Properties

Label 6003.2
Level 6003
Weight 2
Dimension 1041768
Nonzero newspaces 48
Sturm bound 5322240

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Defining parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5322240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6003))\).

Total New Old
Modular forms 1340416 1051976 288440
Cusp forms 1320705 1041768 278937
Eisenstein series 19711 10208 9503

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6003))\)

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
6003.2.a \(\chi_{6003}(1, \cdot)\) 6003.2.a.a 1 1
6003.2.a.b 1
6003.2.a.c 1
6003.2.a.d 2
6003.2.a.e 2
6003.2.a.f 2
6003.2.a.g 4
6003.2.a.h 5
6003.2.a.i 7
6003.2.a.j 7
6003.2.a.k 10
6003.2.a.l 10
6003.2.a.m 11
6003.2.a.n 12
6003.2.a.o 13
6003.2.a.p 14
6003.2.a.q 16
6003.2.a.r 16
6003.2.a.s 20
6003.2.a.t 22
6003.2.a.u 22
6003.2.a.v 30
6003.2.a.w 30
6003.2.d \(\chi_{6003}(3104, \cdot)\) n/a 224 1
6003.2.e \(\chi_{6003}(2899, \cdot)\) n/a 274 1
6003.2.h \(\chi_{6003}(6002, \cdot)\) n/a 240 1
6003.2.i \(\chi_{6003}(2002, \cdot)\) n/a 1232 2
6003.2.l \(\chi_{6003}(505, \cdot)\) n/a 596 2
6003.2.m \(\chi_{6003}(737, \cdot)\) n/a 440 2
6003.2.n \(\chi_{6003}(2000, \cdot)\) n/a 1432 2
6003.2.q \(\chi_{6003}(898, \cdot)\) n/a 1320 2
6003.2.r \(\chi_{6003}(1103, \cdot)\) n/a 1344 2
6003.2.u \(\chi_{6003}(1243, \cdot)\) n/a 1656 6
6003.2.v \(\chi_{6003}(262, \cdot)\) n/a 2800 10
6003.2.w \(\chi_{6003}(1496, \cdot)\) n/a 2640 4
6003.2.x \(\chi_{6003}(1264, \cdot)\) n/a 2864 4
6003.2.ba \(\chi_{6003}(1862, \cdot)\) n/a 1440 6
6003.2.bd \(\chi_{6003}(208, \cdot)\) n/a 1644 6
6003.2.be \(\chi_{6003}(413, \cdot)\) n/a 1440 6
6003.2.bh \(\chi_{6003}(139, \cdot)\) n/a 7920 12
6003.2.bi \(\chi_{6003}(260, \cdot)\) n/a 2400 10
6003.2.bl \(\chi_{6003}(289, \cdot)\) n/a 2980 10
6003.2.bm \(\chi_{6003}(494, \cdot)\) n/a 2240 10
6003.2.bp \(\chi_{6003}(530, \cdot)\) n/a 2640 12
6003.2.bq \(\chi_{6003}(298, \cdot)\) n/a 3576 12
6003.2.bt \(\chi_{6003}(349, \cdot)\) n/a 13440 20
6003.2.bw \(\chi_{6003}(344, \cdot)\) n/a 8592 12
6003.2.bx \(\chi_{6003}(760, \cdot)\) n/a 7920 12
6003.2.ca \(\chi_{6003}(689, \cdot)\) n/a 8592 12
6003.2.cb \(\chi_{6003}(215, \cdot)\) n/a 4800 20
6003.2.cc \(\chi_{6003}(244, \cdot)\) n/a 5960 20
6003.2.ch \(\chi_{6003}(320, \cdot)\) n/a 13440 20
6003.2.ci \(\chi_{6003}(202, \cdot)\) n/a 14320 20
6003.2.cl \(\chi_{6003}(86, \cdot)\) n/a 14320 20
6003.2.cm \(\chi_{6003}(82, \cdot)\) n/a 17880 60
6003.2.cp \(\chi_{6003}(160, \cdot)\) n/a 17184 24
6003.2.cq \(\chi_{6003}(47, \cdot)\) n/a 15840 24
6003.2.ct \(\chi_{6003}(157, \cdot)\) n/a 28640 40
6003.2.cu \(\chi_{6003}(41, \cdot)\) n/a 28640 40
6003.2.cx \(\chi_{6003}(53, \cdot)\) n/a 14400 60
6003.2.cy \(\chi_{6003}(64, \cdot)\) n/a 17880 60
6003.2.db \(\chi_{6003}(80, \cdot)\) n/a 14400 60
6003.2.dc \(\chi_{6003}(16, \cdot)\) n/a 85920 120
6003.2.df \(\chi_{6003}(10, \cdot)\) n/a 35760 120
6003.2.dg \(\chi_{6003}(8, \cdot)\) n/a 28800 120
6003.2.dh \(\chi_{6003}(5, \cdot)\) n/a 85920 120
6003.2.dk \(\chi_{6003}(4, \cdot)\) n/a 85920 120
6003.2.dl \(\chi_{6003}(20, \cdot)\) n/a 85920 120
6003.2.do \(\chi_{6003}(2, \cdot)\) n/a 171840 240
6003.2.dp \(\chi_{6003}(40, \cdot)\) n/a 171840 240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2001))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( ( 1 + T + 2 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( ( 1 - T + 2 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} )^{4} \))(\( 1 - 2 T + 3 T^{2} - 3 T^{3} + 9 T^{4} - 15 T^{5} + 18 T^{6} - 12 T^{7} + 24 T^{8} - 32 T^{9} + 32 T^{10} \))(\( 1 - T + 4 T^{2} - 2 T^{3} + 13 T^{4} - 9 T^{5} + 30 T^{6} - 13 T^{7} + 60 T^{8} - 36 T^{9} + 104 T^{10} - 32 T^{11} + 128 T^{12} - 64 T^{13} + 128 T^{14} \))(\( 1 - 3 T + 9 T^{2} - 18 T^{3} + 38 T^{4} - 62 T^{5} + 105 T^{6} - 144 T^{7} + 210 T^{8} - 248 T^{9} + 304 T^{10} - 288 T^{11} + 288 T^{12} - 192 T^{13} + 128 T^{14} \))(\( 1 + 3 T + 6 T^{2} + 5 T^{3} + T^{4} + 21 T^{6} + 52 T^{7} + 59 T^{8} - 60 T^{10} + 236 T^{12} + 416 T^{13} + 336 T^{14} + 64 T^{16} + 640 T^{17} + 1536 T^{18} + 1536 T^{19} + 1024 T^{20} \))(\( 1 - 3 T + 10 T^{2} - 22 T^{3} + 52 T^{4} - 102 T^{5} + 195 T^{6} - 326 T^{7} + 540 T^{8} - 817 T^{9} + 1219 T^{10} - 1634 T^{11} + 2160 T^{12} - 2608 T^{13} + 3120 T^{14} - 3264 T^{15} + 3328 T^{16} - 2816 T^{17} + 2560 T^{18} - 1536 T^{19} + 1024 T^{20} \))(\( 1 + 2 T + 4 T^{2} + 10 T^{3} + 20 T^{4} + 32 T^{5} + 56 T^{6} + 99 T^{7} + 154 T^{8} + 213 T^{9} + 331 T^{10} + 488 T^{11} + 662 T^{12} + 852 T^{13} + 1232 T^{14} + 1584 T^{15} + 1792 T^{16} + 2048 T^{17} + 2560 T^{18} + 2560 T^{19} + 2048 T^{20} + 2048 T^{21} + 2048 T^{22} \))(\( 1 - 3 T + 11 T^{2} - 25 T^{3} + 58 T^{4} - 110 T^{5} + 207 T^{6} - 346 T^{7} + 577 T^{8} - 875 T^{9} + 1349 T^{10} - 1909 T^{11} + 2807 T^{12} - 3818 T^{13} + 5396 T^{14} - 7000 T^{15} + 9232 T^{16} - 11072 T^{17} + 13248 T^{18} - 14080 T^{19} + 14848 T^{20} - 12800 T^{21} + 11264 T^{22} - 6144 T^{23} + 4096 T^{24} \))(\( 1 + 4 T + 15 T^{2} + 38 T^{3} + 94 T^{4} + 194 T^{5} + 397 T^{6} + 727 T^{7} + 1332 T^{8} + 2231 T^{9} + 3712 T^{10} + 5697 T^{11} + 8688 T^{12} + 12324 T^{13} + 17376 T^{14} + 22788 T^{15} + 29696 T^{16} + 35696 T^{17} + 42624 T^{18} + 46528 T^{19} + 50816 T^{20} + 49664 T^{21} + 48128 T^{22} + 38912 T^{23} + 30720 T^{24} + 16384 T^{25} + 8192 T^{26} \))(\( 1 - 2 T + 10 T^{2} - 18 T^{3} + 56 T^{4} - 92 T^{5} + 220 T^{6} - 337 T^{7} + 686 T^{8} - 985 T^{9} + 1787 T^{10} - 2438 T^{11} + 4096 T^{12} - 5352 T^{13} + 8520 T^{14} - 10704 T^{15} + 16384 T^{16} - 19504 T^{17} + 28592 T^{18} - 31520 T^{19} + 43904 T^{20} - 43136 T^{21} + 56320 T^{22} - 47104 T^{23} + 57344 T^{24} - 36864 T^{25} + 40960 T^{26} - 16384 T^{27} + 16384 T^{28} \))(\( 1 + 3 T + 10 T^{2} + 22 T^{3} + 51 T^{4} + 89 T^{5} + 165 T^{6} + 246 T^{7} + 384 T^{8} + 497 T^{9} + 708 T^{10} + 826 T^{11} + 1154 T^{12} + 1343 T^{13} + 1975 T^{14} + 2394 T^{15} + 3852 T^{16} + 4788 T^{17} + 7900 T^{18} + 10744 T^{19} + 18464 T^{20} + 26432 T^{21} + 45312 T^{22} + 63616 T^{23} + 98304 T^{24} + 125952 T^{25} + 168960 T^{26} + 182272 T^{27} + 208896 T^{28} + 180224 T^{29} + 163840 T^{30} + 98304 T^{31} + 65536 T^{32} \))(\( 1 - T + 4 T^{2} - 3 T^{3} + 12 T^{4} - 13 T^{5} + 37 T^{6} - 41 T^{7} + 86 T^{8} - 118 T^{9} + 231 T^{10} - 304 T^{11} + 521 T^{12} - 640 T^{13} + 1132 T^{14} - 1376 T^{15} + 2456 T^{16} - 2752 T^{17} + 4528 T^{18} - 5120 T^{19} + 8336 T^{20} - 9728 T^{21} + 14784 T^{22} - 15104 T^{23} + 22016 T^{24} - 20992 T^{25} + 37888 T^{26} - 26624 T^{27} + 49152 T^{28} - 24576 T^{29} + 65536 T^{30} - 32768 T^{31} + 65536 T^{32} \))(\( 1 + 2 T + 7 T^{2} + 12 T^{3} + 25 T^{4} + 38 T^{5} + 67 T^{6} + 83 T^{7} + 136 T^{8} + 148 T^{9} + 221 T^{10} + 234 T^{11} + 321 T^{12} + 334 T^{13} + 509 T^{14} + 535 T^{15} + 813 T^{16} + 830 T^{17} + 1044 T^{18} + 1112 T^{19} + 1496 T^{20} + 2224 T^{21} + 4176 T^{22} + 6640 T^{23} + 13008 T^{24} + 17120 T^{25} + 32576 T^{26} + 42752 T^{27} + 82176 T^{28} + 119808 T^{29} + 226304 T^{30} + 303104 T^{31} + 557056 T^{32} + 679936 T^{33} + 1097728 T^{34} + 1245184 T^{35} + 1638400 T^{36} + 1572864 T^{37} + 1835008 T^{38} + 1048576 T^{39} + 1048576 T^{40} \))
$3$ 1
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 + 4 T^{2} + 25 T^{4} \))(\( ( 1 - 2 T + 5 T^{2} )^{2} \))(\( 1 - 2 T + 14 T^{2} - 22 T^{3} + 94 T^{4} - 110 T^{5} + 350 T^{6} - 250 T^{7} + 625 T^{8} \))(\( 1 - 3 T + 16 T^{2} - 32 T^{3} + 132 T^{4} - 227 T^{5} + 660 T^{6} - 800 T^{7} + 2000 T^{8} - 1875 T^{9} + 3125 T^{10} \))(\( 1 - 5 T + 32 T^{2} - 110 T^{3} + 435 T^{4} - 1162 T^{5} + 3436 T^{6} - 7342 T^{7} + 17180 T^{8} - 29050 T^{9} + 54375 T^{10} - 68750 T^{11} + 100000 T^{12} - 78125 T^{13} + 78125 T^{14} \))(\( 1 - 3 T + 26 T^{2} - 60 T^{3} + 295 T^{4} - 554 T^{5} + 2056 T^{6} - 3282 T^{7} + 10280 T^{8} - 13850 T^{9} + 36875 T^{10} - 37500 T^{11} + 81250 T^{12} - 46875 T^{13} + 78125 T^{14} \))(\( 1 + 6 T + 45 T^{2} + 201 T^{3} + 898 T^{4} + 3208 T^{5} + 10848 T^{6} + 32170 T^{7} + 89100 T^{8} + 223637 T^{9} + 523098 T^{10} + 1118185 T^{11} + 2227500 T^{12} + 4021250 T^{13} + 6780000 T^{14} + 10025000 T^{15} + 14031250 T^{16} + 15703125 T^{17} + 17578125 T^{18} + 11718750 T^{19} + 9765625 T^{20} \))(\( 1 - 10 T + 70 T^{2} - 368 T^{3} + 1615 T^{4} - 6157 T^{5} + 20809 T^{6} - 63509 T^{7} + 176219 T^{8} - 447408 T^{9} + 1043891 T^{10} - 2237040 T^{11} + 4405475 T^{12} - 7938625 T^{13} + 13005625 T^{14} - 19240625 T^{15} + 25234375 T^{16} - 28750000 T^{17} + 27343750 T^{18} - 19531250 T^{19} + 9765625 T^{20} \))(\( 1 + 2 T + 28 T^{2} + 47 T^{3} + 393 T^{4} + 517 T^{5} + 3618 T^{6} + 3614 T^{7} + 25024 T^{8} + 19175 T^{9} + 143096 T^{10} + 94058 T^{11} + 715480 T^{12} + 479375 T^{13} + 3128000 T^{14} + 2258750 T^{15} + 11306250 T^{16} + 8078125 T^{17} + 30703125 T^{18} + 18359375 T^{19} + 54687500 T^{20} + 19531250 T^{21} + 48828125 T^{22} \))(\( 1 - 16 T + 151 T^{2} - 1042 T^{3} + 5804 T^{4} - 27347 T^{5} + 112408 T^{6} - 410786 T^{7} + 1353173 T^{8} - 4055040 T^{9} + 11129571 T^{10} - 28094425 T^{11} + 65397143 T^{12} - 140472125 T^{13} + 278239275 T^{14} - 506880000 T^{15} + 845733125 T^{16} - 1283706250 T^{17} + 1756375000 T^{18} - 2136484375 T^{19} + 2267187500 T^{20} - 2035156250 T^{21} + 1474609375 T^{22} - 781250000 T^{23} + 244140625 T^{24} \))(\( 1 + 16 T + 151 T^{2} + 1032 T^{3} + 5658 T^{4} + 26139 T^{5} + 105357 T^{6} + 379082 T^{7} + 1239597 T^{8} + 3730940 T^{9} + 10434096 T^{10} + 27277136 T^{11} + 66909704 T^{12} + 154271046 T^{13} + 334548520 T^{14} + 681928400 T^{15} + 1304262000 T^{16} + 2331837500 T^{17} + 3873740625 T^{18} + 5923156250 T^{19} + 8231015625 T^{20} + 10210546875 T^{21} + 11050781250 T^{22} + 10078125000 T^{23} + 7373046875 T^{24} + 3906250000 T^{25} + 1220703125 T^{26} \))(\( 1 - 3 T + 33 T^{2} - 99 T^{3} + 534 T^{4} - 1595 T^{5} + 5860 T^{6} - 17183 T^{7} + 50676 T^{8} - 141937 T^{9} + 369399 T^{10} - 963721 T^{11} + 2310925 T^{12} - 5570690 T^{13} + 12445672 T^{14} - 27853450 T^{15} + 57773125 T^{16} - 120465125 T^{17} + 230874375 T^{18} - 443553125 T^{19} + 791812500 T^{20} - 1342421875 T^{21} + 2289062500 T^{22} - 3115234375 T^{23} + 5214843750 T^{24} - 4833984375 T^{25} + 8056640625 T^{26} - 3662109375 T^{27} + 6103515625 T^{28} \))(\( 1 + 16 T + 153 T^{2} + 1088 T^{3} + 6372 T^{4} + 32211 T^{5} + 144828 T^{6} + 589852 T^{7} + 2205462 T^{8} + 7640406 T^{9} + 24699256 T^{10} + 74890147 T^{11} + 213843063 T^{12} + 576696630 T^{13} + 1472098531 T^{14} + 3561811102 T^{15} + 8175960316 T^{16} + 17809055510 T^{17} + 36802463275 T^{18} + 72087078750 T^{19} + 133651914375 T^{20} + 234031709375 T^{21} + 385925875000 T^{22} + 596906718750 T^{23} + 861508593750 T^{24} + 1152054687500 T^{25} + 1414335937500 T^{26} + 1572802734375 T^{27} + 1555664062500 T^{28} + 1328125000000 T^{29} + 933837890625 T^{30} + 488281250000 T^{31} + 152587890625 T^{32} \))(\( 1 + 3 T + 33 T^{2} + 83 T^{3} + 572 T^{4} + 1319 T^{5} + 7104 T^{6} + 15349 T^{7} + 69629 T^{8} + 142220 T^{9} + 568036 T^{10} + 1101608 T^{11} + 3968776 T^{12} + 7293890 T^{13} + 24116395 T^{14} + 41856232 T^{15} + 128600972 T^{16} + 209281160 T^{17} + 602909875 T^{18} + 911736250 T^{19} + 2480485000 T^{20} + 3442525000 T^{21} + 8875562500 T^{22} + 11110937500 T^{23} + 27198828125 T^{24} + 29978515625 T^{25} + 69375000000 T^{26} + 64404296875 T^{27} + 139648437500 T^{28} + 101318359375 T^{29} + 201416015625 T^{30} + 91552734375 T^{31} + 152587890625 T^{32} \))(\( 1 - T + 27 T^{2} - 39 T^{3} + 410 T^{4} - 717 T^{5} + 4736 T^{6} - 8813 T^{7} + 45610 T^{8} - 84699 T^{9} + 378699 T^{10} - 688957 T^{11} + 2777258 T^{12} - 4928589 T^{13} + 18374081 T^{14} - 31646695 T^{15} + 111227573 T^{16} - 185409648 T^{17} + 621293905 T^{18} - 1001839322 T^{19} + 3220723704 T^{20} - 5009196610 T^{21} + 15532347625 T^{22} - 23176206000 T^{23} + 69517233125 T^{24} - 98895921875 T^{25} + 287095015625 T^{26} - 385046015625 T^{27} + 1084866406250 T^{28} - 1345619140625 T^{29} + 3698232421875 T^{30} - 4135693359375 T^{31} + 11135253906250 T^{32} - 10758056640625 T^{33} + 28906250000000 T^{34} - 21881103515625 T^{35} + 62561035156250 T^{36} - 29754638671875 T^{37} + 102996826171875 T^{38} - 19073486328125 T^{39} + 95367431640625 T^{40} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( 1 + 4 T + 12 T^{2} + 28 T^{3} + 49 T^{4} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( 1 + 2 T + 14 T^{2} + 26 T^{3} + 150 T^{4} + 182 T^{5} + 686 T^{6} + 686 T^{7} + 2401 T^{8} \))(\( 1 + 5 T + 33 T^{2} + 115 T^{3} + 447 T^{4} + 1151 T^{5} + 3129 T^{6} + 5635 T^{7} + 11319 T^{8} + 12005 T^{9} + 16807 T^{10} \))(\( 1 + 5 T + 44 T^{2} + 172 T^{3} + 851 T^{4} + 2679 T^{5} + 9529 T^{6} + 24079 T^{7} + 66703 T^{8} + 131271 T^{9} + 291893 T^{10} + 412972 T^{11} + 739508 T^{12} + 588245 T^{13} + 823543 T^{14} \))(\( 1 + 5 T + 41 T^{2} + 135 T^{3} + 656 T^{4} + 1638 T^{5} + 6288 T^{6} + 13196 T^{7} + 44016 T^{8} + 80262 T^{9} + 225008 T^{10} + 324135 T^{11} + 689087 T^{12} + 588245 T^{13} + 823543 T^{14} \))(\( 1 - 3 T + 24 T^{2} - 64 T^{3} + 390 T^{4} - 926 T^{5} + 4308 T^{6} - 9374 T^{7} + 38937 T^{8} - 77749 T^{9} + 291264 T^{10} - 544243 T^{11} + 1907913 T^{12} - 3215282 T^{13} + 10343508 T^{14} - 15563282 T^{15} + 45883110 T^{16} - 52706752 T^{17} + 138355224 T^{18} - 121060821 T^{19} + 282475249 T^{20} \))(\( 1 - T + 27 T^{2} - 51 T^{3} + 320 T^{4} - 865 T^{5} + 2581 T^{6} - 7090 T^{7} + 19668 T^{8} - 37113 T^{9} + 146057 T^{10} - 259791 T^{11} + 963732 T^{12} - 2431870 T^{13} + 6196981 T^{14} - 14538055 T^{15} + 37647680 T^{16} - 42000693 T^{17} + 155649627 T^{18} - 40353607 T^{19} + 282475249 T^{20} \))(\( 1 - 3 T + 32 T^{2} - 86 T^{3} + 459 T^{4} - 1013 T^{5} + 4113 T^{6} - 6717 T^{7} + 27974 T^{8} - 34932 T^{9} + 175069 T^{10} - 213418 T^{11} + 1225483 T^{12} - 1711668 T^{13} + 9595082 T^{14} - 16127517 T^{15} + 69127191 T^{16} - 119178437 T^{17} + 378006237 T^{18} - 495772886 T^{19} + 1291315424 T^{20} - 847425747 T^{21} + 1977326743 T^{22} \))(\( 1 + 7 T + 65 T^{2} + 357 T^{3} + 2029 T^{4} + 9030 T^{5} + 39824 T^{6} + 149611 T^{7} + 550512 T^{8} + 1792938 T^{9} + 5690118 T^{10} + 16257543 T^{11} + 45237078 T^{12} + 113802801 T^{13} + 278815782 T^{14} + 614977734 T^{15} + 1321779312 T^{16} + 2514512077 T^{17} + 4685253776 T^{18} + 7436593290 T^{19} + 11696781229 T^{20} + 14406237699 T^{21} + 18360891185 T^{22} + 13841287201 T^{23} + 13841287201 T^{24} \))(\( 1 - T + 44 T^{2} - 22 T^{3} + 972 T^{4} - 11 T^{5} + 14367 T^{6} + 6349 T^{7} + 161924 T^{8} + 130615 T^{9} + 1503898 T^{10} + 1533689 T^{11} + 12019984 T^{12} + 12574506 T^{13} + 84139888 T^{14} + 75150761 T^{15} + 515837014 T^{16} + 313606615 T^{17} + 2721456668 T^{18} + 746953501 T^{19} + 11831842281 T^{20} - 63412811 T^{21} + 39223706004 T^{22} - 6214455478 T^{23} + 87002376692 T^{24} - 13841287201 T^{25} + 96889010407 T^{26} \))(\( 1 + 3 T + 45 T^{2} + 99 T^{3} + 970 T^{4} + 1612 T^{5} + 13841 T^{6} + 17081 T^{7} + 149698 T^{8} + 129304 T^{9} + 1326607 T^{10} + 732200 T^{11} + 10262627 T^{12} + 3642781 T^{13} + 73555142 T^{14} + 25499467 T^{15} + 502868723 T^{16} + 251144600 T^{17} + 3185183407 T^{18} + 2173212328 T^{19} + 17611820002 T^{20} + 14066937983 T^{21} + 79790610641 T^{22} + 65050014484 T^{23} + 274000991530 T^{24} + 195755347557 T^{25} + 622857924045 T^{26} + 290667031221 T^{27} + 678223072849 T^{28} \))(\( 1 - T + 41 T^{2} - 25 T^{3} + 889 T^{4} - 262 T^{5} + 13422 T^{6} + 1475 T^{7} + 154581 T^{8} + 97281 T^{9} + 1445031 T^{10} + 1808766 T^{11} + 11521521 T^{12} + 22075619 T^{13} + 83322450 T^{14} + 200046589 T^{15} + 584108128 T^{16} + 1400326123 T^{17} + 4082800050 T^{18} + 7571937317 T^{19} + 27663171921 T^{20} + 30399930162 T^{21} + 170006452119 T^{22} + 80115086583 T^{23} + 891128703381 T^{24} + 59521570325 T^{25} + 3791382792078 T^{26} - 518059606666 T^{27} + 12304904321689 T^{28} - 2422225260175 T^{29} + 27807145986809 T^{30} - 4747561509943 T^{31} + 33232930569601 T^{32} \))(\( 1 - 13 T + 120 T^{2} - 804 T^{3} + 4551 T^{4} - 21729 T^{5} + 91678 T^{6} - 338046 T^{7} + 1105030 T^{8} - 3108264 T^{9} + 7298782 T^{10} - 12074303 T^{11} + 2434585 T^{12} + 89106998 T^{13} - 474263316 T^{14} + 1720403873 T^{15} - 4979877774 T^{16} + 12042827111 T^{17} - 23238902484 T^{18} + 30563700314 T^{19} + 5845438585 T^{20} - 202932810521 T^{21} + 858694403518 T^{22} - 2559789059352 T^{23} + 6370278049030 T^{24} - 13641375431922 T^{25} + 25896765877822 T^{26} - 42965332798647 T^{27} + 62991698051751 T^{28} - 77898764367228 T^{29} + 81386768741880 T^{30} - 61718299629259 T^{31} + 33232930569601 T^{32} \))(\( 1 - 9 T + 93 T^{2} - 583 T^{3} + 3711 T^{4} - 18395 T^{5} + 89974 T^{6} - 373916 T^{7} + 1522703 T^{8} - 5492013 T^{9} + 19423811 T^{10} - 62344298 T^{11} + 197250576 T^{12} - 576616234 T^{13} + 1677200945 T^{14} - 4582282761 T^{15} + 12620567920 T^{16} - 33184332359 T^{17} + 89195465289 T^{18} - 231925425628 T^{19} + 622248430242 T^{20} - 1623477979396 T^{21} + 4370577799161 T^{22} - 11382225999137 T^{23} + 30301983575920 T^{24} - 77014426364127 T^{25} + 197321013978305 T^{26} - 474868263197062 T^{27} + 1137110317775376 T^{28} - 2515817300182886 T^{29} + 5486745848753939 T^{30} - 10859504177803659 T^{31} + 21076169544824303 T^{32} - 36228351215343812 T^{33} + 61022442756515926 T^{34} - 87331393975401485 T^{35} + 123327405343789311 T^{36} - 135623589654541681 T^{37} + 151442464605671757 T^{38} - 102590056668358287 T^{39} + 79792266297612001 T^{40} \))
