Properties

Label 1890.2.k
Level 1890
Weight 2
Character orbit k
Rep. character \(\chi_{1890}(541,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 88
Newform subspaces 38
Sturm bound 864
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1890.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 38 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).

Total New Old
Modular forms 912 88 824
Cusp forms 816 88 728
Eisenstein series 96 0 96

Trace form

\( 88q - 44q^{4} + 24q^{7} + O(q^{10}) \) \( 88q - 44q^{4} + 24q^{7} - 24q^{13} - 44q^{16} - 24q^{19} - 44q^{25} - 12q^{28} + 12q^{31} + 16q^{34} + 20q^{37} - 72q^{43} + 8q^{46} - 8q^{49} + 12q^{52} + 16q^{55} + 28q^{61} + 88q^{64} + 36q^{67} - 24q^{73} + 48q^{76} + 20q^{79} + 16q^{82} - 104q^{91} + 32q^{94} + 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1890.2.k.a \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.b \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.c \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.d \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.e \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.f \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.g \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.h \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.i \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1890.2.k.j \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.k \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.l \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.m \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.n \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.o \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.p \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.q \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.r \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.s \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1890.2.k.t \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1890.2.k.u \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.v \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.w \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.x \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.y \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.z \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.ba \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.bb \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.bc \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.k.bd \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.k.be \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.bf \(2\) \(15.092\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1890.2.k.bg \(4\) \(15.092\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(-2\) \(-2\) \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1890.2.k.bh \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(-2\) \(0\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+\beta _{2}q^{5}+\beta _{1}q^{7}+\cdots\)
1890.2.k.bi \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(-2\) \(10\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+\beta _{2}q^{5}+(2+\cdots)q^{7}+\cdots\)
1890.2.k.bj \(4\) \(15.092\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(-2\) \(q+(1+\beta _{1})q^{2}+\beta _{1}q^{4}+(1+\beta _{1})q^{5}+\cdots\)
1890.2.k.bk \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(0\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+\cdots\)
1890.2.k.bl \(4\) \(15.092\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(10\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$3$ 1
$5$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$7$ (\( 1 + 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 7 T^{2} + 49 T^{4} \))(\( ( 1 - 5 T + 7 T^{2} )^{2} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 7 T^{2} + 49 T^{4} \))(\( ( 1 - 5 T + 7 T^{2} )^{2} \))
