Properties

Label 6069.2
Level 6069
Weight 2
Dimension 946868
Nonzero newspaces 40
Sturm bound 5326848

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Defining parameters

Level: \( N \) = \( 6069 = 3 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(5326848\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6069))\).

Total New Old
Modular forms 1341312 954240 387072
Cusp forms 1322113 946868 375245
Eisenstein series 19199 7372 11827

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6069))\)

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
6069.2.a \(\chi_{6069}(1, \cdot)\) 6069.2.a.a 1 1
6069.2.a.b 1
6069.2.a.c 1
6069.2.a.d 1
6069.2.a.e 1
6069.2.a.f 2
6069.2.a.g 2
6069.2.a.h 2
6069.2.a.i 2
6069.2.a.j 3
6069.2.a.k 3
6069.2.a.l 3
6069.2.a.m 3
6069.2.a.n 3
6069.2.a.o 3
6069.2.a.p 3
6069.2.a.q 3
6069.2.a.r 3
6069.2.a.s 4
6069.2.a.t 5
6069.2.a.u 5
6069.2.a.v 5
6069.2.a.w 5
6069.2.a.x 6
6069.2.a.y 6
6069.2.a.z 9
6069.2.a.ba 9
6069.2.a.bb 9
6069.2.a.bc 9
6069.2.a.bd 10
6069.2.a.be 10
6069.2.a.bf 15
6069.2.a.bg 15
6069.2.a.bh 15
6069.2.a.bi 15
6069.2.a.bj 16
6069.2.a.bk 16
6069.2.a.bl 24
6069.2.a.bm 24
6069.2.c \(\chi_{6069}(6068, \cdot)\) n/a 692 1
6069.2.d \(\chi_{6069}(3758, \cdot)\) n/a 692 1
6069.2.f \(\chi_{6069}(2311, \cdot)\) n/a 272 1
6069.2.i \(\chi_{6069}(3469, \cdot)\) n/a 722 2
6069.2.k \(\chi_{6069}(2563, \cdot)\) n/a 544 2
6069.2.l \(\chi_{6069}(251, \cdot)\) n/a 1384 2
6069.2.p \(\chi_{6069}(1444, \cdot)\) n/a 720 2
6069.2.r \(\chi_{6069}(290, \cdot)\) n/a 1386 2
6069.2.s \(\chi_{6069}(866, \cdot)\) n/a 1384 2
6069.2.u \(\chi_{6069}(757, \cdot)\) n/a 1072 4
6069.2.w \(\chi_{6069}(1868, \cdot)\) n/a 2768 4
6069.2.y \(\chi_{6069}(38, \cdot)\) n/a 2768 4
6069.2.bb \(\chi_{6069}(1696, \cdot)\) n/a 1440 4
6069.2.bc \(\chi_{6069}(538, \cdot)\) n/a 2880 8
6069.2.bf \(\chi_{6069}(827, \cdot)\) n/a 4320 8
6069.2.bg \(\chi_{6069}(358, \cdot)\) n/a 4864 16
6069.2.bi \(\chi_{6069}(688, \cdot)\) n/a 2880 8
6069.2.bk \(\chi_{6069}(110, \cdot)\) n/a 5536 8
6069.2.bn \(\chi_{6069}(169, \cdot)\) n/a 4864 16
6069.2.bp \(\chi_{6069}(188, \cdot)\) n/a 12992 16
6069.2.bq \(\chi_{6069}(356, \cdot)\) n/a 12992 16
6069.2.bt \(\chi_{6069}(40, \cdot)\) n/a 5760 16
6069.2.bu \(\chi_{6069}(65, \cdot)\) n/a 11072 16
6069.2.bw \(\chi_{6069}(205, \cdot)\) n/a 13056 32
6069.2.by \(\chi_{6069}(293, \cdot)\) n/a 25984 32
6069.2.bz \(\chi_{6069}(64, \cdot)\) n/a 9728 32
6069.2.cc \(\chi_{6069}(101, \cdot)\) n/a 25984 32
6069.2.cd \(\chi_{6069}(341, \cdot)\) n/a 25984 32
6069.2.cf \(\chi_{6069}(16, \cdot)\) n/a 13056 32
6069.2.ci \(\chi_{6069}(83, \cdot)\) n/a 51968 64
6069.2.ck \(\chi_{6069}(43, \cdot)\) n/a 19712 64
6069.2.cm \(\chi_{6069}(4, \cdot)\) n/a 26112 64
6069.2.cp \(\chi_{6069}(47, \cdot)\) n/a 51968 64
6069.2.cq \(\chi_{6069}(29, \cdot)\) n/a 78336 128
6069.2.ct \(\chi_{6069}(97, \cdot)\) n/a 52224 128
6069.2.cv \(\chi_{6069}(26, \cdot)\) n/a 103936 128
6069.2.cx \(\chi_{6069}(25, \cdot)\) n/a 52224 128
6069.2.cz \(\chi_{6069}(11, \cdot)\) n/a 207872 256
6069.2.da \(\chi_{6069}(10, \cdot)\) n/a 104448 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6069))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6069)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2023))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} \))(\( 1 + 2 T^{2} + 4 T^{4} \))(\( 1 - T + T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 - T + T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 5 T^{2} + 7 T^{3} + 10 T^{4} + 8 T^{5} + 8 T^{6} \))(\( 1 + 2 T + 4 T^{2} + 6 T^{3} + 8 T^{4} + 8 T^{5} + 8 T^{6} \))(\( 1 + 2 T + 5 T^{2} + 7 T^{3} + 10 T^{4} + 8 T^{5} + 8 T^{6} \))(\( 1 + 2 T + 4 T^{2} + 6 T^{3} + 8 T^{4} + 8 T^{5} + 8 T^{6} \))(\( 1 + 3 T^{2} + T^{3} + 6 T^{4} + 8 T^{6} \))(\( 1 + T^{2} + 3 T^{3} + 2 T^{4} + 8 T^{6} \))(\( 1 + 3 T^{2} + T^{3} + 6 T^{4} + 8 T^{6} \))(\( 1 + T^{2} + 3 T^{3} + 2 T^{4} + 8 T^{6} \))(\( 1 - T + 2 T^{2} - 2 T^{3} + 4 T^{4} - 4 T^{5} + 8 T^{6} \))(\( 1 - 2 T + 3 T^{2} - 4 T^{3} + 6 T^{4} - 8 T^{5} + 12 T^{6} - 16 T^{7} + 16 T^{8} \))(\( 1 + T + 2 T^{2} - 2 T^{3} - 7 T^{5} - 8 T^{7} + 16 T^{8} + 16 T^{9} + 32 T^{10} \))(\( 1 + T + 2 T^{2} - 2 T^{3} - 7 T^{5} - 8 T^{7} + 16 T^{8} + 16 T^{9} + 32 T^{10} \))(\( 1 + T^{2} + 4 T^{4} - 2 T^{5} + 8 T^{6} + 8 T^{8} + 32 T^{10} \))(\( 1 + T^{2} + 4 T^{4} - 2 T^{5} + 8 T^{6} + 8 T^{8} + 32 T^{10} \))(\( 1 + 6 T^{2} + 20 T^{4} + 46 T^{6} + 80 T^{8} + 96 T^{10} + 64 T^{12} \))(\( 1 + 6 T^{2} + 20 T^{4} + 46 T^{6} + 80 T^{8} + 96 T^{10} + 64 T^{12} \))(\( 1 + 6 T^{2} - 3 T^{3} + 21 T^{4} - 15 T^{5} + 61 T^{6} - 51 T^{7} + 138 T^{8} - 129 T^{9} + 276 T^{10} - 204 T^{11} + 488 T^{12} - 240 T^{13} + 672 T^{14} - 192 T^{15} + 768 T^{16} + 512 T^{18} \))(\( 1 + 6 T^{2} - 3 T^{3} + 21 T^{4} - 15 T^{5} + 63 T^{6} - 39 T^{7} + 156 T^{8} - 83 T^{9} + 312 T^{10} - 156 T^{11} + 504 T^{12} - 240 T^{13} + 672 T^{14} - 192 T^{15} + 768 T^{16} + 512 T^{18} \))(\( 1 + 6 T^{2} - 3 T^{3} + 21 T^{4} - 15 T^{5} + 63 T^{6} - 39 T^{7} + 156 T^{8} - 83 T^{9} + 312 T^{10} - 156 T^{11} + 504 T^{12} - 240 T^{13} + 672 T^{14} - 192 T^{15} + 768 T^{16} + 512 T^{18} \))(\( 1 + 6 T^{2} - 3 T^{3} + 21 T^{4} - 15 T^{5} + 61 T^{6} - 51 T^{7} + 138 T^{8} - 129 T^{9} + 276 T^{10} - 204 T^{11} + 488 T^{12} - 240 T^{13} + 672 T^{14} - 192 T^{15} + 768 T^{16} + 512 T^{18} \))(\( 1 - 4 T + 12 T^{2} - 28 T^{3} + 57 T^{4} - 104 T^{5} + 172 T^{6} - 272 T^{7} + 416 T^{8} - 608 T^{9} + 878 T^{10} - 1216 T^{11} + 1664 T^{12} - 2176 T^{13} + 2752 T^{14} - 3328 T^{15} + 3648 T^{16} - 3584 T^{17} + 3072 T^{18} - 2048 T^{19} + 1024 T^{20} \))(\( 1 - 4 T + 12 T^{2} - 28 T^{3} + 57 T^{4} - 104 T^{5} + 172 T^{6} - 272 T^{7} + 416 T^{8} - 608 T^{9} + 878 T^{10} - 1216 T^{11} + 1664 T^{12} - 2176 T^{13} + 2752 T^{14} - 3328 T^{15} + 3648 T^{16} - 3584 T^{17} + 3072 T^{18} - 2048 T^{19} + 1024 T^{20} \))(\( 1 + 6 T^{2} + 4 T^{3} + 21 T^{4} + 27 T^{5} + 67 T^{6} + 96 T^{7} + 195 T^{8} + 293 T^{9} + 510 T^{10} + 771 T^{11} + 1256 T^{12} + 1737 T^{13} + 2874 T^{14} + 3609 T^{15} + 5748 T^{16} + 6948 T^{17} + 10048 T^{18} + 12336 T^{19} + 16320 T^{20} + 18752 T^{21} + 24960 T^{22} + 24576 T^{23} + 34304 T^{24} + 27648 T^{25} + 43008 T^{26} + 16384 T^{27} + 49152 T^{28} + 32768 T^{30} \))(\( 1 + 6 T^{2} + 4 T^{3} + 21 T^{4} + 27 T^{5} + 65 T^{6} + 108 T^{7} + 201 T^{8} + 325 T^{9} + 546 T^{10} + 873 T^{11} + 1320 T^{12} + 2061 T^{13} + 2928 T^{14} + 4391 T^{15} + 5856 T^{16} + 8244 T^{17} + 10560 T^{18} + 13968 T^{19} + 17472 T^{20} + 20800 T^{21} + 25728 T^{22} + 27648 T^{23} + 33280 T^{24} + 27648 T^{25} + 43008 T^{26} + 16384 T^{27} + 49152 T^{28} + 32768 T^{30} \))(\( 1 + 6 T^{2} + 4 T^{3} + 21 T^{4} + 27 T^{5} + 65 T^{6} + 108 T^{7} + 201 T^{8} + 325 T^{9} + 546 T^{10} + 873 T^{11} + 1320 T^{12} + 2061 T^{13} + 2928 T^{14} + 4391 T^{15} + 5856 T^{16} + 8244 T^{17} + 10560 T^{18} + 13968 T^{19} + 17472 T^{20} + 20800 T^{21} + 25728 T^{22} + 27648 T^{23} + 33280 T^{24} + 27648 T^{25} + 43008 T^{26} + 16384 T^{27} + 49152 T^{28} + 32768 T^{30} \))(\( 1 + 6 T^{2} + 4 T^{3} + 21 T^{4} + 27 T^{5} + 67 T^{6} + 96 T^{7} + 195 T^{8} + 293 T^{9} + 510 T^{10} + 771 T^{11} + 1256 T^{12} + 1737 T^{13} + 2874 T^{14} + 3609 T^{15} + 5748 T^{16} + 6948 T^{17} + 10048 T^{18} + 12336 T^{19} + 16320 T^{20} + 18752 T^{21} + 24960 T^{22} + 24576 T^{23} + 34304 T^{24} + 27648 T^{25} + 43008 T^{26} + 16384 T^{27} + 49152 T^{28} + 32768 T^{30} \))(\( 1 + 4 T + 18 T^{2} + 52 T^{3} + 151 T^{4} + 360 T^{5} + 844 T^{6} + 1760 T^{7} + 3594 T^{8} + 6752 T^{9} + 12424 T^{10} + 21384 T^{11} + 36066 T^{12} + 57408 T^{13} + 89604 T^{14} + 132584 T^{15} + 192446 T^{16} + 265168 T^{17} + 358416 T^{18} + 459264 T^{19} + 577056 T^{20} + 684288 T^{21} + 795136 T^{22} + 864256 T^{23} + 920064 T^{24} + 901120 T^{25} + 864256 T^{26} + 737280 T^{27} + 618496 T^{28} + 425984 T^{29} + 294912 T^{30} + 131072 T^{31} + 65536 T^{32} \))(\( 1 + 4 T + 18 T^{2} + 52 T^{3} + 151 T^{4} + 360 T^{5} + 844 T^{6} + 1760 T^{7} + 3594 T^{8} + 6752 T^{9} + 12424 T^{10} + 21384 T^{11} + 36066 T^{12} + 57408 T^{13} + 89604 T^{14} + 132584 T^{15} + 192446 T^{16} + 265168 T^{17} + 358416 T^{18} + 459264 T^{19} + 577056 T^{20} + 684288 T^{21} + 795136 T^{22} + 864256 T^{23} + 920064 T^{24} + 901120 T^{25} + 864256 T^{26} + 737280 T^{27} + 618496 T^{28} + 425984 T^{29} + 294912 T^{30} + 131072 T^{31} + 65536 T^{32} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{15} \))(\( ( 1 + T )^{15} \))(\( ( 1 - T )^{15} \))(\( ( 1 - T )^{15} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{16} \))
$5$ (\( 1 - 3 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 - 2 T + 9 T^{2} - 10 T^{3} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 + 2 T - 9 T^{3} + 50 T^{5} + 125 T^{6} \))(\( 1 - 3 T + 14 T^{2} - 29 T^{3} + 70 T^{4} - 75 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 9 T^{3} - 50 T^{5} + 125 T^{6} \))(\( 1 + 3 T + 14 T^{2} + 29 T^{3} + 70 T^{4} + 75 T^{5} + 125 T^{6} \))(\( 1 + 12 T^{2} + T^{3} + 60 T^{4} + 125 T^{6} \))(\( 1 - 2 T + 12 T^{2} - 19 T^{3} + 60 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 + 12 T^{2} - T^{3} + 60 T^{4} + 125 T^{6} \))(\( 1 + 2 T + 12 T^{2} + 19 T^{3} + 60 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 + 2 T + 12 T^{2} + 18 T^{3} + 60 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 10 T^{3} + 16 T^{4} - 50 T^{5} + 175 T^{6} - 250 T^{7} + 625 T^{8} \))(\( 1 + 4 T + 10 T^{2} + 7 T^{3} - 7 T^{4} - 66 T^{5} - 35 T^{6} + 175 T^{7} + 1250 T^{8} + 2500 T^{9} + 3125 T^{10} \))(\( 1 - 4 T + 10 T^{2} - 7 T^{3} - 7 T^{4} + 66 T^{5} - 35 T^{6} - 175 T^{7} + 1250 T^{8} - 2500 T^{9} + 3125 T^{10} \))(\( 1 - 3 T + 8 T^{2} - 31 T^{3} + 83 T^{4} - 172 T^{5} + 415 T^{6} - 775 T^{7} + 1000 T^{8} - 1875 T^{9} + 3125 T^{10} \))(\( 1 + 3 T + 8 T^{2} + 31 T^{3} + 83 T^{4} + 172 T^{5} + 415 T^{6} + 775 T^{7} + 1000 T^{8} + 1875 T^{9} + 3125 T^{10} \))(\( 1 - 6 T + 29 T^{2} - 102 T^{3} + 332 T^{4} - 878 T^{5} + 2137 T^{6} - 4390 T^{7} + 8300 T^{8} - 12750 T^{9} + 18125 T^{10} - 18750 T^{11} + 15625 T^{12} \))(\( 1 + 6 T + 29 T^{2} + 102 T^{3} + 332 T^{4} + 878 T^{5} + 2137 T^{6} + 4390 T^{7} + 8300 T^{8} + 12750 T^{9} + 18125 T^{10} + 18750 T^{11} + 15625 T^{12} \))(\( 1 - 3 T + 27 T^{2} - 71 T^{3} + 363 T^{4} - 891 T^{5} + 3315 T^{6} - 7389 T^{7} + 22017 T^{8} - 43267 T^{9} + 110085 T^{10} - 184725 T^{11} + 414375 T^{12} - 556875 T^{13} + 1134375 T^{14} - 1109375 T^{15} + 2109375 T^{16} - 1171875 T^{17} + 1953125 T^{18} \))(\( 1 - 3 T + 27 T^{2} - 69 T^{3} + 381 T^{4} - 831 T^{5} + 3495 T^{6} - 6639 T^{7} + 23223 T^{8} - 38447 T^{9} + 116115 T^{10} - 165975 T^{11} + 436875 T^{12} - 519375 T^{13} + 1190625 T^{14} - 1078125 T^{15} + 2109375 T^{16} - 1171875 T^{17} + 1953125 T^{18} \))(\( 1 + 3 T + 27 T^{2} + 69 T^{3} + 381 T^{4} + 831 T^{5} + 3495 T^{6} + 6639 T^{7} + 23223 T^{8} + 38447 T^{9} + 116115 T^{10} + 165975 T^{11} + 436875 T^{12} + 519375 T^{13} + 1190625 T^{14} + 1078125 T^{15} + 2109375 T^{16} + 1171875 T^{17} + 1953125 T^{18} \))(\( 1 + 3 T + 27 T^{2} + 71 T^{3} + 363 T^{4} + 891 T^{5} + 3315 T^{6} + 7389 T^{7} + 22017 T^{8} + 43267 T^{9} + 110085 T^{10} + 184725 T^{11} + 414375 T^{12} + 556875 T^{13} + 1134375 T^{14} + 1109375 T^{15} + 2109375 T^{16} + 1171875 T^{17} + 1953125 T^{18} \))(\( 1 - 6 T + 41 T^{2} - 166 T^{3} + 686 T^{4} - 2162 T^{5} + 6771 T^{6} - 17922 T^{7} + 47077 T^{8} - 110464 T^{9} + 258656 T^{10} - 552320 T^{11} + 1176925 T^{12} - 2240250 T^{13} + 4231875 T^{14} - 6756250 T^{15} + 10718750 T^{16} - 12968750 T^{17} + 16015625 T^{18} - 11718750 T^{19} + 9765625 T^{20} \))(\( 1 + 6 T + 41 T^{2} + 166 T^{3} + 686 T^{4} + 2162 T^{5} + 6771 T^{6} + 17922 T^{7} + 47077 T^{8} + 110464 T^{9} + 258656 T^{10} + 552320 T^{11} + 1176925 T^{12} + 2240250 T^{13} + 4231875 T^{14} + 6756250 T^{15} + 10718750 T^{16} + 12968750 T^{17} + 16015625 T^{18} + 11718750 T^{19} + 9765625 T^{20} \))(\( 1 + 9 T + 63 T^{2} + 335 T^{3} + 1614 T^{4} + 6798 T^{5} + 26536 T^{6} + 94512 T^{7} + 317013 T^{8} + 990683 T^{9} + 2938239 T^{10} + 8202627 T^{11} + 21836188 T^{12} + 55029774 T^{13} + 132577530 T^{14} + 303091612 T^{15} + 662887650 T^{16} + 1375744350 T^{17} + 2729523500 T^{18} + 5126641875 T^{19} + 9181996875 T^{20} + 15479421875 T^{21} + 24766640625 T^{22} + 36918750000 T^{23} + 51828125000 T^{24} + 66386718750 T^{25} + 78808593750 T^{26} + 81787109375 T^{27} + 76904296875 T^{28} + 54931640625 T^{29} + 30517578125 T^{30} \))(\( 1 + 9 T + 63 T^{2} + 325 T^{3} + 1452 T^{4} + 5586 T^{5} + 19612 T^{6} + 62820 T^{7} + 189609 T^{8} + 539179 T^{9} + 1473201 T^{10} + 3853605 T^{11} + 9763436 T^{12} + 23791290 T^{13} + 56192154 T^{14} + 127666116 T^{15} + 280960770 T^{16} + 594782250 T^{17} + 1220429500 T^{18} + 2408503125 T^{19} + 4603753125 T^{20} + 8424671875 T^{21} + 14813203125 T^{22} + 24539062500 T^{23} + 38304687500 T^{24} + 54550781250 T^{25} + 70898437500 T^{26} + 79345703125 T^{27} + 76904296875 T^{28} + 54931640625 T^{29} + 30517578125 T^{30} \))(\( 1 - 9 T + 63 T^{2} - 325 T^{3} + 1452 T^{4} - 5586 T^{5} + 19612 T^{6} - 62820 T^{7} + 189609 T^{8} - 539179 T^{9} + 1473201 T^{10} - 3853605 T^{11} + 9763436 T^{12} - 23791290 T^{13} + 56192154 T^{14} - 127666116 T^{15} + 280960770 T^{16} - 594782250 T^{17} + 1220429500 T^{18} - 2408503125 T^{19} + 4603753125 T^{20} - 8424671875 T^{21} + 14813203125 T^{22} - 24539062500 T^{23} + 38304687500 T^{24} - 54550781250 T^{25} + 70898437500 T^{26} - 79345703125 T^{27} + 76904296875 T^{28} - 54931640625 T^{29} + 30517578125 T^{30} \))(\( 1 - 9 T + 63 T^{2} - 335 T^{3} + 1614 T^{4} - 6798 T^{5} + 26536 T^{6} - 94512 T^{7} + 317013 T^{8} - 990683 T^{9} + 2938239 T^{10} - 8202627 T^{11} + 21836188 T^{12} - 55029774 T^{13} + 132577530 T^{14} - 303091612 T^{15} + 662887650 T^{16} - 1375744350 T^{17} + 2729523500 T^{18} - 5126641875 T^{19} + 9181996875 T^{20} - 15479421875 T^{21} + 24766640625 T^{22} - 36918750000 T^{23} + 51828125000 T^{24} - 66386718750 T^{25} + 78808593750 T^{26} - 81787109375 T^{27} + 76904296875 T^{28} - 54931640625 T^{29} + 30517578125 T^{30} \))(\( 1 + 4 T + 46 T^{2} + 168 T^{3} + 1033 T^{4} + 3416 T^{5} + 14934 T^{6} + 44812 T^{7} + 155937 T^{8} + 428176 T^{9} + 1261668 T^{10} + 3212232 T^{11} + 8372538 T^{12} + 20097096 T^{13} + 48091452 T^{14} + 110500520 T^{15} + 250246928 T^{16} + 552502600 T^{17} + 1202286300 T^{18} + 2512137000 T^{19} + 5232836250 T^{20} + 10038225000 T^{21} + 19713562500 T^{22} + 33451250000 T^{23} + 60912890625 T^{24} + 87523437500 T^{25} + 145839843750 T^{26} + 166796875000 T^{27} + 252197265625 T^{28} + 205078125000 T^{29} + 280761718750 T^{30} + 122070312500 T^{31} + 152587890625 T^{32} \))(\( 1 - 4 T + 46 T^{2} - 168 T^{3} + 1033 T^{4} - 3416 T^{5} + 14934 T^{6} - 44812 T^{7} + 155937 T^{8} - 428176 T^{9} + 1261668 T^{10} - 3212232 T^{11} + 8372538 T^{12} - 20097096 T^{13} + 48091452 T^{14} - 110500520 T^{15} + 250246928 T^{16} - 552502600 T^{17} + 1202286300 T^{18} - 2512137000 T^{19} + 5232836250 T^{20} - 10038225000 T^{21} + 19713562500 T^{22} - 33451250000 T^{23} + 60912890625 T^{24} - 87523437500 T^{25} + 145839843750 T^{26} - 166796875000 T^{27} + 252197265625 T^{28} - 205078125000 T^{29} + 280761718750 T^{30} - 122070312500 T^{31} + 152587890625 T^{32} \))
$7$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{15} \))(\( ( 1 - T )^{15} \))(\( ( 1 + T )^{15} \))(\( ( 1 - T )^{15} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{16} \))
$11$ (\( 1 - 3 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( ( 1 - 5 T + 11 T^{2} )^{2} \))(\( ( 1 + T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 + 12 T + 74 T^{2} + 293 T^{3} + 814 T^{4} + 1452 T^{5} + 1331 T^{6} \))(\( 1 + 5 T + 36 T^{2} + 105 T^{3} + 396 T^{4} + 605 T^{5} + 1331 T^{6} \))(\( 1 - 12 T + 74 T^{2} - 293 T^{3} + 814 T^{4} - 1452 T^{5} + 1331 T^{6} \))(\( 1 - 5 T + 36 T^{2} - 105 T^{3} + 396 T^{4} - 605 T^{5} + 1331 T^{6} \))(\( 1 - 6 T + 36 T^{2} - 113 T^{3} + 396 T^{4} - 726 T^{5} + 1331 T^{6} \))(\( 1 - 2 T + 10 T^{2} - 65 T^{3} + 110 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( 1 + 6 T + 36 T^{2} + 113 T^{3} + 396 T^{4} + 726 T^{5} + 1331 T^{6} \))(\( 1 + 2 T + 10 T^{2} + 65 T^{3} + 110 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 + 6 T + 38 T^{2} + 128 T^{3} + 418 T^{4} + 726 T^{5} + 1331 T^{6} \))(\( 1 + 2 T + 21 T^{2} - 14 T^{3} + 156 T^{4} - 154 T^{5} + 2541 T^{6} + 2662 T^{7} + 14641 T^{8} \))(\( 1 + 22 T^{2} + 25 T^{3} + 241 T^{4} + 614 T^{5} + 2651 T^{6} + 3025 T^{7} + 29282 T^{8} + 161051 T^{10} \))(\( 1 + 22 T^{2} - 25 T^{3} + 241 T^{4} - 614 T^{5} + 2651 T^{6} - 3025 T^{7} + 29282 T^{8} + 161051 T^{10} \))(\( 1 - 3 T + 46 T^{2} - 105 T^{3} + 913 T^{4} - 1588 T^{5} + 10043 T^{6} - 12705 T^{7} + 61226 T^{8} - 43923 T^{9} + 161051 T^{10} \))(\( 1 + 3 T + 46 T^{2} + 105 T^{3} + 913 T^{4} + 1588 T^{5} + 10043 T^{6} + 12705 T^{7} + 61226 T^{8} + 43923 T^{9} + 161051 T^{10} \))(\( 1 - 2 T + 23 T^{2} - 78 T^{3} + 346 T^{4} - 1346 T^{5} + 4691 T^{6} - 14806 T^{7} + 41866 T^{8} - 103818 T^{9} + 336743 T^{10} - 322102 T^{11} + 1771561 T^{12} \))(\( 1 + 2 T + 23 T^{2} + 78 T^{3} + 346 T^{4} + 1346 T^{5} + 4691 T^{6} + 14806 T^{7} + 41866 T^{8} + 103818 T^{9} + 336743 T^{10} + 322102 T^{11} + 1771561 T^{12} \))(\( 1 - 18 T + 219 T^{2} - 1919 T^{3} + 13767 T^{4} - 82206 T^{5} + 424942 T^{6} - 1910907 T^{7} + 7603209 T^{8} - 26727395 T^{9} + 83635299 T^{10} - 231219747 T^{11} + 565597802 T^{12} - 1203578046 T^{13} + 2217189117 T^{14} - 3399625559 T^{15} + 4267690449 T^{16} - 3858459858 T^{17} + 2357947691 T^{18} \))(\( 1 - 12 T + 129 T^{2} - 909 T^{3} + 5751 T^{4} - 29292 T^{5} + 136956 T^{6} - 555483 T^{7} + 2111463 T^{8} - 7200659 T^{9} + 23226093 T^{10} - 67213443 T^{11} + 182288436 T^{12} - 428864172 T^{13} + 926204301 T^{14} - 1610348949 T^{15} + 2513845059 T^{16} - 2572306572 T^{17} + 2357947691 T^{18} \))(\( 1 + 12 T + 129 T^{2} + 909 T^{3} + 5751 T^{4} + 29292 T^{5} + 136956 T^{6} + 555483 T^{7} + 2111463 T^{8} + 7200659 T^{9} + 23226093 T^{10} + 67213443 T^{11} + 182288436 T^{12} + 428864172 T^{13} + 926204301 T^{14} + 1610348949 T^{15} + 2513845059 T^{16} + 2572306572 T^{17} + 2357947691 T^{18} \))(\( 1 + 18 T + 219 T^{2} + 1919 T^{3} + 13767 T^{4} + 82206 T^{5} + 424942 T^{6} + 1910907 T^{7} + 7603209 T^{8} + 26727395 T^{9} + 83635299 T^{10} + 231219747 T^{11} + 565597802 T^{12} + 1203578046 T^{13} + 2217189117 T^{14} + 3399625559 T^{15} + 4267690449 T^{16} + 3858459858 T^{17} + 2357947691 T^{18} \))(\( 1 - 2 T + 47 T^{2} - 86 T^{3} + 1156 T^{4} - 1422 T^{5} + 18513 T^{6} - 10274 T^{7} + 223703 T^{8} - 1136 T^{9} + 2454356 T^{10} - 12496 T^{11} + 27068063 T^{12} - 13674694 T^{13} + 271048833 T^{14} - 229014522 T^{15} + 2047924516 T^{16} - 1675896706 T^{17} + 10074867407 T^{18} - 4715895382 T^{19} + 25937424601 T^{20} \))(\( 1 + 2 T + 47 T^{2} + 86 T^{3} + 1156 T^{4} + 1422 T^{5} + 18513 T^{6} + 10274 T^{7} + 223703 T^{8} + 1136 T^{9} + 2454356 T^{10} + 12496 T^{11} + 27068063 T^{12} + 13674694 T^{13} + 271048833 T^{14} + 229014522 T^{15} + 2047924516 T^{16} + 1675896706 T^{17} + 10074867407 T^{18} + 4715895382 T^{19} + 25937424601 T^{20} \))(\( 1 + 12 T + 144 T^{2} + 1137 T^{3} + 8646 T^{4} + 53853 T^{5} + 322392 T^{6} + 1699341 T^{7} + 8624340 T^{8} + 39821975 T^{9} + 177410742 T^{10} + 731398002 T^{11} + 2913830185 T^{12} + 10837802157 T^{13} + 38990537040 T^{14} + 131467390133 T^{15} + 428895907440 T^{16} + 1311374060997 T^{17} + 3878307976235 T^{18} + 10708398147282 T^{19} + 28572177409842 T^{20} + 70547057852975 T^{21} + 168063988342140 T^{22} + 364268835197421 T^{23} + 760183471996872 T^{24} + 1396808127037653 T^{25} + 2466804704102706 T^{26} + 3568393064331777 T^{27} + 4971270548726064 T^{28} + 4556998002998892 T^{29} + 4177248169415651 T^{30} \))(\( 1 + 30 T + 498 T^{2} + 5901 T^{3} + 55416 T^{4} + 436113 T^{5} + 2980006 T^{6} + 18113277 T^{7} + 99663006 T^{8} + 502799089 T^{9} + 2348046678 T^{10} + 10221213006 T^{11} + 41686937785 T^{12} + 159874116603 T^{13} + 577975253814 T^{14} + 1972489034873 T^{15} + 6357727791954 T^{16} + 19344768108963 T^{17} + 55485314191835 T^{18} + 149648779620846 T^{19} + 378155265538578 T^{20} + 890739256907929 T^{21} + 1942150040296026 T^{22} + 3882741788963037 T^{23} + 7026698266866146 T^{24} + 11311648055015913 T^{25} + 15810831538579176 T^{26} + 18519865851030621 T^{27} + 17192310647677638 T^{28} + 11392495007497230 T^{29} + 4177248169415651 T^{30} \))(\( 1 - 30 T + 498 T^{2} - 5901 T^{3} + 55416 T^{4} - 436113 T^{5} + 2980006 T^{6} - 18113277 T^{7} + 99663006 T^{8} - 502799089 T^{9} + 2348046678 T^{10} - 10221213006 T^{11} + 41686937785 T^{12} - 159874116603 T^{13} + 577975253814 T^{14} - 1972489034873 T^{15} + 6357727791954 T^{16} - 19344768108963 T^{17} + 55485314191835 T^{18} - 149648779620846 T^{19} + 378155265538578 T^{20} - 890739256907929 T^{21} + 1942150040296026 T^{22} - 3882741788963037 T^{23} + 7026698266866146 T^{24} - 11311648055015913 T^{25} + 15810831538579176 T^{26} - 18519865851030621 T^{27} + 17192310647677638 T^{28} - 11392495007497230 T^{29} + 4177248169415651 T^{30} \))(\( 1 - 12 T + 144 T^{2} - 1137 T^{3} + 8646 T^{4} - 53853 T^{5} + 322392 T^{6} - 1699341 T^{7} + 8624340 T^{8} - 39821975 T^{9} + 177410742 T^{10} - 731398002 T^{11} + 2913830185 T^{12} - 10837802157 T^{13} + 38990537040 T^{14} - 131467390133 T^{15} + 428895907440 T^{16} - 1311374060997 T^{17} + 3878307976235 T^{18} - 10708398147282 T^{19} + 28572177409842 T^{20} - 70547057852975 T^{21} + 168063988342140 T^{22} - 364268835197421 T^{23} + 760183471996872 T^{24} - 1396808127037653 T^{25} + 2466804704102706 T^{26} - 3568393064331777 T^{27} + 4971270548726064 T^{28} - 4556998002998892 T^{29} + 4177248169415651 T^{30} \))(\( 1 - 4 T + 106 T^{2} - 352 T^{3} + 5321 T^{4} - 14472 T^{5} + 168642 T^{6} - 364116 T^{7} + 3807789 T^{8} - 6153968 T^{9} + 65944252 T^{10} - 71998448 T^{11} + 931466054 T^{12} - 588422752 T^{13} + 11430491804 T^{14} - 3916386248 T^{15} + 129269626670 T^{16} - 43080248728 T^{17} + 1383089508284 T^{18} - 783190682912 T^{19} + 13637594496614 T^{20} - 11595422048848 T^{21} + 116824265017372 T^{22} - 119923426744528 T^{23} + 816233389124109 T^{24} - 858566481456156 T^{25} + 4374139159561842 T^{26} - 4129030497082392 T^{27} + 16699577392532441 T^{28} - 12151994674663712 T^{29} + 40253482359823546 T^{30} - 16708992677662604 T^{31} + 45949729863572161 T^{32} \))(\( 1 + 4 T + 106 T^{2} + 352 T^{3} + 5321 T^{4} + 14472 T^{5} + 168642 T^{6} + 364116 T^{7} + 3807789 T^{8} + 6153968 T^{9} + 65944252 T^{10} + 71998448 T^{11} + 931466054 T^{12} + 588422752 T^{13} + 11430491804 T^{14} + 3916386248 T^{15} + 129269626670 T^{16} + 43080248728 T^{17} + 1383089508284 T^{18} + 783190682912 T^{19} + 13637594496614 T^{20} + 11595422048848 T^{21} + 116824265017372 T^{22} + 119923426744528 T^{23} + 816233389124109 T^{24} + 858566481456156 T^{25} + 4374139159561842 T^{26} + 4129030497082392 T^{27} + 16699577392532441 T^{28} + 12151994674663712 T^{29} + 40253482359823546 T^{30} + 16708992677662604 T^{31} + 45949729863572161 T^{32} \))
