Properties

Label 144.3
Level 144
Weight 3
Dimension 493
Nonzero newspaces 8
Newform subspaces 19
Sturm bound 3456
Trace bound 2

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Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 19 \)
Sturm bound: \(3456\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(144))\).

Total New Old
Modular forms 1264 533 731
Cusp forms 1040 493 547
Eisenstein series 224 40 184

Trace form

\( 493q - 6q^{2} - 6q^{3} - 12q^{4} - 15q^{5} - 8q^{6} - 23q^{7} - 10q^{9} + O(q^{10}) \) \( 493q - 6q^{2} - 6q^{3} - 12q^{4} - 15q^{5} - 8q^{6} - 23q^{7} - 10q^{9} + 20q^{10} - 19q^{11} - 8q^{12} + 19q^{13} + 40q^{14} + 27q^{15} + 68q^{16} + 102q^{17} + 92q^{18} + 82q^{19} + 80q^{20} + 31q^{21} - 8q^{22} + 67q^{23} - 40q^{24} - 79q^{25} - 100q^{26} + 66q^{27} - 200q^{28} - 127q^{29} - 220q^{30} - 107q^{31} - 356q^{32} - 75q^{33} - 256q^{34} + 96q^{35} - 204q^{36} + 52q^{37} - 468q^{38} + 129q^{39} - 412q^{40} + 15q^{41} - 208q^{42} + 283q^{43} - 248q^{44} - 171q^{45} - 20q^{46} - 225q^{47} + 44q^{48} - 117q^{49} + 322q^{50} - 320q^{51} + 416q^{52} - 124q^{53} + 300q^{54} - 446q^{55} + 352q^{56} - 316q^{57} + 732q^{58} - 587q^{59} - 524q^{60} + 83q^{61} - 216q^{62} - 339q^{63} + 552q^{64} - 59q^{65} - 608q^{66} - 69q^{67} + 80q^{68} - 103q^{69} + 28q^{70} - 268q^{71} + 104q^{72} - 146q^{73} + 72q^{74} - 62q^{75} - 432q^{76} + 173q^{77} + 532q^{78} - 563q^{79} - 192q^{80} + 646q^{81} - 1544q^{82} - 283q^{83} + 520q^{84} + 308q^{85} - 72q^{86} - 69q^{87} - 844q^{88} + 426q^{89} + 280q^{90} + 142q^{91} - 500q^{92} + 567q^{93} - 84q^{94} + 714q^{95} + 60q^{96} + 429q^{97} + 838q^{98} + 747q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)

We only show spaces with odd 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
144.3.b \(\chi_{144}(55, \cdot)\) None 0 1
144.3.e \(\chi_{144}(17, \cdot)\) 144.3.e.a 2 1
144.3.e.b 2
144.3.g \(\chi_{144}(127, \cdot)\) 144.3.g.a 1 1
144.3.g.b 2
144.3.g.c 2
144.3.h \(\chi_{144}(89, \cdot)\) None 0 1
144.3.j \(\chi_{144}(53, \cdot)\) 144.3.j.a 32 2
144.3.m \(\chi_{144}(19, \cdot)\) 144.3.m.a 6 2
144.3.m.b 16
144.3.m.c 16
144.3.n \(\chi_{144}(41, \cdot)\) None 0 2
144.3.o \(\chi_{144}(31, \cdot)\) 144.3.o.a 8 2
144.3.o.b 8
144.3.o.c 8
144.3.q \(\chi_{144}(65, \cdot)\) 144.3.q.a 2 2
144.3.q.b 4
144.3.q.c 4
144.3.q.d 4
144.3.q.e 8
144.3.t \(\chi_{144}(7, \cdot)\) None 0 2
144.3.v \(\chi_{144}(43, \cdot)\) 144.3.v.a 184 4
144.3.w \(\chi_{144}(5, \cdot)\) 144.3.w.a 184 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 2 T + 6 T^{2} - 8 T^{3} + 24 T^{4} - 32 T^{5} + 64 T^{6} \))(\( 1 + 6 T^{2} + 10 T^{4} - 88 T^{6} - 752 T^{8} - 1408 T^{10} + 2560 T^{12} + 24576 T^{14} + 65536 T^{16} \))(\( 1 - 6 T^{2} - 4 T^{3} + 10 T^{4} + 56 T^{5} + 88 T^{6} - 128 T^{7} - 496 T^{8} - 512 T^{9} + 1408 T^{10} + 3584 T^{11} + 2560 T^{12} - 4096 T^{13} - 24576 T^{14} + 65536 T^{16} \))
$3$ (\( 1 + 3 T + 6 T^{2} - 27 T^{3} - 126 T^{4} - 243 T^{5} + 486 T^{6} + 2187 T^{7} + 6561 T^{8} \))(\( 1 + 3 T^{2} - 72 T^{4} + 243 T^{6} + 6561 T^{8} \))(\( 1 - 3 T + 6 T^{2} + 27 T^{3} - 126 T^{4} + 243 T^{5} + 486 T^{6} - 2187 T^{7} + 6561 T^{8} \))(\( 1 - 3 T + 9 T^{2} \))(\( 1 + 3 T + 12 T^{2} + 27 T^{3} + 81 T^{4} \))(\( 1 - 6 T^{2} + 81 T^{4} \))(\( ( 1 - 3 T )^{4} \))(\( 1 + 10 T + 61 T^{2} + 270 T^{3} + 912 T^{4} + 2430 T^{5} + 4941 T^{6} + 7290 T^{7} + 6561 T^{8} \))
$5$ (\( 1 + 625 T^{4} \))(\( 1 - 32 T^{2} + 625 T^{4} \))(\( 1 - 6 T + 25 T^{2} \))(\( ( 1 + 6 T + 25 T^{2} )^{2} \))(\( ( 1 + 25 T^{2} )^{2} \))(\( 1 - 2 T + 2 T^{2} + 14 T^{3} - 369 T^{4} - 636 T^{5} + 2108 T^{6} - 15900 T^{7} - 230625 T^{8} + 218750 T^{9} + 781250 T^{10} - 19531250 T^{11} + 244140625 T^{12} \))(\( 1 - 344 T^{4} - 8484 T^{8} + 258572952 T^{12} - 94198183354 T^{16} + 101005059375000 T^{20} - 1294555664062500 T^{24} - 20503997802734375000 T^{28} + \)\(23\!\cdots\!25\)\( T^{32} \))(\( 1 - 32 T^{3} - 344 T^{4} - 5664 T^{5} + 512 T^{6} - 145600 T^{7} + 223452 T^{8} + 2255168 T^{9} + 20875776 T^{10} + 67282720 T^{11} + 753060504 T^{12} - 1881828576 T^{13} + 2740220928 T^{14} - 75471830656 T^{15} - 399298967994 T^{16} - 1886795766400 T^{17} + 1712638080000 T^{18} - 29403571500000 T^{19} + 294164259375000 T^{20} + 657057812500000 T^{21} + 5096625000000000 T^{22} + 13764453125000000 T^{23} + 34096069335937500 T^{24} - 555419921875000000 T^{25} + 48828125000000000 T^{26} - 13504028320312500000 T^{27} - 20503997802734375000 T^{28} - 47683715820312500000 T^{29} + \)\(23\!\cdots\!25\)\( T^{32} \))(\( 1 - 3 T - 34 T^{2} + 339 T^{3} + 211 T^{4} - 10296 T^{5} + 50708 T^{6} + 156576 T^{7} - 1757804 T^{8} + 3914400 T^{9} + 31692500 T^{10} - 160875000 T^{11} + 82421875 T^{12} + 3310546875 T^{13} - 8300781250 T^{14} - 18310546875 T^{15} + 152587890625 T^{16} \))(\( ( 1 + 3 T - 17 T^{2} - 72 T^{3} - 174 T^{4} - 1800 T^{5} - 10625 T^{6} + 46875 T^{7} + 390625 T^{8} )^{2} \))(\( 1 - 3 T - 34 T^{2} + 339 T^{3} + 211 T^{4} - 10296 T^{5} + 50708 T^{6} + 156576 T^{7} - 1757804 T^{8} + 3914400 T^{9} + 31692500 T^{10} - 160875000 T^{11} + 82421875 T^{12} + 3310546875 T^{13} - 8300781250 T^{14} - 18310546875 T^{15} + 152587890625 T^{16} \))(\( 1 - 6 T + 37 T^{2} - 150 T^{3} + 625 T^{4} \))(\( 1 - 9 T + 59 T^{2} - 288 T^{3} + 1074 T^{4} - 7200 T^{5} + 36875 T^{6} - 140625 T^{7} + 390625 T^{8} \))(\( ( 1 + 9 T + 52 T^{2} + 225 T^{3} + 625 T^{4} )^{2} \))(\( 1 - 6 T + 33 T^{2} - 126 T^{3} + 116 T^{4} - 3150 T^{5} + 20625 T^{6} - 93750 T^{7} + 390625 T^{8} \))(\( 1 + 6 T + 63 T^{2} + 306 T^{3} + 2461 T^{4} + 15132 T^{5} + 86562 T^{6} + 473928 T^{7} + 2131866 T^{8} + 11848200 T^{9} + 54101250 T^{10} + 236437500 T^{11} + 961328125 T^{12} + 2988281250 T^{13} + 15380859375 T^{14} + 36621093750 T^{15} + 152587890625 T^{16} \))
$7$ (\( ( 1 + 12 T + 49 T^{2} )^{2} \))(\( ( 1 - 4 T + 49 T^{2} )^{2} \))(\( ( 1 - 7 T )( 1 + 7 T ) \))(\( 1 - 50 T^{2} + 2401 T^{4} \))(\( ( 1 - 2 T + 49 T^{2} )( 1 + 2 T + 49 T^{2} ) \))(\( ( 1 + 2 T + 87 T^{2} + 332 T^{3} + 4263 T^{4} + 4802 T^{5} + 117649 T^{6} )^{2} \))(\( ( 1 + 84 T^{2} + 352 T^{3} + 3530 T^{4} + 17248 T^{5} + 201684 T^{6} + 5764801 T^{8} )^{4} \))(\( ( 1 + 168 T^{2} - 448 T^{3} + 15076 T^{4} - 56512 T^{5} + 1070392 T^{6} - 3649664 T^{7} + 60103046 T^{8} - 178833536 T^{9} + 2570011192 T^{10} - 6648580288 T^{11} + 86910139876 T^{12} - 126548911552 T^{13} + 2325336249768 T^{14} + 33232930569601 T^{16} )^{2} \))(\( 1 - 3 T + 82 T^{2} - 237 T^{3} + 2419 T^{4} - 21600 T^{5} + 116980 T^{6} - 2348256 T^{7} + 7641628 T^{8} - 115064544 T^{9} + 280868980 T^{10} - 2541218400 T^{11} + 13945053619 T^{12} - 66946634013 T^{13} + 1134985550482 T^{14} - 2034669218547 T^{15} + 33232930569601 T^{16} \))(\( 1 + 97 T^{2} + 4381 T^{4} + 21922 T^{6} - 3075026 T^{8} + 52634722 T^{10} + 25255593181 T^{12} + 1342604858497 T^{14} + 33232930569601 T^{16} \))(\( 1 + 3 T + 82 T^{2} + 237 T^{3} + 2419 T^{4} + 21600 T^{5} + 116980 T^{6} + 2348256 T^{7} + 7641628 T^{8} + 115064544 T^{9} + 280868980 T^{10} + 2541218400 T^{11} + 13945053619 T^{12} + 66946634013 T^{13} + 1134985550482 T^{14} + 2034669218547 T^{15} + 33232930569601 T^{16} \))(\( ( 1 - 13 T + 49 T^{2} )( 1 + 11 T + 49 T^{2} ) \))(\( 1 - T - 23 T^{2} + 74 T^{3} - 1874 T^{4} + 3626 T^{5} - 55223 T^{6} - 117649 T^{7} + 5764801 T^{8} \))(\( 1 + 2 T - 41 T^{2} - 106 T^{3} - 572 T^{4} - 5194 T^{5} - 98441 T^{6} + 235298 T^{7} + 5764801 T^{8} \))(\( 1 - 6 T + 25 T^{2} + 522 T^{3} - 4044 T^{4} + 25578 T^{5} + 60025 T^{6} - 705894 T^{7} + 5764801 T^{8} \))(\( 1 + 6 T - 127 T^{2} - 714 T^{3} + 10213 T^{4} + 43992 T^{5} - 588922 T^{6} - 917052 T^{7} + 31082074 T^{8} - 44935548 T^{9} - 1414001722 T^{10} + 5175614808 T^{11} + 58875912613 T^{12} - 201687327786 T^{13} - 1757843474527 T^{14} + 4069338437094 T^{15} + 33232930569601 T^{16} \))
