Properties

Label 4010.2
Level 4010
Weight 2
Dimension 147401
Nonzero newspaces 30
Sturm bound 1929600

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Defining parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(1929600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4010))\).

Total New Old
Modular forms 485600 147401 338199
Cusp forms 479201 147401 331800
Eisenstein series 6399 0 6399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4010))\)

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
4010.2.a \(\chi_{4010}(1, \cdot)\) 4010.2.a.a 1 1
4010.2.a.b 1
4010.2.a.c 1
4010.2.a.d 1
4010.2.a.e 1
4010.2.a.f 1
4010.2.a.g 2
4010.2.a.h 9
4010.2.a.i 10
4010.2.a.j 12
4010.2.a.k 15
4010.2.a.l 17
4010.2.a.m 20
4010.2.a.n 22
4010.2.a.o 22
4010.2.b \(\chi_{4010}(3209, \cdot)\) n/a 200 1
4010.2.c \(\chi_{4010}(801, \cdot)\) n/a 134 1
4010.2.d \(\chi_{4010}(4009, \cdot)\) n/a 200 1
4010.2.f \(\chi_{4010}(381, \cdot)\) n/a 268 2
4010.2.i \(\chi_{4010}(3589, \cdot)\) n/a 400 2
4010.2.k \(\chi_{4010}(841, \cdot)\) n/a 536 4
4010.2.m \(\chi_{4010}(1301, \cdot)\) n/a 536 4
4010.2.n \(\chi_{4010}(499, \cdot)\) n/a 808 4
4010.2.p \(\chi_{4010}(29, \cdot)\) n/a 800 4
4010.2.q \(\chi_{4010}(831, \cdot)\) n/a 536 4
4010.2.r \(\chi_{4010}(39, \cdot)\) n/a 800 4
4010.2.u \(\chi_{4010}(147, \cdot)\) n/a 1608 8
4010.2.v \(\chi_{4010}(133, \cdot)\) n/a 1608 8
4010.2.x \(\chi_{4010}(179, \cdot)\) n/a 1600 8
4010.2.ba \(\chi_{4010}(981, \cdot)\) n/a 1072 8
4010.2.bc \(\chi_{4010}(51, \cdot)\) n/a 2680 20
4010.2.be \(\chi_{4010}(239, \cdot)\) n/a 3232 16
4010.2.bf \(\chi_{4010}(151, \cdot)\) n/a 2144 16
4010.2.bh \(\chi_{4010}(629, \cdot)\) n/a 4000 20
4010.2.bi \(\chi_{4010}(41, \cdot)\) n/a 2680 20
4010.2.bj \(\chi_{4010}(489, \cdot)\) n/a 4000 20
4010.2.bm \(\chi_{4010}(153, \cdot)\) n/a 6432 32
4010.2.bn \(\chi_{4010}(33, \cdot)\) n/a 6432 32
4010.2.bo \(\chi_{4010}(81, \cdot)\) n/a 5360 40
4010.2.bp \(\chi_{4010}(49, \cdot)\) n/a 8000 40
4010.2.bu \(\chi_{4010}(11, \cdot)\) n/a 10720 80
4010.2.bv \(\chi_{4010}(9, \cdot)\) n/a 16160 80
4010.2.by \(\chi_{4010}(3, \cdot)\) n/a 32160 160
4010.2.bz \(\chi_{4010}(13, \cdot)\) n/a 32160 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(401))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(802))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2005))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{10} \))(\( ( 1 - T )^{12} \))(\( ( 1 + T )^{15} \))(\( ( 1 + T )^{17} \))(\( ( 1 + T )^{20} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 4 T + 25 T^{2} + 76 T^{3} + 279 T^{4} + 680 T^{5} + 1849 T^{6} + 3715 T^{7} + 8082 T^{8} + 13508 T^{9} + 24246 T^{10} + 33435 T^{11} + 49923 T^{12} + 55080 T^{13} + 67797 T^{14} + 55404 T^{15} + 54675 T^{16} + 26244 T^{17} + 19683 T^{18} \))(\( 1 + 4 T + 20 T^{2} + 58 T^{3} + 182 T^{4} + 434 T^{5} + 1076 T^{6} + 2235 T^{7} + 4753 T^{8} + 8719 T^{9} + 16208 T^{10} + 26157 T^{11} + 42777 T^{12} + 60345 T^{13} + 87156 T^{14} + 105462 T^{15} + 132678 T^{16} + 126846 T^{17} + 131220 T^{18} + 78732 T^{19} + 59049 T^{20} \))(\( 1 + 2 T + 20 T^{2} + 36 T^{3} + 207 T^{4} + 342 T^{5} + 1454 T^{6} + 2201 T^{7} + 7647 T^{8} + 10581 T^{9} + 31620 T^{10} + 39804 T^{11} + 105310 T^{12} + 119412 T^{13} + 284580 T^{14} + 285687 T^{15} + 619407 T^{16} + 534843 T^{17} + 1059966 T^{18} + 747954 T^{19} + 1358127 T^{20} + 708588 T^{21} + 1180980 T^{22} + 354294 T^{23} + 531441 T^{24} \))(\( 1 + 6 T + 31 T^{2} + 112 T^{3} + 364 T^{4} + 1000 T^{5} + 2552 T^{6} + 5871 T^{7} + 12866 T^{8} + 26376 T^{9} + 52680 T^{10} + 100896 T^{11} + 190651 T^{12} + 348714 T^{13} + 629155 T^{14} + 1098434 T^{15} + 1887465 T^{16} + 3138426 T^{17} + 5147577 T^{18} + 8172576 T^{19} + 12801240 T^{20} + 19228104 T^{21} + 28137942 T^{22} + 38519631 T^{23} + 50231016 T^{24} + 59049000 T^{25} + 64481508 T^{26} + 59521392 T^{27} + 49424013 T^{28} + 28697814 T^{29} + 14348907 T^{30} \))(\( 1 - 3 T + 27 T^{2} - 74 T^{3} + 372 T^{4} - 938 T^{5} + 3497 T^{6} - 8144 T^{7} + 25065 T^{8} - 54067 T^{9} + 144730 T^{10} - 289956 T^{11} + 694811 T^{12} - 1295337 T^{13} + 2826331 T^{14} - 4904990 T^{15} + 9848296 T^{16} - 15887336 T^{17} + 29544888 T^{18} - 44144910 T^{19} + 76310937 T^{20} - 104922297 T^{21} + 168839073 T^{22} - 211377924 T^{23} + 316524510 T^{24} - 354733587 T^{25} + 493354395 T^{26} - 480895056 T^{27} + 619483059 T^{28} - 498491658 T^{29} + 593088156 T^{30} - 353939706 T^{31} + 387420489 T^{32} - 129140163 T^{33} + 129140163 T^{34} \))(\( 1 - 4 T + 25 T^{2} - 74 T^{3} + 280 T^{4} - 694 T^{5} + 2074 T^{6} - 4639 T^{7} + 12079 T^{8} - 25278 T^{9} + 59841 T^{10} - 119226 T^{11} + 263159 T^{12} - 503756 T^{13} + 1050631 T^{14} - 1933641 T^{15} + 3835144 T^{16} - 6787892 T^{17} + 12890253 T^{18} - 21982472 T^{19} + 40146458 T^{20} - 65947416 T^{21} + 116012277 T^{22} - 183273084 T^{23} + 310646664 T^{24} - 469874763 T^{25} + 765909999 T^{26} - 1101714372 T^{27} + 1726586199 T^{28} - 2346725358 T^{29} + 3533551209 T^{30} - 4477921866 T^{31} + 6419275839 T^{32} - 7396064397 T^{33} + 9919877706 T^{34} - 9958141458 T^{35} + 12053081880 T^{36} - 9556372062 T^{37} + 9685512225 T^{38} - 4649045868 T^{39} + 3486784401 T^{40} \))
$5$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{9} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{12} \))(\( ( 1 + T )^{15} \))(\( ( 1 + T )^{17} \))(\( ( 1 - T )^{20} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 6 T^{2} + 49 T^{4} \))(\( 1 + 7 T + 65 T^{2} + 312 T^{3} + 1673 T^{4} + 6192 T^{5} + 24524 T^{6} + 74511 T^{7} + 239687 T^{8} + 616764 T^{9} + 1677809 T^{10} + 3651039 T^{11} + 8411732 T^{12} + 14866992 T^{13} + 28118111 T^{14} + 36706488 T^{15} + 53530295 T^{16} + 40353607 T^{17} + 40353607 T^{18} \))(\( 1 + 3 T + 42 T^{2} + 129 T^{3} + 894 T^{4} + 2832 T^{5} + 12609 T^{6} + 39725 T^{7} + 130193 T^{8} + 387735 T^{9} + 1033046 T^{10} + 2714145 T^{11} + 6379457 T^{12} + 13625675 T^{13} + 30274209 T^{14} + 47597424 T^{15} + 105178206 T^{16} + 106237047 T^{17} + 242121642 T^{18} + 121060821 T^{19} + 282475249 T^{20} \))(\( 1 + 9 T + 84 T^{2} + 507 T^{3} + 2905 T^{4} + 13423 T^{5} + 58623 T^{6} + 222202 T^{7} + 801881 T^{8} + 2601035 T^{9} + 8104477 T^{10} + 23118678 T^{11} + 63732314 T^{12} + 161830746 T^{13} + 397119373 T^{14} + 892155005 T^{15} + 1925316281 T^{16} + 3734549014 T^{17} + 6896937327 T^{18} + 11054417689 T^{19} + 16746746905 T^{20} + 20459278749 T^{21} + 23727920916 T^{22} + 17795940687 T^{23} + 13841287201 T^{24} \))(\( 1 + 5 T + 55 T^{2} + 224 T^{3} + 1440 T^{4} + 4965 T^{5} + 24419 T^{6} + 73651 T^{7} + 308231 T^{8} + 833291 T^{9} + 3137426 T^{10} + 7746120 T^{11} + 27147545 T^{12} + 62398907 T^{13} + 208275005 T^{14} + 454838570 T^{15} + 1457925035 T^{16} + 3057546443 T^{17} + 9311607935 T^{18} + 18598434120 T^{19} + 52730718782 T^{20} + 98035852859 T^{21} + 253841482433 T^{22} + 424583358451 T^{23} + 985394729333 T^{24} + 1402489611285 T^{25} + 2847350509920 T^{26} + 3100448333024 T^{27} + 5328895572385 T^{28} + 3391115364245 T^{29} + 4747561509943 T^{30} \))(\( 1 - 4 T + 54 T^{2} - 194 T^{3} + 1421 T^{4} - 4579 T^{5} + 24260 T^{6} - 70066 T^{7} + 305451 T^{8} - 796809 T^{9} + 3110613 T^{10} - 7488895 T^{11} + 27727668 T^{12} - 63462879 T^{13} + 227702190 T^{14} - 503646169 T^{15} + 1737275532 T^{16} - 3693969338 T^{17} + 12160928724 T^{18} - 24678662281 T^{19} + 78101851170 T^{20} - 152374372479 T^{21} + 466018916076 T^{22} - 881061007855 T^{23} + 2561723561859 T^{24} - 4593445320009 T^{25} + 12326049611757 T^{26} - 19791910796434 T^{27} + 47969946785180 T^{28} - 63379254093379 T^{29} + 137679283788347 T^{30} - 131575276132706 T^{31} + 256368321536922 T^{32} - 132931722278404 T^{33} + 232630513987207 T^{34} \))(\( 1 - 11 T + 109 T^{2} - 760 T^{3} + 4810 T^{4} - 25911 T^{5} + 129587 T^{6} - 586561 T^{7} + 2504480 T^{8} - 9960560 T^{9} + 37784799 T^{10} - 135712250 T^{11} + 468685321 T^{12} - 1548757706 T^{13} + 4950678598 T^{14} - 15252837261 T^{15} + 45666591933 T^{16} - 132444676281 T^{17} + 374472954091 T^{18} - 1028761385485 T^{19} + 2759849551454 T^{20} - 7201329698395 T^{21} + 18349174750459 T^{22} - 45428523964383 T^{23} + 109645487231133 T^{24} - 256354435845627 T^{25} + 582442386376102 T^{26} - 1275468567472358 T^{27} + 2701877607186121 T^{28} - 5476478801585750 T^{29} + 10673270505939951 T^{30} - 19695281663256080 T^{31} + 34665226969160480 T^{32} - 56831314833340327 T^{33} + 87888893341283363 T^{34} - 123014066284133073 T^{35} + 159850396039780810 T^{36} - 176799190630277320 T^{37} + 177497082172238941 T^{38} - 125387847039104573 T^{39} + 79792266297612001 T^{40} \))
$11$ (\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( 1 + 11 T + 124 T^{2} + 871 T^{3} + 5868 T^{4} + 30847 T^{5} + 154017 T^{6} + 644266 T^{7} + 2555584 T^{8} + 8704990 T^{9} + 28111424 T^{10} + 77956186 T^{11} + 204996627 T^{12} + 451630927 T^{13} + 945047268 T^{14} + 1543029631 T^{15} + 2416409204 T^{16} + 2357947691 T^{17} + 2357947691 T^{18} \))(\( 1 + 11 T + 103 T^{2} + 616 T^{3} + 3268 T^{4} + 13096 T^{5} + 47861 T^{6} + 133699 T^{7} + 360987 T^{8} + 744096 T^{9} + 2350040 T^{10} + 8185056 T^{11} + 43679427 T^{12} + 177953369 T^{13} + 700732901 T^{14} + 2109123896 T^{15} + 5789461348 T^{16} + 12004097336 T^{17} + 22078964743 T^{18} + 25937424601 T^{19} + 25937424601 T^{20} \))(\( 1 - T + 74 T^{2} - 101 T^{3} + 2792 T^{4} - 4233 T^{5} + 70930 T^{6} - 109593 T^{7} + 1345312 T^{8} - 2025517 T^{9} + 20126898 T^{10} - 28468225 T^{11} + 244570862 T^{12} - 313150475 T^{13} + 2435354658 T^{14} - 2695963127 T^{15} + 19696712992 T^{16} - 17650062243 T^{17} + 125656821730 T^{18} - 82489194843 T^{19} + 598489995752 T^{20} - 238152716791 T^{21} + 1919369420474 T^{22} - 285311670611 T^{23} + 3138428376721 T^{24} \))(\( 1 + 2 T + 93 T^{2} + 252 T^{3} + 4387 T^{4} + 14310 T^{5} + 140615 T^{6} + 505764 T^{7} + 3427648 T^{8} + 12694640 T^{9} + 66907544 T^{10} + 242422076 T^{11} + 1070653474 T^{12} + 3662156648 T^{13} + 14181624706 T^{14} + 44679013096 T^{15} + 155997871766 T^{16} + 443120954408 T^{17} + 1425039773894 T^{18} + 3549301614716 T^{19} + 10775526868744 T^{20} + 22489329133040 T^{21} + 66795162703808 T^{22} + 108415005090084 T^{23} + 331562814569965 T^{24} + 371164546040310 T^{25} + 1251662298970457 T^{26} + 790883950933692 T^{27} + 3210612229385583 T^{28} + 759499667166482 T^{29} + 4177248169415651 T^{30} \))(\( 1 + 8 T + 119 T^{2} + 756 T^{3} + 6421 T^{4} + 34108 T^{5} + 215576 T^{6} + 995396 T^{7} + 5217488 T^{8} + 21644986 T^{9} + 100122992 T^{10} + 383402870 T^{11} + 1624676799 T^{12} + 5837071158 T^{13} + 23056429337 T^{14} + 78020337916 T^{15} + 288444048531 T^{16} + 916491513240 T^{17} + 3172884533841 T^{18} + 9440460887836 T^{19} + 30688107447547 T^{20} + 85460558824278 T^{21} + 261655823155749 T^{22} + 679221571780070 T^{23} + 1951113866135632 T^{24} + 4639794978220666 T^{25} + 12302563782420208 T^{26} + 25818008698136996 T^{27} + 61506348703636936 T^{28} + 107045515073199868 T^{29} + 221670334676180951 T^{30} + 287090874188930196 T^{31} + 497092532160462469 T^{32} + 367597838908577288 T^{33} + 505447028499293771 T^{34} \))(\( 1 - 10 T + 135 T^{2} - 968 T^{3} + 8005 T^{4} - 46606 T^{5} + 297499 T^{6} - 1488356 T^{7} + 7976885 T^{8} - 35418536 T^{9} + 166443123 T^{10} - 670802614 T^{11} + 2842273407 T^{12} - 10592077576 T^{13} + 41364010581 T^{14} - 145097041890 T^{15} + 533021349843 T^{16} - 1791638233136 T^{17} + 6314223167762 T^{18} - 20648559894180 T^{19} + 70901564095950 T^{20} - 227134158835980 T^{21} + 764021003299202 T^{22} - 2384670488304016 T^{23} + 7803965583051363 T^{24} - 23368023693426390 T^{25} + 73278867948886941 T^{26} - 206409626968777496 T^{27} + 609266547020577567 T^{28} - 1581717474798064274 T^{29} + 4317105953167468923 T^{30} - 10105321676755845496 T^{31} + 25034882241840094085 T^{32} - 51382085755692567436 T^{33} + \)\(11\!\cdots\!59\)\( T^{34} - \)\(19\!\cdots\!06\)\( T^{35} + \)\(36\!\cdots\!05\)\( T^{36} - \)\(48\!\cdots\!28\)\( T^{37} + \)\(75\!\cdots\!35\)\( T^{38} - \)\(61\!\cdots\!10\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))
