Properties

Label 630.2.j
Level 630
Weight 2
Character orbit j
Rep. character \(\chi_{630}(211,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 48
Newform subspaces 12
Sturm bound 288
Trace bound 7

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(630, [\chi])\).

Total New Old
Modular forms 304 48 256
Cusp forms 272 48 224
Eisenstein series 32 0 32

Trace form

\( 48q - 4q^{2} - 4q^{3} - 24q^{4} - 4q^{6} + 8q^{8} + 4q^{9} + O(q^{10}) \) \( 48q - 4q^{2} - 4q^{3} - 24q^{4} - 4q^{6} + 8q^{8} + 4q^{9} + 8q^{11} + 8q^{12} - 4q^{15} - 24q^{16} - 8q^{17} + 8q^{18} - 24q^{19} - 4q^{21} + 12q^{22} - 4q^{24} - 24q^{25} + 56q^{27} + 16q^{29} - 4q^{32} - 20q^{33} + 12q^{34} + 8q^{35} - 8q^{36} + 4q^{38} - 36q^{39} + 20q^{41} + 12q^{43} - 16q^{44} - 16q^{45} - 48q^{47} - 4q^{48} - 24q^{49} - 4q^{50} + 12q^{51} + 16q^{53} - 28q^{54} + 60q^{57} - 28q^{59} - 4q^{60} - 48q^{62} - 16q^{63} + 48q^{64} - 12q^{65} - 24q^{66} + 12q^{67} + 4q^{68} - 32q^{69} + 56q^{71} - 4q^{72} - 24q^{73} + 16q^{74} - 4q^{75} + 12q^{76} - 16q^{77} + 8q^{78} + 12q^{79} + 52q^{81} - 24q^{82} + 48q^{83} + 8q^{84} + 12q^{85} + 20q^{86} - 72q^{87} + 12q^{88} - 112q^{89} + 32q^{90} - 24q^{91} + 64q^{93} + 16q^{95} + 8q^{96} + 12q^{97} + 8q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
630.2.j.a \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.b \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(1\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.c \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.d \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.e \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.f \(4\) \(5.031\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-2\) \(2\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
630.2.j.g \(4\) \(5.031\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(2\) \(2\) \(q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots\)
630.2.j.h \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(2\) \(-2\) \(-2\) \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
630.2.j.i \(6\) \(5.031\) 6.0.954288.1 None \(-3\) \(-1\) \(-3\) \(3\) \(q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
630.2.j.j \(6\) \(5.031\) 6.0.954288.1 None \(-3\) \(-1\) \(3\) \(-3\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
630.2.j.k \(6\) \(5.031\) 6.0.954288.1 None \(-3\) \(1\) \(-3\) \(-3\) \(q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots\)
630.2.j.l \(8\) \(5.031\) 8.0.856615824.2 None \(-4\) \(-3\) \(4\) \(4\) \(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{4} \))
$3$ (\( 1 + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + T - 2 T^{2} - 3 T^{3} - 6 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 + T + 4 T^{2} + 3 T^{3} + 12 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 - T - 2 T^{2} + 3 T^{3} - 6 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 + 3 T + 3 T^{2} - 6 T^{3} - 24 T^{4} - 18 T^{5} + 27 T^{6} + 81 T^{7} + 81 T^{8} \))
$5$ (\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{4} \))
$7$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{4} \))
