\!\cdots\!37\)\( T^{18} + \)\(31\!\cdots\!24\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} )^{2} \))
$67$ (\( 1 - 164 T + 300763 T^{2} \))(\( 1 + 244 T + 300763 T^{2} \))(\( 1 - 152 T + 599110 T^{2} - 45715976 T^{3} + 90458382169 T^{4} \))(\( 1 + 908 T + 525193 T^{2} + 273092804 T^{3} + 90458382169 T^{4} \))(\( 1 - 908 T + 525193 T^{2} - 273092804 T^{3} + 90458382169 T^{4} \))(\( 1 + 204 T + 92049 T^{2} - 202232824 T^{3} + 27684933387 T^{4} + 18453509962476 T^{5} + 27206534396294947 T^{6} \))(\( 1 + 424 T + 917806 T^{2} + 255868016 T^{3} + 369880128047 T^{4} + 76955632096208 T^{5} + 83023245905001214 T^{6} + 11535570584029057528 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 424 T + 917806 T^{2} - 255868016 T^{3} + 369880128047 T^{4} - 76955632096208 T^{5} + 83023245905001214 T^{6} - 11535570584029057528 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 804 T + 1172907 T^{2} - 702427600 T^{3} + 618816552222 T^{4} - 292956943717080 T^{5} + 186117122695945386 T^{6} - 63540464286853464400 T^{7} + \)\(31\!\cdots\!29\)\( T^{8} - \)\(65\!\cdots\!44\)\( T^{9} + \)\(24\!\cdots\!43\)\( T^{10} \))(\( 1 + 804 T + 1172907 T^{2} + 702427600 T^{3} + 618816552222 T^{4} + 292956943717080 T^{5} + 186117122695945386 T^{6} + 63540464286853464400 T^{7} + \)\(31\!\cdots\!29\)\( T^{8} + \)\(65\!\cdots\!44\)\( T^{9} + \)\(24\!\cdots\!43\)\( T^{10} \))(\( 1 - 574630 T^{2} + 90458382169 T^{4} \))(\( 1 - 541990 T^{2} + 90458382169 T^{4} \))(\( 1 - 1175116 T^{2} + 525951899734 T^{4} - 106299092220906604 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 225922 T^{2} - 39192080477 T^{4} - 20436538616384818 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 142482 T^{2} + 146353877367 T^{4} - 11082662491564636 T^{6} + \)\(13\!\cdots\!23\)\( T^{8} - \)\(11\!\cdots\!02\)\( T^{10} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 - 1655836 T^{2} + 1365152032162 T^{4} - 714276075785251552 T^{6} + \)\(25\!\cdots\!99\)\( T^{8} - \)\(64\!\cdots\!88\)\( T^{10} + \)\(11\!\cdots\!82\)\( T^{12} - \)\(12\!\cdots\!24\)\( T^{14} + \)\(66\!\cdots\!21\)\( T^{16} \))(\( 1 - 415 T - 128538 T^{2} - 124816645 T^{3} + 90458382169 T^{4} \))(\( 1 + 280 T - 222363 T^{2} + 84213640 T^{3} + 90458382169 T^{4} \))(\( 1 + 1286 T + 648343 T^{2} + 519450122 T^{3} + 423076706692 T^{4} + 156231377043086 T^{5} + 58648058870595967 T^{6} + 34987603233635301842 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 1118 T - 89755 T^{2} + 544724314 T^{3} - 95454149156 T^{4} - 123793400461058 T^{5} + 10648899628386803 T^{6} + 41531516553755134674 T^{7} - \)\(95\!\cdots\!45\)\( T^{8} - \)\(76\!\cdots\!64\)\( T^{9} + \)\(63\!\cdots\!60\)\( T^{10} - \)\(23\!\cdots\!32\)\( T^{11} - \)\(86\!\cdots\!05\)\( T^{12} + \)\(11\!\cdots\!78\)\( T^{13} + \)\(87\!\cdots\!83\)\( T^{14} - \)\(30\!\cdots\!94\)\( T^{15} - \)\(70\!\cdots\!04\)\( T^{16} + \)\(12\!\cdots\!38\)\( T^{17} - \)\(60\!\cdots\!55\)\( T^{18} - \)\(22\!\cdots\!14\)\( T^{19} + \)\(60\!\cdots\!49\)\( T^{20} \))(\( 1 + 1166 T - 161212 T^{2} - 1210036940 T^{3} - 751587178096 T^{4} + 159739362432438 T^{5} + 476016416724908880 T^{6} + \)\(24\!\cdots\!62\)\( T^{7} - \)\(21\!\cdots\!46\)\( T^{8} - \)\(11\!\cdots\!08\)\( T^{9} - \)\(67\!\cdots\!16\)\( T^{10} - \)\(44\!\cdots\!74\)\( T^{11} + \)\(20\!\cdots\!40\)\( T^{12} + \)\(14\!\cdots\!58\)\( T^{13} + \)\(24\!\cdots\!52\)\( T^{14} - \)\(26\!\cdots\!56\)\( T^{15} - \)\(24\!\cdots\!13\)\( T^{16} - \)\(80\!\cdots\!28\)\( T^{17} + \)\(21\!\cdots\!88\)\( T^{18} + \)\(38\!\cdots\!26\)\( T^{19} + \)\(16\!\cdots\!40\)\( T^{20} - \)\(10\!\cdots\!82\)\( T^{21} - \)\(49\!\cdots\!44\)\( T^{22} - \)\(24\!\cdots\!36\)\( T^{23} - \)\(14\!\cdots\!66\)\( T^{24} + \)\(49\!\cdots\!26\)\( T^{25} + \)\(28\!\cdots\!20\)\( T^{26} + \)\(29\!\cdots\!06\)\( T^{27} - \)\(41\!\cdots\!76\)\( T^{28} - \)\(19\!\cdots\!20\)\( T^{29} - \)\(79\!\cdots\!68\)\( T^{30} + \)\(17\!\cdots\!62\)\( T^{31} + \)\(44\!\cdots\!41\)\( T^{32} \))(\( 1 - 1166 T - 161212 T^{2} + 1210036940 T^{3} - 751587178096 T^{4} - 159739362432438 T^{5} + 476016416724908880 T^{6} - \)\(24\!\cdots\!62\)\( T^{7} - \)\(21\!\cdots\!46\)\( T^{8} + \)\(11\!\cdots\!08\)\( T^{9} - \)\(67\!\cdots\!16\)\( T^{10} + \)\(44\!\cdots\!74\)\( T^{11} + \)\(20\!\cdots\!40\)\( T^{12} - \)\(14\!\cdots\!58\)\( T^{13} + \)\(24\!\cdots\!52\)\( T^{14} + \)\(26\!\cdots\!56\)\( T^{15} - \)\(24\!\cdots\!13\)\( T^{16} + \)\(80\!\cdots\!28\)\( T^{17} + \)\(21\!\cdots\!88\)\( T^{18} - \)\(38\!\cdots\!26\)\( T^{19} + \)\(16\!\cdots\!40\)\( T^{20} + \)\(10\!\cdots\!82\)\( T^{21} - \)\(49\!\cdots\!44\)\( T^{22} + \)\(24\!\cdots\!36\)\( T^{23} - \)\(14\!\cdots\!66\)\( T^{24} - \)\(49\!\cdots\!26\)\( T^{25} + \)\(28\!\cdots\!20\)\( T^{26} - \)\(29\!\cdots\!06\)\( T^{27} - \)\(41\!\cdots\!76\)\( T^{28} + \)\(19\!\cdots\!20\)\( T^{29} - \)\(79\!\cdots\!68\)\( T^{30} - \)\(17\!\cdots\!62\)\( T^{31} + \)\(44\!\cdots\!41\)\( T^{32} \))(\( 1 - 1063794 T^{2} + 583098793137 T^{4} - 259526981150249198 T^{6} + \)\(10\!\cdots\!64\)\( T^{8} - \)\(33\!\cdots\!86\)\( T^{10} + \)\(10\!\cdots\!43\)\( T^{12} - \)\(33\!\cdots\!50\)\( T^{14} + \)\(10\!\cdots\!79\)\( T^{16} - \)\(32\!\cdots\!28\)\( T^{18} + \)\(99\!\cdots\!52\)\( T^{20} - \)\(29\!\cdots\!32\)\( T^{22} + \)\(84\!\cdots\!19\)\( T^{24} - \)\(24\!\cdots\!50\)\( T^{26} + \)\(71\!\cdots\!03\)\( T^{28} - \)\(20\!