$11$ (\( 1 - 210 T^{2} + 14641 T^{4} \))(\( ( 1 - 14 T + 121 T^{2} )( 1 + 14 T + 121 T^{2} ) \))(\( ( 1 - 11 T )( 1 + 11 T ) \))(\( 1 + 190 T^{2} + 14641 T^{4} \))(\( ( 1 - 11 T )^{2}( 1 + 11 T )^{2} \))(\( 1 - 18 T + 162 T^{2} - 2146 T^{3} + 17759 T^{4} - 65756 T^{5} + 609308 T^{6} - 7956476 T^{7} + 260009519 T^{8} - 3801769906 T^{9} + 34726138722 T^{10} - 466873642818 T^{11} + 3138428376721 T^{12} \))(\( 1 - 27832 T^{4} + 345241884 T^{8} - 1221720802824 T^{12} - 7510669490883642 T^{16} - \)\(26\!\cdots\!44\)\( T^{20} + \)\(15\!\cdots\!24\)\( T^{24} - \)\(27\!\cdots\!12\)\( T^{28} + \)\(21\!\cdots\!21\)\( T^{32} \))(\( 1 + 32 T + 512 T^{2} + 8480 T^{3} + 137032 T^{4} + 1636576 T^{5} + 18165248 T^{6} + 219655136 T^{7} + 2263228700 T^{8} + 21867108000 T^{9} + 253620152832 T^{10} + 2916953293728 T^{11} + 33797606438392 T^{12} + 431768458252384 T^{13} + 5293166227138048 T^{14} + 61910274521995104 T^{15} + 703855220885889990 T^{16} + 7491143217161407584 T^{17} + 77497246731528160768 T^{18} + \)\(76\!\cdots\!24\)\( T^{19} + \)\(72\!\cdots\!52\)\( T^{20} + \)\(75\!\cdots\!28\)\( T^{21} + \)\(79\!\cdots\!72\)\( T^{22} + \)\(83\!\cdots\!00\)\( T^{23} + \)\(10\!\cdots\!00\)\( T^{24} + \)\(12\!\cdots\!16\)\( T^{25} + \)\(12\!\cdots\!48\)\( T^{26} + \)\(13\!\cdots\!96\)\( T^{27} + \)\(13\!\cdots\!12\)\( T^{28} + \)\(10\!\cdots\!80\)\( T^{29} + \)\(73\!\cdots\!72\)\( T^{30} + \)\(55\!\cdots\!32\)\( T^{31} + \)\(21\!\cdots\!21\)\( T^{32} \))(\( 1 - 18 T + 448 T^{2} - 6120 T^{3} + 93463 T^{4} - 1253556 T^{5} + 16013428 T^{6} - 201806226 T^{7} + 2222076136 T^{8} - 24418553346 T^{9} + 234452599348 T^{10} - 2220750920916 T^{11} + 20034624094903 T^{12} - 158737038558120 T^{13} + 1406015912771008 T^{14} - 6835497004498338 T^{15} + 45949729863572161 T^{16} \))(\( ( 1 + 107 T^{2} - 3192 T^{4} + 1566587 T^{6} + 214358881 T^{8} )^{2} \))(\( 1 + 18 T + 448 T^{2} + 6120 T^{3} + 93463 T^{4} + 1253556 T^{5} + 16013428 T^{6} + 201806226 T^{7} + 2222076136 T^{8} + 24418553346 T^{9} + 234452599348 T^{10} + 2220750920916 T^{11} + 20034624094903 T^{12} + 158737038558120 T^{13} + 1406015912771008 T^{14} + 6835497004498338 T^{15} + 45949729863572161 T^{16} \))(\( 1 - 3 T + 124 T^{2} - 363 T^{3} + 14641 T^{4} \))(\( 1 - 36 T + 683 T^{2} - 9036 T^{3} + 100632 T^{4} - 1093356 T^{5} + 9999803 T^{6} - 63776196 T^{7} + 214358881 T^{8} \))(\( 1 + 18 T + 359 T^{2} + 4518 T^{3} + 61428 T^{4} + 546678 T^{5} + 5256119 T^{6} + 31888098 T^{7} + 214358881 T^{8} \))(\( 1 - 18 T + 249 T^{2} - 2538 T^{3} + 18308 T^{4} - 307098 T^{5} + 3645609 T^{6} - 31888098 T^{7} + 214358881 T^{8} \))(\( 1 + 36 T + 828 T^{2} + 14256 T^{3} + 189103 T^{4} + 2029500 T^{5} + 18127476 T^{6} + 142796448 T^{7} + 1322450688 T^{8} + 17278370208 T^{9} + 265404376116 T^{10} + 3595383049500 T^{11} + 40535907473743 T^{12} + 369763925111856 T^{13} + 2598618695924988 T^{14} + 13670994008996676 T^{15} + 45949729863572161 T^{16} \))
$13$ (\( ( 1 + 8 T + 169 T^{2} )^{2} \))(\( ( 1 - 8 T + 169 T^{2} )^{2} \))(\( 1 - 10 T + 169 T^{2} \))(\( ( 1 + 14 T + 169 T^{2} )^{2} \))(\( ( 1 - 22 T + 169 T^{2} )^{2} \))(\( 1 + 2 T + 2 T^{2} + 1554 T^{3} - 7825 T^{4} - 453380 T^{5} + 316348 T^{6} - 76621220 T^{7} - 223489825 T^{8} + 7500861186 T^{9} + 1631461442 T^{10} + 275716983698 T^{11} + 23298085122481 T^{12} \))(\( ( 1 - 4352 T^{3} + 12636 T^{4} + 622336 T^{5} + 9469952 T^{6} - 45147648 T^{7} - 2135161210 T^{8} - 7629952512 T^{9} + 270471299072 T^{10} + 3003897005824 T^{11} + 10307573390556 T^{12} - 599960156526848 T^{13} + 665416609183179841 T^{16} )^{2} \))(\( 1 + 3200 T^{3} + 7608 T^{4} + 95360 T^{5} + 5120000 T^{6} + 68335872 T^{7} + 2004669468 T^{8} + 7270355200 T^{9} + 184268595200 T^{10} + 4889456013184 T^{11} + 5354592144136 T^{12} + 669839496880000 T^{13} + 7008632866619392 T^{14} + 70586941744778752 T^{15} + 2398056097119178950 T^{16} + 11929193154867609088 T^{17} + \)\(20\!\cdots\!12\)\( T^{18} + \)\(32\!\cdots\!00\)\( T^{19} + \)\(43\!\cdots\!56\)\( T^{20} + \)\(67\!\cdots\!16\)\( T^{21} + \)\(42\!\cdots\!00\)\( T^{22} + \)\(28\!\cdots\!00\)\( T^{23} + \)\(13\!\cdots\!88\)\( T^{24} + \)\(76\!\cdots\!88\)\( T^{25} + \)\(97\!\cdots\!00\)\( T^{26} + \)\(30\!\cdots\!40\)\( T^{27} + \)\(41\!\cdots\!88\)\( T^{28} + \)\(29\!\cdots\!00\)\( T^{29} + \)\(44\!\cdots\!81\)\( T^{32} \))(\( 1 - 5 T - 360 T^{2} - 1561 T^{3} + 77501 T^{4} + 597312 T^{5} - 5007086 T^{6} - 68136458 T^{7} + 60552144 T^{8} - 11515061402 T^{9} - 143007383246 T^{10} + 2883110937408 T^{11} + 63219946608221 T^{12} - 215197105776289 T^{13} - 8387310644093160 T^{14} - 19686881928496445 T^{15} + 665416609183179841 T^{16} \))(\( ( 1 + 5 T - 83 T^{2} - 1150 T^{3} - 21122 T^{4} - 194350 T^{5} - 2370563 T^{6} + 24134045 T^{7} + 815730721 T^{8} )^{2} \))(\( 1 - 5 T - 360 T^{2} - 1561 T^{3} + 77501 T^{4} + 597312 T^{5} - 5007086 T^{6} - 68136458 T^{7} + 60552144 T^{8} - 11515061402 T^{9} - 143007383246 T^{10} + 2883110937408 T^{11} + 63219946608221 T^{12} - 215197105776289 T^{13} - 8387310644093160 T^{14} - 19686881928496445 T^{15} + 665416609183179841 T^{16} \))(\( 1 - 4 T - 153 T^{2} - 676 T^{3} + 28561 T^{4} \))(\( 1 - 5 T - 245 T^{2} + 340 T^{3} + 40114 T^{4} + 57460 T^{5} - 6997445 T^{6} - 24134045 T^{7} + 815730721 T^{8} \))(\( 1 + 10 T - 47 T^{2} - 1910 T^{3} - 23852 T^{4} - 322790 T^{5} - 1342367 T^{6} + 48268090 T^{7} + 815730721 T^{8} \))(\( 1 + 14 T - 95 T^{2} - 658 T^{3} + 22996 T^{4} - 111202 T^{5} - 2713295 T^{6} + 67575326 T^{7} + 815730721 T^{8} \))(\( 1 - 14 T - 129 T^{2} + 1886 T^{3} + 9461 T^{4} - 158556 T^{5} + 4694986 T^{6} - 8508992 T^{7} - 1078024230 T^{8} - 1438019648 T^{9} + 134093495146 T^{10} - 765319527804 T^{11} + 7717628351381 T^{12} + 260001115627214 T^{13} - 3005452980800049 T^{14} - 55123269399790046 T^{15} + 665416609183179841 T^{16} \))
$17$ (\( 1 - 480 T^{2} + 83521 T^{4} \))(\( 1 - 416 T^{2} + 83521 T^{4} \))(\( 1 - 30 T + 289 T^{2} \))(\( ( 1 - 6 T + 289 T^{2} )^{2} \))(\( ( 1 + 289 T^{2} )^{2} \))(\( ( 1 - 2 T + 607 T^{2} + 388 T^{3} + 175423 T^{4} - 167042 T^{5} + 24137569 T^{6} )^{2} \))(\( ( 1 + 1208 T^{2} + 806844 T^{4} + 368107656 T^{6} + 122826347526 T^{8} + 30744719536776 T^{10} + 5628348036726204 T^{12} + 703807662573551288 T^{14} + 48661191875666868481 T^{16} )^{2} \))(\( ( 1 + 968 T^{2} + 2944 T^{3} + 516540 T^{4} + 3209600 T^{5} + 201700088 T^{6} + 1543904000 T^{7} + 63894476806 T^{8} + 446188256000 T^{9} + 16846193049848 T^{10} + 77471941462400 T^{11} + 3603257748574140 T^{12} + 5935086042921856 T^{13} + 563978325638408648 T^{14} + 48661191875666868481 T^{16} )^{2} \))(\( ( 1 - 3 T + 334 T^{2} - 693 T^{3} + 110178 T^{4} - 200277 T^{5} + 27896014 T^{6} - 72412707 T^{7} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 15 T + 608 T^{2} - 4335 T^{3} + 83521 T^{4} )^{4} \))(\( ( 1 - 3 T + 334 T^{2} - 693 T^{3} + 110178 T^{4} - 200277 T^{5} + 27896014 T^{6} - 72412707 T^{7} + 6975757441 T^{8} )^{2} \))(\( 1 - 335 T^{2} + 83521 T^{4} \))(\( 1 - 769 T^{2} + 298176 T^{4} - 64227649 T^{6} + 6975757441 T^{8} \))(\( 1 - 796 T^{2} + 294342 T^{4} - 66482716 T^{6} + 6975757441 T^{8} \))(\( 1 - 516 T^{2} + 135302 T^{4} - 43096836 T^{6} + 6975757441 T^{8} \))(\( 1 - 858 T^{2} + 505105 T^{4} - 204328674 T^{6} + 68217206628 T^{8} - 17065735181154 T^{10} + 3523489962236305 T^{12} - 499889879543134938 T^{14} + 48661191875666868481 T^{16} \))
$19$ (\( ( 1 - 16 T + 361 T^{2} )^{2} \))(\( ( 1 - 16 T + 361 T^{2} )^{2} \))(\( ( 1 - 19 T )( 1 + 19 T ) \))(\( 1 - 674 T^{2} + 130321 T^{4} \))(\( ( 1 - 26 T + 361 T^{2} )( 1 + 26 T + 361 T^{2} ) \))(\( 1 - 30 T + 450 T^{2} - 12014 T^{3} + 441215 T^{4} - 8004292 T^{5} + 113750108 T^{6} - 2889549412 T^{7} + 57499580015 T^{8} - 565209214334 T^{9} + 7642603368450 T^{10} - 183931987734030 T^{11} + 2213314919066161 T^{12} \))(\( ( 1 + 16 T + 128 T^{2} - 7984 T^{3} - 156764 T^{4} + 603504 T^{5} + 61593984 T^{6} + 384035120 T^{7} + 7522568070 T^{8} + 138636678320 T^{9} + 8026989588864 T^{10} + 28392377367024 T^{11} - 2662411276559324 T^{12} - 48950433002283184 T^{13} + 283304309640468608 T^{14} + 12784106972526145936 T^{15} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 + 32 T + 512 T^{2} - 2656 T^{3} - 523448 T^{4} - 8424608 T^{5} + 1945088 T^{6} + 4454446304 T^{7} + 107916937244 T^{8} - 703649376 T^{9} - 30601835632128 T^{10} - 698985761087712 T^{11} + 998616856187896 T^{12} + 253693358084547040 T^{13} + 3161998119961945600 T^{14} - 30474951661580761248 T^{15} - \)\(19\!\cdots\!42\)\( T^{16} - \)\(11\!\cdots\!28\)\( T^{17} + \)\(41\!\cdots\!00\)\( T^{18} + \)\(11\!\cdots\!40\)\( T^{19} + \)\(16\!\cdots\!36\)\( T^{20} - \)\(42\!\cdots\!12\)\( T^{21} - \)\(67\!\cdots\!08\)\( T^{22} - \)\(56\!\cdots\!96\)\( T^{23} + \)\(31\!\cdots\!64\)\( T^{24} + \)\(46\!\cdots\!64\)\( T^{25} + \)\(73\!\cdots\!88\)\( T^{26} - \)\(11\!\cdots\!88\)\( T^{27} - \)\(25\!\cdots\!08\)\( T^{28} - \)\(46\!\cdots\!36\)\( T^{29} + \)\(32\!\cdots\!92\)\( T^{30} + \)\(73\!\cdots\!32\)\( T^{31} + \)\(83\!\cdots\!61\)\( T^{32} \))(\( 1 - 1157 T^{2} + 639226 T^{4} - 232952123 T^{6} + 79410905002 T^{8} - 30358553621483 T^{10} + 10856335068446266 T^{12} - 2560805361359548277 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 589 T^{2} + 294216 T^{4} - 76759069 T^{6} + 16983563041 T^{8} )^{2} \))(\( 1 - 1157 T^{2} + 639226 T^{4} - 232952123 T^{6} + 79410905002 T^{8} - 30358553621483 T^{10} + 10856335068446266 T^{12} - 2560805361359548277 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( ( 1 + 11 T + 361 T^{2} )^{2} \))(\( ( 1 + T + 648 T^{2} + 361 T^{3} + 130321 T^{4} )^{2} \))(\( ( 1 - 20 T + 606 T^{2} - 7220 T^{3} + 130321 T^{4} )^{2} \))(\( ( 1 + 4 T + 342 T^{2} + 1444 T^{3} + 130321 T^{4} )^{2} \))(\( ( 1 + 2 T + 265 T^{2} + 6170 T^{3} + 157036 T^{4} + 2227370 T^{5} + 34535065 T^{6} + 94091762 T^{7} + 16983563041 T^{8} )^{2} \))
