Properties

Label 4016.2
Level 4016
Weight 2
Dimension 282371
Nonzero newspaces 16
Sturm bound 2016000

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Defining parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(2016000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4016))\).

Total New Old
Modular forms 507500 284611 222889
Cusp forms 500501 282371 218130
Eisenstein series 6999 2240 4759

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4016))\)

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
4016.2.a \(\chi_{4016}(1, \cdot)\) 4016.2.a.a 2 1
4016.2.a.b 2
4016.2.a.c 4
4016.2.a.d 5
4016.2.a.e 5
4016.2.a.f 6
4016.2.a.g 7
4016.2.a.h 9
4016.2.a.i 12
4016.2.a.j 14
4016.2.a.k 17
4016.2.a.l 19
4016.2.a.m 23
4016.2.b \(\chi_{4016}(2009, \cdot)\) None 0 1
4016.2.e \(\chi_{4016}(4015, \cdot)\) n/a 126 1
4016.2.f \(\chi_{4016}(2007, \cdot)\) None 0 1
4016.2.j \(\chi_{4016}(1005, \cdot)\) n/a 1000 2
4016.2.k \(\chi_{4016}(1003, \cdot)\) n/a 1004 2
4016.2.m \(\chi_{4016}(113, \cdot)\) n/a 500 4
4016.2.o \(\chi_{4016}(231, \cdot)\) None 0 4
4016.2.r \(\chi_{4016}(2121, \cdot)\) None 0 4
4016.2.s \(\chi_{4016}(2239, \cdot)\) n/a 504 4
4016.2.v \(\chi_{4016}(283, \cdot)\) n/a 4016 8
4016.2.w \(\chi_{4016}(149, \cdot)\) n/a 4016 8
4016.2.y \(\chi_{4016}(241, \cdot)\) n/a 2500 20
4016.2.z \(\chi_{4016}(47, \cdot)\) n/a 2520 20
4016.2.bc \(\chi_{4016}(151, \cdot)\) None 0 20
4016.2.bd \(\chi_{4016}(25, \cdot)\) None 0 20
4016.2.bg \(\chi_{4016}(5, \cdot)\) n/a 20080 40
4016.2.bh \(\chi_{4016}(171, \cdot)\) n/a 20080 40
4016.2.bk \(\chi_{4016}(17, \cdot)\) n/a 12500 100
4016.2.bm \(\chi_{4016}(95, \cdot)\) n/a 12600 100
4016.2.bo \(\chi_{4016}(55, \cdot)\) None 0 100
4016.2.bq \(\chi_{4016}(9, \cdot)\) None 0 100
4016.2.bu \(\chi_{4016}(13, \cdot)\) n/a 100400 200
4016.2.bv \(\chi_{4016}(11, \cdot)\) n/a 100400 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2008))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))
$3$ (\( ( 1 + T + 3 T^{2} )^{2} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( 1 - 2 T + 10 T^{2} - 15 T^{3} + 43 T^{4} - 45 T^{5} + 90 T^{6} - 54 T^{7} + 81 T^{8} \))(\( 1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4} + 32 T^{5} + 75 T^{6} + 90 T^{7} + 162 T^{8} + 162 T^{9} + 243 T^{10} \))(\( 1 - T + 8 T^{2} - 8 T^{3} + 33 T^{4} - 29 T^{5} + 99 T^{6} - 72 T^{7} + 216 T^{8} - 81 T^{9} + 243 T^{10} \))(\( 1 + T + 2 T^{2} + 6 T^{3} + 17 T^{4} + 17 T^{5} + 32 T^{6} + 51 T^{7} + 153 T^{8} + 162 T^{9} + 162 T^{10} + 243 T^{11} + 729 T^{12} \))(\( 1 - 3 T + 15 T^{2} - 36 T^{3} + 107 T^{4} - 206 T^{5} + 468 T^{6} - 751 T^{7} + 1404 T^{8} - 1854 T^{9} + 2889 T^{10} - 2916 T^{11} + 3645 T^{12} - 2187 T^{13} + 2187 T^{14} \))(\( 1 - T + 16 T^{2} - 17 T^{3} + 133 T^{4} - 137 T^{5} + 736 T^{6} - 701 T^{7} + 2947 T^{8} - 2495 T^{9} + 8841 T^{10} - 6309 T^{11} + 19872 T^{12} - 11097 T^{13} + 32319 T^{14} - 12393 T^{15} + 34992 T^{16} - 6561 T^{17} + 19683 T^{18} \))(\( 1 + 3 T + 19 T^{2} + 50 T^{3} + 190 T^{4} + 439 T^{5} + 1282 T^{6} + 2662 T^{7} + 6558 T^{8} + 12352 T^{9} + 26745 T^{10} + 45782 T^{11} + 88754 T^{12} + 137346 T^{13} + 240705 T^{14} + 333504 T^{15} + 531198 T^{16} + 646866 T^{17} + 934578 T^{18} + 960093 T^{19} + 1246590 T^{20} + 984150 T^{21} + 1121931 T^{22} + 531441 T^{23} + 531441 T^{24} \))(\( 1 + 3 T + 15 T^{2} + 38 T^{3} + 121 T^{4} + 246 T^{5} + 588 T^{6} + 943 T^{7} + 1704 T^{8} + 1662 T^{9} + 1559 T^{10} - 3178 T^{11} - 10199 T^{12} - 30997 T^{13} - 51382 T^{14} - 92991 T^{15} - 91791 T^{16} - 85806 T^{17} + 126279 T^{18} + 403866 T^{19} + 1242216 T^{20} + 2062341 T^{21} + 3857868 T^{22} + 4842018 T^{23} + 7144929 T^{24} + 6731586 T^{25} + 7971615 T^{26} + 4782969 T^{27} + 4782969 T^{28} \))(\( 1 + 13 T^{2} - 5 T^{3} + 96 T^{4} - 68 T^{5} + 546 T^{6} - 428 T^{7} + 2687 T^{8} - 1862 T^{9} + 11307 T^{10} - 6854 T^{11} + 41095 T^{12} - 22552 T^{13} + 136637 T^{14} - 64016 T^{15} + 433839 T^{16} - 180530 T^{17} + 1301517 T^{18} - 576144 T^{19} + 3689199 T^{20} - 1826712 T^{21} + 9986085 T^{22} - 4996566 T^{23} + 24728409 T^{24} - 12216582 T^{25} + 52888221 T^{26} - 25272972 T^{27} + 96722262 T^{28} - 36137988 T^{29} + 153055008 T^{30} - 23914845 T^{31} + 186535791 T^{32} + 129140163 T^{34} \))(\( 1 - 6 T + 36 T^{2} - 145 T^{3} + 558 T^{4} - 1779 T^{5} + 5435 T^{6} - 14769 T^{7} + 38715 T^{8} - 93356 T^{9} + 218592 T^{10} - 480072 T^{11} + 1029981 T^{12} - 2099020 T^{13} + 4201067 T^{14} - 8055658 T^{15} + 15234935 T^{16} - 27758354 T^{17} + 50020029 T^{18} - 87076358 T^{19} + 150060087 T^{20} - 249825186 T^{21} + 411343245 T^{22} - 652508298 T^{23} + 1020859281 T^{24} - 1530185580 T^{25} + 2252568447 T^{26} - 3149752392 T^{27} + 4302546336 T^{28} - 5512578444 T^{29} + 6858246105 T^{30} - 7848852129 T^{31} + 8665145505 T^{32} - 8508901851 T^{33} + 8006690106 T^{34} - 6241774545 T^{35} + 4649045868 T^{36} - 2324522934 T^{37} + 1162261467 T^{38} \))
$5$ (\( 1 - 5 T + 13 T^{2} - 25 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 11 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 18 T^{2} + 43 T^{3} + 131 T^{4} + 215 T^{5} + 450 T^{6} + 375 T^{7} + 625 T^{8} \))(\( 1 - 7 T + 34 T^{2} - 116 T^{3} + 333 T^{4} - 786 T^{5} + 1665 T^{6} - 2900 T^{7} + 4250 T^{8} - 4375 T^{9} + 3125 T^{10} \))(\( 1 + 6 T + 31 T^{2} + 102 T^{3} + 315 T^{4} + 727 T^{5} + 1575 T^{6} + 2550 T^{7} + 3875 T^{8} + 3750 T^{9} + 3125 T^{10} \))(\( 1 + T + 16 T^{2} + 22 T^{3} + 139 T^{4} + 169 T^{5} + 848 T^{6} + 845 T^{7} + 3475 T^{8} + 2750 T^{9} + 10000 T^{10} + 3125 T^{11} + 15625 T^{12} \))(\( 1 + 2 T + 24 T^{2} + 35 T^{3} + 276 T^{4} + 331 T^{5} + 2035 T^{6} + 2033 T^{7} + 10175 T^{8} + 8275 T^{9} + 34500 T^{10} + 21875 T^{11} + 75000 T^{12} + 31250 T^{13} + 78125 T^{14} \))(\( 1 + 5 T + 41 T^{2} + 156 T^{3} + 744 T^{4} + 2286 T^{5} + 8057 T^{6} + 20562 T^{7} + 58100 T^{8} + 124071 T^{9} + 290500 T^{10} + 514050 T^{11} + 1007125 T^{12} + 1428750 T^{13} + 2325000 T^{14} + 2437500 T^{15} + 3203125 T^{16} + 1953125 T^{17} + 1953125 T^{18} \))(\( 1 - 5 T + 44 T^{2} - 177 T^{3} + 928 T^{4} - 3155 T^{5} + 12519 T^{6} - 36865 T^{7} + 120738 T^{8} - 312421 T^{9} + 879601 T^{10} - 2013517 T^{11} + 4972218 T^{12} - 10067585 T^{13} + 21990025 T^{14} - 39052625 T^{15} + 75461250 T^{16} - 115203125 T^{17} + 195609375 T^{18} - 246484375 T^{19} + 362500000 T^{20} - 345703125 T^{21} + 429687500 T^{22} - 244140625 T^{23} + 244140625 T^{24} \))(\( 1 + 2 T + 24 T^{2} + 59 T^{3} + 320 T^{4} + 863 T^{5} + 3339 T^{6} + 8624 T^{7} + 28921 T^{8} + 68243 T^{9} + 207217 T^{10} + 458259 T^{11} + 1263673 T^{12} + 2658519 T^{13} + 6736137 T^{14} + 13292595 T^{15} + 31591825 T^{16} + 57282375 T^{17} + 129510625 T^{18} + 213259375 T^{19} + 451890625 T^{20} + 673750000 T^{21} + 1304296875 T^{22} + 1685546875 T^{23} + 3125000000 T^{24} + 2880859375 T^{25} + 5859375000 T^{26} + 2441406250 T^{27} + 6103515625 T^{28} \))(\( 1 - 3 T + 31 T^{2} - 72 T^{3} + 468 T^{4} - 881 T^{5} + 4768 T^{6} - 7539 T^{7} + 39098 T^{8} - 55783 T^{9} + 286603 T^{10} - 389484 T^{11} + 1915432 T^{12} - 2487938 T^{13} + 11481759 T^{14} - 14067935 T^{15} + 62122047 T^{16} - 72647307 T^{17} + 310610235 T^{18} - 351698375 T^{19} + 1435219875 T^{20} - 1554961250 T^{21} + 5985725000 T^{22} - 6085687500 T^{23} + 22390859375 T^{24} - 21790234375 T^{25} + 76363281250 T^{26} - 73623046875 T^{27} + 232812500000 T^{28} - 215087890625 T^{29} + 571289062500 T^{30} - 439453125000 T^{31} + 946044921875 T^{32} - 457763671875 T^{33} + 762939453125 T^{34} \))(\( 1 + 8 T + 67 T^{2} + 371 T^{3} + 1985 T^{4} + 8797 T^{5} + 37460 T^{6} + 142256 T^{7} + 520564 T^{8} + 1756157 T^{9} + 5727835 T^{10} + 17528753 T^{11} + 52007592 T^{12} + 146275818 T^{13} + 399719294 T^{14} + 1041799772 T^{15} + 2641852395 T^{16} + 6412031906 T^{17} + 15154195631 T^{18} + 34334767805 T^{19} + 75770978155 T^{20} + 160300797650 T^{21} + 330231549375 T^{22} + 651124857500 T^{23} + 1249122793750 T^{24} + 2285559656250 T^{25} + 4063093125000 T^{26} + 6847169140625 T^{27} + 11187177734375 T^{28} + 17149970703125 T^{29} + 25418164062500 T^{30} + 34730468750000 T^{31} + 45727539062500 T^{32} + 53692626953125 T^{33} + 60577392578125 T^{34} + 56610107421875 T^{35} + 51116943359375 T^{36} + 30517578125000 T^{37} + 19073486328125 T^{38} \))
$7$ (\( ( 1 - T + 7 T^{2} )^{2} \))(\( 1 - 4 T + 13 T^{2} - 28 T^{3} + 49 T^{4} \))(\( 1 - 3 T + 23 T^{2} - 44 T^{3} + 213 T^{4} - 308 T^{5} + 1127 T^{6} - 1029 T^{7} + 2401 T^{8} \))(\( 1 + T + 16 T^{2} + 171 T^{4} + 39 T^{5} + 1197 T^{6} + 5488 T^{8} + 2401 T^{9} + 16807 T^{10} \))(\( 1 - T + 16 T^{2} - 10 T^{3} + 169 T^{4} - 115 T^{5} + 1183 T^{6} - 490 T^{7} + 5488 T^{8} - 2401 T^{9} + 16807 T^{10} \))(\( 1 + 6 T + 35 T^{2} + 120 T^{3} + 393 T^{4} + 978 T^{5} + 2747 T^{6} + 6846 T^{7} + 19257 T^{8} + 41160 T^{9} + 84035 T^{10} + 100842 T^{11} + 117649 T^{12} \))(\( 1 - 6 T + 49 T^{2} - 217 T^{3} + 1012 T^{4} - 3486 T^{5} + 11665 T^{6} - 31629 T^{7} + 81655 T^{8} - 170814 T^{9} + 347116 T^{10} - 521017 T^{11} + 823543 T^{12} - 705894 T^{13} + 823543 T^{14} \))(\( 1 + 42 T^{2} + 17 T^{3} + 846 T^{4} + 549 T^{5} + 11048 T^{6} + 7998 T^{7} + 103972 T^{8} + 69809 T^{9} + 727804 T^{10} + 391902 T^{11} + 3789464 T^{12} + 1318149 T^{13} + 14218722 T^{14} + 2000033 T^{15} + 34588806 T^{16} + 40353607 T^{18} \))(\( 1 + 5 T + 61 T^{2} + 234 T^{3} + 1656 T^{4} + 5163 T^{5} + 27663 T^{6} + 72782 T^{7} + 329230 T^{8} + 754003 T^{9} + 3052708 T^{10} + 6266814 T^{11} + 23313049 T^{12} + 43867698 T^{13} + 149582692 T^{14} + 258623029 T^{15} + 790481230 T^{16} + 1223247074 T^{17} + 3254524287 T^{18} + 4251952509 T^{19} + 9546510456 T^{20} + 9442744038 T^{21} + 17230990189 T^{22} + 9886633715 T^{23} + 13841287201 T^{24} \))(\( 1 + 8 T + 63 T^{2} + 299 T^{3} + 1414 T^{4} + 4980 T^{5} + 18363 T^{6} + 54402 T^{7} + 178145 T^{8} + 485063 T^{9} + 1521945 T^{10} + 4020493 T^{11} + 12333269 T^{12} + 31560379 T^{13} + 91881835 T^{14} + 220922653 T^{15} + 604330181 T^{16} + 1379029099 T^{17} + 3654189945 T^{18} + 8152453841 T^{19} + 20958581105 T^{20} + 44802386286 T^{21} + 105859040763 T^{22} + 200960962860 T^{23} + 399420002086 T^{24} + 591220696157 T^{25} + 872001093663 T^{26} + 775112083256 T^{27} + 678223072849 T^{28} \))(\( 1 + 3 T + 48 T^{2} + 133 T^{3} + 1239 T^{4} + 3325 T^{5} + 22870 T^{6} + 58943 T^{7} + 332802 T^{8} + 822312 T^{9} + 4028418 T^{10} + 9517541 T^{11} + 41695740 T^{12} + 93949998 T^{13} + 375908581 T^{14} + 804043343 T^{15} + 2979678299 T^{16} + 6011005895 T^{17} + 20857748093 T^{18} + 39398123807 T^{19} + 128936643283 T^{20} + 225573945198 T^{21} + 700780302180 T^{22} + 1119729181109 T^{23} + 3317575444974 T^{24} + 4740465039912 T^{25} + 13429761116814 T^{26} + 16649938601807 T^{27} + 45221462612410 T^{28} + 46022279943325 T^{29} + 120045483894273 T^{30} + 90203668688917 T^{31} + 227882952477264 T^{32} + 99698791708803 T^{33} + 232630513987207 T^{34} \))(\( 1 - 11 T + 109 T^{2} - 732 T^{3} + 4442 T^{4} - 22659 T^{5} + 107125 T^{6} - 460953 T^{7} + 1877593 T^{8} - 7214174 T^{9} + 26543670 T^{10} - 93368788 T^{11} + 316152330 T^{12} - 1029009505 T^{13} + 3237845191 T^{14} - 9836649898 T^{15} + 28990410624 T^{16} - 82733622904 T^{17} + 229265535989 T^{18} - 615627991785 T^{19} + 1604858751923 T^{20} - 4053947522296 T^{21} + 9943710844032 T^{22} - 23617796405098 T^{23} + 54418464125137 T^{24} - 121061939253745 T^{25} + 260365038305190 T^{26} - 538252482431188 T^{27} + 1071132827517690 T^{28} - 2037825596979326 T^{29} + 3712614851369599 T^{30} - 6380182859162553 T^{31} + 10379235239849875 T^{32} - 15367856607685491 T^{33} + 21088668227166806 T^{34} - 24326505176947932 T^{35} + 25356726024605563 T^{36} - 17912549577014939 T^{37} + 11398895185373143 T^{38} \))
