Properties

Label 1008.2.r
Level 1008
Weight 2
Character orbit r
Rep. character \(\chi_{1008}(337,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 72
Newform subspaces 14
Sturm bound 384
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 408 72 336
Cusp forms 360 72 288
Eisenstein series 48 0 48

Trace form

\( 72q + 4q^{9} + O(q^{10}) \) \( 72q + 4q^{9} - 12q^{11} - 12q^{15} + 8q^{17} + 12q^{23} - 36q^{25} + 36q^{27} + 12q^{33} + 24q^{35} + 36q^{39} + 4q^{41} + 12q^{47} - 36q^{49} - 12q^{51} - 4q^{57} - 12q^{59} - 8q^{65} - 80q^{71} + 24q^{73} - 68q^{75} - 20q^{81} + 4q^{87} - 16q^{89} - 24q^{93} + 32q^{95} - 12q^{97} + 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.2.r.a \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-2\) \(-1\) \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
1008.2.r.b \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-2\) \(1\) \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1008.2.r.c \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(1\) \(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1008.2.r.d \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1008.2.r.e \(4\) \(8.049\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-4\) \(-2\) \(-2\) \(q+(-1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1008.2.r.f \(4\) \(8.049\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(-3\) \(2\) \(q+(\beta _{2}+\beta _{3})q^{3}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots\)
1008.2.r.g \(6\) \(8.049\) 6.0.309123.1 None \(0\) \(-2\) \(3\) \(3\) \(q+(-1+\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1008.2.r.h \(6\) \(8.049\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(3\) \(q+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{3}+(-1+\zeta_{18}+\zeta_{18}^{5})q^{5}+\cdots\)
1008.2.r.i \(6\) \(8.049\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(3\) \(q+(\zeta_{18}^{4}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
1008.2.r.j \(6\) \(8.049\) 6.0.309123.1 None \(0\) \(2\) \(-1\) \(-3\) \(q+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
1008.2.r.k \(6\) \(8.049\) 6.0.309123.1 None \(0\) \(4\) \(5\) \(-3\) \(q+(1-\beta _{5})q^{3}+(2+\beta _{2}+2\beta _{4}-\beta _{5})q^{5}+\cdots\)
1008.2.r.l \(8\) \(8.049\) 8.0.2091141441.1 None \(0\) \(1\) \(-3\) \(-4\) \(q+(-\beta _{1}+\beta _{6})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1008.2.r.m \(8\) \(8.049\) 8.0.508277025.1 None \(0\) \(4\) \(4\) \(4\) \(q+(1-\beta _{2})q^{3}+(\beta _{2}-\beta _{3}+\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots\)
1008.2.r.n \(10\) \(8.049\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(-3\) \(-5\) \(q-\beta _{6}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 + 2 T + 4 T^{2} + 3 T^{3} + 12 T^{4} + 18 T^{5} + 27 T^{6} \))(\( 1 + 9 T^{3} + 27 T^{6} \))(\( 1 - 9 T^{3} + 27 T^{6} \))(\( 1 - 2 T - 2 T^{2} + 9 T^{3} - 6 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 - 4 T + 10 T^{2} - 21 T^{3} + 30 T^{4} - 36 T^{5} + 27 T^{6} \))(\( 1 - T + T^{2} + 3 T^{3} + 3 T^{4} + 9 T^{5} + 9 T^{6} - 27 T^{7} + 81 T^{8} \))(\( 1 - 4 T + 3 T^{2} + 11 T^{3} - 32 T^{4} + 33 T^{5} + 27 T^{6} - 108 T^{7} + 81 T^{8} \))(\( 1 - 3 T^{3} + 3 T^{4} + 18 T^{5} + 9 T^{6} - 27 T^{7} + 243 T^{10} \))
$5$ (\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} - 10 T^{3} - 20 T^{4} - 50 T^{5} - 25 T^{6} + 250 T^{7} + 625 T^{8} \))(\( ( 1 + 3 T + 5 T^{2} )^{2}( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} ) \))(\( 1 - 3 T + 15 T^{3} - 27 T^{4} + 6 T^{5} + 61 T^{6} + 30 T^{7} - 675 T^{8} + 1875 T^{9} - 9375 T^{11} + 15625 T^{12} \))(\( 1 + 3 T - 6 T^{2} - 9 T^{3} + 69 T^{4} + 30 T^{5} - 371 T^{6} + 150 T^{7} + 1725 T^{8} - 1125 T^{9} - 3750 T^{10} + 9375 T^{11} + 15625 T^{12} \))(\( 1 - 3 T - 6 T^{2} + 13 T^{3} + 63 T^{4} - 60 T^{5} - 259 T^{6} - 300 T^{7} + 1575 T^{8} + 1625 T^{9} - 3750 T^{10} - 9375 T^{11} + 15625 T^{12} \))(\( 1 + T - 10 T^{2} - 7 T^{3} + 57 T^{4} + 14 T^{5} - 299 T^{6} + 70 T^{7} + 1425 T^{8} - 875 T^{9} - 6250 T^{10} + 3125 T^{11} + 15625 T^{12} \))(\( 1 - 5 T + 8 T^{2} - 7 T^{3} + 9 T^{4} + 62 T^{5} - 299 T^{6} + 310 T^{7} + 225 T^{8} - 875 T^{9} + 5000 T^{10} - 15625 T^{11} + 15625 T^{12} \))(\( 1 + 3 T - 3 T^{2} - 36 T^{3} - 32 T^{4} + 204 T^{5} + 540 T^{6} - 597 T^{7} - 3831 T^{8} - 2985 T^{9} + 13500 T^{10} + 25500 T^{11} - 20000 T^{12} - 112500 T^{13} - 46875 T^{14} + 234375 T^{15} + 390625 T^{16} \))(\( 1 - 4 T + 5 T^{2} + 18 T^{3} - 94 T^{4} + 232 T^{5} - 110 T^{6} - 1011 T^{7} + 3826 T^{8} - 5055 T^{9} - 2750 T^{10} + 29000 T^{11} - 58750 T^{12} + 56250 T^{13} + 78125 T^{14} - 312500 T^{15} + 390625 T^{16} \))(\( 1 + 3 T - 3 T^{2} - 16 T^{3} - 25 T^{4} - 63 T^{5} - 19 T^{6} + 277 T^{7} + 775 T^{8} + 451 T^{9} - 1814 T^{10} + 2255 T^{11} + 19375 T^{12} + 34625 T^{13} - 11875 T^{14} - 196875 T^{15} - 390625 T^{16} - 1250000 T^{17} - 1171875 T^{18} + 5859375 T^{19} + 9765625 T^{20} \))
$7$ (\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 + T + T^{2} )^{5} \))