\cdots\!14\)\( T^{30} + \)\(54\!\cdots\!84\)\( T^{32} - \)\(12\!\cdots\!22\)\( T^{34} + \)\(26\!\cdots\!17\)\( T^{36} - \)\(43\!\cdots\!26\)\( T^{38} + \)\(36\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 144 T + 10368 T^{2} - 43309872 T^{3} + 90458382169 T^{4} )^{2} \))(\( 1 - 178008750862 T^{4} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( ( 1 + 90458382169 T^{4} )^{2} \))(\( ( 1 - 554 T + 153458 T^{2} - 166622702 T^{3} + 90458382169 T^{4} )^{2} \))(\( ( 1 + 144 T + 10368 T^{2} + 43309872 T^{3} + 90458382169 T^{4} )^{2} \))(\( 1 + 178008750862 T^{4} + \)\(23\!\cdots\!83\)\( T^{8} + \)\(14\!\cdots\!82\)\( T^{12} + \)\(66\!\cdots\!21\)\( T^{16} \))(\( ( 1 + 2252 T + 2535752 T^{2} + 2225077036 T^{3} + 1815966182624 T^{4} + 1326362080610140 T^{5} + 857611434080134680 T^{6} + \)\(51\!\cdots\!20\)\( T^{7} + \)\(29\!\cdots\!50\)\( T^{8} + \)\(15\!\cdots\!60\)\( T^{9} + \)\(77\!\cdots\!20\)\( T^{10} + \)\(36\!\cdots\!80\)\( T^{11} + \)\(14\!\cdots\!64\)\( T^{12} + \)\(54\!\cdots\!48\)\( T^{13} + \)\(18\!\cdots\!68\)\( T^{14} + \)\(50\!\cdots\!84\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 429301 T^{2} + 93840966432 T^{4} + 38833873923533869 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 523126 T^{2} + 183202429707 T^{4} + 47321131630540294 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 357110 T^{2} - 69523654751 T^{4} + 5761770765817430 T^{6} + \)\(19\!\cdots\!40\)\( T^{8} + \)\(52\!\cdots\!70\)\( T^{10} - \)\(56\!\cdots\!11\)\( T^{12} + \)\(26\!\cdots\!90\)\( T^{14} + \)\(66\!\cdots\!21\)\( T^{16} \))(\( 1 + 1429434 T^{2} + 1035151227817 T^{4} + 535093848121929118 T^{6} + \)\(21\!\cdots\!04\)\( T^{8} + \)\(65\!\cdots\!06\)\( T^{10} + \)\(12\!\cdots\!63\)\( T^{12} - \)\(32\!\cdots\!30\)\( T^{14} - \)\(16\!\cdots\!01\)\( T^{16} - \)\(85\!\cdots\!92\)\( T^{18} - \)\(30\!\cdots\!68\)\( T^{20} - \)\(77\!\cdots\!48\)\( T^{22} - \)\(13\!\cdots\!61\)\( T^{24} - \)\(24\!\cdots\!70\)\( T^{26} + \)\(83\!\cdots\!23\)\( T^{28} + \)\(39\!\cdots\!94\)\( T^{30} + \)\(11\!\cdots\!24\)\( T^{32} + \)\(26\!\cdots\!02\)\( T^{34} + \)\(46\!\cdots\!97\)\( T^{36} + \)\(57\!\cdots\!86\)\( T^{38} + \)\(36\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 - 672 T + 357911 T^{2} \))(\( 1 + 768 T + 357911 T^{2} \))(\( ( 1 + 952 T + 357911 T^{2} )^{2} \))(\( 1 - 127 T - 221188 T^{2} - 45454697 T^{3} + 128100283921 T^{4} \))(\( 1 - 127 T - 221188 T^{2} - 45454697 T^{3} + 128100283921 T^{4} \))(\( 1 + 136 T + 900677 T^{2} + 112926832 T^{3} + 322362205747 T^{4} + 17421638613256 T^{5} + 45848500718449031 T^{6} \))(\( 1 - 215 T + 982021 T^{2} - 275350320 T^{3} + 449702043326 T^{4} - 98550908381520 T^{5} + 125797168916384341 T^{6} - 9857427654466541665 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} \))(\( 1 - 215 T + 982021 T^{2} - 275350320 T^{3} + 449702043326 T^{4} - 98550908381520 T^{5} + 125797168916384341 T^{6} - 9857427654466541665 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} \))(\( 1 - 440 T + 1467407 T^{2} - 492789840 T^{3} + 952423975862 T^{4} - 247789000795120 T^{5} + 340883017624744282 T^{6} - 63126518417384162640 T^{7} + \)\(67\!\cdots\!17\)\( T^{8} - \)\(72\!\cdots\!40\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} \))(\( 1 - 440 T + 1467407 T^{2} - 492789840 T^{3} + 952423975862 T^{4} - 247789000795120 T^{5} + 340883017624744282 T^{6} - 63126518417384162640 T^{7} + \)\(67\!\cdots\!17\)\( T^{8} - \)\(72\!\cdots\!40\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} \))(\( ( 1 - 672 T + 357911 T^{2} )^{2} \))(\( ( 1 + 768 T + 357911 T^{2} )^{2} \))(\( ( 1 + 952 T + 357911 T^{2} )^{4} \))(\( ( 1 - 127 T - 221188 T^{2} - 45454697 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 + 136 T + 900677 T^{2} + 112926832 T^{3} + 322362205747 T^{4} + 17421638613256 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 - 215 T + 982021 T^{2} - 275350320 T^{3} + 449702043326 T^{4} - 98550908381520 T^{5} + 125797168916384341 T^{6} - 9857427654466541665 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 + 432 T + 357911 T^{2} )^{2} \))(\( ( 1 - 48 T + 357911 T^{2} )^{2} \))(\( ( 1 - 1064 T + 753846 T^{2} - 380817304 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 864 T + 1690919 T^{2} - 959528208 T^{3} + 1093514996270 T^{4} - 459054202031136 T^{5} + 391381045829991970 T^{6} - \)\(12\!\cdots\!68\)\( T^{7} + \)\(77\!\cdots\!89\)\( T^{8} - \)\(14\!\cdots\!24\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 + 724 T + 1612036 T^{2} + 992074752 T^{3} + 1324440151090 T^{4} + 736092038749460 T^{5} + 730541970918164640 T^{6} + \)\(36\!\cdots\!04\)\( T^{7} + \)\(29\!\cdots\!51\)\( T^{8} + \)\(13\!\cdots\!44\)\( T^{9} + \)\(93\!\cdots\!40\)\( T^{10} + \)\(33\!\cdots\!60\)\( T^{11} + \)\(21\!\cdots\!90\)\( T^{12} + \)\(58\!\cdots\!52\)\( T^{13} + \)\(33\!\cdots\!96\)\( T^{14} + \)\(54\!\cdots\!04\)\( T^{15} + \)\(26\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 724 T + 1612036 T^{2} + 992074752 T^{3} + 1324440151090 T^{4} + 736092038749460 T^{5} + 730541970918164640 T^{6} + \)\(36\!\cdots\!04\)\( T^{7} + \)\(29\!\cdots\!51\)\( T^{8} + \)\(13\!\cdots\!44\)\( T^{9} + \)\(93\!\cdots\!40\)\( T^{10} + \)\(33\!\cdots\!60\)\( T^{11} + \)\(21\!\cdots\!90\)\( T^{12} + \)\(58\!\cdots\!52\)\( T^{13} + \)\(33\!\cdots\!96\)\( T^{14} + \)\(54\!