Properties

Label 4014.2
Level 4014
Weight 2
Dimension 118100
Nonzero newspaces 20
Sturm bound 1790208

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Defining parameters

Level: \( N \) = \( 4014\( 4014 = 2 \cdot 3^{2} \cdot 223 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(1790208\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4014))\).

Total New Old
Modular forms 451104 118100 333004
Cusp forms 444001 118100 325901
Eisenstein series 7103 0 7103

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4014))\)

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
4014.2.a \(\chi_{4014}(1, \cdot)\) 4014.2.a.a 1 1
4014.2.a.b 1
4014.2.a.c 1
4014.2.a.d 1
4014.2.a.e 1
4014.2.a.f 1
4014.2.a.g 1
4014.2.a.h 1
4014.2.a.i 1
4014.2.a.j 2
4014.2.a.k 2
4014.2.a.l 2
4014.2.a.m 3
4014.2.a.n 3
4014.2.a.o 3
4014.2.a.p 3
4014.2.a.q 4
4014.2.a.r 5
4014.2.a.s 6
4014.2.a.t 6
4014.2.a.u 6
4014.2.a.v 7
4014.2.a.w 7
4014.2.a.x 8
4014.2.a.y 8
4014.2.a.z 8
4014.2.d \(\chi_{4014}(4013, \cdot)\) 4014.2.d.a 72 1
4014.2.e \(\chi_{4014}(1339, \cdot)\) n/a 444 2
4014.2.f \(\chi_{4014}(1075, \cdot)\) n/a 448 2
4014.2.g \(\chi_{4014}(2269, \cdot)\) n/a 188 2
4014.2.h \(\chi_{4014}(931, \cdot)\) n/a 448 2
4014.2.k \(\chi_{4014}(1337, \cdot)\) n/a 448 2
4014.2.l \(\chi_{4014}(407, \cdot)\) n/a 448 2
4014.2.m \(\chi_{4014}(1601, \cdot)\) n/a 152 2
4014.2.t \(\chi_{4014}(263, \cdot)\) n/a 448 2
4014.2.u \(\chi_{4014}(253, \cdot)\) n/a 3312 36
4014.2.v \(\chi_{4014}(125, \cdot)\) n/a 2592 36
4014.2.y \(\chi_{4014}(31, \cdot)\) n/a 16128 72
4014.2.z \(\chi_{4014}(19, \cdot)\) n/a 6768 72
4014.2.ba \(\chi_{4014}(25, \cdot)\) n/a 16128 72
4014.2.bb \(\chi_{4014}(7, \cdot)\) n/a 16128 72
4014.2.bc \(\chi_{4014}(11, \cdot)\) n/a 16128 72
4014.2.bj \(\chi_{4014}(35, \cdot)\) n/a 5472 72
4014.2.bk \(\chi_{4014}(5, \cdot)\) n/a 16128 72
4014.2.bl \(\chi_{4014}(59, \cdot)\) n/a 16128 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2007))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{8} \))
$3$ 1
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 - 3 T + 15 T^{2} - 29 T^{3} + 75 T^{4} - 75 T^{5} + 125 T^{6} \))(\( 1 - 7 T + 29 T^{2} - 77 T^{3} + 145 T^{4} - 175 T^{5} + 125 T^{6} \))(\( 1 - T + 11 T^{2} - 7 T^{3} + 55 T^{4} - 25 T^{5} + 125 T^{6} \))(\( 1 - T + 7 T^{2} + T^{3} + 35 T^{4} - 25 T^{5} + 125 T^{6} \))(\( 1 + 2 T + 15 T^{2} + 19 T^{3} + 97 T^{4} + 95 T^{5} + 375 T^{6} + 250 T^{7} + 625 T^{8} \))(\( 1 + 5 T + 21 T^{2} + 59 T^{3} + 136 T^{4} + 320 T^{5} + 680 T^{6} + 1475 T^{7} + 2625 T^{8} + 3125 T^{9} + 3125 T^{10} \))(\( 1 + 6 T + 33 T^{2} + 121 T^{3} + 408 T^{4} + 1091 T^{5} + 2684 T^{6} + 5455 T^{7} + 10200 T^{8} + 15125 T^{9} + 20625 T^{10} + 18750 T^{11} + 15625 T^{12} \))(\( 1 + 2 T + 11 T^{2} + 20 T^{3} + 105 T^{4} + 162 T^{5} + 567 T^{6} + 810 T^{7} + 2625 T^{8} + 2500 T^{9} + 6875 T^{10} + 6250 T^{11} + 15625 T^{12} \))(\( 1 - 2 T + 11 T^{2} - 20 T^{3} + 105 T^{4} - 162 T^{5} + 567 T^{6} - 810 T^{7} + 2625 T^{8} - 2500 T^{9} + 6875 T^{10} - 6250 T^{11} + 15625 T^{12} \))(\( 1 + 6 T + 26 T^{2} + 75 T^{3} + 209 T^{4} + 466 T^{5} + 1064 T^{6} + 2146 T^{7} + 5320 T^{8} + 11650 T^{9} + 26125 T^{10} + 46875 T^{11} + 81250 T^{12} + 93750 T^{13} + 78125 T^{14} \))(\( 1 + 2 T + 13 T^{2} + 18 T^{3} + 67 T^{4} + 166 T^{5} + 429 T^{6} + 1296 T^{7} + 2145 T^{8} + 4150 T^{9} + 8375 T^{10} + 11250 T^{11} + 40625 T^{12} + 31250 T^{13} + 78125 T^{14} \))(\( 1 - 6 T + 33 T^{2} - 128 T^{3} + 456 T^{4} - 1368 T^{5} + 3884 T^{6} - 9666 T^{7} + 22992 T^{8} - 48330 T^{9} + 97100 T^{10} - 171000 T^{11} + 285000 T^{12} - 400000 T^{13} + 515625 T^{14} - 468750 T^{15} + 390625 T^{16} \))(\( 1 + 6 T + 33 T^{2} + 128 T^{3} + 456 T^{4} + 1368 T^{5} + 3884 T^{6} + 9666 T^{7} + 22992 T^{8} + 48330 T^{9} + 97100 T^{10} + 171000 T^{11} + 285000 T^{12} + 400000 T^{13} + 515625 T^{14} + 468750 T^{15} + 390625 T^{16} \))(\( 1 + 4 T + 16 T^{2} + 34 T^{3} + 110 T^{4} + 238 T^{5} + 698 T^{6} + 1224 T^{7} + 3288 T^{8} + 6120 T^{9} + 17450 T^{10} + 29750 T^{11} + 68750 T^{12} + 106250 T^{13} + 250000 T^{14} + 312500 T^{15} + 390625 T^{16} \))
$7$ (\( 1 + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 3 T + 21 T^{2} + 41 T^{3} + 147 T^{4} + 147 T^{5} + 343 T^{6} \))(\( 1 + 9 T + 41 T^{2} + 125 T^{3} + 287 T^{4} + 441 T^{5} + 343 T^{6} \))(\( 1 - T + 11 T^{2} - 23 T^{3} + 77 T^{4} - 49 T^{5} + 343 T^{6} \))(\( 1 - 9 T + 43 T^{2} - 137 T^{3} + 301 T^{4} - 441 T^{5} + 343 T^{6} \))(\( 1 + 5 T + 30 T^{2} + 92 T^{3} + 310 T^{4} + 644 T^{5} + 1470 T^{6} + 1715 T^{7} + 2401 T^{8} \))(\( 1 + T + 17 T^{2} + 13 T^{3} + 184 T^{4} + 164 T^{5} + 1288 T^{6} + 637 T^{7} + 5831 T^{8} + 2401 T^{9} + 16807 T^{10} \))(\( 1 - 5 T + 34 T^{2} - 114 T^{3} + 499 T^{4} - 1345 T^{5} + 4468 T^{6} - 9415 T^{7} + 24451 T^{8} - 39102 T^{9} + 81634 T^{10} - 84035 T^{11} + 117649 T^{12} \))(\( 1 - 8 T + 53 T^{2} - 244 T^{3} + 959 T^{4} - 3142 T^{5} + 8933 T^{6} - 21994 T^{7} + 46991 T^{8} - 83692 T^{9} + 127253 T^{10} - 134456 T^{11} + 117649 T^{12} \))(\( 1 - 8 T + 53 T^{2} - 244 T^{3} + 959 T^{4} - 3142 T^{5} + 8933 T^{6} - 21994 T^{7} + 46991 T^{8} - 83692 T^{9} + 127253 T^{10} - 134456 T^{11} + 117649 T^{12} \))(\( 1 - 3 T + 17 T^{2} - 25 T^{3} + 133 T^{4} - 113 T^{5} + 581 T^{6} + 346 T^{7} + 4067 T^{8} - 5537 T^{9} + 45619 T^{10} - 60025 T^{11} + 285719 T^{12} - 352947 T^{13} + 823543 T^{14} \))(\( 1 - 6 T + 41 T^{2} - 164 T^{3} + 701 T^{4} - 2170 T^{5} + 7157 T^{6} - 18328 T^{7} + 50099 T^{8} - 106330 T^{9} + 240443 T^{10} - 393764 T^{11} + 689087 T^{12} - 705894 T^{13} + 823543 T^{14} \))(\( 1 + 6 T + 47 T^{2} + 192 T^{3} + 938 T^{4} + 3082 T^{5} + 11540 T^{6} + 31430 T^{7} + 96232 T^{8} + 220010 T^{9} + 565460 T^{10} + 1057126 T^{11} + 2252138 T^{12} + 3226944 T^{13} + 5529503 T^{14} + 4941258 T^{15} + 5764801 T^{16} \))(\( 1 + 6 T + 47 T^{2} + 192 T^{3} + 938 T^{4} + 3082 T^{5} + 11540 T^{6} + 31430 T^{7} + 96232 T^{8} + 220010 T^{9} + 565460 T^{10} + 1057126 T^{11} + 2252138 T^{12} + 3226944 T^{13} + 5529503 T^{14} + 4941258 T^{15} + 5764801 T^{16} \))(\( 1 - 4 T + 16 T^{2} - 20 T^{3} + 148 T^{4} - 468 T^{5} + 2080 T^{6} - 2820 T^{7} + 9478 T^{8} - 19740 T^{9} + 101920 T^{10} - 160524 T^{11} + 355348 T^{12} - 336140 T^{13} + 1882384 T^{14} - 3294172 T^{15} + 5764801 T^{16} \))
$11$ (\( 1 - 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 9 T + 39 T^{2} + 99 T^{3} + 121 T^{4} \))(\( 1 - 3 T + 13 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 - 9 T + 39 T^{2} - 99 T^{3} + 121 T^{4} \))(\( 1 + 24 T^{2} + 9 T^{3} + 264 T^{4} + 1331 T^{6} \))(\( 1 - 4 T - 6 T^{2} + 81 T^{3} - 66 T^{4} - 484 T^{5} + 1331 T^{6} \))(\( 1 - 8 T + 46 T^{2} - 173 T^{3} + 506 T^{4} - 968 T^{5} + 1331 T^{6} \))(\( 1 + 6 T + 40 T^{2} + 129 T^{3} + 440 T^{4} + 726 T^{5} + 1331 T^{6} \))(\( 1 + 4 T + 31 T^{2} + 123 T^{3} + 456 T^{4} + 1353 T^{5} + 3751 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( 1 + 9 T + 61 T^{2} + 314 T^{3} + 1370 T^{4} + 4797 T^{5} + 15070 T^{6} + 37994 T^{7} + 81191 T^{8} + 131769 T^{9} + 161051 T^{10} \))(\( 1 + T + 40 T^{2} - 25 T^{3} + 615 T^{4} - 1417 T^{5} + 6516 T^{6} - 15587 T^{7} + 74415 T^{8} - 33275 T^{9} + 585640 T^{10} + 161051 T^{11} + 1771561 T^{12} \))(\( 1 + 2 T + 44 T^{2} + 82 T^{3} + 922 T^{4} + 1454 T^{5} + 12305 T^{6} + 15994 T^{7} + 111562 T^{8} + 109142 T^{9} + 644204 T^{10} + 322102 T^{11} + 1771561 T^{12} \))(\( 1 - 2 T + 44 T^{2} - 82 T^{3} + 922 T^{4} - 1454 T^{5} + 12305 T^{6} - 15994 T^{7} + 111562 T^{8} - 109142 T^{9} + 644204 T^{10} - 322102 T^{11} + 1771561 T^{12} \))(\( 1 - T + 29 T^{2} - 58 T^{3} + 525 T^{4} - 1158 T^{5} + 6713 T^{6} - 16614 T^{7} + 73843 T^{8} - 140118 T^{9} + 698775 T^{10} - 849178 T^{11} + 4670479 T^{12} - 1771561 T^{13} + 19487171 T^{14} \))(\( 1 + 9 T + 63 T^{2} + 340 T^{3} + 1713 T^{4} + 7187 T^{5} + 28125 T^{6} + 96298 T^{7} + 309375 T^{8} + 869627 T^{9} + 2280003 T^{10} + 4977940 T^{11} + 10146213 T^{12} + 15944049 T^{13} + 19487171 T^{14} \))(\( 