Properties

Label 63.4
Level 63
Weight 4
Dimension 305
Nonzero newspaces 10
Newform subspaces 20
Sturm bound 1152
Trace bound 2

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 20 \)
Sturm bound: \(1152\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(63))\).

Total New Old
Modular forms 480 349 131
Cusp forms 384 305 79
Eisenstein series 96 44 52

Trace form

\( 305q - 3q^{2} - 6q^{3} + 17q^{4} + 33q^{5} - 30q^{6} + 2q^{7} - 177q^{8} - 102q^{9} + O(q^{10}) \) \( 305q - 3q^{2} - 6q^{3} + 17q^{4} + 33q^{5} - 30q^{6} + 2q^{7} - 177q^{8} - 102q^{9} - 78q^{10} + 123q^{11} + 348q^{12} + 256q^{13} + 603q^{14} + 42q^{15} - 91q^{16} - 615q^{17} - 780q^{18} - 491q^{19} - 1626q^{20} - 393q^{21} - 954q^{22} - 237q^{23} - 102q^{24} + 209q^{25} + 1626q^{26} + 1248q^{27} + 1433q^{28} + 1140q^{29} + 1002q^{30} + 1345q^{31} + 2535q^{32} + 336q^{33} + 1530q^{34} - 3q^{35} - 234q^{36} - 1517q^{37} - 4596q^{38} - 2790q^{39} - 3654q^{40} - 2784q^{41} - 2232q^{42} - 788q^{43} - 3570q^{44} - 54q^{45} - 1218q^{46} - 201q^{47} - 2502q^{48} + 1148q^{49} + 159q^{50} - 1362q^{51} + 3970q^{52} + 2841q^{53} + 336q^{54} + 510q^{55} + 4599q^{56} + 3954q^{57} - 2652q^{58} + 4005q^{59} + 8670q^{60} - 2327q^{61} + 3084q^{62} + 4593q^{63} + 1733q^{64} + 4722q^{65} + 8226q^{66} + 4651q^{67} + 12738q^{68} + 3978q^{69} + 9078q^{70} - 348q^{71} - 1920q^{72} + 3355q^{73} + 90q^{74} - 5718q^{75} - 878q^{76} - 8508q^{77} - 11040q^{78} - 7793q^{79} - 18114q^{80} - 5346q^{81} - 19734q^{82} - 9438q^{83} - 8322q^{84} - 9918q^{85} - 10644q^{86} - 1182q^{87} + 5988q^{88} + 1893q^{89} + 1914q^{90} + 3070q^{91} + 4848q^{92} + 2094q^{93} + 7284q^{94} + 3339q^{95} + 1320q^{96} + 7912q^{97} + 11763q^{98} + 3366q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.4.a \(\chi_{63}(1, \cdot)\) 63.4.a.a 1 1
63.4.a.b 1
63.4.a.c 1
63.4.a.d 2
63.4.a.e 2
63.4.c \(\chi_{63}(62, \cdot)\) 63.4.c.a 4 1
63.4.c.b 4
63.4.e \(\chi_{63}(37, \cdot)\) 63.4.e.a 2 2
63.4.e.b 2
63.4.e.c 6
63.4.e.d 8
63.4.f \(\chi_{63}(22, \cdot)\) 63.4.f.a 2 2
63.4.f.b 16
63.4.f.c 18
63.4.g \(\chi_{63}(4, \cdot)\) 63.4.g.a 44 2
63.4.h \(\chi_{63}(25, \cdot)\) 63.4.h.a 44 2
63.4.i \(\chi_{63}(5, \cdot)\) 63.4.i.a 44 2
63.4.o \(\chi_{63}(20, \cdot)\) 63.4.o.a 44 2
63.4.p \(\chi_{63}(17, \cdot)\) 63.4.p.a 16 2
63.4.s \(\chi_{63}(47, \cdot)\) 63.4.s.a 44 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T + 8 T^{2} \))(\( 1 - T + 8 T^{2} \))(\( 1 - 3 T + 8 T^{2} \))(\( 1 - 3 T^{2} + 64 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 - 47 T^{4} + 4096 T^{8} \))(\( ( 1 - 8 T^{2} + 64 T^{4} )^{2} \))(\( 1 + 3 T + T^{2} + 24 T^{3} + 64 T^{4} \))(\( 1 - 2 T - 4 T^{2} - 16 T^{3} + 64 T^{4} \))(\( 1 - T + T^{2} + 20 T^{3} - 10 T^{4} - 64 T^{5} + 1060 T^{6} - 512 T^{7} - 640 T^{8} + 10240 T^{9} + 4096 T^{10} - 32768 T^{11} + 262144 T^{12} \))(\( 1 - 13 T^{2} + 47 T^{4} + 78 T^{6} - 28 T^{8} + 4992 T^{10} + 192512 T^{12} - 3407872 T^{14} + 16777216 T^{16} \))(\( 1 - T - 7 T^{2} - 8 T^{3} + 64 T^{4} \))(\( 1 + 3 T - 6 T^{2} - 15 T^{3} - 13 T^{4} + 15 T^{5} + 885 T^{6} - 372 T^{7} - 9944 T^{8} - 6948 T^{9} + 5697 T^{10} + 114462 T^{11} + 280316 T^{12} - 1536384 T^{13} - 2583696 T^{14} + 7319616 T^{15} + 22669120 T^{16} + 58556928 T^{17} - 165356544 T^{18} - 786628608 T^{19} + 1148174336 T^{20} + 3750690816 T^{21} + 1493434368 T^{22} - 14571012096 T^{23} - 166832635904 T^{24} - 49928994816 T^{25} + 950261514240 T^{26} + 128849018880 T^{27} - 893353197568 T^{28} - 8246337208320 T^{29} - 26388279066624 T^{30} + 105553116266496 T^{31} + 281474976710656 T^{32} \))(\( 1 - 6 T + 90 T^{3} - 252 T^{4} - 231 T^{5} + 2433 T^{6} - 3066 T^{7} - 4923 T^{8} + 14400 T^{9} - 34659 T^{10} + 185313 T^{11} - 505137 T^{12} - 274038 T^{13} + 6064668 T^{14} - 20259792 T^{15} + 27195696 T^{16} + 96456576 T^{17} - 561577664 T^{18} + 771652608 T^{19} + 1740524544 T^{20} - 10373013504 T^{21} + 24840880128 T^{22} - 8979677184 T^{23} - 132418633728 T^{24} + 388629528576 T^{25} - 581481529344 T^{26} + 1932735283200 T^{27} - 5286030999552 T^{28} - 26336739459072 T^{29} + 167194486898688 T^{30} - 126993593008128 T^{31} - 1108307720798208 T^{32} + 3166593487994880 T^{33} - 13510798882111488 T^{35} + 18014398509481984 T^{36} \))(\( 1 + 16 T^{2} + 111 T^{4} - 996 T^{6} - 22563 T^{8} - 199398 T^{10} - 234688 T^{12} + 11210024 T^{14} + 146432016 T^{16} + 717441536 T^{18} - 961282048 T^{20} - 52270989312 T^{22} - 378544324608 T^{24} - 1069446856704 T^{26} + 7627861917696 T^{28} + 70368744177664 T^{30} + 281474976710656 T^{32} \))
$3$ (\( 1 + 9 T + 27 T^{2} \))(\( 1 - 2 T + 64 T^{2} - 216 T^{3} + 2109 T^{4} - 13158 T^{5} + 54675 T^{6} - 463968 T^{7} + 1372950 T^{8} - 12527136 T^{9} + 39858075 T^{10} - 258988914 T^{11} + 1120809069 T^{12} - 3099363912 T^{13} + 24794911296 T^{14} - 20920706406 T^{15} + 282429536481 T^{16} \))(\( 1 - 9 T + 9 T^{2} + 18 T^{3} + 1269 T^{4} - 8181 T^{5} - 4428 T^{6} + 108621 T^{7} + 413343 T^{8} - 5025726 T^{9} + 11160261 T^{10} + 79184709 T^{11} - 87156324 T^{12} - 4347718821 T^{13} + 18208762983 T^{14} + 6973568802 T^{15} + 94143178827 T^{16} - 2541865828329 T^{17} + 7625597484987 T^{18} \))
$5$ (\( 1 - 4 T + 125 T^{2} \))(\( 1 + 16 T + 125 T^{2} \))(\( 1 - 18 T + 125 T^{2} \))(\( 1 + 174 T^{2} + 15625 T^{4} \))(\( 1 + 6 T + 202 T^{2} + 750 T^{3} + 15625 T^{4} \))(\( ( 1 + 125 T^{2} )^{4} \))(\( ( 1 - 194 T^{2} + 15625 T^{4} )^{2} \))(\( 1 + 3 T - 116 T^{2} + 375 T^{3} + 15625 T^{4} \))(\( 1 - 7 T - 76 T^{2} - 875 T^{3} + 15625 T^{4} \))(\( 1 - 11 T - 62 T^{2} + 1015 T^{3} - 6040 T^{4} + 54313 T^{5} + 121696 T^{6} + 6789125 T^{7} - 94375000 T^{8} + 1982421875 T^{9} - 15136718750 T^{10} - 335693359375 T^{11} + 3814697265625 T^{12} \))(\( 1 - 67 T^{2} - 13939 T^{4} + 859074 T^{6} + 25309934 T^{8} + 13423031250 T^{10} - 3403076171875 T^{12} - 255584716796875 T^{14} + 59604644775390625 T^{16} \))(\( 1 - 14 T + 71 T^{2} - 1750 T^{3} + 15625 T^{4} \))(\( 1 + 30 T + 72 T^{2} - 10440 T^{3} - 166117 T^{4} + 283968 T^{5} + 38626110 T^{6} + 467135070 T^{7} - 196342208 T^{8} - 82657218078 T^{9} - 1137104761158 T^{10} - 2696743553724 T^{11} + 139035171825830 T^{12} + 2250940255089630 T^{13} + 10174499387616861 T^{14} - 175588804032450084 T^{15} - 3536462896978609646 T^{16} - 21948600504056260500 T^{17} + \)\(15\!\cdots\!25\)\( T^{18} + \)\(43\!\cdots\!50\)\( T^{19} + \)\(33\!\cdots\!50\)\( T^{20} - \)\(82\!\cdots\!00\)\( T^{21} - \)\(43\!\cdots\!50\)\( T^{22} - \)\(39\!\cdots\!50\)\( T^{23} - \)\(11\!\cdots\!00\)\( T^{24} + \)\(34\!\cdots\!50\)\( T^{25} + \)\(35\!\cdots\!50\)\( T^{26} + \)\(33\!\cdots\!00\)\( T^{27} - \)\(24\!\cdots\!25\)\( T^{28} - \)\(18\!\cdots\!00\)\( T^{29} + \)\(16\!\cdots\!00\)\( T^{30} + \)\(85\!\cdots\!50\)\( T^{31} + \)\(35\!\cdots\!25\)\( T^{32} \))(\( 1 - 24 T - 135 T^{2} + 4284 T^{3} + 54072 T^{4} - 313044 T^{5} - 15740079 T^{6} - 55778280 T^{7} + 2773664253 T^{8} + 25738770672 T^{9} - 265166877816 T^{10} - 5900298626580 T^{11} + 589682928372 T^{12} + 893960315200164 T^{13} + 5517977552150157 T^{14} - 91672964034914088 T^{15} - 1281826000386231867 T^{16} + 4703053884869404056 T^{17} + \)\(18\!\cdots\!24\)\( T^{18} + \)\(58\!\cdots\!00\)\( T^{19} - \)\(20\!\cdots\!75\)\( T^{20} - \)\(17\!\cdots\!00\)\( T^{21} + \)\(13\!\cdots\!25\)\( T^{22} + \)\(27\!\cdots\!00\)\( T^{23} + \)\(22\!\cdots\!00\)\( T^{24} - \)\(28\!\cdots\!00\)\( T^{25} - \)\(15\!\cdots\!00\)\( T^{26} + \)\(19\!\cdots\!00\)\( T^{27} + \)\(25\!\cdots\!25\)\( T^{28} - \)\(64\!\cdots\!00\)\( T^{29} - \)\(22\!\cdots\!75\)\( T^{30} - \)\(56\!\cdots\!00\)\( T^{31} + \)\(12\!\cdots\!00\)\( T^{32} + \)\(12\!\cdots\!00\)\( T^{33} - \)\(47\!\cdots\!75\)\( T^{34} - \)\(10\!\cdots\!00\)\( T^{35} + \)\(55\!\cdots\!25\)\( T^{36} \))(\( 1 - 490 T^{2} + 101175 T^{4} - 13467734 T^{6} + 2004738389 T^{8} - 380916749220 T^{10} + 60059957637514 T^{12} - 6902983281820528 T^{14} + 756156244566152106 T^{16} - \)\(10\!\cdots\!00\)\( T^{18} + \)\(14\!\cdots\!50\)\( T^{20} - \)\(14\!\cdots\!00\)\( T^{22} + \)\(11\!\cdots\!25\)\( T^{24} - \)\(12\!\cdots\!50\)\( T^{26} + \)\(14\!\cdots\!75\)\( T^{28} - \)\(11\!\cdots\!50\)\( T^{30} + \)\(35\!\cdots\!25\)\( T^{32} \))
$7$ (\( 1 + 7 T \))(\( 1 + 7 T \))(\( 1 - 7 T \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 - 343 T^{2} )^{2} \))(\( ( 1 + 22 T + 343 T^{2} )^{2} \))(\( 1 + 7 T + 343 T^{2} \))(\( 1 - 28 T + 343 T^{2} \))(\( 1 + 13 T + 236 T^{2} + 12145 T^{3} + 80948 T^{4} + 1529437 T^{5} + 40353607 T^{6} \))(\( ( 1 + 6 T - 77 T^{2} + 2058 T^{3} + 117649 T^{4} )^{2} \))(\( 1 - 7 T + 49 T^{2} \))(\( ( 1 - 7 T + 49 T^{2} )^{8} \))(\( ( 1 + 7 T + 49 T^{2} )^{9} \))(\( ( 1 - 28 T + 196 T^{2} + 9604 T^{3} - 262591 T^{4} + 3294172 T^{5} + 23059204 T^{6} - 1129900996 T^{7} + 13841287201 T^{8} )^{2} \))
