Properties

Label 4020.2
Level 4020
Weight 2
Dimension 171928
Nonzero newspaces 48
Sturm bound 1723392

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Defining parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(1723392\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4020))\).

Total New Old
Modular forms 436128 173496 262632
Cusp forms 425569 171928 253641
Eisenstein series 10559 1568 8991

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4020))\)

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
4020.2.a \(\chi_{4020}(1, \cdot)\) 4020.2.a.a 1 1
4020.2.a.b 4
4020.2.a.c 4
4020.2.a.d 4
4020.2.a.e 5
4020.2.a.f 6
4020.2.a.g 6
4020.2.a.h 7
4020.2.a.i 7
4020.2.f \(\chi_{4020}(401, \cdot)\) 4020.2.f.a 46 1
4020.2.f.b 46
4020.2.g \(\chi_{4020}(1609, \cdot)\) 4020.2.g.a 2 1
4020.2.g.b 24
4020.2.g.c 38
4020.2.h \(\chi_{4020}(671, \cdot)\) n/a 528 1
4020.2.i \(\chi_{4020}(1339, \cdot)\) n/a 408 1
4020.2.n \(\chi_{4020}(2279, \cdot)\) n/a 792 1
4020.2.o \(\chi_{4020}(3751, \cdot)\) n/a 272 1
4020.2.p \(\chi_{4020}(2009, \cdot)\) n/a 136 1
4020.2.q \(\chi_{4020}(841, \cdot)\) 4020.2.q.a 2 2
4020.2.q.b 2
4020.2.q.c 2
4020.2.q.d 2
4020.2.q.e 2
4020.2.q.f 2
4020.2.q.g 2
4020.2.q.h 2
4020.2.q.i 4
4020.2.q.j 12
4020.2.q.k 14
4020.2.q.l 22
4020.2.q.m 24
4020.2.r \(\chi_{4020}(133, \cdot)\) n/a 136 2
4020.2.s \(\chi_{4020}(1073, \cdot)\) n/a 264 2
4020.2.t \(\chi_{4020}(403, \cdot)\) n/a 792 2
4020.2.u \(\chi_{4020}(803, \cdot)\) n/a 1616 2
4020.2.z \(\chi_{4020}(1169, \cdot)\) n/a 272 2
4020.2.ba \(\chi_{4020}(2911, \cdot)\) n/a 544 2
4020.2.bb \(\chi_{4020}(2039, \cdot)\) n/a 1616 2
4020.2.bg \(\chi_{4020}(499, \cdot)\) n/a 816 2
4020.2.bh \(\chi_{4020}(431, \cdot)\) n/a 1088 2
4020.2.bi \(\chi_{4020}(1369, \cdot)\) n/a 136 2
4020.2.bj \(\chi_{4020}(641, \cdot)\) n/a 180 2
4020.2.bo \(\chi_{4020}(241, \cdot)\) n/a 440 10
4020.2.bt \(\chi_{4020}(767, \cdot)\) n/a 3232 4
4020.2.bu \(\chi_{4020}(163, \cdot)\) n/a 1632 4
4020.2.bv \(\chi_{4020}(833, \cdot)\) n/a 544 4
4020.2.bw \(\chi_{4020}(97, \cdot)\) n/a 272 4
4020.2.bx \(\chi_{4020}(209, \cdot)\) n/a 1360 10
4020.2.by \(\chi_{4020}(59, \cdot)\) n/a 8080 10
4020.2.bz \(\chi_{4020}(271, \cdot)\) n/a 2720 10
4020.2.ce \(\chi_{4020}(131, \cdot)\) n/a 5440 10
4020.2.cf \(\chi_{4020}(139, \cdot)\) n/a 4080 10
4020.2.cg \(\chi_{4020}(161, \cdot)\) n/a 920 10
4020.2.ch \(\chi_{4020}(349, \cdot)\) n/a 680 10
4020.2.cm \(\chi_{4020}(121, \cdot)\) n/a 920 20
4020.2.cr \(\chi_{4020}(223, \cdot)\) n/a 8160 20
4020.2.cs \(\chi_{4020}(407, \cdot)\) n/a 16160 20
4020.2.ct \(\chi_{4020}(253, \cdot)\) n/a 1360 20
4020.2.cu \(\chi_{4020}(293, \cdot)\) n/a 2720 20
4020.2.cz \(\chi_{4020}(49, \cdot)\) n/a 1360 20
4020.2.da \(\chi_{4020}(41, \cdot)\) n/a 1800 20
4020.2.db \(\chi_{4020}(79, \cdot)\) n/a 8160 20
4020.2.dc \(\chi_{4020}(71, \cdot)\) n/a 10880 20
4020.2.dh \(\chi_{4020}(31, \cdot)\) n/a 5440 20
4020.2.di \(\chi_{4020}(419, \cdot)\) n/a 16160 20
4020.2.dj \(\chi_{4020}(329, \cdot)\) n/a 2720 20
4020.2.dk \(\chi_{4020}(17, \cdot)\) n/a 5440 40
4020.2.dl \(\chi_{4020}(13, \cdot)\) n/a 2720 40
4020.2.dm \(\chi_{4020}(203, \cdot)\) n/a 32320 40
4020.2.dn \(\chi_{4020}(103, \cdot)\) n/a 16320 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(670))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(804))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1005))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2010))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 - T \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( 1 + T^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{12} \))(\( ( 1 + T )^{14} \))
$5$ (\( 1 + T \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( 1 - 2 T + 5 T^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{12} \))(\( ( 1 - T )^{14} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 + T + 16 T^{2} - T^{3} + 123 T^{4} - 7 T^{5} + 784 T^{6} + 343 T^{7} + 2401 T^{8} \))(\( 1 - T + 20 T^{2} - 17 T^{3} + 183 T^{4} - 119 T^{5} + 980 T^{6} - 343 T^{7} + 2401 T^{8} \))(\( 1 + 3 T + 22 T^{2} + 45 T^{3} + 201 T^{4} + 315 T^{5} + 1078 T^{6} + 1029 T^{7} + 2401 T^{8} \))(\( 1 + 3 T + 23 T^{2} + 68 T^{3} + 241 T^{4} + 660 T^{5} + 1687 T^{6} + 3332 T^{7} + 7889 T^{8} + 7203 T^{9} + 16807 T^{10} \))(\( 1 - T + 14 T^{2} - 47 T^{3} + 160 T^{4} - 382 T^{5} + 1698 T^{6} - 2674 T^{7} + 7840 T^{8} - 16121 T^{9} + 33614 T^{10} - 16807 T^{11} + 117649 T^{12} \))(\( 1 - 3 T + 24 T^{2} - 45 T^{3} + 282 T^{4} - 474 T^{5} + 2458 T^{6} - 3318 T^{7} + 13818 T^{8} - 15435 T^{9} + 57624 T^{10} - 50421 T^{11} + 117649 T^{12} \))(\( 1 - 3 T + 21 T^{2} - 36 T^{3} + 192 T^{4} - 103 T^{5} + 1032 T^{6} + 188 T^{7} + 7224 T^{8} - 5047 T^{9} + 65856 T^{10} - 86436 T^{11} + 352947 T^{12} - 352947 T^{13} + 823543 T^{14} \))(\( 1 - T + 19 T^{2} - 8 T^{3} + 128 T^{4} - 41 T^{5} + 498 T^{6} - 444 T^{7} + 3486 T^{8} - 2009 T^{9} + 43904 T^{10} - 19208 T^{11} + 319333 T^{12} - 117649 T^{13} + 823543 T^{14} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} \))(\( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( ( 1 - 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( ( 1 - 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( ( 1 - 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( 1 + T - 5 T^{2} - 8 T^{3} - 20 T^{4} - 56 T^{5} - 245 T^{6} + 343 T^{7} + 2401 T^{8} \))(\( 1 - 2 T + 4 T^{2} - 48 T^{4} + 107 T^{5} + 396 T^{6} - 1161 T^{7} + 2332 T^{8} - 8784 T^{9} - 6359 T^{10} - 549 T^{11} + 84688 T^{12} - 3843 T^{13} - 311591 T^{14} - 3012912 T^{15} + 5599132 T^{16} - 19512927 T^{17} + 46589004 T^{18} + 88119101 T^{19} - 276710448 T^{20} + 1129900996 T^{22} - 3954653486 T^{23} + 13841287201 T^{24} \))(\( 1 - 3 T - 20 T^{2} + 57 T^{3} + 177 T^{4} - 389 T^{5} - 1803 T^{6} + 3303 T^{7} + 18070 T^{8} - 36377 T^{9} - 110178 T^{10} + 123265 T^{11} + 781213 T^{12} + 114570 T^{13} - 6762664 T^{14} + 801990 T^{15} + 38279437 T^{16} + 42279895 T^{17} - 264537378 T^{18} - 611388239 T^{19} + 2125917430 T^{20} + 2720162529 T^{21} - 10393936203 T^{22} - 15697553123 T^{23} + 49998119073 T^{24} + 112707624351 T^{25} - 276825744020 T^{26} - 290667031221 T^{27} + 678223072849 T^{28} \))
$11$ (\( 1 + 2 T + 11 T^{2} \))(\( 1 - 5 T + 48 T^{2} - 161 T^{3} + 813 T^{4} - 1771 T^{5} + 5808 T^{6} - 6655 T^{7} + 14641 T^{8} \))(\( 1 + 5 T + 26 T^{2} + 95 T^{3} + 411 T^{4} + 1045 T^{5} + 3146 T^{6} + 6655 T^{7} + 14641 T^{8} \))(\( 1 + 5 T + 34 T^{2} + 115 T^{3} + 501 T^{4} + 1265 T^{5} + 4114 T^{6} + 6655 T^{7} + 14641 T^{8} \))(\( 1 - 3 T + 29 T^{2} - 60 T^{3} + 385 T^{4} - 712 T^{5} + 4235 T^{6} - 7260 T^{7} + 38599 T^{8} - 43923 T^{9} + 161051 T^{10} \))(\( 1 + 7 T + 52 T^{2} + 241 T^{3} + 1104 T^{4} + 3942 T^{5} + 14534 T^{6} + 43362 T^{7} + 133584 T^{8} + 320771 T^{9} + 761332 T^{10} + 1127357 T^{11} + 1771561 T^{12} \))(\( 1 - 3 T + 30 T^{2} - 75 T^{3} + 348 T^{4} - 876 T^{5} + 3130 T^{6} - 9636 T^{7} + 42108 T^{8} - 99825 T^{9} + 439230 T^{10} - 483153 T^{11} + 1771561 T^{12} \))(\( 1 + 5 T + 21 T^{2} + 58 T^{3} + 292 T^{4} + 1049 T^{5} + 4080 T^{6} + 12192 T^{7} + 44880 T^{8} + 126929 T^{9} + 388652 T^{10} + 849178 T^{11} + 3382071 T^{12} + 8857805 T^{13} + 19487171 T^{14} \))(\( 1 - 5 T + 47 T^{2} - 124 T^{3} + 782 T^{4} - 1205 T^{5} + 8984 T^{6} - 10948 T^{7} + 98824 T^{8} - 145805 T^{9} + 1040842 T^{10} - 1815484 T^{11} + 7569397 T^{12} - 8857805 T^{13} + 19487171 T^{14} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 3 T - 7 T^{2} + 18 T^{3} + 36 T^{4} + 198 T^{5} - 847 T^{6} - 3993 T^{7} + 14641 T^{8} \))(\( 1 + 5 T - 10 T^{2} - 39 T^{3} + 71 T^{4} - 535 T^{5} - 1716 T^{6} - 1332 T^{7} - 1883 T^{8} + 75951 T^{9} - 168035 T^{10} - 92937 T^{11} + 7017904 T^{12} - 1022307 T^{13} - 20332235 T^{14} + 101090781 T^{15} - 27569003 T^{16} - 214519932 T^{17} - 3039998676 T^{18} - 10425636485 T^{19} + 15219480551 T^{20} - 91959959949 T^{21} - 259374246010 T^{22} + 1426558353055 T^{23} + 3138428376721 T^{24} \))(\( 1 - 6 T - 11 T^{2} + 16 T^{3} + 550 T^{4} + 451 T^{5} - 6158 T^{6} - 23818 T^{7} + 26095 T^{8} + 323347 T^{9} + 407400 T^{10} - 2104801 T^{11} - 9984167 T^{12} + 14819849 T^{13} + 70409980 T^{14} + 163018339 T^{15} - 1208084207 T^{16} - 2801490131 T^{17} + 5964743400 T^{18} + 52075357697 T^{19} + 46228884295 T^{20} - 464145438878 T^{21} - 1320021989198 T^{22} + 1063434408641 T^{23} + 14265583530550 T^{24} + 4564986729776 T^{25} - 34522712143931 T^{26} - 207136272863586 T^{27} + 379749833583241 T^{28} \))