$11$ (\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 4 T^{3} + 232 T^{4} + 44 T^{5} - 847 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( ( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} ) \))(\( 1 - 7 T + 5 T^{2} - 2 T^{3} + 381 T^{4} - 803 T^{5} - 1154 T^{6} - 8833 T^{7} + 46101 T^{8} - 2662 T^{9} + 73205 T^{10} - 1127357 T^{11} + 1771561 T^{12} \))(\( 1 - 3 T - 9 T^{2} + 96 T^{3} - 99 T^{4} - 525 T^{5} + 3634 T^{6} - 5775 T^{7} - 11979 T^{8} + 127776 T^{9} - 131769 T^{10} - 483153 T^{11} + 1771561 T^{12} \))(\( 1 - T - 27 T^{2} + 10 T^{3} + 457 T^{4} - 37 T^{5} - 5722 T^{6} - 407 T^{7} + 55297 T^{8} + 13310 T^{9} - 395307 T^{10} - 161051 T^{11} + 1771561 T^{12} \))(\( 1 - 2 T - 10 T^{2} + 96 T^{3} - 133 T^{4} - 730 T^{5} + 2998 T^{6} + 336 T^{7} - 27968 T^{8} + 3696 T^{9} + 362758 T^{10} - 971630 T^{11} - 1947253 T^{12} + 15460896 T^{13} - 17715610 T^{14} - 38974342 T^{15} + 214358881 T^{16} \))
$13$ (\( ( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} \))(\( ( 1 - 5 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} ) \))(\( ( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( 1 + 6 T + 4 T^{2} + 36 T^{3} + 387 T^{4} + 468 T^{5} + 676 T^{6} + 13182 T^{7} + 28561 T^{8} \))(\( 1 - T - 17 T^{2} + 8 T^{3} + 142 T^{4} + 104 T^{5} - 2873 T^{6} - 2197 T^{7} + 28561 T^{8} \))(\( 1 + 4 T - 8 T^{2} - 8 T^{3} + 199 T^{4} - 104 T^{5} - 1352 T^{6} + 8788 T^{7} + 28561 T^{8} \))(\( 1 - 3 T^{2} - 164 T^{3} - 30 T^{4} + 246 T^{5} + 11001 T^{6} + 3198 T^{7} - 5070 T^{8} - 360308 T^{9} - 85683 T^{10} + 4826809 T^{12} \))(\( 1 - 21 T^{2} - 52 T^{3} + 168 T^{4} + 546 T^{5} - 663 T^{6} + 7098 T^{7} + 28392 T^{8} - 114244 T^{9} - 599781 T^{10} + 4826809 T^{12} \))(\( 1 - 2 T - 31 T^{2} + 30 T^{3} + 670 T^{4} - 268 T^{5} - 9707 T^{6} - 3484 T^{7} + 113230 T^{8} + 65910 T^{9} - 885391 T^{10} - 742586 T^{11} + 4826809 T^{12} \))(\( 1 - 3 T - 31 T^{2} + 42 T^{3} + 673 T^{4} - 189 T^{5} - 10438 T^{6} + 1965 T^{7} + 123148 T^{8} + 25545 T^{9} - 1764022 T^{10} - 415233 T^{11} + 19221553 T^{12} + 15594306 T^{13} - 149631079 T^{14} - 188245551 T^{15} + 815730721 T^{16} \))
$17$ (\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( ( 1 + 5 T + 17 T^{2} )^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( ( 1 - 7 T + 17 T^{2} )^{2} \))(\( ( 1 - T + 17 T^{2} )^{4} \))(\( ( 1 - 3 T + 17 T^{2} )^{4} \))(\( ( 1 + 3 T + 17 T^{2} )^{4} \))(\( ( 1 + 5 T + 22 T^{2} + 29 T^{3} + 374 T^{4} + 1445 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 9 T + 54 T^{2} + 225 T^{3} + 918 T^{4} + 2601 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 7 T + 58 T^{2} - 235 T^{3} + 986 T^{4} - 2023 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 2 T + 8 T^{2} + 40 T^{3} + 37 T^{4} + 680 T^{5} + 2312 T^{6} - 9826 T^{7} + 83521 T^{8} )^{2} \))
$19$ (\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 6 T + 35 T^{2} + 114 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 3 T + 32 T^{2} - 57 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 2 T + 15 T^{2} + 38 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 7 T + 64 T^{2} + 263 T^{3} + 1216 T^{4} + 2527 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 + 3 T + 36 T^{2} + 127 T^{3} + 684 T^{4} + 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 + 3 T + 36 T^{2} + 55 T^{3} + 684 T^{4} + 1083 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 3 T + 37 T^{2} - 108 T^{3} + 1098 T^{4} - 2052 T^{5} + 13357 T^{6} - 20577 T^{7} + 130321 T^{8} )^{2} \))
