Properties

Label 2667.2
Level 2667
Weight 2
Dimension 184203
Nonzero newspaces 64
Sturm bound 1032192
Trace bound 8

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Defining parameters

Level: \( N \) = \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(1032192\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2667))\).

Total New Old
Modular forms 261072 186699 74373
Cusp forms 255025 184203 70822
Eisenstein series 6047 2496 3551

Trace form

\( 184203q + 9q^{2} - 245q^{3} - 487q^{4} + 6q^{5} - 255q^{6} - 619q^{7} + 9q^{8} - 257q^{9} + O(q^{10}) \) \( 184203q + 9q^{2} - 245q^{3} - 487q^{4} + 6q^{5} - 255q^{6} - 619q^{7} + 9q^{8} - 257q^{9} - 498q^{10} - 251q^{12} - 490q^{13} - 3q^{14} - 612q^{15} - 471q^{16} + 30q^{17} - 243q^{18} - 472q^{19} + 54q^{20} - 308q^{21} - 1200q^{22} + 24q^{23} - 243q^{24} - 483q^{25} + 42q^{26} - 257q^{27} - 657q^{28} + 18q^{29} - 246q^{30} - 484q^{31} + 57q^{32} - 252q^{33} - 462q^{34} + 6q^{35} - 605q^{36} - 470q^{37} + 72q^{38} - 238q^{39} - 402q^{40} + 78q^{41} - 294q^{42} - 1208q^{43} + 84q^{44} - 246q^{45} - 432q^{46} + 36q^{47} - 203q^{48} - 627q^{49} + 99q^{50} - 222q^{51} - 394q^{52} + 66q^{53} - 243q^{54} - 432q^{55} + 21q^{56} - 658q^{57} - 402q^{58} + 12q^{59} - 222q^{60} - 442q^{61} + 24q^{62} - 344q^{63} - 1147q^{64} + 72q^{65} - 216q^{66} - 432q^{67} + 114q^{68} - 228q^{69} - 576q^{70} + 96q^{71} - 243q^{72} - 370q^{73} + 138q^{74} - 191q^{75} - 364q^{76} + 36q^{77} - 600q^{78} - 420q^{79} + 198q^{80} - 233q^{81} - 414q^{82} + 84q^{83} - 302q^{84} - 1176q^{85} + 144q^{86} - 210q^{87} - 348q^{88} + 150q^{89} - 222q^{90} - 628q^{91} + 168q^{92} - 172q^{93} - 384q^{94} + 132q^{95} - 195q^{96} - 418q^{97} - 3q^{98} - 618q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2667))\)

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
2667.2.a \(\chi_{2667}(1, \cdot)\) 2667.2.a.a 1 1
2667.2.a.b 1
2667.2.a.c 1
2667.2.a.d 1
2667.2.a.e 1
2667.2.a.f 2
2667.2.a.g 2
2667.2.a.h 2
2667.2.a.i 2
2667.2.a.j 7
2667.2.a.k 11
2667.2.a.l 13
2667.2.a.m 14
2667.2.a.n 16
2667.2.a.o 16
2667.2.a.p 18
2667.2.a.q 19
2667.2.d \(\chi_{2667}(2414, \cdot)\) n/a 336 1
2667.2.e \(\chi_{2667}(1142, \cdot)\) n/a 256 1
2667.2.h \(\chi_{2667}(1777, \cdot)\) n/a 172 1
2667.2.i \(\chi_{2667}(361, \cdot)\) n/a 340 2
2667.2.j \(\chi_{2667}(382, \cdot)\) n/a 336 2
2667.2.k \(\chi_{2667}(781, \cdot)\) n/a 340 2
2667.2.l \(\chi_{2667}(400, \cdot)\) n/a 256 2
2667.2.o \(\chi_{2667}(743, \cdot)\) n/a 512 2
2667.2.p \(\chi_{2667}(146, \cdot)\) n/a 672 2
2667.2.q \(\chi_{2667}(1396, \cdot)\) n/a 340 2
2667.2.r \(\chi_{2667}(1417, \cdot)\) n/a 340 2
2667.2.s \(\chi_{2667}(997, \cdot)\) n/a 340 2
2667.2.z \(\chi_{2667}(401, \cdot)\) n/a 676 2
2667.2.ba \(\chi_{2667}(488, \cdot)\) n/a 676 2
2667.2.bb \(\chi_{2667}(509, \cdot)\) n/a 672 2
2667.2.bc \(\chi_{2667}(1544, \cdot)\) n/a 676 2
2667.2.bd \(\chi_{2667}(908, \cdot)\) n/a 676 2
2667.2.be \(\chi_{2667}(380, \cdot)\) n/a 676 2
2667.2.bn \(\chi_{2667}(1378, \cdot)\) n/a 344 2
2667.2.bo \(\chi_{2667}(64, \cdot)\) n/a 768 6
2667.2.bp \(\chi_{2667}(37, \cdot)\) n/a 1026 6
2667.2.bq \(\chi_{2667}(226, \cdot)\) n/a 1026 6
2667.2.br \(\chi_{2667}(22, \cdot)\) n/a 768 6
2667.2.bs \(\chi_{2667}(349, \cdot)\) n/a 1032 6
2667.2.bv \(\chi_{2667}(365, \cdot)\) n/a 1536 6
2667.2.bw \(\chi_{2667}(524, \cdot)\) n/a 2016 6
2667.2.bz \(\chi_{2667}(155, \cdot)\) n/a 1536 6
2667.2.ca \(\chi_{2667}(230, \cdot)\) n/a 2028 6
2667.2.cf \(\chi_{2667}(313, \cdot)\) n/a 1026 6
2667.2.ci \(\chi_{2667}(598, \cdot)\) n/a 1026 6
2667.2.cl \(\chi_{2667}(68, \cdot)\) n/a 2022 6
2667.2.cm \(\chi_{2667}(359, \cdot)\) n/a 2022 6
2667.2.cp \(\chi_{2667}(725, \cdot)\) n/a 2022 6
2667.2.cq \(\chi_{2667}(164, \cdot)\) n/a 2022 6
2667.2.cr \(\chi_{2667}(202, \cdot)\) n/a 1020 6
2667.2.cu \(\chi_{2667}(442, \cdot)\) n/a 1536 12
2667.2.cv \(\chi_{2667}(25, \cdot)\) n/a 2040 12
2667.2.cw \(\chi_{2667}(4, \cdot)\) n/a 2040 12
2667.2.cx \(\chi_{2667}(100, \cdot)\) n/a 2040 12
2667.2.cy \(\chi_{2667}(160, \cdot)\) n/a 2064 12
2667.2.dh \(\chi_{2667}(95, \cdot)\) n/a 4056 12
2667.2.di \(\chi_{2667}(122, \cdot)\) n/a 4056 12
2667.2.dj \(\chi_{2667}(137, \cdot)\) n/a 4056 12
2667.2.dk \(\chi_{2667}(131, \cdot)\) n/a 4056 12
2667.2.dl \(\chi_{2667}(38, \cdot)\) n/a 4056 12
2667.2.dm \(\chi_{2667}(305, \cdot)\) n/a 4056 12
2667.2.dt \(\chi_{2667}(40, \cdot)\) n/a 2040 12
2667.2.du \(\chi_{2667}(10, \cdot)\) n/a 2040 12
2667.2.dv \(\chi_{2667}(250, \cdot)\) n/a 2040 12
2667.2.dw \(\chi_{2667}(188, \cdot)\) n/a 4032 12
2667.2.dx \(\chi_{2667}(281, \cdot)\) n/a 3072 12
2667.2.ea \(\chi_{2667}(148, \cdot)\) n/a 4608 36
2667.2.eb \(\chi_{2667}(79, \cdot)\) n/a 6156 36
2667.2.ec \(\chi_{2667}(163, \cdot)\) n/a 6156 36
2667.2.ef \(\chi_{2667}(55, \cdot)\) n/a 6120 36
2667.2.eg \(\chi_{2667}(23, \cdot)\) n/a 12132 36
2667.2.eh \(\chi_{2667}(17, \cdot)\) n/a 12132 36
2667.2.ek \(\chi_{2667}(206, \cdot)\) n/a 12132 36
2667.2.el \(\chi_{2667}(86, \cdot)\) n/a 12132 36
2667.2.eo \(\chi_{2667}(220, \cdot)\) n/a 6156 36
2667.2.er \(\chi_{2667}(166, \cdot)\) n/a 6156 36
2667.2.ew \(\chi_{2667}(29, \cdot)\) n/a 9216 36
2667.2.ex \(\chi_{2667}(41, \cdot)\) n/a 12168 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2667))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2667)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(381))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(889))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T^{2} + 4 T^{4} \))(\( 1 - T - 2 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 7 T^{2} + 13 T^{3} + 28 T^{4} + 41 T^{5} + 73 T^{6} + 94 T^{7} + 146 T^{8} + 164 T^{9} + 224 T^{10} + 208 T^{11} + 224 T^{12} + 128 T^{13} + 128 T^{14} \))(\( 1 + 2 T + 7 T^{2} + 15 T^{3} + 38 T^{4} + 72 T^{5} + 145 T^{6} + 249 T^{7} + 435 T^{8} + 690 T^{9} + 1061 T^{10} + 1511 T^{11} + 2122 T^{12} + 2760 T^{13} + 3480 T^{14} + 3984 T^{15} + 4640 T^{16} + 4608 T^{17} + 4864 T^{18} + 3840 T^{19} + 3584 T^{20} + 2048 T^{21} + 2048 T^{22} \))(\( 1 - 4 T + 16 T^{2} - 43 T^{3} + 111 T^{4} - 238 T^{5} + 491 T^{6} - 905 T^{7} + 1619 T^{8} - 2672 T^{9} + 4312 T^{10} - 6552 T^{11} + 9792 T^{12} - 13944 T^{13} + 19584 T^{14} - 26208 T^{15} + 34496 T^{16} - 42752 T^{17} + 51808 T^{18} - 57920 T^{19} + 62848 T^{20} - 60928 T^{21} + 56832 T^{22} - 44032 T^{23} + 32768 T^{24} - 16384 T^{25} + 8192 T^{26} \))(\( 1 + 5 T + 19 T^{2} + 54 T^{3} + 136 T^{4} + 302 T^{5} + 627 T^{6} + 1213 T^{7} + 2245 T^{8} + 3945 T^{9} + 6666 T^{10} + 10741 T^{11} + 16698 T^{12} + 24876 T^{13} + 35892 T^{14} + 49752 T^{15} + 66792 T^{16} + 85928 T^{17} + 106656 T^{18} + 126240 T^{19} + 143680 T^{20} + 155264 T^{21} + 160512 T^{22} + 154624 T^{23} + 139264 T^{24} + 110592 T^{25} + 77824 T^{26} + 40960 T^{27} + 16384 T^{28} \))(\( 1 - 4 T + 14 T^{2} - 37 T^{3} + 88 T^{4} - 190 T^{5} + 381 T^{6} - 712 T^{7} + 1274 T^{8} - 2174 T^{9} + 3615 T^{10} - 5835 T^{11} + 9161 T^{12} - 14072 T^{13} + 21098 T^{14} - 30924 T^{15} + 44348 T^{16} - 61848 T^{17} + 84392 T^{18} - 112576 T^{19} + 146576 T^{20} - 186720 T^{21} + 231360 T^{22} - 278272 T^{23} + 326144 T^{24} - 364544 T^{25} + 390144 T^{26} - 389120 T^{27} + 360448 T^{28} - 303104 T^{29} + 229376 T^{30} - 131072 T^{31} + 65536 T^{32} \))(\( 1 - 5 T + 19 T^{2} - 52 T^{3} + 125 T^{4} - 264 T^{5} + 529 T^{6} - 1006 T^{7} + 1858 T^{8} - 3287 T^{9} + 5617 T^{10} - 9208 T^{11} + 14687 T^{12} - 22750 T^{13} + 34532 T^{14} - 50960 T^{15} + 73260 T^{16} - 101920 T^{17} + 138128 T^{18} - 182000 T^{19} + 234992 T^{20} - 294656 T^{21} + 359488 T^{22} - 420736 T^{23} + 475648 T^{24} - 515072 T^{25} + 541696 T^{26} - 540672 T^{27} + 512000 T^{28} - 425984 T^{29} + 311296 T^{30} - 163840 T^{31} + 65536 T^{32} \))(\( 1 + 6 T + 25 T^{2} + 81 T^{3} + 225 T^{4} + 556 T^{5} + 1256 T^{6} + 2640 T^{7} + 5231 T^{8} + 9842 T^{9} + 17724 T^{10} + 30680 T^{11} + 51321 T^{12} + 83210 T^{13} + 131171 T^{14} + 201431 T^{15} + 301850 T^{16} + 441694 T^{17} + 631856 T^{18} + 883388 T^{19} + 1207400 T^{20} + 1611448 T^{21} + 2098736 T^{22} + 2662720 T^{23} + 3284544 T^{24} + 3927040 T^{25} + 4537344 T^{26} + 5039104 T^{27} + 5356544 T^{28} + 5406720 T^{29} + 5144576 T^{30} + 4554752 T^{31} + 3686400 T^{32} + 2654208 T^{33} + 1638400 T^{34} + 786432 T^{35} + 262144 T^{36} \))(\( 1 - 4 T + 16 T^{2} - 43 T^{3} + 114 T^{4} - 251 T^{5} + 541 T^{6} - 1040 T^{7} + 1959 T^{8} - 3404 T^{9} + 5807 T^{10} - 9344 T^{11} + 14813 T^{12} - 22536 T^{13} + 33898 T^{14} - 49667 T^{15} + 72273 T^{16} - 103641 T^{17} + 148038 T^{18} - 209658 T^{19} + 296076 T^{20} - 414564 T^{21} + 578184 T^{22} - 794672 T^{23} + 1084736 T^{24} - 1442304 T^{25} + 1896064 T^{26} - 2392064 T^{27} + 2973184 T^{28} - 3485696 T^{29} + 4012032 T^{30} - 4259840 T^{31} + 4431872 T^{32} - 4112384 T^{33} + 3735552 T^{34} - 2818048 T^{35} + 2097152 T^{36} - 1048576 T^{37} + 524288 T^{38} \))
$3$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{7} \))(\( ( 1 - T )^{11} \))(\( ( 1 + T )^{13} \))(\( ( 1 + T )^{14} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{16} \))(\( ( 1 + T )^{18} \))(\( ( 1 - T )^{19} \))
$5$ (\( 1 + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( 1 + 4 T^{2} + 25 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 198 T^{3} + 701 T^{4} + 2022 T^{5} + 5344 T^{6} + 12315 T^{7} + 26720 T^{8} + 50550 T^{9} + 87625 T^{10} + 123750 T^{11} + 150000 T^{12} + 125000 T^{13} + 78125 T^{14} \))(\( 1 - T + 23 T^{2} - 18 T^{3} + 254 T^{4} - 42 T^{5} + 1659 T^{6} + 1512 T^{7} + 6662 T^{8} + 20507 T^{9} + 19405 T^{10} + 134932 T^{11} + 97025 T^{12} + 512675 T^{13} + 832750 T^{14} + 945000 T^{15} + 5184375 T^{16} - 656250 T^{17} + 19843750 T^{18} - 7031250 T^{19} + 44921875 T^{20} - 9765625 T^{21} + 48828125 T^{22} \))(\( 1 - 12 T + 104 T^{2} - 670 T^{3} + 3638 T^{4} - 16960 T^{5} + 70302 T^{6} - 262027 T^{7} + 890580 T^{8} - 2778820 T^{9} + 8011459 T^{10} - 21421987 T^{11} + 53271576 T^{12} - 123398136 T^{13} + 266357880 T^{14} - 535549675 T^{15} + 1001432375 T^{16} - 1736762500 T^{17} + 2783062500 T^{18} - 4094171875 T^{19} + 5492343750 T^{20} - 6625000000 T^{21} + 7105468750 T^{22} - 6542968750 T^{23} + 5078125000 T^{24} - 2929687500 T^{25} + 1220703125 T^{26} \))(\( 1 + 4 T + 41 T^{2} + 150 T^{3} + 870 T^{4} + 2908 T^{5} + 12492 T^{6} + 38021 T^{7} + 133996 T^{8} + 370873 T^{9} + 1127299 T^{10} + 2836015 T^{11} + 7634651 T^{12} + 17439737 T^{13} + 42178904 T^{14} + 87198685 T^{15} + 190866275 T^{16} + 354501875 T^{17} + 704561875 T^{18} + 1158978125 T^{19} + 2093687500 T^{20} + 2970390625 T^{21} + 4879687500 T^{22} + 5679687500 T^{23} + 8496093750 T^{24} + 7324218750 T^{25} + 10009765625 T^{26} + 4882812500 T^{27} + 6103515625 T^{28} \))(\( 1 - 5 T + 44 T^{2} - 165 T^{3} + 915 T^{4} - 2942 T^{5} + 12907 T^{6} - 37018 T^{7} + 138404 T^{8} - 361252 T^{9} + 1199295 T^{10} - 2886522 T^{11} + 8700809 T^{12} - 19438343 T^{13} + 53957730 T^{14} - 112352057 T^{15} + 289570702 T^{16} - 561760285 T^{17} + 1348943250 T^{18} - 2429792875 T^{19} + 5438005625 T^{20} - 9020381250 T^{21} + 18738984375 T^{22} - 28222812500 T^{23} + 54064062500 T^{24} - 72300781250 T^{25} + 126044921875 T^{26} - 143652343750 T^{27} + 223388671875 T^{28} - 201416015625 T^{29} + 268554687500 T^{30} - 152587890625 T^{31} + 152587890625 T^{32} \))(\( 1 + T + 24 T^{2} + 19 T^{3} + 329 T^{4} + 170 T^{5} + 3169 T^{6} + 250 T^{7} + 23164 T^{8} - 13164 T^{9} + 133265 T^{10} - 205344 T^{11} + 624119 T^{12} - 1857497 T^{13} + 2603502 T^{14} - 12171723 T^{15} + 11656934 T^{16} - 60858615 T^{17} + 65087550 T^{18} - 232187125 T^{19} + 390074375 T^{20} - 641700000 T^{21} + 2082265625 T^{22} - 1028437500 T^{23} + 9048437500 T^{24} + 488281250 T^{25} + 30947265625 T^{26} + 8300781250 T^{27} + 80322265625 T^{28} + 23193359375 T^{29} + 146484375000 T^{30} + 30517578125 T^{31} + 152587890625 T^{32} \))(\( 1 + 10 T + 81 T^{2} + 476 T^{3} + 2454 T^{4} + 10782 T^{5} + 43074 T^{6} + 154195 T^{7} + 511259 T^{8} + 1553151 T^{9} + 4417176 T^{10} + 11648601 T^{11} + 29006707 T^{12} + 67663733 T^{13} + 151179610 T^{14} + 322803966 T^{15} + 682949075 T^{16} + 1441859622 T^{17} + 3174135542 T^{18} + 7209298110 T^{19} + 17073726875 T^{20} + 40350495750 T^{21} + 94487256250 T^{22} + 211449165625 T^{23} + 453229796875 T^{24} + 910046953125 T^{25} + 1725459375000 T^{26} + 3033498046875 T^{27} + 4992763671875 T^{28} + 7529052734375 T^{29} + 10516113281250 T^{30} + 13161621093750 T^{31} + 14978027343750 T^{32} + 14526367187500 T^{33} + 12359619140625 T^{34} + 7629394531250 T^{35} + 3814697265625 T^{36} \))(\( 1 - 5 T + 41 T^{2} - 168 T^{3} + 832 T^{4} - 2996 T^{5} + 11691 T^{6} - 37986 T^{7} + 128552 T^{8} - 382033 T^{9} + 1168939 T^{10} - 3222334 T^{11} + 9102821 T^{12} - 23575655 T^{13} + 62285480 T^{14} - 152712478 T^{15} + 380888120 T^{16} - 886961463 T^{17} + 2101604027 T^{18} - 4656991668 T^{19} + 10508020135 T^{20} - 22174036575 T^{21} + 47611015000 T^{22} - 95445298750 T^{23} + 194642125000 T^{24} - 368369609375 T^{25} + 711157890625 T^{26} - 1258724218750 T^{27} + 2283083984375 T^{28} - 3730791015625 T^{29} + 6276953125000 T^{30} - 9273925781250 T^{31} + 14271240234375 T^{32} - 18286132812500 T^{33} + 25390625000000 T^{34} - 25634765625000 T^{35} + 31280517578125 T^{36} - 19073486328125 T^{37} + 19073486328125 T^{38} \))
$7$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{11} \))(\( ( 1 - T )^{13} \))(\( ( 1 + T )^{14} \))(\( ( 1 + T )^{16} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{18} \))(\( ( 1 - T )^{19} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 2 T + 6 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 + 2 T + 6 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 31 T^{2} + 93 T^{3} + 656 T^{4} + 1715 T^{5} + 9199 T^{6} + 22080 T^{7} + 101189 T^{8} + 207515 T^{9} + 873136 T^{10} + 1361613 T^{11} + 4992581 T^{12} + 5314683 T^{13} + 19487171 T^{14} \))(\( 1 + 7 T + 102 T^{2} + 550 T^{3} + 4620 T^{4} + 20475 T^{5} + 127969 T^{6} + 483479 T^{7} + 2471330 T^{8} + 8122440 T^{9} + 35508279 T^{10} + 102345862 T^{11} + 390591069 T^{12} + 982815240 T^{13} + 3289340230 T^{14} + 7078616039 T^{15} + 20609535419 T^{16} + 36272711475 T^{17} + 90030730020 T^{18} + 117897384550 T^{19} + 240510664482 T^{20} + 181561972207 T^{21} + 285311670611 T^{22} \))(\( 1 - 3 T + 83 T^{2} - 231 T^{3} + 3487 T^{4} - 8594 T^{5} + 96020 T^{6} - 206021 T^{7} + 1938774 T^{8} - 3603777 T^{9} + 30713596 T^{10} - 50136844 T^{11} + 400155761 T^{12} - 591166452 T^{13} + 4401713371 T^{14} - 6066558124 T^{15} + 40879796276 T^{16} - 52762899057 T^{17} + 312241491474 T^{18} - 364978768781 T^{19} + 1871158159420 T^{20} - 1842200223314 T^{21} + 8222163598517 T^{22} - 5991545082831 T^{23} + 23680868660713 T^{24} - 9415285130163 T^{25} + 34522712143931 T^{26} \))(\( 1 + 3 T + 82 T^{2} + 256 T^{3} + 3350 T^{4} + 10553 T^{5} + 92717 T^{6} + 284301 T^{7} + 1964384 T^{8} + 5713164 T^{9} + 33629114 T^{10} + 91772019 T^{11} + 477433889 T^{12} + 1214718248 T^{13} + 5707030766 T^{14} + 13361900728 T^{15} + 57769500569 T^{16} + 122148557289 T^{17} + 492363858074 T^{18} + 920110775364 T^{19} + 3480026083424 T^{20} + 5540222202471 T^{21} + 19874712369677 T^{22} + 24883421983123 T^{23} + 86890372413350 T^{24} + 73039787676416 T^{25} + 257351126891122 T^{26} + 103568136431793 T^{27} + 379749833583241 T^{28} \))(\( 1 - T + 92 T^{2} - 96 T^{3} + 4181 T^{4} - 4100 T^{5} + 126197 T^{6} - 107277 T^{7} + 2867972 T^{8} - 2007877 T^{9} + 52697233 T^{10} - 30067300 T^{11} + 817852019 T^{12} - 392443888 T^{13} + 10985297878 T^{14} - 4676327073 T^{15} + 129047873478 T^{16} - 51439597803 T^{17} + 1329221043238 T^{18} - 522342814928 T^{19} + 11974171410179 T^{20} - 4842368732300 T^{21} + 93356362790713 T^{22} - 39127842445967 T^{23} + 614775268659332 T^{24} - 252953554447407 T^{25} + 3273225172372397 T^{26} - 1169777849505100 T^{27} + 13121769043070501 T^{28} - 3314180365817376 T^{29} + 34936984689658172 T^{30} - 4177248169415651 T^{31} + 45949729863572161 T^{32} \))(\( 1 - 11 T + 127 T^{2} - 927 T^{3} + 6546 T^{4} - 37443 T^{5} + 205797 T^{6} - 996578 T^{7} + 4658508 T^{8} - 19883514 T^{9} + 82587628 T^{10} - 319384657 T^{11} + 1213890104 T^{12} - 4356733405 T^{13} + 15506991000 T^{14} - 52671594431 T^{15} + 178444424018 T^{16} - 579387538741 T^{17} + 1876345911000 T^{18} - 5798812162055 T^{19} + 17772565012664 T^{20} - 51437218394507 T^{21} + 146309020847308 T^{22} - 387473437398894 T^{23} + 998592562009548 T^{24} - 2349878794001398 T^{25} + 5337844170611997 T^{26} - 10682924882687673 T^{27} + 20544152154015666 T^{28} - 32002554157424037 T^{29} + 48228228865071607 T^{30} - 45949729863572161 T^{31} + 45949729863572161 T^{32} \))(\( 1 + 9 T + 123 T^{2} + 853 T^{3} + 7075 T^{4} + 40936 T^{5} + 262862 T^{6} + 1328997 T^{7} + 7225154 T^{8} + 32841991 T^{9} + 157994657 T^{10} + 657379783 T^{11} + 2869404622 T^{12} + 11054117909 T^{13} + 44448793774 T^{14} + 159662650340 T^{15} + 596925478628 T^{16} + 2006578164628 T^{17} + 7011320772848 T^{18} + 22072359810908 T^{19} + 72227982913988 T^{20} + 212510987602540 T^{21} + 650774789645134 T^{22} + 1780276743362359 T^{23} + 5083325321554942 T^{24} + 12810472243263893 T^{25} + 33867557878498817 T^{26} + 77439696846292781 T^{27} + 187401887105613554 T^{28} + 379178354307007167 T^{29} + 824973559961635502 T^{30} + 1413221744323959416 T^{31} + 2686730072601430075 T^{32} + 3563192688511550303 T^{33} + 5651816773219375803 T^{34} + 4549023256493643939 T^{35} + 5559917313492231481 T^{36} \))(\( 1 + 9 T + 114 T^{2} + 846 T^{3} + 6834 T^{4} + 43631 T^{5} + 279049 T^{6} + 1570491 T^{7} + 8622246 T^{8} + 43583626 T^{9} + 213037611 T^{10} + 979860254 T^{11} + 4350940113 T^{12} + 18383133454 T^{13} + 75002259850 T^{14} + 292955898389 T^{15} + 1105867682544 T^{16} + 4009634203784 T^{17} + 14057469809074 T^{18} + 47407746375208 T^{19} + 154632167899814 T^{20} + 485165738657864 T^{21} + 1471909885466064 T^{22} + 4289167308313349 T^{23} + 12079188951102350 T^{24} + 32566842284901694 T^{25} + 84787513992790323 T^{26} + 210041747583815774 T^{27} + 502331542953606201 T^{28} + 1130447013213183226 T^{29} + 2460027410679012306 T^{30} + 4928873519784940011 T^{31} + 9633528301051801619 T^{32} + 16568864989070388071 T^{33} + 28547313989786558934 T^{34} + 38873471464582048206 T^{35} + 57620961248919489894 T^{36} + 50039255821430083329 T^{37} + 61159090448414546291 T^{38} \))