$13$ (\( 1 - 2 T + 13 T^{2} \))(\( 1 + T + 27 T^{2} + 24 T^{3} + 365 T^{4} + 312 T^{5} + 4563 T^{6} + 2197 T^{7} + 28561 T^{8} \))(\( 1 + 5 T + 31 T^{2} + 70 T^{3} + 341 T^{4} + 910 T^{5} + 5239 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( 1 + 9 T + 63 T^{2} + 330 T^{3} + 1271 T^{4} + 4290 T^{5} + 10647 T^{6} + 19773 T^{7} + 28561 T^{8} \))(\( 1 + 11 T + 102 T^{2} + 599 T^{3} + 3098 T^{4} + 11862 T^{5} + 40274 T^{6} + 101231 T^{7} + 224094 T^{8} + 314171 T^{9} + 371293 T^{10} \))(\( 1 - 7 T + 47 T^{2} - 214 T^{3} + 1146 T^{4} - 4513 T^{5} + 18522 T^{6} - 58669 T^{7} + 193674 T^{8} - 470158 T^{9} + 1342367 T^{10} - 2599051 T^{11} + 4826809 T^{12} \))(\( 1 - 3 T + 39 T^{2} - 76 T^{3} + 648 T^{4} - 639 T^{5} + 8106 T^{6} - 8307 T^{7} + 109512 T^{8} - 166972 T^{9} + 1113879 T^{10} - 1113879 T^{11} + 4826809 T^{12} \))(\( 1 - 5 T + 34 T^{2} - 139 T^{3} + 635 T^{4} - 2607 T^{5} + 10740 T^{6} - 37974 T^{7} + 139620 T^{8} - 440583 T^{9} + 1395095 T^{10} - 3969979 T^{11} + 12623962 T^{12} - 24134045 T^{13} + 62748517 T^{14} \))(\( 1 - 9 T + 82 T^{2} - 501 T^{3} + 2853 T^{4} - 13419 T^{5} + 57830 T^{6} - 218514 T^{7} + 751790 T^{8} - 2267811 T^{9} + 6268041 T^{10} - 14309061 T^{11} + 30446026 T^{12} - 43441281 T^{13} + 62748517 T^{14} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))(\( ( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( ( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 3 T - 4 T^{2} - 39 T^{3} + 169 T^{4} \))(\( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} \))(\( ( 1 + 2 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} \))(\( ( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( ( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} )^{6} \))(\( 1 - 9 T - 3 T^{2} + 234 T^{3} - 216 T^{4} - 3440 T^{5} + 5289 T^{6} + 22909 T^{7} - 40116 T^{8} + 156307 T^{9} - 627413 T^{10} - 5854224 T^{11} + 29555027 T^{12} + 38130675 T^{13} - 498920098 T^{14} + 495698775 T^{15} + 4994799563 T^{16} - 12861730128 T^{17} - 17919542693 T^{18} + 58035694951 T^{19} - 193632269844 T^{20} + 1437505775953 T^{21} + 4314399783369 T^{22} - 36479477843120 T^{23} - 29777434239384 T^{24} + 419365532204658 T^{25} - 69894255367443 T^{26} - 2725875959330277 T^{27} + 3937376385699289 T^{28} \))
$17$ (\( 1 - 5 T + 17 T^{2} \))(\( 1 + 4 T + 52 T^{2} + 217 T^{3} + 1187 T^{4} + 3689 T^{5} + 15028 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 + 8 T + 58 T^{2} + 289 T^{3} + 1469 T^{4} + 4913 T^{5} + 16762 T^{6} + 39304 T^{7} + 83521 T^{8} \))(\( 1 + 8 T + 52 T^{2} + 205 T^{3} + 921 T^{4} + 3485 T^{5} + 15028 T^{6} + 39304 T^{7} + 83521 T^{8} \))(\( 1 + 11 T + 115 T^{2} + 695 T^{3} + 4088 T^{4} + 16919 T^{5} + 69496 T^{6} + 200855 T^{7} + 564995 T^{8} + 918731 T^{9} + 1419857 T^{10} \))(\( 1 - 10 T + 82 T^{2} - 461 T^{3} + 2598 T^{4} - 12491 T^{5} + 56936 T^{6} - 212347 T^{7} + 750822 T^{8} - 2264893 T^{9} + 6848722 T^{10} - 14198570 T^{11} + 24137569 T^{12} \))(\( 1 - 6 T + 78 T^{2} - 385 T^{3} + 2724 T^{4} - 11127 T^{5} + 57328 T^{6} - 189159 T^{7} + 787236 T^{8} - 1891505 T^{9} + 6514638 T^{10} - 8519142 T^{11} + 24137569 T^{12} \))(\( 1 - 3 T + 31 T^{2} - 83 T^{3} + 651 T^{4} - 2330 T^{5} + 12209 T^{6} - 39446 T^{7} + 207553 T^{8} - 673370 T^{9} + 3198363 T^{10} - 6932243 T^{11} + 44015567 T^{12} - 72412707 T^{13} + 410338673 T^{14} \))(\( 1 - 11 T + 131 T^{2} - 919 T^{3} + 6497 T^{4} - 34076 T^{5} + 177839 T^{6} - 735646 T^{7} + 3023263 T^{8} - 9847964 T^{9} + 31919761 T^{10} - 76755799 T^{11} + 186001267 T^{12} - 265513259 T^{13} + 410338673 T^{14} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 7 T + 32 T^{2} - 119 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - T - 16 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 - 5 T + 8 T^{2} - 85 T^{3} + 289 T^{4} \))(\( 1 + T - 16 T^{2} + 17 T^{3} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 - 7 T + 32 T^{2} - 119 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 9 T + 35 T^{2} + 108 T^{3} + 450 T^{4} + 1836 T^{5} + 10115 T^{6} + 44217 T^{7} + 83521 T^{8} \))(\( 1 - 9 T + 4 T^{2} + 355 T^{3} - 1746 T^{4} - 1694 T^{5} + 47899 T^{6} - 146091 T^{7} - 390577 T^{8} + 4607833 T^{9} - 10879892 T^{10} - 42482959 T^{11} + 376180152 T^{12} - 722210303 T^{13} - 3144288788 T^{14} + 22638283529 T^{15} - 32621381617 T^{16} - 207428328987 T^{17} + 1156165417531 T^{18} - 695113712062 T^{19} - 12179672491986 T^{20} + 42098696156435 T^{21} + 8063975601796 T^{22} - 308447066768697 T^{23} + 582622237229761 T^{24} \))(\( 1 + 12 T + 13 T^{2} - 120 T^{3} + 1763 T^{4} + 8439 T^{5} - 29854 T^{6} + 48731 T^{7} + 1353310 T^{8} - 587405 T^{9} - 5786839 T^{10} + 84344359 T^{11} + 106817487 T^{12} - 21465324 T^{13} + 3964551862 T^{14} - 364910508 T^{15} + 30870253743 T^{16} + 414383835767 T^{17} - 483322580119 T^{18} - 834031101085 T^{19} + 32665613503390 T^{20} + 19996213873963 T^{21} - 208254262643614 T^{22} + 1000763089758183 T^{23} + 3554197246491587 T^{24} - 4112627556915960 T^{25} + 7574089083986893 T^{26} + 118854936394871244 T^{27} + 168377826559400929 T^{28} \))
$19$ (\( 1 - T + 19 T^{2} \))(\( 1 + 7 T + 79 T^{2} + 368 T^{3} + 2273 T^{4} + 6992 T^{5} + 28519 T^{6} + 48013 T^{7} + 130321 T^{8} \))(\( 1 - 5 T + 51 T^{2} - 224 T^{3} + 1409 T^{4} - 4256 T^{5} + 18411 T^{6} - 34295 T^{7} + 130321 T^{8} \))(\( 1 + 7 T + 55 T^{2} + 232 T^{3} + 1309 T^{4} + 4408 T^{5} + 19855 T^{6} + 48013 T^{7} + 130321 T^{8} \))(\( 1 - 6 T + 43 T^{2} - 258 T^{3} + 1470 T^{4} - 5525 T^{5} + 27930 T^{6} - 93138 T^{7} + 294937 T^{8} - 781926 T^{9} + 2476099 T^{10} \))(\( 1 + 3 T + 73 T^{2} + 170 T^{3} + 2688 T^{4} + 5347 T^{5} + 63764 T^{6} + 101593 T^{7} + 970368 T^{8} + 1166030 T^{9} + 9513433 T^{10} + 7428297 T^{11} + 47045881 T^{12} \))(\( 1 + 3 T + 81 T^{2} + 258 T^{3} + 3060 T^{4} + 9339 T^{5} + 71452 T^{6} + 177441 T^{7} + 1104660 T^{8} + 1769622 T^{9} + 10556001 T^{10} + 7428297 T^{11} + 47045881 T^{12} \))(\( 1 - 2 T + 25 T^{2} - 70 T^{3} + 977 T^{4} - 2063 T^{5} + 20081 T^{6} - 51322 T^{7} + 381539 T^{8} - 744743 T^{9} + 6701243 T^{10} - 9122470 T^{11} + 61902475 T^{12} - 94091762 T^{13} + 893871739 T^{14} \))(\( 1 - 2 T + 73 T^{2} - 22 T^{3} + 2165 T^{4} + 3821 T^{5} + 39189 T^{6} + 134574 T^{7} + 744591 T^{8} + 1379381 T^{9} + 14849735 T^{10} - 2867062 T^{11} + 180755227 T^{12} - 94091762 T^{13} + 893871739 T^{14} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( ( 1 - T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 7 T + 7 T^{2} + 28 T^{3} + 472 T^{4} + 532 T^{5} + 2527 T^{6} + 48013 T^{7} + 130321 T^{8} \))(\( 1 + 11 T + 33 T^{2} - 388 T^{4} - 4838 T^{5} - 28432 T^{6} - 111029 T^{7} - 333428 T^{8} - 54312 T^{9} + 4625736 T^{10} + 47081975 T^{11} + 298793580 T^{12} + 894557525 T^{13} + 1669890696 T^{14} - 372526008 T^{15} - 43452670388 T^{16} - 274918795871 T^{17} - 1337608488592 T^{18} - 4324551473282 T^{19} - 6589622459908 T^{20} + 202325186507433 T^{22} + 1281392847880409 T^{23} + 2213314919066161 T^{24} \))(\( 1 - 14 T + 8 T^{2} + 582 T^{3} + 222 T^{4} - 25358 T^{5} - 8233 T^{6} + 614419 T^{7} + 1938247 T^{8} - 16399564 T^{9} - 65078281 T^{10} + 228533498 T^{11} + 2092709725 T^{12} - 2476014457 T^{13} - 40027234346 T^{14} - 47044274683 T^{15} + 755468210725 T^{16} + 1567511262782 T^{17} - 8481066658201 T^{18} - 40606944020836 T^{19} + 91186537710607 T^{20} + 549211780004641 T^{21} - 139825674516553 T^{22} - 8182714640279882 T^{23} + 1361096709231822 T^{24} + 67797330678763458 T^{25} + 17706519352529288 T^{26} - 588741768471598826 T^{27} + 799006685782884121 T^{28} \))
