Properties

Label 1503.2
Level 1503
Weight 2
Dimension 65487
Nonzero newspaces 8
Sturm bound 334656
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1503 = 3^{2} \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(334656\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1503))\).

Total New Old
Modular forms 84992 66971 18021
Cusp forms 82337 65487 16850
Eisenstein series 2655 1484 1171

Trace form

\( 65487q - 249q^{2} - 332q^{3} - 249q^{4} - 249q^{5} - 332q^{6} - 249q^{7} - 249q^{8} - 332q^{9} + O(q^{10}) \) \( 65487q - 249q^{2} - 332q^{3} - 249q^{4} - 249q^{5} - 332q^{6} - 249q^{7} - 249q^{8} - 332q^{9} - 747q^{10} - 249q^{11} - 332q^{12} - 249q^{13} - 249q^{14} - 332q^{15} - 249q^{16} - 249q^{17} - 332q^{18} - 747q^{19} - 249q^{20} - 332q^{21} - 249q^{22} - 249q^{23} - 332q^{24} - 249q^{25} - 249q^{26} - 332q^{27} - 747q^{28} - 249q^{29} - 332q^{30} - 249q^{31} - 249q^{32} - 332q^{33} - 249q^{34} - 249q^{35} - 332q^{36} - 747q^{37} - 249q^{38} - 332q^{39} - 249q^{40} - 249q^{41} - 332q^{42} - 249q^{43} - 249q^{44} - 332q^{45} - 747q^{46} - 249q^{47} - 332q^{48} - 249q^{49} - 249q^{50} - 332q^{51} - 249q^{52} - 249q^{53} - 332q^{54} - 747q^{55} - 249q^{56} - 332q^{57} - 249q^{58} - 249q^{59} - 332q^{60} - 249q^{61} - 249q^{62} - 332q^{63} - 747q^{64} - 249q^{65} - 332q^{66} - 249q^{67} - 249q^{68} - 332q^{69} - 249q^{70} - 249q^{71} - 332q^{72} - 747q^{73} - 249q^{74} - 332q^{75} - 249q^{76} - 249q^{77} - 332q^{78} - 249q^{79} - 249q^{80} - 332q^{81} - 747q^{82} - 249q^{83} - 332q^{84} - 249q^{85} - 249q^{86} - 332q^{87} - 249q^{88} - 249q^{89} - 332q^{90} - 747q^{91} - 249q^{92} - 332q^{93} - 249q^{94} - 249q^{95} - 332q^{96} - 249q^{97} - 249q^{98} - 332q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1503))\)

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
1503.2.a \(\chi_{1503}(1, \cdot)\) 1503.2.a.a 1 1
1503.2.a.b 2
1503.2.a.c 5
1503.2.a.d 5
1503.2.a.e 8
1503.2.a.f 8
1503.2.a.g 12
1503.2.a.h 14
1503.2.a.i 14
1503.2.c \(\chi_{1503}(1502, \cdot)\) 1503.2.c.a 56 1
1503.2.e \(\chi_{1503}(502, \cdot)\) n/a 332 2
1503.2.g \(\chi_{1503}(500, \cdot)\) n/a 332 2
1503.2.i \(\chi_{1503}(19, \cdot)\) n/a 5658 82
1503.2.k \(\chi_{1503}(17, \cdot)\) n/a 4592 82
1503.2.m \(\chi_{1503}(4, \cdot)\) n/a 27224 164
1503.2.o \(\chi_{1503}(5, \cdot)\) n/a 27224 164

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1503))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1503)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 2 T^{2} \))(\( 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 + 5 T^{2} + 14 T^{4} - T^{5} + 28 T^{6} + 40 T^{8} + 32 T^{10} \))(\( 1 - 4 T + 11 T^{2} - 24 T^{3} + 44 T^{4} - 67 T^{5} + 88 T^{6} - 96 T^{7} + 88 T^{8} - 64 T^{9} + 32 T^{10} \))(\( 1 + 3 T + 8 T^{2} + 14 T^{3} + 25 T^{4} + 36 T^{5} + 57 T^{6} + 81 T^{7} + 125 T^{8} + 162 T^{9} + 228 T^{10} + 288 T^{11} + 400 T^{12} + 448 T^{13} + 512 T^{14} + 384 T^{15} + 256 T^{16} \))(\( 1 - 3 T + 6 T^{2} - 8 T^{3} + 9 T^{4} - 12 T^{5} + 27 T^{6} - 59 T^{7} + 93 T^{8} - 118 T^{9} + 108 T^{10} - 96 T^{11} + 144 T^{12} - 256 T^{13} + 384 T^{14} - 384 T^{15} + 256 T^{16} \))(\( 1 + 2 T + 7 T^{2} + 11 T^{3} + 27 T^{4} + 35 T^{5} + 71 T^{6} + 87 T^{7} + 175 T^{8} + 223 T^{9} + 447 T^{10} + 558 T^{11} + 989 T^{12} + 1116 T^{13} + 1788 T^{14} + 1784 T^{15} + 2800 T^{16} + 2784 T^{17} + 4544 T^{18} + 4480 T^{19} + 6912 T^{20} + 5632 T^{21} + 7168 T^{22} + 4096 T^{23} + 4096 T^{24} \))(\( 1 + 6 T + 24 T^{2} + 74 T^{3} + 196 T^{4} + 462 T^{5} + 1002 T^{6} + 2014 T^{7} + 3803 T^{8} + 6776 T^{9} + 11493 T^{10} + 18614 T^{11} + 28964 T^{12} + 43314 T^{13} + 62433 T^{14} + 86628 T^{15} + 115856 T^{16} + 148912 T^{17} + 183888 T^{18} + 216832 T^{19} + 243392 T^{20} + 257792 T^{21} + 256512 T^{22} + 236544 T^{23} + 200704 T^{24} + 151552 T^{25} + 98304 T^{26} + 49152 T^{27} + 16384 T^{28} \))(\( 1 - 6 T + 24 T^{2} - 74 T^{3} + 196 T^{4} - 462 T^{5} + 1002 T^{6} - 2014 T^{7} + 3803 T^{8} - 6776 T^{9} + 11493 T^{10} - 18614 T^{11} + 28964 T^{12} - 43314 T^{13} + 62433 T^{14} - 86628 T^{15} + 115856 T^{16} - 148912 T^{17} + 183888 T^{18} - 216832 T^{19} + 243392 T^{20} - 257792 T^{21} + 256512 T^{22} - 236544 T^{23} + 200704 T^{24} - 151552 T^{25} + 98304 T^{26} - 49152 T^{27} + 16384 T^{28} \))
$3$ 1
$5$ (\( 1 - 4 T + 5 T^{2} \))(\( ( 1 - T + 5 T^{2} )^{2} \))(\( 1 - T + 16 T^{2} - 18 T^{3} + 132 T^{4} - 129 T^{5} + 660 T^{6} - 450 T^{7} + 2000 T^{8} - 625 T^{9} + 3125 T^{10} \))(\( 1 - 9 T + 50 T^{2} - 192 T^{3} + 586 T^{4} - 1433 T^{5} + 2930 T^{6} - 4800 T^{7} + 6250 T^{8} - 5625 T^{9} + 3125 T^{10} \))(\( 1 + 7 T + 47 T^{2} + 195 T^{3} + 785 T^{4} + 2416 T^{5} + 7321 T^{6} + 18114 T^{7} + 44442 T^{8} + 90570 T^{9} + 183025 T^{10} + 302000 T^{11} + 490625 T^{12} + 609375 T^{13} + 734375 T^{14} + 546875 T^{15} + 390625 T^{16} \))(\( 1 + T + 19 T^{2} + 17 T^{3} + 161 T^{4} + 192 T^{5} + 927 T^{6} + 1582 T^{7} + 4718 T^{8} + 7910 T^{9} + 23175 T^{10} + 24000 T^{11} + 100625 T^{12} + 53125 T^{13} + 296875 T^{14} + 78125 T^{15} + 390625 T^{16} \))(\( 1 + 4 T + 19 T^{2} + 68 T^{3} + 248 T^{4} + 796 T^{5} + 2479 T^{6} + 6892 T^{7} + 19111 T^{8} + 48832 T^{9} + 123526 T^{10} + 288688 T^{11} + 667744 T^{12} + 1443440 T^{13} + 3088150 T^{14} + 6104000 T^{15} + 11944375 T^{16} + 21537500 T^{17} + 38734375 T^{18} + 62187500 T^{19} + 96875000 T^{20} + 132812500 T^{21} + 185546875 T^{22} + 195312500 T^{23} + 244140625 T^{24} \))(\( 1 + 12 T + 101 T^{2} + 640 T^{3} + 3430 T^{4} + 15914 T^{5} + 66064 T^{6} + 248208 T^{7} + 856487 T^{8} + 2731144 T^{9} + 8111350 T^{10} + 22509388 T^{11} + 58623082 T^{12} + 143469404 T^{13} + 330652308 T^{14} + 717347020 T^{15} + 1465577050 T^{16} + 2813673500 T^{17} + 5069593750 T^{18} + 8534825000 T^{19} + 13382609375 T^{20} + 19391250000 T^{21} + 25806250000 T^{22} + 31082031250 T^{23} + 33496093750 T^{24} + 31250000000 T^{25} + 24658203125 T^{26} + 14648437500 T^{27} + 6103515625 T^{28} \))(\( 1 - 12 T + 101 T^{2} - 640 T^{3} + 3430 T^{4} - 15914 T^{5} + 66064 T^{6} - 248208 T^{7} + 856487 T^{8} - 2731144 T^{9} + 8111350 T^{10} - 22509388 T^{11} + 58623082 T^{12} - 143469404 T^{13} + 330652308 T^{14} - 717347020 T^{15} + 1465577050 T^{16} - 2813673500 T^{17} + 5069593750 T^{18} - 8534825000 T^{19} + 13382609375 T^{20} - 19391250000 T^{21} + 25806250000 T^{22} - 31082031250 T^{23} + 33496093750 T^{24} - 31250000000 T^{25} + 24658203125 T^{26} - 14648437500 T^{27} + 6103515625 T^{28} \))
$7$ (\( 1 - 4 T + 7 T^{2} \))(\( 1 + 5 T + 19 T^{2} + 35 T^{3} + 49 T^{4} \))(\( 1 + 4 T + 32 T^{2} + 83 T^{3} + 390 T^{4} + 757 T^{5} + 2730 T^{6} + 4067 T^{7} + 10976 T^{8} + 9604 T^{9} + 16807 T^{10} \))(\( 1 + 4 T + 20 T^{2} + 63 T^{3} + 230 T^{4} + 573 T^{5} + 1610 T^{6} + 3087 T^{7} + 6860 T^{8} + 9604 T^{9} + 16807 T^{10} \))(\( 1 + 4 T + 37 T^{2} + 131 T^{3} + 637 T^{4} + 2096 T^{5} + 7091 T^{6} + 21477 T^{7} + 57412 T^{8} + 150339 T^{9} + 347459 T^{10} + 718928 T^{11} + 1529437 T^{12} + 2201717 T^{13} + 4353013 T^{14} + 3294172 T^{15} + 5764801 T^{16} \))(\( 1 + 25 T^{2} + 7 T^{3} + 245 T^{4} + 304 T^{5} + 1099 T^{6} + 4509 T^{7} + 3708 T^{8} + 31563 T^{9} + 53851 T^{10} + 104272 T^{11} + 588245 T^{12} + 117649 T^{13} + 2941225 T^{14} + 5764801 T^{16} \))(\( 1 - 11 T + 88 T^{2} - 512 T^{3} + 2549 T^{4} - 10848 T^{5} + 41869 T^{6} - 146188 T^{7} + 478105 T^{8} - 1460284 T^{9} + 4272913 T^{10} - 11903480 T^{11} + 32169505 T^{12} - 83324360 T^{13} + 209372737 T^{14} - 500877412 T^{15} + 1147930105 T^{16} - 2456981716 T^{17} + 4925845981 T^{18} - 8933794464 T^{19} + 14694477749 T^{20} - 20661046784 T^{21} + 24857821912 T^{22} - 21750594173 T^{23} + 13841287201 T^{24} \))(\( 1 + 52 T^{2} - 6 T^{3} + 1394 T^{4} - 322 T^{5} + 25509 T^{6} - 8202 T^{7} + 354863 T^{8} - 133288 T^{9} + 3954335 T^{10} - 1561758 T^{11} + 36269970 T^{12} - 13981732 T^{13} + 277464040 T^{14} - 97872124 T^{15} + 1777228530 T^{16} - 535682994 T^{17} + 9494358335 T^{18} - 2240171416 T^{19} + 41749277087 T^{20} - 6754699686 T^{21} + 147054308709 T^{22} - 12993861454 T^{23} + 393770497106 T^{24} - 11863960458 T^{25} + 719746934452 T^{26} + 678223072849 T^{28} \))(\( 1 + 52 T^{2} - 6 T^{3} + 1394 T^{4} - 322 T^{5} + 25509 T^{6} - 8202 T^{7} + 354863 T^{8} - 133288 T^{9} + 3954335 T^{10} - 1561758 T^{11} + 36269970 T^{12} - 13981732 T^{13} + 277464040 T^{14} - 97872124 T^{15} + 1777228530 T^{16} - 535682994 T^{17} + 9494358335 T^{18} - 2240171416 T^{19} + 41749277087 T^{20} - 6754699686 T^{21} + 147054308709 T^{22} - 12993861454 T^{23} + 393770497106 T^{24} - 11863960458 T^{25} + 719746934452 T^{26} + 678223072849 T^{28} \))