\cdots\!04\)\( T^{15} + \)\(26\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 736 T + 1120739 T^{2} + 619752192 T^{3} + 535581261770 T^{4} + 254623498821824 T^{5} + 191690424981362470 T^{6} + 79390431755862104832 T^{7} + \)\(51\!\cdots\!09\)\( T^{8} + \)\(12\!\cdots\!76\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{4} \))(\( ( 1 - 324 T + 357911 T^{2} )^{4} \))(\( ( 1 + 688 T + 357911 T^{2} )^{4} \))(\( ( 1 + 828 T + 357911 T^{2} )^{4} \))(\( ( 1 + 916 T + 357911 T^{2} )^{4} \))(\( ( 1 - 324 T + 357911 T^{2} )^{4} \))(\( ( 1 - 688 T + 115433 T^{2} - 246242768 T^{3} + 128100283921 T^{4} )^{4} \))(\( ( 1 - 1592 T + 1740546 T^{2} - 1313608192 T^{3} + 887743954594 T^{4} - 470154821606912 T^{5} + 222964436777560866 T^{6} - 72990813143770857352 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} )^{4} \))(\( ( 1 + 432 T + 357911 T^{2} )^{4} \))(\( ( 1 - 48 T + 357911 T^{2} )^{4} \))(\( ( 1 - 1064 T + 753846 T^{2} - 380817304 T^{3} + 128100283921 T^{4} )^{4} \))(\( ( 1 - 864 T + 1690919 T^{2} - 959528208 T^{3} + 1093514996270 T^{4} - 459054202031136 T^{5} + 391381045829991970 T^{6} - \)\(12\!\cdots\!68\)\( T^{7} + \)\(77\!\cdots\!89\)\( T^{8} - \)\(14\!\cdots\!24\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{4} \))
$73$ (\( 1 + 82 T + 389017 T^{2} \))(\( 1 - 702 T + 389017 T^{2} \))(\( 1 + 676 T + 655606 T^{2} + 262975492 T^{3} + 151334226289 T^{4} \))(\( 1 - 337 T + 64726 T^{2} - 131098729 T^{3} + 151334226289 T^{4} \))(\( 1 + 337 T + 64726 T^{2} + 131098729 T^{3} + 151334226289 T^{4} \))(\( 1 + 310 T + 450279 T^{2} + 192471924 T^{3} + 175166185743 T^{4} + 46913610149590 T^{5} + 58871586708267913 T^{6} \))(\( 1 - 1207 T + 1581740 T^{2} - 1193773973 T^{3} + 948033109470 T^{4} - 464398369654541 T^{5} + 239371399090362860 T^{6} - 71058005156879370991 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 1207 T + 1581740 T^{2} + 1193773973 T^{3} + 948033109470 T^{4} + 464398369654541 T^{5} + 239371399090362860 T^{6} + 71058005156879370991 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 564 T + 1422205 T^{2} + 573808208 T^{3} + 913296471322 T^{4} + 285146462532088 T^{5} + 355287853384270474 T^{6} + 86836821195957580112 T^{7} + \)\(83\!\cdots\!65\)\( T^{8} + \)\(12\!\cdots\!44\)\( T^{9} + \)\(89\!\cdots\!57\)\( T^{10} \))(\( 1 - 564 T + 1422205 T^{2} - 573808208 T^{3} + 913296471322 T^{4} - 285146462532088 T^{5} + 355287853384270474 T^{6} - 86836821195957580112 T^{7} + \)\(83\!\cdots\!65\)\( T^{8} - \)\(12\!\cdots\!44\)\( T^{9} + \)\(89\!\cdots\!57\)\( T^{10} \))(\( 1 - 771310 T^{2} + 151334226289 T^{4} \))(\( 1 - 285230 T^{2} + 151334226289 T^{4} \))(\( 1 - 854236 T^{2} + 376944814630 T^{4} - 129275144128210204 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 15883 T^{2} + 218497364308 T^{4} - 2403641516148187 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 804458 T^{2} + 433750956447 T^{4} - 209358603495872844 T^{6} + \)\(65\!\cdots\!83\)\( T^{8} - \)\(18\!\cdots\!18\)\( T^{10} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( 1 - 1706631 T^{2} + 1516197275718 T^{4} - 931672616368614617 T^{6} + \)\(42\!\cdots\!82\)\( T^{8} - \)\(14\!\cdots\!13\)\( T^{10} + \)\(34\!\cdots\!78\)\( T^{12} - \)\(59\!\cdots\!39\)\( T^{14} + \)\(52\!\cdots\!41\)\( T^{16} \))(\( 1 + 1113 T + 849752 T^{2} + 432975921 T^{3} + 151334226289 T^{4} \))(\( 1 - 668 T + 57207 T^{2} - 259863356 T^{3} + 151334226289 T^{4} \))(\( 1 + 172 T - 727998 T^{2} - 3517744 T^{3} + 411087581507 T^{4} - 1368462217648 T^{5} - 110171014069939422 T^{6} + 10125912913822081036 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 1652 T + 187071 T^{2} - 576882732 T^{3} + 434002580187 T^{4} + 531471598604920 T^{5} - 187348919748357658 T^{6} - \)\(14\!\cdots\!36\)\( T^{7} + \)\(11\!\cdots\!81\)\( T^{8} + \)\(15\!\cdots\!24\)\( T^{9} - \)\(60\!\cdots\!27\)\( T^{10} + \)\(59\!\cdots\!08\)\( T^{11} + \)\(17\!\cdots\!09\)\( T^{12} - \)\(87\!\cdots\!68\)\( T^{13} - \)\(42\!\cdots\!18\)\( T^{14} + \)\(47\!\cdots\!40\)\( T^{15} + \)\(15\!\cdots\!03\)\( T^{16} - \)\(77\!\cdots\!36\)\( T^{17} + \)\(98\!\cdots\!11\)\( T^{18} + \)\(33\!\cdots\!44\)\( T^{19} + \)\(79\!\cdots\!49\)\( T^{20} \))(\( 1 - 892 T - 1618444 T^{2} + 1459146232 T^{3} + 1488041466252 T^{4} - 1217322595227516 T^{5} - 1081896761435227176 T^{6} + \)\(70\!\cdots\!44\)\( T^{7} + \)\(68\!\cdots\!46\)\( T^{8} - \)\(31\!\cdots\!60\)\( T^{9} - \)\(37\!\cdots\!00\)\( T^{10} + \)\(11\!\cdots\!80\)\( T^{11} + \)\(18\!\cdots\!88\)\( T^{12} - \)\(29\!\cdots\!76\)\( T^{13} - \)\(81\!\cdots\!32\)\( T^{14} + \)\(40\!\cdots\!96\)\( T^{15} + \)\(33\!\cdots\!51\)\( T^{16} + \)\(15\!\cdots\!32\)\( T^{17} - \)\(12\!\cdots\!48\)\( T^{18} - \)\(17\!\cdots\!88\)\( T^{19} + \)\(42\!\cdots\!48\)\( T^{20} + \)\(10\!\cdots\!60\)\( T^{21} - \)\(13\!\cdots\!00\)\( T^{22} - \)\(42\!\cdots\!80\)\( T^{23} + \)\(35\!\cdots\!86\)\( T^{24} + \)\(14\!\cdots\!68\)\( T^{25} - \)\(85\!\cdots\!24\)\( T^{26} - \)\(37\!\cdots\!28\)\( T^{27} + \)\(17\!\cdots\!72\)\( T^{28} + \)\(68\!\cdots\!84\)\( T^{29} - \)\(29\!\cdots\!76\)\( T^{30} - \)\(63\!\cdots\!56\)\( T^{31} + \)\(27\!\cdots\!81\)\( T^{32} \))(\( 1 + 892 T - 1618444 T^{2} - 1459146232 T^{3} + 1488041466252 T^{4} + 1217322595227516 T^{5} - 1081896761435227176 T^{6} - \)\(70\!\cdots\!44\)\( T^{7} + \)\(68\!\cdots\!46\)\( T^{8} + \)\(31\!\cdots\!60\)\( T^{9} - \)\(37\!\cdots\!00\)\( T^{10} - \)\(11\!