$13$ (\( 1 - 5 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 28 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 + 14 T + 154 T^{2} + 1195 T^{3} + 8168 T^{4} + 46697 T^{5} + 243049 T^{6} + 1109064 T^{7} + 4662406 T^{8} + 17476066 T^{9} + 60611278 T^{10} + 187431816 T^{11} + 533978653 T^{12} + 1333713017 T^{13} + 3032721224 T^{14} + 5768036755 T^{15} + 9663271618 T^{16} + 11420230094 T^{17} + 10604499373 T^{18} \))(\( 1 - 6 T + 81 T^{2} - 287 T^{3} + 2372 T^{4} - 4060 T^{5} + 34023 T^{6} + 16767 T^{7} + 283911 T^{8} + 1210928 T^{9} + 2420282 T^{10} + 15742064 T^{11} + 47980959 T^{12} + 36837099 T^{13} + 971730903 T^{14} - 1507449580 T^{15} + 11449190948 T^{16} - 18008824379 T^{17} + 66074188401 T^{18} - 63626996238 T^{19} + 137858491849 T^{20} \))(\( 1 + 6 T + 132 T^{2} + 705 T^{3} + 8226 T^{4} + 39361 T^{5} + 320360 T^{6} + 1372984 T^{7} + 8683928 T^{8} + 33172919 T^{9} + 172580900 T^{10} + 582177315 T^{11} + 2578069132 T^{12} + 7568305095 T^{13} + 29166172100 T^{14} + 72880903043 T^{15} + 248021667608 T^{16} + 509779348312 T^{17} + 1546316531240 T^{18} + 2469844377637 T^{19} + 6710200910946 T^{20} + 7476172057965 T^{21} + 18197320924068 T^{22} + 10752962364222 T^{23} + 23298085122481 T^{24} \))(\( 1 + 13 T + 176 T^{2} + 1462 T^{3} + 11848 T^{4} + 74831 T^{5} + 460613 T^{6} + 2417706 T^{7} + 12485916 T^{8} + 57656725 T^{9} + 264135749 T^{10} + 1110937146 T^{11} + 4649594521 T^{12} + 18096827983 T^{13} + 70046903252 T^{14} + 253346279352 T^{15} + 910609742276 T^{16} + 3058363929127 T^{17} + 10215159162637 T^{18} + 31729475826906 T^{19} + 98071754653457 T^{20} + 278297999140525 T^{21} + 783472712386572 T^{22} + 1972197058546026 T^{23} + 4884570269695649 T^{24} + 10316088803552519 T^{25} + 21233516348550376 T^{26} + 34061800449067222 T^{27} + 53306018760236528 T^{28} + 51185893014090757 T^{29} + 51185893014090757 T^{30} \))(\( 1 - 14 T + 188 T^{2} - 1709 T^{3} + 14688 T^{4} - 104729 T^{5} + 710895 T^{6} - 4286064 T^{7} + 24770030 T^{8} - 131212980 T^{9} + 669741138 T^{10} - 3186738722 T^{11} + 14663661497 T^{12} - 63509366239 T^{13} + 266641393844 T^{14} - 1059405873689 T^{15} + 4085863671859 T^{16} - 14949155109868 T^{17} + 53116227734167 T^{18} - 179039592653441 T^{19} + 585811142275268 T^{20} - 1813891009152079 T^{21} + 5444514868205621 T^{22} - 15381779143998098 T^{23} + 42025263183392346 T^{24} - 107034458779958580 T^{25} + 262673767604191190 T^{26} - 590870319008292336 T^{27} + 1274037863318933115 T^{28} - 2439985156792312649 T^{29} + 4448629565627012064 T^{30} - 6728976243160084901 T^{31} + 9622947886649062316 T^{32} - 9315832528564517774 T^{33} + 8650415919381337933 T^{34} \))(\( 1 + 9 T + 125 T^{2} + 803 T^{3} + 6936 T^{4} + 35787 T^{5} + 245019 T^{6} + 1073173 T^{7} + 6422048 T^{8} + 24590846 T^{9} + 135968394 T^{10} + 462566134 T^{11} + 2458241730 T^{12} + 7521270846 T^{13} + 39614362494 T^{14} + 110604235870 T^{15} + 588518940767 T^{16} + 1528601024818 T^{17} + 8236033085448 T^{18} + 20370448346586 T^{19} + 109643739132620 T^{20} + 264815828505618 T^{21} + 1391889591440712 T^{22} + 3358336451525146 T^{23} + 16808689467246287 T^{24} + 41066578548879910 T^{25} + 191210961415301646 T^{26} + 471948591541835382 T^{27} + 2005263298805187330 T^{28} + 4905282277974033982 T^{29} + 18744397735970620506 T^{30} + 44070740257063185302 T^{31} + \)\(14\!\cdots\!88\)\( T^{32} + \)\(32\!\cdots\!69\)\( T^{33} + \)\(96\!\cdots\!91\)\( T^{34} + \)\(18\!\cdots\!59\)\( T^{35} + \)\(46\!\cdots\!76\)\( T^{36} + \)\(69\!\cdots\!99\)\( T^{37} + \)\(14\!\cdots\!25\)\( T^{38} + \)\(13\!\cdots\!93\)\( T^{39} + \)\(19\!\cdots\!01\)\( T^{40} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 13 T + 155 T^{2} + 1254 T^{3} + 9160 T^{4} + 55284 T^{5} + 309024 T^{6} + 1522263 T^{7} + 7096052 T^{8} + 29952602 T^{9} + 120632884 T^{10} + 439934007 T^{11} + 1518234912 T^{12} + 4617374964 T^{13} + 13005890120 T^{14} + 30268511526 T^{15} + 63602494315 T^{16} + 90684846733 T^{17} + 118587876497 T^{18} \))(\( 1 - 9 T + 152 T^{2} - 1037 T^{3} + 10141 T^{4} - 56380 T^{5} + 409608 T^{6} - 1923285 T^{7} + 11325598 T^{8} - 45513113 T^{9} + 225415358 T^{10} - 773722921 T^{11} + 3273097822 T^{12} - 9449099205 T^{13} + 34210869768 T^{14} - 80051537660 T^{15} + 244779087229 T^{16} - 425521203901 T^{17} + 1060315131032 T^{18} - 1067290888473 T^{19} + 2015993900449 T^{20} \))(\( 1 + 11 T + 162 T^{2} + 1315 T^{3} + 11926 T^{4} + 78747 T^{5} + 549770 T^{6} + 3089744 T^{7} + 17978263 T^{8} + 88128905 T^{9} + 443487026 T^{10} + 1920230718 T^{11} + 8509135824 T^{12} + 32643922206 T^{13} + 128167750514 T^{14} + 432977310265 T^{15} + 1501562504023 T^{16} + 4386994646608 T^{17} + 13270111309130 T^{18} + 32312939482731 T^{19} + 83192883241366 T^{20} + 155943057593555 T^{21} + 326591011872738 T^{22} + 376990859383963 T^{23} + 582622237229761 T^{24} \))(\( 1 - 11 T + 201 T^{2} - 1698 T^{3} + 18103 T^{4} - 126031 T^{5} + 1008183 T^{6} - 6030933 T^{7} + 39819749 T^{8} - 210366617 T^{9} + 1204743745 T^{10} - 5729336560 T^{11} + 29317892855 T^{12} - 127136200733 T^{13} + 591782669287 T^{14} - 2355665873410 T^{15} + 10060305377879 T^{16} - 36742362011837 T^{17} + 144038807596615 T^{18} - 478519918827760 T^{19} + 1710563839544465 T^{20} - 5077738733134073 T^{21} + 16339582963853077 T^{22} - 42070325750922453 T^{23} + 119558281090374951 T^{24} - 254077727267487919 T^{25} + 620424138857080199 T^{26} - 989292558816134178 T^{27} + 1990820184614093337 T^{28} - 1852156092153410219 T^{29} + 2862423051509815793 T^{30} \))(\( 1 + 8 T + 168 T^{2} + 1094 T^{3} + 12936 T^{4} + 72676 T^{5} + 638266 T^{6} + 3230701 T^{7} + 23535657 T^{8} + 110236578 T^{9} + 704135559 T^{10} + 3089429848 T^{11} + 17850678593 T^{12} + 73710688863 T^{13} + 392671629074 T^{14} + 1527388326679 T^{15} + 7581461046292 T^{16} + 27721055960372 T^{17} + 128884837786964 T^{18} + 441415226410231 T^{19} + 1929195713640562 T^{20} + 6156390444526623 T^{21} + 25345410955021201 T^{22} + 74571326126759512 T^{23} + 288934050892173207 T^{24} + 768983629253876898 T^{25} + 2791043585591753529 T^{26} + 6513073510174484749 T^{27} + 21874586168687684378 T^{28} + 42342653712910110436 T^{29} + \)\(12\!\cdots\!32\)\( T^{30} + \)\(18\!\cdots\!26\)\( T^{31} + \)\(48\!\cdots\!24\)\( T^{32} + \)\(38\!\cdots\!48\)\( T^{33} + \)\(82\!\cdots\!77\)\( T^{34} \))(\( 1 + 11 T + 187 T^{2} + 1466 T^{3} + 15045 T^{4} + 95975 T^{5} + 766879 T^{6} + 4276345 T^{7} + 29230872 T^{8} + 148160148 T^{9} + 904326022 T^{10} + 4257130832 T^{11} + 23760103160 T^{12} + 105394177764 T^{13} + 547114384798 T^{14} + 2312777899509 T^{15} + 11321989575037 T^{16} + 45992275060073 T^{17} + 214715852192474 T^{18} + 842066173843817 T^{19} + 3779929420654682 T^{20} + 14315124955344889 T^{21} + 62052881283624986 T^{22} + 225960047370138649 T^{23} + 945623891296665277 T^{24} + 3283813890063150213 T^{25} + 13206011213954276062 T^{26} + 43247307045605867172 T^{27} + \)\(16\!\cdots\!60\)\( T^{28} + \)\(50\!\cdots\!04\)\( T^{29} + \)\(18\!\cdots\!78\)\( T^{30} + \)\(50\!\cdots\!84\)\( T^{31} + \)\(17\!\cdots\!92\)\( T^{32} + \)\(42\!\cdots\!65\)\( T^{33} + \)\(12\!\cdots\!91\)\( T^{34} + \)\(27\!\cdots\!75\)\( T^{35} + \)\(73\!\cdots\!45\)\( T^{36} + \)\(12\!\cdots\!82\)\( T^{37} + \)\(26\!\cdots\!83\)\( T^{38} + \)\(26\!\cdots\!83\)\( T^{39} + \)\(40\!\cdots\!01\)\( T^{40} \))
$19$ (\( 1 - 8 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( 1 + 11 T + 149 T^{2} + 1181 T^{3} + 9356 T^{4} + 58968 T^{5} + 348929 T^{6} + 1847834 T^{7} + 8968293 T^{8} + 40969788 T^{9} + 170397567 T^{10} + 667068074 T^{11} + 2393304011 T^{12} + 7684768728 T^{13} + 23166382244 T^{14} + 55561185461 T^{15} + 133186889111 T^{16} + 186819193451 T^{17} + 322687697779 T^{18} \))(\( 1 + 13 T + 192 T^{2} + 1664 T^{3} + 14659 T^{4} + 97713 T^{5} + 648691 T^{6} + 3562244 T^{7} + 19446002 T^{8} + 91270928 T^{9} + 426588208 T^{10} + 1734147632 T^{11} + 7020006722 T^{12} + 24433431596 T^{13} + 84538059811 T^{14} + 241947061587 T^{15} + 689645569579 T^{16} + 1487402573696 T^{17} + 3260844103872 T^{18} + 4194940071127 T^{19} + 6131066257801 T^{20} \))(\( 1 + 13 T + 196 T^{2} + 1734 T^{3} + 16020 T^{4} + 111826 T^{5} + 798253 T^{6} + 4700466 T^{7} + 28178827 T^{8} + 144966631 T^{9} + 758572667 T^{10} + 3468912550 T^{11} + 16130954328 T^{12} + 65909338450 T^{13} + 273844732787 T^{14} + 994326122029 T^{15} + 3672292913467 T^{16} + 11638819162134 T^{17} + 37554515645893 T^{18} + 99958101085414 T^{19} + 272076679916820 T^{20} + 559540467948786 T^{21} + 1201688986528996 T^{22} + 1514373365676847 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 15 T + 259 T^{2} + 2701 T^{3} + 28615 T^{4} + 235883 T^{5} + 1927308 T^{6} + 13383443 T^{7} + 91572288 T^{8} + 554851665 T^{9} + 3307884597 T^{10} + 17842928505 T^{11} + 94681396897 T^{12} + 459769462949 T^{13} + 2196650574001 T^{14} + 9652630949326 T^{15} + 41736360906019 T^{16} + 165976776124589 T^{17} + 649419701316523 T^{18} + 2325308285700105 T^{19} + 8190649742747103 T^{20} + 26103485404241865 T^{21} + 81853880318768832 T^{22} + 227298547896130163 T^{23} + 621918581431048932 T^{24} + 1446214302088873283 T^{25} + 3333368758372536685 T^{26} + 5978163596397700861 T^{27} + 10891722716724578281 T^{28} + 11985100286743261815 T^{29} + 15181127029874798299 T^{30} \))(\( 1 - 7 T + 133 T^{2} - 705 T^{3} + 8374 T^{4} - 35180 T^{5} + 345811 T^{6} - 1208188 T^{7} + 11190229 T^{8} - 34531294 T^{9} + 315792563 T^{10} - 906583990 T^{11} + 8040380821 T^{12} - 21775619948 T^{13} + 183703598236 T^{14} - 469086364517 T^{15} + 3792015256306 T^{16} - 9233975523846 T^{17} + 72048289869814 T^{18} - 169340177590637 T^{19} + 1260022980300724 T^{20} - 2837820567243308 T^{21} + 19908778910497279 T^{22} - 42651042510045190 T^{23} + 282278047452077057 T^{24} - 586464408536305054 T^{25} + 3610949233629801391 T^{26} - 7407480679880074588 T^{27} + 40283612919852010609 T^{28} - 77864418852747543980 T^{29} + \)\(35\!\cdots\!66\)\( T^{30} - \)\(56\!\cdots\!05\)\( T^{31} + \)\(20\!\cdots\!67\)\( T^{32} - \)\(20\!\cdots\!67\)\( T^{33} + \)\(54\!\cdots\!39\)\( T^{34} \))(\( 1 - 17 T + 328 T^{2} - 3718 T^{3} + 43206 T^{4} - 378002 T^{5} + 3319937 T^{6} - 23893056 T^{7} + 171910607 T^{8} - 1049674263 T^{9} + 6420497259 T^{10} - 33673266646 T^{11} + 178116297884 T^{12} - 799930391474 T^{13} + 3679058705569 T^{14} - 13840172383731 T^{15} + 55520795289792 T^{16} - 166885253979295 T^{17} + 618842889946139 T^{18} - 1519199049734360 T^{19} + 7761996180389628 T^{20} - 28864781944952840 T^{21} + 223402283270556179 T^{22} - 1144665957043984405 T^{23} + 7235525562960983232 T^{24} - 34269636999183945369 T^{25} + \)\(17\!\cdots\!89\)\( T^{26} - \)\(71\!\cdots\!86\)\( T^{27} + \)\(30\!\cdots\!44\)\( T^{28} - \)\(10\!\cdots\!34\)\( T^{29} + \)\(39\!\cdots\!59\)\( T^{30} - \)\(12\!\cdots\!97\)\( T^{31} + \)\(38\!\cdots\!27\)\( T^{32} - \)\(10\!\cdots\!04\)\( T^{33} + \)\(26\!\cdots\!77\)\( T^{34} - \)\(57\!\cdots\!98\)\( T^{35} + \)\(12\!\cdots\!86\)\( T^{36} - \)\(20\!\cdots\!02\)\( T^{37} + \)\(34\!\cdots\!48\)\( T^{38} - \)\(33\!\cdots\!43\)\( T^{39} + \)\(37\!