Properties

Label 6040.2
Level 6040
Weight 2
Dimension 562462
Nonzero newspaces 54
Sturm bound 4377600

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(4377600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6040))\).

Total New Old
Modular forms 1101600 566038 535562
Cusp forms 1087201 562462 524739
Eisenstein series 14399 3576 10823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6040))\)

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
6040.2.a \(\chi_{6040}(1, \cdot)\) 6040.2.a.a 1 1
6040.2.a.b 1
6040.2.a.c 1
6040.2.a.d 1
6040.2.a.e 1
6040.2.a.f 1
6040.2.a.g 1
6040.2.a.h 1
6040.2.a.i 1
6040.2.a.j 1
6040.2.a.k 2
6040.2.a.l 9
6040.2.a.m 12
6040.2.a.n 13
6040.2.a.o 15
6040.2.a.p 19
6040.2.a.q 23
6040.2.a.r 23
6040.2.a.s 24
6040.2.b \(\chi_{6040}(6039, \cdot)\) None 0 1
6040.2.d \(\chi_{6040}(1209, \cdot)\) n/a 224 1
6040.2.g \(\chi_{6040}(3021, \cdot)\) n/a 600 1
6040.2.i \(\chi_{6040}(1811, \cdot)\) n/a 608 1
6040.2.j \(\chi_{6040}(4229, \cdot)\) n/a 900 1
6040.2.l \(\chi_{6040}(3019, \cdot)\) n/a 908 1
6040.2.o \(\chi_{6040}(4831, \cdot)\) None 0 1
6040.2.q \(\chi_{6040}(2081, \cdot)\) n/a 304 2
6040.2.r \(\chi_{6040}(2717, \cdot)\) n/a 1816 2
6040.2.u \(\chi_{6040}(303, \cdot)\) None 0 2
6040.2.w \(\chi_{6040}(907, \cdot)\) n/a 1800 2
6040.2.x \(\chi_{6040}(2113, \cdot)\) n/a 456 2
6040.2.z \(\chi_{6040}(321, \cdot)\) n/a 608 4
6040.2.ba \(\chi_{6040}(1931, \cdot)\) n/a 1216 2
6040.2.bc \(\chi_{6040}(2901, \cdot)\) n/a 1216 2
6040.2.bf \(\chi_{6040}(1089, \cdot)\) n/a 456 2
6040.2.bh \(\chi_{6040}(119, \cdot)\) None 0 2
6040.2.bj \(\chi_{6040}(2751, \cdot)\) None 0 2
6040.2.bm \(\chi_{6040}(939, \cdot)\) n/a 1816 2
6040.2.bo \(\chi_{6040}(269, \cdot)\) n/a 1816 2
6040.2.bq \(\chi_{6040}(1351, \cdot)\) None 0 4
6040.2.bt \(\chi_{6040}(1899, \cdot)\) n/a 3632 4
6040.2.bv \(\chi_{6040}(1669, \cdot)\) n/a 3632 4
6040.2.bw \(\chi_{6040}(691, \cdot)\) n/a 2432 4
6040.2.by \(\chi_{6040}(461, \cdot)\) n/a 2432 4
6040.2.cb \(\chi_{6040}(1529, \cdot)\) n/a 912 4
6040.2.cd \(\chi_{6040}(2559, \cdot)\) None 0 4
6040.2.ce \(\chi_{6040}(33, \cdot)\) n/a 912 4
6040.2.ch \(\chi_{6040}(787, \cdot)\) n/a 3632 4
6040.2.cj \(\chi_{6040}(183, \cdot)\) None 0 4
6040.2.ck \(\chi_{6040}(637, \cdot)\) n/a 3632 4
6040.2.cm \(\chi_{6040}(1361, \cdot)\) n/a 1216 8
6040.2.co \(\chi_{6040}(993, \cdot)\) n/a 1824 8
6040.2.cp \(\chi_{6040}(763, \cdot)\) n/a 7264 8
6040.2.cr \(\chi_{6040}(623, \cdot)\) None 0 8
6040.2.cu \(\chi_{6040}(1597, \cdot)\) n/a 7264 8
6040.2.cv \(\chi_{6040}(81, \cdot)\) n/a 3040 20
6040.2.cw \(\chi_{6040}(189, \cdot)\) n/a 7264 8
6040.2.cy \(\chi_{6040}(499, \cdot)\) n/a 7264 8
6040.2.db \(\chi_{6040}(751, \cdot)\) None 0 8
6040.2.dd \(\chi_{6040}(519, \cdot)\) None 0 8
6040.2.df \(\chi_{6040}(529, \cdot)\) n/a 1824 8
6040.2.di \(\chi_{6040}(581, \cdot)\) n/a 4864 8
6040.2.dk \(\chi_{6040}(451, \cdot)\) n/a 4864 8
6040.2.dm \(\chi_{6040}(131, \cdot)\) n/a 12160 20
6040.2.dp \(\chi_{6040}(9, \cdot)\) n/a 4560 20
6040.2.dr \(\chi_{6040}(179, \cdot)\) n/a 18160 20
6040.2.dt \(\chi_{6040}(631, \cdot)\) None 0 20
6040.2.dv \(\chi_{6040}(261, \cdot)\) n/a 12160 20
6040.2.dx \(\chi_{6040}(29, \cdot)\) n/a 18160 20
6040.2.dz \(\chi_{6040}(79, \cdot)\) None 0 20
6040.2.eb \(\chi_{6040}(197, \cdot)\) n/a 14528 16
6040.2.ec \(\chi_{6040}(167, \cdot)\) None 0 16
6040.2.ee \(\chi_{6040}(227, \cdot)\) n/a 14528 16
6040.2.eh \(\chi_{6040}(113, \cdot)\) n/a 3648 16
6040.2.ei \(\chi_{6040}(121, \cdot)\) n/a 6080 40
6040.2.el \(\chi_{6040}(127, \cdot)\) None 0 40
6040.2.em \(\chi_{6040}(53, \cdot)\) n/a 36320 40
6040.2.ep \(\chi_{6040}(123, \cdot)\) n/a 36320 40
6040.2.eq \(\chi_{6040}(57, \cdot)\) n/a 9120 40
6040.2.er \(\chi_{6040}(259, \cdot)\) n/a 36320 40
6040.2.et \(\chi_{6040}(49, \cdot)\) n/a 9120 40
6040.2.ew \(\chi_{6040}(51, \cdot)\) n/a 24320 40
6040.2.ey \(\chi_{6040}(199, \cdot)\) None 0 40
6040.2.fa \(\chi_{6040}(69, \cdot)\) n/a 36320 40
6040.2.fc \(\chi_{6040}(21, \cdot)\) n/a 24320 40
6040.2.fe \(\chi_{6040}(71, \cdot)\) None 0 40
6040.2.fg \(\chi_{6040}(47, \cdot)\) None 0 80
6040.2.fh \(\chi_{6040}(13, \cdot)\) n/a 72640 80
6040.2.fk \(\chi_{6040}(43, \cdot)\) n/a 72640 80
6040.2.fl \(\chi_{6040}(233, \cdot)\) n/a 18240 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(755))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1510))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3020))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 + 15 T^{2} - 4 T^{3} + 118 T^{4} - 47 T^{5} + 635 T^{6} - 266 T^{7} + 2527 T^{8} - 967 T^{9} + 7581 T^{10} - 2394 T^{11} + 17145 T^{12} - 3807 T^{13} + 28674 T^{14} - 2916 T^{15} + 32805 T^{16} + 19683 T^{18} \))(\( 1 - 3 T + 18 T^{2} - 45 T^{3} + 164 T^{4} - 362 T^{5} + 1032 T^{6} - 2079 T^{7} + 5019 T^{8} - 9327 T^{9} + 19821 T^{10} - 33914 T^{11} + 65018 T^{12} - 101742 T^{13} + 178389 T^{14} - 251829 T^{15} + 406539 T^{16} - 505197 T^{17} + 752328 T^{18} - 791694 T^{19} + 1076004 T^{20} - 885735 T^{21} + 1062882 T^{22} - 531441 T^{23} + 531441 T^{24} \))(\( 1 + 4 T + 25 T^{2} + 74 T^{3} + 281 T^{4} + 679 T^{5} + 2008 T^{6} + 4212 T^{7} + 10674 T^{8} + 20184 T^{9} + 45823 T^{10} + 79398 T^{11} + 164006 T^{12} + 260647 T^{13} + 492018 T^{14} + 714582 T^{15} + 1237221 T^{16} + 1634904 T^{17} + 2593782 T^{18} + 3070548 T^{19} + 4391496 T^{20} + 4454919 T^{21} + 5530923 T^{22} + 4369626 T^{23} + 4428675 T^{24} + 2125764 T^{25} + 1594323 T^{26} \))(\( 1 - 5 T + 26 T^{2} - 91 T^{3} + 310 T^{4} - 874 T^{5} + 2397 T^{6} - 5834 T^{7} + 13891 T^{8} - 30332 T^{9} + 65131 T^{10} - 130558 T^{11} + 258316 T^{12} - 481397 T^{13} + 886876 T^{14} - 1544842 T^{15} + 2660628 T^{16} - 4332573 T^{17} + 6974532 T^{18} - 10575198 T^{19} + 15826833 T^{20} - 22112028 T^{21} + 30379617 T^{22} - 38276874 T^{23} + 47180151 T^{24} - 51608826 T^{25} + 54915570 T^{26} - 48361131 T^{27} + 41452398 T^{28} - 23914845 T^{29} + 14348907 T^{30} \))(\( 1 + 5 T + 28 T^{2} + 105 T^{3} + 385 T^{4} + 1173 T^{5} + 3401 T^{6} + 8801 T^{7} + 21544 T^{8} + 48297 T^{9} + 102298 T^{10} + 200259 T^{11} + 369639 T^{12} + 629345 T^{13} + 1007640 T^{14} + 1476676 T^{15} + 2050061 T^{16} + 2643230 T^{17} + 3589755 T^{18} + 5417718 T^{19} + 10769265 T^{20} + 23789070 T^{21} + 55351647 T^{22} + 119610756 T^{23} + 244856520 T^{24} + 458792505 T^{25} + 808400493 T^{26} + 1313899299 T^{27} + 2013531534 T^{28} + 2851889553 T^{29} + 3816454968 T^{30} + 4677212241 T^{31} + 5422292523 T^{32} + 5610422637 T^{33} + 5524329195 T^{34} + 4519905705 T^{35} + 3615924564 T^{36} + 1937102445 T^{37} + 1162261467 T^{38} \))
$5$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{12} \))(\( ( 1 + T )^{13} \))(\( ( 1 - T )^{15} \))(\( ( 1 - T )^{19} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + T + 10 T^{2} + 7 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 48 T^{2} + 87 T^{3} + 1101 T^{4} + 1789 T^{5} + 15787 T^{6} + 22602 T^{7} + 155425 T^{8} + 191188 T^{9} + 1087975 T^{10} + 1107498 T^{11} + 5414941 T^{12} + 4295389 T^{13} + 18504507 T^{14} + 10235463 T^{15} + 39530064 T^{16} + 11529602 T^{17} + 40353607 T^{18} \))(\( 1 - 5 T + 53 T^{2} - 237 T^{3} + 1423 T^{4} - 5728 T^{5} + 25292 T^{6} - 92019 T^{7} + 329208 T^{8} - 1082072 T^{9} + 3293391 T^{10} - 9729941 T^{11} + 25909424 T^{12} - 68109587 T^{13} + 161376159 T^{14} - 371150696 T^{15} + 790428408 T^{16} - 1546563333 T^{17} + 2975578508 T^{18} - 4717254304 T^{19} + 8203311823 T^{20} - 9563804859 T^{21} + 14971188197 T^{22} - 9886633715 T^{23} + 13841287201 T^{24} \))(\( 1 + 46 T^{2} + 3 T^{3} + 1095 T^{4} + 241 T^{5} + 17737 T^{6} + 7118 T^{7} + 217636 T^{8} + 121206 T^{9} + 2147799 T^{10} + 1391743 T^{11} + 17692018 T^{12} + 11431698 T^{13} + 123844126 T^{14} + 68195407 T^{15} + 736695057 T^{16} + 291015606 T^{17} + 3657808252 T^{18} + 837425582 T^{19} + 14607182191 T^{20} + 1389317041 T^{21} + 44187199665 T^{22} + 847425747 T^{23} + 90957030178 T^{24} + 96889010407 T^{26} \))(\( 1 - 7 T + 84 T^{2} - 466 T^{3} + 3301 T^{4} - 15364 T^{5} + 82145 T^{6} - 331367 T^{7} + 1462068 T^{8} - 5213280 T^{9} + 19821780 T^{10} - 63223382 T^{11} + 212116643 T^{12} - 609156101 T^{13} + 1827630012 T^{14} - 4735701986 T^{15} + 12793410084 T^{16} - 29848648949 T^{17} + 72756008549 T^{18} - 151799340182 T^{19} + 333144656460 T^{20} - 613337178720 T^{21} + 1204075866924 T^{22} - 1910264812967 T^{23} + 3314847047015 T^{24} - 4339949725636 T^{25} + 6527155578643 T^{26} - 6450039835666 T^{27} + 8138676874188 T^{28} - 4747561509943 T^{29} + 4747561509943 T^{30} \))(\( 1 + 8 T + 87 T^{2} + 543 T^{3} + 3565 T^{4} + 18384 T^{5} + 93619 T^{6} + 415955 T^{7} + 1798485 T^{8} + 7097291 T^{9} + 27221401 T^{10} + 97470412 T^{11} + 339791807 T^{12} + 1119899050 T^{13} + 3599730515 T^{14} + 11020265087 T^{15} + 32941393184 T^{16} + 94173390003 T^{17} + 263041879420 T^{18} + 703999382598 T^{19} + 1841293155940 T^{20} + 4614496110147 T^{21} + 11298897862112 T^{22} + 26459656473887 T^{23} + 60500670765605 T^{24} + 131755003333450 T^{25} + 279833164112201 T^{26} + 561897528568012 T^{27} + 1098481717943407 T^{28} + 2004809042450459 T^{29} + 3556192487384355 T^{30} + 5757352617691955 T^{31} + 9070652265292933 T^{32} + 12468452971256016 T^{33} + 16925056782946795 T^{34} + 18045481299293343 T^{35} + 20238854716887009 T^{36} + 13027308783283592 T^{37} + 11398895185373143 T^{38} \))