\cdots\!80\)\( T^{11} + \)\(18\!\cdots\!88\)\( T^{12} + \)\(29\!\cdots\!76\)\( T^{13} - \)\(81\!\cdots\!32\)\( T^{14} - \)\(40\!\cdots\!96\)\( T^{15} + \)\(33\!\cdots\!51\)\( T^{16} - \)\(15\!\cdots\!32\)\( T^{17} - \)\(12\!\cdots\!48\)\( T^{18} + \)\(17\!\cdots\!88\)\( T^{19} + \)\(42\!\cdots\!48\)\( T^{20} - \)\(10\!\cdots\!60\)\( T^{21} - \)\(13\!\cdots\!00\)\( T^{22} + \)\(42\!\cdots\!80\)\( T^{23} + \)\(35\!\cdots\!86\)\( T^{24} - \)\(14\!\cdots\!68\)\( T^{25} - \)\(85\!\cdots\!24\)\( T^{26} + \)\(37\!\cdots\!28\)\( T^{27} + \)\(17\!\cdots\!72\)\( T^{28} - \)\(68\!\cdots\!84\)\( T^{29} - \)\(29\!\cdots\!76\)\( T^{30} + \)\(63\!\cdots\!56\)\( T^{31} + \)\(27\!\cdots\!81\)\( T^{32} \))(\( 1 - 2627747 T^{2} + 3676489000168 T^{4} - 3499491410340553131 T^{6} + \)\(24\!\cdots\!99\)\( T^{8} - \)\(13\!\cdots\!14\)\( T^{10} + \)\(58\!\cdots\!36\)\( T^{12} - \)\(18\!\cdots\!34\)\( T^{14} + \)\(32\!\cdots\!05\)\( T^{16} + \)\(20\!\cdots\!67\)\( T^{18} - \)\(32\!\cdots\!88\)\( T^{20} + \)\(31\!\cdots\!63\)\( T^{22} + \)\(74\!\cdots\!05\)\( T^{24} - \)\(62\!\cdots\!46\)\( T^{26} + \)\(30\!\cdots\!76\)\( T^{28} - \)\(10\!\cdots\!86\)\( T^{30} + \)\(29\!\cdots\!39\)\( T^{32} - \)\(63\!\cdots\!99\)\( T^{34} + \)\(10\!\cdots\!08\)\( T^{36} - \)\(10\!\cdots\!23\)\( T^{38} + \)\(63\!\cdots\!01\)\( T^{40} \))(\( 1 + 268918956578 T^{4} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( ( 1 + 151334226289 T^{4} )^{2} \))(\( 1 - 48396356062 T^{4} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 283756682078 T^{4} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 268918956578 T^{4} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( ( 1 + 151334226289 T^{4} )^{4} \))(\( 1 - 454504886008 T^{4} + \)\(58\!\cdots\!08\)\( T^{8} + \)\(30\!\cdots\!64\)\( T^{12} - \)\(14\!\cdots\!30\)\( T^{16} + \)\(68\!\cdots\!44\)\( T^{20} + \)\(30\!\cdots\!28\)\( T^{24} - \)\(54\!\cdots\!88\)\( T^{28} + \)\(27\!\cdots\!81\)\( T^{32} \))(\( 1 - 460735 T^{2} + 60942513936 T^{4} - 69724974749262415 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 331810 T^{2} - 41236350189 T^{4} + 50214209624953090 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 1485580 T^{2} + 1353366354954 T^{4} + 818425525983723440 T^{6} + \)\(37\!\cdots\!95\)\( T^{8} + \)\(12\!\cdots\!60\)\( T^{10} + \)\(30\!\cdots\!34\)\( T^{12} + \)\(51\!\cdots\!20\)\( T^{14} + \)\(52\!\cdots\!41\)\( T^{16} \))(\( 1 + 2354962 T^{2} + 2809021265943 T^{4} + 2301095094410830266 T^{6} + \)\(14\!\cdots\!19\)\( T^{8} + \)\(74\!\cdots\!44\)\( T^{10} + \)\(30\!\cdots\!86\)\( T^{12} + \)\(10\!\cdots\!24\)\( T^{14} + \)\(25\!\cdots\!05\)\( T^{16} + \)\(50\!\cdots\!78\)\( T^{18} + \)\(11\!\cdots\!97\)\( T^{20} + \)\(75\!\cdots\!42\)\( T^{22} + \)\(59\!\cdots\!05\)\( T^{24} + \)\(35\!\cdots\!56\)\( T^{26} + \)\(16\!\cdots\!26\)\( T^{28} + \)\(59\!\cdots\!56\)\( T^{30} + \)\(17\!\cdots\!59\)\( T^{32} + \)\(41\!\cdots\!14\)\( T^{34} + \)\(77\!\cdots\!83\)\( T^{36} + \)\(98\!\cdots\!58\)\( T^{38} + \)\(63\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 + 1000 T + 493039 T^{2} \))(\( 1 - 440 T + 493039 T^{2} \))(\( 1 - 1014 T + 1120119 T^{2} - 499941546 T^{3} + 243087455521 T^{4} \))(\( 1 + 1119 T + 1281888 T^{2} + 551710641 T^{3} + 243087455521 T^{4} \))(\( 1 + 1119 T + 1281888 T^{2} + 551710641 T^{3} + 243087455521 T^{4} \))(\( 1 + 1034 T + 1094262 T^{2} + 675989052 T^{3} + 539513842218 T^{4} + 251352429008714 T^{5} + 119851595982618319 T^{6} \))(\( 1 + 951 T + 1431057 T^{2} + 665911232 T^{3} + 746318767554 T^{4} + 328320207914048 T^{5} + 347872004835515697 T^{6} + \)\(11\!\cdots\!69\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 + 951 T + 1431057 T^{2} + 665911232 T^{3} + 746318767554 T^{4} + 328320207914048 T^{5} + 347872004835515697 T^{6} + \)\(11\!\cdots\!69\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 1790 T + 3366800 T^{2} - 3670804696 T^{3} + 3768250665575 T^{4} - 2749245121712708 T^{5} + 1857894539904432425 T^{6} - \)\(89\!\cdots\!16\)\( T^{7} + \)\(40\!\cdots\!00\)\( T^{8} - \)\(10\!\cdots\!90\)\( T^{9} + \)\(29\!\cdots\!99\)\( T^{10} \))(\( 1 - 1790 T + 3366800 T^{2} - 3670804696 T^{3} + 3768250665575 T^{4} - 2749245121712708 T^{5} + 1857894539904432425 T^{6} - \)\(89\!\cdots\!16\)\( T^{7} + \)\(40\!\cdots\!00\)\( T^{8} - \)\(10\!\cdots\!90\)\( T^{9} + \)\(29\!\cdots\!99\)\( T^{10} \))(\( ( 1 - 1000 T + 493039 T^{2} )^{2} \))(\( ( 1 + 440 T + 493039 T^{2} )^{2} \))(\( ( 1 + 1014 T + 1120119 T^{2} + 499941546 T^{3} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 1119 T + 1281888 T^{2} - 551710641 T^{3} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 1034 T + 1094262 T^{2} - 675989052 T^{3} + 539513842218 T^{4} - 251352429008714 T^{5} + 119851595982618319 T^{6} )^{2} \))(\( ( 1 - 951 T + 1431057 T^{2} - 665911232 T^{3} + 746318767554 T^{4} - 328320207914048 T^{5} + 347872004835515697 T^{6} - \)\(11\!\cdots\!69\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} )^{2} \))(\( 1 - 103 T - 482430 T^{2} - 50783017 T^{3} + 243087455521 T^{4} \))(\( 1 + 782 T + 118485 T^{2} + 385556498 T^{3} + 243087455521 T^{4} \))(\( 1 - 1240 T + 258714 T^{2} - 363081920 T^{3} + 634365179075 T^{4} - 179013546754880 T^{5} + 62890127967659994 T^{6} - \)\(14\!\cdots\!60\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 + 218 T - 1453667 T^{2} - 1963370 T^{3} + 1085327492763 T^{4} - 157694661811260 T^{5} - 575577812372860958 T^{6} + 81206950854078977836 T^{7} + \)\(26\!