$13$ (\( 1 - T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 33 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 22 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 22 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 - 13 T + 79 T^{2} - 325 T^{3} + 1027 T^{4} - 2197 T^{5} + 2197 T^{6} \))(\( 1 + T + 26 T^{2} + 3 T^{3} + 338 T^{4} + 169 T^{5} + 2197 T^{6} \))(\( 1 - 13 T + 79 T^{2} - 325 T^{3} + 1027 T^{4} - 2197 T^{5} + 2197 T^{6} \))(\( 1 + T + 26 T^{2} + 3 T^{3} + 338 T^{4} + 169 T^{5} + 2197 T^{6} \))(\( 1 - 3 T + 33 T^{2} - 61 T^{3} + 429 T^{4} - 507 T^{5} + 2197 T^{6} \))(\( 1 + 9 T + 61 T^{2} + 243 T^{3} + 793 T^{4} + 1521 T^{5} + 2197 T^{6} \))(\( 1 - 3 T + 33 T^{2} - 61 T^{3} + 429 T^{4} - 507 T^{5} + 2197 T^{6} \))(\( 1 + 9 T + 61 T^{2} + 243 T^{3} + 793 T^{4} + 1521 T^{5} + 2197 T^{6} \))(\( 1 + 2 T + 16 T^{2} - 10 T^{3} + 208 T^{4} + 338 T^{5} + 2197 T^{6} \))(\( 1 - 2 T + 39 T^{2} - 58 T^{3} + 672 T^{4} - 754 T^{5} + 6591 T^{6} - 4394 T^{7} + 28561 T^{8} \))(\( 1 - 3 T + 51 T^{2} - 123 T^{3} + 1198 T^{4} - 2252 T^{5} + 15574 T^{6} - 20787 T^{7} + 112047 T^{8} - 85683 T^{9} + 371293 T^{10} \))(\( 1 - 3 T + 51 T^{2} - 123 T^{3} + 1198 T^{4} - 2252 T^{5} + 15574 T^{6} - 20787 T^{7} + 112047 T^{8} - 85683 T^{9} + 371293 T^{10} \))(\( 1 - 3 T + 28 T^{2} - 95 T^{3} + 543 T^{4} - 1788 T^{5} + 7059 T^{6} - 16055 T^{7} + 61516 T^{8} - 85683 T^{9} + 371293 T^{10} \))(\( 1 - 3 T + 28 T^{2} - 95 T^{3} + 543 T^{4} - 1788 T^{5} + 7059 T^{6} - 16055 T^{7} + 61516 T^{8} - 85683 T^{9} + 371293 T^{10} \))(\( 1 + 2 T + 47 T^{2} + 58 T^{3} + 1072 T^{4} + 978 T^{5} + 16547 T^{6} + 12714 T^{7} + 181168 T^{8} + 127426 T^{9} + 1342367 T^{10} + 742586 T^{11} + 4826809 T^{12} \))(\( 1 + 2 T + 47 T^{2} + 58 T^{3} + 1072 T^{4} + 978 T^{5} + 16547 T^{6} + 12714 T^{7} + 181168 T^{8} + 127426 T^{9} + 1342367 T^{10} + 742586 T^{11} + 4826809 T^{12} \))(\( 1 + 21 T + 276 T^{2} + 2661 T^{3} + 20715 T^{4} + 135090 T^{5} + 758542 T^{6} + 3717540 T^{7} + 16066302 T^{8} + 61488171 T^{9} + 208861926 T^{10} + 628264260 T^{11} + 1666516774 T^{12} + 3858305490 T^{13} + 7691334495 T^{14} + 12844138749 T^{15} + 17318590692 T^{16} + 17130345141 T^{17} + 10604499373 T^{18} \))(\( 1 - 3 T + 96 T^{2} - 243 T^{3} + 4287 T^{4} - 9258 T^{5} + 117306 T^{6} - 216408 T^{7} + 2171706 T^{8} - 3394177 T^{9} + 28232178 T^{10} - 36572952 T^{11} + 257721282 T^{12} - 264417738 T^{13} + 1591733091 T^{14} - 1172914587 T^{15} + 6023857632 T^{16} - 2447192163 T^{17} + 10604499373 T^{18} \))(\( 1 - 3 T + 96 T^{2} - 243 T^{3} + 4287 T^{4} - 9258 T^{5} + 117306 T^{6} - 216408 T^{7} + 2171706 T^{8} - 3394177 T^{9} + 28232178 T^{10} - 36572952 T^{11} + 257721282 T^{12} - 264417738 T^{13} + 1591733091 T^{14} - 1172914587 T^{15} + 6023857632 T^{16} - 2447192163 T^{17} + 10604499373 T^{18} \))(\( 1 + 21 T + 276 T^{2} + 2661 T^{3} + 20715 T^{4} + 135090 T^{5} + 758542 T^{6} + 3717540 T^{7} + 16066302 T^{8} + 61488171 T^{9} + 208861926 T^{10} + 628264260 T^{11} + 1666516774 T^{12} + 3858305490 T^{13} + 7691334495 T^{14} + 12844138749 T^{15} + 17318590692 T^{16} + 17130345141 T^{17} + 10604499373 T^{18} \))(\( 1 - 6 T + 59 T^{2} - 358 T^{3} + 2226 T^{4} - 11706 T^{5} + 58385 T^{6} - 264738 T^{7} + 1131761 T^{8} - 4488632 T^{9} + 16753424 T^{10} - 58352216 T^{11} + 191267609 T^{12} - 581629386 T^{13} + 1667533985 T^{14} - 4346355858 T^{15} + 10744476834 T^{16} - 22463969086 T^{17} + 48128112539 T^{18} - 63626996238 T^{19} + 137858491849 T^{20} \))(\( 1 - 6 T + 59 T^{2} - 358 T^{3} + 2226 T^{4} - 11706 T^{5} + 58385 T^{6} - 264738 T^{7} + 1131761 T^{8} - 4488632 T^{9} + 16753424 T^{10} - 58352216 T^{11} + 191267609 T^{12} - 581629386 T^{13} + 1667533985 T^{14} - 4346355858 T^{15} + 10744476834 T^{16} - 22463969086 T^{17} + 48128112539 T^{18} - 63626996238 T^{19} + 137858491849 T^{20} \))(\( 1 - 27 T + 474 T^{2} - 6205 T^{3} + 66672 T^{4} - 611031 T^{5} + 4914164 T^{6} - 35269707 T^{7} + 228830790 T^{8} - 1353912410 T^{9} + 7355504442 T^{10} - 36871989033 T^{11} + 171194271000 T^{12} - 738105544620 T^{13} + 2960684833965 T^{14} - 11059657580862 T^{15} + 38488902841545 T^{16} - 124739837040780 T^{17} + 376113813387000 T^{18} - 1053100878771513 T^{19} + 2731047310783506 T^{20} - 6535076605799690 T^{21} + 14358792716438430 T^{22} - 28770583520568747 T^{23} + 52112249056819172 T^{24} - 84235812132986319 T^{25} + 119486917791234864 T^{26} - 144564618184994605 T^{27} + 143562800524727922 T^{28} - 106309162413880803 T^{29} + 51185893014090757 T^{30} \))(\( 1 - 3 T + 54 T^{2} - 69 T^{3} + 1692 T^{4} - 723 T^{5} + 40044 T^{6} + 21369 T^{7} + 781782 T^{8} + 934374 T^{9} + 13705230 T^{10} + 22395783 T^{11} + 218096236 T^{12} + 381379704 T^{13} + 3161418549 T^{14} + 5450756074 T^{15} + 41098441137 T^{16} + 64453169976 T^{17} + 479157430492 T^{18} + 639645958263 T^{19} + 5088655962390 T^{20} + 4510044832566 T^{21} + 49055661117294 T^{22} + 17431349777049 T^{23} + 424646572892412 T^{24} - 99671689606827 T^{25} + 3032335386710604 T^{26} - 1607567873451189 T^{27} + 16355255755981662 T^{28} - 11812129157097867 T^{29} + 51185893014090757 T^{30} \))(\( 1 - 3 T + 54 T^{2} - 69 T^{3} + 1692 T^{4} - 723 T^{5} + 40044 T^{6} + 21369 T^{7} + 781782 T^{8} + 934374 T^{9} + 13705230 T^{10} + 22395783 T^{11} + 218096236 T^{12} + 381379704 T^{13} + 3161418549 T^{14} + 5450756074 T^{15} + 41098441137 T^{16} + 64453169976 T^{17} + 479157430492 T^{18} + 639645958263 T^{19} + 5088655962390 T^{20} + 4510044832566 T^{21} + 49055661117294 T^{22} + 17431349777049 T^{23} + 424646572892412 T^{24} - 99671689606827 T^{25} + 3032335386710604 T^{26} - 1607567873451189 T^{27} + 16355255755981662 T^{28} - 11812129157097867 T^{29} + 51185893014090757 T^{30} \))(\( 1 - 27 T + 474 T^{2} - 6205 T^{3} + 66672 T^{4} - 611031 T^{5} + 4914164 T^{6} - 35269707 T^{7} + 228830790 T^{8} - 1353912410 T^{9} + 7355504442 T^{10} - 36871989033 T^{11} + 171194271000 T^{12} - 738105544620 T^{13} + 2960684833965 T^{14} - 11059657580862 T^{15} + 38488902841545 T^{16} - 124739837040780 T^{17} + 376113813387000 T^{18} - 1053100878771513 T^{19} + 2731047310783506 T^{20} - 6535076605799690 T^{21} + 14358792716438430 T^{22} - 28770583520568747 T^{23} + 52112249056819172 T^{24} - 84235812132986319 T^{25} + 119486917791234864 T^{26} - 144564618184994605 T^{27} + 143562800524727922 T^{28} - 106309162413880803 T^{29} + 51185893014090757 T^{30} \))(\( 1 + 12 T + 170 T^{2} + 1368 T^{3} + 11565 T^{4} + 71544 T^{5} + 455870 T^{6} + 2317068 T^{7} + 12186579 T^{8} + 53028432 T^{9} + 242875408 T^{10} + 934582464 T^{11} + 3893456558 T^{12} + 13719069384 T^{13} + 54320906352 T^{14} + 182905480672 T^{15} + 714008629214 T^{16} + 2377771248736 T^{17} + 9180233173488 T^{18} + 30140795436648 T^{19} + 111201012753038 T^{20} + 347003926805952 T^{21} + 1172313205213072 T^{22} + 3327455466835344 T^{23} + 9940966874193459 T^{24} + 24571346153198364 T^{25} + 62845550679203630 T^{26} + 128218323230983128 T^{27} + 269442354441492765 T^{28} + 414333145818202104 T^{29} + 669353985568879130 T^{30} + 614230716169089084 T^{31} + 665416609183179841 T^{32} \))(\( 1 + 12 T + 170 T^{2} + 1368 T^{3} + 11565 T^{4} + 71544 T^{5} + 455870 T^{6} + 2317068 T^{7} + 12186579 T^{8} + 53028432 T^{9} + 242875408 T^{10} + 934582464 T^{11} + 3893456558 T^{12} + 13719069384 T^{13} + 54320906352 T^{14} + 182905480672 T^{15} + 714008629214 T^{16} + 2377771248736 T^{17} + 9180233173488 T^{18} + 30140795436648 T^{19} + 111201012753038 T^{20} + 347003926805952 T^{21} + 1172313205213072 T^{22} + 3327455466835344 T^{23} + 9940966874193459 T^{24} + 24571346153198364 T^{25} + 62845550679203630 T^{26} + 128218323230983128 T^{27} + 269442354441492765 T^{28} + 414333145818202104 T^{29} + 669353985568879130 T^{30} + 614230716169089084 T^{31} + 665416609183179841 T^{32} \))
$17$ 1
$19$ (\( 1 + 7 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 4 T + 15 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 10 T + 61 T^{2} + 190 T^{3} + 361 T^{4} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( 1 + T + 13 T^{2} - 89 T^{3} + 247 T^{4} + 361 T^{5} + 6859 T^{6} \))(\( 1 + 7 T + 70 T^{2} + 271 T^{3} + 1330 T^{4} + 2527 T^{5} + 6859 T^{6} \))(\( 1 + T + 13 T^{2} - 89 T^{3} + 247 T^{4} + 361 T^{5} + 6859 T^{6} \))(\( 1 + 7 T + 70 T^{2} + 271 T^{3} + 1330 T^{4} + 2527 T^{5} + 6859 T^{6} \))(\( 1 - 3 T + 51 T^{2} - 97 T^{3} + 969 T^{4} - 1083 T^{5} + 6859 T^{6} \))(\( 1 + T + 11 T^{2} + 143 T^{3} + 209 T^{4} + 361 T^{5} + 6859 T^{6} \))(\( 1 - 3 T + 51 T^{2} - 97 T^{3} + 969 T^{4} - 1083 T^{5} + 6859 T^{6} \))(\( 1 + T + 11 T^{2} + 143 T^{3} + 209 T^{4} + 361 T^{5} + 6859 T^{6} \))(\( 1 + 4 T + 58 T^{2} + 148 T^{3} + 1102 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 - 10 T + 83 T^{2} - 490 T^{3} + 2400 T^{4} - 9310 T^{5} + 29963 T^{6} - 68590 T^{7} + 130321 T^{8} \))(\( 1 + T + 43 T^{2} + 17 T^{3} + 882 T^{4} - 200 T^{5} + 16758 T^{6} + 6137 T^{7} + 294937 T^{8} + 130321 T^{9} + 2476099 T^{10} \))(\( 1 + T + 43 T^{2} + 17 T^{3} + 882 T^{4} - 200 T^{5} + 16758 T^{6} + 6137 T^{7} + 294937 T^{8} + 130321 T^{9} + 2476099 T^{10} \))(\( 1 - 17 T + 160 T^{2} - 1027 T^{3} + 5331 T^{4} - 24140 T^{5} + 101289 T^{6} - 370747 T^{7} + 1097440 T^{8} - 2215457 T^{9} + 2476099 T^{10} \))(\( 1 - 17 T + 160 T^{2} - 1027 T^{3} + 5331 T^{4} - 24140 T^{5} + 101289 T^{6} - 370747 T^{7} + 1097440 T^{8} - 2215457 T^{9} + 2476099 T^{10} \))(\( 1 + 10 T + 121 T^{2} + 858 T^{3} + 5810 T^{4} + 30962 T^{5} + 147287 T^{6} + 588278 T^{7} + 2097410 T^{8} + 5885022 T^{9} + 15768841 T^{10} + 24760990 T^{11} + 47045881 T^{12} \))(\( 1 + 10 T + 121 T^{2} + 858 T^{3} + 5810 T^{4} + 30962 T^{5} + 147287 T^{6} + 588278 T^{7} + 2097410 T^{8} + 5885022 T^{9} + 15768841 T^{10} + 24760990 T^{11} + 47045881 T^{12} \))(\( 1 + 9 T + 123 T^{2} + 841 T^{3} + 7041 T^{4} + 40431 T^{5} + 259769 T^{6} + 1275165 T^{7} + 6744345 T^{8} + 28427045 T^{9} + 128142555 T^{10} + 460334565 T^{11} + 1781755571 T^{12} + 5269008351 T^{13} + 17434213059 T^{14} + 39565585921 T^{15} + 109946223897 T^{16} + 152852067369 T^{17} + 322687697779 T^{18} \))(\( 1 - 3 T + 123 T^{2} - 387 T^{3} + 7365 T^{4} - 22353 T^{5} + 280809 T^{6} - 773283 T^{7} + 7445157 T^{8} - 17772811 T^{9} + 141457983 T^{10} - 279155163 T^{11} + 1926068931 T^{12} - 2913065313 T^{13} + 18236469135 T^{14} - 18206755947 T^{15} + 109946223897 T^{16} - 50950689123 T^{17} + 322687697779 T^{18} \))(\( 1 - 3 T + 123 T^{2} - 387 T^{3} + 7365 T^{4} - 22353 T^{5} + 280809 T^{6} - 773283 T^{7} + 7445157 T^{8} - 17772811 T^{9} + 141457983 T^{10} - 279155163 T^{11} + 1926068931 T^{12} - 2913065313 T^{13} + 18236469135 T^{14} - 18206755947 T^{15} + 109946223897 T^{16} - 50950689123 T^{17} + 322687697779 T^{18} \))(\( 1 + 9 T + 123 T^{2} + 841 T^{3} + 7041 T^{4} + 40431 T^{5} + 259769 T^{6} + 1275165 T^{7} + 6744345 T^{8} + 28427045 T^{9} + 128142555 T^{10} + 460334565 T^{11} + 1781755571 T^{12} + 5269008351 T^{13} + 17434213059 T^{14} + 39565585921 T^{15} + 109946223897 T^{16} + 152852067369 T^{17} + 322687697779 T^{18} \))(\( 1 - 6 T + 105 T^{2} - 630 T^{3} + 5772 T^{4} - 32962 T^{5} + 219265 T^{6} - 1129366 T^{7} + 6229359 T^{8} - 28188412 T^{9} + 135194368 T^{10} - 535579828 T^{11} + 2248798599 T^{12} - 7746321394 T^{13} + 28574834065 T^{14} - 81617175238 T^{15} + 271548825132 T^{16} - 563139195570 T^{17} + 1783274119305 T^{18} - 1936126186674 T^{19} + 6131066257801 T^{20} \))(\( 1 - 6 T + 105 T^{2} - 630 T^{3} + 5772 T^{4} - 32962 T^{5} + 219265 T^{6} - 1129366 T^{7} + 6229359 T^{8} - 28188412 T^{9} + 135194368 T^{10} - 535579828 T^{11} + 2248798599 T^{12} - 7746321394 T^{13} + 28574834065 T^{14} - 81617175238 T^{15} + 271548825132 T^{16} - 563139195570 T^{17} + 1783274119305 T^{18} - 1936126186674 T^{19} + 6131066257801 T^{20} \))(\( 1 - 15 T + 195 T^{2} - 1767 T^{3} + 14352 T^{4} - 94488 T^{5} + 574680 T^{6} - 2993016 T^{7} + 14878371 T^{8} - 66125059 T^{9} + 301365297 T^{10} - 1304452323 T^{11} + 6188102124 T^{12} - 28035458982 T^{13} + 133970562900 T^{14} - 579045983004 T^{15} + 2545440695100 T^{16} - 10120800692502 T^{17} + 42444192468516 T^{18} - 169997531185683 T^{19} + 746210310536403 T^{20} - 3110911656831979 T^{21} + 13299355359257169 T^{22} - 50832075918721656 T^{23} + 185442166159635720 T^{24} - 579312188567100888 T^{25} + 1671868195707239088 T^{26} - 3910927461989906487 T^{27} + 8200331775140126505 T^{28} - 11985100286743261815 T^{29} + 15181127029874798299 T^{30} \))(\( 1 - 3 T + 147 T^{2} - 299 T^{3} + 10692 T^{4} - 13308 T^{5} + 522544 T^{6} - 315828 T^{7} + 19506939 T^{8} - 2344591 T^{9} + 594098589 T^{10} + 118292721 T^{11} + 15275483172 T^{12} + 5506961790 T^{13} + 336781228884 T^{14} + 130917569980 T^{15} + 6398843348796 T^{16} + 1988013206190 T^{17} + 104774539076748 T^{18} + 15416025693441 T^{19} + 1471046922124311 T^{20} - 110303349179671 T^{21} + 17436701486496921 T^{22} - 5363884748112948 T^{23} + 168618520348229776 T^{24} - 81592229758815708 T^{25} + 1245513848139757548 T^{26} - 661781160800782139 T^{27} + 6181788568951787673 T^{28} - 2397020057348652363 T^{29} + 15181127029874798299 T^{30} \))(\( 1 - 3 T + 147 T^{2} - 299 T^{3} + 10692 T^{4} - 13308 T^{5} + 522544 T^{6} - 315828 T^{7} + 19506939 T^{8} - 2344591 T^{9} + 594098589 T^{10} + 118292721 T^{11} + 15275483172 T^{12} + 5506961790 T^{13} + 336781228884 T^{14} + 130917569980 T^{15} + 6398843348796 T^{16} + 1988013206190 T^{17} + 104774539076748 T^{18} + 15416025693441 T^{19} + 1471046922124311 T^{20} - 110303349179671 T^{21} + 17436701486496921 T^{22} - 5363884748112948 T^{23} + 168618520348229776 T^{24} - 81592229758815708 T^{25} + 1245513848139757548 T^{26} - 661781160800782139 T^{27} + 6181788568951787673 T^{28} - 2397020057348652363 T^{29} + 15181127029874798299 T^{30} \))(\( 1 - 15 T + 195 T^{2} - 1767 T^{3} + 14352 T^{4} - 94488 T^{5} + 574680 T^{6} - 2993016 T^{7} + 14878371 T^{8} - 66125059 T^{9} + 301365297 T^{10} - 1304452323 T^{11} + 6188102124 T^{12} - 28035458982 T^{13} + 133970562900 T^{14} - 579045983004 T^{15} + 2545440695100 T^{16} - 10120800692502 T^{17} + 42444192468516 T^{18} - 169997531185683 T^{19} + 746210310536403 T^{20} - 3110911656831979 T^{21} + 13299355359257169 T^{22} - 50832075918721656 T^{23} + 185442166159635720 T^{24} - 579312188567100888 T^{25} + 1671868195707239088 T^{26} - 3910927461989906487 T^{27} + 8200331775140126505 T^{28} - 11985100286743261815 T^{29} + 15181127029874798299 T^{30} \))(\( 1 + 36 T + 774 T^{2} + 12152 T^{3} + 153759 T^{4} + 1644144 T^{5} + 15345778 T^{6} + 127697740 T^{7} + 962943789 T^{8} + 6660136600 T^{9} + 42661986228 T^{10} + 254952780832 T^{11} + 1429645342816 T^{12} + 7552911572760 T^{13} + 37703589082864 T^{14} + 178156322913520 T^{15} + 797663601866798 T^{16} + 3384970135356880 T^{17} + 13610995658913904 T^{18} + 51805420477560840 T^{19} + 186312810721123936 T^{20} + 631288325665334368 T^{21} + 2007070727306126868 T^{22} + 5953307884619547400 T^{23} + 16354216545420902349 T^{24} + 41206489732181319460 T^{25} + 94085981695504914178 T^{26} + \)\(19\!\cdots\!36\)\( T^{27} + \)\(34\!\cdots\!99\)\( T^{28} + \)\(51\!\cdots\!68\)\( T^{29} + \)\(61\!\cdots\!54\)\( T^{30} + \)\(54\!\cdots\!64\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 + 36 T + 774 T^{2} + 12152 T^{3} + 153759 T^{4} + 1644144 T^{5} + 15345778 T^{6} + 127697740 T^{7} + 962943789 T^{8} + 6660136600 T^{9} + 42661986228 T^{10} + 254952780832 T^{11} + 1429645342816 T^{12} + 7552911572760 T^{13} + 37703589082864 T^{14} + 178156322913520 T^{15} + 797663601866798 T^{16} + 3384970135356880 T^{17} + 13610995658913904 T^{18} + 51805420477560840 T^{19} + 186312810721123936 T^{20} + 631288325665334368 T^{21} + 2007070727306126868 T^{22} + 5953307884619547400 T^{23} + 16354216545420902349 T^{24} + 41206489732181319460 T^{25} + 94085981695504914178 T^{26} + \)\(19\!\cdots\!36\)\( T^{27} + \)\(34\!\cdots\!99\)\( T^{28} + \)\(51\!\cdots\!68\)\( T^{29} + \)\(61\!\cdots\!54\)\( T^{30} + \)\(54\!\cdots\!64\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))
$23$ (\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( 1 - 2 T + 39 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 2 T - 5 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 + 2 T - 5 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 + 20 T^{2} + 91 T^{3} + 460 T^{4} + 12167 T^{6} \))(\( 1 - 11 T + 96 T^{2} - 507 T^{3} + 2208 T^{4} - 5819 T^{5} + 12167 T^{6} \))(\( 1 + 20 T^{2} - 91 T^{3} + 460 T^{4} + 12167 T^{6} \))(\( 1 + 11 T + 96 T^{2} + 507 T^{3} + 2208 T^{4} + 5819 T^{5} + 12167 T^{6} \))(\( 1 + 42 T^{2} - 27 T^{3} + 966 T^{4} + 12167 T^{6} \))(\( 1 - 2 T + 66 T^{2} - 91 T^{3} + 1518 T^{4} - 1058 T^{5} + 12167 T^{6} \))(\( 1 + 42 T^{2} + 27 T^{3} + 966 T^{4} + 12167 T^{6} \))(\( 1 + 2 T + 66 T^{2} + 91 T^{3} + 1518 T^{4} + 1058 T^{5} + 12167 T^{6} \))(\( 1 + 6 T + 74 T^{2} + 268 T^{3} + 1702 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 + 6 T + 29 T^{2} + 70 T^{3} + 548 T^{4} + 1610 T^{5} + 15341 T^{6} + 73002 T^{7} + 279841 T^{8} \))(\( 1 + 4 T + 43 T^{2} + 115 T^{3} + 1439 T^{4} + 4597 T^{5} + 33097 T^{6} + 60835 T^{7} + 523181 T^{8} + 1119364 T^{9} + 6436343 T^{10} \))(\( 1 - 4 T + 43 T^{2} - 115 T^{3} + 1439 T^{4} - 4597 T^{5} + 33097 T^{6} - 60835 T^{7} + 523181 T^{8} - 1119364 T^{9} + 6436343 T^{10} \))(\( 1 - 7 T + 70 T^{2} - 301 T^{3} + 1817 T^{4} - 6492 T^{5} + 41791 T^{6} - 159229 T^{7} + 851690 T^{8} - 1958887 T^{9} + 6436343 T^{10} \))(\( 1 + 7 T + 70 T^{2} + 301 T^{3} + 1817 T^{4} + 6492 T^{5} + 41791 T^{6} + 159229 T^{7} + 851690 T^{8} + 1958887 T^{9} + 6436343 T^{10} \))(\( 1 + 10 T + 131 T^{2} + 1026 T^{3} + 7410 T^{4} + 44578 T^{5} + 226355 T^{6} + 1025294 T^{7} + 3919890 T^{8} + 12483342 T^{9} + 36659171 T^{10} + 64363430 T^{11} + 148035889 T^{12} \))(\( 1 - 10 T + 131 T^{2} - 1026 T^{3} + 7410 T^{4} - 44578 T^{5} + 226355 T^{6} - 1025294 T^{7} + 3919890 T^{8} - 12483342 T^{9} + 36659171 T^{10} - 64363430 T^{11} + 148035889 T^{12} \))(\( 1 + 69 T^{2} + 106 T^{3} + 2088 T^{4} + 7122 T^{5} + 56352 T^{6} + 234714 T^{7} + 1685415 T^{8} + 5845133 T^{9} + 38764545 T^{10} + 124163706 T^{11} + 685634784 T^{12} + 1993027602 T^{13} + 13439084184 T^{14} + 15691804234 T^{15} + 234932955843 T^{16} + 1801152661463 T^{18} \))(\( 1 - 18 T + 297 T^{2} - 3222 T^{3} + 31644 T^{4} - 249930 T^{5} + 1805568 T^{6} - 11168082 T^{7} + 63664623 T^{8} - 317628495 T^{9} + 1464286329 T^{10} - 5907915378 T^{11} + 21968345856 T^{12} - 69940661130 T^{13} + 203671637892 T^{14} - 476971634358 T^{15} + 1011233157759 T^{16} - 1409597735058 T^{17} + 1801152661463 T^{18} \))(\( 1 + 18 T + 297 T^{2} + 3222 T^{3} + 31644 T^{4} + 249930 T^{5} + 1805568 T^{6} + 11168082 T^{7} + 63664623 T^{8} + 317628495 T^{9} + 1464286329 T^{10} + 5907915378 T^{11} + 21968345856 T^{12} + 69940661130 T^{13} + 203671637892 T^{14} + 476971634358 T^{15} + 1011233157759 T^{16} + 1409597735058 T^{17} + 1801152661463 T^{18} \))(\( 1 + 69 T^{2} - 106 T^{3} + 2088 T^{4} - 7122 T^{5} + 56352 T^{6} - 234714 T^{7} + 1685415 T^{8} - 5845133 T^{9} + 38764545 T^{10} - 124163706 T^{11} + 685634784 T^{12} - 1993027602 T^{13} + 13439084184 T^{14} - 15691804234 T^{15} + 234932955843 T^{16} + 1801152661463 T^{18} \))(\( 1 + 18 T + 259 T^{2} + 2610 T^{3} + 22884 T^{4} + 165238 T^{5} + 1087737 T^{6} + 6294090 T^{7} + 34525463 T^{8} + 174175276 T^{9} + 862119372 T^{10} + 4006031348 T^{11} + 18263969927 T^{12} + 76580193030 T^{13} + 304393409817 T^{14} + 1063528444634 T^{15} + 3387653283876 T^{16} + 8886594416670 T^{17} + 20282545187779 T^{18} + 32420747906334 T^{19} + 41426511213649 T^{20} \))(\( 1 - 18 T + 259 T^{2} - 2610 T^{3} + 22884 T^{4} - 165238 T^{5} + 1087737 T^{6} - 6294090 T^{7} + 34525463 T^{8} - 174175276 T^{9} + 862119372 T^{10} - 4006031348 T^{11} + 18263969927 T^{12} - 76580193030 T^{13} + 304393409817 T^{14} - 1063528444634 T^{15} + 3387653283876 T^{16} - 8886594416670 T^{17} + 20282545187779 T^{18} - 32420747906334 T^{19} + 41426511213649 T^{20} \))(\( 1 + 18 T + 321 T^{2} + 3898 T^{3} + 43956 T^{4} + 419124 T^{5} + 3708441 T^{6} + 29617650 T^{7} + 221186862 T^{8} + 1531246547 T^{9} + 9982594707 T^{10} + 61106319852 T^{11} + 353912466425 T^{12} + 1937332495182 T^{13} + 10059954399726 T^{14} + 49515792846789 T^{15} + 231378951193698 T^{16} + 1024848889951278 T^{17} + 4306052978992975 T^{18} + 17100053653703532 T^{19} + 64251403564236501 T^{20} + 226679443863325283 T^{21} + 753102656279677314 T^{22} + 2319387353207809650 T^{23} + 6679468377028509183 T^{24} + 17362845085909423476 T^{25} + 41881705718864575212 T^{26} + 85423206036015211258 T^{27} + \)\(16\!\cdots\!43\)\( T^{28} + \)\(20\!\cdots\!62\)\( T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 + 12 T + 261 T^{2} + 2386 T^{3} + 31032 T^{4} + 237720 T^{5} + 2354497 T^{6} + 15761280 T^{7} + 129649662 T^{8} + 775112995 T^{9} + 5524755723 T^{10} + 29843208876 T^{11} + 188699545649 T^{12} + 925956892896 T^{13} + 5266144430274 T^{14} + 23496635502661 T^{15} + 121121321896302 T^{16} + 489831196341984 T^{17} + 2295907371911383 T^{18} + 8351353415068716 T^{19} + 35559222824440989 T^{20} + 114744541290277555 T^{21} + 441434468372548914 T^{22} + 1234281366089719680 T^{23} + 4240808537956649111 T^{24} + 9847910245708640280 T^{25} + 29567592407584982664 T^{26} + 52288293894800485906 T^{27} + \)\(13\!\cdots\!63\)\( T^{28} + \)\(13\!\cdots\!08\)\( T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 - 12 T + 261 T^{2} - 2386 T^{3} + 31032 T^{4} - 237720 T^{5} + 2354497 T^{6} - 15761280 T^{7} + 129649662 T^{8} - 775112995 T^{9} + 5524755723 T^{10} - 29843208876 T^{11} + 188699545649 T^{12} - 925956892896 T^{13} + 5266144430274 T^{14} - 23496635502661 T^{15} + 121121321896302 T^{16} - 489831196341984 T^{17} + 2295907371911383 T^{18} - 8351353415068716 T^{19} + 35559222824440989 T^{20} - 114744541290277555 T^{21} + 441434468372548914 T^{22} - 1234281366089719680 T^{23} + 4240808537956649111 T^{24} - 9847910245708640280 T^{25} + 29567592407584982664 T^{26} - 52288293894800485906 T^{27} + \)\(13\!\cdots\!63\)\( T^{28} - \)\(13\!\cdots\!08\)\( T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 - 18 T + 321 T^{2} - 3898 T^{3} + 43956 T^{4} - 419124 T^{5} + 3708441 T^{6} - 29617650 T^{7} + 221186862 T^{8} - 1531246547 T^{9} + 9982594707 T^{10} - 61106319852 T^{11} + 353912466425 T^{12} - 1937332495182 T^{13} + 10059954399726 T^{14} - 49515792846789 T^{15} + 231378951193698 T^{16} - 1024848889951278 T^{17} + 4306052978992975 T^{18} - 17100053653703532 T^{19} + 64251403564236501 T^{20} - 226679443863325283 T^{21} + 753102656279677314 T^{22} - 2319387353207809650 T^{23} + 6679468377028509183 T^{24} - 17362845085909423476 T^{25} + 41881705718864575212 T^{26} - 85423206036015211258 T^{27} + \)\(16\!\cdots\!43\)\( T^{28} - \)\(20\!\cdots\!62\)\( T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 + 4 T + 150 T^{2} + 480 T^{3} + 11837 T^{4} + 31152 T^{5} + 664114 T^{6} + 1487788 T^{7} + 29584069 T^{8} + 57815712 T^{9} + 1100977364 T^{10} + 1915674640 T^{11} + 35191513986 T^{12} + 55665645224 T^{13} + 981272634968 T^{14} + 1435562573120 T^{15} + 24048012773518 T^{16} + 33017939181760 T^{17} + 519093223898072 T^{18} + 677283905440408 T^{19} + 9848028465356226 T^{20} + 12329939059441520 T^{21} + 162984162848616596 T^{22} + 196852407454023264 T^{23} + 2316757592011088389 T^{24} + 2679733315892713844 T^{25} + 27511926068141291986 T^{26} + 29681929578534653904 T^{27} + \)\(25\!\cdots\!77\)\( T^{28} + \)\(24\!\cdots\!40\)\( T^{29} + \)\(17\!\cdots\!50\)\( T^{30} + \)\(10\!\cdots\!28\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 4 T + 150 T^{2} - 480 T^{3} + 11837 T^{4} - 31152 T^{5} + 664114 T^{6} - 1487788 T^{7} + 29584069 T^{8} - 57815712 T^{9} + 1100977364 T^{10} - 1915674640 T^{11} + 35191513986 T^{12} - 55665645224 T^{13} + 981272634968 T^{14} - 1435562573120 T^{15} + 24048012773518 T^{16} - 33017939181760 T^{17} + 519093223898072 T^{18} - 677283905440408 T^{19} + 9848028465356226 T^{20} - 12329939059441520 T^{21} + 162984162848616596 T^{22} - 196852407454023264 T^{23} + 2316757592011088389 T^{24} - 2679733315892713844 T^{25} + 27511926068141291986 T^{26} - 29681929578534653904 T^{27} + \)\(25\!\cdots\!77\)\( T^{28} - \)\(24\!\cdots\!40\)\( T^{29} + \)\(17\!\cdots\!50\)\( T^{30} - \)\(10\!\cdots\!28\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))
