Properties

Label 8036.2
Level 8036
Weight 2
Dimension 1100830
Nonzero newspaces 64
Sturm bound 7902720

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Defining parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(7902720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8036))\).

Total New Old
Modular forms 1987680 1108398 879282
Cusp forms 1963681 1100830 862851
Eisenstein series 23999 7568 16431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8036))\)

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
8036.2.a \(\chi_{8036}(1, \cdot)\) 8036.2.a.a 1 1
8036.2.a.b 1
8036.2.a.c 1
8036.2.a.d 1
8036.2.a.e 1
8036.2.a.f 1
8036.2.a.g 2
8036.2.a.h 3
8036.2.a.i 4
8036.2.a.j 5
8036.2.a.k 5
8036.2.a.l 5
8036.2.a.m 8
8036.2.a.n 8
8036.2.a.o 10
8036.2.a.p 10
8036.2.a.q 15
8036.2.a.r 15
8036.2.a.s 20
8036.2.a.t 20
8036.2.c \(\chi_{8036}(8035, \cdot)\) n/a 832 1
8036.2.d \(\chi_{8036}(4509, \cdot)\) n/a 144 1
8036.2.f \(\chi_{8036}(3527, \cdot)\) n/a 800 1
8036.2.i \(\chi_{8036}(165, \cdot)\) n/a 268 2
8036.2.k \(\chi_{8036}(6077, \cdot)\) n/a 286 2
8036.2.l \(\chi_{8036}(1567, \cdot)\) n/a 1664 2
8036.2.n \(\chi_{8036}(2353, \cdot)\) n/a 576 4
8036.2.p \(\chi_{8036}(411, \cdot)\) n/a 1600 2
8036.2.r \(\chi_{8036}(4673, \cdot)\) n/a 280 2
8036.2.u \(\chi_{8036}(4919, \cdot)\) n/a 1664 2
8036.2.v \(\chi_{8036}(1149, \cdot)\) n/a 1128 6
8036.2.x \(\chi_{8036}(489, \cdot)\) n/a 560 4
8036.2.z \(\chi_{8036}(1667, \cdot)\) n/a 3404 4
8036.2.bb \(\chi_{8036}(2157, \cdot)\) n/a 576 4
8036.2.bc \(\chi_{8036}(195, \cdot)\) n/a 3328 4
8036.2.bg \(\chi_{8036}(1371, \cdot)\) n/a 3328 4
8036.2.bi \(\chi_{8036}(1403, \cdot)\) n/a 3328 4
8036.2.bj \(\chi_{8036}(1157, \cdot)\) n/a 560 4
8036.2.bn \(\chi_{8036}(83, \cdot)\) n/a 6720 6
8036.2.bp \(\chi_{8036}(1065, \cdot)\) n/a 1176 6
8036.2.bq \(\chi_{8036}(1147, \cdot)\) n/a 7032 6
8036.2.bs \(\chi_{8036}(961, \cdot)\) n/a 1120 8
8036.2.bu \(\chi_{8036}(979, \cdot)\) n/a 6656 8
8036.2.bv \(\chi_{8036}(197, \cdot)\) n/a 1144 8
8036.2.bx \(\chi_{8036}(821, \cdot)\) n/a 2232 12
8036.2.by \(\chi_{8036}(79, \cdot)\) n/a 6656 8
8036.2.ca \(\chi_{8036}(325, \cdot)\) n/a 1120 8
8036.2.cd \(\chi_{8036}(419, \cdot)\) n/a 14064 12
8036.2.ce \(\chi_{8036}(337, \cdot)\) n/a 2352 12
8036.2.ch \(\chi_{8036}(215, \cdot)\) n/a 6656 8
8036.2.cj \(\chi_{8036}(31, \cdot)\) n/a 6656 8
8036.2.cm \(\chi_{8036}(373, \cdot)\) n/a 1120 8
8036.2.cn \(\chi_{8036}(57, \cdot)\) n/a 4704 24
8036.2.co \(\chi_{8036}(99, \cdot)\) n/a 13616 16
8036.2.cq \(\chi_{8036}(97, \cdot)\) n/a 2240 16
8036.2.cs \(\chi_{8036}(327, \cdot)\) n/a 14064 12
8036.2.cv \(\chi_{8036}(81, \cdot)\) n/a 2352 12
8036.2.cx \(\chi_{8036}(1067, \cdot)\) n/a 13440 12
8036.2.da \(\chi_{8036}(407, \cdot)\) n/a 28128 24
8036.2.dc \(\chi_{8036}(601, \cdot)\) n/a 4704 24
8036.2.de \(\chi_{8036}(361, \cdot)\) n/a 2240 16
8036.2.df \(\chi_{8036}(607, \cdot)\) n/a 13312 16
8036.2.dh \(\chi_{8036}(139, \cdot)\) n/a 28128 24
8036.2.dl \(\chi_{8036}(1007, \cdot)\) n/a 28128 24
8036.2.dm \(\chi_{8036}(113, \cdot)\) n/a 4704 24
8036.2.dp \(\chi_{8036}(9, \cdot)\) n/a 4704 24
8036.2.dq \(\chi_{8036}(255, \cdot)\) n/a 28128 24
8036.2.ds \(\chi_{8036}(37, \cdot)\) n/a 9408 48
8036.2.du \(\chi_{8036}(117, \cdot)\) n/a 4480 32
8036.2.dw \(\chi_{8036}(67, \cdot)\) n/a 26624 32
8036.2.dy \(\chi_{8036}(169, \cdot)\) n/a 9408 48
8036.2.dz \(\chi_{8036}(251, \cdot)\) n/a 56256 48
8036.2.eb \(\chi_{8036}(437, \cdot)\) n/a 9408 48
8036.2.ed \(\chi_{8036}(191, \cdot)\) n/a 56256 48
8036.2.ef \(\chi_{8036}(25, \cdot)\) n/a 9408 48
8036.2.ei \(\chi_{8036}(187, \cdot)\) n/a 56256 48
8036.2.ek \(\chi_{8036}(59, \cdot)\) n/a 56256 48
8036.2.em \(\chi_{8036}(13, \cdot)\) n/a 18816 96
8036.2.eo \(\chi_{8036}(15, \cdot)\) n/a 112512 96
8036.2.er \(\chi_{8036}(87, \cdot)\) n/a 112512 96
8036.2.es \(\chi_{8036}(121, \cdot)\) n/a 18816 96
8036.2.ev \(\chi_{8036}(11, \cdot)\) n/a 225024 192
8036.2.ex \(\chi_{8036}(17, \cdot)\) n/a 37632 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2009))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4018))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 3 T + 5 T^{2} - 9 T^{3} + 9 T^{4} \))(\( 1 - 3 T + 9 T^{2} - 15 T^{3} + 27 T^{4} - 27 T^{5} + 27 T^{6} \))(\( 1 + 2 T + 2 T^{2} - 4 T^{3} - 8 T^{4} - 12 T^{5} + 18 T^{6} + 54 T^{7} + 81 T^{8} \))(\( 1 + 2 T + 7 T^{2} + 14 T^{3} + 31 T^{4} + 59 T^{5} + 93 T^{6} + 126 T^{7} + 189 T^{8} + 162 T^{9} + 243 T^{10} \))(\( 1 + 2 T + 9 T^{2} + 16 T^{3} + 45 T^{4} + 59 T^{5} + 135 T^{6} + 144 T^{7} + 243 T^{8} + 162 T^{9} + 243 T^{10} \))(\( 1 - 2 T + 9 T^{2} - 16 T^{3} + 43 T^{4} - 59 T^{5} + 129 T^{6} - 144 T^{7} + 243 T^{8} - 162 T^{9} + 243 T^{10} \))(\( 1 + 10 T^{2} + 4 T^{3} + 60 T^{4} + 29 T^{5} + 267 T^{6} + 141 T^{7} + 889 T^{8} + 423 T^{9} + 2403 T^{10} + 783 T^{11} + 4860 T^{12} + 972 T^{13} + 7290 T^{14} + 6561 T^{16} \))(\( 1 + 10 T^{2} - 4 T^{3} + 60 T^{4} - 29 T^{5} + 267 T^{6} - 141 T^{7} + 889 T^{8} - 423 T^{9} + 2403 T^{10} - 783 T^{11} + 4860 T^{12} - 972 T^{13} + 7290 T^{14} + 6561 T^{16} \))(\( 1 + 2 T + 12 T^{2} + 22 T^{3} + 83 T^{4} + 130 T^{5} + 402 T^{6} + 542 T^{7} + 1513 T^{8} + 1854 T^{9} + 4817 T^{10} + 5562 T^{11} + 13617 T^{12} + 14634 T^{13} + 32562 T^{14} + 31590 T^{15} + 60507 T^{16} + 48114 T^{17} + 78732 T^{18} + 39366 T^{19} + 59049 T^{20} \))(\( 1 - 2 T + 12 T^{2} - 22 T^{3} + 83 T^{4} - 130 T^{5} + 402 T^{6} - 542 T^{7} + 1513 T^{8} - 1854 T^{9} + 4817 T^{10} - 5562 T^{11} + 13617 T^{12} - 14634 T^{13} + 32562 T^{14} - 31590 T^{15} + 60507 T^{16} - 48114 T^{17} + 78732 T^{18} - 39366 T^{19} + 59049 T^{20} \))(\( 1 + T + 8 T^{2} + 3 T^{3} + 39 T^{4} + 31 T^{5} + 179 T^{6} + 213 T^{7} + 606 T^{8} + 916 T^{9} + 1919 T^{10} + 3696 T^{11} + 6947 T^{12} + 12504 T^{13} + 21048 T^{14} + 35139 T^{15} + 63144 T^{16} + 112536 T^{17} + 187569 T^{18} + 299376 T^{19} + 466317 T^{20} + 667764 T^{21} + 1325322 T^{22} + 1397493 T^{23} + 3523257 T^{24} + 1830519 T^{25} + 6908733 T^{26} + 1594323 T^{27} + 12754584 T^{28} + 4782969 T^{29} + 14348907 T^{30} \))(\( 1 - T + 8 T^{2} - 3 T^{3} + 39 T^{4} - 31 T^{5} + 179 T^{6} - 213 T^{7} + 606 T^{8} - 916 T^{9} + 1919 T^{10} - 3696 T^{11} + 6947 T^{12} - 12504 T^{13} + 21048 T^{14} - 35139 T^{15} + 63144 T^{16} - 112536 T^{17} + 187569 T^{18} - 299376 T^{19} + 466317 T^{20} - 667764 T^{21} + 1325322 T^{22} - 1397493 T^{23} + 3523257 T^{24} - 1830519 T^{25} + 6908733 T^{26} - 1594323 T^{27} + 12754584 T^{28} - 4782969 T^{29} + 14348907 T^{30} \))(\( 1 + 4 T + 30 T^{2} + 100 T^{3} + 438 T^{4} + 1272 T^{5} + 4240 T^{6} + 11012 T^{7} + 30845 T^{8} + 72876 T^{9} + 180194 T^{10} + 392412 T^{11} + 881848 T^{12} + 1790364 T^{13} + 3730214 T^{14} + 7134852 T^{15} + 13991387 T^{16} + 25453628 T^{17} + 47522000 T^{18} + 82831548 T^{19} + 148322703 T^{20} + 248494644 T^{21} + 427698000 T^{22} + 687247956 T^{23} + 1133302347 T^{24} + 1733769036 T^{25} + 2719326006 T^{26} + 3915526068 T^{27} + 5785804728 T^{28} + 7723845396 T^{29} + 10640275506 T^{30} + 12909764772 T^{31} + 16392297645 T^{32} + 17556684876 T^{33} + 20279788560 T^{34} + 18251809704 T^{35} + 18854463798 T^{36} + 12914016300 T^{37} + 11622614670 T^{38} + 4649045868 T^{39} + 3486784401 T^{40} \))(\( 1 - 4 T + 30 T^{2} - 100 T^{3} + 438 T^{4} - 1272 T^{5} + 4240 T^{6} - 11012 T^{7} + 30845 T^{8} - 72876 T^{9} + 180194 T^{10} - 392412 T^{11} + 881848 T^{12} - 1790364 T^{13} + 3730214 T^{14} - 7134852 T^{15} + 13991387 T^{16} - 25453628 T^{17} + 47522000 T^{18} - 82831548 T^{19} + 148322703 T^{20} - 248494644 T^{21} + 427698000 T^{22} - 687247956 T^{23} + 1133302347 T^{24} - 1733769036 T^{25} + 2719326006 T^{26} - 3915526068 T^{27} + 5785804728 T^{28} - 7723845396 T^{29} + 10640275506 T^{30} - 12909764772 T^{31} + 16392297645 T^{32} - 17556684876 T^{33} + 20279788560 T^{34} - 18251809704 T^{35} + 18854463798 T^{36} - 12914016300 T^{37} + 11622614670 T^{38} - 4649045868 T^{39} + 3486784401 T^{40} \))
$5$ (\( 1 + T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 3 T + 9 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T^{2} + 8 T^{3} + 15 T^{4} + 125 T^{6} \))(\( 1 + 4 T + 12 T^{2} + 16 T^{3} + 34 T^{4} + 80 T^{5} + 300 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 + 3 T + 16 T^{2} + 40 T^{3} + 127 T^{4} + 274 T^{5} + 635 T^{6} + 1000 T^{7} + 2000 T^{8} + 1875 T^{9} + 3125 T^{10} \))(\( 1 - 3 T + 16 T^{2} - 48 T^{3} + 143 T^{4} - 322 T^{5} + 715 T^{6} - 1200 T^{7} + 2000 T^{8} - 1875 T^{9} + 3125 T^{10} \))(\( 1 - T + 16 T^{2} - 12 T^{3} + 127 T^{4} - 78 T^{5} + 635 T^{6} - 300 T^{7} + 2000 T^{8} - 625 T^{9} + 3125 T^{10} \))(\( 1 + 22 T^{2} + 12 T^{3} + 258 T^{4} + 183 T^{5} + 2095 T^{6} + 1441 T^{7} + 12249 T^{8} + 7205 T^{9} + 52375 T^{10} + 22875 T^{11} + 161250 T^{12} + 37500 T^{13} + 343750 T^{14} + 390625 T^{16} \))(\( 1 + 22 T^{2} - 12 T^{3} + 258 T^{4} - 183 T^{5} + 2095 T^{6} - 1441 T^{7} + 12249 T^{8} - 7205 T^{9} + 52375 T^{10} - 22875 T^{11} + 161250 T^{12} - 37500 T^{13} + 343750 T^{14} + 390625 T^{16} \))(\( 1 + 4 T + 25 T^{2} + 88 T^{3} + 326 T^{4} + 994 T^{5} + 2938 T^{6} + 7978 T^{7} + 20745 T^{8} + 50112 T^{9} + 116858 T^{10} + 250560 T^{11} + 518625 T^{12} + 997250 T^{13} + 1836250 T^{14} + 3106250 T^{15} + 5093750 T^{16} + 6875000 T^{17} + 9765625 T^{18} + 7812500 T^{19} + 9765625 T^{20} \))(\( 1 - 4 T + 25 T^{2} - 88 T^{3} + 326 T^{4} - 994 T^{5} + 2938 T^{6} - 7978 T^{7} + 20745 T^{8} - 50112 T^{9} + 116858 T^{10} - 250560 T^{11} + 518625 T^{12} - 997250 T^{13} + 1836250 T^{14} - 3106250 T^{15} + 5093750 T^{16} - 6875000 T^{17} + 9765625 T^{18} - 7812500 T^{19} + 9765625 T^{20} \))(\( 1 - 3 T + 26 T^{2} - 75 T^{3} + 351 T^{4} - 983 T^{5} + 3481 T^{6} - 9515 T^{7} + 29060 T^{8} - 75678 T^{9} + 209221 T^{10} - 513824 T^{11} + 1309803 T^{12} - 3067058 T^{13} + 7286756 T^{14} - 16275117 T^{15} + 36433780 T^{16} - 76676450 T^{17} + 163725375 T^{18} - 321140000 T^{19} + 653815625 T^{20} - 1182468750 T^{21} + 2270312500 T^{22} - 3716796875 T^{23} + 6798828125 T^{24} - 9599609375 T^{25} + 17138671875 T^{26} - 18310546875 T^{27} + 31738281250 T^{28} - 18310546875 T^{29} + 30517578125 T^{30} \))(\( 1 + 3 T + 26 T^{2} + 75 T^{3} + 351 T^{4} + 983 T^{5} + 3481 T^{6} + 9515 T^{7} + 29060 T^{8} + 75678 T^{9} + 209221 T^{10} + 513824 T^{11} + 1309803 T^{12} + 3067058 T^{13} + 7286756 T^{14} + 16275117 T^{15} + 36433780 T^{16} + 76676450 T^{17} + 163725375 T^{18} + 321140000 T^{19} + 653815625 T^{20} + 1182468750 T^{21} + 2270312500 T^{22} + 3716796875 T^{23} + 6798828125 T^{24} + 9599609375 T^{25} + 17138671875 T^{26} + 18310546875 T^{27} + 31738281250 T^{28} + 18310546875 T^{29} + 30517578125 T^{30} \))(\( 1 + 8 T + 72 T^{2} + 400 T^{3} + 2237 T^{4} + 9876 T^{5} + 42972 T^{6} + 160960 T^{7} + 592638 T^{8} + 1959204 T^{9} + 6383550 T^{10} + 19135824 T^{11} + 56758118 T^{12} + 157264968 T^{13} + 432551686 T^{14} + 1121760004 T^{15} + 2892510705 T^{16} + 7067419456 T^{17} + 17173284840 T^{18} + 39625592820 T^{19} + 90903287002 T^{20} + 198127964100 T^{21} + 429332121000 T^{22} + 883427432000 T^{23} + 1807819190625 T^{24} + 3505500012500 T^{25} + 6758620093750 T^{26} + 12286325625000 T^{27} + 22171139843750 T^{28} + 37374656250000 T^{29} + 62339355468750 T^{30} + 95664257812500 T^{31} + 144687011718750 T^{32} + 196484375000000 T^{33} + 262280273437500 T^{34} + 301391601562500 T^{35} + 341339111328125 T^{36} + 305175781250000 T^{37} + 274658203125000 T^{38} + 152587890625000 T^{39} + 95367431640625 T^{40} \))(\( 1 - 8 T + 72 T^{2} - 400 T^{3} + 2237 T^{4} - 9876 T^{5} + 42972 T^{6} - 160960 T^{7} + 592638 T^{8} - 1959204 T^{9} + 6383550 T^{10} - 19135824 T^{11} + 56758118 T^{12} - 157264968 T^{13} + 432551686 T^{14} - 1121760004 T^{15} + 2892510705 T^{16} - 7067419456 T^{17} + 17173284840 T^{18} - 39625592820 T^{19} + 90903287002 T^{20} - 198127964100 T^{21} + 429332121000 T^{22} - 883427432000 T^{23} + 1807819190625 T^{24} - 3505500012500 T^{25} + 6758620093750 T^{26} - 12286325625000 T^{27} + 22171139843750 T^{28} - 37374656250000 T^{29} + 62339355468750 T^{30} - 95664257812500 T^{31} + 144687011718750 T^{32} - 196484375000000 T^{33} + 262280273437500 T^{34} - 301391601562500 T^{35} + 341339111328125 T^{36} - 305175781250000 T^{37} + 274658203125000 T^{38} - 152587890625000 T^{39} + 95367431640625 T^{40} \))
$7$ 1
$11$ (\( 1 + 5 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( ( 1 - T + 11 T^{2} )^{2} \))(\( 1 + 6 T + 9 T^{2} - 4 T^{3} + 99 T^{4} + 726 T^{5} + 1331 T^{6} \))(\( 1 - 4 T + 26 T^{2} - 114 T^{3} + 384 T^{4} - 1254 T^{5} + 3146 T^{6} - 5324 T^{7} + 14641 T^{8} \))(\( 1 + 34 T^{2} + 4 T^{3} + 601 T^{4} + 16 T^{5} + 6611 T^{6} + 484 T^{7} + 45254 T^{8} + 161051 T^{10} \))(\( 1 - 6 T + 48 T^{2} - 196 T^{3} + 895 T^{4} - 2836 T^{5} + 9845 T^{6} - 23716 T^{7} + 63888 T^{8} - 87846 T^{9} + 161051 T^{10} \))(\( 1 + 2 T + 26 T^{2} - 10 T^{3} + 165 T^{4} - 728 T^{5} + 1815 T^{6} - 1210 T^{7} + 34606 T^{8} + 29282 T^{9} + 161051 T^{10} \))(\( 1 + 8 T + 89 T^{2} + 522 T^{3} + 3323 T^{4} + 15312 T^{5} + 70852 T^{6} + 264099 T^{7} + 962211 T^{8} + 2905089 T^{9} + 8573092 T^{10} + 20380272 T^{11} + 48652043 T^{12} + 84068622 T^{13} + 157668929 T^{14} + 155897368 T^{15} + 214358881 T^{16} \))(\( 1 + 8 T + 89 T^{2} + 522 T^{3} + 3323 T^{4} + 15312 T^{5} + 70852 T^{6} + 264099 T^{7} + 962211 T^{8} + 2905089 T^{9} + 8573092 T^{10} + 20380272 T^{11} + 48652043 T^{12} + 84068622 T^{13} + 157668929 T^{14} + 155897368 T^{15} + 214358881 T^{16} \))(\( 1 + 60 T^{2} - 48 T^{3} + 1750 T^{4} - 2512 T^{5} + 35046 T^{6} - 60128 T^{7} + 548345 T^{8} - 910432 T^{9} + 6806204 T^{10} - 10014752 T^{11} + 66349745 T^{12} - 80030368 T^{13} + 513108486 T^{14} - 404560112 T^{15} + 3100231750 T^{16} - 935384208 T^{17} + 12861532860 T^{18} + 25937424601 T^{20} \))(\( 1 + 60 T^{2} - 48 T^{3} + 1750 T^{4} - 2512 T^{5} + 35046 T^{6} - 60128 T^{7} + 548345 T^{8} - 910432 T^{9} + 6806204 T^{10} - 10014752 T^{11} + 66349745 T^{12} - 80030368 T^{13} + 513108486 T^{14} - 404560112 T^{15} + 3100231750 T^{16} - 935384208 T^{17} + 12861532860 T^{18} + 25937424601 T^{20} \))(\( 1 - 9 T + 89 T^{2} - 498 T^{3} + 2998 T^{4} - 12910 T^{5} + 62896 T^{6} - 244295 T^{7} + 1118943 T^{8} - 4242745 T^{9} + 18355959 T^{10} - 65389764 T^{11} + 257372053 T^{12} - 841875891 T^{13} + 3082353593 T^{14} - 9581848759 T^{15} + 33905889523 T^{16} - 101866982811 T^{17} + 342562202543 T^{18} - 957371534724 T^{19} + 2956245552909 T^{20} - 7516281574945 T^{21} + 21805033580253 T^{22} - 52366802833895 T^{23} + 148305477973136 T^{24} - 334852151598910 T^{25} + 855364388491778 T^{26} - 1562937331607058 T^{27} + 3072521380809859 T^{28} - 3417748502249169 T^{29} + 4177248169415651 T^{30} \))(\( 1 - 9 T + 89 T^{2} - 498 T^{3} + 2998 T^{4} - 12910 T^{5} + 62896 T^{6} - 244295 T^{7} + 1118943 T^{8} - 4242745 T^{9} + 18355959 T^{10} - 65389764 T^{11} + 257372053 T^{12} - 841875891 T^{13} + 3082353593 T^{14} - 9581848759 T^{15} + 33905889523 T^{16} - 101866982811 T^{17} + 342562202543 T^{18} - 957371534724 T^{19} + 2956245552909 T^{20} - 7516281574945 T^{21} + 21805033580253 T^{22} - 52366802833895 T^{23} + 148305477973136 T^{24} - 334852151598910 T^{25} + 855364388491778 T^{26} - 1562937331607058 T^{27} + 3072521380809859 T^{28} - 3417748502249169 T^{29} + 4177248169415651 T^{30} \))(\( 1 + 8 T + 142 T^{2} + 992 T^{3} + 9964 T^{4} + 61248 T^{5} + 458342 T^{6} + 2512024 T^{7} + 15530598 T^{8} + 76936024 T^{9} + 413551562 T^{10} + 1873362464 T^{11} + 9012640270 T^{12} + 37664981344 T^{13} + 165092145546 T^{14} + 640460360552 T^{15} + 2586564514345 T^{16} + 9350628067040 T^{17} + 35040381858552 T^{18} + 118256665353312 T^{19} + 412895546420908 T^{20} + 1300823318886432 T^{21} + 4239886204884792 T^{22} + 12445685957230240 T^{23} + 37869891054525145 T^{24} + 103146781527260152 T^{25} + 292470806455617306 T^{26} + 733983932162337824 T^{27} + 1931939483132737870 T^{28} + 4417290696394870624 T^{29} + 10726462458000776762 T^{30} + 21950745537607990664 T^{31} + 48741669470646409158 T^{32} + 86721881450646126344 T^{33} + \)\(17\!