\cdots\!29\)\( T^{8} - \)\(96\!\cdots\!90\)\( T^{9} - \)\(12\!\cdots\!41\)\( T^{10} - \)\(47\!\cdots\!10\)\( T^{11} + \)\(64\!\cdots\!09\)\( T^{12} + \)\(97\!\cdots\!84\)\( T^{13} - \)\(34\!\cdots\!78\)\( T^{14} - \)\(45\!\cdots\!40\)\( T^{15} + \)\(15\!\cdots\!43\)\( T^{16} - \)\(13\!\cdots\!30\)\( T^{17} - \)\(50\!\cdots\!27\)\( T^{18} + \)\(37\!\cdots\!62\)\( T^{19} + \)\(84\!\cdots\!01\)\( T^{20} \))(\( 1 - 840 T - 2008472 T^{2} + 200940784 T^{3} + 3653059876319 T^{4} + 812647375809134 T^{5} - 3301414879970917994 T^{6} - \)\(24\!\cdots\!14\)\( T^{7} + \)\(20\!\cdots\!86\)\( T^{8} + \)\(25\!\cdots\!26\)\( T^{9} - \)\(25\!\cdots\!74\)\( T^{10} - \)\(19\!\cdots\!72\)\( T^{11} - \)\(58\!\cdots\!28\)\( T^{12} + \)\(84\!\cdots\!32\)\( T^{13} + \)\(70\!\cdots\!17\)\( T^{14} - \)\(17\!\cdots\!58\)\( T^{15} - \)\(42\!\cdots\!30\)\( T^{16} - \)\(88\!\cdots\!62\)\( T^{17} + \)\(17\!\cdots\!57\)\( T^{18} + \)\(10\!\cdots\!08\)\( T^{19} - \)\(34\!\cdots\!48\)\( T^{20} - \)\(55\!\cdots\!28\)\( T^{21} - \)\(37\!\cdots\!14\)\( T^{22} + \)\(18\!\cdots\!54\)\( T^{23} + \)\(70\!\cdots\!66\)\( T^{24} - \)\(41\!\cdots\!26\)\( T^{25} - \)\(28\!\cdots\!94\)\( T^{26} + \)\(34\!\cdots\!26\)\( T^{27} + \)\(75\!\cdots\!99\)\( T^{28} + \)\(20\!\cdots\!96\)\( T^{29} - \)\(10\!\cdots\!52\)\( T^{30} - \)\(20\!\cdots\!60\)\( T^{31} + \)\(12\!\cdots\!61\)\( T^{32} \))(\( 1 - 840 T - 2008472 T^{2} + 200940784 T^{3} + 3653059876319 T^{4} + 812647375809134 T^{5} - 3301414879970917994 T^{6} - \)\(24\!\cdots\!14\)\( T^{7} + \)\(20\!\cdots\!86\)\( T^{8} + \)\(25\!\cdots\!26\)\( T^{9} - \)\(25\!\cdots\!74\)\( T^{10} - \)\(19\!\cdots\!72\)\( T^{11} - \)\(58\!\cdots\!28\)\( T^{12} + \)\(84\!\cdots\!32\)\( T^{13} + \)\(70\!\cdots\!17\)\( T^{14} - \)\(17\!\cdots\!58\)\( T^{15} - \)\(42\!\cdots\!30\)\( T^{16} - \)\(88\!\cdots\!62\)\( T^{17} + \)\(17\!\cdots\!57\)\( T^{18} + \)\(10\!\cdots\!08\)\( T^{19} - \)\(34\!\cdots\!48\)\( T^{20} - \)\(55\!\cdots\!28\)\( T^{21} - \)\(37\!\cdots\!14\)\( T^{22} + \)\(18\!\cdots\!54\)\( T^{23} + \)\(70\!\cdots\!66\)\( T^{24} - \)\(41\!\cdots\!26\)\( T^{25} - \)\(28\!\cdots\!94\)\( T^{26} + \)\(34\!\cdots\!26\)\( T^{27} + \)\(75\!\cdots\!99\)\( T^{28} + \)\(20\!\cdots\!96\)\( T^{29} - \)\(10\!\cdots\!52\)\( T^{30} - \)\(20\!\cdots\!60\)\( T^{31} + \)\(12\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 23 T - 490582 T^{2} - 501202135 T^{3} - 21157688697 T^{4} + 158473640720330 T^{5} + 191577977326579332 T^{6} + 87280947293160331886 T^{7} - \)\(63\!\cdots\!11\)\( T^{8} - \)\(24\!\cdots\!75\)\( T^{9} - \)\(17\!\cdots\!66\)\( T^{10} - \)\(11\!\cdots\!25\)\( T^{11} - \)\(15\!\cdots\!31\)\( T^{12} + \)\(10\!\cdots\!34\)\( T^{13} + \)\(11\!\cdots\!12\)\( T^{14} + \)\(46\!\cdots\!70\)\( T^{15} - \)\(30\!\cdots\!17\)\( T^{16} - \)\(35\!\cdots\!65\)\( T^{17} - \)\(17\!\cdots\!42\)\( T^{18} + \)\(39\!\cdots\!57\)\( T^{19} + \)\(84\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 - 909349 T^{2} + 243087455521 T^{4} )^{2} \))(\( ( 1 + 929378 T^{2} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 930382 T^{2} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 757594 T^{2} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 909349 T^{2} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 929378 T^{2} + 620656011363 T^{4} - 225920133237195938 T^{6} + \)\(59\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 - 3309042 T^{2} + 5035453141141 T^{4} - 4602570291031234982 T^{6} + \)\(27\!\cdots\!04\)\( T^{8} - \)\(11\!\cdots\!22\)\( T^{10} + \)\(29\!\cdots\!81\)\( T^{12} - \)\(47\!\cdots\!62\)\( T^{14} + \)\(34\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 103 T - 482430 T^{2} + 50783017 T^{3} + 243087455521 T^{4} )^{2} \))(\( ( 1 - 782 T + 118485 T^{2} - 385556498 T^{3} + 243087455521 T^{4} )^{2} \))(\( ( 1 + 1240 T + 258714 T^{2} + 363081920 T^{3} + 634365179075 T^{4} + 179013546754880 T^{5} + 62890127967659994 T^{6} + \)\(14\!\cdots\!60\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 - 218 T - 1453667 T^{2} + 1963370 T^{3} + 1085327492763 T^{4} + 157694661811260 T^{5} - 575577812372860958 T^{6} - 81206950854078977836 T^{7} + \)\(26\!\cdots\!29\)\( T^{8} + \)\(96\!\cdots\!90\)\( T^{9} - \)\(12\!\cdots\!41\)\( T^{10} + \)\(47\!\cdots\!10\)\( T^{11} + \)\(64\!\cdots\!09\)\( T^{12} - \)\(97\!\cdots\!84\)\( T^{13} - \)\(34\!\cdots\!78\)\( T^{14} + \)\(45\!\cdots\!40\)\( T^{15} + \)\(15\!\cdots\!43\)\( T^{16} + \)\(13\!\cdots\!30\)\( T^{17} - \)\(50\!\cdots\!27\)\( T^{18} - \)\(37\!\cdots\!62\)\( T^{19} + \)\(84\!\cdots\!01\)\( T^{20} )^{2} \))