$11$ (\( 1 + 62 T + 1331 T^{2} \))(\( 1 - 8 T + 1331 T^{2} \))(\( 1 - 36 T + 1331 T^{2} \))(\( 1 + 762 T^{2} + 1771561 T^{4} \))(\( 1 - 6 T + 1246 T^{2} - 7986 T^{3} + 1771561 T^{4} \))(\( 1 + 306322 T^{4} + 3138428376721 T^{8} \))(\( ( 1 - 2420 T^{2} + 1771561 T^{4} )^{2} \))(\( 1 + 15 T - 1106 T^{2} + 19965 T^{3} + 1771561 T^{4} \))(\( 1 + 5 T - 1306 T^{2} + 6655 T^{3} + 1771561 T^{4} \))(\( 1 - 35 T - 1400 T^{2} + 113593 T^{3} - 198940 T^{4} - 87110135 T^{5} + 3928586038 T^{6} - 115943589685 T^{7} - 352434345340 T^{8} + 267846352063763 T^{9} - 4393799727409400 T^{10} - 146203685929547785 T^{11} + 5559917313492231481 T^{12} \))(\( 1 - 1387 T^{2} + 1086569 T^{4} + 3753113814 T^{6} - 5845598670130 T^{8} + 6648870061443654 T^{10} + 3410118982865360249 T^{12} - \)\(77\!\cdots\!47\)\( T^{14} + \)\(98\!\cdots\!41\)\( T^{16} \))(\( 1 - 47 T + 878 T^{2} - 62557 T^{3} + 1771561 T^{4} \))(\( 1 + 24 T - 6312 T^{2} - 112236 T^{3} + 20919641 T^{4} + 234941478 T^{5} - 48781328610 T^{6} - 247581606570 T^{7} + 91374825172267 T^{8} + 19514919797334 T^{9} - 148969481247130356 T^{10} + 376103153664918684 T^{11} + \)\(22\!\cdots\!01\)\( T^{12} - \)\(61\!\cdots\!80\)\( T^{13} - \)\(31\!\cdots\!40\)\( T^{14} + \)\(35\!\cdots\!36\)\( T^{15} + \)\(42\!\cdots\!85\)\( T^{16} + \)\(47\!\cdots\!16\)\( T^{17} - \)\(55\!\cdots\!40\)\( T^{18} - \)\(14\!\cdots\!80\)\( T^{19} + \)\(69\!\cdots\!21\)\( T^{20} + \)\(15\!\cdots\!84\)\( T^{21} - \)\(82\!\cdots\!36\)\( T^{22} + \)\(14\!\cdots\!74\)\( T^{23} + \)\(90\!\cdots\!47\)\( T^{24} - \)\(32\!\cdots\!70\)\( T^{25} - \)\(85\!\cdots\!10\)\( T^{26} + \)\(54\!\cdots\!18\)\( T^{27} + \)\(64\!\cdots\!01\)\( T^{28} - \)\(46\!\cdots\!76\)\( T^{29} - \)\(34\!\cdots\!52\)\( T^{30} + \)\(17\!\cdots\!24\)\( T^{31} + \)\(97\!\cdots\!81\)\( T^{32} \))(\( 1 - 111 T + 702 T^{2} + 275031 T^{3} + 1265238 T^{4} - 928261857 T^{5} + 11439493518 T^{6} + 1092829962687 T^{7} + 3152075996304 T^{8} - 2138272282554579 T^{9} + 23019715641124836 T^{10} + 882464328696498459 T^{11} + 22286657835297708522 T^{12} - \)\(24\!\cdots\!53\)\( T^{13} + \)\(90\!\cdots\!78\)\( T^{14} - \)\(89\!\cdots\!41\)\( T^{15} - \)\(63\!\cdots\!02\)\( T^{16} - \)\(27\!\cdots\!59\)\( T^{17} + \)\(30\!\cdots\!06\)\( T^{18} - \)\(36\!\cdots\!29\)\( T^{19} - \)\(11\!\cdots\!22\)\( T^{20} - \)\(21\!\cdots\!31\)\( T^{21} + \)\(28\!\cdots\!38\)\( T^{22} - \)\(10\!\cdots\!03\)\( T^{23} + \)\(12\!\cdots\!82\)\( T^{24} + \)\(65\!\cdots\!49\)\( T^{25} + \)\(22\!\cdots\!76\)\( T^{26} - \)\(28\!\cdots\!09\)\( T^{27} + \)\(55\!\cdots\!04\)\( T^{28} + \)\(25\!\cdots\!97\)\( T^{29} + \)\(35\!\cdots\!98\)\( T^{30} - \)\(38\!\cdots\!87\)\( T^{31} + \)\(69\!\cdots\!98\)\( T^{32} + \)\(20\!\cdots\!81\)\( T^{33} + \)\(68\!\cdots\!62\)\( T^{34} - \)\(14\!\cdots\!21\)\( T^{35} + \)\(17\!\cdots\!41\)\( T^{36} \))(\( 1 + 3202 T^{2} + 1797447 T^{4} - 5608813218 T^{6} - 4531249774539 T^{8} + 15353827063546164 T^{10} + 27034229520225124106 T^{12} + \)\(48\!\cdots\!88\)\( T^{14} - \)\(31\!\cdots\!02\)\( T^{16} + \)\(86\!\cdots\!68\)\( T^{18} + \)\(84\!\cdots\!26\)\( T^{20} + \)\(85\!\cdots\!84\)\( T^{22} - \)\(44\!\cdots\!99\)\( T^{24} - \)\(97\!\cdots\!18\)\( T^{26} + \)\(55\!\cdots\!67\)\( T^{28} + \)\(17\!\cdots\!42\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))
$13$ (\( 1 + 62 T + 2197 T^{2} \))(\( 1 - 28 T + 2197 T^{2} \))(\( 1 + 34 T + 2197 T^{2} \))(\( ( 1 - 82 T + 2197 T^{2} )^{2} \))(\( 1 - 16 T + 2406 T^{2} - 35152 T^{3} + 4826809 T^{4} \))(\( ( 1 - 2197 T^{2} )^{4} \))(\( ( 1 - 3506 T^{2} + 4826809 T^{4} )^{2} \))(\( ( 1 + 64 T + 2197 T^{2} )^{2} \))(\( ( 1 + 14 T + 2197 T^{2} )^{2} \))(\( ( 1 - 62 T + 7016 T^{2} - 253976 T^{3} + 15414152 T^{4} - 299262158 T^{5} + 10604499373 T^{6} )^{2} \))(\( ( 1 - 51 T + 4996 T^{2} - 112047 T^{3} + 4826809 T^{4} )^{4} \))(\( 1 - 86 T + 5199 T^{2} - 188942 T^{3} + 4826809 T^{4} \))(\( 1 + 68 T - 6065 T^{2} - 196604 T^{3} + 34516832 T^{4} - 115057268 T^{5} - 122980759173 T^{6} + 2886205959684 T^{7} + 258268070617101 T^{8} - 13209130095181224 T^{9} - 311290223266507584 T^{10} + 36814066155203942280 T^{11} - \)\(16\!\cdots\!94\)\( T^{12} - \)\(69\!\cdots\!48\)\( T^{13} + \)\(24\!\cdots\!74\)\( T^{14} + \)\(61\!\cdots\!32\)\( T^{15} - \)\(74\!\cdots\!40\)\( T^{16} + \)\(13\!\cdots\!04\)\( T^{17} + \)\(11\!\cdots\!66\)\( T^{18} - \)\(73\!\cdots\!04\)\( T^{19} - \)\(39\!\cdots\!14\)\( T^{20} + \)\(18\!\cdots\!60\)\( T^{21} - \)\(35\!\cdots\!36\)\( T^{22} - \)\(32\!\cdots\!12\)\( T^{23} + \)\(14\!\cdots\!61\)\( T^{24} + \)\(34\!\cdots\!28\)\( T^{25} - \)\(32\!\cdots\!77\)\( T^{26} - \)\(66\!\cdots\!04\)\( T^{27} + \)\(43\!\cdots\!12\)\( T^{28} - \)\(54\!\cdots\!08\)\( T^{29} - \)\(37\!\cdots\!85\)\( T^{30} + \)\(91\!\cdots\!24\)\( T^{31} + \)\(29\!\cdots\!21\)\( T^{32} \))(\( 1 + 18 T - 11790 T^{2} - 333840 T^{3} + 67296114 T^{4} + 2377926054 T^{5} - 248226013230 T^{6} - 9077200849170 T^{7} + 723851944582338 T^{8} + 20640745941737936 T^{9} - 2079987427593942750 T^{10} - 30051189439357231350 T^{11} + \)\(61\!\cdots\!35\)\( T^{12} + \)\(39\!\cdots\!04\)\( T^{13} - \)\(16\!\cdots\!12\)\( T^{14} - \)\(74\!\cdots\!72\)\( T^{15} + \)\(38\!\cdots\!44\)\( T^{16} + \)\(80\!\cdots\!80\)\( T^{17} - \)\(84\!\cdots\!16\)\( T^{18} + \)\(17\!\cdots\!60\)\( T^{19} + \)\(18\!\cdots\!96\)\( T^{20} - \)\(79\!\cdots\!56\)\( T^{21} - \)\(38\!\cdots\!72\)\( T^{22} + \)\(20\!\cdots\!28\)\( T^{23} + \)\(69\!\cdots\!15\)\( T^{24} - \)\(74\!\cdots\!50\)\( T^{25} - \)\(11\!\cdots\!50\)\( T^{26} + \)\(24\!\cdots\!12\)\( T^{27} + \)\(18\!\cdots\!62\)\( T^{28} - \)\(52\!\cdots\!10\)\( T^{29} - \)\(31\!\cdots\!30\)\( T^{30} + \)\(66\!\cdots\!58\)\( T^{31} + \)\(41\!\cdots\!66\)\( T^{32} - \)\(44\!\cdots\!20\)\( T^{33} - \)\(34\!\cdots\!90\)\( T^{34} + \)\(11\!\cdots\!66\)\( T^{35} + \)\(14\!\cdots\!89\)\( T^{36} \))(\( ( 1 - 4502 T^{2} + 10097461 T^{4} - 24107307194 T^{6} + 60089639013832 T^{8} - 116361367329763946 T^{10} + \)\(23\!\cdots\!41\)\( T^{12} - \)\(50\!\cdots\!58\)\( T^{14} + \)\(54\!\cdots\!61\)\( T^{16} )^{2} \))
$17$ (\( 1 + 84 T + 4913 T^{2} \))(\( 1 + 54 T + 4913 T^{2} \))(\( 1 + 42 T + 4913 T^{2} \))(\( 1 + 3670 T^{2} + 24137569 T^{4} \))(\( 1 - 6 T + 9778 T^{2} - 29478 T^{3} + 24137569 T^{4} \))(\( ( 1 + 4913 T^{2} )^{4} \))(\( ( 1 + 5830 T^{2} + 24137569 T^{4} )^{2} \))(\( 1 - 84 T + 2143 T^{2} - 412692 T^{3} + 24137569 T^{4} \))(\( 1 + 21 T - 4472 T^{2} + 103173 T^{3} + 24137569 T^{4} \))(\( 1 - 48 T - 10035 T^{2} + 125232 T^{3} + 74409318 T^{4} + 234420432 T^{5} - 437742983351 T^{6} + 1151707582416 T^{7} + 1796060047467942 T^{8} + 14850996949472304 T^{9} - 5846614150600651635 T^{10} - \)\(13\!\cdots\!64\)\( T^{11} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 - 4256 T^{2} - 33515774 T^{4} - 14275356032 T^{6} + 1645746688812355 T^{8} - 344572391221966208 T^{10} - \)\(19\!\cdots\!14\)\( T^{12} - \)\(59\!\cdots\!04\)\( T^{14} + \)\(33\!\cdots\!21\)\( T^{16} \))(\( ( 1 + 9 T + 4913 T^{2} )^{2} \))(\( ( 1 - 168 T + 30394 T^{2} - 3297180 T^{3} + 380502793 T^{4} - 32690504880 T^{5} + 3022684670725 T^{6} - 221800606656432 T^{7} + 17377623608249734 T^{8} - 1089706380503050416 T^{9} + 72960259804866967525 T^{10} - \)\(38\!\cdots\!60\)\( T^{11} + \)\(22\!\cdots\!73\)\( T^{12} - \)\(94\!\cdots\!40\)\( T^{13} + \)\(42\!\cdots\!46\)\( T^{14} - \)\(11\!\cdots\!56\)\( T^{15} + \)\(33\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 273 T + 54171 T^{2} + 7772238 T^{3} + 968957271 T^{4} + 102002032857 T^{5} + 9773002638042 T^{6} + 833158680136113 T^{7} + 66278147938872399 T^{8} + 4792749919630444854 T^{9} + \)\(32\!\cdots\!87\)\( T^{10} + \)\(20\!\cdots\!97\)\( T^{11} + \)\(11\!\cdots\!74\)\( T^{12} + \)\(59\!\cdots\!77\)\( T^{13} + \)\(27\!\cdots\!03\)\( T^{14} + \)\(10\!\cdots\!42\)\( T^{15} + \)\(37\!\cdots\!07\)\( T^{16} + \)\(92\!\cdots\!33\)\( T^{17} + \)\(16\!\cdots\!73\)\( T^{18} )^{2} \))(\( 1 - 16948 T^{2} + 84203208 T^{4} - 399083701352 T^{6} + 6508712666429186 T^{8} - 42615253832024962764 T^{10} + \)\(11\!\cdots\!04\)\( T^{12} - \)\(92\!\cdots\!84\)\( T^{14} + \)\(77\!\cdots\!75\)\( T^{16} - \)\(22\!\cdots\!96\)\( T^{18} + \)\(66\!\cdots\!44\)\( T^{20} - \)\(59\!\cdots\!76\)\( T^{22} + \)\(22\!\cdots\!06\)\( T^{24} - \)\(32\!\cdots\!48\)\( T^{26} + \)\(16\!\cdots\!48\)\( T^{28} - \)\(80\!\cdots\!72\)\( T^{30} + \)\(11\!\cdots\!41\)\( T^{32} \))