$11$ (\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( ( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} )^{2} \))(\( 1 - 3 T - 7 T^{2} + 18 T^{3} + 36 T^{4} + 198 T^{5} - 847 T^{6} - 3993 T^{7} + 14641 T^{8} \))(\( 1 + 6 T - 30 T^{3} + 162 T^{4} + 402 T^{5} - 821 T^{6} + 4422 T^{7} + 19602 T^{8} - 39930 T^{9} + 966306 T^{11} + 1771561 T^{12} \))(\( 1 - 6 T - 6 T^{2} + 18 T^{3} + 492 T^{4} - 852 T^{5} - 2873 T^{6} - 9372 T^{7} + 59532 T^{8} + 23958 T^{9} - 87846 T^{10} - 966306 T^{11} + 1771561 T^{12} \))(\( 1 - 24 T^{2} + 18 T^{3} + 312 T^{4} - 216 T^{5} - 3593 T^{6} - 2376 T^{7} + 37752 T^{8} + 23958 T^{9} - 351384 T^{10} + 1771561 T^{12} \))(\( 1 - 2 T - 4 T^{2} - 46 T^{3} + 6 T^{4} + 230 T^{5} + 1699 T^{6} + 2530 T^{7} + 726 T^{8} - 61226 T^{9} - 58564 T^{10} - 322102 T^{11} + 1771561 T^{12} \))(\( 1 + 2 T - 10 T^{2} + 34 T^{3} + 48 T^{4} - 416 T^{5} + 31 T^{6} - 4576 T^{7} + 5808 T^{8} + 45254 T^{9} - 146410 T^{10} + 322102 T^{11} + 1771561 T^{12} \))(\( 1 + 7 T - 2 T^{2} - 81 T^{3} + 203 T^{4} + 1468 T^{5} - 675 T^{6} - 3769 T^{7} + 21730 T^{8} - 41459 T^{9} - 81675 T^{10} + 1953908 T^{11} + 2972123 T^{12} - 13045131 T^{13} - 3543122 T^{14} + 136410197 T^{15} + 214358881 T^{16} \))(\( 1 - 6 T + T^{2} + 24 T^{3} + 49 T^{4} + 306 T^{5} - 2153 T^{6} + 1236 T^{7} + 7063 T^{8} + 13596 T^{9} - 260513 T^{10} + 407286 T^{11} + 717409 T^{12} + 3865224 T^{13} + 1771561 T^{14} - 116923026 T^{15} + 214358881 T^{16} \))(\( 1 + 4 T - 6 T^{2} + 10 T^{3} + 191 T^{4} - 240 T^{5} + 1529 T^{6} + 16178 T^{7} - 5837 T^{8} - 14002 T^{9} + 502605 T^{10} - 154022 T^{11} - 706277 T^{12} + 21532918 T^{13} + 22386089 T^{14} - 38652240 T^{15} + 338368151 T^{16} + 194871710 T^{17} - 1286153286 T^{18} + 9431790764 T^{19} + 25937424601 T^{20} \))
$13$ (\( 1 - 6 T + 23 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 23 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 23 T^{2} + 78 T^{3} + 169 T^{4} \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 2 T^{2} - 165 T^{4} - 338 T^{6} + 28561 T^{8} \))(\( ( 1 - 5 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2} \))(\( ( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} )^{3} \))(\( 1 - 3 T + 3 T^{2} - 76 T^{3} + 45 T^{4} + 135 T^{5} + 3246 T^{6} + 1755 T^{7} + 7605 T^{8} - 166972 T^{9} + 85683 T^{10} - 1113879 T^{11} + 4826809 T^{12} \))(\( 1 - 3 T - 21 T^{2} + 60 T^{3} + 285 T^{4} - 417 T^{5} - 3202 T^{6} - 5421 T^{7} + 48165 T^{8} + 131820 T^{9} - 599781 T^{10} - 1113879 T^{11} + 4826809 T^{12} \))(\( 1 + 3 T + 3 T^{2} - 84 T^{3} - 195 T^{4} + 345 T^{5} + 5006 T^{6} + 4485 T^{7} - 32955 T^{8} - 184548 T^{9} + 85683 T^{10} + 1113879 T^{11} + 4826809 T^{12} \))(\( ( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} )^{3} \))(\( 1 - 3 T - 32 T^{2} + 57 T^{3} + 673 T^{4} - 432 T^{5} - 11810 T^{6} + 2142 T^{7} + 166240 T^{8} + 27846 T^{9} - 1995890 T^{10} - 949104 T^{11} + 19221553 T^{12} + 21163701 T^{13} - 154457888 T^{14} - 188245551 T^{15} + 815730721 T^{16} \))(\( 1 + 3 T - 16 T^{2} + 39 T^{3} + 337 T^{4} - 720 T^{5} + 2222 T^{6} + 11778 T^{7} - 44096 T^{8} + 153114 T^{9} + 375518 T^{10} - 1581840 T^{11} + 9625057 T^{12} + 14480427 T^{13} - 77228944 T^{14} + 188245551 T^{15} + 815730721 T^{16} \))(\( 1 + 3 T - 31 T^{2} - 106 T^{3} + 402 T^{4} + 1426 T^{5} - 5437 T^{6} - 15135 T^{7} + 85123 T^{8} + 101952 T^{9} - 1104756 T^{10} + 1325376 T^{11} + 14385787 T^{12} - 33251595 T^{13} - 155286157 T^{14} + 529463818 T^{15} + 1940377218 T^{16} - 6651342802 T^{17} - 25287652351 T^{18} + 31813498119 T^{19} + 137858491849 T^{20} \))
$17$ (\( ( 1 + 5 T + 17 T^{2} )^{2} \))(\( ( 1 - 7 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{4} \))(\( ( 1 + 3 T + 28 T^{2} + 51 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 + 18 T^{2} + 9 T^{3} + 306 T^{4} + 4913 T^{6} )^{2} \))(\( ( 1 - 6 T + 60 T^{2} - 207 T^{3} + 1020 T^{4} - 1734 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 6 T + 54 T^{2} - 203 T^{3} + 918 T^{4} - 1734 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 2 T + 32 T^{2} - 21 T^{3} + 544 T^{4} - 578 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 12 T + 90 T^{2} + 435 T^{3} + 1530 T^{4} + 3468 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} - 189 T^{3} + 807 T^{4} - 3213 T^{5} + 11849 T^{6} - 14739 T^{7} + 83521 T^{8} )^{2} \))(\( ( 1 + 8 T + 35 T^{2} + 167 T^{3} + 886 T^{4} + 2839 T^{5} + 10115 T^{6} + 39304 T^{7} + 83521 T^{8} )^{2} \))(\( ( 1 + 46 T^{2} - 9 T^{3} + 1261 T^{4} - 198 T^{5} + 21437 T^{6} - 2601 T^{7} + 225998 T^{8} + 1419857 T^{10} )^{2} \))
$19$ (\( ( 1 - 7 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 - 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 10 T + 57 T^{2} + 190 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 5 T + 19 T^{2} )^{4} \))(\( ( 1 + 3 T + 21 T^{2} + 65 T^{3} + 399 T^{4} + 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 3 T + 51 T^{2} - 97 T^{3} + 969 T^{4} - 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 9 T + 63 T^{2} - 323 T^{3} + 1197 T^{4} - 3249 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 + 3 T + 33 T^{2} + 35 T^{3} + 627 T^{4} + 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 3 T + 51 T^{2} - 107 T^{3} + 969 T^{4} - 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 4 T + 49 T^{2} - 193 T^{3} + 1297 T^{4} - 3667 T^{5} + 17689 T^{6} - 27436 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - 2 T + 55 T^{2} - 41 T^{3} + 1309 T^{4} - 779 T^{5} + 19855 T^{6} - 13718 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 + T + 42 T^{2} + 66 T^{3} + 1281 T^{4} + 1209 T^{5} + 24339 T^{6} + 23826 T^{7} + 288078 T^{8} + 130321 T^{9} + 2476099 T^{10} )^{2} \))