1 - 11 T + 101 T^{2} - 647 T^{3} + 3759 T^{4} - 17968 T^{5} + 79367 T^{6} - 302769 T^{7} + 1074995 T^{8} - 3330459 T^{9} + 9603407 T^{10} - 23915408 T^{11} + 55035519 T^{12} - 104199997 T^{13} + 178927661 T^{14} - 214358881 T^{15} + 214358881 T^{16} \))(\( 1 + 11 T + 101 T^{2} + 647 T^{3} + 3759 T^{4} + 17968 T^{5} + 79367 T^{6} + 302769 T^{7} + 1074995 T^{8} + 3330459 T^{9} + 9603407 T^{10} + 23915408 T^{11} + 55035519 T^{12} + 104199997 T^{13} + 178927661 T^{14} + 214358881 T^{15} + 214358881 T^{16} \))(\( 1 + 2 T + 38 T^{2} + 32 T^{3} + 738 T^{4} + 304 T^{5} + 11720 T^{6} + 5706 T^{7} + 150992 T^{8} + 62766 T^{9} + 1418120 T^{10} + 404624 T^{11} + 10805058 T^{12} + 5153632 T^{13} + 67319318 T^{14} + 38974342 T^{15} + 214358881 T^{16} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 7 T + 35 T^{2} - 91 T^{3} + 169 T^{4} \))(\( 1 + 3 T + 17 T^{2} + 39 T^{3} + 169 T^{4} \))(\( 1 - 7 T + 35 T^{2} - 91 T^{3} + 169 T^{4} \))(\( 1 + 9 T + 57 T^{2} + 243 T^{3} + 741 T^{4} + 1521 T^{5} + 2197 T^{6} \))(\( 1 + 7 T + 39 T^{2} + 133 T^{3} + 507 T^{4} + 1183 T^{5} + 2197 T^{6} \))(\( 1 + 7 T + 51 T^{2} + 183 T^{3} + 663 T^{4} + 1183 T^{5} + 2197 T^{6} \))(\( 1 - 11 T + 71 T^{2} - 313 T^{3} + 923 T^{4} - 1859 T^{5} + 2197 T^{6} \))(\( 1 + 5 T + 34 T^{2} + 150 T^{3} + 654 T^{4} + 1950 T^{5} + 5746 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( 1 + 41 T^{2} - 54 T^{3} + 735 T^{4} - 1391 T^{5} + 9555 T^{6} - 9126 T^{7} + 90077 T^{8} + 371293 T^{10} \))(\( 1 - 6 T + 68 T^{2} - 322 T^{3} + 2040 T^{4} - 7657 T^{5} + 34410 T^{6} - 99541 T^{7} + 344760 T^{8} - 707434 T^{9} + 1942148 T^{10} - 2227758 T^{11} + 4826809 T^{12} \))(\( 1 + 2 T + 53 T^{2} + 112 T^{3} + 1395 T^{4} + 2548 T^{5} + 22751 T^{6} + 33124 T^{7} + 235755 T^{8} + 246064 T^{9} + 1513733 T^{10} + 742586 T^{11} + 4826809 T^{12} \))(\( 1 + 2 T + 53 T^{2} + 112 T^{3} + 1395 T^{4} + 2548 T^{5} + 22751 T^{6} + 33124 T^{7} + 235755 T^{8} + 246064 T^{9} + 1513733 T^{10} + 742586 T^{11} + 4826809 T^{12} \))(\( 1 - 8 T + 87 T^{2} - 534 T^{3} + 3352 T^{4} - 15709 T^{5} + 72570 T^{6} - 263078 T^{7} + 943410 T^{8} - 2654821 T^{9} + 7364344 T^{10} - 15251574 T^{11} + 32302491 T^{12} - 38614472 T^{13} + 62748517 T^{14} \))(\( 1 + 2 T + 27 T^{2} + 78 T^{3} + 749 T^{4} + 1430 T^{5} + 12173 T^{6} + 26660 T^{7} + 158249 T^{8} + 241670 T^{9} + 1645553 T^{10} + 2227758 T^{11} + 10024911 T^{12} + 9653618 T^{13} + 62748517 T^{14} \))(\( 1 + T + 30 T^{2} + 4 T^{3} + 565 T^{4} - 134 T^{5} + 10013 T^{6} + 1682 T^{7} + 150687 T^{8} + 21866 T^{9} + 1692197 T^{10} - 294398 T^{11} + 16136965 T^{12} + 1485172 T^{13} + 144804270 T^{14} + 62748517 T^{15} + 815730721 T^{16} \))(\( 1 + T + 30 T^{2} + 4 T^{3} + 565 T^{4} - 134 T^{5} + 10013 T^{6} + 1682 T^{7} + 150687 T^{8} + 21866 T^{9} + 1692197 T^{10} - 294398 T^{11} + 16136965 T^{12} + 1485172 T^{13} + 144804270 T^{14} + 62748517 T^{15} + 815730721 T^{16} \))(\( 1 - 10 T + 94 T^{2} - 612 T^{3} + 3610 T^{4} - 18168 T^{5} + 83580 T^{6} - 345814 T^{7} + 1307872 T^{8} - 4495582 T^{9} + 14125020 T^{10} - 39915096 T^{11} + 103105210 T^{12} - 227231316 T^{13} + 453720046 T^{14} - 627485170 T^{15} + 815730721 T^{16} \))
$17$ (\( 1 + 4 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 + 2 T + 22 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 2 T + 22 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 36 T^{2} - 131 T^{3} + 612 T^{4} - 1734 T^{5} + 4913 T^{6} \))(\( 1 - 10 T + 40 T^{2} - 117 T^{3} + 680 T^{4} - 2890 T^{5} + 4913 T^{6} \))(\( 1 - 8 T + 68 T^{2} - 281 T^{3} + 1156 T^{4} - 2312 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 30 T^{2} - 13 T^{3} + 510 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 25 T^{2} - 27 T^{3} + 270 T^{4} - 459 T^{5} + 7225 T^{6} - 9826 T^{7} + 83521 T^{8} \))(\( 1 + 6 T + 80 T^{2} + 341 T^{3} + 2587 T^{4} + 8190 T^{5} + 43979 T^{6} + 98549 T^{7} + 393040 T^{8} + 501126 T^{9} + 1419857 T^{10} \))(\( 1 + 10 T + 97 T^{2} + 649 T^{3} + 3893 T^{4} + 18857 T^{5} + 86090 T^{6} + 320569 T^{7} + 1125077 T^{8} + 3188537 T^{9} + 8101537 T^{10} + 14198570 T^{11} + 24137569 T^{12} \))(\( 1 + 2 T + 82 T^{2} + 156 T^{3} + 3084 T^{4} + 5034 T^{5} + 67215 T^{6} + 85578 T^{7} + 891276 T^{8} + 766428 T^{9} + 6848722 T^{10} + 2839714 T^{11} + 24137569 T^{12} \))(\( 1 - 2 T + 82 T^{2} - 156 T^{3} + 3084 T^{4} - 5034 T^{5} + 67215 T^{6} - 85578 T^{7} + 891276 T^{8} - 766428 T^{9} + 6848722 T^{10} - 2839714 T^{11} + 24137569 T^{12} \))(\( 1 + 16 T + 182 T^{2} + 1459 T^{3} + 9888 T^{4} + 55744 T^{5} + 279481 T^{6} + 1215546 T^{7} + 4751177 T^{8} + 16110016 T^{9} + 48579744 T^{10} + 121857139 T^{11} + 258413974 T^{12} + 386201104 T^{13} + 410338673 T^{14} \))(\( 1 - 7 T + 75 T^{2} - 422 T^{3} + 2657 T^{4} - 13017 T^{5} + 64695 T^{6} - 268656 T^{7} + 1099815 T^{8} - 3761913 T^{9} + 13053841 T^{10} - 35245862 T^{11} + 106489275 T^{12} - 168962983 T^{13} + 410338673 T^{14} \))(\( 1 - 16 T + 184 T^{2} - 1506 T^{3} + 10309 T^{4} - 59680 T^{5} + 307385 T^{6} - 1431328 T^{7} + 6133586 T^{8} - 24332576 T^{9} + 88834265 T^{10} - 293207840 T^{11} + 861017989 T^{12} - 2138304642 T^{13} + 4441312696 T^{14} - 6565418768 T^{15} + 6975757441 T^{16} \))(\( 1 + 16 T + 184 T^{2} + 1506 T^{3} + 10309 T^{4} + 59680 T^{5} + 307385 T^{6} + 1431328 T^{7} + 6133586 T^{8} + 24332576 T^{9} + 88834265 T^{10} + 293207840 T^{11} + 861017989 T^{12} + 2138304642 T^{13} + 4441312696 T^{14} + 6565418768 T^{15} + 6975757441 T^{16} \))(\( 1 + 8 T + 72 T^{2} + 400 T^{3} + 2428 T^{4} + 11088 T^{5} + 54980 T^{6} + 222032 T^{7} + 1013314 T^{8} + 3774544 T^{9} + 15889220 T^{10} + 54475344 T^{11} + 202788988 T^{12} + 567942800 T^{13} + 1737904968 T^{14} + 3282709384 T^{15} + 6975757441 T^{16} \))
$19$ (\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 5 T + 41 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 43 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 41 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 + 3 T + 57 T^{2} + 111 T^{3} + 1083 T^{4} + 1083 T^{5} + 6859 T^{6} \))(\( 1 + T + 27 T^{2} - 5 T^{3} + 513 T^{4} + 361 T^{5} + 6859 T^{6} \))(\( 1 + 9 T + 39 T^{2} + 153 T^{3} + 741 T^{4} + 3249 T^{5} + 6859 T^{6} \))(\( 1 - 5 T + 55 T^{2} - 175 T^{3} + 1045 T^{4} - 1805 T^{5} + 6859 T^{6} \))(\( 1 + 7 T + 48 T^{2} + 210 T^{3} + 998 T^{4} + 3990 T^{5} + 17328 T^{6} + 48013 T^{7} + 130321 T^{8} \))(\( 1 + 4 T + 79 T^{2} + 216 T^{3} + 2575 T^{4} + 5267 T^{5} + 48925 T^{6} + 77976 T^{7} + 541861 T^{8} + 521284 T^{9} + 2476099 T^{10} \))(\( 1 + 4 T + 70 T^{2} + 306 T^{3} + 2570 T^{4} + 10439 T^{5} + 59754 T^{6} + 198341 T^{7} + 927770 T^{8} + 2098854 T^{9} + 9122470 T^{10} + 9904396 T^{11} + 47045881 T^{12} \))(\( 1 + 2 T + 79 T^{2} + 82 T^{3} + 2853 T^{4} + 1532 T^{5} + 65377 T^{6} + 29108 T^{7} + 1029933 T^{8} + 562438 T^{9} + 10295359 T^{10} + 4952198 T^{11} + 47045881 T^{12} \))(\( 1 + 2 T + 79 T^{2} + 82 T^{3} + 2853 T^{4} + 1532 T^{5} + 65377 T^{6} + 29108 T^{7} + 1029933 T^{8} + 562438 T^{9} + 10295359 T^{10} + 4952198 T^{11} + 47045881 T^{12} \))(\( 1 - 2 T + 57 T^{2} + 30 T^{3} + 1522 T^{4} + 1831 T^{5} + 43250 T^{6} + 14418 T^{7} + 821750 T^{8} + 660991 T^{9} + 10439398 T^{10} + 3909630 T^{11} + 141137643 T^{12} - 94091762 T^{13} + 893871739 T^{14} \))(\( 1 + 2 T + 77 T^{2} + 132 T^{3} + 3061 T^{4} + 4686 T^{5} + 81073 T^{6} + 107896 T^{7} + 1540387 T^{8} + 1691646 T^{9} + 20995399 T^{10} + 17202372 T^{11} + 190659623 T^{12} + 94091762 T^{13} + 893871739 T^{14} \))(\( 1 + T + 46 T^{2} + 54 T^{3} + 1665 T^{4} + 2430 T^{5} + 44311 T^{6} + 56050 T^{7} + 957323 T^{8} + 1064950 T^{9} + 15996271 T^{10} + 16667370 T^{11} + 216984465 T^{12} + 133709346 T^{13} + 2164110526 T^{14} + 893871739 T^{15} + 16983563041 T^{16} \))(\( 1 + T + 46 T^{2} + 54 T^{3} + 1665 T^{4} + 2430 T^{5} + 44311 T^{6} + 56050 T^{7} + 957323 T^{8} + 1064950 T^{9} + 15996271 T^{10} + 16667370 T^{11} + 216984465 T^{12} + 133709346 T^{13} + 2164110526 T^{14} + 893871739 T^{15} + 16983563041 T^{16} \))(\( 1 - 16 T + 152 T^{2} - 1056 T^{3} + 6428 T^{4} - 34944 T^{5} + 178280 T^{6} - 847792 T^{7} + 3839846 T^{8} - 16108048 T^{9} + 64359080 T^{10} - 239680896 T^{11} + 837703388 T^{12} - 2614760544 T^{13} + 7150973912 T^{14} - 14301947824 T^{15} + 16983563041 T^{16} \))