\cdots\!01\)\( T^{40} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 4 T + 48 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 204 T^{2} + 1428 T^{3} + 18095 T^{4} + 103135 T^{5} + 939715 T^{6} + 4443747 T^{7} + 31831811 T^{8} + 125006960 T^{9} + 732131653 T^{10} + 2350742163 T^{11} + 11433512405 T^{12} + 28861401535 T^{13} + 116465626585 T^{14} + 211395249492 T^{15} + 694584391188 T^{16} + 704798867529 T^{17} + 1801152661463 T^{18} \))(\( 1 + 3 T + 187 T^{2} + 425 T^{3} + 16093 T^{4} + 27993 T^{5} + 855348 T^{6} + 1169460 T^{7} + 31480234 T^{8} + 35291365 T^{9} + 842951618 T^{10} + 811701395 T^{11} + 16653043786 T^{12} + 14228819820 T^{13} + 239361439668 T^{14} + 180172549599 T^{15} + 2382341561677 T^{16} + 1447050814975 T^{17} + 14644154247547 T^{18} + 5403457984389 T^{19} + 41426511213649 T^{20} \))(\( 1 + 21 T + 349 T^{2} + 4069 T^{3} + 41236 T^{4} + 351240 T^{5} + 2716341 T^{6} + 18804819 T^{7} + 121076813 T^{8} + 718665218 T^{9} + 4018862412 T^{10} + 21002818223 T^{11} + 103985618488 T^{12} + 483064819129 T^{13} + 2125978215948 T^{14} + 8743999707406 T^{15} + 33882256426733 T^{16} + 121034265136917 T^{17} + 402115954762149 T^{18} + 1195910890004280 T^{19} + 3229231789047316 T^{20} + 7328890179492947 T^{21} + 14457852413563501 T^{22} + 20009004916192467 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 3 T + 124 T^{2} + 612 T^{3} + 8498 T^{4} + 51692 T^{5} + 449663 T^{6} + 2750157 T^{7} + 19626301 T^{8} + 111745772 T^{9} + 708496310 T^{10} + 3765357540 T^{11} + 21650852124 T^{12} + 107736805365 T^{13} + 572963668571 T^{14} + 2656934667606 T^{15} + 13178164377133 T^{16} + 56992770038085 T^{17} + 263425917792708 T^{18} + 1053701419351140 T^{19} + 4560125265394330 T^{20} + 16542384700011308 T^{21} + 66824129075281547 T^{22} + 215367504347439117 T^{23} + 809911709211436969 T^{24} + 2141419217655944108 T^{25} + 8096977322752551646 T^{26} + 13411750152396436452 T^{27} + 62500508880121955492 T^{28} + 34778508973616249427 T^{29} + \)\(26\!\cdots\!07\)\( T^{30} \))(\( 1 - T + 258 T^{2} - 586 T^{3} + 32167 T^{4} - 110407 T^{5} + 2627477 T^{6} - 11472227 T^{7} + 159987825 T^{8} - 793118792 T^{9} + 7755873787 T^{10} - 40094248967 T^{11} + 308835875999 T^{12} - 1566359147625 T^{13} + 10221086295673 T^{14} - 48903765882012 T^{15} + 281969559330651 T^{16} - 1242948205696206 T^{17} + 6485299864604973 T^{18} - 25870092151584348 T^{19} + 124359956959453391 T^{20} - 438331510230527625 T^{21} + 1987773628635031657 T^{22} - 5935387789617176663 T^{23} + 26407396433697857789 T^{24} - 62109914046396500552 T^{25} + \)\(28\!\cdots\!75\)\( T^{26} - \)\(47\!\cdots\!23\)\( T^{27} + \)\(25\!\cdots\!79\)\( T^{28} - \)\(24\!\cdots\!47\)\( T^{29} + \)\(16\!\cdots\!61\)\( T^{30} - \)\(67\!\cdots\!74\)\( T^{31} + \)\(68\!\cdots\!06\)\( T^{32} - \)\(61\!\cdots\!61\)\( T^{33} + \)\(14\!\cdots\!03\)\( T^{34} \))(\( 1 + 3 T + 111 T^{2} + 81 T^{3} + 6554 T^{4} - 8790 T^{5} + 281777 T^{6} - 990877 T^{7} + 10440367 T^{8} - 54806504 T^{9} + 368391954 T^{10} - 2188486123 T^{11} + 12502551884 T^{12} - 72140341875 T^{13} + 394333527374 T^{14} - 2106944090532 T^{15} + 11261617726288 T^{16} - 56751441150884 T^{17} + 291511876182384 T^{18} - 1416598262006791 T^{19} + 6953049529150452 T^{20} - 32581760026156193 T^{21} + 154209782500481136 T^{22} - 690494784482805628 T^{23} + 3151462366142160208 T^{24} - 13561014848487004476 T^{25} + 58375514287315925486 T^{26} - \)\(24\!\cdots\!25\)\( T^{27} + \)\(97\!\cdots\!04\)\( T^{28} - \)\(39\!\cdots\!49\)\( T^{29} + \)\(15\!\cdots\!46\)\( T^{30} - \)\(52\!\cdots\!08\)\( T^{31} + \)\(22\!\cdots\!07\)\( T^{32} - \)\(49\!\cdots\!91\)\( T^{33} + \)\(32\!\cdots\!93\)\( T^{34} - \)\(23\!\cdots\!30\)\( T^{35} + \)\(40\!\cdots\!94\)\( T^{36} + \)\(11\!\cdots\!43\)\( T^{37} + \)\(36\!\cdots\!59\)\( T^{38} + \)\(22\!\cdots\!61\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$29$ (\( 1 + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 14 T^{2} + 841 T^{4} \))(\( 1 + 20 T + 368 T^{2} + 4312 T^{3} + 46906 T^{4} + 399688 T^{5} + 3211699 T^{6} + 21630457 T^{7} + 138714394 T^{8} + 764244162 T^{9} + 4022717426 T^{10} + 18191214337 T^{11} + 78330126911 T^{12} + 282691728328 T^{13} + 962095954994 T^{14} + 2564878160152 T^{15} + 6347954481712 T^{16} + 10004928259220 T^{17} + 14507145975869 T^{18} \))(\( 1 + 4 T + 129 T^{2} + 570 T^{3} + 7726 T^{4} + 35616 T^{5} + 303517 T^{6} + 1267961 T^{7} + 9743651 T^{8} + 32792993 T^{9} + 289804684 T^{10} + 950996797 T^{11} + 8194410491 T^{12} + 30924300829 T^{13} + 214671807277 T^{14} + 730525082784 T^{15} + 4595604978046 T^{16} + 9832429496130 T^{17} + 64531787271969 T^{18} + 58028583903476 T^{19} + 420707233300201 T^{20} \))(\( 1 + 10 T + 261 T^{2} + 1966 T^{3} + 30097 T^{4} + 183996 T^{5} + 2161060 T^{6} + 11255937 T^{7} + 112103665 T^{8} + 513250943 T^{9} + 4517680475 T^{10} + 18482818840 T^{11} + 145826528258 T^{12} + 536001746360 T^{13} + 3799369279475 T^{14} + 12517677248827 T^{15} + 79288792284865 T^{16} + 230872200941613 T^{17} + 1285448886080260 T^{18} + 3173908241350764 T^{19} + 15055916290887217 T^{20} + 28521048988558454 T^{21} + 109804587891352461 T^{22} + 122005097657058290 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 28 T + 592 T^{2} - 9056 T^{3} + 118911 T^{4} - 1329738 T^{5} + 13420255 T^{6} - 121873217 T^{7} + 1024877301 T^{8} - 7960726826 T^{9} + 58099319823 T^{10} - 397236746984 T^{11} + 2573553953982 T^{12} - 15741129677616 T^{13} + 91644010024595 T^{14} - 505485533978350 T^{15} + 2657676290713255 T^{16} - 13238290058875056 T^{17} + 62766407383666998 T^{18} - 280958003643590504 T^{19} + 1191683805688206627 T^{20} - 4735225968215109146 T^{21} + 17679006674151762009 T^{22} - 60966639640267565537 T^{23} + \)\(19\!\cdots\!95\)\( T^{24} - \)\(55\!\cdots\!38\)\( T^{25} + \)\(14\!\cdots\!19\)\( T^{26} - \)\(32\!\cdots\!96\)\( T^{27} + \)\(60\!\cdots\!88\)\( T^{28} - \)\(83\!\cdots\!68\)\( T^{29} + \)\(86\!\cdots\!49\)\( T^{30} \))(\( 1 + 18 T + 422 T^{2} + 5366 T^{3} + 74920 T^{4} + 759404 T^{5} + 8051121 T^{6} + 69428979 T^{7} + 613731180 T^{8} + 4684021786 T^{9} + 36208020002 T^{10} + 250319762307 T^{11} + 1736799896485 T^{12} + 11012058661404 T^{13} + 69594977253398 T^{14} + 407119920018492 T^{15} + 2364206156173403 T^{16} + 12786761412429272 T^{17} + 68561978529028687 T^{18} + 342387852735551772 T^{19} + 1697351900233123822 T^{20} + 7788619862096482524 T^{21} + 35623761459988411265 T^{22} + \)\(14\!\cdots\!47\)\( T^{23} + \)\(62\!\cdots\!18\)\( T^{24} + \)\(23\!\cdots\!46\)\( T^{25} + \)\(89\!\cdots\!20\)\( T^{26} + \)\(29\!\cdots\!79\)\( T^{27} + \)\(98\!\cdots\!09\)\( T^{28} + \)\(26\!\cdots\!64\)\( T^{29} + \)\(76\!\cdots\!80\)\( T^{30} + \)\(15\!\cdots\!46\)\( T^{31} + \)\(36\!\cdots\!78\)\( T^{32} + \)\(45\!\cdots\!78\)\( T^{33} + \)\(72\!\cdots\!09\)\( T^{34} \))(\( 1 - 6 T + 279 T^{2} - 1754 T^{3} + 39553 T^{4} - 243622 T^{5} + 3749498 T^{6} - 21733423 T^{7} + 264103463 T^{8} - 1412924349 T^{9} + 14664372197 T^{10} - 71922469734 T^{11} + 670676080400 T^{12} - 3016767543462 T^{13} + 26260811561223 T^{14} - 109030716579071 T^{15} + 912551573568488 T^{16} - 3544260981938023 T^{17} + 29048131149675435 T^{18} - 107588090610467364 T^{19} + 866530819130155742 T^{20} - 3120054627703553556 T^{21} + 24429478296877040835 T^{22} - 86440981088486442947 T^{23} + \)\(64\!\cdots\!28\)\( T^{24} - \)\(22\!\cdots\!79\)\( T^{25} + \)\(15\!\cdots\!83\)\( T^{26} - \)\(52\!\cdots\!58\)\( T^{27} + \)\(33\!\cdots\!00\)\( T^{28} - \)\(10\!\cdots\!46\)\( T^{29} + \)\(61\!\cdots\!97\)\( T^{30} - \)\(17\!\cdots\!21\)\( T^{31} + \)\(93\!\cdots\!83\)\( T^{32} - \)\(22\!\cdots\!47\)\( T^{33} + \)\(11\!\cdots\!38\)\( T^{34} - \)\(21\!\cdots\!78\)\( T^{35} + \)\(98\!\cdots\!13\)\( T^{36} - \)\(12\!\cdots\!86\)\( T^{37} + \)\(58\!\cdots\!19\)\( T^{38} - \)\(36\!\cdots\!14\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$31$ (\( 1 - 5 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( 1 + 11 T + 207 T^{2} + 1833 T^{3} + 20926 T^{4} + 154797 T^{5} + 1326048 T^{6} + 8304128 T^{7} + 57773680 T^{8} + 307226774 T^{9} + 1790984080 T^{10} + 7980267008 T^{11} + 39504295968 T^{12} + 142958280237 T^{13} + 599093613826 T^{14} + 1626794247273 T^{15} + 5695111120977 T^{16} + 9381801411851 T^{17} + 26439622160671 T^{18} \))(\( 1 + 17 T + 216 T^{2} + 2088 T^{3} + 18749 T^{4} + 145342 T^{5} + 1063788 T^{6} + 7150461 T^{7} + 46404448 T^{8} + 277307962 T^{9} + 1596171690 T^{10} + 8596546822 T^{11} + 44594674528 T^{12} + 213019383651 T^{13} + 982430557548 T^{14} + 4161018064642 T^{15} + 16639806515069 T^{16} + 57446338263768 T^{17} + 184224464087256 T^{18} + 449473576731407 T^{19} + 819628286980801 T^{20} \))(\( 1 + 11 T + 227 T^{2} + 1615 T^{3} + 20900 T^{4} + 112977 T^{5} + 1271977 T^{6} + 5946911 T^{7} + 62721163 T^{8} + 260661987 T^{9} + 2517960900 T^{10} + 9282982813 T^{11} + 83977696464 T^{12} + 287772467203 T^{13} + 2419760424900 T^{14} + 7765381254717 T^{15} + 57924311174923 T^{16} + 170255013002561 T^{17} + 1128884269647337 T^{18} + 3108292604418447 T^{19} + 17825422682516900 T^{20} + 42699989789483665 T^{21} + 186055621144641827 T^{22} + 279493245860453141 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 12 T + 312 T^{2} + 3391 T^{3} + 50061 T^{4} + 473669 T^{5} + 5261407 T^{6} + 43653203 T^{7} + 400511494 T^{8} + 2956576801 T^{9} + 23425062532 T^{10} + 155376971917 T^{11} + 1090342519305 T^{12} + 6539376833326 T^{13} + 41213522489050 T^{14} + 224098836266594 T^{15} + 1277619197160550 T^{16} + 6284341136826286 T^{17} + 32482393992615255 T^{18} + 143493896481759757 T^{19} + 670639652413070332 T^{20} + 2623972794046704481 T^{21} + 11019118181442091834 T^{22} + 37231425594292573523 T^{23} + \)\(13\!\cdots\!97\)\( T^{24} + \)\(38\!\cdots\!69\)\( T^{25} + \)\(12\!\cdots\!91\)\( T^{26} + \)\(26\!\cdots\!51\)\( T^{27} + \)\(76\!\cdots\!92\)\( T^{28} + \)\(90\!\cdots\!52\)\( T^{29} + \)\(23\!\cdots\!51\)\( T^{30} \))(\( 1 - 8 T + 312 T^{2} - 1959 T^{3} + 44439 T^{4} - 218039 T^{5} + 3922014 T^{6} - 14675929 T^{7} + 248125485 T^{8} - 684671706 T^{9} + 12521348281 T^{10} - 25349781723 T^{11} + 548292039678 T^{12} - 880790272986 T^{13} + 21689791691904 T^{14} - 31097258913017 T^{15} + 768095225334912 T^{16} - 1028370458485346 T^{17} + 23810951985382272 T^{18} - 29884465815409337 T^{19} + 646160584293512064 T^{20} - 813428313698303706 T^{21} + 15697135596039453378 T^{22} - 22498024591709022363 T^{23} + \)\(34\!\cdots\!91\)\( T^{24} - \)\(58\!\cdots\!46\)\( T^{25} + \)\(65\!\cdots\!35\)\( T^{26} - \)\(12\!\cdots\!29\)\( T^{27} + \)\(99\!\cdots\!34\)\( T^{28} - \)\(17\!\cdots\!79\)\( T^{29} + \)\(10\!\cdots\!49\)\( T^{30} - \)\(14\!\cdots\!39\)\( T^{31} + \)\(73\!\cdots\!12\)\( T^{32} - \)\(58\!\cdots\!48\)\( T^{33} + \)\(22\!\cdots\!11\)\( T^{34} \))(\( 1 - 28 T + 672 T^{2} - 11309 T^{3} + 167975 T^{4} - 2095701 T^{5} + 23693151 T^{6} - 237991181 T^{7} + 2201384919 T^{8} - 18525865649 T^{9} + 144838949648 T^{10} - 1040741709740 T^{11} + 6970732125174 T^{12} - 42986376020677 T^{13} + 246787658105407 T^{14} - 1298130078805857 T^{15} + 6342038871927391 T^{16} - 28318552383402343 T^{17} + 121028837362334126 T^{18} - 513350287388893799 T^{19} + 2580102329863498336 T^{20} - 15913858909055707769 T^{21} + \)\(11\!\cdots\!86\)\( T^{22} - \)\(84\!\cdots\!13\)\( T^{23} + \)\(58\!\cdots\!11\)\( T^{24} - \)\(37\!\cdots\!07\)\( T^{25} + \)\(21\!\cdots\!67\)\( T^{26} - \)\(11\!\cdots\!47\)\( T^{27} + \)\(59\!\cdots\!34\)\( T^{28} - \)\(27\!\cdots\!40\)\( T^{29} + \)\(11\!\cdots\!48\)\( T^{30} - \)\(47\!\cdots\!19\)\( T^{31} + \)\(17\!\cdots\!59\)\( T^{32} - \)\(58\!\cdots\!71\)\( T^{33} + \)\(17\!\cdots\!71\)\( T^{34} - \)\(49\!\cdots\!51\)\( T^{35} + \)\(12\!\cdots\!75\)\( T^{36} - \)\(25\!\cdots\!99\)\( T^{37} + \)\(46\!\cdots\!52\)\( T^{38} - \)\(60\!\cdots\!88\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))