$11$ (\( 1 + T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( ( 1 - T + 11 T^{2} )^{2} \))(\( 1 + 6 T + 79 T^{2} + 412 T^{3} + 2914 T^{4} + 13101 T^{5} + 66735 T^{6} + 255668 T^{7} + 1043569 T^{8} + 3375305 T^{9} + 11479259 T^{10} + 30935828 T^{11} + 88824285 T^{12} + 191811741 T^{13} + 469302614 T^{14} + 729883132 T^{15} + 1539486509 T^{16} + 1286153286 T^{17} + 2357947691 T^{18} \))(\( 1 - 10 T + 141 T^{2} - 1004 T^{3} + 8314 T^{4} - 46853 T^{5} + 289036 T^{6} - 1355948 T^{7} + 6788446 T^{8} - 27225939 T^{9} + 115182463 T^{10} - 400077789 T^{11} + 1459053450 T^{12} - 4400855679 T^{13} + 13937078023 T^{14} - 36237724809 T^{15} + 99389637886 T^{16} - 218376781348 T^{17} + 512044905196 T^{18} - 913032422863 T^{19} + 1782179736634 T^{20} - 2367379481764 T^{21} + 3657176868741 T^{22} - 2853116706110 T^{23} + 3138428376721 T^{24} \))(\( 1 + 14 T + 194 T^{2} + 1724 T^{3} + 14469 T^{4} + 97075 T^{5} + 614158 T^{6} + 3344067 T^{7} + 17227512 T^{8} + 78940743 T^{9} + 343284525 T^{10} + 1349212866 T^{11} + 5042010643 T^{12} + 17144099998 T^{13} + 55462117073 T^{14} + 163254756786 T^{15} + 456911702775 T^{16} + 1155771418263 T^{17} + 2774508035112 T^{18} + 5924218678587 T^{19} + 11968201967018 T^{20} + 20808888373075 T^{21} + 34117145141079 T^{22} + 44716120012124 T^{23} + 55350464098534 T^{24} + 43937997274094 T^{25} + 34522712143931 T^{26} \))(\( 1 - 7 T + 112 T^{2} - 727 T^{3} + 6434 T^{4} - 37328 T^{5} + 244109 T^{6} - 1258208 T^{7} + 6751611 T^{8} - 31034182 T^{9} + 143445213 T^{10} - 591173358 T^{11} + 2413073976 T^{12} - 8953166139 T^{13} + 32697622592 T^{14} - 109396144614 T^{15} + 359673848512 T^{16} - 1083333102819 T^{17} + 3211801462056 T^{18} - 8655369134478 T^{19} + 23101994998863 T^{20} - 54978946498102 T^{21} + 131569798082481 T^{22} - 269708058945248 T^{23} + 575596252902319 T^{24} - 968192185506128 T^{25} + 1835695288711174 T^{26} - 2281637429876167 T^{27} + 3866543760120272 T^{28} - 2658248835082687 T^{29} + 4177248169415651 T^{30} \))(\( 1 + 18 T + 247 T^{2} + 2454 T^{3} + 21181 T^{4} + 156509 T^{5} + 1054756 T^{6} + 6437200 T^{7} + 36707246 T^{8} + 194628472 T^{9} + 977384365 T^{10} + 4629917152 T^{11} + 20942197301 T^{12} + 90115730775 T^{13} + 372151751391 T^{14} + 1469604097856 T^{15} + 5586871636156 T^{16} + 20369777201669 T^{17} + 71617697359258 T^{18} + 241820759643478 T^{19} + 787794670951838 T^{20} + 2464743041401949 T^{21} + 7436126147723636 T^{22} + 21516473596709696 T^{23} + 59935411713271941 T^{24} + 159645514127489775 T^{25} + 408104179920325471 T^{26} + 992463859825426912 T^{27} + 2304621206671251215 T^{28} + 5048161317707839672 T^{29} + 10473005679788947306 T^{30} + 20202691146628421200 T^{31} + 36413037770084085836 T^{32} + 59434266704279465669 T^{33} + 88478293476392903831 T^{34} + \)\(11\!\cdots\!94\)\( T^{35} + \)\(12\!\cdots\!37\)\( T^{36} + \)\(10\!\cdots\!58\)\( T^{37} + 61159090448414546291 T^{38} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( 1 + 9 T + 99 T^{2} + 567 T^{3} + 3445 T^{4} + 13766 T^{5} + 57760 T^{6} + 170408 T^{7} + 605954 T^{8} + 1754767 T^{9} + 7877402 T^{10} + 28798952 T^{11} + 126898720 T^{12} + 393170726 T^{13} + 1279104385 T^{14} + 2736800703 T^{15} + 6212103183 T^{16} + 7341576489 T^{17} + 10604499373 T^{18} \))(\( 1 - 11 T + 155 T^{2} - 1205 T^{3} + 10213 T^{4} - 62872 T^{5} + 403455 T^{6} - 2074409 T^{7} + 10926383 T^{8} - 48212982 T^{9} + 216272033 T^{10} - 829548582 T^{11} + 3224799856 T^{12} - 10784131566 T^{13} + 36549973577 T^{14} - 105923921454 T^{15} + 312068424863 T^{16} - 770213540837 T^{17} + 1947400225095 T^{18} - 3945124760824 T^{19} + 8331057853573 T^{20} - 12778421744465 T^{21} + 21368066236595 T^{22} - 19713764334407 T^{23} + 23298085122481 T^{24} \))(\( 1 - 5 T + 120 T^{2} - 556 T^{3} + 7162 T^{4} - 30241 T^{5} + 277628 T^{6} - 1063383 T^{7} + 7751242 T^{8} - 26846327 T^{9} + 164127574 T^{10} - 511602512 T^{11} + 2707150189 T^{12} - 7537299196 T^{13} + 35192952457 T^{14} - 86460824528 T^{15} + 360588280078 T^{16} - 766757945447 T^{17} + 2877981895906 T^{18} - 5132746634847 T^{19} + 17420745277676 T^{20} - 24668512733761 T^{21} + 75949424509426 T^{22} - 76649321468044 T^{23} + 215059247284440 T^{24} - 116490425612405 T^{25} + 302875106592253 T^{26} \))(\( 1 - 2 T + 103 T^{2} - 229 T^{3} + 5480 T^{4} - 12104 T^{5} + 197291 T^{6} - 411125 T^{7} + 5332914 T^{8} - 10236830 T^{9} + 114781094 T^{10} - 201050431 T^{11} + 2044232320 T^{12} - 3274982462 T^{13} + 30900140413 T^{14} - 45718983610 T^{15} + 401701825369 T^{16} - 553472036078 T^{17} + 4491178407040 T^{18} - 5742201359791 T^{19} + 42617416734542 T^{20} - 49411223175470 T^{21} + 334632444788538 T^{22} - 335367292671125 T^{23} + 2092172285798543 T^{24} - 1668639185340296 T^{25} + 9821038959322760 T^{26} - 5335261493048149 T^{27} + 31196135979002059 T^{28} - 7874752771398578 T^{29} + 51185893014090757 T^{30} \))(\( 1 - 5 T + 103 T^{2} - 415 T^{3} + 5372 T^{4} - 20237 T^{5} + 199251 T^{6} - 742795 T^{7} + 5808966 T^{8} - 21876562 T^{9} + 140058255 T^{10} - 538343803 T^{11} + 2894272436 T^{12} - 11321669092 T^{13} + 52360879452 T^{14} - 205835429828 T^{15} + 841516816285 T^{16} - 3263227299131 T^{17} + 12138647794523 T^{18} - 45310613127736 T^{19} + 157802421328799 T^{20} - 551485413553139 T^{21} + 1848812445378145 T^{22} - 5878865711317508 T^{23} + 19441228014371436 T^{24} - 54647534268287428 T^{25} + 181611303152977412 T^{26} - 439143578567071963 T^{27} + 1485247677330974115 T^{28} - 3015869844161143138 T^{29} + 10410598795507535742 T^{30} - 17305701138553274395 T^{31} + 60348167863613002503 T^{32} - 79680685917396511493 T^{33} + \)\(27\!\cdots\!04\)\( T^{34} - \)\(27\!\cdots\!15\)\( T^{35} + \)\(89\!\cdots\!99\)\( T^{36} - \)\(56\!\cdots\!45\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( 1 + 2 T + 111 T^{2} + 263 T^{3} + 5989 T^{4} + 14562 T^{5} + 205296 T^{6} + 468556 T^{7} + 4877847 T^{8} + 9765154 T^{9} + 82923399 T^{10} + 135412684 T^{11} + 1008619248 T^{12} + 1216232802 T^{13} + 8503523573 T^{14} + 6348180647 T^{15} + 45547592703 T^{16} + 13951514882 T^{17} + 118587876497 T^{18} \))(\( 1 + 4 T + 118 T^{2} + 527 T^{3} + 7449 T^{4} + 32803 T^{5} + 320129 T^{6} + 1321661 T^{7} + 10143121 T^{8} + 38481525 T^{9} + 247165225 T^{10} + 847543192 T^{11} + 4728920234 T^{12} + 14408234264 T^{13} + 71430750025 T^{14} + 189059732325 T^{15} + 847163609041 T^{16} + 1876569622477 T^{17} + 7727135826401 T^{18} + 13460339490419 T^{19} + 51962417178009 T^{20} + 62495810913919 T^{21} + 237887280252982 T^{22} + 137087585230532 T^{23} + 582622237229761 T^{24} \))(\( 1 + 8 T + 180 T^{2} + 1129 T^{3} + 14594 T^{4} + 75971 T^{5} + 733874 T^{6} + 3285476 T^{7} + 26175553 T^{8} + 103059983 T^{9} + 709247720 T^{10} + 2486361391 T^{11} + 15114105422 T^{12} + 47380188116 T^{13} + 256939792174 T^{14} + 718558441999 T^{15} + 3484534048360 T^{16} + 8607672840143 T^{17} + 37165542155921 T^{18} + 79303403647844 T^{19} + 301136883309202 T^{20} + 529955268550211 T^{21} + 1730671469597218 T^{22} + 2276057113606921 T^{23} + 6168941335373940 T^{24} + 4660977897838088 T^{25} + 9904578032905937 T^{26} \))(\( 1 + 3 T + 135 T^{2} + 191 T^{3} + 8257 T^{4} - 428 T^{5} + 326534 T^{6} - 435554 T^{7} + 10120515 T^{8} - 22367840 T^{9} + 267372044 T^{10} - 710136995 T^{11} + 6037518112 T^{12} - 17239853495 T^{13} + 116919420242 T^{14} - 330700272052 T^{15} + 1987630144114 T^{16} - 4982317660055 T^{17} + 29662326484256 T^{18} - 59311351959395 T^{19} + 379630068277708 T^{20} - 539905281380960 T^{21} + 4152838695176595 T^{22} - 3038319056457314 T^{23} + 38722973664071398 T^{24} - 862845389392172 T^{25} + 282983047812125681 T^{26} + 111280847310884351 T^{27} + 1337118034442301495 T^{28} + 505133479678202787 T^{29} + 2862423051509815793 T^{30} \))(\( 1 + 4 T + 129 T^{2} + 555 T^{3} + 8680 T^{4} + 38720 T^{5} + 403087 T^{6} + 1830895 T^{7} + 14546768 T^{8} + 66293924 T^{9} + 437116547 T^{10} + 1967353042 T^{11} + 11423251269 T^{12} + 49921515276 T^{13} + 266126037332 T^{14} + 1112655834529 T^{15} + 5581247893596 T^{16} + 22133710651532 T^{17} + 105465619387167 T^{18} + 396183904285542 T^{19} + 1792915529581839 T^{20} + 6396642378292748 T^{21} + 27420670901237148 T^{22} + 92930127955696609 T^{23} + 377860916988101524 T^{24} + 1204984019559004044 T^{25} + 4687401767067026037 T^{26} + 13723777621805485522 T^{27} + 51836723090431095859 T^{28} + \)\(13\!\cdots\!76\)\( T^{29} + \)\(49\!\cdots\!44\)\( T^{30} + \)\(10\!\cdots\!95\)\( T^{31} + \)\(39\!\cdots\!19\)\( T^{32} + \)\(65\!\cdots\!80\)\( T^{33} + \)\(24\!\cdots\!40\)\( T^{34} + \)\(27\!\cdots\!55\)\( T^{35} + \)\(10\!\cdots\!33\)\( T^{36} + \)\(56\!\cdots\!36\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))
$19$ (\( 1 + 7 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 7 T + 46 T^{2} - 133 T^{3} + 361 T^{4} \))(\( 1 + 10 T + 178 T^{2} + 1313 T^{3} + 13385 T^{4} + 78486 T^{5} + 582240 T^{6} + 2797447 T^{7} + 16391825 T^{8} + 65033423 T^{9} + 311444675 T^{10} + 1009878367 T^{11} + 3993584160 T^{12} + 10228374006 T^{13} + 33142585115 T^{14} + 61771241753 T^{15} + 159109169542 T^{16} + 169835630410 T^{17} + 322687697779 T^{18} \))(\( 1 - 5 T + 171 T^{2} - 851 T^{3} + 14393 T^{4} - 68203 T^{5} + 778818 T^{6} - 3416354 T^{7} + 29913432 T^{8} - 119049473 T^{9} + 854481504 T^{10} - 3032211964 T^{11} + 18557844314 T^{12} - 57612027316 T^{13} + 308467822944 T^{14} - 816560335307 T^{15} + 3898348371672 T^{16} - 8459230723046 T^{17} + 36640178948658 T^{18} - 60964734215017 T^{19} + 244444422849113 T^{20} - 274607230809929 T^{21} + 1048412330083971 T^{22} - 582451294491095 T^{23} + 2213314919066161 T^{24} \))(\( 1 - 16 T + 285 T^{2} - 3085 T^{3} + 33317 T^{4} - 279515 T^{5} + 2286436 T^{6} - 15803987 T^{7} + 105870036 T^{8} - 622402185 T^{9} + 3540840453 T^{10} - 18006321491 T^{11} + 88584668848 T^{12} - 392583388926 T^{13} + 1683108708112 T^{14} - 6500282058251 T^{15} + 24286624667127 T^{16} - 81112075151385 T^{17} + 262144690269564 T^{18} - 743512491727547 T^{19} + 2043780523432204 T^{20} - 4747160623405115 T^{21} + 10750986026902943 T^{22} - 18914339405316085 T^{23} + 33199723785992415 T^{24} - 35413038705058576 T^{25} + 42052983462257059 T^{26} \))(\( 1 - 8 T + 183 T^{2} - 1323 T^{3} + 16330 T^{4} - 107863 T^{5} + 951855 T^{6} - 5757418 T^{7} + 40839169 T^{8} - 225904422 T^{9} + 1373989109 T^{10} - 6939982240 T^{11} + 37586571994 T^{12} - 173413555983 T^{13} + 853052093451 T^{14} - 3601342087998 T^{15} + 16207989775569 T^{16} - 62602293709863 T^{17} + 257806297306846 T^{18} - 904425425499040 T^{19} + 3402133058805791 T^{20} - 10627872554785782 T^{21} + 36504979013344891 T^{22} - 97781471556388138 T^{23} + 307151898569430045 T^{24} - 661315199765189263 T^{25} + 1902285927807916270 T^{26} - 2928215637924531003 T^{27} + 7695695973593041797 T^{28} - 6392053486263072968 T^{29} + 15181127029874798299 T^{30} \))(\( 1 + 27 T + 535 T^{2} + 7831 T^{3} + 97628 T^{4} + 1046136 T^{5} + 10062922 T^{6} + 87462094 T^{7} + 700547907 T^{8} + 5194046040 T^{9} + 36042332073 T^{10} + 234789044331 T^{11} + 1445917508080 T^{12} + 8435292346429 T^{13} + 46841230345474 T^{14} + 247896735734358 T^{15} + 1254523249513997 T^{16} + 6073818712825768 T^{17} + 28195688928536073 T^{18} + 125457254289174004 T^{19} + 535718089642185387 T^{20} + 2192648555330102248 T^{21} + 8604774968416505423 T^{22} + 32306150497637268918 T^{23} + \)\(11\!\cdots\!26\)\( T^{24} + \)\(39\!\cdots\!49\)\( T^{25} + \)\(12\!\cdots\!20\)\( T^{26} + \)\(39\!\cdots\!71\)\( T^{27} + \)\(11\!\cdots\!67\)\( T^{28} + \)\(31\!\cdots\!40\)\( T^{29} + \)\(81\!\cdots\!33\)\( T^{30} + \)\(19\!\cdots\!34\)\( T^{31} + \)\(42\!\cdots\!98\)\( T^{32} + \)\(83\!\cdots\!56\)\( T^{33} + \)\(14\!\cdots\!72\)\( T^{34} + \)\(22\!\cdots\!11\)\( T^{35} + \)\(29\!\cdots\!65\)\( T^{36} + \)\(28\!\cdots\!07\)\( T^{37} + \)\(19\!\cdots\!79\)\( T^{38} \))