$23$ (\( 1 + 3 T + 23 T^{2} \))(\( 1 - 6 T + 56 T^{2} - 152 T^{3} + 1249 T^{4} - 3496 T^{5} + 29624 T^{6} - 73002 T^{7} + 279841 T^{8} \))(\( ( 1 + 3 T + 23 T^{2} )^{4} \))(\( 1 + 12 T + 106 T^{2} + 576 T^{3} + 3099 T^{4} + 13248 T^{5} + 56074 T^{6} + 146004 T^{7} + 279841 T^{8} \))(\( 1 - 3 T + 37 T^{2} - 98 T^{3} + 417 T^{4} - 2453 T^{5} + 9591 T^{6} - 51842 T^{7} + 450179 T^{8} - 839523 T^{9} + 6436343 T^{10} \))(\( 1 + 4 T + 72 T^{2} + 152 T^{3} + 1528 T^{4} - 12 T^{5} + 18638 T^{6} - 276 T^{7} + 808312 T^{8} + 1849384 T^{9} + 20148552 T^{10} + 25745372 T^{11} + 148035889 T^{12} \))(\( 1 - 6 T + 78 T^{2} - 436 T^{3} + 3354 T^{4} - 16590 T^{5} + 93454 T^{6} - 381570 T^{7} + 1774266 T^{8} - 5304812 T^{9} + 21827598 T^{10} - 38618058 T^{11} + 148035889 T^{12} \))(\( 1 + 3 T + 87 T^{2} + 376 T^{3} + 3928 T^{4} + 19960 T^{5} + 119694 T^{6} + 598042 T^{7} + 2752962 T^{8} + 10558840 T^{9} + 47791976 T^{10} + 105220216 T^{11} + 559961841 T^{12} + 444107667 T^{13} + 3404825447 T^{14} \))(\( 1 - 7 T + 119 T^{2} - 704 T^{3} + 6512 T^{4} - 32704 T^{5} + 219182 T^{6} - 929666 T^{7} + 5041186 T^{8} - 17300416 T^{9} + 79231504 T^{10} - 197008064 T^{11} + 765924817 T^{12} - 1036251223 T^{13} + 3404825447 T^{14} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( 1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 + 7 T + 26 T^{2} + 161 T^{3} + 529 T^{4} \))(\( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 + 3 T - 14 T^{2} + 69 T^{3} + 529 T^{4} \))(\( 1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 + 3 T - 14 T^{2} + 69 T^{3} + 529 T^{4} \))(\( ( 1 + 9 T + 23 T^{2} )^{2}( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} ) \))(\( 1 - 19 T + 120 T^{2} - 95 T^{3} - 1424 T^{4} - 2326 T^{5} + 61689 T^{6} - 352863 T^{7} + 2083525 T^{8} - 6539565 T^{9} - 1493768 T^{10} - 115618269 T^{11} + 1361354230 T^{12} - 2659220187 T^{13} - 790203272 T^{14} - 79566887355 T^{15} + 583055719525 T^{16} - 2271147300009 T^{17} + 9132185956521 T^{18} - 7919623989722 T^{19} - 111514843040144 T^{20} - 171109502838985 T^{21} + 4971181345637880 T^{22} - 18103385400364613 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 6 T - 55 T^{2} + 462 T^{3} + 753 T^{4} - 13307 T^{5} + 10046 T^{6} + 152185 T^{7} - 95636 T^{8} - 824917 T^{9} - 12768145 T^{10} + 51517171 T^{11} + 264832895 T^{12} - 956116592 T^{13} - 2075704102 T^{14} - 21990681616 T^{15} + 140096601455 T^{16} + 626809419557 T^{17} - 3573050464945 T^{18} - 5309448758531 T^{19} - 14157560280404 T^{20} + 518163360651695 T^{21} + 786712158132926 T^{22} - 23967938466088141 T^{23} + 31194162943877697 T^{24} + 440198108156234274 T^{25} - 1205304343761117655 T^{26} - 3024218171618804298 T^{27} + 11592836324538749809 T^{28} \))
$29$ (\( 1 + 9 T + 29 T^{2} \))(\( 1 + T + 79 T^{2} + 166 T^{3} + 2863 T^{4} + 4814 T^{5} + 66439 T^{6} + 24389 T^{7} + 707281 T^{8} \))(\( 1 + 5 T + 117 T^{2} + 422 T^{3} + 5095 T^{4} + 12238 T^{5} + 98397 T^{6} + 121945 T^{7} + 707281 T^{8} \))(\( 1 + 9 T + 97 T^{2} + 642 T^{3} + 4125 T^{4} + 18618 T^{5} + 81577 T^{6} + 219501 T^{7} + 707281 T^{8} \))(\( 1 + 2 T + 45 T^{2} - 66 T^{3} + 2142 T^{4} + 1785 T^{5} + 62118 T^{6} - 55506 T^{7} + 1097505 T^{8} + 1414562 T^{9} + 20511149 T^{10} \))(\( 1 - 9 T + 115 T^{2} - 532 T^{3} + 4192 T^{4} - 11455 T^{5} + 107112 T^{6} - 332195 T^{7} + 3525472 T^{8} - 12974948 T^{9} + 81337315 T^{10} - 184600341 T^{11} + 594823321 T^{12} \))(\( 1 - 21 T + 249 T^{2} - 2108 T^{3} + 14766 T^{4} - 90339 T^{5} + 507904 T^{6} - 2619831 T^{7} + 12418206 T^{8} - 51412012 T^{9} + 176112969 T^{10} - 430734129 T^{11} + 594823321 T^{12} \))(\( 1 + 8 T + 195 T^{2} + 1174 T^{3} + 16017 T^{4} + 76183 T^{5} + 746831 T^{6} + 2836022 T^{7} + 21658099 T^{8} + 64069903 T^{9} + 390638613 T^{10} + 830347894 T^{11} + 3999674055 T^{12} + 4758586568 T^{13} + 17249876309 T^{14} \))(\( 1 - 8 T + 173 T^{2} - 1024 T^{3} + 12881 T^{4} - 60359 T^{5} + 566477 T^{6} - 2164546 T^{7} + 16427833 T^{8} - 50761919 T^{9} + 314154709 T^{10} - 724255744 T^{11} + 3548428777 T^{12} - 4758586568 T^{13} + 17249876309 T^{14} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( 1 + 3 T - 20 T^{2} + 87 T^{3} + 841 T^{4} \))(\( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} \))(\( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} \))(\( 1 - 7 T + 20 T^{2} - 203 T^{3} + 841 T^{4} \))(\( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} \))(\( 1 + T - 28 T^{2} + 29 T^{3} + 841 T^{4} \))(\( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 + 3 T - 43 T^{2} - 18 T^{3} + 1602 T^{4} - 522 T^{5} - 36163 T^{6} + 73167 T^{7} + 707281 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 368 T^{3} + 1206 T^{4} - 1655 T^{5} + 89070 T^{6} - 339779 T^{7} + 1355490 T^{8} - 22458518 T^{9} + 53699035 T^{10} - 227990417 T^{11} + 3614850538 T^{12} - 6611722093 T^{13} + 45160888435 T^{14} - 547740795502 T^{15} + 958712322690 T^{16} - 6969257696071 T^{17} + 52980913201470 T^{18} - 28548545291395 T^{19} + 603297174030966 T^{20} - 5338629719119792 T^{21} + 13462631465606432 T^{22} - 97604078125646632 T^{23} + 353814783205469041 T^{24} \))(\( 1 + T - 94 T^{2} + 111 T^{3} + 4141 T^{4} - 11695 T^{5} - 81857 T^{6} + 347769 T^{7} + 213802 T^{8} + 2744015 T^{9} + 736264 T^{10} - 378858495 T^{11} + 1902063729 T^{12} + 6351771646 T^{13} - 90593298388 T^{14} + 184201377734 T^{15} + 1599635596089 T^{16} - 9239979834555 T^{17} + 520745538184 T^{18} + 56282900523235 T^{19} + 127174415676442 T^{20} + 5998972234104621 T^{21} - 40948670625748577 T^{22} - 169661072187787955 T^{23} + 1742148653096132341 T^{24} + 1354256583993347019 T^{25} - 33258589621314089854 T^{26} + 10260628712958602189 T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 + 11 T + 116 T^{2} + 761 T^{3} + 4843 T^{4} + 23591 T^{5} + 111476 T^{6} + 327701 T^{7} + 923521 T^{8} \))(\( 1 + T + 70 T^{2} - 119 T^{3} + 2217 T^{4} - 3689 T^{5} + 67270 T^{6} + 29791 T^{7} + 923521 T^{8} \))(\( 1 + 9 T + 90 T^{2} + 591 T^{3} + 4349 T^{4} + 18321 T^{5} + 86490 T^{6} + 268119 T^{7} + 923521 T^{8} \))(\( 1 - T + 75 T^{2} + 328 T^{3} + 1275 T^{4} + 22862 T^{5} + 39525 T^{6} + 315208 T^{7} + 2234325 T^{8} - 923521 T^{9} + 28629151 T^{10} \))(\( 1 - 3 T + 116 T^{2} - 513 T^{3} + 6456 T^{4} - 31790 T^{5} + 237604 T^{6} - 985490 T^{7} + 6204216 T^{8} - 15282783 T^{9} + 107128436 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 3 T + 114 T^{2} + 209 T^{3} + 6642 T^{4} + 10098 T^{5} + 255648 T^{6} + 313038 T^{7} + 6382962 T^{8} + 6226319 T^{9} + 105281394 T^{10} + 85887453 T^{11} + 887503681 T^{12} \))(\( 1 - 7 T + 103 T^{2} - 752 T^{3} + 6848 T^{4} - 42865 T^{5} + 308936 T^{6} - 1562360 T^{7} + 9577016 T^{8} - 41193265 T^{9} + 204008768 T^{10} - 694487792 T^{11} + 2948802553 T^{12} - 6212525767 T^{13} + 27512614111 T^{14} \))(\( 1 - 9 T + 157 T^{2} - 684 T^{3} + 6900 T^{4} - 2043 T^{5} + 96962 T^{6} + 651768 T^{7} + 3005822 T^{8} - 1963323 T^{9} + 205557900 T^{10} - 631688364 T^{11} + 