$23$ (\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4} \))(\( ( 1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 9 T + 23 T^{2} )^{2}( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} ) \))(\( 1 + 6 T - 18 T^{2} - 30 T^{3} + 612 T^{4} - 2172 T^{5} - 30449 T^{6} - 49956 T^{7} + 323748 T^{8} - 365010 T^{9} - 5037138 T^{10} + 38618058 T^{11} + 148035889 T^{12} \))(\( 1 - 12 T + 48 T^{2} - 54 T^{3} + 420 T^{4} - 6060 T^{5} + 37591 T^{6} - 139380 T^{7} + 222180 T^{8} - 657018 T^{9} + 13432368 T^{10} - 77236116 T^{11} + 148035889 T^{12} \))(\( 1 - 6 T + 12 T^{2} - 130 T^{3} - 18 T^{4} + 3282 T^{5} - 7909 T^{6} + 75486 T^{7} - 9522 T^{8} - 1581710 T^{9} + 3358092 T^{10} - 38618058 T^{11} + 148035889 T^{12} \))(\( 1 - 14 T + 74 T^{2} - 358 T^{3} + 2628 T^{4} - 11188 T^{5} + 33943 T^{6} - 257324 T^{7} + 1390212 T^{8} - 4355786 T^{9} + 20708234 T^{10} - 90108802 T^{11} + 148035889 T^{12} \))(\( 1 - 36 T^{2} + 18 T^{3} + 468 T^{4} - 324 T^{5} - 5393 T^{6} - 7452 T^{7} + 247572 T^{8} + 219006 T^{9} - 10074276 T^{10} + 148035889 T^{12} \))(\( 1 + 2 T - 59 T^{2} - 192 T^{3} + 1775 T^{4} + 6170 T^{5} - 33567 T^{6} - 71510 T^{7} + 655807 T^{8} - 1644730 T^{9} - 17756943 T^{10} + 75070390 T^{11} + 496717775 T^{12} - 1235777856 T^{13} - 8734117451 T^{14} + 6809650894 T^{15} + 78310985281 T^{16} \))(\( 1 - 5 T - 28 T^{2} + 177 T^{3} - 25 T^{4} + 494 T^{5} - 12137 T^{6} - 44331 T^{7} + 708646 T^{8} - 1019613 T^{9} - 6420473 T^{10} + 6010498 T^{11} - 6996025 T^{12} + 1139232711 T^{13} - 4145004892 T^{14} - 17024127235 T^{15} + 78310985281 T^{16} \))(\( 1 + 8 T + 9 T^{2} + 222 T^{3} + 2650 T^{4} + 9138 T^{5} + 54826 T^{6} + 441030 T^{7} + 1653286 T^{8} + 8929410 T^{9} + 60424408 T^{10} + 205376430 T^{11} + 874588294 T^{12} + 5366012010 T^{13} + 15342562666 T^{14} + 58815302334 T^{15} + 392295105850 T^{16} + 755871249234 T^{17} + 704798867529 T^{18} + 14409221291704 T^{19} + 41426511213649 T^{20} \))
$29$ (\( 1 - 4 T - 13 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 - 4 T - 13 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 + 2 T - 25 T^{2} + 58 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 4 T - 22 T^{2} + 80 T^{3} + 139 T^{4} + 2320 T^{5} - 18502 T^{6} - 97556 T^{7} + 707281 T^{8} \))(\( 1 - 6 T + 2 T^{2} + 144 T^{3} - 729 T^{4} + 4176 T^{5} + 1682 T^{6} - 146334 T^{7} + 707281 T^{8} \))(\( 1 - 15 T + 90 T^{2} - 411 T^{3} + 2205 T^{4} - 4110 T^{5} - 17723 T^{6} - 119190 T^{7} + 1854405 T^{8} - 10023879 T^{9} + 63655290 T^{10} - 307667235 T^{11} + 594823321 T^{12} \))(\( 1 + 9 T + 30 T^{2} + 81 T^{3} - 579 T^{4} - 9414 T^{5} - 59051 T^{6} - 273006 T^{7} - 486939 T^{8} + 1975509 T^{9} + 21218430 T^{10} + 184600341 T^{11} + 594823321 T^{12} \))(\( 1 - 3 T - 42 T^{2} + 157 T^{3} + 657 T^{4} - 1554 T^{5} - 10195 T^{6} - 45066 T^{7} + 552537 T^{8} + 3829073 T^{9} - 29705802 T^{10} - 61533447 T^{11} + 594823321 T^{12} \))(\( 1 + T - 46 T^{2} + 149 T^{3} + 897 T^{4} - 4282 T^{5} - 13523 T^{6} - 124178 T^{7} + 754377 T^{8} + 3633961 T^{9} - 32534926 T^{10} + 20511149 T^{11} + 594823321 T^{12} \))(\( 1 + T - 82 T^{2} - 31 T^{3} + 4425 T^{4} + 758 T^{5} - 148595 T^{6} + 21982 T^{7} + 3721425 T^{8} - 756059 T^{9} - 57997042 T^{10} + 20511149 T^{11} + 594823321 T^{12} \))(\( 1 + 9 T + 13 T^{2} + 72 T^{3} + 904 T^{4} + 2970 T^{5} + 29086 T^{6} + 17613 T^{7} - 1095047 T^{8} + 510777 T^{9} + 24461326 T^{10} + 72435330 T^{11} + 639382024 T^{12} + 1476802728 T^{13} + 7732703173 T^{14} + 155248886781 T^{15} + 500246412961 T^{16} \))(\( 1 - T - 49 T^{2} + 294 T^{3} + 1136 T^{4} - 11204 T^{5} + 49096 T^{6} + 227337 T^{7} - 2198075 T^{8} + 6592773 T^{9} + 41289736 T^{10} - 273254356 T^{11} + 803471216 T^{12} + 6030277806 T^{13} - 29146342729 T^{14} - 17249876309 T^{15} + 500246412961 T^{16} \))(\( 1 + 9 T - 52 T^{2} - 657 T^{3} + 1944 T^{4} + 29007 T^{5} - 46389 T^{6} - 788049 T^{7} + 920775 T^{8} + 10497078 T^{9} - 9302769 T^{10} + 304415262 T^{11} + 774371775 T^{12} - 19219727061 T^{13} - 32810058309 T^{14} + 594966899043 T^{15} + 1156336536024 T^{16} - 11333168735013 T^{17} - 26012813473972 T^{18} + 130564313782821 T^{19} + 420707233300201 T^{20} \))
$31$ (\( 1 + 6 T + 5 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} \))(\( ( 1 - 6 T + 5 T^{2} - 186 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} )^{2} \))(\( 1 + 3 T - 6 T^{2} - 221 T^{3} - 639 T^{4} + 2088 T^{5} + 61647 T^{6} + 64728 T^{7} - 614079 T^{8} - 6583811 T^{9} - 5541126 T^{10} + 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 3 T - 6 T^{2} + 319 T^{3} + 171 T^{4} - 1962 T^{5} + 62727 T^{6} - 60822 T^{7} + 164331 T^{8} + 9503329 T^{9} - 5541126 T^{10} + 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 9 T - 18 T^{2} - 79 T^{3} + 2367 T^{4} + 1422 T^{5} - 86865 T^{6} + 44082 T^{7} + 2274687 T^{8} - 2353489 T^{9} - 16623378 T^{10} + 257662359 T^{11} + 887503681 T^{12} \))(\( 1 + 3 T - 48 T^{2} - 147 T^{3} + 1005 T^{4} + 1344 T^{5} - 24505 T^{6} + 41664 T^{7} + 965805 T^{8} - 4379277 T^{9} - 44329008 T^{10} + 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 3 T - 60 T^{2} - 219 T^{3} + 1983 T^{4} + 4746 T^{5} - 51289 T^{6} + 147126 T^{7} + 1905663 T^{8} - 6524229 T^{9} - 55411260 T^{10} + 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 3 T - 41 T^{2} - 354 T^{3} - 128 T^{4} + 9180 T^{5} + 42568 T^{6} - 75933 T^{7} - 1254023 T^{8} - 2353923 T^{9} + 40907848 T^{10} + 273481380 T^{11} - 118210688 T^{12} - 10134719454 T^{13} - 36387650921 T^{14} + 82537842333 T^{15} + 852891037441 T^{16} \))(\( 1 + 11 T - 39 T^{2} - 356 T^{3} + 5954 T^{4} + 25902 T^{5} - 215174 T^{6} - 3835 T^{7} + 11112081 T^{8} - 118885 T^{9} - 206782214 T^{10} + 771646482 T^{11} + 5498644034 T^{12} - 10191977756 T^{13} - 34612643559 T^{14} + 302638755221 T^{15} + 852891037441 T^{16} \))(\( 1 - 3 T - 106 T^{2} + 157 T^{3} + 6498 T^{4} - 2989 T^{5} - 283525 T^{6} - 3627 T^{7} + 9910699 T^{8} + 942522 T^{9} - 316500783 T^{10} + 29218182 T^{11} + 9524181739 T^{12} - 108051957 T^{13} - 261841291525 T^{14} - 85572532339 T^{15} + 5766998919138 T^{16} + 4319480415427 T^{17} - 90406449968746 T^{18} - 79318866482013 T^{19} + 819628286980801 T^{20} \))