$13$ (\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 3 T + 24 T^{2} + 39 T^{3} + 169 T^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 - 4 T + 6 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 3 T + 24 T^{2} + 39 T^{3} + 169 T^{4} \))(\( 1 + 23 T + 289 T^{2} + 2532 T^{3} + 17108 T^{4} + 93828 T^{5} + 430561 T^{6} + 1679255 T^{7} + 5597293 T^{8} + 15856932 T^{9} + 37586276 T^{10} + 72316452 T^{11} + 107303677 T^{12} + 111016607 T^{13} + 62748517 T^{14} \))(\( 1 + 24 T + 346 T^{2} + 3680 T^{3} + 31746 T^{4} + 231850 T^{5} + 1475347 T^{6} + 8317190 T^{7} + 42047204 T^{8} + 192032718 T^{9} + 796510865 T^{10} + 3007998246 T^{11} + 10354641245 T^{12} + 32453529342 T^{13} + 92377707188 T^{14} + 237547263590 T^{15} + 547786013671 T^{16} + 1119095666650 T^{17} + 1992014420682 T^{18} + 3001889053280 T^{19} + 3669156783058 T^{20} + 3308603804376 T^{21} + 1792160394037 T^{22} \))(\( 1 - 21 T + 303 T^{2} - 3206 T^{3} + 28249 T^{4} - 211775 T^{5} + 1406812 T^{6} - 8366101 T^{7} + 45400042 T^{8} - 225933653 T^{9} + 1041869982 T^{10} - 4459348525 T^{11} + 17818659263 T^{12} - 66419150254 T^{13} + 231642570419 T^{14} - 753629900725 T^{15} + 2288988350454 T^{16} - 6452891063333 T^{17} + 16856717794306 T^{18} - 40381571601709 T^{19} + 88275366697804 T^{20} - 172751373439775 T^{21} + 299566502787877 T^{22} - 441974324867894 T^{23} + 543024599393211 T^{24} - 489259787572101 T^{25} + 302875106592253 T^{26} \))(\( 1 + 13 T + 182 T^{2} + 1585 T^{3} + 13608 T^{4} + 92167 T^{5} + 606905 T^{6} + 3422512 T^{7} + 18744862 T^{8} + 91352922 T^{9} + 433195838 T^{10} + 1864962208 T^{11} + 7828834193 T^{12} + 30141395677 T^{13} + 113300440326 T^{14} + 391838143801 T^{15} + 1323072978617 T^{16} + 4097321970976 T^{17} + 12372506329118 T^{18} + 33918700468146 T^{19} + 90477868605358 T^{20} + 214757552414704 T^{21} + 495071053228505 T^{22} + 977384893711291 T^{23} + 1875978357081192 T^{24} + 2840574224548645 T^{25} + 4240251492291542 T^{26} + 3937376385699289 T^{27} + 3937376385699289 T^{28} \))(\( 1 - 20 T + 290 T^{2} - 3026 T^{3} + 26451 T^{4} - 193872 T^{5} + 1250917 T^{6} - 7096516 T^{7} + 36195640 T^{8} - 165179444 T^{9} + 682331085 T^{10} - 2528068092 T^{11} + 8470190389 T^{12} - 25438784618 T^{13} + 70775694820 T^{14} - 192799829316 T^{15} + 616167289950 T^{16} - 2506397781108 T^{17} + 11961092424580 T^{18} - 55889009805746 T^{19} + 241917107700229 T^{20} - 938653986082956 T^{21} + 3293481822057765 T^{22} - 10364765149884548 T^{23} + 29525895514256440 T^{24} - 75254999472484468 T^{25} + 172449531048275533 T^{26} - 347449719912741264 T^{27} + 616257649574744931 T^{28} - 916500072548157578 T^{29} + 1141839151852793810 T^{30} - 1023717860281815140 T^{31} + 665416609183179841 T^{32} \))(\( 1 - 18 T + 219 T^{2} - 1948 T^{3} + 14614 T^{4} - 94646 T^{5} + 555983 T^{6} - 2985822 T^{7} + 14990448 T^{8} - 70533970 T^{9} + 315528362 T^{10} - 1344918094 T^{11} + 5522268604 T^{12} - 21859541176 T^{13} + 84090414036 T^{14} - 314220696382 T^{15} + 1147549597242 T^{16} - 4084869052966 T^{17} + 14211279972084 T^{18} - 48025411963672 T^{19} + 157721513598844 T^{20} - 499358673875542 T^{21} + 1522995137456858 T^{22} - 4425902015622490 T^{23} + 12228168955153008 T^{24} - 31663147526889606 T^{25} + 76646977873682567 T^{26} - 169620812654025902 T^{27} + 340478215979937334 T^{28} - 590000707641708844 T^{29} + 862285428468144291 T^{30} - 921346074253633626 T^{31} + 665416609183179841 T^{32} \))(\( 1 + 25 T + 385 T^{2} + 4370 T^{3} + 40821 T^{4} + 328011 T^{5} + 2348286 T^{6} + 15262673 T^{7} + 91519666 T^{8} + 511265569 T^{9} + 2684450093 T^{10} + 13324020516 T^{11} + 62851127050 T^{12} + 282769818174 T^{13} + 1217464085422 T^{14} + 5026930729070 T^{15} + 19945274556838 T^{16} + 76121573741284 T^{17} + 279708125871724 T^{18} + 989580458636692 T^{19} + 3370751400105622 T^{20} + 11044166811766790 T^{21} + 34771991743737742 T^{22} + 104990454099278982 T^{23} + 303370385705083450 T^{24} + 836062527856574772 T^{25} + 2189788409851407053 T^{26} + 5421715405896988237 T^{27} + 12616763129284202434 T^{28} + 27353158057737880901 T^{29} + 54710567119930417566 T^{30} + 99346366588431498783 T^{31} + \)\(16\!\cdots\!69\)\( T^{32} + \)\(22\!\cdots\!90\)\( T^{33} + \)\(25\!\cdots\!85\)\( T^{34} + \)\(21\!\cdots\!25\)\( T^{35} + \)\(11\!\cdots\!29\)\( T^{36} \))(\( 1 - 24 T + 402 T^{2} - 5026 T^{3} + 52972 T^{4} - 482098 T^{5} + 3925963 T^{6} - 28966932 T^{7} + 196682920 T^{8} - 1238002338 T^{9} + 7283995209 T^{10} - 40243236364 T^{11} + 209809038801 T^{12} - 1035189853758 T^{13} + 4848463373224 T^{14} - 21594807026076 T^{15} + 91636684117992 T^{16} - 370834674951958 T^{17} + 1432622313733372 T^{18} - 5285005449943492 T^{19} + 18624090078533836 T^{20} - 62671060066880902 T^{21} + 201325795007228424 T^{22} - 616769283471756636 T^{23} + 1800200511234458632 T^{24} - 4996663702827798222 T^{25} + 13165206037958208117 T^{26} - 32827644214579138444 T^{27} + 77243122626775503957 T^{28} - \)\(17\!\cdots\!62\)\( T^{29} + \)\(35\!\cdots\!40\)\( T^{30} - \)\(67\!\cdots\!92\)\( T^{31} + \)\(11\!\cdots\!39\)\( T^{32} - \)\(18\!\cdots\!22\)\( T^{33} + \)\(27\!\cdots\!04\)\( T^{34} - \)\(33\!\cdots\!66\)\( T^{35} + \)\(34\!\cdots\!66\)\( T^{36} - \)\(26\!\cdots\!96\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))
$17$ (\( 1 - T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 9 T + 50 T^{2} - 153 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 35 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 37 T^{2} + 102 T^{3} + 289 T^{4} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( 1 - 3 T + 50 T^{2} - 146 T^{3} + 1373 T^{4} - 4645 T^{5} + 30241 T^{6} - 99122 T^{7} + 514097 T^{8} - 1342405 T^{9} + 6745549 T^{10} - 12194066 T^{11} + 70992850 T^{12} - 72412707 T^{13} + 410338673 T^{14} \))(\( 1 + 15 T + 185 T^{2} + 1553 T^{3} + 11942 T^{4} + 75526 T^{5} + 456245 T^{6} + 2418698 T^{7} + 12494286 T^{8} + 58193991 T^{9} + 266122262 T^{10} + 1106913944 T^{11} + 4524078454 T^{12} + 16818063399 T^{13} + 61384427118 T^{14} + 202012075658 T^{15} + 647802656965 T^{16} + 1823014036294 T^{17} + 4900264432966 T^{18} + 10833351305873 T^{19} + 21938757151945 T^{20} + 30239908506735 T^{21} + 34271896307633 T^{22} \))(\( 1 - 17 T + 258 T^{2} - 2538 T^{3} + 22321 T^{4} - 152819 T^{5} + 941699 T^{6} - 4671056 T^{7} + 20527283 T^{8} - 67321211 T^{9} + 167904403 T^{10} - 10092848 T^{11} - 1775763501 T^{12} + 11811409138 T^{13} - 30187979517 T^{14} - 2916833072 T^{15} + 824914331939 T^{16} - 5622734863931 T^{17} + 29145806458531 T^{18} - 112747936502864 T^{19} + 386415518025427 T^{20} - 1066028276376179 T^{21} + 2646999991289537 T^{22} - 5116592519339562 T^{23} + 8842149247369314 T^{24} - 9904578032905937 T^{25} + 9904578032905937 T^{26} \))(\( 1 + 5 T + 130 T^{2} + 468 T^{3} + 7643 T^{4} + 20469 T^{5} + 287362 T^{6} + 594229 T^{7} + 8149596 T^{8} + 13821766 T^{9} + 190977908 T^{10} + 284790841 T^{11} + 3876597272 T^{12} + 5340393118 T^{13} + 69746292016 T^{14} + 90786683006 T^{15} + 1120336611608 T^{16} + 1399177401833 T^{17} + 15950665854068 T^{18} + 19624931207462 T^{19} + 196711435772124 T^{20} + 243835139318117 T^{21} + 2004567609760642 T^{22} + 2427375244017093 T^{23} + 15408241381131707 T^{24} + 16039247471972244 T^{25} + 75740890839868930 T^{26} + 49522890164529685 T^{27} + 168377826559400929 T^{28} \))(\( 1 - 3 T + 119 T^{2} - 197 T^{3} + 7224 T^{4} - 5540 T^{5} + 310835 T^{6} - 34062 T^{7} + 10484647 T^{8} + 4461310 T^{9} + 291065858 T^{10} + 241198952 T^{11} + 6894239766 T^{12} + 7415074569 T^{13} + 141937841380 T^{14} + 165486582283 T^{15} + 2567277444404 T^{16} + 2813271898811 T^{17} + 41020036158820 T^{18} + 36430261357497 T^{19} + 575813799496086 T^{20} + 342468020389864 T^{21} + 7025622231019202 T^{22} + 1830648025241630 T^{23} + 73138354326508327 T^{24} - 4039340249240814 T^{25} + 626641464046064915 T^{26} - 189866305544286820 T^{27} + 4208863041747793464 T^{28} - 1951201872482469589 T^{29} + 20036961360568710551 T^{30} - 8587269154529447379 T^{31} + 48661191875666868481 T^{32} \))(\( 1 + 5 T + 158 T^{2} + 540 T^{3} + 11588 T^{4} + 27066 T^{5} + 558089 T^{6} + 870456 T^{7} + 20459225 T^{8} + 20581469 T^{9} + 610166673 T^{10} + 380514409 T^{11} + 15256129494 T^{12} + 5823688053 T^{13} + 325009231345 T^{14} + 84738254968 T^{15} + 5951336176930 T^{16} + 1440550334456 T^{17} + 93927667858705 T^{18} + 28611779404389 T^{19} + 1274207191468374 T^{20} + 540276047219513 T^{21} + 14727940171037937 T^{22} + 8445372677850637 T^{23} + 142718591030843225 T^{24} + 103225528624072632 T^{25} + 1125104019907681961 T^{26} + 927603145462394778 T^{27} + 6751426485018470468 T^{28} + 5348472137769205980 T^{29} + 26603696596385346782 T^{30} + 14312115257549078965 T^{31} + 48661191875666868481 T^{32} \))(\( 1 + 17 T + 271 T^{2} + 2811 T^{3} + 27324 T^{4} + 215198 T^{5} + 1613920 T^{6} + 10643807 T^{7} + 67598476 T^{8} + 393720197 T^{9} + 2219851055 T^{10} + 11763913489 T^{11} + 60437526881 T^{12} + 296473981529 T^{13} + 1409837991942 T^{14} + 6467854453086 T^{15} + 28753111843606 T^{16} + 124072891149114 T^{17} + 518698939431416 T^{18} + 2109239149534938 T^{19} + 8309649322802134 T^{20} + 31776568928011518 T^{21} + 117751078924987782 T^{22} + 420950657991821353 T^{23} + 1458814975279492289 T^{24} + 4827188650363060097 T^{25} + 15485142514827950255 T^{26} + 46690442096210509909 T^{27} + \)\(13\!\cdots\!24\)\( T^{28} + \)\(36\!\cdots\!31\)\( T^{29} + \)\(94\!\cdots\!20\)\( T^{30} + \)\(21\!\cdots\!26\)\( T^{31} + \)\(46\!\cdots\!96\)\( T^{32} + \)\(80\!\cdots\!23\)\( T^{33} + \)\(13\!\cdots\!51\)\( T^{34} + \)\(14\!\cdots\!09\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))(\( 1 - 17 T + 284 T^{2} - 3184 T^{3} + 32551 T^{4} - 278609 T^{5} + 2179544 T^{6} - 15312493 T^{7} + 99697602 T^{8} - 601566144 T^{9} + 3415708339 T^{10} - 18303102870 T^{11} + 93623696982 T^{12} - 457896515162 T^{13} + 2163836903127 T^{14} - 9881182119343 T^{15} + 43988887312946 T^{16} - 190801647107236 T^{17} + 811083332879856 T^{18} - 3375158517221308 T^{19} + 13788416658957552 T^{20} - 55141676013991204 T^{21} + 216117403368503698 T^{22} - 825286211789646703 T^{23} + 3072338973763192839 T^{24} - 11052508729582321178 T^{25} + 38417423580947984886 T^{26} - \)\(12\!\cdots\!70\)\( T^{27} + \)\(40\!\cdots\!83\)\( T^{28} - \)\(12\!\cdots\!56\)\( T^{29} + \)\(34\!\cdots\!66\)\( T^{30} - \)\(89\!\cdots\!73\)\( T^{31} + \)\(21\!\cdots\!28\)\( T^{32} - \)\(46\!\cdots\!61\)\( T^{33} + \)\(93\!\cdots\!43\)\( T^{34} - \)\(15\!\cdots\!04\)\( T^{35} + \)\(23\!\cdots\!68\)\( T^{36} - \)\(23\!\cdots\!53\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))
$19$ (\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( 1 + 8 T + 36 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 36 T^{2} - 76 T^{3} + 361 T^{4} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( 1 + 9 T + 127 T^{2} + 828 T^{3} + 6701 T^{4} + 34195 T^{5} + 201852 T^{6} + 825304 T^{7} + 3835188 T^{8} + 12344395 T^{9} + 45962159 T^{10} + 107905788 T^{11} + 314464573 T^{12} + 423412929 T^{13} + 893871739 T^{14} \))(\( 1 + 19 T + 234 T^{2} + 2045 T^{3} + 14527 T^{4} + 83422 T^{5} + 399009 T^{6} + 1485464 T^{7} + 3888135 T^{8} + 1769859 T^{9} - 45008345 T^{10} - 294336390 T^{11} - 855158555 T^{12} + 638919099 T^{13} + 26668717965 T^{14} + 193587153944 T^{15} + 987985785891 T^{16} + 3924661484782 T^{17} + 12985274752453 T^{18} + 34731386418845 T^{19} + 75508921280286 T^{20} + 116490258898219 T^{21} + 116490258898219 T^{22} \))(\( 1 - 5 T + 173 T^{2} - 864 T^{3} + 14502 T^{4} - 70542 T^{5} + 782707 T^{6} - 3630922 T^{7} + 30483684 T^{8} - 132517839 T^{9} + 909405816 T^{10} - 3646806238 T^{11} + 21484456413 T^{12} - 78131794348 T^{13} + 408204671847 T^{14} - 1316497051918 T^{15} + 6237614491944 T^{16} - 17269857296319 T^{17} + 75480619468716 T^{18} - 170819924332282 T^{19} + 699639667217473 T^{20} - 1198054504038222 T^{21} + 4679616993191058 T^{22} - 5297241246740064 T^{23} + 20152814789391887 T^{24} - 11066574595330805 T^{25} + 42052983462257059 T^{26} \))(\( 1 - 21 T + 374 T^{2} - 4569 T^{3} + 49627 T^{4} - 447130 T^{5} + 3686027 T^{6} - 26871562 T^{7} + 182306081 T^{8} - 1126820515 T^{9} + 6549395980 T^{10} - 35231461213 T^{11} + 179334900367 T^{12} - 851666403346 T^{13} + 3838575491950 T^{14} - 16181661663574 T^{15} + 64739899032487 T^{16} - 241652592459967 T^{17} + 853523833509580 T^{18} - 2790119150370985 T^{19} + 8576750192302361 T^{20} - 24019729854586318 T^{21} + 62601871925328107 T^{22} - 144283350307924270 T^{23} + 304266425175890227 T^{24} - 532243992905962611 T^{25} + 827779779730744214 T^{26} - 883112652707398239 T^{27} + 799006685782884121 T^{28} \))(\( 1 - 13 T + 224 T^{2} - 2227 T^{3} + 23556 T^{4} - 193353 T^{5} + 1589551 T^{6} - 11232515 T^{7} + 77919882 T^{8} - 486334465 T^{9} + 2959429581 T^{10} - 16577586969 T^{11} + 90351387300 T^{12} - 458691179259 T^{13} + 2264953054380 T^{14} - 10477514679859 T^{15} + 47144548718330 T^{16} - 199072778917321 T^{17} + 817648052631180 T^{18} - 3146162798537481 T^{19} + 11774683144323300 T^{20} - 41047746516353931 T^{21} + 139228971895605861 T^{22} - 434720633965184635 T^{23} + 1323357228094281162 T^{24} - 3624594405618084185 T^{25} + 9745642501153837351 T^{26} - 22523741028747338307 T^{27} + 52136846233522488516 T^{28} - 93651994170446470393 T^{29} + \)\(17\!\cdots\!04\)\( T^{30} - \)\(19\!\cdots\!87\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 + 11 T + 181 T^{2} + 1462 T^{3} + 14335 T^{4} + 95375 T^{5} + 719296 T^{6} + 4211650 T^{7} + 26971845 T^{8} + 143986816 T^{9} + 822044549 T^{10} + 4072545605 T^{11} + 21330650499 T^{12} + 99112960004 T^{13} + 484717258250 T^{14} + 2123022393713 T^{15} + 9768224694024 T^{16} + 40337425480547 T^{17} + 174982930228250 T^{18} + 679815792667436 T^{19} + 2779831703680179 T^{20} + 10084026099994895 T^{21} + 38673810028952669 T^{22} + 128705745610993024 T^{23} + 458078029889580645 T^{24} + 1359047642350925350 T^{25} + 4410051434971228096 T^{26} + 11110258442417637125 T^{27} + 31727869364813417935 T^{28} + 61481461821819820258 T^{29} + \)\(14\!\cdots\!01\)\( T^{30} + \)\(16\!\cdots\!89\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 + 5 T + 147 T^{2} + 706 T^{3} + 11220 T^{4} + 54388 T^{5} + 598059 T^{6} + 2947928 T^{7} + 24930876 T^{8} + 123855871 T^{9} + 863216513 T^{10} + 4247612067 T^{11} + 25659749354 T^{12} + 122670371696 T^{13} + 666353734551 T^{14} + 3046885890738 T^{15} + 15241373221617 T^{16} + 65964543118195 T^{17} + 307973464968892 T^{18} + 1253326319245705 T^{19} + 5502135733003737 T^{20} + 20898590324571942 T^{21} + 86839885040420871 T^{22} + 303743984686093904 T^{23} + 1207185514598110874 T^{24} + 3796820384926674513 T^{25} + 14660492066567696033 T^{26} + 39966765869402810509 T^{27} + \)\(15\!\cdots\!76\)\( T^{28} + \)\(34\!\cdots\!32\)\( T^{29} + \)\(13\!\cdots\!99\)\( T^{30} + \)\(22\!\cdots\!92\)\( T^{31} + \)\(89\!\cdots\!20\)\( T^{32} + \)\(10\!\cdots\!94\)\( T^{33} + \)\(42\!\cdots\!07\)\( T^{34} + \)\(27\!\cdots\!95\)\( T^{35} + \)\(10\!\cdots\!41\)\( T^{36} \))(\( 1 - 23 T + 416 T^{2} - 5333 T^{3} + 59693 T^{4} - 564360 T^{5} + 4868647 T^{6} - 37688990 T^{7} + 272710055 T^{8} - 1823898623 T^{9} + 11572107859 T^{10} - 69036155352 T^{11} + 394624910977 T^{12} - 2144671314045 T^{13} + 11249450770817 T^{14} - 56533025766972 T^{15} + 275667627613884 T^{16} - 1294507948679753 T^{17} + 5918690016197407 T^{18} - 26130047561244090 T^{19} + 112455110307750733 T^{20} - 467317369473390833 T^{21} + 1890804257803630356 T^{22} - 7367440450977558012 T^{23} + 27854753804169202883 T^{24} - \)\(10\!