Properties

Label 2672.2
Level 2672
Weight 2
Dimension 124745
Nonzero newspaces 8
Sturm bound 892416
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2672\( 2672 = 2^{4} \cdot 167 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(892416\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2672))\).

Total New Old
Modular forms 225428 126229 99199
Cusp forms 220781 124745 96036
Eisenstein series 4647 1484 3163

Trace form

\( 124745q - 328q^{2} - 245q^{3} - 332q^{4} - 411q^{5} - 340q^{6} - 249q^{7} - 340q^{8} - 83q^{9} + O(q^{10}) \) \( 124745q - 328q^{2} - 245q^{3} - 332q^{4} - 411q^{5} - 340q^{6} - 249q^{7} - 340q^{8} - 83q^{9} - 332q^{10} - 253q^{11} - 324q^{12} - 411q^{13} - 324q^{14} - 257q^{15} - 316q^{16} - 739q^{17} - 336q^{18} - 261q^{19} - 340q^{20} - 423q^{21} - 332q^{22} - 249q^{23} - 332q^{24} - 83q^{25} - 340q^{26} - 233q^{27} - 348q^{28} - 427q^{29} - 324q^{30} - 217q^{31} - 348q^{32} - 739q^{33} - 340q^{34} - 241q^{35} - 324q^{36} - 427q^{37} - 308q^{38} - 249q^{39} - 316q^{40} - 83q^{41} - 332q^{42} - 269q^{43} - 324q^{44} - 419q^{45} - 356q^{46} - 281q^{47} - 348q^{48} - 759q^{49} - 320q^{50} - 257q^{51} - 324q^{52} - 395q^{53} - 332q^{54} - 249q^{55} - 316q^{56} - 83q^{57} - 308q^{58} - 237q^{59} - 332q^{60} - 379q^{61} - 364q^{62} - 257q^{63} - 332q^{64} - 755q^{65} - 340q^{66} - 229q^{67} - 332q^{68} - 391q^{69} - 348q^{70} - 249q^{71} - 340q^{72} - 83q^{73} - 332q^{74} - 261q^{75} - 356q^{76} - 423q^{77} - 324q^{78} - 249q^{79} - 348q^{80} - 767q^{81} - 332q^{82} - 245q^{83} - 316q^{84} - 423q^{85} - 332q^{86} - 249q^{87} - 348q^{88} - 83q^{89} - 324q^{90} - 257q^{91} - 284q^{92} - 447q^{93} - 300q^{94} - 225q^{95} - 300q^{96} - 739q^{97} - 320q^{98} - 245q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2672))\)

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
2672.2.a \(\chi_{2672}(1, \cdot)\) 2672.2.a.a 1 1
2672.2.a.b 2
2672.2.a.c 2
2672.2.a.d 2
2672.2.a.e 2
2672.2.a.f 2
2672.2.a.g 2
2672.2.a.h 3
2672.2.a.i 3
2672.2.a.j 5
2672.2.a.k 7
2672.2.a.l 7
2672.2.a.m 9
2672.2.a.n 12
2672.2.a.o 12
2672.2.a.p 12
2672.2.b \(\chi_{2672}(2671, \cdot)\) 2672.2.b.a 28 1
2672.2.b.b 56
2672.2.c \(\chi_{2672}(1337, \cdot)\) None 0 1
2672.2.h \(\chi_{2672}(1335, \cdot)\) None 0 1
2672.2.j \(\chi_{2672}(669, \cdot)\) n/a 664 2
2672.2.l \(\chi_{2672}(667, \cdot)\) n/a 668 2
2672.2.m \(\chi_{2672}(33, \cdot)\) n/a 6806 82
2672.2.n \(\chi_{2672}(23, \cdot)\) None 0 82
2672.2.s \(\chi_{2672}(9, \cdot)\) None 0 82
2672.2.t \(\chi_{2672}(15, \cdot)\) n/a 6888 82
2672.2.u \(\chi_{2672}(35, \cdot)\) n/a 54776 164
2672.2.w \(\chi_{2672}(21, \cdot)\) n/a 54776 164

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2672))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2672)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1336))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T^{2} \))(\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4} \))(\( 1 + T + 3 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4} \))(\( 1 + T + 2 T^{2} - 2 T^{3} + 6 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 - T + 4 T^{2} - 2 T^{3} + 12 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 + 3 T + 9 T^{2} + 19 T^{3} + 45 T^{4} + 83 T^{5} + 135 T^{6} + 171 T^{7} + 243 T^{8} + 243 T^{9} + 243 T^{10} \))(\( 1 - 4 T + 15 T^{2} - 40 T^{3} + 93 T^{4} - 185 T^{5} + 355 T^{6} - 599 T^{7} + 1065 T^{8} - 1665 T^{9} + 2511 T^{10} - 3240 T^{11} + 3645 T^{12} - 2916 T^{13} + 2187 T^{14} \))(\( 1 - 6 T + 27 T^{2} - 88 T^{3} + 249 T^{4} - 587 T^{5} + 1241 T^{6} - 2263 T^{7} + 3723 T^{8} - 5283 T^{9} + 6723 T^{10} - 7128 T^{11} + 6561 T^{12} - 4374 T^{13} + 2187 T^{14} \))(\( 1 - T + 14 T^{2} - 16 T^{3} + 107 T^{4} - 123 T^{5} + 570 T^{6} - 610 T^{7} + 2245 T^{8} - 2147 T^{9} + 6735 T^{10} - 5490 T^{11} + 15390 T^{12} - 9963 T^{13} + 26001 T^{14} - 11664 T^{15} + 30618 T^{16} - 6561 T^{17} + 19683 T^{18} \))(\( 1 + 5 T + 21 T^{2} + 65 T^{3} + 180 T^{4} + 416 T^{5} + 858 T^{6} + 1532 T^{7} + 2456 T^{8} + 3338 T^{9} + 4105 T^{10} + 4482 T^{11} + 6566 T^{12} + 13446 T^{13} + 36945 T^{14} + 90126 T^{15} + 198936 T^{16} + 372276 T^{17} + 625482 T^{18} + 909792 T^{19} + 1180980 T^{20} + 1279395 T^{21} + 1240029 T^{22} + 885735 T^{23} + 531441 T^{24} \))(\( 1 + 3 T + 14 T^{2} + 28 T^{3} + 79 T^{4} + 120 T^{5} + 267 T^{6} + 376 T^{7} + 859 T^{8} + 1572 T^{9} + 3591 T^{10} + 6916 T^{11} + 12959 T^{12} + 20748 T^{13} + 32319 T^{14} + 42444 T^{15} + 69579 T^{16} + 91368 T^{17} + 194643 T^{18} + 262440 T^{19} + 518319 T^{20} + 551124 T^{21} + 826686 T^{22} + 531441 T^{23} + 531441 T^{24} \))(\( 1 - T + 11 T^{2} - 13 T^{3} + 68 T^{4} - 90 T^{5} + 326 T^{6} - 480 T^{7} + 1314 T^{8} - 2062 T^{9} + 4559 T^{10} - 7212 T^{11} + 14242 T^{12} - 21636 T^{13} + 41031 T^{14} - 55674 T^{15} + 106434 T^{16} - 116640 T^{17} + 237654 T^{18} - 196830 T^{19} + 446148 T^{20} - 255879 T^{21} + 649539 T^{22} - 177147 T^{23} + 531441 T^{24} \))
$5$ (\( 1 - 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} + 25 T^{4} \))(\( ( 1 + 3 T + 5 T^{2} )^{2} \))(\( 1 - 2 T + 9 T^{2} - 10 T^{3} + 25 T^{4} \))(\( ( 1 + T + 5 T^{2} )^{2} \))(\( ( 1 + T + 5 T^{2} )^{2} \))(\( 1 + 4 T + 9 T^{2} + 20 T^{3} + 25 T^{4} \))(\( ( 1 + T + 5 T^{2} )^{3} \))(\( 1 + 2 T^{2} + 16 T^{3} + 10 T^{4} + 125 T^{6} \))(\( ( 1 - 2 T + 5 T^{2} )^{5} \))(\( 1 + 2 T + 18 T^{2} + 18 T^{3} + 128 T^{4} - 2 T^{5} + 545 T^{6} - 452 T^{7} + 2725 T^{8} - 50 T^{9} + 16000 T^{10} + 11250 T^{11} + 56250 T^{12} + 31250 T^{13} + 78125 T^{14} \))(\( 1 + 16 T^{2} - 6 T^{3} + 142 T^{4} - 104 T^{5} + 893 T^{6} - 708 T^{7} + 4465 T^{8} - 2600 T^{9} + 17750 T^{10} - 3750 T^{11} + 50000 T^{12} + 78125 T^{14} \))(\( 1 + 8 T + 53 T^{2} + 254 T^{3} + 1063 T^{4} + 3774 T^{5} + 12035 T^{6} + 34178 T^{7} + 88336 T^{8} + 206612 T^{9} + 441680 T^{10} + 854450 T^{11} + 1504375 T^{12} + 2358750 T^{13} + 3321875 T^{14} + 3968750 T^{15} + 4140625 T^{16} + 3125000 T^{17} + 1953125 T^{18} \))(\( 1 + 2 T + 23 T^{2} + 48 T^{3} + 303 T^{4} + 618 T^{5} + 3004 T^{6} + 5842 T^{7} + 23765 T^{8} + 43696 T^{9} + 154685 T^{10} + 262994 T^{11} + 843222 T^{12} + 1314970 T^{13} + 3867125 T^{14} + 5462000 T^{15} + 14853125 T^{16} + 18256250 T^{17} + 46937500 T^{18} + 48281250 T^{19} + 118359375 T^{20} + 93750000 T^{21} + 224609375 T^{22} + 97656250 T^{23} + 244140625 T^{24} \))(\( 1 - 4 T + 19 T^{2} - 68 T^{3} + 248 T^{4} - 796 T^{5} + 2479 T^{6} - 6892 T^{7} + 19111 T^{8} - 48832 T^{9} + 123526 T^{10} - 288688 T^{11} + 667744 T^{12} - 1443440 T^{13} + 3088150 T^{14} - 6104000 T^{15} + 11944375 T^{16} - 21537500 T^{17} + 38734375 T^{18} - 62187500 T^{19} + 96875000 T^{20} - 132812500 T^{21} + 185546875 T^{22} - 195312500 T^{23} + 244140625 T^{24} \))(\( 1 - 8 T + 53 T^{2} - 248 T^{3} + 1047 T^{4} - 3688 T^{5} + 12156 T^{6} - 35512 T^{7} + 99309 T^{8} - 254088 T^{9} + 634687 T^{10} - 1479832 T^{11} + 3411222 T^{12} - 7399160 T^{13} + 15867175 T^{14} - 31761000 T^{15} + 62068125 T^{16} - 110975000 T^{17} + 189937500 T^{18} - 288125000 T^{19} + 408984375 T^{20} - 484375000 T^{21} + 517578125 T^{22} - 390625000 T^{23} + 244140625 T^{24} \))
$7$ (\( 1 + T + 7 T^{2} \))(\( 1 - 7 T + 25 T^{2} - 49 T^{3} + 49 T^{4} \))(\( 1 + 3 T + 13 T^{2} + 21 T^{3} + 49 T^{4} \))(\( ( 1 - 3 T + 7 T^{2} )^{2} \))(\( 1 + 9 T^{2} + 49 T^{4} \))(\( 1 - 5 T + 19 T^{2} - 35 T^{3} + 49 T^{4} \))(\( ( 1 - 3 T + 7 T^{2} )^{2} \))(\( ( 1 + T + 7 T^{2} )^{3} \))(\( 1 + 8 T^{2} - 16 T^{3} + 56 T^{4} + 343 T^{6} \))(\( 1 + 9 T + 51 T^{2} + 223 T^{3} + 787 T^{4} + 2265 T^{5} + 5509 T^{6} + 10927 T^{7} + 17493 T^{8} + 21609 T^{9} + 16807 T^{10} \))(\( 1 - 12 T + 87 T^{2} - 466 T^{3} + 2053 T^{4} - 7675 T^{5} + 24829 T^{6} - 70131 T^{7} + 173803 T^{8} - 376075 T^{9} + 704179 T^{10} - 1118866 T^{11} + 1462209 T^{12} - 1411788 T^{13} + 823543 T^{14} \))(\( 1 - T + 32 T^{2} - 34 T^{3} + 529 T^{4} - 495 T^{5} + 5487 T^{6} - 4415 T^{7} + 38409 T^{8} - 24255 T^{9} + 181447 T^{10} - 81634 T^{11} + 537824 T^{12} - 117649 T^{13} + 823543 T^{14} \))(\( 1 + 2 T + 34 T^{2} + 72 T^{3} + 567 T^{4} + 1231 T^{5} + 6391 T^{6} + 13376 T^{7} + 55371 T^{8} + 106443 T^{9} + 387597 T^{10} + 655424 T^{11} + 2192113 T^{12} + 2955631 T^{13} + 9529569 T^{14} + 8470728 T^{15} + 28000462 T^{16} + 11529602 T^{17} + 40353607 T^{18} \))(\( 1 + 10 T + 82 T^{2} + 476 T^{3} + 2479 T^{4} + 10943 T^{5} + 44794 T^{6} + 164522 T^{7} + 569513 T^{8} + 1817643 T^{9} + 5531118 T^{10} + 15745437 T^{11} + 42979650 T^{12} + 110218059 T^{13} + 271024782 T^{14} + 623451549 T^{15} + 1367400713 T^{16} + 2765121254 T^{17} + 5269969306 T^{18} + 9012031049 T^{19} + 14290941679 T^{20} + 19208316932 T^{21} + 23162970418 T^{22} + 19773267430 T^{23} + 13841287201 T^{24} \))(\( 1 + 11 T + 88 T^{2} + 512 T^{3} + 2549 T^{4} + 10848 T^{5} + 41869 T^{6} + 146188 T^{7} + 478105 T^{8} + 1460284 T^{9} + 4272913 T^{10} + 11903480 T^{11} + 32169505 T^{12} + 83324360 T^{13} + 209372737 T^{14} + 500877412 T^{15} + 1147930105 T^{16} + 2456981716 T^{17} + 4925845981 T^{18} + 8933794464 T^{19} + 14694477749 T^{20} + 20661046784 T^{21} + 24857821912 T^{22} + 21750594173 T^{23} + 13841287201 T^{24} \))(\( 1 - 4 T + 40 T^{2} - 136 T^{3} + 833 T^{4} - 2529 T^{5} + 12154 T^{6} - 33386 T^{7} + 137681 T^{8} - 347839 T^{9} + 1274382 T^{10} - 2958957 T^{11} + 9776074 T^{12} - 20712699 T^{13} + 62444718 T^{14} - 119308777 T^{15} + 330572081 T^{16} - 561118502 T^{17} + 1429905946 T^{18} - 2082740247 T^{19} + 4802079233 T^{20} - 5488090552 T^{21} + 11299009960 T^{22} - 7909306972 T^{23} + 13841287201 T^{24} \))