\cdots\!22\)\( T^{34} + \)\(25\!\cdots\!48\)\( T^{35} + \)\(45\!\cdots\!04\)\( T^{36} + \)\(50\!\cdots\!32\)\( T^{37} + \)\(78\!\cdots\!02\)\( T^{38} + \)\(48\!\cdots\!28\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( 1 + 8 T + 142 T^{2} + 992 T^{3} + 9964 T^{4} + 61248 T^{5} + 458342 T^{6} + 2512024 T^{7} + 15530598 T^{8} + 76936024 T^{9} + 413551562 T^{10} + 1873362464 T^{11} + 9012640270 T^{12} + 37664981344 T^{13} + 165092145546 T^{14} + 640460360552 T^{15} + 2586564514345 T^{16} + 9350628067040 T^{17} + 35040381858552 T^{18} + 118256665353312 T^{19} + 412895546420908 T^{20} + 1300823318886432 T^{21} + 4239886204884792 T^{22} + 12445685957230240 T^{23} + 37869891054525145 T^{24} + 103146781527260152 T^{25} + 292470806455617306 T^{26} + 733983932162337824 T^{27} + 1931939483132737870 T^{28} + 4417290696394870624 T^{29} + 10726462458000776762 T^{30} + 21950745537607990664 T^{31} + 48741669470646409158 T^{32} + 86721881450646126344 T^{33} + \)\(17\!\cdots\!22\)\( T^{34} + \)\(25\!\cdots\!48\)\( T^{35} + \)\(45\!\cdots\!04\)\( T^{36} + \)\(50\!\cdots\!32\)\( T^{37} + \)\(78\!\cdots\!02\)\( T^{38} + \)\(48\!\cdots\!28\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2} \))(\( 1 - 3 T + 21 T^{2} - 21 T^{3} + 273 T^{4} - 507 T^{5} + 2197 T^{6} \))(\( 1 + 12 T^{2} + 48 T^{3} + 118 T^{4} + 624 T^{5} + 2028 T^{6} + 28561 T^{8} \))(\( 1 + 7 T + 72 T^{2} + 326 T^{3} + 1883 T^{4} + 6081 T^{5} + 24479 T^{6} + 55094 T^{7} + 158184 T^{8} + 199927 T^{9} + 371293 T^{10} \))(\( 1 + 7 T + 60 T^{2} + 328 T^{3} + 1513 T^{4} + 6189 T^{5} + 19669 T^{6} + 55432 T^{7} + 131820 T^{8} + 199927 T^{9} + 371293 T^{10} \))(\( 1 - T + 42 T^{2} - 4 T^{3} + 835 T^{4} + 131 T^{5} + 10855 T^{6} - 676 T^{7} + 92274 T^{8} - 28561 T^{9} + 371293 T^{10} \))(\( 1 + 7 T + 87 T^{2} + 414 T^{3} + 2973 T^{4} + 10570 T^{5} + 58450 T^{6} + 170152 T^{7} + 839348 T^{8} + 2211976 T^{9} + 9878050 T^{10} + 23222290 T^{11} + 84911853 T^{12} + 153715302 T^{13} + 419932383 T^{14} + 439239619 T^{15} + 815730721 T^{16} \))(\( 1 - 7 T + 87 T^{2} - 414 T^{3} + 2973 T^{4} - 10570 T^{5} + 58450 T^{6} - 170152 T^{7} + 839348 T^{8} - 2211976 T^{9} + 9878050 T^{10} - 23222290 T^{11} + 84911853 T^{12} - 153715302 T^{13} + 419932383 T^{14} - 439239619 T^{15} + 815730721 T^{16} \))(\( 1 + 6 T + 77 T^{2} + 378 T^{3} + 2756 T^{4} + 11378 T^{5} + 63254 T^{6} + 226122 T^{7} + 1083085 T^{8} + 3478468 T^{9} + 15235973 T^{10} + 45220084 T^{11} + 183041365 T^{12} + 496790034 T^{13} + 1806597494 T^{14} + 4224571754 T^{15} + 13302685604 T^{16} + 23718939426 T^{17} + 62811265517 T^{18} + 63626996238 T^{19} + 137858491849 T^{20} \))(\( 1 - 6 T + 77 T^{2} - 378 T^{3} + 2756 T^{4} - 11378 T^{5} + 63254 T^{6} - 226122 T^{7} + 1083085 T^{8} - 3478468 T^{9} + 15235973 T^{10} - 45220084 T^{11} + 183041365 T^{12} - 496790034 T^{13} + 1806597494 T^{14} - 4224571754 T^{15} + 13302685604 T^{16} - 23718939426 T^{17} + 62811265517 T^{18} - 63626996238 T^{19} + 137858491849 T^{20} \))(\( 1 - 7 T + 76 T^{2} - 375 T^{3} + 2621 T^{4} - 10793 T^{5} + 61717 T^{6} - 220271 T^{7} + 1122185 T^{8} - 3552915 T^{9} + 17109259 T^{10} - 48621973 T^{11} + 230086024 T^{12} - 601963629 T^{13} + 2936644665 T^{14} - 7551218442 T^{15} + 38176380645 T^{16} - 101731853301 T^{17} + 505498994728 T^{18} - 1388692170853 T^{19} + 6352548101887 T^{20} - 17149242098235 T^{21} + 70415444549645 T^{22} - 179681821645391 T^{23} + 654477887803441 T^{24} - 1487906702526257 T^{25} + 4697252392770977 T^{26} - 8736781920930375 T^{27} + 23018508101011228 T^{28} - 27561634699895023 T^{29} + 51185893014090757 T^{30} \))(\( 1 + 7 T + 76 T^{2} + 375 T^{3} + 2621 T^{4} + 10793 T^{5} + 61717 T^{6} + 220271 T^{7} + 1122185 T^{8} + 3552915 T^{9} + 17109259 T^{10} + 48621973 T^{11} + 230086024 T^{12} + 601963629 T^{13} + 2936644665 T^{14} + 7551218442 T^{15} + 38176380645 T^{16} + 101731853301 T^{17} + 505498994728 T^{18} + 1388692170853 T^{19} + 6352548101887 T^{20} + 17149242098235 T^{21} + 70415444549645 T^{22} + 179681821645391 T^{23} + 654477887803441 T^{24} + 1487906702526257 T^{25} + 4697252392770977 T^{26} + 8736781920930375 T^{27} + 23018508101011228 T^{28} + 27561634699895023 T^{29} + 51185893014090757 T^{30} \))(\( 1 + 12 T + 194 T^{2} + 1700 T^{3} + 16215 T^{4} + 114764 T^{5} + 829070 T^{6} + 5018428 T^{7} + 30262070 T^{8} + 162395528 T^{9} + 860372336 T^{10} + 4190858120 T^{11} + 20109646694 T^{12} + 90368949632 T^{13} + 400312442964 T^{14} + 1679055021608 T^{15} + 6949980791045 T^{16} + 27425632181028 T^{17} + 106863781088238 T^{18} + 398549262766884 T^{19} + 1467826932439611 T^{20} + 5181140415969492 T^{21} + 18059979003912222 T^{22} + 60254113901718516 T^{23} + 198498401373036245 T^{24} + 623421376137899144 T^{25} + 1932231702510621876 T^{26} + 5670517572255695744 T^{27} + 16404056596751886374 T^{28} + 44441952305871958760 T^{29} + \)\(11\!\cdots\!64\)\( T^{30} + \)\(29\!\cdots\!36\)\( T^{31} + \)\(70\!\cdots\!70\)\( T^{32} + \)\(15\!\cdots\!84\)\( T^{33} + \)\(32\!\cdots\!30\)\( T^{34} + \)\(58\!\cdots\!48\)\( T^{35} + \)\(10\!\cdots\!15\)\( T^{36} + \)\(14\!\cdots\!00\)\( T^{37} + \)\(21\!\cdots\!26\)\( T^{38} + \)\(17\!\cdots\!24\)\( T^{39} + \)\(19\!\cdots\!01\)\( T^{40} \))(\( 1 - 12 T + 194 T^{2} - 1700 T^{3} + 16215 T^{4} - 114764 T^{5} + 829070 T^{6} - 5018428 T^{7} + 30262070 T^{8} - 162395528 T^{9} + 860372336 T^{10} - 4190858120 T^{11} + 20109646694 T^{12} - 90368949632 T^{13} + 400312442964 T^{14} - 1679055021608 T^{15} + 6949980791045 T^{16} - 27425632181028 T^{17} + 106863781088238 T^{18} - 398549262766884 T^{19} + 1467826932439611 T^{20} - 5181140415969492 T^{21} + 18059979003912222 T^{22} - 60254113901718516 T^{23} + 198498401373036245 T^{24} - 623421376137899144 T^{25} + 1932231702510621876 T^{26} - 5670517572255695744 T^{27} + 16404056596751886374 T^{28} - 44441952305871958760 T^{29} + \)\(11\!\cdots\!64\)\( T^{30} - \)\(29\!\cdots\!36\)\( T^{31} + \)\(70\!\cdots\!70\)\( T^{32} - \)\(15\!\cdots\!84\)\( T^{33} + \)\(32\!\cdots\!30\)\( T^{34} - \)\(58\!\cdots\!48\)\( T^{35} + \)\(10\!\cdots\!15\)\( T^{36} - \)\(14\!\cdots\!00\)\( T^{37} + \)\(21\!\cdots\!26\)\( T^{38} - \)\(17\!\cdots\!24\)\( T^{39} + \)\(19\!\cdots\!01\)\( T^{40} \))
$17$ (\( 1 + 3 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 - 2 T - 17 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 3 T + 51 T^{2} + 99 T^{3} + 867 T^{4} + 867 T^{5} + 4913 T^{6} \))(\( 1 - 4 T + 20 T^{2} - 124 T^{3} + 534 T^{4} - 2108 T^{5} + 5780 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( 1 - 3 T + 40 T^{2} - 132 T^{3} + 1135 T^{4} - 2835 T^{5} + 19295 T^{6} - 38148 T^{7} + 196520 T^{8} - 250563 T^{9} + 1419857 T^{10} \))(\( 1 + T + 68 T^{2} + 82 T^{3} + 2041 T^{4} + 2209 T^{5} + 34697 T^{6} + 23698 T^{7} + 334084 T^{8} + 83521 T^{9} + 1419857 T^{10} \))(\( 1 - 3 T + 56 T^{2} - 126 T^{3} + 1591 T^{4} - 3013 T^{5} + 27047 T^{6} - 36414 T^{7} + 275128 T^{8} - 250563 T^{9} + 1419857 T^{10} \))(\( 1 + T + 87 T^{2} + 61 T^{3} + 3759 T^{4} + 1751 T^{5} + 105134 T^{6} + 34539 T^{7} + 2092941 T^{8} + 587163 T^{9} + 30383726 T^{10} + 8602663 T^{11} + 313955439 T^{12} + 86611277 T^{13} + 2099968503 T^{14} + 410338673 T^{15} + 6975757441 T^{16} \))(\( 1 - T + 87 T^{2} - 61 T^{3} + 3759 T^{4} - 1751 T^{5} + 105134 T^{6} - 34539 T^{7} + 2092941 T^{8} - 587163 T^{9} + 30383726 T^{10} - 8602663 T^{11} + 313955439 T^{12} - 86611277 T^{13} + 2099968503 T^{14} - 410338673 T^{15} + 6975757441 T^{16} \))(\( 1 + 12 T + 153 T^{2} + 1250 T^{3} + 9866 T^{4} + 64080 T^{5} + 390146 T^{6} + 2122674 T^{7} + 10664977 T^{8} + 49516210 T^{9} + 211311741 T^{10} + 841775570 T^{11} + 3082178353 T^{12} + 10428697362 T^{13} + 32585384066 T^{14} + 90984436560 T^{15} + 238141255754 T^{16} + 512923341250 T^{17} + 1067290888473 T^{18} + 1423054517964 T^{19} + 2015993900449 T^{20} \))(\( 1 - 12 T + 153 T^{2} - 1250 T^{3} + 9866 T^{4} - 64080 T^{5} + 390146 T^{6} - 2122674 T^{7} + 10664977 T^{8} - 49516210 T^{9} + 211311741 T^{10} - 841775570 T^{11} + 3082178353 T^{12} - 10428697362 T^{13} + 32585384066 T^{14} - 90984436560 T^{15} + 238141255754 T^{16} - 512923341250 T^{17} + 1067290888473 T^{18} - 1423054517964 T^{19} + 2015993900449 T^{20} \))(\( 1 - 3 T + 50 T^{2} - 128 T^{3} + 1899 T^{4} - 4363 T^{5} + 49157 T^{6} - 88690 T^{7} + 1034344 T^{8} - 1427757 T^{9} + 18105190 T^{10} - 15514456 T^{11} + 284744193 T^{12} - 98181573 T^{13} + 4458511390 T^{14} - 907579244 T^{15} + 75794693630 T^{16} - 28374474597 T^{17} + 1398948220209 T^{18} - 1295782879576 T^{19} + 25706780757830 T^{20} - 34462583102733 T^{21} + 424431344385512 T^{22} - 618679927442290 T^{23} + 5829424244963029 T^{24} - 8795781387658987 T^{25} + 65082331088195067 T^{26} - 74575646365409408 T^{27} + 495228901645296850 T^{28} - 505133479678202787 T^{29} + 2862423051509815793 T^{30} \))(\( 1 + 3 T + 50 T^{2} + 128 T^{3} + 1899 T^{4} + 4363 T^{5} + 49157 T^{6} + 88690 T^{7} + 1034344 T^{8} + 1427757 T^{9} + 18105190 T^{10} + 15514456 T^{11} + 284744193 T^{12} + 98181573 T^{13} + 4458511390 T^{14} + 907579244 T^{15} + 75794693630 T^{16} + 28374474597 T^{17} + 1398948220209 T^{18} + 1295782879576 T^{19} + 25706780757830 T^{20} + 34462583102733 T^{21} + 424431344385512 T^{22} + 618679927442290 T^{23} + 5829424244963029 T^{24} + 8795781387658987 T^{25} + 65082331088195067 T^{26} + 74575646365409408 T^{27} + 495228901645296850 T^{28} + 505133479678202787 T^{29} + 2862423051509815793 T^{30} \))(\( 1 + 8 T + 204 T^{2} + 1364 T^{3} + 19837 T^{4} + 115236 T^{5} + 1252068 T^{6} + 6497620 T^{7} + 58571224 T^{8} + 277021276 T^{9} + 2184743874 T^{10} + 9546857708 T^{11} + 67882331020 T^{12} + 276510702884 T^{13} + 1805247496970 T^{14} + 6893991759912 T^{15} + 41807869607761 T^{16} + 150199940099848 T^{17} + 852315750839294 T^{18} + 2884906960753048 T^{19} + 15384600661717447 T^{20} + 49043418332801816 T^{21} + 246319251992555966 T^{22} + 737932305710553224 T^{23} + 3491835077509806481 T^{24} + 9788482458253372584 T^{25} + 43574286020190665930 T^{26} + \)\(11\!\cdots\!32\)\( T^{27} + \)\(47\!\cdots\!20\)\( T^{28} + \)\(11\!\cdots\!76\)\( T^{29} + \)\(44\!\cdots\!26\)\( T^{30} + \)\(94\!\cdots\!08\)\( T^{31} + \)\(34\!\cdots\!64\)\( T^{32} + \)\(64\!\cdots\!40\)\( T^{33} + \)\(21\!\cdots\!72\)\( T^{34} + \)\(32\!\cdots\!48\)\( T^{35} + \)\(96\!\cdots\!97\)\( T^{36} + \)\(11\!\cdots\!28\)\( T^{37} + \)\(28\!\cdots\!36\)\( T^{38} + \)\(19\!\cdots\!24\)\( T^{39} + \)\(40\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 204 T^{2} - 1364 T^{3} + 19837 T^{4} - 115236 T^{5} + 1252068 T^{6} - 6497620 T^{7} + 58571224 T^{8} - 277021276 T^{9} + 2184743874 T^{10} - 9546857708 T^{11} + 67882331020 T^{12} - 276510702884 T^{13} + 1805247496970 T^{14} - 6893991759912 T^{15} + 41807869607761 T^{16} - 150199940099848 T^{17} + 852315750839294 T^{18} - 2884906960753048 T^{19} + 15384600661717447 T^{20} - 49043418332801816 T^{21} + 246319251992555966 T^{22} - 737932305710553224 T^{23} + 3491835077509806481 T^{24} - 9788482458253372584 T^{25} + 43574286020190665930 T^{26} - \)\(11\!\cdots\!32\)\( T^{27} + \)\(47\!\cdots\!20\)\( T^{28} - \)\(11\!\cdots\!76\)\( T^{29} + \)\(44\!\cdots\!26\)\( T^{30} - \)\(94\!\cdots\!08\)\( T^{31} + \)\(34\!\cdots\!64\)\( T^{32} - \)\(64\!\cdots\!40\)\( T^{33} + \)\(21\!\cdots\!72\)\( T^{34} - \)\(32\!\cdots\!48\)\( T^{35} + \)\(96\!\cdots\!97\)\( T^{36} - \)\(11\!\cdots\!28\)\( T^{37} + \)\(28\!\cdots\!36\)\( T^{38} - \)\(19\!\cdots\!24\)\( T^{39} + \)\(40\!\cdots\!01\)\( T^{40} \))
$19$ (\( 1 + 3 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - 3 T + 11 T^{2} - 57 T^{3} + 361 T^{4} \))(\( 1 - 9 T + 63 T^{2} - 269 T^{3} + 1197 T^{4} - 3249 T^{5} + 6859 T^{6} \))(\( 1 + 6 T + 62 T^{2} + 208 T^{3} + 1448 T^{4} + 3952 T^{5} + 22382 T^{6} + 41154 T^{7} + 130321 T^{8} \))(\( 1 + 10 T + 117 T^{2} + 730 T^{3} + 4783 T^{4} + 20523 T^{5} + 90877 T^{6} + 263530 T^{7} + 802503 T^{8} + 1303210 T^{9} + 2476099 T^{10} \))(\( 1 + 2 T + 27 T^{2} - 24 T^{3} + 901 T^{4} + 1287 T^{5} + 17119 T^{6} - 8664 T^{7} + 185193 T^{8} + 260642 T^{9} + 2476099 T^{10} \))(\( 1 - 4 T + 39 T^{2} - 48 T^{3} + 441 T^{4} + 365 T^{5} + 8379 T^{6} - 17328 T^{7} + 267501 T^{8} - 521284 T^{9} + 2476099 T^{10} \))(\( 1 - 4 T + 118 T^{2} - 415 T^{3} + 6581 T^{4} - 20104 T^{5} + 225525 T^{6} - 588263 T^{7} + 5177111 T^{8} - 11176997 T^{9} + 81414525 T^{10} - 137893336 T^{11} + 857642501 T^{12} - 1027581085 T^{13} + 5551413958 T^{14} - 3575486956 T^{15} + 16983563041 T^{16} \))(\( 1 + 4 T + 118 T^{2} + 415 T^{3} + 6581 T^{4} + 20104 T^{5} + 225525 T^{6} + 588263 T^{7} + 5177111 T^{8} + 11176997 T^{9} + 81414525 T^{10} + 137893336 T^{11} + 857642501 T^{12} + 1027581085 T^{13} + 5551413958 T^{14} + 3575486956 T^{15} + 16983563041 T^{16} \))(\( 1 + 8 T + 142 T^{2} + 854 T^{3} + 8779 T^{4} + 41722 T^{5} + 324726 T^{6} + 1272034 T^{7} + 8468743 T^{8} + 28827300 T^{9} + 175736485 T^{10} + 547718700 T^{11} + 3057216223 T^{12} + 8724881206 T^{13} + 42318617046 T^{14} + 103307802478 T^{15} + 413015789299 T^{16} + 763366465106 T^{17} + 2411665951822 T^{18} + 2581501582232 T^{19} + 6131066257801 T^{20} \))(\( 1 - 8 T + 142 T^{2} - 854 T^{3} + 8779 T^{4} - 41722 T^{5} + 324726 T^{6} - 1272034 T^{7} + 8468743 T^{8} - 28827300 T^{9} + 175736485 T^{10} - 547718700 T^{11} + 3057216223 T^{12} - 8724881206 T^{13} + 42318617046 T^{14} - 103307802478 T^{15} + 413015789299 T^{16} - 763366465106 T^{17} + 2411665951822 T^{18} - 2581501582232 T^{19} + 6131066257801 T^{20} \))(\( 1 - 7 T + 118 T^{2} - 440 T^{3} + 5385 T^{4} - 8099 T^{5} + 160785 T^{6} + 56883 T^{7} + 4342870 T^{8} + 8044488 T^{9} + 105632963 T^{10} + 341081490 T^{11} + 2256115895 T^{12} + 9680538834 T^{13} + 45674046668 T^{14} + 205914593365 T^{15} + 867806886692 T^{16} + 3494674519074 T^{17} + 15474698923805 T^{18} + 44450080858290 T^{19} + 261557674051337 T^{20} + 378460025153928 T^{21} + 3881968759150930 T^{22} + 966076016461203 T^{23} + 51883341487396515 T^{24} - 49655505621930299 T^{25} + 627300044166909315 T^{26} - 973858564389110840 T^{27} + 4962252048546332962 T^{28} - 5593046800480188847 T^{29} + 15181127029874798299 T^{30} \))(\( 1 + 7 T + 118 T^{2} + 440 T^{3} + 5385 T^{4} + 8099 T^{5} + 160785 T^{6} - 56883 T^{7} + 4342870 T^{8} - 8044488 T^{9} + 105632963 T^{10} - 341081490 T^{11} + 2256115895 T^{12} - 9680538834 T^{13} + 45674046668 T^{14} - 205914593365 T^{15} + 867806886692 T^{16} - 3494674519074 T^{17} + 15474698923805 T^{18} - 44450080858290 T^{19} + 261557674051337 T^{20} - 378460025153928 T^{21} + 3881968759150930 T^{22} - 966076016461203 T^{23} + 51883341487396515 T^{24} + 49655505621930299 T^{25} + 627300044166909315 T^{26} + 973858564389110840 T^{27} + 4962252048546332962 T^{28} + 5593046800480188847 T^{29} + 15181127029874798299 T^{30} \))(\( 1 + 24 T + 442 T^{2} + 5948 T^{3} + 69172 T^{4} + 689232 T^{5} + 6223974 T^{6} + 50847780 T^{7} + 386362967 T^{8} + 2729413288 T^{9} + 18223922508 T^{10} + 114944678504 T^{11} + 692265483630 T^{12} + 3976725038900 T^{13} + 21951204485116 T^{14} + 116244899280332 T^{15} + 593773138113969 T^{16} + 2919711686019564 T^{17} + 13879126186324128 T^{18} + 63632736387802896 T^{19} + 282340935861651499 T^{20} + 1209021991368255024 T^{21} + 5010364553263010208 T^{22} + 20026302454408189476 T^{23} + 77381109132150554049 T^{24} + \)\(28\!\cdots\!68\)\( T^{25} + \)\(10\!\cdots\!96\)\( T^{26} + \)\(35\!\cdots\!00\)\( T^{27} + \)\(11\!\cdots\!30\)\( T^{28} + \)\(37\!\cdots\!16\)\( T^{29} + \)\(11\!\cdots\!08\)\( T^{30} + \)\(31\!\cdots\!72\)\( T^{31} + \)\(85\!\cdots\!87\)\( T^{32} + \)\(21\!\cdots\!20\)\( T^{33} + \)\(49\!\cdots\!54\)\( T^{34} + \)\(10\!\cdots\!68\)\( T^{35} + \)\(19\!\cdots\!32\)\( T^{36} + \)\(32\!\cdots\!72\)\( T^{37} + \)\(46\!\cdots\!22\)\( T^{38} + \)\(47\!\cdots\!96\)\( T^{39} + \)\(37\!\cdots\!01\)\( T^{40} \))(\( 1 - 24 T + 442 T^{2} - 5948 T^{3} + 69172 T^{4} - 689232 T^{5} + 6223974 T^{6} - 50847780 T^{7} + 386362967 T^{8} - 2729413288 T^{9} + 18223922508 T^{10} - 114944678504 T^{11} + 692265483630 T^{12} - 3976725038900 T^{13} + 21951204485116 T^{14} - 116244899280332 T^{15} + 593773138113969 T^{16} - 2919711686019564 T^{17} + 13879126186324128 T^{18} - 63632736387802896 T^{19} + 282340935861651499 T^{20} - 1209021991368255024 T^{21} + 5010364553263010208 T^{22} - 20026302454408189476 T^{23} + 77381109132150554049 T^{24} - \)\(28\!\cdots\!68\)\( T^{25} + \)\(10\!\cdots\!96\)\( T^{26} - \)\(35\!\cdots\!00\)\( T^{27} + \)\(11\!\cdots\!30\)\( T^{28} - \)\(37\!\cdots\!16\)\( T^{29} + \)\(11\!\cdots\!08\)\( T^{30} - \)\(31\!\cdots\!72\)\( T^{31} + \)\(85\!\cdots\!87\)\( T^{32} - \)\(21\!\cdots\!20\)\( T^{33} + \)\(49\!\cdots\!54\)\( T^{34} - \)\(10\!\cdots\!68\)\( T^{35} + \)\(19\!\cdots\!32\)\( T^{36} - \)\(32\!\cdots\!72\)\( T^{37} + \)\(46\!\cdots\!22\)\( T^{38} - \)\(47\!\cdots\!96\)\( T^{39} + \)\(37\!\cdots\!01\)\( T^{40} \))