4494776707 T^{12} - 7987533129 T^{13} + 27512614111 T^{14} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( 1 - 3 T - 22 T^{2} - 93 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 4 T - 17 T^{2} - 116 T^{3} - 368 T^{4} - 3596 T^{5} - 16337 T^{6} + 119164 T^{7} + 923521 T^{8} \))(\( 1 + 4 T - 109 T^{2} - 606 T^{3} + 5492 T^{4} + 36266 T^{5} - 184734 T^{6} - 1057922 T^{7} + 6973790 T^{8} + 13628888 T^{9} - 332452362 T^{10} - 40779865 T^{11} + 12559806528 T^{12} - 1264175815 T^{13} - 319486719882 T^{14} + 406018202408 T^{15} + 6440441514590 T^{16} - 30287408684222 T^{17} - 163952105005854 T^{18} + 997772463349526 T^{19} + 4684077577625972 T^{20} - 16022411029366626 T^{21} - 89339483280907309 T^{22} + 101633907585619324 T^{23} + 787662783788549761 T^{24} \))(\( 1 - 7 T - 39 T^{2} + 660 T^{3} - 2351 T^{4} - 13913 T^{5} + 146821 T^{6} - 144326 T^{7} - 3076282 T^{8} + 12618238 T^{9} + 70496210 T^{10} - 862571403 T^{11} + 1968366689 T^{12} + 19721322013 T^{13} - 189458995778 T^{14} + 611360982403 T^{15} + 1891600388129 T^{16} - 25696864666773 T^{17} + 65104730355410 T^{18} + 361249441055938 T^{19} - 2730211598794042 T^{20} - 3970785544184186 T^{21} + 125222315008125061 T^{22} - 367854463121415623 T^{23} - 1926946102691863151 T^{24} + 16769594751627188460 T^{25} - 30718848567753440679 T^{26} - \)\(17\!\cdots\!37\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))
$37$ (\( 1 + 11 T + 37 T^{2} \))(\( 1 + 114 T^{2} + 32 T^{3} + 5747 T^{4} + 1184 T^{5} + 156066 T^{6} + 1874161 T^{8} \))(\( 1 - 14 T + 188 T^{2} - 1492 T^{3} + 10941 T^{4} - 55204 T^{5} + 257372 T^{6} - 709142 T^{7} + 1874161 T^{8} \))(\( 1 + 20 T + 258 T^{2} + 2200 T^{3} + 15299 T^{4} + 81400 T^{5} + 353202 T^{6} + 1013060 T^{7} + 1874161 T^{8} \))(\( 1 + 13 T + 135 T^{2} + 922 T^{3} + 5933 T^{4} + 31335 T^{5} + 219521 T^{6} + 1262218 T^{7} + 6838155 T^{8} + 24364093 T^{9} + 69343957 T^{10} \))(\( 1 - 16 T + 256 T^{2} - 2444 T^{3} + 22360 T^{4} - 155208 T^{5} + 1050702 T^{6} - 5742696 T^{7} + 30610840 T^{8} - 123795932 T^{9} + 479785216 T^{10} - 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 + 120 T^{2} - 180 T^{3} + 7944 T^{4} - 10224 T^{5} + 370078 T^{6} - 378288 T^{7} + 10875336 T^{8} - 9117540 T^{9} + 224899320 T^{10} + 2565726409 T^{12} \))(\( 1 + 5 T + 213 T^{2} + 1068 T^{3} + 20860 T^{4} + 95468 T^{5} + 1212318 T^{6} + 4647094 T^{7} + 44855766 T^{8} + 130695692 T^{9} + 1056621580 T^{10} + 2001603948 T^{11} + 14770262841 T^{12} + 12828632045 T^{13} + 94931877133 T^{14} \))(\( 1 - 7 T + 97 T^{2} - 224 T^{3} + 3260 T^{4} + 3352 T^{5} + 85122 T^{6} + 362766 T^{7} + 3149514 T^{8} + 4588888 T^{9} + 165128780 T^{10} - 419812064 T^{11} + 6726363829 T^{12} - 17960084863 T^{13} + 94931877133 T^{14} \))(\( ( 1 - 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( ( 1 - 10 T + 37 T^{2} )( 1 - T + 37 T^{2} ) \))(\( 1 + 5 T - 12 T^{2} + 185 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 28 T^{2} - 111 T^{3} + 1369 T^{4} \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} \))(\( 1 + T + T^{2} - 74 T^{3} - 1406 T^{4} - 2738 T^{5} + 1369 T^{6} + 50653 T^{7} + 1874161 T^{8} \))(\( 1 - 5 T - 35 T^{2} + 148 T^{3} + 910 T^{4} + 4694 T^{5} + 48184 T^{6} - 753797 T^{7} - 2440934 T^{8} + 39099266 T^{9} + 52006098 T^{10} - 569825299 T^{11} - 258124762 T^{12} - 21083536063 T^{13} + 71196348162 T^{14} + 1980495120698 T^{15} - 4574703306374 T^{16} - 52271266754729 T^{17} + 123626961291256 T^{18} + 445610231262302 T^{19} + 3196356303068110 T^{20} + 19234337489671396 T^{21} - 168300453034624715 T^{22} - 889588108897302065 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + 2 T - 144 T^{2} - 58 T^{3} + 11562 T^{4} - 8564 T^{5} - 567933 T^{6} + 1219349 T^{7} + 16972491 T^{8} - 72220508 T^{9} - 82031967 T^{10} + 2604100054 T^{11} - 19609237189 T^{12} - 38834898747 T^{13} + 1110997548598 T^{14} - 1436891253639 T^{15} - 26845045711741 T^{16} + 131905480035262 T^{17} - 153741113304687 T^{18} - 5008055801270156 T^{19} + 43546768385214819 T^{20} + 115755089450246417 T^{21} - 1994852993703715293 T^{22} - 1112992339605039428 T^{23} + 55596852513895170138 T^{24} - 10319222063208703954 T^{25} - \)\(94\!\cdots\!64\)\( T^{26} + \)\(48\!\cdots\!94\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 13 T + 98 T^{2} + 387 T^{3} + 2053 T^{4} + 15867 T^{5} + 164738 T^{6} + 895973 T^{7} + 2825761 T^{8} \))(\( 1 + 17 T + 238 T^{2} + 2123 T^{3} + 16155 T^{4} + 87043 T^{5} + 400078 T^{6} + 1171657 T^{7} + 2825761 T^{8} \))(\( 1 + 11 T + 200 T^{2} + 1379 T^{3} + 13009 T^{4} + 56539 T^{5} + 336200 T^{6} + 758131 T^{7} + 2825761 T^{8} \))(\( 1 + 13 T + 207 T^{2} + 1558 T^{3} + 14601 T^{4} + 81272 T^{5} + 598641 T^{6} + 2618998 T^{7} + 14266647 T^{8} + 36734893 T^{9} + 115856201 T^{10} \))(\( 1 - 7 T + 200 T^{2} - 1161 T^{3} + 17720 T^{4} - 84576 T^{5} + 918738 T^{6} - 3467616 T^{7} + 29787320 T^{8} - 80017281 T^{9} + 565152200 T^{10} - 810993407 T^{11} + 4750104241 T^{12} \))(\( 1 - 9 T + 186 T^{2} - 1421 T^{3} + 16128 T^{4} - 102162 T^{5} + 834046 T^{6} - 4188642 T^{7} + 27111168 T^{8} - 97936741 T^{9} + 525591546 T^{10} - 1042705809 T^{11} + 4750104241 T^{12} \))(\( 1 - 7 T + 201 T^{2} - 1558 T^{3} + 20510 T^{4} - 142227 T^{5} + 1320572 T^{6} - 7391784 T^{7} + 54143452 T^{8} - 239083587 T^{9} + 1413569710 T^{10} - 4402535638 T^{11} + 23287096401 T^{12} - 33250729687 T^{13} + 194754273881 T^{14} \))(\( 1 - 9 T + 119 T^{2} - 696 T^{3} + 6948 T^{4} - 31269 T^{5} + 313624 T^{6} - 1370892 T^{7} + 12858584 T^{8} - 52563189 T^{9} + 478863108 T^{10} - 1966729656 T^{11} + 13786887919 T^{12} - 42750938169 T^{13} + 194754273881 T^{14} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( 1 - 5 T - 16 T^{2} - 205 T^{3} + 1681 T^{4} \))(\( 1 - 11 T + 80 T^{2} - 451 T^{3} + 1681 T^{4} \))(\( 1 + T - 40 T^{2} + 41 T^{3} + 1681 T^{4} \))(\( 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 + 5 T - 16 T^{2} + 205 T^{3} + 1681 T^{4} \))(\( 1 - 7 T + 8 T^{2} - 287 T^{3} + 1681 T^{4} \))(\( 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 - 15 T + 95 T^{2} - 720 T^{3} + 5994 T^{4} - 29520 T^{5} + 159695 T^{6} - 1033815 T^{7} + 2825761 T^{8} \))(\( 1 + 9 T - 112 T^{2} - 853 T^{3} + 9803 T^{4} + 50521 T^{5} - 565952 T^{6} - 1758476 T^{7} + 24242199 T^{8} + 40372655 T^{9} - 791971767 T^{10} - 501901089 T^{11} + 26593085586 T^{12} - 20577944649 T^{13} - 1331304540327 T^{14} + 2782523755255 T^{15} + 68502660488439 T^{16} - 203730348909676 T^{17} - 2688330995402432 T^{18} + 9839180670742001 T^{19} + 78276222021073163 T^{20} - 279256790038048733 T^{21} - 1503337842737068912 T^{22} + 4952961285446235969 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 18 T - 29 T^{2} - 2200 T^{3} - 1130 T^{4} + 183989 T^{5} + 379300 T^{6} - 8058104 T^{7} - 4062155 T^{8} + 263971859 T^{9} - 1279880946 T^{10} - 2948011895 T^{11} + 160106068045 T^{12} + 57760123657 T^{13} - 7992127618244 T^{14} + 2368165069937 T^{15} + 269138300383645 T^{16} - 203179927815295 T^{17} - 3616637661849906 T^{18} + 30582776754647659 T^{19} - 19295659693099355 T^{20} - 1569350193377581624 T^{21} + 3028682139405595300 T^{22} + 60234674727210490429 T^{23} - 15167605020472213130 T^{24} - \)\(12\!\cdots\!00\)\( T^{25} - \)\(65\!\cdots\!49\)\( T^{26} + \)\(16\!\cdots\!78\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))