$19$ (\( 1 - 100 T + 6859 T^{2} \))(\( 1 + 110 T + 6859 T^{2} \))(\( 1 + 124 T + 6859 T^{2} \))(\( ( 1 + 20 T + 6859 T^{2} )^{2} \))(\( 1 - 64 T + 6534 T^{2} - 438976 T^{3} + 47045881 T^{4} \))(\( ( 1 - 6859 T^{2} )^{4} \))(\( ( 1 - 5726 T^{2} + 47045881 T^{4} )^{2} \))(\( 1 - 16 T - 6603 T^{2} - 109744 T^{3} + 47045881 T^{4} \))(\( 1 + 49 T - 4458 T^{2} + 336091 T^{3} + 47045881 T^{4} \))(\( 1 - 202 T + 7946 T^{2} - 627636 T^{3} + 247297462 T^{4} - 17185599794 T^{5} + 349471935958 T^{6} - 117876028987046 T^{7} + 11634326968854022 T^{8} - 202530415883220444 T^{9} + 17587000346899715306 T^{10} - \)\(30\!\cdots\!98\)\( T^{11} + \)\(10\!\cdots\!41\)\( T^{12} \))(\( ( 1 + 111 T + 1361 T^{2} - 306138 T^{3} - 11434020 T^{4} - 2099800542 T^{5} + 64029444041 T^{6} + 35818334453469 T^{7} + 2213314919066161 T^{8} )^{2} \))(\( ( 1 + 131 T + 6859 T^{2} )^{2} \))(\( ( 1 - 176 T + 41892 T^{2} - 4833442 T^{3} + 719223515 T^{4} - 65014349322 T^{5} + 7631904477739 T^{6} - 579970516177592 T^{7} + 59026078922135409 T^{8} - 3978017770462103528 T^{9} + \)\(35\!\cdots\!59\)\( T^{10} - \)\(20\!\cdots\!38\)\( T^{11} + \)\(15\!\cdots\!15\)\( T^{12} - \)\(73\!\cdots\!58\)\( T^{13} + \)\(43\!\cdots\!72\)\( T^{14} - \)\(12\!\cdots\!44\)\( T^{15} + \)\(48\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 45 T + 38925 T^{2} - 2601348 T^{3} + 709193457 T^{4} - 62259072669 T^{5} + 8287221918066 T^{6} - 840378579772851 T^{7} + 71702530972816086 T^{8} - 7149895439436435791 T^{9} + \)\(49\!\cdots\!74\)\( T^{10} - \)\(39\!\cdots\!31\)\( T^{11} + \)\(26\!\cdots\!14\)\( T^{12} - \)\(13\!\cdots\!09\)\( T^{13} + \)\(10\!\cdots\!43\)\( T^{14} - \)\(27\!\cdots\!68\)\( T^{15} + \)\(27\!\cdots\!75\)\( T^{16} - \)\(22\!\cdots\!45\)\( T^{17} + \)\(33\!\cdots\!39\)\( T^{18} )^{2} \))(\( ( 1 + 306 T + 57757 T^{2} + 8122770 T^{3} + 990235135 T^{4} + 107235980892 T^{5} + 10750308055972 T^{6} + 990048157019604 T^{7} + 85251569497003126 T^{8} + 6790740308997463836 T^{9} + \)\(50\!\cdots\!32\)\( T^{10} + \)\(34\!\cdots\!68\)\( T^{11} + \)\(21\!\cdots\!35\)\( T^{12} + \)\(12\!\cdots\!30\)\( T^{13} + \)\(60\!\cdots\!37\)\( T^{14} + \)\(21\!\cdots\!14\)\( T^{15} + \)\(48\!\cdots\!21\)\( T^{16} )^{2} \))
$23$ (\( 1 - 42 T + 12167 T^{2} \))(\( 1 + 48 T + 12167 T^{2} \))(\( 1 + 12167 T^{2} \))(\( 1 + 7234 T^{2} + 148035889 T^{4} \))(\( 1 + 6 T + 7870 T^{2} + 73002 T^{3} + 148035889 T^{4} \))(\( 1 + 220762978 T^{4} + 21914624432020321 T^{8} \))(\( ( 1 - 18284 T^{2} + 148035889 T^{4} )^{2} \))(\( 1 + 84 T - 5111 T^{2} + 1022028 T^{3} + 148035889 T^{4} \))(\( 1 + 159 T + 13114 T^{2} + 1934553 T^{3} + 148035889 T^{4} \))(\( 1 - 216 T + 10827 T^{2} - 387864 T^{3} + 53856198 T^{4} + 24653558952 T^{5} - 5413409425505 T^{6} + 299959851768984 T^{7} + 7972650149090022 T^{8} - 698602275885685032 T^{9} + \)\(23\!\cdots\!67\)\( T^{10} - \)\(57\!\cdots\!12\)\( T^{11} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 - 8216 T^{2} + 118915282 T^{4} + 2854931863264 T^{6} - 29264182010625629 T^{8} + \)\(42\!\cdots\!96\)\( T^{10} + \)\(26\!\cdots\!22\)\( T^{12} - \)\(26\!\cdots\!04\)\( T^{14} + \)\(48\!\cdots\!41\)\( T^{16} \))(\( 1 - 12 T - 12023 T^{2} - 146004 T^{3} + 148035889 T^{4} \))(\( 1 + 228 T - 25525 T^{2} - 8731368 T^{3} + 389743110 T^{4} + 187567739154 T^{5} - 2655559094585 T^{6} - 2320959795806634 T^{7} + 15687067961480891 T^{8} + 14915354307460983396 T^{9} - \)\(20\!\cdots\!94\)\( T^{10} + \)\(72\!\cdots\!22\)\( T^{11} + \)\(10\!\cdots\!27\)\( T^{12} - \)\(22\!\cdots\!12\)\( T^{13} - \)\(20\!\cdots\!83\)\( T^{14} + \)\(15\!\cdots\!30\)\( T^{15} + \)\(31\!\cdots\!32\)\( T^{16} + \)\(18\!\cdots\!10\)\( T^{17} - \)\(30\!\cdots\!87\)\( T^{18} - \)\(40\!\cdots\!56\)\( T^{19} + \)\(22\!\cdots\!67\)\( T^{20} + \)\(19\!\cdots\!54\)\( T^{21} - \)\(68\!\cdots\!86\)\( T^{22} + \)\(58\!\cdots\!08\)\( T^{23} + \)\(75\!\cdots\!31\)\( T^{24} - \)\(13\!\cdots\!98\)\( T^{25} - \)\(18\!\cdots\!65\)\( T^{26} + \)\(16\!\cdots\!82\)\( T^{27} + \)\(41\!\cdots\!10\)\( T^{28} - \)\(11\!\cdots\!16\)\( T^{29} - \)\(39\!\cdots\!25\)\( T^{30} + \)\(43\!\cdots\!04\)\( T^{31} + \)\(23\!\cdots\!81\)\( T^{32} \))(\( 1 - 312 T + 23652 T^{2} + 7593588 T^{3} - 2146907142 T^{4} + 183846066258 T^{5} + 18462658479600 T^{6} - 6811755519336540 T^{7} + 751342821079870584 T^{8} + 1069713603046935900 T^{9} - \)\(12\!\cdots\!80\)\( T^{10} + \)\(19\!\cdots\!60\)\( T^{11} - \)\(10\!\cdots\!72\)\( T^{12} - \)\(11\!\cdots\!42\)\( T^{13} + \)\(31\!\cdots\!38\)\( T^{14} - \)\(31\!\cdots\!84\)\( T^{15} + \)\(51\!\cdots\!76\)\( T^{16} + \)\(31\!\cdots\!32\)\( T^{17} - \)\(52\!\cdots\!70\)\( T^{18} + \)\(38\!\cdots\!44\)\( T^{19} + \)\(76\!\cdots\!64\)\( T^{20} - \)\(56\!\cdots\!92\)\( T^{21} + \)\(70\!\cdots\!98\)\( T^{22} - \)\(31\!\cdots\!94\)\( T^{23} - \)\(33\!\cdots\!68\)\( T^{24} + \)\(75\!\cdots\!80\)\( T^{25} - \)\(60\!\cdots\!80\)\( T^{26} + \)\(62\!\cdots\!00\)\( T^{27} + \)\(53\!\cdots\!16\)\( T^{28} - \)\(58\!\cdots\!20\)\( T^{29} + \)\(19\!\cdots\!00\)\( T^{30} + \)\(23\!\cdots\!46\)\( T^{31} - \)\(33\!\cdots\!18\)\( T^{32} + \)\(14\!\cdots\!84\)\( T^{33} + \)\(54\!\cdots\!12\)\( T^{34} - \)\(87\!\cdots\!24\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))(\( 1 + 54964 T^{2} + 1326151704 T^{4} + 25415665738344 T^{6} + 524305919802157986 T^{8} + \)\(89\!\cdots\!72\)\( T^{10} + \)\(12\!\cdots\!96\)\( T^{12} + \)\(17\!\cdots\!32\)\( T^{14} + \)\(23\!\cdots\!87\)\( T^{16} + \)\(25\!\cdots\!48\)\( T^{18} + \)\(26\!\cdots\!16\)\( T^{20} + \)\(28\!\cdots\!68\)\( T^{22} + \)\(25\!\cdots\!26\)\( T^{24} + \)\(18\!\cdots\!56\)\( T^{26} + \)\(13\!\cdots\!44\)\( T^{28} + \)\(85\!\cdots\!56\)\( T^{30} + \)\(23\!\cdots\!81\)\( T^{32} \))
$29$ (\( 1 - 10 T + 24389 T^{2} \))(\( 1 - 110 T + 24389 T^{2} \))(\( 1 + 102 T + 24389 T^{2} \))(\( 1 - 10806 T^{2} + 594823321 T^{4} \))(\( 1 - 252 T + 56446 T^{2} - 6146028 T^{3} + 594823321 T^{4} \))(\( 1 - 739273358 T^{4} + 353814783205469041 T^{8} \))(\( ( 1 - 32936 T^{2} + 594823321 T^{4} )^{2} \))(\( ( 1 - 297 T + 24389 T^{2} )^{2} \))(\( ( 1 + 58 T + 24389 T^{2} )^{2} \))(\( ( 1 + 53 T + 52695 T^{2} + 3410210 T^{3} + 1285178355 T^{4} + 31525636013 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 + 59371 T^{2} + 1802370044 T^{4} + 35315255391091 T^{6} + 353814783205469041 T^{8} )^{2} \))(\( 1 - 260 T + 43211 T^{2} - 6341140 T^{3} + 594823321 T^{4} \))(\( 1 + 618 T + 78015 T^{2} - 22761822 T^{3} - 3949828339 T^{4} + 1033935290616 T^{5} + 177028776333588 T^{6} - 27273811167129462 T^{7} - 2315043616387851764 T^{8} + \)\(10\!\cdots\!86\)\( T^{9} - \)\(62\!\cdots\!16\)\( T^{10} - \)\(23\!\cdots\!26\)\( T^{11} + \)\(40\!\cdots\!20\)\( T^{12} + \)\(56\!\cdots\!76\)\( T^{13} - \)\(14\!\cdots\!49\)\( T^{14} - \)\(28\!\cdots\!74\)\( T^{15} + \)\(48\!\cdots\!01\)\( T^{16} - \)\(68\!\cdots\!86\)\( T^{17} - \)\(87\!\cdots\!29\)\( T^{18} + \)\(81\!\cdots\!44\)\( T^{19} + \)\(14\!\cdots\!20\)\( T^{20} - \)\(20\!\cdots\!74\)\( T^{21} - \)\(13\!\cdots\!76\)\( T^{22} + \)\(53\!\cdots\!94\)\( T^{23} - \)\(28\!\cdots\!84\)\( T^{24} - \)\(83\!\cdots\!58\)\( T^{25} + \)\(13\!\cdots\!88\)\( T^{26} + \)\(18\!\cdots\!24\)\( T^{27} - \)\(17\!\cdots\!19\)\( T^{28} - \)\(24\!\cdots\!18\)\( T^{29} + \)\(20\!\cdots\!15\)\( T^{30} + \)\(39\!\cdots\!82\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 378 T - 60390 T^{2} + 32343264 T^{3} + 3419158491 T^{4} - 1712659382352 T^{5} - 178308643692966 T^{6} + 67132136829713688 T^{7} + 7500583452138631965 T^{8} - \)\(19\!\cdots\!76\)\( T^{9} - \)\(27\!\cdots\!36\)\( T^{10} + \)\(45\!\cdots\!58\)\( T^{11} + \)\(86\!\cdots\!44\)\( T^{12} - \)\(83\!\cdots\!12\)\( T^{13} - \)\(23\!\cdots\!01\)\( T^{14} + \)\(11\!\cdots\!00\)\( T^{15} + \)\(62\!\cdots\!42\)\( T^{16} - \)\(79\!\cdots\!32\)\( T^{17} - \)\(15\!\cdots\!07\)\( T^{18} - \)\(19\!\cdots\!48\)\( T^{19} + \)\(36\!\cdots\!82\)\( T^{20} + \)\(16\!\cdots\!00\)\( T^{21} - \)\(84\!\cdots\!41\)\( T^{22} - \)\(71\!\cdots\!88\)\( T^{23} + \)\(18\!\cdots\!84\)\( T^{24} + \)\(23\!\cdots\!82\)\( T^{25} - \)\(33\!\cdots\!16\)\( T^{26} - \)\(60\!\cdots\!84\)\( T^{27} + \)\(55\!\cdots\!65\)\( T^{28} + \)\(12\!\cdots\!32\)\( T^{29} - \)\(78\!\cdots\!86\)\( T^{30} - \)\(18\!\cdots\!88\)\( T^{31} + \)\(90\!\cdots\!31\)\( T^{32} + \)\(20\!\cdots\!36\)\( T^{33} - \)\(94\!\cdots\!90\)\( T^{34} - \)\(14\!\cdots\!62\)\( T^{35} + \)\(93\!\cdots\!81\)\( T^{36} \))(\( ( 1 - 102034 T^{2} + 6213617737 T^{4} - 245008733294114 T^{6} + 7064972052959541764 T^{8} - \)\(14\!\cdots\!94\)\( T^{10} + \)\(21\!\cdots\!17\)\( T^{12} - \)\(21\!\cdots\!74\)\( T^{14} + \)\(12\!\cdots\!81\)\( T^{16} )^{2} \))