$23$ (\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 + 6 T - 16 T^{2} + 36 T^{3} + 1347 T^{4} + 828 T^{5} - 8464 T^{6} + 73002 T^{7} + 279841 T^{8} \))(\( ( 1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( 1 - 40 T^{2} + 1071 T^{4} - 21160 T^{6} + 279841 T^{8} \))(\( 1 - 2 T - T^{2} - 70 T^{3} - 30 T^{4} - 448 T^{5} + 22543 T^{6} - 10304 T^{7} - 15870 T^{8} - 851690 T^{9} - 279841 T^{10} - 12872686 T^{11} + 148035889 T^{12} \))(\( 1 - 6 T - 27 T^{2} + 66 T^{3} + 1188 T^{4} + 228 T^{5} - 36713 T^{6} + 5244 T^{7} + 628452 T^{8} + 803022 T^{9} - 7555707 T^{10} - 38618058 T^{11} + 148035889 T^{12} \))(\( 1 - 4 T - 9 T^{2} + 40 T^{3} - 230 T^{4} + 734 T^{5} + 6395 T^{6} + 16882 T^{7} - 121670 T^{8} + 486680 T^{9} - 2518569 T^{10} - 25745372 T^{11} + 148035889 T^{12} \))(\( 1 + 6 T - 38 T^{2} - 276 T^{3} + 862 T^{4} + 5472 T^{5} - 23384 T^{6} - 34122 T^{7} + 740695 T^{8} - 784806 T^{9} - 12370136 T^{10} + 66577824 T^{11} + 241222942 T^{12} - 1776430668 T^{13} - 5625363782 T^{14} + 20428952682 T^{15} + 78310985281 T^{16} \))
$29$ (\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 + 2 T - 25 T^{2} + 58 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 - 6 T - 4 T^{2} + 108 T^{3} - 285 T^{4} + 3132 T^{5} - 3364 T^{6} - 146334 T^{7} + 707281 T^{8} \))(\( ( 1 - 2 T - 25 T^{2} - 58 T^{3} + 841 T^{4} )^{2} \))(\( 1 - 52 T^{2} + 1863 T^{4} - 43732 T^{6} + 707281 T^{8} \))(\( 1 - 20 T + 185 T^{2} - 1456 T^{3} + 11550 T^{4} - 73150 T^{5} + 393937 T^{6} - 2121350 T^{7} + 9713550 T^{8} - 35510384 T^{9} + 130846985 T^{10} - 410222980 T^{11} + 594823321 T^{12} \))(\( 1 - 12 T + 27 T^{2} + 24 T^{3} + 1728 T^{4} - 12198 T^{5} + 40489 T^{6} - 353742 T^{7} + 1453248 T^{8} + 585336 T^{9} + 19096587 T^{10} - 246133788 T^{11} + 594823321 T^{12} \))(\( 1 + 6 T - 27 T^{2} - 354 T^{3} - 54 T^{4} + 6180 T^{5} + 37357 T^{6} + 179220 T^{7} - 45414 T^{8} - 8633706 T^{9} - 19096587 T^{10} + 123066894 T^{11} + 594823321 T^{12} \))(\( 1 + 12 T + 82 T^{2} + 60 T^{3} - 2498 T^{4} - 22590 T^{5} - 36524 T^{6} + 453936 T^{7} + 4700635 T^{8} + 13164144 T^{9} - 30716684 T^{10} - 550947510 T^{11} - 1766787938 T^{12} + 1230668940 T^{13} + 48775512322 T^{14} + 206998515708 T^{15} + 500246412961 T^{16} \))
$31$ (\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 5 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 69 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 + 4 T - 2 T^{2} - 176 T^{3} - 1133 T^{4} - 5456 T^{5} - 1922 T^{6} + 119164 T^{7} + 923521 T^{8} \))(\( ( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} )^{2} \))(\( 1 - 8 T - 29 T^{2} + 152 T^{3} + 2182 T^{4} - 3224 T^{5} - 69337 T^{6} - 99944 T^{7} + 2096902 T^{8} + 4528232 T^{9} - 26782109 T^{10} - 229033208 T^{11} + 887503681 T^{12} \))(\( ( 1 - 11 T + 31 T^{2} )^{3}( 1 + 7 T + 31 T^{2} )^{3} \))(\( 1 + 4 T - 37 T^{2} - 252 T^{3} + 238 T^{4} + 2996 T^{5} + 10951 T^{6} + 92876 T^{7} + 228718 T^{8} - 7507332 T^{9} - 34170277 T^{10} + 114516604 T^{11} + 887503681 T^{12} \))(\( 1 + 2 T + 48 T^{2} - 140 T^{3} - 442 T^{4} - 9642 T^{5} + 16840 T^{6} + 106418 T^{7} + 2843631 T^{8} + 3298958 T^{9} + 16183240 T^{10} - 287244822 T^{11} - 408196282 T^{12} - 4008081140 T^{13} + 42600176688 T^{14} + 55025228222 T^{15} + 852891037441 T^{16} \))