$29$ (\( 1 - 10 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( 1 + 8 T + 66 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 49 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 + 4 T + 49 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 + 9 T + 2 T^{2} - 235 T^{3} + 58 T^{4} + 7569 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 83 T^{2} - 112 T^{3} + 2407 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 2 T^{2} + 235 T^{3} + 58 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 + 2 T + 83 T^{2} + 112 T^{3} + 2407 T^{4} + 1682 T^{5} + 24389 T^{6} \))(\( 1 + 3 T + 54 T^{2} + 211 T^{3} + 1566 T^{4} + 2523 T^{5} + 24389 T^{6} \))(\( 1 + 7 T + 62 T^{2} + 223 T^{3} + 1798 T^{4} + 5887 T^{5} + 24389 T^{6} \))(\( 1 - 3 T + 54 T^{2} - 211 T^{3} + 1566 T^{4} - 2523 T^{5} + 24389 T^{6} \))(\( 1 - 7 T + 62 T^{2} - 223 T^{3} + 1798 T^{4} - 5887 T^{5} + 24389 T^{6} \))(\( 1 + 6 T + 71 T^{2} + 284 T^{3} + 2059 T^{4} + 5046 T^{5} + 24389 T^{6} \))(\( 1 - 4 T + 96 T^{2} - 284 T^{3} + 3918 T^{4} - 8236 T^{5} + 80736 T^{6} - 97556 T^{7} + 707281 T^{8} \))(\( 1 + 13 T + 179 T^{2} + 1462 T^{3} + 11301 T^{4} + 62963 T^{5} + 327729 T^{6} + 1229542 T^{7} + 4365631 T^{8} + 9194653 T^{9} + 20511149 T^{10} \))(\( 1 - 13 T + 179 T^{2} - 1462 T^{3} + 11301 T^{4} - 62963 T^{5} + 327729 T^{6} - 1229542 T^{7} + 4365631 T^{8} - 9194653 T^{9} + 20511149 T^{10} \))(\( 1 - 10 T + 113 T^{2} - 764 T^{3} + 5690 T^{4} - 28884 T^{5} + 165010 T^{6} - 642524 T^{7} + 2755957 T^{8} - 7072810 T^{9} + 20511149 T^{10} \))(\( 1 + 10 T + 113 T^{2} + 764 T^{3} + 5690 T^{4} + 28884 T^{5} + 165010 T^{6} + 642524 T^{7} + 2755957 T^{8} + 7072810 T^{9} + 20511149 T^{10} \))(\( 1 + 4 T + 98 T^{2} + 192 T^{3} + 4807 T^{4} + 7804 T^{5} + 173048 T^{6} + 226316 T^{7} + 4042687 T^{8} + 4682688 T^{9} + 69313538 T^{10} + 82044596 T^{11} + 594823321 T^{12} \))(\( 1 - 4 T + 98 T^{2} - 192 T^{3} + 4807 T^{4} - 7804 T^{5} + 173048 T^{6} - 226316 T^{7} + 4042687 T^{8} - 4682688 T^{9} + 69313538 T^{10} - 82044596 T^{11} + 594823321 T^{12} \))(\( 1 - 6 T + 102 T^{2} - 251 T^{3} + 2760 T^{4} + 6351 T^{5} + 34994 T^{6} + 266010 T^{7} + 2440869 T^{8} + 982303 T^{9} + 70785201 T^{10} + 223714410 T^{11} + 853468666 T^{12} + 4491941631 T^{13} + 56610771240 T^{14} - 149300653571 T^{15} + 1759487383518 T^{16} - 3001478477766 T^{17} + 14507145975869 T^{18} \))(\( 1 - 6 T + 132 T^{2} - 831 T^{3} + 10080 T^{4} - 57351 T^{5} + 535326 T^{6} - 2682294 T^{7} + 20510667 T^{8} - 91215989 T^{9} + 594809343 T^{10} - 2255809254 T^{11} + 13056065814 T^{12} - 40563272631 T^{13} + 206752381920 T^{14} - 494298179751 T^{15} + 2276983672788 T^{16} - 3001478477766 T^{17} + 14507145975869 T^{18} \))(\( 1 + 6 T + 132 T^{2} + 831 T^{3} + 10080 T^{4} + 57351 T^{5} + 535326 T^{6} + 2682294 T^{7} + 20510667 T^{8} + 91215989 T^{9} + 594809343 T^{10} + 2255809254 T^{11} + 13056065814 T^{12} + 40563272631 T^{13} + 206752381920 T^{14} + 494298179751 T^{15} + 2276983672788 T^{16} + 3001478477766 T^{17} + 14507145975869 T^{18} \))(\( 1 + 6 T + 102 T^{2} + 251 T^{3} + 2760 T^{4} - 6351 T^{5} + 34994 T^{6} - 266010 T^{7} + 2440869 T^{8} - 982303 T^{9} + 70785201 T^{10} - 223714410 T^{11} + 853468666 T^{12} - 4491941631 T^{13} + 56610771240 T^{14} + 149300653571 T^{15} + 1759487383518 T^{16} + 3001478477766 T^{17} + 14507145975869 T^{18} \))(\( 1 - 12 T + 198 T^{2} - 1456 T^{3} + 14165 T^{4} - 72764 T^{5} + 566532 T^{6} - 2255812 T^{7} + 17573058 T^{8} - 62716532 T^{9} + 518204236 T^{10} - 1818779428 T^{11} + 14778941778 T^{12} - 55016998868 T^{13} + 400697319492 T^{14} - 1492473245836 T^{15} + 8425672341965 T^{16} - 25115819905904 T^{17} + 99048789766278 T^{18} - 174085751710428 T^{19} + 420707233300201 T^{20} \))(\( 1 + 12 T + 198 T^{2} + 1456 T^{3} + 14165 T^{4} + 72764 T^{5} + 566532 T^{6} + 2255812 T^{7} + 17573058 T^{8} + 62716532 T^{9} + 518204236 T^{10} + 1818779428 T^{11} + 14778941778 T^{12} + 55016998868 T^{13} + 400697319492 T^{14} + 1492473245836 T^{15} + 8425672341965 T^{16} + 25115819905904 T^{17} + 99048789766278 T^{18} + 174085751710428 T^{19} + 420707233300201 T^{20} \))(\( 1 + 18 T + 426 T^{2} + 5375 T^{3} + 75576 T^{4} + 755505 T^{5} + 8035995 T^{6} + 67732674 T^{7} + 596339163 T^{8} + 4388002924 T^{9} + 33411366135 T^{10} + 218829823737 T^{11} + 1475157312449 T^{12} + 8687911542849 T^{13} + 52515614429133 T^{14} + 279272238304299 T^{15} + 1522952818444857 T^{16} + 7306533607536009 T^{17} + 35977611693318661 T^{18} + 154774176562529097 T^{19} + 685305509088539115 T^{20} + 2610086471811390604 T^{21} + 10286776799962589367 T^{22} + 33883027208756787714 T^{23} + \)\(11\!\cdots\!55\)\( T^{24} + \)\(31\!\cdots\!05\)\( T^{25} + \)\(92\!\cdots\!04\)\( T^{26} + \)\(19\!\cdots\!75\)\( T^{27} + \)\(43\!\cdots\!14\)\( T^{28} + \)\(53\!\cdots\!58\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 + 18 T + 288 T^{2} + 3103 T^{3} + 31908 T^{4} + 263895 T^{5} + 2124743 T^{6} + 14603238 T^{7} + 100163595 T^{8} + 604160260 T^{9} + 3738908169 T^{10} + 20724355887 T^{11} + 121333825449 T^{12} + 642349536087 T^{13} + 3665137866537 T^{14} + 18951976793267 T^{15} + 106288998129573 T^{16} + 540215959849167 T^{17} + 2959210668875661 T^{18} + 14657943156113247 T^{19} + 76689302551676181 T^{20} + 359368612269423460 T^{21} + 1727809624414770855 T^{22} + 7305217427115767718 T^{23} + 30823956862205826667 T^{24} + \)\(11\!\cdots\!95\)\( T^{25} + \)\(38\!\cdots\!32\)\( T^{26} + \)\(10\!\cdots\!23\)\( T^{27} + \)\(29\!\cdots\!32\)\( T^{28} + \)\(53\!\cdots\!58\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 - 18 T + 288 T^{2} - 3103 T^{3} + 31908 T^{4} - 263895 T^{5} + 2124743 T^{6} - 14603238 T^{7} + 100163595 T^{8} - 604160260 T^{9} + 3738908169 T^{10} - 20724355887 T^{11} + 121333825449 T^{12} - 642349536087 T^{13} + 3665137866537 T^{14} - 18951976793267 T^{15} + 106288998129573 T^{16} - 540215959849167 T^{17} + 2959210668875661 T^{18} - 14657943156113247 T^{19} + 76689302551676181 T^{20} - 359368612269423460 T^{21} + 1727809624414770855 T^{22} - 7305217427115767718 T^{23} + 30823956862205826667 T^{24} - \)\(11\!\cdots\!95\)\( T^{25} + \)\(38\!\cdots\!32\)\( T^{26} - \)\(10\!\cdots\!23\)\( T^{27} + \)\(29\!\cdots\!32\)\( T^{28} - \)\(53\!\cdots\!58\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 - 18 T + 426 T^{2} - 5375 T^{3} + 75576 T^{4} - 755505 T^{5} + 8035995 T^{6} - 67732674 T^{7} + 596339163 T^{8} - 4388002924 T^{9} + 33411366135 T^{10} - 218829823737 T^{11} + 1475157312449 T^{12} - 8687911542849 T^{13} + 52515614429133 T^{14} - 279272238304299 T^{15} + 1522952818444857 T^{16} - 7306533607536009 T^{17} + 35977611693318661 T^{18} - 154774176562529097 T^{19} + 685305509088539115 T^{20} - 2610086471811390604 T^{21} + 10286776799962589367 T^{22} - 33883027208756787714 T^{23} + \)\(11\!\cdots\!55\)\( T^{24} - \)\(31\!\cdots\!05\)\( T^{25} + \)\(92\!\cdots\!04\)\( T^{26} - \)\(19\!\cdots\!75\)\( T^{27} + \)\(43\!\cdots\!14\)\( T^{28} - \)\(53\!\cdots\!58\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 - 16 T + 364 T^{2} - 4488 T^{3} + 61378 T^{4} - 623576 T^{5} + 6544952 T^{6} - 57109296 T^{7} + 501759624 T^{8} - 3860240176 T^{9} + 29581317928 T^{10} - 203974333736 T^{11} + 1393802386954 T^{12} - 8698591173272 T^{13} + 53667338656628 T^{14} - 304694610347440 T^{15} + 1708505654486606 T^{16} - 8836143700075760 T^{17} + 45134231810224148 T^{18} - 212149940124930808 T^{19} + 985809946047212074 T^{20} - 4183747951434822664 T^{21} + 17595657769489798888 T^{22} - 66588665559032390384 T^{23} + \)\(25\!\cdots\!64\)\( T^{24} - \)\(82\!\cdots\!24\)\( T^{25} + \)\(27\!\cdots\!52\)\( T^{26} - \)\(76\!\cdots\!04\)\( T^{27} + \)\(21\!\cdots\!98\)\( T^{28} - \)\(46\!\cdots\!32\)\( T^{29} + \)\(10\!\cdots\!84\)\( T^{30} - \)\(13\!\cdots\!84\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 16 T + 364 T^{2} + 4488 T^{3} + 61378 T^{4} + 623576 T^{5} + 6544952 T^{6} + 57109296 T^{7} + 501759624 T^{8} + 3860240176 T^{9} + 29581317928 T^{10} + 203974333736 T^{11} + 1393802386954 T^{12} + 8698591173272 T^{13} + 53667338656628 T^{14} + 304694610347440 T^{15} + 1708505654486606 T^{16} + 8836143700075760 T^{17} + 45134231810224148 T^{18} + 212149940124930808 T^{19} + 985809946047212074 T^{20} + 4183747951434822664 T^{21} + 17595657769489798888 T^{22} + 66588665559032390384 T^{23} + \)\(25\!\cdots\!64\)\( T^{24} + \)\(82\!\cdots\!24\)\( T^{25} + \)\(27\!\cdots\!52\)\( T^{26} + \)\(76\!\cdots\!04\)\( T^{27} + \)\(21\!\cdots\!98\)\( T^{28} + \)\(46\!\cdots\!32\)\( T^{29} + \)\(10\!\cdots\!84\)\( T^{30} + \)\(13\!\cdots\!84\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 6 T + 68 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 - 36 T^{2} + 961 T^{4} \))(\( 1 + 6 T + 58 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 58 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + T + 28 T^{2} - 107 T^{3} + 868 T^{4} + 961 T^{5} + 29791 T^{6} \))(\( 1 + 2 T + 81 T^{2} + 134 T^{3} + 2511 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 - T + 28 T^{2} + 107 T^{3} + 868 T^{4} - 961 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 81 T^{2} - 134 T^{3} + 2511 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 - 3 T + 84 T^{2} - 183 T^{3} + 2604 T^{4} - 2883 T^{5} + 29791 T^{6} \))(\( 1 - T + 76 T^{2} - 69 T^{3} + 2356 T^{4} - 961 T^{5} + 29791 T^{6} \))(\( 1 + 3 T + 84 T^{2} + 183 T^{3} + 2604 T^{4} + 2883 T^{5} + 29791 T^{6} \))(\( 1 + T + 76 T^{2} + 69 T^{3} + 2356 T^{4} + 961 T^{5} + 29791 T^{6} \))(\( 1 - 14 T + 151 T^{2} - 932 T^{3} + 4681 T^{4} - 13454 T^{5} + 29791 T^{6} \))(\( 1 - 4 T + 30 T^{2} - 212 T^{3} + 2114 T^{4} - 6572 T^{5} + 28830 T^{6} - 119164 T^{7} + 923521 T^{8} \))(\( 1 + 13 T + 124 T^{2} + 843 T^{3} + 6245 T^{4} + 36412 T^{5} + 193595 T^{6} + 810123 T^{7} + 3694084 T^{8} + 12005773 T^{9} + 28629151 T^{10} \))(\( 1 - 13 T + 124 T^{2} - 843 T^{3} + 6245 T^{4} - 36412 T^{5} + 193595 T^{6} - 810123 T^{7} + 3694084 T^{8} - 12005773 T^{9} + 28629151 T^{10} \))(\( 1 + 14 T + 159 T^{2} + 1298 T^{3} + 9310 T^{4} + 53312 T^{5} + 288610 T^{6} + 1247378 T^{7} + 4736769 T^{8} + 12929294 T^{9} + 28629151 T^{10} \))(\( 1 - 14 T + 159 T^{2} - 1298 T^{3} + 9310 T^{4} - 53312 T^{5} + 288610 T^{6} - 1247378 T^{7} + 4736769 T^{8} - 12929294 T^{9} + 28629151 T^{10} \))(\( 1 + 78 T^{2} + 152 T^{3} + 3881 T^{4} + 9196 T^{5} + 136942 T^{6} + 285076 T^{7} + 3729641 T^{8} + 4528232 T^{9} + 72034638 T^{10} + 887503681 T^{12} \))(\( 1 + 78 T^{2} - 152 T^{3} + 3881 T^{4} - 9196 T^{5} + 136942 T^{6} - 285076 T^{7} + 3729641 T^{8} - 4528232 T^{9} + 72034638 T^{10} + 887503681 T^{12} \))(\( 1 - 30 T + 609 T^{2} - 8974 T^{3} + 107898 T^{4} - 1084593 T^{5} + 9406978 T^{6} - 71179788 T^{7} + 475092744 T^{8} - 2807835099 T^{9} + 14727875064 T^{10} - 68403776268 T^{11} + 280243281598 T^{12} - 1001644411953 T^{13} + 3089028134598 T^{14} - 7964458033294 T^{15} + 16755181993599 T^{16} - 25586731123230 T^{17} + 26439622160671 T^{18} \))(\( 1 - 30 T + 573 T^{2} - 7854 T^{3} + 87882 T^{4} - 825699 T^{5} + 6795186 T^{6} - 49346844 T^{7} + 322028472 T^{8} - 1885250961 T^{9} + 9982882632 T^{10} - 47422317084 T^{11} + 202435386126 T^{12} - 762550366179 T^{13} + 2515987048182 T^{14} - 6970453910574 T^{15} + 15764727885603 T^{16} - 25586731123230 T^{17} + 26439622160671 T^{18} \))(\( 1 + 30 T + 573 T^{2} + 7854 T^{3} + 87882 T^{4} + 825699 T^{5} + 6795186 T^{6} + 49346844 T^{7} + 322028472 T^{8} + 1885250961 T^{9} + 9982882632 T^{10} + 47422317084 T^{11} + 202435386126 T^{12} + 762550366179 T^{13} + 2515987048182 T^{14} + 6970453910574 T^{15} + 15764727885603 T^{16} + 25586731123230 T^{17} + 26439622160671 T^{18} \))(\( 1 + 30 T + 609 T^{2} + 8974 T^{3} + 107898 T^{4} + 1084593 T^{5} + 9406978 T^{6} + 71179788 T^{7} + 475092744 T^{8} + 2807835099 T^{9} + 14727875064 T^{10} + 68403776268 T^{11} + 280243281598 T^{12} + 1001644411953 T^{13} + 3089028134598 T^{14} + 7964458033294 T^{15} + 16755181993599 T^{16} + 25586731123230 T^{17} + 26439622160671 T^{18} \))(\( 1 - 8 T + 226 T^{2} - 1720 T^{3} + 24503 T^{4} - 171780 T^{5} + 1694106 T^{6} - 10617756 T^{7} + 82792512 T^{8} - 454248264 T^{9} + 2976826232 T^{10} - 14081696184 T^{11} + 79563604032 T^{12} - 316313568996 T^{13} + 1564542467226 T^{14} - 4917915558780 T^{15} + 21746502695543 T^{16} - 47321696270920 T^{17} + 192753374461666 T^{18} - 211516977285368 T^{19} + 819628286980801 T^{20} \))(\( 1 + 8 T + 226 T^{2} + 1720 T^{3} + 24503 T^{4} + 171780 T^{5} + 1694106 T^{6} + 10617756 T^{7} + 82792512 T^{8} + 454248264 T^{9} + 2976826232 T^{10} + 14081696184 T^{11} + 79563604032 T^{12} + 316313568996 T^{13} + 1564542467226 T^{14} + 4917915558780 T^{15} + 21746502695543 T^{16} + 47321696270920 T^{17} + 192753374461666 T^{18} + 211516977285368 T^{19} + 819628286980801 T^{20} \))(\( 1 + 18 T + 423 T^{2} + 5662 T^{3} + 80601 T^{4} + 874053 T^{5} + 9524957 T^{6} + 87512742 T^{7} + 792431397 T^{8} + 6332755610 T^{9} + 49515846945 T^{10} + 349707988392 T^{11} + 2409592174119 T^{12} + 15177825115455 T^{13} + 93167409596001 T^{14} + 525552815261832 T^{15} + 2888189697476031 T^{16} + 14585889935952255 T^{17} + 71784160459179129 T^{18} + 322962671147768232 T^{19} + 1417596659081293695 T^{20} + 5620343914748400410 T^{21} + 21801859235101643067 T^{22} + 74638833313686573222 T^{23} + \)\(25\!\cdots\!47\)\( T^{24} + \)\(71\!\cdots\!53\)\( T^{25} + \)\(20\!\cdots\!31\)\( T^{26} + \)\(44\!\cdots\!82\)\( T^{27} + \)\(10\!\cdots\!93\)\( T^{28} + \)\(13\!\cdots\!78\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 + 18 T + 339 T^{2} + 4150 T^{3} + 47481 T^{4} + 440379 T^{5} + 3729097 T^{6} + 27201510 T^{7} + 177677973 T^{8} + 996899898 T^{9} + 4702681845 T^{10} + 16271492172 T^{11} + 18293251895 T^{12} - 308798431095 T^{13} - 3386504114667 T^{14} - 22424168869808 T^{15} - 104981627554677 T^{16} - 296755292282295 T^{17} + 544974267203945 T^{18} + 15027064722177612 T^{19} + 134633788645463595 T^{20} + 884752329063524538 T^{21} + 4888385507173677003 T^{22} + 23199924083861735910 T^{23} + 98595915680491744087 T^{24} + \)\(36\!\cdots\!79\)\( T^{25} + \)\(12\!\cdots\!11\)\( T^{26} + \)\(32\!\cdots\!50\)\( T^{27} + \)\(82\!\cdots\!49\)\( T^{28} + \)\(13\!\cdots\!78\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 - 18 T + 339 T^{2} - 4150 T^{3} + 47481 T^{4} - 440379 T^{5} + 3729097 T^{6} - 27201510 T^{7} + 177677973 T^{8} - 996899898 T^{9} + 4702681845 T^{10} - 16271492172 T^{11} + 18293251895 T^{12} + 308798431095 T^{13} - 3386504114667 T^{14} + 22424168869808 T^{15} - 104981627554677 T^{16} + 296755292282295 T^{17} + 544974267203945 T^{18} - 15027064722177612 T^{19} + 134633788645463595 T^{20} - 884752329063524538 T^{21} + 4888385507173677003 T^{22} - 23199924083861735910 T^{23} + 98595915680491744087 T^{24} - \)\(36\!\cdots\!79\)\( T^{25} + \)\(12\!\cdots\!11\)\( T^{26} - \)\(32\!\cdots\!50\)\( T^{27} + \)\(82\!\cdots\!49\)\( T^{28} - \)\(13\!\cdots\!78\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 - 18 T + 423 T^{2} - 5662 T^{3} + 80601 T^{4} - 874053 T^{5} + 9524957 T^{6} - 87512742 T^{7} + 792431397 T^{8} - 6332755610 T^{9} + 49515846945 T^{10} - 349707988392 T^{11} + 2409592174119 T^{12} - 15177825115455 T^{13} + 93167409596001 T^{14} - 525552815261832 T^{15} + 2888189697476031 T^{16} - 14585889935952255 T^{17} + 71784160459179129 T^{18} - 322962671147768232 T^{19} + 1417596659081293695 T^{20} - 5620343914748400410 T^{21} + 21801859235101643067 T^{22} - 74638833313686573222 T^{23} + \)\(25\!\cdots\!47\)\( T^{24} - \)\(71\!\cdots\!53\)\( T^{25} + \)\(20\!\cdots\!31\)\( T^{26} - \)\(44\!\cdots\!82\)\( T^{27} + \)\(10\!\cdots\!93\)\( T^{28} - \)\(13\!\cdots\!78\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 - 8 T + 284 T^{2} - 2368 T^{3} + 41172 T^{4} - 344080 T^{5} + 4041364 T^{6} - 32696536 T^{7} + 299905218 T^{8} - 2282370424 T^{9} + 17758847064 T^{10} - 124605496312 T^{11} + 862772719594 T^{12} - 5526882242552 T^{13} + 34874280457664 T^{14} - 203805472796152 T^{15} + 1180368719787118 T^{16} - 6317969656680712 T^{17} + 33514183519815104 T^{18} - 164651348887866632 T^{19} + 796788724772170474 T^{20} - 3567349569346191112 T^{21} + 15761042139616042584 T^{22} - 62793976733871453064 T^{23} + \)\(25\!\cdots\!38\)\( T^{24} - \)\(86\!\cdots\!56\)\( T^{25} + \)\(33\!\cdots\!64\)\( T^{26} - \)\(87\!\cdots\!80\)\( T^{27} + \)\(32\!\cdots\!92\)\( T^{28} - \)\(57\!\cdots\!88\)\( T^{29} + \)\(21\!\cdots\!64\)\( T^{30} - \)\(18\!\cdots\!08\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 + 8 T + 284 T^{2} + 2368 T^{3} + 41172 T^{4} + 344080 T^{5} + 4041364 T^{6} + 32696536 T^{7} + 299905218 T^{8} + 2282370424 T^{9} + 17758847064 T^{10} + 124605496312 T^{11} + 862772719594 T^{12} + 5526882242552 T^{13} + 34874280457664 T^{14} + 203805472796152 T^{15} + 1180368719787118 T^{16} + 6317969656680712 T^{17} + 33514183519815104 T^{18} + 164651348887866632 T^{19} + 796788724772170474 T^{20} + 3567349569346191112 T^{21} + 15761042139616042584 T^{22} + 62793976733871453064 T^{23} + \)\(25\!\cdots\!38\)\( T^{24} + \)\(86\!\cdots\!56\)\( T^{25} + \)\(33\!\cdots\!64\)\( T^{26} + \)\(87\!\cdots\!80\)\( T^{27} + \)\(32\!\cdots\!92\)\( T^{28} + \)\(57\!\cdots\!88\)\( T^{29} + \)\(21\!\cdots\!64\)\( T^{30} + \)\(18\!\cdots\!08\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))
$37$ (\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 6 T + 80 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( ( 1 + 5 T + 37 T^{2} )^{2} \))(\( ( 1 - 5 T + 37 T^{2} )^{2} \))(\( 1 - T + 25 T^{2} - 325 T^{3} + 925 T^{4} - 1369 T^{5} + 50653 T^{6} \))(\( 1 - 8 T + 109 T^{2} - 566 T^{3} + 4033 T^{4} - 10952 T^{5} + 50653 T^{6} \))(\( 1 + T + 25 T^{2} + 325 T^{3} + 925 T^{4} + 1369 T^{5} + 50653 T^{6} \))(\( 1 + 8 T + 109 T^{2} + 566 T^{3} + 4033 T^{4} + 10952 T^{5} + 50653 T^{6} \))(\( 1 + 3 T + 21 T^{2} + 111 T^{3} + 777 T^{4} + 4107 T^{5} + 50653 T^{6} \))(\( 1 + T - 7 T^{2} - 35 T^{3} - 259 T^{4} + 1369 T^{5} + 50653 T^{6} \))(\( 1 - 3 T + 21 T^{2} - 111 T^{3} + 777 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 - T - 7 T^{2} + 35 T^{3} - 259 T^{4} - 1369 T^{5} + 50653 T^{6} \))(\( 1 - 4 T + 61 T^{2} - 364 T^{3} + 2257 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 + 106 T^{2} - 56 T^{3} + 5114 T^{4} - 2072 T^{5} + 145114 T^{6} + 1874161 T^{8} \))(\( 1 + 11 T + 206 T^{2} + 1612 T^{3} + 15973 T^{4} + 89153 T^{5} + 591001 T^{6} + 2206828 T^{7} + 10434518 T^{8} + 20615771 T^{9} + 69343957 T^{10} \))(\( 1 - 11 T + 206 T^{2} - 1612 T^{3} + 15973 T^{4} - 89153 T^{5} + 591001 T^{6} - 2206828 T^{7} + 10434518 T^{8} - 20615771 T^{9} + 69343957 T^{10} \))(\( 1 + 4 T + 107 T^{2} + 114 T^{3} + 4280 T^{4} - 2740 T^{5} + 158360 T^{6} + 156066 T^{7} + 5419871 T^{8} + 7496644 T^{9} + 69343957 T^{10} \))(\( 1 - 4 T + 107 T^{2} - 114 T^{3} + 4280 T^{4} + 2740 T^{5} + 158360 T^{6} - 156066 T^{7} + 5419871 T^{8} - 7496644 T^{9} + 69343957 T^{10} \))(\( 1 - 16 T + 210 T^{2} - 1828 T^{3} + 14683 T^{4} - 98340 T^{5} + 639542 T^{6} - 3638580 T^{7} + 20101027 T^{8} - 92593684 T^{9} + 393573810 T^{10} - 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 + 16 T + 210 T^{2} + 1828 T^{3} + 14683 T^{4} + 98340 T^{5} + 639542 T^{6} + 3638580 T^{7} + 20101027 T^{8} + 92593684 T^{9} + 393573810 T^{10} + 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 - 12 T + 297 T^{2} - 2615 T^{3} + 36708 T^{4} - 253005 T^{5} + 2634143 T^{6} - 14959179 T^{7} + 129555237 T^{8} - 634181501 T^{9} + 4793543769 T^{10} - 20479116051 T^{11} + 133427245379 T^{12} - 474172103805 T^{13} + 2545477973556 T^{14} - 6709374559535 T^{15} + 28194767508501 T^{16} - 42149753447052 T^{17} + 129961739795077 T^{18} \))(\( 1 - 12 T + 249 T^{2} - 2241 T^{3} + 28464 T^{4} - 207651 T^{5} + 2017707 T^{6} - 12475077 T^{7} + 100742817 T^{8} - 536816091 T^{9} + 3727484229 T^{10} - 17078380413 T^{11} + 102202912671 T^{12} - 389171405811 T^{13} + 1973806392048 T^{14} - 5749792882569 T^{15} + 23638037406117 T^{16} - 42149753447052 T^{17} + 129961739795077 T^{18} \))(\( 1 + 12 T + 249 T^{2} + 2241 T^{3} + 28464 T^{4} + 207651 T^{5} + 2017707 T^{6} + 12475077 T^{7} + 100742817 T^{8} + 536816091 T^{9} + 3727484229 T^{10} + 17078380413 T^{11} + 102202912671 T^{12} + 389171405811 T^{13} + 1973806392048 T^{14} + 5749792882569 T^{15} + 23638037406117 T^{16} + 42149753447052 T^{17} + 129961739795077 T^{18} \))(\( 1 + 12 T + 297 T^{2} + 2615 T^{3} + 36708 T^{4} + 253005 T^{5} + 2634143 T^{6} + 14959179 T^{7} + 129555237 T^{8} + 634181501 T^{9} + 4793543769 T^{10} + 20479116051 T^{11} + 133427245379 T^{12} + 474172103805 T^{13} + 2545477973556 T^{14} + 6709374559535 T^{15} + 28194767508501 T^{16} + 42149753447052 T^{17} + 129961739795077 T^{18} \))(\( 1 + 24 T + 474 T^{2} + 6436 T^{3} + 77341 T^{4} + 767756 T^{5} + 7014090 T^{6} + 56345492 T^{7} + 424419818 T^{8} + 2877734884 T^{9} + 18400003200 T^{10} + 106476190708 T^{11} + 581030730842 T^{12} + 2854068206276 T^{13} + 13145533928490 T^{14} + 53239239050492 T^{15} + 198435846198469 T^{16} + 610981561227988 T^{17} + 1664915261158554 T^{18} + 3119081755081848 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 24 T + 474 T^{2} - 6436 T^{3} + 77341 T^{4} - 767756 T^{5} + 7014090 T^{6} - 56345492 T^{7} + 424419818 T^{8} - 2877734884 T^{9} + 18400003200 T^{10} - 106476190708 T^{11} + 581030730842 T^{12} - 2854068206276 T^{13} + 13145533928490 T^{14} - 53239239050492 T^{15} + 198435846198469 T^{16} - 610981561227988 T^{17} + 1664915261158554 T^{18} - 3119081755081848 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 24 T + 501 T^{2} + 7329 T^{3} + 98196 T^{4} + 1109751 T^{5} + 11763156 T^{6} + 111779427 T^{7} + 1009936434 T^{8} + 8414512810 T^{9} + 67196472039 T^{10} + 502096771278 T^{11} + 3612070486941 T^{12} + 24497686531656 T^{13} + 160329804558228 T^{14} + 992450717932221 T^{15} + 5932202768654436 T^{16} + 33537332861837064 T^{17} + 182962206375022473 T^{18} + 941010186955147758 T^{19} + 4659669267624118323 T^{20} + 21589337735485799290 T^{21} + 95875161464628163722 T^{22} + \)\(39\!\cdots\!67\)\( T^{23} + \)\(15\!\cdots\!12\)\( T^{24} + \)\(53\!\cdots\!99\)\( T^{25} + \)\(17\!\cdots\!48\)\( T^{26} + \)\(48\!\cdots\!49\)\( T^{27} + \)\(12\!\cdots\!97\)\( T^{28} + \)\(21\!\cdots\!36\)\( T^{29} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 + 93 T^{2} + 191 T^{3} + 7680 T^{4} + 20265 T^{5} + 461504 T^{6} + 1718085 T^{7} + 25551414 T^{8} + 104187070 T^{9} + 1234700295 T^{10} + 5344395234 T^{11} + 56303678893 T^{12} + 230356588824 T^{13} + 2286075894780 T^{14} + 9122378492099 T^{15} + 84584808106860 T^{16} + 315358170100056 T^{17} + 2851950246967129 T^{18} + 10016257116148674 T^{19} + 85619004164367315 T^{20} + 267315516975331630 T^{21} + 2425643694422416062 T^{22} + 6034738262589861285 T^{23} + 59977862762387215808 T^{24} + 97445962307047709985 T^{25} + \)\(13\!\cdots\!40\)\( T^{26} + \)\(12\!\cdots\!71\)\( T^{27} + \)\(22\!\cdots\!21\)\( T^{28} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 + 93 T^{2} - 191 T^{3} + 7680 T^{4} - 20265 T^{5} + 461504 T^{6} - 1718085 T^{7} + 25551414 T^{8} - 104187070 T^{9} + 1234700295 T^{10} - 5344395234 T^{11} + 56303678893 T^{12} - 230356588824 T^{13} + 2286075894780 T^{14} - 9122378492099 T^{15} + 84584808106860 T^{16} - 315358170100056 T^{17} + 2851950246967129 T^{18} - 10016257116148674 T^{19} + 85619004164367315 T^{20} - 267315516975331630 T^{21} + 2425643694422416062 T^{22} - 6034738262589861285 T^{23} + 59977862762387215808 T^{24} - 97445962307047709985 T^{25} + \)\(13\!\cdots\!40\)\( T^{26} - \)\(12\!\cdots\!71\)\( T^{27} + \)\(22\!\cdots\!21\)\( T^{28} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 - 24 T + 501 T^{2} - 7329 T^{3} + 98196 T^{4} - 1109751 T^{5} + 11763156 T^{6} - 111779427 T^{7} + 1009936434 T^{8} - 8414512810 T^{9} + 67196472039 T^{10} - 502096771278 T^{11} + 3612070486941 T^{12} - 24497686531656 T^{13} + 160329804558228 T^{14} - 992450717932221 T^{15} + 5932202768654436 T^{16} - 33537332861837064 T^{17} + 182962206375022473 T^{18} - 941010186955147758 T^{19} + 4659669267624118323 T^{20} - 21589337735485799290 T^{21} + 95875161464628163722 T^{22} - \)\(39\!\cdots\!67\)\( T^{23} + \)\(15\!\cdots\!12\)\( T^{24} - \)\(53\!\cdots\!99\)\( T^{25} + \)\(17\!\cdots\!48\)\( T^{26} - \)\(48\!\cdots\!49\)\( T^{27} + \)\(12\!\cdots\!97\)\( T^{28} - \)\(21\!\cdots\!36\)\( T^{29} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 - 32 T + 844 T^{2} - 15816 T^{3} + 259018 T^{4} - 3586360 T^{5} + 44924784 T^{6} - 503410256 T^{7} + 5209581936 T^{8} - 49520039408 T^{9} + 440368534016 T^{10} - 3650182313736 T^{11} + 28540634729592 T^{12} - 209791843144152 T^{13} + 1461997225902308 T^{14} - 9622169517939392 T^{15} + 60182926938134846 T^{16} - 356020272163757504 T^{17} + 2001474202260259652 T^{18} - 10626586230780731256 T^{19} + 53489744525446872312 T^{20} - \)\(25\!\cdots\!52\)\( T^{21} + \)\(11\!\cdots\!44\)\( T^{22} - \)\(47\!\cdots\!64\)\( T^{23} + \)\(18\!\cdots\!56\)\( T^{24} - \)\(65\!\cdots\!12\)\( T^{25} + \)\(21\!\cdots\!16\)\( T^{26} - \)\(63\!\cdots\!80\)\( T^{27} + \)\(17\!\cdots\!58\)\( T^{28} - \)\(38\!\cdots\!52\)\( T^{29} + \)\(76\!\cdots\!16\)\( T^{30} - \)\(10\!\cdots\!76\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 + 32 T + 844 T^{2} + 15816 T^{3} + 259018 T^{4} + 3586360 T^{5} + 44924784 T^{6} + 503410256 T^{7} + 5209581936 T^{8} + 49520039408 T^{9} + 440368534016 T^{10} + 3650182313736 T^{11} + 28540634729592 T^{12} + 209791843144152 T^{13} + 1461997225902308 T^{14} + 9622169517939392 T^{15} + 60182926938134846 T^{16} + 356020272163757504 T^{17} + 2001474202260259652 T^{18} + 10626586230780731256 T^{19} + 53489744525446872312 T^{20} + \)\(25\!\cdots\!52\)\( T^{21} + \)\(11\!\cdots\!44\)\( T^{22} + \)\(47\!\cdots\!64\)\( T^{23} + \)\(18\!\cdots\!56\)\( T^{24} + \)\(65\!\cdots\!12\)\( T^{25} + \)\(21\!\cdots\!16\)\( T^{26} + \)\(63\!\cdots\!80\)\( T^{27} + \)\(17\!\cdots\!58\)\( T^{28} + \)\(38\!\cdots\!52\)\( T^{29} + \)\(76\!\cdots\!16\)\( T^{30} + \)\(10\!\cdots\!76\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))