$11$ (\( ( 1 + 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( 1 - 3 T + 44 T^{2} - 95 T^{3} + 725 T^{4} - 1045 T^{5} + 5324 T^{6} - 3993 T^{7} + 14641 T^{8} \))(\( 1 + 7 T + 68 T^{2} + 308 T^{3} + 1629 T^{4} + 5083 T^{5} + 17919 T^{6} + 37268 T^{7} + 90508 T^{8} + 102487 T^{9} + 161051 T^{10} \))(\( 1 - 4 T + 26 T^{2} - 100 T^{3} + 413 T^{4} - 1168 T^{5} + 4543 T^{6} - 12100 T^{7} + 34606 T^{8} - 58564 T^{9} + 161051 T^{10} \))(\( 1 + T + 36 T^{2} + 32 T^{3} + 775 T^{4} + 563 T^{5} + 10168 T^{6} + 6193 T^{7} + 93775 T^{8} + 42592 T^{9} + 527076 T^{10} + 161051 T^{11} + 1771561 T^{12} \))(\( 1 - 5 T + 57 T^{2} - 246 T^{3} + 1548 T^{4} - 5621 T^{5} + 25904 T^{6} - 77368 T^{7} + 284944 T^{8} - 680141 T^{9} + 2060388 T^{10} - 3601686 T^{11} + 9179907 T^{12} - 8857805 T^{13} + 19487171 T^{14} \))(\( 1 - 3 T + 68 T^{2} - 217 T^{3} + 2336 T^{4} - 7128 T^{5} + 51619 T^{6} - 142123 T^{7} + 793562 T^{8} - 1890298 T^{9} + 8729182 T^{10} - 17196883 T^{11} + 68704889 T^{12} - 104361048 T^{13} + 376215136 T^{14} - 384428737 T^{15} + 1325127628 T^{16} - 643076643 T^{17} + 2357947691 T^{18} \))(\( 1 + 10 T + 140 T^{2} + 1003 T^{3} + 8199 T^{4} + 46419 T^{5} + 282004 T^{6} + 1327774 T^{7} + 6549093 T^{8} + 26384889 T^{9} + 110215160 T^{10} + 385435349 T^{11} + 1392015790 T^{12} + 4239788839 T^{13} + 13336034360 T^{14} + 35118287259 T^{15} + 95885270613 T^{16} + 213839330474 T^{17} + 499587288244 T^{18} + 904574990649 T^{19} + 1757528465319 T^{20} + 2365021534073 T^{21} + 3631239444140 T^{22} + 2853116706110 T^{23} + 3138428376721 T^{24} \))(\( 1 + 9 T + 100 T^{2} + 687 T^{3} + 4884 T^{4} + 27546 T^{5} + 155686 T^{6} + 756862 T^{7} + 3649790 T^{8} + 15719595 T^{9} + 66852900 T^{10} + 258836085 T^{11} + 987952117 T^{12} + 3464423852 T^{13} + 11971213668 T^{14} + 38108662372 T^{15} + 119542206157 T^{16} + 344510829135 T^{17} + 978793308900 T^{18} + 2531656494345 T^{19} + 6465825622190 T^{20} + 14749099217402 T^{21} + 33372676747366 T^{22} + 64952027096286 T^{23} + 126678381751284 T^{24} + 196009117709757 T^{25} + 313842837672100 T^{26} + 310704409295379 T^{27} + 379749833583241 T^{28} \))(\( 1 - T + 65 T^{2} - 24 T^{3} + 2303 T^{4} - 274 T^{5} + 58221 T^{6} - 2576 T^{7} + 1134784 T^{8} - 81072 T^{9} + 18003396 T^{10} - 3578304 T^{11} + 242692505 T^{12} - 92338862 T^{13} + 2903678795 T^{14} - 1617752920 T^{15} + 32648883056 T^{16} - 20772298142 T^{17} + 359137713616 T^{18} - 195748103320 T^{19} + 3864796476145 T^{20} - 1351933278542 T^{21} + 39085870622755 T^{22} - 6339183812544 T^{23} + 350835256432716 T^{24} - 17378503200432 T^{25} + 2675761312583744 T^{26} - 66814805772176 T^{27} + 16611130774643031 T^{28} - 859929375221554 T^{29} + 79505806067473093 T^{30} - 9113996005997784 T^{31} + 271521131012017315 T^{32} - 45949729863572161 T^{33} + 505447028499293771 T^{34} \))(\( 1 - 15 T + 192 T^{2} - 1627 T^{3} + 12407 T^{4} - 75861 T^{5} + 433675 T^{6} - 2134218 T^{7} + 10162346 T^{8} - 43391414 T^{9} + 185017749 T^{10} - 725505016 T^{11} + 2904468233 T^{12} - 10806579018 T^{13} + 41415218350 T^{14} - 147613875702 T^{15} + 542566795026 T^{16} - 1851888759780 T^{17} + 6517163917931 T^{18} - 21286385181914 T^{19} + 71688803097241 T^{20} - 224078539933380 T^{21} + 722156404179606 T^{22} - 2161214754152982 T^{23} + 6669962330485850 T^{24} - 19144513931707098 T^{25} + 56599869120538843 T^{26} - 155518443389647096 T^{27} + 436262174048567559 T^{28} - 1125461528955775814 T^{29} + 2899435914587013406 T^{30} - 6698090333308739178 T^{31} + 14971637189019276425 T^{32} - 28808202125458245501 T^{33} + 51827118037939981957 T^{34} - 74760210488031905947 T^{35} + 97045829471864404032 T^{36} - 83398759702383472215 T^{37} + 61159090448414546291 T^{38} \))
$13$ (\( 1 + 13 T^{2} + 169 T^{4} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( 1 + 12 T + 100 T^{2} + 545 T^{3} + 2303 T^{4} + 7085 T^{5} + 16900 T^{6} + 26364 T^{7} + 28561 T^{8} \))(\( 1 - 4 T + 42 T^{2} - 70 T^{3} + 593 T^{4} - 396 T^{5} + 7709 T^{6} - 11830 T^{7} + 92274 T^{8} - 114244 T^{9} + 371293 T^{10} \))(\( 1 + 7 T + 58 T^{2} + 264 T^{3} + 1411 T^{4} + 4871 T^{5} + 18343 T^{6} + 44616 T^{7} + 127426 T^{8} + 199927 T^{9} + 371293 T^{10} \))(\( 1 + 5 T + 54 T^{2} + 184 T^{3} + 1209 T^{4} + 3311 T^{5} + 17968 T^{6} + 43043 T^{7} + 204321 T^{8} + 404248 T^{9} + 1542294 T^{10} + 1856465 T^{11} + 4826809 T^{12} \))(\( 1 + T + 49 T^{2} + 10 T^{3} + 1145 T^{4} - 534 T^{5} + 18318 T^{6} - 12855 T^{7} + 238134 T^{8} - 90246 T^{9} + 2515565 T^{10} + 285610 T^{11} + 18193357 T^{12} + 4826809 T^{13} + 62748517 T^{14} \))(\( 1 + 3 T + 90 T^{2} + 229 T^{3} + 3771 T^{4} + 8049 T^{5} + 97678 T^{6} + 175667 T^{7} + 1750123 T^{8} + 2681615 T^{9} + 22751599 T^{10} + 29687723 T^{11} + 214598566 T^{12} + 229887489 T^{13} + 1400145903 T^{14} + 1105339261 T^{15} + 5647366530 T^{16} + 2447192163 T^{17} + 10604499373 T^{18} \))(\( 1 - 3 T + 99 T^{2} - 290 T^{3} + 4978 T^{4} - 13727 T^{5} + 165710 T^{6} - 422960 T^{7} + 4031144 T^{8} - 9416452 T^{9} + 75184897 T^{10} - 158659844 T^{11} + 1099925382 T^{12} - 2062577972 T^{13} + 12706247593 T^{14} - 20687945044 T^{15} + 115133503784 T^{16} - 157042087280 T^{17} + 799850519390 T^{18} - 861348892859 T^{19} + 4060707529138 T^{20} - 3075304818170 T^{21} + 13647990693051 T^{22} - 5376481182111 T^{23} + 23298085122481 T^{24} \))(\( 1 + T + 77 T^{2} + 118 T^{3} + 3157 T^{4} + 5386 T^{5} + 92690 T^{6} + 150851 T^{7} + 2123696 T^{8} + 3170308 T^{9} + 39751641 T^{10} + 54234088 T^{11} + 633863833 T^{12} + 790255061 T^{13} + 8807951688 T^{14} + 10273315793 T^{15} + 107122987777 T^{16} + 119152291336 T^{17} + 1135346618601 T^{18} + 1177113168244 T^{19} + 10250674966064 T^{20} + 9465676537967 T^{21} + 75610080529490 T^{22} + 57115833622978 T^{23} + 435219258767293 T^{24} + 211474926496366 T^{25} + 1793952554431037 T^{26} + 302875106592253 T^{27} + 3937376385699289 T^{28} \))(\( 1 - 22 T + 327 T^{2} - 3591 T^{3} + 32474 T^{4} - 248232 T^{5} + 1651854 T^{6} - 9644200 T^{7} + 49752027 T^{8} - 225212378 T^{9} + 879770185 T^{10} - 2810241288 T^{11} + 6139198039 T^{12} + 1399315966 T^{13} - 109121956145 T^{14} + 759635042868 T^{15} - 3699336995499 T^{16} + 14613844354636 T^{17} - 48091380941487 T^{18} + 128378322244692 T^{19} - 239740937650565 T^{20} + 39965863304926 T^{21} + 2279441257494427 T^{22} - 13564497941089992 T^{23} + 55204274409565645 T^{24} - 183712655484064538 T^{25} + 527595339126979071 T^{26} - 1329534867090125800 T^{27} + 2960387315531594598 T^{28} - 5783330266123703592 T^{29} + 9835566211476823922 T^{30} - 14139118601046146799 T^{31} + 16737787015607677539 T^{32} - 14639165402029956502 T^{33} + 8650415919381337933 T^{34} \))(\( 1 + 8 T + 106 T^{2} + 763 T^{3} + 6300 T^{4} + 39943 T^{5} + 263231 T^{6} + 1490525 T^{7} + 8505999 T^{8} + 43740266 T^{9} + 224155422 T^{10} + 1060968944 T^{11} + 4978995067 T^{12} + 21896457394 T^{13} + 95250018635 T^{14} + 391600830392 T^{15} + 1590987926605 T^{16} + 6138779751362 T^{17} + 23398142032971 T^{18} + 84884689058628 T^{19} + 304175846428623 T^{20} + 1037453777980178 T^{21} + 3495400474751185 T^{22} + 11184511316825912 T^{23} + 35365665169045055 T^{24} + 105690017617475746 T^{25} + 312424556604565639 T^{26} + 865464961647728624 T^{27} + 2377056032053550406 T^{28} + 6029967103834091834 T^{29} + 15244114519518327963 T^{30} + 34726378327185992525 T^{31} + 79726117183385349443 T^{32} + \)\(15\!\cdots\!27\)\( T^{33} + \)\(32\!\cdots\!00\)\( T^{34} + \)\(50\!\cdots\!83\)\( T^{35} + \)\(91\!\cdots\!98\)\( T^{36} + \)\(89\!\cdots\!32\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))
$17$ (\( 1 + 3 T + 7 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - T + 3 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 - T + 44 T^{2} - 17 T^{3} + 949 T^{4} - 289 T^{5} + 12716 T^{6} - 4913 T^{7} + 83521 T^{8} \))(\( 1 - 6 T + 61 T^{2} - 250 T^{3} + 1707 T^{4} - 5563 T^{5} + 29019 T^{6} - 72250 T^{7} + 299693 T^{8} - 501126 T^{9} + 1419857 T^{10} \))(\( 1 + 8 T + 63 T^{2} + 302 T^{3} + 1267 T^{4} + 5331 T^{5} + 21539 T^{6} + 87278 T^{7} + 309519 T^{8} + 668168 T^{9} + 1419857 T^{10} \))(\( 1 - 8 T + 93 T^{2} - 556 T^{3} + 3569 T^{4} - 16744 T^{5} + 77417 T^{6} - 284648 T^{7} + 1031441 T^{8} - 2731628 T^{9} + 7767453 T^{10} - 11358856 T^{11} + 24137569 T^{12} \))(\( 1 + 8 T + 112 T^{2} + 599 T^{3} + 4772 T^{4} + 19059 T^{5} + 115579 T^{6} + 380413 T^{7} + 1964843 T^{8} + 5508051 T^{9} + 23444836 T^{10} + 50029079 T^{11} + 159023984 T^{12} + 193100552 T^{13} + 410338673 T^{14} \))(\( 1 + 11 T + 159 T^{2} + 1158 T^{3} + 9870 T^{4} + 55444 T^{5} + 356037 T^{6} + 1649486 T^{7} + 8633360 T^{8} + 33582711 T^{9} + 146767120 T^{10} + 476701454 T^{11} + 1749209781 T^{12} + 4630738324 T^{13} + 14013988590 T^{14} + 27951304902 T^{15} + 65243849007 T^{16} + 76733331851 T^{17} + 118587876497 T^{18} \))(\( 1 - 2 T + 141 T^{2} - 211 T^{3} + 9189 T^{4} - 8557 T^{5} + 369346 T^{6} - 123771 T^{7} + 10436566 T^{8} + 2186136 T^{9} + 228044014 T^{10} + 123426362 T^{11} + 4167530739 T^{12} + 2098248154 T^{13} + 65904720046 T^{14} + 10740486168 T^{15} + 871672428886 T^{16} - 175737120747 T^{17} + 8915114559874 T^{18} - 3511268024861 T^{19} + 64100235125349 T^{20} - 25022041940867 T^{21} + 284255139963309 T^{22} - 68543792615266 T^{23} + 582622237229761 T^{24} \))(\( 1 + 104 T^{2} + 19 T^{3} + 5532 T^{4} + 2047 T^{5} + 205715 T^{6} + 93642 T^{7} + 6080575 T^{8} + 2798407 T^{9} + 150481407 T^{10} + 68169151 T^{11} + 3176734263 T^{12} + 1420430387 T^{13} + 57926949651 T^{14} + 24147316579 T^{15} + 918076202007 T^{16} + 334915038863 T^{17} + 12568357594047 T^{18} + 3973337767799 T^{19} + 146770298622175 T^{20} + 38424934017066 T^{21} + 1435017941975315 T^{22} + 242749383189359 T^{23} + 11152478257283868 T^{24} + 651166029845027 T^{25} + 60592712671895144 T^{26} + 168377826559400929 T^{28} \))(\( 1 + T + 133 T^{2} + 268 T^{3} + 9244 T^{4} + 27575 T^{5} + 444762 T^{6} + 1692375 T^{7} + 16736710 T^{8} + 72663473 T^{9} + 524899057 T^{10} + 2371518904 T^{11} + 14112267644 T^{12} + 61982655932 T^{13} + 327056280789 T^{14} + 1344039683401 T^{15} + 6505937728089 T^{16} + 24716676967305 T^{17} + 110600941377513 T^{18} + 388427468502889 T^{19} + 1606827507516357 T^{20} + 5176853406096572 T^{21} + 20037402000206908 T^{22} + 57242701180104376 T^{23} + 215386382508331361 T^{24} + 506882762468652593 T^{25} + 1984770898446104870 T^{26} + 3411817677272376375 T^{27} + 15242837145575468346 T^{28} + 16065808191610659575 T^{29} + 91557919336182481628 T^{30} + 45125257517919448972 T^{31} + \)\(38\!\cdots\!69\)\( T^{32} + 48661191875666868481 T^{33} + \)\(82\!\cdots\!77\)\( T^{34} \))(\( 1 + 4 T + 119 T^{2} + 481 T^{3} + 7975 T^{4} + 29831 T^{5} + 372628 T^{6} + 1260042 T^{7} + 13325290 T^{8} + 39739617 T^{9} + 384020857 T^{10} + 983714371 T^{11} + 9249982788 T^{12} + 19726608316 T^{13} + 192764183682 T^{14} + 333485338032 T^{15} + 3612009494007 T^{16} + 5140404188550 T^{17} + 63485845906563 T^{18} + 82326436300519 T^{19} + 1079259380411571 T^{20} + 1485576810490950 T^{21} + 17745802644056391 T^{22} + 27853028917770672 T^{23} + 273697575550173474 T^{24} + 476152369363423804 T^{25} + 3795625662500760324 T^{26} + 6862152843321884611 T^{27} + 45540217962188097929 T^{28} + 80114825478179388033 T^{29} + \)\(45\!\cdots\!70\)\( T^{30} + \)\(73\!\cdots\!62\)\( T^{31} + \)\(36\!\cdots\!36\)\( T^{32} + \)\(50\!\cdots\!99\)\( T^{33} + \)\(22\!\cdots\!75\)\( T^{34} + \)\(23\!\cdots\!61\)\( T^{35} + \)\(98\!\cdots\!63\)\( T^{36} + \)\(56\!\cdots\!36\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))
$19$ (\( 1 + T + 9 T^{2} + 19 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 13 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 - 9 T + 73 T^{2} - 424 T^{3} + 2153 T^{4} - 8056 T^{5} + 26353 T^{6} - 61731 T^{7} + 130321 T^{8} \))(\( 1 - 10 T + 117 T^{2} - 724 T^{3} + 4703 T^{4} - 20163 T^{5} + 89357 T^{6} - 261364 T^{7} + 802503 T^{8} - 1303210 T^{9} + 2476099 T^{10} \))(\( 1 + 3 T + 82 T^{2} + 230 T^{3} + 2885 T^{4} + 6566 T^{5} + 54815 T^{6} + 83030 T^{7} + 562438 T^{8} + 390963 T^{9} + 2476099 T^{10} \))(\( 1 + 3 T + 68 T^{2} + 156 T^{3} + 1985 T^{4} + 3861 T^{5} + 40284 T^{6} + 73359 T^{7} + 716585 T^{8} + 1070004 T^{9} + 8861828 T^{10} + 7428297 T^{11} + 47045881 T^{12} \))(\( 1 - 15 T + 198 T^{2} - 1705 T^{3} + 13153 T^{4} - 79977 T^{5} + 441300 T^{6} - 2015782 T^{7} + 8384700 T^{8} - 28871697 T^{9} + 90216427 T^{10} - 222197305 T^{11} + 490267602 T^{12} - 705688215 T^{13} + 893871739 T^{14} \))(\( 1 + 4 T + 108 T^{2} + 299 T^{3} + 4778 T^{4} + 8024 T^{5} + 118817 T^{6} + 80541 T^{7} + 2161610 T^{8} + 326408 T^{9} + 41070590 T^{10} + 29075301 T^{11} + 814965803 T^{12} + 1045695704 T^{13} + 11830801022 T^{14} + 14066718419 T^{15} + 96538147812 T^{16} + 67934252164 T^{17} + 322687697779 T^{18} \))(\( 1 + 15 T + 275 T^{2} + 2854 T^{3} + 31018 T^{4} + 249838 T^{5} + 2022975 T^{6} + 13349013 T^{7} + 87267683 T^{8} + 485194285 T^{9} + 2656933750 T^{10} + 12617725635 T^{11} + 58890558116 T^{12} + 239736787065 T^{13} + 959153083750 T^{14} + 3327947600815 T^{15} + 11372811716243 T^{16} + 33053477740287 T^{17} + 95172641115975 T^{18} + 223323127528282 T^{19} + 526796158405738 T^{20} + 920950689461266 T^{21} + 1686043220895275 T^{22} + 1747353883473285 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 27 T + 441 T^{2} + 5254 T^{3} + 50682 T^{4} + 414675 T^{5} + 2979448 T^{6} + 19196965 T^{7} + 113021852 T^{8} + 616541144 T^{9} + 3160784719 T^{10} + 15400093521 T^{11} + 72100535921 T^{12} + 326801388214 T^{13} + 1442586078560 T^{14} + 6209226376066 T^{15} + 26028293467481 T^{16} + 105629241460539 T^{17} + 411916625364799 T^{18} + 1526616910117256 T^{19} + 5317212599591612 T^{20} + 17159624488072135 T^{21} + 50601642935381368 T^{22} + 133810521076506825 T^{23} + 310734700077870282 T^{24} + 612039820251242626 T^{25} + 976071879308177001 T^{26} + 1135430553480940593 T^{27} + 799006685782884121 T^{28} \))(\( 1 + 13 T + 222 T^{2} + 2221 T^{3} + 23502 T^{4} + 194998 T^{5} + 1613988 T^{6} + 11594639 T^{7} + 81389501 T^{8} + 519469448 T^{9} + 3214276817 T^{10} + 18520540701 T^{11} + 103165666144 T^{12} + 542091355850 T^{13} + 2751364836018 T^{14} + 13263883720023 T^{15} + 61753665721869 T^{16} + 273906962104534 T^{17} + 1173319648715511 T^{18} + 4788262022928303 T^{19} + 18871611410247462 T^{20} + 70645887585727850 T^{21} + 255448402773492256 T^{22} + 871315153874902581 T^{23} + 2873151208039174763 T^{24} + 8822442117981471368 T^{25} + 26263390701071618279 T^{26} + 71087499944283528839 T^{27} + \)\(18\!\cdots\!72\)\( T^{28} + \)\(43\!\cdots\!78\)\( T^{29} + \)\(98\!\cdots\!18\)\( T^{30} + \)\(17\!\cdots\!41\)\( T^{31} + \)\(33\!\cdots\!78\)\( T^{32} + \)\(37\!\cdots\!53\)\( T^{33} + \)\(54\!\cdots\!39\)\( T^{34} \))(\( 1 - 14 T + 206 T^{2} - 1879 T^{3} + 17921 T^{4} - 134424 T^{5} + 1045199 T^{6} - 6915642 T^{7} + 46981466 T^{8} - 282680334 T^{9} + 1736481625 T^{10} - 9660479784 T^{11} + 54620257741 T^{12} - 283603129994 T^{13} + 1492781661606 T^{14} - 7279463908550 T^{15} + 35920477421638 T^{16} - 165054278935634 T^{17} + 766732643665887 T^{18} - 3324580428588802 T^{19} + 14567920229651853 T^{20} - 59584594695763874 T^{21} + 246378554635015042 T^{22} - 948667016026144550 T^{23} + 3696275179520954994 T^{24} - 13342359104925254714 T^{25} + 48823504771575881599 T^{26} - \)\(16\!\cdots\!44\)\( T^{27} + \)\(56\!\cdots\!75\)\( T^{28} - \)\(17\!\cdots\!34\)\( T^{29} + \)\(54\!\cdots\!54\)\( T^{30} - \)\(15\!\cdots\!62\)\( T^{31} + \)\(43\!\cdots\!41\)\( T^{32} - \)\(10\!\cdots\!04\)\( T^{33} + \)\(27\!\cdots\!79\)\( T^{34} - \)\(54\!\cdots\!99\)\( T^{35} + \)\(11\!\cdots\!34\)\( T^{36} - \)\(14\!\cdots\!74\)\( T^{37} + \)\(19\!\cdots\!79\)\( T^{38} \))