$23$ (\( 1 + 510 T^{2} + 279841 T^{4} \))(\( 1 - 770 T^{2} + 279841 T^{4} \))(\( ( 1 - 23 T )( 1 + 23 T ) \))(\( ( 1 - 23 T )^{2}( 1 + 23 T )^{2} \))(\( ( 1 - 23 T )^{2}( 1 + 23 T )^{2} \))(\( ( 1 + 30 T + 1751 T^{2} + 30772 T^{3} + 926279 T^{4} + 8395230 T^{5} + 148035889 T^{6} )^{2} \))(\( ( 1 + 2600 T^{2} + 3157852 T^{4} + 2464614168 T^{6} + 1453801462342 T^{8} + 689700093387288 T^{10} + 247294501491576412 T^{12} + 56978023523252834600 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 64 T + 3496 T^{2} - 127936 T^{3} + 4410332 T^{4} - 130001728 T^{5} + 3673719192 T^{6} - 94049622208 T^{7} + 2261818535238 T^{8} - 49752250148032 T^{9} + 1028057252408472 T^{10} - 19244921376016192 T^{11} + 345377444336323292 T^{12} - 5299942138629398464 T^{13} + 76613527014343042216 T^{14} - \)\(74\!\cdots\!76\)\( T^{15} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 + 81 T + 4870 T^{2} + 217323 T^{3} + 8414383 T^{4} + 278460504 T^{5} + 8325324592 T^{6} + 221238967356 T^{7} + 5380294547716 T^{8} + 117035413731324 T^{9} + 2329767159149872 T^{10} + 41222148261028056 T^{11} + 658938623261696623 T^{12} + 9002933696483841627 T^{13} + \)\(10\!\cdots\!70\)\( T^{14} + \)\(93\!\cdots\!29\)\( T^{15} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 503 T^{2} - 197699 T^{4} + 54813922 T^{6} + 54024424414 T^{8} + 15339182746402 T^{10} - 15482003479068419 T^{12} - 11023056089306221463 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 81 T + 4870 T^{2} - 217323 T^{3} + 8414383 T^{4} - 278460504 T^{5} + 8325324592 T^{6} - 221238967356 T^{7} + 5380294547716 T^{8} - 117035413731324 T^{9} + 2329767159149872 T^{10} - 41222148261028056 T^{11} + 658938623261696623 T^{12} - 9002933696483841627 T^{13} + \)\(10\!\cdots\!70\)\( T^{14} - \)\(93\!\cdots\!29\)\( T^{15} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 48 T + 1297 T^{2} - 25392 T^{3} + 279841 T^{4} \))(\( 1 + 99 T + 5117 T^{2} + 183150 T^{3} + 4870902 T^{4} + 96886350 T^{5} + 1431946397 T^{6} + 14655553011 T^{7} + 78310985281 T^{8} \))(\( 1 + 18 T + 1175 T^{2} + 19206 T^{3} + 915780 T^{4} + 10159974 T^{5} + 328813175 T^{6} + 2664646002 T^{7} + 78310985281 T^{8} \))(\( 1 + 30 T + 1401 T^{2} + 33030 T^{3} + 1091060 T^{4} + 17472870 T^{5} + 392057241 T^{6} + 4441076670 T^{7} + 78310985281 T^{8} \))(\( 1 - 102 T + 6033 T^{2} - 261630 T^{3} + 9057109 T^{4} - 271036392 T^{5} + 7331036166 T^{6} - 184354538700 T^{7} + 4374045926298 T^{8} - 97523550972300 T^{9} + 2051524491729606 T^{10} - 40123113241072488 T^{11} + 709271129587412629 T^{12} - 10838418128826987870 T^{13} + \)\(13\!\cdots\!93\)\( T^{14} - \)\(11\!\cdots\!18\)\( T^{15} + \)\(61\!\cdots\!61\)\( T^{16} \))
$29$ (\( 1 - 800 T^{2} + 707281 T^{4} \))(\( 1 - 1664 T^{2} + 707281 T^{4} \))(\( 1 + 42 T + 841 T^{2} \))(\( ( 1 + 30 T + 841 T^{2} )^{2} \))(\( ( 1 + 841 T^{2} )^{2} \))(\( 1 - 18 T + 162 T^{2} + 4894 T^{3} + 124463 T^{4} - 24625372 T^{5} + 435069308 T^{6} - 20709937852 T^{7} + 88030315103 T^{8} + 2911065332974 T^{9} + 81039918899682 T^{10} - 7572730199403618 T^{11} + 353814783205469041 T^{12} \))(\( 1 - 1812568 T^{4} + 855482597340 T^{8} + 905028609054258072 T^{12} - \)\(12\!\cdots\!34\)\( T^{16} + \)\(45\!\cdots\!92\)\( T^{20} + \)\(21\!\cdots\!40\)\( T^{24} - \)\(22\!\cdots\!08\)\( T^{28} + \)\(62\!\cdots\!41\)\( T^{32} \))(\( 1 + 32 T + 512 T^{2} - 18368 T^{3} - 1552984 T^{4} - 20596992 T^{5} + 304715776 T^{6} + 25469097376 T^{7} + 491466517980 T^{8} - 9791032230816 T^{9} - 347423504794624 T^{10} - 2649303176415616 T^{11} + 694517140133881240 T^{12} + 20658732330776531008 T^{13} + \)\(19\!\cdots\!28\)\( T^{14} - \)\(11\!\cdots\!40\)\( T^{15} - \)\(82\!\cdots\!10\)\( T^{16} - \)\(96\!\cdots\!40\)\( T^{17} + \)\(13\!\cdots\!68\)\( T^{18} + \)\(12\!\cdots\!68\)\( T^{19} + \)\(34\!\cdots\!40\)\( T^{20} - \)\(11\!\cdots\!16\)\( T^{21} - \)\(12\!\cdots\!84\)\( T^{22} - \)\(29\!\cdots\!96\)\( T^{23} + \)\(12\!\cdots\!80\)\( T^{24} + \)\(53\!\cdots\!36\)\( T^{25} + \)\(53\!\cdots\!76\)\( T^{26} - \)\(30\!\cdots\!72\)\( T^{27} - \)\(19\!\cdots\!04\)\( T^{28} - \)\(19\!\cdots\!28\)\( T^{29} + \)\(45\!\cdots\!32\)\( T^{30} + \)\(23\!\cdots\!32\)\( T^{31} + \)\(62\!\cdots\!41\)\( T^{32} \))(\( 1 - 69 T + 1976 T^{2} - 82905 T^{3} + 2728573 T^{4} - 24459264 T^{5} + 249830930 T^{6} + 10215187926 T^{7} - 1249058812400 T^{8} + 8590973045766 T^{9} + 176700670001330 T^{10} - 14548940641695744 T^{11} + 1364958855752234653 T^{12} - 34878733176753163905 T^{13} + \)\(69\!\cdots\!16\)\( T^{14} - \)\(20\!\cdots\!89\)\( T^{15} + \)\(25\!\cdots\!21\)\( T^{16} \))(\( ( 1 + 33 T - 839 T^{2} + 8118 T^{3} + 2094054 T^{4} + 6827238 T^{5} - 593408759 T^{6} + 19629169593 T^{7} + 500246412961 T^{8} )^{2} \))(\( 1 - 69 T + 1976 T^{2} - 82905 T^{3} + 2728573 T^{4} - 24459264 T^{5} + 249830930 T^{6} + 10215187926 T^{7} - 1249058812400 T^{8} + 8590973045766 T^{9} + 176700670001330 T^{10} - 14548940641695744 T^{11} + 1364958855752234653 T^{12} - 34878733176753163905 T^{13} + \)\(69\!\cdots\!16\)\( T^{14} - \)\(20\!\cdots\!89\)\( T^{15} + \)\(25\!\cdots\!21\)\( T^{16} \))(\( 1 - 78 T + 2869 T^{2} - 65598 T^{3} + 707281 T^{4} \))(\( 1 + 63 T + 2123 T^{2} + 50400 T^{3} + 1045362 T^{4} + 42386400 T^{5} + 1501557563 T^{6} + 37473869223 T^{7} + 500246412961 T^{8} \))(\( 1 - 18 T + 1745 T^{2} - 29466 T^{3} + 2063316 T^{4} - 24780906 T^{5} + 1234205345 T^{6} - 10706819778 T^{7} + 500246412961 T^{8} \))(\( 1 - 6 T + 1409 T^{2} - 8382 T^{3} + 1254420 T^{4} - 7049262 T^{5} + 996558929 T^{6} - 3568939926 T^{7} + 500246412961 T^{8} \))(\( 1 + 114 T + 8599 T^{2} + 486438 T^{3} + 22645933 T^{4} + 890300916 T^{5} + 31365917458 T^{6} + 1000841966952 T^{7} + 29952505780714 T^{8} + 841708094206632 T^{9} + 22184517465611698 T^{10} + 529571747544462036 T^{11} + 11328546751405137613 T^{12} + \)\(20\!\cdots\!38\)\( T^{13} + \)\(30\!\cdots\!59\)\( T^{14} + \)\(33\!\cdots\!34\)\( T^{15} + \)\(25\!\cdots\!21\)\( T^{16} \))
$31$ (\( ( 1 - 4 T + 961 T^{2} )^{2} \))(\( ( 1 + 44 T + 961 T^{2} )^{2} \))(\( ( 1 - 31 T )( 1 + 31 T ) \))(\( 1 - 1490 T^{2} + 923521 T^{4} \))(\( ( 1 - 46 T + 961 T^{2} )( 1 + 46 T + 961 T^{2} ) \))(\( 1 - 3846 T^{2} + 7131791 T^{4} - 8361808916 T^{6} + 6586358756111 T^{8} - 3280218929998086 T^{10} + 787662783788549761 T^{12} \))(\( ( 1 - 3656 T^{2} + 7444644 T^{4} - 10749322008 T^{6} + 11704860550022 T^{8} - 9927224610150168 T^{10} + 6349470144538916004 T^{12} - \)\(28\!\cdots\!16\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 7312 T^{2} + 29025544 T^{4} - 80335806576 T^{6} + 171125889681052 T^{8} - 295006946315669072 T^{10} + \)\(42\!\cdots\!64\)\( T^{12} - \)\(51\!\cdots\!00\)\( T^{14} + \)\(53\!\cdots\!38\)\( T^{16} - \)\(47\!\cdots\!00\)\( T^{18} + \)\(36\!\cdots\!24\)\( T^{20} - \)\(23\!\cdots\!92\)\( T^{22} + \)\(12\!\cdots\!12\)\( T^{24} - \)\(53\!\cdots\!76\)\( T^{26} + \)\(18\!\cdots\!24\)\( T^{28} - \)\(41\!\cdots\!92\)\( T^{30} + \)\(52\!\cdots\!61\)\( T^{32} \))(\( 1 - 45 T + 3520 T^{2} - 128025 T^{3} + 6239425 T^{4} - 221987952 T^{5} + 7979134318 T^{6} - 268603930890 T^{7} + 8040333650992 T^{8} - 258128377585290 T^{9} + 7368898104493678 T^{10} - 197015124537651312 T^{11} + 5321549661285311425 T^{12} - \)\(10\!\cdots\!25\)\( T^{13} + \)\(27\!\cdots\!20\)\( T^{14} - \)\(34\!