$31$ (\( 1 + 48 T + 29791 T^{2} \))(\( 1 - 12 T + 29791 T^{2} \))(\( 1 + 160 T + 29791 T^{2} \))(\( ( 1 - 156 T + 29791 T^{2} )^{2} \))(\( 1 - 40 T - 13890 T^{2} - 1191640 T^{3} + 887503681 T^{4} \))(\( ( 1 - 29791 T^{2} )^{4} \))(\( ( 1 - 2750 T^{2} + 887503681 T^{4} )^{2} \))(\( 1 - 253 T + 34218 T^{2} - 7537123 T^{3} + 887503681 T^{4} \))(\( 1 + 147 T - 8182 T^{2} + 4379277 T^{3} + 887503681 T^{4} \))(\( 1 - 95 T - 70347 T^{2} + 3756594 T^{3} + 3398738767 T^{4} - 83374434539 T^{5} - 110906046363338 T^{6} - 2483807779351349 T^{7} + 3016393166469901327 T^{8} + 99322925971043714574 T^{9} - \)\(55\!\cdots\!67\)\( T^{10} - \)\(22\!\cdots\!45\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} \))(\( ( 1 + 110 T - 31207 T^{2} - 1790250 T^{3} + 627521468 T^{4} - 53333337750 T^{5} - 27696327372967 T^{6} + 2908358437673810 T^{7} + 787662783788549761 T^{8} )^{2} \))(\( 1 - 54 T - 26875 T^{2} - 1608714 T^{3} + 887503681 T^{4} \))(\( 1 + 72 T - 122345 T^{2} - 12759228 T^{3} + 7008800553 T^{4} + 937649058354 T^{5} - 246288843940504 T^{6} - 39508523240638446 T^{7} + 6189681260162427926 T^{8} + \)\(11\!\cdots\!06\)\( T^{9} - \)\(13\!\cdots\!30\)\( T^{10} - \)\(31\!\cdots\!70\)\( T^{11} + \)\(21\!\cdots\!42\)\( T^{12} + \)\(78\!\cdots\!78\)\( T^{13} + \)\(73\!\cdots\!79\)\( T^{14} - \)\(99\!\cdots\!06\)\( T^{15} - \)\(13\!\cdots\!55\)\( T^{16} - \)\(29\!\cdots\!46\)\( T^{17} + \)\(64\!\cdots\!99\)\( T^{18} + \)\(20\!\cdots\!38\)\( T^{19} + \)\(17\!\cdots\!62\)\( T^{20} - \)\(74\!\cdots\!70\)\( T^{21} - \)\(93\!\cdots\!30\)\( T^{22} + \)\(24\!\cdots\!86\)\( T^{23} + \)\(38\!\cdots\!46\)\( T^{24} - \)\(73\!\cdots\!06\)\( T^{25} - \)\(13\!\cdots\!04\)\( T^{26} + \)\(15\!\cdots\!14\)\( T^{27} + \)\(34\!\cdots\!93\)\( T^{28} - \)\(18\!\cdots\!88\)\( T^{29} - \)\(53\!\cdots\!45\)\( T^{30} + \)\(93\!\cdots\!72\)\( T^{31} + \)\(38\!\cdots\!41\)\( T^{32} \))(\( 1 + 18 T - 151704 T^{2} - 4525968 T^{3} + 10857610485 T^{4} + 400645742382 T^{5} - 526464550327740 T^{6} - 16887794293815498 T^{7} + 21797169327038746179 T^{8} + \)\(35\!\cdots\!70\)\( T^{9} - \)\(87\!\cdots\!96\)\( T^{10} - \)\(45\!\cdots\!86\)\( T^{11} + \)\(33\!\cdots\!94\)\( T^{12} + \)\(16\!\cdots\!14\)\( T^{13} - \)\(11\!\cdots\!61\)\( T^{14} - \)\(77\!\cdots\!40\)\( T^{15} + \)\(36\!\cdots\!74\)\( T^{16} + \)\(12\!\cdots\!18\)\( T^{17} - \)\(10\!\cdots\!65\)\( T^{18} + \)\(35\!\cdots\!38\)\( T^{19} + \)\(32\!\cdots\!94\)\( T^{20} - \)\(20\!\cdots\!40\)\( T^{21} - \)\(92\!\cdots\!21\)\( T^{22} + \)\(39\!\cdots\!14\)\( T^{23} + \)\(23\!\cdots\!54\)\( T^{24} - \)\(94\!\cdots\!66\)\( T^{25} - \)\(54\!\cdots\!16\)\( T^{26} + \)\(65\!\cdots\!70\)\( T^{27} + \)\(12\!\cdots\!79\)\( T^{28} - \)\(27\!\cdots\!18\)\( T^{29} - \)\(25\!\cdots\!40\)\( T^{30} + \)\(58\!\cdots\!22\)\( T^{31} + \)\(47\!\cdots\!85\)\( T^{32} - \)\(58\!\cdots\!68\)\( T^{33} - \)\(58\!\cdots\!64\)\( T^{34} + \)\(20\!\cdots\!58\)\( T^{35} + \)\(34\!\cdots\!21\)\( T^{36} \))(\( ( 1 - 564 T + 243388 T^{2} - 77468784 T^{3} + 21469133071 T^{4} - 5073861272220 T^{5} + 1094289736794676 T^{6} - 211880592093523344 T^{7} + 38213365513366414528 T^{8} - \)\(63\!\cdots\!04\)\( T^{9} + \)\(97\!\cdots\!56\)\( T^{10} - \)\(13\!\cdots\!20\)\( T^{11} + \)\(16\!\cdots\!31\)\( T^{12} - \)\(18\!\cdots\!84\)\( T^{13} + \)\(17\!\cdots\!08\)\( T^{14} - \)\(11\!\cdots\!84\)\( T^{15} + \)\(62\!\cdots\!21\)\( T^{16} )^{2} \))
$37$ (\( 1 + 246 T + 50653 T^{2} \))(\( 1 + 246 T + 50653 T^{2} \))(\( 1 - 398 T + 50653 T^{2} \))(\( ( 1 - 186 T + 50653 T^{2} )^{2} \))(\( 1 + 248 T + 98214 T^{2} + 12561944 T^{3} + 2565726409 T^{4} \))(\( ( 1 + 101194 T^{2} + 2565726409 T^{4} )^{2} \))(\( ( 1 + 184 T + 50653 T^{2} )^{4} \))(\( 1 - 316 T + 49203 T^{2} - 16006348 T^{3} + 2565726409 T^{4} \))(\( 1 + 219 T - 2692 T^{2} + 11093007 T^{3} + 2565726409 T^{4} \))(\( 1 + 262 T - 97404 T^{2} - 9678072 T^{3} + 12194182072 T^{4} + 680381910454 T^{5} - 605701122868778 T^{6} + 34463384910226462 T^{7} + 31286934978284739448 T^{8} - \)\(12\!\cdots\!44\)\( T^{9} - \)\(64\!\cdots\!24\)\( T^{10} + \)\(87\!\cdots\!66\)\( T^{11} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( ( 1 - 187 T - 44923 T^{2} + 4004418 T^{3} + 2045720498 T^{4} + 202835784954 T^{5} - 115260127471507 T^{6} - 24302845341679399 T^{7} + 6582952005840035281 T^{8} )^{2} \))(\( ( 1 + 246 T + 50653 T^{2} )^{2} \))(\( ( 1 - 210 T + 273581 T^{2} - 62260500 T^{3} + 37970446276 T^{4} - 8100635347836 T^{5} + 3402478745034716 T^{6} - 624886705874379210 T^{7} + \)\(20\!\cdots\!28\)\( T^{8} - \)\(31\!\cdots\!30\)\( T^{9} + \)\(87\!\cdots\!44\)\( T^{10} - \)\(10\!\cdots\!72\)\( T^{11} + \)\(24\!\cdots\!56\)\( T^{12} - \)\(20\!\cdots\!00\)\( T^{13} + \)\(46\!\cdots\!49\)\( T^{14} - \)\(17\!\cdots\!70\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 36 T + 281574 T^{2} + 8355144 T^{3} + 38702854413 T^{4} + 1148561406576 T^{5} + 3497796368226528 T^{6} + 108726691647213162 T^{7} + \)\(23\!\cdots\!32\)\( T^{8} + \)\(68\!\cdots\!80\)\( T^{9} + \)\(11\!\cdots\!96\)\( T^{10} + \)\(27\!\cdots\!58\)\( T^{11} + \)\(45\!\cdots\!56\)\( T^{12} + \)\(75\!\cdots\!56\)\( T^{13} + \)\(12\!\cdots\!09\)\( T^{14} + \)\(14\!\cdots\!76\)\( T^{15} + \)\(24\!\cdots\!38\)\( T^{16} + \)\(15\!\cdots\!96\)\( T^{17} + \)\(21\!\cdots\!33\)\( T^{18} )^{2} \))(\( ( 1 + 598 T + 47601 T^{2} - 11729418 T^{3} + 10699876539 T^{4} + 3891656263464 T^{5} + 114219217143080 T^{6} + 66547288562775176 T^{7} + 48227467333244423670 T^{8} + \)\(33\!\cdots\!28\)\( T^{9} + \)\(29\!\cdots\!20\)\( T^{10} + \)\(50\!\cdots\!28\)\( T^{11} + \)\(70\!\cdots\!59\)\( T^{12} - \)\(39\!\cdots\!74\)\( T^{13} + \)\(80\!\cdots\!29\)\( T^{14} + \)\(51\!\cdots\!26\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))
$41$ (\( 1 - 248 T + 68921 T^{2} \))(\( 1 + 182 T + 68921 T^{2} \))(\( 1 - 318 T + 68921 T^{2} \))(\( 1 + 110406 T^{2} + 4750104241 T^{4} \))(\( 1 - 450 T + 175642 T^{2} - 31014450 T^{3} + 4750104241 T^{4} \))(\( ( 1 + 68921 T^{2} )^{4} \))(\( ( 1 + 126742 T^{2} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 360 T + 68921 T^{2} )^{2} \))(\( ( 1 + 350 T + 68921 T^{2} )^{2} \))(\( ( 1 + 244 T + 187983 T^{2} + 33933832 T^{3} + 12955976343 T^{4} + 1159025434804 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 + 85540 T^{2} + 8435951270 T^{4} + 406323916775140 T^{6} + 22563490300366186081 T^{8} )^{2} \))(\( 1 + 383 T + 77768 T^{2} + 26396743 T^{3} + 4750104241 T^{4} \))(\( 1 + 420 T - 287838 T^{2} - 111388608 T^{3} + 54335362343 T^{4} + 15821993821032 T^{5} - 8270886127177332 T^{6} - 1582199089188412056 T^{7} + \)\(10\!\cdots\!33\)\( T^{8} + \)\(12\!\cdots\!60\)\( T^{9} - \)\(10\!\cdots\!02\)\( T^{10} - \)\(76\!\cdots\!28\)\( T^{11} + \)\(94\!\cdots\!59\)\( T^{12} + \)\(33\!\cdots\!24\)\( T^{13} - \)\(74\!\cdots\!76\)\( T^{14} - \)\(72\!\cdots\!96\)\( T^{15} + \)\(54\!\cdots\!89\)\( T^{16} - \)\(50\!\cdots\!16\)\( T^{17} - \)\(35\!\cdots\!16\)\( T^{18} + \)\(10\!\cdots\!64\)\( T^{19} + \)\(21\!\cdots\!79\)\( T^{20} - \)\(11\!\cdots\!28\)\( T^{21} - \)\(11\!\cdots\!42\)\( T^{22} + \)\(92\!\cdots\!60\)\( T^{23} + \)\(53\!\cdots\!13\)\( T^{24} - \)\(55\!\cdots\!36\)\( T^{25} - \)\(20\!\cdots\!32\)\( T^{26} + \)\(26\!\cdots\!72\)\( T^{27} + \)\(62\!\cdots\!63\)\( T^{28} - \)\(88\!\cdots\!88\)\( T^{29} - \)\(15\!\cdots\!78\)\( T^{30} + \)\(15\!\cdots\!20\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 - 477 T - 127026 T^{2} + 100179549 T^{3} + 2571445512 T^{4} - 11016504815049 T^{5} + 1080814638078678 T^{6} + 755078533104102165 T^{7} - \)\(14\!\cdots\!48\)\( T^{8} - \)\(45\!\cdots\!21\)\( T^{9} + \)\(14\!\cdots\!62\)\( T^{10} + \)\(27\!\cdots\!73\)\( T^{11} - \)\(13\!\cdots\!36\)\( T^{12} - \)\(11\!\cdots\!33\)\( T^{13} + \)\(10\!\cdots\!90\)\( T^{14} + \)\(91\!\cdots\!65\)\( T^{15} - \)\(58\!\cdots\!00\)\( T^{16} + \)\(79\!\cdots\!71\)\( T^{17} + \)\(33\!\cdots\!44\)\( T^{18} + \)\(54\!\cdots\!91\)\( T^{19} - \)\(27\!\cdots\!00\)\( T^{20} + \)\(30\!\cdots\!65\)\( T^{21} + \)\(23\!\cdots\!90\)\( T^{22} - \)\(18\!\cdots\!33\)\( T^{23} - \)\(14\!\cdots\!56\)\( T^{24} + \)\(20\!\cdots\!93\)\( T^{25} + \)\(75\!\cdots\!82\)\( T^{26} - \)\(15\!\cdots\!01\)\( T^{27} - \)\(35\!\cdots\!48\)\( T^{28} + \)\(12\!\cdots\!65\)\( T^{29} + \)\(12\!\cdots\!98\)\( T^{30} - \)\(87\!\cdots\!89\)\( T^{31} + \)\(14\!\cdots\!72\)\( T^{32} + \)\(37\!\cdots\!49\)\( T^{33} - \)\(32\!\cdots\!46\)\( T^{34} - \)\(85\!\cdots\!57\)\( T^{35} + \)\(12\!\cdots\!61\)\( T^{36} \))(\( ( 1 + 148396 T^{2} + 19955386648 T^{4} + 1828971842691940 T^{6} + \)\(14\!\cdots\!50\)\( T^{8} + \)\(86\!\cdots\!40\)\( T^{10} + \)\(45\!\cdots\!88\)\( T^{12} + \)\(15\!\cdots\!16\)\( T^{14} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))