$11$ (\( 1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4} \))(\( 1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} \))(\( 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} \))(\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( ( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4} )^{2} \))(\( 1 - 2 T + 9 T^{2} + 54 T^{3} - 140 T^{4} + 594 T^{5} + 1089 T^{6} - 2662 T^{7} + 14641 T^{8} \))(\( ( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} )^{2} \))(\( 1 + 2 T + 9 T^{2} - 54 T^{3} - 140 T^{4} - 594 T^{5} + 1089 T^{6} + 2662 T^{7} + 14641 T^{8} \))
$13$ (\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - T + 13 T^{2} )^{2} \))(\( ( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 - T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{4} \))(\( ( 1 - 2 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{4} \))(\( ( 1 - 2 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 5 T + 8 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 + 5 T + 8 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 + 5 T + 8 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - 5 T + 8 T^{2} - 85 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 5 T + 8 T^{2} - 85 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 5 T + 8 T^{2} - 85 T^{3} + 289 T^{4} \))(\( ( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} )^{2} \))(\( 1 + 2 T - 3 T^{2} - 54 T^{3} - 308 T^{4} - 918 T^{5} - 867 T^{6} + 9826 T^{7} + 83521 T^{8} \))(\( 1 - 4 T + 6 T^{2} + 96 T^{3} - 461 T^{4} + 1632 T^{5} + 1734 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( ( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} )^{2} \))(\( 1 - 2 T - 3 T^{2} + 54 T^{3} - 308 T^{4} + 918 T^{5} - 867 T^{6} - 9826 T^{7} + 83521 T^{8} \))(\( 1 + 4 T + 6 T^{2} - 96 T^{3} - 461 T^{4} - 1632 T^{5} + 1734 T^{6} + 19652 T^{7} + 83521 T^{8} \))
$19$ (\( 1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 - T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 + 4 T - 8 T^{2} - 56 T^{3} - 89 T^{4} - 1064 T^{5} - 2888 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 - 10 T + 44 T^{2} - 180 T^{3} + 875 T^{4} - 3420 T^{5} + 15884 T^{6} - 68590 T^{7} + 130321 T^{8} \))(\( ( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} )^{2} \))(\( 1 + 4 T - 8 T^{2} - 56 T^{3} - 89 T^{4} - 1064 T^{5} - 2888 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 - 10 T + 44 T^{2} - 180 T^{3} + 875 T^{4} - 3420 T^{5} + 15884 T^{6} - 68590 T^{7} + 130321 T^{8} \))(\( ( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} )^{2} \))
$23$ (\( 1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 28 T^{2} + 255 T^{4} - 14812 T^{6} + 279841 T^{8} \))(\( 1 - 6 T - 12 T^{2} - 12 T^{3} + 947 T^{4} - 276 T^{5} - 6348 T^{6} - 73002 T^{7} + 279841 T^{8} \))(\( 1 + 4 T - 6 T^{2} - 96 T^{3} - 413 T^{4} - 2208 T^{5} - 3174 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 - 28 T^{2} + 255 T^{4} - 14812 T^{6} + 279841 T^{8} \))(\( 1 + 6 T - 12 T^{2} + 12 T^{3} + 947 T^{4} + 276 T^{5} - 6348 T^{6} + 73002 T^{7} + 279841 T^{8} \))(\( 1 - 4 T - 6 T^{2} + 96 T^{3} - 413 T^{4} + 2208 T^{5} - 3174 T^{6} - 48668 T^{7} + 279841 T^{8} \))
$29$ (\( ( 1 + T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 9 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 9 T + 29 T^{2} )^{2} \))(\( ( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 14 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 4 T + 34 T^{2} + 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{4} \))(\( ( 1 - 14 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 4 T + 34 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{4} \))
$31$ (\( ( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( 1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 5 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 279 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( 1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 279 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 5 T^{2} - 186 T^{3} + 961 T^{4} \))(\( ( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 6 T + 43 T^{2} - 186 T^{3} + 961 T^{4} )( 1 - 50 T^{2} + 961 T^{4} ) \))(\( ( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 6 T + 43 T^{2} - 186 T^{3} + 961 T^{4} )( 1 - 50 T^{2} + 961 T^{4} ) \))