$23$ (\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( 1 - 12 T + 77 T^{2} - 276 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 79 T^{2} + 242 T^{3} + 2587 T^{4} + 5566 T^{5} + 41791 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 + 13 T + 112 T^{2} + 726 T^{3} + 4663 T^{4} + 24345 T^{5} + 107249 T^{6} + 384054 T^{7} + 1362704 T^{8} + 3637933 T^{9} + 6436343 T^{10} \))(\( 1 - 17 T + 194 T^{2} - 1498 T^{3} + 9545 T^{4} - 48923 T^{5} + 219535 T^{6} - 792442 T^{7} + 2360398 T^{8} - 4757297 T^{9} + 6436343 T^{10} \))(\( 1 + 18 T + 233 T^{2} + 2096 T^{3} + 15827 T^{4} + 96048 T^{5} + 506401 T^{6} + 2209104 T^{7} + 8372483 T^{8} + 25502032 T^{9} + 65202953 T^{10} + 115854174 T^{11} + 148035889 T^{12} \))(\( 1 - 5 T + 114 T^{2} - 562 T^{3} + 6547 T^{4} - 28211 T^{5} + 231026 T^{6} - 828297 T^{7} + 5313598 T^{8} - 14923619 T^{9} + 79657349 T^{10} - 157270642 T^{11} + 733743102 T^{12} - 740179445 T^{13} + 3404825447 T^{14} \))(\( 1 - 9 T + 171 T^{2} - 1185 T^{3} + 12954 T^{4} - 74062 T^{5} + 600031 T^{6} - 2917424 T^{7} + 19157887 T^{8} - 79632349 T^{9} + 440631401 T^{10} - 1543317296 T^{11} + 7300577177 T^{12} - 20725584142 T^{13} + 83376387222 T^{14} - 175422528465 T^{15} + 582225151437 T^{16} - 704798867529 T^{17} + 1801152661463 T^{18} \))(\( 1 + 20 T + 365 T^{2} + 4416 T^{3} + 48516 T^{4} + 432668 T^{5} + 3561459 T^{6} + 25491272 T^{7} + 170978142 T^{8} + 1030965126 T^{9} + 5896418020 T^{10} + 30856094338 T^{11} + 154253916053 T^{12} + 709690169774 T^{13} + 3119205132580 T^{14} + 12543752688042 T^{15} + 47846694235422 T^{16} + 164070570098296 T^{17} + 527223749202051 T^{18} + 1473159016502596 T^{19} + 3799335761892996 T^{20} + 7953890153020608 T^{21} + 15120676592981885 T^{22} + 19056195158278540 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 13 T + 190 T^{2} + 1518 T^{3} + 13387 T^{4} + 77351 T^{5} + 513478 T^{6} + 2186676 T^{7} + 11981481 T^{8} + 31447409 T^{9} + 146114163 T^{10} - 206892093 T^{11} - 842453049 T^{12} - 23183395277 T^{13} - 66332617343 T^{14} - 533218091371 T^{15} - 445657662921 T^{16} - 2517256095531 T^{17} + 40888733488083 T^{18} + 202406310785287 T^{19} + 1773689191371609 T^{20} + 7445250089144172 T^{21} + 40210968100117318 T^{22} + 139320959516824513 T^{23} + 554576705617119163 T^{24} + 1446365212513341186 T^{25} + 4163778642083860990 T^{26} + 6552472705174075979 T^{27} + 11592836324538749809 T^{28} \))(\( 1 - 2 T + 246 T^{2} - 472 T^{3} + 30161 T^{4} - 55676 T^{5} + 2449686 T^{6} - 4351793 T^{7} + 147602921 T^{8} - 251800336 T^{9} + 7000359821 T^{10} - 11414484673 T^{11} + 270592769479 T^{12} - 418659247364 T^{13} + 8708044461887 T^{14} - 12658121552351 T^{15} + 236228585975581 T^{16} - 318600146073527 T^{17} + 5433257477438363 T^{18} - 6696146301193679 T^{19} + 105950776967779129 T^{20} - 117158022441589124 T^{21} + 1741627877686775297 T^{22} - 1689753386044429297 T^{23} + 23835003256697164987 T^{24} - 19718732406246854416 T^{25} + \)\(26\!\cdots\!23\)\( T^{26} - \)\(18\!\cdots\!57\)\( T^{27} + \)\(23\!\cdots\!22\)\( T^{28} - \)\(12\!\cdots\!96\)\( T^{29} + \)\(15\!\cdots\!63\)\( T^{30} - \)\(54\!\cdots\!48\)\( T^{31} + \)\(65\!\cdots\!22\)\( T^{32} - \)\(12\!\cdots\!22\)\( T^{33} + \)\(14\!\cdots\!03\)\( T^{34} \))(\( 1 - 28 T + 535 T^{2} - 7358 T^{3} + 84514 T^{4} - 827640 T^{5} + 7294333 T^{6} - 58577261 T^{7} + 440234474 T^{8} - 3114093241 T^{9} + 21000654858 T^{10} - 135166271702 T^{11} + 835529342779 T^{12} - 4960909458413 T^{13} + 28418883546195 T^{14} - 157128667306480 T^{15} + 841331391800273 T^{16} - 4360714597728562 T^{17} + 21921404979061595 T^{18} - 106745007165852307 T^{19} + 504192314518416685 T^{20} - 2306818022198409298 T^{21} + 10236479044033921591 T^{22} - 43971043387712669680 T^{23} + \)\(18\!\cdots\!85\)\( T^{24} - \)\(73\!\cdots\!57\)\( T^{25} + \)\(28\!\cdots\!13\)\( T^{26} - \)\(10\!\cdots\!62\)\( T^{27} + \)\(37\!\cdots\!54\)\( T^{28} - \)\(12\!\cdots\!09\)\( T^{29} + \)\(41\!\cdots\!98\)\( T^{30} - \)\(12\!\cdots\!81\)\( T^{31} + \)\(36\!\cdots\!39\)\( T^{32} - \)\(95\!\cdots\!60\)\( T^{33} + \)\(22\!\cdots\!98\)\( T^{34} - \)\(45\!\cdots\!38\)\( T^{35} + \)\(75\!\cdots\!05\)\( T^{36} - \)\(90\!\cdots\!32\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))
$29$ (\( 1 + 7 T + 67 T^{2} + 203 T^{3} + 841 T^{4} \))(\( 1 - 5 T + 33 T^{2} - 145 T^{3} + 841 T^{4} \))(\( 1 + 12 T + 115 T^{2} + 822 T^{3} + 5299 T^{4} + 23838 T^{5} + 96715 T^{6} + 292668 T^{7} + 707281 T^{8} \))(\( 1 - 4 T + 121 T^{2} - 396 T^{3} + 6485 T^{4} - 16363 T^{5} + 188065 T^{6} - 333036 T^{7} + 2951069 T^{8} - 2829124 T^{9} + 20511149 T^{10} \))(\( 1 + 15 T + 214 T^{2} + 1788 T^{3} + 14073 T^{4} + 77938 T^{5} + 408117 T^{6} + 1503708 T^{7} + 5219246 T^{8} + 10609215 T^{9} + 20511149 T^{10} \))(\( 1 - T + 28 T^{2} + 16 T^{3} + 687 T^{4} + 1345 T^{5} + 5872 T^{6} + 39005 T^{7} + 577767 T^{8} + 390224 T^{9} + 19803868 T^{10} - 20511149 T^{11} + 594823321 T^{12} \))(\( 1 + 132 T^{2} + 90 T^{3} + 8557 T^{4} + 8078 T^{5} + 357562 T^{6} + 322880 T^{7} + 10369298 T^{8} + 6793598 T^{9} + 208696673 T^{10} + 63655290 T^{11} + 2707471668 T^{12} + 17249876309 T^{14} \))(\( 1 + 9 T + 193 T^{2} + 1425 T^{3} + 16900 T^{4} + 108679 T^{5} + 931247 T^{6} + 5328603 T^{7} + 36527203 T^{8} + 183039488 T^{9} + 1059288887 T^{10} + 4481355123 T^{11} + 22712183083 T^{12} + 76866591799 T^{13} + 346638418100 T^{14} + 847623232425 T^{15} + 3329226127637 T^{16} + 4502217716649 T^{17} + 14507145975869 T^{18} \))(\( 1 - 6 T + 263 T^{2} - 1464 T^{3} + 32996 T^{4} - 170821 T^{5} + 2623910 T^{6} - 12596328 T^{7} + 148094014 T^{8} - 653381511 T^{9} + 6282380187 T^{10} - 25073897238 T^{11} + 206197153794 T^{12} - 727143019902 T^{13} + 5283481737267 T^{14} - 15935321671779 T^{15} + 104744082315934 T^{16} - 258365160460872 T^{17} + 1560762860205110 T^{18} - 2946641120979689 T^{19} + 16506130642061156 T^{20} - 21238461708672216 T^{21} + 110646002357952863 T^{22} - 73203058594234974 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 157 T^{2} + 192 T^{3} + 13404 T^{4} + 26074 T^{5} + 840016 T^{6} + 1985546 T^{7} + 42186822 T^{8} + 108389824 T^{9} + 1784428139 T^{10} + 4581335888 T^{11} + 64702247509 T^{12} + 158910539972 T^{13} + 2018754156720 T^{14} + 4608405659188 T^{15} + 54414590155069 T^{16} + 111734200972432 T^{17} + 1262092118580059 T^{18} + 2223199830147776 T^{19} + 25093705564475862 T^{20} + 34250422905829714 T^{21} + 420214990829847376 T^{22} + 378259324174808306 T^{23} + 5639159755155894204 T^{24} + 2342497875015519168 T^{25} + 55548920963258639437 T^{26} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( 1 - 28 T + 602 T^{2} - 9400 T^{3} + 126452 T^{4} - 1451348 T^{5} + 15001278 T^{6} - 139469184 T^{7} + 1195787437 T^{8} - 9465739752 T^{9} + 70192831599 T^{10} - 488740210864 T^{11} + 3228475083182 T^{12} - 20297814483564 T^{13} + 122476315938600 T^{14} - 711585033189976 T^{15} + 4005438718327285 T^{16} - 21871939305117688 T^{17} + 116157722831491265 T^{18} - 598443012912769816 T^{19} + 2987074869426515400 T^{20} - 14356258525749629484 T^{21} + 66219733473933396118 T^{22} - \)\(29\!\cdots\!44\)\( T^{23} + \)\(12\!\cdots\!91\)\( T^{24} - \)\(47\!\cdots\!72\)\( T^{25} + \)\(17\!\cdots\!53\)\( T^{26} - \)\(58\!\cdots\!84\)\( T^{27} + \)\(18\!\cdots\!62\)\( T^{28} - \)\(51\!\cdots\!68\)\( T^{29} + \)\(12\!\cdots\!28\)\( T^{30} - \)\(27\!\cdots\!00\)\( T^{31} + \)\(51\!\cdots\!98\)\( T^{32} - \)\(70\!\cdots\!88\)\( T^{33} + \)\(72\!\cdots\!09\)\( T^{34} \))(\( 1 + 13 T + 295 T^{2} + 3267 T^{3} + 44891 T^{4} + 436062 T^{5} + 4652184 T^{6} + 40412222 T^{7} + 365733059 T^{8} + 2884445183 T^{9} + 23096365298 T^{10} + 167195266176 T^{11} + 1212188888586 T^{12} + 8116702694453 T^{13} + 54024292981305 T^{14} + 336315872241346 T^{15} + 2072563944350431 T^{16} + 12031569672800089 T^{17} + 68999130215806366 T^{18} + 373960687475776762 T^{19} + 2000974776258384614 T^{20} + 10118550094824874849 T^{21} + 50547762038762661659 T^{22} + \)\(23\!\cdots\!26\)\( T^{23} + \)\(11\!\cdots\!45\)\( T^{24} + \)\(48\!\cdots\!13\)\( T^{25} + \)\(20\!\cdots\!74\)\( T^{26} + \)\(83\!\cdots\!36\)\( T^{27} + \)\(33\!\cdots\!62\)\( T^{28} + \)\(12\!\cdots\!83\)\( T^{29} + \)\(44\!\cdots\!11\)\( T^{30} + \)\(14\!\cdots\!02\)\( T^{31} + \)\(47\!\cdots\!76\)\( T^{32} + \)\(12\!\cdots\!22\)\( T^{33} + \)\(38\!\cdots\!59\)\( T^{34} + \)\(81\!\cdots\!07\)\( T^{35} + \)\(21\!\cdots\!55\)\( T^{36} + \)\(27\!\cdots\!93\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))
$31$ (\( 1 + 10 T^{2} + 961 T^{4} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( 1 - 2 T + 74 T^{2} - 135 T^{3} + 2655 T^{4} - 4185 T^{5} + 71114 T^{6} - 59582 T^{7} + 923521 T^{8} \))(\( 1 - 13 T + 171 T^{2} - 1223 T^{3} + 9378 T^{4} - 48892 T^{5} + 290718 T^{6} - 1175303 T^{7} + 5094261 T^{8} - 12005773 T^{9} + 28629151 T^{10} \))(\( 1 - T + 75 T^{2} - 139 T^{3} + 3758 T^{4} - 4900 T^{5} + 116498 T^{6} - 133579 T^{7} + 2234325 T^{8} - 923521 T^{9} + 28629151 T^{10} \))(\( 1 + 6 T + 119 T^{2} + 684 T^{3} + 7365 T^{4} + 37394 T^{5} + 281235 T^{6} + 1159214 T^{7} + 7077765 T^{8} + 20377044 T^{9} + 109898999 T^{10} + 171774906 T^{11} + 887503681 T^{12} \))(\( 1 - 21 T + 323 T^{2} - 3712 T^{3} + 34723 T^{4} - 275114 T^{5} + 1883364 T^{6} - 11173393 T^{7} + 58384284 T^{8} - 264384554 T^{9} + 1034432893 T^{10} - 3428109952 T^{11} + 9247215773 T^{12} - 18637577301 T^{13} + 27512614111 T^{14} \))(\( 1 + 3 T + 181 T^{2} + 710 T^{3} + 16192 T^{4} + 69857 T^{5} + 950879 T^{6} + 3994573 T^{7} + 40050775 T^{8} + 150151518 T^{9} + 1241574025 T^{10} + 3838784653 T^{11} + 28327636289 T^{12} + 64514406497 T^{13} + 463563212992 T^{14} + 630127613510 T^{15} + 4979783154091 T^{16} + 2558673112323 T^{17} + 26439622160671 T^{18} \))(\( 1 + 14 T + 307 T^{2} + 3043 T^{3} + 39363 T^{4} + 309078 T^{5} + 3054515 T^{6} + 20375941 T^{7} + 170212169 T^{8} + 1004678182 T^{9} + 7390624625 T^{10} + 39099308202 T^{11} + 256163422028 T^{12} + 1212078554262 T^{13} + 7102390264625 T^{14} + 29930367719962 T^{15} + 157194512527049 T^{16} + 583345891656091 T^{17} + 2710893306169715 T^{18} + 8503543744199658 T^{19} + 33572349906790083 T^{20} + 80455770234921853 T^{21} + 251625884103105907 T^{22} + 355718676549667634 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 25 T + 503 T^{2} + 6946 T^{3} + 83553 T^{4} + 823630 T^{5} + 7364616 T^{6} + 57517098 T^{7} + 419903137 T^{8} + 2780464125 T^{9} + 17714198221 T^{10} + 105465364251 T^{11} + 621052204731 T^{12} + 3495835300725 T^{13} + 19820760784583 T^{14} + 108370894322475 T^{15} + 596831168746491 T^{16} + 3141918666401541 T^{17} + 16359434055256141 T^{18} + 79602327284707875 T^{19} + 372665579750947297 T^{20} + 1582445722058569878 T^{21} + 6281214980594587656 T^{22} + 21776466000193455730 T^{23} + 68482402262106865953 T^{24} + \)\(17\!\cdots\!26\)\( T^{25} + \)\(39\!\cdots\!83\)\( T^{26} + \)\(61\!\cdots\!75\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 + 12 T + 361 T^{2} + 3663 T^{3} + 63568 T^{4} + 562300 T^{5} + 7276538 T^{6} + 57288091 T^{7} + 608911263 T^{8} + 4327577685 T^{9} + 39671337740 T^{10} + 257001286154 T^{11} + 2090299529775 T^{12} + 12421276415178 T^{13} + 91217472684149 T^{14} + 498870365298137 T^{15} + 3343830717932873 T^{16} + 16838912161949331 T^{17} + 103658752255919063 T^{18} + 479414421051509657 T^{19} + 2717459728733482859 T^{20} + 11471309616221601738 T^{21} + 59843500873157471025 T^{22} + \)\(22\!\cdots\!74\)\( T^{23} + \)\(10\!\cdots\!40\)\( T^{24} + \)\(36\!\cdots\!85\)\( T^{25} + \)\(16\!\cdots\!73\)\( T^{26} + \)\(46\!\cdots\!91\)\( T^{27} + \)\(18\!\cdots\!78\)\( T^{28} + \)\(44\!\cdots\!00\)\( T^{29} + \)\(15\!\cdots\!88\)\( T^{30} + \)\(27\!\cdots\!23\)\( T^{31} + \)\(84\!\cdots\!11\)\( T^{32} + \)\(87\!\cdots\!72\)\( T^{33} + \)\(22\!\cdots\!11\)\( T^{34} \))(\( 1 - 20 T + 405 T^{2} - 5217 T^{3} + 64309 T^{4} - 641682 T^{5} + 6169939 T^{6} - 52651118 T^{7} + 438950289 T^{8} - 3390764709 T^{9} + 25735638484 T^{10} - 184053040687 T^{11} + 1292873394434 T^{12} - 8622846223629 T^{13} + 56548586622041 T^{14} - 354512050135865 T^{15} + 2189967710275750 T^{16} - 12987345695517131 T^{17} + 75873648382152230 T^{18} - 425816559058164984 T^{19} + 2352083099846719130 T^{20} - 12480839213391962891 T^{21} + 65241328056824868250 T^{22} - \)\(32\!\cdots\!65\)\( T^{23} + \)\(16\!\cdots\!91\)\( T^{24} - \)\(76\!\cdots\!49\)\( T^{25} + \)\(35\!\cdots\!74\)\( T^{26} - \)\(15\!\cdots\!67\)\( T^{27} + \)\(68\!\cdots\!64\)\( T^{28} - \)\(27\!\cdots\!09\)\( T^{29} + \)\(11\!\cdots\!59\)\( T^{30} - \)\(41\!\cdots\!98\)\( T^{31} + \)\(15\!\cdots\!49\)\( T^{32} - \)\(48\!\cdots\!22\)\( T^{33} + \)\(15\!\cdots\!59\)\( T^{34} - \)\(37\!\cdots\!77\)\( T^{35} + \)\(91\!\cdots\!55\)\( T^{36} - \)\(13\!\cdots\!20\)\( T^{37} + \)\(21\!\cdots\!71\)\( T^{38} \))