\cdots\!45\)\( T^{15} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 - 251 T^{2} + 804865 T^{4} + 649815406 T^{6} - 360711589466 T^{8} + 600118173564526 T^{10} + 686462144849950465 T^{12} - \)\(19\!\cdots\!11\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 + 45 T + 3520 T^{2} + 128025 T^{3} + 6239425 T^{4} + 221987952 T^{5} + 7979134318 T^{6} + 268603930890 T^{7} + 8040333650992 T^{8} + 258128377585290 T^{9} + 7368898104493678 T^{10} + 197015124537651312 T^{11} + 5321549661285311425 T^{12} + \)\(10\!\cdots\!25\)\( T^{13} + \)\(27\!\cdots\!20\)\( T^{14} + \)\(34\!\cdots\!45\)\( T^{15} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 - 32 T + 63 T^{2} - 30752 T^{3} + 923521 T^{4} \))(\( 1 - 7 T - 1217 T^{2} + 4592 T^{3} + 632146 T^{4} + 4412912 T^{5} - 1123925057 T^{6} - 6212525767 T^{7} + 852891037441 T^{8} \))(\( 1 + 38 T - 353 T^{2} - 4750 T^{3} + 918004 T^{4} - 4564750 T^{5} - 326002913 T^{6} + 33725139878 T^{7} + 852891037441 T^{8} \))(\( 1 + 74 T + 2281 T^{2} + 94202 T^{3} + 4022068 T^{4} + 90528122 T^{5} + 2106551401 T^{6} + 65675272394 T^{7} + 852891037441 T^{8} \))(\( 1 - 50 T - 651 T^{2} + 68990 T^{3} - 334663 T^{4} - 5769840 T^{5} - 1286987822 T^{6} - 24925573940 T^{7} + 3245120663634 T^{8} - 23953476556340 T^{9} - 1188560280361262 T^{10} - 5120754238781040 T^{11} - 285431073263117383 T^{12} + 56546155518805460990 T^{13} - \)\(51\!\cdots\!11\)\( T^{14} - \)\(37\!\cdots\!50\)\( T^{15} + \)\(72\!\cdots\!81\)\( T^{16} \))
$37$ (\( ( 1 - 30 T + 1369 T^{2} )^{2} \))(\( ( 1 + 34 T + 1369 T^{2} )^{2} \))(\( 1 + 70 T + 1369 T^{2} \))(\( ( 1 - 26 T + 1369 T^{2} )^{2} \))(\( ( 1 - 26 T + 1369 T^{2} )^{2} \))(\( 1 - 46 T + 1058 T^{2} + 6594 T^{3} - 356337 T^{4} - 78343460 T^{5} + 4002544124 T^{6} - 107252196740 T^{7} - 667832908257 T^{8} + 16918399940946 T^{9} + 3716203262248418 T^{10} - 221194881131221054 T^{11} + 6582952005840035281 T^{12} \))(\( ( 1 - 48 T + 1152 T^{2} - 50960 T^{3} - 719780 T^{4} + 84286160 T^{5} - 1918088320 T^{6} + 86111407472 T^{7} - 3715717913082 T^{8} + 117886516829168 T^{9} - 3594806323899520 T^{10} + 216255226625199440 T^{11} - 2528212461343257380 T^{12} - \)\(24\!\cdots\!40\)\( T^{13} + \)\(75\!\cdots\!12\)\( T^{14} - \)\(43\!\cdots\!72\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 + 96 T + 4608 T^{2} + 145952 T^{3} + 4040888 T^{4} + 217733344 T^{5} + 12932982272 T^{6} + 602883756192 T^{7} + 21839639792924 T^{8} + 655265530977504 T^{9} + 21703692469355008 T^{10} + 815191556064282016 T^{11} + 35433653736114978312 T^{12} + \)\(14\!\cdots\!40\)\( T^{13} + \)\(50\!\cdots\!52\)\( T^{14} + \)\(14\!\cdots\!84\)\( T^{15} + \)\(43\!\cdots\!90\)\( T^{16} + \)\(20\!\cdots\!96\)\( T^{17} + \)\(95\!\cdots\!72\)\( T^{18} + \)\(37\!\cdots\!60\)\( T^{19} + \)\(12\!\cdots\!52\)\( T^{20} + \)\(39\!\cdots\!84\)\( T^{21} + \)\(14\!\cdots\!48\)\( T^{22} + \)\(59\!\cdots\!56\)\( T^{23} + \)\(26\!\cdots\!84\)\( T^{24} + \)\(10\!\cdots\!68\)\( T^{25} + \)\(29\!\cdots\!72\)\( T^{26} + \)\(68\!\cdots\!36\)\( T^{27} + \)\(17\!\cdots\!68\)\( T^{28} + \)\(86\!\cdots\!68\)\( T^{29} + \)\(37\!\cdots\!68\)\( T^{30} + \)\(10\!\cdots\!04\)\( T^{31} + \)\(15\!\cdots\!81\)\( T^{32} \))(\( ( 1 + 10 T + 1720 T^{2} - 76250 T^{3} + 347470 T^{4} - 104386250 T^{5} + 3223556920 T^{6} + 25657264090 T^{7} + 3512479453921 T^{8} )^{2} \))(\( ( 1 - 10 T + 1818 T^{2} - 13690 T^{3} + 1874161 T^{4} )^{4} \))(\( ( 1 + 10 T + 1720 T^{2} - 76250 T^{3} + 347470 T^{4} - 104386250 T^{5} + 3223556920 T^{6} + 25657264090 T^{7} + 3512479453921 T^{8} )^{2} \))(\( ( 1 + 34 T + 1369 T^{2} )^{2} \))(\( ( 1 + 32 T + 1806 T^{2} + 43808 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 - 64 T + 3546 T^{2} - 87616 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 + 60 T + 3254 T^{2} + 82140 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 - 60 T + 5200 T^{2} - 219060 T^{3} + 10695774 T^{4} - 299893140 T^{5} + 9745637200 T^{6} - 153943584540 T^{7} + 3512479453921 T^{8} )^{2} \))
$41$ (\( 1 - 2912 T^{2} + 2825761 T^{4} \))(\( 1 - 1184 T^{2} + 2825761 T^{4} \))(\( 1 + 18 T + 1681 T^{2} \))(\( ( 1 - 54 T + 1681 T^{2} )^{2} \))(\( ( 1 + 1681 T^{2} )^{2} \))(\( 1 - 5094 T^{2} + 15050223 T^{4} - 31243096276 T^{6} + 42528333194703 T^{8} - 40675209117142374 T^{10} + 22563490300366186081 T^{12} \))(\( ( 1 - 6200 T^{2} + 18860092 T^{4} - 40121913352 T^{6} + 71431934605958 T^{8} - 113374937995460872 T^{10} + \)\(15\!\cdots\!32\)\( T^{12} - \)\(13\!\cdots\!00\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 - 13840 T^{2} + 102706104 T^{4} - 524939980080 T^{6} + 2044068651261084 T^{8} - 6376104819902485008 T^{10} + \)\(16\!\cdots\!68\)\( T^{12} - \)\(35\!\cdots\!72\)\( T^{14} + \)\(64\!\cdots\!06\)\( T^{16} - \)\(99\!\cdots\!92\)\( T^{18} + \)\(13\!\cdots\!28\)\( T^{20} - \)\(14\!\cdots\!48\)\( T^{22} + \)\(13\!\cdots\!44\)\( T^{24} - \)\(94\!\cdots\!80\)\( T^{26} + \)\(52\!\cdots\!44\)\( T^{28} - \)\(19\!\cdots\!40\)\( T^{30} + \)\(40\!\cdots\!81\)\( T^{32} \))(\( 1 - 54 T - 1108 T^{2} - 54648 T^{3} + 6254527 T^{4} + 135074304 T^{5} - 346116544 T^{6} - 221393044530 T^{7} - 6391866656792 T^{8} - 372161707854930 T^{9} - 978042631489984 T^{10} + 641617024280523264 T^{11} + 49941930438518480767 T^{12} - \)\(73\!\cdots\!48\)\( T^{13} - \)\(25\!\cdots\!48\)\( T^{14} - \)\(20\!\cdots\!94\)\( T^{15} + \)\(63\!\cdots\!41\)\( T^{16} \))(\( ( 1 + 72 T + 1471 T^{2} + 25272 T^{3} + 2246304 T^{4} + 42482232 T^{5} + 4156694431 T^{6} + 342007505352 T^{7} + 7984925229121 T^{8} )^{2} \))(\( 1 - 54 T - 1108 T^{2} - 54648 T^{3} + 6254527 T^{4} + 135074304 T^{5} - 346116544 T^{6} - 221393044530 T^{7} - 6391866656792 T^{8} - 372161707854930 T^{9} - 978042631489984 T^{10} + 641617024280523264 T^{11} + 49941930438518480767 T^{12} - \)\(73\!\cdots\!48\)\( T^{13} - \)\(25\!\cdots\!48\)\( T^{14} - \)\(20\!\cdots\!94\)\( T^{15} + \)\(63\!\cdots\!41\)\( T^{16} \))(\( 1 + 21 T + 1828 T^{2} + 35301 T^{3} + 2825761 T^{4} \))(\( 1 + 18 T + 1913 T^{2} + 32490 T^{3} + 613812 T^{4} + 54615690 T^{5} + 5405680793 T^{6} + 85501876338 T^{7} + 7984925229121 T^{8} \))(\( 1 + 126 T + 9329 T^{2} + 508662 T^{3} + 22367460 T^{4} + 855060822 T^{5} + 26361524369 T^{6} + 598513134366 T^{7} + 7984925229121 T^{8} \))(\( ( 1 + 69 T + 3268 T^{2} + 115989 T^{3} + 2825761 T^{4} )^{2} \))(\( 1 - 264 T + 38158 T^{2} - 3940464 T^{3} + 321724129 T^{4} - 21802117680 T^{5} + 1260648967822 T^{6} - 63190156979928 T^{7} + 2768191141578052 T^{8} - 106222653883258968 T^{9} + 3562292687961662542 T^{10} - \)\(10\!\cdots\!80\)\( T^{11} + \)\(25\!\cdots\!09\)\( T^{12} - \)\(52\!\cdots\!64\)\( T^{13} + \)\(86\!\cdots\!98\)\( T^{14} - \)\(10\!\cdots\!04\)\( T^{15} + \)\(63\!\cdots\!41\)\( T^{16} \))
$43$ (\( ( 1 - 8 T + 1849 T^{2} )^{2} \))(\( ( 1 - 40 T + 1849 T^{2} )^{2} \))(\( ( 1 - 43 T )( 1 + 43 T ) \))(\( 1 - 3266 T^{2} + 3418801 T^{4} \))(\( ( 1 - 22 T + 1849 T^{2} )( 1 + 22 T + 1849 T^{2} ) \))(\( 1 + 114 T + 6498 T^{2} + 241730 T^{3} + 12357983 T^{4} + 838941724 T^{5} + 44553879452 T^{6} + 1551203247676 T^{7} + 42249484638383 T^{8} + 1528063089834770 T^{9} + 75949925403851298 T^{10} + 2463708983714404386 T^{11} + 39959630797262576401 T^{12} \))(\( ( 1 + 16 T + 128 T^{2} + 120528 T^{3} - 217180 T^{4} - 199455632 T^{5} + 4100008320 T^{6} - 63109389264 T^{7} - 21163084456442 T^{8} - 116689260749136 T^{9} + 14017112544424320 T^{10} - 1260831462039741968 T^{11} - 2538443336289385180 T^{12} + \)\(26\!\cdots\!72\)\( T^{13} + \)\(51\!\cdots\!28\)\( T^{14} + \)\(11\!\cdots\!84\)\( T^{15} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 160 T + 12800 T^{2} - 978464 T^{3} + 71106632 T^{4} - 3813053664 T^{5} + 178619596288 T^{6} - 8719368905312 T^{7} + 336417491247900 T^{8} - 9339737479444512 T^{9} + 288453906337733120 T^{10} - 7137460469658328480 T^{11} - \)\(12\!\cdots\!76\)\( T^{12} + \)\(13\!\cdots\!84\)\( T^{13} - \)\(44\!\cdots\!20\)\( T^{14} + \)\(28\!\cdots\!76\)\( T^{15} - \)\(17\!\cdots\!30\)\( T^{16} + \)\(53\!\cdots\!24\)\( T^{17} - \)\(15\!\cdots\!20\)\( T^{18} + \)\(83\!\cdots\!16\)\( T^{19} - \)\(15\!\cdots\!76\)\( T^{20} - \)\(15\!\cdots\!20\)\( T^{21} + \)\(11\!\cdots\!20\)\( T^{22} - \)\(69\!\cdots\!88\)\( T^{23} + \)\(45\!\cdots\!00\)\( T^{24} - \)\(22\!\cdots\!88\)\( T^{25} + \)\(83\!\cdots\!88\)\( T^{26} - \)\(32\!\cdots\!36\)\( T^{27} + \)\(11\!\cdots\!32\)\( T^{28} - \)\(28\!\cdots\!36\)\( T^{29} + \)\(69\!