\cdots\!45\)\( T^{25} + \)\(35\!\cdots\!03\)\( T^{26} - \)\(11\!\cdots\!32\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} - \)\(11\!\cdots\!23\)\( T^{29} + \)\(31\!\cdots\!45\)\( T^{30} - \)\(83\!\cdots\!90\)\( T^{31} + \)\(20\!\cdots\!73\)\( T^{32} - \)\(45\!\cdots\!60\)\( T^{33} + \)\(90\!\cdots\!07\)\( T^{34} - \)\(15\!\cdots\!73\)\( T^{35} + \)\(22\!\cdots\!24\)\( T^{36} - \)\(23\!\cdots\!43\)\( T^{37} + \)\(19\!\cdots\!79\)\( T^{38} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 - 3 T + 10 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( 1 + 5 T + 48 T^{2} + 115 T^{3} + 529 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 1067 T^{3} + 8328 T^{4} - 46995 T^{5} + 292164 T^{6} - 1356265 T^{7} + 6719772 T^{8} - 24860355 T^{9} + 101326776 T^{10} - 298590347 T^{11} + 965451450 T^{12} - 1776430668 T^{13} + 3404825447 T^{14} \))(\( 1 + 11 T + 183 T^{2} + 1415 T^{3} + 13556 T^{4} + 84717 T^{5} + 612371 T^{6} + 3414518 T^{7} + 20798264 T^{8} + 108054544 T^{9} + 578865979 T^{10} + 2768846230 T^{11} + 13313917517 T^{12} + 57160853776 T^{13} + 253052478088 T^{14} + 955522131638 T^{15} + 3941429799253 T^{16} + 12541156408413 T^{17} + 46155813759532 T^{18} + 110810044172615 T^{19} + 329610937047729 T^{20} + 455691623350139 T^{21} + 952809757913927 T^{22} \))(\( 1 - 4 T + 184 T^{2} - 613 T^{3} + 16621 T^{4} - 45907 T^{5} + 981152 T^{6} - 2240102 T^{7} + 42577347 T^{8} - 80788590 T^{9} + 1448692280 T^{10} - 2339155653 T^{11} + 40151933279 T^{12} - 57649846102 T^{13} + 923494465417 T^{14} - 1237413340437 T^{15} + 17626238970760 T^{16} - 22607959814190 T^{17} + 274042409322021 T^{18} - 331615491020678 T^{19} + 3340651296974944 T^{20} - 3595022401294867 T^{21} + 29936958386176523 T^{22} - 25394451373966837 T^{23} + 175316995456162568 T^{24} - 87658497728081284 T^{25} + 504036361936467383 T^{26} \))(\( 1 + 10 T + 197 T^{2} + 1651 T^{3} + 18643 T^{4} + 131352 T^{5} + 1107307 T^{6} + 6674025 T^{7} + 46362563 T^{8} + 244354670 T^{9} + 1483666023 T^{10} + 7040607329 T^{11} + 39336210461 T^{12} + 174731022341 T^{13} + 936647851466 T^{14} + 4018813513843 T^{15} + 20808855333869 T^{16} + 85663069371943 T^{17} + 415190583542343 T^{18} + 1572750469771810 T^{19} + 6863323230023507 T^{20} + 22723890153914175 T^{21} + 86714302178548267 T^{22} + 236585004388487976 T^{23} + 772314448556058307 T^{24} + 1573088910315893477 T^{25} + 4317181013108003237 T^{26} + 5040363619364673830 T^{27} + 11592836324538749809 T^{28} \))(\( 1 - 5 T + 182 T^{2} - 756 T^{3} + 15727 T^{4} - 54038 T^{5} + 854995 T^{6} - 2305237 T^{7} + 32132604 T^{8} - 57324585 T^{9} + 857073607 T^{10} - 371762126 T^{11} + 15989916385 T^{12} + 32570990844 T^{13} + 206622863040 T^{14} + 1527911913935 T^{15} + 2891712727590 T^{16} + 35141974020505 T^{17} + 109303494548160 T^{18} + 396291245598948 T^{19} + 4474634191094785 T^{20} - 2392788557345218 T^{21} + 126877653350681623 T^{22} - 195180205746714495 T^{23} + 2516335878884201724 T^{24} - 4152083757852981731 T^{25} + 35419459955113826755 T^{26} - 51487933698152787226 T^{27} + \)\(34\!\cdots\!67\)\( T^{28} - \)\(38\!\cdots\!48\)\( T^{29} + \)\(21\!\cdots\!38\)\( T^{30} - \)\(13\!\cdots\!35\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 13 T + 208 T^{2} - 2018 T^{3} + 20375 T^{4} - 160550 T^{5} + 1275907 T^{6} - 8665917 T^{7} + 58792152 T^{8} - 357162729 T^{9} + 2165764215 T^{10} - 12076345886 T^{11} + 67338196417 T^{12} - 351022119450 T^{13} + 1831885262566 T^{14} - 9017382569929 T^{15} + 44472265582174 T^{16} - 207399799108367 T^{17} + 969067303897414 T^{18} - 4270886127348150 T^{19} + 18843988223529697 T^{20} - 77727504308934898 T^{21} + 320610830931912135 T^{22} - 1216076748419164863 T^{23} + 4604071349910314712 T^{24} - 15608639468567456571 T^{25} + 52856375643073254643 T^{26} - \)\(15\!\cdots\!50\)\( T^{27} + \)\(44\!\cdots\!75\)\( T^{28} - \)\(10\!\cdots\!94\)\( T^{29} + \)\(24\!\cdots\!72\)\( T^{30} - \)\(34\!\cdots\!91\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 14 T + 241 T^{2} + 2165 T^{3} + 22937 T^{4} + 159770 T^{5} + 1348211 T^{6} + 7982781 T^{7} + 59782924 T^{8} + 318639178 T^{9} + 2236451198 T^{10} + 11093814756 T^{11} + 74232434192 T^{12} + 346225007891 T^{13} + 2204529109109 T^{14} + 9680284070456 T^{15} + 58671559445850 T^{16} + 244022213085305 T^{17} + 1413668128204946 T^{18} + 5612510900962015 T^{19} + 31037254946854650 T^{20} + 117780016285238152 T^{21} + 616917630422171669 T^{22} + 2228422905964182613 T^{23} + 10989064388246716688 T^{24} + 37772502785532895932 T^{25} + \)\(17\!\cdots\!38\)\( T^{26} + \)\(57\!\cdots\!14\)\( T^{27} + \)\(24\!\cdots\!76\)\( T^{28} + \)\(76\!\cdots\!87\)\( T^{29} + \)\(29\!\cdots\!31\)\( T^{30} + \)\(80\!\cdots\!10\)\( T^{31} + \)\(26\!\cdots\!33\)\( T^{32} + \)\(57\!\cdots\!55\)\( T^{33} + \)\(14\!\cdots\!01\)\( T^{34} + \)\(19\!\cdots\!42\)\( T^{35} + \)\(32\!\cdots\!69\)\( T^{36} \))(\( 1 + 17 T + 391 T^{2} + 4769 T^{3} + 65448 T^{4} + 640527 T^{5} + 6681855 T^{6} + 55642304 T^{7} + 483186514 T^{8} + 3544873790 T^{9} + 26828147273 T^{10} + 177193952328 T^{11} + 1199885605017 T^{12} + 7232532287266 T^{13} + 44528435308294 T^{14} + 247034068307600 T^{15} + 1396581507639034 T^{16} + 7165658273752720 T^{17} + 37417693376472169 T^{18} + 177916417007843598 T^{19} + 860606947658859887 T^{20} + 3790633226815188880 T^{21} + 16992207203444126678 T^{22} + 69130260709267091600 T^{23} + \)\(28\!\cdots\!42\)\( T^{24} + \)\(10\!\cdots\!74\)\( T^{25} + \)\(40\!\cdots\!99\)\( T^{26} + \)\(13\!\cdots\!68\)\( T^{27} + \)\(48\!\cdots\!99\)\( T^{28} + \)\(14\!\cdots\!10\)\( T^{29} + \)\(46\!\cdots\!78\)\( T^{30} + \)\(12\!\cdots\!84\)\( T^{31} + \)\(33\!\cdots\!65\)\( T^{32} + \)\(74\!\cdots\!43\)\( T^{33} + \)\(17\!\cdots\!36\)\( T^{34} + \)\(29\!\cdots\!09\)\( T^{35} + \)\(55\!\cdots\!73\)\( T^{36} + \)\(55\!\cdots\!73\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))
$29$ (\( 1 + 9 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 41 T^{2} + 841 T^{4} \))(\( 1 + 6 T + 65 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 43 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 9 T + 74 T^{2} - 261 T^{3} + 841 T^{4} \))(\( 1 + 9 T + 107 T^{2} + 652 T^{3} + 4764 T^{4} + 22810 T^{5} + 134487 T^{6} + 612145 T^{7} + 3900123 T^{8} + 19183210 T^{9} + 116189196 T^{10} + 461147212 T^{11} + 2194692943 T^{12} + 5353409889 T^{13} + 17249876309 T^{14} \))(\( 1 + 10 T + 181 T^{2} + 1710 T^{3} + 17914 T^{4} + 147510 T^{5} + 1186021 T^{6} + 8528670 T^{7} + 57349064 T^{8} + 364258800 T^{9} + 2122703783 T^{10} + 11977573672 T^{11} + 61558409707 T^{12} + 306341650800 T^{13} + 1398686321896 T^{14} + 6032166246270 T^{15} + 24326653448129 T^{16} + 87742388080710 T^{17} + 309014284199426 T^{18} + 855421366163310 T^{19} + 2625793421632289 T^{20} + 4207072333002010 T^{21} + 12200509765705829 T^{22} \))(\( 1 - 21 T + 421 T^{2} - 5324 T^{3} + 64636 T^{4} - 613764 T^{5} + 5683567 T^{6} - 44367699 T^{7} + 342010383 T^{8} - 2302116496 T^{9} + 15447960508 T^{10} - 92186196428 T^{11} + 551990408672 T^{12} - 2963927041432 T^{13} + 16007721851488 T^{14} - 77528591195948 T^{15} + 376760308829612 T^{16} - 1628243257407376 T^{17} + 7015025925260067 T^{18} - 26390942064308379 T^{19} + 98040827743914203 T^{20} - 307033239404595204 T^{21} + 937683887296268684 T^{22} - 2239845310090270124 T^{23} + 5136414611362154009 T^{24} - 7430110447314849861 T^{25} + 10260628712958602189 T^{26} \))(\( 1 + 15 T + 325 T^{2} + 3542 T^{3} + 45090 T^{4} + 389302 T^{5} + 3709822 T^{6} + 26645384 T^{7} + 208750551 T^{8} + 1291861725 T^{9} + 8811883923 T^{10} + 48651787808 T^{11} + 303330222126 T^{12} + 1554455012568 T^{13} + 9203796607924 T^{14} + 45079195364472 T^{15} + 255100716807966 T^{16} + 1186568452849312 T^{17} + 6232478072943363 T^{18} + 26497568328872025 T^{19} + 124169696006399871 T^{20} + 459629578205807656 T^{21} + 1855825148223802942 T^{22} + 5647660942697753438 T^{23} + 18969689149506063090 T^{24} + 43214205590130046318 T^{25} + \)\(11\!\cdots\!25\)\( T^{26} + \)\(15\!\cdots\!35\)\( T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( 1 - 22 T + 522 T^{2} - 7766 T^{3} + 112692 T^{4} - 1304358 T^{5} + 14474109 T^{6} - 139071516 T^{7} + 1278513361 T^{8} - 10568056376 T^{9} + 83695188240 T^{10} - 607919137474 T^{11} + 4238256585198 T^{12} - 27397319711554 T^{13} + 170225839422745 T^{14} - 986146653004046 T^{15} + 5495004250987864 T^{16} - 28598252937117334 T^{17} + 143159930954528545 T^{18} - 668193230445090506 T^{19} + 2997638355835426638 T^{20} - 12469120008680697626 T^{21} + 49783849820636945040 T^{22} - \)\(18\!\cdots\!84\)\( T^{23} + \)\(63\!\cdots\!21\)\( T^{24} - \)\(20\!\cdots\!04\)\( T^{25} + \)\(60\!\cdots\!09\)\( T^{26} - \)\(15\!\cdots\!82\)\( T^{27} + \)\(39\!\cdots\!72\)\( T^{28} - \)\(79\!\cdots\!74\)\( T^{29} + \)\(15\!\cdots\!82\)\( T^{30} - \)\(18\!\cdots\!78\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 - 24 T + 472 T^{2} - 6622 T^{3} + 82320 T^{4} - 873128 T^{5} + 8519727 T^{6} - 75217422 T^{7} + 623444003 T^{8} - 4802217916 T^{9} + 35136436698 T^{10} - 242281577588 T^{11} + 1597747487582 T^{12} - 10006074679634 T^{13} + 60158248780719 T^{14} - 344816413108922 T^{15} + 1900626864033788 T^{16} - 9999675980158738 T^{17} + 50593087224584679 T^{18} - 244038155361593626 T^{19} + 1130056440764484542 T^{20} - 4969473537862528612 T^{21} + 20899971964810634058 T^{22} - 82837665059863752044 T^{23} + \)\(31\!\cdots\!83\)\( T^{24} - \)\(10\!\cdots\!18\)\( T^{25} + \)\(35\!\cdots\!27\)\( T^{26} - \)\(10\!\cdots\!12\)\( T^{27} + \)\(29\!\cdots\!20\)\( T^{28} - \)\(67\!\cdots\!58\)\( T^{29} + \)\(14\!\cdots\!32\)\( T^{30} - \)\(20\!\cdots\!76\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 17 T + 417 T^{2} + 5334 T^{3} + 78106 T^{4} + 813038 T^{5} + 9035294 T^{6} + 80040114 T^{7} + 737367708 T^{8} + 5722271524 T^{9} + 45743439048 T^{10} + 317607890130 T^{11} + 2268138488862 T^{12} + 14333282840010 T^{13} + 93413372409634 T^{14} + 545192523955726 T^{15} + 3295455203397803 T^{16} + 17965463101032459 T^{17} + 101749592417859630 T^{18} + 520998429929941311 T^{19} + 2771477826057552323 T^{20} + 13296700466756201414 T^{21} + 66069503451258345154 T^{22} + \)\(29\!\cdots\!90\)\( T^{23} + \)\(13\!\cdots\!02\)\( T^{24} + \)\(54\!\cdots\!70\)\( T^{25} + \)\(22\!\cdots\!28\)\( T^{26} + \)\(83\!\cdots\!56\)\( T^{27} + \)\(31\!\cdots\!08\)\( T^{28} + \)\(97\!\cdots\!06\)\( T^{29} + \)\(31\!\cdots\!54\)\( T^{30} + \)\(83\!\cdots\!82\)\( T^{31} + \)\(23\!\cdots\!86\)\( T^{32} + \)\(46\!\cdots\!66\)\( T^{33} + \)\(10\!\cdots\!57\)\( T^{34} + \)\(12\!\cdots\!53\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 - 2 T + 250 T^{2} - 416 T^{3} + 31743 T^{4} - 40300 T^{5} + 2734376 T^{6} - 2380316 T^{7} + 180736146 T^{8} - 93979076 T^{9} + 9822415154 T^{10} - 2467083804 T^{11} + 457248535436 T^{12} - 31843829608 T^{13} + 18656669806136 T^{14} + 735202286540 T^{15} + 675508971482301 T^{16} + 63722501247098 T^{17} + 21852698540725853 T^{18} + 2340535489419288 T^{19} + 633728257681049737 T^{20} + 53590623548809418 T^{21} + 16474988305481839089 T^{22} + 519994608426297740 T^{23} + \)\(38\!\cdots\!64\)\( T^{24} - 18941452480788688168 T^{25} + \)\(78\!\cdots\!24\)\( T^{26} - \)\(12\!\cdots\!44\)\( T^{27} + \)\(14\!\cdots\!26\)\( T^{28} - \)\(39\!\cdots\!76\)\( T^{29} + \)\(22\!\cdots\!34\)\( T^{30} - \)\(84\!\cdots\!56\)\( T^{31} + \)\(28\!\cdots\!64\)\( T^{32} - \)\(11\!\cdots\!00\)\( T^{33} + \)\(27\!\cdots\!07\)\( T^{34} - \)\(10\!\cdots\!36\)\( T^{35} + \)\(18\!\cdots\!50\)\( T^{36} - \)\(42\!\cdots\!22\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 + 3 T + 26 T^{2} + 93 T^{3} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( 1 - 9 T + 78 T^{2} - 279 T^{3} + 961 T^{4} \))(\( 1 + 33 T + 645 T^{2} + 8883 T^{3} + 95284 T^{4} + 826887 T^{5} + 5965621 T^{6} + 36144101 T^{7} + 184934251 T^{8} + 794638407 T^{9} + 2838605644 T^{10} + 8203637043 T^{11} + 18465802395 T^{12} + 29287621473 T^{13} + 27512614111 T^{14} \))(\( 1 + 20 T + 316 T^{2} + 3441 T^{3} + 34953 T^{4} + 299945 T^{5} + 2479883 T^{6} + 18060107 T^{7} + 127136571 T^{8} + 809510497 T^{9} + 5025593175 T^{10} + 28399375380 T^{11} + 155793388425 T^{12} + 777939587617 T^{13} + 3787525586661 T^{14} + 16678888076747 T^{15} + 70996944869333 T^{16} + 266202291597545 T^{17} + 961648401021783 T^{18} + 2934798059834481 T^{19} + 8354920602772036 T^{20} + 16392565739616020 T^{21} + 25408476896404831 T^{22} \))(\( 1 + 7 T + 217 T^{2} + 1437 T^{3} + 23361 T^{4} + 141394 T^{5} + 1651220 T^{6} + 9026082 T^{7} + 86549696 T^{8} + 428736095 T^{9} + 3637767504 T^{10} + 16521213633 T^{11} + 129439998267 T^{12} + 546785963664 T^{13} + 4012639946277 T^{14} + 15876886301313 T^{15} + 108372731711664 T^{16} + 395946787190495 T^{17} + 2477844315788096 T^{18} + 8010681000007842 T^{19} + 45429378672365420 T^{20} + 120593675347932754 T^{21} + 617656013295435231 T^{22} + 1177805848391411037 T^{23} + 5513639486519848327 T^{24} + 5513639486519848327 T^{25} + 24417546297445042591 T^{26} \))(\( 1 - 33 T + 772 T^{2} - 13150 T^{3} + 188546 T^{4} - 2298977 T^{5} + 24968647 T^{6} - 242769108 T^{7} + 2159103944 T^{8} - 17604871449 T^{9} + 133190121022 T^{10} - 935380216908 T^{11} + 6142523519475 T^{12} - 37677429544483 T^{13} + 216850565998226 T^{14} - 1168000315878973 T^{15} + 5902965102215475 T^{16} - 27865912041906228 T^{17} + 123003873756358462 T^{18} - 504012523049009799 T^{19} + 1916212697961617864 T^{20} - 6679212786475682988 T^{21} + 21295535243328112327 T^{22} - 60784083236072933567 T^{23} + \)\(15\!\cdots\!46\)\( T^{24} - \)\(33\!\cdots\!50\)\( T^{25} + \)\(60\!\cdots\!92\)\( T^{26} - \)\(80\!\cdots\!03\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 - 26 T + 544 T^{2} - 8205 T^{3} + 108390 T^{4} - 1223221 T^{5} + 12591467 T^{6} - 117150234 T^{7} + 1016820642 T^{8} - 8192223962 T^{9} + 62402913981 T^{10} - 447676790195 T^{11} + 3061424282902 T^{12} - 19881426212383 T^{13} + 123673849035384 T^{14} - 733836777735502 T^{15} + 4180499851186114 T^{16} - 22748940109800562 T^{17} + 118850568923004024 T^{18} - 592287568293101953 T^{19} + 2827289615169937942 T^{20} - 12816606425687974445 T^{21} + 55382815863263864061 T^{22} - \)\(22\!\cdots\!82\)\( T^{23} + \)\(86\!\cdots\!22\)\( T^{24} - \)\(30\!\cdots\!14\)\( T^{25} + \)\(10\!\cdots\!67\)\( T^{26} - \)\(31\!\cdots\!51\)\( T^{27} + \)\(85\!\cdots\!90\)\( T^{28} - \)\(20\!\cdots\!55\)\( T^{29} + \)\(41\!\cdots\!24\)\( T^{30} - \)\(61\!\cdots\!26\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 + 42 T + 1103 T^{2} + 21297 T^{3} + 334685 T^{4} + 4460298 T^{5} + 52049742 T^{6} + 541781390 T^{7} + 5109757813 T^{8} + 44140935934 T^{9} + 352708311097 T^{10} + 2626670113330 T^{11} + 18362034468729 T^{12} + 121180561220341 T^{13} + 758925862323514 T^{14} + 4526798708422582 T^{15} + 25783901132438856 T^{16} + 140330759961100042 T^{17} + 729327753692896954 T^{18} + 3610090099315178731 T^{19} + 16957724434595074809 T^{20} + 75199335301711682830 T^{21} + \)\(31\!\cdots\!57\)\( T^{22} + \)\(12\!\cdots\!74\)\( T^{23} + \)\(43\!\cdots\!33\)\( T^{24} + \)\(14\!\cdots\!90\)\( T^{25} + \)\(42\!\cdots\!42\)\( T^{26} + \)\(11\!\cdots\!38\)\( T^{27} + \)\(26\!\cdots\!85\)\( T^{28} + \)\(52\!\cdots\!27\)\( T^{29} + \)\(83\!\cdots\!63\)\( T^{30} + \)\(98\!\cdots\!42\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 5 T + 345 T^{2} - 1457 T^{3} + 56911 T^{4} - 201348 T^{5} + 6039940 T^{6} - 17777850 T^{7} + 469396428 T^{8} - 1148134577 T^{9} + 28833727003 T^{10} - 59197956874 T^{11} + 1470588580318 T^{12} - 2592870701857 T^{13} + 64165914583760 T^{14} - 100158175269391 T^{15} + 2432313210501904 T^{16} - 3462335844380129 T^{17} + 80591864885992316 T^{18} - 107332411175783999 T^{19} + 2337452995292329744 T^{20} - 2983812199450427281 T^{21} + 59258569602308618960 T^{22} - 74231686846940033407 T^{23} + \)\(13\!\cdots\!58\)\( T^{24} - \)\(16\!\cdots\!14\)\( T^{25} + \)\(24\!\cdots\!23\)\( T^{26} - \)\(30\!\cdots\!67\)\( T^{27} + \)\(38\!\cdots\!28\)\( T^{28} - \)\(45\!\cdots\!50\)\( T^{29} + \)\(47\!\cdots\!40\)\( T^{30} - \)\(49\!\cdots\!68\)\( T^{31} + \)\(43\!\cdots\!31\)\( T^{32} - \)\(34\!\cdots\!07\)\( T^{33} + \)\(25\!\cdots\!45\)\( T^{34} - \)\(11\!\cdots\!55\)\( T^{35} + \)\(69\!\cdots\!41\)\( T^{36} \))(\( 1 - 16 T + 444 T^{2} - 5891 T^{3} + 94707 T^{4} - 1068715 T^{5} + 12949771 T^{6} - 127334359 T^{7} + 1280574803 T^{8} - 11191113269 T^{9} + 97892201385 T^{10} - 771667588986 T^{11} + 6026996383307 T^{12} - 43307805557421 T^{13} + 306799204066761 T^{14} - 2023856746847967 T^{15} + 13129737685672700 T^{16} - 79857016141786523 T^{17} + 477117795202829813 T^{18} - 2680713867518439722 T^{19} + 14790651651287724203 T^{20} - 76742592512256848603 T^{21} + \)\(39\!\cdots\!00\)\( T^{22} - \)\(18\!\cdots\!07\)\( T^{23} + \)\(87\!\cdots\!11\)\( T^{24} - \)\(38\!\cdots\!01\)\( T^{25} + \)\(16\!\cdots\!77\)\( T^{26} - \)\(65\!\cdots\!26\)\( T^{27} + \)\(25\!\cdots\!35\)\( T^{28} - \)\(91\!\cdots\!69\)\( T^{29} + \)\(32\!\cdots\!93\)\( T^{30} - \)\(10\!\cdots\!99\)\( T^{31} + \)\(31\!\cdots\!61\)\( T^{32} - \)\(80\!\cdots\!15\)\( T^{33} + \)\(22\!\cdots\!57\)\( T^{34} - \)\(42\!\cdots\!71\)\( T^{35} + \)\(10\!\cdots\!84\)\( T^{36} - \)\(11\!\cdots\!56\)\( T^{37} + \)\(21\!\cdots\!71\)\( T^{38} \))