$11$ (\( 1 + 11 T^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 5 T + 27 T^{2} - 55 T^{3} + 121 T^{4} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 9 T + 41 T^{2} - 99 T^{3} + 121 T^{4} \))(\( 1 + 7 T + 24 T^{2} + 66 T^{3} + 264 T^{4} + 847 T^{5} + 1331 T^{6} \))(\( 1 + 11 T + 66 T^{2} + 258 T^{3} + 726 T^{4} + 1331 T^{5} + 1331 T^{6} \))(\( 1 + 5 T + 43 T^{2} + 191 T^{3} + 849 T^{4} + 3017 T^{5} + 9339 T^{6} + 23111 T^{7} + 57233 T^{8} + 73205 T^{9} + 161051 T^{10} \))(\( 1 - 7 T + 49 T^{2} - 211 T^{3} + 1044 T^{4} - 3820 T^{5} + 15876 T^{6} - 49868 T^{7} + 174636 T^{8} - 462220 T^{9} + 1389564 T^{10} - 3089251 T^{11} + 7891499 T^{12} - 12400927 T^{13} + 19487171 T^{14} \))(\( 1 - 6 T + 57 T^{2} - 280 T^{3} + 1477 T^{4} - 6073 T^{5} + 23343 T^{6} - 81859 T^{7} + 256773 T^{8} - 734833 T^{9} + 1965887 T^{10} - 4099480 T^{11} + 9179907 T^{12} - 10629366 T^{13} + 19487171 T^{14} \))(\( 1 - 10 T + 93 T^{2} - 590 T^{3} + 3378 T^{4} - 16365 T^{5} + 72894 T^{6} - 292609 T^{7} + 1094660 T^{8} - 3753996 T^{9} + 12041260 T^{10} - 35405689 T^{11} + 97021914 T^{12} - 239599965 T^{13} + 544030278 T^{14} - 1045220990 T^{15} + 1812306903 T^{16} - 2143588810 T^{17} + 2357947691 T^{18} \))(\( 1 + 14 T + 160 T^{2} + 1234 T^{3} + 8382 T^{4} + 46483 T^{5} + 238446 T^{6} + 1078238 T^{7} + 4676555 T^{8} + 18581954 T^{9} + 71789378 T^{10} + 256135639 T^{11} + 884942924 T^{12} + 2817492029 T^{13} + 8686514738 T^{14} + 24732580774 T^{15} + 68469441755 T^{16} + 173651308138 T^{17} + 422421634206 T^{18} + 905822169593 T^{19} + 1796756140542 T^{20} + 2909707450694 T^{21} + 4149987936160 T^{22} + 3994363388554 T^{23} + 3138428376721 T^{24} \))(\( 1 + 55 T^{2} + 12 T^{3} + 1596 T^{4} + 688 T^{5} + 31920 T^{6} + 20160 T^{7} + 495320 T^{8} + 392868 T^{9} + 6450124 T^{10} + 5620672 T^{11} + 74530936 T^{12} + 61827392 T^{13} + 780465004 T^{14} + 522907308 T^{15} + 7251980120 T^{16} + 3246788160 T^{17} + 56548227120 T^{18} + 13407173648 T^{19} + 342116774076 T^{20} + 28295372292 T^{21} + 1426558353055 T^{22} + 3138428376721 T^{24} \))(\( 1 + 6 T + 78 T^{2} + 368 T^{3} + 2890 T^{4} + 11755 T^{5} + 71010 T^{6} + 258818 T^{7} + 1309339 T^{8} + 4348186 T^{9} + 19257904 T^{10} + 58566749 T^{11} + 232768628 T^{12} + 644234239 T^{13} + 2330206384 T^{14} + 5787435566 T^{15} + 19170032299 T^{16} + 41682897718 T^{17} + 125798546610 T^{18} + 229071695105 T^{19} + 619497166090 T^{20} + 867724750288 T^{21} + 2023119118878 T^{22} + 1711870023666 T^{23} + 3138428376721 T^{24} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 9 T + 45 T^{2} - 117 T^{3} + 169 T^{4} \))(\( 1 - 9 T + 43 T^{2} - 117 T^{3} + 169 T^{4} \))(\( 1 - 8 T + 34 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 21 T^{2} + 169 T^{4} \))(\( 1 + 5 T + 31 T^{2} + 65 T^{3} + 169 T^{4} \))(\( 1 - 2 T + 7 T^{2} - 26 T^{3} + 169 T^{4} \))(\( 1 - 2 T + 30 T^{2} - 38 T^{3} + 390 T^{4} - 338 T^{5} + 2197 T^{6} \))(\( 1 + 10 T + 60 T^{2} + 256 T^{3} + 780 T^{4} + 1690 T^{5} + 2197 T^{6} \))(\( 1 + 4 T + 45 T^{2} + 160 T^{3} + 1006 T^{4} + 2840 T^{5} + 13078 T^{6} + 27040 T^{7} + 98865 T^{8} + 114244 T^{9} + 371293 T^{10} \))(\( 1 + 9 T + 68 T^{2} + 356 T^{3} + 1658 T^{4} + 6631 T^{5} + 26213 T^{6} + 92808 T^{7} + 340769 T^{8} + 1120639 T^{9} + 3642626 T^{10} + 10167716 T^{11} + 25247924 T^{12} + 43441281 T^{13} + 62748517 T^{14} \))(\( 1 + 2 T + 54 T^{2} + 78 T^{3} + 1412 T^{4} + 1590 T^{5} + 24481 T^{6} + 22964 T^{7} + 318253 T^{8} + 268710 T^{9} + 3102164 T^{10} + 2227758 T^{11} + 20049822 T^{12} + 9653618 T^{13} + 62748517 T^{14} \))(\( 1 + 13 T + 133 T^{2} + 953 T^{3} + 6225 T^{4} + 33638 T^{5} + 169261 T^{6} + 741887 T^{7} + 3086116 T^{8} + 11414650 T^{9} + 40119508 T^{10} + 125378903 T^{11} + 371866417 T^{12} + 960734918 T^{13} + 2311298925 T^{14} + 4599948977 T^{15} + 8345552761 T^{16} + 10604499373 T^{17} + 10604499373 T^{18} \))(\( 1 + 9 T + 124 T^{2} + 784 T^{3} + 6135 T^{4} + 29412 T^{5} + 166800 T^{6} + 624997 T^{7} + 2854483 T^{8} + 8529550 T^{9} + 35235252 T^{10} + 92130964 T^{11} + 416218410 T^{12} + 1197702532 T^{13} + 5954757588 T^{14} + 18739421350 T^{15} + 81526888963 T^{16} + 232057011121 T^{17} + 805111741200 T^{18} + 1845559382004 T^{19} + 5004507973335 T^{20} + 8313927508432 T^{21} + 17094452989276 T^{22} + 16129443546333 T^{23} + 23298085122481 T^{24} \))(\( 1 - 9 T + 109 T^{2} - 645 T^{3} + 4648 T^{4} - 20861 T^{5} + 117121 T^{6} - 441833 T^{7} + 2219655 T^{8} - 7677394 T^{9} + 36384794 T^{10} - 117891114 T^{11} + 516138240 T^{12} - 1532584482 T^{13} + 6149030186 T^{14} - 16867234618 T^{15} + 63395566455 T^{16} - 164049500069 T^{17} + 565320696889 T^{18} - 1308996813137 T^{19} + 3791516391208 T^{20} - 6839902095585 T^{21} + 15026575611541 T^{22} - 16129443546333 T^{23} + 23298085122481 T^{24} \))(\( 1 - 13 T + 166 T^{2} - 1386 T^{3} + 10959 T^{4} - 70182 T^{5} + 426682 T^{6} - 2255577 T^{7} + 11375923 T^{8} - 51440742 T^{9} + 222705776 T^{10} - 876391344 T^{11} + 3307744314 T^{12} - 11393087472 T^{13} + 37637276144 T^{14} - 113015310174 T^{15} + 324907736803 T^{16} - 837479951061 T^{17} + 2059512517738 T^{18} - 4403816420094 T^{19} + 8939592971439 T^{20} - 14697836130978 T^{21} + 22884509646934 T^{22} - 23298085122481 T^{23} + 23298085122481 T^{24} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 + 5 T + 9 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 - T + 31 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 5 T + 29 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 + 5 T + 39 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 - T + 3 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 - 3 T + 44 T^{2} - 104 T^{3} + 748 T^{4} - 867 T^{5} + 4913 T^{6} \))(\( 1 - 9 T + 50 T^{2} - 200 T^{3} + 850 T^{4} - 2601 T^{5} + 4913 T^{6} \))(\( 1 + 2 T + 25 T^{2} + 96 T^{3} + 662 T^{4} + 1308 T^{5} + 11254 T^{6} + 27744 T^{7} + 122825 T^{8} + 167042 T^{9} + 1419857 T^{10} \))(\( 1 + T + 66 T^{2} + 26 T^{3} + 2212 T^{4} + 199 T^{5} + 51705 T^{6} + 1532 T^{7} + 878985 T^{8} + 57511 T^{9} + 10867556 T^{10} + 2171546 T^{11} + 93710562 T^{12} + 24137569 T^{13} + 410338673 T^{14} \))(\( 1 + 9 T + 122 T^{2} + 798 T^{3} + 6216 T^{4} + 31223 T^{5} + 174989 T^{6} + 688740 T^{7} + 2974813 T^{8} + 9023447 T^{9} + 30539208 T^{10} + 66649758 T^{11} + 173222554 T^{12} + 217238121 T^{13} + 410338673 T^{14} \))(\( 1 + 8 T + 92 T^{2} + 500 T^{3} + 3438 T^{4} + 14774 T^{5} + 76420 T^{6} + 279916 T^{7} + 1273329 T^{8} + 4593380 T^{9} + 21646593 T^{10} + 80895724 T^{11} + 375451460 T^{12} + 1233939254 T^{13} + 4881468366 T^{14} + 12068784500 T^{15} + 37751157916 T^{16} + 55806059528 T^{17} + 118587876497 T^{18} \))(\( 1 - 4 T + 97 T^{2} - 264 T^{3} + 4341 T^{4} - 7296 T^{5} + 129101 T^{6} - 117284 T^{7} + 3130755 T^{8} - 1704552 T^{9} + 67580850 T^{10} - 32335528 T^{11} + 1258614414 T^{12} - 549703976 T^{13} + 19530865650 T^{14} - 8374463976 T^{15} + 261483788355 T^{16} - 166526508388 T^{17} + 3116184295469 T^{18} - 2993830958208 T^{19} + 30281763051381 T^{20} - 31307199395208 T^{21} + 195551408343553 T^{22} - 137087585230532 T^{23} + 582622237229761 T^{24} \))(\( 1 - 3 T + 89 T^{2} - 271 T^{3} + 3764 T^{4} - 10083 T^{5} + 102997 T^{6} - 196615 T^{7} + 2062567 T^{8} - 2024678 T^{9} + 33284978 T^{10} - 9244702 T^{11} + 527249480 T^{12} - 157159934 T^{13} + 9619358642 T^{14} - 9947243014 T^{15} + 172267658407 T^{16} - 279165184055 T^{17} + 2486097194293 T^{18} - 4137444839859 T^{19} + 26256751007924 T^{20} - 32137314530687 T^{21} + 179423457139961 T^{22} - 102815688922899 T^{23} + 582622237229761 T^{24} \))(\( 1 - 10 T + 165 T^{2} - 1192 T^{3} + 11741 T^{4} - 68630 T^{5} + 517025 T^{6} - 2584468 T^{7} + 16278147 T^{8} - 71577210 T^{9} + 392465306 T^{10} - 1537406410 T^{11} + 7474717374 T^{12} - 26135908970 T^{13} + 113422473434 T^{14} - 351658832730 T^{15} + 1359567115587 T^{16} - 3669574981076 T^{17} + 12479726612225 T^{18} - 28161543127990 T^{19} + 81902368114781 T^{20} - 141356748784424 T^{21} + 332638993574085 T^{22} - 342718963076330 T^{23} + 582622237229761 T^{24} \))