$37$ (\( 1 + 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 12 T + 92 T^{2} - 444 T^{3} + 1369 T^{4} \))(\( 1 + 25 T + 527 T^{2} + 7600 T^{3} + 95916 T^{4} + 991756 T^{5} + 9178026 T^{6} + 73462489 T^{7} + 532196738 T^{8} + 3397008442 T^{9} + 19691279306 T^{10} + 100570147441 T^{11} + 464894550978 T^{12} + 1858710416716 T^{13} + 6651194979612 T^{14} + 19499520708400 T^{15} + 50029099249091 T^{16} + 87811986348025 T^{17} + 129961739795077 T^{18} \))(\( 1 + 15 T + 318 T^{2} + 3739 T^{3} + 45945 T^{4} + 441510 T^{5} + 4052846 T^{6} + 32751775 T^{7} + 244564024 T^{8} + 1686062901 T^{9} + 10602280982 T^{10} + 62384327337 T^{11} + 334808148856 T^{12} + 1658975659075 T^{13} + 7595685912206 T^{14} + 30616050455070 T^{15} + 117882299861505 T^{16} + 354950288600287 T^{17} + 1116968466346878 T^{18} + 1949426096926155 T^{19} + 4808584372417849 T^{20} \))(\( 1 + 29 T + 634 T^{2} + 10187 T^{3} + 139602 T^{4} + 1636549 T^{5} + 17180810 T^{6} + 161860688 T^{7} + 1397336497 T^{8} + 11054079853 T^{9} + 81045685614 T^{10} + 549653977234 T^{11} + 3471535946572 T^{12} + 20337197157658 T^{13} + 110951543605566 T^{14} + 559922306794009 T^{15} + 2618833566554017 T^{16} + 11224060588662416 T^{17} + 44081257945011290 T^{18} + 155360668590134017 T^{19} + 490349156726279442 T^{20} + 1323920243292449399 T^{21} + 3048642492112916266 T^{22} + 5159611031604351977 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + 23 T + 631 T^{2} + 9862 T^{3} + 160449 T^{4} + 1941751 T^{5} + 23709039 T^{6} + 237293533 T^{7} + 2376900989 T^{8} + 20457880839 T^{9} + 175964491963 T^{10} + 1334117021208 T^{11} + 10109417826565 T^{12} + 68450761317695 T^{13} + 463302787160399 T^{14} + 2818655318051962 T^{15} + 17142203124934763 T^{16} + 93709092243924455 T^{17} + 512072341168996945 T^{18} + 2500350090584206488 T^{19} + 12202074164209117591 T^{20} + 52489325140797377151 T^{21} + \)\(22\!\cdots\!37\)\( T^{22} + \)\(83\!\cdots\!93\)\( T^{23} + \)\(30\!\cdots\!03\)\( T^{24} + \)\(93\!\cdots\!99\)\( T^{25} + \)\(28\!\cdots\!37\)\( T^{26} + \)\(64\!\cdots\!22\)\( T^{27} + \)\(15\!\cdots\!07\)\( T^{28} + \)\(20\!\cdots\!47\)\( T^{29} + \)\(33\!\cdots\!93\)\( T^{30} \))(\( 1 - 49 T + 1469 T^{2} - 32090 T^{3} + 566892 T^{4} - 8466258 T^{5} + 110624422 T^{6} - 1291076383 T^{7} + 13694744232 T^{8} - 133629921796 T^{9} + 1212080214934 T^{10} - 10296247480623 T^{11} + 82429685546352 T^{12} - 624601352421982 T^{13} + 4495064660144854 T^{14} - 30787282954238032 T^{15} + 201000306711998104 T^{16} - 1251645098480898870 T^{17} + 7437011348343929848 T^{18} - 42147790364351865808 T^{19} + \)\(22\!\cdots\!62\)\( T^{20} - \)\(11\!\cdots\!02\)\( T^{21} + \)\(57\!\cdots\!64\)\( T^{22} - \)\(26\!\cdots\!07\)\( T^{23} + \)\(11\!\cdots\!22\)\( T^{24} - \)\(46\!\cdots\!16\)\( T^{25} + \)\(17\!\cdots\!64\)\( T^{26} - \)\(62\!\cdots\!67\)\( T^{27} + \)\(19\!\cdots\!86\)\( T^{28} - \)\(55\!\cdots\!98\)\( T^{29} + \)\(13\!\cdots\!24\)\( T^{30} - \)\(28\!\cdots\!10\)\( T^{31} + \)\(48\!\cdots\!17\)\( T^{32} - \)\(60\!\cdots\!09\)\( T^{33} + \)\(45\!\cdots\!17\)\( T^{34} \))(\( 1 - 33 T + 920 T^{2} - 18109 T^{3} + 313072 T^{4} - 4577405 T^{5} + 60573576 T^{6} - 718614854 T^{7} + 7868440417 T^{8} - 79393277341 T^{9} + 749405759288 T^{10} - 6625840847018 T^{11} + 55371470318800 T^{12} - 438534234155610 T^{13} + 3312305751623064 T^{14} - 23944987027564343 T^{15} + 166488942952783662 T^{16} - 1117799717799449857 T^{17} + 7273115895541291536 T^{18} - 46011991044893902286 T^{19} + \)\(28\!\cdots\!76\)\( T^{20} - \)\(17\!\cdots\!82\)\( T^{21} + \)\(99\!\cdots\!84\)\( T^{22} - \)\(56\!\cdots\!21\)\( T^{23} + \)\(31\!\cdots\!82\)\( T^{24} - \)\(16\!\cdots\!51\)\( T^{25} + \)\(84\!\cdots\!76\)\( T^{26} - \)\(41\!\cdots\!30\)\( T^{27} + \)\(19\!\cdots\!00\)\( T^{28} - \)\(86\!\cdots\!86\)\( T^{29} + \)\(36\!\cdots\!12\)\( T^{30} - \)\(14\!\cdots\!33\)\( T^{31} + \)\(51\!\cdots\!77\)\( T^{32} - \)\(17\!\cdots\!38\)\( T^{33} + \)\(54\!\cdots\!64\)\( T^{34} - \)\(15\!\cdots\!65\)\( T^{35} + \)\(38\!\cdots\!52\)\( T^{36} - \)\(82\!\cdots\!53\)\( T^{37} + \)\(15\!\cdots\!80\)\( T^{38} - \)\(20\!\cdots\!09\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 + 9 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 50 T^{2} + 1681 T^{4} \))(\( 1 + 29 T + 563 T^{2} + 8225 T^{3} + 99790 T^{4} + 1036815 T^{5} + 9513930 T^{6} + 77954978 T^{7} + 577358404 T^{8} + 3876393614 T^{9} + 23671694564 T^{10} + 131042318018 T^{11} + 655709569530 T^{12} + 2929791391215 T^{13} + 11561290297790 T^{14} + 39069607382225 T^{15} + 109646656195003 T^{16} + 231562831644509 T^{17} + 327381934393961 T^{18} \))(\( 1 + 11 T + 238 T^{2} + 2000 T^{3} + 28011 T^{4} + 207360 T^{5} + 2280094 T^{6} + 14946485 T^{7} + 137235898 T^{8} + 799593928 T^{9} + 6373618252 T^{10} + 32783351048 T^{11} + 230693544538 T^{12} + 1030126692685 T^{13} + 6443000701534 T^{14} + 24023941839360 T^{15} + 133055169894651 T^{16} + 389508547762000 T^{17} + 1900412204530798 T^{18} + 3601201278333571 T^{19} + 13422659310152401 T^{20} \))(\( 1 + T + 227 T^{2} + 611 T^{3} + 26416 T^{4} + 110933 T^{5} + 2147305 T^{6} + 11550595 T^{7} + 136264421 T^{8} + 830907243 T^{9} + 7141720354 T^{10} + 44376965029 T^{11} + 317294625780 T^{12} + 1819455566189 T^{13} + 12005231915074 T^{14} + 57266958094803 T^{15} + 385050686549381 T^{16} + 1338208055989595 T^{17} + 10199922587220505 T^{18} + 21604675864440973 T^{19} + 210929784852460336 T^{20} + 200030361914710171 T^{21} + 3046943663404595027 T^{22} + 550329031716248441 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 24 T + 670 T^{2} - 10895 T^{3} + 179923 T^{4} - 2256817 T^{5} + 27807705 T^{6} - 286893495 T^{7} + 2878892760 T^{8} - 25426568643 T^{9} + 218122769030 T^{10} - 1699280099085 T^{11} + 12895674297205 T^{12} - 90796070166964 T^{13} + 625402948135754 T^{14} - 4044538038489338 T^{15} + 25641520873565914 T^{16} - 152628193950666484 T^{17} + 888782768237665805 T^{18} - 4801759432070528685 T^{19} + 25270875371416255030 T^{20} - \)\(12\!\cdots\!63\)\( T^{21} + \)\(56\!\cdots\!60\)\( T^{22} - \)\(22\!\cdots\!95\)\( T^{23} + \)\(91\!\cdots\!05\)\( T^{24} - \)\(30\!\cdots\!17\)\( T^{25} + \)\(99\!\cdots\!43\)\( T^{26} - \)\(24\!\cdots\!95\)\( T^{27} + \)\(61\!\cdots\!70\)\( T^{28} - \)\(91\!\cdots\!64\)\( T^{29} + \)\(15\!\cdots\!01\)\( T^{30} \))(\( 1 + 23 T + 620 T^{2} + 9604 T^{3} + 150152 T^{4} + 1746449 T^{5} + 19856985 T^{6} + 183192678 T^{7} + 1652492326 T^{8} + 12639253899 T^{9} + 97054103390 T^{10} + 660616002064 T^{11} + 4771274246477 T^{12} + 32067998683418 T^{13} + 235132990774778 T^{14} + 1596412759123138 T^{15} + 11325808375103459 T^{16} + 71952763534328646 T^{17} + 464358143379241819 T^{18} + 2683569848085994978 T^{19} + 16205600857188474538 T^{20} + 90616500027653931098 T^{21} + \)\(55\!\cdots\!77\)\( T^{22} + \)\(31\!\cdots\!24\)\( T^{23} + \)\(18\!\cdots\!90\)\( T^{24} + \)\(10\!\cdots\!79\)\( T^{25} + \)\(54\!\cdots\!86\)\( T^{26} + \)\(24\!\cdots\!78\)\( T^{27} + \)\(10\!\cdots\!85\)\( T^{28} + \)\(39\!\cdots\!69\)\( T^{29} + \)\(13\!\cdots\!92\)\( T^{30} + \)\(36\!\cdots\!44\)\( T^{31} + \)\(96\!\cdots\!20\)\( T^{32} + \)\(14\!\cdots\!43\)\( T^{33} + \)\(26\!\cdots\!81\)\( T^{34} \))(\( 1 - 32 T + 942 T^{2} - 19053 T^{3} + 349697 T^{4} - 5380853 T^{5} + 76242290 T^{6} - 965917263 T^{7} + 11420272429 T^{8} - 124364941580 T^{9} + 1277017218691 T^{10} - 12280763635141 T^{11} + 112253680031242 T^{12} - 971318643399844 T^{13} + 8039228992738246 T^{14} - 63459953289904227 T^{15} + 481541267720648344 T^{16} - 3503326536622076286 T^{17} + 24588161616267071735 T^{18} - \)\(16\!\cdots\!69\)\( T^{19} + \)\(10\!\cdots\!26\)\( T^{20} - \)\(68\!\cdots\!29\)\( T^{21} + \)\(41\!\cdots\!35\)\( T^{22} - \)\(24\!\cdots\!06\)\( T^{23} + \)\(13\!\cdots\!84\)\( T^{24} - \)\(73\!\cdots\!27\)\( T^{25} + \)\(38\!\cdots\!86\)\( T^{26} - \)\(18\!\cdots\!64\)\( T^{27} + \)\(89\!\cdots\!82\)\( T^{28} - \)\(40\!\cdots\!01\)\( T^{29} + \)\(17\!\cdots\!91\)\( T^{30} - \)\(68\!\cdots\!80\)\( T^{31} + \)\(25\!\cdots\!49\)\( T^{32} - \)\(89\!\cdots\!23\)\( T^{33} + \)\(28\!\cdots\!90\)\( T^{34} - \)\(83\!\cdots\!53\)\( T^{35} + \)\(22\!\cdots\!77\)\( T^{36} - \)\(49\!\cdots\!93\)\( T^{37} + \)\(10\!\cdots\!82\)\( T^{38} - \)\(14\!\cdots\!52\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$43$ (\( 1 - 5 T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 42 T^{2} + 1849 T^{4} \))(\( 1 + 11 T + 388 T^{2} + 3506 T^{3} + 66348 T^{4} + 499753 T^{5} + 6611727 T^{6} + 41605289 T^{7} + 424683678 T^{8} + 2212249306 T^{9} + 18261398154 T^{10} + 76928179361 T^{11} + 525678578589 T^{12} + 1708556056153 T^{13} + 9753716176164 T^{14} + 22162698849794 T^{15} + 105465621109516 T^{16} + 128570203053611 T^{17} + 502592611936843 T^{18} \))(\( 1 + 11 T + 197 T^{2} + 1901 T^{3} + 22094 T^{4} + 191017 T^{5} + 1740213 T^{6} + 13397158 T^{7} + 106178861 T^{8} + 725466695 T^{9} + 5107982132 T^{10} + 31195067885 T^{11} + 196324713989 T^{12} + 1065167841106 T^{13} + 5949441944613 T^{14} + 28081111756531 T^{15} + 139664195204606 T^{16} + 516727179714407 T^{17} + 2302575454687397 T^{18} + 5528518731305273 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 23 T + 710 T^{2} + 11408 T^{3} + 202944 T^{4} + 2518327 T^{5} + 32679638 T^{6} + 329144290 T^{7} + 3389916092 T^{8} + 28462469768 T^{9} + 242020145644 T^{10} + 1716470265728 T^{11} + 12282801803942 T^{12} + 73808221426304 T^{13} + 447495249295756 T^{14} + 2262965583844376 T^{15} + 11589448525245692 T^{16} + 48386989595240470 T^{17} + 206579856107896262 T^{18} + 684528147453257989 T^{19} + 2372050117137457344 T^{20} + 5733576516975504944 T^{21} + 15344152442431816790 T^{22} + 21373756007838122261 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 24 T + 633 T^{2} + 10211 T^{3} + 161530 T^{4} + 1988610 T^{5} + 23579220 T^{6} + 235622334 T^{7} + 2271701453 T^{8} + 19148162290 T^{9} + 157415248835 T^{10} + 1158540227245 T^{11} + 8489803201446 T^{12} + 57001180431012 T^{13} + 391948398111494 T^{14} + 2520191424987268 T^{15} + 16853781118794242 T^{16} + 105395182616941188 T^{17} + 674998783137367122 T^{18} + 3960818487445433245 T^{19} + 23141370635690913905 T^{20} + \)\(12\!\cdots\!10\)\( T^{21} + \)\(61\!\cdots\!71\)\( T^{22} + \)\(27\!\cdots\!34\)\( T^{23} + \)\(11\!\cdots\!60\)\( T^{24} + \)\(42\!\cdots\!90\)\( T^{25} + \)\(15\!\cdots\!10\)\( T^{26} + \)\(40\!\cdots\!11\)\( T^{27} + \)\(10\!\cdots\!19\)\( T^{28} + \)\(17\!\cdots\!76\)\( T^{29} + \)\(31\!\cdots\!07\)\( T^{30} \))(\( 1 - 35 T + 988 T^{2} - 19244 T^{3} + 328086 T^{4} - 4626589 T^{5} + 59393385 T^{6} - 671846123 T^{7} + 7085796272 T^{8} - 68012421768 T^{9} + 619141166474 T^{10} - 5234558106879 T^{11} + 42543454724555 T^{12} - 325721078958459 T^{13} + 2423010400582732 T^{14} - 17145483709223346 T^{15} + 118724804383340653 T^{16} - 786006320930521050 T^{17} + 5105166588483648079 T^{18} - 31701999378353966754 T^{19} + \)\(19\!\cdots\!24\)\( T^{20} - \)\(11\!\cdots\!59\)\( T^{21} + \)\(62\!\cdots\!65\)\( T^{22} - \)\(33\!\cdots\!71\)\( T^{23} + \)\(16\!\cdots\!18\)\( T^{24} - \)\(79\!\cdots\!68\)\( T^{25} + \)\(35\!\cdots\!96\)\( T^{26} - \)\(14\!\cdots\!27\)\( T^{27} + \)\(55\!\cdots\!95\)\( T^{28} - \)\(18\!\cdots\!89\)\( T^{29} + \)\(56\!\cdots\!98\)\( T^{30} - \)\(14\!\cdots\!56\)\( T^{31} + \)\(31\!\cdots\!16\)\( T^{32} - \)\(47\!\cdots\!35\)\( T^{33} + \)\(58\!\cdots\!43\)\( T^{34} \))(\( 1 - 30 T + 856 T^{2} - 16665 T^{3} + 299663 T^{4} - 4514387 T^{5} + 63414770 T^{6} - 797741034 T^{7} + 9455911046 T^{8} - 103474312852 T^{9} + 1075697205290 T^{10} - 10496289515336 T^{11} + 97896045691830 T^{12} - 865628308270888 T^{13} + 7348985142939734 T^{14} - 59527585557919532 T^{15} + 464424940702494377 T^{16} - 3470866238516529340 T^{17} + 25035376828074798390 T^{18} - \)\(17\!\cdots\!02\)\( T^{19} + \)\(11\!\cdots\!90\)\( T^{20} - \)\(74\!\cdots\!86\)\( T^{21} + \)\(46\!\cdots\!10\)\( T^{22} - \)\(27\!\cdots\!80\)\( T^{23} + \)\(15\!\cdots\!77\)\( T^{24} - \)\(87\!\cdots\!76\)\( T^{25} + \)\(46\!\cdots\!66\)\( T^{26} - \)\(23\!\cdots\!16\)\( T^{27} + \)\(11\!\cdots\!30\)\( T^{28} - \)\(52\!\cdots\!48\)\( T^{29} + \)\(23\!\cdots\!10\)\( T^{30} - \)\(96\!\cdots\!64\)\( T^{31} + \)\(37\!\cdots\!46\)\( T^{32} - \)\(13\!\cdots\!62\)\( T^{33} + \)\(46\!\cdots\!30\)\( T^{34} - \)\(14\!