$37$ (\( 1 + T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 + 12 T + 93 T^{2} + 444 T^{3} + 1369 T^{4} \))(\( 1 - 6 T + 11 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( ( 1 + 7 T + 37 T^{2} )^{2} \))(\( 1 + 5 T + 76 T^{2} + 185 T^{3} + 1369 T^{4} \))(\( 1 + 33 T + 653 T^{2} + 9315 T^{3} + 105122 T^{4} + 971473 T^{5} + 7548399 T^{6} + 49726081 T^{7} + 279290763 T^{8} + 1329946537 T^{9} + 5324744666 T^{10} + 17457809715 T^{11} + 45281603921 T^{12} + 84668971497 T^{13} + 94931877133 T^{14} \))(\( 1 + 22 T + 454 T^{2} + 6487 T^{3} + 83295 T^{4} + 901639 T^{5} + 8870009 T^{6} + 77946725 T^{7} + 629881853 T^{8} + 4654816069 T^{9} + 31844505529 T^{10} + 201114366430 T^{11} + 1178246704573 T^{12} + 6372443198461 T^{13} + 31905405500009 T^{14} + 146084712072725 T^{15} + 615081522685613 T^{16} + 2313358993684351 T^{17} + 7907350705793235 T^{18} + 22785454217585527 T^{19} + 59002629866964958 T^{20} + 105788856193192678 T^{21} + 177917621779460413 T^{22} \))(\( 1 - 7 T + 349 T^{2} - 2305 T^{3} + 57994 T^{4} - 369015 T^{5} + 6147489 T^{6} - 37952961 T^{7} + 468210685 T^{8} - 2784936853 T^{9} + 27265286966 T^{10} - 153098638011 T^{11} + 1255909686356 T^{12} - 6449571361272 T^{13} + 46468658395172 T^{14} - 209592035437059 T^{15} + 1381068580688798 T^{16} - 5219420037355333 T^{17} + 32467581607580545 T^{18} - 97376914337447049 T^{19} + 583592670424469037 T^{20} - 1296157605688657815 T^{21} + 7537001137675695538 T^{22} - 11083786978423141945 T^{23} + 62093250001031684137 T^{24} - 46080664040880246967 T^{25} + \)\(24\!\cdots\!97\)\( T^{26} \))(\( 1 + 29 T + 693 T^{2} + 11721 T^{3} + 173826 T^{4} + 2176097 T^{5} + 24709960 T^{6} + 250869276 T^{7} + 2356076231 T^{8} + 20315367197 T^{9} + 163971869231 T^{10} + 1232026880055 T^{11} + 8724657176274 T^{12} + 57914924180169 T^{13} + 363474458224772 T^{14} + 2142852194666253 T^{15} + 11944055674319106 T^{16} + 62405857555425915 T^{17} + 307309682409840191 T^{18} + 1408747949347978529 T^{19} + 6045047007493884479 T^{20} + 23815491285676665708 T^{21} + 86793226807209753160 T^{22} + \)\(28\!\cdots\!69\)\( T^{23} + \)\(83\!\cdots\!74\)\( T^{24} + \)\(20\!\cdots\!73\)\( T^{25} + \)\(45\!\cdots\!33\)\( T^{26} + \)\(70\!\cdots\!13\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 - 30 T + 806 T^{2} - 14673 T^{3} + 242625 T^{4} - 3312475 T^{5} + 41848747 T^{6} - 466357225 T^{7} + 4870920594 T^{8} - 46271902891 T^{9} + 415447002148 T^{10} - 3448551643407 T^{11} + 27200630462421 T^{12} - 200172652127761 T^{13} + 1404240604044519 T^{14} - 9234259977455106 T^{15} + 57972877864016510 T^{16} - 341667619165838922 T^{17} + 1922405386936946511 T^{18} - 10139345348227477933 T^{19} + 50978360788081403781 T^{20} - \)\(23\!\cdots\!99\)\( T^{21} + \)\(10\!\cdots\!32\)\( T^{22} - \)\(43\!\cdots\!03\)\( T^{23} + \)\(17\!\cdots\!74\)\( T^{24} - \)\(60\!\cdots\!25\)\( T^{25} + \)\(20\!\cdots\!03\)\( T^{26} - \)\(58\!\cdots\!75\)\( T^{27} + \)\(15\!\cdots\!25\)\( T^{28} - \)\(35\!\cdots\!81\)\( T^{29} + \)\(72\!\cdots\!34\)\( T^{30} - \)\(10\!\cdots\!90\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 40 T + 1093 T^{2} - 21915 T^{3} + 365384 T^{4} - 5189918 T^{5} + 65263975 T^{6} - 735690707 T^{7} + 7568509040 T^{8} - 71598368286 T^{9} + 629373118507 T^{10} - 5166707785384 T^{11} + 39884876555089 T^{12} - 290489859017229 T^{13} + 2005230244594602 T^{14} - 13140503504719049 T^{15} + 81949219635694490 T^{16} - 486198629674604813 T^{17} + 2745160204850010138 T^{18} - 14714182828799700537 T^{19} + 74750680129362155329 T^{20} - \)\(35\!\cdots\!88\)\( T^{21} + \)\(16\!\cdots\!63\)\( T^{22} - \)\(67\!\cdots\!38\)\( T^{23} + \)\(26\!\cdots\!40\)\( T^{24} - \)\(95\!\cdots\!39\)\( T^{25} + \)\(31\!\cdots\!75\)\( T^{26} - \)\(92\!\cdots\!34\)\( T^{27} + \)\(24\!\cdots\!04\)\( T^{28} - \)\(53\!\cdots\!55\)\( T^{29} + \)\(98\!\cdots\!77\)\( T^{30} - \)\(13\!\cdots\!20\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 + 15 T + 366 T^{2} + 4166 T^{3} + 63112 T^{4} + 600801 T^{5} + 7118236 T^{6} + 59182921 T^{7} + 595812423 T^{8} + 4428544822 T^{9} + 39581642519 T^{10} + 267508054476 T^{11} + 2185412894544 T^{12} + 13627736681152 T^{13} + 104028964880528 T^{14} + 607397885300872 T^{15} + 4406318113508128 T^{16} + 24433425678421227 T^{17} + 170043359575354066 T^{18} + 904036750101585399 T^{19} + 6032249497392627232 T^{20} + 30766525084145069416 T^{21} + \)\(19\!\cdots\!08\)\( T^{22} + \)\(94\!\cdots\!64\)\( T^{23} + \)\(56\!\cdots\!96\)\( T^{24} + \)\(25\!\cdots\!08\)\( T^{25} + \)\(13\!\cdots\!99\)\( T^{26} + \)\(57\!\cdots\!94\)\( T^{27} + \)\(28\!\cdots\!27\)\( T^{28} + \)\(10\!\cdots\!73\)\( T^{29} + \)\(46\!\cdots\!16\)\( T^{30} + \)\(14\!\cdots\!97\)\( T^{31} + \)\(56\!\cdots\!68\)\( T^{32} + \)\(13\!\cdots\!38\)\( T^{33} + \)\(45\!\cdots\!06\)\( T^{34} + \)\(68\!\cdots\!55\)\( T^{35} + \)\(16\!\cdots\!29\)\( T^{36} \))(\( 1 - 56 T + 1919 T^{2} - 48113 T^{3} + 978205 T^{4} - 16860046 T^{5} + 254586879 T^{6} - 3434890242 T^{7} + 42066352834 T^{8} - 472720007895 T^{9} + 4918349057024 T^{10} - 47690421274916 T^{11} + 433348998146773 T^{12} - 3705349253519629 T^{13} + 29916574318889081 T^{14} - 228662300563992558 T^{15} + 1658031228676445269 T^{16} - 11421713005692758978 T^{17} + 74832242387766162423 T^{18} - \)\(46\!\cdots\!78\)\( T^{19} + \)\(27\!\cdots\!51\)\( T^{20} - \)\(15\!\cdots\!82\)\( T^{21} + \)\(83\!\cdots\!57\)\( T^{22} - \)\(42\!\cdots\!38\)\( T^{23} + \)\(20\!\cdots\!17\)\( T^{24} - \)\(95\!\cdots\!61\)\( T^{25} + \)\(41\!\cdots\!09\)\( T^{26} - \)\(16\!\cdots\!36\)\( T^{27} + \)\(63\!\cdots\!48\)\( T^{28} - \)\(22\!\cdots\!55\)\( T^{29} + \)\(74\!\cdots\!42\)\( T^{30} - \)\(22\!\cdots\!02\)\( T^{31} + \)\(62\!\cdots\!63\)\( T^{32} - \)\(15\!\cdots\!94\)\( T^{33} + \)\(32\!\cdots\!65\)\( T^{34} - \)\(59\!\cdots\!33\)\( T^{35} + \)\(87\!\cdots\!23\)\( T^{36} - \)\(94\!\cdots\!24\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))
$41$ (\( 1 + 3 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + T - 24 T^{2} + 41 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 59 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 85 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 74 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 + 3 T + 170 T^{2} + 50 T^{3} + 11626 T^{4} - 29278 T^{5} + 496448 T^{6} - 2150172 T^{7} + 20354368 T^{8} - 49216318 T^{9} + 801275546 T^{10} + 141288050 T^{11} + 19695554170 T^{12} + 14250312723 T^{13} + 194754273881 T^{14} \))(\( 1 - 9 T + 199 T^{2} - 1511 T^{3} + 21975 T^{4} - 155965 T^{5} + 1759117 T^{6} - 11369627 T^{7} + 108763053 T^{8} - 644974505 T^{9} + 5441506152 T^{10} - 29350169344 T^{11} + 223101752232 T^{12} - 1084202142905 T^{13} + 7496058375813 T^{14} - 32127848561147 T^{15} + 203804612734517 T^{16} - 740850007947565 T^{17} + 4279725168534975 T^{18} - 12065222021201831 T^{19} + 65149004944398239 T^{20} - 120803933791371609 T^{21} + 550329031716248441 T^{22} \))(\( 1 - 21 T + 616 T^{2} - 9402 T^{3} + 160488 T^{4} - 1938936 T^{5} + 24485336 T^{6} - 245110356 T^{7} + 2497863778 T^{8} - 21278259882 T^{9} + 182459787904 T^{10} - 1342887611296 T^{11} + 9902669942613 T^{12} - 63386892075414 T^{13} + 406009467647133 T^{14} - 2257394074588576 T^{15} + 12575311042131584 T^{16} - 60127276922420202 T^{17} + 289393007934587378 T^{18} - 1164299741548619796 T^{19} + 4768623833412309016 T^{20} - 15482258984050955256 T^{21} + 52540871887018012968 T^{22} - \)\(12\!\cdots\!02\)\( T^{23} + \)\(33\!\cdots\!56\)\( T^{24} - \)\(47\!\cdots\!01\)\( T^{25} + \)\(92\!\cdots\!21\)\( T^{26} \))(\( 1 + T + 206 T^{2} + 42 T^{3} + 22600 T^{4} - 5720 T^{5} + 1802471 T^{6} - 973585 T^{7} + 116330717 T^{8} - 88412265 T^{9} + 6386509096 T^{10} - 5890073146 T^{11} + 308288137130 T^{12} - 303314192679 T^{13} + 13329630557542 T^{14} - 12435881899839 T^{15} + 518232358515530 T^{16} - 405949731295466 T^{17} + 18046748329622056 T^{18} - 10243109144705265 T^{19} + 552583032180270797 T^{20} - 189609839736433385 T^{21} + 14392596162658957991 T^{22} - 1872624664733456920 T^{23} + \)\(30\!\cdots\!00\)\( T^{24} + 23113819332082434522 T^{25} + \)\(46\!\cdots\!86\)\( T^{26} + \)\(92\!\cdots\!21\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 - T + 381 T^{2} - 753 T^{3} + 71193 T^{4} - 206003 T^{5} + 8769091 T^{6} - 32248993 T^{7} + 807996980 T^{8} - 3423817656 T^{9} + 59693127474 T^{10} - 269410101834 T^{11} + 3672268203653 T^{12} - 16586234784178 T^{13} + 191391546657934 T^{14} - 826335588463734 T^{15} + 8497746395094842 T^{16} - 33879759127013094 T^{17} + 321729189931987054 T^{18} - 1143139887560331938 T^{19} + 10376952271422704933 T^{20} - 31212830909510372634 T^{21} + \)\(28\!\cdots\!34\)\( T^{22} - \)\(66\!\cdots\!36\)\( T^{23} + \)\(64\!\cdots\!80\)\( T^{24} - \)\(10\!\cdots\!73\)\( T^{25} + \)\(11\!\cdots\!91\)\( T^{26} - \)\(11\!\cdots\!23\)\( T^{27} + \)\(16\!\cdots\!33\)\( T^{28} - \)\(69\!\cdots\!13\)\( T^{29} + \)\(14\!\cdots\!41\)\( T^{30} - \)\(15\!\cdots\!01\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 9 T + 262 T^{2} - 2416 T^{3} + 37769 T^{4} - 315207 T^{5} + 3782416 T^{6} - 28401838 T^{7} + 290262313 T^{8} - 2011916927 T^{9} + 18444064407 T^{10} - 119441768717 T^{11} + 1012122769428 T^{12} - 6182374690503 T^{13} + 49052876571800 T^{14} - 283552719845861 T^{15} + 2125239007937044 T^{16} - 11625661513680301 T^{17} + 82457885517195800 T^{18} - 426095446044157263 T^{19} + 2860017049061634708 T^{20} - 13838069564272264117 T^{21} + 87611228560967850087 T^{22} - \)\(39\!\cdots\!87\)\( T^{23} + \)\(23\!\cdots\!73\)\( T^{24} - \)\(92\!\cdots\!18\)\( T^{25} + \)\(50\!\cdots\!16\)\( T^{26} - \)\(17\!\cdots\!87\)\( T^{27} + \)\(85\!\cdots\!89\)\( T^{28} - \)\(22\!\cdots\!36\)\( T^{29} + \)\(99\!\cdots\!82\)\( T^{30} - \)\(13\!\cdots\!09\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 + 17 T + 587 T^{2} + 7983 T^{3} + 157437 T^{4} + 1804251 T^{5} + 26303394 T^{6} + 262317360 T^{7} + 3118583347 T^{8} + 27662680979 T^{9} + 282270497714 T^{10} + 2263125901586 T^{11} + 20458023064018 T^{12} + 150120482591273 T^{13} + 1228554873931248 T^{14} + 8330642142077100 T^{15} + 62666398844152637 T^{16} + 395131743262021859 T^{17} + 2758290334846420354 T^{18} + 16200401473742896219 T^{19} + \)\(10\!\cdots\!97\)\( T^{20} + \)\(57\!\cdots\!00\)\( T^{21} + \)\(34\!\cdots\!28\)\( T^{22} + \)\(17\!\cdots\!73\)\( T^{23} + \)\(97\!\cdots\!38\)\( T^{24} + \)\(44\!\cdots\!66\)\( T^{25} + \)\(22\!\cdots\!94\)\( T^{26} + \)\(90\!\cdots\!19\)\( T^{27} + \)\(41\!\cdots\!47\)\( T^{28} + \)\(14\!\cdots\!60\)\( T^{29} + \)\(59\!\cdots\!14\)\( T^{30} + \)\(16\!\cdots\!71\)\( T^{31} + \)\(59\!\cdots\!57\)\( T^{32} + \)\(12\!\cdots\!83\)\( T^{33} + \)\(37\!\cdots\!67\)\( T^{34} + \)\(44\!\cdots\!77\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))(\( 1 + 7 T + 372 T^{2} + 2494 T^{3} + 72192 T^{4} + 464718 T^{5} + 9659139 T^{6} + 59703885 T^{7} + 994893253 T^{8} + 5895564041 T^{9} + 83515099021 T^{10} + 473396571593 T^{11} + 5907087984900 T^{12} + 31939933276623 T^{13} + 359380353673970 T^{14} + 1847303925885007 T^{15} + 19050148050782657 T^{16} + 92701601847103523 T^{17} + 886536429602488599 T^{18} + 4062791660052265530 T^{19} + 36347993613702032559 T^{20} + \)\(15\!\cdots\!63\)\( T^{21} + \)\(13\!\cdots\!97\)\( T^{22} + \)\(52\!\cdots\!27\)\( T^{23} + \)\(41\!\cdots\!70\)\( T^{24} + \)\(15\!\cdots\!43\)\( T^{25} + \)\(11\!\cdots\!00\)\( T^{26} + \)\(37\!\cdots\!53\)\( T^{27} + \)\(27\!\cdots\!81\)\( T^{28} + \)\(79\!\cdots\!41\)\( T^{29} + \)\(54\!\cdots\!73\)\( T^{30} + \)\(13\!\cdots\!85\)\( T^{31} + \)\(89\!\cdots\!19\)\( T^{32} + \)\(17\!\cdots\!98\)\( T^{33} + \)\(11\!\cdots\!92\)\( T^{34} + \)\(15\!\cdots\!54\)\( T^{35} + \)\(97\!\cdots\!32\)\( T^{36} + \)\(75\!\cdots\!47\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))
$43$ (\( 1 + 6 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 34 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( 1 - 6 T + 78 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 9 T + 217 T^{2} + 1559 T^{3} + 22058 T^{4} + 131173 T^{5} + 1390533 T^{6} + 6894030 T^{7} + 59792919 T^{8} + 242538877 T^{9} + 1753765406 T^{10} + 5329910759 T^{11} + 31900832131 T^{12} + 56892267441 T^{13} + 271818611107 T^{14} \))(\( 1 + 17 T + 261 T^{2} + 2371 T^{3} + 23234 T^{4} + 176729 T^{5} + 1611187 T^{6} + 11859504 T^{7} + 98425636 T^{8} + 660659206 T^{9} + 4960731363 T^{10} + 30775020746 T^{11} + 213311448609 T^{12} + 1221558871894 T^{13} + 7825527041452 T^{14} + 40545284134704 T^{15} + 236858092251841 T^{16} + 1117168170286721 T^{17} + 6315433610460038 T^{18} + 27712722858191971 T^{19} + 131176671715516023 T^{20} + 367395199325832233 T^{21} + 929293739471222707 T^{22} \))(\( 1 + 9 T + 363 T^{2} + 2829 T^{3} + 62991 T^{4} + 434130 T^{5} + 7053472 T^{6} + 43885133 T^{7} + 580184802 T^{8} + 3304680495 T^{9} + 37503098992 T^{10} + 196157482974 T^{11} + 1966417783053 T^{12} + 9376737802572 T^{13} + 84555964671279 T^{14} + 362695186018926 T^{15} + 2981758891556944 T^{16} + 11298044980986495 T^{17} + 85292064394283286 T^{18} + 277413858146650517 T^{19} + 1917264962522113504 T^{20} + 5074198386514922130 T^{21} + 31658811218513677413 T^{22} + 61138883464281140421 T^{23} + \)\(33\!\cdots\!41\)\( T^{24} + \)\(35\!\cdots\!09\)\( T^{25} + \)\(17\!\cdots\!43\)\( T^{26} \))(\( 1 + 25 T + 530 T^{2} + 7932 T^{3} + 110412 T^{4} + 1292969 T^{5} + 14382905 T^{6} + 142501427 T^{7} + 1353730590 T^{8} + 11754987450 T^{9} + 98445954790 T^{10} + 763920391599 T^{11} + 5734234384189 T^{12} + 40147595965818 T^{13} + 272318392470142 T^{14} + 1726346626530174 T^{15} + 10602599376365461 T^{16} + 60737018574861693 T^{17} + 336567128682006790 T^{18} + 1728082402509040350 T^{19} + 8557422529926968910 T^{20} + 38734539967905549689 T^{21} + \)\(16\!\cdots\!05\)\( T^{22} + \)\(64\!\cdots\!67\)\( T^{23} + \)\(23\!\cdots\!88\)\( T^{24} + \)\(73\!\cdots\!24\)\( T^{25} + \)\(21\!\cdots\!30\)\( T^{26} + \)\(42\!\cdots\!75\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 - 31 T + 852 T^{2} - 15670 T^{3} + 264821 T^{4} - 3665962 T^{5} + 47706251 T^{6} - 544725555 T^{7} + 5919219884 T^{8} - 58255247771 T^{9} + 549520016843 T^{10} - 4775114475230 T^{11} + 39944199949147 T^{12} - 310729232709570 T^{13} + 2332751593885182 T^{14} - 16365338610668583 T^{15} + 110929007559371878 T^{16} - 703709560258749069 T^{17} + 4313257697093701518 T^{18} - 24705149105039781990 T^{19} + \)\(13\!\cdots\!47\)\( T^{20} - \)\(70\!\cdots\!90\)\( T^{21} + \)\(34\!\cdots\!07\)\( T^{22} - \)\(15\!\cdots\!97\)\( T^{23} + \)\(69\!\cdots\!84\)\( T^{24} - \)\(27\!\cdots\!65\)\( T^{25} + \)\(10\!\cdots\!99\)\( T^{26} - \)\(34\!\cdots\!34\)\( T^{27} + \)\(10\!\cdots\!21\)\( T^{28} - \)\(26\!\cdots\!10\)\( T^{29} + \)\(62\!\cdots\!48\)\( T^{30} - \)\(98\!\cdots\!17\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 7 T + 372 T^{2} - 3138 T^{3} + 73315 T^{4} - 666780 T^{5} + 10087481 T^{6} - 91367841 T^{7} + 1064678040 T^{8} - 9159628901 T^{9} + 89637382245 T^{10} - 716798756168 T^{11} + 6144361260517 T^{12} - 45322086179990 T^{13} + 347525991033990 T^{14} - 2355177051473659 T^{15} + 16357027715502558 T^{16} - 101272613213367337 T^{17} + 642575557421847510 T^{18} - 3603423105912464930 T^{19} + 21006348421816780117 T^{20} - \)\(10\!\cdots\!24\)\( T^{21} + \)\(56\!\cdots\!05\)\( T^{22} - \)\(24\!\cdots\!07\)\( T^{23} + \)\(12\!\cdots\!40\)\( T^{24} - \)\(45\!\cdots\!63\)\( T^{25} + \)\(21\!\cdots\!69\)\( T^{26} - \)\(61\!\cdots\!60\)\( T^{27} + \)\(29\!\cdots\!15\)\( T^{28} - \)\(53\!\cdots\!34\)\( T^{29} + \)\(27\!\cdots\!28\)\( T^{30} - \)\(22\!\cdots\!49\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - T + 388 T^{2} - 878 T^{3} + 73702 T^{4} - 275013 T^{5} + 9240295 T^{6} - 48874735 T^{7} + 876579751 T^{8} - 5864621513 T^{9} + 68610867706 T^{10} - 521103359185 T^{11} + 4672717098109 T^{12} - 36435312822151 T^{13} + 282210282216185 T^{14} - 2100029747349757 T^{15} + 15017594037839229 T^{16} - 103445385887703081 T^{17} + 694702110628981988 T^{18} - 4448151593171232483 T^{19} + 27767531375964734421 T^{20} - \)\(16\!\cdots\!99\)\( T^{21} + \)\(96\!\cdots\!85\)\( T^{22} - \)\(53\!\cdots\!93\)\( T^{23} + \)\(29\!\cdots\!41\)\( T^{24} - \)\(14\!\cdots\!95\)\( T^{25} + \)\(80\!\cdots\!06\)\( T^{26} - \)\(29\!\cdots\!59\)\( T^{27} + \)\(18\!\cdots\!99\)\( T^{28} - \)\(45\!\cdots\!45\)\( T^{29} + \)\(36\!\cdots\!95\)\( T^{30} - \)\(47\!\cdots\!59\)\( T^{31} + \)\(54\!\cdots\!98\)\( T^{32} - \)\(27\!\cdots\!46\)\( T^{33} + \)\(53\!\cdots\!88\)\( T^{34} - \)\(58\!\cdots\!43\)\( T^{35} + \)\(25\!\cdots\!49\)\( T^{36} \))(\( 1 - 19 T + 541 T^{2} - 8177 T^{3} + 138902 T^{4} - 1756335 T^{5} + 22810067 T^{6} - 249749424 T^{7} + 2714308406 T^{8} - 26376020952 T^{9} + 251013493425 T^{10} - 2205434613904 T^{11} + 18891895734477 T^{12} - 152330616533600 T^{13} + 1197167503618210 T^{14} - 8968364455463072 T^{15} + 65582001060951154 T^{16} - 460827672059565390 T^{17} + 3166245237871279593 T^{18} - 20989222701232991902 T^{19} + \)\(13\!\cdots\!99\)\( T^{20} - \)\(85\!\cdots\!10\)\( T^{21} + \)\(52\!\cdots\!78\)\( T^{22} - \)\(30\!\cdots\!72\)\( T^{23} + \)\(17\!\cdots\!30\)\( T^{24} - \)\(96\!\cdots\!00\)\( T^{25} + \)\(51\!\cdots\!39\)\( T^{26} - \)\(25\!\cdots\!04\)\( T^{27} + \)\(12\!\cdots\!75\)\( T^{28} - \)\(57\!\cdots\!48\)\( T^{29} + \)\(25\!\cdots\!42\)\( T^{30} - \)\(99\!\cdots\!24\)\( T^{31} + \)\(39\!\cdots\!81\)\( T^{32} - \)\(12\!\cdots\!15\)\( T^{33} + \)\(44\!\cdots\!14\)\( T^{34} - \)\(11\!\cdots\!77\)\( T^{35} + \)\(31\!\cdots\!63\)\( T^{36} - \)\(47\!\cdots\!31\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))