$23$ (\( 1 + 9 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 29 T^{2} + 529 T^{4} \))(\( 1 + 6 T + 105 T^{2} + 601 T^{3} + 5819 T^{4} + 31388 T^{5} + 229739 T^{6} + 1112785 T^{7} + 6942596 T^{8} + 29389157 T^{9} + 159679708 T^{10} + 588663265 T^{11} + 2795234413 T^{12} + 8783649308 T^{13} + 37453079917 T^{14} + 88969569289 T^{15} + 357506671935 T^{16} + 469865911686 T^{17} + 1801152661463 T^{18} \))(\( 1 - 18 T + 367 T^{2} - 4553 T^{3} + 54891 T^{4} - 522034 T^{5} + 4669378 T^{6} - 35885385 T^{7} + 257511339 T^{8} - 1645483248 T^{9} + 9810041903 T^{10} - 52889965641 T^{11} + 266146274438 T^{12} - 1216469209743 T^{13} + 5189512166687 T^{14} - 20020594678416 T^{15} + 72062230617099 T^{16} - 230970646547055 T^{17} + 691235523307042 T^{18} - 1777434647399198 T^{19} + 4298568293059371 T^{20} - 8200648067641039 T^{21} + 15203529615409183 T^{22} - 17150575642450686 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 4 T + 208 T^{2} + 577 T^{3} + 19338 T^{4} + 28323 T^{5} + 1059011 T^{6} - 82927 T^{7} + 38203077 T^{8} - 77496151 T^{9} + 993251086 T^{10} - 4331036769 T^{11} + 21779891225 T^{12} - 128863329834 T^{13} + 500937498175 T^{14} - 2291118450801 T^{15} + 12084885963362 T^{16} - 21686600391991 T^{17} + 245888107227411 T^{18} - 12276172167103 T^{19} + 3605747601452917 T^{20} + 2218002036113763 T^{21} + 34830690167371494 T^{22} + 23903096970275473 T^{23} + 198184429646096816 T^{24} + 87658497728081284 T^{25} + 504036361936467383 T^{26} \))(\( 1 - 15 T + 314 T^{2} - 3218 T^{3} + 39572 T^{4} - 314597 T^{5} + 2922471 T^{6} - 19356629 T^{7} + 150439325 T^{8} - 868735490 T^{9} + 5953482271 T^{10} - 30806961835 T^{11} + 191340028196 T^{12} - 902290213496 T^{13} + 5156303178192 T^{14} - 22416930858984 T^{15} + 118594973098416 T^{16} - 477311522939384 T^{17} + 2328034123060732 T^{18} - 8621051006868235 T^{19} + 38318653940574953 T^{20} - 128604030568000610 T^{21} + 512219641989503275 T^{22} - 1515836688708777749 T^{23} + 5263816419698435073 T^{24} - 13032656148280334453 T^{25} + 37704587740169919244 T^{26} - 70521261422241392978 T^{27} + \)\(15\!\cdots\!62\)\( T^{28} - \)\(17\!\cdots\!35\)\( T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 + 25 T + 483 T^{2} + 6657 T^{3} + 78929 T^{4} + 788614 T^{5} + 7089783 T^{6} + 56746078 T^{7} + 418193193 T^{8} + 2811738201 T^{9} + 17621204996 T^{10} + 101906218735 T^{11} + 553061386246 T^{12} + 2784525495916 T^{13} + 13243571803035 T^{14} + 58857507541326 T^{15} + 252296052575820 T^{16} + 1045218587025787 T^{17} + 4488879747048825 T^{18} + 20343701113662066 T^{19} + 103244234182122975 T^{20} + 552920632536641323 T^{21} + 3069686071690001940 T^{22} + 16470743767872209166 T^{23} + 85240170669461701005 T^{24} + \)\(41\!\cdots\!24\)\( T^{25} + \)\(18\!\cdots\!62\)\( T^{26} + \)\(79\!\cdots\!35\)\( T^{27} + \)\(31\!\cdots\!48\)\( T^{28} + \)\(11\!\cdots\!49\)\( T^{29} + \)\(39\!\cdots\!11\)\( T^{30} + \)\(12\!\cdots\!38\)\( T^{31} + \)\(35\!\cdots\!89\)\( T^{32} + \)\(91\!\cdots\!26\)\( T^{33} + \)\(21\!\cdots\!03\)\( T^{34} + \)\(40\!\cdots\!77\)\( T^{35} + \)\(68\!\cdots\!49\)\( T^{36} + \)\(81\!\cdots\!25\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))
$29$ (\( 1 - 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 + 6 T + 196 T^{2} + 769 T^{3} + 15986 T^{4} + 36539 T^{5} + 754774 T^{6} + 762460 T^{7} + 25518646 T^{8} + 11770109 T^{9} + 740040734 T^{10} + 641228860 T^{11} + 18408183086 T^{12} + 25843340459 T^{13} + 327891227914 T^{14} + 457419133849 T^{15} + 3380975756564 T^{16} + 3001478477766 T^{17} + 14507145975869 T^{18} \))(\( 1 - 16 T + 332 T^{2} - 4127 T^{3} + 50410 T^{4} - 505365 T^{5} + 4664711 T^{6} - 38760038 T^{7} + 294317772 T^{8} - 2067630380 T^{9} + 13372644504 T^{10} - 80514659399 T^{11} + 449227882818 T^{12} - 2334925122571 T^{13} + 11246394027864 T^{14} - 50427437337820 T^{15} + 208165368097932 T^{16} - 795012914663662 T^{17} + 2774678888525231 T^{18} - 8717483740897785 T^{19} + 25217421677364010 T^{20} - 59870991442411363 T^{21} + 139674801455666732 T^{22} - 195208156251293264 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 6 T + 167 T^{2} + 1119 T^{3} + 14556 T^{4} + 95554 T^{5} + 867323 T^{6} + 5155775 T^{7} + 38673431 T^{8} + 204819528 T^{9} + 1375646200 T^{10} + 6728549019 T^{11} + 42400243934 T^{12} + 200835971850 T^{13} + 1229607074086 T^{14} + 5658709724979 T^{15} + 33550635171800 T^{16} + 144864960583368 T^{17} + 793236505582219 T^{18} + 3066775207828775 T^{19} + 14961214469950807 T^{20} + 47800545744075394 T^{21} + 211166016824749164 T^{22} + 470771394062924919 T^{23} + 2037485130872873443 T^{24} + 2122888699232814246 T^{25} + 10260628712958602189 T^{26} \))(\( 1 - 5 T + 285 T^{2} - 1297 T^{3} + 39420 T^{4} - 164025 T^{5} + 3529105 T^{6} - 13467799 T^{7} + 230168464 T^{8} - 807618258 T^{9} + 11678884490 T^{10} - 37767346607 T^{11} + 480799802498 T^{12} - 1435318103556 T^{13} + 16499278352309 T^{14} - 45424943311210 T^{15} + 478479072216961 T^{16} - 1207102525090596 T^{17} + 11726226383123722 T^{18} - 26712126675545567 T^{19} + 239547339928179010 T^{20} - 480390174323794818 T^{21} + 3970377534232519376 T^{22} - 6737218140229742839 T^{23} + 51197241399169167245 T^{24} - 69006503942065469025 T^{25} + \)\(48\!\cdots\!80\)\( T^{26} - \)\(45\!\cdots\!77\)\( T^{27} + \)\(29\!\cdots\!65\)\( T^{28} - \)\(14\!\cdots\!05\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 + 35 T + 756 T^{2} + 12298 T^{3} + 167884 T^{4} + 2006813 T^{5} + 21660828 T^{6} + 214507339 T^{7} + 1974741700 T^{8} + 17035008433 T^{9} + 138669684363 T^{10} + 1070096187532 T^{11} + 7860580603761 T^{12} + 55116418019285 T^{13} + 369831555544579 T^{14} + 2378774068521476 T^{15} + 14689079687025666 T^{16} + 87161365931198394 T^{17} + 497392064222251313 T^{18} + 2730581369496168420 T^{19} + 14424369862445288077 T^{20} + 73302708748137849354 T^{21} + \)\(35\!\cdots\!74\)\( T^{22} + \)\(16\!\cdots\!56\)\( T^{23} + \)\(75\!\cdots\!71\)\( T^{24} + \)\(32\!\cdots\!85\)\( T^{25} + \)\(13\!\cdots\!49\)\( T^{26} + \)\(53\!\cdots\!52\)\( T^{27} + \)\(20\!\cdots\!47\)\( T^{28} + \)\(71\!\cdots\!33\)\( T^{29} + \)\(24\!\cdots\!00\)\( T^{30} + \)\(75\!\cdots\!99\)\( T^{31} + \)\(22\!\cdots\!92\)\( T^{32} + \)\(59\!\cdots\!53\)\( T^{33} + \)\(14\!\cdots\!16\)\( T^{34} + \)\(30\!\cdots\!58\)\( T^{35} + \)\(54\!\cdots\!04\)\( T^{36} + \)\(73\!\cdots\!35\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))
$31$ (\( 1 + 5 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 49 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 9 T + 234 T^{2} - 1732 T^{3} + 25480 T^{4} - 158678 T^{5} + 1691399 T^{6} - 8921024 T^{7} + 75364190 T^{8} - 334756311 T^{9} + 2336289890 T^{10} - 8573104064 T^{11} + 50388467609 T^{12} - 146542465238 T^{13} + 729470767480 T^{14} - 1537156375492 T^{15} + 6437951701974 T^{16} - 7676019336969 T^{17} + 26439622160671 T^{18} \))(\( 1 + T + 240 T^{2} + 34 T^{3} + 28362 T^{4} - 12186 T^{5} + 2206766 T^{6} - 1678769 T^{7} + 126135114 T^{8} - 113523695 T^{9} + 5564527804 T^{10} - 5007076406 T^{11} + 193626966370 T^{12} - 155219368586 T^{13} + 5347511219644 T^{14} - 3381984397745 T^{15} + 116488426616394 T^{16} - 48061731195119 T^{17} + 1958512948105646 T^{18} - 335268715556646 T^{19} + 24189695603901642 T^{20} + 898947153462814 T^{21} + 196710788875392240 T^{22} + 25408476896404831 T^{23} + 787662783788549761 T^{24} \))(\( 1 - 11 T + 238 T^{2} - 2146 T^{3} + 27423 T^{4} - 213083 T^{5} + 2107619 T^{6} - 14608062 T^{7} + 122405479 T^{8} - 768021726 T^{9} + 5651157323 T^{10} - 32220230074 T^{11} + 212385028049 T^{12} - 1101680720195 T^{13} + 6583935869519 T^{14} - 30963641101114 T^{15} + 168353627809493 T^{16} - 709284192417246 T^{17} + 3504364941518329 T^{18} - 12964708797276222 T^{19} + 57986108240011709 T^{20} - 181736580931040603 T^{21} + 725053758512080833 T^{22} - 1758922303860798946 T^{23} + 6047217501344349778 T^{24} - 8664290621674047371 T^{25} + 24417546297445042591 T^{26} \))(\( 1 - 27 T + 654 T^{2} - 10624 T^{3} + 156540 T^{4} - 1886930 T^{5} + 21019985 T^{6} - 204884254 T^{7} + 1871310206 T^{8} - 15442049933 T^{9} + 120601145202 T^{10} - 866328731732 T^{11} + 5931292477740 T^{12} - 37735985874125 T^{13} + 229812434587298 T^{14} - 1306856099382354 T^{15} + 7124185472206238 T^{16} - 36264282425034125 T^{17} + 176699134204352340 T^{18} - 800072776657868372 T^{19} + 3452708396760983502 T^{20} - 13704876157723303373 T^{21} + 51484635579653916866 T^{22} - \)\(17\!\cdots\!14\)\( T^{23} + \)\(55\!\cdots\!35\)\( T^{24} - \)\(15\!\cdots\!30\)\( T^{25} + \)\(39\!\cdots\!40\)\( T^{26} - \)\(83\!\cdots\!64\)\( T^{27} + \)\(15\!\cdots\!14\)\( T^{28} - \)\(20\!\cdots\!67\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 + 26 T + 505 T^{2} + 7507 T^{3} + 97022 T^{4} + 1106201 T^{5} + 11561741 T^{6} + 111535761 T^{7} + 1009177797 T^{8} + 8601913136 T^{9} + 69613352337 T^{10} + 536555748661 T^{11} + 3956081439850 T^{12} + 27961546276091 T^{13} + 189939104670201 T^{14} + 1241754799579918 T^{15} + 7824148963012716 T^{16} + 47555622396051041 T^{17} + 279011364426555775 T^{18} + 1580753440138227764 T^{19} + 8649352297223229025 T^{20} + 45700953122605050401 T^{21} + \)\(23\!\cdots\!56\)\( T^{22} + \)\(11\!\cdots\!78\)\( T^{23} + \)\(54\!\cdots\!51\)\( T^{24} + \)\(24\!\cdots\!71\)\( T^{25} + \)\(10\!\cdots\!50\)\( T^{26} + \)\(45\!\cdots\!01\)\( T^{27} + \)\(18\!\cdots\!27\)\( T^{28} + \)\(70\!\cdots\!36\)\( T^{29} + \)\(25\!\cdots\!07\)\( T^{30} + \)\(87\!\cdots\!21\)\( T^{31} + \)\(28\!\cdots\!31\)\( T^{32} + \)\(83\!\cdots\!21\)\( T^{33} + \)\(22\!\cdots\!22\)\( T^{34} + \)\(54\!\cdots\!67\)\( T^{35} + \)\(11\!\cdots\!55\)\( T^{36} + \)\(18\!\cdots\!66\)\( T^{37} + \)\(21\!\cdots\!71\)\( T^{38} \))