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 7 T + 52 T^{2} - 216 T^{3} + 1010 T^{4} - 3179 T^{5} + 11110 T^{6} - 26136 T^{7} + 69212 T^{8} - 102487 T^{9} + 161051 T^{10} \))(\( 1 - 15 T + 124 T^{2} - 696 T^{3} + 3040 T^{4} - 10921 T^{5} + 33440 T^{6} - 84216 T^{7} + 165044 T^{8} - 219615 T^{9} + 161051 T^{10} \))(\( 1 + 13 T + 129 T^{2} + 897 T^{3} + 5403 T^{4} + 26878 T^{5} + 120351 T^{6} + 466726 T^{7} + 1652716 T^{8} + 5133986 T^{9} + 14562471 T^{10} + 35774618 T^{11} + 79105323 T^{12} + 144462747 T^{13} + 228531369 T^{14} + 253333223 T^{15} + 214358881 T^{16} \))(\( 1 + 5 T + 65 T^{2} + 281 T^{3} + 2021 T^{4} + 7532 T^{5} + 38975 T^{6} + 124436 T^{7} + 512616 T^{8} + 1368796 T^{9} + 4715975 T^{10} + 10025092 T^{11} + 29589461 T^{12} + 45255331 T^{13} + 115151465 T^{14} + 97435855 T^{15} + 214358881 T^{16} \))(\( 1 + 55 T^{2} + 12 T^{3} + 1596 T^{4} + 688 T^{5} + 31920 T^{6} + 20160 T^{7} + 495320 T^{8} + 392868 T^{9} + 6450124 T^{10} + 5620672 T^{11} + 74530936 T^{12} + 61827392 T^{13} + 780465004 T^{14} + 522907308 T^{15} + 7251980120 T^{16} + 3246788160 T^{17} + 56548227120 T^{18} + 13407173648 T^{19} + 342116774076 T^{20} + 28295372292 T^{21} + 1426558353055 T^{22} + 3138428376721 T^{24} \))(\( 1 + 12 T + 137 T^{2} + 924 T^{3} + 5888 T^{4} + 26524 T^{5} + 116284 T^{6} + 365704 T^{7} + 1245761 T^{8} + 3011608 T^{9} + 11702172 T^{10} + 36005440 T^{11} + 187249750 T^{12} + 639420336 T^{13} + 2648993946 T^{14} + 7033623696 T^{15} + 22657219750 T^{16} + 47923240640 T^{17} + 171331500252 T^{18} + 485022480008 T^{19} + 2206941602921 T^{20} + 7126536383384 T^{21} + 24926508118204 T^{22} + 62542204556084 T^{23} + 152719556050688 T^{24} + 263627983644564 T^{25} + 429964687610777 T^{26} + 414272545727172 T^{27} + 379749833583241 T^{28} \))(\( 1 - 12 T + 137 T^{2} - 924 T^{3} + 5888 T^{4} - 26524 T^{5} + 116284 T^{6} - 365704 T^{7} + 1245761 T^{8} - 3011608 T^{9} + 11702172 T^{10} - 36005440 T^{11} + 187249750 T^{12} - 639420336 T^{13} + 2648993946 T^{14} - 7033623696 T^{15} + 22657219750 T^{16} - 47923240640 T^{17} + 171331500252 T^{18} - 485022480008 T^{19} + 2206941602921 T^{20} - 7126536383384 T^{21} + 24926508118204 T^{22} - 62542204556084 T^{23} + 152719556050688 T^{24} - 263627983644564 T^{25} + 429964687610777 T^{26} - 414272545727172 T^{27} + 379749833583241 T^{28} \))
$13$ (\( 1 - 6 T + 13 T^{2} \))(\( 1 + 5 T + 31 T^{2} + 65 T^{3} + 169 T^{4} \))(\( 1 + 8 T + 64 T^{2} + 350 T^{3} + 1603 T^{4} + 6413 T^{5} + 20839 T^{6} + 59150 T^{7} + 140608 T^{8} + 228488 T^{9} + 371293 T^{10} \))(\( 1 + 24 T^{2} - 32 T^{3} + 503 T^{4} - 145 T^{5} + 6539 T^{6} - 5408 T^{7} + 52728 T^{8} + 371293 T^{10} \))(\( 1 + 67 T^{2} - 52 T^{3} + 2166 T^{4} - 2407 T^{5} + 46871 T^{6} - 49521 T^{7} + 723870 T^{8} - 643773 T^{9} + 7921199 T^{10} - 5288179 T^{11} + 61863126 T^{12} - 19307236 T^{13} + 323396203 T^{14} + 815730721 T^{16} \))(\( 1 + 43 T^{2} - 10 T^{3} + 1062 T^{4} - 887 T^{5} + 18051 T^{6} - 22315 T^{7} + 251414 T^{8} - 290095 T^{9} + 3050619 T^{10} - 1948739 T^{11} + 30331782 T^{12} - 3712930 T^{13} + 207552787 T^{14} + 815730721 T^{16} \))(\( 1 - 9 T + 109 T^{2} - 645 T^{3} + 4648 T^{4} - 20861 T^{5} + 117121 T^{6} - 441833 T^{7} + 2219655 T^{8} - 7677394 T^{9} + 36384794 T^{10} - 117891114 T^{11} + 516138240 T^{12} - 1532584482 T^{13} + 6149030186 T^{14} - 16867234618 T^{15} + 63395566455 T^{16} - 164049500069 T^{17} + 565320696889 T^{18} - 1308996813137 T^{19} + 3791516391208 T^{20} - 6839902095585 T^{21} + 15026575611541 T^{22} - 16129443546333 T^{23} + 23298085122481 T^{24} \))(\( 1 + 2 T + 92 T^{2} + 178 T^{3} + 4326 T^{4} + 8798 T^{5} + 136604 T^{6} + 303330 T^{7} + 3238254 T^{8} + 7898934 T^{9} + 61569081 T^{10} + 160967710 T^{11} + 984155055 T^{12} + 2610481632 T^{13} + 13652094166 T^{14} + 33936261216 T^{15} + 166322204295 T^{16} + 353646058870 T^{17} + 1758474522441 T^{18} + 2932818901662 T^{19} + 15630433551486 T^{20} + 19033507661610 T^{21} + 111432079411484 T^{22} + 93298385483654 T^{23} + 596375835738774 T^{24} + 319004550138586 T^{25} + 2143423831268252 T^{26} + 605750213184506 T^{27} + 3937376385699289 T^{28} \))(\( 1 + 2 T + 92 T^{2} + 178 T^{3} + 4326 T^{4} + 8798 T^{5} + 136604 T^{6} + 303330 T^{7} + 3238254 T^{8} + 7898934 T^{9} + 61569081 T^{10} + 160967710 T^{11} + 984155055 T^{12} + 2610481632 T^{13} + 13652094166 T^{14} + 33936261216 T^{15} + 166322204295 T^{16} + 353646058870 T^{17} + 1758474522441 T^{18} + 2932818901662 T^{19} + 15630433551486 T^{20} + 19033507661610 T^{21} + 111432079411484 T^{22} + 93298385483654 T^{23} + 596375835738774 T^{24} + 319004550138586 T^{25} + 2143423831268252 T^{26} + 605750213184506 T^{27} + 3937376385699289 T^{28} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 - 5 T + 39 T^{2} - 85 T^{3} + 289 T^{4} \))(\( 1 + 5 T + 51 T^{2} + 106 T^{3} + 901 T^{4} + 1007 T^{5} + 15317 T^{6} + 30634 T^{7} + 250563 T^{8} + 417605 T^{9} + 1419857 T^{10} \))(\( 1 - 11 T + 75 T^{2} - 390 T^{3} + 2037 T^{4} - 9105 T^{5} + 34629 T^{6} - 112710 T^{7} + 368475 T^{8} - 918731 T^{9} + 1419857 T^{10} \))(\( 1 + 11 T + 116 T^{2} + 683 T^{3} + 4251 T^{4} + 18412 T^{5} + 96214 T^{6} + 371378 T^{7} + 1794794 T^{8} + 6313426 T^{9} + 27805846 T^{10} + 90458156 T^{11} + 355047771 T^{12} + 969762331 T^{13} + 2799958004 T^{14} + 4513725403 T^{15} + 6975757441 T^{16} \))(\( 1 - 7 T + 94 T^{2} - 515 T^{3} + 3983 T^{4} - 19188 T^{5} + 110490 T^{6} - 475150 T^{7} + 2210030 T^{8} - 8077550 T^{9} + 31931610 T^{10} - 94270644 T^{11} + 332664143 T^{12} - 731226355 T^{13} + 2268931486 T^{14} - 2872370711 T^{15} + 6975757441 T^{16} \))(\( 1 + 3 T + 89 T^{2} + 271 T^{3} + 3764 T^{4} + 10083 T^{5} + 102997 T^{6} + 196615 T^{7} + 2062567 T^{8} + 2024678 T^{9} + 33284978 T^{10} + 9244702 T^{11} + 527249480 T^{12} + 157159934 T^{13} + 9619358642 T^{14} + 9947243014 T^{15} + 172267658407 T^{16} + 279165184055 T^{17} + 2486097194293 T^{18} + 4137444839859 T^{19} + 26256751007924 T^{20} + 32137314530687 T^{21} + 179423457139961 T^{22} + 102815688922899 T^{23} + 582622237229761 T^{24} \))(\( 1 + 26 T + 467 T^{2} + 6240 T^{3} + 69389 T^{4} + 660108 T^{5} + 5547310 T^{6} + 41737680 T^{7} + 285097640 T^{8} + 1780774190 T^{9} + 10244083880 T^{10} + 54484105138 T^{11} + 268924628290 T^{12} + 1233975861412 T^{13} + 5272413571728 T^{14} + 20977589644004 T^{15} + 77719217575810 T^{16} + 267680408542994 T^{17} + 855596129741480 T^{18} + 2528444699090830 T^{19} + 6881563957237160 T^{20} + 17126584225298640 T^{21} + 38696689010033710 T^{22} + 78280805978681676 T^{23} + 139887800758255661 T^{24} + 213856632959629920 T^{25} + 272084584786298387 T^{26} + 257519028855554362 T^{27} + 168377826559400929 T^{28} \))(\( 1 - 26 T + 467 T^{2} - 6240 T^{3} + 69389 T^{4} - 660108 T^{5} + 5547310 T^{6} - 41737680 T^{7} + 285097640 T^{8} - 1780774190 T^{9} + 10244083880 T^{10} - 54484105138 T^{11} + 268924628290 T^{12} - 1233975861412 T^{13} + 5272413571728 T^{14} - 20977589644004 T^{15} + 77719217575810 T^{16} - 267680408542994 T^{17} + 855596129741480 T^{18} - 2528444699090830 T^{19} + 6881563957237160 T^{20} - 17126584225298640 T^{21} + 38696689010033710 T^{22} - 78280805978681676 T^{23} + 139887800758255661 T^{24} - 213856632959629920 T^{25} + 272084584786298387 T^{26} - 257519028855554362 T^{27} + 168377826559400929 T^{28} \))