$43$ (\( 1 - 68 T + 79507 T^{2} \))(\( 1 - 128 T + 79507 T^{2} \))(\( 1 + 268 T + 79507 T^{2} \))(\( ( 1 - 164 T + 79507 T^{2} )^{2} \))(\( 1 - 376 T + 161526 T^{2} - 29894632 T^{3} + 6321363049 T^{4} \))(\( ( 1 - 126614 T^{2} + 6321363049 T^{4} )^{2} \))(\( ( 1 + 190 T + 79507 T^{2} )^{4} \))(\( ( 1 - 26 T + 79507 T^{2} )^{2} \))(\( ( 1 + 124 T + 79507 T^{2} )^{2} \))(\( ( 1 - 360 T + 166158 T^{2} - 38975294 T^{3} + 13210724106 T^{4} - 2275690697640 T^{5} + 502592611936843 T^{6} )^{2} \))(\( ( 1 + 419 T + 167730 T^{2} + 33313433 T^{3} + 6321363049 T^{4} )^{4} \))(\( 1 - 169 T - 50946 T^{2} - 13436683 T^{3} + 6321363049 T^{4} \))(\( 1 - 2 T - 174923 T^{2} - 18126802 T^{3} + 6568829129 T^{4} + 3504431725334 T^{5} + 1175920450315236 T^{6} - 266898513634748244 T^{7} - \)\(13\!\cdots\!38\)\( T^{8} - \)\(25\!\cdots\!48\)\( T^{9} + \)\(33\!\cdots\!62\)\( T^{10} + \)\(20\!\cdots\!40\)\( T^{11} + \)\(30\!\cdots\!22\)\( T^{12} - \)\(22\!\cdots\!90\)\( T^{13} - \)\(31\!\cdots\!27\)\( T^{14} + \)\(89\!\cdots\!28\)\( T^{15} + \)\(20\!\cdots\!33\)\( T^{16} + \)\(70\!\cdots\!96\)\( T^{17} - \)\(19\!\cdots\!23\)\( T^{18} - \)\(11\!\cdots\!70\)\( T^{19} + \)\(12\!\cdots\!22\)\( T^{20} + \)\(65\!\cdots\!80\)\( T^{21} + \)\(85\!\cdots\!38\)\( T^{22} - \)\(50\!\cdots\!64\)\( T^{23} - \)\(21\!\cdots\!38\)\( T^{24} - \)\(33\!\cdots\!08\)\( T^{25} + \)\(11\!\cdots\!64\)\( T^{26} + \)\(28\!\cdots\!62\)\( T^{27} + \)\(41\!\cdots\!29\)\( T^{28} - \)\(91\!\cdots\!14\)\( T^{29} - \)\(70\!\cdots\!27\)\( T^{30} - \)\(64\!\cdots\!86\)\( T^{31} + \)\(25\!\cdots\!01\)\( T^{32} \))(\( 1 - 171 T - 426483 T^{2} + 41179794 T^{3} + 94371482016 T^{4} - 2792580312384 T^{5} - 14659227739710609 T^{6} - 180703342390066785 T^{7} + \)\(18\!\cdots\!01\)\( T^{8} + \)\(46\!\cdots\!68\)\( T^{9} - \)\(19\!\cdots\!62\)\( T^{10} - \)\(38\!\cdots\!24\)\( T^{11} + \)\(20\!\cdots\!12\)\( T^{12} + \)\(14\!\cdots\!10\)\( T^{13} - \)\(19\!\cdots\!79\)\( T^{14} + \)\(18\!\cdots\!13\)\( T^{15} + \)\(17\!\cdots\!51\)\( T^{16} - \)\(25\!\cdots\!86\)\( T^{17} - \)\(14\!\cdots\!28\)\( T^{18} - \)\(20\!\cdots\!02\)\( T^{19} + \)\(11\!\cdots\!99\)\( T^{20} + \)\(95\!\cdots\!59\)\( T^{21} - \)\(77\!\cdots\!79\)\( T^{22} + \)\(45\!\cdots\!70\)\( T^{23} + \)\(50\!\cdots\!88\)\( T^{24} - \)\(77\!\cdots\!32\)\( T^{25} - \)\(31\!\cdots\!62\)\( T^{26} + \)\(59\!\cdots\!76\)\( T^{27} + \)\(18\!\cdots\!49\)\( T^{28} - \)\(14\!\cdots\!55\)\( T^{29} - \)\(93\!\cdots\!09\)\( T^{30} - \)\(14\!\cdots\!88\)\( T^{31} + \)\(38\!\cdots\!84\)\( T^{32} + \)\(13\!\cdots\!42\)\( T^{33} - \)\(10\!\cdots\!83\)\( T^{34} - \)\(34\!\cdots\!97\)\( T^{35} + \)\(16\!\cdots\!49\)\( T^{36} \))(\( ( 1 - 82 T + 122239 T^{2} - 47448038 T^{3} + 6939760430 T^{4} - 3772451157266 T^{5} + 772717097746711 T^{6} - 41212594178821126 T^{7} + 39959630797262576401 T^{8} )^{4} \))
$47$ (\( 1 + 324 T + 103823 T^{2} \))(\( 1 + 324 T + 103823 T^{2} \))(\( 1 + 240 T + 103823 T^{2} \))(\( 1 - 13970 T^{2} + 10779215329 T^{4} \))(\( 1 - 12 T + 141790 T^{2} - 1245876 T^{3} + 10779215329 T^{4} \))(\( ( 1 + 103823 T^{2} )^{4} \))(\( ( 1 + 205870 T^{2} + 10779215329 T^{4} )^{2} \))(\( 1 + 30 T - 102923 T^{2} + 3114690 T^{3} + 10779215329 T^{4} \))(\( 1 - 525 T + 171802 T^{2} - 54507075 T^{3} + 10779215329 T^{4} \))(\( 1 + 210 T - 20853 T^{2} - 83809446 T^{3} - 12756928590 T^{4} + 2596137940074 T^{5} + 3698984470026571 T^{6} + 269538829352302902 T^{7} - \)\(13\!\cdots\!10\)\( T^{8} - \)\(93\!\cdots\!82\)\( T^{9} - \)\(24\!\cdots\!73\)\( T^{10} + \)\(25\!\cdots\!30\)\( T^{11} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 - 279692 T^{2} + 37152412138 T^{4} - 5458685013243056 T^{6} + \)\(72\!\cdots\!79\)\( T^{8} - \)\(58\!\cdots\!24\)\( T^{10} + \)\(43\!\cdots\!58\)\( T^{12} - \)\(35\!\cdots\!88\)\( T^{14} + \)\(13\!\cdots\!81\)\( T^{16} \))(\( 1 + 96 T - 94607 T^{2} + 9967008 T^{3} + 10779215329 T^{4} \))(\( 1 + 570 T - 504019 T^{2} - 269131554 T^{3} + 178645227255 T^{4} + 75997022312142 T^{5} - 48054772790072906 T^{6} - 15112394704504881348 T^{7} + \)\(10\!\cdots\!88\)\( T^{8} + \)\(22\!\cdots\!32\)\( T^{9} - \)\(18\!\cdots\!92\)\( T^{10} - \)\(26\!\cdots\!90\)\( T^{11} + \)\(28\!\cdots\!88\)\( T^{12} + \)\(22\!\cdots\!72\)\( T^{13} - \)\(37\!\cdots\!29\)\( T^{14} - \)\(88\!\cdots\!70\)\( T^{15} + \)\(41\!\cdots\!29\)\( T^{16} - \)\(91\!\cdots\!10\)\( T^{17} - \)\(40\!\cdots\!41\)\( T^{18} + \)\(24\!\cdots\!24\)\( T^{19} + \)\(33\!\cdots\!08\)\( T^{20} - \)\(32\!\cdots\!70\)\( T^{21} - \)\(23\!\cdots\!88\)\( T^{22} + \)\(29\!\cdots\!04\)\( T^{23} + \)\(14\!\cdots\!28\)\( T^{24} - \)\(21\!\cdots\!24\)\( T^{25} - \)\(69\!\cdots\!94\)\( T^{26} + \)\(11\!\cdots\!34\)\( T^{27} + \)\(28\!\cdots\!55\)\( T^{28} - \)\(43\!\cdots\!82\)\( T^{29} - \)\(85\!\cdots\!71\)\( T^{30} + \)\(10\!\cdots\!90\)\( T^{31} + \)\(18\!\cdots\!61\)\( T^{32} \))(\( 1 - 654 T - 251046 T^{2} + 153655848 T^{3} + 85771776033 T^{4} - 28676474262762 T^{5} - 16055837602998162 T^{6} + 2281442852927326800 T^{7} + \)\(22\!\cdots\!57\)\( T^{8} + \)\(20\!\cdots\!18\)\( T^{9} - \)\(18\!\cdots\!38\)\( T^{10} - \)\(31\!\cdots\!46\)\( T^{11} + \)\(24\!\cdots\!44\)\( T^{12} + \)\(48\!\cdots\!18\)\( T^{13} + \)\(18\!\cdots\!23\)\( T^{14} - \)\(35\!\cdots\!40\)\( T^{15} - \)\(36\!\cdots\!04\)\( T^{16} + \)\(17\!\cdots\!68\)\( T^{17} + \)\(42\!\cdots\!95\)\( T^{18} + \)\(17\!\cdots\!64\)\( T^{19} - \)\(39\!\cdots\!16\)\( T^{20} - \)\(40\!\cdots\!80\)\( T^{21} + \)\(21\!\cdots\!43\)\( T^{22} + \)\(58\!\cdots\!74\)\( T^{23} + \)\(31\!\cdots\!16\)\( T^{24} - \)\(41\!\cdots\!62\)\( T^{25} - \)\(25\!\cdots\!78\)\( T^{26} + \)\(28\!\cdots\!34\)\( T^{27} + \)\(33\!\cdots\!93\)\( T^{28} + \)\(34\!\cdots\!00\)\( T^{29} - \)\(25\!\cdots\!02\)\( T^{30} - \)\(46\!\cdots\!46\)\( T^{31} + \)\(14\!\cdots\!97\)\( T^{32} + \)\(26\!\cdots\!36\)\( T^{33} - \)\(45\!\cdots\!06\)\( T^{34} - \)\(12\!\cdots\!62\)\( T^{35} + \)\(19\!\cdots\!69\)\( T^{36} \))(\( 1 - 358312 T^{2} + 90535322508 T^{4} - 16795335458693168 T^{6} + \)\(25\!\cdots\!46\)\( T^{8} - \)\(33\!\cdots\!96\)\( T^{10} + \)\(39\!\cdots\!64\)\( T^{12} - \)\(42\!\cdots\!76\)\( T^{14} + \)\(45\!\cdots\!75\)\( T^{16} - \)\(46\!\cdots\!04\)\( T^{18} + \)\(46\!\cdots\!24\)\( T^{20} - \)\(42\!\cdots\!44\)\( T^{22} + \)\(35\!\cdots\!26\)\( T^{24} - \)\(24\!\cdots\!32\)\( T^{26} + \)\(14\!\cdots\!68\)\( T^{28} - \)\(60\!\cdots\!08\)\( T^{30} + \)\(18\!\cdots\!61\)\( T^{32} \))
$53$ (\( 1 + 258 T + 148877 T^{2} \))(\( 1 - 162 T + 148877 T^{2} \))(\( 1 - 498 T + 148877 T^{2} \))(\( 1 + 273130 T^{2} + 22164361129 T^{4} \))(\( 1 - 1104 T + 602230 T^{2} - 164360208 T^{3} + 22164361129 T^{4} \))(\( 1 - 41794002542 T^{4} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( ( 1 - 169736 T^{2} + 22164361129 T^{4} )^{2} \))(\( 1 - 363 T - 17108 T^{2} - 54042351 T^{3} + 22164361129 T^{4} \))(\( 1 - 303 T - 57068 T^{2} - 45109731 T^{3} + 22164361129 T^{4} \))(\( 1 - 393 T - 211446 T^{2} + 23899125 T^{3} + 46453564620 T^{4} + 3425920762143 T^{5} - 9724787230272680 T^{6} + 510040805305563411 T^{7} + \)\(10\!\cdots\!80\)\( T^{8} + \)\(78\!\cdots\!25\)\( T^{9} - \)\(10\!\cdots\!86\)\( T^{10} - \)\(28\!\cdots\!01\)\( T^{11} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 - 574307 T^{2} + 203127896557 T^{4} - 47306765339926238 T^{6} + \)\(82\!\cdots\!02\)\( T^{8} - \)\(10\!\cdots\!02\)\( T^{10} + \)\(99\!\cdots\!37\)\( T^{12} - \)\(62\!\cdots\!23\)\( T^{14} + \)\(24\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 300 T + 148877 T^{2} )^{2} \))(\( ( 1 - 528 T + 603082 T^{2} - 112356498 T^{3} + 113056847713 T^{4} - 1488977365716 T^{5} + 24102465385714279 T^{6} - 3059793563504889246 T^{7} + \)\(52\!\cdots\!50\)\( T^{8} - \)\(45\!\cdots\!42\)\( T^{9} + \)\(53\!\cdots\!91\)\( T^{10} - \)\(49\!\cdots\!28\)\( T^{11} + \)\(55\!\cdots\!33\)\( T^{12} - \)\(82\!\cdots\!86\)\( T^{13} + \)\(65\!\cdots\!98\)\( T^{14} - \)\(85\!\cdots\!84\)\( T^{15} + \)\(24\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 948 T + 1389591 T^{2} + 911764422 T^{3} + 747220561587 T^{4} + 372226870112574 T^{5} + 221418756940245828 T^{6} + 89663338994683246554 T^{7} + \)\(43\!\cdots\!01\)\( T^{8} + \)\(15\!\cdots\!16\)\( T^{9} + \)\(65\!\cdots\!77\)\( T^{10} + \)\(19\!\cdots\!66\)\( T^{11} + \)\(73\!\cdots\!24\)\( T^{12} + \)\(18\!\cdots\!34\)\( T^{13} + \)\(54\!\cdots\!59\)\( T^{14} + \)\(99\!\cdots\!58\)\( T^{15} + \)\(22\!\cdots\!23\)\( T^{16} + \)\(22\!\cdots\!88\)\( T^{17} + \)\(35\!\cdots\!37\)\( T^{18} )^{2} \))(\( 1 + 506674 T^{2} + 85866141819 T^{4} + 10208516436240318 T^{6} + \)\(32\!\cdots\!49\)\( T^{8} + \)\(63\!\cdots\!00\)\( T^{10} + \)\(61\!\cdots\!74\)\( T^{12} + \)\(12\!\cdots\!24\)\( T^{14} + \)\(28\!\cdots\!38\)\( T^{16} + \)\(27\!\cdots\!96\)\( T^{18} + \)\(30\!\cdots\!34\)\( T^{20} + \)\(69\!\cdots\!00\)\( T^{22} + \)\(77\!\cdots\!69\)\( T^{24} + \)\(54\!\cdots\!82\)\( T^{26} + \)\(10\!\cdots\!99\)\( T^{28} + \)\(13\!\cdots\!66\)\( T^{30} + \)\(58\!\cdots\!61\)\( T^{32} \))