$37$ (\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T - 18 T^{2} - 148 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{4} \))(\( ( 1 + 3 T + 33 T^{2} + 115 T^{3} + 1221 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 3 T + 33 T^{2} - 101 T^{3} + 1221 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 15 T + 165 T^{2} + 1167 T^{3} + 6105 T^{4} + 20535 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 3 T + 81 T^{2} + 199 T^{3} + 2997 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 3 T + 57 T^{2} + 303 T^{3} + 2109 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 3 T + 140 T^{2} - 324 T^{3} + 7620 T^{4} - 11988 T^{5} + 191660 T^{6} - 151959 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 27 T + 412 T^{2} - 4104 T^{3} + 29436 T^{4} - 151848 T^{5} + 564028 T^{6} - 1367631 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 3 T + 103 T^{2} + 197 T^{3} + 6112 T^{4} + 11312 T^{5} + 226144 T^{6} + 269693 T^{7} + 5217259 T^{8} + 5622483 T^{9} + 69343957 T^{10} )^{2} \))
$41$ (\( 1 + 3 T - 32 T^{2} + 123 T^{3} + 1681 T^{4} \))(\( 1 + 7 T + 8 T^{2} + 287 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 23 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 - 41 T^{2} + 1681 T^{4} \))(\( 1 + 14 T^{2} - 1485 T^{4} + 23534 T^{6} + 2825761 T^{8} \))(\( 1 + 15 T + 95 T^{2} + 720 T^{3} + 5994 T^{4} + 29520 T^{5} + 159695 T^{6} + 1033815 T^{7} + 2825761 T^{8} \))(\( 1 - 6 T - 90 T^{2} + 210 T^{3} + 7812 T^{4} - 8952 T^{5} - 340301 T^{6} - 367032 T^{7} + 13131972 T^{8} + 14473410 T^{9} - 254318490 T^{10} - 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 114 T^{2} - 18 T^{3} + 8322 T^{4} + 1026 T^{5} - 394913 T^{6} + 42066 T^{7} + 13989282 T^{8} - 1240578 T^{9} - 322136754 T^{10} + 4750104241 T^{12} \))(\( 1 + 6 T - 72 T^{2} - 298 T^{3} + 4398 T^{4} + 8034 T^{5} - 177169 T^{6} + 329394 T^{7} + 7393038 T^{8} - 20538458 T^{9} - 203454792 T^{10} + 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 90 T^{2} + 18 T^{3} + 4410 T^{4} - 810 T^{5} - 194177 T^{6} - 33210 T^{7} + 7413210 T^{8} + 1240578 T^{9} - 254318490 T^{10} + 4750104241 T^{12} \))(\( 1 - 22 T + 206 T^{2} - 1802 T^{3} + 18432 T^{4} - 135116 T^{5} + 808243 T^{6} - 5539756 T^{7} + 30984192 T^{8} - 124195642 T^{9} + 582106766 T^{10} - 2548836422 T^{11} + 4750104241 T^{12} \))(\( 1 - 9 T - 36 T^{2} + 381 T^{3} + 895 T^{4} + 852 T^{5} - 99027 T^{6} - 57981 T^{7} + 4458864 T^{8} - 2377221 T^{9} - 166464387 T^{10} + 58720692 T^{11} + 2529056095 T^{12} + 44141212581 T^{13} - 171003752676 T^{14} - 1752788464929 T^{15} + 7984925229121 T^{16} \))(\( 1 - 2 T - 37 T^{2} + 432 T^{3} - 841 T^{4} - 13042 T^{5} + 100489 T^{6} + 72294 T^{7} - 3776099 T^{8} + 2964054 T^{9} + 168922009 T^{10} - 898867682 T^{11} - 2376465001 T^{12} + 50049878832 T^{13} - 175753856917 T^{14} - 389508547762 T^{15} + 7984925229121 T^{16} \))(\( 1 + 12 T - 30 T^{2} - 790 T^{3} - 277 T^{4} + 13968 T^{5} - 140563 T^{6} - 610562 T^{7} + 9173539 T^{8} + 24360490 T^{9} - 273097535 T^{10} + 998780090 T^{11} + 15420719059 T^{12} - 42080543602 T^{13} - 397197443443 T^{14} + 1618279415568 T^{15} - 1315778874757 T^{16} - 153855876365990 T^{17} - 239547756873630 T^{18} + 3928583212727532 T^{19} + 13422659310152401 T^{20} \))
$43$ (\( 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} \))(\( 1 - 11 T + 78 T^{2} - 473 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 57 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 - 2 T - 39 T^{2} - 86 T^{3} + 1849 T^{4} \))(\( 1 - 4 T - 50 T^{2} + 80 T^{3} + 1819 T^{4} + 3440 T^{5} - 92450 T^{6} - 318028 T^{7} + 3418801 T^{8} \))(\( 1 - T - 11 T^{2} + 74 T^{3} - 1748 T^{4} + 3182 T^{5} - 20339 T^{6} - 79507 T^{7} + 3418801 T^{8} \))(\( 1 - 3 T - 12 T^{2} - 473 T^{3} + 153 T^{4} + 4176 T^{5} + 165435 T^{6} + 179568 T^{7} + 282897 T^{8} - 37606811 T^{9} - 41025612 T^{10} - 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 + 3 T - 114 T^{2} - 149 T^{3} + 9063 T^{4} + 5670 T^{5} - 441093 T^{6} + 243810 T^{7} + 16757487 T^{8} - 11846543 T^{9} - 389743314 T^{10} + 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 + 15 T + 42 T^{2} + 199 T^{3} + 6525 T^{4} + 24624 T^{5} - 76509 T^{6} + 1058832 T^{7} + 12064725 T^{8} + 15821893 T^{9} + 143589642 T^{10} + 2205126645 T^{11} + 6321363049 T^{12} \))(\( 1 - 3 T - 24 T^{2} + 979 T^{3} - 1947 T^{4} - 14820 T^{5} + 386067 T^{6} - 637260 T^{7} - 3600003 T^{8} + 77837353 T^{9} - 82051224 T^{10} - 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 + 3 T - 54 T^{2} - 569 T^{3} + 123 T^{4} + 13170 T^{5} + 115347 T^{6} + 566310 T^{7} + 227427 T^{8} - 45239483 T^{9} - 184615254 T^{10} + 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 + 8 T - 73 T^{2} - 914 T^{3} + 2642 T^{4} + 51508 T^{5} + 63012 T^{6} - 1050915 T^{7} - 5977292 T^{8} - 45189345 T^{9} + 116509188 T^{10} + 4095246556 T^{11} + 9032472242 T^{12} - 134365716902 T^{13} - 461459502577 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 - 11 T - 27 T^{2} + 596 T^{3} + 140 T^{4} - 2688 T^{5} - 152864 T^{6} - 330797 T^{7} + 13009029 T^{8} - 14224271 T^{9} - 282645536 T^{10} - 213714816 T^{11} + 478632140 T^{12} + 87617032028 T^{13} - 170676802323 T^{14} - 2990004722177 T^{15} + 11688200277601 T^{16} \))(\( 1 - 5 T - 88 T^{2} - 275 T^{3} + 6540 T^{4} + 38663 T^{5} - 127543 T^{6} - 2251353 T^{7} - 2752001 T^{8} + 27649602 T^{9} + 456453449 T^{10} + 1188932886 T^{11} - 5088449849 T^{12} - 178998322971 T^{13} - 436044135943 T^{14} + 5683787431709 T^{15} + 41341714340460 T^{16} - 74750118054425 T^{17} - 1028561624428888 T^{18} - 2512963059684215 T^{19} + 21611482313284249 T^{20} \))