$43$ (\( 1 - 10 T + 43 T^{2} \))(\( 1 - 15 T + 240 T^{2} - 2047 T^{3} + 16991 T^{4} - 88021 T^{5} + 443760 T^{6} - 1192605 T^{7} + 3418801 T^{8} \))(\( 1 + 9 T + 136 T^{2} + 807 T^{3} + 7703 T^{4} + 34701 T^{5} + 251464 T^{6} + 715563 T^{7} + 3418801 T^{8} \))(\( 1 - T + 108 T^{2} - 215 T^{3} + 5561 T^{4} - 9245 T^{5} + 199692 T^{6} - 79507 T^{7} + 3418801 T^{8} \))(\( 1 + 9 T + 53 T^{2} + 120 T^{3} + 2299 T^{4} + 15920 T^{5} + 98857 T^{6} + 221880 T^{7} + 4213871 T^{8} + 30769209 T^{9} + 147008443 T^{10} \))(\( 1 - 3 T + 222 T^{2} - 599 T^{3} + 21772 T^{4} - 49864 T^{5} + 1210538 T^{6} - 2144152 T^{7} + 40256428 T^{8} - 47624693 T^{9} + 758973822 T^{10} - 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 + 3 T + 90 T^{2} + 609 T^{3} + 6102 T^{4} + 34602 T^{5} + 344926 T^{6} + 1487886 T^{7} + 11282598 T^{8} + 48419763 T^{9} + 307692090 T^{10} + 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 - 3 T + 211 T^{2} - 416 T^{3} + 19878 T^{4} - 22931 T^{5} + 1168364 T^{6} - 911236 T^{7} + 50239652 T^{8} - 42399419 T^{9} + 1580440146 T^{10} - 1422221216 T^{11} + 31018781473 T^{12} - 18964089147 T^{13} + 271818611107 T^{14} \))(\( 1 - 5 T + 151 T^{2} - 622 T^{3} + 10436 T^{4} - 32797 T^{5} + 484086 T^{6} - 1283088 T^{7} + 20815698 T^{8} - 60641653 T^{9} + 829735052 T^{10} - 2126494222 T^{11} + 22198274893 T^{12} - 31606815245 T^{13} + 271818611107 T^{14} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - T + 78 T^{2} - 43 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 7 T + 202 T^{2} + 1304 T^{3} + 19362 T^{4} + 102444 T^{5} + 1076954 T^{6} + 4405092 T^{7} + 35800338 T^{8} + 103677128 T^{9} + 690597802 T^{10} + 1029059101 T^{11} + 6321363049 T^{12} )^{2} \))(\( ( 1 + 3 T + 165 T^{2} + 625 T^{3} + 14336 T^{4} + 57190 T^{5} + 833372 T^{6} + 3148724 T^{7} + 35834996 T^{8} + 105744310 T^{9} + 1139812352 T^{10} + 2136750625 T^{11} + 24256393095 T^{12} + 18964089147 T^{13} + 271818611107 T^{14} )^{2} \))
$47$ (\( 1 + 5 T + 47 T^{2} \))(\( 1 - 7 T + 139 T^{2} - 726 T^{3} + 9219 T^{4} - 34122 T^{5} + 307051 T^{6} - 726761 T^{7} + 4879681 T^{8} \))(\( 1 + 7 T + 61 T^{2} - 378 T^{3} - 2059 T^{4} - 17766 T^{5} + 134749 T^{6} + 726761 T^{7} + 4879681 T^{8} \))(\( 1 + 5 T + 173 T^{2} + 680 T^{3} + 11869 T^{4} + 31960 T^{5} + 382157 T^{6} + 519115 T^{7} + 4879681 T^{8} \))(\( 1 + 12 T + 221 T^{2} + 2144 T^{3} + 20300 T^{4} + 148487 T^{5} + 954100 T^{6} + 4736096 T^{7} + 22944883 T^{8} + 58556172 T^{9} + 229345007 T^{10} \))(\( 1 - T + 213 T^{2} - 102 T^{3} + 21168 T^{4} - 5801 T^{5} + 1257772 T^{6} - 272647 T^{7} + 46760112 T^{8} - 10589946 T^{9} + 1039372053 T^{10} - 229345007 T^{11} + 10779215329 T^{12} \))(\( 1 - 21 T + 303 T^{2} - 3044 T^{3} + 27474 T^{4} - 213243 T^{5} + 1570804 T^{6} - 10022421 T^{7} + 60690066 T^{8} - 316037212 T^{9} + 1478543343 T^{10} - 4816245147 T^{11} + 10779215329 T^{12} \))(\( 1 + 6 T + 281 T^{2} + 1420 T^{3} + 35583 T^{4} + 150355 T^{5} + 2641311 T^{6} + 9105486 T^{7} + 124141617 T^{8} + 332134195 T^{9} + 3694333809 T^{10} + 6929147020 T^{11} + 64445946967 T^{12} + 64675291974 T^{13} + 506623120463 T^{14} \))(\( 1 - 2 T + 203 T^{2} - 856 T^{3} + 18173 T^{4} - 117683 T^{5} + 1046795 T^{6} - 7697422 T^{7} + 49199365 T^{8} - 259961747 T^{9} + 1886775379 T^{10} - 4177006936 T^{11} + 46557036421 T^{12} - 21558430658 T^{13} + 506623120463 T^{14} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 + 13 T + 122 T^{2} + 611 T^{3} + 2209 T^{4} \))(\( 1 + T - 46 T^{2} + 47 T^{3} + 2209 T^{4} \))(\( 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} \))(\( 1 - T - 46 T^{2} - 47 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 + 7 T + 2 T^{2} + 329 T^{3} + 2209 T^{4} \))(\( 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} \))(\( 1 - 9 T - 25 T^{2} - 108 T^{3} + 5220 T^{4} - 5076 T^{5} - 55225 T^{6} - 934407 T^{7} + 4879681 T^{8} \))(\( 1 + 6 T - 23 T^{2} - 1160 T^{3} - 6572 T^{4} + 16868 T^{5} + 616228 T^{6} + 3244950 T^{7} - 6853044 T^{8} - 219512470 T^{9} - 865976942 T^{10} + 3383470903 T^{11} + 68645946092 T^{12} + 159023132441 T^{13} - 1912943064878 T^{14} - 22790443172810 T^{15} - 33440668598964 T^{16} + 744213080464650 T^{17} + 6642454303759012 T^{18} + 8545718795969884 T^{19} - 156487775941093292 T^{20} - 1298191348799209720 T^{21} - 1209780041424091127 T^{22} + 14832955290504073818 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 - 7 T - 153 T^{2} + 1362 T^{3} + 9935 T^{4} - 114473 T^{5} - 354685 T^{6} + 5522720 T^{7} + 11215060 T^{8} - 156793834 T^{9} - 900317666 T^{10} + 2422525493 T^{11} + 78249322737 T^{12} - 17047291839 T^{13} - 4482369027754 T^{14} - 801222716433 T^{15} + 172852753926033 T^{16} + 251513864259739 T^{17} - 4393263008744546 T^{18} - 35959882956286838 T^{19} + 120889546667654740 T^{20} + 2797937639843419360 T^{21} - 8445506209626700285 T^{22} - \)\(12\!\cdots\!91\)\( T^{23} + \)\(52\!\cdots\!15\)\( T^{24} + \)\(33\!\cdots\!86\)\( T^{25} - \)\(17\!\cdots\!73\)\( T^{26} - \)\(38\!\cdots\!89\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))
$53$ (\( 1 + 12 T + 53 T^{2} \))(\( 1 - 13 T + 169 T^{2} - 1572 T^{3} + 12393 T^{4} - 83316 T^{5} + 474721 T^{6} - 1935401 T^{7} + 7890481 T^{8} \))(\( 1 + 3 T + 161 T^{2} + 582 T^{3} + 11405 T^{4} + 30846 T^{5} + 452249 T^{6} + 446631 T^{7} + 7890481 T^{8} \))(\( 1 + 15 T + 227 T^{2} + 2070 T^{3} + 18489 T^{4} + 109710 T^{5} + 637643 T^{6} + 2233155 T^{7} + 7890481 T^{8} \))(\( 1 + 19 T + 228 T^{2} + 1171 T^{3} + 1956 T^{4} - 25864 T^{5} + 103668 T^{6} + 3289339 T^{7} + 33943956 T^{8} + 149919139 T^{9} + 418195493 T^{10} \))(\( 1 - 7 T + 249 T^{2} - 1418 T^{3} + 28238 T^{4} - 129827 T^{5} + 1892976 T^{6} - 6880831 T^{7} + 79320542 T^{8} - 211107586 T^{9} + 1964729769 T^{10} - 2927368451 T^{11} + 22164361129 T^{12} \))(\( 1 - 15 T + 147 T^{2} - 1020 T^{3} + 8466 T^{4} - 77433 T^{5} + 656404 T^{6} - 4103949 T^{7} + 23780994 T^{8} - 151854540 T^{9} + 1159900707 T^{10} - 6272932395 T^{11} + 22164361129 T^{12} \))(\( 1 + 9 T + 296 T^{2} + 2235 T^{3} + 39989 T^{4} + 254943 T^{5} + 3255898 T^{6} + 17152618 T^{7} + 172562594 T^{8} + 716134887 T^{9} + 5953442353 T^{10} + 17635225035 T^{11} + 123785865928 T^{12} + 199479250161 T^{13} + 1174711139837 T^{14} \))(\( 1 - 15 T + 374 T^{2} - 3975 T^{3} + 57039 T^{4} - 470469 T^{5} + 4901962 T^{6} - 32054298 T^{7} + 259803986 T^{8} - 1321547421 T^{9} + 8491795203 T^{10} - 31364661975 T^{11} + 156405114382 T^{12} - 332465416935 T^{13} + 1174711139837 T^{14} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 14 T + 53 T^{2} )^{2} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 82 T^{2} + 318 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 10 T + 292 T^{2} + 2399 T^{3} + 37181 T^{4} + 241012 T^{5} + 2598106 T^{6} + 12773636 T^{7} + 104441429 T^{8} + 357155923 T^{9} + 2304020452 T^{10} + 4181954930 T^{11} + 22164361129 T^{12} )^{2} \))(\( ( 1 + 6 T + 247 T^{2} + 1145 T^{3} + 30041 T^{4} + 116883 T^{5} + 2344387 T^{6} + 7652092 T^{7} + 124252511 T^{8} + 328324347 T^{9} + 4472413957 T^{10} + 9034600745 T^{11} + 103294286771 T^{12} + 132986166774 T^{13} + 1174711139837 T^{14} )^{2} \))