$47$ (\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 18 T + 158 T^{2} + 846 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 122 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 10 T + 47 T^{2} )^{2} \))(\( 1 - 11 T + 145 T^{2} - 1339 T^{3} + 14705 T^{4} - 119758 T^{5} + 953008 T^{6} - 6346454 T^{7} + 44791376 T^{8} - 264545422 T^{9} + 1526717215 T^{10} - 6533892859 T^{11} + 33255026015 T^{12} - 118571368619 T^{13} + 506623120463 T^{14} \))(\( 1 + 7 T + 348 T^{2} + 2664 T^{3} + 61373 T^{4} + 467056 T^{5} + 7133325 T^{6} + 50680040 T^{7} + 596259485 T^{8} + 3809875568 T^{9} + 37124292907 T^{10} + 208420861194 T^{11} + 1744841766629 T^{12} + 8416015129712 T^{13} + 61905448511155 T^{14} + 247302428267240 T^{15} + 1635992472058275 T^{16} + 5034497194701424 T^{17} + 31092980772175699 T^{18} + 63433267666931304 T^{19} + 389457404639762916 T^{20} + 368193925650810343 T^{21} + 2472159215084012303 T^{22} \))(\( 1 - 23 T + 607 T^{2} - 9855 T^{3} + 158534 T^{4} - 2026095 T^{5} + 24946377 T^{6} - 265384987 T^{7} + 2704629542 T^{8} - 24695815357 T^{9} + 215886050220 T^{10} - 1720118801318 T^{11} + 13126247577063 T^{12} - 91942347287866 T^{13} + 616933636121961 T^{14} - 3799742432111462 T^{15} + 22413937391991060 T^{16} - 120507700977061117 T^{17} + 620293281242396794 T^{18} - 2860641919956865723 T^{19} + 12638411359986412551 T^{20} - 48243928848960653295 T^{21} + \)\(17\!\cdots\!78\)\( T^{22} - \)\(51\!\cdots\!95\)\( T^{23} + \)\(15\!\cdots\!21\)\( T^{24} - \)\(26\!\cdots\!43\)\( T^{25} + \)\(54\!\cdots\!27\)\( T^{26} \))(\( 1 + 9 T + 350 T^{2} + 3582 T^{3} + 68307 T^{4} + 684242 T^{5} + 9374099 T^{6} + 86334288 T^{7} + 965719113 T^{8} + 8092193530 T^{9} + 77594134130 T^{10} + 590988285775 T^{11} + 4991471177695 T^{12} + 34417211240088 T^{13} + 260228788002610 T^{14} + 1617608928284136 T^{15} + 11026159831528255 T^{16} + 61358176794017825 T^{17} + 378634622025612530 T^{18} + 1855904181783204710 T^{19} + 10409694266357883177 T^{20} + 43738946389511335344 T^{21} + \)\(22\!\cdots\!39\)\( T^{22} + \)\(76\!\cdots\!14\)\( T^{23} + \)\(35\!\cdots\!43\)\( T^{24} + \)\(88\!\cdots\!46\)\( T^{25} + \)\(40\!\cdots\!50\)\( T^{26} + \)\(49\!\cdots\!43\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 + T + 360 T^{2} + 1350 T^{3} + 63404 T^{4} + 418163 T^{5} + 7649067 T^{6} + 68548326 T^{7} + 747449622 T^{8} + 7437562764 T^{9} + 63784570875 T^{10} + 597692191691 T^{11} + 4745753222012 T^{12} + 38339036949818 T^{13} + 298426805613138 T^{14} + 2072618878066403 T^{15} + 15494086707737218 T^{16} + 97413087269120941 T^{17} + 659224813599421842 T^{18} + 3980473833240954214 T^{19} + 23157761828140738172 T^{20} + \)\(13\!\cdots\!37\)\( T^{21} + \)\(68\!\cdots\!75\)\( T^{22} + \)\(37\!\cdots\!32\)\( T^{23} + \)\(17\!\cdots\!42\)\( T^{24} + \)\(76\!\cdots\!42\)\( T^{25} + \)\(40\!\cdots\!83\)\( T^{26} + \)\(10\!\cdots\!89\)\( T^{27} + \)\(73\!\cdots\!64\)\( T^{28} + \)\(73\!\cdots\!50\)\( T^{29} + \)\(92\!\cdots\!40\)\( T^{30} + \)\(12\!\cdots\!43\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 31 T + 941 T^{2} - 18281 T^{3} + 336231 T^{4} - 4931218 T^{5} + 68745838 T^{6} - 824945998 T^{7} + 9479210063 T^{8} - 97272427247 T^{9} + 962214491659 T^{10} - 8677297342675 T^{11} + 75838894223815 T^{12} - 611669521060006 T^{13} + 4799477730874298 T^{14} - 34983489091252572 T^{15} + 248573892822537796 T^{16} - 1644223987288870884 T^{17} + 10602046307501324282 T^{18} - 63505364685013002938 T^{19} + \)\(37\!\cdots\!15\)\( T^{20} - \)\(19\!\cdots\!25\)\( T^{21} + \)\(10\!\cdots\!11\)\( T^{22} - \)\(49\!\cdots\!61\)\( T^{23} + \)\(22\!\cdots\!43\)\( T^{24} - \)\(92\!\cdots\!66\)\( T^{25} + \)\(36\!\cdots\!62\)\( T^{26} - \)\(12\!\cdots\!54\)\( T^{27} + \)\(39\!\cdots\!71\)\( T^{28} - \)\(99\!\cdots\!87\)\( T^{29} + \)\(24\!\cdots\!29\)\( T^{30} - \)\(37\!\cdots\!33\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 31 T + 753 T^{2} + 13091 T^{3} + 197274 T^{4} + 2525137 T^{5} + 29473827 T^{6} + 311740727 T^{7} + 3111974218 T^{8} + 29220169105 T^{9} + 264679717261 T^{10} + 2297383543981 T^{11} + 19369688968200 T^{12} + 157133862498639 T^{13} + 1237282175874877 T^{14} + 9385007085387867 T^{15} + 69206387033259215 T^{16} + 493641831656169754 T^{17} + 3436277445562061196 T^{18} + 23201166087839978438 T^{19} + \)\(15\!\cdots\!35\)\( T^{20} + \)\(97\!\cdots\!41\)\( T^{21} + \)\(60\!\cdots\!37\)\( T^{22} + \)\(36\!\cdots\!73\)\( T^{23} + \)\(20\!\cdots\!00\)\( T^{24} + \)\(11\!\cdots\!03\)\( T^{25} + \)\(63\!\cdots\!21\)\( T^{26} + \)\(32\!\cdots\!35\)\( T^{27} + \)\(16\!\cdots\!82\)\( T^{28} + \)\(77\!\cdots\!81\)\( T^{29} + \)\(34\!\cdots\!07\)\( T^{30} + \)\(13\!\cdots\!99\)\( T^{31} + \)\(50\!\cdots\!06\)\( T^{32} + \)\(15\!\cdots\!13\)\( T^{33} + \)\(42\!\cdots\!13\)\( T^{34} + \)\(82\!\cdots\!97\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))(\( 1 - 25 T + 904 T^{2} - 16894 T^{3} + 361649 T^{4} - 5490414 T^{5} + 88619801 T^{6} - 1143888312 T^{7} + 15210985459 T^{8} - 171652595794 T^{9} + 1965291833203 T^{10} - 19743875550578 T^{11} + 199637602810875 T^{12} - 1807202412082554 T^{13} + 16393786057089957 T^{14} - 134786478179220970 T^{15} + 1107872880178406762 T^{16} - 8312551665909679693 T^{17} + 62279110124776561297 T^{18} - \)\(42\!\cdots\!32\)\( T^{19} + \)\(29\!\cdots\!59\)\( T^{20} - \)\(18\!\cdots\!37\)\( T^{21} + \)\(11\!\cdots\!26\)\( T^{22} - \)\(65\!\cdots\!70\)\( T^{23} + \)\(37\!\cdots\!99\)\( T^{24} - \)\(19\!\cdots\!66\)\( T^{25} + \)\(10\!\cdots\!25\)\( T^{26} - \)\(47\!\cdots\!58\)\( T^{27} + \)\(21\!\cdots\!01\)\( T^{28} - \)\(90\!\cdots\!06\)\( T^{29} + \)\(37\!\cdots\!77\)\( T^{30} - \)\(13\!\cdots\!92\)\( T^{31} + \)\(48\!\cdots\!27\)\( T^{32} - \)\(14\!\cdots\!66\)\( T^{33} + \)\(43\!\cdots\!07\)\( T^{34} - \)\(95\!\cdots\!74\)\( T^{35} + \)\(24\!\cdots\!48\)\( T^{36} - \)\(31\!\cdots\!25\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))
$53$ (\( 1 - 11 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( ( 1 + 11 T + 53 T^{2} )^{2} \))(\( 1 + 18 T + 185 T^{2} + 954 T^{3} + 2809 T^{4} \))(\( 1 + 6 T + 91 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 5 T + 74 T^{2} + 265 T^{3} + 2809 T^{4} \))(\( 1 - T + 216 T^{2} + 139 T^{3} + 22869 T^{4} + 30467 T^{5} + 1664224 T^{6} + 2175415 T^{7} + 88203872 T^{8} + 85581803 T^{9} + 3404668113 T^{10} + 1096776859 T^{11} + 90330226488 T^{12} - 22164361129 T^{13} + 1174711139837 T^{14} \))(\( 1 + 28 T + 760 T^{2} + 13988 T^{3} + 232097 T^{4} + 3194819 T^{5} + 39947629 T^{6} + 438470374 T^{7} + 4419138620 T^{8} + 39984022809 T^{9} + 334085184597 T^{10} + 2528924844716 T^{11} + 17706514783641 T^{12} + 112315120070481 T^{13} + 657908100329740 T^{14} + 3459742155109894 T^{15} + 16705918403836097 T^{16} + 70811122057790651 T^{17} + 272646931422748189 T^{18} + 870888549474117668 T^{19} + 2507820329769621080 T^{20} + 4896849170234365372 T^{21} + 9269035929372191597 T^{22} \))(\( 1 - 31 T + 936 T^{2} - 18071 T^{3} + 328569 T^{4} - 4749105 T^{5} + 64916194 T^{6} - 760070261 T^{7} + 8473173808 T^{8} - 83734170303 T^{9} + 791809806079 T^{10} - 6750789985461 T^{11} + 55228222405121 T^{12} - 410273915363592 T^{13} + 2927095787471413 T^{14} - 18962969069159949 T^{15} + 117882268499623283 T^{16} - 660702879826585743 T^{17} + 3543443097911247344 T^{18} - 16846471748217284669 T^{19} + 76257776247619820378 T^{20} - \)\(29\!\cdots\!05\)\( T^{21} + \)\(10\!\cdots\!77\)\( T^{22} - \)\(31\!\cdots\!79\)\( T^{23} + \)\(86\!\cdots\!92\)\( T^{24} - \)\(15\!\cdots\!71\)\( T^{25} + \)\(26\!\cdots\!73\)\( T^{26} \))(\( 1 + 35 T + 934 T^{2} + 17975 T^{3} + 299033 T^{4} + 4227887 T^{5} + 54144485 T^{6} + 622708390 T^{7} + 6648233679 T^{8} + 65496431709 T^{9} + 608126212712 T^{10} + 5291692221571 T^{11} + 43805743758863 T^{12} + 342748023160961 T^{13} + 2563077085008698 T^{14} + 18165645227530933 T^{15} + 123050334218646167 T^{16} + 787811262870825767 T^{17} + 4798408327005994472 T^{18} + 27390312548286087537 T^{19} + \)\(14\!\cdots\!91\)\( T^{20} + \)\(73\!\cdots\!30\)\( T^{21} + \)\(33\!\cdots\!85\)\( T^{22} + \)\(13\!\cdots\!71\)\( T^{23} + \)\(52\!\cdots\!17\)\( T^{24} + \)\(16\!\cdots\!75\)\( T^{25} + \)\(45\!\cdots\!94\)\( T^{26} + \)\(91\!\cdots\!55\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( 1 - 24 T + 623 T^{2} - 9286 T^{3} + 145196 T^{4} - 1667275 T^{5} + 20422321 T^{6} - 202557693 T^{7} + 2163294243 T^{8} - 19651949700 T^{9} + 190486009842 T^{10} - 1611744454580 T^{11} + 14312697141274 T^{12} - 112880703254671 T^{13} + 924871830380006 T^{14} - 6823886144051675 T^{15} + 52193981804810860 T^{16} - 361665965634738775 T^{17} + 2597964971537436854 T^{18} - 16805340458445654467 T^{19} + \)\(11\!\cdots\!94\)\( T^{20} - \)\(67\!\cdots\!40\)\( T^{21} + \)\(42\!\cdots\!18\)\( T^{22} - \)\(23\!\cdots\!00\)\( T^{23} + \)\(13\!\cdots\!23\)\( T^{24} - \)\(66\!\cdots\!69\)\( T^{25} + \)\(35\!\cdots\!29\)\( T^{26} - \)\(15\!\cdots\!75\)\( T^{27} + \)\(71\!\cdots\!36\)\( T^{28} - \)\(24\!\cdots\!78\)\( T^{29} + \)\(85\!\cdots\!87\)\( T^{30} - \)\(17\!\cdots\!68\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 66 T + 2621 T^{2} - 76058 T^{3} + 1781762 T^{4} - 35276871 T^{5} + 609041687 T^{6} - 9347868667 T^{7} + 129408562699 T^{8} - 1632151424402 T^{9} + 18901860842316 T^{10} - 202148349366060 T^{11} + 2005406612147776 T^{12} - 18514212309862079 T^{13} + 159456108398381176 T^{14} - 1283208801034658221 T^{15} + 9658332823518811780 T^{16} - 68010066454836885713 T^{17} + \)\(44\!\cdots\!84\)\( T^{18} - \)\(27\!\cdots\!83\)\( T^{19} + \)\(15\!\cdots\!56\)\( T^{20} - \)\(84\!\cdots\!80\)\( T^{21} + \)\(41\!\cdots\!64\)\( T^{22} - \)\(19\!\cdots\!74\)\( T^{23} + \)\(80\!\cdots\!39\)\( T^{24} - \)\(30\!\cdots\!11\)\( T^{25} + \)\(10\!\cdots\!63\)\( T^{26} - \)\(32\!\cdots\!87\)\( T^{27} + \)\(87\!\cdots\!42\)\( T^{28} - \)\(19\!\cdots\!34\)\( T^{29} + \)\(36\!\cdots\!49\)\( T^{30} - \)\(48\!\cdots\!62\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 + 35 T + 1002 T^{2} + 20303 T^{3} + 359179 T^{4} + 5356293 T^{5} + 72450797 T^{6} + 876498168 T^{7} + 9860866190 T^{8} + 102370151648 T^{9} + 1007118215698 T^{10} + 9336961305420 T^{11} + 83269959064210 T^{12} + 710236502930910 T^{13} + 5888264586633139 T^{14} + 47091839467003009 T^{15} + 367936393518839916 T^{16} + 2782388009045035942 T^{17} + 20583240410282150440 T^{18} + \)\(14\!\cdots\!26\)\( T^{19} + \)\(10\!\cdots\!44\)\( T^{20} + \)\(70\!\cdots\!93\)\( T^{21} + \)\(46\!\cdots\!59\)\( T^{22} + \)\(29\!\cdots\!30\)\( T^{23} + \)\(18\!\cdots\!90\)\( T^{24} + \)\(10\!\cdots\!40\)\( T^{25} + \)\(62\!\cdots\!78\)\( T^{26} + \)\(33\!\cdots\!84\)\( T^{27} + \)\(17\!\cdots\!10\)\( T^{28} + \)\(81\!\cdots\!96\)\( T^{29} + \)\(35\!\cdots\!77\)\( T^{30} + \)\(13\!\cdots\!89\)\( T^{31} + \)\(49\!\cdots\!51\)\( T^{32} + \)\(14\!\cdots\!71\)\( T^{33} + \)\(38\!\cdots\!42\)\( T^{34} + \)\(71\!\cdots\!55\)\( T^{35} + \)\(10\!\cdots\!89\)\( T^{36} \))(\( 1 - 18 T + 729 T^{2} - 10786 T^{3} + 248005 T^{4} - 3156553 T^{5} + 53632959 T^{6} - 604817569 T^{7} + 8403382051 T^{8} - 85661456697 T^{9} + 1025414824379 T^{10} - 9578389113218 T^{11} + 101873882940499 T^{12} - 879848025198707 T^{13} + 8477677851613975 T^{14} - 68061668751127647 T^{15} + 601679391573782590 T^{16} - 4501409880480265273 T^{17} + 36809960564576726564 T^{18} - \)\(25\!\cdots\!92\)\( T^{19} + \)\(19\!\cdots\!92\)\( T^{20} - \)\(12\!\cdots\!57\)\( T^{21} + \)\(89\!\cdots\!30\)\( T^{22} - \)\(53\!\cdots\!07\)\( T^{23} + \)\(35\!\cdots\!75\)\( T^{24} - \)\(19\!\cdots\!03\)\( T^{25} + \)\(11\!\cdots\!63\)\( T^{26} - \)\(59\!\cdots\!98\)\( T^{27} + \)\(33\!\cdots\!07\)\( T^{28} - \)\(14\!\cdots\!53\)\( T^{29} + \)\(77\!\cdots\!47\)\( T^{30} - \)\(29\!\cdots\!29\)\( T^{31} + \)\(13\!\cdots\!07\)\( T^{32} - \)\(43\!\cdots\!57\)\( T^{33} + \)\(18\!\cdots\!85\)\( T^{34} - \)\(41\!\cdots\!06\)\( T^{35} + \)\(14\!\cdots\!77\)\( T^{36} - \)\(19\!\cdots\!02\)\( T^{37} + \)\(57\!\cdots\!17\)\( T^{38} \))
$59$ (\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 13 T + 156 T^{2} + 767 T^{3} + 3481 T^{4} \))(\( 1 + 68 T^{2} + 3481 T^{4} \))(\( 1 + 112 T^{2} + 3481 T^{4} \))(\( 1 + 5 T + 86 T^{2} + 295 T^{3} + 3481 T^{4} \))(\( 1 + 30 T + 570 T^{2} + 7389 T^{3} + 75460 T^{4} + 617301 T^{5} + 4593588 T^{6} + 33613111 T^{7} + 271021692 T^{8} + 2148824781 T^{9} + 15497899340 T^{10} + 89535180429 T^{11} + 407506850430 T^{12} + 1265416009230 T^{13} + 2488651484819 T^{14} \))(\( 1 - 35 T + 929 T^{2} - 17931 T^{3} + 295556 T^{4} - 4135295 T^{5} + 51799617 T^{6} - 579088080 T^{7} + 5930670234 T^{8} - 55413165022 T^{9} + 479604963105 T^{10} - 3821238360890 T^{11} + 28296692823195 T^{12} - 192893227441582 T^{13} + 1218035121988686 T^{14} - 7017019316156880 T^{15} + 37032804872193483 T^{16} - 174428949862959095 T^{17} + 735535878247164364 T^{18} - 2632816576683079851 T^{19} + 8047923115530438331 T^{20} - 17889086365522449035 T^{21} + 30155888444737842659 T^{22} \))(\( 1 - 28 T + 748 T^{2} - 12353 T^{3} + 200007 T^{4} - 2482731 T^{5} + 31037042 T^{6} - 320236588 T^{7} + 3396643521 T^{8} - 30749512300 T^{9} + 290422351830 T^{10} - 2376472711159 T^{11} + 20434393717531 T^{12} - 152974888166578 T^{13} + 1205629229334329 T^{14} - 8272501507544479 T^{15} + 59646652196493570 T^{16} - 372602941113040300 T^{17} + 2428342988203816779 T^{18} - 13507750173213056908 T^{19} + 77240380657689665398 T^{20} - \)\(36\!\cdots\!51\)\( T^{21} + \)\(17\!\cdots\!73\)\( T^{22} - \)\(63\!\cdots\!53\)\( T^{23} + \)\(22\!\cdots\!32\)\( T^{24} - \)\(49\!\cdots\!68\)\( T^{25} + \)\(10\!\cdots\!79\)\( T^{26} \))(\( 1 - 10 T + 389 T^{2} - 3033 T^{3} + 74371 T^{4} - 531008 T^{5} + 10011285 T^{6} - 70337571 T^{7} + 1054894651 T^{8} - 7383068244 T^{9} + 90904277275 T^{10} - 631193665181 T^{11} + 6652047058913 T^{12} - 44814617366759 T^{13} + 421301398427094 T^{14} - 2644062424638781 T^{15} + 23155775812076153 T^{16} - 129633923761208599 T^{17} + 1101519944185271275 T^{18} - 5278334888810860956 T^{19} + 44496019314216454291 T^{20} - \)\(17\!\cdots\!49\)\( T^{21} + \)\(14\!\cdots\!85\)\( T^{22} - \)\(46\!\cdots\!12\)\( T^{23} + \)\(38\!\cdots\!71\)\( T^{24} - \)\(91\!\cdots\!47\)\( T^{25} + \)\(69\!\cdots\!09\)\( T^{26} - \)\(10\!\cdots\!90\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 + 17 T + 846 T^{2} + 11802 T^{3} + 329143 T^{4} + 3917144 T^{5} + 79697417 T^{6} + 829139959 T^{7} + 13603939474 T^{8} + 125686534583 T^{9} + 1749118455509 T^{10} + 14494136574176 T^{11} + 176087374935777 T^{12} + 1316023362978522 T^{13} + 14200806947115068 T^{14} + 95904511241320065 T^{15} + 928657148255566346 T^{16} + 5658366163237883835 T^{17} + 49433008982907551708 T^{18} + \)\(27\!\cdots\!38\)\( T^{19} + \)\(21\!\cdots\!97\)\( T^{20} + \)\(10\!\cdots\!24\)\( T^{21} + \)\(73\!\cdots\!69\)\( T^{22} + \)\(31\!\cdots\!77\)\( T^{23} + \)\(19\!\cdots\!54\)\( T^{24} + \)\(71\!\cdots\!01\)\( T^{25} + \)\(40\!\cdots\!17\)\( T^{26} + \)\(11\!\cdots\!96\)\( T^{27} + \)\(58\!\cdots\!83\)\( T^{28} + \)\(12\!\cdots\!58\)\( T^{29} + \)\(52\!\cdots\!06\)\( T^{30} + \)\(62\!\cdots\!83\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 7 T + 442 T^{2} + 3508 T^{3} + 105593 T^{4} + 856382 T^{5} + 17639389 T^{6} + 139554059 T^{7} + 2261197320 T^{8} + 17115674831 T^{9} + 234152631353 T^{10} + 1678592886254 T^{11} + 20227940459783 T^{12} + 136519444242156 T^{13} + 1488182686904536 T^{14} + 9408447183719123 T^{15} + 94379018439678286 T^{16} + 555098383839428257 T^{17} + 5180363933114689816 T^{18} + 28038226939009757124 T^{19} + \)\(24\!\cdots\!63\)\( T^{20} + \)\(12\!\cdots\!46\)\( T^{21} + \)\(98\!\cdots\!73\)\( T^{22} + \)\(42\!\cdots\!89\)\( T^{23} + \)\(33\!\cdots\!20\)\( T^{24} + \)\(12\!\cdots\!01\)\( T^{25} + \)\(90\!\cdots\!89\)\( T^{26} + \)\(25\!\cdots\!38\)\( T^{27} + \)\(18\!\cdots\!33\)\( T^{28} + \)\(36\!\cdots\!32\)\( T^{29} + \)\(27\!\cdots\!62\)\( T^{30} + \)\(25\!\cdots\!93\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 46 T + 1709 T^{2} + 44939 T^{3} + 1028319 T^{4} + 19836014 T^{5} + 345643777 T^{6} + 5379928797 T^{7} + 77278229780 T^{8} + 1019115860932 T^{9} + 12568554567858 T^{10} + 144505310405158 T^{11} + 1567113639682192 T^{12} + 15990154268072311 T^{13} + 154748085150649455 T^{14} + 1416913606523974460 T^{15} + 12346169576116035044 T^{16} + \)\(10\!