$19$ (\( 1 + 2 T + 19 T^{2} \))(\( 1 - 8 T + 34 T^{2} - 152 T^{3} + 361 T^{4} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( 1 + 4 T + 10 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 33 T^{2} + 361 T^{4} \))(\( 1 + 18 T^{2} + 361 T^{4} \))(\( 1 - 2 T + 19 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 102 T^{3} + 722 T^{4} - 1444 T^{5} + 6859 T^{6} \))(\( 1 - 4 T + 8 T^{2} + 72 T^{3} + 152 T^{4} - 1444 T^{5} + 6859 T^{6} \))(\( 1 + 5 T + 53 T^{2} + 279 T^{3} + 1821 T^{4} + 6547 T^{5} + 34599 T^{6} + 100719 T^{7} + 363527 T^{8} + 651605 T^{9} + 2476099 T^{10} \))(\( 1 - 11 T + 123 T^{2} - 943 T^{3} + 6780 T^{4} - 38558 T^{5} + 207830 T^{6} - 937252 T^{7} + 3948770 T^{8} - 13919438 T^{9} + 46504020 T^{10} - 122892703 T^{11} + 304560177 T^{12} - 517504691 T^{13} + 893871739 T^{14} \))(\( 1 - 3 T + 52 T^{2} - 68 T^{3} + 1203 T^{4} + 321 T^{5} + 16531 T^{6} + 37799 T^{7} + 314089 T^{8} + 115881 T^{9} + 8251377 T^{10} - 8861828 T^{11} + 128757148 T^{12} - 141137643 T^{13} + 893871739 T^{14} \))(\( 1 - T + 74 T^{2} - 124 T^{3} + 3178 T^{4} - 6606 T^{5} + 98399 T^{6} - 201683 T^{7} + 2392182 T^{8} - 4452264 T^{9} + 45451458 T^{10} - 72807563 T^{11} + 674918741 T^{12} - 860900526 T^{13} + 7869042622 T^{14} - 5833689244 T^{15} + 66146508686 T^{16} - 16983563041 T^{17} + 322687697779 T^{18} \))(\( 1 + 9 T + 127 T^{2} + 999 T^{3} + 8513 T^{4} + 55475 T^{5} + 374218 T^{6} + 2092084 T^{7} + 11981297 T^{8} + 59771665 T^{9} + 302921079 T^{10} + 1367448582 T^{11} + 6310019386 T^{12} + 25981523058 T^{13} + 109354509519 T^{14} + 409973850235 T^{15} + 1561414606337 T^{16} + 5180207100316 T^{17} + 17605415496058 T^{18} + 49587534721025 T^{19} + 144581072168033 T^{20} + 322365010081221 T^{21} + 778645414740727 T^{22} + 1048412330083971 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 123 T^{2} + 44 T^{3} + 7924 T^{4} + 5052 T^{5} + 346656 T^{6} + 289044 T^{7} + 11384560 T^{8} + 10701760 T^{9} + 295368344 T^{10} + 279137696 T^{11} + 6209526260 T^{12} + 5303616224 T^{13} + 106627972184 T^{14} + 73403371840 T^{15} + 1483647243760 T^{16} + 715701559356 T^{17} + 16308736923936 T^{18} + 4515840025428 T^{19} + 134577753536884 T^{20} + 14198258702276 T^{21} + 754121149709523 T^{22} + 2213314919066161 T^{24} \))(\( 1 - T + 143 T^{2} - 81 T^{3} + 10035 T^{4} - 1401 T^{5} + 458986 T^{6} + 103028 T^{7} + 15376081 T^{8} + 7311047 T^{9} + 401594583 T^{10} + 231239358 T^{11} + 8453969526 T^{12} + 4393547802 T^{13} + 144975644463 T^{14} + 50146471373 T^{15} + 2003826252001 T^{16} + 255107527772 T^{17} + 21593400736666 T^{18} - 1252314306339 T^{19} + 170430055116435 T^{20} - 26137703520099 T^{21} + 876742474865543 T^{22} - 116490258898219 T^{23} + 2213314919066161 T^{24} \))
$23$ (\( 1 + 2 T + 23 T^{2} \))(\( 1 - 5 T + 41 T^{2} - 115 T^{3} + 529 T^{4} \))(\( 1 - T + 43 T^{2} - 23 T^{3} + 529 T^{4} \))(\( 1 + 12 T + 74 T^{2} + 276 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 45 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + T + 45 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 + 41 T^{2} + 529 T^{4} \))(\( 1 + 4 T - 2 T^{2} - 150 T^{3} - 46 T^{4} + 2116 T^{5} + 12167 T^{6} \))(\( 1 - 10 T + 90 T^{2} - 456 T^{3} + 2070 T^{4} - 5290 T^{5} + 12167 T^{6} \))(\( 1 + 6 T + 63 T^{2} + 192 T^{3} + 1414 T^{4} + 2452 T^{5} + 32522 T^{6} + 101568 T^{7} + 766521 T^{8} + 1679046 T^{9} + 6436343 T^{10} \))(\( 1 - 19 T + 232 T^{2} - 2074 T^{3} + 15558 T^{4} - 100741 T^{5} + 582135 T^{6} - 2958428 T^{7} + 13389105 T^{8} - 53291989 T^{9} + 189294186 T^{10} - 580390234 T^{11} + 1493231576 T^{12} - 2812681891 T^{13} + 3404825447 T^{14} \))(\( 1 - 10 T + 156 T^{2} - 1070 T^{3} + 9810 T^{4} - 52254 T^{5} + 355503 T^{6} - 1519732 T^{7} + 8176569 T^{8} - 27642366 T^{9} + 119358270 T^{10} - 299429870 T^{11} + 1004069508 T^{12} - 1480358890 T^{13} + 3404825447 T^{14} \))(\( 1 - 3 T + 59 T^{2} + 39 T^{3} + 1183 T^{4} + 8810 T^{5} + 24729 T^{6} + 233961 T^{7} + 1236788 T^{8} + 3999570 T^{9} + 28446124 T^{10} + 123765369 T^{11} + 300877743 T^{12} + 2465399210 T^{13} + 7614193769 T^{14} + 5773399671 T^{15} + 200884701373 T^{16} - 234932955843 T^{17} + 1801152661463 T^{18} \))(\( 1 + 15 T + 268 T^{2} + 2898 T^{3} + 30599 T^{4} + 259246 T^{5} + 2053716 T^{6} + 14360493 T^{7} + 93286443 T^{8} + 558477374 T^{9} + 3118163168 T^{10} + 16394322468 T^{11} + 80741669146 T^{12} + 377069416764 T^{13} + 1649508315872 T^{14} + 6794994209458 T^{15} + 26105371495563 T^{16} + 92429058597099 T^{17} + 304023673813524 T^{18} + 882687377832962 T^{19} + 2396237838613319 T^{20} + 5219740412919774 T^{21} + 11102305005257932 T^{22} + 14292146368708905 T^{23} + 21914624432020321 T^{24} \))(\( 1 + T + 111 T^{2} - 17 T^{3} + 6044 T^{4} - 5251 T^{5} + 232339 T^{6} - 271053 T^{7} + 7190087 T^{8} - 9335894 T^{9} + 189133806 T^{10} - 264460122 T^{11} + 4496011768 T^{12} - 6082582806 T^{13} + 100051783374 T^{14} - 113589822298 T^{15} + 2012081136167 T^{16} - 1744590079179 T^{17} + 34394510414371 T^{18} - 17878738422197 T^{19} + 473311595038364 T^{20} - 30619595244871 T^{21} + 4598342744715039 T^{22} + 952809757913927 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 3 T + 156 T^{2} + 544 T^{3} + 12859 T^{4} + 46134 T^{5} + 722980 T^{6} + 2512287 T^{7} + 30281675 T^{8} + 98657940 T^{9} + 984601984 T^{10} + 2937072550 T^{11} + 25361223538 T^{12} + 67552668650 T^{13} + 520854449536 T^{14} + 1200371155980 T^{15} + 8474054213675 T^{16} + 16169940846441 T^{17} + 107026987029220 T^{18} + 157078217171898 T^{19} + 1007000959728379 T^{20} + 979827047835872 T^{21} + 6462535749329244 T^{22} + 2858429273741781 T^{23} + 21914624432020321 T^{24} \))
$29$ (\( 1 + 4 T + 29 T^{2} \))(\( 1 + 8 T + 69 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 61 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 66 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 + 12 T + 89 T^{2} + 348 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 69 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 + 16 T + 117 T^{2} + 464 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 82 T^{2} - 228 T^{3} + 2378 T^{4} - 3364 T^{5} + 24389 T^{6} \))(\( 1 - 18 T + 182 T^{2} - 1166 T^{3} + 5278 T^{4} - 15138 T^{5} + 24389 T^{6} \))(\( 1 + 5 T + 117 T^{2} + 541 T^{3} + 6005 T^{4} + 22981 T^{5} + 174145 T^{6} + 454981 T^{7} + 2853513 T^{8} + 3536405 T^{9} + 20511149 T^{10} \))(\( 1 + 5 T + 162 T^{2} + 702 T^{3} + 12203 T^{4} + 45007 T^{5} + 550271 T^{6} + 1671295 T^{7} + 15957859 T^{8} + 37850887 T^{9} + 297618967 T^{10} + 496511262 T^{11} + 3322806138 T^{12} + 2974116605 T^{13} + 17249876309 T^{14} \))(\( 1 + 5 T + 126 T^{2} + 582 T^{3} + 7819 T^{4} + 31203 T^{5} + 320931 T^{6} + 1074715 T^{7} + 9306999 T^{8} + 26241723 T^{9} + 190697591 T^{10} + 411637542 T^{11} + 2584404774 T^{12} + 2974116605 T^{13} + 17249876309 T^{14} \))(\( 1 + 25 T + 395 T^{2} + 4479 T^{3} + 40930 T^{4} + 309446 T^{5} + 2033900 T^{6} + 11929004 T^{7} + 65912049 T^{8} + 354500133 T^{9} + 1911449421 T^{10} + 10032292364 T^{11} + 49604787100 T^{12} + 218865276326 T^{13} + 839521328570 T^{14} + 2664213654759 T^{15} + 6813701142055 T^{16} + 12506160324025 T^{17} + 14507145975869 T^{18} \))(\( 1 - 17 T + 308 T^{2} - 3084 T^{3} + 32784 T^{4} - 239556 T^{5} + 1971086 T^{6} - 12005398 T^{7} + 88342328 T^{8} - 493352408 T^{9} + 3403529628 T^{10} - 17607784369 T^{11} + 110114806362 T^{12} - 510625746701 T^{13} + 2862368417148 T^{14} - 12032371878712 T^{15} + 62482850090168 T^{16} - 246244507182302 T^{17} + 1172447920496606 T^{18} - 4132311369078804 T^{19} + 16400078402513424 T^{20} - 44740038189579996 T^{21} + 129577827856461908 T^{22} - 207408666016999093 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 6 T + 212 T^{2} + 1082 T^{3} + 21101 T^{4} + 89188 T^{5} + 1306403 T^{6} + 4417266 T^{7} + 57247721 T^{8} + 150616432 T^{9} + 1974753899 T^{10} + 4219750520 T^{11} + 59628660633 T^{12} + 122372765080 T^{13} + 1660768029059 T^{14} + 3673384160048 T^{15} + 40490225356601 T^{16} + 90603201098634 T^{17} + 777078971024363 T^{18} + 1538481968247092 T^{19} + 10555699559890061 T^{20} + 15696731945890258 T^{21} + 89189933459642612 T^{22} + 73203058594234974 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 29 T + 548 T^{2} - 7552 T^{3} + 87152 T^{4} - 863504 T^{5} + 7675970 T^{6} - 61582806 T^{7} + 455093348 T^{8} - 3101918876 T^{9} + 19739486944 T^{10} - 117092823849 T^{11} + 652152687522 T^{12} - 3395691891621 T^{13} + 16600908519904 T^{14} - 75652699466764 T^{15} + 321878878266788 T^{16} - 1263134109704094 T^{17} + 4565845967296370 T^{18} - 14895337192326736 T^{19} + 43597475382377072 T^{20} - 109557966409762688 T^{21} + 230547563848510148 T^{22} - 353814783205469041 T^{23} + 353814783205469041 T^{24} \))
$31$ (\( 1 + T + 31 T^{2} \))(\( 1 + 6 T + 66 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 58 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 79 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 21 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 66 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 + 2 T + 43 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 5 T + 60 T^{2} - 305 T^{3} + 1860 T^{4} - 4805 T^{5} + 29791 T^{6} \))(\( 1 + 4 T + 28 T^{2} + 376 T^{3} + 868 T^{4} + 3844 T^{5} + 29791 T^{6} \))(\( 1 + 9 T + 119 T^{2} + 909 T^{3} + 6257 T^{4} + 39425 T^{5} + 193967 T^{6} + 873549 T^{7} + 3545129 T^{8} + 8311689 T^{9} + 28629151 T^{10} \))(\( 1 - 13 T + 95 T^{2} - 305 T^{3} + 648 T^{4} + 560 T^{5} + 20132 T^{6} - 105568 T^{7} + 624092 T^{8} + 538160 T^{9} + 19304568 T^{10} - 281673905 T^{11} + 2719769345 T^{12} - 11537547853 T^{13} + 27512614111 T^{14} \))(\( 1 - 21 T + 316 T^{2} - 3540 T^{3} + 33161 T^{4} - 259869 T^{5} + 1781471 T^{6} - 10560667 T^{7} + 55225601 T^{8} - 249734109 T^{9} + 987899351 T^{10} - 3269264340 T^{11} + 9046811716 T^{12} - 18637577301 T^{13} + 27512614111 T^{14} \))(\( 1 - T + 156 T^{2} - 46 T^{3} + 12646 T^{4} + 64 T^{5} + 695121 T^{6} + 73599 T^{7} + 28337228 T^{8} + 2988116 T^{9} + 878454068 T^{10} + 70728639 T^{11} + 20708349711 T^{12} + 59105344 T^{13} + 362044243546 T^{14} - 40825169326 T^{15} + 4291967801316 T^{16} - 852891037441 T^{17} + 26439622160671 T^{18} \))(\( 1 + 11 T + 268 T^{2} + 2246 T^{3} + 31422 T^{4} + 208276 T^{5} + 2177752 T^{6} + 11625436 T^{7} + 102606128 T^{8} + 450844454 T^{9} + 3710634278 T^{10} + 14293752563 T^{11} + 118137620686 T^{12} + 443106329453 T^{13} + 3565919541158 T^{14} + 13431107129114 T^{15} + 94758913936688 T^{16} + 332826362684836 T^{17} + 1932762916305112 T^{18} + 5730217216582636 T^{19} + 26799542178471102 T^{20} + 59383391372867066 T^{21} + 219660380910854668 T^{22} + 279493245860453141 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 2 T + 215 T^{2} + 552 T^{3} + 24140 T^{4} + 66360 T^{5} + 1836432 T^{6} + 5016820 T^{7} + 103696828 T^{8} + 270132408 T^{9} + 4543215564 T^{10} + 10915998044 T^{11} + 157730757196 T^{12} + 338395939364 T^{13} + 4366030157004 T^{14} + 8047514566728 T^{15} + 95766198291388 T^{16} + 143627297319820 T^{17} + 1629840159906192 T^{18} + 1825737072405960 T^{19} + 20588789643825740 T^{20} + 14594671432690392 T^{21} + 176220081700872215 T^{22} + 50816953792809662 T^{23} + 787662783788549761 T^{24} \))(\( 1 - 3 T + 184 T^{2} - 496 T^{3} + 17088 T^{4} - 38208 T^{5} + 1061590 T^{6} - 1787402 T^{7} + 49574412 T^{8} - 57911964 T^{9} + 1884191468 T^{10} - 1580225069 T^{11} + 61992076274 T^{12} - 48986977139 T^{13} + 1810708000748 T^{14} - 1725255319524 T^{15} + 45783010544652 T^{16} - 51171801755702 T^{17} + 942165032712790 T^{18} - 1051201959953088 T^{19} + 14574202047791808 T^{20} - 13114052591692816 T^{21} + 150811604804467384 T^{22} - 76225430689214493 T^{23} + 787662783788549761 T^{24} \))