$47$ (\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 2 T^{2} - 2205 T^{4} + 4418 T^{6} + 4879681 T^{8} \))(\( ( 1 - 47 T^{2} + 2209 T^{4} )^{2} \))(\( 1 + 15 T + 48 T^{2} - 3 T^{3} + 3075 T^{4} + 18798 T^{5} + 4399 T^{6} + 883506 T^{7} + 6792675 T^{8} - 311469 T^{9} + 234224688 T^{10} + 3440175105 T^{11} + 10779215329 T^{12} \))(\( 1 - 3 T - 78 T^{2} + 405 T^{3} + 2481 T^{4} - 11064 T^{5} - 57089 T^{6} - 520008 T^{7} + 5480529 T^{8} + 42048315 T^{9} - 380615118 T^{10} - 688035021 T^{11} + 10779215329 T^{12} \))(\( 1 - 9 T - 66 T^{2} + 371 T^{3} + 7077 T^{4} - 20028 T^{5} - 269497 T^{6} - 941316 T^{7} + 15633093 T^{8} + 38518333 T^{9} - 322058946 T^{10} - 2064105063 T^{11} + 10779215329 T^{12} \))(\( 1 - 21 T + 180 T^{2} - 1119 T^{3} + 10053 T^{4} - 100416 T^{5} + 788551 T^{6} - 4719552 T^{7} + 22207077 T^{8} - 116177937 T^{9} + 878342580 T^{10} - 4816245147 T^{11} + 10779215329 T^{12} \))(\( 1 + 9 T - 6 T^{2} - 531 T^{3} - 2433 T^{4} + 3438 T^{5} + 104623 T^{6} + 161586 T^{7} - 5374497 T^{8} - 55130013 T^{9} - 29278086 T^{10} + 2064105063 T^{11} + 10779215329 T^{12} \))(\( 1 + 3 T - 141 T^{2} - 486 T^{3} + 11422 T^{4} + 34152 T^{5} - 635364 T^{6} - 765849 T^{7} + 30578781 T^{8} - 35994903 T^{9} - 1403519076 T^{10} + 3545763096 T^{11} + 55735716382 T^{12} - 111461673402 T^{13} - 1519869361389 T^{14} + 1519869361389 T^{15} + 23811286661761 T^{16} \))(\( 1 + 7 T - 61 T^{2} + 174 T^{3} + 5108 T^{4} - 21898 T^{5} - 62918 T^{6} + 808359 T^{7} - 1538879 T^{8} + 37992873 T^{9} - 138985862 T^{10} - 2273516054 T^{11} + 24925410548 T^{12} + 39906031218 T^{13} - 657532135069 T^{14} + 3546361843241 T^{15} + 23811286661761 T^{16} \))(\( 1 + 3 T - 24 T^{2} - 751 T^{3} - 2770 T^{4} + 11169 T^{5} + 300305 T^{6} + 1566601 T^{7} - 499337 T^{8} - 58566752 T^{9} - 599985995 T^{10} - 2752637344 T^{11} - 1103035433 T^{12} + 162649215623 T^{13} + 1465392602705 T^{14} + 2561554383183 T^{15} - 29858426461330 T^{16} - 380473963467713 T^{17} - 571470879882264 T^{18} + 3357391419308301 T^{19} + 52599132235830049 T^{20} \))
$53$ (\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 4 T + 53 T^{2} )^{2} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 12 T + 118 T^{2} + 636 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 6 T + 82 T^{2} + 318 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 18 T + 198 T^{2} + 1521 T^{3} + 10494 T^{4} + 50562 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 - 6 T + 150 T^{2} - 639 T^{3} + 7950 T^{4} - 16854 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 6 T + 162 T^{2} + 617 T^{3} + 8586 T^{4} + 16854 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 - 6 T + 162 T^{2} - 627 T^{3} + 8586 T^{4} - 16854 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 18 T + 234 T^{2} + 1917 T^{3} + 12402 T^{4} + 50562 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} - 621 T^{3} + 4704 T^{4} - 32913 T^{5} + 165731 T^{6} - 893262 T^{7} + 7890481 T^{8} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} - 197 T^{3} + 2722 T^{4} - 10441 T^{5} + 233147 T^{6} + 595508 T^{7} + 7890481 T^{8} )^{2} \))(\( ( 1 - 30 T + 580 T^{2} - 7683 T^{3} + 79903 T^{4} - 646182 T^{5} + 4234859 T^{6} - 21581547 T^{7} + 86348660 T^{8} - 236714430 T^{9} + 418195493 T^{10} )^{2} \))
$59$ (\( 1 + 7 T - 10 T^{2} + 413 T^{3} + 3481 T^{4} \))(\( 1 - 9 T + 22 T^{2} - 531 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( ( 1 + 2 T - 55 T^{2} + 118 T^{3} + 3481 T^{4} )^{2} \))(\( 1 + 3 T - 37 T^{2} - 216 T^{3} - 1896 T^{4} - 12744 T^{5} - 128797 T^{6} + 616137 T^{7} + 12117361 T^{8} \))(\( 1 + 3 T - 114 T^{2} - 501 T^{3} + 6567 T^{4} + 20406 T^{5} - 323957 T^{6} + 1203954 T^{7} + 22859727 T^{8} - 102894879 T^{9} - 1381379154 T^{10} + 2144772897 T^{11} + 42180533641 T^{12} \))(\( 1 + 3 T - 96 T^{2} - 495 T^{3} + 3615 T^{4} + 15798 T^{5} - 107021 T^{6} + 932082 T^{7} + 12583815 T^{8} - 101662605 T^{9} - 1163266656 T^{10} + 2144772897 T^{11} + 42180533641 T^{12} \))(\( 1 - 3 T - 24 T^{2} - 369 T^{3} - 453 T^{4} + 5694 T^{5} + 333403 T^{6} + 335946 T^{7} - 1576893 T^{8} - 75784851 T^{9} - 290816664 T^{10} - 2144772897 T^{11} + 42180533641 T^{12} \))(\( 1 - 31 T + 476 T^{2} - 5741 T^{3} + 62553 T^{4} - 587576 T^{5} + 4781851 T^{6} - 34666984 T^{7} + 217746993 T^{8} - 1179080839 T^{9} + 5767863836 T^{10} - 22162653269 T^{11} + 42180533641 T^{12} \))(\( 1 + 9 T - 90 T^{2} - 459 T^{3} + 10161 T^{4} + 20556 T^{5} - 598421 T^{6} + 1212804 T^{7} + 35370441 T^{8} - 94268961 T^{9} - 1090562490 T^{10} + 6434318691 T^{11} + 42180533641 T^{12} \))(\( 1 + 10 T - 71 T^{2} - 1536 T^{3} - 346 T^{4} + 106150 T^{5} + 583014 T^{6} - 3064183 T^{7} - 49833644 T^{8} - 180786797 T^{9} + 2029471734 T^{10} + 21800980850 T^{11} - 4192606906 T^{12} - 1098123723264 T^{13} - 2994817888511 T^{14} + 24886514848190 T^{15} + 146830437604321 T^{16} \))(\( 1 + 9 T - 119 T^{2} - 1116 T^{3} + 10336 T^{4} + 79866 T^{5} - 564434 T^{6} - 2176353 T^{7} + 30131725 T^{8} - 128404827 T^{9} - 1964794754 T^{10} + 16402799214 T^{11} + 125245043296 T^{12} - 797855517684 T^{13} - 5019483503279 T^{14} + 22397863363371 T^{15} + 146830437604321 T^{16} \))(\( 1 + 7 T - 84 T^{2} - 891 T^{3} - 548 T^{4} + 21051 T^{5} + 190525 T^{6} + 1336983 T^{7} + 4615039 T^{8} - 49687002 T^{9} - 884146943 T^{10} - 2931533118 T^{11} + 16064950759 T^{12} + 274588231557 T^{13} + 2308660204525 T^{14} + 15049871418249 T^{15} - 23114932435268 T^{16} - 2217388472973729 T^{17} - 12333756758762964 T^{18} + 60640970730584573 T^{19} + 511116753300641401 T^{20} \))