$19$ (\( 1 - 4 T + 19 T^{2} \))(\( 1 + 18 T^{2} + 361 T^{4} \))(\( 1 + 20 T + 248 T^{2} + 2074 T^{3} + 13271 T^{4} + 64971 T^{5} + 252149 T^{6} + 748714 T^{7} + 1701032 T^{8} + 2606420 T^{9} + 2476099 T^{10} \))(\( 1 + 16 T + 156 T^{2} + 1114 T^{3} + 6331 T^{4} + 30103 T^{5} + 120289 T^{6} + 402154 T^{7} + 1070004 T^{8} + 2085136 T^{9} + 2476099 T^{10} \))(\( 1 - 12 T + 157 T^{2} - 1298 T^{3} + 10390 T^{4} - 65307 T^{5} + 390291 T^{6} - 1947317 T^{7} + 9226946 T^{8} - 36999023 T^{9} + 140895051 T^{10} - 447940713 T^{11} + 1354035190 T^{12} - 3213976502 T^{13} + 7386203317 T^{14} - 10726460868 T^{15} + 16983563041 T^{16} \))(\( 1 - 24 T + 353 T^{2} - 3710 T^{3} + 31022 T^{4} - 214835 T^{5} + 1278735 T^{6} - 6653837 T^{7} + 30755986 T^{8} - 126422903 T^{9} + 461623335 T^{10} - 1473553265 T^{11} + 4042818062 T^{12} - 9186327290 T^{13} + 16607195993 T^{14} - 21452921736 T^{15} + 16983563041 T^{16} \))(\( 1 + 123 T^{2} - 44 T^{3} + 7924 T^{4} - 5052 T^{5} + 346656 T^{6} - 289044 T^{7} + 11384560 T^{8} - 10701760 T^{9} + 295368344 T^{10} - 279137696 T^{11} + 6209526260 T^{12} - 5303616224 T^{13} + 106627972184 T^{14} - 73403371840 T^{15} + 1483647243760 T^{16} - 715701559356 T^{17} + 16308736923936 T^{18} - 4515840025428 T^{19} + 134577753536884 T^{20} - 14198258702276 T^{21} + 754121149709523 T^{22} + 2213314919066161 T^{24} \))(\( 1 + 108 T^{2} + 100 T^{3} + 6164 T^{4} + 10482 T^{5} + 254274 T^{6} + 564448 T^{7} + 8391482 T^{8} + 21209702 T^{9} + 231229901 T^{10} + 613500214 T^{11} + 5456931093 T^{12} + 14214864186 T^{13} + 111406539970 T^{14} + 270082419534 T^{15} + 1969952124573 T^{16} + 4207997967826 T^{17} + 30134111928221 T^{18} + 52517321912498 T^{19} + 394784663585642 T^{20} + 504544115335072 T^{21} + 4318478508687234 T^{22} + 3382412448119478 T^{23} + 37791892413085364 T^{24} + 11649025889821900 T^{25} + 239038011259145388 T^{26} + 799006685782884121 T^{28} \))(\( 1 + 108 T^{2} + 100 T^{3} + 6164 T^{4} + 10482 T^{5} + 254274 T^{6} + 564448 T^{7} + 8391482 T^{8} + 21209702 T^{9} + 231229901 T^{10} + 613500214 T^{11} + 5456931093 T^{12} + 14214864186 T^{13} + 111406539970 T^{14} + 270082419534 T^{15} + 1969952124573 T^{16} + 4207997967826 T^{17} + 30134111928221 T^{18} + 52517321912498 T^{19} + 394784663585642 T^{20} + 504544115335072 T^{21} + 4318478508687234 T^{22} + 3382412448119478 T^{23} + 37791892413085364 T^{24} + 11649025889821900 T^{25} + 239038011259145388 T^{26} + 799006685782884121 T^{28} \))
$23$ (\( 1 - 8 T + 23 T^{2} \))(\( 1 + T + 45 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 + T + 38 T^{2} + 66 T^{3} + 1278 T^{4} + 185 T^{5} + 29394 T^{6} + 34914 T^{7} + 462346 T^{8} + 279841 T^{9} + 6436343 T^{10} \))(\( 1 - 9 T + 114 T^{2} - 658 T^{3} + 4866 T^{4} - 20699 T^{5} + 111918 T^{6} - 348082 T^{7} + 1387038 T^{8} - 2518569 T^{9} + 6436343 T^{10} \))(\( 1 + 7 T + 165 T^{2} + 1013 T^{3} + 12309 T^{4} + 65238 T^{5} + 541223 T^{6} + 2417292 T^{7} + 15329148 T^{8} + 55597716 T^{9} + 286306967 T^{10} + 793750746 T^{11} + 3444562869 T^{12} + 6520015459 T^{13} + 24425921685 T^{14} + 23833778129 T^{15} + 78310985281 T^{16} \))(\( 1 + T + 69 T^{2} - 65 T^{3} + 3165 T^{4} - 2232 T^{5} + 113855 T^{6} - 101490 T^{7} + 2806012 T^{8} - 2334270 T^{9} + 60229295 T^{10} - 27156744 T^{11} + 885696765 T^{12} - 418362295 T^{13} + 10214476341 T^{14} + 3404825447 T^{15} + 78310985281 T^{16} \))(\( 1 + T + 111 T^{2} - 17 T^{3} + 6044 T^{4} - 5251 T^{5} + 232339 T^{6} - 271053 T^{7} + 7190087 T^{8} - 9335894 T^{9} + 189133806 T^{10} - 264460122 T^{11} + 4496011768 T^{12} - 6082582806 T^{13} + 100051783374 T^{14} - 113589822298 T^{15} + 2012081136167 T^{16} - 1744590079179 T^{17} + 34394510414371 T^{18} - 17878738422197 T^{19} + 473311595038364 T^{20} - 30619595244871 T^{21} + 4598342744715039 T^{22} + 952809757913927 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 24 T + 395 T^{2} + 4430 T^{3} + 39942 T^{4} + 283318 T^{5} + 1695456 T^{6} + 8346530 T^{7} + 37063497 T^{8} + 154392698 T^{9} + 771775494 T^{10} + 4465086344 T^{11} + 28591796692 T^{12} + 164021373600 T^{13} + 855594339126 T^{14} + 3772491592800 T^{15} + 15125060450068 T^{16} + 54326705547448 T^{17} + 215974426016454 T^{18} + 993724361023414 T^{19} + 5486727727843833 T^{20} + 28418477738148910 T^{21} + 132772829860583136 T^{22} + 510298969740374234 T^{23} + 1654657710895568358 T^{24} + 4220947227558696610 T^{25} + 8656276650648026795 T^{26} + 12096872686475217192 T^{27} + 11592836324538749809 T^{28} \))(\( 1 - 24 T + 395 T^{2} - 4430 T^{3} + 39942 T^{4} - 283318 T^{5} + 1695456 T^{6} - 8346530 T^{7} + 37063497 T^{8} - 154392698 T^{9} + 771775494 T^{10} - 4465086344 T^{11} + 28591796692 T^{12} - 164021373600 T^{13} + 855594339126 T^{14} - 3772491592800 T^{15} + 15125060450068 T^{16} - 54326705547448 T^{17} + 215974426016454 T^{18} - 993724361023414 T^{19} + 5486727727843833 T^{20} - 28418477738148910 T^{21} + 132772829860583136 T^{22} - 510298969740374234 T^{23} + 1654657710895568358 T^{24} - 4220947227558696610 T^{25} + 8656276650648026795 T^{26} - 12096872686475217192 T^{27} + 11592836324538749809 T^{28} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 8 T + 69 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 5 T + 74 T^{2} - 250 T^{3} + 3266 T^{4} - 10091 T^{5} + 94714 T^{6} - 210250 T^{7} + 1804786 T^{8} - 3536405 T^{9} + 20511149 T^{10} \))(\( 1 - T + 56 T^{2} + 30 T^{3} + 1306 T^{4} + 3579 T^{5} + 37874 T^{6} + 25230 T^{7} + 1365784 T^{8} - 707281 T^{9} + 20511149 T^{10} \))(\( 1 + T + 129 T^{2} + 195 T^{3} + 6633 T^{4} + 16732 T^{5} + 181393 T^{6} + 805780 T^{7} + 4241976 T^{8} + 23367620 T^{9} + 152551513 T^{10} + 408076748 T^{11} + 4691394873 T^{12} + 3999674055 T^{13} + 76732208409 T^{14} + 17249876309 T^{15} + 500246412961 T^{16} \))(\( 1 - 11 T + 179 T^{2} - 1685 T^{3} + 15871 T^{4} - 120326 T^{5} + 863835 T^{6} - 5257502 T^{7} + 30730100 T^{8} - 152467558 T^{9} + 726485235 T^{10} - 2934630814 T^{11} + 11225256751 T^{12} - 34561286065 T^{13} + 106473374459 T^{14} - 189748639399 T^{15} + 500246412961 T^{16} \))(\( 1 - 6 T + 212 T^{2} - 1082 T^{3} + 21101 T^{4} - 89188 T^{5} + 1306403 T^{6} - 4417266 T^{7} + 57247721 T^{8} - 150616432 T^{9} + 1974753899 T^{10} - 4219750520 T^{11} + 59628660633 T^{12} - 122372765080 T^{13} + 1660768029059 T^{14} - 3673384160048 T^{15} + 40490225356601 T^{16} - 90603201098634 T^{17} + 777078971024363 T^{18} - 1538481968247092 T^{19} + 10555699559890061 T^{20} - 15696731945890258 T^{21} + 89189933459642612 T^{22} - 73203058594234974 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 16 T + 251 T^{2} + 2588 T^{3} + 26314 T^{4} + 219296 T^{5} + 1802294 T^{6} + 13068460 T^{7} + 93258059 T^{8} + 606986728 T^{9} + 3894586830 T^{10} + 23278278820 T^{11} + 137817541750 T^{12} + 769115415212 T^{13} + 4259238284330 T^{14} + 22304347041148 T^{15} + 115904552611750 T^{16} + 567733942140980 T^{17} + 2754567267709230 T^{18} + 12449995219030472 T^{19} + 55472068364393939 T^{20} + 225429318549114140 T^{21} + 901591108601132534 T^{22} + 3181359083924168224 T^{23} + 11070490137061489114 T^{24} + 31574919273646685452 T^{25} + 88807510584572729291 T^{26} + \)\(16\!\cdots\!24\)\( T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( 1 - 16 T + 251 T^{2} - 2588 T^{3} + 26314 T^{4} - 219296 T^{5} + 1802294 T^{6} - 13068460 T^{7} + 93258059 T^{8} - 606986728 T^{9} + 3894586830 T^{10} - 23278278820 T^{11} + 137817541750 T^{12} - 769115415212 T^{13} + 4259238284330 T^{14} - 22304347041148 T^{15} + 115904552611750 T^{16} - 567733942140980 T^{17} + 2754567267709230 T^{18} - 12449995219030472 T^{19} + 55472068364393939 T^{20} - 225429318549114140 T^{21} + 901591108601132534 T^{22} - 3181359083924168224 T^{23} + 11070490137061489114 T^{24} - 31574919273646685452 T^{25} + 88807510584572729291 T^{26} - \)\(16\!\cdots\!24\)\( T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 - 6 T + 66 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 18 T + 273 T^{2} + 2579 T^{3} + 21028 T^{4} + 125483 T^{5} + 651868 T^{6} + 2478419 T^{7} + 8132943 T^{8} + 16623378 T^{9} + 28629151 T^{10} \))(\( 1 + 18 T + 245 T^{2} + 2311 T^{3} + 17740 T^{4} + 108663 T^{5} + 549940 T^{6} + 2220871 T^{7} + 7298795 T^{8} + 16623378 T^{9} + 28629151 T^{10} \))(\( 1 + 2 T + 42 T^{2} - 147 T^{3} + 2272 T^{4} + 556 T^{5} + 120062 T^{6} - 147459 T^{7} + 2714766 T^{8} - 4571229 T^{9} + 115379582 T^{10} + 16563796 T^{11} + 2098239712 T^{12} - 4208485197 T^{13} + 37275154602 T^{14} + 55025228222 T^{15} + 852891037441 T^{16} \))(\( 1 - 30 T + 494 T^{2} - 5767 T^{3} + 53036 T^{4} - 409236 T^{5} + 2761738 T^{6} - 16906143 T^{7} + 96763478 T^{8} - 524090433 T^{9} + 2654030218 T^{10} - 12191549676 T^{11} + 48979859756 T^{12} - 165104313817 T^{13} + 438426818414 T^{14} - 825378423330 T^{15} + 852891037441 T^{16} \))(\( 1 - 2 T + 215 T^{2} - 552 T^{3} + 24140 T^{4} - 66360 T^{5} + 1836432 T^{6} - 5016820 T^{7} + 103696828 T^{8} - 270132408 T^{9} + 4543215564 T^{10} - 10915998044 T^{11} + 157730757196 T^{12} - 338395939364 T^{13} + 4366030157004 T^{14} - 8047514566728 T^{15} + 95766198291388 T^{16} - 143627297319820 T^{17} + 1629840159906192 T^{18} - 1825737072405960 T^{19} + 20588789643825740 T^{20} - 14594671432690392 T^{21} + 176220081700872215 T^{22} - 50816953792809662 T^{23} + 787662783788549761 T^{24} \))(\( 1 - 8 T + 302 T^{2} - 2178 T^{3} + 43971 T^{4} - 287864 T^{5} + 4130345 T^{6} - 24679312 T^{7} + 281786583 T^{8} - 1541345010 T^{9} + 14851568619 T^{10} - 74353357944 T^{11} + 625737338609 T^{12} - 2856210573848 T^{13} + 21448165431204 T^{14} - 88542527789288 T^{15} + 601333582403249 T^{16} - 2215060886509704 T^{17} + 13715735502587499 T^{18} - 44127399034386510 T^{19} + 250086629668912023 T^{20} - 678992387580971632 T^{21} + 3522734232039247145 T^{22} - 7611015393659396744 T^{23} + 36039875406832800771 T^{24} - 55339662680369721918 T^{25} + \)\(23\!