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - 3 T + 20 T^{2} - 33 T^{3} + 121 T^{4} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 4 T + 6 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 16 T^{2} + 48 T^{3} + 94 T^{4} + 528 T^{5} + 1936 T^{6} + 14641 T^{8} \))(\( 1 - 8 T + 71 T^{2} - 359 T^{3} + 1734 T^{4} - 5961 T^{5} + 19074 T^{6} - 43439 T^{7} + 94501 T^{8} - 117128 T^{9} + 161051 T^{10} \))(\( 1 - 12 T + 116 T^{2} - 783 T^{3} + 4536 T^{4} - 21382 T^{5} + 88915 T^{6} - 312885 T^{7} + 978065 T^{8} - 2587222 T^{9} + 6037416 T^{10} - 11463903 T^{11} + 18681916 T^{12} - 21258732 T^{13} + 19487171 T^{14} \))(\( 1 - 4 T + 43 T^{2} - 177 T^{3} + 1011 T^{4} - 3683 T^{5} + 15431 T^{6} - 49616 T^{7} + 169741 T^{8} - 445643 T^{9} + 1345641 T^{10} - 2591457 T^{11} + 6925193 T^{12} - 7086244 T^{13} + 19487171 T^{14} \))(\( 1 + 9 T + 93 T^{2} + 587 T^{3} + 3694 T^{4} + 18662 T^{5} + 90162 T^{6} + 385219 T^{7} + 1545610 T^{8} + 5708547 T^{9} + 19626536 T^{10} + 62794017 T^{11} + 187018810 T^{12} + 512726489 T^{13} + 1320061842 T^{14} + 3005533762 T^{15} + 6544146334 T^{16} + 11438969377 T^{17} + 19935375933 T^{18} + 21221529219 T^{19} + 25937424601 T^{20} \))(\( 1 + 46 T^{2} + 69 T^{3} + 1079 T^{4} + 2926 T^{5} + 19000 T^{6} + 64647 T^{7} + 270077 T^{8} + 988343 T^{9} + 3200721 T^{10} + 10871773 T^{11} + 32679317 T^{12} + 86045157 T^{13} + 278179000 T^{14} + 471235226 T^{15} + 1911514319 T^{16} + 1344614799 T^{17} + 9860508526 T^{18} + 25937424601 T^{20} \))(\( 1 + 11 T + 107 T^{2} + 665 T^{3} + 3853 T^{4} + 17357 T^{5} + 77380 T^{6} + 292567 T^{7} + 1161868 T^{8} + 4068001 T^{9} + 15108568 T^{10} + 48975106 T^{11} + 166194248 T^{12} + 492228121 T^{13} + 1546446308 T^{14} + 4283473447 T^{15} + 12462126380 T^{16} + 30748984277 T^{17} + 75084069863 T^{18} + 142548655865 T^{19} + 252300402937 T^{20} + 285311670611 T^{21} + 285311670611 T^{22} \))(\( 1 - 6 T + 69 T^{2} - 283 T^{3} + 2102 T^{4} - 7523 T^{5} + 45973 T^{6} - 153816 T^{7} + 788320 T^{8} - 2463728 T^{9} + 11074500 T^{10} - 32738381 T^{11} + 132642913 T^{12} - 360122191 T^{13} + 1340014500 T^{14} - 3279221968 T^{15} + 11541793120 T^{16} - 24772220616 T^{17} + 81443973853 T^{18} - 146601987433 T^{19} + 450582367862 T^{20} - 667299196553 T^{21} + 1789682297469 T^{22} - 1711870023666 T^{23} + 3138428376721 T^{24} \))(\( 1 + 10 T + 129 T^{2} + 957 T^{3} + 7486 T^{4} + 44779 T^{5} + 267592 T^{6} + 1348334 T^{7} + 6669056 T^{8} + 29027357 T^{9} + 123280921 T^{10} + 470069885 T^{11} + 1745640195 T^{12} + 5867812140 T^{13} + 19202042145 T^{14} + 56878456085 T^{15} + 164086905851 T^{16} + 424989533837 T^{17} + 1074058137856 T^{18} + 2388655929374 T^{19} + 5214611062232 T^{20} + 9598776332299 T^{21} + 17651596414826 T^{22} + 24822115343157 T^{23} + 36805205508819 T^{24} + 31384283767210 T^{25} + 34522712143931 T^{26} \))(\( 1 - 12 T + 139 T^{2} - 1121 T^{3} + 8287 T^{4} - 52293 T^{5} + 304414 T^{6} - 1606898 T^{7} + 7904531 T^{8} - 36145022 T^{9} + 155180105 T^{10} - 626725645 T^{11} + 2387643533 T^{12} - 8604818257 T^{13} + 29318443452 T^{14} - 94653000827 T^{15} + 288904867493 T^{16} - 834171833495 T^{17} + 2271991917305 T^{18} - 5821191938122 T^{19} + 14003358842891 T^{20} - 31313896105558 T^{21} + 65253844400734 T^{22} - 123304158605463 T^{23} + 214943437668487 T^{24} - 319834382754931 T^{25} + 436241544364219 T^{26} - 414272545727172 T^{27} + 379749833583241 T^{28} \))(\( 1 + 4 T + 87 T^{2} + 305 T^{3} + 3846 T^{4} + 12369 T^{5} + 116999 T^{6} + 351654 T^{7} + 2743519 T^{8} + 7762962 T^{9} + 52405763 T^{10} + 139857014 T^{11} + 840621025 T^{12} + 2111707908 T^{13} + 11524132159 T^{14} + 27123517842 T^{15} + 136290044578 T^{16} + 298358696262 T^{17} + 1394419991239 T^{18} + 2810683225548 T^{19} + 12307532427025 T^{20} + 22524111961714 T^{21} + 92840005906043 T^{22} + 151278167960502 T^{23} + 588097662842239 T^{24} + 829181737330914 T^{25} + 3034652740892399 T^{26} + 3529020053787459 T^{27} + 12070395536868966 T^{28} + 10529427203898955 T^{29} + 33038235521741967 T^{30} + 16708992677662604 T^{31} + 45949729863572161 T^{32} \))(\( 1 + 8 T + 124 T^{2} + 819 T^{3} + 7197 T^{4} + 40910 T^{5} + 267126 T^{6} + 1341878 T^{7} + 7228206 T^{8} + 32646945 T^{9} + 152778984 T^{10} + 627549447 T^{11} + 2623058407 T^{12} + 9868098664 T^{13} + 37405543590 T^{14} + 129284753107 T^{15} + 448129229178 T^{16} + 1422132284177 T^{17} + 4526070774390 T^{18} + 13134439321784 T^{19} + 38404198136887 T^{20} + 101067465988797 T^{21} + 270657289674024 T^{22} + 636196599842595 T^{23} + 1549430149797486 T^{24} + 3164078131703698 T^{25} + 6928560483966726 T^{26} + 11672100444696010 T^{27} + 22587269027261037 T^{28} + 28274101245879489 T^{29} + 47088979364321884 T^{30} + 33417985355325208 T^{31} + 45949729863572161 T^{32} \))(\( 1 + 73 T^{2} - 47 T^{3} + 3033 T^{4} - 3811 T^{5} + 91636 T^{6} - 163856 T^{7} + 2231051 T^{8} - 4953696 T^{9} + 46062463 T^{10} - 116768915 T^{11} + 829973932 T^{12} - 2266227913 T^{13} + 13265281121 T^{14} - 37356687648 T^{15} + 189734815108 T^{16} - 533198439656 T^{17} + 2439922967707 T^{18} - 6663484842834 T^{19} + 28267289746614 T^{20} - 73298333271174 T^{21} + 295230679092547 T^{22} - 709687123182136 T^{23} + 2777907427996228 T^{24} - 6016331902398048 T^{25} + 23500254687999881 T^{26} - 44162370865604123 T^{27} + 177912283322690092 T^{28} - 275334993504825265 T^{29} + 1194741660998852263 T^{30} - 1413347281459028256 T^{31} + 7001993768311763771 T^{32} - 5656753521055957936 T^{33} + 34798755750233872276 T^{34} - 15919492773643045961 T^{35} + \)\(13\!\cdots\!13\)\( T^{36} - 23756010339466807237 T^{37} + \)\(40\!\cdots\!13\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))
$13$ (\( 1 + 5 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 3 T + 24 T^{2} + 39 T^{3} + 169 T^{4} \))(\( ( 1 - T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 + 14 T^{2} - 24 T^{3} + 151 T^{4} - 312 T^{5} + 2366 T^{6} + 28561 T^{8} \))(\( 1 - 5 T + 61 T^{2} - 237 T^{3} + 1563 T^{4} - 4463 T^{5} + 20319 T^{6} - 40053 T^{7} + 134017 T^{8} - 142805 T^{9} + 371293 T^{10} \))(\( 1 + 13 T + 118 T^{2} + 720 T^{3} + 3455 T^{4} + 13353 T^{5} + 45817 T^{6} + 159073 T^{7} + 595621 T^{8} + 2256657 T^{9} + 7590635 T^{10} + 20563920 T^{11} + 43812574 T^{12} + 62748517 T^{13} + 62748517 T^{14} \))(\( 1 + 18 T + 210 T^{2} + 1721 T^{3} + 11354 T^{4} + 61060 T^{5} + 279708 T^{6} + 1085552 T^{7} + 3636204 T^{8} + 10319140 T^{9} + 24944738 T^{10} + 49153481 T^{11} + 77971530 T^{12} + 86882562 T^{13} + 62748517 T^{14} \))(\( 1 + 16 T + 163 T^{2} + 1291 T^{3} + 8628 T^{4} + 50465 T^{5} + 264346 T^{6} + 1260110 T^{7} + 5517709 T^{8} + 22294412 T^{9} + 83497771 T^{10} + 289827356 T^{11} + 932492821 T^{12} + 2768461670 T^{13} + 7549986106 T^{14} + 18737301245 T^{15} + 41645708052 T^{16} + 81008335447 T^{17} + 132964107523 T^{18} + 169671989968 T^{19} + 137858491849 T^{20} \))(\( 1 + 13 T + 145 T^{2} + 1138 T^{3} + 7974 T^{4} + 46970 T^{5} + 253908 T^{6} + 1216997 T^{7} + 5428597 T^{8} + 21924657 T^{9} + 82839053 T^{10} + 285020541 T^{11} + 917432893 T^{12} + 2673742409 T^{13} + 7251866388 T^{14} + 17439632210 T^{15} + 38488974966 T^{16} + 71407812346 T^{17} + 118280954545 T^{18} + 137858491849 T^{19} + 137858491849 T^{20} \))(\( 1 + 5 T + 84 T^{2} + 350 T^{3} + 3206 T^{4} + 11152 T^{5} + 72699 T^{6} + 212361 T^{7} + 1121757 T^{8} + 2859915 T^{9} + 14089132 T^{10} + 35296207 T^{11} + 183158716 T^{12} + 483325635 T^{13} + 2464500129 T^{14} + 6065242521 T^{15} + 26992629807 T^{16} + 53828573968 T^{17} + 201171745502 T^{18} + 285505752350 T^{19} + 890777947332 T^{20} + 689292459245 T^{21} + 1792160394037 T^{22} \))(\( 1 + 15 T + 166 T^{2} + 1273 T^{3} + 8652 T^{4} + 49483 T^{5} + 266267 T^{6} + 1274153 T^{7} + 5845861 T^{8} + 24481580 T^{9} + 100038580 T^{10} + 379622217 T^{11} + 1417566029 T^{12} + 4935088821 T^{13} + 16906520020 T^{14} + 53786031260 T^{15} + 166963636021 T^{16} + 473084089829 T^{17} + 1285219952003 T^{18} + 3104984866711 T^{19} + 7057702198092 T^{20} + 13499527701829 T^{21} + 22884509646934 T^{22} + 26882405910555 T^{23} + 23298085122481 T^{24} \))(\( 1 - 7 T + 133 T^{2} - 776 T^{3} + 8208 T^{4} - 41012 T^{5} + 316653 T^{6} - 1383298 T^{7} + 8656894 T^{8} - 33553565 T^{9} + 179349201 T^{10} - 621906575 T^{11} + 2919955615 T^{12} - 9072659644 T^{13} + 37959422995 T^{14} - 105102211175 T^{15} + 394030194597 T^{16} - 958323369965 T^{17} + 3214244143942 T^{18} - 6676915236082 T^{19} + 19869506153601 T^{20} - 33454748329652 T^{21} + 87041730853584 T^{22} - 106978189674824 T^{23} + 238357332406921 T^{24} - 163086595857367 T^{25} + 302875106592253 T^{26} \))(\( 1 - 13 T + 177 T^{2} - 1487 T^{3} + 12289 T^{4} - 78917 T^{5} + 496496 T^{6} - 2629018 T^{7} + 13720162 T^{8} - 62633382 T^{9} + 284605872 T^{10} - 1157550439 T^{11} + 4740009622 T^{12} - 17623247216 T^{13} + 66511477178 T^{14} - 229102213808 T^{15} + 801061626118 T^{16} - 2543138314483 T^{17} + 8128628310192 T^{18} - 23255336302926 T^{19} + 66224601423058 T^{20} - 164966980666306 T^{21} + 405007040053616 T^{22} - 836875277019041 T^{23} + 1694143006332361 T^{24} - 2664942505933019 T^{25} + 4123761066679137 T^{26} - 3937376385699289 T^{27} + 3937376385699289 T^{28} \))(\( 1 - 15 T + 193 T^{2} - 1750 T^{3} + 14182 T^{4} - 97594 T^{5} + 618110 T^{6} - 3532117 T^{7} + 18918983 T^{8} - 94054959 T^{9} + 443969101 T^{10} - 1977759271 T^{11} + 8449925802 T^{12} - 34448927420 T^{13} + 135720783671 T^{14} - 513755415830 T^{15} + 1887460003930 T^{16} - 6678820405790 T^{17} + 22936812440399 T^{18} - 75684293541740 T^{19} + 241338330830922 T^{20} - 734328173007403 T^{21} + 2142954052428709 T^{22} - 5901809193745803 T^{23} + 15432795643176743 T^{24} - 37456332511862641 T^{25} + 85211712396785390 T^{26} - 174904101495646978 T^{27} + 330413443207025542 T^{28} - 530031436536442750 T^{29} + 759913642439962777 T^{30} - 767788395211361355 T^{31} + 665416609183179841 T^{32} \))(\( 1 - 19 T + 298 T^{2} - 3314 T^{3} + 32145 T^{4} - 263999 T^{5} + 1957100 T^{6} - 13012182 T^{7} + 79750453 T^{8} - 450160393 T^{9} + 2373582126 T^{10} - 11690911651 T^{11} + 54236880926 T^{12} - 236892228119 T^{13} + 979270962230 T^{14} - 3826389950627 T^{15} + 14181759836002 T^{16} - 49743069358151 T^{17} + 165496792616870 T^{18} - 520452225177443 T^{19} + 1549059556127486 T^{20} - 4340753659634743 T^{21} + 11456827568015934 T^{22} - 28246897072887181 T^{23} + 65054894525766613 T^{24} - 137987675860361886 T^{25} + 269802854397677900 T^{26} - 473128551865373963 T^{27} + 748916946262151745 T^{28} - 1003728103246726442 T^{29} + 1173338162938388122 T^{30} - 972531967267724383 T^{31} + 665416609183179841 T^{32} \))(\( 1 - 21 T + 301 T^{2} - 3163 T^{3} + 27637 T^{4} - 206057 T^{5} + 1364242 T^{6} - 8139280 T^{7} + 44625688 T^{8} - 227253048 T^{9} + 1088899906 T^{10} - 4956051849 T^{11} + 21651182355 T^{12} - 91555662621 T^{13} + 377574054643 T^{14} - 1525983394811 T^{15} + 6058490078215 T^{16} - 23625172277730 T^{17} + 90322393264348 T^{18} - 337747420812184 T^{19} + 1232943029423520 T^{20} - 4390716470558392 T^{21} + 15264484461674812 T^{22} - 51904503494172810 T^{23} + 173036535123898615 T^{24} - 566586952609560623 T^{25} + 1822477845117324187 T^{26} - 5744982052420083057 T^{27} + 17661534592946627955 T^{28} - 52556448725275990677 T^{29} + \)\(15\!\cdots\!94\)\( T^{30} - \)\(40\!\cdots\!76\)\( T^{31} + \)\(10\!\cdots\!28\)\( T^{32} - \)\(24\!\cdots\!40\)\( T^{33} + \)\(53\!\cdots\!38\)\( T^{34} - \)\(10\!\cdots\!49\)\( T^{35} + \)\(18\!\cdots\!17\)\( T^{36} - \)\(27\!\cdots\!79\)\( T^{37} + \)\(33\!\cdots\!29\)\( T^{38} - \)\(30\!\cdots\!17\)\( T^{39} + \)\(19\!\cdots\!01\)\( T^{40} \))
$17$ (\( 1 - 5 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( 1 + 2 T + 29 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 + 14 T^{2} + 289 T^{4} \))(\( 1 + 2 T + 24 T^{2} + 80 T^{3} + 593 T^{4} + 1360 T^{5} + 6936 T^{6} + 9826 T^{7} + 83521 T^{8} \))(\( 1 + 2 T + 80 T^{2} + 125 T^{3} + 2634 T^{4} + 3097 T^{5} + 44778 T^{6} + 36125 T^{7} + 393040 T^{8} + 167042 T^{9} + 1419857 T^{10} \))(\( 1 - 12 T + 117 T^{2} - 781 T^{3} + 4831 T^{4} - 25246 T^{5} + 125970 T^{6} - 537609 T^{7} + 2141490 T^{8} - 7296094 T^{9} + 23734703 T^{10} - 65229901 T^{11} + 166123269 T^{12} - 289650828 T^{13} + 410338673 T^{14} \))(\( 1 - 3 T + 80 T^{2} - 188 T^{3} + 3142 T^{4} - 6147 T^{5} + 77998 T^{6} - 126724 T^{7} + 1325966 T^{8} - 1776483 T^{9} + 15436646 T^{10} - 15701948 T^{11} + 113588560 T^{12} - 72412707 T^{13} + 410338673 T^{14} \))(\( 1 + 90 T^{2} - 43 T^{3} + 4171 T^{4} - 3309 T^{5} + 132803 T^{6} - 121588 T^{7} + 3209008 T^{8} - 2910200 T^{9} + 61136062 T^{10} - 49473400 T^{11} + 927403312 T^{12} - 597361844 T^{13} + 11091839363 T^{14} - 4698306813 T^{15} + 100677800299 T^{16} - 17644562939 T^{17} + 627818169690 T^{18} + 2015993900449 T^{20} \))(\( 1 - 22 T + 279 T^{2} - 2560 T^{3} + 18885 T^{4} - 118890 T^{5} + 669412 T^{6} - 3469737 T^{7} + 16851864 T^{8} - 76822830 T^{9} + 327849375 T^{10} - 1305988110 T^{11} + 4870188696 T^{12} - 17046817881 T^{13} + 55909959652 T^{14} - 168806798730 T^{15} + 455837990565 T^{16} - 1050467002880 T^{17} + 1946236326039 T^{18} - 2608933282934 T^{19} + 2015993900449 T^{20} \))(\( 1 + 15 T + 187 T^{2} + 1517 T^{3} + 10634 T^{4} + 56023 T^{5} + 250369 T^{6} + 755250 T^{7} + 1190337 T^{8} - 6597342 T^{9} - 60323812 T^{10} - 321154542 T^{11} - 1025504804 T^{12} - 1906631838 T^{13} + 5848125681 T^{14} + 63079235250 T^{15} + 355488177233 T^{16} + 1352259028087 T^{17} + 4363541448682 T^{18} + 10582224037997 T^{19} + 22175932904939 T^{20} + 30239908506735 T^{21} + 34271896307633 T^{22} \))(\( 1 - 18 T + 275 T^{2} - 2930 T^{3} + 27660 T^{4} - 217720 T^{5} + 1561467 T^{6} - 9894935 T^{7} + 58087329 T^{8} - 309237988 T^{9} + 1539835855 T^{10} - 7039278989 T^{11} + 30235172546 T^{12} - 119667742813 T^{13} + 445012562095 T^{14} - 1519286235044 T^{15} + 4851511805409 T^{16} - 14049392724295 T^{17} + 37690017453723 T^{18} - 89338935885560 T^{19} + 192949450818060 T^{20} - 347462478136210 T^{21} + 554398322623475 T^{22} - 616894133537394 T^{23} + 582622237229761 T^{24} \))(\( 1 + 26 T + 443 T^{2} + 5624 T^{3} + 59015 T^{4} + 529758 T^{5} + 4192795 T^{6} + 29699383 T^{7} + 190783229 T^{8} + 1119794260 T^{9} + 6045356912 T^{10} + 30129093102 T^{11} + 139068012694 T^{12} + 595198333880 T^{13} + 2364156215798 T^{14} + 8707307906478 T^{15} + 29700838508656 T^{16} + 93526336389460 T^{17} + 270884903178253 T^{18} + 716870906419927 T^{19} + 1720465936461035 T^{20} + 3695463310429278 T^{21} + 6998463531470455 T^{22} + 11337949696125176 T^{23} + 15182450064281419 T^{24} + 15148178167973786 T^{25} + 9904578032905937 T^{26} \))(\( 1 - 14 T + 208 T^{2} - 1889 T^{3} + 16926 T^{4} - 117195 T^{5} + 798635 T^{6} - 4583479 T^{7} + 26201988 T^{8} - 132050361 T^{9} + 671563025 T^{10} - 3086940621 T^{11} + 14399017325 T^{12} - 61266330337 T^{13} + 264303495568 T^{14} - 1041527615729 T^{15} + 4161316006925 T^{16} - 15166139270973 T^{17} + 56089615411025 T^{18} - 187492629418377 T^{19} + 632452293287172 T^{20} - 1880778690583367 T^{21} + 5571084043893035 T^{22} - 13897906186065915 T^{23} + 34122712758999774 T^{24} - 64739612125118737 T^{25} + 121185425343790288 T^{26} - 138664092460683118 T^{27} + 168377826559400929 T^{28} \))(\( 1 + 20 T + 318 T^{2} + 3634 T^{3} + 35651 T^{4} + 295522 T^{5} + 2190070 T^{6} + 14437961 T^{7} + 87119572 T^{8} + 479762707 T^{9} + 2459921959 T^{10} + 11733318129 T^{11} + 53092304636 T^{12} + 228644231681 T^{13} + 959837015325 T^{14} + 3951257438490 T^{15} + 16310811598792 T^{16} + 67171376454330 T^{17} + 277392897428925 T^{18} + 1123329110248753 T^{19} + 4434322375503356 T^{20} + 16659633878687553 T^{21} + 59376536019977671 T^{22} + 196865192545267811 T^{23} + 607725002635735252 T^{24} + 1712167135936502617 T^{25} + 4415167761556341430 T^{26} + 10128099340624319426 T^{27} + 20771065379478209411 T^{28} + 35993236571580175058 T^{29} + 53544148845889495422 T^{30} + 57248461030196315860 T^{31} + 48661191875666868481 T^{32} \))(\( 1 - 4 T + 105 T^{2} - 299 T^{3} + 5458 T^{4} - 12698 T^{5} + 197720 T^{6} - 425660 T^{7} + 5655591 T^{8} - 12646197 T^{9} + 135952466 T^{10} - 334122711 T^{11} + 2846433090 T^{12} - 7686727064 T^{13} + 53717007117 T^{14} - 152110631623 T^{15} + 940947036552 T^{16} - 2585880737591 T^{17} + 15524215056813 T^{18} - 37764890065432 T^{19} + 237736938109890 T^{20} - 474406470072327 T^{21} + 3281562028795154 T^{22} - 5189223695476581 T^{23} + 39452031001502631 T^{24} - 50478115509713020 T^{25} + 398602313996776280 T^{26} - 435184539314323834 T^{27} + 3179952170800035538 T^{28} - 2961468831838875163 T^{29} + 17679671788737097545 T^{30} - 11449692206039263172 T^{31} + 48661191875666868481 T^{32} \))(\( 1 - 4 T + 168 T^{2} - 619 T^{3} + 13433 T^{4} - 47287 T^{5} + 688249 T^{6} - 2398160 T^{7} + 25709641 T^{8} - 91244692 T^{9} + 757956498 T^{10} - 2784205789 T^{11} + 18734675684 T^{12} - 71205881473 T^{13} + 408455222260 T^{14} - 1580820886684 T^{15} + 8161638451030 T^{16} - 31416124339492 T^{17} + 152493040628985 T^{18} - 573166662265880 T^{19} + 2675816091260806 T^{20} - 9743833258519960 T^{21} + 44070488741776665 T^{22} - 154347418879924196 T^{23} + 681668205068476630 T^{24} - 2244539601704484188 T^{25} + 9859116110711085940 T^{26} - 29218526913426105329 T^{27} + \)\(13\!\cdots\!44\)\( T^{28} - \)\(33\!\cdots\!33\)\( T^{29} + \)\(15\!\cdots\!02\)\( T^{30} - \)\(31\!\cdots\!36\)\( T^{31} + \)\(14\!\cdots\!01\)\( T^{32} - \)\(23\!\cdots\!20\)\( T^{33} + \)\(11\!\cdots\!21\)\( T^{34} - \)\(13\!\cdots\!91\)\( T^{35} + \)\(65\!\cdots\!73\)\( T^{36} - \)\(51\!\cdots\!63\)\( T^{37} + \)\(23\!\cdots\!12\)\( T^{38} - \)\(95\!\cdots\!12\)\( T^{39} + \)\(40\!\cdots\!01\)\( T^{40} \))