$23$ (\( 1 + T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 + 3 T + 45 T^{2} + 69 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 51 T^{2} - 101 T^{3} + 1173 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 + 12 T + 108 T^{2} + 700 T^{3} + 3718 T^{4} + 16100 T^{5} + 57132 T^{6} + 146004 T^{7} + 279841 T^{8} \))(\( 1 - 12 T + 163 T^{2} - 1174 T^{3} + 8623 T^{4} - 41305 T^{5} + 198329 T^{6} - 621046 T^{7} + 1983221 T^{8} - 3358092 T^{9} + 6436343 T^{10} \))(\( 1 - 4 T + 23 T^{2} - 58 T^{3} + 1051 T^{4} - 4157 T^{5} + 24173 T^{6} - 30682 T^{7} + 279841 T^{8} - 1119364 T^{9} + 6436343 T^{10} \))(\( 1 + 8 T + 83 T^{2} + 574 T^{3} + 3355 T^{4} + 18011 T^{5} + 77165 T^{6} + 303646 T^{7} + 1009861 T^{8} + 2238728 T^{9} + 6436343 T^{10} \))(\( 1 + 3 T + 137 T^{2} + 183 T^{3} + 7715 T^{4} - 1513 T^{5} + 252455 T^{6} - 332692 T^{7} + 6224545 T^{8} - 7651916 T^{9} + 133548695 T^{10} - 18408671 T^{11} + 2158973315 T^{12} + 1177850769 T^{13} + 20280916793 T^{14} + 10214476341 T^{15} + 78310985281 T^{16} \))(\( 1 + 3 T + 137 T^{2} + 183 T^{3} + 7715 T^{4} - 1513 T^{5} + 252455 T^{6} - 332692 T^{7} + 6224545 T^{8} - 7651916 T^{9} + 133548695 T^{10} - 18408671 T^{11} + 2158973315 T^{12} + 1177850769 T^{13} + 20280916793 T^{14} + 10214476341 T^{15} + 78310985281 T^{16} \))(\( 1 - 4 T + 150 T^{2} - 472 T^{3} + 10995 T^{4} - 29014 T^{5} + 530388 T^{6} - 1210146 T^{7} + 18532865 T^{8} - 36844898 T^{9} + 487837739 T^{10} - 847432654 T^{11} + 9803885585 T^{12} - 14723846382 T^{13} + 148424308308 T^{14} - 186744055802 T^{15} + 1627654599555 T^{16} - 1607077610984 T^{17} + 11746647792150 T^{18} - 7204610645852 T^{19} + 41426511213649 T^{20} \))(\( 1 - 4 T + 150 T^{2} - 472 T^{3} + 10995 T^{4} - 29014 T^{5} + 530388 T^{6} - 1210146 T^{7} + 18532865 T^{8} - 36844898 T^{9} + 487837739 T^{10} - 847432654 T^{11} + 9803885585 T^{12} - 14723846382 T^{13} + 148424308308 T^{14} - 186744055802 T^{15} + 1627654599555 T^{16} - 1607077610984 T^{17} + 11746647792150 T^{18} - 7204610645852 T^{19} + 41426511213649 T^{20} \))(\( 1 + T + 100 T^{2} - 240 T^{3} + 5823 T^{4} - 23139 T^{5} + 307392 T^{6} - 1276767 T^{7} + 12804893 T^{8} - 57452087 T^{9} + 449235292 T^{10} - 2003430672 T^{11} + 13871296909 T^{12} - 58567273319 T^{13} + 364132115290 T^{14} - 1474508609730 T^{15} + 8375038651670 T^{16} - 30982087585751 T^{17} + 168772069491803 T^{18} - 560642042683152 T^{19} + 2891432427017156 T^{20} - 8504970773950343 T^{21} + 43598425532512171 T^{22} - 99984881744266527 T^{23} + 553659918912434496 T^{24} - 958568042972624211 T^{25} + 5548211220332796921 T^{26} - 5259509863684877040 T^{27} + 50403636193646738300 T^{28} + 11592836324538749809 T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 + T + 100 T^{2} - 240 T^{3} + 5823 T^{4} - 23139 T^{5} + 307392 T^{6} - 1276767 T^{7} + 12804893 T^{8} - 57452087 T^{9} + 449235292 T^{10} - 2003430672 T^{11} + 13871296909 T^{12} - 58567273319 T^{13} + 364132115290 T^{14} - 1474508609730 T^{15} + 8375038651670 T^{16} - 30982087585751 T^{17} + 168772069491803 T^{18} - 560642042683152 T^{19} + 2891432427017156 T^{20} - 8504970773950343 T^{21} + 43598425532512171 T^{22} - 99984881744266527 T^{23} + 553659918912434496 T^{24} - 958568042972624211 T^{25} + 5548211220332796921 T^{26} - 5259509863684877040 T^{27} + 50403636193646738300 T^{28} + 11592836324538749809 T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 - 8 T + 224 T^{2} - 1604 T^{3} + 25586 T^{4} - 164324 T^{5} + 1949088 T^{6} - 11272892 T^{7} + 110293819 T^{8} - 575766952 T^{9} + 4917180158 T^{10} - 23186904576 T^{11} + 179684057376 T^{12} - 766054796244 T^{13} + 5564463719942 T^{14} - 21547403690928 T^{15} + 151225681694129 T^{16} - 539520406114572 T^{17} + 3750834473275234 T^{18} - 12680390219549800 T^{19} + 88013214377958071 T^{20} - 291648975049645400 T^{21} + 1984191436362598786 T^{22} - 6564344781195997524 T^{23} + 42319145990966753489 T^{24} - \)\(13\!\cdots\!04\)\( T^{25} + \)\(82\!\cdots\!38\)\( T^{26} - \)\(26\!\cdots\!68\)\( T^{27} + \)\(14\!\cdots\!56\)\( T^{28} - \)\(41\!\cdots\!88\)\( T^{29} + \)\(20\!\cdots\!42\)\( T^{30} - \)\(54\!\cdots\!04\)\( T^{31} + \)\(24\!\cdots\!99\)\( T^{32} - \)\(56\!\cdots\!36\)\( T^{33} + \)\(22\!\cdots\!92\)\( T^{34} - \)\(43\!\cdots\!68\)\( T^{35} + \)\(15\!\cdots\!46\)\( T^{36} - \)\(22\!\cdots\!12\)\( T^{37} + \)\(72\!\cdots\!56\)\( T^{38} - \)\(59\!\cdots\!96\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 224 T^{2} - 1604 T^{3} + 25586 T^{4} - 164324 T^{5} + 1949088 T^{6} - 11272892 T^{7} + 110293819 T^{8} - 575766952 T^{9} + 4917180158 T^{10} - 23186904576 T^{11} + 179684057376 T^{12} - 766054796244 T^{13} + 5564463719942 T^{14} - 21547403690928 T^{15} + 151225681694129 T^{16} - 539520406114572 T^{17} + 3750834473275234 T^{18} - 12680390219549800 T^{19} + 88013214377958071 T^{20} - 291648975049645400 T^{21} + 1984191436362598786 T^{22} - 6564344781195997524 T^{23} + 42319145990966753489 T^{24} - \)\(13\!\cdots\!04\)\( T^{25} + \)\(82\!\cdots\!38\)\( T^{26} - \)\(26\!\cdots\!68\)\( T^{27} + \)\(14\!\cdots\!56\)\( T^{28} - \)\(41\!\cdots\!88\)\( T^{29} + \)\(20\!\cdots\!42\)\( T^{30} - \)\(54\!\cdots\!04\)\( T^{31} + \)\(24\!\cdots\!99\)\( T^{32} - \)\(56\!\cdots\!36\)\( T^{33} + \)\(22\!\cdots\!92\)\( T^{34} - \)\(43\!\cdots\!68\)\( T^{35} + \)\(15\!\cdots\!46\)\( T^{36} - \)\(22\!\cdots\!12\)\( T^{37} + \)\(72\!\cdots\!56\)\( T^{38} - \)\(59\!\cdots\!96\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$29$ (\( 1 + 10 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 17 T + 127 T^{2} - 493 T^{3} + 841 T^{4} \))(\( 1 + 12 T + 123 T^{2} + 704 T^{3} + 3567 T^{4} + 10092 T^{5} + 24389 T^{6} \))(\( 1 + 4 T + 76 T^{2} + 348 T^{3} + 2870 T^{4} + 10092 T^{5} + 63916 T^{6} + 97556 T^{7} + 707281 T^{8} \))(\( 1 + 3 T + 124 T^{2} + 284 T^{3} + 6667 T^{4} + 11690 T^{5} + 193343 T^{6} + 238844 T^{7} + 3024236 T^{8} + 2121843 T^{9} + 20511149 T^{10} \))(\( 1 - 11 T + 114 T^{2} - 876 T^{3} + 6109 T^{4} - 32522 T^{5} + 177161 T^{6} - 736716 T^{7} + 2780346 T^{8} - 7780091 T^{9} + 20511149 T^{10} \))(\( 1 + 9 T + 68 T^{2} + 24 T^{3} - 1301 T^{4} - 16106 T^{5} - 37729 T^{6} + 20184 T^{7} + 1658452 T^{8} + 6365529 T^{9} + 20511149 T^{10} \))(\( 1 + 4 T + 138 T^{2} + 516 T^{3} + 9467 T^{4} + 33071 T^{5} + 440608 T^{6} + 1382028 T^{7} + 14949058 T^{8} + 40078812 T^{9} + 370551328 T^{10} + 806568619 T^{11} + 6695829227 T^{12} + 10583752884 T^{13} + 82085618298 T^{14} + 68999505236 T^{15} + 500246412961 T^{16} \))(\( 1 + 4 T + 138 T^{2} + 516 T^{3} + 9467 T^{4} + 33071 T^{5} + 440608 T^{6} + 1382028 T^{7} + 14949058 T^{8} + 40078812 T^{9} + 370551328 T^{10} + 806568619 T^{11} + 6695829227 T^{12} + 10583752884 T^{13} + 82085618298 T^{14} + 68999505236 T^{15} + 500246412961 T^{16} \))(\( 1 - 2 T + 169 T^{2} - 200 T^{3} + 13298 T^{4} - 8180 T^{5} + 689398 T^{6} - 273872 T^{7} + 27573885 T^{8} - 10844658 T^{9} + 890329250 T^{10} - 314495082 T^{11} + 23189637285 T^{12} - 6679464208 T^{13} + 487598106838 T^{14} - 167781198820 T^{15} + 7909960522658 T^{16} - 3449975261800 T^{17} + 84541643790409 T^{18} - 29014291951738 T^{19} + 420707233300201 T^{20} \))(\( 1 - 2 T + 169 T^{2} - 200 T^{3} + 13298 T^{4} - 8180 T^{5} + 689398 T^{6} - 273872 T^{7} + 27573885 T^{8} - 10844658 T^{9} + 890329250 T^{10} - 314495082 T^{11} + 23189637285 T^{12} - 6679464208 T^{13} + 487598106838 T^{14} - 167781198820 T^{15} + 7909960522658 T^{16} - 3449975261800 T^{17} + 84541643790409 T^{18} - 29014291951738 T^{19} + 420707233300201 T^{20} \))(\( 1 - 18 T + 351 T^{2} - 3938 T^{3} + 45998 T^{4} - 391789 T^{5} + 3532456 T^{6} - 25324251 T^{7} + 196317762 T^{8} - 1257094469 T^{9} + 8801517748 T^{10} - 51641736178 T^{11} + 332842157595 T^{12} - 1810862813908 T^{13} + 10895718454521 T^{14} - 55671549974722 T^{15} + 315975835181109 T^{16} - 1522935626496628 T^{17} + 8117687381584455 T^{18} - 36525218805712018 T^{19} + 180529241955372452 T^{20} - 747749106861311549 T^{21} + 3386457111759700458 T^{22} - 12668365723674017211 T^{23} + 51245854845334304264 T^{24} - \)\(16\!\cdots\!89\)\( T^{25} + \)\(56\!\cdots\!42\)\( T^{26} - \)\(13\!\cdots\!58\)\( T^{27} + \)\(36\!\cdots\!39\)\( T^{28} - \)\(53\!\cdots\!58\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 - 18 T + 351 T^{2} - 3938 T^{3} + 45998 T^{4} - 391789 T^{5} + 3532456 T^{6} - 25324251 T^{7} + 196317762 T^{8} - 1257094469 T^{9} + 8801517748 T^{10} - 51641736178 T^{11} + 332842157595 T^{12} - 1810862813908 T^{13} + 10895718454521 T^{14} - 55671549974722 T^{15} + 315975835181109 T^{16} - 1522935626496628 T^{17} + 8117687381584455 T^{18} - 36525218805712018 T^{19} + 180529241955372452 T^{20} - 747749106861311549 T^{21} + 3386457111759700458 T^{22} - 12668365723674017211 T^{23} + 51245854845334304264 T^{24} - \)\(16\!\cdots\!89\)\( T^{25} + \)\(56\!\cdots\!42\)\( T^{26} - \)\(13\!\cdots\!58\)\( T^{27} + \)\(36\!\cdots\!39\)\( T^{28} - \)\(53\!\cdots\!58\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 + 12 T + 372 T^{2} + 3900 T^{3} + 68255 T^{4} + 641676 T^{5} + 8277632 T^{6} + 70822400 T^{7} + 746135170 T^{8} + 5863304764 T^{9} + 53174262038 T^{10} + 386094445984 T^{11} + 3108561209242 T^{12} + 20939598180832 T^{13} + 152594143829102 T^{14} + 956108937529028 T^{15} + 6385477457957389 T^{16} + 37270237580395268 T^{17} + 229952446886288440 T^{18} + 1250667711151805704 T^{19} + 7163785976565568494 T^{20} + 36269363623402365416 T^{21} + \)\(19\!\cdots\!40\)\( T^{22} + \)\(90\!\cdots\!52\)\( T^{23} + \)\(45\!\cdots\!09\)\( T^{24} + \)\(19\!\cdots\!72\)\( T^{25} + \)\(90\!\cdots\!42\)\( T^{26} + \)\(36\!\cdots\!88\)\( T^{27} + \)\(15\!\cdots\!62\)\( T^{28} + \)\(56\!\cdots\!96\)\( T^{29} + \)\(22\!\cdots\!38\)\( T^{30} + \)\(71\!\cdots\!56\)\( T^{31} + \)\(26\!\cdots\!70\)\( T^{32} + \)\(72\!\cdots\!00\)\( T^{33} + \)\(24\!\cdots\!92\)\( T^{34} + \)\(55\!\cdots\!24\)\( T^{35} + \)\(17\!\cdots\!55\)\( T^{36} + \)\(28\!\cdots\!00\)\( T^{37} + \)\(78\!\cdots\!92\)\( T^{38} + \)\(73\!\cdots\!28\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( 1 + 12 T + 372 T^{2} + 3900 T^{3} + 68255 T^{4} + 641676 T^{5} + 8277632 T^{6} + 70822400 T^{7} + 746135170 T^{8} + 5863304764 T^{9} + 53174262038 T^{10} + 386094445984 T^{11} + 3108561209242 T^{12} + 20939598180832 T^{13} + 152594143829102 T^{14} + 956108937529028 T^{15} + 6385477457957389 T^{16} + 37270237580395268 T^{17} + 229952446886288440 T^{18} + 1250667711151805704 T^{19} + 7163785976565568494 T^{20} + 36269363623402365416 T^{21} + \)\(19\!\cdots\!40\)\( T^{22} + \)\(90\!\cdots\!52\)\( T^{23} + \)\(45\!\cdots\!09\)\( T^{24} + \)\(19\!\cdots\!72\)\( T^{25} + \)\(90\!\cdots\!42\)\( T^{26} + \)\(36\!\cdots\!88\)\( T^{27} + \)\(15\!\cdots\!62\)\( T^{28} + \)\(56\!\cdots\!96\)\( T^{29} + \)\(22\!\cdots\!38\)\( T^{30} + \)\(71\!\cdots\!56\)\( T^{31} + \)\(26\!\cdots\!70\)\( T^{32} + \)\(72\!\cdots\!00\)\( T^{33} + \)\(24\!\cdots\!92\)\( T^{34} + \)\(55\!\cdots\!24\)\( T^{35} + \)\(17\!\cdots\!55\)\( T^{36} + \)\(28\!\cdots\!00\)\( T^{37} + \)\(78\!\cdots\!92\)\( T^{38} + \)\(73\!\cdots\!28\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$31$ (\( 1 + 11 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 11 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 11 T + 63 T^{2} + 341 T^{3} + 961 T^{4} \))(\( 1 - 12 T + 93 T^{2} - 552 T^{3} + 2883 T^{4} - 11532 T^{5} + 29791 T^{6} \))(\( 1 - 8 T + 92 T^{2} - 712 T^{3} + 3846 T^{4} - 22072 T^{5} + 88412 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( 1 + 7 T + 162 T^{2} + 842 T^{3} + 10229 T^{4} + 38742 T^{5} + 317099 T^{6} + 809162 T^{7} + 4826142 T^{8} + 6464647 T^{9} + 28629151 T^{10} \))(\( 1 + 13 T + 130 T^{2} + 830 T^{3} + 4765 T^{4} + 25298 T^{5} + 147715 T^{6} + 797630 T^{7} + 3872830 T^{8} + 12005773 T^{9} + 28629151 T^{10} \))(\( 1 - 11 T + 112 T^{2} - 656 T^{3} + 5003 T^{4} - 25610 T^{5} + 155093 T^{6} - 630416 T^{7} + 3336592 T^{8} - 10158731 T^{9} + 28629151 T^{10} \))(\( 1 - 4 T + 136 T^{2} - 326 T^{3} + 9390 T^{4} - 15989 T^{5} + 452251 T^{6} - 616687 T^{7} + 16188363 T^{8} - 19117297 T^{9} + 434613211 T^{10} - 476328299 T^{11} + 8671862190 T^{12} - 9333103226 T^{13} + 120700500616 T^{14} - 110050456444 T^{15} + 852891037441 T^{16} \))(\( 1 + 4 T + 136 T^{2} + 326 T^{3} + 9390 T^{4} + 15989 T^{5} + 452251 T^{6} + 616687 T^{7} + 16188363 T^{8} + 19117297 T^{9} + 434613211 T^{10} + 476328299 T^{11} + 8671862190 T^{12} + 9333103226 T^{13} + 120700500616 T^{14} + 110050456444 T^{15} + 852891037441 T^{16} \))(\( 1 + 8 T + 173 T^{2} + 1172 T^{3} + 15518 T^{4} + 93450 T^{5} + 940146 T^{6} + 5050870 T^{7} + 42210833 T^{8} + 203386776 T^{9} + 1475895842 T^{10} + 6304990056 T^{11} + 40564610513 T^{12} + 150470468170 T^{13} + 868244574066 T^{14} + 2675394160950 T^{15} + 13772282121758 T^{16} + 32244783738092 T^{17} + 147550149477293 T^{18} + 211516977285368 T^{19} + 819628286980801 T^{20} \))(\( 1 - 8 T + 173 T^{2} - 1172 T^{3} + 15518 T^{4} - 93450 T^{5} + 940146 T^{6} - 5050870 T^{7} + 42210833 T^{8} - 203386776 T^{9} + 1475895842 T^{10} - 6304990056 T^{11} + 40564610513 T^{12} - 150470468170 T^{13} + 868244574066 T^{14} - 2675394160950 T^{15} + 13772282121758 T^{16} - 32244783738092 T^{17} + 147550149477293 T^{18} - 211516977285368 T^{19} + 819628286980801 T^{20} \))(\( 1 - 30 T + 729 T^{2} - 12702 T^{3} + 192287 T^{4} - 2469077 T^{5} + 28541588 T^{6} - 295094480 T^{7} + 2801338765 T^{8} - 24357725643 T^{9} + 196723756650 T^{10} - 1473344847030 T^{11} + 10319381498616 T^{12} - 67463739856866 T^{13} + 413955859752302 T^{14} - 2377693087445112 T^{15} + 12832631652321362 T^{16} - 64832654002448226 T^{17} + 307424694225269256 T^{18} - 1360664906473992630 T^{19} + 5632034134420104150 T^{20} - 21617571168950591883 T^{21} + 77072152435630312915 T^{22} - \)\(25\!\cdots\!80\)\( T^{23} + \)\(75\!\cdots\!48\)\( T^{24} - \)\(20\!\cdots\!77\)\( T^{25} + \)\(48\!\cdots\!97\)\( T^{26} - \)\(10\!\cdots\!22\)\( T^{27} + \)\(17\!\cdots\!39\)\( T^{28} - \)\(22\!\cdots\!30\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 + 30 T + 729 T^{2} + 12702 T^{3} + 192287 T^{4} + 2469077 T^{5} + 28541588 T^{6} + 295094480 T^{7} + 2801338765 T^{8} + 24357725643 T^{9} + 196723756650 T^{10} + 1473344847030 T^{11} + 10319381498616 T^{12} + 67463739856866 T^{13} + 413955859752302 T^{14} + 2377693087445112 T^{15} + 12832631652321362 T^{16} + 64832654002448226 T^{17} + 307424694225269256 T^{18} + 1360664906473992630 T^{19} + 5632034134420104150 T^{20} + 21617571168950591883 T^{21} + 77072152435630312915 T^{22} + \)\(25\!\cdots\!80\)\( T^{23} + \)\(75\!\cdots\!48\)\( T^{24} + \)\(20\!\cdots\!77\)\( T^{25} + \)\(48\!\cdots\!97\)\( T^{26} + \)\(10\!\cdots\!22\)\( T^{27} + \)\(17\!\cdots\!39\)\( T^{28} + \)\(22\!\cdots\!30\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 + 366 T^{2} - 200 T^{3} + 64893 T^{4} - 66076 T^{5} + 7487952 T^{6} - 10495888 T^{7} + 637833274 T^{8} - 1075441548 T^{9} + 43108352406 T^{10} - 80651055032 T^{11} + 2420742392118 T^{12} - 4765258606976 T^{13} + 116381484643210 T^{14} - 232551995261652 T^{15} + 4881847246546661 T^{16} - 9645402933660120 T^{17} + 180712343974789634 T^{18} - 344947354297833756 T^{19} + 5939483468474401498 T^{20} - 10693367983232846436 T^{21} + \)\(17\!\cdots\!74\)\( T^{22} - \)\(28\!\cdots\!20\)\( T^{23} + \)\(45\!\cdots\!81\)\( T^{24} - \)\(66\!\cdots\!52\)\( T^{25} + \)\(10\!\cdots\!10\)\( T^{26} - \)\(13\!\cdots\!36\)\( T^{27} + \)\(20\!\cdots\!38\)\( T^{28} - \)\(21\!\cdots\!72\)\( T^{29} + \)\(35\!\cdots\!06\)\( T^{30} - \)\(27\!\cdots\!88\)\( T^{31} + \)\(50\!\cdots\!14\)\( T^{32} - \)\(25\!\cdots\!08\)\( T^{33} + \)\(56\!\cdots\!92\)\( T^{34} - \)\(15\!\cdots\!76\)\( T^{35} + \)\(47\!\cdots\!33\)\( T^{36} - \)\(45\!\cdots\!00\)\( T^{37} + \)\(25\!\cdots\!06\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( 1 + 366 T^{2} + 200 T^{3} + 64893 T^{4} + 66076 T^{5} + 7487952 T^{6} + 10495888 T^{7} + 637833274 T^{8} + 1075441548 T^{9} + 43108352406 T^{10} + 80651055032 T^{11} + 2420742392118 T^{12} + 4765258606976 T^{13} + 116381484643210 T^{14} + 232551995261652 T^{15} + 4881847246546661 T^{16} + 9645402933660120 T^{17} + 180712343974789634 T^{18} + 344947354297833756 T^{19} + 5939483468474401498 T^{20} + 10693367983232846436 T^{21} + \)\(17\!\cdots\!74\)\( T^{22} + \)\(28\!\cdots\!20\)\( T^{23} + \)\(45\!\cdots\!81\)\( T^{24} + \)\(66\!\cdots\!52\)\( T^{25} + \)\(10\!\cdots\!10\)\( T^{26} + \)\(13\!\cdots\!36\)\( T^{27} + \)\(20\!\cdots\!38\)\( T^{28} + \)\(21\!\cdots\!72\)\( T^{29} + \)\(35\!\cdots\!06\)\( T^{30} + \)\(27\!\cdots\!88\)\( T^{31} + \)\(50\!\cdots\!14\)\( T^{32} + \)\(25\!\cdots\!08\)\( T^{33} + \)\(56\!\cdots\!92\)\( T^{34} + \)\(15\!\cdots\!76\)\( T^{35} + \)\(47\!\cdots\!33\)\( T^{36} + \)\(45\!\cdots\!00\)\( T^{37} + \)\(25\!\cdots\!06\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))