\cdots\!00\)\( T^{30} - \)\(16\!\cdots\!40\)\( T^{31} + \)\(18\!\cdots\!01\)\( T^{32} \))(\( 1 + 4210 T^{2} + 9163465 T^{4} + 282271716 T^{5} + 12018514642 T^{6} + 1023475278060 T^{7} + 9810745543012 T^{8} + 1892405789132940 T^{9} + 41088909876584242 T^{10} + 1784341995300222084 T^{11} + \)\(10\!\cdots\!65\)\( T^{12} + \)\(16\!\cdots\!10\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} \))(\( 1 + 3166 T^{2} + 4082065 T^{4} - 2837087426 T^{6} - 10655428250876 T^{8} - 9699437329096226 T^{10} + 47711993266185326065 T^{12} + \)\(12\!\cdots\!66\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} \))(\( 1 + 4210 T^{2} + 9163465 T^{4} - 282271716 T^{5} + 12018514642 T^{6} - 1023475278060 T^{7} + 9810745543012 T^{8} - 1892405789132940 T^{9} + 41088909876584242 T^{10} - 1784341995300222084 T^{11} + \)\(10\!\cdots\!65\)\( T^{12} + \)\(16\!\cdots\!10\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 22 T + 1849 T^{2} )( 1 + 83 T + 1849 T^{2} ) \))(\( ( 1 - 23 T - 1320 T^{2} - 42527 T^{3} + 3418801 T^{4} )^{2} \))(\( 1 - 46 T - 1625 T^{2} - 1978 T^{3} + 6663796 T^{4} - 3657322 T^{5} - 5555551625 T^{6} - 290782700254 T^{7} + 11688200277601 T^{8} \))(\( 1 + 10 T - 2087 T^{2} - 15110 T^{3} + 1179268 T^{4} - 27938390 T^{5} - 7135037687 T^{6} + 63213630490 T^{7} + 11688200277601 T^{8} \))(\( 1 - 28 T - 2364 T^{2} - 141848 T^{3} + 7021127 T^{4} + 338054892 T^{5} + 12175270060 T^{6} - 693178978408 T^{7} - 23735268373680 T^{8} - 1281687931076392 T^{9} + 41624825456398060 T^{10} + 2136967702822485708 T^{11} + 82064338550471876327 T^{12} - \)\(30\!\cdots\!52\)\( T^{13} - \)\(94\!\cdots\!64\)\( T^{14} - \)\(20\!\cdots\!72\)\( T^{15} + \)\(13\!\cdots\!01\)\( T^{16} \))
$47$ (\( 1 - 4130 T^{2} + 4879681 T^{4} \))(\( 1 + 2782 T^{2} + 4879681 T^{4} \))(\( ( 1 - 47 T )( 1 + 47 T ) \))(\( 1 - 2690 T^{2} + 4879681 T^{4} \))(\( ( 1 - 47 T )^{2}( 1 + 47 T )^{2} \))(\( 1 - 4678 T^{2} + 12462287 T^{4} - 24905944212 T^{6} + 60811985090447 T^{8} - 111389199003717958 T^{10} + \)\(11\!\cdots\!41\)\( T^{12} \))(\( ( 1 - 6312 T^{2} + 26526428 T^{4} - 83137920920 T^{6} + 212859158930374 T^{8} - 405686533092826520 T^{10} + \)\(63\!\cdots\!08\)\( T^{12} - \)\(73\!\cdots\!92\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 24144 T^{2} + 280869112 T^{4} - 2097883923184 T^{6} + 11327375509374492 T^{8} - 47271044690493269328 T^{10} + \)\(15\!\cdots\!16\)\( T^{12} - \)\(44\!\cdots\!04\)\( T^{14} + \)\(10\!\cdots\!58\)\( T^{16} - \)\(21\!\cdots\!24\)\( T^{18} + \)\(37\!\cdots\!76\)\( T^{20} - \)\(54\!\cdots\!48\)\( T^{22} + \)\(64\!\cdots\!32\)\( T^{24} - \)\(58\!\cdots\!84\)\( T^{26} + \)\(37\!\cdots\!72\)\( T^{28} - \)\(15\!\cdots\!84\)\( T^{30} + \)\(32\!\cdots\!41\)\( T^{32} \))(\( 1 - 207 T + 24406 T^{2} - 2095461 T^{3} + 142092151 T^{4} - 7940274480 T^{5} + 383592144688 T^{6} - 17253891231516 T^{7} + 786328390118740 T^{8} - 38113845730418844 T^{9} + 1871807300183284528 T^{10} - 85589928391283503920 T^{11} + \)\(33\!\cdots\!11\)\( T^{12} - \)\(11\!\cdots\!89\)\( T^{13} + \)\(28\!\cdots\!46\)\( T^{14} - \)\(53\!\cdots\!83\)\( T^{15} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 + 2977 T^{2} + 5326621 T^{4} - 18527222558 T^{6} - 54554955650546 T^{8} - 90406935899043998 T^{10} + \)\(12\!\cdots\!81\)\( T^{12} + \)\(34\!\cdots\!57\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 + 207 T + 24406 T^{2} + 2095461 T^{3} + 142092151 T^{4} + 7940274480 T^{5} + 383592144688 T^{6} + 17253891231516 T^{7} + 786328390118740 T^{8} + 38113845730418844 T^{9} + 1871807300183284528 T^{10} + 85589928391283503920 T^{11} + \)\(33\!\cdots\!11\)\( T^{12} + \)\(11\!\cdots\!89\)\( T^{13} + \)\(28\!\cdots\!46\)\( T^{14} + \)\(53\!\cdots\!83\)\( T^{15} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 - 84 T + 4561 T^{2} - 185556 T^{3} + 4879681 T^{4} \))(\( 1 - 81 T + 6929 T^{2} - 384102 T^{3} + 22437966 T^{4} - 848481318 T^{5} + 33811309649 T^{6} - 873116441649 T^{7} + 23811286661761 T^{8} \))(\( 1 + 54 T + 4751 T^{2} + 204066 T^{3} + 11548308 T^{4} + 450781794 T^{5} + 23183364431 T^{6} + 582077627766 T^{7} + 23811286661761 T^{8} \))(\( 1 + 174 T + 16745 T^{2} + 1157622 T^{3} + 61675956 T^{4} + 2557186998 T^{5} + 81710258345 T^{6} + 1875583467246 T^{7} + 23811286661761 T^{8} \))(\( 1 + 150 T + 16249 T^{2} + 1312350 T^{3} + 88432117 T^{4} + 5053131000 T^{5} + 262267521478 T^{6} + 12644089287900 T^{7} + 595883042253514 T^{8} + 27930793236971100 T^{9} + 1279781841473288518 T^{10} + 54468787134645099000 T^{11} + \)\(21\!\cdots\!37\)\( T^{12} + \)\(69\!\cdots\!50\)\( T^{13} + \)\(18\!\cdots\!09\)\( T^{14} + \)\(38\!\cdots\!50\)\( T^{15} + \)\(56\!\cdots\!21\)\( T^{16} \))
$53$ (\( 1 - 3168 T^{2} + 7890481 T^{4} \))(\( 1 - 4160 T^{2} + 7890481 T^{4} \))(\( 1 + 90 T + 2809 T^{2} \))(\( ( 1 - 18 T + 2809 T^{2} )^{2} \))(\( ( 1 + 2809 T^{2} )^{2} \))(\( 1 + 78 T + 3042 T^{2} + 270110 T^{3} + 31648463 T^{4} + 1389102820 T^{5} + 48555101564 T^{6} + 3901989821380 T^{7} + 249721595980703 T^{8} + 5986815584554190 T^{9} + 189393978231360162 T^{10} + 13641222688510017822 T^{11} + \)\(49\!\cdots\!41\)\( T^{12} \))(\( 1 - 41116504 T^{4} + 844846897443036 T^{8} - \)\(11\!\cdots\!20\)\( T^{12} + \)\(10\!\cdots\!98\)\( T^{16} - \)\(69\!\cdots\!20\)\( T^{20} + \)\(32\!\cdots\!56\)\( T^{24} - \)\(99\!\cdots\!24\)\( T^{28} + \)\(15\!\cdots\!41\)\( T^{32} \))(\( 1 - 160 T + 12800 T^{2} - 602944 T^{3} + 3948712 T^{4} + 1481707264 T^{5} - 105845942272 T^{6} + 3791430241760 T^{7} + 34861972067036 T^{8} - 14471440004155872 T^{9} + 1098860393015073792 T^{10} - 54880211634179791488 T^{11} + \)\(13\!\cdots\!12\)\( T^{12} + \)\(17\!\cdots\!00\)\( T^{13} - \)\(18\!\cdots\!48\)\( T^{14} - \)\(16\!\cdots\!08\)\( T^{15} + \)\(51\!\cdots\!54\)\( T^{16} - \)\(46\!\cdots\!72\)\( T^{17} - \)\(14\!\cdots\!88\)\( T^{18} + \)\(38\!\cdots\!00\)\( T^{19} + \)\(84\!\cdots\!32\)\( T^{20} - \)\(95\!\cdots\!12\)\( T^{21} + \)\(53\!\cdots\!72\)\( T^{22} - \)\(19\!\cdots\!68\)\( T^{23} + \)\(13\!\cdots\!56\)\( T^{24} + \)\(41\!\cdots\!40\)\( T^{25} - \)\(32\!\cdots\!72\)\( T^{26} + \)\(12\!\cdots\!76\)\( T^{27} + \)\(95\!\cdots\!72\)\( T^{28} - \)\(40\!\cdots\!76\)\( T^{29} + \)\(24\!\cdots\!00\)\( T^{30} - \)\(85\!\cdots\!40\)\( T^{31} + \)\(15\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 126 T + 12208 T^{2} + 787698 T^{3} + 46295070 T^{4} + 2212643682 T^{5} + 96326992048 T^{6} + 2792709502254 T^{7} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 90 T + 6698 T^{2} - 252810 T^{3} + 7890481 T^{4} )^{4} \))(\( ( 1 + 126 T + 12208 T^{2} + 787698 T^{3} + 46295070 T^{4} + 2212643682 T^{5} + 96326992048 T^{6} + 2792709502254 T^{7} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 53 T )^{2}( 1 + 53 T )^{2} \))(\( 1 - 7204 T^{2} + 26018214 T^{4} - 56843025124 T^{6} + 62259690411361 T^{8} \))(\( 1 - 2236 T^{2} - 2409114 T^{4} - 17643115516 T^{6} + 62259690411361 T^{8} \))(\( 1 - 996 T^{2} - 9136858 T^{4} - 7858919076 T^{6} + 62259690411361 T^{8} \))(\( 1 - 15456 T^{2} + 115082620 T^{4} - 547509829536 T^{6} + 1820499555493830 T^{8} - 4320115907267046816 T^{10} + \)\(71\!\cdots\!20\)\( T^{12} - \)\(75\!\cdots\!96\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} \))