$37$ (\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{2} \))(\( ( 1 + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 10 T + 66 T^{2} - 370 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 8 T + 84 T^{2} + 296 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 4 T + 105 T^{2} + 278 T^{3} + 3885 T^{4} + 5476 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 63 T^{2} + 34 T^{3} + 2331 T^{4} + 50653 T^{6} )^{2} \))(\( ( 1 - 10 T + 77 T^{2} - 394 T^{3} + 2849 T^{4} - 13690 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 4 T + 64 T^{2} + 322 T^{3} + 2962 T^{4} + 11914 T^{5} + 87616 T^{6} + 202612 T^{7} + 1874161 T^{8} )^{2} \))
$41$ (\( 1 - 41 T^{2} + 1681 T^{4} \))(\( 1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 - 41 T^{2} + 1681 T^{4} \))(\( 1 - 5 T - 16 T^{2} - 205 T^{3} + 1681 T^{4} \))(\( 1 + 8 T - 31 T^{2} + 104 T^{3} + 4720 T^{4} + 4264 T^{5} - 52111 T^{6} + 551368 T^{7} + 2825761 T^{8} \))(\( 1 - 7 T - 37 T^{2} - 28 T^{3} + 3706 T^{4} - 1148 T^{5} - 62197 T^{6} - 482447 T^{7} + 2825761 T^{8} \))(\( 1 - 18 T + 167 T^{2} - 1350 T^{3} + 9684 T^{4} - 55350 T^{5} + 280727 T^{6} - 1240578 T^{7} + 2825761 T^{8} \))(\( 1 - 7 T - 41 T^{2} + 212 T^{3} + 1463 T^{4} + 2003 T^{5} - 99386 T^{6} + 82123 T^{7} + 2459303 T^{8} + 14611252 T^{9} - 115856201 T^{10} - 810993407 T^{11} + 4750104241 T^{12} \))(\( 1 - 15 T + 45 T^{2} - 222 T^{3} + 6435 T^{4} - 26835 T^{5} - 33662 T^{6} - 1100235 T^{7} + 10817235 T^{8} - 15300462 T^{9} + 127159245 T^{10} - 1737843015 T^{11} + 4750104241 T^{12} \))(\( 1 + 7 T + 51 T^{2} + 656 T^{3} + 2431 T^{4} + 13585 T^{5} + 167534 T^{6} + 556985 T^{7} + 4086511 T^{8} + 45212176 T^{9} + 144113811 T^{10} + 810993407 T^{11} + 4750104241 T^{12} \))(\( 1 - T - 148 T^{2} + 111 T^{3} + 13211 T^{4} - 6980 T^{5} - 807632 T^{6} + 117150 T^{7} + 37798900 T^{8} + 4803150 T^{9} - 1357629392 T^{10} - 481068580 T^{11} + 37331128571 T^{12} + 12860038311 T^{13} - 703015427668 T^{14} - 194754273881 T^{15} + 7984925229121 T^{16} \))
$43$ (\( 1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 + 2 T - 39 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( 1 - 9 T + 38 T^{2} - 387 T^{3} + 1849 T^{4} \))(\( 1 + 2 T + 25 T^{2} - 214 T^{3} - 1580 T^{4} - 9202 T^{5} + 46225 T^{6} + 159014 T^{7} + 3418801 T^{8} \))(\( 1 + 13 T + 49 T^{2} + 442 T^{3} + 5284 T^{4} + 19006 T^{5} + 90601 T^{6} + 1033591 T^{7} + 3418801 T^{8} \))(\( 1 - 2 T - 59 T^{2} + 46 T^{3} + 1948 T^{4} + 1978 T^{5} - 109091 T^{6} - 159014 T^{7} + 3418801 T^{8} \))(\( 1 - 15 T + 93 T^{2} - 286 T^{3} - 957 T^{4} + 30741 T^{5} - 288834 T^{6} + 1321863 T^{7} - 1769493 T^{8} - 22739002 T^{9} + 317948493 T^{10} - 2205126645 T^{11} + 6321363049 T^{12} \))(\( ( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} )^{3} \))(\( 1 + 17 T + 85 T^{2} + 442 T^{3} + 7123 T^{4} + 41837 T^{5} + 124334 T^{6} + 1798991 T^{7} + 13170427 T^{8} + 35142094 T^{9} + 290598085 T^{10} + 2499143531 T^{11} + 6321363049 T^{12} \))(\( 1 - 5 T - 96 T^{2} + 203 T^{3} + 6131 T^{4} - 1356 T^{5} - 261476 T^{6} + 65884 T^{7} + 8587152 T^{8} + 2833012 T^{9} - 483469124 T^{10} - 107811492 T^{11} + 20960668931 T^{12} + 29842713929 T^{13} - 606850852704 T^{14} - 1359093055535 T^{15} + 11688200277601 T^{16} \))