$37$ (\( 1 - 7 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 6 T + 70 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 21 T + 237 T^{2} + 1733 T^{3} + 8769 T^{4} + 28749 T^{5} + 50653 T^{6} \))(\( 1 - 16 T + 212 T^{2} - 1740 T^{3} + 12626 T^{4} - 64380 T^{5} + 290228 T^{6} - 810448 T^{7} + 1874161 T^{8} \))(\( 1 - T + 129 T^{2} - 293 T^{3} + 7484 T^{4} - 18756 T^{5} + 276908 T^{6} - 401117 T^{7} + 6534237 T^{8} - 1874161 T^{9} + 69343957 T^{10} \))(\( 1 - 5 T + 117 T^{2} - 517 T^{3} + 6812 T^{4} - 26316 T^{5} + 252044 T^{6} - 707773 T^{7} + 5926401 T^{8} - 9370805 T^{9} + 69343957 T^{10} \))(\( 1 + 11 T + 145 T^{2} + 663 T^{3} + 4956 T^{4} + 12852 T^{5} + 183372 T^{6} + 907647 T^{7} + 7344685 T^{8} + 20615771 T^{9} + 69343957 T^{10} \))(\( 1 + 31 T + 643 T^{2} + 9644 T^{3} + 117278 T^{4} + 1183925 T^{5} + 10234846 T^{6} + 76402804 T^{7} + 497661632 T^{8} + 2826903748 T^{9} + 14011504174 T^{10} + 59969353025 T^{11} + 219797853758 T^{12} + 668753121308 T^{13} + 1649762080987 T^{14} + 2942888191123 T^{15} + 3512479453921 T^{16} \))(\( 1 + 31 T + 643 T^{2} + 9644 T^{3} + 117278 T^{4} + 1183925 T^{5} + 10234846 T^{6} + 76402804 T^{7} + 497661632 T^{8} + 2826903748 T^{9} + 14011504174 T^{10} + 59969353025 T^{11} + 219797853758 T^{12} + 668753121308 T^{13} + 1649762080987 T^{14} + 2942888191123 T^{15} + 3512479453921 T^{16} \))(\( 1 + 2 T + 207 T^{2} + 440 T^{3} + 23279 T^{4} + 49382 T^{5} + 1758529 T^{6} + 3562350 T^{7} + 97635520 T^{8} + 181110266 T^{9} + 4119614704 T^{10} + 6701079842 T^{11} + 133663026880 T^{12} + 180443714550 T^{13} + 3295766469169 T^{14} + 3424343284574 T^{15} + 59727545075111 T^{16} + 41770025938520 T^{17} + 727083246961647 T^{18} + 259923479590154 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 2 T + 207 T^{2} + 440 T^{3} + 23279 T^{4} + 49382 T^{5} + 1758529 T^{6} + 3562350 T^{7} + 97635520 T^{8} + 181110266 T^{9} + 4119614704 T^{10} + 6701079842 T^{11} + 133663026880 T^{12} + 180443714550 T^{13} + 3295766469169 T^{14} + 3424343284574 T^{15} + 59727545075111 T^{16} + 41770025938520 T^{17} + 727083246961647 T^{18} + 259923479590154 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 23 T + 400 T^{2} - 5145 T^{3} + 58100 T^{4} - 567646 T^{5} + 5181174 T^{6} - 43727378 T^{7} + 355029388 T^{8} - 2734178148 T^{9} + 20402693048 T^{10} - 144984533863 T^{11} + 997358220188 T^{12} - 6561885310287 T^{13} + 41976916551657 T^{14} - 258407011673340 T^{15} + 1553145912411309 T^{16} - 8983220989782903 T^{17} + 50519185927182764 T^{18} - 271724358969213943 T^{19} + 1414803469404710936 T^{20} - 7015153081234310532 T^{21} + 33703606240220184604 T^{22} - \)\(15\!\cdots\!38\)\( T^{23} + \)\(67\!\cdots\!98\)\( T^{24} - \)\(27\!\cdots\!54\)\( T^{25} + \)\(10\!\cdots\!00\)\( T^{26} - \)\(33\!\cdots\!45\)\( T^{27} + \)\(97\!\cdots\!00\)\( T^{28} - \)\(20\!\cdots\!47\)\( T^{29} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 - 23 T + 400 T^{2} - 5145 T^{3} + 58100 T^{4} - 567646 T^{5} + 5181174 T^{6} - 43727378 T^{7} + 355029388 T^{8} - 2734178148 T^{9} + 20402693048 T^{10} - 144984533863 T^{11} + 997358220188 T^{12} - 6561885310287 T^{13} + 41976916551657 T^{14} - 258407011673340 T^{15} + 1553145912411309 T^{16} - 8983220989782903 T^{17} + 50519185927182764 T^{18} - 271724358969213943 T^{19} + 1414803469404710936 T^{20} - 7015153081234310532 T^{21} + 33703606240220184604 T^{22} - \)\(15\!\cdots\!38\)\( T^{23} + \)\(67\!\cdots\!98\)\( T^{24} - \)\(27\!\cdots\!54\)\( T^{25} + \)\(10\!\cdots\!00\)\( T^{26} - \)\(33\!\cdots\!45\)\( T^{27} + \)\(97\!\cdots\!00\)\( T^{28} - \)\(20\!\cdots\!47\)\( T^{29} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 - 12 T + 414 T^{2} - 4100 T^{3} + 82723 T^{4} - 714876 T^{5} + 10950648 T^{6} - 85102596 T^{7} + 1090533699 T^{8} - 7755996252 T^{9} + 87298936098 T^{10} - 574754531056 T^{11} + 5846021890633 T^{12} - 35909756683808 T^{13} + 335961485822006 T^{14} - 1935713494053164 T^{15} + 16848638971526184 T^{16} - 91370333355176520 T^{17} + 745252319804448866 T^{18} - 3810432221941255680 T^{19} + 29246522638093731856 T^{20} - \)\(14\!\cdots\!60\)\( T^{21} + \)\(10\!\cdots\!54\)\( T^{22} - \)\(46\!\cdots\!60\)\( T^{23} + \)\(31\!\cdots\!24\)\( T^{24} - \)\(13\!\cdots\!48\)\( T^{25} + \)\(86\!\cdots\!54\)\( T^{26} - \)\(34\!\cdots\!64\)\( T^{27} + \)\(20\!\cdots\!93\)\( T^{28} - \)\(74\!\cdots\!12\)\( T^{29} + \)\(41\!\cdots\!02\)\( T^{30} - \)\(13\!\cdots\!76\)\( T^{31} + \)\(71\!\cdots\!19\)\( T^{32} - \)\(20\!\cdots\!12\)\( T^{33} + \)\(98\!\cdots\!72\)\( T^{34} - \)\(23\!\cdots\!68\)\( T^{35} + \)\(10\!\cdots\!43\)\( T^{36} - \)\(18\!\cdots\!00\)\( T^{37} + \)\(69\!\cdots\!06\)\( T^{38} - \)\(74\!\cdots\!76\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))(\( 1 - 12 T + 414 T^{2} - 4100 T^{3} + 82723 T^{4} - 714876 T^{5} + 10950648 T^{6} - 85102596 T^{7} + 1090533699 T^{8} - 7755996252 T^{9} + 87298936098 T^{10} - 574754531056 T^{11} + 5846021890633 T^{12} - 35909756683808 T^{13} + 335961485822006 T^{14} - 1935713494053164 T^{15} + 16848638971526184 T^{16} - 91370333355176520 T^{17} + 745252319804448866 T^{18} - 3810432221941255680 T^{19} + 29246522638093731856 T^{20} - \)\(14\!\cdots\!60\)\( T^{21} + \)\(10\!\cdots\!54\)\( T^{22} - \)\(46\!\cdots\!60\)\( T^{23} + \)\(31\!\cdots\!24\)\( T^{24} - \)\(13\!\cdots\!48\)\( T^{25} + \)\(86\!\cdots\!54\)\( T^{26} - \)\(34\!\cdots\!64\)\( T^{27} + \)\(20\!\cdots\!93\)\( T^{28} - \)\(74\!\cdots\!12\)\( T^{29} + \)\(41\!\cdots\!02\)\( T^{30} - \)\(13\!\cdots\!76\)\( T^{31} + \)\(71\!\cdots\!19\)\( T^{32} - \)\(20\!\cdots\!12\)\( T^{33} + \)\(98\!\cdots\!72\)\( T^{34} - \)\(23\!\cdots\!68\)\( T^{35} + \)\(10\!\cdots\!43\)\( T^{36} - \)\(18\!\cdots\!00\)\( T^{37} + \)\(69\!\cdots\!06\)\( T^{38} - \)\(74\!\cdots\!76\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{8} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{15} \))(\( ( 1 - T )^{15} \))(\( ( 1 - T )^{20} \))(\( ( 1 + T )^{20} \))
$43$ (\( 1 - 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 16 T + 137 T^{2} + 688 T^{3} + 1849 T^{4} \))(\( 1 + 3 T + 93 T^{2} + 239 T^{3} + 3999 T^{4} + 5547 T^{5} + 79507 T^{6} \))(\( 1 - 4 T + 124 T^{2} - 244 T^{3} + 6678 T^{4} - 10492 T^{5} + 229276 T^{6} - 318028 T^{7} + 3418801 T^{8} \))(\( 1 - 13 T + 234 T^{2} - 2046 T^{3} + 20829 T^{4} - 128475 T^{5} + 895647 T^{6} - 3783054 T^{7} + 18604638 T^{8} - 44444413 T^{9} + 147008443 T^{10} \))(\( 1 - 29 T + 522 T^{2} - 6438 T^{3} + 61101 T^{4} - 448587 T^{5} + 2627343 T^{6} - 11903862 T^{7} + 41502654 T^{8} - 99145229 T^{9} + 147008443 T^{10} \))(\( 1 + 27 T + 382 T^{2} + 3986 T^{3} + 34437 T^{4} + 248301 T^{5} + 1480791 T^{6} + 7370114 T^{7} + 30371674 T^{8} + 92307627 T^{9} + 147008443 T^{10} \))(\( 1 + 8 T + 288 T^{2} + 2036 T^{3} + 38055 T^{4} + 236033 T^{5} + 3024756 T^{6} + 16054528 T^{7} + 158339468 T^{8} + 690344704 T^{9} + 5592773844 T^{10} + 18766275731 T^{11} + 130102472055 T^{12} + 299309189948 T^{13} + 1820552558112 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 + 8 T + 288 T^{2} + 2036 T^{3} + 38055 T^{4} + 236033 T^{5} + 3024756 T^{6} + 16054528 T^{7} + 158339468 T^{8} + 690344704 T^{9} + 5592773844 T^{10} + 18766275731 T^{11} + 130102472055 T^{12} + 299309189948 T^{13} + 1820552558112 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 + 2 T + 221 T^{2} + 468 T^{3} + 25826 T^{4} + 55060 T^{5} + 2056468 T^{6} + 4339622 T^{7} + 123599993 T^{8} + 247838392 T^{9} + 5913403015 T^{10} + 10657050856 T^{11} + 228536387057 T^{12} + 345030326354 T^{13} + 7030654854868 T^{14} + 8094284871580 T^{15} + 163255522103474 T^{16} + 127211109998076 T^{17} + 2583092261349821 T^{18} + 1005185223873686 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 2 T + 221 T^{2} + 468 T^{3} + 25826 T^{4} + 55060 T^{5} + 2056468 T^{6} + 4339622 T^{7} + 123599993 T^{8} + 247838392 T^{9} + 5913403015 T^{10} + 10657050856 T^{11} + 228536387057 T^{12} + 345030326354 T^{13} + 7030654854868 T^{14} + 8094284871580 T^{15} + 163255522103474 T^{16} + 127211109998076 T^{17} + 2583092261349821 T^{18} + 1005185223873686 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 12 T + 269 T^{2} - 2316 T^{3} + 34068 T^{4} - 253607 T^{5} + 3153596 T^{6} - 21954583 T^{7} + 240692362 T^{8} - 1568196355 T^{9} + 15411762010 T^{10} - 94482346296 T^{11} + 854049383983 T^{12} - 4960571657906 T^{13} + 41710893999939 T^{14} - 228266308319210 T^{15} + 1793568441997377 T^{16} - 9172096995468194 T^{17} + 67902904372336381 T^{18} - 323016339999111096 T^{19} + 2265659136976650430 T^{20} - 9913138492073486395 T^{21} + 65424663542903264734 T^{22} - \)\(25\!\cdots\!83\)\( T^{23} + \)\(15\!\cdots\!28\)\( T^{24} - \)\(54\!\cdots\!43\)\( T^{25} + \)\(31\!\cdots\!76\)\( T^{26} - \)\(92\!\cdots\!16\)\( T^{27} + \)\(46\!\cdots\!67\)\( T^{28} - \)\(88\!\cdots\!88\)\( T^{29} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 - 12 T + 269 T^{2} - 2316 T^{3} + 34068 T^{4} - 253607 T^{5} + 3153596 T^{6} - 21954583 T^{7} + 240692362 T^{8} - 1568196355 T^{9} + 15411762010 T^{10} - 94482346296 T^{11} + 854049383983 T^{12} - 4960571657906 T^{13} + 41710893999939 T^{14} - 228266308319210 T^{15} + 1793568441997377 T^{16} - 9172096995468194 T^{17} + 67902904372336381 T^{18} - 323016339999111096 T^{19} + 2265659136976650430 T^{20} - 9913138492073486395 T^{21} + 65424663542903264734 T^{22} - \)\(25\!\cdots\!83\)\( T^{23} + \)\(15\!\cdots\!28\)\( T^{24} - \)\(54\!\cdots\!43\)\( T^{25} + \)\(31\!\cdots\!76\)\( T^{26} - \)\(92\!\cdots\!16\)\( T^{27} + \)\(46\!\cdots\!67\)\( T^{28} - \)\(88\!\cdots\!88\)\( T^{29} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 - 4 T + 362 T^{2} - 1816 T^{3} + 68417 T^{4} - 376728 T^{5} + 8859796 T^{6} - 50098400 T^{7} + 873099406 T^{8} - 4884181768 T^{9} + 69429029716 T^{10} - 376406649008 T^{11} + 4640398136768 T^{12} - 24165516805592 T^{13} + 269513852332750 T^{14} - 1347357682359948 T^{15} + 14004381065462057 T^{16} - 67481618639288864 T^{17} + 667084060401896952 T^{18} - 3111440283755638144 T^{19} + 29620566888741233631 T^{20} - \)\(13\!\cdots\!92\)\( T^{21} + \)\(12\!\cdots\!48\)\( T^{22} - \)\(53\!\cdots\!48\)\( T^{23} + \)\(47\!\cdots\!57\)\( T^{24} - \)\(19\!\cdots\!64\)\( T^{25} + \)\(17\!\cdots\!50\)\( T^{26} - \)\(65\!\cdots\!44\)\( T^{27} + \)\(54\!\cdots\!68\)\( T^{28} - \)\(18\!\cdots\!44\)\( T^{29} + \)\(15\!\cdots\!84\)\( T^{30} - \)\(45\!\cdots\!76\)\( T^{31} + \)\(34\!\cdots\!06\)\( T^{32} - \)\(86\!\cdots\!00\)\( T^{33} + \)\(65\!\cdots\!04\)\( T^{34} - \)\(11\!\cdots\!96\)\( T^{35} + \)\(93\!\cdots\!17\)\( T^{36} - \)\(10\!\cdots\!88\)\( T^{37} + \)\(91\!\cdots\!38\)\( T^{38} - \)\(43\!\cdots\!28\)\( T^{39} + \)\(46\!\cdots\!01\)\( T^{40} \))(\( 1 - 4 T + 362 T^{2} - 1816 T^{3} + 68417 T^{4} - 376728 T^{5} + 8859796 T^{6} - 50098400 T^{7} + 873099406 T^{8} - 4884181768 T^{9} + 69429029716 T^{10} - 376406649008 T^{11} + 4640398136768 T^{12} - 24165516805592 T^{13} + 269513852332750 T^{14} - 1347357682359948 T^{15} + 14004381065462057 T^{16} - 67481618639288864 T^{17} + 667084060401896952 T^{18} - 3111440283755638144 T^{19} + 29620566888741233631 T^{20} - \)\(13\!\cdots\!92\)\( T^{21} + \)\(12\!\cdots\!48\)\( T^{22} - \)\(53\!\cdots\!48\)\( T^{23} + \)\(47\!\cdots\!57\)\( T^{24} - \)\(19\!\cdots\!64\)\( T^{25} + \)\(17\!\cdots\!50\)\( T^{26} - \)\(65\!\cdots\!44\)\( T^{27} + \)\(54\!\cdots\!68\)\( T^{28} - \)\(18\!\cdots\!44\)\( T^{29} + \)\(15\!\cdots\!84\)\( T^{30} - \)\(45\!\cdots\!76\)\( T^{31} + \)\(34\!\cdots\!06\)\( T^{32} - \)\(86\!\cdots\!00\)\( T^{33} + \)\(65\!\cdots\!04\)\( T^{34} - \)\(11\!\cdots\!96\)\( T^{35} + \)\(93\!\cdots\!17\)\( T^{36} - \)\(10\!\cdots\!88\)\( T^{37} + \)\(91\!\cdots\!38\)\( T^{38} - \)\(43\!\cdots\!28\)\( T^{39} + \)\(46\!\cdots\!01\)\( T^{40} \))
$47$ (\( 1 + 7 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 18 T + 162 T^{2} - 846 T^{3} + 2209 T^{4} \))(\( 1 - 3 T + 51 T^{2} + 99 T^{3} + 2397 T^{4} - 6627 T^{5} + 103823 T^{6} \))(\( 1 - 6 T + 126 T^{2} - 640 T^{3} + 8608 T^{4} - 30080 T^{5} + 278334 T^{6} - 622938 T^{7} + 4879681 T^{8} \))(\( 1 + 9 T + 169 T^{2} + 1585 T^{3} + 12862 T^{4} + 109216 T^{5} + 604514 T^{6} + 3501265 T^{7} + 17546087 T^{8} + 43917129 T^{9} + 229345007 T^{10} \))(\( 1 + 7 T + 161 T^{2} + 1027 T^{3} + 12666 T^{4} + 67144 T^{5} + 595302 T^{6} + 2268643 T^{7} + 16715503 T^{8} + 34157767 T^{9} + 229345007 T^{10} \))(\( 1 - 3 T + 167 T^{2} - 461 T^{3} + 13280 T^{4} - 29348 T^{5} + 624160 T^{6} - 1018349 T^{7} + 17338441 T^{8} - 14639043 T^{9} + 229345007 T^{10} \))(\( 1 - 24 T + 521 T^{2} - 7118 T^{3} + 90467 T^{4} - 890901 T^{5} + 8363341 T^{6} - 64948086 T^{7} + 485629743 T^{8} - 3052560042 T^{9} + 18474620269 T^{10} - 92496014523 T^{11} + 441450101027 T^{12} - 1632477759826 T^{13} + 5615971186409 T^{14} - 12158954891112 T^{15} + 23811286661761 T^{16} \))(\( 1 + 24 T + 521 T^{2} + 7118 T^{3} + 90467 T^{4} + 890901 T^{5} + 8363341 T^{6} + 64948086 T^{7} + 485629743 T^{8} + 3052560042 T^{9} + 18474620269 T^{10} + 92496014523 T^{11} + 441450101027 T^{12} + 1632477759826 T^{13} + 5615971186409 T^{14} + 12158954891112 T^{15} + 23811286661761 T^{16} \))(\( 1 - 14 T + 347 T^{2} - 4286 T^{3} + 61213 T^{4} - 634688 T^{5} + 6842191 T^{6} - 59787324 T^{7} + 525899550 T^{8} - 3920374812 T^{9} + 28988297588 T^{10} - 184257616164 T^{11} + 1161712105950 T^{12} - 6207299339652 T^{13} + 33387709421071 T^{14} - 145562523802816 T^{15} + 659828107934077 T^{16} - 2171386694304418 T^{17} + 8262516471631067 T^{18} - 15667826623438738 T^{19} + 52599132235830049 T^{20} \))(\( 1 + 14 T + 347 T^{2} + 4286 T^{3} + 61213 T^{4} + 634688 T^{5} + 6842191 T^{6} + 59787324 T^{7} + 525899550 T^{8} + 3920374812 T^{9} + 28988297588 T^{10} + 184257616164 T^{11} + 1161712105950 T^{12} + 6207299339652 T^{13} + 33387709421071 T^{14} + 145562523802816 T^{15} + 659828107934077 T^{16} + 2171386694304418 T^{17} + 8262516471631067 T^{18} + 15667826623438738 T^{19} + 52599132235830049 T^{20} \))(\( 1 + 16 T + 460 T^{2} + 6182 T^{3} + 103105 T^{4} + 1195645 T^{5} + 15130362 T^{6} + 154307107 T^{7} + 1634434125 T^{8} + 14876354705 T^{9} + 137984024424 T^{10} + 1134183253390 T^{11} + 9424749493183 T^{12} + 70531837481534 T^{13} + 531469788689268 T^{14} + 3633615760597546 T^{15} + 24979080068395596 T^{16} + 155804828996708606 T^{17} + 978505766630738609 T^{18} + 5534452472085368590 T^{19} + 31645947047410450968 T^{20} + \)\(16\!