$37$ (\( 1 + 3 T + 37 T^{2} \))(\( 1 - 2 T - 5 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 77 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 65 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 25 T^{2} - 111 T^{3} + 1369 T^{4} \))(\( 1 + 12 T + 105 T^{2} + 444 T^{3} + 1369 T^{4} \))(\( 1 + 3 T + 65 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 91 T^{2} + 223 T^{3} + 3367 T^{4} + 5476 T^{5} + 50653 T^{6} \))(\( 1 - T + 106 T^{2} - 70 T^{3} + 3922 T^{4} - 1369 T^{5} + 50653 T^{6} \))(\( 1 - 8 T + 141 T^{2} - 1104 T^{3} + 8998 T^{4} - 60080 T^{5} + 332926 T^{6} - 1511376 T^{7} + 7142073 T^{8} - 14993288 T^{9} + 69343957 T^{10} \))(\( 1 + 26 T + 404 T^{2} + 4432 T^{3} + 39662 T^{4} + 308446 T^{5} + 2171097 T^{6} + 13871632 T^{7} + 80330589 T^{8} + 422262574 T^{9} + 2008999286 T^{10} + 8306281552 T^{11} + 28014958628 T^{12} + 66708886634 T^{13} + 94931877133 T^{14} \))(\( 1 - 19 T + 360 T^{2} - 4286 T^{3} + 46858 T^{4} - 399525 T^{5} + 3092377 T^{6} - 19755620 T^{7} + 114417949 T^{8} - 546949725 T^{9} + 2373498274 T^{10} - 8032654046 T^{11} + 24963824520 T^{12} - 48748801771 T^{13} + 94931877133 T^{14} \))(\( 1 + 35 T + 763 T^{2} + 11917 T^{3} + 150667 T^{4} + 1593626 T^{5} + 14655455 T^{6} + 118318739 T^{7} + 851803426 T^{8} + 5469266198 T^{9} + 31516726762 T^{10} + 161978353691 T^{11} + 742342762115 T^{12} + 2986711697786 T^{13} + 10447845969319 T^{14} + 30575761616053 T^{15} + 72433022252479 T^{16} + 122936780887235 T^{17} + 129961739795077 T^{18} \))(\( 1 + 29 T + 631 T^{2} + 9945 T^{3} + 134321 T^{4} + 1544182 T^{5} + 15965302 T^{6} + 148019388 T^{7} + 1262977605 T^{8} + 9884449483 T^{9} + 72006725027 T^{10} + 485946774853 T^{11} + 3066780197650 T^{12} + 17980030669561 T^{13} + 98577206561963 T^{14} + 500677019662399 T^{15} + 2367023371164405 T^{16} + 10264250076638316 T^{17} + 40962596969060518 T^{18} + 146592095894990206 T^{19} + 471799752730122641 T^{20} + 1292469502262040765 T^{21} + 3034216738995662719 T^{22} + 5159611031604351977 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 34 T + 721 T^{2} - 10994 T^{3} + 136136 T^{4} - 1426586 T^{5} + 13262837 T^{6} - 111888490 T^{7} + 878750471 T^{8} - 6481238924 T^{9} + 45307548946 T^{10} - 299446846172 T^{11} + 1874841412864 T^{12} - 11079533308364 T^{13} + 62026034507074 T^{14} - 328294195217372 T^{15} + 1646919861479831 T^{16} - 7758790639354930 T^{17} + 34028811149162333 T^{18} - 135428486871657938 T^{19} + 478174902938989256 T^{20} - 1428799367307076538 T^{21} + 3466989332513269129 T^{22} - 6049199140501654042 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 41 T + 1033 T^{2} - 18759 T^{3} + 275331 T^{4} - 3406272 T^{5} + 36890664 T^{6} - 356083210 T^{7} + 3115607565 T^{8} - 24911189221 T^{9} + 183516644463 T^{10} - 1249548077529 T^{11} + 7892527209182 T^{12} - 46233278868573 T^{13} + 251234286269847 T^{14} - 1261826467611313 T^{15} + 5839150189627965 T^{16} - 24692218802661970 T^{17} + 94651350870345576 T^{18} - 323363794985578176 T^{19} + 967094480527522851 T^{20} - 2437952276815849443 T^{21} + 4967267656707638017 T^{22} - 7294622492957876933 T^{23} + 6582952005840035281 T^{24} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))(\( 1 + 77 T^{2} + 1681 T^{4} \))(\( 1 - 2 T + 31 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 86 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 93 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 3 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 71 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 + 2 T + 114 T^{2} + 150 T^{3} + 4674 T^{4} + 3362 T^{5} + 68921 T^{6} \))(\( 1 - 16 T + 196 T^{2} - 1398 T^{3} + 8036 T^{4} - 26896 T^{5} + 68921 T^{6} \))(\( 1 + 4 T + 109 T^{2} + 424 T^{3} + 6474 T^{4} + 20392 T^{5} + 265434 T^{6} + 712744 T^{7} + 7512389 T^{8} + 11303044 T^{9} + 115856201 T^{10} \))(\( 1 + 2 T + 146 T^{2} + 266 T^{3} + 11268 T^{4} + 21566 T^{5} + 619985 T^{6} + 1112908 T^{7} + 25419385 T^{8} + 36252446 T^{9} + 776601828 T^{10} + 751652426 T^{11} + 16915005346 T^{12} + 9500208482 T^{13} + 194754273881 T^{14} \))(\( 1 + 22 T + 270 T^{2} + 2078 T^{3} + 13932 T^{4} + 101594 T^{5} + 873197 T^{6} + 6232516 T^{7} + 35801077 T^{8} + 170779514 T^{9} + 960207372 T^{10} + 5871931358 T^{11} + 31281174270 T^{12} + 104502293302 T^{13} + 194754273881 T^{14} \))(\( 1 + 16 T + 303 T^{2} + 2844 T^{3} + 31747 T^{4} + 213788 T^{5} + 1872807 T^{6} + 10023732 T^{7} + 81015990 T^{8} + 398200168 T^{9} + 3321655590 T^{10} + 16849893492 T^{11} + 129075731247 T^{12} + 604113792668 T^{13} + 3678086813147 T^{14} + 13509296461404 T^{15} + 59010544985943 T^{16} + 127758803665936 T^{17} + 327381934393961 T^{18} \))(\( 1 - 14 T + 330 T^{2} - 3554 T^{3} + 49735 T^{4} - 449836 T^{5} + 4743290 T^{6} - 37513844 T^{7} + 327083851 T^{8} - 2326331990 T^{9} + 17697320220 T^{10} - 115153987482 T^{11} + 790833981402 T^{12} - 4721313486762 T^{13} + 29749195289820 T^{14} - 160333127082790 T^{15} + 924260789885611 T^{16} - 4346211450746644 T^{17} + 22531121945292890 T^{18} - 87607483545533516 T^{19} + 397130256270332935 T^{20} - 1163515394836137394 T^{21} + 4429477572350292330 T^{22} - 7704606444027478174 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 14 T + 339 T^{2} + 3588 T^{3} + 53932 T^{4} + 480564 T^{5} + 5599015 T^{6} + 43529766 T^{7} + 424099143 T^{8} + 2922923404 T^{9} + 24710309430 T^{10} + 152033575416 T^{11} + 1136390796760 T^{12} + 6233376592056 T^{13} + 41538030151830 T^{14} + 201450803927084 T^{15} + 1198402818422823 T^{16} + 5043193319178966 T^{17} + 26595904896922615 T^{18} + 93591892873348884 T^{19} + 430642987456953772 T^{20} + 1174646380605532068 T^{21} + 4550281506141663939 T^{22} + 7704606444027478174 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 20 T + 462 T^{2} - 6324 T^{3} + 87975 T^{4} - 937816 T^{5} + 9887402 T^{6} - 87412528 T^{7} + 762361555 T^{8} - 5818085772 T^{9} + 44034155752 T^{10} - 298034708708 T^{11} + 2010901084426 T^{12} - 12219423057028 T^{13} + 74021415819112 T^{14} - 400988289492012 T^{15} + 2154251550018355 T^{16} - 10127283413886128 T^{17} + 46966190172671882 T^{18} - 182643674113983896 T^{19} + 702473797031919975 T^{20} - 2070363353107409364 T^{21} + 6201268601290409262 T^{22} - 11006580634324968820 T^{23} + 22563490300366186081 T^{24} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 - 6 T + 75 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 109 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( ( 1 + 2 T + 43 T^{2} )^{2} \))(\( 1 + 9 T + 75 T^{2} + 387 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 15 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 - 5 T - 9 T^{2} - 215 T^{3} + 1849 T^{4} \))(\( 1 - 7 T + 84 T^{2} - 502 T^{3} + 3612 T^{4} - 12943 T^{5} + 79507 T^{6} \))(\( 1 - 11 T + 94 T^{2} - 572 T^{3} + 4042 T^{4} - 20339 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 135 T^{2} + 992 T^{3} + 9706 T^{4} + 56752 T^{5} + 417358 T^{6} + 1834208 T^{7} + 10733445 T^{8} + 27350408 T^{9} + 147008443 T^{10} \))(\( 1 - 24 T + 514 T^{2} - 7062 T^{3} + 86260 T^{4} - 816360 T^{5} + 6931999 T^{6} - 47907988 T^{7} + 298075957 T^{8} - 1509449640 T^{9} + 6858273820 T^{10} - 24143572662 T^{11} + 75562339702 T^{12} - 151712713176 T^{13} + 271818611107 T^{14} \))(\( 1 - 19 T + 330 T^{2} - 3778 T^{3} + 40164 T^{4} - 339037 T^{5} + 2712855 T^{6} - 18187404 T^{7} + 116652765 T^{8} - 626879413 T^{9} + 3193319148 T^{10} - 12916230178 T^{11} + 48512786190 T^{12} - 120105897931 T^{13} + 271818611107 T^{14} \))(\( 1 + 9 T + 277 T^{2} + 1841 T^{3} + 33599 T^{4} + 176736 T^{5} + 2548969 T^{6} + 11255519 T^{7} + 141367302 T^{8} + 545391838 T^{9} + 6078793986 T^{10} + 20811454631 T^{11} + 202660878283 T^{12} + 604225213536 T^{13} + 4939336676357 T^{14} + 11637629373209 T^{15} + 75293755276639 T^{16} + 105193802498409 T^{17} + 502592611936843 T^{18} \))(\( 1 + 15 T + 258 T^{2} + 1904 T^{3} + 16807 T^{4} + 43956 T^{5} + 334214 T^{6} - 930811 T^{7} + 18567651 T^{8} + 73256050 T^{9} + 1947741960 T^{10} + 8094843132 T^{11} + 100281619882 T^{12} + 348078254676 T^{13} + 3601374884040 T^{14} + 5824368767350 T^{15} + 63479103806451 T^{16} - 136837075837273 T^{17} + 2112688030058486 T^{18} + 11948058869819292 T^{19} + 196443582065640007 T^{20} + 956936333127749072 T^{21} + 5575762436827336242 T^{22} + 13939406092068340605 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 6 T + 255 T^{2} + 1748 T^{3} + 32440 T^{4} + 226068 T^{5} + 2746475 T^{6} + 18002290 T^{7} + 172552423 T^{8} + 1047703492 T^{9} + 8712770270 T^{10} + 50501656128 T^{11} + 388449379296 T^{12} + 2171571213504 T^{13} + 16109912229230 T^{14} + 83299761538444 T^{15} + 589922396304823 T^{16} + 2646488623334470 T^{17} + 17361465580002275 T^{18} + 61449489775737276 T^{19} + 379165217005376440 T^{20} + 878531885665601564 T^{21} + 5510927989887483495 T^{22} + 5575762436827336242 T^{23} + 39959630797262576401 T^{24} \))(\( 1 - T + 322 T^{2} - 210 T^{3} + 52081 T^{4} - 20518 T^{5} + 5574006 T^{6} - 1198663 T^{7} + 438696187 T^{8} - 47048986 T^{9} + 26694033368 T^{10} - 1531431188 T^{11} + 1285689958822 T^{12} - 65851541084 T^{13} + 49357267697432 T^{14} - 3740723729902 T^{15} + 1499814962811787 T^{16} - 176213581311709 T^{17} + 35235315563304294 T^{18} - 5577174262693426 T^{19} + 608733158657737681 T^{20} - 105544448506737030 T^{21} + 6958897304877528178 T^{22} - 929293739471222707 T^{23} + 39959630797262576401 T^{24} \))