$47$ (\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 9 T + 34 T^{2} - 423 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( ( 1 + 4 T - 31 T^{2} + 188 T^{3} + 2209 T^{4} )^{2} \))(\( 1 - 7 T - 49 T^{2} - 28 T^{3} + 5092 T^{4} - 1316 T^{5} - 108241 T^{6} - 726761 T^{7} + 4879681 T^{8} \))(\( 1 + 2 T^{2} - 2205 T^{4} + 4418 T^{6} + 4879681 T^{8} \))(\( 1 + 2 T - 53 T^{2} - 310 T^{3} + 146 T^{4} + 5786 T^{5} + 91051 T^{6} + 271942 T^{7} + 322514 T^{8} - 32185130 T^{9} - 258623093 T^{10} + 458690014 T^{11} + 10779215329 T^{12} \))(\( 1 - 6 T + 27 T^{2} - 798 T^{3} + 1890 T^{4} - 4830 T^{5} + 262699 T^{6} - 227010 T^{7} + 4175010 T^{8} - 82850754 T^{9} + 131751387 T^{10} - 1376070042 T^{11} + 10779215329 T^{12} \))(\( 1 + 14 T + 27 T^{2} - 218 T^{3} + 2530 T^{4} + 26870 T^{5} + 101579 T^{6} + 1262890 T^{7} + 5588770 T^{8} - 22633414 T^{9} + 131751387 T^{10} + 3210830098 T^{11} + 10779215329 T^{12} \))(\( 1 + 11 T - T^{2} - 600 T^{3} - 3319 T^{4} - 1385 T^{5} + 62146 T^{6} + 274965 T^{7} - 366314 T^{8} + 12923355 T^{9} + 137280514 T^{10} - 143794855 T^{11} - 16195661239 T^{12} - 137607004200 T^{13} - 10779215329 T^{14} + 5572854325093 T^{15} + 23811286661761 T^{16} \))
$53$ (\( ( 1 + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 104 T^{2} - 530 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 10 T + 98 T^{2} + 530 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 - 12 T + 88 T^{2} - 636 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 33 T^{2} + 478 T^{3} + 1749 T^{4} + 148877 T^{6} )^{2} \))(\( ( 1 + 12 T + 159 T^{2} + 1110 T^{3} + 8427 T^{4} + 33708 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 6 T + 153 T^{2} + 582 T^{3} + 8109 T^{4} + 16854 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 - 22 T + 368 T^{2} - 3856 T^{3} + 33406 T^{4} - 204368 T^{5} + 1033712 T^{6} - 3275294 T^{7} + 7890481 T^{8} )^{2} \))
$59$ (\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 22 T^{2} + 531 T^{3} + 3481 T^{4} \))(\( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 5 T - 34 T^{2} + 295 T^{3} + 3481 T^{4} \))(\( 1 + 10 T - 31 T^{2} + 130 T^{3} + 7780 T^{4} + 7670 T^{5} - 107911 T^{6} + 2053790 T^{7} + 12117361 T^{8} \))(\( 1 + 5 T - 25 T^{2} - 340 T^{3} - 2456 T^{4} - 20060 T^{5} - 87025 T^{6} + 1026895 T^{7} + 12117361 T^{8} \))(\( 1 + 6 T - 67 T^{2} - 90 T^{3} + 5004 T^{4} - 5310 T^{5} - 233227 T^{6} + 1232274 T^{7} + 12117361 T^{8} \))(\( 1 - 7 T + 37 T^{2} - 766 T^{3} + 1823 T^{4} - 10363 T^{5} + 347974 T^{6} - 611417 T^{7} + 6345863 T^{8} - 157320314 T^{9} + 448342357 T^{10} - 5004470093 T^{11} + 42180533641 T^{12} \))(\( 1 - 3 T - 87 T^{2} + 582 T^{3} + 2247 T^{4} - 18219 T^{5} + 24910 T^{6} - 1074921 T^{7} + 7821807 T^{8} + 119530578 T^{9} - 1054210407 T^{10} - 2144772897 T^{11} + 42180533641 T^{12} \))(\( 1 + 29 T + 393 T^{2} + 4534 T^{3} + 51631 T^{4} + 462485 T^{5} + 3526142 T^{6} + 27286615 T^{7} + 179727511 T^{8} + 931188386 T^{9} + 4762122873 T^{10} + 20732804671 T^{11} + 42180533641 T^{12} \))(\( 1 + T - 94 T^{2} + 879 T^{3} + 4265 T^{4} - 70672 T^{5} + 348742 T^{6} + 2910810 T^{7} - 25645700 T^{8} + 171737790 T^{9} + 1213970902 T^{10} - 14514544688 T^{11} + 51680544665 T^{12} + 628418458821 T^{13} - 3964970162254 T^{14} + 2488651484819 T^{15} + 146830437604321 T^{16} \))