$61$ (\( 1 - 12 T + 83 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 45 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} \))(\( 1 + 5 T - 36 T^{2} + 305 T^{3} + 3721 T^{4} \))(\( 1 + 18 T + 127 T^{2} + 1350 T^{3} + 15324 T^{4} + 82350 T^{5} + 472567 T^{6} + 4085658 T^{7} + 13845841 T^{8} \))(\( 1 - 11 T + 43 T^{2} + 484 T^{3} - 5018 T^{4} + 29524 T^{5} + 160003 T^{6} - 2496791 T^{7} + 13845841 T^{8} \))(\( 1 - 6 T - 102 T^{2} + 698 T^{3} + 6048 T^{4} - 26604 T^{5} - 259509 T^{6} - 1622844 T^{7} + 22504608 T^{8} + 158432738 T^{9} - 1412275782 T^{10} - 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 + 6 T - 132 T^{2} - 418 T^{3} + 13698 T^{4} + 19134 T^{5} - 893289 T^{6} + 1167174 T^{7} + 50970258 T^{8} - 94878058 T^{9} - 1827651012 T^{10} + 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 - 12 T - 48 T^{2} + 478 T^{3} + 8460 T^{4} - 30636 T^{5} - 395685 T^{6} - 1868796 T^{7} + 31479660 T^{8} + 108496918 T^{9} - 664600368 T^{10} - 10135155612 T^{11} + 51520374361 T^{12} \))(\( 1 + 6 T + 48 T^{2} + 642 T^{3} + 3018 T^{4} + 35394 T^{5} + 438671 T^{6} + 2159034 T^{7} + 11229978 T^{8} + 145721802 T^{9} + 664600368 T^{10} + 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 - 6 T - 126 T^{2} + 358 T^{3} + 12372 T^{4} - 11472 T^{5} - 838653 T^{6} - 699792 T^{7} + 46036212 T^{8} + 81259198 T^{9} - 1744575966 T^{10} - 5067577806 T^{11} + 51520374361 T^{12} \))(\( 1 - 20 T + 161 T^{2} - 562 T^{3} - 931 T^{4} + 2180 T^{5} - 139869 T^{6} + 5694174 T^{7} - 64208639 T^{8} + 347344614 T^{9} - 520452549 T^{10} + 494818580 T^{11} - 12890477971 T^{12} - 474663121162 T^{13} + 8294780272121 T^{14} - 62854856720420 T^{15} + 191707312997281 T^{16} \))(\( 1 + 7 T - 144 T^{2} - 1315 T^{3} + 11783 T^{4} + 112692 T^{5} - 470051 T^{6} - 3262925 T^{7} + 21742764 T^{8} - 199038425 T^{9} - 1749059771 T^{10} + 25578942852 T^{11} + 163145544503 T^{12} - 1110644135815 T^{13} - 7418933907984 T^{14} + 21999199852147 T^{15} + 191707312997281 T^{16} \))(\( 1 + 14 T - 67 T^{2} - 1032 T^{3} + 10040 T^{4} + 70122 T^{5} - 675608 T^{6} - 3001836 T^{7} + 20748698 T^{8} - 6195900 T^{9} - 1395441908 T^{10} - 377949900 T^{11} + 77205905258 T^{12} - 681359737116 T^{13} - 9354360946328 T^{14} + 59224781818722 T^{15} + 517264558584440 T^{16} - 3243310606773672 T^{17} - 12844389970817827 T^{18} + 163718045299677974 T^{19} + 713342911662882601 T^{20} \))
$67$ (\( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 14 T^{2} - 603 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 77 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 16 T + 82 T^{2} + 640 T^{3} + 8635 T^{4} + 42880 T^{5} + 368098 T^{6} + 4812208 T^{7} + 20151121 T^{8} \))(\( ( 1 - 13 T + 67 T^{2} )^{2}( 1 + 13 T + 102 T^{2} + 871 T^{3} + 4489 T^{4} ) \))(\( 1 + 6 T - 138 T^{2} - 446 T^{3} + 14148 T^{4} + 16668 T^{5} - 1033545 T^{6} + 1116756 T^{7} + 63510372 T^{8} - 134140298 T^{9} - 2780854698 T^{10} + 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 + 12 T - 78 T^{2} - 518 T^{3} + 15318 T^{4} + 50094 T^{5} - 815637 T^{6} + 3356298 T^{7} + 68762502 T^{8} - 155795234 T^{9} - 1571787438 T^{10} + 16201501284 T^{11} + 90458382169 T^{12} \))(\( 1 + 12 T - 12 T^{2} - 690 T^{3} - 1488 T^{4} + 2856 T^{5} - 34441 T^{6} + 191352 T^{7} - 6679632 T^{8} - 207526470 T^{9} - 241813452 T^{10} + 16201501284 T^{11} + 90458382169 T^{12} \))(\( 1 - 6 T - 150 T^{2} + 506 T^{3} + 17268 T^{4} - 28236 T^{5} - 1220289 T^{6} - 1891812 T^{7} + 77516052 T^{8} + 152186078 T^{9} - 3022668150 T^{10} - 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 + 6 T^{2} - 1366 T^{3} + 438 T^{4} - 4098 T^{5} + 1065603 T^{6} - 274566 T^{7} + 1966182 T^{8} - 410842258 T^{9} + 120906726 T^{10} + 90458382169 T^{12} \))(\( 1 + 11 T - 82 T^{2} - 689 T^{3} + 8039 T^{4} + 18292 T^{5} - 590799 T^{6} - 1428153 T^{7} + 17009218 T^{8} - 95686251 T^{9} - 2652096711 T^{10} + 5501556796 T^{11} + 161994861719 T^{12} - 930236198723 T^{13} - 7417587337858 T^{14} + 66667827658553 T^{15} + 406067677556641 T^{16} \))(\( 1 - 12 T - 139 T^{2} + 1338 T^{3} + 22729 T^{4} - 133506 T^{5} - 1954153 T^{6} + 2368722 T^{7} + 170018875 T^{8} + 158704374 T^{9} - 8772192817 T^{10} - 40153665078 T^{11} + 458014829209 T^{12} + 1806467393166 T^{13} - 12573715121491 T^{14} - 72728539263876 T^{15} + 406067677556641 T^{16} \))(\( 1 - 8 T - 142 T^{2} + 1462 T^{3} + 7779 T^{4} - 110116 T^{5} - 343663 T^{6} + 6410154 T^{7} + 10809007 T^{8} - 209041554 T^{9} + 61061861 T^{10} - 14005784118 T^{11} + 48521632423 T^{12} + 1927937147502 T^{13} - 6925194696223 T^{14} - 148670376282412 T^{15} + 703675754892651 T^{16} + 8860760366982226 T^{17} - 57661610213043022 T^{18} - 217652275170359576 T^{19} + 1822837804551761449 T^{20} \))