\cdots\!09\)\( T^{35} + \)\(40\!\cdots\!63\)\( T^{36} - \)\(97\!\cdots\!95\)\( T^{37} + \)\(21\!\cdots\!44\)\( T^{38} - \)\(32\!\cdots\!10\)\( T^{39} + \)\(46\!\cdots\!01\)\( T^{40} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 102 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 3 T + 263 T^{2} + 906 T^{3} + 31922 T^{4} + 118986 T^{5} + 2468778 T^{6} + 9354601 T^{7} + 142747902 T^{8} + 512493344 T^{9} + 6709151394 T^{10} + 20664313609 T^{11} + 256315938294 T^{12} + 580613723466 T^{13} + 7321151313454 T^{14} + 9765969088074 T^{15} + 133241880681769 T^{16} + 71433859985283 T^{17} + 1119130473102767 T^{18} \))(\( 1 - 3 T + 194 T^{2} - 323 T^{3} + 17109 T^{4} - 940 T^{5} + 811722 T^{6} + 2405797 T^{7} + 19065686 T^{8} + 231609061 T^{9} + 317343936 T^{10} + 10885625867 T^{11} + 42116100374 T^{12} + 249777061931 T^{13} + 3960944420682 T^{14} - 215584306580 T^{15} + 184421595063861 T^{16} - 163639267909549 T^{17} + 4619389612381634 T^{18} - 3357391419308301 T^{19} + 52599132235830049 T^{20} \))(\( 1 + 17 T + 392 T^{2} + 4877 T^{3} + 68596 T^{4} + 711925 T^{5} + 7758454 T^{6} + 70749814 T^{7} + 647419321 T^{8} + 5286513139 T^{9} + 42174957618 T^{10} + 310368551078 T^{11} + 2203921132484 T^{12} + 14587321900666 T^{13} + 93164481378162 T^{14} + 548861653630397 T^{15} + 3159199759716601 T^{16} + 16226116587078698 T^{17} + 83630046286141366 T^{18} + 360677665035621275 T^{19} + 1633359019850157556 T^{20} + 5457999317322194659 T^{21} + 20618859836445379208 T^{22} + 42026706656428209151 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 3 T + 401 T^{2} + 970 T^{3} + 77369 T^{4} + 157503 T^{5} + 9765541 T^{6} + 17991539 T^{7} + 922365787 T^{8} + 1645286933 T^{9} + 70075625135 T^{10} + 124136668578 T^{11} + 4454494334671 T^{12} + 7725569022889 T^{13} + 242157704454975 T^{14} + 398192294240194 T^{15} + 11381412109383825 T^{16} + 17065781971561801 T^{17} + 462478965308547233 T^{18} + 605747343063363618 T^{19} + 16071494737115950945 T^{20} + 17734902128796995957 T^{21} + \)\(46\!\cdots\!81\)\( T^{22} + \)\(42\!\cdots\!79\)\( T^{23} + \)\(10\!\cdots\!47\)\( T^{24} + \)\(82\!\cdots\!47\)\( T^{25} + \)\(19\!\cdots\!07\)\( T^{26} + \)\(11\!\cdots\!70\)\( T^{27} + \)\(21\!\cdots\!27\)\( T^{28} + \)\(77\!\cdots\!07\)\( T^{29} + \)\(12\!\cdots\!43\)\( T^{30} \))(\( 1 - 11 T + 384 T^{2} - 4411 T^{3} + 82948 T^{4} - 906429 T^{5} + 12678465 T^{6} - 127861773 T^{7} + 1485841582 T^{8} - 13777717043 T^{9} + 139695948802 T^{10} - 1193142692196 T^{11} + 10836120090361 T^{12} - 85417448655262 T^{13} + 705428280282542 T^{14} - 5138863786936380 T^{15} + 38926778372285253 T^{16} - 262021781331596670 T^{17} + 1829558583497406891 T^{18} - 11351750105342463420 T^{19} + 73239680343774358066 T^{20} - \)\(41\!\cdots\!22\)\( T^{21} + \)\(24\!\cdots\!27\)\( T^{22} - \)\(12\!\cdots\!84\)\( T^{23} + \)\(70\!\cdots\!26\)\( T^{24} - \)\(32\!\cdots\!23\)\( T^{25} + \)\(16\!\cdots\!94\)\( T^{26} - \)\(67\!\cdots\!77\)\( T^{27} + \)\(31\!\cdots\!95\)\( T^{28} - \)\(10\!\cdots\!89\)\( T^{29} + \)\(45\!\cdots\!96\)\( T^{30} - \)\(11\!\cdots\!59\)\( T^{31} + \)\(46\!\cdots\!12\)\( T^{32} - \)\(62\!\cdots\!31\)\( T^{33} + \)\(26\!\cdots\!87\)\( T^{34} \))(\( 1 - 13 T + 545 T^{2} - 6712 T^{3} + 151015 T^{4} - 1726403 T^{5} + 28006418 T^{6} - 294963660 T^{7} + 3878399311 T^{8} - 37634958770 T^{9} + 425669221389 T^{10} - 3820578959723 T^{11} + 38456235420320 T^{12} - 320862713801166 T^{13} + 2935213631999119 T^{14} - 22868067052871623 T^{15} + 192742167062395496 T^{16} - 1406526534033716800 T^{17} + 11021027114470315793 T^{18} - 75435176263696806234 T^{19} + \)\(55\!\cdots\!54\)\( T^{20} - \)\(35\!\cdots\!98\)\( T^{21} + \)\(24\!\cdots\!37\)\( T^{22} - \)\(14\!\cdots\!00\)\( T^{23} + \)\(94\!\cdots\!76\)\( T^{24} - \)\(52\!\cdots\!61\)\( T^{25} + \)\(31\!\cdots\!51\)\( T^{26} - \)\(16\!\cdots\!58\)\( T^{27} + \)\(91\!\cdots\!20\)\( T^{28} - \)\(42\!\cdots\!41\)\( T^{29} + \)\(22\!\cdots\!61\)\( T^{30} - \)\(93\!\cdots\!10\)\( T^{31} + \)\(45\!\cdots\!51\)\( T^{32} - \)\(16\!\cdots\!20\)\( T^{33} + \)\(71\!\cdots\!42\)\( T^{34} - \)\(20\!\cdots\!29\)\( T^{35} + \)\(85\!\cdots\!15\)\( T^{36} - \)\(17\!\cdots\!44\)\( T^{37} + \)\(68\!\cdots\!05\)\( T^{38} - \)\(76\!\cdots\!79\)\( T^{39} + \)\(27\!\cdots\!01\)\( T^{40} \))
$53$ (\( 1 + 9 T + 53 T^{2} \))(\( 1 + 5 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 4 T + 92 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 + 9 T + 412 T^{2} + 3087 T^{3} + 77174 T^{4} + 489029 T^{5} + 8728308 T^{6} + 47009594 T^{7} + 662187581 T^{8} + 3012842556 T^{9} + 35095941793 T^{10} + 132049949546 T^{11} + 1299444310116 T^{12} + 3858674032949 T^{13} + 32273818976782 T^{14} + 68421382805223 T^{15} + 483980989612844 T^{16} + 560337213702249 T^{17} + 3299763591802133 T^{18} \))(\( 1 - 25 T + 427 T^{2} - 5582 T^{3} + 64602 T^{4} - 665382 T^{5} + 6336438 T^{6} - 56080783 T^{7} + 467737103 T^{8} - 3708855556 T^{9} + 27786225496 T^{10} - 196569344468 T^{11} + 1313873522327 T^{12} - 8349138730691 T^{13} + 49997543646678 T^{14} - 278259753523326 T^{15} + 1431862057655658 T^{16} - 6557237582570134 T^{17} + 26584887805651147 T^{18} - 82494089795053325 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 47 T + 1464 T^{2} + 32355 T^{3} + 578376 T^{4} + 8518229 T^{5} + 108098757 T^{6} + 1193284165 T^{7} + 11776836649 T^{8} + 104961651929 T^{9} + 867297393463 T^{10} + 6724540398031 T^{11} + 50010776341666 T^{12} + 356400641095643 T^{13} + 2436238378237567 T^{14} + 15626375854233733 T^{15} + 92924905819038169 T^{16} + 499026059671268345 T^{17} + 2395939887744016653 T^{18} + 10006458497982588673 T^{19} + 36009510701361329736 T^{20} + \)\(10\!\cdots\!15\)\( T^{21} + \)\(25\!\cdots\!36\)\( T^{22} + \)\(43\!\cdots\!59\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 10 T + 543 T^{2} - 5046 T^{3} + 142187 T^{4} - 1247932 T^{5} + 24070770 T^{6} - 201295291 T^{7} + 2971827729 T^{8} - 23712807344 T^{9} + 285290440864 T^{10} - 2159702552932 T^{11} + 22094046458624 T^{12} - 156803608878674 T^{13} + 1408981472813102 T^{14} - 9215493938942538 T^{15} + 74676018059094406 T^{16} - 440461337340195266 T^{17} + 3289295354620565248 T^{18} - 17041091959561440292 T^{19} + \)\(11\!\cdots\!52\)\( T^{20} - \)\(52\!\cdots\!76\)\( T^{21} + \)\(34\!\cdots\!73\)\( T^{22} - \)\(12\!\cdots\!51\)\( T^{23} + \)\(79\!\cdots\!10\)\( T^{24} - \)\(21\!\cdots\!68\)\( T^{25} + \)\(13\!\cdots\!39\)\( T^{26} - \)\(24\!\cdots\!86\)\( T^{27} + \)\(14\!\cdots\!39\)\( T^{28} - \)\(13\!\cdots\!90\)\( T^{29} + \)\(73\!\cdots\!57\)\( T^{30} \))(\( 1 + 3 T + 326 T^{2} + 983 T^{3} + 57566 T^{4} + 166663 T^{5} + 7322872 T^{6} + 20720442 T^{7} + 747555581 T^{8} + 2093893066 T^{9} + 64373966381 T^{10} + 177949646220 T^{11} + 4807103795182 T^{12} + 13012418387745 T^{13} + 317328395006692 T^{14} + 833181625135947 T^{15} + 18727586656157603 T^{16} + 47032320818661622 T^{17} + 992562092776352959 T^{18} + 2340407185006875123 T^{19} + 47242899463411284884 T^{20} + \)\(10\!\cdots\!45\)\( T^{21} + \)\(20\!\cdots\!26\)\( T^{22} + \)\(39\!\cdots\!80\)\( T^{23} + \)\(75\!\cdots\!97\)\( T^{24} + \)\(13\!\cdots\!26\)\( T^{25} + \)\(24\!\cdots\!73\)\( T^{26} + \)\(36\!\cdots\!58\)\( T^{27} + \)\(67\!\cdots\!84\)\( T^{28} + \)\(81\!\cdots\!83\)\( T^{29} + \)\(14\!\cdots\!18\)\( T^{30} + \)\(13\!\cdots\!27\)\( T^{31} + \)\(23\!\cdots\!82\)\( T^{32} + \)\(11\!\cdots\!63\)\( T^{33} + \)\(20\!\cdots\!13\)\( T^{34} \))(\( 1 + 580 T^{2} - 94 T^{3} + 168300 T^{4} - 37522 T^{5} + 32529045 T^{6} - 6734733 T^{7} + 4709063900 T^{8} - 650592727 T^{9} + 544673756091 T^{10} - 22341386100 T^{11} + 52434444393602 T^{12} + 3172847169196 T^{13} + 4318179455645649 T^{14} + 632502433537527 T^{15} + 309916584861821571 T^{16} + 63053809635564805 T^{17} + 19616370967515961547 T^{18} + 4421096949156420672 T^{19} + \)\(11\!\cdots\!80\)\( T^{20} + \)\(23\!\cdots\!16\)\( T^{21} + \)\(55\!\cdots\!23\)\( T^{22} + \)\(93\!\cdots\!85\)\( T^{23} + \)\(24\!\cdots\!51\)\( T^{24} + \)\(26\!\cdots\!11\)\( T^{25} + \)\(95\!\cdots\!21\)\( T^{26} + \)\(37\!\cdots\!52\)\( T^{27} + \)\(32\!\cdots\!22\)\( T^{28} - \)\(73\!\cdots\!00\)\( T^{29} + \)\(95\!\cdots\!59\)\( T^{30} - \)\(60\!\cdots\!19\)\( T^{31} + \)\(23\!\cdots\!00\)\( T^{32} - \)\(17\!\cdots\!09\)\( T^{33} + \)\(44\!\cdots\!05\)\( T^{34} - \)\(27\!\cdots\!54\)\( T^{35} + \)\(65\!\cdots\!00\)\( T^{36} - \)\(19\!\cdots\!22\)\( T^{37} + \)\(63\!\cdots\!20\)\( T^{38} + \)\(30\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 2 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 12 T + 122 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 10 T + 383 T^{2} + 3454 T^{3} + 70659 T^{4} + 570721 T^{5} + 8282388 T^{6} + 58937689 T^{7} + 677699543 T^{8} + 4158111660 T^{9} + 39984273037 T^{10} + 205162095409 T^{11} + 1701028565052 T^{12} + 6915632387281 T^{13} + 50515836043041 T^{14} + 145691563196014 T^{15} + 953153518685677 T^{16} + 1468304376043210 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 46 T + 1370 T^{2} + 29248 T^{3} + 507730 T^{4} + 7358451 T^{5} + 92806871 T^{6} + 1028827578 T^{7} + 10218323913 T^{8} + 91125712475 T^{9} + 736477435704 T^{10} + 5376417036025 T^{11} + 35569985541153 T^{12} + 211299579142062 T^{13} + 1124574359187431 T^{14} + 5260735422900849 T^{15} + 21416322345544930 T^{16} + 72788078627986112 T^{17} + 201157699517919770 T^{18} + 398497807658127194 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 14 T + 524 T^{2} - 6332 T^{3} + 130961 T^{4} - 1388671 T^{5} + 20825935 T^{6} - 196142214 T^{7} + 2364188051 T^{8} - 19891125494 T^{9} + 202847297785 T^{10} - 1522847324069 T^{11} + 13522000135294 T^{12} - 89847992120071 T^{13} + 706111443589585 T^{14} - 4085219462832226 T^{15} + 28647720085853411 T^{16} - 140226834848257986 T^{17} + 878449051872779335 T^{18} - 3455918146075085549 T^{19} + 19229060939099482481 T^{20} - 54854089523723073748 T^{21} + \)\(26\!\cdots\!24\)\( T^{22} - \)\(42\!\cdots\!26\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 - 2 T + 463 T^{2} - 150 T^{3} + 104394 T^{4} + 156515 T^{5} + 15471899 T^{6} + 51012401 T^{7} + 1741164753 T^{8} + 8242535757 T^{9} + 162572604430 T^{10} + 889165031536 T^{11} + 13096949454895 T^{12} + 72082252835202 T^{13} + 908833329431935 T^{14} + 4691296748869402 T^{15} + 53621166436484165 T^{16} + 250918322119338162 T^{17} + 2689838382096880205 T^{18} + 10774333675698096496 T^{19} + \)\(11\!\cdots\!70\)\( T^{20} + \)\(34\!\cdots\!37\)\( T^{21} + \)\(43\!\cdots\!07\)\( T^{22} + \)\(74\!\cdots\!21\)\( T^{23} + \)\(13\!\cdots\!61\)\( T^{24} + \)\(79\!\cdots\!15\)\( T^{25} + \)\(31\!\cdots\!46\)\( T^{26} - \)\(26\!\cdots\!50\)\( T^{27} + \)\(48\!\cdots\!77\)\( T^{28} - \)\(12\!\cdots\!22\)\( T^{29} + \)\(36\!\cdots\!99\)\( T^{30} \))(\( 1 + 6 T + 505 T^{2} + 3070 T^{3} + 125887 T^{4} + 791977 T^{5} + 20728636 T^{6} + 136434219 T^{7} + 2551071979 T^{8} + 17573070808 T^{9} + 252273029925 T^{10} + 1801537488571 T^{11} + 21061805277486 T^{12} + 153170139109455 T^{13} + 1537327626331605 T^{14} + 11116274112352084 T^{15} + 100337494047722842 T^{16} + 701253578712838004 T^{17} + 5919912148815647678 T^{18} + 38695750185097604404 T^{19} + \)\(31\!\cdots\!95\)\( T^{20} + \)\(18\!\cdots\!55\)\( T^{21} + \)\(15\!\cdots\!14\)\( T^{22} + \)\(75\!\cdots\!11\)\( T^{23} + \)\(62\!\cdots\!75\)\( T^{24} + \)\(25\!\cdots\!68\)\( T^{25} + \)\(22\!\cdots\!81\)\( T^{26} + \)\(69\!\cdots\!19\)\( T^{27} + \)\(62\!\cdots\!24\)\( T^{28} + \)\(14\!\cdots\!37\)\( T^{29} + \)\(13\!\cdots\!73\)\( T^{30} + \)\(19\!\cdots\!70\)\( T^{31} + \)\(18\!\cdots\!95\)\( T^{32} + \)\(12\!\cdots\!46\)\( T^{33} + \)\(12\!\cdots\!19\)\( T^{34} \))(\( 1 - 52 T + 1878 T^{2} - 50022 T^{3} + 1116871 T^{4} - 21390055 T^{5} + 365572667 T^{6} - 5645806566 T^{7} + 80247743447 T^{8} - 1057776840220 T^{9} + 13063792894135 T^{10} - 151898601180455 T^{11} + 1673407854431448 T^{12} - 17520989353594035 T^{13} + 175071493851574117 T^{14} - 1672684747762174640 T^{15} + 15322812599928299672 T^{16} - \)\(13\!\cdots\!30\)\( T^{17} + \)\(11\!\cdots\!87\)\( T^{18} - \)\(92\!\cdots\!13\)\( T^{19} + \)\(72\!\cdots\!98\)\( T^{20} - \)\(54\!\cdots\!67\)\( T^{21} + \)\(39\!\cdots\!47\)\( T^{22} - \)\(27\!\cdots\!70\)\( T^{23} + \)\(18\!\cdots\!92\)\( T^{24} - \)\(11\!\cdots\!60\)\( T^{25} + \)\(73\!\cdots\!97\)\( T^{26} - \)\(43\!\cdots\!65\)\( T^{27} + \)\(24\!\cdots\!08\)\( T^{28} - \)\(13\!\cdots\!45\)\( T^{29} + \)\(66\!\cdots\!35\)\( T^{30} - \)\(31\!\cdots\!80\)\( T^{31} + \)\(14\!\cdots\!07\)\( T^{32} - \)\(59\!\cdots\!14\)\( T^{33} + \)\(22\!\cdots\!87\)\( T^{34} - \)\(78\!\cdots\!45\)\( T^{35} + \)\(24\!\cdots\!11\)\( T^{36} - \)\(63\!\cdots\!18\)\( T^{37} + \)\(14\!\cdots\!38\)\( T^{38} - \)\(23\!\cdots\!28\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))