$61$ (\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 116 T^{2} - 4 T^{3} + 10435 T^{4} - 244 T^{5} - 431636 T^{6} + 453962 T^{7} + 13845841 T^{8} \))(\( 1 + 10 T^{2} - 3621 T^{4} + 37210 T^{6} + 13845841 T^{8} \))(\( 1 + 4 T - 56 T^{2} - 200 T^{3} + 487 T^{4} - 12200 T^{5} - 208376 T^{6} + 907924 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T - 129 T^{2} + 396 T^{3} + 17716 T^{4} - 28610 T^{5} - 1115471 T^{6} - 1745210 T^{7} + 65921236 T^{8} + 89884476 T^{9} - 1786113489 T^{10} - 6756770408 T^{11} + 51520374361 T^{12} \))(\( 1 - 147 T^{2} + 164 T^{3} + 12642 T^{4} - 12054 T^{5} - 857463 T^{6} - 735294 T^{7} + 47040882 T^{8} + 37224884 T^{9} - 2035338627 T^{10} + 51520374361 T^{12} \))(\( 1 - 2 T - 169 T^{2} + 138 T^{3} + 18892 T^{4} - 7096 T^{5} - 1328027 T^{6} - 432856 T^{7} + 70297132 T^{8} + 31323378 T^{9} - 2339947129 T^{10} - 1689192602 T^{11} + 51520374361 T^{12} \))(\( 1 + 4 T - 132 T^{2} - 1084 T^{3} + 7670 T^{4} + 88086 T^{5} - 11348 T^{6} - 2901056 T^{7} - 12506193 T^{8} - 176964416 T^{9} - 42225908 T^{10} + 19993848366 T^{11} + 106197600470 T^{12} - 915542390284 T^{13} - 6800689415652 T^{14} + 12570971344084 T^{15} + 191707312997281 T^{16} \))
$67$ (\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 + 9 T + 14 T^{2} + 603 T^{3} + 4489 T^{4} \))(\( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} \))(\( 1 - 3 T - 58 T^{2} - 201 T^{3} + 4489 T^{4} \))(\( ( 1 - 9 T + 14 T^{2} - 603 T^{3} + 4489 T^{4} )^{2} \))(\( 1 + 3 T - 119 T^{2} - 18 T^{3} + 11292 T^{4} - 1206 T^{5} - 534191 T^{6} + 902289 T^{7} + 20151121 T^{8} \))(\( 1 - 2 T + 85 T^{2} + 430 T^{3} + 1804 T^{4} + 28810 T^{5} + 381565 T^{6} - 601526 T^{7} + 20151121 T^{8} \))(\( 1 + 3 T - 111 T^{2} - 606 T^{3} + 4911 T^{4} + 23187 T^{5} - 170386 T^{6} + 1553529 T^{7} + 22045479 T^{8} - 182262378 T^{9} - 2236774431 T^{10} + 4050375321 T^{11} + 90458382169 T^{12} \))(\( 1 - 9 T - 39 T^{2} + 1226 T^{3} - 4017 T^{4} - 34041 T^{5} + 602526 T^{6} - 2280747 T^{7} - 18032313 T^{8} + 368735438 T^{9} - 785893719 T^{10} - 12151125963 T^{11} + 90458382169 T^{12} \))(\( 1 - T - 71 T^{2} - 86 T^{3} + 367 T^{4} + 5663 T^{5} + 249758 T^{6} + 379421 T^{7} + 1647463 T^{8} - 25865618 T^{9} - 1430729591 T^{10} - 1350125107 T^{11} + 90458382169 T^{12} \))(\( 1 + 21 T + 92 T^{2} - 519 T^{3} + 1771 T^{4} + 52092 T^{5} - 121444 T^{6} + 3350544 T^{7} + 82422040 T^{8} + 224486448 T^{9} - 545162116 T^{10} + 15667346196 T^{11} + 35687635291 T^{12} - 700714930533 T^{13} + 8322171159548 T^{14} + 127274943711783 T^{15} + 406067677556641 T^{16} \))