$59$ (\( 1 - 690 T^{2} + 12117361 T^{4} \))(\( 1 - 5810 T^{2} + 12117361 T^{4} \))(\( ( 1 - 59 T )( 1 + 59 T ) \))(\( 1 - 6530 T^{2} + 12117361 T^{4} \))(\( ( 1 - 59 T )^{2}( 1 + 59 T )^{2} \))(\( 1 + 206 T + 21218 T^{2} + 1942462 T^{3} + 171214239 T^{4} + 11916831972 T^{5} + 708622973852 T^{6} + 41482492094532 T^{7} + 2074664742303279 T^{8} + 81934083737364142 T^{9} + 3115448225088482978 T^{10} + \)\(10\!\cdots\!06\)\( T^{11} + \)\(17\!\cdots\!81\)\( T^{12} \))(\( 1 - 11621240 T^{4} - 131007530650980 T^{8} + \)\(57\!\cdots\!44\)\( T^{12} + \)\(25\!\cdots\!66\)\( T^{16} + \)\(84\!\cdots\!24\)\( T^{20} - \)\(28\!\cdots\!80\)\( T^{24} - \)\(36\!\cdots\!40\)\( T^{28} + \)\(46\!\cdots\!81\)\( T^{32} \))(\( 1 - 128 T + 8192 T^{2} - 1121408 T^{3} + 136226184 T^{4} - 9279937408 T^{5} + 700645040128 T^{6} - 71627082366848 T^{7} + 5234572115355804 T^{8} - 316007889653226112 T^{9} + 25502997282495045632 T^{10} - \)\(19\!\cdots\!80\)\( T^{11} + \)\(10\!\cdots\!40\)\( T^{12} - \)\(69\!\cdots\!16\)\( T^{13} + \)\(51\!\cdots\!56\)\( T^{14} - \)\(29\!\cdots\!24\)\( T^{15} + \)\(15\!\cdots\!38\)\( T^{16} - \)\(10\!\cdots\!44\)\( T^{17} + \)\(62\!\cdots\!16\)\( T^{18} - \)\(29\!\cdots\!56\)\( T^{19} + \)\(16\!\cdots\!40\)\( T^{20} - \)\(98\!\cdots\!80\)\( T^{21} + \)\(45\!\cdots\!92\)\( T^{22} - \)\(19\!\cdots\!32\)\( T^{23} + \)\(11\!\cdots\!64\)\( T^{24} - \)\(53\!\cdots\!08\)\( T^{25} + \)\(18\!\cdots\!28\)\( T^{26} - \)\(84\!\cdots\!48\)\( T^{27} + \)\(43\!\cdots\!24\)\( T^{28} - \)\(12\!\cdots\!28\)\( T^{29} + \)\(31\!\cdots\!32\)\( T^{30} - \)\(17\!\cdots\!28\)\( T^{31} + \)\(46\!\cdots\!81\)\( T^{32} \))(\( 1 + 306 T + 52768 T^{2} + 6596136 T^{3} + 655249567 T^{4} + 54840345300 T^{5} + 4031461665844 T^{6} + 267864455425266 T^{7} + 16404403358884120 T^{8} + 932436169335350946 T^{9} + 48850676362693117684 T^{10} + \)\(23\!\cdots\!00\)\( T^{11} + \)\(96\!\cdots\!07\)\( T^{12} + \)\(33\!\cdots\!36\)\( T^{13} + \)\(93\!\cdots\!08\)\( T^{14} + \)\(18\!\cdots\!66\)\( T^{15} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( ( 1 + 3587 T^{2} + 749208 T^{4} + 43464973907 T^{6} + 146830437604321 T^{8} )^{2} \))(\( 1 - 306 T + 52768 T^{2} - 6596136 T^{3} + 655249567 T^{4} - 54840345300 T^{5} + 4031461665844 T^{6} - 267864455425266 T^{7} + 16404403358884120 T^{8} - 932436169335350946 T^{9} + 48850676362693117684 T^{10} - \)\(23\!\cdots\!00\)\( T^{11} + \)\(96\!\cdots\!07\)\( T^{12} - \)\(33\!\cdots\!36\)\( T^{13} + \)\(93\!\cdots\!08\)\( T^{14} - \)\(18\!\cdots\!66\)\( T^{15} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 + 87 T + 6004 T^{2} + 302847 T^{3} + 12117361 T^{4} \))(\( 1 + 126 T + 11993 T^{2} + 844326 T^{3} + 51207492 T^{4} + 2939098806 T^{5} + 145323510473 T^{6} + 5314747238766 T^{7} + 146830437604321 T^{8} \))(\( 1 + 126 T + 10535 T^{2} + 660618 T^{3} + 33793140 T^{4} + 2299611258 T^{5} + 127656398135 T^{6} + 5314747238766 T^{7} + 146830437604321 T^{8} \))(\( 1 - 18 T + 6969 T^{2} - 123498 T^{3} + 35331908 T^{4} - 429896538 T^{5} + 84445888809 T^{6} - 759249605538 T^{7} + 146830437604321 T^{8} \))(\( 1 - 108 T + 14820 T^{2} - 1180656 T^{3} + 104177575 T^{4} - 7489417356 T^{5} + 509063599692 T^{6} - 32920352322696 T^{7} + 1903340903262096 T^{8} - 114595746435304776 T^{9} + 6168507409427452812 T^{10} - \)\(31\!\cdots\!96\)\( T^{11} + \)\(15\!\cdots\!75\)\( T^{12} - \)\(60\!\cdots\!56\)\( T^{13} + \)\(26\!\cdots\!20\)\( T^{14} - \)\(66\!\cdots\!88\)\( T^{15} + \)\(21\!\cdots\!41\)\( T^{16} \))
$61$ (\( ( 1 + 14 T + 3721 T^{2} )^{2} \))(\( ( 1 - 50 T + 3721 T^{2} )^{2} \))(\( 1 + 22 T + 3721 T^{2} \))(\( ( 1 + 70 T + 3721 T^{2} )^{2} \))(\( ( 1 - 74 T + 3721 T^{2} )^{2} \))(\( 1 - 30 T + 450 T^{2} - 111694 T^{3} + 33268655 T^{4} - 582006980 T^{5} + 8727089468 T^{6} - 2165647972580 T^{7} + 460632507413855 T^{8} - 5754516693877534 T^{9} + 86268290848776450 T^{10} - 21400287349886478030 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} \))(\( ( 1 + 16 T + 128 T^{2} + 6576 T^{3} - 8849956 T^{4} - 175483376 T^{5} - 1653317760 T^{6} - 420993646800 T^{7} - 32622960575354 T^{8} - 1566517359742800 T^{9} - 22891574827436160 T^{10} - 9040969225652122736 T^{11} - \)\(16\!\cdots\!36\)\( T^{12} + \)\(46\!\cdots\!76\)\( T^{13} + \)\(33\!\cdots\!88\)\( T^{14} + \)\(15\!\cdots\!56\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 + 32 T + 512 T^{2} - 38048 T^{3} - 60439624 T^{4} - 1520787552 T^{5} - 16996289024 T^{6} + 2981900088544 T^{7} + 2018049968078364 T^{8} + 40394929489472928 T^{9} + 275088896591278592 T^{10} - \)\(10\!\cdots\!56\)\( T^{11} - \)\(45\!\cdots\!20\)\( T^{12} - \)\(71\!\cdots\!16\)\( T^{13} - \)\(18\!\cdots\!28\)\( T^{14} + \)\(23\!\cdots\!64\)\( T^{15} + \)\(72\!\cdots\!42\)\( T^{16} + \)\(88\!\cdots\!44\)\( T^{17} - \)\(26\!\cdots\!48\)\( T^{18} - \)\(36\!\cdots\!76\)\( T^{19} - \)\(86\!\cdots\!20\)\( T^{20} - \)\(75\!\cdots\!56\)\( T^{21} + \)\(73\!\cdots\!32\)\( T^{22} + \)\(39\!\cdots\!48\)\( T^{23} + \)\(74\!\cdots\!04\)\( T^{24} + \)\(40\!\cdots\!64\)\( T^{25} - \)\(86\!\cdots\!24\)\( T^{26} - \)\(28\!\cdots\!92\)\( T^{27} - \)\(42\!\cdots\!84\)\( T^{28} - \)\(99\!\cdots\!28\)\( T^{29} + \)\(49\!\cdots\!72\)\( T^{30} + \)\(11\!\cdots\!32\)\( T^{31} + \)\(13\!\cdots\!21\)\( T^{32} \))(\( 1 - 7 T - 8478 T^{2} - 347909 T^{3} + 38508983 T^{4} + 2257992504 T^{5} - 39583245248 T^{6} - 5257966541956 T^{7} - 30952228546836 T^{8} - 19564893502618276 T^{9} - 548063319967813568 T^{10} + \)\(11\!\cdots\!44\)\( T^{11} + \)\(73\!\cdots\!23\)\( T^{12} - \)\(24\!\cdots\!09\)\( T^{13} - \)\(22\!\cdots\!38\)\( T^{14} - \)\(69\!\cdots\!87\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} \))(\( ( 1 + 7 T - 7169 T^{2} - 1568 T^{3} + 38071354 T^{4} - 5834528 T^{5} - 99260834129 T^{6} + 360642620527 T^{7} + 191707312997281 T^{8} )^{2} \))(\( 1 - 7 T - 8478 T^{2} - 347909 T^{3} + 38508983 T^{4} + 2257992504 T^{5} - 39583245248 T^{6} - 5257966541956 T^{7} - 30952228546836 T^{8} - 19564893502618276 T^{9} - 548063319967813568 T^{10} + \)\(11\!\cdots\!44\)\( T^{11} + \)\(73\!\cdots\!23\)\( T^{12} - \)\(24\!\cdots\!09\)\( T^{13} - \)\(22\!\cdots\!38\)\( T^{14} - \)\(69\!\cdots\!87\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} \))(\( 1 + 56 T - 585 T^{2} + 208376 T^{3} + 13845841 T^{4} \))(\( 1 - 41 T - 5513 T^{2} + 10168 T^{3} + 31652794 T^{4} + 37835128 T^{5} - 76332121433 T^{6} - 2112335348801 T^{7} + 191707312997281 T^{8} \))(\( 1 - 62 T - 2615 T^{2} + 60946 T^{3} + 13569316 T^{4} + 226780066 T^{5} - 36206874215 T^{6} - 3194263210382 T^{7} + 191707312997281 T^{8} \))(\( 1 + 62 T - 4463 T^{2} + 53630 T^{3} + 40856884 T^{4} + 199557230 T^{5} - 61793988383 T^{6} + 3194263210382 T^{7} + 191707312997281 T^{8} \))(\( 1 - 14 T - 6633 T^{2} + 472862 T^{3} + 19891733 T^{4} - 2361270204 T^{5} + 99631636810 T^{6} + 5929775489824 T^{7} - 599620944879702 T^{8} + 22064694597635104 T^{9} + 1379483801841007210 T^{10} - \)\(12\!\cdots\!44\)\( T^{11} + \)\(38\!\cdots\!73\)\( T^{12} + \)\(33\!\cdots\!62\)\( T^{13} - \)\(17\!\cdots\!93\)\( T^{14} - \)\(13\!\cdots\!74\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} \))
$67$ (\( ( 1 - 88 T + 4489 T^{2} )^{2} \))(\( ( 1 + 8 T + 4489 T^{2} )^{2} \))(\( ( 1 - 67 T )( 1 + 67 T ) \))(\( 1 + 4894 T^{2} + 20151121 T^{4} \))(\( ( 1 - 122 T + 4489 T^{2} )( 1 + 122 T + 4489 T^{2} ) \))(\( 1 + 226 T + 25538 T^{2} + 2083538 T^{3} + 120508479 T^{4} + 5203289532 T^{5} + 268963196252 T^{6} + 23357566709148 T^{7} + 2428380941854959 T^{8} + 188473476667633922 T^{9} + 10370156349441497858 T^{10} + \)\(41\!\cdots\!74\)\( T^{11} + \)\(81\!\cdots\!61\)\( T^{12} \))(\( ( 1 + 128 T + 8192 T^{2} + 693376 T^{3} + 50920004 T^{4} + 2251590016 T^{5} + 111451987968 T^{6} + 7277319415168 T^{7} + 468898776356806 T^{8} + 32667886854689152 T^{9} + 2245882495233712128 T^{10} + \)\(20\!\cdots\!04\)\( T^{11} + \)\(20\!\cdots\!64\)\( T^{12} + \)\(12\!\cdots\!24\)\( T^{13} + \)\(67\!\cdots\!12\)\( T^{14} + \)\(47\!\cdots\!12\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 320 T + 51200 T^{2} - 6047552 T^{3} + 641735304 T^{4} - 64228593856 T^{5} + 5982745065472 T^{6} - 525110406070976 T^{7} + 43992629224199580 T^{8} - 3502096836597496384 T^{9} + \)\(26\!\cdots\!12\)\( T^{10} - \)\(19\!\cdots\!80\)\( T^{11} + \)\(14\!\cdots\!20\)\( T^{12} - \)\(10\!\cdots\!88\)\( T^{13} + \)\(71\!\cdots\!04\)\( T^{14} - \)\(48\!\cdots\!52\)\( T^{15} + \)\(32\!\cdots\!74\)\( T^{16} - \)\(21\!\cdots\!28\)\( T^{17} + \)\(14\!\cdots\!84\)\( T^{18} - \)\(93\!\cdots\!72\)\( T^{19} + \)\(58\!\cdots\!20\)\( T^{20} - \)\(36\!\cdots\!20\)\( T^{21} + \)\(21\!\cdots\!32\)\( T^{22} - \)\(12\!\cdots\!36\)\( T^{23} + \)\(72\!\cdots\!80\)\( T^{24} - \)\(38\!\cdots\!84\)\( T^{25} + \)\(19\!\cdots\!72\)\( T^{26} - \)\(95\!\cdots\!84\)\( T^{27} + \)\(42\!\cdots\!84\)\( T^{28} - \)\(18\!\cdots\!88\)\( T^{29} + \)\(69\!\cdots\!00\)\( T^{30} - \)\(19\!\cdots\!80\)\( T^{31} + \)\(27\!\cdots\!61\)\( T^{32} \))(\( 1 - 12 T + 11866 T^{2} - 141816 T^{3} + 66010801 T^{4} - 721613340 T^{5} + 400272803818 T^{6} - 3347530167216 T^{7} + 2268475959596500 T^{8} - 15027062920632624 T^{9} + 8065945702745779978 T^{10} - 65275975287968534460 T^{11} + \)\(26\!\cdots\!41\)\( T^{12} - \)\(25\!\cdots\!84\)\( T^{13} + \)\(97\!\cdots\!26\)\( T^{14} - \)\(44\!