$59$ (\( 1 + 120 T + 205379 T^{2} \))(\( 1 + 810 T + 205379 T^{2} \))(\( 1 - 132 T + 205379 T^{2} \))(\( 1 + 386134 T^{2} + 42180533641 T^{4} \))(\( 1 + 804 T + 380614 T^{2} + 165124716 T^{3} + 42180533641 T^{4} \))(\( ( 1 + 205379 T^{2} )^{4} \))(\( ( 1 + 403654 T^{2} + 42180533641 T^{4} )^{2} \))(\( 1 + 15 T - 205154 T^{2} + 3080685 T^{3} + 42180533641 T^{4} \))(\( 1 + 105 T - 194354 T^{2} + 21564795 T^{3} + 42180533641 T^{4} \))(\( 1 - 1143 T + 557208 T^{2} - 118327563 T^{3} - 14314666608 T^{4} + 27063102119841 T^{5} - 16891447327378130 T^{6} + 5558192850270824739 T^{7} - \)\(60\!\cdots\!28\)\( T^{8} - \)\(10\!\cdots\!57\)\( T^{9} + \)\(99\!\cdots\!48\)\( T^{10} - \)\(41\!\cdots\!57\)\( T^{11} + \)\(75\!\cdots\!21\)\( T^{12} \))(\( 1 - 615851 T^{2} + 202986056233 T^{4} - 56612306828303786 T^{6} + \)\(13\!\cdots\!02\)\( T^{8} - \)\(23\!\cdots\!26\)\( T^{10} + \)\(36\!\cdots\!73\)\( T^{12} - \)\(46\!\cdots\!71\)\( T^{14} + \)\(31\!\cdots\!61\)\( T^{16} \))(\( 1 + 429 T - 21338 T^{2} + 88107591 T^{3} + 42180533641 T^{4} \))(\( 1 - 150 T - 946117 T^{2} + 200189070 T^{3} + 428040629955 T^{4} - 107278598640996 T^{5} - 129587827131610502 T^{6} + 31309587455023028910 T^{7} + \)\(32\!\cdots\!18\)\( T^{8} - \)\(58\!\cdots\!30\)\( T^{9} - \)\(81\!\cdots\!26\)\( T^{10} + \)\(89\!\cdots\!28\)\( T^{11} + \)\(19\!\cdots\!14\)\( T^{12} - \)\(13\!\cdots\!46\)\( T^{13} - \)\(43\!\cdots\!67\)\( T^{14} + \)\(10\!\cdots\!64\)\( T^{15} + \)\(89\!\cdots\!65\)\( T^{16} + \)\(22\!\cdots\!56\)\( T^{17} - \)\(18\!\cdots\!47\)\( T^{18} - \)\(11\!\cdots\!94\)\( T^{19} + \)\(34\!\cdots\!34\)\( T^{20} + \)\(32\!\cdots\!72\)\( T^{21} - \)\(61\!\cdots\!46\)\( T^{22} - \)\(90\!\cdots\!70\)\( T^{23} + \)\(10\!\cdots\!98\)\( T^{24} + \)\(20\!\cdots\!90\)\( T^{25} - \)\(17\!\cdots\!02\)\( T^{26} - \)\(29\!\cdots\!84\)\( T^{27} + \)\(24\!\cdots\!55\)\( T^{28} + \)\(23\!\cdots\!30\)\( T^{29} - \)\(22\!\cdots\!77\)\( T^{30} - \)\(73\!\cdots\!50\)\( T^{31} + \)\(10\!\cdots\!21\)\( T^{32} \))(\( 1 - 957 T - 98361 T^{2} + 735477084 T^{3} - 430472366334 T^{4} - 49716354336762 T^{5} + 192187410340337805 T^{6} - 91904385221774360049 T^{7} - \)\(61\!\cdots\!81\)\( T^{8} + \)\(28\!\cdots\!02\)\( T^{9} - \)\(12\!\cdots\!44\)\( T^{10} - \)\(36\!\cdots\!02\)\( T^{11} + \)\(30\!\cdots\!30\)\( T^{12} - \)\(12\!\cdots\!04\)\( T^{13} - \)\(90\!\cdots\!67\)\( T^{14} + \)\(29\!\cdots\!63\)\( T^{15} - \)\(91\!\cdots\!89\)\( T^{16} - \)\(23\!\cdots\!18\)\( T^{17} + \)\(26\!\cdots\!32\)\( T^{18} - \)\(47\!\cdots\!22\)\( T^{19} - \)\(38\!\cdots\!49\)\( T^{20} + \)\(25\!\cdots\!57\)\( T^{21} - \)\(16\!\cdots\!27\)\( T^{22} - \)\(47\!\cdots\!96\)\( T^{23} + \)\(23\!\cdots\!30\)\( T^{24} - \)\(56\!\cdots\!18\)\( T^{25} - \)\(41\!\cdots\!84\)\( T^{26} + \)\(18\!\cdots\!38\)\( T^{27} - \)\(82\!\cdots\!81\)\( T^{28} - \)\(25\!\cdots\!71\)\( T^{29} + \)\(10\!\cdots\!05\)\( T^{30} - \)\(57\!\cdots\!18\)\( T^{31} - \)\(10\!\cdots\!54\)\( T^{32} + \)\(35\!\cdots\!16\)\( T^{33} - \)\(98\!\cdots\!81\)\( T^{34} - \)\(19\!\cdots\!63\)\( T^{35} + \)\(42\!\cdots\!61\)\( T^{36} \))(\( 1 - 399442 T^{2} + 89994325083 T^{4} - 32591407040941742 T^{6} + \)\(78\!\cdots\!45\)\( T^{8} - \)\(13\!\cdots\!56\)\( T^{10} + \)\(43\!\cdots\!26\)\( T^{12} - \)\(98\!\cdots\!64\)\( T^{14} + \)\(16\!\cdots\!22\)\( T^{16} - \)\(41\!\cdots\!24\)\( T^{18} + \)\(77\!\cdots\!06\)\( T^{20} - \)\(10\!\cdots\!76\)\( T^{22} + \)\(24\!\cdots\!45\)\( T^{24} - \)\(43\!\cdots\!42\)\( T^{26} + \)\(50\!\cdots\!03\)\( T^{28} - \)\(94\!\cdots\!02\)\( T^{30} + \)\(10\!\cdots\!21\)\( T^{32} \))
$61$ (\( 1 - 622 T + 226981 T^{2} \))(\( 1 + 488 T + 226981 T^{2} \))(\( 1 - 398 T + 226981 T^{2} \))(\( ( 1 - 790 T + 226981 T^{2} )^{2} \))(\( 1 + 428 T + 425886 T^{2} + 97147868 T^{3} + 51520374361 T^{4} \))(\( ( 1 - 226981 T^{2} )^{4} \))(\( ( 1 - 24170 T^{2} + 51520374361 T^{4} )^{2} \))(\( 1 - 118 T - 213057 T^{2} - 26783758 T^{3} + 51520374361 T^{4} \))(\( 1 - 413 T - 56412 T^{2} - 93743153 T^{3} + 51520374361 T^{4} \))(\( 1 - 70 T - 335143 T^{2} - 129510330 T^{3} + 42145697866 T^{4} + 25171752927730 T^{5} - 316289217432887 T^{6} + 5713509651289083130 T^{7} + \)\(21\!\cdots\!26\)\( T^{8} - \)\(15\!\cdots\!30\)\( T^{9} - \)\(88\!\cdots\!03\)\( T^{10} - \)\(42\!\cdots\!70\)\( T^{11} + \)\(13\!\cdots\!81\)\( T^{12} \))(\( ( 1 + 666 T - 19198 T^{2} + 5855472 T^{3} + 61942105719 T^{4} + 1329080890032 T^{5} - 989088146982478 T^{6} + 7788301297827537906 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} )^{2} \))(\( 1 - 380 T - 82581 T^{2} - 86252780 T^{3} + 51520374361 T^{4} \))(\( 1 + 578 T - 1145735 T^{2} - 501446726 T^{3} + 837776641016 T^{4} + 251069047448050 T^{5} - 421088343940353753 T^{6} - 74043629095730306598 T^{7} + \)\(16\!\cdots\!99\)\( T^{8} + \)\(12\!\cdots\!52\)\( T^{9} - \)\(48\!\cdots\!12\)\( T^{10} - \)\(44\!\cdots\!40\)\( T^{11} + \)\(11\!\cdots\!09\)\( T^{12} - \)\(29\!\cdots\!26\)\( T^{13} - \)\(26\!\cdots\!71\)\( T^{14} + \)\(45\!\cdots\!78\)\( T^{15} + \)\(57\!\cdots\!72\)\( T^{16} + \)\(10\!\cdots\!18\)\( T^{17} - \)\(13\!\cdots\!31\)\( T^{18} - \)\(34\!\cdots\!66\)\( T^{19} + \)\(31\!\cdots\!89\)\( T^{20} - \)\(27\!\cdots\!40\)\( T^{21} - \)\(66\!\cdots\!72\)\( T^{22} + \)\(40\!\cdots\!72\)\( T^{23} + \)\(11\!\cdots\!59\)\( T^{24} - \)\(11\!\cdots\!58\)\( T^{25} - \)\(15\!\cdots\!53\)\( T^{26} + \)\(20\!\cdots\!50\)\( T^{27} + \)\(15\!\cdots\!76\)\( T^{28} - \)\(21\!\cdots\!66\)\( T^{29} - \)\(11\!\cdots\!35\)\( T^{30} + \)\(12\!\cdots\!78\)\( T^{31} + \)\(49\!\cdots\!81\)\( T^{32} \))(\( 1 - 198 T - 887778 T^{2} - 287437260 T^{3} + 528889911822 T^{4} + 307113774288822 T^{5} - 116372190688624860 T^{6} - \)\(17\!\cdots\!38\)\( T^{7} - \)\(13\!\cdots\!26\)\( T^{8} + \)\(50\!\cdots\!72\)\( T^{9} + \)\(22\!\cdots\!86\)\( T^{10} - \)\(68\!\cdots\!58\)\( T^{11} - \)\(76\!\cdots\!20\)\( T^{12} - \)\(11\!\cdots\!82\)\( T^{13} + \)\(12\!\cdots\!98\)\( T^{14} + \)\(60\!\cdots\!76\)\( T^{15} + \)\(33\!\cdots\!70\)\( T^{16} - \)\(77\!\cdots\!54\)\( T^{17} - \)\(41\!\cdots\!02\)\( T^{18} - \)\(17\!\cdots\!74\)\( T^{19} + \)\(17\!\cdots\!70\)\( T^{20} + \)\(70\!\cdots\!16\)\( T^{21} + \)\(33\!\cdots\!58\)\( T^{22} - \)\(70\!\cdots\!82\)\( T^{23} - \)\(10\!\cdots\!20\)\( T^{24} - \)\(21\!\cdots\!38\)\( T^{25} + \)\(16\!\cdots\!26\)\( T^{26} + \)\(81\!\cdots\!12\)\( T^{27} - \)\(49\!\cdots\!26\)\( T^{28} - \)\(14\!\cdots\!78\)\( T^{29} - \)\(21\!\cdots\!60\)\( T^{30} + \)\(13\!\cdots\!02\)\( T^{31} + \)\(50\!\cdots\!62\)\( T^{32} - \)\(62\!\cdots\!60\)\( T^{33} - \)\(44\!\cdots\!18\)\( T^{34} - \)\(22\!\cdots\!78\)\( T^{35} + \)\(25\!\cdots\!41\)\( T^{36} \))(\( ( 1 + 816 T + 837478 T^{2} + 502269216 T^{3} + 333755818642 T^{4} + 188353178559720 T^{5} + 93910648157586304 T^{6} + 50370689927417233344 T^{7} + \)\(21\!\cdots\!87\)\( T^{8} + \)\(11\!\cdots\!64\)\( T^{9} + \)\(48\!\cdots\!44\)\( T^{10} + \)\(22\!\cdots\!20\)\( T^{11} + \)\(88\!\cdots\!82\)\( T^{12} + \)\(30\!\cdots\!16\)\( T^{13} + \)\(11\!\cdots\!18\)\( T^{14} + \)\(25\!\cdots\!76\)\( T^{15} + \)\(70\!\cdots\!41\)\( T^{16} )^{2} \))
$67$ (\( 1 - 904 T + 300763 T^{2} \))(\( 1 - 244 T + 300763 T^{2} \))(\( 1 - 92 T + 300763 T^{2} \))(\( ( 1 + 44 T + 300763 T^{2} )^{2} \))(\( 1 - 148 T + 440790 T^{2} - 44512924 T^{3} + 90458382169 T^{4} \))(\( ( 1 - 740 T + 300763 T^{2} )^{4} \))(\( ( 1 - 296 T + 300763 T^{2} )^{4} \))(\( 1 - 370 T - 163863 T^{2} - 111282310 T^{3} + 90458382169 T^{4} \))(\( 1 + 415 T - 128538 T^{2} + 124816645 T^{3} + 90458382169 T^{4} \))(\( 1 - 628 T - 202942 T^{2} + 436381932 T^{3} - 77667044702 T^{4} - 73528811914784 T^{5} + 76060129771959310 T^{6} - 22114746057926180192 T^{7} - \)\(70\!\cdots\!38\)\( T^{8} + \)\(11\!\cdots\!04\)\( T^{9} - \)\(16\!\cdots\!62\)\( T^{10} - \)\(15\!\cdots\!04\)\( T^{11} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( ( 1 + 945 T + 85661 T^{2} + 194516910 T^{3} + 292789368252 T^{4} + 58503489402330 T^{5} + 7748755474978709 T^{6} + 25710175004498724915 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} )^{2} \))(\( 1 - 155 T - 276738 T^{2} - 46618265 T^{3} + 90458382169 T^{4} \))(\( 1 - 898 T - 791450 T^{2} + 1047042856 T^{3} + 204780930149 T^{4} - 606381046616276 T^{5} + 43407094416136272 T^{6} + \)\(23\!\cdots\!40\)\( T^{7} - \)\(65\!\cdots\!51\)\( T^{8} - \)\(67\!\cdots\!24\)\( T^{9} + \)\(35\!\cdots\!60\)\( T^{10} + \)\(13\!\cdots\!80\)\( T^{11} - \)\(13\!\cdots\!05\)\( T^{12} - \)\(17\!\cdots\!58\)\( T^{13} + \)\(38\!\cdots\!12\)\( T^{14} + \)\(11\!\cdots\!04\)\( T^{15} - \)\(11\!\cdots\!23\)\( T^{16} + \)\(33\!\cdots\!52\)\( T^{17} + \)\(35\!\cdots\!28\)\( T^{18} - \)\(48\!\cdots\!26\)\( T^{19} - \)\(10\!\cdots\!05\)\( T^{20} + \)\(33\!\cdots\!40\)\( T^{21} + \)\(26\!\cdots\!40\)\( T^{22} - \)\(15\!\cdots\!08\)\( T^{23} - \)\(44\!\cdots\!71\)\( T^{24} + \)\(47\!\cdots\!20\)\( T^{25} + \)\(26\!\cdots\!28\)\( T^{26} - \)\(11\!\cdots\!12\)\( T^{27} + \)\(11\!\cdots\!69\)\( T^{28} + \)\(17\!\cdots\!68\)\( T^{29} - \)\(39\!\cdots\!50\)\( T^{30} - \)\(13\!\cdots\!86\)\( T^{31} + \)\(44\!\cdots\!41\)\( T^{32} \))(\( 1 - 333 T - 1732230 T^{2} + 528423009 T^{3} + 1536024854412 T^{4} - 412920519370443 T^{5} - 968545743628278552 T^{6} + \)\(22\!\cdots\!51\)\( T^{7} + \)\(49\!\cdots\!18\)\( T^{8} - \)\(90\!\cdots\!95\)\( T^{9} - \)\(21\!\cdots\!74\)\( T^{10} + \)\(29\!\cdots\!79\)\( T^{11} + \)\(85\!\cdots\!76\)\( T^{12} - \)\(74\!\cdots\!11\)\( T^{13} - \)\(30\!\cdots\!04\)\( T^{14} + \)\(14\!\cdots\!01\)\( T^{15} + \)\(10\!\cdots\!50\)\( T^{16} - \)\(15\!\cdots\!09\)\( T^{17} - \)\(31\!\cdots\!66\)\( T^{18} - \)\(46\!\cdots\!67\)\( T^{19} + \)\(92\!\cdots\!50\)\( T^{20} + \)\(39\!\cdots\!47\)\( T^{21} - \)\(25\!\cdots\!44\)\( T^{22} - \)\(18\!\cdots\!73\)\( T^{23} + \)\(63\!\cdots\!84\)\( T^{24} + \)\(65\!\cdots\!93\)\( T^{25} - \)\(14\!\cdots\!54\)\( T^{26} - \)\(18\!\cdots\!85\)\( T^{27} + \)\(30\!\cdots\!82\)\( T^{28} + \)\(40\!\cdots\!37\)\( T^{29} - \)\(53\!\cdots\!12\)\( T^{30} - \)\(68\!\cdots\!29\)\( T^{31} + \)\(76\!\cdots\!68\)\( T^{32} + \)\(78\!\cdots\!63\)\( T^{33} - \)\(77\!\cdots\!30\)\( T^{34} - \)\(44\!\cdots\!39\)\( T^{35} + \)\(40\!\cdots\!29\)\( T^{36} \))(\( ( 1 - 154 T - 1009305 T^{2} + 101871994 T^{3} + 602011276205 T^{4} - 36961847361936 T^{5} - 261850611517253414 T^{6} + 4431016160230762340 T^{7} + \)\(89\!\cdots\!66\)\( T^{8} + \)\(13\!\cdots\!20\)\( T^{9} - \)\(23\!\cdots\!66\)\( T^{10} - \)\(10\!\cdots\!92\)\( T^{11} + \)\(49\!\cdots\!05\)\( T^{12} + \)\(25\!\cdots\!42\)\( T^{13} - \)\(74\!\cdots\!45\)\( T^{14} - \)\(34\!\cdots\!18\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} )^{2} \))