\cdots\!22\)\( T^{26} - \)\(19\!\cdots\!28\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 - 8 T + 302 T^{2} - 2178 T^{3} + 43971 T^{4} - 287864 T^{5} + 4130345 T^{6} - 24679312 T^{7} + 281786583 T^{8} - 1541345010 T^{9} + 14851568619 T^{10} - 74353357944 T^{11} + 625737338609 T^{12} - 2856210573848 T^{13} + 21448165431204 T^{14} - 88542527789288 T^{15} + 601333582403249 T^{16} - 2215060886509704 T^{17} + 13715735502587499 T^{18} - 44127399034386510 T^{19} + 250086629668912023 T^{20} - 678992387580971632 T^{21} + 3522734232039247145 T^{22} - 7611015393659396744 T^{23} + 36039875406832800771 T^{24} - 55339662680369721918 T^{25} + \)\(23\!\cdots\!22\)\( T^{26} - \)\(19\!\cdots\!28\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 + 12 T + 105 T^{2} + 444 T^{3} + 1369 T^{4} \))(\( 1 + 17 T + 208 T^{2} + 1432 T^{3} + 8968 T^{4} + 45509 T^{5} + 331816 T^{6} + 1960408 T^{7} + 10535824 T^{8} + 31860737 T^{9} + 69343957 T^{10} \))(\( 1 - 7 T + 108 T^{2} - 806 T^{3} + 6788 T^{4} - 38669 T^{5} + 251156 T^{6} - 1103414 T^{7} + 5470524 T^{8} - 13119127 T^{9} + 69343957 T^{10} \))(\( 1 + 9 T + 189 T^{2} + 1437 T^{3} + 17491 T^{4} + 112148 T^{5} + 1044441 T^{6} + 5719578 T^{7} + 44753916 T^{8} + 211624386 T^{9} + 1429839729 T^{10} + 5680632644 T^{11} + 32780950051 T^{12} + 99647266209 T^{13} + 484922291301 T^{14} + 854386894197 T^{15} + 3512479453921 T^{16} \))(\( 1 - 11 T + 189 T^{2} - 1649 T^{3} + 17551 T^{4} - 135404 T^{5} + 1078209 T^{6} - 7208484 T^{7} + 46667124 T^{8} - 266713908 T^{9} + 1476068121 T^{10} - 6858618812 T^{11} + 32893399711 T^{12} - 114348185093 T^{13} + 484922291301 T^{14} - 1044250648463 T^{15} + 3512479453921 T^{16} \))(\( 1 - 34 T + 721 T^{2} - 10994 T^{3} + 136136 T^{4} - 1426586 T^{5} + 13262837 T^{6} - 111888490 T^{7} + 878750471 T^{8} - 6481238924 T^{9} + 45307548946 T^{10} - 299446846172 T^{11} + 1874841412864 T^{12} - 11079533308364 T^{13} + 62026034507074 T^{14} - 328294195217372 T^{15} + 1646919861479831 T^{16} - 7758790639354930 T^{17} + 34028811149162333 T^{18} - 135428486871657938 T^{19} + 478174902938989256 T^{20} - 1428799367307076538 T^{21} + 3466989332513269129 T^{22} - 6049199140501654042 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + 8 T + 367 T^{2} + 2638 T^{3} + 64506 T^{4} + 416352 T^{5} + 7214172 T^{6} + 41863122 T^{7} + 577721515 T^{8} + 3023928872 T^{9} + 35455595340 T^{10} + 168271395126 T^{11} + 1744187268678 T^{12} + 7545465755138 T^{13} + 70730759308874 T^{14} + 279182232940106 T^{15} + 2387792370820182 T^{16} + 8523450977317278 T^{17} + 66449494018009740 T^{18} + 209691193671026504 T^{19} + 1482275348082989635 T^{20} + 3974144754107789226 T^{21} + 25339630927052168412 T^{22} + 54109830287159899104 T^{23} + \)\(31\!\cdots\!94\)\( T^{24} + \)\(46\!\cdots\!94\)\( T^{25} + \)\(24\!\cdots\!27\)\( T^{26} + \)\(19\!\cdots\!76\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 + 8 T + 367 T^{2} + 2638 T^{3} + 64506 T^{4} + 416352 T^{5} + 7214172 T^{6} + 41863122 T^{7} + 577721515 T^{8} + 3023928872 T^{9} + 35455595340 T^{10} + 168271395126 T^{11} + 1744187268678 T^{12} + 7545465755138 T^{13} + 70730759308874 T^{14} + 279182232940106 T^{15} + 2387792370820182 T^{16} + 8523450977317278 T^{17} + 66449494018009740 T^{18} + 209691193671026504 T^{19} + 1482275348082989635 T^{20} + 3974144754107789226 T^{21} + 25339630927052168412 T^{22} + 54109830287159899104 T^{23} + \)\(31\!\cdots\!94\)\( T^{24} + \)\(46\!\cdots\!94\)\( T^{25} + \)\(24\!\cdots\!27\)\( T^{26} + \)\(19\!\cdots\!76\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 + 2 T + 3 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 165 T^{2} + 1039 T^{3} + 11876 T^{4} + 65025 T^{5} + 486916 T^{6} + 1746559 T^{7} + 11371965 T^{8} + 16954566 T^{9} + 115856201 T^{10} \))(\( 1 - 10 T + 85 T^{2} - 521 T^{3} + 2706 T^{4} - 9015 T^{5} + 110946 T^{6} - 875801 T^{7} + 5858285 T^{8} - 28257610 T^{9} + 115856201 T^{10} \))(\( 1 + 4 T + 140 T^{2} + 355 T^{3} + 11350 T^{4} + 28966 T^{5} + 691586 T^{6} + 1546337 T^{7} + 31338264 T^{8} + 63399817 T^{9} + 1162556066 T^{10} + 1996365686 T^{11} + 32072387350 T^{12} + 41128951355 T^{13} + 665014593740 T^{14} + 779017095524 T^{15} + 7984925229121 T^{16} \))(\( 1 + 10 T + 232 T^{2} + 1869 T^{3} + 25858 T^{4} + 173932 T^{5} + 1795868 T^{6} + 10291247 T^{7} + 87043884 T^{8} + 421941127 T^{9} + 3018854108 T^{10} + 11987567372 T^{11} + 73068527938 T^{12} + 216535239669 T^{13} + 1102024183912 T^{14} + 1947542738810 T^{15} + 7984925229121 T^{16} \))(\( 1 - 14 T + 339 T^{2} - 3588 T^{3} + 53932 T^{4} - 480564 T^{5} + 5599015 T^{6} - 43529766 T^{7} + 424099143 T^{8} - 2922923404 T^{9} + 24710309430 T^{10} - 152033575416 T^{11} + 1136390796760 T^{12} - 6233376592056 T^{13} + 41538030151830 T^{14} - 201450803927084 T^{15} + 1198402818422823 T^{16} - 5043193319178966 T^{17} + 26595904896922615 T^{18} - 93591892873348884 T^{19} + 430642987456953772 T^{20} - 1174646380605532068 T^{21} + 4550281506141663939 T^{22} - 7704606444027478174 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 26 T + 748 T^{2} + 13010 T^{3} + 224509 T^{4} + 3000584 T^{5} + 38899723 T^{6} + 425624652 T^{7} + 4492145263 T^{8} + 41628252730 T^{9} + 371700011745 T^{10} + 2973416119806 T^{11} + 22920068572349 T^{12} + 159850260984846 T^{13} + 1074458698822158 T^{14} + 6553860700378686 T^{15} + 38528635270118669 T^{16} + 204930812393149326 T^{17} + 1050335396888562945 T^{18} + 4822891215565678730 T^{19} + 21338158264964360383 T^{20} + 82892220046113314412 T^{21} + \)\(31\!\cdots\!83\)\( T^{22} + \)\(98\!\cdots\!24\)\( T^{23} + \)\(30\!\cdots\!09\)\( T^{24} + \)\(71\!\cdots\!10\)\( T^{25} + \)\(16\!\cdots\!88\)\( T^{26} + \)\(24\!\cdots\!46\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 - 26 T + 748 T^{2} - 13010 T^{3} + 224509 T^{4} - 3000584 T^{5} + 38899723 T^{6} - 425624652 T^{7} + 4492145263 T^{8} - 41628252730 T^{9} + 371700011745 T^{10} - 2973416119806 T^{11} + 22920068572349 T^{12} - 159850260984846 T^{13} + 1074458698822158 T^{14} - 6553860700378686 T^{15} + 38528635270118669 T^{16} - 204930812393149326 T^{17} + 1050335396888562945 T^{18} - 4822891215565678730 T^{19} + 21338158264964360383 T^{20} - 82892220046113314412 T^{21} + \)\(31\!\cdots\!83\)\( T^{22} - \)\(98\!\cdots\!24\)\( T^{23} + \)\(30\!\cdots\!09\)\( T^{24} - \)\(71\!\cdots\!10\)\( T^{25} + \)\(16\!\cdots\!88\)\( T^{26} - \)\(24\!\cdots\!46\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))
$43$ (\( 1 + 6 T + 43 T^{2} \))(\( 1 + 6 T + 15 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 163 T^{2} + 1031 T^{3} + 11132 T^{4} + 55845 T^{5} + 478676 T^{6} + 1906319 T^{7} + 12959641 T^{8} + 34188010 T^{9} + 147008443 T^{10} \))(\( 1 - 6 T + 89 T^{2} - 79 T^{3} + 1118 T^{4} + 15267 T^{5} + 48074 T^{6} - 146071 T^{7} + 7076123 T^{8} - 20512806 T^{9} + 147008443 T^{10} \))(\( 1 - 2 T + 306 T^{2} - 625 T^{3} + 42368 T^{4} - 81466 T^{5} + 3468520 T^{6} - 5843465 T^{7} + 183436652 T^{8} - 251268995 T^{9} + 6413293480 T^{10} - 6477117262 T^{11} + 144847760768 T^{12} - 91880276875 T^{13} + 1934337092994 T^{14} - 543637222214 T^{15} + 11688200277601 T^{16} \))(\( 1 - 24 T + 480 T^{2} - 6573 T^{3} + 79642 T^{4} - 786764 T^{5} + 7047644 T^{6} - 54159389 T^{7} + 381070708 T^{8} - 2328853727 T^{9} + 13031093756 T^{10} - 62553245348 T^{11} + 272280149242 T^{12} - 966286495839 T^{13} + 3034254263520 T^{14} - 6523646666568 T^{15} + 11688200277601 T^{16} \))(\( 1 - 6 T + 255 T^{2} - 1748 T^{3} + 32440 T^{4} - 226068 T^{5} + 2746475 T^{6} - 18002290 T^{7} + 172552423 T^{8} - 1047703492 T^{9} + 8712770270 T^{10} - 50501656128 T^{11} + 388449379296 T^{12} - 2171571213504 T^{13} + 16109912229230 T^{14} - 83299761538444 T^{15} + 589922396304823 T^{16} - 2646488623334470 T^{17} + 17361465580002275 T^{18} - 61449489775737276 T^{19} + 379165217005376440 T^{20} - 878531885665601564 T^{21} + 5510927989887483495 T^{22} - 5575762436827336242 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 6 T + 282 T^{2} + 1660 T^{3} + 38531 T^{4} + 214740 T^{5} + 3403919 T^{6} + 16959498 T^{7} + 217807469 T^{8} + 905480210 T^{9} + 10822632373 T^{10} + 35383900490 T^{11} + 456940524673 T^{12} + 1216941844454 T^{13} + 18941684033374 T^{14} + 52328499311522 T^{15} + 844883030120377 T^{16} + 2813267776258430 T^{17} + 37000426379444773 T^{18} + 133113235839413030 T^{19} + 1376840086332812981 T^{20} + 4609907191431944286 T^{21} + 39785687000731318319 T^{22} + \)\(10\!\cdots\!20\)\( T^{23} + \)\(83\!\cdots\!19\)\( T^{24} + \)\(15\!\cdots\!20\)\( T^{25} + \)\(11\!\cdots\!82\)\( T^{26} + \)\(10\!\cdots\!58\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 + 6 T + 282 T^{2} + 1660 T^{3} + 38531 T^{4} + 214740 T^{5} + 3403919 T^{6} + 16959498 T^{7} + 217807469 T^{8} + 905480210 T^{9} + 10822632373 T^{10} + 35383900490 T^{11} + 456940524673 T^{12} + 1216941844454 T^{13} + 18941684033374 T^{14} + 52328499311522 T^{15} + 844883030120377 T^{16} + 2813267776258430 T^{17} + 37000426379444773 T^{18} + 133113235839413030 T^{19} + 1376840086332812981 T^{20} + 4609907191431944286 T^{21} + 39785687000731318319 T^{22} + \)\(10\!\cdots\!20\)\( T^{23} + \)\(83\!\cdots\!19\)\( T^{24} + \)\(15\!\cdots\!20\)\( T^{25} + \)\(11\!\cdots\!82\)\( T^{26} + \)\(10\!\cdots\!58\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))
