Properties

Label 1470.2.i
Level $1470$
Weight $2$
Character orbit 1470.i
Rep. character $\chi_{1470}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $24$
Sturm bound $672$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 24 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

Total New Old
Modular forms 736 56 680
Cusp forms 608 56 552
Eisenstein series 128 0 128

Trace form

\( 56q - 28q^{4} - 28q^{9} + O(q^{10}) \) \( 56q - 28q^{4} - 28q^{9} + 4q^{10} - 4q^{11} - 16q^{13} - 28q^{16} - 8q^{17} - 4q^{19} + 16q^{22} - 28q^{25} - 4q^{26} + 32q^{29} - 8q^{31} + 8q^{33} + 16q^{34} + 56q^{36} - 48q^{37} - 8q^{38} - 40q^{39} + 4q^{40} - 24q^{41} + 48q^{43} - 4q^{44} + 12q^{46} - 16q^{47} + 8q^{51} + 8q^{52} - 24q^{53} + 16q^{55} + 80q^{57} + 8q^{58} + 32q^{59} + 8q^{61} - 32q^{62} + 56q^{64} - 4q^{65} - 40q^{67} - 8q^{68} + 32q^{69} + 32q^{71} - 8q^{73} - 4q^{74} + 8q^{76} - 32q^{78} - 56q^{79} - 28q^{81} + 16q^{82} - 16q^{83} + 16q^{85} - 8q^{88} + 8q^{89} - 8q^{90} - 56q^{93} - 12q^{94} + 64q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1470.2.i.a \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.b \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.c \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.d \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.e \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.f \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.g \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.h \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.i \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.j \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.k \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.l \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.m \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.n \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.o \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.p \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.q \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.r \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.s \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.t \(2\) \(11.738\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.u \(4\) \(11.738\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-2\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1470.2.i.v \(4\) \(11.738\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(2\) \(0\) \(q+(-1-\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
1470.2.i.w \(4\) \(11.738\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(2\) \(0\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
1470.2.i.x \(4\) \(11.738\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(2\) \(-2\) \(0\) \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$3$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$5$ (\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))
$7$ 1
$11$ (\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T - 8 T^{2} + 8 T^{3} + 279 T^{4} + 88 T^{5} - 968 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( 1 + 4 T - 8 T^{2} + 8 T^{3} + 279 T^{4} + 88 T^{5} - 968 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 56 T^{3} - 233 T^{4} + 616 T^{5} + 968 T^{6} - 5324 T^{7} + 14641 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 56 T^{3} - 233 T^{4} + 616 T^{5} + 968 T^{6} - 5324 T^{7} + 14641 T^{8} \))
$13$ (\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 7 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 - 6 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 6 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 32 T^{2} + 735 T^{4} - 9248 T^{6} + 83521 T^{8} \))(\( 1 - 32 T^{2} + 735 T^{4} - 9248 T^{6} + 83521 T^{8} \))(\( 1 - 8 T + 16 T^{2} - 112 T^{3} + 927 T^{4} - 1904 T^{5} + 4624 T^{6} - 39304 T^{7} + 83521 T^{8} \))(\( 1 + 8 T + 16 T^{2} + 112 T^{3} + 927 T^{4} + 1904 T^{5} + 4624 T^{6} + 39304 T^{7} + 83521 T^{8} \))
$19$ (\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( ( 1 - T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 3 T - 10 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 - T + 19 T^{2} ) \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8} \))(\( 1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8} \))(\( 1 + 8 T + 18 T^{2} + 64 T^{3} + 539 T^{4} + 1216 T^{5} + 6498 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 - 8 T + 18 T^{2} - 64 T^{3} + 539 T^{4} - 1216 T^{5} + 6498 T^{6} - 54872 T^{7} + 130321 T^{8} \))
$23$ (\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 7 T + 26 T^{2} + 161 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 26 T^{2} - 16 T^{3} + 867 T^{4} - 368 T^{5} - 13754 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 + 4 T - 26 T^{2} - 16 T^{3} + 867 T^{4} - 368 T^{5} - 13754 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 + 12 T + 70 T^{2} + 336 T^{3} + 1635 T^{4} + 7728 T^{5} + 37030 T^{6} + 146004 T^{7} + 279841 T^{8} \))(\( 1 + 12 T + 70 T^{2} + 336 T^{3} + 1635 T^{4} + 7728 T^{5} + 37030 T^{6} + 146004 T^{7} + 279841 T^{8} \))
$29$ (\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 8 T + 56 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 8 T + 56 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 8 T + 72 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 8 T + 72 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))