$71$ (\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 15 T + 71 T^{2} )^{2} \))(\( ( 1 + 3 T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 143 T^{2} + 710 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 3 T + 70 T^{2} + 213 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 15 T + 231 T^{2} - 1833 T^{3} + 16401 T^{4} - 75615 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 9 T + 159 T^{2} + 1305 T^{3} + 11289 T^{4} + 45369 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 21 T + 249 T^{2} + 2115 T^{3} + 17679 T^{4} + 105861 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 17 T + 119 T^{2} + 507 T^{3} + 8449 T^{4} + 85697 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 9 T + 207 T^{2} + 1197 T^{3} + 14697 T^{4} + 45369 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 3 T + 276 T^{2} - 630 T^{3} + 29126 T^{4} - 44730 T^{5} + 1391316 T^{6} - 1073733 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 - 12 T + 167 T^{2} - 591 T^{3} + 7587 T^{4} - 41961 T^{5} + 841847 T^{6} - 4294932 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 - 9 T + 306 T^{2} - 2174 T^{3} + 40411 T^{4} - 221049 T^{5} + 2869181 T^{6} - 10959134 T^{7} + 109520766 T^{8} - 228705129 T^{9} + 1804229351 T^{10} )^{2} \))
$73$ (\( ( 1 - T + 73 T^{2} )^{2} \))(\( ( 1 - 13 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 126 T^{2} + 292 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 7 T + 84 T^{2} - 511 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 9 T + 207 T^{2} - 1235 T^{3} + 15111 T^{4} - 47961 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 + 21 T + 303 T^{2} + 2797 T^{3} + 22119 T^{4} + 111909 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 - 3 T + 105 T^{2} - 475 T^{3} + 7665 T^{4} - 15987 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 + 3 T + 195 T^{2} + 359 T^{3} + 14235 T^{4} + 15987 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 - 3 T + 51 T^{2} - 681 T^{3} + 3723 T^{4} - 15987 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 + 24 T + 425 T^{2} + 4923 T^{3} + 48495 T^{4} + 359379 T^{5} + 2264825 T^{6} + 9336408 T^{7} + 28398241 T^{8} )^{2} \))(\( ( 1 - 13 T + 232 T^{2} - 1504 T^{3} + 18820 T^{4} - 109792 T^{5} + 1236328 T^{6} - 5057221 T^{7} + 28398241 T^{8} )^{2} \))(\( ( 1 - 15 T + 247 T^{2} - 2719 T^{3} + 26596 T^{4} - 243028 T^{5} + 1941508 T^{6} - 14489551 T^{7} + 96087199 T^{8} - 425973615 T^{9} + 2073071593 T^{10} )^{2} \))
$79$ (\( 1 + 6 T - 43 T^{2} + 474 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - 6 T - 107 T^{2} + 90 T^{3} + 11364 T^{4} + 7110 T^{5} - 667787 T^{6} - 2958234 T^{7} + 38950081 T^{8} \))(\( 1 - 7 T - 47 T^{2} + 434 T^{3} - 896 T^{4} + 34286 T^{5} - 293327 T^{6} - 3451273 T^{7} + 38950081 T^{8} \))(\( 1 - 3 T + 6 T^{2} - 1787 T^{3} + 2439 T^{4} - 14634 T^{5} + 1719519 T^{6} - 1156086 T^{7} + 15221799 T^{8} - 881060693 T^{9} + 233700486 T^{10} - 9231169197 T^{11} + 243087455521 T^{12} \))(\( 1 + 21 T + 84 T^{2} + 499 T^{3} + 25767 T^{4} + 195678 T^{5} + 408327 T^{6} + 15458562 T^{7} + 160811847 T^{8} + 246026461 T^{9} + 3271806804 T^{10} + 64618184379 T^{11} + 243087455521 T^{12} \))(\( 1 + 15 T + 30 T^{2} + 59 T^{3} + 1125 T^{4} - 89100 T^{5} - 1368633 T^{6} - 7038900 T^{7} + 7021125 T^{8} + 29089301 T^{9} + 1168502430 T^{10} + 46155845985 T^{11} + 243087455521 T^{12} \))(\( 1 + 9 T - 114 T^{2} - 351 T^{3} + 13143 T^{4} - 15786 T^{5} - 1414609 T^{6} - 1247094 T^{7} + 82025463 T^{8} - 173056689 T^{9} - 4440309234 T^{10} + 27693507591 T^{11} + 243087455521 T^{12} \))(\( 1 - 15 T + 36 T^{2} + 367 T^{3} - 3225 T^{4} + 51726 T^{5} - 676905 T^{6} + 4086354 T^{7} - 20127225 T^{8} + 180945313 T^{9} + 1402202916 T^{10} - 46155845985 T^{11} + 243087455521 T^{12} \))(\( 1 + 21 T + 133 T^{2} - 252 T^{3} - 9896 T^{4} - 136080 T^{5} - 973784 T^{6} + 2121567 T^{7} + 81625693 T^{8} + 167603793 T^{9} - 6077385944 T^{10} - 67092747120 T^{11} - 385450001576 T^{12} - 775418212548 T^{13} + 32330631584293 T^{14} + 403282088709339 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 22 T + 237 T^{2} - 1616 T^{3} + 2882 T^{4} + 87342 T^{5} - 574370 T^{6} - 1050079 T^{7} + 29800944 T^{8} - 82956241 T^{9} - 3584643170 T^{10} + 43063012338 T^{11} + 112254133442 T^{12} - 4972523140784 T^{13} + 57611726958477 T^{14} - 422485997695498 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 3 T - 271 T^{2} + 1532 T^{3} + 38715 T^{4} - 263753 T^{5} - 3446203 T^{6} + 24313053 T^{7} + 236347015 T^{8} - 845708523 T^{9} - 15972358530 T^{10} - 66810973317 T^{11} + 1475041720615 T^{12} + 11987283338067 T^{13} - 134229885992443 T^{14} - 811582856405447 T^{15} + 9411130840495515 T^{16} + 29420388566795588 T^{17} - 411136487484678031 T^{18} - 359554787947854957 T^{19} + 9468276082626847201 T^{20} \))