$37$ (\( 1 + 3 T + 73 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( 1 - T + 63 T^{2} - 37 T^{3} + 1369 T^{4} \))(\( 1 + 13 T + 176 T^{2} + 1251 T^{3} + 9627 T^{4} + 46287 T^{5} + 240944 T^{6} + 658489 T^{7} + 1874161 T^{8} \))(\( 1 - 16 T + 163 T^{2} - 1254 T^{3} + 9303 T^{4} - 59013 T^{5} + 344211 T^{6} - 1716726 T^{7} + 8256439 T^{8} - 29986576 T^{9} + 69343957 T^{10} \))(\( 1 + 5 T + 54 T^{2} - 70 T^{3} - 1555 T^{4} - 17902 T^{5} - 57535 T^{6} - 95830 T^{7} + 2735262 T^{8} + 9370805 T^{9} + 69343957 T^{10} \))(\( 1 + 13 T + 250 T^{2} + 2314 T^{3} + 24501 T^{4} + 167949 T^{5} + 1229888 T^{6} + 6214113 T^{7} + 33541869 T^{8} + 117211042 T^{9} + 468540250 T^{10} + 901471441 T^{11} + 2565726409 T^{12} \))(\( 1 + T + 107 T^{2} - 80 T^{3} + 5714 T^{4} - 14045 T^{5} + 214630 T^{6} - 801168 T^{7} + 7941310 T^{8} - 19227605 T^{9} + 289431242 T^{10} - 149932880 T^{11} + 7419803399 T^{12} + 2565726409 T^{13} + 94931877133 T^{14} \))(\( 1 + 10 T + 293 T^{2} + 2525 T^{3} + 39913 T^{4} + 292183 T^{5} + 3273928 T^{6} + 20233887 T^{7} + 177240541 T^{8} + 915619550 T^{9} + 6557900017 T^{10} + 27700191303 T^{11} + 165834274984 T^{12} + 547597983463 T^{13} + 2767725355741 T^{14} + 6478459182725 T^{15} + 27815039999969 T^{16} + 35124794539210 T^{17} + 129961739795077 T^{18} \))(\( 1 - 5 T + 312 T^{2} - 1415 T^{3} + 48022 T^{4} - 198367 T^{5} + 4789573 T^{6} - 17999713 T^{7} + 343463566 T^{8} - 1167787725 T^{9} + 18608835879 T^{10} - 56684284147 T^{11} + 780021299974 T^{12} - 2097318513439 T^{13} + 25475496318351 T^{14} - 59151951634425 T^{15} + 643706020318126 T^{16} - 1248171324284341 T^{17} + 12288733933933357 T^{18} - 18831351671241811 T^{19} + 168676288336194262 T^{20} - 183895861810033955 T^{21} + 1500278324194368888 T^{22} - 889588108897302065 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + T + 206 T^{2} + 417 T^{3} + 22954 T^{4} + 67484 T^{5} + 1814134 T^{6} + 6641756 T^{7} + 115182508 T^{8} + 460182755 T^{9} + 6224084362 T^{10} + 24574724091 T^{11} + 290341422433 T^{12} + 1073562144200 T^{13} + 11624734096484 T^{14} + 39721799335400 T^{15} + 397477407310777 T^{16} + 1244783499381423 T^{17} + 11664936171970282 T^{18} + 31910893174861535 T^{19} + 295526802630453772 T^{20} + 630514364539365548 T^{21} + 6372108401659519414 T^{22} + 8770338048330976268 T^{23} + \)\(11\!\cdots\!46\)\( T^{24} + 74191648282034992221 T^{25} + \)\(13\!\cdots\!86\)\( T^{26} + \)\(24\!\cdots\!97\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 - 27 T + 629 T^{2} - 10426 T^{3} + 153823 T^{4} - 1935194 T^{5} + 22315383 T^{6} - 232647766 T^{7} + 2267662294 T^{8} - 20538267480 T^{9} + 176186972446 T^{10} - 1425612728754 T^{11} + 11014966015165 T^{12} - 80957098803430 T^{13} + 570820778990653 T^{14} - 3845674010664990 T^{15} + 24911778549511730 T^{16} - 154483347658623386 T^{17} + 921735806331934010 T^{18} - 5264727720600371310 T^{19} + 28913784918213546409 T^{20} - \)\(15\!\cdots\!30\)\( T^{21} + \)\(76\!\cdots\!05\)\( T^{22} - \)\(36\!\cdots\!86\)\( T^{23} + \)\(16\!\cdots\!18\)\( T^{24} - \)\(72\!\cdots\!80\)\( T^{25} + \)\(29\!\cdots\!38\)\( T^{26} - \)\(11\!\cdots\!34\)\( T^{27} + \)\(39\!\cdots\!79\)\( T^{28} - \)\(12\!\cdots\!14\)\( T^{29} + \)\(37\!\cdots\!31\)\( T^{30} - \)\(93\!\cdots\!14\)\( T^{31} + \)\(20\!\cdots\!97\)\( T^{32} - \)\(33\!\cdots\!07\)\( T^{33} + \)\(45\!\cdots\!17\)\( T^{34} \))(\( 1 + 16 T + 433 T^{2} + 5297 T^{3} + 86384 T^{4} + 878473 T^{5} + 11066225 T^{6} + 98333130 T^{7} + 1050286754 T^{8} + 8410002971 T^{9} + 79754186703 T^{10} + 586434675088 T^{11} + 5064387035573 T^{12} + 34590874009057 T^{13} + 276110515965634 T^{14} + 1764116091799734 T^{15} + 13132979193833710 T^{16} + 78793501349803963 T^{17} + 549876488783014335 T^{18} + 3102198011165143550 T^{19} + 20345430084971530395 T^{20} + \)\(10\!\cdots\!47\)\( T^{21} + \)\(66\!\cdots\!30\)\( T^{22} + \)\(33\!\cdots\!74\)\( T^{23} + \)\(19\!\cdots\!38\)\( T^{24} + \)\(88\!\cdots\!13\)\( T^{25} + \)\(48\!\cdots\!09\)\( T^{26} + \)\(20\!\cdots\!48\)\( T^{27} + \)\(10\!\cdots\!31\)\( T^{28} + \)\(40\!\cdots\!79\)\( T^{29} + \)\(18\!\cdots\!02\)\( T^{30} + \)\(64\!\cdots\!30\)\( T^{31} + \)\(26\!\cdots\!25\)\( T^{32} + \)\(79\!\cdots\!97\)\( T^{33} + \)\(28\!\cdots\!12\)\( T^{34} + \)\(65\!\cdots\!77\)\( T^{35} + \)\(19\!\cdots\!61\)\( T^{36} + \)\(27\!\cdots\!64\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))
$41$ (\( 1 + 9 T + 73 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 + T + 21 T^{2} + 41 T^{3} + 1681 T^{4} \))(\( 1 - T + 129 T^{2} + 4 T^{3} + 7095 T^{4} + 164 T^{5} + 216849 T^{6} - 68921 T^{7} + 2825761 T^{8} \))(\( 1 - 6 T + 123 T^{2} - 768 T^{3} + 8837 T^{4} - 40071 T^{5} + 362317 T^{6} - 1291008 T^{7} + 8477283 T^{8} - 16954566 T^{9} + 115856201 T^{10} \))(\( 1 + 12 T + 161 T^{2} + 1212 T^{3} + 11153 T^{4} + 67159 T^{5} + 457273 T^{6} + 2037372 T^{7} + 11096281 T^{8} + 33909132 T^{9} + 115856201 T^{10} \))(\( 1 - 4 T + 149 T^{2} - 476 T^{3} + 9989 T^{4} - 26584 T^{5} + 453769 T^{6} - 1089944 T^{7} + 16791509 T^{8} - 32806396 T^{9} + 421038389 T^{10} - 463424804 T^{11} + 4750104241 T^{12} \))(\( 1 + 10 T + 183 T^{2} + 1925 T^{3} + 18522 T^{4} + 156974 T^{5} + 1223611 T^{6} + 7778621 T^{7} + 50168051 T^{8} + 263873294 T^{9} + 1276554762 T^{10} + 5439589925 T^{11} + 21201684783 T^{12} + 47501042410 T^{13} + 194754273881 T^{14} \))(\( 1 + 23 T + 518 T^{2} + 7507 T^{3} + 100089 T^{4} + 1066086 T^{5} + 10400915 T^{6} + 86647669 T^{7} + 662535855 T^{8} + 4425715811 T^{9} + 27163970055 T^{10} + 145654731589 T^{11} + 716841462715 T^{12} + 3012504241446 T^{13} + 11595931301889 T^{14} + 35659032537187 T^{15} + 100882713870358 T^{16} + 183653280269783 T^{17} + 327381934393961 T^{18} \))(\( 1 + 258 T^{2} + 473 T^{3} + 33090 T^{4} + 98836 T^{5} + 2993547 T^{6} + 9926755 T^{7} + 211013443 T^{8} + 685203796 T^{9} + 11761926780 T^{10} + 36494399132 T^{11} + 530959735377 T^{12} + 1496270364412 T^{13} + 19771798917180 T^{14} + 47224930824116 T^{15} + 596273557705123 T^{16} + 1150076122557755 T^{17} + 14219660300332827 T^{18} + 19248733413302516 T^{19} + 264221175831613890 T^{20} + 154851654968343553 T^{21} + 3463046102019319458 T^{22} + 22563490300366186081 T^{24} \))(\( 1 - 10 T + 271 T^{2} - 2287 T^{3} + 35114 T^{4} - 272478 T^{5} + 3121403 T^{6} - 22996332 T^{7} + 218558009 T^{8} - 1529053321 T^{9} + 12761407637 T^{10} - 84350370261 T^{11} + 639294414953 T^{12} - 3977962213993 T^{13} + 27952401522009 T^{14} - 163096450773713 T^{15} + 1074653911535993 T^{16} - 5813511868758381 T^{17} + 36060688005736757 T^{18} - 177150308897493521 T^{19} + 1038173325455416169 T^{20} - 4478633940586404492 T^{21} + 24924169564953976763 T^{22} - 89204374719797705358 T^{23} + \)\(47\!\cdots\!14\)\( T^{24} - \)\(12\!\cdots\!67\)\( T^{25} + \)\(61\!\cdots\!51\)\( T^{26} - \)\(92\!\cdots\!10\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 + T + 370 T^{2} - 141 T^{3} + 66419 T^{4} - 126865 T^{5} + 7811356 T^{6} - 27158711 T^{7} + 693005062 T^{8} - 3345604560 T^{9} + 50737727474 T^{10} - 285769580321 T^{11} + 3222700257040 T^{12} - 18557932001698 T^{13} + 179352486137175 T^{14} - 974668139909303 T^{15} + 8626071655372911 T^{16} - 43172980681404095 T^{17} + 353668937870289351 T^{18} - 1638417143187538343 T^{19} + 12361152697060238175 T^{20} - 52440280491050142178 T^{21} + \)\(37\!\cdots\!40\)\( T^{22} - \)\(13\!\cdots\!61\)\( T^{23} + \)\(98\!\cdots\!94\)\( T^{24} - \)\(26\!\cdots\!60\)\( T^{25} + \)\(22\!\cdots\!82\)\( T^{26} - \)\(36\!\cdots\!11\)\( T^{27} + \)\(42\!\cdots\!96\)\( T^{28} - \)\(28\!\cdots\!65\)\( T^{29} + \)\(61\!\cdots\!99\)\( T^{30} - \)\(53\!\cdots\!01\)\( T^{31} + \)\(57\!\cdots\!70\)\( T^{32} + \)\(63\!\cdots\!41\)\( T^{33} + \)\(26\!\cdots\!81\)\( T^{34} \))(\( 1 - 2 T + 252 T^{2} - 689 T^{3} + 37762 T^{4} - 114252 T^{5} + 4106335 T^{6} - 13127406 T^{7} + 356924105 T^{8} - 1159800490 T^{9} + 26005965917 T^{10} - 84249039220 T^{11} + 1638726935883 T^{12} - 5212255293993 T^{13} + 91175699305654 T^{14} - 282130974817083 T^{15} + 4545214341428713 T^{16} - 13572370355034642 T^{17} + 204987213180311607 T^{18} - 586405341734573143 T^{19} + 8404475740392775887 T^{20} - 22815154566813233202 T^{21} + \)\(31\!\cdots\!73\)\( T^{22} - \)\(79\!\cdots\!63\)\( T^{23} + \)\(10\!\cdots\!54\)\( T^{24} - \)\(24\!\cdots\!13\)\( T^{25} + \)\(31\!\cdots\!23\)\( T^{26} - \)\(67\!\cdots\!20\)\( T^{27} + \)\(85\!\cdots\!37\)\( T^{28} - \)\(15\!\cdots\!90\)\( T^{29} + \)\(19\!\cdots\!05\)\( T^{30} - \)\(29\!\cdots\!86\)\( T^{31} + \)\(37\!\cdots\!35\)\( T^{32} - \)\(43\!\cdots\!72\)\( T^{33} + \)\(58\!\cdots\!62\)\( T^{34} - \)\(43\!\cdots\!49\)\( T^{35} + \)\(65\!\cdots\!12\)\( T^{36} - \)\(21\!\cdots\!42\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))
$43$ (\( 1 + 13 T + 99 T^{2} + 559 T^{3} + 1849 T^{4} \))(\( 1 + 3 T - 13 T^{2} + 129 T^{3} + 1849 T^{4} \))(\( 1 - 5 T + 38 T^{2} + 65 T^{3} + 1009 T^{4} + 2795 T^{5} + 70262 T^{6} - 397535 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T + 99 T^{2} - 568 T^{3} + 6133 T^{4} - 35897 T^{5} + 263719 T^{6} - 1050232 T^{7} + 7871193 T^{8} - 27350408 T^{9} + 147008443 T^{10} \))(\( 1 + T + 172 T^{2} + 286 T^{3} + 12855 T^{4} + 20906 T^{5} + 552765 T^{6} + 528814 T^{7} + 13675204 T^{8} + 3418801 T^{9} + 147008443 T^{10} \))(\( 1 - 5 T + 106 T^{2} - 152 T^{3} + 5533 T^{4} + 4289 T^{5} + 220872 T^{6} + 184427 T^{7} + 10230517 T^{8} - 12085064 T^{9} + 362392906 T^{10} - 735042215 T^{11} + 6321363049 T^{12} \))(\( 1 - 23 T + 479 T^{2} - 6374 T^{3} + 76418 T^{4} - 709137 T^{5} + 5980176 T^{6} - 41069820 T^{7} + 257147568 T^{8} - 1311194313 T^{9} + 6075765926 T^{10} - 21791437574 T^{11} + 70417044197 T^{12} - 145391350127 T^{13} + 271818611107 T^{14} \))(\( 1 + 229 T^{2} - 505 T^{3} + 25033 T^{4} - 95093 T^{5} + 1850150 T^{6} - 8235541 T^{7} + 103295925 T^{8} - 437280466 T^{9} + 4441724775 T^{10} - 15227515309 T^{11} + 147099876050 T^{12} - 325104043493 T^{13} + 3680062353619 T^{14} - 3192288339745 T^{15} + 62246461943503 T^{16} + 502592611936843 T^{18} \))(\( 1 + 21 T + 566 T^{2} + 8605 T^{3} + 137410 T^{4} + 1651519 T^{5} + 19709307 T^{6} + 195788145 T^{7} + 1892909276 T^{8} + 15920662733 T^{9} + 129322691089 T^{10} + 932042200511 T^{11} + 6470033718086 T^{12} + 40077814621973 T^{13} + 239117655823561 T^{14} + 1265804131912631 T^{15} + 6471480125698076 T^{16} + 28782510354308235 T^{17} + 124589684991197043 T^{18} + 448913600796821533 T^{19} + 1606075600145153410 T^{20} + 4324809425716534015 T^{21} + 12232098989318884934 T^{22} + 19515168528895676847 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 35 T + 948 T^{2} + 18609 T^{3} + 311924 T^{4} + 4456696 T^{5} + 56842554 T^{6} + 650599032 T^{7} + 6808036286 T^{8} + 65426928661 T^{9} + 582811610820 T^{10} + 4824699695991 T^{11} + 37308717328405 T^{12} + 269691818544208 T^{13} + 1827487675896028 T^{14} + 11596748197400944 T^{15} + 68983818340220845 T^{16} + 383597398729156437 T^{17} + 1992516917883026820 T^{18} + 9618310912725684823 T^{19} + 43036069014571596014 T^{20} + \)\(17\!\cdots\!24\)\( T^{21} + \)\(66\!\cdots\!54\)\( T^{22} + \)\(22\!\cdots\!28\)\( T^{23} + \)\(67\!\cdots\!76\)\( T^{24} + \)\(17\!\cdots\!63\)\( T^{25} + \)\(37\!\cdots\!48\)\( T^{26} + \)\(60\!\cdots\!05\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 + 9 T + 381 T^{2} + 3330 T^{3} + 74587 T^{4} + 626370 T^{5} + 9994685 T^{6} + 79932102 T^{7} + 1022218640 T^{8} + 7745341120 T^{9} + 84285089900 T^{10} + 602966972786 T^{11} + 5783246060193 T^{12} + 38925473880766 T^{13} + 336561052878383 T^{14} + 2122402402822886 T^{15} + 16793877441281108 T^{16} + 98683122241581038 T^{17} + 722136729975087644 T^{18} + 3924322042819516214 T^{19} + 26758959631201597181 T^{20} + \)\(13\!\cdots\!66\)\( T^{21} + \)\(85\!\cdots\!99\)\( T^{22} + \)\(38\!\cdots\!14\)\( T^{23} + \)\(22\!\cdots\!00\)\( T^{24} + \)\(90\!\cdots\!20\)\( T^{25} + \)\(51\!\cdots\!20\)\( T^{26} + \)\(17\!\cdots\!98\)\( T^{27} + \)\(92\!\cdots\!95\)\( T^{28} + \)\(25\!\cdots\!70\)\( T^{29} + \)\(12\!\cdots\!41\)\( T^{30} + \)\(24\!\cdots\!70\)\( T^{31} + \)\(12\!\cdots\!67\)\( T^{32} + \)\(12\!\cdots\!09\)\( T^{33} + \)\(58\!\cdots\!43\)\( T^{34} \))(\( 1 - 28 T + 795 T^{2} - 14321 T^{3} + 249728 T^{4} - 3458673 T^{5} + 46373301 T^{6} - 534422488 T^{7} + 5999510852 T^{8} - 60178060975 T^{9} + 591918466921 T^{10} - 5319426262908 T^{11} + 47140355784661 T^{12} - 386909199343101 T^{13} + 3143653195629816 T^{14} - 23847714228979176 T^{15} + 179466603028519644 T^{16} - 1266368692235692983 T^{17} + 8871872375658672893 T^{18} - 58381161647973150054 T^{19} + \)\(38\!\cdots\!99\)\( T^{20} - \)\(23\!\cdots\!67\)\( T^{21} + \)\(14\!\cdots\!08\)\( T^{22} - \)\(81\!\cdots\!76\)\( T^{23} + \)\(46\!\cdots\!88\)\( T^{24} - \)\(24\!\cdots\!49\)\( T^{25} + \)\(12\!\cdots\!27\)\( T^{26} - \)\(62\!\cdots\!08\)\( T^{27} + \)\(29\!\cdots\!03\)\( T^{28} - \)\(13\!\cdots\!75\)\( T^{29} + \)\(55\!\cdots\!64\)\( T^{30} - \)\(21\!\cdots\!88\)\( T^{31} + \)\(79\!\cdots\!43\)\( T^{32} - \)\(25\!\cdots\!77\)\( T^{33} + \)\(79\!\cdots\!96\)\( T^{34} - \)\(19\!\cdots\!21\)\( T^{35} + \)\(46\!\cdots\!85\)\( T^{36} - \)\(70\!\cdots\!72\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))