$37$ (\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 6 T^{2} + 1369 T^{4} \))(\( 1 + 12 T + 276 T^{2} + 2684 T^{3} + 35909 T^{4} + 288167 T^{5} + 2851203 T^{6} + 19150173 T^{7} + 151750959 T^{8} + 855268604 T^{9} + 5614785483 T^{10} + 26216586837 T^{11} + 144421985559 T^{12} + 540071352887 T^{13} + 2490072151913 T^{14} + 6886409681756 T^{15} + 26201198088708 T^{16} + 42149753447052 T^{17} + 129961739795077 T^{18} \))(\( 1 - 2 T + 255 T^{2} - 590 T^{3} + 32982 T^{4} - 86555 T^{5} + 2859105 T^{6} - 8108526 T^{7} + 184958463 T^{8} - 535864322 T^{9} + 9410474584 T^{10} - 26222253969 T^{11} + 386206617076 T^{12} - 970223396853 T^{13} + 12882939705496 T^{14} - 27143135502266 T^{15} + 346641937974543 T^{16} - 562277278277382 T^{17} + 7335681204603945 T^{18} - 8216828625246815 T^{19} + 115848597349222422 T^{20} - 76677426479095430 T^{21} + 1226189014966551495 T^{22} - 355835243558920826 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 6 T + 288 T^{2} - 1580 T^{3} + 41221 T^{4} - 207761 T^{5} + 3882367 T^{6} - 18076309 T^{7} + 270389640 T^{8} - 1165896004 T^{9} + 14821805019 T^{10} - 59072018711 T^{11} + 662208710800 T^{12} - 2419941319722 T^{13} + 24501722299600 T^{14} - 80869593615359 T^{15} + 750768889627407 T^{16} - 2185076820752644 T^{17} + 18749887569405480 T^{18} - 46378863378544381 T^{19} + 368560387029213811 T^{20} - 729756243826080881 T^{21} + 5357152876092869017 T^{22} - 7597563308420201420 T^{23} + 51240275072484598944 T^{24} - 39497712035040211686 T^{25} + \)\(24\!\cdots\!97\)\( T^{26} \))(\( 1 + 4 T + 342 T^{2} + 1132 T^{3} + 57624 T^{4} + 163275 T^{5} + 6417097 T^{6} + 15994583 T^{7} + 530753443 T^{8} + 1186930711 T^{9} + 34605400036 T^{10} + 70331963896 T^{11} + 1839417388070 T^{12} + 3420682929346 T^{13} + 81222928474307 T^{14} + 138446947060522 T^{15} + 3005248353549359 T^{16} + 4682914930274674 T^{17} + 93172008957909710 T^{18} + 131813423787291256 T^{19} + 2399675372064182452 T^{20} + 3045339470865846799 T^{21} + 50385420638792718919 T^{22} + 56180644161534109943 T^{23} + \)\(83\!\cdots\!69\)\( T^{24} + \)\(78\!\cdots\!75\)\( T^{25} + \)\(10\!\cdots\!12\)\( T^{26} + \)\(74\!\cdots\!92\)\( T^{27} + \)\(83\!\cdots\!74\)\( T^{28} + \)\(36\!\cdots\!56\)\( T^{29} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 + 10 T + 270 T^{2} + 2394 T^{3} + 37842 T^{4} + 314825 T^{5} + 3792127 T^{6} + 30123787 T^{7} + 303631628 T^{8} + 2309430713 T^{9} + 20449708618 T^{10} + 148909147614 T^{11} + 1194431191170 T^{12} + 8309492269427 T^{13} + 61540830059600 T^{14} + 408036887621621 T^{15} + 2825032416976248 T^{16} + 17821276585784641 T^{17} + 116274960721861956 T^{18} + 696464521225933360 T^{19} + 4302173546708892372 T^{20} + 24397327645939173529 T^{21} + \)\(14\!\cdots\!44\)\( T^{22} + \)\(76\!\cdots\!81\)\( T^{23} + \)\(42\!\cdots\!00\)\( T^{24} + \)\(21\!\cdots\!43\)\( T^{25} + \)\(11\!\cdots\!10\)\( T^{26} + \)\(52\!\cdots\!94\)\( T^{27} + \)\(26\!\cdots\!86\)\( T^{28} + \)\(11\!\cdots\!37\)\( T^{29} + \)\(54\!\cdots\!64\)\( T^{30} + \)\(19\!\cdots\!47\)\( T^{31} + \)\(92\!\cdots\!19\)\( T^{32} + \)\(28\!\cdots\!25\)\( T^{33} + \)\(12\!\cdots\!06\)\( T^{34} + \)\(29\!\cdots\!54\)\( T^{35} + \)\(12\!\cdots\!90\)\( T^{36} + \)\(16\!\cdots\!90\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))
$41$ (\( 1 - 8 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 10 T + 90 T^{2} + 410 T^{3} + 1681 T^{4} \))(\( 1 + 20 T + 408 T^{2} + 5382 T^{3} + 66752 T^{4} + 662951 T^{5} + 6182298 T^{6} + 49271005 T^{7} + 370828921 T^{8} + 2440211572 T^{9} + 15203985761 T^{10} + 82824559405 T^{11} + 426090160458 T^{12} + 1873341080711 T^{13} + 7733633129152 T^{14} + 25565061025062 T^{15} + 79459743743448 T^{16} + 159698504582420 T^{17} + 327381934393961 T^{18} \))(\( 1 - 4 T + 267 T^{2} - 700 T^{3} + 33375 T^{4} - 56845 T^{5} + 2758533 T^{6} - 3467588 T^{7} + 176379019 T^{8} - 202640590 T^{9} + 9313440944 T^{10} - 10497664985 T^{11} + 414700967562 T^{12} - 430404264385 T^{13} + 15655894226864 T^{14} - 13966192103390 T^{15} + 498404953108459 T^{16} - 401741572313188 T^{17} + 13103319302238453 T^{18} - 11070806698765445 T^{19} + 266496879521913375 T^{20} - 229167354075772700 T^{21} + 3583850035810691067 T^{22} - 2201316126864993764 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 18 T + 402 T^{2} + 5278 T^{3} + 72254 T^{4} + 766107 T^{5} + 8137956 T^{6} + 73727947 T^{7} + 661285826 T^{8} + 5286002164 T^{9} + 41629266411 T^{10} + 298362914039 T^{11} + 2101215187046 T^{12} + 13579450259166 T^{13} + 86149822668886 T^{14} + 501548058499559 T^{15} + 2869130670312531 T^{16} + 14936978760946804 T^{17} + 76614063575507026 T^{18} + 350215433724923227 T^{19} + 1584901711655527236 T^{20} + 6117307112506201947 T^{21} + 23654654287701258094 T^{22} + 70844795838984372478 T^{23} + \)\(22\!\cdots\!82\)\( T^{24} + \)\(40\!\cdots\!58\)\( T^{25} + \)\(92\!\cdots\!21\)\( T^{26} \))(\( 1 - 20 T + 592 T^{2} - 8658 T^{3} + 151271 T^{4} - 1784615 T^{5} + 23476382 T^{6} - 234996301 T^{7} + 2544497378 T^{8} - 22236081499 T^{9} + 206969899761 T^{10} - 1605433624426 T^{11} + 13154830002152 T^{12} - 91404805790618 T^{13} + 668146613064223 T^{14} - 4173760166461870 T^{15} + 27394011135633143 T^{16} - 153651478534028858 T^{17} + 906644038578317992 T^{18} - 4536571723991638186 T^{19} + 23978746307660267961 T^{20} - \)\(10\!\cdots\!59\)\( T^{21} + \)\(49\!\cdots\!18\)\( T^{22} - \)\(18\!\cdots\!21\)\( T^{23} + \)\(76\!\cdots\!02\)\( T^{24} - \)\(23\!\cdots\!15\)\( T^{25} + \)\(83\!\cdots\!11\)\( T^{26} - \)\(19\!\cdots\!98\)\( T^{27} + \)\(54\!\cdots\!32\)\( T^{28} - \)\(75\!\cdots\!20\)\( T^{29} + \)\(15\!\cdots\!01\)\( T^{30} \))(\( 1 + 14 T + 424 T^{2} + 4604 T^{3} + 81835 T^{4} + 748985 T^{5} + 10179182 T^{6} + 82890787 T^{7} + 951974493 T^{8} + 7136986289 T^{9} + 72632117051 T^{10} + 511503471494 T^{11} + 4731577791669 T^{12} + 31643979398651 T^{13} + 270180953787955 T^{14} + 1723542871284813 T^{15} + 13724585484282873 T^{16} + 83506658146740621 T^{17} + 625184036814135869 T^{18} + 3617718144565975516 T^{19} + 25632545509379570629 T^{20} + \)\(14\!\cdots\!01\)\( T^{21} + \)\(94\!\cdots\!33\)\( T^{22} + \)\(48\!\cdots\!93\)\( T^{23} + \)\(31\!\cdots\!55\)\( T^{24} + \)\(15\!\cdots\!91\)\( T^{25} + \)\(92\!\cdots\!89\)\( T^{26} + \)\(40\!\cdots\!74\)\( T^{27} + \)\(23\!\cdots\!11\)\( T^{28} + \)\(95\!\cdots\!89\)\( T^{29} + \)\(52\!\cdots\!13\)\( T^{30} + \)\(18\!\cdots\!47\)\( T^{31} + \)\(94\!\cdots\!22\)\( T^{32} + \)\(28\!\cdots\!85\)\( T^{33} + \)\(12\!\cdots\!35\)\( T^{34} + \)\(29\!\cdots\!64\)\( T^{35} + \)\(11\!\cdots\!44\)\( T^{36} + \)\(15\!\cdots\!94\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))
$43$ (\( 1 - 6 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( ( 1 + 2 T + 43 T^{2} )^{2} \))(\( 1 - T + 142 T^{2} - 10 T^{3} + 12667 T^{4} + 5978 T^{5} + 866152 T^{6} + 495413 T^{7} + 46190614 T^{8} + 27052868 T^{9} + 1986196402 T^{10} + 916018637 T^{11} + 68865147064 T^{12} + 20437592378 T^{13} + 1862155947481 T^{14} - 63213630490 T^{15} + 38598242777194 T^{16} - 11688200277601 T^{17} + 502592611936843 T^{18} \))(\( 1 - 7 T + 367 T^{2} - 2305 T^{3} + 62018 T^{4} - 351425 T^{5} + 6465474 T^{6} - 33306226 T^{7} + 474553429 T^{8} - 2245965849 T^{9} + 26849890287 T^{10} - 117795194122 T^{11} + 1253499992400 T^{12} - 5065193347246 T^{13} + 49645447140663 T^{14} - 178570006756443 T^{15} + 1622403737618629 T^{16} - 4896296426466118 T^{17} + 40870608437870226 T^{18} - 95523855408277475 T^{19} + 724878804816258818 T^{20} - 1158475970514423115 T^{21} + 7931414008975319383 T^{22} - 6505056176298558949 T^{23} + 39959630797262576401 T^{24} \))(\( 1 - 7 T + 332 T^{2} - 1690 T^{3} + 52911 T^{4} - 206356 T^{5} + 5602742 T^{6} - 17329187 T^{7} + 446353627 T^{8} - 1134442447 T^{9} + 28351878132 T^{10} - 61688069451 T^{11} + 1474448251091 T^{12} - 2861935589388 T^{13} + 63401274796913 T^{14} - 114061240414899 T^{15} + 2254172774640924 T^{16} - 3878432972246047 T^{17} + 65617751732672761 T^{18} - 109544082371011163 T^{19} + 1522929548830855394 T^{20} - 2411930256484631956 T^{21} + 26592677690190299973 T^{22} - 36523405109450380810 T^{23} + \)\(30\!\cdots\!24\)\( T^{24} - \)\(27\!\cdots\!07\)\( T^{25} + \)\(17\!\cdots\!43\)\( T^{26} \))(\( 1 - 25 T + 702 T^{2} - 11576 T^{3} + 192762 T^{4} - 2416005 T^{5} + 30015940 T^{6} - 306283387 T^{7} + 3101351742 T^{8} - 26905822427 T^{9} + 233779343434 T^{10} - 1784699215484 T^{11} + 13835908280982 T^{12} - 95879420155335 T^{13} + 684132155182855 T^{14} - 4407555954419778 T^{15} + 29417682672862765 T^{16} - 177281047867214415 T^{17} + 1100051559696035874 T^{18} - 6101531462595914684 T^{19} + 34367537283794613262 T^{20} - \)\(17\!\cdots\!23\)\( T^{21} + \)\(84\!\cdots\!94\)\( T^{22} - \)\(35\!\cdots\!87\)\( T^{23} + \)\(15\!\cdots\!20\)\( T^{24} - \)\(52\!\cdots\!45\)\( T^{25} + \)\(17\!\cdots\!34\)\( T^{26} - \)\(46\!\cdots\!76\)\( T^{27} + \)\(12\!\cdots\!86\)\( T^{28} - \)\(18\!\cdots\!25\)\( T^{29} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 + 21 T + 596 T^{2} + 9234 T^{3} + 161038 T^{4} + 2053315 T^{5} + 27773232 T^{6} + 306654655 T^{7} + 3499525009 T^{8} + 34439534170 T^{9} + 345679890922 T^{10} + 3086573198150 T^{11} + 27903332082978 T^{12} + 228654724550094 T^{13} + 1889108123082193 T^{14} + 14311447324461569 T^{15} + 109051257094336819 T^{16} + 767083715981138168 T^{17} + 5420618127619235826 T^{18} + 35470483556462799472 T^{19} + \)\(23\!\cdots\!18\)\( T^{20} + \)\(14\!\cdots\!32\)\( T^{21} + \)\(86\!\cdots\!33\)\( T^{22} + \)\(48\!\cdots\!69\)\( T^{23} + \)\(27\!\cdots\!99\)\( T^{24} + \)\(14\!\cdots\!06\)\( T^{25} + \)\(75\!\cdots\!46\)\( T^{26} + \)\(36\!\cdots\!50\)\( T^{27} + \)\(17\!\cdots\!46\)\( T^{28} + \)\(74\!\cdots\!30\)\( T^{29} + \)\(32\!\cdots\!63\)\( T^{30} + \)\(12\!\cdots\!55\)\( T^{31} + \)\(47\!\cdots\!76\)\( T^{32} + \)\(15\!\cdots\!35\)\( T^{33} + \)\(51\!\cdots\!66\)\( T^{34} + \)\(12\!\cdots\!34\)\( T^{35} + \)\(35\!\cdots\!28\)\( T^{36} + \)\(53\!\cdots\!29\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))