$47$ (\( 1 - T + 47 T^{2} \))(\( 1 - 4 T + 93 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 85 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 31 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 58 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( ( 1 + 7 T + 47 T^{2} )^{2} \))(\( 1 + 6 T + 58 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + T + 23 T^{2} + 266 T^{3} + 1081 T^{4} + 2209 T^{5} + 103823 T^{6} \))(\( 1 - 2 T + 113 T^{2} - 220 T^{3} + 5311 T^{4} - 4418 T^{5} + 103823 T^{6} \))(\( 1 + 13 T + 261 T^{2} + 2283 T^{3} + 25333 T^{4} + 157087 T^{5} + 1190651 T^{6} + 5043147 T^{7} + 27097803 T^{8} + 63435853 T^{9} + 229345007 T^{10} \))(\( 1 - 11 T + 154 T^{2} - 1124 T^{3} + 10727 T^{4} - 58321 T^{5} + 473997 T^{6} - 2317571 T^{7} + 22277859 T^{8} - 128831089 T^{9} + 1113709321 T^{10} - 5484761444 T^{11} + 35319131078 T^{12} - 118571368619 T^{13} + 506623120463 T^{14} \))(\( 1 - 13 T + 179 T^{2} - 2011 T^{3} + 20590 T^{4} - 165352 T^{5} + 1351646 T^{6} - 9741796 T^{7} + 63527362 T^{8} - 365262568 T^{9} + 2137715570 T^{10} - 9813038491 T^{11} + 41052756253 T^{12} - 140129799277 T^{13} + 506623120463 T^{14} \))(\( 1 - T + 272 T^{2} + 136 T^{3} + 32074 T^{4} + 76640 T^{5} + 2223103 T^{6} + 10058089 T^{7} + 113020750 T^{8} + 644899588 T^{9} + 5311975250 T^{10} + 22218318601 T^{11} + 230809222769 T^{12} + 373978751840 T^{13} + 7356011754518 T^{14} + 1465973284744 T^{15} + 137801488765936 T^{16} - 23811286661761 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 17 T + 416 T^{2} + 5222 T^{3} + 75152 T^{4} + 755072 T^{5} + 8230488 T^{6} + 69868476 T^{7} + 639405486 T^{8} + 4787353750 T^{9} + 38964096514 T^{10} + 265590831261 T^{11} + 1982556678638 T^{12} + 12482769069267 T^{13} + 86071689199426 T^{14} + 497037428386250 T^{15} + 3120094801329966 T^{16} + 16023986117299332 T^{17} + 88718202414750552 T^{18} + 382536932814238336 T^{19} + 1789465815204662672 T^{20} + 5844099330542649274 T^{21} + 21881239010105300384 T^{22} + 42026706656428209151 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 2 T + 336 T^{2} + 344 T^{3} + 54457 T^{4} + 3732 T^{5} + 5722257 T^{6} - 4378892 T^{7} + 444390369 T^{8} - 603623948 T^{9} + 27487693525 T^{10} - 44089368444 T^{11} + 1409831184861 T^{12} - 2072200316868 T^{13} + 60720314996725 T^{14} - 62670049153204 T^{15} + 2168483240192289 T^{16} - 1004277016392244 T^{17} + 61681440370877553 T^{18} + 1890717485567916 T^{19} + 1296691237739518777 T^{20} + 384980882747351848 T^{21} + 17673308431238896464 T^{22} + 4944318430168024606 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 5 T + 272 T^{2} + 1154 T^{3} + 38220 T^{4} + 142892 T^{5} + 3793456 T^{6} + 12969688 T^{7} + 294553462 T^{8} + 924023442 T^{9} + 18438929550 T^{10} + 52757098657 T^{11} + 949938052894 T^{12} + 2479583636879 T^{13} + 40731595375950 T^{14} + 95934885818766 T^{15} + 1437326932005622 T^{16} + 2974533185147816 T^{17} + 40890479065087024 T^{18} + 72392390929198996 T^{19} + 910067376212505420 T^{20} + 1291476565960593118 T^{21} + 14306963968145773328 T^{22} + 12360796075420061515 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))
$53$ (\( 1 + 11 T + 53 T^{2} \))(\( 1 + 14 T + 150 T^{2} + 742 T^{3} + 2809 T^{4} \))(\( 1 + 2 T + 94 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 + 22 T + 225 T^{2} + 1166 T^{3} + 2809 T^{4} \))(\( 1 - 5 T + 111 T^{2} - 265 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 126 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 7 T + 117 T^{2} + 371 T^{3} + 2809 T^{4} \))(\( 1 - 26 T + 377 T^{2} - 3349 T^{3} + 19981 T^{4} - 73034 T^{5} + 148877 T^{6} \))(\( 1 - 21 T + 278 T^{2} - 2422 T^{3} + 14734 T^{4} - 58989 T^{5} + 148877 T^{6} \))(\( 1 + 2 T + 141 T^{2} + 216 T^{3} + 11910 T^{4} + 17068 T^{5} + 631230 T^{6} + 606744 T^{7} + 20991657 T^{8} + 15780962 T^{9} + 418195493 T^{10} \))(\( 1 - 4 T + 207 T^{2} - 920 T^{3} + 21673 T^{4} - 86044 T^{5} + 1568415 T^{6} - 5154512 T^{7} + 83125995 T^{8} - 241697596 T^{9} + 3226611221 T^{10} - 7259242520 T^{11} + 86566467051 T^{12} - 88657444516 T^{13} + 1174711139837 T^{14} \))(\( 1 - 5 T + 292 T^{2} - 1358 T^{3} + 39830 T^{4} - 162507 T^{5} + 3267729 T^{6} - 11087924 T^{7} + 173189637 T^{8} - 456482163 T^{9} + 5929770910 T^{10} - 10715273198 T^{11} + 122113083956 T^{12} - 110821805645 T^{13} + 1174711139837 T^{14} \))(\( 1 + 29 T + 726 T^{2} + 12562 T^{3} + 188263 T^{4} + 2341888 T^{5} + 25766913 T^{6} + 247956318 T^{7} + 2138364493 T^{8} + 16409384230 T^{9} + 113333318129 T^{10} + 696509297262 T^{11} + 3836100706701 T^{12} + 18478622768128 T^{13} + 78730738098659 T^{14} + 278428704502498 T^{15} + 852840287521662 T^{16} + 1805531021929469 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 7 T + 90 T^{2} + 488 T^{3} + 12865 T^{4} + 79310 T^{5} + 853506 T^{6} + 3921193 T^{7} + 65117699 T^{8} + 321866540 T^{9} + 3600066580 T^{10} + 15238294818 T^{11} + 207282814582 T^{12} + 807629625354 T^{13} + 10112587023220 T^{14} + 47918524875580 T^{15} + 513809966723219 T^{16} + 1639825239783149 T^{17} + 18917415209768274 T^{18} + 93166340500472470 T^{19} + 800970917142159265 T^{20} + 1610284632799440904 T^{21} + 15739872332896174410 T^{22} + 64883251505605341179 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 10 T + 416 T^{2} - 3966 T^{3} + 86330 T^{4} - 761902 T^{5} + 11674400 T^{6} - 94151882 T^{7} + 1144126111 T^{8} - 8383469412 T^{9} + 85931558464 T^{10} - 568900866028 T^{11} + 5098746497836 T^{12} - 30151745899484 T^{13} + 241381747725376 T^{14} - 1248105775650324 T^{15} + 9027705340449391 T^{16} - 39373892709867826 T^{17} + 258755617564397600 T^{18} - 895014766864089974 T^{19} + 5374879073212795130 T^{20} - 13086862405087259478 T^{21} + 72753187672053428384 T^{22} - 92690359293721915970 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 39 T + 1040 T^{2} - 20272 T^{3} + 328087 T^{4} - 4495172 T^{5} + 54394544 T^{6} - 587035227 T^{7} + 5781909051 T^{8} - 52318711658 T^{9} + 441970840512 T^{10} - 3498408843716 T^{11} + 26210432476442 T^{12} - 185415668716948 T^{13} + 1241496090998208 T^{14} - 7789052835508066 T^{15} + 45622043510643531 T^{16} - 245495486163631911 T^{17} + 1205620316663280176 T^{18} - 5280528623883366964 T^{19} + 20426595047992196407 T^{20} - 66892807533012840176 T^{21} + \)\(18\!\cdots\!60\)\( T^{22} - \)\(36\!\cdots\!83\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))
$59$ (\( 1 - 3 T + 59 T^{2} \))(\( 1 + 10 T + 98 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 10 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 + 10 T + 141 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( 1 - 2 T + 99 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( 1 - 2 T + 114 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( 1 + 10 T + 123 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 164 T^{2} + 881 T^{3} + 9676 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 - 6 T + 176 T^{2} - 706 T^{3} + 10384 T^{4} - 20886 T^{5} + 205379 T^{6} \))(\( 1 + 4 T + 59 T^{2} + 120 T^{3} + 4414 T^{4} + 36008 T^{5} + 260426 T^{6} + 417720 T^{7} + 12117361 T^{8} + 48469444 T^{9} + 714924299 T^{10} \))(\( 1 - 4 T + 321 T^{2} - 944 T^{3} + 46921 T^{4} - 103612 T^{5} + 4159569 T^{6} - 7292384 T^{7} + 245414571 T^{8} - 360673372 T^{9} + 9636588059 T^{10} - 11438788784 T^{11} + 229490699979 T^{12} - 168722134564 T^{13} + 2488651484819 T^{14} \))(\( 1 - 18 T + 418 T^{2} - 5368 T^{3} + 72948 T^{4} - 714158 T^{5} + 7100527 T^{6} - 54300560 T^{7} + 418931093 T^{8} - 2485983998 T^{9} + 14981987292 T^{10} - 65045993848 T^{11} + 298838356982 T^{12} - 759249605538 T^{13} + 2488651484819 T^{14} \))(\( 1 - 14 T + 236 T^{2} - 2756 T^{3} + 33441 T^{4} - 327888 T^{5} + 3255193 T^{6} - 28063996 T^{7} + 240319503 T^{8} - 1866179140 T^{9} + 14178850677 T^{10} - 97690770076 T^{11} + 668548283147 T^{12} - 3973137263568 T^{13} + 23907783482859 T^{14} - 116249550714596 T^{15} + 587321750417284 T^{16} - 2055626126460494 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 32 T + 710 T^{2} + 11554 T^{3} + 163099 T^{4} + 1999788 T^{5} + 22569414 T^{6} + 232762054 T^{7} + 2268422075 T^{8} + 20712796662 T^{9} + 180762854212 T^{10} + 1489434396946 T^{11} + 11760399511698 T^{12} + 87876629419814 T^{13} + 629235495511972 T^{14} + 4253973465644898 T^{15} + 27487289183144075 T^{16} + 166407248289750146 T^{17} + 951989926484656374 T^{18} + 4976775375523218372 T^{19} + 23947897542827150779 T^{20} + \)\(10\!