\cdots\!45\)\( T^{21} + \)\(82\!\cdots\!75\)\( T^{22} + \)\(36\!\cdots\!27\)\( T^{23} + \)\(16\!\cdots\!54\)\( T^{24} + \)\(62\!\cdots\!05\)\( T^{25} + \)\(25\!\cdots\!15\)\( T^{26} + \)\(71\!\cdots\!62\)\( T^{27} + \)\(25\!\cdots\!20\)\( T^{28} + \)\(41\!\cdots\!04\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 - 16 T + 460 T^{2} - 6182 T^{3} + 103105 T^{4} - 1195645 T^{5} + 15130362 T^{6} - 154307107 T^{7} + 1634434125 T^{8} - 14876354705 T^{9} + 137984024424 T^{10} - 1134183253390 T^{11} + 9424749493183 T^{12} - 70531837481534 T^{13} + 531469788689268 T^{14} - 3633615760597546 T^{15} + 24979080068395596 T^{16} - 155804828996708606 T^{17} + 978505766630738609 T^{18} - 5534452472085368590 T^{19} + 31645947047410450968 T^{20} - \)\(16\!\cdots\!45\)\( T^{21} + \)\(82\!\cdots\!75\)\( T^{22} - \)\(36\!\cdots\!27\)\( T^{23} + \)\(16\!\cdots\!54\)\( T^{24} - \)\(62\!\cdots\!05\)\( T^{25} + \)\(25\!\cdots\!15\)\( T^{26} - \)\(71\!\cdots\!62\)\( T^{27} + \)\(25\!\cdots\!20\)\( T^{28} - \)\(41\!\cdots\!04\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 + 4 T + 374 T^{2} + 1096 T^{3} + 70333 T^{4} + 138060 T^{5} + 8812902 T^{6} + 8238792 T^{7} + 825273227 T^{8} - 162954236 T^{9} + 62195044950 T^{10} - 87253393748 T^{11} + 4018555017717 T^{12} - 10192167743020 T^{13} + 235818086464330 T^{14} - 791041310737316 T^{15} + 13050043304896332 T^{16} - 48390279852871812 T^{17} + 684184059349996740 T^{18} - 2536743929071383924 T^{19} + 33454277957904126460 T^{20} - \)\(11\!\cdots\!28\)\( T^{21} + \)\(15\!\cdots\!60\)\( T^{22} - \)\(50\!\cdots\!76\)\( T^{23} + \)\(63\!\cdots\!92\)\( T^{24} - \)\(18\!\cdots\!12\)\( T^{25} + \)\(25\!\cdots\!70\)\( T^{26} - \)\(51\!\cdots\!60\)\( T^{27} + \)\(95\!\cdots\!37\)\( T^{28} - \)\(97\!\cdots\!16\)\( T^{29} + \)\(32\!\cdots\!50\)\( T^{30} - \)\(40\!\cdots\!08\)\( T^{31} + \)\(95\!\cdots\!07\)\( T^{32} + \)\(44\!\cdots\!84\)\( T^{33} + \)\(22\!\cdots\!38\)\( T^{34} + \)\(16\!\cdots\!80\)\( T^{35} + \)\(39\!\cdots\!93\)\( T^{36} + \)\(29\!\cdots\!52\)\( T^{37} + \)\(46\!\cdots\!86\)\( T^{38} + \)\(23\!\cdots\!32\)\( T^{39} + \)\(27\!\cdots\!01\)\( T^{40} \))(\( 1 - 4 T + 374 T^{2} - 1096 T^{3} + 70333 T^{4} - 138060 T^{5} + 8812902 T^{6} - 8238792 T^{7} + 825273227 T^{8} + 162954236 T^{9} + 62195044950 T^{10} + 87253393748 T^{11} + 4018555017717 T^{12} + 10192167743020 T^{13} + 235818086464330 T^{14} + 791041310737316 T^{15} + 13050043304896332 T^{16} + 48390279852871812 T^{17} + 684184059349996740 T^{18} + 2536743929071383924 T^{19} + 33454277957904126460 T^{20} + \)\(11\!\cdots\!28\)\( T^{21} + \)\(15\!\cdots\!60\)\( T^{22} + \)\(50\!\cdots\!76\)\( T^{23} + \)\(63\!\cdots\!92\)\( T^{24} + \)\(18\!\cdots\!12\)\( T^{25} + \)\(25\!\cdots\!70\)\( T^{26} + \)\(51\!\cdots\!60\)\( T^{27} + \)\(95\!\cdots\!37\)\( T^{28} + \)\(97\!\cdots\!16\)\( T^{29} + \)\(32\!\cdots\!50\)\( T^{30} + \)\(40\!\cdots\!08\)\( T^{31} + \)\(95\!\cdots\!07\)\( T^{32} - \)\(44\!\cdots\!84\)\( T^{33} + \)\(22\!\cdots\!38\)\( T^{34} - \)\(16\!\cdots\!80\)\( T^{35} + \)\(39\!\cdots\!93\)\( T^{36} - \)\(29\!\cdots\!52\)\( T^{37} + \)\(46\!\cdots\!86\)\( T^{38} - \)\(23\!\cdots\!32\)\( T^{39} + \)\(27\!\cdots\!01\)\( T^{40} \))
$53$ (\( 1 + 11 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 9 T + 123 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 - 18 T + 231 T^{2} - 1980 T^{3} + 12243 T^{4} - 50562 T^{5} + 148877 T^{6} \))(\( 1 + 16 T + 212 T^{2} + 1824 T^{3} + 15558 T^{4} + 96672 T^{5} + 595508 T^{6} + 2382032 T^{7} + 7890481 T^{8} \))(\( 1 + 3 T + 256 T^{2} + 616 T^{3} + 26671 T^{4} + 48466 T^{5} + 1413563 T^{6} + 1730344 T^{7} + 38112512 T^{8} + 23671443 T^{9} + 418195493 T^{10} \))(\( 1 - 21 T + 354 T^{2} - 4212 T^{3} + 41957 T^{4} - 328646 T^{5} + 2223721 T^{6} - 11831508 T^{7} + 52702458 T^{8} - 165700101 T^{9} + 418195493 T^{10} \))(\( 1 + 19 T + 298 T^{2} + 2774 T^{3} + 25329 T^{4} + 175326 T^{5} + 1342437 T^{6} + 7792166 T^{7} + 44365346 T^{8} + 149919139 T^{9} + 418195493 T^{10} \))(\( 1 + T + 280 T^{2} + 513 T^{3} + 36898 T^{4} + 94390 T^{5} + 3091933 T^{6} + 8855605 T^{7} + 188115325 T^{8} + 469347065 T^{9} + 8685239797 T^{10} + 14052500030 T^{11} + 291142967938 T^{12} + 214534287909 T^{13} + 6206021116120 T^{14} + 1174711139837 T^{15} + 62259690411361 T^{16} \))(\( 1 + T + 280 T^{2} + 513 T^{3} + 36898 T^{4} + 94390 T^{5} + 3091933 T^{6} + 8855605 T^{7} + 188115325 T^{8} + 469347065 T^{9} + 8685239797 T^{10} + 14052500030 T^{11} + 291142967938 T^{12} + 214534287909 T^{13} + 6206021116120 T^{14} + 1174711139837 T^{15} + 62259690411361 T^{16} \))(\( 1 - 8 T + 245 T^{2} - 1196 T^{3} + 23954 T^{4} - 58632 T^{5} + 1591642 T^{6} - 2732816 T^{7} + 116936509 T^{8} - 293998276 T^{9} + 7553425474 T^{10} - 15581908628 T^{11} + 328474653781 T^{12} - 406853447632 T^{13} + 12558820959802 T^{14} - 24519638145576 T^{15} + 530925106484066 T^{16} - 1404954523245052 T^{17} + 15253624150783445 T^{18} - 26398108734417064 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 8 T + 245 T^{2} - 1196 T^{3} + 23954 T^{4} - 58632 T^{5} + 1591642 T^{6} - 2732816 T^{7} + 116936509 T^{8} - 293998276 T^{9} + 7553425474 T^{10} - 15581908628 T^{11} + 328474653781 T^{12} - 406853447632 T^{13} + 12558820959802 T^{14} - 24519638145576 T^{15} + 530925106484066 T^{16} - 1404954523245052 T^{17} + 15253624150783445 T^{18} - 26398108734417064 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 33 T + 863 T^{2} - 15722 T^{3} + 246347 T^{4} - 3183252 T^{5} + 36912998 T^{6} - 375975233 T^{7} + 3571763601 T^{8} - 31328295324 T^{9} + 268476858640 T^{10} - 2219388789806 T^{11} + 18375669724390 T^{12} - 146996823158855 T^{13} + 1154099940434404 T^{14} - 8551045524129902 T^{15} + 61167296843023412 T^{16} - 412914076253223695 T^{17} + 2735714581558010030 T^{18} - 17512045077577236686 T^{19} + \)\(11\!\cdots\!20\)\( T^{20} - \)\(69\!\cdots\!96\)\( T^{21} + \)\(41\!\cdots\!37\)\( T^{22} - \)\(23\!\cdots\!13\)\( T^{23} + \)\(12\!\cdots\!34\)\( T^{24} - \)\(55\!\cdots\!48\)\( T^{25} + \)\(22\!\cdots\!59\)\( T^{26} - \)\(77\!\cdots\!02\)\( T^{27} + \)\(22\!\cdots\!99\)\( T^{28} - \)\(45\!\cdots\!77\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 - 33 T + 863 T^{2} - 15722 T^{3} + 246347 T^{4} - 3183252 T^{5} + 36912998 T^{6} - 375975233 T^{7} + 3571763601 T^{8} - 31328295324 T^{9} + 268476858640 T^{10} - 2219388789806 T^{11} + 18375669724390 T^{12} - 146996823158855 T^{13} + 1154099940434404 T^{14} - 8551045524129902 T^{15} + 61167296843023412 T^{16} - 412914076253223695 T^{17} + 2735714581558010030 T^{18} - 17512045077577236686 T^{19} + \)\(11\!\cdots\!20\)\( T^{20} - \)\(69\!\cdots\!96\)\( T^{21} + \)\(41\!\cdots\!37\)\( T^{22} - \)\(23\!\cdots\!13\)\( T^{23} + \)\(12\!\cdots\!34\)\( T^{24} - \)\(55\!\cdots\!48\)\( T^{25} + \)\(22\!\cdots\!59\)\( T^{26} - \)\(77\!\cdots\!02\)\( T^{27} + \)\(22\!\cdots\!99\)\( T^{28} - \)\(45\!\cdots\!77\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 + 12 T + 512 T^{2} + 5612 T^{3} + 135003 T^{4} + 1361876 T^{5} + 24146848 T^{6} + 224957376 T^{7} + 3265904782 T^{8} + 28191103556 T^{9} + 354427483702 T^{10} + 2845087467008 T^{11} + 32079538394358 T^{12} + 240579990164368 T^{13} + 2492534087391782 T^{14} + 17565005054366700 T^{15} + 170202190083621233 T^{16} + 1134513791108890324 T^{17} + 10410150847987163156 T^{18} + 66034944862846181312 T^{19} + \)\(57\!\cdots\!62\)\( T^{20} + \)\(34\!\cdots\!36\)\( T^{21} + \)\(29\!\cdots\!04\)\( T^{22} + \)\(16\!\cdots\!48\)\( T^{23} + \)\(13\!\cdots\!73\)\( T^{24} + \)\(73\!\cdots\!00\)\( T^{25} + \)\(55\!\cdots\!78\)\( T^{26} + \)\(28\!\cdots\!16\)\( T^{27} + \)\(19\!\cdots\!38\)\( T^{28} + \)\(93\!\cdots\!64\)\( T^{29} + \)\(61\!\cdots\!98\)\( T^{30} + \)\(26\!\cdots\!32\)\( T^{31} + \)\(16\!\cdots\!62\)\( T^{32} + \)\(58\!\cdots\!48\)\( T^{33} + \)\(33\!\cdots\!12\)\( T^{34} + \)\(99\!\cdots\!32\)\( T^{35} + \)\(52\!\cdots\!63\)\( T^{36} + \)\(11\!\cdots\!56\)\( T^{37} + \)\(55\!\cdots\!68\)\( T^{38} + \)\(69\!\cdots\!04\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))(\( 1 + 12 T + 512 T^{2} + 5612 T^{3} + 135003 T^{4} + 1361876 T^{5} + 24146848 T^{6} + 224957376 T^{7} + 3265904782 T^{8} + 28191103556 T^{9} + 354427483702 T^{10} + 2845087467008 T^{11} + 32079538394358 T^{12} + 240579990164368 T^{13} + 2492534087391782 T^{14} + 17565005054366700 T^{15} + 170202190083621233 T^{16} + 1134513791108890324 T^{17} + 10410150847987163156 T^{18} + 66034944862846181312 T^{19} + \)\(57\!\cdots\!62\)\( T^{20} + \)\(34\!\cdots\!36\)\( T^{21} + \)\(29\!\cdots\!04\)\( T^{22} + \)\(16\!\cdots\!48\)\( T^{23} + \)\(13\!\cdots\!73\)\( T^{24} + \)\(73\!\cdots\!00\)\( T^{25} + \)\(55\!\cdots\!78\)\( T^{26} + \)\(28\!\cdots\!16\)\( T^{27} + \)\(19\!\cdots\!38\)\( T^{28} + \)\(93\!\cdots\!64\)\( T^{29} + \)\(61\!\cdots\!98\)\( T^{30} + \)\(26\!\cdots\!32\)\( T^{31} + \)\(16\!\cdots\!62\)\( T^{32} + \)\(58\!\cdots\!48\)\( T^{33} + \)\(33\!\cdots\!12\)\( T^{34} + \)\(99\!\cdots\!32\)\( T^{35} + \)\(52\!\cdots\!63\)\( T^{36} + \)\(11\!\cdots\!56\)\( T^{37} + \)\(55\!\cdots\!68\)\( T^{38} + \)\(69\!\cdots\!04\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 + 7 T + 59 T^{2} \))(\( 1 - 5 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 + T + 89 T^{2} + 59 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 141 T^{2} - 556 T^{3} + 8319 T^{4} - 20886 T^{5} + 205379 T^{6} \))(\( 1 + 12 T + 252 T^{2} + 1996 T^{3} + 22582 T^{4} + 117764 T^{5} + 877212 T^{6} + 2464548 T^{7} + 12117361 T^{8} \))(\( 1 - 3 T + 208 T^{2} - 530 T^{3} + 20587 T^{4} - 40862 T^{5} + 1214633 T^{6} - 1844930 T^{7} + 42718832 T^{8} - 36352083 T^{9} + 714924299 T^{10} \))(\( 1 + 3 T + 32 T^{2} + 122 T^{3} + 2667 T^{4} + 48958 T^{5} + 157353 T^{6} + 424682 T^{7} + 6572128 T^{8} + 36352083 T^{9} + 714924299 T^{10} \))(\( 1 - 15 T + 316 T^{2} - 3050 T^{3} + 36379 T^{4} - 253030 T^{5} + 2146361 T^{6} - 10617050 T^{7} + 64899764 T^{8} - 181760415 T^{9} + 714924299 T^{10} \))(\( 1 - 4 T + 341 T^{2} - 1058 T^{3} + 53761 T^{4} - 131677 T^{5} + 5303445 T^{6} - 10633338 T^{7} + 367344925 T^{8} - 627366942 T^{9} + 18461292045 T^{10} - 27043690583 T^{11} + 651441444721 T^{12} - 756389908342 T^{13} + 14383561971581 T^{14} - 9954605939276 T^{15} + 146830437604321 T^{16} \))(\( 1 + 4 T + 341 T^{2} + 1058 T^{3} + 53761 T^{4} + 131677 T^{5} + 5303445 T^{6} + 10633338 T^{7} + 367344925 T^{8} + 627366942 T^{9} + 18461292045 T^{10} + 27043690583 T^{11} + 651441444721 T^{12} + 756389908342 T^{13} + 14383561971581 T^{14} + 9954605939276 T^{15} + 146830437604321 T^{16} \))(\( 1 + 24 T + 629 T^{2} + 8776 T^{3} + 126918 T^{4} + 1161538 T^{5} + 11387310 T^{6} + 65476022 T^{7} + 482347017 T^{8} + 1374681036 T^{9} + 15949341018 T^{10} + 81106181124 T^{11} + 1679049966177 T^{12} + 13447399922338 T^{13} + 137984146088910 T^{14} + 830411740411862 T^{15} + 5353468968648438 T^{16} + 21840405430771544 T^{17} + 92356345253117909 T^{18} + 207911899647718536 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 24 T + 629 T^{2} - 8776 T^{3} + 126918 T^{4} - 1161538 T^{5} + 11387310 T^{6} - 65476022 T^{7} + 482347017 T^{8} - 1374681036 T^{9} + 15949341018 T^{10} - 81106181124 T^{11} + 1679049966177 T^{12} - 13447399922338 T^{13} + 137984146088910 T^{14} - 830411740411862 T^{15} + 5353468968648438 T^{16} - 21840405430771544 T^{17} + 92356345253117909 T^{18} - 207911899647718536 T^{19} + 511116753300641401 T^{20} \))(\( 1 + 10 T + 438 T^{2} + 3184 T^{3} + 90647 T^{4} + 466961 T^{5} + 11795042 T^{6} + 34131003 T^{7} + 1053566807 T^{8} - 72516125 T^{9} + 66451314548 T^{10} - 316500930128 T^{11} + 3005689076311 T^{12} - 40055060945190 T^{13} + 114526107347490 T^{14} - 2931515365957526 T^{15} + 6757040333501910 T^{16} - 139431667150206390 T^{17} + 617305416803676869 T^{18} - 3835156027196752208 T^{19} + 47507659470857401852 T^{20} - 3058768850077461125 T^{21} + \)\(26\!\cdots\!33\)\( T^{22} + \)\(50\!\cdots\!63\)\( T^{23} + \)\(10\!\cdots\!38\)\( T^{24} + \)\(23\!\cdots\!61\)\( T^{25} + \)\(27\!\cdots\!73\)\( T^{26} + \)\(56\!\cdots\!04\)\( T^{27} + \)\(45\!\cdots\!02\)\( T^{28} + \)\(61\!\cdots\!10\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 - 10 T + 438 T^{2} - 3184 T^{3} + 90647 T^{4} - 466961 T^{5} + 11795042 T^{6} - 34131003 T^{7} + 1053566807 T^{8} + 72516125 T^{9} + 66451314548 T^{10} + 316500930128 T^{11} + 3005689076311 T^{12} + 40055060945190 T^{13} + 114526107347490 T^{14} + 2931515365957526 T^{15} + 6757040333501910 T^{16} + 139431667150206390 T^{17} + 617305416803676869 T^{18} + 3835156027196752208 T^{19} + 47507659470857401852 T^{20} + 3058768850077461125 T^{21} + \)\(26\!\cdots\!33\)\( T^{22} - \)\(50\!\cdots\!63\)\( T^{23} + \)\(10\!\cdots\!38\)\( T^{24} - \)\(23\!\cdots\!61\)\( T^{25} + \)\(27\!\cdots\!73\)\( T^{26} - \)\(56\!\cdots\!04\)\( T^{27} + \)\(45\!\cdots\!02\)\( T^{28} - \)\(61\!\cdots\!10\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 + 16 T + 600 T^{2} + 7152 T^{3} + 160149 T^{4} + 1517188 T^{5} + 26845940 T^{6} + 211678632 T^{7} + 3369110190 T^{8} + 23123338092 T^{9} + 354171762190 T^{10} + 2196705117576 T^{11} + 32918184304670 T^{12} + 187976789926624 T^{13} + 2737276590449382 T^{14} + 14486638251217924 T^{15} + 204335692284544161 T^{16} + 1010492249607485920 T^{17} + 13812880948781473744 T^{18} + 64587694050718683228 T^{19} + \)\(85\!\cdots\!74\)\( T^{20} + \)\(38\!\cdots\!52\)\( T^{21} + \)\(48\!\cdots\!64\)\( T^{22} + \)\(20\!\cdots\!80\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} + \)\(10\!\cdots\!76\)\( T^{25} + \)\(11\!\cdots\!62\)\( T^{26} + \)\(46\!\cdots\!56\)\( T^{27} + \)\(48\!\cdots\!70\)\( T^{28} + \)\(19\!\cdots\!64\)\( T^{29} + \)\(18\!\cdots\!90\)\( T^{30} + \)\(69\!\cdots\!28\)\( T^{31} + \)\(59\!\cdots\!90\)\( T^{32} + \)\(22\!\cdots\!28\)\( T^{33} + \)\(16\!\cdots\!40\)\( T^{34} + \)\(55\!\cdots\!12\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} + \)\(90\!\cdots\!88\)\( T^{37} + \)\(45\!\cdots\!00\)\( T^{38} + \)\(70\!\cdots\!24\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))(\( 1 - 16 T + 600 T^{2} - 7152 T^{3} + 160149 T^{4} - 1517188 T^{5} + 26845940 T^{6} - 211678632 T^{7} + 3369110190 T^{8} - 23123338092 T^{9} + 354171762190 T^{10} - 2196705117576 T^{11} + 32918184304670 T^{12} - 187976789926624 T^{13} + 2737276590449382 T^{14} - 14486638251217924 T^{15} + 204335692284544161 T^{16} - 1010492249607485920 T^{17} + 13812880948781473744 T^{18} - 64587694050718683228 T^{19} + \)\(85\!\cdots\!74\)\( T^{20} - \)\(38\!\cdots\!52\)\( T^{21} + \)\(48\!\cdots\!64\)\( T^{22} - \)\(20\!\cdots\!80\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} - \)\(10\!\cdots\!76\)\( T^{25} + \)\(11\!\cdots\!62\)\( T^{26} - \)\(46\!\cdots\!56\)\( T^{27} + \)\(48\!\cdots\!70\)\( T^{28} - \)\(19\!\cdots\!64\)\( T^{29} + \)\(18\!\cdots\!90\)\( T^{30} - \)\(69\!\cdots\!28\)\( T^{31} + \)\(59\!\cdots\!90\)\( T^{32} - \)\(22\!\cdots\!28\)\( T^{33} + \)\(16\!\cdots\!40\)\( T^{34} - \)\(55\!\cdots\!12\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} - \)\(90\!\cdots\!88\)\( T^{37} + \)\(45\!\cdots\!00\)\( T^{38} - \)\(70\!\cdots\!24\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))