$31$ (\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 6 T + 5 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 69 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 184 T^{3} - 1201 T^{4} + 5704 T^{5} - 119164 T^{7} + 923521 T^{8} \))(\( 1 + 4 T - 184 T^{3} - 1201 T^{4} - 5704 T^{5} + 119164 T^{7} + 923521 T^{8} \))(\( 1 + 12 T + 64 T^{2} + 216 T^{3} + 975 T^{4} + 6696 T^{5} + 61504 T^{6} + 357492 T^{7} + 923521 T^{8} \))(\( 1 - 12 T + 64 T^{2} - 216 T^{3} + 975 T^{4} - 6696 T^{5} + 61504 T^{6} - 357492 T^{7} + 923521 T^{8} \))
$37$ (\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 2 T - 33 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( ( 1 - 10 T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( 1 - 2 T - 33 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 28 T^{2} - 111 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 21 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( ( 1 + T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 21 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 72 T^{2} + 3815 T^{4} - 98568 T^{6} + 1874161 T^{8} \))(\( 1 - 72 T^{2} + 3815 T^{4} - 98568 T^{6} + 1874161 T^{8} \))(\( 1 + 8 T - 8 T^{2} - 16 T^{3} + 1447 T^{4} - 592 T^{5} - 10952 T^{6} + 405224 T^{7} + 1874161 T^{8} \))(\( 1 + 8 T - 8 T^{2} - 16 T^{3} + 1447 T^{4} - 592 T^{5} - 10952 T^{6} + 405224 T^{7} + 1874161 T^{8} \))
$41$ (\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 5 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 9 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 11 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 9 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 110 T^{2} + 492 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 12 T + 110 T^{2} - 492 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 4 T + 14 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 4 T + 14 T^{2} - 164 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 2 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 2 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 6 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 6 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 12 T + 120 T^{2} - 516 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 12 T + 120 T^{2} - 516 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 4 T + 40 T^{2} - 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 4 T + 40 T^{2} - 172 T^{3} + 1849 T^{4} )^{2} \))
$47$ (\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 53 T^{2} - 470 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 11 T + 74 T^{2} + 517 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 10 T + 53 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 2 T - 43 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 5 T - 22 T^{2} + 235 T^{3} + 2209 T^{4} \))(\( 1 - 4 T - 31 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 4 T - 31 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 - 4 T - 32 T^{2} + 184 T^{3} - 657 T^{4} + 8648 T^{5} - 70688 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( 1 + 4 T - 32 T^{2} - 184 T^{3} - 657 T^{4} - 8648 T^{5} - 70688 T^{6} + 415292 T^{7} + 4879681 T^{8} \))(\( 1 - 4 T - 64 T^{2} + 56 T^{3} + 3439 T^{4} + 2632 T^{5} - 141376 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( 1 + 4 T - 64 T^{2} - 56 T^{3} + 3439 T^{4} - 2632 T^{5} - 141376 T^{6} + 415292 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 28 T^{2} - 477 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - T - 52 T^{2} - 53 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 11 T + 68 T^{2} - 583 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 3 T - 44 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 34 T^{2} - 496 T^{3} - 3333 T^{4} - 26288 T^{5} + 95506 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 34 T^{2} - 496 T^{3} - 3333 T^{4} - 26288 T^{5} + 95506 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( 1 + 12 T + 34 T^{2} + 48 T^{3} + 1659 T^{4} + 2544 T^{5} + 95506 T^{6} + 1786524 T^{7} + 7890481 T^{8} \))(\( 1 + 12 T + 34 T^{2} + 48 T^{3} + 1659 T^{4} + 2544 T^{5} + 95506 T^{6} + 1786524 T^{7} + 7890481 T^{8} \))
$59$ (\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 62 T^{2} + 432 T^{3} - 5253 T^{4} + 25488 T^{5} + 215822 T^{6} - 2464548 T^{7} + 12117361 T^{8} \))(\( 1 + 12 T + 62 T^{2} - 432 T^{3} - 5253 T^{4} - 25488 T^{5} + 215822 T^{6} + 2464548 T^{7} + 12117361 T^{8} \))(\( 1 + 12 T - 2 T^{2} + 336 T^{3} + 9339 T^{4} + 19824 T^{5} - 6962 T^{6} + 2464548 T^{7} + 12117361 T^{8} \))(\( 1 - 12 T - 2 T^{2} - 336 T^{3} + 9339 T^{4} - 19824 T^{5} - 6962 T^{6} - 2464548 T^{7} + 12117361 T^{8} \))