$71$ (\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 14 T + 71 T^{2} )^{2} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 14 T + 188 T^{2} - 994 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 15 T + 124 T^{2} + 1065 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 12 T + 172 T^{2} + 852 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 16 T + 67 T^{2} - 62 T^{3} + 4757 T^{4} + 80656 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 12 T + 213 T^{2} - 1542 T^{3} + 15123 T^{4} - 60492 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 10 T - 29 T^{2} + 1082 T^{3} - 2059 T^{4} - 50410 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 17 T + 362 T^{2} - 3707 T^{3} + 41248 T^{4} - 263197 T^{5} + 1824842 T^{6} - 6084487 T^{7} + 25411681 T^{8} )^{2} \))
$73$ (\( ( 1 - 11 T + 73 T^{2} )^{2} \))(\( ( 1 + 7 T + 73 T^{2} )^{2} \))(\( ( 1 - T + 73 T^{2} )^{2} \))(\( ( 1 - 11 T + 73 T^{2} )^{2} \))(\( ( 1 + 11 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 123 T^{2} - 730 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} - 438 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 14 T + 171 T^{2} + 1022 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 7 T + 214 T^{2} + 995 T^{3} + 15622 T^{4} + 37303 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 + 3 T + 126 T^{2} + 55 T^{3} + 9198 T^{4} + 15987 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 - T + 182 T^{2} - 85 T^{3} + 13286 T^{4} - 5329 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 + 10 T + 268 T^{2} + 1828 T^{3} + 27853 T^{4} + 133444 T^{5} + 1428172 T^{6} + 3890170 T^{7} + 28398241 T^{8} )^{2} \))
$79$ (\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 + 2 T - 75 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 - 14 T + 117 T^{2} - 1106 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( 1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( ( 1 - 14 T + 117 T^{2} - 1106 T^{3} + 6241 T^{4} )^{2} \))(\( 1 + 17 T + 133 T^{2} - 34 T^{3} - 4736 T^{4} - 2686 T^{5} + 830053 T^{6} + 8381663 T^{7} + 38950081 T^{8} \))(\( ( 1 + 2 T - 75 T^{2} + 158 T^{3} + 6241 T^{4} )^{2} \))(\( 1 - 6 T - 117 T^{2} + 1186 T^{3} + 5010 T^{4} - 53358 T^{5} + 18795 T^{6} - 4215282 T^{7} + 31267410 T^{8} + 584744254 T^{9} - 4557159477 T^{10} - 18462338394 T^{11} + 243087455521 T^{12} \))(\( 1 + 6 T - 117 T^{2} - 1186 T^{3} + 5010 T^{4} + 53358 T^{5} + 18795 T^{6} + 4215282 T^{7} + 31267410 T^{8} - 584744254 T^{9} - 4557159477 T^{10} + 18462338394 T^{11} + 243087455521 T^{12} \))(\( 1 + 2 T - 197 T^{2} - 278 T^{3} + 23842 T^{4} + 17306 T^{5} - 2114965 T^{6} + 1367174 T^{7} + 148797922 T^{8} - 137064842 T^{9} - 7673165957 T^{10} + 6154112798 T^{11} + 243087455521 T^{12} \))(\( 1 + 25 T + 135 T^{2} + 152 T^{3} + 25385 T^{4} + 267381 T^{5} - 350294 T^{6} + 4515655 T^{7} + 219222990 T^{8} + 356736745 T^{9} - 2186184854 T^{10} + 131829260859 T^{11} + 988747806185 T^{12} + 467712572648 T^{13} + 32816806495335 T^{14} + 480097724653975 T^{15} + 1517108809906561 T^{16} \))