\cdots\!35\)\( T^{17} + \)\(80\!\cdots\!90\)\( T^{18} + \)\(60\!\cdots\!65\)\( T^{19} + \)\(42\!\cdots\!64\)\( T^{20} + \)\(29\!\cdots\!40\)\( T^{21} + \)\(18\!\cdots\!55\)\( T^{22} + \)\(11\!\cdots\!89\)\( T^{23} + \)\(66\!\cdots\!72\)\( T^{24} + \)\(35\!\cdots\!02\)\( T^{25} + \)\(18\!\cdots\!18\)\( T^{26} + \)\(88\!\cdots\!48\)\( T^{27} + \)\(39\!\cdots\!80\)\( T^{28} + \)\(16\!\cdots\!23\)\( T^{29} + \)\(61\!\cdots\!37\)\( T^{30} + \)\(20\!\cdots\!06\)\( T^{31} + \)\(63\!\cdots\!59\)\( T^{32} + \)\(16\!\cdots\!61\)\( T^{33} + \)\(36\!\cdots\!69\)\( T^{34} + \)\(58\!\cdots\!74\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))(\( 1 - 11 T + 625 T^{2} - 6723 T^{3} + 195828 T^{4} - 2071013 T^{5} + 41248883 T^{6} - 425750946 T^{7} + 6571435112 T^{8} - 65378594338 T^{9} + 841495712425 T^{10} - 7973031579512 T^{11} + 89681549643081 T^{12} - 802152520437678 T^{13} + 8123426402651024 T^{14} - 68246189918775774 T^{15} + 633654102053130070 T^{16} - 4987112049848041672 T^{17} + 42904033250390068767 T^{18} - \)\(31\!\cdots\!46\)\( T^{19} + \)\(25\!\cdots\!53\)\( T^{20} - \)\(17\!\cdots\!32\)\( T^{21} + \)\(13\!\cdots\!30\)\( T^{22} - \)\(82\!\cdots\!14\)\( T^{23} + \)\(58\!\cdots\!76\)\( T^{24} - \)\(33\!\cdots\!98\)\( T^{25} + \)\(22\!\cdots\!39\)\( T^{26} - \)\(11\!\cdots\!52\)\( T^{27} + \)\(72\!\cdots\!75\)\( T^{28} - \)\(33\!\cdots\!38\)\( T^{29} + \)\(19\!\cdots\!08\)\( T^{30} - \)\(75\!\cdots\!26\)\( T^{31} + \)\(43\!\cdots\!57\)\( T^{32} - \)\(12\!\cdots\!93\)\( T^{33} + \)\(71\!\cdots\!72\)\( T^{34} - \)\(14\!\cdots\!43\)\( T^{35} + \)\(79\!\cdots\!75\)\( T^{36} - \)\(82\!\cdots\!31\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 7 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 15 T + 174 T^{2} + 915 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 168 T^{2} + 976 T^{3} + 3721 T^{4} \))(\( 1 - 4 T + 120 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 13 T + 160 T^{2} + 793 T^{3} + 3721 T^{4} \))(\( 1 + 19 T + 427 T^{2} + 5649 T^{3} + 75542 T^{4} + 765723 T^{5} + 7510227 T^{6} + 59966461 T^{7} + 458123847 T^{8} + 2849255283 T^{9} + 17146598702 T^{10} + 78215155809 T^{11} + 360642620527 T^{12} + 978887112859 T^{13} + 3142742836021 T^{14} \))(\( 1 + 6 T + 578 T^{2} + 2995 T^{3} + 155515 T^{4} + 699413 T^{5} + 25807191 T^{6} + 100980199 T^{7} + 2944011895 T^{8} + 10017465515 T^{9} + 242968967593 T^{10} + 715340296626 T^{11} + 14821107023173 T^{12} + 37274989181315 T^{13} + 668234763938995 T^{14} + 1398155779502359 T^{15} + 21796658057800491 T^{16} + 36034019592950093 T^{17} + 488743652143805815 T^{18} + 574163402426856595 T^{19} + 6759216441658133498 T^{20} + 4280057469977295606 T^{21} + 43513917611435838661 T^{22} \))(\( 1 - 29 T + 1023 T^{2} - 20439 T^{3} + 425921 T^{4} - 6588276 T^{5} + 102071192 T^{6} - 1292237308 T^{7} + 16152643052 T^{8} - 172446855471 T^{9} + 1807344944080 T^{10} - 16534828328737 T^{11} + 148161174495311 T^{12} - 1169622992942008 T^{13} + 9037831644213971 T^{14} - 61526096211230377 T^{15} + 410232962752222480 T^{16} - 2387671741801446111 T^{17} + 13642462573092550652 T^{18} - 66576549871410860188 T^{19} + \)\(32\!\cdots\!32\)\( T^{20} - \)\(12\!\cdots\!56\)\( T^{21} + \)\(49\!\cdots\!61\)\( T^{22} - \)\(14\!\cdots\!39\)\( T^{23} + \)\(44\!\cdots\!03\)\( T^{24} - \)\(76\!\cdots\!09\)\( T^{25} + \)\(16\!\cdots\!81\)\( T^{26} \))(\( 1 - T + 410 T^{2} - 890 T^{3} + 87588 T^{4} - 279433 T^{5} + 12931865 T^{6} - 50711894 T^{7} + 1484437808 T^{8} - 6339757701 T^{9} + 139727676318 T^{10} - 597738020304 T^{11} + 11017030143027 T^{12} - 44768426473041 T^{13} + 731807583059774 T^{14} - 2730874014855501 T^{15} + 40994369162203467 T^{16} - 135675173586622224 T^{17} + 1934647189598493438 T^{18} - 5354535903500864001 T^{19} + 76478791583782240688 T^{20} - \)\(15\!\cdots\!74\)\( T^{21} + \)\(24\!\cdots\!65\)\( T^{22} - \)\(32\!\cdots\!53\)\( T^{23} + \)\(62\!\cdots\!88\)\( T^{24} - \)\(38\!\cdots\!90\)\( T^{25} + \)\(10\!\cdots\!10\)\( T^{26} - \)\(16\!\cdots\!81\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( 1 - 32 T + 1206 T^{2} - 25791 T^{3} + 574786 T^{4} - 9432859 T^{5} + 157027093 T^{6} - 2115073800 T^{7} + 28728344596 T^{8} - 330500301176 T^{9} + 3837456872265 T^{10} - 38710131992009 T^{11} + 395349964688070 T^{12} - 3560087269732381 T^{13} + 32564374072402884 T^{14} - 264721387143865088 T^{15} + 2190402127678037446 T^{16} - 16148004615775770368 T^{17} + \)\(12\!\cdots\!64\)\( T^{18} - \)\(80\!\cdots\!61\)\( T^{19} + \)\(54\!\cdots\!70\)\( T^{20} - \)\(32\!\cdots\!09\)\( T^{21} + \)\(19\!\cdots\!65\)\( T^{22} - \)\(10\!\cdots\!96\)\( T^{23} + \)\(55\!\cdots\!76\)\( T^{24} - \)\(24\!\cdots\!00\)\( T^{25} + \)\(11\!\cdots\!93\)\( T^{26} - \)\(41\!\cdots\!99\)\( T^{27} + \)\(15\!\cdots\!06\)\( T^{28} - \)\(41\!\cdots\!71\)\( T^{29} + \)\(11\!\cdots\!46\)\( T^{30} - \)\(19\!\cdots\!32\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 6 T + 323 T^{2} - 1803 T^{3} + 51999 T^{4} - 310708 T^{5} + 5859564 T^{6} - 41551842 T^{7} + 551504573 T^{8} - 4527561984 T^{9} + 47537189043 T^{10} - 403868693098 T^{11} + 3813583117651 T^{12} - 30173927981267 T^{13} + 277792860692578 T^{14} - 1985788550129320 T^{15} + 18004760530932760 T^{16} - 121133101557888520 T^{17} + 1033667234637082738 T^{18} - 6848908347115964927 T^{19} + 52802265487280039491 T^{20} - \)\(34\!\cdots\!98\)\( T^{21} + \)\(24\!\cdots\!23\)\( T^{22} - \)\(14\!\cdots\!64\)\( T^{23} + \)\(10\!\cdots\!13\)\( T^{24} - \)\(48\!\cdots\!22\)\( T^{25} + \)\(41\!\cdots\!64\)\( T^{26} - \)\(13\!\cdots\!88\)\( T^{27} + \)\(13\!\cdots\!79\)\( T^{28} - \)\(29\!\cdots\!43\)\( T^{29} + \)\(31\!\cdots\!43\)\( T^{30} - \)\(36\!\cdots\!06\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 + 5 T + 313 T^{2} + 823 T^{3} + 52165 T^{4} + 17522 T^{5} + 6076918 T^{6} - 11076242 T^{7} + 573805076 T^{8} - 2160722153 T^{9} + 47466893999 T^{10} - 243623260628 T^{11} + 3639796890962 T^{12} - 20608000137639 T^{13} + 266055733023234 T^{14} - 1442983180432481 T^{15} + 18359172200402956 T^{16} - 91434935405685095 T^{17} + 1172250317548098592 T^{18} - 5577531059746790795 T^{19} + 68314479757699399276 T^{20} - \)\(32\!\cdots\!61\)\( T^{21} + \)\(36\!\cdots\!94\)\( T^{22} - \)\(17\!\cdots\!39\)\( T^{23} + \)\(18\!\cdots\!82\)\( T^{24} - \)\(76\!\cdots\!88\)\( T^{25} + \)\(90\!\cdots\!19\)\( T^{26} - \)\(25\!\cdots\!73\)\( T^{27} + \)\(40\!\cdots\!76\)\( T^{28} - \)\(48\!\cdots\!62\)\( T^{29} + \)\(16\!\cdots\!78\)\( T^{30} + \)\(28\!\cdots\!82\)\( T^{31} + \)\(51\!\cdots\!65\)\( T^{32} + \)\(49\!\cdots\!23\)\( T^{33} + \)\(11\!\cdots\!93\)\( T^{34} + \)\(11\!\cdots\!05\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))(\( 1 - 26 T + 838 T^{2} - 15329 T^{3} + 298583 T^{4} - 4294165 T^{5} + 63615119 T^{6} - 761644687 T^{7} + 9351456495 T^{8} - 96581854497 T^{9} + 1031428248461 T^{10} - 9443877771964 T^{11} + 90986491118717 T^{12} - 758071858895611 T^{13} + 6812650245376485 T^{14} - 53082743698333913 T^{15} + 458408958260406348 T^{16} - 3427992803436643349 T^{17} + 29015749356968724265 T^{18} - \)\(21\!\cdots\!10\)\( T^{19} + \)\(17\!\cdots\!65\)\( T^{20} - \)\(12\!\cdots\!29\)\( T^{21} + \)\(10\!\cdots\!88\)\( T^{22} - \)\(73\!\cdots\!33\)\( T^{23} + \)\(57\!\cdots\!85\)\( T^{24} - \)\(39\!\cdots\!71\)\( T^{25} + \)\(28\!\cdots\!57\)\( T^{26} - \)\(18\!\cdots\!84\)\( T^{27} + \)\(12\!\cdots\!01\)\( T^{28} - \)\(68\!\cdots\!97\)\( T^{29} + \)\(40\!\cdots\!95\)\( T^{30} - \)\(20\!\cdots\!27\)\( T^{31} + \)\(10\!\cdots\!39\)\( T^{32} - \)\(42\!\cdots\!65\)\( T^{33} + \)\(17\!\cdots\!83\)\( T^{34} - \)\(56\!\cdots\!69\)\( T^{35} + \)\(18\!\cdots\!98\)\( T^{36} - \)\(35\!\cdots\!06\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))
$67$ (\( 1 - 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( ( 1 + 2 T + 67 T^{2} )^{2} \))(\( 1 + 116 T^{2} + 4489 T^{4} \))(\( 1 - 4 T - 12 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 126 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 30 T + 675 T^{2} + 11360 T^{3} + 157485 T^{4} + 1838995 T^{5} + 18608402 T^{6} + 162480644 T^{7} + 1246762934 T^{8} + 8255248555 T^{9} + 47365661055 T^{10} + 228916734560 T^{11} + 911334447225 T^{12} + 2713751465070 T^{13} + 6060711605323 T^{14} \))(\( 1 + 22 T + 283 T^{2} + 2634 T^{3} + 21175 T^{4} + 155113 T^{5} + 1264826 T^{6} + 10435972 T^{7} + 93771899 T^{8} + 1070765649 T^{9} + 11695961050 T^{10} + 106234297972 T^{11} + 783629390350 T^{12} + 4806666998361 T^{13} + 28203117658937 T^{14} + 210296534524612 T^{15} + 1707673338586382 T^{16} + 14031271033380097 T^{17} + 128335568242714525 T^{18} + 1069582262684192394 T^{19} + 7699449234151470001 T^{20} + 40102431700138751878 T^{21} + \)\(12\!\cdots\!83\)\( T^{22} \))(\( 1 + 18 T + 515 T^{2} + 7308 T^{3} + 124920 T^{4} + 1475761 T^{5} + 19125783 T^{6} + 196479200 T^{7} + 2123208520 T^{8} + 19682935334 T^{9} + 187612591758 T^{10} + 1616331925468 T^{11} + 14149667857895 T^{12} + 115112160627838 T^{13} + 948027746478965 T^{14} + 7255714013425852 T^{15} + 56426925934911354 T^{16} + 396633211550609414 T^{17} + 2866597130248311640 T^{18} + 17773190561859384800 T^{19} + \)\(11\!\cdots\!09\)\( T^{20} + \)\(59\!\cdots\!01\)\( T^{21} + \)\(33\!\cdots\!40\)\( T^{22} + \)\(13\!\cdots\!92\)\( T^{23} + \)\(62\!\cdots\!45\)\( T^{24} + \)\(14\!\cdots\!98\)\( T^{25} + \)\(54\!\cdots\!87\)\( T^{26} \))(\( 1 + 38 T + 1174 T^{2} + 23934 T^{3} + 422665 T^{4} + 5839509 T^{5} + 71970295 T^{6} + 723216019 T^{7} + 6601917413 T^{8} + 48533153402 T^{9} + 331369870442 T^{10} + 1636952749842 T^{11} + 8113580369697 T^{12} + 14028985989802 T^{13} + 123870851464306 T^{14} + 939942061316734 T^{15} + 36421862279569833 T^{16} + 492334819900729446 T^{17} + 6677474355031065482 T^{18} + 65525828929922664014 T^{19} + \)\(59\!\cdots\!97\)\( T^{20} + \)\(43\!\cdots\!37\)\( T^{21} + \)\(29\!\cdots\!95\)\( T^{22} + \)\(15\!\cdots\!23\)\( T^{23} + \)\(77\!\cdots\!85\)\( T^{24} + \)\(29\!\cdots\!22\)\( T^{25} + \)\(96\!\cdots\!14\)\( T^{26} + \)\(20\!\cdots\!06\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 - 16 T + 628 T^{2} - 8280 T^{3} + 190794 T^{4} - 2210435 T^{5} + 38583413 T^{6} - 404285065 T^{7} + 5872118516 T^{8} - 56444576871 T^{9} + 715144787325 T^{10} - 6351231831685 T^{11} + 72089223934430 T^{12} - 593244848334966 T^{13} + 6130469576154946 T^{14} - 46757932432905050 T^{15} + 444257383187169606 T^{16} - 3132781473004638350 T^{17} + 27519677927359552594 T^{18} - \)\(17\!\cdots\!58\)\( T^{19} + \)\(14\!\cdots\!30\)\( T^{20} - \)\(85\!\cdots\!95\)\( T^{21} + \)\(64\!\cdots\!25\)\( T^{22} - \)\(34\!\cdots\!33\)\( T^{23} + \)\(23\!\cdots\!56\)\( T^{24} - \)\(10\!\cdots\!55\)\( T^{25} + \)\(70\!\cdots\!37\)\( T^{26} - \)\(26\!\cdots\!05\)\( T^{27} + \)\(15\!\cdots\!34\)\( T^{28} - \)\(45\!\cdots\!60\)\( T^{29} + \)\(23\!\cdots\!12\)\( T^{30} - \)\(39\!\cdots\!88\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 16 T + 766 T^{2} - 9522 T^{3} + 266198 T^{4} - 2737347 T^{5} + 58496417 T^{6} - 519287669 T^{7} + 9388084842 T^{8} - 74027457819 T^{9} + 1185159368461 T^{10} - 8444953971409 T^{11} + 122332956376634 T^{12} - 795520428449380 T^{13} + 10542611262284876 T^{14} - 62937864816399986 T^{15} + 767216039759836106 T^{16} - 4216836942698799062 T^{17} + 47325781956396808364 T^{18} - \)\(23\!\cdots\!40\)\( T^{19} + \)\(24\!\cdots\!14\)\( T^{20} - \)\(11\!\cdots\!63\)\( T^{21} + \)\(10\!\cdots\!09\)\( T^{22} - \)\(44\!\cdots\!37\)\( T^{23} + \)\(38\!\cdots\!22\)\( T^{24} - \)\(14\!\cdots\!43\)\( T^{25} + \)\(10\!\cdots\!33\)\( T^{26} - \)\(33\!\cdots\!01\)\( T^{27} + \)\(21\!\cdots\!78\)\( T^{28} - \)\(52\!\cdots\!14\)\( T^{29} + \)\(28\!\cdots\!14\)\( T^{30} - \)\(39\!\cdots\!88\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 6 T + 660 T^{2} - 2744 T^{3} + 206847 T^{4} - 546815 T^{5} + 41865837 T^{6} - 58775543 T^{7} + 6267210834 T^{8} - 2850792910 T^{9} + 751996954474 T^{10} + 126073507818 T^{11} + 76266450675238 T^{12} + 35752074266697 T^{13} + 6762717540256435 T^{14} + 3616840565032217 T^{15} + 533791607456110448 T^{16} + 269073439163604974 T^{17} + 37755976465866968420 T^{18} + 18027920423961533258 T^{19} + \)\(23\!\cdots\!72\)\( T^{20} + \)\(10\!\cdots\!71\)\( T^{21} + \)\(13\!\cdots\!35\)\( T^{22} + \)\(48\!\cdots\!79\)\( T^{23} + \)\(68\!\cdots\!22\)\( T^{24} + \)\(76\!\cdots\!14\)\( T^{25} + \)\(30\!\cdots\!34\)\( T^{26} - \)\(77\!\cdots\!70\)\( T^{27} + \)\(11\!\cdots\!66\)\( T^{28} - \)\(71\!\cdots\!69\)\( T^{29} + \)\(34\!\cdots\!57\)\( T^{30} - \)\(29\!\cdots\!05\)\( T^{31} + \)\(75\!\cdots\!63\)\( T^{32} - \)\(67\!\cdots\!92\)\( T^{33} + \)\(10\!\cdots\!60\)\( T^{34} - \)\(66\!\cdots\!62\)\( T^{35} + \)\(74\!\cdots\!09\)\( T^{36} \))(\( 1 - 24 T + 1065 T^{2} - 20598 T^{3} + 528809 T^{4} - 8644973 T^{5} + 165769208 T^{6} - 2361709360 T^{7} + 37198542309 T^{8} - 471412532131 T^{9} + 6396164360286 T^{10} - 73119929927616 T^{11} + 878356408508454 T^{12} - 9144679664174609 T^{13} + 98919019711057509 T^{14} - 943722960976640048 T^{15} + 9291719328933613139 T^{16} - 81516068920894131031 T^{17} + \)\(73\!\cdots\!96\)\( T^{18} - \)\(59\!\cdots\!16\)\( T^{19} + \)\(49\!\cdots\!32\)\( T^{20} - \)\(36\!\cdots\!59\)\( T^{21} + \)\(27\!\cdots\!57\)\( T^{22} - \)\(19\!\cdots\!08\)\( T^{23} + \)\(13\!\cdots\!63\)\( T^{24} - \)\(82\!\cdots\!21\)\( T^{25} + \)\(53\!\cdots\!42\)\( T^{26} - \)\(29\!\cdots\!56\)\( T^{27} + \)\(17\!\cdots\!42\)\( T^{28} - \)\(85\!\cdots\!19\)\( T^{29} + \)\(45\!\cdots\!47\)\( T^{30} - \)\(19\!\cdots\!60\)\( T^{31} + \)\(90\!\cdots\!96\)\( T^{32} - \)\(31\!\cdots\!17\)\( T^{33} + \)\(13\!\cdots\!87\)\( T^{34} - \)\(33\!\cdots\!38\)\( T^{35} + \)\(11\!\cdots\!55\)\( T^{36} - \)\(17\!\cdots\!16\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))
$71$ (\( 1 - 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 + 18 T + 206 T^{2} + 1278 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 176 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 172 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( 1 - 8 T + 246 T^{2} - 1787 T^{3} + 34468 T^{4} - 225343 T^{5} + 3268094 T^{6} - 18726838 T^{7} + 232034674 T^{8} - 1135954063 T^{9} + 12336476348 T^{10} - 45410673947 T^{11} + 443840420346 T^{12} - 1024802271368 T^{13} + 9095120158391 T^{14} \))(\( 1 + 22 T + 619 T^{2} + 9193 T^{3} + 157535 T^{4} + 1875828 T^{5} + 25189813 T^{6} + 258501834 T^{7} + 2939448413 T^{8} + 26553256573 T^{9} + 263699709796 T^{10} + 2119146874428 T^{11} + 18722679395516 T^{12} + 133854966384493 T^{13} + 1052060920945243 T^{14} + 6568966143522954 T^{15} + 45448199960801363 T^{16} + 240294099386961588 T^{17} + 1432799754152126185 T^{18} + 5936412212742280873 T^{19} + 28380221944719950189 T^{20} + 71615358122217386422 T^{21} + \)\(23\!\cdots\!71\)\( T^{22} \))(\( 1 - 10 T + 556 T^{2} - 4573 T^{3} + 149491 T^{4} - 1052465 T^{5} + 26282634 T^{6} - 161622081 T^{7} + 3414944265 T^{8} - 18615640006 T^{9} + 350734762938 T^{10} - 1720351297082 T^{11} + 29653858976227 T^{12} - 132764914433646 T^{13} + 2105423987312117 T^{14} - 8672290888590362 T^{15} + 125531829737902518 T^{16} - 473054705443310086 T^{17} + 6161342674942122015 T^{18} - 20703834464002859601 T^{19} + \)\(23\!\cdots\!94\)\( T^{20} - \)\(67\!\cdots\!65\)\( T^{21} + \)\(68\!\cdots\!21\)\( T^{22} - \)\(14\!\cdots\!73\)\( T^{23} + \)\(12\!\cdots\!76\)\( T^{24} - \)\(16\!\cdots\!10\)\( T^{25} + \)\(11\!\cdots\!11\)\( T^{26} \))(\( 1 + 10 T + 621 T^{2} + 5411 T^{3} + 182283 T^{4} + 1425360 T^{5} + 34456003 T^{6} + 247816664 T^{7} + 4799991247 T^{8} + 32264035049 T^{9} + 530496962459 T^{10} + 3348973491864 T^{11} + 48460938627045 T^{12} + 285739722695784 T^{13} + 3734602641050538 T^{14} + 20287520311400664 T^{15} + 244291591618933845 T^{16} + 1198634451446536104 T^{17} + 13480819581477083579 T^{18} + 58211719017098523199 T^{19} + \)\(61\!\cdots\!87\)\( T^{20} + \)\(22\!\cdots\!24\)\( T^{21} + \)\(22\!\cdots\!83\)\( T^{22} + \)\(65\!\cdots\!60\)\( T^{23} + \)\(59\!\cdots\!83\)\( T^{24} + \)\(12\!\cdots\!81\)\( T^{25} + \)\(10\!\cdots\!61\)\( T^{26} + \)\(11\!\cdots\!10\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))(\( 1 + 10 T + 733 T^{2} + 8415 T^{3} + 271870 T^{4} + 3298766 T^{5} + 67832304 T^{6} + 816827387 T^{7} + 12630578324 T^{8} + 144866921557 T^{9} + 1840550492694 T^{10} + 19647637055160 T^{11} + 215273356920058 T^{12} + 2113451975430609 T^{13} + 20509996777358637 T^{14} + 183899987372631804 T^{15} + 1604770401332365030 T^{16} + 13056899103456858084 T^{17} + \)\(10\!\cdots\!17\)\( T^{18} + \)\(75\!\cdots\!99\)\( T^{19} + \)\(54\!\cdots\!98\)\( T^{20} + \)\(35\!\cdots\!60\)\( T^{21} + \)\(23\!\cdots\!74\)\( T^{22} + \)\(13\!\cdots\!87\)\( T^{23} + \)\(81\!\cdots\!64\)\( T^{24} + \)\(37\!\cdots\!97\)\( T^{25} + \)\(22\!\cdots\!04\)\( T^{26} + \)\(76\!\cdots\!86\)\( T^{27} + \)\(44\!