$47$ (\( 1 + 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 86 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 22 T + 376 T^{2} - 4404 T^{3} + 42260 T^{4} - 310347 T^{5} + 1850858 T^{6} - 7701577 T^{7} + 22600745 T^{8} - 51499192 T^{9} + 1062235015 T^{10} - 17012783593 T^{11} + 192161630134 T^{12} - 1514394359307 T^{13} + 9692119995820 T^{14} - 47471664308916 T^{15} + 190490293294088 T^{16} - 523848306558742 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 373 T^{2} - 54 T^{3} + 68901 T^{4} - 17235 T^{5} + 8327671 T^{6} - 2584696 T^{7} + 732655165 T^{8} - 242912206 T^{9} + 49368235556 T^{10} - 15844207299 T^{11} + 2610053872218 T^{12} - 744677743053 T^{13} + 109054432343204 T^{14} - 25219873963538 T^{15} + 3575123488202365 T^{16} - 592787122212872 T^{17} + 89765758898068759 T^{18} - 8731649481179805 T^{19} + 1640621462281994661 T^{20} - 60433045547549418 T^{21} + 19619476323964608277 T^{22} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 22 T + 597 T^{2} + 9204 T^{3} + 145292 T^{4} + 1749919 T^{5} + 20438727 T^{6} + 204362410 T^{7} + 1940934728 T^{8} + 16806052097 T^{9} + 137188101256 T^{10} + 1062343723182 T^{11} + 7745163593679 T^{12} + 54715625823788 T^{13} + 364022688902913 T^{14} + 2346717284509038 T^{15} + 14243280236701688 T^{16} + 82008173102741057 T^{17} + 445143688779703096 T^{18} + 2202866422543382890 T^{19} + 10354731651031370601 T^{20} + 41667822943862147359 T^{21} + \)\(16\!\cdots\!64\)\( T^{22} + \)\(48\!\cdots\!96\)\( T^{23} + \)\(14\!\cdots\!91\)\( T^{24} + \)\(25\!\cdots\!02\)\( T^{25} + \)\(54\!\cdots\!27\)\( T^{26} \))(\( 1 - 35 T + 1058 T^{2} - 22303 T^{3} + 416091 T^{4} - 6511973 T^{5} + 92434535 T^{6} - 1167735175 T^{7} + 13596093140 T^{8} - 144682157195 T^{9} + 1433468206674 T^{10} - 13160580788645 T^{11} + 113197625639101 T^{12} - 908815291751341 T^{13} + 6858913899062018 T^{14} - 48473135287908458 T^{15} + 322368953255914846 T^{16} - 2007572979478712269 T^{17} + 11752517086728383123 T^{18} - 64219436023316022245 T^{19} + \)\(32\!\cdots\!18\)\( T^{20} - \)\(15\!\cdots\!55\)\( T^{21} + \)\(68\!\cdots\!20\)\( T^{22} - \)\(27\!\cdots\!75\)\( T^{23} + \)\(10\!\cdots\!45\)\( T^{24} - \)\(34\!\cdots\!77\)\( T^{25} + \)\(10\!\cdots\!73\)\( T^{26} - \)\(25\!\cdots\!23\)\( T^{27} + \)\(57\!\cdots\!66\)\( T^{28} - \)\(89\!\cdots\!15\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 + 40 T + 1054 T^{2} + 20442 T^{3} + 330523 T^{4} + 4599591 T^{5} + 57356270 T^{6} + 649908779 T^{7} + 6822561735 T^{8} + 66872497541 T^{9} + 619557355221 T^{10} + 5455180703414 T^{11} + 46061513183161 T^{12} + 374366454288919 T^{13} + 2947923948738331 T^{14} + 22533311972141893 T^{15} + 167907295819012305 T^{16} + 1219811438775488341 T^{17} + 8661349157140592161 T^{18} + 60044945349966815104 T^{19} + \)\(40\!\cdots\!67\)\( T^{20} + \)\(26\!\cdots\!69\)\( T^{21} + \)\(17\!\cdots\!15\)\( T^{22} + \)\(10\!\cdots\!33\)\( T^{23} + \)\(67\!\cdots\!17\)\( T^{24} + \)\(40\!\cdots\!51\)\( T^{25} + \)\(23\!\cdots\!43\)\( T^{26} + \)\(12\!\cdots\!54\)\( T^{27} + \)\(69\!\cdots\!07\)\( T^{28} + \)\(35\!\cdots\!09\)\( T^{29} + \)\(16\!\cdots\!05\)\( T^{30} + \)\(75\!\cdots\!39\)\( T^{31} + \)\(31\!\cdots\!90\)\( T^{32} + \)\(11\!\cdots\!79\)\( T^{33} + \)\(39\!\cdots\!89\)\( T^{34} + \)\(11\!\cdots\!82\)\( T^{35} + \)\(28\!\cdots\!98\)\( T^{36} + \)\(50\!\cdots\!60\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))
$53$ (\( 1 + 14 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 7 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( 1 + 35 T + 850 T^{2} + 14180 T^{3} + 194080 T^{4} + 2153766 T^{5} + 21034560 T^{6} + 179691819 T^{7} + 1435774373 T^{8} + 10623299708 T^{9} + 76096041769 T^{10} + 504754319571 T^{11} + 3131562189120 T^{12} + 16994249701446 T^{13} + 81163381281440 T^{14} + 314290640809220 T^{15} + 998504468861450 T^{16} + 2179089164397635 T^{17} + 3299763591802133 T^{18} \))(\( 1 - 39 T + 1073 T^{2} - 21235 T^{3} + 352653 T^{4} - 4948457 T^{5} + 61879929 T^{6} - 691394072 T^{7} + 7085505731 T^{8} - 66533059143 T^{9} + 580845739822 T^{10} - 4696033701050 T^{11} + 35475983531998 T^{12} - 248889786155650 T^{13} + 1631595683159998 T^{14} - 9905242246032411 T^{15} + 55908048345846611 T^{16} - 289137884797317496 T^{17} + 1371529092992879841 T^{18} - 5813007562904381509 T^{19} + 21956066602637690733 T^{20} - 70070479871918294255 T^{21} + \)\(18\!\cdots\!77\)\( T^{22} - \)\(36\!\cdots\!83\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 17 T + 517 T^{2} + 6573 T^{3} + 118122 T^{4} + 1226674 T^{5} + 16797017 T^{6} + 150152470 T^{7} + 1725931736 T^{8} + 13711431986 T^{9} + 138404681578 T^{10} + 992387726269 T^{11} + 8972206200805 T^{12} + 58256637673334 T^{13} + 475526928642665 T^{14} + 2787617123089621 T^{15} + 20605273779287906 T^{16} + 108189793568325266 T^{17} + 721776873220865848 T^{18} + 3328033569491338630 T^{19} + 19731642985931466229 T^{20} + 76372343475665843314 T^{21} + \)\(38\!\cdots\!26\)\( T^{22} + \)\(11\!\cdots\!77\)\( T^{23} + \)\(47\!\cdots\!49\)\( T^{24} + \)\(83\!\cdots\!97\)\( T^{25} + \)\(26\!\cdots\!73\)\( T^{26} \))(\( 1 + 2 T + 501 T^{2} + 1065 T^{3} + 126368 T^{4} + 275499 T^{5} + 21172086 T^{6} + 46100521 T^{7} + 2625273049 T^{8} + 5584221641 T^{9} + 254534369865 T^{10} + 518392662039 T^{11} + 19899651890494 T^{12} + 38051626661586 T^{13} + 1276049033124980 T^{14} + 2244275628406830 T^{15} + 67630598755623940 T^{16} + 106887019292395074 T^{17} + 2962600474501075238 T^{18} + 4090367450358150759 T^{19} + \)\(10\!\cdots\!45\)\( T^{20} + \)\(12\!\cdots\!89\)\( T^{21} + \)\(30\!\cdots\!13\)\( T^{22} + \)\(28\!\cdots\!81\)\( T^{23} + \)\(69\!\cdots\!38\)\( T^{24} + \)\(48\!\cdots\!51\)\( T^{25} + \)\(11\!\cdots\!96\)\( T^{26} + \)\(52\!\cdots\!65\)\( T^{27} + \)\(13\!\cdots\!73\)\( T^{28} + \)\(27\!\cdots\!38\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 + 3 T + 412 T^{2} + 998 T^{3} + 88593 T^{4} + 177385 T^{5} + 13348140 T^{6} + 22498941 T^{7} + 1580929971 T^{8} + 2273397458 T^{9} + 155879855657 T^{10} + 193226190074 T^{11} + 13213544307947 T^{12} + 14274004331766 T^{13} + 982162404430577 T^{14} + 940719453256547 T^{15} + 64825708012701211 T^{16} + 56418963351739284 T^{17} + 3827617461797003727 T^{18} + 3112679846710590048 T^{19} + \)\(20\!\cdots\!31\)\( T^{20} + \)\(15\!\cdots\!56\)\( T^{21} + \)\(96\!\cdots\!47\)\( T^{22} + \)\(74\!\cdots\!07\)\( T^{23} + \)\(41\!\cdots\!61\)\( T^{24} + \)\(31\!\cdots\!14\)\( T^{25} + \)\(15\!\cdots\!39\)\( T^{26} + \)\(12\!\cdots\!14\)\( T^{27} + \)\(51\!\cdots\!81\)\( T^{28} + \)\(39\!\cdots\!42\)\( T^{29} + \)\(14\!\cdots\!87\)\( T^{30} + \)\(11\!\cdots\!81\)\( T^{31} + \)\(34\!\cdots\!20\)\( T^{32} + \)\(24\!\cdots\!65\)\( T^{33} + \)\(64\!\cdots\!01\)\( T^{34} + \)\(38\!\cdots\!58\)\( T^{35} + \)\(84\!\cdots\!56\)\( T^{36} + \)\(32\!\cdots\!67\)\( T^{37} + \)\(57\!\cdots\!17\)\( T^{38} \))
$59$ (\( 1 - T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 13 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( ( 1 + 9 T + 59 T^{2} )^{2} \))(\( 1 - 14 T + 498 T^{2} - 5447 T^{3} + 108700 T^{4} - 970433 T^{5} + 14022556 T^{6} - 104378350 T^{7} + 1196918896 T^{8} - 7458610785 T^{9} + 70618214864 T^{10} - 363341036350 T^{11} + 2879938528724 T^{12} - 11759086987313 T^{13} + 77712271301300 T^{14} - 229757366742527 T^{15} + 1239348439439862 T^{16} - 2055626126460494 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 4 T + 350 T^{2} + 1535 T^{3} + 57100 T^{4} + 225195 T^{5} + 5493801 T^{6} + 15560780 T^{7} + 319966674 T^{8} + 270969040 T^{9} + 10950635520 T^{10} - 35171673695 T^{11} + 353469201160 T^{12} - 2075128748005 T^{13} + 38119162245120 T^{14} + 55651350466160 T^{15} + 3877151696827314 T^{16} + 11124779733393220 T^{17} + 231731457897459441 T^{18} + 560431871123814705 T^{19} + 8384017987206729100 T^{20} + 13297698581635331365 T^{21} + \)\(17\!\cdots\!50\)\( T^{22} + \)\(12\!\cdots\!36\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 6 T + 531 T^{2} + 3011 T^{3} + 137862 T^{4} + 739334 T^{5} + 23234635 T^{6} + 117265119 T^{7} + 2840117773 T^{8} + 13365969432 T^{9} + 266069574110 T^{10} + 1152143341551 T^{11} + 19658171978356 T^{12} + 76948369277422 T^{13} + 1159832146723004 T^{14} + 4010610971939031 T^{15} + 54645103061137690 T^{16} + 161960276722508952 T^{17} + 2030469207939466127 T^{18} + 4946305296895368279 T^{19} + 57822908891977506065 T^{20} + \)\(10\!\cdots\!14\)\( T^{21} + \)\(11\!\cdots\!18\)\( T^{22} + \)\(15\!\cdots\!11\)\( T^{23} + \)\(16\!\cdots\!29\)\( T^{24} + \)\(10\!\cdots\!86\)\( T^{25} + \)\(10\!\cdots\!79\)\( T^{26} \))(\( 1 - 39 T + 1305 T^{2} - 30215 T^{3} + 619400 T^{4} - 10570103 T^{5} + 163941581 T^{6} - 2249674639 T^{7} + 28551056406 T^{8} - 330015630310 T^{9} + 3570603828708 T^{10} - 35769095599899 T^{11} + 338219711313728 T^{12} - 2990021950651696 T^{13} + 25078988874765213 T^{14} - 197593260006048326 T^{15} + 1479660343611147567 T^{16} - 10408266410218553776 T^{17} + 69463226089902142912 T^{18} - \)\(43\!\cdots\!39\)\( T^{19} + \)\(25\!\cdots\!92\)\( T^{20} - \)\(13\!\cdots\!10\)\( T^{21} + \)\(71\!\cdots\!14\)\( T^{22} - \)\(33\!\cdots\!19\)\( T^{23} + \)\(14\!\cdots\!59\)\( T^{24} - \)\(54\!\cdots\!03\)\( T^{25} + \)\(18\!\cdots\!00\)\( T^{26} - \)\(53\!\cdots\!15\)\( T^{27} + \)\(13\!\cdots\!95\)\( T^{28} - \)\(24\!\cdots\!79\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 + 28 T + 834 T^{2} + 16479 T^{3} + 311813 T^{4} + 4943073 T^{5} + 74128844 T^{6} + 1002325477 T^{7} + 12868359737 T^{8} + 153615164976 T^{9} + 1751527999988 T^{10} + 18854002002405 T^{11} + 194823653348045 T^{12} + 1916799758931661 T^{13} + 18167671021569848 T^{14} + 164792443459516498 T^{15} + 1443189299739530571 T^{16} + 12132068388706314585 T^{17} + 98584033478702479197 T^{18} + \)\(77\!\cdots\!48\)\( T^{19} + \)\(58\!\cdots\!23\)\( T^{20} + \)\(42\!\cdots\!85\)\( T^{21} + \)\(29\!\cdots\!09\)\( T^{22} + \)\(19\!\cdots\!78\)\( T^{23} + \)\(12\!\cdots\!52\)\( T^{24} + \)\(80\!\cdots\!01\)\( T^{25} + \)\(48\!\cdots\!55\)\( T^{26} + \)\(27\!\cdots\!05\)\( T^{27} + \)\(15\!\cdots\!32\)\( T^{28} + \)\(78\!\cdots\!76\)\( T^{29} + \)\(38\!\cdots\!83\)\( T^{30} + \)\(17\!\cdots\!37\)\( T^{31} + \)\(77\!\cdots\!76\)\( T^{32} + \)\(30\!\cdots\!53\)\( T^{33} + \)\(11\!\cdots\!87\)\( T^{34} + \)\(35\!\cdots\!39\)\( T^{35} + \)\(10\!\cdots\!46\)\( T^{36} + \)\(21\!\cdots\!88\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))