$41$ (\( 1 + 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 - 20 T + 179 T^{2} - 820 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 41 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( 1 - 7 T + 109 T^{2} - 567 T^{3} + 4469 T^{4} - 11767 T^{5} + 68921 T^{6} \))(\( 1 - 7 T + 136 T^{2} - 579 T^{3} + 5576 T^{4} - 11767 T^{5} + 68921 T^{6} \))(\( 1 + 7 T + 109 T^{2} + 567 T^{3} + 4469 T^{4} + 11767 T^{5} + 68921 T^{6} \))(\( 1 + 7 T + 136 T^{2} + 579 T^{3} + 5576 T^{4} + 11767 T^{5} + 68921 T^{6} \))(\( 1 - 15 T + 159 T^{2} - 1249 T^{3} + 6519 T^{4} - 25215 T^{5} + 68921 T^{6} \))(\( 1 + 3 T + 73 T^{2} + 99 T^{3} + 2993 T^{4} + 5043 T^{5} + 68921 T^{6} \))(\( 1 + 15 T + 159 T^{2} + 1249 T^{3} + 6519 T^{4} + 25215 T^{5} + 68921 T^{6} \))(\( 1 - 3 T + 73 T^{2} - 99 T^{3} + 2993 T^{4} - 5043 T^{5} + 68921 T^{6} \))(\( 1 + 14 T + 184 T^{2} + 1230 T^{3} + 7544 T^{4} + 23534 T^{5} + 68921 T^{6} \))(\( 1 - 18 T + 207 T^{2} - 1578 T^{3} + 10824 T^{4} - 64698 T^{5} + 347967 T^{6} - 1240578 T^{7} + 2825761 T^{8} \))(\( 1 - T + 113 T^{2} + 75 T^{3} + 6090 T^{4} + 9636 T^{5} + 249690 T^{6} + 126075 T^{7} + 7788073 T^{8} - 2825761 T^{9} + 115856201 T^{10} \))(\( 1 + T + 113 T^{2} - 75 T^{3} + 6090 T^{4} - 9636 T^{5} + 249690 T^{6} - 126075 T^{7} + 7788073 T^{8} + 2825761 T^{9} + 115856201 T^{10} \))(\( 1 + T + 90 T^{2} + 347 T^{3} + 4385 T^{4} + 21280 T^{5} + 179785 T^{6} + 583307 T^{7} + 6202890 T^{8} + 2825761 T^{9} + 115856201 T^{10} \))(\( 1 - T + 90 T^{2} - 347 T^{3} + 4385 T^{4} - 21280 T^{5} + 179785 T^{6} - 583307 T^{7} + 6202890 T^{8} - 2825761 T^{9} + 115856201 T^{10} \))(\( 1 - 18 T + 331 T^{2} - 3630 T^{3} + 38410 T^{4} - 295698 T^{5} + 2175241 T^{6} - 12123618 T^{7} + 64567210 T^{8} - 250183230 T^{9} + 935326891 T^{10} - 2085411618 T^{11} + 4750104241 T^{12} \))(\( 1 + 18 T + 331 T^{2} + 3630 T^{3} + 38410 T^{4} + 295698 T^{5} + 2175241 T^{6} + 12123618 T^{7} + 64567210 T^{8} + 250183230 T^{9} + 935326891 T^{10} + 2085411618 T^{11} + 4750104241 T^{12} \))(\( 1 - 9 T + 291 T^{2} - 2337 T^{3} + 40059 T^{4} - 284061 T^{5} + 3422485 T^{6} - 21083007 T^{7} + 199188759 T^{8} - 1045098519 T^{9} + 8166739119 T^{10} - 35440534767 T^{11} + 235881088685 T^{12} - 802688495421 T^{13} + 4641083555859 T^{14} - 11100993611217 T^{15} + 56673493699371 T^{16} - 71864327062089 T^{17} + 327381934393961 T^{18} \))(\( 1 - 15 T + 333 T^{2} - 3483 T^{3} + 46389 T^{4} - 384045 T^{5} + 3869115 T^{6} - 26650065 T^{7} + 220226457 T^{8} - 1289235535 T^{9} + 9029284737 T^{10} - 44798759265 T^{11} + 266663274915 T^{12} - 1085219383245 T^{13} + 5374453308189 T^{14} - 16544613071403 T^{15} + 64853173202373 T^{16} - 119773878436815 T^{17} + 327381934393961 T^{18} \))(\( 1 + 15 T + 333 T^{2} + 3483 T^{3} + 46389 T^{4} + 384045 T^{5} + 3869115 T^{6} + 26650065 T^{7} + 220226457 T^{8} + 1289235535 T^{9} + 9029284737 T^{10} + 44798759265 T^{11} + 266663274915 T^{12} + 1085219383245 T^{13} + 5374453308189 T^{14} + 16544613071403 T^{15} + 64853173202373 T^{16} + 119773878436815 T^{17} + 327381934393961 T^{18} \))(\( 1 + 9 T + 291 T^{2} + 2337 T^{3} + 40059 T^{4} + 284061 T^{5} + 3422485 T^{6} + 21083007 T^{7} + 199188759 T^{8} + 1045098519 T^{9} + 8166739119 T^{10} + 35440534767 T^{11} + 235881088685 T^{12} + 802688495421 T^{13} + 4641083555859 T^{14} + 11100993611217 T^{15} + 56673493699371 T^{16} + 71864327062089 T^{17} + 327381934393961 T^{18} \))(\( 1 - 2 T + 71 T^{2} - 134 T^{3} + 7140 T^{4} - 7142 T^{5} + 253863 T^{6} - 49886 T^{7} + 15431079 T^{8} + 6002284 T^{9} + 392787500 T^{10} + 246093644 T^{11} + 25939643799 T^{12} - 3438193006 T^{13} + 717356164743 T^{14} - 827444987542 T^{15} + 33915744280740 T^{16} - 26097072700054 T^{17} + 566929691267591 T^{18} - 654763868787922 T^{19} + 13422659310152401 T^{20} \))(\( 1 + 2 T + 71 T^{2} + 134 T^{3} + 7140 T^{4} + 7142 T^{5} + 253863 T^{6} + 49886 T^{7} + 15431079 T^{8} - 6002284 T^{9} + 392787500 T^{10} - 246093644 T^{11} + 25939643799 T^{12} + 3438193006 T^{13} + 717356164743 T^{14} + 827444987542 T^{15} + 33915744280740 T^{16} + 26097072700054 T^{17} + 566929691267591 T^{18} + 654763868787922 T^{19} + 13422659310152401 T^{20} \))(\( 1 + 15 T + 447 T^{2} + 5039 T^{3} + 88056 T^{4} + 816312 T^{5} + 10836428 T^{6} + 87201648 T^{7} + 969593745 T^{8} + 6994081163 T^{9} + 68215221891 T^{10} + 448706289555 T^{11} + 3933586051738 T^{12} + 23789949719166 T^{13} + 190206667490382 T^{14} + 1060603067547772 T^{15} + 7798473367105662 T^{16} + 39990905477918046 T^{17} + 271106684271834698 T^{18} + 1267936733479226355 T^{19} + 7903156458663296091 T^{20} + 33222614594264512283 T^{21} + \)\(18\!\cdots\!45\)\( T^{22} + \)\(69\!\cdots\!08\)\( T^{23} + \)\(35\!\cdots\!08\)\( T^{24} + \)\(10\!\cdots\!12\)\( T^{25} + \)\(48\!\cdots\!96\)\( T^{26} + \)\(11\!\cdots\!59\)\( T^{27} + \)\(41\!\cdots\!87\)\( T^{28} + \)\(56\!\cdots\!15\)\( T^{29} + \)\(15\!\cdots\!01\)\( T^{30} \))(\( 1 + 9 T + 201 T^{2} + 1493 T^{3} + 22746 T^{4} + 151854 T^{5} + 1769144 T^{6} + 11124636 T^{7} + 110969205 T^{8} + 695869773 T^{9} + 6032707401 T^{10} + 38655864861 T^{11} + 300637113288 T^{12} + 1942788405900 T^{13} + 13663829967102 T^{14} + 85331968271940 T^{15} + 560217028651182 T^{16} + 3265827310317900 T^{17} + 20720210484922248 T^{18} + 109232235345484221 T^{19} + 698926561224443601 T^{20} + 3305453959911007293 T^{21} + 21611726942926834605 T^{22} + 88829386661187724956 T^{23} + \)\(57\!\cdots\!84\)\( T^{24} + \)\(20\!\cdots\!54\)\( T^{25} + \)\(12\!\cdots\!86\)\( T^{26} + \)\(33\!\cdots\!33\)\( T^{27} + \)\(18\!\cdots\!21\)\( T^{28} + \)\(34\!\cdots\!49\)\( T^{29} + \)\(15\!\cdots\!01\)\( T^{30} \))(\( 1 - 9 T + 201 T^{2} - 1493 T^{3} + 22746 T^{4} - 151854 T^{5} + 1769144 T^{6} - 11124636 T^{7} + 110969205 T^{8} - 695869773 T^{9} + 6032707401 T^{10} - 38655864861 T^{11} + 300637113288 T^{12} - 1942788405900 T^{13} + 13663829967102 T^{14} - 85331968271940 T^{15} + 560217028651182 T^{16} - 3265827310317900 T^{17} + 20720210484922248 T^{18} - 109232235345484221 T^{19} + 698926561224443601 T^{20} - 3305453959911007293 T^{21} + 21611726942926834605 T^{22} - 88829386661187724956 T^{23} + \)\(57\!\cdots\!84\)\( T^{24} - \)\(20\!\cdots\!54\)\( T^{25} + \)\(12\!\cdots\!86\)\( T^{26} - \)\(33\!\cdots\!33\)\( T^{27} + \)\(18\!\cdots\!21\)\( T^{28} - \)\(34\!\cdots\!49\)\( T^{29} + \)\(15\!\cdots\!01\)\( T^{30} \))(\( 1 - 15 T + 447 T^{2} - 5039 T^{3} + 88056 T^{4} - 816312 T^{5} + 10836428 T^{6} - 87201648 T^{7} + 969593745 T^{8} - 6994081163 T^{9} + 68215221891 T^{10} - 448706289555 T^{11} + 3933586051738 T^{12} - 23789949719166 T^{13} + 190206667490382 T^{14} - 1060603067547772 T^{15} + 7798473367105662 T^{16} - 39990905477918046 T^{17} + 271106684271834698 T^{18} - 1267936733479226355 T^{19} + 7903156458663296091 T^{20} - 33222614594264512283 T^{21} + \)\(18\!\cdots\!45\)\( T^{22} - \)\(69\!\cdots\!08\)\( T^{23} + \)\(35\!\cdots\!08\)\( T^{24} - \)\(10\!\cdots\!12\)\( T^{25} + \)\(48\!\cdots\!96\)\( T^{26} - \)\(11\!\cdots\!59\)\( T^{27} + \)\(41\!\cdots\!87\)\( T^{28} - \)\(56\!\cdots\!15\)\( T^{29} + \)\(15\!\cdots\!01\)\( T^{30} \))(\( 1 + 28 T + 590 T^{2} + 9192 T^{3} + 128663 T^{4} + 1555640 T^{5} + 17445970 T^{6} + 177734116 T^{7} + 1713289175 T^{8} + 15362786984 T^{9} + 131547111180 T^{10} + 1061909894152 T^{11} + 8240959622728 T^{12} + 60733344710984 T^{13} + 431776166224960 T^{14} + 2927752489250448 T^{15} + 19186550539896492 T^{16} + 120037852059268368 T^{17} + 725815735424157760 T^{18} + 4185802850825728264 T^{19} + 23286982304479496008 T^{20} + \)\(12\!\cdots\!52\)\( T^{21} + \)\(62\!\cdots\!80\)\( T^{22} + \)\(29\!\cdots\!04\)\( T^{23} + \)\(13\!\cdots\!75\)\( T^{24} + \)\(58\!\cdots\!76\)\( T^{25} + \)\(23\!\cdots\!70\)\( T^{26} + \)\(85\!\cdots\!40\)\( T^{27} + \)\(29\!\cdots\!03\)\( T^{28} + \)\(85\!\cdots\!32\)\( T^{29} + \)\(22\!\cdots\!90\)\( T^{30} + \)\(43\!\cdots\!28\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 28 T + 590 T^{2} - 9192 T^{3} + 128663 T^{4} - 1555640 T^{5} + 17445970 T^{6} - 177734116 T^{7} + 1713289175 T^{8} - 15362786984 T^{9} + 131547111180 T^{10} - 1061909894152 T^{11} + 8240959622728 T^{12} - 60733344710984 T^{13} + 431776166224960 T^{14} - 2927752489250448 T^{15} + 19186550539896492 T^{16} - 120037852059268368 T^{17} + 725815735424157760 T^{18} - 4185802850825728264 T^{19} + 23286982304479496008 T^{20} - \)\(12\!\cdots\!52\)\( T^{21} + \)\(62\!\cdots\!80\)\( T^{22} - \)\(29\!\cdots\!04\)\( T^{23} + \)\(13\!\cdots\!75\)\( T^{24} - \)\(58\!\cdots\!76\)\( T^{25} + \)\(23\!\cdots\!70\)\( T^{26} - \)\(85\!\cdots\!40\)\( T^{27} + \)\(29\!\cdots\!03\)\( T^{28} - \)\(85\!\cdots\!32\)\( T^{29} + \)\(22\!\cdots\!90\)\( T^{30} - \)\(43\!\cdots\!28\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))
$43$ (\( 1 + 11 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - 9 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 2 T - 21 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 87 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 73 T^{2} + 1849 T^{4} \))(\( 1 + 73 T^{2} + 1849 T^{4} \))(\( 1 - 5 T + 37 T^{2} - 53 T^{3} + 1591 T^{4} - 9245 T^{5} + 79507 T^{6} \))(\( 1 + T + 76 T^{2} + 217 T^{3} + 3268 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 - 5 T + 37 T^{2} - 53 T^{3} + 1591 T^{4} - 9245 T^{5} + 79507 T^{6} \))(\( 1 + T + 76 T^{2} + 217 T^{3} + 3268 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 + 3 T + 69 T^{2} + 187 T^{3} + 2967 T^{4} + 5547 T^{5} + 79507 T^{6} \))(\( 1 + 15 T + 157 T^{2} + 1119 T^{3} + 6751 T^{4} + 27735 T^{5} + 79507 T^{6} \))(\( 1 + 3 T + 69 T^{2} + 187 T^{3} + 2967 T^{4} + 5547 T^{5} + 79507 T^{6} \))(\( 1 + 15 T + 157 T^{2} + 1119 T^{3} + 6751 T^{4} + 27735 T^{5} + 79507 T^{6} \))(\( 1 - 2 T + 70 T^{2} - 296 T^{3} + 3010 T^{4} - 3698 T^{5} + 79507 T^{6} \))(\( 1 - 26 T + 373 T^{2} - 3682 T^{3} + 27628 T^{4} - 158326 T^{5} + 689677 T^{6} - 2067182 T^{7} + 3418801 T^{8} \))(\( 1 - T + 30 T^{2} - 266 T^{3} + 1669 T^{4} - 5107 T^{5} + 71767 T^{6} - 491834 T^{7} + 2385210 T^{8} - 3418801 T^{9} + 147008443 T^{10} \))(\( 1 - T + 30 T^{2} - 266 T^{3} + 1669 T^{4} - 5107 T^{5} + 71767 T^{6} - 491834 T^{7} + 2385210 T^{8} - 3418801 T^{9} + 147008443 T^{10} \))(\( 1 + T + 34 T^{2} - 113 T^{3} + 3077 T^{4} + 6808 T^{5} + 132311 T^{6} - 208937 T^{7} + 2703238 T^{8} + 3418801 T^{9} + 147008443 T^{10} \))(\( 1 + T + 34 T^{2} - 113 T^{3} + 3077 T^{4} + 6808 T^{5} + 132311 T^{6} - 208937 T^{7} + 2703238 T^{8} + 3418801 T^{9} + 147008443 T^{10} \))(\( 1 + 26 T + 409 T^{2} + 4642 T^{3} + 44074 T^{4} + 359722 T^{5} + 2549577 T^{6} + 15468046 T^{7} + 81492826 T^{8} + 369071494 T^{9} + 1398289609 T^{10} + 3822219518 T^{11} + 6321363049 T^{12} \))(\( 1 + 26 T + 409 T^{2} + 4642 T^{3} + 44074 T^{4} + 359722 T^{5} + 2549577 T^{6} + 15468046 T^{7} + 81492826 T^{8} + 369071494 T^{9} + 1398289609 T^{10} + 3822219518 T^{11} + 6321363049 T^{12} \))(\( 1 + 138 T^{2} - 18 T^{3} + 13506 T^{4} + 2142 T^{5} + 915652 T^{6} + 15255 T^{7} + 49741707 T^{8} + 6512931 T^{9} + 2138893401 T^{10} + 28206495 T^{11} + 72800743564 T^{12} + 7323071742 T^{13} + 1985496031158 T^{14} - 113784534882 T^{15} + 37510968332766 T^{16} + 502592611936843 T^{18} \))(\( 1 + 12 T + 294 T^{2} + 2862 T^{3} + 39846 T^{4} + 324978 T^{5} + 3325824 T^{6} + 23312991 T^{7} + 193800183 T^{8} + 1176109315 T^{9} + 8333407869 T^{10} + 43105720359 T^{11} + 264426288768 T^{12} + 1111035111378 T^{13} + 5857698419778 T^{14} + 18091741046238 T^{15} + 79914671665458 T^{16} + 140258403331212 T^{17} + 502592611936843 T^{18} \))(\( 1 + 12 T + 294 T^{2} + 2862 T^{3} + 39846 T^{4} + 324978 T^{5} + 3325824 T^{6} + 23312991 T^{7} + 193800183 T^{8} + 1176109315 T^{9} + 8333407869 T^{10} + 43105720359 T^{11} + 264426288768 T^{12} + 1111035111378 T^{13} + 5857698419778 T^{14} + 18091741046238 T^{15} + 79914671665458 T^{16} + 140258403331212 T^{17} + 502592611936843 T^{18} \))(\( 1 + 138 T^{2} - 18 T^{3} + 13506 T^{4} + 2142 T^{5} + 915652 T^{6} + 15255 T^{7} + 49741707 T^{8} + 6512931 T^{9} + 2138893401 T^{10} + 28206495 T^{11} + 72800743564 T^{12} + 7323071742 T^{13} + 1985496031158 T^{14} - 113784534882 T^{15} + 37510968332766 T^{16} + 502592611936843 T^{18} \))(\( 1 - 6 T + 357 T^{2} - 2166 T^{3} + 59932 T^{4} - 351090 T^{5} + 6222483 T^{6} - 33763766 T^{7} + 441575135 T^{8} - 2130582468 T^{9} + 22347739048 T^{10} - 91615046124 T^{11} + 816472424615 T^{12} - 2684455743362 T^{13} + 21273431102883 T^{14} - 51613194252870 T^{15} + 378851930252668 T^{16} - 588759111657762 T^{17} + 4172687499103557 T^{18} - 3015555671621058 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 6 T + 357 T^{2} - 2166 T^{3} + 59932 T^{4} - 351090 T^{5} + 6222483 T^{6} - 33763766 T^{7} + 441575135 T^{8} - 2130582468 T^{9} + 22347739048 T^{10} - 91615046124 T^{11} + 816472424615 T^{12} - 2684455743362 T^{13} + 21273431102883 T^{14} - 51613194252870 T^{15} + 378851930252668 T^{16} - 588759111657762 T^{17} + 4172687499103557 T^{18} - 3015555671621058 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 414 T^{2} - 2 T^{3} + 81306 T^{4} - 3078 T^{5} + 10221401 T^{6} - 876129 T^{7} + 939845637 T^{8} - 122407831 T^{9} + 68331879135 T^{10} - 10692938835 T^{11} + 4107811212345 T^{12} - 664245631659 T^{13} + 208280206655703 T^{14} - 31936272120153 T^{15} + 8956048886195229 T^{16} - 1228190172937491 T^{17} + 326599746059913915 T^{18} - 36557029982036835 T^{19} + 10045363158900536805 T^{20} - 773784339791636719 T^{21} + \)\(25\!\cdots\!59\)\( T^{22} - 10240371221014286529 T^{23} + \)\(51\!\cdots\!43\)\( T^{24} - 66520142560288918422 T^{25} + \)\(75\!\cdots\!42\)\( T^{26} - 79919261594525152802 T^{27} + \)\(71\!\cdots\!02\)\( T^{28} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 - 12 T + 378 T^{2} - 4138 T^{3} + 74622 T^{4} - 748170 T^{5} + 9939117 T^{6} - 91459533 T^{7} + 988510509 T^{8} - 8359420151 T^{9} + 77264618967 T^{10} - 600268036359 T^{11} + 4884656968777 T^{12} - 34795587164811 T^{13} + 253768675207179 T^{14} - 1650458568010513 T^{15} + 10912053033908697 T^{16} - 64337040667735539 T^{17} + 388364421616552939 T^{18} - 2052196962972185559 T^{19} + 11358551333326938381 T^{20} - 52842929653597400399 T^{21} + \)\(26\!\cdots\!63\)\( T^{22} - \)\(10\!\cdots\!33\)\( T^{23} + \)\(49\!\cdots\!31\)\( T^{24} - \)\(16\!\cdots\!30\)\( T^{25} + \)\(69\!\cdots\!54\)\( T^{26} - \)\(16\!\cdots\!38\)\( T^{27} + \)\(64\!\cdots\!54\)\( T^{28} - \)\(88\!\cdots\!88\)\( T^{29} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 - 12 T + 378 T^{2} - 4138 T^{3} + 74622 T^{4} - 748170 T^{5} + 9939117 T^{6} - 91459533 T^{7} + 988510509 T^{8} - 8359420151 T^{9} + 77264618967 T^{10} - 600268036359 T^{11} + 4884656968777 T^{12} - 34795587164811 T^{13} + 253768675207179 T^{14} - 1650458568010513 T^{15} + 10912053033908697 T^{16} - 64337040667735539 T^{17} + 388364421616552939 T^{18} - 2052196962972185559 T^{19} + 11358551333326938381 T^{20} - 52842929653597400399 T^{21} + \)\(26\!\cdots\!63\)\( T^{22} - \)\(10\!\cdots\!33\)\( T^{23} + \)\(49\!\cdots\!31\)\( T^{24} - \)\(16\!\cdots\!30\)\( T^{25} + \)\(69\!\cdots\!54\)\( T^{26} - \)\(16\!\cdots\!38\)\( T^{27} + \)\(64\!\cdots\!54\)\( T^{28} - \)\(88\!\cdots\!88\)\( T^{29} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 + 414 T^{2} - 2 T^{3} + 81306 T^{4} - 3078 T^{5} + 10221401 T^{6} - 876129 T^{7} + 939845637 T^{8} - 122407831 T^{9} + 68331879135 T^{10} - 10692938835 T^{11} + 4107811212345 T^{12} - 664245631659 T^{13} + 208280206655703 T^{14} - 31936272120153 T^{15} + 8956048886195229 T^{16} - 1228190172937491 T^{17} + 326599746059913915 T^{18} - 36557029982036835 T^{19} + 10045363158900536805 T^{20} - 773784339791636719 T^{21} + \)\(25\!\cdots\!59\)\( T^{22} - 10240371221014286529 T^{23} + \)\(51\!\cdots\!43\)\( T^{24} - 66520142560288918422 T^{25} + \)\(75\!\cdots\!42\)\( T^{26} - 79919261594525152802 T^{27} + \)\(71\!\cdots\!02\)\( T^{28} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 + 20 T + 610 T^{2} + 9128 T^{3} + 162875 T^{4} + 1972024 T^{5} + 26329486 T^{6} + 270030444 T^{7} + 2960356457 T^{8} + 26516602592 T^{9} + 250708156244 T^{10} + 2005404207776 T^{11} + 16861411949390 T^{12} + 122437001752072 T^{13} + 934086845332584 T^{14} + 6223950282269296 T^{15} + 43592706614193362 T^{16} + 267629862137579728 T^{17} + 1727126577019947816 T^{18} + 9734598698301988504 T^{19} + 57645812033986481390 T^{20} + \)\(29\!\cdots\!68\)\( T^{21} + \)\(15\!\cdots\!56\)\( T^{22} + \)\(72\!\cdots\!44\)\( T^{23} + \)\(34\!\cdots\!57\)\( T^{24} + \)\(13\!\cdots\!92\)\( T^{25} + \)\(56\!\cdots\!14\)\( T^{26} + \)\(18\!\cdots\!68\)\( T^{27} + \)\(65\!\cdots\!75\)\( T^{28} + \)\(15\!\cdots\!04\)\( T^{29} + \)\(45\!\cdots\!90\)\( T^{30} + \)\(63\!\cdots\!40\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 + 20 T + 610 T^{2} + 9128 T^{3} + 162875 T^{4} + 1972024 T^{5} + 26329486 T^{6} + 270030444 T^{7} + 2960356457 T^{8} + 26516602592 T^{9} + 250708156244 T^{10} + 2005404207776 T^{11} + 16861411949390 T^{12} + 122437001752072 T^{13} + 934086845332584 T^{14} + 6223950282269296 T^{15} + 43592706614193362 T^{16} + 267629862137579728 T^{17} + 1727126577019947816 T^{18} + 9734598698301988504 T^{19} + 57645812033986481390 T^{20} + \)\(29\!\cdots\!68\)\( T^{21} + \)\(15\!\cdots\!56\)\( T^{22} + \)\(72\!\cdots\!44\)\( T^{23} + \)\(34\!\cdots\!57\)\( T^{24} + \)\(13\!\cdots\!92\)\( T^{25} + \)\(56\!\cdots\!14\)\( T^{26} + \)\(18\!\cdots\!68\)\( T^{27} + \)\(65\!\cdots\!75\)\( T^{28} + \)\(15\!\cdots\!04\)\( T^{29} + \)\(45\!\cdots\!90\)\( T^{30} + \)\(63\!\cdots\!40\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))
$47$ (\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 6 T + 100 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 108 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 106 T^{2} - 470 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 106 T^{2} - 470 T^{3} + 2209 T^{4} \))(\( 1 + 20 T + 272 T^{2} + 2161 T^{3} + 12784 T^{4} + 44180 T^{5} + 103823 T^{6} \))(\( 1 - 14 T + 145 T^{2} - 1014 T^{3} + 6815 T^{4} - 30926 T^{5} + 103823 T^{6} \))(\( 1 + 20 T + 272 T^{2} + 2161 T^{3} + 12784 T^{4} + 44180 T^{5} + 103823 T^{6} \))(\( 1 - 14 T + 145 T^{2} - 1014 T^{3} + 6815 T^{4} - 30926 T^{5} + 103823 T^{6} \))(\( 1 + 6 T + 96 T^{2} + 351 T^{3} + 4512 T^{4} + 13254 T^{5} + 103823 T^{6} \))(\( 1 + 8 T + 140 T^{2} + 677 T^{3} + 6580 T^{4} + 17672 T^{5} + 103823 T^{6} \))(\( 1 + 6 T + 96 T^{2} + 351 T^{3} + 4512 T^{4} + 13254 T^{5} + 103823 T^{6} \))(\( 1 + 8 T + 140 T^{2} + 677 T^{3} + 6580 T^{4} + 17672 T^{5} + 103823 T^{6} \))(\( 1 + 2 T + 47 T^{2} - 164 T^{3} + 2209 T^{4} + 4418 T^{5} + 103823 T^{6} \))(\( 1 + 4 T + 94 T^{2} + 404 T^{3} + 6594 T^{4} + 18988 T^{5} + 207646 T^{6} + 415292 T^{7} + 4879681 T^{8} \))(\( 1 + 4 T + 210 T^{2} + 589 T^{3} + 18275 T^{4} + 37538 T^{5} + 858925 T^{6} + 1301101 T^{7} + 21802830 T^{8} + 19518724 T^{9} + 229345007 T^{10} \))(\( 1 + 4 T + 210 T^{2} + 589 T^{3} + 18275 T^{4} + 37538 T^{5} + 858925 T^{6} + 1301101 T^{7} + 21802830 T^{8} + 19518724 T^{9} + 229345007 T^{10} \))(\( 1 - 6 T + 187 T^{2} - 938 T^{3} + 15178 T^{4} - 61696 T^{5} + 713366 T^{6} - 2072042 T^{7} + 19414901 T^{8} - 29278086 T^{9} + 229345007 T^{10} \))(\( 1 - 6 T + 187 T^{2} - 938 T^{3} + 15178 T^{4} - 61696 T^{5} + 713366 T^{6} - 2072042 T^{7} + 19414901 T^{8} - 29278086 T^{9} + 229345007 T^{10} \))(\( 1 + 16 T + 294 T^{2} + 3380 T^{3} + 35353 T^{4} + 302440 T^{5} + 2229378 T^{6} + 14214680 T^{7} + 78094777 T^{8} + 350921740 T^{9} + 1434626214 T^{10} + 3669520112 T^{11} + 10779215329 T^{12} \))(\( 1 + 16 T + 294 T^{2} + 3380 T^{3} + 35353 T^{4} + 302440 T^{5} + 2229378 T^{6} + 14214680 T^{7} + 78094777 T^{8} + 350921740 T^{9} + 1434626214 T^{10} + 3669520112 T^{11} + 10779215329 T^{12} \))(\( 1 + 9 T + 222 T^{2} + 2072 T^{3} + 29490 T^{4} + 237882 T^{5} + 2602214 T^{6} + 18427272 T^{7} + 165174465 T^{8} + 1013376587 T^{9} + 7763199855 T^{10} + 40705843848 T^{11} + 270169664122 T^{12} + 1160788275642 T^{13} + 6763384256430 T^{14} + 22334534161688 T^{15} + 112470332742786 T^{16} + 214301579955849 T^{17} + 1119130473102767 T^{18} \))(\( 1 - 15 T + 294 T^{2} - 2460 T^{3} + 26760 T^{4} - 117726 T^{5} + 887346 T^{6} + 1409376 T^{7} - 3540585 T^{8} + 292308813 T^{9} - 166407495 T^{10} + 3113311584 T^{11} + 92126923758 T^{12} - 574465325406 T^{13} + 6137272387320 T^{14} - 26516869709340 T^{15} + 148947197416122 T^{16} - 357169299926415 T^{17} + 1119130473102767 T^{18} \))(\( 1 - 15 T + 294 T^{2} - 2460 T^{3} + 26760 T^{4} - 117726 T^{5} + 887346 T^{6} + 1409376 T^{7} - 3540585 T^{8} + 292308813 T^{9} - 166407495 T^{10} + 3113311584 T^{11} + 92126923758 T^{12} - 574465325406 T^{13} + 6137272387320 T^{14} - 26516869709340 T^{15} + 148947197416122 T^{16} - 357169299926415 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 9 T + 222 T^{2} + 2072 T^{3} + 29490 T^{4} + 237882 T^{5} + 2602214 T^{6} + 18427272 T^{7} + 165174465 T^{8} + 1013376587 T^{9} + 7763199855 T^{10} + 40705843848 T^{11} + 270169664122 T^{12} + 1160788275642 T^{13} + 6763384256430 T^{14} + 22334534161688 T^{15} + 112470332742786 T^{16} + 214301579955849 T^{17} + 1119130473102767 T^{18} \))(\( 1 - 16 T + 346 T^{2} - 3452 T^{3} + 44735 T^{4} - 323304 T^{5} + 3281214 T^{6} - 18149968 T^{7} + 167944152 T^{8} - 772357332 T^{9} + 7651510112 T^{10} - 36300794604 T^{11} + 370988631768 T^{12} - 1884384127664 T^{13} + 16011277612734 T^{14} - 74148158143128 T^{15} + 482208197742815 T^{16} - 1748863011838276 T^{17} + 8238705184969306 T^{18} - 17906087569644272 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 16 T + 346 T^{2} - 3452 T^{3} + 44735 T^{4} - 323304 T^{5} + 3281214 T^{6} - 18149968 T^{7} + 167944152 T^{8} - 772357332 T^{9} + 7651510112 T^{10} - 36300794604 T^{11} + 370988631768 T^{12} - 1884384127664 T^{13} + 16011277612734 T^{14} - 74148158143128 T^{15} + 482208197742815 T^{16} - 1748863011838276 T^{17} + 8238705184969306 T^{18} - 17906087569644272 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 9 T + 354 T^{2} - 2828 T^{3} + 60957 T^{4} - 458811 T^{5} + 7167154 T^{6} - 52122828 T^{7} + 658185558 T^{8} - 4591465534 T^{9} + 49727340027 T^{10} - 328458589806 T^{11} + 3169777340444 T^{12} - 19675186174542 T^{13} + 173060523267297 T^{14} - 1001656302383316 T^{15} + 8133844593562959 T^{16} - 43462486259563278 T^{17} + 329095792816917412 T^{18} - 1602773139963131886 T^{19} + 11404717146583695189 T^{20} - 49492395666667970686 T^{21} + \)\(33\!\cdots\!54\)\( T^{22} - \)\(12\!\cdots\!08\)\( T^{23} + \)\(80\!\cdots\!18\)\( T^{24} - \)\(24\!\cdots\!39\)\( T^{25} + \)\(15\!\cdots\!71\)\( T^{26} - \)\(32\!\cdots\!48\)\( T^{27} + \)\(19\!\cdots\!58\)\( T^{28} - \)\(23\!\cdots\!21\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 + 15 T + 366 T^{2} + 3964 T^{3} + 56391 T^{4} + 468201 T^{5} + 4978578 T^{6} + 32667924 T^{7} + 294889986 T^{8} + 1592864488 T^{9} + 14170030713 T^{10} + 71506591662 T^{11} + 707999369300 T^{12} + 3762254010096 T^{13} + 37535133902181 T^{14} + 194178015253988 T^{15} + 1764151293402507 T^{16} + 8310819108302064 T^{17} + 73506618518833900 T^{18} + 348929356707819822 T^{19} + 3249825793063199991 T^{20} + 17169829306069336552 T^{21} + \)\(14\!