$47$ (\( 1 - T + 91 T^{2} - 47 T^{3} + 2209 T^{4} \))(\( 1 - 9 T + 113 T^{2} - 423 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 222 T^{2} + 1705 T^{3} + 16451 T^{4} + 80135 T^{5} + 490398 T^{6} + 1245876 T^{7} + 4879681 T^{8} \))(\( 1 + 29 T + 530 T^{2} + 6754 T^{3} + 66085 T^{4} + 508202 T^{5} + 3105995 T^{6} + 14919586 T^{7} + 55026190 T^{8} + 141510749 T^{9} + 229345007 T^{10} \))(\( 1 - 19 T + 332 T^{2} - 3522 T^{3} + 34851 T^{4} - 247598 T^{5} + 1637997 T^{6} - 7780098 T^{7} + 34469236 T^{8} - 92713939 T^{9} + 229345007 T^{10} \))(\( 1 + 8 T + 194 T^{2} + 1024 T^{3} + 16399 T^{4} + 66232 T^{5} + 908508 T^{6} + 3112904 T^{7} + 36225391 T^{8} + 106314752 T^{9} + 946658114 T^{10} + 1834760056 T^{11} + 10779215329 T^{12} \))(\( 1 - 10 T + 175 T^{2} - 1405 T^{3} + 16332 T^{4} - 102894 T^{5} + 981162 T^{6} - 5586582 T^{7} + 46114614 T^{8} - 227292846 T^{9} + 1695637236 T^{10} - 6855951805 T^{11} + 40135376225 T^{12} - 107792153290 T^{13} + 506623120463 T^{14} \))(\( 1 - 11 T + 304 T^{2} - 2379 T^{3} + 35917 T^{4} - 196156 T^{5} + 2190202 T^{6} - 7822829 T^{7} + 89098332 T^{8} - 255370170 T^{9} + 4187621604 T^{10} - 17280629261 T^{11} + 227393342246 T^{12} - 957178706236 T^{13} + 8237384616419 T^{14} - 25643753267691 T^{15} + 154013428620752 T^{16} - 261924153279371 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 27 T + 721 T^{2} + 12646 T^{3} + 205206 T^{4} + 2719622 T^{5} + 33303256 T^{6} + 356780847 T^{7} + 3554349185 T^{8} + 31875619896 T^{9} + 267301104519 T^{10} + 2043077919444 T^{11} + 14644952368176 T^{12} + 96024662213868 T^{13} + 590468139882471 T^{14} + 3309422484462408 T^{15} + 17344090185409985 T^{16} + 81825905852680929 T^{17} + 358982967580811224 T^{18} + 1377823384119824986 T^{19} + 4886218890713327766 T^{20} + 14152523962857591482 T^{21} + 37923974342033465329 T^{22} + 66748298807268332181 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 6 T + 382 T^{2} + 1059 T^{3} + 61842 T^{4} - 36571 T^{5} + 5929810 T^{6} - 26059681 T^{7} + 432153524 T^{8} - 3250819243 T^{9} + 30303276714 T^{10} - 230841065832 T^{11} + 2036943202521 T^{12} - 12145587908550 T^{13} + 110601003501836 T^{14} - 570842631701850 T^{15} + 4499607534368889 T^{16} - 23966611977875736 T^{17} + 147870323619048234 T^{18} - 745559162041569701 T^{19} + 4658275890382169396 T^{20} - 13202436906490352303 T^{21} + \)\(14\!\cdots\!10\)\( T^{22} - 40927720531841291957 T^{23} + \)\(32\!\cdots\!58\)\( T^{24} + \)\(26\!\cdots\!77\)\( T^{25} + \)\(44\!\cdots\!62\)\( T^{26} + \)\(32\!\cdots\!62\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 - 20 T + 539 T^{2} - 8097 T^{3} + 132115 T^{4} - 1605834 T^{5} + 20056685 T^{6} - 206148995 T^{7} + 2142835302 T^{8} - 19167731204 T^{9} + 173224474562 T^{10} - 1379601189521 T^{11} + 11194106900813 T^{12} - 81339011735318 T^{13} + 612242201931411 T^{14} - 4186001600199691 T^{15} + 30249408537814534 T^{16} - 200723203035174160 T^{17} + 1421722201277283098 T^{18} - 9246877534841117419 T^{19} + 63564822131124884253 T^{20} - \)\(39\!\cdots\!58\)\( T^{21} + \)\(25\!\cdots\!91\)\( T^{22} - \)\(14\!\cdots\!09\)\( T^{23} + \)\(87\!\cdots\!06\)\( T^{24} - \)\(45\!\cdots\!44\)\( T^{25} + \)\(23\!\cdots\!34\)\( T^{26} - \)\(10\!\cdots\!55\)\( T^{27} + \)\(49\!\cdots\!55\)\( T^{28} - \)\(18\!\cdots\!94\)\( T^{29} + \)\(72\!\cdots\!05\)\( T^{30} - \)\(20\!\cdots\!93\)\( T^{31} + \)\(65\!\cdots\!77\)\( T^{32} - \)\(11\!\cdots\!20\)\( T^{33} + \)\(26\!\cdots\!87\)\( T^{34} \))(\( 1 - 37 T + 978 T^{2} - 19359 T^{3} + 330366 T^{4} - 4921443 T^{5} + 66764986 T^{6} - 829712514 T^{7} + 9623059649 T^{8} - 104529238390 T^{9} + 1073988693974 T^{10} - 10460746659784 T^{11} + 97157192823338 T^{12} - 861629531013210 T^{13} + 7323218104941353 T^{14} - 59693259205396446 T^{15} + 467764290384534385 T^{16} - 3524369881542455240 T^{17} + 25570816431177422752 T^{18} - \)\(17\!\cdots\!50\)\( T^{19} + \)\(12\!\cdots\!44\)\( T^{20} - \)\(77\!\cdots\!60\)\( T^{21} + \)\(48\!\cdots\!55\)\( T^{22} - \)\(29\!\cdots\!26\)\( T^{23} + \)\(16\!\cdots\!71\)\( T^{24} - \)\(92\!\cdots\!90\)\( T^{25} + \)\(49\!\cdots\!94\)\( T^{26} - \)\(24\!\cdots\!24\)\( T^{27} + \)\(12\!\cdots\!58\)\( T^{28} - \)\(54\!\cdots\!10\)\( T^{29} + \)\(23\!\cdots\!47\)\( T^{30} - \)\(96\!\cdots\!74\)\( T^{31} + \)\(36\!\cdots\!22\)\( T^{32} - \)\(12\!\cdots\!67\)\( T^{33} + \)\(39\!\cdots\!38\)\( T^{34} - \)\(10\!\cdots\!39\)\( T^{35} + \)\(26\!\cdots\!86\)\( T^{36} - \)\(46\!\cdots\!93\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))
$53$ (\( 1 - 6 T - 2 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 2 T - 18 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 - 5 T + 188 T^{2} - 715 T^{3} + 14449 T^{4} - 37895 T^{5} + 528092 T^{6} - 744385 T^{7} + 7890481 T^{8} \))(\( 1 - 25 T + 481 T^{2} - 5989 T^{3} + 62516 T^{4} - 492068 T^{5} + 3313348 T^{6} - 16823101 T^{7} + 71609837 T^{8} - 197262025 T^{9} + 418195493 T^{10} \))(\( 1 + 34 T + 625 T^{2} + 8072 T^{3} + 81586 T^{4} + 661196 T^{5} + 4324058 T^{6} + 22674248 T^{7} + 93048125 T^{8} + 268276354 T^{9} + 418195493 T^{10} \))(\( 1 + 3 T + 212 T^{2} + 824 T^{3} + 21599 T^{4} + 87165 T^{5} + 1392784 T^{6} + 4619745 T^{7} + 60671591 T^{8} + 122674648 T^{9} + 1672781972 T^{10} + 1254586479 T^{11} + 22164361129 T^{12} \))(\( 1 + T + 341 T^{2} + 296 T^{3} + 51270 T^{4} + 37529 T^{5} + 4404456 T^{6} + 2612924 T^{7} + 233436168 T^{8} + 105418961 T^{9} + 7632923790 T^{10} + 2335582376 T^{11} + 142604663113 T^{12} + 22164361129 T^{13} + 1174711139837 T^{14} \))(\( 1 + 21 T + 571 T^{2} + 8372 T^{3} + 131947 T^{4} + 1483676 T^{5} + 17016111 T^{6} + 152931868 T^{7} + 1376311042 T^{8} + 10036793022 T^{9} + 72944485226 T^{10} + 429585617212 T^{11} + 2533307557347 T^{12} + 11706917288156 T^{13} + 55179640714871 T^{14} + 185560031371988 T^{15} + 670760060846927 T^{16} + 1307453498638581 T^{17} + 3299763591802133 T^{18} \))(\( 1 - 22 T + 457 T^{2} - 6131 T^{3} + 81712 T^{4} - 864884 T^{5} + 9238431 T^{6} - 83791862 T^{7} + 777068847 T^{8} - 6324907486 T^{9} + 53066638192 T^{10} - 395846312399 T^{11} + 3050517811680 T^{12} - 20979854557147 T^{13} + 149064186681328 T^{14} - 941633251793222 T^{15} + 6131446972945407 T^{16} - 35041379038477966 T^{17} + 204763920949348599 T^{18} - 1015988869466783908 T^{19} + 5087363822893130032 T^{20} - 20230850581338877423 T^{21} + 79923573957039463393 T^{22} - \)\(20\!\cdots\!34\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + T + 336 T^{2} + 657 T^{3} + 55960 T^{4} + 176338 T^{5} + 6430150 T^{6} + 27382410 T^{7} + 584794578 T^{8} + 2927367915 T^{9} + 44477723032 T^{10} + 239086649523 T^{11} + 2895999634685 T^{12} + 15648142913420 T^{13} + 164010413112036 T^{14} + 829351574411260 T^{15} + 8134862973830165 T^{16} + 35594503121035671 T^{17} + 350950628507258392 T^{18} + 1224212068405807095 T^{19} + 12961598213073158562 T^{20} + 32166422062584067170 T^{21} + \)\(40\!\cdots\!50\)\( T^{22} + \)\(58\!\cdots\!54\)\( T^{23} + \)\(97\!\cdots\!40\)\( T^{24} + \)\(60\!\cdots\!29\)\( T^{25} + \)\(16\!\cdots\!76\)\( T^{26} + \)\(26\!\cdots\!73\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( 1 - T + 441 T^{2} + 322 T^{3} + 101481 T^{4} + 197494 T^{5} + 16305137 T^{6} + 44655998 T^{7} + 2032908942 T^{8} + 6502234464 T^{9} + 206464610670 T^{10} + 704884913034 T^{11} + 17527521175563 T^{12} + 60528664390346 T^{13} + 1262670466507339 T^{14} + 4244148057212694 T^{15} + 77865100767818918 T^{16} + 246569452473215298 T^{17} + 4126850340694402654 T^{18} + 11921811892710457446 T^{19} + \)\(18\!\cdots\!03\)\( T^{20} + \)\(47\!\cdots\!26\)\( T^{21} + \)\(73\!\cdots\!59\)\( T^{22} + \)\(15\!\cdots\!86\)\( T^{23} + \)\(24\!\cdots\!90\)\( T^{24} + \)\(40\!\cdots\!04\)\( T^{25} + \)\(67\!\cdots\!86\)\( T^{26} + \)\(78\!\cdots\!02\)\( T^{27} + \)\(15\!\cdots\!89\)\( T^{28} + \)\(97\!\cdots\!54\)\( T^{29} + \)\(26\!\cdots\!13\)\( T^{30} + \)\(44\!\cdots\!18\)\( T^{31} + \)\(32\!\cdots\!37\)\( T^{32} - \)\(38\!\cdots\!21\)\( T^{33} + \)\(20\!\cdots\!13\)\( T^{34} \))(\( 1 + 37 T + 1169 T^{2} + 25468 T^{3} + 499604 T^{4} + 8164847 T^{5} + 123648490 T^{6} + 1663415860 T^{7} + 21093616691 T^{8} + 245069327634 T^{9} + 2714128730081 T^{10} + 28030811005848 T^{11} + 278124385839559 T^{12} + 2602114800649150 T^{13} + 23520023015593165 T^{14} + 201909756210416460 T^{15} + 1681037739749985753 T^{16} + 13351541419509911796 T^{17} + \)\(10\!\cdots\!79\)\( T^{18} + \)\(76\!\cdots\!00\)\( T^{19} + \)\(54\!\cdots\!87\)\( T^{20} + \)\(37\!\cdots\!64\)\( T^{21} + \)\(25\!\cdots\!81\)\( T^{22} + \)\(15\!\cdots\!60\)\( T^{23} + \)\(98\!\cdots\!45\)\( T^{24} + \)\(57\!\cdots\!50\)\( T^{25} + \)\(32\!\cdots\!83\)\( T^{26} + \)\(17\!\cdots\!28\)\( T^{27} + \)\(89\!\cdots\!73\)\( T^{28} + \)\(42\!\cdots\!66\)\( T^{29} + \)\(19\!\cdots\!27\)\( T^{30} + \)\(81\!\cdots\!60\)\( T^{31} + \)\(32\!\cdots\!70\)\( T^{32} + \)\(11\!\cdots\!43\)\( T^{33} + \)\(36\!\cdots\!28\)\( T^{34} + \)\(98\!\cdots\!28\)\( T^{35} + \)\(24\!\cdots\!97\)\( T^{36} + \)\(40\!\cdots\!93\)\( T^{37} + \)\(57\!\cdots\!17\)\( T^{38} \))
$59$ (\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( 1 + 6 T + 173 T^{2} + 946 T^{3} + 14003 T^{4} + 55814 T^{5} + 602213 T^{6} + 1232274 T^{7} + 12117361 T^{8} \))(\( 1 + 11 T + 293 T^{2} + 2373 T^{3} + 34336 T^{4} + 203496 T^{5} + 2025824 T^{6} + 8260413 T^{7} + 60176047 T^{8} + 133290971 T^{9} + 714924299 T^{10} \))(\( 1 - 10 T + 259 T^{2} - 1968 T^{3} + 27990 T^{4} - 163116 T^{5} + 1651410 T^{6} - 6850608 T^{7} + 53193161 T^{8} - 121173610 T^{9} + 714924299 T^{10} \))(\( 1 - 5 T + 122 T^{2} - 96 T^{3} + 7917 T^{4} + 4213 T^{5} + 555224 T^{6} + 248567 T^{7} + 27559077 T^{8} - 19716384 T^{9} + 1478318042 T^{10} - 3574621495 T^{11} + 42180533641 T^{12} \))(\( 1 - 4 T + 192 T^{2} - 766 T^{3} + 17341 T^{4} - 80260 T^{5} + 1108838 T^{6} - 5770956 T^{7} + 65421442 T^{8} - 279385060 T^{9} + 3561477239 T^{10} - 9281898526 T^{11} + 137265465408 T^{12} - 168722134564 T^{13} + 2488651484819 T^{14} \))(\( 1 - 4 T + 400 T^{2} - 1232 T^{3} + 76098 T^{4} - 190184 T^{5} + 9093980 T^{6} - 18940360 T^{7} + 750071737 T^{8} - 1319289400 T^{9} + 44254232483 T^{10} - 65931393160 T^{11} + 1867712518420 T^{12} - 2304528184424 T^{13} + 54404309305302 T^{14} - 51966417445712 T^{15} + 995460593927600 T^{16} - 587321750417284 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 23 T + 463 T^{2} + 5991 T^{3} + 76539 T^{4} + 797165 T^{5} + 8616593 T^{6} + 80045466 T^{7} + 761614967 T^{8} + 6355022897 T^{9} + 55110088864 T^{10} + 428918254928 T^{11} + 3481229277834 T^{12} + 25306177040752 T^{13} + 191838219335584 T^{14} + 1305188247562963 T^{15} + 9228763498142087 T^{16} + 57226448668178334 T^{17} + 363452490907305113 T^{18} + 1983865860895738135 T^{19} + 11238254863797125019 T^{20} + 51900007949561739549 T^{21} + \)\(23\!\cdots\!63\)\( T^{22} + \)\(69\!\cdots\!57\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 30 T + 779 T^{2} + 13424 T^{3} + 209000 T^{4} + 2609668 T^{5} + 30561096 T^{6} + 309458644 T^{7} + 3067074882 T^{8} + 27703864660 T^{9} + 254359244333 T^{10} + 2182190578586 T^{11} + 19036964650525 T^{12} + 153468834699824 T^{13} + 1232796925002464 T^{14} + 9054661247289616 T^{15} + 66267673948477525 T^{16} + 448176118839414094 T^{17} + 3082162787270165213 T^{18} + 19806166021641373340 T^{19} + \)\(12\!\cdots\!62\)\( T^{20} + \)\(77\!\cdots\!36\)\( T^{21} + \)\(44\!\cdots\!16\)\( T^{22} + \)\(22\!\cdots\!52\)\( T^{23} + \)\(10\!\cdots\!00\)\( T^{24} + \)\(40\!\cdots\!16\)\( T^{25} + \)\(13\!\cdots\!99\)\( T^{26} + \)\(31\!\cdots\!70\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 - 20 T + 734 T^{2} - 12408 T^{3} + 265020 T^{4} - 3848930 T^{5} + 62041502 T^{6} - 789606768 T^{7} + 10542318489 T^{8} - 119467599956 T^{9} + 1381468079645 T^{10} - 14098607773024 T^{11} + 144713205438578 T^{12} - 1340202733600798 T^{13} + 12387676412233544 T^{14} - 104573297813556984 T^{15} + 877737340473617637 T^{16} - 6765212874797431024 T^{17} + 51786503087943440583 T^{18} - \)\(36\!\cdots\!04\)\( T^{19} + \)\(25\!\cdots\!76\)\( T^{20} - \)\(16\!\cdots\!78\)\( T^{21} + \)\(10\!\cdots\!22\)\( T^{22} - \)\(59\!\cdots\!84\)\( T^{23} + \)\(34\!\cdots\!55\)\( T^{24} - \)\(17\!\cdots\!76\)\( T^{25} + \)\(91\!\cdots\!71\)\( T^{26} - \)\(40\!\cdots\!68\)\( T^{27} + \)\(18\!\cdots\!18\)\( T^{28} - \)\(68\!\cdots\!30\)\( T^{29} + \)\(27\!\cdots\!80\)\( T^{30} - \)\(76\!\cdots\!88\)\( T^{31} + \)\(26\!\cdots\!66\)\( T^{32} - \)\(43\!\cdots\!20\)\( T^{33} + \)\(12\!\cdots\!19\)\( T^{34} \))(\( 1 - 32 T + 952 T^{2} - 18790 T^{3} + 335659 T^{4} - 4877288 T^{5} + 64659406 T^{6} - 744373672 T^{7} + 7897382483 T^{8} - 75001234072 T^{9} + 664756713559 T^{10} - 5402287760152 T^{11} + 42052001722839 T^{12} - 312369219526600 T^{13} + 2342413480172083 T^{14} - 17719625435757784 T^{15} + 140139416136991777 T^{16} - 1117137759102826776 T^{17} + 8964214316433501483 T^{18} - 69599971239624987524 T^{19} + \)\(52\!\cdots\!97\)\( T^{20} - \)\(38\!\cdots\!56\)\( T^{21} + \)\(28\!\cdots\!83\)\( T^{22} - \)\(21\!\cdots\!24\)\( T^{23} + \)\(16\!\cdots\!17\)\( T^{24} - \)\(13\!\cdots\!00\)\( T^{25} + \)\(10\!\cdots\!41\)\( T^{26} - \)\(79\!\cdots\!92\)\( T^{27} + \)\(57\!\cdots\!01\)\( T^{28} - \)\(38\!\cdots\!72\)\( T^{29} + \)\(23\!\cdots\!97\)\( T^{30} - \)\(13\!\cdots\!32\)\( T^{31} + \)\(67\!\cdots\!74\)\( T^{32} - \)\(30\!\cdots\!68\)\( T^{33} + \)\(12\!\cdots\!41\)\( T^{34} - \)\(40\!\cdots\!90\)\( T^{35} + \)\(12\!\cdots\!88\)\( T^{36} - \)\(24\!\cdots\!72\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))