$61$ (\( 1 + 14 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 10 T + 130 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 22 T + 620 T^{2} + 9359 T^{3} + 152725 T^{4} + 1760123 T^{5} + 21079971 T^{6} + 195959042 T^{7} + 1876678719 T^{8} + 14447579032 T^{9} + 114477401859 T^{10} + 729163595282 T^{11} + 4784752897551 T^{12} + 24370383198443 T^{13} + 128990970070225 T^{14} + 482179183644599 T^{15} + 1948500558333020 T^{16} + 4217560885940182 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 32 T + 995 T^{2} + 20277 T^{3} + 380678 T^{4} + 5818630 T^{5} + 81958011 T^{6} + 1008758892 T^{7} + 11507197045 T^{8} + 118259200130 T^{9} + 1131558630826 T^{10} + 9889032493271 T^{11} + 80655507146600 T^{12} + 603230982089531 T^{13} + 4210529665303546 T^{14} + 26842591504707530 T^{15} + 159326820640739845 T^{16} + 851994028784058492 T^{17} + 4222507408602955971 T^{18} + 18286457747956871230 T^{19} + 72978756497178936518 T^{20} + \)\(23\!\cdots\!57\)\( T^{21} + \)\(70\!\cdots\!95\)\( T^{22} + \)\(13\!\cdots\!52\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 10 T + 561 T^{2} - 5233 T^{3} + 154029 T^{4} - 1339188 T^{5} + 27415743 T^{6} - 221150773 T^{7} + 3527520185 T^{8} - 26196554633 T^{9} + 346113595797 T^{10} - 2341761498458 T^{11} + 26617840240960 T^{12} - 161858915327202 T^{13} + 1623688254698560 T^{14} - 8713694535762218 T^{15} + 78561210087598857 T^{16} - 362713330196331353 T^{17} + 2979330499953835685 T^{18} - 11393770615184531053 T^{19} + 86160629907442878603 T^{20} - \)\(25\!\cdots\!28\)\( T^{21} + \)\(18\!\cdots\!89\)\( T^{22} - \)\(37\!\cdots\!33\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} - \)\(26\!\cdots\!10\)\( T^{25} + \)\(16\!\cdots\!81\)\( T^{26} \))(\( 1 - 23 T + 786 T^{2} - 14322 T^{3} + 283157 T^{4} - 4266020 T^{5} + 63232257 T^{6} - 811733173 T^{7} + 9932480960 T^{8} - 111072676284 T^{9} + 1176017440650 T^{10} - 11644534827070 T^{11} + 109405782823559 T^{12} - 970259556868769 T^{13} + 8194703922341442 T^{14} - 65532501113010326 T^{15} + 499876939262827962 T^{16} - 3610335811108689449 T^{17} + 24833033991074245379 T^{18} - \)\(16\!\cdots\!70\)\( T^{19} + \)\(99\!\cdots\!50\)\( T^{20} - \)\(57\!\cdots\!24\)\( T^{21} + \)\(31\!\cdots\!60\)\( T^{22} - \)\(15\!\cdots\!13\)\( T^{23} + \)\(73\!\cdots\!37\)\( T^{24} - \)\(30\!\cdots\!20\)\( T^{25} + \)\(12\!\cdots\!77\)\( T^{26} - \)\(38\!\cdots\!62\)\( T^{27} + \)\(12\!\cdots\!66\)\( T^{28} - \)\(22\!\cdots\!43\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 + 46 T + 1446 T^{2} + 33221 T^{3} + 645076 T^{4} + 10758279 T^{5} + 162008665 T^{6} + 2216232209 T^{7} + 28251487284 T^{8} + 336372180939 T^{9} + 3798545625234 T^{10} + 40686985743326 T^{11} + 417543179461438 T^{12} + 4100061559925217 T^{13} + 38797876798529420 T^{14} + 353056458691331983 T^{15} + 3106272555322987178 T^{16} + 26354879086383658111 T^{17} + \)\(21\!\cdots\!62\)\( T^{18} + \)\(17\!\cdots\!34\)\( T^{19} + \)\(13\!\cdots\!82\)\( T^{20} + \)\(98\!\cdots\!31\)\( T^{21} + \)\(70\!\cdots\!18\)\( T^{22} + \)\(48\!\cdots\!03\)\( T^{23} + \)\(32\!\cdots\!20\)\( T^{24} + \)\(21\!\cdots\!37\)\( T^{25} + \)\(13\!\cdots\!98\)\( T^{26} + \)\(77\!\cdots\!06\)\( T^{27} + \)\(44\!\cdots\!94\)\( T^{28} + \)\(23\!\cdots\!39\)\( T^{29} + \)\(12\!\cdots\!24\)\( T^{30} + \)\(58\!\cdots\!89\)\( T^{31} + \)\(26\!\cdots\!65\)\( T^{32} + \)\(10\!\cdots\!39\)\( T^{33} + \)\(38\!\cdots\!76\)\( T^{34} + \)\(12\!\cdots\!81\)\( T^{35} + \)\(32\!\cdots\!66\)\( T^{36} + \)\(62\!\cdots\!26\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))
$67$ (\( 1 - 13 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 423 T^{2} - 1756 T^{3} + 85338 T^{4} - 363041 T^{5} + 10913597 T^{6} - 45397750 T^{7} + 987881219 T^{8} - 3719759597 T^{9} + 66188041673 T^{10} - 203790499750 T^{11} + 3282406174511 T^{12} - 7315683118961 T^{13} + 115216976381166 T^{14} - 158844919088764 T^{15} + 2563681009051629 T^{16} - 1624270710226564 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 4 T + 495 T^{2} - 2334 T^{3} + 120862 T^{4} - 613667 T^{5} + 19567446 T^{6} - 100204094 T^{7} + 2349488220 T^{8} - 11605195795 T^{9} + 219970063029 T^{10} - 1011683317879 T^{11} + 16437292090748 T^{12} - 67782782297893 T^{13} + 987445612937181 T^{14} - 3490413502891585 T^{15} + 47344821409294620 T^{16} - 135288063133588058 T^{17} + 1770039508339270374 T^{18} - 3719258708703749441 T^{19} + 49078151644850744542 T^{20} - 63500051280952406298 T^{21} + \)\(90\!\cdots\!55\)\( T^{22} - \)\(48\!\cdots\!32\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 12 T + 665 T^{2} - 7140 T^{3} + 208013 T^{4} - 2021955 T^{5} + 41130040 T^{6} - 364569506 T^{7} + 5807596282 T^{8} - 47005474760 T^{9} + 623398964827 T^{10} - 4584842194264 T^{11} + 52519403082702 T^{12} - 347271203945123 T^{13} + 3518800006541034 T^{14} - 20581356610051096 T^{15} + 187495342858263001 T^{16} - 947213009551205960 T^{17} + 7840981551648052174 T^{18} - 32978367700911538514 T^{19} + \)\(24\!\cdots\!20\)\( T^{20} - \)\(82\!\cdots\!55\)\( T^{21} + \)\(56\!\cdots\!11\)\( T^{22} - \)\(13\!\cdots\!60\)\( T^{23} + \)\(81\!\cdots\!95\)\( T^{24} - \)\(98\!\cdots\!32\)\( T^{25} + \)\(54\!\cdots\!87\)\( T^{26} \))(\( 1 - 32 T + 991 T^{2} - 21236 T^{3} + 416924 T^{4} - 6930159 T^{5} + 106468485 T^{6} - 1471208004 T^{7} + 19000635277 T^{8} - 226536817371 T^{9} + 2544073950885 T^{10} - 26726471566662 T^{11} + 265769342627684 T^{12} - 2489210260894379 T^{13} + 22129061901794521 T^{14} - 185837808364801502 T^{15} + 1482647147420232907 T^{16} - 11174064861154867331 T^{17} + 79933584796730122892 T^{18} - \)\(53\!\cdots\!02\)\( T^{19} + \)\(34\!\cdots\!95\)\( T^{20} - \)\(20\!\cdots\!99\)\( T^{21} + \)\(11\!\cdots\!71\)\( T^{22} - \)\(59\!\cdots\!64\)\( T^{23} + \)\(28\!\cdots\!95\)\( T^{24} - \)\(12\!\cdots\!91\)\( T^{25} + \)\(50\!\cdots\!92\)\( T^{26} - \)\(17\!\cdots\!96\)\( T^{27} + \)\(54\!\cdots\!17\)\( T^{28} - \)\(11\!\cdots\!28\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 + 42 T + 1575 T^{2} + 39878 T^{3} + 908009 T^{4} + 16969283 T^{5} + 290907710 T^{6} + 4373018796 T^{7} + 61331474684 T^{8} + 780283200836 T^{9} + 9405518849175 T^{10} + 105231969621198 T^{11} + 1131917940357961 T^{12} + 11498704416367879 T^{13} + 113622583192346603 T^{14} + 1071932815093372898 T^{15} + 9891341460679541474 T^{16} + 87446819829371019123 T^{17} + \)\(75\!\cdots\!50\)\( T^{18} + \)\(62\!\cdots\!98\)\( T^{19} + \)\(50\!\cdots\!50\)\( T^{20} + \)\(39\!\cdots\!47\)\( T^{21} + \)\(29\!\cdots\!62\)\( T^{22} + \)\(21\!\cdots\!58\)\( T^{23} + \)\(15\!\cdots\!21\)\( T^{24} + \)\(10\!\cdots\!51\)\( T^{25} + \)\(68\!\cdots\!03\)\( T^{26} + \)\(42\!\cdots\!18\)\( T^{27} + \)\(25\!\cdots\!25\)\( T^{28} + \)\(14\!\cdots\!64\)\( T^{29} + \)\(74\!\cdots\!72\)\( T^{30} + \)\(35\!\cdots\!56\)\( T^{31} + \)\(15\!\cdots\!70\)\( T^{32} + \)\(62\!\cdots\!07\)\( T^{33} + \)\(22\!\cdots\!87\)\( T^{34} + \)\(65\!\cdots\!18\)\( T^{35} + \)\(17\!\cdots\!25\)\( T^{36} + \)\(31\!\cdots\!78\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))
$71$ (\( 1 - 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 2 T + 126 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 + 22 T + 614 T^{2} + 9413 T^{3} + 156739 T^{4} + 1912189 T^{5} + 23879047 T^{6} + 241533430 T^{7} + 2432107105 T^{8} + 20614628884 T^{9} + 172679604455 T^{10} + 1217570020630 T^{11} + 8546573590817 T^{12} + 48591936879709 T^{13} + 282793104246389 T^{14} + 1205807972548373 T^{15} + 5584403777252074 T^{16} + 14206577687406742 T^{17} + 45848500718449031 T^{18} \))(\( 1 - 24 T + 573 T^{2} - 8229 T^{3} + 122860 T^{4} - 1394684 T^{5} + 16813349 T^{6} - 166412378 T^{7} + 1764351545 T^{8} - 15998237484 T^{9} + 155570574382 T^{10} - 1313986932737 T^{11} + 11848956998900 T^{12} - 93293072224327 T^{13} + 784231265459662 T^{14} - 5725945176135924 T^{15} + 44835138633397145 T^{16} - 300246096757306678 T^{17} + 2153794780562861429 T^{18} - 12684818562985393444 T^{19} + 79337278848854196460 T^{20} - \)\(37\!\cdots\!99\)\( T^{21} + \)\(18\!\cdots\!73\)\( T^{22} - \)\(55\!\cdots\!04\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 16 T + 600 T^{2} + 9303 T^{3} + 191257 T^{4} + 2644019 T^{5} + 40586319 T^{6} + 491218314 T^{7} + 6227913258 T^{8} + 66330165858 T^{9} + 723295569155 T^{10} + 6828672615759 T^{11} + 65271622158806 T^{12} + 547640621279510 T^{13} + 4634285173275226 T^{14} + 34423338656041119 T^{15} + 258875440451835205 T^{16} + 1685561015460587298 T^{17} + 11236583895565635558 T^{18} + 62925205490594929194 T^{19} + \)\(36\!\cdots\!29\)\( T^{20} + \)\(17\!\cdots\!59\)\( T^{21} + \)\(87\!\cdots\!67\)\( T^{22} + \)\(30\!\cdots\!03\)\( T^{23} + \)\(13\!\cdots\!00\)\( T^{24} + \)\(26\!