$61$ (\( 1 + T + 61 T^{2} \))(\( 1 - 3 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 + 3 T + 61 T^{2} \))(\( 1 - 6 T + 79 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 30 T + 471 T^{2} - 4532 T^{3} + 28731 T^{4} - 111630 T^{5} + 226981 T^{6} \))(\( 1 + 24 T + 420 T^{2} + 4824 T^{3} + 44086 T^{4} + 294264 T^{5} + 1562820 T^{6} + 5447544 T^{7} + 13845841 T^{8} \))(\( 1 + 16 T + 174 T^{2} + 270 T^{3} - 7827 T^{4} - 122124 T^{5} - 477447 T^{6} + 1004670 T^{7} + 39494694 T^{8} + 221533456 T^{9} + 844596301 T^{10} \))(\( 1 - 8 T + 138 T^{2} - 1074 T^{3} + 13585 T^{4} - 83436 T^{5} + 828685 T^{6} - 3996354 T^{7} + 31323378 T^{8} - 110766728 T^{9} + 844596301 T^{10} \))(\( 1 + 190 T^{2} + 30 T^{3} + 18957 T^{4} + 5364 T^{5} + 1156377 T^{6} + 111630 T^{7} + 43126390 T^{8} + 844596301 T^{10} \))(\( 1 + 4 T + 355 T^{2} + 1441 T^{3} + 61684 T^{4} + 231523 T^{5} + 6694222 T^{6} + 22066564 T^{7} + 491179868 T^{8} + 1346060404 T^{9} + 24909200062 T^{10} + 52551322063 T^{11} + 854066856244 T^{12} + 1217063269741 T^{13} + 18289732898155 T^{14} + 12570971344084 T^{15} + 191707312997281 T^{16} \))(\( 1 - 4 T + 355 T^{2} - 1441 T^{3} + 61684 T^{4} - 231523 T^{5} + 6694222 T^{6} - 22066564 T^{7} + 491179868 T^{8} - 1346060404 T^{9} + 24909200062 T^{10} - 52551322063 T^{11} + 854066856244 T^{12} - 1217063269741 T^{13} + 18289732898155 T^{14} - 12570971344084 T^{15} + 191707312997281 T^{16} \))(\( 1 + 14 T + 528 T^{2} + 6362 T^{3} + 130430 T^{4} + 1349402 T^{5} + 19744598 T^{6} + 175069242 T^{7} + 2021257345 T^{8} + 15296907412 T^{9} + 145932869524 T^{10} + 933111352132 T^{11} + 7521098580745 T^{12} + 39737391618402 T^{13} + 273380564516918 T^{14} + 1139699937762002 T^{15} + 6719802427905230 T^{16} + 19994129922765602 T^{17} + 101221461262564368 T^{18} + 163718045299677974 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 14 T + 528 T^{2} - 6362 T^{3} + 130430 T^{4} - 1349402 T^{5} + 19744598 T^{6} - 175069242 T^{7} + 2021257345 T^{8} - 15296907412 T^{9} + 145932869524 T^{10} - 933111352132 T^{11} + 7521098580745 T^{12} - 39737391618402 T^{13} + 273380564516918 T^{14} - 1139699937762002 T^{15} + 6719802427905230 T^{16} - 19994129922765602 T^{17} + 101221461262564368 T^{18} - 163718045299677974 T^{19} + 713342911662882601 T^{20} \))(\( 1 - T + 523 T^{2} - 129 T^{3} + 136932 T^{4} + 51712 T^{5} + 23976824 T^{6} + 20622714 T^{7} + 3155814965 T^{8} + 3736521011 T^{9} + 331449399927 T^{10} + 447634864256 T^{11} + 28677224204791 T^{12} + 39659467357703 T^{13} + 2076688162703281 T^{14} + 2726716307441572 T^{15} + 126677977924900141 T^{16} + 147572878038012863 T^{17} + 6509185027227665971 T^{18} + 6197881156545159296 T^{19} + \)\(27\!\cdots\!27\)\( T^{20} + \)\(19\!\cdots\!71\)\( T^{21} + \)\(99\!\cdots\!65\)\( T^{22} + \)\(39\!\cdots\!34\)\( T^{23} + \)\(28\!\cdots\!84\)\( T^{24} + \)\(36\!\cdots\!12\)\( T^{25} + \)\(59\!\cdots\!52\)\( T^{26} - \)\(34\!\cdots\!09\)\( T^{27} + \)\(84\!\cdots\!63\)\( T^{28} - \)\(98\!\cdots\!41\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 + T + 523 T^{2} + 129 T^{3} + 136932 T^{4} - 51712 T^{5} + 23976824 T^{6} - 20622714 T^{7} + 3155814965 T^{8} - 3736521011 T^{9} + 331449399927 T^{10} - 447634864256 T^{11} + 28677224204791 T^{12} - 39659467357703 T^{13} + 2076688162703281 T^{14} - 2726716307441572 T^{15} + 126677977924900141 T^{16} - 147572878038012863 T^{17} + 6509185027227665971 T^{18} - 6197881156545159296 T^{19} + \)\(27\!\cdots\!27\)\( T^{20} - \)\(19\!\cdots\!71\)\( T^{21} + \)\(99\!\cdots\!65\)\( T^{22} - \)\(39\!\cdots\!34\)\( T^{23} + \)\(28\!\cdots\!84\)\( T^{24} - \)\(36\!\cdots\!12\)\( T^{25} + \)\(59\!\cdots\!52\)\( T^{26} + \)\(34\!\cdots\!09\)\( T^{27} + \)\(84\!\cdots\!63\)\( T^{28} + \)\(98\!\cdots\!41\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 + 68 T + 2746 T^{2} + 80188 T^{3} + 1878988 T^{4} + 37113284 T^{5} + 640367622 T^{6} + 9880068788 T^{7} + 138898695230 T^{8} + 1804249453812 T^{9} + 21905924713998 T^{10} + 250758694746204 T^{11} + 2725099373231954 T^{12} + 28254058109831964 T^{13} + 280527819775663110 T^{14} + 2674075904274351012 T^{15} + 24521277038835470769 T^{16} + \)\(21\!\cdots\!80\)\( T^{17} + \)\(18\!\cdots\!40\)\( T^{18} + \)\(15\!\cdots\!44\)\( T^{19} + \)\(12\!\cdots\!64\)\( T^{20} + \)\(92\!\cdots\!84\)\( T^{21} + \)\(68\!\cdots\!40\)\( T^{22} + \)\(49\!\cdots\!80\)\( T^{23} + \)\(33\!\cdots\!29\)\( T^{24} + \)\(22\!\cdots\!12\)\( T^{25} + \)\(14\!\cdots\!10\)\( T^{26} + \)\(88\!\cdots\!44\)\( T^{27} + \)\(52\!\cdots\!74\)\( T^{28} + \)\(29\!\cdots\!64\)\( T^{29} + \)\(15\!\cdots\!98\)\( T^{30} + \)\(78\!\cdots\!32\)\( T^{31} + \)\(36\!\cdots\!30\)\( T^{32} + \)\(15\!\cdots\!28\)\( T^{33} + \)\(63\!\cdots\!02\)\( T^{34} + \)\(22\!\cdots\!84\)\( T^{35} + \)\(69\!\cdots\!68\)\( T^{36} + \)\(17\!\cdots\!48\)\( T^{37} + \)\(37\!\cdots\!26\)\( T^{38} + \)\(56\!\cdots\!88\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))(\( 1 - 68 T + 2746 T^{2} - 80188 T^{3} + 1878988 T^{4} - 37113284 T^{5} + 640367622 T^{6} - 9880068788 T^{7} + 138898695230 T^{8} - 1804249453812 T^{9} + 21905924713998 T^{10} - 250758694746204 T^{11} + 2725099373231954 T^{12} - 28254058109831964 T^{13} + 280527819775663110 T^{14} - 2674075904274351012 T^{15} + 24521277038835470769 T^{16} - \)\(21\!\cdots\!80\)\( T^{17} + \)\(18\!\cdots\!40\)\( T^{18} - \)\(15\!\cdots\!44\)\( T^{19} + \)\(12\!\cdots\!64\)\( T^{20} - \)\(92\!\cdots\!84\)\( T^{21} + \)\(68\!\cdots\!40\)\( T^{22} - \)\(49\!\cdots\!80\)\( T^{23} + \)\(33\!\cdots\!29\)\( T^{24} - \)\(22\!\cdots\!12\)\( T^{25} + \)\(14\!\cdots\!10\)\( T^{26} - \)\(88\!\cdots\!44\)\( T^{27} + \)\(52\!\cdots\!74\)\( T^{28} - \)\(29\!\cdots\!64\)\( T^{29} + \)\(15\!\cdots\!98\)\( T^{30} - \)\(78\!\cdots\!32\)\( T^{31} + \)\(36\!\cdots\!30\)\( T^{32} - \)\(15\!\cdots\!28\)\( T^{33} + \)\(63\!\cdots\!02\)\( T^{34} - \)\(22\!\cdots\!84\)\( T^{35} + \)\(69\!\cdots\!68\)\( T^{36} - \)\(17\!\cdots\!48\)\( T^{37} + \)\(37\!\cdots\!26\)\( T^{38} - \)\(56\!\cdots\!88\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))
$67$ (\( 1 - 7 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 7 T + 117 T^{2} + 469 T^{3} + 4489 T^{4} \))(\( 1 + 18 T + 261 T^{2} + 2276 T^{3} + 17487 T^{4} + 80802 T^{5} + 300763 T^{6} \))(\( 1 - 28 T + 538 T^{2} - 6638 T^{3} + 64208 T^{4} - 444746 T^{5} + 2415082 T^{6} - 8421364 T^{7} + 20151121 T^{8} \))(\( 1 - 19 T + 360 T^{2} - 4400 T^{3} + 48887 T^{4} - 419922 T^{5} + 3275429 T^{6} - 19751600 T^{7} + 108274680 T^{8} - 382871299 T^{9} + 1350125107 T^{10} \))(\( 1 - 3 T - 10 T^{2} - 696 T^{3} + 4469 T^{4} - 15122 T^{5} + 299423 T^{6} - 3124344 T^{7} - 3007630 T^{8} - 60453363 T^{9} + 1350125107 T^{10} \))(\( 1 + 21 T + 310 T^{2} + 3174 T^{3} + 31197 T^{4} + 258962 T^{5} + 2090199 T^{6} + 14248086 T^{7} + 93236530 T^{8} + 423173541 T^{9} + 1350125107 T^{10} \))(\( 1 + 340 T^{2} + 68 T^{3} + 59697 T^{4} + 16147 T^{5} + 6764659 T^{6} + 1849089 T^{7} + 536944362 T^{8} + 123888963 T^{9} + 30366554251 T^{10} + 4856420161 T^{11} + 1202961470337 T^{12} + 91808507276 T^{13} + 30755849937460 T^{14} + 406067677556641 T^{16} \))(\( 1 + 340 T^{2} + 68 T^{3} + 59697 T^{4} + 16147 T^{5} + 6764659 T^{6} + 1849089 T^{7} + 536944362 T^{8} + 123888963 T^{9} + 30366554251 T^{10} + 4856420161 T^{11} + 1202961470337 T^{12} + 91808507276 T^{13} + 30755849937460 T^{14} + 406067677556641 T^{16} \))(\( 1 + 8 T + 449 T^{2} + 2320 T^{3} + 87078 T^{4} + 265904 T^{5} + 10436462 T^{6} + 16581400 T^{7} + 935678857 T^{8} + 796918512 T^{9} + 68666864514 T^{10} + 53393540304 T^{11} + 4200262389073 T^{12} + 4987071608200 T^{13} + 210306408573902 T^{14} + 359003666451728 T^{15} + 7876935002512182 T^{16} + 14060850924349360 T^{17} + 182324387222931809 T^{18} + 217652275170359576 T^{19} + 1822837804551761449 T^{20} \))(\( 1 + 8 T + 449 T^{2} + 2320 T^{3} + 87078 T^{4} + 265904 T^{5} + 10436462 T^{6} + 16581400 T^{7} + 935678857 T^{8} + 796918512 T^{9} + 68666864514 T^{10} + 53393540304 T^{11} + 4200262389073 T^{12} + 4987071608200 T^{13} + 210306408573902 T^{14} + 359003666451728 T^{15} + 7876935002512182 T^{16} + 14060850924349360 T^{17} + 182324387222931809 T^{18} + 217652275170359576 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 20 T + 429 T^{2} - 5822 T^{3} + 73632 T^{4} - 722379 T^{5} + 6792071 T^{6} - 53130812 T^{7} + 435608371 T^{8} - 3414484347 T^{9} + 30999954694 T^{10} - 278288722590 T^{11} + 2671766006547 T^{12} - 23401501064390 T^{13} + 206689542780553 T^{14} - 1689647377929920 T^{15} + 13848199366297051 T^{16} - 105049338278046710 T^{17} + 803568359427095361 T^{18} - 5607829721846523390 T^{19} + 41853817148231902258 T^{20} - \)\(30\!\cdots\!43\)\( T^{21} + \)\(26\!\cdots\!33\)\( T^{22} - \)\(21\!\cdots\!92\)\( T^{23} + \)\(18\!\cdots\!37\)\( T^{24} - \)\(13\!\cdots\!71\)\( T^{25} + \)\(89\!\cdots\!56\)\( T^{26} - \)\(47\!\cdots\!42\)\( T^{27} + \)\(23\!\cdots\!23\)\( T^{28} - \)\(73\!\cdots\!80\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 - 20 T + 429 T^{2} - 5822 T^{3} + 73632 T^{4} - 722379 T^{5} + 6792071 T^{6} - 53130812 T^{7} + 435608371 T^{8} - 3414484347 T^{9} + 30999954694 T^{10} - 278288722590 T^{11} + 2671766006547 T^{12} - 23401501064390 T^{13} + 206689542780553 T^{14} - 1689647377929920 T^{15} + 13848199366297051 T^{16} - 105049338278046710 T^{17} + 803568359427095361 T^{18} - 5607829721846523390 T^{19} + 41853817148231902258 T^{20} - \)\(30\!\cdots\!43\)\( T^{21} + \)\(26\!\cdots\!33\)\( T^{22} - \)\(21\!\cdots\!92\)\( T^{23} + \)\(18\!\cdots\!37\)\( T^{24} - \)\(13\!\cdots\!71\)\( T^{25} + \)\(89\!\cdots\!56\)\( T^{26} - \)\(47\!\cdots\!42\)\( T^{27} + \)\(23\!\cdots\!23\)\( T^{28} - \)\(73\!\cdots\!80\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 - 4 T + 964 T^{2} - 4156 T^{3} + 456375 T^{4} - 2061116 T^{5} + 141287868 T^{6} - 652790288 T^{7} + 32101542726 T^{8} - 148762145132 T^{9} + 5690411521150 T^{10} - 26012669512256 T^{11} + 816354810670358 T^{12} - 3628940346767312 T^{13} + 97022283322151438 T^{14} - 414055046813706044 T^{15} + 9698391419487720521 T^{16} - 39254578625509580396 T^{17} + \)\(82\!\cdots\!24\)\( T^{18} - \)\(31\!\cdots\!48\)\( T^{19} + \)\(59\!\cdots\!90\)\( T^{20} - \)\(20\!\cdots\!16\)\( T^{21} + \)\(36\!\cdots\!36\)\( T^{22} - \)\(11\!\cdots\!48\)\( T^{23} + \)\(19\!\cdots\!41\)\( T^{24} - \)\(55\!\cdots\!08\)\( T^{25} + \)\(87\!\cdots\!22\)\( T^{26} - \)\(21\!\cdots\!76\)\( T^{27} + \)\(33\!\cdots\!78\)\( T^{28} - \)\(70\!\cdots\!32\)\( T^{29} + \)\(10\!\cdots\!50\)\( T^{30} - \)\(18\!\cdots\!56\)\( T^{31} + \)\(26\!\cdots\!86\)\( T^{32} - \)\(35\!\cdots\!56\)\( T^{33} + \)\(51\!\cdots\!72\)\( T^{34} - \)\(50\!\cdots\!88\)\( T^{35} + \)\(75\!\cdots\!75\)\( T^{36} - \)\(45\!\cdots\!12\)\( T^{37} + \)\(71\!\cdots\!76\)\( T^{38} - \)\(19\!\cdots\!12\)\( T^{39} + \)\(33\!\cdots\!01\)\( T^{40} \))(\( 1 - 4 T + 964 T^{2} - 4156 T^{3} + 456375 T^{4} - 2061116 T^{5} + 141287868 T^{6} - 652790288 T^{7} + 32101542726 T^{8} - 148762145132 T^{9} + 5690411521150 T^{10} - 26012669512256 T^{11} + 816354810670358 T^{12} - 3628940346767312 T^{13} + 97022283322151438 T^{14} - 414055046813706044 T^{15} + 9698391419487720521 T^{16} - 39254578625509580396 T^{17} + \)\(82\!\cdots\!24\)\( T^{18} - \)\(31\!\cdots\!48\)\( T^{19} + \)\(59\!\cdots\!90\)\( T^{20} - \)\(20\!\cdots\!16\)\( T^{21} + \)\(36\!\cdots\!36\)\( T^{22} - \)\(11\!\cdots\!48\)\( T^{23} + \)\(19\!\cdots\!41\)\( T^{24} - \)\(55\!\cdots\!08\)\( T^{25} + \)\(87\!\cdots\!22\)\( T^{26} - \)\(21\!\cdots\!76\)\( T^{27} + \)\(33\!\cdots\!78\)\( T^{28} - \)\(70\!\cdots\!32\)\( T^{29} + \)\(10\!\cdots\!50\)\( T^{30} - \)\(18\!\cdots\!56\)\( T^{31} + \)\(26\!\cdots\!86\)\( T^{32} - \)\(35\!\cdots\!56\)\( T^{33} + \)\(51\!\cdots\!72\)\( T^{34} - \)\(50\!\cdots\!88\)\( T^{35} + \)\(75\!\cdots\!75\)\( T^{36} - \)\(45\!\cdots\!12\)\( T^{37} + \)\(71\!\cdots\!76\)\( T^{38} - \)\(19\!\cdots\!12\)\( T^{39} + \)\(33\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 10 T + 115 T^{2} + 710 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 177 T^{2} - 1728 T^{3} + 12567 T^{4} - 60492 T^{5} + 357911 T^{6} \))(\( 1 + 2 T + 98 T^{2} - 268 T^{3} + 3408 T^{4} - 19028 T^{5} + 494018 T^{6} + 715822 T^{7} + 25411681 T^{8} \))(\( 1 + 12 T + 286 T^{2} + 2964 T^{3} + 35425 T^{4} + 300480 T^{5} + 2515175 T^{6} + 14941524 T^{7} + 102362546 T^{8} + 304940172 T^{9} + 1804229351 T^{10} \))(\( 1 - 22 T + 152 T^{2} - 652 T^{3} + 13507 T^{4} - 179324 T^{5} + 958997 T^{6} - 3286732 T^{7} + 54402472 T^{8} - 559056982 T^{9} + 1804229351 T^{10} \))(\( 1 + 16 T + 338 T^{2} + 4312 T^{3} + 46713 T^{4} + 451448 T^{5} + 3316623 T^{6} + 21736792 T^{7} + 120973918 T^{8} + 406586896 T^{9} + 1804229351 T^{10} \))(\( 1 - 8 T + 341 T^{2} - 2537 T^{3} + 60540 T^{4} - 400543 T^{5} + 7099493 T^{6} - 41272935 T^{7} + 591932642 T^{8} - 2930378385 T^{9} + 35788544213 T^{10} - 143358745673 T^{11} + 1538423167740 T^{12} - 4577329863487 T^{13} + 43682196817061 T^{14} - 72760961267128 T^{15} + 645753531245761 T^{16} \))(\( 1 - 8 T + 341 T^{2} - 2537 T^{3} + 60540 T^{4} - 400543 T^{5} + 7099493 T^{6} - 41272935 T^{7} + 591932642 T^{8} - 2930378385 T^{9} + 35788544213 T^{10} - 143358745673 T^{11} + 1538423167740 T^{12} - 4577329863487 T^{13} + 43682196817061 T^{14} - 72760961267128 T^{15} + 645753531245761 T^{16} \))(\( 1 - 10 T + 444 T^{2} - 4262 T^{3} + 86730 T^{4} - 810086 T^{5} + 9918442 T^{6} - 94008490 T^{7} + 789911765 T^{8} - 7996076064 T^{9} + 55295925748 T^{10} - 567721400544 T^{11} + 3981945207365 T^{12} - 33646672664390 T^{13} + 252044284121002 T^{14} - 1461580938034186 T^{15} + 11110137624468330 T^{16} - 38763402115062442 T^{17} + 286714567873117884 T^{18} - 458485007184490310 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 10 T + 444 T^{2} - 4262 T^{3} + 86730 T^{4} - 810086 T^{5} + 9918442 T^{6} - 94008490 T^{7} + 789911765 T^{8} - 7996076064 T^{9} + 55295925748 T^{10} - 567721400544 T^{11} + 3981945207365 T^{12} - 33646672664390 T^{13} + 252044284121002 T^{14} - 1461580938034186 T^{15} + 11110137624468330 T^{16} - 38763402115062442 T^{17} + 286714567873117884 T^{18} - 458485007184490310 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 5 T + 673 T^{2} - 3977 T^{3} + 223612 T^{4} - 1485542 T^{5} + 49080265 T^{6} - 348399794 T^{7} + 8003819994 T^{8} - 57819268023 T^{9} + 1028517214635 T^{10} - 7247014954358 T^{11} + 107290099585961 T^{12} - 713261170497997 T^{13} + 9210290678641452 T^{14} - 56332695950174480 T^{15} + 653930638183543092 T^{16} - 3595549560480402877 T^{17} + 38400306832910887471 T^{18} - \)\(18\!\cdots\!98\)\( T^{19} + \)\(18\!\cdots\!85\)\( T^{20} - \)\(74\!\cdots\!83\)\( T^{21} + \)\(72\!\cdots\!54\)\( T^{22} - \)\(22\!\cdots\!34\)\( T^{23} + \)\(22\!\cdots\!15\)\( T^{24} - \)\(48\!\cdots\!42\)\( T^{25} + \)\(51\!\cdots\!52\)\( T^{26} - \)\(65\!\cdots\!57\)\( T^{27} + \)\(78\!\cdots\!03\)\( T^{28} - \)\(41\!\cdots\!05\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 - 5 T + 673 T^{2} - 3977 T^{3} + 223612 T^{4} - 1485542 T^{5} + 49080265 T^{6} - 348399794 T^{7} + 8003819994 T^{8} - 57819268023 T^{9} + 1028517214635 T^{10} - 7247014954358 T^{11} + 107290099585961 T^{12} - 713261170497997 T^{13} + 9210290678641452 T^{14} - 56332695950174480 T^{15} + 653930638183543092 T^{16} - 3595549560480402877 T^{17} + 38400306832910887471 T^{18} - \)\(18\!\cdots\!98\)\( T^{19} + \)\(18\!\cdots\!85\)\( T^{20} - \)\(74\!\cdots\!83\)\( T^{21} + \)\(72\!\cdots\!54\)\( T^{22} - \)\(22\!\cdots\!34\)\( T^{23} + \)\(22\!\cdots\!15\)\( T^{24} - \)\(48\!\cdots\!42\)\( T^{25} + \)\(51\!\cdots\!52\)\( T^{26} - \)\(65\!\cdots\!57\)\( T^{27} + \)\(78\!\cdots\!03\)\( T^{28} - \)\(41\!\cdots\!05\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 - 8 T + 874 T^{2} - 6608 T^{3} + 368744 T^{4} - 2610424 T^{5} + 100404914 T^{6} - 660904456 T^{7} + 19947410094 T^{8} - 121657957840 T^{9} + 3106217030942 T^{10} - 17569063338760 T^{11} + 398194221131546 T^{12} - 2099453527999864 T^{13} + 43527546864216302 T^{14} - 215467526265102368 T^{15} + 4154554567737912833 T^{16} - 19417901038856108816 T^{17} + \)\(35\!\cdots\!52\)\( T^{18} - \)\(15\!\cdots\!16\)\( T^{19} + \)\(26\!\cdots\!20\)\( T^{20} - \)\(11\!\cdots\!36\)\( T^{21} + \)\(17\!\cdots\!32\)\( T^{22} - \)\(69\!\cdots\!76\)\( T^{23} + \)\(10\!\cdots\!73\)\( T^{24} - \)\(38\!\cdots\!68\)\( T^{25} + \)\(55\!\cdots\!42\)\( T^{26} - \)\(19\!\cdots\!24\)\( T^{27} + \)\(25\!\cdots\!06\)\( T^{28} - \)\(80\!\cdots\!60\)\( T^{29} + \)\(10\!\cdots\!42\)\( T^{30} - \)\(28\!\cdots\!40\)\( T^{31} + \)\(32\!\cdots\!54\)\( T^{32} - \)\(77\!\cdots\!16\)\( T^{33} + \)\(83\!\cdots\!34\)\( T^{34} - \)\(15\!\cdots\!24\)\( T^{35} + \)\(15\!\cdots\!24\)\( T^{36} - \)\(19\!\cdots\!28\)\( T^{37} + \)\(18\!\cdots\!14\)\( T^{38} - \)\(11\!\cdots\!48\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 874 T^{2} - 6608 T^{3} + 368744 T^{4} - 2610424 T^{5} + 100404914 T^{6} - 660904456 T^{7} + 19947410094 T^{8} - 121657957840 T^{9} + 3106217030942 T^{10} - 17569063338760 T^{11} + 398194221131546 T^{12} - 2099453527999864 T^{13} + 43527546864216302 T^{14} - 215467526265102368 T^{15} + 4154554567737912833 T^{16} - 19417901038856108816 T^{17} + \)\(35\!\cdots\!52\)\( T^{18} - \)\(15\!\cdots\!16\)\( T^{19} + \)\(26\!\cdots\!20\)\( T^{20} - \)\(11\!\cdots\!36\)\( T^{21} + \)\(17\!\cdots\!32\)\( T^{22} - \)\(69\!\cdots\!76\)\( T^{23} + \)\(10\!\cdots\!73\)\( T^{24} - \)\(38\!\cdots\!68\)\( T^{25} + \)\(55\!\cdots\!42\)\( T^{26} - \)\(19\!\cdots\!24\)\( T^{27} + \)\(25\!\cdots\!06\)\( T^{28} - \)\(80\!\cdots\!60\)\( T^{29} + \)\(10\!\cdots\!42\)\( T^{30} - \)\(28\!\cdots\!40\)\( T^{31} + \)\(32\!\cdots\!54\)\( T^{32} - \)\(77\!\cdots\!16\)\( T^{33} + \)\(83\!\cdots\!34\)\( T^{34} - \)\(15\!\cdots\!24\)\( T^{35} + \)\(15\!\cdots\!24\)\( T^{36} - \)\(19\!\cdots\!28\)\( T^{37} + \)\(18\!\cdots\!14\)\( T^{38} - \)\(11\!\cdots\!48\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))