$61$ (\( 1 - 14 T + 119 T^{2} - 854 T^{3} + 3721 T^{4} \))(\( 1 - 4 T + 121 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 21 T + 401 T^{2} + 4332 T^{3} + 42001 T^{4} + 264252 T^{5} + 1492121 T^{6} + 4766601 T^{7} + 13845841 T^{8} \))(\( 1 - 11 T + 282 T^{2} - 2318 T^{3} + 33067 T^{4} - 201041 T^{5} + 2017087 T^{6} - 8625278 T^{7} + 64008642 T^{8} - 152304251 T^{9} + 844596301 T^{10} \))(\( 1 + 134 T^{2} + 54 T^{3} + 8185 T^{4} + 4644 T^{5} + 499285 T^{6} + 200934 T^{7} + 30415454 T^{8} + 844596301 T^{10} \))(\( 1 + 61 T + 1886 T^{2} + 38382 T^{3} + 568285 T^{4} + 6417813 T^{5} + 56554408 T^{6} + 391486593 T^{7} + 2114588485 T^{8} + 8711984742 T^{9} + 26113256126 T^{10} + 51520374361 T^{11} + 51520374361 T^{12} \))(\( 1 - 3 T + 162 T^{2} + 61 T^{3} + 11799 T^{4} + 53561 T^{5} + 692826 T^{6} + 4721098 T^{7} + 42262386 T^{8} + 199300481 T^{9} + 2678148819 T^{10} + 844596301 T^{11} + 136824600762 T^{12} - 154561123083 T^{13} + 3142742836021 T^{14} \))(\( 1 + 11 T + 363 T^{2} + 3178 T^{3} + 64388 T^{4} + 484001 T^{5} + 7421927 T^{6} + 48387836 T^{7} + 610501909 T^{8} + 3456902892 T^{9} + 37240616449 T^{10} + 180051137756 T^{11} + 1684636412387 T^{12} + 6701400889841 T^{13} + 54381866628788 T^{14} + 163731749719258 T^{15} + 1140815649475623 T^{16} + 2108780442970091 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 4 T + 515 T^{2} - 2183 T^{3} + 126825 T^{4} - 553350 T^{5} + 20068525 T^{6} - 86790548 T^{7} + 2298315906 T^{8} - 9463792069 T^{9} + 201443760970 T^{10} - 761468440966 T^{11} + 13837315630820 T^{12} - 46449574898926 T^{13} + 749572234569370 T^{14} - 2148100987613689 T^{15} + 31822116602246946 T^{16} - 73302975802562948 T^{17} + 1033937920873087525 T^{18} - 1739036748312220350 T^{19} + 24313279970880162825 T^{20} - 25528320920656929803 T^{21} + \)\(36\!\cdots\!15\)\( T^{22} - \)\(17\!\cdots\!44\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 3 T + 403 T^{2} - 1236 T^{3} + 82870 T^{4} - 256913 T^{5} + 11777036 T^{6} - 35236793 T^{7} + 1301617432 T^{8} - 3621165890 T^{9} + 118008463253 T^{10} - 302860230171 T^{11} + 9025363533113 T^{12} - 21515936469586 T^{13} + 592385566983864 T^{14} - 1312472124644746 T^{15} + 33583377706713473 T^{16} - 68743517904443751 T^{17} + 1633926418855380773 T^{18} - 3058423316001372890 T^{19} + 67059817371443460952 T^{20} - \)\(11\!\cdots\!53\)\( T^{21} + \)\(22\!\cdots\!16\)\( T^{22} - \)\(30\!\cdots\!33\)\( T^{23} + \)\(59\!\cdots\!70\)\( T^{24} - \)\(53\!\cdots\!96\)\( T^{25} + \)\(10\!\cdots\!63\)\( T^{26} - \)\(48\!\cdots\!43\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( 1 - 59 T + 2112 T^{2} - 55415 T^{3} + 1177562 T^{4} - 21221476 T^{5} + 335021876 T^{6} - 4728841013 T^{7} + 60639557803 T^{8} - 714705093420 T^{9} + 7819314243897 T^{10} - 80060921611007 T^{11} + 773076350787456 T^{12} - 7089636137923804 T^{13} + 62176250216536602 T^{14} - 524679013289345893 T^{15} + 4282737142918878503 T^{16} - 33929936279905333490 T^{17} + \)\(26\!\cdots\!83\)\( T^{18} - \)\(19\!\cdots\!53\)\( T^{19} + \)\(14\!\cdots\!62\)\( T^{20} - \)\(98\!\cdots\!64\)\( T^{21} + \)\(65\!\cdots\!56\)\( T^{22} - \)\(41\!\cdots\!27\)\( T^{23} + \)\(24\!\cdots\!37\)\( T^{24} - \)\(13\!\cdots\!20\)\( T^{25} + \)\(70\!\cdots\!23\)\( T^{26} - \)\(33\!\cdots\!13\)\( T^{27} + \)\(14\!\cdots\!36\)\( T^{28} - \)\(56\!\cdots\!96\)\( T^{29} + \)\(19\!\cdots\!22\)\( T^{30} - \)\(54\!\cdots\!15\)\( T^{31} + \)\(12\!\cdots\!12\)\( T^{32} - \)\(21\!\cdots\!99\)\( T^{33} + \)\(22\!\cdots\!21\)\( T^{34} \))(\( 1 + 7 T + 373 T^{2} + 1464 T^{3} + 72641 T^{4} + 155126 T^{5} + 10849508 T^{6} + 11940304 T^{7} + 1359391559 T^{8} + 515279945 T^{9} + 145828250858 T^{10} - 23210933856 T^{11} + 13706013765858 T^{12} - 7117859420813 T^{13} + 1147404585906229 T^{14} - 831976516643152 T^{15} + 86153129544462099 T^{16} - 70894625436126353 T^{17} + 5818343767347833826 T^{18} - 4828695528054928304 T^{19} + \)\(35\!\cdots\!86\)\( T^{20} - \)\(26\!\cdots\!13\)\( T^{21} + \)\(19\!\cdots\!19\)\( T^{22} - \)\(11\!\cdots\!32\)\( T^{23} + \)\(96\!\cdots\!29\)\( T^{24} - \)\(36\!\cdots\!93\)\( T^{25} + \)\(43\!\cdots\!18\)\( T^{26} - \)\(44\!\cdots\!36\)\( T^{27} + \)\(17\!\cdots\!78\)\( T^{28} + \)\(36\!\cdots\!45\)\( T^{29} + \)\(59\!\cdots\!99\)\( T^{30} + \)\(31\!\cdots\!84\)\( T^{31} + \)\(17\!\cdots\!48\)\( T^{32} + \)\(15\!\cdots\!66\)\( T^{33} + \)\(43\!\cdots\!41\)\( T^{34} + \)\(53\!\cdots\!04\)\( T^{35} + \)\(83\!\cdots\!33\)\( T^{36} + \)\(95\!\cdots\!67\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))
$67$ (\( 1 + 20 T + 221 T^{2} + 1340 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 133 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 17 T + 242 T^{2} + 2035 T^{3} + 19291 T^{4} + 136345 T^{5} + 1086338 T^{6} + 5112971 T^{7} + 20151121 T^{8} \))(\( 1 - 6 T + 32 T^{2} + 152 T^{3} + 5791 T^{4} - 64428 T^{5} + 387997 T^{6} + 682328 T^{7} + 9624416 T^{8} - 120906726 T^{9} + 1350125107 T^{10} \))(\( 1 - 11 T + 328 T^{2} - 2684 T^{3} + 43483 T^{4} - 262229 T^{5} + 2913361 T^{6} - 12048476 T^{7} + 98650264 T^{8} - 221662331 T^{9} + 1350125107 T^{10} \))(\( 1 - 13 T + 156 T^{2} - 1026 T^{3} + 10455 T^{4} - 87493 T^{5} + 1010848 T^{6} - 5862031 T^{7} + 46932495 T^{8} - 308582838 T^{9} + 3143574876 T^{10} - 17551626391 T^{11} + 90458382169 T^{12} \))(\( 1 - 28 T + 648 T^{2} - 9931 T^{3} + 135284 T^{4} - 1472821 T^{5} + 14791793 T^{6} - 125329735 T^{7} + 991050131 T^{8} - 6611493469 T^{9} + 40688421692 T^{10} - 200120782651 T^{11} + 874881069336 T^{12} - 2532834700732 T^{13} + 6060711605323 T^{14} \))(\( 1 - 4 T + 463 T^{2} - 1319 T^{3} + 96965 T^{4} - 183954 T^{5} + 12423379 T^{6} - 15236907 T^{7} + 1114089690 T^{8} - 1022393523 T^{9} + 74644009230 T^{10} - 68398475523 T^{11} + 3736492738177 T^{12} - 3706879312434 T^{13} + 130914881000255 T^{14} - 119314606080911 T^{15} + 2806109473264549 T^{16} - 1624270710226564 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 26 T + 734 T^{2} + 12241 T^{3} + 194371 T^{4} + 2301401 T^{5} + 24936552 T^{6} + 208315088 T^{7} + 1508590671 T^{8} + 6757901265 T^{9} + 10934295138 T^{10} - 306038227373 T^{11} - 3111488124494 T^{12} - 20504561233991 T^{13} + 49084050874482 T^{14} + 2032526658165195 T^{15} + 30399793150792191 T^{16} + 281251430475714416 T^{17} + 2255720150793141288 T^{18} + 13948127749201957523 T^{19} + 78927780554361867811 T^{20} + \)\(33\!\cdots\!27\)\( T^{21} + \)\(13\!\cdots\!66\)\( T^{22} + \)\(31\!\cdots\!58\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 + 22 T + 694 T^{2} + 10439 T^{3} + 193492 T^{4} + 2285571 T^{5} + 32492463 T^{6} + 328286398 T^{7} + 3998651363 T^{8} + 36396393149 T^{9} + 399795726501 T^{10} + 3357364823787 T^{11} + 33894768425127 T^{12} + 263865853266971 T^{13} + 2457414462651723 T^{14} + 17679012168887057 T^{15} + 152153615460395103 T^{16} + 1009771116496649481 T^{17} + 8056332060004557621 T^{18} + 49139684194707691943 T^{19} + \)\(36\!\cdots\!47\)\( T^{20} + \)\(19\!\cdots\!54\)\( T^{21} + \)\(13\!\cdots\!83\)\( T^{22} + \)\(62\!\cdots\!37\)\( T^{23} + \)\(35\!\cdots\!08\)\( T^{24} + \)\(12\!\cdots\!37\)\( T^{25} + \)\(56\!\cdots\!34\)\( T^{26} + \)\(12\!\cdots\!14\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 15 T + 739 T^{2} + 10078 T^{3} + 268868 T^{4} + 3345611 T^{5} + 64094448 T^{6} + 730468759 T^{7} + 11245254118 T^{8} + 117840395659 T^{9} + 1545847478289 T^{10} + 14948642880732 T^{11} + 172926454422394 T^{12} + 1547119860739074 T^{13} + 16118788783198125 T^{14} + 133524216140123901 T^{15} + 1269632332199075877 T^{16} + 9722118088107106935 T^{17} + 85065366257338083759 T^{18} + \)\(59\!\cdots\!89\)\( T^{19} + \)\(48\!\cdots\!75\)\( T^{20} + \)\(31\!\cdots\!54\)\( T^{21} + \)\(23\!\cdots\!58\)\( T^{22} + \)\(13\!\cdots\!08\)\( T^{23} + \)\(93\!\cdots\!47\)\( T^{24} + \)\(47\!\cdots\!19\)\( T^{25} + \)\(30\!\cdots\!46\)\( T^{26} + \)\(13\!\cdots\!91\)\( T^{27} + \)\(78\!\cdots\!84\)\( T^{28} + \)\(27\!\cdots\!71\)\( T^{29} + \)\(14\!\cdots\!16\)\( T^{30} + \)\(37\!\cdots\!62\)\( T^{31} + \)\(18\!\cdots\!77\)\( T^{32} + \)\(24\!\cdots\!15\)\( T^{33} + \)\(11\!\cdots\!27\)\( T^{34} \))(\( 1 - 45 T + 1918 T^{2} - 54641 T^{3} + 1428188 T^{4} - 30747644 T^{5} + 612056281 T^{6} - 10751002816 T^{7} + 176297257568 T^{8} - 2633062404829 T^{9} + 36996136230153 T^{10} - 481629334199938 T^{11} + 5932022620473347 T^{12} - 68382935486817391 T^{13} + 748774876446608998 T^{14} - 7721042535844920931 T^{15} + 75822371411990625652 T^{16} - \)\(70\!\cdots\!96\)\( T^{17} + \)\(62\!\cdots\!87\)\( T^{18} - \)\(52\!\cdots\!11\)\( T^{19} + \)\(41\!\cdots\!29\)\( T^{20} - \)\(31\!\cdots\!44\)\( T^{21} + \)\(22\!\cdots\!76\)\( T^{22} - \)\(15\!\cdots\!51\)\( T^{23} + \)\(10\!\cdots\!86\)\( T^{24} - \)\(61\!\cdots\!79\)\( T^{25} + \)\(35\!\cdots\!81\)\( T^{26} - \)\(19\!\cdots\!58\)\( T^{27} + \)\(10\!\cdots\!91\)\( T^{28} - \)\(47\!\cdots\!21\)\( T^{29} + \)\(21\!\cdots\!44\)\( T^{30} - \)\(87\!\cdots\!76\)\( T^{31} + \)\(33\!\cdots\!47\)\( T^{32} - \)\(11\!\cdots\!76\)\( T^{33} + \)\(35\!\cdots\!84\)\( T^{34} - \)\(90\!\cdots\!21\)\( T^{35} + \)\(21\!\cdots\!86\)\( T^{36} - \)\(33\!\cdots\!05\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))