\cdots\!56\)\( T^{25} + \)\(11\!\cdots\!11\)\( T^{26} \))(\( 1 - 30 T + 1236 T^{2} - 27311 T^{3} + 657652 T^{4} - 11593205 T^{5} + 207630185 T^{6} - 3052828373 T^{7} + 44377613727 T^{8} - 559208794785 T^{9} + 6885681211534 T^{10} - 75640524373453 T^{11} + 807741028833350 T^{12} - 7813951774661788 T^{13} + 73322025601429983 T^{14} - 627494556611979870 T^{15} + 5205863817701528793 T^{16} - 39390130896070073308 T^{17} + \)\(28\!\cdots\!50\)\( T^{18} - \)\(19\!\cdots\!93\)\( T^{19} + \)\(12\!\cdots\!34\)\( T^{20} - \)\(71\!\cdots\!85\)\( T^{21} + \)\(40\!\cdots\!57\)\( T^{22} - \)\(19\!\cdots\!53\)\( T^{23} + \)\(95\!\cdots\!35\)\( T^{24} - \)\(37\!\cdots\!05\)\( T^{25} + \)\(15\!\cdots\!92\)\( T^{26} - \)\(44\!\cdots\!51\)\( T^{27} + \)\(14\!\cdots\!96\)\( T^{28} - \)\(24\!\cdots\!30\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 + 46 T + 1416 T^{2} + 31979 T^{3} + 610138 T^{4} + 10061445 T^{5} + 150970465 T^{6} + 2079366941 T^{7} + 26960668746 T^{8} + 329623790121 T^{9} + 3852796195242 T^{10} + 43000970977110 T^{11} + 462356794054962 T^{12} + 4780075558168587 T^{13} + 47827348859556946 T^{14} + 462049404462359699 T^{15} + 4331617893151475920 T^{16} + 39302095847057353817 T^{17} + \)\(34\!\cdots\!18\)\( T^{18} + \)\(29\!\cdots\!46\)\( T^{19} + \)\(24\!\cdots\!78\)\( T^{20} + \)\(19\!\cdots\!97\)\( T^{21} + \)\(15\!\cdots\!20\)\( T^{22} + \)\(11\!\cdots\!19\)\( T^{23} + \)\(86\!\cdots\!46\)\( T^{24} + \)\(61\!\cdots\!27\)\( T^{25} + \)\(42\!\cdots\!42\)\( T^{26} + \)\(27\!\cdots\!10\)\( T^{27} + \)\(17\!\cdots\!02\)\( T^{28} + \)\(10\!\cdots\!21\)\( T^{29} + \)\(62\!\cdots\!66\)\( T^{30} + \)\(34\!\cdots\!81\)\( T^{31} + \)\(17\!\cdots\!15\)\( T^{32} + \)\(83\!\cdots\!45\)\( T^{33} + \)\(35\!\cdots\!38\)\( T^{34} + \)\(13\!\cdots\!59\)\( T^{35} + \)\(41\!\cdots\!56\)\( T^{36} + \)\(96\!\cdots\!06\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))
$73$ (\( 1 - 7 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 7 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 - T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 2 T + 79 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 34 T + 964 T^{2} + 18065 T^{3} + 297862 T^{4} + 3921795 T^{5} + 47265018 T^{6} + 488688038 T^{7} + 4783584224 T^{8} + 41674504091 T^{9} + 349201648352 T^{10} + 2604218554502 T^{11} + 18386895507306 T^{12} + 111372079562595 T^{13} + 617489250834166 T^{14} + 2733852797910785 T^{15} + 10649692172409508 T^{16} + 27419643124398754 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 10 T + 644 T^{2} + 5195 T^{3} + 192240 T^{4} + 1274477 T^{5} + 35994559 T^{6} + 199038168 T^{7} + 4807466626 T^{8} + 22589788876 T^{9} + 491516311680 T^{10} + 2014694402495 T^{11} + 39977243151166 T^{12} + 147072691382135 T^{13} + 2619290424942720 T^{14} + 8787811899174892 T^{15} + 136523595844604866 T^{16} + 412620372003561624 T^{17} + 5447208736878761551 T^{18} + 14079655322423187269 T^{19} + \)\(15\!\cdots\!40\)\( T^{20} + \)\(30\!\cdots\!35\)\( T^{21} + \)\(27\!\cdots\!56\)\( T^{22} + \)\(31\!\cdots\!70\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 24 T + 769 T^{2} + 11939 T^{3} + 226244 T^{4} + 2622242 T^{5} + 37785377 T^{6} + 347504349 T^{7} + 4251509561 T^{8} + 32017232498 T^{9} + 362496888988 T^{10} + 2337189970097 T^{11} + 26773382950040 T^{12} + 163671899929078 T^{13} + 1954456955352920 T^{14} + 12454885350646913 T^{15} + 141017452263444796 T^{16} + 909233084631236018 T^{17} + 8813683698277000673 T^{18} + 52589301787977630861 T^{19} + \)\(41\!\cdots\!69\)\( T^{20} + \)\(21\!\cdots\!02\)\( T^{21} + \)\(13\!\cdots\!72\)\( T^{22} + \)\(51\!\cdots\!11\)\( T^{23} + \)\(24\!\cdots\!13\)\( T^{24} + \)\(54\!\cdots\!04\)\( T^{25} + \)\(16\!\cdots\!33\)\( T^{26} \))(\( 1 - 7 T + 583 T^{2} - 3893 T^{3} + 164476 T^{4} - 1051095 T^{5} + 30328551 T^{6} - 184327331 T^{7} + 4158209336 T^{8} - 23829000050 T^{9} + 456578515114 T^{10} - 2460208029889 T^{11} + 42270731409214 T^{12} - 215251983612670 T^{13} + 3432994492168803 T^{14} - 16610860472146262 T^{15} + 250608597928322619 T^{16} - 1147077820671918430 T^{17} + 16444033120618202638 T^{18} - 69865580542923025249 T^{19} + \)\(94\!\cdots\!02\)\( T^{20} - \)\(36\!\cdots\!50\)\( T^{21} + \)\(45\!\cdots\!92\)\( T^{22} - \)\(14\!\cdots\!11\)\( T^{23} + \)\(17\!\cdots\!63\)\( T^{24} - \)\(45\!\cdots\!55\)\( T^{25} + \)\(51\!\cdots\!52\)\( T^{26} - \)\(89\!\cdots\!53\)\( T^{27} + \)\(97\!\cdots\!39\)\( T^{28} - \)\(85\!\cdots\!63\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 - 31 T + 1294 T^{2} - 29370 T^{3} + 741362 T^{4} - 13655959 T^{5} + 263513554 T^{6} - 4142758475 T^{7} + 66520605294 T^{8} - 918746991765 T^{9} + 12799746997835 T^{10} - 158132703251184 T^{11} + 1957544533024645 T^{12} - 21886220625034447 T^{13} + 244276817435380915 T^{14} - 2490133454428234836 T^{15} + 25287937970432991546 T^{16} - \)\(23\!\cdots\!44\)\( T^{17} + \)\(21\!\cdots\!99\)\( T^{18} - \)\(18\!\cdots\!84\)\( T^{19} + \)\(16\!\cdots\!27\)\( T^{20} - \)\(12\!\cdots\!76\)\( T^{21} + \)\(98\!\cdots\!82\)\( T^{22} - \)\(70\!\cdots\!76\)\( T^{23} + \)\(50\!\cdots\!95\)\( T^{24} - \)\(33\!\cdots\!83\)\( T^{25} + \)\(21\!\cdots\!65\)\( T^{26} - \)\(12\!\cdots\!04\)\( T^{27} + \)\(75\!\cdots\!55\)\( T^{28} - \)\(39\!\cdots\!85\)\( T^{29} + \)\(20\!\cdots\!38\)\( T^{30} - \)\(94\!\cdots\!75\)\( T^{31} + \)\(44\!\cdots\!82\)\( T^{32} - \)\(16\!\cdots\!31\)\( T^{33} + \)\(66\!\cdots\!34\)\( T^{34} - \)\(19\!\cdots\!70\)\( T^{35} + \)\(61\!\cdots\!82\)\( T^{36} - \)\(10\!\cdots\!39\)\( T^{37} + \)\(25\!\cdots\!37\)\( T^{38} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( 1 - 8 T + 361 T^{2} - 3121 T^{3} + 65108 T^{4} - 603177 T^{5} + 7790243 T^{6} - 75572458 T^{7} + 721910187 T^{8} - 6894365900 T^{9} + 57030904773 T^{10} - 471647710378 T^{11} + 3840893618477 T^{12} - 23493793007337 T^{13} + 200340988026092 T^{14} - 758675948681041 T^{15} + 6932611144003399 T^{16} - 12136870479252488 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 32 T + 1208 T^{2} - 26731 T^{3} + 598942 T^{4} - 10225332 T^{5} + 170346951 T^{6} - 2364896674 T^{7} + 31669466693 T^{8} - 367543872768 T^{9} + 4098646312177 T^{10} - 40314255770695 T^{11} + 380553530514200 T^{12} - 3184826205884905 T^{13} + 25579651634296657 T^{14} - 181213463485661952 T^{15} + 1233528292919152133 T^{16} - 7276920443705516926 T^{17} + 41409206874350466471 T^{18} - \)\(19\!\cdots\!88\)\( T^{19} + \)\(90\!\cdots\!62\)\( T^{20} - \)\(32\!\cdots\!89\)\( T^{21} + \)\(11\!\cdots\!08\)\( T^{22} - \)\(23\!\cdots\!28\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 36 T + 1053 T^{2} - 20715 T^{3} + 364974 T^{4} - 5262753 T^{5} + 71788931 T^{6} - 863654022 T^{7} + 10121381914 T^{8} - 107845195310 T^{9} + 1131093082394 T^{10} - 10924126266943 T^{11} + 104640315620113 T^{12} - 931578148956794 T^{13} + 8266584933988927 T^{14} - 68177472031991263 T^{15} + 557673002250455366 T^{16} - 4200579092785320110 T^{17} + 31144062985196567686 T^{18} - \)\(20\!\cdots\!62\)\( T^{19} + \)\(13\!\cdots\!29\)\( T^{20} - \)\(79\!\cdots\!33\)\( T^{21} + \)\(43\!\cdots\!06\)\( T^{22} - \)\(19\!\cdots\!15\)\( T^{23} + \)\(78\!\cdots\!87\)\( T^{24} - \)\(21\!\cdots\!76\)\( T^{25} + \)\(46\!\cdots\!39\)\( T^{26} \))(\( 1 - 38 T + 1485 T^{2} - 37017 T^{3} + 876231 T^{4} - 16709753 T^{5} + 299688498 T^{6} - 4689010953 T^{7} + 69102003990 T^{8} - 921578723941 T^{9} + 11613388640965 T^{10} - 135003888913283 T^{11} + 1487000481031499 T^{12} - 15263660272623196 T^{13} + 148710765475130805 T^{14} - 1356310036247888950 T^{15} + 11748150472535333595 T^{16} - 95260503761441366236 T^{17} + \)\(73\!\cdots\!61\)\( T^{18} - \)\(52\!\cdots\!23\)\( T^{19} + \)\(35\!\cdots\!35\)\( T^{20} - \)\(22\!\cdots\!61\)\( T^{21} + \)\(13\!\cdots\!10\)\( T^{22} - \)\(71\!\cdots\!33\)\( T^{23} + \)\(35\!\cdots\!62\)\( T^{24} - \)\(15\!\cdots\!53\)\( T^{25} + \)\(65\!\cdots\!49\)\( T^{26} - \)\(21\!\cdots\!97\)\( T^{27} + \)\(69\!\cdots\!15\)\( T^{28} - \)\(14\!\cdots\!78\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 + 56 T + 1751 T^{2} + 40251 T^{3} + 768165 T^{4} + 12982463 T^{5} + 200498578 T^{6} + 2871717245 T^{7} + 38535946843 T^{8} + 488856506209 T^{9} + 5906021798132 T^{10} + 68290067433246 T^{11} + 758626958932316 T^{12} + 8125309517850771 T^{13} + 84172064243536311 T^{14} + 845374015350145971 T^{15} + 8245992766585914749 T^{16} + 78232615790179343445 T^{17} + \)\(72\!\cdots\!46\)\( T^{18} + \)\(65\!\cdots\!74\)\( T^{19} + \)\(57\!\cdots\!34\)\( T^{20} + \)\(48\!\cdots\!45\)\( T^{21} + \)\(40\!\cdots\!11\)\( T^{22} + \)\(32\!\cdots\!51\)\( T^{23} + \)\(25\!\cdots\!89\)\( T^{24} + \)\(19\!\cdots\!91\)\( T^{25} + \)\(14\!\cdots\!44\)\( T^{26} + \)\(10\!\cdots\!06\)\( T^{27} + \)\(70\!\cdots\!08\)\( T^{28} + \)\(46\!\cdots\!09\)\( T^{29} + \)\(28\!\cdots\!97\)\( T^{30} + \)\(16\!\cdots\!45\)\( T^{31} + \)\(93\!\cdots\!42\)\( T^{32} + \)\(47\!\cdots\!03\)\( T^{33} + \)\(22\!\cdots\!35\)\( T^{34} + \)\(92\!\cdots\!71\)\( T^{35} + \)\(31\!\cdots\!09\)\( T^{36} + \)\(80\!\cdots\!16\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))