\cdots\!18\)\( T^{22} + \)\(77\!\cdots\!64\)\( T^{23} + \)\(55\!\cdots\!26\)\( T^{24} + \)\(24\!\cdots\!49\)\( T^{25} + \)\(13\!\cdots\!73\)\( T^{26} + \)\(46\!\cdots\!24\)\( T^{27} + \)\(19\!\cdots\!82\)\( T^{28} + \)\(38\!\cdots\!35\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 + 15 T + 366 T^{2} + 3964 T^{3} + 56391 T^{4} + 468201 T^{5} + 4978578 T^{6} + 32667924 T^{7} + 294889986 T^{8} + 1592864488 T^{9} + 14170030713 T^{10} + 71506591662 T^{11} + 707999369300 T^{12} + 3762254010096 T^{13} + 37535133902181 T^{14} + 194178015253988 T^{15} + 1764151293402507 T^{16} + 8310819108302064 T^{17} + 73506618518833900 T^{18} + 348929356707819822 T^{19} + 3249825793063199991 T^{20} + 17169829306069336552 T^{21} + \)\(14\!\cdots\!18\)\( T^{22} + \)\(77\!\cdots\!64\)\( T^{23} + \)\(55\!\cdots\!26\)\( T^{24} + \)\(24\!\cdots\!49\)\( T^{25} + \)\(13\!\cdots\!73\)\( T^{26} + \)\(46\!\cdots\!24\)\( T^{27} + \)\(19\!\cdots\!82\)\( T^{28} + \)\(38\!\cdots\!35\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 - 9 T + 354 T^{2} - 2828 T^{3} + 60957 T^{4} - 458811 T^{5} + 7167154 T^{6} - 52122828 T^{7} + 658185558 T^{8} - 4591465534 T^{9} + 49727340027 T^{10} - 328458589806 T^{11} + 3169777340444 T^{12} - 19675186174542 T^{13} + 173060523267297 T^{14} - 1001656302383316 T^{15} + 8133844593562959 T^{16} - 43462486259563278 T^{17} + 329095792816917412 T^{18} - 1602773139963131886 T^{19} + 11404717146583695189 T^{20} - 49492395666667970686 T^{21} + \)\(33\!\cdots\!54\)\( T^{22} - \)\(12\!\cdots\!08\)\( T^{23} + \)\(80\!\cdots\!18\)\( T^{24} - \)\(24\!\cdots\!39\)\( T^{25} + \)\(15\!\cdots\!71\)\( T^{26} - \)\(32\!\cdots\!48\)\( T^{27} + \)\(19\!\cdots\!58\)\( T^{28} - \)\(23\!\cdots\!21\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 + 32 T + 844 T^{2} + 15296 T^{3} + 246764 T^{4} + 3304944 T^{5} + 41030560 T^{6} + 452505896 T^{7} + 4735449658 T^{8} + 45474862752 T^{9} + 419831989708 T^{10} + 3617479553392 T^{11} + 30182462244230 T^{12} + 237203301571376 T^{13} + 1812299365025856 T^{14} + 13103976537954952 T^{15} + 92279132887993142 T^{16} + 615886897283882744 T^{17} + 4003369297342115904 T^{18} + 24627158379044970448 T^{19} + \)\(14\!\cdots\!30\)\( T^{20} + \)\(82\!\cdots\!44\)\( T^{21} + \)\(45\!\cdots\!32\)\( T^{22} + \)\(23\!\cdots\!76\)\( T^{23} + \)\(11\!\cdots\!38\)\( T^{24} + \)\(50\!\cdots\!32\)\( T^{25} + \)\(21\!\cdots\!40\)\( T^{26} + \)\(81\!\cdots\!32\)\( T^{27} + \)\(28\!\cdots\!24\)\( T^{28} + \)\(83\!\cdots\!92\)\( T^{29} + \)\(21\!\cdots\!36\)\( T^{30} + \)\(38\!\cdots\!76\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 32 T + 844 T^{2} + 15296 T^{3} + 246764 T^{4} + 3304944 T^{5} + 41030560 T^{6} + 452505896 T^{7} + 4735449658 T^{8} + 45474862752 T^{9} + 419831989708 T^{10} + 3617479553392 T^{11} + 30182462244230 T^{12} + 237203301571376 T^{13} + 1812299365025856 T^{14} + 13103976537954952 T^{15} + 92279132887993142 T^{16} + 615886897283882744 T^{17} + 4003369297342115904 T^{18} + 24627158379044970448 T^{19} + \)\(14\!\cdots\!30\)\( T^{20} + \)\(82\!\cdots\!44\)\( T^{21} + \)\(45\!\cdots\!32\)\( T^{22} + \)\(23\!\cdots\!76\)\( T^{23} + \)\(11\!\cdots\!38\)\( T^{24} + \)\(50\!\cdots\!32\)\( T^{25} + \)\(21\!\cdots\!40\)\( T^{26} + \)\(81\!\cdots\!32\)\( T^{27} + \)\(28\!\cdots\!24\)\( T^{28} + \)\(83\!\cdots\!92\)\( T^{29} + \)\(21\!\cdots\!36\)\( T^{30} + \)\(38\!\cdots\!76\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 + 4 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 40 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 92 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 109 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 109 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 + 19 T + 263 T^{2} + 2141 T^{3} + 13939 T^{4} + 53371 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 137 T^{2} - 514 T^{3} + 7261 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 + 19 T + 263 T^{2} + 2141 T^{3} + 13939 T^{4} + 53371 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 137 T^{2} - 514 T^{3} + 7261 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 - 3 T + 33 T^{2} - 261 T^{3} + 1749 T^{4} - 8427 T^{5} + 148877 T^{6} \))(\( 1 - 3 T + 123 T^{2} - 323 T^{3} + 6519 T^{4} - 8427 T^{5} + 148877 T^{6} \))(\( 1 - 3 T + 33 T^{2} - 261 T^{3} + 1749 T^{4} - 8427 T^{5} + 148877 T^{6} \))(\( 1 - 3 T + 123 T^{2} - 323 T^{3} + 6519 T^{4} - 8427 T^{5} + 148877 T^{6} \))(\( 1 + 4 T - 19 T^{2} - 244 T^{3} - 1007 T^{4} + 11236 T^{5} + 148877 T^{6} \))(\( 1 - 20 T + 262 T^{2} - 2644 T^{3} + 22338 T^{4} - 140132 T^{5} + 735958 T^{6} - 2977540 T^{7} + 7890481 T^{8} \))(\( 1 + 19 T + 378 T^{2} + 4126 T^{3} + 44951 T^{4} + 328013 T^{5} + 2382403 T^{6} + 11589934 T^{7} + 56275506 T^{8} + 149919139 T^{9} + 418195493 T^{10} \))(\( 1 + 19 T + 378 T^{2} + 4126 T^{3} + 44951 T^{4} + 328013 T^{5} + 2382403 T^{6} + 11589934 T^{7} + 56275506 T^{8} + 149919139 T^{9} + 418195493 T^{10} \))(\( 1 - 6 T + 103 T^{2} - 806 T^{3} + 9564 T^{4} - 45320 T^{5} + 506892 T^{6} - 2264054 T^{7} + 15334331 T^{8} - 47342886 T^{9} + 418195493 T^{10} \))(\( 1 - 6 T + 103 T^{2} - 806 T^{3} + 9564 T^{4} - 45320 T^{5} + 506892 T^{6} - 2264054 T^{7} + 15334331 T^{8} - 47342886 T^{9} + 418195493 T^{10} \))(\( 1 - 12 T + 266 T^{2} - 2204 T^{3} + 30071 T^{4} - 198816 T^{5} + 2034058 T^{6} - 10537248 T^{7} + 84469439 T^{8} - 328124908 T^{9} + 2098867946 T^{10} - 5018345916 T^{11} + 22164361129 T^{12} \))(\( 1 - 12 T + 266 T^{2} - 2204 T^{3} + 30071 T^{4} - 198816 T^{5} + 2034058 T^{6} - 10537248 T^{7} + 84469439 T^{8} - 328124908 T^{9} + 2098867946 T^{10} - 5018345916 T^{11} + 22164361129 T^{12} \))(\( 1 + 153 T^{2} - 267 T^{3} + 14526 T^{4} - 46530 T^{5} + 1077021 T^{6} - 3967515 T^{7} + 69603120 T^{8} - 239455751 T^{9} + 3688965360 T^{10} - 11144749635 T^{11} + 160343655417 T^{12} - 367144080930 T^{13} + 6074707731318 T^{14} - 5917884421443 T^{15} + 179730804395061 T^{16} + 3299763591802133 T^{18} \))(\( 1 + 6 T + 339 T^{2} + 1977 T^{3} + 55506 T^{4} + 303000 T^{5} + 5808789 T^{6} + 28480587 T^{7} + 426301872 T^{8} + 1810706175 T^{9} + 22593999216 T^{10} + 80001968883 T^{11} + 864795079953 T^{12} + 2390815743000 T^{13} + 23212359034458 T^{14} + 43818941952033 T^{15} + 398227076404743 T^{16} + 373558142468166 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 6 T + 339 T^{2} + 1977 T^{3} + 55506 T^{4} + 303000 T^{5} + 5808789 T^{6} + 28480587 T^{7} + 426301872 T^{8} + 1810706175 T^{9} + 22593999216 T^{10} + 80001968883 T^{11} + 864795079953 T^{12} + 2390815743000 T^{13} + 23212359034458 T^{14} + 43818941952033 T^{15} + 398227076404743 T^{16} + 373558142468166 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 153 T^{2} - 267 T^{3} + 14526 T^{4} - 46530 T^{5} + 1077021 T^{6} - 3967515 T^{7} + 69603120 T^{8} - 239455751 T^{9} + 3688965360 T^{10} - 11144749635 T^{11} + 160343655417 T^{12} - 367144080930 T^{13} + 6074707731318 T^{14} - 5917884421443 T^{15} + 179730804395061 T^{16} + 3299763591802133 T^{18} \))(\( 1 + 12 T + 446 T^{2} + 4508 T^{3} + 92061 T^{4} + 796656 T^{5} + 11680310 T^{6} + 87114016 T^{7} + 1013644770 T^{8} + 6508572088 T^{9} + 63036707560 T^{10} + 344954320664 T^{11} + 2847328158930 T^{12} + 12969273360032 T^{13} + 92163264129110 T^{14} + 333157948671408 T^{15} + 2040473249896869 T^{16} + 5295597818385196 T^{17} + 27767821923467006 T^{18} + 39597163101625596 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 12 T + 446 T^{2} + 4508 T^{3} + 92061 T^{4} + 796656 T^{5} + 11680310 T^{6} + 87114016 T^{7} + 1013644770 T^{8} + 6508572088 T^{9} + 63036707560 T^{10} + 344954320664 T^{11} + 2847328158930 T^{12} + 12969273360032 T^{13} + 92163264129110 T^{14} + 333157948671408 T^{15} + 2040473249896869 T^{16} + 5295597818385196 T^{17} + 27767821923467006 T^{18} + 39597163101625596 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 12 T + 327 T^{2} + 3473 T^{3} + 53064 T^{4} + 487062 T^{5} + 5616934 T^{6} + 46087893 T^{7} + 439725291 T^{8} + 3385452076 T^{9} + 27983519328 T^{10} + 209178677415 T^{11} + 1562478260057 T^{12} + 11690774772795 T^{13} + 82278442199583 T^{14} + 626391502315503 T^{15} + 4360757436577899 T^{16} + 32839386336781155 T^{17} + 232617075922505989 T^{18} + 1650520379748186615 T^{19} + 11702581661247988704 T^{20} + 75036382397386753804 T^{21} + \)\(51\!\cdots\!67\)\( T^{22} + \)\(28\!\cdots\!73\)\( T^{23} + \)\(18\!\cdots\!22\)\( T^{24} + \)\(85\!\cdots\!38\)\( T^{25} + \)\(49\!\cdots\!08\)\( T^{26} + \)\(17\!\cdots\!93\)\( T^{27} + \)\(85\!\cdots\!71\)\( T^{28} + \)\(16\!\cdots\!28\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 - 6 T + 249 T^{2} - 275 T^{3} + 28632 T^{4} + 69768 T^{5} + 2843778 T^{6} + 12603177 T^{7} + 241992825 T^{8} + 1517296294 T^{9} + 17619776328 T^{10} + 128958848343 T^{11} + 1199769491573 T^{12} + 8838195404517 T^{13} + 70110282980025 T^{14} + 521934173654201 T^{15} + 3715844997941325 T^{16} + 24826490891288253 T^{17} + 178618082596913521 T^{18} + 1017547342632322983 T^{19} + 7368511048037689704 T^{20} + 33629902999909355926 T^{21} + \)\(28\!\cdots\!25\)\( T^{22} + \)\(78\!\cdots\!97\)\( T^{23} + \)\(93\!\cdots\!74\)\( T^{24} + \)\(12\!\cdots\!32\)\( T^{25} + \)\(26\!\cdots\!04\)\( T^{26} - \)\(13\!\cdots\!75\)\( T^{27} + \)\(64\!\cdots\!77\)\( T^{28} - \)\(82\!\cdots\!14\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 - 6 T + 249 T^{2} - 275 T^{3} + 28632 T^{4} + 69768 T^{5} + 2843778 T^{6} + 12603177 T^{7} + 241992825 T^{8} + 1517296294 T^{9} + 17619776328 T^{10} + 128958848343 T^{11} + 1199769491573 T^{12} + 8838195404517 T^{13} + 70110282980025 T^{14} + 521934173654201 T^{15} + 3715844997941325 T^{16} + 24826490891288253 T^{17} + 178618082596913521 T^{18} + 1017547342632322983 T^{19} + 7368511048037689704 T^{20} + 33629902999909355926 T^{21} + \)\(28\!\cdots\!25\)\( T^{22} + \)\(78\!\cdots\!97\)\( T^{23} + \)\(93\!\cdots\!74\)\( T^{24} + \)\(12\!\cdots\!32\)\( T^{25} + \)\(26\!\cdots\!04\)\( T^{26} - \)\(13\!\cdots\!75\)\( T^{27} + \)\(64\!\cdots\!77\)\( T^{28} - \)\(82\!\cdots\!14\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 + 12 T + 327 T^{2} + 3473 T^{3} + 53064 T^{4} + 487062 T^{5} + 5616934 T^{6} + 46087893 T^{7} + 439725291 T^{8} + 3385452076 T^{9} + 27983519328 T^{10} + 209178677415 T^{11} + 1562478260057 T^{12} + 11690774772795 T^{13} + 82278442199583 T^{14} + 626391502315503 T^{15} + 4360757436577899 T^{16} + 32839386336781155 T^{17} + 232617075922505989 T^{18} + 1650520379748186615 T^{19} + 11702581661247988704 T^{20} + 75036382397386753804 T^{21} + \)\(51\!\cdots\!67\)\( T^{22} + \)\(28\!\cdots\!73\)\( T^{23} + \)\(18\!\cdots\!22\)\( T^{24} + \)\(85\!\cdots\!38\)\( T^{25} + \)\(49\!\cdots\!08\)\( T^{26} + \)\(17\!\cdots\!93\)\( T^{27} + \)\(85\!\cdots\!71\)\( T^{28} + \)\(16\!\cdots\!28\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 + 16 T + 548 T^{2} + 6648 T^{3} + 136600 T^{4} + 1377920 T^{5} + 21982636 T^{6} + 194107416 T^{7} + 2637226488 T^{8} + 20956475536 T^{9} + 252758233796 T^{10} + 1834538169912 T^{11} + 20065364411974 T^{12} + 134111570413168 T^{13} + 1345921891498924 T^{14} + 8317910829572584 T^{15} + 77076039393661418 T^{16} + 440849273967346952 T^{17} + 3780694593220477516 T^{18} + 19966128268401212336 T^{19} + \)\(15\!\cdots\!94\)\( T^{20} + \)\(76\!\cdots\!16\)\( T^{21} + \)\(56\!\cdots\!84\)\( T^{22} + \)\(24\!\cdots\!32\)\( T^{23} + \)\(16\!\cdots\!68\)\( T^{24} + \)\(64\!\cdots\!28\)\( T^{25} + \)\(38\!\cdots\!64\)\( T^{26} + \)\(12\!\cdots\!40\)\( T^{27} + \)\(67\!\cdots\!00\)\( T^{28} + \)\(17\!\cdots\!04\)\( T^{29} + \)\(75\!\cdots\!12\)\( T^{30} + \)\(11\!\cdots\!12\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 + 16 T + 548 T^{2} + 6648 T^{3} + 136600 T^{4} + 1377920 T^{5} + 21982636 T^{6} + 194107416 T^{7} + 2637226488 T^{8} + 20956475536 T^{9} + 252758233796 T^{10} + 1834538169912 T^{11} + 20065364411974 T^{12} + 134111570413168 T^{13} + 1345921891498924 T^{14} + 8317910829572584 T^{15} + 77076039393661418 T^{16} + 440849273967346952 T^{17} + 3780694593220477516 T^{18} + 19966128268401212336 T^{19} + \)\(15\!\cdots\!94\)\( T^{20} + \)\(76\!\cdots\!16\)\( T^{21} + \)\(56\!\cdots\!84\)\( T^{22} + \)\(24\!\cdots\!32\)\( T^{23} + \)\(16\!\cdots\!68\)\( T^{24} + \)\(64\!\cdots\!28\)\( T^{25} + \)\(38\!\cdots\!64\)\( T^{26} + \)\(12\!\cdots\!40\)\( T^{27} + \)\(67\!\cdots\!00\)\( T^{28} + \)\(17\!\cdots\!04\)\( T^{29} + \)\(75\!\cdots\!12\)\( T^{30} + \)\(11\!\cdots\!12\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 6 T + 100 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 + 16 T + 164 T^{2} + 944 T^{3} + 3481 T^{4} \))(\( 1 + 2 T + 106 T^{2} + 118 T^{3} + 3481 T^{4} \))(\( 1 + 2 T + 106 T^{2} + 118 T^{3} + 3481 T^{4} \))(\( 1 + 5 T + 183 T^{2} + 591 T^{3} + 10797 T^{4} + 17405 T^{5} + 205379 T^{6} \))(\( 1 + 14 T + 193 T^{2} + 1422 T^{3} + 11387 T^{4} + 48734 T^{5} + 205379 T^{6} \))(\( 1 + 5 T + 183 T^{2} + 591 T^{3} + 10797 T^{4} + 17405 T^{5} + 205379 T^{6} \))(\( 1 + 14 T + 193 T^{2} + 1422 T^{3} + 11387 T^{4} + 48734 T^{5} + 205379 T^{6} \))(\( 1 - 9 T + 33 T^{2} + 81 T^{3} + 1947 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 135 T^{2} - 229 T^{3} + 7965 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 - 9 T + 33 T^{2} + 81 T^{3} + 1947 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 135 T^{2} - 229 T^{3} + 7965 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 + 2 T + 99 T^{2} + 84 T^{3} + 5841 T^{4} + 6962 T^{5} + 205379 T^{6} \))(\( 1 - 4 T + 110 T^{2} - 404 T^{3} + 8866 T^{4} - 23836 T^{5} + 382910 T^{6} - 821516 T^{7} + 12117361 T^{8} \))(\( 1 - 3 T + 141 T^{2} - 41 T^{3} + 9630 T^{4} + 7820 T^{5} + 568170 T^{6} - 142721 T^{7} + 28958439 T^{8} - 36352083 T^{9} + 714924299 T^{10} \))(\( 1 - 3 T + 141 T^{2} - 41 T^{3} + 9630 T^{4} + 7820 T^{5} + 568170 T^{6} - 142721 T^{7} + 28958439 T^{8} - 36352083 T^{9} + 714924299 T^{10} \))(\( 1 - 26 T + 491 T^{2} - 6414 T^{3} + 68414 T^{4} - 576224 T^{5} + 4036426 T^{6} - 22327134 T^{7} + 100841089 T^{8} - 315051386 T^{9} + 714924299 T^{10} \))(\( 1 - 26 T + 491 T^{2} - 6414 T^{3} + 68414 T^{4} - 576224 T^{5} + 4036426 T^{6} - 22327134 T^{7} + 100841089 T^{8} - 315051386 T^{9} + 714924299 T^{10} \))(\( 1 + 12 T + 86 T^{2} + 1032 T^{3} + 13613 T^{4} + 102640 T^{5} + 653242 T^{6} + 6055760 T^{7} + 47386853 T^{8} + 211951128 T^{9} + 1042093046 T^{10} + 8579091588 T^{11} + 42180533641 T^{12} \))(\( 1 + 12 T + 86 T^{2} + 1032 T^{3} + 13613 T^{4} + 102640 T^{5} + 653242 T^{6} + 6055760 T^{7} + 47386853 T^{8} + 211951128 T^{9} + 1042093046 T^{10} + 8579091588 T^{11} + 42180533641 T^{12} \))(\( 1 + 3 T + 246 T^{2} + 189 T^{3} + 29403 T^{4} - 44049 T^{5} + 2424513 T^{6} - 7841796 T^{7} + 162746523 T^{8} - 612296737 T^{9} + 9602044857 T^{10} - 27297291876 T^{11} + 497944055427 T^{12} - 533757634689 T^{13} + 21020919163497 T^{14} + 7972120858149 T^{15} + 612208265265474 T^{16} + 440491312812963 T^{17} + 8662995818654939 T^{18} \))(\( 1 - 3 T + 288 T^{2} - 1827 T^{3} + 43335 T^{4} - 338043 T^{5} + 4734231 T^{6} - 35023224 T^{7} + 381620979 T^{8} - 2463176367 T^{9} + 22515637761 T^{10} - 121915842744 T^{11} + 972311628549 T^{12} - 4096189064523 T^{13} + 30981244497165 T^{14} - 77063834962107 T^{15} + 716731627627872 T^{16} - 440491312812963 T^{17} + 8662995818654939 T^{18} \))(\( 1 - 3 T + 288 T^{2} - 1827 T^{3} + 43335 T^{4} - 338043 T^{5} + 4734231 T^{6} - 35023224 T^{7} + 381620979 T^{8} - 2463176367 T^{9} + 22515637761 T^{10} - 121915842744 T^{11} + 972311628549 T^{12} - 4096189064523 T^{13} + 30981244497165 T^{14} - 77063834962107 T^{15} + 716731627627872 T^{16} - 440491312812963 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 3 T + 246 T^{2} + 189 T^{3} + 29403 T^{4} - 44049 T^{5} + 2424513 T^{6} - 7841796 T^{7} + 162746523 T^{8} - 612296737 T^{9} + 9602044857 T^{10} - 27297291876 T^{11} + 497944055427 T^{12} - 533757634689 T^{13} + 21020919163497 T^{14} + 7972120858149 T^{15} + 612208265265474 T^{16} + 440491312812963 T^{17} + 8662995818654939 T^{18} \))(\( 1 - 20 T + 618 T^{2} - 9016 T^{3} + 160851 T^{4} - 1858392 T^{5} + 24351302 T^{6} - 232096896 T^{7} + 2434545420 T^{8} - 19516464300 T^{9} + 170267580496 T^{10} - 1151471393700 T^{11} + 8474652607020 T^{12} - 47667828403584 T^{13} + 295073517154022 T^{14} - 1328609597867208 T^{15} + 6784781016688491 T^{16} - 22437681787128104 T^{17} + 90741210439470378 T^{18} - 173259916373098780 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 20 T + 618 T^{2} - 9016 T^{3} + 160851 T^{4} - 1858392 T^{5} + 24351302 T^{6} - 232096896 T^{7} + 2434545420 T^{8} - 19516464300 T^{9} + 170267580496 T^{10} - 1151471393700 T^{11} + 8474652607020 T^{12} - 47667828403584 T^{13} + 295073517154022 T^{14} - 1328609597867208 T^{15} + 6784781016688491 T^{16} - 22437681787128104 T^{17} + 90741210439470378 T^{18} - 173259916373098780 T^{19} + 511116753300641401 T^{20} \))(\( 1 + 15 T + 612 T^{2} + 7141 T^{3} + 169026 T^{4} + 1651068 T^{5} + 29535557 T^{6} + 253450017 T^{7} + 3778054137 T^{8} + 29350931553 T^{9} + 381532332426 T^{10} + 2727694973313 T^{11} + 31683606223308 T^{12} + 209660710824516 T^{13} + 2208882631580277 T^{14} + 13496593815419986 T^{15} + 130324075263236343 T^{16} + 729828934380140196 T^{17} + 6507147362536773732 T^{18} + 33052464689518986993 T^{19} + \)\(27\!\cdots\!74\)\( T^{20} + \)\(12\!\cdots\!73\)\( T^{21} + \)\(94\!\cdots\!03\)\( T^{22} + \)\(37\!\cdots\!57\)\( T^{23} + \)\(25\!\cdots\!23\)\( T^{24} + \)\(84\!\cdots\!68\)\( T^{25} + \)\(50\!\cdots\!34\)\( T^{26} + \)\(12\!\cdots\!21\)\( T^{27} + \)\(64\!\cdots\!48\)\( T^{28} + \)\(92\!\cdots\!15\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 + 21 T + 642 T^{2} + 10497 T^{3} + 195114 T^{4} + 2648844 T^{5} + 37942005 T^{6} + 444827265 T^{7} + 5343741285 T^{8} + 55453307767 T^{9} + 581797865922 T^{10} + 5424795906849 T^{11} + 50803118313906 T^{12} + 429195659361624 T^{13} + 3630306376429953 T^{14} + 27881329875021530 T^{15} + 214188076209367227 T^{16} + 1494030090237813144 T^{17} + 10433893636191700374 T^{18} + 65734210354611705489 T^{19} + \)\(41\!\cdots\!78\)\( T^{20} + \)\(23\!\cdots\!47\)\( T^{21} + \)\(13\!\cdots\!15\)\( T^{22} + \)\(65\!\cdots\!65\)\( T^{23} + \)\(32\!\cdots\!95\)\( T^{24} + \)\(13\!\cdots\!44\)\( T^{25} + \)\(58\!\cdots\!26\)\( T^{26} + \)\(18\!\cdots\!57\)\( T^{27} + \)\(67\!\cdots\!18\)\( T^{28} + \)\(13\!\cdots\!81\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 + 21 T + 642 T^{2} + 10497 T^{3} + 195114 T^{4} + 2648844 T^{5} + 37942005 T^{6} + 444827265 T^{7} + 5343741285 T^{8} + 55453307767 T^{9} + 581797865922 T^{10} + 5424795906849 T^{11} + 50803118313906 T^{12} + 429195659361624 T^{13} + 3630306376429953 T^{14} + 27881329875021530 T^{15} + 214188076209367227 T^{16} + 1494030090237813144 T^{17} + 10433893636191700374 T^{18} + 65734210354611705489 T^{19} + \)\(41\!\cdots\!78\)\( T^{20} + \)\(23\!\cdots\!47\)\( T^{21} + \)\(13\!\cdots\!15\)\( T^{22} + \)\(65\!\cdots\!65\)\( T^{23} + \)\(32\!\cdots\!95\)\( T^{24} + \)\(13\!\cdots\!44\)\( T^{25} + \)\(58\!\cdots\!26\)\( T^{26} + \)\(18\!\cdots\!57\)\( T^{27} + \)\(67\!\cdots\!18\)\( T^{28} + \)\(13\!\cdots\!81\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 + 15 T + 612 T^{2} + 7141 T^{3} + 169026 T^{4} + 1651068 T^{5} + 29535557 T^{6} + 253450017 T^{7} + 3778054137 T^{8} + 29350931553 T^{9} + 381532332426 T^{10} + 2727694973313 T^{11} + 31683606223308 T^{12} + 209660710824516 T^{13} + 2208882631580277 T^{14} + 13496593815419986 T^{15} + 130324075263236343 T^{16} + 729828934380140196 T^{17} + 6507147362536773732 T^{18} + 33052464689518986993 T^{19} + \)\(27\!\cdots\!74\)\( T^{20} + \)\(12\!\cdots\!73\)\( T^{21} + \)\(94\!\cdots\!03\)\( T^{22} + \)\(37\!\cdots\!57\)\( T^{23} + \)\(25\!\cdots\!23\)\( T^{24} + \)\(84\!\cdots\!68\)\( T^{25} + \)\(50\!\cdots\!34\)\( T^{26} + \)\(12\!\cdots\!21\)\( T^{27} + \)\(64\!\cdots\!48\)\( T^{28} + \)\(92\!\cdots\!15\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 + 64 T + 2528 T^{2} + 73120 T^{3} + 1717612 T^{4} + 34196088 T^{5} + 596133180 T^{6} + 9270405432 T^{7} + 130561789286 T^{8} + 1681747302640 T^{9} + 19975741638424 T^{10} + 220023190093064 T^{11} + 2257899855913446 T^{12} + 21655891273563072 T^{13} + 194631108199142404 T^{14} + 1641580735613173736 T^{15} + 13007808520754896126 T^{16} + 96853263401177250424 T^{17} + \)\(67\!\cdots\!24\)\( T^{18} + \)\(44\!\cdots\!88\)\( T^{19} + \)\(27\!\cdots\!06\)\( T^{20} + \)\(15\!\cdots\!36\)\( T^{21} + \)\(84\!\cdots\!84\)\( T^{22} + \)\(41\!\cdots\!60\)\( T^{23} + \)\(19\!\cdots\!06\)\( T^{24} + \)\(80\!\cdots\!48\)\( T^{25} + \)\(30\!\cdots\!80\)\( T^{26} + \)\(10\!\cdots\!92\)\( T^{27} + \)\(30\!\cdots\!72\)\( T^{28} + \)\(76\!\cdots\!80\)\( T^{29} + \)\(15\!\cdots\!08\)\( T^{30} + \)\(23\!\cdots\!36\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 64 T + 2528 T^{2} + 73120 T^{3} + 1717612 T^{4} + 34196088 T^{5} + 596133180 T^{6} + 9270405432 T^{7} + 130561789286 T^{8} + 1681747302640 T^{9} + 19975741638424 T^{10} + 220023190093064 T^{11} + 2257899855913446 T^{12} + 21655891273563072 T^{13} + 194631108199142404 T^{14} + 1641580735613173736 T^{15} + 13007808520754896126 T^{16} + 96853263401177250424 T^{17} + \)\(67\!\cdots\!24\)\( T^{18} + \)\(44\!\cdots\!88\)\( T^{19} + \)\(27\!\cdots\!06\)\( T^{20} + \)\(15\!\cdots\!36\)\( T^{21} + \)\(84\!\cdots\!84\)\( T^{22} + \)\(41\!\cdots\!60\)\( T^{23} + \)\(19\!\cdots\!06\)\( T^{24} + \)\(80\!\cdots\!48\)\( T^{25} + \)\(30\!\cdots\!80\)\( T^{26} + \)\(10\!\cdots\!92\)\( T^{27} + \)\(30\!\cdots\!72\)\( T^{28} + \)\(76\!\cdots\!80\)\( T^{29} + \)\(15\!\cdots\!08\)\( T^{30} + \)\(23\!