$61$ (\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 45 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )( 1 - T + 61 T^{2} ) \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 61 T^{2} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )( 1 - T + 61 T^{2} ) \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 18 T^{2} - 48 T^{3} + 3371 T^{4} - 2928 T^{5} + 66978 T^{6} - 2723772 T^{7} + 13845841 T^{8} \))(\( 1 + 12 T + 18 T^{2} + 48 T^{3} + 3371 T^{4} + 2928 T^{5} + 66978 T^{6} + 2723772 T^{7} + 13845841 T^{8} \))(\( 1 + 12 T + 18 T^{2} + 48 T^{3} + 3371 T^{4} + 2928 T^{5} + 66978 T^{6} + 2723772 T^{7} + 13845841 T^{8} \))(\( 1 - 12 T + 18 T^{2} - 48 T^{3} + 3371 T^{4} - 2928 T^{5} + 66978 T^{6} - 2723772 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 77 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 77 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 77 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 14 T + 129 T^{2} + 938 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 67 T^{2} + 4489 T^{4} \))(\( 1 - 67 T^{2} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 14 T + 129 T^{2} + 938 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 67 T^{2} + 4489 T^{4} \))(\( 1 - 4 T - 24 T^{2} + 376 T^{3} - 3961 T^{4} + 25192 T^{5} - 107736 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T - 24 T^{2} + 376 T^{3} - 3961 T^{4} + 25192 T^{5} - 107736 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 + 4 T - 72 T^{2} - 184 T^{3} + 2183 T^{4} - 12328 T^{5} - 323208 T^{6} + 1203052 T^{7} + 20151121 T^{8} \))(\( 1 + 4 T - 72 T^{2} - 184 T^{3} + 2183 T^{4} - 12328 T^{5} - 323208 T^{6} + 1203052 T^{7} + 20151121 T^{8} \))
$71$ (\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 14 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 16 T + 198 T^{2} - 1136 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 16 T + 198 T^{2} - 1136 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 + 14 T + 123 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 14 T + 123 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 - 14 T + 123 T^{2} - 1022 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 14 T + 123 T^{2} - 1022 T^{3} + 5329 T^{4} \))(\( 1 + 14 T + 123 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 6 T - 37 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 6 T - 37 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 + 6 T - 37 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 + 4 T - 102 T^{2} - 112 T^{3} + 7427 T^{4} - 8176 T^{5} - 543558 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 - 4 T - 102 T^{2} + 112 T^{3} + 7427 T^{4} + 8176 T^{5} - 543558 T^{6} - 1556068 T^{7} + 28398241 T^{8} \))(\( ( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} )^{2} \))
$79$ (\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 79 T^{2} + 6241 T^{4} \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 177 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 65 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 - 79 T^{2} + 6241 T^{4} \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 177 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 - 30 T^{2} - 5341 T^{4} - 187230 T^{6} + 38950081 T^{8} \))(\( 1 - 30 T^{2} - 5341 T^{4} - 187230 T^{6} + 38950081 T^{8} \))(\( ( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 16 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 16 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 8 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 8 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 8 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 16 T + 222 T^{2} + 1328 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 16 T + 222 T^{2} - 1328 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 16 T + 222 T^{2} + 1328 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 16 T + 222 T^{2} - 1328 T^{3} + 6889 T^{4} )^{2} \))
$89$ (\( 1 + 10 T + 11 T^{2} + 890 T^{3} + 7921 T^{4} \))(\( 1 - 2 T - 85 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 + 2 T - 85 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 + 14 T + 107 T^{2} + 1246 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 2 T - 85 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 - 10 T + 11 T^{2} - 890 T^{3} + 7921 T^{4} \))(\( 1 - 18 T + 235 T^{2} - 1602 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 10 T + 11 T^{2} + 890 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 + 18 T + 235 T^{2} + 1602 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 - 18 T + 235 T^{2} - 1602 T^{3} + 7921 T^{4} \))(\( 1 + 18 T + 235 T^{2} + 1602 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 14 T + 107 T^{2} + 1246 T^{3} + 7921 T^{4} \))(\( 1 + 4 T - 94 T^{2} - 272 T^{3} + 2755 T^{4} - 24208 T^{5} - 744574 T^{6} + 2819876 T^{7} + 62742241 T^{8} \))(\( 1 - 4 T - 94 T^{2} + 272 T^{3} + 2755 T^{4} + 24208 T^{5} - 744574 T^{6} - 2819876 T^{7} + 62742241 T^{8} \))(\( 1 - 4 T - 158 T^{2} + 16 T^{3} + 20931 T^{4} + 1424 T^{5} - 1251518 T^{6} - 2819876 T^{7} + 62742241 T^{8} \))(\( 1 + 4 T - 158 T^{2} - 16 T^{3} + 20931 T^{4} - 1424 T^{5} - 1251518 T^{6} + 2819876 T^{7} + 62742241 T^{8} \))
$97$ (\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 6 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 16 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 16 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 12 T + 222 T^{2} - 1164 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 12 T + 222 T^{2} + 1164 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 4 T + 126 T^{2} + 388 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 4 T + 126 T^{2} - 388 T^{3} + 9409 T^{4} )^{2} \))
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