$19$ (\( 1 - 5 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 2 T + 22 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( 1 + 4 T + 22 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 20 T^{2} - 112 T^{3} + 873 T^{4} - 2128 T^{5} + 7220 T^{6} - 27436 T^{7} + 130321 T^{8} \))(\( 1 + 9 T + 89 T^{2} + 438 T^{3} + 2569 T^{4} + 9583 T^{5} + 48811 T^{6} + 158118 T^{7} + 610451 T^{8} + 1172889 T^{9} + 2476099 T^{10} \))(\( 1 + 5 T + 71 T^{2} + 264 T^{3} + 2600 T^{4} + 7812 T^{5} + 64394 T^{6} + 167594 T^{7} + 1223486 T^{8} + 2820132 T^{9} + 17833400 T^{10} + 34404744 T^{11} + 175803029 T^{12} + 235229405 T^{13} + 893871739 T^{14} \))(\( 1 + 4 T + 96 T^{2} + 250 T^{3} + 3793 T^{4} + 5980 T^{5} + 90955 T^{6} + 101614 T^{7} + 1728145 T^{8} + 2158780 T^{9} + 26016187 T^{10} + 32580250 T^{11} + 237705504 T^{12} + 188183524 T^{13} + 893871739 T^{14} \))(\( 1 - T + 143 T^{2} - 168 T^{3} + 9740 T^{4} - 12024 T^{5} + 418797 T^{6} - 500881 T^{7} + 12620907 T^{8} - 13739056 T^{9} + 278516040 T^{10} - 261042064 T^{11} + 4556147427 T^{12} - 3435542779 T^{13} + 54578043837 T^{14} - 29772614376 T^{15} + 458226880940 T^{16} - 150170452152 T^{17} + 2428649514863 T^{18} - 322687697779 T^{19} + 6131066257801 T^{20} \))(\( 1 + 2 T + 95 T^{2} + 311 T^{3} + 4337 T^{4} + 18975 T^{5} + 138780 T^{6} + 661855 T^{7} + 3627427 T^{8} + 16047275 T^{9} + 77334365 T^{10} + 304898225 T^{11} + 1309501147 T^{12} + 4539663445 T^{13} + 18085948380 T^{14} + 46983978525 T^{15} + 204037985897 T^{16} + 277994110829 T^{17} + 1613438488895 T^{18} + 645375395558 T^{19} + 6131066257801 T^{20} \))(\( 1 + 6 T + 80 T^{2} + 576 T^{3} + 4431 T^{4} + 26764 T^{5} + 174475 T^{6} + 923308 T^{7} + 5030336 T^{8} + 24438270 T^{9} + 118842117 T^{10} + 508708424 T^{11} + 2258000223 T^{12} + 8822215470 T^{13} + 34503074624 T^{14} + 120326421868 T^{15} + 432017373025 T^{16} + 1259135959084 T^{17} + 3960745675509 T^{18} + 9782532311616 T^{19} + 25815015822320 T^{20} + 36786397546806 T^{21} + 116490258898219 T^{22} \))(\( 1 + 6 T + 109 T^{2} + 357 T^{3} + 4376 T^{4} + 4409 T^{5} + 99783 T^{6} - 124994 T^{7} + 2170382 T^{8} - 4573836 T^{9} + 56249733 T^{10} - 77379748 T^{11} + 1244276232 T^{12} - 1470215212 T^{13} + 20306153613 T^{14} - 31371941124 T^{15} + 282846352622 T^{16} - 309497518406 T^{17} + 4694379143823 T^{18} + 3941080497251 T^{19} + 74320071867416 T^{20} + 115199508107103 T^{21} + 668286222100309 T^{22} + 698941553389314 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 131 T^{2} - 239 T^{3} + 8327 T^{4} - 28235 T^{5} + 371127 T^{6} - 1572979 T^{7} + 13335630 T^{8} - 56977156 T^{9} + 391663148 T^{10} - 1539858034 T^{11} + 9262692275 T^{12} - 32779561110 T^{13} + 175991153225 T^{14} - 555888750274 T^{15} + 2686417532132 T^{16} - 7425319947076 T^{17} + 33020340107370 T^{18} - 74002182849499 T^{19} + 331739936879853 T^{20} - 479530902462635 T^{21} + 2687020459405733 T^{22} - 1465324835614439 T^{23} + 15260223915666689 T^{24} + 42052983462257059 T^{26} \))(\( 1 + 9 T + 184 T^{2} + 1407 T^{3} + 16433 T^{4} + 109832 T^{5} + 951768 T^{6} + 5660364 T^{7} + 40108696 T^{8} + 214599308 T^{9} + 1304579992 T^{10} + 6316022728 T^{11} + 33841102070 T^{12} + 148435363378 T^{13} + 712050960576 T^{14} + 2820271904182 T^{15} + 12216637847270 T^{16} + 43321599891352 T^{17} + 170014169137432 T^{18} + 531369131939492 T^{19} + 1886948939081176 T^{20} + 5059639412052996 T^{21} + 16164411828406488 T^{22} + 35441435222463128 T^{23} + 100751811814443833 T^{24} + 163901794269794133 T^{25} + 407249945108173624 T^{26} + 378476851160313531 T^{27} + 799006685782884121 T^{28} \))(\( 1 + 4 T + 162 T^{2} + 703 T^{3} + 13635 T^{4} + 60384 T^{5} + 779746 T^{6} + 3423643 T^{7} + 33618775 T^{8} + 144056893 T^{9} + 1156283192 T^{10} + 4778942484 T^{11} + 32844550826 T^{12} + 129483358143 T^{13} + 787683013956 T^{14} + 2924003086674 T^{15} + 16151768751174 T^{16} + 55556058646806 T^{17} + 284353568038116 T^{18} + 888126353502837 T^{19} + 4280334708195146 T^{20} + 11833134705689916 T^{21} + 54398361453132152 T^{22} + 128768385460846927 T^{23} + 570966584573694775 T^{24} + 1104767477687188897 T^{25} + 4780674390255298546 T^{26} + 7034147793310056096 T^{27} + 30178548921467105235 T^{28} + 29563247373966712477 T^{29} + \)\(12\!\cdots\!02\)\( T^{30} + 60724508119499193196 T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 - 19 T + 306 T^{2} - 3175 T^{3} + 29574 T^{4} - 213809 T^{5} + 1447182 T^{6} - 8077449 T^{7} + 44238549 T^{8} - 205703372 T^{9} + 1006667408 T^{10} - 4274869164 T^{11} + 20791502522 T^{12} - 87804548738 T^{13} + 437819221792 T^{14} - 1826900858190 T^{15} + 8801375311540 T^{16} - 34711116305610 T^{17} + 158052739066912 T^{18} - 602251399793942 T^{19} + 2709569400169562 T^{20} - 10584999262111236 T^{21} + 47359555083346448 T^{22} - 183872430847803908 T^{23} + 751328185783867509 T^{24} - 2606493421737285771 T^{25} + 8872768729096966782 T^{26} - 24906665764769306171 T^{27} + 65456575416462645414 T^{28} - \)\(13\!\cdots\!25\)\( T^{29} + \)\(24\!\cdots\!26\)\( T^{30} - \)\(28\!\cdots\!81\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 - 7 T + 206 T^{2} - 1441 T^{3} + 21594 T^{4} - 148311 T^{5} + 1532868 T^{6} - 10173127 T^{7} + 82557992 T^{8} - 522709431 T^{9} + 3579868022 T^{10} - 21420969929 T^{11} + 129424965062 T^{12} - 727382090943 T^{13} + 3987290830474 T^{14} - 20976856836709 T^{15} + 106125178431079 T^{16} - 522115505502926 T^{17} + 2460886478873694 T^{18} - 11327402839776084 T^{19} + 49943143618540832 T^{20} - 215220653955745596 T^{21} + 888380018873403534 T^{22} - 3581190252244569434 T^{23} + 13830339378316646359 T^{24} - 51940774236518318191 T^{25} + \)\(18\!\cdots\!94\)\( T^{26} - \)\(65\!\cdots\!77\)\( T^{27} + \)\(21\!\cdots\!42\)\( T^{28} - \)\(69\!\cdots\!91\)\( T^{29} + \)\(21\!\cdots\!22\)\( T^{30} - \)\(60\!\cdots\!89\)\( T^{31} + \)\(18\!\cdots\!12\)\( T^{32} - \)\(42\!\cdots\!93\)\( T^{33} + \)\(12\!\cdots\!28\)\( T^{34} - \)\(22\!\cdots\!89\)\( T^{35} + \)\(62\!\cdots\!14\)\( T^{36} - \)\(78\!\cdots\!99\)\( T^{37} + \)\(21\!\cdots\!46\)\( T^{38} - \)\(13\!\cdots\!53\)\( T^{39} + \)\(37\!\cdots\!01\)\( T^{40} \))
$23$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{11} \))(\( ( 1 - T )^{12} \))(\( ( 1 - T )^{13} \))(\( ( 1 - T )^{14} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{20} \))
$29$ (\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{10} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{11} \))(\( ( 1 - T )^{12} \))(\( ( 1 + T )^{13} \))(\( ( 1 - T )^{14} \))(\( ( 1 - T )^{16} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{20} \))
$31$ (\( 1 + 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 9 T + 78 T^{2} + 279 T^{3} + 961 T^{4} \))(\( 1 + 16 T + 120 T^{2} + 496 T^{3} + 961 T^{4} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( 1 - 2 T + 86 T^{2} - 234 T^{3} + 3414 T^{4} - 7254 T^{5} + 82646 T^{6} - 59582 T^{7} + 923521 T^{8} \))(\( 1 + 6 T + 115 T^{2} + 685 T^{3} + 6096 T^{4} + 31077 T^{5} + 188976 T^{6} + 658285 T^{7} + 3425965 T^{8} + 5541126 T^{9} + 28629151 T^{10} \))(\( 1 + 8 T + 163 T^{2} + 973 T^{3} + 12089 T^{4} + 58707 T^{5} + 556093 T^{6} + 2238228 T^{7} + 17238883 T^{8} + 56417427 T^{9} + 360143399 T^{10} + 898585933 T^{11} + 4666551613 T^{12} + 7100029448 T^{13} + 27512614111 T^{14} \))(\( 1 + 22 T + 385 T^{2} + 4655 T^{3} + 47023 T^{4} + 387247 T^{5} + 2731617 T^{6} + 16373192 T^{7} + 84680127 T^{8} + 372144367 T^{9} + 1400862193 T^{10} + 4298990255 T^{11} + 11022223135 T^{12} + 19525080982 T^{13} + 27512614111 T^{14} \))(\( 1 - 17 T + 259 T^{2} - 2743 T^{3} + 27138 T^{4} - 223526 T^{5} + 1759704 T^{6} - 12219295 T^{7} + 81812734 T^{8} - 494132507 T^{9} + 2889244638 T^{10} - 15318107717 T^{11} + 78622037374 T^{12} - 364025017345 T^{13} + 1625123597784 T^{14} - 6399359606426 T^{15} + 24085074894978 T^{16} - 75467100506473 T^{17} + 220898778697219 T^{18} - 449473576731407 T^{19} + 819628286980801 T^{20} \))(\( 1 + 22 T + 430 T^{2} + 5551 T^{3} + 65126 T^{4} + 617363 T^{5} + 5422722 T^{6} + 41104187 T^{7} + 291555454 T^{8} + 1830808995 T^{9} + 10796917527 T^{10} + 56755078845 T^{11} + 280184791294 T^{12} + 1224534834917 T^{13} + 5007997644162 T^{14} + 17674578548813 T^{15} + 57799564728806 T^{16} + 152722520930161 T^{17} + 366743146099630 T^{18} + 581671687534762 T^{19} + 819628286980801 T^{20} \))(\( 1 - 35 T + 740 T^{2} - 11594 T^{3} + 147509 T^{4} - 1594455 T^{5} + 15077700 T^{6} - 127032607 T^{7} + 965714594 T^{8} - 6680895592 T^{9} + 42287192376 T^{10} - 245648352538 T^{11} + 1310902963656 T^{12} - 6420340663912 T^{13} + 28769603469854 T^{14} - 117317280249247 T^{15} + 431661750032700 T^{16} - 1415084681688855 T^{17} + 4058358194899499 T^{18} - 9888418688090954 T^{19} + 19565320398896540 T^{20} - 28686990044328035 T^{21} + 25408476896404831 T^{22} \))(\( 1 - 16 T + 397 T^{2} - 4753 T^{3} + 67843 T^{4} - 653566 T^{5} + 6860588 T^{6} - 55290793 T^{7} + 466499848 T^{8} - 3212098525 T^{9} + 22711219041 T^{10} - 134878897381 T^{11} + 815898095197 T^{12} - 4181245818811 T^{13} + 21825481498401 T^{14} - 95691627158275 T^{15} + 430822406124808 T^{16} - 1582928461706743 T^{17} + 6088797103824428 T^{18} - 17981309154069826 T^{19} + 57862686653109763 T^{20} - 125667524129669263 T^{21} + 325392429931377997 T^{22} - 406535630342477296 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 6 T + 219 T^{2} + 1177 T^{3} + 23675 T^{4} + 114348 T^{5} + 1673197 T^{6} + 7240633 T^{7} + 87128432 T^{8} + 338263472 T^{9} + 3614888285 T^{10} + 12755260394 T^{11} + 127117776313 T^{12} + 417702954404 T^{13} + 3940651065703 T^{14} + 12257805238634 T^{15} + 107691136898435 T^{16} + 312393419924912 T^{17} + 2494413036121232 T^{18} + 6426088440270073 T^{19} + 46034023392682867 T^{20} + 97526384349303468 T^{21} + 625958054653885925 T^{22} + 964702493776402777 T^{23} + 5564456440312657989 T^{24} + 4725976702731298566 T^{25} + 24417546297445042591 T^{26} \))(\( 1 + 28 T + 572 T^{2} + 8327 T^{3} + 101681 T^{4} + 1034552 T^{5} + 9267436 T^{6} + 72684144 T^{7} + 513558687 T^{8} + 3250981745 T^{9} + 18879768188 T^{10} + 100774249494 T^{11} + 515723640143 T^{12} + 2609190143976 T^{13} + 14031300428920 T^{14} + 80884894463256 T^{15} + 495610418177423 T^{16} + 3002165666675754 T^{17} + 17435862396749948 T^{18} + 93072847275848495 T^{19} + 455785225122026847 T^{20} + 1999730805860355984 T^{21} + 7904113104458071276 T^{22} + 27353163985566504392 T^{23} + 83340623848494826481 T^{24} + \)\(21\!\cdots\!37\)\( T^{25} + \)\(45\!\cdots\!92\)\( T^{26} + \)\(68\!\cdots\!48\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 + 233 T^{2} + 411 T^{3} + 27649 T^{4} + 85522 T^{5} + 2307254 T^{6} + 8925993 T^{7} + 151860395 T^{8} + 635536599 T^{9} + 8212180782 T^{10} + 34789676356 T^{11} + 373071508736 T^{12} + 1540593820289 T^{13} + 14475921162419 T^{14} + 56653078471506 T^{15} + 483416812385190 T^{16} + 1756245432616686 T^{17} + 13911360237084659 T^{18} + 45895830500229599 T^{19} + 344539372819379456 T^{20} + 995998897637053756 T^{21} + 7288340673062458542 T^{22} + 17485273201704348489 T^{23} + \)\(12\!\cdots\!95\)\( T^{24} + \)\(23\!\cdots\!03\)\( T^{25} + \)\(18\!\cdots\!54\)\( T^{26} + \)\(21\!\cdots\!82\)\( T^{27} + \)\(21\!\cdots\!89\)\( T^{28} + \)\(10\!\cdots\!01\)\( T^{29} + \)\(17\!\cdots\!93\)\( T^{30} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 24 T + 546 T^{2} - 8297 T^{3} + 116585 T^{4} - 1349216 T^{5} + 14569250 T^{6} - 139005886 T^{7} + 1250373298 T^{8} - 10270921065 T^{9} + 80220563558 T^{10} - 582685198433 T^{11} + 4050433584927 T^{12} - 26465173663698 T^{13} + 166223733105942 T^{14} - 987027398318235 T^{15} + 5646756334450186 T^{16} - 30597849347865285 T^{17} + 159741007514810262 T^{18} - 788423988615227118 T^{19} + 3740660474785367967 T^{20} - 16681782531403320383 T^{21} + 71196045449619456998 T^{22} - \)\(28\!\cdots\!15\)\( T^{23} + \)\(10\!\cdots\!18\)\( T^{24} - \)\(36\!\cdots\!06\)\( T^{25} + \)\(11\!\cdots\!50\)\( T^{26} - \)\(34\!\cdots\!96\)\( T^{27} + \)\(91\!\cdots\!85\)\( T^{28} - \)\(20\!\cdots\!27\)\( T^{29} + \)\(41\!\cdots\!66\)\( T^{30} - \)\(56\!\cdots\!24\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 28 T + 734 T^{2} - 12443 T^{3} + 195429 T^{4} - 2441390 T^{5} + 28616380 T^{6} - 286109548 T^{7} + 2720474403 T^{8} - 22805231081 T^{9} + 184428733252 T^{10} - 1340489657632 T^{11} + 9562630355712 T^{12} - 62167212657734 T^{13} + 405178142932552 T^{14} - 2433533660272167 T^{15} + 14981131940984620 T^{16} - 85549761961121342 T^{17} + 508708968702325082 T^{18} - 2807453646036113993 T^{19} + 16234616358335702678 T^{20} - 87031063027119533783 T^{21} + \)\(48\!\cdots\!02\)\( T^{22} - \)\(25\!\cdots\!22\)\( T^{23} + \)\(13\!\cdots\!20\)\( T^{24} - \)\(69\!\cdots\!17\)\( T^{25} + \)\(35\!\cdots\!12\)\( T^{26} - \)\(17\!\cdots\!74\)\( T^{27} + \)\(81\!\cdots\!92\)\( T^{28} - \)\(35\!\cdots\!72\)\( T^{29} + \)\(15\!\cdots\!52\)\( T^{30} - \)\(57\!\cdots\!11\)\( T^{31} + \)\(21\!\cdots\!83\)\( T^{32} - \)\(69\!\cdots\!68\)\( T^{33} + \)\(21\!\cdots\!80\)\( T^{34} - \)\(57\!\cdots\!90\)\( T^{35} + \)\(14\!\cdots\!49\)\( T^{36} - \)\(28\!\cdots\!73\)\( T^{37} + \)\(51\!\cdots\!94\)\( T^{38} - \)\(60\!\cdots\!88\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))
$37$ (\( 1 - 5 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 - 9 T + 90 T^{2} - 333 T^{3} + 1369 T^{4} \))(\( 1 - 10 T + 75 T^{2} - 370 T^{3} + 1369 T^{4} \))(\( 1 + 54 T^{2} + 1369 T^{4} \))(\( 1 - 4 T + 92 T^{2} - 336 T^{3} + 4905 T^{4} - 12432 T^{5} + 125948 T^{6} - 202612 T^{7} + 1874161 T^{8} \))(\( 1 - 10 T + 161 T^{2} - 1277 T^{3} + 11230 T^{4} - 67939 T^{5} + 415510 T^{6} - 1748213 T^{7} + 8155133 T^{8} - 18741610 T^{9} + 69343957 T^{10} \))(\( 1 + 24 T + 405 T^{2} + 4845 T^{3} + 49327 T^{4} + 416707 T^{5} + 3121913 T^{6} + 20087224 T^{7} + 115510781 T^{8} + 570471883 T^{9} + 2498560531 T^{10} + 9080310045 T^{11} + 28084302585 T^{12} + 61577433816 T^{13} + 94931877133 T^{14} \))(\( 1 + 25 T + 383 T^{2} + 4139 T^{3} + 35920 T^{4} + 263242 T^{5} + 1744343 T^{6} + 10831352 T^{7} + 64540691 T^{8} + 360378298 T^{9} + 1819455760 T^{10} + 7757152379 T^{11} + 26558735531 T^{12} + 64143160225 T^{13} + 94931877133 T^{14} \))(\( 1 - T + 38 T^{2} + 310 T^{3} + 3419 T^{4} - 2611 T^{5} + 200805 T^{6} + 734164 T^{7} + 4826007 T^{8} + 10544103 T^{9} + 413407761 T^{10} + 390131811 T^{11} + 6606803583 T^{12} + 37187609092 T^{13} + 376340899605 T^{14} - 181057071727 T^{15} + 8772218592371 T^{16} + 29428881911230 T^{17} + 133474219248998 T^{18} - 129961739795077 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 9 T + 272 T^{2} + 2244 T^{3} + 36506 T^{4} + 266344 T^{5} + 3108815 T^{6} + 19865478 T^{7} + 184485854 T^{8} + 1025174520 T^{9} + 7957552221 T^{10} + 37931457240 T^{11} + 252561134126 T^{12} + 1006246057134 T^{13} + 5826419829215 T^{14} + 18469346883208 T^{15} + 93664408286954 T^{16} + 213027132286452 T^{17} + 955394411466512 T^{18} + 1169655658155693 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 28 T + 617 T^{2} + 9207 T^{3} + 118856 T^{4} + 1241639 T^{5} + 11728670 T^{6} + 95688335 T^{7} + 730296367 T^{8} + 5015228404 T^{9} + 33274323831 T^{10} + 204290941550 T^{11} + 1231149981747 T^{12} + 6865847685076 T^{13} + 36991701877651 T^{14} + 179335345611935 T^{15} + 813312388147190 T^{16} + 3185705972744351 T^{17} + 11283223188519848 T^{18} + 32339398332250647 T^{19} + 80186393453562509 T^{20} + 134640362427699772 T^{21} + 177917621779460413 T^{22} \))(\( 1 + T + 144 T^{2} + 268 T^{3} + 11671 T^{4} + 16087 T^{5} + 689449 T^{6} + 258592 T^{7} + 31233836 T^{8} - 24273612 T^{9} + 1203162288 T^{10} - 2025452524 T^{11} + 44091152134 T^{12} - 74941743388 T^{13} + 1647129172272 T^{14} - 1229531268636 T^{15} + 58537237311596 T^{16} + 17931792528544 T^{17} + 1768937506958641 T^{18} + 1527169107438571 T^{19} + 40994147706711991 T^{20} + 34829746265080636 T^{21} + 692436149628170256 T^{22} + 177917621779460413 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 15 T + 404 T^{2} - 4658 T^{3} + 73032 T^{4} - 695636 T^{5} + 8157306 T^{6} - 66709445 T^{7} + 642020904 T^{8} - 4610206838 T^{9} + 38118060931 T^{10} - 243399565516 T^{11} + 1771690302159 T^{12} - 10108357803174 T^{13} + 65552541179883 T^{14} - 333214005191404 T^{15} + 1930794140337943 T^{16} - 8640269857712918 T^{17} + 44520269960077128 T^{18} - 171158184766233005 T^{19} + 774388370928283698 T^{20} - 2443407157407788756 T^{21} + 9491365780714063464 T^{22} - 22398386006722340642 T^{23} + 71878719198902006852 T^{24} - 98744280087600529215 T^{25} + \)\(24\!\cdots\!97\)\( T^{26} \))(\( 1 + 12 T + 304 T^{2} + 2885 T^{3} + 42862 T^{4} + 341274 T^{5} + 3808952 T^{6} + 26105941 T^{7} + 241811446 T^{8} + 1455530727 T^{9} + 11923120230 T^{10} + 64695546402 T^{11} + 495142685963 T^{12} + 2521698703959 T^{13} + 18795047013204 T^{14} + 93302852046483 T^{15} + 677850337083347 T^{16} + 3277023511900506 T^{17} + 22345846933377030 T^{18} + 100932260145266739 T^{19} + 620422013000677414 T^{20} + 2478285983453347153 T^{21} + 13378865640971300792 T^{22} + 44352562786825108098 T^{23} + \)\(20\!\cdots\!38\)\( T^{24} + \)\(51\!\cdots\!05\)\( T^{25} + \)\(20\!\cdots\!24\)\( T^{26} + \)\(29\!\cdots\!64\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 - 5 T + 285 T^{2} - 1339 T^{3} + 41237 T^{4} - 188625 T^{5} + 4060511 T^{6} - 18570522 T^{7} + 305421340 T^{8} - 1413924211 T^{9} + 18662771011 T^{10} - 87416923987 T^{11} + 963231740724 T^{12} - 4505250808383 T^{13} + 43078895001993 T^{14} - 196151157407296 T^{15} + 1694967246538164 T^{16} - 7257592824069952 T^{17} + 58975007257728417 T^{18} - 228204469197024099 T^{19} + 1805251362427032564 T^{20} - 6061835418026796559 T^{21} + 47883564448042329499 T^{22} - \)\(13\!\cdots\!63\)\( T^{23} + \)\(10\!\cdots\!40\)\( T^{24} - \)\(24\!\cdots\!94\)\( T^{25} + \)\(19\!\cdots\!39\)\( T^{26} - \)\(33\!\cdots\!25\)\( T^{27} + \)\(27\!\cdots\!97\)\( T^{28} - \)\(32\!\cdots\!83\)\( T^{29} + \)\(25\!\cdots\!65\)\( T^{30} - \)\(16\!\cdots\!65\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 26 T + 718 T^{2} - 12561 T^{3} + 212768 T^{4} - 2882628 T^{5} + 37271932 T^{6} - 417045923 T^{7} + 4448849589 T^{8} - 42578173809 T^{9} + 389157534608 T^{10} - 3252297755891 T^{11} + 26006216634590 T^{12} - 192148833268307 T^{13} + 1360288879833426 T^{14} - 8945905826461451 T^{15} + 56411283830063528 T^{16} - 330998515579073687 T^{17} + 1862235476491960194 T^{18} - 9732914851539554471 T^{19} + 48739836974099828990 T^{20} - \)\(22\!\cdots\!87\)\( T^{21} + \)\(99\!\cdots\!72\)\( T^{22} - \)\(40\!\cdots\!97\)\( T^{23} + \)\(15\!\cdots\!69\)\( T^{24} - \)\(54\!\cdots\!71\)\( T^{25} + \)\(17\!\cdots\!68\)\( T^{26} - \)\(51\!\cdots\!64\)\( T^{27} + \)\(14\!\cdots\!08\)\( T^{28} - \)\(30\!\cdots\!17\)\( T^{29} + \)\(64\!\cdots\!02\)\( T^{30} - \)\(86\!\cdots\!18\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 14 T + 384 T^{2} - 3803 T^{3} + 61172 T^{4} - 464658 T^{5} + 5850756 T^{6} - 36539181 T^{7} + 419482784 T^{8} - 2343294339 T^{9} + 26315153804 T^{10} - 138788107216 T^{11} + 1498002688124 T^{12} - 7419001222863 T^{13} + 75550131694104 T^{14} - 349617353886428 T^{15} + 3424235107091679 T^{16} - 15141415688005494 T^{17} + 144053314275522840 T^{18} - 614955419688354484 T^{19} + 5591421800765102880 T^{20} - 22753350528469115908 T^{21} + \)\(19\!\cdots\!60\)\( T^{22} - \)\(76\!\cdots\!82\)\( T^{23} + \)\(64\!\cdots\!19\)\( T^{24} - \)\(24\!\cdots\!96\)\( T^{25} + \)\(19\!\cdots\!36\)\( T^{26} - \)\(70\!\cdots\!79\)\( T^{27} + \)\(52\!\cdots\!04\)\( T^{28} - \)\(18\!\cdots\!32\)\( T^{29} + \)\(12\!