$71$ (\( 1 - 678 T + 357911 T^{2} \))(\( 1 - 768 T + 357911 T^{2} \))(\( 1 - 720 T + 357911 T^{2} \))(\( 1 + 518146 T^{2} + 128100283921 T^{4} \))(\( 1 + 954 T + 930526 T^{2} + 341447094 T^{3} + 128100283921 T^{4} \))(\( 1 - 197404987358 T^{4} + \)\(16\!\cdots\!41\)\( T^{8} \))(\( ( 1 - 607244 T^{2} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 342 T + 357911 T^{2} )^{2} \))(\( ( 1 - 432 T + 357911 T^{2} )^{2} \))(\( ( 1 + 318 T + 742929 T^{2} + 256167372 T^{3} + 265902461319 T^{4} + 40735890286878 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 + 874364 T^{2} + 392544633894 T^{4} + 112006276650301244 T^{6} + \)\(16\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 - 72 T + 357911 T^{2} )^{2} \))(\( ( 1 - 882 T + 1565920 T^{2} - 1172203578 T^{3} + 1342300776931 T^{4} - 886834221035832 T^{5} + 765294077320357237 T^{6} - \)\(44\!\cdots\!26\)\( T^{7} + \)\(31\!\cdots\!95\)\( T^{8} - \)\(15\!\cdots\!86\)\( T^{9} + \)\(98\!\cdots\!77\)\( T^{10} - \)\(40\!\cdots\!92\)\( T^{11} + \)\(22\!\cdots\!71\)\( T^{12} - \)\(68\!\cdots\!78\)\( T^{13} + \)\(32\!\cdots\!20\)\( T^{14} - \)\(66\!\cdots\!22\)\( T^{15} + \)\(26\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 2826 T + 5263047 T^{2} + 6924084732 T^{3} + 7456807599435 T^{4} + 6647912633823210 T^{5} + 5231634779026552794 T^{6} + \)\(36\!\cdots\!26\)\( T^{7} + \)\(23\!\cdots\!18\)\( T^{8} + \)\(14\!\cdots\!00\)\( T^{9} + \)\(85\!\cdots\!98\)\( T^{10} + \)\(46\!\cdots\!46\)\( T^{11} + \)\(23\!\cdots\!14\)\( T^{12} + \)\(10\!\cdots\!10\)\( T^{13} + \)\(43\!\cdots\!85\)\( T^{14} + \)\(14\!\cdots\!52\)\( T^{15} + \)\(39\!\cdots\!37\)\( T^{16} + \)\(76\!\cdots\!06\)\( T^{17} + \)\(96\!\cdots\!91\)\( T^{18} )^{2} \))(\( ( 1 - 2546056 T^{2} + 2933736697204 T^{4} - 1997708473027518488 T^{6} + \)\(87\!\cdots\!74\)\( T^{8} - \)\(25\!\cdots\!48\)\( T^{10} + \)\(48\!\cdots\!64\)\( T^{12} - \)\(53\!\cdots\!16\)\( T^{14} + \)\(26\!\cdots\!81\)\( T^{16} )^{2} \))
$73$ (\( 1 + 642 T + 389017 T^{2} \))(\( 1 + 702 T + 389017 T^{2} \))(\( 1 + 502 T + 389017 T^{2} \))(\( ( 1 - 126 T + 389017 T^{2} )^{2} \))(\( 1 - 1072 T + 1063278 T^{2} - 417026224 T^{3} + 151334226289 T^{4} \))(\( ( 1 - 389017 T^{2} )^{4} \))(\( ( 1 - 130682 T^{2} + 151334226289 T^{4} )^{2} \))(\( 1 + 362 T - 257973 T^{2} + 140824154 T^{3} + 151334226289 T^{4} \))(\( 1 - 1113 T + 849752 T^{2} - 432975921 T^{3} + 151334226289 T^{4} \))(\( 1 + 988 T - 186552 T^{2} - 102237300 T^{3} + 281568890272 T^{4} - 16988127696596 T^{5} - 164639785652996186 T^{6} - 6608670472146686132 T^{7} + \)\(42\!\cdots\!08\)\( T^{8} - \)\(60\!\cdots\!00\)\( T^{9} - \)\(42\!\cdots\!92\)\( T^{10} + \)\(88\!\cdots\!16\)\( T^{11} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( ( 1 + 875 T - 201451 T^{2} + 165411750 T^{3} + 486060622862 T^{4} + 64347982749750 T^{5} - 30486431220145339 T^{6} + 51512638369734423875 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} )^{2} \))(\( ( 1 - 117 T + 389017 T^{2} )^{2} \))(\( ( 1 - 972 T + 1718351 T^{2} - 1080282636 T^{3} + 1082261782252 T^{4} - 376474331161008 T^{5} + 293371917050729072 T^{6} - 2405960897454683676 T^{7} + \)\(57\!\cdots\!52\)\( T^{8} - \)\(93\!\cdots\!92\)\( T^{9} + \)\(44\!\cdots\!08\)\( T^{10} - \)\(22\!\cdots\!04\)\( T^{11} + \)\(24\!\cdots\!92\)\( T^{12} - \)\(96\!\cdots\!52\)\( T^{13} + \)\(59\!\cdots\!19\)\( T^{14} - \)\(13\!\cdots\!56\)\( T^{15} + \)\(52\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 153 T + 2081772 T^{2} - 57071499 T^{3} + 1958269856463 T^{4} + 263808176386464 T^{5} + 1132889252675869788 T^{6} + \)\(34\!\cdots\!20\)\( T^{7} + \)\(49\!\cdots\!36\)\( T^{8} + \)\(18\!\cdots\!04\)\( T^{9} + \)\(19\!\cdots\!12\)\( T^{10} + \)\(52\!\cdots\!80\)\( T^{11} + \)\(66\!\cdots\!44\)\( T^{12} + \)\(60\!\cdots\!44\)\( T^{13} + \)\(17\!\cdots\!91\)\( T^{14} - \)\(19\!\cdots\!31\)\( T^{15} + \)\(28\!\cdots\!56\)\( T^{16} - \)\(80\!\cdots\!73\)\( T^{17} + \)\(20\!\cdots\!97\)\( T^{18} )^{2} \))(\( ( 1 - 2034 T + 2450047 T^{2} - 2178403830 T^{3} + 1347031106821 T^{4} - 430919574332148 T^{5} - 113107388808572534 T^{6} + \)\(30\!\cdots\!80\)\( T^{7} - \)\(25\!\cdots\!10\)\( T^{8} + \)\(11\!\cdots\!60\)\( T^{9} - \)\(17\!\cdots\!26\)\( T^{10} - \)\(25\!\cdots\!24\)\( T^{11} + \)\(30\!\cdots\!41\)\( T^{12} - \)\(19\!\cdots\!10\)\( T^{13} + \)\(84\!\cdots\!43\)\( T^{14} - \)\(27\!\cdots\!82\)\( T^{15} + \)\(52\!\cdots\!41\)\( T^{16} )^{2} \))
$79$ (\( 1 - 740 T + 493039 T^{2} \))(\( 1 - 440 T + 493039 T^{2} \))(\( 1 + 1024 T + 493039 T^{2} \))(\( ( 1 + 712 T + 493039 T^{2} )^{2} \))(\( 1 + 572 T + 901662 T^{2} + 282018308 T^{3} + 243087455521 T^{4} \))(\( ( 1 + 1384 T + 493039 T^{2} )^{4} \))(\( ( 1 - 836 T + 493039 T^{2} )^{4} \))(\( 1 + 467 T - 274950 T^{2} + 230249213 T^{3} + 243087455521 T^{4} \))(\( 1 - 103 T - 482430 T^{2} - 50783017 T^{3} + 243087455521 T^{4} \))(\( 1 + 861 T - 479895 T^{2} - 258646666 T^{3} + 325257480351 T^{4} - 27564282842211 T^{5} - 246706047980056146 T^{6} - 13590266448240869229 T^{7} + \)\(79\!\cdots\!71\)\( T^{8} - \)\(30\!\cdots\!54\)\( T^{9} - \)\(28\!\cdots\!95\)\( T^{10} + \)\(25\!\cdots\!39\)\( T^{11} + \)\(14\!\cdots\!61\)\( T^{12} \))(\( ( 1 + 4 T - 900953 T^{2} - 340436 T^{3} + 568649794816 T^{4} - 167848225004 T^{5} - 219010372314011513 T^{6} + 479406383930473276 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} )^{2} \))(\( 1 - 526 T - 216363 T^{2} - 259338514 T^{3} + 243087455521 T^{4} \))(\( 1 - 158 T - 1631978 T^{2} + 326581604 T^{3} + 1003734307967 T^{4} - 276658431385546 T^{5} - 294010705461071412 T^{6} + \)\(16\!\cdots\!94\)\( T^{7} + \)\(10\!\cdots\!84\)\( T^{8} - \)\(77\!\cdots\!36\)\( T^{9} - \)\(89\!\cdots\!86\)\( T^{10} + \)\(15\!\cdots\!56\)\( T^{11} + \)\(53\!\cdots\!98\)\( T^{12} + \)\(92\!\cdots\!86\)\( T^{13} - \)\(20\!\cdots\!95\)\( T^{14} - \)\(39\!\cdots\!96\)\( T^{15} + \)\(81\!\cdots\!30\)\( T^{16} - \)\(19\!\cdots\!44\)\( T^{17} - \)\(49\!\cdots\!95\)\( T^{18} + \)\(11\!\cdots\!34\)\( T^{19} + \)\(31\!\cdots\!18\)\( T^{20} + \)\(44\!\cdots\!44\)\( T^{21} - \)\(12\!\cdots\!46\)\( T^{22} - \)\(55\!\cdots\!44\)\( T^{23} + \)\(35\!\cdots\!04\)\( T^{24} + \)\(27\!\cdots\!46\)\( T^{25} - \)\(24\!\cdots\!12\)\( T^{26} - \)\(11\!\cdots\!94\)\( T^{27} + \)\(20\!\cdots\!07\)\( T^{28} + \)\(33\!\cdots\!76\)\( T^{29} - \)\(81\!\cdots\!98\)\( T^{30} - \)\(39\!\cdots\!42\)\( T^{31} + \)\(12\!\cdots\!61\)\( T^{32} \))(\( 1 + 1152 T - 2310273 T^{2} - 2463307860 T^{3} + 3542715673650 T^{4} + 3068374894454970 T^{5} - 3930405513412520391 T^{6} - \)\(26\!\cdots\!06\)\( T^{7} + \)\(33\!\cdots\!23\)\( T^{8} + \)\(17\!\cdots\!64\)\( T^{9} - \)\(23\!\cdots\!14\)\( T^{10} - \)\(89\!\cdots\!18\)\( T^{11} + \)\(13\!\cdots\!36\)\( T^{12} + \)\(37\!\cdots\!18\)\( T^{13} - \)\(63\!\cdots\!91\)\( T^{14} - \)\(12\!\cdots\!96\)\( T^{15} + \)\(28\!\cdots\!25\)\( T^{16} + \)\(20\!\cdots\!76\)\( T^{17} - \)\(13\!\cdots\!88\)\( T^{18} + \)\(10\!\cdots\!64\)\( T^{19} + \)\(70\!\cdots\!25\)\( T^{20} - \)\(14\!\cdots\!24\)\( T^{21} - \)\(37\!\cdots\!31\)\( T^{22} + \)\(10\!\cdots\!82\)\( T^{23} + \)\(18\!\cdots\!96\)\( T^{24} - \)\(63\!\cdots\!22\)\( T^{25} - \)\(80\!\cdots\!34\)\( T^{26} + \)\(29\!\cdots\!76\)\( T^{27} + \)\(28\!\cdots\!23\)\( T^{28} - \)\(11\!\cdots\!34\)\( T^{29} - \)\(81\!\cdots\!11\)\( T^{30} + \)\(31\!\cdots\!30\)\( T^{31} + \)\(17\!\cdots\!50\)\( T^{32} - \)\(60\!\cdots\!40\)\( T^{33} - \)\(28\!\cdots\!53\)\( T^{34} + \)\(69\!\cdots\!08\)\( T^{35} + \)\(29\!\cdots\!81\)\( T^{36} \))(\( ( 1 + 1088 T - 269028 T^{2} - 1109682680 T^{3} - 391267378201 T^{4} + 358084200932532 T^{5} + 285753619209423700 T^{6} - 15705523238748286852 T^{7} - \)\(10\!\cdots\!68\)\( T^{8} - \)\(77\!\cdots\!28\)\( T^{9} + \)\(69\!\cdots\!00\)\( T^{10} + \)\(42\!\cdots\!08\)\( T^{11} - \)\(23\!\cdots\!41\)\( T^{12} - \)\(32\!\cdots\!20\)\( T^{13} - \)\(38\!\cdots\!08\)\( T^{14} + \)\(77\!\cdots\!52\)\( T^{15} + \)\(34\!\cdots\!81\)\( T^{16} )^{2} \))