\cdots\!70\)\( T^{28} + \)\(98\!\cdots\!65\)\( T^{29} + \)\(60\!\cdots\!73\)\( T^{30} + \)\(58\!\cdots\!10\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 - 46 T + 1696 T^{2} - 44053 T^{3} + 1001168 T^{4} - 19136619 T^{5} + 332551066 T^{6} - 5155299858 T^{7} + 74144424281 T^{8} - 977582113019 T^{9} + 12099134092469 T^{10} - 139298259299498 T^{11} + 1516078883966442 T^{12} - 15474989005321276 T^{13} + 149928022065044389 T^{14} - 1368030361292835759 T^{15} + 11870282787987010192 T^{16} - 97130155651791338889 T^{17} + \)\(75\!\cdots\!49\)\( T^{18} - \)\(55\!\cdots\!36\)\( T^{19} + \)\(38\!\cdots\!02\)\( T^{20} - \)\(25\!\cdots\!98\)\( T^{21} + \)\(15\!\cdots\!49\)\( T^{22} - \)\(88\!\cdots\!29\)\( T^{23} + \)\(47\!\cdots\!41\)\( T^{24} - \)\(23\!\cdots\!98\)\( T^{25} + \)\(10\!\cdots\!66\)\( T^{26} - \)\(44\!\cdots\!49\)\( T^{27} + \)\(16\!\cdots\!88\)\( T^{28} - \)\(51\!\cdots\!83\)\( T^{29} + \)\(14\!\cdots\!76\)\( T^{30} - \)\(27\!\cdots\!46\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 22 T + 816 T^{2} + 13317 T^{3} + 296343 T^{4} + 3949811 T^{5} + 67461988 T^{6} + 771642797 T^{7} + 11118168119 T^{8} + 112487037082 T^{9} + 1438298463717 T^{10} + 13144317642374 T^{11} + 154065969757915 T^{12} + 1293495497977143 T^{13} + 14217749002563904 T^{14} + 111372864315380429 T^{15} + 1165348206806512150 T^{16} + 8636949642215036499 T^{17} + 86585290392974234382 T^{18} + \)\(61\!\cdots\!29\)\( T^{19} + \)\(58\!\cdots\!50\)\( T^{20} + \)\(39\!\cdots\!19\)\( T^{21} + \)\(36\!\cdots\!24\)\( T^{22} + \)\(23\!\cdots\!93\)\( T^{23} + \)\(19\!\cdots\!15\)\( T^{24} + \)\(11\!\cdots\!34\)\( T^{25} + \)\(92\!\cdots\!37\)\( T^{26} + \)\(51\!\cdots\!42\)\( T^{27} + \)\(36\!\cdots\!19\)\( T^{28} + \)\(17\!\cdots\!87\)\( T^{29} + \)\(11\!\cdots\!08\)\( T^{30} + \)\(46\!\cdots\!21\)\( T^{31} + \)\(24\!\cdots\!83\)\( T^{32} + \)\(78\!\cdots\!67\)\( T^{33} + \)\(34\!\cdots\!36\)\( T^{34} + \)\(65\!\cdots\!02\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 + 32 T + 1227 T^{2} + 28835 T^{3} + 680427 T^{4} + 12842100 T^{5} + 234406211 T^{6} + 3740306330 T^{7} + 57238298625 T^{8} + 796894059719 T^{9} + 10634242395334 T^{10} + 131843183828886 T^{11} + 1569149036104108 T^{12} + 17561592195883763 T^{13} + 189022343080292513 T^{14} + 1927041274911330686 T^{15} + 18922276766488552162 T^{16} + \)\(17\!\cdots\!86\)\( T^{17} + \)\(15\!\cdots\!38\)\( T^{18} + \)\(13\!\cdots\!34\)\( T^{19} + \)\(11\!\cdots\!98\)\( T^{20} + \)\(89\!\cdots\!26\)\( T^{21} + \)\(67\!\cdots\!82\)\( T^{22} + \)\(48\!\cdots\!66\)\( T^{23} + \)\(34\!\cdots\!63\)\( T^{24} + \)\(22\!\cdots\!23\)\( T^{25} + \)\(14\!\cdots\!28\)\( T^{26} + \)\(85\!\cdots\!46\)\( T^{27} + \)\(48\!\cdots\!54\)\( T^{28} + \)\(25\!\cdots\!19\)\( T^{29} + \)\(13\!\cdots\!75\)\( T^{30} + \)\(61\!\cdots\!30\)\( T^{31} + \)\(27\!\cdots\!21\)\( T^{32} + \)\(10\!\cdots\!00\)\( T^{33} + \)\(39\!\cdots\!77\)\( T^{34} + \)\(12\!\cdots\!35\)\( T^{35} + \)\(36\!\cdots\!57\)\( T^{36} + \)\(67\!\cdots\!52\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 7 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 + 13 T + 184 T^{2} + 949 T^{3} + 5329 T^{4} \))(\( 1 - 4 T - 12 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 108 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 + 13 T + 184 T^{2} + 949 T^{3} + 5329 T^{4} \))(\( 1 + 20 T + 510 T^{2} + 6961 T^{3} + 102634 T^{4} + 1069123 T^{5} + 11655826 T^{6} + 97527765 T^{7} + 850875298 T^{8} + 5697356467 T^{9} + 39926370778 T^{10} + 197680155601 T^{11} + 1057266512430 T^{12} + 3026684525780 T^{13} + 11047398519097 T^{14} \))(\( 1 + 29 T + 576 T^{2} + 8358 T^{3} + 105962 T^{4} + 1144815 T^{5} + 11352193 T^{6} + 99293139 T^{7} + 816363138 T^{8} + 6266682434 T^{9} + 49949153545 T^{10} + 406427719068 T^{11} + 3646288208785 T^{12} + 33395150690786 T^{13} + 317579138855346 T^{14} + 2819750490968499 T^{15} + 23533908826553449 T^{16} + 173249692269041535 T^{17} + 1170604441880556314 T^{18} + 6740393448050728998 T^{19} + 33910033943962317888 T^{20} + \)\(12\!\cdots\!21\)\( T^{21} + \)\(31\!\cdots\!77\)\( T^{22} \))(\( 1 - 24 T + 870 T^{2} - 15387 T^{3} + 325681 T^{4} - 4669441 T^{5} + 74019844 T^{6} - 905055656 T^{7} + 11773114747 T^{8} - 126039249920 T^{9} + 1404528656478 T^{10} - 13325817517321 T^{11} + 130094309435051 T^{12} - 1097731775448310 T^{13} + 9496884588758723 T^{14} - 71013281549803609 T^{15} + 546385524357102126 T^{16} - 3579292994687390720 T^{17} + 24406509743135081971 T^{18} - \)\(13\!\cdots\!84\)\( T^{19} + \)\(81\!\cdots\!68\)\( T^{20} - \)\(37\!\cdots\!21\)\( T^{21} + \)\(19\!\cdots\!53\)\( T^{22} - \)\(66\!\cdots\!63\)\( T^{23} + \)\(27\!\cdots\!90\)\( T^{24} - \)\(54\!\cdots\!04\)\( T^{25} + \)\(16\!\cdots\!33\)\( T^{26} \))(\( 1 - 8 T + 547 T^{2} - 3939 T^{3} + 156457 T^{4} - 1057340 T^{5} + 30751475 T^{6} - 195813211 T^{7} + 4575405639 T^{8} - 27362929950 T^{9} + 541643272461 T^{10} - 3022765696423 T^{11} + 52384471961759 T^{12} - 270009836377377 T^{13} + 4193767875322650 T^{14} - 19710718055548521 T^{15} + 279156851084213711 T^{16} - 1175907242925386191 T^{17} + 15381716187376141101 T^{18} - 56725312780593910350 T^{19} + \)\(69\!\cdots\!71\)\( T^{20} - \)\(21\!\cdots\!67\)\( T^{21} + \)\(24\!\cdots\!75\)\( T^{22} - \)\(62\!\cdots\!20\)\( T^{23} + \)\(67\!\cdots\!93\)\( T^{24} - \)\(12\!\cdots\!03\)\( T^{25} + \)\(12\!\cdots\!87\)\( T^{26} - \)\(13\!\cdots\!64\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( 1 - 23 T + 844 T^{2} - 14258 T^{3} + 313221 T^{4} - 4311528 T^{5} + 72723743 T^{6} - 863577203 T^{7} + 12288571822 T^{8} - 130212669665 T^{9} + 1636466187575 T^{10} - 15774708137328 T^{11} + 179347554825123 T^{12} - 1589309353137782 T^{13} + 16565296817973582 T^{14} - 135691770432833349 T^{15} + 1306081775474694290 T^{16} - 9905499241596834477 T^{17} + 88276466742981218478 T^{18} - \)\(61\!\cdots\!94\)\( T^{19} + \)\(50\!\cdots\!43\)\( T^{20} - \)\(32\!\cdots\!04\)\( T^{21} + \)\(24\!\cdots\!75\)\( T^{22} - \)\(14\!\cdots\!05\)\( T^{23} + \)\(99\!\cdots\!82\)\( T^{24} - \)\(50\!\cdots\!39\)\( T^{25} + \)\(31\!\cdots\!07\)\( T^{26} - \)\(13\!\cdots\!56\)\( T^{27} + \)\(71\!\cdots\!41\)\( T^{28} - \)\(23\!\cdots\!14\)\( T^{29} + \)\(10\!\cdots\!96\)\( T^{30} - \)\(20\!\cdots\!11\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 39 T + 1449 T^{2} - 35633 T^{3} + 819016 T^{4} - 15354005 T^{5} + 270847213 T^{6} - 4181000932 T^{7} + 61166945860 T^{8} - 808996878016 T^{9} + 10194855445346 T^{10} - 118177368250479 T^{11} + 1310024305648818 T^{12} - 13487234128627491 T^{13} + 133088301010306108 T^{14} - 1225754844226755877 T^{15} + 10832013228567582618 T^{16} - 89480103628553179021 T^{17} + \)\(70\!\cdots\!32\)\( T^{18} - \)\(52\!\cdots\!47\)\( T^{19} + \)\(37\!\cdots\!38\)\( T^{20} - \)\(24\!\cdots\!47\)\( T^{21} + \)\(15\!\cdots\!94\)\( T^{22} - \)\(89\!\cdots\!52\)\( T^{23} + \)\(49\!\cdots\!60\)\( T^{24} - \)\(24\!\cdots\!16\)\( T^{25} + \)\(11\!\cdots\!37\)\( T^{26} - \)\(48\!\cdots\!85\)\( T^{27} + \)\(18\!\cdots\!36\)\( T^{28} - \)\(59\!\cdots\!89\)\( T^{29} + \)\(17\!\cdots\!41\)\( T^{30} - \)\(34\!\cdots\!23\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 + 16 T + 774 T^{2} + 11991 T^{3} + 310425 T^{4} + 4494649 T^{5} + 84044592 T^{6} + 1122180182 T^{7} + 17029645739 T^{8} + 209114736738 T^{9} + 2728250649635 T^{10} + 30858797839849 T^{11} + 357339169674251 T^{12} + 3732467329882239 T^{13} + 39092259481718292 T^{14} + 377781559757387694 T^{15} + 3620052404771985744 T^{16} + 32383355156256234226 T^{17} + \)\(28\!\cdots\!94\)\( T^{18} + \)\(23\!\cdots\!98\)\( T^{19} + \)\(19\!\cdots\!76\)\( T^{20} + \)\(14\!\cdots\!98\)\( T^{21} + \)\(11\!\cdots\!72\)\( T^{22} + \)\(77\!\cdots\!27\)\( T^{23} + \)\(54\!\cdots\!39\)\( T^{24} + \)\(34\!\cdots\!53\)\( T^{25} + \)\(22\!\cdots\!35\)\( T^{26} + \)\(12\!\cdots\!94\)\( T^{27} + \)\(73\!\cdots\!11\)\( T^{28} + \)\(35\!\cdots\!14\)\( T^{29} + \)\(19\!\cdots\!32\)\( T^{30} + \)\(75\!\cdots\!17\)\( T^{31} + \)\(37\!\cdots\!25\)\( T^{32} + \)\(10\!\cdots\!87\)\( T^{33} + \)\(50\!\cdots\!14\)\( T^{34} + \)\(75\!\cdots\!48\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))(\( 1 - 51 T + 2082 T^{2} - 60320 T^{3} + 1520884 T^{4} - 32377455 T^{5} + 624053883 T^{6} - 10764805837 T^{7} + 171927543584 T^{8} - 2527267835368 T^{9} + 34877971935503 T^{10} - 450100748228450 T^{11} + 5502830968614309 T^{12} - 63523695181462276 T^{13} + 698837312980657430 T^{14} - 7303189643834057099 T^{15} + 73007994854064934486 T^{16} - \)\(69\!\cdots\!98\)\( T^{17} + \)\(63\!\cdots\!58\)\( T^{18} - \)\(55\!\cdots\!84\)\( T^{19} + \)\(46\!\cdots\!34\)\( T^{20} - \)\(37\!\cdots\!42\)\( T^{21} + \)\(28\!\cdots\!62\)\( T^{22} - \)\(20\!\cdots\!59\)\( T^{23} + \)\(14\!\cdots\!90\)\( T^{24} - \)\(96\!\cdots\!64\)\( T^{25} + \)\(60\!\cdots\!73\)\( T^{26} - \)\(36\!\cdots\!50\)\( T^{27} + \)\(20\!\cdots\!39\)\( T^{28} - \)\(10\!\cdots\!32\)\( T^{29} + \)\(53\!\cdots\!68\)\( T^{30} - \)\(24\!\cdots\!77\)\( T^{31} + \)\(10\!\cdots\!39\)\( T^{32} - \)\(39\!\cdots\!95\)\( T^{33} + \)\(13\!\cdots\!88\)\( T^{34} - \)\(39\!\cdots\!20\)\( T^{35} + \)\(98\!\cdots\!46\)\( T^{36} - \)\(17\!\cdots\!19\)\( T^{37} + \)\(25\!\cdots\!37\)\( T^{38} \))
$79$ (\( 1 + 13 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 13 T + 162 T^{2} + 1027 T^{3} + 6241 T^{4} \))(\( ( 1 + 11 T + 79 T^{2} )^{2} \))(\( 1 + 2 T + 135 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 94 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 8 T + 273 T^{2} - 2858 T^{3} + 45901 T^{4} - 424499 T^{5} + 5436714 T^{6} - 39832374 T^{7} + 429500406 T^{8} - 2649298259 T^{9} + 22630983139 T^{10} - 111319331498 T^{11} + 840036396927 T^{12} - 1944699644168 T^{13} + 19203908986159 T^{14} \))(\( 1 + 20 T + 558 T^{2} + 8066 T^{3} + 147283 T^{4} + 1803439 T^{5} + 25866209 T^{6} + 275681257 T^{7} + 3338940595 T^{8} + 31609800198 T^{9} + 333856936437 T^{10} + 2814728702072 T^{11} + 26374697978523 T^{12} + 197276763035718 T^{13} + 1646227932018205 T^{14} + 10737807290331817 T^{15} + 79591783921321391 T^{16} + 438393397697336719 T^{17} + 2828409327208455997 T^{18} + 12236999660706321026 T^{19} + 66877190558301022002 T^{20} + \)\(18\!\cdots\!20\)\( T^{21} + \)\(74\!\cdots\!79\)\( T^{22} \))(\( 1 + 28 T + 1025 T^{2} + 19014 T^{3} + 398721 T^{4} + 5420565 T^{5} + 81531672 T^{6} + 832892678 T^{7} + 9725170712 T^{8} + 72303138705 T^{9} + 699331712541 T^{10} + 3412737965740 T^{11} + 35417479052632 T^{12} + 139160460017484 T^{13} + 2797980845157928 T^{14} + 21298897644183340 T^{15} + 344797808219502099 T^{16} + 2816213109113985105 T^{17} + 29924898770726986088 T^{18} + \)\(20\!\cdots\!38\)\( T^{19} + \)\(15\!\cdots\!48\)\( T^{20} + \)\(82\!\cdots\!65\)\( T^{21} + \)\(47\!\cdots\!99\)\( T^{22} + \)\(18\!\cdots\!14\)\( T^{23} + \)\(76\!\cdots\!75\)\( T^{24} + \)\(16\!\cdots\!48\)\( T^{25} + \)\(46\!\cdots\!39\)\( T^{26} \))(\( 1 - 26 T + 995 T^{2} - 18888 T^{3} + 423915 T^{4} - 6445491 T^{5} + 108617293 T^{6} - 1396649186 T^{7} + 19434091386 T^{8} - 218844443965 T^{9} + 2638999284435 T^{10} - 26567340357667 T^{11} + 284690572139722 T^{12} - 2585314414532307 T^{13} + 24906831120291546 T^{14} - 204239838748052253 T^{15} + 1776753860724005002 T^{16} - 13098734922603780013 T^{17} + \)\(10\!\cdots\!35\)\( T^{18} - \)\(67\!\cdots\!35\)\( T^{19} + \)\(47\!\cdots\!06\)\( T^{20} - \)\(26\!\cdots\!74\)\( T^{21} + \)\(16\!\cdots\!73\)\( T^{22} - \)\(77\!\cdots\!29\)\( T^{23} + \)\(40\!\cdots\!15\)\( T^{24} - \)\(14\!\cdots\!52\)\( T^{25} + \)\(58\!\cdots\!95\)\( T^{26} - \)\(12\!\cdots\!14\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 - 48 T + 1790 T^{2} - 48298 T^{3} + 1116249 T^{4} - 21951489 T^{5} + 387171727 T^{6} - 6133408839 T^{7} + 89467750466 T^{8} - 1204253173348 T^{9} + 15175235165324 T^{10} - 179254222560342 T^{11} + 2002963195844289 T^{12} - 21170098555741523 T^{13} + 212885951986436599 T^{14} - 2034025008309474401 T^{15} + 18535129089765807910 T^{16} - \)\(16\!\cdots\!79\)\( T^{17} + \)\(13\!\cdots\!59\)\( T^{18} - \)\(10\!\cdots\!97\)\( T^{19} + \)\(78\!\cdots\!09\)\( T^{20} - \)\(55\!\cdots\!58\)\( T^{21} + \)\(36\!\cdots\!04\)\( T^{22} - \)\(23\!\cdots\!32\)\( T^{23} + \)\(13\!\cdots\!26\)\( T^{24} - \)\(73\!\cdots\!41\)\( T^{25} + \)\(36\!\cdots\!27\)\( T^{26} - \)\(16\!\cdots\!31\)\( T^{27} + \)\(65\!\cdots\!09\)\( T^{28} - \)\(22\!\cdots\!22\)\( T^{29} + \)\(66\!\cdots\!90\)\( T^{30} - \)\(13\!\cdots\!52\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 4 T + 523 T^{2} - 2502 T^{3} + 139646 T^{4} - 789723 T^{5} + 25317681 T^{6} - 164597190 T^{7} + 3543641120 T^{8} - 25365204188 T^{9} + 414143422875 T^{10} - 3092572364282 T^{11} + 42450546057593 T^{12} - 314223074160542 T^{13} + 3907176098450002 T^{14} - 27774453730301147 T^{15} + 324801875822633630 T^{16} - 2194181844693790613 T^{17} + 24384686030426462482 T^{18} - \)\(15\!\cdots\!38\)\( T^{19} + \)\(16\!\cdots\!33\)\( T^{20} - \)\(95\!\cdots\!18\)\( T^{21} + \)\(10\!\cdots\!75\)\( T^{22} - \)\(48\!\cdots\!92\)\( T^{23} + \)\(53\!\cdots\!20\)\( T^{24} - \)\(19\!\cdots\!10\)\( T^{25} + \)\(23\!\cdots\!81\)\( T^{26} - \)\(59\!\cdots\!17\)\( T^{27} + \)\(82\!\cdots\!86\)\( T^{28} - \)\(11\!\cdots\!78\)\( T^{29} + \)\(19\!\cdots\!63\)\( T^{30} - \)\(11\!\cdots\!96\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 46 T + 1652 T^{2} - 41934 T^{3} + 913375 T^{4} - 16648169 T^{5} + 272067184 T^{6} - 3944716283 T^{7} + 52754177710 T^{8} - 647408799368 T^{9} + 7513495891584 T^{10} - 82278295480761 T^{11} + 872957218286027 T^{12} - 8937344998796532 T^{13} + 90009306584051938 T^{14} - 881338931700124702 T^{15} + 8477537143157484023 T^{16} - 78804698976013235469 T^{17} + \)\(71\!\cdots\!12\)\( T^{18} - \)\(62\!\cdots\!51\)\( T^{19} + \)\(52\!\cdots\!43\)\( T^{20} - \)\(43\!\cdots\!78\)\( T^{21} + \)\(35\!\cdots\!78\)\( T^{22} - \)\(27\!\cdots\!68\)\( T^{23} + \)\(21\!\cdots\!67\)\( T^{24} - \)\(15\!\cdots\!99\)\( T^{25} + \)\(11\!\cdots\!24\)\( T^{26} - \)\(77\!\cdots\!92\)\( T^{27} + \)\(49\!\cdots\!10\)\( T^{28} - \)\(29\!\cdots\!57\)\( T^{29} + \)\(16\!\cdots\!44\)\( T^{30} - \)\(77\!\cdots\!91\)\( T^{31} + \)\(33\!\cdots\!75\)\( T^{32} - \)\(12\!\cdots\!66\)\( T^{33} + \)\(38\!\cdots\!92\)\( T^{34} - \)\(83\!\cdots\!14\)\( T^{35} + \)\(14\!\cdots\!61\)\( T^{36} \))(\( 1 - 30 T + 1323 T^{2} - 30260 T^{3} + 793055 T^{4} - 14916571 T^{5} + 296531429 T^{6} - 4783765086 T^{7} + 78863642538 T^{8} - 1120203367049 T^{9} + 16007575831074 T^{10} - 203725377221417 T^{11} + 2588519002910803 T^{12} - 29871844374454987 T^{13} + 342857430889264467 T^{14} - 3616829807433295478 T^{15} + 37877700456738271513 T^{16} - \)\(36\!\cdots\!51\)\( T^{17} + \)\(35\!\cdots\!65\)\( T^{18} - \)\(31\!\cdots\!06\)\( T^{19} + \)\(27\!\cdots\!35\)\( T^{20} - \)\(22\!\cdots\!91\)\( T^{21} + \)\(18\!\cdots\!07\)\( T^{22} - \)\(14\!\cdots\!18\)\( T^{23} + \)\(10\!\cdots\!33\)\( T^{24} - \)\(72\!\cdots\!27\)\( T^{25} + \)\(49\!\cdots\!77\)\( T^{26} - \)\(30\!\cdots\!37\)\( T^{27} + \)\(19\!\cdots\!06\)\( T^{28} - \)\(10\!\cdots\!49\)\( T^{29} + \)\(58\!\cdots\!02\)\( T^{30} - \)\(28\!\cdots\!26\)\( T^{31} + \)\(13\!\cdots\!31\)\( T^{32} - \)\(55\!\cdots\!51\)\( T^{33} + \)\(23\!\cdots\!45\)\( T^{34} - \)\(69\!\cdots\!60\)\( T^{35} + \)\(24\!\cdots\!57\)\( T^{36} - \)\(43\!\cdots\!30\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))