\cdots\!96\)\( T^{30} - \)\(41\!\cdots\!07\)\( T^{31} + \)\(27\!\cdots\!04\)\( T^{32} - \)\(88\!\cdots\!57\)\( T^{33} + \)\(52\!\cdots\!84\)\( T^{34} - \)\(15\!\cdots\!94\)\( T^{35} + \)\(75\!\cdots\!52\)\( T^{36} - \)\(17\!\cdots\!51\)\( T^{37} + \)\(64\!\cdots\!36\)\( T^{38} - \)\(87\!\cdots\!22\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 11 T + 108 T^{2} + 451 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 32 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 6 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 118 T^{2} + 450 T^{3} + 5950 T^{4} + 18450 T^{5} + 198358 T^{6} + 413526 T^{7} + 2825761 T^{8} \))(\( 1 - 11 T + 184 T^{2} - 1340 T^{3} + 12920 T^{4} - 71977 T^{5} + 529720 T^{6} - 2252540 T^{7} + 12681464 T^{8} - 31083371 T^{9} + 115856201 T^{10} \))(\( 1 + 9 T + 100 T^{2} - 232 T^{3} - 1699 T^{4} - 37702 T^{5} + 118878 T^{6} - 5494 T^{7} + 4873998 T^{8} - 63377062 T^{9} - 117096779 T^{10} - 655576552 T^{11} + 11585620100 T^{12} + 42750938169 T^{13} + 194754273881 T^{14} \))(\( 1 - 13 T + 266 T^{2} - 2638 T^{3} + 30449 T^{4} - 241362 T^{5} + 2003812 T^{6} - 12720406 T^{7} + 82156292 T^{8} - 405729522 T^{9} + 2098575529 T^{10} - 7454357518 T^{11} + 30817749466 T^{12} - 61751355133 T^{13} + 194754273881 T^{14} \))(\( 1 + 247 T^{2} - 257 T^{3} + 27758 T^{4} - 66436 T^{5} + 1908038 T^{6} - 7623594 T^{7} + 94884916 T^{8} - 503304539 T^{9} + 4027740914 T^{10} - 20635486099 T^{11} + 159501543796 T^{12} - 525425722074 T^{13} + 5391659366918 T^{14} - 7697022569636 T^{15} + 131853393521678 T^{16} - 50051848387417 T^{17} + 1972276531592887 T^{18} + 13422659310152401 T^{20} \))(\( 1 - 25 T + 495 T^{2} - 6723 T^{3} + 81455 T^{4} - 815800 T^{5} + 7630229 T^{6} - 62837308 T^{7} + 492494695 T^{8} - 3473801813 T^{9} + 23398531031 T^{10} - 142425874333 T^{11} + 827883582295 T^{12} - 4330810104668 T^{13} + 21561203529269 T^{14} - 94515488775800 T^{15} + 386919740950655 T^{16} - 1309332983301963 T^{17} + 3952537988414895 T^{18} - 8184548359849025 T^{19} + 13422659310152401 T^{20} \))(\( 1 + 10 T + 228 T^{2} + 1439 T^{3} + 21527 T^{4} + 100809 T^{5} + 1421858 T^{6} + 5953934 T^{7} + 80939232 T^{8} + 313060821 T^{9} + 3868196546 T^{10} + 13739665526 T^{11} + 158596058386 T^{12} + 526255240101 T^{13} + 5578412808672 T^{14} + 16824394493774 T^{15} + 164731066241458 T^{16} + 478853258430969 T^{17} + 4192475253836287 T^{18} + 11490307404705119 T^{19} + 74643081041823108 T^{20} + 134226593101524010 T^{21} + 550329031716248441 T^{22} \))(\( 1 + 3 T + 267 T^{2} + 1253 T^{3} + 38030 T^{4} + 203473 T^{5} + 3795696 T^{6} + 20268147 T^{7} + 284183426 T^{8} + 1439876239 T^{9} + 16521954046 T^{10} + 76833132697 T^{11} + 759993748432 T^{12} + 3150158440577 T^{13} + 27773404751326 T^{14} + 99237710268119 T^{15} + 803034442037186 T^{16} + 2348190512729547 T^{17} + 18029951667146736 T^{18} + 39627236369388713 T^{19} + 303666706463471630 T^{20} + 410209563795633133 T^{21} + 3583850035810691067 T^{22} + 1650987095148745323 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 9 T + 312 T^{2} + 2384 T^{3} + 46289 T^{4} + 307268 T^{5} + 4430238 T^{6} + 25887442 T^{7} + 312053432 T^{8} + 1627381936 T^{9} + 17524169596 T^{10} + 83059990388 T^{11} + 828356088124 T^{12} + 3638235256906 T^{13} + 33962599613084 T^{14} + 139623843842228 T^{15} + 1207783292725916 T^{16} + 4598592406853296 T^{17} + 36153325140531832 T^{18} + 122968048032841522 T^{19} + 862807784810013678 T^{20} + 2453512005301551428 T^{21} + 15154182361162060729 T^{22} + 31999619795403323984 T^{23} + \)\(17\!\cdots\!92\)\( T^{24} + \)\(20\!\cdots\!29\)\( T^{25} + \)\(92\!\cdots\!21\)\( T^{26} \))(\( 1 - 25 T + 563 T^{2} - 8607 T^{3} + 121790 T^{4} - 1433577 T^{5} + 15853304 T^{6} - 156316437 T^{7} + 1459584908 T^{8} - 12547879865 T^{9} + 102600090629 T^{10} - 785560142479 T^{11} + 5735202560101 T^{12} - 39539710215930 T^{13} + 260203302026272 T^{14} - 1621128118853130 T^{15} + 9640875503529781 T^{16} - 54141590579795159 T^{17} + 289923334695893669 T^{18} - 1453749691763292865 T^{19} + 6933180461590394828 T^{20} - 30443294183600081997 T^{21} + \)\(12\!\cdots\!84\)\( T^{22} - \)\(46\!\cdots\!97\)\( T^{23} + \)\(16\!\cdots\!90\)\( T^{24} - \)\(47\!\cdots\!87\)\( T^{25} + \)\(12\!\cdots\!03\)\( T^{26} - \)\(23\!\cdots\!25\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 + 7 T + 479 T^{2} + 3737 T^{3} + 113000 T^{4} + 927971 T^{5} + 17487630 T^{6} + 143932917 T^{7} + 1982002515 T^{8} + 15741652212 T^{9} + 173398279305 T^{10} + 1294524515988 T^{11} + 12037605284290 T^{12} + 83034933842372 T^{13} + 673331302488874 T^{14} + 4239158475190508 T^{15} + 30592154579437316 T^{16} + 173805497482810828 T^{17} + 1131869919483797194 T^{18} + 5722850675350120612 T^{19} + 34015395545740594690 T^{20} + \)\(14\!\cdots\!88\)\( T^{21} + \)\(82\!\cdots\!05\)\( T^{22} + \)\(30\!\cdots\!72\)\( T^{23} + \)\(15\!\cdots\!15\)\( T^{24} + \)\(47\!\cdots\!37\)\( T^{25} + \)\(23\!\cdots\!30\)\( T^{26} + \)\(51\!\cdots\!11\)\( T^{27} + \)\(25\!\cdots\!00\)\( T^{28} + \)\(34\!\cdots\!77\)\( T^{29} + \)\(18\!\cdots\!19\)\( T^{30} + \)\(10\!\cdots\!07\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 15 T + 427 T^{2} - 4333 T^{3} + 72902 T^{4} - 542103 T^{5} + 7245402 T^{6} - 41306237 T^{7} + 521320635 T^{8} - 2411087708 T^{9} + 31913258818 T^{10} - 127776076240 T^{11} + 1761167235846 T^{12} - 6289776758660 T^{13} + 86170188359457 T^{14} - 279550070438288 T^{15} + 3734275000083968 T^{16} - 11461552887969808 T^{17} + 144852086632247217 T^{18} - 433497703983605860 T^{19} + 4976637689531428806 T^{20} - 14803650771852764240 T^{21} + \)\(15\!\cdots\!38\)\( T^{22} - \)\(46\!\cdots\!48\)\( T^{23} + \)\(41\!\cdots\!35\)\( T^{24} - \)\(13\!\cdots\!57\)\( T^{25} + \)\(97\!\cdots\!02\)\( T^{26} - \)\(29\!\cdots\!23\)\( T^{27} + \)\(16\!\cdots\!62\)\( T^{28} - \)\(40\!\cdots\!93\)\( T^{29} + \)\(16\!\cdots\!47\)\( T^{30} - \)\(23\!\cdots\!15\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 + 7 T + 479 T^{2} + 3033 T^{3} + 111924 T^{4} + 649297 T^{5} + 17050658 T^{6} + 92016777 T^{7} + 1912340620 T^{8} + 9765477291 T^{9} + 169201987053 T^{10} + 831514315257 T^{11} + 12361443058494 T^{12} + 59254741384169 T^{13} + 770247956920639 T^{14} + 3624728678993295 T^{15} + 41904106814273651 T^{16} + 193018006334304006 T^{17} + 2022878003909591075 T^{18} + 9007468644099125876 T^{19} + 87485259650824791324 T^{20} + \)\(36\!\cdots\!16\)\( T^{21} + \)\(34\!\cdots\!75\)\( T^{22} + \)\(13\!\cdots\!26\)\( T^{23} + \)\(11\!\cdots\!11\)\( T^{24} + \)\(41\!\cdots\!95\)\( T^{25} + \)\(36\!\cdots\!99\)\( T^{26} + \)\(11\!\cdots\!89\)\( T^{27} + \)\(98\!\cdots\!74\)\( T^{28} + \)\(27\!\cdots\!77\)\( T^{29} + \)\(22\!\cdots\!53\)\( T^{30} + \)\(53\!\cdots\!31\)\( T^{31} + \)\(43\!\cdots\!20\)\( T^{32} + \)\(85\!\cdots\!17\)\( T^{33} + \)\(64\!\cdots\!38\)\( T^{34} + \)\(10\!\cdots\!97\)\( T^{35} + \)\(71\!\cdots\!84\)\( T^{36} + \)\(79\!\cdots\!73\)\( T^{37} + \)\(51\!\cdots\!59\)\( T^{38} + \)\(30\!\cdots\!27\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$43$ (\( 1 - T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 8 T + 34 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 87 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 80 T^{2} - 216 T^{3} + 3109 T^{4} - 9288 T^{5} + 147920 T^{6} + 3418801 T^{8} \))(\( 1 + 9 T + 140 T^{2} + 922 T^{3} + 10096 T^{4} + 53457 T^{5} + 434128 T^{6} + 1704778 T^{7} + 11130980 T^{8} + 30769209 T^{9} + 147008443 T^{10} \))(\( 1 + T + 186 T^{2} - 122 T^{3} + 16897 T^{4} - 23864 T^{5} + 1024474 T^{6} - 1457402 T^{7} + 44052382 T^{8} - 44124536 T^{9} + 1343429779 T^{10} - 417093722 T^{11} + 27343570398 T^{12} + 6321363049 T^{13} + 271818611107 T^{14} \))(\( 1 + 2 T + 167 T^{2} + 179 T^{3} + 12436 T^{4} + 420 T^{5} + 603809 T^{6} - 305536 T^{7} + 25963787 T^{8} + 776580 T^{9} + 988749052 T^{10} + 611965379 T^{11} + 24550409981 T^{12} + 12642726098 T^{13} + 271818611107 T^{14} \))(\( 1 + 5 T + 306 T^{2} + 1414 T^{3} + 46131 T^{4} + 193980 T^{5} + 4452501 T^{6} + 16809587 T^{7} + 302756922 T^{8} + 1008755844 T^{9} + 15108863806 T^{10} + 43376501292 T^{11} + 559797548778 T^{12} + 1336479833609 T^{13} + 15222214871301 T^{14} + 28516697773140 T^{15} + 291610798813419 T^{16} + 384351516105298 T^{17} + 3576589284945906 T^{18} + 2512963059684215 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 3 T + 247 T^{2} - 665 T^{3} + 31054 T^{4} - 74510 T^{5} + 2630158 T^{6} - 5674198 T^{7} + 165896276 T^{8} - 321130465 T^{9} + 8083839367 T^{10} - 13808609995 T^{11} + 306742214324 T^{12} - 451138460386 T^{13} + 8991986800558 T^{14} - 10953599087930 T^{15} + 196303608123646 T^{16} - 180759376386155 T^{17} + 2886985468567447 T^{18} - 1507777835810529 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 6 T + 249 T^{2} + 1421 T^{3} + 32256 T^{4} + 174058 T^{5} + 2861763 T^{6} + 14515904 T^{7} + 192474612 T^{8} + 905291064 T^{9} + 10258637493 T^{10} + 43907837686 T^{11} + 441121412199 T^{12} + 1673883177336 T^{13} + 15303078976284 T^{14} + 49626987111104 T^{15} + 420703322865009 T^{16} + 1100283809582842 T^{17} + 8767781119867392 T^{18} + 16608932594471021 T^{19} + 125145560372273907 T^{20} + 129668893879705494 T^{21} + 929293739471222707 T^{22} \))(\( 1 + 23 T + 534 T^{2} + 7164 T^{3} + 95402 T^{4} + 896932 T^{5} + 8597959 T^{6} + 60154369 T^{7} + 454291076 T^{8} + 2379928831 T^{9} + 15740252883 T^{10} + 66376399142 T^{11} + 532701233829 T^{12} + 2854185163106 T^{13} + 29103727580667 T^{14} + 189221001566317 T^{15} + 1553130784919876 T^{16} + 8843200126337467 T^{17} + 54350820319416991 T^{18} + 243802810497423724 T^{19} + 1115077682883690602 T^{20} + 3600573471915543252 T^{21} + 11540531555293788966 T^{22} + 21373756007838122261 T^{23} + 39959630797262576401 T^{24} \))(\( 1 - T + 309 T^{2} - 215 T^{3} + 44138 T^{4} - 26154 T^{5} + 3866259 T^{6} - 3087745 T^{7} + 235173405 T^{8} - 334018968 T^{9} + 11008331369 T^{10} - 26221003985 T^{11} + 457110290538 T^{12} - 1382586516876 T^{13} + 19655742493134 T^{14} - 48482636368265 T^{15} + 875239402155083 T^{16} - 1141944381817368 T^{17} + 34572476104058415 T^{18} - 19518757147734505 T^{19} + 1050921151559938713 T^{20} - 305693190060376554 T^{21} + 22183432705668376334 T^{22} - 4646468697356113535 T^{23} + \)\(28\!\cdots\!63\)\( T^{24} - 39959630797262576401 T^{25} + \)\(17\!\cdots\!43\)\( T^{26} \))(\( 1 - 5 T + 297 T^{2} - 1219 T^{3} + 46823 T^{4} - 174090 T^{5} + 5132797 T^{6} - 17834622 T^{7} + 430864094 T^{8} - 1416867538 T^{9} + 29103005409 T^{10} - 90407818422 T^{11} + 1625566361842 T^{12} - 4719120486698 T^{13} + 76160620269810 T^{14} - 202922180928014 T^{15} + 3005672203045858 T^{16} - 7188054419277954 T^{17} + 99497383995294609 T^{18} - 208291490698623334 T^{19} + 2723648362952462606 T^{20} - 4847782181658346554 T^{21} + 59993159320269579997 T^{22} - 87496347812084997870 T^{23} + \)\(10\!\cdots\!27\)\( T^{24} - \)\(11\!\cdots\!33\)\( T^{25} + \)\(11\!\cdots\!97\)\( T^{26} - \)\(85\!\cdots\!15\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 + 17 T + 513 T^{2} + 7205 T^{3} + 124688 T^{4} + 1493488 T^{5} + 19330948 T^{6} + 201987772 T^{7} + 2160610148 T^{8} + 20032919829 T^{9} + 185964243015 T^{10} + 1549827842217 T^{11} + 12822536040455 T^{12} + 96941169343511 T^{13} + 725554514257835 T^{14} + 5003884842566475 T^{15} + 34140214704561310 T^{16} + 215167048230358425 T^{17} + 1341550296862736915 T^{18} + 7707501550994529077 T^{19} + 43837699037643594455 T^{20} + \)\(22\!\cdots\!31\)\( T^{21} + \)\(11\!\cdots\!35\)\( T^{22} + \)\(54\!\cdots\!03\)\( T^{23} + \)\(25\!\cdots\!48\)\( T^{24} + \)\(10\!\cdots\!96\)\( T^{25} + \)\(41\!\cdots\!52\)\( T^{26} + \)\(13\!\cdots\!16\)\( T^{27} + \)\(49\!\cdots\!88\)\( T^{28} + \)\(12\!\cdots\!15\)\( T^{29} + \)\(37\!\cdots\!37\)\( T^{30} + \)\(54\!\cdots\!19\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 33 T + 849 T^{2} - 14973 T^{3} + 227662 T^{4} - 2816959 T^{5} + 31287178 T^{6} - 298052951 T^{7} + 2595602135 T^{8} - 19610166260 T^{9} + 135473232502 T^{10} - 785905431788 T^{11} + 4000938206578 T^{12} - 13776936930866 T^{13} + 20903687462007 T^{14} + 285879832687618 T^{15} - 2444438322463504 T^{16} + 12292832805567574 T^{17} + 38650918117250943 T^{18} - 1095362924562363062 T^{19} + 13678411541587072978 T^{20} - \)\(11\!\cdots\!84\)\( T^{21} + \)\(85\!\cdots\!98\)\( T^{22} - \)\(53\!\cdots\!20\)\( T^{23} + \)\(30\!\cdots\!35\)\( T^{24} - \)\(14\!\cdots\!93\)\( T^{25} + \)\(67\!\cdots\!22\)\( T^{26} - \)\(26\!\cdots\!13\)\( T^{27} + \)\(90\!\cdots\!62\)\( T^{28} - \)\(25\!\cdots\!39\)\( T^{29} + \)\(62\!\cdots\!01\)\( T^{30} - \)\(10\!\cdots\!31\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 3 T + 347 T^{2} - 881 T^{3} + 62672 T^{4} - 150103 T^{5} + 7836966 T^{6} - 19114103 T^{7} + 760747202 T^{8} - 1976582771 T^{9} + 61037238543 T^{10} - 171148563521 T^{11} + 4209454598974 T^{12} - 12607701901679 T^{13} + 256102399277881 T^{14} - 800311005423689 T^{15} + 13977998993261533 T^{16} - 44276426802708506 T^{17} + 691244233050498015 T^{18} - 2154155385698601420 T^{19} + 31126330649301424100 T^{20} - 92628681585039861060 T^{21} + \)\(12\!\cdots\!35\)\( T^{22} - \)\(35\!\cdots\!42\)\( T^{23} + \)\(47\!\cdots\!33\)\( T^{24} - \)\(11\!\cdots\!27\)\( T^{25} + \)\(16\!\cdots\!69\)\( T^{26} - \)\(34\!\cdots\!53\)\( T^{27} + \)\(49\!\cdots\!74\)\( T^{28} - \)\(86\!\cdots\!03\)\( T^{29} + \)\(13\!\cdots\!07\)\( T^{30} - \)\(18\!\cdots\!97\)\( T^{31} + \)\(30\!\cdots\!02\)\( T^{32} - \)\(32\!\cdots\!29\)\( T^{33} + \)\(57\!\cdots\!34\)\( T^{34} - \)\(47\!\cdots\!21\)\( T^{35} + \)\(85\!\cdots\!72\)\( T^{36} - \)\(51\!\cdots\!83\)\( T^{37} + \)\(87\!\cdots\!03\)\( T^{38} - \)\(32\!\cdots\!21\)\( T^{39} + \)\(46\!\cdots\!01\)\( T^{40} \))
$47$ (\( 1 + 6 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 86 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 20 T + 188 T^{2} - 940 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 30 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 2 T + 182 T^{2} + 274 T^{3} + 12694 T^{4} + 12878 T^{5} + 402038 T^{6} + 207646 T^{7} + 4879681 T^{8} \))(\( 1 - 13 T + 90 T^{2} - 567 T^{3} + 5553 T^{4} - 45003 T^{5} + 260991 T^{6} - 1252503 T^{7} + 9344070 T^{8} - 63435853 T^{9} + 229345007 T^{10} \))(\( 1 + 27 T + 555 T^{2} + 7940 T^{3} + 95954 T^{4} + 943823 T^{5} + 8122004 T^{6} + 59256915 T^{7} + 381734188 T^{8} + 2084905007 T^{9} + 9962232142 T^{10} + 38744667140 T^{11} + 127286478885 T^{12} + 291038813883 T^{13} + 506623120463 T^{14} \))(\( 1 - 25 T + 432 T^{2} - 4881 T^{3} + 44174 T^{4} - 308602 T^{5} + 1991113 T^{6} - 12529824 T^{7} + 93582311 T^{8} - 681701818 T^{9} + 4586277202 T^{10} - 23817722961 T^{11} + 99077043024 T^{12} - 269480383225 T^{13} + 506623120463 T^{14} \))(\( 1 + 15 T + 419 T^{2} + 4988 T^{3} + 78043 T^{4} + 768230 T^{5} + 8720656 T^{6} + 72871106 T^{7} + 661923720 T^{8} + 4756090233 T^{9} + 36267801154 T^{10} + 223536240951 T^{11} + 1462189497480 T^{12} + 7565696838238 T^{13} + 42554019390736 T^{14} + 176189714727610 T^{15} + 841242301921147 T^{16} + 2527036124869444 T^{17} + 9976929111277859 T^{18} + 16786957096541505 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 17 T + 313 T^{2} - 2557 T^{3} + 25054 T^{4} - 85032 T^{5} + 579788 T^{6} + 4662563 T^{7} - 30698536 T^{8} + 639621255 T^{9} - 3017746273 T^{10} + 30062198985 T^{11} - 67813066024 T^{12} + 484081278349 T^{13} + 2829180487628 T^{14} - 19501664635224 T^{15} + 270062460852766 T^{16} - 1295435319023891 T^{17} + 7452932725131193 T^{18} - 19025218042747039 T^{19} + 52599132235830049 T^{20} \))(\( 1 + 15 T + 243 T^{2} + 2292 T^{3} + 28624 T^{4} + 260365 T^{5} + 2746148 T^{6} + 21501459 T^{7} + 190723757 T^{8} + 1362389332 T^{9} + 11104441367 T^{10} + 72604894898 T^{11} + 521908744249 T^{12} + 3009518034388 T^{13} + 19801512623011 T^{14} + 104920260954579 T^{15} + 629815332283036 T^{16} + 2806530399135085 T^{17} + 14501580200132912 T^{18} + 54575469028756212 T^{19} + 271948704963972381 T^{20} + 788986983537450735 T^{21} + 2472159215084012303 T^{22} \))(\( 1 - 35 T + 786 T^{2} - 13088 T^{3} + 181182 T^{4} - 2157152 T^{5} + 23003847 T^{6} - 223443780 T^{7} + 2017433324 T^{8} - 17029593972 T^{9} + 135477644983 T^{10} - 1014476657609 T^{11} + 7169245407477 T^{12} - 47680402907623 T^{13} + 299270117767447 T^{14} - 1768063534954956 T^{15} + 9844431059889644 T^{16} - 51245715288206460 T^{17} + 247963420208370663 T^{18} - 1092863077553001376 T^{19} + 4314176539951181502 T^{20} - 14647179631969014496 T^{21} + 41342917937362418514 T^{22} - 86525572527940430605 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 15 T + 538 T^{2} + 6818 T^{3} + 134254 T^{4} + 1473084 T^{5} + 20819660 T^{6} + 200522045 T^{7} + 2252696337 T^{8} + 19173221203 T^{9} + 180161912833 T^{10} + 1357141814693 T^{11} + 10973804183039 T^{12} + 72929252644700 T^{13} + 515768796602833 T^{14} + 2997926268656837 T^{15} + 18704950276060559 T^{16} + 93559203213076243 T^{17} + 516644657178139359 T^{18} + 2161470301266427805 T^{19} + 10547721116178702580 T^{20} + 35076025400853540924 T^{21} + \)\(15\!\cdots\!18\)\( T^{22} + \)\(35\!\cdots\!82\)\( T^{23} + \)\(13\!\cdots\!14\)\( T^{24} + \)\(17\!\cdots\!15\)\( T^{25} + \)\(54\!\cdots\!27\)\( T^{26} \))(\( 1 - 17 T + 476 T^{2} - 5509 T^{3} + 90642 T^{4} - 798086 T^{5} + 10209828 T^{6} - 74193631 T^{7} + 843621786 T^{8} - 5421861566 T^{9} + 57988161744 T^{10} - 341708483626 T^{11} + 3434636562755 T^{12} - 18683810508297 T^{13} + 174525409046848 T^{14} - 878139093889959 T^{15} + 7587112167125795 T^{16} - 35477199895502198 T^{17} + 282963731087123664 T^{18} - 1243476878807300962 T^{19} + 9093580887529557594 T^{20} - 37588208855700371153 T^{21} + \)\(24\!\cdots\!08\)\( T^{22} - \)\(89\!\cdots\!62\)\( T^{23} + \)\(47\!\cdots\!58\)\( T^{24} - \)\(13\!\cdots\!27\)\( T^{25} + \)\(55\!\cdots\!16\)\( T^{26} - \)\(92\!\cdots\!59\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 + 29 T + 866 T^{2} + 16104 T^{3} + 288964 T^{4} + 4059574 T^{5} + 54737743 T^{6} + 625314880 T^{7} + 6889440501 T^{8} + 66797235645 T^{9} + 629927859687 T^{10} + 5348449236143 T^{11} + 44672448605843 T^{12} + 341591995236157 T^{13} + 2602589459913176 T^{14} + 18379631794667350 T^{15} + 130553878485010118 T^{16} + 863842694349365450 T^{17} + 5749120116948205784 T^{18} + 35465105721403528211 T^{19} + \)\(21\!\cdots\!83\)\( T^{20} + \)\(12\!\cdots\!01\)\( T^{21} + \)\(67\!\cdots\!23\)\( T^{22} + \)\(33\!\cdots\!35\)\( T^{23} + \)\(16\!\cdots\!61\)\( T^{24} + \)\(69\!\cdots\!60\)\( T^{25} + \)\(28\!\cdots\!07\)\( T^{26} + \)\(10\!\cdots\!22\)\( T^{27} + \)\(33\!\cdots\!24\)\( T^{28} + \)\(87\!\cdots\!08\)\( T^{29} + \)\(22\!\cdots\!54\)\( T^{30} + \)\(34\!\cdots\!47\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 13 T + 577 T^{2} + 6704 T^{3} + 159740 T^{4} + 1669359 T^{5} + 28317255 T^{6} + 267574444 T^{7} + 3613396300 T^{8} + 31002497946 T^{9} + 353131896133 T^{10} + 2759377979105 T^{11} + 27412240369956 T^{12} + 195352502747250 T^{13} + 1727408754101875 T^{14} + 11218490075789707 T^{15} + 89413246954024486 T^{16} + 527269033562116229 T^{17} + 3815845937811041875 T^{18} + 20282082892727736750 T^{19} + \)\(13\!\cdots\!36\)\( T^{20} + \)\(63\!\cdots\!35\)\( T^{21} + \)\(38\!\cdots\!57\)\( T^{22} + \)\(15\!\cdots\!98\)\( T^{23} + \)\(86\!\cdots\!00\)\( T^{24} + \)\(29\!\cdots\!48\)\( T^{25} + \)\(14\!\cdots\!95\)\( T^{26} + \)\(41\!\cdots\!77\)\( T^{27} + \)\(18\!\cdots\!40\)\( T^{28} + \)\(36\!\cdots\!08\)\( T^{29} + \)\(14\!\cdots\!13\)\( T^{30} + \)\(15\!\cdots\!59\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 3 T + 220 T^{2} + 455 T^{3} + 29369 T^{4} + 32791 T^{5} + 3053842 T^{6} + 1350802 T^{7} + 263467845 T^{8} - 35923295 T^{9} + 19795789858 T^{10} - 11956563230 T^{11} + 1339059446476 T^{12} - 1185220997750 T^{13} + 82693897224342 T^{14} - 86528288754835 T^{15} + 4705956226316154 T^{16} - 5264505627410837 T^{17} + 247969141553411418 T^{18} - 275049900373265592 T^{19} + 12108087115108416246 T^{20} - 12927345317543482824 T^{21} + \)\(54\!\cdots\!62\)\( T^{22} - \)\(54\!\cdots\!51\)\( T^{23} + \)\(22\!\cdots\!74\)\( T^{24} - \)\(19\!\cdots\!45\)\( T^{25} + \)\(89\!\cdots\!18\)\( T^{26} - \)\(60\!\cdots\!50\)\( T^{27} + \)\(31\!\cdots\!36\)\( T^{28} - \)\(13\!\cdots\!10\)\( T^{29} + \)\(10\!\cdots\!42\)\( T^{30} - \)\(88\!\cdots\!85\)\( T^{31} + \)\(30\!\cdots\!45\)\( T^{32} + \)\(73\!\cdots\!54\)\( T^{33} + \)\(78\!\cdots\!98\)\( T^{34} + \)\(39\!\cdots\!13\)\( T^{35} + \)\(16\!\cdots\!49\)\( T^{36} + \)\(12\!\cdots\!85\)\( T^{37} + \)\(27\!\cdots\!80\)\( T^{38} + \)\(17\!\cdots\!49\)\( T^{39} + \)\(27\!\cdots\!01\)\( T^{40} \))