$37$ (\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 28 T^{2} - 111 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 28 T^{2} - 111 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 44 T^{2} - 56 T^{3} + 1639 T^{4} - 2072 T^{5} - 60236 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 6 T - 40 T^{2} + 12 T^{3} + 3075 T^{4} + 444 T^{5} - 54760 T^{6} + 303918 T^{7} + 1874161 T^{8} \))(\( 1 - 12 T + 62 T^{2} - 96 T^{3} + 27 T^{4} - 3552 T^{5} + 84878 T^{6} - 607836 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T - 44 T^{2} - 56 T^{3} + 1639 T^{4} - 2072 T^{5} - 60236 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 6 T - 40 T^{2} + 12 T^{3} + 3075 T^{4} + 444 T^{5} - 54760 T^{6} + 303918 T^{7} + 1874161 T^{8} \))(\( 1 - 12 T + 62 T^{2} - 96 T^{3} + 27 T^{4} - 3552 T^{5} + 84878 T^{6} - 607836 T^{7} + 1874161 T^{8} \))
$41$ (\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 4 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{4} \))(\( ( 1 + 4 T + 41 T^{2} )^{4} \))(\( ( 1 + 4 T - 26 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 41 T^{2} )^{4} \))(\( ( 1 - 4 T + 41 T^{2} )^{4} \))(\( ( 1 - 4 T - 26 T^{2} - 164 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 18 T^{2} - 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T - 22 T^{2} + 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T + 62 T^{2} + 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 4 T + 18 T^{2} - 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T - 22 T^{2} + 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T + 62 T^{2} + 172 T^{3} + 1849 T^{4} )^{2} \))
$47$ (\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 53 T^{2} - 470 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 53 T^{2} - 470 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 10 T + 53 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 10 T + 53 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 76 T^{2} + 3567 T^{4} - 167884 T^{6} + 4879681 T^{8} \))(\( 1 - 6 T - 60 T^{2} - 12 T^{3} + 5315 T^{4} - 564 T^{5} - 132540 T^{6} - 622938 T^{7} + 4879681 T^{8} \))(\( 1 - 8 T - 18 T^{2} + 96 T^{3} + 1507 T^{4} + 4512 T^{5} - 39762 T^{6} - 830584 T^{7} + 4879681 T^{8} \))(\( 1 - 76 T^{2} + 3567 T^{4} - 167884 T^{6} + 4879681 T^{8} \))(\( 1 + 6 T - 60 T^{2} + 12 T^{3} + 5315 T^{4} + 564 T^{5} - 132540 T^{6} + 622938 T^{7} + 4879681 T^{8} \))(\( 1 + 8 T - 18 T^{2} - 96 T^{3} + 1507 T^{4} - 4512 T^{5} - 39762 T^{6} + 830584 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 4 T - 37 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 + 2 T - 49 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 - 3 T - 44 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 7 T - 4 T^{2} + 371 T^{3} + 2809 T^{4} \))(\( 1 - 11 T + 68 T^{2} - 583 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 9 T + 28 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 11 T + 68 T^{2} + 583 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 7 T - 4 T^{2} - 371 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 28 T^{2} - 477 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 91 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 + 4 T - 37 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 61 T^{2} + 54 T^{3} + 4692 T^{4} + 2862 T^{5} - 171349 T^{6} - 893262 T^{7} + 7890481 T^{8} \))(\( 1 - 16 T + 93 T^{2} - 912 T^{3} + 10192 T^{4} - 48336 T^{5} + 261237 T^{6} - 2382032 T^{7} + 7890481 T^{8} \))(\( ( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} )^{2} \))(\( 1 + 6 T - 61 T^{2} - 54 T^{3} + 4692 T^{4} - 2862 T^{5} - 171349 T^{6} + 893262 T^{7} + 7890481 T^{8} \))(\( 1 + 16 T + 93 T^{2} + 912 T^{3} + 10192 T^{4} + 48336 T^{5} + 261237 T^{6} + 2382032 T^{7} + 7890481 T^{8} \))(\( ( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} )^{2} \))