$23$ (\( 1 - 2 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( 1 - 6 T + 60 T^{2} - 225 T^{3} + 1380 T^{4} - 3174 T^{5} + 12167 T^{6} \))(\( 1 - 12 T + 110 T^{2} - 581 T^{3} + 2530 T^{4} - 6348 T^{5} + 12167 T^{6} \))(\( 1 - 8 T + 82 T^{2} - 365 T^{3} + 1886 T^{4} - 4232 T^{5} + 12167 T^{6} \))(\( 1 - 2 T + 38 T^{2} - 17 T^{3} + 874 T^{4} - 1058 T^{5} + 12167 T^{6} \))(\( 1 - 4 T + 35 T^{2} - 207 T^{3} + 1066 T^{4} - 4761 T^{5} + 18515 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 + 16 T + 182 T^{2} + 1407 T^{3} + 9129 T^{4} + 46862 T^{5} + 209967 T^{6} + 744303 T^{7} + 2214394 T^{8} + 4477456 T^{9} + 6436343 T^{10} \))(\( 1 + 2 T + 65 T^{2} + 235 T^{3} + 2357 T^{4} + 9465 T^{5} + 62842 T^{6} + 217695 T^{7} + 1246853 T^{8} + 2859245 T^{9} + 18189665 T^{10} + 12872686 T^{11} + 148035889 T^{12} \))(\( 1 + 22 T + 330 T^{2} + 3376 T^{3} + 27572 T^{4} + 177050 T^{5} + 944549 T^{6} + 4072150 T^{7} + 14585588 T^{8} + 41075792 T^{9} + 92347530 T^{10} + 141599546 T^{11} + 148035889 T^{12} \))(\( 1 - 22 T + 330 T^{2} - 3376 T^{3} + 27572 T^{4} - 177050 T^{5} + 944549 T^{6} - 4072150 T^{7} + 14585588 T^{8} - 41075792 T^{9} + 92347530 T^{10} - 141599546 T^{11} + 148035889 T^{12} \))(\( 1 + 8 T + 94 T^{2} + 389 T^{3} + 2978 T^{4} + 6480 T^{5} + 54941 T^{6} + 63078 T^{7} + 1263643 T^{8} + 3427920 T^{9} + 36233326 T^{10} + 108858149 T^{11} + 605016242 T^{12} + 1184287112 T^{13} + 3404825447 T^{14} \))(\( 1 + 15 T + 205 T^{2} + 1902 T^{3} + 15529 T^{4} + 103889 T^{5} + 615469 T^{6} + 3131844 T^{7} + 14155787 T^{8} + 54957281 T^{9} + 188941343 T^{10} + 532257582 T^{11} + 1319450315 T^{12} + 2220538335 T^{13} + 3404825447 T^{14} \))(\( 1 - 14 T + 168 T^{2} - 1496 T^{3} + 11853 T^{4} - 79684 T^{5} + 493823 T^{6} - 2703978 T^{7} + 13676166 T^{8} - 62191494 T^{9} + 261232367 T^{10} - 969515228 T^{11} + 3316955373 T^{12} - 9628769128 T^{13} + 24870029352 T^{14} - 47667556258 T^{15} + 78310985281 T^{16} \))(\( 1 + 14 T + 168 T^{2} + 1496 T^{3} + 11853 T^{4} + 79684 T^{5} + 493823 T^{6} + 2703978 T^{7} + 13676166 T^{8} + 62191494 T^{9} + 261232367 T^{10} + 969515228 T^{11} + 3316955373 T^{12} + 9628769128 T^{13} + 24870029352 T^{14} + 47667556258 T^{15} + 78310985281 T^{16} \))(\( 1 - 4 T + 48 T^{2} - 100 T^{3} + 1164 T^{4} - 692 T^{5} + 34832 T^{6} - 68628 T^{7} + 1062054 T^{8} - 1578444 T^{9} + 18426128 T^{10} - 8419564 T^{11} + 325734924 T^{12} - 643634300 T^{13} + 7105722672 T^{14} - 13619301788 T^{15} + 78310985281 T^{16} \))
$29$ (\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 7 T + 67 T^{2} + 203 T^{3} + 841 T^{4} \))(\( 1 - 3 T + 29 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 7 T + 67 T^{2} - 203 T^{3} + 841 T^{4} \))(\( 1 - 3 T + 27 T^{2} + 59 T^{3} + 783 T^{4} - 2523 T^{5} + 24389 T^{6} \))(\( 1 - 7 T + 73 T^{2} - 399 T^{3} + 2117 T^{4} - 5887 T^{5} + 24389 T^{6} \))(\( 1 - 15 T + 121 T^{2} - 689 T^{3} + 3509 T^{4} - 12615 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 109 T^{2} - 535 T^{3} + 3161 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 + 9 T + 116 T^{2} + 626 T^{3} + 4734 T^{4} + 18154 T^{5} + 97556 T^{6} + 219501 T^{7} + 707281 T^{8} \))(\( 1 + 8 T + 87 T^{2} + 554 T^{3} + 3949 T^{4} + 18747 T^{5} + 114521 T^{6} + 465914 T^{7} + 2121843 T^{8} + 5658248 T^{9} + 20511149 T^{10} \))(\( 1 + 6 T + 142 T^{2} + 710 T^{3} + 9120 T^{4} + 36961 T^{5} + 338694 T^{6} + 1071869 T^{7} + 7669920 T^{8} + 17316190 T^{9} + 100433902 T^{10} + 123066894 T^{11} + 594823321 T^{12} \))(\( 1 + 8 T + 91 T^{2} + 558 T^{3} + 4893 T^{4} + 23934 T^{5} + 161495 T^{6} + 694086 T^{7} + 4115013 T^{8} + 13609062 T^{9} + 64362571 T^{10} + 164089192 T^{11} + 594823321 T^{12} \))(\( 1 - 8 T + 91 T^{2} - 558 T^{3} + 4893 T^{4} - 23934 T^{5} + 161495 T^{6} - 694086 T^{7} + 4115013 T^{8} - 13609062 T^{9} + 64362571 T^{10} - 164089192 T^{11} + 594823321 T^{12} \))(\( 1 + 4 T + 101 T^{2} + 216 T^{3} + 2780 T^{4} - 3931 T^{5} - 11736 T^{6} - 397206 T^{7} - 340344 T^{8} - 3305971 T^{9} + 67801420 T^{10} + 152772696 T^{11} + 2071626049 T^{12} + 2379293284 T^{13} + 17249876309 T^{14} \))(\( 1 + 9 T + 107 T^{2} + 722 T^{3} + 4829 T^{4} + 23967 T^{5} + 139055 T^{6} + 602588 T^{7} + 4032595 T^{8} + 20156247 T^{9} + 117774481 T^{10} + 510656882 T^{11} + 2194692943 T^{12} + 5353409889 T^{13} + 17249876309 T^{14} \))(\( 1 - 21 T + 258 T^{2} - 2290 T^{3} + 16073 T^{4} - 95508 T^{5} + 522069 T^{6} - 2762546 T^{7} + 14727627 T^{8} - 80113834 T^{9} + 439060029 T^{10} - 2329344612 T^{11} + 11368127513 T^{12} - 46970531210 T^{13} + 153464416818 T^{14} - 362247402489 T^{15} + 500246412961 T^{16} \))(\( 1 + 21 T + 258 T^{2} + 2290 T^{3} + 16073 T^{4} + 95508 T^{5} + 522069 T^{6} + 2762546 T^{7} + 14727627 T^{8} + 80113834 T^{9} + 439060029 T^{10} + 2329344612 T^{11} + 11368127513 T^{12} + 46970531210 T^{13} + 153464416818 T^{14} + 362247402489 T^{15} + 500246412961 T^{16} \))(\( 1 + 8 T + 184 T^{2} + 1256 T^{3} + 16060 T^{4} + 92664 T^{5} + 854216 T^{6} + 4129944 T^{7} + 30109862 T^{8} + 119768376 T^{9} + 718395656 T^{10} + 2259982296 T^{11} + 11358932860 T^{12} + 25762003144 T^{13} + 109447491064 T^{14} + 137999010472 T^{15} + 500246412961 T^{16} \))
$31$ (\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 6 T + 58 T^{2} - 186 T^{3} + 961 T^{4} \))(\( ( 1 - 6 T + 31 T^{2} )^{2} \))(\( 1 - 6 T + 58 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 9 T + 81 T^{2} + 379 T^{3} + 2511 T^{4} + 8649 T^{5} + 29791 T^{6} \))(\( 1 + 5 T + 99 T^{2} + 311 T^{3} + 3069 T^{4} + 4805 T^{5} + 29791 T^{6} \))(\( 1 - T + 23 T^{2} + 179 T^{3} + 713 T^{4} - 961 T^{5} + 29791 T^{6} \))(\( 1 + 5 T + 57 T^{2} + 141 T^{3} + 1767 T^{4} + 4805 T^{5} + 29791 T^{6} \))(\( 1 + T + 78 T^{2} + 118 T^{3} + 3036 T^{4} + 3658 T^{5} + 74958 T^{6} + 29791 T^{7} + 923521 T^{8} \))(\( 1 + T + 101 T^{2} + 143 T^{3} + 5000 T^{4} + 6444 T^{5} + 155000 T^{6} + 137423 T^{7} + 3008891 T^{8} + 923521 T^{9} + 28629151 T^{10} \))(\( 1 + 5 T + 126 T^{2} + 530 T^{3} + 7933 T^{4} + 27909 T^{5} + 306992 T^{6} + 865179 T^{7} + 7623613 T^{8} + 15789230 T^{9} + 116363646 T^{10} + 143145755 T^{11} + 887503681 T^{12} \))(\( 1 + 12 T + 163 T^{2} + 1446 T^{3} + 11543 T^{4} + 77210 T^{5} + 461997 T^{6} + 2393510 T^{7} + 11092823 T^{8} + 43077786 T^{9} + 150533923 T^{10} + 343549812 T^{11} + 887503681 T^{12} \))(\( 1 + 12 T + 163 T^{2} + 1446 T^{3} + 11543 T^{4} + 77210 T^{5} + 461997 T^{6} + 2393510 T^{7} + 11092823 T^{8} + 43077786 T^{9} + 150533923 T^{10} + 343549812 T^{11} + 887503681 T^{12} \))(\( 1 - 11 T + 167 T^{2} - 1267 T^{3} + 11993 T^{4} - 74685 T^{5} + 552771 T^{6} - 2866186 T^{7} + 17135901 T^{8} - 71772285 T^{9} + 357283463 T^{10} - 1170101107 T^{11} + 4781068217 T^{12} - 9762540491 T^{13} + 27512614111 T^{14} \))(\( 1 + 2 T + 125 T^{2} - 100 T^{3} + 6369 T^{4} - 22362 T^{5} + 216297 T^{6} - 1064192 T^{7} + 6705207 T^{8} - 21489882 T^{9} + 189738879 T^{10} - 92352100 T^{11} + 3578643875 T^{12} + 1775007362 T^{13} + 27512614111 T^{14} \))(\( 1 + 6 T + 93 T^{2} + 502 T^{3} + 6586 T^{4} + 30218 T^{5} + 288086 T^{6} + 1229152 T^{7} + 10731368 T^{8} + 38103712 T^{9} + 276850646 T^{10} + 900224438 T^{11} + 6082309306 T^{12} + 14371833802 T^{13} + 82537842333 T^{14} + 165075684666 T^{15} + 852891037441 T^{16} \))(\( 1 + 6 T + 93 T^{2} + 502 T^{3} + 6586 T^{4} + 30218 T^{5} + 288086 T^{6} + 1229152 T^{7} + 10731368 T^{8} + 38103712 T^{9} + 276850646 T^{10} + 900224438 T^{11} + 6082309306 T^{12} + 14371833802 T^{13} + 82537842333 T^{14} + 165075684666 T^{15} + 852891037441 T^{16} \))(\( 1 - 12 T + 180 T^{2} - 1292 T^{3} + 11692 T^{4} - 58972 T^{5} + 426416 T^{6} - 1697396 T^{7} + 12644594 T^{8} - 52619276 T^{9} + 409785776 T^{10} - 1756834852 T^{11} + 10797807532 T^{12} - 36988863092 T^{13} + 159750662580 T^{14} - 330151369332 T^{15} + 852891037441 T^{16} \))