$47$ (\( 1 + 8 T + 47 T^{2} \))(\( ( 1 + 7 T + 47 T^{2} )^{2} \))(\( 1 - 3 T + 172 T^{2} - 341 T^{3} + 13415 T^{4} - 19347 T^{5} + 630505 T^{6} - 753269 T^{7} + 17857556 T^{8} - 14639043 T^{9} + 229345007 T^{10} \))(\( 1 - 7 T + 178 T^{2} - 799 T^{3} + 13385 T^{4} - 45389 T^{5} + 629095 T^{6} - 1764991 T^{7} + 18480494 T^{8} - 34157767 T^{9} + 229345007 T^{10} \))(\( 1 + 17 T + 343 T^{2} + 3782 T^{3} + 46162 T^{4} + 389283 T^{5} + 3631945 T^{6} + 25382322 T^{7} + 198853598 T^{8} + 1192969134 T^{9} + 8022966505 T^{10} + 40416528909 T^{11} + 225255834322 T^{12} + 867382816474 T^{13} + 3697270857847 T^{14} + 8612593047871 T^{15} + 23811286661761 T^{16} \))(\( 1 - 3 T + 73 T^{2} - 628 T^{3} + 6578 T^{4} - 33029 T^{5} + 475607 T^{6} - 2491768 T^{7} + 21399806 T^{8} - 117113096 T^{9} + 1050615863 T^{10} - 3429169867 T^{11} + 32098541618 T^{12} - 144028664396 T^{13} + 786882719017 T^{14} - 1519869361389 T^{15} + 23811286661761 T^{16} \))(\( 1 + 2 T + 336 T^{2} + 344 T^{3} + 54457 T^{4} + 3732 T^{5} + 5722257 T^{6} - 4378892 T^{7} + 444390369 T^{8} - 603623948 T^{9} + 27487693525 T^{10} - 44089368444 T^{11} + 1409831184861 T^{12} - 2072200316868 T^{13} + 60720314996725 T^{14} - 62670049153204 T^{15} + 2168483240192289 T^{16} - 1004277016392244 T^{17} + 61681440370877553 T^{18} + 1890717485567916 T^{19} + 1296691237739518777 T^{20} + 384980882747351848 T^{21} + 17673308431238896464 T^{22} + 4944318430168024606 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 24 T + 475 T^{2} + 6644 T^{3} + 80414 T^{4} + 848248 T^{5} + 8194983 T^{6} + 73704656 T^{7} + 627215954 T^{8} + 5027760264 T^{9} + 38811285448 T^{10} + 286173333844 T^{11} + 2068072950787 T^{12} + 14562423408036 T^{13} + 100854293912192 T^{14} + 684433900177692 T^{15} + 4568373148288483 T^{16} + 29711374039685612 T^{17} + 189386692186182088 T^{18} + 1153091712941401848 T^{19} + 6760895825950158866 T^{20} + 37340482815371975728 T^{21} + \)\(19\!\cdots\!63\)\( T^{22} + \)\(94\!\cdots\!16\)\( T^{23} + \)\(42\!\cdots\!86\)\( T^{24} + \)\(16\!\cdots\!32\)\( T^{25} + \)\(55\!\cdots\!75\)\( T^{26} + \)\(13\!\cdots\!48\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 - 24 T + 475 T^{2} - 6644 T^{3} + 80414 T^{4} - 848248 T^{5} + 8194983 T^{6} - 73704656 T^{7} + 627215954 T^{8} - 5027760264 T^{9} + 38811285448 T^{10} - 286173333844 T^{11} + 2068072950787 T^{12} - 14562423408036 T^{13} + 100854293912192 T^{14} - 684433900177692 T^{15} + 4568373148288483 T^{16} - 29711374039685612 T^{17} + 189386692186182088 T^{18} - 1153091712941401848 T^{19} + 6760895825950158866 T^{20} - 37340482815371975728 T^{21} + \)\(19\!\cdots\!63\)\( T^{22} - \)\(94\!\cdots\!16\)\( T^{23} + \)\(42\!\cdots\!86\)\( T^{24} - \)\(16\!\cdots\!32\)\( T^{25} + \)\(55\!\cdots\!75\)\( T^{26} - \)\(13\!\cdots\!48\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))
$53$ (\( 1 + 12 T + 53 T^{2} \))(\( 1 - 10 T + 126 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 15 T + 200 T^{2} + 1763 T^{3} + 13441 T^{4} + 101901 T^{5} + 712373 T^{6} + 4952267 T^{7} + 29775400 T^{8} + 118357215 T^{9} + 418195493 T^{10} \))(\( 1 - 9 T + 138 T^{2} - 183 T^{3} + 2319 T^{4} + 34225 T^{5} + 122907 T^{6} - 514047 T^{7} + 20545026 T^{8} - 71014329 T^{9} + 418195493 T^{10} \))(\( 1 + 9 T + 371 T^{2} + 2932 T^{3} + 62840 T^{4} + 427509 T^{5} + 6314527 T^{6} + 36165056 T^{7} + 411010840 T^{8} + 1916747968 T^{9} + 17737506343 T^{10} + 63646257393 T^{11} + 495837826040 T^{12} + 1226149185476 T^{13} + 8222977978859 T^{14} + 10572400258533 T^{15} + 62259690411361 T^{16} \))(\( 1 - 25 T + 579 T^{2} - 8774 T^{3} + 120610 T^{4} - 1329957 T^{5} + 13375065 T^{6} - 114505786 T^{7} + 896980008 T^{8} - 6068806658 T^{9} + 37570557585 T^{10} - 198000008289 T^{11} + 951670913410 T^{12} - 3669247255582 T^{13} + 12833165093691 T^{14} - 29367778495925 T^{15} + 62259690411361 T^{16} \))(\( 1 + 10 T + 416 T^{2} + 3966 T^{3} + 86330 T^{4} + 761902 T^{5} + 11674400 T^{6} + 94151882 T^{7} + 1144126111 T^{8} + 8383469412 T^{9} + 85931558464 T^{10} + 568900866028 T^{11} + 5098746497836 T^{12} + 30151745899484 T^{13} + 241381747725376 T^{14} + 1248105775650324 T^{15} + 9027705340449391 T^{16} + 39373892709867826 T^{17} + 258755617564397600 T^{18} + 895014766864089974 T^{19} + 5374879073212795130 T^{20} + 13086862405087259478 T^{21} + 72753187672053428384 T^{22} + 92690359293721915970 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 38 T + 1101 T^{2} + 22606 T^{3} + 399326 T^{4} + 5943884 T^{5} + 79924901 T^{6} + 960896588 T^{7} + 10698492214 T^{8} + 109457449812 T^{9} + 1050964757836 T^{10} + 9401053502688 T^{11} + 79462678451505 T^{12} + 629815515646850 T^{13} + 4730510944624794 T^{14} + 33380222329283050 T^{15} + 223210663770277545 T^{16} + 1399600642319681376 T^{17} + 8292617453374559116 T^{18} + 45774612186652097316 T^{19} + \)\(23\!\cdots\!06\)\( T^{20} + \)\(11\!\cdots\!56\)\( T^{21} + \)\(49\!\cdots\!61\)\( T^{22} + \)\(19\!\cdots\!72\)\( T^{23} + \)\(69\!\cdots\!74\)\( T^{24} + \)\(20\!\cdots\!82\)\( T^{25} + \)\(54\!\cdots\!41\)\( T^{26} + \)\(98\!\cdots\!74\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( 1 - 38 T + 1101 T^{2} - 22606 T^{3} + 399326 T^{4} - 5943884 T^{5} + 79924901 T^{6} - 960896588 T^{7} + 10698492214 T^{8} - 109457449812 T^{9} + 1050964757836 T^{10} - 9401053502688 T^{11} + 79462678451505 T^{12} - 629815515646850 T^{13} + 4730510944624794 T^{14} - 33380222329283050 T^{15} + 223210663770277545 T^{16} - 1399600642319681376 T^{17} + 8292617453374559116 T^{18} - 45774612186652097316 T^{19} + \)\(23\!\cdots\!06\)\( T^{20} - \)\(11\!\cdots\!56\)\( T^{21} + \)\(49\!\cdots\!61\)\( T^{22} - \)\(19\!\cdots\!72\)\( T^{23} + \)\(69\!\cdots\!74\)\( T^{24} - \)\(20\!\cdots\!82\)\( T^{25} + \)\(54\!\cdots\!41\)\( T^{26} - \)\(98\!\cdots\!74\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))
$59$ (\( 1 + 12 T + 59 T^{2} \))(\( 1 - 2 T + 114 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( 1 - 17 T + 222 T^{2} - 1631 T^{3} + 11419 T^{4} - 68367 T^{5} + 673721 T^{6} - 5677511 T^{7} + 45594138 T^{8} - 205995137 T^{9} + 714924299 T^{10} \))(\( 1 - 37 T + 764 T^{2} - 11069 T^{3} + 121669 T^{4} - 1047931 T^{5} + 7178471 T^{6} - 38531189 T^{7} + 156909556 T^{8} - 448342357 T^{9} + 714924299 T^{10} \))(\( 1 + 29 T + 741 T^{2} + 12436 T^{3} + 187204 T^{4} + 2234733 T^{5} + 24274943 T^{6} + 220913290 T^{7} + 1841244926 T^{8} + 13033884110 T^{9} + 84501076583 T^{10} + 458967228807 T^{11} + 2268418448644 T^{12} + 8890798582364 T^{13} + 31255775427981 T^{14} + 72170893059751 T^{15} + 146830437604321 T^{16} \))(\( 1 + 45 T + 1223 T^{2} + 23998 T^{3} + 374940 T^{4} + 4846851 T^{5} + 53304093 T^{6} + 504932174 T^{7} + 4157961070 T^{8} + 29790998266 T^{9} + 185551547733 T^{10} + 995441411529 T^{11} + 4543283333340 T^{12} + 17156753327402 T^{13} + 51586792642943 T^{14} + 111989316816855 T^{15} + 146830437604321 T^{16} \))(\( 1 - 28 T + 668 T^{2} - 10196 T^{3} + 145714 T^{4} - 1636716 T^{5} + 18251276 T^{6} - 172162052 T^{7} + 1672497151 T^{8} - 14180893624 T^{9} + 126122113016 T^{10} - 986576008488 T^{11} + 8091055420924 T^{12} - 58207984500792 T^{13} + 439031075408696 T^{14} - 2912457751603496 T^{15} + 20266251750138511 T^{16} - 123082834340501548 T^{17} + 769848561309175916 T^{18} - 4073215703627014404 T^{19} + 21395250385076030194 T^{20} - 88327905367005758044 T^{21} + \)\(34\!\cdots\!68\)\( T^{22} - \)\(84\!