\cdots\!06\)\( T^{21} + \)\(36\!\cdots\!10\)\( T^{22} + \)\(96\!\cdots\!88\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 - 28 T + 668 T^{2} - 10196 T^{3} + 145714 T^{4} - 1636716 T^{5} + 18251276 T^{6} - 172162052 T^{7} + 1672497151 T^{8} - 14180893624 T^{9} + 126122113016 T^{10} - 986576008488 T^{11} + 8091055420924 T^{12} - 58207984500792 T^{13} + 439031075408696 T^{14} - 2912457751603496 T^{15} + 20266251750138511 T^{16} - 123082834340501548 T^{17} + 769848561309175916 T^{18} - 4073215703627014404 T^{19} + 21395250385076030194 T^{20} - 88327905367005758044 T^{21} + \)\(34\!\cdots\!68\)\( T^{22} - \)\(84\!\cdots\!52\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 8 T + 360 T^{2} + 2574 T^{3} + 64925 T^{4} + 419628 T^{5} + 7794256 T^{6} + 46045554 T^{7} + 706940547 T^{8} + 3846500746 T^{9} + 52187047304 T^{10} + 263973152262 T^{11} + 3297051899198 T^{12} + 15574415983458 T^{13} + 181663111665224 T^{14} + 789990476712734 T^{15} + 8566253813536467 T^{16} + 32919085415516646 T^{17} + 328765877414566096 T^{18} + 1044307845271627332 T^{19} + 9532966161460540925 T^{20} + 22298551237217812986 T^{21} + \)\(18\!\cdots\!60\)\( T^{22} + \)\(24\!\cdots\!72\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))
$61$ (\( 1 + 4 T + 61 T^{2} \))(\( 1 + 20 T + 217 T^{2} + 1220 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 21 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 + 50 T^{2} + 3721 T^{4} \))(\( 1 + 5 T + 127 T^{2} + 305 T^{3} + 3721 T^{4} \))(\( 1 + 117 T^{2} + 3721 T^{4} \))(\( 1 - 9 T + 131 T^{2} - 549 T^{3} + 3721 T^{4} \))(\( 1 - T + 44 T^{2} + 546 T^{3} + 2684 T^{4} - 3721 T^{5} + 226981 T^{6} \))(\( 1 + 11 T + 62 T^{2} + 480 T^{3} + 3782 T^{4} + 40931 T^{5} + 226981 T^{6} \))(\( 1 - 11 T + 229 T^{2} - 2491 T^{3} + 24489 T^{4} - 221163 T^{5} + 1493829 T^{6} - 9269011 T^{7} + 51978649 T^{8} - 152304251 T^{9} + 844596301 T^{10} \))(\( 1 + 5 T + 210 T^{2} + 398 T^{3} + 22363 T^{4} + 26651 T^{5} + 1945003 T^{6} + 2595919 T^{7} + 118645183 T^{8} + 99168371 T^{9} + 5075976103 T^{10} + 5510644718 T^{11} + 177365223210 T^{12} + 257601871805 T^{13} + 3142742836021 T^{14} \))(\( 1 - 26 T + 537 T^{2} - 6694 T^{3} + 72271 T^{4} - 555381 T^{5} + 4325959 T^{6} - 29289133 T^{7} + 263883499 T^{8} - 2066572701 T^{9} + 16404143851 T^{10} - 92684059654 T^{11} + 453548213637 T^{12} - 1339529733386 T^{13} + 3142742836021 T^{14} \))(\( 1 + 28 T + 488 T^{2} + 6082 T^{3} + 61351 T^{4} + 542901 T^{5} + 4384253 T^{6} + 33042120 T^{7} + 240205165 T^{8} + 1799569925 T^{9} + 14652515065 T^{10} + 122949728520 T^{11} + 995142130193 T^{12} + 7516920924741 T^{13} + 51816827662651 T^{14} + 313346916863602 T^{15} + 1533658503978248 T^{16} + 5367804763923868 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 8 T + 593 T^{2} + 4174 T^{3} + 164810 T^{4} + 1024441 T^{5} + 28619615 T^{6} + 157483913 T^{7} + 3485187899 T^{8} + 16996065526 T^{9} + 315625078990 T^{10} + 1362184283202 T^{11} + 21896493361504 T^{12} + 83093241275322 T^{13} + 1174440918921790 T^{14} + 3857783949157006 T^{15} + 48255357504678059 T^{16} + 133010330386805813 T^{17} + 1474493278867691015 T^{18} + 3219554613676189261 T^{19} + 31595282255081881610 T^{20} + 48811365791489704534 T^{21} + \)\(42\!\cdots\!93\)\( T^{22} + \)\(34\!\cdots\!88\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 2 T + 436 T^{2} - 1038 T^{3} + 96193 T^{4} - 245604 T^{5} + 14171095 T^{6} - 36275338 T^{7} + 1548507881 T^{8} - 3796228844 T^{9} + 131946978859 T^{10} - 299278550144 T^{11} + 8976427949089 T^{12} - 18255991558784 T^{13} + 490974708334339 T^{14} - 861671819239964 T^{15} + 21440393907572921 T^{16} - 30638016292324738 T^{17} + 730100119505295295 T^{18} - 771870211498101684 T^{19} + 18440901559147451233 T^{20} - 12138523644361838358 T^{21} + \)\(31\!\cdots\!36\)\( T^{22} - 87027835222871677322 T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 30 T + 843 T^{2} - 15790 T^{3} + 274782 T^{4} - 3898493 T^{5} + 51874541 T^{6} - 601780665 T^{7} + 6604262409 T^{8} - 65123828282 T^{9} + 611139914150 T^{10} - 5226719073036 T^{11} + 42670329733292 T^{12} - 318829863455196 T^{13} + 2274051620552150 T^{14} - 14781871667276642 T^{15} + 91441567237290969 T^{16} - 508261723672320165 T^{17} + 2672595772125043301 T^{18} - 12251960947028016353 T^{19} + 52677718880018867742 T^{20} - \)\(18\!\cdots\!90\)\( T^{21} + \)\(60\!\cdots\!43\)\( T^{22} - \)\(13\!\cdots\!30\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))
$67$ (\( 1 - 3 T + 67 T^{2} \))(\( 1 + 8 T + 145 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 2 T + 83 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 - 2 T + 133 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 + 11 T + 153 T^{2} + 737 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 133 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + T + 73 T^{2} + 67 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 61 T^{2} + 605 T^{3} + 4087 T^{4} + 35912 T^{5} + 300763 T^{6} \))(\( 1 - 29 T + 476 T^{2} - 4740 T^{3} + 31892 T^{4} - 130181 T^{5} + 300763 T^{6} \))(\( 1 + 28 T + 491 T^{2} + 5616 T^{3} + 53302 T^{4} + 436232 T^{5} + 3571234 T^{6} + 25210224 T^{7} + 147674633 T^{8} + 564231388 T^{9} + 1350125107 T^{10} \))(\( 1 - 42 T + 1060 T^{2} - 19258 T^{3} + 278042 T^{4} - 3324230 T^{5} + 33867347 T^{6} - 297649804 T^{7} + 2269112249 T^{8} - 14922468470 T^{9} + 83624746046 T^{10} - 388070288218 T^{11} + 1431132613420 T^{12} - 3799252051098 T^{13} + 6060711605323 T^{14} \))(\( 1 - 27 T + 586 T^{2} - 8768 T^{3} + 117100 T^{4} - 1283653 T^{5} + 12863415 T^{6} - 109990832 T^{7} + 861848805 T^{8} - 5762318317 T^{9} + 35219347300 T^{10} - 176685028928 T^{11} + 791173312702 T^{12} - 2442376318563 T^{13} + 6060711605323 T^{14} \))(\( 1 + 19 T + 373 T^{2} + 4527 T^{3} + 55745 T^{4} + 463082 T^{5} + 4103863 T^{6} + 24884529 T^{7} + 197147226 T^{8} + 1121891190 T^{9} + 13208864142 T^{10} + 111706650681 T^{11} + 1234290147469 T^{12} + 9331621414922 T^{13} + 75262724089715 T^{14} + 409505096079063 T^{15} + 2260645428785479 T^{16} + 7715285873576179 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 39 T + 1027 T^{2} + 19953 T^{3} + 327827 T^{4} + 4668260 T^{5} + 60334624 T^{6} + 711808264 T^{7} + 7810781633 T^{8} + 79587200761 T^{9} + 760914720237 T^{10} + 6811012689499 T^{11} + 57514505185654 T^{12} + 456337850196433 T^{13} + 3415746179143893 T^{14} + 23936885262480643 T^{15} + 157396005791160593 T^{16} + 961030208596484248 T^{17} + 5457772475814919456 T^{18} + 28292977558665147980 T^{19} + \)\(13\!\cdots\!07\)\( T^{20} + \)\(54\!\cdots\!91\)\( T^{21} + \)\(18\!\cdots\!23\)\( T^{22} + \)\(47\!\cdots\!37\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 + 28 T + 849 T^{2} + 15350 T^{3} + 282852 T^{4} + 3942978 T^{5} + 55516261 T^{6} + 642715788 T^{7} + 7500440119 T^{8} + 74700374352 T^{9} + 749275246162 T^{10} + 6523249807428 T^{11} + 57171174721064 T^{12} + 437057737097676 T^{13} + 3363496580021218 T^{14} + 22467108691230576 T^{15} + 151142276391223399 T^{16} + 867746722044089316 T^{17} + 5021911154131950109 T^{18} + 23897252524133271894 T^{19} + \)\(11\!\cdots\!32\)\( T^{20} + \)\(41\!\cdots\!50\)\( T^{21} + \)\(15\!\cdots\!01\)\( T^{22} + \)\(34\!\cdots\!24\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 9 T + 601 T^{2} - 3775 T^{3} + 157069 T^{4} - 604972 T^{5} + 23942342 T^{6} - 34337308 T^{7} + 2438929425 T^{8} + 2442927869 T^{9} + 188022122801 T^{10} + 539005678755 T^{11} + 12811914209986 T^{12} + 36113380476585 T^{13} + 844031309253689 T^{14} + 734742314664047 T^{15} + 49147161953635425 T^{16} - 46359661637591956 T^{17} + 2165785522656899798 T^{18} - 3666560821295465956 T^{19} + 63780644046144045229 T^{20} - \)\(10\!\cdots\!25\)\( T^{21} + \)\(10\!\cdots\!49\)\( T^{22} - \)\(10\!\cdots\!47\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))