$83$ (\( 1 + 468 T + 571787 T^{2} \))(\( 1 - 1302 T + 571787 T^{2} \))(\( 1 - 204 T + 571787 T^{2} \))(\( 1 - 1001450 T^{2} + 326940373369 T^{4} \))(\( 1 + 1944 T + 1957030 T^{2} + 1111553928 T^{3} + 326940373369 T^{4} \))(\( ( 1 + 571787 T^{2} )^{4} \))(\( ( 1 - 350042 T^{2} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 477 T + 571787 T^{2} )^{2} \))(\( ( 1 + 1092 T + 571787 T^{2} )^{2} \))(\( ( 1 + 519 T + 1583745 T^{2} + 545598870 T^{3} + 905564802315 T^{4} + 169682053778511 T^{5} + 186940255267540403 T^{6} )^{2} \))(\( ( 1 + 1482323 T^{2} + 1051851285456 T^{4} + 484631235073456187 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} )^{2} \))(\( 1 + 576 T - 240011 T^{2} + 329349312 T^{3} + 326940373369 T^{4} \))(\( 1 + 2958 T + 2046194 T^{2} - 1191819780 T^{3} - 156888285003 T^{4} + 2954536317243036 T^{5} + 1354865827302829804 T^{6} - \)\(96\!\cdots\!52\)\( T^{7} + \)\(25\!\cdots\!17\)\( T^{8} + \)\(90\!\cdots\!24\)\( T^{9} - \)\(57\!\cdots\!04\)\( T^{10} - \)\(67\!\cdots\!52\)\( T^{11} + \)\(24\!\cdots\!15\)\( T^{12} - \)\(26\!\cdots\!58\)\( T^{13} - \)\(13\!\cdots\!52\)\( T^{14} + \)\(69\!\cdots\!52\)\( T^{15} + \)\(56\!\cdots\!77\)\( T^{16} + \)\(39\!\cdots\!24\)\( T^{17} - \)\(43\!\cdots\!88\)\( T^{18} - \)\(49\!\cdots\!74\)\( T^{19} + \)\(25\!\cdots\!15\)\( T^{20} - \)\(41\!\cdots\!64\)\( T^{21} - \)\(20\!\cdots\!36\)\( T^{22} + \)\(18\!\cdots\!92\)\( T^{23} + \)\(28\!\cdots\!57\)\( T^{24} - \)\(62\!\cdots\!04\)\( T^{25} + \)\(50\!\cdots\!96\)\( T^{26} + \)\(63\!\cdots\!68\)\( T^{27} - \)\(19\!\cdots\!43\)\( T^{28} - \)\(83\!\cdots\!60\)\( T^{29} + \)\(81\!\cdots\!66\)\( T^{30} + \)\(67\!\cdots\!94\)\( T^{31} + \)\(13\!\cdots\!41\)\( T^{32} \))(\( 1 - 1890 T - 1259001 T^{2} + 3565334466 T^{3} + 1727740592604 T^{4} - 4244684325885126 T^{5} - 2320472508559383597 T^{6} + \)\(38\!\cdots\!36\)\( T^{7} + \)\(24\!\cdots\!66\)\( T^{8} - \)\(26\!\cdots\!76\)\( T^{9} - \)\(20\!\cdots\!19\)\( T^{10} + \)\(14\!\cdots\!40\)\( T^{11} + \)\(14\!\cdots\!84\)\( T^{12} - \)\(64\!\cdots\!34\)\( T^{13} - \)\(90\!\cdots\!89\)\( T^{14} + \)\(22\!\cdots\!86\)\( T^{15} + \)\(51\!\cdots\!52\)\( T^{16} - \)\(46\!\cdots\!14\)\( T^{17} - \)\(28\!\cdots\!07\)\( T^{18} - \)\(26\!\cdots\!18\)\( T^{19} + \)\(16\!\cdots\!88\)\( T^{20} + \)\(42\!\cdots\!58\)\( T^{21} - \)\(96\!\cdots\!29\)\( T^{22} - \)\(39\!\cdots\!38\)\( T^{23} + \)\(51\!\cdots\!56\)\( T^{24} + \)\(29\!\cdots\!20\)\( T^{25} - \)\(23\!\cdots\!99\)\( T^{26} - \)\(17\!\cdots\!52\)\( T^{27} + \)\(92\!\cdots\!34\)\( T^{28} + \)\(81\!\cdots\!68\)\( T^{29} - \)\(28\!\cdots\!57\)\( T^{30} - \)\(29\!\cdots\!22\)\( T^{31} + \)\(68\!\cdots\!56\)\( T^{32} + \)\(81\!\cdots\!38\)\( T^{33} - \)\(16\!\cdots\!41\)\( T^{34} - \)\(14\!\cdots\!30\)\( T^{35} + \)\(42\!\cdots\!29\)\( T^{36} \))(\( ( 1 + 2632486 T^{2} + 3636170382349 T^{4} + 3366834686358200962 T^{6} + \)\(22\!\cdots\!84\)\( T^{8} + \)\(11\!\cdots\!78\)\( T^{10} + \)\(38\!\cdots\!89\)\( T^{12} + \)\(91\!\cdots\!74\)\( T^{14} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))
$89$ (\( 1 + 200 T + 704969 T^{2} \))(\( 1 + 730 T + 704969 T^{2} \))(\( 1 + 354 T + 704969 T^{2} \))(\( 1 - 709626 T^{2} + 496981290961 T^{4} \))(\( 1 + 366 T + 1156090 T^{2} + 258018654 T^{3} + 496981290961 T^{4} \))(\( ( 1 + 704969 T^{2} )^{4} \))(\( ( 1 + 926422 T^{2} + 496981290961 T^{4} )^{2} \))(\( 1 - 906 T + 115867 T^{2} - 638701914 T^{3} + 496981290961 T^{4} \))(\( 1 + 329 T - 596728 T^{2} + 231934801 T^{3} + 496981290961 T^{4} \))(\( 1 - 1766 T + 725929 T^{2} + 728159446 T^{3} - 335534377858 T^{4} - 846551335831238 T^{5} + 1249625385561159997 T^{6} - \)\(59\!\cdots\!22\)\( T^{7} - \)\(16\!\cdots\!38\)\( T^{8} + \)\(25\!\cdots\!14\)\( T^{9} + \)\(17\!\cdots\!09\)\( T^{10} - \)\(30\!\cdots\!34\)\( T^{11} + \)\(12\!\cdots\!81\)\( T^{12} \))(\( 1 - 627904 T^{2} - 652647550942 T^{4} - 33246513557593344 T^{6} + \)\(65\!\cdots\!67\)\( T^{8} - \)\(16\!\cdots\!84\)\( T^{10} - \)\(16\!\cdots\!82\)\( T^{12} - \)\(77\!\cdots\!24\)\( T^{14} + \)\(61\!\cdots\!41\)\( T^{16} \))(\( ( 1 + 278 T + 704969 T^{2} )^{2} \))(\( ( 1 - 4380 T + 10823694 T^{2} - 19914754776 T^{3} + 29899723956313 T^{4} - 38260156523638452 T^{5} + 42933634978495882653 T^{6} - \)\(42\!\cdots\!56\)\( T^{7} + \)\(37\!\cdots\!62\)\( T^{8} - \)\(30\!\cdots\!64\)\( T^{9} + \)\(21\!\cdots\!33\)\( T^{10} - \)\(13\!\cdots\!68\)\( T^{11} + \)\(73\!\cdots\!73\)\( T^{12} - \)\(34\!\cdots\!24\)\( T^{13} + \)\(13\!\cdots\!14\)\( T^{14} - \)\(37\!\cdots\!20\)\( T^{15} + \)\(61\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 1302 T + 2637747 T^{2} + 1784744028 T^{3} + 3054189577995 T^{4} + 2033343768333426 T^{5} + 3526920405043686474 T^{6} + \)\(20\!\cdots\!02\)\( T^{7} + \)\(27\!\cdots\!55\)\( T^{8} + \)\(12\!\cdots\!16\)\( T^{9} + \)\(19\!\cdots\!95\)\( T^{10} + \)\(10\!\cdots\!22\)\( T^{11} + \)\(12\!\cdots\!66\)\( T^{12} + \)\(50\!\cdots\!46\)\( T^{13} + \)\(53\!\cdots\!55\)\( T^{14} + \)\(21\!\cdots\!68\)\( T^{15} + \)\(22\!\cdots\!83\)\( T^{16} + \)\(79\!\cdots\!82\)\( T^{17} + \)\(43\!\cdots\!29\)\( T^{18} )^{2} \))(\( 1 - 2548864 T^{2} + 4462766350596 T^{4} - 5306850100326352640 T^{6} + \)\(51\!\cdots\!26\)\( T^{8} - \)\(40\!\cdots\!68\)\( T^{10} + \)\(27\!\cdots\!80\)\( T^{12} - \)\(17\!\cdots\!04\)\( T^{14} + \)\(11\!\cdots\!27\)\( T^{16} - \)\(87\!\cdots\!44\)\( T^{18} + \)\(67\!\cdots\!80\)\( T^{20} - \)\(49\!\cdots\!08\)\( T^{22} + \)\(31\!\cdots\!66\)\( T^{24} - \)\(16\!\cdots\!40\)\( T^{26} + \)\(67\!\cdots\!56\)\( T^{28} - \)\(19\!\cdots\!44\)\( T^{30} + \)\(37\!\cdots\!81\)\( T^{32} \))
$97$ (\( 1 + 1266 T + 912673 T^{2} \))(\( 1 - 294 T + 912673 T^{2} \))(\( 1 + 286 T + 912673 T^{2} \))(\( ( 1 - 798 T + 912673 T^{2} )^{2} \))(\( 1 - 808 T + 903054 T^{2} - 737439784 T^{3} + 832972004929 T^{4} \))(\( ( 1 - 912673 T^{2} )^{4} \))(\( ( 1 - 1504778 T^{2} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 503 T + 912673 T^{2} )^{2} \))(\( ( 1 + 882 T + 912673 T^{2} )^{2} \))(\( ( 1 - 19 T + 2168419 T^{2} + 10094878 T^{3} + 1979057473987 T^{4} - 15826468093651 T^{5} + 760231058654565217 T^{6} )^{2} \))(\( ( 1 - 1505 T + 1992044 T^{2} - 1373572865 T^{3} + 832972004929 T^{4} )^{4} \))(\( 1 - 201 T - 872272 T^{2} - 183447273 T^{3} + 832972004929 T^{4} \))(\( 1 - 60 T - 3109535 T^{2} + 2828204676 T^{3} + 4865749520445 T^{4} - 7975237084169220 T^{5} - 624844777429079932 T^{6} + \)\(11\!\cdots\!12\)\( T^{7} - \)\(80\!\cdots\!40\)\( T^{8} - \)\(65\!\cdots\!40\)\( T^{9} + \)\(13\!\cdots\!28\)\( T^{10} - \)\(36\!\cdots\!20\)\( T^{11} - \)\(86\!\cdots\!92\)\( T^{12} + \)\(97\!\cdots\!76\)\( T^{13} - \)\(16\!\cdots\!31\)\( T^{14} - \)\(45\!\cdots\!64\)\( T^{15} + \)\(67\!\cdots\!49\)\( T^{16} - \)\(41\!\cdots\!72\)\( T^{17} - \)\(13\!\cdots\!99\)\( T^{18} + \)\(74\!\cdots\!92\)\( T^{19} - \)\(59\!\cdots\!72\)\( T^{20} - \)\(23\!\cdots\!60\)\( T^{21} + \)\(80\!\cdots\!92\)\( T^{22} - \)\(34\!\cdots\!80\)\( T^{23} - \)\(38\!\cdots\!40\)\( T^{24} + \)\(51\!\cdots\!56\)\( T^{25} - \)\(25\!\cdots\!68\)\( T^{26} - \)\(29\!\cdots\!40\)\( T^{27} + \)\(16\!\cdots\!45\)\( T^{28} + \)\(86\!\cdots\!08\)\( T^{29} - \)\(86\!\cdots\!15\)\( T^{30} - \)\(15\!\cdots\!20\)\( T^{31} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( 1 - 1737 T - 1233891 T^{2} + 3264015786 T^{3} + 895203537786 T^{4} - 2970294593054454 T^{5} - 210857292003178851 T^{6} + \)\(61\!\cdots\!43\)\( T^{7} - \)\(50\!\cdots\!07\)\( T^{8} + \)\(33\!\cdots\!80\)\( T^{9} - \)\(11\!\cdots\!72\)\( T^{10} - \)\(40\!\cdots\!96\)\( T^{11} + \)\(15\!\cdots\!68\)\( T^{12} + \)\(30\!\cdots\!96\)\( T^{13} - \)\(36\!\cdots\!15\)\( T^{14} - \)\(14\!\cdots\!61\)\( T^{15} - \)\(16\!\cdots\!15\)\( T^{16} - \)\(29\!\cdots\!38\)\( T^{17} + \)\(32\!\cdots\!78\)\( T^{18} - \)\(26\!\cdots\!74\)\( T^{19} - \)\(14\!\cdots\!35\)\( T^{20} - \)\(11\!\cdots\!37\)\( T^{21} - \)\(24\!\cdots\!15\)\( T^{22} + \)\(19\!\cdots\!28\)\( T^{23} + \)\(89\!\cdots\!52\)\( T^{24} - \)\(21\!\cdots\!12\)\( T^{25} - \)\(55\!\cdots\!32\)\( T^{26} + \)\(14\!\cdots\!40\)\( T^{27} - \)\(20\!\cdots\!43\)\( T^{28} + \)\(22\!\cdots\!11\)\( T^{29} - \)\(70\!\cdots\!71\)\( T^{30} - \)\(90\!\cdots\!82\)\( T^{31} + \)\(24\!\cdots\!74\)\( T^{32} + \)\(82\!\cdots\!02\)\( T^{33} - \)\(28\!\cdots\!51\)\( T^{34} - \)\(36\!\cdots\!61\)\( T^{35} + \)\(19\!\cdots\!69\)\( T^{36} \))(\( ( 1 - 2978570 T^{2} + 5898756336049 T^{4} - 7901916867899068322 T^{6} + \)\(83\!\cdots\!24\)\( T^{8} - \)\(65\!\cdots\!38\)\( T^{10} + \)\(40\!\cdots\!09\)\( T^{12} - \)\(17\!\cdots\!30\)\( T^{14} + \)\(48\!\cdots\!81\)\( T^{16} )^{2} \))
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