\cdots\!52\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 10 T + 543 T^{2} + 4200 T^{3} + 135414 T^{4} + 813708 T^{5} + 21140429 T^{6} + 97524910 T^{7} + 2375722486 T^{8} + 8278655814 T^{9} + 209504477712 T^{10} + 554296600500 T^{11} + 15367912283095 T^{12} + 33032858265318 T^{13} + 971150421246016 T^{14} + 1948938637653762 T^{15} + 53495702657453695 T^{16} + 113840881514089500 T^{17} + 2538641387552758032 T^{18} + 5918612204486224386 T^{19} + \)\(10\!\cdots\!26\)\( T^{20} + \)\(24\!\cdots\!90\)\( T^{21} + \)\(31\!\cdots\!09\)\( T^{22} + \)\(70\!\cdots\!12\)\( T^{23} + \)\(69\!\cdots\!14\)\( T^{24} + \)\(12\!\cdots\!00\)\( T^{25} + \)\(96\!\cdots\!83\)\( T^{26} + \)\(10\!\cdots\!90\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 - 10 T + 543 T^{2} - 4200 T^{3} + 135414 T^{4} - 813708 T^{5} + 21140429 T^{6} - 97524910 T^{7} + 2375722486 T^{8} - 8278655814 T^{9} + 209504477712 T^{10} - 554296600500 T^{11} + 15367912283095 T^{12} - 33032858265318 T^{13} + 971150421246016 T^{14} - 1948938637653762 T^{15} + 53495702657453695 T^{16} - 113840881514089500 T^{17} + 2538641387552758032 T^{18} - 5918612204486224386 T^{19} + \)\(10\!\cdots\!26\)\( T^{20} - \)\(24\!\cdots\!90\)\( T^{21} + \)\(31\!\cdots\!09\)\( T^{22} - \)\(70\!\cdots\!12\)\( T^{23} + \)\(69\!\cdots\!14\)\( T^{24} - \)\(12\!\cdots\!00\)\( T^{25} + \)\(96\!\cdots\!83\)\( T^{26} - \)\(10\!\cdots\!90\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))
$61$ (\( 1 - 2 T + 61 T^{2} \))(\( 1 + 117 T^{2} + 3721 T^{4} \))(\( 1 + 2 T + 158 T^{2} + 962 T^{3} + 12461 T^{4} + 93871 T^{5} + 760121 T^{6} + 3579602 T^{7} + 35862998 T^{8} + 27691682 T^{9} + 844596301 T^{10} \))(\( 1 + 2 T + 74 T^{2} - 366 T^{3} + 8477 T^{4} + 9987 T^{5} + 517097 T^{6} - 1361886 T^{7} + 16796594 T^{8} + 27691682 T^{9} + 844596301 T^{10} \))(\( 1 + 12 T + 389 T^{2} + 4096 T^{3} + 72802 T^{4} + 647219 T^{5} + 8262029 T^{6} + 61325593 T^{7} + 615125834 T^{8} + 3740861173 T^{9} + 30743009909 T^{10} + 146906415839 T^{11} + 1008004916482 T^{12} + 3459466448896 T^{13} + 20041425626429 T^{14} + 37712914032252 T^{15} + 191707312997281 T^{16} \))(\( 1 - 16 T + 449 T^{2} - 5808 T^{3} + 91382 T^{4} - 952529 T^{5} + 10887925 T^{6} - 91603311 T^{7} + 824334746 T^{8} - 5587801971 T^{9} + 40513968925 T^{10} - 216205984949 T^{11} + 1265260642262 T^{12} - 4905415316208 T^{13} + 23132648088089 T^{14} - 50283885376336 T^{15} + 191707312997281 T^{16} \))(\( 1 - 2 T + 436 T^{2} - 1038 T^{3} + 96193 T^{4} - 245604 T^{5} + 14171095 T^{6} - 36275338 T^{7} + 1548507881 T^{8} - 3796228844 T^{9} + 131946978859 T^{10} - 299278550144 T^{11} + 8976427949089 T^{12} - 18255991558784 T^{13} + 490974708334339 T^{14} - 861671819239964 T^{15} + 21440393907572921 T^{16} - 30638016292324738 T^{17} + 730100119505295295 T^{18} - 771870211498101684 T^{19} + 18440901559147451233 T^{20} - 12138523644361838358 T^{21} + \)\(31\!\cdots\!36\)\( T^{22} - 87027835222871677322 T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 + 4 T + 412 T^{2} + 744 T^{3} + 85496 T^{4} + 32626 T^{5} + 12399266 T^{6} - 6510256 T^{7} + 1403149254 T^{8} - 1504772318 T^{9} + 129973897001 T^{10} - 175584974106 T^{11} + 10098399185925 T^{12} - 14346897904162 T^{13} + 666660829411622 T^{14} - 875160772153882 T^{15} + 37576143370826925 T^{16} - 39854453007553986 T^{17} + 1799597912026222841 T^{18} - 1270925133629995718 T^{19} + 72290774850437876694 T^{20} - 20460060404662731376 T^{21} + \)\(23\!\cdots\!46\)\( T^{22} + \)\(38\!\cdots\!66\)\( T^{23} + \)\(60\!\cdots\!96\)\( T^{24} + \)\(32\!\cdots\!84\)\( T^{25} + \)\(10\!\cdots\!52\)\( T^{26} + \)\(64\!\cdots\!24\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( 1 + 4 T + 412 T^{2} + 744 T^{3} + 85496 T^{4} + 32626 T^{5} + 12399266 T^{6} - 6510256 T^{7} + 1403149254 T^{8} - 1504772318 T^{9} + 129973897001 T^{10} - 175584974106 T^{11} + 10098399185925 T^{12} - 14346897904162 T^{13} + 666660829411622 T^{14} - 875160772153882 T^{15} + 37576143370826925 T^{16} - 39854453007553986 T^{17} + 1799597912026222841 T^{18} - 1270925133629995718 T^{19} + 72290774850437876694 T^{20} - 20460060404662731376 T^{21} + \)\(23\!\cdots\!46\)\( T^{22} + \)\(38\!\cdots\!66\)\( T^{23} + \)\(60\!\cdots\!96\)\( T^{24} + \)\(32\!\cdots\!84\)\( T^{25} + \)\(10\!\cdots\!52\)\( T^{26} + \)\(64\!\cdots\!24\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))
$67$ (\( 1 + 2 T + 67 T^{2} \))(\( 1 + 4 T + 133 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 24 T + 332 T^{2} + 3300 T^{3} + 29991 T^{4} + 250177 T^{5} + 2009397 T^{6} + 14813700 T^{7} + 99853316 T^{8} + 483626904 T^{9} + 1350125107 T^{10} \))(\( 1 + 116 T^{2} + 558 T^{3} + 2479 T^{4} + 75523 T^{5} + 166093 T^{6} + 2504862 T^{7} + 34888508 T^{8} + 1350125107 T^{10} \))(\( 1 + 359 T^{2} - 320 T^{3} + 64940 T^{4} - 71061 T^{5} + 7533739 T^{6} - 8111583 T^{7} + 600908932 T^{8} - 543476061 T^{9} + 33818954371 T^{10} - 21372519543 T^{11} + 1308613797740 T^{12} - 432040034240 T^{13} + 32474559198671 T^{14} + 406067677556641 T^{16} \))(\( 1 - 18 T + 475 T^{2} - 6870 T^{3} + 105772 T^{4} - 1204725 T^{5} + 13774321 T^{6} - 126193127 T^{7} + 1141351048 T^{8} - 8454939509 T^{9} + 61832926969 T^{10} - 362336705175 T^{11} + 2131424370412 T^{12} - 9275359485090 T^{13} + 42967731530275 T^{14} - 109092808895814 T^{15} + 406067677556641 T^{16} \))(\( 1 - 28 T + 849 T^{2} - 15350 T^{3} + 282852 T^{4} - 3942978 T^{5} + 55516261 T^{6} - 642715788 T^{7} + 7500440119 T^{8} - 74700374352 T^{9} + 749275246162 T^{10} - 6523249807428 T^{11} + 57171174721064 T^{12} - 437057737097676 T^{13} + 3363496580021218 T^{14} - 22467108691230576 T^{15} + 151142276391223399 T^{16} - 867746722044089316 T^{17} + 5021911154131950109 T^{18} - 23897252524133271894 T^{19} + \)\(11\!\cdots\!32\)\( T^{20} - \)\(41\!\cdots\!50\)\( T^{21} + \)\(15\!\cdots\!01\)\( T^{22} - \)\(34\!\cdots\!24\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 + 6 T + 498 T^{2} + 3796 T^{3} + 120628 T^{4} + 1114272 T^{5} + 19516706 T^{6} + 201027386 T^{7} + 2452257470 T^{8} + 25242587690 T^{9} + 257641258179 T^{10} + 2404663550768 T^{11} + 22896645930919 T^{12} + 187238511196152 T^{13} + 1691329586861428 T^{14} + 12544980250142184 T^{15} + 102783043583895391 T^{16} + 723233823519635984 T^{17} + 5191760168157268659 T^{18} + 34080651405918132830 T^{19} + \)\(22\!\cdots\!30\)\( T^{20} + \)\(12\!\cdots\!78\)\( T^{21} + \)\(79\!\cdots\!46\)\( T^{22} + \)\(30\!\cdots\!84\)\( T^{23} + \)\(21\!\cdots\!72\)\( T^{24} + \)\(46\!\cdots\!68\)\( T^{25} + \)\(40\!\cdots\!78\)\( T^{26} + \)\(32\!\cdots\!22\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 6 T + 498 T^{2} + 3796 T^{3} + 120628 T^{4} + 1114272 T^{5} + 19516706 T^{6} + 201027386 T^{7} + 2452257470 T^{8} + 25242587690 T^{9} + 257641258179 T^{10} + 2404663550768 T^{11} + 22896645930919 T^{12} + 187238511196152 T^{13} + 1691329586861428 T^{14} + 12544980250142184 T^{15} + 102783043583895391 T^{16} + 723233823519635984 T^{17} + 5191760168157268659 T^{18} + 34080651405918132830 T^{19} + \)\(22\!\cdots\!30\)\( T^{20} + \)\(12\!\cdots\!78\)\( T^{21} + \)\(79\!\cdots\!46\)\( T^{22} + \)\(30\!\cdots\!84\)\( T^{23} + \)\(21\!\cdots\!72\)\( T^{24} + \)\(46\!\cdots\!68\)\( T^{25} + \)\(40\!\cdots\!78\)\( T^{26} + \)\(32\!\cdots\!22\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))