$83$ (\( 1 - 16 T + 173 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( ( 1 - 2 T - 79 T^{2} - 166 T^{3} + 6889 T^{4} )^{2} \))(\( 1 - 12 T + 74 T^{2} + 1152 T^{3} - 13941 T^{4} + 95616 T^{5} + 509786 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))(\( 1 + 18 T - 198 T^{3} + 23814 T^{4} + 132750 T^{5} - 711245 T^{6} + 11018250 T^{7} + 164054646 T^{8} - 113213826 T^{9} + 70902731574 T^{11} + 326940373369 T^{12} \))(\( 1 + 18 T + 30 T^{2} - 702 T^{3} + 8088 T^{4} + 126648 T^{5} + 719359 T^{6} + 10511784 T^{7} + 55718232 T^{8} - 401394474 T^{9} + 1423749630 T^{10} + 70902731574 T^{11} + 326940373369 T^{12} \))(\( 1 + 6 T - 42 T^{2} - 2610 T^{3} - 9624 T^{4} + 83688 T^{5} + 2759119 T^{6} + 6946104 T^{7} - 66299736 T^{8} - 1492364070 T^{9} - 1993249482 T^{10} + 23634243858 T^{11} + 326940373369 T^{12} \))(\( 1 - 20 T + 38 T^{2} - 346 T^{3} + 32058 T^{4} - 183754 T^{5} - 606869 T^{6} - 15251582 T^{7} + 220847562 T^{8} - 197838302 T^{9} + 1803416198 T^{10} - 78780812860 T^{11} + 326940373369 T^{12} \))(\( 1 + 12 T - 144 T^{2} - 582 T^{3} + 34812 T^{4} + 90444 T^{5} - 2656433 T^{6} + 7506852 T^{7} + 239819868 T^{8} - 332780034 T^{9} - 6833998224 T^{10} + 47268487716 T^{11} + 326940373369 T^{12} \))(\( 1 + 8 T - 259 T^{2} - 1146 T^{3} + 49577 T^{4} + 119878 T^{5} - 6175577 T^{6} - 3335418 T^{7} + 604903483 T^{8} - 276839694 T^{9} - 42543549953 T^{10} + 68544681986 T^{11} + 2352841180217 T^{12} - 4514140576878 T^{13} - 84677556702571 T^{14} + 217088407917016 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 6 T - 113 T^{2} + 1704 T^{3} + 3151 T^{4} - 166296 T^{5} + 1416277 T^{6} + 7918434 T^{7} - 172589093 T^{8} + 657230022 T^{9} + 9756732253 T^{10} - 95085890952 T^{11} + 149541169471 T^{12} + 6712125255672 T^{13} - 36944262190697 T^{14} - 162816305937762 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 20 T + 98 T^{2} + 318 T^{3} + 879 T^{4} - 169800 T^{5} - 2124519 T^{6} - 6011178 T^{7} + 51057123 T^{8} + 1398046658 T^{9} + 18343755493 T^{10} + 116037872614 T^{11} + 351732520347 T^{12} - 3437113435086 T^{13} - 100826104672599 T^{14} - 668849101181400 T^{15} + 287380588191351 T^{16} + 8629264214701386 T^{17} + 220724638749626018 T^{18} + 3738805105350808060 T^{19} + 15516041187205853449 T^{20} \))
$89$ (\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 4 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 24 T + 298 T^{2} + 2136 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 18 T + 226 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 6 T + 72 T^{2} + 21 T^{3} + 6408 T^{4} - 47526 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 12 T + 204 T^{2} - 1323 T^{3} + 18156 T^{4} - 95052 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 + 18 T + 318 T^{2} + 3241 T^{3} + 28302 T^{4} + 142578 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 12 T + 216 T^{2} - 1425 T^{3} + 19224 T^{4} - 95052 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 + 2 T + 116 T^{2} + 735 T^{3} + 10324 T^{4} + 15842 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 6 T + 263 T^{2} - 1377 T^{3} + 32646 T^{4} - 122553 T^{5} + 2083223 T^{6} - 4229814 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 14 T + 323 T^{2} + 2963 T^{3} + 41152 T^{4} + 263707 T^{5} + 2558483 T^{6} + 9869566 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 12 T + 292 T^{2} + 2463 T^{3} + 41383 T^{4} + 291726 T^{5} + 3683087 T^{6} + 19509423 T^{7} + 205850948 T^{8} + 752906892 T^{9} + 5584059449 T^{10} )^{2} \))
$97$ (\( ( 1 - 19 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( 1 + 7 T - 48 T^{2} + 679 T^{3} + 9409 T^{4} \))(\( 1 - 2 T - 93 T^{2} - 194 T^{3} + 9409 T^{4} \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - 4 T - 158 T^{2} + 80 T^{3} + 19315 T^{4} + 7760 T^{5} - 1486622 T^{6} - 3650692 T^{7} + 88529281 T^{8} \))(\( 1 + T - 119 T^{2} - 74 T^{3} + 4894 T^{4} - 7178 T^{5} - 1119671 T^{6} + 912673 T^{7} + 88529281 T^{8} \))(\( 1 - 15 T - 84 T^{2} + 1139 T^{3} + 22203 T^{4} - 134028 T^{5} - 1218567 T^{6} - 13000716 T^{7} + 208908027 T^{8} + 1039534547 T^{9} - 7436459604 T^{10} - 128810103855 T^{11} + 832972004929 T^{12} \))(\( 1 - 3 T - 114 T^{2} + 149 T^{3} + 2421 T^{4} + 11502 T^{5} + 340233 T^{6} + 1115694 T^{7} + 22779189 T^{8} + 135988277 T^{9} - 10092338034 T^{10} - 25762020771 T^{11} + 832972004929 T^{12} \))(\( 1 + 15 T + 168 T^{2} + 1477 T^{3} + 2385 T^{4} - 42462 T^{5} - 510111 T^{6} - 4118814 T^{7} + 22440465 T^{8} + 1348018021 T^{9} + 14872919208 T^{10} + 128810103855 T^{11} + 832972004929 T^{12} \))(\( 1 - 9 T - 66 T^{2} + 2023 T^{3} - 7707 T^{4} - 73950 T^{5} + 1766073 T^{6} - 7173150 T^{7} - 72515163 T^{8} + 1846337479 T^{9} - 5842932546 T^{10} - 77286062313 T^{11} + 832972004929 T^{12} \))(\( 1 + 3 T - 168 T^{2} + 573 T^{3} + 14223 T^{4} - 78504 T^{5} - 1297807 T^{6} - 7614888 T^{7} + 133824207 T^{8} + 522961629 T^{9} - 14872919208 T^{10} + 25762020771 T^{11} + 832972004929 T^{12} \))(\( 1 - 16 T - 175 T^{2} + 2086 T^{3} + 49490 T^{4} - 309968 T^{5} - 6453258 T^{6} + 6735477 T^{7} + 823825414 T^{8} + 653341269 T^{9} - 60718704522 T^{10} - 282899424464 T^{11} + 4381314116690 T^{12} + 17913191776102 T^{13} - 145770100862575 T^{14} - 1292772551649808 T^{15} + 7837433594376961 T^{16} \))(\( 1 + T - 123 T^{2} - 856 T^{3} - 4138 T^{4} + 70242 T^{5} + 167026 T^{6} - 386291 T^{7} + 107246157 T^{8} - 37470227 T^{9} + 1571547634 T^{10} + 64107976866 T^{11} - 366334164778 T^{12} - 7350763259992 T^{13} - 102455556606267 T^{14} + 80798284478113 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 37 T + 608 T^{2} + 4491 T^{3} - 11038 T^{4} - 630495 T^{5} - 6947105 T^{6} - 31739955 T^{7} + 128335391 T^{8} + 3636093960 T^{9} + 40545974467 T^{10} + 352701114120 T^{11} + 1207507693919 T^{12} - 28968199949715 T^{13} - 615022210681505 T^{14} - 5414275095337215 T^{15} - 9194344990406302 T^{16} + 362865095591205483 T^{17} + 4765159625381192288 T^{18} + 28128549170218913029 T^{19} + 73742412689492826049 T^{20} \))
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