\cdots\!48\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( ( 1 + 8411 T^{2} + 50593800 T^{4} + 169491078731 T^{6} + 406067677556641 T^{8} )^{2} \))(\( 1 + 12 T + 11866 T^{2} + 141816 T^{3} + 66010801 T^{4} + 721613340 T^{5} + 400272803818 T^{6} + 3347530167216 T^{7} + 2268475959596500 T^{8} + 15027062920632624 T^{9} + 8065945702745779978 T^{10} + 65275975287968534460 T^{11} + \)\(26\!\cdots\!41\)\( T^{12} + \)\(25\!\cdots\!84\)\( T^{13} + \)\(97\!\cdots\!26\)\( T^{14} + \)\(44\!\cdots\!48\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( 1 + 31 T - 3528 T^{2} + 139159 T^{3} + 20151121 T^{4} \))(\( 1 + 116 T + 3787 T^{2} + 80156 T^{3} + 12934456 T^{4} + 359820284 T^{5} + 76312295227 T^{6} + 10493172331604 T^{7} + 406067677556641 T^{8} \))(\( 1 - 106 T - 65 T^{2} - 246238 T^{3} + 57123076 T^{4} - 1105362382 T^{5} - 1309822865 T^{6} - 9588588509914 T^{7} + 406067677556641 T^{8} \))(\( 1 - 22 T + 985 T^{2} + 208538 T^{3} - 22072796 T^{4} + 936127082 T^{5} + 19848854185 T^{6} - 1990084407718 T^{7} + 406067677556641 T^{8} \))(\( 1 - 20 T - 15756 T^{2} + 141560 T^{3} + 151491335 T^{4} - 601531260 T^{5} - 1010166803204 T^{6} + 1012785207880 T^{7} + 5163639663893904 T^{8} + 4546392798173320 T^{9} - 20355993481546991684 T^{10} - 54413544603680102940 T^{11} + \)\(61\!\cdots\!35\)\( T^{12} + \)\(25\!\cdots\!40\)\( T^{13} - \)\(12\!\cdots\!16\)\( T^{14} - \)\(73\!\cdots\!80\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} \))
$71$ (\( 1 - 9282 T^{2} + 25411681 T^{4} \))(\( 1 - 7490 T^{2} + 25411681 T^{4} \))(\( ( 1 - 71 T )( 1 + 71 T ) \))(\( 1 - 3170 T^{2} + 25411681 T^{4} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 130 T + 11575 T^{2} - 918796 T^{3} + 58349575 T^{4} - 3303518530 T^{5} + 128100283921 T^{6} )^{2} \))(\( ( 1 + 776 T^{2} + 40385436 T^{4} - 127559387592 T^{6} + 690614216465094 T^{8} - 3241498466043262152 T^{10} + \)\(26\!\cdots\!96\)\( T^{12} + \)\(12\!\cdots\!16\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 256 T + 68104 T^{2} + 10692864 T^{3} + 1610923548 T^{4} + 179723087616 T^{5} + 18972832358712 T^{6} + 1588998739085056 T^{7} + 125568612540426694 T^{8} + 8010142643727767296 T^{9} + \)\(48\!\cdots\!72\)\( T^{10} + \)\(23\!\cdots\!36\)\( T^{11} + \)\(10\!\cdots\!28\)\( T^{12} + \)\(34\!\cdots\!64\)\( T^{13} + \)\(11\!\cdots\!64\)\( T^{14} + \)\(21\!\cdots\!36\)\( T^{15} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 14120 T^{2} + 150082588 T^{4} - 1080637518872 T^{6} + 6319440918414790 T^{8} - 27460815906206743832 T^{10} + \)\(96\!\cdots\!68\)\( T^{12} - \)\(23\!\cdots\!20\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 7922 T^{2} + 25411681 T^{4} )^{4} \))(\( 1 - 14120 T^{2} + 150082588 T^{4} - 1080637518872 T^{6} + 6319440918414790 T^{8} - 27460815906206743832 T^{10} + \)\(96\!\cdots\!68\)\( T^{12} - \)\(23\!\cdots\!20\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))(\( 1 - 9110 T^{2} + 25411681 T^{4} \))(\( 1 - 18616 T^{2} + 137194926 T^{4} - 473063853496 T^{6} + 645753531245761 T^{8} \))(\( 1 - 12460 T^{2} + 77194662 T^{4} - 316629545260 T^{6} + 645753531245761 T^{8} \))(\( 1 - 16452 T^{2} + 117605702 T^{4} - 418072975812 T^{6} + 645753531245761 T^{8} \))(\( 1 - 13464 T^{2} + 105773404 T^{4} - 696180849192 T^{6} + 3915811319568198 T^{8} - 17691125657976211752 T^{10} + \)\(68\!\cdots\!44\)\( T^{12} - \)\(22\!\cdots\!24\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))
$73$ (\( ( 1 + 80 T + 5329 T^{2} )^{2} \))(\( ( 1 + 16 T + 5329 T^{2} )^{2} \))(\( 1 + 110 T + 5329 T^{2} \))(\( ( 1 - 82 T + 5329 T^{2} )^{2} \))(\( ( 1 - 46 T + 5329 T^{2} )^{2} \))(\( 1 - 13126 T^{2} + 103571951 T^{4} - 653716749588 T^{6} + 2941261225338191 T^{8} - 10585595166201707206 T^{10} + \)\(22\!\cdots\!21\)\( T^{12} \))(\( ( 1 - 22536 T^{2} + 300646172 T^{4} - 2600139782456 T^{6} + 16379358145749190 T^{8} - 73839396175873059896 T^{10} + \)\(24\!\cdots\!32\)\( T^{12} - \)\(51\!\cdots\!56\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 42768 T^{2} + 946714744 T^{4} - 14391245893936 T^{6} + 167549428359087132 T^{8} - \)\(15\!\cdots\!24\)\( T^{10} + \)\(12\!\cdots\!76\)\( T^{12} - \)\(83\!\cdots\!96\)\( T^{14} + \)\(47\!\cdots\!22\)\( T^{16} - \)\(23\!\cdots\!36\)\( T^{18} + \)\(10\!\cdots\!56\)\( T^{20} - \)\(36\!\cdots\!04\)\( T^{22} + \)\(10\!\cdots\!52\)\( T^{24} - \)\(26\!\cdots\!36\)\( T^{26} + \)\(49\!\cdots\!04\)\( T^{28} - \)\(63\!\cdots\!08\)\( T^{30} + \)\(42\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 37 T + 20314 T^{2} - 565891 T^{3} + 160126666 T^{4} - 3015633139 T^{5} + 576881867674 T^{6} - 5599366372693 T^{7} + 806460091894081 T^{8} )^{2} \))(\( ( 1 + 55 T + 5508 T^{2} + 293095 T^{3} + 28398241 T^{4} )^{4} \))(\( ( 1 - 37 T + 20314 T^{2} - 565891 T^{3} + 160126666 T^{4} - 3015633139 T^{5} + 576881867674 T^{6} - 5599366372693 T^{7} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 65 T + 5329 T^{2} )^{2} \))(\( ( 1 - 43 T + 10452 T^{2} - 229147 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 104 T + 11418 T^{2} + 554216 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 - 20 T + 7302 T^{2} - 106580 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 38 T + 11485 T^{2} + 120314 T^{3} + 68572624 T^{4} + 641153306 T^{5} + 326153797885 T^{6} + 5750700598982 T^{7} + 806460091894081 T^{8} )^{2} \))
$79$ (\( ( 1 + 100 T + 6241 T^{2} )^{2} \))(\( ( 1 - 76 T + 6241 T^{2} )^{2} \))(\( ( 1 - 79 T )( 1 + 79 T ) \))(\( 1 - 6674 T^{2} + 38950081 T^{4} \))(\( ( 1 - 142 T + 6241 T^{2} )( 1 + 142 T + 6241 T^{2} ) \))(\( 1 - 70 T^{2} + 84324175 T^{4} + 17226941804 T^{6} + 3284433446508175 T^{8} - 106197616693459270 T^{10} + \)\(59\!\cdots\!41\)\( T^{12} \))(\( ( 1 - 35304 T^{2} + 608675620 T^{4} - 6614894483704 T^{6} + 49280941921260934 T^{8} - \)\(25\!\cdots\!24\)\( T^{10} + \)\(92\!\cdots\!20\)\( T^{12} - \)\(20\!\cdots\!64\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 62928 T^{2} + 1905826568 T^{4} - 37296559235888 T^{6} + 534425714020543644 T^{8} - \)\(60\!\cdots\!08\)\( T^{10} + \)\(55\!\cdots\!96\)\( T^{12} - \)\(43\!\cdots\!36\)\( T^{14} + \)\(29\!\cdots\!62\)\( T^{16} - \)\(16\!\cdots\!16\)\( T^{18} + \)\(84\!\cdots\!56\)\( T^{20} - \)\(35\!\cdots\!28\)\( T^{22} + \)\(12\!\cdots\!24\)\( T^{24} - \)\(33\!\cdots\!88\)\( T^{26} + \)\(66\!\cdots\!08\)\( T^{28} - \)\(85\!\cdots\!08\)\( T^{30} + \)\(52\!\cdots\!41\)\( T^{32} \))(\( 1 - 33 T + 13924 T^{2} - 447513 T^{3} + 83250565 T^{4} - 4145960160 T^{5} + 461050019242 T^{6} - 35083235957766 T^{7} + 3234248047096936 T^{8} - 218954475612417606 T^{9} + 17957935594527458602 T^{10} - \)\(10\!\cdots\!60\)\( T^{11} + \)\(12\!\cdots\!65\)\( T^{12} - \)\(42\!\cdots\!13\)\( T^{13} + \)\(82\!\cdots\!84\)\( T^{14} - \)\(12\!\cdots\!73\)\( T^{15} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 + 20869 T^{2} + 251340865 T^{4} + 2217834902446 T^{6} + 15439711699511014 T^{8} + 86384849094898798126 T^{10} + \)\(38\!\cdots\!65\)\( T^{12} + \)\(12\!\cdots\!29\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 + 33 T + 13924 T^{2} + 447513 T^{3} + 83250565 T^{4} + 4145960160 T^{5} + 461050019242 T^{6} + 35083235957766 T^{7} + 3234248047096936 T^{8} + 218954475612417606 T^{9} + 17957935594527458602 T^{10} + \)\(10\!\cdots\!60\)\( T^{11} + \)\(12\!\cdots\!65\)\( T^{12} + \)\(42\!\cdots\!13\)\( T^{13} + \)\(82\!\cdots\!84\)\( T^{14} + \)\(12\!\cdots\!73\)\( T^{15} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 - 38 T - 4797 T^{2} - 237158 T^{3} + 38950081 T^{4} \))(\( 1 + 83 T - 5459 T^{2} - 11122 T^{3} + 70528774 T^{4} - 69412402 T^{5} - 212628492179 T^{6} + 20176258808243 T^{7} + 1517108809906561 T^{8} \))(\( 1 + 14 T - 10985 T^{2} - 18214 T^{3} + 84841444 T^{4} - 113673574 T^{5} - 427866639785 T^{6} + 3403224377294 T^{7} + 1517108809906561 T^{8} \))(\( 1 - 86 T - 2231 T^{2} + 245530 T^{3} + 7570612 T^{4} + 1532352730 T^{5} - 86897630711 T^{6} - 20905521174806 T^{7} + 1517108809906561 T^{8} \))(\( 1 + 26 T - 12687 T^{2} - 773558 T^{3} + 64925093 T^{4} + 5836272936 T^{5} - 59707396922 T^{6} - 18106848362500 T^{7} - 289214375790438 T^{8} - 113004840630362500 T^{9} - 2325607946411050682 T^{10} + \)\(14\!\cdots\!56\)\( T^{11} + \)\(98\!\cdots\!73\)\( T^{12} - \)\(73\!\cdots\!58\)\( T^{13} - \)\(74\!\cdots\!67\)\( T^{14} + \)\(95\!\cdots\!06\)\( T^{15} + \)\(23\!\cdots\!21\)\( T^{16} \))