\cdots\!36\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 10 T + 144 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 36 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 70 T^{2} + 3721 T^{4} \))(\( 1 + 70 T^{2} + 3721 T^{4} \))(\( 1 + 9 T + 147 T^{2} + 747 T^{3} + 8967 T^{4} + 33489 T^{5} + 226981 T^{6} \))(\( 1 - 6 T + 59 T^{2} - 742 T^{3} + 3599 T^{4} - 22326 T^{5} + 226981 T^{6} \))(\( 1 - 9 T + 147 T^{2} - 747 T^{3} + 8967 T^{4} - 33489 T^{5} + 226981 T^{6} \))(\( 1 + 6 T + 59 T^{2} + 742 T^{3} + 3599 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 - 9 T + 153 T^{2} - 1061 T^{3} + 9333 T^{4} - 33489 T^{5} + 226981 T^{6} \))(\( 1 + 13 T + 169 T^{2} + 1145 T^{3} + 10309 T^{4} + 48373 T^{5} + 226981 T^{6} \))(\( 1 + 9 T + 153 T^{2} + 1061 T^{3} + 9333 T^{4} + 33489 T^{5} + 226981 T^{6} \))(\( 1 - 13 T + 169 T^{2} - 1145 T^{3} + 10309 T^{4} - 48373 T^{5} + 226981 T^{6} \))(\( 1 - 12 T + 165 T^{2} - 1356 T^{3} + 10065 T^{4} - 44652 T^{5} + 226981 T^{6} \))(\( 1 - 4 T + 86 T^{2} + 60 T^{3} + 2082 T^{4} + 3660 T^{5} + 320006 T^{6} - 907924 T^{7} + 13845841 T^{8} \))(\( 1 - 5 T + 129 T^{2} - 629 T^{3} + 12458 T^{4} - 47364 T^{5} + 759938 T^{6} - 2340509 T^{7} + 29280549 T^{8} - 69229205 T^{9} + 844596301 T^{10} \))(\( 1 + 5 T + 129 T^{2} + 629 T^{3} + 12458 T^{4} + 47364 T^{5} + 759938 T^{6} + 2340509 T^{7} + 29280549 T^{8} + 69229205 T^{9} + 844596301 T^{10} \))(\( 1 - 14 T + 265 T^{2} - 2298 T^{3} + 26762 T^{4} - 178416 T^{5} + 1632482 T^{6} - 8550858 T^{7} + 60149965 T^{8} - 193841774 T^{9} + 844596301 T^{10} \))(\( 1 + 14 T + 265 T^{2} + 2298 T^{3} + 26762 T^{4} + 178416 T^{5} + 1632482 T^{6} + 8550858 T^{7} + 60149965 T^{8} + 193841774 T^{9} + 844596301 T^{10} \))(\( 1 - 20 T + 440 T^{2} - 5736 T^{3} + 71617 T^{4} - 676320 T^{5} + 5921890 T^{6} - 41255520 T^{7} + 266486857 T^{8} - 1301963016 T^{9} + 6092170040 T^{10} - 16891926020 T^{11} + 51520374361 T^{12} \))(\( 1 + 20 T + 440 T^{2} + 5736 T^{3} + 71617 T^{4} + 676320 T^{5} + 5921890 T^{6} + 41255520 T^{7} + 266486857 T^{8} + 1301963016 T^{9} + 6092170040 T^{10} + 16891926020 T^{11} + 51520374361 T^{12} \))(\( 1 - 33 T + 825 T^{2} - 14918 T^{3} + 227739 T^{4} - 2927769 T^{5} + 33326638 T^{6} - 334980822 T^{7} + 3048029490 T^{8} - 24937379371 T^{9} + 185929798890 T^{10} - 1246463638662 T^{11} + 7564513619878 T^{12} - 40537424058729 T^{13} + 192347516993439 T^{14} - 768580944717398 T^{15} + 2592762839717325 T^{16} - 6326341328910273 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 3 T + 333 T^{2} - 666 T^{3} + 56091 T^{4} - 83199 T^{5} + 6317706 T^{6} - 7523154 T^{7} + 515478702 T^{8} - 517413533 T^{9} + 31444200822 T^{10} - 27993656034 T^{11} + 1433999225586 T^{12} - 1151960125359 T^{13} + 47374251119391 T^{14} - 34312569324426 T^{15} + 1046533364394993 T^{16} - 575121938991843 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 3 T + 333 T^{2} + 666 T^{3} + 56091 T^{4} + 83199 T^{5} + 6317706 T^{6} + 7523154 T^{7} + 515478702 T^{8} + 517413533 T^{9} + 31444200822 T^{10} + 27993656034 T^{11} + 1433999225586 T^{12} + 1151960125359 T^{13} + 47374251119391 T^{14} + 34312569324426 T^{15} + 1046533364394993 T^{16} + 575121938991843 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 33 T + 825 T^{2} + 14918 T^{3} + 227739 T^{4} + 2927769 T^{5} + 33326638 T^{6} + 334980822 T^{7} + 3048029490 T^{8} + 24937379371 T^{9} + 185929798890 T^{10} + 1246463638662 T^{11} + 7564513619878 T^{12} + 40537424058729 T^{13} + 192347516993439 T^{14} + 768580944717398 T^{15} + 2592762839717325 T^{16} + 6326341328910273 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 4 T + 228 T^{2} - 1048 T^{3} + 34423 T^{4} - 143152 T^{5} + 3565226 T^{6} - 13980936 T^{7} + 294987208 T^{8} - 1046855340 T^{9} + 19636482804 T^{10} - 63858175740 T^{11} + 1097647400968 T^{12} - 3173406834216 T^{13} + 49363552325066 T^{14} - 120905649680752 T^{15} + 1773485846628703 T^{16} - 3293594492150008 T^{17} + 43709267363380068 T^{18} - 46776584371336564 T^{19} + 713342911662882601 T^{20} \))(\( 1 + 4 T + 228 T^{2} + 1048 T^{3} + 34423 T^{4} + 143152 T^{5} + 3565226 T^{6} + 13980936 T^{7} + 294987208 T^{8} + 1046855340 T^{9} + 19636482804 T^{10} + 63858175740 T^{11} + 1097647400968 T^{12} + 3173406834216 T^{13} + 49363552325066 T^{14} + 120905649680752 T^{15} + 1773485846628703 T^{16} + 3293594492150008 T^{17} + 43709267363380068 T^{18} + 46776584371336564 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 3 T + 405 T^{2} - 1038 T^{3} + 80514 T^{4} - 240402 T^{5} + 10594849 T^{6} - 43622604 T^{7} + 1032842034 T^{8} - 6051295179 T^{9} + 79877019699 T^{10} - 647575153632 T^{11} + 5261078236318 T^{12} - 54760131408720 T^{13} + 321962053159656 T^{14} - 3718982200870668 T^{15} + 19639685242739016 T^{16} - 203762448971847120 T^{17} + 1194164799157695958 T^{18} - 8966222612739244512 T^{19} + 67463835372679533399 T^{20} - \)\(31\!\cdots\!19\)\( T^{21} + \)\(32\!\cdots\!14\)\( T^{22} - \)\(83\!\cdots\!24\)\( T^{23} + \)\(12\!\cdots\!09\)\( T^{24} - \)\(17\!\cdots\!02\)\( T^{25} + \)\(35\!\cdots\!54\)\( T^{26} - \)\(27\!\cdots\!98\)\( T^{27} + \)\(65\!\cdots\!05\)\( T^{28} - \)\(29\!\cdots\!23\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 + 39 T + 1209 T^{2} + 26638 T^{3} + 513018 T^{4} + 8343606 T^{5} + 123463665 T^{6} + 1634928084 T^{7} + 20128663590 T^{8} + 227928702367 T^{9} + 2430337412319 T^{10} + 24189324814608 T^{11} + 228434422882886 T^{12} + 2030019678424500 T^{13} + 17187328985303460 T^{14} + 137436799730025756 T^{15} + 1048427068103511060 T^{16} + 7553703223417564500 T^{17} + 51850273740380347166 T^{18} + \)\(33\!\cdots\!28\)\( T^{19} + \)\(20\!\cdots\!19\)\( T^{20} + \)\(11\!\cdots\!87\)\( T^{21} + \)\(63\!\cdots\!90\)\( T^{22} + \)\(31\!\cdots\!04\)\( T^{23} + \)\(14\!\cdots\!65\)\( T^{24} + \)\(59\!\cdots\!06\)\( T^{25} + \)\(22\!\cdots\!98\)\( T^{26} + \)\(70\!\cdots\!98\)\( T^{27} + \)\(19\!\cdots\!29\)\( T^{28} + \)\(38\!\cdots\!99\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 - 39 T + 1209 T^{2} - 26638 T^{3} + 513018 T^{4} - 8343606 T^{5} + 123463665 T^{6} - 1634928084 T^{7} + 20128663590 T^{8} - 227928702367 T^{9} + 2430337412319 T^{10} - 24189324814608 T^{11} + 228434422882886 T^{12} - 2030019678424500 T^{13} + 17187328985303460 T^{14} - 137436799730025756 T^{15} + 1048427068103511060 T^{16} - 7553703223417564500 T^{17} + 51850273740380347166 T^{18} - \)\(33\!\cdots\!28\)\( T^{19} + \)\(20\!\cdots\!19\)\( T^{20} - \)\(11\!\cdots\!87\)\( T^{21} + \)\(63\!\cdots\!90\)\( T^{22} - \)\(31\!\cdots\!04\)\( T^{23} + \)\(14\!\cdots\!65\)\( T^{24} - \)\(59\!\cdots\!06\)\( T^{25} + \)\(22\!\cdots\!98\)\( T^{26} - \)\(70\!\cdots\!98\)\( T^{27} + \)\(19\!\cdots\!29\)\( T^{28} - \)\(38\!\cdots\!99\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 + 3 T + 405 T^{2} + 1038 T^{3} + 80514 T^{4} + 240402 T^{5} + 10594849 T^{6} + 43622604 T^{7} + 1032842034 T^{8} + 6051295179 T^{9} + 79877019699 T^{10} + 647575153632 T^{11} + 5261078236318 T^{12} + 54760131408720 T^{13} + 321962053159656 T^{14} + 3718982200870668 T^{15} + 19639685242739016 T^{16} + 203762448971847120 T^{17} + 1194164799157695958 T^{18} + 8966222612739244512 T^{19} + 67463835372679533399 T^{20} + \)\(31\!\cdots\!19\)\( T^{21} + \)\(32\!\cdots\!14\)\( T^{22} + \)\(83\!\cdots\!24\)\( T^{23} + \)\(12\!\cdots\!09\)\( T^{24} + \)\(17\!\cdots\!02\)\( T^{25} + \)\(35\!\cdots\!54\)\( T^{26} + \)\(27\!\cdots\!98\)\( T^{27} + \)\(65\!\cdots\!05\)\( T^{28} + \)\(29\!\cdots\!23\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 + 8 T + 456 T^{2} + 3216 T^{3} + 107592 T^{4} + 699232 T^{5} + 17569396 T^{6} + 106144640 T^{7} + 2212290062 T^{8} + 12433895144 T^{9} + 227236509864 T^{10} + 1189368198672 T^{11} + 19696483032146 T^{12} + 96220048159504 T^{13} + 1471407916389636 T^{14} + 6724244751245488 T^{15} + 95896882459231514 T^{16} + 410178929825974768 T^{17} + 5475108856885835556 T^{18} + 21840122751292377424 T^{19} + \)\(27\!\cdots\!86\)\( T^{20} + \)\(10\!\cdots\!72\)\( T^{21} + \)\(11\!\cdots\!04\)\( T^{22} + \)\(39\!\cdots\!24\)\( T^{23} + \)\(42\!\cdots\!22\)\( T^{24} + \)\(12\!\cdots\!40\)\( T^{25} + \)\(12\!\cdots\!96\)\( T^{26} + \)\(30\!\cdots\!52\)\( T^{27} + \)\(28\!\cdots\!32\)\( T^{28} + \)\(52\!\cdots\!96\)\( T^{29} + \)\(45\!\cdots\!96\)\( T^{30} + \)\(48\!\cdots\!08\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 8 T + 456 T^{2} - 3216 T^{3} + 107592 T^{4} - 699232 T^{5} + 17569396 T^{6} - 106144640 T^{7} + 2212290062 T^{8} - 12433895144 T^{9} + 227236509864 T^{10} - 1189368198672 T^{11} + 19696483032146 T^{12} - 96220048159504 T^{13} + 1471407916389636 T^{14} - 6724244751245488 T^{15} + 95896882459231514 T^{16} - 410178929825974768 T^{17} + 5475108856885835556 T^{18} - 21840122751292377424 T^{19} + \)\(27\!\cdots\!86\)\( T^{20} - \)\(10\!\cdots\!72\)\( T^{21} + \)\(11\!\cdots\!04\)\( T^{22} - \)\(39\!\cdots\!24\)\( T^{23} + \)\(42\!\cdots\!22\)\( T^{24} - \)\(12\!\cdots\!40\)\( T^{25} + \)\(12\!\cdots\!96\)\( T^{26} - \)\(30\!\cdots\!52\)\( T^{27} + \)\(28\!\cdots\!32\)\( T^{28} - \)\(52\!\cdots\!96\)\( T^{29} + \)\(45\!\cdots\!96\)\( T^{30} - \)\(48\!\cdots\!08\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))
$67$ (\( 1 + 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 16 T + 186 T^{2} + 1072 T^{3} + 4489 T^{4} \))(\( 1 + 4 T + 106 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 118 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 118 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 144 T^{2} - 1037 T^{3} + 9648 T^{4} - 40401 T^{5} + 300763 T^{6} \))(\( 1 + 12 T + 89 T^{2} + 604 T^{3} + 5963 T^{4} + 53868 T^{5} + 300763 T^{6} \))(\( 1 - 9 T + 144 T^{2} - 1037 T^{3} + 9648 T^{4} - 40401 T^{5} + 300763 T^{6} \))(\( 1 + 12 T + 89 T^{2} + 604 T^{3} + 5963 T^{4} + 53868 T^{5} + 300763 T^{6} \))(\( 1 + 3 T + 120 T^{2} + 23 T^{3} + 8040 T^{4} + 13467 T^{5} + 300763 T^{6} \))(\( 1 - 5 T + 128 T^{2} - 793 T^{3} + 8576 T^{4} - 22445 T^{5} + 300763 T^{6} \))(\( 1 + 3 T + 120 T^{2} + 23 T^{3} + 8040 T^{4} + 13467 T^{5} + 300763 T^{6} \))(\( 1 - 5 T + 128 T^{2} - 793 T^{3} + 8576 T^{4} - 22445 T^{5} + 300763 T^{6} \))(\( 1 - 12 T + 93 T^{2} - 920 T^{3} + 6231 T^{4} - 53868 T^{5} + 300763 T^{6} \))(\( 1 - 28 T + 512 T^{2} - 6300 T^{3} + 59694 T^{4} - 422100 T^{5} + 2298368 T^{6} - 8421364 T^{7} + 20151121 T^{8} \))(\( 1 + 11 T + 234 T^{2} + 2225 T^{3} + 26993 T^{4} + 210384 T^{5} + 1808531 T^{6} + 9988025 T^{7} + 70378542 T^{8} + 221662331 T^{9} + 1350125107 T^{10} \))(\( 1 + 11 T + 234 T^{2} + 2225 T^{3} + 26993 T^{4} + 210384 T^{5} + 1808531 T^{6} + 9988025 T^{7} + 70378542 T^{8} + 221662331 T^{9} + 1350125107 T^{10} \))(\( 1 + 4 T + 191 T^{2} - 348 T^{3} + 11402 T^{4} - 87152 T^{5} + 763934 T^{6} - 1562172 T^{7} + 57445733 T^{8} + 80604484 T^{9} + 1350125107 T^{10} \))(\( 1 + 4 T + 191 T^{2} - 348 T^{3} + 11402 T^{4} - 87152 T^{5} + 763934 T^{6} - 1562172 T^{7} + 57445733 T^{8} + 80604484 T^{9} + 1350125107 T^{10} \))(\( 1 + 28 T + 634 T^{2} + 9952 T^{3} + 129219 T^{4} + 1369980 T^{5} + 12224408 T^{6} + 91788660 T^{7} + 580064091 T^{8} + 2993193376 T^{9} + 12775810714 T^{10} + 37803502996 T^{11} + 90458382169 T^{12} \))(\( 1 + 28 T + 634 T^{2} + 9952 T^{3} + 129219 T^{4} + 1369980 T^{5} + 12224408 T^{6} + 91788660 T^{7} + 580064091 T^{8} + 2993193376 T^{9} + 12775810714 T^{10} + 37803502996 T^{11} + 90458382169 T^{12} \))(\( 1 + 15 T + 441 T^{2} + 5122 T^{3} + 92805 T^{4} + 904887 T^{5} + 12386222 T^{6} + 102849678 T^{7} + 1150437630 T^{8} + 8170791449 T^{9} + 77079321210 T^{10} + 461692204542 T^{11} + 3725317287386 T^{12} + 18234487428327 T^{13} + 125298360555135 T^{14} + 463327833469618 T^{15} + 2672773817947443 T^{16} + 6091015163349615 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 3 T + 225 T^{2} + 1362 T^{3} + 33717 T^{4} + 213555 T^{5} + 3577398 T^{6} + 23502546 T^{7} + 301086138 T^{8} + 1768560221 T^{9} + 20172771246 T^{10} + 105502928994 T^{11} + 1075948954674 T^{12} + 4303372645155 T^{13} + 45522168232719 T^{14} + 123204316514178 T^{15} + 1363660111197675 T^{16} + 1218203032669923 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 3 T + 225 T^{2} + 1362 T^{3} + 33717 T^{4} + 213555 T^{5} + 3577398 T^{6} + 23502546 T^{7} + 301086138 T^{8} + 1768560221 T^{9} + 20172771246 T^{10} + 105502928994 T^{11} + 1075948954674 T^{12} + 4303372645155 T^{13} + 45522168232719 T^{14} + 123204316514178 T^{15} + 1363660111197675 T^{16} + 1218203032669923 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 15 T + 441 T^{2} + 5122 T^{3} + 92805 T^{4} + 904887 T^{5} + 12386222 T^{6} + 102849678 T^{7} + 1150437630 T^{8} + 8170791449 T^{9} + 77079321210 T^{10} + 461692204542 T^{11} + 3725317287386 T^{12} + 18234487428327 T^{13} + 125298360555135 T^{14} + 463327833469618 T^{15} + 2672773817947443 T^{16} + 6091015163349615 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 20 T + 630 T^{2} - 9248 T^{3} + 169969 T^{4} - 2006492 T^{5} + 27434596 T^{6} - 271627180 T^{7} + 3008480358 T^{8} - 25397834508 T^{9} + 236383789932 T^{10} - 1701654912036 T^{11} + 13505068327062 T^{12} - 81695405538340 T^{13} + 552837863582116 T^{14} - 2709015226194644 T^{15} + 15375120758882761 T^{16} - 56049460926027104 T^{17} + 255822636860683830 T^{18} - 544130687925898940 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 20 T + 630 T^{2} - 9248 T^{3} + 169969 T^{4} - 2006492 T^{5} + 27434596 T^{6} - 271627180 T^{7} + 3008480358 T^{8} - 25397834508 T^{9} + 236383789932 T^{10} - 1701654912036 T^{11} + 13505068327062 T^{12} - 81695405538340 T^{13} + 552837863582116 T^{14} - 2709015226194644 T^{15} + 15375120758882761 T^{16} - 56049460926027104 T^{17} + 255822636860683830 T^{18} - 544130687925898940 T^{19} + 1822837804551761449 T^{20} \))(\( 1 + 3 T + 540 T^{2} + 1899 T^{3} + 151614 T^{4} + 572595 T^{5} + 28981114 T^{6} + 112408584 T^{7} + 4192429599 T^{8} + 16169381017 T^{9} + 484433477112 T^{10} + 1810551685431 T^{11} + 46065259755136 T^{12} + 163189365640488 T^{13} + 3663769134686055 T^{14} + 12047798656634197 T^{15} + 245472532023965685 T^{16} + 732557062360150632 T^{17} + 13854725719733968768 T^{18} + 36484646089874018151 T^{19} + \)\(65\!\cdots\!84\)\( T^{20} + \)\(14\!\cdots\!73\)\( T^{21} + \)\(25\!\cdots\!77\)\( T^{22} + \)\(45\!\cdots\!44\)\( T^{23} + \)\(78\!\cdots\!58\)\( T^{24} + \)\(10\!\cdots\!55\)\( T^{25} + \)\(18\!\cdots\!62\)\( T^{26} + \)\(15\!\cdots\!39\)\( T^{27} + \)\(29\!\cdots\!80\)\( T^{28} + \)\(11\!\cdots\!87\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 - 57 T + 2172 T^{2} - 60961 T^{3} + 1416558 T^{4} - 28043241 T^{5} + 490021602 T^{6} - 7659293052 T^{7} + 108803552859 T^{8} - 1414767181135 T^{9} + 16981534149456 T^{10} - 188897018828121 T^{11} + 1956587535977564 T^{12} - 18907294335451248 T^{13} + 170896307876152803 T^{14} - 1445378386447897767 T^{15} + 11450052627702237801 T^{16} - 84874844271840652272 T^{17} + \)\(58\!\cdots\!32\)\( T^{18} - \)\(38\!\cdots\!41\)\( T^{19} + \)\(22\!\cdots\!92\)\( T^{20} - \)\(12\!\cdots\!15\)\( T^{21} + \)\(65\!\cdots\!57\)\( T^{22} - \)\(31\!\cdots\!32\)\( T^{23} + \)\(13\!\cdots\!94\)\( T^{24} - \)\(51\!\cdots\!09\)\( T^{25} + \)\(17\!\cdots\!14\)\( T^{26} - \)\(49\!\cdots\!21\)\( T^{27} + \)\(11\!\cdots\!64\)\( T^{28} - \)\(20\!\cdots\!53\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 - 57 T + 2172 T^{2} - 60961 T^{3} + 1416558 T^{4} - 28043241 T^{5} + 490021602 T^{6} - 7659293052 T^{7} + 108803552859 T^{8} - 1414767181135 T^{9} + 16981534149456 T^{10} - 188897018828121 T^{11} + 1956587535977564 T^{12} - 18907294335451248 T^{13} + 170896307876152803 T^{14} - 1445378386447897767 T^{15} + 11450052627702237801 T^{16} - 84874844271840652272 T^{17} + \)\(58\!\cdots\!32\)\( T^{18} - \)\(38\!\cdots\!41\)\( T^{19} + \)\(22\!\cdots\!92\)\( T^{20} - \)\(12\!\cdots\!15\)\( T^{21} + \)\(65\!\cdots\!57\)\( T^{22} - \)\(31\!\cdots\!32\)\( T^{23} + \)\(13\!\cdots\!94\)\( T^{24} - \)\(51\!\cdots\!09\)\( T^{25} + \)\(17\!\cdots\!14\)\( T^{26} - \)\(49\!\cdots\!21\)\( T^{27} + \)\(11\!\cdots\!64\)\( T^{28} - \)\(20\!\cdots\!53\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 + 3 T + 540 T^{2} + 1899 T^{3} + 151614 T^{4} + 572595 T^{5} + 28981114 T^{6} + 112408584 T^{7} + 4192429599 T^{8} + 16169381017 T^{9} + 484433477112 T^{10} + 1810551685431 T^{11} + 46065259755136 T^{12} + 163189365640488 T^{13} + 3663769134686055 T^{14} + 12047798656634197 T^{15} + 245472532023965685 T^{16} + 732557062360150632 T^{17} + 13854725719733968768 T^{18} + 36484646089874018151 T^{19} + \)\(65\!\cdots\!84\)\( T^{20} + \)\(14\!\cdots\!73\)\( T^{21} + \)\(25\!\cdots\!77\)\( T^{22} + \)\(45\!\cdots\!44\)\( T^{23} + \)\(78\!\cdots\!58\)\( T^{24} + \)\(10\!\cdots\!55\)\( T^{25} + \)\(18\!\cdots\!62\)\( T^{26} + \)\(15\!\cdots\!39\)\( T^{27} + \)\(29\!\cdots\!80\)\( T^{28} + \)\(11\!\cdots\!87\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 + 48 T + 1588 T^{2} + 38600 T^{3} + 789792 T^{4} + 13841712 T^{5} + 217103552 T^{6} + 3071967032 T^{7} + 40054011296 T^{8} + 483374852008 T^{9} + 5468386026752 T^{10} + 58145386617616 T^{11} + 586154072687492 T^{12} + 5609300585187944 T^{13} + 51268701662901276 T^{14} + 447478210022003104 T^{15} + 3744418423048532630 T^{16} + 29981040071474207968 T^{17} + \)\(23\!\cdots\!64\)\( T^{18} + \)\(16\!\cdots\!72\)\( T^{19} + \)\(11\!\cdots\!32\)\( T^{20} + \)\(78\!\cdots\!12\)\( T^{21} + \)\(49\!\cdots\!88\)\( T^{22} + \)\(29\!\cdots\!84\)\( T^{23} + \)\(16\!\cdots\!36\)\( T^{24} + \)\(83\!\cdots\!04\)\( T^{25} + \)\(39\!\cdots\!48\)\( T^{26} + \)\(16\!\cdots\!96\)\( T^{27} + \)\(64\!\cdots\!12\)\( T^{28} + \)\(21\!\cdots\!00\)\( T^{29} + \)\(58\!\cdots\!52\)\( T^{30} + \)\(11\!\cdots\!64\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 + 48 T + 1588 T^{2} + 38600 T^{3} + 789792 T^{4} + 13841712 T^{5} + 217103552 T^{6} + 3071967032 T^{7} + 40054011296 T^{8} + 483374852008 T^{9} + 5468386026752 T^{10} + 58145386617616 T^{11} + 586154072687492 T^{12} + 5609300585187944 T^{13} + 51268701662901276 T^{14} + 447478210022003104 T^{15} + 3744418423048532630 T^{16} + 29981040071474207968 T^{17} + \)\(23\!\cdots\!64\)\( T^{18} + \)\(16\!\cdots\!72\)\( T^{19} + \)\(11\!\cdots\!32\)\( T^{20} + \)\(78\!\cdots\!12\)\( T^{21} + \)\(49\!\cdots\!88\)\( T^{22} + \)\(29\!\cdots\!84\)\( T^{23} + \)\(16\!\cdots\!36\)\( T^{24} + \)\(83\!\cdots\!04\)\( T^{25} + \)\(39\!\cdots\!48\)\( T^{26} + \)\(16\!\cdots\!96\)\( T^{27} + \)\(64\!\cdots\!12\)\( T^{28} + \)\(21\!\cdots\!00\)\( T^{29} + \)\(58\!\cdots\!52\)\( T^{30} + \)\(11\!\cdots\!64\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))
$71$ (\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 130 T^{2} + 5041 T^{4} \))(\( ( 1 + 2 T + 71 T^{2} )^{2} \))(\( 1 + 2 T + 91 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 - 2 T + 91 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 - 3 T + 188 T^{2} - 343 T^{3} + 13348 T^{4} - 15123 T^{5} + 357911 T^{6} \))(\( 1 + 8 T + 81 T^{2} + 396 T^{3} + 5751 T^{4} + 40328 T^{5} + 357911 T^{6} \))(\( 1 + 3 T + 188 T^{2} + 343 T^{3} + 13348 T^{4} + 15123 T^{5} + 357911 T^{6} \))(\( 1 - 8 T + 81 T^{2} - 396 T^{3} + 5751 T^{4} - 40328 T^{5} + 357911 T^{6} \))(\( 1 + 3 T + 132 T^{2} + 639 T^{3} + 9372 T^{4} + 15123 T^{5} + 357911 T^{6} \))(\( 1 - 13 T + 136 T^{2} - 1333 T^{3} + 9656 T^{4} - 65533 T^{5} + 357911 T^{6} \))(\( 1 - 3 T + 132 T^{2} - 639 T^{3} + 9372 T^{4} - 15123 T^{5} + 357911 T^{6} \))(\( 1 + 13 T + 136 T^{2} + 1333 T^{3} + 9656 T^{4} + 65533 T^{5} + 357911 T^{6} \))(\( 1 + 41 T^{2} - 352 T^{3} + 2911 T^{4} + 357911 T^{6} \))(\( 1 + 4 T + 80 T^{2} - 268 T^{3} + 4414 T^{4} - 19028 T^{5} + 403280 T^{6} + 1431644 T^{7} + 25411681 T^{8} \))(\( 1 + 31 T + 677 T^{2} + 10002 T^{3} + 119521 T^{4} + 1105953 T^{5} + 8485991 T^{6} + 50420082 T^{7} + 242305747 T^{8} + 787762111 T^{9} + 1804229351 T^{10} \))(\( 1 - 31 T + 677 T^{2} - 10002 T^{3} + 119521 T^{4} - 1105953 T^{5} + 8485991 T^{6} - 50420082 T^{7} + 242305747 T^{8} - 787762111 T^{9} + 1804229351 T^{10} \))(\( 1 - 16 T + 323 T^{2} - 3876 T^{3} + 43946 T^{4} - 392872 T^{5} + 3120166 T^{6} - 19538916 T^{7} + 115605253 T^{8} - 406586896 T^{9} + 1804229351 T^{10} \))(\( 1 + 16 T + 323 T^{2} + 3876 T^{3} + 43946 T^{4} + 392872 T^{5} + 3120166 T^{6} + 19538916 T^{7} + 115605253 T^{8} + 406586896 T^{9} + 1804229351 T^{10} \))(\( 1 - 20 T + 422 T^{2} - 5368 T^{3} + 70999 T^{4} - 675460 T^{5} + 6565248 T^{6} - 47957660 T^{7} + 357905959 T^{8} - 1921266248 T^{9} + 10723729382 T^{10} - 36084587020 T^{11} + 128100283921 T^{12} \))(\( 1 + 20 T + 422 T^{2} + 5368 T^{3} + 70999 T^{4} + 675460 T^{5} + 6565248 T^{6} + 47957660 T^{7} + 357905959 T^{8} + 1921266248 T^{9} + 10723729382 T^{10} + 36084587020 T^{11} + 128100283921 T^{12} \))(\( 1 + 483 T^{2} + 476 T^{3} + 107232 T^{4} + 196824 T^{5} + 14688688 T^{6} + 34312518 T^{7} + 1407390513 T^{8} + 3228790331 T^{9} + 99924726423 T^{10} + 172969403238 T^{11} + 5257243010768 T^{12} + 5001628701144 T^{13} + 193471121766432 T^{14} + 60975735146396 T^{15} + 4392943036502853 T^{16} + 45848500718449031 T^{18} \))(\( 1 - 12 T + 375 T^{2} - 2904 T^{3} + 61860 T^{4} - 349788 T^{5} + 6706872 T^{6} - 28969788 T^{7} + 561141141 T^{8} - 2079376101 T^{9} + 39841021011 T^{10} - 146036701308 T^{11} + 2400463264392 T^{12} - 8888701073628 T^{13} + 111609627652860 T^{14} - 372003224506584 T^{15} + 3410670059396625 T^{16} - 7749042374949132 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 12 T + 375 T^{2} + 2904 T^{3} + 61860 T^{4} + 349788 T^{5} + 6706872 T^{6} + 28969788 T^{7} + 561141141 T^{8} + 2079376101 T^{9} + 39841021011 T^{10} + 146036701308 T^{11} + 2400463264392 T^{12} + 8888701073628 T^{13} + 111609627652860 T^{14} + 372003224506584 T^{15} + 3410670059396625 T^{16} + 7749042374949132 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 483 T^{2} - 476 T^{3} + 107232 T^{4} - 196824 T^{5} + 14688688 T^{6} - 34312518 T^{7} + 1407390513 T^{8} - 3228790331 T^{9} + 99924726423 T^{10} - 172969403238 T^{11} + 5257243010768 T^{12} - 5001628701144 T^{13} + 193471121766432 T^{14} - 60975735146396 T^{15} + 4392943036502853 T^{16} + 45848500718449031 T^{18} \))(\( 1 - 20 T + 606 T^{2} - 8824 T^{3} + 161273 T^{4} - 1915212 T^{5} + 26546668 T^{6} - 266891404 T^{7} + 3025998550 T^{8} - 26097694084 T^{9} + 250402439964 T^{10} - 1852936279964 T^{11} + 15254058690550 T^{12} - 95523369297044 T^{13} + 674595458828908 T^{14} - 3455481703787412 T^{15} + 20659117088791433 T^{16} - 80255340277642184 T^{17} + 391326639934931166 T^{18} - 916970014368980620 T^{19} + 3255243551009881201 T^{20} \))(\( 1 + 20 T + 606 T^{2} + 8824 T^{3} + 161273 T^{4} + 1915212 T^{5} + 26546668 T^{6} + 266891404 T^{7} + 3025998550 T^{8} + 26097694084 T^{9} + 250402439964 T^{10} + 1852936279964 T^{11} + 15254058690550 T^{12} + 95523369297044 T^{13} + 674595458828908 T^{14} + 3455481703787412 T^{15} + 20659117088791433 T^{16} + 80255340277642184 T^{17} + 391326639934931166 T^{18} + 916970014368980620 T^{19} + 3255243551009881201 T^{20} \))(\( 1 + 60 T + 2109 T^{2} + 54176 T^{3} + 1133202 T^{4} + 20299644 T^{5} + 322180017 T^{6} + 4622882304 T^{7} + 60897167352 T^{8} + 743998939207 T^{9} + 8499219170991 T^{10} + 91281096905376 T^{11} + 925652180167817 T^{12} + 8886236820981552 T^{13} + 80921076213714942 T^{14} + 699612643766511723 T^{15} + 5745396411173760882 T^{16} + 44795519814568003632 T^{17} + \)\(33\!\cdots\!87\)\( T^{18} + \)\(23\!\cdots\!56\)\( T^{19} + \)\(15\!\cdots\!41\)\( T^{20} + \)\(95\!\cdots\!47\)\( T^{21} + \)\(55\!\cdots\!32\)\( T^{22} + \)\(29\!\cdots\!44\)\( T^{23} + \)\(14\!\cdots\!27\)\( T^{24} + \)\(66\!\cdots\!44\)\( T^{25} + \)\(26\!\cdots\!42\)\( T^{26} + \)\(88\!\cdots\!16\)\( T^{27} + \)\(24\!\cdots\!99\)\( T^{28} + \)\(49\!\cdots\!60\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 + 72 T + 3057 T^{2} + 93124 T^{3} + 2261778 T^{4} + 45975264 T^{5} + 810672497 T^{6} + 12678638910 T^{7} + 179075378520 T^{8} + 2312532467199 T^{9} + 27584859891123 T^{10} + 306088854387270 T^{11} + 3178119784324537 T^{12} + 30995895531916650 T^{13} + 284831702125489326 T^{14} + 2469767997656070783 T^{15} + 20223050850909742146 T^{16} + \)\(15\!\cdots\!50\)\( T^{17} + \)\(11\!\cdots\!07\)\( T^{18} + \)\(77\!\cdots\!70\)\( T^{19} + \)\(49\!\cdots\!73\)\( T^{20} + \)\(29\!\cdots\!79\)\( T^{21} + \)\(16\!\cdots\!20\)\( T^{22} + \)\(81\!\cdots\!10\)\( T^{23} + \)\(37\!\cdots\!07\)\( T^{24} + \)\(14\!\cdots\!64\)\( T^{25} + \)\(52\!\cdots\!38\)\( T^{26} + \)\(15\!\cdots\!84\)\( T^{27} + \)\(35\!\cdots\!27\)\( T^{28} + \)\(59\!\cdots\!32\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 - 72 T + 3057 T^{2} - 93124 T^{3} + 2261778 T^{4} - 45975264 T^{5} + 810672497 T^{6} - 12678638910 T^{7} + 179075378520 T^{8} - 2312532467199 T^{9} + 27584859891123 T^{10} - 306088854387270 T^{11} + 3178119784324537 T^{12} - 30995895531916650 T^{13} + 284831702125489326 T^{14} - 2469767997656070783 T^{15} + 20223050850909742146 T^{16} - \)\(15\!\cdots\!50\)\( T^{17} + \)\(11\!\cdots\!07\)\( T^{18} - \)\(77\!\cdots\!70\)\( T^{19} + \)\(49\!\cdots\!73\)\( T^{20} - \)\(29\!\cdots\!79\)\( T^{21} + \)\(16\!\cdots\!20\)\( T^{22} - \)\(81\!\cdots\!10\)\( T^{23} + \)\(37\!\cdots\!07\)\( T^{24} - \)\(14\!\cdots\!64\)\( T^{25} + \)\(52\!\cdots\!38\)\( T^{26} - \)\(15\!\cdots\!84\)\( T^{27} + \)\(35\!\cdots\!27\)\( T^{28} - \)\(59\!\cdots\!32\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 - 60 T + 2109 T^{2} - 54176 T^{3} + 1133202 T^{4} - 20299644 T^{5} + 322180017 T^{6} - 4622882304 T^{7} + 60897167352 T^{8} - 743998939207 T^{9} + 8499219170991 T^{10} - 91281096905376 T^{11} + 925652180167817 T^{12} - 8886236820981552 T^{13} + 80921076213714942 T^{14} - 699612643766511723 T^{15} + 5745396411173760882 T^{16} - 44795519814568003632 T^{17} + \)\(33\!\cdots\!87\)\( T^{18} - \)\(23\!\cdots\!56\)\( T^{19} + \)\(15\!\cdots\!41\)\( T^{20} - \)\(95\!\cdots\!47\)\( T^{21} + \)\(55\!\cdots\!32\)\( T^{22} - \)\(29\!\cdots\!44\)\( T^{23} + \)\(14\!\cdots\!27\)\( T^{24} - \)\(66\!\cdots\!44\)\( T^{25} + \)\(26\!\cdots\!42\)\( T^{26} - \)\(88\!\cdots\!16\)\( T^{27} + \)\(24\!\cdots\!99\)\( T^{28} - \)\(49\!\cdots\!60\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 - 40 T + 1220 T^{2} - 28080 T^{3} + 553724 T^{4} - 9520992 T^{5} + 147453352 T^{6} - 2084632184 T^{7} + 27266965684 T^{8} - 332898035608 T^{9} + 3821413117744 T^{10} - 41478229902144 T^{11} + 427614065904832 T^{12} - 4200892052513488 T^{13} + 39435658935681268 T^{14} - 354250327094299656 T^{15} + 3049411851091955198 T^{16} - 25151773223695275576 T^{17} + \)\(19\!\cdots\!88\)\( T^{18} - \)\(15\!\cdots\!68\)\( T^{19} + \)\(10\!\cdots\!92\)\( T^{20} - \)\(74\!\cdots\!44\)\( T^{21} + \)\(48\!\cdots\!24\)\( T^{22} - \)\(30\!\cdots\!28\)\( T^{23} + \)\(17\!\cdots\!24\)\( T^{24} - \)\(95\!\cdots\!04\)\( T^{25} + \)\(47\!\cdots\!52\)\( T^{26} - \)\(22\!\cdots\!32\)\( T^{27} + \)\(90\!\cdots\!84\)\( T^{28} - \)\(32\!\cdots\!80\)\( T^{29} + \)\(10\!\cdots\!20\)\( T^{30} - \)\(23\!\cdots\!40\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 40 T + 1220 T^{2} + 28080 T^{3} + 553724 T^{4} + 9520992 T^{5} + 147453352 T^{6} + 2084632184 T^{7} + 27266965684 T^{8} + 332898035608 T^{9} + 3821413117744 T^{10} + 41478229902144 T^{11} + 427614065904832 T^{12} + 4200892052513488 T^{13} + 39435658935681268 T^{14} + 354250327094299656 T^{15} + 3049411851091955198 T^{16} + 25151773223695275576 T^{17} + \)\(19\!\cdots\!88\)\( T^{18} + \)\(15\!\cdots\!68\)\( T^{19} + \)\(10\!\cdots\!92\)\( T^{20} + \)\(74\!\cdots\!44\)\( T^{21} + \)\(48\!\cdots\!24\)\( T^{22} + \)\(30\!\cdots\!28\)\( T^{23} + \)\(17\!\cdots\!24\)\( T^{24} + \)\(95\!\cdots\!04\)\( T^{25} + \)\(47\!\cdots\!52\)\( T^{26} + \)\(22\!\cdots\!32\)\( T^{27} + \)\(90\!\cdots\!84\)\( T^{28} + \)\(32\!\cdots\!80\)\( T^{29} + \)\(10\!\cdots\!20\)\( T^{30} + \)\(23\!\cdots\!40\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))