$61$ (\( 1 + T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( 1 + 10 T + 265 T^{2} + 2420 T^{3} + 38202 T^{4} + 294768 T^{5} + 3824699 T^{6} + 26084475 T^{7} + 291676029 T^{8} + 1807841310 T^{9} + 17792237769 T^{10} + 97060331475 T^{11} + 868134003719 T^{12} + 4081310859888 T^{13} + 32265267890802 T^{14} + 124679305953620 T^{15} + 832826851545565 T^{16} + 1917073129972810 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 54 T + 1716 T^{2} + 39282 T^{3} + 715319 T^{4} + 10864488 T^{5} + 141988979 T^{6} + 1627514861 T^{7} + 16582577610 T^{8} + 151415379327 T^{9} + 1245270340302 T^{10} + 9236338138947 T^{11} + 61703771286810 T^{12} + 369414950664641 T^{13} + 1965956826986339 T^{14} + 9176106377058888 T^{15} + 36853502667536159 T^{16} + 123453224084576922 T^{17} + 328969749103334196 T^{18} + 631483889013043614 T^{19} + 713342911662882601 T^{20} \))(\( 1 + 22 T + 747 T^{2} + 12648 T^{3} + 249186 T^{4} + 3419700 T^{5} + 49881736 T^{6} + 572715499 T^{7} + 6736313418 T^{8} + 65910665846 T^{9} + 649967327993 T^{10} + 5468019382925 T^{11} + 46067190229586 T^{12} + 333549182358425 T^{13} + 2418528427461953 T^{14} + 14960468844390926 T^{15} + 93269924511794538 T^{16} + 483713391980769199 T^{17} + 2569925712496570696 T^{18} + 10747237676341013700 T^{19} + 47770778496540463266 T^{20} + \)\(14\!\cdots\!68\)\( T^{21} + \)\(53\!\cdots\!47\)\( T^{22} + \)\(95\!\cdots\!42\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 15 T + 389 T^{2} - 5718 T^{3} + 88147 T^{4} - 1115189 T^{5} + 13813374 T^{6} - 151905572 T^{7} + 1642521631 T^{8} - 16248582125 T^{9} + 158174949974 T^{10} - 1443924047098 T^{11} + 12904926633618 T^{12} - 109365180859199 T^{13} + 908852281342766 T^{14} - 7161600945424696 T^{15} + 55439989161908726 T^{16} - 406947837977079479 T^{17} + 2929173152225247258 T^{18} - 19992342772195419418 T^{19} + \)\(13\!\cdots\!74\)\( T^{20} - \)\(83\!\cdots\!25\)\( T^{21} + \)\(51\!\cdots\!51\)\( T^{22} - \)\(29\!\cdots\!32\)\( T^{23} + \)\(16\!\cdots\!34\)\( T^{24} - \)\(79\!\cdots\!89\)\( T^{25} + \)\(38\!\cdots\!67\)\( T^{26} - \)\(15\!\cdots\!78\)\( T^{27} + \)\(62\!\cdots\!09\)\( T^{28} - \)\(14\!\cdots\!15\)\( T^{29} + \)\(60\!\cdots\!01\)\( T^{30} \))(\( 1 - 6 T + 638 T^{2} - 3040 T^{3} + 193424 T^{4} - 701244 T^{5} + 37488494 T^{6} - 97507187 T^{7} + 5298503792 T^{8} - 9207825017 T^{9} + 592081822043 T^{10} - 646238486588 T^{11} + 55187808991560 T^{12} - 37819521253901 T^{13} + 4425405985772070 T^{14} - 2128325343747833 T^{15} + 309116768894991602 T^{16} - 125849450850605128 T^{17} + 18856122902594487722 T^{18} - 7919498604085686593 T^{19} + \)\(10\!\cdots\!70\)\( T^{20} - \)\(52\!\cdots\!41\)\( T^{21} + \)\(46\!\cdots\!60\)\( T^{22} - \)\(33\!\cdots\!68\)\( T^{23} + \)\(18\!\cdots\!03\)\( T^{24} - \)\(17\!\cdots\!77\)\( T^{25} + \)\(61\!\cdots\!72\)\( T^{26} - \)\(69\!\cdots\!87\)\( T^{27} + \)\(16\!\cdots\!34\)\( T^{28} - \)\(18\!\cdots\!24\)\( T^{29} + \)\(31\!\cdots\!44\)\( T^{30} - \)\(30\!\cdots\!40\)\( T^{31} + \)\(38\!\cdots\!38\)\( T^{32} - \)\(22\!\cdots\!66\)\( T^{33} + \)\(22\!\cdots\!21\)\( T^{34} \))(\( 1 - 25 T + 809 T^{2} - 13066 T^{3} + 249287 T^{4} - 3013197 T^{5} + 43802961 T^{6} - 425295829 T^{7} + 5280074813 T^{8} - 42617209014 T^{9} + 488390063830 T^{10} - 3333662338553 T^{11} + 38095080824968 T^{12} - 226541564136203 T^{13} + 2776119292967903 T^{14} - 15273161628830562 T^{15} + 201717876443814384 T^{16} - 1077035925100860262 T^{17} + 14266608901344242433 T^{18} - 73582750774492550021 T^{19} + \)\(92\!\cdots\!02\)\( T^{20} - \)\(44\!\cdots\!81\)\( T^{21} + \)\(53\!\cdots\!93\)\( T^{22} - \)\(24\!\cdots\!22\)\( T^{23} + \)\(27\!\cdots\!44\)\( T^{24} - \)\(12\!\cdots\!62\)\( T^{25} + \)\(14\!\cdots\!83\)\( T^{26} - \)\(71\!\cdots\!63\)\( T^{27} + \)\(73\!\cdots\!08\)\( T^{28} - \)\(38\!\cdots\!73\)\( T^{29} + \)\(34\!\cdots\!30\)\( T^{30} - \)\(18\!\cdots\!54\)\( T^{31} + \)\(14\!\cdots\!73\)\( T^{32} - \)\(68\!\cdots\!49\)\( T^{33} + \)\(43\!\cdots\!01\)\( T^{34} - \)\(18\!\cdots\!97\)\( T^{35} + \)\(91\!\cdots\!07\)\( T^{36} - \)\(29\!\cdots\!86\)\( T^{37} + \)\(11\!\cdots\!29\)\( T^{38} - \)\(20\!\cdots\!25\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 8 T + 100 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 16 T + 404 T^{2} + 4911 T^{3} + 77694 T^{4} + 806081 T^{5} + 9931975 T^{6} + 88694538 T^{7} + 900379838 T^{8} + 6936558622 T^{9} + 60325449146 T^{10} + 398149781082 T^{11} + 2987170596925 T^{12} + 16243435766801 T^{13} + 104896620063258 T^{14} + 444241114831959 T^{15} + 2448527488550492 T^{16} + 6497082840906256 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 26 T + 703 T^{2} + 12197 T^{3} + 199474 T^{4} + 2642918 T^{5} + 32795787 T^{6} + 354040609 T^{7} + 3605991281 T^{8} + 32798357058 T^{9} + 283115362804 T^{10} + 2197489922886 T^{11} + 16187294860409 T^{12} + 106482315684667 T^{13} + 660871872127227 T^{14} + 3568269947542226 T^{15} + 18044095324779106 T^{16} + 73922499450124631 T^{17} + 285465577322318623 T^{18} + 707369894303668622 T^{19} + 1822837804551761449 T^{20} \))(\( 1 + 28 T + 689 T^{2} + 10891 T^{3} + 161345 T^{4} + 1947730 T^{5} + 23126622 T^{6} + 246374126 T^{7} + 2578192547 T^{8} + 24871330110 T^{9} + 231020161059 T^{10} + 2012513191251 T^{11} + 16898953980082 T^{12} + 134838383813817 T^{13} + 1037049502993851 T^{14} + 7480375857873930 T^{15} + 51953469975895187 T^{16} + 332635893227781482 T^{17} + 2091996811154003118 T^{18} + 11804629815035766790 T^{19} + 65516989435376242145 T^{20} + \)\(29\!\cdots\!77\)\( T^{21} + \)\(12\!\cdots\!61\)\( T^{22} + \)\(34\!\cdots\!24\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 + 48 T + 1592 T^{2} + 38385 T^{3} + 766595 T^{4} + 12922937 T^{5} + 191808331 T^{6} + 2533174721 T^{7} + 30436073067 T^{8} + 335320152411 T^{9} + 3442600223787 T^{10} + 33181003249279 T^{11} + 304499434952000 T^{12} + 2678122793808180 T^{13} + 22830875118700093 T^{14} + 189112920995810334 T^{15} + 1529668632952906231 T^{16} + 12022093221404920020 T^{17} + 91582163554468376000 T^{18} + \)\(66\!\cdots\!59\)\( T^{19} + \)\(46\!\cdots\!09\)\( T^{20} + \)\(30\!\cdots\!59\)\( T^{21} + \)\(18\!\cdots\!41\)\( T^{22} + \)\(10\!\cdots\!61\)\( T^{23} + \)\(52\!\cdots\!57\)\( T^{24} + \)\(23\!\cdots\!13\)\( T^{25} + \)\(93\!\cdots\!85\)\( T^{26} + \)\(31\!\cdots\!85\)\( T^{27} + \)\(87\!\cdots\!04\)\( T^{28} + \)\(17\!\cdots\!92\)\( T^{29} + \)\(24\!\cdots\!43\)\( T^{30} \))(\( 1 - 55 T + 1924 T^{2} - 48966 T^{3} + 1023988 T^{4} - 18256637 T^{5} + 289485380 T^{6} - 4152995037 T^{7} + 55024408171 T^{8} - 678804428324 T^{9} + 7881424800095 T^{10} - 86436352053773 T^{11} + 901118103211499 T^{12} - 8945554207616791 T^{13} + 84922104254306328 T^{14} - 771322655140452430 T^{15} + 6720698510301434406 T^{16} - 56140486494129784436 T^{17} + \)\(45\!\cdots\!02\)\( T^{18} - \)\(34\!\cdots\!70\)\( T^{19} + \)\(25\!\cdots\!64\)\( T^{20} - \)\(18\!\cdots\!11\)\( T^{21} + \)\(12\!\cdots\!93\)\( T^{22} - \)\(78\!\cdots\!37\)\( T^{23} + \)\(47\!\cdots\!85\)\( T^{24} - \)\(27\!\cdots\!84\)\( T^{25} + \)\(14\!\cdots\!37\)\( T^{26} - \)\(75\!\cdots\!13\)\( T^{27} + \)\(35\!\cdots\!40\)\( T^{28} - \)\(14\!\cdots\!57\)\( T^{29} + \)\(56\!\cdots\!56\)\( T^{30} - \)\(17\!\cdots\!14\)\( T^{31} + \)\(47\!\cdots\!32\)\( T^{32} - \)\(90\!\cdots\!55\)\( T^{33} + \)\(11\!\cdots\!27\)\( T^{34} \))(\( 1 - 40 T + 1284 T^{2} - 28673 T^{3} + 562703 T^{4} - 9190003 T^{5} + 137172557 T^{6} - 1807316403 T^{7} + 22182723544 T^{8} - 246076933121 T^{9} + 2563472310635 T^{10} - 24267573215354 T^{11} + 215479037907315 T^{12} - 1714952393890307 T^{13} + 12561359328564502 T^{14} - 77177585048238639 T^{15} + 389509735111653839 T^{16} - 808108512380630575 T^{17} - 8673410536585896382 T^{18} + \)\(17\!\cdots\!67\)\( T^{19} - \)\(16\!\cdots\!88\)\( T^{20} + \)\(11\!\cdots\!89\)\( T^{21} - \)\(38\!\cdots\!98\)\( T^{22} - \)\(24\!\cdots\!25\)\( T^{23} + \)\(78\!\cdots\!19\)\( T^{24} - \)\(10\!\cdots\!73\)\( T^{25} + \)\(11\!\cdots\!38\)\( T^{26} - \)\(10\!\cdots\!61\)\( T^{27} + \)\(87\!\cdots\!15\)\( T^{28} - \)\(66\!\cdots\!38\)\( T^{29} + \)\(46\!\cdots\!15\)\( T^{30} - \)\(30\!\cdots\!43\)\( T^{31} + \)\(18\!\cdots\!84\)\( T^{32} - \)\(99\!\cdots\!61\)\( T^{33} + \)\(50\!\cdots\!53\)\( T^{34} - \)\(22\!\cdots\!29\)\( T^{35} + \)\(92\!\cdots\!43\)\( T^{36} - \)\(31\!\cdots\!71\)\( T^{37} + \)\(95\!\cdots\!56\)\( T^{38} - \)\(19\!\cdots\!20\)\( T^{39} + \)\(33\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 + 3 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 13 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 + 16 T + 198 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 427 T^{2} + 2671 T^{3} + 81571 T^{4} + 382243 T^{5} + 9559831 T^{6} + 33024958 T^{7} + 821306390 T^{8} + 2341152544 T^{9} + 58312753690 T^{10} + 166478813278 T^{11} + 3421568673041 T^{12} + 9713437180483 T^{13} + 147172792390421 T^{14} + 342155858352991 T^{15} + 3883616307632957 T^{16} + 5166028249966088 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 16 T + 658 T^{2} + 7807 T^{3} + 181148 T^{4} + 1676154 T^{5} + 28845062 T^{6} + 216422887 T^{7} + 3107133973 T^{8} + 19751330864 T^{9} + 250233628330 T^{10} + 1402344491344 T^{11} + 15663062357893 T^{12} + 77460131909057 T^{13} + 733001513969222 T^{14} + 3024166243596054 T^{15} + 23205110231721308 T^{16} + 71005603076558537 T^{17} + 424905823559710738 T^{18} + 733576011495184496 T^{19} + 3255243551009881201 T^{20} \))(\( 1 + 18 T + 377 T^{2} + 4677 T^{3} + 69343 T^{4} + 736011 T^{5} + 8984892 T^{6} + 86228572 T^{7} + 948563309 T^{8} + 8397539729 T^{9} + 83744230371 T^{10} + 690029166881 T^{11} + 6400390234166 T^{12} + 48992070848551 T^{13} + 422154665300211 T^{14} + 3005571841946119 T^{15} + 24104588216612429 T^{16} + 155576120497216772 T^{17} + 1150967216199521532 T^{18} + 6694108482897518301 T^{19} + 44778487117174805023 T^{20} + \)\(21\!\cdots\!87\)\( T^{21} + \)\(12\!\cdots\!77\)\( T^{22} + \)\(41\!\cdots\!78\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 - 15 T + 663 T^{2} - 8211 T^{3} + 213443 T^{4} - 2322873 T^{5} + 45583572 T^{6} - 448093563 T^{7} + 7261879909 T^{8} - 65272750573 T^{9} + 913732624716 T^{10} - 7548608662237 T^{11} + 93698588670850 T^{12} - 711831534976219 T^{13} + 7964442188083044 T^{14} - 55476205029348554 T^{15} + 565475395353896124 T^{16} - 3588342767815119979 T^{17} + 33535755569772594350 T^{18} - \)\(19\!\cdots\!97\)\( T^{19} + \)\(16\!\cdots\!16\)\( T^{20} - \)\(83\!\cdots\!33\)\( T^{21} + \)\(66\!\cdots\!19\)\( T^{22} - \)\(28\!\cdots\!43\)\( T^{23} + \)\(20\!\cdots\!32\)\( T^{24} - \)\(75\!\cdots\!73\)\( T^{25} + \)\(49\!\cdots\!53\)\( T^{26} - \)\(13\!\cdots\!51\)\( T^{27} + \)\(77\!\cdots\!93\)\( T^{28} - \)\(12\!\cdots\!15\)\( T^{29} + \)\(58\!