$83$ (\( 1 + 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 17 T + 83 T^{2} \))(\( 1 - 15 T + 116 T^{2} - 1245 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 170 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( 1 - 3 T + 130 T^{2} - 249 T^{3} + 6889 T^{4} \))(\( 1 + 34 T + 962 T^{2} + 18636 T^{3} + 304656 T^{4} + 4073018 T^{5} + 46715214 T^{6} + 458242049 T^{7} + 3877362762 T^{8} + 28059021002 T^{9} + 174198340272 T^{10} + 884433270156 T^{11} + 3789357098566 T^{12} + 11115972694546 T^{13} + 27136050989627 T^{14} \))(\( 1 - 17 T + 727 T^{2} - 10718 T^{3} + 256585 T^{4} - 3261797 T^{5} + 56903318 T^{6} - 626753150 T^{7} + 8759367643 T^{8} - 83774195962 T^{9} + 980570063180 T^{10} - 8118034148760 T^{11} + 81387315243940 T^{12} - 577120435982218 T^{13} + 5008492546488041 T^{14} - 29744652180461150 T^{15} + 224144482323553474 T^{16} - 1066413129033884093 T^{17} + 6962703643173443795 T^{18} - 24140068144066241438 T^{19} + \)\(13\!\cdots\!81\)\( T^{20} - \)\(26\!\cdots\!33\)\( T^{21} + \)\(12\!\cdots\!67\)\( T^{22} \))(\( 1 - 26 T + 912 T^{2} - 16870 T^{3} + 351403 T^{4} - 5167744 T^{5} + 81355420 T^{6} - 1007182561 T^{7} + 13151871421 T^{8} - 142231819988 T^{9} + 1621508875722 T^{10} - 15730315041009 T^{11} + 161523128267333 T^{12} - 1428718611245444 T^{13} + 13406419646188639 T^{14} - 108366140317511001 T^{15} + 927157695522455214 T^{16} - 6750083369404720148 T^{17} + 51805756058829163703 T^{18} - \)\(32\!\cdots\!09\)\( T^{19} + \)\(22\!\cdots\!40\)\( T^{20} - \)\(11\!\cdots\!04\)\( T^{21} + \)\(65\!\cdots\!09\)\( T^{22} - \)\(26\!\cdots\!30\)\( T^{23} + \)\(11\!\cdots\!04\)\( T^{24} - \)\(27\!\cdots\!86\)\( T^{25} + \)\(88\!\cdots\!63\)\( T^{26} \))(\( 1 + 30 T + 969 T^{2} + 18676 T^{3} + 365335 T^{4} + 5350552 T^{5} + 79155481 T^{6} + 943348279 T^{7} + 11483465659 T^{8} + 115946714119 T^{9} + 1228033468687 T^{10} + 10957644918809 T^{11} + 107585686563309 T^{12} + 906460220784007 T^{13} + 8857114926688414 T^{14} + 75236198325072581 T^{15} + 741157794734635701 T^{16} + 6265438915191041683 T^{17} + 58280406555691094527 T^{18} + \)\(45\!\cdots\!17\)\( T^{19} + \)\(37\!\cdots\!71\)\( T^{20} + \)\(25\!\cdots\!33\)\( T^{21} + \)\(17\!\cdots\!21\)\( T^{22} + \)\(10\!\cdots\!56\)\( T^{23} + \)\(56\!\cdots\!15\)\( T^{24} + \)\(24\!\cdots\!92\)\( T^{25} + \)\(10\!\cdots\!09\)\( T^{26} + \)\(26\!\cdots\!90\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 - 9 T + 922 T^{2} - 8751 T^{3} + 425274 T^{4} - 4060279 T^{5} + 129458581 T^{6} - 1203835783 T^{7} + 28912374714 T^{8} - 256282046515 T^{9} + 4995921340093 T^{10} - 41580737482759 T^{11} + 688346845936766 T^{12} - 5315373706784247 T^{13} + 76961879728256332 T^{14} - 545261754693266101 T^{15} + 7047910466107914458 T^{16} - 45256725639541086383 T^{17} + \)\(53\!\cdots\!48\)\( T^{18} - \)\(30\!\cdots\!89\)\( T^{19} + \)\(32\!\cdots\!86\)\( T^{20} - \)\(16\!\cdots\!37\)\( T^{21} + \)\(16\!\cdots\!17\)\( T^{22} - \)\(69\!\cdots\!05\)\( T^{23} + \)\(65\!\cdots\!74\)\( T^{24} - \)\(22\!\cdots\!49\)\( T^{25} + \)\(20\!\cdots\!69\)\( T^{26} - \)\(52\!\cdots\!93\)\( T^{27} + \)\(45\!\cdots\!14\)\( T^{28} - \)\(77\!\cdots\!13\)\( T^{29} + \)\(67\!\cdots\!38\)\( T^{30} - \)\(55\!\cdots\!63\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 15 T + 838 T^{2} - 11765 T^{3} + 347274 T^{4} - 4483083 T^{5} + 94328215 T^{6} - 1114931415 T^{7} + 18851537694 T^{8} - 204626105391 T^{9} + 2955643532351 T^{10} - 29598435804255 T^{11} + 378062838968094 T^{12} - 3501719008421705 T^{13} + 40369874910747532 T^{14} - 345564045988135983 T^{15} + 3640146863496575154 T^{16} - 28681815817015286589 T^{17} + \)\(27\!\cdots\!48\)\( T^{18} - \)\(20\!\cdots\!35\)\( T^{19} + \)\(17\!\cdots\!74\)\( T^{20} - \)\(11\!\cdots\!65\)\( T^{21} + \)\(96\!\cdots\!19\)\( T^{22} - \)\(55\!\cdots\!57\)\( T^{23} + \)\(42\!\cdots\!54\)\( T^{24} - \)\(20\!\cdots\!45\)\( T^{25} + \)\(14\!\cdots\!35\)\( T^{26} - \)\(57\!\cdots\!61\)\( T^{27} + \)\(37\!\cdots\!14\)\( T^{28} - \)\(10\!\cdots\!95\)\( T^{29} + \)\(61\!\cdots\!02\)\( T^{30} - \)\(91\!\cdots\!05\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 46 T + 1803 T^{2} + 49450 T^{3} + 1213637 T^{4} + 25057794 T^{5} + 476001267 T^{6} + 8084141739 T^{7} + 128449477860 T^{8} + 1877750632737 T^{9} + 25963046510186 T^{10} + 335627644220575 T^{11} + 4134348251646044 T^{12} + 48084643546611681 T^{13} + 535631470942771309 T^{14} + 5667781749956354908 T^{15} + 57627441353791009762 T^{16} + \)\(55\!\cdots\!66\)\( T^{17} + \)\(52\!\cdots\!58\)\( T^{18} + \)\(46\!\cdots\!78\)\( T^{19} + \)\(39\!\cdots\!18\)\( T^{20} + \)\(32\!\cdots\!96\)\( T^{21} + \)\(25\!\cdots\!89\)\( T^{22} + \)\(18\!\cdots\!83\)\( T^{23} + \)\(13\!\cdots\!36\)\( T^{24} + \)\(91\!\cdots\!25\)\( T^{25} + \)\(58\!\cdots\!26\)\( T^{26} + \)\(35\!\cdots\!11\)\( T^{27} + \)\(19\!\cdots\!40\)\( T^{28} + \)\(10\!\cdots\!13\)\( T^{29} + \)\(50\!\cdots\!87\)\( T^{30} + \)\(22\!\cdots\!22\)\( T^{31} + \)\(89\!\cdots\!73\)\( T^{32} + \)\(30\!\cdots\!50\)\( T^{33} + \)\(91\!\cdots\!43\)\( T^{34} + \)\(19\!\cdots\!58\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))(\( 1 - T + 913 T^{2} - 180 T^{3} + 412053 T^{4} + 180103 T^{5} + 122830140 T^{6} + 112698348 T^{7} + 27225502887 T^{8} + 34293478900 T^{9} + 4787033795008 T^{10} + 7085502677768 T^{11} + 695564964961644 T^{12} + 1111539579594292 T^{13} + 85892305345946283 T^{14} + 140345510451137812 T^{15} + 9192190781252108163 T^{16} + 14778538914349895882 T^{17} + \)\(86\!\cdots\!08\)\( T^{18} + \)\(13\!\cdots\!36\)\( T^{19} + \)\(71\!\cdots\!64\)\( T^{20} + \)\(10\!\cdots\!98\)\( T^{21} + \)\(52\!\cdots\!81\)\( T^{22} + \)\(66\!\cdots\!52\)\( T^{23} + \)\(33\!\cdots\!69\)\( T^{24} + \)\(36\!\cdots\!48\)\( T^{25} + \)\(18\!\cdots\!88\)\( T^{26} + \)\(15\!\cdots\!88\)\( T^{27} + \)\(89\!\cdots\!24\)\( T^{28} + \)\(53\!\cdots\!00\)\( T^{29} + \)\(35\!\cdots\!29\)\( T^{30} + \)\(12\!\cdots\!28\)\( T^{31} + \)\(10\!\cdots\!20\)\( T^{32} + \)\(13\!\cdots\!87\)\( T^{33} + \)\(25\!\cdots\!71\)\( T^{34} - \)\(91\!\cdots\!80\)\( T^{35} + \)\(38\!\cdots\!99\)\( T^{36} - \)\(34\!\cdots\!09\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))
$89$ (\( 1 - 12 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 + 5 T + 78 T^{2} + 445 T^{3} + 7921 T^{4} \))(\( 1 - 24 T + 314 T^{2} - 2136 T^{3} + 7921 T^{4} \))(\( 1 + 82 T^{2} + 7921 T^{4} \))(\( 1 - 23 T + 272 T^{2} - 2047 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 151 T^{2} + 2659 T^{3} + 35240 T^{4} + 317069 T^{5} + 3805221 T^{6} + 40673821 T^{7} + 338664669 T^{8} + 2511503549 T^{9} + 24843107560 T^{10} + 166831618819 T^{11} + 843192976799 T^{12} + 5963775491532 T^{13} + 44231334895529 T^{14} \))(\( 1 + T + 464 T^{2} - 24 T^{3} + 111297 T^{4} - 87447 T^{5} + 18619837 T^{6} - 19886272 T^{7} + 2448903052 T^{8} - 2538261642 T^{9} + 263858245381 T^{10} - 245368640400 T^{11} + 23483383838909 T^{12} - 20105570466282 T^{13} + 1726400735665388 T^{14} - 1247709270415552 T^{15} + 103974276738689813 T^{16} - 43459522950666567 T^{17} + 4922814879867691113 T^{18} - 94478131336849944 T^{19} + \)\(16\!\cdots\!76\)\( T^{20} + 31181719929966183601 T^{21} + \)\(27\!\cdots\!89\)\( T^{22} \))(\( 1 - 44 T + 1789 T^{2} - 48025 T^{3} + 1179457 T^{4} - 23460109 T^{5} + 431592848 T^{6} - 6880773166 T^{7} + 102377806578 T^{8} - 1360607322250 T^{9} + 16975488400752 T^{10} - 191986074688377 T^{11} + 2045012097441543 T^{12} - 19868978401857274 T^{13} + 182006076672297327 T^{14} - 1520721697606634217 T^{15} + 11967193082389736688 T^{16} - 85367552518974162250 T^{17} + \)\(57\!\cdots\!22\)\( T^{18} - \)\(34\!\cdots\!26\)\( T^{19} + \)\(19\!\cdots\!92\)\( T^{20} - \)\(92\!\cdots\!29\)\( T^{21} + \)\(41\!\cdots\!13\)\( T^{22} - \)\(14\!\cdots\!25\)\( T^{23} + \)\(49\!\cdots\!21\)\( T^{24} - \)\(10\!\cdots\!24\)\( T^{25} + \)\(21\!\cdots\!69\)\( T^{26} \))(\( 1 - 4 T + 780 T^{2} - 1881 T^{3} + 289356 T^{4} - 274990 T^{5} + 69261693 T^{6} + 17925425 T^{7} + 12271686510 T^{8} + 13239275906 T^{9} + 1735603354082 T^{10} + 2547188943427 T^{11} + 202853568948719 T^{12} + 309799827574717 T^{13} + 19768290680155150 T^{14} + 27572184654149813 T^{15} + 1606803119642803199 T^{16} + 1795689242258788763 T^{17} + \)\(10\!\cdots\!62\)\( T^{18} + 73928903720817335794 T^{19} + \)\(60\!\cdots\!10\)\( T^{20} + \)\(79\!\cdots\!25\)\( T^{21} + \)\(27\!\cdots\!33\)\( T^{22} - \)\(96\!\cdots\!10\)\( T^{23} + \)\(90\!\cdots\!56\)\( T^{24} - \)\(52\!\cdots\!09\)\( T^{25} + \)\(19\!\cdots\!80\)\( T^{26} - \)\(87\!\cdots\!76\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( 1 - 17 T + 1127 T^{2} - 15983 T^{3} + 586311 T^{4} - 7166681 T^{5} + 191074546 T^{6} - 2062455143 T^{7} + 44443133398 T^{8} - 431204254609 T^{9} + 7927842129958 T^{10} - 69953463871825 T^{11} + 1131788728858665 T^{12} - 9138323523354515 T^{13} + 132584056451488545 T^{14} - 980924964406358011 T^{15} + 12914003614443073682 T^{16} - 87302321832165862979 T^{17} + \)\(10\!\cdots\!45\)\( T^{18} - \)\(64\!\cdots\!35\)\( T^{19} + \)\(71\!\cdots\!65\)\( T^{20} - \)\(39\!\cdots\!25\)\( T^{21} + \)\(39\!\cdots\!38\)\( T^{22} - \)\(19\!\cdots\!61\)\( T^{23} + \)\(17\!\cdots\!38\)\( T^{24} - \)\(72\!\cdots\!87\)\( T^{25} + \)\(59\!\cdots\!46\)\( T^{26} - \)\(19\!\cdots\!09\)\( T^{27} + \)\(14\!\cdots\!31\)\( T^{28} - \)\(35\!\cdots\!27\)\( T^{29} + \)\(22\!\cdots\!07\)\( T^{30} - \)\(29\!\cdots\!33\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 + T + 543 T^{2} - 671 T^{3} + 152533 T^{4} - 517635 T^{5} + 30165176 T^{6} - 157224139 T^{7} + 4823063548 T^{8} - 30855005869 T^{9} + 665165199182 T^{10} - 4562642804149 T^{11} + 80959528623427 T^{12} - 549124327434249 T^{13} + 8716291116419723 T^{14} - 56211725364021865 T^{15} + 827104459422306710 T^{16} - 5002843557397945985 T^{17} + 69041741933160625883 T^{18} - \)\(38\!\cdots\!81\)\( T^{19} + \)\(50\!\cdots\!07\)\( T^{20} - \)\(25\!\cdots\!01\)\( T^{21} + \)\(33\!\cdots\!02\)\( T^{22} - \)\(13\!\cdots\!01\)\( T^{23} + \)\(18\!\cdots\!88\)\( T^{24} - \)\(55\!\cdots\!51\)\( T^{25} + \)\(94\!\cdots\!76\)\( T^{26} - \)\(14\!\cdots\!15\)\( T^{27} + \)\(37\!\cdots\!93\)\( T^{28} - \)\(14\!\cdots\!99\)\( T^{29} + \)\(10\!\cdots\!63\)\( T^{30} + \)\(17\!\cdots\!49\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 + 42 T + 1798 T^{2} + 48793 T^{3} + 1279302 T^{4} + 26760790 T^{5} + 539059369 T^{6} + 9388573567 T^{7} + 157864657375 T^{8} + 2384001838238 T^{9} + 34852410451996 T^{10} + 467195821431568 T^{11} + 6075757390898767 T^{12} + 73334134581530775 T^{13} + 860024600762049203 T^{14} + 9427780194222755892 T^{15} + \)\(10\!\cdots\!59\)\( T^{16} + \)\(10\!\cdots\!07\)\( T^{17} + \)\(97\!\cdots\!68\)\( T^{18} + \)\(89\!\cdots\!23\)\( T^{19} + \)\(79\!\cdots\!39\)\( T^{20} + \)\(66\!\cdots\!48\)\( T^{21} + \)\(53\!\cdots\!23\)\( T^{22} + \)\(40\!\cdots\!75\)\( T^{23} + \)\(30\!\cdots\!87\)\( T^{24} + \)\(20\!\cdots\!72\)\( T^{25} + \)\(13\!\cdots\!76\)\( T^{26} + \)\(83\!\cdots\!42\)\( T^{27} + \)\(49\!\cdots\!75\)\( T^{28} + \)\(26\!\cdots\!63\)\( T^{29} + \)\(13\!\cdots\!49\)\( T^{30} + \)\(58\!\cdots\!10\)\( T^{31} + \)\(25\!\cdots\!82\)\( T^{32} + \)\(84\!\cdots\!57\)\( T^{33} + \)\(27\!\cdots\!78\)\( T^{34} + \)\(57\!\cdots\!18\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))(\( 1 - 5 T + 900 T^{2} - 5208 T^{3} + 408753 T^{4} - 2600183 T^{5} + 124544985 T^{6} - 845207354 T^{7} + 28548725824 T^{8} - 202656062858 T^{9} + 5238694079121 T^{10} - 38292815208174 T^{11} + 800260312469475 T^{12} - 5932265418022598 T^{13} + 104523943291455492 T^{14} - 772530166737831198 T^{15} + 11892279508870100778 T^{16} - 85898464458081369316 T^{17} + \)\(11\!\cdots\!55\)\( T^{18} - \)\(82\!\cdots\!80\)\( T^{19} + \)\(10\!\cdots\!95\)\( T^{20} - \)\(68\!\cdots\!36\)\( T^{21} + \)\(83\!\cdots\!82\)\( T^{22} - \)\(48\!\cdots\!18\)\( T^{23} + \)\(58\!\cdots\!08\)\( T^{24} - \)\(29\!\cdots\!78\)\( T^{25} + \)\(35\!\cdots\!75\)\( T^{26} - \)\(15\!\cdots\!94\)\( T^{27} + \)\(18\!\cdots\!89\)\( T^{28} - \)\(63\!\cdots\!58\)\( T^{29} + \)\(79\!\cdots\!36\)\( T^{30} - \)\(20\!\cdots\!34\)\( T^{31} + \)\(27\!\cdots\!65\)\( T^{32} - \)\(50\!\cdots\!03\)\( T^{33} + \)\(71\!\cdots\!97\)\( T^{34} - \)\(80\!\cdots\!88\)\( T^{35} + \)\(12\!\cdots\!00\)\( T^{36} - \)\(61\!\cdots\!05\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))
$97$ (\( 1 + 7 T + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 - 3 T + 90 T^{2} - 291 T^{3} + 9409 T^{4} \))(\( 1 - 14 T + 225 T^{2} - 1358 T^{3} + 9409 T^{4} \))(\( 1 - 10 T + 165 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 + 26 T + 346 T^{2} + 2522 T^{3} + 9409 T^{4} \))(\( 1 - 7 T + 326 T^{2} - 2842 T^{3} + 55405 T^{4} - 456619 T^{5} + 7188211 T^{6} - 47880078 T^{7} + 697256467 T^{8} - 4296328171 T^{9} + 50566647565 T^{10} - 251600216602 T^{11} + 2799472923782 T^{12} - 5830804034503 T^{13} + 80798284478113 T^{14} \))(\( 1 + 45 T + 1820 T^{2} + 48766 T^{3} + 1176007 T^{4} + 22870361 T^{5} + 405854399 T^{6} + 6187284940 T^{7} + 86893093162 T^{8} + 1076504810282 T^{9} + 12349988741891 T^{10} + 126294350302956 T^{11} + 1197948907963427 T^{12} + 10128833759943338 T^{13} + 79304980015442026 T^{14} + 547755887080328140 T^{15} + 3485209819013240543 T^{16} + 19050370455620009369 T^{17} + 95019348134252234791 T^{18} + \)\(38\!\cdots\!26\)\( T^{19} + \)\(13\!\cdots\!40\)\( T^{20} + \)\(33\!\cdots\!05\)\( T^{21} + \)\(71\!\cdots\!53\)\( T^{22} \))(\( 1 - 17 T + 998 T^{2} - 14430 T^{3} + 471225 T^{4} - 5972993 T^{5} + 141228807 T^{6} - 1591368836 T^{7} + 30095354665 T^{8} - 303043084483 T^{9} + 4820083155707 T^{10} - 43368648096954 T^{11} + 597070384172585 T^{12} - 4777592162764534 T^{13} + 57915827264740745 T^{14} - 408055609944240186 T^{15} + 4399159753968574811 T^{16} - 26828186381302246723 T^{17} + \)\(25\!\cdots\!05\)\( T^{18} - \)\(13\!\cdots\!44\)\( T^{19} + \)\(11\!\cdots\!91\)\( T^{20} - \)\(46\!\cdots\!73\)\( T^{21} + \)\(35\!\cdots\!25\)\( T^{22} - \)\(10\!\cdots\!70\)\( T^{23} + \)\(71\!\cdots\!94\)\( T^{24} - \)\(11\!\cdots\!97\)\( T^{25} + \)\(67\!\cdots\!77\)\( T^{26} \))(\( 1 - 15 T + 688 T^{2} - 9074 T^{3} + 232439 T^{4} - 2674739 T^{5} + 50852864 T^{6} - 510202963 T^{7} + 8088855856 T^{8} - 71493024766 T^{9} + 1014684615820 T^{10} - 8074806425495 T^{11} + 108805877810262 T^{12} - 810761204923202 T^{13} + 10784014670664272 T^{14} - 78643836877550594 T^{15} + 1023754504316755158 T^{16} - 7369657804775798135 T^{17} + 89829299480305825420 T^{18} - \)\(61\!\cdots\!62\)\( T^{19} + \)\(67\!\cdots\!24\)\( T^{20} - \)\(41\!\cdots\!19\)\( T^{21} + \)\(39\!\cdots\!04\)\( T^{22} - \)\(20\!\cdots\!63\)\( T^{23} + \)\(17\!\cdots\!11\)\( T^{24} - \)\(64\!\cdots\!22\)\( T^{25} + \)\(47\!\cdots\!08\)\( T^{26} - \)\(10\!\cdots\!55\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 - 17 T + 913 T^{2} - 13489 T^{3} + 407538 T^{4} - 5428802 T^{5} + 120440919 T^{6} - 1477034756 T^{7} + 26668402651 T^{8} - 304251849558 T^{9} + 4714542700790 T^{10} - 50215256728296 T^{11} + 689165255502424 T^{12} - 6848160468346513 T^{13} + 84938546496995736 T^{14} - 784702342845576967 T^{15} + 8914605800421217636 T^{16} - 76116127256020965799 T^{17} + \)\(79\!\cdots\!24\)\( T^{18} - \)\(62\!\cdots\!49\)\( T^{19} + \)\(61\!\cdots\!44\)\( T^{20} - \)\(43\!\cdots\!72\)\( T^{21} + \)\(39\!\cdots\!10\)\( T^{22} - \)\(24\!\cdots\!54\)\( T^{23} + \)\(20\!\cdots\!11\)\( T^{24} - \)\(11\!\cdots\!52\)\( T^{25} + \)\(88\!\cdots\!31\)\( T^{26} - \)\(38\!\cdots\!06\)\( T^{27} + \)\(28\!\cdots\!58\)\( T^{28} - \)\(90\!\cdots\!53\)\( T^{29} + \)\(59\!\cdots\!97\)\( T^{30} - \)\(10\!\cdots\!81\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 41 T + 1499 T^{2} - 38587 T^{3} + 902626 T^{4} - 17930470 T^{5} + 329984509 T^{6} - 5477364638 T^{7} + 85335761433 T^{8} - 1232122907558 T^{9} + 16844252420378 T^{10} - 216472222887038 T^{11} + 2649198951432652 T^{12} - 30719144250882281 T^{13} + 340398004753863806 T^{14} - 3588518828385646187 T^{15} + 36211946895519678800 T^{16} - \)\(34\!\cdots\!39\)\( T^{17} + \)\(32\!\cdots\!54\)\( T^{18} - \)\(28\!\cdots\!13\)\( T^{19} + \)\(23\!\cdots\!12\)\( T^{20} - \)\(18\!\cdots\!66\)\( T^{21} + \)\(14\!\cdots\!62\)\( T^{22} - \)\(99\!\cdots\!54\)\( T^{23} + \)\(66\!\cdots\!13\)\( T^{24} - \)\(41\!\cdots\!46\)\( T^{25} + \)\(24\!\cdots\!41\)\( T^{26} - \)\(12\!\cdots\!10\)\( T^{27} + \)\(62\!\cdots\!66\)\( T^{28} - \)\(25\!\cdots\!99\)\( T^{29} + \)\(97\!\cdots\!31\)\( T^{30} - \)\(25\!\cdots\!13\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 35 T + 1444 T^{2} + 34718 T^{3} + 871617 T^{4} + 16689897 T^{5} + 324272940 T^{6} + 5304501825 T^{7} + 87089442417 T^{8} + 1261878995611 T^{9} + 18253738121908 T^{10} + 239093914197707 T^{11} + 3119110855161003 T^{12} + 37405451259827487 T^{13} + 446307927225846884 T^{14} + 4938726924768483995 T^{15} + 54347074761442941730 T^{16} + \)\(55\!\cdots\!57\)\( T^{17} + \)\(56\!\cdots\!04\)\( T^{18} + \)\(54\!\cdots\!29\)\( T^{19} + \)\(51\!\cdots\!70\)\( T^{20} + \)\(45\!\cdots\!35\)\( T^{21} + \)\(39\!\cdots\!04\)\( T^{22} + \)\(32\!\cdots\!59\)\( T^{23} + \)\(25\!\cdots\!87\)\( T^{24} + \)\(19\!\cdots\!91\)\( T^{25} + \)\(14\!\cdots\!88\)\( T^{26} + \)\(95\!\cdots\!87\)\( T^{27} + \)\(64\!\cdots\!33\)\( T^{28} + \)\(37\!\cdots\!25\)\( T^{29} + \)\(22\!\cdots\!40\)\( T^{30} + \)\(11\!\cdots\!69\)\( T^{31} + \)\(56\!\cdots\!73\)\( T^{32} + \)\(21\!\cdots\!74\)\( T^{33} + \)\(88\!\cdots\!24\)\( T^{34} + \)\(20\!\cdots\!95\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))(\( 1 - 5 T + 1119 T^{2} - 7425 T^{3} + 626161 T^{4} - 4997793 T^{5} + 234060233 T^{6} - 2106203122 T^{7} + 65583827219 T^{8} - 634772102388 T^{9} + 14616979308761 T^{10} - 146747567731490 T^{11} + 2681647163351003 T^{12} - 27114376204648986 T^{13} + 413553226986122049 T^{14} - 4106187033289173770 T^{15} + 54307299971976751138 T^{16} - \)\(51\!\cdots\!28\)\( T^{17} + \)\(61\!\cdots\!00\)\( T^{18} - \)\(54\!\cdots\!70\)\( T^{19} + \)\(59\!\cdots\!00\)\( T^{20} - \)\(48\!\cdots\!52\)\( T^{21} + \)\(49\!\cdots\!74\)\( T^{22} - \)\(36\!\cdots\!70\)\( T^{23} + \)\(35\!\cdots\!93\)\( T^{24} - \)\(22\!\cdots\!94\)\( T^{25} + \)\(21\!\cdots\!39\)\( T^{26} - \)\(11\!\cdots\!90\)\( T^{27} + \)\(11\!\cdots\!37\)\( T^{28} - \)\(46\!\cdots\!12\)\( T^{29} + \)\(46\!\cdots\!07\)\( T^{30} - \)\(14\!\cdots\!02\)\( T^{31} + \)\(15\!\cdots\!41\)\( T^{32} - \)\(32\!\cdots\!17\)\( T^{33} + \)\(39\!\cdots\!73\)\( T^{34} - \)\(45\!\cdots\!25\)\( T^{35} + \)\(66\!\cdots\!03\)\( T^{36} - \)\(28\!\cdots\!45\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))
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