$59$ (\( 1 - 7 T + 59 T^{2} \))(\( 1 - T + 85 T^{2} + 80 T^{3} + 3389 T^{4} + 4720 T^{5} + 295885 T^{6} - 205379 T^{7} + 12117361 T^{8} \))(\( 1 + 23 T + 255 T^{2} + 1812 T^{3} + 11745 T^{4} + 106908 T^{5} + 887655 T^{6} + 4723717 T^{7} + 12117361 T^{8} \))(\( 1 - 7 T + 145 T^{2} - 692 T^{3} + 9879 T^{4} - 40828 T^{5} + 504745 T^{6} - 1437653 T^{7} + 12117361 T^{8} \))(\( 1 - 6 T + 127 T^{2} - 562 T^{3} + 9064 T^{4} - 21293 T^{5} + 534776 T^{6} - 1956322 T^{7} + 26083133 T^{8} - 72704166 T^{9} + 714924299 T^{10} \))(\( 1 - 5 T + 313 T^{2} - 1348 T^{3} + 43144 T^{4} - 151913 T^{5} + 3320862 T^{6} - 8962867 T^{7} + 150184264 T^{8} - 276850892 T^{9} + 3792733993 T^{10} - 3574621495 T^{11} + 42180533641 T^{12} \))(\( 1 - 15 T + 345 T^{2} - 3492 T^{3} + 46986 T^{4} - 360735 T^{5} + 3571414 T^{6} - 21283365 T^{7} + 163558266 T^{8} - 717183468 T^{9} + 4180489545 T^{10} - 10723864485 T^{11} + 42180533641 T^{12} \))(\( 1 + 22 T + 499 T^{2} + 6902 T^{3} + 92099 T^{4} + 937655 T^{5} + 9110405 T^{6} + 71721796 T^{7} + 537513895 T^{8} + 3263977055 T^{9} + 18915200521 T^{10} + 83634025622 T^{11} + 356747225201 T^{12} + 927971740102 T^{13} + 2488651484819 T^{14} \))(\( 1 + 197 T^{2} + 108 T^{3} + 22893 T^{4} + 15603 T^{5} + 1834513 T^{6} + 1268472 T^{7} + 108236267 T^{8} + 54314043 T^{9} + 4701741447 T^{10} + 1308674988 T^{11} + 140840086903 T^{12} + 2488651484819 T^{14} \))(\( ( 1 + 2 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 94 T^{2} - 354 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 3 T + 70 T^{2} - 98 T^{3} + 1610 T^{4} - 9168 T^{5} + 82294 T^{6} - 540912 T^{7} + 5604410 T^{8} - 20127142 T^{9} + 848215270 T^{10} - 2144772897 T^{11} + 42180533641 T^{12} )^{2} \))(\( ( 1 + T + 289 T^{2} + 403 T^{3} + 39692 T^{4} + 63484 T^{5} + 3413740 T^{6} + 5088680 T^{7} + 201410660 T^{8} + 220987804 T^{9} + 8151903268 T^{10} + 4883296483 T^{11} + 206613122411 T^{12} + 42180533641 T^{13} + 2488651484819 T^{14} )^{2} \))
$61$ (\( 1 - 8 T + 61 T^{2} \))(\( 1 + 15 T + 201 T^{2} + 1958 T^{3} + 15667 T^{4} + 119438 T^{5} + 747921 T^{6} + 3404715 T^{7} + 13845841 T^{8} \))(\( 1 + 27 T + 483 T^{2} + 5690 T^{3} + 52101 T^{4} + 347090 T^{5} + 1797243 T^{6} + 6128487 T^{7} + 13845841 T^{8} \))(\( 1 + 7 T + 163 T^{2} + 1264 T^{3} + 12505 T^{4} + 77104 T^{5} + 606523 T^{6} + 1588867 T^{7} + 13845841 T^{8} \))(\( 1 + 3 T + 238 T^{2} + 663 T^{3} + 25704 T^{4} + 59788 T^{5} + 1567944 T^{6} + 2467023 T^{7} + 54021478 T^{8} + 41537523 T^{9} + 844596301 T^{10} \))(\( 1 - 15 T + 415 T^{2} - 4412 T^{3} + 66966 T^{4} - 528689 T^{5} + 5538276 T^{6} - 32250029 T^{7} + 249180486 T^{8} - 1001440172 T^{9} + 5746024015 T^{10} - 12668944515 T^{11} + 51520374361 T^{12} \))(\( 1 - 15 T + 333 T^{2} - 3566 T^{3} + 46368 T^{4} - 386895 T^{5} + 3658196 T^{6} - 23600595 T^{7} + 172535328 T^{8} - 809414246 T^{9} + 4610665053 T^{10} - 12668944515 T^{11} + 51520374361 T^{12} \))(\( 1 - 19 T + 472 T^{2} - 6161 T^{3} + 88213 T^{4} - 867977 T^{5} + 8973786 T^{6} - 68695318 T^{7} + 547400946 T^{8} - 3229742417 T^{9} + 20022674953 T^{10} - 85304226401 T^{11} + 398649454072 T^{12} - 978887112859 T^{13} + 3142742836021 T^{14} \))(\( 1 - 11 T + 214 T^{2} - 883 T^{3} + 12641 T^{4} + 24563 T^{5} + 347856 T^{6} + 4536294 T^{7} + 21219216 T^{8} + 91398923 T^{9} + 2869266821 T^{10} - 12225877603 T^{11} + 180743608414 T^{12} - 566724117971 T^{13} + 3142742836021 T^{14} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} \))(\( 1 - 9 T + 20 T^{2} - 549 T^{3} + 3721 T^{4} \))(\( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} \))(\( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} \))(\( 1 + 3 T - 52 T^{2} + 183 T^{3} + 3721 T^{4} \))(\( 1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4} \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + T + 61 T^{2} ) \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( ( 1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4} )^{2} \))(\( 1 - 27 T + 151 T^{2} + 1702 T^{3} - 6246 T^{4} - 320230 T^{5} + 2445536 T^{6} + 10370959 T^{7} - 96143610 T^{8} - 1233847964 T^{9} + 14003131220 T^{10} - 9804089745 T^{11} - 438692150218 T^{12} - 598049474445 T^{13} + 52105651269620 T^{14} - 280060044716684 T^{15} - 1331189137226010 T^{16} + 8759273609222659 T^{17} + 125994930233302496 T^{18} - 1006400538379004830 T^{19} - 1197403876981017126 T^{20} + 19903436650003707982 T^{21} + \)\(10\!\cdots\!51\)\( T^{22} - \)\(11\!\cdots\!47\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 250 T^{2} - 1082 T^{3} + 35548 T^{4} + 260866 T^{5} - 2717433 T^{6} - 36918565 T^{7} + 78765775 T^{8} + 3261082584 T^{9} + 10157211285 T^{10} - 189570224500 T^{11} - 1612043826243 T^{12} + 4675152702057 T^{13} + 127013861698650 T^{14} + 285184314825477 T^{15} - 5998415077450203 T^{16} - 43028839127234500 T^{17} + 140635132455515685 T^{18} + 2754298287701921784 T^{19} + 4058042214834294775 T^{20} - \)\(11\!\cdots\!65\)\( T^{21} - \)\(52\!\cdots\!73\)\( T^{22} + \)\(30\!\cdots\!06\)\( T^{23} + \)\(25\!\cdots\!48\)\( T^{24} - \)\(47\!\cdots\!02\)\( T^{25} - \)\(66\!\cdots\!50\)\( T^{26} + \)\(98\!\cdots\!41\)\( T^{28} \))
$67$ (\( 1 + T \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{7} \))(\( 1 + T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} \))(\( 1 - 3 T - 9 T^{2} + 945 T^{3} - 6138 T^{4} - 52035 T^{5} + 480724 T^{6} - 3486345 T^{7} - 27553482 T^{8} + 284221035 T^{9} - 181360089 T^{10} - 4050375321 T^{11} + 90458382169 T^{12} \))(\( 1 - 25 T + 298 T^{2} - 2382 T^{3} + 12789 T^{4} - 5772 T^{5} - 884312 T^{6} + 10995854 T^{7} - 59248904 T^{8} - 25910508 T^{9} + 3846458007 T^{10} - 47999970222 T^{11} + 402337281886 T^{12} - 2261459554225 T^{13} + 6060711605323 T^{14} \))
$71$ (\( 1 - 4 T + 71 T^{2} \))(\( 1 + 6 T - 32 T^{2} + 305 T^{3} + 11555 T^{4} + 21655 T^{5} - 161312 T^{6} + 2147466 T^{7} + 25411681 T^{8} \))(\( 1 + 20 T + 310 T^{2} + 3443 T^{3} + 32439 T^{4} + 244453 T^{5} + 1562710 T^{6} + 7158220 T^{7} + 25411681 T^{8} \))(\( 1 + 94 T^{2} - 285 T^{3} + 7761 T^{4} - 20235 T^{5} + 473854 T^{6} + 25411681 T^{8} \))(\( 1 - 6 T + 311 T^{2} - 1489 T^{3} + 41597 T^{4} - 152470 T^{5} + 2953387 T^{6} - 7506049 T^{7} + 111310321 T^{8} - 152470086 T^{9} + 1804229351 T^{10} \))(\( 1 + 12 T + 362 T^{2} + 3665 T^{3} + 58658 T^{4} + 478899 T^{5} + 5395088 T^{6} + 34001829 T^{7} + 295694978 T^{8} + 1311743815 T^{9} + 9199028522 T^{10} + 21650752212 T^{11} + 128100283921 T^{12} \))(\( 1 - 18 T + 300 T^{2} - 3057 T^{3} + 34512 T^{4} - 321813 T^{5} + 3065020 T^{6} - 22848723 T^{7} + 173974992 T^{8} - 1094133927 T^{9} + 7623504300 T^{10} - 32476128318 T^{11} + 128100283921 T^{12} \))(\( 1 + 253 T^{2} - 419 T^{3} + 30766 T^{4} - 116730 T^{5} + 2499824 T^{6} - 12048814 T^{7} + 177487504 T^{8} - 588435930 T^{9} + 11011489826 T^{10} - 10647494339 T^{11} + 456470025803 T^{12} + 9095120158391 T^{14} \))(\( 1 - 18 T + 527 T^{2} - 6351 T^{3} + 105570 T^{4} - 953004 T^{5} + 11665102 T^{6} - 84162318 T^{7} + 828222242 T^{8} - 4804093164 T^{9} + 37784664270 T^{10} - 161389586031 T^{11} + 950828867977 T^{12} - 2305805110578 T^{13} + 9095120158391 T^{14} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( 1 + T - 70 T^{2} + 71 T^{3} + 5041 T^{4} \))(\( 1 + 15 T + 154 T^{2} + 1065 T^{3} + 5041 T^{4} \))(\( 1 + 3 T - 62 T^{2} + 213 T^{3} + 5041 T^{4} \))(\( 1 + 15 T + 154 T^{2} + 1065 T^{3} + 5041 T^{4} \))(\( 1 + 15 T + 154 T^{2} + 1065 T^{3} + 5041 T^{4} \))(\( 1 - 13 T + 98 T^{2} - 923 T^{3} + 5041 T^{4} \))(\( 1 + 7 T - 22 T^{2} + 497 T^{3} + 5041 T^{4} \))(\( 1 + 3 T - 62 T^{2} + 213 T^{3} + 5041 T^{4} \))(\( 1 + 9 T - 7 T^{2} - 486 T^{3} - 3048 T^{4} - 34506 T^{5} - 35287 T^{6} + 3221199 T^{7} + 25411681 T^{8} \))(\( 1 - 25 T + 66 T^{2} + 2427 T^{3} - 921 T^{4} - 287069 T^{5} - 349824 T^{6} + 22779568 T^{7} + 109032831 T^{8} - 1504395045 T^{9} - 10745043831 T^{10} + 19122129269 T^{11} + 1224386041720 T^{12} + 1357671178099 T^{13} - 54165765952071 T^{14} - 538439534950995 T^{15} + 2770707519898911 T^{16} + 41099565188700368 T^{17} - 44812553722379904 T^{18} - 2610927048749145979 T^{19} - 594739002277345881 T^{20} + \)\(11\!\cdots\!37\)\( T^{21} + \)\(21\!\cdots\!66\)\( T^{22} - \)\(57\!\cdots\!75\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 - 22 T - 17 T^{2} + 820 T^{3} + 49824 T^{4} - 364769 T^{5} - 2625066 T^{6} - 31439174 T^{7} + 604960277 T^{8} + 1291494445 T^{9} + 13047003346 T^{10} - 519002271697 T^{11} - 392108245783 T^{12} - 2884405046697 T^{13} + 359176316454548 T^{14} - 204792758315487 T^{15} - 1976617666992103 T^{16} - 185756622065344967 T^{17} + 331546287034484626 T^{18} + 2330152184322455195 T^{19} + 77495583244626806117 T^{20} - \)\(28\!\cdots\!34\)\( T^{21} - \)\(16\!\cdots\!26\)\( T^{22} - \)\(16\!\cdots\!39\)\( T^{23} + \)\(16\!\cdots\!24\)\( T^{24} + \)\(18\!\cdots\!20\)\( T^{25} - \)\(27\!\cdots\!97\)\( T^{26} - \)\(25\!\cdots\!42\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))