\cdots\!51\)\( T^{30} \))(\( 1 - 5 T + 519 T^{2} - 2571 T^{3} + 131433 T^{4} - 690169 T^{5} + 21872731 T^{6} - 125504274 T^{7} + 2740776719 T^{8} - 17009452359 T^{9} + 283405432950 T^{10} - 1808238452159 T^{11} + 25827998546402 T^{12} - 157892004302432 T^{13} + 2152907138729751 T^{14} - 12051306559758872 T^{15} + 165790853562412576 T^{16} - 865664769327601806 T^{17} + 11771150602931292896 T^{18} - 60750636367744473752 T^{19} + \)\(77\!\cdots\!61\)\( T^{20} - \)\(40\!\cdots\!92\)\( T^{21} + \)\(46\!\cdots\!02\)\( T^{22} - \)\(23\!\cdots\!39\)\( T^{23} + \)\(25\!\cdots\!50\)\( T^{24} - \)\(10\!\cdots\!99\)\( T^{25} + \)\(12\!\cdots\!89\)\( T^{26} - \)\(40\!\cdots\!74\)\( T^{27} + \)\(50\!\cdots\!01\)\( T^{28} - \)\(11\!\cdots\!29\)\( T^{29} + \)\(15\!\cdots\!63\)\( T^{30} - \)\(21\!\cdots\!51\)\( T^{31} + \)\(30\!\cdots\!69\)\( T^{32} - \)\(20\!\cdots\!05\)\( T^{33} + \)\(29\!\cdots\!91\)\( T^{34} \))(\( 1 - 25 T + 1179 T^{2} - 23627 T^{3} + 642303 T^{4} - 10843765 T^{5} + 219746522 T^{6} - 3227326843 T^{7} + 53701111244 T^{8} - 701374155508 T^{9} + 10064549875983 T^{10} - 118735729776174 T^{11} + 1512292614445371 T^{12} - 16295701656776826 T^{13} + 187615065116936644 T^{14} - 1860880499290935897 T^{15} + 19599269848882745602 T^{16} - \)\(17\!\cdots\!41\)\( T^{17} + \)\(17\!\cdots\!56\)\( T^{18} - \)\(14\!\cdots\!40\)\( T^{19} + \)\(13\!\cdots\!14\)\( T^{20} - \)\(10\!\cdots\!40\)\( T^{21} + \)\(88\!\cdots\!96\)\( T^{22} - \)\(64\!\cdots\!51\)\( T^{23} + \)\(49\!\cdots\!62\)\( T^{24} - \)\(33\!\cdots\!47\)\( T^{25} + \)\(24\!\cdots\!24\)\( T^{26} - \)\(14\!\cdots\!66\)\( T^{27} + \)\(97\!\cdots\!31\)\( T^{28} - \)\(54\!\cdots\!94\)\( T^{29} + \)\(32\!\cdots\!83\)\( T^{30} - \)\(16\!\cdots\!68\)\( T^{31} + \)\(88\!\cdots\!04\)\( T^{32} - \)\(37\!\cdots\!73\)\( T^{33} + \)\(18\!\cdots\!82\)\( T^{34} - \)\(63\!\cdots\!15\)\( T^{35} + \)\(26\!\cdots\!63\)\( T^{36} - \)\(69\!\cdots\!57\)\( T^{37} + \)\(24\!\cdots\!19\)\( T^{38} - \)\(37\!\cdots\!75\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))
$73$ (\( 1 + 7 T + 73 T^{2} \))(\( 1 - 9 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 4 T + 78 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 22 T + 445 T^{2} + 5498 T^{3} + 63365 T^{4} + 546992 T^{5} + 4813565 T^{6} + 35010851 T^{7} + 303068460 T^{8} + 2291105682 T^{9} + 22123997580 T^{10} + 186572824979 T^{11} + 1872558615605 T^{12} + 15533610641072 T^{13} + 131360181490445 T^{14} + 832035576136922 T^{15} + 4916092340998165 T^{16} + 17742122021669782 T^{17} + 58871586708267913 T^{18} \))(\( 1 - 4 T + 516 T^{2} - 1626 T^{3} + 129718 T^{4} - 334152 T^{5} + 20927890 T^{6} - 45246887 T^{7} + 2391701595 T^{8} - 4417520027 T^{9} + 201898642960 T^{10} - 322478961971 T^{11} + 12745377799755 T^{12} - 17601808240079 T^{13} + 594315263841490 T^{14} - 692721018944136 T^{15} + 19630773165756502 T^{16} - 17963069992051722 T^{17} + 416133407417345796 T^{18} - 235486346833071652 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 2 T + 607 T^{2} + 546 T^{3} + 180491 T^{4} + 38574 T^{5} + 34940912 T^{6} - 6463501 T^{7} + 4890792591 T^{8} - 1878185724 T^{9} + 519673391213 T^{10} - 228111031597 T^{11} + 42893697332658 T^{12} - 16652105306581 T^{13} + 2769339501774077 T^{14} - 730646175793308 T^{15} + 138889906680232431 T^{16} - 13399300314427093 T^{17} + 5287755883352035568 T^{18} + 426142350475647678 T^{19} + \)\(14\!\cdots\!71\)\( T^{20} + 32143886342714280498 T^{21} + \)\(26\!\cdots\!43\)\( T^{22} + \)\(62\!\cdots\!54\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 47 T + 1559 T^{2} + 37738 T^{3} + 752946 T^{4} + 12574770 T^{5} + 181347212 T^{6} + 2260880209 T^{7} + 24449694563 T^{8} + 224566017024 T^{9} + 1676008441763 T^{10} + 8568786631506 T^{11} + 1004664725920 T^{12} - 655617077444017 T^{13} - 9938682894055628 T^{14} - 98983151195635290 T^{15} - 725523851266060844 T^{16} - 3493783405699166593 T^{17} + 390831657683220640 T^{18} + \)\(24\!\cdots\!46\)\( T^{19} + \)\(34\!\cdots\!59\)\( T^{20} + \)\(33\!\cdots\!36\)\( T^{21} + \)\(27\!\cdots\!11\)\( T^{22} + \)\(18\!\cdots\!29\)\( T^{23} + \)\(10\!\cdots\!56\)\( T^{24} + \)\(54\!\cdots\!30\)\( T^{25} + \)\(23\!\cdots\!42\)\( T^{26} + \)\(86\!\cdots\!98\)\( T^{27} + \)\(26\!\cdots\!47\)\( T^{28} + \)\(57\!\cdots\!23\)\( T^{29} + \)\(89\!\cdots\!57\)\( T^{30} \))(\( 1 - 62 T + 2345 T^{2} - 65692 T^{3} + 1499365 T^{4} - 29226596 T^{5} + 501467717 T^{6} - 7727718481 T^{7} + 108535496076 T^{8} - 1404999495118 T^{9} + 16917098044148 T^{10} - 190944343123749 T^{11} + 2034492673305731 T^{12} - 20595616166752516 T^{13} + 199272873329354339 T^{14} - 1852574097883943422 T^{15} + 16619414049924542894 T^{16} - \)\(14\!\cdots\!84\)\( T^{17} + \)\(12\!\cdots\!62\)\( T^{18} - \)\(98\!\cdots\!38\)\( T^{19} + \)\(77\!\cdots\!63\)\( T^{20} - \)\(58\!\cdots\!56\)\( T^{21} + \)\(42\!\cdots\!83\)\( T^{22} - \)\(28\!\cdots\!61\)\( T^{23} + \)\(18\!\cdots\!56\)\( T^{24} - \)\(11\!\cdots\!58\)\( T^{25} + \)\(63\!\cdots\!88\)\( T^{26} - \)\(33\!\cdots\!69\)\( T^{27} + \)\(15\!\cdots\!09\)\( T^{28} - \)\(66\!\cdots\!16\)\( T^{29} + \)\(25\!\cdots\!45\)\( T^{30} - \)\(80\!\cdots\!28\)\( T^{31} + \)\(20\!\cdots\!65\)\( T^{32} - \)\(40\!\cdots\!82\)\( T^{33} + \)\(47\!\cdots\!53\)\( T^{34} \))(\( 1 + 5 T + 804 T^{2} + 3251 T^{3} + 323509 T^{4} + 1074418 T^{5} + 87431704 T^{6} + 242424263 T^{7} + 17867342220 T^{8} + 42008911292 T^{9} + 2936371625912 T^{10} + 5940568696023 T^{11} + 402422635461418 T^{12} + 711191350050545 T^{13} + 47060618620907168 T^{14} + 73860683416004584 T^{15} + 4766499495805964611 T^{16} + 6763244830835519256 T^{17} + \)\(42\!\cdots\!56\)\( T^{18} + \)\(55\!\cdots\!99\)\( T^{19} + \)\(32\!\cdots\!18\)\( T^{20} + \)\(40\!\cdots\!27\)\( T^{21} + \)\(22\!\cdots\!24\)\( T^{22} + \)\(26\!\cdots\!52\)\( T^{23} + \)\(13\!\cdots\!51\)\( T^{24} + \)\(15\!\cdots\!12\)\( T^{25} + \)\(71\!\cdots\!52\)\( T^{26} + \)\(78\!\cdots\!65\)\( T^{27} + \)\(32\!\cdots\!58\)\( T^{28} + \)\(34\!\cdots\!99\)\( T^{29} + \)\(12\!\cdots\!88\)\( T^{30} + \)\(13\!\cdots\!84\)\( T^{31} + \)\(40\!\cdots\!20\)\( T^{32} + \)\(40\!\cdots\!79\)\( T^{33} + \)\(10\!\cdots\!36\)\( T^{34} + \)\(95\!\cdots\!26\)\( T^{35} + \)\(21\!\cdots\!49\)\( T^{36} + \)\(15\!\cdots\!03\)\( T^{37} + \)\(27\!\cdots\!76\)\( T^{38} + \)\(12\!\cdots\!85\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 + T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 24 T + 270 T^{2} + 1896 T^{3} + 6241 T^{4} \))(\( 1 + 9 T + 306 T^{2} + 2670 T^{3} + 49718 T^{4} + 425525 T^{5} + 6075105 T^{6} + 46257105 T^{7} + 590046696 T^{8} + 3928870030 T^{9} + 46613688984 T^{10} + 288690592305 T^{11} + 2995263694095 T^{12} + 16574233217525 T^{13} + 152985090045482 T^{14} + 649043506241070 T^{15} + 5876396149764654 T^{16} + 13653979289159049 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 19 T + 701 T^{2} + 10669 T^{3} + 223488 T^{4} + 2834077 T^{5} + 43314051 T^{6} + 466164732 T^{7} + 5686462673 T^{8} + 52208581403 T^{9} + 529742938534 T^{10} + 4124477930837 T^{11} + 35489213542193 T^{12} + 229837393300548 T^{13} + 1687085794888131 T^{14} + 8720614768108723 T^{15} + 54327129259477248 T^{16} + 204886504973330371 T^{17} + 1063493275744499261 T^{18} + 2277180323669748061 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + 39 T + 1280 T^{2} + 28792 T^{3} + 576222 T^{4} + 9524009 T^{5} + 144520164 T^{6} + 1929852318 T^{7} + 24089980562 T^{8} + 272304248612 T^{9} + 2904521634968 T^{10} + 28411976889090 T^{11} + 263234863218358 T^{12} + 2244546174238110 T^{13} + 18127119523835288 T^{14} + 134256614431411868 T^{15} + 938306694178325522 T^{16} + 5938264424226882882 T^{17} + 35131038938237625444 T^{18} + \)\(18\!\cdots\!31\)\( T^{19} + \)\(87\!\cdots\!42\)\( T^{20} + \)\(34\!\cdots\!48\)\( T^{21} + \)\(12\!\cdots\!80\)\( T^{22} + \)\(29\!\cdots\!81\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 + 34 T + 921 T^{2} + 16993 T^{3} + 277114 T^{4} + 3717092 T^{5} + 46357492 T^{6} + 512837484 T^{7} + 5472746443 T^{8} + 54448201310 T^{9} + 539647942747 T^{10} + 5175038299729 T^{11} + 50074493425156 T^{12} + 471585554932132 T^{13} + 4407517487335866 T^{14} + 39568188481271700 T^{15} + 348193881499533414 T^{16} + 2943165448331435812 T^{17} + 24688678163845489084 T^{18} + \)\(20\!\cdots\!49\)\( T^{19} + \)\(16\!\cdots\!53\)\( T^{20} + \)\(13\!\cdots\!10\)\( T^{21} + \)\(10\!\cdots\!37\)\( T^{22} + \)\(77\!\cdots\!24\)\( T^{23} + \)\(55\!\cdots\!48\)\( T^{24} + \)\(35\!\cdots\!92\)\( T^{25} + \)\(20\!\cdots\!06\)\( T^{26} + \)\(10\!\cdots\!13\)\( T^{27} + \)\(42\!\cdots\!19\)\( T^{28} + \)\(12\!\cdots\!54\)\( T^{29} + \)\(29\!\cdots\!99\)\( T^{30} \))(\( 1 + 3 T + 585 T^{2} + 1043 T^{3} + 177679 T^{4} + 64512 T^{5} + 36697381 T^{6} - 39312354 T^{7} + 5837371543 T^{8} - 13647513730 T^{9} + 771378841851 T^{10} - 2486630200488 T^{11} + 88642184872350 T^{12} - 321453678475485 T^{13} + 9015673700440774 T^{14} - 32833650134036701 T^{15} + 810513346635652698 T^{16} - 2807305074783810208 T^{17} + 64030554384216563142 T^{18} - \)\(20\!\cdots\!41\)\( T^{19} + \)\(44\!\cdots\!86\)\( T^{20} - \)\(12\!\cdots\!85\)\( T^{21} + \)\(27\!\cdots\!50\)\( T^{22} - \)\(60\!\cdots\!48\)\( T^{23} + \)\(14\!\cdots\!09\)\( T^{24} - \)\(20\!\cdots\!30\)\( T^{25} + \)\(69\!\cdots\!17\)\( T^{26} - \)\(37\!\cdots\!54\)\( T^{27} + \)\(27\!\cdots\!99\)\( T^{28} + \)\(38\!\cdots\!92\)\( T^{29} + \)\(82\!\cdots\!81\)\( T^{30} + \)\(38\!\cdots\!83\)\( T^{31} + \)\(17\!\cdots\!15\)\( T^{32} + \)\(69\!\cdots\!63\)\( T^{33} + \)\(18\!\cdots\!59\)\( T^{34} \))(\( 1 - 40 T + 1811 T^{2} - 48477 T^{3} + 1319282 T^{4} - 27369850 T^{5} + 564440865 T^{6} - 9727465556 T^{7} + 165765052229 T^{8} - 2469431623547 T^{9} + 36363007841360 T^{10} - 480299833255876 T^{11} + 6278599655046057 T^{12} - 74807860002705982 T^{13} + 883599841612642101 T^{14} - 9611050821905146937 T^{15} + \)\(10\!\cdots\!80\)\( T^{16} - \)\(10\!\cdots\!14\)\( T^{17} + \)\(10\!\cdots\!83\)\( T^{18} - \)\(95\!\cdots\!23\)\( T^{19} + \)\(88\!\cdots\!94\)\( T^{20} - \)\(75\!\cdots\!17\)\( T^{21} + \)\(64\!\cdots\!03\)\( T^{22} - \)\(51\!\cdots\!46\)\( T^{23} + \)\(40\!\cdots\!80\)\( T^{24} - \)\(29\!\cdots\!63\)\( T^{25} + \)\(21\!\cdots\!21\)\( T^{26} - \)\(14\!\cdots\!38\)\( T^{27} + \)\(95\!\cdots\!77\)\( T^{28} - \)\(57\!\cdots\!44\)\( T^{29} + \)\(34\!\cdots\!60\)\( T^{30} - \)\(18\!\cdots\!13\)\( T^{31} + \)\(97\!\cdots\!89\)\( T^{32} - \)\(45\!\cdots\!84\)\( T^{33} + \)\(20\!\cdots\!65\)\( T^{34} - \)\(79\!\cdots\!50\)\( T^{35} + \)\(30\!\cdots\!22\)\( T^{36} - \)\(88\!\cdots\!43\)\( T^{37} + \)\(26\!\cdots\!71\)\( T^{38} - \)\(45\!\cdots\!60\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))