$83$ (\( 1 - 448 T + 571787 T^{2} \))(\( 1 - 1302 T + 571787 T^{2} \))(\( 1 - 376 T + 458918 T^{2} - 214991912 T^{3} + 326940373369 T^{4} \))(\( 1 - 1517 T + 1670096 T^{2} - 867400879 T^{3} + 326940373369 T^{4} \))(\( 1 + 1517 T + 1670096 T^{2} + 867400879 T^{3} + 326940373369 T^{4} \))(\( 1 - 1660 T + 2204369 T^{2} - 1855605736 T^{3} + 1260429537403 T^{4} - 542721019792540 T^{5} + 186940255267540403 T^{6} \))(\( 1 - 3035 T + 5488190 T^{2} - 6563721455 T^{3} + 5816729995458 T^{4} - 3753050599590085 T^{5} + 1794310887720012110 T^{6} - \)\(56\!\cdots\!05\)\( T^{7} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 + 3035 T + 5488190 T^{2} + 6563721455 T^{3} + 5816729995458 T^{4} + 3753050599590085 T^{5} + 1794310887720012110 T^{6} + \)\(56\!\cdots\!05\)\( T^{7} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 + 1656 T + 3466257 T^{2} + 3716076720 T^{3} + 4273940284148 T^{4} + 3169585577722288 T^{5} + 2443783493252132476 T^{6} + \)\(12\!\cdots\!80\)\( T^{7} + \)\(64\!\cdots\!71\)\( T^{8} + \)\(17\!\cdots\!16\)\( T^{9} + \)\(61\!\cdots\!07\)\( T^{10} \))(\( 1 - 1656 T + 3466257 T^{2} - 3716076720 T^{3} + 4273940284148 T^{4} - 3169585577722288 T^{5} + 2443783493252132476 T^{6} - \)\(12\!\cdots\!80\)\( T^{7} + \)\(64\!\cdots\!71\)\( T^{8} - \)\(17\!\cdots\!16\)\( T^{9} + \)\(61\!\cdots\!07\)\( T^{10} \))(\( 1 - 942870 T^{2} + 326940373369 T^{4} \))(\( 1 + 551630 T^{2} + 326940373369 T^{4} \))(\( 1 - 776460 T^{2} + 702812559638 T^{4} - 253856122306093740 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 1038903 T^{2} + 811407129068 T^{4} - 339659334714174207 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 1653138 T^{2} + 1219490719447 T^{4} - 685677675218773724 T^{6} + \)\(39\!\cdots\!43\)\( T^{8} - \)\(17\!\cdots\!18\)\( T^{10} + \)\(34\!\cdots\!09\)\( T^{12} \))(\( 1 - 1765155 T^{2} + 1911900235166 T^{4} - 1571804084646173285 T^{6} + \)\(10\!\cdots\!86\)\( T^{8} - \)\(51\!\cdots\!65\)\( T^{10} + \)\(20\!\cdots\!26\)\( T^{12} - \)\(61\!\cdots\!95\)\( T^{14} + \)\(11\!\cdots\!21\)\( T^{16} \))(\( ( 1 + 1092 T + 571787 T^{2} )^{2} \))(\( ( 1 + 768 T + 571787 T^{2} )^{2} \))(\( ( 1 - 1906 T + 2051733 T^{2} - 1089826022 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 1502 T + 2544639 T^{2} - 2916185966 T^{3} + 2925083074177 T^{4} - 2334912952153996 T^{5} + 1672524475734444299 T^{6} - \)\(95\!\cdots\!54\)\( T^{7} + \)\(47\!\cdots\!17\)\( T^{8} - \)\(16\!\cdots\!22\)\( T^{9} + \)\(61\!\cdots\!07\)\( T^{10} )^{2} \))(\( ( 1 + 1146 T + 3416020 T^{2} + 3387553522 T^{3} + 5478658983621 T^{4} + 4848757329217062 T^{5} + 5490388377352564865 T^{6} + \)\(42\!\cdots\!74\)\( T^{7} + \)\(37\!\cdots\!26\)\( T^{8} + \)\(24\!\cdots\!38\)\( T^{9} + \)\(17\!\cdots\!85\)\( T^{10} + \)\(90\!\cdots\!86\)\( T^{11} + \)\(58\!\cdots\!81\)\( T^{12} + \)\(20\!\cdots\!54\)\( T^{13} + \)\(11\!\cdots\!80\)\( T^{14} + \)\(22\!\cdots\!18\)\( T^{15} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 1146 T + 3416020 T^{2} - 3387553522 T^{3} + 5478658983621 T^{4} - 4848757329217062 T^{5} + 5490388377352564865 T^{6} - \)\(42\!\cdots\!74\)\( T^{7} + \)\(37\!\cdots\!26\)\( T^{8} - \)\(24\!\cdots\!38\)\( T^{9} + \)\(17\!\cdots\!85\)\( T^{10} - \)\(90\!\cdots\!86\)\( T^{11} + \)\(58\!\cdots\!81\)\( T^{12} - \)\(20\!\cdots\!54\)\( T^{13} + \)\(11\!\cdots\!80\)\( T^{14} - \)\(22\!\cdots\!18\)\( T^{15} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 3839289 T^{2} + 6907901943196 T^{4} + 7907786449656750719 T^{6} + \)\(65\!\cdots\!67\)\( T^{8} + \)\(42\!\cdots\!64\)\( T^{10} + \)\(21\!\cdots\!23\)\( T^{12} + \)\(84\!\cdots\!59\)\( T^{14} + \)\(24\!\cdots\!64\)\( T^{16} + \)\(43\!\cdots\!69\)\( T^{18} + \)\(37\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 - 563973123022 T^{4} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( ( 1 + 326940373369 T^{4} )^{2} \))(\( 1 + 648698638898 T^{4} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 142535619682 T^{4} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 563973123022 T^{4} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( ( 1 + 326940373369 T^{4} )^{4} \))(\( 1 - 501476514268 T^{4} + \)\(49\!\cdots\!28\)\( T^{8} - \)\(16\!\cdots\!96\)\( T^{12} + \)\(82\!\cdots\!70\)\( T^{16} - \)\(17\!\cdots\!56\)\( T^{20} + \)\(56\!\cdots\!88\)\( T^{24} - \)\(61\!\cdots\!08\)\( T^{28} + \)\(13\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 48890 T^{2} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 553750 T^{2} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 470630 T^{2} + 709072254163 T^{4} - 153867947918652470 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} )^{2} \))(\( ( 1 - 2833274 T^{2} + 3565131146811 T^{4} - 2713390792484305664 T^{6} + \)\(15\!\cdots\!97\)\( T^{8} - \)\(83\!\cdots\!54\)\( T^{10} + \)\(50\!\cdots\!93\)\( T^{12} - \)\(29\!\cdots\!04\)\( T^{14} + \)\(12\!\cdots\!99\)\( T^{16} - \)\(32\!\cdots\!54\)\( T^{18} + \)\(37\!\cdots\!49\)\( T^{20} )^{2} \))
$89$ (\( 1 + 870 T + 704969 T^{2} \))(\( 1 - 730 T + 704969 T^{2} \))(\( 1 + 216 T + 1417730 T^{2} + 152273304 T^{3} + 496981290961 T^{4} \))(\( 1 + 1713 T + 2140568 T^{2} + 1207611897 T^{3} + 496981290961 T^{4} \))(\( 1 + 1713 T + 2140568 T^{2} + 1207611897 T^{3} + 496981290961 T^{4} \))(\( 1 - 242 T + 1427227 T^{2} - 347564516 T^{3} + 1006150790963 T^{4} - 120269472412562 T^{5} + 350356403707485209 T^{6} \))(\( 1 - 2819 T + 5531118 T^{2} - 7041312813 T^{3} + 6955665197242 T^{4} - 4963907252467797 T^{5} + 2748862164097624398 T^{6} - \)\(98\!\cdots\!71\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 2819 T + 5531118 T^{2} - 7041312813 T^{3} + 6955665197242 T^{4} - 4963907252467797 T^{5} + 2748862164097624398 T^{6} - \)\(98\!\cdots\!71\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 746 T + 1733225 T^{2} + 126840160 T^{3} + 408516498430 T^{4} + 989188619900372 T^{5} + 287991467381698670 T^{6} + 63037186462499793760 T^{7} + \)\(60\!\cdots\!25\)\( T^{8} - \)\(18\!\cdots\!66\)\( T^{9} + \)\(17\!