$71$ (\( 1 + 3 T + 115 T^{2} + 213 T^{3} + 5041 T^{4} \))(\( 1 + 9 T + 161 T^{2} + 639 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 210 T^{2} - 1635 T^{3} + 22127 T^{4} - 116085 T^{5} + 1058610 T^{6} - 3579110 T^{7} + 25411681 T^{8} \))(\( 1 + 15 T + 300 T^{2} + 2752 T^{3} + 33867 T^{4} + 239018 T^{5} + 2404557 T^{6} + 13872832 T^{7} + 107373300 T^{8} + 381175215 T^{9} + 1804229351 T^{10} \))(\( 1 - T + 124 T^{2} + 10 T^{3} + 13175 T^{4} - 21722 T^{5} + 935425 T^{6} + 50410 T^{7} + 44380964 T^{8} - 25411681 T^{9} + 1804229351 T^{10} \))(\( 1 + 22 T + 398 T^{2} + 5466 T^{3} + 64191 T^{4} + 655668 T^{5} + 5763460 T^{6} + 46552428 T^{7} + 323586831 T^{8} + 1956341526 T^{9} + 10113849038 T^{10} + 39693045722 T^{11} + 128100283921 T^{12} \))(\( 1 - 18 T + 509 T^{2} - 6143 T^{3} + 99682 T^{4} - 906794 T^{5} + 10907742 T^{6} - 79739874 T^{7} + 774449682 T^{8} - 4571148554 T^{9} + 35677284302 T^{10} - 156103956383 T^{11} + 918352739659 T^{12} - 2305805110578 T^{13} + 9095120158391 T^{14} \))(\( 1 - 19 T + 476 T^{2} - 5215 T^{3} + 76213 T^{4} - 550470 T^{5} + 6501366 T^{6} - 32177773 T^{7} + 411733912 T^{8} - 1744233622 T^{9} + 29233107752 T^{10} - 162208153693 T^{11} + 2326910406426 T^{12} - 13988368040070 T^{13} + 137505731527763 T^{14} - 668042980648015 T^{15} + 4329277195394116 T^{16} - 12269317093669459 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 23 T + 815 T^{2} + 13944 T^{3} + 290174 T^{4} + 4016108 T^{5} + 62482250 T^{6} + 729493421 T^{7} + 9247078025 T^{8} + 93075600870 T^{9} + 1000403940743 T^{10} + 8767603232972 T^{11} + 81491494383600 T^{12} + 622499829541012 T^{13} + 5043036265285463 T^{14} + 33312781382982570 T^{15} + 234983796953410025 T^{16} + 1316173441529599771 T^{17} + 8003993965022902250 T^{18} + 36526984829075362228 T^{19} + \)\(18\!\cdots\!14\)\( T^{20} + \)\(63\!\cdots\!64\)\( T^{21} + \)\(26\!\cdots\!15\)\( T^{22} + \)\(53\!\cdots\!33\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 6 T + 440 T^{2} + 951 T^{3} + 96092 T^{4} - 58657 T^{5} + 14918598 T^{6} - 40123203 T^{7} + 1874503078 T^{8} - 7242827855 T^{9} + 200997151216 T^{10} - 842990815480 T^{11} + 18428438400077 T^{12} - 74289209148314 T^{13} + 1428760173206436 T^{14} - 5274533849530294 T^{15} + 92897757974788157 T^{16} - 301715685759262280 T^{17} + 5107675488609754096 T^{18} - 13067722600231372105 T^{19} + \)\(24\!\cdots\!38\)\( T^{20} - \)\(36\!\cdots\!73\)\( T^{21} + \)\(96\!\cdots\!78\)\( T^{22} - \)\(26\!\cdots\!67\)\( T^{23} + \)\(31\!\cdots\!92\)\( T^{24} + \)\(21\!\cdots\!21\)\( T^{25} + \)\(72\!\cdots\!40\)\( T^{26} + \)\(69\!\cdots\!66\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))(\( 1 - 26 T + 1007 T^{2} - 19849 T^{3} + 446241 T^{4} - 7194988 T^{5} + 120762359 T^{6} - 1665305267 T^{7} + 22992215838 T^{8} - 279200807408 T^{9} + 3339644446146 T^{10} - 36445396630849 T^{11} + 389968744645311 T^{12} - 3880328825560916 T^{13} + 37900927653943305 T^{14} - 347306265647546659 T^{15} + 3132356239603608570 T^{16} - 26587811659247253100 T^{17} + \)\(22\!\cdots\!70\)\( T^{18} - \)\(17\!\cdots\!19\)\( T^{19} + \)\(13\!\cdots\!55\)\( T^{20} - \)\(98\!\cdots\!96\)\( T^{21} + \)\(70\!\cdots\!61\)\( T^{22} - \)\(46\!\cdots\!29\)\( T^{23} + \)\(30\!\cdots\!86\)\( T^{24} - \)\(18\!\cdots\!88\)\( T^{25} + \)\(10\!\cdots\!78\)\( T^{26} - \)\(54\!\cdots\!67\)\( T^{27} + \)\(27\!\cdots\!89\)\( T^{28} - \)\(11\!\cdots\!08\)\( T^{29} + \)\(51\!\cdots\!51\)\( T^{30} - \)\(16\!\cdots\!69\)\( T^{31} + \)\(59\!\cdots\!57\)\( T^{32} - \)\(10\!\cdots\!46\)\( T^{33} + \)\(29\!\cdots\!91\)\( T^{34} \))(\( 1 - 49 T + 1754 T^{2} - 44561 T^{3} + 953082 T^{4} - 17033763 T^{5} + 270400262 T^{6} - 3801050320 T^{7} + 48928829721 T^{8} - 575873040154 T^{9} + 6344317178214 T^{10} - 65347156270492 T^{11} + 641067107467026 T^{12} - 5979678872761462 T^{13} + 53884285367136673 T^{14} - 468469307668254768 T^{15} + 3995212095000677909 T^{16} - 33464611033845211212 T^{17} + \)\(28\!\cdots\!24\)\( T^{18} - \)\(23\!\cdots\!94\)\( T^{19} + \)\(19\!\cdots\!04\)\( T^{20} - \)\(16\!\cdots\!92\)\( T^{21} + \)\(14\!\cdots\!99\)\( T^{22} - \)\(11\!\cdots\!08\)\( T^{23} + \)\(97\!\cdots\!23\)\( T^{24} - \)\(76\!\cdots\!02\)\( T^{25} + \)\(58\!\cdots\!66\)\( T^{26} - \)\(42\!\cdots\!12\)\( T^{27} + \)\(29\!\cdots\!34\)\( T^{28} - \)\(18\!\cdots\!54\)\( T^{29} + \)\(11\!\cdots\!91\)\( T^{30} - \)\(62\!\cdots\!20\)\( T^{31} + \)\(31\!\cdots\!82\)\( T^{32} - \)\(14\!\cdots\!03\)\( T^{33} + \)\(55\!\cdots\!82\)\( T^{34} - \)\(18\!\cdots\!81\)\( T^{35} + \)\(51\!\cdots\!14\)\( T^{36} - \)\(10\!\cdots\!89\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))
$73$ (\( 1 + 12 T + 130 T^{2} + 876 T^{3} + 5329 T^{4} \))(\( 1 - 8 T + 82 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 162 T^{2} + 697 T^{3} + 13533 T^{4} + 50881 T^{5} + 863298 T^{6} + 778034 T^{7} + 28398241 T^{8} \))(\( 1 + 9 T + 159 T^{2} + 1799 T^{3} + 21272 T^{4} + 138124 T^{5} + 1552856 T^{6} + 9586871 T^{7} + 61853703 T^{8} + 255584169 T^{9} + 2073071593 T^{10} \))(\( 1 - 3 T + 283 T^{2} - 953 T^{3} + 35808 T^{4} - 107372 T^{5} + 2613984 T^{6} - 5078537 T^{7} + 110091811 T^{8} - 85194723 T^{9} + 2073071593 T^{10} \))(\( 1 - 6 T + 155 T^{2} - 1180 T^{3} + 23493 T^{4} - 140690 T^{5} + 1759919 T^{6} - 10270370 T^{7} + 125194197 T^{8} - 459040060 T^{9} + 4401727355 T^{10} - 12438429558 T^{11} + 151334226289 T^{12} \))(\( 1 + 7 T + 277 T^{2} + 2034 T^{3} + 44471 T^{4} + 290456 T^{5} + 4664818 T^{6} + 26135103 T^{7} + 340531714 T^{8} + 1547840024 T^{9} + 17299975007 T^{10} + 57762022194 T^{11} + 574240831261 T^{12} + 1059339584023 T^{13} + 11047398519097 T^{14} \))(\( 1 + 31 T + 975 T^{2} + 18708 T^{3} + 343818 T^{4} + 4818451 T^{5} + 64286029 T^{6} + 702746801 T^{7} + 7317435477 T^{8} + 64040954134 T^{9} + 534172789821 T^{10} + 3744937702529 T^{11} + 25008358143493 T^{12} + 136835532744691 T^{13} + 712759328962074 T^{14} + 2831160705414612 T^{15} + 10771213556119575 T^{16} + 25000262848716511 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 8 T + 635 T^{2} + 4195 T^{3} + 189057 T^{4} + 1034616 T^{5} + 35458617 T^{6} + 161383993 T^{7} + 4745268235 T^{8} + 18194832974 T^{9} + 485587865335 T^{10} + 1612273953570 T^{11} + 39501142360716 T^{12} + 117695998610610 T^{13} + 2587697734370215 T^{14} + 7078099339046558 T^{15} + 134757270947174635 T^{16} + 334560571453210849 T^{17} + 5366102368972982313 T^{18} + 11429815266234061752 T^{19} + \)\(15\!\cdots\!17\)\( T^{20} + \)\(24\!\cdots\!35\)\( T^{21} + \)\(27\!\cdots\!15\)\( T^{22} + \)\(25\!\cdots\!16\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 5 T + 509 T^{2} - 2246 T^{3} + 131047 T^{4} - 543096 T^{5} + 22785570 T^{6} - 92847232 T^{7} + 3016491029 T^{8} - 12396170995 T^{9} + 324499520677 T^{10} - 1340853514487 T^{11} + 29471947693033 T^{12} - 118946765135011 T^{13} + 2308572431873909 T^{14} - 8683113854855803 T^{15} + 157056009256172857 T^{16} - 521614811645189279 T^{17} + 9215215592569929157 T^{18} - 25698149951705045035 T^{19} + \)\(45\!\cdots\!81\)\( T^{20} - \)\(10\!\cdots\!04\)\( T^{21} + \)\(18\!\cdots\!70\)\( T^{22} - \)\(31\!\cdots\!48\)\( T^{23} + \)\(56\!\cdots\!03\)\( T^{24} - \)\(70\!\cdots\!42\)\( T^{25} + \)\(11\!\cdots\!89\)\( T^{26} - \)\(83\!\cdots\!65\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( 1 - 8 T + 581 T^{2} - 3373 T^{3} + 161686 T^{4} - 646934 T^{5} + 29717152 T^{6} - 74294097 T^{7} + 4174267013 T^{8} - 5314756935 T^{9} + 484566969456 T^{10} - 144409053834 T^{11} + 48456663741423 T^{12} + 21161696177878 T^{13} + 4284608404951523 T^{14} + 3849114453674043 T^{15} + 341995284726843055 T^{16} + 352083483795091715 T^{17} + 24965655785059543015 T^{18} + 20511930923628975147 T^{19} + \)\(16\!\cdots\!91\)\( T^{20} + \)\(60\!\cdots\!98\)\( T^{21} + \)\(10\!\cdots\!39\)\( T^{22} - \)\(21\!\cdots\!26\)\( T^{23} + \)\(53\!\cdots\!32\)\( T^{24} - \)\(42\!\cdots\!35\)\( T^{25} + \)\(24\!\cdots\!69\)\( T^{26} - \)\(31\!\cdots\!53\)\( T^{27} + \)\(93\!\cdots\!04\)\( T^{28} - \)\(14\!\cdots\!14\)\( T^{29} + \)\(27\!\cdots\!38\)\( T^{30} - \)\(41\!\cdots\!57\)\( T^{31} + \)\(51\!\cdots\!17\)\( T^{32} - \)\(52\!\cdots\!88\)\( T^{33} + \)\(47\!\cdots\!53\)\( T^{34} \))(\( 1 - 16 T + 991 T^{2} - 14609 T^{3} + 478441 T^{4} - 6556476 T^{5} + 150401605 T^{6} - 1923830006 T^{7} + 34631637591 T^{8} - 413916478771 T^{9} + 6217974600238 T^{10} - 69391003639581 T^{11} + 903552039709648 T^{12} - 9399790238999045 T^{13} + 108765125899905461 T^{14} - 1052581583047709299 T^{15} + 11004629424568627428 T^{16} - 98818147534782712689 T^{17} + \)\(94\!\cdots\!88\)\( T^{18} - \)\(78\!\cdots\!64\)\( T^{19} + \)\(68\!\cdots\!24\)\( T^{20} - \)\(52\!\cdots\!81\)\( T^{21} + \)\(42\!\cdots\!76\)\( T^{22} - \)\(29\!\cdots\!59\)\( T^{23} + \)\(22\!\cdots\!73\)\( T^{24} - \)\(14\!\cdots\!05\)\( T^{25} + \)\(99\!\cdots\!56\)\( T^{26} - \)\(55\!\cdots\!61\)\( T^{27} + \)\(36\!\cdots\!94\)\( T^{28} - \)\(17\!\cdots\!79\)\( T^{29} + \)\(10\!\cdots\!07\)\( T^{30} - \)\(44\!\cdots\!26\)\( T^{31} + \)\(25\!\cdots\!65\)\( T^{32} - \)\(80\!\cdots\!84\)\( T^{33} + \)\(42\!\cdots\!37\)\( T^{34} - \)\(95\!\cdots\!49\)\( T^{35} + \)\(47\!\cdots\!23\)\( T^{36} - \)\(55\!\cdots\!04\)\( T^{37} + \)\(25\!\cdots\!37\)\( T^{38} \))
$79$ (\( 1 - 24 T + 289 T^{2} - 1896 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 163 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 - 21 T + 296 T^{2} - 2355 T^{3} + 21235 T^{4} - 186045 T^{5} + 1847336 T^{6} - 10353819 T^{7} + 38950081 T^{8} \))(\( 1 - 29 T + 426 T^{2} - 2590 T^{3} - 4859 T^{4} + 200521 T^{5} - 383861 T^{6} - 16164190 T^{7} + 210034614 T^{8} - 1129552349 T^{9} + 3077056399 T^{10} \))(\( 1 + 35 T + 848 T^{2} + 13730 T^{3} + 176739 T^{4} + 1738679 T^{5} + 13962381 T^{6} + 85688930 T^{7} + 418097072 T^{8} + 1363252835 T^{9} + 3077056399 T^{10} \))(\( 1 + 28 T + 627 T^{2} + 9560 T^{3} + 125279 T^{4} + 1350546 T^{5} + 12950923 T^{6} + 106693134 T^{7} + 781866239 T^{8} + 4713452840 T^{9} + 24421700787 T^{10} + 86157579172 T^{11} + 243087455521 T^{12} \))(\( 1 - 30 T + 864 T^{2} - 15277 T^{3} + 251870 T^{4} - 3126597 T^{5} + 36178295 T^{6} - 332923983 T^{7} + 2858085305 T^{8} - 19513091877 T^{9} + 124181732930 T^{10} - 595040387437 T^{11} + 2658576728736 T^{12} - 7292623665630 T^{13} + 19203908986159 T^{14} \))(\( 1 + 4 T + 497 T^{2} + 1179 T^{3} + 116109 T^{4} + 148892 T^{5} + 17277791 T^{6} + 11543951 T^{7} + 1835589466 T^{8} + 818930763 T^{9} + 145011567814 T^{10} + 72045798191 T^{11} + 8518624796849 T^{12} + 5799355460252 T^{13} + 357273941431491 T^{14} + 286600110059259 T^{15} + 9544342766121023 T^{16} + 6068435239626244 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 37 T + 1170 T^{2} + 26323 T^{3} + 524294 T^{4} + 8813126 T^{5} + 134846261 T^{6} + 1837624125 T^{7} + 23158328723 T^{8} + 266053942831 T^{9} + 2851382404096 T^{10} + 28152678898468 T^{11} + 260296843460799 T^{12} + 2224061632978972 T^{13} + 17795477583963136 T^{14} + 131174969919453409 T^{15} + 902018779585476563 T^{16} + 5654473072788025875 T^{17} + 32779434473010656981 T^{18} + \)\(16\!\cdots\!34\)\( T^{19} + \)\(79\!\cdots\!34\)\( T^{20} + \)\(31\!\cdots\!37\)\( T^{21} + \)\(11\!\cdots\!70\)\( T^{22} + \)\(27\!\cdots\!23\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 + 56 T + 2178 T^{2} + 61573 T^{3} + 1444638 T^{4} + 28678155 T^{5} + 502092413 T^{6} + 7837978292 T^{7} + 111253380003 T^{8} + 1445274307857 T^{9} + 17375055426959 T^{10} + 193997565121459 T^{11} + 2024946369538101 T^{12} + 19782596308792413 T^{13} + 181527502415863181 T^{14} + 1562825108394600627 T^{15} + 12637690292287288341 T^{16} + 95648365509919023901 T^{17} + \)\(67\!\cdots\!79\)\( T^{18} + \)\(44\!\cdots\!43\)\( T^{19} + \)\(27\!\cdots\!63\)\( T^{20} + \)\(15\!\cdots\!28\)\( T^{21} + \)\(76\!\cdots\!93\)\( T^{22} + \)\(34\!\cdots\!45\)\( T^{23} + \)\(13\!\cdots\!38\)\( T^{24} + \)\(46\!\cdots\!67\)\( T^{25} + \)\(12\!\cdots\!98\)\( T^{26} + \)\(26\!\cdots\!84\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 + 33 T + 1353 T^{2} + 32406 T^{3} + 807998 T^{4} + 15511805 T^{5} + 295820068 T^{6} + 4788030417 T^{7} + 75771882238 T^{8} + 1064743445583 T^{9} + 14544158476409 T^{10} + 180674985423206 T^{11} + 2177306441772962 T^{12} + 24183639832001318 T^{13} + 260411110563583929 T^{14} + 2603558555285058439 T^{15} + 25231939994033822625 T^{16} + \)\(22\!\cdots\!01\)\( T^{17} + \)\(19\!\cdots\!75\)\( T^{18} + \)\(16\!\cdots\!99\)\( T^{19} + \)\(12\!\cdots\!31\)\( T^{20} + \)\(94\!\cdots\!58\)\( T^{21} + \)\(66\!\cdots\!38\)\( T^{22} + \)\(43\!\cdots\!26\)\( T^{23} + \)\(27\!\cdots\!31\)\( T^{24} + \)\(16\!\cdots\!63\)\( T^{25} + \)\(90\!\cdots\!22\)\( T^{26} + \)\(45\!\cdots\!17\)\( T^{27} + \)\(22\!\cdots\!72\)\( T^{28} + \)\(91\!\cdots\!05\)\( T^{29} + \)\(37\!\cdots\!22\)\( T^{30} + \)\(11\!\cdots\!86\)\( T^{31} + \)\(39\!\cdots\!47\)\( T^{32} + \)\(75\!\cdots\!93\)\( T^{33} + \)\(18\!\cdots\!59\)\( T^{34} \))(\( 1 - 33 T + 856 T^{2} - 18633 T^{3} + 356050 T^{4} - 6081544 T^{5} + 96300949 T^{6} - 1420112580 T^{7} + 19695300700 T^{8} - 259010414059 T^{9} + 3246108938509 T^{10} - 38891882965358 T^{11} + 447325591962679 T^{12} - 4949749130109503 T^{13} + 52789416862330412 T^{14} - 543624833729230867 T^{15} + 5412536814779891262 T^{16} - 52123926589365922156 T^{17} + \)\(48\!\cdots\!99\)\( T^{18} - \)\(43\!\cdots\!01\)\( T^{19} + \)\(38\!\cdots\!21\)\( T^{20} - \)\(32\!\cdots\!96\)\( T^{21} + \)\(26\!\cdots\!18\)\( T^{22} - \)\(21\!\cdots\!27\)\( T^{23} + \)\(16\!\cdots\!88\)\( T^{24} - \)\(12\!\cdots\!63\)\( T^{25} + \)\(85\!\cdots\!61\)\( T^{26} - \)\(59\!\cdots\!38\)\( T^{27} + \)\(38\!\cdots\!71\)\( T^{28} - \)\(24\!\cdots\!59\)\( T^{29} + \)\(14\!\cdots\!00\)\( T^{30} - \)\(83\!\cdots\!80\)\( T^{31} + \)\(44\!\cdots\!11\)\( T^{32} - \)\(22\!\cdots\!64\)\( T^{33} + \)\(10\!\cdots\!50\)\( T^{34} - \)\(42\!\cdots\!93\)\( T^{35} + \)\(15\!\cdots\!04\)\( T^{36} - \)\(47\!\cdots\!13\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))