$59$ (\( 1 - 13 T + 110 T^{2} - 767 T^{3} + 3481 T^{4} \))(\( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 + 15 T + 166 T^{2} + 885 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 - 5 T - 34 T^{2} - 295 T^{3} + 3481 T^{4} \))(\( 1 - 11 T + 62 T^{2} - 649 T^{3} + 3481 T^{4} \))(\( 1 - 5 T - 34 T^{2} - 295 T^{3} + 3481 T^{4} \))(\( 1 + T - 58 T^{2} + 59 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 22 T^{2} + 531 T^{3} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 9 T + 22 T^{2} - 531 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 + 5 T - 34 T^{2} + 295 T^{3} + 3481 T^{4} \))(\( 1 - T - 58 T^{2} - 59 T^{3} + 3481 T^{4} \))(\( 1 + 5 T - 34 T^{2} + 295 T^{3} + 3481 T^{4} \))(\( 1 + 11 T + 62 T^{2} + 649 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 22 T^{2} + 531 T^{3} + 3481 T^{4} \))(\( 1 - 9 T + 22 T^{2} - 531 T^{3} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 + 13 T + 110 T^{2} + 767 T^{3} + 3481 T^{4} \))(\( 1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( ( 1 + 9 T + 22 T^{2} + 531 T^{3} + 3481 T^{4} )^{2} \))(\( 1 - 6 T - 63 T^{2} + 114 T^{3} + 4196 T^{4} + 6726 T^{5} - 219303 T^{6} - 1232274 T^{7} + 12117361 T^{8} \))(\( 1 - 14 T + 57 T^{2} - 294 T^{3} + 4276 T^{4} - 17346 T^{5} + 198417 T^{6} - 2875306 T^{7} + 12117361 T^{8} \))(\( ( 1 - 9 T + 22 T^{2} - 531 T^{3} + 3481 T^{4} )^{2} \))(\( 1 + 6 T - 63 T^{2} - 114 T^{3} + 4196 T^{4} - 6726 T^{5} - 219303 T^{6} + 1232274 T^{7} + 12117361 T^{8} \))(\( 1 + 14 T + 57 T^{2} + 294 T^{3} + 4276 T^{4} + 17346 T^{5} + 198417 T^{6} + 2875306 T^{7} + 12117361 T^{8} \))
$61$ (\( 1 + 12 T + 83 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 5 T - 36 T^{2} + 305 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )( 1 - T + 61 T^{2} ) \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )( 1 - T + 61 T^{2} ) \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 83 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 5 T - 36 T^{2} + 305 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 38 T^{2} - 272 T^{3} - 1781 T^{4} - 16592 T^{5} - 141398 T^{6} + 907924 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T - 46 T^{2} + 96 T^{3} + 4475 T^{4} + 5856 T^{5} - 171166 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 12 T + 14 T^{2} - 96 T^{3} + 4395 T^{4} - 5856 T^{5} + 52094 T^{6} - 2723772 T^{7} + 13845841 T^{8} \))(\( 1 + 4 T - 38 T^{2} - 272 T^{3} - 1781 T^{4} - 16592 T^{5} - 141398 T^{6} + 907924 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T - 46 T^{2} + 96 T^{3} + 4475 T^{4} + 5856 T^{5} - 171166 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 12 T + 14 T^{2} - 96 T^{3} + 4395 T^{4} - 5856 T^{5} + 52094 T^{6} - 2723772 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 + 6 T - 31 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 14 T + 129 T^{2} + 938 T^{3} + 4489 T^{4} \))(\( 1 - 6 T - 31 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4} \))(\( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} \))(\( ( 1 - 5 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} \))(\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 - 67 T^{2} + 4489 T^{4} \))(\( 1 + 9 T + 14 T^{2} + 603 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 14 T^{2} - 603 T^{3} + 4489 T^{4} \))(\( 1 - 67 T^{2} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - T - 66 T^{2} - 67 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( ( 1 - 5 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} \))(\( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} \))(\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 14 T^{2} - 603 T^{3} + 4489 T^{4} \))(\( 1 - 67 T^{2} + 4489 T^{4} \))(\( 1 - 67 T^{2} + 4489 T^{4} \))(\( 1 + 9 T + 14 T^{2} + 603 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - T - 66 T^{2} - 67 T^{3} + 4489 T^{4} \))(\( 1 + 6 T - 31 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 14 T + 129 T^{2} + 938 T^{3} + 4489 T^{4} \))(\( 1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4} \))(\( 1 - 6 T - 31 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 - 14 T + 85 T^{2} + 322 T^{3} - 5300 T^{4} + 21574 T^{5} + 381565 T^{6} - 4210682 T^{7} + 20151121 T^{8} \))(\( ( 1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4} )^{2} \))(\( 1 - 16 T + 86 T^{2} - 576 T^{3} + 7259 T^{4} - 38592 T^{5} + 386054 T^{6} - 4812208 T^{7} + 20151121 T^{8} \))(\( 1 - 14 T + 85 T^{2} + 322 T^{3} - 5300 T^{4} + 21574 T^{5} + 381565 T^{6} - 4210682 T^{7} + 20151121 T^{8} \))(\( ( 1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4} )^{2} \))(\( 1 - 16 T + 86 T^{2} - 576 T^{3} + 7259 T^{4} - 38592 T^{5} + 386054 T^{6} - 4812208 T^{7} + 20151121 T^{8} \))