\cdots\!49\)\( T^{10} \))(\( 1 - 746 T + 1733225 T^{2} + 126840160 T^{3} + 408516498430 T^{4} + 989188619900372 T^{5} + 287991467381698670 T^{6} + 63037186462499793760 T^{7} + \)\(60\!\cdots\!25\)\( T^{8} - \)\(18\!\cdots\!66\)\( T^{9} + \)\(17\!\cdots\!49\)\( T^{10} \))(\( ( 1 - 870 T + 704969 T^{2} )^{2} \))(\( ( 1 + 730 T + 704969 T^{2} )^{2} \))(\( ( 1 - 216 T + 1417730 T^{2} - 152273304 T^{3} + 496981290961 T^{4} )^{2} \))(\( ( 1 - 1713 T + 2140568 T^{2} - 1207611897 T^{3} + 496981290961 T^{4} )^{2} \))(\( ( 1 + 242 T + 1427227 T^{2} + 347564516 T^{3} + 1006150790963 T^{4} + 120269472412562 T^{5} + 350356403707485209 T^{6} )^{2} \))(\( ( 1 + 2819 T + 5531118 T^{2} + 7041312813 T^{3} + 6955665197242 T^{4} + 4963907252467797 T^{5} + 2748862164097624398 T^{6} + \)\(98\!\cdots\!71\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} )^{2} \))(\( 1 - 329 T - 596728 T^{2} - 231934801 T^{3} + 496981290961 T^{4} \))(\( 1 - 1194 T + 720667 T^{2} - 841732986 T^{3} + 496981290961 T^{4} \))(\( 1 + 650 T - 883111 T^{2} - 67812550 T^{3} + 909789389860 T^{4} - 47805745560950 T^{5} - 438889644841859671 T^{6} + \)\(22\!\cdots\!50\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 2322 T + 885553 T^{2} - 27254778 T^{3} + 2336719735260 T^{4} + 1546137721242198 T^{5} - 1544579435132215297 T^{6} - \)\(76\!\cdots\!66\)\( T^{7} + \)\(50\!\cdots\!63\)\( T^{8} - \)\(79\!\cdots\!44\)\( T^{9} - \)\(15\!\cdots\!20\)\( T^{10} - \)\(55\!\cdots\!36\)\( T^{11} + \)\(24\!\cdots\!43\)\( T^{12} - \)\(26\!\cdots\!94\)\( T^{13} - \)\(38\!\cdots\!37\)\( T^{14} + \)\(26\!\cdots\!02\)\( T^{15} + \)\(28\!\cdots\!60\)\( T^{16} - \)\(23\!\cdots\!42\)\( T^{17} + \)\(54\!\cdots\!73\)\( T^{18} + \)\(99\!\cdots\!38\)\( T^{19} + \)\(30\!\cdots\!01\)\( T^{20} \))(\( 1 + 2678 T - 182939 T^{2} - 5535014430 T^{3} - 214319400560 T^{4} + 8765677069815078 T^{5} + 164101013399486579 T^{6} - \)\(99\!\cdots\!54\)\( T^{7} + \)\(21\!\cdots\!27\)\( T^{8} + \)\(99\!\cdots\!12\)\( T^{9} - \)\(42\!\cdots\!84\)\( T^{10} - \)\(74\!\cdots\!68\)\( T^{11} + \)\(61\!\cdots\!33\)\( T^{12} + \)\(42\!\cdots\!22\)\( T^{13} - \)\(60\!\cdots\!91\)\( T^{14} - \)\(10\!\cdots\!82\)\( T^{15} + \)\(49\!\cdots\!08\)\( T^{16} - \)\(73\!\cdots\!58\)\( T^{17} - \)\(30\!\cdots\!51\)\( T^{18} + \)\(14\!\cdots\!98\)\( T^{19} + \)\(15\!\cdots\!93\)\( T^{20} - \)\(12\!\cdots\!32\)\( T^{21} - \)\(52\!\cdots\!04\)\( T^{22} + \)\(86\!\cdots\!68\)\( T^{23} + \)\(13\!\cdots\!07\)\( T^{24} - \)\(42\!\cdots\!66\)\( T^{25} + \)\(49\!\cdots\!79\)\( T^{26} + \)\(18\!\cdots\!82\)\( T^{27} - \)\(32\!\cdots\!60\)\( T^{28} - \)\(58\!\cdots\!70\)\( T^{29} - \)\(13\!\cdots\!19\)\( T^{30} + \)\(14\!\cdots\!22\)\( T^{31} + \)\(37\!\cdots\!81\)\( T^{32} \))(\( 1 + 2678 T - 182939 T^{2} - 5535014430 T^{3} - 214319400560 T^{4} + 8765677069815078 T^{5} + 164101013399486579 T^{6} - \)\(99\!\cdots\!54\)\( T^{7} + \)\(21\!\cdots\!27\)\( T^{8} + \)\(99\!\cdots\!12\)\( T^{9} - \)\(42\!\cdots\!84\)\( T^{10} - \)\(74\!\cdots\!68\)\( T^{11} + \)\(61\!\cdots\!33\)\( T^{12} + \)\(42\!\cdots\!22\)\( T^{13} - \)\(60\!\cdots\!91\)\( T^{14} - \)\(10\!\cdots\!82\)\( T^{15} + \)\(49\!\cdots\!08\)\( T^{16} - \)\(73\!\cdots\!58\)\( T^{17} - \)\(30\!\cdots\!51\)\( T^{18} + \)\(14\!\cdots\!98\)\( T^{19} + \)\(15\!\cdots\!93\)\( T^{20} - \)\(12\!\cdots\!32\)\( T^{21} - \)\(52\!\cdots\!04\)\( T^{22} + \)\(86\!\cdots\!68\)\( T^{23} + \)\(13\!\cdots\!07\)\( T^{24} - \)\(42\!\cdots\!66\)\( T^{25} + \)\(49\!\cdots\!79\)\( T^{26} + \)\(18\!\cdots\!82\)\( T^{27} - \)\(32\!\cdots\!60\)\( T^{28} - \)\(58\!\cdots\!70\)\( T^{29} - \)\(13\!\cdots\!19\)\( T^{30} + \)\(14\!\cdots\!22\)\( T^{31} + \)\(37\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 2938 T + 2564153 T^{2} - 1165926318 T^{3} + 2792164847900 T^{4} - 3018079716233822 T^{5} - 308766378555648137 T^{6} + \)\(71\!\cdots\!34\)\( T^{7} + \)\(10\!\cdots\!23\)\( T^{8} + \)\(25\!\cdots\!56\)\( T^{9} - \)\(15\!\cdots\!40\)\( T^{10} + \)\(18\!\cdots\!64\)\( T^{11} + \)\(50\!\cdots\!03\)\( T^{12} + \)\(25\!\cdots\!06\)\( T^{13} - \)\(76\!\cdots\!77\)\( T^{14} - \)\(52\!\cdots\!78\)\( T^{15} + \)\(34\!\cdots\!00\)\( T^{16} - \)\(10\!\cdots\!02\)\( T^{17} + \)\(15\!\cdots\!73\)\( T^{18} - \)\(12\!\cdots\!02\)\( T^{19} + \)\(30\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 + 633778 T^{2} + 496981290961 T^{4} )^{2} \))(\( ( 1 + 704969 T^{2} )^{4} \))(\( ( 1 + 704969 T^{2} )^{4} \))(\( ( 1 + 1409918 T^{2} + 496981290961 T^{4} )^{2} \))(\( ( 1 + 633778 T^{2} + 496981290961 T^{4} )^{2} \))(\( ( 1 + 704969 T^{2} )^{8} \))(\( ( 1 + 2745112 T^{2} + 4127085754748 T^{4} + 4427611292803540904 T^{6} + \)\(35\!\cdots\!70\)\( T^{8} + \)\(22\!\cdots\!44\)\( T^{10} + \)\(10\!\cdots\!08\)\( T^{12} + \)\(33\!\cdots\!72\)\( T^{14} + \)\(61\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 329 T - 596728 T^{2} + 231934801 T^{3} + 496981290961 T^{4} )^{2} \))(\( ( 1 + 1194 T + 720667 T^{2} + 841732986 T^{3} + 496981290961 T^{4} )^{2} \))(\( ( 1 - 650 T - 883111 T^{2} + 67812550 T^{3} + 909789389860 T^{4} + 47805745560950 T^{5} - 438889644841859671 T^{6} - \)\(22\!\cdots\!50\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} )^{2} \))(\( ( 1 - 2322 T + 885553 T^{2} + 27254778 T^{3} + 2336719735260 T^{4} - 1546137721242198 T^{5} - 1544579435132215297 T^{6} + \)\(76\!\cdots\!66\)\( T^{7} + \)\(50\!\cdots\!63\)\( T^{8} + \)\(79\!\cdots\!44\)\( T^{9} - \)\(15\!\cdots\!20\)\( T^{10} + \)\(55\!\cdots\!36\)\( T^{11} + \)\(24\!\cdots\!43\)\( T^{12} + \)\(26\!\cdots\!94\)\( T^{13} - \)\(38\!\cdots\!37\)\( T^{14} - \)\(26\!\cdots\!02\)\( T^{15} + \)\(28\!\cdots\!60\)\( T^{16} + \)\(23\!\cdots\!42\)\( T^{17} + \)\(54\!\cdots\!73\)\( T^{18} - \)\(99\!\cdots\!38\)\( T^{19} + \)\(30\!\cdots\!01\)\( T^{20} )^{2} \))