$73$ (\( 1 - 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 134 T^{2} + 5329 T^{4} \))(\( 1 - 12 T + 174 T^{2} - 876 T^{3} + 5329 T^{4} \))(\( 1 - 18 T + 214 T^{2} - 1314 T^{3} + 5329 T^{4} \))(\( 1 + 18 T + 214 T^{2} + 1314 T^{3} + 5329 T^{4} \))(\( 1 + 5 T + 106 T^{2} + 941 T^{3} + 7738 T^{4} + 26645 T^{5} + 389017 T^{6} \))(\( 1 - 6 T + 87 T^{2} - 164 T^{3} + 6351 T^{4} - 31974 T^{5} + 389017 T^{6} \))(\( 1 - 5 T + 106 T^{2} - 941 T^{3} + 7738 T^{4} - 26645 T^{5} + 389017 T^{6} \))(\( 1 + 6 T + 87 T^{2} + 164 T^{3} + 6351 T^{4} + 31974 T^{5} + 389017 T^{6} \))(\( 1 - 15 T + 246 T^{2} - 2139 T^{3} + 17958 T^{4} - 79935 T^{5} + 389017 T^{6} \))(\( 1 - 9 T + 166 T^{2} - 909 T^{3} + 12118 T^{4} - 47961 T^{5} + 389017 T^{6} \))(\( 1 + 15 T + 246 T^{2} + 2139 T^{3} + 17958 T^{4} + 79935 T^{5} + 389017 T^{6} \))(\( 1 + 9 T + 166 T^{2} + 909 T^{3} + 12118 T^{4} + 47961 T^{5} + 389017 T^{6} \))(\( 1 - 22 T + 319 T^{2} - 2980 T^{3} + 23287 T^{4} - 117238 T^{5} + 389017 T^{6} \))(\( 1 + 8 T + 116 T^{2} - 360 T^{3} + 630 T^{4} - 26280 T^{5} + 618164 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + 13 T + 222 T^{2} + 1435 T^{3} + 15587 T^{4} + 77520 T^{5} + 1137851 T^{6} + 7647115 T^{7} + 86361774 T^{8} + 369177133 T^{9} + 2073071593 T^{10} \))(\( 1 - 13 T + 222 T^{2} - 1435 T^{3} + 15587 T^{4} - 77520 T^{5} + 1137851 T^{6} - 7647115 T^{7} + 86361774 T^{8} - 369177133 T^{9} + 2073071593 T^{10} \))(\( 1 + 14 T + 357 T^{2} + 3512 T^{3} + 50594 T^{4} + 364212 T^{5} + 3693362 T^{6} + 18715448 T^{7} + 138879069 T^{8} + 397575374 T^{9} + 2073071593 T^{10} \))(\( 1 - 14 T + 357 T^{2} - 3512 T^{3} + 50594 T^{4} - 364212 T^{5} + 3693362 T^{6} - 18715448 T^{7} + 138879069 T^{8} - 397575374 T^{9} + 2073071593 T^{10} \))(\( 1 - 36 T + 634 T^{2} - 7412 T^{3} + 74815 T^{4} - 752648 T^{5} + 6990252 T^{6} - 54943304 T^{7} + 398689135 T^{8} - 2883394004 T^{9} + 18004484794 T^{10} - 74630577348 T^{11} + 151334226289 T^{12} \))(\( 1 + 36 T + 634 T^{2} + 7412 T^{3} + 74815 T^{4} + 752648 T^{5} + 6990252 T^{6} + 54943304 T^{7} + 398689135 T^{8} + 2883394004 T^{9} + 18004484794 T^{10} + 74630577348 T^{11} + 151334226289 T^{12} \))(\( 1 - 21 T + 669 T^{2} - 10392 T^{3} + 190086 T^{4} - 2351538 T^{5} + 31387456 T^{6} - 319007214 T^{7} + 3373933260 T^{8} - 28403486253 T^{9} + 246297127980 T^{10} - 1699989443406 T^{11} + 12210253970752 T^{12} - 66779542844658 T^{13} + 394061886826998 T^{14} - 1572665279595288 T^{15} + 7390709609275893 T^{16} - 16935661929775701 T^{17} + 58871586708267913 T^{18} \))(\( 1 - 15 T + 285 T^{2} - 2784 T^{3} + 45510 T^{4} - 408930 T^{5} + 5084844 T^{6} - 37369506 T^{7} + 447175056 T^{8} - 3176887383 T^{9} + 32643779088 T^{10} - 199142097474 T^{11} + 1978090758348 T^{12} - 11612892692130 T^{13} + 94345488197430 T^{14} - 421314485988576 T^{15} + 3148508577942645 T^{16} - 12096901378411215 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 15 T + 285 T^{2} + 2784 T^{3} + 45510 T^{4} + 408930 T^{5} + 5084844 T^{6} + 37369506 T^{7} + 447175056 T^{8} + 3176887383 T^{9} + 32643779088 T^{10} + 199142097474 T^{11} + 1978090758348 T^{12} + 11612892692130 T^{13} + 94345488197430 T^{14} + 421314485988576 T^{15} + 3148508577942645 T^{16} + 12096901378411215 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 21 T + 669 T^{2} + 10392 T^{3} + 190086 T^{4} + 2351538 T^{5} + 31387456 T^{6} + 319007214 T^{7} + 3373933260 T^{8} + 28403486253 T^{9} + 246297127980 T^{10} + 1699989443406 T^{11} + 12210253970752 T^{12} + 66779542844658 T^{13} + 394061886826998 T^{14} + 1572665279595288 T^{15} + 7390709609275893 T^{16} + 16935661929775701 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 20 T + 422 T^{2} + 5908 T^{3} + 83645 T^{4} + 974736 T^{5} + 11328072 T^{6} + 114836560 T^{7} + 1153800722 T^{8} + 10433697048 T^{9} + 93401872804 T^{10} + 761659884504 T^{11} + 6148604047538 T^{12} + 44673374061520 T^{13} + 321697318721352 T^{14} + 2020697512274448 T^{15} + 12658351357943405 T^{16} + 65268030450825076 T^{17} + 340326158779302182 T^{18} + 1177431734165358260 T^{19} + 4297625829703557649 T^{20} \))(\( 1 - 20 T + 422 T^{2} - 5908 T^{3} + 83645 T^{4} - 974736 T^{5} + 11328072 T^{6} - 114836560 T^{7} + 1153800722 T^{8} - 10433697048 T^{9} + 93401872804 T^{10} - 761659884504 T^{11} + 6148604047538 T^{12} - 44673374061520 T^{13} + 321697318721352 T^{14} - 2020697512274448 T^{15} + 12658351357943405 T^{16} - 65268030450825076 T^{17} + 340326158779302182 T^{18} - 1177431734165358260 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 15 T + 555 T^{2} + 8468 T^{3} + 170553 T^{4} + 2382141 T^{5} + 36578963 T^{6} + 454695834 T^{7} + 5906683191 T^{8} + 66094061374 T^{9} + 754311004539 T^{10} + 7688590169274 T^{11} + 78800271051165 T^{12} + 734774571727494 T^{13} + 6857129731983849 T^{14} + 58575440203131888 T^{15} + 500570470434820977 T^{16} + 3915613692735815526 T^{17} + 30654645043511054805 T^{18} + \)\(21\!\cdots\!34\)\( T^{19} + \)\(15\!\cdots\!27\)\( T^{20} + \)\(10\!\cdots\!86\)\( T^{21} + \)\(65\!\cdots\!27\)\( T^{22} + \)\(36\!\cdots\!54\)\( T^{23} + \)\(21\!\cdots\!19\)\( T^{24} + \)\(10\!\cdots\!09\)\( T^{25} + \)\(53\!\cdots\!81\)\( T^{26} + \)\(19\!\cdots\!28\)\( T^{27} + \)\(92\!\cdots\!15\)\( T^{28} + \)\(18\!\cdots\!35\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 + 21 T + 891 T^{2} + 15220 T^{3} + 371049 T^{4} + 5367915 T^{5} + 97187319 T^{6} + 1222132518 T^{7} + 18079607811 T^{8} + 201134227798 T^{9} + 2549668018299 T^{10} + 25392194960550 T^{11} + 283348747760909 T^{12} + 2544030249576474 T^{13} + 25385034248721321 T^{14} + 205988265367358400 T^{15} + 1853107500156656433 T^{16} + 13557137199993029946 T^{17} + \)\(11\!\cdots\!53\)\( T^{18} + \)\(72\!\cdots\!50\)\( T^{19} + \)\(52\!\cdots\!07\)\( T^{20} + \)\(30\!\cdots\!22\)\( T^{21} + \)\(19\!\cdots\!67\)\( T^{22} + \)\(98\!\cdots\!58\)\( T^{23} + \)\(57\!\cdots\!47\)\( T^{24} + \)\(23\!\cdots\!35\)\( T^{25} + \)\(11\!\cdots\!73\)\( T^{26} + \)\(34\!\cdots\!20\)\( T^{27} + \)\(14\!\cdots\!03\)\( T^{28} + \)\(25\!\cdots\!89\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 - 21 T + 891 T^{2} - 15220 T^{3} + 371049 T^{4} - 5367915 T^{5} + 97187319 T^{6} - 1222132518 T^{7} + 18079607811 T^{8} - 201134227798 T^{9} + 2549668018299 T^{10} - 25392194960550 T^{11} + 283348747760909 T^{12} - 2544030249576474 T^{13} + 25385034248721321 T^{14} - 205988265367358400 T^{15} + 1853107500156656433 T^{16} - 13557137199993029946 T^{17} + \)\(11\!\cdots\!53\)\( T^{18} - \)\(72\!\cdots\!50\)\( T^{19} + \)\(52\!\cdots\!07\)\( T^{20} - \)\(30\!\cdots\!22\)\( T^{21} + \)\(19\!\cdots\!67\)\( T^{22} - \)\(98\!\cdots\!58\)\( T^{23} + \)\(57\!\cdots\!47\)\( T^{24} - \)\(23\!\cdots\!35\)\( T^{25} + \)\(11\!\cdots\!73\)\( T^{26} - \)\(34\!\cdots\!20\)\( T^{27} + \)\(14\!\cdots\!03\)\( T^{28} - \)\(25\!\cdots\!89\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 - 15 T + 555 T^{2} - 8468 T^{3} + 170553 T^{4} - 2382141 T^{5} + 36578963 T^{6} - 454695834 T^{7} + 5906683191 T^{8} - 66094061374 T^{9} + 754311004539 T^{10} - 7688590169274 T^{11} + 78800271051165 T^{12} - 734774571727494 T^{13} + 6857129731983849 T^{14} - 58575440203131888 T^{15} + 500570470434820977 T^{16} - 3915613692735815526 T^{17} + 30654645043511054805 T^{18} - \)\(21\!\cdots\!34\)\( T^{19} + \)\(15\!\cdots\!27\)\( T^{20} - \)\(10\!\cdots\!86\)\( T^{21} + \)\(65\!\cdots\!27\)\( T^{22} - \)\(36\!\cdots\!54\)\( T^{23} + \)\(21\!\cdots\!19\)\( T^{24} - \)\(10\!\cdots\!09\)\( T^{25} + \)\(53\!\cdots\!81\)\( T^{26} - \)\(19\!\cdots\!28\)\( T^{27} + \)\(92\!\cdots\!15\)\( T^{28} - \)\(18\!\cdots\!35\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 - 24 T + 900 T^{2} - 17320 T^{3} + 393458 T^{4} - 6343128 T^{5} + 110340548 T^{6} - 1538927944 T^{7} + 22281446640 T^{8} - 274265997208 T^{9} + 3440201876060 T^{10} - 37857718646536 T^{11} + 420471789860526 T^{12} - 4169144601592824 T^{13} + 41519080797307228 T^{14} - 372421833775799432 T^{15} + 3348148910062390494 T^{16} - 27186793865633358536 T^{17} + \)\(22\!\cdots\!12\)\( T^{18} - \)\(16\!\cdots\!08\)\( T^{19} + \)\(11\!\cdots\!66\)\( T^{20} - \)\(78\!\cdots\!48\)\( T^{21} + \)\(52\!\cdots\!40\)\( T^{22} - \)\(30\!\cdots\!76\)\( T^{23} + \)\(17\!\cdots\!40\)\( T^{24} - \)\(90\!\cdots\!72\)\( T^{25} + \)\(47\!\cdots\!52\)\( T^{26} - \)\(19\!\cdots\!56\)\( T^{27} + \)\(90\!\cdots\!18\)\( T^{28} - \)\(28\!\cdots\!60\)\( T^{29} + \)\(10\!\cdots\!00\)\( T^{30} - \)\(21\!\cdots\!68\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 + 24 T + 900 T^{2} + 17320 T^{3} + 393458 T^{4} + 6343128 T^{5} + 110340548 T^{6} + 1538927944 T^{7} + 22281446640 T^{8} + 274265997208 T^{9} + 3440201876060 T^{10} + 37857718646536 T^{11} + 420471789860526 T^{12} + 4169144601592824 T^{13} + 41519080797307228 T^{14} + 372421833775799432 T^{15} + 3348148910062390494 T^{16} + 27186793865633358536 T^{17} + \)\(22\!\cdots\!12\)\( T^{18} + \)\(16\!\cdots\!08\)\( T^{19} + \)\(11\!\cdots\!66\)\( T^{20} + \)\(78\!\cdots\!48\)\( T^{21} + \)\(52\!\cdots\!40\)\( T^{22} + \)\(30\!\cdots\!76\)\( T^{23} + \)\(17\!\cdots\!40\)\( T^{24} + \)\(90\!\cdots\!72\)\( T^{25} + \)\(47\!\cdots\!52\)\( T^{26} + \)\(19\!\cdots\!56\)\( T^{27} + \)\(90\!\cdots\!18\)\( T^{28} + \)\(28\!\cdots\!60\)\( T^{29} + \)\(10\!\cdots\!00\)\( T^{30} + \)\(21\!\cdots\!68\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))
$79$ (\( 1 + 16 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 10 T + 156 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 - 4 T - 316 T^{3} + 6241 T^{4} \))(\( 1 + 12 T + 181 T^{2} + 948 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 181 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 - 13 T + 256 T^{2} - 1957 T^{3} + 20224 T^{4} - 81133 T^{5} + 493039 T^{6} \))(\( 1 - 2 T - 21 T^{2} + 898 T^{3} - 1659 T^{4} - 12482 T^{5} + 493039 T^{6} \))(\( 1 + 13 T + 256 T^{2} + 1957 T^{3} + 20224 T^{4} + 81133 T^{5} + 493039 T^{6} \))(\( 1 + 2 T - 21 T^{2} - 898 T^{3} - 1659 T^{4} + 12482 T^{5} + 493039 T^{6} \))(\( ( 1 - 7 T + 79 T^{2} )^{3} \))(\( ( 1 - 13 T + 79 T^{2} )^{3} \))(\( ( 1 + 7 T + 79 T^{2} )^{3} \))(\( ( 1 + 13 T + 79 T^{2} )^{3} \))(\( 1 + 2 T + 223 T^{2} + 284 T^{3} + 17617 T^{4} + 12482 T^{5} + 493039 T^{6} \))(\( 1 - 8 T + 74 T^{2} - 360 T^{3} - 534 T^{4} - 28440 T^{5} + 461834 T^{6} - 3944312 T^{7} + 38950081 T^{8} \))(\( 1 + 5 T + 273 T^{2} + 866 T^{3} + 33857 T^{4} + 79239 T^{5} + 2674703 T^{6} + 5404706 T^{7} + 134599647 T^{8} + 194750405 T^{9} + 3077056399 T^{10} \))(\( 1 - 5 T + 273 T^{2} - 866 T^{3} + 33857 T^{4} - 79239 T^{5} + 2674703 T^{6} - 5404706 T^{7} + 134599647 T^{8} - 194750405 T^{9} + 3077056399 T^{10} \))(\( 1 + 10 T + 381 T^{2} + 3006 T^{3} + 58836 T^{4} + 350000 T^{5} + 4648044 T^{6} + 18760446 T^{7} + 187847859 T^{8} + 389500810 T^{9} + 3077056399 T^{10} \))(\( 1 - 10 T + 381 T^{2} - 3006 T^{3} + 58836 T^{4} - 350000 T^{5} + 4648044 T^{6} - 18760446 T^{7} + 187847859 T^{8} - 389500810 T^{9} + 3077056399 T^{10} \))(\( 1 + 12 T + 402 T^{2} + 4320 T^{3} + 72235 T^{4} + 653060 T^{5} + 7374422 T^{6} + 51591740 T^{7} + 450818635 T^{8} + 2129928480 T^{9} + 15657932562 T^{10} + 36924676788 T^{11} + 243087455521 T^{12} \))(\( 1 - 12 T + 402 T^{2} - 4320 T^{3} + 72235 T^{4} - 653060 T^{5} + 7374422 T^{6} - 51591740 T^{7} + 450818635 T^{8} - 2129928480 T^{9} + 15657932562 T^{10} - 36924676788 T^{11} + 243087455521 T^{12} \))(\( 1 - 30 T + 978 T^{2} - 19449 T^{3} + 370335 T^{4} - 5471349 T^{5} + 75622518 T^{6} - 873175935 T^{7} + 9391027695 T^{8} - 86509645657 T^{9} + 741891187905 T^{10} - 5449491010335 T^{11} + 37284850652202 T^{12} - 213109486729269 T^{13} + 1139541681523665 T^{14} - 4727807922427929 T^{15} + 18781422988463502 T^{16} - 45513264297196830 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 18 T + 594 T^{2} + 8565 T^{3} + 164259 T^{4} + 1957437 T^{5} + 27696642 T^{6} + 276847119 T^{7} + 3138674391 T^{8} + 26366393369 T^{9} + 247955276889 T^{10} + 1727802869679 T^{11} + 13655524675038 T^{12} + 76242329702397 T^{13} + 505434207043341 T^{14} + 2082044056537365 T^{15} + 11407121937778446 T^{16} + 27307958578318098 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 18 T + 594 T^{2} - 8565 T^{3} + 164259 T^{4} - 1957437 T^{5} + 27696642 T^{6} - 276847119 T^{7} + 3138674391 T^{8} - 26366393369 T^{9} + 247955276889 T^{10} - 1727802869679 T^{11} + 13655524675038 T^{12} - 76242329702397 T^{13} + 505434207043341 T^{14} - 2082044056537365 T^{15} + 11407121937778446 T^{16} - 27307958578318098 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 30 T + 978 T^{2} + 19449 T^{3} + 370335 T^{4} + 5471349 T^{5} + 75622518 T^{6} + 873175935 T^{7} + 9391027695 T^{8} + 86509645657 T^{9} + 741891187905 T^{10} + 5449491010335 T^{11} + 37284850652202 T^{12} + 213109486729269 T^{13} + 1139541681523665 T^{14} + 4727807922427929 T^{15} + 18781422988463502 T^{16} + 45513264297196830 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 20 T + 566 T^{2} + 8504 T^{3} + 142281 T^{4} + 1768492 T^{5} + 22645362 T^{6} + 245838652 T^{7} + 2638129806 T^{8} + 25425634932 T^{9} + 236538598976 T^{10} + 2008625159628 T^{11} + 16464568119246 T^{12} + 121208043143428 T^{13} + 882038684174322 T^{14} + 5441749625180308 T^{15} + 34586726258983401 T^{16} + 163310042018296136 T^{17} + 858683586407113526 T^{18} + 2397031919652366380 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 20 T + 566 T^{2} - 8504 T^{3} + 142281 T^{4} - 1768492 T^{5} + 22645362 T^{6} - 245838652 T^{7} + 2638129806 T^{8} - 25425634932 T^{9} + 236538598976 T^{10} - 2008625159628 T^{11} + 16464568119246 T^{12} - 121208043143428 T^{13} + 882038684174322 T^{14} - 5441749625180308 T^{15} + 34586726258983401 T^{16} - 163310042018296136 T^{17} + 858683586407113526 T^{18} - 2397031919652366380 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + 42 T + 1374 T^{2} + 32249 T^{3} + 665739 T^{4} + 11698869 T^{5} + 188530763 T^{6} + 2733854481 T^{7} + 37102778445 T^{8} + 465014297218 T^{9} + 5519580733176 T^{10} + 61360213865160 T^{11} + 650621847414933 T^{12} + 6511550051002326 T^{13} + 62401866547807650 T^{14} + 566448562540938807 T^{15} + 4929747457276804350 T^{16} + 40638583868305516566 T^{17} + \)\(32\!\cdots\!87\)\( T^{18} + \)\(23\!\cdots\!60\)\( T^{19} + \)\(16\!\cdots\!24\)\( T^{20} + \)\(11\!\cdots\!78\)\( T^{21} + \)\(71\!\cdots\!55\)\( T^{22} + \)\(41\!\cdots\!41\)\( T^{23} + \)\(22\!\cdots\!97\)\( T^{24} + \)\(11\!\cdots\!69\)\( T^{25} + \)\(49\!\cdots\!81\)\( T^{26} + \)\(19\!\cdots\!09\)\( T^{27} + \)\(64\!\cdots\!86\)\( T^{28} + \)\(15\!\cdots\!02\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 - 30 T + 894 T^{2} - 18613 T^{3} + 362583 T^{4} - 6003237 T^{5} + 92841303 T^{6} - 1303070829 T^{7} + 17191897821 T^{8} - 211542708454 T^{9} + 2464082452596 T^{10} - 27136084639728 T^{11} + 284375605529381 T^{12} - 2836481330522226 T^{13} + 27014922814816470 T^{14} - 245596852256704455 T^{15} + 2134178902370501130 T^{16} - 17702479983789212466 T^{17} + \)\(14\!\cdots\!59\)\( T^{18} - \)\(10\!\cdots\!68\)\( T^{19} + \)\(75\!\cdots\!04\)\( T^{20} - \)\(51\!\cdots\!34\)\( T^{21} + \)\(33\!\cdots\!39\)\( T^{22} - \)\(19\!\cdots\!69\)\( T^{23} + \)\(11\!\cdots\!57\)\( T^{24} - \)\(56\!\cdots\!37\)\( T^{25} + \)\(27\!\cdots\!57\)\( T^{26} - \)\(10\!\cdots\!33\)\( T^{27} + \)\(41\!\cdots\!66\)\( T^{28} - \)\(11\!\cdots\!30\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 + 30 T + 894 T^{2} + 18613 T^{3} + 362583 T^{4} + 6003237 T^{5} + 92841303 T^{6} + 1303070829 T^{7} + 17191897821 T^{8} + 211542708454 T^{9} + 2464082452596 T^{10} + 27136084639728 T^{11} + 284375605529381 T^{12} + 2836481330522226 T^{13} + 27014922814816470 T^{14} + 245596852256704455 T^{15} + 2134178902370501130 T^{16} + 17702479983789212466 T^{17} + \)\(14\!\cdots\!59\)\( T^{18} + \)\(10\!\cdots\!68\)\( T^{19} + \)\(75\!\cdots\!04\)\( T^{20} + \)\(51\!\cdots\!34\)\( T^{21} + \)\(33\!\cdots\!39\)\( T^{22} + \)\(19\!\cdots\!69\)\( T^{23} + \)\(11\!\cdots\!57\)\( T^{24} + \)\(56\!\cdots\!37\)\( T^{25} + \)\(27\!\cdots\!57\)\( T^{26} + \)\(10\!\cdots\!33\)\( T^{27} + \)\(41\!\cdots\!66\)\( T^{28} + \)\(11\!\cdots\!30\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 - 42 T + 1374 T^{2} - 32249 T^{3} + 665739 T^{4} - 11698869 T^{5} + 188530763 T^{6} - 2733854481 T^{7} + 37102778445 T^{8} - 465014297218 T^{9} + 5519580733176 T^{10} - 61360213865160 T^{11} + 650621847414933 T^{12} - 6511550051002326 T^{13} + 62401866547807650 T^{14} - 566448562540938807 T^{15} + 4929747457276804350 T^{16} - 40638583868305516566 T^{17} + \)\(32\!\cdots\!87\)\( T^{18} - \)\(23\!\cdots\!60\)\( T^{19} + \)\(16\!\cdots\!24\)\( T^{20} - \)\(11\!\cdots\!78\)\( T^{21} + \)\(71\!\cdots\!55\)\( T^{22} - \)\(41\!\cdots\!41\)\( T^{23} + \)\(22\!\cdots\!97\)\( T^{24} - \)\(11\!\cdots\!69\)\( T^{25} + \)\(49\!\cdots\!81\)\( T^{26} - \)\(19\!\cdots\!09\)\( T^{27} + \)\(64\!\cdots\!86\)\( T^{28} - \)\(15\!\cdots\!02\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 - 8 T + 616 T^{2} - 3904 T^{3} + 186376 T^{4} - 967744 T^{5} + 37758652 T^{6} - 162657880 T^{7} + 5800632244 T^{8} - 20677056888 T^{9} + 723634720012 T^{10} - 2129853094608 T^{11} + 76768228146362 T^{12} - 189377602974096 T^{13} + 7146703764025832 T^{14} - 15490639503621992 T^{15} + 595033565693724322 T^{16} - 1223760520786137368 T^{17} + 44602578191285217512 T^{18} - 93370543992745317744 T^{19} + \)\(29\!\cdots\!22\)\( T^{20} - \)\(65\!\cdots\!92\)\( T^{21} + \)\(17\!\cdots\!52\)\( T^{22} - \)\(39\!\cdots\!92\)\( T^{23} + \)\(88\!\cdots\!84\)\( T^{24} - \)\(19\!\cdots\!20\)\( T^{25} + \)\(35\!\cdots\!52\)\( T^{26} - \)\(72\!\cdots\!76\)\( T^{27} + \)\(11\!\cdots\!16\)\( T^{28} - \)\(18\!\cdots\!56\)\( T^{29} + \)\(22\!\cdots\!96\)\( T^{30} - \)\(23\!\cdots\!92\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 + 8 T + 616 T^{2} + 3904 T^{3} + 186376 T^{4} + 967744 T^{5} + 37758652 T^{6} + 162657880 T^{7} + 5800632244 T^{8} + 20677056888 T^{9} + 723634720012 T^{10} + 2129853094608 T^{11} + 76768228146362 T^{12} + 189377602974096 T^{13} + 7146703764025832 T^{14} + 15490639503621992 T^{15} + 595033565693724322 T^{16} + 1223760520786137368 T^{17} + 44602578191285217512 T^{18} + 93370543992745317744 T^{19} + \)\(29\!\cdots\!22\)\( T^{20} + \)\(65\!\cdots\!92\)\( T^{21} + \)\(17\!\cdots\!52\)\( T^{22} + \)\(39\!\cdots\!92\)\( T^{23} + \)\(88\!\cdots\!84\)\( T^{24} + \)\(19\!\cdots\!20\)\( T^{25} + \)\(35\!\cdots\!52\)\( T^{26} + \)\(72\!\cdots\!76\)\( T^{27} + \)\(11\!\cdots\!16\)\( T^{28} + \)\(18\!\cdots\!56\)\( T^{29} + \)\(22\!\cdots\!96\)\( T^{30} + \)\(23\!\cdots\!92\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 10 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 12 T + 154 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( 1 + 6 T + 254 T^{2} + 997 T^{3} + 21082 T^{4} + 41334 T^{5} + 571787 T^{6} \))(\( 1 + 16 T + 273 T^{2} + 2640 T^{3} + 22659 T^{4} + 110224 T^{5} + 571787 T^{6} \))(\( 1 + 6 T + 254 T^{2} + 997 T^{3} + 21082 T^{4} + 41334 T^{5} + 571787 T^{6} \))(\( 1 + 16 T + 273 T^{2} + 2640 T^{3} + 22659 T^{4} + 110224 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 240 T^{2} - 945 T^{3} + 19920 T^{4} - 41334 T^{5} + 571787 T^{6} \))(\( 1 + 26 T + 450 T^{2} + 4793 T^{3} + 37350 T^{4} + 179114 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 240 T^{2} - 945 T^{3} + 19920 T^{4} - 41334 T^{5} + 571787 T^{6} \))(\( 1 + 26 T + 450 T^{2} + 4793 T^{3} + 37350 T^{4} + 179114 T^{5} + 571787 T^{6} \))(\( 1 - 24 T + 413 T^{2} - 4256 T^{3} + 34279 T^{4} - 165336 T^{5} + 571787 T^{6} \))(\( 1 - 28 T + 576 T^{2} - 7644 T^{3} + 81902 T^{4} - 634452 T^{5} + 3968064 T^{6} - 16010036 T^{7} + 47458321 T^{8} \))(\( 1 + 2 T + 122 T^{2} - 377 T^{3} + 17717 T^{4} + 17826 T^{5} + 1470511 T^{6} - 2597153 T^{7} + 69758014 T^{8} + 94916642 T^{9} + 3939040643 T^{10} \))(\( 1 + 2 T + 122 T^{2} - 377 T^{3} + 17717 T^{4} + 17826 T^{5} + 1470511 T^{6} - 2597153 T^{7} + 69758014 T^{8} + 94916642 T^{9} + 3939040643 T^{10} \))(\( 1 - 8 T + 103 T^{2} - 1328 T^{3} + 16802 T^{4} - 97936 T^{5} + 1394566 T^{6} - 9148592 T^{7} + 58894061 T^{8} - 379666568 T^{9} + 3939040643 T^{10} \))(\( 1 - 8 T + 103 T^{2} - 1328 T^{3} + 16802 T^{4} - 97936 T^{5} + 1394566 T^{6} - 9148592 T^{7} + 58894061 T^{8} - 379666568 T^{9} + 3939040643 T^{10} \))(\( 1 + 12 T + 224 T^{2} + 1180 T^{3} + 9611 T^{4} - 86240 T^{5} - 341072 T^{6} - 7157920 T^{7} + 66210179 T^{8} + 674708660 T^{9} + 10630663904 T^{10} + 47268487716 T^{11} + 326940373369 T^{12} \))(\( 1 + 12 T + 224 T^{2} + 1180 T^{3} + 9611 T^{4} - 86240 T^{5} - 341072 T^{6} - 7157920 T^{7} + 66210179 T^{8} + 674708660 T^{9} + 10630663904 T^{10} + 47268487716 T^{11} + 326940373369 T^{12} \))(\( 1 + 405 T^{2} + 1199 T^{3} + 76854 T^{4} + 452895 T^{5} + 9588291 T^{6} + 78902508 T^{7} + 931583136 T^{8} + 8229578495 T^{9} + 77321400288 T^{10} + 543559377612 T^{11} + 5482460146017 T^{12} + 21493636289295 T^{13} + 302731029577122 T^{14} + 392001507669431 T^{15} + 10990100650798935 T^{16} + 186940255267540403 T^{18} \))(\( 1 - 24 T + 555 T^{2} - 8691 T^{3} + 132726 T^{4} - 1649895 T^{5} + 19953621 T^{6} - 211152102 T^{7} + 2178331728 T^{8} - 20104915311 T^{9} + 180801533424 T^{10} - 1454626830678 T^{11} + 11409221090727 T^{12} - 78301246526295 T^{13} + 522813108382818 T^{14} - 2841438784949979 T^{15} + 15060508299242985 T^{16} - 54055013571336984 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 24 T + 555 T^{2} - 8691 T^{3} + 132726 T^{4} - 1649895 T^{5} + 19953621 T^{6} - 211152102 T^{7} + 2178331728 T^{8} - 20104915311 T^{9} + 180801533424 T^{10} - 1454626830678 T^{11} + 11409221090727 T^{12} - 78301246526295 T^{13} + 522813108382818 T^{14} - 2841438784949979 T^{15} + 15060508299242985 T^{16} - 54055013571336984 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 405 T^{2} + 1199 T^{3} + 76854 T^{4} + 452895 T^{5} + 9588291 T^{6} + 78902508 T^{7} + 931583136 T^{8} + 8229578495 T^{9} + 77321400288 T^{10} + 543559377612 T^{11} + 5482460146017 T^{12} + 21493636289295 T^{13} + 302731029577122 T^{14} + 392001507669431 T^{15} + 10990100650798935 T^{16} + 186940255267540403 T^{18} \))(\( 1 - 36 T + 1164 T^{2} - 24868 T^{3} + 484833 T^{4} - 7611848 T^{5} + 110869984 T^{6} - 1385960296 T^{7} + 16221223814 T^{8} - 167060621648 T^{9} + 1616987761128 T^{10} - 13866031596784 T^{11} + 111748010854646 T^{12} - 792474079768952 T^{13} + 5261703289936864 T^{14} - 29983378640338264 T^{15} + 158511482041612377 T^{16} - 674819316010044236 T^{17} + 2621668158209843724 T^{18} - 6729849189631454508 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 36 T + 1164 T^{2} - 24868 T^{3} + 484833 T^{4} - 7611848 T^{5} + 110869984 T^{6} - 1385960296 T^{7} + 16221223814 T^{8} - 167060621648 T^{9} + 1616987761128 T^{10} - 13866031596784 T^{11} + 111748010854646 T^{12} - 792474079768952 T^{13} + 5261703289936864 T^{14} - 29983378640338264 T^{15} + 158511482041612377 T^{16} - 674819316010044236 T^{17} + 2621668158209843724 T^{18} - 6729849189631454508 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 12 T + 879 T^{2} + 9933 T^{3} + 379923 T^{4} + 3993807 T^{5} + 106881966 T^{6} + 1037761077 T^{7} + 21854704317 T^{8} + 195231967630 T^{9} + 3439491394386 T^{10} + 28186230213393 T^{11} + 430635857293282 T^{12} + 3225145096201431 T^{13} + 43709701254370368 T^{14} + 297405413859198970 T^{15} + 3627905204112740544 T^{16} + 22218024567731658159 T^{17} + \)\(24\!