$71$ (\( 1 - 12 T + 71 T^{2} \))(\( 1 - 11 T + 141 T^{2} - 781 T^{3} + 5041 T^{4} \))(\( 1 + T + 63 T^{2} + 77 T^{3} + 4051 T^{4} + 28891 T^{5} + 287621 T^{6} + 388157 T^{7} + 22548393 T^{8} + 25411681 T^{9} + 1804229351 T^{10} \))(\( 1 + 13 T + 97 T^{2} + 1015 T^{3} + 10325 T^{4} + 77487 T^{5} + 733075 T^{6} + 5116615 T^{7} + 34717367 T^{8} + 330351853 T^{9} + 1804229351 T^{10} \))(\( 1 + 13 T + 534 T^{2} + 5116 T^{3} + 118293 T^{4} + 877603 T^{5} + 15080094 T^{6} + 90574920 T^{7} + 1280201724 T^{8} + 6430819320 T^{9} + 76018753854 T^{10} + 314103767333 T^{11} + 3006023980533 T^{12} + 9230437359716 T^{13} + 68405551613814 T^{14} + 118236562059083 T^{15} + 645753531245761 T^{16} \))(\( 1 + 21 T + 408 T^{2} + 4842 T^{3} + 53937 T^{4} + 469505 T^{5} + 3864512 T^{6} + 29321392 T^{7} + 233979356 T^{8} + 2081818832 T^{9} + 19481004992 T^{10} + 168041004055 T^{11} + 1370629838097 T^{12} + 8736078517542 T^{13} + 52264915839768 T^{14} + 190997523326211 T^{15} + 645753531245761 T^{16} \))(\( 1 - 9 T + 567 T^{2} - 5311 T^{3} + 156896 T^{4} - 1466349 T^{5} + 28329979 T^{6} - 252668907 T^{7} + 3739585015 T^{8} - 30670653834 T^{9} + 379907284894 T^{10} - 2802006636918 T^{11} + 30339404350608 T^{12} - 198942471221178 T^{13} + 1915112623150654 T^{14} - 10977364384380774 T^{15} + 95029141473560215 T^{16} - 455872658094489357 T^{17} + 3629078353375967659 T^{18} - 13336620349136484459 T^{19} + \)\(10\!\cdots\!56\)\( T^{20} - \)\(24\!\cdots\!41\)\( T^{21} + \)\(18\!\cdots\!67\)\( T^{22} - \)\(20\!\cdots\!39\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 32 T + 1221 T^{2} + 26256 T^{3} + 591619 T^{4} + 9792358 T^{5} + 164767059 T^{6} + 2242173642 T^{7} + 30744445668 T^{8} + 357004838934 T^{9} + 4166749925144 T^{10} + 42193451081430 T^{11} + 429233686902364 T^{12} + 3834619563919972 T^{13} + 34415745454421528 T^{14} + 272257989038318012 T^{15} + 2163767015674816924 T^{16} + 15101500270005692730 T^{17} + \)\(10\!\cdots\!64\)\( T^{18} + \)\(64\!\cdots\!34\)\( T^{19} + \)\(39\!\cdots\!28\)\( T^{20} + \)\(20\!\cdots\!22\)\( T^{21} + \)\(10\!\cdots\!99\)\( T^{22} + \)\(44\!\cdots\!98\)\( T^{23} + \)\(19\!\cdots\!19\)\( T^{24} + \)\(60\!\cdots\!76\)\( T^{25} + \)\(20\!\cdots\!61\)\( T^{26} + \)\(37\!\cdots\!52\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))(\( 1 - 32 T + 1221 T^{2} - 26256 T^{3} + 591619 T^{4} - 9792358 T^{5} + 164767059 T^{6} - 2242173642 T^{7} + 30744445668 T^{8} - 357004838934 T^{9} + 4166749925144 T^{10} - 42193451081430 T^{11} + 429233686902364 T^{12} - 3834619563919972 T^{13} + 34415745454421528 T^{14} - 272257989038318012 T^{15} + 2163767015674816924 T^{16} - 15101500270005692730 T^{17} + \)\(10\!\cdots\!64\)\( T^{18} - \)\(64\!\cdots\!34\)\( T^{19} + \)\(39\!\cdots\!28\)\( T^{20} - \)\(20\!\cdots\!22\)\( T^{21} + \)\(10\!\cdots\!99\)\( T^{22} - \)\(44\!\cdots\!98\)\( T^{23} + \)\(19\!\cdots\!19\)\( T^{24} - \)\(60\!\cdots\!76\)\( T^{25} + \)\(20\!\cdots\!61\)\( T^{26} - \)\(37\!\cdots\!52\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 19 T + 225 T^{2} + 1387 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 256 T^{2} - 646 T^{3} + 32717 T^{4} - 64257 T^{5} + 2388341 T^{6} - 3442534 T^{7} + 99588352 T^{8} - 56796482 T^{9} + 2073071593 T^{10} \))(\( 1 + 6 T + 350 T^{2} + 1712 T^{3} + 50031 T^{4} + 186001 T^{5} + 3652263 T^{6} + 9123248 T^{7} + 136155950 T^{8} + 170389446 T^{9} + 2073071593 T^{10} \))(\( 1 + 20 T + 415 T^{2} + 5020 T^{3} + 66722 T^{4} + 623383 T^{5} + 6619959 T^{6} + 52721729 T^{7} + 512092382 T^{8} + 3848686217 T^{9} + 35277761511 T^{10} + 242506584511 T^{11} + 1894787436002 T^{12} + 10406819396860 T^{13} + 62803703909935 T^{14} + 220947970381940 T^{15} + 806460091894081 T^{16} \))(\( 1 + 8 T + 361 T^{2} + 2398 T^{3} + 62862 T^{4} + 365975 T^{5} + 7401469 T^{6} + 38062427 T^{7} + 634690566 T^{8} + 2778557171 T^{9} + 39442428301 T^{10} + 142370496575 T^{11} + 1785170225742 T^{12} + 4971225680014 T^{13} + 54631655690329 T^{14} + 88379188152776 T^{15} + 806460091894081 T^{16} \))(\( 1 - 61 T + 2263 T^{2} - 61453 T^{3} + 1350684 T^{4} - 25082241 T^{5} + 405789051 T^{6} - 5819222145 T^{7} + 74966261383 T^{8} - 874663299866 T^{9} + 9301701526878 T^{10} - 90483767786106 T^{11} + 807146180879736 T^{12} - 6605315048385738 T^{13} + 49568767436732862 T^{14} - 340258892923971722 T^{15} + 2128909957623427303 T^{16} - 12063664122156026985 T^{17} + 61409772069632561739 T^{18} - \)\(27\!\cdots\!77\)\( T^{19} + \)\(10\!\cdots\!04\)\( T^{20} - \)\(36\!\cdots\!89\)\( T^{21} + \)\(97\!\cdots\!87\)\( T^{22} - \)\(19\!\cdots\!97\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 528 T^{2} - 206 T^{3} + 137462 T^{4} - 127272 T^{5} + 23713662 T^{6} - 35062306 T^{7} + 3087932914 T^{8} - 5971338154 T^{9} + 327232382785 T^{10} - 720792642320 T^{11} + 29468587230347 T^{12} - 66453040472174 T^{13} + 2302694973877050 T^{14} - 4851071954468702 T^{15} + 157038101350519163 T^{16} - 280400591337399440 T^{17} + 9292824069332681185 T^{18} - 12379011499254459322 T^{19} + \)\(46\!\cdots\!46\)\( T^{20} - \)\(38\!\cdots\!82\)\( T^{21} + \)\(19\!\cdots\!22\)\( T^{22} - \)\(74\!\cdots\!36\)\( T^{23} + \)\(59\!\cdots\!38\)\( T^{24} - \)\(64\!\cdots\!62\)\( T^{25} + \)\(12\!\cdots\!88\)\( T^{26} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( 1 + 528 T^{2} - 206 T^{3} + 137462 T^{4} - 127272 T^{5} + 23713662 T^{6} - 35062306 T^{7} + 3087932914 T^{8} - 5971338154 T^{9} + 327232382785 T^{10} - 720792642320 T^{11} + 29468587230347 T^{12} - 66453040472174 T^{13} + 2302694973877050 T^{14} - 4851071954468702 T^{15} + 157038101350519163 T^{16} - 280400591337399440 T^{17} + 9292824069332681185 T^{18} - 12379011499254459322 T^{19} + \)\(46\!\cdots\!46\)\( T^{20} - \)\(38\!\cdots\!82\)\( T^{21} + \)\(19\!\cdots\!22\)\( T^{22} - \)\(74\!\cdots\!36\)\( T^{23} + \)\(59\!\cdots\!38\)\( T^{24} - \)\(64\!\cdots\!62\)\( T^{25} + \)\(12\!\cdots\!88\)\( T^{26} + \)\(12\!\cdots\!09\)\( T^{28} \))
$79$ (\( 1 + 2 T + 79 T^{2} \))(\( 1 - 2 T + 139 T^{2} - 158 T^{3} + 6241 T^{4} \))(\( 1 + 6 T + 209 T^{2} + 425 T^{3} + 21440 T^{4} + 23747 T^{5} + 1693760 T^{6} + 2652425 T^{7} + 103045151 T^{8} + 233700486 T^{9} + 3077056399 T^{10} \))(\( 1 - 14 T + 439 T^{2} - 4305 T^{3} + 72074 T^{4} - 504519 T^{5} + 5693846 T^{6} - 26867505 T^{7} + 216444121 T^{8} - 545301134 T^{9} + 3077056399 T^{10} \))(\( 1 - 8 T + 168 T^{2} - 573 T^{3} + 22756 T^{4} - 69216 T^{5} + 2102300 T^{6} - 2692689 T^{7} + 175872908 T^{8} - 212722431 T^{9} + 13120454300 T^{10} - 34126187424 T^{11} + 886348043236 T^{12} - 1763153316627 T^{13} + 40838692527528 T^{14} - 153631271889272 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 10 T + 266 T^{2} - 1825 T^{3} + 37702 T^{4} - 229058 T^{5} + 4155060 T^{6} - 23409469 T^{7} + 372961876 T^{8} - 1849348051 T^{9} + 25931729460 T^{10} - 112934527262 T^{11} + 1468495953862 T^{12} - 5615627928175 T^{13} + 64661263168586 T^{14} - 192039089861590 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 427 T^{2} - 1180 T^{3} + 95292 T^{4} - 474180 T^{5} + 15149935 T^{6} - 94423472 T^{7} + 1950616551 T^{8} - 12357400976 T^{9} + 208925853190 T^{10} - 1214936220104 T^{11} + 18336406212664 T^{12} - 95979961388216 T^{13} + 1303906249758790 T^{14} - 6092680619806064 T^{15} + 75976672661390631 T^{16} - 290546348733397328 T^{17} + 3682759150458541135 T^{18} - 9106109563056874620 T^{19} + \)\(14\!\cdots\!12\)\( T^{20} - \)\(14\!\cdots\!20\)\( T^{21} + \)\(40\!\cdots\!27\)\( T^{22} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 + 28 T + 926 T^{2} + 19486 T^{3} + 399235 T^{4} + 6742560 T^{5} + 107891119 T^{6} + 1531739308 T^{7} + 20612487509 T^{8} + 253439280462 T^{9} + 2962371633649 T^{10} + 32098882315696 T^{11} + 331348038270553 T^{12} + 3192774659632742 T^{13} + 29342599253216918 T^{14} + 252229198110986618 T^{15} + 2067943106846521273 T^{16} + 15826000838048440144 T^{17} + \)\(11\!\cdots\!69\)\( T^{18} + \)\(77\!\cdots\!38\)\( T^{19} + \)\(50\!\cdots\!89\)\( T^{20} + \)\(29\!\cdots\!72\)\( T^{21} + \)\(16\!\cdots\!59\)\( T^{22} + \)\(80\!\cdots\!40\)\( T^{23} + \)\(37\!\cdots\!35\)\( T^{24} + \)\(14\!\cdots\!94\)\( T^{25} + \)\(54\!\cdots\!66\)\( T^{26} + \)\(13\!\cdots\!92\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 + 28 T + 926 T^{2} + 19486 T^{3} + 399235 T^{4} + 6742560 T^{5} + 107891119 T^{6} + 1531739308 T^{7} + 20612487509 T^{8} + 253439280462 T^{9} + 2962371633649 T^{10} + 32098882315696 T^{11} + 331348038270553 T^{12} + 3192774659632742 T^{13} + 29342599253216918 T^{14} + 252229198110986618 T^{15} + 2067943106846521273 T^{16} + 15826000838048440144 T^{17} + \)\(11\!\cdots\!69\)\( T^{18} + \)\(77\!\cdots\!38\)\( T^{19} + \)\(50\!\cdots\!89\)\( T^{20} + \)\(29\!\cdots\!72\)\( T^{21} + \)\(16\!\cdots\!59\)\( T^{22} + \)\(80\!\cdots\!40\)\( T^{23} + \)\(37\!\cdots\!35\)\( T^{24} + \)\(14\!\cdots\!94\)\( T^{25} + \)\(54\!\cdots\!66\)\( T^{26} + \)\(13\!\cdots\!92\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))