$97$ (\( 1 + 1026 T + 912673 T^{2} \))(\( 1 + 294 T + 912673 T^{2} \))(\( 1 + 2742 T + 3608187 T^{2} + 2502549366 T^{3} + 832972004929 T^{4} \))(\( 1 + 1764 T + 1844934 T^{2} + 1609955172 T^{3} + 832972004929 T^{4} \))(\( 1 - 1764 T + 1844934 T^{2} - 1609955172 T^{3} + 832972004929 T^{4} \))(\( 1 + 100 T + 2266056 T^{2} + 184512618 T^{3} + 2068168127688 T^{4} + 83297200492900 T^{5} + 760231058654565217 T^{6} \))(\( 1 - 1100 T + 625060 T^{2} + 1205286580 T^{3} - 1327506690522 T^{4} + 1100032518828340 T^{5} + 520657481400920740 T^{6} - \)\(83\!\cdots\!00\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 + 1100 T + 625060 T^{2} - 1205286580 T^{3} - 1327506690522 T^{4} - 1100032518828340 T^{5} + 520657481400920740 T^{6} + \)\(83\!\cdots\!00\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 + 518 T + 3950578 T^{2} + 1339313360 T^{3} + 6506315346693 T^{4} + 1569203693813924 T^{5} + 5938138346412340389 T^{6} + \)\(11\!\cdots\!40\)\( T^{7} + \)\(30\!\cdots\!26\)\( T^{8} + \)\(35\!\cdots\!38\)\( T^{9} + \)\(63\!\cdots\!93\)\( T^{10} \))(\( 1 - 518 T + 3950578 T^{2} - 1339313360 T^{3} + 6506315346693 T^{4} - 1569203693813924 T^{5} + 5938138346412340389 T^{6} - \)\(11\!\cdots\!40\)\( T^{7} + \)\(30\!\cdots\!26\)\( T^{8} - \)\(35\!\cdots\!38\)\( T^{9} + \)\(63\!\cdots\!93\)\( T^{10} \))(\( 1 - 772670 T^{2} + 832972004929 T^{4} \))(\( 1 - 1738910 T^{2} + 832972004929 T^{4} \))(\( 1 + 302190 T^{2} + 960976713683 T^{4} + 251715810169494510 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 - 578172 T^{2} - 610196372602 T^{4} - 481601090033809788 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 - 4522112 T^{2} + 9234443526912 T^{4} - 10842927360521653566 T^{6} + \)\(76\!\cdots\!48\)\( T^{8} - \)\(31\!\cdots\!92\)\( T^{10} + \)\(57\!\cdots\!89\)\( T^{12} \))(\( 1 - 40120 T^{2} + 387317098556 T^{4} - 349128100340730440 T^{6} - \)\(69\!\cdots\!34\)\( T^{8} - \)\(29\!\cdots\!60\)\( T^{10} + \)\(26\!\cdots\!96\)\( T^{12} - \)\(23\!\cdots\!80\)\( T^{14} + \)\(48\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 882 T + 912673 T^{2} )^{2} \))(\( ( 1 + 902 T + 912673 T^{2} )^{2} \))(\( ( 1 - 628 T + 1423942 T^{2} - 573158644 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 + 598 T + 4425037 T^{2} + 2054168072 T^{3} + 7929732195026 T^{4} + 2752469564393540 T^{5} + 7237252471630964498 T^{6} + \)\(17\!\cdots\!88\)\( T^{7} + \)\(33\!\cdots\!29\)\( T^{8} + \)\(41\!\cdots\!18\)\( T^{9} + \)\(63\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 + 664 T + 2601074 T^{2} + 849188910 T^{3} + 4238296189015 T^{4} + 857926081559752 T^{5} + 5162277704515872633 T^{6} + \)\(63\!\cdots\!48\)\( T^{7} + \)\(51\!\cdots\!63\)\( T^{8} + \)\(57\!\cdots\!04\)\( T^{9} + \)\(43\!\cdots\!57\)\( T^{10} + \)\(65\!\cdots\!84\)\( T^{11} + \)\(29\!\cdots\!15\)\( T^{12} + \)\(53\!\cdots\!30\)\( T^{13} + \)\(15\!\cdots\!86\)\( T^{14} + \)\(35\!\cdots\!08\)\( T^{15} + \)\(48\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 664 T + 2601074 T^{2} - 849188910 T^{3} + 4238296189015 T^{4} - 857926081559752 T^{5} + 5162277704515872633 T^{6} - \)\(63\!\cdots\!48\)\( T^{7} + \)\(51\!\cdots\!63\)\( T^{8} - \)\(57\!\cdots\!04\)\( T^{9} + \)\(43\!\cdots\!57\)\( T^{10} - \)\(65\!\cdots\!84\)\( T^{11} + \)\(29\!\cdots\!15\)\( T^{12} - \)\(53\!\cdots\!30\)\( T^{13} + \)\(15\!\cdots\!86\)\( T^{14} - \)\(35\!\cdots\!08\)\( T^{15} + \)\(48\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 3893530 T^{2} + 9172577050349 T^{4} + 15424484400745116216 T^{6} + \)\(19\!\cdots\!18\)\( T^{8} + \)\(20\!\cdots\!68\)\( T^{10} + \)\(16\!\cdots\!22\)\( T^{12} + \)\(10\!\cdots\!56\)\( T^{14} + \)\(53\!\cdots\!61\)\( T^{16} + \)\(18\!\cdots\!30\)\( T^{18} + \)\(40\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 + 1499220776423 T^{4} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( ( 1 + 832972004929 T^{4} )^{2} \))(\( 1 - 859766289982 T^{4} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 - 1665717085762 T^{4} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 + 1499220776423 T^{4} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( ( 1 + 832972004929 T^{4} )^{4} \))(\( 1 - 1933745575038 T^{4} + \)\(56\!\cdots\!93\)\( T^{8} + \)\(12\!\cdots\!34\)\( T^{12} - \)\(15\!\cdots\!80\)\( T^{16} + \)\(86\!\cdots\!94\)\( T^{20} + \)\(27\!\cdots\!33\)\( T^{24} - \)\(64\!\cdots\!98\)\( T^{28} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 1047422 T^{2} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 1011742 T^{2} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 2453500 T^{2} + 2973667572358 T^{4} - 2043696814093301500 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 - 8492470 T^{2} + 32983631827309 T^{4} - 77141661602385589896 T^{6} + \)\(12\!\cdots\!78\)\( T^{8} - \)\(13\!\cdots\!28\)\( T^{10} + \)\(10\!\cdots\!62\)\( T^{12} - \)\(53\!\cdots\!36\)\( T^{14} + \)\(19\!\cdots\!01\)\( T^{16} - \)\(40\!\cdots\!70\)\( T^{18} + \)\(40\!\cdots\!49\)\( T^{20} )^{2} \))
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