$71$ (\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 3 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - T + 71 T^{2} )^{2} \))(\( ( 1 + 2 T + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 15 T + 71 T^{2} )^{2} \))(\( ( 1 - 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 13 T + 71 T^{2} )^{2} \))(\( ( 1 + T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 15 T + 71 T^{2} )^{2} \))(\( ( 1 - 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 - T + 71 T^{2} )^{2} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 13 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 3 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 + T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T - 11 T^{2} + 426 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 16 T + 199 T^{2} + 1136 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 4 T + 118 T^{2} + 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 6 T - 11 T^{2} - 426 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 16 T + 199 T^{2} - 1136 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 4 T + 118 T^{2} - 284 T^{3} + 5041 T^{4} )^{2} \))
$73$ (\( 1 - 9 T + 8 T^{2} - 657 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 4 T - 57 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 + 8 T - 9 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 96 T^{2} - 949 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 96 T^{2} - 949 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 - T - 72 T^{2} - 73 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 - 4 T - 57 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 96 T^{2} - 949 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 + 8 T - 9 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 - T - 72 T^{2} - 73 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 96 T^{2} - 949 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 - 9 T + 8 T^{2} - 657 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 28 T^{2} - 632 T^{3} - 6353 T^{4} - 46136 T^{5} + 149212 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 - 14 T + 8 T^{2} - 588 T^{3} + 15707 T^{4} - 42924 T^{5} + 42632 T^{6} - 5446238 T^{7} + 28398241 T^{8} \))(\( 1 + 6 T - 91 T^{2} - 114 T^{3} + 8172 T^{4} - 8322 T^{5} - 484939 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 + 4 T + 28 T^{2} - 632 T^{3} - 6353 T^{4} - 46136 T^{5} + 149212 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 - 14 T + 8 T^{2} - 588 T^{3} + 15707 T^{4} - 42924 T^{5} + 42632 T^{6} - 5446238 T^{7} + 28398241 T^{8} \))(\( 1 + 6 T - 91 T^{2} - 114 T^{3} + 8172 T^{4} - 8322 T^{5} - 484939 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 14 T + 117 T^{2} + 1106 T^{3} + 6241 T^{4} \))(\( 1 - 7 T - 30 T^{2} - 553 T^{3} + 6241 T^{4} \))(\( 1 - 2 T - 75 T^{2} - 158 T^{3} + 6241 T^{4} \))(\( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 + 14 T + 117 T^{2} + 1106 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 10 T + 21 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4} \))(\( 1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 + 14 T + 117 T^{2} + 1106 T^{3} + 6241 T^{4} \))(\( 1 + 10 T + 21 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 14 T + 117 T^{2} + 1106 T^{3} + 6241 T^{4} \))(\( 1 - 7 T - 30 T^{2} - 553 T^{3} + 6241 T^{4} \))(\( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 - 2 T - 75 T^{2} - 158 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 92 T^{2} + 16 T^{3} + 13039 T^{4} + 1264 T^{5} - 574172 T^{6} - 3944312 T^{7} + 38950081 T^{8} \))(\( 1 + 10 T - 76 T^{2} + 180 T^{3} + 16835 T^{4} + 14220 T^{5} - 474316 T^{6} + 4930390 T^{7} + 38950081 T^{8} \))(\( 1 - 10 T - 55 T^{2} + 30 T^{3} + 9884 T^{4} + 2370 T^{5} - 343255 T^{6} - 4930390 T^{7} + 38950081 T^{8} \))(\( 1 - 8 T - 92 T^{2} + 16 T^{3} + 13039 T^{4} + 1264 T^{5} - 574172 T^{6} - 3944312 T^{7} + 38950081 T^{8} \))(\( 1 + 10 T - 76 T^{2} + 180 T^{3} + 16835 T^{4} + 14220 T^{5} - 474316 T^{6} + 4930390 T^{7} + 38950081 T^{8} \))(\( 1 - 10 T - 55 T^{2} + 30 T^{3} + 9884 T^{4} + 2370 T^{5} - 343255 T^{6} - 4930390 T^{7} + 38950081 T^{8} \))