$53$ (\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 8 T + 54 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( 1 - 8 T + 156 T^{2} - 856 T^{3} + 10614 T^{4} - 45368 T^{5} + 438204 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + T + 216 T^{2} + 192 T^{3} + 20850 T^{4} + 14373 T^{5} + 1105050 T^{6} + 539328 T^{7} + 32157432 T^{8} + 7890481 T^{9} + 418195493 T^{10} \))(\( 1 - T + 266 T^{2} - 824 T^{3} + 30639 T^{4} - 148452 T^{5} + 2179032 T^{6} - 11405030 T^{7} + 115488696 T^{8} - 417001668 T^{9} + 4561442403 T^{10} - 6501756344 T^{11} + 111240001138 T^{12} - 22164361129 T^{13} + 1174711139837 T^{14} \))(\( 1 - 5 T + 162 T^{2} - 932 T^{3} + 12979 T^{4} - 102946 T^{5} + 809118 T^{6} - 7139802 T^{7} + 42883254 T^{8} - 289175314 T^{9} + 1932274583 T^{10} - 7353928292 T^{11} + 67747669866 T^{12} - 110821805645 T^{13} + 1174711139837 T^{14} \))(\( 1 + 35 T + 829 T^{2} + 13989 T^{3} + 195802 T^{4} + 2299297 T^{5} + 24060150 T^{6} + 225074557 T^{7} + 1950241193 T^{8} + 15591379682 T^{9} + 117587685970 T^{10} + 826343123146 T^{11} + 5478227511137 T^{12} + 33508424822489 T^{13} + 189846156432150 T^{14} + 961555642468421 T^{15} + 4339826237780458 T^{16} + 16433034135179793 T^{17} + 51613283351018269 T^{18} + 115491725713074655 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 43 T + 1108 T^{2} - 20557 T^{3} + 306875 T^{4} - 3849325 T^{5} + 42092239 T^{6} - 409427041 T^{7} + 3616962404 T^{8} - 29372469128 T^{9} + 221665477065 T^{10} - 1556740863784 T^{11} + 10160047392836 T^{12} - 60954269582957 T^{13} + 332128012076959 T^{14} - 1609770366092225 T^{15} + 6801688321461875 T^{16} - 24148536901629209 T^{17} + 68983736975787988 T^{18} - 141889834447491719 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 7 T + 252 T^{2} - 1046 T^{3} + 30049 T^{4} - 56128 T^{5} + 2444244 T^{6} - 432858 T^{7} + 168007971 T^{8} + 112638471 T^{9} + 10281805295 T^{10} + 8391601472 T^{11} + 544935680635 T^{12} + 316401465039 T^{13} + 25012522698567 T^{14} - 3415457824698 T^{15} + 1022171824592292 T^{16} - 1244041261448512 T^{17} + 35298895040962013 T^{18} - 65123636170283606 T^{19} + 831540425134137516 T^{20} - 1224212292558591343 T^{21} + 9269035929372191597 T^{22} \))(\( 1 - 45 T + 1319 T^{2} - 27726 T^{3} + 472754 T^{4} - 6715967 T^{5} + 82858250 T^{6} - 900211755 T^{7} + 8822903856 T^{8} - 78903314982 T^{9} + 656800907646 T^{10} - 5138994786863 T^{11} + 38323412840667 T^{12} - 272366723703739 T^{13} + 1844953749577614 T^{14} - 11746888824575214 T^{15} + 69616955240594736 T^{16} - 376464498686620215 T^{17} + 1836500175516964250 T^{18} - 7889321249677677379 T^{19} + 29433517680732558194 T^{20} - 91489245346305939558 T^{21} + \)\(23\!\cdots\!31\)\( T^{22} - \)\(41\!\cdots\!65\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 43 T + 1315 T^{2} + 28796 T^{3} + 527234 T^{4} + 8099301 T^{5} + 110085139 T^{6} + 1326292478 T^{7} + 14556860056 T^{8} + 145603343341 T^{9} + 1350391398871 T^{10} + 11596807768092 T^{11} + 93303826685684 T^{12} + 700534218536522 T^{13} + 4945102814341252 T^{14} + 32575433020570428 T^{15} + 201042220289717867 T^{16} + 1148880414168637021 T^{17} + 6087613267650927608 T^{18} + 29396425445068287662 T^{19} + \)\(12\!\cdots\!43\)\( T^{20} + \)\(50\!\cdots\!61\)\( T^{21} + \)\(17\!\cdots\!22\)\( T^{22} + \)\(50\!\cdots\!04\)\( T^{23} + \)\(12\!\cdots\!55\)\( T^{24} + \)\(21\!\cdots\!63\)\( T^{25} + \)\(26\!\cdots\!73\)\( T^{26} \))(\( 1 - 17 T + 451 T^{2} - 6199 T^{3} + 103714 T^{4} - 1212805 T^{5} + 15785236 T^{6} - 162135273 T^{7} + 1781542164 T^{8} - 16346188245 T^{9} + 157363232837 T^{10} - 1303467112035 T^{11} + 11220283418081 T^{12} - 84285002735454 T^{13} + 655369971693480 T^{14} - 4467105144979062 T^{15} + 31517776121389529 T^{16} - 194056273238434695 T^{17} + 1241671598798924597 T^{18} - 6835902251788579785 T^{19} + 39486743889436143156 T^{20} - \)\(19\!\cdots\!01\)\( T^{21} + \)\(98\!\cdots\!96\)\( T^{22} - \)\(40\!\cdots\!65\)\( T^{23} + \)\(18\!\cdots\!86\)\( T^{24} - \)\(57\!\cdots\!03\)\( T^{25} + \)\(22\!\cdots\!91\)\( T^{26} - \)\(44\!\cdots\!41\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( 1 + 63 T + 2345 T^{2} + 63312 T^{3} + 1370906 T^{4} + 25004561 T^{5} + 397150870 T^{6} + 5614072755 T^{7} + 71799158661 T^{8} + 840804285427 T^{9} + 9101064515451 T^{10} + 91708149305311 T^{11} + 865122714883027 T^{12} + 7672397016244700 T^{13} + 64172863595393290 T^{14} + 507317180372376107 T^{15} + 3795670584889688578 T^{16} + 26887810559735933671 T^{17} + \)\(18\!\cdots\!10\)\( T^{18} + \)\(11\!\cdots\!00\)\( T^{19} + \)\(68\!\cdots\!87\)\( T^{20} + \)\(38\!\cdots\!23\)\( T^{21} + \)\(20\!\cdots\!79\)\( T^{22} + \)\(98\!\cdots\!99\)\( T^{23} + \)\(44\!\cdots\!21\)\( T^{24} + \)\(18\!\cdots\!15\)\( T^{25} + \)\(69\!\cdots\!30\)\( T^{26} + \)\(23\!\cdots\!17\)\( T^{27} + \)\(67\!\cdots\!46\)\( T^{28} + \)\(16\!\cdots\!76\)\( T^{29} + \)\(32\!\cdots\!05\)\( T^{30} + \)\(46\!\cdots\!91\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 + 5 T + 459 T^{2} + 1939 T^{3} + 104759 T^{4} + 409362 T^{5} + 15995137 T^{6} + 62125282 T^{7} + 1837174966 T^{8} + 7385859436 T^{9} + 168847447731 T^{10} + 708468232808 T^{11} + 12909505399193 T^{12} + 55503752465943 T^{13} + 843207959471281 T^{14} + 3572246791815617 T^{15} + 47824741115119442 T^{16} + 189329079966227701 T^{17} + 2368571158154828329 T^{18} + 8263232155872196011 T^{19} + \)\(10\!\cdots\!33\)\( T^{20} + \)\(29\!\cdots\!44\)\( T^{21} + \)\(37\!\cdots\!99\)\( T^{22} + \)\(86\!\cdots\!32\)\( T^{23} + \)\(11\!\cdots\!26\)\( T^{24} + \)\(20\!\cdots\!06\)\( T^{25} + \)\(27\!\cdots\!13\)\( T^{26} + \)\(37\!\cdots\!14\)\( T^{27} + \)\(51\!\cdots\!19\)\( T^{28} + \)\(50\!\cdots\!47\)\( T^{29} + \)\(63\!\cdots\!71\)\( T^{30} + \)\(36\!\cdots\!85\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 19 T + 771 T^{2} - 13045 T^{3} + 297433 T^{4} - 4446370 T^{5} + 75343953 T^{6} - 1000209050 T^{7} + 13969343581 T^{8} - 166226634293 T^{9} + 2010454187510 T^{10} - 21643768295159 T^{11} + 232886942885068 T^{12} - 2285759140151649 T^{13} + 22232806260698970 T^{14} - 200086387459444507 T^{15} + 1776686645323641746 T^{16} - 14718052278784708623 T^{17} + \)\(12\!\cdots\!64\)\( T^{18} - \)\(91\!\cdots\!37\)\( T^{19} + \)\(68\!\cdots\!62\)\( T^{20} - \)\(48\!\cdots\!61\)\( T^{21} + \)\(33\!\cdots\!76\)\( T^{22} - \)\(21\!\cdots\!71\)\( T^{23} + \)\(14\!\cdots\!26\)\( T^{24} - \)\(83\!\cdots\!51\)\( T^{25} + \)\(49\!\cdots\!30\)\( T^{26} - \)\(26\!\cdots\!13\)\( T^{27} + \)\(14\!\cdots\!48\)\( T^{28} - \)\(71\!\cdots\!47\)\( T^{29} + \)\(35\!\cdots\!90\)\( T^{30} - \)\(15\!\cdots\!21\)\( T^{31} + \)\(68\!\cdots\!21\)\( T^{32} - \)\(26\!\cdots\!50\)\( T^{33} + \)\(10\!\cdots\!57\)\( T^{34} - \)\(32\!\cdots\!90\)\( T^{35} + \)\(11\!\cdots\!93\)\( T^{36} - \)\(26\!\cdots\!85\)\( T^{37} + \)\(83\!\cdots\!19\)\( T^{38} - \)\(10\!\cdots\!23\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 + 9 T + 59 T^{2} \))(\( 1 - 11 T + 59 T^{2} \))(\( 1 + T + 59 T^{2} \))(\( 1 + 15 T + 170 T^{2} + 885 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 121 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( 1 - 22 T + 366 T^{2} - 4156 T^{3} + 36359 T^{4} - 245204 T^{5} + 1274046 T^{6} - 4518338 T^{7} + 12117361 T^{8} \))(\( 1 + 6 T + 91 T^{2} + 8 T^{3} - 4194 T^{4} - 42652 T^{5} - 247446 T^{6} + 27848 T^{7} + 18689489 T^{8} + 72704166 T^{9} + 714924299 T^{10} \))(\( 1 + 8 T + 377 T^{2} + 2640 T^{3} + 62673 T^{4} + 373048 T^{5} + 5969217 T^{6} + 28925920 T^{7} + 352183803 T^{8} + 1298580088 T^{9} + 12871718067 T^{10} + 31989833040 T^{11} + 269526460723 T^{12} + 337444269128 T^{13} + 2488651484819 T^{14} \))(\( 1 + 11 T + 203 T^{2} + 1834 T^{3} + 22191 T^{4} + 181693 T^{5} + 1772309 T^{6} + 13197356 T^{7} + 104566231 T^{8} + 632473333 T^{9} + 4557565389 T^{10} + 22223240074 T^{11} + 145129632697 T^{12} + 463985870051 T^{13} + 2488651484819 T^{14} \))(\( 1 + 49 T + 1468 T^{2} + 31983 T^{3} + 560352 T^{4} + 8241655 T^{5} + 104905012 T^{6} + 1175707141 T^{7} + 11745929719 T^{8} + 105340650908 T^{9} + 851722841840 T^{10} + 6215098403572 T^{11} + 40887581351839 T^{12} + 241465556911439 T^{13} + 1271171901113332 T^{14} + 5892159423474845 T^{15} + 23635946386801632 T^{16} + 79594540438966077 T^{17} + 215547082403143228 T^{18} + 424486795114092011 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 7 T + 368 T^{2} - 2593 T^{3} + 66263 T^{4} - 460573 T^{5} + 7816897 T^{6} - 52222655 T^{7} + 676063465 T^{8} - 4192119863 T^{9} + 45083176781 T^{10} - 247335071917 T^{11} + 2353376921665 T^{12} - 10725436661245 T^{13} + 94720162848817 T^{14} - 329274829163327 T^{15} + 2795008700653583 T^{16} - 6453073300135667 T^{17} + 54033601038390128 T^{18} - 60640970730584573 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 20 T + 459 T^{2} - 6128 T^{3} + 81930 T^{4} - 851924 T^{5} + 8552108 T^{6} - 76180464 T^{7} + 645277215 T^{8} - 5291221496 T^{9} + 40997839179 T^{10} - 324105866432 T^{11} + 2418872511561 T^{12} - 18418742027576 T^{13} + 132526389139485 T^{14} - 923106183435504 T^{15} + 6114109816872292 T^{16} - 35934608941575284 T^{17} + 203895216151220670 T^{18} - 899776921639279088 T^{19} + 3976315080762617001 T^{20} - 10222335066012828020 T^{21} + 30155888444737842659 T^{22} \))(\( 1 - 11 T + 322 T^{2} - 3387 T^{3} + 58100 T^{4} - 586022 T^{5} + 7471787 T^{6} - 70370122 T^{7} + 744998638 T^{8} - 6427574750 T^{9} + 59555314996 T^{10} - 467466370186 T^{11} + 3886847698992 T^{12} - 27580515840974 T^{13} + 207312051501076 T^{14} - 1320088874580250 T^{15} + 9027417441154318 T^{16} - 50309310141394478 T^{17} + 315163962911886467 T^{18} - 1458404520436600018 T^{19} + 8530848424811050100 T^{20} - 29341566837784278393 T^{21} + \)\(16\!\cdots\!22\)\( T^{22} - \)\(33\!\cdots\!49\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 - 9 T + 248 T^{2} - 3047 T^{3} + 48131 T^{4} - 494885 T^{5} + 6608818 T^{6} - 62816390 T^{7} + 687722697 T^{8} - 6044502246 T^{9} + 59622236678 T^{10} - 470861754348 T^{11} + 4184281778788 T^{12} - 30794504149682 T^{13} + 246872624948492 T^{14} - 1639069766885388 T^{15} + 12245155346690962 T^{16} - 73243415780092806 T^{17} + 491669667059114403 T^{18} - 2649628851601175990 T^{19} + 16447044728598533942 T^{20} - 72664181113814398085 T^{21} + \)\(41\!\cdots\!09\)\( T^{22} - \)\(15\!\cdots\!47\)\( T^{23} + \)\(74\!\cdots\!32\)\( T^{24} - \)\(16\!\cdots\!29\)\( T^{25} + \)\(10\!\cdots\!79\)\( T^{26} \))(\( 1 - 18 T + 638 T^{2} - 9332 T^{3} + 189406 T^{4} - 2362986 T^{5} + 35603330 T^{6} - 389556630 T^{7} + 4800237280 T^{8} - 46805333984 T^{9} + 494611111946 T^{10} - 4334161949190 T^{11} + 40310964925849 T^{12} - 318364997149716 T^{13} + 2644086692075628 T^{14} - 18783534831833244 T^{15} + 140322468906880369 T^{16} - 890145846962693010 T^{17} + 5993381398061094506 T^{18} - 33462270587972077216 T^{19} + \)\(20\!\cdots\!80\)\( T^{20} - \)\(96\!\cdots\!70\)\( T^{21} + \)\(52\!\cdots\!30\)\( T^{22} - \)\(20\!\cdots\!54\)\( T^{23} + \)\(96\!\cdots\!06\)\( T^{24} - \)\(28\!\cdots\!88\)\( T^{25} + \)\(11\!\cdots\!78\)\( T^{26} - \)\(18\!\cdots\!22\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 + 11 T + 581 T^{2} + 5608 T^{3} + 170450 T^{4} + 1484025 T^{5} + 33371964 T^{6} + 265309873 T^{7} + 4861313076 T^{8} + 35523364556 T^{9} + 557181999478 T^{10} + 3753509547737 T^{11} + 51882494368759 T^{12} + 322292125090558 T^{13} + 3998789482813805 T^{14} + 22855714893812772 T^{15} + 257642804366027452 T^{16} + 1348487178734953548 T^{17} + 13919786189674855205 T^{18} + 66192034358973711482 T^{19} + \)\(62\!\cdots\!99\)\( T^{20} + \)\(26\!\cdots\!63\)\( T^{21} + \)\(23\!\cdots\!98\)\( T^{22} + \)\(88\!\cdots\!64\)\( T^{23} + \)\(71\!\cdots\!96\)\( T^{24} + \)\(22\!\cdots\!47\)\( T^{25} + \)\(17\!\cdots\!64\)\( T^{26} + \)\(44\!\cdots\!75\)\( T^{27} + \)\(30\!\cdots\!50\)\( T^{28} + \)\(58\!\cdots\!32\)\( T^{29} + \)\(35\!\cdots\!41\)\( T^{30} + \)\(40\!\cdots\!89\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 2 T + 456 T^{2} + 410 T^{3} + 105694 T^{4} + 1578 T^{5} + 16738484 T^{6} - 11214982 T^{7} + 2043859457 T^{8} - 2364599752 T^{9} + 204440098008 T^{10} - 298947595392 T^{11} + 17293348708774 T^{12} - 27860047508768 T^{13} + 1258623500826412 T^{14} - 2043515480003328 T^{15} + 79558310545440212 T^{16} - 120567413320196352 T^{17} + 4381268406376740172 T^{18} - 5721868697303263072 T^{19} + \)\(20\!\cdots\!14\)\( T^{20} - \)\(21\!\cdots\!08\)\( T^{21} + \)\(86\!\cdots\!28\)\( T^{22} - \)\(58\!\cdots\!88\)\( T^{23} + \)\(30\!\cdots\!97\)\( T^{24} - \)\(97\!\cdots\!98\)\( T^{25} + \)\(85\!\cdots\!84\)\( T^{26} + \)\(47\!\cdots\!02\)\( T^{27} + \)\(18\!\cdots\!14\)\( T^{28} + \)\(43\!\cdots\!90\)\( T^{29} + \)\(28\!\cdots\!16\)\( T^{30} + \)\(73\!\cdots\!98\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 20 T + 850 T^{2} + 14944 T^{3} + 359194 T^{4} + 5554132 T^{5} + 99417320 T^{6} + 1364452652 T^{7} + 20136013888 T^{8} + 248042865464 T^{9} + 3169580665114 T^{10} + 35396074222236 T^{11} + 402433552754022 T^{12} + 4106531088799116 T^{13} + 42228011673478494 T^{14} + 396014313052177864 T^{15} + 3721339647187461071 T^{16} + 32195426419238706616 T^{17} + \)\(27\!\cdots\!14\)\( T^{18} + \)\(22\!\cdots\!08\)\( T^{19} + \)\(17\!\cdots\!32\)\( T^{20} + \)\(13\!\cdots\!72\)\( T^{21} + \)\(96\!\cdots\!34\)\( T^{22} + \)\(66\!\cdots\!64\)\( T^{23} + \)\(45\!\cdots\!31\)\( T^{24} + \)\(28\!\cdots\!36\)\( T^{25} + \)\(17\!\cdots\!54\)\( T^{26} + \)\(10\!\cdots\!04\)\( T^{27} + \)\(59\!\cdots\!62\)\( T^{28} + \)\(30\!\cdots\!04\)\( T^{29} + \)\(16\!\cdots\!14\)\( T^{30} + \)\(74\!\cdots\!76\)\( T^{31} + \)\(35\!\cdots\!28\)\( T^{32} + \)\(14\!\cdots\!08\)\( T^{33} + \)\(61\!\cdots\!20\)\( T^{34} + \)\(20\!\cdots\!68\)\( T^{35} + \)\(77\!\cdots\!54\)\( T^{36} + \)\(19\!\cdots\!36\)\( T^{37} + \)\(63\!\cdots\!50\)\( T^{38} + \)\(88\!\cdots\!80\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + 3 T + 18 T^{2} + 183 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 162 T^{2} + 976 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 166 T^{2} + 976 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 252 T^{2} + 2192 T^{3} + 21062 T^{4} + 133712 T^{5} + 937692 T^{6} + 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 23 T + 389 T^{2} - 4749 T^{3} + 48365 T^{4} - 408493 T^{5} + 2950265 T^{6} - 17671029 T^{7} + 88295609 T^{8} - 318454343 T^{9} + 844596301 T^{10} \))(\( 1 - T + 293 T^{2} - 629 T^{3} + 40490 T^{4} - 112038 T^{5} + 3530870 T^{6} - 9478320 T^{7} + 215383070 T^{8} - 416893398 T^{9} + 9190460690 T^{10} - 8709033989 T^{11} + 247466716193 T^{12} - 51520374361 T^{13} + 3142742836021 T^{14} \))(\( 1 + 33 T + 797 T^{2} + 13241 T^{3} + 183526 T^{4} + 2058638 T^{5} + 20168438 T^{6} + 167441348 T^{7} + 1230274718 T^{8} + 7660191998 T^{9} + 41656915006 T^{10} + 183332780681 T^{11} + 673143251897 T^{12} + 1700172353913 T^{13} + 3142742836021 T^{14} \))(\( 1 - 8 T + 210 T^{2} - 1139 T^{3} + 23892 T^{4} - 120640 T^{5} + 2053215 T^{6} - 10056420 T^{7} + 145717704 T^{8} - 700052357 T^{9} + 9112309312 T^{10} - 42703193777 T^{11} + 542215576584 T^{12} - 2282616268020 T^{13} + 28428488428815 T^{14} - 101892097752640 T^{15} + 1230924784233012 T^{16} - 3579584090227919 T^{17} + 40258535729429010 T^{18} - 93553168742673128 T^{19} + 713342911662882601 T^{20} \))(\( 1 + 6 T + 442 T^{2} + 2408 T^{3} + 93753 T^{4} + 455424 T^{5} + 12598899 T^{6} + 54110890 T^{7} + 1194644788 T^{8} + 4506335398 T^{9} + 83995741755 T^{10} + 274886459278 T^{11} + 4445273256148 T^{12} + 12282143923090 T^{13} + 174442352329059 T^{14} + 384649425786624 T^{15} + 4830189657466833 T^{16} + 7567724749138568 T^{17} + 84734632344798202 T^{18} + 70164876557004846 T^{19} + 713342911662882601 T^{20} \))(\( 1 + 20 T + 539 T^{2} + 8475 T^{3} + 137126 T^{4} + 1767407 T^{5} + 21877875 T^{6} + 237530632 T^{7} + 2435554719 T^{8} + 22657355053 T^{9} + 198679093064 T^{10} + 1597886764642 T^{11} + 12119424676904 T^{12} + 84308018152213 T^{13} + 552824645673339 T^{14} + 3288811363301512 T^{15} + 18477972298740375 T^{16} + 91057470288251927 T^{17} + 430951754132215646 T^{18} + 1624719477651956475 T^{19} + 6303144744037601999 T^{20} + 14266858233257652020 T^{21} + 43513917611435838661 T^{22} \))(\( 1 - 4 T + 444 T^{2} - 1466 T^{3} + 93276 T^{4} - 240684 T^{5} + 12441225 T^{6} - 22951404 T^{7} + 1203204535 T^{8} - 1421375134 T^{9} + 92409857416 T^{10} - 69967907024 T^{11} + 6031571155150 T^{12} - 4268042328464 T^{13} + 343857079444936 T^{14} - 322625149290454 T^{15} + 16659378682088935 T^{16} - 19384670921156604 T^{17} + 640976569509432225 T^{18} - 756407916744878364 T^{19} + 17881691327134382556 T^{20} - 17143618172094850706 T^{21} + \)\(31\!