$83$ (\( 1 + 15 T + 83 T^{2} \))(\( 1 + 10 T + 83 T^{2} \))(\( 1 - 11 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 5 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 10 T + 83 T^{2} \))(\( 1 - 10 T + 123 T^{2} - 830 T^{3} + 6889 T^{4} \))(\( 1 + 3 T + 511 T^{2} + 1653 T^{3} + 125955 T^{4} + 425658 T^{5} + 19783154 T^{6} + 65916258 T^{7} + 2208335548 T^{8} + 6686212487 T^{9} + 183291850484 T^{10} + 454097101362 T^{11} + 11311750276198 T^{12} + 20201014000218 T^{13} + 496141864189065 T^{14} + 540432437178957 T^{15} + 13866522055699397 T^{16} + 6756876696417123 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 9 T + 767 T^{2} - 6769 T^{3} + 286605 T^{4} - 2407178 T^{5} + 68318501 T^{6} - 534452349 T^{7} + 11506512135 T^{8} - 82238330606 T^{9} + 1437899185287 T^{10} - 9202188223588 T^{11} + 136466743467514 T^{12} - 763781622557804 T^{13} + 9905687487442143 T^{14} - 47022808342212922 T^{15} + 546079746493225335 T^{16} - 2105229524457820407 T^{17} + 22336076224950399869 T^{18} - 65321304949108342606 T^{19} + \)\(64\!\cdots\!05\)\( T^{20} - \)\(12\!\cdots\!07\)\( T^{21} + \)\(11\!\cdots\!83\)\( T^{22} - \)\(11\!\cdots\!03\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - T + 303 T^{2} - 723 T^{3} + 71270 T^{4} - 154547 T^{5} + 11552741 T^{6} - 29244559 T^{7} + 1581532486 T^{8} - 3595884588 T^{9} + 177033915977 T^{10} - 414290554931 T^{11} + 17131502248919 T^{12} - 35242187307005 T^{13} + 1421914686660277 T^{14} - 2854047632919659 T^{15} + 101225691714740899 T^{16} - 170654645056256748 T^{17} + 6229720740578828498 T^{18} - 9561227038471749271 T^{19} + \)\(31\!\cdots\!07\)\( T^{20} - \)\(34\!\cdots\!27\)\( T^{21} + \)\(13\!\cdots\!10\)\( T^{22} - \)\(11\!\cdots\!27\)\( T^{23} + \)\(39\!\cdots\!01\)\( T^{24} - \)\(10\!\cdots\!61\)\( T^{25} + \)\(88\!\cdots\!63\)\( T^{26} \))(\( 1 - 29 T + 1185 T^{2} - 25389 T^{3} + 600153 T^{4} - 10276532 T^{5} + 179001262 T^{6} - 2563506102 T^{7} + 36020968176 T^{8} - 445565013881 T^{9} + 5311836590620 T^{10} - 58364817616840 T^{11} + 613314019969625 T^{12} - 6147154425437853 T^{13} + 58842171714124416 T^{14} - 548426223370991568 T^{15} + 4883900252272326528 T^{16} - 42347746836841369317 T^{17} + \)\(35\!\cdots\!75\)\( T^{18} - \)\(27\!\cdots\!40\)\( T^{19} + \)\(20\!\cdots\!60\)\( T^{20} - \)\(14\!\cdots\!89\)\( T^{21} + \)\(97\!\cdots\!52\)\( T^{22} - \)\(57\!\cdots\!82\)\( T^{23} + \)\(33\!\cdots\!86\)\( T^{24} - \)\(15\!\cdots\!68\)\( T^{25} + \)\(77\!\cdots\!51\)\( T^{26} - \)\(27\!\cdots\!29\)\( T^{27} + \)\(10\!\cdots\!55\)\( T^{28} - \)\(21\!\cdots\!41\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 + 25 T + 1051 T^{2} + 20585 T^{3} + 510946 T^{4} + 8368347 T^{5} + 157295265 T^{6} + 2243056623 T^{7} + 35101450564 T^{8} + 448135896138 T^{9} + 6135824348909 T^{10} + 71553214836029 T^{11} + 883311764321072 T^{12} + 9542482089027602 T^{13} + 108253626347253710 T^{14} + 1093294901011008236 T^{15} + 11535043282104115171 T^{16} + \)\(10\!\cdots\!89\)\( T^{17} + \)\(10\!\cdots\!07\)\( T^{18} + \)\(96\!\cdots\!72\)\( T^{19} + \)\(89\!\cdots\!81\)\( T^{20} + \)\(75\!\cdots\!21\)\( T^{21} + \)\(65\!\cdots\!77\)\( T^{22} + \)\(51\!\cdots\!56\)\( T^{23} + \)\(42\!\cdots\!30\)\( T^{24} + \)\(31\!\cdots\!38\)\( T^{25} + \)\(23\!\cdots\!44\)\( T^{26} + \)\(16\!\cdots\!89\)\( T^{27} + \)\(11\!\cdots\!27\)\( T^{28} + \)\(69\!\cdots\!62\)\( T^{29} + \)\(45\!\cdots\!88\)\( T^{30} + \)\(23\!\cdots\!03\)\( T^{31} + \)\(13\!\cdots\!95\)\( T^{32} + \)\(61\!\cdots\!63\)\( T^{33} + \)\(31\!\cdots\!22\)\( T^{34} + \)\(10\!\cdots\!85\)\( T^{35} + \)\(44\!\cdots\!73\)\( T^{36} + \)\(87\!\cdots\!25\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))
$89$ (\( 1 + 12 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 16 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 22 T + 282 T^{2} + 1958 T^{3} + 7921 T^{4} \))(\( 1 + 5 T + 494 T^{2} + 1934 T^{3} + 115913 T^{4} + 331352 T^{5} + 17489158 T^{6} + 35044073 T^{7} + 1953083326 T^{8} + 3088810680 T^{9} + 173824416014 T^{10} + 277584102233 T^{11} + 12329314226102 T^{12} + 20789767039832 T^{13} + 647265082911937 T^{14} + 961161816718574 T^{15} + 21850279438391326 T^{16} + 19682944028510405 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 15 T + 483 T^{2} - 5211 T^{3} + 96324 T^{4} - 826853 T^{5} + 11988900 T^{6} - 93547398 T^{7} + 1258290761 T^{8} - 10540139229 T^{9} + 134590686313 T^{10} - 1182018629254 T^{11} + 13237557681668 T^{12} - 105199658003606 T^{13} + 1066092826285273 T^{14} - 7430471412128901 T^{15} + 78947982174735401 T^{16} - 522374231731263702 T^{17} + 5958258999202332900 T^{18} - 36572811952372840237 T^{19} + \)\(37\!\cdots\!44\)\( T^{20} - \)\(18\!\cdots\!99\)\( T^{21} + \)\(15\!\cdots\!83\)\( T^{22} - \)\(41\!\cdots\!35\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 53 T + 2002 T^{2} + 54398 T^{3} + 1233571 T^{4} + 23443428 T^{5} + 392806234 T^{6} + 5817829435 T^{7} + 78328510257 T^{8} + 961260034545 T^{9} + 10984234874496 T^{10} + 117218879048135 T^{11} + 1188942226035487 T^{12} + 11452514746162508 T^{13} + 105815858117158343 T^{14} + 928490740940277335 T^{15} + 7743545075238570624 T^{16} + 60311608751090715345 T^{17} + \)\(43\!\cdots\!93\)\( T^{18} + \)\(28\!\cdots\!35\)\( T^{19} + \)\(17\!\cdots\!86\)\( T^{20} + \)\(92\!\cdots\!68\)\( T^{21} + \)\(43\!\cdots\!39\)\( T^{22} + \)\(16\!\cdots\!98\)\( T^{23} + \)\(55\!\cdots\!78\)\( T^{24} + \)\(13\!\cdots\!13\)\( T^{25} + \)\(21\!\cdots\!69\)\( T^{26} \))(\( 1 - 19 T + 1190 T^{2} - 19912 T^{3} + 669280 T^{4} - 9950377 T^{5} + 236525874 T^{6} - 3142538391 T^{7} + 58821873944 T^{8} - 700736154159 T^{9} + 10913498105048 T^{10} - 116702861037044 T^{11} + 1561368359376938 T^{12} - 14970132876839669 T^{13} + 175453434740369589 T^{14} - 1502547658278786074 T^{15} + 15615355691892893421 T^{16} - \)\(11\!\cdots\!49\)\( T^{17} + \)\(11\!\cdots\!22\)\( T^{18} - \)\(73\!\cdots\!04\)\( T^{19} + \)\(60\!\cdots\!52\)\( T^{20} - \)\(34\!\cdots\!99\)\( T^{21} + \)\(26\!\cdots\!76\)\( T^{22} - \)\(12\!\cdots\!71\)\( T^{23} + \)\(82\!\cdots\!66\)\( T^{24} - \)\(31\!\cdots\!77\)\( T^{25} + \)\(18\!\cdots\!20\)\( T^{26} - \)\(49\!\cdots\!52\)\( T^{27} + \)\(26\!\cdots\!10\)\( T^{28} - \)\(37\!\cdots\!79\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 + 7 T + 964 T^{2} + 4454 T^{3} + 437542 T^{4} + 1166643 T^{5} + 128078168 T^{6} + 140924113 T^{7} + 27834247843 T^{8} - 1650657100 T^{9} + 4860448158536 T^{10} - 3964771674614 T^{11} + 714056828966148 T^{12} - 879984127345524 T^{13} + 90678035997531389 T^{14} - 128074711932031809 T^{15} + 10126341138806063407 T^{16} - 14697176129571376618 T^{17} + \)\(10\!\cdots\!90\)\( T^{18} - \)\(14\!\cdots\!40\)\( T^{19} + \)\(89\!\cdots\!10\)\( T^{20} - \)\(11\!\cdots\!78\)\( T^{21} + \)\(71\!\cdots\!83\)\( T^{22} - \)\(80\!\cdots\!69\)\( T^{23} + \)\(50\!\cdots\!61\)\( T^{24} - \)\(43\!\cdots\!64\)\( T^{25} + \)\(31\!\cdots\!92\)\( T^{26} - \)\(15\!\cdots\!34\)\( T^{27} + \)\(17\!\cdots\!24\)\( T^{28} - \)\(51\!\cdots\!00\)\( T^{29} + \)\(77\!\cdots\!27\)\( T^{30} + \)\(34\!\cdots\!73\)\( T^{31} + \)\(28\!\cdots\!92\)\( T^{32} + \)\(22\!\cdots\!63\)\( T^{33} + \)\(76\!\cdots\!58\)\( T^{34} + \)\(69\!\cdots\!94\)\( T^{35} + \)\(13\!\cdots\!56\)\( T^{36} + \)\(85\!\cdots\!67\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))
$97$ (\( 1 + 12 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 4 T + 130 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( 1 + 33 T + 1084 T^{2} + 21618 T^{3} + 420709 T^{4} + 6238212 T^{5} + 91075788 T^{6} + 1091216741 T^{7} + 12895551382 T^{8} + 127980390584 T^{9} + 1250868484054 T^{10} + 10267258316069 T^{11} + 83122412661324 T^{12} + 552264423085572 T^{13} + 3612771332182213 T^{14} + 18007188802555122 T^{15} + 87585340374274492 T^{16} + 258635308614439713 T^{17} + 760231058654565217 T^{18} \))(\( 1 - 15 T + 647 T^{2} - 10235 T^{3} + 217588 T^{4} - 3311979 T^{5} + 50610296 T^{6} - 690685452 T^{7} + 8896369343 T^{8} - 105921681527 T^{9} + 1219816901553 T^{10} - 12751757948264 T^{11} + 132534100467000 T^{12} - 1236920520981608 T^{13} + 11477257226712177 T^{14} - 96671858844291671 T^{15} + 787589181446232383 T^{16} - 5931150986883841164 T^{17} + 42156959729170148984 T^{18} - \)\(26\!\cdots\!27\)\( T^{19} + \)\(17\!\cdots\!68\)\( T^{20} - \)\(77\!\cdots\!95\)\( T^{21} + \)\(47\!\cdots\!03\)\( T^{22} - \)\(10\!\cdots\!95\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 + 21 T + 651 T^{2} + 9907 T^{3} + 188399 T^{4} + 2321362 T^{5} + 32954330 T^{6} + 328855618 T^{7} + 3712298851 T^{8} + 29150841566 T^{9} + 273248536763 T^{10} + 1576167435891 T^{11} + 14933500499341 T^{12} + 82452835579798 T^{13} + 1448549548436077 T^{14} + 14830159404298419 T^{15} + 249386561793097499 T^{16} + 2580703044382894046 T^{17} + 31878773369207144707 T^{18} + \)\(27\!\cdots\!22\)\( T^{19} + \)\(26\!\cdots\!90\)\( T^{20} + \)\(18\!\cdots\!82\)\( T^{21} + \)\(14\!\cdots\!83\)\( T^{22} + \)\(73\!\cdots\!43\)\( T^{23} + \)\(46\!\cdots\!03\)\( T^{24} + \)\(14\!\cdots\!61\)\( T^{25} + \)\(67\!\cdots\!77\)\( T^{26} \))(\( 1 + 8 T + 1079 T^{2} + 8047 T^{3} + 564101 T^{4} + 3938060 T^{5} + 190168386 T^{6} + 1243438406 T^{7} + 46322170917 T^{8} + 282873276440 T^{9} + 8645373821974 T^{10} + 49011429523145 T^{11} + 1277914773988946 T^{12} + 6665406320437460 T^{13} + 152384590518767700 T^{14} + 722493776397475588 T^{15} + 14781305280320466900 T^{16} + 62714808068996061140 T^{17} + \)\(11\!\cdots\!58\)\( T^{18} + \)\(43\!\cdots\!45\)\( T^{19} + \)\(74\!\cdots\!18\)\( T^{20} + \)\(23\!\cdots\!60\)\( T^{21} + \)\(37\!\cdots\!21\)\( T^{22} + \)\(97\!\cdots\!66\)\( T^{23} + \)\(14\!\cdots\!62\)\( T^{24} + \)\(29\!\cdots\!40\)\( T^{25} + \)\(40\!\cdots\!53\)\( T^{26} + \)\(55\!\cdots\!27\)\( T^{27} + \)\(72\!\cdots\!83\)\( T^{28} + \)\(52\!\cdots\!52\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 - 39 T + 1812 T^{2} - 48290 T^{3} + 1343996 T^{4} - 28015607 T^{5} + 591847844 T^{6} - 10331773501 T^{7} + 181372882043 T^{8} - 2762894411788 T^{9} + 42260825462822 T^{10} - 576732763030202 T^{11} + 7902903390374710 T^{12} - 98237879336580364 T^{13} + 1226269306796116981 T^{14} - 14025839064140651091 T^{15} + \)\(16\!\cdots\!39\)\( T^{16} - \)\(17\!\cdots\!58\)\( T^{17} + \)\(18\!\cdots\!48\)\( T^{18} - \)\(17\!\cdots\!32\)\( T^{19} + \)\(17\!\cdots\!56\)\( T^{20} - \)\(16\!\cdots\!22\)\( T^{21} + \)\(14\!\cdots\!47\)\( T^{22} - \)\(12\!\cdots\!71\)\( T^{23} + \)\(10\!\cdots\!17\)\( T^{24} - \)\(81\!\cdots\!56\)\( T^{25} + \)\(63\!\cdots\!30\)\( T^{26} - \)\(45\!\cdots\!22\)\( T^{27} + \)\(32\!\cdots\!74\)\( T^{28} - \)\(20\!\cdots\!12\)\( T^{29} + \)\(12\!\cdots\!79\)\( T^{30} - \)\(71\!\cdots\!41\)\( T^{31} + \)\(39\!\cdots\!88\)\( T^{32} - \)\(18\!\cdots\!83\)\( T^{33} + \)\(85\!\cdots\!28\)\( T^{34} - \)\(29\!\cdots\!90\)\( T^{35} + \)\(10\!\cdots\!44\)\( T^{36} - \)\(22\!\cdots\!71\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))
show more
show less