$73$ (\( 1 + 5 T + 73 T^{2} \))(\( 1 + T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 5 T + 73 T^{2} \))(\( 1 - T + 73 T^{2} \))(\( ( 1 + 7 T + 73 T^{2} )^{2} \))(\( 1 - 12 T + 219 T^{2} - 1688 T^{3} + 15987 T^{4} - 63948 T^{5} + 389017 T^{6} \))(\( 1 + 8 T + 212 T^{2} + 1060 T^{3} + 19890 T^{4} + 77380 T^{5} + 1129748 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + 4 T + 282 T^{2} + 914 T^{3} + 36665 T^{4} + 94644 T^{5} + 2676545 T^{6} + 4870706 T^{7} + 109702794 T^{8} + 113592964 T^{9} + 2073071593 T^{10} \))(\( 1 - 16 T + 338 T^{2} - 4158 T^{3} + 47185 T^{4} - 439204 T^{5} + 3444505 T^{6} - 22157982 T^{7} + 131487746 T^{8} - 454371856 T^{9} + 2073071593 T^{10} \))(\( 1 - 10 T + 222 T^{2} - 2492 T^{3} + 25941 T^{4} - 257572 T^{5} + 1893693 T^{6} - 13279868 T^{7} + 86361774 T^{8} - 283982410 T^{9} + 2073071593 T^{10} \))(\( 1 - 11 T + 474 T^{2} - 4040 T^{3} + 94652 T^{4} - 643511 T^{5} + 11124356 T^{6} - 63241059 T^{7} + 927349325 T^{8} - 4616597307 T^{9} + 59281693124 T^{10} - 250336718687 T^{11} + 2687950307132 T^{12} - 8375209235720 T^{13} + 71732423260986 T^{14} - 121521383710067 T^{15} + 806460091894081 T^{16} \))(\( 1 + 11 T + 474 T^{2} + 4040 T^{3} + 94652 T^{4} + 643511 T^{5} + 11124356 T^{6} + 63241059 T^{7} + 927349325 T^{8} + 4616597307 T^{9} + 59281693124 T^{10} + 250336718687 T^{11} + 2687950307132 T^{12} + 8375209235720 T^{13} + 71732423260986 T^{14} + 121521383710067 T^{15} + 806460091894081 T^{16} \))(\( 1 + 44 T + 1220 T^{2} + 24508 T^{3} + 403542 T^{4} + 5667300 T^{5} + 70965058 T^{6} + 804708756 T^{7} + 8403572217 T^{8} + 80839769728 T^{9} + 719421847316 T^{10} + 5901303190144 T^{11} + 44782636344393 T^{12} + 313045386132852 T^{13} + 2015282819662978 T^{14} + 11748718639008900 T^{15} + 61069716345115638 T^{16} + 270749642906029276 T^{17} + 983881312110778820 T^{18} + 2590349815163788172 T^{19} + 4297625829703557649 T^{20} \))(\( 1 - 44 T + 1220 T^{2} - 24508 T^{3} + 403542 T^{4} - 5667300 T^{5} + 70965058 T^{6} - 804708756 T^{7} + 8403572217 T^{8} - 80839769728 T^{9} + 719421847316 T^{10} - 5901303190144 T^{11} + 44782636344393 T^{12} - 313045386132852 T^{13} + 2015282819662978 T^{14} - 11748718639008900 T^{15} + 61069716345115638 T^{16} - 270749642906029276 T^{17} + 983881312110778820 T^{18} - 2590349815163788172 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 3 T + 583 T^{2} + 555 T^{3} + 162403 T^{4} - 132936 T^{5} + 29712937 T^{6} - 66363985 T^{7} + 4114280860 T^{8} - 13241903644 T^{9} + 463723711956 T^{10} - 1765474643243 T^{11} + 44185799832094 T^{12} - 179873270172127 T^{13} + 3652540420576382 T^{14} - 14631397178604766 T^{15} + 266635450702075886 T^{16} - 958544656747264783 T^{17} + 17189027293281711598 T^{18} - 50136374398203735563 T^{19} + \)\(96\!\cdots\!08\)\( T^{20} - \)\(20\!\cdots\!16\)\( T^{21} + \)\(45\!\cdots\!20\)\( T^{22} - \)\(53\!\cdots\!85\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} - \)\(57\!\cdots\!64\)\( T^{25} + \)\(50\!\cdots\!31\)\( T^{26} + \)\(12\!\cdots\!55\)\( T^{27} + \)\(97\!\cdots\!39\)\( T^{28} + \)\(36\!\cdots\!27\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 - 3 T + 583 T^{2} - 555 T^{3} + 162403 T^{4} + 132936 T^{5} + 29712937 T^{6} + 66363985 T^{7} + 4114280860 T^{8} + 13241903644 T^{9} + 463723711956 T^{10} + 1765474643243 T^{11} + 44185799832094 T^{12} + 179873270172127 T^{13} + 3652540420576382 T^{14} + 14631397178604766 T^{15} + 266635450702075886 T^{16} + 958544656747264783 T^{17} + 17189027293281711598 T^{18} + 50136374398203735563 T^{19} + \)\(96\!\cdots\!08\)\( T^{20} + \)\(20\!\cdots\!16\)\( T^{21} + \)\(45\!\cdots\!20\)\( T^{22} + \)\(53\!\cdots\!85\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} + \)\(57\!\cdots\!64\)\( T^{25} + \)\(50\!\cdots\!31\)\( T^{26} - \)\(12\!\cdots\!55\)\( T^{27} + \)\(97\!\cdots\!39\)\( T^{28} - \)\(36\!\cdots\!27\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 + 48 T + 1494 T^{2} + 33256 T^{3} + 598148 T^{4} + 8939320 T^{5} + 116257546 T^{6} + 1342575896 T^{7} + 14264801870 T^{8} + 142480859576 T^{9} + 1376060227538 T^{10} + 12947573383648 T^{11} + 119527307724954 T^{12} + 1075306586055696 T^{13} + 9483832704310266 T^{14} + 82276567800105240 T^{15} + 713707218156263457 T^{16} + 6206964800767534632 T^{17} + 54355099696009499380 T^{18} + \)\(47\!\cdots\!28\)\( T^{19} + \)\(40\!\cdots\!04\)\( T^{20} + \)\(34\!\cdots\!44\)\( T^{21} + \)\(28\!\cdots\!20\)\( T^{22} + \)\(24\!\cdots\!44\)\( T^{23} + \)\(20\!\cdots\!37\)\( T^{24} + \)\(17\!\cdots\!20\)\( T^{25} + \)\(14\!\cdots\!74\)\( T^{26} + \)\(11\!\cdots\!12\)\( T^{27} + \)\(96\!\cdots\!74\)\( T^{28} + \)\(76\!\cdots\!24\)\( T^{29} + \)\(59\!\cdots\!62\)\( T^{30} + \)\(44\!\cdots\!52\)\( T^{31} + \)\(32\!\cdots\!70\)\( T^{32} + \)\(22\!\cdots\!68\)\( T^{33} + \)\(14\!\cdots\!14\)\( T^{34} + \)\(79\!\cdots\!40\)\( T^{35} + \)\(38\!\cdots\!28\)\( T^{36} + \)\(15\!\cdots\!68\)\( T^{37} + \)\(51\!\cdots\!86\)\( T^{38} + \)\(12\!\cdots\!76\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))(\( 1 - 48 T + 1494 T^{2} - 33256 T^{3} + 598148 T^{4} - 8939320 T^{5} + 116257546 T^{6} - 1342575896 T^{7} + 14264801870 T^{8} - 142480859576 T^{9} + 1376060227538 T^{10} - 12947573383648 T^{11} + 119527307724954 T^{12} - 1075306586055696 T^{13} + 9483832704310266 T^{14} - 82276567800105240 T^{15} + 713707218156263457 T^{16} - 6206964800767534632 T^{17} + 54355099696009499380 T^{18} - \)\(47\!\cdots\!28\)\( T^{19} + \)\(40\!\cdots\!04\)\( T^{20} - \)\(34\!\cdots\!44\)\( T^{21} + \)\(28\!\cdots\!20\)\( T^{22} - \)\(24\!\cdots\!44\)\( T^{23} + \)\(20\!\cdots\!37\)\( T^{24} - \)\(17\!\cdots\!20\)\( T^{25} + \)\(14\!\cdots\!74\)\( T^{26} - \)\(11\!\cdots\!12\)\( T^{27} + \)\(96\!\cdots\!74\)\( T^{28} - \)\(76\!\cdots\!24\)\( T^{29} + \)\(59\!\cdots\!62\)\( T^{30} - \)\(44\!\cdots\!52\)\( T^{31} + \)\(32\!\cdots\!70\)\( T^{32} - \)\(22\!\cdots\!68\)\( T^{33} + \)\(14\!\cdots\!14\)\( T^{34} - \)\(79\!\cdots\!40\)\( T^{35} + \)\(38\!\cdots\!28\)\( T^{36} - \)\(15\!\cdots\!68\)\( T^{37} + \)\(51\!\cdots\!86\)\( T^{38} - \)\(12\!\cdots\!76\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 - 9 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 26 T + 314 T^{2} + 2054 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 177 T^{2} - 1744 T^{3} + 13983 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 + 18 T + 366 T^{2} + 4224 T^{3} + 45328 T^{4} + 333696 T^{5} + 2284206 T^{6} + 8874702 T^{7} + 38950081 T^{8} \))(\( 1 - 28 T + 579 T^{2} - 8320 T^{3} + 100402 T^{4} - 956712 T^{5} + 7931758 T^{6} - 51925120 T^{7} + 285469581 T^{8} - 1090602268 T^{9} + 3077056399 T^{10} \))(\( 1 - 4 T + 107 T^{2} + 144 T^{3} + 11770 T^{4} - 28216 T^{5} + 929830 T^{6} + 898704 T^{7} + 52755173 T^{8} - 155800324 T^{9} + 3077056399 T^{10} \))(\( 1 + 14 T + 315 T^{2} + 3176 T^{3} + 45082 T^{4} + 346676 T^{5} + 3561478 T^{6} + 19821416 T^{7} + 155307285 T^{8} + 545301134 T^{9} + 3077056399 T^{10} \))(\( 1 - 14 T + 483 T^{2} - 5250 T^{3} + 107571 T^{4} - 967249 T^{5} + 14893663 T^{6} - 112979804 T^{7} + 1409336805 T^{8} - 8925404516 T^{9} + 92951350783 T^{10} - 476891479711 T^{11} + 4189899163251 T^{12} - 16154546094750 T^{13} + 117411241016643 T^{14} - 268854725806226 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 14 T + 483 T^{2} - 5250 T^{3} + 107571 T^{4} - 967249 T^{5} + 14893663 T^{6} - 112979804 T^{7} + 1409336805 T^{8} - 8925404516 T^{9} + 92951350783 T^{10} - 476891479711 T^{11} + 4189899163251 T^{12} - 16154546094750 T^{13} + 117411241016643 T^{14} - 268854725806226 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 10 T + 614 T^{2} - 5902 T^{3} + 179069 T^{4} - 1630352 T^{5} + 32727400 T^{6} - 275265280 T^{7} + 4153988066 T^{8} - 31232651988 T^{9} + 382732416868 T^{10} - 2467379507052 T^{11} + 25925039519906 T^{12} - 135716518385920 T^{13} + 1274734880919400 T^{14} - 5016685054222448 T^{15} + 43529427572689949 T^{16} - 113341470836310418 T^{17} + 931504809282628454 T^{18} - 1198515959826183190 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 10 T + 614 T^{2} - 5902 T^{3} + 179069 T^{4} - 1630352 T^{5} + 32727400 T^{6} - 275265280 T^{7} + 4153988066 T^{8} - 31232651988 T^{9} + 382732416868 T^{10} - 2467379507052 T^{11} + 25925039519906 T^{12} - 135716518385920 T^{13} + 1274734880919400 T^{14} - 5016685054222448 T^{15} + 43529427572689949 T^{16} - 113341470836310418 T^{17} + 931504809282628454 T^{18} - 1198515959826183190 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 25 T + 867 T^{2} - 15594 T^{3} + 324404 T^{4} - 4707655 T^{5} + 75412400 T^{6} - 941871353 T^{7} + 12777037715 T^{8} - 142497901288 T^{9} + 1711757913945 T^{10} - 17371634352920 T^{11} + 188916919425901 T^{12} - 1760893570473008 T^{13} + 17547537073774455 T^{14} - 150880781779786061 T^{15} + 1386255428828181945 T^{16} - 10989736773322042928 T^{17} + 93143409036826803139 T^{18} - \)\(67\!\cdots\!20\)\( T^{19} + \)\(52\!\cdots\!55\)\( T^{20} - \)\(34\!\cdots\!48\)\( T^{21} + \)\(24\!\cdots\!85\)\( T^{22} - \)\(14\!\cdots\!33\)\( T^{23} + \)\(90\!\cdots\!00\)\( T^{24} - \)\(44\!\cdots\!55\)\( T^{25} + \)\(24\!\cdots\!16\)\( T^{26} - \)\(92\!\cdots\!54\)\( T^{27} + \)\(40\!\cdots\!13\)\( T^{28} - \)\(92\!\cdots\!25\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 - 25 T + 867 T^{2} - 15594 T^{3} + 324404 T^{4} - 4707655 T^{5} + 75412400 T^{6} - 941871353 T^{7} + 12777037715 T^{8} - 142497901288 T^{9} + 1711757913945 T^{10} - 17371634352920 T^{11} + 188916919425901 T^{12} - 1760893570473008 T^{13} + 17547537073774455 T^{14} - 150880781779786061 T^{15} + 1386255428828181945 T^{16} - 10989736773322042928 T^{17} + 93143409036826803139 T^{18} - \)\(67\!\cdots\!20\)\( T^{19} + \)\(52\!\cdots\!55\)\( T^{20} - \)\(34\!\cdots\!48\)\( T^{21} + \)\(24\!\cdots\!85\)\( T^{22} - \)\(14\!\cdots\!33\)\( T^{23} + \)\(90\!\cdots\!00\)\( T^{24} - \)\(44\!\cdots\!55\)\( T^{25} + \)\(24\!\cdots\!16\)\( T^{26} - \)\(92\!\cdots\!54\)\( T^{27} + \)\(40\!\cdots\!13\)\( T^{28} - \)\(92\!\cdots\!25\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 + 20 T + 936 T^{2} + 18068 T^{3} + 457182 T^{4} + 8086332 T^{5} + 151587824 T^{6} + 2407195644 T^{7} + 37630638349 T^{8} + 536777135360 T^{9} + 7375070117720 T^{10} + 95320730703424 T^{11} + 1181426005717928 T^{12} + 13965857953973408 T^{13} + 158429454783904840 T^{14} + 1725932412403134048 T^{15} + 18076051380908681650 T^{16} + \)\(18\!\cdots\!80\)\( T^{17} + \)\(17\!\cdots\!16\)\( T^{18} + \)\(16\!\cdots\!72\)\( T^{19} + \)\(15\!\cdots\!32\)\( T^{20} + \)\(13\!\cdots\!88\)\( T^{21} + \)\(11\!\cdots\!56\)\( T^{22} + \)\(89\!\cdots\!20\)\( T^{23} + \)\(70\!\cdots\!50\)\( T^{24} + \)\(53\!\cdots\!52\)\( T^{25} + \)\(38\!\cdots\!40\)\( T^{26} + \)\(26\!\cdots\!72\)\( T^{27} + \)\(17\!\cdots\!08\)\( T^{28} + \)\(11\!\cdots\!56\)\( T^{29} + \)\(69\!\cdots\!20\)\( T^{30} + \)\(40\!\cdots\!40\)\( T^{31} + \)\(22\!\cdots\!09\)\( T^{32} + \)\(11\!\cdots\!16\)\( T^{33} + \)\(55\!\cdots\!44\)\( T^{34} + \)\(23\!\cdots\!68\)\( T^{35} + \)\(10\!\cdots\!22\)\( T^{36} + \)\(32\!\cdots\!12\)\( T^{37} + \)\(13\!\cdots\!96\)\( T^{38} + \)\(22\!\cdots\!80\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))(\( 1 + 20 T + 936 T^{2} + 18068 T^{3} + 457182 T^{4} + 8086332 T^{5} + 151587824 T^{6} + 2407195644 T^{7} + 37630638349 T^{8} + 536777135360 T^{9} + 7375070117720 T^{10} + 95320730703424 T^{11} + 1181426005717928 T^{12} + 13965857953973408 T^{13} + 158429454783904840 T^{14} + 1725932412403134048 T^{15} + 18076051380908681650 T^{16} + \)\(18\!\cdots\!80\)\( T^{17} + \)\(17\!\cdots\!16\)\( T^{18} + \)\(16\!\cdots\!72\)\( T^{19} + \)\(15\!\cdots\!32\)\( T^{20} + \)\(13\!\cdots\!88\)\( T^{21} + \)\(11\!\cdots\!56\)\( T^{22} + \)\(89\!\cdots\!20\)\( T^{23} + \)\(70\!\cdots\!50\)\( T^{24} + \)\(53\!\cdots\!52\)\( T^{25} + \)\(38\!\cdots\!40\)\( T^{26} + \)\(26\!\cdots\!72\)\( T^{27} + \)\(17\!\cdots\!08\)\( T^{28} + \)\(11\!\cdots\!56\)\( T^{29} + \)\(69\!\cdots\!20\)\( T^{30} + \)\(40\!\cdots\!40\)\( T^{31} + \)\(22\!\cdots\!09\)\( T^{32} + \)\(11\!\cdots\!16\)\( T^{33} + \)\(55\!\cdots\!44\)\( T^{34} + \)\(23\!\cdots\!68\)\( T^{35} + \)\(10\!\cdots\!22\)\( T^{36} + \)\(32\!\cdots\!12\)\( T^{37} + \)\(13\!\cdots\!96\)\( T^{38} + \)\(22\!\cdots\!80\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))
$83$ (\( 1 + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 49 T^{2} + 6889 T^{4} \))(\( 1 - 18 T + 309 T^{2} - 2852 T^{3} + 25647 T^{4} - 124002 T^{5} + 571787 T^{6} \))(\( 1 - 12 T + 252 T^{2} - 1644 T^{3} + 24598 T^{4} - 136452 T^{5} + 1736028 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))(\( 1 + 18 T + 418 T^{2} + 4746 T^{3} + 63337 T^{4} + 530832 T^{5} + 5256971 T^{6} + 32695194 T^{7} + 239006966 T^{8} + 854249778 T^{9} + 3939040643 T^{10} \))(\( 1 - 6 T + 326 T^{2} - 1666 T^{3} + 48333 T^{4} - 199160 T^{5} + 4011639 T^{6} - 11477074 T^{7} + 186402562 T^{8} - 284749926 T^{9} + 3939040643 T^{10} \))(\( 1 - 2 T + 114 T^{2} - 338 T^{3} + 12089 T^{4} - 78912 T^{5} + 1003387 T^{6} - 2328482 T^{7} + 65183718 T^{8} - 94916642 T^{9} + 3939040643 T^{10} \))(\( 1 + 42 T + 1200 T^{2} + 24924 T^{3} + 427571 T^{4} + 6160059 T^{5} + 77219520 T^{6} + 845604102 T^{7} + 8200816788 T^{8} + 70185140466 T^{9} + 531965273280 T^{10} + 3522241655433 T^{11} + 20291801768291 T^{12} + 98176648986132 T^{13} + 392328448042800 T^{14} + 1139714141564334 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 42 T + 1200 T^{2} - 24924 T^{3} + 427571 T^{4} - 6160059 T^{5} + 77219520 T^{6} - 845604102 T^{7} + 8200816788 T^{8} - 70185140466 T^{9} + 531965273280 T^{10} - 3522241655433 T^{11} + 20291801768291 T^{12} - 98176648986132 T^{13} + 392328448042800 T^{14} - 1139714141564334 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 20 T + 528 T^{2} + 7496 T^{3} + 121918 T^{4} + 1442276 T^{5} + 18880926 T^{6} + 198399444 T^{7} + 2251070337 T^{8} + 21080323924 T^{9} + 210699872260 T^{10} + 1749666885692 T^{11} + 15507623551593 T^{12} + 113442222886428 T^{13} + 896057046885246 T^{14} + 5681183782423468 T^{15} + 39859916440401742 T^{16} + 203411838218243992 T^{17} + 1189210298569413648 T^{18} + 3738805105350808060 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 20 T + 528 T^{2} - 7496 T^{3} + 121918 T^{4} - 1442276 T^{5} + 18880926 T^{6} - 198399444 T^{7} + 2251070337 T^{8} - 21080323924 T^{9} + 210699872260 T^{10} - 1749666885692 T^{11} + 15507623551593 T^{12} - 113442222886428 T^{13} + 896057046885246 T^{14} - 5681183782423468 T^{15} + 39859916440401742 T^{16} - 203411838218243992 T^{17} + 1189210298569413648 T^{18} - 3738805105350808060 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 18 T + 957 T^{2} - 13278 T^{3} + 406532 T^{4} - 4526403 T^{5} + 104640076 T^{6} - 950016557 T^{7} + 18638437942 T^{8} - 138413158803 T^{9} + 2492847506614 T^{10} - 15191914173358 T^{11} + 268012339072371 T^{12} - 1377333735196800 T^{13} + 24729349092135191 T^{14} - 115390514275133166 T^{15} + 2052535974647220853 T^{16} - 9488452101770755200 T^{17} + \)\(15\!