\cdots\!44\)\( T^{22} - \)\(17\!\cdots\!44\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 20 T + 491 T^{2} - 6662 T^{3} + 102320 T^{4} - 1158288 T^{5} + 14386931 T^{6} - 146172204 T^{7} + 1564997432 T^{8} - 14416278202 T^{9} + 136902142177 T^{10} - 1156374492284 T^{11} + 9961381576960 T^{12} - 77273889474880 T^{13} + 607644276194560 T^{14} - 4302869485788764 T^{15} + 31074185133477637 T^{16} - 199605495796657882 T^{17} + 1321791042141699032 T^{18} - 7530846671252461644 T^{19} + 45214424332578441551 T^{20} - \)\(22\!\cdots\!28\)\( T^{21} + \)\(11\!\cdots\!20\)\( T^{22} - \)\(47\!\cdots\!62\)\( T^{23} + \)\(21\!\cdots\!51\)\( T^{24} - \)\(53\!\cdots\!20\)\( T^{25} + \)\(16\!\cdots\!81\)\( T^{26} \))(\( 1 + 13 T + 596 T^{2} + 6434 T^{3} + 165632 T^{4} + 1535224 T^{5} + 29236284 T^{6} + 238761328 T^{7} + 3747057210 T^{8} + 27488969596 T^{9} + 374836174492 T^{10} + 2499571361745 T^{11} + 30415369892253 T^{12} + 185108931897456 T^{13} + 2037221839194280 T^{14} + 11291644845744816 T^{15} + 113175591369073413 T^{16} + 567355207260241845 T^{17} + 5189922073064487772 T^{18} + 23217082039083064396 T^{19} + \)\(19\!\cdots\!10\)\( T^{20} + \)\(75\!\cdots\!88\)\( T^{21} + \)\(56\!\cdots\!04\)\( T^{22} + \)\(17\!\cdots\!84\)\( T^{23} + \)\(11\!\cdots\!32\)\( T^{24} + \)\(27\!\cdots\!74\)\( T^{25} + \)\(15\!\cdots\!16\)\( T^{26} + \)\(21\!\cdots\!53\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( 1 + 430 T^{2} - 442 T^{3} + 96022 T^{4} - 176950 T^{5} + 14719103 T^{6} - 37933840 T^{7} + 1731467400 T^{8} - 5670296486 T^{9} + 166556630888 T^{10} - 649179906236 T^{11} + 13666457049488 T^{12} - 59356051906612 T^{13} + 984542318044971 T^{14} - 4416129220363530 T^{15} + 63361352311918146 T^{16} - 269383882442175330 T^{17} + 3663481965445337091 T^{18} - 13472696017814698372 T^{19} + \)\(18\!\cdots\!08\)\( T^{20} - \)\(54\!\cdots\!36\)\( T^{21} + \)\(85\!\cdots\!68\)\( T^{22} - \)\(17\!\cdots\!06\)\( T^{23} + \)\(33\!\cdots\!00\)\( T^{24} - \)\(44\!\cdots\!40\)\( T^{25} + \)\(10\!\cdots\!03\)\( T^{26} - \)\(76\!\cdots\!50\)\( T^{27} + \)\(25\!\cdots\!62\)\( T^{28} - \)\(71\!\cdots\!02\)\( T^{29} + \)\(42\!\cdots\!30\)\( T^{30} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 29 T + 944 T^{2} - 19058 T^{3} + 382210 T^{4} - 6113816 T^{5} + 94573042 T^{6} - 1272502554 T^{7} + 16439619025 T^{8} - 192257946445 T^{9} + 2155532568934 T^{10} - 22340216230423 T^{11} + 222004378224474 T^{12} - 2062961303066295 T^{13} + 18389585981128520 T^{14} - 154188399183324000 T^{15} + 1240580780851833988 T^{16} - 9405492350182764000 T^{17} + 68427649435779222920 T^{18} - \)\(46\!\cdots\!95\)\( T^{19} + \)\(30\!\cdots\!34\)\( T^{20} - \)\(18\!\cdots\!23\)\( T^{21} + \)\(11\!\cdots\!74\)\( T^{22} - \)\(60\!\cdots\!45\)\( T^{23} + \)\(31\!\cdots\!25\)\( T^{24} - \)\(14\!\cdots\!14\)\( T^{25} + \)\(67\!\cdots\!42\)\( T^{26} - \)\(26\!\cdots\!76\)\( T^{27} + \)\(10\!\cdots\!10\)\( T^{28} - \)\(30\!\cdots\!98\)\( T^{29} + \)\(93\!\cdots\!04\)\( T^{30} - \)\(17\!\cdots\!29\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 15 T + 632 T^{2} - 9178 T^{3} + 214368 T^{4} - 2896282 T^{5} + 50100198 T^{6} - 623402438 T^{7} + 8906308926 T^{8} - 102103383754 T^{9} + 1270478817982 T^{10} - 13469241787695 T^{11} + 150321742884866 T^{12} - 1479978782393335 T^{13} + 15075703455738050 T^{14} - 138321830366923864 T^{15} + 1300058924253812145 T^{16} - 11142344236564741201 T^{17} + 97284222403134078882 T^{18} - \)\(77\!\cdots\!14\)\( T^{19} + \)\(63\!\cdots\!00\)\( T^{20} - \)\(47\!\cdots\!54\)\( T^{21} + \)\(36\!\cdots\!22\)\( T^{22} - \)\(25\!\cdots\!81\)\( T^{23} + \)\(18\!\cdots\!45\)\( T^{24} - \)\(11\!\cdots\!64\)\( T^{25} + \)\(77\!\cdots\!50\)\( T^{26} - \)\(46\!\cdots\!35\)\( T^{27} + \)\(28\!\cdots\!46\)\( T^{28} - \)\(15\!\cdots\!95\)\( T^{29} + \)\(90\!\cdots\!82\)\( T^{30} - \)\(44\!\cdots\!94\)\( T^{31} + \)\(23\!\cdots\!46\)\( T^{32} - \)\(10\!\cdots\!78\)\( T^{33} + \)\(49\!\cdots\!18\)\( T^{34} - \)\(17\!\cdots\!82\)\( T^{35} + \)\(78\!\cdots\!48\)\( T^{36} - \)\(20\!\cdots\!38\)\( T^{37} + \)\(86\!\cdots\!92\)\( T^{38} - \)\(12\!\cdots\!15\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 - 17 T + 202 T^{2} - 1139 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( 1 - 4 T + 212 T^{2} - 676 T^{3} + 20262 T^{4} - 45292 T^{5} + 951668 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 + 10 T + 202 T^{2} + 1197 T^{3} + 16424 T^{4} + 70105 T^{5} + 1100408 T^{6} + 5373333 T^{7} + 60754126 T^{8} + 201511210 T^{9} + 1350125107 T^{10} \))(\( 1 + 16 T + 389 T^{2} + 3875 T^{3} + 53383 T^{4} + 375776 T^{5} + 4164638 T^{6} + 25313577 T^{7} + 279030746 T^{8} + 1686858464 T^{9} + 16055631229 T^{10} + 78085593875 T^{11} + 525198666623 T^{12} + 1447334114704 T^{13} + 6060711605323 T^{14} \))(\( 1 - 8 T + 182 T^{2} - 2291 T^{3} + 24185 T^{4} - 260917 T^{5} + 2432692 T^{6} - 20277336 T^{7} + 162990364 T^{8} - 1171256413 T^{9} + 7273953155 T^{10} - 46166218211 T^{11} + 245722769474 T^{12} - 723667057352 T^{13} + 6060711605323 T^{14} \))(\( 1 - 35 T + 1062 T^{2} - 21178 T^{3} + 376716 T^{4} - 5351357 T^{5} + 69609399 T^{6} - 773864453 T^{7} + 8037621732 T^{8} - 73671757791 T^{9} + 638591078308 T^{10} - 4936007771997 T^{11} + 36080883954948 T^{12} - 232749794477639 T^{13} + 1402707421986279 T^{14} - 7225001442220199 T^{15} + 34077119897177004 T^{16} - 128353750377530494 T^{17} + 431243873565152742 T^{18} - 952228703870323145 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 11 T + 440 T^{2} - 3258 T^{3} + 82372 T^{4} - 437749 T^{5} + 9931812 T^{6} - 43101729 T^{7} + 945457911 T^{8} - 3694828149 T^{9} + 72034637003 T^{10} - 247553485983 T^{11} + 4244160562479 T^{12} - 12963405319227 T^{13} + 200137145361252 T^{14} - 591015915464143 T^{15} + 7451237856024868 T^{16} - 19745798410142334 T^{17} + 178669778124922040 T^{18} - 299271878359244417 T^{19} + 1822837804551761449 T^{20} \))(\( 1 + 39 T + 1072 T^{2} + 20960 T^{3} + 340805 T^{4} + 4604354 T^{5} + 54800454 T^{6} + 574727854 T^{7} + 5531614723 T^{8} + 49152332927 T^{9} + 419703286294 T^{10} + 3456693252772 T^{11} + 28120120181698 T^{12} + 220644822509303 T^{13} + 1663705038933649 T^{14} + 11581410528024334 T^{15} + 73987468820398578 T^{16} + 416502413773363826 T^{17} + 2065520818652105015 T^{18} + 8511178521587195360 T^{19} + 29165404872828183184 T^{20} + 71090674377518696511 T^{21} + \)\(12\!\cdots\!83\)\( T^{22} \))(\( 1 + 19 T + 582 T^{2} + 8498 T^{3} + 157935 T^{4} + 1947356 T^{5} + 27739678 T^{6} + 298026009 T^{7} + 3521843485 T^{8} + 33428296182 T^{9} + 340561826459 T^{10} + 2872813898074 T^{11} + 25727396379516 T^{12} + 192478531170958 T^{13} + 1528782038974451 T^{14} + 10053994644586866 T^{15} + 70969094209296685 T^{16} + 402372397289907963 T^{17} + 2509286393769001582 T^{18} + 11802363108895375988 T^{19} + 64132298654908096335 T^{20} + \)\(23\!\cdots\!06\)\( T^{21} + \)\(10\!\cdots\!18\)\( T^{22} + \)\(23\!\cdots\!77\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - T + 345 T^{2} - 1033 T^{3} + 60225 T^{4} - 315162 T^{5} + 7588143 T^{6} - 51308407 T^{7} + 804912719 T^{8} - 5664080339 T^{9} + 74276768870 T^{10} - 488828629460 T^{11} + 5871020311353 T^{12} - 35427149740492 T^{13} + 393358360860651 T^{14} - 2194351717645940 T^{15} + 22339703835647810 T^{16} - 114137568264910019 T^{17} + 1086732870865535933 T^{18} - 4641275488888594783 T^{19} + 45989546342950485189 T^{20} - \)\(12\!\cdots\!42\)\( T^{21} + \)\(16\!\cdots\!75\)\( T^{22} - \)\(18\!\cdots\!17\)\( T^{23} + \)\(42\!\cdots\!35\)\( T^{24} - \)\(81\!\cdots\!61\)\( T^{25} + \)\(54\!\cdots\!87\)\( T^{26} \))(\( 1 - 2 T + 412 T^{2} - 85 T^{3} + 81873 T^{4} + 59025 T^{5} + 11064257 T^{6} + 6768182 T^{7} + 1156961567 T^{8} - 227617176 T^{9} + 98345725864 T^{10} - 115483783745 T^{11} + 7193333316815 T^{12} - 13468582820631 T^{13} + 489649450710742 T^{14} - 902395048982277 T^{15} + 32290873259182535 T^{16} - 34733249250497435 T^{17} + 1981776621718293544 T^{18} - 307311664102037832 T^{19} + \)\(10\!\cdots\!23\)\( T^{20} + 41019999194338232786 T^{21} + \)\(44\!\cdots\!37\)\( T^{22} + \)\(16\!\cdots\!75\)\( T^{23} + \)\(14\!\cdots\!77\)\( T^{24} - \)\(10\!\cdots\!55\)\( T^{25} + \)\(33\!\cdots\!32\)\( T^{26} - \)\(10\!\cdots\!74\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 13 T + 670 T^{2} + 8188 T^{3} + 230543 T^{4} + 2619614 T^{5} + 53087488 T^{6} + 558208387 T^{7} + 9073012510 T^{8} + 88068094121 T^{9} + 1213486439819 T^{10} + 10855099028016 T^{11} + 130938836056731 T^{12} + 1077211910225838 T^{13} + 11603480018277103 T^{14} + 87507315070039515 T^{15} + 852538297434471918 T^{16} + 5862990109692647505 T^{17} + 52088021802045915367 T^{18} + \)\(32\!\cdots\!94\)\( T^{19} + \)\(26\!\cdots\!51\)\( T^{20} + \)\(14\!\cdots\!12\)\( T^{21} + \)\(10\!\cdots\!11\)\( T^{22} + \)\(53\!\cdots\!83\)\( T^{23} + \)\(36\!\cdots\!10\)\( T^{24} + \)\(15\!\cdots\!89\)\( T^{25} + \)\(96\!\cdots\!12\)\( T^{26} + \)\(31\!\cdots\!62\)\( T^{27} + \)\(18\!\cdots\!23\)\( T^{28} + \)\(44\!\cdots\!56\)\( T^{29} + \)\(24\!\cdots\!30\)\( T^{30} + \)\(31\!\cdots\!59\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 32 T + 899 T^{2} - 17381 T^{3} + 299650 T^{4} - 4367598 T^{5} + 58180816 T^{6} - 704246868 T^{7} + 7965286745 T^{8} - 84941529999 T^{9} + 863331531798 T^{10} - 8444234612619 T^{11} + 79746261365378 T^{12} - 730107612862990 T^{13} + 6478611978227839 T^{14} - 55688515897313891 T^{15} + 463482632727338148 T^{16} - 3731130565120030697 T^{17} + 29082489170264769271 T^{18} - \)\(21\!\cdots\!70\)\( T^{19} + \)\(16\!\cdots\!38\)\( T^{20} - \)\(11\!\cdots\!33\)\( T^{21} + \)\(78\!\cdots\!62\)\( T^{22} - \)\(51\!\cdots\!77\)\( T^{23} + \)\(32\!\cdots\!45\)\( T^{24} - \)\(19\!\cdots\!96\)\( T^{25} + \)\(10\!\cdots\!84\)\( T^{26} - \)\(53\!\cdots\!34\)\( T^{27} + \)\(24\!\cdots\!50\)\( T^{28} - \)\(95\!\cdots\!47\)\( T^{29} + \)\(33\!\cdots\!71\)\( T^{30} - \)\(78\!\cdots\!76\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 20 T + 814 T^{2} - 12903 T^{3} + 305961 T^{4} - 4047653 T^{5} + 72254961 T^{6} - 824255236 T^{7} + 12233558357 T^{8} - 122983674302 T^{9} + 1601693140998 T^{10} - 14406388234225 T^{11} + 170654313648350 T^{12} - 1389771538600015 T^{13} + 15404833617631740 T^{14} - 115030417424373978 T^{15} + 1223404814530070450 T^{16} - 8525247538987629756 T^{17} + 88790021430906710023 T^{18} - \)\(59\!\cdots\!00\)\( T^{19} + \)\(60\!\cdots\!06\)\( T^{20} - \)\(39\!\cdots\!00\)\( T^{21} + \)\(39\!\cdots\!47\)\( T^{22} - \)\(25\!\cdots\!28\)\( T^{23} + \)\(24\!\cdots\!50\)\( T^{24} - \)\(15\!\cdots\!46\)\( T^{25} + \)\(13\!\cdots\!60\)\( T^{26} - \)\(84\!\cdots\!45\)\( T^{27} + \)\(69\!\cdots\!50\)\( T^{28} - \)\(39\!\cdots\!75\)\( T^{29} + \)\(29\!\cdots\!02\)\( T^{30} - \)\(15\!\cdots\!66\)\( T^{31} + \)\(10\!\cdots\!77\)\( T^{32} - \)\(45\!\cdots\!32\)\( T^{33} + \)\(26\!\cdots\!69\)\( T^{34} - \)\(99\!\cdots\!79\)\( T^{35} + \)\(50\!\cdots\!41\)\( T^{36} - \)\(14\!\cdots\!81\)\( T^{37} + \)\(60\!\cdots\!26\)\( T^{38} - \)\(99\!\cdots\!60\)\( T^{39} + \)\(33\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 - 3 T + 71 T^{2} \))(\( 1 - 15 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 25 T + 294 T^{2} + 1775 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 113 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( 1 - 22 T + 414 T^{2} - 4964 T^{3} + 48903 T^{4} - 352444 T^{5} + 2086974 T^{6} - 7874042 T^{7} + 25411681 T^{8} \))(\( 1 - 11 T + 357 T^{2} - 3005 T^{3} + 50921 T^{4} - 315865 T^{5} + 3615391 T^{6} - 15148205 T^{7} + 127774227 T^{8} - 279528491 T^{9} + 1804229351 T^{10} \))(\( 1 - 13 T + 521 T^{2} - 5337 T^{3} + 113902 T^{4} - 926278 T^{5} + 13634702 T^{6} - 87029512 T^{7} + 968063842 T^{8} - 4669367398 T^{9} + 40766778722 T^{10} - 135622141497 T^{11} + 940003491871 T^{12} - 1665303690973 T^{13} + 9095120158391 T^{14} \))(\( 1 - 6 T + 302 T^{2} - 1347 T^{3} + 42856 T^{4} - 163270 T^{5} + 4135912 T^{6} - 13977690 T^{7} + 293649752 T^{8} - 823044070 T^{9} + 15338633816 T^{10} - 34229534307 T^{11} + 544877264002 T^{12} - 768601703526 T^{13} + 9095120158391 T^{14} \))(\( 1 + 30 T + 649 T^{2} + 10715 T^{3} + 160512 T^{4} + 2062967 T^{5} + 24445546 T^{6} + 262904570 T^{7} + 2669117543 T^{8} + 24756823700 T^{9} + 216918645355 T^{10} + 1757734482700 T^{11} + 13455021534263 T^{12} + 94096437553270 T^{13} + 621202416822826 T^{14} + 3722065611544417 T^{15} + 20561632772727552 T^{16} + 97454212497159565 T^{17} + 419094041778498889 T^{18} + 1375455021553470930 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 17 T + 487 T^{2} - 5429 T^{3} + 95541 T^{4} - 839054 T^{5} + 12202961 T^{6} - 93606104 T^{7} + 1206692029 T^{8} - 8257557627 T^{9} + 95318141337 T^{10} - 586286591517 T^{11} + 6082934518189 T^{12} - 33502654288744 T^{13} + 310097752187441 T^{14} - 1513845853873954 T^{15} + 12238829226096261 T^{16} - 49377407339904739 T^{17} + 314481969716685607 T^{18} - 779424512213633527 T^{19} + 3255243551009881201 T^{20} \))(\( 1 + 49 T + 1561 T^{2} + 35931 T^{3} + 670365 T^{4} + 10461619 T^{5} + 141823527 T^{6} + 1699994043 T^{7} + 18416834909 T^{8} + 182866016817 T^{9} + 1690497985987 T^{10} + 14666905550090 T^{11} + 120025357005077 T^{12} + 921827590774497 T^{13} + 6591587799115099 T^{14} + 43199706322616283 T^{15} + 255882170075740977 T^{16} + 1340136364173328099 T^{17} + 6097050224979782715 T^{18} + 23202570131191438491 T^{19} + 71569509621498937391 T^{20} + \)\(15\!\cdots\!49\)\( T^{21} + \)\(23\!\cdots\!71\)\( T^{22} \))(\( 1 + 19 T + 557 T^{2} + 8669 T^{3} + 147428 T^{4} + 1886187 T^{5} + 24513358 T^{6} + 263684591 T^{7} + 2890644180 T^{8} + 27203252247 T^{9} + 264256344608 T^{10} + 2267894906725 T^{11} + 20188824935908 T^{12} + 161020538377475 T^{13} + 1332116233168928 T^{14} + 9736343214976017 T^{15} + 73456127786666580 T^{16} + 475747478488630441 T^{17} + 3140168119657116718 T^{18} + 17155097406195045117 T^{19} + 95202151604500052708 T^{20} + \)\(39\!\cdots\!39\)\( T^{21} + \)\(18\!\cdots\!57\)\( T^{22} + \)\(43\!\cdots\!49\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 17 T + 411 T^{2} + 4819 T^{3} + 72983 T^{4} + 696550 T^{5} + 8552058 T^{6} + 72895639 T^{7} + 826016480 T^{8} + 6823981862 T^{9} + 75438996290 T^{10} + 609685710595 T^{11} + 6338553518754 T^{12} + 47648490220692 T^{13} + 450037299831534 T^{14} + 3073425667109395 T^{15} + 27000446601150190 T^{16} + 173408850226930022 T^{17} + 1490323177625704480 T^{18} + 9337952052502720519 T^{19} + 77781995111529018678 T^{20} + \)\(44\!\cdots\!50\)\( T^{21} + \)\(33\!\cdots\!73\)\( T^{22} + \)\(15\!\cdots\!19\)\( T^{23} + \)\(94\!\cdots\!81\)\( T^{24} + \)\(27\!\cdots\!97\)\( T^{25} + \)\(11\!\cdots\!11\)\( T^{26} \))(\( 1 - 55 T + 1906 T^{2} - 47988 T^{3} + 984493 T^{4} - 17083015 T^{5} + 260576902 T^{6} - 3557771614 T^{7} + 44369235966 T^{8} - 510923883358 T^{9} + 5499327498984 T^{10} - 55655727934707 T^{11} + 533182660015140 T^{12} - 4844300269336289 T^{13} + 41867190182528960 T^{14} - 343945319122876519 T^{15} + 2687773789136320740 T^{16} - 19919797240838917077 T^{17} + \)\(13\!\cdots\!04\)\( T^{18} - \)\(92\!\cdots\!58\)\( T^{19} + \)\(56\!\cdots\!86\)\( T^{20} - \)\(32\!\cdots\!74\)\( T^{21} + \)\(16\!\cdots\!22\)\( T^{22} - \)\(78\!\cdots\!65\)\( T^{23} + \)\(32\!\cdots\!93\)\( T^{24} - \)\(11\!\cdots\!48\)\( T^{25} + \)\(31\!\cdots\!46\)\( T^{26} - \)\(64\!\cdots\!05\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))(\( 1 - 23 T + 884 T^{2} - 15988 T^{3} + 350501 T^{4} - 5252152 T^{5} + 84915421 T^{6} - 1089093351 T^{7} + 14332646888 T^{8} - 161103070680 T^{9} + 1821849114561 T^{10} - 18326234398836 T^{11} + 185017677286106 T^{12} - 1701877538128570 T^{13} + 15819528055733742 T^{14} - 135879776864301866 T^{15} + 1188115050713486000 T^{16} - 9647464157365432486 T^{17} + 79746240928953793422 T^{18} - \)\(60\!\cdots\!70\)\( T^{19} + \)\(47\!\cdots\!86\)\( T^{20} - \)\(33\!\cdots\!36\)\( T^{21} + \)\(23\!\cdots\!81\)\( T^{22} - \)\(14\!\cdots\!80\)\( T^{23} + \)\(92\!\cdots\!68\)\( T^{24} - \)\(49\!\cdots\!81\)\( T^{25} + \)\(27\!\cdots\!21\)\( T^{26} - \)\(12\!\cdots\!92\)\( T^{27} + \)\(57\!\cdots\!41\)\( T^{28} - \)\(18\!\cdots\!68\)\( T^{29} + \)\(73\!\cdots\!04\)\( T^{30} - \)\(13\!\cdots\!73\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 29 T + 932 T^{2} + 17858 T^{3} + 345833 T^{4} + 5076239 T^{5} + 74234648 T^{6} + 890327184 T^{7} + 10665643953 T^{8} + 108028812469 T^{9} + 1106635368452 T^{10} + 9678586554561 T^{11} + 88074708018966 T^{12} + 687500520363023 T^{13} + 5917159166967580 T^{14} + 44483733398901865 T^{15} + 397289714357614342 T^{16} + 3158345071322032415 T^{17} + 29828399360683570780 T^{18} + \)\(24\!\cdots\!53\)\( T^{19} + \)\(22\!\cdots\!46\)\( T^{20} + \)\(17\!\cdots\!11\)\( T^{21} + \)\(14\!\cdots\!92\)\( T^{22} + \)\(98\!\cdots\!79\)\( T^{23} + \)\(68\!\cdots\!33\)\( T^{24} + \)\(40\!\cdots\!04\)\( T^{25} + \)\(24\!\cdots\!48\)\( T^{26} + \)\(11\!\cdots\!69\)\( T^{27} + \)\(56\!\cdots\!53\)\( T^{28} + \)\(20\!\cdots\!38\)\( T^{29} + \)\(77\!\cdots\!92\)\( T^{30} + \)\(17\!\cdots\!79\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 63 T + 2590 T^{2} + 78606 T^{3} + 1970879 T^{4} + 42229125 T^{5} + 800998266 T^{6} + 13664206408 T^{7} + 213204472880 T^{8} + 3070903631126 T^{9} + 41242902030686 T^{10} + 519647975394003 T^{11} + 6184547496360173 T^{12} + 69833932774379894 T^{13} + 751885537417647114 T^{14} + 7744065320700227311 T^{15} + 76579426796513361691 T^{16} + \)\(72\!\cdots\!30\)\( T^{17} + \)\(66\!\cdots\!44\)\( T^{18} + \)\(59\!\cdots\!46\)\( T^{19} + \)\(50\!\cdots\!04\)\( T^{20} + \)\(42\!\cdots\!66\)\( T^{21} + \)\(33\!\cdots\!04\)\( T^{22} + \)\(26\!\cdots\!30\)\( T^{23} + \)\(19\!\cdots\!71\)\( T^{24} + \)\(13\!\cdots\!61\)\( T^{25} + \)\(96\!\cdots\!94\)\( T^{26} + \)\(63\!\cdots\!54\)\( T^{27} + \)\(39\!\cdots\!53\)\( T^{28} + \)\(23\!\cdots\!93\)\( T^{29} + \)\(13\!\cdots\!86\)\( T^{30} + \)\(70\!\cdots\!46\)\( T^{31} + \)\(34\!\cdots\!80\)\( T^{32} + \)\(15\!\cdots\!88\)\( T^{33} + \)\(66\!\cdots\!46\)\( T^{34} + \)\(24\!\cdots\!75\)\( T^{35} + \)\(82\!\cdots\!59\)\( T^{36} + \)\(23\!\cdots\!46\)\( T^{37} + \)\(54\!\cdots\!90\)\( T^{38} + \)\(94\!\cdots\!53\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))