$83$ (\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 - 15 T + 142 T^{2} - 1245 T^{3} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 - 4 T - 142 T^{2} + 32 T^{3} + 16747 T^{4} + 2656 T^{5} - 978238 T^{6} - 2287148 T^{7} + 47458321 T^{8} \))(\( 1 + 7 T - 121 T^{2} + 28 T^{3} + 17944 T^{4} + 2324 T^{5} - 833569 T^{6} + 4002509 T^{7} + 47458321 T^{8} \))(\( 1 - 24 T + 290 T^{2} - 2880 T^{3} + 27099 T^{4} - 239040 T^{5} + 1997810 T^{6} - 13722888 T^{7} + 47458321 T^{8} \))(\( 1 - 8 T - 161 T^{2} + 568 T^{3} + 22478 T^{4} - 22712 T^{5} - 2097341 T^{6} - 1885096 T^{7} + 154850942 T^{8} + 324775016 T^{9} - 7640789681 T^{10} - 31512325144 T^{11} + 326940373369 T^{12} \))(\( 1 - 24 T + 279 T^{2} - 1752 T^{3} - 954 T^{4} + 219576 T^{5} - 2920493 T^{6} + 18224808 T^{7} - 6572106 T^{8} - 1001770824 T^{9} + 13240871559 T^{10} - 94536975432 T^{11} + 326940373369 T^{12} \))(\( 1 + 12 T - 81 T^{2} - 420 T^{3} + 13230 T^{4} - 14532 T^{5} - 1616717 T^{6} - 1206156 T^{7} + 91141470 T^{8} - 240150540 T^{9} - 3844124001 T^{10} + 47268487716 T^{11} + 326940373369 T^{12} \))(\( 1 + 23 T + 209 T^{2} + 1890 T^{3} + 15209 T^{4} - 14951 T^{5} - 1103450 T^{6} - 15006849 T^{7} - 178990154 T^{8} - 1245568467 T^{9} - 7601667050 T^{10} - 8548787437 T^{11} + 721793604089 T^{12} + 7444786815270 T^{13} + 68330538034121 T^{14} + 624129172761421 T^{15} + 2252292232139041 T^{16} \))
$89$ (\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 8 T + 182 T^{2} + 712 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 8 T + 62 T^{2} + 712 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 12 T + 190 T^{2} + 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{6} \))(\( ( 1 + 18 T + 279 T^{2} + 2556 T^{3} + 24831 T^{4} + 142578 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 22 T + 343 T^{2} - 3604 T^{3} + 30527 T^{4} - 174262 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 16 T + 332 T^{2} - 3280 T^{3} + 40582 T^{4} - 291920 T^{5} + 2629772 T^{6} - 11279504 T^{7} + 62742241 T^{8} )^{2} \))
$97$ (\( 1 + 17 T + 192 T^{2} + 1649 T^{3} + 9409 T^{4} \))(\( 1 + 11 T + 24 T^{2} + 1067 T^{3} + 9409 T^{4} \))(\( 1 - 13 T + 72 T^{2} - 1261 T^{3} + 9409 T^{4} \))(\( 1 - 7 T - 48 T^{2} - 679 T^{3} + 9409 T^{4} \))(\( 1 - 17 T + 192 T^{2} - 1649 T^{3} + 9409 T^{4} \))(\( ( 1 - T - 96 T^{2} - 97 T^{3} + 9409 T^{4} )^{2} \))(\( 1 + 10 T + 13 T^{2} - 1070 T^{3} - 11540 T^{4} - 103790 T^{5} + 122317 T^{6} + 9126730 T^{7} + 88529281 T^{8} \))(\( 1 - 2 T + 25 T^{2} + 430 T^{3} - 9356 T^{4} + 41710 T^{5} + 235225 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 + 3 T + 3 T^{2} + 2756 T^{3} + 3561 T^{4} + 16521 T^{5} + 3611334 T^{6} + 1602537 T^{7} + 33505449 T^{8} + 2515326788 T^{9} + 265587843 T^{10} + 25762020771 T^{11} + 832972004929 T^{12} \))(\( 1 - 9 T - 165 T^{2} + 1316 T^{3} + 20769 T^{4} - 89355 T^{5} - 1691610 T^{6} - 8667435 T^{7} + 195415521 T^{8} + 1201077668 T^{9} - 14607331365 T^{10} - 77286062313 T^{11} + 832972004929 T^{12} \))(\( 1 - 5 T - 229 T^{2} + 444 T^{3} + 35593 T^{4} - 18343 T^{5} - 3933482 T^{6} - 1779271 T^{7} + 334894537 T^{8} + 405226812 T^{9} - 20273205349 T^{10} - 42936701285 T^{11} + 832972004929 T^{12} \))(\( 1 + 2 T - 48 T^{2} - 224 T^{3} - 10381 T^{4} - 26592 T^{5} + 310252 T^{6} + 3241598 T^{7} + 53462304 T^{8} + 314435006 T^{9} + 2919161068 T^{10} - 24269800416 T^{11} - 919022466061 T^{12} - 1923564217568 T^{13} - 39982656236592 T^{14} + 161596568956226 T^{15} + 7837433594376961 T^{16} \))
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