$83$ (\( 1 + 21 T + 247 T^{2} + 1743 T^{3} + 6889 T^{4} \))(\( 1 - 17 T + 207 T^{2} - 1411 T^{3} + 6889 T^{4} \))(\( 1 - T + 122 T^{2} - 297 T^{3} + 12743 T^{4} - 24651 T^{5} + 840458 T^{6} - 571787 T^{7} + 47458321 T^{8} \))(\( 1 - 9 T + 416 T^{2} - 2882 T^{3} + 69119 T^{4} - 354626 T^{5} + 5736877 T^{6} - 19854098 T^{7} + 237863392 T^{8} - 427124889 T^{9} + 3939040643 T^{10} \))(\( 1 + 3 T + 126 T^{2} + 320 T^{3} + 16065 T^{4} + 60618 T^{5} + 1333395 T^{6} + 2204480 T^{7} + 72045162 T^{8} + 142374963 T^{9} + 3939040643 T^{10} \))(\( 1 + 14 T + 246 T^{2} + 1978 T^{3} + 28727 T^{4} + 273460 T^{5} + 3322100 T^{6} + 22697180 T^{7} + 197900303 T^{8} + 1130994686 T^{9} + 11674746966 T^{10} + 55146569002 T^{11} + 326940373369 T^{12} \))(\( 1 + 13 T + 485 T^{2} + 5360 T^{3} + 109330 T^{4} + 996823 T^{5} + 14416686 T^{6} + 106582888 T^{7} + 1196584938 T^{8} + 6867113647 T^{9} + 62513472710 T^{10} + 254376600560 T^{11} + 1910434711855 T^{12} + 4250224853797 T^{13} + 27136050989627 T^{14} \))(\( 1 - 22 T + 697 T^{2} - 10747 T^{3} + 202141 T^{4} - 2458553 T^{5} + 34682944 T^{6} - 349803141 T^{7} + 4025119603 T^{8} - 34396711778 T^{9} + 334084927049 T^{10} - 2409793838349 T^{11} + 19831256500928 T^{12} - 116678797469513 T^{13} + 796241614616663 T^{14} - 3513628192596643 T^{15} + 18913827539770019 T^{16} - 49550429107058902 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 30 T + 998 T^{2} + 19521 T^{3} + 386595 T^{4} + 5774396 T^{5} + 86624835 T^{6} + 1074210737 T^{7} + 13455746937 T^{8} + 145378443767 T^{9} + 1590934546399 T^{10} + 15272101715923 T^{11} + 148277925367526 T^{12} + 1267584442421609 T^{13} + 10959948090142711 T^{14} + 83125504226201629 T^{15} + 638587157430912777 T^{16} + 4231359752189983891 T^{17} + 28321155897928019115 T^{18} + \)\(15\!\cdots\!92\)\( T^{19} + \)\(87\!\cdots\!95\)\( T^{20} + \)\(36\!\cdots\!63\)\( T^{21} + \)\(15\!\cdots\!02\)\( T^{22} + \)\(38\!\cdots\!10\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 28 T + 1194 T^{2} - 24258 T^{3} + 597660 T^{4} - 9577457 T^{5} + 174046785 T^{6} - 2306100582 T^{7} + 33960396380 T^{8} - 384505903734 T^{9} + 4841020526267 T^{10} - 48162250372593 T^{11} + 538120608580119 T^{12} - 4819591768627718 T^{13} + 48926682521657972 T^{14} - 400026116796100594 T^{15} + 3707112872508439791 T^{16} - 27538548653793833691 T^{17} + \)\(22\!\cdots\!07\)\( T^{18} - \)\(15\!\cdots\!62\)\( T^{19} + \)\(11\!\cdots\!20\)\( T^{20} - \)\(62\!\cdots\!14\)\( T^{21} + \)\(39\!\cdots\!85\)\( T^{22} - \)\(17\!\cdots\!71\)\( T^{23} + \)\(92\!\cdots\!40\)\( T^{24} - \)\(31\!\cdots\!86\)\( T^{25} + \)\(12\!\cdots\!34\)\( T^{26} - \)\(24\!\cdots\!64\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 + 581 T^{2} + 182 T^{3} + 180307 T^{4} + 64291 T^{5} + 39429864 T^{6} + 10639717 T^{7} + 6767265501 T^{8} + 978598957 T^{9} + 963090953338 T^{10} + 30597338308 T^{11} + 117355310194685 T^{12} - 5664290130289 T^{13} + 12476694291222476 T^{14} - 1130794417610287 T^{15} + 1169345388231792369 T^{16} - 116200485002181054 T^{17} + 97055667223238766627 T^{18} - 7790042742917267143 T^{19} + \)\(71\!\cdots\!12\)\( T^{20} - \)\(26\!\cdots\!69\)\( T^{21} + \)\(46\!\cdots\!55\)\( T^{22} + \)\(10\!\cdots\!52\)\( T^{23} + \)\(26\!\cdots\!26\)\( T^{24} + \)\(22\!\cdots\!37\)\( T^{25} + \)\(12\!\cdots\!03\)\( T^{26} + \)\(16\!\cdots\!33\)\( T^{27} + \)\(50\!\cdots\!88\)\( T^{28} + \)\(68\!\cdots\!51\)\( T^{29} + \)\(15\!\cdots\!41\)\( T^{30} + \)\(13\!\cdots\!78\)\( T^{31} + \)\(35\!\cdots\!67\)\( T^{32} + \)\(42\!\cdots\!23\)\( T^{34} \))(\( 1 - 43 T + 1508 T^{2} - 37882 T^{3} + 840373 T^{4} - 15937851 T^{5} + 277958379 T^{6} - 4399409689 T^{7} + 65478186374 T^{8} - 909344821776 T^{9} + 12025890837761 T^{10} - 150600828649685 T^{11} + 1809506105787199 T^{12} - 20766729625407617 T^{13} + 229780959491279600 T^{14} - 2441594431390736045 T^{15} + 25091658027287709184 T^{16} - \)\(24\!\cdots\!05\)\( T^{17} + \)\(23\!\cdots\!83\)\( T^{18} - \)\(22\!\cdots\!06\)\( T^{19} + \)\(19\!\cdots\!89\)\( T^{20} - \)\(17\!\cdots\!45\)\( T^{21} + \)\(14\!\cdots\!08\)\( T^{22} - \)\(11\!\cdots\!45\)\( T^{23} + \)\(90\!\cdots\!00\)\( T^{24} - \)\(67\!\cdots\!73\)\( T^{25} + \)\(49\!\cdots\!73\)\( T^{26} - \)\(33\!\cdots\!85\)\( T^{27} + \)\(22\!\cdots\!83\)\( T^{28} - \)\(14\!\cdots\!24\)\( T^{29} + \)\(84\!\cdots\!58\)\( T^{30} - \)\(47\!\cdots\!29\)\( T^{31} + \)\(24\!\cdots\!77\)\( T^{32} - \)\(11\!\cdots\!79\)\( T^{33} + \)\(51\!\cdots\!11\)\( T^{34} - \)\(19\!\cdots\!42\)\( T^{35} + \)\(63\!\cdots\!84\)\( T^{36} - \)\(15\!\cdots\!87\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))
$89$ (\( 1 + 12 T + 97 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 53 T^{2} + 7921 T^{4} \))(\( 1 - 5 T + 257 T^{2} - 1080 T^{3} + 32393 T^{4} - 96120 T^{5} + 2035697 T^{6} - 3524845 T^{7} + 62742241 T^{8} \))(\( 1 + 9 T + 302 T^{2} + 1778 T^{3} + 37739 T^{4} + 172799 T^{5} + 3358771 T^{6} + 14083538 T^{7} + 212900638 T^{8} + 564680169 T^{9} + 5584059449 T^{10} \))(\( 1 - 15 T + 450 T^{2} - 4826 T^{3} + 79871 T^{4} - 621321 T^{5} + 7108519 T^{6} - 38226746 T^{7} + 317236050 T^{8} - 941133615 T^{9} + 5584059449 T^{10} \))(\( 1 - 18 T + 339 T^{2} - 2768 T^{3} + 23317 T^{4} - 2718 T^{5} + 223443 T^{6} - 241902 T^{7} + 184693957 T^{8} - 1951354192 T^{9} + 21269619699 T^{10} - 100513070082 T^{11} + 496981290961 T^{12} \))(\( 1 + 109 T^{2} - 211 T^{3} + 18778 T^{4} + 41946 T^{5} + 1597555 T^{6} + 597701 T^{7} + 142182395 T^{8} + 332254266 T^{9} + 13237907882 T^{10} - 13238612851 T^{11} + 608662479941 T^{12} + 44231334895529 T^{14} \))(\( 1 + 36 T + 1250 T^{2} + 27317 T^{3} + 556616 T^{4} + 8813319 T^{5} + 130176166 T^{6} + 1596565568 T^{7} + 18315953568 T^{8} + 178565859993 T^{9} + 1630119867552 T^{10} + 12646395864128 T^{11} + 91770161568854 T^{12} + 552967384707879 T^{13} + 3108176834264584 T^{14} + 13576037925181637 T^{15} + 55289168619411250 T^{16} + 141717197005274916 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 3 T + 695 T^{2} - 656 T^{3} + 229968 T^{4} + 161447 T^{5} + 49555045 T^{6} + 88908024 T^{7} + 7925590920 T^{8} + 18070410375 T^{9} + 993701773490 T^{10} + 2286483477062 T^{11} + 99101678422277 T^{12} + 203497029458518 T^{13} + 7871111747814290 T^{14} + 12739079131653375 T^{15} + 497269335570051720 T^{16} + 496467691509118776 T^{17} + 24627930237730448245 T^{18} + 7141016324878470463 T^{19} + \)\(90\!\cdots\!08\)\( T^{20} - \)\(22\!\cdots\!04\)\( T^{21} + \)\(21\!\cdots\!95\)\( T^{22} - \)\(83\!\cdots\!67\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 24 T + 669 T^{2} + 10517 T^{3} + 185238 T^{4} + 2263722 T^{5} + 31585183 T^{6} + 325130743 T^{7} + 4027076643 T^{8} + 37730303200 T^{9} + 449488705240 T^{10} + 4053222457673 T^{11} + 47081758898733 T^{12} + 407899267298090 T^{13} + 4474499931731100 T^{14} + 36303034789530010 T^{15} + 372934612236864093 T^{16} + 2857396182763277137 T^{17} + 28201928670946042840 T^{18} + \)\(21\!\cdots\!00\)\( T^{19} + \)\(20\!\cdots\!23\)\( T^{20} + \)\(14\!\cdots\!47\)\( T^{21} + \)\(12\!\cdots\!23\)\( T^{22} + \)\(79\!\cdots\!98\)\( T^{23} + \)\(57\!\cdots\!38\)\( T^{24} + \)\(29\!\cdots\!13\)\( T^{25} + \)\(16\!\cdots\!49\)\( T^{26} + \)\(52\!\cdots\!56\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( 1 - 11 T + 1018 T^{2} - 10217 T^{3} + 499889 T^{4} - 4640361 T^{5} + 158874258 T^{6} - 1379474804 T^{7} + 36937331775 T^{8} - 302341492178 T^{9} + 6716122844629 T^{10} - 51998242411620 T^{11} + 994168111675971 T^{12} - 7269598825192290 T^{13} + 122782314292295471 T^{14} - 842720446308890714 T^{15} + 12831305239642471183 T^{16} - 81825398892517969620 T^{17} + \)\(11\!\cdots\!87\)\( T^{18} - \)\(66\!\cdots\!94\)\( T^{19} + \)\(86\!\cdots\!99\)\( T^{20} - \)\(45\!\cdots\!90\)\( T^{21} + \)\(55\!\cdots\!79\)\( T^{22} - \)\(25\!\cdots\!20\)\( T^{23} + \)\(29\!\cdots\!41\)\( T^{24} - \)\(11\!\cdots\!18\)\( T^{25} + \)\(12\!\cdots\!75\)\( T^{26} - \)\(43\!\cdots\!04\)\( T^{27} + \)\(44\!\cdots\!62\)\( T^{28} - \)\(11\!\cdots\!81\)\( T^{29} + \)\(10\!\cdots\!41\)\( T^{30} - \)\(19\!\cdots\!97\)\( T^{31} + \)\(17\!\cdots\!82\)\( T^{32} - \)\(17\!\cdots\!71\)\( T^{33} + \)\(13\!\cdots\!29\)\( T^{34} \))(\( 1 - 3 T + 819 T^{2} - 4460 T^{3} + 342244 T^{4} - 2607357 T^{5} + 98529533 T^{6} - 918753610 T^{7} + 22068299362 T^{8} - 229633703147 T^{9} + 4084817881958 T^{10} - 44236481470254 T^{11} + 643940245028507 T^{12} - 6898431655878476 T^{13} + 87622815454377775 T^{14} - 898527223206629076 T^{15} + 10341643988289122401 T^{16} - 99733165433583186620 T^{17} + \)\(10\!\cdots\!97\)\( T^{18} - \)\(95\!\cdots\!00\)\( T^{19} + \)\(94\!\cdots\!33\)\( T^{20} - \)\(78\!\cdots\!20\)\( T^{21} + \)\(72\!\cdots\!69\)\( T^{22} - \)\(56\!\cdots\!16\)\( T^{23} + \)\(48\!\cdots\!75\)\( T^{24} - \)\(34\!\cdots\!36\)\( T^{25} + \)\(28\!\cdots\!03\)\( T^{26} - \)\(17\!\cdots\!74\)\( T^{27} + \)\(14\!\cdots\!22\)\( T^{28} - \)\(71\!\cdots\!47\)\( T^{29} + \)\(61\!\cdots\!18\)\( T^{30} - \)\(22\!\cdots\!10\)\( T^{31} + \)\(21\!\cdots\!77\)\( T^{32} - \)\(51\!\cdots\!37\)\( T^{33} + \)\(59\!\cdots\!56\)\( T^{34} - \)\(69\!\cdots\!60\)\( T^{35} + \)\(11\!\cdots\!51\)\( T^{36} - \)\(36\!\cdots\!43\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))
$97$ (\( 1 + 28 T + 377 T^{2} + 2716 T^{3} + 9409 T^{4} \))(\( 1 - 16 T + 213 T^{2} - 1552 T^{3} + 9409 T^{4} \))(\( 1 - 6 T + 308 T^{2} - 1804 T^{3} + 41253 T^{4} - 174988 T^{5} + 2897972 T^{6} - 5476038 T^{7} + 88529281 T^{8} \))(\( 1 + 6 T + 392 T^{2} + 1594 T^{3} + 66059 T^{4} + 196320 T^{5} + 6407723 T^{6} + 14997946 T^{7} + 357767816 T^{8} + 531175686 T^{9} + 8587340257 T^{10} \))(\( 1 + 2 T + 132 T^{2} - 318 T^{3} + 18695 T^{4} + 9736 T^{5} + 1813415 T^{6} - 2992062 T^{7} + 120472836 T^{8} + 177058562 T^{9} + 8587340257 T^{10} \))(\( 1 - 16 T + 258 T^{2} - 1728 T^{3} + 15615 T^{4} + 49936 T^{5} - 330564 T^{6} + 4843792 T^{7} + 146921535 T^{8} - 1577098944 T^{9} + 22840554498 T^{10} - 137397444112 T^{11} + 832972004929 T^{12} \))(\( 1 + 2 T + 455 T^{2} - 86 T^{3} + 89144 T^{4} - 192034 T^{5} + 10939992 T^{6} - 31982204 T^{7} + 1061179224 T^{8} - 1806847906 T^{9} + 81359321912 T^{10} - 7613518166 T^{11} + 3907239816935 T^{12} + 1665944009858 T^{13} + 80798284478113 T^{14} \))(\( 1 + 38 T + 1014 T^{2} + 20302 T^{3} + 362890 T^{4} + 5556782 T^{5} + 76897379 T^{6} + 945841020 T^{7} + 10761247144 T^{8} + 110399206676 T^{9} + 1043840972968 T^{10} + 8899418157180 T^{11} + 70182161584067 T^{12} + 491937915133742 T^{13} + 3116259905862730 T^{14} + 16910997644068558 T^{15} + 81929460460806582 T^{16} + 297822476586324518 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 4 T + 705 T^{2} + 2332 T^{3} + 244683 T^{4} + 665112 T^{5} + 55974764 T^{6} + 126126264 T^{7} + 9477471873 T^{8} + 18038171780 T^{9} + 1258847536915 T^{10} + 2084337404684 T^{11} + 135161661133350 T^{12} + 202180728254348 T^{13} + 11844496474833235 T^{14} + 16462952352967940 T^{15} + 839033770614413313 T^{16} + 1083089144312209848 T^{17} + 46625411394507611756 T^{18} + 53739908585806693656 T^{19} + \)\(19\!\cdots\!63\)\( T^{20} + \)\(17\!\cdots\!44\)\( T^{21} + \)\(51\!\cdots\!45\)\( T^{22} + \)\(28\!\cdots\!12\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 6 T + 832 T^{2} - 5918 T^{3} + 341876 T^{4} - 2755486 T^{5} + 92593566 T^{6} - 810972134 T^{7} + 18572514318 T^{8} - 169569347650 T^{9} + 2931193224296 T^{10} - 26741162517482 T^{11} + 376439434844093 T^{12} - 3283902645684332 T^{13} + 40023991828359028 T^{14} - 318538556631380204 T^{15} + 3541918642448071037 T^{16} - 24405937018317849386 T^{17} + \)\(25\!\cdots\!76\)\( T^{18} - \)\(14\!\cdots\!50\)\( T^{19} + \)\(15\!\cdots\!22\)\( T^{20} - \)\(65\!\cdots\!42\)\( T^{21} + \)\(72\!\cdots\!26\)\( T^{22} - \)\(20\!\cdots\!62\)\( T^{23} + \)\(25\!\cdots\!24\)\( T^{24} - \)\(42\!\cdots\!54\)\( T^{25} + \)\(57\!\cdots\!12\)\( T^{26} - \)\(40\!\cdots\!62\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 + 10 T + 907 T^{2} + 8664 T^{3} + 415183 T^{4} + 3860446 T^{5} + 127714355 T^{6} + 1170394080 T^{7} + 29623108956 T^{8} + 268520719860 T^{9} + 5502372876200 T^{10} + 49124502273872 T^{11} + 847939461439269 T^{12} + 7377586202846146 T^{13} + 110804220390412409 T^{14} + 924869826743967992 T^{15} + 12437415583741272176 T^{16} + 97631790166212328132 T^{17} + \)\(12\!\cdots\!72\)\( T^{18} + \)\(87\!\cdots\!28\)\( T^{19} + \)\(10\!\cdots\!57\)\( T^{20} + \)\(65\!\cdots\!26\)\( T^{21} + \)\(72\!\cdots\!33\)\( T^{22} + \)\(40\!\cdots\!88\)\( T^{23} + \)\(44\!\cdots\!00\)\( T^{24} + \)\(21\!\cdots\!60\)\( T^{25} + \)\(22\!\cdots\!52\)\( T^{26} + \)\(86\!\cdots\!20\)\( T^{27} + \)\(91\!\cdots\!15\)\( T^{28} + \)\(26\!\cdots\!86\)\( T^{29} + \)\(27\!\cdots\!91\)\( T^{30} + \)\(56\!\cdots\!16\)\( T^{31} + \)\(57\!\cdots\!51\)\( T^{32} + \)\(61\!\cdots\!10\)\( T^{33} + \)\(59\!\cdots\!37\)\( T^{34} \))(\( 1 - 8 T + 890 T^{2} - 6082 T^{3} + 385725 T^{4} - 2233764 T^{5} + 110223871 T^{6} - 535057282 T^{7} + 23729758344 T^{8} - 95665077484 T^{9} + 4158695895895 T^{10} - 13887010827068 T^{11} + 622510038322209 T^{12} - 1733297928812820 T^{13} + 81941954371299436 T^{14} - 193608012338911838 T^{15} + 9652566563722421324 T^{16} - 20012195963743566420 T^{17} + \)\(10\!\cdots\!09\)\( T^{18} - \)\(19\!\cdots\!92\)\( T^{19} + \)\(99\!\cdots\!73\)\( T^{20} - \)\(18\!\cdots\!80\)\( T^{21} + \)\(88\!\cdots\!52\)\( T^{22} - \)\(17\!\cdots\!78\)\( T^{23} + \)\(70\!\cdots\!52\)\( T^{24} - \)\(14\!\cdots\!80\)\( T^{25} + \)\(50\!\cdots\!17\)\( T^{26} - \)\(10\!\cdots\!48\)\( T^{27} + \)\(31\!\cdots\!15\)\( T^{28} - \)\(70\!\cdots\!16\)\( T^{29} + \)\(16\!\cdots\!32\)\( T^{30} - \)\(37\!\cdots\!62\)\( T^{31} + \)\(74\!\cdots\!67\)\( T^{32} - \)\(14\!\cdots\!16\)\( T^{33} + \)\(24\!\cdots\!25\)\( T^{34} - \)\(37\!\cdots\!22\)\( T^{35} + \)\(53\!\cdots\!30\)\( T^{36} - \)\(46\!\cdots\!12\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))
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