$73$ (\( 1 + 5 T + 73 T^{2} \))(\( 1 - 8 T + 172 T^{2} - 415 T^{3} + 11367 T^{4} - 30295 T^{5} + 916588 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + 2 T + 160 T^{2} + 317 T^{3} + 16077 T^{4} + 23141 T^{5} + 852640 T^{6} + 778034 T^{7} + 28398241 T^{8} \))(\( 1 + 26 T + 468 T^{2} + 5485 T^{3} + 53951 T^{4} + 400405 T^{5} + 2493972 T^{6} + 10114442 T^{7} + 28398241 T^{8} \))(\( 1 + 21 T + 465 T^{2} + 5845 T^{3} + 72518 T^{4} + 625715 T^{5} + 5293814 T^{6} + 31148005 T^{7} + 180892905 T^{8} + 596363061 T^{9} + 2073071593 T^{10} \))(\( 1 - 12 T + 320 T^{2} - 3055 T^{3} + 50012 T^{4} - 385121 T^{5} + 4601870 T^{6} - 28113833 T^{7} + 266513948 T^{8} - 1188446935 T^{9} + 9087437120 T^{10} - 24876859116 T^{11} + 151334226289 T^{12} \))(\( 1 + 6 T + 228 T^{2} + 1709 T^{3} + 28116 T^{4} + 226017 T^{5} + 2344662 T^{6} + 16499241 T^{7} + 149830164 T^{8} + 664830053 T^{9} + 6474798948 T^{10} + 12438429558 T^{11} + 151334226289 T^{12} \))(\( 1 - 23 T + 289 T^{2} - 1759 T^{3} + 6547 T^{4} - 96526 T^{5} + 2159079 T^{6} - 25271472 T^{7} + 157612767 T^{8} - 514387054 T^{9} + 2546894299 T^{10} - 49952505919 T^{11} + 599117690377 T^{12} - 3480687204647 T^{13} + 11047398519097 T^{14} \))(\( 1 - 21 T + 511 T^{2} - 6561 T^{3} + 92751 T^{4} - 882216 T^{5} + 9543917 T^{6} - 75489564 T^{7} + 696705941 T^{8} - 4701329064 T^{9} + 36081715767 T^{10} - 186320859201 T^{11} + 1059339584023 T^{12} - 3178018752069 T^{13} + 11047398519097 T^{14} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( 1 + 5 T - 48 T^{2} + 365 T^{3} + 5329 T^{4} \))(\( 1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4} \))(\( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} \))(\( 1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 - 5 T - 48 T^{2} - 365 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 10 T + 73 T^{2} ) \))(\( ( 1 - 13 T + 96 T^{2} - 949 T^{3} + 5329 T^{4} )^{2} \))(\( 1 + 8 T - 13 T^{2} - 410 T^{3} - 9332 T^{4} - 91230 T^{5} + 69722 T^{6} + 6044840 T^{7} + 55975786 T^{8} + 340615830 T^{9} + 20999164 T^{10} - 25331655699 T^{11} - 349115977166 T^{12} - 1849210866027 T^{13} + 111904544956 T^{14} + 132505348339110 T^{15} + 1589613860992426 T^{16} + 12531386088230120 T^{17} + 10551324925321658 T^{18} - 1007854166897219310 T^{19} - 7525885577555563892 T^{20} - 24137350550389844330 T^{21} - 55869135786146249437 T^{22} + \)\(25\!\cdots\!16\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 15 T - 305 T^{2} - 3966 T^{3} + 75355 T^{4} + 692695 T^{5} - 13270379 T^{6} - 81309244 T^{7} + 1857676842 T^{8} + 7051146754 T^{9} - 209843950998 T^{10} - 423003183473 T^{11} + 19720732477631 T^{12} + 12001986433031 T^{13} - 1563096084841678 T^{14} + 876145009611263 T^{15} + 105091783373295599 T^{16} - 164555429425116041 T^{17} - 5959199092833394518 T^{18} + 14617532033791559122 T^{19} + \)\(28\!\cdots\!38\)\( T^{20} - \)\(89\!\cdots\!68\)\( T^{21} - \)\(10\!\cdots\!99\)\( T^{22} + \)\(40\!\cdots\!35\)\( T^{23} + \)\(32\!\cdots\!95\)\( T^{24} - \)\(12\!\cdots\!82\)\( T^{25} - \)\(69\!\cdots\!05\)\( T^{26} + \)\(25\!\cdots\!95\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))
$79$ (\( 1 - 4 T + 79 T^{2} \))(\( 1 + T + 214 T^{2} + 227 T^{3} + 23337 T^{4} + 17933 T^{5} + 1335574 T^{6} + 493039 T^{7} + 38950081 T^{8} \))(\( 1 + 17 T + 394 T^{2} + 4021 T^{3} + 49295 T^{4} + 317659 T^{5} + 2458954 T^{6} + 8381663 T^{7} + 38950081 T^{8} \))(\( 1 + 9 T + 292 T^{2} + 1917 T^{3} + 33915 T^{4} + 151443 T^{5} + 1822372 T^{6} + 4437351 T^{7} + 38950081 T^{8} \))(\( 1 + T + 23 T^{2} - 362 T^{3} + 4893 T^{4} - 32514 T^{5} + 386547 T^{6} - 2259242 T^{7} + 11339897 T^{8} + 38950081 T^{9} + 3077056399 T^{10} \))(\( 1 - 9 T + 214 T^{2} - 971 T^{3} + 14970 T^{4} - 38514 T^{5} + 890304 T^{6} - 3042606 T^{7} + 93427770 T^{8} - 478740869 T^{9} + 8335317334 T^{10} - 27693507591 T^{11} + 243087455521 T^{12} \))(\( 1 - 9 T + 84 T^{2} - 1001 T^{3} + 2028 T^{4} + 27336 T^{5} + 181484 T^{6} + 2159544 T^{7} + 12656748 T^{8} - 493532039 T^{9} + 3271806804 T^{10} - 27693507591 T^{11} + 243087455521 T^{12} \))(\( 1 - 25 T + 651 T^{2} - 9530 T^{3} + 142430 T^{4} - 1499035 T^{5} + 16738302 T^{6} - 142494620 T^{7} + 1322325858 T^{8} - 9355477435 T^{9} + 70223544770 T^{10} - 371194271930 T^{11} + 2003163715749 T^{12} - 6077186388025 T^{13} + 19203908986159 T^{14} \))(\( 1 - 5 T + 385 T^{2} - 628 T^{3} + 60698 T^{4} + 73721 T^{5} + 5848464 T^{6} + 14581032 T^{7} + 462028656 T^{8} + 460092761 T^{9} + 29926481222 T^{10} - 24460650868 T^{11} + 1184666713615 T^{12} - 1215437277605 T^{13} + 19203908986159 T^{14} \))(\( ( 1 - 14 T + 79 T^{2} )^{2} \))(\( 1 + 9 T + 2 T^{2} + 711 T^{3} + 6241 T^{4} \))(\( 1 - 3 T - 70 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4} \))(\( 1 - 3 T - 70 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 - 3 T - 70 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4} \))(\( ( 1 - 4 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( ( 1 + 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 - 20 T + 175 T^{2} - 1340 T^{3} + 12784 T^{4} - 105860 T^{5} + 1092175 T^{6} - 9860780 T^{7} + 38950081 T^{8} \))(\( 1 + 2 T - 254 T^{2} + 354 T^{3} + 30644 T^{4} - 104573 T^{5} - 2255531 T^{6} + 2220835 T^{7} + 156777095 T^{8} + 785447464 T^{9} - 19907349612 T^{10} - 43426772841 T^{11} + 2128421622846 T^{12} - 3430715054439 T^{13} - 124241768928492 T^{14} + 387256232203096 T^{15} + 6106480549194695 T^{16} + 6833634547873165 T^{17} - 548291291638736651 T^{18} - 2008210374409605107 T^{19} + 46490282370776655284 T^{20} + 42427464977846884926 T^{21} - \)\(24\!\cdots\!54\)\( T^{22} + \)\(14\!\cdots\!58\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 9 T - 290 T^{2} + 971 T^{3} + 58957 T^{4} + 39935 T^{5} - 7304652 T^{6} - 31245424 T^{7} + 627140605 T^{8} + 4416045423 T^{9} - 33081571720 T^{10} - 353555917085 T^{11} + 956394409296 T^{12} + 11107915331417 T^{13} - 6705152277818 T^{14} + 877525311181943 T^{15} + 5968857508416336 T^{16} - 174316855803671315 T^{17} - 1288529898101309320 T^{18} + 13588420827116811777 T^{19} + \)\(15\!\cdots\!05\)\( T^{20} - \)\(60\!\cdots\!16\)\( T^{21} - \)\(11\!\cdots\!72\)\( T^{22} + \)\(47\!\cdots\!65\)\( T^{23} + \)\(55\!\cdots\!57\)\( T^{24} + \)\(72\!\cdots\!09\)\( T^{25} - \)\(17\!\cdots\!90\)\( T^{26} - \)\(42\!