$83$ (\( 1 + 3150 T^{2} + 47458321 T^{4} \))(\( 1 + 334 T^{2} + 47458321 T^{4} \))(\( ( 1 - 83 T )( 1 + 83 T ) \))(\( 1 - 13346 T^{2} + 47458321 T^{4} \))(\( ( 1 - 83 T )^{2}( 1 + 83 T )^{2} \))(\( 1 + 318 T + 50562 T^{2} + 6712846 T^{3} + 819490815 T^{4} + 81203275140 T^{5} + 6918697616348 T^{6} + 559409362439460 T^{7} + 38891658154821615 T^{8} + 2194700377608598174 T^{9} + \)\(11\!\cdots\!42\)\( T^{10} + \)\(49\!\cdots\!82\)\( T^{11} + \)\(10\!\cdots\!61\)\( T^{12} \))(\( 1 - 47654840 T^{4} - 1328477750370788 T^{8} + \)\(67\!\cdots\!96\)\( T^{12} + \)\(24\!\cdots\!06\)\( T^{16} + \)\(15\!\cdots\!36\)\( T^{20} - \)\(67\!\cdots\!28\)\( T^{24} - \)\(54\!\cdots\!40\)\( T^{28} + \)\(25\!\cdots\!61\)\( T^{32} \))(\( 1 - 160 T + 12800 T^{2} - 895904 T^{3} + 107479624 T^{4} - 16432771168 T^{5} + 1654826188288 T^{6} - 174484645067104 T^{7} + 18280323695716892 T^{8} - 1483531366054758688 T^{9} + \)\(11\!\cdots\!96\)\( T^{10} - \)\(11\!\cdots\!36\)\( T^{11} + \)\(13\!\cdots\!00\)\( T^{12} - \)\(12\!\cdots\!44\)\( T^{13} + \)\(89\!\cdots\!76\)\( T^{14} - \)\(74\!\cdots\!76\)\( T^{15} + \)\(61\!\cdots\!66\)\( T^{16} - \)\(51\!\cdots\!64\)\( T^{17} + \)\(42\!\cdots\!96\)\( T^{18} - \)\(39\!\cdots\!36\)\( T^{19} + \)\(30\!\cdots\!00\)\( T^{20} - \)\(17\!\cdots\!64\)\( T^{21} + \)\(12\!\cdots\!56\)\( T^{22} - \)\(10\!\cdots\!52\)\( T^{23} + \)\(92\!\cdots\!52\)\( T^{24} - \)\(60\!\cdots\!36\)\( T^{25} + \)\(39\!\cdots\!88\)\( T^{26} - \)\(27\!\cdots\!52\)\( T^{27} + \)\(12\!\cdots\!04\)\( T^{28} - \)\(70\!\cdots\!76\)\( T^{29} + \)\(69\!\cdots\!00\)\( T^{30} - \)\(59\!\cdots\!40\)\( T^{31} + \)\(25\!\cdots\!61\)\( T^{32} \))(\( 1 - 549 T + 157876 T^{2} - 31517541 T^{3} + 4848813277 T^{4} - 610140548160 T^{5} + 65668976887426 T^{6} - 6260783050033902 T^{7} + 542374558465652968 T^{8} - 43130534431683550878 T^{9} + \)\(31\!\cdots\!46\)\( T^{10} - \)\(19\!\cdots\!40\)\( T^{11} + \)\(10\!\cdots\!57\)\( T^{12} - \)\(48\!\cdots\!09\)\( T^{13} + \)\(16\!\cdots\!36\)\( T^{14} - \)\(40\!\cdots\!21\)\( T^{15} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 + 16837 T^{2} + 138536161 T^{4} + 842384844142 T^{6} + 5304047075446774 T^{8} + 39978170338826005582 T^{10} + \)\(31\!\cdots\!01\)\( T^{12} + \)\(17\!\cdots\!57\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 + 549 T + 157876 T^{2} + 31517541 T^{3} + 4848813277 T^{4} + 610140548160 T^{5} + 65668976887426 T^{6} + 6260783050033902 T^{7} + 542374558465652968 T^{8} + 43130534431683550878 T^{9} + \)\(31\!\cdots\!46\)\( T^{10} + \)\(19\!\cdots\!40\)\( T^{11} + \)\(10\!\cdots\!57\)\( T^{12} + \)\(48\!\cdots\!09\)\( T^{13} + \)\(16\!\cdots\!36\)\( T^{14} + \)\(40\!\cdots\!21\)\( T^{15} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 - 84 T + 9241 T^{2} - 578676 T^{3} + 47458321 T^{4} \))(\( 1 - 81 T + 16289 T^{2} - 1142262 T^{3} + 166474326 T^{4} - 7869042918 T^{5} + 773048590769 T^{6} - 26482170242889 T^{7} + 2252292232139041 T^{8} \))(\( 1 - 378 T + 72863 T^{2} - 9538830 T^{3} + 917456196 T^{4} - 65712999870 T^{5} + 3457955643023 T^{6} - 123583461133482 T^{7} + 2252292232139041 T^{8} \))(\( 1 - 66 T + 9321 T^{2} - 519354 T^{3} + 24465668 T^{4} - 3577829706 T^{5} + 442359010041 T^{6} - 21578064642354 T^{7} + 2252292232139041 T^{8} \))(\( 1 + 246 T + 54825 T^{2} + 8524638 T^{3} + 1254860197 T^{4} + 148166306376 T^{5} + 16481417300694 T^{6} + 1562002778781228 T^{7} + 140096195439334362 T^{8} + 10760637143023879692 T^{9} + \)\(78\!\cdots\!74\)\( T^{10} + \)\(48\!\cdots\!44\)\( T^{11} + \)\(28\!\cdots\!77\)\( T^{12} + \)\(13\!\cdots\!62\)\( T^{13} + \)\(58\!\cdots\!25\)\( T^{14} + \)\(18\!\cdots\!34\)\( T^{15} + \)\(50\!\cdots\!81\)\( T^{16} \))
$89$ (\( 1 + 6208 T^{2} + 62742241 T^{4} \))(\( 1 - 15680 T^{2} + 62742241 T^{4} \))(\( 1 - 78 T + 7921 T^{2} \))(\( ( 1 + 114 T + 7921 T^{2} )^{2} \))(\( ( 1 + 7921 T^{2} )^{2} \))(\( 1 - 31238 T^{2} + 466178479 T^{4} - 4433595811988 T^{6} + 29249082478431439 T^{8} - \)\(12\!\cdots\!78\)\( T^{10} + \)\(24\!\cdots\!21\)\( T^{12} \))(\( ( 1 - 17608 T^{2} + 140263452 T^{4} - 1652317947000 T^{6} + 18439815418282950 T^{8} - \)\(10\!\cdots\!00\)\( T^{10} + \)\(55\!\cdots\!12\)\( T^{12} - \)\(43\!\cdots\!68\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 81008 T^{2} + 3201135736 T^{4} - 82544801381712 T^{6} + 1567286911309649436 T^{8} - \)\(23\!\cdots\!04\)\( T^{10} + \)\(28\!\cdots\!72\)\( T^{12} - \)\(29\!\cdots\!36\)\( T^{14} + \)\(25\!\cdots\!10\)\( T^{16} - \)\(18\!\cdots\!76\)\( T^{18} + \)\(11\!\cdots\!32\)\( T^{20} - \)\(57\!\cdots\!84\)\( T^{22} + \)\(24\!\cdots\!96\)\( T^{24} - \)\(80\!\cdots\!12\)\( T^{26} + \)\(19\!\cdots\!76\)\( T^{28} - \)\(31\!\cdots\!48\)\( T^{30} + \)\(24\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 84 T + 30700 T^{2} + 1886940 T^{3} + 359702982 T^{4} + 14946451740 T^{5} + 1926186798700 T^{6} + 41746428440724 T^{7} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 228 T + 27158 T^{2} - 1805988 T^{3} + 62742241 T^{4} )^{4} \))(\( ( 1 + 84 T + 30700 T^{2} + 1886940 T^{3} + 359702982 T^{4} + 14946451740 T^{5} + 1926186798700 T^{6} + 41746428440724 T^{7} + 3936588805702081 T^{8} )^{2} \))(\( 1 - 290 T^{2} + 62742241 T^{4} \))(\( 1 - 6916 T^{2} + 69013446 T^{4} - 433925338756 T^{6} + 3936588805702081 T^{8} \))(\( 1 - 8860 T^{2} + 51019782 T^{4} - 555896255260 T^{6} + 3936588805702081 T^{8} \))(\( 1 - 25924 T^{2} + 285535302 T^{4} - 1626529855684 T^{6} + 3936588805702081 T^{8} \))(\( 1 - 28448 T^{2} + 504887356 T^{4} - 6266477720288 T^{6} + 56631012864364294 T^{8} - \)\(39\!\cdots\!08\)\( T^{10} + \)\(19\!\cdots\!36\)\( T^{12} - \)\(70\!\cdots\!08\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} \))
$97$ (\( ( 1 + 112 T + 9409 T^{2} )^{2} \))(\( ( 1 - 176 T + 9409 T^{2} )^{2} \))(\( 1 - 130 T + 9409 T^{2} \))(\( ( 1 - 34 T + 9409 T^{2} )^{2} \))(\( ( 1 + 2 T + 9409 T^{2} )^{2} \))(\( ( 1 + 2 T + 10687 T^{2} + 557564 T^{3} + 100553983 T^{4} + 177058562 T^{5} + 832972004929 T^{6} )^{2} \))(\( ( 1 + 25252 T^{2} - 77824 T^{3} + 327999814 T^{4} - 732246016 T^{5} + 2235541403812 T^{6} + 7837433594376961 T^{8} )^{4} \))(\( ( 1 + 38216 T^{2} + 116224 T^{3} + 770481564 T^{4} + 3485408768 T^{5} + 10857255215864 T^{6} + 49274039499776 T^{7} + 116292098553803590 T^{8} + 463619437653392384 T^{9} + \)\(96\!\cdots\!84\)\( T^{10} + \)\(29\!\cdots\!72\)\( T^{11} + \)\(60\!\cdots\!04\)\( T^{12} + \)\(85\!\cdots\!76\)\( T^{13} + \)\(26\!\cdots\!56\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 10 T - 22548 T^{2} + 828296 T^{3} + 272325791 T^{4} - 14518511616 T^{5} - 1388516520704 T^{6} + 83318070893038 T^{7} + 5416086623373288 T^{8} + 783939729032594542 T^{9} - \)\(12\!\cdots\!24\)\( T^{10} - \)\(12\!\cdots\!64\)\( T^{11} + \)\(21\!\cdots\!51\)\( T^{12} + \)\(61\!\cdots\!04\)\( T^{13} - \)\(15\!\cdots\!68\)\( T^{14} + \)\(65\!\cdots\!90\)\( T^{15} + \)\(61\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 100 T - 2813 T^{2} + 600500 T^{3} - 18446312 T^{4} + 5650104500 T^{5} - 249032867453 T^{6} - 83297200492900 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( 1 + 10 T - 22548 T^{2} + 828296 T^{3} + 272325791 T^{4} - 14518511616 T^{5} - 1388516520704 T^{6} + 83318070893038 T^{7} + 5416086623373288 T^{8} + 783939729032594542 T^{9} - \)\(12\!\cdots\!24\)\( T^{10} - \)\(12\!\cdots\!64\)\( T^{11} + \)\(21\!\cdots\!51\)\( T^{12} + \)\(61\!\cdots\!04\)\( T^{13} - \)\(15\!\cdots\!68\)\( T^{14} + \)\(65\!\cdots\!90\)\( T^{15} + \)\(61\!\cdots\!21\)\( T^{16} \))(\( 1 - 115 T + 3816 T^{2} - 1082035 T^{3} + 88529281 T^{4} \))(\( 1 + 196 T + 10291 T^{2} + 1824172 T^{3} + 341030200 T^{4} + 17163634348 T^{5} + 911054830771 T^{6} + 163262512966084 T^{7} + 7837433594376961 T^{8} \))(\( 1 - 14 T - 8087 T^{2} + 147490 T^{3} - 21765356 T^{4} + 1387733410 T^{5} - 715936295447 T^{6} - 11661608069006 T^{7} + 7837433594376961 T^{8} \))(\( 1 - 242 T + 25489 T^{2} - 3450194 T^{3} + 454397668 T^{4} - 32462875346 T^{5} + 2256522843409 T^{6} - 201579225192818 T^{7} + 7837433594376961 T^{8} \))(\( 1 + 236 T + 438 T^{2} - 1185512 T^{3} + 510091505 T^{4} + 51879290952 T^{5} - 3191784386426 T^{6} + 104812309462772 T^{7} + 86158688483213604 T^{8} + 986179019735221748 T^{9} - \)\(28\!\cdots\!06\)\( T^{10} + \)\(43\!\cdots\!08\)\( T^{11} + \)\(39\!\cdots\!05\)\( T^{12} - \)\(87\!\cdots\!88\)\( T^{13} + \)\(30\!\cdots\!58\)\( T^{14} + \)\(15\!\cdots\!84\)\( T^{15} + \)\(61\!\cdots\!21\)\( T^{16} \))
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