\cdots\!34\)\( T^{18} + \)\(13\!\cdots\!53\)\( T^{19} + \)\(13\!\cdots\!98\)\( T^{20} + \)\(63\!\cdots\!70\)\( T^{21} + \)\(59\!\cdots\!59\)\( T^{22} + \)\(23\!\cdots\!57\)\( T^{23} + \)\(19\!\cdots\!98\)\( T^{24} + \)\(61\!\cdots\!43\)\( T^{25} + \)\(48\!\cdots\!41\)\( T^{26} + \)\(10\!\cdots\!13\)\( T^{27} + \)\(77\!\cdots\!77\)\( T^{28} + \)\(88\!\cdots\!48\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 + 36 T + 1317 T^{2} + 30839 T^{3} + 682455 T^{4} + 12215481 T^{5} + 205439462 T^{6} + 3034285425 T^{7} + 42307402593 T^{8} + 539164879558 T^{9} + 6525870882882 T^{10} + 73811614905627 T^{11} + 796880946640772 T^{12} + 8139353654101053 T^{13} + 79607023485949620 T^{14} + 740750397757950234 T^{15} + 6607382949333818460 T^{16} + 56072007323102154117 T^{17} + \)\(45\!\cdots\!64\)\( T^{18} + \)\(35\!\cdots\!67\)\( T^{19} + \)\(25\!\cdots\!26\)\( T^{20} + \)\(17\!\cdots\!02\)\( T^{21} + \)\(11\!\cdots\!11\)\( T^{22} + \)\(68\!\cdots\!25\)\( T^{23} + \)\(38\!\cdots\!86\)\( T^{24} + \)\(18\!\cdots\!69\)\( T^{25} + \)\(87\!\cdots\!85\)\( T^{26} + \)\(32\!\cdots\!79\)\( T^{27} + \)\(11\!\cdots\!71\)\( T^{28} + \)\(26\!\cdots\!44\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 + 36 T + 1317 T^{2} + 30839 T^{3} + 682455 T^{4} + 12215481 T^{5} + 205439462 T^{6} + 3034285425 T^{7} + 42307402593 T^{8} + 539164879558 T^{9} + 6525870882882 T^{10} + 73811614905627 T^{11} + 796880946640772 T^{12} + 8139353654101053 T^{13} + 79607023485949620 T^{14} + 740750397757950234 T^{15} + 6607382949333818460 T^{16} + 56072007323102154117 T^{17} + \)\(45\!\cdots\!64\)\( T^{18} + \)\(35\!\cdots\!67\)\( T^{19} + \)\(25\!\cdots\!26\)\( T^{20} + \)\(17\!\cdots\!02\)\( T^{21} + \)\(11\!\cdots\!11\)\( T^{22} + \)\(68\!\cdots\!25\)\( T^{23} + \)\(38\!\cdots\!86\)\( T^{24} + \)\(18\!\cdots\!69\)\( T^{25} + \)\(87\!\cdots\!85\)\( T^{26} + \)\(32\!\cdots\!79\)\( T^{27} + \)\(11\!\cdots\!71\)\( T^{28} + \)\(26\!\cdots\!44\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 + 12 T + 879 T^{2} + 9933 T^{3} + 379923 T^{4} + 3993807 T^{5} + 106881966 T^{6} + 1037761077 T^{7} + 21854704317 T^{8} + 195231967630 T^{9} + 3439491394386 T^{10} + 28186230213393 T^{11} + 430635857293282 T^{12} + 3225145096201431 T^{13} + 43709701254370368 T^{14} + 297405413859198970 T^{15} + 3627905204112740544 T^{16} + 22218024567731658159 T^{17} + \)\(24\!\cdots\!34\)\( T^{18} + \)\(13\!\cdots\!53\)\( T^{19} + \)\(13\!\cdots\!98\)\( T^{20} + \)\(63\!\cdots\!70\)\( T^{21} + \)\(59\!\cdots\!59\)\( T^{22} + \)\(23\!\cdots\!57\)\( T^{23} + \)\(19\!\cdots\!98\)\( T^{24} + \)\(61\!\cdots\!43\)\( T^{25} + \)\(48\!\cdots\!41\)\( T^{26} + \)\(10\!\cdots\!13\)\( T^{27} + \)\(77\!\cdots\!77\)\( T^{28} + \)\(88\!\cdots\!48\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 + 40 T + 1344 T^{2} + 32440 T^{3} + 701330 T^{4} + 12932760 T^{5} + 220131600 T^{6} + 3380558888 T^{7} + 48732431420 T^{8} + 650463425704 T^{9} + 8232488517408 T^{10} + 97812316551000 T^{11} + 1108669517034534 T^{12} + 11886643842362040 T^{13} + 121999270728457968 T^{14} + 1188968190486437736 T^{15} + 11109566231987397334 T^{16} + 98684359810374332088 T^{17} + \)\(84\!\cdots\!52\)\( T^{18} + \)\(67\!\cdots\!80\)\( T^{19} + \)\(52\!\cdots\!14\)\( T^{20} + \)\(38\!\cdots\!00\)\( T^{21} + \)\(26\!\cdots\!52\)\( T^{22} + \)\(17\!\cdots\!08\)\( T^{23} + \)\(10\!\cdots\!20\)\( T^{24} + \)\(63\!\cdots\!64\)\( T^{25} + \)\(34\!\cdots\!00\)\( T^{26} + \)\(16\!\cdots\!20\)\( T^{27} + \)\(74\!\cdots\!30\)\( T^{28} + \)\(28\!\cdots\!20\)\( T^{29} + \)\(98\!\cdots\!76\)\( T^{30} + \)\(24\!\cdots\!80\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 40 T + 1344 T^{2} + 32440 T^{3} + 701330 T^{4} + 12932760 T^{5} + 220131600 T^{6} + 3380558888 T^{7} + 48732431420 T^{8} + 650463425704 T^{9} + 8232488517408 T^{10} + 97812316551000 T^{11} + 1108669517034534 T^{12} + 11886643842362040 T^{13} + 121999270728457968 T^{14} + 1188968190486437736 T^{15} + 11109566231987397334 T^{16} + 98684359810374332088 T^{17} + \)\(84\!\cdots\!52\)\( T^{18} + \)\(67\!\cdots\!80\)\( T^{19} + \)\(52\!\cdots\!14\)\( T^{20} + \)\(38\!\cdots\!00\)\( T^{21} + \)\(26\!\cdots\!52\)\( T^{22} + \)\(17\!\cdots\!08\)\( T^{23} + \)\(10\!\cdots\!20\)\( T^{24} + \)\(63\!\cdots\!64\)\( T^{25} + \)\(34\!\cdots\!00\)\( T^{26} + \)\(16\!\cdots\!20\)\( T^{27} + \)\(74\!\cdots\!30\)\( T^{28} + \)\(28\!\cdots\!20\)\( T^{29} + \)\(98\!\cdots\!76\)\( T^{30} + \)\(24\!\cdots\!80\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 + 8 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 - 16 T + 89 T^{2} \))(\( 1 + 4 T + 74 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 234 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 - 22 T + 286 T^{2} - 1958 T^{3} + 7921 T^{4} \))(\( 1 - 22 T + 286 T^{2} - 1958 T^{3} + 7921 T^{4} \))(\( 1 + 7 T + 218 T^{2} + 1295 T^{3} + 19402 T^{4} + 55447 T^{5} + 704969 T^{6} \))(\( 1 + 8 T + 203 T^{2} + 1504 T^{3} + 18067 T^{4} + 63368 T^{5} + 704969 T^{6} \))(\( 1 + 7 T + 218 T^{2} + 1295 T^{3} + 19402 T^{4} + 55447 T^{5} + 704969 T^{6} \))(\( 1 + 8 T + 203 T^{2} + 1504 T^{3} + 18067 T^{4} + 63368 T^{5} + 704969 T^{6} \))(\( ( 1 - T + 89 T^{2} )^{3} \))(\( 1 - 33 T + 610 T^{2} - 7009 T^{3} + 54290 T^{4} - 261393 T^{5} + 704969 T^{6} \))(\( ( 1 - T + 89 T^{2} )^{3} \))(\( 1 - 33 T + 610 T^{2} - 7009 T^{3} + 54290 T^{4} - 261393 T^{5} + 704969 T^{6} \))(\( 1 + 10 T + 203 T^{2} + 1124 T^{3} + 18067 T^{4} + 79210 T^{5} + 704969 T^{6} \))(\( 1 + 28 T + 592 T^{2} + 7988 T^{3} + 88798 T^{4} + 710932 T^{5} + 4689232 T^{6} + 19739132 T^{7} + 62742241 T^{8} \))(\( 1 - 5 T + 270 T^{2} - 839 T^{3} + 33831 T^{4} - 76528 T^{5} + 3010959 T^{6} - 6645719 T^{7} + 190341630 T^{8} - 313711205 T^{9} + 5584059449 T^{10} \))(\( 1 - 5 T + 270 T^{2} - 839 T^{3} + 33831 T^{4} - 76528 T^{5} + 3010959 T^{6} - 6645719 T^{7} + 190341630 T^{8} - 313711205 T^{9} + 5584059449 T^{10} \))(\( 1 - 24 T + 589 T^{2} - 8336 T^{3} + 114842 T^{4} - 1100272 T^{5} + 10220938 T^{6} - 66029456 T^{7} + 415226741 T^{8} - 1505813784 T^{9} + 5584059449 T^{10} \))(\( 1 - 24 T + 589 T^{2} - 8336 T^{3} + 114842 T^{4} - 1100272 T^{5} + 10220938 T^{6} - 66029456 T^{7} + 415226741 T^{8} - 1505813784 T^{9} + 5584059449 T^{10} \))(\( 1 + 32 T + 702 T^{2} + 10528 T^{3} + 134815 T^{4} + 1429568 T^{5} + 14315748 T^{6} + 127231552 T^{7} + 1067869615 T^{8} + 7421913632 T^{9} + 44045053182 T^{10} + 178689902368 T^{11} + 496981290961 T^{12} \))(\( 1 + 32 T + 702 T^{2} + 10528 T^{3} + 134815 T^{4} + 1429568 T^{5} + 14315748 T^{6} + 127231552 T^{7} + 1067869615 T^{8} + 7421913632 T^{9} + 44045053182 T^{10} + 178689902368 T^{11} + 496981290961 T^{12} \))(\( 1 + 12 T + 399 T^{2} + 2343 T^{3} + 59493 T^{4} + 81864 T^{5} + 5768434 T^{6} - 10964487 T^{7} + 551057481 T^{8} - 1442663521 T^{9} + 49044115809 T^{10} - 86849701527 T^{11} + 4066567148546 T^{12} + 5136330817224 T^{13} + 332212448799357 T^{14} + 1164427164721623 T^{15} + 17648302623316071 T^{16} + 47239065668424972 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 549 T^{2} - 633 T^{3} + 145521 T^{4} - 274176 T^{5} + 24666300 T^{6} - 53979489 T^{7} + 2969184267 T^{8} - 6147670243 T^{9} + 264257399763 T^{10} - 427571532369 T^{11} + 17388976844700 T^{12} - 17202416668416 T^{13} + 812597915077929 T^{14} - 314589157178313 T^{15} + 24283002857645421 T^{16} + 350356403707485209 T^{18} \))(\( 1 + 549 T^{2} - 633 T^{3} + 145521 T^{4} - 274176 T^{5} + 24666300 T^{6} - 53979489 T^{7} + 2969184267 T^{8} - 6147670243 T^{9} + 264257399763 T^{10} - 427571532369 T^{11} + 17388976844700 T^{12} - 17202416668416 T^{13} + 812597915077929 T^{14} - 314589157178313 T^{15} + 24283002857645421 T^{16} + 350356403707485209 T^{18} \))(\( 1 + 12 T + 399 T^{2} + 2343 T^{3} + 59493 T^{4} + 81864 T^{5} + 5768434 T^{6} - 10964487 T^{7} + 551057481 T^{8} - 1442663521 T^{9} + 49044115809 T^{10} - 86849701527 T^{11} + 4066567148546 T^{12} + 5136330817224 T^{13} + 332212448799357 T^{14} + 1164427164721623 T^{15} + 17648302623316071 T^{16} + 47239065668424972 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 32 T + 894 T^{2} - 17376 T^{3} + 305761 T^{4} - 4506496 T^{5} + 61247712 T^{6} - 744023808 T^{7} + 8443359246 T^{8} - 88030522496 T^{9} + 862716055876 T^{10} - 7834716502144 T^{11} + 66879848587566 T^{12} - 524513719901952 T^{13} + 3842818707002592 T^{14} - 25164541570680704 T^{15} + 151957496505526321 T^{16} - 768563675144711904 T^{17} + 3519310392297660414 T^{18} - 11211404918639526688 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 32 T + 894 T^{2} - 17376 T^{3} + 305761 T^{4} - 4506496 T^{5} + 61247712 T^{6} - 744023808 T^{7} + 8443359246 T^{8} - 88030522496 T^{9} + 862716055876 T^{10} - 7834716502144 T^{11} + 66879848587566 T^{12} - 524513719901952 T^{13} + 3842818707002592 T^{14} - 25164541570680704 T^{15} + 151957496505526321 T^{16} - 768563675144711904 T^{17} + 3519310392297660414 T^{18} - 11211404918639526688 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 12 T + 765 T^{2} - 6867 T^{3} + 275220 T^{4} - 1986312 T^{5} + 66069005 T^{6} - 407964780 T^{7} + 12134591601 T^{8} - 66311846503 T^{9} + 1798842584430 T^{10} - 8846132833911 T^{11} + 221675797940349 T^{12} - 995949070127109 T^{13} + 23143972467637005 T^{14} - 95860175808207604 T^{15} + 2059813549619693445 T^{16} - 7888912584476830389 T^{17} + \)\(15\!\cdots\!81\)\( T^{18} - \)\(55\!\cdots\!51\)\( T^{19} + \)\(10\!\cdots\!70\)\( T^{20} - \)\(32\!\cdots\!83\)\( T^{21} + \)\(53\!\cdots\!29\)\( T^{22} - \)\(16\!\cdots\!80\)\( T^{23} + \)\(23\!\cdots\!45\)\( T^{24} - \)\(61\!\cdots\!12\)\( T^{25} + \)\(76\!\cdots\!80\)\( T^{26} - \)\(16\!\cdots\!07\)\( T^{27} + \)\(16\!\cdots\!85\)\( T^{28} - \)\(23\!\cdots\!92\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 + 24 T + 759 T^{2} + 14701 T^{3} + 287184 T^{4} + 4625472 T^{5} + 71015205 T^{6} + 986746842 T^{7} + 12947637999 T^{8} + 159526832215 T^{9} + 1868221776468 T^{10} + 20835198871413 T^{11} + 223517795484513 T^{12} + 2293722839182161 T^{13} + 22875732724011015 T^{14} + 218482842218744936 T^{15} + 2035940212436980335 T^{16} + 18168578609161897281 T^{17} + \)\(15\!\cdots\!97\)\( T^{18} + \)\(13\!\cdots\!33\)\( T^{19} + \)\(10\!\cdots\!32\)\( T^{20} + \)\(79\!\cdots\!15\)\( T^{21} + \)\(57\!\cdots\!71\)\( T^{22} + \)\(38\!\cdots\!02\)\( T^{23} + \)\(24\!\cdots\!45\)\( T^{24} + \)\(14\!\cdots\!72\)\( T^{25} + \)\(79\!\cdots\!76\)\( T^{26} + \)\(36\!\cdots\!21\)\( T^{27} + \)\(16\!\cdots\!71\)\( T^{28} + \)\(46\!\cdots\!84\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 + 24 T + 759 T^{2} + 14701 T^{3} + 287184 T^{4} + 4625472 T^{5} + 71015205 T^{6} + 986746842 T^{7} + 12947637999 T^{8} + 159526832215 T^{9} + 1868221776468 T^{10} + 20835198871413 T^{11} + 223517795484513 T^{12} + 2293722839182161 T^{13} + 22875732724011015 T^{14} + 218482842218744936 T^{15} + 2035940212436980335 T^{16} + 18168578609161897281 T^{17} + \)\(15\!\cdots\!97\)\( T^{18} + \)\(13\!\cdots\!33\)\( T^{19} + \)\(10\!\cdots\!32\)\( T^{20} + \)\(79\!\cdots\!15\)\( T^{21} + \)\(57\!\cdots\!71\)\( T^{22} + \)\(38\!\cdots\!02\)\( T^{23} + \)\(24\!\cdots\!45\)\( T^{24} + \)\(14\!\cdots\!72\)\( T^{25} + \)\(79\!\cdots\!76\)\( T^{26} + \)\(36\!\cdots\!21\)\( T^{27} + \)\(16\!\cdots\!71\)\( T^{28} + \)\(46\!\cdots\!84\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 - 12 T + 765 T^{2} - 6867 T^{3} + 275220 T^{4} - 1986312 T^{5} + 66069005 T^{6} - 407964780 T^{7} + 12134591601 T^{8} - 66311846503 T^{9} + 1798842584430 T^{10} - 8846132833911 T^{11} + 221675797940349 T^{12} - 995949070127109 T^{13} + 23143972467637005 T^{14} - 95860175808207604 T^{15} + 2059813549619693445 T^{16} - 7888912584476830389 T^{17} + \)\(15\!\cdots\!81\)\( T^{18} - \)\(55\!\cdots\!51\)\( T^{19} + \)\(10\!\cdots\!70\)\( T^{20} - \)\(32\!\cdots\!83\)\( T^{21} + \)\(53\!\cdots\!29\)\( T^{22} - \)\(16\!\cdots\!80\)\( T^{23} + \)\(23\!\cdots\!45\)\( T^{24} - \)\(61\!\cdots\!12\)\( T^{25} + \)\(76\!\cdots\!80\)\( T^{26} - \)\(16\!\cdots\!07\)\( T^{27} + \)\(16\!\cdots\!85\)\( T^{28} - \)\(23\!\cdots\!92\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 + 24 T + 1140 T^{2} + 22120 T^{3} + 608292 T^{4} + 10022968 T^{5} + 205523788 T^{6} + 2959193160 T^{7} + 49716586420 T^{8} + 636854471640 T^{9} + 9188603930788 T^{10} + 105924827078184 T^{11} + 1348031289706588 T^{12} + 14081421752798648 T^{13} + 160609517815722268 T^{14} + 1524991878114879560 T^{15} + 15733353409536274966 T^{16} + \)\(13\!\cdots\!40\)\( T^{17} + \)\(12\!\cdots\!28\)\( T^{18} + \)\(99\!\cdots\!12\)\( T^{19} + \)\(84\!\cdots\!08\)\( T^{20} + \)\(59\!\cdots\!16\)\( T^{21} + \)\(45\!\cdots\!68\)\( T^{22} + \)\(28\!\cdots\!60\)\( T^{23} + \)\(19\!\cdots\!20\)\( T^{24} + \)\(10\!\cdots\!40\)\( T^{25} + \)\(64\!\cdots\!88\)\( T^{26} + \)\(27\!\cdots\!52\)\( T^{27} + \)\(15\!\cdots\!32\)\( T^{28} + \)\(48\!\cdots\!80\)\( T^{29} + \)\(22\!\cdots\!40\)\( T^{30} + \)\(41\!\cdots\!76\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 + 24 T + 1140 T^{2} + 22120 T^{3} + 608292 T^{4} + 10022968 T^{5} + 205523788 T^{6} + 2959193160 T^{7} + 49716586420 T^{8} + 636854471640 T^{9} + 9188603930788 T^{10} + 105924827078184 T^{11} + 1348031289706588 T^{12} + 14081421752798648 T^{13} + 160609517815722268 T^{14} + 1524991878114879560 T^{15} + 15733353409536274966 T^{16} + \)\(13\!\cdots\!40\)\( T^{17} + \)\(12\!\cdots\!28\)\( T^{18} + \)\(99\!\cdots\!12\)\( T^{19} + \)\(84\!\cdots\!08\)\( T^{20} + \)\(59\!\cdots\!16\)\( T^{21} + \)\(45\!\cdots\!68\)\( T^{22} + \)\(28\!\cdots\!60\)\( T^{23} + \)\(19\!\cdots\!20\)\( T^{24} + \)\(10\!\cdots\!40\)\( T^{25} + \)\(64\!\cdots\!88\)\( T^{26} + \)\(27\!\cdots\!52\)\( T^{27} + \)\(15\!\cdots\!32\)\( T^{28} + \)\(48\!\cdots\!80\)\( T^{29} + \)\(22\!\cdots\!40\)\( T^{30} + \)\(41\!\cdots\!76\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))
$97$ (\( 1 - 4 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 8 T + 178 T^{2} - 776 T^{3} + 9409 T^{4} \))(\( 1 + 10 T + 102 T^{2} + 970 T^{3} + 9409 T^{4} \))(\( 1 - 10 T + 102 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 + 21 T + 389 T^{2} + 4165 T^{3} + 37733 T^{4} + 197589 T^{5} + 912673 T^{6} \))(\( 1 - 30 T + 575 T^{2} - 6644 T^{3} + 55775 T^{4} - 282270 T^{5} + 912673 T^{6} \))(\( 1 - 21 T + 389 T^{2} - 4165 T^{3} + 37733 T^{4} - 197589 T^{5} + 912673 T^{6} \))(\( 1 + 30 T + 575 T^{2} + 6644 T^{3} + 55775 T^{4} + 282270 T^{5} + 912673 T^{6} \))(\( 1 - 3 T + 183 T^{2} - 39 T^{3} + 17751 T^{4} - 28227 T^{5} + 912673 T^{6} \))(\( 1 - 9 T + 139 T^{2} - 1813 T^{3} + 13483 T^{4} - 84681 T^{5} + 912673 T^{6} \))(\( 1 + 3 T + 183 T^{2} + 39 T^{3} + 17751 T^{4} + 28227 T^{5} + 912673 T^{6} \))(\( 1 + 9 T + 139 T^{2} + 1813 T^{3} + 13483 T^{4} + 84681 T^{5} + 912673 T^{6} \))(\( 1 - 6 T + 275 T^{2} - 1100 T^{3} + 26675 T^{4} - 56454 T^{5} + 912673 T^{6} \))(\( 1 + 4 T + 184 T^{2} + 44 T^{3} + 20014 T^{4} + 4268 T^{5} + 1731256 T^{6} + 3650692 T^{7} + 88529281 T^{8} \))(\( 1 - 3 T + 73 T^{2} + 997 T^{3} + 17676 T^{4} - 58860 T^{5} + 1714572 T^{6} + 9380773 T^{7} + 66625129 T^{8} - 265587843 T^{9} + 8587340257 T^{10} \))(\( 1 + 3 T + 73 T^{2} - 997 T^{3} + 17676 T^{4} + 58860 T^{5} + 1714572 T^{6} - 9380773 T^{7} + 66625129 T^{8} + 265587843 T^{9} + 8587340257 T^{10} \))(\( 1 + 14 T + 477 T^{2} + 4696 T^{3} + 89026 T^{4} + 645044 T^{5} + 8635522 T^{6} + 44184664 T^{7} + 435345021 T^{8} + 1239409934 T^{9} + 8587340257 T^{10} \))(\( 1 - 14 T + 477 T^{2} - 4696 T^{3} + 89026 T^{4} - 645044 T^{5} + 8635522 T^{6} - 44184664 T^{7} + 435345021 T^{8} - 1239409934 T^{9} + 8587340257 T^{10} \))(\( 1 - 36 T + 780 T^{2} - 9836 T^{3} + 81027 T^{4} - 306224 T^{5} + 933736 T^{6} - 29703728 T^{7} + 762383043 T^{8} - 8977051628 T^{9} + 69052839180 T^{10} - 309144249252 T^{11} + 832972004929 T^{12} \))(\( 1 + 36 T + 780 T^{2} + 9836 T^{3} + 81027 T^{4} + 306224 T^{5} + 933736 T^{6} + 29703728 T^{7} + 762383043 T^{8} + 8977051628 T^{9} + 69052839180 T^{10} + 309144249252 T^{11} + 832972004929 T^{12} \))(\( 1 + 435 T^{2} + 1128 T^{3} + 93120 T^{4} + 390543 T^{5} + 14445307 T^{6} + 61562556 T^{7} + 1800901236 T^{8} + 6652252001 T^{9} + 174687419892 T^{10} + 579242089404 T^{11} + 13183841675611 T^{12} + 34574490989583 T^{13} + 799653124731840 T^{14} + 939592421559912 T^{15} + 35147253747979155 T^{16} + 760231058654565217 T^{18} \))(\( 1 - 36 T + 1095 T^{2} - 23592 T^{3} + 441744 T^{4} - 6994107 T^{5} + 98921787 T^{6} - 1245846024 T^{7} + 14203862652 T^{8} - 146762437341 T^{9} + 1377774677244 T^{10} - 11722165239816 T^{11} + 90283244106651 T^{12} - 619183263947067 T^{13} + 3793406034488208 T^{14} - 19651475540284968 T^{15} + 88474121503533735 T^{16} - 282147609397570596 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 36 T + 1095 T^{2} + 23592 T^{3} + 441744 T^{4} + 6994107 T^{5} + 98921787 T^{6} + 1245846024 T^{7} + 14203862652 T^{8} + 146762437341 T^{9} + 1377774677244 T^{10} + 11722165239816 T^{11} + 90283244106651 T^{12} + 619183263947067 T^{13} + 3793406034488208 T^{14} + 19651475540284968 T^{15} + 88474121503533735 T^{16} + 282147609397570596 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 435 T^{2} - 1128 T^{3} + 93120 T^{4} - 390543 T^{5} + 14445307 T^{6} - 61562556 T^{7} + 1800901236 T^{8} - 6652252001 T^{9} + 174687419892 T^{10} - 579242089404 T^{11} + 13183841675611 T^{12} - 34574490989583 T^{13} + 799653124731840 T^{14} - 939592421559912 T^{15} + 35147253747979155 T^{16} + 760231058654565217 T^{18} \))(\( 1 + 36 T + 1352 T^{2} + 31436 T^{3} + 696409 T^{4} + 12063848 T^{5} + 196337184 T^{6} + 2696256088 T^{7} + 34737678982 T^{8} + 389219957200 T^{9} + 4093415170800 T^{10} + 37754335848400 T^{11} + 326846821541638 T^{12} + 2460800132603224 T^{13} + 17381589733084704 T^{14} + 103596367584728936 T^{15} + 580089200980599961 T^{16} + 2539974870853960268 T^{17} + 10596210219597651272 T^{18} + 27368318111564347812 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 36 T + 1352 T^{2} - 31436 T^{3} + 696409 T^{4} - 12063848 T^{5} + 196337184 T^{6} - 2696256088 T^{7} + 34737678982 T^{8} - 389219957200 T^{9} + 4093415170800 T^{10} - 37754335848400 T^{11} + 326846821541638 T^{12} - 2460800132603224 T^{13} + 17381589733084704 T^{14} - 103596367584728936 T^{15} + 580089200980599961 T^{16} - 2539974870853960268 T^{17} + 10596210219597651272 T^{18} - 27368318111564347812 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 30 T + 1131 T^{2} - 26600 T^{3} + 624237 T^{4} - 11960487 T^{5} + 219548486 T^{6} - 3567716454 T^{7} + 55176339651 T^{8} - 781042302314 T^{9} + 10529212133676 T^{10} - 131988647545458 T^{11} + 1578849596319856 T^{12} - 17698250384017665 T^{13} + 189599217682490754 T^{14} - 1909634152078169888 T^{15} + 18391124115201603138 T^{16} - \)\(16\!\cdots\!85\)\( T^{17} + \)\(14\!\cdots\!88\)\( T^{18} - \)\(11\!\cdots\!98\)\( T^{19} + \)\(90\!\cdots\!32\)\( T^{20} - \)\(65\!\cdots\!06\)\( T^{21} + \)\(44\!\cdots\!63\)\( T^{22} - \)\(27\!\cdots\!94\)\( T^{23} + \)\(16\!\cdots\!62\)\( T^{24} - \)\(88\!\cdots\!63\)\( T^{25} + \)\(44\!\cdots\!61\)\( T^{26} - \)\(18\!\cdots\!00\)\( T^{27} + \)\(76\!\cdots\!87\)\( T^{28} - \)\(19\!\cdots\!70\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 + 18 T + 855 T^{2} + 11088 T^{3} + 321333 T^{4} + 3212295 T^{5} + 76613146 T^{6} + 625005882 T^{7} + 13938491979 T^{8} + 97567098838 T^{9} + 2110186227480 T^{10} + 13016694311442 T^{11} + 271712191260768 T^{12} + 1498946620615233 T^{13} + 30107796987009558 T^{14} + 152885453576667240 T^{15} + 2920456307739927126 T^{16} + 14103588753368727297 T^{17} + \)\(24\!\cdots\!64\)\( T^{18} + \)\(11\!\cdots\!02\)\( T^{19} + \)\(18\!\cdots\!60\)\( T^{20} + \)\(81\!\cdots\!02\)\( T^{21} + \)\(11\!\cdots\!27\)\( T^{22} + \)\(48\!\cdots\!02\)\( T^{23} + \)\(58\!\cdots\!82\)\( T^{24} + \)\(23\!\cdots\!55\)\( T^{25} + \)\(22\!\cdots\!49\)\( T^{26} + \)\(76\!\cdots\!08\)\( T^{27} + \)\(57\!\cdots\!35\)\( T^{28} + \)\(11\!\cdots\!42\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 - 18 T + 855 T^{2} - 11088 T^{3} + 321333 T^{4} - 3212295 T^{5} + 76613146 T^{6} - 625005882 T^{7} + 13938491979 T^{8} - 97567098838 T^{9} + 2110186227480 T^{10} - 13016694311442 T^{11} + 271712191260768 T^{12} - 1498946620615233 T^{13} + 30107796987009558 T^{14} - 152885453576667240 T^{15} + 2920456307739927126 T^{16} - 14103588753368727297 T^{17} + \)\(24\!\cdots\!64\)\( T^{18} - \)\(11\!\cdots\!02\)\( T^{19} + \)\(18\!\cdots\!60\)\( T^{20} - \)\(81\!\cdots\!02\)\( T^{21} + \)\(11\!\cdots\!27\)\( T^{22} - \)\(48\!\cdots\!02\)\( T^{23} + \)\(58\!\cdots\!82\)\( T^{24} - \)\(23\!\cdots\!55\)\( T^{25} + \)\(22\!\cdots\!49\)\( T^{26} - \)\(76\!\cdots\!08\)\( T^{27} + \)\(57\!\cdots\!35\)\( T^{28} - \)\(11\!\cdots\!42\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 + 30 T + 1131 T^{2} + 26600 T^{3} + 624237 T^{4} + 11960487 T^{5} + 219548486 T^{6} + 3567716454 T^{7} + 55176339651 T^{8} + 781042302314 T^{9} + 10529212133676 T^{10} + 131988647545458 T^{11} + 1578849596319856 T^{12} + 17698250384017665 T^{13} + 189599217682490754 T^{14} + 1909634152078169888 T^{15} + 18391124115201603138 T^{16} + \)\(16\!\cdots\!85\)\( T^{17} + \)\(14\!\cdots\!88\)\( T^{18} + \)\(11\!\cdots\!98\)\( T^{19} + \)\(90\!\cdots\!32\)\( T^{20} + \)\(65\!\cdots\!06\)\( T^{21} + \)\(44\!\cdots\!63\)\( T^{22} + \)\(27\!\cdots\!94\)\( T^{23} + \)\(16\!\cdots\!62\)\( T^{24} + \)\(88\!\cdots\!63\)\( T^{25} + \)\(44\!\cdots\!61\)\( T^{26} + \)\(18\!\cdots\!00\)\( T^{27} + \)\(76\!\cdots\!87\)\( T^{28} + \)\(19\!\cdots\!70\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 - 24 T + 1048 T^{2} - 19872 T^{3} + 513088 T^{4} - 8326336 T^{5} + 162947088 T^{6} - 2348731000 T^{7} + 38166677220 T^{8} - 498146127624 T^{9} + 7034745494144 T^{10} - 83999239308256 T^{11} + 1057977212217872 T^{12} - 11615517852618880 T^{13} + 132548445199714552 T^{14} - 1340033641328478696 T^{15} + 13986038362547118278 T^{16} - \)\(12\!\cdots\!12\)\( T^{17} + \)\(12\!\cdots\!68\)\( T^{18} - \)\(10\!\cdots\!40\)\( T^{19} + \)\(93\!\cdots\!32\)\( T^{20} - \)\(72\!\cdots\!92\)\( T^{21} + \)\(58\!\cdots\!76\)\( T^{22} - \)\(40\!\cdots\!12\)\( T^{23} + \)\(29\!\cdots\!20\)\( T^{24} - \)\(17\!\cdots\!00\)\( T^{25} + \)\(12\!\cdots\!12\)\( T^{26} - \)\(59\!\cdots\!08\)\( T^{27} + \)\(35\!\cdots\!08\)\( T^{28} - \)\(13\!\cdots\!44\)\( T^{29} + \)\(68\!\cdots\!12\)\( T^{30} - \)\(15\!\cdots\!32\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 24 T + 1048 T^{2} + 19872 T^{3} + 513088 T^{4} + 8326336 T^{5} + 162947088 T^{6} + 2348731000 T^{7} + 38166677220 T^{8} + 498146127624 T^{9} + 7034745494144 T^{10} + 83999239308256 T^{11} + 1057977212217872 T^{12} + 11615517852618880 T^{13} + 132548445199714552 T^{14} + 1340033641328478696 T^{15} + 13986038362547118278 T^{16} + \)\(12\!\cdots\!12\)\( T^{17} + \)\(12\!\cdots\!68\)\( T^{18} + \)\(10\!\cdots\!40\)\( T^{19} + \)\(93\!\cdots\!32\)\( T^{20} + \)\(72\!\cdots\!92\)\( T^{21} + \)\(58\!\cdots\!76\)\( T^{22} + \)\(40\!\cdots\!12\)\( T^{23} + \)\(29\!\cdots\!20\)\( T^{24} + \)\(17\!\cdots\!00\)\( T^{25} + \)\(12\!\cdots\!12\)\( T^{26} + \)\(59\!\cdots\!08\)\( T^{27} + \)\(35\!\cdots\!08\)\( T^{28} + \)\(13\!\cdots\!44\)\( T^{29} + \)\(68\!\cdots\!12\)\( T^{30} + \)\(15\!\cdots\!32\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))
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