\cdots\!77\)\( T^{18} - \)\(72\!\cdots\!18\)\( T^{19} + \)\(98\!\cdots\!02\)\( T^{20} - \)\(45\!\cdots\!07\)\( T^{21} + \)\(50\!\cdots\!34\)\( T^{22} - \)\(21\!\cdots\!37\)\( T^{23} + \)\(19\!\cdots\!28\)\( T^{24} - \)\(70\!\cdots\!47\)\( T^{25} + \)\(52\!\cdots\!44\)\( T^{26} - \)\(14\!\cdots\!58\)\( T^{27} + \)\(84\!\cdots\!91\)\( T^{28} - \)\(13\!\cdots\!22\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 + 18 T + 957 T^{2} + 13278 T^{3} + 406532 T^{4} + 4526403 T^{5} + 104640076 T^{6} + 950016557 T^{7} + 18638437942 T^{8} + 138413158803 T^{9} + 2492847506614 T^{10} + 15191914173358 T^{11} + 268012339072371 T^{12} + 1377333735196800 T^{13} + 24729349092135191 T^{14} + 115390514275133166 T^{15} + 2052535974647220853 T^{16} + 9488452101770755200 T^{17} + \)\(15\!\cdots\!77\)\( T^{18} + \)\(72\!\cdots\!18\)\( T^{19} + \)\(98\!\cdots\!02\)\( T^{20} + \)\(45\!\cdots\!07\)\( T^{21} + \)\(50\!\cdots\!34\)\( T^{22} + \)\(21\!\cdots\!37\)\( T^{23} + \)\(19\!\cdots\!28\)\( T^{24} + \)\(70\!\cdots\!47\)\( T^{25} + \)\(52\!\cdots\!44\)\( T^{26} + \)\(14\!\cdots\!58\)\( T^{27} + \)\(84\!\cdots\!91\)\( T^{28} + \)\(13\!\cdots\!22\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 - 8 T + 844 T^{2} - 7192 T^{3} + 372340 T^{4} - 3255184 T^{5} + 113045612 T^{6} - 989158864 T^{7} + 26286771966 T^{8} - 226434233416 T^{9} + 4946391546212 T^{10} - 41465008968600 T^{11} + 778056222842042 T^{12} - 6291772550614808 T^{13} + 104429188772228900 T^{14} - 808563541486623240 T^{15} + 12119228017148642625 T^{16} - 89221305839101878056 T^{17} + \)\(12\!\cdots\!12\)\( T^{18} - \)\(85\!\cdots\!24\)\( T^{19} + \)\(10\!\cdots\!32\)\( T^{20} - \)\(70\!\cdots\!92\)\( T^{21} + \)\(84\!\cdots\!68\)\( T^{22} - \)\(51\!\cdots\!72\)\( T^{23} + \)\(57\!\cdots\!25\)\( T^{24} - \)\(31\!\cdots\!20\)\( T^{25} + \)\(34\!\cdots\!00\)\( T^{26} - \)\(17\!\cdots\!16\)\( T^{27} + \)\(17\!\cdots\!22\)\( T^{28} - \)\(77\!\cdots\!00\)\( T^{29} + \)\(76\!\cdots\!88\)\( T^{30} - \)\(29\!\cdots\!72\)\( T^{31} + \)\(28\!\cdots\!26\)\( T^{32} - \)\(87\!\cdots\!32\)\( T^{33} + \)\(83\!\cdots\!48\)\( T^{34} - \)\(19\!\cdots\!88\)\( T^{35} + \)\(18\!\cdots\!40\)\( T^{36} - \)\(30\!\cdots\!16\)\( T^{37} + \)\(29\!\cdots\!96\)\( T^{38} - \)\(23\!\cdots\!76\)\( T^{39} + \)\(24\!\cdots\!01\)\( T^{40} \))(\( 1 + 8 T + 844 T^{2} + 7192 T^{3} + 372340 T^{4} + 3255184 T^{5} + 113045612 T^{6} + 989158864 T^{7} + 26286771966 T^{8} + 226434233416 T^{9} + 4946391546212 T^{10} + 41465008968600 T^{11} + 778056222842042 T^{12} + 6291772550614808 T^{13} + 104429188772228900 T^{14} + 808563541486623240 T^{15} + 12119228017148642625 T^{16} + 89221305839101878056 T^{17} + \)\(12\!\cdots\!12\)\( T^{18} + \)\(85\!\cdots\!24\)\( T^{19} + \)\(10\!\cdots\!32\)\( T^{20} + \)\(70\!\cdots\!92\)\( T^{21} + \)\(84\!\cdots\!68\)\( T^{22} + \)\(51\!\cdots\!72\)\( T^{23} + \)\(57\!\cdots\!25\)\( T^{24} + \)\(31\!\cdots\!20\)\( T^{25} + \)\(34\!\cdots\!00\)\( T^{26} + \)\(17\!\cdots\!16\)\( T^{27} + \)\(17\!\cdots\!22\)\( T^{28} + \)\(77\!\cdots\!00\)\( T^{29} + \)\(76\!\cdots\!88\)\( T^{30} + \)\(29\!\cdots\!72\)\( T^{31} + \)\(28\!\cdots\!26\)\( T^{32} + \)\(87\!\cdots\!32\)\( T^{33} + \)\(83\!\cdots\!48\)\( T^{34} + \)\(19\!\cdots\!88\)\( T^{35} + \)\(18\!\cdots\!40\)\( T^{36} + \)\(30\!\cdots\!16\)\( T^{37} + \)\(29\!\cdots\!96\)\( T^{38} + \)\(23\!\cdots\!76\)\( T^{39} + \)\(24\!\cdots\!01\)\( T^{40} \))
$89$ (\( 1 + 3 T + 89 T^{2} \))(\( 1 - 5 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))(\( 1 + 5 T + 89 T^{2} \))(\( 1 + T + 97 T^{2} + 89 T^{3} + 7921 T^{4} \))(\( 1 - 3 T + 153 T^{2} - 265 T^{3} + 13617 T^{4} - 23763 T^{5} + 704969 T^{6} \))(\( 1 + 4 T + 228 T^{2} + 796 T^{3} + 29014 T^{4} + 70844 T^{5} + 1805988 T^{6} + 2819876 T^{7} + 62742241 T^{8} \))(\( 1 + 217 T^{2} - 1284 T^{3} + 17623 T^{4} - 224799 T^{5} + 1568447 T^{6} - 10170564 T^{7} + 152978273 T^{8} + 5584059449 T^{10} \))(\( 1 - 20 T + 491 T^{2} - 6302 T^{3} + 87253 T^{4} - 799619 T^{5} + 7765517 T^{6} - 49918142 T^{7} + 346139779 T^{8} - 1254844820 T^{9} + 5584059449 T^{10} \))(\( 1 + 6 T + 305 T^{2} + 1284 T^{3} + 45117 T^{4} + 153431 T^{5} + 4015413 T^{6} + 10170564 T^{7} + 215015545 T^{8} + 376453446 T^{9} + 5584059449 T^{10} \))(\( 1 + 11 T + 348 T^{2} + 2729 T^{3} + 52037 T^{4} + 403057 T^{5} + 6261873 T^{6} + 54404070 T^{7} + 655489911 T^{8} + 4841962230 T^{9} + 49600296033 T^{10} + 284142690233 T^{11} + 3264917994917 T^{12} + 15238898236321 T^{13} + 172949489254428 T^{14} + 486544683850819 T^{15} + 3936588805702081 T^{16} \))(\( 1 - 11 T + 348 T^{2} - 2729 T^{3} + 52037 T^{4} - 403057 T^{5} + 6261873 T^{6} - 54404070 T^{7} + 655489911 T^{8} - 4841962230 T^{9} + 49600296033 T^{10} - 284142690233 T^{11} + 3264917994917 T^{12} - 15238898236321 T^{13} + 172949489254428 T^{14} - 486544683850819 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 6 T + 178 T^{2} + 40 T^{3} + 19025 T^{4} - 13312 T^{5} + 2644880 T^{6} + 1951728 T^{7} + 298984707 T^{8} - 249612878 T^{9} + 23616419385 T^{10} - 22215546142 T^{11} + 2368257864147 T^{12} + 1375907736432 T^{13} + 165945698376080 T^{14} - 74334999385088 T^{15} + 9455069060533025 T^{16} + 1769253395821160 T^{17} + 700712807414970418 T^{18} + 2102138422244911254 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 6 T + 178 T^{2} - 40 T^{3} + 19025 T^{4} + 13312 T^{5} + 2644880 T^{6} - 1951728 T^{7} + 298984707 T^{8} + 249612878 T^{9} + 23616419385 T^{10} + 22215546142 T^{11} + 2368257864147 T^{12} - 1375907736432 T^{13} + 165945698376080 T^{14} + 74334999385088 T^{15} + 9455069060533025 T^{16} - 1769253395821160 T^{17} + 700712807414970418 T^{18} - 2102138422244911254 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 11 T + 645 T^{2} + 8338 T^{3} + 217386 T^{4} + 3018655 T^{5} + 52577251 T^{6} + 707493399 T^{7} + 10081479552 T^{8} + 123380688221 T^{9} + 1563746987133 T^{10} + 17312911230666 T^{11} + 197999214628080 T^{12} + 2021153054738361 T^{13} + 20843092796609928 T^{14} + 197072121359103194 T^{15} + 1855035258898283592 T^{16} + 16009553346582557481 T^{17} + \)\(13\!\cdots\!20\)\( T^{18} + \)\(10\!\cdots\!06\)\( T^{19} + \)\(87\!\cdots\!17\)\( T^{20} + \)\(61\!\cdots\!81\)\( T^{21} + \)\(44\!\cdots\!08\)\( T^{22} + \)\(27\!\cdots\!19\)\( T^{23} + \)\(18\!\cdots\!59\)\( T^{24} + \)\(94\!\cdots\!55\)\( T^{25} + \)\(60\!\cdots\!54\)\( T^{26} + \)\(20\!\cdots\!98\)\( T^{27} + \)\(14\!\cdots\!05\)\( T^{28} + \)\(21\!\cdots\!51\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 - 11 T + 645 T^{2} - 8338 T^{3} + 217386 T^{4} - 3018655 T^{5} + 52577251 T^{6} - 707493399 T^{7} + 10081479552 T^{8} - 123380688221 T^{9} + 1563746987133 T^{10} - 17312911230666 T^{11} + 197999214628080 T^{12} - 2021153054738361 T^{13} + 20843092796609928 T^{14} - 197072121359103194 T^{15} + 1855035258898283592 T^{16} - 16009553346582557481 T^{17} + \)\(13\!\cdots\!20\)\( T^{18} - \)\(10\!\cdots\!06\)\( T^{19} + \)\(87\!\cdots\!17\)\( T^{20} - \)\(61\!\cdots\!81\)\( T^{21} + \)\(44\!\cdots\!08\)\( T^{22} - \)\(27\!\cdots\!19\)\( T^{23} + \)\(18\!\cdots\!59\)\( T^{24} - \)\(94\!\cdots\!55\)\( T^{25} + \)\(60\!\cdots\!54\)\( T^{26} - \)\(20\!\cdots\!98\)\( T^{27} + \)\(14\!\cdots\!05\)\( T^{28} - \)\(21\!\cdots\!51\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 + 60 T + 3064 T^{2} + 109736 T^{3} + 3469110 T^{4} + 92247504 T^{5} + 2226138806 T^{6} + 47923058388 T^{7} + 952895395711 T^{8} + 17367055631856 T^{9} + 295721937917720 T^{10} + 4684930005199444 T^{11} + 69874023790081134 T^{12} + 978367239015143448 T^{13} + 12963332685038076396 T^{14} + \)\(16\!\cdots\!80\)\( T^{15} + \)\(19\!\cdots\!71\)\( T^{16} + \)\(21\!\cdots\!04\)\( T^{17} + \)\(23\!\cdots\!62\)\( T^{18} + \)\(23\!\cdots\!64\)\( T^{19} + \)\(22\!\cdots\!11\)\( T^{20} + \)\(20\!\cdots\!96\)\( T^{21} + \)\(18\!\cdots\!02\)\( T^{22} + \)\(15\!\cdots\!76\)\( T^{23} + \)\(12\!\cdots\!11\)\( T^{24} + \)\(90\!\cdots\!20\)\( T^{25} + \)\(64\!\cdots\!56\)\( T^{26} + \)\(43\!\cdots\!92\)\( T^{27} + \)\(27\!\cdots\!54\)\( T^{28} + \)\(16\!\cdots\!96\)\( T^{29} + \)\(92\!\cdots\!20\)\( T^{30} + \)\(48\!\cdots\!84\)\( T^{31} + \)\(23\!\cdots\!31\)\( T^{32} + \)\(10\!\cdots\!72\)\( T^{33} + \)\(43\!\cdots\!46\)\( T^{34} + \)\(16\!\cdots\!96\)\( T^{35} + \)\(53\!\cdots\!10\)\( T^{36} + \)\(15\!\cdots\!44\)\( T^{37} + \)\(37\!\cdots\!84\)\( T^{38} + \)\(65\!\cdots\!40\)\( T^{39} + \)\(97\!\cdots\!01\)\( T^{40} \))(\( 1 - 60 T + 3064 T^{2} - 109736 T^{3} + 3469110 T^{4} - 92247504 T^{5} + 2226138806 T^{6} - 47923058388 T^{7} + 952895395711 T^{8} - 17367055631856 T^{9} + 295721937917720 T^{10} - 4684930005199444 T^{11} + 69874023790081134 T^{12} - 978367239015143448 T^{13} + 12963332685038076396 T^{14} - \)\(16\!\cdots\!80\)\( T^{15} + \)\(19\!\cdots\!71\)\( T^{16} - \)\(21\!\cdots\!04\)\( T^{17} + \)\(23\!\cdots\!62\)\( T^{18} - \)\(23\!\cdots\!64\)\( T^{19} + \)\(22\!\cdots\!11\)\( T^{20} - \)\(20\!\cdots\!96\)\( T^{21} + \)\(18\!\cdots\!02\)\( T^{22} - \)\(15\!\cdots\!76\)\( T^{23} + \)\(12\!\cdots\!11\)\( T^{24} - \)\(90\!\cdots\!20\)\( T^{25} + \)\(64\!\cdots\!56\)\( T^{26} - \)\(43\!\cdots\!92\)\( T^{27} + \)\(27\!\cdots\!54\)\( T^{28} - \)\(16\!\cdots\!96\)\( T^{29} + \)\(92\!\cdots\!20\)\( T^{30} - \)\(48\!\cdots\!84\)\( T^{31} + \)\(23\!\cdots\!31\)\( T^{32} - \)\(10\!\cdots\!72\)\( T^{33} + \)\(43\!\cdots\!46\)\( T^{34} - \)\(16\!\cdots\!96\)\( T^{35} + \)\(53\!\cdots\!10\)\( T^{36} - \)\(15\!\cdots\!44\)\( T^{37} + \)\(37\!\cdots\!84\)\( T^{38} - \)\(65\!\cdots\!40\)\( T^{39} + \)\(97\!\cdots\!01\)\( T^{40} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 7 T + 47 T^{2} - 679 T^{3} + 9409 T^{4} \))(\( 1 + 3 T + 231 T^{2} + 349 T^{3} + 22407 T^{4} + 28227 T^{5} + 912673 T^{6} \))(\( 1 + 16 T + 268 T^{2} + 3376 T^{3} + 38118 T^{4} + 327472 T^{5} + 2521612 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 4 T + 405 T^{2} + 1326 T^{3} + 71967 T^{4} + 181845 T^{5} + 6980799 T^{6} + 12476334 T^{7} + 369632565 T^{8} + 354117124 T^{9} + 8587340257 T^{10} \))(\( 1 - 24 T + 363 T^{2} - 2360 T^{3} + 3237 T^{4} + 115965 T^{5} + 313989 T^{6} - 22205240 T^{7} + 331300299 T^{8} - 2124702744 T^{9} + 8587340257 T^{10} \))(\( 1 + 20 T + 207 T^{2} + 2236 T^{3} + 33747 T^{4} + 423407 T^{5} + 3273459 T^{6} + 21038524 T^{7} + 188923311 T^{8} + 1770585620 T^{9} + 8587340257 T^{10} \))(\( 1 + 16 T + 693 T^{2} + 8103 T^{3} + 198454 T^{4} + 1794697 T^{5} + 32962752 T^{6} + 243374175 T^{7} + 3748103050 T^{8} + 23607294975 T^{9} + 310146533568 T^{10} + 1637971495081 T^{11} + 17568989931574 T^{12} + 69583218102471 T^{13} + 577249599415797 T^{14} + 1292772551649808 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 16 T + 693 T^{2} - 8103 T^{3} + 198454 T^{4} - 1794697 T^{5} + 32962752 T^{6} - 243374175 T^{7} + 3748103050 T^{8} - 23607294975 T^{9} + 310146533568 T^{10} - 1637971495081 T^{11} + 17568989931574 T^{12} - 69583218102471 T^{13} + 577249599415797 T^{14} - 1292772551649808 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 46 T + 1292 T^{2} + 26530 T^{3} + 430839 T^{4} + 5783946 T^{5} + 66062922 T^{6} + 659196450 T^{7} + 5979674797 T^{8} + 52593327006 T^{9} + 491620931417 T^{10} + 5101552719582 T^{11} + 56262760164973 T^{12} + 601630801610850 T^{13} + 5848502985419082 T^{14} + 49668712330114122 T^{15} + 358876825631605431 T^{16} + 2143578487204337890 T^{17} + 10125964203935033612 T^{18} + 34970628698109999982 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 46 T + 1292 T^{2} - 26530 T^{3} + 430839 T^{4} - 5783946 T^{5} + 66062922 T^{6} - 659196450 T^{7} + 5979674797 T^{8} - 52593327006 T^{9} + 491620931417 T^{10} - 5101552719582 T^{11} + 56262760164973 T^{12} - 601630801610850 T^{13} + 5848502985419082 T^{14} - 49668712330114122 T^{15} + 358876825631605431 T^{16} - 2143578487204337890 T^{17} + 10125964203935033612 T^{18} - 34970628698109999982 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 16 T + 870 T^{2} - 13555 T^{3} + 394150 T^{4} - 5742512 T^{5} + 120559588 T^{6} - 1613534841 T^{7} + 27451908702 T^{8} - 335768070768 T^{9} + 4892169113610 T^{10} - 54643508317377 T^{11} + 702367249354834 T^{12} - 7159961181650448 T^{13} + 82579753815804149 T^{14} - 766573984600929574 T^{15} + 8010236120133002453 T^{16} - 67368074758149065232 T^{17} + \)\(64\!\cdots\!82\)\( T^{18} - \)\(48\!\cdots\!37\)\( T^{19} + \)\(42\!\cdots\!70\)\( T^{20} - \)\(27\!\cdots\!72\)\( T^{21} + \)\(22\!\cdots\!26\)\( T^{22} - \)\(12\!\cdots\!01\)\( T^{23} + \)\(91\!\cdots\!96\)\( T^{24} - \)\(42\!\cdots\!88\)\( T^{25} + \)\(28\!\cdots\!50\)\( T^{26} - \)\(94\!\cdots\!55\)\( T^{27} + \)\(58\!\cdots\!90\)\( T^{28} - \)\(10\!\cdots\!04\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 + 16 T + 870 T^{2} + 13555 T^{3} + 394150 T^{4} + 5742512 T^{5} + 120559588 T^{6} + 1613534841 T^{7} + 27451908702 T^{8} + 335768070768 T^{9} + 4892169113610 T^{10} + 54643508317377 T^{11} + 702367249354834 T^{12} + 7159961181650448 T^{13} + 82579753815804149 T^{14} + 766573984600929574 T^{15} + 8010236120133002453 T^{16} + 67368074758149065232 T^{17} + \)\(64\!\cdots\!82\)\( T^{18} + \)\(48\!\cdots\!37\)\( T^{19} + \)\(42\!\cdots\!70\)\( T^{20} + \)\(27\!\cdots\!72\)\( T^{21} + \)\(22\!\cdots\!26\)\( T^{22} + \)\(12\!\cdots\!01\)\( T^{23} + \)\(91\!\cdots\!96\)\( T^{24} + \)\(42\!\cdots\!88\)\( T^{25} + \)\(28\!\cdots\!50\)\( T^{26} + \)\(94\!\cdots\!55\)\( T^{27} + \)\(58\!\cdots\!90\)\( T^{28} + \)\(10\!\cdots\!04\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 + 40 T + 1682 T^{2} + 45380 T^{3} + 1181790 T^{4} + 25037632 T^{5} + 506502396 T^{6} + 9044350868 T^{7} + 154470490273 T^{8} + 2419186654120 T^{9} + 36384002638630 T^{10} + 512269362167364 T^{11} + 6953901987187436 T^{12} + 89457001024798496 T^{13} + 1113239218578782266 T^{14} + 13227501904031877232 T^{15} + \)\(15\!\cdots\!63\)\( T^{16} + \)\(16\!\cdots\!56\)\( T^{17} + \)\(18\!\cdots\!84\)\( T^{18} + \)\(18\!\cdots\!40\)\( T^{19} + \)\(18\!\cdots\!39\)\( T^{20} + \)\(18\!\cdots\!80\)\( T^{21} + \)\(17\!\cdots\!56\)\( T^{22} + \)\(15\!\cdots\!88\)\( T^{23} + \)\(13\!\cdots\!03\)\( T^{24} + \)\(11\!\cdots\!24\)\( T^{25} + \)\(92\!\cdots\!14\)\( T^{26} + \)\(72\!\cdots\!48\)\( T^{27} + \)\(54\!\cdots\!96\)\( T^{28} + \)\(38\!\cdots\!88\)\( T^{29} + \)\(26\!\cdots\!70\)\( T^{30} + \)\(17\!\cdots\!60\)\( T^{31} + \)\(10\!\cdots\!93\)\( T^{32} + \)\(60\!\cdots\!36\)\( T^{33} + \)\(33\!\cdots\!24\)\( T^{34} + \)\(15\!\cdots\!76\)\( T^{35} + \)\(72\!\cdots\!90\)\( T^{36} + \)\(27\!\cdots\!60\)\( T^{37} + \)\(97\!\cdots\!98\)\( T^{38} + \)\(22\!\cdots\!20\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))(\( 1 - 40 T + 1682 T^{2} - 45380 T^{3} + 1181790 T^{4} - 25037632 T^{5} + 506502396 T^{6} - 9044350868 T^{7} + 154470490273 T^{8} - 2419186654120 T^{9} + 36384002638630 T^{10} - 512269362167364 T^{11} + 6953901987187436 T^{12} - 89457001024798496 T^{13} + 1113239218578782266 T^{14} - 13227501904031877232 T^{15} + \)\(15\!\cdots\!63\)\( T^{16} - \)\(16\!\cdots\!56\)\( T^{17} + \)\(18\!\cdots\!84\)\( T^{18} - \)\(18\!\cdots\!40\)\( T^{19} + \)\(18\!\cdots\!39\)\( T^{20} - \)\(18\!\cdots\!80\)\( T^{21} + \)\(17\!\cdots\!56\)\( T^{22} - \)\(15\!\cdots\!88\)\( T^{23} + \)\(13\!\cdots\!03\)\( T^{24} - \)\(11\!\cdots\!24\)\( T^{25} + \)\(92\!\cdots\!14\)\( T^{26} - \)\(72\!\cdots\!48\)\( T^{27} + \)\(54\!\cdots\!96\)\( T^{28} - \)\(38\!\cdots\!88\)\( T^{29} + \)\(26\!\cdots\!70\)\( T^{30} - \)\(17\!\cdots\!60\)\( T^{31} + \)\(10\!\cdots\!93\)\( T^{32} - \)\(60\!\cdots\!36\)\( T^{33} + \)\(33\!\cdots\!24\)\( T^{34} - \)\(15\!\cdots\!76\)\( T^{35} + \)\(72\!\cdots\!90\)\( T^{36} - \)\(27\!\cdots\!60\)\( T^{37} + \)\(97\!\cdots\!98\)\( T^{38} - \)\(22\!\cdots\!20\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))
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