$83$ (\( 1 - 3 T + 83 T^{2} \))(\( 1 + 5 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 8 T + 110 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 - 11 T + 474 T^{2} - 3846 T^{3} + 97672 T^{4} - 547461 T^{5} + 11848717 T^{6} - 42502105 T^{7} + 1056612310 T^{8} - 2868090410 T^{9} + 87698821730 T^{10} - 292797001345 T^{11} + 6774942347279 T^{12} - 25981579872981 T^{13} + 384733977683096 T^{14} - 1257412675977174 T^{15} + 12862488169083198 T^{16} - 24775214553529451 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 19 T + 687 T^{2} - 11547 T^{3} + 227142 T^{4} - 3257653 T^{5} + 46742113 T^{6} - 563300086 T^{7} + 6536553969 T^{8} - 66156590137 T^{9} + 643472849516 T^{10} - 5490996981371 T^{11} + 45030320292441 T^{12} - 322087666273682 T^{13} + 2218302202972273 T^{14} - 12832027567790879 T^{15} + 74261890287781398 T^{16} - 313339980777222969 T^{17} + 1547324763479521167 T^{18} - 3551864850083267657 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 5 T + 320 T^{2} + 2558 T^{3} + 65050 T^{4} + 598605 T^{5} + 10645776 T^{6} + 95974594 T^{7} + 1402228546 T^{8} + 11915660442 T^{9} + 152449757362 T^{10} + 1201994024908 T^{11} + 13850165462714 T^{12} + 99765504067364 T^{13} + 1050226378466818 T^{14} + 6813219737149854 T^{15} + 66547412451431266 T^{16} + 378047826461423942 T^{17} + 3480533980242739344 T^{18} + 16243775802645670335 T^{19} + \)\(14\!\cdots\!50\)\( T^{20} + \)\(47\!\cdots\!74\)\( T^{21} + \)\(49\!\cdots\!80\)\( T^{22} + \)\(64\!\cdots\!35\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 32 T + 1135 T^{2} + 24891 T^{3} + 547502 T^{4} + 9525526 T^{5} + 162347934 T^{6} + 2383310138 T^{7} + 34049494927 T^{8} + 435862259404 T^{9} + 5422285931239 T^{10} + 61693834835533 T^{11} + 682305282543888 T^{12} + 6976719981736934 T^{13} + 69375411735134418 T^{14} + 640856113990023532 T^{15} + 5758159174016156694 T^{16} + 48062623954185738326 T^{17} + \)\(39\!\cdots\!56\)\( T^{18} + \)\(29\!\cdots\!93\)\( T^{19} + \)\(21\!\cdots\!77\)\( T^{20} + \)\(14\!\cdots\!76\)\( T^{21} + \)\(92\!\cdots\!29\)\( T^{22} + \)\(53\!\cdots\!58\)\( T^{23} + \)\(30\!\cdots\!02\)\( T^{24} + \)\(14\!\cdots\!74\)\( T^{25} + \)\(70\!\cdots\!34\)\( T^{26} + \)\(26\!\cdots\!51\)\( T^{27} + \)\(10\!\cdots\!05\)\( T^{28} + \)\(23\!\cdots\!28\)\( T^{29} + \)\(61\!\cdots\!07\)\( T^{30} \))(\( 1 - 7 T + 848 T^{2} - 5302 T^{3} + 363344 T^{4} - 2065443 T^{5} + 104359263 T^{6} - 545448991 T^{7} + 22432325052 T^{8} - 108460590636 T^{9} + 3817692384918 T^{10} - 17124472064727 T^{11} + 531403985345169 T^{12} - 2212501967360181 T^{13} + 61689215608266670 T^{14} - 238030226504530236 T^{15} + 6039763231142169521 T^{16} - 21520308264914614218 T^{17} + \)\(50\!\cdots\!43\)\( T^{18} - \)\(16\!\cdots\!04\)\( T^{19} + \)\(35\!\cdots\!90\)\( T^{20} - \)\(10\!\cdots\!01\)\( T^{21} + \)\(20\!\cdots\!67\)\( T^{22} - \)\(55\!\cdots\!63\)\( T^{23} + \)\(10\!\cdots\!86\)\( T^{24} - \)\(24\!\cdots\!76\)\( T^{25} + \)\(41\!\cdots\!56\)\( T^{26} - \)\(84\!\cdots\!59\)\( T^{27} + \)\(13\!\cdots\!21\)\( T^{28} - \)\(22\!\cdots\!23\)\( T^{29} + \)\(32\!\cdots\!72\)\( T^{30} - \)\(39\!\cdots\!58\)\( T^{31} + \)\(51\!\cdots\!36\)\( T^{32} - \)\(35\!\cdots\!67\)\( T^{33} + \)\(42\!\cdots\!23\)\( T^{34} \))(\( 1 - 10 T + 938 T^{2} - 8915 T^{3} + 437497 T^{4} - 4047595 T^{5} + 135198370 T^{6} - 1234894620 T^{7} + 31094638166 T^{8} - 282741954734 T^{9} + 5672941324764 T^{10} - 51540855872926 T^{11} + 855297468978862 T^{12} - 7757780277247158 T^{13} + 109698914421900540 T^{14} - 987728555306949406 T^{15} + 12229665929165323865 T^{16} - \)\(10\!\cdots\!02\)\( T^{17} + \)\(12\!\cdots\!04\)\( T^{18} - \)\(10\!\cdots\!60\)\( T^{19} + \)\(10\!\cdots\!94\)\( T^{20} - \)\(85\!\cdots\!80\)\( T^{21} + \)\(82\!\cdots\!56\)\( T^{22} - \)\(61\!\cdots\!74\)\( T^{23} + \)\(58\!\cdots\!65\)\( T^{24} - \)\(38\!\cdots\!58\)\( T^{25} + \)\(35\!\cdots\!60\)\( T^{26} - \)\(21\!\cdots\!66\)\( T^{27} + \)\(19\!\cdots\!42\)\( T^{28} - \)\(96\!\cdots\!78\)\( T^{29} + \)\(88\!\cdots\!36\)\( T^{30} - \)\(36\!\cdots\!78\)\( T^{31} + \)\(33\!\cdots\!26\)\( T^{32} - \)\(10\!\cdots\!60\)\( T^{33} + \)\(99\!\cdots\!30\)\( T^{34} - \)\(24\!\cdots\!65\)\( T^{35} + \)\(22\!\cdots\!57\)\( T^{36} - \)\(37\!\cdots\!45\)\( T^{37} + \)\(32\!\cdots\!42\)\( T^{38} - \)\(29\!\cdots\!70\)\( T^{39} + \)\(24\!\cdots\!01\)\( T^{40} \))
$89$ (\( 1 - 15 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( 1 + 28 T + 502 T^{2} + 6163 T^{3} + 75886 T^{4} + 967153 T^{5} + 12492667 T^{6} + 135318502 T^{7} + 1302126084 T^{8} + 11889195164 T^{9} + 115889221476 T^{10} + 1071857854342 T^{11} + 8806942962323 T^{12} + 60681346609873 T^{13} + 423751935346814 T^{14} + 3062895696192643 T^{15} + 22204130117555558 T^{16} + 110224486559658268 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 30 T + 1011 T^{2} + 20699 T^{3} + 418614 T^{4} + 6544860 T^{5} + 98981835 T^{6} + 1250450097 T^{7} + 15230285299 T^{8} + 159866982622 T^{9} + 1617442689892 T^{10} + 14228161453358 T^{11} + 120639089853379 T^{12} + 881528554431993 T^{13} + 6210342146192235 T^{14} + 36546887325382140 T^{15} + 208043326134348054 T^{16} + 915544401002554771 T^{17} + 3979891282564803891 T^{18} + 10510692111224556270 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 8 T + 514 T^{2} + 4157 T^{3} + 136934 T^{4} + 1110429 T^{5} + 25021642 T^{6} + 201108030 T^{7} + 3508301548 T^{8} + 27557573181 T^{9} + 400998482658 T^{10} + 3009007792643 T^{11} + 38641229406062 T^{12} + 267801693545227 T^{13} + 3176308981134018 T^{14} + 19427234807836389 T^{15} + 220118701225289068 T^{16} + 1122999195191275470 T^{17} + 12435287943123977962 T^{18} + 49115756976707371941 T^{19} + \)\(53\!\cdots\!54\)\( T^{20} + \)\(14\!\cdots\!13\)\( T^{21} + \)\(16\!\cdots\!14\)\( T^{22} + \)\(22\!\cdots\!12\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 25 T + 1018 T^{2} - 18600 T^{3} + 443982 T^{4} - 6606737 T^{5} + 119469217 T^{6} - 1543977228 T^{7} + 23326536924 T^{8} - 271475845653 T^{9} + 3586000833545 T^{10} - 38193837010312 T^{11} + 451500197042975 T^{12} - 4426424853940601 T^{13} + 47534310321073314 T^{14} - 429364443286779416 T^{15} + 4230553618575524946 T^{16} - 35061711268063500521 T^{17} + \)\(31\!\cdots\!75\)\( T^{18} - \)\(23\!\cdots\!92\)\( T^{19} + \)\(20\!\cdots\!05\)\( T^{20} - \)\(13\!\cdots\!33\)\( T^{21} + \)\(10\!\cdots\!96\)\( T^{22} - \)\(60\!\cdots\!68\)\( T^{23} + \)\(41\!\cdots\!53\)\( T^{24} - \)\(20\!\cdots\!37\)\( T^{25} + \)\(12\!\cdots\!98\)\( T^{26} - \)\(45\!\cdots\!00\)\( T^{27} + \)\(22\!\cdots\!42\)\( T^{28} - \)\(48\!\cdots\!25\)\( T^{29} + \)\(17\!\cdots\!49\)\( T^{30} \))(\( 1 + 18 T + 973 T^{2} + 13541 T^{3} + 423651 T^{4} + 4707002 T^{5} + 113091725 T^{6} + 1018344814 T^{7} + 21456097611 T^{8} + 158520556203 T^{9} + 3209494793181 T^{10} + 19969966846364 T^{11} + 410153301259870 T^{12} + 2249075818418931 T^{13} + 46721366186577296 T^{14} + 235166727751100061 T^{15} + 4740958967140044580 T^{16} + 22244931566777751028 T^{17} + \)\(42\!\cdots\!20\)\( T^{18} + \)\(18\!\cdots\!81\)\( T^{19} + \)\(32\!\cdots\!24\)\( T^{20} + \)\(14\!\cdots\!71\)\( T^{21} + \)\(22\!\cdots\!30\)\( T^{22} + \)\(99\!\cdots\!04\)\( T^{23} + \)\(14\!\cdots\!49\)\( T^{24} + \)\(62\!\cdots\!43\)\( T^{25} + \)\(75\!\cdots\!99\)\( T^{26} + \)\(31\!\cdots\!14\)\( T^{27} + \)\(31\!\cdots\!25\)\( T^{28} + \)\(11\!\cdots\!42\)\( T^{29} + \)\(93\!\cdots\!19\)\( T^{30} + \)\(26\!\cdots\!81\)\( T^{31} + \)\(16\!\cdots\!77\)\( T^{32} + \)\(27\!\cdots\!98\)\( T^{33} + \)\(13\!\cdots\!29\)\( T^{34} \))(\( 1 - 17 T + 846 T^{2} - 13042 T^{3} + 368030 T^{4} - 5072331 T^{5} + 107208364 T^{6} - 1327865531 T^{7} + 23321848051 T^{8} - 261915573704 T^{9} + 4032316846037 T^{10} - 41403697198507 T^{11} + 578136461074171 T^{12} - 5471945286248959 T^{13} + 71086330842501118 T^{14} - 626350947584957666 T^{15} + 7727728719959675218 T^{16} - 64202582847234225602 T^{17} + \)\(76\!\cdots\!23\)\( T^{18} - \)\(60\!\cdots\!61\)\( T^{19} + \)\(70\!\cdots\!34\)\( T^{20} - \)\(54\!\cdots\!29\)\( T^{21} + \)\(60\!\cdots\!83\)\( T^{22} - \)\(45\!\cdots\!38\)\( T^{23} + \)\(48\!\cdots\!38\)\( T^{24} - \)\(34\!\cdots\!34\)\( T^{25} + \)\(35\!\cdots\!98\)\( T^{26} - \)\(24\!\cdots\!11\)\( T^{27} + \)\(22\!\cdots\!51\)\( T^{28} - \)\(14\!\cdots\!63\)\( T^{29} + \)\(12\!\cdots\!37\)\( T^{30} - \)\(72\!\cdots\!56\)\( T^{31} + \)\(57\!\cdots\!71\)\( T^{32} - \)\(29\!\cdots\!39\)\( T^{33} + \)\(20\!\cdots\!24\)\( T^{34} - \)\(88\!\cdots\!19\)\( T^{35} + \)\(57\!\cdots\!30\)\( T^{36} - \)\(17\!\cdots\!18\)\( T^{37} + \)\(10\!\cdots\!26\)\( T^{38} - \)\(18\!\cdots\!53\)\( T^{39} + \)\(97\!\cdots\!01\)\( T^{40} \))
$97$ (\( 1 - 14 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 3 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 24 T + 336 T^{2} + 2328 T^{3} + 9409 T^{4} \))(\( 1 + 28 T + 915 T^{2} + 17360 T^{3} + 342597 T^{4} + 5017891 T^{5} + 74248348 T^{6} + 883806883 T^{7} + 10524022081 T^{8} + 103749957330 T^{9} + 1020830141857 T^{10} + 8315738962147 T^{11} + 67764462514204 T^{12} + 444230282366371 T^{13} + 2941997010027429 T^{14} + 14460394005567440 T^{15} + 73930430297473395 T^{16} + 219448140642554908 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 16 T + 640 T^{2} + 6946 T^{3} + 179074 T^{4} + 1534105 T^{5} + 33304185 T^{6} + 244454186 T^{7} + 4690150175 T^{8} + 30216640161 T^{9} + 513900985612 T^{10} + 2931014095617 T^{11} + 44129622996575 T^{12} + 223106735299178 T^{13} + 2948395552340985 T^{14} + 13173881624964985 T^{15} + 149163628810655746 T^{16} + 561224883984972898 T^{17} + 5015957500401255040 T^{18} + 12163696938473043472 T^{19} + 73742412689492826049 T^{20} \))(\( 1 + 32 T + 1110 T^{2} + 23592 T^{3} + 498483 T^{4} + 8248923 T^{5} + 133984853 T^{6} + 1854692468 T^{7} + 25171997923 T^{8} + 301987005962 T^{9} + 3554048841815 T^{10} + 37560019017727 T^{11} + 389515614831966 T^{12} + 3643321844719519 T^{13} + 33440045552637335 T^{14} + 275615386692356426 T^{15} + 2228458877456683363 T^{16} + 15926875294811084276 T^{17} + \)\(11\!\cdots\!37\)\( T^{18} + \)\(66\!\cdots\!99\)\( T^{19} + \)\(39\!\cdots\!63\)\( T^{20} + \)\(17\!\cdots\!64\)\( T^{21} + \)\(81\!\cdots\!90\)\( T^{22} + \)\(22\!\cdots\!96\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 + 34 T + 1261 T^{2} + 28182 T^{3} + 644608 T^{4} + 11385135 T^{5} + 203469675 T^{6} + 3065540581 T^{7} + 46427042747 T^{8} + 617169579093 T^{9} + 8213466618766 T^{10} + 98045796310932 T^{11} + 1169552401922133 T^{12} + 12661735697433550 T^{13} + 136848774462950549 T^{14} + 1349177368408284450 T^{15} + 13274331122906203253 T^{16} + \)\(11\!\cdots\!50\)\( T^{17} + \)\(10\!\cdots\!09\)\( T^{18} + \)\(86\!\cdots\!92\)\( T^{19} + \)\(70\!\cdots\!62\)\( T^{20} + \)\(51\!\cdots\!97\)\( T^{21} + \)\(37\!\cdots\!11\)\( T^{22} + \)\(24\!\cdots\!41\)\( T^{23} + \)\(15\!\cdots\!75\)\( T^{24} + \)\(83\!\cdots\!15\)\( T^{25} + \)\(46\!\cdots\!24\)\( T^{26} + \)\(19\!\cdots\!62\)\( T^{27} + \)\(84\!\cdots\!97\)\( T^{28} + \)\(22\!\cdots\!46\)\( T^{29} + \)\(63\!\cdots\!93\)\( T^{30} \))(\( 1 - 63 T + 2743 T^{2} - 88452 T^{3} + 2371828 T^{4} - 54312415 T^{5} + 1099276687 T^{6} - 19936891951 T^{7} + 329338675273 T^{8} - 4997505682608 T^{9} + 70378212269780 T^{10} - 925790691893063 T^{11} + 11467680553211171 T^{12} - 134550426960870441 T^{13} + 1506101640687965527 T^{14} - 16167059496128328282 T^{15} + \)\(16\!\cdots\!38\)\( T^{16} - \)\(16\!\cdots\!44\)\( T^{17} + \)\(16\!\cdots\!86\)\( T^{18} - \)\(15\!\cdots\!38\)\( T^{19} + \)\(13\!\cdots\!71\)\( T^{20} - \)\(11\!\cdots\!21\)\( T^{21} + \)\(98\!\cdots\!47\)\( T^{22} - \)\(77\!\cdots\!27\)\( T^{23} + \)\(56\!\cdots\!40\)\( T^{24} - \)\(39\!\cdots\!88\)\( T^{25} + \)\(25\!\cdots\!41\)\( T^{26} - \)\(14\!\cdots\!99\)\( T^{27} + \)\(78\!\cdots\!11\)\( T^{28} - \)\(37\!\cdots\!15\)\( T^{29} + \)\(15\!\cdots\!56\)\( T^{30} - \)\(57\!\cdots\!88\)\( T^{31} + \)\(17\!\cdots\!99\)\( T^{32} - \)\(38\!\cdots\!23\)\( T^{33} + \)\(59\!\cdots\!37\)\( T^{34} \))(\( 1 + 2 T + 909 T^{2} + 2372 T^{3} + 414784 T^{4} + 1241355 T^{5} + 128264569 T^{6} + 402347181 T^{7} + 30420162456 T^{8} + 94138802251 T^{9} + 5901608783321 T^{10} + 17396802161192 T^{11} + 972566457145183 T^{12} + 2687077808715671 T^{13} + 139522059303651822 T^{14} + 359592587249436223 T^{15} + 17715158909625088629 T^{16} + 42681247133183014345 T^{17} + \)\(20\!\cdots\!75\)\( T^{18} + \)\(45\!\cdots\!08\)\( T^{19} + \)\(20\!\cdots\!22\)\( T^{20} + \)\(44\!\cdots\!76\)\( T^{21} + \)\(18\!\cdots\!75\)\( T^{22} + \)\(38\!\cdots\!85\)\( T^{23} + \)\(15\!\cdots\!49\)\( T^{24} + \)\(30\!\cdots\!11\)\( T^{25} + \)\(11\!\cdots\!38\)\( T^{26} + \)\(21\!\cdots\!23\)\( T^{27} + \)\(76\!\cdots\!63\)\( T^{28} + \)\(13\!\cdots\!64\)\( T^{29} + \)\(43\!\cdots\!29\)\( T^{30} + \)\(67\!\cdots\!03\)\( T^{31} + \)\(21\!\cdots\!96\)\( T^{32} + \)\(27\!\cdots\!37\)\( T^{33} + \)\(83\!\cdots\!61\)\( T^{34} + \)\(78\!\cdots\!15\)\( T^{35} + \)\(25\!\cdots\!64\)\( T^{36} + \)\(14\!\cdots\!64\)\( T^{37} + \)\(52\!\cdots\!01\)\( T^{38} + \)\(11\!\cdots\!66\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))
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