$37$ (\( 1 - 3 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 - 2 T + 62 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 58 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 2 T + 62 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 12 T^{2} - 203 T^{3} + 444 T^{4} + 8214 T^{5} + 50653 T^{6} \))(\( 1 + 4 T + 72 T^{2} + 337 T^{3} + 2664 T^{4} + 5476 T^{5} + 50653 T^{6} \))(\( 1 - 8 T + 124 T^{2} - 589 T^{3} + 4588 T^{4} - 10952 T^{5} + 50653 T^{6} \))(\( 1 - 4 T - 10 T^{2} + 413 T^{3} - 370 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 + 11 T + 155 T^{2} + 1129 T^{3} + 8591 T^{4} + 41773 T^{5} + 212195 T^{6} + 557183 T^{7} + 1874161 T^{8} \))(\( 1 + 2 T + 72 T^{2} - 51 T^{3} + 3779 T^{4} - 146 T^{5} + 139823 T^{6} - 69819 T^{7} + 3647016 T^{8} + 3748322 T^{9} + 69343957 T^{10} \))(\( 1 - T + 127 T^{2} + 61 T^{3} + 8406 T^{4} + 5520 T^{5} + 382600 T^{6} + 204240 T^{7} + 11507814 T^{8} + 3089833 T^{9} + 238018447 T^{10} - 69343957 T^{11} + 2565726409 T^{12} \))(\( 1 + 146 T^{2} + 16 T^{3} + 9794 T^{4} + 1096 T^{5} + 426551 T^{6} + 40552 T^{7} + 13407986 T^{8} + 810448 T^{9} + 273627506 T^{10} + 2565726409 T^{12} \))(\( 1 + 146 T^{2} + 16 T^{3} + 9794 T^{4} + 1096 T^{5} + 426551 T^{6} + 40552 T^{7} + 13407986 T^{8} + 810448 T^{9} + 273627506 T^{10} + 2565726409 T^{12} \))(\( 1 - 17 T + 280 T^{2} - 2814 T^{3} + 27841 T^{4} - 212197 T^{5} + 1603258 T^{6} - 9844176 T^{7} + 59320546 T^{8} - 290497693 T^{9} + 1410230173 T^{10} - 5273889054 T^{11} + 19416307960 T^{12} - 43617348953 T^{13} + 94931877133 T^{14} \))(\( 1 - 5 T + 51 T^{2} - 402 T^{3} + 3485 T^{4} - 16691 T^{5} + 132407 T^{6} - 755612 T^{7} + 4899059 T^{8} - 22849979 T^{9} + 176525705 T^{10} - 753412722 T^{11} + 3536541807 T^{12} - 12828632045 T^{13} + 94931877133 T^{14} \))(\( 1 + 14 T + 248 T^{2} + 2542 T^{3} + 27627 T^{4} + 224696 T^{5} + 1859201 T^{6} + 12366486 T^{7} + 83220526 T^{8} + 457559982 T^{9} + 2545246169 T^{10} + 11381526488 T^{11} + 51777445947 T^{12} + 176272338694 T^{13} + 636300149432 T^{14} + 1329046279862 T^{15} + 3512479453921 T^{16} \))(\( 1 + 14 T + 248 T^{2} + 2542 T^{3} + 27627 T^{4} + 224696 T^{5} + 1859201 T^{6} + 12366486 T^{7} + 83220526 T^{8} + 457559982 T^{9} + 2545246169 T^{10} + 11381526488 T^{11} + 51777445947 T^{12} + 176272338694 T^{13} + 636300149432 T^{14} + 1329046279862 T^{15} + 3512479453921 T^{16} \))(\( 1 - 16 T + 272 T^{2} - 2720 T^{3} + 28236 T^{4} - 221248 T^{5} + 1805744 T^{6} - 11915088 T^{7} + 80272582 T^{8} - 440858256 T^{9} + 2472063536 T^{10} - 11206874944 T^{11} + 52918809996 T^{12} - 188615563040 T^{13} + 697877583248 T^{14} - 1518910034128 T^{15} + 3512479453921 T^{16} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 4 T + 41 T^{2} )^{2} \))(\( 1 - 6 T + 96 T^{2} - 333 T^{3} + 3936 T^{4} - 10086 T^{5} + 68921 T^{6} \))(\( 1 - 2 T + 24 T^{2} + 117 T^{3} + 984 T^{4} - 3362 T^{5} + 68921 T^{6} \))(\( 1 - 6 T + 90 T^{2} - 491 T^{3} + 3690 T^{4} - 10086 T^{5} + 68921 T^{6} \))(\( 1 + 8 T + 26 T^{2} + 101 T^{3} + 1066 T^{4} + 13448 T^{5} + 68921 T^{6} \))(\( 1 + 14 T + 139 T^{2} + 1245 T^{3} + 9124 T^{4} + 51045 T^{5} + 233659 T^{6} + 964894 T^{7} + 2825761 T^{8} \))(\( 1 + 4 T + 96 T^{2} - 57 T^{3} + 3551 T^{4} - 12502 T^{5} + 145591 T^{6} - 95817 T^{7} + 6616416 T^{8} + 11303044 T^{9} + 115856201 T^{10} \))(\( 1 + 12 T + 251 T^{2} + 1995 T^{3} + 23819 T^{4} + 141129 T^{5} + 1246146 T^{6} + 5786289 T^{7} + 40039739 T^{8} + 137497395 T^{9} + 709266011 T^{10} + 1390274412 T^{11} + 4750104241 T^{12} \))(\( 1 + 28 T + 540 T^{2} + 7068 T^{3} + 74874 T^{4} + 627126 T^{5} + 4445591 T^{6} + 25712166 T^{7} + 125863194 T^{8} + 487133628 T^{9} + 1525910940 T^{10} + 3243973628 T^{11} + 4750104241 T^{12} \))(\( 1 - 28 T + 540 T^{2} - 7068 T^{3} + 74874 T^{4} - 627126 T^{5} + 4445591 T^{6} - 25712166 T^{7} + 125863194 T^{8} - 487133628 T^{9} + 1525910940 T^{10} - 3243973628 T^{11} + 4750104241 T^{12} \))(\( 1 + 18 T + 244 T^{2} + 2031 T^{3} + 15320 T^{4} + 87734 T^{5} + 576219 T^{6} + 3259314 T^{7} + 23624979 T^{8} + 147480854 T^{9} + 1055869720 T^{10} + 5739120591 T^{11} + 28268913044 T^{12} + 85501876338 T^{13} + 194754273881 T^{14} \))(\( 1 - 33 T + 655 T^{2} - 9442 T^{3} + 107781 T^{4} - 1018431 T^{5} + 8167163 T^{6} - 56270876 T^{7} + 334853683 T^{8} - 1711982511 T^{9} + 7428374301 T^{10} - 26680835362 T^{11} + 75885811655 T^{12} - 156753439953 T^{13} + 194754273881 T^{14} \))(\( 1 - 16 T + 358 T^{2} - 4364 T^{3} + 53943 T^{4} - 518694 T^{5} + 4533887 T^{6} - 34838962 T^{7} + 234118138 T^{8} - 1428397442 T^{9} + 7621464047 T^{10} - 35748909174 T^{11} + 152430025623 T^{12} - 505596461164 T^{13} + 1700537318278 T^{14} - 3116068382096 T^{15} + 7984925229121 T^{16} \))(\( 1 + 16 T + 358 T^{2} + 4364 T^{3} + 53943 T^{4} + 518694 T^{5} + 4533887 T^{6} + 34838962 T^{7} + 234118138 T^{8} + 1428397442 T^{9} + 7621464047 T^{10} + 35748909174 T^{11} + 152430025623 T^{12} + 505596461164 T^{13} + 1700537318278 T^{14} + 3116068382096 T^{15} + 7984925229121 T^{16} \))(\( 1 + 16 T + 328 T^{2} + 3536 T^{3} + 42780 T^{4} + 356016 T^{5} + 3229304 T^{6} + 21927280 T^{7} + 160620166 T^{8} + 899018480 T^{9} + 5428460024 T^{10} + 24536978736 T^{11} + 120886055580 T^{12} + 409667526736 T^{13} + 1558034191048 T^{14} + 3116068382096 T^{15} + 7984925229121 T^{16} \))
$43$ (\( 1 - 6 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 3 T + 59 T^{2} + 129 T^{3} + 1849 T^{4} \))(\( 1 - 15 T + 141 T^{2} - 645 T^{3} + 1849 T^{4} \))(\( 1 + 3 T + 59 T^{2} + 129 T^{3} + 1849 T^{4} \))(\( 1 + 102 T^{2} + 27 T^{3} + 4386 T^{4} + 79507 T^{6} \))(\( 1 + 6 T + 134 T^{2} + 503 T^{3} + 5762 T^{4} + 11094 T^{5} + 79507 T^{6} \))(\( 1 - 12 T + 132 T^{2} - 835 T^{3} + 5676 T^{4} - 22188 T^{5} + 79507 T^{6} \))(\( 1 - 2 T + 86 T^{2} - 43 T^{3} + 3698 T^{4} - 3698 T^{5} + 79507 T^{6} \))(\( 1 + 22 T + 343 T^{2} + 3395 T^{3} + 26448 T^{4} + 145985 T^{5} + 634207 T^{6} + 1749154 T^{7} + 3418801 T^{8} \))(\( 1 - 3 T + 27 T^{2} + 246 T^{3} + 2882 T^{4} - 10727 T^{5} + 123926 T^{6} + 454854 T^{7} + 2146689 T^{8} - 10256403 T^{9} + 147008443 T^{10} \))(\( 1 + 11 T + 246 T^{2} + 1877 T^{3} + 24479 T^{4} + 143495 T^{5} + 1364840 T^{6} + 6170285 T^{7} + 45261671 T^{8} + 149234639 T^{9} + 841025046 T^{10} + 1617092873 T^{11} + 6321363049 T^{12} \))(\( 1 - 14 T + 246 T^{2} - 2256 T^{3} + 23498 T^{4} - 162252 T^{5} + 1270461 T^{6} - 6976836 T^{7} + 43447802 T^{8} - 179367792 T^{9} + 841025046 T^{10} - 2058118202 T^{11} + 6321363049 T^{12} \))(\( 1 - 14 T + 246 T^{2} - 2256 T^{3} + 23498 T^{4} - 162252 T^{5} + 1270461 T^{6} - 6976836 T^{7} + 43447802 T^{8} - 179367792 T^{9} + 841025046 T^{10} - 2058118202 T^{11} + 6321363049 T^{12} \))(\( 1 + T + 19 T^{2} + 56 T^{3} + 1695 T^{4} - 6240 T^{5} - 6539 T^{6} - 47162 T^{7} - 281177 T^{8} - 11537760 T^{9} + 134764365 T^{10} + 191452856 T^{11} + 2793160417 T^{12} + 6321363049 T^{13} + 271818611107 T^{14} \))(\( 1 - 20 T + 373 T^{2} - 4328 T^{3} + 47717 T^{4} - 402636 T^{5} + 3292073 T^{6} - 21857328 T^{7} + 141559139 T^{8} - 744473964 T^{9} + 3793835519 T^{10} - 14796570728 T^{11} + 54834149239 T^{12} - 126427260980 T^{13} + 271818611107 T^{14} \))(\( 1 + 29 T + 587 T^{2} + 8661 T^{3} + 106007 T^{4} + 1089814 T^{5} + 9793353 T^{6} + 76899377 T^{7} + 536926075 T^{8} + 3306673211 T^{9} + 18107909697 T^{10} + 86647841698 T^{11} + 362416837607 T^{12} + 1273240124823 T^{13} + 3710640109763 T^{14} + 7882739722103 T^{15} + 11688200277601 T^{16} \))(\( 1 + 29 T + 587 T^{2} + 8661 T^{3} + 106007 T^{4} + 1089814 T^{5} + 9793353 T^{6} + 76899377 T^{7} + 536926075 T^{8} + 3306673211 T^{9} + 18107909697 T^{10} + 86647841698 T^{11} + 362416837607 T^{12} + 1273240124823 T^{13} + 3710640109763 T^{14} + 7882739722103 T^{15} + 11688200277601 T^{16} \))(\( 1 - 12 T + 160 T^{2} - 1628 T^{3} + 14796 T^{4} - 128092 T^{5} + 1004448 T^{6} - 7054892 T^{7} + 49383750 T^{8} - 303360356 T^{9} + 1857224352 T^{10} - 10184210644 T^{11} + 50584579596 T^{12} - 239329745204 T^{13} + 1011418087840 T^{14} - 3261823333284 T^{15} + 11688200277601 T^{16} \))