$73$ (\( 1 - 8 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 + 2 T + 130 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 292 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 22 T + 458 T^{2} + 5314 T^{3} + 56718 T^{4} + 387922 T^{5} + 2440682 T^{6} + 8558374 T^{7} + 28398241 T^{8} \))(\( 1 - 31 T + 648 T^{2} - 9721 T^{3} + 114923 T^{4} - 1087551 T^{5} + 8389379 T^{6} - 51803209 T^{7} + 252083016 T^{8} - 880345471 T^{9} + 2073071593 T^{10} \))(\( 1 + 23 T + 452 T^{2} + 6121 T^{3} + 70148 T^{4} + 672782 T^{5} + 6097489 T^{6} + 50887564 T^{7} + 445116697 T^{8} + 3585255278 T^{9} + 27288764516 T^{10} + 173825633161 T^{11} + 937028360036 T^{12} + 3480687204647 T^{13} + 11047398519097 T^{14} \))(\( 1 - 15 T + 438 T^{2} - 5215 T^{3} + 83728 T^{4} - 810862 T^{5} + 9403735 T^{6} - 74481820 T^{7} + 686472655 T^{8} - 4321083598 T^{9} + 32571615376 T^{10} - 148096826815 T^{11} + 908005357734 T^{12} - 2270013394335 T^{13} + 11047398519097 T^{14} \))(\( 1 + 15 T + 633 T^{2} + 8266 T^{3} + 181121 T^{4} + 2073532 T^{5} + 31324558 T^{6} + 315193028 T^{7} + 3690028070 T^{8} + 32453555007 T^{9} + 313999225218 T^{10} + 2369109515511 T^{11} + 19664159585030 T^{12} + 122615446173476 T^{13} + 889562347302478 T^{14} + 4298580286376476 T^{15} + 27409806399689969 T^{16} + 91317796158855802 T^{17} + 510489238168953273 T^{18} + 883073800624018695 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 44 T + 1512 T^{2} + 35899 T^{3} + 726529 T^{4} + 12037217 T^{5} + 176244267 T^{6} + 2227972384 T^{7} + 25319414428 T^{8} + 253707899388 T^{9} + 2301758109781 T^{10} + 18520676655324 T^{11} + 134927159486812 T^{12} + 866719132906528 T^{13} + 5005027169134347 T^{14} + 24954012621476681 T^{15} + 109948704091520881 T^{16} + 396590559437063203 T^{17} + 1219367658943850472 T^{18} + 2590349815163788172 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 3 T + 196 T^{2} - 159 T^{3} + 31858 T^{4} - 26254 T^{5} + 3900187 T^{6} - 6625858 T^{7} + 402069132 T^{8} - 632169893 T^{9} + 34172795610 T^{10} - 62902441758 T^{11} + 2494614079530 T^{12} - 3368833359797 T^{13} + 156411727523244 T^{14} - 188162712315778 T^{15} + 8085366877087891 T^{16} - 3973128776991406 T^{17} + 351948022021392226 T^{18} - 128227154611158879 T^{19} + 11538830994820510948 T^{20} + 12892877489110672947 T^{21} + \)\(31\!\cdots\!77\)\( T^{22} \))(\( 1 - 10 T + 470 T^{2} - 5607 T^{3} + 123348 T^{4} - 1452955 T^{5} + 22746543 T^{6} - 243632885 T^{7} + 3115488575 T^{8} - 29875682425 T^{9} + 326956400646 T^{10} - 2804767203394 T^{11} + 26870758635114 T^{12} - 204748005847762 T^{13} + 1742350659042534 T^{14} - 11622148349926225 T^{15} + 88474395385596575 T^{16} - 505068413014135805 T^{17} + 3442330485654468927 T^{18} - 16051372915314581635 T^{19} + 99475239414951103188 T^{20} - \)\(33\!\cdots\!91\)\( T^{21} + \)\(20\!\cdots\!30\)\( T^{22} - \)\(31\!\cdots\!70\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 26 T + 771 T^{2} - 14457 T^{3} + 266822 T^{4} - 3998594 T^{5} + 57241185 T^{6} - 724874106 T^{7} + 8706447990 T^{8} - 96138348524 T^{9} + 1005759688137 T^{10} - 9859920644507 T^{11} + 91592280066474 T^{12} - 803840006556492 T^{13} + 6686236444852602 T^{14} - 52543517114577803 T^{15} + 391257616599991329 T^{16} - 2730159990726546284 T^{17} + 18049090004000948070 T^{18} - \)\(10\!\cdots\!34\)\( T^{19} + \)\(63\!\cdots\!45\)\( T^{20} - \)\(32\!\cdots\!14\)\( T^{21} + \)\(15\!\cdots\!86\)\( T^{22} - \)\(62\!\cdots\!93\)\( T^{23} + \)\(24\!\cdots\!67\)\( T^{24} - \)\(59\!\cdots\!46\)\( T^{25} + \)\(16\!\cdots\!33\)\( T^{26} \))(\( 1 - 19 T + 865 T^{2} - 13222 T^{3} + 339511 T^{4} - 4344852 T^{5} + 81804908 T^{6} - 899882588 T^{7} + 13751393653 T^{8} - 132600600224 T^{9} + 1735580768935 T^{10} - 14902256067743 T^{11} + 172536300488083 T^{12} - 1334594221796352 T^{13} + 13913248462638488 T^{14} - 97425378191133696 T^{15} + 919445945300994307 T^{16} - 5797230948705178631 T^{17} + 49287440951181443335 T^{18} - \)\(27\!\cdots\!32\)\( T^{19} + \)\(20\!\cdots\!17\)\( T^{20} - \)\(99\!\cdots\!36\)\( T^{21} + \)\(65\!\cdots\!48\)\( T^{22} - \)\(25\!\cdots\!76\)\( T^{23} + \)\(14\!\cdots\!39\)\( T^{24} - \)\(41\!\cdots\!94\)\( T^{25} + \)\(19\!\cdots\!65\)\( T^{26} - \)\(31\!\cdots\!27\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( 1 + 38 T + 1102 T^{2} + 23637 T^{3} + 449118 T^{4} + 7416121 T^{5} + 112854931 T^{6} + 1568043333 T^{7} + 20466071212 T^{8} + 249509182915 T^{9} + 2887586787526 T^{10} + 31589362290113 T^{11} + 330110919046364 T^{12} + 3282626306498577 T^{13} + 31291315331137657 T^{14} + 284805720605396682 T^{15} + 2488970007910991602 T^{16} + 20790817604193957786 T^{17} + \)\(16\!\cdots\!53\)\( T^{18} + \)\(12\!\cdots\!09\)\( T^{19} + \)\(93\!\cdots\!24\)\( T^{20} + \)\(65\!\cdots\!09\)\( T^{21} + \)\(43\!\cdots\!14\)\( T^{22} + \)\(27\!\cdots\!55\)\( T^{23} + \)\(16\!\cdots\!72\)\( T^{24} + \)\(92\!\cdots\!29\)\( T^{25} + \)\(48\!\cdots\!19\)\( T^{26} + \)\(23\!\cdots\!17\)\( T^{27} + \)\(10\!\cdots\!78\)\( T^{28} + \)\(39\!\cdots\!21\)\( T^{29} + \)\(13\!\cdots\!18\)\( T^{30} + \)\(33\!\cdots\!66\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 19 T + 799 T^{2} - 12074 T^{3} + 294238 T^{4} - 3713937 T^{5} + 67555519 T^{6} - 731881822 T^{7} + 10961775828 T^{8} - 103764840872 T^{9} + 1353185769425 T^{10} - 11374809129845 T^{11} + 134695985357378 T^{12} - 1027001886511736 T^{13} + 11440507882026129 T^{14} - 81420620955130623 T^{15} + 872041110559406614 T^{16} - 5943705329724535479 T^{17} + 60966466503317241441 T^{18} - \)\(39\!\cdots\!12\)\( T^{19} + \)\(38\!\cdots\!98\)\( T^{20} - \)\(23\!\cdots\!85\)\( T^{21} + \)\(20\!\cdots\!25\)\( T^{22} - \)\(11\!\cdots\!84\)\( T^{23} + \)\(88\!\cdots\!68\)\( T^{24} - \)\(43\!\cdots\!86\)\( T^{25} + \)\(29\!\cdots\!31\)\( T^{26} - \)\(11\!\cdots\!49\)\( T^{27} + \)\(67\!\cdots\!98\)\( T^{28} - \)\(20\!\cdots\!42\)\( T^{29} + \)\(97\!\cdots\!91\)\( T^{30} - \)\(16\!\cdots\!83\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 19 T + 769 T^{2} - 10982 T^{3} + 276918 T^{4} - 3345467 T^{5} + 66999737 T^{6} - 718002144 T^{7} + 12387233437 T^{8} - 120457948023 T^{9} + 1864921663172 T^{10} - 16704013939955 T^{11} + 237570269110792 T^{12} - 1979196282339905 T^{13} + 26221041043135092 T^{14} - 204595515703267829 T^{15} + 2546979484335337090 T^{16} - 18708000306500559833 T^{17} + \)\(21\!\cdots\!82\)\( T^{18} - \)\(15\!\cdots\!55\)\( T^{19} + \)\(16\!\cdots\!56\)\( T^{20} - \)\(11\!\cdots\!15\)\( T^{21} + \)\(11\!\cdots\!78\)\( T^{22} - \)\(72\!\cdots\!61\)\( T^{23} + \)\(72\!\cdots\!90\)\( T^{24} - \)\(42\!\cdots\!97\)\( T^{25} + \)\(39\!\cdots\!88\)\( T^{26} - \)\(21\!\cdots\!85\)\( T^{27} + \)\(19\!\cdots\!52\)\( T^{28} - \)\(98\!\cdots\!15\)\( T^{29} + \)\(80\!\cdots\!28\)\( T^{30} - \)\(37\!\cdots\!71\)\( T^{31} + \)\(28\!\cdots\!77\)\( T^{32} - \)\(12\!\cdots\!52\)\( T^{33} + \)\(81\!\cdots\!33\)\( T^{34} - \)\(29\!\cdots\!19\)\( T^{35} + \)\(18\!\cdots\!98\)\( T^{36} - \)\(52\!\cdots\!46\)\( T^{37} + \)\(26\!\cdots\!61\)\( T^{38} - \)\(48\!\cdots\!03\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 - 13 T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( ( 1 + 2 T + 79 T^{2} )^{2} \))(\( 1 - 2 T + 135 T^{2} - 158 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 174 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 + 20 T + 316 T^{2} + 3064 T^{3} + 30313 T^{4} + 242056 T^{5} + 1972156 T^{6} + 9860780 T^{7} + 38950081 T^{8} \))(\( 1 - 8 T + 333 T^{2} - 2069 T^{3} + 48048 T^{4} - 229967 T^{5} + 3795792 T^{6} - 12912629 T^{7} + 164181987 T^{8} - 311600648 T^{9} + 3077056399 T^{10} \))(\( 1 + 44 T + 1245 T^{2} + 25061 T^{3} + 405173 T^{4} + 5369531 T^{5} + 60465031 T^{6} + 579089508 T^{7} + 4776737449 T^{8} + 33511242971 T^{9} + 199766090747 T^{10} + 976127979941 T^{11} + 3830935216755 T^{12} + 10695848042924 T^{13} + 19203908986159 T^{14} \))(\( 1 + 15 T + 565 T^{2} + 6921 T^{3} + 135750 T^{4} + 1345178 T^{5} + 17992607 T^{6} + 140941514 T^{7} + 1421415953 T^{8} + 8395255898 T^{9} + 66930044250 T^{10} + 269573510601 T^{11} + 1738536865435 T^{12} + 3646311832815 T^{13} + 19203908986159 T^{14} \))(\( 1 - 24 T + 711 T^{2} - 11703 T^{3} + 206161 T^{4} - 2694049 T^{5} + 36083162 T^{6} - 400300042 T^{7} + 4441321528 T^{8} - 42742258912 T^{9} + 405407419410 T^{10} - 3376638454048 T^{11} + 27718287656248 T^{12} - 197363532407638 T^{13} + 1405442082636122 T^{14} - 8289740714669551 T^{15} + 50115152917664881 T^{16} - 224743346865018777 T^{17} + 1078664363843564871 T^{18} - 2876438303582839656 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 5 T + 453 T^{2} - 1654 T^{3} + 91613 T^{4} - 178830 T^{5} + 10951097 T^{6} + 1909376 T^{7} + 919392184 T^{8} + 2065356423 T^{9} + 69768644457 T^{10} + 163163157417 T^{11} + 5737926620344 T^{12} + 941396833664 T^{13} + 426546115188857 T^{14} - 550269995833170 T^{15} + 22269971062645373 T^{16} - 31763265463106986 T^{17} + 687250290887672133 T^{18} - 599257979913091595 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 41 T + 1189 T^{2} - 26193 T^{3} + 483626 T^{4} - 7709044 T^{5} + 109460517 T^{6} - 1399418794 T^{7} + 16364772946 T^{8} - 175822723067 T^{9} + 1749124610179 T^{10} - 16126404005754 T^{11} + 138180844204141 T^{12} - 1097309614661147 T^{13} + 8068471288522894 T^{14} - 54507475379222314 T^{15} + 336816184272698283 T^{16} - 1873971890459431924 T^{17} + 9287509687340132534 T^{18} - 39737631057882552273 T^{19} + \)\(14\!\cdots\!91\)\( T^{20} - \)\(38\!\cdots\!41\)\( T^{21} + \)\(74\!\cdots\!79\)\( T^{22} \))(\( 1 - 17 T + 726 T^{2} - 9471 T^{3} + 233843 T^{4} - 2476541 T^{5} + 46166955 T^{6} - 412420874 T^{7} + 6460192964 T^{8} - 50180892217 T^{9} + 696914226932 T^{10} - 4825821191556 T^{11} + 60765805192315 T^{12} - 381239874132924 T^{13} + 4349441690282612 T^{14} - 24741136917777463 T^{15} + 251625039223430084 T^{16} - 1269042289422872726 T^{17} + 11222607620102508555 T^{18} - 47559267964491196019 T^{19} + \)\(35\!\cdots\!23\)\( T^{20} - \)\(11\!\cdots\!49\)\( T^{21} + \)\(68\!\cdots\!26\)\( T^{22} - \)\(12\!\cdots\!43\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 5 T + 339 T^{2} - 2040 T^{3} + 58251 T^{4} - 365198 T^{5} + 7585540 T^{6} - 45405015 T^{7} + 871129057 T^{8} - 4953738105 T^{9} + 88251798724 T^{10} - 484381708717 T^{11} + 7805005889985 T^{12} - 41126444625392 T^{13} + 616595465308815 T^{14} - 3023026244102797 T^{15} + 43511578591082236 T^{16} - 192948500442536505 T^{17} + 2680513239196685743 T^{18} - 11037389564242837815 T^{19} + \)\(14\!\cdots\!60\)\( T^{20} - \)\(55\!\cdots\!78\)\( T^{21} + \)\(69\!\cdots\!69\)\( T^{22} - \)\(19\!\cdots\!40\)\( T^{23} + \)\(25\!\cdots\!81\)\( T^{24} - \)\(29\!\cdots\!05\)\( T^{25} + \)\(46\!\cdots\!39\)\( T^{26} \))(\( 1 + 68 T + 2854 T^{2} + 87913 T^{3} + 2199796 T^{4} + 46646952 T^{5} + 865021420 T^{6} + 14282158063 T^{7} + 212976079418 T^{8} + 2894813443275 T^{9} + 36133541437366 T^{10} + 416213385145996 T^{11} + 4441578912784593 T^{12} + 44010249013254925 T^{13} + 405564900431154960 T^{14} + 3476809672047139075 T^{15} + 27719893994688644913 T^{16} + \)\(20\!\cdots\!44\)\( T^{17} + \)\(14\!\cdots\!46\)\( T^{18} + \)\(89\!\cdots\!25\)\( T^{19} + \)\(51\!\cdots\!78\)\( T^{20} + \)\(27\!\cdots\!17\)\( T^{21} + \)\(13\!\cdots\!20\)\( T^{22} + \)\(55\!\cdots\!88\)\( T^{23} + \)\(20\!\cdots\!96\)\( T^{24} + \)\(65\!\cdots\!27\)\( T^{25} + \)\(16\!\cdots\!14\)\( T^{26} + \)\(31\!\cdots\!52\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 + 27 T + 693 T^{2} + 9018 T^{3} + 123643 T^{4} + 857696 T^{5} + 9649395 T^{6} + 34236492 T^{7} + 874865634 T^{8} + 3707513929 T^{9} + 117694754759 T^{10} + 461194101439 T^{11} + 11627414069339 T^{12} + 25230497718801 T^{13} + 855497369602862 T^{14} + 175508400238644 T^{15} + 60554252891018408 T^{16} + 13865163618852876 T^{17} + 5339159083691461742 T^{18} + 12439619364779926239 T^{19} + \)\(45\!\cdots\!59\)\( T^{20} + \)\(14\!\cdots\!61\)\( T^{21} + \)\(28\!\cdots\!39\)\( T^{22} + \)\(71\!\cdots\!11\)\( T^{23} + \)\(13\!\cdots\!74\)\( T^{24} + \)\(41\!\cdots\!48\)\( T^{25} + \)\(91\!\cdots\!95\)\( T^{26} + \)\(64\!\cdots\!84\)\( T^{27} + \)\(73\!\cdots\!63\)\( T^{28} + \)\(42\!\cdots\!02\)\( T^{29} + \)\(25\!\cdots\!33\)\( T^{30} + \)\(78\!\cdots\!73\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 56 T + 2220 T^{2} - 63209 T^{3} + 1497077 T^{4} - 29816776 T^{5} + 523750220 T^{6} - 8188556978 T^{7} + 116694081790 T^{8} - 1528622743781 T^{9} + 18678888346970 T^{10} - 214455360319749 T^{11} + 2333837789894623 T^{12} - 24184707860680170 T^{13} + 239494812428915022 T^{14} - 2270495102884056799 T^{15} + 20615177670016269722 T^{16} - \)\(17\!\cdots\!21\)\( T^{17} + \)\(14\!\cdots\!02\)\( T^{18} - \)\(11\!\cdots\!30\)\( T^{19} + \)\(90\!\cdots\!63\)\( T^{20} - \)\(65\!\cdots\!51\)\( T^{21} + \)\(45\!\cdots\!70\)\( T^{22} - \)\(29\!\cdots\!79\)\( T^{23} + \)\(17\!\cdots\!90\)\( T^{24} - \)\(98\!\cdots\!82\)\( T^{25} + \)\(49\!\cdots\!20\)\( T^{26} - \)\(22\!\cdots\!04\)\( T^{27} + \)\(88\!\cdots\!57\)\( T^{28} - \)\(29\!\cdots\!51\)\( T^{29} + \)\(81\!\cdots\!20\)\( T^{30} - \)\(16\!\cdots\!44\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 32 T + 1430 T^{2} - 33799 T^{3} + 909433 T^{4} - 17532202 T^{5} + 360187910 T^{6} - 5951638450 T^{7} + 101789545993 T^{8} - 1483644502631 T^{9} + 22048084895066 T^{10} - 288634171288938 T^{11} + 3819726063800976 T^{12} - 45443454703136376 T^{13} + 543762219529712722 T^{14} - 5924597129880906313 T^{15} + 64725468439977681990 T^{16} - \)\(64\!\cdots\!24\)\( T^{17} + \)\(65\!\cdots\!24\)\( T^{18} - \)\(60\!\cdots\!41\)\( T^{19} + \)\(55\!\cdots\!06\)\( T^{20} - \)\(47\!\cdots\!39\)\( T^{21} + \)\(40\!\cdots\!84\)\( T^{22} - \)\(31\!\cdots\!36\)\( T^{23} + \)\(25\!\cdots\!90\)\( T^{24} - \)\(18\!\cdots\!87\)\( T^{25} + \)\(13\!\cdots\!62\)\( T^{26} - \)\(87\!\cdots\!84\)\( T^{27} + \)\(57\!\cdots\!36\)\( T^{28} - \)\(34\!\cdots\!22\)\( T^{29} + \)\(20\!\cdots\!66\)\( T^{30} - \)\(11\!\cdots\!49\)\( T^{31} + \)\(60\!\cdots\!13\)\( T^{32} - \)\(27\!\cdots\!50\)\( T^{33} + \)\(13\!\cdots\!10\)\( T^{34} - \)\(51\!\cdots\!98\)\( T^{35} + \)\(20\!\cdots\!93\)\( T^{36} - \)\(61\!\cdots\!41\)\( T^{37} + \)\(20\!\cdots\!30\)\( T^{38} - \)\(36\!\cdots\!08\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 6 T + 158 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 - 20 T + 260 T^{2} - 1660 T^{3} + 6889 T^{4} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( 1 - 10 T + 210 T^{2} - 2706 T^{3} + 21014 T^{4} - 224598 T^{5} + 1446690 T^{6} - 5717870 T^{7} + 47458321 T^{8} \))(\( 1 + 7 T + 130 T^{2} + 1342 T^{3} + 15890 T^{4} + 85583 T^{5} + 1318870 T^{6} + 9245038 T^{7} + 74332310 T^{8} + 332208247 T^{9} + 3939040643 T^{10} \))(\( 1 + 21 T + 540 T^{2} + 8096 T^{3} + 119997 T^{4} + 1418842 T^{5} + 15465914 T^{6} + 148208926 T^{7} + 1283670862 T^{8} + 9774402538 T^{9} + 68612724639 T^{10} + 384222566816 T^{11} + 2127081947220 T^{12} + 6865747840749 T^{13} + 27136050989627 T^{14} \))(\( 1 + 21 T + 408 T^{2} + 4818 T^{3} + 59881 T^{4} + 573036 T^{5} + 6250008 T^{6} + 53935978 T^{7} + 518750664 T^{8} + 3947645004 T^{9} + 34239177347 T^{10} + 228654190578 T^{11} + 1607128582344 T^{12} + 6865747840749 T^{13} + 27136050989627 T^{14} \))(\( 1 + T + 429 T^{2} - 783 T^{3} + 80674 T^{4} - 393897 T^{5} + 9292852 T^{6} - 77038357 T^{7} + 807855057 T^{8} - 9174603004 T^{9} + 65503788806 T^{10} - 761492049332 T^{11} + 5565313487673 T^{12} - 44049531033959 T^{13} + 441023153221492 T^{14} - 1551576292155771 T^{15} + 26375587681170706 T^{16} - 21247527924877941 T^{17} + 966233367587648589 T^{18} + 186940255267540403 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - 32 T + 1006 T^{2} - 20223 T^{3} + 380602 T^{4} - 5730612 T^{5} + 80923753 T^{6} - 985170346 T^{7} + 11305014451 T^{8} - 115208135432 T^{9} + 1109307126255 T^{10} - 9562275240856 T^{11} + 77880244552939 T^{12} - 563307596628302 T^{13} + 3840505446398713 T^{14} - 22573113577263516 T^{15} + 124434159984988138 T^{16} - 548772359163226821 T^{17} + 2265805985531875246 T^{18} - 5982088168561292896 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 13 T + 502 T^{2} + 5300 T^{3} + 117049 T^{4} + 987588 T^{5} + 16724796 T^{6} + 110612382 T^{7} + 1685329611 T^{8} + 8817785535 T^{9} + 140832263751 T^{10} + 668486929788 T^{11} + 11689077891333 T^{12} + 60745724550615 T^{13} + 963649562284857 T^{14} + 5249477931530622 T^{15} + 65879651189883828 T^{16} + 322882389454743972 T^{17} + 3176247632284850723 T^{18} + 11937148830336917300 T^{19} + 93844008144305282306 T^{20} + \)\(20\!\cdots\!37\)\( T^{21} + \)\(12\!\cdots\!67\)\( T^{22} \))(\( 1 - 12 T + 358 T^{2} - 6137 T^{3} + 78325 T^{4} - 1167568 T^{5} + 13032043 T^{6} - 133237621 T^{7} + 1396486127 T^{8} - 11948659334 T^{9} + 105414867948 T^{10} - 932526228440 T^{11} + 7908158278756 T^{12} - 77399676960520 T^{13} + 726203025293772 T^{14} - 6832088074609858 T^{15} + 66274886887212767 T^{16} - 524828404295630303 T^{17} + 4260701004180862867 T^{18} - 31683184781856817136 T^{19} + \)\(17\!\cdots\!25\)\( T^{20} - \)\(11\!\cdots\!11\)\( T^{21} + \)\(55\!\cdots\!42\)\( T^{22} - \)\(15\!\cdots\!04\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 4 T + 589 T^{2} + 2547 T^{3} + 182867 T^{4} + 825229 T^{5} + 38696874 T^{6} + 176614203 T^{7} + 6158379204 T^{8} + 27559881015 T^{9} + 773307881825 T^{10} + 3290559088410 T^{11} + 78527868396960 T^{12} + 307578321495216 T^{13} + 6517813076947680 T^{14} + 22668661560056490 T^{15} + 442167393825071275 T^{16} + 1307945679931675815 T^{17} + 24258105979561988172 T^{18} + 57742313471088359907 T^{19} + \)\(10\!