Properties

Label 3840.2.k
Level $3840$
Weight $2$
Character orbit 3840.k
Rep. character $\chi_{3840}(1921,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $30$
Sturm bound $1536$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3840.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(1536\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(23\), \(31\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3840, [\chi])\).

Total New Old
Modular forms 816 64 752
Cusp forms 720 64 656
Eisenstein series 96 0 96

Trace form

\( 64q - 64q^{9} + O(q^{10}) \) \( 64q - 64q^{9} - 64q^{25} + 128q^{49} - 64q^{57} - 64q^{73} + 64q^{81} + 64q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3840.2.k.a \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-iq^{3}-iq^{5}-4q^{7}-q^{9}+6iq^{13}+\cdots\)
3840.2.k.b \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}+iq^{5}-4q^{7}-q^{9}+2iq^{11}+\cdots\)
3840.2.k.c \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-iq^{3}-iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots\)
3840.2.k.d \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-iq^{3}+iq^{5}-4q^{7}-q^{9}+2iq^{13}+\cdots\)
3840.2.k.e \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-iq^{5}-4q^{7}-q^{9}+6iq^{11}+\cdots\)
3840.2.k.f \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-iq^{5}-4q^{7}-q^{9}-2iq^{13}+\cdots\)
3840.2.k.g \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{11}+\cdots\)
3840.2.k.h \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+iq^{3}+iq^{5}-2q^{7}-q^{9}-6iq^{11}+\cdots\)
3840.2.k.i \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{11}+\cdots\)
3840.2.k.j \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}-4iq^{11}+6iq^{13}+\cdots\)
3840.2.k.k \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{5}-q^{9}-4iq^{11}+2iq^{13}+\cdots\)
3840.2.k.l \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}-2iq^{11}+4iq^{13}+\cdots\)
3840.2.k.m \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}+4iq^{11}-2iq^{13}+\cdots\)
3840.2.k.n \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}+2iq^{13}-q^{15}+\cdots\)
3840.2.k.o \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-q^{9}+4iq^{11}+6iq^{13}+\cdots\)
3840.2.k.p \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-q^{9}+4iq^{11}+2iq^{13}+\cdots\)
3840.2.k.q \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-q^{9}+2iq^{11}+4iq^{13}+\cdots\)
3840.2.k.r \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-q^{9}-4iq^{11}-2iq^{13}+\cdots\)
3840.2.k.s \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-q^{9}-2iq^{13}+q^{15}+\cdots\)
3840.2.k.t \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q-iq^{3}-iq^{5}+2q^{7}-q^{9}+2iq^{11}+\cdots\)
3840.2.k.u \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}-iq^{5}+2q^{7}-q^{9}+2iq^{11}+\cdots\)
3840.2.k.v \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}-iq^{5}+2q^{7}-q^{9}-6iq^{11}+\cdots\)
3840.2.k.w \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+iq^{5}+4q^{7}-q^{9}+2iq^{13}+\cdots\)
3840.2.k.x \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+iq^{5}+4q^{7}-q^{9}+6iq^{11}+\cdots\)
3840.2.k.y \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}-iq^{5}+4q^{7}-q^{9}-2iq^{13}+\cdots\)
3840.2.k.z \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+iq^{5}+4q^{7}-q^{9}-6iq^{13}+\cdots\)
3840.2.k.ba \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+iq^{5}+4q^{7}-q^{9}-2iq^{11}+\cdots\)
3840.2.k.bb \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+iq^{5}+4q^{7}-q^{9}-4iq^{11}+\cdots\)
3840.2.k.bc \(4\) \(30.663\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1+\beta _{3})q^{7}-q^{9}+\cdots\)
3840.2.k.bd \(4\) \(30.663\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{3}-\beta _{1}q^{5}+(1-\beta _{3})q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$5$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$7$ (\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 2 T - 2 T^{2} - 14 T^{3} + 49 T^{4} )^{2} \))
$11$ (\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 18 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 121 T^{4} )^{2} \))
$13$ (\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 16 T^{2} + 334 T^{4} - 2704 T^{6} + 28561 T^{8} \))(\( 1 - 16 T^{2} + 334 T^{4} - 2704 T^{6} + 28561 T^{8} \))
$17$ (\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 26 T^{2} - 102 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 6 T + 26 T^{2} - 102 T^{3} + 289 T^{4} )^{2} \))
$19$ (\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 40 T^{2} + 1054 T^{4} - 14440 T^{6} + 130321 T^{8} \))(\( 1 - 40 T^{2} + 1054 T^{4} - 14440 T^{6} + 130321 T^{8} \))
$23$ (\( ( 1 - 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 2 T + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( ( 1 + 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 8 T + 23 T^{2} )^{2} \))(\( ( 1 - 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 - 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 2 T + 30 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 2 T + 30 T^{2} + 46 T^{3} + 529 T^{4} )^{2} \))
$29$ (\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( ( 1 + 10 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 10 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 10 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 10 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 6 T + 54 T^{2} + 186 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 6 T + 54 T^{2} - 186 T^{3} + 961 T^{4} )^{2} \))
$37$ (\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 112 T^{2} + 5806 T^{4} - 153328 T^{6} + 1874161 T^{8} \))(\( 1 - 112 T^{2} + 5806 T^{4} - 153328 T^{6} + 1874161 T^{8} \))
$41$ (\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{4} \))(\( ( 1 - 2 T + 41 T^{2} )^{4} \))
$43$ (\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 28 T^{2} + 2806 T^{4} - 51772 T^{6} + 3418801 T^{8} \))(\( 1 - 28 T^{2} + 2806 T^{4} - 51772 T^{6} + 3418801 T^{8} \))
$47$ (\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 6 T + 47 T^{2} )^{2} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( ( 1 - 2 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 2 T + 47 T^{2} )^{2} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( ( 1 - 6 T + 47 T^{2} )^{2} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 18 T + 158 T^{2} + 846 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 - 18 T + 158 T^{2} - 846 T^{3} + 2209 T^{4} )^{2} \))
$53$ (\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( ( 1 - 6 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 6 T^{2} + 2809 T^{4} )^{2} \))
$59$ (\( ( 1 - 59 T^{2} )^{2} \))(\( 1 + 78 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 114 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 114 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( 1 + 78 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( ( 1 - 82 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 3481 T^{4} )^{2} \))
$61$ (\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( ( 1 - 118 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 118 T^{2} + 3721 T^{4} )^{2} \))
$67$ (\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 + 122 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 + 122 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 124 T^{2} + 11734 T^{4} - 556636 T^{6} + 20151121 T^{8} \))(\( 1 - 124 T^{2} + 11734 T^{4} - 556636 T^{6} + 20151121 T^{8} \))
$71$ (\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{4} \))(\( ( 1 + 8 T + 71 T^{2} )^{4} \))
$73$ (\( ( 1 - 14 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 14 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 14 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 14 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 14 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 14 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 + 8 T + 94 T^{2} + 584 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 8 T + 94 T^{2} + 584 T^{3} + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 6 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 6 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 2 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 2 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 6 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 6 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 18 T + 222 T^{2} + 1422 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 18 T + 222 T^{2} - 1422 T^{3} + 6241 T^{4} )^{2} \))
$83$ (\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( ( 1 - 150 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 150 T^{2} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{4} \))(\( ( 1 - 10 T + 89 T^{2} )^{4} \))
$97$ (\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{4} \))(\( ( 1 - 10 T + 97 T^{2} )^{4} \))
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