$47$ (\( 1 + 9 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 5 T + 97 T^{2} + 235 T^{3} + 2209 T^{4} \))(\( 1 + 9 T + 113 T^{2} + 423 T^{3} + 2209 T^{4} \))(\( 1 - 5 T + 97 T^{2} - 235 T^{3} + 2209 T^{4} \))(\( 1 - 15 T + 123 T^{2} - 781 T^{3} + 5781 T^{4} - 33135 T^{5} + 103823 T^{6} \))(\( 1 + 5 T + 77 T^{2} + 289 T^{3} + 3619 T^{4} + 11045 T^{5} + 103823 T^{6} \))(\( 1 - 9 T + 129 T^{2} - 799 T^{3} + 6063 T^{4} - 19881 T^{5} + 103823 T^{6} \))(\( 1 - 11 T + 147 T^{2} - 881 T^{3} + 6909 T^{4} - 24299 T^{5} + 103823 T^{6} \))(\( 1 - 8 T + 181 T^{2} - 1085 T^{3} + 12569 T^{4} - 50995 T^{5} + 399829 T^{6} - 830584 T^{7} + 4879681 T^{8} \))(\( 1 + 18 T + 275 T^{2} + 2774 T^{3} + 24661 T^{4} + 177861 T^{5} + 1159067 T^{6} + 6127766 T^{7} + 28551325 T^{8} + 87834258 T^{9} + 229345007 T^{10} \))(\( 1 + 5 T + 204 T^{2} + 1111 T^{3} + 19280 T^{4} + 101170 T^{5} + 1117673 T^{6} + 4754990 T^{7} + 42589520 T^{8} + 115347353 T^{9} + 995454924 T^{10} + 1146725035 T^{11} + 10779215329 T^{12} \))(\( 1 + 2 T + 161 T^{2} + 258 T^{3} + 11803 T^{4} + 18340 T^{5} + 608617 T^{6} + 861980 T^{7} + 26072827 T^{8} + 26786334 T^{9} + 785628641 T^{10} + 458690014 T^{11} + 10779215329 T^{12} \))(\( 1 - 2 T + 161 T^{2} - 258 T^{3} + 11803 T^{4} - 18340 T^{5} + 608617 T^{6} - 861980 T^{7} + 26072827 T^{8} - 26786334 T^{9} + 785628641 T^{10} - 458690014 T^{11} + 10779215329 T^{12} \))(\( 1 + 5 T + 61 T^{2} - 128 T^{3} + 2482 T^{4} - 14063 T^{5} + 41963 T^{6} - 1627436 T^{7} + 1972261 T^{8} - 31065167 T^{9} + 257688686 T^{10} - 624599168 T^{11} + 13990045427 T^{12} + 53896076645 T^{13} + 506623120463 T^{14} \))(\( 1 - 2 T + 113 T^{2} + 20 T^{3} + 8501 T^{4} + 906 T^{5} + 518921 T^{6} + 118368 T^{7} + 24389287 T^{8} + 2001354 T^{9} + 882599323 T^{10} + 97593620 T^{11} + 25915985791 T^{12} - 21558430658 T^{13} + 506623120463 T^{14} \))(\( 1 - 9 T + 192 T^{2} - 856 T^{3} + 13037 T^{4} - 5994 T^{5} + 396723 T^{6} + 2875252 T^{7} + 8189679 T^{8} + 135136844 T^{9} + 876361107 T^{10} - 622315062 T^{11} + 63616401197 T^{12} - 196319325992 T^{13} + 2069609343168 T^{14} - 4559608084167 T^{15} + 23811286661761 T^{16} \))(\( 1 + 9 T + 192 T^{2} + 856 T^{3} + 13037 T^{4} + 5994 T^{5} + 396723 T^{6} - 2875252 T^{7} + 8189679 T^{8} - 135136844 T^{9} + 876361107 T^{10} + 622315062 T^{11} + 63616401197 T^{12} + 196319325992 T^{13} + 2069609343168 T^{14} + 4559608084167 T^{15} + 23811286661761 T^{16} \))(\( 1 - 4 T + 136 T^{2} - 700 T^{3} + 13996 T^{4} - 64068 T^{5} + 950924 T^{6} - 4077972 T^{7} + 52261874 T^{8} - 191664684 T^{9} + 2100591116 T^{10} - 6651731964 T^{11} + 68296015276 T^{12} - 160541504900 T^{13} + 1465973284744 T^{14} - 2026492481852 T^{15} + 23811286661761 T^{16} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 + 3 T + 79 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 - 5 T + 81 T^{2} - 265 T^{3} + 2809 T^{4} \))(\( 1 - 3 T + 79 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 57 T^{2} - 145 T^{3} + 3021 T^{4} - 25281 T^{5} + 148877 T^{6} \))(\( 1 - 5 T + 81 T^{2} - 111 T^{3} + 4293 T^{4} - 14045 T^{5} + 148877 T^{6} \))(\( 1 - 11 T + 131 T^{2} - 1121 T^{3} + 6943 T^{4} - 30899 T^{5} + 148877 T^{6} \))(\( 1 + 3 T + 91 T^{2} + 29 T^{3} + 4823 T^{4} + 8427 T^{5} + 148877 T^{6} \))(\( 1 + 3 T + 146 T^{2} + 380 T^{3} + 10800 T^{4} + 20140 T^{5} + 410114 T^{6} + 446631 T^{7} + 7890481 T^{8} \))(\( 1 + 26 T + 501 T^{2} + 6338 T^{3} + 66181 T^{4} + 524547 T^{5} + 3507593 T^{6} + 17803442 T^{7} + 74587377 T^{8} + 205152506 T^{9} + 418195493 T^{10} \))(\( 1 + 4 T + 232 T^{2} + 684 T^{3} + 24888 T^{4} + 57715 T^{5} + 1635504 T^{6} + 3058895 T^{7} + 69910392 T^{8} + 101831868 T^{9} + 1830591592 T^{10} + 1672781972 T^{11} + 22164361129 T^{12} \))(\( 1 + 26 T + 491 T^{2} + 6142 T^{3} + 65029 T^{4} + 553746 T^{5} + 4352587 T^{6} + 29348538 T^{7} + 182666461 T^{8} + 914402534 T^{9} + 3874226171 T^{10} + 10873082818 T^{11} + 22164361129 T^{12} \))(\( 1 - 26 T + 491 T^{2} - 6142 T^{3} + 65029 T^{4} - 553746 T^{5} + 4352587 T^{6} - 29348538 T^{7} + 182666461 T^{8} - 914402534 T^{9} + 3874226171 T^{10} - 10873082818 T^{11} + 22164361129 T^{12} \))(\( 1 + 6 T + 189 T^{2} + 1106 T^{3} + 17250 T^{4} + 106541 T^{5} + 1103088 T^{6} + 6768406 T^{7} + 58463664 T^{8} + 299273669 T^{9} + 2568128250 T^{10} + 8726871986 T^{11} + 79038948177 T^{12} + 132986166774 T^{13} + 1174711139837 T^{14} \))(\( 1 - 13 T + 259 T^{2} - 2626 T^{3} + 33677 T^{4} - 278539 T^{5} + 2685015 T^{6} - 18247356 T^{7} + 142305795 T^{8} - 782416051 T^{9} + 5013730729 T^{10} - 20720403106 T^{11} + 108312632687 T^{12} - 288136694677 T^{13} + 1174711139837 T^{14} \))(\( 1 - 11 T + 284 T^{2} - 1808 T^{3} + 30979 T^{4} - 128438 T^{5} + 2235793 T^{6} - 7349734 T^{7} + 132132131 T^{8} - 389535902 T^{9} + 6280342537 T^{10} - 19121464126 T^{11} + 244439210899 T^{12} - 756097451344 T^{13} + 6294678560636 T^{14} - 12921822538207 T^{15} + 62259690411361 T^{16} \))(\( 1 + 11 T + 284 T^{2} + 1808 T^{3} + 30979 T^{4} + 128438 T^{5} + 2235793 T^{6} + 7349734 T^{7} + 132132131 T^{8} + 389535902 T^{9} + 6280342537 T^{10} + 19121464126 T^{11} + 244439210899 T^{12} + 756097451344 T^{13} + 6294678560636 T^{14} + 12921822538207 T^{15} + 62259690411361 T^{16} \))(\( 1 - 8 T + 328 T^{2} - 2232 T^{3} + 50076 T^{4} - 290568 T^{5} + 4697784 T^{6} - 23153656 T^{7} + 298519718 T^{8} - 1227143768 T^{9} + 13196075256 T^{10} - 43258892136 T^{11} + 395123726556 T^{12} - 933412340376 T^{13} + 7269910450312 T^{14} - 9397689118696 T^{15} + 62259690411361 T^{16} \))
$59$ (\( 1 + 14 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 11 T + 59 T^{2} \))(\( 1 - 3 T + 117 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 + 7 T + 119 T^{2} + 413 T^{3} + 3481 T^{4} \))(\( 1 + 3 T + 117 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 168 T^{2} + 711 T^{3} + 9912 T^{4} + 20886 T^{5} + 205379 T^{6} \))(\( 1 + 8 T + 98 T^{2} + 775 T^{3} + 5782 T^{4} + 27848 T^{5} + 205379 T^{6} \))(\( 1 - 8 T + 30 T^{2} - 187 T^{3} + 1770 T^{4} - 27848 T^{5} + 205379 T^{6} \))(\( 1 - 6 T + 114 T^{2} - 789 T^{3} + 6726 T^{4} - 20886 T^{5} + 205379 T^{6} \))(\( 1 - 6 T + 135 T^{2} - 553 T^{3} + 8832 T^{4} - 32627 T^{5} + 469935 T^{6} - 1232274 T^{7} + 12117361 T^{8} \))(\( 1 + 21 T + 191 T^{2} + 1174 T^{3} + 7728 T^{4} + 57933 T^{5} + 455952 T^{6} + 4086694 T^{7} + 39227389 T^{8} + 254464581 T^{9} + 714924299 T^{10} \))(\( 1 + T + 198 T^{2} + 531 T^{3} + 16363 T^{4} + 74891 T^{5} + 963204 T^{6} + 4418569 T^{7} + 56959603 T^{8} + 109056249 T^{9} + 2399237478 T^{10} + 714924299 T^{11} + 42180533641 T^{12} \))(\( 1 + 4 T + 178 T^{2} - 18 T^{3} + 12718 T^{4} - 53854 T^{5} + 669709 T^{6} - 3177386 T^{7} + 44271358 T^{8} - 3696822 T^{9} + 2156890258 T^{10} + 2859697196 T^{11} + 42180533641 T^{12} \))(\( 1 - 4 T + 178 T^{2} + 18 T^{3} + 12718 T^{4} + 53854 T^{5} + 669709 T^{6} + 3177386 T^{7} + 44271358 T^{8} + 3696822 T^{9} + 2156890258 T^{10} - 2859697196 T^{11} + 42180533641 T^{12} \))(\( 1 - 7 T + 221 T^{2} - 1540 T^{3} + 25061 T^{4} - 148516 T^{5} + 1965993 T^{6} - 9737770 T^{7} + 115993587 T^{8} - 516984196 T^{9} + 5147003119 T^{10} - 18660735940 T^{11} + 157998270079 T^{12} - 295263735487 T^{13} + 2488651484819 T^{14} \))(\( 1 + 9 T + 203 T^{2} + 1630 T^{3} + 23925 T^{4} + 170923 T^{5} + 1964329 T^{6} + 12171514 T^{7} + 115895411 T^{8} + 594982963 T^{9} + 4913692575 T^{10} + 19751298430 T^{11} + 145129632697 T^{12} + 379624802769 T^{13} + 2488651484819 T^{14} \))(\( 1 - 21 T + 471 T^{2} - 6327 T^{3} + 82527 T^{4} - 835620 T^{5} + 8145533 T^{6} - 68273733 T^{7} + 555976677 T^{8} - 4028150247 T^{9} + 28354600373 T^{10} - 171618799980 T^{11} + 1000009451247 T^{12} - 4523326039773 T^{13} + 19867031344911 T^{14} - 52261681181199 T^{15} + 146830437604321 T^{16} \))(\( 1 + 21 T + 471 T^{2} + 6327 T^{3} + 82527 T^{4} + 835620 T^{5} + 8145533 T^{6} + 68273733 T^{7} + 555976677 T^{8} + 4028150247 T^{9} + 28354600373 T^{10} + 171618799980 T^{11} + 1000009451247 T^{12} + 4523326039773 T^{13} + 19867031344911 T^{14} + 52261681181199 T^{15} + 146830437604321 T^{16} \))(\( 1 + 348 T^{2} - 102 T^{3} + 58026 T^{4} - 21534 T^{5} + 6032534 T^{6} - 2177220 T^{7} + 426474240 T^{8} - 128455980 T^{9} + 20999250854 T^{10} - 4422631386 T^{11} + 703121989386 T^{12} - 72922278498 T^{13} + 14678825707068 T^{14} + 146830437604321 T^{16} \))