$83$ (\( ( 1 - 7 T + 83 T^{2} )^{2} \))(\( ( 1 + 9 T + 83 T^{2} )^{2} \))(\( ( 1 - 15 T + 83 T^{2} )^{2} \))(\( ( 1 + 15 T + 83 T^{2} )^{2} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( ( 1 - 9 T + 83 T^{2} )^{2} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( ( 1 - 15 T + 83 T^{2} )^{2} \))(\( ( 1 - 18 T + 83 T^{2} )^{2} \))(\( ( 1 + T + 83 T^{2} )^{2} \))(\( ( 1 - 8 T + 83 T^{2} )^{2} \))(\( ( 1 - 14 T + 83 T^{2} )^{2} \))(\( ( 1 - 5 T + 83 T^{2} )^{2} \))(\( ( 1 + 3 T + 83 T^{2} )^{2} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 9 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 15 T + 83 T^{2} )^{2} \))(\( ( 1 + 9 T + 83 T^{2} )^{2} \))(\( ( 1 + 18 T + 83 T^{2} )^{2} \))(\( ( 1 + 14 T + 83 T^{2} )^{2} \))(\( ( 1 + 5 T + 83 T^{2} )^{2} \))(\( ( 1 - T + 83 T^{2} )^{2} \))(\( ( 1 + 8 T + 83 T^{2} )^{2} \))(\( ( 1 - 9 T + 83 T^{2} )^{2} \))(\( ( 1 - 3 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 7 T + 83 T^{2} )^{2} \))(\( ( 1 - 9 T + 83 T^{2} )^{2} \))(\( ( 1 + 15 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 - 15 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 184 T^{2} - 996 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 2 T + 160 T^{2} + 166 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 9 T + 83 T^{2} )^{4} \))(\( ( 1 + 12 T + 184 T^{2} + 996 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 2 T + 160 T^{2} - 166 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 9 T + 83 T^{2} )^{4} \))
$89$ (\( 1 - 2 T - 85 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 - 18 T + 235 T^{2} - 1602 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 167 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 - 2 T - 85 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 55 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 55 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 8 T - 25 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 - 2 T - 85 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 4 T - 73 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 167 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 4 T - 73 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 167 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 + 8 T - 25 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 + 2 T - 85 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 12 T + 55 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 2 T - 85 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 + 18 T + 235 T^{2} + 1602 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 2 T - 85 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 167 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 - 160 T^{2} + 17679 T^{4} - 1267360 T^{6} + 62742241 T^{8} \))(\( 1 - 6 T + 24 T^{2} + 996 T^{3} - 10981 T^{4} + 88644 T^{5} + 190104 T^{6} - 4229814 T^{7} + 62742241 T^{8} \))(\( 1 - 16 T + 42 T^{2} - 576 T^{3} + 15091 T^{4} - 51264 T^{5} + 332682 T^{6} - 11279504 T^{7} + 62742241 T^{8} \))(\( 1 - 160 T^{2} + 17679 T^{4} - 1267360 T^{6} + 62742241 T^{8} \))(\( 1 + 6 T + 24 T^{2} - 996 T^{3} - 10981 T^{4} - 88644 T^{5} + 190104 T^{6} + 4229814 T^{7} + 62742241 T^{8} \))(\( 1 + 16 T + 42 T^{2} + 576 T^{3} + 15091 T^{4} + 51264 T^{5} + 332682 T^{6} + 11279504 T^{7} + 62742241 T^{8} \))
$97$ (\( ( 1 - 17 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 19 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 7 T + 97 T^{2} )^{2} \))(\( ( 1 + 19 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 7 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 - 17 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 - 5 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 8 T + 192 T^{2} + 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 6 T + 28 T^{2} - 582 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 18 T + 247 T^{2} - 1746 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 8 T + 192 T^{2} + 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 6 T + 28 T^{2} - 582 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 18 T + 247 T^{2} - 1746 T^{3} + 9409 T^{4} )^{2} \))
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