\cdots\!98\)\( T^{20} + \)\(18\!\cdots\!89\)\( T^{21} + \)\(34\!\cdots\!01\)\( T^{22} + \)\(39\!\cdots\!03\)\( T^{23} + \)\(75\!\cdots\!63\)\( T^{24} + \)\(42\!\cdots\!44\)\( T^{25} + \)\(88\!\cdots\!63\)\( T^{26} \))(\( 1 - 21 T + 889 T^{2} - 15799 T^{3} + 375156 T^{4} - 5788987 T^{5} + 100461402 T^{6} - 1370905001 T^{7} + 19213943114 T^{8} - 234724212595 T^{9} + 2794963467615 T^{10} - 30778046565473 T^{11} + 320655847170681 T^{12} - 3188405195562274 T^{13} + 29585454778993340 T^{14} - 264637631231668742 T^{15} + 2208998131158821409 T^{16} - 17598486911532110251 T^{17} + \)\(13\!\cdots\!15\)\( T^{18} - \)\(92\!\cdots\!85\)\( T^{19} + \)\(62\!\cdots\!66\)\( T^{20} - \)\(37\!\cdots\!27\)\( T^{21} + \)\(22\!\cdots\!82\)\( T^{22} - \)\(10\!\cdots\!61\)\( T^{23} + \)\(58\!\cdots\!44\)\( T^{24} - \)\(20\!\cdots\!33\)\( T^{25} + \)\(95\!\cdots\!29\)\( T^{26} - \)\(18\!\cdots\!23\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 + 36 T + 1196 T^{2} + 27517 T^{3} + 571881 T^{4} + 9920614 T^{5} + 158245423 T^{6} + 2231747673 T^{7} + 29379555190 T^{8} + 351597127364 T^{9} + 3980053468120 T^{10} + 41759240431813 T^{11} + 421455095839285 T^{12} + 4024465951535984 T^{13} + 37861643012502909 T^{14} + 345281369780647867 T^{15} + 3174230346311553110 T^{16} + 28658353691793772961 T^{17} + \)\(26\!\cdots\!01\)\( T^{18} + \)\(23\!\cdots\!08\)\( T^{19} + \)\(20\!\cdots\!85\)\( T^{20} + \)\(16\!\cdots\!59\)\( T^{21} + \)\(13\!\cdots\!80\)\( T^{22} + \)\(95\!\cdots\!28\)\( T^{23} + \)\(66\!\cdots\!90\)\( T^{24} + \)\(41\!\cdots\!19\)\( T^{25} + \)\(24\!\cdots\!27\)\( T^{26} + \)\(12\!\cdots\!38\)\( T^{27} + \)\(61\!\cdots\!41\)\( T^{28} + \)\(24\!\cdots\!71\)\( T^{29} + \)\(88\!\cdots\!84\)\( T^{30} + \)\(22\!\cdots\!52\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 5 T + 619 T^{2} + 1789 T^{3} + 189875 T^{4} + 196844 T^{5} + 39294993 T^{6} - 23525976 T^{7} + 6261812710 T^{8} - 12148150242 T^{9} + 826900900131 T^{10} - 2371817048838 T^{11} + 94316828196477 T^{12} - 314513109217841 T^{13} + 9454726181158001 T^{14} - 32241383639665305 T^{15} + 835772322462085234 T^{16} - 2676034842092220315 T^{17} + 65133608661997468889 T^{18} - \)\(17\!\cdots\!67\)\( T^{19} + \)\(44\!\cdots\!17\)\( T^{20} - \)\(93\!\cdots\!34\)\( T^{21} + \)\(27\!\cdots\!39\)\( T^{22} - \)\(32\!\cdots\!34\)\( T^{23} + \)\(14\!\cdots\!10\)\( T^{24} - \)\(43\!\cdots\!28\)\( T^{25} + \)\(60\!\cdots\!57\)\( T^{26} + \)\(25\!\cdots\!48\)\( T^{27} + \)\(20\!\cdots\!75\)\( T^{28} + \)\(15\!\cdots\!07\)\( T^{29} + \)\(45\!\cdots\!51\)\( T^{30} + \)\(30\!\cdots\!35\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 21 T + 1119 T^{2} - 19471 T^{3} + 599759 T^{4} - 9037206 T^{5} + 208286349 T^{6} - 2790710326 T^{7} + 53051147853 T^{8} - 643058468719 T^{9} + 10596342405190 T^{10} - 117601394018569 T^{11} + 1729819168571668 T^{12} - 17729018166575289 T^{13} + 237214420638684586 T^{14} - 2259038398021528647 T^{15} + 27841006306951857538 T^{16} - \)\(24\!\cdots\!61\)\( T^{17} + \)\(28\!\cdots\!36\)\( T^{18} - \)\(23\!\cdots\!27\)\( T^{19} + \)\(25\!\cdots\!66\)\( T^{20} - \)\(19\!\cdots\!41\)\( T^{21} + \)\(19\!\cdots\!04\)\( T^{22} - \)\(14\!\cdots\!07\)\( T^{23} + \)\(13\!\cdots\!98\)\( T^{24} - \)\(88\!\cdots\!21\)\( T^{25} + \)\(77\!\cdots\!34\)\( T^{26} - \)\(48\!\cdots\!03\)\( T^{27} + \)\(38\!\cdots\!88\)\( T^{28} - \)\(21\!\cdots\!07\)\( T^{29} + \)\(16\!\cdots\!10\)\( T^{30} - \)\(82\!\cdots\!73\)\( T^{31} + \)\(56\!\cdots\!33\)\( T^{32} - \)\(24\!\cdots\!38\)\( T^{33} + \)\(15\!\cdots\!21\)\( T^{34} - \)\(55\!\cdots\!42\)\( T^{35} + \)\(30\!\cdots\!79\)\( T^{36} - \)\(81\!\cdots\!33\)\( T^{37} + \)\(39\!\cdots\!71\)\( T^{38} - \)\(60\!\cdots\!87\)\( T^{39} + \)\(24\!\cdots\!01\)\( T^{40} \))
$89$ (\( 1 - 9 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 10 T + 50 T^{2} + 890 T^{3} + 7921 T^{4} \))(\( 1 + 6 T + 181 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 2 T^{2} + 7921 T^{4} \))(\( 1 - 14 T + 164 T^{2} - 1808 T^{3} + 23557 T^{4} - 160912 T^{5} + 1299044 T^{6} - 9869566 T^{7} + 62742241 T^{8} \))(\( 1 + 3 T + 295 T^{2} + 1825 T^{3} + 37881 T^{4} + 278011 T^{5} + 3371409 T^{6} + 14455825 T^{7} + 207965855 T^{8} + 188226723 T^{9} + 5584059449 T^{10} \))(\( 1 - 5 T + 428 T^{2} - 2396 T^{3} + 90651 T^{4} - 477799 T^{5} + 12139591 T^{6} - 54121615 T^{7} + 1080423599 T^{8} - 3784645879 T^{9} + 63906144819 T^{10} - 150330409436 T^{11} + 2389977444172 T^{12} - 2484906454805 T^{13} + 44231334895529 T^{14} \))(\( 1 + 8 T + 432 T^{2} + 2603 T^{3} + 85202 T^{4} + 395462 T^{5} + 10586330 T^{6} + 40422326 T^{7} + 942183370 T^{8} + 3132454502 T^{9} + 60064768738 T^{10} + 163318053323 T^{11} + 2412313681968 T^{12} + 3975850327688 T^{13} + 44231334895529 T^{14} \))(\( 1 + 15 T + 657 T^{2} + 9561 T^{3} + 211960 T^{4} + 2864098 T^{5} + 43638725 T^{6} + 529420307 T^{7} + 6274334785 T^{8} + 66647999115 T^{9} + 653070127936 T^{10} + 5931671921235 T^{11} + 49699005831985 T^{12} + 373224904405483 T^{13} + 2737991400882725 T^{14} + 15993293499762002 T^{15} + 105340154432093560 T^{16} + 422895792936152769 T^{17} + 2586338845346267217 T^{18} + 5255346055612278135 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 10 T + 554 T^{2} - 5842 T^{3} + 155645 T^{4} - 1640385 T^{5} + 28935836 T^{6} - 290928628 T^{7} + 3903118975 T^{8} - 35927833885 T^{9} + 397465410729 T^{10} - 3197577215765 T^{11} + 30916605400975 T^{12} - 205095663952532 T^{13} + 1815499195848476 T^{14} - 9160007359247865 T^{15} + 77352653031624845 T^{16} - 258399458459680418 T^{17} + 2180870198358952874 T^{18} - 3503564037074852090 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 34 T + 1201 T^{2} + 26387 T^{3} + 559512 T^{4} + 9300775 T^{5} + 147852867 T^{6} + 1992121814 T^{7} + 25687764507 T^{8} + 290370740809 T^{9} + 3147129733888 T^{10} + 30308852282314 T^{11} + 280094546316032 T^{12} + 2300026637948089 T^{13} + 18109077656735283 T^{14} + 124990186955345174 T^{15} + 825619199033090283 T^{16} + 4622311166437794775 T^{17} + 24747962650067221848 T^{18} + \)\(10\!\cdots\!47\)\( T^{19} + \)\(42\!\cdots\!09\)\( T^{20} + \)\(10\!\cdots\!34\)\( T^{21} + \)\(27\!\cdots\!89\)\( T^{22} \))(\( 1 - 20 T + 684 T^{2} - 10502 T^{3} + 216198 T^{4} - 2804069 T^{5} + 44593072 T^{6} - 509986178 T^{7} + 6856781124 T^{8} - 70502587428 T^{9} + 834633343019 T^{10} - 7761428330603 T^{11} + 82316339528600 T^{12} - 690767121423667 T^{13} + 6611130710053499 T^{14} - 49702138556529732 T^{15} + 430209813766258884 T^{16} - 2847793136120295922 T^{17} + 22161922490476822192 T^{18} - \)\(12\!\cdots\!01\)\( T^{19} + \)\(85\!\cdots\!38\)\( T^{20} - \)\(36\!\cdots\!18\)\( T^{21} + \)\(21\!\cdots\!84\)\( T^{22} - \)\(55\!\cdots\!80\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 48 T + 1594 T^{2} + 38770 T^{3} + 792883 T^{4} + 13825325 T^{5} + 215573747 T^{6} + 3023761998 T^{7} + 39145660911 T^{8} + 469173717361 T^{9} + 5295811844460 T^{10} + 56323668994780 T^{11} + 571147707266589 T^{12} + 5506317450879454 T^{13} + 50832145946726421 T^{14} + 446139782107652380 T^{15} + 3733383180177121740 T^{16} + 29437010445529746001 T^{17} + \)\(21\!\cdots\!39\)\( T^{18} + \)\(15\!\cdots\!78\)\( T^{19} + \)\(95\!\cdots\!63\)\( T^{20} + \)\(54\!\cdots\!25\)\( T^{21} + \)\(27\!\cdots\!47\)\( T^{22} + \)\(12\!\cdots\!70\)\( T^{23} + \)\(44\!\cdots\!66\)\( T^{24} + \)\(11\!\cdots\!08\)\( T^{25} + \)\(21\!\cdots\!69\)\( T^{26} \))(\( 1 - 17 T + 605 T^{2} - 7757 T^{3} + 170857 T^{4} - 1865051 T^{5} + 32707576 T^{6} - 317061790 T^{7} + 4820161984 T^{8} - 42568948494 T^{9} + 590976178888 T^{10} - 4867467377397 T^{11} + 63043309074110 T^{12} - 487765585730110 T^{13} + 5943840388880014 T^{14} - 43411137129979790 T^{15} + 499366051176025310 T^{16} - 3431413609576185693 T^{17} + 37079169841050008008 T^{18} - \)\(23\!\cdots\!06\)\( T^{19} + \)\(23\!\cdots\!24\)\( T^{20} - \)\(14\!\cdots\!10\)\( T^{21} + \)\(12\!\cdots\!56\)\( T^{22} - \)\(65\!\cdots\!59\)\( T^{23} + \)\(53\!\cdots\!57\)\( T^{24} - \)\(21\!\cdots\!73\)\( T^{25} + \)\(14\!\cdots\!05\)\( T^{26} - \)\(37\!\cdots\!73\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( 1 - 16 T + 811 T^{2} - 11248 T^{3} + 323872 T^{4} - 4023539 T^{5} + 86234371 T^{6} - 978851675 T^{7} + 17292857403 T^{8} - 181368267110 T^{9} + 2777395005049 T^{10} - 27066173146294 T^{11} + 369771559980595 T^{12} - 3354466560687775 T^{13} + 41625490530195845 T^{14} - 351042231905929943 T^{15} + 4002398398064518426 T^{16} - 31242758639627764927 T^{17} + \)\(32\!\cdots\!45\)\( T^{18} - \)\(23\!\cdots\!75\)\( T^{19} + \)\(23\!\cdots\!95\)\( T^{20} - \)\(15\!\cdots\!06\)\( T^{21} + \)\(13\!\cdots\!89\)\( T^{22} - \)\(80\!\cdots\!90\)\( T^{23} + \)\(68\!\cdots\!43\)\( T^{24} - \)\(34\!\cdots\!75\)\( T^{25} + \)\(26\!\cdots\!71\)\( T^{26} - \)\(11\!\cdots\!71\)\( T^{27} + \)\(79\!\cdots\!12\)\( T^{28} - \)\(24\!\cdots\!12\)\( T^{29} + \)\(15\!\cdots\!51\)\( T^{30} - \)\(27\!\cdots\!84\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 + 7 T + 578 T^{2} + 3482 T^{3} + 170640 T^{4} + 922484 T^{5} + 35410568 T^{6} + 179607028 T^{7} + 5872703627 T^{8} + 28816908881 T^{9} + 823168298384 T^{10} + 3930733809449 T^{11} + 99853059470828 T^{12} + 460024212013485 T^{13} + 10626189131305926 T^{14} + 46732143059635336 T^{15} + 1002391679183032880 T^{16} + 4159160732307544904 T^{17} + 84170044109074239846 T^{18} + \)\(32\!\cdots\!65\)\( T^{19} + \)\(62\!\cdots\!48\)\( T^{20} + \)\(21\!\cdots\!01\)\( T^{21} + \)\(40\!\cdots\!24\)\( T^{22} + \)\(12\!\cdots\!49\)\( T^{23} + \)\(23\!\cdots\!87\)\( T^{24} + \)\(62\!\cdots\!52\)\( T^{25} + \)\(11\!\cdots\!68\)\( T^{26} + \)\(25\!\cdots\!76\)\( T^{27} + \)\(42\!\cdots\!40\)\( T^{28} + \)\(76\!\cdots\!58\)\( T^{29} + \)\(11\!\cdots\!98\)\( T^{30} + \)\(12\!\cdots\!43\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 13 T + 1227 T^{2} - 13857 T^{3} + 731036 T^{4} - 7298054 T^{5} + 283553347 T^{6} - 2535583981 T^{7} + 80777199578 T^{8} - 653711712400 T^{9} + 18035127148077 T^{10} - 133173693213556 T^{11} + 3282443098361722 T^{12} - 22259188527282398 T^{13} + 499356299606160985 T^{14} - 3125596297317945832 T^{15} + 64535473127533893589 T^{16} - \)\(37\!\cdots\!66\)\( T^{17} + \)\(71\!\cdots\!52\)\( T^{18} - \)\(38\!\cdots\!95\)\( T^{19} + \)\(68\!\cdots\!28\)\( T^{20} - \)\(34\!\cdots\!55\)\( T^{21} + \)\(56\!\cdots\!92\)\( T^{22} - \)\(26\!\cdots\!54\)\( T^{23} + \)\(40\!\cdots\!49\)\( T^{24} - \)\(17\!\cdots\!68\)\( T^{25} + \)\(24\!\cdots\!85\)\( T^{26} - \)\(98\!\cdots\!42\)\( T^{27} + \)\(12\!\cdots\!82\)\( T^{28} - \)\(46\!\cdots\!04\)\( T^{29} + \)\(56\!\cdots\!77\)\( T^{30} - \)\(18\!\cdots\!00\)\( T^{31} + \)\(19\!\cdots\!38\)\( T^{32} - \)\(55\!\cdots\!89\)\( T^{33} + \)\(55\!\cdots\!27\)\( T^{34} - \)\(12\!\cdots\!46\)\( T^{35} + \)\(11\!\cdots\!96\)\( T^{36} - \)\(19\!\cdots\!53\)\( T^{37} + \)\(15\!\cdots\!87\)\( T^{38} - \)\(14\!\cdots\!17\)\( T^{39} + \)\(97\!\cdots\!01\)\( T^{40} \))
$97$ (\( 1 + 6 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 42 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - 24 T + 314 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( 1 - 8 T + 30 T^{2} - 776 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 364 T^{2} + 2296 T^{3} + 51862 T^{4} + 222712 T^{5} + 3424876 T^{6} + 7301384 T^{7} + 88529281 T^{8} \))(\( 1 - 3 T + 217 T^{2} + 949 T^{3} + 10747 T^{4} + 244897 T^{5} + 1042459 T^{6} + 8929141 T^{7} + 198050041 T^{8} - 265587843 T^{9} + 8587340257 T^{10} \))(\( 1 + 55 T + 1849 T^{2} + 43681 T^{3} + 811452 T^{4} + 12227790 T^{5} + 154536730 T^{6} + 1648617028 T^{7} + 14990062810 T^{8} + 115051276110 T^{9} + 740590331196 T^{10} + 3867047523361 T^{11} + 15877992135193 T^{12} + 45813460271095 T^{13} + 80798284478113 T^{14} \))(\( 1 - 13 T + 555 T^{2} - 6021 T^{3} + 142804 T^{4} - 1285466 T^{5} + 21777034 T^{6} - 159349292 T^{7} + 2112372298 T^{8} - 12094949594 T^{9} + 130333355092 T^{10} - 533034800901 T^{11} + 4765973842635 T^{12} - 10828636064077 T^{13} + 80798284478113 T^{14} \))(\( 1 + 35 T + 968 T^{2} + 20626 T^{3} + 382128 T^{4} + 6160478 T^{5} + 89500494 T^{6} + 1179846288 T^{7} + 14229403627 T^{8} + 158127626653 T^{9} + 1619442398156 T^{10} + 15338379785341 T^{11} + 133884458726443 T^{12} + 1076813851207824 T^{13} + 7923414382964814 T^{14} + 52902120731762846 T^{15} + 318301926299508912 T^{16} + 1666545415645558738 T^{17} + 7586635719356898248 T^{18} + 26608087052909782595 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 6 T + 456 T^{2} - 3944 T^{3} + 108368 T^{4} - 1175483 T^{5} + 18618490 T^{6} - 212770829 T^{7} + 2555320728 T^{8} - 27177265474 T^{9} + 279700991985 T^{10} - 2636194750978 T^{11} + 24043012729752 T^{12} - 194190190815917 T^{13} + 1648281533005690 T^{14} - 10094272487319131 T^{15} + 90267510230145872 T^{16} - 318668433981677672 T^{17} + 3573869719035894216 T^{18} - 4561386351927391302 T^{19} + 73742412689492826049 T^{20} \))(\( 1 + 11 T + 727 T^{2} + 8119 T^{3} + 252528 T^{4} + 2751124 T^{5} + 56605078 T^{6} + 574477674 T^{7} + 9226377413 T^{8} + 84145091209 T^{9} + 1150431401949 T^{10} + 9286762453998 T^{11} + 111591845989053 T^{12} + 791721163185481 T^{13} + 8420665552654949 T^{14} + 50858095429772394 T^{15} + 486087065060025046 T^{16} + 2291609274088290196 T^{17} + 20403829182688919664 T^{18} + 63632123352746546359 T^{19} + \)\(55\!\cdots\!59\)\( T^{20} + \)\(81\!\cdots\!39\)\( T^{21} + \)\(71\!\cdots\!53\)\( T^{22} \))(\( 1 + 12 T + 796 T^{2} + 7580 T^{3} + 297199 T^{4} + 2298359 T^{5} + 70288656 T^{6} + 447238351 T^{7} + 11967689156 T^{8} + 63828920543 T^{9} + 1579738479959 T^{10} + 7308273286367 T^{11} + 168939726182442 T^{12} + 708902508777599 T^{13} + 14863759357934231 T^{14} + 58254932398741439 T^{15} + 1059490916212176836 T^{16} + 3840587896016596207 T^{17} + 58548482712084785424 T^{18} + \)\(18\!\cdots\!67\)\( T^{19} + \)\(23\!\cdots\!39\)\( T^{20} + \)\(57\!\cdots\!60\)\( T^{21} + \)\(58\!\cdots\!04\)\( T^{22} + \)\(85\!\cdots\!36\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 30 T + 1113 T^{2} - 22870 T^{3} + 505329 T^{4} - 8025669 T^{5} + 133001593 T^{6} - 1736062668 T^{7} + 23652981736 T^{8} - 265217381024 T^{9} + 3155425042003 T^{10} - 31742477150988 T^{11} + 346837094966997 T^{12} - 3257920191910950 T^{13} + 33643198211798709 T^{14} - 298664967513646092 T^{15} + 2879871239360004019 T^{16} - 23479504050757763744 T^{17} + \)\(20\!\cdots\!52\)\( T^{18} - \)\(14\!\cdots\!72\)\( T^{19} + \)\(10\!\cdots\!09\)\( T^{20} - \)\(62\!\cdots\!09\)\( T^{21} + \)\(38\!\cdots\!93\)\( T^{22} - \)\(16\!\cdots\!30\)\( T^{23} + \)\(79\!\cdots\!89\)\( T^{24} - \)\(20\!\cdots\!30\)\( T^{25} + \)\(67\!\cdots\!77\)\( T^{26} \))(\( 1 - 25 T + 998 T^{2} - 18478 T^{3} + 440564 T^{4} - 6808974 T^{5} + 124249438 T^{6} - 1688787414 T^{7} + 25703112526 T^{8} - 313958756704 T^{9} + 4151947080722 T^{10} - 46013431741105 T^{11} + 541103217274109 T^{12} - 5455834895034788 T^{13} + 57822196357889364 T^{14} - 529215984818374436 T^{15} + 5091240171332091581 T^{16} - 41995216787449523665 T^{17} + \)\(36\!\cdots\!82\)\( T^{18} - \)\(26\!\cdots\!28\)\( T^{19} + \)\(21\!\cdots\!54\)\( T^{20} - \)\(13\!\cdots\!82\)\( T^{21} + \)\(97\!\cdots\!18\)\( T^{22} - \)\(51\!\cdots\!58\)\( T^{23} + \)\(32\!\cdots\!36\)\( T^{24} - \)\(13\!\cdots\!34\)\( T^{25} + \)\(69\!\cdots\!18\)\( T^{26} - \)\(16\!\cdots\!25\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 + 30 T + 926 T^{2} + 17818 T^{3} + 357637 T^{4} + 5630907 T^{5} + 91483144 T^{6} + 1261788379 T^{7} + 17841643467 T^{8} + 223742731957 T^{9} + 2856843348275 T^{10} + 33124989986201 T^{11} + 388835507548649 T^{12} + 4209189925697002 T^{13} + 45935998553919015 T^{14} + 465832374979483898 T^{15} + 4752194657058211340 T^{16} + 45185740373009938106 T^{17} + \)\(43\!\cdots\!35\)\( T^{18} + \)\(38\!\cdots\!46\)\( T^{19} + \)\(34\!\cdots\!69\)\( T^{20} + \)\(28\!\cdots\!57\)\( T^{21} + \)\(23\!\cdots\!75\)\( T^{22} + \)\(18\!\cdots\!41\)\( T^{23} + \)\(13\!\cdots\!87\)\( T^{24} + \)\(95\!\cdots\!43\)\( T^{25} + \)\(67\!\cdots\!56\)\( T^{26} + \)\(40\!\cdots\!71\)\( T^{27} + \)\(24\!\cdots\!17\)\( T^{28} + \)\(11\!\cdots\!86\)\( T^{29} + \)\(60\!\cdots\!94\)\( T^{30} + \)\(18\!\cdots\!90\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 35 T + 1878 T^{2} - 49186 T^{3} + 1529353 T^{4} - 32288323 T^{5} + 742439004 T^{6} - 13162301860 T^{7} + 244609704726 T^{8} - 3731903967818 T^{9} + 58541323697864 T^{10} - 780371593286307 T^{11} + 10585401042878535 T^{12} - 124417086367441608 T^{13} + 1479896786950776582 T^{14} - 15407385163006573471 T^{15} + \)\(16\!\cdots\!54\)\( T^{16} - \)\(14\!\cdots\!87\)\( T^{17} + \)\(13\!\cdots\!38\)\( T^{18} - \)\(11\!\cdots\!84\)\( T^{19} + \)\(93\!\cdots\!35\)\( T^{20} - \)\(67\!\cdots\!99\)\( T^{21} + \)\(48\!\cdots\!56\)\( T^{22} - \)\(30\!\cdots\!34\)\( T^{23} + \)\(19\!\cdots\!86\)\( T^{24} - \)\(10\!\cdots\!20\)\( T^{25} + \)\(54\!\cdots\!96\)\( T^{26} - \)\(23\!\cdots\!19\)\( T^{27} + \)\(10\!\cdots\!73\)\( T^{28} - \)\(33\!\cdots\!22\)\( T^{29} + \)\(12\!\cdots\!82\)\( T^{30} - \)\(22\!\cdots\!55\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 9 T + 772 T^{2} + 3956 T^{3} + 295553 T^{4} + 671337 T^{5} + 79467812 T^{6} + 499520 T^{7} + 17138414889 T^{8} - 30145470491 T^{9} + 3144529120192 T^{10} - 9528963923781 T^{11} + 505253771785252 T^{12} - 1941916199657855 T^{13} + 72070436975111872 T^{14} - 308292019346329785 T^{15} + 9183383407813211734 T^{16} - 40631474133499742421 T^{17} + \)\(10\!\cdots\!52\)\( T^{18} - \)\(45\!\cdots\!29\)\( T^{19} + \)\(10\!\cdots\!22\)\( T^{20} - \)\(44\!\cdots\!13\)\( T^{21} + \)\(98\!\cdots\!68\)\( T^{22} - \)\(37\!\cdots\!33\)\( T^{23} + \)\(81\!\cdots\!54\)\( T^{24} - \)\(26\!\cdots\!45\)\( T^{25} + \)\(60\!\cdots\!88\)\( T^{26} - \)\(15\!\cdots\!15\)\( T^{27} + \)\(39\!\cdots\!72\)\( T^{28} - \)\(72\!\cdots\!77\)\( T^{29} + \)\(23\!\cdots\!08\)\( T^{30} - \)\(21\!\cdots\!23\)\( T^{31} + \)\(11\!\cdots\!49\)\( T^{32} + \)\(33\!\cdots\!40\)\( T^{33} + \)\(51\!\cdots\!28\)\( T^{34} + \)\(42\!\cdots\!41\)\( T^{35} + \)\(18\!\cdots\!13\)\( T^{36} + \)\(23\!\cdots\!72\)\( T^{37} + \)\(44\!\cdots\!08\)\( T^{38} + \)\(50\!\cdots\!97\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))
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