$61$ (\( 1 - 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 9 T + 139 T^{2} + 549 T^{3} + 3721 T^{4} \))(\( 1 - 3 T - 27 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 + 9 T + 139 T^{2} + 549 T^{3} + 3721 T^{4} \))(\( 1 + 15 T + 237 T^{2} + 1833 T^{3} + 14457 T^{4} + 55815 T^{5} + 226981 T^{6} \))(\( 1 + 15 T + 167 T^{2} + 1703 T^{3} + 10187 T^{4} + 55815 T^{5} + 226981 T^{6} \))(\( 1 - 3 T + 93 T^{2} + 61 T^{3} + 5673 T^{4} - 11163 T^{5} + 226981 T^{6} \))(\( 1 + T + 55 T^{2} - 463 T^{3} + 3355 T^{4} + 3721 T^{5} + 226981 T^{6} \))(\( 1 + 9 T + 236 T^{2} + 1484 T^{3} + 21094 T^{4} + 90524 T^{5} + 878156 T^{6} + 2042829 T^{7} + 13845841 T^{8} \))(\( 1 + 20 T + 309 T^{2} + 3002 T^{3} + 27263 T^{4} + 201443 T^{5} + 1663043 T^{6} + 11170442 T^{7} + 70137129 T^{8} + 276916820 T^{9} + 844596301 T^{10} \))(\( 1 + 8 T + 96 T^{2} + 868 T^{3} + 12058 T^{4} + 71629 T^{5} + 630206 T^{6} + 4369369 T^{7} + 44867818 T^{8} + 197019508 T^{9} + 1329200736 T^{10} + 6756770408 T^{11} + 51520374361 T^{12} \))(\( 1 + 6 T + 145 T^{2} + 358 T^{3} + 13345 T^{4} + 44368 T^{5} + 1081027 T^{6} + 2706448 T^{7} + 49656745 T^{8} + 81259198 T^{9} + 2007646945 T^{10} + 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 + 6 T + 145 T^{2} + 358 T^{3} + 13345 T^{4} + 44368 T^{5} + 1081027 T^{6} + 2706448 T^{7} + 49656745 T^{8} + 81259198 T^{9} + 2007646945 T^{10} + 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 - 24 T + 565 T^{2} - 8504 T^{3} + 115340 T^{4} - 1255803 T^{5} + 12166384 T^{6} - 100810822 T^{7} + 742149424 T^{8} - 4672842963 T^{9} + 26179988540 T^{10} - 117745031864 T^{11} + 477196910065 T^{12} - 1236488984664 T^{13} + 3142742836021 T^{14} \))(\( 1 - 8 T + 239 T^{2} - 2446 T^{3} + 30153 T^{4} - 299532 T^{5} + 2695533 T^{6} - 21956832 T^{7} + 164427513 T^{8} - 1114558572 T^{9} + 6844158093 T^{10} - 33866927086 T^{11} + 201858515939 T^{12} - 412162994888 T^{13} + 3142742836021 T^{14} \))(\( 1 - 3 T + 198 T^{2} + 222 T^{3} + 15669 T^{4} + 110866 T^{5} + 795949 T^{6} + 11947206 T^{7} + 43070391 T^{8} + 728779566 T^{9} + 2961726229 T^{10} + 25164475546 T^{11} + 216950482629 T^{12} + 187500378822 T^{13} + 10201034123478 T^{14} - 9428228508063 T^{15} + 191707312997281 T^{16} \))(\( 1 - 3 T + 198 T^{2} + 222 T^{3} + 15669 T^{4} + 110866 T^{5} + 795949 T^{6} + 11947206 T^{7} + 43070391 T^{8} + 728779566 T^{9} + 2961726229 T^{10} + 25164475546 T^{11} + 216950482629 T^{12} + 187500378822 T^{13} + 10201034123478 T^{14} - 9428228508063 T^{15} + 191707312997281 T^{16} \))(\( 1 - 26 T + 594 T^{2} - 8944 T^{3} + 123630 T^{4} - 1373152 T^{5} + 14358788 T^{6} - 127671414 T^{7} + 1075004504 T^{8} - 7787956254 T^{9} + 53429050148 T^{10} - 311679414112 T^{11} + 1711761322830 T^{12} - 7554069316144 T^{13} + 30603102370434 T^{14} - 81711313736546 T^{15} + 191707312997281 T^{16} \))
$67$ (\( 1 + 3 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 - 2 T + 122 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 90 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 2 T + 122 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 + 3 T + 57 T^{2} + 653 T^{3} + 3819 T^{4} + 13467 T^{5} + 300763 T^{6} \))(\( 1 - 13 T + 185 T^{2} - 1365 T^{3} + 12395 T^{4} - 58357 T^{5} + 300763 T^{6} \))(\( 1 + 11 T + 123 T^{2} + 601 T^{3} + 8241 T^{4} + 49379 T^{5} + 300763 T^{6} \))(\( 1 - 15 T + 201 T^{2} - 1537 T^{3} + 13467 T^{4} - 67335 T^{5} + 300763 T^{6} \))(\( 1 + 22 T + 443 T^{2} + 5021 T^{3} + 51131 T^{4} + 336407 T^{5} + 1988627 T^{6} + 6616786 T^{7} + 20151121 T^{8} \))(\( 1 + 5 T + 207 T^{2} + 1391 T^{3} + 20426 T^{4} + 142580 T^{5} + 1368542 T^{6} + 6244199 T^{7} + 62257941 T^{8} + 100755605 T^{9} + 1350125107 T^{10} \))(\( 1 + 6 T + 341 T^{2} + 1697 T^{3} + 51708 T^{4} + 207911 T^{5} + 4466256 T^{6} + 13930037 T^{7} + 232117212 T^{8} + 510394811 T^{9} + 6871532261 T^{10} + 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 - 18 T + 357 T^{2} - 4422 T^{3} + 52655 T^{4} - 514304 T^{5} + 4532217 T^{6} - 34458368 T^{7} + 236368295 T^{8} - 1329973986 T^{9} + 7193950197 T^{10} - 24302251926 T^{11} + 90458382169 T^{12} \))(\( 1 - 18 T + 357 T^{2} - 4422 T^{3} + 52655 T^{4} - 514304 T^{5} + 4532217 T^{6} - 34458368 T^{7} + 236368295 T^{8} - 1329973986 T^{9} + 7193950197 T^{10} - 24302251926 T^{11} + 90458382169 T^{12} \))(\( 1 + 4 T + 334 T^{2} + 1393 T^{3} + 54365 T^{4} + 208604 T^{5} + 5511936 T^{6} + 17838814 T^{7} + 369299712 T^{8} + 936423356 T^{9} + 16350980495 T^{10} + 28070511553 T^{11} + 450941785738 T^{12} + 361833528676 T^{13} + 6060711605323 T^{14} \))(\( 1 - 29 T + 547 T^{2} - 7824 T^{3} + 93989 T^{4} - 1001607 T^{5} + 9666465 T^{6} - 83193754 T^{7} + 647653155 T^{8} - 4496213823 T^{9} + 28268413607 T^{10} - 157662370704 T^{11} + 738518433529 T^{12} - 2623293082901 T^{13} + 6060711605323 T^{14} \))(\( 1 + 20 T + 443 T^{2} + 5246 T^{3} + 70214 T^{4} + 662146 T^{5} + 7410764 T^{6} + 62681818 T^{7} + 594236152 T^{8} + 4199681806 T^{9} + 33266919596 T^{10} + 199149017398 T^{11} + 1414890809894 T^{12} + 7082756311322 T^{13} + 40073063300867 T^{14} + 121214232106460 T^{15} + 406067677556641 T^{16} \))(\( 1 + 20 T + 443 T^{2} + 5246 T^{3} + 70214 T^{4} + 662146 T^{5} + 7410764 T^{6} + 62681818 T^{7} + 594236152 T^{8} + 4199681806 T^{9} + 33266919596 T^{10} + 199149017398 T^{11} + 1414890809894 T^{12} + 7082756311322 T^{13} + 40073063300867 T^{14} + 121214232106460 T^{15} + 406067677556641 T^{16} \))(\( 1 + 10 T + 386 T^{2} + 2680 T^{3} + 66446 T^{4} + 364212 T^{5} + 7427496 T^{6} + 34595050 T^{7} + 590663576 T^{8} + 2317868350 T^{9} + 33342029544 T^{10} + 109541493756 T^{11} + 1338961385966 T^{12} + 3618335286760 T^{13} + 34916935517234 T^{14} + 60607116053230 T^{15} + 406067677556641 T^{16} \))
$71$ (\( 1 + 10 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 8 T + 106 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 + 4 T - 34 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 568 T^{3} + 5041 T^{4} \))(\( ( 1 + 3 T + 71 T^{2} )^{3} \))(\( 1 - 7 T + 108 T^{2} - 315 T^{3} + 7668 T^{4} - 35287 T^{5} + 357911 T^{6} \))(\( 1 - 11 T + 156 T^{2} - 959 T^{3} + 11076 T^{4} - 55451 T^{5} + 357911 T^{6} \))(\( 1 - 15 T + 268 T^{2} - 2163 T^{3} + 19028 T^{4} - 75615 T^{5} + 357911 T^{6} \))(\( 1 + 5 T + 215 T^{2} + 624 T^{3} + 19864 T^{4} + 44304 T^{5} + 1083815 T^{6} + 1789555 T^{7} + 25411681 T^{8} \))(\( 1 + 17 T + 390 T^{2} + 4187 T^{3} + 54301 T^{4} + 418152 T^{5} + 3855371 T^{6} + 21106667 T^{7} + 139585290 T^{8} + 431998577 T^{9} + 1804229351 T^{10} \))(\( 1 + T + 157 T^{2} - 254 T^{3} + 17047 T^{4} - 15675 T^{5} + 1462102 T^{6} - 1112925 T^{7} + 85933927 T^{8} - 90909394 T^{9} + 3989633917 T^{10} + 1804229351 T^{11} + 128100283921 T^{12} \))(\( 1 + 12 T + 311 T^{2} + 2688 T^{3} + 43470 T^{4} + 315580 T^{5} + 3864635 T^{6} + 22406180 T^{7} + 219132270 T^{8} + 962064768 T^{9} + 7903032791 T^{10} + 21650752212 T^{11} + 128100283921 T^{12} \))(\( 1 - 12 T + 311 T^{2} - 2688 T^{3} + 43470 T^{4} - 315580 T^{5} + 3864635 T^{6} - 22406180 T^{7} + 219132270 T^{8} - 962064768 T^{9} + 7903032791 T^{10} - 21650752212 T^{11} + 128100283921 T^{12} \))(\( 1 - 7 T + 304 T^{2} - 2759 T^{3} + 42642 T^{4} - 454357 T^{5} + 3931755 T^{6} - 41713722 T^{7} + 279154605 T^{8} - 2290413637 T^{9} + 15262040862 T^{10} - 70110827879 T^{11} + 548485722704 T^{12} - 896701987447 T^{13} + 9095120158391 T^{14} \))(\( 1 + 73 T^{2} + 48 T^{3} + 7885 T^{4} - 42944 T^{5} + 476501 T^{6} - 2121440 T^{7} + 33831571 T^{8} - 216480704 T^{9} + 2822128235 T^{10} + 1219760688 T^{11} + 131708742623 T^{12} + 9095120158391 T^{14} \))(\( 1 - 32 T + 641 T^{2} - 9004 T^{3} + 110069 T^{4} - 1213992 T^{5} + 12786174 T^{6} - 122742572 T^{7} + 1089839354 T^{8} - 8714722612 T^{9} + 64455103134 T^{10} - 434501090712 T^{11} + 2797038315989 T^{12} - 16245281076404 T^{13} + 82112281993361 T^{14} - 291043845068512 T^{15} + 645753531245761 T^{16} \))(\( 1 + 32 T + 641 T^{2} + 9004 T^{3} + 110069 T^{4} + 1213992 T^{5} + 12786174 T^{6} + 122742572 T^{7} + 1089839354 T^{8} + 8714722612 T^{9} + 64455103134 T^{10} + 434501090712 T^{11} + 2797038315989 T^{12} + 16245281076404 T^{13} + 82112281993361 T^{14} + 291043845068512 T^{15} + 645753531245761 T^{16} \))(\( 1 + 8 T + 248 T^{2} + 1816 T^{3} + 33980 T^{4} + 226392 T^{5} + 3435336 T^{6} + 19612232 T^{7} + 269503430 T^{8} + 1392468472 T^{9} + 17317528776 T^{10} + 81028187112 T^{11} + 863488920380 T^{12} + 3276480501416 T^{13} + 31768870412408 T^{14} + 72760961267128 T^{15} + 645753531245761 T^{16} \))