$83$ (\( 1 + 8 T + 83 T^{2} \))(\( 1 - 2 T + 87 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 - 7 T + 286 T^{2} - 1971 T^{3} + 41947 T^{4} - 223037 T^{5} + 3481601 T^{6} - 13578219 T^{7} + 163531082 T^{8} - 332208247 T^{9} + 3939040643 T^{10} \))(\( 1 - 5 T + 246 T^{2} + 331 T^{3} + 18969 T^{4} + 134411 T^{5} + 1574427 T^{6} + 2280259 T^{7} + 140659602 T^{8} - 237291605 T^{9} + 3939040643 T^{10} \))(\( 1 + 33 T + 921 T^{2} + 17544 T^{3} + 295768 T^{4} + 4076215 T^{5} + 50726539 T^{6} + 543414180 T^{7} + 5301266758 T^{8} + 45103376940 T^{9} + 349455127171 T^{10} + 2330726746205 T^{11} + 14036652685528 T^{12} + 69106529040792 T^{13} + 301112083872849 T^{14} + 895489682657691 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 7 T + 397 T^{2} + 3500 T^{3} + 78910 T^{4} + 711159 T^{5} + 10765451 T^{6} + 84640014 T^{7} + 1058869618 T^{8} + 7025121162 T^{9} + 74163191939 T^{10} + 406631471133 T^{11} + 3744936110110 T^{12} + 13786642250500 T^{13} + 129795328227493 T^{14} + 189952356927389 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 16 T + 651 T^{2} - 9008 T^{3} + 209704 T^{4} - 2612920 T^{5} + 44543431 T^{6} - 502710712 T^{7} + 6909206119 T^{8} - 70557447080 T^{9} + 822114410918 T^{10} - 7547188829640 T^{11} + 76761076758592 T^{12} - 626416672860120 T^{13} + 5663546176814102 T^{14} - 40343830993531960 T^{15} + 327899321850666199 T^{16} - 1980197926239467816 T^{17} + 14563045962276289039 T^{18} - 70904330351816180840 T^{19} + \)\(47\!\cdots\!64\)\( T^{20} - \)\(16\!\cdots\!24\)\( T^{21} + \)\(10\!\cdots\!99\)\( T^{22} - \)\(20\!\cdots\!72\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 10 T + 403 T^{2} + 2030 T^{3} + 82110 T^{4} + 223410 T^{5} + 12782889 T^{6} + 6421776 T^{7} + 1547705126 T^{8} - 2643242502 T^{9} + 161596673968 T^{10} - 528368251022 T^{11} + 15206798296887 T^{12} - 63588302755798 T^{13} + 1295954098341040 T^{14} - 5277829128731234 T^{15} + 104759633467254543 T^{16} - 302114097147116314 T^{17} + 7669106825705687728 T^{18} - 10411839644683008786 T^{19} + \)\(50\!\cdots\!94\)\( T^{20} + \)\(17\!\cdots\!52\)\( T^{21} + \)\(28\!\cdots\!49\)\( T^{22} + \)\(41\!\cdots\!30\)\( T^{23} + \)\(12\!\cdots\!90\)\( T^{24} + \)\(26\!\cdots\!10\)\( T^{25} + \)\(43\!\cdots\!83\)\( T^{26} + \)\(88\!\cdots\!30\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 - 10 T + 403 T^{2} - 2030 T^{3} + 82110 T^{4} - 223410 T^{5} + 12782889 T^{6} - 6421776 T^{7} + 1547705126 T^{8} + 2643242502 T^{9} + 161596673968 T^{10} + 528368251022 T^{11} + 15206798296887 T^{12} + 63588302755798 T^{13} + 1295954098341040 T^{14} + 5277829128731234 T^{15} + 104759633467254543 T^{16} + 302114097147116314 T^{17} + 7669106825705687728 T^{18} + 10411839644683008786 T^{19} + \)\(50\!\cdots\!94\)\( T^{20} - \)\(17\!\cdots\!52\)\( T^{21} + \)\(28\!\cdots\!49\)\( T^{22} - \)\(41\!\cdots\!30\)\( T^{23} + \)\(12\!\cdots\!90\)\( T^{24} - \)\(26\!\cdots\!10\)\( T^{25} + \)\(43\!\cdots\!83\)\( T^{26} - \)\(88\!\cdots\!30\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))
$89$ (\( 1 - 6 T + 89 T^{2} \))(\( 1 - 2 T + 54 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 290 T^{2} + 322 T^{3} + 42889 T^{4} + 40245 T^{5} + 3817121 T^{6} + 2550562 T^{7} + 204441010 T^{8} + 5584059449 T^{10} \))(\( 1 - 30 T + 662 T^{2} - 9524 T^{3} + 118385 T^{4} - 1164809 T^{5} + 10536265 T^{6} - 75439604 T^{7} + 466689478 T^{8} - 1882267230 T^{9} + 5584059449 T^{10} \))(\( 1 + 4 T + 513 T^{2} + 2094 T^{3} + 127678 T^{4} + 487693 T^{5} + 19972765 T^{6} + 67413913 T^{7} + 2130074694 T^{8} + 5999838257 T^{9} + 158204271565 T^{10} + 343808446517 T^{11} + 8010803846398 T^{12} + 11693020486206 T^{13} + 254951402262993 T^{14} + 176925339582116 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 26 T + 761 T^{2} + 12182 T^{3} + 203638 T^{4} + 2354455 T^{5} + 29224825 T^{6} + 274376689 T^{7} + 2923563118 T^{8} + 24419525321 T^{9} + 231489838825 T^{10} + 1659817786895 T^{11} + 12776704472758 T^{12} + 68025012207718 T^{13} + 378202762421321 T^{14} + 1150014707283754 T^{15} + 3936588805702081 T^{16} \))(\( 1 - 12 T + 697 T^{2} - 6680 T^{3} + 227732 T^{4} - 1834756 T^{5} + 48216552 T^{6} - 338563596 T^{7} + 7544000400 T^{8} - 47120413712 T^{9} + 925586563900 T^{10} - 5192252357770 T^{11} + 91437739905100 T^{12} - 462110459841530 T^{13} + 7331571172651900 T^{14} - 33218430934134928 T^{15} + 473327491200896400 T^{16} - 1890559247331218604 T^{17} + 23962724258648186472 T^{18} - 81153707087581205924 T^{19} + \)\(89\!\cdots\!92\)\( T^{20} - \)\(23\!\cdots\!20\)\( T^{21} + \)\(21\!\cdots\!97\)\( T^{22} - \)\(33\!\cdots\!68\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 44 T + 1672 T^{2} + 43744 T^{3} + 1029092 T^{4} + 20107108 T^{5} + 361913220 T^{6} + 5755314876 T^{7} + 85517741812 T^{8} + 1154634395808 T^{9} + 14690164208739 T^{10} + 172275093038392 T^{11} + 1912972392748275 T^{12} + 19717806434099180 T^{13} + 192867499403655162 T^{14} + 1754884772634827020 T^{15} + 15152654322959086275 T^{16} + \)\(12\!\cdots\!48\)\( T^{17} + \)\(92\!\cdots\!99\)\( T^{18} + \)\(64\!\cdots\!92\)\( T^{19} + \)\(42\!\cdots\!32\)\( T^{20} + \)\(25\!\cdots\!04\)\( T^{21} + \)\(14\!\cdots\!20\)\( T^{22} + \)\(70\!\cdots\!72\)\( T^{23} + \)\(32\!\cdots\!92\)\( T^{24} + \)\(12\!\cdots\!16\)\( T^{25} + \)\(41\!\cdots\!12\)\( T^{26} + \)\(96\!\cdots\!36\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( 1 - 44 T + 1672 T^{2} - 43744 T^{3} + 1029092 T^{4} - 20107108 T^{5} + 361913220 T^{6} - 5755314876 T^{7} + 85517741812 T^{8} - 1154634395808 T^{9} + 14690164208739 T^{10} - 172275093038392 T^{11} + 1912972392748275 T^{12} - 19717806434099180 T^{13} + 192867499403655162 T^{14} - 1754884772634827020 T^{15} + 15152654322959086275 T^{16} - \)\(12\!\cdots\!48\)\( T^{17} + \)\(92\!\cdots\!99\)\( T^{18} - \)\(64\!\cdots\!92\)\( T^{19} + \)\(42\!\cdots\!32\)\( T^{20} - \)\(25\!\cdots\!04\)\( T^{21} + \)\(14\!\cdots\!20\)\( T^{22} - \)\(70\!\cdots\!72\)\( T^{23} + \)\(32\!\cdots\!92\)\( T^{24} - \)\(12\!\cdots\!16\)\( T^{25} + \)\(41\!\cdots\!12\)\( T^{26} - \)\(96\!\cdots\!36\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))
$97$ (\( 1 - 10 T + 97 T^{2} \))(\( 1 + 21 T + 293 T^{2} + 2037 T^{3} + 9409 T^{4} \))(\( 1 + 13 T + 373 T^{2} + 3843 T^{3} + 59509 T^{4} + 500039 T^{5} + 5772373 T^{6} + 36158787 T^{7} + 340427029 T^{8} + 1150880653 T^{9} + 8587340257 T^{10} \))(\( 1 + 9 T + 437 T^{2} + 3063 T^{3} + 80677 T^{4} + 428251 T^{5} + 7825669 T^{6} + 28819767 T^{7} + 398838101 T^{8} + 796763529 T^{9} + 8587340257 T^{10} \))(\( 1 + 31 T + 826 T^{2} + 15984 T^{3} + 265829 T^{4} + 3793587 T^{5} + 48345108 T^{6} + 548722798 T^{7} + 5707233480 T^{8} + 53226111406 T^{9} + 454879121172 T^{10} + 3462304428051 T^{11} + 23533650238949 T^{12} + 137260046667888 T^{13} + 688034876071354 T^{14} + 2504746818821503 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 3 T + 402 T^{2} + 2024 T^{3} + 73933 T^{4} + 595959 T^{5} + 8542284 T^{6} + 96913774 T^{7} + 827247384 T^{8} + 9400636078 T^{9} + 80374350156 T^{10} + 543915688407 T^{11} + 6545235332173 T^{12} + 17380776680168 T^{13} + 334854745981458 T^{14} + 242394853434339 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 73 T + 3010 T^{2} - 87102 T^{3} + 1967135 T^{4} - 36575228 T^{5} + 582031485 T^{6} - 8144116778 T^{7} + 102571284139 T^{8} - 1186076744056 T^{9} + 12844235600713 T^{10} - 132620387939348 T^{11} + 1324602883633461 T^{12} - 12864177630116756 T^{13} + 120851412767108617 T^{14} - 1082500220227821688 T^{15} + 9080562036072374059 T^{16} - 69936301865428531946 T^{17} + \)\(48\!\cdots\!65\)\( T^{18} - \)\(29\!\cdots\!64\)\( T^{19} + \)\(15\!\cdots\!35\)\( T^{20} - \)\(66\!\cdots\!34\)\( T^{21} + \)\(22\!\cdots\!90\)\( T^{22} - \)\(52\!\cdots\!69\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 + 2 T + 843 T^{2} + 1204 T^{3} + 360287 T^{4} + 355350 T^{5} + 102380513 T^{6} + 66455592 T^{7} + 21502400796 T^{8} + 8750298536 T^{9} + 3521431933440 T^{10} + 884827423734 T^{11} + 463065802729656 T^{12} + 79616104931582 T^{13} + 49635490385604272 T^{14} + 7722762178363454 T^{15} + 4356986137883333304 T^{16} + 807558099301580982 T^{17} + \)\(31\!\cdots\!40\)\( T^{18} + 75141790878960963752 T^{19} + \)\(17\!\cdots\!84\)\( T^{20} + \)\(53\!\cdots\!96\)\( T^{21} + \)\(80\!\cdots\!93\)\( T^{22} + \)\(27\!\cdots\!50\)\( T^{23} + \)\(26\!\cdots\!63\)\( T^{24} + \)\(86\!\cdots\!12\)\( T^{25} + \)\(58\!\cdots\!63\)\( T^{26} + \)\(13\!\cdots\!54\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 + 2 T + 843 T^{2} + 1204 T^{3} + 360287 T^{4} + 355350 T^{5} + 102380513 T^{6} + 66455592 T^{7} + 21502400796 T^{8} + 8750298536 T^{9} + 3521431933440 T^{10} + 884827423734 T^{11} + 463065802729656 T^{12} + 79616104931582 T^{13} + 49635490385604272 T^{14} + 7722762178363454 T^{15} + 4356986137883333304 T^{16} + 807558099301580982 T^{17} + \)\(31\!\cdots\!40\)\( T^{18} + 75141790878960963752 T^{19} + \)\(17\!\cdots\!84\)\( T^{20} + \)\(53\!\cdots\!96\)\( T^{21} + \)\(80\!\cdots\!93\)\( T^{22} + \)\(27\!\cdots\!50\)\( T^{23} + \)\(26\!\cdots\!63\)\( T^{24} + \)\(86\!\cdots\!12\)\( T^{25} + \)\(58\!\cdots\!63\)\( T^{26} + \)\(13\!\cdots\!54\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))
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