$71$ (\( 1 + 6 T + 71 T^{2} \))(\( 1 + 11 T + 161 T^{2} + 781 T^{3} + 5041 T^{4} \))(\( 1 - 3 T + 115 T^{2} - 213 T^{3} + 5041 T^{4} \))(\( 1 + 12 T + 106 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( 1 + 4 T - 34 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 - 11 T + 141 T^{2} - 781 T^{3} + 5041 T^{4} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( 1 + 10 T + 205 T^{2} + 1260 T^{3} + 14555 T^{4} + 50410 T^{5} + 357911 T^{6} \))(\( ( 1 - 4 T + 71 T^{2} )^{3} \))(\( 1 + 2 T + 175 T^{2} + 320 T^{3} + 17542 T^{4} + 36060 T^{5} + 1245482 T^{6} + 1613120 T^{7} + 62634425 T^{8} + 50823362 T^{9} + 1804229351 T^{10} \))(\( 1 + 9 T + 320 T^{2} + 2246 T^{3} + 49410 T^{4} + 293863 T^{5} + 5051659 T^{6} + 25462260 T^{7} + 358667789 T^{8} + 1481363383 T^{9} + 17684382510 T^{10} + 57074635526 T^{11} + 577353392320 T^{12} + 1152902555289 T^{13} + 9095120158391 T^{14} \))(\( 1 - 46 T + 1357 T^{2} - 28004 T^{3} + 457241 T^{4} - 6006866 T^{5} + 65915325 T^{6} - 603704184 T^{7} + 4679988075 T^{8} - 30280611506 T^{9} + 163651583551 T^{10} - 711628714724 T^{11} + 2448339229307 T^{12} - 5892613060366 T^{13} + 9095120158391 T^{14} \))(\( 1 - 9 T + 336 T^{2} - 3512 T^{3} + 59605 T^{4} - 653252 T^{5} + 7286033 T^{6} - 77748744 T^{7} + 665144243 T^{8} - 6510156198 T^{9} + 47225241253 T^{10} - 391931418504 T^{11} + 2607751357063 T^{12} - 16600231436612 T^{13} + 107541090466355 T^{14} - 449888197130552 T^{15} + 3055960373219376 T^{16} - 5811781781211849 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 35 T + 965 T^{2} + 18827 T^{3} + 320068 T^{4} + 4564809 T^{5} + 59233681 T^{6} + 683322497 T^{7} + 7374100007 T^{8} + 73103273734 T^{9} + 693289648154 T^{10} + 6177140226134 T^{11} + 53453933493352 T^{12} + 438576956055514 T^{13} + 3494873116344314 T^{14} + 26164465805409674 T^{15} + 187388277039981767 T^{16} + 1232870505286009447 T^{17} + 7587851353785943201 T^{18} + 41517486355104662319 T^{19} + \)\(20\!\cdots\!48\)\( T^{20} + \)\(86\!\cdots\!37\)\( T^{21} + \)\(31\!\cdots\!65\)\( T^{22} + \)\(80\!\cdots\!85\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 - 9 T + 567 T^{2} - 5311 T^{3} + 156896 T^{4} - 1466349 T^{5} + 28329979 T^{6} - 252668907 T^{7} + 3739585015 T^{8} - 30670653834 T^{9} + 379907284894 T^{10} - 2802006636918 T^{11} + 30339404350608 T^{12} - 198942471221178 T^{13} + 1915112623150654 T^{14} - 10977364384380774 T^{15} + 95029141473560215 T^{16} - 455872658094489357 T^{17} + 3629078353375967659 T^{18} - 13336620349136484459 T^{19} + \)\(10\!\cdots\!56\)\( T^{20} - \)\(24\!\cdots\!41\)\( T^{21} + \)\(18\!\cdots\!67\)\( T^{22} - \)\(20\!\cdots\!39\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 29 T + 933 T^{2} + 18131 T^{3} + 349216 T^{4} + 5237441 T^{5} + 75956737 T^{6} + 938754783 T^{7} + 11147389591 T^{8} + 117660839402 T^{9} + 1191836294858 T^{10} + 10951471090550 T^{11} + 96586453776592 T^{12} + 777554447429050 T^{13} + 6008046762379178 T^{14} + 42112108691209222 T^{15} + 283273908269212471 T^{16} + 1693728932880235833 T^{17} + 9730079575412725777 T^{18} + 47635155217483517431 T^{19} + \)\(22\!\cdots\!76\)\( T^{20} + \)\(83\!\cdots\!61\)\( T^{21} + \)\(30\!\cdots\!33\)\( T^{22} + \)\(67\!\cdots\!59\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))(\( 1 - T + 115 T^{2} - 73 T^{3} + 5329 T^{4} \))(\( 1 + 17 T + 189 T^{2} + 1241 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 178 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 - T + 145 T^{2} - 73 T^{3} + 5329 T^{4} \))(\( 1 + 19 T + 225 T^{2} + 1387 T^{3} + 5329 T^{4} \))(\( 1 - 5 T + 151 T^{2} - 365 T^{3} + 5329 T^{4} \))(\( 1 + 17 T + 254 T^{2} + 2286 T^{3} + 18542 T^{4} + 90593 T^{5} + 389017 T^{6} \))(\( 1 + 7 T + 66 T^{2} + 100 T^{3} + 4818 T^{4} + 37303 T^{5} + 389017 T^{6} \))(\( 1 - 8 T + 241 T^{2} - 616 T^{3} + 19206 T^{4} + 4320 T^{5} + 1402038 T^{6} - 3282664 T^{7} + 93753097 T^{8} - 227185928 T^{9} + 2073071593 T^{10} \))(\( 1 - 27 T + 614 T^{2} - 10216 T^{3} + 143660 T^{4} - 1707773 T^{5} + 17858693 T^{6} - 161388576 T^{7} + 1303684589 T^{8} - 9100722317 T^{9} + 55886182220 T^{10} - 290116430056 T^{11} + 1272865958102 T^{12} - 4086024109803 T^{13} + 11047398519097 T^{14} \))(\( 1 + 25 T + 468 T^{2} + 5668 T^{3} + 55638 T^{4} + 413863 T^{5} + 2707213 T^{6} + 19340664 T^{7} + 197626549 T^{8} + 2205475927 T^{9} + 21644127846 T^{10} + 160961229988 T^{11} + 970197505524 T^{12} + 3783355657225 T^{13} + 11047398519097 T^{14} \))(\( 1 + 160 T^{2} - 1178 T^{3} + 13812 T^{4} - 174332 T^{5} + 1312718 T^{6} - 13146518 T^{7} + 138980941 T^{8} - 746538888 T^{9} + 10145608693 T^{10} - 70057794422 T^{11} + 510669618206 T^{12} - 4950722150012 T^{13} + 28633264842516 T^{14} - 178271718568442 T^{15} + 1767583763055520 T^{16} + 58871586708267913 T^{18} \))(\( 1 + 12 T + 369 T^{2} + 3938 T^{3} + 76243 T^{4} + 768288 T^{5} + 11261961 T^{6} + 104835486 T^{7} + 1302550371 T^{8} + 11200420910 T^{9} + 123899449814 T^{10} + 976028791990 T^{11} + 9844713826450 T^{12} + 71250101815270 T^{13} + 660260168058806 T^{14} + 4357154141145470 T^{15} + 36990139350297411 T^{16} + 217331467964949198 T^{17} + 1704320154431892729 T^{18} + 8487583713439995936 T^{19} + 61486936786280417683 T^{20} + \)\(23\!\cdots\!94\)\( T^{21} + \)\(15\!\cdots\!81\)\( T^{22} + \)\(37\!\cdots\!24\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 61 T + 2263 T^{2} - 61453 T^{3} + 1350684 T^{4} - 25082241 T^{5} + 405789051 T^{6} - 5819222145 T^{7} + 74966261383 T^{8} - 874663299866 T^{9} + 9301701526878 T^{10} - 90483767786106 T^{11} + 807146180879736 T^{12} - 6605315048385738 T^{13} + 49568767436732862 T^{14} - 340258892923971722 T^{15} + 2128909957623427303 T^{16} - 12063664122156026985 T^{17} + 61409772069632561739 T^{18} - \)\(27\!\cdots\!77\)\( T^{19} + \)\(10\!\cdots\!04\)\( T^{20} - \)\(36\!\cdots\!89\)\( T^{21} + \)\(97\!\cdots\!87\)\( T^{22} - \)\(19\!\cdots\!97\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 12 T + 635 T^{2} - 7394 T^{3} + 194695 T^{4} - 2147414 T^{5} + 38452515 T^{6} - 390830824 T^{7} + 5462001571 T^{8} - 50006017692 T^{9} + 586344593106 T^{10} - 4769156371240 T^{11} + 48581803711146 T^{12} - 348148415100520 T^{13} + 3124630336661874 T^{14} - 19453190984488764 T^{15} + 155111236955636611 T^{16} - 810220278903182632 T^{17} + 5819181606391166835 T^{18} - 23723338243488165158 T^{19} + \)\(15\!\cdots\!95\)\( T^{20} - \)\(43\!\cdots\!22\)\( T^{21} + \)\(27\!\cdots\!15\)\( T^{22} - \)\(37\!\cdots\!24\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))
$79$ (\( 1 - 12 T + 79 T^{2} \))(\( ( 1 - 3 T + 79 T^{2} )^{2} \))(\( 1 + 20 T + 245 T^{2} + 1580 T^{3} + 6241 T^{4} \))(\( 1 + 86 T^{2} + 6241 T^{4} \))(\( 1 + 12 T + 189 T^{2} + 948 T^{3} + 6241 T^{4} \))(\( 1 + 2 T + 139 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 149 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 + 14 T + 226 T^{2} + 2192 T^{3} + 17854 T^{4} + 87374 T^{5} + 493039 T^{6} \))(\( 1 - 2 T + 166 T^{2} - 308 T^{3} + 13114 T^{4} - 12482 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 139 T^{2} - 1552 T^{3} + 15962 T^{4} - 195500 T^{5} + 1260998 T^{6} - 9686032 T^{7} + 68532421 T^{8} - 389500810 T^{9} + 3077056399 T^{10} \))(\( 1 - 8 T + 314 T^{2} - 2854 T^{3} + 52244 T^{4} - 477640 T^{5} + 5822187 T^{6} - 47351668 T^{7} + 459952773 T^{8} - 2980951240 T^{9} + 25758329516 T^{10} - 111163531174 T^{11} + 966195709286 T^{12} - 1944699644168 T^{13} + 19203908986159 T^{14} \))(\( 1 - 22 T + 460 T^{2} - 7210 T^{3} + 96802 T^{4} - 1132698 T^{5} + 11996871 T^{6} - 110259820 T^{7} + 947752809 T^{8} - 7069168218 T^{9} + 47727161278 T^{10} - 280830084010 T^{11} + 1415445943540 T^{12} - 5347924021462 T^{13} + 19203908986159 T^{14} \))(\( 1 - 18 T + 613 T^{2} - 8232 T^{3} + 162407 T^{4} - 1767190 T^{5} + 26081621 T^{6} - 239485944 T^{7} + 2879648274 T^{8} - 22496197200 T^{9} + 227492213646 T^{10} - 1494631776504 T^{11} + 12859256336219 T^{12} - 68832193642390 T^{13} + 499735498592393 T^{14} - 2001095933848872 T^{15} + 11771996208515467 T^{16} - 27307958578318098 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 36 T + 1156 T^{2} + 26026 T^{3} + 521709 T^{4} + 8832620 T^{5} + 135692808 T^{6} + 1863508050 T^{7} + 23540265499 T^{8} + 272195166550 T^{9} + 2918160542324 T^{10} + 28938160763594 T^{11} + 267029484011502 T^{12} + 2286114700323926 T^{13} + 18212239944644084 T^{14} + 134202832720645450 T^{15} + 916895247947555419 T^{16} + 5734119369840511950 T^{17} + 32985219429219592968 T^{18} + \)\(16\!\cdots\!80\)\( T^{19} + \)\(79\!\cdots\!49\)\( T^{20} + \)\(31\!\cdots\!94\)\( T^{21} + \)\(10\!\cdots\!56\)\( T^{22} + \)\(26\!\cdots\!44\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 + 427 T^{2} + 1180 T^{3} + 95292 T^{4} + 474180 T^{5} + 15149935 T^{6} + 94423472 T^{7} + 1950616551 T^{8} + 12357400976 T^{9} + 208925853190 T^{10} + 1214936220104 T^{11} + 18336406212664 T^{12} + 95979961388216 T^{13} + 1303906249758790 T^{14} + 6092680619806064 T^{15} + 75976672661390631 T^{16} + 290546348733397328 T^{17} + 3682759150458541135 T^{18} + 9106109563056874620 T^{19} + \)\(14\!\cdots\!12\)\( T^{20} + \)\(14\!\cdots\!20\)\( T^{21} + \)\(40\!\cdots\!27\)\( T^{22} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 2 T + 478 T^{2} - 662 T^{3} + 116823 T^{4} - 163500 T^{5} + 19383770 T^{6} - 31924712 T^{7} + 2440536275 T^{8} - 4660284782 T^{9} + 248660799624 T^{10} - 498568629982 T^{11} + 21281094687146 T^{12} - 39386921768578 T^{13} + 1551892050453384 T^{14} - 2297702148632498 T^{15} + 95059085594688275 T^{16} - 98234139345832088 T^{17} + 4711951327704294170 T^{18} - 3139839119236996500 T^{19} + \)\(17\!\cdots\!03\)\( T^{20} - 79341756540493327178 T^{21} + \)\(45\!\cdots\!78\)\( T^{22} - \)\(14\!\cdots\!58\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))