$73$ (\( 1 - 13 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 13 T + 73 T^{2} \))(\( 1 + 15 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 + 7 T + 129 T^{2} + 511 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 157 T^{2} - 949 T^{3} + 5329 T^{4} \))(\( 1 + 7 T + 129 T^{2} + 511 T^{3} + 5329 T^{4} \))(\( 1 + 12 T + 246 T^{2} + 1769 T^{3} + 17958 T^{4} + 63948 T^{5} + 389017 T^{6} \))(\( 1 - 8 T + 210 T^{2} - 1139 T^{3} + 15330 T^{4} - 42632 T^{5} + 389017 T^{6} \))(\( 1 - 24 T + 358 T^{2} - 3687 T^{3} + 26134 T^{4} - 127896 T^{5} + 389017 T^{6} \))(\( 1 + 4 T + 54 T^{2} + 705 T^{3} + 3942 T^{4} + 21316 T^{5} + 389017 T^{6} \))(\( 1 + 3 T + 159 T^{2} + 527 T^{3} + 16559 T^{4} + 38471 T^{5} + 847311 T^{6} + 1167051 T^{7} + 28398241 T^{8} \))(\( 1 - 5 T + 247 T^{2} - 1122 T^{3} + 28636 T^{4} - 113547 T^{5} + 2090428 T^{6} - 5979138 T^{7} + 96087199 T^{8} - 141991205 T^{9} + 2073071593 T^{10} \))(\( 1 + 10 T + 249 T^{2} + 2366 T^{3} + 32637 T^{4} + 293431 T^{5} + 2852527 T^{6} + 21420463 T^{7} + 173922573 T^{8} + 920414222 T^{9} + 7071162009 T^{10} + 20730715930 T^{11} + 151334226289 T^{12} \))(\( 1 + 20 T + 432 T^{2} + 5194 T^{3} + 66924 T^{4} + 598592 T^{5} + 5963879 T^{6} + 43697216 T^{7} + 356637996 T^{8} + 2020554298 T^{9} + 12268040112 T^{10} + 41461431860 T^{11} + 151334226289 T^{12} \))(\( 1 + 20 T + 432 T^{2} + 5194 T^{3} + 66924 T^{4} + 598592 T^{5} + 5963879 T^{6} + 43697216 T^{7} + 356637996 T^{8} + 2020554298 T^{9} + 12268040112 T^{10} + 41461431860 T^{11} + 151334226289 T^{12} \))(\( 1 - 28 T + 674 T^{2} - 10822 T^{3} + 155858 T^{4} - 1792357 T^{5} + 18944622 T^{6} - 168136784 T^{7} + 1382957406 T^{8} - 9551470453 T^{9} + 60631411586 T^{10} - 307325764102 T^{11} + 1397250253682 T^{12} - 4237358336092 T^{13} + 11047398519097 T^{14} \))(\( 1 + 37 T + 983 T^{2} + 18018 T^{3} + 274469 T^{4} + 3384747 T^{5} + 36363747 T^{6} + 330718412 T^{7} + 2654553531 T^{8} + 18037316763 T^{9} + 106773106973 T^{10} + 511679506338 T^{11} + 2037829375919 T^{12} + 5599366372693 T^{13} + 11047398519097 T^{14} \))(\( 1 - 13 T + 373 T^{2} - 3779 T^{3} + 59871 T^{4} - 487622 T^{5} + 5786257 T^{6} - 41105185 T^{7} + 440500479 T^{8} - 3000678505 T^{9} + 30834963553 T^{10} - 189693247574 T^{11} + 1700231086911 T^{12} - 7834137549947 T^{13} + 56447666405797 T^{14} - 143616180748261 T^{15} + 806460091894081 T^{16} \))(\( 1 - 13 T + 373 T^{2} - 3779 T^{3} + 59871 T^{4} - 487622 T^{5} + 5786257 T^{6} - 41105185 T^{7} + 440500479 T^{8} - 3000678505 T^{9} + 30834963553 T^{10} - 189693247574 T^{11} + 1700231086911 T^{12} - 7834137549947 T^{13} + 56447666405797 T^{14} - 143616180748261 T^{15} + 806460091894081 T^{16} \))(\( 1 - 8 T + 376 T^{2} - 2672 T^{3} + 70292 T^{4} - 439776 T^{5} + 8578872 T^{6} - 46802504 T^{7} + 739256326 T^{8} - 3416582792 T^{9} + 45716808888 T^{10} - 171080340192 T^{11} + 1996169156372 T^{12} - 5539247296496 T^{13} + 56901669084664 T^{14} - 88379188152776 T^{15} + 806460091894081 T^{16} \))
$79$ (\( 1 + 15 T + 79 T^{2} \))(\( 1 + 5 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 5 T + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 + 5 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + T + 77 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 7 T + 169 T^{2} + 553 T^{3} + 6241 T^{4} \))(\( 1 + T + 77 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 216 T^{2} - 37 T^{3} + 17064 T^{4} + 493039 T^{6} \))(\( 1 + 6 T + 74 T^{2} + 1481 T^{3} + 5846 T^{4} + 37446 T^{5} + 493039 T^{6} \))(\( 1 - 16 T + 64 T^{2} + 249 T^{3} + 5056 T^{4} - 99856 T^{5} + 493039 T^{6} \))(\( 1 - 22 T + 270 T^{2} - 2387 T^{3} + 21330 T^{4} - 137302 T^{5} + 493039 T^{6} \))(\( 1 + 29 T + 523 T^{2} + 6871 T^{3} + 70149 T^{4} + 542809 T^{5} + 3264043 T^{6} + 14298131 T^{7} + 38950081 T^{8} \))(\( 1 + 21 T + 385 T^{2} + 3818 T^{3} + 39648 T^{4} + 299687 T^{5} + 3132192 T^{6} + 23828138 T^{7} + 189820015 T^{8} + 817951701 T^{9} + 3077056399 T^{10} \))(\( 1 + 10 T + 165 T^{2} + 1548 T^{3} + 19319 T^{4} + 124055 T^{5} + 1493471 T^{6} + 9800345 T^{7} + 120569879 T^{8} + 763224372 T^{9} + 6426763365 T^{10} + 30770563990 T^{11} + 243087455521 T^{12} \))(\( 1 - 12 T + 404 T^{2} - 4826 T^{3} + 71522 T^{4} - 769226 T^{5} + 7243841 T^{6} - 60768854 T^{7} + 446368802 T^{8} - 2379406214 T^{9} + 15735832724 T^{10} - 36924676788 T^{11} + 243087455521 T^{12} \))(\( 1 - 12 T + 404 T^{2} - 4826 T^{3} + 71522 T^{4} - 769226 T^{5} + 7243841 T^{6} - 60768854 T^{7} + 446368802 T^{8} - 2379406214 T^{9} + 15735832724 T^{10} - 36924676788 T^{11} + 243087455521 T^{12} \))(\( 1 + 278 T^{2} + 350 T^{3} + 42298 T^{4} + 68845 T^{5} + 4389542 T^{6} + 7723498 T^{7} + 346773818 T^{8} + 429661645 T^{9} + 20854563622 T^{10} + 13632528350 T^{11} + 855421678922 T^{12} + 19203908986159 T^{14} \))(\( 1 - 32 T + 825 T^{2} - 14640 T^{3} + 224645 T^{4} - 2807072 T^{5} + 31109933 T^{6} - 292707104 T^{7} + 2457684707 T^{8} - 17518936352 T^{9} + 110758746155 T^{10} - 570229185840 T^{11} + 2538571529175 T^{12} - 7778798576672 T^{13} + 19203908986159 T^{14} \))(\( 1 - 21 T + 521 T^{2} - 8025 T^{3} + 126065 T^{4} - 1520426 T^{5} + 18280415 T^{6} - 180049441 T^{7} + 1753921105 T^{8} - 14223905839 T^{9} + 114088070015 T^{10} - 749629314614 T^{11} + 4910241961265 T^{12} - 24693377601975 T^{13} + 126648564326441 T^{14} - 403282088709339 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 21 T + 521 T^{2} - 8025 T^{3} + 126065 T^{4} - 1520426 T^{5} + 18280415 T^{6} - 180049441 T^{7} + 1753921105 T^{8} - 14223905839 T^{9} + 114088070015 T^{10} - 749629314614 T^{11} + 4910241961265 T^{12} - 24693377601975 T^{13} + 126648564326441 T^{14} - 403282088709339 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 16 T + 256 T^{2} - 3296 T^{3} + 50092 T^{4} - 519744 T^{5} + 5530816 T^{6} - 53429616 T^{7} + 543655078 T^{8} - 4220939664 T^{9} + 34517822656 T^{10} - 256254062016 T^{11} + 1951087457452 T^{12} - 10141977891104 T^{13} + 62230388613376 T^{14} - 307262543778544 T^{15} + 1517108809906561 T^{16} \))