\cdots\!51\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 - 18 T + 424 T^{2} - 4637 T^{3} + 56685 T^{4} - 384871 T^{5} + 2920936 T^{6} - 10292166 T^{7} + 47458321 T^{8} \))(\( 1 - 10 T + 240 T^{2} - 1505 T^{3} + 25403 T^{4} - 124915 T^{5} + 1653360 T^{6} - 5717870 T^{7} + 47458321 T^{8} \))(\( 1 + 8 T + 296 T^{2} + 2009 T^{3} + 35359 T^{4} + 166747 T^{5} + 2039144 T^{6} + 4574296 T^{7} + 47458321 T^{8} \))(\( 1 + 8 T + 111 T^{2} + 377 T^{3} + 14981 T^{4} + 112874 T^{5} + 1243423 T^{6} + 2597153 T^{7} + 63468357 T^{8} + 379666568 T^{9} + 3939040643 T^{10} \))(\( 1 + 2 T + 132 T^{2} - 319 T^{3} + 18328 T^{4} - 37297 T^{5} + 1553942 T^{6} - 3095651 T^{7} + 126261592 T^{8} - 182400053 T^{9} + 6264498372 T^{10} + 7878081286 T^{11} + 326940373369 T^{12} \))(\( 1 - 24 T + 708 T^{2} - 10769 T^{3} + 174270 T^{4} - 1854945 T^{5} + 20317210 T^{6} - 153960435 T^{7} + 1200546030 T^{8} - 6157574203 T^{9} + 33600491268 T^{10} - 94536975432 T^{11} + 326940373369 T^{12} \))(\( 1 + 20 T + 403 T^{2} + 4687 T^{3} + 61584 T^{4} + 626492 T^{5} + 7349918 T^{6} + 65413042 T^{7} + 610043194 T^{8} + 4315903388 T^{9} + 35212930608 T^{10} + 222437150527 T^{11} + 1587433379129 T^{12} + 6538807467380 T^{13} + 27136050989627 T^{14} \))(\( 1 - 6 T + 431 T^{2} - 2205 T^{3} + 82446 T^{4} - 361914 T^{5} + 9684928 T^{6} - 36558774 T^{7} + 803849024 T^{8} - 2493225546 T^{9} + 47141551002 T^{10} - 104645597805 T^{11} + 1697726517133 T^{12} - 1961642240214 T^{13} + 27136050989627 T^{14} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 + 11 T + 38 T^{2} + 913 T^{3} + 6889 T^{4} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 + 11 T + 38 T^{2} + 913 T^{3} + 6889 T^{4} \))(\( 1 - 7 T - 34 T^{2} - 581 T^{3} + 6889 T^{4} \))(\( 1 - 11 T + 38 T^{2} - 913 T^{3} + 6889 T^{4} \))(\( 1 + 17 T + 206 T^{2} + 1411 T^{3} + 6889 T^{4} \))(\( 1 + 15 T + 142 T^{2} + 1245 T^{3} + 6889 T^{4} \))(\( 1 - 3 T - 85 T^{2} + 216 T^{3} + 1200 T^{4} + 17928 T^{5} - 585565 T^{6} - 1715361 T^{7} + 47458321 T^{8} \))(\( 1 - 20 T + 131 T^{2} - 1714 T^{3} + 14638 T^{4} + 93416 T^{5} - 900524 T^{6} + 12623066 T^{7} - 198497842 T^{8} + 47393114 T^{9} + 2206202642 T^{10} - 56276030963 T^{11} + 1636885001364 T^{12} - 4670910569929 T^{13} + 15198530000738 T^{14} + 27098766474718 T^{15} - 9420374303443282 T^{16} + 49722770013271438 T^{17} - 294417652787745356 T^{18} + 2534941339246995832 T^{19} + 32969053694051282158 T^{20} - \)\(32\!\cdots\!42\)\( T^{21} + \)\(20\!\cdots\!19\)\( T^{22} - \)\(25\!\cdots\!40\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + T - 299 T^{2} + 1040 T^{3} + 46121 T^{4} - 338171 T^{5} - 3970157 T^{6} + 54632160 T^{7} + 144189246 T^{8} - 5524282328 T^{9} + 13760244348 T^{10} + 359721042959 T^{11} - 3019786479455 T^{12} - 11121758694339 T^{13} + 306888352958254 T^{14} - 923105971630137 T^{15} - 20803309056965495 T^{16} + 205683815990397733 T^{17} + 653038093305819708 T^{18} - 21760372613398656904 T^{19} + 47141285923034589774 T^{20} + \)\(14\!\cdots\!20\)\( T^{21} - \)\(89\!\cdots\!37\)\( T^{22} - \)\(63\!\cdots\!13\)\( T^{23} + \)\(71\!\cdots\!29\)\( T^{24} + \)\(13\!\cdots\!80\)\( T^{25} - \)\(31\!\cdots\!39\)\( T^{26} + \)\(88\!\cdots\!63\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))
$89$ (\( 1 + 9 T + 89 T^{2} \))(\( 1 + 24 T + 542 T^{2} + 6953 T^{3} + 81163 T^{4} + 618817 T^{5} + 4293182 T^{6} + 16919256 T^{7} + 62742241 T^{8} \))(\( 1 + 18 T + 144 T^{2} - 297 T^{3} - 9529 T^{4} - 26433 T^{5} + 1140624 T^{6} + 12689442 T^{7} + 62742241 T^{8} \))(\( 1 - 10 T + 196 T^{2} - 2345 T^{3} + 22821 T^{4} - 208705 T^{5} + 1552516 T^{6} - 7049690 T^{7} + 62742241 T^{8} \))(\( 1 + 29 T + 747 T^{2} + 11591 T^{3} + 161040 T^{4} + 1600867 T^{5} + 14332560 T^{6} + 91812311 T^{7} + 526611843 T^{8} + 1819524989 T^{9} + 5584059449 T^{10} \))(\( 1 - 10 T + 362 T^{2} - 3087 T^{3} + 60038 T^{4} - 436915 T^{5} + 6351790 T^{6} - 38885435 T^{7} + 475560998 T^{8} - 2176239303 T^{9} + 22712691242 T^{10} - 55840594490 T^{11} + 496981290961 T^{12} \))(\( 1 - 24 T + 276 T^{2} - 1213 T^{3} - 5016 T^{4} + 173625 T^{5} - 1927802 T^{6} + 15452625 T^{7} - 39731736 T^{8} - 855127397 T^{9} + 17316858516 T^{10} - 134017426776 T^{11} + 496981290961 T^{12} \))(\( 1 - T + 533 T^{2} - 347 T^{3} + 127527 T^{4} - 53386 T^{5} + 17869735 T^{6} - 5417092 T^{7} + 1590406415 T^{8} - 422870506 T^{9} + 89902581663 T^{10} - 21771557627 T^{11} + 2976303686317 T^{12} - 496981290961 T^{13} + 44231334895529 T^{14} \))(\( 1 - 7 T + 365 T^{2} - 1685 T^{3} + 61205 T^{4} - 158422 T^{5} + 6655073 T^{6} - 11367164 T^{7} + 592301497 T^{8} - 1254860662 T^{9} + 43147627645 T^{10} - 105720676085 T^{11} + 2038181698885 T^{12} - 3478869036727 T^{13} + 44231334895529 T^{14} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 - 18 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 46 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 6 T + 278 T^{2} - 1201 T^{3} + 41023 T^{4} - 169406 T^{5} + 4354474 T^{6} - 15077134 T^{7} + 324943183 T^{8} - 846667769 T^{9} + 17442342998 T^{10} - 33504356694 T^{11} + 496981290961 T^{12} )^{2} \))(\( ( 1 + 6 T + 509 T^{2} + 2393 T^{3} + 116955 T^{4} + 439711 T^{5} + 16028883 T^{6} + 48830780 T^{7} + 1426570587 T^{8} + 3482950831 T^{9} + 82449649395 T^{10} + 150142182713 T^{11} + 2842286259541 T^{12} + 2981887745766 T^{13} + 44231334895529 T^{14} )^{2} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 + 23 T + 511 T^{2} + 6898 T^{3} + 80385 T^{4} + 669106 T^{5} + 4807999 T^{6} + 20991479 T^{7} + 88529281 T^{8} \))(\( 1 + 11 T + 173 T^{2} + 2468 T^{3} + 24581 T^{4} + 239396 T^{5} + 1627757 T^{6} + 10039403 T^{7} + 88529281 T^{8} \))(\( 1 + 11 T + 339 T^{2} + 2662 T^{3} + 46799 T^{4} + 258214 T^{5} + 3189651 T^{6} + 10039403 T^{7} + 88529281 T^{8} \))(\( 1 + 13 T + 172 T^{2} + 1289 T^{3} + 26352 T^{4} + 245878 T^{5} + 2556144 T^{6} + 12128201 T^{7} + 156979756 T^{8} + 1150880653 T^{9} + 8587340257 T^{10} \))(\( 1 - 37 T + 881 T^{2} - 15720 T^{3} + 230894 T^{4} - 2872481 T^{5} + 30509558 T^{6} - 278630657 T^{7} + 2172481646 T^{8} - 14347219560 T^{9} + 77994296561 T^{10} - 317731589509 T^{11} + 832972004929 T^{12} \))(\( 1 - 9 T + 453 T^{2} - 2388 T^{3} + 81744 T^{4} - 252837 T^{5} + 9145678 T^{6} - 24525189 T^{7} + 769129296 T^{8} - 2179463124 T^{9} + 40103764293 T^{10} - 77286062313 T^{11} + 832972004929 T^{12} \))(\( 1 - 3 T + 454 T^{2} - 1093 T^{3} + 99495 T^{4} - 175093 T^{5} + 13812188 T^{6} - 19147754 T^{7} + 1339782236 T^{8} - 1647450037 T^{9} + 90806400135 T^{10} - 96762504133 T^{11} + 3898652476678 T^{12} - 2498916014787 T^{13} + 80798284478113 T^{14} \))(\( 1 + 9 T + 394 T^{2} + 3615 T^{3} + 86565 T^{4} + 702723 T^{5} + 12173822 T^{6} + 85552134 T^{7} + 1180860734 T^{8} + 6611920707 T^{9} + 79005538245 T^{10} + 320033350815 T^{11} + 3383412061258 T^{12} + 7496748044361 T^{13} + 80798284478113 T^{14} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 7 T - 48 T^{2} - 679 T^{3} + 9409 T^{4} \))(\( 1 + 9 T - 16 T^{2} + 873 T^{3} + 9409 T^{4} \))(\( 1 + 13 T + 72 T^{2} + 1261 T^{3} + 9409 T^{4} \))(\( 1 + 13 T + 72 T^{2} + 1261 T^{3} + 9409 T^{4} \))(\( 1 - 17 T + 192 T^{2} - 1649 T^{3} + 9409 T^{4} \))(\( 1 + 7 T - 48 T^{2} + 679 T^{3} + 9409 T^{4} \))(\( 1 - T - 96 T^{2} - 97 T^{3} + 9409 T^{4} \))(\( 1 + 17 T + 192 T^{2} + 1649 T^{3} + 9409 T^{4} \))(\( ( 1 - T - 96 T^{2} - 97 T^{3} + 9409 T^{4} )^{2} \))(\( 1 + T - 74 T^{2} - 3085 T^{3} + 512 T^{4} + 161294 T^{5} + 5154103 T^{6} + 4425829 T^{7} - 201336043 T^{8} - 7008527843 T^{9} - 13501932242 T^{10} + 195913282487 T^{11} + 7566580882136 T^{12} + 19003588401239 T^{13} - 127039680464978 T^{14} - 6396494132054339 T^{15} - 17824135126175083 T^{16} + 38006099542298053 T^{17} + 4293223509520573687 T^{18} + 13032278496612758222 T^{19} + 4012766000321004032 T^{20} - \)\(23\!\cdots\!45\)\( T^{21} - \)\(54\!\cdots\!26\)\( T^{22} + \)\(71\!\cdots\!53\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 16 T - 305 T^{2} + 4468 T^{3} + 66659 T^{4} - 627781 T^{5} - 13361122 T^{6} + 73927187 T^{7} + 2109835734 T^{8} - 7502842347 T^{9} - 269438721123 T^{10} + 493586727995 T^{11} + 30832175504259 T^{12} - 14324354895126 T^{13} - 3192872878082918 T^{14} - 1389462424827222 T^{15} + 290099939319572931 T^{16} + 450483279799380635 T^{17} - 23853216254578702563 T^{18} - 64429460128317463179 T^{19} + \)\(17\!\cdots\!86\)\( T^{20} + \)\(59\!\cdots\!31\)\( T^{21} - \)\(10\!\cdots\!42\)\( T^{22} - \)\(47\!\cdots\!77\)\( T^{23} + \)\(49\!\cdots\!91\)\( T^{24} + \)\(31\!\cdots\!04\)\( T^{25} - \)\(21\!\cdots\!05\)\( T^{26} - \)\(10\!\cdots\!32\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))
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