$83$ (\( 1 + 7 T + 83 T^{2} \))(\( 1 - 14 T + 135 T^{2} - 1162 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 157 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 + 10 T + 93 T^{2} + 830 T^{3} + 6889 T^{4} \))(\( 1 + 23 T + 287 T^{2} + 1909 T^{3} + 6889 T^{4} \))(\( 1 - 2 T + 87 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 + T + 15 T^{2} + 83 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 231 T^{2} - 1943 T^{3} + 19173 T^{4} - 82668 T^{5} + 571787 T^{6} \))(\( 1 - 19 T + 362 T^{2} - 3368 T^{3} + 30046 T^{4} - 130891 T^{5} + 571787 T^{6} \))(\( 1 + 2 T + 179 T^{2} + 656 T^{3} + 20622 T^{4} + 69980 T^{5} + 1711626 T^{6} + 4519184 T^{7} + 102349873 T^{8} + 94916642 T^{9} + 3939040643 T^{10} \))(\( 1 + 16 T + 238 T^{2} + 1826 T^{3} + 19504 T^{4} + 186096 T^{5} + 2712391 T^{6} + 24177788 T^{7} + 225128453 T^{8} + 1282015344 T^{9} + 11152133648 T^{10} + 86658894146 T^{11} + 937491673034 T^{12} + 5231045973904 T^{13} + 27136050989627 T^{14} \))(\( 1 + T + 344 T^{2} - 140 T^{3} + 59570 T^{4} - 62633 T^{5} + 6942631 T^{6} - 7393352 T^{7} + 576238373 T^{8} - 431478737 T^{9} + 34061351590 T^{10} - 6644164940 T^{11} + 1355029981192 T^{12} + 326940373369 T^{13} + 27136050989627 T^{14} \))(\( 1 - 13 T + 673 T^{2} - 7417 T^{3} + 205967 T^{4} - 1935852 T^{5} + 37738433 T^{6} - 301498679 T^{7} + 4568581146 T^{8} - 30624712542 T^{9} + 379192235118 T^{10} - 2077024399631 T^{11} + 21578345389771 T^{12} - 91872285624492 T^{13} + 811312384116781 T^{14} - 2424916749277873 T^{15} + 18262562316018971 T^{16} - 29279799017807533 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 25 T + 783 T^{2} + 14775 T^{3} + 287637 T^{4} + 4408358 T^{5} + 66832046 T^{6} + 866074036 T^{7} + 10989644649 T^{8} + 123351930903 T^{9} + 1350839330659 T^{10} + 13295933048579 T^{11} + 127458076112610 T^{12} + 1103562443032057 T^{13} + 9305932148909851 T^{14} + 70531030515233661 T^{15} + 521550083428174329 T^{16} + 3411500827651045148 T^{17} + 21850094072254182974 T^{18} + \)\(11\!\cdots\!66\)\( T^{19} + \)\(64\!\cdots\!17\)\( T^{20} + \)\(27\!\cdots\!25\)\( T^{21} + \)\(12\!\cdots\!67\)\( T^{22} + \)\(32\!\cdots\!75\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 16 T + 651 T^{2} - 9008 T^{3} + 209704 T^{4} - 2612920 T^{5} + 44543431 T^{6} - 502710712 T^{7} + 6909206119 T^{8} - 70557447080 T^{9} + 822114410918 T^{10} - 7547188829640 T^{11} + 76761076758592 T^{12} - 626416672860120 T^{13} + 5663546176814102 T^{14} - 40343830993531960 T^{15} + 327899321850666199 T^{16} - 1980197926239467816 T^{17} + 14563045962276289039 T^{18} - 70904330351816180840 T^{19} + \)\(47\!\cdots\!64\)\( T^{20} - \)\(16\!\cdots\!24\)\( T^{21} + \)\(10\!\cdots\!99\)\( T^{22} - \)\(20\!\cdots\!72\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 5 T + 575 T^{2} - 3737 T^{3} + 167083 T^{4} - 1276028 T^{5} + 32443144 T^{6} - 271988078 T^{7} + 4692313117 T^{8} - 40595516297 T^{9} + 533788509385 T^{10} - 4470477865035 T^{11} + 49073769984782 T^{12} - 371049662797905 T^{13} + 3677269041153265 T^{14} - 23211988476912739 T^{15} + 222689302139096557 T^{16} - 1071372093653454154 T^{17} + 10606973612624232136 T^{18} - 34626360872191761556 T^{19} + \)\(37\!\cdots\!03\)\( T^{20} - \)\(69\!\cdots\!11\)\( T^{21} + \)\(89\!\cdots\!75\)\( T^{22} - \)\(64\!\cdots\!35\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))
$89$ (\( 1 - 3 T + 89 T^{2} \))(\( 1 + 2 T + 174 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 + 6 T + 70 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 6 T + 155 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 2 T + 54 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 + 2 T + 54 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 - 6 T + 182 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 173 T^{2} + 74 T^{3} + 15397 T^{4} + 23763 T^{5} + 704969 T^{6} \))(\( 1 - 12 T + 179 T^{2} - 2144 T^{3} + 15931 T^{4} - 95052 T^{5} + 704969 T^{6} \))(\( 1 + 17 T + 485 T^{2} + 5689 T^{3} + 89097 T^{4} + 743149 T^{5} + 7929633 T^{6} + 45062569 T^{7} + 341909965 T^{8} + 1066618097 T^{9} + 5584059449 T^{10} \))(\( 1 - 9 T + 261 T^{2} - 1817 T^{3} + 33900 T^{4} - 261500 T^{5} + 4225720 T^{6} - 30821292 T^{7} + 376089080 T^{8} - 2071341500 T^{9} + 23898449100 T^{10} - 114002651897 T^{11} + 1457439516189 T^{12} - 4472831618649 T^{13} + 44231334895529 T^{14} \))(\( 1 + 3 T + 21 T^{2} + 135 T^{3} + 2712 T^{4} - 6152 T^{5} + 710964 T^{6} + 8512188 T^{7} + 63275796 T^{8} - 48729992 T^{9} + 1911875928 T^{10} + 8470202535 T^{11} + 117265248429 T^{12} + 1490943872883 T^{13} + 44231334895529 T^{14} \))(\( 1 + 21 T + 709 T^{2} + 11529 T^{3} + 229075 T^{4} + 3006419 T^{5} + 44380307 T^{6} + 482662319 T^{7} + 5716348292 T^{8} + 51903552752 T^{9} + 508754997988 T^{10} + 3823168228799 T^{11} + 31286740645483 T^{12} + 188629465444979 T^{13} + 1279168418279675 T^{14} + 5729697303489369 T^{15} + 31360016440930061 T^{16} + 82668364919743701 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 23 T + 825 T^{2} - 15753 T^{3} + 330433 T^{4} - 5305955 T^{5} + 84153798 T^{6} - 1153158478 T^{7} + 15132045743 T^{8} - 179133937149 T^{9} + 2021024761073 T^{10} - 20856731697130 T^{11} + 205426750778462 T^{12} - 1856249121044570 T^{13} + 16008537132459233 T^{14} - 126283872537993381 T^{15} + 949418460830330063 T^{16} - 6439305495270358622 T^{17} + 41822863169311219878 T^{18} - \)\(23\!\cdots\!95\)\( T^{19} + \)\(13\!\cdots\!73\)\( T^{20} - \)\(55\!\cdots\!77\)\( T^{21} + \)\(25\!\cdots\!25\)\( T^{22} - \)\(63\!\cdots\!47\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 12 T + 697 T^{2} + 6680 T^{3} + 227732 T^{4} + 1834756 T^{5} + 48216552 T^{6} + 338563596 T^{7} + 7544000400 T^{8} + 47120413712 T^{9} + 925586563900 T^{10} + 5192252357770 T^{11} + 91437739905100 T^{12} + 462110459841530 T^{13} + 7331571172651900 T^{14} + 33218430934134928 T^{15} + 473327491200896400 T^{16} + 1890559247331218604 T^{17} + 23962724258648186472 T^{18} + 81153707087581205924 T^{19} + \)\(89\!\cdots\!92\)\( T^{20} + \)\(23\!\cdots\!20\)\( T^{21} + \)\(21\!\cdots\!97\)\( T^{22} + \)\(33\!\cdots\!68\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 7 T + 525 T^{2} - 2629 T^{3} + 131137 T^{4} - 350743 T^{5} + 21160946 T^{6} - 7265218 T^{7} + 2583323699 T^{8} + 4194750279 T^{9} + 267349298145 T^{10} + 731344991270 T^{11} + 24912791136118 T^{12} + 65089704223030 T^{13} + 2117673790606545 T^{14} + 2957168909436351 T^{15} + 162083518103669459 T^{16} - 40569409221944882 T^{17} + 10516594261036009106 T^{18} - 15513831095262528047 T^{19} + \)\(51\!\cdots\!97\)\( T^{20} - \)\(92\!\cdots\!61\)\( T^{21} + \)\(16\!\cdots\!25\)\( T^{22} - \)\(19\!\cdots\!23\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))
$97$ (\( 1 - 7 T + 97 T^{2} \))(\( 1 - 3 T - 15 T^{2} - 291 T^{3} + 9409 T^{4} \))(\( 1 + 9 T + 133 T^{2} + 873 T^{3} + 9409 T^{4} \))(\( 1 - 2 T + 187 T^{2} - 194 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 158 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 21 T + 293 T^{2} + 2037 T^{3} + 9409 T^{4} \))(\( 1 - 2 T + 70 T^{2} - 194 T^{3} + 9409 T^{4} \))(\( 1 + 27 T + 441 T^{2} + 4930 T^{3} + 42777 T^{4} + 254043 T^{5} + 912673 T^{6} \))(\( 1 - 12 T + 75 T^{2} + 48 T^{3} + 7275 T^{4} - 112908 T^{5} + 912673 T^{6} \))(\( 1 + 27 T + 521 T^{2} + 8059 T^{3} + 104425 T^{4} + 1093259 T^{5} + 10129225 T^{6} + 75827131 T^{7} + 475502633 T^{8} + 2390290587 T^{9} + 8587340257 T^{10} \))(\( 1 + 8 T + 417 T^{2} + 3412 T^{3} + 94457 T^{4} + 671935 T^{5} + 13479577 T^{6} + 82425871 T^{7} + 1307518969 T^{8} + 6322236415 T^{9} + 86208353561 T^{10} + 302061906772 T^{11} + 3580920887169 T^{12} + 6663776039432 T^{13} + 80798284478113 T^{14} \))(\( 1 - 11 T + 517 T^{2} - 5591 T^{3} + 125912 T^{4} - 1249988 T^{5} + 18637548 T^{6} - 157305852 T^{7} + 1807842156 T^{8} - 11761137092 T^{9} + 114916482776 T^{10} - 494967210071 T^{11} + 4439654912869 T^{12} - 9162692054219 T^{13} + 80798284478113 T^{14} \))(\( 1 - 2 T + 615 T^{2} - 1236 T^{3} + 171368 T^{4} - 352849 T^{5} + 29435302 T^{6} - 61397603 T^{7} + 3635999768 T^{8} - 7173227220 T^{9} + 352691977496 T^{10} - 577690046627 T^{11} + 26864805382246 T^{12} - 31237468271569 T^{13} + 1471595325161576 T^{14} - 1029553398092244 T^{15} + 49690944954039495 T^{16} - 15674867188753922 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 2 T + 599 T^{2} + 1134 T^{3} + 186500 T^{4} + 298077 T^{5} + 39910011 T^{6} + 53566567 T^{7} + 6513962669 T^{8} + 7655493132 T^{9} + 851815353522 T^{10} + 900196244348 T^{11} + 91127580291916 T^{12} + 87319035701756 T^{13} + 8014730661288498 T^{14} + 6986961883261836 T^{15} + 576676431547410989 T^{16} + 459994337228387719 T^{17} + 33243921879408444219 T^{18} + 24084110242382488701 T^{19} + \)\(14\!\cdots\!00\)\( T^{20} + \)\(86\!\cdots\!78\)\( T^{21} + \)\(44\!\cdots\!51\)\( T^{22} + \)\(14\!\cdots\!06\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 73 T + 3010 T^{2} - 87102 T^{3} + 1967135 T^{4} - 36575228 T^{5} + 582031485 T^{6} - 8144116778 T^{7} + 102571284139 T^{8} - 1186076744056 T^{9} + 12844235600713 T^{10} - 132620387939348 T^{11} + 1324602883633461 T^{12} - 12864177630116756 T^{13} + 120851412767108617 T^{14} - 1082500220227821688 T^{15} + 9080562036072374059 T^{16} - 69936301865428531946 T^{17} + \)\(48\!\cdots\!65\)\( T^{18} - \)\(29\!\cdots\!64\)\( T^{19} + \)\(15\!\cdots\!35\)\( T^{20} - \)\(66\!\cdots\!34\)\( T^{21} + \)\(22\!\cdots\!90\)\( T^{22} - \)\(52\!\cdots\!69\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 + 14 T + 471 T^{2} + 4178 T^{3} + 85936 T^{4} + 546301 T^{5} + 9377607 T^{6} + 39835307 T^{7} + 587492441 T^{8} - 333339196 T^{9} + 5928057546 T^{10} - 362031342048 T^{11} - 1474830902652 T^{12} - 35117040178656 T^{13} + 55777093450314 T^{14} - 304229684030908 T^{15} + 52010283394664921 T^{16} + 342079335451053899 T^{17} + 7811284104226224903 T^{18} + 44140183608677610013 T^{19} + \)\(67\!\cdots\!96\)\( T^{20} + \)\(31\!\cdots\!26\)\( T^{21} + \)\(34\!\cdots\!79\)\( T^{22} + \)\(10\!\cdots\!42\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))
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