$83$ (\( 1 - 7 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 11 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 4 T + 118 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( 1 - 4 T + 118 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 + 3 T + 123 T^{2} + 819 T^{3} + 10209 T^{4} + 20667 T^{5} + 571787 T^{6} \))(\( 1 - T + 233 T^{2} - 179 T^{3} + 19339 T^{4} - 6889 T^{5} + 571787 T^{6} \))(\( 1 - T + 75 T^{2} - 401 T^{3} + 6225 T^{4} - 6889 T^{5} + 571787 T^{6} \))(\( 1 + 15 T + 177 T^{2} + 1491 T^{3} + 14691 T^{4} + 103335 T^{5} + 571787 T^{6} \))(\( 1 - 12 T + 327 T^{2} - 2665 T^{3} + 40215 T^{4} - 221195 T^{5} + 2252703 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))(\( 1 + 11 T + 213 T^{2} + 2511 T^{3} + 31820 T^{4} + 244036 T^{5} + 2641060 T^{6} + 17298279 T^{7} + 121790631 T^{8} + 522041531 T^{9} + 3939040643 T^{10} \))(\( 1 - 6 T + 243 T^{2} - 2429 T^{3} + 38130 T^{4} - 303279 T^{5} + 4244252 T^{6} - 25172157 T^{7} + 262677570 T^{8} - 1388870623 T^{9} + 11532372003 T^{10} - 23634243858 T^{11} + 326940373369 T^{12} \))(\( 1 + 12 T + 427 T^{2} + 4648 T^{3} + 81391 T^{4} + 743694 T^{5} + 8769517 T^{6} + 61726602 T^{7} + 560702599 T^{8} + 2657665976 T^{9} + 20264703067 T^{10} + 47268487716 T^{11} + 326940373369 T^{12} \))(\( 1 - 12 T + 427 T^{2} - 4648 T^{3} + 81391 T^{4} - 743694 T^{5} + 8769517 T^{6} - 61726602 T^{7} + 560702599 T^{8} - 2657665976 T^{9} + 20264703067 T^{10} - 47268487716 T^{11} + 326940373369 T^{12} \))(\( 1 - 2 T + 124 T^{2} - 227 T^{3} + 9871 T^{4} - 46034 T^{5} + 748440 T^{6} - 4215522 T^{7} + 62120520 T^{8} - 317128226 T^{9} + 5644109477 T^{10} - 10773038867 T^{11} + 488441039732 T^{12} - 653880746738 T^{13} + 27136050989627 T^{14} \))(\( 1 - 6 T + 381 T^{2} - 2108 T^{3} + 73989 T^{4} - 359722 T^{5} + 9067089 T^{6} - 37267848 T^{7} + 752568387 T^{8} - 2478124858 T^{9} + 42305948343 T^{10} - 100042140668 T^{11} + 1500774484983 T^{12} - 1961642240214 T^{13} + 27136050989627 T^{14} \))(\( 1 - 28 T + 617 T^{2} - 9216 T^{3} + 127226 T^{4} - 1485538 T^{5} + 17135118 T^{6} - 174639662 T^{7} + 1708967588 T^{8} - 14495091946 T^{9} + 118043827902 T^{10} - 849411316406 T^{11} + 6037932347546 T^{12} - 36302198565888 T^{13} + 201722210368673 T^{14} - 759809427709556 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 28 T + 617 T^{2} + 9216 T^{3} + 127226 T^{4} + 1485538 T^{5} + 17135118 T^{6} + 174639662 T^{7} + 1708967588 T^{8} + 14495091946 T^{9} + 118043827902 T^{10} + 849411316406 T^{11} + 6037932347546 T^{12} + 36302198565888 T^{13} + 201722210368673 T^{14} + 759809427709556 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 44 T + 1184 T^{2} - 21900 T^{3} + 313388 T^{4} - 3561932 T^{5} + 34360992 T^{6} - 298331788 T^{7} + 2638545734 T^{8} - 24761538404 T^{9} + 236712873888 T^{10} - 2036666412484 T^{11} + 14872868301548 T^{12} - 86264990081700 T^{13} + 387097402068896 T^{14} - 1193986243543588 T^{15} + 2252292232139041 T^{16} \))
$89$ (\( 1 + 4 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 5 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 + 20 T + 226 T^{2} + 1780 T^{3} + 7921 T^{4} \))(\( 1 - 10 T + 198 T^{2} - 890 T^{3} + 7921 T^{4} \))(\( 1 - 20 T + 226 T^{2} - 1780 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 141 T^{2} + 477 T^{3} + 12549 T^{4} + 23763 T^{5} + 704969 T^{6} \))(\( 1 - 27 T + 489 T^{2} - 5353 T^{3} + 43521 T^{4} - 213867 T^{5} + 704969 T^{6} \))(\( 1 - 9 T + 201 T^{2} - 1685 T^{3} + 17889 T^{4} - 71289 T^{5} + 704969 T^{6} \))(\( 1 + 3 T - 17 T^{2} - 1617 T^{3} - 1513 T^{4} + 23763 T^{5} + 704969 T^{6} \))(\( 1 + 9 T + 186 T^{2} + 2446 T^{3} + 17334 T^{4} + 217694 T^{5} + 1473306 T^{6} + 6344721 T^{7} + 62742241 T^{8} \))(\( 1 - 5 T + 391 T^{2} - 1393 T^{3} + 64134 T^{4} - 168644 T^{5} + 5707926 T^{6} - 11033953 T^{7} + 275642879 T^{8} - 313711205 T^{9} + 5584059449 T^{10} \))(\( 1 - 3 T + 212 T^{2} + 432 T^{3} + 27629 T^{4} + 18147 T^{5} + 3437316 T^{6} + 1615083 T^{7} + 218849309 T^{8} + 304546608 T^{9} + 13301355092 T^{10} - 16752178347 T^{11} + 496981290961 T^{12} \))(\( 1 - 2 T + 145 T^{2} + 98 T^{3} - 675 T^{4} + 113172 T^{5} - 1106865 T^{6} + 10072308 T^{7} - 5346675 T^{8} + 69086962 T^{9} + 9097624945 T^{10} - 11168118898 T^{11} + 496981290961 T^{12} \))(\( 1 + 2 T + 145 T^{2} - 98 T^{3} - 675 T^{4} - 113172 T^{5} - 1106865 T^{6} - 10072308 T^{7} - 5346675 T^{8} - 69086962 T^{9} + 9097624945 T^{10} + 11168118898 T^{11} + 496981290961 T^{12} \))(\( 1 + 5 T + 427 T^{2} + 1871 T^{3} + 90273 T^{4} + 340543 T^{5} + 11970235 T^{6} + 38144970 T^{7} + 1065350915 T^{8} + 2697441103 T^{9} + 63639666537 T^{10} + 117390732911 T^{11} + 2384393384723 T^{12} + 2484906454805 T^{13} + 44231334895529 T^{14} \))(\( 1 - 17 T + 447 T^{2} - 7166 T^{3} + 104309 T^{4} - 1338359 T^{5} + 14938191 T^{6} - 148859160 T^{7} + 1329498999 T^{8} - 10601141639 T^{9} + 73534611421 T^{10} - 449610899006 T^{11} + 2496074573703 T^{12} - 8448681946337 T^{13} + 44231334895529 T^{14} \))(\( 1 - 54 T + 1663 T^{2} - 36914 T^{3} + 650736 T^{4} - 9564914 T^{5} + 121318598 T^{6} - 1354932734 T^{7} + 13504663096 T^{8} - 120589013326 T^{9} + 960964614758 T^{10} - 6742967857666 T^{11} + 40828634939376 T^{12} - 206129970500386 T^{13} + 826479886868143 T^{14} - 2388492084358566 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 54 T + 1663 T^{2} + 36914 T^{3} + 650736 T^{4} + 9564914 T^{5} + 121318598 T^{6} + 1354932734 T^{7} + 13504663096 T^{8} + 120589013326 T^{9} + 960964614758 T^{10} + 6742967857666 T^{11} + 40828634939376 T^{12} + 206129970500386 T^{13} + 826479886868143 T^{14} + 2388492084358566 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 292 T^{2} - 784 T^{3} + 42156 T^{4} - 178408 T^{5} + 4613000 T^{6} - 19010800 T^{7} + 446258050 T^{8} - 1691961200 T^{9} + 36539573000 T^{10} - 125772109352 T^{11} + 2644961911596 T^{12} - 4377902608016 T^{13} + 145118536960612 T^{14} + 3936588805702081 T^{16} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 16 T + 206 T^{2} + 1552 T^{3} + 9409 T^{4} \))(\( 1 - 24 T + 318 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( 1 + 16 T + 206 T^{2} + 1552 T^{3} + 9409 T^{4} \))(\( 1 + 27 T + 507 T^{2} + 5697 T^{3} + 49179 T^{4} + 254043 T^{5} + 912673 T^{6} \))(\( 1 - 3 T + 203 T^{2} - 289 T^{3} + 19691 T^{4} - 28227 T^{5} + 912673 T^{6} \))(\( 1 + 27 T + 409 T^{2} + 4467 T^{3} + 39673 T^{4} + 254043 T^{5} + 912673 T^{6} \))(\( 1 + T + 173 T^{2} + 413 T^{3} + 16781 T^{4} + 9409 T^{5} + 912673 T^{6} \))(\( 1 + 29 T + 630 T^{2} + 8898 T^{3} + 102354 T^{4} + 863106 T^{5} + 5927670 T^{6} + 26467517 T^{7} + 88529281 T^{8} \))(\( 1 + 11 T + 347 T^{2} + 3389 T^{3} + 60520 T^{4} + 444664 T^{5} + 5870440 T^{6} + 31887101 T^{7} + 316697531 T^{8} + 973822091 T^{9} + 8587340257 T^{10} \))(\( 1 - 3 T + 506 T^{2} - 1466 T^{3} + 113327 T^{4} - 280531 T^{5} + 14292972 T^{6} - 27211507 T^{7} + 1066293743 T^{8} - 1337978618 T^{9} + 44795816186 T^{10} - 25762020771 T^{11} + 832972004929 T^{12} \))(\( 1 + 6 T + 283 T^{2} + 2374 T^{3} + 46809 T^{4} + 416110 T^{5} + 5208643 T^{6} + 40362670 T^{7} + 440425881 T^{8} + 2166685702 T^{9} + 25053786523 T^{10} + 51524041542 T^{11} + 832972004929 T^{12} \))(\( 1 + 6 T + 283 T^{2} + 2374 T^{3} + 46809 T^{4} + 416110 T^{5} + 5208643 T^{6} + 40362670 T^{7} + 440425881 T^{8} + 2166685702 T^{9} + 25053786523 T^{10} + 51524041542 T^{11} + 832972004929 T^{12} \))(\( 1 - 23 T + 477 T^{2} - 5871 T^{3} + 66981 T^{4} - 495073 T^{5} + 4100541 T^{6} - 25668914 T^{7} + 397752477 T^{8} - 4658141857 T^{9} + 61131750213 T^{10} - 519755408751 T^{11} + 4096161302589 T^{12} - 19158356113367 T^{13} + 80798284478113 T^{14} \))(\( 1 - 12 T + 251 T^{2} - 2024 T^{3} + 40393 T^{4} - 296116 T^{5} + 5234683 T^{6} - 36247216 T^{7} + 507764251 T^{8} - 2786155444 T^{9} + 36865600489 T^{10} - 179183264744 T^{11} + 2155422404507 T^{12} - 9995664059148 T^{13} + 80798284478113 T^{14} \))(\( 1 - 10 T + 597 T^{2} - 5938 T^{3} + 165132 T^{4} - 1584880 T^{5} + 28137136 T^{6} - 245736968 T^{7} + 3263822916 T^{8} - 23836485896 T^{9} + 264742312624 T^{10} - 1446477184240 T^{11} + 14619017230092 T^{12} - 50991626446066 T^{13} + 497284286942613 T^{14} - 807982844781130 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 10 T + 597 T^{2} - 5938 T^{3} + 165132 T^{4} - 1584880 T^{5} + 28137136 T^{6} - 245736968 T^{7} + 3263822916 T^{8} - 23836485896 T^{9} + 264742312624 T^{10} - 1446477184240 T^{11} + 14619017230092 T^{12} - 50991626446066 T^{13} + 497284286942613 T^{14} - 807982844781130 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 12 T + 536 T^{2} - 3284 T^{3} + 94044 T^{4} + 59460 T^{5} + 5663016 T^{6} + 95080348 T^{7} + 130249670 T^{8} + 9222793756 T^{9} + 53283317544 T^{10} + 54267536580 T^{11} + 8325647702364 T^{12} - 28200825403988 T^{13} + 446472994641944 T^{14} - 969579413737356 T^{15} + 7837433594376961 T^{16} \))
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